Identifier
Mp00109:
Permutations
—descent word⟶
Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Images
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[1]=>=>
[1,2]=>0=>1
[2,1]=>1=>0
[1,2,3]=>00=>11
[1,3,2]=>01=>10
[2,1,3]=>10=>01
[2,3,1]=>01=>10
[3,1,2]=>10=>01
[3,2,1]=>11=>00
[1,2,3,4]=>000=>111
[1,2,4,3]=>001=>110
[1,3,2,4]=>010=>101
[1,3,4,2]=>001=>110
[1,4,2,3]=>010=>101
[1,4,3,2]=>011=>100
[2,1,3,4]=>100=>011
[2,1,4,3]=>101=>010
[2,3,1,4]=>010=>101
[2,3,4,1]=>001=>110
[2,4,1,3]=>010=>101
[2,4,3,1]=>011=>100
[3,1,2,4]=>100=>011
[3,1,4,2]=>101=>010
[3,2,1,4]=>110=>001
[3,2,4,1]=>101=>010
[3,4,1,2]=>010=>101
[3,4,2,1]=>011=>100
[4,1,2,3]=>100=>011
[4,1,3,2]=>101=>010
[4,2,1,3]=>110=>001
[4,2,3,1]=>101=>010
[4,3,1,2]=>110=>001
[4,3,2,1]=>111=>000
[1,2,3,4,5]=>0000=>1111
[1,2,3,5,4]=>0001=>1110
[1,2,4,3,5]=>0010=>1101
[1,2,4,5,3]=>0001=>1110
[1,2,5,3,4]=>0010=>1101
[1,2,5,4,3]=>0011=>1100
[1,3,2,4,5]=>0100=>1011
[1,3,2,5,4]=>0101=>1010
[1,3,4,2,5]=>0010=>1101
[1,3,4,5,2]=>0001=>1110
[1,3,5,2,4]=>0010=>1101
[1,3,5,4,2]=>0011=>1100
[1,4,2,3,5]=>0100=>1011
[1,4,2,5,3]=>0101=>1010
[1,4,3,2,5]=>0110=>1001
[1,4,3,5,2]=>0101=>1010
[1,4,5,2,3]=>0010=>1101
[1,4,5,3,2]=>0011=>1100
[1,5,2,3,4]=>0100=>1011
[1,5,2,4,3]=>0101=>1010
[1,5,3,2,4]=>0110=>1001
[1,5,3,4,2]=>0101=>1010
[1,5,4,2,3]=>0110=>1001
[1,5,4,3,2]=>0111=>1000
[2,1,3,4,5]=>1000=>0111
[2,1,3,5,4]=>1001=>0110
[2,1,4,3,5]=>1010=>0101
[2,1,4,5,3]=>1001=>0110
[2,1,5,3,4]=>1010=>0101
[2,1,5,4,3]=>1011=>0100
[2,3,1,4,5]=>0100=>1011
[2,3,1,5,4]=>0101=>1010
[2,3,4,1,5]=>0010=>1101
[2,3,4,5,1]=>0001=>1110
[2,3,5,1,4]=>0010=>1101
[2,3,5,4,1]=>0011=>1100
[2,4,1,3,5]=>0100=>1011
[2,4,1,5,3]=>0101=>1010
[2,4,3,1,5]=>0110=>1001
[2,4,3,5,1]=>0101=>1010
[2,4,5,1,3]=>0010=>1101
[2,4,5,3,1]=>0011=>1100
[2,5,1,3,4]=>0100=>1011
[2,5,1,4,3]=>0101=>1010
[2,5,3,1,4]=>0110=>1001
[2,5,3,4,1]=>0101=>1010
[2,5,4,1,3]=>0110=>1001
[2,5,4,3,1]=>0111=>1000
[3,1,2,4,5]=>1000=>0111
[3,1,2,5,4]=>1001=>0110
[3,1,4,2,5]=>1010=>0101
[3,1,4,5,2]=>1001=>0110
[3,1,5,2,4]=>1010=>0101
[3,1,5,4,2]=>1011=>0100
[3,2,1,4,5]=>1100=>0011
[3,2,1,5,4]=>1101=>0010
[3,2,4,1,5]=>1010=>0101
[3,2,4,5,1]=>1001=>0110
[3,2,5,1,4]=>1010=>0101
[3,2,5,4,1]=>1011=>0100
[3,4,1,2,5]=>0100=>1011
[3,4,1,5,2]=>0101=>1010
[3,4,2,1,5]=>0110=>1001
[3,4,2,5,1]=>0101=>1010
[3,4,5,1,2]=>0010=>1101
[3,4,5,2,1]=>0011=>1100
[3,5,1,2,4]=>0100=>1011
[3,5,1,4,2]=>0101=>1010
[3,5,2,1,4]=>0110=>1001
[3,5,2,4,1]=>0101=>1010
[3,5,4,1,2]=>0110=>1001
[3,5,4,2,1]=>0111=>1000
[4,1,2,3,5]=>1000=>0111
[4,1,2,5,3]=>1001=>0110
[4,1,3,2,5]=>1010=>0101
[4,1,3,5,2]=>1001=>0110
[4,1,5,2,3]=>1010=>0101
[4,1,5,3,2]=>1011=>0100
[4,2,1,3,5]=>1100=>0011
[4,2,1,5,3]=>1101=>0010
[4,2,3,1,5]=>1010=>0101
[4,2,3,5,1]=>1001=>0110
[4,2,5,1,3]=>1010=>0101
[4,2,5,3,1]=>1011=>0100
[4,3,1,2,5]=>1100=>0011
[4,3,1,5,2]=>1101=>0010
[4,3,2,1,5]=>1110=>0001
[4,3,2,5,1]=>1101=>0010
[4,3,5,1,2]=>1010=>0101
[4,3,5,2,1]=>1011=>0100
[4,5,1,2,3]=>0100=>1011
[4,5,1,3,2]=>0101=>1010
[4,5,2,1,3]=>0110=>1001
[4,5,2,3,1]=>0101=>1010
[4,5,3,1,2]=>0110=>1001
[4,5,3,2,1]=>0111=>1000
[5,1,2,3,4]=>1000=>0111
[5,1,2,4,3]=>1001=>0110
[5,1,3,2,4]=>1010=>0101
[5,1,3,4,2]=>1001=>0110
[5,1,4,2,3]=>1010=>0101
[5,1,4,3,2]=>1011=>0100
[5,2,1,3,4]=>1100=>0011
[5,2,1,4,3]=>1101=>0010
[5,2,3,1,4]=>1010=>0101
[5,2,3,4,1]=>1001=>0110
[5,2,4,1,3]=>1010=>0101
[5,2,4,3,1]=>1011=>0100
[5,3,1,2,4]=>1100=>0011
[5,3,1,4,2]=>1101=>0010
[5,3,2,1,4]=>1110=>0001
[5,3,2,4,1]=>1101=>0010
[5,3,4,1,2]=>1010=>0101
[5,3,4,2,1]=>1011=>0100
[5,4,1,2,3]=>1100=>0011
[5,4,1,3,2]=>1101=>0010
[5,4,2,1,3]=>1110=>0001
[5,4,2,3,1]=>1101=>0010
[5,4,3,1,2]=>1110=>0001
[5,4,3,2,1]=>1111=>0000
[1,2,3,4,5,6]=>00000=>11111
[1,2,3,4,6,5]=>00001=>11110
[1,2,3,5,4,6]=>00010=>11101
[1,2,3,5,6,4]=>00001=>11110
[1,2,3,6,4,5]=>00010=>11101
[1,2,3,6,5,4]=>00011=>11100
[1,2,4,3,5,6]=>00100=>11011
[1,2,4,3,6,5]=>00101=>11010
[1,2,4,5,3,6]=>00010=>11101
[1,2,4,5,6,3]=>00001=>11110
[1,2,4,6,3,5]=>00010=>11101
[1,2,4,6,5,3]=>00011=>11100
[1,2,5,3,4,6]=>00100=>11011
[1,2,5,3,6,4]=>00101=>11010
[1,2,5,4,3,6]=>00110=>11001
[1,2,5,4,6,3]=>00101=>11010
[1,2,5,6,3,4]=>00010=>11101
[1,2,5,6,4,3]=>00011=>11100
[1,2,6,3,4,5]=>00100=>11011
[1,2,6,3,5,4]=>00101=>11010
[1,2,6,4,3,5]=>00110=>11001
[1,2,6,4,5,3]=>00101=>11010
[1,2,6,5,3,4]=>00110=>11001
[1,2,6,5,4,3]=>00111=>11000
[1,3,2,4,5,6]=>01000=>10111
[1,3,2,4,6,5]=>01001=>10110
[1,3,2,5,4,6]=>01010=>10101
[1,3,2,5,6,4]=>01001=>10110
[1,3,2,6,4,5]=>01010=>10101
[1,3,2,6,5,4]=>01011=>10100
[1,3,4,2,5,6]=>00100=>11011
[1,3,4,2,6,5]=>00101=>11010
[1,3,4,5,2,6]=>00010=>11101
[1,3,4,5,6,2]=>00001=>11110
[1,3,4,6,2,5]=>00010=>11101
[1,3,4,6,5,2]=>00011=>11100
[1,3,5,2,4,6]=>00100=>11011
[1,3,5,2,6,4]=>00101=>11010
[1,3,5,4,2,6]=>00110=>11001
[1,3,5,4,6,2]=>00101=>11010
[1,3,5,6,2,4]=>00010=>11101
[1,3,5,6,4,2]=>00011=>11100
[1,3,6,2,4,5]=>00100=>11011
[1,3,6,2,5,4]=>00101=>11010
[1,3,6,4,2,5]=>00110=>11001
[1,3,6,4,5,2]=>00101=>11010
[1,3,6,5,2,4]=>00110=>11001
[1,3,6,5,4,2]=>00111=>11000
[1,4,2,3,5,6]=>01000=>10111
[1,4,2,3,6,5]=>01001=>10110
[1,4,2,5,3,6]=>01010=>10101
[1,4,2,5,6,3]=>01001=>10110
[1,4,2,6,3,5]=>01010=>10101
[1,4,2,6,5,3]=>01011=>10100
[1,4,3,2,5,6]=>01100=>10011
[1,4,3,2,6,5]=>01101=>10010
[1,4,3,5,2,6]=>01010=>10101
[1,4,3,5,6,2]=>01001=>10110
[1,4,3,6,2,5]=>01010=>10101
[1,4,3,6,5,2]=>01011=>10100
[1,4,5,2,3,6]=>00100=>11011
[1,4,5,2,6,3]=>00101=>11010
[1,4,5,3,2,6]=>00110=>11001
[1,4,5,3,6,2]=>00101=>11010
[1,4,5,6,2,3]=>00010=>11101
[1,4,5,6,3,2]=>00011=>11100
[1,4,6,2,3,5]=>00100=>11011
[1,4,6,2,5,3]=>00101=>11010
[1,4,6,3,2,5]=>00110=>11001
[1,4,6,3,5,2]=>00101=>11010
[1,4,6,5,2,3]=>00110=>11001
[1,4,6,5,3,2]=>00111=>11000
[1,5,2,3,4,6]=>01000=>10111
[1,5,2,3,6,4]=>01001=>10110
[1,5,2,4,3,6]=>01010=>10101
[1,5,2,4,6,3]=>01001=>10110
[1,5,2,6,3,4]=>01010=>10101
[1,5,2,6,4,3]=>01011=>10100
[1,5,3,2,4,6]=>01100=>10011
[1,5,3,2,6,4]=>01101=>10010
[1,5,3,4,2,6]=>01010=>10101
[1,5,3,4,6,2]=>01001=>10110
[1,5,3,6,2,4]=>01010=>10101
[1,5,3,6,4,2]=>01011=>10100
[1,5,4,2,3,6]=>01100=>10011
[1,5,4,2,6,3]=>01101=>10010
[1,5,4,3,2,6]=>01110=>10001
[1,5,4,3,6,2]=>01101=>10010
[1,5,4,6,2,3]=>01010=>10101
[1,5,4,6,3,2]=>01011=>10100
[1,5,6,2,3,4]=>00100=>11011
[1,5,6,2,4,3]=>00101=>11010
[1,5,6,3,2,4]=>00110=>11001
[1,5,6,3,4,2]=>00101=>11010
[1,5,6,4,2,3]=>00110=>11001
[1,5,6,4,3,2]=>00111=>11000
[1,6,2,3,4,5]=>01000=>10111
[1,6,2,3,5,4]=>01001=>10110
[1,6,2,4,3,5]=>01010=>10101
[1,6,2,4,5,3]=>01001=>10110
[1,6,2,5,3,4]=>01010=>10101
[1,6,2,5,4,3]=>01011=>10100
[1,6,3,2,4,5]=>01100=>10011
[1,6,3,2,5,4]=>01101=>10010
[1,6,3,4,2,5]=>01010=>10101
[1,6,3,4,5,2]=>01001=>10110
[1,6,3,5,2,4]=>01010=>10101
[1,6,3,5,4,2]=>01011=>10100
[1,6,4,2,3,5]=>01100=>10011
[1,6,4,2,5,3]=>01101=>10010
[1,6,4,3,2,5]=>01110=>10001
[1,6,4,3,5,2]=>01101=>10010
[1,6,4,5,2,3]=>01010=>10101
[1,6,4,5,3,2]=>01011=>10100
[1,6,5,2,3,4]=>01100=>10011
[1,6,5,2,4,3]=>01101=>10010
[1,6,5,3,2,4]=>01110=>10001
[1,6,5,3,4,2]=>01101=>10010
[1,6,5,4,2,3]=>01110=>10001
[1,6,5,4,3,2]=>01111=>10000
[2,1,3,4,5,6]=>10000=>01111
[2,1,3,4,6,5]=>10001=>01110
[2,1,3,5,4,6]=>10010=>01101
[2,1,3,5,6,4]=>10001=>01110
[2,1,3,6,4,5]=>10010=>01101
[2,1,3,6,5,4]=>10011=>01100
[2,1,4,3,5,6]=>10100=>01011
[2,1,4,3,6,5]=>10101=>01010
[2,1,4,5,3,6]=>10010=>01101
[2,1,4,5,6,3]=>10001=>01110
[2,1,4,6,3,5]=>10010=>01101
[2,1,4,6,5,3]=>10011=>01100
[2,1,5,3,4,6]=>10100=>01011
[2,1,5,3,6,4]=>10101=>01010
[2,1,5,4,3,6]=>10110=>01001
[2,1,5,4,6,3]=>10101=>01010
[2,1,5,6,3,4]=>10010=>01101
[2,1,5,6,4,3]=>10011=>01100
[2,1,6,3,4,5]=>10100=>01011
[2,1,6,3,5,4]=>10101=>01010
[2,1,6,4,3,5]=>10110=>01001
[2,1,6,4,5,3]=>10101=>01010
[2,1,6,5,3,4]=>10110=>01001
[2,1,6,5,4,3]=>10111=>01000
[2,3,1,4,5,6]=>01000=>10111
[2,3,1,4,6,5]=>01001=>10110
[2,3,1,5,4,6]=>01010=>10101
[2,3,1,5,6,4]=>01001=>10110
[2,3,1,6,4,5]=>01010=>10101
[2,3,1,6,5,4]=>01011=>10100
[2,3,4,1,5,6]=>00100=>11011
[2,3,4,1,6,5]=>00101=>11010
[2,3,4,5,1,6]=>00010=>11101
[2,3,4,5,6,1]=>00001=>11110
[2,3,4,6,1,5]=>00010=>11101
[2,3,4,6,5,1]=>00011=>11100
[2,3,5,1,4,6]=>00100=>11011
[2,3,5,1,6,4]=>00101=>11010
[2,3,5,4,1,6]=>00110=>11001
[2,3,5,4,6,1]=>00101=>11010
[2,3,5,6,1,4]=>00010=>11101
[2,3,5,6,4,1]=>00011=>11100
[2,3,6,1,4,5]=>00100=>11011
[2,3,6,1,5,4]=>00101=>11010
[2,3,6,4,1,5]=>00110=>11001
[2,3,6,4,5,1]=>00101=>11010
[2,3,6,5,1,4]=>00110=>11001
[2,3,6,5,4,1]=>00111=>11000
[2,4,1,3,5,6]=>01000=>10111
[2,4,1,3,6,5]=>01001=>10110
[2,4,1,5,3,6]=>01010=>10101
[2,4,1,5,6,3]=>01001=>10110
[2,4,1,6,3,5]=>01010=>10101
[2,4,1,6,5,3]=>01011=>10100
[2,4,3,1,5,6]=>01100=>10011
[2,4,3,1,6,5]=>01101=>10010
[2,4,3,5,1,6]=>01010=>10101
[2,4,3,5,6,1]=>01001=>10110
[2,4,3,6,1,5]=>01010=>10101
[2,4,3,6,5,1]=>01011=>10100
[2,4,5,1,3,6]=>00100=>11011
[2,4,5,1,6,3]=>00101=>11010
[2,4,5,3,1,6]=>00110=>11001
[2,4,5,3,6,1]=>00101=>11010
[2,4,5,6,1,3]=>00010=>11101
[2,4,5,6,3,1]=>00011=>11100
[2,4,6,1,3,5]=>00100=>11011
[2,4,6,1,5,3]=>00101=>11010
[2,4,6,3,1,5]=>00110=>11001
[2,4,6,3,5,1]=>00101=>11010
[2,4,6,5,1,3]=>00110=>11001
[2,4,6,5,3,1]=>00111=>11000
[2,5,1,3,4,6]=>01000=>10111
[2,5,1,3,6,4]=>01001=>10110
[2,5,1,4,3,6]=>01010=>10101
[2,5,1,4,6,3]=>01001=>10110
[2,5,1,6,3,4]=>01010=>10101
[2,5,1,6,4,3]=>01011=>10100
[2,5,3,1,4,6]=>01100=>10011
[2,5,3,1,6,4]=>01101=>10010
[2,5,3,4,1,6]=>01010=>10101
[2,5,3,4,6,1]=>01001=>10110
[2,5,3,6,1,4]=>01010=>10101
[2,5,3,6,4,1]=>01011=>10100
[2,5,4,1,3,6]=>01100=>10011
[2,5,4,1,6,3]=>01101=>10010
[2,5,4,3,1,6]=>01110=>10001
[2,5,4,3,6,1]=>01101=>10010
[2,5,4,6,1,3]=>01010=>10101
[2,5,4,6,3,1]=>01011=>10100
[2,5,6,1,3,4]=>00100=>11011
[2,5,6,1,4,3]=>00101=>11010
[2,5,6,3,1,4]=>00110=>11001
[2,5,6,3,4,1]=>00101=>11010
[2,5,6,4,1,3]=>00110=>11001
[2,5,6,4,3,1]=>00111=>11000
[2,6,1,3,4,5]=>01000=>10111
[2,6,1,3,5,4]=>01001=>10110
[2,6,1,4,3,5]=>01010=>10101
[2,6,1,4,5,3]=>01001=>10110
[2,6,1,5,3,4]=>01010=>10101
[2,6,1,5,4,3]=>01011=>10100
[2,6,3,1,4,5]=>01100=>10011
[2,6,3,1,5,4]=>01101=>10010
[2,6,3,4,1,5]=>01010=>10101
[2,6,3,4,5,1]=>01001=>10110
[2,6,3,5,1,4]=>01010=>10101
[2,6,3,5,4,1]=>01011=>10100
[2,6,4,1,3,5]=>01100=>10011
[2,6,4,1,5,3]=>01101=>10010
[2,6,4,3,1,5]=>01110=>10001
[2,6,4,3,5,1]=>01101=>10010
[2,6,4,5,1,3]=>01010=>10101
[2,6,4,5,3,1]=>01011=>10100
[2,6,5,1,3,4]=>01100=>10011
[2,6,5,1,4,3]=>01101=>10010
[2,6,5,3,1,4]=>01110=>10001
[2,6,5,3,4,1]=>01101=>10010
[2,6,5,4,1,3]=>01110=>10001
[2,6,5,4,3,1]=>01111=>10000
[3,1,2,4,5,6]=>10000=>01111
[3,1,2,4,6,5]=>10001=>01110
[3,1,2,5,4,6]=>10010=>01101
[3,1,2,5,6,4]=>10001=>01110
[3,1,2,6,4,5]=>10010=>01101
[3,1,2,6,5,4]=>10011=>01100
[3,1,4,2,5,6]=>10100=>01011
[3,1,4,2,6,5]=>10101=>01010
[3,1,4,5,2,6]=>10010=>01101
[3,1,4,5,6,2]=>10001=>01110
[3,1,4,6,2,5]=>10010=>01101
[3,1,4,6,5,2]=>10011=>01100
[3,1,5,2,4,6]=>10100=>01011
[3,1,5,2,6,4]=>10101=>01010
[3,1,5,4,2,6]=>10110=>01001
[3,1,5,4,6,2]=>10101=>01010
[3,1,5,6,2,4]=>10010=>01101
[3,1,5,6,4,2]=>10011=>01100
[3,1,6,2,4,5]=>10100=>01011
[3,1,6,2,5,4]=>10101=>01010
[3,1,6,4,2,5]=>10110=>01001
[3,1,6,4,5,2]=>10101=>01010
[3,1,6,5,2,4]=>10110=>01001
[3,1,6,5,4,2]=>10111=>01000
[3,2,1,4,5,6]=>11000=>00111
[3,2,1,4,6,5]=>11001=>00110
[3,2,1,5,4,6]=>11010=>00101
[3,2,1,5,6,4]=>11001=>00110
[3,2,1,6,4,5]=>11010=>00101
[3,2,1,6,5,4]=>11011=>00100
[3,2,4,1,5,6]=>10100=>01011
[3,2,4,1,6,5]=>10101=>01010
[3,2,4,5,1,6]=>10010=>01101
[3,2,4,5,6,1]=>10001=>01110
[3,2,4,6,1,5]=>10010=>01101
[3,2,4,6,5,1]=>10011=>01100
[3,2,5,1,4,6]=>10100=>01011
[3,2,5,1,6,4]=>10101=>01010
[3,2,5,4,1,6]=>10110=>01001
[3,2,5,4,6,1]=>10101=>01010
[3,2,5,6,1,4]=>10010=>01101
[3,2,5,6,4,1]=>10011=>01100
[3,2,6,1,4,5]=>10100=>01011
[3,2,6,1,5,4]=>10101=>01010
[3,2,6,4,1,5]=>10110=>01001
[3,2,6,4,5,1]=>10101=>01010
[3,2,6,5,1,4]=>10110=>01001
[3,2,6,5,4,1]=>10111=>01000
[3,4,1,2,5,6]=>01000=>10111
[3,4,1,2,6,5]=>01001=>10110
[3,4,1,5,2,6]=>01010=>10101
[3,4,1,5,6,2]=>01001=>10110
[3,4,1,6,2,5]=>01010=>10101
[3,4,1,6,5,2]=>01011=>10100
[3,4,2,1,5,6]=>01100=>10011
[3,4,2,1,6,5]=>01101=>10010
[3,4,2,5,1,6]=>01010=>10101
[3,4,2,5,6,1]=>01001=>10110
[3,4,2,6,1,5]=>01010=>10101
[3,4,2,6,5,1]=>01011=>10100
[3,4,5,1,2,6]=>00100=>11011
[3,4,5,1,6,2]=>00101=>11010
[3,4,5,2,1,6]=>00110=>11001
[3,4,5,2,6,1]=>00101=>11010
[3,4,5,6,1,2]=>00010=>11101
[3,4,5,6,2,1]=>00011=>11100
[3,4,6,1,2,5]=>00100=>11011
[3,4,6,1,5,2]=>00101=>11010
[3,4,6,2,1,5]=>00110=>11001
[3,4,6,2,5,1]=>00101=>11010
[3,4,6,5,1,2]=>00110=>11001
[3,4,6,5,2,1]=>00111=>11000
[3,5,1,2,4,6]=>01000=>10111
[3,5,1,2,6,4]=>01001=>10110
[3,5,1,4,2,6]=>01010=>10101
[3,5,1,4,6,2]=>01001=>10110
[3,5,1,6,2,4]=>01010=>10101
[3,5,1,6,4,2]=>01011=>10100
[3,5,2,1,4,6]=>01100=>10011
[3,5,2,1,6,4]=>01101=>10010
[3,5,2,4,1,6]=>01010=>10101
[3,5,2,4,6,1]=>01001=>10110
[3,5,2,6,1,4]=>01010=>10101
[3,5,2,6,4,1]=>01011=>10100
[3,5,4,1,2,6]=>01100=>10011
[3,5,4,1,6,2]=>01101=>10010
[3,5,4,2,1,6]=>01110=>10001
[3,5,4,2,6,1]=>01101=>10010
[3,5,4,6,1,2]=>01010=>10101
[3,5,4,6,2,1]=>01011=>10100
[3,5,6,1,2,4]=>00100=>11011
[3,5,6,1,4,2]=>00101=>11010
[3,5,6,2,1,4]=>00110=>11001
[3,5,6,2,4,1]=>00101=>11010
[3,5,6,4,1,2]=>00110=>11001
[3,5,6,4,2,1]=>00111=>11000
[3,6,1,2,4,5]=>01000=>10111
[3,6,1,2,5,4]=>01001=>10110
[3,6,1,4,2,5]=>01010=>10101
[3,6,1,4,5,2]=>01001=>10110
[3,6,1,5,2,4]=>01010=>10101
[3,6,1,5,4,2]=>01011=>10100
[3,6,2,1,4,5]=>01100=>10011
[3,6,2,1,5,4]=>01101=>10010
[3,6,2,4,1,5]=>01010=>10101
[3,6,2,4,5,1]=>01001=>10110
[3,6,2,5,1,4]=>01010=>10101
[3,6,2,5,4,1]=>01011=>10100
[3,6,4,1,2,5]=>01100=>10011
[3,6,4,1,5,2]=>01101=>10010
[3,6,4,2,1,5]=>01110=>10001
[3,6,4,2,5,1]=>01101=>10010
[3,6,4,5,1,2]=>01010=>10101
[3,6,4,5,2,1]=>01011=>10100
[3,6,5,1,2,4]=>01100=>10011
[3,6,5,1,4,2]=>01101=>10010
[3,6,5,2,1,4]=>01110=>10001
[3,6,5,2,4,1]=>01101=>10010
[3,6,5,4,1,2]=>01110=>10001
[3,6,5,4,2,1]=>01111=>10000
[4,1,2,3,5,6]=>10000=>01111
[4,1,2,3,6,5]=>10001=>01110
[4,1,2,5,3,6]=>10010=>01101
[4,1,2,5,6,3]=>10001=>01110
[4,1,2,6,3,5]=>10010=>01101
[4,1,2,6,5,3]=>10011=>01100
[4,1,3,2,5,6]=>10100=>01011
[4,1,3,2,6,5]=>10101=>01010
[4,1,3,5,2,6]=>10010=>01101
[4,1,3,5,6,2]=>10001=>01110
[4,1,3,6,2,5]=>10010=>01101
[4,1,3,6,5,2]=>10011=>01100
[4,1,5,2,3,6]=>10100=>01011
[4,1,5,2,6,3]=>10101=>01010
[4,1,5,3,2,6]=>10110=>01001
[4,1,5,3,6,2]=>10101=>01010
[4,1,5,6,2,3]=>10010=>01101
[4,1,5,6,3,2]=>10011=>01100
[4,1,6,2,3,5]=>10100=>01011
[4,1,6,2,5,3]=>10101=>01010
[4,1,6,3,2,5]=>10110=>01001
[4,1,6,3,5,2]=>10101=>01010
[4,1,6,5,2,3]=>10110=>01001
[4,1,6,5,3,2]=>10111=>01000
[4,2,1,3,5,6]=>11000=>00111
[4,2,1,3,6,5]=>11001=>00110
[4,2,1,5,3,6]=>11010=>00101
[4,2,1,5,6,3]=>11001=>00110
[4,2,1,6,3,5]=>11010=>00101
[4,2,1,6,5,3]=>11011=>00100
[4,2,3,1,5,6]=>10100=>01011
[4,2,3,1,6,5]=>10101=>01010
[4,2,3,5,1,6]=>10010=>01101
[4,2,3,5,6,1]=>10001=>01110
[4,2,3,6,1,5]=>10010=>01101
[4,2,3,6,5,1]=>10011=>01100
[4,2,5,1,3,6]=>10100=>01011
[4,2,5,1,6,3]=>10101=>01010
[4,2,5,3,1,6]=>10110=>01001
[4,2,5,3,6,1]=>10101=>01010
[4,2,5,6,1,3]=>10010=>01101
[4,2,5,6,3,1]=>10011=>01100
[4,2,6,1,3,5]=>10100=>01011
[4,2,6,1,5,3]=>10101=>01010
[4,2,6,3,1,5]=>10110=>01001
[4,2,6,3,5,1]=>10101=>01010
[4,2,6,5,1,3]=>10110=>01001
[4,2,6,5,3,1]=>10111=>01000
[4,3,1,2,5,6]=>11000=>00111
[4,3,1,2,6,5]=>11001=>00110
[4,3,1,5,2,6]=>11010=>00101
[4,3,1,5,6,2]=>11001=>00110
[4,3,1,6,2,5]=>11010=>00101
[4,3,1,6,5,2]=>11011=>00100
[4,3,2,1,5,6]=>11100=>00011
[4,3,2,1,6,5]=>11101=>00010
[4,3,2,5,1,6]=>11010=>00101
[4,3,2,5,6,1]=>11001=>00110
[4,3,2,6,1,5]=>11010=>00101
[4,3,2,6,5,1]=>11011=>00100
[4,3,5,1,2,6]=>10100=>01011
[4,3,5,1,6,2]=>10101=>01010
[4,3,5,2,1,6]=>10110=>01001
[4,3,5,2,6,1]=>10101=>01010
[4,3,5,6,1,2]=>10010=>01101
[4,3,5,6,2,1]=>10011=>01100
[4,3,6,1,2,5]=>10100=>01011
[4,3,6,1,5,2]=>10101=>01010
[4,3,6,2,1,5]=>10110=>01001
[4,3,6,2,5,1]=>10101=>01010
[4,3,6,5,1,2]=>10110=>01001
[4,3,6,5,2,1]=>10111=>01000
[4,5,1,2,3,6]=>01000=>10111
[4,5,1,2,6,3]=>01001=>10110
[4,5,1,3,2,6]=>01010=>10101
[4,5,1,3,6,2]=>01001=>10110
[4,5,1,6,2,3]=>01010=>10101
[4,5,1,6,3,2]=>01011=>10100
[4,5,2,1,3,6]=>01100=>10011
[4,5,2,1,6,3]=>01101=>10010
[4,5,2,3,1,6]=>01010=>10101
[4,5,2,3,6,1]=>01001=>10110
[4,5,2,6,1,3]=>01010=>10101
[4,5,2,6,3,1]=>01011=>10100
[4,5,3,1,2,6]=>01100=>10011
[4,5,3,1,6,2]=>01101=>10010
[4,5,3,2,1,6]=>01110=>10001
[4,5,3,2,6,1]=>01101=>10010
[4,5,3,6,1,2]=>01010=>10101
[4,5,3,6,2,1]=>01011=>10100
[4,5,6,1,2,3]=>00100=>11011
[4,5,6,1,3,2]=>00101=>11010
[4,5,6,2,1,3]=>00110=>11001
[4,5,6,2,3,1]=>00101=>11010
[4,5,6,3,1,2]=>00110=>11001
[4,5,6,3,2,1]=>00111=>11000
[4,6,1,2,3,5]=>01000=>10111
[4,6,1,2,5,3]=>01001=>10110
[4,6,1,3,2,5]=>01010=>10101
[4,6,1,3,5,2]=>01001=>10110
[4,6,1,5,2,3]=>01010=>10101
[4,6,1,5,3,2]=>01011=>10100
[4,6,2,1,3,5]=>01100=>10011
[4,6,2,1,5,3]=>01101=>10010
[4,6,2,3,1,5]=>01010=>10101
[4,6,2,3,5,1]=>01001=>10110
[4,6,2,5,1,3]=>01010=>10101
[4,6,2,5,3,1]=>01011=>10100
[4,6,3,1,2,5]=>01100=>10011
[4,6,3,1,5,2]=>01101=>10010
[4,6,3,2,1,5]=>01110=>10001
[4,6,3,2,5,1]=>01101=>10010
[4,6,3,5,1,2]=>01010=>10101
[4,6,3,5,2,1]=>01011=>10100
[4,6,5,1,2,3]=>01100=>10011
[4,6,5,1,3,2]=>01101=>10010
[4,6,5,2,1,3]=>01110=>10001
[4,6,5,2,3,1]=>01101=>10010
[4,6,5,3,1,2]=>01110=>10001
[4,6,5,3,2,1]=>01111=>10000
[5,1,2,3,4,6]=>10000=>01111
[5,1,2,3,6,4]=>10001=>01110
[5,1,2,4,3,6]=>10010=>01101
[5,1,2,4,6,3]=>10001=>01110
[5,1,2,6,3,4]=>10010=>01101
[5,1,2,6,4,3]=>10011=>01100
[5,1,3,2,4,6]=>10100=>01011
[5,1,3,2,6,4]=>10101=>01010
[5,1,3,4,2,6]=>10010=>01101
[5,1,3,4,6,2]=>10001=>01110
[5,1,3,6,2,4]=>10010=>01101
[5,1,3,6,4,2]=>10011=>01100
[5,1,4,2,3,6]=>10100=>01011
[5,1,4,2,6,3]=>10101=>01010
[5,1,4,3,2,6]=>10110=>01001
[5,1,4,3,6,2]=>10101=>01010
[5,1,4,6,2,3]=>10010=>01101
[5,1,4,6,3,2]=>10011=>01100
[5,1,6,2,3,4]=>10100=>01011
[5,1,6,2,4,3]=>10101=>01010
[5,1,6,3,2,4]=>10110=>01001
[5,1,6,3,4,2]=>10101=>01010
[5,1,6,4,2,3]=>10110=>01001
[5,1,6,4,3,2]=>10111=>01000
[5,2,1,3,4,6]=>11000=>00111
[5,2,1,3,6,4]=>11001=>00110
[5,2,1,4,3,6]=>11010=>00101
[5,2,1,4,6,3]=>11001=>00110
[5,2,1,6,3,4]=>11010=>00101
[5,2,1,6,4,3]=>11011=>00100
[5,2,3,1,4,6]=>10100=>01011
[5,2,3,1,6,4]=>10101=>01010
[5,2,3,4,1,6]=>10010=>01101
[5,2,3,4,6,1]=>10001=>01110
[5,2,3,6,1,4]=>10010=>01101
[5,2,3,6,4,1]=>10011=>01100
[5,2,4,1,3,6]=>10100=>01011
[5,2,4,1,6,3]=>10101=>01010
[5,2,4,3,1,6]=>10110=>01001
[5,2,4,3,6,1]=>10101=>01010
[5,2,4,6,1,3]=>10010=>01101
[5,2,4,6,3,1]=>10011=>01100
[5,2,6,1,3,4]=>10100=>01011
[5,2,6,1,4,3]=>10101=>01010
[5,2,6,3,1,4]=>10110=>01001
[5,2,6,3,4,1]=>10101=>01010
[5,2,6,4,1,3]=>10110=>01001
[5,2,6,4,3,1]=>10111=>01000
[5,3,1,2,4,6]=>11000=>00111
[5,3,1,2,6,4]=>11001=>00110
[5,3,1,4,2,6]=>11010=>00101
[5,3,1,4,6,2]=>11001=>00110
[5,3,1,6,2,4]=>11010=>00101
[5,3,1,6,4,2]=>11011=>00100
[5,3,2,1,4,6]=>11100=>00011
[5,3,2,1,6,4]=>11101=>00010
[5,3,2,4,1,6]=>11010=>00101
[5,3,2,4,6,1]=>11001=>00110
[5,3,2,6,1,4]=>11010=>00101
[5,3,2,6,4,1]=>11011=>00100
[5,3,4,1,2,6]=>10100=>01011
[5,3,4,1,6,2]=>10101=>01010
[5,3,4,2,1,6]=>10110=>01001
[5,3,4,2,6,1]=>10101=>01010
[5,3,4,6,1,2]=>10010=>01101
[5,3,4,6,2,1]=>10011=>01100
[5,3,6,1,2,4]=>10100=>01011
[5,3,6,1,4,2]=>10101=>01010
[5,3,6,2,1,4]=>10110=>01001
[5,3,6,2,4,1]=>10101=>01010
[5,3,6,4,1,2]=>10110=>01001
[5,3,6,4,2,1]=>10111=>01000
[5,4,1,2,3,6]=>11000=>00111
[5,4,1,2,6,3]=>11001=>00110
[5,4,1,3,2,6]=>11010=>00101
[5,4,1,3,6,2]=>11001=>00110
[5,4,1,6,2,3]=>11010=>00101
[5,4,1,6,3,2]=>11011=>00100
[5,4,2,1,3,6]=>11100=>00011
[5,4,2,1,6,3]=>11101=>00010
[5,4,2,3,1,6]=>11010=>00101
[5,4,2,3,6,1]=>11001=>00110
[5,4,2,6,1,3]=>11010=>00101
[5,4,2,6,3,1]=>11011=>00100
[5,4,3,1,2,6]=>11100=>00011
[5,4,3,1,6,2]=>11101=>00010
[5,4,3,2,1,6]=>11110=>00001
[5,4,3,2,6,1]=>11101=>00010
[5,4,3,6,1,2]=>11010=>00101
[5,4,3,6,2,1]=>11011=>00100
[5,4,6,1,2,3]=>10100=>01011
[5,4,6,1,3,2]=>10101=>01010
[5,4,6,2,1,3]=>10110=>01001
[5,4,6,2,3,1]=>10101=>01010
[5,4,6,3,1,2]=>10110=>01001
[5,4,6,3,2,1]=>10111=>01000
[5,6,1,2,3,4]=>01000=>10111
[5,6,1,2,4,3]=>01001=>10110
[5,6,1,3,2,4]=>01010=>10101
[5,6,1,3,4,2]=>01001=>10110
[5,6,1,4,2,3]=>01010=>10101
[5,6,1,4,3,2]=>01011=>10100
[5,6,2,1,3,4]=>01100=>10011
[5,6,2,1,4,3]=>01101=>10010
[5,6,2,3,1,4]=>01010=>10101
[5,6,2,3,4,1]=>01001=>10110
[5,6,2,4,1,3]=>01010=>10101
[5,6,2,4,3,1]=>01011=>10100
[5,6,3,1,2,4]=>01100=>10011
[5,6,3,1,4,2]=>01101=>10010
[5,6,3,2,1,4]=>01110=>10001
[5,6,3,2,4,1]=>01101=>10010
[5,6,3,4,1,2]=>01010=>10101
[5,6,3,4,2,1]=>01011=>10100
[5,6,4,1,2,3]=>01100=>10011
[5,6,4,1,3,2]=>01101=>10010
[5,6,4,2,1,3]=>01110=>10001
[5,6,4,2,3,1]=>01101=>10010
[5,6,4,3,1,2]=>01110=>10001
[5,6,4,3,2,1]=>01111=>10000
[6,1,2,3,4,5]=>10000=>01111
[6,1,2,3,5,4]=>10001=>01110
[6,1,2,4,3,5]=>10010=>01101
[6,1,2,4,5,3]=>10001=>01110
[6,1,2,5,3,4]=>10010=>01101
[6,1,2,5,4,3]=>10011=>01100
[6,1,3,2,4,5]=>10100=>01011
[6,1,3,2,5,4]=>10101=>01010
[6,1,3,4,2,5]=>10010=>01101
[6,1,3,4,5,2]=>10001=>01110
[6,1,3,5,2,4]=>10010=>01101
[6,1,3,5,4,2]=>10011=>01100
[6,1,4,2,3,5]=>10100=>01011
[6,1,4,2,5,3]=>10101=>01010
[6,1,4,3,2,5]=>10110=>01001
[6,1,4,3,5,2]=>10101=>01010
[6,1,4,5,2,3]=>10010=>01101
[6,1,4,5,3,2]=>10011=>01100
[6,1,5,2,3,4]=>10100=>01011
[6,1,5,2,4,3]=>10101=>01010
[6,1,5,3,2,4]=>10110=>01001
[6,1,5,3,4,2]=>10101=>01010
[6,1,5,4,2,3]=>10110=>01001
[6,1,5,4,3,2]=>10111=>01000
[6,2,1,3,4,5]=>11000=>00111
[6,2,1,3,5,4]=>11001=>00110
[6,2,1,4,3,5]=>11010=>00101
[6,2,1,4,5,3]=>11001=>00110
[6,2,1,5,3,4]=>11010=>00101
[6,2,1,5,4,3]=>11011=>00100
[6,2,3,1,4,5]=>10100=>01011
[6,2,3,1,5,4]=>10101=>01010
[6,2,3,4,1,5]=>10010=>01101
[6,2,3,4,5,1]=>10001=>01110
[6,2,3,5,1,4]=>10010=>01101
[6,2,3,5,4,1]=>10011=>01100
[6,2,4,1,3,5]=>10100=>01011
[6,2,4,1,5,3]=>10101=>01010
[6,2,4,3,1,5]=>10110=>01001
[6,2,4,3,5,1]=>10101=>01010
[6,2,4,5,1,3]=>10010=>01101
[6,2,4,5,3,1]=>10011=>01100
[6,2,5,1,3,4]=>10100=>01011
[6,2,5,1,4,3]=>10101=>01010
[6,2,5,3,1,4]=>10110=>01001
[6,2,5,3,4,1]=>10101=>01010
[6,2,5,4,1,3]=>10110=>01001
[6,2,5,4,3,1]=>10111=>01000
[6,3,1,2,4,5]=>11000=>00111
[6,3,1,2,5,4]=>11001=>00110
[6,3,1,4,2,5]=>11010=>00101
[6,3,1,4,5,2]=>11001=>00110
[6,3,1,5,2,4]=>11010=>00101
[6,3,1,5,4,2]=>11011=>00100
[6,3,2,1,4,5]=>11100=>00011
[6,3,2,1,5,4]=>11101=>00010
[6,3,2,4,1,5]=>11010=>00101
[6,3,2,4,5,1]=>11001=>00110
[6,3,2,5,1,4]=>11010=>00101
[6,3,2,5,4,1]=>11011=>00100
[6,3,4,1,2,5]=>10100=>01011
[6,3,4,1,5,2]=>10101=>01010
[6,3,4,2,1,5]=>10110=>01001
[6,3,4,2,5,1]=>10101=>01010
[6,3,4,5,1,2]=>10010=>01101
[6,3,4,5,2,1]=>10011=>01100
[6,3,5,1,2,4]=>10100=>01011
[6,3,5,1,4,2]=>10101=>01010
[6,3,5,2,1,4]=>10110=>01001
[6,3,5,2,4,1]=>10101=>01010
[6,3,5,4,1,2]=>10110=>01001
[6,3,5,4,2,1]=>10111=>01000
[6,4,1,2,3,5]=>11000=>00111
[6,4,1,2,5,3]=>11001=>00110
[6,4,1,3,2,5]=>11010=>00101
[6,4,1,3,5,2]=>11001=>00110
[6,4,1,5,2,3]=>11010=>00101
[6,4,1,5,3,2]=>11011=>00100
[6,4,2,1,3,5]=>11100=>00011
[6,4,2,1,5,3]=>11101=>00010
[6,4,2,3,1,5]=>11010=>00101
[6,4,2,3,5,1]=>11001=>00110
[6,4,2,5,1,3]=>11010=>00101
[6,4,2,5,3,1]=>11011=>00100
[6,4,3,1,2,5]=>11100=>00011
[6,4,3,1,5,2]=>11101=>00010
[6,4,3,2,1,5]=>11110=>00001
[6,4,3,2,5,1]=>11101=>00010
[6,4,3,5,1,2]=>11010=>00101
[6,4,3,5,2,1]=>11011=>00100
[6,4,5,1,2,3]=>10100=>01011
[6,4,5,1,3,2]=>10101=>01010
[6,4,5,2,1,3]=>10110=>01001
[6,4,5,2,3,1]=>10101=>01010
[6,4,5,3,1,2]=>10110=>01001
[6,4,5,3,2,1]=>10111=>01000
[6,5,1,2,3,4]=>11000=>00111
[6,5,1,2,4,3]=>11001=>00110
[6,5,1,3,2,4]=>11010=>00101
[6,5,1,3,4,2]=>11001=>00110
[6,5,1,4,2,3]=>11010=>00101
[6,5,1,4,3,2]=>11011=>00100
[6,5,2,1,3,4]=>11100=>00011
[6,5,2,1,4,3]=>11101=>00010
[6,5,2,3,1,4]=>11010=>00101
[6,5,2,3,4,1]=>11001=>00110
[6,5,2,4,1,3]=>11010=>00101
[6,5,2,4,3,1]=>11011=>00100
[6,5,3,1,2,4]=>11100=>00011
[6,5,3,1,4,2]=>11101=>00010
[6,5,3,2,1,4]=>11110=>00001
[6,5,3,2,4,1]=>11101=>00010
[6,5,3,4,1,2]=>11010=>00101
[6,5,3,4,2,1]=>11011=>00100
[6,5,4,1,2,3]=>11100=>00011
[6,5,4,1,3,2]=>11101=>00010
[6,5,4,2,1,3]=>11110=>00001
[6,5,4,2,3,1]=>11101=>00010
[6,5,4,3,1,2]=>11110=>00001
[6,5,4,3,2,1]=>11111=>00000
[1,2,3,4,5,6,7]=>000000=>111111
[1,2,3,4,5,7,6]=>000001=>111110
[1,2,3,4,6,5,7]=>000010=>111101
[1,2,3,4,6,7,5]=>000001=>111110
[1,2,3,4,7,5,6]=>000010=>111101
[1,2,3,4,7,6,5]=>000011=>111100
[1,2,3,5,4,6,7]=>000100=>111011
[1,2,3,5,4,7,6]=>000101=>111010
[1,2,3,5,6,4,7]=>000010=>111101
[1,2,3,5,6,7,4]=>000001=>111110
[1,2,3,5,7,4,6]=>000010=>111101
[1,2,3,5,7,6,4]=>000011=>111100
[1,2,3,6,4,5,7]=>000100=>111011
[1,2,3,6,4,7,5]=>000101=>111010
[1,2,3,6,5,4,7]=>000110=>111001
[1,2,3,6,5,7,4]=>000101=>111010
[1,2,3,6,7,4,5]=>000010=>111101
[1,2,3,6,7,5,4]=>000011=>111100
[1,2,3,7,4,5,6]=>000100=>111011
[1,2,3,7,4,6,5]=>000101=>111010
[1,2,3,7,5,4,6]=>000110=>111001
[1,2,3,7,5,6,4]=>000101=>111010
[1,2,3,7,6,4,5]=>000110=>111001
[1,2,3,7,6,5,4]=>000111=>111000
[1,2,4,3,5,6,7]=>001000=>110111
[1,2,4,3,5,7,6]=>001001=>110110
[1,2,4,3,6,5,7]=>001010=>110101
[1,2,4,3,6,7,5]=>001001=>110110
[1,2,4,3,7,5,6]=>001010=>110101
[1,2,4,3,7,6,5]=>001011=>110100
[1,2,4,5,3,6,7]=>000100=>111011
[1,2,4,5,3,7,6]=>000101=>111010
[1,2,4,5,6,3,7]=>000010=>111101
[1,2,4,5,6,7,3]=>000001=>111110
[1,2,4,5,7,3,6]=>000010=>111101
[1,2,4,5,7,6,3]=>000011=>111100
[1,2,4,6,3,5,7]=>000100=>111011
[1,2,4,6,3,7,5]=>000101=>111010
[1,2,4,6,5,3,7]=>000110=>111001
[1,2,4,6,5,7,3]=>000101=>111010
[1,2,4,6,7,3,5]=>000010=>111101
[1,2,4,6,7,5,3]=>000011=>111100
[1,2,4,7,3,5,6]=>000100=>111011
[1,2,4,7,3,6,5]=>000101=>111010
[1,2,4,7,5,3,6]=>000110=>111001
[1,2,4,7,5,6,3]=>000101=>111010
[1,2,4,7,6,3,5]=>000110=>111001
[1,2,4,7,6,5,3]=>000111=>111000
[1,2,5,3,4,6,7]=>001000=>110111
[1,2,5,3,4,7,6]=>001001=>110110
[1,2,5,3,6,4,7]=>001010=>110101
[1,2,5,3,6,7,4]=>001001=>110110
[1,2,5,3,7,4,6]=>001010=>110101
[1,2,5,3,7,6,4]=>001011=>110100
[1,2,5,4,3,6,7]=>001100=>110011
[1,2,5,4,3,7,6]=>001101=>110010
[1,2,5,4,6,3,7]=>001010=>110101
[1,2,5,4,6,7,3]=>001001=>110110
[1,2,5,4,7,3,6]=>001010=>110101
[1,2,5,4,7,6,3]=>001011=>110100
[1,2,5,6,3,4,7]=>000100=>111011
[1,2,5,6,3,7,4]=>000101=>111010
[1,2,5,6,4,3,7]=>000110=>111001
[1,2,5,6,4,7,3]=>000101=>111010
[1,2,5,6,7,3,4]=>000010=>111101
[1,2,5,6,7,4,3]=>000011=>111100
[1,2,5,7,3,4,6]=>000100=>111011
[1,2,5,7,3,6,4]=>000101=>111010
[1,2,5,7,4,3,6]=>000110=>111001
[1,2,5,7,4,6,3]=>000101=>111010
[1,2,5,7,6,3,4]=>000110=>111001
[1,2,5,7,6,4,3]=>000111=>111000
[1,2,6,3,4,5,7]=>001000=>110111
[1,2,6,3,4,7,5]=>001001=>110110
[1,2,6,3,5,4,7]=>001010=>110101
[1,2,6,3,5,7,4]=>001001=>110110
[1,2,6,3,7,4,5]=>001010=>110101
[1,2,6,3,7,5,4]=>001011=>110100
[1,2,6,4,3,5,7]=>001100=>110011
[1,2,6,4,3,7,5]=>001101=>110010
[1,2,6,4,5,3,7]=>001010=>110101
[1,2,6,4,5,7,3]=>001001=>110110
[1,2,6,4,7,3,5]=>001010=>110101
[1,2,6,4,7,5,3]=>001011=>110100
[1,2,6,5,3,4,7]=>001100=>110011
[1,2,6,5,3,7,4]=>001101=>110010
[1,2,6,5,4,3,7]=>001110=>110001
[1,2,6,5,4,7,3]=>001101=>110010
[1,2,6,5,7,3,4]=>001010=>110101
[1,2,6,5,7,4,3]=>001011=>110100
[1,2,6,7,3,4,5]=>000100=>111011
[1,2,6,7,3,5,4]=>000101=>111010
[1,2,6,7,4,3,5]=>000110=>111001
[1,2,6,7,4,5,3]=>000101=>111010
[1,2,6,7,5,3,4]=>000110=>111001
[1,2,6,7,5,4,3]=>000111=>111000
[1,2,7,3,4,5,6]=>001000=>110111
[1,2,7,3,4,6,5]=>001001=>110110
[1,2,7,3,5,4,6]=>001010=>110101
[1,2,7,3,5,6,4]=>001001=>110110
[1,2,7,3,6,4,5]=>001010=>110101
[1,2,7,3,6,5,4]=>001011=>110100
[1,2,7,4,3,5,6]=>001100=>110011
[1,2,7,4,3,6,5]=>001101=>110010
[1,2,7,4,5,3,6]=>001010=>110101
[1,2,7,4,5,6,3]=>001001=>110110
[1,2,7,4,6,3,5]=>001010=>110101
[1,2,7,4,6,5,3]=>001011=>110100
[1,2,7,5,3,4,6]=>001100=>110011
[1,2,7,5,3,6,4]=>001101=>110010
[1,2,7,5,4,3,6]=>001110=>110001
[1,2,7,5,4,6,3]=>001101=>110010
[1,2,7,5,6,3,4]=>001010=>110101
[1,2,7,5,6,4,3]=>001011=>110100
[1,2,7,6,3,4,5]=>001100=>110011
[1,2,7,6,3,5,4]=>001101=>110010
[1,2,7,6,4,3,5]=>001110=>110001
[1,2,7,6,4,5,3]=>001101=>110010
[1,2,7,6,5,3,4]=>001110=>110001
[1,2,7,6,5,4,3]=>001111=>110000
[1,3,2,4,5,6,7]=>010000=>101111
[1,3,2,4,5,7,6]=>010001=>101110
[1,3,2,4,6,5,7]=>010010=>101101
[1,3,2,4,6,7,5]=>010001=>101110
[1,3,2,4,7,5,6]=>010010=>101101
[1,3,2,4,7,6,5]=>010011=>101100
[1,3,2,5,4,6,7]=>010100=>101011
[1,3,2,5,4,7,6]=>010101=>101010
[1,3,2,5,6,4,7]=>010010=>101101
[1,3,2,5,6,7,4]=>010001=>101110
[1,3,2,5,7,4,6]=>010010=>101101
[1,3,2,5,7,6,4]=>010011=>101100
[1,3,2,6,4,5,7]=>010100=>101011
[1,3,2,6,4,7,5]=>010101=>101010
[1,3,2,6,5,4,7]=>010110=>101001
[1,3,2,6,5,7,4]=>010101=>101010
[1,3,2,6,7,4,5]=>010010=>101101
[1,3,2,6,7,5,4]=>010011=>101100
[1,3,2,7,4,5,6]=>010100=>101011
[1,3,2,7,4,6,5]=>010101=>101010
[1,3,2,7,5,4,6]=>010110=>101001
[1,3,2,7,5,6,4]=>010101=>101010
[1,3,2,7,6,4,5]=>010110=>101001
[1,3,2,7,6,5,4]=>010111=>101000
[1,3,4,2,5,6,7]=>001000=>110111
[1,3,4,2,5,7,6]=>001001=>110110
[1,3,4,2,6,5,7]=>001010=>110101
[1,3,4,2,6,7,5]=>001001=>110110
[1,3,4,2,7,5,6]=>001010=>110101
[1,3,4,2,7,6,5]=>001011=>110100
[1,3,4,5,2,6,7]=>000100=>111011
[1,3,4,5,2,7,6]=>000101=>111010
[1,3,4,5,6,2,7]=>000010=>111101
[1,3,4,5,6,7,2]=>000001=>111110
[1,3,4,5,7,2,6]=>000010=>111101
[1,3,4,5,7,6,2]=>000011=>111100
[1,3,4,6,2,5,7]=>000100=>111011
[1,3,4,6,2,7,5]=>000101=>111010
[1,3,4,6,5,2,7]=>000110=>111001
[1,3,4,6,5,7,2]=>000101=>111010
[1,3,4,6,7,2,5]=>000010=>111101
[1,3,4,6,7,5,2]=>000011=>111100
[1,3,4,7,2,5,6]=>000100=>111011
[1,3,4,7,2,6,5]=>000101=>111010
[1,3,4,7,5,2,6]=>000110=>111001
[1,3,4,7,5,6,2]=>000101=>111010
[1,3,4,7,6,2,5]=>000110=>111001
[1,3,4,7,6,5,2]=>000111=>111000
[1,3,5,2,4,6,7]=>001000=>110111
[1,3,5,2,4,7,6]=>001001=>110110
[1,3,5,2,6,4,7]=>001010=>110101
[1,3,5,2,6,7,4]=>001001=>110110
[1,3,5,2,7,4,6]=>001010=>110101
[1,3,5,2,7,6,4]=>001011=>110100
[1,3,5,4,2,6,7]=>001100=>110011
[1,3,5,4,2,7,6]=>001101=>110010
[1,3,5,4,6,2,7]=>001010=>110101
[1,3,5,4,6,7,2]=>001001=>110110
[1,3,5,4,7,2,6]=>001010=>110101
[1,3,5,4,7,6,2]=>001011=>110100
[1,3,5,6,2,4,7]=>000100=>111011
[1,3,5,6,2,7,4]=>000101=>111010
[1,3,5,6,4,2,7]=>000110=>111001
[1,3,5,6,4,7,2]=>000101=>111010
[1,3,5,6,7,2,4]=>000010=>111101
[1,3,5,6,7,4,2]=>000011=>111100
[1,3,5,7,2,4,6]=>000100=>111011
[1,3,5,7,2,6,4]=>000101=>111010
[1,3,5,7,4,2,6]=>000110=>111001
[1,3,5,7,4,6,2]=>000101=>111010
[1,3,5,7,6,2,4]=>000110=>111001
[1,3,5,7,6,4,2]=>000111=>111000
[1,3,6,2,4,5,7]=>001000=>110111
[1,3,6,2,4,7,5]=>001001=>110110
[1,3,6,2,5,4,7]=>001010=>110101
[1,3,6,2,5,7,4]=>001001=>110110
[1,3,6,2,7,4,5]=>001010=>110101
[1,3,6,2,7,5,4]=>001011=>110100
[1,3,6,4,2,5,7]=>001100=>110011
[1,3,6,4,2,7,5]=>001101=>110010
[1,3,6,4,5,2,7]=>001010=>110101
[1,3,6,4,5,7,2]=>001001=>110110
[1,3,6,4,7,2,5]=>001010=>110101
[1,3,6,4,7,5,2]=>001011=>110100
[1,3,6,5,2,4,7]=>001100=>110011
[1,3,6,5,2,7,4]=>001101=>110010
[1,3,6,5,4,2,7]=>001110=>110001
[1,3,6,5,4,7,2]=>001101=>110010
[1,3,6,5,7,2,4]=>001010=>110101
[1,3,6,5,7,4,2]=>001011=>110100
[1,3,6,7,2,4,5]=>000100=>111011
[1,3,6,7,2,5,4]=>000101=>111010
[1,3,6,7,4,2,5]=>000110=>111001
[1,3,6,7,4,5,2]=>000101=>111010
[1,3,6,7,5,2,4]=>000110=>111001
[1,3,6,7,5,4,2]=>000111=>111000
[1,3,7,2,4,5,6]=>001000=>110111
[1,3,7,2,4,6,5]=>001001=>110110
[1,3,7,2,5,4,6]=>001010=>110101
[1,3,7,2,5,6,4]=>001001=>110110
[1,3,7,2,6,4,5]=>001010=>110101
[1,3,7,2,6,5,4]=>001011=>110100
[1,3,7,4,2,5,6]=>001100=>110011
[1,3,7,4,2,6,5]=>001101=>110010
[1,3,7,4,5,2,6]=>001010=>110101
[1,3,7,4,5,6,2]=>001001=>110110
[1,3,7,4,6,2,5]=>001010=>110101
[1,3,7,4,6,5,2]=>001011=>110100
[1,3,7,5,2,4,6]=>001100=>110011
[1,3,7,5,2,6,4]=>001101=>110010
[1,3,7,5,4,2,6]=>001110=>110001
[1,3,7,5,4,6,2]=>001101=>110010
[1,3,7,5,6,2,4]=>001010=>110101
[1,3,7,5,6,4,2]=>001011=>110100
[1,3,7,6,2,4,5]=>001100=>110011
[1,3,7,6,2,5,4]=>001101=>110010
[1,3,7,6,4,2,5]=>001110=>110001
[1,3,7,6,4,5,2]=>001101=>110010
[1,3,7,6,5,2,4]=>001110=>110001
[1,3,7,6,5,4,2]=>001111=>110000
[1,4,2,3,5,6,7]=>010000=>101111
[1,4,2,3,5,7,6]=>010001=>101110
[1,4,2,3,6,5,7]=>010010=>101101
[1,4,2,3,6,7,5]=>010001=>101110
[1,4,2,3,7,5,6]=>010010=>101101
[1,4,2,3,7,6,5]=>010011=>101100
[1,4,2,5,3,6,7]=>010100=>101011
[1,4,2,5,3,7,6]=>010101=>101010
[1,4,2,5,6,3,7]=>010010=>101101
[1,4,2,5,6,7,3]=>010001=>101110
[1,4,2,5,7,3,6]=>010010=>101101
[1,4,2,5,7,6,3]=>010011=>101100
[1,4,2,6,3,5,7]=>010100=>101011
[1,4,2,6,3,7,5]=>010101=>101010
[1,4,2,6,5,3,7]=>010110=>101001
[1,4,2,6,5,7,3]=>010101=>101010
[1,4,2,6,7,3,5]=>010010=>101101
[1,4,2,6,7,5,3]=>010011=>101100
[1,4,2,7,3,5,6]=>010100=>101011
[1,4,2,7,3,6,5]=>010101=>101010
[1,4,2,7,5,3,6]=>010110=>101001
[1,4,2,7,5,6,3]=>010101=>101010
[1,4,2,7,6,3,5]=>010110=>101001
[1,4,2,7,6,5,3]=>010111=>101000
[1,4,3,2,5,6,7]=>011000=>100111
[1,4,3,2,5,7,6]=>011001=>100110
[1,4,3,2,6,5,7]=>011010=>100101
[1,4,3,2,6,7,5]=>011001=>100110
[1,4,3,2,7,5,6]=>011010=>100101
[1,4,3,2,7,6,5]=>011011=>100100
[1,4,3,5,2,6,7]=>010100=>101011
[1,4,3,5,2,7,6]=>010101=>101010
[1,4,3,5,6,2,7]=>010010=>101101
[1,4,3,5,6,7,2]=>010001=>101110
[1,4,3,5,7,2,6]=>010010=>101101
[1,4,3,5,7,6,2]=>010011=>101100
[1,4,3,6,2,5,7]=>010100=>101011
[1,4,3,6,2,7,5]=>010101=>101010
[1,4,3,6,5,2,7]=>010110=>101001
[1,4,3,6,5,7,2]=>010101=>101010
[1,4,3,6,7,2,5]=>010010=>101101
[1,4,3,6,7,5,2]=>010011=>101100
[1,4,3,7,2,5,6]=>010100=>101011
[1,4,3,7,2,6,5]=>010101=>101010
[1,4,3,7,5,2,6]=>010110=>101001
[1,4,3,7,5,6,2]=>010101=>101010
[1,4,3,7,6,2,5]=>010110=>101001
[1,4,3,7,6,5,2]=>010111=>101000
[1,4,5,2,3,6,7]=>001000=>110111
[1,4,5,2,3,7,6]=>001001=>110110
[1,4,5,2,6,3,7]=>001010=>110101
[1,4,5,2,6,7,3]=>001001=>110110
[1,4,5,2,7,3,6]=>001010=>110101
[1,4,5,2,7,6,3]=>001011=>110100
[1,4,5,3,2,6,7]=>001100=>110011
[1,4,5,3,2,7,6]=>001101=>110010
[1,4,5,3,6,2,7]=>001010=>110101
[1,4,5,3,6,7,2]=>001001=>110110
[1,4,5,3,7,2,6]=>001010=>110101
[1,4,5,3,7,6,2]=>001011=>110100
[1,4,5,6,2,3,7]=>000100=>111011
[1,4,5,6,2,7,3]=>000101=>111010
[1,4,5,6,3,2,7]=>000110=>111001
[1,4,5,6,3,7,2]=>000101=>111010
[1,4,5,6,7,2,3]=>000010=>111101
[1,4,5,6,7,3,2]=>000011=>111100
[1,4,5,7,2,3,6]=>000100=>111011
[1,4,5,7,2,6,3]=>000101=>111010
[1,4,5,7,3,2,6]=>000110=>111001
[1,4,5,7,3,6,2]=>000101=>111010
[1,4,5,7,6,2,3]=>000110=>111001
[1,4,5,7,6,3,2]=>000111=>111000
[1,4,6,2,3,5,7]=>001000=>110111
[1,4,6,2,3,7,5]=>001001=>110110
[1,4,6,2,5,3,7]=>001010=>110101
[1,4,6,2,5,7,3]=>001001=>110110
[1,4,6,2,7,3,5]=>001010=>110101
[1,4,6,2,7,5,3]=>001011=>110100
[1,4,6,3,2,5,7]=>001100=>110011
[1,4,6,3,2,7,5]=>001101=>110010
[1,4,6,3,5,2,7]=>001010=>110101
[1,4,6,3,5,7,2]=>001001=>110110
[1,4,6,3,7,2,5]=>001010=>110101
[1,4,6,3,7,5,2]=>001011=>110100
[1,4,6,5,2,3,7]=>001100=>110011
[1,4,6,5,2,7,3]=>001101=>110010
[1,4,6,5,3,2,7]=>001110=>110001
[1,4,6,5,3,7,2]=>001101=>110010
[1,4,6,5,7,2,3]=>001010=>110101
[1,4,6,5,7,3,2]=>001011=>110100
[1,4,6,7,2,3,5]=>000100=>111011
[1,4,6,7,2,5,3]=>000101=>111010
[1,4,6,7,3,2,5]=>000110=>111001
[1,4,6,7,3,5,2]=>000101=>111010
[1,4,6,7,5,2,3]=>000110=>111001
[1,4,6,7,5,3,2]=>000111=>111000
[1,4,7,2,3,5,6]=>001000=>110111
[1,4,7,2,3,6,5]=>001001=>110110
[1,4,7,2,5,3,6]=>001010=>110101
[1,4,7,2,5,6,3]=>001001=>110110
[1,4,7,2,6,3,5]=>001010=>110101
[1,4,7,2,6,5,3]=>001011=>110100
[1,4,7,3,2,5,6]=>001100=>110011
[1,4,7,3,2,6,5]=>001101=>110010
[1,4,7,3,5,2,6]=>001010=>110101
[1,4,7,3,5,6,2]=>001001=>110110
[1,4,7,3,6,2,5]=>001010=>110101
[1,4,7,3,6,5,2]=>001011=>110100
[1,4,7,5,2,3,6]=>001100=>110011
[1,4,7,5,2,6,3]=>001101=>110010
[1,4,7,5,3,2,6]=>001110=>110001
[1,4,7,5,3,6,2]=>001101=>110010
[1,4,7,5,6,2,3]=>001010=>110101
[1,4,7,5,6,3,2]=>001011=>110100
[1,4,7,6,2,3,5]=>001100=>110011
[1,4,7,6,2,5,3]=>001101=>110010
[1,4,7,6,3,2,5]=>001110=>110001
[1,4,7,6,3,5,2]=>001101=>110010
[1,4,7,6,5,2,3]=>001110=>110001
[1,4,7,6,5,3,2]=>001111=>110000
[1,5,2,3,4,6,7]=>010000=>101111
[1,5,2,3,4,7,6]=>010001=>101110
[1,5,2,3,6,4,7]=>010010=>101101
[1,5,2,3,6,7,4]=>010001=>101110
[1,5,2,3,7,4,6]=>010010=>101101
[1,5,2,3,7,6,4]=>010011=>101100
[1,5,2,4,3,6,7]=>010100=>101011
[1,5,2,4,3,7,6]=>010101=>101010
[1,5,2,4,6,3,7]=>010010=>101101
[1,5,2,4,6,7,3]=>010001=>101110
[1,5,2,4,7,3,6]=>010010=>101101
[1,5,2,4,7,6,3]=>010011=>101100
[1,5,2,6,3,4,7]=>010100=>101011
[1,5,2,6,3,7,4]=>010101=>101010
[1,5,2,6,4,3,7]=>010110=>101001
[1,5,2,6,4,7,3]=>010101=>101010
[1,5,2,6,7,3,4]=>010010=>101101
[1,5,2,6,7,4,3]=>010011=>101100
[1,5,2,7,3,4,6]=>010100=>101011
[1,5,2,7,3,6,4]=>010101=>101010
[1,5,2,7,4,3,6]=>010110=>101001
[1,5,2,7,4,6,3]=>010101=>101010
[1,5,2,7,6,3,4]=>010110=>101001
[1,5,2,7,6,4,3]=>010111=>101000
[1,5,3,2,4,6,7]=>011000=>100111
[1,5,3,2,4,7,6]=>011001=>100110
[1,5,3,2,6,4,7]=>011010=>100101
[1,5,3,2,6,7,4]=>011001=>100110
[1,5,3,2,7,4,6]=>011010=>100101
[1,5,3,2,7,6,4]=>011011=>100100
[1,5,3,4,2,6,7]=>010100=>101011
[1,5,3,4,2,7,6]=>010101=>101010
[1,5,3,4,6,2,7]=>010010=>101101
[1,5,3,4,6,7,2]=>010001=>101110
[1,5,3,4,7,2,6]=>010010=>101101
[1,5,3,4,7,6,2]=>010011=>101100
[1,5,3,6,2,4,7]=>010100=>101011
[1,5,3,6,2,7,4]=>010101=>101010
[1,5,3,6,4,2,7]=>010110=>101001
[1,5,3,6,4,7,2]=>010101=>101010
[1,5,3,6,7,2,4]=>010010=>101101
[1,5,3,6,7,4,2]=>010011=>101100
[1,5,3,7,2,4,6]=>010100=>101011
[1,5,3,7,2,6,4]=>010101=>101010
[1,5,3,7,4,2,6]=>010110=>101001
[1,5,3,7,4,6,2]=>010101=>101010
[1,5,3,7,6,2,4]=>010110=>101001
[1,5,3,7,6,4,2]=>010111=>101000
[1,5,4,2,3,6,7]=>011000=>100111
[1,5,4,2,3,7,6]=>011001=>100110
[1,5,4,2,6,3,7]=>011010=>100101
[1,5,4,2,6,7,3]=>011001=>100110
[1,5,4,2,7,3,6]=>011010=>100101
[1,5,4,2,7,6,3]=>011011=>100100
[1,5,4,3,2,6,7]=>011100=>100011
[1,5,4,3,2,7,6]=>011101=>100010
[1,5,4,3,6,2,7]=>011010=>100101
[1,5,4,3,6,7,2]=>011001=>100110
[1,5,4,3,7,2,6]=>011010=>100101
[1,5,4,3,7,6,2]=>011011=>100100
[1,5,4,6,2,3,7]=>010100=>101011
[1,5,4,6,2,7,3]=>010101=>101010
[1,5,4,6,3,2,7]=>010110=>101001
[1,5,4,6,3,7,2]=>010101=>101010
[1,5,4,6,7,2,3]=>010010=>101101
[1,5,4,6,7,3,2]=>010011=>101100
[1,5,4,7,2,3,6]=>010100=>101011
[1,5,4,7,2,6,3]=>010101=>101010
[1,5,4,7,3,2,6]=>010110=>101001
[1,5,4,7,3,6,2]=>010101=>101010
[1,5,4,7,6,2,3]=>010110=>101001
[1,5,4,7,6,3,2]=>010111=>101000
[1,5,6,2,3,4,7]=>001000=>110111
[1,5,6,2,3,7,4]=>001001=>110110
[1,5,6,2,4,3,7]=>001010=>110101
[1,5,6,2,4,7,3]=>001001=>110110
[1,5,6,2,7,3,4]=>001010=>110101
[1,5,6,2,7,4,3]=>001011=>110100
[1,5,6,3,2,4,7]=>001100=>110011
[1,5,6,3,2,7,4]=>001101=>110010
[1,5,6,3,4,2,7]=>001010=>110101
[1,5,6,3,4,7,2]=>001001=>110110
[1,5,6,3,7,2,4]=>001010=>110101
[1,5,6,3,7,4,2]=>001011=>110100
[1,5,6,4,2,3,7]=>001100=>110011
[1,5,6,4,2,7,3]=>001101=>110010
[1,5,6,4,3,2,7]=>001110=>110001
[1,5,6,4,3,7,2]=>001101=>110010
[1,5,6,4,7,2,3]=>001010=>110101
[1,5,6,4,7,3,2]=>001011=>110100
[1,5,6,7,2,3,4]=>000100=>111011
[1,5,6,7,2,4,3]=>000101=>111010
[1,5,6,7,3,2,4]=>000110=>111001
[1,5,6,7,3,4,2]=>000101=>111010
[1,5,6,7,4,2,3]=>000110=>111001
[1,5,6,7,4,3,2]=>000111=>111000
[1,5,7,2,3,4,6]=>001000=>110111
[1,5,7,2,3,6,4]=>001001=>110110
[1,5,7,2,4,3,6]=>001010=>110101
[1,5,7,2,4,6,3]=>001001=>110110
[1,5,7,2,6,3,4]=>001010=>110101
[1,5,7,2,6,4,3]=>001011=>110100
[1,5,7,3,2,4,6]=>001100=>110011
[1,5,7,3,2,6,4]=>001101=>110010
[1,5,7,3,4,2,6]=>001010=>110101
[1,5,7,3,4,6,2]=>001001=>110110
[1,5,7,3,6,2,4]=>001010=>110101
[1,5,7,3,6,4,2]=>001011=>110100
[1,5,7,4,2,3,6]=>001100=>110011
[1,5,7,4,2,6,3]=>001101=>110010
[1,5,7,4,3,2,6]=>001110=>110001
[1,5,7,4,3,6,2]=>001101=>110010
[1,5,7,4,6,2,3]=>001010=>110101
[1,5,7,4,6,3,2]=>001011=>110100
[1,5,7,6,2,3,4]=>001100=>110011
[1,5,7,6,2,4,3]=>001101=>110010
[1,5,7,6,3,2,4]=>001110=>110001
[1,5,7,6,3,4,2]=>001101=>110010
[1,5,7,6,4,2,3]=>001110=>110001
[1,5,7,6,4,3,2]=>001111=>110000
[1,6,2,3,4,5,7]=>010000=>101111
[1,6,2,3,4,7,5]=>010001=>101110
[1,6,2,3,5,4,7]=>010010=>101101
[1,6,2,3,5,7,4]=>010001=>101110
[1,6,2,3,7,4,5]=>010010=>101101
[1,6,2,3,7,5,4]=>010011=>101100
[1,6,2,4,3,5,7]=>010100=>101011
[1,6,2,4,3,7,5]=>010101=>101010
[1,6,2,4,5,3,7]=>010010=>101101
[1,6,2,4,5,7,3]=>010001=>101110
[1,6,2,4,7,3,5]=>010010=>101101
[1,6,2,4,7,5,3]=>010011=>101100
[1,6,2,5,3,4,7]=>010100=>101011
[1,6,2,5,3,7,4]=>010101=>101010
[1,6,2,5,4,3,7]=>010110=>101001
[1,6,2,5,4,7,3]=>010101=>101010
[1,6,2,5,7,3,4]=>010010=>101101
[1,6,2,5,7,4,3]=>010011=>101100
[1,6,2,7,3,4,5]=>010100=>101011
[1,6,2,7,3,5,4]=>010101=>101010
[1,6,2,7,4,3,5]=>010110=>101001
[1,6,2,7,4,5,3]=>010101=>101010
[1,6,2,7,5,3,4]=>010110=>101001
[1,6,2,7,5,4,3]=>010111=>101000
[1,6,3,2,4,5,7]=>011000=>100111
[1,6,3,2,4,7,5]=>011001=>100110
[1,6,3,2,5,4,7]=>011010=>100101
[1,6,3,2,5,7,4]=>011001=>100110
[1,6,3,2,7,4,5]=>011010=>100101
[1,6,3,2,7,5,4]=>011011=>100100
[1,6,3,4,2,5,7]=>010100=>101011
[1,6,3,4,2,7,5]=>010101=>101010
[1,6,3,4,5,2,7]=>010010=>101101
[1,6,3,4,5,7,2]=>010001=>101110
[1,6,3,4,7,2,5]=>010010=>101101
[1,6,3,4,7,5,2]=>010011=>101100
[1,6,3,5,2,4,7]=>010100=>101011
[1,6,3,5,2,7,4]=>010101=>101010
[1,6,3,5,4,2,7]=>010110=>101001
[1,6,3,5,4,7,2]=>010101=>101010
[1,6,3,5,7,2,4]=>010010=>101101
[1,6,3,5,7,4,2]=>010011=>101100
[1,6,3,7,2,4,5]=>010100=>101011
[1,6,3,7,2,5,4]=>010101=>101010
[1,6,3,7,4,2,5]=>010110=>101001
[1,6,3,7,4,5,2]=>010101=>101010
[1,6,3,7,5,2,4]=>010110=>101001
[1,6,3,7,5,4,2]=>010111=>101000
[1,6,4,2,3,5,7]=>011000=>100111
[1,6,4,2,3,7,5]=>011001=>100110
[1,6,4,2,5,3,7]=>011010=>100101
[1,6,4,2,5,7,3]=>011001=>100110
[1,6,4,2,7,3,5]=>011010=>100101
[1,6,4,2,7,5,3]=>011011=>100100
[1,6,4,3,2,5,7]=>011100=>100011
[1,6,4,3,2,7,5]=>011101=>100010
[1,6,4,3,5,2,7]=>011010=>100101
[1,6,4,3,5,7,2]=>011001=>100110
[1,6,4,3,7,2,5]=>011010=>100101
[1,6,4,3,7,5,2]=>011011=>100100
[1,6,4,5,2,3,7]=>010100=>101011
[1,6,4,5,2,7,3]=>010101=>101010
[1,6,4,5,3,2,7]=>010110=>101001
[1,6,4,5,3,7,2]=>010101=>101010
[1,6,4,5,7,2,3]=>010010=>101101
[1,6,4,5,7,3,2]=>010011=>101100
[1,6,4,7,2,3,5]=>010100=>101011
[1,6,4,7,2,5,3]=>010101=>101010
[1,6,4,7,3,2,5]=>010110=>101001
[1,6,4,7,3,5,2]=>010101=>101010
[1,6,4,7,5,2,3]=>010110=>101001
[1,6,4,7,5,3,2]=>010111=>101000
[1,6,5,2,3,4,7]=>011000=>100111
[1,6,5,2,3,7,4]=>011001=>100110
[1,6,5,2,4,3,7]=>011010=>100101
[1,6,5,2,4,7,3]=>011001=>100110
[1,6,5,2,7,3,4]=>011010=>100101
[1,6,5,2,7,4,3]=>011011=>100100
[1,6,5,3,2,4,7]=>011100=>100011
[1,6,5,3,2,7,4]=>011101=>100010
[1,6,5,3,4,2,7]=>011010=>100101
[1,6,5,3,4,7,2]=>011001=>100110
[1,6,5,3,7,2,4]=>011010=>100101
[1,6,5,3,7,4,2]=>011011=>100100
[1,6,5,4,2,3,7]=>011100=>100011
[1,6,5,4,2,7,3]=>011101=>100010
[1,6,5,4,3,2,7]=>011110=>100001
[1,6,5,4,3,7,2]=>011101=>100010
[1,6,5,4,7,2,3]=>011010=>100101
[1,6,5,4,7,3,2]=>011011=>100100
[1,6,5,7,2,3,4]=>010100=>101011
[1,6,5,7,2,4,3]=>010101=>101010
[1,6,5,7,3,2,4]=>010110=>101001
[1,6,5,7,3,4,2]=>010101=>101010
[1,6,5,7,4,2,3]=>010110=>101001
[1,6,5,7,4,3,2]=>010111=>101000
[1,6,7,2,3,4,5]=>001000=>110111
[1,6,7,2,3,5,4]=>001001=>110110
[1,6,7,2,4,3,5]=>001010=>110101
[1,6,7,2,4,5,3]=>001001=>110110
[1,6,7,2,5,3,4]=>001010=>110101
[1,6,7,2,5,4,3]=>001011=>110100
[1,6,7,3,2,4,5]=>001100=>110011
[1,6,7,3,2,5,4]=>001101=>110010
[1,6,7,3,4,2,5]=>001010=>110101
[1,6,7,3,4,5,2]=>001001=>110110
[1,6,7,3,5,2,4]=>001010=>110101
[1,6,7,3,5,4,2]=>001011=>110100
[1,6,7,4,2,3,5]=>001100=>110011
[1,6,7,4,2,5,3]=>001101=>110010
[1,6,7,4,3,2,5]=>001110=>110001
[1,6,7,4,3,5,2]=>001101=>110010
[1,6,7,4,5,2,3]=>001010=>110101
[1,6,7,4,5,3,2]=>001011=>110100
[1,6,7,5,2,3,4]=>001100=>110011
[1,6,7,5,2,4,3]=>001101=>110010
[1,6,7,5,3,2,4]=>001110=>110001
[1,6,7,5,3,4,2]=>001101=>110010
[1,6,7,5,4,2,3]=>001110=>110001
[1,6,7,5,4,3,2]=>001111=>110000
[1,7,2,3,4,5,6]=>010000=>101111
[1,7,2,3,4,6,5]=>010001=>101110
[1,7,2,3,5,4,6]=>010010=>101101
[1,7,2,3,5,6,4]=>010001=>101110
[1,7,2,3,6,4,5]=>010010=>101101
[1,7,2,3,6,5,4]=>010011=>101100
[1,7,2,4,3,5,6]=>010100=>101011
[1,7,2,4,3,6,5]=>010101=>101010
[1,7,2,4,5,3,6]=>010010=>101101
[1,7,2,4,5,6,3]=>010001=>101110
[1,7,2,4,6,3,5]=>010010=>101101
[1,7,2,4,6,5,3]=>010011=>101100
[1,7,2,5,3,4,6]=>010100=>101011
[1,7,2,5,3,6,4]=>010101=>101010
[1,7,2,5,4,3,6]=>010110=>101001
[1,7,2,5,4,6,3]=>010101=>101010
[1,7,2,5,6,3,4]=>010010=>101101
[1,7,2,5,6,4,3]=>010011=>101100
[1,7,2,6,3,4,5]=>010100=>101011
[1,7,2,6,3,5,4]=>010101=>101010
[1,7,2,6,4,3,5]=>010110=>101001
[1,7,2,6,4,5,3]=>010101=>101010
[1,7,2,6,5,3,4]=>010110=>101001
[1,7,2,6,5,4,3]=>010111=>101000
[1,7,3,2,4,5,6]=>011000=>100111
[1,7,3,2,4,6,5]=>011001=>100110
[1,7,3,2,5,4,6]=>011010=>100101
[1,7,3,2,5,6,4]=>011001=>100110
[1,7,3,2,6,4,5]=>011010=>100101
[1,7,3,2,6,5,4]=>011011=>100100
[1,7,3,4,2,5,6]=>010100=>101011
[1,7,3,4,2,6,5]=>010101=>101010
[1,7,3,4,5,2,6]=>010010=>101101
[1,7,3,4,5,6,2]=>010001=>101110
[1,7,3,4,6,2,5]=>010010=>101101
[1,7,3,4,6,5,2]=>010011=>101100
[1,7,3,5,2,4,6]=>010100=>101011
[1,7,3,5,2,6,4]=>010101=>101010
[1,7,3,5,4,2,6]=>010110=>101001
[1,7,3,5,4,6,2]=>010101=>101010
[1,7,3,5,6,2,4]=>010010=>101101
[1,7,3,5,6,4,2]=>010011=>101100
[1,7,3,6,2,4,5]=>010100=>101011
[1,7,3,6,2,5,4]=>010101=>101010
[1,7,3,6,4,2,5]=>010110=>101001
[1,7,3,6,4,5,2]=>010101=>101010
[1,7,3,6,5,2,4]=>010110=>101001
[1,7,3,6,5,4,2]=>010111=>101000
[1,7,4,2,3,5,6]=>011000=>100111
[1,7,4,2,3,6,5]=>011001=>100110
[1,7,4,2,5,3,6]=>011010=>100101
[1,7,4,2,5,6,3]=>011001=>100110
[1,7,4,2,6,3,5]=>011010=>100101
[1,7,4,2,6,5,3]=>011011=>100100
[1,7,4,3,2,5,6]=>011100=>100011
[1,7,4,3,2,6,5]=>011101=>100010
[1,7,4,3,5,2,6]=>011010=>100101
[1,7,4,3,5,6,2]=>011001=>100110
[1,7,4,3,6,2,5]=>011010=>100101
[1,7,4,3,6,5,2]=>011011=>100100
[1,7,4,5,2,3,6]=>010100=>101011
[1,7,4,5,2,6,3]=>010101=>101010
[1,7,4,5,3,2,6]=>010110=>101001
[1,7,4,5,3,6,2]=>010101=>101010
[1,7,4,5,6,2,3]=>010010=>101101
[1,7,4,5,6,3,2]=>010011=>101100
[1,7,4,6,2,3,5]=>010100=>101011
[1,7,4,6,2,5,3]=>010101=>101010
[1,7,4,6,3,2,5]=>010110=>101001
[1,7,4,6,3,5,2]=>010101=>101010
[1,7,4,6,5,2,3]=>010110=>101001
[1,7,4,6,5,3,2]=>010111=>101000
[1,7,5,2,3,4,6]=>011000=>100111
[1,7,5,2,3,6,4]=>011001=>100110
[1,7,5,2,4,3,6]=>011010=>100101
[1,7,5,2,4,6,3]=>011001=>100110
[1,7,5,2,6,3,4]=>011010=>100101
[1,7,5,2,6,4,3]=>011011=>100100
[1,7,5,3,2,4,6]=>011100=>100011
[1,7,5,3,2,6,4]=>011101=>100010
[1,7,5,3,4,2,6]=>011010=>100101
[1,7,5,3,4,6,2]=>011001=>100110
[1,7,5,3,6,2,4]=>011010=>100101
[1,7,5,3,6,4,2]=>011011=>100100
[1,7,5,4,2,3,6]=>011100=>100011
[1,7,5,4,2,6,3]=>011101=>100010
[1,7,5,4,3,2,6]=>011110=>100001
[1,7,5,4,3,6,2]=>011101=>100010
[1,7,5,4,6,2,3]=>011010=>100101
[1,7,5,4,6,3,2]=>011011=>100100
[1,7,5,6,2,3,4]=>010100=>101011
[1,7,5,6,2,4,3]=>010101=>101010
[1,7,5,6,3,2,4]=>010110=>101001
[1,7,5,6,3,4,2]=>010101=>101010
[1,7,5,6,4,2,3]=>010110=>101001
[1,7,5,6,4,3,2]=>010111=>101000
[1,7,6,2,3,4,5]=>011000=>100111
[1,7,6,2,3,5,4]=>011001=>100110
[1,7,6,2,4,3,5]=>011010=>100101
[1,7,6,2,4,5,3]=>011001=>100110
[1,7,6,2,5,3,4]=>011010=>100101
[1,7,6,2,5,4,3]=>011011=>100100
[1,7,6,3,2,4,5]=>011100=>100011
[1,7,6,3,2,5,4]=>011101=>100010
[1,7,6,3,4,2,5]=>011010=>100101
[1,7,6,3,4,5,2]=>011001=>100110
[1,7,6,3,5,2,4]=>011010=>100101
[1,7,6,3,5,4,2]=>011011=>100100
[1,7,6,4,2,3,5]=>011100=>100011
[1,7,6,4,2,5,3]=>011101=>100010
[1,7,6,4,3,2,5]=>011110=>100001
[1,7,6,4,3,5,2]=>011101=>100010
[1,7,6,4,5,2,3]=>011010=>100101
[1,7,6,4,5,3,2]=>011011=>100100
[1,7,6,5,2,3,4]=>011100=>100011
[1,7,6,5,2,4,3]=>011101=>100010
[1,7,6,5,3,2,4]=>011110=>100001
[1,7,6,5,3,4,2]=>011101=>100010
[1,7,6,5,4,2,3]=>011110=>100001
[1,7,6,5,4,3,2]=>011111=>100000
[2,1,3,4,5,6,7]=>100000=>011111
[2,1,3,4,5,7,6]=>100001=>011110
[2,1,3,4,6,5,7]=>100010=>011101
[2,1,3,4,6,7,5]=>100001=>011110
[2,1,3,4,7,5,6]=>100010=>011101
[2,1,3,4,7,6,5]=>100011=>011100
[2,1,3,5,4,6,7]=>100100=>011011
[2,1,3,5,4,7,6]=>100101=>011010
[2,1,3,5,6,4,7]=>100010=>011101
[2,1,3,5,6,7,4]=>100001=>011110
[2,1,3,5,7,4,6]=>100010=>011101
[2,1,3,5,7,6,4]=>100011=>011100
[2,1,3,6,4,5,7]=>100100=>011011
[2,1,3,6,4,7,5]=>100101=>011010
[2,1,3,6,5,4,7]=>100110=>011001
[2,1,3,6,5,7,4]=>100101=>011010
[2,1,3,6,7,4,5]=>100010=>011101
[2,1,3,6,7,5,4]=>100011=>011100
[2,1,3,7,4,5,6]=>100100=>011011
[2,1,3,7,4,6,5]=>100101=>011010
[2,1,3,7,5,4,6]=>100110=>011001
[2,1,3,7,5,6,4]=>100101=>011010
[2,1,3,7,6,4,5]=>100110=>011001
[2,1,3,7,6,5,4]=>100111=>011000
[2,1,4,3,5,6,7]=>101000=>010111
[2,1,4,3,5,7,6]=>101001=>010110
[2,1,4,3,6,5,7]=>101010=>010101
[2,1,4,3,6,7,5]=>101001=>010110
[2,1,4,3,7,5,6]=>101010=>010101
[2,1,4,3,7,6,5]=>101011=>010100
[2,1,4,5,3,6,7]=>100100=>011011
[2,1,4,5,3,7,6]=>100101=>011010
[2,1,4,5,6,3,7]=>100010=>011101
[2,1,4,5,6,7,3]=>100001=>011110
[2,1,4,5,7,3,6]=>100010=>011101
[2,1,4,5,7,6,3]=>100011=>011100
[2,1,4,6,3,5,7]=>100100=>011011
[2,1,4,6,3,7,5]=>100101=>011010
[2,1,4,6,5,3,7]=>100110=>011001
[2,1,4,6,5,7,3]=>100101=>011010
[2,1,4,6,7,3,5]=>100010=>011101
[2,1,4,6,7,5,3]=>100011=>011100
[2,1,4,7,3,5,6]=>100100=>011011
[2,1,4,7,3,6,5]=>100101=>011010
[2,1,4,7,5,3,6]=>100110=>011001
[2,1,4,7,5,6,3]=>100101=>011010
[2,1,4,7,6,3,5]=>100110=>011001
[2,1,4,7,6,5,3]=>100111=>011000
[2,1,5,3,4,6,7]=>101000=>010111
[2,1,5,3,4,7,6]=>101001=>010110
[2,1,5,3,6,4,7]=>101010=>010101
[2,1,5,3,6,7,4]=>101001=>010110
[2,1,5,3,7,4,6]=>101010=>010101
[2,1,5,3,7,6,4]=>101011=>010100
[2,1,5,4,3,6,7]=>101100=>010011
[2,1,5,4,3,7,6]=>101101=>010010
[2,1,5,4,6,3,7]=>101010=>010101
[2,1,5,4,6,7,3]=>101001=>010110
[2,1,5,4,7,3,6]=>101010=>010101
[2,1,5,4,7,6,3]=>101011=>010100
[2,1,5,6,3,4,7]=>100100=>011011
[2,1,5,6,3,7,4]=>100101=>011010
[2,1,5,6,4,3,7]=>100110=>011001
[2,1,5,6,4,7,3]=>100101=>011010
[2,1,5,6,7,3,4]=>100010=>011101
[2,1,5,6,7,4,3]=>100011=>011100
[2,1,5,7,3,4,6]=>100100=>011011
[2,1,5,7,3,6,4]=>100101=>011010
[2,1,5,7,4,3,6]=>100110=>011001
[2,1,5,7,4,6,3]=>100101=>011010
[2,1,5,7,6,3,4]=>100110=>011001
[2,1,5,7,6,4,3]=>100111=>011000
[2,1,6,3,4,5,7]=>101000=>010111
[2,1,6,3,4,7,5]=>101001=>010110
[2,1,6,3,5,4,7]=>101010=>010101
[2,1,6,3,5,7,4]=>101001=>010110
[2,1,6,3,7,4,5]=>101010=>010101
[2,1,6,3,7,5,4]=>101011=>010100
[2,1,6,4,3,5,7]=>101100=>010011
[2,1,6,4,3,7,5]=>101101=>010010
[2,1,6,4,5,3,7]=>101010=>010101
[2,1,6,4,5,7,3]=>101001=>010110
[2,1,6,4,7,3,5]=>101010=>010101
[2,1,6,4,7,5,3]=>101011=>010100
[2,1,6,5,3,4,7]=>101100=>010011
[2,1,6,5,3,7,4]=>101101=>010010
[2,1,6,5,4,3,7]=>101110=>010001
[2,1,6,5,4,7,3]=>101101=>010010
[2,1,6,5,7,3,4]=>101010=>010101
[2,1,6,5,7,4,3]=>101011=>010100
[2,1,6,7,3,4,5]=>100100=>011011
[2,1,6,7,3,5,4]=>100101=>011010
[2,1,6,7,4,3,5]=>100110=>011001
[2,1,6,7,4,5,3]=>100101=>011010
[2,1,6,7,5,3,4]=>100110=>011001
[2,1,6,7,5,4,3]=>100111=>011000
[2,1,7,3,4,5,6]=>101000=>010111
[2,1,7,3,4,6,5]=>101001=>010110
[2,1,7,3,5,4,6]=>101010=>010101
[2,1,7,3,5,6,4]=>101001=>010110
[2,1,7,3,6,4,5]=>101010=>010101
[2,1,7,3,6,5,4]=>101011=>010100
[2,1,7,4,3,5,6]=>101100=>010011
[2,1,7,4,3,6,5]=>101101=>010010
[2,1,7,4,5,3,6]=>101010=>010101
[2,1,7,4,5,6,3]=>101001=>010110
[2,1,7,4,6,3,5]=>101010=>010101
[2,1,7,4,6,5,3]=>101011=>010100
[2,1,7,5,3,4,6]=>101100=>010011
[2,1,7,5,3,6,4]=>101101=>010010
[2,1,7,5,4,3,6]=>101110=>010001
[2,1,7,5,4,6,3]=>101101=>010010
[2,1,7,5,6,3,4]=>101010=>010101
[2,1,7,5,6,4,3]=>101011=>010100
[2,1,7,6,3,4,5]=>101100=>010011
[2,1,7,6,3,5,4]=>101101=>010010
[2,1,7,6,4,3,5]=>101110=>010001
[2,1,7,6,4,5,3]=>101101=>010010
[2,1,7,6,5,3,4]=>101110=>010001
[2,1,7,6,5,4,3]=>101111=>010000
[2,3,1,4,5,6,7]=>010000=>101111
[2,3,1,4,5,7,6]=>010001=>101110
[2,3,1,4,6,5,7]=>010010=>101101
[2,3,1,4,6,7,5]=>010001=>101110
[2,3,1,4,7,5,6]=>010010=>101101
[2,3,1,4,7,6,5]=>010011=>101100
[2,3,1,5,4,6,7]=>010100=>101011
[2,3,1,5,4,7,6]=>010101=>101010
[2,3,1,5,6,4,7]=>010010=>101101
[2,3,1,5,6,7,4]=>010001=>101110
[2,3,1,5,7,4,6]=>010010=>101101
[2,3,1,5,7,6,4]=>010011=>101100
[2,3,1,6,4,5,7]=>010100=>101011
[2,3,1,6,4,7,5]=>010101=>101010
[2,3,1,6,5,4,7]=>010110=>101001
[2,3,1,6,5,7,4]=>010101=>101010
[2,3,1,6,7,4,5]=>010010=>101101
[2,3,1,6,7,5,4]=>010011=>101100
[2,3,1,7,4,5,6]=>010100=>101011
[2,3,1,7,4,6,5]=>010101=>101010
[2,3,1,7,5,4,6]=>010110=>101001
[2,3,1,7,5,6,4]=>010101=>101010
[2,3,1,7,6,4,5]=>010110=>101001
[2,3,1,7,6,5,4]=>010111=>101000
[2,3,4,1,5,6,7]=>001000=>110111
[2,3,4,1,5,7,6]=>001001=>110110
[2,3,4,1,6,5,7]=>001010=>110101
[2,3,4,1,6,7,5]=>001001=>110110
[2,3,4,1,7,5,6]=>001010=>110101
[2,3,4,1,7,6,5]=>001011=>110100
[2,3,4,5,1,6,7]=>000100=>111011
[2,3,4,5,1,7,6]=>000101=>111010
[2,3,4,5,6,1,7]=>000010=>111101
[2,3,4,5,6,7,1]=>000001=>111110
[2,3,4,5,7,1,6]=>000010=>111101
[2,3,4,5,7,6,1]=>000011=>111100
[2,3,4,6,1,5,7]=>000100=>111011
[2,3,4,6,1,7,5]=>000101=>111010
[2,3,4,6,5,1,7]=>000110=>111001
[2,3,4,6,5,7,1]=>000101=>111010
[2,3,4,6,7,1,5]=>000010=>111101
[2,3,4,6,7,5,1]=>000011=>111100
[2,3,4,7,1,5,6]=>000100=>111011
[2,3,4,7,1,6,5]=>000101=>111010
[2,3,4,7,5,1,6]=>000110=>111001
[2,3,4,7,5,6,1]=>000101=>111010
[2,3,4,7,6,1,5]=>000110=>111001
[2,3,4,7,6,5,1]=>000111=>111000
[2,3,5,1,4,6,7]=>001000=>110111
[2,3,5,1,4,7,6]=>001001=>110110
[2,3,5,1,6,4,7]=>001010=>110101
[2,3,5,1,6,7,4]=>001001=>110110
[2,3,5,1,7,4,6]=>001010=>110101
[2,3,5,1,7,6,4]=>001011=>110100
[2,3,5,4,1,6,7]=>001100=>110011
[2,3,5,4,1,7,6]=>001101=>110010
[2,3,5,4,6,1,7]=>001010=>110101
[2,3,5,4,6,7,1]=>001001=>110110
[2,3,5,4,7,1,6]=>001010=>110101
[2,3,5,4,7,6,1]=>001011=>110100
[2,3,5,6,1,4,7]=>000100=>111011
[2,3,5,6,1,7,4]=>000101=>111010
[2,3,5,6,4,1,7]=>000110=>111001
[2,3,5,6,4,7,1]=>000101=>111010
[2,3,5,6,7,1,4]=>000010=>111101
[2,3,5,6,7,4,1]=>000011=>111100
[2,3,5,7,1,4,6]=>000100=>111011
[2,3,5,7,1,6,4]=>000101=>111010
[2,3,5,7,4,1,6]=>000110=>111001
[2,3,5,7,4,6,1]=>000101=>111010
[2,3,5,7,6,1,4]=>000110=>111001
[2,3,5,7,6,4,1]=>000111=>111000
[2,3,6,1,4,5,7]=>001000=>110111
[2,3,6,1,4,7,5]=>001001=>110110
[2,3,6,1,5,4,7]=>001010=>110101
[2,3,6,1,5,7,4]=>001001=>110110
[2,3,6,1,7,4,5]=>001010=>110101
[2,3,6,1,7,5,4]=>001011=>110100
[2,3,6,4,1,5,7]=>001100=>110011
[2,3,6,4,1,7,5]=>001101=>110010
[2,3,6,4,5,1,7]=>001010=>110101
[2,3,6,4,5,7,1]=>001001=>110110
[2,3,6,4,7,1,5]=>001010=>110101
[2,3,6,4,7,5,1]=>001011=>110100
[2,3,6,5,1,4,7]=>001100=>110011
[2,3,6,5,1,7,4]=>001101=>110010
[2,3,6,5,4,1,7]=>001110=>110001
[2,3,6,5,4,7,1]=>001101=>110010
[2,3,6,5,7,1,4]=>001010=>110101
[2,3,6,5,7,4,1]=>001011=>110100
[2,3,6,7,1,4,5]=>000100=>111011
[2,3,6,7,1,5,4]=>000101=>111010
[2,3,6,7,4,1,5]=>000110=>111001
[2,3,6,7,4,5,1]=>000101=>111010
[2,3,6,7,5,1,4]=>000110=>111001
[2,3,6,7,5,4,1]=>000111=>111000
[2,3,7,1,4,5,6]=>001000=>110111
[2,3,7,1,4,6,5]=>001001=>110110
[2,3,7,1,5,4,6]=>001010=>110101
[2,3,7,1,5,6,4]=>001001=>110110
[2,3,7,1,6,4,5]=>001010=>110101
[2,3,7,1,6,5,4]=>001011=>110100
[2,3,7,4,1,5,6]=>001100=>110011
[2,3,7,4,1,6,5]=>001101=>110010
[2,3,7,4,5,1,6]=>001010=>110101
[2,3,7,4,5,6,1]=>001001=>110110
[2,3,7,4,6,1,5]=>001010=>110101
[2,3,7,4,6,5,1]=>001011=>110100
[2,3,7,5,1,4,6]=>001100=>110011
[2,3,7,5,1,6,4]=>001101=>110010
[2,3,7,5,4,1,6]=>001110=>110001
[2,3,7,5,4,6,1]=>001101=>110010
[2,3,7,5,6,1,4]=>001010=>110101
[2,3,7,5,6,4,1]=>001011=>110100
[2,3,7,6,1,4,5]=>001100=>110011
[2,3,7,6,1,5,4]=>001101=>110010
[2,3,7,6,4,1,5]=>001110=>110001
[2,3,7,6,4,5,1]=>001101=>110010
[2,3,7,6,5,1,4]=>001110=>110001
[2,3,7,6,5,4,1]=>001111=>110000
[2,4,1,3,5,6,7]=>010000=>101111
[2,4,1,3,5,7,6]=>010001=>101110
[2,4,1,3,6,5,7]=>010010=>101101
[2,4,1,3,6,7,5]=>010001=>101110
[2,4,1,3,7,5,6]=>010010=>101101
[2,4,1,3,7,6,5]=>010011=>101100
[2,4,1,5,3,6,7]=>010100=>101011
[2,4,1,5,3,7,6]=>010101=>101010
[2,4,1,5,6,3,7]=>010010=>101101
[2,4,1,5,6,7,3]=>010001=>101110
[2,4,1,5,7,3,6]=>010010=>101101
[2,4,1,5,7,6,3]=>010011=>101100
[2,4,1,6,3,5,7]=>010100=>101011
[2,4,1,6,3,7,5]=>010101=>101010
[2,4,1,6,5,3,7]=>010110=>101001
[2,4,1,6,5,7,3]=>010101=>101010
[2,4,1,6,7,3,5]=>010010=>101101
[2,4,1,6,7,5,3]=>010011=>101100
[2,4,1,7,3,5,6]=>010100=>101011
[2,4,1,7,3,6,5]=>010101=>101010
[2,4,1,7,5,3,6]=>010110=>101001
[2,4,1,7,5,6,3]=>010101=>101010
[2,4,1,7,6,3,5]=>010110=>101001
[2,4,1,7,6,5,3]=>010111=>101000
[2,4,3,1,5,6,7]=>011000=>100111
[2,4,3,1,5,7,6]=>011001=>100110
[2,4,3,1,6,5,7]=>011010=>100101
[2,4,3,1,6,7,5]=>011001=>100110
[2,4,3,1,7,5,6]=>011010=>100101
[2,4,3,1,7,6,5]=>011011=>100100
[2,4,3,5,1,6,7]=>010100=>101011
[2,4,3,5,1,7,6]=>010101=>101010
[2,4,3,5,6,1,7]=>010010=>101101
[2,4,3,5,6,7,1]=>010001=>101110
[2,4,3,5,7,1,6]=>010010=>101101
[2,4,3,5,7,6,1]=>010011=>101100
[2,4,3,6,1,5,7]=>010100=>101011
[2,4,3,6,1,7,5]=>010101=>101010
[2,4,3,6,5,1,7]=>010110=>101001
[2,4,3,6,5,7,1]=>010101=>101010
[2,4,3,6,7,1,5]=>010010=>101101
[2,4,3,6,7,5,1]=>010011=>101100
[2,4,3,7,1,5,6]=>010100=>101011
[2,4,3,7,1,6,5]=>010101=>101010
[2,4,3,7,5,1,6]=>010110=>101001
[2,4,3,7,5,6,1]=>010101=>101010
[2,4,3,7,6,1,5]=>010110=>101001
[2,4,3,7,6,5,1]=>010111=>101000
[2,4,5,1,3,6,7]=>001000=>110111
[2,4,5,1,3,7,6]=>001001=>110110
[2,4,5,1,6,3,7]=>001010=>110101
[2,4,5,1,6,7,3]=>001001=>110110
[2,4,5,1,7,3,6]=>001010=>110101
[2,4,5,1,7,6,3]=>001011=>110100
[2,4,5,3,1,6,7]=>001100=>110011
[2,4,5,3,1,7,6]=>001101=>110010
[2,4,5,3,6,1,7]=>001010=>110101
[2,4,5,3,6,7,1]=>001001=>110110
[2,4,5,3,7,1,6]=>001010=>110101
[2,4,5,3,7,6,1]=>001011=>110100
[2,4,5,6,1,3,7]=>000100=>111011
[2,4,5,6,1,7,3]=>000101=>111010
[2,4,5,6,3,1,7]=>000110=>111001
[2,4,5,6,3,7,1]=>000101=>111010
[2,4,5,6,7,1,3]=>000010=>111101
[2,4,5,6,7,3,1]=>000011=>111100
[2,4,5,7,1,3,6]=>000100=>111011
[2,4,5,7,1,6,3]=>000101=>111010
[2,4,5,7,3,1,6]=>000110=>111001
[2,4,5,7,3,6,1]=>000101=>111010
[2,4,5,7,6,1,3]=>000110=>111001
[2,4,5,7,6,3,1]=>000111=>111000
[2,4,6,1,3,5,7]=>001000=>110111
[2,4,6,1,3,7,5]=>001001=>110110
[2,4,6,1,5,3,7]=>001010=>110101
[2,4,6,1,5,7,3]=>001001=>110110
[2,4,6,1,7,3,5]=>001010=>110101
[2,4,6,1,7,5,3]=>001011=>110100
[2,4,6,3,1,5,7]=>001100=>110011
[2,4,6,3,1,7,5]=>001101=>110010
[2,4,6,3,5,1,7]=>001010=>110101
[2,4,6,3,5,7,1]=>001001=>110110
[2,4,6,3,7,1,5]=>001010=>110101
[2,4,6,3,7,5,1]=>001011=>110100
[2,4,6,5,1,3,7]=>001100=>110011
[2,4,6,5,1,7,3]=>001101=>110010
[2,4,6,5,3,1,7]=>001110=>110001
[2,4,6,5,3,7,1]=>001101=>110010
[2,4,6,5,7,1,3]=>001010=>110101
[2,4,6,5,7,3,1]=>001011=>110100
[2,4,6,7,1,3,5]=>000100=>111011
[2,4,6,7,1,5,3]=>000101=>111010
[2,4,6,7,3,1,5]=>000110=>111001
[2,4,6,7,3,5,1]=>000101=>111010
[2,4,6,7,5,1,3]=>000110=>111001
[2,4,6,7,5,3,1]=>000111=>111000
[2,4,7,1,3,5,6]=>001000=>110111
[2,4,7,1,3,6,5]=>001001=>110110
[2,4,7,1,5,3,6]=>001010=>110101
[2,4,7,1,5,6,3]=>001001=>110110
[2,4,7,1,6,3,5]=>001010=>110101
[2,4,7,1,6,5,3]=>001011=>110100
[2,4,7,3,1,5,6]=>001100=>110011
[2,4,7,3,1,6,5]=>001101=>110010
[2,4,7,3,5,1,6]=>001010=>110101
[2,4,7,3,5,6,1]=>001001=>110110
[2,4,7,3,6,1,5]=>001010=>110101
[2,4,7,3,6,5,1]=>001011=>110100
[2,4,7,5,1,3,6]=>001100=>110011
[2,4,7,5,1,6,3]=>001101=>110010
[2,4,7,5,3,1,6]=>001110=>110001
[2,4,7,5,3,6,1]=>001101=>110010
[2,4,7,5,6,1,3]=>001010=>110101
[2,4,7,5,6,3,1]=>001011=>110100
[2,4,7,6,1,3,5]=>001100=>110011
[2,4,7,6,1,5,3]=>001101=>110010
[2,4,7,6,3,1,5]=>001110=>110001
[2,4,7,6,3,5,1]=>001101=>110010
[2,4,7,6,5,1,3]=>001110=>110001
[2,4,7,6,5,3,1]=>001111=>110000
[2,5,1,3,4,6,7]=>010000=>101111
[2,5,1,3,4,7,6]=>010001=>101110
[2,5,1,3,6,4,7]=>010010=>101101
[2,5,1,3,6,7,4]=>010001=>101110
[2,5,1,3,7,4,6]=>010010=>101101
[2,5,1,3,7,6,4]=>010011=>101100
[2,5,1,4,3,6,7]=>010100=>101011
[2,5,1,4,3,7,6]=>010101=>101010
[2,5,1,4,6,3,7]=>010010=>101101
[2,5,1,4,6,7,3]=>010001=>101110
[2,5,1,4,7,3,6]=>010010=>101101
[2,5,1,4,7,6,3]=>010011=>101100
[2,5,1,6,3,4,7]=>010100=>101011
[2,5,1,6,3,7,4]=>010101=>101010
[2,5,1,6,4,3,7]=>010110=>101001
[2,5,1,6,4,7,3]=>010101=>101010
[2,5,1,6,7,3,4]=>010010=>101101
[2,5,1,6,7,4,3]=>010011=>101100
[2,5,1,7,3,4,6]=>010100=>101011
[2,5,1,7,3,6,4]=>010101=>101010
[2,5,1,7,4,3,6]=>010110=>101001
[2,5,1,7,4,6,3]=>010101=>101010
[2,5,1,7,6,3,4]=>010110=>101001
[2,5,1,7,6,4,3]=>010111=>101000
[2,5,3,1,4,6,7]=>011000=>100111
[2,5,3,1,4,7,6]=>011001=>100110
[2,5,3,1,6,4,7]=>011010=>100101
[2,5,3,1,6,7,4]=>011001=>100110
[2,5,3,1,7,4,6]=>011010=>100101
[2,5,3,1,7,6,4]=>011011=>100100
[2,5,3,4,1,6,7]=>010100=>101011
[2,5,3,4,1,7,6]=>010101=>101010
[2,5,3,4,6,1,7]=>010010=>101101
[2,5,3,4,6,7,1]=>010001=>101110
[2,5,3,4,7,1,6]=>010010=>101101
[2,5,3,4,7,6,1]=>010011=>101100
[2,5,3,6,1,4,7]=>010100=>101011
[2,5,3,6,1,7,4]=>010101=>101010
[2,5,3,6,4,1,7]=>010110=>101001
[2,5,3,6,4,7,1]=>010101=>101010
[2,5,3,6,7,1,4]=>010010=>101101
[2,5,3,6,7,4,1]=>010011=>101100
[2,5,3,7,1,4,6]=>010100=>101011
[2,5,3,7,1,6,4]=>010101=>101010
[2,5,3,7,4,1,6]=>010110=>101001
[2,5,3,7,4,6,1]=>010101=>101010
[2,5,3,7,6,1,4]=>010110=>101001
[2,5,3,7,6,4,1]=>010111=>101000
[2,5,4,1,3,6,7]=>011000=>100111
[2,5,4,1,3,7,6]=>011001=>100110
[2,5,4,1,6,3,7]=>011010=>100101
[2,5,4,1,6,7,3]=>011001=>100110
[2,5,4,1,7,3,6]=>011010=>100101
[2,5,4,1,7,6,3]=>011011=>100100
[2,5,4,3,1,6,7]=>011100=>100011
[2,5,4,3,1,7,6]=>011101=>100010
[2,5,4,3,6,1,7]=>011010=>100101
[2,5,4,3,6,7,1]=>011001=>100110
[2,5,4,3,7,1,6]=>011010=>100101
[2,5,4,3,7,6,1]=>011011=>100100
[2,5,4,6,1,3,7]=>010100=>101011
[2,5,4,6,1,7,3]=>010101=>101010
[2,5,4,6,3,1,7]=>010110=>101001
[2,5,4,6,3,7,1]=>010101=>101010
[2,5,4,6,7,1,3]=>010010=>101101
[2,5,4,6,7,3,1]=>010011=>101100
[2,5,4,7,1,3,6]=>010100=>101011
[2,5,4,7,1,6,3]=>010101=>101010
[2,5,4,7,3,1,6]=>010110=>101001
[2,5,4,7,3,6,1]=>010101=>101010
[2,5,4,7,6,1,3]=>010110=>101001
[2,5,4,7,6,3,1]=>010111=>101000
[2,5,6,1,3,4,7]=>001000=>110111
[2,5,6,1,3,7,4]=>001001=>110110
[2,5,6,1,4,3,7]=>001010=>110101
[2,5,6,1,4,7,3]=>001001=>110110
[2,5,6,1,7,3,4]=>001010=>110101
[2,5,6,1,7,4,3]=>001011=>110100
[2,5,6,3,1,4,7]=>001100=>110011
[2,5,6,3,1,7,4]=>001101=>110010
[2,5,6,3,4,1,7]=>001010=>110101
[2,5,6,3,4,7,1]=>001001=>110110
[2,5,6,3,7,1,4]=>001010=>110101
[2,5,6,3,7,4,1]=>001011=>110100
[2,5,6,4,1,3,7]=>001100=>110011
[2,5,6,4,1,7,3]=>001101=>110010
[2,5,6,4,3,1,7]=>001110=>110001
[2,5,6,4,3,7,1]=>001101=>110010
[2,5,6,4,7,1,3]=>001010=>110101
[2,5,6,4,7,3,1]=>001011=>110100
[2,5,6,7,1,3,4]=>000100=>111011
[2,5,6,7,1,4,3]=>000101=>111010
[2,5,6,7,3,1,4]=>000110=>111001
[2,5,6,7,3,4,1]=>000101=>111010
[2,5,6,7,4,1,3]=>000110=>111001
[2,5,6,7,4,3,1]=>000111=>111000
[2,5,7,1,3,4,6]=>001000=>110111
[2,5,7,1,3,6,4]=>001001=>110110
[2,5,7,1,4,3,6]=>001010=>110101
[2,5,7,1,4,6,3]=>001001=>110110
[2,5,7,1,6,3,4]=>001010=>110101
[2,5,7,1,6,4,3]=>001011=>110100
[2,5,7,3,1,4,6]=>001100=>110011
[2,5,7,3,1,6,4]=>001101=>110010
[2,5,7,3,4,1,6]=>001010=>110101
[2,5,7,3,4,6,1]=>001001=>110110
[2,5,7,3,6,1,4]=>001010=>110101
[2,5,7,3,6,4,1]=>001011=>110100
[2,5,7,4,1,3,6]=>001100=>110011
[2,5,7,4,1,6,3]=>001101=>110010
[2,5,7,4,3,1,6]=>001110=>110001
[2,5,7,4,3,6,1]=>001101=>110010
[2,5,7,4,6,1,3]=>001010=>110101
[2,5,7,4,6,3,1]=>001011=>110100
[2,5,7,6,1,3,4]=>001100=>110011
[2,5,7,6,1,4,3]=>001101=>110010
[2,5,7,6,3,1,4]=>001110=>110001
[2,5,7,6,3,4,1]=>001101=>110010
[2,5,7,6,4,1,3]=>001110=>110001
[2,5,7,6,4,3,1]=>001111=>110000
[2,6,1,3,4,5,7]=>010000=>101111
[2,6,1,3,4,7,5]=>010001=>101110
[2,6,1,3,5,4,7]=>010010=>101101
[2,6,1,3,5,7,4]=>010001=>101110
[2,6,1,3,7,4,5]=>010010=>101101
[2,6,1,3,7,5,4]=>010011=>101100
[2,6,1,4,3,5,7]=>010100=>101011
[2,6,1,4,3,7,5]=>010101=>101010
[2,6,1,4,5,3,7]=>010010=>101101
[2,6,1,4,5,7,3]=>010001=>101110
[2,6,1,4,7,3,5]=>010010=>101101
[2,6,1,4,7,5,3]=>010011=>101100
[2,6,1,5,3,4,7]=>010100=>101011
[2,6,1,5,3,7,4]=>010101=>101010
[2,6,1,5,4,3,7]=>010110=>101001
[2,6,1,5,4,7,3]=>010101=>101010
[2,6,1,5,7,3,4]=>010010=>101101
[2,6,1,5,7,4,3]=>010011=>101100
[2,6,1,7,3,4,5]=>010100=>101011
[2,6,1,7,3,5,4]=>010101=>101010
[2,6,1,7,4,3,5]=>010110=>101001
[2,6,1,7,4,5,3]=>010101=>101010
[2,6,1,7,5,3,4]=>010110=>101001
[2,6,1,7,5,4,3]=>010111=>101000
[2,6,3,1,4,5,7]=>011000=>100111
[2,6,3,1,4,7,5]=>011001=>100110
[2,6,3,1,5,4,7]=>011010=>100101
[2,6,3,1,5,7,4]=>011001=>100110
[2,6,3,1,7,4,5]=>011010=>100101
[2,6,3,1,7,5,4]=>011011=>100100
[2,6,3,4,1,5,7]=>010100=>101011
[2,6,3,4,1,7,5]=>010101=>101010
[2,6,3,4,5,1,7]=>010010=>101101
[2,6,3,4,5,7,1]=>010001=>101110
[2,6,3,4,7,1,5]=>010010=>101101
[2,6,3,4,7,5,1]=>010011=>101100
[2,6,3,5,1,4,7]=>010100=>101011
[2,6,3,5,1,7,4]=>010101=>101010
[2,6,3,5,4,1,7]=>010110=>101001
[2,6,3,5,4,7,1]=>010101=>101010
[2,6,3,5,7,1,4]=>010010=>101101
[2,6,3,5,7,4,1]=>010011=>101100
[2,6,3,7,1,4,5]=>010100=>101011
[2,6,3,7,1,5,4]=>010101=>101010
[2,6,3,7,4,1,5]=>010110=>101001
[2,6,3,7,4,5,1]=>010101=>101010
[2,6,3,7,5,1,4]=>010110=>101001
[2,6,3,7,5,4,1]=>010111=>101000
[2,6,4,1,3,5,7]=>011000=>100111
[2,6,4,1,3,7,5]=>011001=>100110
[2,6,4,1,5,3,7]=>011010=>100101
[2,6,4,1,5,7,3]=>011001=>100110
[2,6,4,1,7,3,5]=>011010=>100101
[2,6,4,1,7,5,3]=>011011=>100100
[2,6,4,3,1,5,7]=>011100=>100011
[2,6,4,3,1,7,5]=>011101=>100010
[2,6,4,3,5,1,7]=>011010=>100101
[2,6,4,3,5,7,1]=>011001=>100110
[2,6,4,3,7,1,5]=>011010=>100101
[2,6,4,3,7,5,1]=>011011=>100100
[2,6,4,5,1,3,7]=>010100=>101011
[2,6,4,5,1,7,3]=>010101=>101010
[2,6,4,5,3,1,7]=>010110=>101001
[2,6,4,5,3,7,1]=>010101=>101010
[2,6,4,5,7,1,3]=>010010=>101101
[2,6,4,5,7,3,1]=>010011=>101100
[2,6,4,7,1,3,5]=>010100=>101011
[2,6,4,7,1,5,3]=>010101=>101010
[2,6,4,7,3,1,5]=>010110=>101001
[2,6,4,7,3,5,1]=>010101=>101010
[2,6,4,7,5,1,3]=>010110=>101001
[2,6,4,7,5,3,1]=>010111=>101000
[2,6,5,1,3,4,7]=>011000=>100111
[2,6,5,1,3,7,4]=>011001=>100110
[2,6,5,1,4,3,7]=>011010=>100101
[2,6,5,1,4,7,3]=>011001=>100110
[2,6,5,1,7,3,4]=>011010=>100101
[2,6,5,1,7,4,3]=>011011=>100100
[2,6,5,3,1,4,7]=>011100=>100011
[2,6,5,3,1,7,4]=>011101=>100010
[2,6,5,3,4,1,7]=>011010=>100101
[2,6,5,3,4,7,1]=>011001=>100110
[2,6,5,3,7,1,4]=>011010=>100101
[2,6,5,3,7,4,1]=>011011=>100100
[2,6,5,4,1,3,7]=>011100=>100011
[2,6,5,4,1,7,3]=>011101=>100010
[2,6,5,4,3,1,7]=>011110=>100001
[2,6,5,4,3,7,1]=>011101=>100010
[2,6,5,4,7,1,3]=>011010=>100101
[2,6,5,4,7,3,1]=>011011=>100100
[2,6,5,7,1,3,4]=>010100=>101011
[2,6,5,7,1,4,3]=>010101=>101010
[2,6,5,7,3,1,4]=>010110=>101001
[2,6,5,7,3,4,1]=>010101=>101010
[2,6,5,7,4,1,3]=>010110=>101001
[2,6,5,7,4,3,1]=>010111=>101000
[2,6,7,1,3,4,5]=>001000=>110111
[2,6,7,1,3,5,4]=>001001=>110110
[2,6,7,1,4,3,5]=>001010=>110101
[2,6,7,1,4,5,3]=>001001=>110110
[2,6,7,1,5,3,4]=>001010=>110101
[2,6,7,1,5,4,3]=>001011=>110100
[2,6,7,3,1,4,5]=>001100=>110011
[2,6,7,3,1,5,4]=>001101=>110010
[2,6,7,3,4,1,5]=>001010=>110101
[2,6,7,3,4,5,1]=>001001=>110110
[2,6,7,3,5,1,4]=>001010=>110101
[2,6,7,3,5,4,1]=>001011=>110100
[2,6,7,4,1,3,5]=>001100=>110011
[2,6,7,4,1,5,3]=>001101=>110010
[2,6,7,4,3,1,5]=>001110=>110001
[2,6,7,4,3,5,1]=>001101=>110010
[2,6,7,4,5,1,3]=>001010=>110101
[2,6,7,4,5,3,1]=>001011=>110100
[2,6,7,5,1,3,4]=>001100=>110011
[2,6,7,5,1,4,3]=>001101=>110010
[2,6,7,5,3,1,4]=>001110=>110001
[2,6,7,5,3,4,1]=>001101=>110010
[2,6,7,5,4,1,3]=>001110=>110001
[2,6,7,5,4,3,1]=>001111=>110000
[2,7,1,3,4,5,6]=>010000=>101111
[2,7,1,3,4,6,5]=>010001=>101110
[2,7,1,3,5,4,6]=>010010=>101101
[2,7,1,3,5,6,4]=>010001=>101110
[2,7,1,3,6,4,5]=>010010=>101101
[2,7,1,3,6,5,4]=>010011=>101100
[2,7,1,4,3,5,6]=>010100=>101011
[2,7,1,4,3,6,5]=>010101=>101010
[2,7,1,4,5,3,6]=>010010=>101101
[2,7,1,4,5,6,3]=>010001=>101110
[2,7,1,4,6,3,5]=>010010=>101101
[2,7,1,4,6,5,3]=>010011=>101100
[2,7,1,5,3,4,6]=>010100=>101011
[2,7,1,5,3,6,4]=>010101=>101010
[2,7,1,5,4,3,6]=>010110=>101001
[2,7,1,5,4,6,3]=>010101=>101010
[2,7,1,5,6,3,4]=>010010=>101101
[2,7,1,5,6,4,3]=>010011=>101100
[2,7,1,6,3,4,5]=>010100=>101011
[2,7,1,6,3,5,4]=>010101=>101010
[2,7,1,6,4,3,5]=>010110=>101001
[2,7,1,6,4,5,3]=>010101=>101010
[2,7,1,6,5,3,4]=>010110=>101001
[2,7,1,6,5,4,3]=>010111=>101000
[2,7,3,1,4,5,6]=>011000=>100111
[2,7,3,1,4,6,5]=>011001=>100110
[2,7,3,1,5,4,6]=>011010=>100101
[2,7,3,1,5,6,4]=>011001=>100110
[2,7,3,1,6,4,5]=>011010=>100101
[2,7,3,1,6,5,4]=>011011=>100100
[2,7,3,4,1,5,6]=>010100=>101011
[2,7,3,4,1,6,5]=>010101=>101010
[2,7,3,4,5,1,6]=>010010=>101101
[2,7,3,4,5,6,1]=>010001=>101110
[2,7,3,4,6,1,5]=>010010=>101101
[2,7,3,4,6,5,1]=>010011=>101100
[2,7,3,5,1,4,6]=>010100=>101011
[2,7,3,5,1,6,4]=>010101=>101010
[2,7,3,5,4,1,6]=>010110=>101001
[2,7,3,5,4,6,1]=>010101=>101010
[2,7,3,5,6,1,4]=>010010=>101101
[2,7,3,5,6,4,1]=>010011=>101100
[2,7,3,6,1,4,5]=>010100=>101011
[2,7,3,6,1,5,4]=>010101=>101010
[2,7,3,6,4,1,5]=>010110=>101001
[2,7,3,6,4,5,1]=>010101=>101010
[2,7,3,6,5,1,4]=>010110=>101001
[2,7,3,6,5,4,1]=>010111=>101000
[2,7,4,1,3,5,6]=>011000=>100111
[2,7,4,1,3,6,5]=>011001=>100110
[2,7,4,1,5,3,6]=>011010=>100101
[2,7,4,1,5,6,3]=>011001=>100110
[2,7,4,1,6,3,5]=>011010=>100101
[2,7,4,1,6,5,3]=>011011=>100100
[2,7,4,3,1,5,6]=>011100=>100011
[2,7,4,3,1,6,5]=>011101=>100010
[2,7,4,3,5,1,6]=>011010=>100101
[2,7,4,3,5,6,1]=>011001=>100110
[2,7,4,3,6,1,5]=>011010=>100101
[2,7,4,3,6,5,1]=>011011=>100100
[2,7,4,5,1,3,6]=>010100=>101011
[2,7,4,5,1,6,3]=>010101=>101010
[2,7,4,5,3,1,6]=>010110=>101001
[2,7,4,5,3,6,1]=>010101=>101010
[2,7,4,5,6,1,3]=>010010=>101101
[2,7,4,5,6,3,1]=>010011=>101100
[2,7,4,6,1,3,5]=>010100=>101011
[2,7,4,6,1,5,3]=>010101=>101010
[2,7,4,6,3,1,5]=>010110=>101001
[2,7,4,6,3,5,1]=>010101=>101010
[2,7,4,6,5,1,3]=>010110=>101001
[2,7,4,6,5,3,1]=>010111=>101000
[2,7,5,1,3,4,6]=>011000=>100111
[2,7,5,1,3,6,4]=>011001=>100110
[2,7,5,1,4,3,6]=>011010=>100101
[2,7,5,1,4,6,3]=>011001=>100110
[2,7,5,1,6,3,4]=>011010=>100101
[2,7,5,1,6,4,3]=>011011=>100100
[2,7,5,3,1,4,6]=>011100=>100011
[2,7,5,3,1,6,4]=>011101=>100010
[2,7,5,3,4,1,6]=>011010=>100101
[2,7,5,3,4,6,1]=>011001=>100110
[2,7,5,3,6,1,4]=>011010=>100101
[2,7,5,3,6,4,1]=>011011=>100100
[2,7,5,4,1,3,6]=>011100=>100011
[2,7,5,4,1,6,3]=>011101=>100010
[2,7,5,4,3,1,6]=>011110=>100001
[2,7,5,4,3,6,1]=>011101=>100010
[2,7,5,4,6,1,3]=>011010=>100101
[2,7,5,4,6,3,1]=>011011=>100100
[2,7,5,6,1,3,4]=>010100=>101011
[2,7,5,6,1,4,3]=>010101=>101010
[2,7,5,6,3,1,4]=>010110=>101001
[2,7,5,6,3,4,1]=>010101=>101010
[2,7,5,6,4,1,3]=>010110=>101001
[2,7,5,6,4,3,1]=>010111=>101000
[2,7,6,1,3,4,5]=>011000=>100111
[2,7,6,1,3,5,4]=>011001=>100110
[2,7,6,1,4,3,5]=>011010=>100101
[2,7,6,1,4,5,3]=>011001=>100110
[2,7,6,1,5,3,4]=>011010=>100101
[2,7,6,1,5,4,3]=>011011=>100100
[2,7,6,3,1,4,5]=>011100=>100011
[2,7,6,3,1,5,4]=>011101=>100010
[2,7,6,3,4,1,5]=>011010=>100101
[2,7,6,3,4,5,1]=>011001=>100110
[2,7,6,3,5,1,4]=>011010=>100101
[2,7,6,3,5,4,1]=>011011=>100100
[2,7,6,4,1,3,5]=>011100=>100011
[2,7,6,4,1,5,3]=>011101=>100010
[2,7,6,4,3,1,5]=>011110=>100001
[2,7,6,4,3,5,1]=>011101=>100010
[2,7,6,4,5,1,3]=>011010=>100101
[2,7,6,4,5,3,1]=>011011=>100100
[2,7,6,5,1,3,4]=>011100=>100011
[2,7,6,5,1,4,3]=>011101=>100010
[2,7,6,5,3,1,4]=>011110=>100001
[2,7,6,5,3,4,1]=>011101=>100010
[2,7,6,5,4,1,3]=>011110=>100001
[2,7,6,5,4,3,1]=>011111=>100000
[3,1,2,4,5,6,7]=>100000=>011111
[3,1,2,4,5,7,6]=>100001=>011110
[3,1,2,4,6,5,7]=>100010=>011101
[3,1,2,4,6,7,5]=>100001=>011110
[3,1,2,4,7,5,6]=>100010=>011101
[3,1,2,4,7,6,5]=>100011=>011100
[3,1,2,5,4,6,7]=>100100=>011011
[3,1,2,5,4,7,6]=>100101=>011010
[3,1,2,5,6,4,7]=>100010=>011101
[3,1,2,5,6,7,4]=>100001=>011110
[3,1,2,5,7,4,6]=>100010=>011101
[3,1,2,5,7,6,4]=>100011=>011100
[3,1,2,6,4,5,7]=>100100=>011011
[3,1,2,6,4,7,5]=>100101=>011010
[3,1,2,6,5,4,7]=>100110=>011001
[3,1,2,6,5,7,4]=>100101=>011010
[3,1,2,6,7,4,5]=>100010=>011101
[3,1,2,6,7,5,4]=>100011=>011100
[3,1,2,7,4,5,6]=>100100=>011011
[3,1,2,7,4,6,5]=>100101=>011010
[3,1,2,7,5,4,6]=>100110=>011001
[3,1,2,7,5,6,4]=>100101=>011010
[3,1,2,7,6,4,5]=>100110=>011001
[3,1,2,7,6,5,4]=>100111=>011000
[3,1,4,2,5,6,7]=>101000=>010111
[3,1,4,2,5,7,6]=>101001=>010110
[3,1,4,2,6,5,7]=>101010=>010101
[3,1,4,2,6,7,5]=>101001=>010110
[3,1,4,2,7,5,6]=>101010=>010101
[3,1,4,2,7,6,5]=>101011=>010100
[3,1,4,5,2,6,7]=>100100=>011011
[3,1,4,5,2,7,6]=>100101=>011010
[3,1,4,5,6,2,7]=>100010=>011101
[3,1,4,5,6,7,2]=>100001=>011110
[3,1,4,5,7,2,6]=>100010=>011101
[3,1,4,5,7,6,2]=>100011=>011100
[3,1,4,6,2,5,7]=>100100=>011011
[3,1,4,6,2,7,5]=>100101=>011010
[3,1,4,6,5,2,7]=>100110=>011001
[3,1,4,6,5,7,2]=>100101=>011010
[3,1,4,6,7,2,5]=>100010=>011101
[3,1,4,6,7,5,2]=>100011=>011100
[3,1,4,7,2,5,6]=>100100=>011011
[3,1,4,7,2,6,5]=>100101=>011010
[3,1,4,7,5,2,6]=>100110=>011001
[3,1,4,7,5,6,2]=>100101=>011010
[3,1,4,7,6,2,5]=>100110=>011001
[3,1,4,7,6,5,2]=>100111=>011000
[3,1,5,2,4,6,7]=>101000=>010111
[3,1,5,2,4,7,6]=>101001=>010110
[3,1,5,2,6,4,7]=>101010=>010101
[3,1,5,2,6,7,4]=>101001=>010110
[3,1,5,2,7,4,6]=>101010=>010101
[3,1,5,2,7,6,4]=>101011=>010100
[3,1,5,4,2,6,7]=>101100=>010011
[3,1,5,4,2,7,6]=>101101=>010010
[3,1,5,4,6,2,7]=>101010=>010101
[3,1,5,4,6,7,2]=>101001=>010110
[3,1,5,4,7,2,6]=>101010=>010101
[3,1,5,4,7,6,2]=>101011=>010100
[3,1,5,6,2,4,7]=>100100=>011011
[3,1,5,6,2,7,4]=>100101=>011010
[3,1,5,6,4,2,7]=>100110=>011001
[3,1,5,6,4,7,2]=>100101=>011010
[3,1,5,6,7,2,4]=>100010=>011101
[3,1,5,6,7,4,2]=>100011=>011100
[3,1,5,7,2,4,6]=>100100=>011011
[3,1,5,7,2,6,4]=>100101=>011010
[3,1,5,7,4,2,6]=>100110=>011001
[3,1,5,7,4,6,2]=>100101=>011010
[3,1,5,7,6,2,4]=>100110=>011001
[3,1,5,7,6,4,2]=>100111=>011000
[3,1,6,2,4,5,7]=>101000=>010111
[3,1,6,2,4,7,5]=>101001=>010110
[3,1,6,2,5,4,7]=>101010=>010101
[3,1,6,2,5,7,4]=>101001=>010110
[3,1,6,2,7,4,5]=>101010=>010101
[3,1,6,2,7,5,4]=>101011=>010100
[3,1,6,4,2,5,7]=>101100=>010011
[3,1,6,4,2,7,5]=>101101=>010010
[3,1,6,4,5,2,7]=>101010=>010101
[3,1,6,4,5,7,2]=>101001=>010110
[3,1,6,4,7,2,5]=>101010=>010101
[3,1,6,4,7,5,2]=>101011=>010100
[3,1,6,5,2,4,7]=>101100=>010011
[3,1,6,5,2,7,4]=>101101=>010010
[3,1,6,5,4,2,7]=>101110=>010001
[3,1,6,5,4,7,2]=>101101=>010010
[3,1,6,5,7,2,4]=>101010=>010101
[3,1,6,5,7,4,2]=>101011=>010100
[3,1,6,7,2,4,5]=>100100=>011011
[3,1,6,7,2,5,4]=>100101=>011010
[3,1,6,7,4,2,5]=>100110=>011001
[3,1,6,7,4,5,2]=>100101=>011010
[3,1,6,7,5,2,4]=>100110=>011001
[3,1,6,7,5,4,2]=>100111=>011000
[3,1,7,2,4,5,6]=>101000=>010111
[3,1,7,2,4,6,5]=>101001=>010110
[3,1,7,2,5,4,6]=>101010=>010101
[3,1,7,2,5,6,4]=>101001=>010110
[3,1,7,2,6,4,5]=>101010=>010101
[3,1,7,2,6,5,4]=>101011=>010100
[3,1,7,4,2,5,6]=>101100=>010011
[3,1,7,4,2,6,5]=>101101=>010010
[3,1,7,4,5,2,6]=>101010=>010101
[3,1,7,4,5,6,2]=>101001=>010110
[3,1,7,4,6,2,5]=>101010=>010101
[3,1,7,4,6,5,2]=>101011=>010100
[3,1,7,5,2,4,6]=>101100=>010011
[3,1,7,5,2,6,4]=>101101=>010010
[3,1,7,5,4,2,6]=>101110=>010001
[3,1,7,5,4,6,2]=>101101=>010010
[3,1,7,5,6,2,4]=>101010=>010101
[3,1,7,5,6,4,2]=>101011=>010100
[3,1,7,6,2,4,5]=>101100=>010011
[3,1,7,6,2,5,4]=>101101=>010010
[3,1,7,6,4,2,5]=>101110=>010001
[3,1,7,6,4,5,2]=>101101=>010010
[3,1,7,6,5,2,4]=>101110=>010001
[3,1,7,6,5,4,2]=>101111=>010000
[3,2,1,4,5,6,7]=>110000=>001111
[3,2,1,4,5,7,6]=>110001=>001110
[3,2,1,4,6,5,7]=>110010=>001101
[3,2,1,4,6,7,5]=>110001=>001110
[3,2,1,4,7,5,6]=>110010=>001101
[3,2,1,4,7,6,5]=>110011=>001100
[3,2,1,5,4,6,7]=>110100=>001011
[3,2,1,5,4,7,6]=>110101=>001010
[3,2,1,5,6,4,7]=>110010=>001101
[3,2,1,5,6,7,4]=>110001=>001110
[3,2,1,5,7,4,6]=>110010=>001101
[3,2,1,5,7,6,4]=>110011=>001100
[3,2,1,6,4,5,7]=>110100=>001011
[3,2,1,6,4,7,5]=>110101=>001010
[3,2,1,6,5,4,7]=>110110=>001001
[3,2,1,6,5,7,4]=>110101=>001010
[3,2,1,6,7,4,5]=>110010=>001101
[3,2,1,6,7,5,4]=>110011=>001100
[3,2,1,7,4,5,6]=>110100=>001011
[3,2,1,7,4,6,5]=>110101=>001010
[3,2,1,7,5,4,6]=>110110=>001001
[3,2,1,7,5,6,4]=>110101=>001010
[3,2,1,7,6,4,5]=>110110=>001001
[3,2,1,7,6,5,4]=>110111=>001000
[3,2,4,1,5,6,7]=>101000=>010111
[3,2,4,1,5,7,6]=>101001=>010110
[3,2,4,1,6,5,7]=>101010=>010101
[3,2,4,1,6,7,5]=>101001=>010110
[3,2,4,1,7,5,6]=>101010=>010101
[3,2,4,1,7,6,5]=>101011=>010100
[3,2,4,5,1,6,7]=>100100=>011011
[3,2,4,5,1,7,6]=>100101=>011010
[3,2,4,5,6,1,7]=>100010=>011101
[3,2,4,5,6,7,1]=>100001=>011110
[3,2,4,5,7,1,6]=>100010=>011101
[3,2,4,5,7,6,1]=>100011=>011100
[3,2,4,6,1,5,7]=>100100=>011011
[3,2,4,6,1,7,5]=>100101=>011010
[3,2,4,6,5,1,7]=>100110=>011001
[3,2,4,6,5,7,1]=>100101=>011010
[3,2,4,6,7,1,5]=>100010=>011101
[3,2,4,6,7,5,1]=>100011=>011100
[3,2,4,7,1,5,6]=>100100=>011011
[3,2,4,7,1,6,5]=>100101=>011010
[3,2,4,7,5,1,6]=>100110=>011001
[3,2,4,7,5,6,1]=>100101=>011010
[3,2,4,7,6,1,5]=>100110=>011001
[3,2,4,7,6,5,1]=>100111=>011000
[3,2,5,1,4,6,7]=>101000=>010111
[3,2,5,1,4,7,6]=>101001=>010110
[3,2,5,1,6,4,7]=>101010=>010101
[3,2,5,1,6,7,4]=>101001=>010110
[3,2,5,1,7,4,6]=>101010=>010101
[3,2,5,1,7,6,4]=>101011=>010100
[3,2,5,4,1,6,7]=>101100=>010011
[3,2,5,4,1,7,6]=>101101=>010010
[3,2,5,4,6,1,7]=>101010=>010101
[3,2,5,4,6,7,1]=>101001=>010110
[3,2,5,4,7,1,6]=>101010=>010101
[3,2,5,4,7,6,1]=>101011=>010100
[3,2,5,6,1,4,7]=>100100=>011011
[3,2,5,6,1,7,4]=>100101=>011010
[3,2,5,6,4,1,7]=>100110=>011001
[3,2,5,6,4,7,1]=>100101=>011010
[3,2,5,6,7,1,4]=>100010=>011101
[3,2,5,6,7,4,1]=>100011=>011100
[3,2,5,7,1,4,6]=>100100=>011011
[3,2,5,7,1,6,4]=>100101=>011010
[3,2,5,7,4,1,6]=>100110=>011001
[3,2,5,7,4,6,1]=>100101=>011010
[3,2,5,7,6,1,4]=>100110=>011001
[3,2,5,7,6,4,1]=>100111=>011000
[3,2,6,1,4,5,7]=>101000=>010111
[3,2,6,1,4,7,5]=>101001=>010110
[3,2,6,1,5,4,7]=>101010=>010101
[3,2,6,1,5,7,4]=>101001=>010110
[3,2,6,1,7,4,5]=>101010=>010101
[3,2,6,1,7,5,4]=>101011=>010100
[3,2,6,4,1,5,7]=>101100=>010011
[3,2,6,4,1,7,5]=>101101=>010010
[3,2,6,4,5,1,7]=>101010=>010101
[3,2,6,4,5,7,1]=>101001=>010110
[3,2,6,4,7,1,5]=>101010=>010101
[3,2,6,4,7,5,1]=>101011=>010100
[3,2,6,5,1,4,7]=>101100=>010011
[3,2,6,5,1,7,4]=>101101=>010010
[3,2,6,5,4,1,7]=>101110=>010001
[3,2,6,5,4,7,1]=>101101=>010010
[3,2,6,5,7,1,4]=>101010=>010101
[3,2,6,5,7,4,1]=>101011=>010100
[3,2,6,7,1,4,5]=>100100=>011011
[3,2,6,7,1,5,4]=>100101=>011010
[3,2,6,7,4,1,5]=>100110=>011001
[3,2,6,7,4,5,1]=>100101=>011010
[3,2,6,7,5,1,4]=>100110=>011001
[3,2,6,7,5,4,1]=>100111=>011000
[3,2,7,1,4,5,6]=>101000=>010111
[3,2,7,1,4,6,5]=>101001=>010110
[3,2,7,1,5,4,6]=>101010=>010101
[3,2,7,1,5,6,4]=>101001=>010110
[3,2,7,1,6,4,5]=>101010=>010101
[3,2,7,1,6,5,4]=>101011=>010100
[3,2,7,4,1,5,6]=>101100=>010011
[3,2,7,4,1,6,5]=>101101=>010010
[3,2,7,4,5,1,6]=>101010=>010101
[3,2,7,4,5,6,1]=>101001=>010110
[3,2,7,4,6,1,5]=>101010=>010101
[3,2,7,4,6,5,1]=>101011=>010100
[3,2,7,5,1,4,6]=>101100=>010011
[3,2,7,5,1,6,4]=>101101=>010010
[3,2,7,5,4,1,6]=>101110=>010001
[3,2,7,5,4,6,1]=>101101=>010010
[3,2,7,5,6,1,4]=>101010=>010101
[3,2,7,5,6,4,1]=>101011=>010100
[3,2,7,6,1,4,5]=>101100=>010011
[3,2,7,6,1,5,4]=>101101=>010010
[3,2,7,6,4,1,5]=>101110=>010001
[3,2,7,6,4,5,1]=>101101=>010010
[3,2,7,6,5,1,4]=>101110=>010001
[3,2,7,6,5,4,1]=>101111=>010000
[3,4,1,2,5,6,7]=>010000=>101111
[3,4,1,2,5,7,6]=>010001=>101110
[3,4,1,2,6,5,7]=>010010=>101101
[3,4,1,2,6,7,5]=>010001=>101110
[3,4,1,2,7,5,6]=>010010=>101101
[3,4,1,2,7,6,5]=>010011=>101100
[3,4,1,5,2,6,7]=>010100=>101011
[3,4,1,5,2,7,6]=>010101=>101010
[3,4,1,5,6,2,7]=>010010=>101101
[3,4,1,5,6,7,2]=>010001=>101110
[3,4,1,5,7,2,6]=>010010=>101101
[3,4,1,5,7,6,2]=>010011=>101100
[3,4,1,6,2,5,7]=>010100=>101011
[3,4,1,6,2,7,5]=>010101=>101010
[3,4,1,6,5,2,7]=>010110=>101001
[3,4,1,6,5,7,2]=>010101=>101010
[3,4,1,6,7,2,5]=>010010=>101101
[3,4,1,6,7,5,2]=>010011=>101100
[3,4,1,7,2,5,6]=>010100=>101011
[3,4,1,7,2,6,5]=>010101=>101010
[3,4,1,7,5,2,6]=>010110=>101001
[3,4,1,7,5,6,2]=>010101=>101010
[3,4,1,7,6,2,5]=>010110=>101001
[3,4,1,7,6,5,2]=>010111=>101000
[3,4,2,1,5,6,7]=>011000=>100111
[3,4,2,1,5,7,6]=>011001=>100110
[3,4,2,1,6,5,7]=>011010=>100101
[3,4,2,1,6,7,5]=>011001=>100110
[3,4,2,1,7,5,6]=>011010=>100101
[3,4,2,1,7,6,5]=>011011=>100100
[3,4,2,5,1,6,7]=>010100=>101011
[3,4,2,5,1,7,6]=>010101=>101010
[3,4,2,5,6,1,7]=>010010=>101101
[3,4,2,5,6,7,1]=>010001=>101110
[3,4,2,5,7,1,6]=>010010=>101101
[3,4,2,5,7,6,1]=>010011=>101100
[3,4,2,6,1,5,7]=>010100=>101011
[3,4,2,6,1,7,5]=>010101=>101010
[3,4,2,6,5,1,7]=>010110=>101001
[3,4,2,6,5,7,1]=>010101=>101010
[3,4,2,6,7,1,5]=>010010=>101101
[3,4,2,6,7,5,1]=>010011=>101100
[3,4,2,7,1,5,6]=>010100=>101011
[3,4,2,7,1,6,5]=>010101=>101010
[3,4,2,7,5,1,6]=>010110=>101001
[3,4,2,7,5,6,1]=>010101=>101010
[3,4,2,7,6,1,5]=>010110=>101001
[3,4,2,7,6,5,1]=>010111=>101000
[3,4,5,1,2,6,7]=>001000=>110111
[3,4,5,1,2,7,6]=>001001=>110110
[3,4,5,1,6,2,7]=>001010=>110101
[3,4,5,1,6,7,2]=>001001=>110110
[3,4,5,1,7,2,6]=>001010=>110101
[3,4,5,1,7,6,2]=>001011=>110100
[3,4,5,2,1,6,7]=>001100=>110011
[3,4,5,2,1,7,6]=>001101=>110010
[3,4,5,2,6,1,7]=>001010=>110101
[3,4,5,2,6,7,1]=>001001=>110110
[3,4,5,2,7,1,6]=>001010=>110101
[3,4,5,2,7,6,1]=>001011=>110100
[3,4,5,6,1,2,7]=>000100=>111011
[3,4,5,6,1,7,2]=>000101=>111010
[3,4,5,6,2,1,7]=>000110=>111001
[3,4,5,6,2,7,1]=>000101=>111010
[3,4,5,6,7,1,2]=>000010=>111101
[3,4,5,6,7,2,1]=>000011=>111100
[3,4,5,7,1,2,6]=>000100=>111011
[3,4,5,7,1,6,2]=>000101=>111010
[3,4,5,7,2,1,6]=>000110=>111001
[3,4,5,7,2,6,1]=>000101=>111010
[3,4,5,7,6,1,2]=>000110=>111001
[3,4,5,7,6,2,1]=>000111=>111000
[3,4,6,1,2,5,7]=>001000=>110111
[3,4,6,1,2,7,5]=>001001=>110110
[3,4,6,1,5,2,7]=>001010=>110101
[3,4,6,1,5,7,2]=>001001=>110110
[3,4,6,1,7,2,5]=>001010=>110101
[3,4,6,1,7,5,2]=>001011=>110100
[3,4,6,2,1,5,7]=>001100=>110011
[3,4,6,2,1,7,5]=>001101=>110010
[3,4,6,2,5,1,7]=>001010=>110101
[3,4,6,2,5,7,1]=>001001=>110110
[3,4,6,2,7,1,5]=>001010=>110101
[3,4,6,2,7,5,1]=>001011=>110100
[3,4,6,5,1,2,7]=>001100=>110011
[3,4,6,5,1,7,2]=>001101=>110010
[3,4,6,5,2,1,7]=>001110=>110001
[3,4,6,5,2,7,1]=>001101=>110010
[3,4,6,5,7,1,2]=>001010=>110101
[3,4,6,5,7,2,1]=>001011=>110100
[3,4,6,7,1,2,5]=>000100=>111011
[3,4,6,7,1,5,2]=>000101=>111010
[3,4,6,7,2,1,5]=>000110=>111001
[3,4,6,7,2,5,1]=>000101=>111010
[3,4,6,7,5,1,2]=>000110=>111001
[3,4,6,7,5,2,1]=>000111=>111000
[3,4,7,1,2,5,6]=>001000=>110111
[3,4,7,1,2,6,5]=>001001=>110110
[3,4,7,1,5,2,6]=>001010=>110101
[3,4,7,1,5,6,2]=>001001=>110110
[3,4,7,1,6,2,5]=>001010=>110101
[3,4,7,1,6,5,2]=>001011=>110100
[3,4,7,2,1,5,6]=>001100=>110011
[3,4,7,2,1,6,5]=>001101=>110010
[3,4,7,2,5,1,6]=>001010=>110101
[3,4,7,2,5,6,1]=>001001=>110110
[3,4,7,2,6,1,5]=>001010=>110101
[3,4,7,2,6,5,1]=>001011=>110100
[3,4,7,5,1,2,6]=>001100=>110011
[3,4,7,5,1,6,2]=>001101=>110010
[3,4,7,5,2,1,6]=>001110=>110001
[3,4,7,5,2,6,1]=>001101=>110010
[3,4,7,5,6,1,2]=>001010=>110101
[3,4,7,5,6,2,1]=>001011=>110100
[3,4,7,6,1,2,5]=>001100=>110011
[3,4,7,6,1,5,2]=>001101=>110010
[3,4,7,6,2,1,5]=>001110=>110001
[3,4,7,6,2,5,1]=>001101=>110010
[3,4,7,6,5,1,2]=>001110=>110001
[3,4,7,6,5,2,1]=>001111=>110000
[3,5,1,2,4,6,7]=>010000=>101111
[3,5,1,2,4,7,6]=>010001=>101110
[3,5,1,2,6,4,7]=>010010=>101101
[3,5,1,2,6,7,4]=>010001=>101110
[3,5,1,2,7,4,6]=>010010=>101101
[3,5,1,2,7,6,4]=>010011=>101100
[3,5,1,4,2,6,7]=>010100=>101011
[3,5,1,4,2,7,6]=>010101=>101010
[3,5,1,4,6,2,7]=>010010=>101101
[3,5,1,4,6,7,2]=>010001=>101110
[3,5,1,4,7,2,6]=>010010=>101101
[3,5,1,4,7,6,2]=>010011=>101100
[3,5,1,6,2,4,7]=>010100=>101011
[3,5,1,6,2,7,4]=>010101=>101010
[3,5,1,6,4,2,7]=>010110=>101001
[3,5,1,6,4,7,2]=>010101=>101010
[3,5,1,6,7,2,4]=>010010=>101101
[3,5,1,6,7,4,2]=>010011=>101100
[3,5,1,7,2,4,6]=>010100=>101011
[3,5,1,7,2,6,4]=>010101=>101010
[3,5,1,7,4,2,6]=>010110=>101001
[3,5,1,7,4,6,2]=>010101=>101010
[3,5,1,7,6,2,4]=>010110=>101001
[3,5,1,7,6,4,2]=>010111=>101000
[3,5,2,1,4,6,7]=>011000=>100111
[3,5,2,1,4,7,6]=>011001=>100110
[3,5,2,1,6,4,7]=>011010=>100101
[3,5,2,1,6,7,4]=>011001=>100110
[3,5,2,1,7,4,6]=>011010=>100101
[3,5,2,1,7,6,4]=>011011=>100100
[3,5,2,4,1,6,7]=>010100=>101011
[3,5,2,4,1,7,6]=>010101=>101010
[3,5,2,4,6,1,7]=>010010=>101101
[3,5,2,4,6,7,1]=>010001=>101110
[3,5,2,4,7,1,6]=>010010=>101101
[3,5,2,4,7,6,1]=>010011=>101100
[3,5,2,6,1,4,7]=>010100=>101011
[3,5,2,6,1,7,4]=>010101=>101010
[3,5,2,6,4,1,7]=>010110=>101001
[3,5,2,6,4,7,1]=>010101=>101010
[3,5,2,6,7,1,4]=>010010=>101101
[3,5,2,6,7,4,1]=>010011=>101100
[3,5,2,7,1,4,6]=>010100=>101011
[3,5,2,7,1,6,4]=>010101=>101010
[3,5,2,7,4,1,6]=>010110=>101001
[3,5,2,7,4,6,1]=>010101=>101010
[3,5,2,7,6,1,4]=>010110=>101001
[3,5,2,7,6,4,1]=>010111=>101000
[3,5,4,1,2,6,7]=>011000=>100111
[3,5,4,1,2,7,6]=>011001=>100110
[3,5,4,1,6,2,7]=>011010=>100101
[3,5,4,1,6,7,2]=>011001=>100110
[3,5,4,1,7,2,6]=>011010=>100101
[3,5,4,1,7,6,2]=>011011=>100100
[3,5,4,2,1,6,7]=>011100=>100011
[3,5,4,2,1,7,6]=>011101=>100010
[3,5,4,2,6,1,7]=>011010=>100101
[3,5,4,2,6,7,1]=>011001=>100110
[3,5,4,2,7,1,6]=>011010=>100101
[3,5,4,2,7,6,1]=>011011=>100100
[3,5,4,6,1,2,7]=>010100=>101011
[3,5,4,6,1,7,2]=>010101=>101010
[3,5,4,6,2,1,7]=>010110=>101001
[3,5,4,6,2,7,1]=>010101=>101010
[3,5,4,6,7,1,2]=>010010=>101101
[3,5,4,6,7,2,1]=>010011=>101100
[3,5,4,7,1,2,6]=>010100=>101011
[3,5,4,7,1,6,2]=>010101=>101010
[3,5,4,7,2,1,6]=>010110=>101001
[3,5,4,7,2,6,1]=>010101=>101010
[3,5,4,7,6,1,2]=>010110=>101001
[3,5,4,7,6,2,1]=>010111=>101000
[3,5,6,1,2,4,7]=>001000=>110111
[3,5,6,1,2,7,4]=>001001=>110110
[3,5,6,1,4,2,7]=>001010=>110101
[3,5,6,1,4,7,2]=>001001=>110110
[3,5,6,1,7,2,4]=>001010=>110101
[3,5,6,1,7,4,2]=>001011=>110100
[3,5,6,2,1,4,7]=>001100=>110011
[3,5,6,2,1,7,4]=>001101=>110010
[3,5,6,2,4,1,7]=>001010=>110101
[3,5,6,2,4,7,1]=>001001=>110110
[3,5,6,2,7,1,4]=>001010=>110101
[3,5,6,2,7,4,1]=>001011=>110100
[3,5,6,4,1,2,7]=>001100=>110011
[3,5,6,4,1,7,2]=>001101=>110010
[3,5,6,4,2,1,7]=>001110=>110001
[3,5,6,4,2,7,1]=>001101=>110010
[3,5,6,4,7,1,2]=>001010=>110101
[3,5,6,4,7,2,1]=>001011=>110100
[3,5,6,7,1,2,4]=>000100=>111011
[3,5,6,7,1,4,2]=>000101=>111010
[3,5,6,7,2,1,4]=>000110=>111001
[3,5,6,7,2,4,1]=>000101=>111010
[3,5,6,7,4,1,2]=>000110=>111001
[3,5,6,7,4,2,1]=>000111=>111000
[3,5,7,1,2,4,6]=>001000=>110111
[3,5,7,1,2,6,4]=>001001=>110110
[3,5,7,1,4,2,6]=>001010=>110101
[3,5,7,1,4,6,2]=>001001=>110110
[3,5,7,1,6,2,4]=>001010=>110101
[3,5,7,1,6,4,2]=>001011=>110100
[3,5,7,2,1,4,6]=>001100=>110011
[3,5,7,2,1,6,4]=>001101=>110010
[3,5,7,2,4,1,6]=>001010=>110101
[3,5,7,2,4,6,1]=>001001=>110110
[3,5,7,2,6,1,4]=>001010=>110101
[3,5,7,2,6,4,1]=>001011=>110100
[3,5,7,4,1,2,6]=>001100=>110011
[3,5,7,4,1,6,2]=>001101=>110010
[3,5,7,4,2,1,6]=>001110=>110001
[3,5,7,4,2,6,1]=>001101=>110010
[3,5,7,4,6,1,2]=>001010=>110101
[3,5,7,4,6,2,1]=>001011=>110100
[3,5,7,6,1,2,4]=>001100=>110011
[3,5,7,6,1,4,2]=>001101=>110010
[3,5,7,6,2,1,4]=>001110=>110001
[3,5,7,6,2,4,1]=>001101=>110010
[3,5,7,6,4,1,2]=>001110=>110001
[3,5,7,6,4,2,1]=>001111=>110000
[3,6,1,2,4,5,7]=>010000=>101111
[3,6,1,2,4,7,5]=>010001=>101110
[3,6,1,2,5,4,7]=>010010=>101101
[3,6,1,2,5,7,4]=>010001=>101110
[3,6,1,2,7,4,5]=>010010=>101101
[3,6,1,2,7,5,4]=>010011=>101100
[3,6,1,4,2,5,7]=>010100=>101011
[3,6,1,4,2,7,5]=>010101=>101010
[3,6,1,4,5,2,7]=>010010=>101101
[3,6,1,4,5,7,2]=>010001=>101110
[3,6,1,4,7,2,5]=>010010=>101101
[3,6,1,4,7,5,2]=>010011=>101100
[3,6,1,5,2,4,7]=>010100=>101011
[3,6,1,5,2,7,4]=>010101=>101010
[3,6,1,5,4,2,7]=>010110=>101001
[3,6,1,5,4,7,2]=>010101=>101010
[3,6,1,5,7,2,4]=>010010=>101101
[3,6,1,5,7,4,2]=>010011=>101100
[3,6,1,7,2,4,5]=>010100=>101011
[3,6,1,7,2,5,4]=>010101=>101010
[3,6,1,7,4,2,5]=>010110=>101001
[3,6,1,7,4,5,2]=>010101=>101010
[3,6,1,7,5,2,4]=>010110=>101001
[3,6,1,7,5,4,2]=>010111=>101000
[3,6,2,1,4,5,7]=>011000=>100111
[3,6,2,1,4,7,5]=>011001=>100110
[3,6,2,1,5,4,7]=>011010=>100101
[3,6,2,1,5,7,4]=>011001=>100110
[3,6,2,1,7,4,5]=>011010=>100101
[3,6,2,1,7,5,4]=>011011=>100100
[3,6,2,4,1,5,7]=>010100=>101011
[3,6,2,4,1,7,5]=>010101=>101010
[3,6,2,4,5,1,7]=>010010=>101101
[3,6,2,4,5,7,1]=>010001=>101110
[3,6,2,4,7,1,5]=>010010=>101101
[3,6,2,4,7,5,1]=>010011=>101100
[3,6,2,5,1,4,7]=>010100=>101011
[3,6,2,5,1,7,4]=>010101=>101010
[3,6,2,5,4,1,7]=>010110=>101001
[3,6,2,5,4,7,1]=>010101=>101010
[3,6,2,5,7,1,4]=>010010=>101101
[3,6,2,5,7,4,1]=>010011=>101100
[3,6,2,7,1,4,5]=>010100=>101011
[3,6,2,7,1,5,4]=>010101=>101010
[3,6,2,7,4,1,5]=>010110=>101001
[3,6,2,7,4,5,1]=>010101=>101010
[3,6,2,7,5,1,4]=>010110=>101001
[3,6,2,7,5,4,1]=>010111=>101000
[3,6,4,1,2,5,7]=>011000=>100111
[3,6,4,1,2,7,5]=>011001=>100110
[3,6,4,1,5,2,7]=>011010=>100101
[3,6,4,1,5,7,2]=>011001=>100110
[3,6,4,1,7,2,5]=>011010=>100101
[3,6,4,1,7,5,2]=>011011=>100100
[3,6,4,2,1,5,7]=>011100=>100011
[3,6,4,2,1,7,5]=>011101=>100010
[3,6,4,2,5,1,7]=>011010=>100101
[3,6,4,2,5,7,1]=>011001=>100110
[3,6,4,2,7,1,5]=>011010=>100101
[3,6,4,2,7,5,1]=>011011=>100100
[3,6,4,5,1,2,7]=>010100=>101011
[3,6,4,5,1,7,2]=>010101=>101010
[3,6,4,5,2,1,7]=>010110=>101001
[3,6,4,5,2,7,1]=>010101=>101010
[3,6,4,5,7,1,2]=>010010=>101101
[3,6,4,5,7,2,1]=>010011=>101100
[3,6,4,7,1,2,5]=>010100=>101011
[3,6,4,7,1,5,2]=>010101=>101010
[3,6,4,7,2,1,5]=>010110=>101001
[3,6,4,7,2,5,1]=>010101=>101010
[3,6,4,7,5,1,2]=>010110=>101001
[3,6,4,7,5,2,1]=>010111=>101000
[3,6,5,1,2,4,7]=>011000=>100111
[3,6,5,1,2,7,4]=>011001=>100110
[3,6,5,1,4,2,7]=>011010=>100101
[3,6,5,1,4,7,2]=>011001=>100110
[3,6,5,1,7,2,4]=>011010=>100101
[3,6,5,1,7,4,2]=>011011=>100100
[3,6,5,2,1,4,7]=>011100=>100011
[3,6,5,2,1,7,4]=>011101=>100010
[3,6,5,2,4,1,7]=>011010=>100101
[3,6,5,2,4,7,1]=>011001=>100110
[3,6,5,2,7,1,4]=>011010=>100101
[3,6,5,2,7,4,1]=>011011=>100100
[3,6,5,4,1,2,7]=>011100=>100011
[3,6,5,4,1,7,2]=>011101=>100010
[3,6,5,4,2,1,7]=>011110=>100001
[3,6,5,4,2,7,1]=>011101=>100010
[3,6,5,4,7,1,2]=>011010=>100101
[3,6,5,4,7,2,1]=>011011=>100100
[3,6,5,7,1,2,4]=>010100=>101011
[3,6,5,7,1,4,2]=>010101=>101010
[3,6,5,7,2,1,4]=>010110=>101001
[3,6,5,7,2,4,1]=>010101=>101010
[3,6,5,7,4,1,2]=>010110=>101001
[3,6,5,7,4,2,1]=>010111=>101000
[3,6,7,1,2,4,5]=>001000=>110111
[3,6,7,1,2,5,4]=>001001=>110110
[3,6,7,1,4,2,5]=>001010=>110101
[3,6,7,1,4,5,2]=>001001=>110110
[3,6,7,1,5,2,4]=>001010=>110101
[3,6,7,1,5,4,2]=>001011=>110100
[3,6,7,2,1,4,5]=>001100=>110011
[3,6,7,2,1,5,4]=>001101=>110010
[3,6,7,2,4,1,5]=>001010=>110101
[3,6,7,2,4,5,1]=>001001=>110110
[3,6,7,2,5,1,4]=>001010=>110101
[3,6,7,2,5,4,1]=>001011=>110100
[3,6,7,4,1,2,5]=>001100=>110011
[3,6,7,4,1,5,2]=>001101=>110010
[3,6,7,4,2,1,5]=>001110=>110001
[3,6,7,4,2,5,1]=>001101=>110010
[3,6,7,4,5,1,2]=>001010=>110101
[3,6,7,4,5,2,1]=>001011=>110100
[3,6,7,5,1,2,4]=>001100=>110011
[3,6,7,5,1,4,2]=>001101=>110010
[3,6,7,5,2,1,4]=>001110=>110001
[3,6,7,5,2,4,1]=>001101=>110010
[3,6,7,5,4,1,2]=>001110=>110001
[3,6,7,5,4,2,1]=>001111=>110000
[3,7,1,2,4,5,6]=>010000=>101111
[3,7,1,2,4,6,5]=>010001=>101110
[3,7,1,2,5,4,6]=>010010=>101101
[3,7,1,2,5,6,4]=>010001=>101110
[3,7,1,2,6,4,5]=>010010=>101101
[3,7,1,2,6,5,4]=>010011=>101100
[3,7,1,4,2,5,6]=>010100=>101011
[3,7,1,4,2,6,5]=>010101=>101010
[3,7,1,4,5,2,6]=>010010=>101101
[3,7,1,4,5,6,2]=>010001=>101110
[3,7,1,4,6,2,5]=>010010=>101101
[3,7,1,4,6,5,2]=>010011=>101100
[3,7,1,5,2,4,6]=>010100=>101011
[3,7,1,5,2,6,4]=>010101=>101010
[3,7,1,5,4,2,6]=>010110=>101001
[3,7,1,5,4,6,2]=>010101=>101010
[3,7,1,5,6,2,4]=>010010=>101101
[3,7,1,5,6,4,2]=>010011=>101100
[3,7,1,6,2,4,5]=>010100=>101011
[3,7,1,6,2,5,4]=>010101=>101010
[3,7,1,6,4,2,5]=>010110=>101001
[3,7,1,6,4,5,2]=>010101=>101010
[3,7,1,6,5,2,4]=>010110=>101001
[3,7,1,6,5,4,2]=>010111=>101000
[3,7,2,1,4,5,6]=>011000=>100111
[3,7,2,1,4,6,5]=>011001=>100110
[3,7,2,1,5,4,6]=>011010=>100101
[3,7,2,1,5,6,4]=>011001=>100110
[3,7,2,1,6,4,5]=>011010=>100101
[3,7,2,1,6,5,4]=>011011=>100100
[3,7,2,4,1,5,6]=>010100=>101011
[3,7,2,4,1,6,5]=>010101=>101010
[3,7,2,4,5,1,6]=>010010=>101101
[3,7,2,4,5,6,1]=>010001=>101110
[3,7,2,4,6,1,5]=>010010=>101101
[3,7,2,4,6,5,1]=>010011=>101100
[3,7,2,5,1,4,6]=>010100=>101011
[3,7,2,5,1,6,4]=>010101=>101010
[3,7,2,5,4,1,6]=>010110=>101001
[3,7,2,5,4,6,1]=>010101=>101010
[3,7,2,5,6,1,4]=>010010=>101101
[3,7,2,5,6,4,1]=>010011=>101100
[3,7,2,6,1,4,5]=>010100=>101011
[3,7,2,6,1,5,4]=>010101=>101010
[3,7,2,6,4,1,5]=>010110=>101001
[3,7,2,6,4,5,1]=>010101=>101010
[3,7,2,6,5,1,4]=>010110=>101001
[3,7,2,6,5,4,1]=>010111=>101000
[3,7,4,1,2,5,6]=>011000=>100111
[3,7,4,1,2,6,5]=>011001=>100110
[3,7,4,1,5,2,6]=>011010=>100101
[3,7,4,1,5,6,2]=>011001=>100110
[3,7,4,1,6,2,5]=>011010=>100101
[3,7,4,1,6,5,2]=>011011=>100100
[3,7,4,2,1,5,6]=>011100=>100011
[3,7,4,2,1,6,5]=>011101=>100010
[3,7,4,2,5,1,6]=>011010=>100101
[3,7,4,2,5,6,1]=>011001=>100110
[3,7,4,2,6,1,5]=>011010=>100101
[3,7,4,2,6,5,1]=>011011=>100100
[3,7,4,5,1,2,6]=>010100=>101011
[3,7,4,5,1,6,2]=>010101=>101010
[3,7,4,5,2,1,6]=>010110=>101001
[3,7,4,5,2,6,1]=>010101=>101010
[3,7,4,5,6,1,2]=>010010=>101101
[3,7,4,5,6,2,1]=>010011=>101100
[3,7,4,6,1,2,5]=>010100=>101011
[3,7,4,6,1,5,2]=>010101=>101010
[3,7,4,6,2,1,5]=>010110=>101001
[3,7,4,6,2,5,1]=>010101=>101010
[3,7,4,6,5,1,2]=>010110=>101001
[3,7,4,6,5,2,1]=>010111=>101000
[3,7,5,1,2,4,6]=>011000=>100111
[3,7,5,1,2,6,4]=>011001=>100110
[3,7,5,1,4,2,6]=>011010=>100101
[3,7,5,1,4,6,2]=>011001=>100110
[3,7,5,1,6,2,4]=>011010=>100101
[3,7,5,1,6,4,2]=>011011=>100100
[3,7,5,2,1,4,6]=>011100=>100011
[3,7,5,2,1,6,4]=>011101=>100010
[3,7,5,2,4,1,6]=>011010=>100101
[3,7,5,2,4,6,1]=>011001=>100110
[3,7,5,2,6,1,4]=>011010=>100101
[3,7,5,2,6,4,1]=>011011=>100100
[3,7,5,4,1,2,6]=>011100=>100011
[3,7,5,4,1,6,2]=>011101=>100010
[3,7,5,4,2,1,6]=>011110=>100001
[3,7,5,4,2,6,1]=>011101=>100010
[3,7,5,4,6,1,2]=>011010=>100101
[3,7,5,4,6,2,1]=>011011=>100100
[3,7,5,6,1,2,4]=>010100=>101011
[3,7,5,6,1,4,2]=>010101=>101010
[3,7,5,6,2,1,4]=>010110=>101001
[3,7,5,6,2,4,1]=>010101=>101010
[3,7,5,6,4,1,2]=>010110=>101001
[3,7,5,6,4,2,1]=>010111=>101000
[3,7,6,1,2,4,5]=>011000=>100111
[3,7,6,1,2,5,4]=>011001=>100110
[3,7,6,1,4,2,5]=>011010=>100101
[3,7,6,1,4,5,2]=>011001=>100110
[3,7,6,1,5,2,4]=>011010=>100101
[3,7,6,1,5,4,2]=>011011=>100100
[3,7,6,2,1,4,5]=>011100=>100011
[3,7,6,2,1,5,4]=>011101=>100010
[3,7,6,2,4,1,5]=>011010=>100101
[3,7,6,2,4,5,1]=>011001=>100110
[3,7,6,2,5,1,4]=>011010=>100101
[3,7,6,2,5,4,1]=>011011=>100100
[3,7,6,4,1,2,5]=>011100=>100011
[3,7,6,4,1,5,2]=>011101=>100010
[3,7,6,4,2,1,5]=>011110=>100001
[3,7,6,4,2,5,1]=>011101=>100010
[3,7,6,4,5,1,2]=>011010=>100101
[3,7,6,4,5,2,1]=>011011=>100100
[3,7,6,5,1,2,4]=>011100=>100011
[3,7,6,5,1,4,2]=>011101=>100010
[3,7,6,5,2,1,4]=>011110=>100001
[3,7,6,5,2,4,1]=>011101=>100010
[3,7,6,5,4,1,2]=>011110=>100001
[3,7,6,5,4,2,1]=>011111=>100000
[4,1,2,3,5,6,7]=>100000=>011111
[4,1,2,3,5,7,6]=>100001=>011110
[4,1,2,3,6,5,7]=>100010=>011101
[4,1,2,3,6,7,5]=>100001=>011110
[4,1,2,3,7,5,6]=>100010=>011101
[4,1,2,3,7,6,5]=>100011=>011100
[4,1,2,5,3,6,7]=>100100=>011011
[4,1,2,5,3,7,6]=>100101=>011010
[4,1,2,5,6,3,7]=>100010=>011101
[4,1,2,5,6,7,3]=>100001=>011110
[4,1,2,5,7,3,6]=>100010=>011101
[4,1,2,5,7,6,3]=>100011=>011100
[4,1,2,6,3,5,7]=>100100=>011011
[4,1,2,6,3,7,5]=>100101=>011010
[4,1,2,6,5,3,7]=>100110=>011001
[4,1,2,6,5,7,3]=>100101=>011010
[4,1,2,6,7,3,5]=>100010=>011101
[4,1,2,6,7,5,3]=>100011=>011100
[4,1,2,7,3,5,6]=>100100=>011011
[4,1,2,7,3,6,5]=>100101=>011010
[4,1,2,7,5,3,6]=>100110=>011001
[4,1,2,7,5,6,3]=>100101=>011010
[4,1,2,7,6,3,5]=>100110=>011001
[4,1,2,7,6,5,3]=>100111=>011000
[4,1,3,2,5,6,7]=>101000=>010111
[4,1,3,2,5,7,6]=>101001=>010110
[4,1,3,2,6,5,7]=>101010=>010101
[4,1,3,2,6,7,5]=>101001=>010110
[4,1,3,2,7,5,6]=>101010=>010101
[4,1,3,2,7,6,5]=>101011=>010100
[4,1,3,5,2,6,7]=>100100=>011011
[4,1,3,5,2,7,6]=>100101=>011010
[4,1,3,5,6,2,7]=>100010=>011101
[4,1,3,5,6,7,2]=>100001=>011110
[4,1,3,5,7,2,6]=>100010=>011101
[4,1,3,5,7,6,2]=>100011=>011100
[4,1,3,6,2,5,7]=>100100=>011011
[4,1,3,6,2,7,5]=>100101=>011010
[4,1,3,6,5,2,7]=>100110=>011001
[4,1,3,6,5,7,2]=>100101=>011010
[4,1,3,6,7,2,5]=>100010=>011101
[4,1,3,6,7,5,2]=>100011=>011100
[4,1,3,7,2,5,6]=>100100=>011011
[4,1,3,7,2,6,5]=>100101=>011010
[4,1,3,7,5,2,6]=>100110=>011001
[4,1,3,7,5,6,2]=>100101=>011010
[4,1,3,7,6,2,5]=>100110=>011001
[4,1,3,7,6,5,2]=>100111=>011000
[4,1,5,2,3,6,7]=>101000=>010111
[4,1,5,2,3,7,6]=>101001=>010110
[4,1,5,2,6,3,7]=>101010=>010101
[4,1,5,2,6,7,3]=>101001=>010110
[4,1,5,2,7,3,6]=>101010=>010101
[4,1,5,2,7,6,3]=>101011=>010100
[4,1,5,3,2,6,7]=>101100=>010011
[4,1,5,3,2,7,6]=>101101=>010010
[4,1,5,3,6,2,7]=>101010=>010101
[4,1,5,3,6,7,2]=>101001=>010110
[4,1,5,3,7,2,6]=>101010=>010101
[4,1,5,3,7,6,2]=>101011=>010100
[4,1,5,6,2,3,7]=>100100=>011011
[4,1,5,6,2,7,3]=>100101=>011010
[4,1,5,6,3,2,7]=>100110=>011001
[4,1,5,6,3,7,2]=>100101=>011010
[4,1,5,6,7,2,3]=>100010=>011101
[4,1,5,6,7,3,2]=>100011=>011100
[4,1,5,7,2,3,6]=>100100=>011011
[4,1,5,7,2,6,3]=>100101=>011010
[4,1,5,7,3,2,6]=>100110=>011001
[4,1,5,7,3,6,2]=>100101=>011010
[4,1,5,7,6,2,3]=>100110=>011001
[4,1,5,7,6,3,2]=>100111=>011000
[4,1,6,2,3,5,7]=>101000=>010111
[4,1,6,2,3,7,5]=>101001=>010110
[4,1,6,2,5,3,7]=>101010=>010101
[4,1,6,2,5,7,3]=>101001=>010110
[4,1,6,2,7,3,5]=>101010=>010101
[4,1,6,2,7,5,3]=>101011=>010100
[4,1,6,3,2,5,7]=>101100=>010011
[4,1,6,3,2,7,5]=>101101=>010010
[4,1,6,3,5,2,7]=>101010=>010101
[4,1,6,3,5,7,2]=>101001=>010110
[4,1,6,3,7,2,5]=>101010=>010101
[4,1,6,3,7,5,2]=>101011=>010100
[4,1,6,5,2,3,7]=>101100=>010011
[4,1,6,5,2,7,3]=>101101=>010010
[4,1,6,5,3,2,7]=>101110=>010001
[4,1,6,5,3,7,2]=>101101=>010010
[4,1,6,5,7,2,3]=>101010=>010101
[4,1,6,5,7,3,2]=>101011=>010100
[4,1,6,7,2,3,5]=>100100=>011011
[4,1,6,7,2,5,3]=>100101=>011010
[4,1,6,7,3,2,5]=>100110=>011001
[4,1,6,7,3,5,2]=>100101=>011010
[4,1,6,7,5,2,3]=>100110=>011001
[4,1,6,7,5,3,2]=>100111=>011000
[4,1,7,2,3,5,6]=>101000=>010111
[4,1,7,2,3,6,5]=>101001=>010110
[4,1,7,2,5,3,6]=>101010=>010101
[4,1,7,2,5,6,3]=>101001=>010110
[4,1,7,2,6,3,5]=>101010=>010101
[4,1,7,2,6,5,3]=>101011=>010100
[4,1,7,3,2,5,6]=>101100=>010011
[4,1,7,3,2,6,5]=>101101=>010010
[4,1,7,3,5,2,6]=>101010=>010101
[4,1,7,3,5,6,2]=>101001=>010110
[4,1,7,3,6,2,5]=>101010=>010101
[4,1,7,3,6,5,2]=>101011=>010100
[4,1,7,5,2,3,6]=>101100=>010011
[4,1,7,5,2,6,3]=>101101=>010010
[4,1,7,5,3,2,6]=>101110=>010001
[4,1,7,5,3,6,2]=>101101=>010010
[4,1,7,5,6,2,3]=>101010=>010101
[4,1,7,5,6,3,2]=>101011=>010100
[4,1,7,6,2,3,5]=>101100=>010011
[4,1,7,6,2,5,3]=>101101=>010010
[4,1,7,6,3,2,5]=>101110=>010001
[4,1,7,6,3,5,2]=>101101=>010010
[4,1,7,6,5,2,3]=>101110=>010001
[4,1,7,6,5,3,2]=>101111=>010000
[4,2,1,3,5,6,7]=>110000=>001111
[4,2,1,3,5,7,6]=>110001=>001110
[4,2,1,3,6,5,7]=>110010=>001101
[4,2,1,3,6,7,5]=>110001=>001110
[4,2,1,3,7,5,6]=>110010=>001101
[4,2,1,3,7,6,5]=>110011=>001100
[4,2,1,5,3,6,7]=>110100=>001011
[4,2,1,5,3,7,6]=>110101=>001010
[4,2,1,5,6,3,7]=>110010=>001101
[4,2,1,5,6,7,3]=>110001=>001110
[4,2,1,5,7,3,6]=>110010=>001101
[4,2,1,5,7,6,3]=>110011=>001100
[4,2,1,6,3,5,7]=>110100=>001011
[4,2,1,6,3,7,5]=>110101=>001010
[4,2,1,6,5,3,7]=>110110=>001001
[4,2,1,6,5,7,3]=>110101=>001010
[4,2,1,6,7,3,5]=>110010=>001101
[4,2,1,6,7,5,3]=>110011=>001100
[4,2,1,7,3,5,6]=>110100=>001011
[4,2,1,7,3,6,5]=>110101=>001010
[4,2,1,7,5,3,6]=>110110=>001001
[4,2,1,7,5,6,3]=>110101=>001010
[4,2,1,7,6,3,5]=>110110=>001001
[4,2,1,7,6,5,3]=>110111=>001000
[4,2,3,1,5,6,7]=>101000=>010111
[4,2,3,1,5,7,6]=>101001=>010110
[4,2,3,1,6,5,7]=>101010=>010101
[4,2,3,1,6,7,5]=>101001=>010110
[4,2,3,1,7,5,6]=>101010=>010101
[4,2,3,1,7,6,5]=>101011=>010100
[4,2,3,5,1,6,7]=>100100=>011011
[4,2,3,5,1,7,6]=>100101=>011010
[4,2,3,5,6,1,7]=>100010=>011101
[4,2,3,5,6,7,1]=>100001=>011110
[4,2,3,5,7,1,6]=>100010=>011101
[4,2,3,5,7,6,1]=>100011=>011100
[4,2,3,6,1,5,7]=>100100=>011011
[4,2,3,6,1,7,5]=>100101=>011010
[4,2,3,6,5,1,7]=>100110=>011001
[4,2,3,6,5,7,1]=>100101=>011010
[4,2,3,6,7,1,5]=>100010=>011101
[4,2,3,6,7,5,1]=>100011=>011100
[4,2,3,7,1,5,6]=>100100=>011011
[4,2,3,7,1,6,5]=>100101=>011010
[4,2,3,7,5,1,6]=>100110=>011001
[4,2,3,7,5,6,1]=>100101=>011010
[4,2,3,7,6,1,5]=>100110=>011001
[4,2,3,7,6,5,1]=>100111=>011000
[4,2,5,1,3,6,7]=>101000=>010111
[4,2,5,1,3,7,6]=>101001=>010110
[4,2,5,1,6,3,7]=>101010=>010101
[4,2,5,1,6,7,3]=>101001=>010110
[4,2,5,1,7,3,6]=>101010=>010101
[4,2,5,1,7,6,3]=>101011=>010100
[4,2,5,3,1,6,7]=>101100=>010011
[4,2,5,3,1,7,6]=>101101=>010010
[4,2,5,3,6,1,7]=>101010=>010101
[4,2,5,3,6,7,1]=>101001=>010110
[4,2,5,3,7,1,6]=>101010=>010101
[4,2,5,3,7,6,1]=>101011=>010100
[4,2,5,6,1,3,7]=>100100=>011011
[4,2,5,6,1,7,3]=>100101=>011010
[4,2,5,6,3,1,7]=>100110=>011001
[4,2,5,6,3,7,1]=>100101=>011010
[4,2,5,6,7,1,3]=>100010=>011101
[4,2,5,6,7,3,1]=>100011=>011100
[4,2,5,7,1,3,6]=>100100=>011011
[4,2,5,7,1,6,3]=>100101=>011010
[4,2,5,7,3,1,6]=>100110=>011001
[4,2,5,7,3,6,1]=>100101=>011010
[4,2,5,7,6,1,3]=>100110=>011001
[4,2,5,7,6,3,1]=>100111=>011000
[4,2,6,1,3,5,7]=>101000=>010111
[4,2,6,1,3,7,5]=>101001=>010110
[4,2,6,1,5,3,7]=>101010=>010101
[4,2,6,1,5,7,3]=>101001=>010110
[4,2,6,1,7,3,5]=>101010=>010101
[4,2,6,1,7,5,3]=>101011=>010100
[4,2,6,3,1,5,7]=>101100=>010011
[4,2,6,3,1,7,5]=>101101=>010010
[4,2,6,3,5,1,7]=>101010=>010101
[4,2,6,3,5,7,1]=>101001=>010110
[4,2,6,3,7,1,5]=>101010=>010101
[4,2,6,3,7,5,1]=>101011=>010100
[4,2,6,5,1,3,7]=>101100=>010011
[4,2,6,5,1,7,3]=>101101=>010010
[4,2,6,5,3,1,7]=>101110=>010001
[4,2,6,5,3,7,1]=>101101=>010010
[4,2,6,5,7,1,3]=>101010=>010101
[4,2,6,5,7,3,1]=>101011=>010100
[4,2,6,7,1,3,5]=>100100=>011011
[4,2,6,7,1,5,3]=>100101=>011010
[4,2,6,7,3,1,5]=>100110=>011001
[4,2,6,7,3,5,1]=>100101=>011010
[4,2,6,7,5,1,3]=>100110=>011001
[4,2,6,7,5,3,1]=>100111=>011000
[4,2,7,1,3,5,6]=>101000=>010111
[4,2,7,1,3,6,5]=>101001=>010110
[4,2,7,1,5,3,6]=>101010=>010101
[4,2,7,1,5,6,3]=>101001=>010110
[4,2,7,1,6,3,5]=>101010=>010101
[4,2,7,1,6,5,3]=>101011=>010100
[4,2,7,3,1,5,6]=>101100=>010011
[4,2,7,3,1,6,5]=>101101=>010010
[4,2,7,3,5,1,6]=>101010=>010101
[4,2,7,3,5,6,1]=>101001=>010110
[4,2,7,3,6,1,5]=>101010=>010101
[4,2,7,3,6,5,1]=>101011=>010100
[4,2,7,5,1,3,6]=>101100=>010011
[4,2,7,5,1,6,3]=>101101=>010010
[4,2,7,5,3,1,6]=>101110=>010001
[4,2,7,5,3,6,1]=>101101=>010010
[4,2,7,5,6,1,3]=>101010=>010101
[4,2,7,5,6,3,1]=>101011=>010100
[4,2,7,6,1,3,5]=>101100=>010011
[4,2,7,6,1,5,3]=>101101=>010010
[4,2,7,6,3,1,5]=>101110=>010001
[4,2,7,6,3,5,1]=>101101=>010010
[4,2,7,6,5,1,3]=>101110=>010001
[4,2,7,6,5,3,1]=>101111=>010000
[4,3,1,2,5,6,7]=>110000=>001111
[4,3,1,2,5,7,6]=>110001=>001110
[4,3,1,2,6,5,7]=>110010=>001101
[4,3,1,2,6,7,5]=>110001=>001110
[4,3,1,2,7,5,6]=>110010=>001101
[4,3,1,2,7,6,5]=>110011=>001100
[4,3,1,5,2,6,7]=>110100=>001011
[4,3,1,5,2,7,6]=>110101=>001010
[4,3,1,5,6,2,7]=>110010=>001101
[4,3,1,5,6,7,2]=>110001=>001110
[4,3,1,5,7,2,6]=>110010=>001101
[4,3,1,5,7,6,2]=>110011=>001100
[4,3,1,6,2,5,7]=>110100=>001011
[4,3,1,6,2,7,5]=>110101=>001010
[4,3,1,6,5,2,7]=>110110=>001001
[4,3,1,6,5,7,2]=>110101=>001010
[4,3,1,6,7,2,5]=>110010=>001101
[4,3,1,6,7,5,2]=>110011=>001100
[4,3,1,7,2,5,6]=>110100=>001011
[4,3,1,7,2,6,5]=>110101=>001010
[4,3,1,7,5,2,6]=>110110=>001001
[4,3,1,7,5,6,2]=>110101=>001010
[4,3,1,7,6,2,5]=>110110=>001001
[4,3,1,7,6,5,2]=>110111=>001000
[4,3,2,1,5,6,7]=>111000=>000111
[4,3,2,1,5,7,6]=>111001=>000110
[4,3,2,1,6,5,7]=>111010=>000101
[4,3,2,1,6,7,5]=>111001=>000110
[4,3,2,1,7,5,6]=>111010=>000101
[4,3,2,1,7,6,5]=>111011=>000100
[4,3,2,5,1,6,7]=>110100=>001011
[4,3,2,5,1,7,6]=>110101=>001010
[4,3,2,5,6,1,7]=>110010=>001101
[4,3,2,5,6,7,1]=>110001=>001110
[4,3,2,5,7,1,6]=>110010=>001101
[4,3,2,5,7,6,1]=>110011=>001100
[4,3,2,6,1,5,7]=>110100=>001011
[4,3,2,6,1,7,5]=>110101=>001010
[4,3,2,6,5,1,7]=>110110=>001001
[4,3,2,6,5,7,1]=>110101=>001010
[4,3,2,6,7,1,5]=>110010=>001101
[4,3,2,6,7,5,1]=>110011=>001100
[4,3,2,7,1,5,6]=>110100=>001011
[4,3,2,7,1,6,5]=>110101=>001010
[4,3,2,7,5,1,6]=>110110=>001001
[4,3,2,7,5,6,1]=>110101=>001010
[4,3,2,7,6,1,5]=>110110=>001001
[4,3,2,7,6,5,1]=>110111=>001000
[4,3,5,1,2,6,7]=>101000=>010111
[4,3,5,1,2,7,6]=>101001=>010110
[4,3,5,1,6,2,7]=>101010=>010101
[4,3,5,1,6,7,2]=>101001=>010110
[4,3,5,1,7,2,6]=>101010=>010101
[4,3,5,1,7,6,2]=>101011=>010100
[4,3,5,2,1,6,7]=>101100=>010011
[4,3,5,2,1,7,6]=>101101=>010010
[4,3,5,2,6,1,7]=>101010=>010101
[4,3,5,2,6,7,1]=>101001=>010110
[4,3,5,2,7,1,6]=>101010=>010101
[4,3,5,2,7,6,1]=>101011=>010100
[4,3,5,6,1,2,7]=>100100=>011011
[4,3,5,6,1,7,2]=>100101=>011010
[4,3,5,6,2,1,7]=>100110=>011001
[4,3,5,6,2,7,1]=>100101=>011010
[4,3,5,6,7,1,2]=>100010=>011101
[4,3,5,6,7,2,1]=>100011=>011100
[4,3,5,7,1,2,6]=>100100=>011011
[4,3,5,7,1,6,2]=>100101=>011010
[4,3,5,7,2,1,6]=>100110=>011001
[4,3,5,7,2,6,1]=>100101=>011010
[4,3,5,7,6,1,2]=>100110=>011001
[4,3,5,7,6,2,1]=>100111=>011000
[4,3,6,1,2,5,7]=>101000=>010111
[4,3,6,1,2,7,5]=>101001=>010110
[4,3,6,1,5,2,7]=>101010=>010101
[4,3,6,1,5,7,2]=>101001=>010110
[4,3,6,1,7,2,5]=>101010=>010101
[4,3,6,1,7,5,2]=>101011=>010100
[4,3,6,2,1,5,7]=>101100=>010011
[4,3,6,2,1,7,5]=>101101=>010010
[4,3,6,2,5,1,7]=>101010=>010101
[4,3,6,2,5,7,1]=>101001=>010110
[4,3,6,2,7,1,5]=>101010=>010101
[4,3,6,2,7,5,1]=>101011=>010100
[4,3,6,5,1,2,7]=>101100=>010011
[4,3,6,5,1,7,2]=>101101=>010010
[4,3,6,5,2,1,7]=>101110=>010001
[4,3,6,5,2,7,1]=>101101=>010010
[4,3,6,5,7,1,2]=>101010=>010101
[4,3,6,5,7,2,1]=>101011=>010100
[4,3,6,7,1,2,5]=>100100=>011011
[4,3,6,7,1,5,2]=>100101=>011010
[4,3,6,7,2,1,5]=>100110=>011001
[4,3,6,7,2,5,1]=>100101=>011010
[4,3,6,7,5,1,2]=>100110=>011001
[4,3,6,7,5,2,1]=>100111=>011000
[4,3,7,1,2,5,6]=>101000=>010111
[4,3,7,1,2,6,5]=>101001=>010110
[4,3,7,1,5,2,6]=>101010=>010101
[4,3,7,1,5,6,2]=>101001=>010110
[4,3,7,1,6,2,5]=>101010=>010101
[4,3,7,1,6,5,2]=>101011=>010100
[4,3,7,2,1,5,6]=>101100=>010011
[4,3,7,2,1,6,5]=>101101=>010010
[4,3,7,2,5,1,6]=>101010=>010101
[4,3,7,2,5,6,1]=>101001=>010110
[4,3,7,2,6,1,5]=>101010=>010101
[4,3,7,2,6,5,1]=>101011=>010100
[4,3,7,5,1,2,6]=>101100=>010011
[4,3,7,5,1,6,2]=>101101=>010010
[4,3,7,5,2,1,6]=>101110=>010001
[4,3,7,5,2,6,1]=>101101=>010010
[4,3,7,5,6,1,2]=>101010=>010101
[4,3,7,5,6,2,1]=>101011=>010100
[4,3,7,6,1,2,5]=>101100=>010011
[4,3,7,6,1,5,2]=>101101=>010010
[4,3,7,6,2,1,5]=>101110=>010001
[4,3,7,6,2,5,1]=>101101=>010010
[4,3,7,6,5,1,2]=>101110=>010001
[4,3,7,6,5,2,1]=>101111=>010000
[4,5,1,2,3,6,7]=>010000=>101111
[4,5,1,2,3,7,6]=>010001=>101110
[4,5,1,2,6,3,7]=>010010=>101101
[4,5,1,2,6,7,3]=>010001=>101110
[4,5,1,2,7,3,6]=>010010=>101101
[4,5,1,2,7,6,3]=>010011=>101100
[4,5,1,3,2,6,7]=>010100=>101011
[4,5,1,3,2,7,6]=>010101=>101010
[4,5,1,3,6,2,7]=>010010=>101101
[4,5,1,3,6,7,2]=>010001=>101110
[4,5,1,3,7,2,6]=>010010=>101101
[4,5,1,3,7,6,2]=>010011=>101100
[4,5,1,6,2,3,7]=>010100=>101011
[4,5,1,6,2,7,3]=>010101=>101010
[4,5,1,6,3,2,7]=>010110=>101001
[4,5,1,6,3,7,2]=>010101=>101010
[4,5,1,6,7,2,3]=>010010=>101101
[4,5,1,6,7,3,2]=>010011=>101100
[4,5,1,7,2,3,6]=>010100=>101011
[4,5,1,7,2,6,3]=>010101=>101010
[4,5,1,7,3,2,6]=>010110=>101001
[4,5,1,7,3,6,2]=>010101=>101010
[4,5,1,7,6,2,3]=>010110=>101001
[4,5,1,7,6,3,2]=>010111=>101000
[4,5,2,1,3,6,7]=>011000=>100111
[4,5,2,1,3,7,6]=>011001=>100110
[4,5,2,1,6,3,7]=>011010=>100101
[4,5,2,1,6,7,3]=>011001=>100110
[4,5,2,1,7,3,6]=>011010=>100101
[4,5,2,1,7,6,3]=>011011=>100100
[4,5,2,3,1,6,7]=>010100=>101011
[4,5,2,3,1,7,6]=>010101=>101010
[4,5,2,3,6,1,7]=>010010=>101101
[4,5,2,3,6,7,1]=>010001=>101110
[4,5,2,3,7,1,6]=>010010=>101101
[4,5,2,3,7,6,1]=>010011=>101100
[4,5,2,6,1,3,7]=>010100=>101011
[4,5,2,6,1,7,3]=>010101=>101010
[4,5,2,6,3,1,7]=>010110=>101001
[4,5,2,6,3,7,1]=>010101=>101010
[4,5,2,6,7,1,3]=>010010=>101101
[4,5,2,6,7,3,1]=>010011=>101100
[4,5,2,7,1,3,6]=>010100=>101011
[4,5,2,7,1,6,3]=>010101=>101010
[4,5,2,7,3,1,6]=>010110=>101001
[4,5,2,7,3,6,1]=>010101=>101010
[4,5,2,7,6,1,3]=>010110=>101001
[4,5,2,7,6,3,1]=>010111=>101000
[4,5,3,1,2,6,7]=>011000=>100111
[4,5,3,1,2,7,6]=>011001=>100110
[4,5,3,1,6,2,7]=>011010=>100101
[4,5,3,1,6,7,2]=>011001=>100110
[4,5,3,1,7,2,6]=>011010=>100101
[4,5,3,1,7,6,2]=>011011=>100100
[4,5,3,2,1,6,7]=>011100=>100011
[4,5,3,2,1,7,6]=>011101=>100010
[4,5,3,2,6,1,7]=>011010=>100101
[4,5,3,2,6,7,1]=>011001=>100110
[4,5,3,2,7,1,6]=>011010=>100101
[4,5,3,2,7,6,1]=>011011=>100100
[4,5,3,6,1,2,7]=>010100=>101011
[4,5,3,6,1,7,2]=>010101=>101010
[4,5,3,6,2,1,7]=>010110=>101001
[4,5,3,6,2,7,1]=>010101=>101010
[4,5,3,6,7,1,2]=>010010=>101101
[4,5,3,6,7,2,1]=>010011=>101100
[4,5,3,7,1,2,6]=>010100=>101011
[4,5,3,7,1,6,2]=>010101=>101010
[4,5,3,7,2,1,6]=>010110=>101001
[4,5,3,7,2,6,1]=>010101=>101010
[4,5,3,7,6,1,2]=>010110=>101001
[4,5,3,7,6,2,1]=>010111=>101000
[4,5,6,1,2,3,7]=>001000=>110111
[4,5,6,1,2,7,3]=>001001=>110110
[4,5,6,1,3,2,7]=>001010=>110101
[4,5,6,1,3,7,2]=>001001=>110110
[4,5,6,1,7,2,3]=>001010=>110101
[4,5,6,1,7,3,2]=>001011=>110100
[4,5,6,2,1,3,7]=>001100=>110011
[4,5,6,2,1,7,3]=>001101=>110010
[4,5,6,2,3,1,7]=>001010=>110101
[4,5,6,2,3,7,1]=>001001=>110110
[4,5,6,2,7,1,3]=>001010=>110101
[4,5,6,2,7,3,1]=>001011=>110100
[4,5,6,3,1,2,7]=>001100=>110011
[4,5,6,3,1,7,2]=>001101=>110010
[4,5,6,3,2,1,7]=>001110=>110001
[4,5,6,3,2,7,1]=>001101=>110010
[4,5,6,3,7,1,2]=>001010=>110101
[4,5,6,3,7,2,1]=>001011=>110100
[4,5,6,7,1,2,3]=>000100=>111011
[4,5,6,7,1,3,2]=>000101=>111010
[4,5,6,7,2,1,3]=>000110=>111001
[4,5,6,7,2,3,1]=>000101=>111010
[4,5,6,7,3,1,2]=>000110=>111001
[4,5,6,7,3,2,1]=>000111=>111000
[4,5,7,1,2,3,6]=>001000=>110111
[4,5,7,1,2,6,3]=>001001=>110110
[4,5,7,1,3,2,6]=>001010=>110101
[4,5,7,1,3,6,2]=>001001=>110110
[4,5,7,1,6,2,3]=>001010=>110101
[4,5,7,1,6,3,2]=>001011=>110100
[4,5,7,2,1,3,6]=>001100=>110011
[4,5,7,2,1,6,3]=>001101=>110010
[4,5,7,2,3,1,6]=>001010=>110101
[4,5,7,2,3,6,1]=>001001=>110110
[4,5,7,2,6,1,3]=>001010=>110101
[4,5,7,2,6,3,1]=>001011=>110100
[4,5,7,3,1,2,6]=>001100=>110011
[4,5,7,3,1,6,2]=>001101=>110010
[4,5,7,3,2,1,6]=>001110=>110001
[4,5,7,3,2,6,1]=>001101=>110010
[4,5,7,3,6,1,2]=>001010=>110101
[4,5,7,3,6,2,1]=>001011=>110100
[4,5,7,6,1,2,3]=>001100=>110011
[4,5,7,6,1,3,2]=>001101=>110010
[4,5,7,6,2,1,3]=>001110=>110001
[4,5,7,6,2,3,1]=>001101=>110010
[4,5,7,6,3,1,2]=>001110=>110001
[4,5,7,6,3,2,1]=>001111=>110000
[4,6,1,2,3,5,7]=>010000=>101111
[4,6,1,2,3,7,5]=>010001=>101110
[4,6,1,2,5,3,7]=>010010=>101101
[4,6,1,2,5,7,3]=>010001=>101110
[4,6,1,2,7,3,5]=>010010=>101101
[4,6,1,2,7,5,3]=>010011=>101100
[4,6,1,3,2,5,7]=>010100=>101011
[4,6,1,3,2,7,5]=>010101=>101010
[4,6,1,3,5,2,7]=>010010=>101101
[4,6,1,3,5,7,2]=>010001=>101110
[4,6,1,3,7,2,5]=>010010=>101101
[4,6,1,3,7,5,2]=>010011=>101100
[4,6,1,5,2,3,7]=>010100=>101011
[4,6,1,5,2,7,3]=>010101=>101010
[4,6,1,5,3,2,7]=>010110=>101001
[4,6,1,5,3,7,2]=>010101=>101010
[4,6,1,5,7,2,3]=>010010=>101101
[4,6,1,5,7,3,2]=>010011=>101100
[4,6,1,7,2,3,5]=>010100=>101011
[4,6,1,7,2,5,3]=>010101=>101010
[4,6,1,7,3,2,5]=>010110=>101001
[4,6,1,7,3,5,2]=>010101=>101010
[4,6,1,7,5,2,3]=>010110=>101001
[4,6,1,7,5,3,2]=>010111=>101000
[4,6,2,1,3,5,7]=>011000=>100111
[4,6,2,1,3,7,5]=>011001=>100110
[4,6,2,1,5,3,7]=>011010=>100101
[4,6,2,1,5,7,3]=>011001=>100110
[4,6,2,1,7,3,5]=>011010=>100101
[4,6,2,1,7,5,3]=>011011=>100100
[4,6,2,3,1,5,7]=>010100=>101011
[4,6,2,3,1,7,5]=>010101=>101010
[4,6,2,3,5,1,7]=>010010=>101101
[4,6,2,3,5,7,1]=>010001=>101110
[4,6,2,3,7,1,5]=>010010=>101101
[4,6,2,3,7,5,1]=>010011=>101100
[4,6,2,5,1,3,7]=>010100=>101011
[4,6,2,5,1,7,3]=>010101=>101010
[4,6,2,5,3,1,7]=>010110=>101001
[4,6,2,5,3,7,1]=>010101=>101010
[4,6,2,5,7,1,3]=>010010=>101101
[4,6,2,5,7,3,1]=>010011=>101100
[4,6,2,7,1,3,5]=>010100=>101011
[4,6,2,7,1,5,3]=>010101=>101010
[4,6,2,7,3,1,5]=>010110=>101001
[4,6,2,7,3,5,1]=>010101=>101010
[4,6,2,7,5,1,3]=>010110=>101001
[4,6,2,7,5,3,1]=>010111=>101000
[4,6,3,1,2,5,7]=>011000=>100111
[4,6,3,1,2,7,5]=>011001=>100110
[4,6,3,1,5,2,7]=>011010=>100101
[4,6,3,1,5,7,2]=>011001=>100110
[4,6,3,1,7,2,5]=>011010=>100101
[4,6,3,1,7,5,2]=>011011=>100100
[4,6,3,2,1,5,7]=>011100=>100011
[4,6,3,2,1,7,5]=>011101=>100010
[4,6,3,2,5,1,7]=>011010=>100101
[4,6,3,2,5,7,1]=>011001=>100110
[4,6,3,2,7,1,5]=>011010=>100101
[4,6,3,2,7,5,1]=>011011=>100100
[4,6,3,5,1,2,7]=>010100=>101011
[4,6,3,5,1,7,2]=>010101=>101010
[4,6,3,5,2,1,7]=>010110=>101001
[4,6,3,5,2,7,1]=>010101=>101010
[4,6,3,5,7,1,2]=>010010=>101101
[4,6,3,5,7,2,1]=>010011=>101100
[4,6,3,7,1,2,5]=>010100=>101011
[4,6,3,7,1,5,2]=>010101=>101010
[4,6,3,7,2,1,5]=>010110=>101001
[4,6,3,7,2,5,1]=>010101=>101010
[4,6,3,7,5,1,2]=>010110=>101001
[4,6,3,7,5,2,1]=>010111=>101000
[4,6,5,1,2,3,7]=>011000=>100111
[4,6,5,1,2,7,3]=>011001=>100110
[4,6,5,1,3,2,7]=>011010=>100101
[4,6,5,1,3,7,2]=>011001=>100110
[4,6,5,1,7,2,3]=>011010=>100101
[4,6,5,1,7,3,2]=>011011=>100100
[4,6,5,2,1,3,7]=>011100=>100011
[4,6,5,2,1,7,3]=>011101=>100010
[4,6,5,2,3,1,7]=>011010=>100101
[4,6,5,2,3,7,1]=>011001=>100110
[4,6,5,2,7,1,3]=>011010=>100101
[4,6,5,2,7,3,1]=>011011=>100100
[4,6,5,3,1,2,7]=>011100=>100011
[4,6,5,3,1,7,2]=>011101=>100010
[4,6,5,3,2,1,7]=>011110=>100001
[4,6,5,3,2,7,1]=>011101=>100010
[4,6,5,3,7,1,2]=>011010=>100101
[4,6,5,3,7,2,1]=>011011=>100100
[4,6,5,7,1,2,3]=>010100=>101011
[4,6,5,7,1,3,2]=>010101=>101010
[4,6,5,7,2,1,3]=>010110=>101001
[4,6,5,7,2,3,1]=>010101=>101010
[4,6,5,7,3,1,2]=>010110=>101001
[4,6,5,7,3,2,1]=>010111=>101000
[4,6,7,1,2,3,5]=>001000=>110111
[4,6,7,1,2,5,3]=>001001=>110110
[4,6,7,1,3,2,5]=>001010=>110101
[4,6,7,1,3,5,2]=>001001=>110110
[4,6,7,1,5,2,3]=>001010=>110101
[4,6,7,1,5,3,2]=>001011=>110100
[4,6,7,2,1,3,5]=>001100=>110011
[4,6,7,2,1,5,3]=>001101=>110010
[4,6,7,2,3,1,5]=>001010=>110101
[4,6,7,2,3,5,1]=>001001=>110110
[4,6,7,2,5,1,3]=>001010=>110101
[4,6,7,2,5,3,1]=>001011=>110100
[4,6,7,3,1,2,5]=>001100=>110011
[4,6,7,3,1,5,2]=>001101=>110010
[4,6,7,3,2,1,5]=>001110=>110001
[4,6,7,3,2,5,1]=>001101=>110010
[4,6,7,3,5,1,2]=>001010=>110101
[4,6,7,3,5,2,1]=>001011=>110100
[4,6,7,5,1,2,3]=>001100=>110011
[4,6,7,5,1,3,2]=>001101=>110010
[4,6,7,5,2,1,3]=>001110=>110001
[4,6,7,5,2,3,1]=>001101=>110010
[4,6,7,5,3,1,2]=>001110=>110001
[4,6,7,5,3,2,1]=>001111=>110000
[4,7,1,2,3,5,6]=>010000=>101111
[4,7,1,2,3,6,5]=>010001=>101110
[4,7,1,2,5,3,6]=>010010=>101101
[4,7,1,2,5,6,3]=>010001=>101110
[4,7,1,2,6,3,5]=>010010=>101101
[4,7,1,2,6,5,3]=>010011=>101100
[4,7,1,3,2,5,6]=>010100=>101011
[4,7,1,3,2,6,5]=>010101=>101010
[4,7,1,3,5,2,6]=>010010=>101101
[4,7,1,3,5,6,2]=>010001=>101110
[4,7,1,3,6,2,5]=>010010=>101101
[4,7,1,3,6,5,2]=>010011=>101100
[4,7,1,5,2,3,6]=>010100=>101011
[4,7,1,5,2,6,3]=>010101=>101010
[4,7,1,5,3,2,6]=>010110=>101001
[4,7,1,5,3,6,2]=>010101=>101010
[4,7,1,5,6,2,3]=>010010=>101101
[4,7,1,5,6,3,2]=>010011=>101100
[4,7,1,6,2,3,5]=>010100=>101011
[4,7,1,6,2,5,3]=>010101=>101010
[4,7,1,6,3,2,5]=>010110=>101001
[4,7,1,6,3,5,2]=>010101=>101010
[4,7,1,6,5,2,3]=>010110=>101001
[4,7,1,6,5,3,2]=>010111=>101000
[4,7,2,1,3,5,6]=>011000=>100111
[4,7,2,1,3,6,5]=>011001=>100110
[4,7,2,1,5,3,6]=>011010=>100101
[4,7,2,1,5,6,3]=>011001=>100110
[4,7,2,1,6,3,5]=>011010=>100101
[4,7,2,1,6,5,3]=>011011=>100100
[4,7,2,3,1,5,6]=>010100=>101011
[4,7,2,3,1,6,5]=>010101=>101010
[4,7,2,3,5,1,6]=>010010=>101101
[4,7,2,3,5,6,1]=>010001=>101110
[4,7,2,3,6,1,5]=>010010=>101101
[4,7,2,3,6,5,1]=>010011=>101100
[4,7,2,5,1,3,6]=>010100=>101011
[4,7,2,5,1,6,3]=>010101=>101010
[4,7,2,5,3,1,6]=>010110=>101001
[4,7,2,5,3,6,1]=>010101=>101010
[4,7,2,5,6,1,3]=>010010=>101101
[4,7,2,5,6,3,1]=>010011=>101100
[4,7,2,6,1,3,5]=>010100=>101011
[4,7,2,6,1,5,3]=>010101=>101010
[4,7,2,6,3,1,5]=>010110=>101001
[4,7,2,6,3,5,1]=>010101=>101010
[4,7,2,6,5,1,3]=>010110=>101001
[4,7,2,6,5,3,1]=>010111=>101000
[4,7,3,1,2,5,6]=>011000=>100111
[4,7,3,1,2,6,5]=>011001=>100110
[4,7,3,1,5,2,6]=>011010=>100101
[4,7,3,1,5,6,2]=>011001=>100110
[4,7,3,1,6,2,5]=>011010=>100101
[4,7,3,1,6,5,2]=>011011=>100100
[4,7,3,2,1,5,6]=>011100=>100011
[4,7,3,2,1,6,5]=>011101=>100010
[4,7,3,2,5,1,6]=>011010=>100101
[4,7,3,2,5,6,1]=>011001=>100110
[4,7,3,2,6,1,5]=>011010=>100101
[4,7,3,2,6,5,1]=>011011=>100100
[4,7,3,5,1,2,6]=>010100=>101011
[4,7,3,5,1,6,2]=>010101=>101010
[4,7,3,5,2,1,6]=>010110=>101001
[4,7,3,5,2,6,1]=>010101=>101010
[4,7,3,5,6,1,2]=>010010=>101101
[4,7,3,5,6,2,1]=>010011=>101100
[4,7,3,6,1,2,5]=>010100=>101011
[4,7,3,6,1,5,2]=>010101=>101010
[4,7,3,6,2,1,5]=>010110=>101001
[4,7,3,6,2,5,1]=>010101=>101010
[4,7,3,6,5,1,2]=>010110=>101001
[4,7,3,6,5,2,1]=>010111=>101000
[4,7,5,1,2,3,6]=>011000=>100111
[4,7,5,1,2,6,3]=>011001=>100110
[4,7,5,1,3,2,6]=>011010=>100101
[4,7,5,1,3,6,2]=>011001=>100110
[4,7,5,1,6,2,3]=>011010=>100101
[4,7,5,1,6,3,2]=>011011=>100100
[4,7,5,2,1,3,6]=>011100=>100011
[4,7,5,2,1,6,3]=>011101=>100010
[4,7,5,2,3,1,6]=>011010=>100101
[4,7,5,2,3,6,1]=>011001=>100110
[4,7,5,2,6,1,3]=>011010=>100101
[4,7,5,2,6,3,1]=>011011=>100100
[4,7,5,3,1,2,6]=>011100=>100011
[4,7,5,3,1,6,2]=>011101=>100010
[4,7,5,3,2,1,6]=>011110=>100001
[4,7,5,3,2,6,1]=>011101=>100010
[4,7,5,3,6,1,2]=>011010=>100101
[4,7,5,3,6,2,1]=>011011=>100100
[4,7,5,6,1,2,3]=>010100=>101011
[4,7,5,6,1,3,2]=>010101=>101010
[4,7,5,6,2,1,3]=>010110=>101001
[4,7,5,6,2,3,1]=>010101=>101010
[4,7,5,6,3,1,2]=>010110=>101001
[4,7,5,6,3,2,1]=>010111=>101000
[4,7,6,1,2,3,5]=>011000=>100111
[4,7,6,1,2,5,3]=>011001=>100110
[4,7,6,1,3,2,5]=>011010=>100101
[4,7,6,1,3,5,2]=>011001=>100110
[4,7,6,1,5,2,3]=>011010=>100101
[4,7,6,1,5,3,2]=>011011=>100100
[4,7,6,2,1,3,5]=>011100=>100011
[4,7,6,2,1,5,3]=>011101=>100010
[4,7,6,2,3,1,5]=>011010=>100101
[4,7,6,2,3,5,1]=>011001=>100110
[4,7,6,2,5,1,3]=>011010=>100101
[4,7,6,2,5,3,1]=>011011=>100100
[4,7,6,3,1,2,5]=>011100=>100011
[4,7,6,3,1,5,2]=>011101=>100010
[4,7,6,3,2,1,5]=>011110=>100001
[4,7,6,3,2,5,1]=>011101=>100010
[4,7,6,3,5,1,2]=>011010=>100101
[4,7,6,3,5,2,1]=>011011=>100100
[4,7,6,5,1,2,3]=>011100=>100011
[4,7,6,5,1,3,2]=>011101=>100010
[4,7,6,5,2,1,3]=>011110=>100001
[4,7,6,5,2,3,1]=>011101=>100010
[4,7,6,5,3,1,2]=>011110=>100001
[4,7,6,5,3,2,1]=>011111=>100000
[5,1,2,3,4,6,7]=>100000=>011111
[5,1,2,3,4,7,6]=>100001=>011110
[5,1,2,3,6,4,7]=>100010=>011101
[5,1,2,3,6,7,4]=>100001=>011110
[5,1,2,3,7,4,6]=>100010=>011101
[5,1,2,3,7,6,4]=>100011=>011100
[5,1,2,4,3,6,7]=>100100=>011011
[5,1,2,4,3,7,6]=>100101=>011010
[5,1,2,4,6,3,7]=>100010=>011101
[5,1,2,4,6,7,3]=>100001=>011110
[5,1,2,4,7,3,6]=>100010=>011101
[5,1,2,4,7,6,3]=>100011=>011100
[5,1,2,6,3,4,7]=>100100=>011011
[5,1,2,6,3,7,4]=>100101=>011010
[5,1,2,6,4,3,7]=>100110=>011001
[5,1,2,6,4,7,3]=>100101=>011010
[5,1,2,6,7,3,4]=>100010=>011101
[5,1,2,6,7,4,3]=>100011=>011100
[5,1,2,7,3,4,6]=>100100=>011011
[5,1,2,7,3,6,4]=>100101=>011010
[5,1,2,7,4,3,6]=>100110=>011001
[5,1,2,7,4,6,3]=>100101=>011010
[5,1,2,7,6,3,4]=>100110=>011001
[5,1,2,7,6,4,3]=>100111=>011000
[5,1,3,2,4,6,7]=>101000=>010111
[5,1,3,2,4,7,6]=>101001=>010110
[5,1,3,2,6,4,7]=>101010=>010101
[5,1,3,2,6,7,4]=>101001=>010110
[5,1,3,2,7,4,6]=>101010=>010101
[5,1,3,2,7,6,4]=>101011=>010100
[5,1,3,4,2,6,7]=>100100=>011011
[5,1,3,4,2,7,6]=>100101=>011010
[5,1,3,4,6,2,7]=>100010=>011101
[5,1,3,4,6,7,2]=>100001=>011110
[5,1,3,4,7,2,6]=>100010=>011101
[5,1,3,4,7,6,2]=>100011=>011100
[5,1,3,6,2,4,7]=>100100=>011011
[5,1,3,6,2,7,4]=>100101=>011010
[5,1,3,6,4,2,7]=>100110=>011001
[5,1,3,6,4,7,2]=>100101=>011010
[5,1,3,6,7,2,4]=>100010=>011101
[5,1,3,6,7,4,2]=>100011=>011100
[5,1,3,7,2,4,6]=>100100=>011011
[5,1,3,7,2,6,4]=>100101=>011010
[5,1,3,7,4,2,6]=>100110=>011001
[5,1,3,7,4,6,2]=>100101=>011010
[5,1,3,7,6,2,4]=>100110=>011001
[5,1,3,7,6,4,2]=>100111=>011000
[5,1,4,2,3,6,7]=>101000=>010111
[5,1,4,2,3,7,6]=>101001=>010110
[5,1,4,2,6,3,7]=>101010=>010101
[5,1,4,2,6,7,3]=>101001=>010110
[5,1,4,2,7,3,6]=>101010=>010101
[5,1,4,2,7,6,3]=>101011=>010100
[5,1,4,3,2,6,7]=>101100=>010011
[5,1,4,3,2,7,6]=>101101=>010010
[5,1,4,3,6,2,7]=>101010=>010101
[5,1,4,3,6,7,2]=>101001=>010110
[5,1,4,3,7,2,6]=>101010=>010101
[5,1,4,3,7,6,2]=>101011=>010100
[5,1,4,6,2,3,7]=>100100=>011011
[5,1,4,6,2,7,3]=>100101=>011010
[5,1,4,6,3,2,7]=>100110=>011001
[5,1,4,6,3,7,2]=>100101=>011010
[5,1,4,6,7,2,3]=>100010=>011101
[5,1,4,6,7,3,2]=>100011=>011100
[5,1,4,7,2,3,6]=>100100=>011011
[5,1,4,7,2,6,3]=>100101=>011010
[5,1,4,7,3,2,6]=>100110=>011001
[5,1,4,7,3,6,2]=>100101=>011010
[5,1,4,7,6,2,3]=>100110=>011001
[5,1,4,7,6,3,2]=>100111=>011000
[5,1,6,2,3,4,7]=>101000=>010111
[5,1,6,2,3,7,4]=>101001=>010110
[5,1,6,2,4,3,7]=>101010=>010101
[5,1,6,2,4,7,3]=>101001=>010110
[5,1,6,2,7,3,4]=>101010=>010101
[5,1,6,2,7,4,3]=>101011=>010100
[5,1,6,3,2,4,7]=>101100=>010011
[5,1,6,3,2,7,4]=>101101=>010010
[5,1,6,3,4,2,7]=>101010=>010101
[5,1,6,3,4,7,2]=>101001=>010110
[5,1,6,3,7,2,4]=>101010=>010101
[5,1,6,3,7,4,2]=>101011=>010100
[5,1,6,4,2,3,7]=>101100=>010011
[5,1,6,4,2,7,3]=>101101=>010010
[5,1,6,4,3,2,7]=>101110=>010001
[5,1,6,4,3,7,2]=>101101=>010010
[5,1,6,4,7,2,3]=>101010=>010101
[5,1,6,4,7,3,2]=>101011=>010100
[5,1,6,7,2,3,4]=>100100=>011011
[5,1,6,7,2,4,3]=>100101=>011010
[5,1,6,7,3,2,4]=>100110=>011001
[5,1,6,7,3,4,2]=>100101=>011010
[5,1,6,7,4,2,3]=>100110=>011001
[5,1,6,7,4,3,2]=>100111=>011000
[5,1,7,2,3,4,6]=>101000=>010111
[5,1,7,2,3,6,4]=>101001=>010110
[5,1,7,2,4,3,6]=>101010=>010101
[5,1,7,2,4,6,3]=>101001=>010110
[5,1,7,2,6,3,4]=>101010=>010101
[5,1,7,2,6,4,3]=>101011=>010100
[5,1,7,3,2,4,6]=>101100=>010011
[5,1,7,3,2,6,4]=>101101=>010010
[5,1,7,3,4,2,6]=>101010=>010101
[5,1,7,3,4,6,2]=>101001=>010110
[5,1,7,3,6,2,4]=>101010=>010101
[5,1,7,3,6,4,2]=>101011=>010100
[5,1,7,4,2,3,6]=>101100=>010011
[5,1,7,4,2,6,3]=>101101=>010010
[5,1,7,4,3,2,6]=>101110=>010001
[5,1,7,4,3,6,2]=>101101=>010010
[5,1,7,4,6,2,3]=>101010=>010101
[5,1,7,4,6,3,2]=>101011=>010100
[5,1,7,6,2,3,4]=>101100=>010011
[5,1,7,6,2,4,3]=>101101=>010010
[5,1,7,6,3,2,4]=>101110=>010001
[5,1,7,6,3,4,2]=>101101=>010010
[5,1,7,6,4,2,3]=>101110=>010001
[5,1,7,6,4,3,2]=>101111=>010000
[5,2,1,3,4,6,7]=>110000=>001111
[5,2,1,3,4,7,6]=>110001=>001110
[5,2,1,3,6,4,7]=>110010=>001101
[5,2,1,3,6,7,4]=>110001=>001110
[5,2,1,3,7,4,6]=>110010=>001101
[5,2,1,3,7,6,4]=>110011=>001100
[5,2,1,4,3,6,7]=>110100=>001011
[5,2,1,4,3,7,6]=>110101=>001010
[5,2,1,4,6,3,7]=>110010=>001101
[5,2,1,4,6,7,3]=>110001=>001110
[5,2,1,4,7,3,6]=>110010=>001101
[5,2,1,4,7,6,3]=>110011=>001100
[5,2,1,6,3,4,7]=>110100=>001011
[5,2,1,6,3,7,4]=>110101=>001010
[5,2,1,6,4,3,7]=>110110=>001001
[5,2,1,6,4,7,3]=>110101=>001010
[5,2,1,6,7,3,4]=>110010=>001101
[5,2,1,6,7,4,3]=>110011=>001100
[5,2,1,7,3,4,6]=>110100=>001011
[5,2,1,7,3,6,4]=>110101=>001010
[5,2,1,7,4,3,6]=>110110=>001001
[5,2,1,7,4,6,3]=>110101=>001010
[5,2,1,7,6,3,4]=>110110=>001001
[5,2,1,7,6,4,3]=>110111=>001000
[5,2,3,1,4,6,7]=>101000=>010111
[5,2,3,1,4,7,6]=>101001=>010110
[5,2,3,1,6,4,7]=>101010=>010101
[5,2,3,1,6,7,4]=>101001=>010110
[5,2,3,1,7,4,6]=>101010=>010101
[5,2,3,1,7,6,4]=>101011=>010100
[5,2,3,4,1,6,7]=>100100=>011011
[5,2,3,4,1,7,6]=>100101=>011010
[5,2,3,4,6,1,7]=>100010=>011101
[5,2,3,4,6,7,1]=>100001=>011110
[5,2,3,4,7,1,6]=>100010=>011101
[5,2,3,4,7,6,1]=>100011=>011100
[5,2,3,6,1,4,7]=>100100=>011011
[5,2,3,6,1,7,4]=>100101=>011010
[5,2,3,6,4,1,7]=>100110=>011001
[5,2,3,6,4,7,1]=>100101=>011010
[5,2,3,6,7,1,4]=>100010=>011101
[5,2,3,6,7,4,1]=>100011=>011100
[5,2,3,7,1,4,6]=>100100=>011011
[5,2,3,7,1,6,4]=>100101=>011010
[5,2,3,7,4,1,6]=>100110=>011001
[5,2,3,7,4,6,1]=>100101=>011010
[5,2,3,7,6,1,4]=>100110=>011001
[5,2,3,7,6,4,1]=>100111=>011000
[5,2,4,1,3,6,7]=>101000=>010111
[5,2,4,1,3,7,6]=>101001=>010110
[5,2,4,1,6,3,7]=>101010=>010101
[5,2,4,1,6,7,3]=>101001=>010110
[5,2,4,1,7,3,6]=>101010=>010101
[5,2,4,1,7,6,3]=>101011=>010100
[5,2,4,3,1,6,7]=>101100=>010011
[5,2,4,3,1,7,6]=>101101=>010010
[5,2,4,3,6,1,7]=>101010=>010101
[5,2,4,3,6,7,1]=>101001=>010110
[5,2,4,3,7,1,6]=>101010=>010101
[5,2,4,3,7,6,1]=>101011=>010100
[5,2,4,6,1,3,7]=>100100=>011011
[5,2,4,6,1,7,3]=>100101=>011010
[5,2,4,6,3,1,7]=>100110=>011001
[5,2,4,6,3,7,1]=>100101=>011010
[5,2,4,6,7,1,3]=>100010=>011101
[5,2,4,6,7,3,1]=>100011=>011100
[5,2,4,7,1,3,6]=>100100=>011011
[5,2,4,7,1,6,3]=>100101=>011010
[5,2,4,7,3,1,6]=>100110=>011001
[5,2,4,7,3,6,1]=>100101=>011010
[5,2,4,7,6,1,3]=>100110=>011001
[5,2,4,7,6,3,1]=>100111=>011000
[5,2,6,1,3,4,7]=>101000=>010111
[5,2,6,1,3,7,4]=>101001=>010110
[5,2,6,1,4,3,7]=>101010=>010101
[5,2,6,1,4,7,3]=>101001=>010110
[5,2,6,1,7,3,4]=>101010=>010101
[5,2,6,1,7,4,3]=>101011=>010100
[5,2,6,3,1,4,7]=>101100=>010011
[5,2,6,3,1,7,4]=>101101=>010010
[5,2,6,3,4,1,7]=>101010=>010101
[5,2,6,3,4,7,1]=>101001=>010110
[5,2,6,3,7,1,4]=>101010=>010101
[5,2,6,3,7,4,1]=>101011=>010100
[5,2,6,4,1,3,7]=>101100=>010011
[5,2,6,4,1,7,3]=>101101=>010010
[5,2,6,4,3,1,7]=>101110=>010001
[5,2,6,4,3,7,1]=>101101=>010010
[5,2,6,4,7,1,3]=>101010=>010101
[5,2,6,4,7,3,1]=>101011=>010100
[5,2,6,7,1,3,4]=>100100=>011011
[5,2,6,7,1,4,3]=>100101=>011010
[5,2,6,7,3,1,4]=>100110=>011001
[5,2,6,7,3,4,1]=>100101=>011010
[5,2,6,7,4,1,3]=>100110=>011001
[5,2,6,7,4,3,1]=>100111=>011000
[5,2,7,1,3,4,6]=>101000=>010111
[5,2,7,1,3,6,4]=>101001=>010110
[5,2,7,1,4,3,6]=>101010=>010101
[5,2,7,1,4,6,3]=>101001=>010110
[5,2,7,1,6,3,4]=>101010=>010101
[5,2,7,1,6,4,3]=>101011=>010100
[5,2,7,3,1,4,6]=>101100=>010011
[5,2,7,3,1,6,4]=>101101=>010010
[5,2,7,3,4,1,6]=>101010=>010101
[5,2,7,3,4,6,1]=>101001=>010110
[5,2,7,3,6,1,4]=>101010=>010101
[5,2,7,3,6,4,1]=>101011=>010100
[5,2,7,4,1,3,6]=>101100=>010011
[5,2,7,4,1,6,3]=>101101=>010010
[5,2,7,4,3,1,6]=>101110=>010001
[5,2,7,4,3,6,1]=>101101=>010010
[5,2,7,4,6,1,3]=>101010=>010101
[5,2,7,4,6,3,1]=>101011=>010100
[5,2,7,6,1,3,4]=>101100=>010011
[5,2,7,6,1,4,3]=>101101=>010010
[5,2,7,6,3,1,4]=>101110=>010001
[5,2,7,6,3,4,1]=>101101=>010010
[5,2,7,6,4,1,3]=>101110=>010001
[5,2,7,6,4,3,1]=>101111=>010000
[5,3,1,2,4,6,7]=>110000=>001111
[5,3,1,2,4,7,6]=>110001=>001110
[5,3,1,2,6,4,7]=>110010=>001101
[5,3,1,2,6,7,4]=>110001=>001110
[5,3,1,2,7,4,6]=>110010=>001101
[5,3,1,2,7,6,4]=>110011=>001100
[5,3,1,4,2,6,7]=>110100=>001011
[5,3,1,4,2,7,6]=>110101=>001010
[5,3,1,4,6,2,7]=>110010=>001101
[5,3,1,4,6,7,2]=>110001=>001110
[5,3,1,4,7,2,6]=>110010=>001101
[5,3,1,4,7,6,2]=>110011=>001100
[5,3,1,6,2,4,7]=>110100=>001011
[5,3,1,6,2,7,4]=>110101=>001010
[5,3,1,6,4,2,7]=>110110=>001001
[5,3,1,6,4,7,2]=>110101=>001010
[5,3,1,6,7,2,4]=>110010=>001101
[5,3,1,6,7,4,2]=>110011=>001100
[5,3,1,7,2,4,6]=>110100=>001011
[5,3,1,7,2,6,4]=>110101=>001010
[5,3,1,7,4,2,6]=>110110=>001001
[5,3,1,7,4,6,2]=>110101=>001010
[5,3,1,7,6,2,4]=>110110=>001001
[5,3,1,7,6,4,2]=>110111=>001000
[5,3,2,1,4,6,7]=>111000=>000111
[5,3,2,1,4,7,6]=>111001=>000110
[5,3,2,1,6,4,7]=>111010=>000101
[5,3,2,1,6,7,4]=>111001=>000110
[5,3,2,1,7,4,6]=>111010=>000101
[5,3,2,1,7,6,4]=>111011=>000100
[5,3,2,4,1,6,7]=>110100=>001011
[5,3,2,4,1,7,6]=>110101=>001010
[5,3,2,4,6,1,7]=>110010=>001101
[5,3,2,4,6,7,1]=>110001=>001110
[5,3,2,4,7,1,6]=>110010=>001101
[5,3,2,4,7,6,1]=>110011=>001100
[5,3,2,6,1,4,7]=>110100=>001011
[5,3,2,6,1,7,4]=>110101=>001010
[5,3,2,6,4,1,7]=>110110=>001001
[5,3,2,6,4,7,1]=>110101=>001010
[5,3,2,6,7,1,4]=>110010=>001101
[5,3,2,6,7,4,1]=>110011=>001100
[5,3,2,7,1,4,6]=>110100=>001011
[5,3,2,7,1,6,4]=>110101=>001010
[5,3,2,7,4,1,6]=>110110=>001001
[5,3,2,7,4,6,1]=>110101=>001010
[5,3,2,7,6,1,4]=>110110=>001001
[5,3,2,7,6,4,1]=>110111=>001000
[5,3,4,1,2,6,7]=>101000=>010111
[5,3,4,1,2,7,6]=>101001=>010110
[5,3,4,1,6,2,7]=>101010=>010101
[5,3,4,1,6,7,2]=>101001=>010110
[5,3,4,1,7,2,6]=>101010=>010101
[5,3,4,1,7,6,2]=>101011=>010100
[5,3,4,2,1,6,7]=>101100=>010011
[5,3,4,2,1,7,6]=>101101=>010010
[5,3,4,2,6,1,7]=>101010=>010101
[5,3,4,2,6,7,1]=>101001=>010110
[5,3,4,2,7,1,6]=>101010=>010101
[5,3,4,2,7,6,1]=>101011=>010100
[5,3,4,6,1,2,7]=>100100=>011011
[5,3,4,6,1,7,2]=>100101=>011010
[5,3,4,6,2,1,7]=>100110=>011001
[5,3,4,6,2,7,1]=>100101=>011010
[5,3,4,6,7,1,2]=>100010=>011101
[5,3,4,6,7,2,1]=>100011=>011100
[5,3,4,7,1,2,6]=>100100=>011011
[5,3,4,7,1,6,2]=>100101=>011010
[5,3,4,7,2,1,6]=>100110=>011001
[5,3,4,7,2,6,1]=>100101=>011010
[5,3,4,7,6,1,2]=>100110=>011001
[5,3,4,7,6,2,1]=>100111=>011000
[5,3,6,1,2,4,7]=>101000=>010111
[5,3,6,1,2,7,4]=>101001=>010110
[5,3,6,1,4,2,7]=>101010=>010101
[5,3,6,1,4,7,2]=>101001=>010110
[5,3,6,1,7,2,4]=>101010=>010101
[5,3,6,1,7,4,2]=>101011=>010100
[5,3,6,2,1,4,7]=>101100=>010011
[5,3,6,2,1,7,4]=>101101=>010010
[5,3,6,2,4,1,7]=>101010=>010101
[5,3,6,2,4,7,1]=>101001=>010110
[5,3,6,2,7,1,4]=>101010=>010101
[5,3,6,2,7,4,1]=>101011=>010100
[5,3,6,4,1,2,7]=>101100=>010011
[5,3,6,4,1,7,2]=>101101=>010010
[5,3,6,4,2,1,7]=>101110=>010001
[5,3,6,4,2,7,1]=>101101=>010010
[5,3,6,4,7,1,2]=>101010=>010101
[5,3,6,4,7,2,1]=>101011=>010100
[5,3,6,7,1,2,4]=>100100=>011011
[5,3,6,7,1,4,2]=>100101=>011010
[5,3,6,7,2,1,4]=>100110=>011001
[5,3,6,7,2,4,1]=>100101=>011010
[5,3,6,7,4,1,2]=>100110=>011001
[5,3,6,7,4,2,1]=>100111=>011000
[5,3,7,1,2,4,6]=>101000=>010111
[5,3,7,1,2,6,4]=>101001=>010110
[5,3,7,1,4,2,6]=>101010=>010101
[5,3,7,1,4,6,2]=>101001=>010110
[5,3,7,1,6,2,4]=>101010=>010101
[5,3,7,1,6,4,2]=>101011=>010100
[5,3,7,2,1,4,6]=>101100=>010011
[5,3,7,2,1,6,4]=>101101=>010010
[5,3,7,2,4,1,6]=>101010=>010101
[5,3,7,2,4,6,1]=>101001=>010110
[5,3,7,2,6,1,4]=>101010=>010101
[5,3,7,2,6,4,1]=>101011=>010100
[5,3,7,4,1,2,6]=>101100=>010011
[5,3,7,4,1,6,2]=>101101=>010010
[5,3,7,4,2,1,6]=>101110=>010001
[5,3,7,4,2,6,1]=>101101=>010010
[5,3,7,4,6,1,2]=>101010=>010101
[5,3,7,4,6,2,1]=>101011=>010100
[5,3,7,6,1,2,4]=>101100=>010011
[5,3,7,6,1,4,2]=>101101=>010010
[5,3,7,6,2,1,4]=>101110=>010001
[5,3,7,6,2,4,1]=>101101=>010010
[5,3,7,6,4,1,2]=>101110=>010001
[5,3,7,6,4,2,1]=>101111=>010000
[5,4,1,2,3,6,7]=>110000=>001111
[5,4,1,2,3,7,6]=>110001=>001110
[5,4,1,2,6,3,7]=>110010=>001101
[5,4,1,2,6,7,3]=>110001=>001110
[5,4,1,2,7,3,6]=>110010=>001101
[5,4,1,2,7,6,3]=>110011=>001100
[5,4,1,3,2,6,7]=>110100=>001011
[5,4,1,3,2,7,6]=>110101=>001010
[5,4,1,3,6,2,7]=>110010=>001101
[5,4,1,3,6,7,2]=>110001=>001110
[5,4,1,3,7,2,6]=>110010=>001101
[5,4,1,3,7,6,2]=>110011=>001100
[5,4,1,6,2,3,7]=>110100=>001011
[5,4,1,6,2,7,3]=>110101=>001010
[5,4,1,6,3,2,7]=>110110=>001001
[5,4,1,6,3,7,2]=>110101=>001010
[5,4,1,6,7,2,3]=>110010=>001101
[5,4,1,6,7,3,2]=>110011=>001100
[5,4,1,7,2,3,6]=>110100=>001011
[5,4,1,7,2,6,3]=>110101=>001010
[5,4,1,7,3,2,6]=>110110=>001001
[5,4,1,7,3,6,2]=>110101=>001010
[5,4,1,7,6,2,3]=>110110=>001001
[5,4,1,7,6,3,2]=>110111=>001000
[5,4,2,1,3,6,7]=>111000=>000111
[5,4,2,1,3,7,6]=>111001=>000110
[5,4,2,1,6,3,7]=>111010=>000101
[5,4,2,1,6,7,3]=>111001=>000110
[5,4,2,1,7,3,6]=>111010=>000101
[5,4,2,1,7,6,3]=>111011=>000100
[5,4,2,3,1,6,7]=>110100=>001011
[5,4,2,3,1,7,6]=>110101=>001010
[5,4,2,3,6,1,7]=>110010=>001101
[5,4,2,3,6,7,1]=>110001=>001110
[5,4,2,3,7,1,6]=>110010=>001101
[5,4,2,3,7,6,1]=>110011=>001100
[5,4,2,6,1,3,7]=>110100=>001011
[5,4,2,6,1,7,3]=>110101=>001010
[5,4,2,6,3,1,7]=>110110=>001001
[5,4,2,6,3,7,1]=>110101=>001010
[5,4,2,6,7,1,3]=>110010=>001101
[5,4,2,6,7,3,1]=>110011=>001100
[5,4,2,7,1,3,6]=>110100=>001011
[5,4,2,7,1,6,3]=>110101=>001010
[5,4,2,7,3,1,6]=>110110=>001001
[5,4,2,7,3,6,1]=>110101=>001010
[5,4,2,7,6,1,3]=>110110=>001001
[5,4,2,7,6,3,1]=>110111=>001000
[5,4,3,1,2,6,7]=>111000=>000111
[5,4,3,1,2,7,6]=>111001=>000110
[5,4,3,1,6,2,7]=>111010=>000101
[5,4,3,1,6,7,2]=>111001=>000110
[5,4,3,1,7,2,6]=>111010=>000101
[5,4,3,1,7,6,2]=>111011=>000100
[5,4,3,2,1,6,7]=>111100=>000011
[5,4,3,2,1,7,6]=>111101=>000010
[5,4,3,2,6,1,7]=>111010=>000101
[5,4,3,2,6,7,1]=>111001=>000110
[5,4,3,2,7,1,6]=>111010=>000101
[5,4,3,2,7,6,1]=>111011=>000100
[5,4,3,6,1,2,7]=>110100=>001011
[5,4,3,6,1,7,2]=>110101=>001010
[5,4,3,6,2,1,7]=>110110=>001001
[5,4,3,6,2,7,1]=>110101=>001010
[5,4,3,6,7,1,2]=>110010=>001101
[5,4,3,6,7,2,1]=>110011=>001100
[5,4,3,7,1,2,6]=>110100=>001011
[5,4,3,7,1,6,2]=>110101=>001010
[5,4,3,7,2,1,6]=>110110=>001001
[5,4,3,7,2,6,1]=>110101=>001010
[5,4,3,7,6,1,2]=>110110=>001001
[5,4,3,7,6,2,1]=>110111=>001000
[5,4,6,1,2,3,7]=>101000=>010111
[5,4,6,1,2,7,3]=>101001=>010110
[5,4,6,1,3,2,7]=>101010=>010101
[5,4,6,1,3,7,2]=>101001=>010110
[5,4,6,1,7,2,3]=>101010=>010101
[5,4,6,1,7,3,2]=>101011=>010100
[5,4,6,2,1,3,7]=>101100=>010011
[5,4,6,2,1,7,3]=>101101=>010010
[5,4,6,2,3,1,7]=>101010=>010101
[5,4,6,2,3,7,1]=>101001=>010110
[5,4,6,2,7,1,3]=>101010=>010101
[5,4,6,2,7,3,1]=>101011=>010100
[5,4,6,3,1,2,7]=>101100=>010011
[5,4,6,3,1,7,2]=>101101=>010010
[5,4,6,3,2,1,7]=>101110=>010001
[5,4,6,3,2,7,1]=>101101=>010010
[5,4,6,3,7,1,2]=>101010=>010101
[5,4,6,3,7,2,1]=>101011=>010100
[5,4,6,7,1,2,3]=>100100=>011011
[5,4,6,7,1,3,2]=>100101=>011010
[5,4,6,7,2,1,3]=>100110=>011001
[5,4,6,7,2,3,1]=>100101=>011010
[5,4,6,7,3,1,2]=>100110=>011001
[5,4,6,7,3,2,1]=>100111=>011000
[5,4,7,1,2,3,6]=>101000=>010111
[5,4,7,1,2,6,3]=>101001=>010110
[5,4,7,1,3,2,6]=>101010=>010101
[5,4,7,1,3,6,2]=>101001=>010110
[5,4,7,1,6,2,3]=>101010=>010101
[5,4,7,1,6,3,2]=>101011=>010100
[5,4,7,2,1,3,6]=>101100=>010011
[5,4,7,2,1,6,3]=>101101=>010010
[5,4,7,2,3,1,6]=>101010=>010101
[5,4,7,2,3,6,1]=>101001=>010110
[5,4,7,2,6,1,3]=>101010=>010101
[5,4,7,2,6,3,1]=>101011=>010100
[5,4,7,3,1,2,6]=>101100=>010011
[5,4,7,3,1,6,2]=>101101=>010010
[5,4,7,3,2,1,6]=>101110=>010001
[5,4,7,3,2,6,1]=>101101=>010010
[5,4,7,3,6,1,2]=>101010=>010101
[5,4,7,3,6,2,1]=>101011=>010100
[5,4,7,6,1,2,3]=>101100=>010011
[5,4,7,6,1,3,2]=>101101=>010010
[5,4,7,6,2,1,3]=>101110=>010001
[5,4,7,6,2,3,1]=>101101=>010010
[5,4,7,6,3,1,2]=>101110=>010001
[5,4,7,6,3,2,1]=>101111=>010000
[5,6,1,2,3,4,7]=>010000=>101111
[5,6,1,2,3,7,4]=>010001=>101110
[5,6,1,2,4,3,7]=>010010=>101101
[5,6,1,2,4,7,3]=>010001=>101110
[5,6,1,2,7,3,4]=>010010=>101101
[5,6,1,2,7,4,3]=>010011=>101100
[5,6,1,3,2,4,7]=>010100=>101011
[5,6,1,3,2,7,4]=>010101=>101010
[5,6,1,3,4,2,7]=>010010=>101101
[5,6,1,3,4,7,2]=>010001=>101110
[5,6,1,3,7,2,4]=>010010=>101101
[5,6,1,3,7,4,2]=>010011=>101100
[5,6,1,4,2,3,7]=>010100=>101011
[5,6,1,4,2,7,3]=>010101=>101010
[5,6,1,4,3,2,7]=>010110=>101001
[5,6,1,4,3,7,2]=>010101=>101010
[5,6,1,4,7,2,3]=>010010=>101101
[5,6,1,4,7,3,2]=>010011=>101100
[5,6,1,7,2,3,4]=>010100=>101011
[5,6,1,7,2,4,3]=>010101=>101010
[5,6,1,7,3,2,4]=>010110=>101001
[5,6,1,7,3,4,2]=>010101=>101010
[5,6,1,7,4,2,3]=>010110=>101001
[5,6,1,7,4,3,2]=>010111=>101000
[5,6,2,1,3,4,7]=>011000=>100111
[5,6,2,1,3,7,4]=>011001=>100110
[5,6,2,1,4,3,7]=>011010=>100101
[5,6,2,1,4,7,3]=>011001=>100110
[5,6,2,1,7,3,4]=>011010=>100101
[5,6,2,1,7,4,3]=>011011=>100100
[5,6,2,3,1,4,7]=>010100=>101011
[5,6,2,3,1,7,4]=>010101=>101010
[5,6,2,3,4,1,7]=>010010=>101101
[5,6,2,3,4,7,1]=>010001=>101110
[5,6,2,3,7,1,4]=>010010=>101101
[5,6,2,3,7,4,1]=>010011=>101100
[5,6,2,4,1,3,7]=>010100=>101011
[5,6,2,4,1,7,3]=>010101=>101010
[5,6,2,4,3,1,7]=>010110=>101001
[5,6,2,4,3,7,1]=>010101=>101010
[5,6,2,4,7,1,3]=>010010=>101101
[5,6,2,4,7,3,1]=>010011=>101100
[5,6,2,7,1,3,4]=>010100=>101011
[5,6,2,7,1,4,3]=>010101=>101010
[5,6,2,7,3,1,4]=>010110=>101001
[5,6,2,7,3,4,1]=>010101=>101010
[5,6,2,7,4,1,3]=>010110=>101001
[5,6,2,7,4,3,1]=>010111=>101000
[5,6,3,1,2,4,7]=>011000=>100111
[5,6,3,1,2,7,4]=>011001=>100110
[5,6,3,1,4,2,7]=>011010=>100101
[5,6,3,1,4,7,2]=>011001=>100110
[5,6,3,1,7,2,4]=>011010=>100101
[5,6,3,1,7,4,2]=>011011=>100100
[5,6,3,2,1,4,7]=>011100=>100011
[5,6,3,2,1,7,4]=>011101=>100010
[5,6,3,2,4,1,7]=>011010=>100101
[5,6,3,2,4,7,1]=>011001=>100110
[5,6,3,2,7,1,4]=>011010=>100101
[5,6,3,2,7,4,1]=>011011=>100100
[5,6,3,4,1,2,7]=>010100=>101011
[5,6,3,4,1,7,2]=>010101=>101010
[5,6,3,4,2,1,7]=>010110=>101001
[5,6,3,4,2,7,1]=>010101=>101010
[5,6,3,4,7,1,2]=>010010=>101101
[5,6,3,4,7,2,1]=>010011=>101100
[5,6,3,7,1,2,4]=>010100=>101011
[5,6,3,7,1,4,2]=>010101=>101010
[5,6,3,7,2,1,4]=>010110=>101001
[5,6,3,7,2,4,1]=>010101=>101010
[5,6,3,7,4,1,2]=>010110=>101001
[5,6,3,7,4,2,1]=>010111=>101000
[5,6,4,1,2,3,7]=>011000=>100111
[5,6,4,1,2,7,3]=>011001=>100110
[5,6,4,1,3,2,7]=>011010=>100101
[5,6,4,1,3,7,2]=>011001=>100110
[5,6,4,1,7,2,3]=>011010=>100101
[5,6,4,1,7,3,2]=>011011=>100100
[5,6,4,2,1,3,7]=>011100=>100011
[5,6,4,2,1,7,3]=>011101=>100010
[5,6,4,2,3,1,7]=>011010=>100101
[5,6,4,2,3,7,1]=>011001=>100110
[5,6,4,2,7,1,3]=>011010=>100101
[5,6,4,2,7,3,1]=>011011=>100100
[5,6,4,3,1,2,7]=>011100=>100011
[5,6,4,3,1,7,2]=>011101=>100010
[5,6,4,3,2,1,7]=>011110=>100001
[5,6,4,3,2,7,1]=>011101=>100010
[5,6,4,3,7,1,2]=>011010=>100101
[5,6,4,3,7,2,1]=>011011=>100100
[5,6,4,7,1,2,3]=>010100=>101011
[5,6,4,7,1,3,2]=>010101=>101010
[5,6,4,7,2,1,3]=>010110=>101001
[5,6,4,7,2,3,1]=>010101=>101010
[5,6,4,7,3,1,2]=>010110=>101001
[5,6,4,7,3,2,1]=>010111=>101000
[5,6,7,1,2,3,4]=>001000=>110111
[5,6,7,1,2,4,3]=>001001=>110110
[5,6,7,1,3,2,4]=>001010=>110101
[5,6,7,1,3,4,2]=>001001=>110110
[5,6,7,1,4,2,3]=>001010=>110101
[5,6,7,1,4,3,2]=>001011=>110100
[5,6,7,2,1,3,4]=>001100=>110011
[5,6,7,2,1,4,3]=>001101=>110010
[5,6,7,2,3,1,4]=>001010=>110101
[5,6,7,2,3,4,1]=>001001=>110110
[5,6,7,2,4,1,3]=>001010=>110101
[5,6,7,2,4,3,1]=>001011=>110100
[5,6,7,3,1,2,4]=>001100=>110011
[5,6,7,3,1,4,2]=>001101=>110010
[5,6,7,3,2,1,4]=>001110=>110001
[5,6,7,3,2,4,1]=>001101=>110010
[5,6,7,3,4,1,2]=>001010=>110101
[5,6,7,3,4,2,1]=>001011=>110100
[5,6,7,4,1,2,3]=>001100=>110011
[5,6,7,4,1,3,2]=>001101=>110010
[5,6,7,4,2,1,3]=>001110=>110001
[5,6,7,4,2,3,1]=>001101=>110010
[5,6,7,4,3,1,2]=>001110=>110001
[5,6,7,4,3,2,1]=>001111=>110000
[5,7,1,2,3,4,6]=>010000=>101111
[5,7,1,2,3,6,4]=>010001=>101110
[5,7,1,2,4,3,6]=>010010=>101101
[5,7,1,2,4,6,3]=>010001=>101110
[5,7,1,2,6,3,4]=>010010=>101101
[5,7,1,2,6,4,3]=>010011=>101100
[5,7,1,3,2,4,6]=>010100=>101011
[5,7,1,3,2,6,4]=>010101=>101010
[5,7,1,3,4,2,6]=>010010=>101101
[5,7,1,3,4,6,2]=>010001=>101110
[5,7,1,3,6,2,4]=>010010=>101101
[5,7,1,3,6,4,2]=>010011=>101100
[5,7,1,4,2,3,6]=>010100=>101011
[5,7,1,4,2,6,3]=>010101=>101010
[5,7,1,4,3,2,6]=>010110=>101001
[5,7,1,4,3,6,2]=>010101=>101010
[5,7,1,4,6,2,3]=>010010=>101101
[5,7,1,4,6,3,2]=>010011=>101100
[5,7,1,6,2,3,4]=>010100=>101011
[5,7,1,6,2,4,3]=>010101=>101010
[5,7,1,6,3,2,4]=>010110=>101001
[5,7,1,6,3,4,2]=>010101=>101010
[5,7,1,6,4,2,3]=>010110=>101001
[5,7,1,6,4,3,2]=>010111=>101000
[5,7,2,1,3,4,6]=>011000=>100111
[5,7,2,1,3,6,4]=>011001=>100110
[5,7,2,1,4,3,6]=>011010=>100101
[5,7,2,1,4,6,3]=>011001=>100110
[5,7,2,1,6,3,4]=>011010=>100101
[5,7,2,1,6,4,3]=>011011=>100100
[5,7,2,3,1,4,6]=>010100=>101011
[5,7,2,3,1,6,4]=>010101=>101010
[5,7,2,3,4,1,6]=>010010=>101101
[5,7,2,3,4,6,1]=>010001=>101110
[5,7,2,3,6,1,4]=>010010=>101101
[5,7,2,3,6,4,1]=>010011=>101100
[5,7,2,4,1,3,6]=>010100=>101011
[5,7,2,4,1,6,3]=>010101=>101010
[5,7,2,4,3,1,6]=>010110=>101001
[5,7,2,4,3,6,1]=>010101=>101010
[5,7,2,4,6,1,3]=>010010=>101101
[5,7,2,4,6,3,1]=>010011=>101100
[5,7,2,6,1,3,4]=>010100=>101011
[5,7,2,6,1,4,3]=>010101=>101010
[5,7,2,6,3,1,4]=>010110=>101001
[5,7,2,6,3,4,1]=>010101=>101010
[5,7,2,6,4,1,3]=>010110=>101001
[5,7,2,6,4,3,1]=>010111=>101000
[5,7,3,1,2,4,6]=>011000=>100111
[5,7,3,1,2,6,4]=>011001=>100110
[5,7,3,1,4,2,6]=>011010=>100101
[5,7,3,1,4,6,2]=>011001=>100110
[5,7,3,1,6,2,4]=>011010=>100101
[5,7,3,1,6,4,2]=>011011=>100100
[5,7,3,2,1,4,6]=>011100=>100011
[5,7,3,2,1,6,4]=>011101=>100010
[5,7,3,2,4,1,6]=>011010=>100101
[5,7,3,2,4,6,1]=>011001=>100110
[5,7,3,2,6,1,4]=>011010=>100101
[5,7,3,2,6,4,1]=>011011=>100100
[5,7,3,4,1,2,6]=>010100=>101011
[5,7,3,4,1,6,2]=>010101=>101010
[5,7,3,4,2,1,6]=>010110=>101001
[5,7,3,4,2,6,1]=>010101=>101010
[5,7,3,4,6,1,2]=>010010=>101101
[5,7,3,4,6,2,1]=>010011=>101100
[5,7,3,6,1,2,4]=>010100=>101011
[5,7,3,6,1,4,2]=>010101=>101010
[5,7,3,6,2,1,4]=>010110=>101001
[5,7,3,6,2,4,1]=>010101=>101010
[5,7,3,6,4,1,2]=>010110=>101001
[5,7,3,6,4,2,1]=>010111=>101000
[5,7,4,1,2,3,6]=>011000=>100111
[5,7,4,1,2,6,3]=>011001=>100110
[5,7,4,1,3,2,6]=>011010=>100101
[5,7,4,1,3,6,2]=>011001=>100110
[5,7,4,1,6,2,3]=>011010=>100101
[5,7,4,1,6,3,2]=>011011=>100100
[5,7,4,2,1,3,6]=>011100=>100011
[5,7,4,2,1,6,3]=>011101=>100010
[5,7,4,2,3,1,6]=>011010=>100101
[5,7,4,2,3,6,1]=>011001=>100110
[5,7,4,2,6,1,3]=>011010=>100101
[5,7,4,2,6,3,1]=>011011=>100100
[5,7,4,3,1,2,6]=>011100=>100011
[5,7,4,3,1,6,2]=>011101=>100010
[5,7,4,3,2,1,6]=>011110=>100001
[5,7,4,3,2,6,1]=>011101=>100010
[5,7,4,3,6,1,2]=>011010=>100101
[5,7,4,3,6,2,1]=>011011=>100100
[5,7,4,6,1,2,3]=>010100=>101011
[5,7,4,6,1,3,2]=>010101=>101010
[5,7,4,6,2,1,3]=>010110=>101001
[5,7,4,6,2,3,1]=>010101=>101010
[5,7,4,6,3,1,2]=>010110=>101001
[5,7,4,6,3,2,1]=>010111=>101000
[5,7,6,1,2,3,4]=>011000=>100111
[5,7,6,1,2,4,3]=>011001=>100110
[5,7,6,1,3,2,4]=>011010=>100101
[5,7,6,1,3,4,2]=>011001=>100110
[5,7,6,1,4,2,3]=>011010=>100101
[5,7,6,1,4,3,2]=>011011=>100100
[5,7,6,2,1,3,4]=>011100=>100011
[5,7,6,2,1,4,3]=>011101=>100010
[5,7,6,2,3,1,4]=>011010=>100101
[5,7,6,2,3,4,1]=>011001=>100110
[5,7,6,2,4,1,3]=>011010=>100101
[5,7,6,2,4,3,1]=>011011=>100100
[5,7,6,3,1,2,4]=>011100=>100011
[5,7,6,3,1,4,2]=>011101=>100010
[5,7,6,3,2,1,4]=>011110=>100001
[5,7,6,3,2,4,1]=>011101=>100010
[5,7,6,3,4,1,2]=>011010=>100101
[5,7,6,3,4,2,1]=>011011=>100100
[5,7,6,4,1,2,3]=>011100=>100011
[5,7,6,4,1,3,2]=>011101=>100010
[5,7,6,4,2,1,3]=>011110=>100001
[5,7,6,4,2,3,1]=>011101=>100010
[5,7,6,4,3,1,2]=>011110=>100001
[5,7,6,4,3,2,1]=>011111=>100000
[6,1,2,3,4,5,7]=>100000=>011111
[6,1,2,3,4,7,5]=>100001=>011110
[6,1,2,3,5,4,7]=>100010=>011101
[6,1,2,3,5,7,4]=>100001=>011110
[6,1,2,3,7,4,5]=>100010=>011101
[6,1,2,3,7,5,4]=>100011=>011100
[6,1,2,4,3,5,7]=>100100=>011011
[6,1,2,4,3,7,5]=>100101=>011010
[6,1,2,4,5,3,7]=>100010=>011101
[6,1,2,4,5,7,3]=>100001=>011110
[6,1,2,4,7,3,5]=>100010=>011101
[6,1,2,4,7,5,3]=>100011=>011100
[6,1,2,5,3,4,7]=>100100=>011011
[6,1,2,5,3,7,4]=>100101=>011010
[6,1,2,5,4,3,7]=>100110=>011001
[6,1,2,5,4,7,3]=>100101=>011010
[6,1,2,5,7,3,4]=>100010=>011101
[6,1,2,5,7,4,3]=>100011=>011100
[6,1,2,7,3,4,5]=>100100=>011011
[6,1,2,7,3,5,4]=>100101=>011010
[6,1,2,7,4,3,5]=>100110=>011001
[6,1,2,7,4,5,3]=>100101=>011010
[6,1,2,7,5,3,4]=>100110=>011001
[6,1,2,7,5,4,3]=>100111=>011000
[6,1,3,2,4,5,7]=>101000=>010111
[6,1,3,2,4,7,5]=>101001=>010110
[6,1,3,2,5,4,7]=>101010=>010101
[6,1,3,2,5,7,4]=>101001=>010110
[6,1,3,2,7,4,5]=>101010=>010101
[6,1,3,2,7,5,4]=>101011=>010100
[6,1,3,4,2,5,7]=>100100=>011011
[6,1,3,4,2,7,5]=>100101=>011010
[6,1,3,4,5,2,7]=>100010=>011101
[6,1,3,4,5,7,2]=>100001=>011110
[6,1,3,4,7,2,5]=>100010=>011101
[6,1,3,4,7,5,2]=>100011=>011100
[6,1,3,5,2,4,7]=>100100=>011011
[6,1,3,5,2,7,4]=>100101=>011010
[6,1,3,5,4,2,7]=>100110=>011001
[6,1,3,5,4,7,2]=>100101=>011010
[6,1,3,5,7,2,4]=>100010=>011101
[6,1,3,5,7,4,2]=>100011=>011100
[6,1,3,7,2,4,5]=>100100=>011011
[6,1,3,7,2,5,4]=>100101=>011010
[6,1,3,7,4,2,5]=>100110=>011001
[6,1,3,7,4,5,2]=>100101=>011010
[6,1,3,7,5,2,4]=>100110=>011001
[6,1,3,7,5,4,2]=>100111=>011000
[6,1,4,2,3,5,7]=>101000=>010111
[6,1,4,2,3,7,5]=>101001=>010110
[6,1,4,2,5,3,7]=>101010=>010101
[6,1,4,2,5,7,3]=>101001=>010110
[6,1,4,2,7,3,5]=>101010=>010101
[6,1,4,2,7,5,3]=>101011=>010100
[6,1,4,3,2,5,7]=>101100=>010011
[6,1,4,3,2,7,5]=>101101=>010010
[6,1,4,3,5,2,7]=>101010=>010101
[6,1,4,3,5,7,2]=>101001=>010110
[6,1,4,3,7,2,5]=>101010=>010101
[6,1,4,3,7,5,2]=>101011=>010100
[6,1,4,5,2,3,7]=>100100=>011011
[6,1,4,5,2,7,3]=>100101=>011010
[6,1,4,5,3,2,7]=>100110=>011001
[6,1,4,5,3,7,2]=>100101=>011010
[6,1,4,5,7,2,3]=>100010=>011101
[6,1,4,5,7,3,2]=>100011=>011100
[6,1,4,7,2,3,5]=>100100=>011011
[6,1,4,7,2,5,3]=>100101=>011010
[6,1,4,7,3,2,5]=>100110=>011001
[6,1,4,7,3,5,2]=>100101=>011010
[6,1,4,7,5,2,3]=>100110=>011001
[6,1,4,7,5,3,2]=>100111=>011000
[6,1,5,2,3,4,7]=>101000=>010111
[6,1,5,2,3,7,4]=>101001=>010110
[6,1,5,2,4,3,7]=>101010=>010101
[6,1,5,2,4,7,3]=>101001=>010110
[6,1,5,2,7,3,4]=>101010=>010101
[6,1,5,2,7,4,3]=>101011=>010100
[6,1,5,3,2,4,7]=>101100=>010011
[6,1,5,3,2,7,4]=>101101=>010010
[6,1,5,3,4,2,7]=>101010=>010101
[6,1,5,3,4,7,2]=>101001=>010110
[6,1,5,3,7,2,4]=>101010=>010101
[6,1,5,3,7,4,2]=>101011=>010100
[6,1,5,4,2,3,7]=>101100=>010011
[6,1,5,4,2,7,3]=>101101=>010010
[6,1,5,4,3,2,7]=>101110=>010001
[6,1,5,4,3,7,2]=>101101=>010010
[6,1,5,4,7,2,3]=>101010=>010101
[6,1,5,4,7,3,2]=>101011=>010100
[6,1,5,7,2,3,4]=>100100=>011011
[6,1,5,7,2,4,3]=>100101=>011010
[6,1,5,7,3,2,4]=>100110=>011001
[6,1,5,7,3,4,2]=>100101=>011010
[6,1,5,7,4,2,3]=>100110=>011001
[6,1,5,7,4,3,2]=>100111=>011000
[6,1,7,2,3,4,5]=>101000=>010111
[6,1,7,2,3,5,4]=>101001=>010110
[6,1,7,2,4,3,5]=>101010=>010101
[6,1,7,2,4,5,3]=>101001=>010110
[6,1,7,2,5,3,4]=>101010=>010101
[6,1,7,2,5,4,3]=>101011=>010100
[6,1,7,3,2,4,5]=>101100=>010011
[6,1,7,3,2,5,4]=>101101=>010010
[6,1,7,3,4,2,5]=>101010=>010101
[6,1,7,3,4,5,2]=>101001=>010110
[6,1,7,3,5,2,4]=>101010=>010101
[6,1,7,3,5,4,2]=>101011=>010100
[6,1,7,4,2,3,5]=>101100=>010011
[6,1,7,4,2,5,3]=>101101=>010010
[6,1,7,4,3,2,5]=>101110=>010001
[6,1,7,4,3,5,2]=>101101=>010010
[6,1,7,4,5,2,3]=>101010=>010101
[6,1,7,4,5,3,2]=>101011=>010100
[6,1,7,5,2,3,4]=>101100=>010011
[6,1,7,5,2,4,3]=>101101=>010010
[6,1,7,5,3,2,4]=>101110=>010001
[6,1,7,5,3,4,2]=>101101=>010010
[6,1,7,5,4,2,3]=>101110=>010001
[6,1,7,5,4,3,2]=>101111=>010000
[6,2,1,3,4,5,7]=>110000=>001111
[6,2,1,3,4,7,5]=>110001=>001110
[6,2,1,3,5,4,7]=>110010=>001101
[6,2,1,3,5,7,4]=>110001=>001110
[6,2,1,3,7,4,5]=>110010=>001101
[6,2,1,3,7,5,4]=>110011=>001100
[6,2,1,4,3,5,7]=>110100=>001011
[6,2,1,4,3,7,5]=>110101=>001010
[6,2,1,4,5,3,7]=>110010=>001101
[6,2,1,4,5,7,3]=>110001=>001110
[6,2,1,4,7,3,5]=>110010=>001101
[6,2,1,4,7,5,3]=>110011=>001100
[6,2,1,5,3,4,7]=>110100=>001011
[6,2,1,5,3,7,4]=>110101=>001010
[6,2,1,5,4,3,7]=>110110=>001001
[6,2,1,5,4,7,3]=>110101=>001010
[6,2,1,5,7,3,4]=>110010=>001101
[6,2,1,5,7,4,3]=>110011=>001100
[6,2,1,7,3,4,5]=>110100=>001011
[6,2,1,7,3,5,4]=>110101=>001010
[6,2,1,7,4,3,5]=>110110=>001001
[6,2,1,7,4,5,3]=>110101=>001010
[6,2,1,7,5,3,4]=>110110=>001001
[6,2,1,7,5,4,3]=>110111=>001000
[6,2,3,1,4,5,7]=>101000=>010111
[6,2,3,1,4,7,5]=>101001=>010110
[6,2,3,1,5,4,7]=>101010=>010101
[6,2,3,1,5,7,4]=>101001=>010110
[6,2,3,1,7,4,5]=>101010=>010101
[6,2,3,1,7,5,4]=>101011=>010100
[6,2,3,4,1,5,7]=>100100=>011011
[6,2,3,4,1,7,5]=>100101=>011010
[6,2,3,4,5,1,7]=>100010=>011101
[6,2,3,4,5,7,1]=>100001=>011110
[6,2,3,4,7,1,5]=>100010=>011101
[6,2,3,4,7,5,1]=>100011=>011100
[6,2,3,5,1,4,7]=>100100=>011011
[6,2,3,5,1,7,4]=>100101=>011010
[6,2,3,5,4,1,7]=>100110=>011001
[6,2,3,5,4,7,1]=>100101=>011010
[6,2,3,5,7,1,4]=>100010=>011101
[6,2,3,5,7,4,1]=>100011=>011100
[6,2,3,7,1,4,5]=>100100=>011011
[6,2,3,7,1,5,4]=>100101=>011010
[6,2,3,7,4,1,5]=>100110=>011001
[6,2,3,7,4,5,1]=>100101=>011010
[6,2,3,7,5,1,4]=>100110=>011001
[6,2,3,7,5,4,1]=>100111=>011000
[6,2,4,1,3,5,7]=>101000=>010111
[6,2,4,1,3,7,5]=>101001=>010110
[6,2,4,1,5,3,7]=>101010=>010101
[6,2,4,1,5,7,3]=>101001=>010110
[6,2,4,1,7,3,5]=>101010=>010101
[6,2,4,1,7,5,3]=>101011=>010100
[6,2,4,3,1,5,7]=>101100=>010011
[6,2,4,3,1,7,5]=>101101=>010010
[6,2,4,3,5,1,7]=>101010=>010101
[6,2,4,3,5,7,1]=>101001=>010110
[6,2,4,3,7,1,5]=>101010=>010101
[6,2,4,3,7,5,1]=>101011=>010100
[6,2,4,5,1,3,7]=>100100=>011011
[6,2,4,5,1,7,3]=>100101=>011010
[6,2,4,5,3,1,7]=>100110=>011001
[6,2,4,5,3,7,1]=>100101=>011010
[6,2,4,5,7,1,3]=>100010=>011101
[6,2,4,5,7,3,1]=>100011=>011100
[6,2,4,7,1,3,5]=>100100=>011011
[6,2,4,7,1,5,3]=>100101=>011010
[6,2,4,7,3,1,5]=>100110=>011001
[6,2,4,7,3,5,1]=>100101=>011010
[6,2,4,7,5,1,3]=>100110=>011001
[6,2,4,7,5,3,1]=>100111=>011000
[6,2,5,1,3,4,7]=>101000=>010111
[6,2,5,1,3,7,4]=>101001=>010110
[6,2,5,1,4,3,7]=>101010=>010101
[6,2,5,1,4,7,3]=>101001=>010110
[6,2,5,1,7,3,4]=>101010=>010101
[6,2,5,1,7,4,3]=>101011=>010100
[6,2,5,3,1,4,7]=>101100=>010011
[6,2,5,3,1,7,4]=>101101=>010010
[6,2,5,3,4,1,7]=>101010=>010101
[6,2,5,3,4,7,1]=>101001=>010110
[6,2,5,3,7,1,4]=>101010=>010101
[6,2,5,3,7,4,1]=>101011=>010100
[6,2,5,4,1,3,7]=>101100=>010011
[6,2,5,4,1,7,3]=>101101=>010010
[6,2,5,4,3,1,7]=>101110=>010001
[6,2,5,4,3,7,1]=>101101=>010010
[6,2,5,4,7,1,3]=>101010=>010101
[6,2,5,4,7,3,1]=>101011=>010100
[6,2,5,7,1,3,4]=>100100=>011011
[6,2,5,7,1,4,3]=>100101=>011010
[6,2,5,7,3,1,4]=>100110=>011001
[6,2,5,7,3,4,1]=>100101=>011010
[6,2,5,7,4,1,3]=>100110=>011001
[6,2,5,7,4,3,1]=>100111=>011000
[6,2,7,1,3,4,5]=>101000=>010111
[6,2,7,1,3,5,4]=>101001=>010110
[6,2,7,1,4,3,5]=>101010=>010101
[6,2,7,1,4,5,3]=>101001=>010110
[6,2,7,1,5,3,4]=>101010=>010101
[6,2,7,1,5,4,3]=>101011=>010100
[6,2,7,3,1,4,5]=>101100=>010011
[6,2,7,3,1,5,4]=>101101=>010010
[6,2,7,3,4,1,5]=>101010=>010101
[6,2,7,3,4,5,1]=>101001=>010110
[6,2,7,3,5,1,4]=>101010=>010101
[6,2,7,3,5,4,1]=>101011=>010100
[6,2,7,4,1,3,5]=>101100=>010011
[6,2,7,4,1,5,3]=>101101=>010010
[6,2,7,4,3,1,5]=>101110=>010001
[6,2,7,4,3,5,1]=>101101=>010010
[6,2,7,4,5,1,3]=>101010=>010101
[6,2,7,4,5,3,1]=>101011=>010100
[6,2,7,5,1,3,4]=>101100=>010011
[6,2,7,5,1,4,3]=>101101=>010010
[6,2,7,5,3,1,4]=>101110=>010001
[6,2,7,5,3,4,1]=>101101=>010010
[6,2,7,5,4,1,3]=>101110=>010001
[6,2,7,5,4,3,1]=>101111=>010000
[6,3,1,2,4,5,7]=>110000=>001111
[6,3,1,2,4,7,5]=>110001=>001110
[6,3,1,2,5,4,7]=>110010=>001101
[6,3,1,2,5,7,4]=>110001=>001110
[6,3,1,2,7,4,5]=>110010=>001101
[6,3,1,2,7,5,4]=>110011=>001100
[6,3,1,4,2,5,7]=>110100=>001011
[6,3,1,4,2,7,5]=>110101=>001010
[6,3,1,4,5,2,7]=>110010=>001101
[6,3,1,4,5,7,2]=>110001=>001110
[6,3,1,4,7,2,5]=>110010=>001101
[6,3,1,4,7,5,2]=>110011=>001100
[6,3,1,5,2,4,7]=>110100=>001011
[6,3,1,5,2,7,4]=>110101=>001010
[6,3,1,5,4,2,7]=>110110=>001001
[6,3,1,5,4,7,2]=>110101=>001010
[6,3,1,5,7,2,4]=>110010=>001101
[6,3,1,5,7,4,2]=>110011=>001100
[6,3,1,7,2,4,5]=>110100=>001011
[6,3,1,7,2,5,4]=>110101=>001010
[6,3,1,7,4,2,5]=>110110=>001001
[6,3,1,7,4,5,2]=>110101=>001010
[6,3,1,7,5,2,4]=>110110=>001001
[6,3,1,7,5,4,2]=>110111=>001000
[6,3,2,1,4,5,7]=>111000=>000111
[6,3,2,1,4,7,5]=>111001=>000110
[6,3,2,1,5,4,7]=>111010=>000101
[6,3,2,1,5,7,4]=>111001=>000110
[6,3,2,1,7,4,5]=>111010=>000101
[6,3,2,1,7,5,4]=>111011=>000100
[6,3,2,4,1,5,7]=>110100=>001011
[6,3,2,4,1,7,5]=>110101=>001010
[6,3,2,4,5,1,7]=>110010=>001101
[6,3,2,4,5,7,1]=>110001=>001110
[6,3,2,4,7,1,5]=>110010=>001101
[6,3,2,4,7,5,1]=>110011=>001100
[6,3,2,5,1,4,7]=>110100=>001011
[6,3,2,5,1,7,4]=>110101=>001010
[6,3,2,5,4,1,7]=>110110=>001001
[6,3,2,5,4,7,1]=>110101=>001010
[6,3,2,5,7,1,4]=>110010=>001101
[6,3,2,5,7,4,1]=>110011=>001100
[6,3,2,7,1,4,5]=>110100=>001011
[6,3,2,7,1,5,4]=>110101=>001010
[6,3,2,7,4,1,5]=>110110=>001001
[6,3,2,7,4,5,1]=>110101=>001010
[6,3,2,7,5,1,4]=>110110=>001001
[6,3,2,7,5,4,1]=>110111=>001000
[6,3,4,1,2,5,7]=>101000=>010111
[6,3,4,1,2,7,5]=>101001=>010110
[6,3,4,1,5,2,7]=>101010=>010101
[6,3,4,1,5,7,2]=>101001=>010110
[6,3,4,1,7,2,5]=>101010=>010101
[6,3,4,1,7,5,2]=>101011=>010100
[6,3,4,2,1,5,7]=>101100=>010011
[6,3,4,2,1,7,5]=>101101=>010010
[6,3,4,2,5,1,7]=>101010=>010101
[6,3,4,2,5,7,1]=>101001=>010110
[6,3,4,2,7,1,5]=>101010=>010101
[6,3,4,2,7,5,1]=>101011=>010100
[6,3,4,5,1,2,7]=>100100=>011011
[6,3,4,5,1,7,2]=>100101=>011010
[6,3,4,5,2,1,7]=>100110=>011001
[6,3,4,5,2,7,1]=>100101=>011010
[6,3,4,5,7,1,2]=>100010=>011101
[6,3,4,5,7,2,1]=>100011=>011100
[6,3,4,7,1,2,5]=>100100=>011011
[6,3,4,7,1,5,2]=>100101=>011010
[6,3,4,7,2,1,5]=>100110=>011001
[6,3,4,7,2,5,1]=>100101=>011010
[6,3,4,7,5,1,2]=>100110=>011001
[6,3,4,7,5,2,1]=>100111=>011000
[6,3,5,1,2,4,7]=>101000=>010111
[6,3,5,1,2,7,4]=>101001=>010110
[6,3,5,1,4,2,7]=>101010=>010101
[6,3,5,1,4,7,2]=>101001=>010110
[6,3,5,1,7,2,4]=>101010=>010101
[6,3,5,1,7,4,2]=>101011=>010100
[6,3,5,2,1,4,7]=>101100=>010011
[6,3,5,2,1,7,4]=>101101=>010010
[6,3,5,2,4,1,7]=>101010=>010101
[6,3,5,2,4,7,1]=>101001=>010110
[6,3,5,2,7,1,4]=>101010=>010101
[6,3,5,2,7,4,1]=>101011=>010100
[6,3,5,4,1,2,7]=>101100=>010011
[6,3,5,4,1,7,2]=>101101=>010010
[6,3,5,4,2,1,7]=>101110=>010001
[6,3,5,4,2,7,1]=>101101=>010010
[6,3,5,4,7,1,2]=>101010=>010101
[6,3,5,4,7,2,1]=>101011=>010100
[6,3,5,7,1,2,4]=>100100=>011011
[6,3,5,7,1,4,2]=>100101=>011010
[6,3,5,7,2,1,4]=>100110=>011001
[6,3,5,7,2,4,1]=>100101=>011010
[6,3,5,7,4,1,2]=>100110=>011001
[6,3,5,7,4,2,1]=>100111=>011000
[6,3,7,1,2,4,5]=>101000=>010111
[6,3,7,1,2,5,4]=>101001=>010110
[6,3,7,1,4,2,5]=>101010=>010101
[6,3,7,1,4,5,2]=>101001=>010110
[6,3,7,1,5,2,4]=>101010=>010101
[6,3,7,1,5,4,2]=>101011=>010100
[6,3,7,2,1,4,5]=>101100=>010011
[6,3,7,2,1,5,4]=>101101=>010010
[6,3,7,2,4,1,5]=>101010=>010101
[6,3,7,2,4,5,1]=>101001=>010110
[6,3,7,2,5,1,4]=>101010=>010101
[6,3,7,2,5,4,1]=>101011=>010100
[6,3,7,4,1,2,5]=>101100=>010011
[6,3,7,4,1,5,2]=>101101=>010010
[6,3,7,4,2,1,5]=>101110=>010001
[6,3,7,4,2,5,1]=>101101=>010010
[6,3,7,4,5,1,2]=>101010=>010101
[6,3,7,4,5,2,1]=>101011=>010100
[6,3,7,5,1,2,4]=>101100=>010011
[6,3,7,5,1,4,2]=>101101=>010010
[6,3,7,5,2,1,4]=>101110=>010001
[6,3,7,5,2,4,1]=>101101=>010010
[6,3,7,5,4,1,2]=>101110=>010001
[6,3,7,5,4,2,1]=>101111=>010000
[6,4,1,2,3,5,7]=>110000=>001111
[6,4,1,2,3,7,5]=>110001=>001110
[6,4,1,2,5,3,7]=>110010=>001101
[6,4,1,2,5,7,3]=>110001=>001110
[6,4,1,2,7,3,5]=>110010=>001101
[6,4,1,2,7,5,3]=>110011=>001100
[6,4,1,3,2,5,7]=>110100=>001011
[6,4,1,3,2,7,5]=>110101=>001010
[6,4,1,3,5,2,7]=>110010=>001101
[6,4,1,3,5,7,2]=>110001=>001110
[6,4,1,3,7,2,5]=>110010=>001101
[6,4,1,3,7,5,2]=>110011=>001100
[6,4,1,5,2,3,7]=>110100=>001011
[6,4,1,5,2,7,3]=>110101=>001010
[6,4,1,5,3,2,7]=>110110=>001001
[6,4,1,5,3,7,2]=>110101=>001010
[6,4,1,5,7,2,3]=>110010=>001101
[6,4,1,5,7,3,2]=>110011=>001100
[6,4,1,7,2,3,5]=>110100=>001011
[6,4,1,7,2,5,3]=>110101=>001010
[6,4,1,7,3,2,5]=>110110=>001001
[6,4,1,7,3,5,2]=>110101=>001010
[6,4,1,7,5,2,3]=>110110=>001001
[6,4,1,7,5,3,2]=>110111=>001000
[6,4,2,1,3,5,7]=>111000=>000111
[6,4,2,1,3,7,5]=>111001=>000110
[6,4,2,1,5,3,7]=>111010=>000101
[6,4,2,1,5,7,3]=>111001=>000110
[6,4,2,1,7,3,5]=>111010=>000101
[6,4,2,1,7,5,3]=>111011=>000100
[6,4,2,3,1,5,7]=>110100=>001011
[6,4,2,3,1,7,5]=>110101=>001010
[6,4,2,3,5,1,7]=>110010=>001101
[6,4,2,3,5,7,1]=>110001=>001110
[6,4,2,3,7,1,5]=>110010=>001101
[6,4,2,3,7,5,1]=>110011=>001100
[6,4,2,5,1,3,7]=>110100=>001011
[6,4,2,5,1,7,3]=>110101=>001010
[6,4,2,5,3,1,7]=>110110=>001001
[6,4,2,5,3,7,1]=>110101=>001010
[6,4,2,5,7,1,3]=>110010=>001101
[6,4,2,5,7,3,1]=>110011=>001100
[6,4,2,7,1,3,5]=>110100=>001011
[6,4,2,7,1,5,3]=>110101=>001010
[6,4,2,7,3,1,5]=>110110=>001001
[6,4,2,7,3,5,1]=>110101=>001010
[6,4,2,7,5,1,3]=>110110=>001001
[6,4,2,7,5,3,1]=>110111=>001000
[6,4,3,1,2,5,7]=>111000=>000111
[6,4,3,1,2,7,5]=>111001=>000110
[6,4,3,1,5,2,7]=>111010=>000101
[6,4,3,1,5,7,2]=>111001=>000110
[6,4,3,1,7,2,5]=>111010=>000101
[6,4,3,1,7,5,2]=>111011=>000100
[6,4,3,2,1,5,7]=>111100=>000011
[6,4,3,2,1,7,5]=>111101=>000010
[6,4,3,2,5,1,7]=>111010=>000101
[6,4,3,2,5,7,1]=>111001=>000110
[6,4,3,2,7,1,5]=>111010=>000101
[6,4,3,2,7,5,1]=>111011=>000100
[6,4,3,5,1,2,7]=>110100=>001011
[6,4,3,5,1,7,2]=>110101=>001010
[6,4,3,5,2,1,7]=>110110=>001001
[6,4,3,5,2,7,1]=>110101=>001010
[6,4,3,5,7,1,2]=>110010=>001101
[6,4,3,5,7,2,1]=>110011=>001100
[6,4,3,7,1,2,5]=>110100=>001011
[6,4,3,7,1,5,2]=>110101=>001010
[6,4,3,7,2,1,5]=>110110=>001001
[6,4,3,7,2,5,1]=>110101=>001010
[6,4,3,7,5,1,2]=>110110=>001001
[6,4,3,7,5,2,1]=>110111=>001000
[6,4,5,1,2,3,7]=>101000=>010111
[6,4,5,1,2,7,3]=>101001=>010110
[6,4,5,1,3,2,7]=>101010=>010101
[6,4,5,1,3,7,2]=>101001=>010110
[6,4,5,1,7,2,3]=>101010=>010101
[6,4,5,1,7,3,2]=>101011=>010100
[6,4,5,2,1,3,7]=>101100=>010011
[6,4,5,2,1,7,3]=>101101=>010010
[6,4,5,2,3,1,7]=>101010=>010101
[6,4,5,2,3,7,1]=>101001=>010110
[6,4,5,2,7,1,3]=>101010=>010101
[6,4,5,2,7,3,1]=>101011=>010100
[6,4,5,3,1,2,7]=>101100=>010011
[6,4,5,3,1,7,2]=>101101=>010010
[6,4,5,3,2,1,7]=>101110=>010001
[6,4,5,3,2,7,1]=>101101=>010010
[6,4,5,3,7,1,2]=>101010=>010101
[6,4,5,3,7,2,1]=>101011=>010100
[6,4,5,7,1,2,3]=>100100=>011011
[6,4,5,7,1,3,2]=>100101=>011010
[6,4,5,7,2,1,3]=>100110=>011001
[6,4,5,7,2,3,1]=>100101=>011010
[6,4,5,7,3,1,2]=>100110=>011001
[6,4,5,7,3,2,1]=>100111=>011000
[6,4,7,1,2,3,5]=>101000=>010111
[6,4,7,1,2,5,3]=>101001=>010110
[6,4,7,1,3,2,5]=>101010=>010101
[6,4,7,1,3,5,2]=>101001=>010110
[6,4,7,1,5,2,3]=>101010=>010101
[6,4,7,1,5,3,2]=>101011=>010100
[6,4,7,2,1,3,5]=>101100=>010011
[6,4,7,2,1,5,3]=>101101=>010010
[6,4,7,2,3,1,5]=>101010=>010101
[6,4,7,2,3,5,1]=>101001=>010110
[6,4,7,2,5,1,3]=>101010=>010101
[6,4,7,2,5,3,1]=>101011=>010100
[6,4,7,3,1,2,5]=>101100=>010011
[6,4,7,3,1,5,2]=>101101=>010010
[6,4,7,3,2,1,5]=>101110=>010001
[6,4,7,3,2,5,1]=>101101=>010010
[6,4,7,3,5,1,2]=>101010=>010101
[6,4,7,3,5,2,1]=>101011=>010100
[6,4,7,5,1,2,3]=>101100=>010011
[6,4,7,5,1,3,2]=>101101=>010010
[6,4,7,5,2,1,3]=>101110=>010001
[6,4,7,5,2,3,1]=>101101=>010010
[6,4,7,5,3,1,2]=>101110=>010001
[6,4,7,5,3,2,1]=>101111=>010000
[6,5,1,2,3,4,7]=>110000=>001111
[6,5,1,2,3,7,4]=>110001=>001110
[6,5,1,2,4,3,7]=>110010=>001101
[6,5,1,2,4,7,3]=>110001=>001110
[6,5,1,2,7,3,4]=>110010=>001101
[6,5,1,2,7,4,3]=>110011=>001100
[6,5,1,3,2,4,7]=>110100=>001011
[6,5,1,3,2,7,4]=>110101=>001010
[6,5,1,3,4,2,7]=>110010=>001101
[6,5,1,3,4,7,2]=>110001=>001110
[6,5,1,3,7,2,4]=>110010=>001101
[6,5,1,3,7,4,2]=>110011=>001100
[6,5,1,4,2,3,7]=>110100=>001011
[6,5,1,4,2,7,3]=>110101=>001010
[6,5,1,4,3,2,7]=>110110=>001001
[6,5,1,4,3,7,2]=>110101=>001010
[6,5,1,4,7,2,3]=>110010=>001101
[6,5,1,4,7,3,2]=>110011=>001100
[6,5,1,7,2,3,4]=>110100=>001011
[6,5,1,7,2,4,3]=>110101=>001010
[6,5,1,7,3,2,4]=>110110=>001001
[6,5,1,7,3,4,2]=>110101=>001010
[6,5,1,7,4,2,3]=>110110=>001001
[6,5,1,7,4,3,2]=>110111=>001000
[6,5,2,1,3,4,7]=>111000=>000111
[6,5,2,1,3,7,4]=>111001=>000110
[6,5,2,1,4,3,7]=>111010=>000101
[6,5,2,1,4,7,3]=>111001=>000110
[6,5,2,1,7,3,4]=>111010=>000101
[6,5,2,1,7,4,3]=>111011=>000100
[6,5,2,3,1,4,7]=>110100=>001011
[6,5,2,3,1,7,4]=>110101=>001010
[6,5,2,3,4,1,7]=>110010=>001101
[6,5,2,3,4,7,1]=>110001=>001110
[6,5,2,3,7,1,4]=>110010=>001101
[6,5,2,3,7,4,1]=>110011=>001100
[6,5,2,4,1,3,7]=>110100=>001011
[6,5,2,4,1,7,3]=>110101=>001010
[6,5,2,4,3,1,7]=>110110=>001001
[6,5,2,4,3,7,1]=>110101=>001010
[6,5,2,4,7,1,3]=>110010=>001101
[6,5,2,4,7,3,1]=>110011=>001100
[6,5,2,7,1,3,4]=>110100=>001011
[6,5,2,7,1,4,3]=>110101=>001010
[6,5,2,7,3,1,4]=>110110=>001001
[6,5,2,7,3,4,1]=>110101=>001010
[6,5,2,7,4,1,3]=>110110=>001001
[6,5,2,7,4,3,1]=>110111=>001000
[6,5,3,1,2,4,7]=>111000=>000111
[6,5,3,1,2,7,4]=>111001=>000110
[6,5,3,1,4,2,7]=>111010=>000101
[6,5,3,1,4,7,2]=>111001=>000110
[6,5,3,1,7,2,4]=>111010=>000101
[6,5,3,1,7,4,2]=>111011=>000100
[6,5,3,2,1,4,7]=>111100=>000011
[6,5,3,2,1,7,4]=>111101=>000010
[6,5,3,2,4,1,7]=>111010=>000101
[6,5,3,2,4,7,1]=>111001=>000110
[6,5,3,2,7,1,4]=>111010=>000101
[6,5,3,2,7,4,1]=>111011=>000100
[6,5,3,4,1,2,7]=>110100=>001011
[6,5,3,4,1,7,2]=>110101=>001010
[6,5,3,4,2,1,7]=>110110=>001001
[6,5,3,4,2,7,1]=>110101=>001010
[6,5,3,4,7,1,2]=>110010=>001101
[6,5,3,4,7,2,1]=>110011=>001100
[6,5,3,7,1,2,4]=>110100=>001011
[6,5,3,7,1,4,2]=>110101=>001010
[6,5,3,7,2,1,4]=>110110=>001001
[6,5,3,7,2,4,1]=>110101=>001010
[6,5,3,7,4,1,2]=>110110=>001001
[6,5,3,7,4,2,1]=>110111=>001000
[6,5,4,1,2,3,7]=>111000=>000111
[6,5,4,1,2,7,3]=>111001=>000110
[6,5,4,1,3,2,7]=>111010=>000101
[6,5,4,1,3,7,2]=>111001=>000110
[6,5,4,1,7,2,3]=>111010=>000101
[6,5,4,1,7,3,2]=>111011=>000100
[6,5,4,2,1,3,7]=>111100=>000011
[6,5,4,2,1,7,3]=>111101=>000010
[6,5,4,2,3,1,7]=>111010=>000101
[6,5,4,2,3,7,1]=>111001=>000110
[6,5,4,2,7,1,3]=>111010=>000101
[6,5,4,2,7,3,1]=>111011=>000100
[6,5,4,3,1,2,7]=>111100=>000011
[6,5,4,3,1,7,2]=>111101=>000010
[6,5,4,3,2,1,7]=>111110=>000001
[6,5,4,3,2,7,1]=>111101=>000010
[6,5,4,3,7,1,2]=>111010=>000101
[6,5,4,3,7,2,1]=>111011=>000100
[6,5,4,7,1,2,3]=>110100=>001011
[6,5,4,7,1,3,2]=>110101=>001010
[6,5,4,7,2,1,3]=>110110=>001001
[6,5,4,7,2,3,1]=>110101=>001010
[6,5,4,7,3,1,2]=>110110=>001001
[6,5,4,7,3,2,1]=>110111=>001000
[6,5,7,1,2,3,4]=>101000=>010111
[6,5,7,1,2,4,3]=>101001=>010110
[6,5,7,1,3,2,4]=>101010=>010101
[6,5,7,1,3,4,2]=>101001=>010110
[6,5,7,1,4,2,3]=>101010=>010101
[6,5,7,1,4,3,2]=>101011=>010100
[6,5,7,2,1,3,4]=>101100=>010011
[6,5,7,2,1,4,3]=>101101=>010010
[6,5,7,2,3,1,4]=>101010=>010101
[6,5,7,2,3,4,1]=>101001=>010110
[6,5,7,2,4,1,3]=>101010=>010101
[6,5,7,2,4,3,1]=>101011=>010100
[6,5,7,3,1,2,4]=>101100=>010011
[6,5,7,3,1,4,2]=>101101=>010010
[6,5,7,3,2,1,4]=>101110=>010001
[6,5,7,3,2,4,1]=>101101=>010010
[6,5,7,3,4,1,2]=>101010=>010101
[6,5,7,3,4,2,1]=>101011=>010100
[6,5,7,4,1,2,3]=>101100=>010011
[6,5,7,4,1,3,2]=>101101=>010010
[6,5,7,4,2,1,3]=>101110=>010001
[6,5,7,4,2,3,1]=>101101=>010010
[6,5,7,4,3,1,2]=>101110=>010001
[6,5,7,4,3,2,1]=>101111=>010000
[6,7,1,2,3,4,5]=>010000=>101111
[6,7,1,2,3,5,4]=>010001=>101110
[6,7,1,2,4,3,5]=>010010=>101101
[6,7,1,2,4,5,3]=>010001=>101110
[6,7,1,2,5,3,4]=>010010=>101101
[6,7,1,2,5,4,3]=>010011=>101100
[6,7,1,3,2,4,5]=>010100=>101011
[6,7,1,3,2,5,4]=>010101=>101010
[6,7,1,3,4,2,5]=>010010=>101101
[6,7,1,3,4,5,2]=>010001=>101110
[6,7,1,3,5,2,4]=>010010=>101101
[6,7,1,3,5,4,2]=>010011=>101100
[6,7,1,4,2,3,5]=>010100=>101011
[6,7,1,4,2,5,3]=>010101=>101010
[6,7,1,4,3,2,5]=>010110=>101001
[6,7,1,4,3,5,2]=>010101=>101010
[6,7,1,4,5,2,3]=>010010=>101101
[6,7,1,4,5,3,2]=>010011=>101100
[6,7,1,5,2,3,4]=>010100=>101011
[6,7,1,5,2,4,3]=>010101=>101010
[6,7,1,5,3,2,4]=>010110=>101001
[6,7,1,5,3,4,2]=>010101=>101010
[6,7,1,5,4,2,3]=>010110=>101001
[6,7,1,5,4,3,2]=>010111=>101000
[6,7,2,1,3,4,5]=>011000=>100111
[6,7,2,1,3,5,4]=>011001=>100110
[6,7,2,1,4,3,5]=>011010=>100101
[6,7,2,1,4,5,3]=>011001=>100110
[6,7,2,1,5,3,4]=>011010=>100101
[6,7,2,1,5,4,3]=>011011=>100100
[6,7,2,3,1,4,5]=>010100=>101011
[6,7,2,3,1,5,4]=>010101=>101010
[6,7,2,3,4,1,5]=>010010=>101101
[6,7,2,3,4,5,1]=>010001=>101110
[6,7,2,3,5,1,4]=>010010=>101101
[6,7,2,3,5,4,1]=>010011=>101100
[6,7,2,4,1,3,5]=>010100=>101011
[6,7,2,4,1,5,3]=>010101=>101010
[6,7,2,4,3,1,5]=>010110=>101001
[6,7,2,4,3,5,1]=>010101=>101010
[6,7,2,4,5,1,3]=>010010=>101101
[6,7,2,4,5,3,1]=>010011=>101100
[6,7,2,5,1,3,4]=>010100=>101011
[6,7,2,5,1,4,3]=>010101=>101010
[6,7,2,5,3,1,4]=>010110=>101001
[6,7,2,5,3,4,1]=>010101=>101010
[6,7,2,5,4,1,3]=>010110=>101001
[6,7,2,5,4,3,1]=>010111=>101000
[6,7,3,1,2,4,5]=>011000=>100111
[6,7,3,1,2,5,4]=>011001=>100110
[6,7,3,1,4,2,5]=>011010=>100101
[6,7,3,1,4,5,2]=>011001=>100110
[6,7,3,1,5,2,4]=>011010=>100101
[6,7,3,1,5,4,2]=>011011=>100100
[6,7,3,2,1,4,5]=>011100=>100011
[6,7,3,2,1,5,4]=>011101=>100010
[6,7,3,2,4,1,5]=>011010=>100101
[6,7,3,2,4,5,1]=>011001=>100110
[6,7,3,2,5,1,4]=>011010=>100101
[6,7,3,2,5,4,1]=>011011=>100100
[6,7,3,4,1,2,5]=>010100=>101011
[6,7,3,4,1,5,2]=>010101=>101010
[6,7,3,4,2,1,5]=>010110=>101001
[6,7,3,4,2,5,1]=>010101=>101010
[6,7,3,4,5,1,2]=>010010=>101101
[6,7,3,4,5,2,1]=>010011=>101100
[6,7,3,5,1,2,4]=>010100=>101011
[6,7,3,5,1,4,2]=>010101=>101010
[6,7,3,5,2,1,4]=>010110=>101001
[6,7,3,5,2,4,1]=>010101=>101010
[6,7,3,5,4,1,2]=>010110=>101001
[6,7,3,5,4,2,1]=>010111=>101000
[6,7,4,1,2,3,5]=>011000=>100111
[6,7,4,1,2,5,3]=>011001=>100110
[6,7,4,1,3,2,5]=>011010=>100101
[6,7,4,1,3,5,2]=>011001=>100110
[6,7,4,1,5,2,3]=>011010=>100101
[6,7,4,1,5,3,2]=>011011=>100100
[6,7,4,2,1,3,5]=>011100=>100011
[6,7,4,2,1,5,3]=>011101=>100010
[6,7,4,2,3,1,5]=>011010=>100101
[6,7,4,2,3,5,1]=>011001=>100110
[6,7,4,2,5,1,3]=>011010=>100101
[6,7,4,2,5,3,1]=>011011=>100100
[6,7,4,3,1,2,5]=>011100=>100011
[6,7,4,3,1,5,2]=>011101=>100010
[6,7,4,3,2,1,5]=>011110=>100001
[6,7,4,3,2,5,1]=>011101=>100010
[6,7,4,3,5,1,2]=>011010=>100101
[6,7,4,3,5,2,1]=>011011=>100100
[6,7,4,5,1,2,3]=>010100=>101011
[6,7,4,5,1,3,2]=>010101=>101010
[6,7,4,5,2,1,3]=>010110=>101001
[6,7,4,5,2,3,1]=>010101=>101010
[6,7,4,5,3,1,2]=>010110=>101001
[6,7,4,5,3,2,1]=>010111=>101000
[6,7,5,1,2,3,4]=>011000=>100111
[6,7,5,1,2,4,3]=>011001=>100110
[6,7,5,1,3,2,4]=>011010=>100101
[6,7,5,1,3,4,2]=>011001=>100110
[6,7,5,1,4,2,3]=>011010=>100101
[6,7,5,1,4,3,2]=>011011=>100100
[6,7,5,2,1,3,4]=>011100=>100011
[6,7,5,2,1,4,3]=>011101=>100010
[6,7,5,2,3,1,4]=>011010=>100101
[6,7,5,2,3,4,1]=>011001=>100110
[6,7,5,2,4,1,3]=>011010=>100101
[6,7,5,2,4,3,1]=>011011=>100100
[6,7,5,3,1,2,4]=>011100=>100011
[6,7,5,3,1,4,2]=>011101=>100010
[6,7,5,3,2,1,4]=>011110=>100001
[6,7,5,3,2,4,1]=>011101=>100010
[6,7,5,3,4,1,2]=>011010=>100101
[6,7,5,3,4,2,1]=>011011=>100100
[6,7,5,4,1,2,3]=>011100=>100011
[6,7,5,4,1,3,2]=>011101=>100010
[6,7,5,4,2,1,3]=>011110=>100001
[6,7,5,4,2,3,1]=>011101=>100010
[6,7,5,4,3,1,2]=>011110=>100001
[6,7,5,4,3,2,1]=>011111=>100000
[7,1,2,3,4,5,6]=>100000=>011111
[7,1,2,3,4,6,5]=>100001=>011110
[7,1,2,3,5,4,6]=>100010=>011101
[7,1,2,3,5,6,4]=>100001=>011110
[7,1,2,3,6,4,5]=>100010=>011101
[7,1,2,3,6,5,4]=>100011=>011100
[7,1,2,4,3,5,6]=>100100=>011011
[7,1,2,4,3,6,5]=>100101=>011010
[7,1,2,4,5,3,6]=>100010=>011101
[7,1,2,4,5,6,3]=>100001=>011110
[7,1,2,4,6,3,5]=>100010=>011101
[7,1,2,4,6,5,3]=>100011=>011100
[7,1,2,5,3,4,6]=>100100=>011011
[7,1,2,5,3,6,4]=>100101=>011010
[7,1,2,5,4,3,6]=>100110=>011001
[7,1,2,5,4,6,3]=>100101=>011010
[7,1,2,5,6,3,4]=>100010=>011101
[7,1,2,5,6,4,3]=>100011=>011100
[7,1,2,6,3,4,5]=>100100=>011011
[7,1,2,6,3,5,4]=>100101=>011010
[7,1,2,6,4,3,5]=>100110=>011001
[7,1,2,6,4,5,3]=>100101=>011010
[7,1,2,6,5,3,4]=>100110=>011001
[7,1,2,6,5,4,3]=>100111=>011000
[7,1,3,2,4,5,6]=>101000=>010111
[7,1,3,2,4,6,5]=>101001=>010110
[7,1,3,2,5,4,6]=>101010=>010101
[7,1,3,2,5,6,4]=>101001=>010110
[7,1,3,2,6,4,5]=>101010=>010101
[7,1,3,2,6,5,4]=>101011=>010100
[7,1,3,4,2,5,6]=>100100=>011011
[7,1,3,4,2,6,5]=>100101=>011010
[7,1,3,4,5,2,6]=>100010=>011101
[7,1,3,4,5,6,2]=>100001=>011110
[7,1,3,4,6,2,5]=>100010=>011101
[7,1,3,4,6,5,2]=>100011=>011100
[7,1,3,5,2,4,6]=>100100=>011011
[7,1,3,5,2,6,4]=>100101=>011010
[7,1,3,5,4,2,6]=>100110=>011001
[7,1,3,5,4,6,2]=>100101=>011010
[7,1,3,5,6,2,4]=>100010=>011101
[7,1,3,5,6,4,2]=>100011=>011100
[7,1,3,6,2,4,5]=>100100=>011011
[7,1,3,6,2,5,4]=>100101=>011010
[7,1,3,6,4,2,5]=>100110=>011001
[7,1,3,6,4,5,2]=>100101=>011010
[7,1,3,6,5,2,4]=>100110=>011001
[7,1,3,6,5,4,2]=>100111=>011000
[7,1,4,2,3,5,6]=>101000=>010111
[7,1,4,2,3,6,5]=>101001=>010110
[7,1,4,2,5,3,6]=>101010=>010101
[7,1,4,2,5,6,3]=>101001=>010110
[7,1,4,2,6,3,5]=>101010=>010101
[7,1,4,2,6,5,3]=>101011=>010100
[7,1,4,3,2,5,6]=>101100=>010011
[7,1,4,3,2,6,5]=>101101=>010010
[7,1,4,3,5,2,6]=>101010=>010101
[7,1,4,3,5,6,2]=>101001=>010110
[7,1,4,3,6,2,5]=>101010=>010101
[7,1,4,3,6,5,2]=>101011=>010100
[7,1,4,5,2,3,6]=>100100=>011011
[7,1,4,5,2,6,3]=>100101=>011010
[7,1,4,5,3,2,6]=>100110=>011001
[7,1,4,5,3,6,2]=>100101=>011010
[7,1,4,5,6,2,3]=>100010=>011101
[7,1,4,5,6,3,2]=>100011=>011100
[7,1,4,6,2,3,5]=>100100=>011011
[7,1,4,6,2,5,3]=>100101=>011010
[7,1,4,6,3,2,5]=>100110=>011001
[7,1,4,6,3,5,2]=>100101=>011010
[7,1,4,6,5,2,3]=>100110=>011001
[7,1,4,6,5,3,2]=>100111=>011000
[7,1,5,2,3,4,6]=>101000=>010111
[7,1,5,2,3,6,4]=>101001=>010110
[7,1,5,2,4,3,6]=>101010=>010101
[7,1,5,2,4,6,3]=>101001=>010110
[7,1,5,2,6,3,4]=>101010=>010101
[7,1,5,2,6,4,3]=>101011=>010100
[7,1,5,3,2,4,6]=>101100=>010011
[7,1,5,3,2,6,4]=>101101=>010010
[7,1,5,3,4,2,6]=>101010=>010101
[7,1,5,3,4,6,2]=>101001=>010110
[7,1,5,3,6,2,4]=>101010=>010101
[7,1,5,3,6,4,2]=>101011=>010100
[7,1,5,4,2,3,6]=>101100=>010011
[7,1,5,4,2,6,3]=>101101=>010010
[7,1,5,4,3,2,6]=>101110=>010001
[7,1,5,4,3,6,2]=>101101=>010010
[7,1,5,4,6,2,3]=>101010=>010101
[7,1,5,4,6,3,2]=>101011=>010100
[7,1,5,6,2,3,4]=>100100=>011011
[7,1,5,6,2,4,3]=>100101=>011010
[7,1,5,6,3,2,4]=>100110=>011001
[7,1,5,6,3,4,2]=>100101=>011010
[7,1,5,6,4,2,3]=>100110=>011001
[7,1,5,6,4,3,2]=>100111=>011000
[7,1,6,2,3,4,5]=>101000=>010111
[7,1,6,2,3,5,4]=>101001=>010110
[7,1,6,2,4,3,5]=>101010=>010101
[7,1,6,2,4,5,3]=>101001=>010110
[7,1,6,2,5,3,4]=>101010=>010101
[7,1,6,2,5,4,3]=>101011=>010100
[7,1,6,3,2,4,5]=>101100=>010011
[7,1,6,3,2,5,4]=>101101=>010010
[7,1,6,3,4,2,5]=>101010=>010101
[7,1,6,3,4,5,2]=>101001=>010110
[7,1,6,3,5,2,4]=>101010=>010101
[7,1,6,3,5,4,2]=>101011=>010100
[7,1,6,4,2,3,5]=>101100=>010011
[7,1,6,4,2,5,3]=>101101=>010010
[7,1,6,4,3,2,5]=>101110=>010001
[7,1,6,4,3,5,2]=>101101=>010010
[7,1,6,4,5,2,3]=>101010=>010101
[7,1,6,4,5,3,2]=>101011=>010100
[7,1,6,5,2,3,4]=>101100=>010011
[7,1,6,5,2,4,3]=>101101=>010010
[7,1,6,5,3,2,4]=>101110=>010001
[7,1,6,5,3,4,2]=>101101=>010010
[7,1,6,5,4,2,3]=>101110=>010001
[7,1,6,5,4,3,2]=>101111=>010000
[7,2,1,3,4,5,6]=>110000=>001111
[7,2,1,3,4,6,5]=>110001=>001110
[7,2,1,3,5,4,6]=>110010=>001101
[7,2,1,3,5,6,4]=>110001=>001110
[7,2,1,3,6,4,5]=>110010=>001101
[7,2,1,3,6,5,4]=>110011=>001100
[7,2,1,4,3,5,6]=>110100=>001011
[7,2,1,4,3,6,5]=>110101=>001010
[7,2,1,4,5,3,6]=>110010=>001101
[7,2,1,4,5,6,3]=>110001=>001110
[7,2,1,4,6,3,5]=>110010=>001101
[7,2,1,4,6,5,3]=>110011=>001100
[7,2,1,5,3,4,6]=>110100=>001011
[7,2,1,5,3,6,4]=>110101=>001010
[7,2,1,5,4,3,6]=>110110=>001001
[7,2,1,5,4,6,3]=>110101=>001010
[7,2,1,5,6,3,4]=>110010=>001101
[7,2,1,5,6,4,3]=>110011=>001100
[7,2,1,6,3,4,5]=>110100=>001011
[7,2,1,6,3,5,4]=>110101=>001010
[7,2,1,6,4,3,5]=>110110=>001001
[7,2,1,6,4,5,3]=>110101=>001010
[7,2,1,6,5,3,4]=>110110=>001001
[7,2,1,6,5,4,3]=>110111=>001000
[7,2,3,1,4,5,6]=>101000=>010111
[7,2,3,1,4,6,5]=>101001=>010110
[7,2,3,1,5,4,6]=>101010=>010101
[7,2,3,1,5,6,4]=>101001=>010110
[7,2,3,1,6,4,5]=>101010=>010101
[7,2,3,1,6,5,4]=>101011=>010100
[7,2,3,4,1,5,6]=>100100=>011011
[7,2,3,4,1,6,5]=>100101=>011010
[7,2,3,4,5,1,6]=>100010=>011101
[7,2,3,4,5,6,1]=>100001=>011110
[7,2,3,4,6,1,5]=>100010=>011101
[7,2,3,4,6,5,1]=>100011=>011100
[7,2,3,5,1,4,6]=>100100=>011011
[7,2,3,5,1,6,4]=>100101=>011010
[7,2,3,5,4,1,6]=>100110=>011001
[7,2,3,5,4,6,1]=>100101=>011010
[7,2,3,5,6,1,4]=>100010=>011101
[7,2,3,5,6,4,1]=>100011=>011100
[7,2,3,6,1,4,5]=>100100=>011011
[7,2,3,6,1,5,4]=>100101=>011010
[7,2,3,6,4,1,5]=>100110=>011001
[7,2,3,6,4,5,1]=>100101=>011010
[7,2,3,6,5,1,4]=>100110=>011001
[7,2,3,6,5,4,1]=>100111=>011000
[7,2,4,1,3,5,6]=>101000=>010111
[7,2,4,1,3,6,5]=>101001=>010110
[7,2,4,1,5,3,6]=>101010=>010101
[7,2,4,1,5,6,3]=>101001=>010110
[7,2,4,1,6,3,5]=>101010=>010101
[7,2,4,1,6,5,3]=>101011=>010100
[7,2,4,3,1,5,6]=>101100=>010011
[7,2,4,3,1,6,5]=>101101=>010010
[7,2,4,3,5,1,6]=>101010=>010101
[7,2,4,3,5,6,1]=>101001=>010110
[7,2,4,3,6,1,5]=>101010=>010101
[7,2,4,3,6,5,1]=>101011=>010100
[7,2,4,5,1,3,6]=>100100=>011011
[7,2,4,5,1,6,3]=>100101=>011010
[7,2,4,5,3,1,6]=>100110=>011001
[7,2,4,5,3,6,1]=>100101=>011010
[7,2,4,5,6,1,3]=>100010=>011101
[7,2,4,5,6,3,1]=>100011=>011100
[7,2,4,6,1,3,5]=>100100=>011011
[7,2,4,6,1,5,3]=>100101=>011010
[7,2,4,6,3,1,5]=>100110=>011001
[7,2,4,6,3,5,1]=>100101=>011010
[7,2,4,6,5,1,3]=>100110=>011001
[7,2,4,6,5,3,1]=>100111=>011000
[7,2,5,1,3,4,6]=>101000=>010111
[7,2,5,1,3,6,4]=>101001=>010110
[7,2,5,1,4,3,6]=>101010=>010101
[7,2,5,1,4,6,3]=>101001=>010110
[7,2,5,1,6,3,4]=>101010=>010101
[7,2,5,1,6,4,3]=>101011=>010100
[7,2,5,3,1,4,6]=>101100=>010011
[7,2,5,3,1,6,4]=>101101=>010010
[7,2,5,3,4,1,6]=>101010=>010101
[7,2,5,3,4,6,1]=>101001=>010110
[7,2,5,3,6,1,4]=>101010=>010101
[7,2,5,3,6,4,1]=>101011=>010100
[7,2,5,4,1,3,6]=>101100=>010011
[7,2,5,4,1,6,3]=>101101=>010010
[7,2,5,4,3,1,6]=>101110=>010001
[7,2,5,4,3,6,1]=>101101=>010010
[7,2,5,4,6,1,3]=>101010=>010101
[7,2,5,4,6,3,1]=>101011=>010100
[7,2,5,6,1,3,4]=>100100=>011011
[7,2,5,6,1,4,3]=>100101=>011010
[7,2,5,6,3,1,4]=>100110=>011001
[7,2,5,6,3,4,1]=>100101=>011010
[7,2,5,6,4,1,3]=>100110=>011001
[7,2,5,6,4,3,1]=>100111=>011000
[7,2,6,1,3,4,5]=>101000=>010111
[7,2,6,1,3,5,4]=>101001=>010110
[7,2,6,1,4,3,5]=>101010=>010101
[7,2,6,1,4,5,3]=>101001=>010110
[7,2,6,1,5,3,4]=>101010=>010101
[7,2,6,1,5,4,3]=>101011=>010100
[7,2,6,3,1,4,5]=>101100=>010011
[7,2,6,3,1,5,4]=>101101=>010010
[7,2,6,3,4,1,5]=>101010=>010101
[7,2,6,3,4,5,1]=>101001=>010110
[7,2,6,3,5,1,4]=>101010=>010101
[7,2,6,3,5,4,1]=>101011=>010100
[7,2,6,4,1,3,5]=>101100=>010011
[7,2,6,4,1,5,3]=>101101=>010010
[7,2,6,4,3,1,5]=>101110=>010001
[7,2,6,4,3,5,1]=>101101=>010010
[7,2,6,4,5,1,3]=>101010=>010101
[7,2,6,4,5,3,1]=>101011=>010100
[7,2,6,5,1,3,4]=>101100=>010011
[7,2,6,5,1,4,3]=>101101=>010010
[7,2,6,5,3,1,4]=>101110=>010001
[7,2,6,5,3,4,1]=>101101=>010010
[7,2,6,5,4,1,3]=>101110=>010001
[7,2,6,5,4,3,1]=>101111=>010000
[7,3,1,2,4,5,6]=>110000=>001111
[7,3,1,2,4,6,5]=>110001=>001110
[7,3,1,2,5,4,6]=>110010=>001101
[7,3,1,2,5,6,4]=>110001=>001110
[7,3,1,2,6,4,5]=>110010=>001101
[7,3,1,2,6,5,4]=>110011=>001100
[7,3,1,4,2,5,6]=>110100=>001011
[7,3,1,4,2,6,5]=>110101=>001010
[7,3,1,4,5,2,6]=>110010=>001101
[7,3,1,4,5,6,2]=>110001=>001110
[7,3,1,4,6,2,5]=>110010=>001101
[7,3,1,4,6,5,2]=>110011=>001100
[7,3,1,5,2,4,6]=>110100=>001011
[7,3,1,5,2,6,4]=>110101=>001010
[7,3,1,5,4,2,6]=>110110=>001001
[7,3,1,5,4,6,2]=>110101=>001010
[7,3,1,5,6,2,4]=>110010=>001101
[7,3,1,5,6,4,2]=>110011=>001100
[7,3,1,6,2,4,5]=>110100=>001011
[7,3,1,6,2,5,4]=>110101=>001010
[7,3,1,6,4,2,5]=>110110=>001001
[7,3,1,6,4,5,2]=>110101=>001010
[7,3,1,6,5,2,4]=>110110=>001001
[7,3,1,6,5,4,2]=>110111=>001000
[7,3,2,1,4,5,6]=>111000=>000111
[7,3,2,1,4,6,5]=>111001=>000110
[7,3,2,1,5,4,6]=>111010=>000101
[7,3,2,1,5,6,4]=>111001=>000110
[7,3,2,1,6,4,5]=>111010=>000101
[7,3,2,1,6,5,4]=>111011=>000100
[7,3,2,4,1,5,6]=>110100=>001011
[7,3,2,4,1,6,5]=>110101=>001010
[7,3,2,4,5,1,6]=>110010=>001101
[7,3,2,4,5,6,1]=>110001=>001110
[7,3,2,4,6,1,5]=>110010=>001101
[7,3,2,4,6,5,1]=>110011=>001100
[7,3,2,5,1,4,6]=>110100=>001011
[7,3,2,5,1,6,4]=>110101=>001010
[7,3,2,5,4,1,6]=>110110=>001001
[7,3,2,5,4,6,1]=>110101=>001010
[7,3,2,5,6,1,4]=>110010=>001101
[7,3,2,5,6,4,1]=>110011=>001100
[7,3,2,6,1,4,5]=>110100=>001011
[7,3,2,6,1,5,4]=>110101=>001010
[7,3,2,6,4,1,5]=>110110=>001001
[7,3,2,6,4,5,1]=>110101=>001010
[7,3,2,6,5,1,4]=>110110=>001001
[7,3,2,6,5,4,1]=>110111=>001000
[7,3,4,1,2,5,6]=>101000=>010111
[7,3,4,1,2,6,5]=>101001=>010110
[7,3,4,1,5,2,6]=>101010=>010101
[7,3,4,1,5,6,2]=>101001=>010110
[7,3,4,1,6,2,5]=>101010=>010101
[7,3,4,1,6,5,2]=>101011=>010100
[7,3,4,2,1,5,6]=>101100=>010011
[7,3,4,2,1,6,5]=>101101=>010010
[7,3,4,2,5,1,6]=>101010=>010101
[7,3,4,2,5,6,1]=>101001=>010110
[7,3,4,2,6,1,5]=>101010=>010101
[7,3,4,2,6,5,1]=>101011=>010100
[7,3,4,5,1,2,6]=>100100=>011011
[7,3,4,5,1,6,2]=>100101=>011010
[7,3,4,5,2,1,6]=>100110=>011001
[7,3,4,5,2,6,1]=>100101=>011010
[7,3,4,5,6,1,2]=>100010=>011101
[7,3,4,5,6,2,1]=>100011=>011100
[7,3,4,6,1,2,5]=>100100=>011011
[7,3,4,6,1,5,2]=>100101=>011010
[7,3,4,6,2,1,5]=>100110=>011001
[7,3,4,6,2,5,1]=>100101=>011010
[7,3,4,6,5,1,2]=>100110=>011001
[7,3,4,6,5,2,1]=>100111=>011000
[7,3,5,1,2,4,6]=>101000=>010111
[7,3,5,1,2,6,4]=>101001=>010110
[7,3,5,1,4,2,6]=>101010=>010101
[7,3,5,1,4,6,2]=>101001=>010110
[7,3,5,1,6,2,4]=>101010=>010101
[7,3,5,1,6,4,2]=>101011=>010100
[7,3,5,2,1,4,6]=>101100=>010011
[7,3,5,2,1,6,4]=>101101=>010010
[7,3,5,2,4,1,6]=>101010=>010101
[7,3,5,2,4,6,1]=>101001=>010110
[7,3,5,2,6,1,4]=>101010=>010101
[7,3,5,2,6,4,1]=>101011=>010100
[7,3,5,4,1,2,6]=>101100=>010011
[7,3,5,4,1,6,2]=>101101=>010010
[7,3,5,4,2,1,6]=>101110=>010001
[7,3,5,4,2,6,1]=>101101=>010010
[7,3,5,4,6,1,2]=>101010=>010101
[7,3,5,4,6,2,1]=>101011=>010100
[7,3,5,6,1,2,4]=>100100=>011011
[7,3,5,6,1,4,2]=>100101=>011010
[7,3,5,6,2,1,4]=>100110=>011001
[7,3,5,6,2,4,1]=>100101=>011010
[7,3,5,6,4,1,2]=>100110=>011001
[7,3,5,6,4,2,1]=>100111=>011000
[7,3,6,1,2,4,5]=>101000=>010111
[7,3,6,1,2,5,4]=>101001=>010110
[7,3,6,1,4,2,5]=>101010=>010101
[7,3,6,1,4,5,2]=>101001=>010110
[7,3,6,1,5,2,4]=>101010=>010101
[7,3,6,1,5,4,2]=>101011=>010100
[7,3,6,2,1,4,5]=>101100=>010011
[7,3,6,2,1,5,4]=>101101=>010010
[7,3,6,2,4,1,5]=>101010=>010101
[7,3,6,2,4,5,1]=>101001=>010110
[7,3,6,2,5,1,4]=>101010=>010101
[7,3,6,2,5,4,1]=>101011=>010100
[7,3,6,4,1,2,5]=>101100=>010011
[7,3,6,4,1,5,2]=>101101=>010010
[7,3,6,4,2,1,5]=>101110=>010001
[7,3,6,4,2,5,1]=>101101=>010010
[7,3,6,4,5,1,2]=>101010=>010101
[7,3,6,4,5,2,1]=>101011=>010100
[7,3,6,5,1,2,4]=>101100=>010011
[7,3,6,5,1,4,2]=>101101=>010010
[7,3,6,5,2,1,4]=>101110=>010001
[7,3,6,5,2,4,1]=>101101=>010010
[7,3,6,5,4,1,2]=>101110=>010001
[7,3,6,5,4,2,1]=>101111=>010000
[7,4,1,2,3,5,6]=>110000=>001111
[7,4,1,2,3,6,5]=>110001=>001110
[7,4,1,2,5,3,6]=>110010=>001101
[7,4,1,2,5,6,3]=>110001=>001110
[7,4,1,2,6,3,5]=>110010=>001101
[7,4,1,2,6,5,3]=>110011=>001100
[7,4,1,3,2,5,6]=>110100=>001011
[7,4,1,3,2,6,5]=>110101=>001010
[7,4,1,3,5,2,6]=>110010=>001101
[7,4,1,3,5,6,2]=>110001=>001110
[7,4,1,3,6,2,5]=>110010=>001101
[7,4,1,3,6,5,2]=>110011=>001100
[7,4,1,5,2,3,6]=>110100=>001011
[7,4,1,5,2,6,3]=>110101=>001010
[7,4,1,5,3,2,6]=>110110=>001001
[7,4,1,5,3,6,2]=>110101=>001010
[7,4,1,5,6,2,3]=>110010=>001101
[7,4,1,5,6,3,2]=>110011=>001100
[7,4,1,6,2,3,5]=>110100=>001011
[7,4,1,6,2,5,3]=>110101=>001010
[7,4,1,6,3,2,5]=>110110=>001001
[7,4,1,6,3,5,2]=>110101=>001010
[7,4,1,6,5,2,3]=>110110=>001001
[7,4,1,6,5,3,2]=>110111=>001000
[7,4,2,1,3,5,6]=>111000=>000111
[7,4,2,1,3,6,5]=>111001=>000110
[7,4,2,1,5,3,6]=>111010=>000101
[7,4,2,1,5,6,3]=>111001=>000110
[7,4,2,1,6,3,5]=>111010=>000101
[7,4,2,1,6,5,3]=>111011=>000100
[7,4,2,3,1,5,6]=>110100=>001011
[7,4,2,3,1,6,5]=>110101=>001010
[7,4,2,3,5,1,6]=>110010=>001101
[7,4,2,3,5,6,1]=>110001=>001110
[7,4,2,3,6,1,5]=>110010=>001101
[7,4,2,3,6,5,1]=>110011=>001100
[7,4,2,5,1,3,6]=>110100=>001011
[7,4,2,5,1,6,3]=>110101=>001010
[7,4,2,5,3,1,6]=>110110=>001001
[7,4,2,5,3,6,1]=>110101=>001010
[7,4,2,5,6,1,3]=>110010=>001101
[7,4,2,5,6,3,1]=>110011=>001100
[7,4,2,6,1,3,5]=>110100=>001011
[7,4,2,6,1,5,3]=>110101=>001010
[7,4,2,6,3,1,5]=>110110=>001001
[7,4,2,6,3,5,1]=>110101=>001010
[7,4,2,6,5,1,3]=>110110=>001001
[7,4,2,6,5,3,1]=>110111=>001000
[7,4,3,1,2,5,6]=>111000=>000111
[7,4,3,1,2,6,5]=>111001=>000110
[7,4,3,1,5,2,6]=>111010=>000101
[7,4,3,1,5,6,2]=>111001=>000110
[7,4,3,1,6,2,5]=>111010=>000101
[7,4,3,1,6,5,2]=>111011=>000100
[7,4,3,2,1,5,6]=>111100=>000011
[7,4,3,2,1,6,5]=>111101=>000010
[7,4,3,2,5,1,6]=>111010=>000101
[7,4,3,2,5,6,1]=>111001=>000110
[7,4,3,2,6,1,5]=>111010=>000101
[7,4,3,2,6,5,1]=>111011=>000100
[7,4,3,5,1,2,6]=>110100=>001011
[7,4,3,5,1,6,2]=>110101=>001010
[7,4,3,5,2,1,6]=>110110=>001001
[7,4,3,5,2,6,1]=>110101=>001010
[7,4,3,5,6,1,2]=>110010=>001101
[7,4,3,5,6,2,1]=>110011=>001100
[7,4,3,6,1,2,5]=>110100=>001011
[7,4,3,6,1,5,2]=>110101=>001010
[7,4,3,6,2,1,5]=>110110=>001001
[7,4,3,6,2,5,1]=>110101=>001010
[7,4,3,6,5,1,2]=>110110=>001001
[7,4,3,6,5,2,1]=>110111=>001000
[7,4,5,1,2,3,6]=>101000=>010111
[7,4,5,1,2,6,3]=>101001=>010110
[7,4,5,1,3,2,6]=>101010=>010101
[7,4,5,1,3,6,2]=>101001=>010110
[7,4,5,1,6,2,3]=>101010=>010101
[7,4,5,1,6,3,2]=>101011=>010100
[7,4,5,2,1,3,6]=>101100=>010011
[7,4,5,2,1,6,3]=>101101=>010010
[7,4,5,2,3,1,6]=>101010=>010101
[7,4,5,2,3,6,1]=>101001=>010110
[7,4,5,2,6,1,3]=>101010=>010101
[7,4,5,2,6,3,1]=>101011=>010100
[7,4,5,3,1,2,6]=>101100=>010011
[7,4,5,3,1,6,2]=>101101=>010010
[7,4,5,3,2,1,6]=>101110=>010001
[7,4,5,3,2,6,1]=>101101=>010010
[7,4,5,3,6,1,2]=>101010=>010101
[7,4,5,3,6,2,1]=>101011=>010100
[7,4,5,6,1,2,3]=>100100=>011011
[7,4,5,6,1,3,2]=>100101=>011010
[7,4,5,6,2,1,3]=>100110=>011001
[7,4,5,6,2,3,1]=>100101=>011010
[7,4,5,6,3,1,2]=>100110=>011001
[7,4,5,6,3,2,1]=>100111=>011000
[7,4,6,1,2,3,5]=>101000=>010111
[7,4,6,1,2,5,3]=>101001=>010110
[7,4,6,1,3,2,5]=>101010=>010101
[7,4,6,1,3,5,2]=>101001=>010110
[7,4,6,1,5,2,3]=>101010=>010101
[7,4,6,1,5,3,2]=>101011=>010100
[7,4,6,2,1,3,5]=>101100=>010011
[7,4,6,2,1,5,3]=>101101=>010010
[7,4,6,2,3,1,5]=>101010=>010101
[7,4,6,2,3,5,1]=>101001=>010110
[7,4,6,2,5,1,3]=>101010=>010101
[7,4,6,2,5,3,1]=>101011=>010100
[7,4,6,3,1,2,5]=>101100=>010011
[7,4,6,3,1,5,2]=>101101=>010010
[7,4,6,3,2,1,5]=>101110=>010001
[7,4,6,3,2,5,1]=>101101=>010010
[7,4,6,3,5,1,2]=>101010=>010101
[7,4,6,3,5,2,1]=>101011=>010100
[7,4,6,5,1,2,3]=>101100=>010011
[7,4,6,5,1,3,2]=>101101=>010010
[7,4,6,5,2,1,3]=>101110=>010001
[7,4,6,5,2,3,1]=>101101=>010010
[7,4,6,5,3,1,2]=>101110=>010001
[7,4,6,5,3,2,1]=>101111=>010000
[7,5,1,2,3,4,6]=>110000=>001111
[7,5,1,2,3,6,4]=>110001=>001110
[7,5,1,2,4,3,6]=>110010=>001101
[7,5,1,2,4,6,3]=>110001=>001110
[7,5,1,2,6,3,4]=>110010=>001101
[7,5,1,2,6,4,3]=>110011=>001100
[7,5,1,3,2,4,6]=>110100=>001011
[7,5,1,3,2,6,4]=>110101=>001010
[7,5,1,3,4,2,6]=>110010=>001101
[7,5,1,3,4,6,2]=>110001=>001110
[7,5,1,3,6,2,4]=>110010=>001101
[7,5,1,3,6,4,2]=>110011=>001100
[7,5,1,4,2,3,6]=>110100=>001011
[7,5,1,4,2,6,3]=>110101=>001010
[7,5,1,4,3,2,6]=>110110=>001001
[7,5,1,4,3,6,2]=>110101=>001010
[7,5,1,4,6,2,3]=>110010=>001101
[7,5,1,4,6,3,2]=>110011=>001100
[7,5,1,6,2,3,4]=>110100=>001011
[7,5,1,6,2,4,3]=>110101=>001010
[7,5,1,6,3,2,4]=>110110=>001001
[7,5,1,6,3,4,2]=>110101=>001010
[7,5,1,6,4,2,3]=>110110=>001001
[7,5,1,6,4,3,2]=>110111=>001000
[7,5,2,1,3,4,6]=>111000=>000111
[7,5,2,1,3,6,4]=>111001=>000110
[7,5,2,1,4,3,6]=>111010=>000101
[7,5,2,1,4,6,3]=>111001=>000110
[7,5,2,1,6,3,4]=>111010=>000101
[7,5,2,1,6,4,3]=>111011=>000100
[7,5,2,3,1,4,6]=>110100=>001011
[7,5,2,3,1,6,4]=>110101=>001010
[7,5,2,3,4,1,6]=>110010=>001101
[7,5,2,3,4,6,1]=>110001=>001110
[7,5,2,3,6,1,4]=>110010=>001101
[7,5,2,3,6,4,1]=>110011=>001100
[7,5,2,4,1,3,6]=>110100=>001011
[7,5,2,4,1,6,3]=>110101=>001010
[7,5,2,4,3,1,6]=>110110=>001001
[7,5,2,4,3,6,1]=>110101=>001010
[7,5,2,4,6,1,3]=>110010=>001101
[7,5,2,4,6,3,1]=>110011=>001100
[7,5,2,6,1,3,4]=>110100=>001011
[7,5,2,6,1,4,3]=>110101=>001010
[7,5,2,6,3,1,4]=>110110=>001001
[7,5,2,6,3,4,1]=>110101=>001010
[7,5,2,6,4,1,3]=>110110=>001001
[7,5,2,6,4,3,1]=>110111=>001000
[7,5,3,1,2,4,6]=>111000=>000111
[7,5,3,1,2,6,4]=>111001=>000110
[7,5,3,1,4,2,6]=>111010=>000101
[7,5,3,1,4,6,2]=>111001=>000110
[7,5,3,1,6,2,4]=>111010=>000101
[7,5,3,1,6,4,2]=>111011=>000100
[7,5,3,2,1,4,6]=>111100=>000011
[7,5,3,2,1,6,4]=>111101=>000010
[7,5,3,2,4,1,6]=>111010=>000101
[7,5,3,2,4,6,1]=>111001=>000110
[7,5,3,2,6,1,4]=>111010=>000101
[7,5,3,2,6,4,1]=>111011=>000100
[7,5,3,4,1,2,6]=>110100=>001011
[7,5,3,4,1,6,2]=>110101=>001010
[7,5,3,4,2,1,6]=>110110=>001001
[7,5,3,4,2,6,1]=>110101=>001010
[7,5,3,4,6,1,2]=>110010=>001101
[7,5,3,4,6,2,1]=>110011=>001100
[7,5,3,6,1,2,4]=>110100=>001011
[7,5,3,6,1,4,2]=>110101=>001010
[7,5,3,6,2,1,4]=>110110=>001001
[7,5,3,6,2,4,1]=>110101=>001010
[7,5,3,6,4,1,2]=>110110=>001001
[7,5,3,6,4,2,1]=>110111=>001000
[7,5,4,1,2,3,6]=>111000=>000111
[7,5,4,1,2,6,3]=>111001=>000110
[7,5,4,1,3,2,6]=>111010=>000101
[7,5,4,1,3,6,2]=>111001=>000110
[7,5,4,1,6,2,3]=>111010=>000101
[7,5,4,1,6,3,2]=>111011=>000100
[7,5,4,2,1,3,6]=>111100=>000011
[7,5,4,2,1,6,3]=>111101=>000010
[7,5,4,2,3,1,6]=>111010=>000101
[7,5,4,2,3,6,1]=>111001=>000110
[7,5,4,2,6,1,3]=>111010=>000101
[7,5,4,2,6,3,1]=>111011=>000100
[7,5,4,3,1,2,6]=>111100=>000011
[7,5,4,3,1,6,2]=>111101=>000010
[7,5,4,3,2,1,6]=>111110=>000001
[7,5,4,3,2,6,1]=>111101=>000010
[7,5,4,3,6,1,2]=>111010=>000101
[7,5,4,3,6,2,1]=>111011=>000100
[7,5,4,6,1,2,3]=>110100=>001011
[7,5,4,6,1,3,2]=>110101=>001010
[7,5,4,6,2,1,3]=>110110=>001001
[7,5,4,6,2,3,1]=>110101=>001010
[7,5,4,6,3,1,2]=>110110=>001001
[7,5,4,6,3,2,1]=>110111=>001000
[7,5,6,1,2,3,4]=>101000=>010111
[7,5,6,1,2,4,3]=>101001=>010110
[7,5,6,1,3,2,4]=>101010=>010101
[7,5,6,1,3,4,2]=>101001=>010110
[7,5,6,1,4,2,3]=>101010=>010101
[7,5,6,1,4,3,2]=>101011=>010100
[7,5,6,2,1,3,4]=>101100=>010011
[7,5,6,2,1,4,3]=>101101=>010010
[7,5,6,2,3,1,4]=>101010=>010101
[7,5,6,2,3,4,1]=>101001=>010110
[7,5,6,2,4,1,3]=>101010=>010101
[7,5,6,2,4,3,1]=>101011=>010100
[7,5,6,3,1,2,4]=>101100=>010011
[7,5,6,3,1,4,2]=>101101=>010010
[7,5,6,3,2,1,4]=>101110=>010001
[7,5,6,3,2,4,1]=>101101=>010010
[7,5,6,3,4,1,2]=>101010=>010101
[7,5,6,3,4,2,1]=>101011=>010100
[7,5,6,4,1,2,3]=>101100=>010011
[7,5,6,4,1,3,2]=>101101=>010010
[7,5,6,4,2,1,3]=>101110=>010001
[7,5,6,4,2,3,1]=>101101=>010010
[7,5,6,4,3,1,2]=>101110=>010001
[7,5,6,4,3,2,1]=>101111=>010000
[7,6,1,2,3,4,5]=>110000=>001111
[7,6,1,2,3,5,4]=>110001=>001110
[7,6,1,2,4,3,5]=>110010=>001101
[7,6,1,2,4,5,3]=>110001=>001110
[7,6,1,2,5,3,4]=>110010=>001101
[7,6,1,2,5,4,3]=>110011=>001100
[7,6,1,3,2,4,5]=>110100=>001011
[7,6,1,3,2,5,4]=>110101=>001010
[7,6,1,3,4,2,5]=>110010=>001101
[7,6,1,3,4,5,2]=>110001=>001110
[7,6,1,3,5,2,4]=>110010=>001101
[7,6,1,3,5,4,2]=>110011=>001100
[7,6,1,4,2,3,5]=>110100=>001011
[7,6,1,4,2,5,3]=>110101=>001010
[7,6,1,4,3,2,5]=>110110=>001001
[7,6,1,4,3,5,2]=>110101=>001010
[7,6,1,4,5,2,3]=>110010=>001101
[7,6,1,4,5,3,2]=>110011=>001100
[7,6,1,5,2,3,4]=>110100=>001011
[7,6,1,5,2,4,3]=>110101=>001010
[7,6,1,5,3,2,4]=>110110=>001001
[7,6,1,5,3,4,2]=>110101=>001010
[7,6,1,5,4,2,3]=>110110=>001001
[7,6,1,5,4,3,2]=>110111=>001000
[7,6,2,1,3,4,5]=>111000=>000111
[7,6,2,1,3,5,4]=>111001=>000110
[7,6,2,1,4,3,5]=>111010=>000101
[7,6,2,1,4,5,3]=>111001=>000110
[7,6,2,1,5,3,4]=>111010=>000101
[7,6,2,1,5,4,3]=>111011=>000100
[7,6,2,3,1,4,5]=>110100=>001011
[7,6,2,3,1,5,4]=>110101=>001010
[7,6,2,3,4,1,5]=>110010=>001101
[7,6,2,3,4,5,1]=>110001=>001110
[7,6,2,3,5,1,4]=>110010=>001101
[7,6,2,3,5,4,1]=>110011=>001100
[7,6,2,4,1,3,5]=>110100=>001011
[7,6,2,4,1,5,3]=>110101=>001010
[7,6,2,4,3,1,5]=>110110=>001001
[7,6,2,4,3,5,1]=>110101=>001010
[7,6,2,4,5,1,3]=>110010=>001101
[7,6,2,4,5,3,1]=>110011=>001100
[7,6,2,5,1,3,4]=>110100=>001011
[7,6,2,5,1,4,3]=>110101=>001010
[7,6,2,5,3,1,4]=>110110=>001001
[7,6,2,5,3,4,1]=>110101=>001010
[7,6,2,5,4,1,3]=>110110=>001001
[7,6,2,5,4,3,1]=>110111=>001000
[7,6,3,1,2,4,5]=>111000=>000111
[7,6,3,1,2,5,4]=>111001=>000110
[7,6,3,1,4,2,5]=>111010=>000101
[7,6,3,1,4,5,2]=>111001=>000110
[7,6,3,1,5,2,4]=>111010=>000101
[7,6,3,1,5,4,2]=>111011=>000100
[7,6,3,2,1,4,5]=>111100=>000011
[7,6,3,2,1,5,4]=>111101=>000010
[7,6,3,2,4,1,5]=>111010=>000101
[7,6,3,2,4,5,1]=>111001=>000110
[7,6,3,2,5,1,4]=>111010=>000101
[7,6,3,2,5,4,1]=>111011=>000100
[7,6,3,4,1,2,5]=>110100=>001011
[7,6,3,4,1,5,2]=>110101=>001010
[7,6,3,4,2,1,5]=>110110=>001001
[7,6,3,4,2,5,1]=>110101=>001010
[7,6,3,4,5,1,2]=>110010=>001101
[7,6,3,4,5,2,1]=>110011=>001100
[7,6,3,5,1,2,4]=>110100=>001011
[7,6,3,5,1,4,2]=>110101=>001010
[7,6,3,5,2,1,4]=>110110=>001001
[7,6,3,5,2,4,1]=>110101=>001010
[7,6,3,5,4,1,2]=>110110=>001001
[7,6,3,5,4,2,1]=>110111=>001000
[7,6,4,1,2,3,5]=>111000=>000111
[7,6,4,1,2,5,3]=>111001=>000110
[7,6,4,1,3,2,5]=>111010=>000101
[7,6,4,1,3,5,2]=>111001=>000110
[7,6,4,1,5,2,3]=>111010=>000101
[7,6,4,1,5,3,2]=>111011=>000100
[7,6,4,2,1,3,5]=>111100=>000011
[7,6,4,2,1,5,3]=>111101=>000010
[7,6,4,2,3,1,5]=>111010=>000101
[7,6,4,2,3,5,1]=>111001=>000110
[7,6,4,2,5,1,3]=>111010=>000101
[7,6,4,2,5,3,1]=>111011=>000100
[7,6,4,3,1,2,5]=>111100=>000011
[7,6,4,3,1,5,2]=>111101=>000010
[7,6,4,3,2,1,5]=>111110=>000001
[7,6,4,3,2,5,1]=>111101=>000010
[7,6,4,3,5,1,2]=>111010=>000101
[7,6,4,3,5,2,1]=>111011=>000100
[7,6,4,5,1,2,3]=>110100=>001011
[7,6,4,5,1,3,2]=>110101=>001010
[7,6,4,5,2,1,3]=>110110=>001001
[7,6,4,5,2,3,1]=>110101=>001010
[7,6,4,5,3,1,2]=>110110=>001001
[7,6,4,5,3,2,1]=>110111=>001000
[7,6,5,1,2,3,4]=>111000=>000111
[7,6,5,1,2,4,3]=>111001=>000110
[7,6,5,1,3,2,4]=>111010=>000101
[7,6,5,1,3,4,2]=>111001=>000110
[7,6,5,1,4,2,3]=>111010=>000101
[7,6,5,1,4,3,2]=>111011=>000100
[7,6,5,2,1,3,4]=>111100=>000011
[7,6,5,2,1,4,3]=>111101=>000010
[7,6,5,2,3,1,4]=>111010=>000101
[7,6,5,2,3,4,1]=>111001=>000110
[7,6,5,2,4,1,3]=>111010=>000101
[7,6,5,2,4,3,1]=>111011=>000100
[7,6,5,3,1,2,4]=>111100=>000011
[7,6,5,3,1,4,2]=>111101=>000010
[7,6,5,3,2,1,4]=>111110=>000001
[7,6,5,3,2,4,1]=>111101=>000010
[7,6,5,3,4,1,2]=>111010=>000101
[7,6,5,3,4,2,1]=>111011=>000100
[7,6,5,4,1,2,3]=>111100=>000011
[7,6,5,4,1,3,2]=>111101=>000010
[7,6,5,4,2,1,3]=>111110=>000001
[7,6,5,4,2,3,1]=>111101=>000010
[7,6,5,4,3,1,2]=>111110=>000001
[7,6,5,4,3,2,1]=>111111=>000000
[8,7,6,5,4,3,2,1]=>1111111=>0000000
[7,8,6,5,4,3,2,1]=>0111111=>1000000
[8,6,7,5,4,3,2,1]=>1011111=>0100000
[7,6,8,5,4,3,2,1]=>1011111=>0100000
[6,7,8,5,4,3,2,1]=>0011111=>1100000
[8,7,5,6,4,3,2,1]=>1101111=>0010000
[7,8,5,6,4,3,2,1]=>0101111=>1010000
[8,6,5,7,4,3,2,1]=>1101111=>0010000
[8,5,6,7,4,3,2,1]=>1001111=>0110000
[7,6,5,8,4,3,2,1]=>1101111=>0010000
[6,7,5,8,4,3,2,1]=>0101111=>1010000
[7,5,6,8,4,3,2,1]=>1001111=>0110000
[6,5,7,8,4,3,2,1]=>1001111=>0110000
[5,6,7,8,4,3,2,1]=>0001111=>1110000
[8,7,6,4,5,3,2,1]=>1110111=>0001000
[7,8,6,4,5,3,2,1]=>0110111=>1001000
[8,6,7,4,5,3,2,1]=>1010111=>0101000
[7,6,8,4,5,3,2,1]=>1010111=>0101000
[8,7,5,4,6,3,2,1]=>1110111=>0001000
[8,7,4,5,6,3,2,1]=>1100111=>0011000
[8,6,5,4,7,3,2,1]=>1110111=>0001000
[8,5,6,4,7,3,2,1]=>1010111=>0101000
[8,6,4,5,7,3,2,1]=>1100111=>0011000
[8,5,4,6,7,3,2,1]=>1100111=>0011000
[8,4,5,6,7,3,2,1]=>1000111=>0111000
[7,6,5,4,8,3,2,1]=>1110111=>0001000
[6,7,5,4,8,3,2,1]=>0110111=>1001000
[7,5,6,4,8,3,2,1]=>1010111=>0101000
[6,5,7,4,8,3,2,1]=>1010111=>0101000
[5,6,7,4,8,3,2,1]=>0010111=>1101000
[7,6,4,5,8,3,2,1]=>1100111=>0011000
[6,7,4,5,8,3,2,1]=>0100111=>1011000
[7,5,4,6,8,3,2,1]=>1100111=>0011000
[7,4,5,6,8,3,2,1]=>1000111=>0111000
[6,5,4,7,8,3,2,1]=>1100111=>0011000
[5,6,4,7,8,3,2,1]=>0100111=>1011000
[6,4,5,7,8,3,2,1]=>1000111=>0111000
[5,4,6,7,8,3,2,1]=>1000111=>0111000
[4,5,6,7,8,3,2,1]=>0000111=>1111000
[8,7,6,5,3,4,2,1]=>1111011=>0000100
[7,8,6,5,3,4,2,1]=>0111011=>1000100
[8,6,7,5,3,4,2,1]=>1011011=>0100100
[7,6,8,5,3,4,2,1]=>1011011=>0100100
[8,7,5,6,3,4,2,1]=>1101011=>0010100
[7,8,5,6,3,4,2,1]=>0101011=>1010100
[8,5,6,7,3,4,2,1]=>1001011=>0110100
[7,6,5,8,3,4,2,1]=>1101011=>0010100
[6,7,5,8,3,4,2,1]=>0101011=>1010100
[6,5,7,8,3,4,2,1]=>1001011=>0110100
[5,6,7,8,3,4,2,1]=>0001011=>1110100
[8,7,6,4,3,5,2,1]=>1111011=>0000100
[7,8,6,4,3,5,2,1]=>0111011=>1000100
[8,6,7,4,3,5,2,1]=>1011011=>0100100
[7,6,8,4,3,5,2,1]=>1011011=>0100100
[6,7,8,4,3,5,2,1]=>0011011=>1100100
[8,7,6,3,4,5,2,1]=>1110011=>0001100
[7,8,6,3,4,5,2,1]=>0110011=>1001100
[8,6,7,3,4,5,2,1]=>1010011=>0101100
[7,6,8,3,4,5,2,1]=>1010011=>0101100
[6,7,8,3,4,5,2,1]=>0010011=>1101100
[8,7,5,4,3,6,2,1]=>1111011=>0000100
[7,8,5,4,3,6,2,1]=>0111011=>1000100
[8,7,4,5,3,6,2,1]=>1101011=>0010100
[8,7,5,3,4,6,2,1]=>1110011=>0001100
[7,8,5,3,4,6,2,1]=>0110011=>1001100
[8,7,4,3,5,6,2,1]=>1110011=>0001100
[8,7,3,4,5,6,2,1]=>1100011=>0011100
[7,8,3,4,5,6,2,1]=>0100011=>1011100
[8,6,5,4,3,7,2,1]=>1111011=>0000100
[8,6,4,5,3,7,2,1]=>1101011=>0010100
[8,6,4,3,5,7,2,1]=>1110011=>0001100
[8,5,4,3,6,7,2,1]=>1110011=>0001100
[8,5,3,4,6,7,2,1]=>1100011=>0011100
[8,4,3,5,6,7,2,1]=>1100011=>0011100
[8,3,4,5,6,7,2,1]=>1000011=>0111100
[7,6,5,4,3,8,2,1]=>1111011=>0000100
[6,7,5,4,3,8,2,1]=>0111011=>1000100
[7,5,6,4,3,8,2,1]=>1011011=>0100100
[6,5,7,4,3,8,2,1]=>1011011=>0100100
[5,6,7,4,3,8,2,1]=>0011011=>1100100
[6,7,4,5,3,8,2,1]=>0101011=>1010100
[7,5,4,6,3,8,2,1]=>1101011=>0010100
[7,4,5,6,3,8,2,1]=>1001011=>0110100
[6,5,4,7,3,8,2,1]=>1101011=>0010100
[6,4,5,7,3,8,2,1]=>1001011=>0110100
[5,4,6,7,3,8,2,1]=>1001011=>0110100
[4,5,6,7,3,8,2,1]=>0001011=>1110100
[7,6,5,3,4,8,2,1]=>1110011=>0001100
[7,6,4,3,5,8,2,1]=>1110011=>0001100
[7,6,3,4,5,8,2,1]=>1100011=>0011100
[7,5,4,3,6,8,2,1]=>1110011=>0001100
[7,5,3,4,6,8,2,1]=>1100011=>0011100
[7,3,4,5,6,8,2,1]=>1000011=>0111100
[6,5,4,3,7,8,2,1]=>1110011=>0001100
[4,5,6,3,7,8,2,1]=>0010011=>1101100
[6,5,3,4,7,8,2,1]=>1100011=>0011100
[6,3,4,5,7,8,2,1]=>1000011=>0111100
[5,4,3,6,7,8,2,1]=>1100011=>0011100
[5,3,4,6,7,8,2,1]=>1000011=>0111100
[4,3,5,6,7,8,2,1]=>1000011=>0111100
[3,4,5,6,7,8,2,1]=>0000011=>1111100
[8,7,6,5,4,2,3,1]=>1111101=>0000010
[7,8,6,5,4,2,3,1]=>0111101=>1000010
[8,6,7,5,4,2,3,1]=>1011101=>0100010
[7,6,8,5,4,2,3,1]=>1011101=>0100010
[8,7,5,6,4,2,3,1]=>1101101=>0010010
[8,6,5,7,4,2,3,1]=>1101101=>0010010
[8,5,6,7,4,2,3,1]=>1001101=>0110010
[7,6,5,8,4,2,3,1]=>1101101=>0010010
[6,7,5,8,4,2,3,1]=>0101101=>1010010
[7,5,6,8,4,2,3,1]=>1001101=>0110010
[5,6,7,8,4,2,3,1]=>0001101=>1110010
[8,7,6,4,5,2,3,1]=>1110101=>0001010
[8,6,7,4,5,2,3,1]=>1010101=>0101010
[7,6,8,4,5,2,3,1]=>1010101=>0101010
[8,7,5,4,6,2,3,1]=>1110101=>0001010
[8,7,4,5,6,2,3,1]=>1100101=>0011010
[7,8,4,5,6,2,3,1]=>0100101=>1011010
[8,6,5,4,7,2,3,1]=>1110101=>0001010
[8,5,6,4,7,2,3,1]=>1010101=>0101010
[8,6,4,5,7,2,3,1]=>1100101=>0011010
[8,4,5,6,7,2,3,1]=>1000101=>0111010
[7,6,5,4,8,2,3,1]=>1110101=>0001010
[7,5,6,4,8,2,3,1]=>1010101=>0101010
[6,5,7,4,8,2,3,1]=>1010101=>0101010
[6,7,4,5,8,2,3,1]=>0100101=>1011010
[4,5,6,7,8,2,3,1]=>0000101=>1111010
[8,7,6,5,3,2,4,1]=>1111101=>0000010
[7,8,6,5,3,2,4,1]=>0111101=>1000010
[8,6,7,5,3,2,4,1]=>1011101=>0100010
[7,6,8,5,3,2,4,1]=>1011101=>0100010
[6,7,8,5,3,2,4,1]=>0011101=>1100010
[8,7,5,6,3,2,4,1]=>1101101=>0010010
[8,6,5,7,3,2,4,1]=>1101101=>0010010
[8,5,6,7,3,2,4,1]=>1001101=>0110010
[7,6,5,8,3,2,4,1]=>1101101=>0010010
[6,7,5,8,3,2,4,1]=>0101101=>1010010
[5,6,7,8,3,2,4,1]=>0001101=>1110010
[8,7,6,5,2,3,4,1]=>1111001=>0000110
[8,6,7,5,2,3,4,1]=>1011001=>0100110
[7,6,8,5,2,3,4,1]=>1011001=>0100110
[6,7,8,5,2,3,4,1]=>0011001=>1100110
[8,7,5,6,2,3,4,1]=>1101001=>0010110
[7,8,5,6,2,3,4,1]=>0101001=>1010110
[8,6,5,7,2,3,4,1]=>1101001=>0010110
[8,5,6,7,2,3,4,1]=>1001001=>0110110
[7,6,5,8,2,3,4,1]=>1101001=>0010110
[6,7,5,8,2,3,4,1]=>0101001=>1010110
[6,5,7,8,2,3,4,1]=>1001001=>0110110
[5,6,7,8,2,3,4,1]=>0001001=>1110110
[8,7,6,4,3,2,5,1]=>1111101=>0000010
[7,8,6,4,3,2,5,1]=>0111101=>1000010
[8,6,7,4,3,2,5,1]=>1011101=>0100010
[7,6,8,4,3,2,5,1]=>1011101=>0100010
[6,7,8,4,3,2,5,1]=>0011101=>1100010
[8,7,6,3,4,2,5,1]=>1110101=>0001010
[7,8,6,3,4,2,5,1]=>0110101=>1001010
[8,6,7,3,4,2,5,1]=>1010101=>0101010
[7,6,8,3,4,2,5,1]=>1010101=>0101010
[6,7,8,3,4,2,5,1]=>0010101=>1101010
[8,7,6,4,2,3,5,1]=>1111001=>0000110
[8,6,7,4,2,3,5,1]=>1011001=>0100110
[7,6,8,4,2,3,5,1]=>1011001=>0100110
[6,7,8,4,2,3,5,1]=>0011001=>1100110
[8,7,6,3,2,4,5,1]=>1111001=>0000110
[7,8,6,3,2,4,5,1]=>0111001=>1000110
[8,6,7,3,2,4,5,1]=>1011001=>0100110
[6,7,8,3,2,4,5,1]=>0011001=>1100110
[8,7,6,2,3,4,5,1]=>1110001=>0001110
[7,8,6,2,3,4,5,1]=>0110001=>1001110
[8,6,7,2,3,4,5,1]=>1010001=>0101110
[7,6,8,2,3,4,5,1]=>1010001=>0101110
[6,7,8,2,3,4,5,1]=>0010001=>1101110
[8,7,5,4,3,2,6,1]=>1111101=>0000010
[7,8,5,4,3,2,6,1]=>0111101=>1000010
[8,7,5,3,4,2,6,1]=>1110101=>0001010
[7,8,5,3,4,2,6,1]=>0110101=>1001010
[8,7,4,3,5,2,6,1]=>1110101=>0001010
[8,7,5,3,2,4,6,1]=>1111001=>0000110
[8,7,4,3,2,5,6,1]=>1111001=>0000110
[7,8,4,3,2,5,6,1]=>0111001=>1000110
[7,8,3,4,2,5,6,1]=>0101001=>1010110
[7,8,4,2,3,5,6,1]=>0110001=>1001110
[7,8,3,2,4,5,6,1]=>0110001=>1001110
[8,7,2,3,4,5,6,1]=>1100001=>0011110
[7,8,2,3,4,5,6,1]=>0100001=>1011110
[8,6,5,4,3,2,7,1]=>1111101=>0000010
[8,5,6,4,3,2,7,1]=>1011101=>0100010
[8,6,4,5,3,2,7,1]=>1101101=>0010010
[8,5,4,6,3,2,7,1]=>1101101=>0010010
[8,6,5,3,4,2,7,1]=>1110101=>0001010
[8,5,6,3,4,2,7,1]=>1010101=>0101010
[8,6,4,3,5,2,7,1]=>1110101=>0001010
[8,6,3,4,5,2,7,1]=>1100101=>0011010
[8,5,4,3,6,2,7,1]=>1110101=>0001010
[8,4,5,3,6,2,7,1]=>1010101=>0101010
[8,4,3,5,6,2,7,1]=>1100101=>0011010
[8,3,4,5,6,2,7,1]=>1000101=>0111010
[8,6,5,4,2,3,7,1]=>1111001=>0000110
[8,5,6,4,2,3,7,1]=>1011001=>0100110
[8,6,4,5,2,3,7,1]=>1101001=>0010110
[8,6,5,3,2,4,7,1]=>1111001=>0000110
[8,6,4,3,2,5,7,1]=>1111001=>0000110
[8,6,4,2,3,5,7,1]=>1110001=>0001110
[8,6,2,3,4,5,7,1]=>1100001=>0011110
[8,5,4,3,2,6,7,1]=>1111001=>0000110
[8,4,5,3,2,6,7,1]=>1011001=>0100110
[8,5,3,4,2,6,7,1]=>1101001=>0010110
[8,3,4,5,2,6,7,1]=>1001001=>0110110
[8,5,4,2,3,6,7,1]=>1110001=>0001110
[8,4,5,2,3,6,7,1]=>1010001=>0101110
[8,5,2,3,4,6,7,1]=>1100001=>0011110
[8,4,3,2,5,6,7,1]=>1110001=>0001110
[8,3,4,2,5,6,7,1]=>1010001=>0101110
[8,4,2,3,5,6,7,1]=>1100001=>0011110
[8,3,2,4,5,6,7,1]=>1100001=>0011110
[8,2,3,4,5,6,7,1]=>1000001=>0111110
[7,6,5,4,3,2,8,1]=>1111101=>0000010
[6,7,5,4,3,2,8,1]=>0111101=>1000010
[7,5,6,4,3,2,8,1]=>1011101=>0100010
[6,5,7,4,3,2,8,1]=>1011101=>0100010
[5,6,7,4,3,2,8,1]=>0011101=>1100010
[7,6,4,5,3,2,8,1]=>1101101=>0010010
[6,7,4,5,3,2,8,1]=>0101101=>1010010
[7,4,5,6,3,2,8,1]=>1001101=>0110010
[6,5,4,7,3,2,8,1]=>1101101=>0010010
[6,4,5,7,3,2,8,1]=>1001101=>0110010
[4,5,6,7,3,2,8,1]=>0001101=>1110010
[7,6,5,3,4,2,8,1]=>1110101=>0001010
[7,5,6,3,4,2,8,1]=>1010101=>0101010
[6,5,7,3,4,2,8,1]=>1010101=>0101010
[5,6,7,3,4,2,8,1]=>0010101=>1101010
[7,6,4,3,5,2,8,1]=>1110101=>0001010
[7,6,3,4,5,2,8,1]=>1100101=>0011010
[7,5,4,3,6,2,8,1]=>1110101=>0001010
[7,4,5,3,6,2,8,1]=>1010101=>0101010
[7,5,3,4,6,2,8,1]=>1100101=>0011010
[7,3,4,5,6,2,8,1]=>1000101=>0111010
[6,5,4,3,7,2,8,1]=>1110101=>0001010
[6,4,5,3,7,2,8,1]=>1010101=>0101010
[5,4,6,3,7,2,8,1]=>1010101=>0101010
[4,5,6,3,7,2,8,1]=>0010101=>1101010
[6,5,3,4,7,2,8,1]=>1100101=>0011010
[5,6,3,4,7,2,8,1]=>0100101=>1011010
[6,4,3,5,7,2,8,1]=>1100101=>0011010
[6,3,4,5,7,2,8,1]=>1000101=>0111010
[5,4,3,6,7,2,8,1]=>1100101=>0011010
[4,5,3,6,7,2,8,1]=>0100101=>1011010
[4,3,5,6,7,2,8,1]=>1000101=>0111010
[3,4,5,6,7,2,8,1]=>0000101=>1111010
[7,6,5,4,2,3,8,1]=>1111001=>0000110
[6,7,5,4,2,3,8,1]=>0111001=>1000110
[7,5,6,4,2,3,8,1]=>1011001=>0100110
[6,5,7,4,2,3,8,1]=>1011001=>0100110
[5,6,7,4,2,3,8,1]=>0011001=>1100110
[7,6,4,5,2,3,8,1]=>1101001=>0010110
[6,7,4,5,2,3,8,1]=>0101001=>1010110
[7,5,4,6,2,3,8,1]=>1101001=>0010110
[7,4,5,6,2,3,8,1]=>1001001=>0110110
[6,5,4,7,2,3,8,1]=>1101001=>0010110
[5,6,4,7,2,3,8,1]=>0101001=>1010110
[6,4,5,7,2,3,8,1]=>1001001=>0110110
[5,4,6,7,2,3,8,1]=>1001001=>0110110
[4,5,6,7,2,3,8,1]=>0001001=>1110110
[7,6,5,3,2,4,8,1]=>1111001=>0000110
[6,7,5,3,2,4,8,1]=>0111001=>1000110
[6,5,7,3,2,4,8,1]=>1011001=>0100110
[7,6,5,2,3,4,8,1]=>1110001=>0001110
[7,5,6,2,3,4,8,1]=>1010001=>0101110
[5,6,7,2,3,4,8,1]=>0010001=>1101110
[6,7,4,3,2,5,8,1]=>0111001=>1000110
[7,6,4,2,3,5,8,1]=>1110001=>0001110
[7,6,3,2,4,5,8,1]=>1110001=>0001110
[6,7,3,2,4,5,8,1]=>0110001=>1001110
[7,6,2,3,4,5,8,1]=>1100001=>0011110
[6,7,2,3,4,5,8,1]=>0100001=>1011110
[7,5,4,3,2,6,8,1]=>1111001=>0000110
[7,4,3,5,2,6,8,1]=>1101001=>0010110
[7,5,4,2,3,6,8,1]=>1110001=>0001110
[7,4,5,2,3,6,8,1]=>1010001=>0101110
[7,5,3,2,4,6,8,1]=>1110001=>0001110
[7,5,2,3,4,6,8,1]=>1100001=>0011110
[7,4,3,2,5,6,8,1]=>1110001=>0001110
[7,4,2,3,5,6,8,1]=>1100001=>0011110
[7,3,2,4,5,6,8,1]=>1100001=>0011110
[7,2,3,4,5,6,8,1]=>1000001=>0111110
[6,5,4,3,2,7,8,1]=>1111001=>0000110
[5,4,6,3,2,7,8,1]=>1011001=>0100110
[4,5,6,3,2,7,8,1]=>0011001=>1100110
[6,5,3,4,2,7,8,1]=>1101001=>0010110
[6,3,4,5,2,7,8,1]=>1001001=>0110110
[5,4,3,6,2,7,8,1]=>1101001=>0010110
[4,3,5,6,2,7,8,1]=>1001001=>0110110
[3,4,5,6,2,7,8,1]=>0001001=>1110110
[6,5,4,2,3,7,8,1]=>1110001=>0001110
[5,6,4,2,3,7,8,1]=>0110001=>1001110
[6,4,5,2,3,7,8,1]=>1010001=>0101110
[5,4,6,2,3,7,8,1]=>1010001=>0101110
[4,5,6,2,3,7,8,1]=>0010001=>1101110
[6,5,3,2,4,7,8,1]=>1110001=>0001110
[6,5,2,3,4,7,8,1]=>1100001=>0011110
[6,2,3,4,5,7,8,1]=>1000001=>0111110
[5,4,3,2,6,7,8,1]=>1110001=>0001110
[4,5,3,2,6,7,8,1]=>0110001=>1001110
[5,3,4,2,6,7,8,1]=>1010001=>0101110
[4,3,5,2,6,7,8,1]=>1010001=>0101110
[3,4,5,2,6,7,8,1]=>0010001=>1101110
[5,4,2,3,6,7,8,1]=>1100001=>0011110
[4,5,2,3,6,7,8,1]=>0100001=>1011110
[5,3,2,4,6,7,8,1]=>1100001=>0011110
[5,2,3,4,6,7,8,1]=>1000001=>0111110
[4,3,2,5,6,7,8,1]=>1100001=>0011110
[3,4,2,5,6,7,8,1]=>0100001=>1011110
[4,2,3,5,6,7,8,1]=>1000001=>0111110
[3,2,4,5,6,7,8,1]=>1000001=>0111110
[2,3,4,5,6,7,8,1]=>0000001=>1111110
[8,7,6,5,4,3,1,2]=>1111110=>0000001
[7,8,6,5,4,3,1,2]=>0111110=>1000001
[8,6,7,5,4,3,1,2]=>1011110=>0100001
[7,6,8,5,4,3,1,2]=>1011110=>0100001
[6,7,8,5,4,3,1,2]=>0011110=>1100001
[8,7,5,6,4,3,1,2]=>1101110=>0010001
[7,8,5,6,4,3,1,2]=>0101110=>1010001
[8,6,5,7,4,3,1,2]=>1101110=>0010001
[7,6,5,8,4,3,1,2]=>1101110=>0010001
[6,7,5,8,4,3,1,2]=>0101110=>1010001
[7,5,6,8,4,3,1,2]=>1001110=>0110001
[6,5,7,8,4,3,1,2]=>1001110=>0110001
[5,6,7,8,4,3,1,2]=>0001110=>1110001
[8,7,6,4,5,3,1,2]=>1110110=>0001001
[7,8,6,4,5,3,1,2]=>0110110=>1001001
[8,6,7,4,5,3,1,2]=>1010110=>0101001
[6,7,8,4,5,3,1,2]=>0010110=>1101001
[8,7,5,4,6,3,1,2]=>1110110=>0001001
[8,5,6,4,7,3,1,2]=>1010110=>0101001
[8,6,4,5,7,3,1,2]=>1100110=>0011001
[8,5,4,6,7,3,1,2]=>1100110=>0011001
[7,6,5,4,8,3,1,2]=>1110110=>0001001
[7,5,6,4,8,3,1,2]=>1010110=>0101001
[6,5,7,4,8,3,1,2]=>1010110=>0101001
[7,6,4,5,8,3,1,2]=>1100110=>0011001
[6,7,4,5,8,3,1,2]=>0100110=>1011001
[6,5,4,7,8,3,1,2]=>1100110=>0011001
[5,6,4,7,8,3,1,2]=>0100110=>1011001
[5,4,6,7,8,3,1,2]=>1000110=>0111001
[4,5,6,7,8,3,1,2]=>0000110=>1111001
[8,7,6,5,3,4,1,2]=>1111010=>0000101
[7,8,6,5,3,4,1,2]=>0111010=>1000101
[7,6,8,5,3,4,1,2]=>1011010=>0100101
[6,7,8,5,3,4,1,2]=>0011010=>1100101
[8,7,5,6,3,4,1,2]=>1101010=>0010101
[7,8,5,6,3,4,1,2]=>0101010=>1010101
[8,6,5,7,3,4,1,2]=>1101010=>0010101
[8,5,6,7,3,4,1,2]=>1001010=>0110101
[7,6,5,8,3,4,1,2]=>1101010=>0010101
[6,7,5,8,3,4,1,2]=>0101010=>1010101
[7,5,6,8,3,4,1,2]=>1001010=>0110101
[6,5,7,8,3,4,1,2]=>1001010=>0110101
[5,6,7,8,3,4,1,2]=>0001010=>1110101
[6,7,8,4,3,5,1,2]=>0011010=>1100101
[8,7,6,3,4,5,1,2]=>1110010=>0001101
[8,6,7,3,4,5,1,2]=>1010010=>0101101
[7,8,5,4,3,6,1,2]=>0111010=>1000101
[8,7,4,5,3,6,1,2]=>1101010=>0010101
[7,8,4,5,3,6,1,2]=>0101010=>1010101
[7,8,5,3,4,6,1,2]=>0110010=>1001101
[8,7,4,3,5,6,1,2]=>1110010=>0001101
[7,8,4,3,5,6,1,2]=>0110010=>1001101
[8,7,3,4,5,6,1,2]=>1100010=>0011101
[7,8,3,4,5,6,1,2]=>0100010=>1011101
[8,6,5,4,3,7,1,2]=>1111010=>0000101
[8,5,4,3,6,7,1,2]=>1110010=>0001101
[8,5,3,4,6,7,1,2]=>1100010=>0011101
[8,4,3,5,6,7,1,2]=>1100010=>0011101
[8,3,4,5,6,7,1,2]=>1000010=>0111101
[7,6,5,4,3,8,1,2]=>1111010=>0000101
[7,5,6,4,3,8,1,2]=>1011010=>0100101
[6,5,7,4,3,8,1,2]=>1011010=>0100101
[5,6,7,4,3,8,1,2]=>0011010=>1100101
[6,7,4,5,3,8,1,2]=>0101010=>1010101
[5,6,4,7,3,8,1,2]=>0101010=>1010101
[5,4,6,7,3,8,1,2]=>1001010=>0110101
[4,5,6,7,3,8,1,2]=>0001010=>1110101
[7,6,5,3,4,8,1,2]=>1110010=>0001101
[7,5,6,3,4,8,1,2]=>1010010=>0101101
[5,6,7,3,4,8,1,2]=>0010010=>1101101
[7,6,4,3,5,8,1,2]=>1110010=>0001101
[7,6,3,4,5,8,1,2]=>1100010=>0011101
[7,5,4,3,6,8,1,2]=>1110010=>0001101
[7,5,3,4,6,8,1,2]=>1100010=>0011101
[7,3,4,5,6,8,1,2]=>1000010=>0111101
[6,5,4,3,7,8,1,2]=>1110010=>0001101
[5,6,4,3,7,8,1,2]=>0110010=>1001101
[5,4,6,3,7,8,1,2]=>1010010=>0101101
[4,5,6,3,7,8,1,2]=>0010010=>1101101
[6,5,3,4,7,8,1,2]=>1100010=>0011101
[5,6,3,4,7,8,1,2]=>0100010=>1011101
[6,4,3,5,7,8,1,2]=>1100010=>0011101
[6,3,4,5,7,8,1,2]=>1000010=>0111101
[5,4,3,6,7,8,1,2]=>1100010=>0011101
[4,5,3,6,7,8,1,2]=>0100010=>1011101
[5,3,4,6,7,8,1,2]=>1000010=>0111101
[4,3,5,6,7,8,1,2]=>1000010=>0111101
[3,4,5,6,7,8,1,2]=>0000010=>1111101
[8,7,6,5,4,2,1,3]=>1111110=>0000001
[7,8,6,5,4,2,1,3]=>0111110=>1000001
[8,6,7,5,4,2,1,3]=>1011110=>0100001
[7,6,8,5,4,2,1,3]=>1011110=>0100001
[6,7,8,5,4,2,1,3]=>0011110=>1100001
[8,7,5,6,4,2,1,3]=>1101110=>0010001
[7,8,5,6,4,2,1,3]=>0101110=>1010001
[8,6,5,7,4,2,1,3]=>1101110=>0010001
[7,6,5,8,4,2,1,3]=>1101110=>0010001
[6,7,5,8,4,2,1,3]=>0101110=>1010001
[7,5,6,8,4,2,1,3]=>1001110=>0110001
[6,5,7,8,4,2,1,3]=>1001110=>0110001
[5,6,7,8,4,2,1,3]=>0001110=>1110001
[8,7,6,4,5,2,1,3]=>1110110=>0001001
[8,6,7,4,5,2,1,3]=>1010110=>0101001
[7,6,8,4,5,2,1,3]=>1010110=>0101001
[8,7,4,5,6,2,1,3]=>1100110=>0011001
[8,6,5,4,7,2,1,3]=>1110110=>0001001
[8,6,4,5,7,2,1,3]=>1100110=>0011001
[8,4,5,6,7,2,1,3]=>1000110=>0111001
[7,6,5,4,8,2,1,3]=>1110110=>0001001
[6,7,5,4,8,2,1,3]=>0110110=>1001001
[7,5,6,4,8,2,1,3]=>1010110=>0101001
[6,5,7,4,8,2,1,3]=>1010110=>0101001
[5,6,7,4,8,2,1,3]=>0010110=>1101001
[7,6,4,5,8,2,1,3]=>1100110=>0011001
[7,4,5,6,8,2,1,3]=>1000110=>0111001
[5,4,6,7,8,2,1,3]=>1000110=>0111001
[4,5,6,7,8,2,1,3]=>0000110=>1111001
[8,7,6,5,4,1,2,3]=>1111100=>0000011
[7,8,6,5,4,1,2,3]=>0111100=>1000011
[7,6,8,5,4,1,2,3]=>1011100=>0100011
[6,7,8,5,4,1,2,3]=>0011100=>1100011
[7,8,5,6,4,1,2,3]=>0101100=>1010011
[8,6,5,7,4,1,2,3]=>1101100=>0010011
[8,5,6,7,4,1,2,3]=>1001100=>0110011
[7,6,5,8,4,1,2,3]=>1101100=>0010011
[6,7,5,8,4,1,2,3]=>0101100=>1010011
[7,5,6,8,4,1,2,3]=>1001100=>0110011
[6,5,7,8,4,1,2,3]=>1001100=>0110011
[5,6,7,8,4,1,2,3]=>0001100=>1110011
[8,7,6,4,5,1,2,3]=>1110100=>0001011
[8,6,7,4,5,1,2,3]=>1010100=>0101011
[6,7,8,4,5,1,2,3]=>0010100=>1101011
[8,7,5,4,6,1,2,3]=>1110100=>0001011
[7,8,5,4,6,1,2,3]=>0110100=>1001011
[8,7,4,5,6,1,2,3]=>1100100=>0011011
[7,8,4,5,6,1,2,3]=>0100100=>1011011
[8,5,6,4,7,1,2,3]=>1010100=>0101011
[8,6,4,5,7,1,2,3]=>1100100=>0011011
[8,5,4,6,7,1,2,3]=>1100100=>0011011
[8,4,5,6,7,1,2,3]=>1000100=>0111011
[7,6,5,4,8,1,2,3]=>1110100=>0001011
[6,7,5,4,8,1,2,3]=>0110100=>1001011
[7,5,6,4,8,1,2,3]=>1010100=>0101011
[6,5,7,4,8,1,2,3]=>1010100=>0101011
[5,6,7,4,8,1,2,3]=>0010100=>1101011
[7,6,4,5,8,1,2,3]=>1100100=>0011011
[6,7,4,5,8,1,2,3]=>0100100=>1011011
[7,5,4,6,8,1,2,3]=>1100100=>0011011
[7,4,5,6,8,1,2,3]=>1000100=>0111011
[6,5,4,7,8,1,2,3]=>1100100=>0011011
[5,6,4,7,8,1,2,3]=>0100100=>1011011
[6,4,5,7,8,1,2,3]=>1000100=>0111011
[5,4,6,7,8,1,2,3]=>1000100=>0111011
[4,5,6,7,8,1,2,3]=>0000100=>1111011
[8,7,6,5,3,2,1,4]=>1111110=>0000001
[7,8,6,5,3,2,1,4]=>0111110=>1000001
[8,6,7,5,3,2,1,4]=>1011110=>0100001
[7,6,8,5,3,2,1,4]=>1011110=>0100001
[6,7,8,5,3,2,1,4]=>0011110=>1100001
[8,7,5,6,3,2,1,4]=>1101110=>0010001
[7,8,5,6,3,2,1,4]=>0101110=>1010001
[8,6,5,7,3,2,1,4]=>1101110=>0010001
[8,5,6,7,3,2,1,4]=>1001110=>0110001
[7,6,5,8,3,2,1,4]=>1101110=>0010001
[6,7,5,8,3,2,1,4]=>0101110=>1010001
[7,5,6,8,3,2,1,4]=>1001110=>0110001
[6,5,7,8,3,2,1,4]=>1001110=>0110001
[5,6,7,8,3,2,1,4]=>0001110=>1110001
[8,7,6,5,2,3,1,4]=>1111010=>0000101
[7,8,6,5,2,3,1,4]=>0111010=>1000101
[8,6,7,5,2,3,1,4]=>1011010=>0100101
[7,6,8,5,2,3,1,4]=>1011010=>0100101
[6,7,8,5,2,3,1,4]=>0011010=>1100101
[8,7,5,6,2,3,1,4]=>1101010=>0010101
[7,8,5,6,2,3,1,4]=>0101010=>1010101
[8,6,5,7,2,3,1,4]=>1101010=>0010101
[8,5,6,7,2,3,1,4]=>1001010=>0110101
[7,6,5,8,2,3,1,4]=>1101010=>0010101
[6,7,5,8,2,3,1,4]=>0101010=>1010101
[7,5,6,8,2,3,1,4]=>1001010=>0110101
[6,5,7,8,2,3,1,4]=>1001010=>0110101
[5,6,7,8,2,3,1,4]=>0001010=>1110101
[8,7,6,5,3,1,2,4]=>1111100=>0000011
[7,8,6,5,3,1,2,4]=>0111100=>1000011
[8,6,7,5,3,1,2,4]=>1011100=>0100011
[7,6,8,5,3,1,2,4]=>1011100=>0100011
[8,7,5,6,3,1,2,4]=>1101100=>0010011
[7,8,5,6,3,1,2,4]=>0101100=>1010011
[7,6,5,8,3,1,2,4]=>1101100=>0010011
[6,7,5,8,3,1,2,4]=>0101100=>1010011
[7,5,6,8,3,1,2,4]=>1001100=>0110011
[6,5,7,8,3,1,2,4]=>1001100=>0110011
[5,6,7,8,3,1,2,4]=>0001100=>1110011
[8,7,6,5,2,1,3,4]=>1111100=>0000011
[7,8,6,5,2,1,3,4]=>0111100=>1000011
[7,6,8,5,2,1,3,4]=>1011100=>0100011
[6,7,8,5,2,1,3,4]=>0011100=>1100011
[8,7,5,6,2,1,3,4]=>1101100=>0010011
[7,8,5,6,2,1,3,4]=>0101100=>1010011
[8,6,5,7,2,1,3,4]=>1101100=>0010011
[8,5,6,7,2,1,3,4]=>1001100=>0110011
[7,6,5,8,2,1,3,4]=>1101100=>0010011
[6,7,5,8,2,1,3,4]=>0101100=>1010011
[7,5,6,8,2,1,3,4]=>1001100=>0110011
[6,5,7,8,2,1,3,4]=>1001100=>0110011
[5,6,7,8,2,1,3,4]=>0001100=>1110011
[8,7,6,5,1,2,3,4]=>1111000=>0000111
[7,8,6,5,1,2,3,4]=>0111000=>1000111
[8,6,7,5,1,2,3,4]=>1011000=>0100111
[7,6,8,5,1,2,3,4]=>1011000=>0100111
[6,7,8,5,1,2,3,4]=>0011000=>1100111
[8,7,5,6,1,2,3,4]=>1101000=>0010111
[7,8,5,6,1,2,3,4]=>0101000=>1010111
[8,6,5,7,1,2,3,4]=>1101000=>0010111
[8,5,6,7,1,2,3,4]=>1001000=>0110111
[7,6,5,8,1,2,3,4]=>1101000=>0010111
[6,7,5,8,1,2,3,4]=>0101000=>1010111
[7,5,6,8,1,2,3,4]=>1001000=>0110111
[6,5,7,8,1,2,3,4]=>1001000=>0110111
[5,6,7,8,1,2,3,4]=>0001000=>1110111
[8,7,6,4,3,2,1,5]=>1111110=>0000001
[7,8,6,4,3,2,1,5]=>0111110=>1000001
[8,6,7,4,3,2,1,5]=>1011110=>0100001
[7,6,8,4,3,2,1,5]=>1011110=>0100001
[6,7,8,4,3,2,1,5]=>0011110=>1100001
[8,7,6,3,4,2,1,5]=>1110110=>0001001
[7,8,6,3,4,2,1,5]=>0110110=>1001001
[6,7,8,3,4,2,1,5]=>0010110=>1101001
[8,7,6,4,2,3,1,5]=>1111010=>0000101
[8,6,7,4,2,3,1,5]=>1011010=>0100101
[7,6,8,4,2,3,1,5]=>1011010=>0100101
[6,7,8,4,2,3,1,5]=>0011010=>1100101
[8,7,6,3,2,4,1,5]=>1111010=>0000101
[8,6,7,3,2,4,1,5]=>1011010=>0100101
[6,7,8,3,2,4,1,5]=>0011010=>1100101
[8,7,6,2,3,4,1,5]=>1110010=>0001101
[8,6,7,2,3,4,1,5]=>1010010=>0101101
[7,6,8,2,3,4,1,5]=>1010010=>0101101
[6,7,8,2,3,4,1,5]=>0010010=>1101101
[8,7,6,4,3,1,2,5]=>1111100=>0000011
[6,7,8,4,3,1,2,5]=>0011100=>1100011
[8,7,6,3,4,1,2,5]=>1110100=>0001011
[7,8,6,3,4,1,2,5]=>0110100=>1001011
[8,6,7,3,4,1,2,5]=>1010100=>0101011
[6,7,8,3,4,1,2,5]=>0010100=>1101011
[8,7,6,4,2,1,3,5]=>1111100=>0000011
[7,8,6,4,2,1,3,5]=>0111100=>1000011
[8,6,7,4,2,1,3,5]=>1011100=>0100011
[6,7,8,4,2,1,3,5]=>0011100=>1100011
[8,7,6,4,1,2,3,5]=>1111000=>0000111
[7,8,6,4,1,2,3,5]=>0111000=>1000111
[7,6,8,4,1,2,3,5]=>1011000=>0100111
[6,7,8,4,1,2,3,5]=>0011000=>1100111
[8,7,6,3,2,1,4,5]=>1111100=>0000011
[7,8,6,3,2,1,4,5]=>0111100=>1000011
[8,6,7,3,2,1,4,5]=>1011100=>0100011
[7,6,8,3,2,1,4,5]=>1011100=>0100011
[6,7,8,3,2,1,4,5]=>0011100=>1100011
[8,7,6,2,3,1,4,5]=>1110100=>0001011
[7,8,6,2,3,1,4,5]=>0110100=>1001011
[8,6,7,2,3,1,4,5]=>1010100=>0101011
[7,6,8,2,3,1,4,5]=>1010100=>0101011
[6,7,8,2,3,1,4,5]=>0010100=>1101011
[8,7,6,3,1,2,4,5]=>1111000=>0000111
[7,8,6,3,1,2,4,5]=>0111000=>1000111
[8,6,7,3,1,2,4,5]=>1011000=>0100111
[7,6,8,3,1,2,4,5]=>1011000=>0100111
[6,7,8,3,1,2,4,5]=>0011000=>1100111
[8,7,6,2,1,3,4,5]=>1111000=>0000111
[7,8,6,2,1,3,4,5]=>0111000=>1000111
[8,6,7,2,1,3,4,5]=>1011000=>0100111
[6,7,8,2,1,3,4,5]=>0011000=>1100111
[8,7,6,1,2,3,4,5]=>1110000=>0001111
[7,8,6,1,2,3,4,5]=>0110000=>1001111
[8,6,7,1,2,3,4,5]=>1010000=>0101111
[7,6,8,1,2,3,4,5]=>1010000=>0101111
[6,7,8,1,2,3,4,5]=>0010000=>1101111
[8,7,5,4,3,2,1,6]=>1111110=>0000001
[7,8,5,4,3,2,1,6]=>0111110=>1000001
[8,7,4,5,3,2,1,6]=>1101110=>0010001
[7,8,4,5,3,2,1,6]=>0101110=>1010001
[8,7,5,3,4,2,1,6]=>1110110=>0001001
[8,7,4,3,5,2,1,6]=>1110110=>0001001
[8,7,3,4,5,2,1,6]=>1100110=>0011001
[7,8,3,4,5,2,1,6]=>0100110=>1011001
[8,7,4,5,2,3,1,6]=>1101010=>0010101
[7,8,4,5,2,3,1,6]=>0101010=>1010101
[8,7,5,3,2,4,1,6]=>1111010=>0000101
[7,8,5,2,3,4,1,6]=>0110010=>1001101
[8,7,4,3,2,5,1,6]=>1111010=>0000101
[7,8,4,3,2,5,1,6]=>0111010=>1000101
[8,7,3,4,2,5,1,6]=>1101010=>0010101
[7,8,3,4,2,5,1,6]=>0101010=>1010101
[8,7,2,3,4,5,1,6]=>1100010=>0011101
[7,8,2,3,4,5,1,6]=>0100010=>1011101
[8,7,5,4,3,1,2,6]=>1111100=>0000011
[7,8,5,4,3,1,2,6]=>0111100=>1000011
[8,7,5,3,4,1,2,6]=>1110100=>0001011
[7,8,5,3,4,1,2,6]=>0110100=>1001011
[8,7,3,4,5,1,2,6]=>1100100=>0011011
[7,8,3,4,5,1,2,6]=>0100100=>1011011
[7,8,5,4,2,1,3,6]=>0111100=>1000011
[8,7,5,4,1,2,3,6]=>1111000=>0000111
[7,8,5,4,1,2,3,6]=>0111000=>1000111
[8,7,4,5,1,2,3,6]=>1101000=>0010111
[7,8,4,5,1,2,3,6]=>0101000=>1010111
[8,7,5,3,2,1,4,6]=>1111100=>0000011
[7,8,5,3,2,1,4,6]=>0111100=>1000011
[8,7,5,2,3,1,4,6]=>1110100=>0001011
[8,7,5,3,1,2,4,6]=>1111000=>0000111
[7,8,5,3,1,2,4,6]=>0111000=>1000111
[8,7,5,2,1,3,4,6]=>1111000=>0000111
[7,8,5,2,1,3,4,6]=>0111000=>1000111
[8,7,5,1,2,3,4,6]=>1110000=>0001111
[7,8,5,1,2,3,4,6]=>0110000=>1001111
[8,7,4,3,2,1,5,6]=>1111100=>0000011
[7,8,4,3,2,1,5,6]=>0111100=>1000011
[8,7,3,4,2,1,5,6]=>1101100=>0010011
[7,8,3,4,2,1,5,6]=>0101100=>1010011
[7,8,4,2,3,1,5,6]=>0110100=>1001011
[8,7,3,2,4,1,5,6]=>1110100=>0001011
[7,8,3,2,4,1,5,6]=>0110100=>1001011
[8,7,2,3,4,1,5,6]=>1100100=>0011011
[7,8,2,3,4,1,5,6]=>0100100=>1011011
[7,8,4,3,1,2,5,6]=>0111000=>1000111
[8,7,3,4,1,2,5,6]=>1101000=>0010111
[7,8,3,4,1,2,5,6]=>0101000=>1010111
[8,7,4,2,1,3,5,6]=>1111000=>0000111
[7,8,4,2,1,3,5,6]=>0111000=>1000111
[8,7,4,1,2,3,5,6]=>1110000=>0001111
[7,8,4,1,2,3,5,6]=>0110000=>1001111
[8,7,3,2,1,4,5,6]=>1111000=>0000111
[7,8,3,2,1,4,5,6]=>0111000=>1000111
[8,7,2,3,1,4,5,6]=>1101000=>0010111
[7,8,2,3,1,4,5,6]=>0101000=>1010111
[7,8,3,1,2,4,5,6]=>0110000=>1001111
[8,7,2,1,3,4,5,6]=>1110000=>0001111
[7,8,2,1,3,4,5,6]=>0110000=>1001111
[8,7,1,2,3,4,5,6]=>1100000=>0011111
[7,8,1,2,3,4,5,6]=>0100000=>1011111
[8,6,5,4,3,2,1,7]=>1111110=>0000001
[8,5,6,4,3,2,1,7]=>1011110=>0100001
[8,6,4,5,3,2,1,7]=>1101110=>0010001
[8,5,4,6,3,2,1,7]=>1101110=>0010001
[8,4,5,6,3,2,1,7]=>1001110=>0110001
[8,6,5,3,4,2,1,7]=>1110110=>0001001
[8,5,6,3,4,2,1,7]=>1010110=>0101001
[8,6,4,3,5,2,1,7]=>1110110=>0001001
[8,4,5,3,6,2,1,7]=>1010110=>0101001
[8,4,3,5,6,2,1,7]=>1100110=>0011001
[8,3,4,5,6,2,1,7]=>1000110=>0111001
[8,6,5,4,2,3,1,7]=>1111010=>0000101
[8,5,6,4,2,3,1,7]=>1011010=>0100101
[8,6,4,5,2,3,1,7]=>1101010=>0010101
[8,4,5,6,2,3,1,7]=>1001010=>0110101
[8,6,5,3,2,4,1,7]=>1111010=>0000101
[8,6,5,2,3,4,1,7]=>1110010=>0001101
[8,5,6,2,3,4,1,7]=>1010010=>0101101
[8,6,4,3,2,5,1,7]=>1111010=>0000101
[8,6,4,2,3,5,1,7]=>1110010=>0001101
[8,6,3,2,4,5,1,7]=>1110010=>0001101
[8,5,4,3,2,6,1,7]=>1111010=>0000101
[8,4,3,5,2,6,1,7]=>1101010=>0010101
[8,5,4,2,3,6,1,7]=>1110010=>0001101
[8,4,5,2,3,6,1,7]=>1010010=>0101101
[8,5,3,2,4,6,1,7]=>1110010=>0001101
[8,5,2,3,4,6,1,7]=>1100010=>0011101
[8,3,4,2,5,6,1,7]=>1010010=>0101101
[8,3,2,4,5,6,1,7]=>1100010=>0011101
[8,2,3,4,5,6,1,7]=>1000010=>0111101
[8,6,5,4,3,1,2,7]=>1111100=>0000011
[8,6,4,5,3,1,2,7]=>1101100=>0010011
[8,6,5,3,4,1,2,7]=>1110100=>0001011
[8,5,6,3,4,1,2,7]=>1010100=>0101011
[8,6,3,4,5,1,2,7]=>1100100=>0011011
[8,5,4,3,6,1,2,7]=>1110100=>0001011
[8,4,5,3,6,1,2,7]=>1010100=>0101011
[8,5,3,4,6,1,2,7]=>1100100=>0011011
[8,4,3,5,6,1,2,7]=>1100100=>0011011
[8,3,4,5,6,1,2,7]=>1000100=>0111011
[8,6,5,4,2,1,3,7]=>1111100=>0000011
[8,5,6,4,2,1,3,7]=>1011100=>0100011
[8,6,4,5,2,1,3,7]=>1101100=>0010011
[8,4,5,6,2,1,3,7]=>1001100=>0110011
[8,6,5,4,1,2,3,7]=>1111000=>0000111
[8,5,6,4,1,2,3,7]=>1011000=>0100111
[8,6,4,5,1,2,3,7]=>1101000=>0010111
[8,4,5,6,1,2,3,7]=>1001000=>0110111
[8,6,5,3,2,1,4,7]=>1111100=>0000011
[8,5,6,3,2,1,4,7]=>1011100=>0100011
[8,6,5,2,3,1,4,7]=>1110100=>0001011
[8,5,6,2,3,1,4,7]=>1010100=>0101011
[8,5,6,3,1,2,4,7]=>1011000=>0100111
[8,6,5,2,1,3,4,7]=>1111000=>0000111
[8,5,6,2,1,3,4,7]=>1011000=>0100111
[8,6,5,1,2,3,4,7]=>1110000=>0001111
[8,5,6,1,2,3,4,7]=>1010000=>0101111
[8,6,4,3,2,1,5,7]=>1111100=>0000011
[8,6,3,4,2,1,5,7]=>1101100=>0010011
[8,6,4,2,3,1,5,7]=>1110100=>0001011
[8,6,3,2,4,1,5,7]=>1110100=>0001011
[8,6,2,3,4,1,5,7]=>1100100=>0011011
[8,6,4,3,1,2,5,7]=>1111000=>0000111
[8,6,3,4,1,2,5,7]=>1101000=>0010111
[8,6,4,2,1,3,5,7]=>1111000=>0000111
[8,6,4,1,2,3,5,7]=>1110000=>0001111
[8,6,1,2,3,4,5,7]=>1100000=>0011111
[8,5,4,3,2,1,6,7]=>1111100=>0000011
[8,4,5,3,2,1,6,7]=>1011100=>0100011
[8,4,3,5,2,1,6,7]=>1101100=>0010011
[8,3,4,5,2,1,6,7]=>1001100=>0110011
[8,4,5,2,3,1,6,7]=>1010100=>0101011
[8,5,2,3,4,1,6,7]=>1100100=>0011011
[8,4,2,3,5,1,6,7]=>1100100=>0011011
[8,2,3,4,5,1,6,7]=>1000100=>0111011
[8,5,3,4,1,2,6,7]=>1101000=>0010111
[8,3,4,5,1,2,6,7]=>1001000=>0110111
[8,5,4,2,1,3,6,7]=>1111000=>0000111
[8,5,4,1,2,3,6,7]=>1110000=>0001111
[8,4,5,1,2,3,6,7]=>1010000=>0101111
[8,5,3,2,1,4,6,7]=>1111000=>0000111
[8,5,3,1,2,4,6,7]=>1110000=>0001111
[8,5,2,1,3,4,6,7]=>1110000=>0001111
[8,5,1,2,3,4,6,7]=>1100000=>0011111
[8,4,3,2,1,5,6,7]=>1111000=>0000111
[8,3,4,2,1,5,6,7]=>1011000=>0100111
[8,4,2,3,1,5,6,7]=>1101000=>0010111
[8,2,3,4,1,5,6,7]=>1001000=>0110111
[8,3,4,1,2,5,6,7]=>1010000=>0101111
[8,4,2,1,3,5,6,7]=>1110000=>0001111
[8,4,1,2,3,5,6,7]=>1100000=>0011111
[8,3,2,1,4,5,6,7]=>1110000=>0001111
[8,2,3,1,4,5,6,7]=>1010000=>0101111
[8,3,1,2,4,5,6,7]=>1100000=>0011111
[8,2,1,3,4,5,6,7]=>1100000=>0011111
[8,1,2,3,4,5,6,7]=>1000000=>0111111
[7,6,5,4,3,2,1,8]=>1111110=>0000001
[6,7,5,4,3,2,1,8]=>0111110=>1000001
[7,5,6,4,3,2,1,8]=>1011110=>0100001
[6,5,7,4,3,2,1,8]=>1011110=>0100001
[5,6,7,4,3,2,1,8]=>0011110=>1100001
[7,6,4,5,3,2,1,8]=>1101110=>0010001
[6,7,4,5,3,2,1,8]=>0101110=>1010001
[7,5,4,6,3,2,1,8]=>1101110=>0010001
[7,4,5,6,3,2,1,8]=>1001110=>0110001
[6,5,4,7,3,2,1,8]=>1101110=>0010001
[5,6,4,7,3,2,1,8]=>0101110=>1010001
[5,4,6,7,3,2,1,8]=>1001110=>0110001
[4,5,6,7,3,2,1,8]=>0001110=>1110001
[7,6,5,3,4,2,1,8]=>1110110=>0001001
[6,7,5,3,4,2,1,8]=>0110110=>1001001
[7,5,6,3,4,2,1,8]=>1010110=>0101001
[6,5,7,3,4,2,1,8]=>1010110=>0101001
[5,6,7,3,4,2,1,8]=>0010110=>1101001
[7,6,4,3,5,2,1,8]=>1110110=>0001001
[6,7,4,3,5,2,1,8]=>0110110=>1001001
[7,6,3,4,5,2,1,8]=>1100110=>0011001
[7,5,4,3,6,2,1,8]=>1110110=>0001001
[7,4,5,3,6,2,1,8]=>1010110=>0101001
[7,3,4,5,6,2,1,8]=>1000110=>0111001
[6,5,4,3,7,2,1,8]=>1110110=>0001001
[5,6,4,3,7,2,1,8]=>0110110=>1001001
[5,4,6,3,7,2,1,8]=>1010110=>0101001
[5,4,3,6,7,2,1,8]=>1100110=>0011001
[3,4,5,6,7,2,1,8]=>0000110=>1111001
[7,6,5,4,2,3,1,8]=>1111010=>0000101
[6,7,5,4,2,3,1,8]=>0111010=>1000101
[7,5,6,4,2,3,1,8]=>1011010=>0100101
[5,6,7,4,2,3,1,8]=>0011010=>1100101
[7,6,4,5,2,3,1,8]=>1101010=>0010101
[6,7,4,5,2,3,1,8]=>0101010=>1010101
[7,5,4,6,2,3,1,8]=>1101010=>0010101
[7,4,5,6,2,3,1,8]=>1001010=>0110101
[6,5,4,7,2,3,1,8]=>1101010=>0010101
[5,6,4,7,2,3,1,8]=>0101010=>1010101
[5,4,6,7,2,3,1,8]=>1001010=>0110101
[4,5,6,7,2,3,1,8]=>0001010=>1110101
[7,6,5,3,2,4,1,8]=>1111010=>0000101
[6,5,7,3,2,4,1,8]=>1011010=>0100101
[5,6,7,3,2,4,1,8]=>0011010=>1100101
[7,6,5,2,3,4,1,8]=>1110010=>0001101
[6,7,5,2,3,4,1,8]=>0110010=>1001101
[7,5,6,2,3,4,1,8]=>1010010=>0101101
[6,5,7,2,3,4,1,8]=>1010010=>0101101
[5,6,7,2,3,4,1,8]=>0010010=>1101101
[7,6,4,3,2,5,1,8]=>1111010=>0000101
[6,7,4,3,2,5,1,8]=>0111010=>1000101
[6,7,3,4,2,5,1,8]=>0101010=>1010101
[7,6,4,2,3,5,1,8]=>1110010=>0001101
[6,7,4,2,3,5,1,8]=>0110010=>1001101
[7,6,3,2,4,5,1,8]=>1110010=>0001101
[6,7,3,2,4,5,1,8]=>0110010=>1001101
[7,6,2,3,4,5,1,8]=>1100010=>0011101
[6,7,2,3,4,5,1,8]=>0100010=>1011101
[7,5,4,3,2,6,1,8]=>1111010=>0000101
[7,4,5,3,2,6,1,8]=>1011010=>0100101
[7,5,3,4,2,6,1,8]=>1101010=>0010101
[7,4,3,5,2,6,1,8]=>1101010=>0010101
[7,5,4,2,3,6,1,8]=>1110010=>0001101
[7,4,5,2,3,6,1,8]=>1010010=>0101101
[7,5,3,2,4,6,1,8]=>1110010=>0001101
[7,4,2,3,5,6,1,8]=>1100010=>0011101
[7,2,3,4,5,6,1,8]=>1000010=>0111101
[6,5,4,3,2,7,1,8]=>1111010=>0000101
[5,6,4,3,2,7,1,8]=>0111010=>1000101
[5,4,6,3,2,7,1,8]=>1011010=>0100101
[5,6,3,4,2,7,1,8]=>0101010=>1010101
[6,3,4,5,2,7,1,8]=>1001010=>0110101
[5,4,3,6,2,7,1,8]=>1101010=>0010101
[4,5,3,6,2,7,1,8]=>0101010=>1010101
[5,3,4,6,2,7,1,8]=>1001010=>0110101
[4,3,5,6,2,7,1,8]=>1001010=>0110101
[3,4,5,6,2,7,1,8]=>0001010=>1110101
[5,4,6,2,3,7,1,8]=>1010010=>0101101
[6,5,3,2,4,7,1,8]=>1110010=>0001101
[6,4,2,3,5,7,1,8]=>1100010=>0011101
[6,3,2,4,5,7,1,8]=>1100010=>0011101
[6,2,3,4,5,7,1,8]=>1000010=>0111101
[5,4,3,2,6,7,1,8]=>1110010=>0001101
[3,4,5,2,6,7,1,8]=>0010010=>1101101
[5,4,2,3,6,7,1,8]=>1100010=>0011101
[4,5,2,3,6,7,1,8]=>0100010=>1011101
[5,2,3,4,6,7,1,8]=>1000010=>0111101
[4,3,2,5,6,7,1,8]=>1100010=>0011101
[3,4,2,5,6,7,1,8]=>0100010=>1011101
[4,2,3,5,6,7,1,8]=>1000010=>0111101
[3,2,4,5,6,7,1,8]=>1000010=>0111101
[2,3,4,5,6,7,1,8]=>0000010=>1111101
[7,6,5,4,3,1,2,8]=>1111100=>0000011
[6,7,5,4,3,1,2,8]=>0111100=>1000011
[7,5,6,4,3,1,2,8]=>1011100=>0100011
[7,6,4,5,3,1,2,8]=>1101100=>0010011
[7,4,5,6,3,1,2,8]=>1001100=>0110011
[5,4,6,7,3,1,2,8]=>1001100=>0110011
[4,5,6,7,3,1,2,8]=>0001100=>1110011
[7,6,5,3,4,1,2,8]=>1110100=>0001011
[7,5,6,3,4,1,2,8]=>1010100=>0101011
[6,7,3,4,5,1,2,8]=>0100100=>1011011
[7,5,3,4,6,1,2,8]=>1100100=>0011011
[6,5,4,3,7,1,2,8]=>1110100=>0001011
[5,6,3,4,7,1,2,8]=>0100100=>1011011
[6,4,3,5,7,1,2,8]=>1100100=>0011011
[6,3,4,5,7,1,2,8]=>1000100=>0111011
[4,3,5,6,7,1,2,8]=>1000100=>0111011
[3,4,5,6,7,1,2,8]=>0000100=>1111011
[7,6,5,4,2,1,3,8]=>1111100=>0000011
[6,5,7,4,2,1,3,8]=>1011100=>0100011
[7,6,4,5,2,1,3,8]=>1101100=>0010011
[7,5,4,6,2,1,3,8]=>1101100=>0010011
[7,4,5,6,2,1,3,8]=>1001100=>0110011
[5,4,6,7,2,1,3,8]=>1001100=>0110011
[4,5,6,7,2,1,3,8]=>0001100=>1110011
[7,6,5,4,1,2,3,8]=>1111000=>0000111
[7,5,6,4,1,2,3,8]=>1011000=>0100111
[5,6,7,4,1,2,3,8]=>0011000=>1100111
[7,6,4,5,1,2,3,8]=>1101000=>0010111
[7,5,4,6,1,2,3,8]=>1101000=>0010111
[7,4,5,6,1,2,3,8]=>1001000=>0110111
[5,4,6,7,1,2,3,8]=>1001000=>0110111
[4,5,6,7,1,2,3,8]=>0001000=>1110111
[7,6,5,3,2,1,4,8]=>1111100=>0000011
[7,6,5,2,3,1,4,8]=>1110100=>0001011
[6,7,5,2,3,1,4,8]=>0110100=>1001011
[7,5,6,2,3,1,4,8]=>1010100=>0101011
[6,5,7,2,3,1,4,8]=>1010100=>0101011
[5,6,7,2,3,1,4,8]=>0010100=>1101011
[7,5,6,3,1,2,4,8]=>1011000=>0100111
[7,6,5,2,1,3,4,8]=>1111000=>0000111
[6,7,5,2,1,3,4,8]=>0111000=>1000111
[7,5,6,2,1,3,4,8]=>1011000=>0100111
[5,6,7,2,1,3,4,8]=>0011000=>1100111
[7,6,5,1,2,3,4,8]=>1110000=>0001111
[6,7,5,1,2,3,4,8]=>0110000=>1001111
[7,5,6,1,2,3,4,8]=>1010000=>0101111
[6,5,7,1,2,3,4,8]=>1010000=>0101111
[5,6,7,1,2,3,4,8]=>0010000=>1101111
[7,6,4,3,2,1,5,8]=>1111100=>0000011
[6,7,4,3,2,1,5,8]=>0111100=>1000011
[7,6,3,4,2,1,5,8]=>1101100=>0010011
[7,6,3,2,4,1,5,8]=>1110100=>0001011
[6,7,3,2,4,1,5,8]=>0110100=>1001011
[7,6,2,3,4,1,5,8]=>1100100=>0011011
[6,7,2,3,4,1,5,8]=>0100100=>1011011
[7,6,4,3,1,2,5,8]=>1111000=>0000111
[6,7,3,4,1,2,5,8]=>0101000=>1010111
[7,6,4,2,1,3,5,8]=>1111000=>0000111
[7,6,3,2,1,4,5,8]=>1111000=>0000111
[6,7,3,2,1,4,5,8]=>0111000=>1000111
[7,6,2,3,1,4,5,8]=>1101000=>0010111
[6,7,2,3,1,4,5,8]=>0101000=>1010111
[6,7,3,1,2,4,5,8]=>0110000=>1001111
[7,6,1,2,3,4,5,8]=>1100000=>0011111
[6,7,1,2,3,4,5,8]=>0100000=>1011111
[7,5,4,3,2,1,6,8]=>1111100=>0000011
[7,4,5,3,2,1,6,8]=>1011100=>0100011
[7,4,3,5,2,1,6,8]=>1101100=>0010011
[7,3,4,5,2,1,6,8]=>1001100=>0110011
[7,5,4,2,3,1,6,8]=>1110100=>0001011
[7,5,3,2,4,1,6,8]=>1110100=>0001011
[7,5,2,3,4,1,6,8]=>1100100=>0011011
[7,4,2,3,5,1,6,8]=>1100100=>0011011
[7,2,3,4,5,1,6,8]=>1000100=>0111011
[7,5,4,3,1,2,6,8]=>1111000=>0000111
[7,5,3,4,1,2,6,8]=>1101000=>0010111
[7,4,5,2,1,3,6,8]=>1011000=>0100111
[7,4,5,1,2,3,6,8]=>1010000=>0101111
[7,5,3,2,1,4,6,8]=>1111000=>0000111
[7,5,2,3,1,4,6,8]=>1101000=>0010111
[7,5,3,1,2,4,6,8]=>1110000=>0001111
[7,5,1,2,3,4,6,8]=>1100000=>0011111
[7,4,3,2,1,5,6,8]=>1111000=>0000111
[7,2,3,4,1,5,6,8]=>1001000=>0110111
[7,4,3,1,2,5,6,8]=>1110000=>0001111
[7,3,4,1,2,5,6,8]=>1010000=>0101111
[7,4,1,2,3,5,6,8]=>1100000=>0011111
[7,3,2,1,4,5,6,8]=>1110000=>0001111
[7,2,3,1,4,5,6,8]=>1010000=>0101111
[7,3,1,2,4,5,6,8]=>1100000=>0011111
[7,2,1,3,4,5,6,8]=>1100000=>0011111
[7,1,2,3,4,5,6,8]=>1000000=>0111111
[6,5,4,3,2,1,7,8]=>1111100=>0000011
[5,6,4,3,2,1,7,8]=>0111100=>1000011
[5,4,6,3,2,1,7,8]=>1011100=>0100011
[4,5,6,3,2,1,7,8]=>0011100=>1100011
[6,5,3,4,2,1,7,8]=>1101100=>0010011
[5,6,3,4,2,1,7,8]=>0101100=>1010011
[5,4,3,6,2,1,7,8]=>1101100=>0010011
[3,4,5,6,2,1,7,8]=>0001100=>1110011
[5,4,6,2,3,1,7,8]=>1010100=>0101011
[5,6,3,2,4,1,7,8]=>0110100=>1001011
[6,5,2,3,4,1,7,8]=>1100100=>0011011
[5,6,2,3,4,1,7,8]=>0100100=>1011011
[6,4,3,2,5,1,7,8]=>1110100=>0001011
[6,2,3,4,5,1,7,8]=>1000100=>0111011
[5,4,3,2,6,1,7,8]=>1110100=>0001011
[4,5,3,2,6,1,7,8]=>0110100=>1001011
[4,3,5,2,6,1,7,8]=>1010100=>0101011
[3,4,5,2,6,1,7,8]=>0010100=>1101011
[5,3,2,4,6,1,7,8]=>1100100=>0011011
[5,2,3,4,6,1,7,8]=>1000100=>0111011
[4,3,2,5,6,1,7,8]=>1100100=>0011011
[3,4,2,5,6,1,7,8]=>0100100=>1011011
[4,2,3,5,6,1,7,8]=>1000100=>0111011
[3,2,4,5,6,1,7,8]=>1000100=>0111011
[2,3,4,5,6,1,7,8]=>0000100=>1111011
[6,5,4,3,1,2,7,8]=>1111000=>0000111
[6,4,5,3,1,2,7,8]=>1011000=>0100111
[5,4,6,3,1,2,7,8]=>1011000=>0100111
[5,6,3,4,1,2,7,8]=>0101000=>1010111
[5,4,3,6,1,2,7,8]=>1101000=>0010111
[4,3,5,6,1,2,7,8]=>1001000=>0110111
[3,4,5,6,1,2,7,8]=>0001000=>1110111
[6,5,4,2,1,3,7,8]=>1111000=>0000111
[5,6,4,2,1,3,7,8]=>0111000=>1000111
[6,4,5,2,1,3,7,8]=>1011000=>0100111
[4,5,6,2,1,3,7,8]=>0011000=>1100111
[6,5,4,1,2,3,7,8]=>1110000=>0001111
[4,5,6,1,2,3,7,8]=>0010000=>1101111
[6,5,3,2,1,4,7,8]=>1111000=>0000111
[5,6,3,2,1,4,7,8]=>0111000=>1000111
[5,6,2,1,3,4,7,8]=>0110000=>1001111
[6,4,3,2,1,5,7,8]=>1111000=>0000111
[6,3,4,2,1,5,7,8]=>1011000=>0100111
[6,4,3,1,2,5,7,8]=>1110000=>0001111
[6,4,2,1,3,5,7,8]=>1110000=>0001111
[6,4,1,2,3,5,7,8]=>1100000=>0011111
[6,3,2,1,4,5,7,8]=>1110000=>0001111
[6,2,3,1,4,5,7,8]=>1010000=>0101111
[6,3,1,2,4,5,7,8]=>1100000=>0011111
[6,2,1,3,4,5,7,8]=>1100000=>0011111
[6,1,2,3,4,5,7,8]=>1000000=>0111111
[5,4,3,2,1,6,7,8]=>1111000=>0000111
[4,5,3,2,1,6,7,8]=>0111000=>1000111
[5,3,4,2,1,6,7,8]=>1011000=>0100111
[4,3,5,2,1,6,7,8]=>1011000=>0100111
[3,4,5,2,1,6,7,8]=>0011000=>1100111
[5,4,2,3,1,6,7,8]=>1101000=>0010111
[4,5,2,3,1,6,7,8]=>0101000=>1010111
[5,3,2,4,1,6,7,8]=>1101000=>0010111
[5,2,3,4,1,6,7,8]=>1001000=>0110111
[4,3,2,5,1,6,7,8]=>1101000=>0010111
[3,4,2,5,1,6,7,8]=>0101000=>1010111
[4,2,3,5,1,6,7,8]=>1001000=>0110111
[3,2,4,5,1,6,7,8]=>1001000=>0110111
[2,3,4,5,1,6,7,8]=>0001000=>1110111
[5,4,3,1,2,6,7,8]=>1110000=>0001111
[5,3,4,1,2,6,7,8]=>1010000=>0101111
[4,3,5,1,2,6,7,8]=>1010000=>0101111
[3,4,5,1,2,6,7,8]=>0010000=>1101111
[5,4,2,1,3,6,7,8]=>1110000=>0001111
[4,5,2,1,3,6,7,8]=>0110000=>1001111
[5,4,1,2,3,6,7,8]=>1100000=>0011111
[4,5,1,2,3,6,7,8]=>0100000=>1011111
[5,3,2,1,4,6,7,8]=>1110000=>0001111
[5,2,3,1,4,6,7,8]=>1010000=>0101111
[5,3,1,2,4,6,7,8]=>1100000=>0011111
[5,2,1,3,4,6,7,8]=>1100000=>0011111
[5,1,2,3,4,6,7,8]=>1000000=>0111111
[4,3,2,1,5,6,7,8]=>1110000=>0001111
[3,4,2,1,5,6,7,8]=>0110000=>1001111
[4,2,3,1,5,6,7,8]=>1010000=>0101111
[3,2,4,1,5,6,7,8]=>1010000=>0101111
[2,3,4,1,5,6,7,8]=>0010000=>1101111
[4,3,1,2,5,6,7,8]=>1100000=>0011111
[3,4,1,2,5,6,7,8]=>0100000=>1011111
[4,2,1,3,5,6,7,8]=>1100000=>0011111
[4,1,2,3,5,6,7,8]=>1000000=>0111111
[3,2,1,4,5,6,7,8]=>1100000=>0011111
[2,3,1,4,5,6,7,8]=>0100000=>1011111
[3,1,2,4,5,6,7,8]=>1000000=>0111111
[2,1,3,4,5,6,7,8]=>1000000=>0111111
[1,2,3,4,5,6,7,8]=>0000000=>1111111
[6,8,7,5,4,3,2,1]=>0111111=>1000000
[5,8,7,6,4,3,2,1]=>0111111=>1000000
[5,7,8,6,4,3,2,1]=>0011111=>1100000
[6,5,8,7,4,3,2,1]=>1011111=>0100000
[5,6,8,7,4,3,2,1]=>0011111=>1100000
[5,7,6,8,4,3,2,1]=>0101111=>1010000
[4,8,7,6,5,3,2,1]=>0111111=>1000000
[4,7,8,6,5,3,2,1]=>0011111=>1100000
[4,6,8,7,5,3,2,1]=>0011111=>1100000
[4,7,6,8,5,3,2,1]=>0101111=>1010000
[4,6,7,8,5,3,2,1]=>0001111=>1110000
[5,4,7,8,6,3,2,1]=>1001111=>0110000
[4,5,8,7,6,3,2,1]=>0011111=>1100000
[4,5,7,8,6,3,2,1]=>0001111=>1110000
[6,5,4,8,7,3,2,1]=>1101111=>0010000
[5,6,4,8,7,3,2,1]=>0101111=>1010000
[4,6,5,8,7,3,2,1]=>0101111=>1010000
[4,5,6,8,7,3,2,1]=>0001111=>1110000
[5,7,6,4,8,3,2,1]=>0110111=>1001000
[4,7,6,5,8,3,2,1]=>0110111=>1001000
[4,6,7,5,8,3,2,1]=>0010111=>1101000
[5,4,7,6,8,3,2,1]=>1010111=>0101000
[4,5,7,6,8,3,2,1]=>0010111=>1101000
[4,6,5,7,8,3,2,1]=>0100111=>1011000
[3,8,7,6,5,4,2,1]=>0111111=>1000000
[3,7,8,6,5,4,2,1]=>0011111=>1100000
[3,6,8,7,5,4,2,1]=>0011111=>1100000
[3,7,6,8,5,4,2,1]=>0101111=>1010000
[3,5,8,7,6,4,2,1]=>0011111=>1100000
[3,5,7,8,6,4,2,1]=>0001111=>1110000
[3,5,6,8,7,4,2,1]=>0001111=>1110000
[3,7,6,5,8,4,2,1]=>0110111=>1001000
[3,6,7,5,8,4,2,1]=>0010111=>1101000
[3,5,7,6,8,4,2,1]=>0010111=>1101000
[3,5,6,7,8,4,2,1]=>0000111=>1111000
[4,3,8,7,6,5,2,1]=>1011111=>0100000
[4,3,7,8,6,5,2,1]=>1001111=>0110000
[4,3,6,7,8,5,2,1]=>1000111=>0111000
[3,4,8,7,6,5,2,1]=>0011111=>1100000
[3,4,6,7,8,5,2,1]=>0000111=>1111000
[5,4,3,8,7,6,2,1]=>1101111=>0010000
[5,4,3,7,8,6,2,1]=>1100111=>0011000
[3,5,4,7,8,6,2,1]=>0100111=>1011000
[3,4,5,8,7,6,2,1]=>0001111=>1110000
[3,4,5,7,8,6,2,1]=>0000111=>1111000
[6,5,4,3,8,7,2,1]=>1110111=>0001000
[5,6,4,3,8,7,2,1]=>0110111=>1001000
[4,5,6,3,8,7,2,1]=>0010111=>1101000
[4,3,6,5,8,7,2,1]=>1010111=>0101000
[5,4,3,6,8,7,2,1]=>1100111=>0011000
[4,5,3,6,8,7,2,1]=>0100111=>1011000
[3,4,5,6,8,7,2,1]=>0000111=>1111000
[5,7,6,4,3,8,2,1]=>0111011=>1000100
[4,7,6,5,3,8,2,1]=>0111011=>1000100
[5,4,7,6,3,8,2,1]=>1011011=>0100100
[3,7,6,5,4,8,2,1]=>0111011=>1000100
[3,5,7,6,4,8,2,1]=>0011011=>1100100
[3,5,6,7,4,8,2,1]=>0001011=>1110100
[4,3,7,6,5,8,2,1]=>1011011=>0100100
[3,4,7,6,5,8,2,1]=>0011011=>1100100
[3,4,6,7,5,8,2,1]=>0001011=>1110100
[4,5,3,7,6,8,2,1]=>0101011=>1010100
[3,5,4,7,6,8,2,1]=>0101011=>1010100
[4,3,5,7,6,8,2,1]=>1001011=>0110100
[3,4,5,7,6,8,2,1]=>0001011=>1110100
[3,6,5,4,7,8,2,1]=>0110011=>1001100
[3,5,6,4,7,8,2,1]=>0010011=>1101100
[4,3,6,5,7,8,2,1]=>1010011=>0101100
[3,4,6,5,7,8,2,1]=>0010011=>1101100
[3,5,4,6,7,8,2,1]=>0100011=>1011100
[2,8,7,6,5,4,3,1]=>0111111=>1000000
[2,7,8,6,5,4,3,1]=>0011111=>1100000
[2,6,8,7,5,4,3,1]=>0011111=>1100000
[2,7,6,8,5,4,3,1]=>0101111=>1010000
[2,6,7,8,5,4,3,1]=>0001111=>1110000
[2,5,8,7,6,4,3,1]=>0011111=>1100000
[2,6,7,5,8,4,3,1]=>0010111=>1101000
[2,6,5,7,8,4,3,1]=>0100111=>1011000
[2,5,6,7,8,4,3,1]=>0000111=>1111000
[2,4,8,7,6,5,3,1]=>0011111=>1100000
[2,4,7,8,6,5,3,1]=>0001111=>1110000
[2,4,6,8,7,5,3,1]=>0001111=>1110000
[2,4,6,7,8,5,3,1]=>0000111=>1111000
[2,5,4,8,7,6,3,1]=>0101111=>1010000
[2,5,4,7,8,6,3,1]=>0100111=>1011000
[2,4,5,7,8,6,3,1]=>0000111=>1111000
[2,6,5,4,8,7,3,1]=>0110111=>1001000
[2,5,6,4,8,7,3,1]=>0010111=>1101000
[2,4,6,5,8,7,3,1]=>0010111=>1101000
[2,4,5,6,8,7,3,1]=>0000111=>1111000
[2,7,6,5,4,8,3,1]=>0111011=>1000100
[2,6,7,5,4,8,3,1]=>0011011=>1100100
[2,5,6,7,4,8,3,1]=>0001011=>1110100
[2,4,7,6,5,8,3,1]=>0011011=>1100100
[2,4,6,7,5,8,3,1]=>0001011=>1110100
[2,5,4,7,6,8,3,1]=>0101011=>1010100
[2,6,5,4,7,8,3,1]=>0110011=>1001100
[2,5,6,4,7,8,3,1]=>0010011=>1101100
[2,4,6,5,7,8,3,1]=>0010011=>1101100
[2,5,4,6,7,8,3,1]=>0100011=>1011100
[2,4,5,6,7,8,3,1]=>0000011=>1111100
[3,2,8,7,6,5,4,1]=>1011111=>0100000
[3,2,6,8,7,5,4,1]=>1001111=>0110000
[3,2,5,7,8,6,4,1]=>1000111=>0111000
[3,2,6,5,8,7,4,1]=>1010111=>0101000
[3,2,5,7,6,8,4,1]=>1001011=>0110100
[3,2,5,6,7,8,4,1]=>1000011=>0111100
[2,3,8,7,6,5,4,1]=>0011111=>1100000
[2,3,6,7,8,5,4,1]=>0000111=>1111000
[2,3,5,7,8,6,4,1]=>0000111=>1111000
[2,3,6,5,8,7,4,1]=>0010111=>1101000
[2,3,5,6,8,7,4,1]=>0000111=>1111000
[2,3,7,6,5,8,4,1]=>0011011=>1100100
[2,3,5,7,6,8,4,1]=>0001011=>1110100
[2,3,5,6,7,8,4,1]=>0000011=>1111100
[4,3,2,8,7,6,5,1]=>1101111=>0010000
[4,3,2,7,8,6,5,1]=>1100111=>0011000
[3,4,2,8,7,6,5,1]=>0101111=>1010000
[3,4,2,7,8,6,5,1]=>0100111=>1011000
[2,4,3,8,7,6,5,1]=>0101111=>1010000
[2,4,3,6,8,7,5,1]=>0100111=>1011000
[2,4,3,6,7,8,5,1]=>0100011=>1011100
[3,2,4,8,7,6,5,1]=>1001111=>0110000
[3,2,4,7,8,6,5,1]=>1000111=>0111000
[2,3,4,8,7,6,5,1]=>0001111=>1110000
[2,3,4,7,8,6,5,1]=>0000111=>1111000
[2,3,4,6,8,7,5,1]=>0000111=>1111000
[2,3,4,7,6,8,5,1]=>0001011=>1110100
[2,3,4,6,7,8,5,1]=>0000011=>1111100
[5,4,3,2,8,7,6,1]=>1110111=>0001000
[5,4,3,2,7,8,6,1]=>1110011=>0001100
[3,5,4,2,7,8,6,1]=>0110011=>1001100
[3,4,5,2,7,8,6,1]=>0010011=>1101100
[2,5,4,3,8,7,6,1]=>0110111=>1001000
[2,5,4,3,7,8,6,1]=>0110011=>1001100
[2,4,5,3,8,7,6,1]=>0010111=>1101000
[2,4,5,3,7,8,6,1]=>0010011=>1101100
[3,2,5,4,7,8,6,1]=>1010011=>0101100
[2,3,5,4,8,7,6,1]=>0010111=>1101000
[2,3,5,4,7,8,6,1]=>0010011=>1101100
[4,3,2,5,8,7,6,1]=>1100111=>0011000
[4,3,2,5,7,8,6,1]=>1100011=>0011100
[3,4,2,5,8,7,6,1]=>0100111=>1011000
[3,4,2,5,7,8,6,1]=>0100011=>1011100
[2,4,3,5,8,7,6,1]=>0100111=>1011000
[3,2,4,5,7,8,6,1]=>1000011=>0111100
[2,3,4,5,8,7,6,1]=>0000111=>1111000
[2,3,4,5,7,8,6,1]=>0000011=>1111100
[6,5,4,3,2,8,7,1]=>1111011=>0000100
[4,6,5,3,2,8,7,1]=>0111011=>1000100
[5,4,6,3,2,8,7,1]=>1011011=>0100100
[4,5,6,3,2,8,7,1]=>0011011=>1100100
[3,6,5,4,2,8,7,1]=>0111011=>1000100
[3,5,6,4,2,8,7,1]=>0011011=>1100100
[4,3,6,5,2,8,7,1]=>1011011=>0100100
[5,4,3,6,2,8,7,1]=>1101011=>0010100
[4,5,3,6,2,8,7,1]=>0101011=>1010100
[3,5,4,6,2,8,7,1]=>0101011=>1010100
[3,4,5,6,2,8,7,1]=>0001011=>1110100
[2,6,5,4,3,8,7,1]=>0111011=>1000100
[2,4,6,5,3,8,7,1]=>0011011=>1100100
[2,4,5,6,3,8,7,1]=>0001011=>1110100
[3,2,6,5,4,8,7,1]=>1011011=>0100100
[2,3,5,6,4,8,7,1]=>0001011=>1110100
[4,3,2,6,5,8,7,1]=>1101011=>0010100
[2,4,3,6,5,8,7,1]=>0101011=>1010100
[3,2,4,6,5,8,7,1]=>1001011=>0110100
[2,3,4,6,5,8,7,1]=>0001011=>1110100
[5,4,3,2,6,8,7,1]=>1110011=>0001100
[4,5,3,2,6,8,7,1]=>0110011=>1001100
[2,5,4,3,6,8,7,1]=>0110011=>1001100
[2,4,5,3,6,8,7,1]=>0010011=>1101100
[3,2,5,4,6,8,7,1]=>1010011=>0101100
[4,3,2,5,6,8,7,1]=>1100011=>0011100
[3,4,2,5,6,8,7,1]=>0100011=>1011100
[2,4,3,5,6,8,7,1]=>0100011=>1011100
[3,2,4,5,6,8,7,1]=>1000011=>0111100
[2,3,4,5,6,8,7,1]=>0000011=>1111100
[5,7,6,4,3,2,8,1]=>0111101=>1000010
[4,7,6,5,3,2,8,1]=>0111101=>1000010
[4,6,7,5,3,2,8,1]=>0011101=>1100010
[4,6,5,7,3,2,8,1]=>0101101=>1010010
[3,5,7,6,4,2,8,1]=>0011101=>1100010
[3,5,6,7,4,2,8,1]=>0001101=>1110010
[4,3,7,6,5,2,8,1]=>1011101=>0100010
[4,3,6,7,5,2,8,1]=>1001101=>0110010
[3,4,7,6,5,2,8,1]=>0011101=>1100010
[3,4,6,7,5,2,8,1]=>0001101=>1110010
[5,4,3,7,6,2,8,1]=>1101101=>0010010
[4,5,3,7,6,2,8,1]=>0101101=>1010010
[3,5,4,7,6,2,8,1]=>0101101=>1010010
[3,4,5,7,6,2,8,1]=>0001101=>1110010
[4,6,5,3,7,2,8,1]=>0110101=>1001010
[3,6,5,4,7,2,8,1]=>0110101=>1001010
[3,5,6,4,7,2,8,1]=>0010101=>1101010
[4,3,6,5,7,2,8,1]=>1010101=>0101010
[3,4,6,5,7,2,8,1]=>0010101=>1101010
[3,5,4,6,7,2,8,1]=>0100101=>1011010
[2,7,6,5,4,3,8,1]=>0111101=>1000010
[2,6,5,7,4,3,8,1]=>0101101=>1010010
[2,5,6,7,4,3,8,1]=>0001101=>1110010
[2,4,6,7,5,3,8,1]=>0001101=>1110010
[2,5,4,7,6,3,8,1]=>0101101=>1010010
[2,4,6,5,7,3,8,1]=>0010101=>1101010
[2,5,4,6,7,3,8,1]=>0100101=>1011010
[2,4,5,6,7,3,8,1]=>0000101=>1111010
[3,2,7,6,5,4,8,1]=>1011101=>0100010
[3,2,6,7,5,4,8,1]=>1001101=>0110010
[3,2,5,7,6,4,8,1]=>1001101=>0110010
[3,2,6,5,7,4,8,1]=>1010101=>0101010
[3,2,5,6,7,4,8,1]=>1000101=>0111010
[2,3,7,6,5,4,8,1]=>0011101=>1100010
[2,3,5,7,6,4,8,1]=>0001101=>1110010
[2,3,5,6,7,4,8,1]=>0000101=>1111010
[4,3,2,7,6,5,8,1]=>1101101=>0010010
[4,3,2,6,7,5,8,1]=>1100101=>0011010
[3,4,2,7,6,5,8,1]=>0101101=>1010010
[3,4,2,6,7,5,8,1]=>0100101=>1011010
[2,4,3,7,6,5,8,1]=>0101101=>1010010
[2,4,3,6,7,5,8,1]=>0100101=>1011010
[3,2,4,7,6,5,8,1]=>1001101=>0110010
[2,3,4,7,6,5,8,1]=>0001101=>1110010
[2,3,4,6,7,5,8,1]=>0000101=>1111010
[5,4,3,2,7,6,8,1]=>1110101=>0001010
[3,5,4,2,7,6,8,1]=>0110101=>1001010
[4,3,5,2,7,6,8,1]=>1010101=>0101010
[3,4,5,2,7,6,8,1]=>0010101=>1101010
[2,5,4,3,7,6,8,1]=>0110101=>1001010
[3,2,5,4,7,6,8,1]=>1010101=>0101010
[2,3,5,4,7,6,8,1]=>0010101=>1101010
[4,3,2,5,7,6,8,1]=>1100101=>0011010
[3,4,2,5,7,6,8,1]=>0100101=>1011010
[2,4,3,5,7,6,8,1]=>0100101=>1011010
[3,2,4,5,7,6,8,1]=>1000101=>0111010
[2,3,4,5,7,6,8,1]=>0000101=>1111010
[3,6,5,4,2,7,8,1]=>0111001=>1000110
[3,5,6,4,2,7,8,1]=>0011001=>1100110
[3,4,6,5,2,7,8,1]=>0011001=>1100110
[3,5,4,6,2,7,8,1]=>0101001=>1010110
[2,6,5,4,3,7,8,1]=>0111001=>1000110
[2,5,6,4,3,7,8,1]=>0011001=>1100110
[2,4,6,5,3,7,8,1]=>0011001=>1100110
[2,5,4,6,3,7,8,1]=>0101001=>1010110
[2,4,5,6,3,7,8,1]=>0001001=>1110110
[3,2,5,6,4,7,8,1]=>1001001=>0110110
[2,3,6,5,4,7,8,1]=>0011001=>1100110
[2,3,5,6,4,7,8,1]=>0001001=>1110110
[4,3,2,6,5,7,8,1]=>1101001=>0010110
[3,4,2,6,5,7,8,1]=>0101001=>1010110
[2,4,3,6,5,7,8,1]=>0101001=>1010110
[2,3,4,6,5,7,8,1]=>0001001=>1110110
[3,5,4,2,6,7,8,1]=>0110001=>1001110
[2,5,4,3,6,7,8,1]=>0110001=>1001110
[2,4,5,3,6,7,8,1]=>0010001=>1101110
[3,2,5,4,6,7,8,1]=>1010001=>0101110
[2,3,5,4,6,7,8,1]=>0010001=>1101110
[2,4,3,5,6,7,8,1]=>0100001=>1011110
[1,8,7,6,5,4,3,2]=>0111111=>1000000
[1,7,8,6,5,4,3,2]=>0011111=>1100000
[1,6,8,7,5,4,3,2]=>0011111=>1100000
[1,7,6,8,5,4,3,2]=>0101111=>1010000
[1,6,7,8,5,4,3,2]=>0001111=>1110000
[1,5,8,7,6,4,3,2]=>0011111=>1100000
[1,6,5,8,7,4,3,2]=>0101111=>1010000
[1,7,6,5,8,4,3,2]=>0110111=>1001000
[1,6,7,5,8,4,3,2]=>0010111=>1101000
[1,5,7,6,8,4,3,2]=>0010111=>1101000
[1,6,5,7,8,4,3,2]=>0100111=>1011000
[1,5,6,7,8,4,3,2]=>0000111=>1111000
[1,4,8,7,6,5,3,2]=>0011111=>1100000
[1,4,7,8,6,5,3,2]=>0001111=>1110000
[1,4,6,8,7,5,3,2]=>0001111=>1110000
[1,4,6,7,8,5,3,2]=>0000111=>1111000
[1,5,4,7,8,6,3,2]=>0100111=>1011000
[1,4,5,8,7,6,3,2]=>0001111=>1110000
[1,4,5,7,8,6,3,2]=>0000111=>1111000
[1,6,5,4,8,7,3,2]=>0110111=>1001000
[1,4,6,5,8,7,3,2]=>0010111=>1101000
[1,7,6,5,4,8,3,2]=>0111011=>1000100
[1,4,7,6,5,8,3,2]=>0011011=>1100100
[1,4,6,7,5,8,3,2]=>0001011=>1110100
[1,6,5,4,7,8,3,2]=>0110011=>1001100
[1,5,6,4,7,8,3,2]=>0010011=>1101100
[1,5,4,6,7,8,3,2]=>0100011=>1011100
[1,4,5,6,7,8,3,2]=>0000011=>1111100
[1,3,8,7,6,5,4,2]=>0011111=>1100000
[1,3,7,8,6,5,4,2]=>0001111=>1110000
[1,3,6,8,7,5,4,2]=>0001111=>1110000
[1,3,6,7,8,5,4,2]=>0000111=>1111000
[1,3,5,8,7,6,4,2]=>0001111=>1110000
[1,3,5,7,8,6,4,2]=>0000111=>1111000
[1,3,5,6,8,7,4,2]=>0000111=>1111000
[1,3,6,7,5,8,4,2]=>0001011=>1110100
[1,3,5,7,6,8,4,2]=>0001011=>1110100
[1,3,6,5,7,8,4,2]=>0010011=>1101100
[1,3,5,6,7,8,4,2]=>0000011=>1111100
[1,4,3,8,7,6,5,2]=>0101111=>1010000
[1,4,3,7,8,6,5,2]=>0100111=>1011000
[1,4,3,6,8,7,5,2]=>0100111=>1011000
[1,4,3,7,6,8,5,2]=>0101011=>1010100
[1,4,3,6,7,8,5,2]=>0100011=>1011100
[1,3,4,8,7,6,5,2]=>0001111=>1110000
[1,3,4,7,6,8,5,2]=>0001011=>1110100
[1,3,4,6,7,8,5,2]=>0000011=>1111100
[1,5,4,3,8,7,6,2]=>0110111=>1001000
[1,4,5,3,8,7,6,2]=>0010111=>1101000
[1,4,5,3,7,8,6,2]=>0010011=>1101100
[1,3,5,4,8,7,6,2]=>0010111=>1101000
[1,3,5,4,7,8,6,2]=>0010011=>1101100
[1,4,3,5,8,7,6,2]=>0100111=>1011000
[1,4,3,5,7,8,6,2]=>0100011=>1011100
[1,3,4,5,8,7,6,2]=>0000111=>1111000
[1,3,4,5,7,8,6,2]=>0000011=>1111100
[1,6,5,4,3,8,7,2]=>0111011=>1000100
[1,5,6,4,3,8,7,2]=>0011011=>1100100
[1,4,6,5,3,8,7,2]=>0011011=>1100100
[1,4,5,6,3,8,7,2]=>0001011=>1110100
[1,3,6,5,4,8,7,2]=>0011011=>1100100
[1,4,3,6,5,8,7,2]=>0101011=>1010100
[1,5,4,3,6,8,7,2]=>0110011=>1001100
[1,4,5,3,6,8,7,2]=>0010011=>1101100
[1,3,4,5,6,8,7,2]=>0000011=>1111100
[1,7,6,5,4,3,8,2]=>0111101=>1000010
[1,6,7,5,4,3,8,2]=>0011101=>1100010
[1,6,5,7,4,3,8,2]=>0101101=>1010010
[1,4,6,7,5,3,8,2]=>0001101=>1110010
[1,5,6,4,7,3,8,2]=>0010101=>1101010
[1,4,6,5,7,3,8,2]=>0010101=>1101010
[1,5,4,6,7,3,8,2]=>0100101=>1011010
[1,4,5,6,7,3,8,2]=>0000101=>1111010
[1,3,5,7,6,4,8,2]=>0001101=>1110010
[1,3,6,5,7,4,8,2]=>0010101=>1101010
[1,3,5,6,7,4,8,2]=>0000101=>1111010
[1,4,3,6,7,5,8,2]=>0100101=>1011010
[1,3,4,7,6,5,8,2]=>0001101=>1110010
[1,3,4,6,7,5,8,2]=>0000101=>1111010
[1,3,5,4,7,6,8,2]=>0010101=>1101010
[1,3,4,5,7,6,8,2]=>0000101=>1111010
[1,6,5,4,3,7,8,2]=>0111001=>1000110
[1,5,4,6,3,7,8,2]=>0101001=>1010110
[1,3,5,6,4,7,8,2]=>0001001=>1110110
[1,4,3,6,5,7,8,2]=>0101001=>1010110
[1,3,4,6,5,7,8,2]=>0001001=>1110110
[1,5,4,3,6,7,8,2]=>0110001=>1001110
[1,4,5,3,6,7,8,2]=>0010001=>1101110
[1,3,5,4,6,7,8,2]=>0010001=>1101110
[1,4,3,5,6,7,8,2]=>0100001=>1011110
[1,3,4,5,6,7,8,2]=>0000001=>1111110
[2,1,8,7,6,5,4,3]=>1011111=>0100000
[2,1,7,8,6,5,4,3]=>1001111=>0110000
[2,1,6,8,7,5,4,3]=>1001111=>0110000
[2,1,7,6,8,5,4,3]=>1010111=>0101000
[2,1,6,7,8,5,4,3]=>1000111=>0111000
[2,1,5,8,7,6,4,3]=>1001111=>0110000
[2,1,5,7,8,6,4,3]=>1000111=>0111000
[2,1,6,5,8,7,4,3]=>1010111=>0101000
[2,1,5,6,8,7,4,3]=>1000111=>0111000
[2,1,7,6,5,8,4,3]=>1011011=>0100100
[2,1,6,7,5,8,4,3]=>1001011=>0110100
[2,1,5,7,6,8,4,3]=>1001011=>0110100
[2,1,6,5,7,8,4,3]=>1010011=>0101100
[2,1,5,6,7,8,4,3]=>1000011=>0111100
[2,1,4,8,7,6,5,3]=>1001111=>0110000
[2,1,4,7,8,6,5,3]=>1000111=>0111000
[2,1,4,6,8,7,5,3]=>1000111=>0111000
[2,1,4,7,6,8,5,3]=>1001011=>0110100
[2,1,4,6,7,8,5,3]=>1000011=>0111100
[2,1,5,4,8,7,6,3]=>1010111=>0101000
[2,1,5,4,7,8,6,3]=>1010011=>0101100
[2,1,4,5,8,7,6,3]=>1000111=>0111000
[2,1,4,5,7,8,6,3]=>1000011=>0111100
[2,1,6,5,4,8,7,3]=>1011011=>0100100
[2,1,5,6,4,8,7,3]=>1001011=>0110100
[2,1,4,6,5,8,7,3]=>1001011=>0110100
[2,1,5,4,6,8,7,3]=>1010011=>0101100
[2,1,4,5,6,8,7,3]=>1000011=>0111100
[2,1,7,6,5,4,8,3]=>1011101=>0100010
[2,1,6,7,5,4,8,3]=>1001101=>0110010
[2,1,5,7,6,4,8,3]=>1001101=>0110010
[2,1,6,5,7,4,8,3]=>1010101=>0101010
[2,1,5,6,7,4,8,3]=>1000101=>0111010
[2,1,4,7,6,5,8,3]=>1001101=>0110010
[2,1,4,6,7,5,8,3]=>1000101=>0111010
[2,1,5,4,7,6,8,3]=>1010101=>0101010
[2,1,5,6,4,7,8,3]=>1001001=>0110110
[2,1,5,4,6,7,8,3]=>1010001=>0101110
[2,1,4,5,6,7,8,3]=>1000001=>0111110
[1,2,8,7,6,5,4,3]=>0011111=>1100000
[1,2,7,8,6,5,4,3]=>0001111=>1110000
[1,2,7,6,8,5,4,3]=>0010111=>1101000
[1,2,6,7,8,5,4,3]=>0000111=>1111000
[1,2,5,8,7,6,4,3]=>0001111=>1110000
[1,2,6,5,8,7,4,3]=>0010111=>1101000
[1,2,5,6,8,7,4,3]=>0000111=>1111000
[1,2,7,6,5,8,4,3]=>0011011=>1100100
[1,2,5,7,6,8,4,3]=>0001011=>1110100
[1,2,6,5,7,8,4,3]=>0010011=>1101100
[1,2,5,6,7,8,4,3]=>0000011=>1111100
[1,2,4,8,7,6,5,3]=>0001111=>1110000
[1,2,4,7,8,6,5,3]=>0000111=>1111000
[1,2,4,6,8,7,5,3]=>0000111=>1111000
[1,2,4,7,6,8,5,3]=>0001011=>1110100
[1,2,4,6,7,8,5,3]=>0000011=>1111100
[1,2,5,4,8,7,6,3]=>0010111=>1101000
[1,2,4,5,8,7,6,3]=>0000111=>1111000
[1,2,4,5,7,8,6,3]=>0000011=>1111100
[1,2,6,5,4,8,7,3]=>0011011=>1100100
[1,2,5,4,6,8,7,3]=>0010011=>1101100
[1,2,4,5,6,8,7,3]=>0000011=>1111100
[1,2,7,6,5,4,8,3]=>0011101=>1100010
[1,2,5,7,6,4,8,3]=>0001101=>1110010
[1,2,5,6,7,4,8,3]=>0000101=>1111010
[1,2,4,7,6,5,8,3]=>0001101=>1110010
[1,2,5,4,7,6,8,3]=>0010101=>1101010
[1,2,6,5,4,7,8,3]=>0011001=>1100110
[1,2,5,6,4,7,8,3]=>0001001=>1110110
[1,2,4,6,5,7,8,3]=>0001001=>1110110
[1,2,5,4,6,7,8,3]=>0010001=>1101110
[1,2,4,5,6,7,8,3]=>0000001=>1111110
[3,2,1,8,7,6,5,4]=>1101111=>0010000
[3,2,1,7,8,6,5,4]=>1100111=>0011000
[3,2,1,6,8,7,5,4]=>1100111=>0011000
[3,2,1,7,6,8,5,4]=>1101011=>0010100
[3,2,1,6,7,8,5,4]=>1100011=>0011100
[3,2,1,5,8,7,6,4]=>1100111=>0011000
[3,2,1,5,7,8,6,4]=>1100011=>0011100
[3,2,1,6,5,8,7,4]=>1101011=>0010100
[3,2,1,5,6,8,7,4]=>1100011=>0011100
[3,2,1,7,6,5,8,4]=>1101101=>0010010
[3,2,1,6,7,5,8,4]=>1100101=>0011010
[3,2,1,5,7,6,8,4]=>1100101=>0011010
[3,2,1,6,5,7,8,4]=>1101001=>0010110
[3,2,1,5,6,7,8,4]=>1100001=>0011110
[2,3,1,8,7,6,5,4]=>0101111=>1010000
[2,3,1,7,8,6,5,4]=>0100111=>1011000
[2,3,1,6,8,7,5,4]=>0100111=>1011000
[2,3,1,7,6,8,5,4]=>0101011=>1010100
[2,3,1,6,7,8,5,4]=>0100011=>1011100
[2,3,1,5,7,8,6,4]=>0100011=>1011100
[2,3,1,6,5,8,7,4]=>0101011=>1010100
[2,3,1,7,6,5,8,4]=>0101101=>1010010
[2,3,1,6,7,5,8,4]=>0100101=>1011010
[2,3,1,5,7,6,8,4]=>0100101=>1011010
[2,3,1,5,6,7,8,4]=>0100001=>1011110
[1,3,2,8,7,6,5,4]=>0101111=>1010000
[1,3,2,6,8,7,5,4]=>0100111=>1011000
[1,3,2,7,6,8,5,4]=>0101011=>1010100
[1,3,2,6,7,8,5,4]=>0100011=>1011100
[1,3,2,5,8,7,6,4]=>0100111=>1011000
[1,3,2,5,7,8,6,4]=>0100011=>1011100
[1,3,2,6,5,8,7,4]=>0101011=>1010100
[1,3,2,5,6,8,7,4]=>0100011=>1011100
[1,3,2,7,6,5,8,4]=>0101101=>1010010
[1,3,2,6,7,5,8,4]=>0100101=>1011010
[1,3,2,5,7,6,8,4]=>0100101=>1011010
[1,3,2,6,5,7,8,4]=>0101001=>1010110
[1,3,2,5,6,7,8,4]=>0100001=>1011110
[2,1,3,8,7,6,5,4]=>1001111=>0110000
[2,1,3,7,8,6,5,4]=>1000111=>0111000
[2,1,3,6,8,7,5,4]=>1000111=>0111000
[2,1,3,6,7,8,5,4]=>1000011=>0111100
[2,1,3,6,5,8,7,4]=>1001011=>0110100
[2,1,3,5,7,6,8,4]=>1000101=>0111010
[2,1,3,5,6,7,8,4]=>1000001=>0111110
[1,2,3,8,7,6,5,4]=>0001111=>1110000
[1,2,3,7,8,6,5,4]=>0000111=>1111000
[1,2,3,6,8,7,5,4]=>0000111=>1111000
[1,2,3,7,6,8,5,4]=>0001011=>1110100
[1,2,3,6,7,8,5,4]=>0000011=>1111100
[1,2,3,5,8,7,6,4]=>0000111=>1111000
[1,2,3,5,7,8,6,4]=>0000011=>1111100
[1,2,3,6,5,8,7,4]=>0001011=>1110100
[1,2,3,5,6,8,7,4]=>0000011=>1111100
[1,2,3,7,6,5,8,4]=>0001101=>1110010
[1,2,3,6,7,5,8,4]=>0000101=>1111010
[1,2,3,5,7,6,8,4]=>0000101=>1111010
[1,2,3,6,5,7,8,4]=>0001001=>1110110
[1,2,3,5,6,7,8,4]=>0000001=>1111110
[4,3,2,1,8,7,6,5]=>1110111=>0001000
[4,3,2,1,7,8,6,5]=>1110011=>0001100
[4,3,2,1,6,8,7,5]=>1110011=>0001100
[4,3,2,1,7,6,8,5]=>1110101=>0001010
[4,3,2,1,6,7,8,5]=>1110001=>0001110
[3,4,2,1,8,7,6,5]=>0110111=>1001000
[3,4,2,1,7,8,6,5]=>0110011=>1001100
[3,4,2,1,6,8,7,5]=>0110011=>1001100
[3,4,2,1,7,6,8,5]=>0110101=>1001010
[3,4,2,1,6,7,8,5]=>0110001=>1001110
[2,4,3,1,8,7,6,5]=>0110111=>1001000
[2,4,3,1,7,8,6,5]=>0110011=>1001100
[2,4,3,1,6,8,7,5]=>0110011=>1001100
[2,4,3,1,7,6,8,5]=>0110101=>1001010
[2,4,3,1,6,7,8,5]=>0110001=>1001110
[3,2,4,1,8,7,6,5]=>1010111=>0101000
[3,2,4,1,7,8,6,5]=>1010011=>0101100
[3,2,4,1,6,8,7,5]=>1010011=>0101100
[3,2,4,1,7,6,8,5]=>1010101=>0101010
[3,2,4,1,6,7,8,5]=>1010001=>0101110
[2,3,4,1,8,7,6,5]=>0010111=>1101000
[2,3,4,1,7,8,6,5]=>0010011=>1101100
[2,3,4,1,6,8,7,5]=>0010011=>1101100
[2,3,4,1,7,6,8,5]=>0010101=>1101010
[2,3,4,1,6,7,8,5]=>0010001=>1101110
[1,4,3,2,8,7,6,5]=>0110111=>1001000
[1,4,3,2,6,8,7,5]=>0110011=>1001100
[1,4,3,2,7,6,8,5]=>0110101=>1001010
[1,4,3,2,6,7,8,5]=>0110001=>1001110
[1,3,4,2,8,7,6,5]=>0010111=>1101000
[1,3,4,2,7,8,6,5]=>0010011=>1101100
[1,3,4,2,6,8,7,5]=>0010011=>1101100
[1,3,4,2,7,6,8,5]=>0010101=>1101010
[1,3,4,2,6,7,8,5]=>0010001=>1101110
[2,1,4,3,8,7,6,5]=>1010111=>0101000
[2,1,4,3,7,8,6,5]=>1010011=>0101100
[2,1,4,3,6,8,7,5]=>1010011=>0101100
[2,1,4,3,7,6,8,5]=>1010101=>0101010
[2,1,4,3,6,7,8,5]=>1010001=>0101110
[1,2,4,3,8,7,6,5]=>0010111=>1101000
[1,2,4,3,7,8,6,5]=>0010011=>1101100
[1,2,4,3,6,8,7,5]=>0010011=>1101100
[1,2,4,3,7,6,8,5]=>0010101=>1101010
[1,2,4,3,6,7,8,5]=>0010001=>1101110
[3,2,1,4,8,7,6,5]=>1100111=>0011000
[3,2,1,4,7,8,6,5]=>1100011=>0011100
[3,2,1,4,6,8,7,5]=>1100011=>0011100
[3,2,1,4,7,6,8,5]=>1100101=>0011010
[3,2,1,4,6,7,8,5]=>1100001=>0011110
[2,3,1,4,8,7,6,5]=>0100111=>1011000
[2,3,1,4,7,8,6,5]=>0100011=>1011100
[2,3,1,4,7,6,8,5]=>0100101=>1011010
[2,3,1,4,6,7,8,5]=>0100001=>1011110
[1,3,2,4,8,7,6,5]=>0100111=>1011000
[1,3,2,4,6,8,7,5]=>0100011=>1011100
[1,3,2,4,7,6,8,5]=>0100101=>1011010
[1,3,2,4,6,7,8,5]=>0100001=>1011110
[2,1,3,4,8,7,6,5]=>1000111=>0111000
[2,1,3,4,7,8,6,5]=>1000011=>0111100
[2,1,3,4,7,6,8,5]=>1000101=>0111010
[2,1,3,4,6,7,8,5]=>1000001=>0111110
[1,2,3,4,8,7,6,5]=>0000111=>1111000
[1,2,3,4,7,8,6,5]=>0000011=>1111100
[1,2,3,4,6,8,7,5]=>0000011=>1111100
[1,2,3,4,7,6,8,5]=>0000101=>1111010
[1,2,3,4,6,7,8,5]=>0000001=>1111110
[5,4,3,2,1,8,7,6]=>1111011=>0000100
[5,4,3,2,1,7,8,6]=>1111001=>0000110
[4,5,3,2,1,8,7,6]=>0111011=>1000100
[3,5,4,2,1,8,7,6]=>0111011=>1000100
[3,5,4,2,1,7,8,6]=>0111001=>1000110
[4,3,5,2,1,8,7,6]=>1011011=>0100100
[3,4,5,2,1,8,7,6]=>0011011=>1100100
[3,4,5,2,1,7,8,6]=>0011001=>1100110
[2,5,4,3,1,8,7,6]=>0111011=>1000100
[2,5,4,3,1,7,8,6]=>0111001=>1000110
[2,4,5,3,1,8,7,6]=>0011011=>1100100
[2,4,5,3,1,7,8,6]=>0011001=>1100110
[3,2,5,4,1,8,7,6]=>1011011=>0100100
[3,2,5,4,1,7,8,6]=>1011001=>0100110
[2,3,5,4,1,8,7,6]=>0011011=>1100100
[4,3,2,5,1,8,7,6]=>1101011=>0010100
[4,3,2,5,1,7,8,6]=>1101001=>0010110
[3,4,2,5,1,8,7,6]=>0101011=>1010100
[3,4,2,5,1,7,8,6]=>0101001=>1010110
[2,4,3,5,1,8,7,6]=>0101011=>1010100
[2,4,3,5,1,7,8,6]=>0101001=>1010110
[3,2,4,5,1,8,7,6]=>1001011=>0110100
[2,3,4,5,1,8,7,6]=>0001011=>1110100
[2,3,4,5,1,7,8,6]=>0001001=>1110110
[1,5,4,3,2,8,7,6]=>0111011=>1000100
[1,5,4,3,2,7,8,6]=>0111001=>1000110
[1,4,5,3,2,8,7,6]=>0011011=>1100100
[1,4,5,3,2,7,8,6]=>0011001=>1100110
[1,3,5,4,2,7,8,6]=>0011001=>1100110
[1,4,3,5,2,8,7,6]=>0101011=>1010100
[1,4,3,5,2,7,8,6]=>0101001=>1010110
[1,3,4,5,2,8,7,6]=>0001011=>1110100
[1,3,4,5,2,7,8,6]=>0001001=>1110110
[2,1,5,4,3,8,7,6]=>1011011=>0100100
[2,1,4,5,3,8,7,6]=>1001011=>0110100
[1,2,5,4,3,8,7,6]=>0011011=>1100100
[1,2,5,4,3,7,8,6]=>0011001=>1100110
[1,2,4,5,3,8,7,6]=>0001011=>1110100
[1,2,4,5,3,7,8,6]=>0001001=>1110110
[1,3,2,5,4,8,7,6]=>0101011=>1010100
[1,3,2,5,4,7,8,6]=>0101001=>1010110
[2,1,3,5,4,8,7,6]=>1001011=>0110100
[2,1,3,5,4,7,8,6]=>1001001=>0110110
[1,2,3,5,4,8,7,6]=>0001011=>1110100
[1,2,3,5,4,7,8,6]=>0001001=>1110110
[4,3,2,1,5,8,7,6]=>1110011=>0001100
[4,3,2,1,5,7,8,6]=>1110001=>0001110
[2,4,3,1,5,8,7,6]=>0110011=>1001100
[3,2,4,1,5,8,7,6]=>1010011=>0101100
[3,2,4,1,5,7,8,6]=>1010001=>0101110
[2,3,4,1,5,8,7,6]=>0010011=>1101100
[2,3,4,1,5,7,8,6]=>0010001=>1101110
[1,4,3,2,5,8,7,6]=>0110011=>1001100
[1,4,3,2,5,7,8,6]=>0110001=>1001110
[1,3,4,2,5,8,7,6]=>0010011=>1101100
[1,3,4,2,5,7,8,6]=>0010001=>1101110
[2,1,4,3,5,8,7,6]=>1010011=>0101100
[2,1,4,3,5,7,8,6]=>1010001=>0101110
[1,2,4,3,5,8,7,6]=>0010011=>1101100
[1,2,4,3,5,7,8,6]=>0010001=>1101110
[3,2,1,4,5,8,7,6]=>1100011=>0011100
[3,2,1,4,5,7,8,6]=>1100001=>0011110
[2,3,1,4,5,7,8,6]=>0100001=>1011110
[1,3,2,4,5,8,7,6]=>0100011=>1011100
[1,3,2,4,5,7,8,6]=>0100001=>1011110
[2,1,3,4,5,8,7,6]=>1000011=>0111100
[2,1,3,4,5,7,8,6]=>1000001=>0111110
[1,2,3,4,5,8,7,6]=>0000011=>1111100
[1,2,3,4,5,7,8,6]=>0000001=>1111110
[6,5,4,3,2,1,8,7]=>1111101=>0000010
[5,6,4,3,2,1,8,7]=>0111101=>1000010
[4,6,5,3,2,1,8,7]=>0111101=>1000010
[5,4,6,3,2,1,8,7]=>1011101=>0100010
[4,5,6,3,2,1,8,7]=>0011101=>1100010
[3,6,5,4,2,1,8,7]=>0111101=>1000010
[3,5,6,4,2,1,8,7]=>0011101=>1100010
[4,3,6,5,2,1,8,7]=>1011101=>0100010
[3,4,6,5,2,1,8,7]=>0011101=>1100010
[5,4,3,6,2,1,8,7]=>1101101=>0010010
[4,5,3,6,2,1,8,7]=>0101101=>1010010
[4,3,5,6,2,1,8,7]=>1001101=>0110010
[3,4,5,6,2,1,8,7]=>0001101=>1110010
[2,6,5,4,3,1,8,7]=>0111101=>1000010
[2,5,6,4,3,1,8,7]=>0011101=>1100010
[2,4,6,5,3,1,8,7]=>0011101=>1100010
[3,2,6,5,4,1,8,7]=>1011101=>0100010
[3,2,5,6,4,1,8,7]=>1001101=>0110010
[2,3,6,5,4,1,8,7]=>0011101=>1100010
[2,3,5,6,4,1,8,7]=>0001101=>1110010
[4,3,2,6,5,1,8,7]=>1101101=>0010010
[3,4,2,6,5,1,8,7]=>0101101=>1010010
[2,4,3,6,5,1,8,7]=>0101101=>1010010
[5,4,3,2,6,1,8,7]=>1110101=>0001010
[4,5,3,2,6,1,8,7]=>0110101=>1001010
[3,5,4,2,6,1,8,7]=>0110101=>1001010
[4,3,5,2,6,1,8,7]=>1010101=>0101010
[3,4,5,2,6,1,8,7]=>0010101=>1101010
[2,5,4,3,6,1,8,7]=>0110101=>1001010
[2,4,5,3,6,1,8,7]=>0010101=>1101010
[3,2,5,4,6,1,8,7]=>1010101=>0101010
[4,3,2,5,6,1,8,7]=>1100101=>0011010
[3,4,2,5,6,1,8,7]=>0100101=>1011010
[2,4,3,5,6,1,8,7]=>0100101=>1011010
[2,3,4,5,6,1,8,7]=>0000101=>1111010
[1,6,5,4,3,2,8,7]=>0111101=>1000010
[1,5,6,4,3,2,8,7]=>0011101=>1100010
[1,5,4,6,3,2,8,7]=>0101101=>1010010
[1,3,6,5,4,2,8,7]=>0011101=>1100010
[1,3,4,5,6,2,8,7]=>0000101=>1111010
[2,1,6,5,4,3,8,7]=>1011101=>0100010
[2,1,5,6,4,3,8,7]=>1001101=>0110010
[2,1,4,6,5,3,8,7]=>1001101=>0110010
[2,1,5,4,6,3,8,7]=>1010101=>0101010
[2,1,4,5,6,3,8,7]=>1000101=>0111010
[1,2,4,5,6,3,8,7]=>0000101=>1111010
[3,2,1,6,5,4,8,7]=>1101101=>0010010
[2,3,1,6,5,4,8,7]=>0101101=>1010010
[1,3,2,6,5,4,8,7]=>0101101=>1010010
[1,3,2,5,6,4,8,7]=>0100101=>1011010
[2,1,3,5,6,4,8,7]=>1000101=>0111010
[1,2,3,6,5,4,8,7]=>0001101=>1110010
[1,2,3,5,6,4,8,7]=>0000101=>1111010
[4,3,2,1,6,5,8,7]=>1110101=>0001010
[3,4,2,1,6,5,8,7]=>0110101=>1001010
[2,4,3,1,6,5,8,7]=>0110101=>1001010
[3,2,4,1,6,5,8,7]=>1010101=>0101010
[2,3,4,1,6,5,8,7]=>0010101=>1101010
[1,3,4,2,6,5,8,7]=>0010101=>1101010
[2,1,4,3,6,5,8,7]=>1010101=>0101010
[1,2,4,3,6,5,8,7]=>0010101=>1101010
[2,3,1,4,6,5,8,7]=>0100101=>1011010
[1,3,2,4,6,5,8,7]=>0100101=>1011010
[2,1,3,4,6,5,8,7]=>1000101=>0111010
[1,2,3,4,6,5,8,7]=>0000101=>1111010
[5,4,3,2,1,6,8,7]=>1111001=>0000110
[4,5,3,2,1,6,8,7]=>0111001=>1000110
[3,5,4,2,1,6,8,7]=>0111001=>1000110
[4,3,5,2,1,6,8,7]=>1011001=>0100110
[3,4,5,2,1,6,8,7]=>0011001=>1100110
[2,5,4,3,1,6,8,7]=>0111001=>1000110
[2,4,5,3,1,6,8,7]=>0011001=>1100110
[3,2,5,4,1,6,8,7]=>1011001=>0100110
[2,3,5,4,1,6,8,7]=>0011001=>1100110
[2,4,3,5,1,6,8,7]=>0101001=>1010110
[2,3,4,5,1,6,8,7]=>0001001=>1110110
[1,4,5,3,2,6,8,7]=>0011001=>1100110
[1,3,5,4,2,6,8,7]=>0011001=>1100110
[1,3,4,5,2,6,8,7]=>0001001=>1110110
[2,1,4,5,3,6,8,7]=>1001001=>0110110
[1,2,5,4,3,6,8,7]=>0011001=>1100110
[2,1,3,5,4,6,8,7]=>1001001=>0110110
[1,2,3,5,4,6,8,7]=>0001001=>1110110
[4,3,2,1,5,6,8,7]=>1110001=>0001110
[3,2,4,1,5,6,8,7]=>1010001=>0101110
[2,3,4,1,5,6,8,7]=>0010001=>1101110
[1,4,3,2,5,6,8,7]=>0110001=>1001110
[1,3,4,2,5,6,8,7]=>0010001=>1101110
[2,1,4,3,5,6,8,7]=>1010001=>0101110
[1,2,4,3,5,6,8,7]=>0010001=>1101110
[3,2,1,4,5,6,8,7]=>1100001=>0011110
[2,3,1,4,5,6,8,7]=>0100001=>1011110
[1,3,2,4,5,6,8,7]=>0100001=>1011110
[2,1,3,4,5,6,8,7]=>1000001=>0111110
[1,2,3,4,5,6,8,7]=>0000001=>1111110
[5,7,6,4,3,2,1,8]=>0111110=>1000001
[4,7,6,5,3,2,1,8]=>0111110=>1000001
[4,6,7,5,3,2,1,8]=>0011110=>1100001
[5,4,7,6,3,2,1,8]=>1011110=>0100001
[4,5,7,6,3,2,1,8]=>0011110=>1100001
[4,6,5,7,3,2,1,8]=>0101110=>1010001
[3,5,7,6,4,2,1,8]=>0011110=>1100001
[3,5,6,7,4,2,1,8]=>0001110=>1110001
[4,3,7,6,5,2,1,8]=>1011110=>0100001
[3,4,7,6,5,2,1,8]=>0011110=>1100001
[5,4,3,7,6,2,1,8]=>1101110=>0010001
[4,5,3,7,6,2,1,8]=>0101110=>1010001
[3,5,4,7,6,2,1,8]=>0101110=>1010001
[4,3,5,7,6,2,1,8]=>1001110=>0110001
[3,6,5,4,7,2,1,8]=>0110110=>1001001
[3,5,6,4,7,2,1,8]=>0010110=>1101001
[4,3,6,5,7,2,1,8]=>1010110=>0101001
[2,7,6,5,4,3,1,8]=>0111110=>1000001
[2,6,7,5,4,3,1,8]=>0011110=>1100001
[2,5,7,6,4,3,1,8]=>0011110=>1100001
[2,5,6,7,4,3,1,8]=>0001110=>1110001
[2,4,6,7,5,3,1,8]=>0001110=>1110001
[2,5,4,7,6,3,1,8]=>0101110=>1010001
[2,5,6,4,7,3,1,8]=>0010110=>1101001
[2,5,4,6,7,3,1,8]=>0100110=>1011001
[2,4,5,6,7,3,1,8]=>0000110=>1111001
[3,2,7,6,5,4,1,8]=>1011110=>0100001
[3,2,6,7,5,4,1,8]=>1001110=>0110001
[3,2,5,7,6,4,1,8]=>1001110=>0110001
[3,2,6,5,7,4,1,8]=>1010110=>0101001
[3,2,5,6,7,4,1,8]=>1000110=>0111001
[2,3,7,6,5,4,1,8]=>0011110=>1100001
[2,3,6,7,5,4,1,8]=>0001110=>1110001
[2,3,5,7,6,4,1,8]=>0001110=>1110001
[2,3,6,5,7,4,1,8]=>0010110=>1101001
[2,3,5,6,7,4,1,8]=>0000110=>1111001
[4,3,2,6,7,5,1,8]=>1100110=>0011001
[3,4,2,7,6,5,1,8]=>0101110=>1010001
[3,4,2,6,7,5,1,8]=>0100110=>1011001
[3,2,4,6,7,5,1,8]=>1000110=>0111001
[2,3,4,7,6,5,1,8]=>0001110=>1110001
[2,3,4,6,7,5,1,8]=>0000110=>1111001
[5,4,3,2,7,6,1,8]=>1110110=>0001001
[4,5,3,2,7,6,1,8]=>0110110=>1001001
[3,5,4,2,7,6,1,8]=>0110110=>1001001
[4,3,5,2,7,6,1,8]=>1010110=>0101001
[3,4,5,2,7,6,1,8]=>0010110=>1101001
[3,2,5,4,7,6,1,8]=>1010110=>0101001
[4,3,2,5,7,6,1,8]=>1100110=>0011001
[3,4,2,5,7,6,1,8]=>0100110=>1011001
[2,3,4,5,7,6,1,8]=>0000110=>1111001
[3,6,5,4,2,7,1,8]=>0111010=>1000101
[3,5,6,4,2,7,1,8]=>0011010=>1100101
[3,4,6,5,2,7,1,8]=>0011010=>1100101
[3,5,4,6,2,7,1,8]=>0101010=>1010101
[2,5,4,6,3,7,1,8]=>0101010=>1010101
[3,2,6,5,4,7,1,8]=>1011010=>0100101
[2,3,5,6,4,7,1,8]=>0001010=>1110101
[4,3,2,6,5,7,1,8]=>1101010=>0010101
[3,4,2,6,5,7,1,8]=>0101010=>1010101
[2,4,3,6,5,7,1,8]=>0101010=>1010101
[2,3,4,6,5,7,1,8]=>0001010=>1110101
[3,5,4,2,6,7,1,8]=>0110010=>1001101
[2,5,4,3,6,7,1,8]=>0110010=>1001101
[2,4,5,3,6,7,1,8]=>0010010=>1101101
[2,3,5,4,6,7,1,8]=>0010010=>1101101
[1,7,6,5,4,3,2,8]=>0111110=>1000001
[1,6,7,5,4,3,2,8]=>0011110=>1100001
[1,6,5,7,4,3,2,8]=>0101110=>1010001
[1,5,6,7,4,3,2,8]=>0001110=>1110001
[1,4,7,6,5,3,2,8]=>0011110=>1100001
[1,4,6,7,5,3,2,8]=>0001110=>1110001
[1,5,4,7,6,3,2,8]=>0101110=>1010001
[1,5,6,4,7,3,2,8]=>0010110=>1101001
[1,4,6,5,7,3,2,8]=>0010110=>1101001
[1,5,4,6,7,3,2,8]=>0100110=>1011001
[1,4,5,6,7,3,2,8]=>0000110=>1111001
[1,3,7,6,5,4,2,8]=>0011110=>1100001
[1,3,6,7,5,4,2,8]=>0001110=>1110001
[1,3,5,7,6,4,2,8]=>0001110=>1110001
[1,3,6,5,7,4,2,8]=>0010110=>1101001
[1,3,5,6,7,4,2,8]=>0000110=>1111001
[1,3,4,6,7,5,2,8]=>0000110=>1111001
[1,3,5,4,7,6,2,8]=>0010110=>1101001
[1,4,3,5,7,6,2,8]=>0100110=>1011001
[1,3,4,5,7,6,2,8]=>0000110=>1111001
[1,5,4,6,3,7,2,8]=>0101010=>1010101
[1,4,5,6,3,7,2,8]=>0001010=>1110101
[1,3,6,5,4,7,2,8]=>0011010=>1100101
[1,3,5,6,4,7,2,8]=>0001010=>1110101
[1,4,3,6,5,7,2,8]=>0101010=>1010101
[1,3,4,6,5,7,2,8]=>0001010=>1110101
[1,5,4,3,6,7,2,8]=>0110010=>1001101
[1,4,5,3,6,7,2,8]=>0010010=>1101101
[1,3,5,4,6,7,2,8]=>0010010=>1101101
[1,3,4,5,6,7,2,8]=>0000010=>1111101
[2,1,7,6,5,4,3,8]=>1011110=>0100001
[2,1,6,7,5,4,3,8]=>1001110=>0110001
[2,1,5,6,7,4,3,8]=>1000110=>0111001
[2,1,4,6,7,5,3,8]=>1000110=>0111001
[2,1,4,5,6,7,3,8]=>1000010=>0111101
[1,2,7,6,5,4,3,8]=>0011110=>1100001
[1,2,6,7,5,4,3,8]=>0001110=>1110001
[1,2,5,7,6,4,3,8]=>0001110=>1110001
[1,2,5,6,7,4,3,8]=>0000110=>1111001
[1,2,4,6,7,5,3,8]=>0000110=>1111001
[1,2,5,6,4,7,3,8]=>0001010=>1110101
[1,2,5,4,6,7,3,8]=>0010010=>1101101
[1,2,4,5,6,7,3,8]=>0000010=>1111101
[3,2,1,7,6,5,4,8]=>1101110=>0010001
[3,2,1,6,7,5,4,8]=>1100110=>0011001
[3,2,1,5,7,6,4,8]=>1100110=>0011001
[3,2,1,5,6,7,4,8]=>1100010=>0011101
[2,3,1,6,7,5,4,8]=>0100110=>1011001
[2,3,1,6,5,7,4,8]=>0101010=>1010101
[2,3,1,5,6,7,4,8]=>0100010=>1011101
[1,3,2,7,6,5,4,8]=>0101110=>1010001
[1,3,2,6,7,5,4,8]=>0100110=>1011001
[1,3,2,5,7,6,4,8]=>0100110=>1011001
[1,3,2,6,5,7,4,8]=>0101010=>1010101
[1,3,2,5,6,7,4,8]=>0100010=>1011101
[2,1,3,6,7,5,4,8]=>1000110=>0111001
[1,2,3,7,6,5,4,8]=>0001110=>1110001
[1,2,3,6,7,5,4,8]=>0000110=>1111001
[1,2,3,5,7,6,4,8]=>0000110=>1111001
[1,2,3,6,5,7,4,8]=>0001010=>1110101
[1,2,3,5,6,7,4,8]=>0000010=>1111101
[4,3,2,1,7,6,5,8]=>1110110=>0001001
[4,3,2,1,6,7,5,8]=>1110010=>0001101
[3,2,4,1,7,6,5,8]=>1010110=>0101001
[3,2,4,1,6,7,5,8]=>1010010=>0101101
[2,3,4,1,7,6,5,8]=>0010110=>1101001
[2,3,4,1,6,7,5,8]=>0010010=>1101101
[1,4,3,2,7,6,5,8]=>0110110=>1001001
[1,4,3,2,6,7,5,8]=>0110010=>1001101
[1,3,4,2,6,7,5,8]=>0010010=>1101101
[1,2,4,3,6,7,5,8]=>0010010=>1101101
[3,2,1,4,7,6,5,8]=>1100110=>0011001
[2,3,1,4,6,7,5,8]=>0100010=>1011101
[1,3,2,4,7,6,5,8]=>0100110=>1011001
[2,1,3,4,6,7,5,8]=>1000010=>0111101
[1,2,3,4,7,6,5,8]=>0000110=>1111001
[1,2,3,4,6,7,5,8]=>0000010=>1111101
[5,4,3,2,1,7,6,8]=>1111010=>0000101
[4,5,3,2,1,7,6,8]=>0111010=>1000101
[3,5,4,2,1,7,6,8]=>0111010=>1000101
[3,4,5,2,1,7,6,8]=>0011010=>1100101
[2,5,4,3,1,7,6,8]=>0111010=>1000101
[2,4,5,3,1,7,6,8]=>0011010=>1100101
[3,2,5,4,1,7,6,8]=>1011010=>0100101
[2,3,5,4,1,7,6,8]=>0011010=>1100101
[3,4,2,5,1,7,6,8]=>0101010=>1010101
[2,4,3,5,1,7,6,8]=>0101010=>1010101
[2,3,4,5,1,7,6,8]=>0001010=>1110101
[1,5,4,3,2,7,6,8]=>0111010=>1000101
[1,4,5,3,2,7,6,8]=>0011010=>1100101
[1,3,5,4,2,7,6,8]=>0011010=>1100101
[1,4,3,5,2,7,6,8]=>0101010=>1010101
[1,3,4,5,2,7,6,8]=>0001010=>1110101
[2,1,5,4,3,7,6,8]=>1011010=>0100101
[1,2,4,5,3,7,6,8]=>0001010=>1110101
[3,2,1,5,4,7,6,8]=>1101010=>0010101
[2,3,1,5,4,7,6,8]=>0101010=>1010101
[1,3,2,5,4,7,6,8]=>0101010=>1010101
[1,2,3,5,4,7,6,8]=>0001010=>1110101
[4,3,2,1,5,7,6,8]=>1110010=>0001101
[3,2,4,1,5,7,6,8]=>1010010=>0101101
[2,3,4,1,5,7,6,8]=>0010010=>1101101
[1,4,3,2,5,7,6,8]=>0110010=>1001101
[1,3,4,2,5,7,6,8]=>0010010=>1101101
[1,2,4,3,5,7,6,8]=>0010010=>1101101
[2,3,1,4,5,7,6,8]=>0100010=>1011101
[1,3,2,4,5,7,6,8]=>0100010=>1011101
[2,1,3,4,5,7,6,8]=>1000010=>0111101
[1,2,3,4,5,7,6,8]=>0000010=>1111101
[3,6,5,4,2,1,7,8]=>0111100=>1000011
[4,3,6,5,2,1,7,8]=>1011100=>0100011
[2,4,6,5,3,1,7,8]=>0011100=>1100011
[2,4,5,6,3,1,7,8]=>0001100=>1110011
[2,3,6,5,4,1,7,8]=>0011100=>1100011
[2,3,5,6,4,1,7,8]=>0001100=>1110011
[4,3,2,6,5,1,7,8]=>1101100=>0010011
[2,4,3,6,5,1,7,8]=>0101100=>1010011
[2,3,4,6,5,1,7,8]=>0001100=>1110011
[3,5,4,2,6,1,7,8]=>0110100=>1001011
[2,3,5,4,6,1,7,8]=>0010100=>1101011
[1,6,5,4,3,2,7,8]=>0111100=>1000011
[1,5,6,4,3,2,7,8]=>0011100=>1100011
[1,4,6,5,3,2,7,8]=>0011100=>1100011
[1,5,4,6,3,2,7,8]=>0101100=>1010011
[1,4,5,6,3,2,7,8]=>0001100=>1110011
[1,3,5,6,4,2,7,8]=>0001100=>1110011
[1,4,3,6,5,2,7,8]=>0101100=>1010011
[1,5,4,3,6,2,7,8]=>0110100=>1001011
[1,4,5,3,6,2,7,8]=>0010100=>1101011
[1,3,5,4,6,2,7,8]=>0010100=>1101011
[1,4,3,5,6,2,7,8]=>0100100=>1011011
[1,3,4,5,6,2,7,8]=>0000100=>1111011
[2,1,5,6,4,3,7,8]=>1001100=>0110011
[2,1,4,6,5,3,7,8]=>1001100=>0110011
[1,2,6,5,4,3,7,8]=>0011100=>1100011
[1,2,5,6,4,3,7,8]=>0001100=>1110011
[1,2,4,6,5,3,7,8]=>0001100=>1110011
[1,2,4,5,6,3,7,8]=>0000100=>1111011
[3,2,1,6,5,4,7,8]=>1101100=>0010011
[3,2,1,5,6,4,7,8]=>1100100=>0011011
[2,3,1,6,5,4,7,8]=>0101100=>1010011
[2,3,1,5,6,4,7,8]=>0100100=>1011011
[1,3,2,6,5,4,7,8]=>0101100=>1010011
[1,3,2,5,6,4,7,8]=>0100100=>1011011
[1,2,3,6,5,4,7,8]=>0001100=>1110011
[1,2,3,5,6,4,7,8]=>0000100=>1111011
[4,3,2,1,6,5,7,8]=>1110100=>0001011
[2,4,3,1,6,5,7,8]=>0110100=>1001011
[3,2,4,1,6,5,7,8]=>1010100=>0101011
[2,3,4,1,6,5,7,8]=>0010100=>1101011
[2,1,4,3,6,5,7,8]=>1010100=>0101011
[1,2,4,3,6,5,7,8]=>0010100=>1101011
[1,3,2,4,6,5,7,8]=>0100100=>1011011
[2,1,3,4,6,5,7,8]=>1000100=>0111011
[1,2,3,4,6,5,7,8]=>0000100=>1111011
[3,5,4,2,1,6,7,8]=>0111000=>1000111
[2,5,4,3,1,6,7,8]=>0111000=>1000111
[2,4,5,3,1,6,7,8]=>0011000=>1100111
[3,2,5,4,1,6,7,8]=>1011000=>0100111
[2,3,5,4,1,6,7,8]=>0011000=>1100111
[2,4,3,5,1,6,7,8]=>0101000=>1010111
[1,5,4,3,2,6,7,8]=>0111000=>1000111
[1,4,5,3,2,6,7,8]=>0011000=>1100111
[1,3,5,4,2,6,7,8]=>0011000=>1100111
[1,3,4,5,2,6,7,8]=>0001000=>1110111
[2,1,5,4,3,6,7,8]=>1011000=>0100111
[2,1,4,5,3,6,7,8]=>1001000=>0110111
[1,2,5,4,3,6,7,8]=>0011000=>1100111
[3,2,1,5,4,6,7,8]=>1101000=>0010111
[2,3,1,5,4,6,7,8]=>0101000=>1010111
[1,3,2,5,4,6,7,8]=>0101000=>1010111
[1,2,3,5,4,6,7,8]=>0001000=>1110111
[2,4,3,1,5,6,7,8]=>0110000=>1001111
[1,4,3,2,5,6,7,8]=>0110000=>1001111
[1,3,4,2,5,6,7,8]=>0010000=>1101111
[2,1,4,3,5,6,7,8]=>1010000=>0101111
[1,2,4,3,5,6,7,8]=>0010000=>1101111
[1,3,2,4,5,6,7,8]=>0100000=>1011111
[1,2,3,4,8,6,7,5]=>0000101=>1111010
[1,2,3,5,8,6,7,4]=>0000101=>1111010
[1,2,3,7,5,6,4,8]=>0001010=>1110101
[1,2,3,7,5,6,8,4]=>0001001=>1110110
[1,2,3,8,5,6,7,4]=>0001001=>1110110
[1,2,3,8,5,7,6,4]=>0001011=>1110100
[1,2,3,8,6,5,7,4]=>0001101=>1110010
[1,2,3,8,6,7,5,4]=>0001011=>1110100
[1,2,4,5,8,6,7,3]=>0000101=>1111010
[1,2,4,7,5,6,8,3]=>0001001=>1110110
[1,2,4,8,5,6,7,3]=>0001001=>1110110
[1,2,4,8,6,5,7,3]=>0001101=>1110010
[1,2,5,4,8,6,7,3]=>0010101=>1101010
[1,2,6,4,5,3,7,8]=>0010100=>1101011
[1,2,6,4,5,7,8,3]=>0010001=>1101110
[1,2,6,4,5,8,7,3]=>0010011=>1101100
[1,2,7,4,5,6,8,3]=>0010001=>1101110
[1,2,8,4,5,6,7,3]=>0010001=>1101110
[1,2,8,4,6,7,5,3]=>0010011=>1101100
[1,2,8,4,7,6,5,3]=>0010111=>1101000
[1,2,7,5,4,6,3,8]=>0011010=>1100101
[1,2,7,5,4,6,8,3]=>0011001=>1100110
[1,2,8,5,4,6,7,3]=>0011001=>1100110
[1,2,8,5,4,7,6,3]=>0011011=>1100100
[1,2,8,5,6,4,7,3]=>0010101=>1101010
[1,2,8,5,6,7,4,3]=>0010011=>1101100
[1,2,8,6,5,4,7,3]=>0011101=>1100010
[1,2,8,6,5,7,4,3]=>0011011=>1100100
[1,2,8,7,5,6,4,3]=>0011011=>1100100
[1,3,2,4,8,6,7,5]=>0100101=>1011010
[1,3,2,7,5,6,8,4]=>0101001=>1010110
[1,3,2,8,5,7,6,4]=>0101011=>1010100
[1,3,2,8,6,5,7,4]=>0101101=>1010010
[1,3,2,8,6,7,5,4]=>0101011=>1010100
[1,3,4,2,8,6,7,5]=>0010101=>1101010
[1,3,4,5,8,6,7,2]=>0000101=>1111010
[1,3,4,8,5,6,7,2]=>0001001=>1110110
[1,3,4,8,6,5,7,2]=>0001101=>1110010
[1,3,4,8,6,7,5,2]=>0001011=>1110100
[1,3,6,4,5,2,8,7]=>0010101=>1101010
[1,3,6,4,5,7,2,8]=>0010010=>1101101
[1,3,6,4,5,7,8,2]=>0010001=>1101110
[1,3,6,4,5,8,7,2]=>0010011=>1101100
[1,3,7,4,5,6,2,8]=>0010010=>1101101
[1,3,7,4,5,6,8,2]=>0010001=>1101110
[1,3,8,4,5,6,7,2]=>0010001=>1101110
[1,3,8,4,6,5,7,2]=>0010101=>1101010
[1,3,8,5,4,6,7,2]=>0011001=>1100110
[1,3,8,5,4,7,6,2]=>0011011=>1100100
[1,3,8,5,6,7,4,2]=>0010011=>1101100
[1,3,8,5,7,6,4,2]=>0010111=>1101000
[1,3,8,6,5,7,4,2]=>0011011=>1100100
[1,3,8,7,5,6,4,2]=>0011011=>1100100
[1,4,3,5,8,6,7,2]=>0100101=>1011010
[1,4,3,8,5,6,7,2]=>0101001=>1010110
[1,4,3,8,5,7,6,2]=>0101011=>1010100
[1,4,3,8,6,5,7,2]=>0101101=>1010010
[1,4,3,8,6,7,5,2]=>0101011=>1010100
[1,5,3,4,2,6,7,8]=>0101000=>1010111
[1,5,3,4,2,7,8,6]=>0101001=>1010110
[1,5,3,4,2,8,7,6]=>0101011=>1010100
[1,5,3,4,6,2,7,8]=>0100100=>1011011
[1,5,3,4,6,2,8,7]=>0100101=>1011010
[1,5,3,4,6,7,2,8]=>0100010=>1011101
[1,5,3,4,6,7,8,2]=>0100001=>1011110
[1,5,3,4,7,6,2,8]=>0100110=>1011001
[1,5,3,4,8,6,7,2]=>0100101=>1011010
[1,6,3,4,5,2,7,8]=>0100100=>1011011
[1,6,3,4,5,8,7,2]=>0100011=>1011100
[1,7,3,4,5,6,2,8]=>0100010=>1011101
[1,7,3,4,5,6,8,2]=>0100001=>1011110
[1,8,3,4,5,6,7,2]=>0100001=>1011110
[1,8,3,4,6,7,5,2]=>0100011=>1011100
[1,6,3,5,4,2,7,8]=>0101100=>1010011
[1,6,3,5,4,8,7,2]=>0101011=>1010100
[1,7,3,5,4,6,2,8]=>0101010=>1010101
[1,8,3,5,4,6,7,2]=>0101001=>1010110
[1,8,3,5,4,7,6,2]=>0101011=>1010100
[1,8,3,5,6,4,7,2]=>0100101=>1011010
[1,8,3,5,6,7,4,2]=>0100011=>1011100
[1,8,3,5,7,6,4,2]=>0100111=>1011000
[1,7,3,6,5,4,2,8]=>0101110=>1010001
[1,7,3,6,5,4,8,2]=>0101101=>1010010
[1,8,3,6,5,4,7,2]=>0101101=>1010010
[1,8,3,7,5,6,4,2]=>0101011=>1010100
[1,8,3,7,6,5,4,2]=>0101111=>1010000
[1,6,4,3,5,2,7,8]=>0110100=>1001011
[1,6,4,3,5,8,7,2]=>0110011=>1001100
[1,8,4,3,5,6,7,2]=>0110001=>1001110
[1,8,4,3,5,7,6,2]=>0110011=>1001100
[1,7,4,3,6,5,8,2]=>0110101=>1001010
[1,8,4,3,6,5,7,2]=>0110101=>1001010
[1,8,4,3,6,7,5,2]=>0110011=>1001100
[1,6,4,5,3,2,7,8]=>0101100=>1010011
[1,6,4,5,3,2,8,7]=>0101101=>1010010
[1,6,4,5,3,8,7,2]=>0101011=>1010100
[1,7,4,5,3,6,8,2]=>0101001=>1010110
[1,8,4,5,3,6,7,2]=>0101001=>1010110
[1,7,4,5,6,3,2,8]=>0100110=>1011001
[1,7,4,5,6,3,8,2]=>0100101=>1011010
[1,8,4,5,6,3,7,2]=>0100101=>1011010
[1,8,4,5,6,7,3,2]=>0100011=>1011100
[1,7,4,6,5,3,2,8]=>0101110=>1010001
[1,8,4,6,5,3,7,2]=>0101101=>1010010
[1,8,4,6,5,7,3,2]=>0101011=>1010100
[1,8,4,7,6,5,3,2]=>0101111=>1010000
[1,7,5,4,3,6,2,8]=>0111010=>1000101
[1,7,5,4,3,6,8,2]=>0111001=>1000110
[1,8,5,4,3,6,7,2]=>0111001=>1000110
[1,8,5,4,3,7,6,2]=>0111011=>1000100
[1,8,5,4,6,3,7,2]=>0110101=>1001010
[1,8,5,4,6,7,3,2]=>0110011=>1001100
[1,8,5,4,7,6,3,2]=>0110111=>1001000
[1,7,6,4,5,3,2,8]=>0110110=>1001001
[1,8,6,4,5,3,7,2]=>0110101=>1001010
[1,8,6,4,5,7,3,2]=>0110011=>1001100
[1,8,7,4,5,6,3,2]=>0110011=>1001100
[1,8,7,4,6,5,3,2]=>0110111=>1001000
[1,8,6,5,4,3,7,2]=>0111101=>1000010
[1,8,6,5,4,7,3,2]=>0111011=>1000100
[1,8,7,5,4,6,3,2]=>0111011=>1000100
[1,8,7,5,6,4,3,2]=>0110111=>1001000
[2,1,3,4,8,6,7,5]=>1000101=>0111010
[2,1,3,5,8,6,7,4]=>1000101=>0111010
[2,1,3,8,5,6,7,4]=>1001001=>0110110
[2,1,3,8,5,7,6,4]=>1001011=>0110100
[2,1,3,8,6,5,7,4]=>1001101=>0110010
[2,1,3,8,6,7,5,4]=>1001011=>0110100
[2,1,4,3,8,6,7,5]=>1010101=>0101010
[2,1,4,5,8,6,7,3]=>1000101=>0111010
[2,1,4,8,5,6,7,3]=>1001001=>0110110
[2,1,4,8,5,7,6,3]=>1001011=>0110100
[2,1,4,8,6,5,7,3]=>1001101=>0110010
[2,1,4,8,6,7,5,3]=>1001011=>0110100
[2,1,5,4,8,6,7,3]=>1010101=>0101010
[2,1,6,4,5,3,8,7]=>1010101=>0101010
[2,1,6,4,5,7,8,3]=>1010001=>0101110
[2,1,6,4,5,8,7,3]=>1010011=>0101100
[2,1,8,4,5,6,7,3]=>1010001=>0101110
[2,1,8,4,5,7,6,3]=>1010011=>0101100
[2,1,7,4,6,5,8,3]=>1010101=>0101010
[2,1,8,4,6,5,7,3]=>1010101=>0101010
[2,1,8,4,6,7,5,3]=>1010011=>0101100
[2,1,8,4,7,6,5,3]=>1010111=>0101000
[2,1,7,5,4,6,8,3]=>1011001=>0100110
[2,1,8,5,4,6,7,3]=>1011001=>0100110
[2,1,8,5,4,7,6,3]=>1011011=>0100100
[2,1,7,5,6,4,8,3]=>1010101=>0101010
[2,1,8,5,6,4,7,3]=>1010101=>0101010
[2,1,8,5,6,7,4,3]=>1010011=>0101100
[2,1,8,5,7,6,4,3]=>1010111=>0101000
[2,1,8,6,5,4,7,3]=>1011101=>0100010
[2,1,8,6,5,7,4,3]=>1011011=>0100100
[2,1,8,7,5,6,4,3]=>1011011=>0100100
[2,3,1,7,5,6,4,8]=>0101010=>1010101
[2,3,1,8,5,6,7,4]=>0101001=>1010110
[2,3,1,8,6,7,5,4]=>0101011=>1010100
[2,3,4,1,8,6,7,5]=>0010101=>1101010
[2,3,4,5,8,6,7,1]=>0000101=>1111010
[2,3,4,7,5,6,1,8]=>0001010=>1110101
[2,3,4,7,5,6,8,1]=>0001001=>1110110
[2,3,4,8,5,6,7,1]=>0001001=>1110110
[2,3,4,8,5,7,6,1]=>0001011=>1110100
[2,3,4,8,6,5,7,1]=>0001101=>1110010
[2,3,4,8,6,7,5,1]=>0001011=>1110100
[2,3,5,4,8,6,7,1]=>0010101=>1101010
[2,3,6,4,5,1,7,8]=>0010100=>1101011
[2,3,6,4,5,1,8,7]=>0010101=>1101010
[2,3,6,4,5,7,8,1]=>0010001=>1101110
[2,3,6,4,5,8,7,1]=>0010011=>1101100
[2,3,7,4,5,6,8,1]=>0010001=>1101110
[2,3,8,4,5,6,7,1]=>0010001=>1101110
[2,3,7,4,6,5,8,1]=>0010101=>1101010
[2,3,8,4,6,7,5,1]=>0010011=>1101100
[2,3,7,5,4,6,1,8]=>0011010=>1100101
[2,3,7,5,4,6,8,1]=>0011001=>1100110
[2,3,8,5,4,6,7,1]=>0011001=>1100110
[2,3,7,5,6,4,1,8]=>0010110=>1101001
[2,3,7,5,6,4,8,1]=>0010101=>1101010
[2,3,8,5,6,4,7,1]=>0010101=>1101010
[2,3,8,5,6,7,4,1]=>0010011=>1101100
[2,3,8,5,7,6,4,1]=>0010111=>1101000
[2,3,8,6,5,4,7,1]=>0011101=>1100010
[2,4,3,1,8,6,7,5]=>0110101=>1001010
[2,4,3,5,8,6,7,1]=>0100101=>1011010
[2,4,3,7,5,6,8,1]=>0101001=>1010110
[2,4,3,8,5,6,7,1]=>0101001=>1010110
[2,4,3,8,5,7,6,1]=>0101011=>1010100
[2,4,3,8,6,5,7,1]=>0101101=>1010010
[2,4,3,8,6,7,5,1]=>0101011=>1010100
[2,5,3,4,1,6,7,8]=>0101000=>1010111
[2,5,3,4,1,8,7,6]=>0101011=>1010100
[2,5,3,4,6,7,1,8]=>0100010=>1011101
[2,5,3,4,6,7,8,1]=>0100001=>1011110
[2,5,3,4,6,8,7,1]=>0100011=>1011100
[2,5,3,4,7,6,8,1]=>0100101=>1011010
[2,5,3,4,8,6,7,1]=>0100101=>1011010
[2,5,3,4,8,7,6,1]=>0100111=>1011000
[2,6,3,4,5,1,7,8]=>0100100=>1011011
[2,6,3,4,5,7,8,1]=>0100001=>1011110
[2,6,3,4,5,8,7,1]=>0100011=>1011100
[2,7,3,4,5,6,1,8]=>0100010=>1011101
[2,8,3,4,5,6,7,1]=>0100001=>1011110
[2,8,3,4,5,7,6,1]=>0100011=>1011100
[2,6,3,5,4,1,7,8]=>0101100=>1010011
[2,6,3,5,4,1,8,7]=>0101101=>1010010
[2,6,3,5,4,7,8,1]=>0101001=>1010110
[2,6,3,5,4,8,7,1]=>0101011=>1010100
[2,7,3,5,4,6,8,1]=>0101001=>1010110
[2,8,3,5,4,7,6,1]=>0101011=>1010100
[2,7,3,5,6,4,8,1]=>0100101=>1011010
[2,8,3,5,6,7,4,1]=>0100011=>1011100
[2,8,3,5,7,6,4,1]=>0100111=>1011000
[2,7,3,6,5,4,1,8]=>0101110=>1010001
[2,8,3,7,5,6,4,1]=>0101011=>1010100
[2,8,3,7,6,5,4,1]=>0101111=>1010000
[2,5,4,3,8,6,7,1]=>0110101=>1001010
[2,6,4,3,5,1,8,7]=>0110101=>1001010
[2,6,4,3,5,7,8,1]=>0110001=>1001110
[2,6,4,3,5,8,7,1]=>0110011=>1001100
[2,7,4,3,5,6,8,1]=>0110001=>1001110
[2,8,4,3,5,6,7,1]=>0110001=>1001110
[2,8,4,3,5,7,6,1]=>0110011=>1001100
[2,7,4,3,6,5,8,1]=>0110101=>1001010
[2,8,4,3,6,5,7,1]=>0110101=>1001010
[2,8,4,3,6,7,5,1]=>0110011=>1001100
[2,8,4,3,7,6,5,1]=>0110111=>1001000
[2,6,4,5,3,1,7,8]=>0101100=>1010011
[2,6,4,5,3,1,8,7]=>0101101=>1010010
[2,6,4,5,3,7,8,1]=>0101001=>1010110
[2,6,4,5,3,8,7,1]=>0101011=>1010100
[2,8,4,5,3,6,7,1]=>0101001=>1010110
[2,7,4,5,6,3,1,8]=>0100110=>1011001
[2,7,4,5,6,3,8,1]=>0100101=>1011010
[2,8,4,5,6,3,7,1]=>0100101=>1011010
[2,8,4,5,6,7,3,1]=>0100011=>1011100
[2,7,4,6,5,3,1,8]=>0101110=>1010001
[2,7,4,6,5,3,8,1]=>0101101=>1010010
[2,8,4,6,5,3,7,1]=>0101101=>1010010
[2,8,4,7,6,5,3,1]=>0101111=>1010000
[2,7,5,4,3,6,8,1]=>0111001=>1000110
[2,8,5,4,3,6,7,1]=>0111001=>1000110
[2,8,5,4,3,7,6,1]=>0111011=>1000100
[2,7,5,4,6,3,8,1]=>0110101=>1001010
[2,8,5,4,6,7,3,1]=>0110011=>1001100
[2,8,5,4,7,6,3,1]=>0110111=>1001000
[2,7,6,4,5,3,8,1]=>0110101=>1001010
[2,8,7,4,5,6,3,1]=>0110011=>1001100
[2,8,7,4,6,5,3,1]=>0110111=>1001000
[2,8,7,5,4,6,3,1]=>0111011=>1000100
[2,8,7,5,6,4,3,1]=>0110111=>1001000
[3,2,1,4,8,6,7,5]=>1100101=>0011010
[3,2,1,5,8,6,7,4]=>1100101=>0011010
[3,2,1,7,5,6,8,4]=>1101001=>0010110
[3,2,1,8,5,6,7,4]=>1101001=>0010110
[3,2,1,8,5,7,6,4]=>1101011=>0010100
[3,2,1,8,6,5,7,4]=>1101101=>0010010
[3,2,1,8,6,7,5,4]=>1101011=>0010100
[3,2,4,1,8,6,7,5]=>1010101=>0101010
[3,2,4,5,8,6,7,1]=>1000101=>0111010
[3,2,4,7,5,6,8,1]=>1001001=>0110110
[3,2,4,8,5,6,7,1]=>1001001=>0110110
[3,2,4,8,6,7,5,1]=>1001011=>0110100
[3,2,5,4,8,6,7,1]=>1010101=>0101010
[3,2,6,4,5,1,8,7]=>1010101=>0101010
[3,2,6,4,5,7,1,8]=>1010010=>0101101
[3,2,7,4,5,6,1,8]=>1010010=>0101101
[3,2,8,4,5,6,7,1]=>1010001=>0101110
[3,2,7,4,6,5,1,8]=>1010110=>0101001
[3,2,7,4,6,5,8,1]=>1010101=>0101010
[3,2,8,4,6,5,7,1]=>1010101=>0101010
[3,2,7,5,4,6,1,8]=>1011010=>0100101
[3,2,8,5,4,6,7,1]=>1011001=>0100110
[3,2,8,5,4,7,6,1]=>1011011=>0100100
[3,2,7,5,6,4,1,8]=>1010110=>0101001
[3,2,7,5,6,4,8,1]=>1010101=>0101010
[3,2,8,5,6,4,7,1]=>1010101=>0101010
[3,2,8,5,7,6,4,1]=>1010111=>0101000
[3,2,8,6,5,7,4,1]=>1011011=>0100100
[3,2,8,7,5,6,4,1]=>1011011=>0100100
[4,2,3,1,5,7,6,8]=>1010010=>0101101
[4,2,3,1,5,7,8,6]=>1010001=>0101110
[4,2,3,1,6,5,8,7]=>1010101=>0101010
[4,2,3,1,6,7,8,5]=>1010001=>0101110
[4,2,3,1,6,8,7,5]=>1010011=>0101100
[4,2,3,1,7,6,8,5]=>1010101=>0101010
[4,2,3,1,8,6,7,5]=>1010101=>0101010
[4,2,3,1,8,7,6,5]=>1010111=>0101000
[4,2,3,5,1,6,8,7]=>1001001=>0110110
[4,2,3,5,1,7,8,6]=>1001001=>0110110
[4,2,3,5,1,8,7,6]=>1001011=>0110100
[4,2,3,5,6,1,8,7]=>1000101=>0111010
[4,2,3,5,6,8,7,1]=>1000011=>0111100
[4,2,3,5,7,6,1,8]=>1000110=>0111001
[4,2,3,5,8,7,6,1]=>1000111=>0111000
[4,2,3,6,5,1,7,8]=>1001100=>0110011
[4,2,3,6,5,1,8,7]=>1001101=>0110010
[4,2,3,6,5,8,7,1]=>1001011=>0110100
[4,2,3,7,5,6,1,8]=>1001010=>0110101
[4,2,3,7,5,6,8,1]=>1001001=>0110110
[4,2,3,8,5,6,7,1]=>1001001=>0110110
[4,2,3,8,5,7,6,1]=>1001011=>0110100
[4,2,3,7,6,5,8,1]=>1001101=>0110010
[4,2,3,8,6,7,5,1]=>1001011=>0110100
[4,2,3,8,7,6,5,1]=>1001111=>0110000
[5,2,3,4,1,6,8,7]=>1001001=>0110110
[5,2,3,4,1,7,8,6]=>1001001=>0110110
[5,2,3,4,1,8,7,6]=>1001011=>0110100
[5,2,3,4,6,1,8,7]=>1000101=>0111010
[5,2,3,4,7,6,1,8]=>1000110=>0111001
[5,2,3,4,8,6,7,1]=>1000101=>0111010
[5,2,3,4,8,7,6,1]=>1000111=>0111000
[6,2,3,4,5,1,8,7]=>1000101=>0111010
[6,2,3,4,5,8,7,1]=>1000011=>0111100
[8,2,3,4,5,7,6,1]=>1000011=>0111100
[7,2,3,4,6,5,1,8]=>1000110=>0111001
[8,2,3,4,7,6,5,1]=>1000111=>0111000
[6,2,3,5,4,1,7,8]=>1001100=>0110011
[6,2,3,5,4,1,8,7]=>1001101=>0110010
[6,2,3,5,4,7,1,8]=>1001010=>0110101
[6,2,3,5,4,7,8,1]=>1001001=>0110110
[7,2,3,5,4,6,1,8]=>1001010=>0110101
[8,2,3,5,4,6,7,1]=>1001001=>0110110
[8,2,3,5,4,7,6,1]=>1001011=>0110100
[7,2,3,5,6,4,1,8]=>1000110=>0111001
[8,2,3,5,6,7,4,1]=>1000011=>0111100
[8,2,3,5,7,6,4,1]=>1000111=>0111000
[7,2,3,6,5,4,1,8]=>1001110=>0110001
[8,2,3,6,5,4,7,1]=>1001101=>0110010
[8,2,3,7,5,6,4,1]=>1001011=>0110100
[8,2,3,7,6,5,4,1]=>1001111=>0110000
[5,2,4,3,1,6,7,8]=>1011000=>0100111
[5,2,4,3,1,6,8,7]=>1011001=>0100110
[5,2,4,3,1,7,6,8]=>1011010=>0100101
[5,2,4,3,1,8,7,6]=>1011011=>0100100
[5,2,4,3,6,1,7,8]=>1010100=>0101011
[5,2,4,3,6,1,8,7]=>1010101=>0101010
[5,2,4,3,6,7,1,8]=>1010010=>0101101
[5,2,4,3,7,6,1,8]=>1010110=>0101001
[5,2,4,3,7,6,8,1]=>1010101=>0101010
[5,2,4,3,8,7,6,1]=>1010111=>0101000
[6,2,4,3,5,1,8,7]=>1010101=>0101010
[7,2,4,3,6,5,1,8]=>1010110=>0101001
[7,2,4,3,6,5,8,1]=>1010101=>0101010
[8,2,4,3,6,5,7,1]=>1010101=>0101010
[8,2,4,3,6,7,5,1]=>1010011=>0101100
[8,2,4,3,7,6,5,1]=>1010111=>0101000
[6,2,4,5,3,1,7,8]=>1001100=>0110011
[6,2,4,5,3,1,8,7]=>1001101=>0110010
[6,2,4,5,3,8,7,1]=>1001011=>0110100
[7,2,4,5,3,6,1,8]=>1001010=>0110101
[7,2,4,5,3,6,8,1]=>1001001=>0110110
[8,2,4,5,3,7,6,1]=>1001011=>0110100
[8,2,4,5,6,3,7,1]=>1000101=>0111010
[8,2,4,5,6,7,3,1]=>1000011=>0111100
[8,2,4,5,7,6,3,1]=>1000111=>0111000
[7,2,4,6,5,3,1,8]=>1001110=>0110001
[7,2,4,6,5,3,8,1]=>1001101=>0110010
[8,2,4,7,5,6,3,1]=>1001011=>0110100
[8,2,4,7,6,5,3,1]=>1001111=>0110000
[6,2,5,4,3,1,7,8]=>1011100=>0100011
[6,2,5,4,3,1,8,7]=>1011101=>0100010
[6,2,5,4,3,7,1,8]=>1011010=>0100101
[6,2,5,4,3,7,8,1]=>1011001=>0100110
[7,2,5,4,3,6,1,8]=>1011010=>0100101
[8,2,5,4,3,6,7,1]=>1011001=>0100110
[8,2,5,4,3,7,6,1]=>1011011=>0100100
[7,2,5,4,6,3,8,1]=>1010101=>0101010
[8,2,5,4,7,6,3,1]=>1010111=>0101000
[7,2,6,4,5,3,1,8]=>1010110=>0101001
[7,2,6,4,5,3,8,1]=>1010101=>0101010
[8,2,6,4,5,3,7,1]=>1010101=>0101010
[8,2,6,4,5,7,3,1]=>1010011=>0101100
[8,2,7,4,5,6,3,1]=>1010011=>0101100
[8,2,7,4,6,5,3,1]=>1010111=>0101000
[7,2,6,5,4,3,1,8]=>1011110=>0100001
[7,2,6,5,4,3,8,1]=>1011101=>0100010
[8,2,6,5,4,3,7,1]=>1011101=>0100010
[8,2,6,5,4,7,3,1]=>1011011=>0100100
[8,2,7,5,4,6,3,1]=>1011011=>0100100
[8,2,7,5,6,4,3,1]=>1010111=>0101000
[8,2,7,6,5,4,3,1]=>1011111=>0100000
[4,3,2,1,8,6,7,5]=>1110101=>0001010
[4,3,2,7,5,6,8,1]=>1101001=>0010110
[4,3,2,8,5,6,7,1]=>1101001=>0010110
[4,3,2,8,5,7,6,1]=>1101011=>0010100
[4,3,2,8,6,7,5,1]=>1101011=>0010100
[5,3,2,4,1,6,8,7]=>1101001=>0010110
[5,3,2,4,1,7,6,8]=>1101010=>0010101
[5,3,2,4,1,8,7,6]=>1101011=>0010100
[5,3,2,4,6,1,8,7]=>1100101=>0011010
[5,3,2,4,7,6,1,8]=>1100110=>0011001
[8,3,2,4,6,5,7,1]=>1100101=>0011010
[8,3,2,4,6,7,5,1]=>1100011=>0011100
[8,3,2,4,7,6,5,1]=>1100111=>0011000
[6,3,2,5,4,1,7,8]=>1101100=>0010011
[6,3,2,5,4,1,8,7]=>1101101=>0010010
[6,3,2,5,4,7,1,8]=>1101010=>0010101
[6,3,2,5,4,7,8,1]=>1101001=>0010110
[6,3,2,5,4,8,7,1]=>1101011=>0010100
[7,3,2,5,4,6,1,8]=>1101010=>0010101
[8,3,2,5,4,7,6,1]=>1101011=>0010100
[7,3,2,5,6,4,8,1]=>1100101=>0011010
[8,3,2,5,6,4,7,1]=>1100101=>0011010
[8,3,2,5,6,7,4,1]=>1100011=>0011100
[8,3,2,5,7,6,4,1]=>1100111=>0011000
[8,3,2,6,5,7,4,1]=>1101011=>0010100
[8,3,2,7,5,6,4,1]=>1101011=>0010100
[8,3,2,7,6,5,4,1]=>1101111=>0010000
[5,3,4,2,1,6,8,7]=>1011001=>0100110
[5,3,4,2,1,7,8,6]=>1011001=>0100110
[5,3,4,2,1,8,7,6]=>1011011=>0100100
[5,3,4,2,6,1,8,7]=>1010101=>0101010
[5,3,4,2,7,6,1,8]=>1010110=>0101001
[5,3,4,2,7,6,8,1]=>1010101=>0101010
[5,3,4,2,8,6,7,1]=>1010101=>0101010
[6,3,4,2,5,1,8,7]=>1010101=>0101010
[7,3,4,2,6,5,1,8]=>1010110=>0101001
[7,3,4,2,6,5,8,1]=>1010101=>0101010
[8,3,4,2,6,5,7,1]=>1010101=>0101010
[6,3,4,5,2,1,8,7]=>1001101=>0110010
[6,3,4,5,2,8,7,1]=>1001011=>0110100
[8,3,4,5,2,7,6,1]=>1001011=>0110100
[8,3,4,5,7,6,2,1]=>1000111=>0111000
[7,3,4,6,5,2,1,8]=>1001110=>0110001
[8,3,4,7,6,5,2,1]=>1001111=>0110000
[6,3,5,4,2,1,8,7]=>1011101=>0100010
[6,3,5,4,2,7,1,8]=>1011010=>0100101
[6,3,5,4,2,7,8,1]=>1011001=>0100110
[6,3,5,4,2,8,7,1]=>1011011=>0100100
[7,3,5,4,2,6,1,8]=>1011010=>0100101
[8,3,5,4,2,6,7,1]=>1011001=>0100110
[8,3,5,4,2,7,6,1]=>1011011=>0100100
[7,3,5,4,6,2,1,8]=>1010110=>0101001
[7,3,5,4,6,2,8,1]=>1010101=>0101010
[8,3,5,4,6,7,2,1]=>1010011=>0101100
[8,3,5,4,7,6,2,1]=>1010111=>0101000
[7,3,6,4,5,2,1,8]=>1010110=>0101001
[7,3,6,4,5,2,8,1]=>1010101=>0101010
[8,3,6,4,5,2,7,1]=>1010101=>0101010
[8,3,6,4,5,7,2,1]=>1010011=>0101100
[8,3,7,4,5,6,2,1]=>1010011=>0101100
[8,3,7,4,6,5,2,1]=>1010111=>0101000
[7,3,6,5,4,2,1,8]=>1011110=>0100001
[7,3,6,5,4,2,8,1]=>1011101=>0100010
[8,3,6,5,4,2,7,1]=>1011101=>0100010
[8,3,6,5,4,7,2,1]=>1011011=>0100100
[8,3,7,5,4,6,2,1]=>1011011=>0100100
[8,3,7,5,6,4,2,1]=>1010111=>0101000
[8,3,7,6,5,4,2,1]=>1011111=>0100000
[5,4,3,2,8,6,7,1]=>1110101=>0001010
[6,4,3,2,5,1,8,7]=>1110101=>0001010
[6,4,3,2,5,8,7,1]=>1110011=>0001100
[8,4,3,2,5,7,6,1]=>1110011=>0001100
[7,4,3,2,6,5,1,8]=>1110110=>0001001
[7,4,3,2,6,5,8,1]=>1110101=>0001010
[8,4,3,2,6,5,7,1]=>1110101=>0001010
[8,4,3,2,6,7,5,1]=>1110011=>0001100
[8,4,3,2,7,6,5,1]=>1110111=>0001000
[6,4,3,5,2,1,8,7]=>1101101=>0010010
[8,4,3,5,2,7,6,1]=>1101011=>0010100
[8,4,3,5,7,6,2,1]=>1100111=>0011000
[7,4,3,6,5,2,1,8]=>1101110=>0010001
[7,4,3,6,5,2,8,1]=>1101101=>0010010
[8,4,3,7,5,6,2,1]=>1101011=>0010100
[8,4,3,7,6,5,2,1]=>1101111=>0010000
[6,5,3,4,2,1,8,7]=>1101101=>0010010
[8,5,3,4,2,7,6,1]=>1101011=>0010100
[8,5,3,4,7,6,2,1]=>1100111=>0011000
[8,7,3,4,6,5,2,1]=>1100111=>0011000
[7,6,3,5,4,2,1,8]=>1101110=>0010001
[7,6,3,5,4,2,8,1]=>1101101=>0010010
[8,6,3,5,4,2,7,1]=>1101101=>0010010
[8,6,3,5,4,7,2,1]=>1101011=>0010100
[8,7,3,5,4,6,2,1]=>1101011=>0010100
[8,7,3,5,6,4,2,1]=>1100111=>0011000
[8,7,3,6,5,4,2,1]=>1101111=>0010000
[8,5,4,3,2,7,6,1]=>1111011=>0000100
[8,5,4,3,7,6,2,1]=>1110111=>0001000
[8,7,4,3,6,5,2,1]=>1110111=>0001000
[8,7,4,6,5,3,2,1]=>1101111=>0010000
[2,4,1,3,6,5,8,7]=>0100101=>1011010
[2,1,4,6,3,5,8,7]=>1001001=>0110110
[2,4,1,6,3,5,8,7]=>0101001=>1010110
[2,4,6,1,3,5,8,7]=>0010001=>1101110
[2,1,4,3,6,8,5,7]=>1010010=>0101101
[2,4,1,3,6,8,5,7]=>0100010=>1011101
[2,1,4,6,3,8,5,7]=>1001010=>0110101
[2,4,1,6,3,8,5,7]=>0101010=>1010101
[2,4,6,1,3,8,5,7]=>0010010=>1101101
[2,1,4,6,8,3,5,7]=>1000100=>0111011
[2,4,1,6,8,3,5,7]=>0100100=>1011011
[2,4,6,1,8,3,5,7]=>0010100=>1101011
[2,4,6,8,1,3,5,7]=>0001000=>1110111
[2,4,1,3,6,5,7,8]=>0100100=>1011011
[2,1,4,6,3,5,7,8]=>1001000=>0110111
[2,4,1,6,3,5,7,8]=>0101000=>1010111
[2,4,6,1,3,5,7,8]=>0010000=>1101111
[2,1,4,6,3,7,5,8]=>1001010=>0110101
[2,4,1,6,3,7,5,8]=>0101010=>1010101
[2,4,6,1,3,7,5,8]=>0010010=>1101101
[2,4,6,7,1,3,5,8]=>0001000=>1110111
[2,4,1,3,6,7,8,5]=>0100001=>1011110
[2,1,4,6,3,7,8,5]=>1001001=>0110110
[2,4,1,6,3,7,8,5]=>0101001=>1010110
[2,4,6,1,3,7,8,5]=>0010001=>1101110
[2,1,4,6,7,3,8,5]=>1000101=>0111010
[2,4,1,6,7,3,8,5]=>0100101=>1011010
[2,4,6,1,7,3,8,5]=>0010101=>1101010
[2,4,6,7,1,3,8,5]=>0001001=>1110110
[2,1,4,6,7,8,3,5]=>1000010=>0111101
[2,4,1,6,7,8,3,5]=>0100010=>1011101
[2,4,6,1,7,8,3,5]=>0010010=>1101101
[2,4,6,7,1,8,3,5]=>0001010=>1110101
[2,4,6,7,8,1,3,5]=>0000100=>1111011
[2,1,4,3,7,5,8,6]=>1010101=>0101010
[2,4,1,3,7,5,8,6]=>0100101=>1011010
[2,1,4,7,3,5,8,6]=>1001001=>0110110
[2,4,1,7,3,5,8,6]=>0101001=>1010110
[2,4,7,1,3,5,8,6]=>0010001=>1101110
[2,1,4,3,7,8,5,6]=>1010010=>0101101
[2,4,1,3,7,8,5,6]=>0100010=>1011101
[2,4,1,7,3,8,5,6]=>0101010=>1010101
[2,1,4,7,8,3,5,6]=>1000100=>0111011
[2,4,1,7,8,3,5,6]=>0100100=>1011011
[2,4,7,1,8,3,5,6]=>0010100=>1101011
[2,4,7,8,1,3,5,6]=>0001000=>1110111
[2,4,1,5,3,7,6,8]=>0101010=>1010101
[2,4,5,1,3,7,6,8]=>0010010=>1101101
[2,4,5,1,7,3,6,8]=>0010100=>1101011
[2,4,1,3,5,7,8,6]=>0100001=>1011110
[2,4,1,5,3,7,8,6]=>0101001=>1010110
[2,4,5,1,3,7,8,6]=>0010001=>1101110
[2,1,4,5,7,3,8,6]=>1000101=>0111010
[2,4,1,5,7,3,8,6]=>0100101=>1011010
[2,4,5,1,7,3,8,6]=>0010101=>1101010
[2,4,5,7,1,3,8,6]=>0001001=>1110110
[2,1,4,5,7,8,3,6]=>1000010=>0111101
[2,4,5,1,7,8,3,6]=>0010010=>1101101
[2,4,5,7,1,8,3,6]=>0001010=>1110101
[2,4,5,7,8,1,3,6]=>0000100=>1111011
[2,1,4,3,8,5,6,7]=>1010100=>0101011
[2,4,1,3,8,5,6,7]=>0100100=>1011011
[2,1,4,8,3,5,6,7]=>1001000=>0110111
[2,4,1,8,3,5,6,7]=>0101000=>1010111
[2,4,8,1,3,5,6,7]=>0010000=>1101111
[2,1,4,3,5,8,6,7]=>1010010=>0101101
[2,4,1,5,3,8,6,7]=>0101010=>1010101
[2,1,4,5,8,3,6,7]=>1000100=>0111011
[2,4,1,5,8,3,6,7]=>0100100=>1011011
[2,4,5,1,8,3,6,7]=>0010100=>1101011
[2,4,5,8,1,3,6,7]=>0001000=>1110111
[2,4,1,5,3,6,8,7]=>0101001=>1010110
[2,4,1,5,6,3,8,7]=>0100101=>1011010
[2,4,5,1,6,3,8,7]=>0010101=>1101010
[2,4,5,6,1,3,8,7]=>0001001=>1110110
[2,1,4,5,6,8,3,7]=>1000010=>0111101
[2,4,1,5,6,8,3,7]=>0100010=>1011101
[2,4,5,1,6,8,3,7]=>0010010=>1101101
[2,4,5,6,1,8,3,7]=>0001010=>1110101
[2,4,5,6,8,1,3,7]=>0000100=>1111011
[2,4,1,3,5,6,7,8]=>0100000=>1011111
[2,4,1,5,3,6,7,8]=>0101000=>1010111
[2,4,5,1,3,6,7,8]=>0010000=>1101111
[2,4,1,5,6,3,7,8]=>0100100=>1011011
[2,4,5,1,6,3,7,8]=>0010100=>1101011
[2,4,5,6,1,3,7,8]=>0001000=>1110111
[2,4,1,5,6,7,3,8]=>0100010=>1011101
[2,4,5,6,1,7,3,8]=>0001010=>1110101
[2,4,5,6,7,1,3,8]=>0000100=>1111011
[2,4,1,5,6,7,8,3]=>0100001=>1011110
[2,4,5,1,6,7,8,3]=>0010001=>1101110
[2,4,5,6,1,7,8,3]=>0001001=>1110110
[2,4,5,6,7,1,8,3]=>0000101=>1111010
[2,4,5,6,7,8,1,3]=>0000010=>1111101
[2,1,5,3,6,4,8,7]=>1010101=>0101010
[2,5,1,3,6,4,8,7]=>0100101=>1011010
[2,1,5,6,3,4,8,7]=>1001001=>0110110
[2,5,1,6,3,4,8,7]=>0101001=>1010110
[2,5,6,1,3,4,8,7]=>0010001=>1101110
[2,1,5,3,6,8,4,7]=>1010010=>0101101
[2,5,1,3,6,8,4,7]=>0100010=>1011101
[2,5,1,6,3,8,4,7]=>0101010=>1010101
[2,5,6,1,3,8,4,7]=>0010010=>1101101
[2,1,5,6,8,3,4,7]=>1000100=>0111011
[2,5,1,6,8,3,4,7]=>0100100=>1011011
[2,5,6,8,1,3,4,7]=>0001000=>1110111
[2,5,1,3,6,4,7,8]=>0100100=>1011011
[2,1,5,6,3,4,7,8]=>1001000=>0110111
[2,5,1,6,3,4,7,8]=>0101000=>1010111
[2,1,5,3,6,7,4,8]=>1010010=>0101101
[2,1,5,6,3,7,4,8]=>1001010=>0110101
[2,5,1,6,3,7,4,8]=>0101010=>1010101
[2,5,6,1,3,7,4,8]=>0010010=>1101101
[2,1,5,6,7,3,4,8]=>1000100=>0111011
[2,5,1,6,7,3,4,8]=>0100100=>1011011
[2,5,6,1,7,3,4,8]=>0010100=>1101011
[2,1,5,3,6,7,8,4]=>1010001=>0101110
[2,5,1,3,6,7,8,4]=>0100001=>1011110
[2,1,5,6,3,7,8,4]=>1001001=>0110110
[2,5,1,6,3,7,8,4]=>0101001=>1010110
[2,5,6,1,3,7,8,4]=>0010001=>1101110
[2,1,5,6,7,3,8,4]=>1000101=>0111010
[2,5,1,6,7,3,8,4]=>0100101=>1011010
[2,5,6,7,1,3,8,4]=>0001001=>1110110
[2,1,5,6,7,8,3,4]=>1000010=>0111101
[2,5,1,6,7,8,3,4]=>0100010=>1011101
[2,5,6,1,7,8,3,4]=>0010010=>1101101
[2,5,6,7,1,8,3,4]=>0001010=>1110101
[2,5,6,7,8,1,3,4]=>0000100=>1111011
[2,1,5,3,7,4,8,6]=>1010101=>0101010
[2,5,1,3,7,4,8,6]=>0100101=>1011010
[2,1,5,7,3,4,8,6]=>1001001=>0110110
[2,5,1,7,3,4,8,6]=>0101001=>1010110
[2,5,7,1,3,4,8,6]=>0010001=>1101110
[2,1,5,3,7,8,4,6]=>1010010=>0101101
[2,5,1,3,7,8,4,6]=>0100010=>1011101
[2,1,5,7,3,8,4,6]=>1001010=>0110101
[2,1,5,7,8,3,4,6]=>1000100=>0111011
[2,5,1,7,8,3,4,6]=>0100100=>1011011
[2,5,7,1,8,3,4,6]=>0010100=>1101011
[2,5,7,8,1,3,4,6]=>0001000=>1110111
[2,5,1,3,7,4,6,8]=>0100100=>1011011
[2,1,5,7,3,4,6,8]=>1001000=>0110111
[2,3,5,1,4,7,6,8]=>0010010=>1101101
[2,3,5,7,1,4,6,8]=>0001000=>1110111
[2,3,5,1,7,4,8,6]=>0010101=>1101010
[2,3,5,7,1,4,8,6]=>0001001=>1110110
[2,3,1,5,7,8,4,6]=>0100010=>1011101
[2,3,5,7,1,8,4,6]=>0001010=>1110101
[2,3,5,7,8,1,4,6]=>0000100=>1111011
[2,1,5,3,8,4,6,7]=>1010100=>0101011
[2,5,1,3,8,4,6,7]=>0100100=>1011011
[2,1,5,8,3,4,6,7]=>1001000=>0110111
[2,5,1,8,3,4,6,7]=>0101000=>1010111
[2,5,8,1,3,4,6,7]=>0010000=>1101111
[2,3,5,1,4,8,6,7]=>0010010=>1101101
[2,1,3,5,8,4,6,7]=>1000100=>0111011
[2,3,5,1,8,4,6,7]=>0010100=>1101011
[2,3,5,8,1,4,6,7]=>0001000=>1110111
[2,1,5,3,4,6,8,7]=>1010001=>0101110
[2,3,5,1,6,4,8,7]=>0010101=>1101010
[2,3,5,6,1,4,8,7]=>0001001=>1110110
[2,3,1,5,6,8,4,7]=>0100010=>1011101
[2,3,5,1,6,8,4,7]=>0010010=>1101101
[2,3,5,6,1,8,4,7]=>0001010=>1110101
[2,3,5,6,8,1,4,7]=>0000100=>1111011
[2,1,5,3,4,6,7,8]=>1010000=>0101111
[2,5,1,3,4,6,7,8]=>0100000=>1011111
[2,3,5,1,4,6,7,8]=>0010000=>1101111
[2,3,5,1,6,4,7,8]=>0010100=>1101011
[2,3,5,6,1,4,7,8]=>0001000=>1110111
[2,3,5,6,1,7,4,8]=>0001010=>1110101
[2,3,5,6,7,1,4,8]=>0000100=>1111011
[2,3,5,1,6,7,8,4]=>0010001=>1101110
[2,3,5,6,1,7,8,4]=>0001001=>1110110
[2,3,5,6,7,1,8,4]=>0000101=>1111010
[2,3,5,6,7,8,1,4]=>0000010=>1111101
[2,1,6,3,7,4,8,5]=>1010101=>0101010
[2,6,1,3,7,4,8,5]=>0100101=>1011010
[2,1,6,7,3,4,8,5]=>1001001=>0110110
[2,6,1,7,3,4,8,5]=>0101001=>1010110
[2,6,7,1,3,4,8,5]=>0010001=>1101110
[2,1,6,3,7,8,4,5]=>1010010=>0101101
[2,6,1,3,7,8,4,5]=>0100010=>1011101
[2,1,6,7,3,8,4,5]=>1001010=>0110101
[2,6,1,7,3,8,4,5]=>0101010=>1010101
[2,1,6,7,8,3,4,5]=>1000100=>0111011
[2,6,1,7,8,3,4,5]=>0100100=>1011011
[2,6,7,1,8,3,4,5]=>0010100=>1101011
[2,6,7,8,1,3,4,5]=>0001000=>1110111
[2,1,6,3,7,4,5,8]=>1010100=>0101011
[2,6,1,7,3,4,5,8]=>0101000=>1010111
[2,6,7,1,3,4,5,8]=>0010000=>1101111
[2,6,1,3,4,7,5,8]=>0100010=>1011101
[2,3,1,6,4,7,5,8]=>0101010=>1010101
[2,3,6,1,4,7,5,8]=>0010010=>1101101
[2,3,6,7,1,4,5,8]=>0001000=>1110111
[2,1,6,3,4,7,8,5]=>1010001=>0101110
[2,6,1,3,4,7,8,5]=>0100001=>1011110
[2,3,6,1,4,7,8,5]=>0010001=>1101110
[2,1,3,6,7,4,8,5]=>1000101=>0111010
[2,3,6,7,1,4,8,5]=>0001001=>1110110
[2,1,3,6,7,8,4,5]=>1000010=>0111101
[2,3,1,6,7,8,4,5]=>0100010=>1011101
[2,3,6,1,7,8,4,5]=>0010010=>1101101
[2,3,6,7,1,8,4,5]=>0001010=>1110101
[2,3,6,7,8,1,4,5]=>0000100=>1111011
[2,1,6,3,8,4,5,7]=>1010100=>0101011
[2,6,1,3,8,4,5,7]=>0100100=>1011011
[2,1,6,8,3,4,5,7]=>1001000=>0110111
[2,6,1,8,3,4,5,7]=>0101000=>1010111
[2,6,8,1,3,4,5,7]=>0010000=>1101111
[2,1,6,3,4,8,5,7]=>1010010=>0101101
[2,6,1,3,4,8,5,7]=>0100010=>1011101
[2,3,1,6,4,8,5,7]=>0101010=>1010101
[2,3,6,1,4,8,5,7]=>0010010=>1101101
[2,3,1,6,8,4,5,7]=>0100100=>1011011
[2,3,6,1,8,4,5,7]=>0010100=>1101011
[2,3,6,8,1,4,5,7]=>0001000=>1110111
[2,1,6,3,4,5,8,7]=>1010001=>0101110
[2,6,1,3,4,5,8,7]=>0100001=>1011110
[2,1,3,6,4,5,8,7]=>1001001=>0110110
[2,3,6,1,4,5,8,7]=>0010001=>1101110
[2,3,4,1,6,8,5,7]=>0010010=>1101101
[2,3,4,6,1,8,5,7]=>0001010=>1110101
[2,3,4,6,8,1,5,7]=>0000100=>1111011
[2,6,1,3,4,5,7,8]=>0100000=>1011111
[2,1,3,6,4,5,7,8]=>1001000=>0110111
[2,3,1,6,4,5,7,8]=>0101000=>1010111
[2,3,6,1,4,5,7,8]=>0010000=>1101111
[2,3,4,6,1,5,7,8]=>0001000=>1110111
[2,3,4,6,1,7,5,8]=>0001010=>1110101
[2,3,4,6,7,1,5,8]=>0000100=>1111011
[2,3,4,6,1,7,8,5]=>0001001=>1110110
[2,3,4,6,7,8,1,5]=>0000010=>1111101
[2,1,7,3,8,4,5,6]=>1010100=>0101011
[2,7,1,3,8,4,5,6]=>0100100=>1011011
[2,1,7,8,3,4,5,6]=>1001000=>0110111
[2,7,1,8,3,4,5,6]=>0101000=>1010111
[2,7,8,1,3,4,5,6]=>0010000=>1101111
[2,1,7,3,4,8,5,6]=>1010010=>0101101
[2,7,1,3,4,8,5,6]=>0100010=>1011101
[2,1,3,7,4,8,5,6]=>1001010=>0110101
[2,3,1,7,4,8,5,6]=>0101010=>1010101
[2,3,7,1,4,8,5,6]=>0010010=>1101101
[2,1,3,7,8,4,5,6]=>1000100=>0111011
[2,3,1,7,8,4,5,6]=>0100100=>1011011
[2,3,7,8,1,4,5,6]=>0001000=>1110111
[2,1,7,3,4,5,8,6]=>1010001=>0101110
[2,7,1,3,4,5,8,6]=>0100001=>1011110
[2,3,1,7,4,5,8,6]=>0101001=>1010110
[2,3,7,1,4,5,8,6]=>0010001=>1101110
[2,1,3,4,7,5,8,6]=>1000101=>0111010
[2,3,4,1,7,5,8,6]=>0010101=>1101010
[2,3,4,7,1,5,8,6]=>0001001=>1110110
[2,1,3,4,7,8,5,6]=>1000010=>0111101
[2,3,1,4,7,8,5,6]=>0100010=>1011101
[2,3,4,1,7,8,5,6]=>0010010=>1101101
[2,3,4,7,1,8,5,6]=>0001010=>1110101
[2,3,4,7,8,1,5,6]=>0000100=>1111011
[2,1,7,3,4,5,6,8]=>1010000=>0101111
[2,7,1,3,4,5,6,8]=>0100000=>1011111
[2,3,7,1,4,5,6,8]=>0010000=>1101111
[2,1,3,4,7,5,6,8]=>1000100=>0111011
[2,3,1,4,7,5,6,8]=>0100100=>1011011
[2,3,4,1,7,5,6,8]=>0010100=>1101011
[2,3,4,7,1,5,6,8]=>0001000=>1110111
[2,3,4,5,7,1,6,8]=>0000100=>1111011
[2,3,4,5,7,1,8,6]=>0000101=>1111010
[2,3,4,5,7,8,1,6]=>0000010=>1111101
[2,1,8,3,4,5,6,7]=>1010000=>0101111
[2,8,1,3,4,5,6,7]=>0100000=>1011111
[2,1,3,8,4,5,6,7]=>1001000=>0110111
[2,3,1,8,4,5,6,7]=>0101000=>1010111
[2,3,8,1,4,5,6,7]=>0010000=>1101111
[2,1,3,4,8,5,6,7]=>1000100=>0111011
[2,3,1,4,8,5,6,7]=>0100100=>1011011
[2,3,4,1,8,5,6,7]=>0010100=>1101011
[2,3,4,8,1,5,6,7]=>0001000=>1110111
[2,1,3,4,5,8,6,7]=>1000010=>0111101
[2,3,1,4,5,8,6,7]=>0100010=>1011101
[2,3,4,1,5,8,6,7]=>0010010=>1101101
[2,3,4,5,1,8,6,7]=>0001010=>1110101
[2,3,4,5,8,1,6,7]=>0000100=>1111011
[2,3,4,5,6,8,1,7]=>0000010=>1111101
[3,1,4,2,6,5,8,7]=>1010101=>0101010
[3,4,1,2,6,5,8,7]=>0100101=>1011010
[3,1,4,6,2,5,8,7]=>1001001=>0110110
[3,4,1,6,2,5,8,7]=>0101001=>1010110
[3,4,6,1,2,5,8,7]=>0010001=>1101110
[3,1,4,2,6,8,5,7]=>1010010=>0101101
[3,4,1,2,6,8,5,7]=>0100010=>1011101
[3,1,4,6,2,8,5,7]=>1001010=>0110101
[3,4,1,6,2,8,5,7]=>0101010=>1010101
[3,1,4,6,8,2,5,7]=>1000100=>0111011
[3,4,1,6,8,2,5,7]=>0100100=>1011011
[3,4,6,8,1,2,5,7]=>0001000=>1110111
[3,1,4,2,6,5,7,8]=>1010100=>0101011
[3,4,1,2,6,5,7,8]=>0100100=>1011011
[3,1,4,2,6,7,5,8]=>1010010=>0101101
[3,4,1,2,6,7,5,8]=>0100010=>1011101
[3,4,1,6,2,7,5,8]=>0101010=>1010101
[3,4,6,1,2,7,5,8]=>0010010=>1101101
[3,4,1,6,7,2,5,8]=>0100100=>1011011
[3,4,6,7,1,2,5,8]=>0001000=>1110111
[3,1,4,2,6,7,8,5]=>1010001=>0101110
[3,4,1,2,6,7,8,5]=>0100001=>1011110
[3,1,4,6,2,7,8,5]=>1001001=>0110110
[3,4,1,6,2,7,8,5]=>0101001=>1010110
[3,4,6,1,2,7,8,5]=>0010001=>1101110
[3,1,4,6,7,2,8,5]=>1000101=>0111010
[3,4,1,6,7,2,8,5]=>0100101=>1011010
[3,4,6,1,7,2,8,5]=>0010101=>1101010
[3,4,6,7,1,2,8,5]=>0001001=>1110110
[3,1,4,6,7,8,2,5]=>1000010=>0111101
[3,4,1,6,7,8,2,5]=>0100010=>1011101
[3,4,6,1,7,8,2,5]=>0010010=>1101101
[3,4,6,7,1,8,2,5]=>0001010=>1110101
[3,4,6,7,8,1,2,5]=>0000100=>1111011
[3,1,4,2,7,5,8,6]=>1010101=>0101010
[3,4,1,2,7,5,8,6]=>0100101=>1011010
[3,1,4,7,2,5,8,6]=>1001001=>0110110
[3,4,1,7,2,5,8,6]=>0101001=>1010110
[3,4,7,1,2,5,8,6]=>0010001=>1101110
[3,1,4,2,7,8,5,6]=>1010010=>0101101
[3,4,1,2,7,8,5,6]=>0100010=>1011101
[3,1,4,7,2,8,5,6]=>1001010=>0110101
[3,4,7,1,8,2,5,6]=>0010100=>1101011
[3,4,7,8,1,2,5,6]=>0001000=>1110111
[3,1,4,2,7,5,6,8]=>1010100=>0101011
[3,4,1,2,7,5,6,8]=>0100100=>1011011
[3,4,1,2,5,7,6,8]=>0100010=>1011101
[3,1,4,5,2,7,6,8]=>1001010=>0110101
[3,4,1,5,2,7,6,8]=>0101010=>1010101
[3,4,1,5,7,2,6,8]=>0100100=>1011011
[3,4,5,7,1,2,6,8]=>0001000=>1110111
[3,1,4,2,5,7,8,6]=>1010001=>0101110
[3,4,1,2,5,7,8,6]=>0100001=>1011110
[3,1,4,5,2,7,8,6]=>1001001=>0110110
[3,4,5,1,2,7,8,6]=>0010001=>1101110
[3,1,4,5,7,2,8,6]=>1000101=>0111010
[3,4,1,5,7,2,8,6]=>0100101=>1011010
[3,4,5,7,1,2,8,6]=>0001001=>1110110
[3,1,4,5,7,8,2,6]=>1000010=>0111101
[3,4,1,5,7,8,2,6]=>0100010=>1011101
[3,4,5,1,7,8,2,6]=>0010010=>1101101
[3,4,5,7,1,8,2,6]=>0001010=>1110101
[3,4,5,7,8,1,2,6]=>0000100=>1111011
[3,1,4,2,8,5,6,7]=>1010100=>0101011
[3,4,1,2,8,5,6,7]=>0100100=>1011011
[3,1,4,8,2,5,6,7]=>1001000=>0110111
[3,4,1,8,2,5,6,7]=>0101000=>1010111
[3,4,8,1,2,5,6,7]=>0010000=>1101111
[3,1,4,2,5,8,6,7]=>1010010=>0101101
[3,4,1,2,5,8,6,7]=>0100010=>1011101
[3,4,1,5,2,8,6,7]=>0101010=>1010101
[3,4,5,1,2,8,6,7]=>0010010=>1101101
[3,1,4,5,8,2,6,7]=>1000100=>0111011
[3,4,1,5,8,2,6,7]=>0100100=>1011011
[3,4,5,8,1,2,6,7]=>0001000=>1110111
[3,4,1,2,5,6,8,7]=>0100001=>1011110
[3,4,5,1,2,6,8,7]=>0010001=>1101110
[3,1,4,5,6,2,8,7]=>1000101=>0111010
[3,4,1,5,6,2,8,7]=>0100101=>1011010
[3,4,5,1,6,2,8,7]=>0010101=>1101010
[3,4,5,6,1,2,8,7]=>0001001=>1110110
[3,1,4,5,6,8,2,7]=>1000010=>0111101
[3,4,1,5,6,8,2,7]=>0100010=>1011101
[3,4,5,6,1,8,2,7]=>0001010=>1110101
[3,4,5,6,8,1,2,7]=>0000100=>1111011
[3,1,4,2,5,6,7,8]=>1010000=>0101111
[3,1,4,5,2,6,7,8]=>1001000=>0110111
[3,4,1,5,2,6,7,8]=>0101000=>1010111
[3,1,4,5,6,2,7,8]=>1000100=>0111011
[3,4,1,5,6,2,7,8]=>0100100=>1011011
[3,4,5,1,6,2,7,8]=>0010100=>1101011
[3,1,4,5,6,7,2,8]=>1000010=>0111101
[3,4,1,5,6,7,2,8]=>0100010=>1011101
[3,4,5,1,6,7,2,8]=>0010010=>1101101
[3,4,5,6,1,7,2,8]=>0001010=>1110101
[3,1,4,5,6,7,8,2]=>1000001=>0111110
[3,4,1,5,6,7,8,2]=>0100001=>1011110
[3,4,5,1,6,7,8,2]=>0010001=>1101110
[3,4,5,6,1,7,8,2]=>0001001=>1110110
[3,4,5,6,7,1,8,2]=>0000101=>1111010
[3,1,5,2,6,4,8,7]=>1010101=>0101010
[3,5,1,2,6,4,8,7]=>0100101=>1011010
[3,1,5,6,2,4,8,7]=>1001001=>0110110
[3,5,1,6,2,4,8,7]=>0101001=>1010110
[3,5,6,1,2,4,8,7]=>0010001=>1101110
[3,1,5,2,6,8,4,7]=>1010010=>0101101
[3,5,1,2,6,8,4,7]=>0100010=>1011101
[3,1,5,6,2,8,4,7]=>1001010=>0110101
[3,5,6,1,2,8,4,7]=>0010010=>1101101
[3,1,5,6,8,2,4,7]=>1000100=>0111011
[3,5,1,6,8,2,4,7]=>0100100=>1011011
[3,5,6,1,8,2,4,7]=>0010100=>1101011
[3,5,6,8,1,2,4,7]=>0001000=>1110111
[3,1,5,6,2,4,7,8]=>1001000=>0110111
[3,5,1,6,2,4,7,8]=>0101000=>1010111
[3,5,6,1,2,4,7,8]=>0010000=>1101111
[3,5,1,2,6,7,4,8]=>0100010=>1011101
[3,5,1,6,2,7,4,8]=>0101010=>1010101
[3,5,6,1,2,7,4,8]=>0010010=>1101101
[3,5,1,6,7,2,4,8]=>0100100=>1011011
[3,5,6,1,7,2,4,8]=>0010100=>1101011
[3,5,6,7,1,2,4,8]=>0001000=>1110111
[3,1,5,2,6,7,8,4]=>1010001=>0101110
[3,5,1,2,6,7,8,4]=>0100001=>1011110
[3,1,5,6,2,7,8,4]=>1001001=>0110110
[3,5,1,6,2,7,8,4]=>0101001=>1010110
[3,5,6,1,2,7,8,4]=>0010001=>1101110
[3,1,5,6,7,2,8,4]=>1000101=>0111010
[3,5,1,6,7,2,8,4]=>0100101=>1011010
[3,5,6,1,7,2,8,4]=>0010101=>1101010
[3,5,6,7,1,2,8,4]=>0001001=>1110110
[3,1,5,6,7,8,2,4]=>1000010=>0111101
[3,5,1,6,7,8,2,4]=>0100010=>1011101
[3,5,6,1,7,8,2,4]=>0010010=>1101101
[3,5,6,7,1,8,2,4]=>0001010=>1110101
[3,5,6,7,8,1,2,4]=>0000100=>1111011
[3,1,5,2,7,4,8,6]=>1010101=>0101010
[3,5,1,2,7,4,8,6]=>0100101=>1011010
[3,1,5,7,2,4,8,6]=>1001001=>0110110
[3,5,1,7,2,4,8,6]=>0101001=>1010110
[3,5,7,1,2,4,8,6]=>0010001=>1101110
[3,1,5,2,7,8,4,6]=>1010010=>0101101
[3,5,1,2,7,8,4,6]=>0100010=>1011101
[3,1,5,7,2,8,4,6]=>1001010=>0110101
[3,5,1,7,2,8,4,6]=>0101010=>1010101
[3,1,5,7,8,2,4,6]=>1000100=>0111011
[3,5,1,7,8,2,4,6]=>0100100=>1011011
[3,5,7,8,1,2,4,6]=>0001000=>1110111
[3,1,5,2,7,4,6,8]=>1010100=>0101011
[3,5,1,2,7,4,6,8]=>0100100=>1011011
[3,1,5,7,2,4,6,8]=>1001000=>0110111
[3,5,1,7,2,4,6,8]=>0101000=>1010111
[3,5,7,1,2,4,6,8]=>0010000=>1101111
[3,1,5,2,4,7,6,8]=>1010010=>0101101
[3,5,1,2,4,7,6,8]=>0100010=>1011101
[3,1,2,5,4,7,6,8]=>1001010=>0110101
[1,3,5,2,4,7,6,8]=>0010010=>1101101
[3,1,2,5,7,4,6,8]=>1000100=>0111011
[1,3,2,5,7,4,6,8]=>0100100=>1011011
[1,3,5,2,7,4,6,8]=>0010100=>1101011
[1,3,5,7,2,4,6,8]=>0001000=>1110111
[3,1,5,2,4,7,8,6]=>1010001=>0101110
[3,5,1,2,4,7,8,6]=>0100001=>1011110
[1,3,5,2,4,7,8,6]=>0010001=>1101110
[3,1,2,5,7,4,8,6]=>1000101=>0111010
[1,3,2,5,7,4,8,6]=>0100101=>1011010
[1,3,5,2,7,4,8,6]=>0010101=>1101010
[1,3,5,7,2,4,8,6]=>0001001=>1110110
[3,1,2,5,7,8,4,6]=>1000010=>0111101
[1,3,2,5,7,8,4,6]=>0100010=>1011101
[1,3,5,2,7,8,4,6]=>0010010=>1101101
[1,3,5,7,2,8,4,6]=>0001010=>1110101
[1,3,5,7,8,2,4,6]=>0000100=>1111011
[3,1,5,2,8,4,6,7]=>1010100=>0101011
[3,5,1,2,8,4,6,7]=>0100100=>1011011
[3,1,5,8,2,4,6,7]=>1001000=>0110111
[3,5,1,8,2,4,6,7]=>0101000=>1010111
[3,1,5,2,4,8,6,7]=>1010010=>0101101
[3,5,1,2,4,8,6,7]=>0100010=>1011101
[1,3,2,5,4,8,6,7]=>0101010=>1010101
[1,3,5,2,4,8,6,7]=>0010010=>1101101
[3,1,2,5,8,4,6,7]=>1000100=>0111011
[1,3,2,5,8,4,6,7]=>0100100=>1011011
[1,3,5,2,8,4,6,7]=>0010100=>1101011
[1,3,5,8,2,4,6,7]=>0001000=>1110111
[3,1,5,2,4,6,8,7]=>1010001=>0101110
[3,5,1,2,4,6,8,7]=>0100001=>1011110
[3,1,2,5,4,6,8,7]=>1001001=>0110110
[1,3,5,2,4,6,8,7]=>0010001=>1101110
[1,3,5,6,2,4,8,7]=>0001001=>1110110
[3,1,2,5,6,8,4,7]=>1000010=>0111101
[1,3,5,2,6,8,4,7]=>0010010=>1101101
[1,3,5,6,2,8,4,7]=>0001010=>1110101
[1,3,5,6,8,2,4,7]=>0000100=>1111011
[3,1,5,2,4,6,7,8]=>1010000=>0101111
[3,5,1,2,4,6,7,8]=>0100000=>1011111
[1,3,5,2,4,6,7,8]=>0010000=>1101111
[3,1,2,5,6,4,7,8]=>1000100=>0111011
[1,3,5,2,6,4,7,8]=>0010100=>1101011
[1,3,5,6,2,4,7,8]=>0001000=>1110111
[3,1,2,5,6,7,4,8]=>1000010=>0111101
[1,3,5,2,6,7,4,8]=>0010010=>1101101
[1,3,5,6,2,7,4,8]=>0001010=>1110101
[1,3,5,6,7,2,4,8]=>0000100=>1111011
[3,1,2,5,6,7,8,4]=>1000001=>0111110
[1,3,5,2,6,7,8,4]=>0010001=>1101110
[1,3,5,6,2,7,8,4]=>0001001=>1110110
[1,3,5,6,7,2,8,4]=>0000101=>1111010
[1,3,5,6,7,8,2,4]=>0000010=>1111101
[3,1,6,2,7,4,8,5]=>1010101=>0101010
[3,6,1,2,7,4,8,5]=>0100101=>1011010
[3,6,1,7,2,4,8,5]=>0101001=>1010110
[3,6,7,1,2,4,8,5]=>0010001=>1101110
[3,6,1,2,7,8,4,5]=>0100010=>1011101
[3,1,6,7,2,8,4,5]=>1001010=>0110101
[3,6,1,7,2,8,4,5]=>0101010=>1010101
[3,6,7,1,2,8,4,5]=>0010010=>1101101
[3,6,1,7,8,2,4,5]=>0100100=>1011011
[3,6,7,8,1,2,4,5]=>0001000=>1110111
[3,1,6,2,7,4,5,8]=>1010100=>0101011
[3,1,6,7,2,4,5,8]=>1001000=>0110111
[3,6,7,1,2,4,5,8]=>0010000=>1101111
[3,1,6,2,4,7,5,8]=>1010010=>0101101
[3,6,1,2,4,7,5,8]=>0100010=>1011101
[3,1,2,6,4,7,5,8]=>1001010=>0110101
[1,3,2,6,4,7,5,8]=>0101010=>1010101
[1,3,6,2,4,7,5,8]=>0010010=>1101101
[1,3,2,6,7,4,5,8]=>0100100=>1011011
[1,3,6,2,7,4,5,8]=>0010100=>1101011
[3,1,6,2,4,7,8,5]=>1010001=>0101110
[3,6,1,2,4,7,8,5]=>0100001=>1011110
[3,1,2,6,4,7,8,5]=>1001001=>0110110
[1,3,2,6,4,7,8,5]=>0101001=>1010110
[1,3,6,2,4,7,8,5]=>0010001=>1101110
[3,1,2,6,7,4,8,5]=>1000101=>0111010
[1,3,2,6,7,4,8,5]=>0100101=>1011010
[1,3,6,2,7,4,8,5]=>0010101=>1101010
[3,1,2,6,7,8,4,5]=>1000010=>0111101
[1,3,2,6,7,8,4,5]=>0100010=>1011101
[1,3,6,2,7,8,4,5]=>0010010=>1101101
[1,3,6,7,8,2,4,5]=>0000100=>1111011
[3,1,6,2,8,4,5,7]=>1010100=>0101011
[3,1,6,8,2,4,5,7]=>1001000=>0110111
[3,6,1,8,2,4,5,7]=>0101000=>1010111
[3,6,8,1,2,4,5,7]=>0010000=>1101111
[3,1,6,2,4,8,5,7]=>1010010=>0101101
[3,6,1,2,4,8,5,7]=>0100010=>1011101
[1,3,2,6,4,8,5,7]=>0101010=>1010101
[1,3,6,2,4,8,5,7]=>0010010=>1101101
[3,1,2,6,8,4,5,7]=>1000100=>0111011
[1,3,2,6,8,4,5,7]=>0100100=>1011011
[3,1,6,2,4,5,8,7]=>1010001=>0101110
[3,6,1,2,4,5,8,7]=>0100001=>1011110
[3,1,2,6,4,5,8,7]=>1001001=>0110110
[1,3,6,2,4,5,8,7]=>0010001=>1101110
[3,1,2,4,6,5,8,7]=>1000101=>0111010
[1,3,4,6,2,5,8,7]=>0001001=>1110110
[3,1,2,4,6,8,5,7]=>1000010=>0111101
[1,3,2,4,6,8,5,7]=>0100010=>1011101
[1,3,4,6,8,2,5,7]=>0000100=>1111011
[3,1,6,2,4,5,7,8]=>1010000=>0101111
[3,6,1,2,4,5,7,8]=>0100000=>1011111
[1,3,2,6,4,5,7,8]=>0101000=>1010111
[1,3,6,2,4,5,7,8]=>0010000=>1101111
[1,3,4,6,2,5,7,8]=>0001000=>1110111
[3,1,2,4,6,7,5,8]=>1000010=>0111101
[1,3,4,6,2,7,5,8]=>0001010=>1110101
[1,3,4,6,7,2,5,8]=>0000100=>1111011
[3,1,2,4,6,7,8,5]=>1000001=>0111110
[1,3,4,6,7,2,8,5]=>0000101=>1111010
[1,3,4,6,7,8,2,5]=>0000010=>1111101
[3,1,7,2,8,4,5,6]=>1010100=>0101011
[3,7,1,2,8,4,5,6]=>0100100=>1011011
[3,1,7,8,2,4,5,6]=>1001000=>0110111
[3,7,1,8,2,4,5,6]=>0101000=>1010111
[3,7,8,1,2,4,5,6]=>0010000=>1101111
[3,7,1,2,4,8,5,6]=>0100010=>1011101
[3,1,2,7,4,8,5,6]=>1001010=>0110101
[1,3,2,7,4,8,5,6]=>0101010=>1010101
[1,3,7,2,4,8,5,6]=>0010010=>1101101
[3,1,2,7,8,4,5,6]=>1000100=>0111011
[1,3,7,2,8,4,5,6]=>0010100=>1101011
[1,3,7,8,2,4,5,6]=>0001000=>1110111
[3,1,7,2,4,5,8,6]=>1010001=>0101110
[3,7,1,2,4,5,8,6]=>0100001=>1011110
[1,3,7,2,4,5,8,6]=>0010001=>1101110
[3,1,2,4,7,5,8,6]=>1000101=>0111010
[1,3,2,4,7,5,8,6]=>0100101=>1011010
[1,3,4,2,7,5,8,6]=>0010101=>1101010
[3,1,2,4,7,8,5,6]=>1000010=>0111101
[1,3,2,4,7,8,5,6]=>0100010=>1011101
[1,3,4,2,7,8,5,6]=>0010010=>1101101
[1,3,4,7,8,2,5,6]=>0000100=>1111011
[3,1,7,2,4,5,6,8]=>1010000=>0101111
[3,7,1,2,4,5,6,8]=>0100000=>1011111
[1,3,2,7,4,5,6,8]=>0101000=>1010111
[1,3,7,2,4,5,6,8]=>0010000=>1101111
[3,1,2,4,7,5,6,8]=>1000100=>0111011
[1,3,4,7,2,5,6,8]=>0001000=>1110111
[3,1,2,4,5,7,6,8]=>1000010=>0111101
[1,3,4,5,7,2,6,8]=>0000100=>1111011
[3,1,2,4,5,7,8,6]=>1000001=>0111110
[1,3,4,5,7,2,8,6]=>0000101=>1111010
[1,3,4,5,7,8,2,6]=>0000010=>1111101
[3,1,8,2,4,5,6,7]=>1010000=>0101111
[3,8,1,2,4,5,6,7]=>0100000=>1011111
[3,1,2,8,4,5,6,7]=>1001000=>0110111
[1,3,2,8,4,5,6,7]=>0101000=>1010111
[1,3,8,2,4,5,6,7]=>0010000=>1101111
[3,1,2,4,8,5,6,7]=>1000100=>0111011
[1,3,2,4,8,5,6,7]=>0100100=>1011011
[1,3,4,2,8,5,6,7]=>0010100=>1101011
[1,3,4,8,2,5,6,7]=>0001000=>1110111
[3,1,2,4,5,8,6,7]=>1000010=>0111101
[1,3,2,4,5,8,6,7]=>0100010=>1011101
[1,3,4,2,5,8,6,7]=>0010010=>1101101
[1,3,4,5,2,8,6,7]=>0001010=>1110101
[1,3,4,5,8,2,6,7]=>0000100=>1111011
[3,1,2,4,5,6,8,7]=>1000001=>0111110
[1,3,4,5,6,8,2,7]=>0000010=>1111101
[4,1,5,2,6,3,8,7]=>1010101=>0101010
[4,5,1,2,6,3,8,7]=>0100101=>1011010
[4,1,5,6,2,3,8,7]=>1001001=>0110110
[4,5,1,6,2,3,8,7]=>0101001=>1010110
[4,5,6,1,2,3,8,7]=>0010001=>1101110
[4,1,5,2,6,8,3,7]=>1010010=>0101101
[4,5,1,2,6,8,3,7]=>0100010=>1011101
[4,1,5,6,2,8,3,7]=>1001010=>0110101
[4,5,1,6,2,8,3,7]=>0101010=>1010101
[4,5,6,1,2,8,3,7]=>0010010=>1101101
[4,1,5,6,8,2,3,7]=>1000100=>0111011
[4,5,1,6,8,2,3,7]=>0100100=>1011011
[4,5,6,1,8,2,3,7]=>0010100=>1101011
[4,5,6,8,1,2,3,7]=>0001000=>1110111
[4,1,5,2,6,3,7,8]=>1010100=>0101011
[4,1,5,6,2,3,7,8]=>1001000=>0110111
[4,5,1,6,2,3,7,8]=>0101000=>1010111
[4,5,1,2,6,7,3,8]=>0100010=>1011101
[4,5,1,6,2,7,3,8]=>0101010=>1010101
[4,5,6,1,2,7,3,8]=>0010010=>1101101
[4,1,5,6,7,2,3,8]=>1000100=>0111011
[4,5,1,6,7,2,3,8]=>0100100=>1011011
[4,5,6,1,7,2,3,8]=>0010100=>1101011
[4,1,5,2,6,7,8,3]=>1010001=>0101110
[4,5,1,2,6,7,8,3]=>0100001=>1011110
[4,5,1,6,2,7,8,3]=>0101001=>1010110
[4,5,6,1,2,7,8,3]=>0010001=>1101110
[4,1,5,6,7,2,8,3]=>1000101=>0111010
[4,5,1,6,7,2,8,3]=>0100101=>1011010
[4,5,6,1,7,2,8,3]=>0010101=>1101010
[4,5,6,7,1,2,8,3]=>0001001=>1110110
[4,1,5,6,7,8,2,3]=>1000010=>0111101
[4,5,1,6,7,8,2,3]=>0100010=>1011101
[4,5,6,1,7,8,2,3]=>0010010=>1101101
[4,5,6,7,1,8,2,3]=>0001010=>1110101
[4,1,5,2,7,3,8,6]=>1010101=>0101010
[4,5,1,7,2,3,8,6]=>0101001=>1010110
[4,5,7,1,2,3,8,6]=>0010001=>1101110
[4,1,5,2,7,8,3,6]=>1010010=>0101101
[4,5,1,2,7,8,3,6]=>0100010=>1011101
[4,1,5,7,2,8,3,6]=>1001010=>0110101
[4,5,1,7,2,8,3,6]=>0101010=>1010101
[4,5,7,1,2,8,3,6]=>0010010=>1101101
[4,5,1,7,8,2,3,6]=>0100100=>1011011
[4,5,7,8,1,2,3,6]=>0001000=>1110111
[4,1,5,2,7,3,6,8]=>1010100=>0101011
[4,5,1,2,7,3,6,8]=>0100100=>1011011
[4,1,5,7,2,3,6,8]=>1001000=>0110111
[4,5,1,7,2,3,6,8]=>0101000=>1010111
[4,1,5,2,3,7,6,8]=>1010010=>0101101
[4,5,1,2,3,7,6,8]=>0100010=>1011101
[4,1,2,5,3,7,6,8]=>1001010=>0110101
[1,4,2,5,3,7,6,8]=>0101010=>1010101
[1,4,5,2,3,7,6,8]=>0010010=>1101101
[4,1,2,5,7,3,6,8]=>1000100=>0111011
[1,4,2,5,7,3,6,8]=>0100100=>1011011
[1,4,5,2,7,3,6,8]=>0010100=>1101011
[1,4,5,7,2,3,6,8]=>0001000=>1110111
[4,1,5,2,3,7,8,6]=>1010001=>0101110
[4,1,2,5,3,7,8,6]=>1001001=>0110110
[1,4,2,5,3,7,8,6]=>0101001=>1010110
[1,4,5,2,3,7,8,6]=>0010001=>1101110
[4,1,2,5,7,3,8,6]=>1000101=>0111010
[1,4,2,5,7,3,8,6]=>0100101=>1011010
[1,4,5,2,7,3,8,6]=>0010101=>1101010
[1,4,5,7,2,3,8,6]=>0001001=>1110110
[4,1,2,5,7,8,3,6]=>1000010=>0111101
[1,4,2,5,7,8,3,6]=>0100010=>1011101
[1,4,5,2,7,8,3,6]=>0010010=>1101101
[1,4,5,7,8,2,3,6]=>0000100=>1111011
[4,1,5,2,8,3,6,7]=>1010100=>0101011
[4,5,1,2,8,3,6,7]=>0100100=>1011011
[4,1,5,8,2,3,6,7]=>1001000=>0110111
[4,5,1,8,2,3,6,7]=>0101000=>1010111
[4,5,8,1,2,3,6,7]=>0010000=>1101111
[4,1,5,2,3,8,6,7]=>1010010=>0101101
[4,5,1,2,3,8,6,7]=>0100010=>1011101
[4,1,2,5,3,8,6,7]=>1001010=>0110101
[1,4,2,5,3,8,6,7]=>0101010=>1010101
[1,4,5,2,3,8,6,7]=>0010010=>1101101
[4,1,2,5,8,3,6,7]=>1000100=>0111011
[1,4,2,5,8,3,6,7]=>0100100=>1011011
[1,4,5,2,8,3,6,7]=>0010100=>1101011
[1,4,5,8,2,3,6,7]=>0001000=>1110111
[1,4,2,5,3,6,8,7]=>0101001=>1010110
[4,1,2,5,6,3,8,7]=>1000101=>0111010
[1,4,5,2,6,3,8,7]=>0010101=>1101010
[1,4,5,6,2,3,8,7]=>0001001=>1110110
[4,1,2,5,6,8,3,7]=>1000010=>0111101
[1,4,2,5,6,8,3,7]=>0100010=>1011101
[1,4,5,2,6,8,3,7]=>0010010=>1101101
[1,4,5,6,2,8,3,7]=>0001010=>1110101
[1,4,5,6,8,2,3,7]=>0000100=>1111011
[4,1,5,2,3,6,7,8]=>1010000=>0101111
[4,1,2,5,3,6,7,8]=>1001000=>0110111
[1,4,2,5,3,6,7,8]=>0101000=>1010111
[1,4,5,2,3,6,7,8]=>0010000=>1101111
[4,1,2,5,6,3,7,8]=>1000100=>0111011
[1,4,5,2,6,3,7,8]=>0010100=>1101011
[1,4,5,6,2,3,7,8]=>0001000=>1110111
[4,1,2,5,6,7,3,8]=>1000010=>0111101
[1,4,2,5,6,7,3,8]=>0100010=>1011101
[1,4,5,2,6,7,3,8]=>0010010=>1101101
[1,4,5,6,2,7,3,8]=>0001010=>1110101
[1,4,5,6,7,2,3,8]=>0000100=>1111011
[4,1,2,5,6,7,8,3]=>1000001=>0111110
[1,4,2,5,6,7,8,3]=>0100001=>1011110
[1,4,5,2,6,7,8,3]=>0010001=>1101110
[1,4,5,6,2,7,8,3]=>0001001=>1110110
[1,4,5,6,7,2,8,3]=>0000101=>1111010
[1,4,5,6,7,8,2,3]=>0000010=>1111101
[4,1,6,2,7,3,8,5]=>1010101=>0101010
[4,1,6,7,2,3,8,5]=>1001001=>0110110
[4,6,7,1,2,3,8,5]=>0010001=>1101110
[4,6,1,2,7,8,3,5]=>0100010=>1011101
[4,6,1,7,2,8,3,5]=>0101010=>1010101
[4,6,7,1,2,8,3,5]=>0010010=>1101101
[4,1,6,7,8,2,3,5]=>1000100=>0111011
[4,6,1,7,8,2,3,5]=>0100100=>1011011
[4,6,7,1,8,2,3,5]=>0010100=>1101011
[4,6,7,8,1,2,3,5]=>0001000=>1110111
[4,1,6,2,7,3,5,8]=>1010100=>0101011
[4,6,1,2,7,3,5,8]=>0100100=>1011011
[4,1,6,7,2,3,5,8]=>1001000=>0110111
[4,6,1,7,2,3,5,8]=>0101000=>1010111
[4,6,7,1,2,3,5,8]=>0010000=>1101111
[4,1,6,2,3,7,5,8]=>1010010=>0101101
[4,6,1,2,3,7,5,8]=>0100010=>1011101
[4,1,2,6,3,7,5,8]=>1001010=>0110101
[1,4,2,6,3,7,5,8]=>0101010=>1010101
[4,1,2,6,7,3,5,8]=>1000100=>0111011
[1,4,2,6,7,3,5,8]=>0100100=>1011011
[1,4,6,2,7,3,5,8]=>0010100=>1101011
[1,4,6,7,2,3,5,8]=>0001000=>1110111
[4,1,6,2,3,7,8,5]=>1010001=>0101110
[4,1,2,6,3,7,8,5]=>1001001=>0110110
[1,4,6,2,3,7,8,5]=>0010001=>1101110
[4,1,2,6,7,3,8,5]=>1000101=>0111010
[1,4,6,2,7,3,8,5]=>0010101=>1101010
[1,4,6,7,2,3,8,5]=>0001001=>1110110
[1,4,2,6,7,8,3,5]=>0100010=>1011101
[1,4,6,2,7,8,3,5]=>0010010=>1101101
[1,4,6,7,2,8,3,5]=>0001010=>1110101
[1,4,6,7,8,2,3,5]=>0000100=>1111011
[4,1,6,2,8,3,5,7]=>1010100=>0101011
[4,6,1,2,8,3,5,7]=>0100100=>1011011
[4,1,6,8,2,3,5,7]=>1001000=>0110111
[4,6,1,8,2,3,5,7]=>0101000=>1010111
[4,6,8,1,2,3,5,7]=>0010000=>1101111
[4,1,6,2,3,8,5,7]=>1010010=>0101101
[4,6,1,2,3,8,5,7]=>0100010=>1011101
[4,1,2,6,3,8,5,7]=>1001010=>0110101
[1,4,2,6,3,8,5,7]=>0101010=>1010101
[1,4,6,2,3,8,5,7]=>0010010=>1101101
[1,4,2,6,8,3,5,7]=>0100100=>1011011
[1,4,6,2,8,3,5,7]=>0010100=>1101011
[1,4,6,8,2,3,5,7]=>0001000=>1110111
[4,1,6,2,3,5,8,7]=>1010001=>0101110
[4,6,1,2,3,5,8,7]=>0100001=>1011110
[4,1,2,6,3,5,8,7]=>1001001=>0110110
[1,4,2,6,3,5,8,7]=>0101001=>1010110
[1,4,6,2,3,5,8,7]=>0010001=>1101110
[4,1,2,3,6,5,8,7]=>1000101=>0111010
[1,4,2,3,6,5,8,7]=>0100101=>1011010
[1,2,4,6,3,5,8,7]=>0001001=>1110110
[4,1,2,3,6,8,5,7]=>1000010=>0111101
[1,2,4,3,6,8,5,7]=>0010010=>1101101
[1,2,4,6,8,3,5,7]=>0000100=>1111011
[4,1,6,2,3,5,7,8]=>1010000=>0101111
[4,6,1,2,3,5,7,8]=>0100000=>1011111
[1,4,2,6,3,5,7,8]=>0101000=>1010111
[1,4,6,2,3,5,7,8]=>0010000=>1101111
[4,1,2,3,6,5,7,8]=>1000100=>0111011
[1,4,2,3,6,5,7,8]=>0100100=>1011011
[1,2,4,6,3,5,7,8]=>0001000=>1110111
[4,1,2,3,6,7,5,8]=>1000010=>0111101
[1,4,2,3,6,7,5,8]=>0100010=>1011101
[1,2,4,6,7,3,5,8]=>0000100=>1111011
[4,1,2,3,6,7,8,5]=>1000001=>0111110
[1,4,2,3,6,7,8,5]=>0100001=>1011110
[1,2,4,6,7,3,8,5]=>0000101=>1111010
[1,2,4,6,7,8,3,5]=>0000010=>1111101
[4,1,7,2,8,3,5,6]=>1010100=>0101011
[4,7,1,2,8,3,5,6]=>0100100=>1011011
[4,1,7,8,2,3,5,6]=>1001000=>0110111
[4,7,1,8,2,3,5,6]=>0101000=>1010111
[4,7,8,1,2,3,5,6]=>0010000=>1101111
[4,7,1,2,3,8,5,6]=>0100010=>1011101
[1,4,2,7,3,8,5,6]=>0101010=>1010101
[1,4,7,2,3,8,5,6]=>0010010=>1101101
[4,1,2,7,8,3,5,6]=>1000100=>0111011
[1,4,2,7,8,3,5,6]=>0100100=>1011011
[1,4,7,2,8,3,5,6]=>0010100=>1101011
[1,4,7,8,2,3,5,6]=>0001000=>1110111
[4,1,7,2,3,5,8,6]=>1010001=>0101110
[4,7,1,2,3,5,8,6]=>0100001=>1011110
[4,1,2,7,3,5,8,6]=>1001001=>0110110
[1,4,2,7,3,5,8,6]=>0101001=>1010110
[1,4,7,2,3,5,8,6]=>0010001=>1101110
[4,1,2,3,7,5,8,6]=>1000101=>0111010
[1,4,2,3,7,5,8,6]=>0100101=>1011010
[1,2,4,3,7,5,8,6]=>0010101=>1101010
[1,2,4,7,3,5,8,6]=>0001001=>1110110
[4,1,2,3,7,8,5,6]=>1000010=>0111101
[1,4,2,3,7,8,5,6]=>0100010=>1011101
[1,2,4,3,7,8,5,6]=>0010010=>1101101
[1,2,4,7,3,8,5,6]=>0001010=>1110101
[1,2,4,7,8,3,5,6]=>0000100=>1111011
[4,1,7,2,3,5,6,8]=>1010000=>0101111
[4,7,1,2,3,5,6,8]=>0100000=>1011111
[4,1,2,7,3,5,6,8]=>1001000=>0110111
[1,4,2,7,3,5,6,8]=>0101000=>1010111
[1,4,7,2,3,5,6,8]=>0010000=>1101111
[4,1,2,3,7,5,6,8]=>1000100=>0111011
[1,4,2,3,7,5,6,8]=>0100100=>1011011
[1,2,4,3,7,5,6,8]=>0010100=>1101011
[1,2,4,7,3,5,6,8]=>0001000=>1110111
[4,1,2,3,5,7,6,8]=>1000010=>0111101
[1,4,2,3,5,7,6,8]=>0100010=>1011101
[1,2,4,5,7,3,6,8]=>0000100=>1111011
[4,1,2,3,5,7,8,6]=>1000001=>0111110
[1,4,2,3,5,7,8,6]=>0100001=>1011110
[1,2,4,5,7,3,8,6]=>0000101=>1111010
[1,2,4,5,7,8,3,6]=>0000010=>1111101
[4,1,8,2,3,5,6,7]=>1010000=>0101111
[4,8,1,2,3,5,6,7]=>0100000=>1011111
[4,1,2,8,3,5,6,7]=>1001000=>0110111
[1,4,2,8,3,5,6,7]=>0101000=>1010111
[1,4,8,2,3,5,6,7]=>0010000=>1101111
[4,1,2,3,8,5,6,7]=>1000100=>0111011
[1,4,2,3,8,5,6,7]=>0100100=>1011011
[1,2,4,3,8,5,6,7]=>0010100=>1101011
[1,2,4,8,3,5,6,7]=>0001000=>1110111
[4,1,2,3,5,8,6,7]=>1000010=>0111101
[1,4,2,3,5,8,6,7]=>0100010=>1011101
[1,2,4,3,5,8,6,7]=>0010010=>1101101
[1,2,4,5,3,8,6,7]=>0001010=>1110101
[1,2,4,5,8,3,6,7]=>0000100=>1111011
[4,1,2,3,5,6,8,7]=>1000001=>0111110
[1,4,2,3,5,6,8,7]=>0100001=>1011110
[1,2,4,5,6,8,3,7]=>0000010=>1111101
[1,4,2,3,5,6,7,8]=>0100000=>1011111
[5,1,6,2,7,3,8,4]=>1010101=>0101010
[5,6,1,2,7,3,8,4]=>0100101=>1011010
[5,1,6,7,2,3,8,4]=>1001001=>0110110
[5,6,1,7,2,3,8,4]=>0101001=>1010110
[5,6,7,1,2,3,8,4]=>0010001=>1101110
[5,6,1,2,7,8,3,4]=>0100010=>1011101
[5,1,6,7,2,8,3,4]=>1001010=>0110101
[5,6,7,1,2,8,3,4]=>0010010=>1101101
[5,1,6,7,8,2,3,4]=>1000100=>0111011
[5,6,1,7,8,2,3,4]=>0100100=>1011011
[5,6,7,1,8,2,3,4]=>0010100=>1101011
[5,1,6,2,7,3,4,8]=>1010100=>0101011
[5,6,1,2,7,3,4,8]=>0100100=>1011011
[5,6,1,7,2,3,4,8]=>0101000=>1010111
[5,1,6,2,3,7,4,8]=>1010010=>0101101
[5,1,2,6,3,7,4,8]=>1001010=>0110101
[1,5,2,6,3,7,4,8]=>0101010=>1010101
[5,1,2,6,7,3,4,8]=>1000100=>0111011
[1,5,2,6,7,3,4,8]=>0100100=>1011011
[1,5,6,2,7,3,4,8]=>0010100=>1101011
[1,5,6,7,2,3,4,8]=>0001000=>1110111
[5,1,6,2,3,7,8,4]=>1010001=>0101110
[5,6,1,2,3,7,8,4]=>0100001=>1011110
[5,1,2,6,3,7,8,4]=>1001001=>0110110
[1,5,2,6,3,7,8,4]=>0101001=>1010110
[1,5,6,2,3,7,8,4]=>0010001=>1101110
[5,1,2,6,7,3,8,4]=>1000101=>0111010
[1,5,6,7,2,3,8,4]=>0001001=>1110110
[5,1,2,6,7,8,3,4]=>1000010=>0111101
[1,5,2,6,7,8,3,4]=>0100010=>1011101
[1,5,6,2,7,8,3,4]=>0010010=>1101101
[1,5,6,7,2,8,3,4]=>0001010=>1110101
[1,5,6,7,8,2,3,4]=>0000100=>1111011
[5,1,6,2,8,3,4,7]=>1010100=>0101011
[5,6,1,2,8,3,4,7]=>0100100=>1011011
[5,6,1,8,2,3,4,7]=>0101000=>1010111
[5,6,8,1,2,3,4,7]=>0010000=>1101111
[5,1,6,2,3,8,4,7]=>1010010=>0101101
[5,6,1,2,3,8,4,7]=>0100010=>1011101
[5,1,2,6,3,8,4,7]=>1001010=>0110101
[1,5,2,6,3,8,4,7]=>0101010=>1010101
[1,5,6,2,3,8,4,7]=>0010010=>1101101
[5,1,2,6,8,3,4,7]=>1000100=>0111011
[1,5,2,6,8,3,4,7]=>0100100=>1011011
[1,5,6,2,8,3,4,7]=>0010100=>1101011
[1,5,6,8,2,3,4,7]=>0001000=>1110111
[5,1,6,2,3,4,8,7]=>1010001=>0101110
[5,6,1,2,3,4,8,7]=>0100001=>1011110
[5,1,2,6,3,4,8,7]=>1001001=>0110110
[1,5,2,6,3,4,8,7]=>0101001=>1010110
[1,5,6,2,3,4,8,7]=>0010001=>1101110
[1,5,2,3,6,4,8,7]=>0100101=>1011010
[1,2,5,3,6,4,8,7]=>0010101=>1101010
[1,2,5,6,3,4,8,7]=>0001001=>1110110
[5,1,2,3,6,8,4,7]=>1000010=>0111101
[1,5,2,3,6,8,4,7]=>0100010=>1011101
[1,2,5,6,3,8,4,7]=>0001010=>1110101
[5,1,6,2,3,4,7,8]=>1010000=>0101111
[5,1,2,6,3,4,7,8]=>1001000=>0110111
[1,5,2,6,3,4,7,8]=>0101000=>1010111
[1,5,6,2,3,4,7,8]=>0010000=>1101111
[5,1,2,3,6,4,7,8]=>1000100=>0111011
[1,5,2,3,6,4,7,8]=>0100100=>1011011
[1,2,5,3,6,4,7,8]=>0010100=>1101011
[1,2,5,6,3,4,7,8]=>0001000=>1110111
[5,1,2,3,6,7,4,8]=>1000010=>0111101
[1,5,2,3,6,7,4,8]=>0100010=>1011101
[1,2,5,3,6,7,4,8]=>0010010=>1101101
[1,2,5,6,3,7,4,8]=>0001010=>1110101
[5,1,2,3,6,7,8,4]=>1000001=>0111110
[1,5,2,3,6,7,8,4]=>0100001=>1011110
[1,2,5,3,6,7,8,4]=>0010001=>1101110
[1,2,5,6,3,7,8,4]=>0001001=>1110110
[1,2,5,6,7,3,8,4]=>0000101=>1111010
[1,2,5,6,7,8,3,4]=>0000010=>1111101
[5,1,7,2,8,3,4,6]=>1010100=>0101011
[5,7,1,2,8,3,4,6]=>0100100=>1011011
[5,1,7,8,2,3,4,6]=>1001000=>0110111
[5,7,1,8,2,3,4,6]=>0101000=>1010111
[5,7,8,1,2,3,4,6]=>0010000=>1101111
[5,1,7,2,3,8,4,6]=>1010010=>0101101
[5,7,1,2,3,8,4,6]=>0100010=>1011101
[5,1,2,7,3,8,4,6]=>1001010=>0110101
[1,5,2,7,3,8,4,6]=>0101010=>1010101
[1,5,7,2,3,8,4,6]=>0010010=>1101101
[5,1,2,7,8,3,4,6]=>1000100=>0111011
[1,5,2,7,8,3,4,6]=>0100100=>1011011
[1,5,7,2,8,3,4,6]=>0010100=>1101011
[1,5,7,8,2,3,4,6]=>0001000=>1110111
[5,1,7,2,3,4,8,6]=>1010001=>0101110
[5,7,1,2,3,4,8,6]=>0100001=>1011110
[5,1,2,7,3,4,8,6]=>1001001=>0110110
[1,5,2,7,3,4,8,6]=>0101001=>1010110
[1,5,7,2,3,4,8,6]=>0010001=>1101110
[5,1,2,3,7,4,8,6]=>1000101=>0111010
[1,5,2,3,7,4,8,6]=>0100101=>1011010
[1,2,5,3,7,4,8,6]=>0010101=>1101010
[1,2,5,7,3,4,8,6]=>0001001=>1110110
[5,1,2,3,7,8,4,6]=>1000010=>0111101
[1,5,2,3,7,8,4,6]=>0100010=>1011101
[1,2,5,7,3,8,4,6]=>0001010=>1110101
[1,2,5,7,8,3,4,6]=>0000100=>1111011
[5,7,1,2,3,4,6,8]=>0100000=>1011111
[5,1,2,7,3,4,6,8]=>1001000=>0110111
[1,5,2,7,3,4,6,8]=>0101000=>1010111
[1,5,7,2,3,4,6,8]=>0010000=>1101111
[1,5,2,3,7,4,6,8]=>0100100=>1011011
[1,2,5,3,7,4,6,8]=>0010100=>1101011
[1,2,5,7,3,4,6,8]=>0001000=>1110111
[1,5,2,3,4,7,6,8]=>0100010=>1011101
[1,2,5,3,4,7,6,8]=>0010010=>1101101
[1,2,3,5,7,4,6,8]=>0000100=>1111011
[5,1,2,3,4,7,8,6]=>1000001=>0111110
[1,5,2,3,4,7,8,6]=>0100001=>1011110
[1,2,5,3,4,7,8,6]=>0010001=>1101110
[1,2,3,5,7,4,8,6]=>0000101=>1111010
[1,2,3,5,7,8,4,6]=>0000010=>1111101
[5,1,8,2,3,4,6,7]=>1010000=>0101111
[5,8,1,2,3,4,6,7]=>0100000=>1011111
[5,1,2,8,3,4,6,7]=>1001000=>0110111
[1,5,2,8,3,4,6,7]=>0101000=>1010111
[1,5,8,2,3,4,6,7]=>0010000=>1101111
[5,1,2,3,8,4,6,7]=>1000100=>0111011
[1,5,2,3,8,4,6,7]=>0100100=>1011011
[1,2,5,3,8,4,6,7]=>0010100=>1101011
[1,2,5,8,3,4,6,7]=>0001000=>1110111
[5,1,2,3,4,8,6,7]=>1000010=>0111101
[1,5,2,3,4,8,6,7]=>0100010=>1011101
[1,2,5,3,4,8,6,7]=>0010010=>1101101
[1,2,3,5,4,8,6,7]=>0001010=>1110101
[1,2,3,5,8,4,6,7]=>0000100=>1111011
[5,1,2,3,4,6,8,7]=>1000001=>0111110
[1,5,2,3,4,6,8,7]=>0100001=>1011110
[1,2,5,3,4,6,8,7]=>0010001=>1101110
[1,2,3,5,6,8,4,7]=>0000010=>1111101
[1,5,2,3,4,6,7,8]=>0100000=>1011111
[1,2,5,3,4,6,7,8]=>0010000=>1101111
[6,1,7,2,8,3,4,5]=>1010100=>0101011
[6,7,1,2,8,3,4,5]=>0100100=>1011011
[6,1,7,8,2,3,4,5]=>1001000=>0110111
[6,7,1,8,2,3,4,5]=>0101000=>1010111
[6,1,7,2,3,8,4,5]=>1010010=>0101101
[6,7,1,2,3,8,4,5]=>0100010=>1011101
[6,1,2,7,3,8,4,5]=>1001010=>0110101
[1,6,2,7,3,8,4,5]=>0101010=>1010101
[1,6,7,2,3,8,4,5]=>0010010=>1101101
[6,1,2,7,8,3,4,5]=>1000100=>0111011
[1,6,2,7,8,3,4,5]=>0100100=>1011011
[1,6,7,2,8,3,4,5]=>0010100=>1101011
[1,6,7,8,2,3,4,5]=>0001000=>1110111
[6,1,7,2,3,4,8,5]=>1010001=>0101110
[6,7,1,2,3,4,8,5]=>0100001=>1011110
[6,1,2,7,3,4,8,5]=>1001001=>0110110
[1,6,2,7,3,4,8,5]=>0101001=>1010110
[1,6,7,2,3,4,8,5]=>0010001=>1101110
[6,1,2,3,7,4,8,5]=>1000101=>0111010
[1,6,2,3,7,4,8,5]=>0100101=>1011010
[1,2,6,3,7,4,8,5]=>0010101=>1101010
[6,1,2,3,7,8,4,5]=>1000010=>0111101
[1,6,2,3,7,8,4,5]=>0100010=>1011101
[1,2,6,3,7,8,4,5]=>0010010=>1101101
[1,2,6,7,3,8,4,5]=>0001010=>1110101
[1,2,6,7,8,3,4,5]=>0000100=>1111011
[6,1,7,2,3,4,5,8]=>1010000=>0101111
[6,1,2,7,3,4,5,8]=>1001000=>0110111
[1,6,2,7,3,4,5,8]=>0101000=>1010111
[1,6,7,2,3,4,5,8]=>0010000=>1101111
[6,1,2,3,7,4,5,8]=>1000100=>0111011
[1,6,2,3,7,4,5,8]=>0100100=>1011011
[1,2,6,3,7,4,5,8]=>0010100=>1101011
[1,2,6,7,3,4,5,8]=>0001000=>1110111
[6,1,2,3,4,7,5,8]=>1000010=>0111101
[1,6,2,3,4,7,5,8]=>0100010=>1011101
[1,2,6,3,4,7,5,8]=>0010010=>1101101
[1,2,3,6,4,7,5,8]=>0001010=>1110101
[1,2,3,6,7,4,5,8]=>0000100=>1111011
[6,1,2,3,4,7,8,5]=>1000001=>0111110
[1,6,2,3,4,7,8,5]=>0100001=>1011110
[1,2,6,3,4,7,8,5]=>0010001=>1101110
[1,2,3,6,4,7,8,5]=>0001001=>1110110
[1,2,3,6,7,4,8,5]=>0000101=>1111010
[1,2,3,6,7,8,4,5]=>0000010=>1111101
[6,1,8,2,3,4,5,7]=>1010000=>0101111
[6,8,1,2,3,4,5,7]=>0100000=>1011111
[6,1,2,8,3,4,5,7]=>1001000=>0110111
[1,6,2,8,3,4,5,7]=>0101000=>1010111
[1,6,8,2,3,4,5,7]=>0010000=>1101111
[6,1,2,3,8,4,5,7]=>1000100=>0111011
[1,6,2,3,8,4,5,7]=>0100100=>1011011
[1,2,6,3,8,4,5,7]=>0010100=>1101011
[1,2,6,8,3,4,5,7]=>0001000=>1110111
[6,1,2,3,4,8,5,7]=>1000010=>0111101
[1,6,2,3,4,8,5,7]=>0100010=>1011101
[1,2,6,3,4,8,5,7]=>0010010=>1101101
[1,2,3,6,4,8,5,7]=>0001010=>1110101
[1,2,3,6,8,4,5,7]=>0000100=>1111011
[6,1,2,3,4,5,8,7]=>1000001=>0111110
[1,6,2,3,4,5,8,7]=>0100001=>1011110
[1,2,6,3,4,5,8,7]=>0010001=>1101110
[1,2,3,6,4,5,8,7]=>0001001=>1110110
[1,2,3,4,6,8,5,7]=>0000010=>1111101
[1,6,2,3,4,5,7,8]=>0100000=>1011111
[1,2,6,3,4,5,7,8]=>0010000=>1101111
[1,2,3,6,4,5,7,8]=>0001000=>1110111
[7,1,8,2,3,4,5,6]=>1010000=>0101111
[7,1,2,8,3,4,5,6]=>1001000=>0110111
[1,7,2,8,3,4,5,6]=>0101000=>1010111
[1,7,8,2,3,4,5,6]=>0010000=>1101111
[7,1,2,3,8,4,5,6]=>1000100=>0111011
[1,7,2,3,8,4,5,6]=>0100100=>1011011
[1,2,7,3,8,4,5,6]=>0010100=>1101011
[1,2,7,8,3,4,5,6]=>0001000=>1110111
[7,1,2,3,4,8,5,6]=>1000010=>0111101
[1,7,2,3,4,8,5,6]=>0100010=>1011101
[1,2,7,3,4,8,5,6]=>0010010=>1101101
[1,2,3,7,4,8,5,6]=>0001010=>1110101
[1,2,3,7,8,4,5,6]=>0000100=>1111011
[7,1,2,3,4,5,8,6]=>1000001=>0111110
[1,7,2,3,4,5,8,6]=>0100001=>1011110
[1,2,7,3,4,5,8,6]=>0010001=>1101110
[1,2,3,7,4,5,8,6]=>0001001=>1110110
[1,2,3,4,7,5,8,6]=>0000101=>1111010
[1,2,3,4,7,8,5,6]=>0000010=>1111101
[1,7,2,3,4,5,6,8]=>0100000=>1011111
[1,2,7,3,4,5,6,8]=>0010000=>1101111
[1,2,3,7,4,5,6,8]=>0001000=>1110111
[1,2,3,4,7,5,6,8]=>0000100=>1111011
[1,8,2,3,4,5,6,7]=>0100000=>1011111
[1,2,8,3,4,5,6,7]=>0010000=>1101111
[1,2,3,8,4,5,6,7]=>0001000=>1110111
[1,2,3,4,8,5,6,7]=>0000100=>1111011
[1,2,3,4,5,8,6,7]=>0000010=>1111101
[5,3,2,6,1,4,8,7]=>1101001=>0010110
[7,3,2,5,4,8,1,6]=>1101010=>0010101
[8,4,5,2,3,7,6,1]=>1010011=>0101100
[7,4,5,2,3,8,1,6]=>1010010=>0101101
[6,4,5,2,3,1,8,7]=>1010101=>0101010
[5,4,6,2,1,3,8,7]=>1011001=>0100110
[3,6,1,5,4,2,8,7]=>0101101=>1010010
[4,6,5,1,3,2,8,7]=>0110101=>1001010
[5,6,4,3,1,2,8,7]=>0111001=>1000110
[7,5,4,3,2,8,1,6]=>1111010=>0000101
[8,6,4,3,7,2,5,1]=>1110101=>0001010
[7,6,4,3,8,2,1,5]=>1110110=>0001001
[6,7,4,3,8,1,2,5]=>0110100=>1001011
[5,7,4,3,1,8,2,6]=>0111010=>1000101
[4,7,5,1,3,8,2,6]=>0110010=>1001101
[3,7,1,5,4,8,2,6]=>0101010=>1010101
[2,1,7,5,4,8,3,6]=>1011010=>0100101
[3,8,1,5,4,7,6,2]=>0101011=>1010100
[4,8,5,1,3,7,6,2]=>0110011=>1001100
[5,8,4,3,1,7,6,2]=>0111011=>1000100
[6,8,4,3,7,1,5,2]=>0110101=>1001010
[7,8,4,3,6,5,1,2]=>0110110=>1001001
[6,8,5,7,3,1,4,2]=>0101101=>1010010
[5,8,6,7,1,3,4,2]=>0101001=>1010110
[4,8,6,1,7,3,5,2]=>0110101=>1001010
[3,8,1,6,7,4,5,2]=>0100101=>1011010
[2,1,8,6,7,4,5,3]=>1010101=>0101010
[2,1,7,6,8,4,3,5]=>1010110=>0101001
[3,7,1,6,8,4,2,5]=>0100110=>1011001
[4,7,6,1,8,3,2,5]=>0110110=>1001001
[5,7,6,8,1,3,2,4]=>0101010=>1010101
[5,4,7,2,1,8,3,6]=>1011010=>0100101
[6,4,7,2,8,1,3,5]=>1010100=>0101011
[7,4,6,2,8,3,1,5]=>1010110=>0101001
[8,4,6,2,7,3,5,1]=>1010101=>0101010
[8,3,2,6,7,4,5,1]=>1100101=>0011010
[7,3,2,6,8,4,1,5]=>1100110=>0011001
[6,3,2,7,8,1,4,5]=>1100100=>0011011
[5,3,2,7,1,8,4,6]=>1101010=>0010101
[4,3,2,1,7,8,5,6]=>1110010=>0001101
[3,4,1,2,8,7,6,5]=>0100111=>1011000
[5,3,2,8,1,7,6,4]=>1101011=>0010100
[6,3,2,8,7,1,5,4]=>1101101=>0010010
[7,3,2,8,6,5,1,4]=>1101110=>0010001
[8,4,7,2,6,5,3,1]=>1010111=>0101000
[7,4,8,2,6,5,1,3]=>1010110=>0101001
[6,4,8,2,7,1,5,3]=>1010101=>0101010
[5,4,8,2,1,7,6,3]=>1011011=>0100100
[4,5,8,1,2,7,6,3]=>0010011=>1101100
[3,5,1,8,2,7,6,4]=>0101011=>1010100
[2,1,5,8,3,7,6,4]=>1001011=>0110100
[2,1,6,8,7,3,5,4]=>1001101=>0110010
[3,6,1,8,7,2,5,4]=>0101101=>1010010
[4,6,8,1,7,2,5,3]=>0010101=>1101010
[5,6,8,7,1,2,4,3]=>0011001=>1100110
[6,5,8,7,2,1,4,3]=>1011101=>0100010
[7,5,8,6,2,4,1,3]=>1011010=>0100101
[8,5,7,6,2,4,3,1]=>1011011=>0100100
[5,7,8,6,1,4,2,3]=>0011010=>1100101
[4,7,8,1,6,5,2,3]=>0010110=>1101001
[3,7,1,8,6,5,2,4]=>0101110=>1010001
[2,1,7,8,6,5,3,4]=>1001110=>0110001
[3,8,1,7,6,5,4,2]=>0101111=>1010000
[4,8,7,1,6,5,3,2]=>0110111=>1001000
[5,8,7,6,1,4,3,2]=>0111011=>1000100
[6,8,7,5,4,1,3,2]=>0111101=>1000010
[2,1,4,3,6,5,8,7,10,9]=>101010101=>010101010
[3,4,1,2,6,5,8,7,10,9]=>010010101=>101101010
[4,3,2,1,6,5,8,7,10,9]=>111010101=>000101010
[6,3,2,5,4,1,8,7,10,9]=>110110101=>001001010
[8,3,2,5,4,7,6,1,10,9]=>110101101=>001010010
[10,3,2,5,4,7,6,9,8,1]=>110101011=>001010100
[4,5,6,1,2,3,8,7,10,9]=>001000101=>110111010
[3,5,1,6,2,4,8,7,10,9]=>010100101=>101011010
[2,1,5,6,3,4,8,7,10,9]=>100100101=>011011010
[2,1,6,5,4,3,8,7,10,9]=>101110101=>010001010
[6,5,4,3,2,1,8,7,10,9]=>111110101=>000001010
[8,5,4,3,2,7,6,1,10,9]=>111101101=>000010010
[10,5,4,3,2,7,6,9,8,1]=>111101011=>000010100
[2,1,8,5,4,7,6,3,10,9]=>101101101=>010010010
[8,7,4,3,6,5,2,1,10,9]=>111011101=>000100010
[10,7,4,3,6,5,2,9,8,1]=>111011011=>000100100
[2,1,10,5,4,7,6,9,8,3]=>101101011=>010010100
[10,9,4,3,6,5,8,7,2,1]=>111010111=>000101000
[8,9,5,6,3,4,10,1,2,7]=>010100100=>101011011
[5,6,7,8,1,2,3,4,10,9]=>000100001=>111011110
[4,6,7,1,8,2,3,5,10,9]=>001010001=>110101110
[3,6,1,7,8,2,4,5,10,9]=>010010001=>101101110
[2,1,6,7,8,3,4,5,10,9]=>100010001=>011101110
[2,1,5,7,3,8,4,6,10,9]=>100101001=>011010110
[3,5,1,7,2,8,4,6,10,9]=>010101001=>101010110
[4,5,7,1,2,8,3,6,10,9]=>001001001=>110110110
[3,4,1,2,7,8,5,6,10,9]=>010001001=>101110110
[2,1,4,3,7,8,5,6,10,9]=>101001001=>010110110
[2,1,4,3,8,7,6,5,10,9]=>101011101=>010100010
[4,3,2,1,8,7,6,5,10,9]=>111011101=>000100010
[8,3,2,7,6,5,4,1,10,9]=>110111101=>001000010
[10,3,2,7,6,5,4,9,8,1]=>110111011=>001000100
[2,1,8,7,6,5,4,3,10,9]=>101111101=>010000010
[8,7,6,5,4,3,2,1,10,9]=>111111101=>000000010
[9,7,6,5,4,3,2,10,1,8]=>111111010=>000000101
[10,7,6,5,4,3,2,9,8,1]=>111111011=>000000100
[2,1,10,7,6,5,4,9,8,3]=>101111011=>010000100
[10,9,6,5,4,3,8,7,2,1]=>111110111=>000001000
[2,1,4,3,10,7,6,9,8,5]=>101011011=>010100100
[4,3,2,1,10,7,6,9,8,5]=>111011011=>000100100
[10,3,2,9,6,5,8,7,4,1]=>110110111=>001001000
[2,1,10,9,6,5,8,7,4,3]=>101110111=>010001000
[10,9,8,5,4,7,6,3,2,1]=>111101111=>000010000
[10,8,9,6,7,4,5,2,3,1]=>101010101=>010101010
[2,1,7,8,9,10,3,4,5,6]=>100001000=>011110111
[3,7,1,8,9,10,2,4,5,6]=>010001000=>101110111
[4,7,8,1,9,10,2,3,5,6]=>001001000=>110110111
[5,7,8,9,1,10,2,3,4,6]=>000101000=>111010111
[6,7,8,9,10,1,2,3,4,5]=>000010000=>111101111
[5,6,8,9,1,2,10,3,4,7]=>000100100=>111011011
[4,6,8,1,9,2,10,3,5,7]=>001010100=>110101011
[3,6,1,8,9,2,10,4,5,7]=>010010100=>101101011
[2,1,6,8,9,3,10,4,5,7]=>100010100=>011101011
[2,1,5,8,3,9,10,4,6,7]=>100100100=>011011011
[3,5,1,8,2,9,10,4,6,7]=>010100100=>101011011
[4,5,8,1,2,9,10,3,6,7]=>001000100=>110111011
[7,3,2,8,9,10,1,4,5,6]=>110001000=>001110111
[3,4,1,2,8,9,10,5,6,7]=>010000100=>101111011
[2,1,4,3,8,9,10,5,6,7]=>101000100=>010111011
[2,1,4,3,7,9,5,10,6,8]=>101001010=>010110101
[3,4,1,2,7,9,5,10,6,8]=>010001010=>101110101
[4,5,7,1,2,9,3,10,6,8]=>001001010=>110110101
[3,5,1,7,2,9,4,10,6,8]=>010101010=>101010101
[2,1,5,7,3,9,4,10,6,8]=>100101010=>011010101
[2,1,6,7,9,3,4,10,5,8]=>100010010=>011101101
[3,6,1,7,9,2,4,10,5,8]=>010010010=>101101101
[4,6,7,1,9,2,3,10,5,8]=>001010010=>110101101
[5,6,7,9,1,2,3,10,4,8]=>000100010=>111011101
[8,5,4,3,2,9,10,1,6,7]=>111100100=>000011011
[2,1,5,6,3,4,9,10,7,8]=>100100010=>011011101
[3,5,1,6,2,4,9,10,7,8]=>010100010=>101011101
[4,5,6,1,2,3,9,10,7,8]=>001000010=>110111101
[3,4,1,2,6,5,9,10,7,8]=>010010010=>101101101
[2,1,4,3,6,5,9,10,7,8]=>101010010=>010101101
[2,1,4,3,6,5,10,9,8,7]=>101010111=>010101000
[4,3,2,1,6,5,10,9,8,7]=>111010111=>000101000
[6,3,2,5,4,1,10,9,8,7]=>110110111=>001001000
[10,3,2,5,4,9,8,7,6,1]=>110101111=>001010000
[2,1,6,5,4,3,10,9,8,7]=>101110111=>010001000
[6,5,4,3,2,1,10,9,8,7]=>111110111=>000001000
[10,5,4,3,2,9,8,7,6,1]=>111101111=>000010000
[2,1,10,5,4,9,8,7,6,3]=>101101111=>010010000
[10,9,4,3,8,7,6,5,2,1]=>111011111=>000100000
[9,7,5,10,3,8,2,6,1,4]=>110101010=>001010101
[2,1,4,3,10,9,8,7,6,5]=>101011111=>010100000
[4,3,2,1,10,9,8,7,6,5]=>111011111=>000100000
[10,3,2,9,8,7,6,5,4,1]=>110111111=>001000000
[2,1,10,9,8,7,6,5,4,3]=>101111111=>010000000
[9,10,8,7,6,5,4,3,1,2]=>011111110=>100000001
[10,9,8,7,6,5,4,3,2,1]=>111111111=>000000000
[3,2,5,1,4,6,7,8]=>1010000=>0101111
[4,2,5,1,3,6,7,8]=>1010000=>0101111
[5,2,4,1,3,6,7,8]=>1010000=>0101111
[3,2,6,1,4,5,7,8]=>1010000=>0101111
[4,2,6,1,3,5,7,8]=>1010000=>0101111
[5,3,6,1,2,4,7,8]=>1010000=>0101111
[6,2,4,1,3,5,7,8]=>1010000=>0101111
[6,3,5,1,2,4,7,8]=>1010000=>0101111
[5,2,7,1,3,4,6,8]=>1010000=>0101111
[5,3,7,1,2,4,6,8]=>1010000=>0101111
[5,4,7,1,2,3,6,8]=>1010000=>0101111
[6,2,7,1,3,4,5,8]=>1010000=>0101111
[6,3,7,1,2,4,5,8]=>1010000=>0101111
[6,4,7,1,2,3,5,8]=>1010000=>0101111
[7,3,5,1,2,4,6,8]=>1010000=>0101111
[7,3,6,1,2,4,5,8]=>1010000=>0101111
[7,4,6,1,2,3,5,8]=>1010000=>0101111
[3,2,8,1,4,5,6,7]=>1010000=>0101111
[4,2,8,1,3,5,6,7]=>1010000=>0101111
[5,2,8,1,3,4,6,7]=>1010000=>0101111
[5,4,8,1,2,3,6,7]=>1010000=>0101111
[6,2,8,1,3,4,5,7]=>1010000=>0101111
[6,3,8,1,2,4,5,7]=>1010000=>0101111
[6,4,8,1,2,3,5,7]=>1010000=>0101111
[6,5,8,1,2,3,4,7]=>1010000=>0101111
[7,2,8,1,3,4,5,6]=>1010000=>0101111
[7,3,8,1,2,4,5,6]=>1010000=>0101111
[7,4,8,1,2,3,5,6]=>1010000=>0101111
[7,5,8,1,2,3,4,6]=>1010000=>0101111
[8,2,4,1,3,5,6,7]=>1010000=>0101111
[8,3,5,1,2,4,6,7]=>1010000=>0101111
[8,3,6,1,2,4,5,7]=>1010000=>0101111
[8,3,7,1,2,4,5,6]=>1010000=>0101111
[8,4,7,1,2,3,5,6]=>1010000=>0101111
[8,5,7,1,2,3,4,6]=>1010000=>0101111
[3,2,5,7,1,4,6,8]=>1001000=>0110111
[4,2,5,7,1,3,6,8]=>1001000=>0110111
[4,3,5,7,1,2,6,8]=>1001000=>0110111
[5,2,4,7,1,3,6,8]=>1001000=>0110111
[5,3,4,7,1,2,6,8]=>1001000=>0110111
[4,2,6,7,1,3,5,8]=>1001000=>0110111
[5,2,6,7,1,3,4,8]=>1001000=>0110111
[5,3,6,7,1,2,4,8]=>1001000=>0110111
[6,2,5,7,1,3,4,8]=>1001000=>0110111
[6,3,5,7,1,2,4,8]=>1001000=>0110111
[7,2,4,6,1,3,5,8]=>1001000=>0110111
[7,3,4,6,1,2,5,8]=>1001000=>0110111
[7,3,5,6,1,2,4,8]=>1001000=>0110111
[3,2,5,8,1,4,6,7]=>1001000=>0110111
[4,2,5,8,1,3,6,7]=>1001000=>0110111
[4,3,5,8,1,2,6,7]=>1001000=>0110111
[5,2,4,8,1,3,6,7]=>1001000=>0110111
[3,2,6,8,1,4,5,7]=>1001000=>0110111
[4,2,6,8,1,3,5,7]=>1001000=>0110111
[4,3,6,8,1,2,5,7]=>1001000=>0110111
[5,2,6,8,1,3,4,7]=>1001000=>0110111
[6,2,4,8,1,3,5,7]=>1001000=>0110111
[6,3,4,8,1,2,5,7]=>1001000=>0110111
[6,2,5,8,1,3,4,7]=>1001000=>0110111
[6,3,5,8,1,2,4,7]=>1001000=>0110111
[6,4,5,8,1,2,3,7]=>1001000=>0110111
[3,2,7,8,1,4,5,6]=>1001000=>0110111
[4,3,7,8,1,2,5,6]=>1001000=>0110111
[5,3,7,8,1,2,4,6]=>1001000=>0110111
[6,2,7,8,1,3,4,5]=>1001000=>0110111
[6,3,7,8,1,2,4,5]=>1001000=>0110111
[6,4,7,8,1,2,3,5]=>1001000=>0110111
[7,2,4,8,1,3,5,6]=>1001000=>0110111
[7,3,4,8,1,2,5,6]=>1001000=>0110111
[7,3,5,8,1,2,4,6]=>1001000=>0110111
[7,4,5,8,1,2,3,6]=>1001000=>0110111
[7,4,6,8,1,2,3,5]=>1001000=>0110111
[8,2,4,6,1,3,5,7]=>1001000=>0110111
[8,3,4,6,1,2,5,7]=>1001000=>0110111
[8,2,5,6,1,3,4,7]=>1001000=>0110111
[8,3,5,6,1,2,4,7]=>1001000=>0110111
[8,2,4,7,1,3,5,6]=>1001000=>0110111
[8,2,5,7,1,3,4,6]=>1001000=>0110111
[8,3,5,7,1,2,4,6]=>1001000=>0110111
[8,2,6,7,1,3,4,5]=>1001000=>0110111
[8,4,6,7,1,2,3,5]=>1001000=>0110111
[3,6,2,5,1,4,7,8]=>0101000=>1010111
[4,6,2,5,1,3,7,8]=>0101000=>1010111
[4,6,3,5,1,2,7,8]=>0101000=>1010111
[3,7,2,5,1,4,6,8]=>0101000=>1010111
[4,7,3,5,1,2,6,8]=>0101000=>1010111
[5,7,2,4,1,3,6,8]=>0101000=>1010111
[5,7,3,4,1,2,6,8]=>0101000=>1010111
[3,7,2,6,1,4,5,8]=>0101000=>1010111
[4,7,3,6,1,2,5,8]=>0101000=>1010111
[5,7,2,6,1,3,4,8]=>0101000=>1010111
[5,7,3,6,1,2,4,8]=>0101000=>1010111
[6,7,2,5,1,3,4,8]=>0101000=>1010111
[4,8,2,5,1,3,6,7]=>0101000=>1010111
[5,8,2,4,1,3,6,7]=>0101000=>1010111
[5,8,3,4,1,2,6,7]=>0101000=>1010111
[3,8,2,6,1,4,5,7]=>0101000=>1010111
[4,8,2,6,1,3,5,7]=>0101000=>1010111
[5,8,3,6,1,2,4,7]=>0101000=>1010111
[5,8,4,6,1,2,3,7]=>0101000=>1010111
[6,8,2,4,1,3,5,7]=>0101000=>1010111
[6,8,3,4,1,2,5,7]=>0101000=>1010111
[6,8,3,5,1,2,4,7]=>0101000=>1010111
[6,8,4,5,1,2,3,7]=>0101000=>1010111
[3,8,2,7,1,4,5,6]=>0101000=>1010111
[4,8,2,7,1,3,5,6]=>0101000=>1010111
[4,8,3,7,1,2,5,6]=>0101000=>1010111
[5,8,2,7,1,3,4,6]=>0101000=>1010111
[5,8,3,7,1,2,4,6]=>0101000=>1010111
[5,8,4,7,1,2,3,6]=>0101000=>1010111
[6,8,2,7,1,3,4,5]=>0101000=>1010111
[6,8,3,7,1,2,4,5]=>0101000=>1010111
[6,8,5,7,1,2,3,4]=>0101000=>1010111
[7,8,2,4,1,3,5,6]=>0101000=>1010111
[7,8,2,5,1,3,4,6]=>0101000=>1010111
[7,8,3,5,1,2,4,6]=>0101000=>1010111
[7,8,4,6,1,2,3,5]=>0101000=>1010111
[4,3,2,6,1,5,7,8]=>1101000=>0010111
[5,3,2,6,1,4,7,8]=>1101000=>0010111
[6,3,2,5,1,4,7,8]=>1101000=>0010111
[6,4,2,5,1,3,7,8]=>1101000=>0010111
[6,5,2,4,1,3,7,8]=>1101000=>0010111
[4,3,2,7,1,5,6,8]=>1101000=>0010111
[5,3,2,7,1,4,6,8]=>1101000=>0010111
[5,4,3,7,1,2,6,8]=>1101000=>0010111
[6,3,2,7,1,4,5,8]=>1101000=>0010111
[6,4,2,7,1,3,5,8]=>1101000=>0010111
[6,4,3,7,1,2,5,8]=>1101000=>0010111
[6,5,3,7,1,2,4,8]=>1101000=>0010111
[7,3,2,5,1,4,6,8]=>1101000=>0010111
[7,4,2,5,1,3,6,8]=>1101000=>0010111
[7,3,2,6,1,4,5,8]=>1101000=>0010111
[7,4,2,6,1,3,5,8]=>1101000=>0010111
[7,4,3,6,1,2,5,8]=>1101000=>0010111
[7,5,2,6,1,3,4,8]=>1101000=>0010111
[7,5,3,6,1,2,4,8]=>1101000=>0010111
[7,6,3,5,1,2,4,8]=>1101000=>0010111
[4,3,2,8,1,5,6,7]=>1101000=>0010111
[5,3,2,8,1,4,6,7]=>1101000=>0010111
[5,4,3,8,1,2,6,7]=>1101000=>0010111
[6,3,2,8,1,4,5,7]=>1101000=>0010111
[6,4,2,8,1,3,5,7]=>1101000=>0010111
[6,4,3,8,1,2,5,7]=>1101000=>0010111
[6,5,2,8,1,3,4,7]=>1101000=>0010111
[6,5,3,8,1,2,4,7]=>1101000=>0010111
[6,5,4,8,1,2,3,7]=>1101000=>0010111
[7,3,2,8,1,4,5,6]=>1101000=>0010111
[7,4,2,8,1,3,5,6]=>1101000=>0010111
[7,4,3,8,1,2,5,6]=>1101000=>0010111
[7,5,3,8,1,2,4,6]=>1101000=>0010111
[7,5,4,8,1,2,3,6]=>1101000=>0010111
[7,6,2,8,1,3,4,5]=>1101000=>0010111
[8,3,2,5,1,4,6,7]=>1101000=>0010111
[8,4,2,5,1,3,6,7]=>1101000=>0010111
[8,3,2,6,1,4,5,7]=>1101000=>0010111
[8,4,2,6,1,3,5,7]=>1101000=>0010111
[8,5,3,6,1,2,4,7]=>1101000=>0010111
[8,6,2,4,1,3,5,7]=>1101000=>0010111
[8,6,2,5,1,3,4,7]=>1101000=>0010111
[8,3,2,7,1,4,5,6]=>1101000=>0010111
[8,4,2,7,1,3,5,6]=>1101000=>0010111
[8,4,3,7,1,2,5,6]=>1101000=>0010111
[8,5,2,7,1,3,4,6]=>1101000=>0010111
[8,5,3,7,1,2,4,6]=>1101000=>0010111
[8,5,4,7,1,2,3,6]=>1101000=>0010111
[8,6,3,7,1,2,4,5]=>1101000=>0010111
[8,7,2,4,1,3,5,6]=>1101000=>0010111
[8,7,2,5,1,3,4,6]=>1101000=>0010111
[8,7,3,5,1,2,4,6]=>1101000=>0010111
[8,7,2,6,1,3,4,5]=>1101000=>0010111
[8,7,3,6,1,2,4,5]=>1101000=>0010111
[8,7,4,6,1,2,3,5]=>1101000=>0010111
[3,6,2,5,8,1,4,7]=>0100100=>1011011
[4,6,3,5,8,1,2,7]=>0100100=>1011011
[5,6,2,4,8,1,3,7]=>0100100=>1011011
[4,7,2,5,8,1,3,6]=>0100100=>1011011
[4,7,3,5,8,1,2,6]=>0100100=>1011011
[5,7,2,4,8,1,3,6]=>0100100=>1011011
[5,7,3,4,8,1,2,6]=>0100100=>1011011
[3,7,2,6,8,1,4,5]=>0100100=>1011011
[4,7,3,6,8,1,2,5]=>0100100=>1011011
[5,7,2,6,8,1,3,4]=>0100100=>1011011
[5,7,4,6,8,1,2,3]=>0100100=>1011011
[6,7,3,4,8,1,2,5]=>0100100=>1011011
[6,7,3,5,8,1,2,4]=>0100100=>1011011
[3,8,2,5,7,1,4,6]=>0100100=>1011011
[4,8,2,5,7,1,3,6]=>0100100=>1011011
[4,8,3,5,7,1,2,6]=>0100100=>1011011
[5,8,2,4,7,1,3,6]=>0100100=>1011011
[3,8,2,6,7,1,4,5]=>0100100=>1011011
[4,8,3,6,7,1,2,5]=>0100100=>1011011
[5,8,2,6,7,1,3,4]=>0100100=>1011011
[5,8,3,6,7,1,2,4]=>0100100=>1011011
[6,8,2,5,7,1,3,4]=>0100100=>1011011
[6,8,3,5,7,1,2,4]=>0100100=>1011011
[6,8,4,5,7,1,2,3]=>0100100=>1011011
[7,8,2,4,6,1,3,5]=>0100100=>1011011
[7,8,2,5,6,1,3,4]=>0100100=>1011011
[7,8,3,5,6,1,2,4]=>0100100=>1011011
[4,3,2,6,8,1,5,7]=>1100100=>0011011
[5,3,2,6,8,1,4,7]=>1100100=>0011011
[5,4,2,6,8,1,3,7]=>1100100=>0011011
[5,4,3,6,8,1,2,7]=>1100100=>0011011
[6,3,2,5,8,1,4,7]=>1100100=>0011011
[6,4,3,5,8,1,2,7]=>1100100=>0011011
[6,5,2,4,8,1,3,7]=>1100100=>0011011
[4,3,2,7,8,1,5,6]=>1100100=>0011011
[5,3,2,7,8,1,4,6]=>1100100=>0011011
[5,4,2,7,8,1,3,6]=>1100100=>0011011
[5,4,3,7,8,1,2,6]=>1100100=>0011011
[6,4,2,7,8,1,3,5]=>1100100=>0011011
[6,4,3,7,8,1,2,5]=>1100100=>0011011
[6,5,2,7,8,1,3,4]=>1100100=>0011011
[7,4,2,5,8,1,3,6]=>1100100=>0011011
[7,4,3,5,8,1,2,6]=>1100100=>0011011
[7,5,3,4,8,1,2,6]=>1100100=>0011011
[7,3,2,6,8,1,4,5]=>1100100=>0011011
[7,5,2,6,8,1,3,4]=>1100100=>0011011
[7,5,3,6,8,1,2,4]=>1100100=>0011011
[7,6,2,4,8,1,3,5]=>1100100=>0011011
[7,6,3,5,8,1,2,4]=>1100100=>0011011
[8,3,2,5,7,1,4,6]=>1100100=>0011011
[8,4,2,5,7,1,3,6]=>1100100=>0011011
[8,5,2,4,7,1,3,6]=>1100100=>0011011
[8,3,2,6,7,1,4,5]=>1100100=>0011011
[8,4,2,6,7,1,3,5]=>1100100=>0011011
[8,5,2,6,7,1,3,4]=>1100100=>0011011
[8,5,3,6,7,1,2,4]=>1100100=>0011011
[8,6,2,4,7,1,3,5]=>1100100=>0011011
[8,6,3,5,7,1,2,4]=>1100100=>0011011
[8,7,2,4,6,1,3,5]=>1100100=>0011011
[8,7,3,4,6,1,2,5]=>1100100=>0011011
[8,7,2,5,6,1,3,4]=>1100100=>0011011
[8,7,3,5,6,1,2,4]=>1100100=>0011011
[4,3,7,2,6,1,5,8]=>1010100=>0101011
[5,3,7,2,6,1,4,8]=>1010100=>0101011
[5,4,7,2,6,1,3,8]=>1010100=>0101011
[6,3,7,2,5,1,4,8]=>1010100=>0101011
[6,4,7,2,5,1,3,8]=>1010100=>0101011
[6,4,7,3,5,1,2,8]=>1010100=>0101011
[7,3,6,2,5,1,4,8]=>1010100=>0101011
[4,3,8,2,6,1,5,7]=>1010100=>0101011
[5,3,8,2,6,1,4,7]=>1010100=>0101011
[5,4,8,2,6,1,3,7]=>1010100=>0101011
[5,4,8,3,6,1,2,7]=>1010100=>0101011
[6,4,8,2,5,1,3,7]=>1010100=>0101011
[6,4,8,3,5,1,2,7]=>1010100=>0101011
[6,5,8,2,4,1,3,7]=>1010100=>0101011
[6,5,8,3,4,1,2,7]=>1010100=>0101011
[4,3,8,2,7,1,5,6]=>1010100=>0101011
[5,3,8,2,7,1,4,6]=>1010100=>0101011
[5,4,8,2,7,1,3,6]=>1010100=>0101011
[5,4,8,3,7,1,2,6]=>1010100=>0101011
[6,3,8,2,7,1,4,5]=>1010100=>0101011
[6,4,8,2,7,1,3,5]=>1010100=>0101011
[6,4,8,3,7,1,2,5]=>1010100=>0101011
[7,3,8,2,5,1,4,6]=>1010100=>0101011
[7,4,8,3,5,1,2,6]=>1010100=>0101011
[7,5,8,2,4,1,3,6]=>1010100=>0101011
[7,5,8,3,4,1,2,6]=>1010100=>0101011
[7,3,8,2,6,1,4,5]=>1010100=>0101011
[7,4,8,2,6,1,3,5]=>1010100=>0101011
[7,5,8,2,6,1,3,4]=>1010100=>0101011
[7,5,8,3,6,1,2,4]=>1010100=>0101011
[7,5,8,4,6,1,2,3]=>1010100=>0101011
[7,6,8,2,5,1,3,4]=>1010100=>0101011
[7,6,8,3,5,1,2,4]=>1010100=>0101011
[8,3,6,2,5,1,4,7]=>1010100=>0101011
[8,5,6,2,4,1,3,7]=>1010100=>0101011
[8,3,7,2,5,1,4,6]=>1010100=>0101011
[8,5,7,2,4,1,3,6]=>1010100=>0101011
[8,3,7,2,6,1,4,5]=>1010100=>0101011
[8,4,7,2,6,1,3,5]=>1010100=>0101011
[8,4,7,3,6,1,2,5]=>1010100=>0101011
[8,5,7,2,6,1,3,4]=>1010100=>0101011
[8,6,7,2,4,1,3,5]=>1010100=>0101011
[8,6,7,2,5,1,3,4]=>1010100=>0101011
[8,6,7,3,5,1,2,4]=>1010100=>0101011
[5,4,3,2,7,1,6,8]=>1110100=>0001011
[6,4,3,2,7,1,5,8]=>1110100=>0001011
[6,5,3,2,7,1,4,8]=>1110100=>0001011
[6,5,4,2,7,1,3,8]=>1110100=>0001011
[7,5,3,2,6,1,4,8]=>1110100=>0001011
[7,5,4,2,6,1,3,8]=>1110100=>0001011
[7,6,3,2,5,1,4,8]=>1110100=>0001011
[5,4,3,2,8,1,6,7]=>1110100=>0001011
[6,5,3,2,8,1,4,7]=>1110100=>0001011
[6,5,4,2,8,1,3,7]=>1110100=>0001011
[6,5,4,3,8,1,2,7]=>1110100=>0001011
[7,5,3,2,8,1,4,6]=>1110100=>0001011
[7,5,4,2,8,1,3,6]=>1110100=>0001011
[7,6,3,2,8,1,4,5]=>1110100=>0001011
[7,6,4,3,8,1,2,5]=>1110100=>0001011
[7,6,5,2,8,1,3,4]=>1110100=>0001011
[8,5,3,2,6,1,4,7]=>1110100=>0001011
[8,5,4,2,6,1,3,7]=>1110100=>0001011
[8,6,4,2,5,1,3,7]=>1110100=>0001011
[8,6,5,2,4,1,3,7]=>1110100=>0001011
[8,5,3,2,7,1,4,6]=>1110100=>0001011
[8,6,3,2,7,1,4,5]=>1110100=>0001011
[8,6,4,2,7,1,3,5]=>1110100=>0001011
[8,6,4,3,7,1,2,5]=>1110100=>0001011
[8,7,3,2,6,1,4,5]=>1110100=>0001011
[8,7,4,2,6,1,3,5]=>1110100=>0001011
[8,7,4,3,6,1,2,5]=>1110100=>0001011
[8,7,5,2,6,1,3,4]=>1110100=>0001011
[8,7,6,2,4,1,3,5]=>1110100=>0001011
[8,7,6,2,5,1,3,4]=>1110100=>0001011
[8,7,6,3,5,1,2,4]=>1110100=>0001011
[4,8,3,7,2,6,1,5]=>0101010=>1010101
[5,8,3,7,2,6,1,4]=>0101010=>1010101
[5,8,4,7,2,6,1,3]=>0101010=>1010101
[5,8,4,7,3,6,1,2]=>0101010=>1010101
[6,8,3,7,2,5,1,4]=>0101010=>1010101
[6,8,4,7,2,5,1,3]=>0101010=>1010101
[6,8,4,7,3,5,1,2]=>0101010=>1010101
[6,8,5,7,2,4,1,3]=>0101010=>1010101
[6,8,5,7,3,4,1,2]=>0101010=>1010101
[7,8,3,6,2,5,1,4]=>0101010=>1010101
[7,8,4,6,2,5,1,3]=>0101010=>1010101
[7,8,4,6,3,5,1,2]=>0101010=>1010101
[7,8,5,6,2,4,1,3]=>0101010=>1010101
[5,4,3,8,2,7,1,6]=>1101010=>0010101
[6,4,3,8,2,7,1,5]=>1101010=>0010101
[6,5,3,8,2,7,1,4]=>1101010=>0010101
[6,5,4,8,2,7,1,3]=>1101010=>0010101
[6,5,4,8,3,7,1,2]=>1101010=>0010101
[7,4,3,8,2,6,1,5]=>1101010=>0010101
[7,5,3,8,2,6,1,4]=>1101010=>0010101
[7,5,4,8,2,6,1,3]=>1101010=>0010101
[7,6,3,8,2,5,1,4]=>1101010=>0010101
[7,6,4,8,2,5,1,3]=>1101010=>0010101
[7,6,5,8,2,4,1,3]=>1101010=>0010101
[8,4,3,7,2,6,1,5]=>1101010=>0010101
[8,5,3,7,2,6,1,4]=>1101010=>0010101
[8,5,4,7,2,6,1,3]=>1101010=>0010101
[8,5,4,7,3,6,1,2]=>1101010=>0010101
[8,6,3,7,2,5,1,4]=>1101010=>0010101
[8,6,4,7,2,5,1,3]=>1101010=>0010101
[8,6,5,7,2,4,1,3]=>1101010=>0010101
[8,7,3,6,2,5,1,4]=>1101010=>0010101
[8,7,4,6,2,5,1,3]=>1101010=>0010101
[8,7,4,6,3,5,1,2]=>1101010=>0010101
[8,7,5,6,2,4,1,3]=>1101010=>0010101
[6,5,4,3,2,8,1,7]=>1111010=>0000101
[7,6,4,3,2,8,1,5]=>1111010=>0000101
[7,6,5,4,2,8,1,3]=>1111010=>0000101
[8,5,4,3,2,7,1,6]=>1111010=>0000101
[8,6,4,3,2,7,1,5]=>1111010=>0000101
[8,6,5,3,2,7,1,4]=>1111010=>0000101
[8,6,5,4,2,7,1,3]=>1111010=>0000101
[8,7,4,3,2,6,1,5]=>1111010=>0000101
[8,7,5,3,2,6,1,4]=>1111010=>0000101
[8,7,5,4,2,6,1,3]=>1111010=>0000101
[8,7,6,3,2,5,1,4]=>1111010=>0000101
[8,7,6,4,2,5,1,3]=>1111010=>0000101
[8,7,6,5,2,4,1,3]=>1111010=>0000101
[8,1,2,3,4,7,5,6]=>1000010=>0111101
[8,1,2,3,6,4,5,7]=>1000100=>0111011
[8,1,2,3,7,4,5,6]=>1000100=>0111011
[7,1,2,3,6,4,8,5]=>1000101=>0111010
[5,1,2,3,8,7,4,6]=>1000110=>0111001
[8,1,2,3,6,7,4,5]=>1000010=>0111101
[4,1,2,8,3,7,5,6]=>1001010=>0110101
[8,1,2,5,3,4,6,7]=>1001000=>0110111
[7,1,2,5,3,4,8,6]=>1001001=>0110110
[8,1,2,6,3,4,5,7]=>1001000=>0110111
[7,1,2,6,3,4,8,5]=>1001001=>0110110
[6,1,2,5,3,8,4,7]=>1001010=>0110101
[8,1,2,5,3,7,4,6]=>1001010=>0110101
[8,1,2,6,3,7,4,5]=>1001010=>0110101
[6,1,2,5,3,7,8,4]=>1001001=>0110110
[4,1,2,8,6,3,5,7]=>1001100=>0110011
[4,1,2,8,7,3,5,6]=>1001100=>0110011
[4,1,2,7,6,3,8,5]=>1001101=>0110010
[8,1,2,5,6,3,4,7]=>1000100=>0111011
[8,1,2,5,7,3,4,6]=>1000100=>0111011
[8,1,2,7,6,3,4,5]=>1001100=>0110011
[7,1,2,5,6,3,8,4]=>1000101=>0111010
[4,1,2,5,8,7,3,6]=>1000110=>0111001
[4,1,2,8,6,7,3,5]=>1001010=>0110101
[8,1,2,5,6,7,3,4]=>1000010=>0111101
[3,1,8,2,4,7,5,6]=>1010010=>0101101
[3,1,8,2,6,4,5,7]=>1010100=>0101011
[3,1,8,2,7,4,5,6]=>1010100=>0101011
[3,1,7,2,6,4,8,5]=>1010101=>0101010
[3,1,5,2,8,7,4,6]=>1010110=>0101001
[3,1,8,2,6,7,4,5]=>1010010=>0101101
[8,1,4,2,3,5,6,7]=>1010000=>0101111
[7,1,4,2,3,5,8,6]=>1010001=>0101110
[6,1,4,2,3,8,5,7]=>1010010=>0101101
[8,1,4,2,3,7,5,6]=>1010010=>0101101
[6,1,4,2,3,7,8,5]=>1010001=>0101110
[8,1,5,2,3,4,6,7]=>1010000=>0101111
[7,1,5,2,3,4,8,6]=>1010001=>0101110
[8,1,7,2,3,4,5,6]=>1010000=>0101111
[6,1,5,2,3,8,4,7]=>1010010=>0101101
[8,1,5,2,3,7,4,6]=>1010010=>0101101
[6,1,8,2,3,7,4,5]=>1010010=>0101101
[6,1,5,2,3,7,8,4]=>1010001=>0101110
[5,1,4,2,8,3,6,7]=>1010100=>0101011
[5,1,4,2,7,3,8,6]=>1010101=>0101010
[8,1,4,2,6,3,5,7]=>1010100=>0101011
[8,1,4,2,7,3,5,6]=>1010100=>0101011
[7,1,4,2,6,3,8,5]=>1010101=>0101010
[8,1,5,2,6,3,4,7]=>1010100=>0101011
[8,1,5,2,7,3,4,6]=>1010100=>0101011
[7,1,8,2,6,3,4,5]=>1010100=>0101011
[7,1,5,2,6,3,8,4]=>1010101=>0101010
[5,1,4,2,6,8,3,7]=>1010010=>0101101
[5,1,4,2,8,7,3,6]=>1010110=>0101001
[8,1,4,2,6,7,3,5]=>1010010=>0101101
[8,1,5,2,6,7,3,4]=>1010010=>0101101
[5,1,4,2,6,7,8,3]=>1010001=>0101110
[3,1,4,8,2,7,5,6]=>1001010=>0110101
[3,1,8,5,2,4,6,7]=>1011000=>0100111
[3,1,7,5,2,4,8,6]=>1011001=>0100110
[3,1,8,6,2,4,5,7]=>1011000=>0100111
[3,1,7,6,2,4,8,5]=>1011001=>0100110
[3,1,6,5,2,8,4,7]=>1011010=>0100101
[3,1,8,5,2,7,4,6]=>1011010=>0100101
[3,1,8,6,2,7,4,5]=>1011010=>0100101
[3,1,6,5,2,7,8,4]=>1011001=>0100110
[8,1,4,5,2,3,6,7]=>1001000=>0110111
[7,1,4,5,2,3,8,6]=>1001001=>0110110
[8,1,4,6,2,3,5,7]=>1001000=>0110111
[7,1,4,8,2,3,5,6]=>1001000=>0110111
[7,1,4,6,2,3,8,5]=>1001001=>0110110
[8,1,6,5,2,3,4,7]=>1011000=>0100111
[7,1,8,5,2,3,4,6]=>1011000=>0100111
[7,1,8,6,2,3,4,5]=>1011000=>0100111
[7,1,6,5,2,3,8,4]=>1011001=>0100110
[6,1,4,5,2,8,3,7]=>1001010=>0110101
[8,1,4,5,2,7,3,6]=>1001010=>0110101
[8,1,4,6,2,7,3,5]=>1001010=>0110101
[8,1,6,5,2,7,3,4]=>1011010=>0100101
[6,1,4,5,2,7,8,3]=>1001001=>0110110
[3,1,4,8,6,2,5,7]=>1001100=>0110011
[3,1,4,8,7,2,5,6]=>1001100=>0110011
[3,1,4,7,6,2,8,5]=>1001101=>0110010
[3,1,8,5,6,2,4,7]=>1010100=>0101011
[3,1,8,5,7,2,4,6]=>1010100=>0101011
[3,1,8,7,6,2,4,5]=>1011100=>0100011
[3,1,7,5,6,2,8,4]=>1010101=>0101010
[8,1,4,5,6,2,3,7]=>1000100=>0111011
[8,1,4,5,7,2,3,6]=>1000100=>0111011
[8,1,4,7,6,2,3,5]=>1001100=>0110011
[8,1,7,5,6,2,3,4]=>1010100=>0101011
[7,1,4,5,6,2,8,3]=>1000101=>0111010
[3,1,4,5,8,7,2,6]=>1000110=>0111001
[3,1,4,8,6,7,2,5]=>1001010=>0110101
[3,1,8,5,6,7,2,4]=>1010010=>0101101
[8,1,4,5,6,7,2,3]=>1000010=>0111101
[2,8,1,3,4,7,5,6]=>0100010=>1011101
[2,8,1,3,6,4,5,7]=>0100100=>1011011
[2,8,1,3,7,4,5,6]=>0100100=>1011011
[2,7,1,3,6,4,8,5]=>0100101=>1011010
[2,5,1,3,8,7,4,6]=>0100110=>1011001
[2,8,1,3,6,7,4,5]=>0100010=>1011101
[2,4,1,8,3,7,5,6]=>0101010=>1010101
[2,8,1,5,3,4,6,7]=>0101000=>1010111
[2,7,1,5,3,4,8,6]=>0101001=>1010110
[2,8,1,6,3,4,5,7]=>0101000=>1010111
[2,7,1,6,3,4,8,5]=>0101001=>1010110
[2,6,1,5,3,8,4,7]=>0101010=>1010101
[2,8,1,5,3,7,4,6]=>0101010=>1010101
[2,6,1,5,3,7,8,4]=>0101001=>1010110
[2,4,1,8,6,3,5,7]=>0101100=>1010011
[2,4,1,8,7,3,5,6]=>0101100=>1010011
[2,4,1,7,6,3,8,5]=>0101101=>1010010
[2,8,1,5,6,3,4,7]=>0100100=>1011011
[2,8,1,5,7,3,4,6]=>0100100=>1011011
[2,8,1,7,6,3,4,5]=>0101100=>1010011
[2,7,1,5,6,3,8,4]=>0100101=>1011010
[2,4,1,5,8,7,3,6]=>0100110=>1011001
[2,4,1,8,6,7,3,5]=>0101010=>1010101
[2,8,1,5,6,7,3,4]=>0100010=>1011101
[7,3,1,2,4,5,8,6]=>1100001=>0011110
[6,3,1,2,4,8,5,7]=>1100010=>0011101
[8,3,1,2,4,7,5,6]=>1100010=>0011101
[6,3,1,2,4,7,8,5]=>1100001=>0011110
[5,3,1,2,8,4,6,7]=>1100100=>0011011
[5,3,1,2,7,4,8,6]=>1100101=>0011010
[8,3,1,2,6,4,5,7]=>1100100=>0011011
[8,3,1,2,7,4,5,6]=>1100100=>0011011
[7,3,1,2,6,4,8,5]=>1100101=>0011010
[5,3,1,2,6,8,4,7]=>1100010=>0011101
[5,3,1,2,8,7,4,6]=>1100110=>0011001
[8,3,1,2,6,7,4,5]=>1100010=>0011101
[5,3,1,2,6,7,8,4]=>1100001=>0011110
[7,4,1,2,3,5,8,6]=>1100001=>0011110
[6,4,1,2,3,8,5,7]=>1100010=>0011101
[8,4,1,2,3,7,5,6]=>1100010=>0011101
[6,4,1,2,3,7,8,5]=>1100001=>0011110
[7,6,1,2,3,4,8,5]=>1100001=>0011110
[5,8,1,2,3,7,4,6]=>0100010=>1011101
[8,6,1,2,3,7,4,5]=>1100010=>0011101
[5,4,1,2,8,3,6,7]=>1100100=>0011011
[5,4,1,2,7,3,8,6]=>1100101=>0011010
[8,4,1,2,6,3,5,7]=>1100100=>0011011
[8,4,1,2,7,3,5,6]=>1100100=>0011011
[7,4,1,2,6,3,8,5]=>1100101=>0011010
[5,8,1,2,6,3,4,7]=>0100100=>1011011
[5,8,1,2,7,3,4,6]=>0100100=>1011011
[8,7,1,2,6,3,4,5]=>1100100=>0011011
[5,7,1,2,6,3,8,4]=>0100101=>1011010
[5,4,1,2,6,8,3,7]=>1100010=>0011101
[5,4,1,2,8,7,3,6]=>1100110=>0011001
[8,4,1,2,6,7,3,5]=>1100010=>0011101
[5,8,1,2,6,7,3,4]=>0100010=>1011101
[5,4,1,2,6,7,8,3]=>1100001=>0011110
[4,3,1,8,2,5,6,7]=>1101000=>0010111
[4,3,1,7,2,5,8,6]=>1101001=>0010110
[4,3,1,6,2,8,5,7]=>1101010=>0010101
[4,3,1,8,2,7,5,6]=>1101010=>0010101
[4,3,1,6,2,7,8,5]=>1101001=>0010110
[8,3,1,5,2,4,6,7]=>1101000=>0010111
[7,3,1,5,2,4,8,6]=>1101001=>0010110
[8,3,1,6,2,4,5,7]=>1101000=>0010111
[7,3,1,8,2,4,5,6]=>1101000=>0010111
[7,3,1,6,2,4,8,5]=>1101001=>0010110
[6,3,1,5,2,8,4,7]=>1101010=>0010101
[8,3,1,5,2,7,4,6]=>1101010=>0010101
[8,3,1,6,2,7,4,5]=>1101010=>0010101
[6,3,1,5,2,7,8,4]=>1101001=>0010110
[8,4,1,5,2,3,6,7]=>1101000=>0010111
[7,4,1,5,2,3,8,6]=>1101001=>0010110
[8,4,1,6,2,3,5,7]=>1101000=>0010111
[7,4,1,8,2,3,5,6]=>1101000=>0010111
[7,4,1,6,2,3,8,5]=>1101001=>0010110
[6,8,1,5,2,3,4,7]=>0101000=>1010111
[8,7,1,5,2,3,4,6]=>1101000=>0010111
[8,7,1,6,2,3,4,5]=>1101000=>0010111
[6,7,1,5,2,3,8,4]=>0101001=>1010110
[6,4,1,5,2,8,3,7]=>1101010=>0010101
[8,4,1,5,2,7,3,6]=>1101010=>0010101
[8,4,1,6,2,7,3,5]=>1101010=>0010101
[6,8,1,5,2,7,3,4]=>0101010=>1010101
[6,4,1,5,2,7,8,3]=>1101001=>0010110
[4,3,1,5,8,2,6,7]=>1100100=>0011011
[4,3,1,5,7,2,8,6]=>1100101=>0011010
[4,3,1,8,6,2,5,7]=>1101100=>0010011
[4,3,1,8,7,2,5,6]=>1101100=>0010011
[4,3,1,7,6,2,8,5]=>1101101=>0010010
[8,3,1,5,6,2,4,7]=>1100100=>0011011
[8,3,1,5,7,2,4,6]=>1100100=>0011011
[8,3,1,7,6,2,4,5]=>1101100=>0010011
[7,3,1,5,6,2,8,4]=>1100101=>0011010
[8,4,1,5,6,2,3,7]=>1100100=>0011011
[8,4,1,5,7,2,3,6]=>1100100=>0011011
[8,4,1,7,6,2,3,5]=>1101100=>0010011
[7,8,1,5,6,2,3,4]=>0100100=>1011011
[7,4,1,5,6,2,8,3]=>1100101=>0011010
[4,3,1,5,6,8,2,7]=>1100010=>0011101
[4,3,1,5,8,7,2,6]=>1100110=>0011001
[4,3,1,8,6,7,2,5]=>1101010=>0010101
[8,3,1,5,6,7,2,4]=>1100010=>0011101
[8,4,1,5,6,7,2,3]=>1100010=>0011101
[4,3,1,5,6,7,8,2]=>1100001=>0011110
[2,3,8,1,4,7,5,6]=>0010010=>1101101
[2,3,8,1,6,4,5,7]=>0010100=>1101011
[2,3,8,1,7,4,5,6]=>0010100=>1101011
[2,3,7,1,6,4,8,5]=>0010101=>1101010
[2,3,5,1,8,7,4,6]=>0010110=>1101001
[2,3,8,1,6,7,4,5]=>0010010=>1101101
[2,8,4,1,3,5,6,7]=>0110000=>1001111
[2,7,4,1,3,5,8,6]=>0110001=>1001110
[2,6,4,1,3,8,5,7]=>0110010=>1001101
[2,8,4,1,3,7,5,6]=>0110010=>1001101
[2,6,4,1,3,7,8,5]=>0110001=>1001110
[2,8,5,1,3,4,6,7]=>0110000=>1001111
[2,7,5,1,3,4,8,6]=>0110001=>1001110
[2,8,7,1,3,4,5,6]=>0110000=>1001111
[2,6,5,1,3,8,4,7]=>0110010=>1001101
[2,8,5,1,3,7,4,6]=>0110010=>1001101
[2,6,8,1,3,7,4,5]=>0010010=>1101101
[2,6,5,1,3,7,8,4]=>0110001=>1001110
[2,5,4,1,8,3,6,7]=>0110100=>1001011
[2,5,4,1,7,3,8,6]=>0110101=>1001010
[2,8,4,1,6,3,5,7]=>0110100=>1001011
[2,8,4,1,7,3,5,6]=>0110100=>1001011
[2,7,4,1,6,3,8,5]=>0110101=>1001010
[2,8,5,1,6,3,4,7]=>0110100=>1001011
[2,8,5,1,7,3,4,6]=>0110100=>1001011
[2,7,8,1,6,3,4,5]=>0010100=>1101011
[2,7,5,1,6,3,8,4]=>0110101=>1001010
[2,5,4,1,6,8,3,7]=>0110010=>1001101
[2,5,4,1,8,7,3,6]=>0110110=>1001001
[2,8,4,1,6,7,3,5]=>0110010=>1001101
[2,8,5,1,6,7,3,4]=>0110010=>1001101
[2,5,4,1,6,7,8,3]=>0110001=>1001110
[7,3,4,1,2,5,8,6]=>1010001=>0101110
[6,3,4,1,2,8,5,7]=>1010010=>0101101
[8,3,4,1,2,7,5,6]=>1010010=>0101101
[6,3,4,1,2,7,8,5]=>1010001=>0101110
[7,3,5,1,2,4,8,6]=>1010001=>0101110
[6,3,7,1,2,4,8,5]=>1010001=>0101110
[6,3,5,1,2,8,4,7]=>1010010=>0101101
[8,3,5,1,2,7,4,6]=>1010010=>0101101
[6,3,8,1,2,7,4,5]=>1010010=>0101101
[6,3,5,1,2,7,8,4]=>1010001=>0101110
[7,5,4,1,2,3,8,6]=>1110001=>0001110
[6,8,4,1,2,3,5,7]=>0110000=>1001111
[6,7,4,1,2,3,8,5]=>0110001=>1001110
[6,8,5,1,2,3,4,7]=>0110000=>1001111
[6,7,5,1,2,3,8,4]=>0110001=>1001110
[6,5,4,1,2,8,3,7]=>1110010=>0001101
[8,5,4,1,2,7,3,6]=>1110010=>0001101
[6,8,4,1,2,7,3,5]=>0110010=>1001101
[6,8,5,1,2,7,3,4]=>0110010=>1001101
[6,5,4,1,2,7,8,3]=>1110001=>0001110
[5,3,4,1,8,2,6,7]=>1010100=>0101011
[5,3,4,1,7,2,8,6]=>1010101=>0101010
[8,3,4,1,6,2,5,7]=>1010100=>0101011
[8,3,4,1,7,2,5,6]=>1010100=>0101011
[7,3,4,1,6,2,8,5]=>1010101=>0101010
[8,3,5,1,6,2,4,7]=>1010100=>0101011
[8,3,5,1,7,2,4,6]=>1010100=>0101011
[7,3,8,1,6,2,4,5]=>1010100=>0101011
[7,3,5,1,6,2,8,4]=>1010101=>0101010
[8,5,4,1,6,2,3,7]=>1110100=>0001011
[8,5,4,1,7,2,3,6]=>1110100=>0001011
[7,8,4,1,6,2,3,5]=>0110100=>1001011
[7,8,5,1,6,2,3,4]=>0110100=>1001011
[7,5,4,1,6,2,8,3]=>1110101=>0001010
[5,3,4,1,6,8,2,7]=>1010010=>0101101
[5,3,4,1,8,7,2,6]=>1010110=>0101001
[8,3,4,1,6,7,2,5]=>1010010=>0101101
[8,3,5,1,6,7,2,4]=>1010010=>0101101
[8,5,4,1,6,7,2,3]=>1110010=>0001101
[5,3,4,1,6,7,8,2]=>1010001=>0101110
[2,3,4,8,1,7,5,6]=>0001010=>1110101
[2,3,8,5,1,4,6,7]=>0011000=>1100111
[2,3,7,5,1,4,8,6]=>0011001=>1100110
[2,3,8,6,1,4,5,7]=>0011000=>1100111
[2,3,7,6,1,4,8,5]=>0011001=>1100110
[2,3,6,5,1,8,4,7]=>0011010=>1100101
[2,3,8,5,1,7,4,6]=>0011010=>1100101
[2,3,8,6,1,7,4,5]=>0011010=>1100101
[2,3,6,5,1,7,8,4]=>0011001=>1100110
[2,8,4,5,1,3,6,7]=>0101000=>1010111
[2,7,4,5,1,3,8,6]=>0101001=>1010110
[2,8,4,6,1,3,5,7]=>0101000=>1010111
[2,7,4,8,1,3,5,6]=>0101000=>1010111
[2,7,4,6,1,3,8,5]=>0101001=>1010110
[2,8,6,5,1,3,4,7]=>0111000=>1000111
[2,7,8,5,1,3,4,6]=>0011000=>1100111
[2,7,8,6,1,3,4,5]=>0011000=>1100111
[2,7,6,5,1,3,8,4]=>0111001=>1000110
[2,6,4,5,1,8,3,7]=>0101010=>1010101
[2,8,4,5,1,7,3,6]=>0101010=>1010101
[2,8,4,6,1,7,3,5]=>0101010=>1010101
[2,8,6,5,1,7,3,4]=>0111010=>1000101
[2,6,4,5,1,7,8,3]=>0101001=>1010110
[7,3,4,5,1,2,8,6]=>1001001=>0110110
[7,3,4,6,1,2,8,5]=>1001001=>0110110
[8,3,6,5,1,2,4,7]=>1011000=>0100111
[7,3,8,5,1,2,4,6]=>1011000=>0100111
[7,3,8,6,1,2,4,5]=>1011000=>0100111
[7,3,6,5,1,2,8,4]=>1011001=>0100110
[7,6,4,5,1,2,8,3]=>1101001=>0010110
[6,3,4,5,1,8,2,7]=>1001010=>0110101
[8,3,4,5,1,7,2,6]=>1001010=>0110101
[8,3,4,6,1,7,2,5]=>1001010=>0110101
[8,3,6,5,1,7,2,4]=>1011010=>0100101
[8,6,4,5,1,7,2,3]=>1101010=>0010101
[6,3,4,5,1,7,8,2]=>1001001=>0110110
[2,3,4,8,6,1,5,7]=>0001100=>1110011
[2,3,4,8,7,1,5,6]=>0001100=>1110011
[2,3,4,7,6,1,8,5]=>0001101=>1110010
[2,3,8,5,6,1,4,7]=>0010100=>1101011
[2,3,8,5,7,1,4,6]=>0010100=>1101011
[2,3,8,7,6,1,4,5]=>0011100=>1100011
[2,3,7,5,6,1,8,4]=>0010101=>1101010
[2,8,4,5,6,1,3,7]=>0100100=>1011011
[2,8,4,5,7,1,3,6]=>0100100=>1011011
[2,8,4,7,6,1,3,5]=>0101100=>1010011
[2,8,7,5,6,1,3,4]=>0110100=>1001011
[2,7,4,5,6,1,8,3]=>0100101=>1011010
[8,3,4,5,7,1,2,6]=>1000100=>0111011
[8,3,4,7,6,1,2,5]=>1001100=>0110011
[8,3,7,5,6,1,2,4]=>1010100=>0101011
[7,3,4,5,6,1,8,2]=>1000101=>0111010
[2,3,4,5,8,7,1,6]=>0000110=>1111001
[2,3,4,8,6,7,1,5]=>0001010=>1110101
[2,3,8,5,6,7,1,4]=>0010010=>1101101
[2,8,4,5,6,7,1,3]=>0100010=>1011101
[9,1,2,3,4,5,6,7,8]=>10000000=>01111111
[8,1,2,3,4,5,6,9,7]=>10000001=>01111110
[7,1,2,3,4,5,9,6,8]=>10000010=>01111101
[9,1,2,3,4,5,8,6,7]=>10000010=>01111101
[7,1,2,3,4,5,8,9,6]=>10000001=>01111110
[6,1,2,3,4,9,5,7,8]=>10000100=>01111011
[6,1,2,3,4,8,5,9,7]=>10000101=>01111010
[9,1,2,3,4,7,5,6,8]=>10000100=>01111011
[9,1,2,3,4,8,5,6,7]=>10000100=>01111011
[8,1,2,3,4,7,5,9,6]=>10000101=>01111010
[6,1,2,3,4,7,9,5,8]=>10000010=>01111101
[6,1,2,3,4,9,8,5,7]=>10000110=>01111001
[9,1,2,3,4,7,8,5,6]=>10000010=>01111101
[6,1,2,3,4,7,8,9,5]=>10000001=>01111110
[5,1,2,3,8,4,6,9,7]=>10001001=>01110110
[9,1,2,3,6,4,5,7,8]=>10001000=>01110111
[8,1,2,3,9,4,5,6,7]=>10001000=>01110111
[5,1,2,3,9,8,4,6,7]=>10001100=>01110011
[9,1,2,3,6,8,4,5,7]=>10000100=>01111011
[5,1,2,3,6,9,8,4,7]=>10000110=>01111001
[5,1,2,3,6,7,8,9,4]=>10000001=>01111110
[4,1,2,8,3,5,6,9,7]=>10010001=>01101110
[4,1,2,9,3,5,8,6,7]=>10010010=>01101101
[4,1,2,9,3,8,5,6,7]=>10010100=>01101011
[9,1,2,5,3,4,6,7,8]=>10010000=>01101111
[9,1,2,8,3,4,5,6,7]=>10010000=>01101111
[7,1,2,8,3,4,5,9,6]=>10010001=>01101110
[4,1,2,5,9,3,6,7,8]=>10001000=>01110111
[4,1,2,8,9,3,5,6,7]=>10001000=>01110111
[8,1,2,5,9,3,4,6,7]=>10001000=>01110111
[8,1,2,9,6,3,4,5,7]=>10011000=>01100111
[4,1,2,5,9,8,3,6,7]=>10001100=>01110011
[9,1,2,8,6,7,3,4,5]=>10010100=>01101011
[4,1,2,5,6,7,9,3,8]=>10000010=>01111101
[4,1,2,9,6,7,8,3,5]=>10010010=>01101101
[9,1,2,5,6,7,8,3,4]=>10000010=>01111101
[4,1,2,5,6,7,8,9,3]=>10000001=>01111110
[3,1,9,2,4,5,6,7,8]=>10100000=>01011111
[3,1,8,2,4,5,6,9,7]=>10100001=>01011110
[3,1,9,2,4,5,8,6,7]=>10100010=>01011101
[3,1,5,2,7,4,9,6,8]=>10101010=>01010101
[8,1,4,2,3,5,6,9,7]=>10100001=>01011110
[9,1,4,2,3,5,8,6,7]=>10100010=>01011101
[6,1,4,2,3,7,8,9,5]=>10100001=>01011110
[9,1,8,2,3,4,5,6,7]=>10100000=>01011111
[8,1,7,2,3,4,5,9,6]=>10100001=>01011110
[3,1,4,9,2,5,6,7,8]=>10010000=>01101111
[3,1,4,9,2,5,8,6,7]=>10010010=>01101101
[3,1,9,8,2,4,5,6,7]=>10110000=>01001111
[9,1,4,5,2,3,6,7,8]=>10010000=>01101111
[7,1,4,5,2,3,8,9,6]=>10010001=>01101110
[7,1,4,9,2,3,5,6,8]=>10010000=>01101111
[9,1,4,8,2,3,5,6,7]=>10010000=>01101111
[9,1,6,5,2,3,4,7,8]=>10110000=>01001111
[7,1,9,6,2,3,4,5,8]=>10110000=>01001111
[9,1,8,6,2,3,4,5,7]=>10110000=>01001111
[7,1,8,9,2,3,4,5,6]=>10010000=>01101111
[3,1,4,8,9,2,5,6,7]=>10001000=>01110111
[3,1,8,9,7,2,4,5,6]=>10011000=>01100111
[8,1,4,5,6,2,3,9,7]=>10001001=>01110110
[8,1,4,9,7,2,3,5,6]=>10011000=>01100111
[8,1,9,5,6,2,3,4,7]=>10101000=>01010111
[8,1,9,7,6,2,3,4,5]=>10111000=>01000111
[7,1,4,5,6,2,8,9,3]=>10001001=>01110110
[3,1,4,5,6,9,2,7,8]=>10000100=>01111011
[3,1,4,5,6,8,2,9,7]=>10000101=>01111010
[3,1,4,9,8,7,2,5,6]=>10011100=>01100011
[3,1,9,8,6,7,2,4,5]=>10110100=>01001011
[9,1,4,5,6,7,2,3,8]=>10000100=>01111011
[9,1,4,8,6,7,2,3,5]=>10010100=>01101011
[9,1,8,5,6,7,2,3,4]=>10100100=>01011011
[8,1,4,5,6,7,2,9,3]=>10000101=>01111010
[3,1,4,5,6,7,9,2,8]=>10000010=>01111101
[3,1,4,9,6,7,8,2,5]=>10010010=>01101101
[3,1,9,5,6,7,8,2,4]=>10100010=>01011101
[9,1,4,5,6,7,8,2,3]=>10000010=>01111101
[3,1,4,5,6,7,8,9,2]=>10000001=>01111110
[2,9,1,3,4,5,6,7,8]=>01000000=>10111111
[2,8,1,3,4,5,6,9,7]=>01000001=>10111110
[2,7,1,3,4,5,9,6,8]=>01000010=>10111101
[2,9,1,3,4,5,8,6,7]=>01000010=>10111101
[2,7,1,3,4,5,8,9,6]=>01000001=>10111110
[2,6,1,3,4,9,5,7,8]=>01000100=>10111011
[2,9,1,3,4,8,5,6,7]=>01000100=>10111011
[2,8,1,3,9,4,5,6,7]=>01001000=>10110111
[2,9,1,3,8,7,4,5,6]=>01001100=>10110011
[2,9,1,3,6,7,8,4,5]=>01000010=>10111101
[2,5,1,3,6,7,8,9,4]=>01000001=>10111110
[2,4,1,6,3,8,5,9,7]=>01010101=>10101010
[2,9,1,8,3,4,5,6,7]=>01010000=>10101111
[2,7,1,6,3,4,8,9,5]=>01010001=>10101110
[2,6,1,5,3,7,8,9,4]=>01010001=>10101110
[2,4,1,5,9,3,6,7,8]=>01001000=>10110111
[2,4,1,8,9,3,5,6,7]=>01001000=>10110111
[2,8,1,9,7,3,4,5,6]=>01011000=>10100111
[2,9,1,8,6,7,3,4,5]=>01010100=>10101011
[2,4,1,5,6,7,9,3,8]=>01000010=>10111101
[2,4,1,5,6,9,8,3,7]=>01000110=>10111001
[2,9,1,5,6,7,8,3,4]=>01000010=>10111101
[2,4,1,5,6,7,8,9,3]=>01000001=>10111110
[9,3,1,2,4,5,6,7,8]=>11000000=>00111111
[8,3,1,2,4,5,6,9,7]=>11000001=>00111110
[9,3,1,2,4,5,8,6,7]=>11000010=>00111101
[6,3,1,2,4,7,8,9,5]=>11000001=>00111110
[9,3,1,2,6,7,8,4,5]=>11000010=>00111101
[5,3,1,2,6,7,8,9,4]=>11000001=>00111110
[9,4,1,2,3,5,6,7,8]=>11000000=>00111111
[7,4,1,2,3,5,8,9,6]=>11000001=>00111110
[6,4,1,2,3,7,8,9,5]=>11000001=>00111110
[5,9,1,2,3,4,6,7,8]=>01000000=>10111111
[5,8,1,2,3,4,6,9,7]=>01000001=>10111110
[5,7,1,2,3,4,8,9,6]=>01000001=>10111110
[9,6,1,2,3,4,5,7,8]=>11000000=>00111111
[8,6,1,2,3,4,5,9,7]=>11000001=>00111110
[9,7,1,2,3,4,5,6,8]=>11000000=>00111111
[8,9,1,2,3,4,5,6,7]=>01000000=>10111111
[8,7,1,2,3,4,5,9,6]=>11000001=>00111110
[7,6,1,2,3,4,9,5,8]=>11000010=>00111101
[9,6,1,2,3,4,8,5,7]=>11000010=>00111101
[9,7,1,2,3,4,8,5,6]=>11000010=>00111101
[7,6,1,2,3,4,8,9,5]=>11000001=>00111110
[5,6,1,2,3,9,4,7,8]=>01000100=>10111011
[5,9,1,2,3,8,4,6,7]=>01000100=>10111011
[9,6,1,2,3,7,4,5,8]=>11000100=>00111011
[9,8,1,2,3,7,4,5,6]=>11000100=>00111011
[8,6,1,2,3,7,4,9,5]=>11000101=>00111010
[5,6,1,2,3,7,9,4,8]=>01000010=>10111101
[9,6,1,2,3,7,8,4,5]=>11000010=>00111101
[5,6,1,2,3,7,8,9,4]=>01000001=>10111110
[5,4,1,2,9,3,6,7,8]=>11001000=>00110111
[8,4,1,2,9,3,5,6,7]=>11001000=>00110111
[5,9,1,2,6,3,4,7,8]=>01001000=>10110111
[9,7,1,2,6,3,8,4,5]=>11001010=>00110101
[5,4,1,2,6,9,3,7,8]=>11000100=>00111011
[9,8,1,2,6,7,3,4,5]=>11000100=>00111011
[5,4,1,2,6,7,9,3,8]=>11000010=>00111101
[5,4,1,2,6,7,8,9,3]=>11000001=>00111110
[4,3,1,9,2,5,6,7,8]=>11010000=>00101111
[9,3,1,8,2,4,5,6,7]=>11010000=>00101111
[9,4,1,5,2,3,6,7,8]=>11010000=>00101111
[9,4,1,8,2,3,5,6,7]=>11010000=>00101111
[6,9,1,5,2,3,4,7,8]=>01010000=>10101111
[9,7,1,6,2,3,4,5,8]=>11010000=>00101111
[8,7,1,9,2,3,4,5,6]=>11010000=>00101111
[8,7,1,6,2,3,4,9,5]=>11010001=>00101110
[9,4,1,6,2,8,3,5,7]=>11010100=>00101011
[9,8,1,6,2,7,3,4,5]=>11010100=>00101011
[4,3,1,5,9,2,6,7,8]=>11001000=>00110111
[9,8,1,7,6,2,3,4,5]=>11011000=>00100111
[4,3,1,5,6,8,2,9,7]=>11000101=>00111010
[4,3,1,5,9,8,2,6,7]=>11001100=>00110011
[4,3,1,5,8,7,2,9,6]=>11001101=>00110010
[8,9,1,5,6,7,2,3,4]=>01000100=>10111011
[4,3,1,5,6,7,9,2,8]=>11000010=>00111101
[4,3,1,5,6,9,8,2,7]=>11000110=>00111001
[9,3,1,5,6,7,8,2,4]=>11000010=>00111101
[9,4,1,5,6,7,8,2,3]=>11000010=>00111101
[4,3,1,5,6,7,8,9,2]=>11000001=>00111110
[2,3,9,1,4,5,6,7,8]=>00100000=>11011111
[2,3,8,1,4,5,6,9,7]=>00100001=>11011110
[2,3,9,1,4,5,8,6,7]=>00100010=>11011101
[2,3,9,1,4,7,8,5,6]=>00100010=>11011101
[2,3,9,1,8,7,4,5,6]=>00101100=>11010011
[2,3,8,1,6,7,4,9,5]=>00100101=>11011010
[2,3,5,1,6,7,9,4,8]=>00100010=>11011101
[2,3,9,1,6,7,8,4,5]=>00100010=>11011101
[2,3,5,1,6,7,8,9,4]=>00100001=>11011110
[2,9,4,1,3,5,6,7,8]=>01100000=>10011111
[2,6,4,1,3,7,8,9,5]=>01100001=>10011110
[2,9,5,1,3,4,6,7,8]=>01100000=>10011111
[2,6,9,1,3,4,5,7,8]=>00100000=>11011111
[2,9,7,1,3,4,5,6,8]=>01100000=>10011111
[2,9,8,1,3,4,5,6,7]=>01100000=>10011111
[2,6,7,1,3,4,8,9,5]=>00100001=>11011110
[2,9,4,1,6,3,5,7,8]=>01101000=>10010111
[2,8,4,1,9,3,5,6,7]=>01101000=>10010111
[2,9,4,1,6,3,8,5,7]=>01101010=>10010101
[2,9,8,1,7,3,4,5,6]=>01101000=>10010111
[2,9,5,1,6,7,8,3,4]=>01100010=>10011101
[9,3,4,1,2,5,6,7,8]=>10100000=>01011111
[6,3,4,1,2,7,8,9,5]=>10100001=>01011110
[9,3,7,1,2,4,5,6,8]=>10100000=>01011111
[9,3,8,1,2,4,5,6,7]=>10100000=>01011111
[9,5,4,1,2,3,6,7,8]=>11100000=>00011111
[8,5,4,1,2,3,6,9,7]=>11100001=>00011110
[6,9,4,1,2,3,5,7,8]=>01100000=>10011111
[6,8,4,1,2,3,5,9,7]=>01100001=>10011110
[9,7,4,1,2,3,5,6,8]=>11100000=>00011111
[9,8,4,1,2,3,5,6,7]=>11100000=>00011111
[6,9,5,1,2,3,4,7,8]=>01100000=>10011111
[6,8,5,1,2,3,4,9,7]=>01100001=>10011110
[8,7,5,1,2,3,4,9,6]=>11100001=>00011110
[6,7,9,1,2,3,4,5,8]=>00100000=>11011111
[6,9,8,1,2,3,4,5,7]=>01100000=>10011111
[9,7,8,1,2,3,4,5,6]=>10100000=>01011111
[6,7,8,1,2,3,4,9,5]=>00100001=>11011110
[6,5,4,1,2,8,3,9,7]=>11100101=>00011010
[9,8,5,1,7,2,3,4,6]=>11101000=>00010111
[7,8,9,1,6,2,3,4,5]=>00101000=>11010111
[7,8,5,1,6,2,3,9,4]=>01101001=>10010110
[5,3,4,1,6,8,2,9,7]=>10100101=>01011010
[9,3,4,1,8,7,2,5,6]=>10101100=>01010011
[8,3,4,1,6,7,2,9,5]=>10100101=>01011010
[9,5,4,1,8,7,2,3,6]=>11101100=>00010011
[8,5,4,1,6,7,2,9,3]=>11100101=>00011010
[5,3,4,1,9,7,8,2,6]=>10101010=>01010101
[9,3,5,1,6,7,8,2,4]=>10100010=>01011101
[9,5,4,1,6,7,8,2,3]=>11100010=>00011101
[5,3,4,1,6,7,8,9,2]=>10100001=>01011110
[2,3,4,9,1,5,6,7,8]=>00010000=>11101111
[2,3,4,9,1,5,8,6,7]=>00010010=>11101101
[2,3,4,9,1,7,8,5,6]=>00010010=>11101101
[2,3,4,6,1,7,8,9,5]=>00010001=>11101110
[2,3,9,5,1,4,6,7,8]=>00110000=>11001111
[2,3,9,6,1,4,5,7,8]=>00110000=>11001111
[2,3,7,9,1,4,5,6,8]=>00010000=>11101111
[2,3,9,8,1,4,5,6,7]=>00110000=>11001111
[2,3,9,5,1,7,4,6,8]=>00110100=>11001011
[2,3,9,6,1,7,8,4,5]=>00110010=>11001101
[2,9,4,5,1,3,6,7,8]=>01010000=>10101111
[2,7,4,5,1,3,8,9,6]=>01010001=>10101110
[2,9,8,6,1,3,4,5,7]=>01110000=>10001111
[2,7,8,9,1,3,4,5,6]=>00010000=>11101111
[2,8,9,6,1,7,3,4,5]=>00110100=>11001011
[2,9,6,5,1,7,8,3,4]=>01110010=>10001101
[7,3,4,5,1,2,8,9,6]=>10010001=>01101110
[9,3,4,8,1,2,5,6,7]=>10010000=>01101111
[7,3,4,8,1,2,5,9,6]=>10010001=>01101110
[7,3,8,9,1,2,4,5,6]=>10010000=>01101111
[9,8,4,5,1,2,3,6,7]=>11010000=>00101111
[7,8,4,6,1,2,3,9,5]=>01010001=>10101110
[9,8,6,5,1,2,3,4,7]=>11110000=>00001111
[7,8,9,6,1,2,3,4,5]=>00110000=>11001111
[7,8,6,5,1,2,3,9,4]=>01110001=>10001110
[8,3,9,6,1,7,2,4,5]=>10110100=>01001011
[8,3,6,5,1,7,2,9,4]=>10110101=>01001010
[8,6,4,5,1,7,2,9,3]=>11010101=>00101010
[6,3,4,5,1,7,9,2,8]=>10010010=>01101101
[6,3,4,5,1,9,8,2,7]=>10010110=>01101001
[9,3,4,6,1,7,8,2,5]=>10010010=>01101101
[6,3,4,5,1,7,8,9,2]=>10010001=>01101110
[2,3,4,5,9,1,6,7,8]=>00001000=>11110111
[2,3,4,5,8,1,6,9,7]=>00001001=>11110110
[2,3,4,5,9,1,8,6,7]=>00001010=>11110101
[2,3,4,5,7,1,8,9,6]=>00001001=>11110110
[2,3,4,9,6,1,5,7,8]=>00011000=>11100111
[2,3,4,9,7,1,5,6,8]=>00011000=>11100111
[2,3,4,9,6,1,8,5,7]=>00011010=>11100101
[2,3,4,9,7,1,8,5,6]=>00011010=>11100101
[2,3,9,5,6,1,4,7,8]=>00101000=>11010111
[2,3,8,5,6,1,4,9,7]=>00101001=>11010110
[2,3,9,5,6,1,8,4,7]=>00101010=>11010101
[2,8,4,5,6,1,3,9,7]=>01001001=>10110110
[2,8,9,5,7,1,3,4,6]=>00101000=>11010111
[2,8,9,7,6,1,3,4,5]=>00111000=>11000111
[2,9,7,5,6,1,8,3,4]=>01101010=>10010101
[8,3,4,5,6,1,2,9,7]=>10001001=>01110110
[8,3,4,7,6,1,2,9,5]=>10011001=>01100110
[8,3,9,7,6,1,2,4,5]=>10111000=>01000111
[8,3,7,5,6,1,2,9,4]=>10101001=>01010110
[9,7,4,5,6,1,2,3,8]=>11001000=>00110111
[8,9,4,5,6,1,2,3,7]=>01001000=>10110111
[8,9,7,5,6,1,2,3,4]=>01101000=>10010111
[8,7,4,5,6,1,2,9,3]=>11001001=>00110110
[7,3,4,5,6,1,9,2,8]=>10001010=>01110101
[9,3,4,5,6,1,8,2,7]=>10001010=>01110101
[9,3,7,5,6,1,8,2,4]=>10101010=>01010101
[7,3,4,5,6,1,8,9,2]=>10001001=>01110110
[2,3,4,5,6,9,1,7,8]=>00000100=>11111011
[2,3,4,5,6,8,1,9,7]=>00000101=>11111010
[2,3,4,5,9,7,1,6,8]=>00001100=>11110011
[2,3,4,5,9,8,1,6,7]=>00001100=>11110011
[2,3,4,9,6,7,1,5,8]=>00010100=>11101011
[2,3,9,5,6,7,1,4,8]=>00100100=>11011011
[2,3,9,5,6,8,1,4,7]=>00100100=>11011011
[2,9,4,5,6,7,1,3,8]=>01000100=>10111011
[2,9,4,5,6,8,1,3,7]=>01000100=>10111011
[2,9,4,5,8,7,1,3,6]=>01001100=>10110011
[2,9,4,8,6,7,1,3,5]=>01010100=>10101011
[2,9,8,5,6,7,1,3,4]=>01100100=>10011011
[2,8,4,5,6,7,1,9,3]=>01000101=>10111010
[9,3,4,5,6,7,1,2,8]=>10000100=>01111011
[9,3,4,5,6,8,1,2,7]=>10000100=>01111011
[9,8,4,5,6,7,1,2,3]=>11000100=>00111011
[8,3,4,5,6,7,1,9,2]=>10000101=>01111010
[2,3,4,5,6,7,9,1,8]=>00000010=>11111101
[2,3,4,5,6,9,8,1,7]=>00000110=>11111001
[2,3,4,5,9,7,8,1,6]=>00001010=>11110101
[2,3,4,9,6,7,8,1,5]=>00010010=>11101101
[2,3,9,5,6,7,8,1,4]=>00100010=>11011101
[2,9,4,5,6,7,8,1,3]=>01000010=>10111101
[9,3,4,5,6,7,8,1,2]=>10000010=>01111101
[2,3,4,5,6,7,8,9,1]=>00000001=>11111110
[3,5,2,6,1,4,8,7]=>0101001=>1010110
[3,5,2,6,4,1,8,7]=>0101101=>1010010
[3,5,2,7,4,8,1,6]=>0101010=>1010101
[3,5,2,7,4,8,6,1]=>0101011=>1010100
[4,5,7,2,3,8,6,1]=>0010011=>1101100
[4,5,7,2,3,8,1,6]=>0010010=>1101101
[4,5,6,2,3,1,8,7]=>0010101=>1101010
[4,5,6,2,1,3,8,7]=>0011001=>1100110
[3,5,1,6,4,2,8,7]=>0101101=>1010010
[4,5,6,1,3,2,8,7]=>0010101=>1101010
[4,5,6,3,1,2,8,7]=>0011001=>1100110
[4,5,7,3,2,8,1,6]=>0011010=>1100101
[4,5,7,3,2,8,6,1]=>0011011=>1100100
[4,6,7,3,8,2,5,1]=>0010101=>1101010
[4,6,7,3,8,2,1,5]=>0010110=>1101001
[4,6,7,3,8,1,2,5]=>0010100=>1101011
[4,5,7,3,1,8,2,6]=>0011010=>1100101
[4,5,7,1,3,8,2,6]=>0010010=>1101101
[3,5,1,7,4,8,2,6]=>0101010=>1010101
[2,1,5,7,4,8,3,6]=>1001010=>0110101
[2,1,5,7,4,8,6,3]=>1001011=>0110100
[3,5,1,7,4,8,6,2]=>0101011=>1010100
[4,5,7,1,3,8,6,2]=>0010011=>1101100
[4,5,7,3,1,8,6,2]=>0011011=>1100100
[4,6,7,3,8,1,5,2]=>0010101=>1101010
[4,6,7,3,8,5,1,2]=>0010110=>1101001
[4,6,7,3,8,5,2,1]=>0010111=>1101000
[5,6,7,8,3,1,4,2]=>0001101=>1110010
[5,6,7,8,1,3,4,2]=>0001001=>1110110
[4,6,7,1,8,3,5,2]=>0010101=>1101010
[3,6,1,7,8,4,5,2]=>0100101=>1011010
[2,1,6,7,8,4,5,3]=>1000101=>0111010
[2,1,6,7,8,4,3,5]=>1000110=>0111001
[3,6,1,7,8,4,2,5]=>0100110=>1011001
[4,6,7,1,8,3,2,5]=>0010110=>1101001
[5,6,7,8,1,3,2,4]=>0001010=>1110101
[4,5,7,2,1,8,3,6]=>0011010=>1100101
[4,6,7,2,8,1,3,5]=>0010100=>1101011
[4,6,7,2,8,3,1,5]=>0010110=>1101001
[4,6,7,2,8,3,5,1]=>0010101=>1101010
[3,6,2,7,8,4,5,1]=>0100101=>1011010
[3,6,2,7,8,4,1,5]=>0100110=>1011001
[3,6,2,7,8,1,4,5]=>0100100=>1011011
[3,5,2,7,1,8,4,6]=>0101010=>1010101
[3,4,2,1,7,8,5,6]=>0110010=>1001101
[3,4,1,2,7,8,6,5]=>0100011=>1011100
[3,5,2,7,1,8,6,4]=>0101011=>1010100
[3,6,2,7,8,1,5,4]=>0100101=>1011010
[3,6,2,7,8,5,1,4]=>0100110=>1011001
[3,6,2,7,8,5,4,1]=>0100111=>1011000
[4,6,7,2,8,5,3,1]=>0010111=>1101000
[4,6,7,2,8,5,1,3]=>0010110=>1101001
[4,6,7,2,8,1,5,3]=>0010101=>1101010
[4,5,7,2,1,8,6,3]=>0011011=>1100100
[4,5,7,1,2,8,6,3]=>0010011=>1101100
[3,5,1,7,2,8,6,4]=>0101011=>1010100
[2,1,5,7,3,8,6,4]=>1001011=>0110100
[2,1,6,7,8,3,5,4]=>1000101=>0111010
[3,6,1,7,8,2,5,4]=>0100101=>1011010
[4,6,7,1,8,2,5,3]=>0010101=>1101010
[5,6,7,8,1,2,4,3]=>0001001=>1110110
[5,6,7,8,2,1,4,3]=>0001101=>1110010
[5,6,7,8,2,4,1,3]=>0001010=>1110101
[5,6,7,8,2,4,3,1]=>0001011=>1110100
[5,6,7,8,1,4,2,3]=>0001010=>1110101
[4,6,7,1,8,5,2,3]=>0010110=>1101001
[3,6,1,7,8,5,2,4]=>0100110=>1011001
[2,1,6,7,8,5,3,4]=>1000110=>0111001
[3,6,1,7,8,5,4,2]=>0100111=>1011000
[4,6,7,1,8,5,3,2]=>0010111=>1101000
[5,6,7,8,1,4,3,2]=>0001011=>1110100
[5,6,7,8,4,1,3,2]=>0001101=>1110010
[3,4,2,1,6,5,8,7,10,9]=>011010101=>100101010
[3,5,2,6,4,1,8,7,10,9]=>010110101=>101001010
[3,5,2,7,4,8,6,1,10,9]=>010101101=>101010010
[3,5,2,7,4,9,6,10,8,1]=>010101011=>101010100
[2,1,5,6,4,3,8,7,10,9]=>100110101=>011001010
[4,5,6,3,2,1,8,7,10,9]=>001110101=>110001010
[4,5,7,3,2,8,6,1,10,9]=>001101101=>110010010
[4,5,7,3,2,9,6,10,8,1]=>001101011=>110010100
[2,1,5,7,4,8,6,3,10,9]=>100101101=>011010010
[4,6,7,3,8,5,2,1,10,9]=>001011101=>110100010
[4,6,7,3,9,5,2,10,8,1]=>001011011=>110100100
[2,1,5,7,4,9,6,10,8,3]=>100101011=>011010100
[4,6,8,3,9,5,10,7,2,1]=>001010111=>110101000
[2,1,4,3,7,8,6,5,10,9]=>101001101=>010110010
[3,4,2,1,7,8,6,5,10,9]=>011001101=>100110010
[3,6,2,7,8,5,4,1,10,9]=>010011101=>101100010
[3,6,2,7,9,5,4,10,8,1]=>010011011=>101100100
[2,1,6,7,8,5,4,3,10,9]=>100011101=>011100010
[5,6,7,8,4,3,2,1,10,9]=>000111101=>111000010
[5,6,7,9,4,3,2,10,8,1]=>000111011=>111000100
[2,1,6,7,9,5,4,10,8,3]=>100011011=>011100100
[5,6,8,9,4,3,10,7,2,1]=>000110111=>111001000
[2,1,4,3,7,9,6,10,8,5]=>101001011=>010110100
[3,4,2,1,7,9,6,10,8,5]=>011001011=>100110100
[3,6,2,8,9,5,10,7,4,1]=>010010111=>101101000
[2,1,6,8,9,5,10,7,4,3]=>100010111=>011101000
[5,7,8,9,4,10,6,3,2,1]=>000101111=>111010000
[6,7,8,9,10,1,4,5,3,2]=>000010011=>111101100
[6,7,8,9,10,1,4,5,2,3]=>000010010=>111101101
[6,7,8,9,10,4,3,2,1,5]=>000011110=>111100001
[6,7,8,9,10,1,3,4,5,2]=>000010001=>111101110
[6,7,8,9,10,3,4,1,2,5]=>000010100=>111101011
[6,7,8,9,10,3,4,2,1,5]=>000010110=>111101001
[6,7,8,9,10,2,3,4,1,5]=>000010010=>111101101
[2,1,4,3,6,5,9,10,8,7]=>101010011=>010101100
[3,4,2,1,6,5,9,10,8,7]=>011010011=>100101100
[3,5,2,6,4,1,9,10,8,7]=>010110011=>101001100
[3,5,2,8,4,9,10,7,6,1]=>010100111=>101011000
[2,1,5,6,4,3,9,10,8,7]=>100110011=>011001100
[4,5,6,3,2,1,9,10,8,7]=>001110011=>110001100
[4,5,8,3,2,9,10,7,6,1]=>001100111=>110011000
[2,1,5,8,4,9,10,7,6,3]=>100100111=>011011000
[4,7,8,3,9,10,6,5,2,1]=>001001111=>110110000
[2,1,4,3,8,9,10,7,6,5]=>101000111=>010111000
[3,4,2,1,8,9,10,7,6,5]=>011000111=>100111000
[3,7,2,8,9,10,6,5,4,1]=>010001111=>101110000
[2,1,7,8,9,10,6,5,4,3]=>100001111=>011110000
[6,7,8,9,10,1,5,4,3,2]=>000010111=>111101000
[6,7,8,9,10,5,4,3,2,1]=>000011111=>111100000
[6,5,8,7,3,4,1,2]=>1011010=>0100101
[3,6,7,4,5,8,1,2]=>0010010=>1101101
[2,6,7,4,5,1,8,3]=>0010101=>1101010
[1,6,7,4,5,2,3,8]=>0010100=>1101011
[1,5,4,7,6,2,3,8]=>0101100=>1010011
[2,5,4,7,6,1,8,3]=>0101101=>1010010
[3,5,4,7,6,8,1,2]=>0101010=>1010101
[4,5,3,7,8,6,1,2]=>0100110=>1011001
[5,4,3,8,7,6,1,2]=>1101110=>0010001
[6,4,8,3,7,5,1,2]=>1010110=>0101001
[6,3,8,4,5,7,1,2]=>1010010=>0101101
[5,3,4,8,6,7,1,2]=>1001010=>0110101
[4,3,5,6,8,7,1,2]=>1000110=>0111001
[3,2,5,6,1,8,7,4]=>1001011=>0110100
[4,2,5,6,8,1,7,3]=>1000101=>0111010
[5,2,4,8,6,1,7,3]=>1001101=>0110010
[6,2,8,4,5,1,7,3]=>1010101=>0101010
[7,8,2,4,5,1,6,3]=>0100101=>1011010
[7,8,1,4,5,2,3,6]=>0100100=>1011011
[6,1,8,4,5,2,3,7]=>1010100=>0101011
[5,1,4,8,6,2,3,7]=>1001100=>0110011
[4,1,3,2,8,6,5,7]=>1010110=>0101001
[5,1,3,8,2,6,4,7]=>1001010=>0110101
[6,1,8,3,2,5,4,7]=>1011010=>0100101
[7,8,1,3,2,5,4,6]=>0101010=>1010101
[7,8,2,3,1,5,6,4]=>0101001=>1010110
[6,2,8,3,1,5,7,4]=>1011001=>0100110
[5,2,3,8,1,6,7,4]=>1001001=>0110110
[6,3,8,2,1,7,5,4]=>1011011=>0100100
[7,8,3,2,1,6,5,4]=>0111011=>1000100
[7,8,4,2,6,1,5,3]=>0110101=>1001010
[5,4,2,8,7,1,6,3]=>1101101=>0010010
[4,5,2,7,8,1,6,3]=>0100101=>1011010
[2,5,3,7,1,6,8,4]=>0101001=>1010110
[1,5,3,7,2,6,4,8]=>0101010=>1010101
[1,6,7,3,2,5,4,8]=>0011010=>1100101
[2,6,7,3,1,5,8,4]=>0011001=>1100110
[3,6,7,2,1,8,5,4]=>0011011=>1100100
[7,8,5,6,2,1,4,3]=>0101101=>1010010
[6,5,8,7,1,2,3,4]=>1011000=>0100111
[5,4,1,8,7,2,3,6]=>1101100=>0010011
[6,4,8,1,7,2,3,5]=>1010100=>0101011
[7,8,3,1,2,6,4,5]=>0110010=>1001101
[5,3,1,8,2,7,4,6]=>1101010=>0010101
[4,3,1,2,8,7,5,6]=>1100110=>0011001
[4,2,1,3,8,5,7,6]=>1100101=>0011010
[5,2,1,8,3,4,7,6]=>1101001=>0010110
[6,2,8,1,3,4,7,5]=>1010001=>0101110
[7,8,2,1,3,4,6,5]=>0110001=>1001110
[4,3,1,2,6,5,8,7]=>1100101=>0011010
[5,3,1,6,2,4,8,7]=>1101001=>0010110
[6,3,1,5,2,4,8,7]=>1101001=>0010110
[7,3,1,5,2,8,4,6]=>1101010=>0010101
[8,4,5,1,2,7,3,6]=>1010010=>0101101
[7,4,5,1,2,8,3,6]=>1010010=>0101101
[6,4,5,1,2,3,8,7]=>1010001=>0101110
[5,4,6,1,2,3,8,7]=>1010001=>0101110
[2,1,6,5,3,4,8,7]=>1011001=>0100110
[3,6,1,5,2,4,8,7]=>0101001=>1010110
[4,6,5,1,2,3,8,7]=>0110001=>1001110
[5,6,4,1,2,3,8,7]=>0110001=>1001110
[6,5,4,1,2,3,8,7]=>1110001=>0001110
[7,5,4,1,2,8,3,6]=>1110010=>0001101
[8,6,4,1,7,2,3,5]=>1110100=>0001011
[7,6,4,1,8,2,3,5]=>1110100=>0001011
[6,7,4,1,8,2,3,5]=>0110100=>1001011
[5,7,4,1,2,8,3,6]=>0110010=>1001101
[4,7,5,1,2,8,3,6]=>0110010=>1001101
[3,7,1,5,2,8,4,6]=>0101010=>1010101
[2,1,7,5,3,8,4,6]=>1011010=>0100101
[2,1,8,5,3,7,4,6]=>1011010=>0100101
[3,8,1,5,2,7,4,6]=>0101010=>1010101
[4,8,5,1,2,7,3,6]=>0110010=>1001101
[5,8,4,1,2,7,3,6]=>0110010=>1001101
[6,8,4,1,7,2,3,5]=>0110100=>1001011
[8,7,4,1,6,2,3,5]=>1110100=>0001011
[5,8,6,7,1,2,3,4]=>0101000=>1010111
[4,8,6,1,7,2,3,5]=>0110100=>1001011
[3,8,1,6,7,2,4,5]=>0100100=>1011011
[2,1,8,6,7,3,4,5]=>1010100=>0101011
[2,1,7,6,8,3,4,5]=>1010100=>0101011
[3,7,1,6,8,2,4,5]=>0100100=>1011011
[4,7,6,1,8,2,3,5]=>0110100=>1001011
[5,7,6,8,1,2,3,4]=>0101000=>1010111
[5,4,7,1,2,8,3,6]=>1010010=>0101101
[6,4,7,1,8,2,3,5]=>1010100=>0101011
[7,4,6,1,8,2,3,5]=>1010100=>0101011
[8,4,6,1,7,2,3,5]=>1010100=>0101011
[8,3,1,6,7,2,4,5]=>1100100=>0011011
[7,3,1,6,8,2,4,5]=>1100100=>0011011
[6,3,1,7,8,2,4,5]=>1100100=>0011011
[5,3,1,7,2,8,4,6]=>1101010=>0010101
[4,3,1,2,7,8,5,6]=>1100010=>0011101
[2,1,4,3,8,7,5,6]=>1010110=>0101001
[3,4,1,2,8,7,5,6]=>0100110=>1011001
[6,3,1,8,7,2,4,5]=>1101100=>0010011
[7,3,1,8,6,2,4,5]=>1101100=>0010011
[8,4,7,1,6,2,3,5]=>1010100=>0101011
[7,4,8,1,6,2,3,5]=>1010100=>0101011
[5,4,8,1,2,7,3,6]=>1010010=>0101101
[4,5,8,1,2,7,3,6]=>0010010=>1101101
[3,5,1,8,2,7,4,6]=>0101010=>1010101
[2,1,5,8,3,7,4,6]=>1001010=>0110101
[2,1,6,8,7,3,4,5]=>1001100=>0110011
[3,6,1,8,7,2,4,5]=>0101100=>1010011
[4,6,8,1,7,2,3,5]=>0010100=>1101011
[5,6,8,7,1,2,3,4]=>0011000=>1100111
[7,5,8,6,1,2,3,4]=>1011000=>0100111
[8,5,7,6,1,2,3,4]=>1011000=>0100111
[5,7,8,6,1,2,3,4]=>0011000=>1100111
[4,7,8,1,6,2,3,5]=>0010100=>1101011
[3,7,1,8,6,2,4,5]=>0101100=>1010011
[2,1,7,8,6,3,4,5]=>1001100=>0110011
[2,1,8,7,6,3,4,5]=>1011100=>0100011
[3,8,1,7,6,2,4,5]=>0101100=>1010011
[4,8,7,1,6,2,3,5]=>0110100=>1001011
[5,8,7,6,1,2,3,4]=>0111000=>1000111
[6,8,7,5,1,2,3,4]=>0111000=>1000111
[6,4,7,3,8,5,1,2]=>1010110=>0101001
[6,4,7,3,5,8,1,2]=>1010010=>0101101
[6,4,7,2,5,1,8,3]=>1010101=>0101010
[5,4,2,7,6,1,3,8]=>1101100=>0010011
[5,4,2,7,6,1,8,3]=>1101101=>0010010
[5,4,3,7,6,8,1,2]=>1101010=>0010101
[5,4,3,7,8,6,1,2]=>1100110=>0011001
[6,4,8,3,5,7,1,2]=>1010010=>0101101
[5,4,3,8,6,7,1,2]=>1101010=>0010101
[5,4,3,6,8,7,1,2]=>1100110=>0011001
[5,4,2,6,7,1,8,3]=>1100101=>0011010
[5,4,2,6,7,1,3,8]=>1100100=>0011011
[5,3,2,6,1,7,4,8]=>1101010=>0010101
[5,3,2,6,1,7,8,4]=>1101001=>0010110
[5,3,2,6,1,8,7,4]=>1101011=>0010100
[5,4,2,6,8,1,7,3]=>1100101=>0011010
[5,4,2,8,6,1,7,3]=>1101101=>0010010
[6,4,8,2,5,1,7,3]=>1010101=>0101010
[7,8,4,2,5,1,6,3]=>0110101=>1001010
[7,8,4,2,5,1,3,6]=>0110100=>1001011
[5,4,2,8,6,1,3,7]=>1101100=>0010011
[5,3,2,6,1,8,4,7]=>1101010=>0010101
[4,3,2,1,6,8,5,7]=>1110010=>0001101
[4,3,2,1,8,6,5,7]=>1110110=>0001001
[5,3,2,8,1,6,4,7]=>1101010=>0010101
[6,3,8,2,1,5,4,7]=>1011010=>0100101
[7,8,3,2,1,5,4,6]=>0111010=>1000101
[7,8,3,2,1,5,6,4]=>0111001=>1000110
[6,3,8,2,1,5,7,4]=>1011001=>0100110
[5,3,2,8,1,6,7,4]=>1101001=>0010110
[5,4,2,7,8,1,6,3]=>1100101=>0011010
[5,3,2,7,1,8,6,4]=>1101011=>0010100
[5,3,2,7,1,6,8,4]=>1101001=>0010110
[5,3,2,7,1,6,4,8]=>1101010=>0010101
[6,3,7,2,1,5,4,8]=>1011010=>0100101
[6,3,7,2,1,5,8,4]=>1011001=>0100110
[6,3,7,2,1,8,5,4]=>1011011=>0100100
[6,4,7,2,8,1,5,3]=>1010101=>0101010
[6,5,7,8,2,1,4,3]=>1001101=>0110010
[6,5,8,7,2,1,3,4]=>1011100=>0100011
[6,3,7,2,1,8,4,5]=>1011010=>0100101
[6,3,7,2,1,4,8,5]=>1011001=>0100110
[6,3,7,2,1,4,5,8]=>1011000=>0100111
[5,3,2,7,1,4,8,6]=>1101001=>0010110
[5,4,2,8,7,1,3,6]=>1101100=>0010011
[7,8,4,2,6,1,3,5]=>0110100=>1001011
[7,8,3,2,1,6,4,5]=>0111010=>1000101
[6,3,8,2,1,7,4,5]=>1011010=>0100101
[5,3,2,8,1,7,4,6]=>1101010=>0010101
[4,3,2,1,8,7,5,6]=>1110110=>0001001
[4,3,2,1,7,5,8,6]=>1110101=>0001010
[4,3,2,1,7,5,6,8]=>1110100=>0001011
[4,3,2,1,8,5,7,6]=>1110101=>0001010
[5,3,2,8,1,4,7,6]=>1101001=>0010110
[6,3,8,2,1,4,7,5]=>1011001=>0100110
[7,8,3,2,1,4,6,5]=>0111001=>1000110
[6,3,8,2,1,4,5,7]=>1011000=>0100111
[4,3,2,1,8,5,6,7]=>1110100=>0001011
[4,3,2,1,5,8,6,7]=>1110010=>0001101
[7,8,5,6,1,2,4,3]=>0101001=>1010110
[7,8,4,1,6,2,5,3]=>0110101=>1001010
[7,8,1,4,6,2,5,3]=>0100101=>1011010
[6,1,8,4,7,2,5,3]=>1010101=>0101010
[1,6,8,4,7,2,5,3]=>0010101=>1101010
[1,6,8,3,2,7,5,4]=>0011011=>1100100
[6,1,8,3,2,7,5,4]=>1011011=>0100100
[7,8,1,3,2,6,5,4]=>0101011=>1010100
[7,8,3,1,2,6,5,4]=>0110011=>1001100
[7,8,3,4,6,5,1,2]=>0100110=>1011001
[7,8,2,4,6,1,5,3]=>0100101=>1011010
[7,8,2,3,1,6,5,4]=>0101011=>1010100
[7,8,2,1,3,6,5,4]=>0110011=>1001100
[7,8,1,2,3,6,5,4]=>0100011=>1011100
[6,1,8,2,3,7,5,4]=>1010011=>0101100
[1,6,8,2,3,7,5,4]=>0010011=>1101100
[1,5,2,8,3,7,6,4]=>0101011=>1010100
[5,1,2,8,3,7,6,4]=>1001011=>0110100
[5,2,1,8,3,7,6,4]=>1101011=>0010100
[6,2,8,1,3,7,5,4]=>1010011=>0101100
[6,2,8,3,1,7,5,4]=>1011011=>0100100
[6,2,8,4,7,1,5,3]=>1010101=>0101010
[6,3,8,4,7,5,1,2]=>1010110=>0101001
[3,6,8,4,7,5,1,2]=>0010110=>1101001
[2,6,8,4,7,1,5,3]=>0010101=>1101010
[2,6,8,3,1,7,5,4]=>0011011=>1100100
[2,6,8,1,3,7,5,4]=>0010011=>1101100
[2,5,1,8,3,7,6,4]=>0101011=>1010100
[1,2,5,8,3,7,6,4]=>0001011=>1110100
[2,4,1,3,8,7,6,5]=>0100111=>1011000
[2,5,3,8,1,7,6,4]=>0101011=>1010100
[2,5,4,8,7,1,6,3]=>0101101=>1010010
[3,5,4,8,7,6,1,2]=>0101110=>1010001
[5,3,4,8,7,6,1,2]=>1001110=>0110001
[5,2,4,8,7,1,6,3]=>1001101=>0110010
[5,2,3,8,1,7,6,4]=>1001011=>0110100
[4,2,1,3,8,7,6,5]=>1100111=>0011000
[4,1,2,3,8,7,6,5]=>1000111=>0111000
[1,4,2,3,8,7,6,5]=>0100111=>1011000
[4,1,3,2,8,7,6,5]=>1010111=>0101000
[4,3,1,2,8,7,6,5]=>1100111=>0011000
[6,3,8,1,2,7,5,4]=>1010011=>0101100
[5,3,1,8,2,7,6,4]=>1101011=>0010100
[5,1,3,8,2,7,6,4]=>1001011=>0110100
[1,5,3,8,2,7,6,4]=>0101011=>1010100
[1,5,4,8,7,2,6,3]=>0101101=>1010010
[5,1,4,8,7,2,6,3]=>1001101=>0110010
[5,4,1,8,7,2,6,3]=>1101101=>0010010
[6,4,8,1,7,2,5,3]=>1010101=>0101010
[6,5,8,7,1,2,4,3]=>1011001=>0100110
[5,6,8,7,3,4,1,2]=>0011010=>1100101
[5,6,8,7,2,1,4,3]=>0011101=>1100010
[4,5,1,8,7,2,6,3]=>0101101=>1010010
[4,1,5,8,7,2,6,3]=>1001101=>0110010
[1,4,5,8,7,2,6,3]=>0001101=>1110010
[1,3,5,8,2,7,6,4]=>0001011=>1110100
[3,1,5,8,2,7,6,4]=>1001011=>0110100
[3,6,8,1,2,7,5,4]=>0010011=>1101100
[3,6,8,2,1,7,5,4]=>0011011=>1100100
[4,6,8,2,7,1,5,3]=>0010101=>1101010
[4,6,8,3,7,5,1,2]=>0010110=>1101001
[4,5,3,8,7,6,1,2]=>0101110=>1010001
[4,5,2,8,7,1,6,3]=>0101101=>1010010
[3,5,2,8,1,7,6,4]=>0101011=>1010100
[3,1,4,2,8,7,6,5]=>1010111=>0101000
[3,1,2,4,8,7,6,5]=>1000111=>0111000
[3,2,5,8,1,7,6,4]=>1001011=>0110100
[4,2,5,8,7,1,6,3]=>1001101=>0110010
[4,3,5,8,7,6,1,2]=>1001110=>0110001
[3,4,5,8,7,6,1,2]=>0001110=>1110001
[2,4,5,8,7,1,6,3]=>0001101=>1110010
[2,3,5,8,1,7,6,4]=>0001011=>1110100
[4,1,3,2,6,5,8,7]=>1010101=>0101010
[5,1,3,2,6,4,8,7]=>1010101=>0101010
[6,1,3,2,5,4,8,7]=>1010101=>0101010
[7,1,3,2,5,4,8,6]=>1010101=>0101010
[8,1,3,2,5,4,7,6]=>1010101=>0101010
[8,1,4,2,5,3,7,6]=>1010101=>0101010
[7,1,4,2,5,3,8,6]=>1010101=>0101010
[6,1,4,2,5,3,8,7]=>1010101=>0101010
[5,1,4,2,6,3,8,7]=>1010101=>0101010
[2,1,6,3,5,4,8,7]=>1010101=>0101010
[3,1,6,2,5,4,8,7]=>1010101=>0101010
[4,1,6,2,5,3,8,7]=>1010101=>0101010
[6,2,5,1,4,3,8,7]=>1010101=>0101010
[5,2,6,1,4,3,8,7]=>1010101=>0101010
[5,2,7,1,4,3,8,6]=>1010101=>0101010
[5,2,8,1,4,3,7,6]=>1010101=>0101010
[6,2,8,1,4,3,7,5]=>1010101=>0101010
[6,2,7,1,4,3,8,5]=>1010101=>0101010
[7,2,6,1,4,3,8,5]=>1010101=>0101010
[7,2,5,1,4,3,8,6]=>1010101=>0101010
[4,1,7,2,5,3,8,6]=>1010101=>0101010
[3,1,7,2,5,4,8,6]=>1010101=>0101010
[2,1,7,3,5,4,8,6]=>1010101=>0101010
[2,1,8,3,5,4,7,6]=>1010101=>0101010
[3,1,8,2,5,4,7,6]=>1010101=>0101010
[4,1,8,2,5,3,7,6]=>1010101=>0101010
[8,2,5,1,4,3,7,6]=>1010101=>0101010
[8,2,6,1,4,3,7,5]=>1010101=>0101010
[7,1,4,3,8,2,6,5]=>1010101=>0101010
[8,1,4,3,7,2,6,5]=>1010101=>0101010
[8,1,5,3,7,2,6,4]=>1010101=>0101010
[7,1,5,3,8,2,6,4]=>1010101=>0101010
[8,2,6,1,5,3,7,4]=>1010101=>0101010
[5,1,8,2,6,3,7,4]=>1010101=>0101010
[4,1,8,2,6,3,7,5]=>1010101=>0101010
[3,1,8,2,6,4,7,5]=>1010101=>0101010
[2,1,8,3,6,4,7,5]=>1010101=>0101010
[2,1,7,3,6,4,8,5]=>1010101=>0101010
[4,1,7,2,6,3,8,5]=>1010101=>0101010
[5,1,7,2,6,3,8,4]=>1010101=>0101010
[7,2,6,1,5,3,8,4]=>1010101=>0101010
[6,2,7,1,5,3,8,4]=>1010101=>0101010
[6,2,8,1,5,3,7,4]=>1010101=>0101010
[8,1,5,2,6,3,7,4]=>1010101=>0101010
[6,1,5,2,7,3,8,4]=>1010101=>0101010
[6,1,4,2,7,3,8,5]=>1010101=>0101010
[8,1,4,2,6,3,7,5]=>1010101=>0101010
[8,1,3,2,6,4,7,5]=>1010101=>0101010
[7,1,3,2,6,4,8,5]=>1010101=>0101010
[6,1,3,2,7,4,8,5]=>1010101=>0101010
[5,1,3,2,7,4,8,6]=>1010101=>0101010
[4,1,3,2,7,5,8,6]=>1010101=>0101010
[2,1,4,3,8,5,7,6]=>1010101=>0101010
[3,1,4,2,8,5,7,6]=>1010101=>0101010
[4,1,3,2,8,5,7,6]=>1010101=>0101010
[5,1,3,2,8,4,7,6]=>1010101=>0101010
[6,1,3,2,8,4,7,5]=>1010101=>0101010
[8,4,7,1,3,2,6,5]=>1010101=>0101010
[7,4,8,1,3,2,6,5]=>1010101=>0101010
[7,3,8,1,4,2,6,5]=>1010101=>0101010
[8,3,7,1,4,2,6,5]=>1010101=>0101010
[6,1,4,2,8,3,7,5]=>1010101=>0101010
[5,1,4,2,8,3,7,6]=>1010101=>0101010
[4,1,5,2,8,3,7,6]=>1010101=>0101010
[3,1,5,2,8,4,7,6]=>1010101=>0101010
[2,1,5,3,8,4,7,6]=>1010101=>0101010
[2,1,6,3,8,4,7,5]=>1010101=>0101010
[3,1,6,2,8,4,7,5]=>1010101=>0101010
[4,1,6,2,8,3,7,5]=>1010101=>0101010
[5,1,6,2,8,3,7,4]=>1010101=>0101010
[6,1,5,2,8,3,7,4]=>1010101=>0101010
[8,3,7,1,5,2,6,4]=>1010101=>0101010
[7,3,8,1,5,2,6,4]=>1010101=>0101010
[6,2,7,3,8,1,5,4]=>1010101=>0101010
[6,2,8,3,7,1,5,4]=>1010101=>0101010
[8,3,7,2,6,1,5,4]=>1010101=>0101010
[5,1,8,3,7,2,6,4]=>1010101=>0101010
[4,1,8,3,7,2,6,5]=>1010101=>0101010
[3,1,8,4,7,2,6,5]=>1010101=>0101010
[2,1,8,4,7,3,6,5]=>1010101=>0101010
[2,1,7,4,8,3,6,5]=>1010101=>0101010
[3,1,7,4,8,2,6,5]=>1010101=>0101010
[4,1,7,3,8,2,6,5]=>1010101=>0101010
[5,1,7,3,8,2,6,4]=>1010101=>0101010
[7,3,8,2,6,1,5,4]=>1010101=>0101010
[8,2,6,3,7,1,5,4]=>1010101=>0101010
[7,2,6,3,8,1,5,4]=>1010101=>0101010
[3,4,2,6,8,1,5,7]=>0100100=>1011011
[5,3,6,2,8,1,4,7]=>1010100=>0101011
[5,3,6,2,4,8,1,7]=>1010010=>0101101
[5,7,3,8,2,4,1,6]=>0101010=>1010101
[5,7,3,8,2,4,6,1]=>0101001=>1010110
[7,4,2,5,8,3,6,1]=>1100101=>0011010
[7,4,2,5,8,3,1,6]=>1100110=>0011001
[4,5,2,6,3,8,1,7]=>0101010=>1010101
[4,5,2,1,6,8,3,7]=>0110010=>1001101
[5,3,1,6,8,2,4,7]=>1100100=>0011011
[5,6,2,8,1,3,4,7]=>0101000=>1010111
[3,5,6,1,4,8,2,7]=>0010010=>1101101
[4,1,5,6,3,8,2,7]=>1001010=>0110101
[4,5,1,6,3,8,2,7]=>0101010=>1010101
[4,5,6,3,2,8,1,7]=>0011010=>1100101
[7,4,5,3,8,2,1,6]=>1010110=>0101001
[7,4,5,3,8,2,6,1]=>1010101=>0101010
[6,7,4,8,3,2,5,1]=>0101101=>1010010
[6,7,4,8,3,2,1,5]=>0101110=>1010001
[6,7,4,1,8,3,2,5]=>0110110=>1001001
[7,4,5,3,1,8,2,6]=>1011010=>0100101
[4,7,1,5,8,3,2,6]=>0100110=>1011001
[5,3,7,8,1,4,2,6]=>1001010=>0110101
[7,5,8,2,4,6,1,3]=>1010010=>0101101
[7,3,5,8,1,4,6,2]=>1001001=>0110110
[4,5,1,7,8,3,6,2]=>0100101=>1011010
[7,4,1,5,8,3,6,2]=>1100101=>0011010
[6,7,4,3,8,1,5,2]=>0110101=>1001010
[6,7,4,8,3,1,5,2]=>0101101=>1010010
[6,7,4,8,3,5,2,1]=>0101011=>1010100
[5,6,7,3,8,4,2,1]=>0010111=>1101000
[5,6,7,3,1,8,4,2]=>0011011=>1100100
[5,6,1,7,3,8,4,2]=>0101011=>1010100
[5,1,6,7,3,8,4,2]=>1001011=>0110100
[6,4,7,1,8,3,5,2]=>1010101=>0101010
[6,7,8,3,1,4,5,2]=>0011001=>1100110
[6,7,2,8,4,5,1,3]=>0101010=>1010101
[6,7,2,8,4,1,3,5]=>0101100=>1010011
[6,1,7,4,8,3,2,5]=>1010110=>0101001
[5,1,6,7,3,2,8,4]=>1001101=>0110010
[5,6,1,7,3,2,8,4]=>0101101=>1010010
[5,6,7,3,2,1,8,4]=>0011101=>1100010
[5,6,7,3,2,8,4,1]=>0011011=>1100100
[5,6,2,7,3,8,4,1]=>0101011=>1010100
[5,6,2,7,3,1,8,4]=>0101101=>1010010
[5,6,2,1,7,3,8,4]=>0110101=>1001010
[6,1,7,4,2,8,3,5]=>1011010=>0100101
[6,7,2,1,8,3,4,5]=>0110100=>1001011
[7,5,8,2,1,3,4,6]=>1011000=>0100111
[5,7,3,1,8,2,4,6]=>0110100=>1001011
[4,7,1,5,2,8,3,6]=>0101010=>1010101
[7,4,2,5,1,8,3,6]=>1101010=>0010101
[6,7,4,2,1,8,3,5]=>0111010=>1000101
[6,7,4,2,8,3,1,5]=>0110110=>1001001
[6,7,4,2,8,3,5,1]=>0110101=>1001010
[3,6,7,2,8,4,5,1]=>0010101=>1101010
[3,6,7,2,8,4,1,5]=>0010110=>1101001
[3,6,7,2,1,8,4,5]=>0011010=>1100101
[5,7,3,8,2,1,4,6]=>0101100=>1010011
[3,4,7,8,2,1,5,6]=>0001100=>1110011
[3,7,8,1,4,6,2,5]=>0010010=>1101101
[3,4,7,8,2,6,1,5]=>0001010=>1110101
[5,7,3,8,2,6,1,4]=>0101010=>1010101
[3,6,7,2,8,5,1,4]=>0010110=>1101001
[3,6,7,8,5,2,1,4]=>0001110=>1110001
[3,6,7,8,5,2,4,1]=>0001101=>1110010
[6,4,7,8,2,5,3,1]=>1001011=>0110100
[6,4,7,8,2,1,5,3]=>1001101=>0110010
[4,1,5,7,8,2,6,3]=>1000101=>0111010
[5,3,7,8,1,6,2,4]=>1001010=>0110101
[6,7,2,8,5,1,3,4]=>0101100=>1010011
[6,4,1,7,8,2,5,3]=>1100101=>0011010
[5,1,6,2,7,8,4,3]=>1010011=>0101100
[5,6,2,1,7,8,4,3]=>0110011=>1001100
[5,6,2,7,1,8,4,3]=>0101011=>1010100
[5,6,2,7,8,4,3,1]=>0100111=>1011000
[5,6,7,2,8,4,3,1]=>0010111=>1101000
[5,6,7,2,1,8,4,3]=>0011011=>1100100
[5,6,1,7,2,8,4,3]=>0101011=>1010100
[5,1,6,7,2,8,4,3]=>1001011=>0110100
[6,4,7,1,8,2,5,3]=>1010101=>0101010
[3,6,7,1,8,5,2,4]=>0010110=>1101001
[6,7,8,5,2,4,1,3]=>0011010=>1100101
[6,7,8,3,5,1,4,2]=>0010101=>1101010
[4,6,7,8,1,5,3,2]=>0001011=>1110100
[5,1,6,7,8,4,3,2]=>1000111=>0111000
[5,6,1,7,8,4,3,2]=>0100111=>1011000
[5,6,7,1,8,4,3,2]=>0010111=>1101000
[8,6,1,3,4,2,5,7]=>1100100=>0011011
[8,3,2,5,1,6,4,7]=>1101010=>0010101
[8,5,3,6,2,4,1,7]=>1101010=>0010101
[5,3,2,7,4,1,8,6]=>1101101=>0010010
[7,5,3,8,2,4,6,1]=>1101001=>0010110
[7,2,4,5,8,3,6,1]=>1000101=>0111010
[2,4,5,3,7,1,8,6]=>0010101=>1101010
[8,2,4,5,6,3,1,7]=>1000110=>0111001
[8,2,4,5,6,1,3,7]=>1000100=>0111011
[8,1,2,4,5,6,3,7]=>1000010=>0111101
[8,2,5,1,3,6,4,7]=>1010010=>0101101
[8,5,6,2,1,4,3,7]=>1011010=>0100101
[8,5,3,6,4,1,2,7]=>1101100=>0010011
[8,4,1,5,6,3,2,7]=>1100110=>0011001
[8,1,4,5,6,3,2,7]=>1000110=>0111001
[4,5,3,7,2,1,8,6]=>0101101=>1010010
[7,4,5,8,3,2,6,1]=>1001101=>0110010
[4,3,6,7,2,8,5,1]=>1001011=>0110100
[4,3,6,7,2,8,1,5]=>1001010=>0110101
[1,4,3,6,7,2,8,5]=>0100101=>1011010
[4,5,3,7,1,8,2,6]=>0101010=>1010101
[4,1,5,3,7,2,8,6]=>1010101=>0101010
[5,3,4,7,1,2,8,6]=>1001001=>0110110
[7,5,8,2,1,4,6,3]=>1011001=>0100110
[7,5,3,8,4,1,6,2]=>1101101=>0010010
[7,4,5,8,3,6,1,2]=>1001010=>0110101
[4,3,6,7,8,1,5,2]=>1000101=>0111010
[1,6,4,7,8,3,5,2]=>0100101=>1011010
[6,4,7,8,3,5,2,1]=>1001011=>0110100
[3,5,6,7,8,4,1,2]=>0000110=>1111001
[3,1,5,6,7,8,4,2]=>1000011=>0111100
[4,6,1,7,8,3,5,2]=>0100101=>1011010
[3,6,7,1,4,8,5,2]=>0010011=>1101100
[6,2,4,1,7,8,5,3]=>1010011=>0101100
[2,6,7,1,4,8,3,5]=>0010010=>1101101
[4,3,6,7,8,1,2,5]=>1000100=>0111011
[1,5,3,6,7,8,2,4]=>0100010=>1011101
[3,5,6,7,8,2,1,4]=>0000110=>1111001
[3,5,6,7,8,2,4,1]=>0000101=>1111010
[5,2,7,1,3,8,4,6]=>1010010=>0101101
[5,3,1,7,8,2,4,6]=>1100100=>0011011
[4,5,2,7,8,1,3,6]=>0100100=>1011011
[4,2,6,7,8,3,1,5]=>1000110=>0111001
[4,2,6,7,8,3,5,1]=>1000101=>0111010
[3,6,2,7,4,8,5,1]=>0101011=>1010100
[3,6,2,7,4,8,1,5]=>0101010=>1010101
[3,2,1,6,4,7,8,5]=>1101001=>0010110
[3,7,4,2,1,5,8,6]=>0111001=>1000110
[1,7,3,4,2,5,8,6]=>0101001=>1010110
[4,7,2,1,3,5,8,6]=>0110001=>1001110
[7,8,4,2,1,3,6,5]=>0111001=>1000110
[7,8,1,3,4,2,6,5]=>0100101=>1011010
[7,8,3,4,2,1,6,5]=>0101101=>1010010
[6,3,2,7,1,8,5,4]=>1101011=>0010100
[3,6,2,7,1,8,5,4]=>0101011=>1010100
[6,7,3,8,2,5,4,1]=>0101011=>1010100
[6,4,7,8,5,2,3,1]=>1001101=>0110010
[2,6,4,7,8,1,5,3]=>0100101=>1011010
[4,6,2,7,8,1,5,3]=>0100101=>1011010
[7,4,5,8,6,2,1,3]=>1001110=>0110001
[7,4,1,5,8,6,2,3]=>1100110=>0011001
[7,5,3,8,6,1,2,4]=>1101100=>0010011
[7,5,8,2,1,6,3,4]=>1011010=>0100101
[6,2,7,1,3,8,5,4]=>1010011=>0101100
[6,3,1,7,8,2,5,4]=>1100101=>0011010
[4,6,1,7,8,5,2,3]=>0100110=>1011001
[5,1,2,6,7,8,4,3]=>1000011=>0111100
[5,2,6,7,8,4,1,3]=>1000110=>0111001
[5,2,6,7,8,4,3,1]=>1000111=>0111000
[2,5,6,7,8,4,1,3]=>0000110=>1111001
[1,5,2,6,7,8,4,3]=>0100011=>1011100
[1,6,4,7,8,5,2,3]=>0100110=>1011001
[2,6,7,1,3,8,5,4]=>0010011=>1101100
[6,7,8,2,1,5,4,3]=>0011011=>1100100
[6,7,3,8,5,1,4,2]=>0101101=>1010010
[6,4,7,8,5,3,1,2]=>1001110=>0110001
[4,5,2,3,7,6,1,8]=>0100110=>1011001
[6,4,3,7,2,5,1,8]=>1101010=>0010101
[8,4,3,6,5,1,2,7]=>1101100=>0010011
[1,5,6,3,4,8,7,2]=>0010011=>1101100
[4,6,2,7,3,5,1,8]=>0101010=>1010101
[3,2,6,7,4,5,1,8]=>1001010=>0110101
[4,7,2,6,5,3,1,8]=>0101110=>1010001
[5,7,6,2,4,3,1,8]=>0110110=>1001001
[1,7,5,4,8,3,6,2]=>0110101=>1001010
[8,7,5,4,1,3,2,6]=>1111010=>0000101
[6,8,5,4,2,1,3,7]=>0111100=>1000011
[5,8,6,2,4,1,3,7]=>0110100=>1001011
[4,8,2,6,5,1,3,7]=>0101100=>1010011
[3,2,8,6,5,1,4,7]=>1011100=>0100011
[4,1,2,6,5,8,7,3]=>1001011=>0110100
[5,1,6,2,4,8,7,3]=>1010011=>0101100
[6,1,5,4,2,8,7,3]=>1011011=>0100100
[7,1,5,4,8,2,6,3]=>1010101=>0101010
[8,1,5,4,7,6,2,3]=>1010110=>0101001
[1,8,6,7,4,5,3,2]=>0101011=>1010100
[8,1,6,7,4,5,2,3]=>1001010=>0110101
[7,1,6,8,4,2,5,3]=>1001101=>0110010
[6,1,7,8,2,4,5,3]=>1001001=>0110110
[5,1,7,2,8,4,6,3]=>1010101=>0101010
[4,1,2,7,8,5,6,3]=>1000101=>0111010
[3,2,1,7,8,5,6,4]=>1100101=>0011010
[3,2,8,7,1,5,4,6]=>1011010=>0100101
[4,8,2,7,1,5,3,6]=>0101010=>1010101
[5,8,7,2,1,4,3,6]=>0111010=>1000101
[6,8,7,1,2,4,3,5]=>0110010=>1001101
[7,8,6,1,4,2,3,5]=>0110100=>1001011
[8,7,6,1,4,3,2,5]=>1110110=>0001001
[1,7,6,8,4,3,5,2]=>0101101=>1010010
[1,6,7,8,3,4,5,2]=>0001001=>1110110
[8,6,7,1,3,4,2,5]=>1010010=>0101101
[7,6,8,1,3,2,4,5]=>1010100=>0101011
[5,7,8,2,1,3,4,6]=>0011000=>1100111
[4,7,2,8,1,3,5,6]=>0101000=>1010111
[3,2,6,8,4,1,5,7]=>1001100=>0110011
[4,6,2,8,3,1,5,7]=>0101100=>1010011
[5,6,8,2,3,1,4,7]=>0010100=>1101011
[6,5,8,3,2,1,4,7]=>1011100=>0100011
[7,5,8,3,1,2,4,6]=>1011000=>0100111
[8,5,7,3,1,4,2,6]=>1011010=>0100101
[1,5,7,3,8,4,6,2]=>0010101=>1101010
[1,4,3,7,8,5,6,2]=>0100101=>1011010
[8,4,3,7,1,5,2,6]=>1101010=>0010101
[6,4,3,8,2,1,5,7]=>1101100=>0010011
[4,5,2,3,8,1,6,7]=>0100100=>1011011
[3,2,5,4,8,1,6,7]=>1010100=>0101011
[4,5,2,3,1,8,7,6]=>0101011=>1010100
[6,4,3,1,2,8,7,5]=>1110011=>0001100
[7,4,3,1,8,2,6,5]=>1110101=>0001010
[8,4,3,1,7,6,2,5]=>1110110=>0001001
[1,5,8,3,7,6,4,2]=>0010111=>1101000
[8,5,1,3,7,6,2,4]=>1100110=>0011001
[7,5,1,3,8,2,6,4]=>1100101=>0011010
[6,5,1,3,2,8,7,4]=>1101011=>0010100
[5,6,1,2,3,8,7,4]=>0100011=>1011100
[4,6,2,1,3,8,7,5]=>0110011=>1001100
[3,2,6,1,4,8,7,5]=>1010011=>0101100
[3,2,7,1,8,4,6,5]=>1010101=>0101010
[4,7,2,1,8,3,6,5]=>0110101=>1001010
[5,7,1,2,8,3,6,4]=>0100101=>1011010
[6,7,1,8,2,3,5,4]=>0101001=>1010110
[7,6,1,8,3,2,5,4]=>1101101=>0010010
[8,6,1,7,3,5,2,4]=>1101010=>0010101
[1,6,8,7,3,5,4,2]=>0011011=>1100100
[1,7,8,6,5,3,4,2]=>0011101=>1100010
[8,7,1,6,5,3,2,4]=>1101110=>0010001
[7,8,1,6,5,2,3,4]=>0101100=>1010011
[6,8,1,7,2,5,3,4]=>0101010=>1010101
[5,8,1,2,7,6,3,4]=>0100110=>1011001
[4,8,2,1,7,6,3,5]=>0110110=>1001001
[3,2,8,1,7,6,4,5]=>1010110=>0101001
[4,1,2,8,7,6,5,3]=>1001111=>0110000
[5,1,8,2,7,6,4,3]=>1010111=>0101000
[6,1,8,7,2,5,4,3]=>1011011=>0100100
[7,1,8,6,5,2,4,3]=>1011101=>0100010
[8,1,7,6,5,4,2,3]=>1011110=>0100001
[3,1,2,6,5,8,7,4]=>1001011=>0110100
[3,1,6,2,4,8,7,5]=>1010011=>0101100
[3,1,5,2,4,8,7,6]=>1010011=>0101100
[4,5,1,2,3,8,7,6]=>0100011=>1011100
[4,6,1,2,3,8,7,5]=>0100011=>1011100
[1,6,5,3,4,8,7,2]=>0110011=>1001100
[6,1,5,2,4,8,7,3]=>1010011=>0101100
[6,5,1,2,3,8,7,4]=>1100011=>0011100
[6,4,1,2,3,8,7,5]=>1100011=>0011100
[5,4,1,2,3,8,7,6]=>1100011=>0011100
[5,4,1,2,7,3,6,8]=>1100100=>0011011
[6,4,1,7,2,3,5,8]=>1101000=>0010111
[6,4,1,8,2,3,5,7]=>1101000=>0010111
[7,4,1,2,8,3,6,5]=>1100101=>0011010
[7,5,1,2,8,3,6,4]=>1100101=>0011010
[7,1,5,2,8,4,6,3]=>1010101=>0101010
[1,7,5,3,8,4,6,2]=>0110101=>1001010
[1,8,5,3,7,4,6,2]=>0110101=>1001010
[8,1,5,2,7,4,6,3]=>1010101=>0101010
[8,5,1,2,7,3,6,4]=>1100101=>0011010
[8,4,1,2,7,3,6,5]=>1100101=>0011010
[8,4,1,7,2,3,5,6]=>1101000=>0010111
[7,4,1,6,2,3,5,8]=>1101000=>0010111
[8,6,1,7,2,3,5,4]=>1101001=>0010110
[8,1,6,7,2,4,5,3]=>1001001=>0110110
[1,8,6,7,3,4,5,2]=>0101001=>1010110
[1,7,6,8,3,4,5,2]=>0101001=>1010110
[7,1,6,8,2,4,5,3]=>1001001=>0110110
[7,6,1,8,2,3,5,4]=>1101001=>0010110
[4,7,1,2,8,3,6,5]=>0100101=>1011010
[3,1,7,2,8,4,6,5]=>1010101=>0101010
[3,1,2,7,8,5,6,4]=>1000101=>0111010
[1,4,3,8,7,5,6,2]=>0101101=>1010010
[4,1,2,8,7,5,6,3]=>1001101=>0110010
[3,1,2,8,7,5,6,4]=>1001101=>0110010
[3,1,8,2,7,4,6,5]=>1010101=>0101010
[3,1,8,7,2,4,5,6]=>1011000=>0100111
[3,1,7,6,2,4,5,8]=>1011000=>0100111
[4,7,1,6,2,3,5,8]=>0101000=>1010111
[4,8,1,6,2,3,5,7]=>0101000=>1010111
[4,8,1,7,2,3,5,6]=>0101000=>1010111
[4,8,1,2,7,3,6,5]=>0100101=>1011010
[5,8,1,2,7,3,6,4]=>0100101=>1011010
[5,1,8,2,7,4,6,3]=>1010101=>0101010
[1,5,8,3,7,4,6,2]=>0010101=>1101010
[1,6,8,7,3,4,5,2]=>0011001=>1100110
[6,1,8,7,2,4,5,3]=>1011001=>0100110
[6,8,1,7,2,3,5,4]=>0101001=>1010110
[6,8,7,1,2,3,4,5]=>0110000=>1001111
[5,8,7,1,2,3,4,6]=>0110000=>1001111
[5,8,6,1,2,3,4,7]=>0110000=>1001111
[5,7,6,1,2,3,4,8]=>0110000=>1001111
[7,8,1,6,2,3,5,4]=>0101001=>1010110
[7,1,8,6,2,4,5,3]=>1011001=>0100110
[1,7,8,6,3,4,5,2]=>0011001=>1100110
[1,8,7,6,3,4,5,2]=>0111001=>1000110
[8,1,7,6,2,4,5,3]=>1011001=>0100110
[8,7,1,6,2,3,5,4]=>1101001=>0010110
[3,2,5,1,6,4,8,7]=>1010101=>0101010
[3,2,5,4,7,1,8,6]=>1010101=>0101010
[4,2,5,3,7,6,8,1]=>1010101=>0101010
[4,2,5,3,7,1,8,6]=>1010101=>0101010
[4,2,5,3,6,1,8,7]=>1010101=>0101010
[4,2,5,1,6,3,8,7]=>1010101=>0101010
[3,1,5,4,6,2,8,7]=>1010101=>0101010
[4,1,5,3,6,2,8,7]=>1010101=>0101010
[4,3,5,1,6,2,8,7]=>1010101=>0101010
[4,3,5,2,7,1,8,6]=>1010101=>0101010
[4,3,6,2,7,5,8,1]=>1010101=>0101010
[4,3,6,2,7,1,8,5]=>1010101=>0101010
[4,3,6,1,7,2,8,5]=>1010101=>0101010
[4,3,5,1,7,2,8,6]=>1010101=>0101010
[3,1,5,4,7,2,8,6]=>1010101=>0101010
[2,1,5,4,7,3,8,6]=>1010101=>0101010
[3,1,5,4,7,6,8,2]=>1010101=>0101010
[4,1,5,3,7,6,8,2]=>1010101=>0101010
[4,3,5,1,7,6,8,2]=>1010101=>0101010
[4,3,6,1,7,5,8,2]=>1010101=>0101010
[4,3,6,5,7,1,8,2]=>1010101=>0101010
[5,3,6,4,7,2,8,1]=>1010101=>0101010
[5,3,6,4,7,1,8,2]=>1010101=>0101010
[5,3,6,1,7,4,8,2]=>1010101=>0101010
[5,1,6,3,7,4,8,2]=>1010101=>0101010
[4,1,6,3,7,5,8,2]=>1010101=>0101010
[3,1,6,4,7,5,8,2]=>1010101=>0101010
[2,1,6,4,7,5,8,3]=>1010101=>0101010
[2,1,6,4,7,3,8,5]=>1010101=>0101010
[3,1,6,4,7,2,8,5]=>1010101=>0101010
[4,1,6,3,7,2,8,5]=>1010101=>0101010
[5,1,6,3,7,2,8,4]=>1010101=>0101010
[5,3,6,1,7,2,8,4]=>1010101=>0101010
[5,3,6,2,7,1,8,4]=>1010101=>0101010
[5,3,6,2,7,4,8,1]=>1010101=>0101010
[5,2,6,3,7,4,8,1]=>1010101=>0101010
[5,2,6,3,7,1,8,4]=>1010101=>0101010
[5,2,6,1,7,3,8,4]=>1010101=>0101010
[4,2,5,1,7,3,8,6]=>1010101=>0101010
[4,2,6,1,7,3,8,5]=>1010101=>0101010
[4,2,6,3,7,1,8,5]=>1010101=>0101010
[4,2,6,3,7,5,8,1]=>1010101=>0101010
[3,2,6,4,7,5,8,1]=>1010101=>0101010
[3,2,6,4,7,1,8,5]=>1010101=>0101010
[3,2,6,1,7,4,8,5]=>1010101=>0101010
[3,2,5,1,7,4,8,6]=>1010101=>0101010
[3,2,4,1,7,5,8,6]=>1010101=>0101010
[3,1,4,2,7,6,8,5]=>1010101=>0101010
[3,2,5,1,7,6,8,4]=>1010101=>0101010
[3,2,6,1,7,5,8,4]=>1010101=>0101010
[3,2,6,5,7,1,8,4]=>1010101=>0101010
[4,2,6,5,7,3,8,1]=>1010101=>0101010
[4,2,6,5,7,1,8,3]=>1010101=>0101010
[4,2,6,1,7,5,8,3]=>1010101=>0101010
[4,2,5,1,7,6,8,3]=>1010101=>0101010
[4,1,5,2,7,6,8,3]=>1010101=>0101010
[3,1,5,2,7,6,8,4]=>1010101=>0101010
[2,1,5,3,7,6,8,4]=>1010101=>0101010
[2,1,6,3,7,5,8,4]=>1010101=>0101010
[3,1,6,2,7,5,8,4]=>1010101=>0101010
[4,1,6,2,7,5,8,3]=>1010101=>0101010
[5,1,6,2,7,4,8,3]=>1010101=>0101010
[5,2,6,1,7,4,8,3]=>1010101=>0101010
[5,2,6,4,7,1,8,3]=>1010101=>0101010
[5,2,6,4,7,3,8,1]=>1010101=>0101010
[5,4,6,2,7,3,8,1]=>1010101=>0101010
[5,4,6,2,7,1,8,3]=>1010101=>0101010
[5,4,6,1,7,2,8,3]=>1010101=>0101010
[5,1,6,4,7,2,8,3]=>1010101=>0101010
[4,1,6,5,7,2,8,3]=>1010101=>0101010
[3,1,6,5,7,2,8,4]=>1010101=>0101010
[2,1,6,5,7,3,8,4]=>1010101=>0101010
[3,1,6,5,7,4,8,2]=>1010101=>0101010
[4,1,6,5,7,3,8,2]=>1010101=>0101010
[5,1,6,4,7,3,8,2]=>1010101=>0101010
[5,4,6,1,7,3,8,2]=>1010101=>0101010
[5,4,6,3,7,1,8,2]=>1010101=>0101010
[8,3,5,2,1,6,4,7]=>1011010=>0100101
[8,6,3,5,2,4,1,7]=>1101010=>0010101
[3,7,5,2,4,1,8,6]=>0110101=>1001010
[8,3,7,5,2,4,6,1]=>1011001=>0100110
[8,2,4,5,7,3,6,1]=>1000101=>0111010
[2,4,5,7,3,1,8,6]=>0001101=>1110010
[8,2,4,6,5,3,1,7]=>1001110=>0110001
[8,2,5,4,6,1,3,7]=>1010100=>0101011
[8,6,3,5,1,4,2,7]=>1101010=>0010101
[8,6,1,4,5,3,2,7]=>1100110=>0011001
[8,1,5,6,4,3,2,7]=>1001110=>0110001
[5,7,4,3,2,1,8,6]=>0111101=>1000010
[8,5,7,4,3,2,6,1]=>1011101=>0100010
[4,6,8,3,2,7,5,1]=>0011011=>1100100
[4,7,6,3,2,8,1,5]=>0111010=>1000101
[1,4,6,7,3,2,8,5]=>0001101=>1110010
[5,4,7,3,1,8,2,6]=>1011010=>0100101
[1,7,4,5,3,2,8,6]=>0101101=>1010010
[3,7,5,1,4,2,8,6]=>0110101=>1001010
[5,7,4,2,1,3,8,6]=>0111001=>1000110
[8,5,7,4,2,1,6,3]=>1011101=>0100010
[8,3,7,5,1,4,6,2]=>1011001=>0100110
[8,4,1,7,5,3,6,2]=>1101101=>0010010
[4,6,3,8,7,1,5,2]=>0101101=>1010010
[1,7,4,8,6,3,5,2]=>0101101=>1010010
[8,4,7,6,3,5,2,1]=>1011011=>0100100
[3,6,5,8,7,4,1,2]=>0101110=>1010001
[3,1,5,8,6,7,4,2]=>1001011=>0110100
[4,8,1,6,7,3,5,2]=>0100101=>1011010
[3,6,4,1,8,7,5,2]=>0110111=>1001000
[8,2,6,1,4,7,5,3]=>1010011=>0101100
[2,7,6,8,1,4,3,5]=>0101010=>1010101
[3,7,1,6,4,8,2,5]=>0101010=>1010101
[1,7,3,5,6,8,2,4]=>0100010=>1011101
[1,3,6,7,5,8,2,4]=>0001010=>1110101
[3,7,6,5,8,2,1,4]=>0110110=>1001001
[3,6,8,5,7,2,4,1]=>0010101=>1101010
[2,3,5,7,6,8,1,4]=>0001010=>1110101
[2,1,6,5,7,8,3,4]=>1010010=>0101101
[4,2,7,6,8,3,1,5]=>1010110=>0101001
[4,2,6,8,7,3,5,1]=>1001101=>0110010
[3,8,2,4,6,7,5,1]=>0100011=>1011100
[3,7,2,6,4,8,1,5]=>0101010=>1010101
[3,2,6,1,4,7,8,5]=>1010001=>0101110
[5,3,7,2,1,8,4,6]=>1011010=>0100101
[4,7,3,2,1,5,8,6]=>0111001=>1000110
[8,7,6,1,3,4,2,5]=>1110010=>0001101
[8,5,7,3,2,1,6,4]=>1011101=>0100010
[8,3,6,7,2,1,5,4]=>1001101=>0110010
[3,7,8,6,2,1,5,4]=>0011101=>1100010
[8,7,6,3,5,2,4,1]=>1110101=>0001010
[2,7,4,8,1,6,5,3]=>0101011=>1010100
[4,6,8,2,1,7,5,3]=>0011011=>1100100
[8,4,1,5,7,2,6,3]=>1100101=>0011010
[8,5,3,7,1,6,2,4]=>1101010=>0010101
[8,5,7,2,1,3,6,4]=>1011001=>0100110
[8,2,6,7,1,3,5,4]=>1001001=>0110110
[8,3,6,1,7,5,2,4]=>1010110=>0101001
[4,6,1,8,7,2,5,3]=>0101101=>1010010
[8,1,2,5,6,7,4,3]=>1000011=>0111100
[8,2,6,5,7,4,1,3]=>1010110=>0101001
[2,1,7,8,5,6,4,3]=>1001011=>0110100
[8,2,5,7,6,4,3,1]=>1001111=>0110000
[2,7,6,8,5,4,1,3]=>0101110=>1010001
[1,7,2,5,8,6,4,3]=>0100111=>1011000
[1,7,4,8,2,6,5,3]=>0101011=>1010100
[3,7,8,1,6,5,2,4]=>0010110=>1101001
[2,7,8,6,1,3,5,4]=>0011001=>1100110
[8,7,6,3,5,1,4,2]=>1110101=>0001010
[8,4,7,6,5,1,3,2]=>1011101=>0100010
[8,7,1,5,6,4,3,2]=>1100111=>0011000
[8,1,6,7,5,4,3,2]=>1001111=>0110000
[6,5,3,1,2,4,8,7]=>1110001=>0001110
[4,6,3,5,1,2,8,7]=>0101001=>1010110
[8,5,3,7,2,1,4,6]=>1101100=>0010011
[6,8,1,4,5,7,3,2]=>0100011=>1011100
[8,7,2,4,5,1,3,6]=>1100100=>0011011
[3,6,2,4,5,1,8,7]=>0100101=>1011010
[2,6,1,4,5,3,8,7]=>0100101=>1011010
[6,1,2,4,5,3,8,7]=>1000101=>0111010
[5,6,3,2,1,4,8,7]=>0111001=>1000110
[5,4,3,6,1,2,8,7]=>1101001=>0010110
[6,3,1,4,5,2,8,7]=>1100101=>0011010
[3,1,6,4,5,2,8,7]=>1010101=>0101010
[8,3,7,4,5,1,2,6]=>1010100=>0101011
[5,8,7,4,2,6,3,1]=>0111011=>1000100
[2,8,7,4,1,6,3,5]=>0111010=>1000101
[8,1,7,4,2,6,3,5]=>1011010=>0100101
[3,7,8,4,5,1,2,6]=>0010100=>1101011
[2,1,8,7,5,3,4,6]=>1011100=>0100011
[2,1,6,8,5,7,3,4]=>1001010=>0110101
[5,6,3,8,1,7,2,4]=>0101010=>1010101
[7,6,1,4,5,8,3,2]=>1100011=>0011100
[3,7,6,4,5,8,2,1]=>0110011=>1001100
[8,5,7,4,1,6,3,2]=>1011011=>0100100
[5,1,8,4,7,6,2,3]=>1010110=>0101001
[2,5,8,4,7,6,1,3]=>0010110=>1101001
[2,4,8,3,5,6,7,1]=>0010001=>1101110
[4,1,8,3,5,6,7,2]=>1010001=>0101110
[3,8,4,2,5,6,7,1]=>0110001=>1001110
[8,4,1,3,5,6,7,2]=>1100001=>0011110
[7,5,8,4,3,6,1,2]=>1011010=>0100101
[6,5,3,8,4,1,7,2]=>1101101=>0010010
[2,1,5,8,4,6,7,3]=>1001001=>0110110
[2,1,4,8,3,6,7,5]=>1001001=>0110110
[6,4,3,8,2,1,7,5]=>1101101=>0010010
[7,3,8,4,2,6,1,5]=>1011010=>0100101
[8,3,1,2,5,6,7,4]=>1100001=>0011110
[3,1,8,2,5,6,7,4]=>1010001=>0101110
[2,3,8,1,5,6,7,4]=>0010001=>1101110
[4,3,8,2,5,6,7,1]=>1010001=>0101110
[4,8,2,3,5,6,7,1]=>0100001=>1011110
[3,8,2,1,5,6,7,4]=>0110001=>1001110
[2,8,1,3,5,6,7,4]=>0100001=>1011110
[8,1,2,3,5,6,7,4]=>1000001=>0111110
[7,8,2,4,3,6,1,5]=>0101010=>1010101
[6,8,3,2,4,1,7,5]=>0110101=>1001010
[2,1,8,3,4,6,7,5]=>1010001=>0101110
[2,1,7,8,5,4,3,6]=>1001110=>0110001
[5,7,3,8,1,4,2,6]=>0101010=>1010101
[7,1,8,4,5,3,2,6]=>1010110=>0101001
[2,7,8,4,5,3,1,6]=>0010110=>1101001
[8,7,1,4,3,6,2,5]=>1101010=>0010101
[3,8,7,4,2,6,1,5]=>0111010=>1000101
[5,7,8,4,3,6,2,1]=>0011011=>1100100
[5,6,3,8,4,2,7,1]=>0101101=>1010010
[4,8,3,6,2,1,7,5]=>0101101=>1010010
[8,6,3,1,4,2,7,5]=>1110101=>0001010
[7,5,3,8,2,4,1,6]=>1101010=>0010101
[2,4,3,1,8,5,7,6]=>0110101=>1001010
[4,1,3,2,6,8,7,5]=>1010011=>0101100
[7,5,3,6,2,8,1,4]=>1101010=>0010101
[8,6,3,5,1,2,7,4]=>1101001=>0010110
[5,8,3,2,6,1,7,4]=>0110101=>1001010
[4,5,3,8,6,2,7,1]=>0101101=>1010010
[3,5,8,4,7,6,2,1]=>0010111=>1101000
[5,8,2,4,7,6,1,3]=>0100110=>1011001
[8,7,5,4,1,6,2,3]=>1111010=>0000101
[2,7,6,4,5,8,1,3]=>0110010=>1001101
[7,1,6,4,5,8,2,3]=>1010010=>0101101
[5,7,3,6,1,8,2,4]=>0101010=>1010101
[2,1,7,6,5,8,3,4]=>1011010=>0100101
[2,1,8,5,3,6,7,4]=>1011001=>0100110
[6,8,3,5,2,1,7,4]=>0101101=>1010010
[7,8,5,4,2,6,1,3]=>0111010=>1000101
[8,1,4,2,5,6,7,3]=>1010001=>0101110
[2,8,4,1,5,6,7,3]=>0110001=>1001110
[4,8,1,2,5,6,7,3]=>0100001=>1011110
[3,4,8,1,5,6,7,2]=>0010001=>1101110
[3,4,2,8,5,6,7,1]=>0101001=>1010110
[2,4,1,8,5,6,7,3]=>0101001=>1010110
[4,1,2,8,5,6,7,3]=>1001001=>0110110
[8,4,2,1,5,6,7,3]=>1110001=>0001110
[7,5,2,4,8,6,1,3]=>1100110=>0011001
[6,5,3,2,8,1,7,4]=>1110101=>0001010
[2,1,5,3,8,6,7,4]=>1010101=>0101010
[6,4,3,5,8,1,7,2]=>1100101=>0011010
[7,3,5,4,8,6,1,2]=>1010110=>0101001
[8,3,4,1,5,6,7,2]=>1010001=>0101110
[4,3,1,8,5,6,7,2]=>1101001=>0010110
[3,1,4,8,5,6,7,2]=>1001001=>0110110
[6,5,3,7,2,8,4,1]=>1101011=>0010100
[6,3,7,4,5,8,2,1]=>1010011=>0101100
[6,7,2,4,5,8,3,1]=>0100011=>1011100
[5,1,7,4,8,6,3,2]=>1010111=>0101000
[2,5,7,4,8,6,3,1]=>0010111=>1101000
[5,6,3,7,1,8,4,2]=>0101011=>1010100
[3,8,7,4,5,2,1,6]=>0110110=>1001001
[3,7,5,4,8,6,2,1]=>0110111=>1001000
[5,7,1,4,8,6,2,3]=>0100110=>1011001
[5,6,3,1,8,2,7,4]=>0110101=>1001010
[4,6,3,5,8,2,7,1]=>0100101=>1011010
[4,6,3,8,1,2,7,5]=>0101001=>1010110
[3,7,8,4,1,6,2,5]=>0011010=>1100101
[3,2,5,1,6,8,4,7]=>1010010=>0101101
[3,6,2,5,4,8,1,7]=>0101010=>1010101
[3,5,2,4,7,1,8,6]=>0100101=>1011010
[3,5,8,2,4,7,6,1]=>0010011=>1101100
[4,2,5,8,3,7,6,1]=>1001011=>0110100
[4,2,6,5,3,8,1,7]=>1011010=>0100101
[5,4,2,1,6,8,3,7]=>1110010=>0001101
[6,3,5,1,4,8,2,7]=>1010010=>0101101
[4,6,1,5,3,8,2,7]=>0101010=>1010101
[5,1,6,4,3,8,2,7]=>1011010=>0100101
[5,4,3,2,7,1,8,6]=>1110101=>0001010
[5,4,3,8,2,7,6,1]=>1101011=>0010100
[4,3,6,2,8,7,5,1]=>1010111=>0101000
[4,3,7,6,2,1,8,5]=>1011101=>0100010
[6,4,3,1,7,2,8,5]=>1110101=>0001010
[7,5,4,3,1,8,2,6]=>1111010=>0000101
[1,4,7,5,8,3,2,6]=>0010110=>1101001
[7,1,3,5,8,4,2,6]=>1000110=>0111001
[7,2,5,8,4,1,3,6]=>1001100=>0110011
[2,8,5,7,4,6,1,3]=>0101010=>1010101
[3,5,8,7,1,4,6,2]=>0011001=>1100110
[1,4,5,8,7,3,6,2]=>0001101=>1110010
[1,5,4,8,7,3,6,2]=>0101101=>1010010
[6,4,3,8,1,7,5,2]=>1101011=>0010100
[4,3,7,1,8,6,5,2]=>1010111=>0101000
[4,8,3,7,6,5,2,1]=>0101111=>1010000
[5,3,8,7,6,4,2,1]=>1011111=>0100000
[7,5,3,1,8,6,4,2]=>1110111=>0001000
[1,8,6,5,3,7,4,2]=>0111011=>1000100
[1,5,8,6,3,7,4,2]=>0011011=>1100100
[4,6,1,8,7,3,5,2]=>0101101=>1010010
[6,8,7,3,1,4,5,2]=>0111001=>1000110
[6,2,8,7,4,5,1,3]=>1011010=>0100101
[7,6,2,8,4,1,3,5]=>1101100=>0010011
[7,3,1,6,8,4,2,5]=>1100110=>0011001
[1,7,6,4,8,3,2,5]=>0110110=>1001001
[5,7,1,6,3,2,8,4]=>0101101=>1010010
[6,1,7,5,3,2,8,4]=>1011101=>0100010
[7,6,5,3,2,1,8,4]=>1111101=>0000010
[6,5,3,2,8,7,4,1]=>1110111=>0001000
[5,2,6,3,8,7,4,1]=>1010111=>0101000
[5,2,7,6,3,1,8,4]=>1011101=>0100010
[6,5,2,1,7,3,8,4]=>1110101=>0001010
[5,2,7,4,1,8,3,6]=>1011010=>0100101
[4,7,2,6,3,1,8,5]=>0101101=>1010010
[2,4,8,6,3,7,5,1]=>0011011=>1100100
[3,8,6,2,4,7,5,1]=>0110011=>1001100
[7,3,6,2,4,1,8,5]=>1010101=>0101010
[3,6,7,2,1,4,8,5]=>0011001=>1100110
[4,3,7,8,2,1,5,6]=>1001100=>0110011
[8,3,7,1,4,6,2,5]=>1010010=>0101101
[3,8,2,5,7,1,6,4]=>0100101=>1011010
[8,3,6,2,7,1,5,4]=>1010101=>0101010
[7,8,3,6,2,1,5,4]=>0101101=>1010010
[8,7,3,6,2,5,4,1]=>1101011=>0010100
[4,7,8,2,1,6,5,3]=>0011011=>1100100
[4,2,6,8,1,7,5,3]=>1001011=>0110100
[5,4,8,2,7,1,6,3]=>1010101=>0101010
[4,8,1,5,7,2,6,3]=>0100101=>1011010
[5,8,3,7,1,6,2,4]=>0101010=>1010101
[5,8,7,2,6,1,3,4]=>0110100=>1001011
[8,6,2,7,5,1,3,4]=>1101100=>0010011
[3,6,8,1,7,5,2,4]=>0010110=>1101001
[5,1,6,8,2,7,4,3]=>1001011=>0110100
[6,5,2,8,1,7,4,3]=>1101011=>0010100
[5,2,7,1,8,6,4,3]=>1010111=>0101000
[5,8,2,7,6,4,3,1]=>0101111=>1010000
[6,2,8,7,5,4,3,1]=>1011111=>0100000
[7,6,2,1,8,5,4,3]=>1110111=>0001000
[6,1,7,2,8,5,4,3]=>1010111=>0101000
[7,5,1,8,2,6,4,3]=>1101011=>0010100
[4,7,1,8,6,2,5,3]=>0101101=>1010010
[7,8,3,1,6,5,2,4]=>0110110=>1001001
[8,7,4,6,1,5,3,2]=>1101011=>0010100
[8,5,7,1,6,4,3,2]=>1010111=>0101000
[6,8,1,7,5,4,3,2]=>0101111=>1010000
[7,1,8,6,5,4,3,2]=>1011111=>0100000
[5,4,2,3,7,6,1,8]=>1100110=>0011001
[6,4,2,7,3,5,1,8]=>1101010=>0010101
[7,4,2,6,3,5,1,8]=>1101010=>0010101
[8,4,2,6,3,1,5,7]=>1101100=>0010011
[3,2,7,6,4,5,1,8]=>1011010=>0100101
[4,7,2,6,3,5,1,8]=>0101010=>1010101
[5,7,6,2,3,4,1,8]=>0110010=>1001101
[1,6,5,2,3,8,4,7]=>0110010=>1001101
[1,7,5,2,8,3,4,6]=>0110100=>1001011
[6,8,5,2,3,1,4,7]=>0110100=>1001011
[5,8,6,2,3,1,4,7]=>0110100=>1001011
[4,8,2,6,3,1,5,7]=>0101100=>1010011
[3,2,8,6,4,1,5,7]=>1011100=>0100011
[3,2,1,6,4,8,5,7]=>1101010=>0010101
[7,1,5,2,8,3,4,6]=>1010100=>0101011
[1,8,5,2,7,3,4,6]=>0110100=>1001011
[1,8,6,7,2,3,4,5]=>0101000=>1010111
[8,1,6,7,2,3,4,5]=>1001000=>0110111
[7,1,6,8,2,3,4,5]=>1001000=>0110111
[3,2,1,7,8,4,5,6]=>1100100=>0011011
[3,2,8,7,1,4,5,6]=>1011000=>0100111
[5,8,7,2,1,3,4,6]=>0111000=>1000111
[1,7,6,8,2,3,4,5]=>0101000=>1010111
[6,5,8,2,3,1,4,7]=>1010100=>0101011
[8,5,7,2,1,3,4,6]=>1011000=>0100111
[6,4,2,8,3,1,5,7]=>1101100=>0010011
[5,4,2,3,8,1,6,7]=>1100100=>0011011
[3,2,5,4,1,8,6,7]=>1011010=>0100101
[4,5,2,3,1,8,6,7]=>0101010=>1010101
[5,4,2,3,1,8,6,7]=>1101010=>0010101
[6,4,2,1,3,8,5,7]=>1110010=>0001101
[7,4,2,1,8,3,5,6]=>1110100=>0001011
[8,4,2,1,7,3,5,6]=>1110100=>0001011
[1,4,2,8,7,3,5,6]=>0101100=>1010011
[1,5,8,2,7,3,4,6]=>0010100=>1101011
[8,5,1,2,7,3,4,6]=>1100100=>0011011
[7,5,1,2,8,3,4,6]=>1100100=>0011011
[6,5,1,2,3,8,4,7]=>1100010=>0011101
[4,6,2,1,3,8,5,7]=>0110010=>1001101
[3,2,6,1,4,8,5,7]=>1010010=>0101101
[3,2,7,1,8,4,5,6]=>1010100=>0101011
[4,7,2,1,8,3,5,6]=>0110100=>1001011
[7,6,1,8,2,3,4,5]=>1101000=>0010111
[8,6,1,7,2,3,4,5]=>1101000=>0010111
[1,6,8,7,2,3,4,5]=>0011000=>1100111
[1,7,8,6,2,3,4,5]=>0011000=>1100111
[7,8,1,6,2,3,4,5]=>0101000=>1010111
[6,8,1,7,2,3,4,5]=>0101000=>1010111
[4,8,2,1,7,3,5,6]=>0110100=>1001011
[3,2,8,1,7,4,5,6]=>1010100=>0101011
[3,2,1,8,7,4,5,6]=>1101100=>0010011
[5,1,8,2,7,3,4,6]=>1010100=>0101011
[6,1,8,7,2,3,4,5]=>1011000=>0100111
[8,1,7,6,2,3,4,5]=>1011000=>0100111
[1,8,7,6,2,3,4,5]=>0111000=>1000111
[6,3,5,1,2,4,8,7]=>1010001=>0101110
[4,3,5,6,1,2,8,7]=>1001001=>0110110
[8,3,7,5,2,1,4,6]=>1011100=>0100011
[6,3,7,5,1,8,4,2]=>1011011=>0100100
[6,5,2,7,1,8,3,4]=>1101010=>0010101
[8,5,2,7,4,1,3,6]=>1101100=>0010011
[2,6,1,5,4,3,8,7]=>0101101=>1010010
[6,4,3,5,1,2,8,7]=>1101001=>0010110
[5,3,1,4,6,2,8,7]=>1100101=>0011010
[3,1,4,6,5,2,8,7]=>1001101=>0110010
[5,7,4,6,2,8,3,1]=>0101011=>1010100
[8,1,4,7,2,6,3,5]=>1001010=>0110101
[3,4,7,8,5,2,1,6]=>0001110=>1110001
[2,1,8,5,7,3,4,6]=>1010100=>0101011
[8,6,3,5,1,7,4,2]=>1101011=>0010100
[5,8,2,4,6,7,3,1]=>0100011=>1011100
[3,4,8,6,5,7,1,2]=>0011010=>1100101
[7,5,4,8,1,6,3,2]=>1101011=>0010100
[5,1,4,6,8,2,7,3]=>1000101=>0111010
[2,5,4,6,7,1,8,3]=>0100101=>1011010
[2,4,6,3,7,5,8,1]=>0010101=>1101010
[4,1,6,3,8,5,7,2]=>1010101=>0101010
[3,7,4,2,8,6,5,1]=>0110111=>1001000
[7,4,1,3,5,8,6,2]=>1100011=>0011100
[6,5,8,4,1,7,3,2]=>1011011=>0100100
[8,5,3,7,4,1,6,2]=>1101101=>0010010
[2,1,4,8,3,7,6,5]=>1001011=>0110100
[7,4,3,8,2,1,6,5]=>1101101=>0010010
[6,3,7,4,1,8,2,5]=>1011010=>0100101
[8,3,1,2,5,7,6,4]=>1100011=>0011100
[3,1,8,2,7,6,5,4]=>1010111=>0101000
[2,3,8,1,6,7,5,4]=>0010011=>1101100
[4,3,7,2,6,8,5,1]=>1010011=>0101100
[4,7,2,3,8,5,6,1]=>0100101=>1011010
[3,8,2,1,7,5,6,4]=>0110101=>1001010
[2,8,1,3,6,5,7,4]=>0100101=>1011010
[2,7,8,5,4,3,1,6]=>0011110=>1100001
[8,7,1,6,3,4,2,5]=>1101010=>0010101
[3,8,6,7,2,4,1,5]=>0101010=>1010101
[5,3,8,7,4,2,6,1]=>1011101=>0100010
[4,3,8,7,2,1,6,5]=>1011101=>0100010
[8,3,6,1,4,2,7,5]=>1010101=>0101010
[7,3,5,8,2,4,1,6]=>1001010=>0110101
[2,3,4,1,8,5,7,6]=>0010101=>1101010
[4,1,3,2,6,7,8,5]=>1010001=>0101110
[8,3,5,6,2,7,1,4]=>1001010=>0110101
[5,3,6,1,8,7,2,4]=>1010110=>0101001
[5,6,2,8,7,4,1,3]=>0101110=>1010001
[7,8,5,6,1,4,2,3]=>0101010=>1010101
[2,8,6,5,4,7,1,3]=>0111010=>1000101
[8,1,6,4,5,7,2,3]=>1010010=>0101101
[5,8,3,6,1,7,2,4]=>0101010=>1010101
[2,1,8,6,5,7,3,4]=>1011010=>0100101
[2,1,7,5,3,6,8,4]=>1011001=>0100110
[6,7,3,5,2,1,8,4]=>0101101=>1010010
[7,1,4,2,5,6,8,3]=>1010001=>0101110
[2,7,4,1,6,5,8,3]=>0110101=>1001010
[4,6,1,2,8,7,3,5]=>0100110=>1011001
[2,4,1,5,8,7,6,3]=>0100111=>1011000
[4,1,2,5,8,6,7,3]=>1000101=>0111010
[6,4,2,1,5,8,7,3]=>1110011=>0001100
[8,5,2,4,6,1,7,3]=>1100101=>0011010
[7,5,3,2,6,8,1,4]=>1110010=>0001101
[2,1,5,3,6,8,7,4]=>1010011=>0101100
[7,3,5,4,6,1,8,2]=>1010101=>0101010
[6,3,4,1,5,7,8,2]=>1010001=>0101110
[4,3,1,5,7,6,8,2]=>1100101=>0011010
[3,1,4,5,6,8,7,2]=>1000011=>0111100
[4,5,2,6,3,1,8,7]=>0101101=>1010010
[6,5,2,1,4,3,8,7]=>1110101=>0001010
[6,5,2,7,4,8,3,1]=>1101011=>0010100
[8,5,2,7,4,1,6,3]=>1101101=>0010010
[8,3,7,5,2,1,6,4]=>1011101=>0100010
[6,3,7,5,2,8,4,1]=>1011011=>0100100
[3,1,6,5,4,2,8,7]=>1011101=>0100010
[5,6,3,2,4,1,8,7]=>0110101=>1001010
[3,6,2,4,1,5,8,7]=>0101001=>1010110
[2,6,1,3,5,4,8,7]=>0100101=>1011010
[6,7,2,3,4,8,5,1]=>0100011=>1011100
[8,7,2,3,4,1,6,5]=>1100101=>0011010
[5,1,7,3,8,4,6,2]=>1010101=>0101010
[2,5,7,3,8,6,4,1]=>0010111=>1101000
[7,6,1,3,5,8,4,2]=>1100011=>0011100
[3,6,7,4,1,8,5,2]=>0011011=>1100100
[5,6,3,7,4,8,1,2]=>0101010=>1010101
[2,1,6,7,4,8,5,3]=>1001011=>0110100
[2,1,8,7,4,3,6,5]=>1011101=>0100010
[5,8,3,7,4,2,6,1]=>0101101=>1010010
[3,8,7,4,1,2,6,5]=>0111001=>1000110
[7,8,1,3,5,2,6,4]=>0100101=>1011010
[5,8,7,3,2,6,1,4]=>0111010=>1000101
[2,8,6,3,1,5,7,4]=>0111001=>1000110
[8,1,6,3,2,5,4,7]=>1011010=>0100101
[2,8,4,1,6,3,7,5]=>0110101=>1001010
[4,8,1,2,7,6,3,5]=>0100110=>1011001
[3,8,4,2,5,7,1,6]=>0110010=>1001101
[6,8,3,5,2,7,4,1]=>0101011=>1010100
[2,1,5,3,8,7,6,4]=>1010111=>0101000
[6,5,3,2,8,7,1,4]=>1110110=>0001001
[7,5,2,4,8,1,6,3]=>1100101=>0011010
[3,4,2,8,5,7,6,1]=>0101011=>1010100
[2,4,1,8,7,6,5,3]=>0101111=>1010000
[8,4,2,1,7,5,3,6]=>1110110=>0001001
[4,3,1,8,6,7,5,2]=>1101011=>0010100
[3,1,4,8,6,5,7,2]=>1001101=>0110010
[7,1,6,5,4,8,2,3]=>1011010=>0100101
[3,7,5,6,8,4,2,1]=>0100111=>1011000
[5,7,1,6,8,2,4,3]=>0100101=>1011010
[8,6,2,5,1,7,4,3]=>1101011=>0010100
[5,6,2,1,8,7,3,4]=>0110110=>1001001
[4,6,2,5,8,3,7,1]=>0100101=>1011010
[7,5,2,6,3,8,1,4]=>1101010=>0010101
[4,1,2,3,6,8,7,5]=>1000011=>0111100
[2,4,3,1,8,5,6,7]=>0110100=>1001011
[7,5,2,8,3,4,6,1]=>1101001=>0010110
[5,6,2,8,4,3,1,7]=>0101110=>1010001
[4,7,2,8,1,5,3,6]=>0101010=>1010101
[8,7,2,1,4,5,6,3]=>1110001=>0001110
[3,6,8,7,1,5,4,2]=>0011011=>1100100
[5,7,8,6,3,4,1,2]=>0011010=>1100101
[7,1,8,5,4,3,6,2]=>1011101=>0100010
[2,7,8,4,5,3,6,1]=>0010101=>1101010
[5,7,3,8,1,4,6,2]=>0101001=>1010110
[2,1,7,8,5,4,6,3]=>1001101=>0110010
[2,1,5,8,4,6,3,7]=>1001010=>0110101
[6,5,3,8,4,1,2,7]=>1101100=>0010011
[7,5,8,4,3,6,2,1]=>1011011=>0100100
[2,4,8,3,5,6,1,7]=>0010010=>1101101
[4,1,8,3,6,5,2,7]=>1010110=>0101001
[3,4,8,1,7,2,5,6]=>0010100=>1101011
[8,4,1,3,7,2,6,5]=>1100101=>0011010
[3,1,8,2,4,7,6,5]=>1010011=>0101100
[2,3,8,1,4,6,7,5]=>0010001=>1101110
[4,3,8,2,5,1,7,6]=>1010101=>0101010
[6,3,8,4,2,5,7,1]=>1011001=>0100110
[7,4,3,8,2,5,1,6]=>1101010=>0010101
[2,1,4,8,3,5,7,6]=>1001001=>0110110
[6,8,2,4,3,5,1,7]=>0101010=>1010101
[4,8,2,3,5,1,6,7]=>0100100=>1011011
[3,8,2,1,4,6,5,7]=>0110010=>1001101
[2,8,1,3,4,5,7,6]=>0100001=>1011110
[2,8,4,1,6,5,3,7]=>0110110=>1001001
[2,8,4,1,6,5,7,3]=>0110101=>1001010
[2,8,7,6,1,4,3,5]=>0111010=>1000101
[2,8,5,6,7,4,3,1]=>0100111=>1011000
[7,5,8,6,1,4,2,3]=>1011010=>0100101
[3,5,7,6,1,4,2,8]=>0011010=>1100101
[3,5,7,2,4,1,6,8]=>0010100=>1101011
[7,5,8,2,4,1,6,3]=>1010101=>0101010
[2,8,5,3,4,7,6,1]=>0110011=>1001100
[2,8,5,3,4,1,7,6]=>0110101=>1001010
[2,8,5,3,4,1,6,7]=>0110100=>1001011
[2,8,7,6,1,4,5,3]=>0111001=>1000110
[2,8,5,3,6,1,7,4]=>0110101=>1001010
[2,8,5,6,7,4,1,3]=>0100110=>1011001
[2,8,5,3,4,7,1,6]=>0110010=>1001101
[2,8,5,3,4,6,1,7]=>0110010=>1001101
[2,8,5,3,4,6,7,1]=>0110001=>1001110
[3,5,7,2,4,6,1,8]=>0010010=>1101101
[6,5,2,7,3,1,4,8]=>1101100=>0010011
[6,5,2,8,3,1,7,4]=>1101101=>0010010
[6,5,2,8,3,1,4,7]=>1101100=>0010011
[7,5,8,2,4,6,3,1]=>1010011=>0101100
[7,5,8,6,1,4,3,2]=>1011011=>0100100
[6,5,8,2,1,3,7,4]=>1011001=>0100110
[3,5,6,2,1,8,7,4]=>0011011=>1100100
[3,5,7,6,1,4,8,2]=>0011001=>1100110
[3,5,7,2,4,1,8,6]=>0010101=>1101010
[3,5,7,2,4,6,8,1]=>0010001=>1101110
[6,5,2,7,3,1,8,4]=>1101101=>0010010
[4,5,2,6,3,1,7,8]=>0101100=>1010011
[4,1,2,3,7,6,8,5]=>1000101=>0111010
[6,5,2,7,3,4,8,1]=>1101001=>0010110
[5,1,6,7,4,3,8,2]=>1001101=>0110010
[5,1,2,6,4,8,7,3]=>1001011=>0110100
[5,1,2,8,6,4,7,3]=>1001101=>0110010
[5,1,6,8,7,3,4,2]=>1001101=>0110010
[6,5,2,8,3,7,4,1]=>1101011=>0010100
[4,1,2,3,8,7,5,6]=>1000110=>0111001
[4,1,2,3,8,6,5,7]=>1000110=>0111001
[4,1,2,3,8,6,7,5]=>1000101=>0111010
[4,1,2,3,7,6,5,8]=>1000110=>0111001
[4,1,2,3,8,5,7,6]=>1000101=>0111010
[7,1,6,8,4,3,5,2]=>1001101=>0110010
[6,1,2,8,4,5,7,3]=>1001001=>0110110
[5,6,8,2,3,1,7,4]=>0010101=>1101010
[6,5,8,2,4,3,1,7]=>1010110=>0101001
[6,5,8,2,4,3,7,1]=>1010101=>0101010
[7,5,2,8,3,4,1,6]=>1101010=>0010101
[6,5,2,8,3,7,1,4]=>1101010=>0010101
[6,5,2,7,3,4,1,8]=>1101010=>0010101
[5,1,6,7,4,3,2,8]=>1001110=>0110001
[5,1,6,8,7,3,2,4]=>1001110=>0110001
[7,1,6,8,4,3,2,5]=>1001110=>0110001
[5,7,8,6,3,4,2,1]=>0011011=>1100100
[4,1,8,3,6,5,7,2]=>1010101=>0101010
[4,1,8,3,6,2,7,5]=>1010101=>0101010
[3,1,4,8,6,2,7,5]=>1001101=>0110010
[3,1,4,8,6,5,2,7]=>1001110=>0110001
[7,1,6,5,8,3,2,4]=>1010110=>0101001
[4,1,6,7,8,3,2,5]=>1000110=>0111001
[4,1,6,5,7,3,2,8]=>1010110=>0101001
[4,5,2,6,3,7,1,8]=>0101010=>1010101
[4,5,2,7,3,8,1,6]=>0101010=>1010101
[3,5,6,2,4,8,7,1]=>0010011=>1101100
[3,5,6,2,4,8,1,7]=>0010010=>1101101
[3,7,5,6,8,4,1,2]=>0100110=>1011001
[3,6,5,2,8,1,7,4]=>0110101=>1001010
[6,1,2,5,8,4,7,3]=>1000101=>0111010
[7,1,6,5,8,3,4,2]=>1010101=>0101010
[7,5,2,6,3,8,4,1]=>1101011=>0010100
[4,1,2,3,5,8,7,6]=>1000011=>0111100
[4,1,2,3,7,8,6,5]=>1000011=>0111100
[4,5,2,7,3,8,6,1]=>0101011=>1010100
[4,1,6,7,8,3,5,2]=>1000101=>0111010
[4,1,2,6,8,5,7,3]=>1000101=>0111010
[4,1,2,5,6,8,7,3]=>1000011=>0111100
[4,5,2,6,3,7,8,1]=>0101001=>1010110
[7,8,5,6,1,4,3,2]=>0101011=>1010100
[7,8,4,2,1,5,3,6]=>0111010=>1000101
[7,8,2,1,6,5,3,4]=>0110110=>1001001
[6,4,1,2,5,7,3,8]=>1100010=>0011101
[2,4,8,1,5,7,3,6]=>0010010=>1101101
[4,3,8,1,7,2,5,6]=>1010100=>0101011
[6,3,1,4,7,2,5,8]=>1100100=>0011011
[7,8,3,4,5,1,6,2]=>0100101=>1011010
[7,8,3,5,4,2,1,6]=>0101110=>1010001
[7,8,4,1,2,3,6,5]=>0110001=>1001110
[7,8,3,6,5,4,1,2]=>0101110=>1010001
[7,8,2,1,5,3,4,6]=>0110100=>1001011
[7,8,2,6,4,1,3,5]=>0101100=>1010011
[7,8,2,5,6,4,1,3]=>0100110=>1011001
[7,8,1,6,5,4,3,2]=>0101111=>1010000
[6,2,1,7,5,4,3,8]=>1101110=>0010001
[2,1,8,7,5,4,3,6]=>1011110=>0100001
[1,3,8,2,6,4,7,5]=>0010101=>1101010
[5,3,7,1,6,4,8,2]=>1010101=>0101010
[5,3,6,2,7,4,1,8]=>1010110=>0101001
[6,1,2,5,8,7,4,3]=>1000111=>0111000
[6,3,1,8,4,2,7,5]=>1101101=>0010010
[6,4,2,1,5,3,8,7]=>1110101=>0001010
[6,4,3,7,5,8,1,2]=>1101010=>0010101
[4,3,8,7,5,6,1,2]=>1011010=>0100101
[2,4,7,1,5,3,6,8]=>0010100=>1101011
[1,3,7,6,4,2,8,5]=>0011101=>1100010
[2,1,7,5,6,8,4,3]=>1010011=>0101100
[3,7,2,8,6,4,1,5]=>0101110=>1010001
[3,8,1,7,6,4,5,2]=>0101101=>1010010
[1,8,5,7,3,6,4,2]=>0101011=>1010100
[2,7,5,8,3,6,1,4]=>0101010=>1010101
[1,5,6,8,2,4,7,3]=>0001001=>1110110
[2,6,8,5,3,1,4,7]=>0011100=>1100011
[2,6,1,4,7,3,5,8]=>0100100=>1011011
[5,6,7,3,8,4,1,2]=>0010110=>1101001
[5,2,8,1,4,7,3,6]=>1010010=>0101101
[4,6,7,5,2,1,3,8]=>0011100=>1100011
[4,5,6,7,2,8,1,3]=>0001010=>1110101
[4,5,7,6,1,8,3,2]=>0011011=>1100100
[1,5,8,6,2,7,3,4]=>0011010=>1100101
[1,6,5,8,3,2,7,4]=>0101101=>1010010
[4,6,5,7,1,2,8,3]=>0101001=>1010110
[4,7,5,6,3,1,8,2]=>0101101=>1010010
[5,1,6,3,4,2,8,7]=>1010101=>0101010
[5,7,1,4,2,3,8,6]=>0101001=>1010110
[5,7,6,4,3,8,1,2]=>0111010=>1000101
[6,3,4,5,8,7,1,2]=>1000110=>0111001
[6,2,4,1,8,3,7,5]=>1010101=>0101010
[6,2,3,5,4,8,1,7]=>1001010=>0110101
[6,1,3,4,5,8,7,2]=>1000011=>0111100
[5,1,4,2,7,6,8,3]=>1010101=>0101010
[1,6,2,4,7,8,3,5]=>0100010=>1011101
[5,7,2,4,1,6,3,8]=>0101010=>1010101
[6,1,4,2,8,5,3,7]=>1010110=>0101001
[6,7,5,8,1,4,3,2]=>0101011=>1010100
[5,8,7,6,3,4,1,2]=>0111010=>1000101
[5,8,7,6,2,3,1,4]=>0111010=>1000101
[4,1,7,2,6,5,3,8]=>1010110=>0101001
[4,8,2,1,5,6,3,7]=>0110010=>1001101
[4,2,7,8,1,6,3,5]=>1001010=>0110101
[2,1,8,7,6,5,3,4]=>1011110=>0100001
[3,1,4,7,8,2,6,5]=>1000101=>0111010
[3,1,7,4,5,6,8,2]=>1010001=>0101110
[4,2,7,1,6,3,8,5]=>1010101=>0101010
[4,3,7,5,6,8,1,2]=>1010010=>0101101
[4,8,6,3,5,7,1,2]=>0110010=>1001101
[4,8,1,2,5,3,7,6]=>0100101=>1011010
[3,8,6,5,2,4,1,7]=>0111010=>1000101
[3,8,5,6,1,4,7,2]=>0101001=>1010110
[5,3,7,8,2,1,6,4]=>1001101=>0110010
[5,2,8,7,1,6,4,3]=>1011011=>0100100
[1,6,8,7,5,2,4,3]=>0011101=>1100010
[3,6,7,8,5,1,4,2]=>0001101=>1110010
[3,7,6,8,5,2,1,4]=>0101110=>1010001
[3,7,8,5,1,2,4,6]=>0011000=>1100111
[3,7,1,6,4,2,5,8]=>0101100=>1010011
[4,1,8,6,2,3,5,7]=>1011000=>0100111
[4,7,8,6,3,5,1,2]=>0011010=>1100101
[3,8,7,6,5,4,1,2]=>0111110=>1000001
[2,1,7,6,5,3,4,8]=>1011100=>0100011
[2,8,1,6,4,5,3,7]=>0101010=>1010101
[2,8,7,5,1,4,3,6]=>0111010=>1000101
[2,8,6,7,5,1,3,4]=>0101100=>1010011
[2,7,8,6,5,4,1,3]=>0011110=>1100001
[6,4,2,7,1,3,8,5]=>1101001=>0010110
[7,4,2,5,1,3,8,6]=>1101001=>0010110
[7,5,3,6,1,8,2,4]=>1101010=>0010101
[8,5,3,6,1,7,2,4]=>1101010=>0010101
[7,3,6,2,4,8,1,5]=>1010010=>0101101
[4,3,7,1,2,5,8,6]=>1010001=>0101110
[3,6,2,7,1,4,8,5]=>0101001=>1010110
[5,3,6,7,1,2,8,4]=>1001001=>0110110
[6,3,7,4,1,2,8,5]=>1011001=>0100110
[4,7,1,5,2,3,8,6]=>0101001=>1010110
[3,7,5,1,2,4,8,6]=>0110001=>1001110
[7,6,4,2,3,8,1,5]=>1110010=>0001101
[8,6,4,2,3,7,1,5]=>1110010=>0001101
[4,7,6,3,8,1,2,5]=>0110100=>1001011
[5,7,4,2,3,8,1,6]=>0110010=>1001101
[3,7,6,1,4,8,2,5]=>0110010=>1001101
[6,4,7,5,2,8,1,3]=>1011010=>0100101
[7,4,8,5,2,6,1,3]=>1011010=>0100101
[5,8,2,6,3,7,1,4]=>0101010=>1010101
[3,8,6,2,4,7,1,5]=>0110010=>1001101
[3,8,5,7,1,2,4,6]=>0101000=>1010111
[2,8,5,7,1,3,4,6]=>0101000=>1010111
[4,8,6,2,7,1,3,5]=>0110100=>1001011
[2,6,5,8,1,3,4,7]=>0101000=>1010111
[3,6,5,8,1,2,4,7]=>0101000=>1010111
[2,5,7,4,8,1,3,6]=>0010100=>1101011
[5,4,6,7,2,8,1,3]=>1001010=>0110101
[3,5,7,1,4,8,2,6]=>0010010=>1101101
[5,3,7,2,4,8,1,6]=>1010010=>0101101
[5,4,7,3,8,1,2,6]=>1010100=>0101011
[7,4,6,3,8,1,2,5]=>1010100=>0101011
[8,4,6,3,7,1,2,5]=>1010100=>0101011
[8,4,1,6,7,2,3,5]=>1100100=>0011011
[7,4,1,6,8,2,3,5]=>1100100=>0011011
[6,5,3,7,1,8,2,4]=>1101010=>0010101
[6,5,1,2,7,8,3,4]=>1100010=>0011101
[5,3,6,4,7,8,1,2]=>1010010=>0101101
[6,3,7,4,8,5,1,2]=>1010110=>0101001
[4,7,1,5,8,6,2,3]=>0100110=>1011001
[7,5,1,2,8,6,3,4]=>1100110=>0011001
[7,5,3,8,1,6,2,4]=>1101010=>0010101
[7,6,1,8,5,2,3,4]=>1101100=>0010011
[8,6,1,7,5,2,3,4]=>1101100=>0010011
[5,7,2,8,1,6,3,4]=>0101010=>1010101
[6,3,7,8,5,1,2,4]=>1001100=>0110011
[3,6,8,2,7,1,4,5]=>0010100=>1101011
[2,4,8,7,1,3,5,6]=>0011000=>1100111
[4,3,8,7,1,2,5,6]=>1011000=>0100111
[5,3,8,7,1,2,4,6]=>1011000=>0100111
[8,3,7,6,1,2,4,5]=>1011000=>0100111
[8,4,7,6,1,2,3,5]=>1011000=>0100111
[5,4,8,7,1,2,3,6]=>1011000=>0100111
[3,5,8,7,1,2,4,6]=>0011000=>1100111
[2,5,8,7,1,3,4,6]=>0011000=>1100111
[4,6,8,2,7,1,3,5]=>0010100=>1101011
[6,8,4,7,5,1,2,3]=>0101100=>1010011
[5,8,7,1,6,2,3,4]=>0110100=>1001011
[2,8,7,6,1,3,4,5]=>0111000=>1000111
[3,8,7,6,1,2,4,5]=>0111000=>1000111
[4,8,7,6,1,2,3,5]=>0111000=>1000111
[5,6,3,1,4,2,8,7]=>0110101=>1001010
[7,5,3,8,2,1,6,4]=>1101101=>0010010
[3,8,7,4,5,1,6,2]=>0110101=>1001010
[6,7,1,4,5,8,2,3]=>0100010=>1011101
[2,1,7,8,5,3,6,4]=>1001101=>0110010
[5,7,3,8,1,2,6,4]=>0101001=>1010110
[8,7,1,4,5,3,2,6]=>1100110=>0011001
[2,7,8,4,1,6,5,3]=>0011011=>1100100
[7,1,8,4,2,6,5,3]=>1011011=>0100100
[7,5,1,4,8,6,3,2]=>1100111=>0011000
[6,5,3,1,8,4,7,2]=>1110101=>0001010
[6,4,3,8,1,5,7,2]=>1101001=>0010110
[8,6,3,1,2,5,7,4]=>1110001=>0001110
[8,7,1,4,2,6,5,3]=>1101011=>0010100
[7,3,8,4,1,6,5,2]=>1011011=>0100100
[2,3,4,5,6,7,8,1,9]=>00000010=>11111101
[2,3,4,5,6,8,9,1,7]=>00000010=>11111101
[2,3,4,5,7,8,9,1,6]=>00000010=>11111101
[2,3,4,6,7,8,9,1,5]=>00000010=>11111101
[2,3,5,6,7,8,9,1,4]=>00000010=>11111101
[2,4,5,6,7,8,9,1,3]=>00000010=>11111101
[3,4,5,6,7,8,9,1,2]=>00000010=>11111101
[2,3,4,5,6,7,8,9,10,1]=>000000001=>111111110
[2,3,4,5,6,7,8,9,1,10]=>000000010=>111111101
[2,3,4,5,6,7,1,8,9]=>00000100=>11111011
[2,3,4,5,6,7,8,10,1,9]=>000000010=>111111101
[2,3,4,5,6,1,9,7,8]=>00001010=>11110101
[2,3,4,5,6,7,9,10,1,8]=>000000010=>111111101
[2,3,4,5,1,8,9,6,7]=>00010010=>11101101
[2,3,4,5,6,8,9,10,1,7]=>000000010=>111111101
[2,3,4,1,7,8,9,5,6]=>00100010=>11011101
[2,3,4,5,7,8,9,10,1,6]=>000000010=>111111101
[2,3,1,6,7,8,9,4,5]=>01000010=>10111101
[2,3,4,6,7,8,9,10,1,5]=>000000010=>111111101
[2,1,5,6,7,8,9,3,4]=>10000010=>01111101
[2,3,5,6,7,8,9,10,1,4]=>000000010=>111111101
[1,4,5,6,7,8,9,2,3]=>00000010=>11111101
[2,4,5,6,7,8,9,10,1,3]=>000000010=>111111101
[3,4,5,6,7,8,9,10,1,2]=>000000010=>111111101
[3,6,4,5,7,2,8,1]=>0100101=>1011010
[5,3,2,7,4,6,8,1]=>1101001=>0010110
[7,5,3,6,2,4,8,1]=>1101001=>0010110
[6,3,2,5,1,8,4,7]=>1101010=>0010101
[8,5,3,6,2,7,1,4]=>1101010=>0010101
[8,2,6,3,4,7,1,5]=>1010010=>0101101
[7,2,6,3,4,5,8,1]=>1010001=>0101110
[6,2,7,3,4,5,8,1]=>1010001=>0101110
[4,2,5,7,3,6,8,1]=>1001001=>0110110
[5,4,7,6,2,3,8,1]=>1011001=>0100110
[6,7,3,5,2,4,8,1]=>0101001=>1010110
[3,7,6,2,4,5,8,1]=>0110001=>1001110
[2,7,6,3,4,5,8,1]=>0110001=>1001110
[6,5,3,1,2,8,4,7]=>1110010=>0001101
[8,6,5,2,3,7,1,4]=>1110010=>0001101
[8,5,2,1,7,3,4,6]=>1110100=>0001011
[7,5,2,1,8,3,4,6]=>1110100=>0001011
[1,6,3,2,8,4,5,7]=>0110100=>1001011
[5,6,2,3,1,8,4,7]=>0101010=>1010101
[4,2,6,5,1,8,3,7]=>1011010=>0100101
[5,4,8,6,2,7,1,3]=>1011010=>0100101
[6,8,3,5,2,7,1,4]=>0101010=>1010101
[7,8,5,2,3,6,1,4]=>0110010=>1001101
[6,8,2,1,7,3,4,5]=>0110100=>1001011
[1,8,6,3,7,2,4,5]=>0110100=>1001011
[1,8,2,7,3,4,5,6]=>0101000=>1010111
[2,8,1,7,3,4,5,6]=>0101000=>1010111
[3,8,6,1,7,2,4,5]=>0110100=>1001011
[4,8,1,5,7,2,3,6]=>0100100=>1011011
[4,2,8,3,7,1,5,6]=>1010100=>0101011
[8,1,2,7,3,4,5,6]=>1001000=>0110111
[3,6,2,7,1,8,4,5]=>0101010=>1010101
[6,3,7,1,2,8,4,5]=>1010010=>0101101
[7,2,6,1,8,3,4,5]=>1010100=>0101011
[7,3,1,5,8,2,4,6]=>1100100=>0011011
[3,2,1,5,8,4,6,7]=>1100100=>0011011
[5,4,1,3,6,8,2,7]=>1100010=>0011101
[1,5,3,4,6,8,2,7]=>0100010=>1011101
[4,3,5,1,6,8,2,7]=>1010010=>0101101
[5,4,6,3,8,7,1,2]=>1010110=>0101001
[3,6,4,5,8,7,1,2]=>0100110=>1011001
[6,5,3,4,8,7,1,2]=>1100110=>0011001
[5,3,2,8,7,1,4,6]=>1101100=>0010011
[5,3,1,8,7,2,4,6]=>1101100=>0010011
[8,5,3,7,6,1,2,4]=>1101100=>0010011
[6,1,8,3,7,2,4,5]=>1010100=>0101011
[6,3,8,1,7,2,4,5]=>1010100=>0101011
[7,6,8,2,3,5,1,4]=>1010010=>0101101
[3,7,8,2,4,6,1,5]=>0010010=>1101101
[6,7,3,8,2,5,1,4]=>0101010=>1010101
[5,4,7,8,2,6,1,3]=>1001010=>0110101
[4,2,5,8,7,1,3,6]=>1001100=>0110011
[2,3,8,7,1,4,5,6]=>0011000=>1100111
[7,2,8,6,1,3,4,5]=>1011000=>0100111
[2,1,8,7,3,4,5,6]=>1011000=>0100111
[8,2,7,6,1,3,4,5]=>1011000=>0100111
[1,2,8,7,3,4,5,6]=>0011000=>1100111
[1,3,8,7,2,4,5,6]=>0011000=>1100111
[1,7,8,3,6,2,4,5]=>0010100=>1101011
[4,1,5,8,7,2,3,6]=>1001100=>0110011
[5,4,8,7,6,1,2,3]=>1011100=>0100011
[6,8,3,7,5,1,2,4]=>0101100=>1010011
[7,8,6,2,5,1,3,4]=>0110100=>1001011
[8,1,6,7,3,2,5,4]=>1001101=>0110010
[8,1,6,7,3,2,4,5]=>1001100=>0110011
[8,1,5,3,7,2,4,6]=>1010100=>0101011
[8,1,5,3,6,2,4,7]=>1010100=>0101011
[7,5,1,3,6,2,4,8]=>1100100=>0011011
[7,5,8,3,6,2,4,1]=>1010101=>0101010
[7,4,8,3,2,6,5,1]=>1011011=>0100100
[7,4,1,3,2,6,5,8]=>1101010=>0010101
[8,1,4,3,2,6,5,7]=>1011010=>0100101
[8,1,4,3,2,7,5,6]=>1011010=>0100101
[8,1,4,3,2,7,6,5]=>1011011=>0100100
[8,1,5,4,6,7,2,3]=>1010010=>0101101
[8,1,5,3,6,2,7,4]=>1010101=>0101010
[8,1,4,3,2,6,7,5]=>1011001=>0100110
[8,1,4,3,2,5,7,6]=>1011001=>0100110
[8,1,4,3,2,5,6,7]=>1011000=>0100111
[7,4,1,3,2,5,6,8]=>1101000=>0010111
[7,4,8,3,2,5,6,1]=>1011001=>0100110
[6,4,3,8,2,5,7,1]=>1101001=>0010110
[6,4,3,1,2,5,8,7]=>1110001=>0001110
[7,4,1,3,2,5,8,6]=>1101001=>0010110
[7,4,1,3,2,6,8,5]=>1101001=>0010110
[7,5,1,3,6,2,8,4]=>1100101=>0011010
[7,5,1,4,6,8,2,3]=>1100010=>0011101
[7,5,8,3,6,2,1,4]=>1010110=>0101001
[7,4,8,3,2,6,1,5]=>1011010=>0100101
[7,4,8,3,2,5,1,6]=>1011010=>0100101
[6,4,3,8,2,5,1,7]=>1101010=>0010101
[6,4,3,7,2,5,8,1]=>1101001=>0010110
[5,4,3,2,8,6,1,7]=>1110110=>0001001
[5,4,3,2,8,7,1,6]=>1110110=>0001001
[6,5,3,8,7,2,1,4]=>1101110=>0010001
[6,5,4,8,7,1,2,3]=>1101100=>0010011
[6,5,4,1,7,8,2,3]=>1110010=>0001101
[6,5,3,1,7,2,8,4]=>1110101=>0001010
[6,4,3,1,2,7,8,5]=>1110001=>0001110
[5,4,3,2,1,8,6,7]=>1111010=>0000101
[6,5,3,1,8,2,7,4]=>1110101=>0001010
[6,5,4,1,8,7,2,3]=>1110110=>0001001
[7,5,1,4,8,6,2,3]=>1100110=>0011001
[7,4,1,3,2,8,6,5]=>1101011=>0010100
[7,4,1,3,2,8,5,6]=>1101010=>0010101
[6,4,3,1,2,8,5,7]=>1110010=>0001101
[6,4,3,1,2,7,5,8]=>1110010=>0001101
[6,4,3,8,2,7,5,1]=>1101011=>0010100
[6,5,3,8,7,2,4,1]=>1101101=>0010010
[6,5,3,1,7,2,4,8]=>1110100=>0001011
[6,5,3,1,8,2,4,7]=>1110100=>0001011
[7,5,1,3,8,2,4,6]=>1100100=>0011011
[7,6,1,8,3,2,4,5]=>1101100=>0010011
[7,6,1,8,4,5,2,3]=>1101010=>0010101
[7,6,8,1,4,5,2,3]=>1010010=>0101101
[7,6,8,1,3,2,5,4]=>1010101=>0101010
[6,5,3,7,8,2,4,1]=>1100101=>0011010
[6,4,3,7,2,8,5,1]=>1101011=>0010100
[6,4,3,7,2,1,5,8]=>1101100=>0010011
[7,4,8,3,2,1,5,6]=>1011100=>0100011
[7,4,8,3,2,1,6,5]=>1011101=>0100010
[7,5,8,3,1,2,6,4]=>1011001=>0100110
[7,5,8,4,1,6,2,3]=>1011010=>0100101
[6,5,4,8,1,7,2,3]=>1101010=>0010101
[6,5,3,8,1,2,7,4]=>1101001=>0010110
[5,4,3,2,8,1,7,6]=>1110101=>0001010
[6,4,3,7,2,1,8,5]=>1101101=>0010010
[6,5,3,7,1,2,8,4]=>1101001=>0010110
[6,5,4,7,1,8,2,3]=>1101010=>0010101
[6,5,3,7,8,2,1,4]=>1100110=>0011001
[6,4,3,7,2,8,1,5]=>1101010=>0010101
[5,4,3,2,7,8,1,6]=>1110010=>0001101
[5,4,3,2,6,8,1,7]=>1110010=>0001101
[5,6,2,1,3,4,8,7]=>0110001=>1001110
[5,8,2,7,4,1,3,6]=>0101100=>1010011
[5,3,7,8,2,1,4,6]=>1001100=>0110011
[7,6,1,2,5,8,3,4]=>1100010=>0011101
[2,1,7,8,4,3,5,6]=>1001100=>0110011
[8,3,7,4,1,5,6,2]=>1011001=>0100110
[7,8,1,2,5,4,6,3]=>0100101=>1011010
[2,6,8,3,1,4,7,5]=>0011001=>1100110
[6,1,8,3,2,4,5,7]=>1011000=>0100111
[8,4,1,3,7,6,2,5]=>1100110=>0011001
[5,8,7,4,2,1,6,3]=>0111101=>1000010
[7,5,1,6,8,3,4,2]=>1100101=>0011010
[6,5,2,1,8,7,4,3]=>1110111=>0001000
[4,7,2,8,1,3,6,5]=>0101001=>1010110
[7,3,8,6,1,2,5,4]=>1011001=>0100110
[3,4,7,1,8,2,6,5]=>0010101=>1101010
[1,8,2,4,3,5,6,7]=>0101000=>1010111
[1,7,2,4,3,5,6,8]=>0101000=>1010111
[1,6,2,4,3,5,7,8]=>0101000=>1010111
[1,5,2,4,3,6,7,8]=>0101000=>1010111
[1,6,2,5,3,4,7,8]=>0101000=>1010111
[1,7,2,5,3,4,6,8]=>0101000=>1010111
[1,8,2,5,3,4,6,7]=>0101000=>1010111
[1,8,2,6,3,4,5,7]=>0101000=>1010111
[1,7,2,6,3,4,5,8]=>0101000=>1010111
[1,8,2,7,3,5,4,6]=>0101010=>1010101
[1,7,2,8,3,5,4,6]=>0101010=>1010101
[1,6,2,8,3,5,4,7]=>0101010=>1010101
[1,5,2,8,3,6,4,7]=>0101010=>1010101
[1,4,2,8,3,6,5,7]=>0101010=>1010101
[1,3,2,8,4,6,5,7]=>0101010=>1010101
[1,2,3,8,4,6,5,7]=>0001010=>1110101
[1,2,3,7,4,6,5,8]=>0001010=>1110101
[1,3,2,7,4,6,5,8]=>0101010=>1010101
[1,4,2,7,3,6,5,8]=>0101010=>1010101
[1,5,2,7,3,6,4,8]=>0101010=>1010101
[1,6,2,7,3,5,4,8]=>0101010=>1010101
[1,7,2,6,3,5,4,8]=>0101010=>1010101
[1,8,2,6,3,5,4,7]=>0101010=>1010101
[1,8,2,5,3,6,4,7]=>0101010=>1010101
[1,7,2,5,3,6,4,8]=>0101010=>1010101
[1,6,2,5,3,7,4,8]=>0101010=>1010101
[1,5,2,4,3,7,6,8]=>0101010=>1010101
[1,6,2,4,3,7,5,8]=>0101010=>1010101
[1,7,2,4,3,6,5,8]=>0101010=>1010101
[1,8,2,4,3,6,5,7]=>0101010=>1010101
[1,8,2,3,4,6,5,7]=>0100010=>1011101
[1,7,2,3,4,6,5,8]=>0100010=>1011101
[1,8,2,3,4,7,5,6]=>0100010=>1011101
[1,8,2,4,3,7,5,6]=>0101010=>1010101
[1,7,2,4,3,8,5,6]=>0101010=>1010101
[1,6,2,4,3,8,5,7]=>0101010=>1010101
[1,5,2,4,3,8,6,7]=>0101010=>1010101
[1,6,2,5,3,8,4,7]=>0101010=>1010101
[1,7,2,5,3,8,4,6]=>0101010=>1010101
[1,8,2,5,3,7,4,6]=>0101010=>1010101
[1,8,2,6,3,7,4,5]=>0101010=>1010101
[1,7,2,6,3,8,4,5]=>0101010=>1010101
[1,2,3,8,4,7,5,6]=>0001010=>1110101
[1,3,2,8,4,7,5,6]=>0101010=>1010101
[1,4,2,8,3,7,5,6]=>0101010=>1010101
[1,5,2,8,3,7,4,6]=>0101010=>1010101
[1,6,2,8,3,7,4,5]=>0101010=>1010101
[1,7,2,8,3,6,4,5]=>0101010=>1010101
[1,8,2,7,3,6,4,5]=>0101010=>1010101
[4,6,3,7,2,5,1,8]=>0101010=>1010101
[4,6,3,7,5,2,1,8]=>0101110=>1010001
[4,6,3,8,5,1,7,2]=>0101101=>1010010
[4,6,3,8,5,1,2,7]=>0101100=>1010011
[5,6,8,3,4,1,2,7]=>0010100=>1101011
[5,6,8,3,4,1,7,2]=>0010101=>1101010
[4,6,2,7,5,3,1,8]=>0101110=>1010001
[5,6,7,2,4,3,1,8]=>0010110=>1101001
[5,6,8,4,3,1,7,2]=>0011101=>1100010
[5,6,8,4,3,1,2,7]=>0011100=>1100011
[5,7,8,4,1,6,2,3]=>0011010=>1100101
[5,7,8,4,1,6,3,2]=>0011011=>1100100
[5,7,8,4,1,3,6,2]=>0011001=>1100110
[5,6,8,4,2,1,7,3]=>0011101=>1100010
[5,6,8,2,4,1,7,3]=>0010101=>1101010
[4,6,2,8,5,1,7,3]=>0101101=>1010010
[3,2,6,8,5,1,7,4]=>1001101=>0110010
[3,2,6,8,5,1,4,7]=>1001100=>0110011
[4,6,2,8,5,1,3,7]=>0101100=>1010011
[5,6,8,2,4,1,3,7]=>0010100=>1101011
[5,6,8,4,2,1,3,7]=>0011100=>1100011
[5,7,8,4,1,3,2,6]=>0011010=>1100101
[5,7,8,4,1,2,6,3]=>0011001=>1100110
[5,7,8,4,1,2,3,6]=>0011000=>1100111
[6,7,8,1,5,2,3,4]=>0010100=>1101011
[6,7,8,1,5,2,4,3]=>0010101=>1101010
[6,7,8,1,5,3,2,4]=>0010110=>1101001
[6,7,8,1,3,5,2,4]=>0010010=>1101101
[5,7,8,2,1,6,3,4]=>0011010=>1100101
[4,7,2,8,1,6,3,5]=>0101010=>1010101
[3,2,7,8,1,6,4,5]=>1001010=>0110101
[3,2,7,8,1,6,5,4]=>1001011=>0110100
[4,7,2,8,1,6,5,3]=>0101011=>1010100
[5,7,8,2,1,6,4,3]=>0011011=>1100100
[6,7,8,1,3,5,4,2]=>0010011=>1101100
[6,7,8,1,5,3,4,2]=>0010101=>1101010
[6,7,8,1,5,4,3,2]=>0010111=>1101000
[6,7,8,1,5,4,2,3]=>0010110=>1101001
[6,7,8,1,4,5,2,3]=>0010010=>1101101
[6,7,8,1,4,5,3,2]=>0010011=>1101100
[6,7,8,1,4,3,5,2]=>0010101=>1101010
[6,7,8,1,3,4,5,2]=>0010001=>1101110
[5,7,8,2,1,4,6,3]=>0011001=>1100110
[4,7,2,8,1,5,6,3]=>0101001=>1010110
[3,2,7,8,1,5,6,4]=>1001001=>0110110
[3,2,6,8,4,1,7,5]=>1001101=>0110010
[4,6,2,8,3,1,7,5]=>0101101=>1010010
[5,6,8,3,2,1,7,4]=>0011101=>1100010
[5,7,8,3,1,4,6,2]=>0011001=>1100110
[5,7,8,3,1,6,4,2]=>0011011=>1100100
[5,7,8,3,1,6,2,4]=>0011010=>1100101
[4,7,3,8,1,6,2,5]=>0101010=>1010101
[4,7,3,8,1,6,5,2]=>0101011=>1010100
[4,7,3,8,1,5,6,2]=>0101001=>1010110
[4,6,3,8,2,1,7,5]=>0101101=>1010010
[4,5,3,2,8,1,7,6]=>0110101=>1001010
[4,5,2,3,8,1,7,6]=>0100101=>1011010
[3,2,5,4,8,1,7,6]=>1010101=>0101010
[4,5,3,2,8,1,6,7]=>0110100=>1001011
[4,6,3,8,2,1,5,7]=>0101100=>1010011
[4,7,3,8,1,5,2,6]=>0101010=>1010101
[4,7,3,8,1,2,6,5]=>0101001=>1010110
[4,7,3,8,1,2,5,6]=>0101000=>1010111
[5,7,8,3,1,2,4,6]=>0011000=>1100111
[5,7,8,3,1,2,6,4]=>0011001=>1100110
[5,7,8,3,1,4,2,6]=>0011010=>1100101
[5,6,8,3,2,1,4,7]=>0011100=>1100011
[3,2,7,8,1,5,4,6]=>1001010=>0110101
[5,7,8,2,1,4,3,6]=>0011010=>1100101
[6,7,8,1,3,4,2,5]=>0010010=>1101101
[6,7,8,1,4,3,2,5]=>0010110=>1101001
[6,7,8,1,4,2,5,3]=>0010101=>1101010
[6,7,8,1,4,2,3,5]=>0010100=>1101011
[6,7,8,1,2,5,3,4]=>0010010=>1101101
[6,7,8,1,2,5,4,3]=>0010011=>1101100
[6,7,8,1,2,4,5,3]=>0010001=>1101110
[6,7,8,1,3,2,5,4]=>0010101=>1101010
[5,7,8,2,1,3,6,4]=>0011001=>1100110
[3,2,7,8,1,4,6,5]=>1001001=>0110110
[6,7,8,1,3,2,4,5]=>0010100=>1101011
[6,7,8,1,2,4,3,5]=>0010010=>1101101
[6,7,8,1,2,3,5,4]=>0010001=>1101110
[7,2,8,5,1,6,4,3]=>1011011=>0100100
[1,3,7,5,2,6,4,8]=>0011010=>1100101
[1,3,7,5,4,2,6,8]=>0011100=>1100011
[7,2,8,5,4,1,6,3]=>1011101=>0100010
[2,8,5,4,3,1,7,6]=>0111101=>1000010
[2,8,4,5,6,1,7,3]=>0100101=>1011010
[2,8,6,5,7,3,1,4]=>0110110=>1001001
[2,8,4,5,3,7,1,6]=>0101010=>1010101
[2,8,4,3,5,6,1,7]=>0110010=>1001101
[7,2,8,4,5,6,1,3]=>1010010=>0101101
[1,6,3,7,5,2,4,8]=>0101100=>1010011
[6,2,3,8,5,1,7,4]=>1001101=>0110010
[6,3,2,8,5,1,4,7]=>1101100=>0010011
[7,4,8,2,5,6,3,1]=>1010011=>0101100
[7,4,8,5,2,1,3,6]=>1011100=>0100011
[6,4,8,5,1,3,7,2]=>1011001=>0100110
[6,3,7,5,2,1,8,4]=>1011101=>0100010
[4,3,7,5,1,2,8,6]=>1011001=>0100110
[4,3,7,1,5,6,8,2]=>1010001=>0101110
[3,6,1,7,5,2,8,4]=>0101101=>1010010
[3,4,1,2,7,6,8,5]=>0100101=>1011010
[3,4,2,1,7,5,8,6]=>0110101=>1001010
[3,6,5,7,1,4,8,2]=>0101001=>1010110
[6,5,2,7,4,1,8,3]=>1101101=>0010010
[3,5,2,6,4,8,7,1]=>0101011=>1010100
[5,3,1,8,6,4,7,2]=>1101101=>0010010
[5,6,1,8,7,2,4,3]=>0101101=>1010010
[6,3,5,8,2,7,4,1]=>1001011=>0110100
[6,5,8,4,2,3,7,1]=>1011001=>0100110
[6,2,5,8,3,7,1,4]=>1001010=>0110101
[1,6,5,7,3,4,2,8]=>0101010=>1010101
[1,5,2,7,4,6,3,8]=>0101010=>1010101
[5,2,1,8,7,6,3,4]=>1101110=>0010001
[7,1,3,8,4,6,2,5]=>1001010=>0110101
[2,3,4,8,6,1,7,5]=>0001101=>1110010
[2,3,4,8,6,5,1,7]=>0001110=>1110001
[2,7,3,5,8,6,1,4]=>0100110=>1011001
[3,2,4,7,8,6,1,5]=>1000110=>0111001
[1,5,4,6,2,7,3,8]=>0101010=>1010101
[5,2,4,7,1,8,3,6]=>1001010=>0110101
[5,3,6,4,1,8,7,2]=>1011011=>0100100
[5,3,6,1,4,8,2,7]=>1010010=>0101101
[7,3,5,6,8,4,2,1]=>1000111=>0111000
[6,3,5,1,8,2,7,4]=>1010101=>0101010
[2,6,1,5,8,4,7,3]=>0100101=>1011010
[2,7,6,5,8,3,4,1]=>0110101=>1001010
[5,7,1,6,3,8,4,2]=>0101011=>1010100
[3,2,4,1,7,8,5,6]=>1010010=>0101101
[3,1,4,2,7,8,6,5]=>1010011=>0101100
[5,1,4,7,2,8,6,3]=>1001011=>0110100
[3,6,4,7,8,2,5,1]=>0100101=>1011010
[3,1,4,6,8,5,7,2]=>1000101=>0111010
[6,3,4,5,7,1,8,2]=>1000101=>0111010
[2,5,4,6,1,7,8,3]=>0101001=>1010110
[7,2,1,4,3,6,5,8]=>1101010=>0010101
[7,3,4,1,2,6,5,8]=>1010010=>0101101
[7,4,3,2,1,6,5,8]=>1111010=>0000101
[7,6,3,2,5,4,1,8]=>1110110=>0001001
[6,7,3,2,5,4,8,1]=>0110101=>1001010
[1,8,3,2,5,4,7,6]=>0110101=>1001010
[1,8,4,5,2,3,7,6]=>0101001=>1010110
[7,3,5,1,6,2,4,8]=>1010100=>0101011
[7,2,1,5,6,3,4,8]=>1100100=>0011011
[7,2,1,6,5,4,3,8]=>1101110=>0010001
[7,3,6,1,5,4,2,8]=>1010110=>0101001
[7,4,6,5,1,3,2,8]=>1011010=>0100101
[1,8,5,4,3,2,7,6]=>0111101=>1000010
[1,8,6,4,3,7,2,5]=>0111010=>1000101
[6,5,7,4,3,1,8,2]=>1011101=>0100010
[6,4,7,5,1,3,8,2]=>1011001=>0100110
[6,3,7,1,5,4,8,2]=>1010101=>0101010
[6,2,1,7,5,4,8,3]=>1101101=>0010010
[3,2,1,8,5,4,7,6]=>1101101=>0010010
[2,3,8,1,5,4,7,6]=>0010101=>1101010
[2,4,8,5,1,3,7,6]=>0011001=>1100110
[2,5,8,4,3,1,7,6]=>0011101=>1100010
[2,6,8,4,3,7,1,5]=>0011010=>1100101
[2,7,8,4,3,6,5,1]=>0011011=>1100100
[1,8,7,4,3,6,5,2]=>0111011=>1000100
[1,8,7,5,6,3,4,2]=>0110101=>1001010
[2,7,8,5,6,3,4,1]=>0010101=>1101010
[2,6,8,5,7,3,1,4]=>0010110=>1101001
[2,5,8,6,7,1,3,4]=>0010100=>1101011
[2,4,8,6,1,7,3,5]=>0011010=>1100101
[3,2,1,8,6,7,4,5]=>1101010=>0010101
[5,2,1,7,6,8,4,3]=>1101011=>0010100
[5,3,7,1,6,8,4,2]=>1010011=>0101100
[5,4,7,6,1,8,3,2]=>1011011=>0100100
[4,5,7,6,8,1,3,2]=>0010101=>1101010
[4,6,7,5,8,3,1,2]=>0010110=>1101001
[1,8,6,5,7,3,2,4]=>0110110=>1001001
[1,8,5,6,7,2,3,4]=>0100100=>1011011
[4,7,5,6,8,2,3,1]=>0100101=>1011010
[4,6,5,7,8,2,1,3]=>0100110=>1011001
[5,4,6,7,1,8,2,3]=>1001010=>0110101
[5,3,6,1,7,8,2,4]=>1010010=>0101101
[5,2,1,6,7,8,3,4]=>1100010=>0011101
[6,2,1,5,7,3,8,4]=>1100101=>0011010
[6,3,5,1,7,2,8,4]=>1010101=>0101010
[6,4,5,7,1,2,8,3]=>1001001=>0110110
[6,5,4,7,2,1,8,3]=>1101101=>0010010
[5,6,4,7,2,8,1,3]=>0101010=>1010101
[1,8,4,6,2,7,3,5]=>0101010=>1010101
[1,8,3,2,6,7,4,5]=>0110010=>1001101
[5,7,3,2,6,8,4,1]=>0110011=>1001100
[5,6,3,2,7,8,1,4]=>0110010=>1001101
[6,5,3,2,7,1,8,4]=>1110101=>0001010
[6,4,3,2,1,7,8,5]=>1111001=>0000110
[6,2,1,4,3,7,8,5]=>1101001=>0010110
[5,2,1,4,3,8,7,6]=>1101011=>0010100
[5,3,4,1,2,8,7,6]=>1010011=>0101100
[4,6,3,2,8,7,1,5]=>0110110=>1001001
[4,7,3,2,8,6,5,1]=>0110111=>1001000
[1,8,3,2,7,6,5,4]=>0110111=>1001000
[1,8,4,7,2,6,5,3]=>0101011=>1010100
[3,7,4,8,2,6,5,1]=>0101011=>1010100
[3,6,4,8,2,7,1,5]=>0101010=>1010101
[3,5,4,8,2,1,7,6]=>0101101=>1010010
[3,4,5,8,1,2,7,6]=>0001001=>1110110
[4,3,5,1,8,2,7,6]=>1010101=>0101010
[4,2,1,5,8,3,7,6]=>1100101=>0011010
[4,2,1,6,8,7,3,5]=>1100110=>0011001
[4,3,6,1,8,7,2,5]=>1010110=>0101001
[3,4,6,8,1,7,2,5]=>0001010=>1110101
[3,5,6,8,7,1,2,4]=>0001100=>1110011
[3,6,5,8,7,2,1,4]=>0101110=>1010001
[3,7,5,8,6,2,4,1]=>0101101=>1010010
[1,8,5,7,6,2,4,3]=>0101101=>1010010
[1,8,6,7,5,4,2,3]=>0101110=>1010001
[3,6,7,8,5,4,1,2]=>0001110=>1110001
[3,5,7,8,6,1,4,2]=>0001101=>1110010
[3,4,7,8,1,6,5,2]=>0001011=>1110100
[4,2,1,7,8,6,5,3]=>1100111=>0011000
[2,3,8,1,7,6,5,4]=>0010111=>1101000
[2,4,8,7,1,6,5,3]=>0011011=>1100100
[2,5,8,7,6,1,4,3]=>0011101=>1100010
[2,6,8,7,5,4,1,3]=>0011110=>1100001
[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101=>01010101010
[2,1,4,3,6,5,8,7,12,11,10,9]=>10101010111=>01010101000
[2,1,4,3,6,5,10,9,8,7,12,11]=>10101011101=>01010100010
[2,1,4,3,6,5,12,11,10,9,8,7]=>10101011111=>01010100000
[2,1,4,3,8,7,6,5,10,9,12,11]=>10101110101=>01010001010
[2,1,4,3,8,7,6,5,12,11,10,9]=>10101110111=>01010001000
[2,1,4,3,10,9,8,7,6,5,12,11]=>10101111101=>01010000010
[2,1,4,3,12,11,8,7,10,9,6,5]=>10101110111=>01010001000
[2,1,4,3,12,11,10,9,8,7,6,5]=>10101111111=>01010000000
[2,1,6,5,4,3,8,7,10,9,12,11]=>10111010101=>01000101010
[2,1,6,5,4,3,8,7,12,11,10,9]=>10111010111=>01000101000
[2,1,6,5,4,3,10,9,8,7,12,11]=>10111011101=>01000100010
[2,1,6,5,4,3,12,11,10,9,8,7]=>10111011111=>01000100000
[2,1,12,5,4,11,10,9,8,7,6,3]=>10110111111=>01001000000
[2,1,8,7,6,5,4,3,10,9,12,11]=>10111110101=>01000001010
[2,1,8,7,6,5,4,3,12,11,10,9]=>10111110111=>01000001000
[2,1,12,7,6,5,4,11,10,9,8,3]=>10111101111=>01000010000
[2,1,10,9,6,5,8,7,4,3,12,11]=>10111011101=>01000100010
[2,1,12,11,6,5,8,7,10,9,4,3]=>10111010111=>01000101000
[2,1,12,11,6,5,10,9,8,7,4,3]=>10111011111=>01000100000
[2,1,10,9,8,7,6,5,4,3,12,11]=>10111111101=>01000000010
[2,1,12,9,8,7,6,5,4,11,10,3]=>10111111011=>01000000100
[2,1,12,11,8,7,6,5,10,9,4,3]=>10111110111=>01000001000
[2,1,12,11,10,7,6,9,8,5,4,3]=>10111101111=>01000010000
[2,1,12,11,10,9,8,7,6,5,4,3]=>10111111111=>01000000000
[4,3,2,1,6,5,8,7,10,9,12,11]=>11101010101=>00010101010
[4,3,2,1,6,5,8,7,12,11,10,9]=>11101010111=>00010101000
[4,3,2,1,6,5,10,9,8,7,12,11]=>11101011101=>00010100010
[4,3,2,1,6,5,12,9,8,11,10,7]=>11101011011=>00010100100
[4,3,2,1,6,5,12,11,10,9,8,7]=>11101011111=>00010100000
[4,3,2,1,8,7,6,5,10,9,12,11]=>11101110101=>00010001010
[4,3,2,1,8,7,6,5,12,11,10,9]=>11101110111=>00010001000
[4,3,2,1,10,7,6,9,8,5,12,11]=>11101101101=>00010010010
[4,3,2,1,12,7,6,9,8,11,10,5]=>11101101011=>00010010100
[4,3,2,1,12,7,6,11,10,9,8,5]=>11101101111=>00010010000
[4,3,2,1,10,9,8,7,6,5,12,11]=>11101111101=>00010000010
[4,3,2,1,12,9,8,7,6,11,10,5]=>11101111011=>00010000100
[4,3,2,1,12,11,8,7,10,9,6,5]=>11101110111=>00010001000
[4,3,2,1,12,11,10,9,8,7,6,5]=>11101111111=>00010000000
[6,3,2,5,4,1,8,7,12,11,10,9]=>11011010111=>00100101000
[6,3,2,5,4,1,10,9,8,7,12,11]=>11011011101=>00100100010
[6,3,2,5,4,1,12,9,8,11,10,7]=>11011011011=>00100100100
[8,3,2,5,4,7,6,1,12,11,10,9]=>11010110111=>00101001000
[12,3,2,5,4,9,8,7,6,11,10,1]=>11010111011=>00101000100
[12,3,2,5,4,11,8,7,10,9,6,1]=>11010110111=>00101001000
[12,3,2,5,4,11,10,9,8,7,6,1]=>11010111111=>00101000000
[8,3,2,7,6,5,4,1,12,11,10,9]=>11011110111=>00100001000
[10,3,2,7,6,5,4,9,8,1,12,11]=>11011101101=>00100010010
[12,3,2,7,6,5,4,9,8,11,10,1]=>11011101011=>00100010100
[12,3,2,7,6,5,4,11,10,9,8,1]=>11011101111=>00100010000
[10,3,2,9,6,5,8,7,4,1,12,11]=>11011011101=>00100100010
[12,3,2,9,6,5,8,7,4,11,10,1]=>11011011011=>00100100100
[12,3,2,11,6,5,8,7,10,9,4,1]=>11011010111=>00100101000
[10,3,2,9,8,7,6,5,4,1,12,11]=>11011111101=>00100000010
[12,3,2,11,8,7,6,5,10,9,4,1]=>11011110111=>00100001000
[12,3,2,11,10,7,6,9,8,5,4,1]=>11011101111=>00100010000
[12,3,2,11,10,9,8,7,6,5,4,1]=>11011111111=>00100000000
[6,5,4,3,2,1,8,7,10,9,12,11]=>11111010101=>00000101010
[6,5,4,3,2,1,8,7,12,11,10,9]=>11111010111=>00000101000
[6,5,4,3,2,1,10,9,8,7,12,11]=>11111011101=>00000100010
[6,5,4,3,2,1,12,9,8,11,10,7]=>11111011011=>00000100100
[6,5,4,3,2,1,12,11,10,9,8,7]=>11111011111=>00000100000
[8,5,4,3,2,7,6,1,10,9,12,11]=>11110110101=>00001001010
[8,5,4,3,2,7,6,1,12,11,10,9]=>11110110111=>00001001000
[10,5,4,3,2,7,6,9,8,1,12,11]=>11110101101=>00001010010
[12,5,4,3,2,7,6,9,8,11,10,1]=>11110101011=>00001010100
[12,5,4,3,2,7,6,11,10,9,8,1]=>11110101111=>00001010000
[10,5,4,3,2,9,8,7,6,1,12,11]=>11110111101=>00001000010
[12,5,4,3,2,9,8,7,6,11,10,1]=>11110111011=>00001000100
[12,5,4,3,2,11,8,7,10,9,6,1]=>11110110111=>00001001000
[12,5,4,3,2,11,10,9,8,7,6,1]=>11110111111=>00001000000
[8,7,4,3,6,5,2,1,10,9,12,11]=>11101110101=>00010001010
[8,7,4,3,6,5,2,1,12,11,10,9]=>11101110111=>00010001000
[10,7,4,3,6,5,2,9,8,1,12,11]=>11101101101=>00010010010
[12,7,4,3,6,5,2,9,8,11,10,1]=>11101101011=>00010010100
[12,7,4,3,6,5,2,11,10,9,8,1]=>11101101111=>00010010000
[10,9,4,3,6,5,8,7,2,1,12,11]=>11101011101=>00010100010
[12,9,4,3,6,5,8,7,2,11,10,1]=>11101011011=>00010100100
[12,11,4,3,6,5,8,7,10,9,2,1]=>11101010111=>00010101000
[12,11,4,3,6,5,10,9,8,7,2,1]=>11101011111=>00010100000
[10,9,4,3,8,7,6,5,2,1,12,11]=>11101111101=>00010000010
[12,9,4,3,8,7,6,5,2,11,10,1]=>11101111011=>00010000100
[12,11,4,3,8,7,6,5,10,9,2,1]=>11101110111=>00010001000
[12,11,4,3,10,7,6,9,8,5,2,1]=>11101101111=>00010010000
[12,11,4,3,10,9,8,7,6,5,2,1]=>11101111111=>00010000000
[8,7,6,5,4,3,2,1,10,9,12,11]=>11111110101=>00000001010
[8,7,6,5,4,3,2,1,12,11,10,9]=>11111110111=>00000001000
[10,7,6,5,4,3,2,9,8,1,12,11]=>11111101101=>00000010010
[12,7,6,5,4,3,2,9,8,11,10,1]=>11111101011=>00000010100
[12,7,6,5,4,3,2,11,10,9,8,1]=>11111101111=>00000010000
[10,9,6,5,4,3,8,7,2,1,12,11]=>11111011101=>00000100010
[12,9,6,5,4,3,8,7,2,11,10,1]=>11111011011=>00000100100
[12,11,6,5,4,3,8,7,10,9,2,1]=>11111010111=>00000101000
[12,11,6,5,4,3,10,9,8,7,2,1]=>11111011111=>00000100000
[10,9,8,5,4,7,6,3,2,1,12,11]=>11110111101=>00001000010
[12,9,8,5,4,7,6,3,2,11,10,1]=>11110111011=>00001000100
[12,11,8,5,4,7,6,3,10,9,2,1]=>11110110111=>00001001000
[12,11,10,5,4,7,6,9,8,3,2,1]=>11110101111=>00001010000
[12,11,10,5,4,9,8,7,6,3,2,1]=>11110111111=>00001000000
[10,9,8,7,6,5,4,3,2,1,12,11]=>11111111101=>00000000010
[12,9,8,7,6,5,4,3,2,11,10,1]=>11111111011=>00000000100
[12,11,8,7,6,5,4,3,10,9,2,1]=>11111110111=>00000001000
[12,11,10,7,6,5,4,9,8,3,2,1]=>11111101111=>00000010000
[12,11,10,9,6,5,8,7,4,3,2,1]=>11111011111=>00000100000
[12,11,10,9,8,7,6,5,4,3,2,1]=>11111111111=>00000000000
[7,4,6,1,8,3,5,2]=>1010101=>0101010
[8,3,5,1,7,4,6,2]=>1010101=>0101010
[8,3,4,1,7,5,6,2]=>1010101=>0101010
[4,8,3,1,7,5,6,2]=>0110101=>1001010
[4,6,2,1,7,5,8,3]=>0110101=>1001010
[1,4,6,2,7,5,8,3]=>0010101=>1101010
[1,7,5,2,6,8,4,3]=>0110011=>1001100
[7,5,2,1,6,8,4,3]=>1110011=>0001100
[6,8,4,3,1,7,5,2]=>0111011=>1000100
[3,6,8,4,1,7,5,2]=>0011011=>1100100
[3,6,7,5,1,8,4,2]=>0011011=>1100100
[7,5,6,1,8,3,4,2]=>1010101=>0101010
[3,4,6,5,7,1,8,2]=>0010101=>1101010
[4,7,5,6,1,8,3,2]=>0101011=>1010100
[6,7,5,1,8,4,3,2]=>0110111=>1001000
[6,8,4,1,7,5,3,2]=>0110111=>1001000
[6,7,5,3,1,8,4,2]=>0111011=>1000100
[8,4,2,1,6,7,5,3]=>1110011=>0001100
[1,8,4,2,6,7,5,3]=>0110011=>1001100
[1,5,3,2,7,6,8,4]=>0110101=>1001010
[5,3,2,1,7,6,8,4]=>1110101=>0001010
[2,5,3,1,7,6,8,4]=>0110101=>1001010
[2,8,4,1,6,7,5,3]=>0110011=>1001100
[2,7,5,1,6,8,4,3]=>0110011=>1001100
[2,4,6,1,7,5,8,3]=>0010101=>1101010
[4,7,1,6,5,8,2,3]=>0101010=>1010101
[4,8,2,6,5,7,1,3]=>0101010=>1010101
[4,6,1,2,7,5,8,3]=>0100101=>1011010
[7,5,1,2,6,8,4,3]=>1100011=>0011100
[8,4,1,2,6,7,5,3]=>1100011=>0011100
[5,3,1,2,7,6,8,4]=>1100101=>0011010
[1,2,5,3,7,6,8,4]=>0010101=>1101010
[4,3,1,2,7,6,8,5]=>1100101=>0011010
[3,5,1,2,7,6,8,4]=>0100101=>1011010
[6,7,1,5,8,2,3,4]=>0100100=>1011011
[2,7,6,1,5,8,3,4]=>0110010=>1001101
[2,3,5,1,7,6,8,4]=>0010101=>1101010
[7,6,1,5,8,3,2,4]=>1100110=>0011001
[3,6,7,1,5,8,2,4]=>0010010=>1101101
[7,1,6,5,8,2,4,3]=>1010101=>0101010
[7,5,1,6,8,4,2,3]=>1100110=>0011001
[8,4,1,6,7,5,2,3]=>1100110=>0011001
[5,2,3,1,7,6,8,4]=>1010101=>0101010
[3,5,2,1,7,6,8,4]=>0110101=>1001010
[1,3,5,2,7,6,8,4]=>0010101=>1101010
[1,7,6,2,5,8,3,4]=>0110010=>1001101
[7,6,2,1,5,8,3,4]=>1110010=>0001101
[8,3,1,5,7,6,2,4]=>1100110=>0011001
[6,2,4,1,7,5,8,3]=>1010101=>0101010
[6,2,5,1,7,4,8,3]=>1010101=>0101010
[7,1,6,4,8,2,5,3]=>1010101=>0101010
[8,2,6,4,7,1,5,3]=>1010101=>0101010
[6,1,5,2,7,4,8,3]=>1010101=>0101010
[7,6,2,5,8,3,1,4]=>1100110=>0011001
[8,3,5,7,6,2,1,4]=>1001110=>0110001
[1,8,3,5,7,6,2,4]=>0100110=>1011001
[1,5,2,3,7,6,8,4]=>0100101=>1011010
[5,2,1,3,7,6,8,4]=>1100101=>0011010
[7,5,2,6,8,4,1,3]=>1100110=>0011001
[8,4,2,6,7,5,1,3]=>1100110=>0011001
[6,1,4,2,7,5,8,3]=>1010101=>0101010
[8,2,6,5,7,1,4,3]=>1010101=>0101010
[3,6,8,2,5,7,1,4]=>0010010=>1101101
[8,3,2,5,7,6,1,4]=>1100110=>0011001
[5,1,3,2,7,6,8,4]=>1010101=>0101010
[4,1,3,2,7,6,8,5]=>1010101=>0101010
[4,2,1,3,7,6,8,5]=>1100101=>0011010
[1,4,2,3,7,6,8,5]=>0100101=>1011010
[2,4,1,3,7,6,8,5]=>0100101=>1011010
[2,5,1,3,7,6,8,4]=>0100101=>1011010
[2,8,3,5,7,6,1,4]=>0100110=>1011001
[6,8,2,3,5,7,1,4]=>0100010=>1011101
[6,7,1,3,5,8,2,4]=>0100010=>1011101
[8,3,5,7,6,1,2,4]=>1001100=>0110011
[5,1,2,3,7,6,8,4]=>1000101=>0111010
[3,1,2,4,7,6,8,5]=>1000101=>0111010
[10,8,9,5,6,7,1,2,3,4]=>101001000=>010110111
[10,8,9,4,5,6,1,2,3,7]=>101001000=>010110111
[10,7,8,5,6,9,1,2,3,4]=>101001000=>010110111
[10,7,8,4,5,9,1,2,3,6]=>101001000=>010110111
[10,6,7,4,5,8,1,2,3,9]=>101001000=>010110111
[10,7,8,3,4,9,1,2,5,6]=>101001000=>010110111
[10,6,7,3,4,8,1,2,5,9]=>101001000=>010110111
[9,8,10,5,6,7,1,2,3,4]=>101001000=>010110111
[9,8,10,4,5,6,1,2,3,7]=>101001000=>010110111
[9,7,10,5,6,8,1,2,3,4]=>101001000=>010110111
[9,7,10,4,5,8,1,2,3,6]=>101001000=>010110111
[9,6,10,4,5,7,1,2,3,8]=>101001000=>010110111
[9,7,10,3,4,8,1,2,5,6]=>101001000=>010110111
[9,6,10,3,4,7,1,2,5,8]=>101001000=>010110111
[8,7,9,5,6,10,1,2,3,4]=>101001000=>010110111
[8,7,9,4,5,10,1,2,3,6]=>101001000=>010110111
[8,6,9,4,5,10,1,2,3,7]=>101001000=>010110111
[7,6,8,4,5,9,1,2,3,10]=>101001000=>010110111
[8,7,9,3,4,10,1,2,5,6]=>101001000=>010110111
[8,6,9,3,4,10,1,2,5,7]=>101001000=>010110111
[7,6,8,3,4,9,1,2,5,10]=>101001000=>010110111
[9,6,10,5,7,8,1,2,3,4]=>101001000=>010110111
[9,6,10,4,7,8,1,2,3,5]=>101001000=>010110111
[9,5,10,4,6,7,1,2,3,8]=>101001000=>010110111
[9,6,10,3,7,8,1,2,4,5]=>101001000=>010110111
[9,5,10,3,6,7,1,2,4,8]=>101001000=>010110111
[8,6,9,5,7,10,1,2,3,4]=>101001000=>010110111
[8,6,9,4,7,10,1,2,3,5]=>101001000=>010110111
[8,5,9,4,6,10,1,2,3,7]=>101001000=>010110111
[7,5,8,4,6,9,1,2,3,10]=>101001000=>010110111
[8,6,9,3,7,10,1,2,4,5]=>101001000=>010110111
[8,5,9,3,6,10,1,2,4,7]=>101001000=>010110111
[7,5,8,3,6,9,1,2,4,10]=>101001000=>010110111
[8,4,9,3,5,10,1,2,6,7]=>101001000=>010110111
[7,4,8,3,5,9,1,2,6,10]=>101001000=>010110111
[9,6,10,2,7,8,1,3,4,5]=>101001000=>010110111
[9,5,10,2,6,7,1,3,4,8]=>101001000=>010110111
[8,6,9,2,7,10,1,3,4,5]=>101001000=>010110111
[8,5,9,2,6,10,1,3,4,7]=>101001000=>010110111
[7,5,8,2,6,9,1,3,4,10]=>101001000=>010110111
[8,4,9,2,5,10,1,3,6,7]=>101001000=>010110111
[7,4,8,2,5,9,1,3,6,10]=>101001000=>010110111
[8,1,2,4,3,6,5,7]=>1001010=>0110101
[8,1,3,5,6,2,7,4]=>1000101=>0111010
[8,1,3,4,2,6,7,5]=>1001001=>0110110
[8,1,3,2,4,5,7,6]=>1010001=>0101110
[2,7,8,3,4,5,6,1]=>0010001=>1101110
[2,6,3,8,4,5,7,1]=>0101001=>1010110
[6,3,2,1,4,5,8,7]=>1110001=>0001110
[7,3,1,4,2,6,8,5]=>1101001=>0010110
[7,4,1,5,6,8,2,3]=>1100010=>0011101
[4,7,8,5,6,1,2,3]=>0010100=>1101011
[3,7,8,5,6,2,1,4]=>0010110=>1101001
[3,7,8,4,2,6,1,5]=>0011010=>1100101
[3,7,8,2,4,5,1,6]=>0010010=>1101101
[3,6,2,8,4,5,1,7]=>0101010=>1010101
[2,3,6,7,4,5,8,1]=>0001001=>1110110
[3,5,2,4,8,6,1,7]=>0100110=>1011001
[3,5,4,2,8,7,1,6]=>0110110=>1001001
[4,6,5,8,7,1,2,3]=>0101100=>1010011
[6,4,5,1,7,8,2,3]=>1010010=>0101101
[7,4,1,2,3,8,5,6]=>1100010=>0011101
[6,2,4,1,3,7,5,8]=>1010010=>0101101
[2,6,4,8,3,7,5,1]=>0101011=>1010100
[2,6,5,8,7,3,4,1]=>0101101=>1010010
[6,2,5,1,7,3,4,8]=>1010100=>0101011
[6,5,2,1,8,3,4,7]=>1110100=>0001011
[2,5,6,7,8,3,4,1]=>0000101=>1111010
[2,4,6,7,3,8,5,1]=>0001011=>1110100
[4,2,6,7,3,1,5,8]=>1001100=>0110011
[4,7,8,2,3,1,5,6]=>0010100=>1101011
[4,7,8,3,2,1,6,5]=>0011101=>1100010
[5,6,4,8,1,7,2,3]=>0101010=>1010101
[5,6,3,8,1,2,7,4]=>0101001=>1010110
[4,2,5,3,7,1,6,8]=>1010100=>0101011
[4,3,6,7,2,1,8,5]=>1001101=>0110010
[3,4,6,7,2,8,1,5]=>0001010=>1110101
[3,4,5,2,7,8,1,6]=>0010010=>1101101
[3,4,2,5,6,8,1,7]=>0100010=>1011101
[5,2,7,8,6,4,1,3]=>1001110=>0110001
[5,1,2,7,8,6,4,3]=>1000111=>0111000
[4,7,1,8,6,5,2,3]=>0101110=>1010001
[4,7,1,2,8,6,5,3]=>0100111=>1011000
[4,6,8,1,2,7,5,3]=>0010011=>1101100
[6,8,7,1,5,3,2,4]=>0110110=>1001001
[6,8,7,3,5,1,2,4]=>0110100=>1001011
[7,8,1,6,3,5,2,4]=>0101010=>1010101
[7,8,1,3,6,5,2,4]=>0100110=>1011001
[7,8,3,6,5,2,1,4]=>0101110=>1010001
[4,7,2,8,6,1,5,3]=>0101101=>1010010
[1,7,3,4,8,6,5,2]=>0100111=>1011000
[4,2,7,1,8,6,5,3]=>1010111=>0101000
[7,8,2,3,6,5,1,4]=>0100110=>1011001
[8,5,7,1,6,2,3,4]=>1010100=>0101011
[8,5,7,1,2,6,3,4]=>1010010=>0101101
[6,8,2,7,1,3,5,4]=>0101001=>1010110
[6,8,7,2,5,3,1,4]=>0110110=>1001001
[6,2,4,8,7,1,5,3]=>1001101=>0110010
[1,6,8,3,7,4,5,2]=>0010101=>1101010
[1,6,8,3,4,7,5,2]=>0010011=>1101100
[6,2,4,8,1,7,5,3]=>1001011=>0110100
[6,8,7,2,3,5,1,4]=>0110010=>1001101
[6,8,2,1,7,3,5,4]=>0110101=>1001010
[8,5,7,2,1,6,3,4]=>1011010=>0100101
[8,5,7,1,2,3,6,4]=>1010001=>0101110
[8,7,6,2,1,4,3,5]=>1111010=>0000101
[8,5,7,2,3,1,6,4]=>1010101=>0101010
[5,8,4,2,7,1,6,3]=>0110101=>1001010
[1,8,7,5,3,4,6,2]=>0111001=>1000110
[1,8,7,3,5,4,6,2]=>0110101=>1001010
[8,2,5,4,7,1,6,3]=>1010101=>0101010
[8,5,2,7,3,1,6,4]=>1101101=>0010010
[8,7,6,2,4,3,1,5]=>1110110=>0001001
[8,7,6,1,2,4,3,5]=>1110010=>0001101
[8,7,6,1,4,2,3,5]=>1110100=>0001011
[8,7,6,4,1,3,2,5]=>1111010=>0000101
[5,8,4,7,2,1,6,3]=>0101101=>1010010
[1,8,7,5,4,3,6,2]=>0111101=>1000010
[1,6,8,4,3,7,5,2]=>0011011=>1100100
[6,8,7,3,2,5,1,4]=>0111010=>1000101
[6,8,1,7,3,2,5,4]=>0101101=>1010010
[8,5,7,3,1,6,2,4]=>1011010=>0100101
[8,5,7,1,3,2,6,4]=>1010101=>0101010
[8,5,7,3,1,2,6,4]=>1011001=>0100110
[5,8,4,7,1,2,6,3]=>0101001=>1010110
[5,8,4,1,7,2,6,3]=>0110101=>1001010
[5,8,4,7,1,6,2,3]=>0101010=>1010101
[8,1,2,6,5,7,4,3]=>1001011=>0110100
[8,2,5,6,7,4,1,3]=>1000110=>0111001
[4,8,5,7,1,6,2,3]=>0101010=>1010101
[4,8,5,7,1,2,6,3]=>0101001=>1010110
[4,8,5,1,7,2,6,3]=>0110101=>1001010
[8,5,3,1,7,2,6,4]=>1110101=>0001010
[8,5,3,7,1,2,6,4]=>1101001=>0010110
[6,8,1,3,7,2,5,4]=>0100101=>1011010
[4,6,2,8,1,7,5,3]=>0101011=>1010100
[1,6,4,8,3,7,5,2]=>0101011=>1010100
[1,8,7,4,5,3,6,2]=>0110101=>1001010
[4,8,5,7,2,1,6,3]=>0101101=>1010010
[8,5,3,7,2,1,6,4]=>1101101=>0010010
[8,7,6,3,1,4,2,5]=>1111010=>0000101
[8,7,6,1,3,2,4,5]=>1110100=>0001011
[8,5,3,2,7,1,6,4]=>1110101=>0001010
[4,8,5,2,7,1,6,3]=>0110101=>1001010
[1,8,7,4,3,5,6,2]=>0111001=>1000110
[1,8,7,3,4,5,6,2]=>0110001=>1001110
[8,2,4,5,7,1,6,3]=>1000101=>0111010
[8,5,2,3,7,1,6,4]=>1100101=>0011010
[6,3,1,5,4,2,8,7]=>1101101=>0010010
[8,3,1,5,2,7,6,4]=>1101011=>0010100
[8,5,4,2,1,7,3,6]=>1111010=>0000101
[8,5,4,2,1,7,6,3]=>1111011=>0000100
[6,5,4,2,1,3,8,7]=>1111001=>0000110
[6,5,4,2,3,1,8,7]=>1110101=>0001010
[6,3,2,5,1,4,8,7]=>1101001=>0010110
[6,5,4,3,1,2,8,7]=>1111001=>0000110
[6,5,4,1,3,2,8,7]=>1110101=>0001010
[8,5,4,1,2,7,6,3]=>1110011=>0001100
[8,7,4,1,6,3,2,5]=>1110110=>0001001
[8,7,4,1,6,3,5,2]=>1110101=>0001010
[8,7,4,1,6,5,3,2]=>1110111=>0001000
[8,5,4,1,3,7,6,2]=>1110011=>0001100
[8,5,4,3,1,7,6,2]=>1111011=>0000100
[8,3,2,5,1,7,6,4]=>1101011=>0010100
[2,1,8,5,3,7,6,4]=>1011011=>0100100
[8,3,2,5,1,7,4,6]=>1101010=>0010101
[8,5,4,3,1,7,2,6]=>1111010=>0000101
[8,5,4,1,3,7,2,6]=>1110010=>0001101
[8,7,4,1,6,5,2,3]=>1110110=>0001001
[8,7,4,1,6,2,5,3]=>1110101=>0001010
[8,7,6,5,2,1,4,3]=>1111101=>0000010
[8,7,4,3,6,2,1,5]=>1110110=>0001001
[8,3,2,7,6,4,1,5]=>1101110=>0010001
[2,1,8,7,6,4,3,5]=>1011110=>0100001
[2,1,8,7,6,4,5,3]=>1011101=>0100010
[8,3,2,7,6,4,5,1]=>1101101=>0010010
[8,7,4,3,6,2,5,1]=>1110101=>0001010
[8,7,6,5,2,4,3,1]=>1111011=>0000100
[8,5,4,2,3,7,6,1]=>1110011=>0001100
[8,7,4,2,6,5,3,1]=>1110111=>0001000
[8,7,4,2,6,3,5,1]=>1110101=>0001010
[8,7,4,2,6,3,1,5]=>1110110=>0001001
[8,3,1,7,6,4,2,5]=>1101110=>0010001
[8,3,1,7,6,4,5,2]=>1101101=>0010010
[8,3,1,7,6,5,4,2]=>1101111=>0010000
[8,3,1,5,4,7,6,2]=>1101011=>0010100
[8,3,1,5,4,7,2,6]=>1101010=>0010101
[8,3,1,7,6,5,2,4]=>1101110=>0010001
[8,3,1,7,6,2,5,4]=>1101101=>0010010
[8,7,4,2,6,1,5,3]=>1110101=>0001010
[8,7,4,2,6,5,1,3]=>1110110=>0001001
[8,5,4,2,3,7,1,6]=>1110010=>0001101
[8,3,2,5,4,7,1,6]=>1101010=>0010101
[2,1,8,5,4,7,3,6]=>1011010=>0100101
[8,3,2,7,6,5,1,4]=>1101110=>0010001
[8,7,4,3,6,5,1,2]=>1110110=>0001001
[8,7,6,5,3,1,4,2]=>1111101=>0000010
[8,7,6,5,1,3,2,4]=>1111010=>0000101
[8,7,6,5,1,3,4,2]=>1111001=>0000110
[8,7,6,5,1,4,3,2]=>1111011=>0000100
[8,7,6,5,4,1,3,2]=>1111101=>0000010
[8,7,4,3,6,1,5,2]=>1110101=>0001010
[8,3,2,7,6,1,5,4]=>1101101=>0010010
[2,1,8,7,6,3,5,4]=>1011101=>0100010
[8,3,2,7,6,1,4,5]=>1101100=>0010011
[8,7,6,5,1,4,2,3]=>1111010=>0000101
[8,7,6,5,1,2,4,3]=>1111001=>0000110
[7,3,5,1,8,4,6,2]=>1010101=>0101010
[7,3,4,1,8,5,6,2]=>1010101=>0101010
[4,5,6,2,1,8,7,3]=>0011011=>1100100
[1,6,5,2,7,4,3,8]=>0110110=>1001001
[7,4,3,1,8,6,5,2]=>1110111=>0001000
[7,6,5,1,8,4,3,2]=>1110111=>0001000
[7,6,4,1,8,5,3,2]=>1110111=>0001000
[6,4,2,1,8,7,5,3]=>1110111=>0001000
[1,6,4,2,7,5,3,8]=>0110110=>1001001
[1,5,3,2,7,6,4,8]=>0110110=>1001001
[5,3,2,1,8,7,6,4]=>1110111=>0001000
[2,5,3,1,7,8,6,4]=>0110011=>1001100
[2,6,4,1,7,8,5,3]=>0110011=>1001100
[2,6,5,1,7,8,4,3]=>0110011=>1001100
[4,5,7,1,6,8,2,3]=>0010010=>1101101
[6,5,1,2,8,4,3,7]=>1100110=>0011001
[6,4,1,2,8,5,3,7]=>1100110=>0011001
[5,3,1,2,8,6,4,7]=>1100110=>0011001
[4,3,1,2,8,6,5,7]=>1100110=>0011001
[6,1,2,5,8,3,4,7]=>1000100=>0111011
[7,1,3,4,8,2,5,6]=>1000100=>0111011
[7,1,5,6,8,2,3,4]=>1000100=>0111011
[2,6,1,5,7,8,3,4]=>0100010=>1011101
[7,4,1,6,8,5,2,3]=>1100110=>0011001
[5,2,3,1,8,6,7,4]=>1010101=>0101010
[3,5,2,1,6,8,7,4]=>0110011=>1001100
[1,6,2,5,7,3,4,8]=>0100100=>1011011
[6,2,1,5,8,7,3,4]=>1100110=>0011001
[7,3,1,5,8,6,2,4]=>1100110=>0011001
[6,2,4,1,8,5,7,3]=>1010101=>0101010
[6,2,5,1,8,4,7,3]=>1010101=>0101010
[7,3,1,4,8,6,2,5]=>1100110=>0011001
[6,2,1,4,8,7,3,5]=>1100110=>0011001
[1,6,2,4,7,3,5,8]=>0100100=>1011011
[5,2,1,3,8,7,4,6]=>1100110=>0011001
[7,4,1,3,8,5,2,6]=>1100110=>0011001
[7,5,1,3,8,4,2,6]=>1100110=>0011001
[3,6,7,1,4,8,2,5]=>0010010=>1101101
[7,6,1,4,8,3,2,5]=>1100110=>0011001
[4,2,1,3,8,7,5,6]=>1100110=>0011001
[2,6,1,4,7,8,3,5]=>0100010=>1011101
[7,1,4,6,8,2,3,5]=>1000100=>0111011
[7,1,3,5,8,2,4,6]=>1000100=>0111011
[6,1,2,4,8,3,5,7]=>1000100=>0111011
[5,2,3,1,6,4,8,7]=>1010101=>0101010
[7,4,5,2,3,1,8,6]=>1010101=>0101010
[8,6,7,3,5,2,4,1]=>1010101=>0101010
[7,3,5,2,4,1,8,6]=>1010101=>0101010
[6,3,5,2,4,1,8,7]=>1010101=>0101010
[5,2,4,1,6,3,8,7]=>1010101=>0101010
[4,1,6,3,5,2,8,7]=>1010101=>0101010
[6,3,4,1,5,2,8,7]=>1010101=>0101010
[5,2,6,3,4,1,8,7]=>1010101=>0101010
[5,2,7,3,4,1,8,6]=>1010101=>0101010
[5,2,8,6,7,3,4,1]=>1010101=>0101010
[6,2,8,5,7,3,4,1]=>1010101=>0101010
[6,2,7,3,4,1,8,5]=>1010101=>0101010
[7,3,4,1,5,2,8,6]=>1010101=>0101010
[4,1,7,3,5,2,8,6]=>1010101=>0101010
[3,1,7,4,5,2,8,6]=>1010101=>0101010
[2,1,7,4,5,3,8,6]=>1010101=>0101010
[3,1,8,6,7,4,5,2]=>1010101=>0101010
[4,1,8,6,7,3,5,2]=>1010101=>0101010
[8,6,7,3,4,1,5,2]=>1010101=>0101010
[8,5,7,3,4,1,6,2]=>1010101=>0101010
[8,5,6,2,7,3,4,1]=>1010101=>0101010
[8,4,7,3,5,1,6,2]=>1010101=>0101010
[5,1,8,4,7,3,6,2]=>1010101=>0101010
[4,1,8,5,7,3,6,2]=>1010101=>0101010
[3,1,8,5,7,4,6,2]=>1010101=>0101010
[2,1,8,5,7,4,6,3]=>1010101=>0101010
[2,1,7,4,6,3,8,5]=>1010101=>0101010
[3,1,7,4,6,2,8,5]=>1010101=>0101010
[4,1,7,3,6,2,8,5]=>1010101=>0101010
[5,1,7,3,6,2,8,4]=>1010101=>0101010
[6,2,7,3,5,1,8,4]=>1010101=>0101010
[6,2,8,4,7,3,5,1]=>1010101=>0101010
[8,4,7,3,6,2,5,1]=>1010101=>0101010
[7,3,6,2,5,1,8,4]=>1010101=>0101010
[6,2,5,1,7,3,8,4]=>1010101=>0101010
[5,2,4,1,7,3,8,6]=>1010101=>0101010
[6,2,4,1,7,3,8,5]=>1010101=>0101010
[8,5,7,3,6,2,4,1]=>1010101=>0101010
[8,5,7,4,6,2,3,1]=>1010101=>0101010
[7,4,6,2,3,1,8,5]=>1010101=>0101010
[6,2,3,1,7,4,8,5]=>1010101=>0101010
[5,2,3,1,7,4,8,6]=>1010101=>0101010
[4,2,3,1,7,5,8,6]=>1010101=>0101010
[3,1,4,2,8,6,7,5]=>1010101=>0101010
[6,2,3,1,8,5,7,4]=>1010101=>0101010
[8,5,6,2,3,1,7,4]=>1010101=>0101010
[7,4,8,5,6,2,3,1]=>1010101=>0101010
[7,3,8,5,6,2,4,1]=>1010101=>0101010
[8,5,6,2,4,1,7,3]=>1010101=>0101010
[5,2,4,1,8,6,7,3]=>1010101=>0101010
[4,1,5,2,8,6,7,3]=>1010101=>0101010
[3,1,5,2,8,6,7,4]=>1010101=>0101010
[2,1,6,3,8,5,7,4]=>1010101=>0101010
[3,1,6,2,8,5,7,4]=>1010101=>0101010
[4,1,6,2,8,5,7,3]=>1010101=>0101010
[5,1,6,2,8,4,7,3]=>1010101=>0101010
[8,4,6,2,5,1,7,3]=>1010101=>0101010
[7,3,8,4,6,2,5,1]=>1010101=>0101010
[6,2,7,3,8,4,5,1]=>1010101=>0101010
[8,4,5,1,6,2,7,3]=>1010101=>0101010
[5,1,8,4,6,2,7,3]=>1010101=>0101010
[4,1,8,5,6,2,7,3]=>1010101=>0101010
[3,1,8,5,6,2,7,4]=>1010101=>0101010
[2,1,8,5,6,3,7,4]=>1010101=>0101010
[2,1,7,4,8,5,6,3]=>1010101=>0101010
[3,1,7,4,8,5,6,2]=>1010101=>0101010
[4,1,7,3,8,5,6,2]=>1010101=>0101010
[7,3,8,4,5,1,6,2]=>1010101=>0101010
[8,4,5,1,7,3,6,2]=>1010101=>0101010
[7,3,6,2,8,4,5,1]=>1010101=>0101010
[7,8,5,6,1,3,4,2]=>0101001=>1010110
[7,8,1,3,6,2,5,4]=>0100101=>1011010
[1,3,8,4,7,2,5,6]=>0010100=>1101011
[3,6,1,4,7,2,5,8]=>0100100=>1011011
[4,6,1,2,5,7,3,8]=>0100010=>1011101
[1,4,8,2,5,7,3,6]=>0010010=>1101101
[7,8,2,4,5,6,1,3]=>0100010=>1011101
[7,8,1,5,4,6,3,2]=>0101011=>1010100
[7,8,2,1,6,3,4,5]=>0110100=>1001011
[7,8,3,5,6,4,1,2]=>0100110=>1011001
[7,8,1,4,2,3,6,5]=>0101001=>1010110
[7,8,5,1,4,2,6,3]=>0110101=>1001010
[7,8,4,5,3,1,6,2]=>0101101=>1010010
[1,5,8,4,3,2,7,6]=>0011101=>1100010
[5,6,1,4,3,2,7,8]=>0101100=>1010011
[2,6,4,8,3,7,1,5]=>0101010=>1010101
[1,4,6,8,3,7,5,2]=>0001011=>1110100
[2,4,8,5,3,1,6,7]=>0011100=>1100011
[2,5,8,1,4,7,6,3]=>0010011=>1101100
[3,5,8,4,7,6,1,2]=>0010110=>1101001
[1,6,2,4,7,3,8,5]=>0100101=>1011010
[5,6,2,1,4,7,8,3]=>0110001=>1001110
[4,6,2,5,3,1,8,7]=>0101101=>1010010
[4,7,5,1,3,6,8,2]=>0110001=>1001110
[7,5,3,6,2,4,1,8]=>1101010=>0010101
[5,7,3,6,1,4,8,2]=>0101001=>1010110
[5,3,6,7,2,1,8,4]=>1001101=>0110010
[6,1,7,5,2,4,8,3]=>1011001=>0100110
[6,3,1,2,4,5,8,7]=>1100001=>0011110
[1,4,7,2,5,3,8,6]=>0010101=>1101010
[4,6,7,8,3,5,1,2]=>0001010=>1110101
[3,6,1,8,4,2,5,7]=>0101100=>1010011
[1,6,7,5,8,2,4,3]=>0010101=>1101010
[3,5,6,7,8,1,4,2]=>0000101=>1111010
[3,6,5,7,8,2,1,4]=>0100110=>1011001
[5,2,7,6,1,4,3,8]=>1011010=>0100101
[2,5,7,6,8,1,3,4]=>0010100=>1101011
[2,7,5,6,8,4,1,3]=>0100110=>1011001
[2,1,6,8,4,5,3,7]=>1001010=>0110101
[2,7,1,8,5,3,4,6]=>0101100=>1010011
[3,7,6,8,5,4,1,2]=>0101110=>1010001
[4,3,8,5,6,7,1,2]=>1010010=>0101101
[4,2,8,1,6,3,7,5]=>1010101=>0101010
[3,1,8,5,4,6,7,2]=>1011001=>0100110
[3,2,8,4,5,6,1,7]=>1010010=>0101101
[3,4,2,8,6,1,7,5]=>0101101=>1010010
[3,4,7,1,5,2,6,8]=>0010100=>1101011
[4,3,7,8,1,2,6,5]=>1001001=>0110110
[1,7,3,8,5,2,6,4]=>0101101=>1010010
[4,1,8,3,6,2,5,7]=>1010100=>0101011
[5,7,8,6,3,2,1,4]=>0011110=>1100001
[5,7,8,6,1,3,4,2]=>0011001=>1100110
[7,6,5,8,1,3,4,2]=>1101001=>0010110
[1,6,4,3,8,2,5,7]=>0110100=>1001011
[7,1,3,4,8,2,6,5]=>1000101=>0111010
[3,6,5,4,1,2,7,8]=>0111000=>1000111
[2,4,5,1,7,8,6,3]=>0010011=>1101100
[2,6,3,4,5,8,1,7]=>0100010=>1011101
[2,6,4,1,8,3,7,5]=>0110101=>1001010
[7,3,6,4,8,5,1,2]=>1010110=>0101001
[7,2,1,4,8,3,5,6]=>1100100=>0011011
[7,1,6,5,3,8,4,2]=>1011011=>0100100
[7,2,5,6,3,8,1,4]=>1001010=>0110101
[6,5,2,7,1,8,4,3]=>1101011=>0010100
[5,6,2,7,3,1,4,8]=>0101100=>1010011
[5,6,7,4,2,8,1,3]=>0011010=>1100101
[5,7,6,4,1,8,3,2]=>0111011=>1000100
[6,7,1,5,2,8,3,4]=>0101010=>1010101
[1,7,5,2,4,8,3,6]=>0110010=>1001101
[6,1,5,2,8,3,4,7]=>1010100=>0101011
[6,7,5,3,8,4,1,2]=>0110110=>1001001
[1,6,5,4,2,3,8,7]=>0111001=>1000110
[7,1,5,3,4,2,8,6]=>1010101=>0101010
[7,6,1,5,3,2,8,4]=>1101101=>0010010
[7,5,6,4,1,2,8,3]=>1011001=>0100110
[6,7,5,4,3,1,8,2]=>0111101=>1000010
[7,5,2,4,3,1,6,8]=>1101100=>0010011
[7,4,6,1,2,5,3,8]=>1010010=>0101101
[7,1,4,2,5,3,6,8]=>1010100=>0101011
[6,8,1,4,2,5,7,3]=>0101001=>1010110
[1,6,4,2,5,7,3,8]=>0110010=>1001101
[1,6,3,7,5,4,2,8]=>0101110=>1010001
[6,8,1,3,7,5,4,2]=>0100111=>1011000
[7,1,3,5,6,4,2,8]=>1000110=>0111001
[7,3,1,6,4,5,2,8]=>1101010=>0010101
[7,4,2,6,5,1,3,8]=>1101100=>0010011
[7,4,6,3,1,5,2,8]=>1011010=>0100101
[7,2,4,1,5,3,6,8]=>1010100=>0101011
[7,2,3,5,4,1,6,8]=>1001100=>0110011
[6,8,1,2,3,4,7,5]=>0100001=>1011110
[1,5,7,2,3,8,6,4]=>0010011=>1101100
[5,1,8,2,3,6,7,4]=>1010001=>0101110
[5,8,2,3,7,6,4,1]=>0100111=>1011000
[6,2,8,1,3,7,4,5]=>1010010=>0101101
[6,8,2,3,5,4,7,1]=>0100101=>1011010
[6,8,2,4,1,5,7,3]=>0101001=>1010110
[6,8,3,1,2,4,7,5]=>0110001=>1001110
[2,6,4,1,5,7,3,8]=>0110010=>1001101
[2,6,3,5,7,1,4,8]=>0100100=>1011011
[2,5,1,7,8,3,6,4]=>0100101=>1011010
[2,5,3,6,8,4,7,1]=>0100101=>1011010
[2,1,4,7,8,5,6,3]=>1000101=>0111010
[2,4,7,6,8,5,1,3]=>0010110=>1101001
[2,5,3,7,6,1,8,4]=>0101101=>1010010
[2,5,7,8,1,4,6,3]=>0001001=>1110110
[3,5,7,4,1,6,2,8]=>0011010=>1100101
[5,3,4,1,8,6,7,2]=>1010101=>0101010
[5,2,8,4,6,1,7,3]=>1010101=>0101010
[5,2,1,8,6,3,7,4]=>1101101=>0010010
[4,2,8,6,5,3,7,1]=>1011101=>0100010
[4,2,8,5,7,6,3,1]=>1010111=>0101000
[1,4,2,7,5,8,6,3]=>0101011=>1010100
[4,1,8,6,7,5,3,2]=>1010111=>0101000
[5,3,8,7,6,2,4,1]=>1011101=>0100010
[5,8,4,7,6,2,1,3]=>0101110=>1010001
[5,8,7,4,3,6,1,2]=>0111010=>1000101
[6,4,8,3,1,7,2,5]=>1011010=>0100101
[6,4,2,8,7,1,3,5]=>1101100=>0010011
[6,3,8,7,2,5,1,4]=>1011010=>0100101
[5,8,3,7,1,6,4,2]=>0101011=>1010100
[5,1,3,8,6,7,2,4]=>1001010=>0110101
[1,5,3,7,8,6,2,4]=>0100110=>1011001
[1,5,7,6,4,2,8,3]=>0011101=>1100010
[5,8,7,4,1,6,2,3]=>0111010=>1000101
[6,4,8,1,2,7,3,5]=>1010010=>0101101
[6,8,5,1,2,3,7,4]=>0110001=>1001110
[6,8,5,2,4,3,7,1]=>0110101=>1001010
[6,8,5,3,1,2,7,4]=>0111001=>1000110
[4,5,1,2,7,6,3,8]=>0100110=>1011001
[4,5,1,2,6,8,7,3]=>0100011=>1011100
[3,5,6,1,8,4,7,2]=>0010101=>1101010
[3,5,7,1,2,8,6,4]=>0010011=>1101100
[3,6,2,7,5,1,4,8]=>0101100=>1010011
[4,2,6,1,7,3,5,8]=>1010100=>0101011
[4,6,3,1,2,7,5,8]=>0110010=>1001101
[4,5,3,1,7,6,2,8]=>0110110=>1001001
[4,2,5,7,1,6,3,8]=>1001010=>0110101
[3,5,2,7,8,1,6,4]=>0100101=>1011010
[3,1,4,7,5,6,2,8]=>1001010=>0110101
[3,4,6,5,8,7,1,2]=>0010110=>1101001
[3,1,4,5,8,6,7,2]=>1000101=>0111010
[3,4,6,8,5,2,7,1]=>0001101=>1110010
[3,5,6,2,8,4,7,1]=>0010101=>1101010
[4,2,5,6,1,8,7,3]=>1001011=>0110100
[4,5,3,1,6,8,7,2]=>0110011=>1001100
[2,1,7,5,8,6,4,3]=>1010111=>0101000
[1,2,7,5,3,8,6,4]=>0011011=>1100100
[4,1,2,7,3,8,6,5]=>1001011=>0110100
[6,4,1,7,5,2,3,8]=>1101100=>0010011
[6,1,3,7,5,2,4,8]=>1001100=>0110011
[3,1,2,6,8,5,4,7]=>1000110=>0111001
[3,7,1,2,5,4,8,6]=>0100101=>1011010
[1,3,7,2,4,8,6,5]=>0010011=>1101100
[2,4,1,7,8,6,5,3]=>0100111=>1011000
[3,4,7,5,1,8,6,2]=>0011011=>1100100
[2,7,4,1,5,8,6,3]=>0110011=>1001100
[2,3,7,1,5,8,6,4]=>0010011=>1101100
[5,2,8,1,3,7,4,6]=>1010010=>0101101
[2,1,6,8,3,4,7,5]=>1001001=>0110110
[2,6,8,3,1,5,7,4]=>0011001=>1100110
[2,8,6,4,1,5,7,3]=>0111001=>1000110
[3,6,4,8,5,1,7,2]=>0101101=>1010010
[6,3,7,4,5,1,8,2]=>1010101=>0101010
[2,6,3,7,5,8,1,4]=>0101010=>1010101
[5,2,1,7,8,3,4,6]=>1100100=>0011011
[4,7,2,3,6,8,1,5]=>0100010=>1011101
[5,2,7,3,6,8,1,4]=>1010010=>0101101
[5,7,4,6,2,8,1,3]=>0101010=>1010101
[5,7,3,4,6,1,8,2]=>0100101=>1011010
[5,3,8,4,6,1,7,2]=>1010101=>0101010
[8,5,2,4,1,6,7,3]=>1101001=>0010110
[8,2,3,5,1,6,7,4]=>1001001=>0110110
[4,2,8,3,6,7,1,5]=>1010010=>0101101
[2,4,8,1,7,3,5,6]=>0010100=>1101011
[8,4,1,3,6,2,5,7]=>1100100=>0011011
[4,8,3,1,7,2,5,6]=>0110100=>1001011
[5,2,8,4,7,1,6,3]=>1010101=>0101010
[5,8,4,7,3,1,6,2]=>0101101=>1010010
[4,6,8,3,1,7,5,2]=>0011011=>1100100
[6,3,8,2,7,1,5,4]=>1010101=>0101010
[6,3,1,8,2,4,7,5]=>1101001=>0010110
[5,3,8,1,2,6,4,7]=>1010010=>0101101
[5,7,4,1,6,2,3,8]=>0110100=>1001011
[8,5,4,1,2,6,3,7]=>1110010=>0001101
[5,1,8,4,2,7,3,6]=>1011010=>0100101
[1,6,2,8,5,3,7,4]=>0101101=>1010010
[6,8,5,3,1,7,4,2]=>0111011=>1000100
[8,4,5,1,2,6,3,7]=>1010010=>0101101
[5,6,3,7,1,2,4,8]=>0101000=>1010111
[1,6,3,7,2,8,4,5]=>0101010=>1010101
[6,3,2,7,8,5,1,4]=>1100110=>0011001
[4,5,7,8,3,1,6,2]=>0001101=>1110010
[4,7,2,5,8,1,6,3]=>0100101=>1011010
[8,1,3,4,6,2,5,7]=>1000100=>0111011
[3,8,2,4,6,7,1,5]=>0100010=>1011101
[3,5,6,8,2,7,1,4]=>0001010=>1110101
[2,4,5,6,8,1,7,3]=>0000101=>1111010
[4,8,3,5,6,1,7,2]=>0100101=>1011010
[5,6,2,3,7,8,1,4]=>0100010=>1011101
[5,8,7,3,4,1,2,6]=>0110100=>1001011
[6,8,7,3,4,1,2,5]=>0110100=>1001011
[6,8,4,7,1,5,3,2]=>0101011=>1010100
[6,8,4,7,2,5,3,1]=>0101011=>1010100
[5,4,8,7,2,6,3,1]=>1011011=>0100100
[5,4,8,7,1,6,3,2]=>1011011=>0100100
[5,3,8,7,6,1,2,4]=>1011100=>0100011
[4,3,8,7,6,1,2,5]=>1011100=>0100011
[4,8,3,7,5,1,2,6]=>0101100=>1010011
[8,3,4,6,5,1,2,7]=>1001100=>0110011
[3,8,4,7,5,1,2,6]=>0101100=>1010011
[3,4,8,7,6,1,2,5]=>0011100=>1100011
[3,5,8,7,6,1,2,4]=>0011100=>1100011
[4,5,8,7,6,1,2,3]=>0011100=>1100011
[4,5,8,7,1,6,3,2]=>0011011=>1100100
[4,5,8,7,2,6,3,1]=>0011011=>1100100
[3,5,8,2,7,6,4,1]=>0010111=>1101000
[3,5,8,1,7,6,4,2]=>0010111=>1101000
[2,5,8,1,7,6,4,3]=>0010111=>1101000
[2,5,8,7,1,6,3,4]=>0011010=>1100101
[2,4,8,7,1,6,3,5]=>0011010=>1100101
[2,8,4,7,1,5,3,6]=>0101010=>1010101
[8,2,4,6,1,5,3,7]=>1001010=>0110101
[8,1,4,6,2,5,3,7]=>1001010=>0110101
[1,8,4,7,2,5,3,6]=>0101010=>1010101
[1,4,8,7,2,6,3,5]=>0011010=>1100101
[1,5,8,7,2,6,3,4]=>0011010=>1100101
[1,5,8,2,7,6,4,3]=>0010111=>1101000
[2,5,8,3,7,6,4,1]=>0010111=>1101000
[1,4,2,8,7,6,5,3]=>0101111=>1010000
[1,3,8,2,7,6,4,5]=>0010110=>1101001
[1,8,3,2,7,5,4,6]=>0110110=>1001001
[8,1,3,2,6,5,4,7]=>1010110=>0101001
[8,2,3,1,6,5,4,7]=>1010110=>0101001
[2,8,3,1,7,5,4,6]=>0110110=>1001001
[2,3,8,1,7,6,4,5]=>0010110=>1101001
[3,4,1,8,7,6,5,2]=>0101111=>1010000
[4,3,1,8,7,6,5,2]=>1101111=>0010000
[4,2,1,8,7,6,5,3]=>1101111=>0010000
[3,8,2,1,7,5,4,6]=>0110110=>1001001
[8,3,2,1,6,5,4,7]=>1110110=>0001001
[8,4,2,6,1,5,3,7]=>1101010=>0010101
[4,2,8,7,1,6,3,5]=>1011010=>0100101
[5,2,8,7,1,6,3,4]=>1011010=>0100101
[5,2,8,1,7,6,4,3]=>1010111=>0101000
[5,3,8,1,7,6,4,2]=>1010111=>0101000
[5,3,8,2,7,6,4,1]=>1010111=>0101000
[6,8,3,2,7,5,4,1]=>0110111=>1001000
[6,8,3,1,7,5,4,2]=>0110111=>1001000
[6,8,2,1,7,5,4,3]=>0110111=>1001000
[6,8,2,7,1,5,3,4]=>0101010=>1010101
[6,8,7,2,1,4,3,5]=>0111010=>1000101
[8,5,6,1,2,4,3,7]=>1010010=>0101101
[5,8,7,1,2,4,3,6]=>0110010=>1001101
[6,8,1,2,7,5,4,3]=>0100111=>1011000
[6,8,2,3,7,5,4,1]=>0100111=>1011000
[5,2,8,3,7,6,4,1]=>1010111=>0101000
[5,1,8,3,7,6,4,2]=>1010111=>0101000
[5,1,8,7,2,6,3,4]=>1011010=>0100101
[4,1,8,7,2,6,3,5]=>1011010=>0100101
[4,8,1,7,2,5,3,6]=>0101010=>1010101
[8,4,1,6,2,5,3,7]=>1101010=>0010101
[8,3,1,2,6,5,4,7]=>1100110=>0011001
[3,8,1,2,7,5,4,6]=>0100110=>1011001
[3,1,8,2,7,6,4,5]=>1010110=>0101001
[3,1,2,8,7,6,5,4]=>1001111=>0110000
[4,1,3,8,7,6,5,2]=>1001111=>0110000
[3,1,4,8,7,6,5,2]=>1001111=>0110000
[2,1,8,3,7,6,4,5]=>1010110=>0101001
[2,8,1,3,7,5,4,6]=>0100110=>1011001
[8,2,1,3,6,5,4,7]=>1100110=>0011001
[8,1,2,3,6,5,4,7]=>1000110=>0111001
[1,8,2,3,7,5,4,6]=>0100110=>1011001
[1,2,8,3,7,6,4,5]=>0010110=>1101001
[1,4,3,6,8,2,5,7]=>0100100=>1011011
[3,1,6,2,5,8,4,7]=>1010010=>0101101
[3,5,1,8,2,4,7,6]=>0101001=>1010110
[1,4,5,2,8,3,7,6]=>0010101=>1101010
[1,4,2,6,5,8,3,7]=>0101010=>1010101
[1,5,4,2,6,8,3,7]=>0110010=>1001101
[3,1,6,5,8,2,4,7]=>1010100=>0101011
[1,6,4,2,5,8,3,7]=>0110010=>1001101
[1,5,2,6,4,8,3,7]=>0101010=>1010101
[1,2,6,5,4,8,3,7]=>0011010=>1100101
[1,2,5,4,7,3,8,6]=>0010101=>1101010
[4,1,2,6,3,8,7,5]=>1001011=>0110100
[7,1,5,4,2,8,3,6]=>1011010=>0100101
[1,4,7,5,2,8,3,6]=>0011010=>1100101
[7,1,3,5,2,8,4,6]=>1001010=>0110101
[7,2,5,1,8,3,4,6]=>1010100=>0101011
[1,4,5,2,8,7,3,6]=>0010110=>1101001
[1,6,4,2,8,3,7,5]=>0110101=>1001010
[1,4,2,8,3,7,6,5]=>0101011=>1010100
[1,2,5,3,8,7,6,4]=>0010111=>1101000
[1,2,8,6,5,3,7,4]=>0011101=>1100010
[1,5,2,8,6,3,7,4]=>0101101=>1010010
[1,6,4,2,8,7,3,5]=>0110110=>1001001
[6,2,1,8,7,3,4,5]=>1101100=>0010011
[7,6,2,1,8,3,4,5]=>1110100=>0001011
[7,3,1,6,2,8,4,5]=>1101010=>0010101
[1,7,6,4,2,8,3,5]=>0111010=>1000101
[1,7,5,2,6,3,8,4]=>0110101=>1001010
[1,6,2,7,5,3,8,4]=>0101101=>1010010
[1,2,7,6,5,3,8,4]=>0011101=>1100010
[1,2,6,5,3,8,7,4]=>0011011=>1100100
[1,5,2,6,3,8,7,4]=>0101011=>1010100
[1,5,2,7,6,3,8,4]=>0101101=>1010010
[1,6,5,2,7,3,8,4]=>0110101=>1001010
[1,5,7,4,2,8,3,6]=>0011010=>1100101
[4,1,2,8,6,3,7,5]=>1001101=>0110010
[3,1,8,6,2,4,7,5]=>1011001=>0100110
[4,3,7,1,8,2,5,6]=>1010100=>0101011
[8,3,1,6,2,4,7,5]=>1101001=>0010110
[7,1,8,3,2,4,6,5]=>1011001=>0100110
[1,8,7,3,2,4,6,5]=>0111001=>1000110
[1,4,2,8,7,3,6,5]=>0101101=>1010010
[1,7,4,2,8,3,6,5]=>0110101=>1001010
[8,1,5,4,2,7,3,6]=>1011010=>0100101
[1,4,8,5,2,7,3,6]=>0011010=>1100101
[8,5,3,1,7,2,4,6]=>1110100=>0001011
[8,6,2,1,7,3,4,5]=>1110100=>0001011
[1,8,6,4,2,7,3,5]=>0111010=>1000101
[1,8,5,2,6,3,7,4]=>0110101=>1001010
[1,5,2,7,3,8,6,4]=>0101011=>1010100
[1,2,8,5,3,7,6,4]=>0011011=>1100100
[1,2,6,3,8,7,5,4]=>0010111=>1101000
[1,2,7,6,3,8,5,4]=>0011011=>1100100
[1,6,2,7,3,8,5,4]=>0101011=>1010100
[1,7,2,8,5,3,6,4]=>0101101=>1010010
[1,7,4,2,8,6,3,5]=>0110110=>1001001
[7,1,8,3,2,6,4,5]=>1011010=>0100101
[7,2,1,8,6,3,4,5]=>1101100=>0010011
[1,8,7,3,2,6,4,5]=>0111010=>1000101
[1,4,2,8,7,6,3,5]=>0101110=>1010001
[1,2,8,7,5,3,6,4]=>0011101=>1100010
[1,2,8,6,3,7,5,4]=>0011011=>1100100
[1,2,7,3,8,6,5,4]=>0010111=>1101000
[4,1,7,3,6,5,8,2]=>1010101=>0101010
[5,1,8,7,6,2,4,3]=>1011101=>0100010
[8,1,7,6,3,4,5,2]=>1011001=>0100110
[5,7,8,6,2,4,1,3]=>0011010=>1100101
[5,7,1,6,2,4,3,8]=>0101010=>1010101
[6,4,1,5,2,7,3,8]=>1101010=>0010101
[8,1,4,5,3,7,6,2]=>1001011=>0110100
[6,1,4,5,3,8,7,2]=>1001011=>0110100
[6,1,4,5,3,7,8,2]=>1001001=>0110110
[5,1,7,8,6,2,4,3]=>1001101=>0110010
[6,1,4,8,3,5,7,2]=>1001001=>0110110
[7,1,8,6,3,4,5,2]=>1011001=>0100110
[7,1,4,5,3,8,6,2]=>1001011=>0110100
[7,1,4,5,3,6,8,2]=>1001001=>0110110
[8,1,4,5,3,6,7,2]=>1001001=>0110110
[7,4,1,5,2,6,3,8]=>1101010=>0010101
[6,3,5,7,2,1,4,8]=>1001100=>0110011
[6,3,5,8,2,1,7,4]=>1001101=>0110010
[6,3,5,7,2,1,8,4]=>1001101=>0110010
[8,4,5,7,3,6,1,2]=>1001010=>0110101
[6,4,5,8,3,7,2,1]=>1001011=>0110100
[5,8,7,6,2,4,1,3]=>0111010=>1000101
[5,4,8,6,3,1,7,2]=>1011101=>0100010
[5,4,1,8,2,3,7,6]=>1101001=>0010110
[5,8,1,6,2,4,3,7]=>0101010=>1010101
[8,4,1,5,2,6,3,7]=>1101010=>0010101
[6,3,5,8,2,1,4,7]=>1001100=>0110011
[2,3,4,1,8,6,5,7]=>0010110=>1101001
[8,3,5,6,2,1,4,7]=>1001100=>0110011
[2,3,8,5,1,4,7,6]=>0011001=>1100110
[2,3,8,6,1,5,7,4]=>0011001=>1100110
[2,8,6,7,1,3,5,4]=>0101001=>1010110
[8,3,5,7,2,1,6,4]=>1001101=>0110010
[2,3,8,5,6,1,7,4]=>0010101=>1101010
[7,4,5,6,3,1,8,2]=>1001101=>0110010
[8,4,5,6,3,1,7,2]=>1001101=>0110010
[7,3,5,6,2,8,1,4]=>1001010=>0110101
[7,3,5,8,2,1,6,4]=>1001101=>0110010
[7,3,5,6,2,1,4,8]=>1001100=>0110011
[2,7,6,5,1,3,4,8]=>0111000=>1000111
[2,7,6,8,1,3,5,4]=>0101001=>1010110
[2,7,6,5,8,3,1,4]=>0110110=>1001001
[8,7,5,6,1,4,2,3]=>1101010=>0010101
[2,6,4,1,8,5,7,3]=>0110101=>1001010
[2,6,1,3,8,5,7,4]=>0100101=>1011010
[2,7,1,3,6,5,8,4]=>0100101=>1011010
[2,7,6,8,4,3,1,5]=>0101110=>1010001
[2,7,6,1,8,3,4,5]=>0110100=>1001011
[2,7,6,1,4,3,5,8]=>0110100=>1001011
[7,3,5,1,2,8,4,6]=>1010010=>0101101
[8,4,1,5,2,3,7,6]=>1101001=>0010110
[7,8,1,6,3,4,2,5]=>0101010=>1010101
[6,4,1,8,3,2,7,5]=>1101101=>0010010
[2,3,8,6,4,1,7,5]=>0011101=>1100010
[2,8,6,7,4,3,1,5]=>0101110=>1010001
[8,3,5,7,2,4,1,6]=>1001010=>0110101
[2,3,4,1,8,7,5,6]=>0010110=>1101001
[2,8,6,1,7,3,4,5]=>0110100=>1001011
[2,3,8,1,6,4,7,5]=>0010101=>1101010
[2,3,8,1,4,5,7,6]=>0010001=>1101110
[2,8,6,1,4,3,5,7]=>0110100=>1001011
[1,2,3,4,5,6,7,9,8]=>00000001=>11111110
[2,1,3,4,5,6,7,8,9]=>10000000=>01111111
[1,2,3,4,5,6,7,8,10,9]=>000000001=>111111110
[2,1,3,4,5,6,7,8,9,10]=>100000000=>011111111
[1,2,3,4,5,6,7,8,9,11,10]=>0000000001=>1111111110
[9,1,2,3,4,5,6,7,10,8]=>100000001=>011111110
[1,8,2,3,4,5,6,9,7]=>01000001=>10111110
[7,1,2,3,4,5,6,9,8]=>10000001=>01111110
[2,1,9,3,4,5,6,7,8]=>10100000=>01011111
[2,8,1,3,4,5,6,7,9]=>01000000=>10111111
[2,10,1,3,4,5,6,7,8,9]=>010000000=>101111111
[2,1,3,4,5,6,7,8,9,10,11]=>1000000000=>0111111111
[8,4,3,6,5,1,7,2]=>1101101=>0010010
[8,5,6,3,4,1,7,2]=>1010101=>0101010
[8,6,5,4,3,1,7,2]=>1111101=>0000010
[1,7,6,5,4,2,3,8]=>0111100=>1000011
[1,8,6,5,2,7,3,4]=>0111010=>1000101
[8,7,5,4,1,6,3,2]=>1111011=>0000100
[7,8,5,4,1,3,6,2]=>0111001=>1000110
[6,8,5,4,2,1,7,3]=>0111101=>1000010
[5,8,6,2,4,1,7,3]=>0110101=>1001010
[4,8,2,6,5,1,7,3]=>0101101=>1010010
[3,2,8,6,5,1,7,4]=>1011101=>0100010
[3,2,1,7,6,4,5,8]=>1101100=>0010011
[4,1,3,7,6,2,5,8]=>1001100=>0110011
[5,1,7,3,6,2,4,8]=>1010100=>0101011
[6,1,7,5,3,2,4,8]=>1011100=>0100011
[7,1,6,5,2,4,3,8]=>1011010=>0100101
[8,1,6,5,2,3,7,4]=>1011001=>0100110
[1,2,7,6,3,4,5,8]=>0011000=>1100111
[1,2,8,3,7,4,5,6]=>0010100=>1101011
[8,1,7,2,6,3,5,4]=>1010101=>0101010
[7,1,8,2,6,4,3,5]=>1010110=>0101001
[6,1,8,2,4,7,3,5]=>1010010=>0101101
[5,1,8,3,2,7,4,6]=>1011010=>0100101
[4,1,3,8,2,7,5,6]=>1001010=>0110101
[3,2,1,8,4,7,5,6]=>1101010=>0010101
[3,2,8,7,1,6,5,4]=>1011011=>0100100
[4,8,2,7,1,6,5,3]=>0101011=>1010100
[5,8,7,2,1,6,4,3]=>0111011=>1000100
[6,8,7,1,3,5,4,2]=>0110011=>1001100
[7,8,6,1,5,3,4,2]=>0110101=>1001010
[8,7,6,1,5,4,3,2]=>1110111=>0001000
[1,8,7,2,6,5,3,4]=>0110110=>1001001
[1,7,8,2,5,6,3,4]=>0010010=>1101101
[8,6,7,1,4,5,3,2]=>1010011=>0101100
[7,6,8,1,4,3,5,2]=>1010101=>0101010
[6,5,8,3,2,1,7,4]=>1011101=>0100010
[7,5,8,3,1,4,6,2]=>1011001=>0100110
[8,5,7,3,1,6,4,2]=>1011011=>0100100
[1,6,8,4,2,7,3,5]=>0011010=>1100101
[1,5,4,8,2,7,3,6]=>0101010=>1010101
[8,4,3,7,1,6,5,2]=>1101011=>0010100
[7,4,3,8,1,5,6,2]=>1101001=>0010110
[6,4,3,1,5,2,7,8]=>1110100=>0001011
[7,4,3,1,2,6,5,8]=>1110010=>0001101
[8,4,3,1,2,5,7,6]=>1110001=>0001110
[1,5,4,2,3,6,7,8]=>0110000=>1001111
[8,5,1,4,2,3,7,6]=>1101001=>0010110
[7,5,1,4,2,6,3,8]=>1101010=>0010101
[6,5,1,4,3,2,7,8]=>1101100=>0010011
[5,6,1,3,4,2,7,8]=>0100100=>1011011
[4,6,2,1,5,3,7,8]=>0110100=>1001011
[3,2,6,1,5,4,7,8]=>1010100=>0101011
[3,2,7,1,4,6,5,8]=>1010010=>0101101
[4,7,2,1,3,6,5,8]=>0110010=>1001101
[5,7,1,3,2,6,4,8]=>0101010=>1010101
[6,7,1,2,4,5,3,8]=>0100010=>1011101
[7,6,1,2,5,4,3,8]=>1100110=>0011001
[8,6,1,2,5,3,7,4]=>1100101=>0011010
[1,7,2,3,6,4,5,8]=>0100100=>1011011
[8,7,1,2,3,6,5,4]=>1100011=>0011100
[7,8,1,2,3,5,6,4]=>0100001=>1011110
[6,8,1,2,4,3,7,5]=>0100101=>1011010
[5,8,1,3,2,4,7,6]=>0101001=>1010110
[4,8,2,1,3,5,7,6]=>0110001=>1001110
[3,2,8,1,4,5,7,6]=>1010001=>0101110
[4,1,3,2,5,6,7,8]=>1010000=>0101111
[5,1,2,4,3,6,7,8]=>1001000=>0110111
[6,1,2,3,5,4,7,8]=>1000100=>0111011
[7,1,2,3,4,6,5,8]=>1000010=>0111101
[8,1,2,3,4,5,7,6]=>1000001=>0111110
[6,7,3,8,5,1,2,4]=>0101100=>1010011
[6,7,4,5,1,8,3,2]=>0101011=>1010100
[5,4,7,6,8,1,2,3]=>1010100=>0101011
[5,3,7,8,6,1,2,4]=>1001100=>0110011
[3,8,4,5,7,1,2,6]=>0100100=>1011011
[3,4,8,6,7,1,2,5]=>0010100=>1101011
[4,5,6,7,1,8,3,2]=>0001011=>1110100
[3,5,6,2,7,4,8,1]=>0010101=>1101010
[3,5,6,1,7,8,4,2]=>0010011=>1101100
[2,5,6,1,8,7,4,3]=>0010111=>1101000
[2,5,6,8,1,7,3,4]=>0001010=>1110101
[8,2,4,5,1,6,3,7]=>1001010=>0110101
[1,4,8,6,2,3,7,5]=>0011001=>1100110
[1,5,6,8,2,3,7,4]=>0001001=>1110110
[1,5,6,2,8,4,7,3]=>0010101=>1101010
[2,5,6,3,4,7,8,1]=>0010001=>1101110
[1,4,2,6,8,5,7,3]=>0100101=>1011010
[8,1,3,2,5,4,6,7]=>1010100=>0101011
[8,2,3,1,5,6,4,7]=>1010010=>0101101
[2,8,3,1,5,7,4,6]=>0110010=>1001101
[2,4,1,6,8,7,5,3]=>0100111=>1011000
[3,4,1,6,7,8,5,2]=>0100011=>1011100
[4,3,1,7,6,8,5,2]=>1101011=>0010100
[5,2,7,8,1,6,3,4]=>1001010=>0110101
[5,3,7,2,6,4,8,1]=>1010101=>0101010
[6,7,3,1,5,8,4,2]=>0110011=>1001100
[6,7,2,1,8,5,4,3]=>0110111=>1001000
[6,7,2,8,1,5,3,4]=>0101010=>1010101
[6,7,8,2,1,4,3,5]=>0011010=>1100101
[6,7,1,2,8,4,5,3]=>0100101=>1011010
[6,7,1,3,4,8,5,2]=>0100011=>1011100
[5,2,7,3,4,6,8,1]=>1010001=>0101110
[5,1,7,3,4,8,6,2]=>1010011=>0101100
[5,1,7,8,2,3,6,4]=>1001001=>0110110
[4,1,8,7,2,3,6,5]=>1011001=>0100110
[3,8,1,2,7,4,5,6]=>0100100=>1011011
[4,1,3,7,5,8,6,2]=>1001011=>0110100
[3,1,4,5,7,8,6,2]=>1000011=>0111100
[2,1,8,3,4,7,6,5]=>1010011=>0101100
[8,2,1,3,4,6,5,7]=>1100010=>0011101
[1,8,2,3,4,5,7,6]=>0100001=>1011110
[1,2,8,3,4,6,7,5]=>0010001=>1101110
[4,2,1,6,5,8,7,3]=>1101011=>0010100
[5,2,6,1,4,8,7,3]=>1010011=>0101100
[5,2,6,4,1,8,7,3]=>1011011=>0100100
[5,2,7,4,8,1,6,3]=>1010101=>0101010
[5,2,7,4,8,6,1,3]=>1010110=>0101001
[5,7,2,3,8,6,1,4]=>0100110=>1011001
[5,7,2,3,8,1,6,4]=>0100101=>1011010
[5,6,2,3,1,8,7,4]=>0101011=>1010100
[5,6,2,1,3,8,7,4]=>0110011=>1001100
[5,1,6,4,2,8,7,3]=>1011011=>0100100
[5,6,1,3,2,8,7,4]=>0101011=>1010100
[5,6,3,1,2,8,7,4]=>0110011=>1001100
[5,6,3,2,1,8,7,4]=>0111011=>1000100
[5,7,3,2,8,1,6,4]=>0110101=>1001010
[5,7,3,2,8,6,1,4]=>0110110=>1001001
[6,7,3,8,2,1,5,4]=>0101101=>1010010
[6,7,3,8,1,2,5,4]=>0101001=>1010110
[5,7,3,1,8,2,6,4]=>0110101=>1001010
[5,7,1,3,8,2,6,4]=>0100101=>1011010
[5,1,7,4,8,2,6,3]=>1010101=>0101010
[1,5,7,4,8,3,6,2]=>0010101=>1101010
[1,5,7,4,8,6,3,2]=>0010111=>1101000
[5,1,7,4,8,6,2,3]=>1010110=>0101001
[5,7,1,3,8,6,2,4]=>0100110=>1011001
[5,7,3,1,8,6,2,4]=>0110110=>1001001
[6,7,3,8,1,5,2,4]=>0101010=>1010101
[6,7,3,8,5,2,1,4]=>0101110=>1010001
[6,7,8,3,1,4,2,5]=>0011010=>1100101
[6,7,1,8,3,5,2,4]=>0101010=>1010101
[6,1,7,8,4,5,2,3]=>1001010=>0110101
[1,6,7,8,4,5,3,2]=>0001011=>1110100
[1,6,7,8,4,3,5,2]=>0001101=>1110010
[6,1,7,8,4,2,5,3]=>1001101=>0110010
[6,7,1,8,3,2,5,4]=>0101101=>1010010
[5,7,2,1,8,3,6,4]=>0110101=>1001010
[6,7,2,8,1,3,5,4]=>0101001=>1010110
[6,7,2,8,3,1,5,4]=>0101101=>1010010
[6,7,2,8,3,5,1,4]=>0101010=>1010101
[6,2,7,8,4,5,1,3]=>1001010=>0110101
[6,2,7,8,4,1,5,3]=>1001101=>0110010
[6,2,7,8,1,4,5,3]=>1001001=>0110110
[5,2,7,1,8,4,6,3]=>1010101=>0101010
[4,2,1,7,8,5,6,3]=>1100101=>0011010
[4,1,2,7,8,6,5,3]=>1000111=>0111000
[6,2,7,8,1,5,4,3]=>1001011=>0110100
[6,2,7,8,5,1,4,3]=>1001101=>0110010
[6,2,7,8,5,4,1,3]=>1001110=>0110001
[6,7,2,8,5,3,1,4]=>0101110=>1010001
[5,7,2,1,8,6,3,4]=>0110110=>1001001
[5,7,1,2,8,6,3,4]=>0100110=>1011001
[5,1,7,2,8,6,4,3]=>1010111=>0101000
[1,5,7,3,8,6,4,2]=>0010111=>1101000
[1,6,7,8,3,5,4,2]=>0001011=>1110100
[6,1,7,8,2,5,4,3]=>1001011=>0110100
[6,7,1,8,2,5,3,4]=>0101010=>1010101
[6,7,8,2,4,1,3,5]=>0010100=>1101011
[6,7,8,2,4,3,1,5]=>0010110=>1101001
[6,7,1,8,5,2,3,4]=>0101100=>1010011
[6,1,7,8,5,2,4,3]=>1001101=>0110010
[1,6,7,8,5,3,4,2]=>0001101=>1110010
[6,1,7,8,5,4,2,3]=>1001110=>0110001
[6,7,1,8,5,3,2,4]=>0101110=>1010001
[6,7,8,4,1,3,2,5]=>0011010=>1100101
[6,3,8,5,2,7,4,1]=>1011011=>0100100
[6,5,2,8,4,7,3,1]=>1101011=>0010100
[6,3,4,5,8,7,2,1]=>1000111=>0111000
[3,8,4,7,5,2,1,6]=>0101110=>1010001
[5,8,1,4,7,2,3,6]=>0100100=>1011011
[5,6,1,4,8,7,3,2]=>0100111=>1011000
[3,6,4,8,5,7,1,2]=>0101010=>1010101
[5,1,4,8,6,3,7,2]=>1001101=>0110010
[3,4,7,1,8,6,5,2]=>0010111=>1101000
[6,3,8,4,2,7,1,5]=>1011010=>0100101
[3,6,8,7,1,4,2,5]=>0011010=>1100101
[5,3,7,1,6,8,2,4]=>1010010=>0101101
[4,3,8,5,6,7,2,1]=>1010011=>0101100
[5,8,1,7,6,2,4,3]=>0101101=>1010010
[4,6,1,2,7,8,5,3]=>0100011=>1011100
[3,6,4,2,8,7,5,1]=>0110111=>1001000
[6,3,7,5,2,8,1,4]=>1011010=>0100101
[6,5,2,7,4,8,1,3]=>1101010=>0010101
[5,7,1,4,8,3,2,6]=>0100110=>1011001
[7,8,3,5,1,4,6,2]=>0101001=>1010110
[5,8,1,4,6,7,2,3]=>0100010=>1011101
[6,5,8,4,3,7,2,1]=>1011011=>0100100
[6,3,7,4,2,8,5,1]=>1011011=>0100100
[8,7,1,6,2,4,5,3]=>1101001=>0010110
[3,8,6,7,1,4,5,2]=>0101001=>1010110
[5,3,8,7,4,1,2,6]=>1011100=>0100011
[4,3,8,7,1,5,6,2]=>1011001=>0100110
[8,3,6,1,2,5,7,4]=>1010001=>0101110
[5,6,1,8,7,3,2,4]=>0101110=>1010001
[5,4,2,7,3,6,8,1]=>1101001=>0010110
[7,5,3,6,4,2,8,1]=>1101101=>0010010
[6,4,1,5,3,8,2,7]=>1101010=>0010101
[8,2,6,3,4,7,5,1]=>1010011=>0101100
[7,2,6,3,5,4,8,1]=>1010101=>0101010
[6,2,7,4,3,5,8,1]=>1011001=>0100110
[3,7,6,4,5,2,8,1]=>0110101=>1001010
[2,7,6,5,3,4,8,1]=>0111001=>1000110
[6,5,4,3,1,8,2,7]=>1111010=>0000101
[8,6,5,4,2,7,3,1]=>1111011=>0000100
[8,5,4,1,7,2,6,3]=>1110101=>0001010
[7,5,4,1,8,3,2,6]=>1110110=>0001001
[1,6,5,2,8,3,4,7]=>0110100=>1001011
[1,6,5,3,4,8,2,7]=>0110010=>1001101
[5,4,6,3,1,8,2,7]=>1011010=>0100101
[6,5,8,4,2,7,3,1]=>1011011=>0100100
[5,8,2,6,4,7,3,1]=>0101011=>1010100
[7,8,5,3,2,6,4,1]=>0111011=>1000100
[6,8,3,1,7,2,5,4]=>0110101=>1001010
[1,8,6,3,7,5,2,4]=>0110110=>1001001
[8,7,5,2,6,4,3,1]=>1110111=>0001000
[8,7,1,6,2,5,4,3]=>1101011=>0010100
[2,8,1,7,3,5,6,4]=>0101001=>1010110
[4,8,1,3,7,2,6,5]=>0100101=>1011010
[4,2,8,5,7,3,6,1]=>1010101=>0101010
[5,1,7,6,8,3,2,4]=>1010110=>0101001
[6,7,3,1,8,4,2,5]=>0110110=>1001001
[1,7,3,8,4,5,2,6]=>0101010=>1010101
[1,7,2,8,5,3,4,6]=>0101100=>1010011
[7,6,1,8,4,3,2,5]=>1101110=>0010001
[8,6,1,7,4,2,5,3]=>1101101=>0010010
[8,1,2,7,3,4,6,5]=>1001001=>0110110
[7,1,2,8,3,5,4,6]=>1001010=>0110101
[8,2,6,1,7,3,5,4]=>1010101=>0101010
[8,3,1,4,7,5,6,2]=>1100101=>0011010
[4,2,1,5,8,3,6,7]=>1100100=>0011011
[5,4,3,1,6,8,2,7]=>1110010=>0001101
[4,7,5,6,8,3,2,1]=>0100111=>1011000
[6,5,4,8,2,7,3,1]=>1101011=>0010100
[6,5,1,8,7,4,2,3]=>1101110=>0010001
[8,6,4,7,5,3,2,1]=>1101111=>0010000
[5,1,8,3,7,6,2,4]=>1010110=>0101001
[5,4,8,1,7,2,6,3]=>1010101=>0101010
[3,6,8,2,4,7,5,1]=>0010011=>1101100
[5,7,3,8,2,6,4,1]=>0101011=>1010100
[4,7,2,8,6,3,5,1]=>0101101=>1010010
[2,3,8,7,4,5,6,1]=>0011001=>1100110
[7,2,8,6,4,3,5,1]=>1011101=>0100010
[2,1,8,7,5,6,3,4]=>1011010=>0100101
[8,2,7,6,3,5,4,1]=>1011011=>0100100
[8,1,7,6,5,2,4,3]=>1011101=>0100010
[7,1,8,6,5,3,2,4]=>1011110=>0100001
[1,2,8,7,6,3,4,5]=>0011100=>1100011
[1,3,8,7,4,6,2,5]=>0011010=>1100101
[5,1,6,8,7,4,2,3]=>1001110=>0110001
[6,8,4,7,5,3,2,1]=>0101111=>1010000
[6,8,7,2,5,4,3,1]=>0110111=>1001000
[3,8,7,6,4,5,2,1]=>0111011=>1000100
[2,8,7,6,5,3,4,1]=>0111101=>1000010
[1,8,7,6,5,4,2,3]=>0111110=>1000001
[5,8,6,7,3,4,1,2]=>0101010=>1010101
[4,8,6,7,3,5,1,2]=>0101010=>1010101
[3,8,6,7,4,5,1,2]=>0101010=>1010101
[2,8,6,7,4,5,1,3]=>0101010=>1010101
[1,8,6,7,4,5,2,3]=>0101010=>1010101
[1,8,5,7,4,6,2,3]=>0101010=>1010101
[3,8,5,7,4,6,1,2]=>0101010=>1010101
[4,8,5,7,3,6,1,2]=>0101010=>1010101
[7,8,3,6,4,5,1,2]=>0101010=>1010101
[6,8,3,7,4,5,1,2]=>0101010=>1010101
[5,8,3,7,4,6,1,2]=>0101010=>1010101
[3,7,4,8,5,6,1,2]=>0101010=>1010101
[4,7,3,8,5,6,1,2]=>0101010=>1010101
[4,7,2,8,5,6,1,3]=>0101010=>1010101
[4,7,1,8,5,6,2,3]=>0101010=>1010101
[3,7,1,8,5,6,2,4]=>0101010=>1010101
[3,7,2,8,5,6,1,4]=>0101010=>1010101
[2,7,3,8,5,6,1,4]=>0101010=>1010101
[2,7,4,8,5,6,1,3]=>0101010=>1010101
[5,8,2,7,4,6,1,3]=>0101010=>1010101
[6,8,2,7,4,5,1,3]=>0101010=>1010101
[7,8,2,6,4,5,1,3]=>0101010=>1010101
[7,8,1,6,4,5,2,3]=>0101010=>1010101
[6,8,1,7,4,5,2,3]=>0101010=>1010101
[5,8,1,7,4,6,2,3]=>0101010=>1010101
[1,7,4,8,5,6,2,3]=>0101010=>1010101
[1,7,3,8,5,6,2,4]=>0101010=>1010101
[2,8,5,6,1,7,3,4]=>0101010=>1010101
[1,8,5,6,2,7,3,4]=>0101010=>1010101
[1,7,3,8,4,6,2,5]=>0101010=>1010101
[4,8,1,7,3,6,2,5]=>0101010=>1010101
[5,8,1,7,3,6,2,4]=>0101010=>1010101
[6,8,1,7,3,5,2,4]=>0101010=>1010101
[7,8,2,6,3,5,1,4]=>0101010=>1010101
[6,8,2,7,3,5,1,4]=>0101010=>1010101
[5,8,2,7,3,6,1,4]=>0101010=>1010101
[4,8,2,7,3,6,1,5]=>0101010=>1010101
[2,7,3,8,4,6,1,5]=>0101010=>1010101
[3,7,2,8,4,6,1,5]=>0101010=>1010101
[3,7,1,8,4,6,2,5]=>0101010=>1010101
[1,8,4,7,3,6,2,5]=>0101010=>1010101
[2,8,4,7,3,6,1,5]=>0101010=>1010101
[3,8,4,7,2,6,1,5]=>0101010=>1010101
[4,8,5,7,2,6,1,3]=>0101010=>1010101
[3,8,5,7,2,6,1,4]=>0101010=>1010101
[2,8,5,7,3,6,1,4]=>0101010=>1010101
[1,8,5,7,3,6,2,4]=>0101010=>1010101
[1,8,6,7,3,5,2,4]=>0101010=>1010101
[2,8,6,7,3,5,1,4]=>0101010=>1010101
[3,8,6,7,2,5,1,4]=>0101010=>1010101
[4,8,6,7,2,5,1,3]=>0101010=>1010101
[5,8,6,7,2,4,1,3]=>0101010=>1010101
[6,8,5,7,1,4,2,3]=>0101010=>1010101
[5,8,6,7,1,4,2,3]=>0101010=>1010101
[4,8,6,7,1,5,2,3]=>0101010=>1010101
[3,8,6,7,1,5,2,4]=>0101010=>1010101
[1,5,2,8,6,7,3,4]=>0101010=>1010101
[2,5,1,8,6,7,3,4]=>0101010=>1010101
[2,6,1,8,5,7,3,4]=>0101010=>1010101
[1,6,2,8,5,7,3,4]=>0101010=>1010101
[3,8,5,7,1,6,2,4]=>0101010=>1010101
[6,8,4,7,1,5,2,3]=>0101010=>1010101
[7,8,4,6,1,5,2,3]=>0101010=>1010101
[7,8,3,6,1,5,2,4]=>0101010=>1010101
[6,8,3,7,1,5,2,4]=>0101010=>1010101
[4,8,3,7,1,6,2,5]=>0101010=>1010101
[3,8,4,7,1,6,2,5]=>0101010=>1010101
[1,6,2,8,4,7,3,5]=>0101010=>1010101
[2,6,1,8,4,7,3,5]=>0101010=>1010101
[3,7,2,6,1,8,4,5]=>0101010=>1010101
[3,7,1,6,2,8,4,5]=>0101010=>1010101
[4,8,1,6,2,7,3,5]=>0101010=>1010101
[5,8,1,6,2,7,3,4]=>0101010=>1010101
[7,8,1,5,2,6,3,4]=>0101010=>1010101
[7,8,2,5,1,6,3,4]=>0101010=>1010101
[6,8,2,5,1,7,3,4]=>0101010=>1010101
[5,8,2,6,1,7,3,4]=>0101010=>1010101
[4,8,2,6,1,7,3,5]=>0101010=>1010101
[1,7,3,6,2,8,4,5]=>0101010=>1010101
[2,7,3,6,1,8,4,5]=>0101010=>1010101
[1,2,3,4,5,6,7,8,9]=>00000000=>11111111
[1,2,3,4,5,6,8,9,7]=>00000001=>11111110
[1,2,3,4,5,7,8,9,6]=>00000001=>11111110
[1,2,3,4,6,7,8,9,5]=>00000001=>11111110
[1,2,3,5,6,7,8,9,4]=>00000001=>11111110
[1,2,4,5,6,7,8,9,3]=>00000001=>11111110
[1,3,4,5,6,7,8,9,2]=>00000001=>11111110
[1,2,3,4,5,6,7,8,9,10]=>000000000=>111111111
[1,2,3,4,5,6,9,8,7]=>00000011=>11111100
[1,2,3,4,5,6,7,9,10,8]=>000000001=>111111110
[1,2,3,4,5,8,7,9,6]=>00000101=>11111010
[1,2,3,4,5,6,8,9,10,7]=>000000001=>111111110
[1,2,3,4,7,6,8,9,5]=>00001001=>11110110
[1,2,3,4,5,7,8,9,10,6]=>000000001=>111111110
[1,2,3,6,5,7,8,9,4]=>00010001=>11101110
[1,2,3,4,6,7,8,9,10,5]=>000000001=>111111110
[1,2,5,4,6,7,8,9,3]=>00100001=>11011110
[1,2,3,5,6,7,8,9,10,4]=>000000001=>111111110
[1,4,3,5,6,7,8,9,2]=>01000001=>10111110
[1,2,4,5,6,7,8,9,10,3]=>000000001=>111111110
[3,2,4,5,6,7,8,9,1]=>10000001=>01111110
[1,3,4,5,6,7,8,9,10,2]=>000000001=>111111110
[6,7,4,8,3,5,1,2]=>0101010=>1010101
[6,7,4,5,2,8,1,3]=>0101010=>1010101
[5,7,4,6,2,3,1,8]=>0101010=>1010101
[5,7,4,6,3,8,1,2]=>0101010=>1010101
[5,7,4,8,3,6,1,2]=>0101010=>1010101
[6,8,4,5,3,7,1,2]=>0101010=>1010101
[5,8,4,6,3,7,1,2]=>0101010=>1010101
[5,6,4,8,3,7,1,2]=>0101010=>1010101
[5,6,3,7,2,4,1,8]=>0101010=>1010101
[5,6,3,7,2,8,1,4]=>0101010=>1010101
[5,6,3,8,2,7,1,4]=>0101010=>1010101
[5,6,4,8,2,7,1,3]=>0101010=>1010101
[5,8,4,6,2,7,1,3]=>0101010=>1010101
[6,8,4,5,2,7,1,3]=>0101010=>1010101
[7,8,4,5,2,6,1,3]=>0101010=>1010101
[6,8,4,5,2,3,1,7]=>0101010=>1010101
[5,8,4,6,2,3,1,7]=>0101010=>1010101
[5,6,4,8,2,3,1,7]=>0101010=>1010101
[5,6,3,8,2,4,1,7]=>0101010=>1010101
[5,6,3,4,2,8,1,7]=>0101010=>1010101
[4,6,3,5,2,7,1,8]=>0101010=>1010101
[4,6,3,5,2,8,1,7]=>0101010=>1010101
[4,6,3,8,2,5,1,7]=>0101010=>1010101
[4,8,3,6,2,5,1,7]=>0101010=>1010101
[5,8,3,6,2,4,1,7]=>0101010=>1010101
[6,8,3,5,2,4,1,7]=>0101010=>1010101
[7,8,3,5,2,4,1,6]=>0101010=>1010101
[7,8,3,5,2,6,1,4]=>0101010=>1010101
[5,8,3,6,2,7,1,4]=>0101010=>1010101
[4,8,3,6,2,7,1,5]=>0101010=>1010101
[4,6,3,8,2,7,1,5]=>0101010=>1010101
[4,6,3,7,2,8,1,5]=>0101010=>1010101
[4,7,3,6,2,5,1,8]=>0101010=>1010101
[4,7,3,6,2,8,1,5]=>0101010=>1010101
[4,7,3,8,2,6,1,5]=>0101010=>1010101
[5,7,4,8,2,6,1,3]=>0101010=>1010101
[5,7,3,6,2,8,1,4]=>0101010=>1010101
[5,7,3,6,2,4,1,8]=>0101010=>1010101
[6,7,3,5,2,4,1,8]=>0101010=>1010101
[6,7,3,5,2,8,1,4]=>0101010=>1010101
[6,7,4,8,2,5,1,3]=>0101010=>1010101
[6,7,5,8,2,4,1,3]=>0101010=>1010101
[6,8,5,7,2,3,1,4]=>0101010=>1010101
[6,7,4,8,2,3,1,5]=>0101010=>1010101
[6,7,3,8,2,4,1,5]=>0101010=>1010101
[6,7,3,4,2,8,1,5]=>0101010=>1010101
[5,7,3,4,2,6,1,8]=>0101010=>1010101
[5,7,3,4,2,8,1,6]=>0101010=>1010101
[5,7,4,8,2,3,1,6]=>0101010=>1010101
[5,8,4,7,2,3,1,6]=>0101010=>1010101
[6,8,4,7,2,3,1,5]=>0101010=>1010101
[7,8,4,6,2,3,1,5]=>0101010=>1010101
[7,8,3,6,2,4,1,5]=>0101010=>1010101
[6,8,3,7,2,4,1,5]=>0101010=>1010101
[5,8,3,7,2,4,1,6]=>0101010=>1010101
[4,8,3,7,2,5,1,6]=>0101010=>1010101
[4,7,3,8,2,5,1,6]=>0101010=>1010101
[4,7,3,5,2,8,1,6]=>0101010=>1010101
[4,7,3,5,2,6,1,8]=>0101010=>1010101
[4,5,3,7,2,6,1,8]=>0101010=>1010101
[4,5,3,7,2,8,1,6]=>0101010=>1010101
[4,5,3,8,2,7,1,6]=>0101010=>1010101
[4,8,3,5,2,7,1,6]=>0101010=>1010101
[5,8,3,4,2,7,1,6]=>0101010=>1010101
[6,8,3,4,2,7,1,5]=>0101010=>1010101
[7,8,3,4,2,6,1,5]=>0101010=>1010101
[6,8,3,4,2,5,1,7]=>0101010=>1010101
[5,8,3,4,2,6,1,7]=>0101010=>1010101
[4,8,3,5,2,6,1,7]=>0101010=>1010101
[4,5,3,8,2,6,1,7]=>0101010=>1010101
[4,5,3,6,2,8,1,7]=>0101010=>1010101
[4,7,5,2,1,8,3,6]=>0111010=>1000101
[4,8,5,2,1,7,6,3]=>0111011=>1000100
[4,6,5,2,1,3,8,7]=>0111001=>1000110
[5,6,4,2,3,1,8,7]=>0110101=>1001010
[6,4,5,3,1,2,8,7]=>1011001=>0100110
[5,4,6,1,3,2,8,7]=>1010101=>0101010
[4,6,8,1,7,3,2,5]=>0010110=>1101001
[4,7,8,1,6,3,5,2]=>0010101=>1101010
[7,4,8,1,6,5,3,2]=>1010111=>0101000
[5,4,8,1,3,7,6,2]=>1010011=>0101100
[8,4,5,3,1,7,6,2]=>1011011=>0100100
[5,4,7,1,3,8,2,6]=>1010010=>0101101
[6,4,8,1,7,5,2,3]=>1010110=>0101001
[5,6,8,7,2,1,3,4]=>0011100=>1100011
[8,5,7,6,4,2,1,3]=>1011110=>0100001
[8,4,6,3,7,2,1,5]=>1010110=>0101001
[6,3,2,8,7,4,1,5]=>1101110=>0010001
[2,1,6,8,7,4,3,5]=>1001110=>0110001
[2,1,7,8,6,4,5,3]=>1001101=>0110010
[7,3,2,8,6,4,5,1]=>1101101=>0010010
[7,6,8,5,2,4,3,1]=>1011011=>0100100
[5,7,8,6,2,3,1,4]=>0011010=>1100101
[5,8,7,6,3,2,1,4]=>0111110=>1000001
[6,8,7,5,3,2,4,1]=>0111101=>1000010
[5,8,4,2,3,7,6,1]=>0110011=>1001100
[7,8,4,2,6,5,3,1]=>0110111=>1001000
[4,8,7,2,6,3,5,1]=>0110101=>1001010
[4,8,6,2,7,3,1,5]=>0110110=>1001001
[3,6,1,8,7,4,2,5]=>0101110=>1010001
[3,7,1,8,6,4,5,2]=>0101101=>1010010
[3,8,1,6,7,5,2,4]=>0100110=>1011001
[3,7,1,6,8,2,5,4]=>0100101=>1011010
[4,7,6,2,8,1,3,5]=>0110100=>1001011
[6,7,4,2,8,1,5,3]=>0110101=>1001010
[6,8,4,2,7,5,1,3]=>0110110=>1001001
[2,1,8,6,7,5,3,4]=>1010110=>0101001
[8,3,2,6,7,5,1,4]=>1100110=>0011001
[8,6,4,3,7,5,1,2]=>1110110=>0001001
[5,8,6,7,3,1,2,4]=>0101100=>1010011
[6,7,5,8,1,3,4,2]=>0101001=>1010110
[7,6,5,8,1,4,3,2]=>1101011=>0010100
[8,6,5,7,4,1,3,2]=>1101101=>0010010
[7,6,4,3,8,1,5,2]=>1110101=>0001010
[7,3,2,6,8,1,5,4]=>1100101=>0011010
[2,1,7,6,8,3,5,4]=>1010101=>0101010
[7,5,6,8,1,4,2,3]=>1001010=>0110101
[6,5,7,8,1,2,4,3]=>1001001=>0110110
[8,1,3,7,4,6,5,2]=>1001011=>0110100
[5,2,8,7,4,6,1,3]=>1011010=>0100101
[1,6,2,5,4,7,3,8]=>0101010=>1010101
[6,2,7,5,4,8,3,1]=>1011011=>0100100
[8,1,3,5,4,7,6,2]=>1001011=>0110100
[6,1,5,4,3,8,7,2]=>1011011=>0100100
[6,1,8,3,4,5,7,2]=>1010001=>0101110
[7,1,5,3,4,8,6,2]=>1010011=>0101100
[7,1,4,3,5,6,8,2]=>1010001=>0101110
[8,1,3,4,5,6,7,2]=>1000001=>0111110
[1,7,2,4,5,6,3,8]=>0100010=>1011101
[6,3,2,7,5,1,8,4]=>1101101=>0010010
[8,4,7,2,5,6,1,3]=>1010010=>0101101
[6,5,8,2,4,7,3,1]=>1010011=>0101100
[8,5,2,1,4,3,7,6]=>1110101=>0001010
[6,5,2,8,4,1,3,7]=>1101100=>0010011
[5,6,2,1,4,8,3,7]=>0110010=>1001101
[3,6,1,8,5,2,4,7]=>0101100=>1010011
[1,2,6,3,5,4,7,8]=>0010100=>1101011
[3,4,1,2,8,6,5,7]=>0100110=>1011001
[4,3,1,2,6,8,5,7]=>1100010=>0011101
[5,8,1,6,3,2,4,7]=>0101100=>1010011
[6,3,8,5,2,1,4,7]=>1011100=>0100011
[8,3,1,5,2,4,7,6]=>1101001=>0010110
[3,8,2,6,1,5,7,4]=>0101001=>1010110
[3,8,6,7,2,1,5,4]=>0101101=>1010010
[8,5,6,4,2,1,7,3]=>1011101=>0100010
[7,2,5,8,3,1,6,4]=>1001101=>0110010
[1,7,5,6,3,2,4,8]=>0101100=>1010011
[6,1,2,3,8,5,7,4]=>1000101=>0111010
[7,1,2,3,6,5,8,4]=>1000101=>0111010
[7,2,1,3,8,6,4,5]=>1100110=>0011001
[1,5,7,3,2,4,6,8]=>0011000=>1100111
[5,2,7,3,1,8,4,6]=>1011010=>0100101
[5,8,2,4,1,3,7,6]=>0101001=>1010110
[8,7,2,6,3,4,1,5]=>1101010=>0010101
[4,8,1,6,3,2,7,5]=>0101101=>1010010
[3,1,8,6,4,2,7,5]=>1011101=>0100010
[8,1,6,7,4,3,2,5]=>1001110=>0110001
[3,5,8,7,2,4,1,6]=>0011010=>1100101
[4,2,1,3,7,8,5,6]=>1100010=>0011101
[2,4,1,3,8,7,5,6]=>0100110=>1011001
[2,5,8,3,1,7,4,6]=>0011010=>1100101
[8,6,1,3,7,2,4,5]=>1100100=>0011011
[2,8,1,3,6,4,7,5]=>0100101=>1011010
[6,8,2,3,4,1,5,7]=>0100100=>1011011
[5,1,8,3,2,4,6,7]=>1011000=>0100111
[9,8,7,6,5,4,3,2,1]=>11111111=>00000000
[8,9,7,6,5,4,3,2,1]=>01111111=>10000000
[8,7,9,6,5,4,3,2,1]=>10111111=>01000000
[8,7,6,9,5,4,3,2,1]=>11011111=>00100000
[8,7,6,5,9,4,3,2,1]=>11101111=>00010000
[8,7,6,5,4,9,3,2,1]=>11110111=>00001000
[8,7,6,5,4,3,9,2,1]=>11111011=>00000100
[8,7,6,5,4,3,2,9,1]=>11111101=>00000010
[8,7,6,5,4,3,2,1,9]=>11111110=>00000001
[9,10,8,7,6,5,4,3,2,1]=>011111111=>100000000
[7,8,9,6,5,4,3,2,1]=>00111111=>11000000
[9,8,10,7,6,5,4,3,2,1]=>101111111=>010000000
[8,6,7,9,5,4,3,2,1]=>10011111=>01100000
[9,8,7,10,6,5,4,3,2,1]=>110111111=>001000000
[8,7,5,6,9,4,3,2,1]=>11001111=>00110000
[9,8,7,6,10,5,4,3,2,1]=>111011111=>000100000
[8,7,6,4,5,9,3,2,1]=>11100111=>00011000
[9,8,7,6,5,10,4,3,2,1]=>111101111=>000010000
[8,7,6,5,3,4,9,2,1]=>11110011=>00001100
[9,8,7,6,5,4,10,3,2,1]=>111110111=>000001000
[8,7,6,5,4,2,3,9,1]=>11111001=>00000110
[9,8,7,6,5,4,3,10,2,1]=>111111011=>000000100
[8,7,6,5,4,3,1,2,9]=>11111100=>00000011
[9,8,7,6,5,4,3,2,10,1]=>111111101=>000000010
[9,8,7,6,5,4,3,2,1,10]=>111111110=>000000001
[1,4,2,7,8,6,3,5]=>0100110=>1011001
[1,6,2,4,8,5,3,7]=>0100110=>1011001
[1,6,2,4,7,5,3,8]=>0100110=>1011001
[1,7,3,8,5,2,4,6]=>0101100=>1010011
[1,7,3,2,8,6,4,5]=>0110110=>1001001
[4,2,5,7,8,6,1,3]=>1000110=>0111001
[7,2,3,1,8,5,6,4]=>1010101=>0101010
[8,2,5,1,7,3,4,6]=>1010100=>0101011
[6,2,1,8,3,4,7,5]=>1101001=>0010110
[6,2,8,3,5,1,7,4]=>1010101=>0101010
[6,2,4,8,5,7,1,3]=>1001010=>0110101
[1,3,6,4,8,5,7,2]=>0010101=>1101010
[1,3,6,4,7,5,8,2]=>0010101=>1101010
[6,2,4,7,5,8,1,3]=>1001010=>0110101
[6,2,1,3,7,8,4,5]=>1100010=>0011101
[7,8,2,1,4,3,5,6]=>0110100=>1001011
[7,6,4,2,3,1,8,5]=>1110101=>0001010
[5,7,2,3,1,6,8,4]=>0101001=>1010110
[7,5,4,2,6,8,1,3]=>1110010=>0001101
[1,7,5,3,4,6,8,2]=>0110001=>1001110
[8,2,5,4,6,7,1,3]=>1010010=>0101101
[5,2,6,3,1,8,7,4]=>1011011=>0100100
[8,2,6,4,3,1,7,5]=>1011101=>0100010
[8,2,7,4,1,3,5,6]=>1011000=>0100111
[1,2,8,4,3,5,6,7]=>0011000=>1100111
[1,7,4,2,3,5,6,8]=>0110000=>1001111
[6,8,4,1,3,2,5,7]=>0110100=>1001011
[1,8,7,4,3,2,5,6]=>0111100=>1000011
[1,6,3,8,2,4,7,5]=>0101001=>1010110
[5,3,8,1,2,7,4,6]=>1010010=>0101101
[5,1,8,3,2,6,4,7]=>1011010=>0100101
[5,7,3,1,2,6,4,8]=>0110010=>1001101
[1,7,5,4,2,6,3,8]=>0111010=>1000101
[1,5,8,2,4,6,3,7]=>0010010=>1101101
[1,5,8,4,2,7,3,6]=>0011010=>1100101
[1,4,6,2,8,3,7,5]=>0010101=>1101010
[5,3,1,6,7,2,4,8]=>1100100=>0011011
[5,3,6,1,2,8,4,7]=>1010010=>0101101
[1,6,3,2,7,8,4,5]=>0110010=>1001101
[1,7,4,5,3,8,6,2]=>0101011=>1010100
[6,3,4,1,2,5,8,7]=>1010001=>0101110
[6,3,1,4,2,7,5,8]=>1101010=>0010101
[1,8,3,2,4,5,6,7]=>0110000=>1001111
[8,6,3,2,4,1,7,5]=>1110101=>0001010
[8,5,3,2,6,7,1,4]=>1110010=>0001101
[4,5,2,6,8,1,7,3]=>0100101=>1011010
[4,2,5,6,7,8,1,3]=>1000010=>0111101
[5,2,3,6,7,1,8,4]=>1000101=>0111010
[6,2,3,4,1,7,8,5]=>1001001=>0110110
[7,2,3,1,4,5,8,6]=>1010001=>0101110
[8,6,1,4,3,2,5,7]=>1101100=>0010011
[8,3,1,6,5,2,4,7]=>1101100=>0010011
[3,7,5,1,8,2,4,6]=>0110100=>1001011
[4,1,5,2,8,7,3,6]=>1010110=>0101001
[8,1,2,4,6,5,3,7]=>1000110=>0111001
[8,1,2,5,4,6,3,7]=>1001010=>0110101
[8,2,6,5,1,3,4,7]=>1011000=>0100111
[8,3,1,6,2,5,4,7]=>1101010=>0010101
[8,1,2,6,4,5,3,7]=>1001010=>0110101
[8,1,2,5,6,4,3,7]=>1000110=>0111001
[8,1,2,6,5,4,3,7]=>1001110=>0110001
[1,7,5,4,2,8,3,6]=>0111010=>1000101
[5,1,4,8,2,7,3,6]=>1001010=>0110101
[1,4,6,8,2,7,3,5]=>0001010=>1110101
[1,4,7,6,2,8,3,5]=>0011010=>1100101
[5,1,4,7,2,8,3,6]=>1001010=>0110101
[1,7,4,5,2,8,3,6]=>0101010=>1010101
[3,7,5,1,2,8,4,6]=>0110010=>1001101
[5,7,2,8,1,3,4,6]=>0101000=>1010111
[5,2,8,7,1,3,4,6]=>1011000=>0100111
[4,1,5,8,2,7,3,6]=>1001010=>0110101
[1,4,6,2,8,7,3,5]=>0010110=>1101001
[1,4,2,8,6,7,3,5]=>0101010=>1010101
[3,1,2,6,4,8,7,5]=>1001011=>0110100
[2,1,7,6,3,4,8,5]=>1011001=>0100110
[3,1,2,7,4,6,8,5]=>1001001=>0110110
[1,4,7,2,6,8,3,5]=>0010010=>1101101
[1,2,3,6,8,5,7,4]=>0000101=>1111010
[5,1,4,2,7,8,3,6]=>1010010=>0101101
[1,4,2,7,6,8,3,5]=>0101010=>1010101
[1,4,2,6,8,7,3,5]=>0100110=>1011001
[3,1,2,8,4,6,7,5]=>1001001=>0110110
[3,1,2,7,6,4,8,5]=>1001101=>0110010
[5,3,7,1,8,2,4,6]=>1010100=>0101011
[1,7,4,3,2,5,8,6]=>0111001=>1000110
[4,8,7,2,1,3,5,6]=>0111000=>1000111
[1,8,7,3,4,2,5,6]=>0110100=>1001011
[3,1,7,8,2,6,4,5]=>1001010=>0110101
[1,4,2,7,8,3,6,5]=>0100101=>1011010
[5,2,8,1,3,4,7,6]=>1010001=>0101110
[2,1,8,6,3,4,7,5]=>1011001=>0100110
[1,4,2,6,8,3,7,5]=>0100101=>1011010
[1,2,3,7,8,5,6,4]=>0000101=>1111010
[1,2,3,7,5,8,6,4]=>0001011=>1110100
[1,4,2,7,3,8,6,5]=>0101011=>1010100
[3,1,7,2,8,6,4,5]=>1010110=>0101001
[2,1,7,8,3,4,6,5]=>1001001=>0110110
[1,2,3,8,7,5,6,4]=>0001101=>1110010
[10,1,2,3,4,5,6,7,8,9]=>100000000=>011111111
[10,1,2,3,4,5,6,9,7,8]=>100000010=>011111101
[10,1,2,3,4,5,9,6,7,8]=>100000100=>011111011
[9,1,2,3,4,10,5,6,7,8]=>100001000=>011110111
[10,1,2,3,9,4,5,6,7,8]=>100010000=>011101111
[10,1,2,9,3,4,5,6,7,8]=>100100000=>011011111
[9,1,10,2,3,4,5,6,7,8]=>101000000=>010111111
[10,9,1,2,3,4,5,6,7,8]=>110000000=>001111111
[11,1,2,3,4,5,6,7,8,9,10]=>1000000000=>0111111111
[10,1,2,3,4,5,6,7,8,11,9]=>1000000001=>0111111110
[8,1,2,3,4,5,6,9,10,7]=>100000001=>011111110
[11,1,2,3,4,5,6,7,10,8,9]=>1000000010=>0111111101
[7,1,2,3,4,5,10,9,6,8]=>100000110=>011111001
[11,1,2,3,4,5,6,10,7,8,9]=>1000000100=>0111111011
[6,1,2,3,4,10,9,5,7,8]=>100001100=>011110011
[10,1,2,3,4,5,11,6,7,8,9]=>1000001000=>0111110111
[5,1,2,3,9,10,4,6,7,8]=>100001000=>011110111
[11,1,2,3,4,10,5,6,7,8,9]=>1000010000=>0111101111
[4,1,2,10,9,3,5,6,7,8]=>100110000=>011001111
[11,1,2,3,10,4,5,6,7,8,9]=>1000100000=>0111011111
[3,1,10,9,2,4,5,6,7,8]=>101100000=>010011111
[10,1,2,11,3,4,5,6,7,8,9]=>1001000000=>0110111111
[2,9,10,1,3,4,5,6,7,8]=>001000000=>110111111
[11,1,10,2,3,4,5,6,7,8,9]=>1010000000=>0101111111
[11,10,1,2,3,4,5,6,7,8,9]=>1100000000=>0011111111
[4,7,8,5,6,2,1,3]=>0010110=>1101001
[5,7,8,4,2,6,1,3]=>0011010=>1100101
[6,7,8,4,2,5,1,3]=>0011010=>1100101
[8,6,3,7,2,1,5,4]=>1101101=>0010010
[7,6,3,8,2,1,5,4]=>1101101=>0010010
[6,7,8,3,2,1,5,4]=>0011101=>1100010
[5,7,8,3,2,1,6,4]=>0011101=>1100010
[2,7,8,4,3,5,6,1]=>0011001=>1100110
[3,7,8,4,2,5,1,6]=>0011010=>1100101
[4,7,8,3,2,1,5,6]=>0011100=>1100011
[5,7,8,3,2,1,4,6]=>0011100=>1100011
[7,6,3,8,2,1,4,5]=>1101100=>0010011
[8,6,3,7,2,1,4,5]=>1101100=>0010011
[5,6,3,8,2,1,4,7]=>0101100=>1010011
[3,6,4,8,2,5,1,7]=>0101010=>1010101
[2,6,4,8,3,5,7,1]=>0101001=>1010110
[2,6,4,7,3,5,8,1]=>0101001=>1010110
[3,6,4,7,2,5,1,8]=>0101010=>1010101
[4,6,3,7,2,1,5,8]=>0101100=>1010011
[5,6,3,7,2,1,4,8]=>0101100=>1010011
[8,4,3,2,1,6,5,7]=>1111010=>0000101
[6,4,3,2,1,7,5,8]=>1111010=>0000101
[4,5,3,2,7,1,6,8]=>0110100=>1001011
[3,5,4,2,8,6,1,7]=>0110110=>1001001
[6,4,3,2,1,8,5,7]=>1111010=>0000101
[7,4,3,2,1,8,5,6]=>1111010=>0000101
[8,4,3,2,1,7,5,6]=>1111010=>0000101
[8,4,3,2,1,7,6,5]=>1111011=>0000100
[7,4,3,2,1,8,6,5]=>1111011=>0000100
[6,4,3,2,1,8,7,5]=>1111011=>0000100
[5,6,3,8,2,1,7,4]=>0101101=>1010010
[7,5,3,2,8,1,6,4]=>1110101=>0001010
[8,5,4,2,7,6,1,3]=>1110110=>0001001
[7,5,4,2,8,6,1,3]=>1110110=>0001001
[6,5,4,2,8,7,1,3]=>1110110=>0001001
[4,6,5,8,7,2,1,3]=>0101110=>1010001
[2,6,5,7,8,3,4,1]=>0100101=>1011010
[6,5,4,2,7,8,1,3]=>1110010=>0001101
[8,5,4,2,6,7,1,3]=>1110010=>0001101
[8,5,3,2,6,1,7,4]=>1110101=>0001010
[7,5,3,2,6,1,8,4]=>1110101=>0001010
[5,6,3,7,2,1,8,4]=>0101101=>1010010
[4,6,3,7,2,1,8,5]=>0101101=>1010010
[3,6,4,7,2,8,1,5]=>0101010=>1010101
[2,6,4,7,3,8,5,1]=>0101011=>1010100
[3,5,4,2,7,8,1,6]=>0110010=>1001101
[4,5,3,2,7,1,8,6]=>0110101=>1001010
[7,4,3,2,1,6,8,5]=>1111001=>0000110
[8,4,3,2,1,6,7,5]=>1111001=>0000110
[8,4,3,2,1,5,7,6]=>1111001=>0000110
[7,4,3,2,1,5,8,6]=>1111001=>0000110
[6,4,3,2,1,5,8,7]=>1111001=>0000110
[3,5,4,2,6,8,1,7]=>0110010=>1001101
[5,6,3,4,1,2,8,7]=>0101001=>1010110
[8,5,3,7,2,6,4,1]=>1101011=>0010100
[8,5,7,4,2,6,3,1]=>1011011=>0100100
[7,5,8,4,2,6,1,3]=>1011010=>0100101
[2,1,7,8,5,6,3,4]=>1001010=>0110101
[6,8,3,7,5,1,4,2]=>0101101=>1010010
[5,7,3,8,1,6,2,4]=>0101010=>1010101
[3,2,6,4,8,5,1,7]=>1010110=>0101001
[3,5,2,4,1,7,6,8]=>0101010=>1010101
[4,2,5,8,3,1,6,7]=>1001100=>0110011
[3,1,5,4,2,8,6,7]=>1011010=>0100101
[4,1,5,8,3,2,6,7]=>1001100=>0110011
[4,3,8,5,2,1,6,7]=>1011100=>0100011
[4,7,3,5,2,1,6,8]=>0101100=>1010011
[4,3,2,7,5,1,6,8]=>1101100=>0010011
[4,3,6,2,5,1,7,8]=>1010100=>0101011
[4,6,3,2,5,1,7,8]=>0110100=>1001011
[4,5,1,7,3,2,6,8]=>0101100=>1010011
[5,2,1,4,3,7,8,6]=>1101001=>0010110
[4,3,1,5,7,2,6,8]=>1100100=>0011011
[4,3,6,1,5,2,7,8]=>1010100=>0101011
[4,6,3,1,5,2,7,8]=>0110100=>1001011
[5,3,6,4,1,2,7,8]=>1011000=>0100111
[4,3,6,1,7,2,5,8]=>1010100=>0101011
[6,2,4,1,3,7,8,5]=>1010001=>0101110
[3,6,4,1,2,7,5,8]=>0110010=>1001101
[4,6,3,1,7,2,5,8]=>0110100=>1001011
[5,6,2,7,1,3,4,8]=>0101000=>1010111
[4,5,2,7,3,1,6,8]=>0101100=>1010011
[4,6,2,1,7,3,5,8]=>0110100=>1001011
[3,2,6,1,4,7,5,8]=>1010010=>0101101
[3,5,2,7,4,6,1,8]=>0101010=>1010101
[3,7,2,4,8,5,1,6]=>0100110=>1011001
[7,3,1,4,6,8,2,5]=>1100010=>0011101
[3,2,6,1,5,7,4,8]=>1010010=>0101101
[6,3,2,1,5,7,4,8]=>1110010=>0001101
[6,4,2,1,5,3,7,8]=>1110100=>0001011
[4,2,6,1,5,3,7,8]=>1010100=>0101011
[4,2,1,7,5,3,6,8]=>1101100=>0010011
[7,4,1,5,6,2,3,8]=>1100100=>0011011
[7,3,1,5,2,6,4,8]=>1101010=>0010101
[6,3,5,1,2,7,4,8]=>1010010=>0101101
[5,2,6,4,1,3,7,8]=>1011000=>0100111
[3,6,5,1,2,7,4,8]=>0110010=>1001101
[6,5,2,1,4,7,8,3]=>1110001=>0001110
[6,5,3,1,4,7,2,8]=>1110010=>0001101
[2,3,1,8,5,4,7,6]=>0101101=>1010010
[2,4,1,5,8,3,7,6]=>0100101=>1011010
[2,4,1,5,3,8,7,6]=>0101011=>1010100
[3,4,5,1,2,8,7,6]=>0010011=>1101100
[3,4,5,1,8,2,7,6]=>0010101=>1101010
[1,8,4,5,3,2,7,6]=>0101101=>1010010
[2,4,8,5,3,1,7,6]=>0011101=>1100010
[3,4,5,8,2,1,7,6]=>0001101=>1110010
[3,4,5,2,8,1,7,6]=>0010101=>1101010
[3,4,6,2,1,7,8,5]=>0011001=>1100110
[3,4,6,2,1,7,5,8]=>0011010=>1100101
[3,5,6,2,7,1,4,8]=>0010100=>1101011
[3,5,6,2,7,1,8,4]=>0010101=>1101010
[3,5,6,2,7,8,1,4]=>0010010=>1101101
[3,4,6,2,8,7,1,5]=>0010110=>1101001
[3,4,6,8,2,7,1,5]=>0001010=>1110101
[2,4,8,6,3,7,1,5]=>0011010=>1100101
[1,8,4,6,3,7,2,5]=>0101010=>1010101
[1,8,4,6,3,7,5,2]=>0101011=>1010100
[3,4,6,8,2,7,5,1]=>0001011=>1110100
[3,4,6,2,8,7,5,1]=>0010111=>1101000
[3,5,6,2,7,8,4,1]=>0010011=>1101100
[3,5,6,2,7,4,1,8]=>0010110=>1101001
[4,5,6,7,2,8,3,1]=>0001011=>1110100
[3,5,6,8,7,2,4,1]=>0001101=>1110010
[2,5,8,6,7,3,4,1]=>0010101=>1101010
[1,8,5,6,7,3,4,2]=>0100101=>1011010
[1,8,5,6,7,3,2,4]=>0100110=>1011001
[2,5,8,6,7,3,1,4]=>0010110=>1101001
[3,5,6,8,7,2,1,4]=>0001110=>1110001
[4,5,6,7,2,1,8,3]=>0001101=>1110010
[3,4,6,1,8,7,2,5]=>0010110=>1101001
[2,4,1,6,8,7,3,5]=>0100110=>1011001
[2,3,1,8,6,7,4,5]=>0101010=>1010101
[1,8,3,2,6,7,5,4]=>0110011=>1001100
[2,5,1,6,7,8,4,3]=>0100011=>1011100
[2,5,1,6,7,4,8,3]=>0100101=>1011010
[2,5,1,6,7,4,3,8]=>0100110=>1011001
[3,5,6,1,7,4,2,8]=>0010110=>1101001
[3,5,6,1,7,4,8,2]=>0010101=>1101010
[3,4,6,1,8,7,5,2]=>0010111=>1101000
[3,4,6,8,1,7,5,2]=>0001011=>1110100
[2,4,8,6,1,7,5,3]=>0011011=>1100100
[1,8,4,6,2,7,5,3]=>0101011=>1010100
[1,8,5,6,7,2,4,3]=>0100101=>1011010
[2,5,8,6,7,1,4,3]=>0010101=>1101010
[3,5,6,8,7,1,4,2]=>0001101=>1110010
[4,5,6,7,8,1,3,2]=>0000101=>1111010
[4,5,6,7,1,3,8,2]=>0001001=>1110110
[4,5,6,7,1,3,2,8]=>0001010=>1110101
[4,5,6,7,3,1,8,2]=>0001101=>1110010
[3,5,6,8,7,4,1,2]=>0001110=>1110001
[2,5,8,6,7,4,1,3]=>0010110=>1101001
[1,8,5,6,7,4,2,3]=>0100110=>1011001
[1,8,5,6,7,4,3,2]=>0100111=>1011000
[2,5,8,6,7,4,3,1]=>0010111=>1101000
[8,2,5,3,7,1,6,4]=>1010101=>0101010
[8,2,4,3,7,1,6,5]=>1010101=>0101010
[5,8,2,4,3,7,1,6]=>0101010=>1010101
[4,2,5,6,1,8,3,7]=>1001010=>0110101
[4,2,5,6,1,7,3,8]=>1001010=>0110101
[6,1,5,7,3,2,4,8]=>1001100=>0110011
[6,1,5,8,3,2,4,7]=>1001100=>0110011
[3,8,2,4,7,1,5,6]=>0100100=>1011011
[3,6,8,2,4,7,1,5]=>0010010=>1101101
[4,3,5,6,7,1,8,2]=>1000101=>0111010
[3,7,1,5,6,8,2,4]=>0100010=>1011101
[3,7,1,5,8,2,4,6]=>0100100=>1011011
[8,3,2,4,6,1,5,7]=>1100100=>0011011
[7,3,2,4,6,1,5,8]=>1100100=>0011011
[3,2,5,1,7,4,6,8]=>1010100=>0101011
[3,2,5,1,8,4,6,7]=>1010100=>0101011
[3,2,5,1,7,8,4,6]=>1010010=>0101101
[7,8,3,2,4,6,1,5]=>0110010=>1001101
[6,1,5,7,8,3,2,4]=>1000110=>0111001
[4,2,5,6,1,7,8,3]=>1001001=>0110110
[5,7,6,1,8,3,4,2]=>0110101=>1001010
[5,8,6,1,7,3,4,2]=>0110101=>1001010
[6,1,5,8,7,3,2,4]=>1001110=>0110001
[8,7,3,2,4,6,1,5]=>1110010=>0001101
[3,2,5,1,8,7,4,6]=>1010110=>0101001
[3,2,5,1,6,4,7,8]=>1010100=>0101011
[3,2,4,1,8,7,5,6]=>1010110=>0101001
[3,2,5,1,6,8,7,4]=>1010011=>0101100
[3,8,6,5,1,7,4,2]=>0111011=>1000100
[3,7,6,5,1,8,4,2]=>0111011=>1000100
[6,5,1,7,8,4,2,3]=>1100110=>0011001
[3,2,5,1,6,7,8,4]=>1010001=>0101110
[3,2,4,1,8,5,6,7]=>1010100=>0101011
[3,2,4,1,7,5,6,8]=>1010100=>0101011
[3,2,4,1,6,8,5,7]=>1010010=>0101101
[3,2,4,1,8,5,7,6]=>1010101=>0101010
[8,3,2,4,7,6,1,5]=>1100110=>0011001
[3,2,5,1,8,4,7,6]=>1010101=>0101010
[3,2,5,1,6,7,4,8]=>1010010=>0101101
[6,5,1,7,4,2,3,8]=>1101100=>0010011
[6,5,1,8,4,2,3,7]=>1101100=>0010011
[8,4,2,3,7,5,1,6]=>1100110=>0011001
[4,2,6,1,8,3,7,5]=>1010101=>0101010
[5,2,6,1,8,3,7,4]=>1010101=>0101010
[8,4,6,1,7,3,5,2]=>1010101=>0101010
[5,2,6,1,8,4,7,3]=>1010101=>0101010
[7,4,2,3,8,5,1,6]=>1100110=>0011001
[8,5,1,6,4,2,3,7]=>1101100=>0010011
[7,5,1,6,4,2,3,8]=>1101100=>0010011
[3,2,5,1,7,6,4,8]=>1010110=>0101001
[3,2,5,1,8,6,4,7]=>1010110=>0101001
[7,3,2,4,8,6,1,5]=>1100110=>0011001
[8,6,1,5,7,3,2,4]=>1100110=>0011001
[4,2,6,1,8,5,7,3]=>1010101=>0101010
[8,5,6,1,7,3,4,2]=>1010101=>0101010
[3,6,8,5,1,7,4,2]=>0011011=>1100100
[8,5,1,6,7,4,2,3]=>1100110=>0011001
[3,2,5,1,8,6,7,4]=>1010101=>0101010
[3,2,4,1,8,6,5,7]=>1010110=>0101001
[3,2,4,1,5,8,6,7]=>1010010=>0101101
[3,2,5,1,7,8,6,4]=>1010011=>0101100
[7,8,5,1,6,4,2,3]=>0110110=>1001001
[3,8,5,1,7,6,4,2]=>0110111=>1001000
[3,7,5,1,8,6,4,2]=>0110111=>1001000
[8,7,5,1,6,4,2,3]=>1110110=>0001001
[3,2,5,1,8,7,6,4]=>1010111=>0101000
[6,5,7,3,1,8,4,2]=>1011011=>0100100
[4,6,3,7,1,8,5,2]=>0101011=>1010100
[4,6,3,7,5,1,8,2]=>0101101=>1010010
[4,2,6,1,7,5,3,8]=>1010110=>0101001
[2,5,7,4,1,6,3,8]=>0011010=>1100101
[2,5,7,4,1,6,8,3]=>0011001=>1100110
[5,4,7,3,6,1,8,2]=>1010101=>0101010
[5,4,7,8,3,1,6,2]=>1001101=>0110010
[4,3,7,5,1,8,6,2]=>1011011=>0100100
[6,4,3,8,5,1,7,2]=>1101101=>0010010
[5,8,4,3,6,1,7,2]=>0110101=>1001010
[5,4,8,3,6,1,7,2]=>1010101=>0101010
[5,4,3,6,7,1,8,2]=>1100101=>0011010
[2,5,4,6,1,7,3,8]=>0101010=>1010101
[3,2,5,8,1,6,7,4]=>1001001=>0110110
[2,5,4,6,8,1,7,3]=>0100101=>1011010
[5,2,8,4,1,6,7,3]=>1011001=>0100110
[4,6,2,1,8,5,7,3]=>0110101=>1001010
[2,4,1,7,5,8,6,3]=>0101011=>1010100
[2,4,1,7,5,3,8,6]=>0101101=>1010010
[2,6,4,1,8,5,3,7]=>0110110=>1001001
[5,4,8,2,1,6,3,7]=>1011010=>0100101
[2,5,8,4,1,6,3,7]=>0011010=>1100101
[3,2,5,6,1,8,4,7]=>1001010=>0110101
[4,8,3,2,6,1,5,7]=>0110100=>1001011
[3,5,2,8,1,6,4,7]=>0101010=>1010101
[3,2,1,6,8,5,4,7]=>1100110=>0011001
[3,2,7,1,5,4,8,6]=>1010101=>0101010
[3,2,7,1,5,8,6,4]=>1010011=>0101100
[3,8,2,5,1,6,7,4]=>0101001=>1010110
[4,8,3,2,6,7,1,5]=>0110010=>1001101
[4,3,8,2,6,7,1,5]=>1010010=>0101101
[4,3,2,6,7,8,1,5]=>1100010=>0011101
[4,3,2,6,7,1,5,8]=>1100100=>0011011
[4,3,7,2,6,8,1,5]=>1010010=>0101101
[4,3,7,8,2,6,1,5]=>1001010=>0110101
[2,5,7,4,8,1,6,3]=>0010101=>1101010
[3,2,5,7,8,1,6,4]=>1000101=>0111010
[3,2,5,7,1,6,8,4]=>1001001=>0110110
[3,2,5,7,1,6,4,8]=>1001010=>0110101
[6,3,2,7,1,5,4,8]=>1101010=>0010101
[6,3,2,7,1,5,8,4]=>1101001=>0010110
[6,3,2,7,8,1,5,4]=>1100101=>0011010
[4,2,6,1,7,8,5,3]=>1010011=>0101100
[6,5,2,1,7,8,4,3]=>1110011=>0001100
[2,1,7,5,3,8,6,4]=>1011011=>0100100
[6,2,1,8,5,3,7,4]=>1101101=>0010010
[6,3,2,7,1,4,8,5]=>1101001=>0010110
[6,3,2,1,4,7,8,5]=>1110001=>0001110
[6,3,2,1,4,7,5,8]=>1110010=>0001101
[3,5,2,1,7,4,6,8]=>0110100=>1001011
[3,5,2,1,7,8,4,6]=>0110010=>1001101
[5,8,4,2,1,7,3,6]=>0111010=>1000101
[4,6,2,1,8,3,7,5]=>0110101=>1001010
[2,4,1,7,3,8,6,5]=>0101011=>1010100
[3,2,7,1,4,8,6,5]=>1010011=>0101100
[3,5,8,2,1,7,4,6]=>0011010=>1100101
[4,8,3,7,2,1,5,6]=>0101100=>1010011
[4,3,7,2,8,1,5,6]=>1010100=>0101011
[4,3,7,2,1,5,6,8]=>1011000=>0100111
[4,8,3,2,7,1,5,6]=>0110100=>1001011
[3,5,2,8,1,7,4,6]=>0101010=>1010101
[6,3,2,8,1,4,7,5]=>1101001=>0010110
[3,2,1,4,7,5,8,6]=>1100101=>0011010
[5,3,2,1,8,4,6,7]=>1110100=>0001011
[4,8,3,2,1,5,6,7]=>0111000=>1000111
[4,3,8,2,1,5,6,7]=>1011000=>0100111
[1,9,8,7,6,5,4,3,2]=>01111111=>10000000
[8,7,6,4,5,3,2,1,9]=>11101110=>00010001
[1,9,8,7,5,6,4,3,2]=>01110111=>10001000
[1,10,9,8,7,6,5,4,3,2]=>011111111=>100000000
[10,9,8,7,6,5,4,3,2,1,11]=>1111111110=>0000000001
[9,8,7,5,6,4,3,2,1,10]=>111011110=>000100001
[8,7,5,4,6,3,2,1,9]=>11101110=>00010001
[8,7,4,6,5,3,2,1,9]=>11011110=>00100001
[1,9,8,6,5,7,4,3,2]=>01110111=>10001000
[1,9,8,5,7,6,4,3,2]=>01101111=>10010000
[1,10,9,8,6,7,5,4,3,2]=>011101111=>100010000
[1,11,10,9,8,7,6,5,4,3,2]=>0111111111=>1000000000
[6,2,3,1,5,4,8,7]=>1010101=>0101010
[8,4,5,2,3,1,7,6]=>1010101=>0101010
[8,6,7,2,5,3,4,1]=>1010101=>0101010
[8,2,5,3,4,1,7,6]=>1010101=>0101010
[6,2,5,3,4,1,8,7]=>1010101=>0101010
[6,1,5,2,4,3,8,7]=>1010101=>0101010
[6,4,5,1,3,2,8,7]=>1010101=>0101010
[6,1,5,3,4,2,8,7]=>1010101=>0101010
[6,3,5,1,4,2,8,7]=>1010101=>0101010
[8,3,5,2,4,1,7,6]=>1010101=>0101010
[8,3,7,5,6,2,4,1]=>1010101=>0101010
[8,3,7,2,4,1,6,5]=>1010101=>0101010
[8,3,5,1,4,2,7,6]=>1010101=>0101010
[8,1,5,3,4,2,7,6]=>1010101=>0101010
[8,4,5,1,3,2,7,6]=>1010101=>0101010
[2,1,8,4,5,3,7,6]=>1010101=>0101010
[8,6,7,4,5,1,3,2]=>1010101=>0101010
[8,6,7,1,5,3,4,2]=>1010101=>0101010
[8,6,7,3,5,1,4,2]=>1010101=>0101010
[8,3,7,5,6,1,4,2]=>1010101=>0101010
[8,5,7,3,6,1,4,2]=>1010101=>0101010
[8,3,7,4,6,2,5,1]=>1010101=>0101010
[8,3,7,4,6,1,5,2]=>1010101=>0101010
[8,3,7,1,6,4,5,2]=>1010101=>0101010
[8,1,7,3,6,4,5,2]=>1010101=>0101010
[8,1,7,5,6,3,4,2]=>1010101=>0101010
[8,4,7,5,6,1,3,2]=>1010101=>0101010
[2,1,8,4,7,5,6,3]=>1010101=>0101010
[8,1,7,3,4,2,6,5]=>1010101=>0101010
[8,1,7,3,6,2,5,4]=>1010101=>0101010
[8,3,7,1,6,2,5,4]=>1010101=>0101010
[8,3,7,2,6,4,5,1]=>1010101=>0101010
[8,2,7,3,6,4,5,1]=>1010101=>0101010
[8,2,7,3,6,1,5,4]=>1010101=>0101010
[8,2,7,1,6,3,5,4]=>1010101=>0101010
[8,1,7,2,4,3,6,5]=>1010101=>0101010
[8,1,3,2,7,4,6,5]=>1010101=>0101010
[2,1,8,3,7,4,6,5]=>1010101=>0101010
[8,1,5,2,4,3,7,6]=>1010101=>0101010
[8,2,7,1,4,3,6,5]=>1010101=>0101010
[8,2,7,3,4,1,6,5]=>1010101=>0101010
[8,2,7,5,6,3,4,1]=>1010101=>0101010
[8,4,7,5,6,2,3,1]=>1010101=>0101010
[8,4,7,2,3,1,6,5]=>1010101=>0101010
[8,2,3,1,7,4,6,5]=>1010101=>0101010
[8,2,3,1,5,4,7,6]=>1010101=>0101010
[4,2,3,1,8,5,7,6]=>1010101=>0101010
[4,1,3,2,8,6,7,5]=>1010101=>0101010
[8,6,7,2,3,1,5,4]=>1010101=>0101010
[8,2,3,1,7,5,6,4]=>1010101=>0101010
[8,5,7,2,6,3,4,1]=>1010101=>0101010
[8,5,7,2,6,1,4,3]=>1010101=>0101010
[8,2,7,5,6,1,4,3]=>1010101=>0101010
[8,6,7,2,5,1,4,3]=>1010101=>0101010
[8,6,7,1,5,2,4,3]=>1010101=>0101010
[8,6,7,1,3,2,5,4]=>1010101=>0101010
[2,1,8,6,7,3,5,4]=>1010101=>0101010
[2,1,8,3,7,5,6,4]=>1010101=>0101010
[8,1,3,2,7,5,6,4]=>1010101=>0101010
[8,1,7,5,6,2,4,3]=>1010101=>0101010
[8,1,7,2,6,4,5,3]=>1010101=>0101010
[8,2,7,1,6,4,5,3]=>1010101=>0101010
[8,2,7,4,6,1,5,3]=>1010101=>0101010
[8,2,7,4,6,3,5,1]=>1010101=>0101010
[8,4,7,2,6,3,5,1]=>1010101=>0101010
[8,4,7,2,6,1,5,3]=>1010101=>0101010
[8,4,7,1,6,2,5,3]=>1010101=>0101010
[8,1,7,4,6,2,5,3]=>1010101=>0101010
[8,5,7,1,6,2,4,3]=>1010101=>0101010
[2,1,8,5,7,3,6,4]=>1010101=>0101010
[8,5,7,4,6,1,3,2]=>1010101=>0101010
[8,5,7,1,6,3,4,2]=>1010101=>0101010
[8,1,7,4,6,3,5,2]=>1010101=>0101010
[8,4,7,1,6,3,5,2]=>1010101=>0101010
[8,4,7,3,6,1,5,2]=>1010101=>0101010
[2,4,8,3,6,1,7,5]=>0010101=>1101010
[6,5,8,1,3,2,7,4]=>1010101=>0101010
[4,5,8,6,3,2,7,1]=>0011101=>1100010
[6,5,8,7,3,1,2,4]=>1011100=>0100011
[1,5,8,7,3,6,2,4]=>0011010=>1100101
[1,7,2,8,4,6,5,3]=>0101011=>1010100
[6,7,2,8,4,1,5,3]=>0101101=>1010010
[3,6,2,8,4,5,7,1]=>0101001=>1010110
[2,6,1,8,4,5,7,3]=>0101001=>1010110
[2,8,4,6,1,5,7,3]=>0101001=>1010110
[6,3,1,8,4,5,7,2]=>1101001=>0010110
[3,1,6,8,4,5,7,2]=>1001001=>0110110
[2,3,6,8,4,5,7,1]=>0001001=>1110110
[6,3,7,8,4,1,5,2]=>1001101=>0110010
[1,3,7,8,4,6,5,2]=>0001011=>1110100
[1,5,7,8,2,4,6,3]=>0001001=>1110110
[5,1,7,8,2,4,6,3]=>1001001=>0110110
[3,6,7,8,4,2,5,1]=>0001101=>1110010
[7,6,1,8,4,2,5,3]=>1101101=>0010010
[5,6,8,7,3,2,1,4]=>0011110=>1100001
[2,8,3,7,1,6,5,4]=>0101011=>1010100
[5,2,8,7,3,6,1,4]=>1011010=>0100101
[7,2,1,8,4,6,5,3]=>1101011=>0010100
[3,2,7,8,4,6,5,1]=>1001011=>0110100
[5,2,7,8,1,4,6,3]=>1001001=>0110110
[1,2,7,8,5,4,6,3]=>0001101=>1110010
[4,2,1,3,8,5,6,7]=>1100100=>0011011
[7,2,5,8,3,4,6,1]=>1001001=>0110110
[6,2,8,5,4,3,1,7]=>1011110=>0100001
[2,8,3,5,4,1,6,7]=>0101100=>1010011
[2,8,4,5,3,1,6,7]=>0101100=>1010011
[6,4,8,5,2,3,1,7]=>1011010=>0100101
[7,3,5,8,2,4,6,1]=>1001001=>0110110
[4,3,1,2,8,5,6,7]=>1100100=>0011011
[3,4,2,1,8,5,6,7]=>0110100=>1001011
[2,7,6,8,4,3,5,1]=>0101101=>1010010
[5,7,1,8,3,4,6,2]=>0101001=>1010110
[3,7,5,8,1,4,6,2]=>0101001=>1010110
[1,7,5,8,3,4,6,2]=>0101001=>1010110
[1,6,8,5,4,3,2,7]=>0011110=>1100001
[4,6,8,5,1,3,2,7]=>0011010=>1100101
[5,6,8,1,4,3,2,7]=>0010110=>1101001
[7,5,8,6,3,4,2,1]=>1011011=>0100100
[2,4,8,3,6,5,1,7]=>0010110=>1101001
[2,8,4,1,5,6,3,7]=>0110010=>1001101
[4,1,8,3,5,6,2,7]=>1010010=>0101101
[5,6,8,4,1,3,2,7]=>0011010=>1100101
[4,6,8,1,5,3,2,7]=>0010110=>1101001
[1,6,8,4,5,3,2,7]=>0010110=>1101001
[1,7,3,8,5,4,6,2]=>0101101=>1010010
[3,7,1,8,5,4,6,2]=>0101101=>1010010
[2,7,3,8,4,6,5,1]=>0101011=>1010100
[7,1,3,8,4,6,5,2]=>1001011=>0110100
[5,7,8,4,3,6,1,2]=>0011010=>1100101
[2,8,7,4,1,6,5,3]=>0111011=>1000100
[2,8,5,4,3,1,6,7]=>0111100=>1000011
[6,5,8,4,2,3,1,7]=>1011010=>0100101
[4,1,3,2,8,5,6,7]=>1010100=>0101011
[1,4,3,2,8,5,6,7]=>0110100=>1001011
[7,3,2,8,5,4,6,1]=>1101101=>0010010
[6,4,8,2,5,3,1,7]=>1010110=>0101001
[2,8,4,3,5,1,6,7]=>0110100=>1001011
[2,8,3,4,5,1,6,7]=>0100100=>1011011
[6,2,8,4,5,3,1,7]=>1010110=>0101001
[7,2,3,8,5,4,6,1]=>1001101=>0110010
[4,2,3,1,8,5,6,7]=>1010100=>0101011
[3,2,1,4,8,5,6,7]=>1100100=>0011011
[5,1,3,2,4,8,6,7]=>1010010=>0101101
[2,8,1,5,3,4,7,6]=>0101001=>1010110
[1,2,8,4,5,3,7,6]=>0010101=>1101010
[1,4,2,8,5,3,6,7]=>0101100=>1010011
[1,8,4,2,5,3,6,7]=>0110100=>1001011
[8,1,5,3,2,4,6,7]=>1011000=>0100111
[3,8,1,5,2,4,6,7]=>0101000=>1010111
[3,5,1,4,8,2,6,7]=>0100100=>1011011
[1,5,2,8,4,3,6,7]=>0101100=>1010011
[1,2,8,5,4,3,6,7]=>0011100=>1100011
[1,2,5,4,3,8,6,7]=>0011010=>1100101
[1,2,4,8,5,3,7,6]=>0001101=>1110010
[1,2,7,4,8,5,3,6]=>0010110=>1101001
[1,5,2,7,8,4,3,6]=>0100110=>1011001
[5,1,2,7,4,8,3,6]=>1001010=>0110101
[8,3,5,1,4,7,2,6]=>1010010=>0101101
[2,8,1,5,4,7,3,6]=>0101010=>1010101
[1,2,8,5,7,4,3,6]=>0010110=>1101001
[1,2,4,8,7,5,3,6]=>0001110=>1110001
[2,8,1,4,3,7,6,5]=>0101011=>1010100
[6,1,2,8,7,4,3,5]=>1001110=>0110001
[6,4,1,2,8,7,3,5]=>1100110=>0011001
[3,6,4,8,1,7,2,5]=>0101010=>1010101
[7,6,1,4,2,8,3,5]=>1101010=>0010101
[7,1,6,2,8,4,3,5]=>1010110=>0101001
[1,6,7,2,8,4,3,5]=>0010110=>1101001
[6,7,1,4,2,8,3,5]=>0101010=>1010101
[6,3,7,1,4,8,2,5]=>1010010=>0101101
[3,7,8,1,5,2,4,6]=>0010100=>1101011
[7,1,2,8,5,3,4,6]=>1001100=>0110011
[1,7,2,8,4,5,3,6]=>0101010=>1010101
[1,4,2,7,8,5,3,6]=>0100110=>1011001
[6,1,2,8,4,3,7,5]=>1001101=>0110010
[6,4,1,2,8,3,7,5]=>1100101=>0011010
[7,6,1,3,2,4,8,5]=>1101001=>0010110
[6,7,1,3,2,4,8,5]=>0101001=>1010110
[1,2,7,3,5,8,4,6]=>0010010=>1101101
[1,2,7,5,8,3,4,6]=>0010100=>1101011
[5,8,1,3,7,2,4,6]=>0100100=>1011011
[1,2,5,8,7,3,4,6]=>0001100=>1110011
[1,2,5,8,3,7,4,6]=>0001010=>1110101
[2,8,1,7,3,5,4,6]=>0101010=>1010101
[8,6,1,3,2,4,7,5]=>1101001=>0010110
[4,2,8,1,7,3,6,5]=>1010101=>0101010
[2,8,1,7,4,3,6,5]=>0101101=>1010010
[7,1,2,8,4,3,6,5]=>1001101=>0110010
[1,2,8,4,7,5,3,6]=>0010110=>1101001
[1,2,8,7,4,5,3,6]=>0011010=>1100101
[2,8,1,7,5,3,4,6]=>0101100=>1010011
[8,3,7,1,5,2,4,6]=>1010100=>0101011
[3,8,6,1,4,7,2,5]=>0110010=>1001101
[8,6,1,4,2,7,3,5]=>1101010=>0010101
[8,1,6,2,7,4,3,5]=>1010110=>0101001
[7,1,2,8,6,4,3,5]=>1001110=>0110001
[7,4,1,2,8,6,3,5]=>1100110=>0011001
[3,7,4,8,1,6,2,5]=>0101010=>1010101
[3,4,8,7,1,6,2,5]=>0011010=>1100101
[4,2,8,1,7,6,3,5]=>1010110=>0101001
[2,8,1,7,6,4,3,5]=>0101110=>1010001
[7,8,3,4,1,5,2,6]=>0101010=>1010101
[7,8,3,4,1,6,2,5]=>0101010=>1010101
[6,8,3,4,1,7,2,5]=>0101010=>1010101
[6,7,3,4,1,8,2,5]=>0101010=>1010101
[5,7,3,4,1,8,2,6]=>0101010=>1010101
[5,8,3,4,1,7,2,6]=>0101010=>1010101
[5,8,3,4,1,6,2,7]=>0101010=>1010101
[6,8,3,4,1,5,2,7]=>0101010=>1010101
[6,7,3,4,1,5,2,8]=>0101010=>1010101
[5,7,3,4,1,6,2,8]=>0101010=>1010101
[5,6,2,8,3,4,1,7]=>0101010=>1010101
[5,6,2,7,3,4,1,8]=>0101010=>1010101
[4,6,2,8,3,5,1,7]=>0101010=>1010101
[4,7,3,5,1,6,2,8]=>0101010=>1010101
[4,8,3,5,1,6,2,7]=>0101010=>1010101
[4,8,3,5,1,7,2,6]=>0101010=>1010101
[4,7,3,5,1,8,2,6]=>0101010=>1010101
[5,6,2,3,1,7,4,8]=>0101010=>1010101
[5,6,2,4,1,8,3,7]=>0101010=>1010101
[5,6,2,4,1,7,3,8]=>0101010=>1010101
[4,6,2,5,1,7,3,8]=>0101010=>1010101
[4,6,2,5,1,8,3,7]=>0101010=>1010101
[4,5,1,8,3,7,2,6]=>0101010=>1010101
[4,5,1,7,3,8,2,6]=>0101010=>1010101
[4,6,2,7,3,8,1,5]=>0101010=>1010101
[5,6,2,7,3,8,1,4]=>0101010=>1010101
[5,6,2,7,4,8,1,3]=>0101010=>1010101
[5,6,3,8,4,7,1,2]=>0101010=>1010101
[5,6,2,8,4,7,1,3]=>0101010=>1010101
[5,6,2,8,3,7,1,4]=>0101010=>1010101
[4,6,2,8,3,7,1,5]=>0101010=>1010101
[4,5,1,7,3,6,2,8]=>0101010=>1010101
[4,5,1,8,3,6,2,7]=>0101010=>1010101
[9,2,1,3,4,5,6,7,8]=>11000000=>00111111
[10,2,1,3,4,5,6,7,8,9]=>110000000=>001111111
[9,2,3,1,4,5,6,7,8]=>10100000=>01011111
[4,2,3,5,6,7,8,9,1]=>10000001=>01111110
[3,4,2,5,6,7,8,9,1]=>01000001=>10111110
[3,2,4,5,6,7,8,9,10,1]=>100000001=>011111110
[2,3,4,5,6,7,8,9,10,11,1]=>0000000001=>1111111110
[6,5,3,2,1,4,8,7]=>1111001=>0000110
[4,6,3,5,2,1,8,7]=>0101101=>1010010
[8,7,3,5,2,4,1,6]=>1101010=>0010101
[6,8,2,4,5,7,3,1]=>0100011=>1011100
[8,7,2,4,5,3,1,6]=>1100110=>0011001
[3,6,1,4,5,2,8,7]=>0100101=>1011010
[8,3,7,4,5,2,1,6]=>1010110=>0101001
[6,3,8,4,5,7,2,1]=>1010011=>0101100
[5,8,7,4,3,6,2,1]=>0111011=>1000100
[2,8,7,4,3,6,1,5]=>0111010=>1000101
[8,1,7,4,3,6,2,5]=>1011010=>0100101
[8,7,3,5,1,4,2,6]=>1101010=>0010101
[2,1,6,8,5,7,4,3]=>1001011=>0110100
[6,8,3,5,1,7,4,2]=>0101011=>1010100
[5,1,8,4,7,6,3,2]=>1010111=>0101000
[2,5,8,4,7,6,3,1]=>0010111=>1101000
[4,3,8,1,5,6,7,2]=>1010001=>0101110
[4,8,1,3,5,6,7,2]=>0100001=>1011110
[5,8,7,4,1,6,3,2]=>0111011=>1000100
[5,8,3,6,1,4,7,2]=>0101001=>1010110
[4,8,3,6,1,2,7,5]=>0101001=>1010110
[3,8,7,4,1,6,2,5]=>0111010=>1000101
[3,8,1,2,5,6,7,4]=>0100001=>1011110
[8,7,1,4,2,6,3,5]=>1101010=>0010101
[8,6,3,1,2,4,7,5]=>1110001=>0001110
[8,1,7,4,5,2,3,6]=>1010100=>0101011
[2,8,7,4,5,1,3,6]=>0110100=>1001011
[8,7,2,4,1,6,3,5]=>1101010=>0010101
[5,8,3,6,2,4,7,1]=>0101001=>1010110
[8,6,3,2,1,4,7,5]=>1111001=>0000110
[8,7,3,5,2,1,4,6]=>1101100=>0010011
[5,8,3,6,2,1,7,4]=>0101101=>1010010
[5,8,7,4,2,6,1,3]=>0111010=>1000101
[2,6,8,4,5,7,1,3]=>0010010=>1101101
[6,1,8,4,5,7,2,3]=>1010010=>0101101
[6,8,3,5,1,7,2,4]=>0101010=>1010101
[2,1,5,8,3,6,7,4]=>1001001=>0110110
[5,8,3,6,1,2,7,4]=>0101001=>1010110
[4,1,8,2,5,6,7,3]=>1010001=>0101110
[2,4,8,1,5,6,7,3]=>0010001=>1101110
[4,8,2,1,5,6,7,3]=>0110001=>1001110
[3,4,8,2,5,6,7,1]=>0010001=>1101110
[5,8,1,4,7,6,2,3]=>0100110=>1011001
[5,8,3,1,6,2,7,4]=>0110101=>1001010
[4,5,3,8,6,1,7,2]=>0101101=>1010010
[3,4,1,8,5,6,7,2]=>0101001=>1010110
[2,4,6,8,10,1,3,5,7,9]=>000010000=>111101111
[2,4,6,9,10,1,3,5,7,8]=>000010000=>111101111
[2,4,7,8,10,1,3,5,6,9]=>000010000=>111101111
[2,4,7,9,10,1,3,5,6,8]=>000010000=>111101111
[2,4,8,9,10,1,3,5,6,7]=>000010000=>111101111
[2,5,6,8,10,1,3,4,7,9]=>000010000=>111101111
[2,5,6,9,10,1,3,4,7,8]=>000010000=>111101111
[2,5,7,8,10,1,3,4,6,9]=>000010000=>111101111
[2,5,7,9,10,1,3,4,6,8]=>000010000=>111101111
[2,5,8,9,10,1,3,4,6,7]=>000010000=>111101111
[2,6,7,8,10,1,3,4,5,9]=>000010000=>111101111
[2,6,7,9,10,1,3,4,5,8]=>000010000=>111101111
[2,6,8,9,10,1,3,4,5,7]=>000010000=>111101111
[2,7,8,9,10,1,3,4,5,6]=>000010000=>111101111
[3,4,6,8,10,1,2,5,7,9]=>000010000=>111101111
[3,4,6,9,10,1,2,5,7,8]=>000010000=>111101111
[3,4,7,8,10,1,2,5,6,9]=>000010000=>111101111
[3,4,7,9,10,1,2,5,6,8]=>000010000=>111101111
[3,4,8,9,10,1,2,5,6,7]=>000010000=>111101111
[3,5,6,8,10,1,2,4,7,9]=>000010000=>111101111
[3,5,6,9,10,1,2,4,7,8]=>000010000=>111101111
[3,5,7,8,10,1,2,4,6,9]=>000010000=>111101111
[3,5,7,9,10,1,2,4,6,8]=>000010000=>111101111
[3,5,8,9,10,1,2,4,6,7]=>000010000=>111101111
[3,6,7,8,10,1,2,4,5,9]=>000010000=>111101111
[3,6,7,9,10,1,2,4,5,8]=>000010000=>111101111
[3,6,8,9,10,1,2,4,5,7]=>000010000=>111101111
[3,7,8,9,10,1,2,4,5,6]=>000010000=>111101111
[4,5,6,8,10,1,2,3,7,9]=>000010000=>111101111
[4,5,6,9,10,1,2,3,7,8]=>000010000=>111101111
[4,5,7,8,10,1,2,3,6,9]=>000010000=>111101111
[4,5,7,9,10,1,2,3,6,8]=>000010000=>111101111
[4,5,8,9,10,1,2,3,6,7]=>000010000=>111101111
[4,6,7,8,10,1,2,3,5,9]=>000010000=>111101111
[4,6,7,9,10,1,2,3,5,8]=>000010000=>111101111
[4,6,8,9,10,1,2,3,5,7]=>000010000=>111101111
[4,7,8,9,10,1,2,3,5,6]=>000010000=>111101111
[5,6,7,8,10,1,2,3,4,9]=>000010000=>111101111
[5,6,7,9,10,1,2,3,4,8]=>000010000=>111101111
[5,6,8,9,10,1,2,3,4,7]=>000010000=>111101111
[5,7,8,9,10,1,2,3,4,6]=>000010000=>111101111
[2,4,6,8,10,12,1,3,5,7,9,11]=>00000100000=>11111011111
[2,4,6,8,11,12,1,3,5,7,9,10]=>00000100000=>11111011111
[2,4,6,9,10,12,1,3,5,7,8,11]=>00000100000=>11111011111
[2,4,6,9,11,12,1,3,5,7,8,10]=>00000100000=>11111011111
[2,4,6,10,11,12,1,3,5,7,8,9]=>00000100000=>11111011111
[2,4,7,8,10,12,1,3,5,6,9,11]=>00000100000=>11111011111
[2,4,7,8,11,12,1,3,5,6,9,10]=>00000100000=>11111011111
[2,4,7,9,10,12,1,3,5,6,8,11]=>00000100000=>11111011111
[2,4,7,9,11,12,1,3,5,6,8,10]=>00000100000=>11111011111
[2,4,7,10,11,12,1,3,5,6,8,9]=>00000100000=>11111011111
[2,4,8,9,10,12,1,3,5,6,7,11]=>00000100000=>11111011111
[2,4,8,9,11,12,1,3,5,6,7,10]=>00000100000=>11111011111
[2,4,8,10,11,12,1,3,5,6,7,9]=>00000100000=>11111011111
[2,4,9,10,11,12,1,3,5,6,7,8]=>00000100000=>11111011111
[2,5,6,8,10,12,1,3,4,7,9,11]=>00000100000=>11111011111
[2,5,6,8,11,12,1,3,4,7,9,10]=>00000100000=>11111011111
[2,5,6,9,10,12,1,3,4,7,8,11]=>00000100000=>11111011111
[2,5,6,9,11,12,1,3,4,7,8,10]=>00000100000=>11111011111
[2,5,6,10,11,12,1,3,4,7,8,9]=>00000100000=>11111011111
[2,5,7,8,10,12,1,3,4,6,9,11]=>00000100000=>11111011111
[2,5,7,8,11,12,1,3,4,6,9,10]=>00000100000=>11111011111
[2,5,7,9,10,12,1,3,4,6,8,11]=>00000100000=>11111011111
[2,5,7,9,11,12,1,3,4,6,8,10]=>00000100000=>11111011111
[2,5,7,10,11,12,1,3,4,6,8,9]=>00000100000=>11111011111
[2,5,8,9,10,12,1,3,4,6,7,11]=>00000100000=>11111011111
[2,5,8,9,11,12,1,3,4,6,7,10]=>00000100000=>11111011111
[2,5,8,10,11,12,1,3,4,6,7,9]=>00000100000=>11111011111
[2,5,9,10,11,12,1,3,4,6,7,8]=>00000100000=>11111011111
[2,6,7,8,10,12,1,3,4,5,9,11]=>00000100000=>11111011111
[2,6,7,8,11,12,1,3,4,5,9,10]=>00000100000=>11111011111
[2,6,7,9,10,12,1,3,4,5,8,11]=>00000100000=>11111011111
[2,6,7,9,11,12,1,3,4,5,8,10]=>00000100000=>11111011111
[2,6,7,10,11,12,1,3,4,5,8,9]=>00000100000=>11111011111
[2,6,8,9,10,12,1,3,4,5,7,11]=>00000100000=>11111011111
[2,6,8,9,11,12,1,3,4,5,7,10]=>00000100000=>11111011111
[2,6,8,10,11,12,1,3,4,5,7,9]=>00000100000=>11111011111
[2,6,9,10,11,12,1,3,4,5,7,8]=>00000100000=>11111011111
[2,7,8,9,10,12,1,3,4,5,6,11]=>00000100000=>11111011111
[2,7,8,9,11,12,1,3,4,5,6,10]=>00000100000=>11111011111
[2,7,8,10,11,12,1,3,4,5,6,9]=>00000100000=>11111011111
[2,7,9,10,11,12,1,3,4,5,6,8]=>00000100000=>11111011111
[2,8,9,10,11,12,1,3,4,5,6,7]=>00000100000=>11111011111
[3,4,6,8,10,12,1,2,5,7,9,11]=>00000100000=>11111011111
[3,4,6,8,11,12,1,2,5,7,9,10]=>00000100000=>11111011111
[3,4,6,9,10,12,1,2,5,7,8,11]=>00000100000=>11111011111
[3,4,6,9,11,12,1,2,5,7,8,10]=>00000100000=>11111011111
[3,4,6,10,11,12,1,2,5,7,8,9]=>00000100000=>11111011111
[3,4,7,8,10,12,1,2,5,6,9,11]=>00000100000=>11111011111
[3,4,7,8,11,12,1,2,5,6,9,10]=>00000100000=>11111011111
[3,4,7,9,10,12,1,2,5,6,8,11]=>00000100000=>11111011111
[3,4,7,9,11,12,1,2,5,6,8,10]=>00000100000=>11111011111
[3,4,7,10,11,12,1,2,5,6,8,9]=>00000100000=>11111011111
[3,4,8,9,10,12,1,2,5,6,7,11]=>00000100000=>11111011111
[3,4,8,9,11,12,1,2,5,6,7,10]=>00000100000=>11111011111
[3,4,8,10,11,12,1,2,5,6,7,9]=>00000100000=>11111011111
[3,4,9,10,11,12,1,2,5,6,7,8]=>00000100000=>11111011111
[3,5,6,8,10,12,1,2,4,7,9,11]=>00000100000=>11111011111
[3,5,6,8,11,12,1,2,4,7,9,10]=>00000100000=>11111011111
[3,5,6,9,10,12,1,2,4,7,8,11]=>00000100000=>11111011111
[3,5,6,9,11,12,1,2,4,7,8,10]=>00000100000=>11111011111
[3,5,6,10,11,12,1,2,4,7,8,9]=>00000100000=>11111011111
[3,5,7,8,10,12,1,2,4,6,9,11]=>00000100000=>11111011111
[3,5,7,8,11,12,1,2,4,6,9,10]=>00000100000=>11111011111
[3,5,7,9,10,12,1,2,4,6,8,11]=>00000100000=>11111011111
[3,5,7,9,11,12,1,2,4,6,8,10]=>00000100000=>11111011111
[3,5,7,10,11,12,1,2,4,6,8,9]=>00000100000=>11111011111
[3,5,8,9,10,12,1,2,4,6,7,11]=>00000100000=>11111011111
[3,5,8,9,11,12,1,2,4,6,7,10]=>00000100000=>11111011111
[3,5,8,10,11,12,1,2,4,6,7,9]=>00000100000=>11111011111
[3,5,9,10,11,12,1,2,4,6,7,8]=>00000100000=>11111011111
[3,6,7,8,10,12,1,2,4,5,9,11]=>00000100000=>11111011111
[3,6,7,8,11,12,1,2,4,5,9,10]=>00000100000=>11111011111
[3,6,7,9,10,12,1,2,4,5,8,11]=>00000100000=>11111011111
[3,6,7,9,11,12,1,2,4,5,8,10]=>00000100000=>11111011111
[3,6,7,10,11,12,1,2,4,5,8,9]=>00000100000=>11111011111
[3,6,8,9,10,12,1,2,4,5,7,11]=>00000100000=>11111011111
[3,6,8,9,11,12,1,2,4,5,7,10]=>00000100000=>11111011111
[3,6,8,10,11,12,1,2,4,5,7,9]=>00000100000=>11111011111
[3,6,9,10,11,12,1,2,4,5,7,8]=>00000100000=>11111011111
[3,7,8,9,10,12,1,2,4,5,6,11]=>00000100000=>11111011111
[3,7,8,9,11,12,1,2,4,5,6,10]=>00000100000=>11111011111
[3,7,8,10,11,12,1,2,4,5,6,9]=>00000100000=>11111011111
[3,7,9,10,11,12,1,2,4,5,6,8]=>00000100000=>11111011111
[3,8,9,10,11,12,1,2,4,5,6,7]=>00000100000=>11111011111
[4,5,6,8,10,12,1,2,3,7,9,11]=>00000100000=>11111011111
[4,5,6,8,11,12,1,2,3,7,9,10]=>00000100000=>11111011111
[4,5,6,9,10,12,1,2,3,7,8,11]=>00000100000=>11111011111
[4,5,6,9,11,12,1,2,3,7,8,10]=>00000100000=>11111011111
[4,5,6,10,11,12,1,2,3,7,8,9]=>00000100000=>11111011111
[4,5,7,8,10,12,1,2,3,6,9,11]=>00000100000=>11111011111
[4,5,7,8,11,12,1,2,3,6,9,10]=>00000100000=>11111011111
[4,5,7,9,10,12,1,2,3,6,8,11]=>00000100000=>11111011111
[4,5,7,9,11,12,1,2,3,6,8,10]=>00000100000=>11111011111
[4,5,7,10,11,12,1,2,3,6,8,9]=>00000100000=>11111011111
[4,5,8,9,10,12,1,2,3,6,7,11]=>00000100000=>11111011111
[4,5,8,9,11,12,1,2,3,6,7,10]=>00000100000=>11111011111
[4,5,8,10,11,12,1,2,3,6,7,9]=>00000100000=>11111011111
[4,5,9,10,11,12,1,2,3,6,7,8]=>00000100000=>11111011111
[4,6,7,8,10,12,1,2,3,5,9,11]=>00000100000=>11111011111
[4,6,7,8,11,12,1,2,3,5,9,10]=>00000100000=>11111011111
[4,6,7,9,10,12,1,2,3,5,8,11]=>00000100000=>11111011111
[4,6,7,9,11,12,1,2,3,5,8,10]=>00000100000=>11111011111
[4,6,7,10,11,12,1,2,3,5,8,9]=>00000100000=>11111011111
[4,6,8,9,10,12,1,2,3,5,7,11]=>00000100000=>11111011111
[4,6,8,9,11,12,1,2,3,5,7,10]=>00000100000=>11111011111
[4,6,8,10,11,12,1,2,3,5,7,9]=>00000100000=>11111011111
[4,6,9,10,11,12,1,2,3,5,7,8]=>00000100000=>11111011111
[4,7,8,9,10,12,1,2,3,5,6,11]=>00000100000=>11111011111
[4,7,8,9,11,12,1,2,3,5,6,10]=>00000100000=>11111011111
[4,7,8,10,11,12,1,2,3,5,6,9]=>00000100000=>11111011111
[4,7,9,10,11,12,1,2,3,5,6,8]=>00000100000=>11111011111
[4,8,9,10,11,12,1,2,3,5,6,7]=>00000100000=>11111011111
[5,6,7,8,10,12,1,2,3,4,9,11]=>00000100000=>11111011111
[5,6,7,8,11,12,1,2,3,4,9,10]=>00000100000=>11111011111
[5,6,7,9,10,12,1,2,3,4,8,11]=>00000100000=>11111011111
[5,6,7,9,11,12,1,2,3,4,8,10]=>00000100000=>11111011111
[5,6,7,10,11,12,1,2,3,4,8,9]=>00000100000=>11111011111
[5,6,8,9,10,12,1,2,3,4,7,11]=>00000100000=>11111011111
[5,6,8,9,11,12,1,2,3,4,7,10]=>00000100000=>11111011111
[5,6,8,10,11,12,1,2,3,4,7,9]=>00000100000=>11111011111
[5,6,9,10,11,12,1,2,3,4,7,8]=>00000100000=>11111011111
[5,7,8,9,10,12,1,2,3,4,6,11]=>00000100000=>11111011111
[5,7,8,9,11,12,1,2,3,4,6,10]=>00000100000=>11111011111
[5,7,8,10,11,12,1,2,3,4,6,9]=>00000100000=>11111011111
[5,7,9,10,11,12,1,2,3,4,6,8]=>00000100000=>11111011111
[5,8,9,10,11,12,1,2,3,4,6,7]=>00000100000=>11111011111
[6,7,8,9,10,12,1,2,3,4,5,11]=>00000100000=>11111011111
[6,7,8,9,11,12,1,2,3,4,5,10]=>00000100000=>11111011111
[6,7,8,10,11,12,1,2,3,4,5,9]=>00000100000=>11111011111
[6,7,9,10,11,12,1,2,3,4,5,8]=>00000100000=>11111011111
[6,8,9,10,11,12,1,2,3,4,5,7]=>00000100000=>11111011111
[7,8,9,10,11,12,1,2,3,4,5,6]=>00000100000=>11111011111
[4,5,7,6,2,3,8,1]=>0011001=>1100110
[3,5,7,2,6,4,8,1]=>0010101=>1101010
[2,5,7,3,6,4,8,1]=>0010101=>1101010
[1,5,7,3,6,8,4,2]=>0010011=>1101100
[8,4,3,7,6,1,5,2]=>1101101=>0010010
[6,7,2,3,5,4,8,1]=>0100101=>1011010
[5,2,7,3,6,4,8,1]=>1010101=>0101010
[8,3,4,7,6,1,5,2]=>1001101=>0110010
[8,2,4,7,1,6,5,3]=>1001011=>0110100
[3,1,4,7,6,8,5,2]=>1001011=>0110100
[4,1,3,7,6,8,5,2]=>1001011=>0110100
[5,1,7,3,6,8,4,2]=>1010011=>0101100
[6,7,1,3,5,8,4,2]=>0100011=>1011100
[5,8,7,3,6,1,4,2]=>0110101=>1001010
[4,8,3,7,6,1,5,2]=>0101101=>1010010
[3,8,4,7,6,1,5,2]=>0101101=>1010010
[2,8,4,7,1,6,5,3]=>0101011=>1010100
[8,1,4,7,2,6,5,3]=>1001011=>0110100
[8,1,3,2,7,6,5,4]=>1010111=>0101000
[2,8,3,1,7,6,5,4]=>0110111=>1001000
[3,8,2,1,7,6,5,4]=>0110111=>1001000
[6,7,1,2,8,5,4,3]=>0100111=>1011000
[8,2,3,1,7,6,5,4]=>1010111=>0101000
[8,3,2,1,7,6,5,4]=>1110111=>0001000
[3,4,1,7,6,8,5,2]=>0101011=>1010100
[1,4,2,7,8,6,5,3]=>0100111=>1011000
[8,4,2,7,1,6,5,3]=>1101011=>0010100
[8,5,7,2,1,6,4,3]=>1011011=>0100100
[1,5,7,2,8,6,4,3]=>0010111=>1101000
[2,5,7,1,8,6,4,3]=>0010111=>1101000
[3,5,7,1,6,8,4,2]=>0010011=>1101100
[6,7,4,5,8,1,3,2]=>0100101=>1011010
[5,4,7,6,8,1,3,2]=>1010101=>0101010
[2,5,7,8,1,6,4,3]=>0001011=>1110100
[1,5,7,8,2,6,4,3]=>0001011=>1110100
[8,5,7,1,2,6,4,3]=>1010011=>0101100
[8,4,1,7,2,6,5,3]=>1101011=>0010100
[1,4,8,7,2,6,5,3]=>0011011=>1100100
[3,4,8,7,6,1,5,2]=>0011101=>1100010
[4,3,8,7,6,1,5,2]=>1011101=>0100010
[5,3,7,8,6,1,4,2]=>1001101=>0110010
[6,7,2,8,1,5,4,3]=>0101011=>1010100
[5,2,7,8,1,6,4,3]=>1001011=>0110100
[4,2,8,7,1,6,5,3]=>1011011=>0100100
[3,2,8,1,7,6,5,4]=>1010111=>0101000
[1,3,8,2,7,6,5,4]=>0010111=>1101000
[8,3,1,2,7,6,5,4]=>1100111=>0011000
[8,2,1,3,7,6,5,4]=>1100111=>0011000
[1,2,8,3,7,6,5,4]=>0010111=>1101000
[2,1,8,3,7,6,5,4]=>1010111=>0101000
[4,1,8,7,2,6,5,3]=>1011011=>0100100
[5,1,7,8,2,6,4,3]=>1001011=>0110100
[6,7,1,8,2,5,4,3]=>0101011=>1010100
[5,8,7,1,2,6,4,3]=>0110011=>1001100
[4,8,1,7,2,6,5,3]=>0101011=>1010100
[3,8,1,2,7,6,5,4]=>0100111=>1011000
[2,8,1,3,7,6,5,4]=>0100111=>1011000
[1,8,2,3,7,6,5,4]=>0100111=>1011000
[8,1,2,3,7,6,5,4]=>1000111=>0111000
[3,1,4,5,6,7,8,9,10,2]=>100000001=>011111110
[2,3,4,5,6,7,8,9,11,1,10]=>0000000010=>1111111101
[10,3,4,5,6,7,8,1,2,9]=>100000100=>011111011
[10,1,4,5,6,7,8,9,2,3]=>100000010=>011111101
[3,1,4,5,6,7,8,9,10,11,2]=>1000000001=>0111111110
[2,3,4,5,6,7,8,9,10,12,1,11]=>00000000010=>11111111101
[11,3,4,5,6,7,8,9,1,2,10]=>1000000100=>0111111011
[2,10,4,5,6,7,8,1,3,9]=>010000100=>101111011
[8,3,4,5,6,7,1,10,2,9]=>100001010=>011110101
[3,1,10,5,6,7,8,9,2,4]=>101000010=>010111101
[9,1,4,5,6,7,8,2,10,3]=>100000101=>011111010
[11,1,4,5,6,7,8,9,10,2,3]=>1000000010=>0111111101
[3,1,4,5,6,7,8,9,10,11,12,2]=>10000000001=>01111111110
[6,7,1,8,4,5,2,3]=>0101010=>1010101
[3,7,1,5,8,2,6,4]=>0100101=>1011010
[2,7,1,5,8,3,6,4]=>0100101=>1011010
[2,6,5,1,8,3,7,4]=>0110101=>1001010
[3,6,5,1,8,2,7,4]=>0110101=>1001010
[4,6,5,1,8,7,2,3]=>0110110=>1001001
[5,6,4,1,8,7,2,3]=>0110110=>1001001
[8,1,4,5,7,6,2,3]=>1000110=>0111001
[6,4,5,1,8,7,2,3]=>1010110=>0101001
[5,4,6,1,8,7,2,3]=>1010110=>0101001
[4,5,6,1,8,7,2,3]=>0010110=>1101001
[3,5,6,1,8,2,7,4]=>0010101=>1101010
[2,5,6,1,8,3,7,4]=>0010101=>1101010
[2,4,6,1,3,8,7,5]=>0010011=>1101100
[3,4,6,1,2,8,7,5]=>0010011=>1101100
[4,3,6,1,2,8,7,5]=>1010011=>0101100
[5,3,6,1,8,2,7,4]=>1010101=>0101010
[7,3,1,5,8,2,6,4]=>1100101=>0011010
[8,1,3,5,7,2,6,4]=>1000101=>0111010
[8,1,2,5,7,3,6,4]=>1000101=>0111010
[7,2,1,5,8,3,6,4]=>1100101=>0011010
[6,2,5,1,8,3,7,4]=>1010101=>0101010
[4,2,6,1,3,8,7,5]=>1010011=>0101100
[2,3,6,1,4,8,7,5]=>0010011=>1101100
[4,2,5,3,1,8,7,6]=>1011011=>0100100
[6,2,4,1,3,8,7,5]=>1010011=>0101100
[7,2,1,4,3,8,6,5]=>1101011=>0010100
[8,1,2,4,3,7,6,5]=>1001011=>0110100
[8,1,3,4,2,7,6,5]=>1001011=>0110100
[7,3,1,4,2,8,6,5]=>1101011=>0010100
[6,3,4,1,2,8,7,5]=>1010011=>0101100
[4,6,3,1,2,8,7,5]=>0110011=>1001100
[3,6,4,1,2,8,7,5]=>0110011=>1001100
[2,6,4,1,3,8,7,5]=>0110011=>1001100
[2,7,1,4,3,8,6,5]=>0101011=>1010100
[3,7,1,4,2,8,6,5]=>0101011=>1010100
[4,7,1,3,2,8,6,5]=>0101011=>1010100
[8,1,6,7,2,3,5,4]=>1001001=>0110110
[4,7,1,2,3,8,6,5]=>0100011=>1011100
[3,7,1,2,4,8,6,5]=>0100011=>1011100
[2,7,1,3,4,8,6,5]=>0100011=>1011100
[2,6,3,1,4,8,7,5]=>0110011=>1001100
[3,6,2,1,4,8,7,5]=>0110011=>1001100
[5,6,2,1,8,3,7,4]=>0110101=>1001010
[6,5,2,1,8,3,7,4]=>1110101=>0001010
[8,1,5,2,7,3,6,4]=>1010101=>0101010
[8,1,4,2,3,7,6,5]=>1010011=>0101100
[7,4,1,2,3,8,6,5]=>1100011=>0011100
[6,4,2,1,3,8,7,5]=>1110011=>0001100
[5,4,2,3,1,8,7,6]=>1101011=>0010100
[3,5,2,4,1,8,7,6]=>0101011=>1010100
[6,3,2,1,4,8,7,5]=>1110011=>0001100
[7,3,1,2,4,8,6,5]=>1100011=>0011100
[8,1,3,2,4,7,6,5]=>1010011=>0101100
[8,1,2,3,4,7,6,5]=>1000011=>0111100
[7,2,1,3,4,8,6,5]=>1100011=>0011100
[6,2,3,1,4,8,7,5]=>1010011=>0101100
[2,4,3,6,1,5,8,7]=>0101001=>1010110
[2,4,3,6,5,8,1,7]=>0101010=>1010101
[2,4,6,3,5,8,7,1]=>0010011=>1101100
[2,4,6,3,5,8,1,7]=>0010010=>1101101
[2,4,6,3,5,1,8,7]=>0010101=>1101010
[2,4,6,3,1,5,8,7]=>0011001=>1100110
[2,4,1,6,5,3,8,7]=>0101101=>1010010
[2,4,6,1,5,3,8,7]=>0010101=>1101010
[4,2,6,5,3,1,8,7]=>1011101=>0100010
[4,2,6,5,1,3,8,7]=>1011001=>0100110
[4,2,6,5,1,8,7,3]=>1011011=>0100100
[4,2,6,5,8,1,7,3]=>1010101=>0101010
[4,2,6,5,8,1,3,7]=>1010100=>0101011
[4,2,6,5,8,3,1,7]=>1010110=>0101001
[2,4,6,1,5,8,3,7]=>0010010=>1101101
[2,4,1,6,5,8,3,7]=>0101010=>1010101
[2,1,4,6,5,8,3,7]=>1001010=>0110101
[2,4,1,6,5,8,7,3]=>0101011=>1010100
[2,4,6,1,5,8,7,3]=>0010011=>1101100
[4,2,6,5,3,8,7,1]=>1011011=>0100100
[4,2,6,5,8,3,7,1]=>1010101=>0101010
[2,6,4,3,8,7,1,5]=>0110110=>1001001
[2,6,4,3,8,7,5,1]=>0110111=>1001000
[4,2,6,8,5,3,7,1]=>1001101=>0110010
[2,4,6,8,1,5,7,3]=>0001001=>1110110
[2,4,6,1,8,5,7,3]=>0010101=>1101010
[2,4,1,6,8,5,7,3]=>0100101=>1011010
[2,1,4,6,8,5,7,3]=>1000101=>0111010
[2,1,4,6,8,5,3,7]=>1000110=>0111001
[2,4,1,6,8,5,3,7]=>0100110=>1011001
[2,4,6,1,8,5,3,7]=>0010110=>1101001
[2,4,6,8,1,5,3,7]=>0001010=>1110101
[4,2,6,8,5,3,1,7]=>1001110=>0110001
[4,2,6,8,5,1,3,7]=>1001100=>0110011
[4,2,6,8,5,1,7,3]=>1001101=>0110010
[2,4,6,8,3,5,7,1]=>0001001=>1110110
[2,4,6,8,3,5,1,7]=>0001010=>1110101
[2,4,6,8,3,1,5,7]=>0001100=>1110011
[2,4,6,3,1,8,5,7]=>0011010=>1100101
[2,4,6,3,8,1,5,7]=>0010100=>1101011
[2,4,6,3,8,5,1,7]=>0010110=>1101001
[2,4,6,3,8,5,7,1]=>0010101=>1101010
[2,4,3,6,8,5,7,1]=>0100101=>1011010
[2,4,3,6,8,5,1,7]=>0100110=>1011001
[2,4,3,6,8,1,5,7]=>0100100=>1011011
[2,4,3,6,1,8,5,7]=>0101010=>1010101
[2,4,3,1,6,8,5,7]=>0110010=>1001101
[2,4,1,3,6,8,7,5]=>0100011=>1011100
[2,4,3,6,1,8,7,5]=>0101011=>1010100
[2,4,3,6,8,1,7,5]=>0100101=>1011010
[4,6,5,2,8,7,3,1]=>0110111=>1001000
[4,6,5,2,8,7,1,3]=>0110110=>1001001
[4,6,2,5,8,7,1,3]=>0100110=>1011001
[4,6,2,5,8,7,3,1]=>0100111=>1011000
[2,4,6,3,8,1,7,5]=>0010101=>1101010
[2,4,6,3,1,8,7,5]=>0011011=>1100100
[2,4,1,6,3,8,7,5]=>0101011=>1010100
[2,1,4,6,3,8,7,5]=>1001011=>0110100
[2,1,4,6,8,3,7,5]=>1000101=>0111010
[2,4,1,6,8,3,7,5]=>0100101=>1011010
[2,4,6,1,8,3,7,5]=>0010101=>1101010
[2,4,6,8,1,3,7,5]=>0001001=>1110110
[2,4,6,8,3,1,7,5]=>0001101=>1110010
[4,6,2,8,5,7,3,1]=>0101011=>1010100
[4,6,2,8,5,7,1,3]=>0101010=>1010101
[6,2,4,8,7,1,3,5]=>1001100=>0110011
[6,4,2,8,7,5,3,1]=>1101111=>0010000
[2,6,4,8,1,7,5,3]=>0101011=>1010100
[2,6,4,1,8,7,5,3]=>0110111=>1001000
[2,6,1,4,8,7,5,3]=>0100111=>1011000
[2,1,6,4,8,7,5,3]=>1010111=>0101000
[2,1,6,4,8,7,3,5]=>1010110=>0101001
[2,6,1,4,8,7,3,5]=>0100110=>1011001
[2,6,4,1,8,7,3,5]=>0110110=>1001001
[2,6,4,8,1,7,3,5]=>0101010=>1010101
[6,4,2,8,7,5,1,3]=>1101110=>0010001
[6,2,4,8,7,3,5,1]=>1001101=>0110010
[6,2,4,8,7,3,1,5]=>1001110=>0110001
[1,6,4,7,3,8,2,5]=>0101010=>1010101
[1,3,7,4,5,8,2,6]=>0010010=>1101101
[5,2,4,7,3,6,8,1]=>1001001=>0110110
[1,7,6,3,4,8,2,5]=>0110010=>1001101
[8,1,6,3,7,2,4,5]=>1010100=>0101011
[7,1,6,3,8,2,4,5]=>1010100=>0101011
[1,2,7,4,8,3,5,6]=>0010100=>1101011
[6,1,7,3,4,8,2,5]=>1010010=>0101101
[2,1,7,4,5,8,3,6]=>1010010=>0101101
[5,1,4,7,3,8,2,6]=>1001010=>0110101
[4,3,1,7,5,8,2,6]=>1101010=>0010101
[2,8,6,3,7,1,4,5]=>0110100=>1001011
[6,8,1,3,7,2,4,5]=>0100100=>1011011
[5,8,2,1,7,3,4,6]=>0110100=>1001011
[5,7,2,1,8,3,4,6]=>0110100=>1001011
[6,7,1,3,8,2,4,5]=>0100100=>1011011
[5,1,2,4,8,3,6,7]=>1000100=>0111011
[4,3,6,1,5,8,2,7]=>1010010=>0101101
[2,6,1,4,5,8,3,7]=>0100010=>1011101
[6,5,1,3,4,8,2,7]=>1100010=>0011101
[1,6,2,4,8,3,5,7]=>0100100=>1011011
[8,5,1,3,7,2,4,6]=>1100100=>0011011
[1,5,3,2,8,4,6,7]=>0110100=>1001011
[6,4,2,1,5,8,3,7]=>1110010=>0001101
[2,5,3,4,1,8,6,7]=>0101010=>1010101
[4,3,5,2,1,8,6,7]=>1011010=>0100101
[2,6,4,8,7,1,3,5]=>0101100=>1010011
[1,6,4,8,7,2,3,5]=>0101100=>1010011
[2,7,8,3,6,1,4,5]=>0010100=>1101011
[4,3,2,8,7,1,5,6]=>1101100=>0010011
[5,2,4,8,7,1,3,6]=>1001100=>0110011
[6,2,8,3,7,1,4,5]=>1010100=>0101011
[5,1,4,8,7,2,3,6]=>1001100=>0110011
[4,8,2,5,1,3,7,6]=>0101001=>1010110
[4,7,2,5,1,3,8,6]=>0101001=>1010110
[3,7,2,1,5,4,8,6]=>0110101=>1001010
[3,8,2,1,5,4,7,6]=>0110101=>1001010
[8,3,2,1,5,4,6,7]=>1110100=>0001011
[8,3,2,1,6,4,5,7]=>1110100=>0001011
[8,4,2,5,1,6,3,7]=>1101010=>0010101
[8,3,2,1,5,6,4,7]=>1110010=>0001101
[8,3,2,1,4,6,5,7]=>1110010=>0001101
[3,8,2,1,4,5,7,6]=>0110001=>1001110
[3,7,2,1,4,5,8,6]=>0110001=>1001110
[3,2,7,1,4,6,8,5]=>1010001=>0101110
[3,2,8,1,4,6,7,5]=>1010001=>0101110
[3,2,8,1,4,7,6,5]=>1010011=>0101100
[3,8,2,1,4,7,5,6]=>0110010=>1001101
[3,8,2,1,5,7,4,6]=>0110010=>1001101
[4,8,2,5,1,7,3,6]=>0101010=>1010101
[4,7,2,5,1,8,3,6]=>0101010=>1010101
[3,7,2,1,5,8,4,6]=>0110010=>1001101
[3,7,2,1,4,8,5,6]=>0110010=>1001101
[3,2,1,7,5,8,6,4]=>1101011=>0010100
[3,2,7,1,6,8,4,5]=>1010010=>0101101
[4,2,7,6,1,8,3,5]=>1011010=>0100101
[4,3,7,6,8,1,2,5]=>1010100=>0101011
[4,3,8,6,7,1,2,5]=>1010100=>0101011
[4,2,8,6,1,7,3,5]=>1011010=>0100101
[3,2,8,1,6,7,4,5]=>1010010=>0101101
[3,2,1,8,7,5,6,4]=>1101101=>0010010
[3,8,2,1,7,4,5,6]=>0110100=>1001011
[3,2,8,1,7,4,6,5]=>1010101=>0101010
[3,2,8,1,6,4,7,5]=>1010101=>0101010
[3,2,7,1,6,4,8,5]=>1010101=>0101010
[4,2,7,6,1,3,8,5]=>1011001=>0100110
[4,2,8,6,1,3,7,5]=>1011001=>0100110
[4,2,8,7,1,3,6,5]=>1011001=>0100110
[5,7,8,3,4,1,2,6]=>0010100=>1101011
[4,2,7,8,1,3,6,5]=>1001001=>0110110
[4,2,6,8,1,3,7,5]=>1001001=>0110110
[4,2,6,7,1,3,8,5]=>1001001=>0110110
[3,2,6,1,8,4,7,5]=>1010101=>0101010
[3,7,2,1,8,4,5,6]=>0110100=>1001011
[3,7,2,1,8,5,4,6]=>0110110=>1001001
[4,7,3,8,5,1,2,6]=>0101100=>1010011
[4,3,7,8,6,1,2,5]=>1001100=>0110011
[3,2,7,1,8,6,4,5]=>1010110=>0101001
[3,2,1,6,8,5,7,4]=>1100101=>0011010
[3,2,6,1,8,7,4,5]=>1010110=>0101001
[4,2,6,8,1,7,3,5]=>1001010=>0110101
[4,3,6,8,7,1,2,5]=>1001100=>0110011
[4,2,6,7,1,8,3,5]=>1001010=>0110101
[3,2,6,1,7,8,4,5]=>1010010=>0101101
[3,4,6,8,7,5,1,2]=>0001110=>1110001
[5,3,6,4,8,7,1,2]=>1010110=>0101001
[1,4,6,2,7,8,5,3]=>0010011=>1101100
[3,1,8,5,4,2,6,7]=>1011100=>0100011
[1,2,7,5,4,8,6,3]=>0011011=>1100100
[6,3,7,5,4,8,1,2]=>1011010=>0100101
[7,3,8,5,4,6,1,2]=>1011010=>0100101
[3,8,7,5,4,6,1,2]=>0111010=>1000101
[4,3,6,7,8,5,1,2]=>1000110=>0111001
[4,5,6,3,8,7,1,2]=>0010110=>1101001
[3,6,8,5,4,7,1,2]=>0011010=>1100101
[6,8,3,5,4,7,1,2]=>0101010=>1010101
[7,6,3,5,4,8,1,2]=>1101010=>0010101
[1,6,2,5,4,8,7,3]=>0101011=>1010100
[7,1,2,5,8,3,6,4]=>1000101=>0111010
[1,8,2,5,7,3,6,4]=>0100101=>1011010
[6,2,1,5,4,8,7,3]=>1101011=>0010100
[4,1,6,2,8,7,5,3]=>1010111=>0101000
[7,8,1,2,4,6,5,3]=>0100011=>1011100
[7,8,3,1,4,2,6,5]=>0110101=>1001010
[4,3,6,1,8,2,7,5]=>1010101=>0101010
[2,3,8,5,4,1,6,7]=>0011100=>1100011
[4,8,1,5,2,3,7,6]=>0101001=>1010110
[7,5,1,6,4,3,2,8]=>1101110=>0010001
[5,8,1,6,4,3,2,7]=>0101110=>1010001
[6,1,5,7,4,3,2,8]=>1001110=>0110001
[1,5,8,6,4,3,2,7]=>0011110=>1100001
[3,4,6,1,5,8,2,7]=>0010010=>1101101
[7,8,4,1,5,3,2,6]=>0110110=>1001001
[7,8,5,1,6,3,2,4]=>0110110=>1001001
[2,6,1,5,7,3,8,4]=>0100101=>1011010
[1,6,8,7,4,3,2,5]=>0011110=>1100001
[6,8,1,7,4,3,2,5]=>0101110=>1010001
[5,6,1,7,4,3,2,8]=>0101110=>1010001
[5,1,7,6,4,3,2,8]=>1011110=>0100001
[6,1,7,8,4,3,2,5]=>1001110=>0110001
[7,1,8,6,4,3,2,5]=>1011110=>0100001
[1,8,7,6,4,3,2,5]=>0111110=>1000001
[2,1,7,5,6,3,8,4]=>1010101=>0101010
[3,1,6,7,5,8,2,4]=>1001010=>0110101
[7,8,1,6,5,3,2,4]=>0101110=>1010001
[7,8,2,1,4,5,6,3]=>0110001=>1001110
[2,8,1,5,4,6,7,3]=>0101001=>1010110
[7,2,1,5,4,6,8,3]=>1101001=>0010110
[1,2,8,5,6,3,7,4]=>0010101=>1101010
[6,1,2,5,7,3,8,4]=>1000101=>0111010
[4,2,1,5,6,3,7,8]=>1100100=>0011011
[4,3,6,1,5,7,2,8]=>1010010=>0101101
[5,1,6,3,7,8,2,4]=>1010010=>0101101
[1,3,6,8,5,7,2,4]=>0001010=>1110101
[2,4,6,3,7,1,8,5]=>0010101=>1101010
[1,3,6,4,8,7,2,5]=>0010110=>1101001
[4,1,6,7,3,8,2,5]=>1001010=>0110101
[5,4,6,1,3,7,2,8]=>1010010=>0101101
[6,4,1,5,2,3,7,8]=>1101000=>0010111
[4,1,7,5,2,3,8,6]=>1011001=>0100110
[1,2,4,5,8,3,7,6]=>0000101=>1111010
[7,2,3,5,4,1,8,6]=>1001101=>0110010
[2,8,3,5,4,1,7,6]=>0101101=>1010010
[4,2,6,3,8,1,7,5]=>1010101=>0101010
[7,8,2,3,4,1,6,5]=>0100101=>1011010
[7,8,1,4,6,3,2,5]=>0100110=>1011001
[3,1,6,4,7,8,2,5]=>1010010=>0101101
[1,8,5,7,4,3,2,6]=>0101110=>1010001
[7,1,5,8,4,3,2,6]=>1001110=>0110001
[5,1,8,7,4,3,2,6]=>1011110=>0100001
[6,5,1,8,4,3,2,7]=>1101110=>0010001
[6,5,7,1,4,3,2,8]=>1010110=>0101001
[7,5,8,1,4,3,2,6]=>1010110=>0101001
[5,8,7,1,4,3,2,6]=>0110110=>1001001
[1,5,7,8,4,3,2,6]=>0001110=>1110001
[2,4,7,5,1,3,8,6]=>0011001=>1100110
[7,8,4,6,1,3,2,5]=>0101010=>1010101
[7,8,5,4,1,3,2,6]=>0111010=>1000101
[3,5,6,4,1,8,2,7]=>0011010=>1100101
[2,6,4,5,1,3,8,7]=>0101001=>1010110
[1,6,5,8,4,3,2,7]=>0101110=>1010001
[6,8,5,1,4,3,2,7]=>0110110=>1001001
[7,6,5,1,4,3,2,8]=>1110110=>0001001
[1,2,3,4,5,6,9,7,8]=>00000010=>11111101
[1,2,3,4,5,8,6,9,7]=>00000101=>11111010
[1,2,3,4,7,5,8,9,6]=>00001001=>11110110
[1,2,3,6,4,7,8,9,5]=>00010001=>11101110
[1,2,5,3,6,7,8,9,4]=>00100001=>11011110
[1,4,2,5,6,7,8,9,3]=>01000001=>10111110
[9,8,1,2,3,4,5,6,7]=>11000000=>00111111
[7,8,9,1,2,3,4,5,6]=>00100000=>11011111
[9,8,7,1,2,3,4,5,6]=>11100000=>00011111
[6,7,8,9,1,2,3,4,5]=>00010000=>11101111
[9,6,7,8,1,2,3,4,5]=>10010000=>01101111
[8,9,6,7,1,2,3,4,5]=>01010000=>10101111
[9,8,6,7,1,2,3,4,5]=>11010000=>00101111
[9,8,7,6,1,2,3,4,5]=>11110000=>00001111
[9,5,6,7,8,1,2,3,4]=>10001000=>01110111
[8,9,5,6,7,1,2,3,4]=>01001000=>10110111
[9,8,5,6,7,1,2,3,4]=>11001000=>00110111
[9,7,8,5,6,1,2,3,4]=>10101000=>01010111
[9,8,7,5,6,1,2,3,4]=>11101000=>00010111
[9,8,7,6,5,1,2,3,4]=>11111000=>00000111
[7,8,9,4,5,6,1,2,3]=>00100100=>11011011
[9,7,8,4,5,6,1,2,3]=>10100100=>01011011
[9,8,7,4,5,6,1,2,3]=>11100100=>00011011
[8,9,6,7,4,5,1,2,3]=>01010100=>10101011
[9,8,6,7,4,5,1,2,3]=>11010100=>00101011
[9,8,7,6,4,5,1,2,3]=>11110100=>00001011
[9,8,7,6,5,4,1,2,3]=>11111100=>00000011
[9,7,8,5,6,3,4,1,2]=>10101010=>01010101
[9,8,7,5,6,3,4,1,2]=>11101010=>00010101
[9,8,7,6,5,3,4,1,2]=>11111010=>00000101
[9,8,7,6,5,4,3,1,2]=>11111110=>00000001
[9,10,1,2,3,4,5,6,7,8]=>010000000=>101111111
[8,9,10,1,2,3,4,5,6,7]=>001000000=>110111111
[10,8,9,1,2,3,4,5,6,7]=>101000000=>010111111
[10,9,8,1,2,3,4,5,6,7]=>111000000=>000111111
[7,8,9,10,1,2,3,4,5,6]=>000100000=>111011111
[10,7,8,9,1,2,3,4,5,6]=>100100000=>011011111
[9,10,7,8,1,2,3,4,5,6]=>010100000=>101011111
[10,9,7,8,1,2,3,4,5,6]=>110100000=>001011111
[10,9,8,7,1,2,3,4,5,6]=>111100000=>000011111
[10,6,7,8,9,1,2,3,4,5]=>100010000=>011101111
[9,10,6,7,8,1,2,3,4,5]=>010010000=>101101111
[10,9,6,7,8,1,2,3,4,5]=>110010000=>001101111
[10,8,9,6,7,1,2,3,4,5]=>101010000=>010101111
[10,9,8,6,7,1,2,3,4,5]=>111010000=>000101111
[10,9,8,7,6,1,2,3,4,5]=>111110000=>000001111
[9,10,5,6,7,8,1,2,3,4]=>010001000=>101110111
[10,9,5,6,7,8,1,2,3,4]=>110001000=>001110111
[8,9,10,5,6,7,1,2,3,4]=>001001000=>110110111
[10,9,8,5,6,7,1,2,3,4]=>111001000=>000110111
[9,10,7,8,5,6,1,2,3,4]=>010101000=>101010111
[10,9,7,8,5,6,1,2,3,4]=>110101000=>001010111
[10,9,8,7,5,6,1,2,3,4]=>111101000=>000010111
[10,9,8,7,6,5,1,2,3,4]=>111111000=>000000111
[10,7,8,9,4,5,6,1,2,3]=>100100100=>011011011
[9,10,7,8,4,5,6,1,2,3]=>010100100=>101011011
[10,9,7,8,4,5,6,1,2,3]=>110100100=>001011011
[10,9,8,7,4,5,6,1,2,3]=>111100100=>000011011
[10,8,9,6,7,4,5,1,2,3]=>101010100=>010101011
[10,9,8,6,7,4,5,1,2,3]=>111010100=>000101011
[10,9,8,7,6,4,5,1,2,3]=>111110100=>000001011
[10,9,8,7,6,5,4,1,2,3]=>111111100=>000000011
[9,10,7,8,5,6,3,4,1,2]=>010101010=>101010101
[10,9,7,8,5,6,3,4,1,2]=>110101010=>001010101
[10,9,8,7,5,6,3,4,1,2]=>111101010=>000010101
[10,9,8,7,6,5,3,4,1,2]=>111111010=>000000101
[10,9,8,7,6,5,4,3,1,2]=>111111110=>000000001
[3,4,6,2,7,1,5,8]=>0010100=>1101011
[3,6,2,5,4,1,7,8]=>0101100=>1010011
[3,2,7,5,4,1,6,8]=>1011100=>0100011
[4,3,6,2,8,1,5,7]=>1010100=>0101011
[6,1,2,5,4,7,8,3]=>1001001=>0110110
[6,2,4,5,1,3,7,8]=>1001000=>0110111
[4,2,8,5,1,3,7,6]=>1011001=>0100110
[4,3,6,8,1,7,2,5]=>1001010=>0110101
[5,3,6,4,1,7,2,8]=>1011010=>0100101
[6,2,1,5,8,3,7,4]=>1100101=>0011010
[1,6,7,4,8,3,5,2]=>0010101=>1101010
[1,4,6,3,7,5,8,2]=>0010101=>1101010
[4,6,7,2,5,8,1,3]=>0010010=>1101101
[2,4,6,1,7,5,3,8]=>0010110=>1101001
[2,7,5,4,1,6,3,8]=>0111010=>1000101
[7,5,4,6,2,8,1,3]=>1101010=>0010101
[1,7,5,4,3,8,6,2]=>0111011=>1000100
[1,4,6,3,5,8,7,2]=>0010011=>1101100
[1,5,8,4,3,6,7,2]=>0011001=>1100110
[5,4,6,2,7,8,1,3]=>1010010=>0101101
[2,5,4,1,6,7,3,8]=>0110010=>1001101
[5,6,3,2,7,1,4,8]=>0110100=>1001011
[5,6,3,2,7,1,8,4]=>0110101=>1001010
[8,5,6,3,2,7,1,4]=>1011010=>0100101
[5,4,6,2,8,1,7,3]=>1010101=>0101010
[2,4,1,7,8,5,3,6]=>0100110=>1011001
[2,5,4,1,6,3,8,7]=>0110101=>1001010
[5,6,3,2,1,8,4,7]=>0111010=>1000101
[3,5,2,1,6,4,7,8]=>0110100=>1001011
[6,8,4,3,2,1,5,7]=>0111100=>1000011
[5,3,8,2,1,6,4,7]=>1011010=>0100101
[3,7,5,8,2,1,4,6]=>0101100=>1010011
[7,3,2,8,5,1,6,4]=>1101101=>0010010
[8,4,6,3,2,1,7,5]=>1011101=>0100010
[8,6,4,3,2,1,7,5]=>1111101=>0000010
[7,6,4,3,2,1,8,5]=>1111101=>0000010
[7,8,4,3,2,1,6,5]=>0111101=>1000010
[5,4,7,2,1,8,6,3]=>1011011=>0100100
[7,5,8,3,2,6,1,4]=>1011010=>0100101
[5,7,3,2,1,6,8,4]=>0111001=>1000110
[5,7,3,2,1,6,4,8]=>0111010=>1000101
[6,3,7,2,5,1,8,4]=>1010101=>0101010
[6,7,8,3,5,2,1,4]=>0010110=>1101001
[6,2,5,7,8,4,1,3]=>1000110=>0111001
[2,1,5,7,8,6,3,4]=>1000110=>0111001
[3,6,7,2,8,1,4,5]=>0010100=>1101011
[6,3,7,2,8,1,4,5]=>1010100=>0101011
[3,2,6,1,7,4,5,8]=>1010100=>0101011
[3,5,2,1,4,7,6,8]=>0110010=>1001101
[7,3,5,2,1,8,4,6]=>1011010=>0100101
[2,5,4,1,3,7,8,6]=>0110001=>1001110
[2,5,8,4,1,3,7,6]=>0011001=>1100110
[2,4,1,7,8,3,6,5]=>0100101=>1011010
[3,7,2,8,6,1,4,5]=>0101100=>1010011
[3,6,8,2,1,7,4,5]=>0011010=>1100101
[5,3,8,2,1,4,7,6]=>1011001=>0100110
[4,8,7,3,2,1,5,6]=>0111100=>1000011
[4,7,3,2,1,5,6,8]=>0111000=>1000111
[8,4,7,3,2,1,5,6]=>1011100=>0100011
[8,3,5,2,1,4,7,6]=>1011001=>0100110
[7,3,2,8,6,1,4,5]=>1101100=>0010011
[3,5,2,1,4,6,8,7]=>0110001=>1001110
[7,8,6,5,4,3,2,1,9]=>01111110=>10000001
[1,8,9,7,6,5,4,3,2]=>00111111=>11000000
[8,9,7,6,5,4,3,2,1,10]=>011111110=>100000001
[7,6,8,5,4,3,2,1,9]=>10111110=>01000001
[6,8,7,5,4,3,2,1,9]=>01111110=>10000001
[1,8,7,9,6,5,4,3,2]=>01011111=>10100000
[1,7,9,8,6,5,4,3,2]=>00111111=>11000000
[1,9,10,8,7,6,5,4,3,2]=>001111111=>110000000
[7,8,3,5,4,6,1,2]=>0101010=>1010101
[8,6,3,7,5,2,4,1]=>1101101=>0010010
[5,4,1,6,3,2,8,7]=>1101101=>0010010
[5,4,1,6,2,3,8,7]=>1101001=>0010110
[5,7,1,6,2,8,3,4]=>0101010=>1010101
[5,7,1,6,2,8,4,3]=>0101011=>1010100
[2,7,6,5,1,8,3,4]=>0111010=>1000101
[2,7,6,5,1,8,4,3]=>0111011=>1000100
[2,3,6,5,1,4,8,7]=>0011001=>1100110
[2,3,6,4,1,5,8,7]=>0011001=>1100110
[2,3,6,1,5,4,8,7]=>0010101=>1101010
[2,7,6,1,4,8,5,3]=>0110011=>1001100
[2,7,6,1,4,8,3,5]=>0110010=>1001101
[7,3,5,1,8,4,2,6]=>1010110=>0101001
[7,3,5,1,8,6,4,2]=>1010111=>0101000
[2,7,6,1,5,8,4,3]=>0110011=>1001100
[2,7,6,4,1,8,5,3]=>0111011=>1000100
[2,1,7,6,3,8,5,4]=>1011011=>0100100
[2,1,7,6,3,8,4,5]=>1011010=>0100101
[5,7,3,6,2,8,4,1]=>0101011=>1010100
[2,7,6,4,1,8,3,5]=>0111010=>1000101
[7,3,5,1,8,6,2,4]=>1010110=>0101001
[6,3,5,1,8,2,4,7]=>1010100=>0101011
[2,3,4,8,7,6,1,5]=>0001110=>1110001
[2,3,4,8,5,7,1,6]=>0001010=>1110101
[7,3,5,4,8,1,2,6]=>1010100=>0101011
[6,4,3,5,8,7,2,1]=>1100111=>0011000
[2,1,4,5,8,7,3,6]=>1000110=>0111001
[6,4,3,5,8,7,1,2]=>1100110=>0011001
[7,3,5,4,8,1,6,2]=>1010101=>0101010
[2,3,4,8,7,5,6,1]=>0001101=>1110010
[2,3,4,8,7,5,1,6]=>0001110=>1110001
[2,7,6,5,4,8,1,3]=>0111010=>1000101
[7,3,5,6,8,4,1,2]=>1000110=>0111001
[7,3,5,6,8,1,4,2]=>1000101=>0111010
[7,3,5,6,8,1,2,4]=>1000100=>0111011
[6,4,1,5,8,7,2,3]=>1100110=>0011001
[6,4,1,5,8,7,3,2]=>1100111=>0011000
[6,4,1,5,8,3,7,2]=>1100101=>0011010
[5,7,1,6,3,8,2,4]=>0101010=>1010101
[6,4,1,5,8,3,2,7]=>1100110=>0011001
[7,4,1,5,8,2,3,6]=>1100100=>0011011
[7,4,1,5,8,2,6,3]=>1100101=>0011010
[6,3,5,7,8,2,1,4]=>1000110=>0111001
[6,3,5,7,8,2,4,1]=>1000101=>0111010
[2,7,6,4,5,8,3,1]=>0110011=>1001100
[5,7,3,6,1,8,4,2]=>0101011=>1010100
[2,1,4,5,8,6,3,7]=>1000110=>0111001
[7,3,5,4,8,6,2,1]=>1010111=>0101000
[2,3,4,8,5,6,1,7]=>0001010=>1110101
[2,3,4,8,7,1,6,5]=>0001101=>1110010
[2,3,4,8,1,7,6,5]=>0001011=>1110100
[2,3,4,8,1,6,7,5]=>0001001=>1110110
[2,3,4,8,5,1,7,6]=>0001101=>1110010
[6,3,5,4,8,2,7,1]=>1010101=>0101010
[7,4,3,5,8,2,1,6]=>1100110=>0011001
[2,1,4,5,8,3,7,6]=>1000101=>0111010
[7,4,3,5,8,2,6,1]=>1100101=>0011010
[6,3,5,4,8,2,1,7]=>1010110=>0101001
[2,3,4,8,5,1,6,7]=>0001100=>1110011
[2,3,4,8,1,6,5,7]=>0001010=>1110101
[2,3,4,8,1,5,7,6]=>0001001=>1110110
[7,8,2,6,1,5,3,4]=>0101010=>1010101
[7,8,1,6,2,5,3,4]=>0101010=>1010101
[1,8,6,7,2,5,3,4]=>0101010=>1010101
[1,8,5,7,2,6,3,4]=>0101010=>1010101
[5,8,1,7,2,6,3,4]=>0101010=>1010101
[5,8,2,7,1,6,3,4]=>0101010=>1010101
[2,8,6,7,1,5,3,4]=>0101010=>1010101
[2,8,5,7,1,6,3,4]=>0101010=>1010101
[2,8,1,7,5,6,3,4]=>0101010=>1010101
[1,8,2,7,5,6,3,4]=>0101010=>1010101
[1,8,2,7,4,6,3,5]=>0101010=>1010101
[2,8,1,7,4,6,3,5]=>0101010=>1010101
[2,8,4,7,1,6,3,5]=>0101010=>1010101
[4,8,2,7,1,6,3,5]=>0101010=>1010101
[4,8,1,7,2,6,3,5]=>0101010=>1010101
[1,8,4,7,2,6,3,5]=>0101010=>1010101
[4,8,1,7,5,6,2,3]=>0101010=>1010101
[1,8,4,7,5,6,2,3]=>0101010=>1010101
[1,8,3,7,5,6,2,4]=>0101010=>1010101
[3,8,1,7,5,6,2,4]=>0101010=>1010101
[3,8,1,7,4,6,2,5]=>0101010=>1010101
[1,8,3,7,4,6,2,5]=>0101010=>1010101
[1,8,3,7,2,6,4,5]=>0101010=>1010101
[3,8,1,7,2,6,4,5]=>0101010=>1010101
[3,8,2,7,1,6,4,5]=>0101010=>1010101
[3,8,2,7,4,6,1,5]=>0101010=>1010101
[3,8,2,7,5,6,1,4]=>0101010=>1010101
[4,8,2,7,5,6,1,3]=>0101010=>1010101
[4,8,3,7,5,6,1,2]=>0101010=>1010101
[3,8,4,7,5,6,1,2]=>0101010=>1010101
[2,8,4,7,5,6,1,3]=>0101010=>1010101
[2,8,3,7,5,6,1,4]=>0101010=>1010101
[2,8,3,7,4,6,1,5]=>0101010=>1010101
[2,8,3,7,1,6,4,5]=>0101010=>1010101
[2,8,1,7,3,6,4,5]=>0101010=>1010101
[7,5,2,8,6,4,1,3]=>1101110=>0010001
[7,5,1,8,6,2,3,4]=>1101100=>0010011
[7,4,8,6,1,5,2,3]=>1011010=>0100101
[7,1,8,4,5,2,6,3]=>1010101=>0101010
[6,8,1,7,4,2,5,3]=>0101101=>1010010
[1,6,7,4,2,8,5,3]=>0011011=>1100100
[1,6,7,3,8,5,2,4]=>0010110=>1101001
[7,1,8,3,5,6,2,4]=>1010010=>0101101
[7,3,8,6,2,5,1,4]=>1011010=>0100101
[7,4,2,8,6,1,3,5]=>1101100=>0010011
[7,3,1,8,4,2,5,6]=>1101100=>0010011
[7,2,8,4,1,5,3,6]=>1011010=>0100101
[7,2,8,3,5,1,6,4]=>1010101=>0101010
[7,2,8,3,4,6,1,5]=>1010010=>0101101
[1,5,7,8,2,6,3,4]=>0001010=>1110101
[6,2,3,8,5,7,4,1]=>1001011=>0110100
[6,2,4,8,5,3,1,7]=>1001110=>0110001
[6,3,1,4,8,5,2,7]=>1100110=>0011001
[2,6,3,7,8,5,4,1]=>0100111=>1011000
[2,6,3,7,8,4,5,1]=>0100101=>1011010
[2,4,7,3,5,6,8,1]=>0010001=>1101110
[2,4,7,3,6,8,5,1]=>0010011=>1101100
[2,5,3,7,8,1,6,4]=>0100101=>1011010
[3,1,5,4,7,8,2,6]=>1010010=>0101101
[5,3,1,4,8,2,6,7]=>1100100=>0011011
[5,2,4,8,6,1,3,7]=>1001100=>0110011
[5,2,3,8,4,6,7,1]=>1001001=>0110110
[4,8,2,3,6,1,7,5]=>0100101=>1011010
[4,8,2,3,5,7,1,6]=>0100010=>1011101
[1,4,7,8,3,6,2,5]=>0001010=>1110101
[4,8,1,3,6,7,2,5]=>0100010=>1011101
[5,3,8,2,4,7,1,6]=>1010010=>0101101
[5,4,3,8,1,2,7,6]=>1101001=>0010110
[6,4,2,8,1,3,7,5]=>1101001=>0010110
[6,3,8,2,5,1,7,4]=>1010101=>0101010
[6,3,8,1,4,7,2,5]=>1010010=>0101101
[5,8,1,3,6,2,7,4]=>0100101=>1011010
[1,5,7,4,2,6,8,3]=>0011001=>1100110
[5,8,1,4,2,6,3,7]=>0101010=>1010101
[5,8,4,1,2,7,6,3]=>0110011=>1001100
[6,5,1,2,8,7,3,4]=>1100110=>0011001
[6,5,3,1,4,2,8,7]=>1110101=>0001010
[5,3,1,6,4,2,7,8]=>1101100=>0010011
[5,2,6,4,1,7,3,8]=>1011010=>0100101
[4,6,1,7,5,2,8,3]=>0101101=>1010010
[4,5,1,7,2,6,3,8]=>0101010=>1010101
[3,5,6,1,2,8,7,4]=>0010011=>1101100
[3,5,7,1,8,6,2,4]=>0010110=>1101001
[3,6,2,7,5,1,8,4]=>0101101=>1010010
[4,2,5,7,1,8,6,3]=>1001011=>0110100
[3,4,7,2,8,6,1,5]=>0010110=>1101001
[3,4,5,8,2,7,1,6]=>0001010=>1110101
[3,4,6,2,8,1,5,7]=>0010100=>1101011
[3,5,2,6,8,1,7,4]=>0100101=>1011010
[4,2,5,6,1,3,8,7]=>1001001=>0110110
[4,3,1,2,5,6,8,7]=>1100001=>0011110
[5,3,6,8,4,7,2,1]=>1001011=>0110100
[3,7,2,5,4,8,6,1]=>0101011=>1010100
[8,4,2,5,7,3,6,1]=>1100101=>0011010
[3,1,6,5,4,8,2,7]=>1011010=>0100101
[4,1,6,5,8,3,2,7]=>1010110=>0101001
[5,1,6,8,4,3,2,7]=>1001110=>0110001
[8,5,4,7,6,3,2,1]=>1101111=>0010000
[2,7,1,5,4,3,8,6]=>0101101=>1010010
[8,2,1,5,4,3,7,6]=>1101101=>0010010
[8,4,1,5,7,3,2,6]=>1100110=>0011001
[8,4,6,1,7,3,2,5]=>1010110=>0101001
[8,3,6,1,4,7,2,5]=>1010010=>0101101
[2,7,6,1,4,3,8,5]=>0110101=>1001010
[6,7,8,5,1,3,2,4]=>0011010=>1100101
[5,7,2,8,4,3,6,1]=>0101101=>1010010
[6,7,8,2,4,3,5,1]=>0010101=>1101010
[4,7,6,2,8,3,5,1]=>0110101=>1001010
[8,3,6,2,4,7,5,1]=>1010011=>0101100
[3,7,6,2,4,8,5,1]=>0110011=>1001100
[5,7,3,8,4,6,2,1]=>0101011=>1010100
[4,7,3,5,8,6,2,1]=>0100111=>1011000
[8,7,2,1,4,3,6,5]=>1110101=>0001010
[8,7,3,1,4,6,2,5]=>1110010=>0001101
[8,7,6,3,2,5,4,1]=>1111011=>0000100
[8,7,3,5,1,6,2,4]=>1101010=>0010101
[8,7,2,5,1,3,6,4]=>1101001=>0010110
[8,4,6,5,7,1,2,3]=>1010100=>0101011
[4,7,6,5,8,1,2,3]=>0110100=>1001011
[3,7,6,5,1,8,2,4]=>0111010=>1000101
[8,1,2,3,4,5,6,7,9]=>10000000=>01111111
[1,9,2,3,4,5,6,7,8]=>01000000=>10111111
[9,1,2,3,4,5,6,7,8,10]=>100000000=>011111111
[7,8,1,2,3,4,5,6,9]=>01000000=>10111111
[1,8,9,2,3,4,5,6,7]=>00100000=>11011111
[1,10,2,3,4,5,6,7,8,9]=>010000000=>101111111
[10,1,2,3,4,5,6,7,8,9,11]=>1000000000=>0111111111
[8,9,1,2,3,4,5,6,7,10]=>010000000=>101111111
[7,1,8,2,3,4,5,6,9]=>10100000=>01011111
[6,8,1,2,3,4,5,7,9]=>01000000=>10111111
[1,8,2,9,3,4,5,6,7]=>01010000=>10101111
[1,7,9,2,3,4,5,6,8]=>00100000=>11011111
[1,9,10,2,3,4,5,6,7,8]=>001000000=>110111111
[1,11,2,3,4,5,6,7,8,9,10]=>0100000000=>1011111111
[3,6,4,8,7,5,1,2]=>0101110=>1010001
[5,6,4,3,8,7,1,2]=>0110110=>1001001
[1,6,2,4,7,8,5,3]=>0100011=>1011100
[3,6,2,4,8,1,5,7]=>0100100=>1011011
[3,4,7,2,8,1,6,5]=>0010101=>1101010
[1,4,7,2,5,8,6,3]=>0010011=>1101100
[7,3,8,4,5,6,1,2]=>1010010=>0101101
[3,5,6,4,8,7,1,2]=>0010110=>1101001
[4,6,8,5,3,7,1,2]=>0011010=>1100101
[6,8,5,3,4,7,1,2]=>0110010=>1001101
[1,6,5,4,2,8,7,3]=>0111011=>1000100
[1,8,5,2,7,3,6,4]=>0110101=>1001010
[4,2,7,5,1,8,6,3]=>1011011=>0100100
[7,8,1,4,2,6,5,3]=>0101011=>1010100
[1,3,6,4,8,2,5,7]=>0010100=>1101011
[4,1,7,5,3,2,6,8]=>1011100=>0100011
[6,5,1,3,4,2,8,7]=>1100101=>0011010
[4,8,5,3,1,7,2,6]=>0111010=>1000101
[7,4,5,3,2,8,1,6]=>1011010=>0100101
[5,8,3,6,1,4,2,7]=>0101010=>1010101
[2,5,8,6,4,1,3,7]=>0011100=>1100011
[1,4,6,2,5,8,3,7]=>0010010=>1101101
[3,6,2,5,8,1,7,4]=>0100101=>1011010
[1,6,8,7,4,2,3,5]=>0011100=>1100011
[6,1,7,8,2,4,3,5]=>1001010=>0110101
[7,1,8,6,3,4,2,5]=>1011010=>0100101
[7,2,1,4,5,6,8,3]=>1100001=>0011110
[1,2,8,3,6,5,7,4]=>0010101=>1101010
[6,1,3,2,7,5,8,4]=>1010101=>0101010
[1,6,3,8,5,7,2,4]=>0101010=>1010101
[2,6,4,1,7,5,8,3]=>0110101=>1001010
[7,6,5,8,1,4,2,3]=>1101010=>0010101
[5,8,6,7,3,2,1,4]=>0101110=>1010001
[1,6,4,3,7,2,8,5]=>0110101=>1001010
[2,6,3,4,8,7,1,5]=>0100110=>1011001
[7,1,3,4,5,2,8,6]=>1000101=>0111010
[1,8,3,5,4,2,7,6]=>0101101=>1010010
[4,1,6,3,8,2,7,5]=>1010101=>0101010
[7,8,2,4,6,3,1,5]=>0100110=>1011001
[3,2,6,4,7,8,1,5]=>1010010=>0101101
[2,8,5,7,4,3,1,6]=>0101110=>1010001
[7,2,5,8,3,4,1,6]=>1001010=>0110101
[5,3,8,7,1,2,6,4]=>1011001=>0100110
[6,5,3,8,2,1,7,4]=>1101101=>0010010
[7,5,8,4,1,2,3,6]=>1011000=>0100111
[5,8,7,4,1,3,2,6]=>0111010=>1000101
[3,5,7,8,4,1,2,6]=>0001100=>1110011
[1,4,7,5,3,8,2,6]=>0011010=>1100101
[2,4,6,7,3,1,8,5]=>0001101=>1110010
[7,8,4,6,3,1,2,5]=>0101100=>1010011
[2,6,4,5,3,8,1,7]=>0101010=>1010101
[3,6,5,8,4,2,1,7]=>0101110=>1010001
[5,6,8,4,2,3,1,7]=>0011010=>1100101
[6,8,5,4,3,1,2,7]=>0111100=>1000011
[6,1,4,2,8,5,7,3]=>1010101=>0101010
[4,8,6,5,3,2,7,1]=>0111101=>1000010
[8,6,5,1,2,4,7,3]=>1110001=>0001110
[6,7,5,8,2,1,4,3]=>0101101=>1010010
[1,7,5,8,2,6,4,3]=>0101011=>1010100
[1,3,8,5,7,6,2,4]=>0010110=>1101001
[6,3,8,5,7,1,2,4]=>1010100=>0101011
[8,3,1,5,6,2,7,4]=>1100101=>0011010
[6,8,5,2,1,4,7,3]=>0111001=>1000110
[3,8,2,5,6,1,7,4]=>0100101=>1011010
[2,8,1,5,6,3,7,4]=>0100101=>1011010
[8,1,2,5,6,3,7,4]=>1000101=>0111010
[1,8,2,5,7,6,3,4]=>0100110=>1011001
[5,1,8,6,2,7,3,4]=>1011010=>0100101
[2,5,8,6,1,7,3,4]=>0011010=>1100101
[8,6,1,5,7,2,3,4]=>1100100=>0011011
[3,8,6,5,7,1,2,4]=>0110100=>1001011
[7,6,5,8,1,2,4,3]=>1101001=>0010110
[5,1,7,6,8,4,2,3]=>1010110=>0101001
[5,1,3,7,8,6,2,4]=>1000110=>0111001
[7,2,5,8,1,6,4,3]=>1001011=>0110100
[3,2,8,5,7,6,1,4]=>1010110=>0101001
[8,2,1,5,7,6,3,4]=>1100110=>0011001
[5,2,8,6,1,7,3,4]=>1011010=>0100101
[1,2,8,6,5,7,3,4]=>0011010=>1100101
[4,2,1,3,6,7,8,5]=>1100001=>0011110
[8,2,5,6,3,7,1,4]=>1001010=>0110101
[7,2,6,5,4,1,8,3]=>1011101=>0100010
[6,1,3,5,4,7,8,2]=>1001001=>0110110
[6,1,5,3,4,7,8,2]=>1010001=>0101110
[7,5,6,2,4,1,8,3]=>1010101=>0101010
[8,5,2,6,3,7,1,4]=>1101010=>0010101
[4,3,1,2,6,7,8,5]=>1100001=>0011110
[8,1,6,5,7,3,2,4]=>1010110=>0101001
[3,5,8,6,2,7,1,4]=>0011010=>1100101
[5,8,1,6,3,7,2,4]=>0101010=>1010101
[1,8,5,6,3,7,2,4]=>0101010=>1010101
[1,7,6,5,4,2,8,3]=>0111101=>1000010
[5,7,6,1,4,2,8,3]=>0110101=>1001010
[7,1,4,2,6,5,8,3]=>1010101=>0101010
[4,1,7,3,5,6,8,2]=>1010001=>0101110
[2,7,4,1,5,6,8,3]=>0110001=>1001110
[5,7,6,4,1,2,8,3]=>0111001=>1000110
[4,7,6,1,5,2,8,3]=>0110101=>1001010
[1,7,6,4,5,2,8,3]=>0110101=>1001010
[1,8,3,6,5,7,2,4]=>0101010=>1010101
[3,8,1,6,5,7,2,4]=>0101010=>1010101
[8,1,3,5,7,6,2,4]=>1000110=>0111001
[7,8,5,4,1,6,2,3]=>0111010=>1000101
[6,1,5,4,3,7,8,2]=>1011001=>0100110
[7,5,6,4,2,1,8,3]=>1011101=>0100010
[8,3,2,6,5,7,1,4]=>1101010=>0010101
[7,4,6,2,5,1,8,3]=>1010101=>0101010
[6,1,4,3,5,7,8,2]=>1010001=>0101110
[6,1,3,4,5,7,8,2]=>1000001=>0111110
[7,2,6,4,5,1,8,3]=>1010101=>0101010
[8,2,3,6,5,7,1,4]=>1001010=>0110101
[5,4,7,3,6,8,1,2]=>1010010=>0101101
[3,4,7,8,5,6,1,2]=>0001010=>1110101
[3,4,7,2,5,1,6,8]=>0010100=>1101011
[1,4,7,2,5,8,3,6]=>0010010=>1101101
[3,6,2,4,7,1,5,8]=>0100100=>1011011
[6,8,3,4,5,7,1,2]=>0100010=>1011101
[4,3,6,7,5,8,1,2]=>1001010=>0110101
[6,3,7,5,8,4,1,2]=>1010110=>0101001
[7,3,8,6,4,5,1,2]=>1011010=>0100101
[3,2,7,6,5,1,4,8]=>1011100=>0100011
[1,2,7,6,5,8,3,4]=>0011010=>1100101
[4,8,2,6,1,5,3,7]=>0101010=>1010101
[2,3,8,6,4,1,5,7]=>0011100=>1100011
[4,3,6,2,5,1,8,7]=>1010101=>0101010
[7,8,3,2,5,1,4,6]=>0110100=>1001011
[7,8,1,2,5,6,3,4]=>0100010=>1011101
[4,1,6,2,5,7,3,8]=>1010010=>0101101
[6,1,2,5,8,7,3,4]=>1000110=>0111001
[2,1,8,6,4,7,3,5]=>1011010=>0100101
[7,1,3,6,8,4,2,5]=>1000110=>0111001
[1,8,3,6,7,4,5,2]=>0100101=>1011010
[7,1,5,8,3,6,2,4]=>1001010=>0110101
[5,1,8,7,2,3,6,4]=>1011001=>0100110
[6,1,5,7,4,2,8,3]=>1001101=>0110010
[3,1,6,4,7,2,5,8]=>1010100=>0101011
[2,4,7,5,1,8,3,6]=>0011010=>1100101
[6,5,7,1,4,2,3,8]=>1010100=>0101011
[5,6,8,1,3,2,4,7]=>0010100=>1101011
[6,8,5,1,3,4,2,7]=>0110010=>1001101
[2,8,3,4,5,1,7,6]=>0100101=>1011010
[6,2,4,3,1,5,7,8]=>1011000=>0100111
[4,2,8,3,1,7,5,6]=>1011010=>0100101
[1,3,7,4,8,2,5,6]=>0010100=>1101011
[5,3,7,4,1,6,2,8]=>1011010=>0100101
[2,4,7,3,6,1,8,5]=>0010101=>1101010
[5,8,7,6,3,1,2,4]=>0111100=>1000011
[7,5,6,8,1,4,3,2]=>1001011=>0110100
[2,4,7,1,6,5,3,8]=>0010110=>1101001
[1,2,7,8,5,4,3,6]=>0001110=>1110001
[6,3,1,2,8,4,5,7]=>1100100=>0011011
[4,2,1,3,6,5,8,7]=>1100101=>0011010
[2,8,1,4,5,6,3,7]=>0100010=>1011101
[7,2,1,5,4,6,3,8]=>1101010=>0010101
[4,2,6,1,8,5,3,7]=>1010110=>0101001
[7,8,2,1,4,5,3,6]=>0110010=>1001101
[7,8,4,1,5,3,6,2]=>0110101=>1001010
[3,4,6,1,5,8,7,2]=>0010011=>1101100
[7,5,1,6,4,3,8,2]=>1101101=>0010010
[5,8,1,6,3,4,7,2]=>0101001=>1010110
[6,5,1,8,2,7,4,3]=>1101011=>0010100
[6,8,1,7,5,2,3,4]=>0101100=>1010011
[7,6,1,8,5,3,2,4]=>1101110=>0010001
[5,6,1,7,4,8,2,3]=>0101010=>1010101
[3,6,1,5,7,4,2,8]=>0100110=>1011001
[2,5,6,1,7,4,8,3]=>0010101=>1101010
[3,1,7,5,6,4,8,2]=>1010101=>0101010
[5,1,7,6,4,8,3,2]=>1011011=>0100100
[6,1,7,8,5,3,4,2]=>1001101=>0110010
[7,1,8,6,5,4,2,3]=>1011110=>0100001
[2,6,5,7,3,4,8,1]=>0101001=>1010110
[1,6,4,7,5,8,2,3]=>0101010=>1010101
[8,5,3,6,2,7,4,1]=>1101011=>0010100
[1,3,7,4,6,8,2,5]=>0010010=>1101101
[4,7,5,6,3,2,8,1]=>0101101=>1010010
[1,7,6,5,4,8,2,3]=>0111010=>1000101
[8,1,6,5,7,2,4,3]=>1010101=>0101010
[1,2,7,6,8,3,4,5]=>0010100=>1101011
[6,1,7,5,3,8,2,4]=>1011010=>0100101
[2,1,7,5,6,8,3,4]=>1010010=>0101101
[5,4,1,7,6,8,2,3]=>1101010=>0010101
[4,8,5,6,2,7,3,1]=>0101011=>1010100
[3,8,6,4,2,7,5,1]=>0111011=>1000100
[7,8,5,2,4,6,3,1]=>0110011=>1001100
[2,8,6,3,7,4,5,1]=>0110101=>1001010
[7,8,1,6,2,4,5,3]=>0101001=>1010110
[6,8,1,4,7,2,5,3]=>0100101=>1011010
[3,8,4,1,7,2,6,5]=>0110101=>1001010
[5,4,7,1,8,3,2,6]=>1010110=>0101001
[3,7,4,1,8,5,2,6]=>0110110=>1001001
[6,7,1,4,8,3,2,5]=>0100110=>1011001
[2,7,1,8,4,5,3,6]=>0101010=>1010101
[6,1,2,8,4,3,5,7]=>1001100=>0110011
[6,5,1,4,3,8,2,7]=>1101010=>0010101
[1,6,2,5,8,3,4,7]=>0100100=>1011011
[8,5,1,3,7,2,6,4]=>1100101=>0011010
[8,4,2,1,7,3,6,5]=>1110101=>0001010
[7,4,2,1,8,5,3,6]=>1110110=>0001001
[1,5,4,2,8,3,6,7]=>0110100=>1001011
[6,4,3,1,5,8,2,7]=>1110010=>0001101
[3,7,6,8,4,5,2,1]=>0101011=>1010100
[2,7,6,8,5,3,4,1]=>0101101=>1010010
[1,7,6,8,5,4,2,3]=>0101110=>1010001
[1,4,8,6,7,5,2,3]=>0010110=>1101001
[2,4,8,6,7,3,5,1]=>0010101=>1101010
[7,3,8,5,4,6,2,1]=>1011011=>0100100
[3,4,8,5,6,7,2,1]=>0010011=>1101100
[6,3,5,8,4,7,2,1]=>1001011=>0110100
[5,4,3,8,6,7,2,1]=>1101011=>0010100
[5,4,2,8,7,3,6,1]=>1101101=>0010010
[6,2,5,8,7,3,4,1]=>1001101=>0110010
[3,2,8,5,7,4,6,1]=>1010101=>0101010
[1,3,8,7,5,6,2,4]=>0011010=>1100101
[2,1,8,7,4,6,3,5]=>1011010=>0100101
[3,1,8,5,7,6,2,4]=>1010110=>0101001
[6,1,5,8,7,4,2,3]=>1001110=>0110001
[5,4,1,8,7,6,2,3]=>1101110=>0010001
[5,8,6,7,4,3,2,1]=>0101111=>1010000
[4,8,7,5,6,3,2,1]=>0110111=>1001000
[4,2,1,6,3,5,8,7]=>1101001=>0010110
[6,2,1,4,3,5,8,7]=>1101001=>0010110
[6,2,1,4,3,8,5,7]=>1101010=>0010101
[8,2,1,4,3,6,5,7]=>1101010=>0010101
[8,2,4,1,3,6,5,7]=>1010010=>0101101
[6,2,4,1,3,8,5,7]=>1010010=>0101101
[6,2,4,1,3,5,8,7]=>1010001=>0101110
[4,2,6,1,3,5,8,7]=>1010001=>0101110
[2,1,6,4,3,5,8,7]=>1011001=>0100110
[2,6,1,4,3,5,8,7]=>0101001=>1010110
[2,6,4,1,3,5,8,7]=>0110001=>1001110
[4,6,2,1,3,5,8,7]=>0110001=>1001110
[6,4,2,1,3,5,8,7]=>1110001=>0001110
[8,4,2,1,3,6,5,7]=>1110010=>0001101
[8,4,2,1,6,3,5,7]=>1110100=>0001011
[6,4,2,1,8,3,5,7]=>1110100=>0001011
[4,6,2,1,8,3,5,7]=>0110100=>1001011
[2,6,1,4,3,8,5,7]=>0101010=>1010101
[2,1,6,4,3,8,5,7]=>1011010=>0100101
[2,1,8,4,3,6,5,7]=>1011010=>0100101
[2,8,1,4,3,6,5,7]=>0101010=>1010101
[2,8,4,1,3,6,5,7]=>0110010=>1001101
[4,8,2,1,3,6,5,7]=>0110010=>1001101
[4,8,2,1,6,3,5,7]=>0110100=>1001011
[6,8,2,1,4,3,5,7]=>0110100=>1001011
[8,6,2,1,4,3,5,7]=>1110100=>0001011
[2,8,1,4,6,3,5,7]=>0100100=>1011011
[2,1,8,4,6,3,5,7]=>1010100=>0101011
[2,1,6,4,8,3,5,7]=>1010100=>0101011
[2,6,1,4,8,3,5,7]=>0100100=>1011011
[2,6,4,1,8,3,5,7]=>0110100=>1001011
[2,6,4,8,1,3,5,7]=>0101000=>1010111
[4,6,2,8,1,3,5,7]=>0101000=>1010111
[4,2,6,1,3,8,5,7]=>1010010=>0101101
[4,2,6,1,8,3,5,7]=>1010100=>0101011
[6,2,4,1,8,3,5,7]=>1010100=>0101011
[8,2,4,1,6,3,5,7]=>1010100=>0101011
[8,2,1,4,6,3,5,7]=>1100100=>0011011
[6,2,1,4,8,3,5,7]=>1100100=>0011011
[4,2,1,6,8,3,5,7]=>1100100=>0011011
[4,2,1,6,3,8,5,7]=>1101010=>0010101
[4,2,1,3,6,8,5,7]=>1100010=>0011101
[2,1,4,3,8,6,5,7]=>1010110=>0101001
[2,4,1,3,8,6,5,7]=>0100110=>1011001
[4,2,1,3,8,6,5,7]=>1100110=>0011001
[4,2,1,8,3,6,5,7]=>1101010=>0010101
[4,2,1,8,6,3,5,7]=>1101100=>0010011
[6,2,1,8,4,3,5,7]=>1101100=>0010011
[8,2,1,6,4,3,5,7]=>1101100=>0010011
[8,2,6,1,4,3,5,7]=>1010100=>0101011
[6,2,8,1,4,3,5,7]=>1010100=>0101011
[4,2,8,1,6,3,5,7]=>1010100=>0101011
[4,2,8,1,3,6,5,7]=>1010010=>0101101
[2,4,8,1,3,6,5,7]=>0010010=>1101101
[2,4,1,8,3,6,5,7]=>0101010=>1010101
[2,1,4,8,3,6,5,7]=>1001010=>0110101
[2,1,4,8,6,3,5,7]=>1001100=>0110011
[2,4,8,1,6,3,5,7]=>0010100=>1101011
[2,4,8,6,1,3,5,7]=>0011000=>1100111
[4,2,8,6,1,3,5,7]=>1011000=>0100111
[6,2,8,4,1,3,5,7]=>1011000=>0100111
[8,2,6,4,1,3,5,7]=>1011000=>0100111
[8,4,6,2,1,3,5,7]=>1011000=>0100111
[6,4,8,2,1,3,5,7]=>1011000=>0100111
[4,6,8,2,1,3,5,7]=>0011000=>1100111
[2,6,8,4,1,3,5,7]=>0011000=>1100111
[2,6,8,1,4,3,5,7]=>0010100=>1101011
[2,6,1,8,4,3,5,7]=>0101100=>1010011
[2,1,6,8,4,3,5,7]=>1001100=>0110011
[2,1,8,6,4,3,5,7]=>1011100=>0100011
[2,8,1,6,4,3,5,7]=>0101100=>1010011
[2,8,6,4,1,3,5,7]=>0111000=>1000111
[4,8,6,2,1,3,5,7]=>0111000=>1000111
[6,8,4,2,1,3,5,7]=>0111000=>1000111
[3,2,6,1,5,4,8,7]=>1010101=>0101010
[5,2,4,3,8,1,7,6]=>1010101=>0101010
[6,2,4,1,5,3,8,7]=>1010101=>0101010
[4,3,6,1,5,2,8,7]=>1010101=>0101010
[4,3,5,2,8,1,7,6]=>1010101=>0101010
[4,3,7,2,6,5,8,1]=>1010101=>0101010
[4,3,8,2,6,1,7,5]=>1010101=>0101010
[4,3,8,1,7,2,6,5]=>1010101=>0101010
[4,3,8,1,5,2,7,6]=>1010101=>0101010
[5,1,8,3,4,2,7,6]=>1010101=>0101010
[5,4,8,1,3,2,7,6]=>1010101=>0101010
[2,1,5,4,8,3,7,6]=>1010101=>0101010
[5,1,7,6,8,3,4,2]=>1010101=>0101010
[4,3,7,6,8,1,5,2]=>1010101=>0101010
[4,3,7,1,8,5,6,2]=>1010101=>0101010
[4,3,6,5,8,1,7,2]=>1010101=>0101010
[6,3,5,4,7,2,8,1]=>1010101=>0101010
[6,3,5,4,8,1,7,2]=>1010101=>0101010
[7,1,6,3,8,4,5,2]=>1010101=>0101010
[7,4,6,5,8,1,3,2]=>1010101=>0101010
[2,1,8,4,6,3,7,5]=>1010101=>0101010
[8,4,6,1,3,2,7,5]=>1010101=>0101010
[8,1,6,3,4,2,7,5]=>1010101=>0101010
[8,1,6,3,7,2,5,4]=>1010101=>0101010
[8,3,5,1,7,2,6,4]=>1010101=>0101010
[8,3,5,2,6,1,7,4]=>1010101=>0101010
[7,3,5,2,6,4,8,1]=>1010101=>0101010
[8,2,6,3,5,1,7,4]=>1010101=>0101010
[8,2,7,1,5,3,6,4]=>1010101=>0101010
[8,2,4,1,5,3,7,6]=>1010101=>0101010
[8,2,4,1,7,3,6,5]=>1010101=>0101010
[8,2,4,3,6,1,7,5]=>1010101=>0101010
[3,2,8,4,6,1,7,5]=>1010101=>0101010
[3,2,8,1,5,4,7,6]=>1010101=>0101010
[3,2,7,6,8,1,5,4]=>1010101=>0101010
[3,2,7,1,8,5,6,4]=>1010101=>0101010
[3,2,6,5,8,1,7,4]=>1010101=>0101010
[6,5,7,2,4,3,8,1]=>1010101=>0101010
[6,5,8,2,4,1,7,3]=>1010101=>0101010
[7,2,4,1,8,5,6,3]=>1010101=>0101010
[7,6,8,2,4,1,5,3]=>1010101=>0101010
[7,6,8,1,5,2,4,3]=>1010101=>0101010
[2,1,7,3,8,5,6,4]=>1010101=>0101010
[7,1,3,2,8,5,6,4]=>1010101=>0101010
[7,1,8,5,6,2,4,3]=>1010101=>0101010
[7,1,8,2,6,4,5,3]=>1010101=>0101010
[7,2,8,1,5,4,6,3]=>1010101=>0101010
[6,2,7,4,5,3,8,1]=>1010101=>0101010
[5,4,7,2,6,3,8,1]=>1010101=>0101010
[5,4,8,2,6,1,7,3]=>1010101=>0101010
[6,5,8,1,7,2,4,3]=>1010101=>0101010
[2,1,6,5,8,3,7,4]=>1010101=>0101010
[6,5,7,4,8,1,3,2]=>1010101=>0101010
[6,5,7,1,8,3,4,2]=>1010101=>0101010
[6,1,7,4,8,3,5,2]=>1010101=>0101010
[5,4,7,1,8,3,6,2]=>1010101=>0101010
[5,4,6,3,8,1,7,2]=>1010101=>0101010
[2,1,4,3,6,5,8,7,11,12,10,9]=>10101010011=>01010101100
[2,1,4,3,6,5,9,10,8,7,12,11]=>10101001101=>01010110010
[2,1,4,3,6,5,9,11,8,12,10,7]=>10101001011=>01010110100
[2,1,4,3,6,5,10,11,12,9,8,7]=>10101000111=>01010111000
[2,1,4,3,7,8,6,5,10,9,12,11]=>10100110101=>01011001010
[2,1,4,3,7,8,6,5,11,12,10,9]=>10100110011=>01011001100
[2,1,4,3,7,9,6,10,8,5,12,11]=>10100101101=>01011010010
[2,1,4,3,7,9,6,11,8,12,10,5]=>10100101011=>01011010100
[2,1,4,3,7,10,6,11,12,9,8,5]=>10100100111=>01011011000
[2,1,4,3,8,9,10,7,6,5,12,11]=>10100011101=>01011100010
[2,1,4,3,8,9,11,7,6,12,10,5]=>10100011011=>01011100100
[2,1,4,3,8,10,11,7,12,9,6,5]=>10100010111=>01011101000
[2,1,4,3,9,10,11,12,8,7,6,5]=>10100001111=>01011110000
[2,1,5,6,4,3,8,7,10,9,12,11]=>10011010101=>01100101010
[2,1,5,6,4,3,8,7,11,12,10,9]=>10011010011=>01100101100
[2,1,5,6,4,3,9,10,8,7,12,11]=>10011001101=>01100110010
[2,1,5,6,4,3,9,11,8,12,10,7]=>10011001011=>01100110100
[2,1,5,6,4,3,10,11,12,9,8,7]=>10011000111=>01100111000
[2,1,5,7,4,8,6,3,10,9,12,11]=>10010110101=>01101001010
[2,1,5,7,4,8,6,3,11,12,10,9]=>10010110011=>01101001100
[2,1,5,7,4,9,6,10,8,3,12,11]=>10010101101=>01101010010
[2,1,5,7,4,9,6,11,8,12,10,3]=>10010101011=>01101010100
[2,1,5,7,4,10,6,11,12,9,8,3]=>10010100111=>01101011000
[2,1,5,8,4,9,10,7,6,3,12,11]=>10010011101=>01101100010
[2,1,5,8,4,9,11,7,6,12,10,3]=>10010011011=>01101100100
[2,1,5,8,4,10,11,7,12,9,6,3]=>10010010111=>01101101000
[2,1,5,9,4,10,11,12,8,7,6,3]=>10010001111=>01101110000
[2,1,6,7,8,5,4,3,10,9,12,11]=>10001110101=>01110001010
[2,1,6,7,8,5,4,3,11,12,10,9]=>10001110011=>01110001100
[2,1,6,7,9,5,4,10,8,3,12,11]=>10001101101=>01110010010
[2,1,6,7,9,5,4,11,8,12,10,3]=>10001101011=>01110010100
[2,1,6,7,10,5,4,11,12,9,8,3]=>10001100111=>01110011000
[2,1,6,8,9,5,10,7,4,3,12,11]=>10001011101=>01110100010
[2,1,6,8,9,5,11,7,4,12,10,3]=>10001011011=>01110100100
[2,1,6,8,10,5,11,7,12,9,4,3]=>10001010111=>01110101000
[2,1,6,9,10,5,11,12,8,7,4,3]=>10001001111=>01110110000
[2,1,7,8,9,10,6,5,4,3,12,11]=>10000111101=>01111000010
[2,1,7,8,9,11,6,5,4,12,10,3]=>10000111011=>01111000100
[2,1,7,8,10,11,6,5,12,9,4,3]=>10000110111=>01111001000
[2,1,7,9,10,11,6,12,8,5,4,3]=>10000101111=>01111010000
[2,1,8,9,10,11,12,7,6,5,4,3]=>10000011111=>01111100000
[3,4,2,1,6,5,8,7,10,9,12,11]=>01101010101=>10010101010
[3,4,2,1,7,8,6,5,11,12,10,9]=>01100110011=>10011001100
[3,4,2,1,8,9,10,7,6,5,12,11]=>01100011101=>10011100010
[3,4,2,1,9,10,11,12,8,7,6,5]=>01100001111=>10011110000
[3,5,2,7,4,9,6,11,8,12,10,1]=>01010101011=>10101010100
[3,5,2,7,4,10,6,11,12,9,8,1]=>01010100111=>10101011000
[3,5,2,8,4,9,11,7,6,12,10,1]=>01010011011=>10101100100
[3,5,2,8,4,10,11,7,12,9,6,1]=>01010010111=>10101101000
[3,5,2,9,4,10,11,12,8,7,6,1]=>01010001111=>10101110000
[3,6,2,7,8,5,4,1,10,9,12,11]=>01001110101=>10110001010
[3,6,2,7,8,5,4,1,11,12,10,9]=>01001110011=>10110001100
[3,6,2,7,9,5,4,11,8,12,10,1]=>01001101011=>10110010100
[3,6,2,7,10,5,4,11,12,9,8,1]=>01001100111=>10110011000
[3,6,2,8,9,5,11,7,4,12,10,1]=>01001011011=>10110100100
[3,6,2,8,10,5,11,7,12,9,4,1]=>01001010111=>10110101000
[3,6,2,9,10,5,11,12,8,7,4,1]=>01001001111=>10110110000
[3,7,2,8,9,10,6,5,4,1,12,11]=>01000111101=>10111000010
[3,7,2,8,9,11,6,5,4,12,10,1]=>01000111011=>10111000100
[3,7,2,8,10,11,6,5,12,9,4,1]=>01000110111=>10111001000
[3,7,2,9,10,11,6,12,8,5,4,1]=>01000101111=>10111010000
[3,8,2,9,10,11,12,7,6,5,4,1]=>01000011111=>10111100000
[4,5,6,3,2,1,8,7,10,9,12,11]=>00111010101=>11000101010
[4,5,6,3,2,1,10,11,12,9,8,7]=>00111000111=>11000111000
[4,5,7,3,2,8,6,1,11,12,10,9]=>00110110011=>11001001100
[4,5,7,3,2,9,6,11,8,12,10,1]=>00110101011=>11001010100
[4,5,7,3,2,10,6,11,12,9,8,1]=>00110100111=>11001011000
[4,5,8,3,2,9,11,7,6,12,10,1]=>00110011011=>11001100100
[4,5,8,3,2,10,11,7,12,9,6,1]=>00110010111=>11001101000
[4,5,9,3,2,10,11,12,8,7,6,1]=>00110001111=>11001110000
[4,6,7,3,8,5,2,1,10,9,12,11]=>00101110101=>11010001010
[4,6,7,3,9,5,2,10,8,1,12,11]=>00101101101=>11010010010
[4,6,7,3,9,5,2,11,8,12,10,1]=>00101101011=>11010010100
[4,6,7,3,10,5,2,11,12,9,8,1]=>00101100111=>11010011000
[4,6,8,3,9,5,11,7,2,12,10,1]=>00101011011=>11010100100
[4,6,8,3,10,5,11,7,12,9,2,1]=>00101010111=>11010101000
[4,6,9,3,10,5,11,12,8,7,2,1]=>00101001111=>11010110000
[4,7,8,3,9,11,6,5,2,12,10,1]=>00100111011=>11011000100
[4,7,8,3,10,11,6,5,12,9,2,1]=>00100110111=>11011001000
[4,7,9,3,10,11,6,12,8,5,2,1]=>00100101111=>11011010000
[4,8,9,3,10,11,12,7,6,5,2,1]=>00100011111=>11011100000
[5,6,7,8,4,3,2,1,10,9,12,11]=>00011110101=>11100001010
[5,6,7,9,4,3,2,11,8,12,10,1]=>00011101011=>11100010100
[5,6,7,10,4,3,2,11,12,9,8,1]=>00011100111=>11100011000
[5,6,8,9,4,3,10,7,2,1,12,11]=>00011011101=>11100100010
[5,6,8,9,4,3,11,7,2,12,10,1]=>00011011011=>11100100100
[5,6,8,10,4,3,11,7,12,9,2,1]=>00011010111=>11100101000
[5,6,9,10,4,3,11,12,8,7,2,1]=>00011001111=>11100110000
[5,7,8,9,4,10,6,3,2,1,12,11]=>00010111101=>11101000010
[5,7,8,9,4,11,6,3,2,12,10,1]=>00010111011=>11101000100
[5,7,8,10,4,11,6,3,12,9,2,1]=>00010110111=>11101001000
[5,7,9,10,4,11,6,12,8,3,2,1]=>00010101111=>11101010000
[5,8,9,10,4,11,12,7,6,3,2,1]=>00010011111=>11101100000
[6,7,8,9,10,5,4,3,2,1,12,11]=>00001111101=>11110000010
[6,7,8,9,11,5,4,3,2,12,10,1]=>00001111011=>11110000100
[6,7,8,10,11,5,4,3,12,9,2,1]=>00001110111=>11110001000
[6,7,9,10,11,5,4,12,8,3,2,1]=>00001101111=>11110010000
[6,8,9,10,11,5,12,7,4,3,2,1]=>00001011111=>11110100000
[7,8,9,10,11,12,6,5,4,3,2,1]=>00000111111=>11111000000
[2,8,3,1,5,4,6,7]=>0110100=>1001011
[2,5,3,4,7,1,8,6]=>0100101=>1011010
[2,4,8,3,5,7,6,1]=>0010011=>1101100
[4,2,5,3,1,8,6,7]=>1011010=>0100101
[4,2,1,8,5,3,6,7]=>1101100=>0010011
[5,4,1,3,8,2,6,7]=>1100100=>0011011
[5,1,4,8,3,2,6,7]=>1001100=>0110011
[1,5,8,4,3,2,6,7]=>0011100=>1100011
[1,8,5,4,3,2,6,7]=>0111100=>1000011
[1,7,4,3,8,5,2,6]=>0110110=>1001001
[1,5,7,3,8,4,2,6]=>0010110=>1101001
[5,1,4,7,8,3,2,6]=>1000110=>0111001
[4,8,1,5,7,3,6,2]=>0100101=>1011010
[8,1,5,3,7,4,6,2]=>1010101=>0101010
[3,8,4,7,6,5,2,1]=>0101111=>1010000
[1,6,8,5,3,7,4,2]=>0011011=>1100100
[6,8,1,7,4,3,5,2]=>0101101=>1010010
[6,4,8,1,7,3,5,2]=>1010101=>0101010
[6,4,8,7,1,5,2,3]=>1011010=>0100101
[7,6,4,1,3,8,2,5]=>1110010=>0001101
[1,7,5,6,3,2,8,4]=>0101101=>1010010
[4,2,1,7,8,5,3,6]=>1100110=>0011001
[2,7,4,6,3,1,8,5]=>0101101=>1010010
[2,6,8,4,3,7,5,1]=>0011011=>1100100
[6,2,4,8,3,7,5,1]=>1001011=>0110100
[7,2,6,3,4,1,8,5]=>1010101=>0101010
[2,6,7,3,1,4,8,5]=>0011001=>1100110
[2,7,1,8,3,5,4,6]=>0101010=>1010101
[2,1,7,3,5,8,4,6]=>1010010=>0101101
[8,7,1,3,6,2,4,5]=>1100100=>0011011
[8,2,1,7,3,5,6,4]=>1101001=>0010110
[7,8,2,6,3,1,5,4]=>0101101=>1010010
[8,7,2,6,3,5,4,1]=>1101011=>0010100
[1,2,8,7,4,5,6,3]=>0011001=>1100110
[8,3,7,1,5,6,2,4]=>1010010=>0101101
[8,6,1,2,7,5,3,4]=>1100110=>0011001
[8,1,6,2,7,4,5,3]=>1010101=>0101010
[1,8,5,2,6,7,4,3]=>0110011=>1001100
[5,2,1,8,6,7,4,3]=>1101011=>0010100
[2,8,5,7,6,4,3,1]=>0101111=>1010000
[1,7,8,5,2,6,4,3]=>0011011=>1100100
[7,8,1,6,4,2,5,3]=>0101101=>1010010
[7,8,6,1,5,3,2,4]=>0110110=>1001001
[7,3,8,6,1,5,2,4]=>1011010=>0100101
[8,7,6,1,5,3,4,2]=>1110101=>0001010
[8,7,1,6,4,5,3,2]=>1101011=>0010100
[8,1,7,5,6,4,3,2]=>1010111=>0101000
[1,8,6,7,5,4,3,2]=>0101111=>1010000
[6,3,5,2,1,4,8,7]=>1011001=>0100110
[6,3,5,7,2,8,4,1]=>1001011=>0110100
[8,5,2,7,4,3,1,6]=>1101110=>0010001
[4,5,3,6,1,2,8,7]=>0101001=>1010110
[3,5,1,4,6,2,8,7]=>0100101=>1011010
[8,3,4,5,7,2,1,6]=>1000110=>0111001
[5,7,4,6,3,8,2,1]=>0101011=>1010100
[2,8,4,6,3,7,1,5]=>0101010=>1010101
[8,1,4,7,3,6,2,5]=>1001010=>0110101
[8,3,4,7,5,1,2,6]=>1001100=>0110011
[8,5,1,4,7,3,2,6]=>1100110=>0011001
[8,5,3,7,1,4,2,6]=>1101010=>0010101
[2,1,8,5,7,4,3,6]=>1010110=>0101001
[6,5,3,7,1,8,4,2]=>1101011=>0010100
[6,5,1,4,7,8,3,2]=>1100011=>0011100
[6,3,4,7,5,8,1,2]=>1001010=>0110101
[5,1,4,6,8,3,7,2]=>1000101=>0111010
[4,7,1,3,5,8,6,2]=>0100011=>1011100
[4,8,3,7,1,2,6,5]=>0101001=>1010110
[3,8,6,4,1,7,2,5]=>0111010=>1000101
[3,8,1,2,5,7,6,4]=>0100011=>1011100
[2,8,7,5,4,1,3,6]=>0111100=>1000011
[8,7,2,6,4,1,3,5]=>1101100=>0010011
[3,8,6,7,4,2,1,5]=>0101110=>1010001
[5,7,6,8,4,2,3,1]=>0101101=>1010010
[5,3,7,8,2,4,6,1]=>1001001=>0110110
[8,3,6,2,1,4,7,5]=>1011001=>0100110
[5,3,7,6,2,1,8,4]=>1011101=>0100010
[5,3,6,2,8,7,1,4]=>1010110=>0101001
[5,7,8,6,4,2,1,3]=>0011110=>1100001
[2,6,7,5,4,8,1,3]=>0011010=>1100101
[6,1,7,4,5,8,2,3]=>1010010=>0101101
[6,7,3,5,1,8,2,4]=>0101010=>1010101
[2,1,6,7,5,8,3,4]=>1001010=>0110101
[2,1,5,7,3,6,8,4]=>1001001=>0110110
[5,7,3,6,1,2,8,4]=>0101001=>1010110
[4,1,7,2,5,6,8,3]=>1010001=>0101110
[2,4,7,1,6,5,8,3]=>0010101=>1101010
[4,6,2,1,8,7,5,3]=>0110111=>1001000
[3,4,6,2,7,8,5,1]=>0010011=>1101100
[4,6,1,2,5,8,7,3]=>0100011=>1011100
[5,6,1,4,8,2,7,3]=>0100101=>1011010
[5,6,3,1,8,7,2,4]=>0110110=>1001001
[3,5,6,4,7,1,8,2]=>0010101=>1101010
[3,4,6,1,5,7,8,2]=>0010001=>1101110
[3,4,1,5,7,6,8,2]=>0100101=>1011010
[3,8,2,7,1,6,5,4]=>0101011=>1010100
[3,8,2,7,6,1,5,4]=>0101101=>1010010
[3,8,2,7,6,5,1,4]=>0101110=>1010001
[3,8,2,7,6,5,4,1]=>0101111=>1010000
[4,8,7,2,6,5,3,1]=>0110111=>1001000
[4,8,7,2,6,5,1,3]=>0110110=>1001001
[4,8,7,2,6,1,5,3]=>0110101=>1001010
[4,8,7,2,1,6,5,3]=>0111011=>1000100
[4,8,7,3,1,6,5,2]=>0111011=>1000100
[4,8,7,3,2,1,6,5]=>0111101=>1000010
[4,8,7,3,2,6,1,5]=>0111010=>1000101
[4,8,7,3,2,6,5,1]=>0111011=>1000100
[4,8,7,3,6,2,5,1]=>0110101=>1001010
[4,8,7,3,6,2,1,5]=>0110110=>1001001
[4,8,7,3,6,1,5,2]=>0110101=>1001010
[4,8,7,3,6,5,1,2]=>0110110=>1001001
[4,8,7,3,6,5,2,1]=>0110111=>1001000
[5,8,7,6,3,4,2,1]=>0111011=>1000100
[5,8,7,6,3,1,4,2]=>0111101=>1000010
[5,8,7,6,3,2,4,1]=>0111101=>1000010
[5,8,7,6,2,4,3,1]=>0111011=>1000100
[5,8,7,6,2,1,4,3]=>0111101=>1000010
[5,8,7,6,4,2,3,1]=>0111101=>1000010
[5,8,7,6,4,2,1,3]=>0111110=>1000001
[5,8,7,6,4,1,3,2]=>0111101=>1000010
[5,8,7,6,4,3,1,2]=>0111110=>1000001
[7,3,4,2,1,6,5,8]=>1011010=>0100101
[7,3,5,2,6,1,4,8]=>1010100=>0101011
[7,3,5,2,6,4,1,8]=>1010110=>0101001
[6,3,5,2,7,4,8,1]=>1010101=>0101010
[7,2,1,5,6,4,3,8]=>1100110=>0011001
[7,3,5,1,6,4,2,8]=>1010110=>0101001
[7,4,5,6,1,3,2,8]=>1001010=>0110101
[1,4,5,7,3,2,8,6]=>0001101=>1110010
[1,4,6,7,3,8,2,5]=>0001010=>1110101
[6,4,5,7,3,1,8,2]=>1001101=>0110010
[6,4,5,7,1,3,8,2]=>1001001=>0110110
[6,3,5,1,7,4,8,2]=>1010101=>0101010
[6,2,1,5,7,4,8,3]=>1100101=>0011010
[3,2,1,5,7,4,8,6]=>1100101=>0011010
[2,4,6,7,3,8,1,5]=>0001010=>1110101
[1,4,6,7,3,8,5,2]=>0001011=>1110100
[1,5,6,7,8,3,4,2]=>0000101=>1111010
[2,5,6,7,8,3,1,4]=>0000110=>1111001
[3,2,1,6,7,8,4,5]=>1100010=>0011101
[5,2,1,6,7,8,4,3]=>1100011=>0011100
[5,3,6,1,7,8,4,2]=>1010011=>0101100
[5,4,6,7,1,8,3,2]=>1001011=>0110100
[1,5,6,7,8,3,2,4]=>0000110=>1111001
[6,4,5,7,2,1,8,3]=>1001101=>0110010
[5,4,6,7,2,8,3,1]=>1001011=>0110100
[5,3,6,2,7,8,4,1]=>1010011=>0101100
[5,3,6,2,7,8,1,4]=>1010010=>0101101
[6,3,5,2,7,1,8,4]=>1010101=>0101010
[6,3,4,2,1,7,8,5]=>1011001=>0100110
[5,3,4,1,2,7,8,6]=>1010001=>0101110
[4,3,6,2,7,8,1,5]=>1010010=>0101101
[4,3,6,2,7,8,5,1]=>1010011=>0101100
[1,3,6,2,7,8,5,4]=>0010011=>1101100
[1,4,6,7,2,8,5,3]=>0001011=>1110100
[3,4,6,7,2,8,5,1]=>0001011=>1110100
[3,4,5,7,2,1,8,6]=>0001101=>1110010
[4,2,1,5,7,3,8,6]=>1100101=>0011010
[4,2,1,6,7,8,3,5]=>1100010=>0011101
[4,3,6,1,7,8,2,5]=>1010010=>0101101
[1,5,6,7,8,2,4,3]=>0000101=>1111010
[1,5,6,7,8,4,2,3]=>0000110=>1111001
[3,4,6,7,1,8,5,2]=>0001011=>1110100
[4,3,6,1,7,8,5,2]=>1010011=>0101100
[4,2,1,6,7,8,5,3]=>1100011=>0011100
[2,3,6,1,7,8,5,4]=>0010011=>1101100
[2,4,6,7,1,8,5,3]=>0001011=>1110100
[2,5,6,7,8,1,4,3]=>0000101=>1111010
[2,1,4,3,6,5,8,7,9]=>10101010=>01010101
[2,4,1,3,6,5,8,7,9]=>01001010=>10110101
[2,4,1,6,3,5,8,7,9]=>01010010=>10101101
[2,4,1,6,3,8,5,7,9]=>01010100=>10101011
[2,4,1,6,3,7,5,9,8]=>01010101=>10101010
[2,4,1,5,3,7,6,9,8]=>01010101=>10101010
[2,3,1,5,4,7,6,9,8]=>01010101=>10101010
[1,3,2,5,4,7,6,9,8]=>01010101=>10101010
[2,4,1,3,6,5,8,7,10,9]=>010010101=>101101010
[2,4,6,1,3,5,8,7,9]=>00100010=>11011101
[2,4,1,6,3,5,8,7,10,9]=>010100101=>101011010
[2,4,1,6,8,3,5,7,9]=>01001000=>10110111
[2,4,1,6,3,8,5,7,10,9]=>010101001=>101010110
[2,4,1,6,3,8,9,5,7]=>01010010=>10101101
[2,4,1,6,3,8,5,10,7,9]=>010101010=>101010101
[2,4,1,6,3,7,5,8,9]=>01010100=>10101011
[2,4,1,6,3,8,5,9,7,10]=>010101010=>101010101
[2,4,1,5,3,8,6,9,7]=>01010101=>10101010
[2,4,1,6,3,7,5,9,8,10]=>010101010=>101010101
[2,3,1,6,4,7,5,9,8]=>01010101=>10101010
[2,4,1,5,3,7,6,9,8,10]=>010101010=>101010101
[1,4,2,5,3,7,6,9,8]=>01010101=>10101010
[2,3,1,5,4,7,6,9,8,10]=>010101010=>101010101
[1,3,2,5,4,7,6,9,8,10]=>010101010=>101010101
[7,1,2,3,4,5,6,8,9]=>10000000=>01111111
[1,4,3,6,2,5,7,8]=>0101000=>1010111
[1,4,3,7,2,5,6,8]=>0101000=>1010111
[1,4,3,7,6,8,2,5]=>0101010=>1010101
[1,4,3,7,5,8,2,6]=>0101010=>1010101
[1,4,3,7,2,6,5,8]=>0101010=>1010101
[1,5,3,7,4,8,2,6]=>0101010=>1010101
[1,3,2,6,5,8,4,7]=>0101010=>1010101
[1,5,4,8,2,6,3,7]=>0101010=>1010101
[1,5,4,8,3,7,2,6]=>0101010=>1010101
[1,2,3,6,5,8,4,7]=>0001010=>1110101
[6,8,2,4,5,7,1,3]=>0100010=>1011101
[3,7,8,4,5,2,6,1]=>0010101=>1101010
[7,8,1,4,5,3,6,2]=>0100101=>1011010
[3,8,7,4,1,6,5,2]=>0111011=>1000100
[4,8,3,6,1,5,7,2]=>0101001=>1010110
[5,8,3,1,6,4,7,2]=>0110101=>1001010
[5,8,1,4,7,6,3,2]=>0100111=>1011000
[7,5,1,8,6,2,4,3]=>1101101=>0010010
[7,4,1,8,2,6,3,5]=>1101010=>0010101
[7,1,8,4,2,6,3,5]=>1011010=>0100101
[1,6,3,8,5,2,4,7]=>0101100=>1010011
[6,1,3,8,5,2,4,7]=>1001100=>0110011
[7,1,8,3,6,2,5,4]=>1010101=>0101010
[7,3,1,8,4,2,6,5]=>1101101=>0010010
[7,2,8,4,1,6,5,3]=>1011011=>0100100
[7,2,8,3,6,5,1,4]=>1010110=>0101001
[7,2,8,3,6,1,5,4]=>1010101=>0101010
[7,1,8,2,3,6,5,4]=>1010011=>0101100
[6,1,2,8,3,5,4,7]=>1001010=>0110101
[1,5,2,3,8,4,7,6]=>0100101=>1011010
[5,1,2,3,8,4,7,6]=>1000101=>0111010
[5,2,3,8,1,4,7,6]=>1001001=>0110110
[6,2,8,1,3,5,4,7]=>1010010=>0101101
[6,2,4,1,8,7,3,5]=>1010110=>0101001
[6,3,1,4,2,8,5,7]=>1101010=>0010101
[3,1,6,4,2,8,5,7]=>1011010=>0100101
[2,6,3,8,7,1,5,4]=>0101101=>1010010
[2,6,3,8,5,1,4,7]=>0101100=>1010011
[2,5,1,8,3,4,7,6]=>0101001=>1010110
[2,5,1,3,8,4,7,6]=>0100101=>1011010
[1,2,5,3,8,4,7,6]=>0010101=>1101010
[1,2,4,8,3,7,6,5]=>0001011=>1110100
[2,4,8,1,3,7,6,5]=>0010011=>1101100
[2,4,8,3,7,1,6,5]=>0010101=>1101010
[2,4,8,3,7,6,1,5]=>0010110=>1101001
[2,5,3,8,1,7,4,6]=>0101010=>1010101
[2,5,4,1,3,8,7,6]=>0110011=>1001100
[3,1,5,4,8,2,7,6]=>1010101=>0101010
[5,3,1,4,8,2,7,6]=>1100101=>0011010
[5,2,3,8,4,7,1,6]=>1001010=>0110101
[4,8,2,3,7,6,1,5]=>0100110=>1011001
[4,8,2,3,7,1,6,5]=>0100101=>1011010
[4,8,1,2,3,7,6,5]=>0100011=>1011100
[1,4,8,2,3,7,6,5]=>0010011=>1101100
[1,4,8,3,7,2,6,5]=>0010101=>1101010
[6,3,8,1,5,2,4,7]=>1010100=>0101011
[5,3,8,1,2,4,7,6]=>1010001=>0101110
[5,1,3,8,2,4,7,6]=>1001001=>0110110
[1,5,3,8,2,4,7,6]=>0101001=>1010110
[1,5,4,8,2,7,6,3]=>0101011=>1010100
[5,1,4,8,2,7,6,3]=>1001011=>0110100
[5,4,8,1,2,7,6,3]=>1010011=>0101100
[6,5,1,2,8,7,4,3]=>1100111=>0011000
[5,3,1,6,4,2,8,7]=>1101101=>0010010
[5,1,6,2,8,7,4,3]=>1010111=>0101000
[4,1,5,8,2,7,6,3]=>1001011=>0110100
[4,1,2,5,8,7,6,3]=>1000111=>0111000
[1,4,2,5,8,7,6,3]=>0100111=>1011000
[1,3,5,2,8,7,4,6]=>0010110=>1101001
[3,5,1,2,8,7,4,6]=>0100110=>1011001
[3,6,2,8,7,5,1,4]=>0101110=>1010001
[4,2,6,1,8,7,3,5]=>1010110=>0101001
[4,3,1,5,8,2,7,6]=>1100101=>0011010
[3,5,2,8,7,1,4,6]=>0101100=>1010011
[3,4,8,7,2,6,1,5]=>0011010=>1100101
[3,4,8,7,1,2,6,5]=>0011001=>1100110
[3,4,8,1,7,2,6,5]=>0010101=>1101010
[1,3,4,8,7,2,6,5]=>0001101=>1110010
[1,3,4,8,2,7,6,5]=>0001011=>1110100
[3,4,8,1,2,7,6,5]=>0010011=>1101100
[3,4,8,2,7,1,6,5]=>0010101=>1101010
[3,4,8,2,7,6,1,5]=>0010110=>1101001
[4,2,5,8,1,7,6,3]=>1001011=>0110100
[4,3,1,2,5,8,7,6]=>1100011=>0011100
[3,1,4,2,5,8,7,6]=>1010011=>0101100
[2,3,5,1,8,7,6,4]=>0010111=>1101000
[7,8,2,1,5,3,6,4]=>0110101=>1001010
[6,4,1,2,7,3,5,8]=>1100100=>0011011
[2,3,7,5,4,1,8,6]=>0011101=>1100010
[6,3,1,5,4,2,7,8]=>1101100=>0010011
[7,8,1,5,4,2,6,3]=>0101101=>1010010
[7,8,3,5,4,1,6,2]=>0101101=>1010010
[7,8,2,5,4,1,3,6]=>0101100=>1010011
[7,8,2,5,4,6,1,3]=>0101010=>1010101
[6,2,1,5,4,7,3,8]=>1101010=>0010101
[5,3,6,1,4,7,8,2]=>1010001=>0101110
[5,3,6,2,4,7,1,8]=>1010010=>0101101
[6,4,2,1,7,3,8,5]=>1110101=>0001010
[4,3,7,5,8,6,1,2]=>1010110=>0101001
[4,2,7,1,8,3,6,5]=>1010101=>0101010
[3,2,6,7,4,8,1,5]=>1001010=>0110101
[3,1,6,7,4,8,5,2]=>1001011=>0110100
[1,7,6,5,3,8,4,2]=>0111011=>1000100
[2,7,6,5,3,8,1,4]=>0111010=>1000101
[1,7,6,5,2,4,8,3]=>0111001=>1000110
[2,7,6,5,3,1,4,8]=>0111100=>1000011
[2,7,1,4,8,3,5,6]=>0100100=>1011011
[3,7,6,4,8,5,1,2]=>0110110=>1001001
[5,7,6,3,8,4,1,2]=>0110110=>1001001
[5,1,6,2,4,8,3,7]=>1010010=>0101101
[4,7,6,5,2,1,3,8]=>0111100=>1000011
[4,7,6,5,2,8,1,3]=>0111010=>1000101
[4,7,6,5,1,8,3,2]=>0111011=>1000100
[1,7,6,5,2,8,3,4]=>0111010=>1000101
[1,7,6,5,3,2,8,4]=>0111101=>1000010
[4,7,6,5,1,2,8,3]=>0111001=>1000110
[4,7,6,5,3,1,8,2]=>0111101=>1000010
[6,1,3,5,4,8,7,2]=>1001011=>0110100
[5,2,6,3,4,1,7,8]=>1010100=>0101011
[5,1,6,2,4,7,8,3]=>1010001=>0101110
[1,2,6,3,4,8,7,5]=>0010011=>1101100
[1,7,2,4,8,3,6,5]=>0100101=>1011010
[6,1,4,2,8,3,5,7]=>1010100=>0101011
[4,1,8,2,6,3,5,7]=>1010100=>0101011
[4,7,2,1,5,3,6,8]=>0110100=>1001011
[4,7,1,6,2,3,8,5]=>0101001=>1010110
[1,7,2,6,8,3,5,4]=>0100101=>1011010
[1,2,6,7,4,8,5,3]=>0001011=>1110100
[3,1,6,7,4,2,8,5]=>1001101=>0110010
[3,2,8,5,4,6,1,7]=>1011010=>0100101
[4,7,6,3,5,8,1,2]=>0110010=>1001101
[4,7,1,2,5,3,8,6]=>0100101=>1011010
[3,7,6,5,2,4,1,8]=>0111010=>1000101
[3,7,6,5,1,4,8,2]=>0111001=>1000110
[3,7,6,5,2,1,8,4]=>0111101=>1000010
[1,7,6,5,8,2,4,3]=>0110101=>1001010
[3,7,6,5,8,1,4,2]=>0110101=>1001010
[3,7,6,5,1,2,4,8]=>0111000=>1000111
[3,1,6,8,4,2,5,7]=>1001100=>0110011
[4,7,6,8,3,5,1,2]=>0101010=>1010101
[2,7,6,5,1,4,3,8]=>0111010=>1000101
[2,7,6,5,8,1,3,4]=>0110100=>1001011
[2,7,6,5,8,4,1,3]=>0110110=>1001001
[6,3,2,1,7,4,8,5]=>1110101=>0001010
[4,2,1,7,3,5,8,6]=>1101001=>0010110
[7,3,1,5,4,2,8,6]=>1101101=>0010010
[8,4,1,5,2,7,6,3]=>1101011=>0010100
[8,2,5,1,3,7,6,4]=>1010011=>0101100
[4,3,7,2,1,5,8,6]=>1011001=>0100110
[4,7,2,5,3,1,8,6]=>0101101=>1010010
[2,7,5,4,1,3,8,6]=>0111001=>1000110
[7,5,4,3,2,1,8,6]=>1111101=>0000010
[6,5,2,1,8,4,3,7]=>1110110=>0001001
[4,6,3,2,8,1,5,7]=>0110100=>1001011
[5,7,4,3,2,8,1,6]=>0111010=>1000101
[1,7,6,2,4,8,3,5]=>0110010=>1001101
[2,7,3,6,4,8,1,5]=>0101010=>1010101
[6,2,7,5,3,8,1,4]=>1011010=>0100101
[7,1,8,5,3,6,4,2]=>1011011=>0100100
[5,8,3,2,7,1,6,4]=>0110101=>1001010
[8,7,3,1,6,5,4,2]=>1110111=>0001000
[8,7,2,6,1,5,4,3]=>1101011=>0010100
[1,8,5,7,4,3,6,2]=>0101101=>1010010
[1,8,5,7,2,4,6,3]=>0101001=>1010110
[3,8,6,1,7,2,5,4]=>0110101=>1001010
[7,2,8,5,6,1,4,3]=>1010101=>0101010
[6,3,7,5,8,2,1,4]=>1010110=>0101001
[3,7,2,6,8,4,1,5]=>0100110=>1011001
[3,6,5,8,1,4,2,7]=>0101010=>1010101
[2,6,5,8,4,1,3,7]=>0101100=>1010011
[6,5,4,8,3,2,1,7]=>1101110=>0010001
[8,4,3,7,2,1,6,5]=>1101101=>0010010
[8,2,4,7,1,3,6,5]=>1001001=>0110110
[6,2,5,8,1,4,3,7]=>1001010=>0110101
[4,3,6,8,2,1,5,7]=>1001100=>0110011
[6,3,5,1,8,4,2,7]=>1010110=>0101001
[8,4,1,5,7,3,6,2]=>1100101=>0011010
[6,4,2,5,8,3,1,7]=>1100110=>0011001
[5,4,1,6,8,2,3,7]=>1100100=>0011011
[6,3,7,4,8,5,2,1]=>1010111=>0101000
[4,7,2,5,8,6,3,1]=>0100111=>1011000
[6,3,1,8,4,7,5,2]=>1101011=>0010100
[6,5,3,8,7,4,1,2]=>1101110=>0010001
[5,4,8,1,7,6,2,3]=>1010110=>0101001
[5,2,8,1,7,3,6,4]=>1010101=>0101010
[5,7,3,8,1,6,4,2]=>0101011=>1010100
[6,4,7,8,1,5,3,2]=>1001011=>0110100
[2,5,8,7,1,3,6,4]=>0011001=>1100110
[5,3,8,7,2,1,6,4]=>1011101=>0100010
[8,3,7,6,1,5,4,2]=>1011011=>0100100
[8,2,7,6,5,1,4,3]=>1011101=>0100010
[4,3,8,7,6,2,1,5]=>1011110=>0100001
[2,4,8,7,6,1,3,5]=>0011100=>1100011
[3,5,8,7,2,6,1,4]=>0011010=>1100101
[4,7,3,8,6,5,1,2]=>0101110=>1010001
[7,5,8,6,4,3,2,1]=>1011111=>0100000
[5,8,7,3,6,4,2,1]=>0110111=>1001000
[4,8,7,6,2,5,3,1]=>0111011=>1000100
[3,8,7,6,5,1,4,2]=>0111101=>1000010
[2,8,7,6,5,4,1,3]=>0111110=>1000001
[3,4,1,2,5,6,7,8,9]=>01000000=>10111111
[3,2,1,4,5,6,7,8,9]=>11000000=>00111111
[4,5,6,1,2,3,7,8,9]=>00100000=>11011111
[4,2,5,1,3,6,7,8,9]=>10100000=>01011111
[4,3,2,1,5,6,7,8,9]=>11100000=>00011111
[5,6,7,8,1,2,3,4,9]=>00010000=>11101111
[5,2,6,7,1,3,4,8,9]=>10010000=>01101111
[5,6,3,4,1,2,7,8,9]=>01010000=>10101111
[5,3,2,6,1,4,7,8,9]=>11010000=>00101111
[5,4,3,2,1,6,7,8,9]=>11110000=>00001111
[6,2,7,8,9,1,3,4,5]=>10001000=>01110111
[6,7,3,4,8,1,2,5,9]=>01001000=>10110111
[6,3,2,7,8,1,4,5,9]=>11001000=>00110111
[6,4,7,2,5,1,3,8,9]=>10101000=>01010111
[6,4,3,2,7,1,5,8,9]=>11101000=>00010111
[6,5,4,3,2,1,7,8,9]=>11111000=>00000111
[7,4,8,2,5,9,1,3,6]=>10100100=>01011011
[7,4,3,2,8,9,1,5,6]=>11100100=>00011011
[7,8,5,6,3,4,1,2,9]=>01010100=>10101011
[7,5,3,8,2,6,1,4,9]=>11010100=>00101011
[7,5,4,3,2,8,1,6,9]=>11110100=>00001011
[7,6,5,4,3,2,1,8,9]=>11111100=>00000011
[8,6,9,4,7,2,5,1,3]=>10101010=>01010101
[8,6,4,3,9,2,7,1,5]=>11101010=>00010101
[8,6,5,4,3,2,9,1,7]=>11111010=>00000101
[3,4,1,2,5,6,7,8,9,10]=>010000000=>101111111
[3,2,1,4,5,6,7,8,9,10]=>110000000=>001111111
[4,5,6,1,2,3,7,8,9,10]=>001000000=>110111111
[4,2,5,1,3,6,7,8,9,10]=>101000000=>010111111
[4,3,2,1,5,6,7,8,9,10]=>111000000=>000111111
[5,6,7,8,1,2,3,4,9,10]=>000100000=>111011111
[5,2,6,7,1,3,4,8,9,10]=>100100000=>011011111
[5,6,3,4,1,2,7,8,9,10]=>010100000=>101011111
[5,3,2,6,1,4,7,8,9,10]=>110100000=>001011111
[5,4,3,2,1,6,7,8,9,10]=>111100000=>000011111
[6,2,7,8,9,1,3,4,5,10]=>100010000=>011101111
[6,7,3,4,8,1,2,5,9,10]=>010010000=>101101111
[6,3,2,7,8,1,4,5,9,10]=>110010000=>001101111
[6,4,7,2,5,1,3,8,9,10]=>101010000=>010101111
[6,4,3,2,7,1,5,8,9,10]=>111010000=>000101111
[6,5,4,3,2,1,7,8,9,10]=>111110000=>000001111
[7,8,3,4,9,10,1,2,5,6]=>010001000=>101110111
[7,8,9,4,5,6,1,2,3,10]=>001001000=>110110111
[7,4,3,2,8,9,1,5,6,10]=>111001000=>000110111
[7,8,5,6,3,4,1,2,9,10]=>010101000=>101010111
[7,5,3,8,2,6,1,4,9,10]=>110101000=>001010111
[7,5,4,3,2,8,1,6,9,10]=>111101000=>000010111
[7,6,5,4,3,2,1,8,9,10]=>111111000=>000000111
[8,5,9,10,2,6,7,1,3,4]=>100100100=>011011011
[8,5,3,9,2,6,10,1,4,7]=>110100100=>001011011
[8,6,9,4,7,2,5,1,3,10]=>101010100=>010101011
[8,6,4,3,9,2,7,1,5,10]=>111010100=>000101011
[8,6,5,4,3,2,9,1,7,10]=>111110100=>000001011
[8,7,6,5,4,3,2,1,9,10]=>111111100=>000000011
[9,7,5,4,3,10,2,8,1,6]=>111101010=>000010101
[3,6,5,1,2,4,8,7]=>0110001=>1001110
[3,7,5,8,2,4,1,6]=>0101010=>1010101
[3,8,5,7,2,4,1,6]=>0101010=>1010101
[5,1,7,8,4,3,2,6]=>1001110=>0110001
[5,1,2,6,4,3,8,7]=>1001101=>0110010
[6,1,2,5,4,3,8,7]=>1001101=>0110010
[5,1,2,4,6,3,8,7]=>1000101=>0111010
[4,1,2,6,5,3,8,7]=>1001101=>0110010
[4,1,5,7,8,3,2,6]=>1000110=>0111001
[4,1,5,8,7,3,2,6]=>1001110=>0110001
[4,7,1,8,3,6,2,5]=>0101010=>1010101
[4,1,7,8,5,2,3,6]=>1001100=>0110011
[5,1,7,4,8,2,3,6]=>1010100=>0101011
[7,5,3,8,1,4,2,6]=>1101010=>0010101
[2,1,5,8,7,3,4,6]=>1001100=>0110011
[5,1,8,4,7,2,3,6]=>1010100=>0101011
[4,1,8,7,5,2,3,6]=>1011100=>0100011
[4,7,1,6,3,2,8,5]=>0101101=>1010010
[6,1,2,3,7,5,8,4]=>1000101=>0111010
[7,1,2,3,8,6,5,4]=>1000111=>0111000
[7,1,2,3,5,8,6,4]=>1000011=>0111100
[6,8,1,4,3,7,2,5]=>0101010=>1010101
[8,7,3,2,4,1,6,5]=>1110101=>0001010
[2,1,7,3,4,8,6,5]=>1010011=>0101100
[7,8,3,2,4,1,6,5]=>0110101=>1001010
[6,7,1,4,3,8,2,5]=>0101010=>1010101
[8,1,2,3,5,7,6,4]=>1000011=>0111100
[8,1,2,3,6,7,5,4]=>1000011=>0111100
[7,1,2,3,6,8,5,4]=>1000011=>0111100
[7,1,2,3,8,5,6,4]=>1000101=>0111010
[8,1,2,3,7,5,6,4]=>1000101=>0111010
[8,1,2,3,6,5,7,4]=>1000101=>0111010
[7,1,8,5,4,3,2,6]=>1011110=>0100001
[7,8,2,6,3,4,1,5]=>0101010=>1010101
[6,8,2,7,3,4,1,5]=>0101010=>1010101
[6,7,2,8,3,4,1,5]=>0101010=>1010101
[3,8,7,1,4,2,6,5]=>0110101=>1001010
[3,7,8,1,4,2,6,5]=>0010101=>1101010
[3,6,8,1,4,2,7,5]=>0010101=>1101010
[3,5,7,8,2,4,1,6]=>0001010=>1110101
[3,6,7,1,4,2,8,5]=>0010101=>1101010
[7,6,2,8,3,1,4,5]=>1101100=>0010011
[8,6,2,7,3,1,4,5]=>1101100=>0010011
[8,1,7,5,4,3,2,6]=>1011110=>0100001
[8,1,7,4,5,3,2,6]=>1010110=>0101001
[5,8,3,7,1,4,2,6]=>0101010=>1010101
[2,1,7,3,4,6,8,5]=>1010001=>0101110
[6,7,3,2,4,1,8,5]=>0110101=>1001010
[8,7,2,4,3,6,1,5]=>1101010=>0010101
[7,1,2,3,5,6,8,4]=>1000001=>0111110
[6,1,2,3,8,7,4,5]=>1000110=>0111001
[5,1,2,3,7,8,6,4]=>1000011=>0111100
[5,1,2,3,8,7,6,4]=>1000111=>0111000
[5,1,2,3,8,6,7,4]=>1000101=>0111010
[6,1,2,3,5,8,7,4]=>1000011=>0111100
[8,6,2,4,3,1,7,5]=>1101101=>0010010
[7,6,3,2,4,8,1,5]=>1110010=>0001101
[2,1,6,3,4,8,7,5]=>1010011=>0101100
[8,6,3,2,4,7,1,5]=>1110010=>0001101
[7,6,2,4,3,1,8,5]=>1101101=>0010010
[6,1,2,3,5,7,8,4]=>1000001=>0111110
[5,1,2,3,6,8,7,4]=>1000011=>0111100
[7,8,1,2,6,3,5,4]=>0100101=>1011010
[1,4,8,2,7,3,5,6]=>0010100=>1101011
[1,2,8,5,4,7,3,6]=>0011010=>1100101
[1,3,8,5,4,2,7,6]=>0011101=>1100010
[2,3,6,8,4,7,1,5]=>0001010=>1110101
[1,3,6,8,4,7,5,2]=>0001011=>1110100
[2,4,8,1,7,3,6,5]=>0010101=>1101010
[3,4,8,5,7,6,1,2]=>0010110=>1101001
[1,2,6,8,4,5,7,3]=>0001001=>1110110
[7,5,1,2,4,3,6,8]=>1100100=>0011011
[7,4,6,1,5,2,3,8]=>1010100=>0101011
[7,1,4,2,6,3,5,8]=>1010100=>0101011
[6,8,1,4,7,2,3,5]=>0100100=>1011011
[1,6,4,2,8,3,5,7]=>0110100=>1001011
[1,6,3,8,5,4,2,7]=>0101110=>1010001
[6,8,1,7,3,5,4,2]=>0101011=>1010100
[7,1,3,6,5,4,2,8]=>1001110=>0110001
[7,3,1,6,5,4,2,8]=>1101110=>0010001
[7,2,1,4,6,3,5,8]=>1100100=>0011011
[7,2,3,6,5,1,4,8]=>1001100=>0110011
[7,1,2,3,6,5,4,8]=>1000110=>0111001
[6,8,1,2,7,3,5,4]=>0100101=>1011010
[1,6,2,3,8,5,4,7]=>0100110=>1011001
[1,5,8,2,7,6,3,4]=>0010110=>1101001
[5,1,8,2,7,6,3,4]=>1010110=>0101001
[5,8,2,7,6,3,4,1]=>0101101=>1010010
[6,2,8,1,7,3,5,4]=>1010101=>0101010
[6,8,2,1,7,4,3,5]=>0110110=>1001001
[3,6,4,1,2,8,5,7]=>0110010=>1001101
[2,1,6,3,8,5,4,7]=>1010110=>0101001
[2,5,1,8,7,6,3,4]=>0101110=>1010001
[2,5,3,8,7,4,6,1]=>0101101=>1010010
[1,2,5,3,8,7,4,6]=>0010110=>1101001
[2,4,8,7,6,5,1,3]=>0011110=>1100001
[2,5,3,8,7,1,6,4]=>0101101=>1010010
[2,5,8,4,1,7,6,3]=>0011011=>1100100
[3,5,8,7,1,4,2,6]=>0011010=>1100101
[5,3,8,4,1,7,6,2]=>1011011=>0100100
[4,2,8,7,6,3,5,1]=>1011101=>0100010
[4,2,8,7,6,5,3,1]=>1011111=>0100000
[4,1,8,7,6,5,3,2]=>1011111=>0100000
[4,3,8,7,6,5,1,2]=>1011110=>0100001
[6,3,1,8,7,2,5,4]=>1101101=>0010010
[5,8,3,7,6,1,4,2]=>0101101=>1010010
[5,1,3,8,7,6,2,4]=>1001110=>0110001
[1,5,3,8,7,6,2,4]=>0101110=>1010001
[1,5,8,4,7,2,6,3]=>0010101=>1101010
[5,1,8,4,7,2,6,3]=>1010101=>0101010
[5,8,7,4,6,1,2,3]=>0110100=>1001011
[6,8,5,1,2,4,7,3]=>0110001=>1001110
[5,6,3,1,2,4,8,7]=>0110001=>1001110
[5,6,2,4,3,1,8,7]=>0101101=>1010010
[5,6,1,2,4,3,8,7]=>0100101=>1011010
[4,5,8,1,7,2,3,6]=>0010100=>1101011
[4,5,8,1,7,2,6,3]=>0010101=>1101010
[1,3,2,5,8,7,4,6]=>0100110=>1011001
[3,5,1,8,7,4,6,2]=>0101101=>1010010
[3,5,1,8,7,2,6,4]=>0101101=>1010010
[4,3,6,1,2,8,5,7]=>1010010=>0101101
[4,5,8,3,1,7,2,6]=>0011010=>1100101
[4,5,2,8,7,1,3,6]=>0101100=>1010011
[3,2,5,8,7,1,6,4]=>1001101=>0110010
[3,4,8,7,6,2,1,5]=>0011110=>1100001
[3,1,4,8,7,6,2,5]=>1001110=>0110001
[3,4,8,7,6,5,1,2]=>0011110=>1100001
[1,3,4,8,7,6,2,5]=>0001110=>1110001
[3,4,8,7,6,2,5,1]=>0011101=>1100010
[3,2,5,8,7,4,6,1]=>1001101=>0110010
[4,5,8,3,1,7,6,2]=>0011011=>1100100
[2,1,3,5,8,7,4,6]=>1000110=>0111001
[1,2,7,5,8,6,4,3]=>0010111=>1101000
[7,1,4,8,2,6,5,3]=>1001011=>0110100
[6,8,1,3,7,5,2,4]=>0100110=>1011001
[3,7,8,1,2,6,5,4]=>0010011=>1101100
[1,3,7,8,2,6,5,4]=>0001011=>1110100
[2,3,7,8,1,6,5,4]=>0001011=>1110100
[2,7,8,1,3,6,5,4]=>0010011=>1101100
[8,1,2,6,7,3,5,4]=>1000101=>0111010
[8,1,2,6,7,5,3,4]=>1000110=>0111001
[8,2,5,7,1,3,6,4]=>1001001=>0110110
[2,8,1,6,7,3,5,4]=>0100101=>1011010
[2,6,8,3,7,1,5,4]=>0010101=>1101010
[2,8,6,4,7,1,5,3]=>0110101=>1001010
[6,8,3,4,1,7,5,2]=>0101011=>1010100
[6,8,3,7,4,1,5,2]=>0101101=>1010010
[2,6,8,3,7,5,1,4]=>0010110=>1101001
[2,8,1,6,7,5,3,4]=>0100110=>1011001
[8,2,5,7,1,6,3,4]=>1001010=>0110101
[8,4,7,2,3,6,1,5]=>1010010=>0101101
[8,5,7,4,2,6,1,3]=>1011010=>0100101
[8,3,5,7,4,1,6,2]=>1001101=>0110010
[8,5,2,4,7,1,6,3]=>1100101=>0011010
[8,2,3,5,7,1,6,4]=>1000101=>0111010
[8,2,4,7,3,6,1,5]=>1001010=>0110101
[8,2,7,1,4,6,3,5]=>1010010=>0101101
[8,7,1,2,4,6,3,5]=>1100010=>0011101
[8,7,1,4,6,2,3,5]=>1100100=>0011011
[8,4,7,1,3,6,2,5]=>1010010=>0101101
[1,6,8,3,7,2,5,4]=>0010101=>1101010
[8,3,5,7,1,2,6,4]=>1001001=>0110110
[5,8,7,1,3,6,2,4]=>0110010=>1001101
[8,5,4,7,1,6,2,3]=>1101010=>0010101
[8,5,4,7,1,2,6,3]=>1101001=>0010110
[8,5,1,4,7,2,6,3]=>1100101=>0011010
[1,4,6,8,2,7,5,3]=>0001011=>1110100
[1,6,5,8,2,7,4,3]=>0101011=>1010100
[8,5,6,3,1,7,4,2]=>1011011=>0100100
[5,6,2,8,1,7,4,3]=>0101011=>1010100
[1,8,4,5,7,2,6,3]=>0100101=>1011010
[5,8,7,3,6,1,2,4]=>0110100=>1001011
[8,3,5,7,1,6,2,4]=>1001010=>0110101
[1,6,8,3,7,5,2,4]=>0010110=>1101001
[6,3,8,2,7,5,1,4]=>1010110=>0101001
[6,8,4,2,7,1,5,3]=>0110101=>1001010
[8,6,4,7,3,1,5,2]=>1101101=>0010010
[8,4,5,7,3,1,6,2]=>1001101=>0110010
[8,4,2,5,7,1,6,3]=>1100101=>0011010
[8,3,4,7,2,6,1,5]=>1001010=>0110101
[8,7,1,3,4,6,2,5]=>1100010=>0011101
[8,3,7,2,4,6,1,5]=>1010010=>0101101
[2,8,4,5,7,1,6,3]=>0100101=>1011010
[8,7,3,4,5,1,6,2]=>1100101=>0011010
[8,7,4,5,2,6,1,3]=>1101010=>0010101
[5,8,7,2,3,6,1,4]=>0110010=>1001101
[8,7,2,3,4,6,1,5]=>1100010=>0011101
[8,7,2,3,6,1,4,5]=>1100100=>0011011
[1,3,2,8,5,4,7,6]=>0101101=>1010010
[4,2,8,5,3,7,1,6]=>1011010=>0100101
[5,2,1,8,4,3,7,6]=>1101101=>0010010
[6,2,8,4,3,7,5,1]=>1011011=>0100100
[7,2,8,4,3,1,6,5]=>1011101=>0100010
[7,3,4,8,2,1,6,5]=>1001101=>0110010
[6,3,4,8,2,7,5,1]=>1001011=>0110100
[5,3,4,1,8,2,7,6]=>1010101=>0101010
[8,1,4,5,2,3,7,6]=>1001001=>0110110
[8,1,5,4,3,2,7,6]=>1011101=>0100010
[3,5,4,2,8,1,7,6]=>0110101=>1001010
[4,5,3,2,8,7,1,6]=>0110110=>1001001
[6,4,3,2,8,7,5,1]=>1110111=>0001000
[6,5,3,2,1,7,8,4]=>1111001=>0000110
[5,6,3,2,7,8,4,1]=>0110011=>1001100
[4,1,6,3,2,7,8,5]=>1011001=>0100110
[3,6,4,2,7,8,1,5]=>0110010=>1001101
[8,1,6,4,3,7,2,5]=>1011010=>0100101
[8,1,7,4,3,6,5,2]=>1011011=>0100100
[2,7,4,1,3,6,5,8]=>0110010=>1001101
[3,7,4,2,6,1,5,8]=>0110100=>1001011
[4,1,7,3,2,6,5,8]=>1011010=>0100101
[5,7,3,2,6,4,8,1]=>0110101=>1001010
[6,7,3,2,5,4,1,8]=>0110110=>1001001
[7,6,3,2,1,5,4,8]=>1111010=>0000101
[4,7,5,6,2,3,8,1]=>0101001=>1010110
[3,1,7,5,6,2,4,8]=>1010100=>0101011
[2,7,5,6,1,3,4,8]=>0101000=>1010111
[2,6,5,7,1,3,8,4]=>0101001=>1010110
[4,6,5,7,2,8,1,3]=>0101010=>1010101
[5,6,4,7,2,8,3,1]=>0101011=>1010100
[6,5,4,1,7,2,8,3]=>1110101=>0001010
[7,5,4,6,2,1,8,3]=>1101101=>0010010
[6,4,5,7,1,8,2,3]=>1001010=>0110101
[5,4,6,1,7,8,2,3]=>1010010=>0101101
[8,1,5,6,7,2,3,4]=>1000100=>0111011
[2,1,4,6,8,7,3,5]=>1000110=>0111001
[3,4,6,8,7,1,2,5]=>0001100=>1110011
[4,3,1,6,8,7,2,5]=>1100110=>0011001
[5,3,6,8,7,2,4,1]=>1001101=>0110010
[6,3,5,1,8,7,2,4]=>1010110=>0101001
[7,3,5,8,6,2,1,4]=>1001110=>0110001
[7,2,8,5,6,3,1,4]=>1010110=>0101001
[6,2,8,5,1,7,3,4]=>1011010=>0100101
[4,2,1,8,6,7,3,5]=>1101010=>0010101
[1,3,2,8,6,7,4,5]=>0101010=>1010101
[2,3,8,6,7,1,4,5]=>0010100=>1101011
[8,1,3,2,6,7,4,5]=>1010010=>0101101
[2,3,8,7,1,6,5,4]=>0011011=>1100100
[4,2,8,7,6,1,5,3]=>1011101=>0100010
[5,2,8,7,6,4,1,3]=>1011110=>0100001
[7,2,1,8,6,5,4,3]=>1101111=>0010000
[7,3,6,1,8,5,4,2]=>1010111=>0101000
[6,3,7,8,5,4,2,1]=>1001111=>0110000
[5,3,7,8,6,4,1,2]=>1001110=>0110001
[4,3,1,7,8,6,5,2]=>1100111=>0011000
[3,4,7,8,6,1,5,2]=>0001101=>1110010
[8,1,5,7,6,2,4,3]=>1001101=>0110010
[3,5,7,6,8,1,4,2]=>0010101=>1101010
[4,5,7,6,8,3,1,2]=>0010110=>1101001
[5,4,1,7,6,8,3,2]=>1101011=>0010100
[6,4,7,5,8,3,2,1]=>1010111=>0101000
[7,4,6,5,1,8,3,2]=>1011011=>0100100
[7,5,6,4,3,1,8,2]=>1011101=>0100010
[6,5,1,7,4,3,8,2]=>1101101=>0010010
[4,6,7,5,3,8,1,2]=>0011010=>1100101
[3,6,7,5,1,4,8,2]=>0011001=>1100110
[8,1,6,7,5,4,2,3]=>1001110=>0110001
[8,1,7,6,5,4,3,2]=>1011111=>0100000
[2,7,6,1,5,4,3,8]=>0110110=>1001001
[3,7,6,5,1,4,2,8]=>0111010=>1000101
[4,7,6,5,3,1,2,8]=>0111100=>1000011
[8,6,4,3,1,5,7,2]=>1111001=>0000110
[8,6,4,1,5,2,7,3]=>1110101=>0001010
[8,6,5,1,3,2,7,4]=>1110101=>0001010
[8,6,3,1,7,2,4,5]=>1110100=>0001011
[8,7,3,1,5,2,4,6]=>1110100=>0001011
[5,3,1,7,2,4,6,8]=>1101000=>0010111
[8,7,1,2,4,5,3,6]=>1100010=>0011101
[8,6,1,2,4,7,3,5]=>1100010=>0011101
[8,5,1,2,6,7,3,4]=>1100010=>0011101
[8,5,1,6,4,2,7,3]=>1101101=>0010010
[8,5,1,3,6,4,7,2]=>1100101=>0011010
[8,6,1,5,3,4,7,2]=>1101001=>0010110
[8,6,1,5,2,4,7,3]=>1101001=>0010110
[8,6,1,2,5,7,3,4]=>1100010=>0011101
[8,6,1,2,7,4,3,5]=>1100110=>0011001
[8,7,1,2,5,4,3,6]=>1100110=>0011001
[5,1,4,2,3,8,6,7]=>1010010=>0101101
[5,1,4,2,7,3,6,8]=>1010100=>0101011
[7,1,5,8,2,6,3,4]=>1001010=>0110101
[5,7,8,1,2,4,6,3]=>0010001=>1101110
[5,7,8,1,3,4,6,2]=>0010001=>1101110
[5,8,1,7,3,4,6,2]=>0101001=>1010110
[8,1,5,7,2,4,6,3]=>1001001=>0110110
[8,4,1,2,7,6,3,5]=>1100110=>0011001
[1,4,2,3,8,7,5,6]=>0100110=>1011001
[1,4,2,7,6,3,5,8]=>0101100=>1010011
[6,1,2,8,7,5,3,4]=>1001110=>0110001
[6,1,2,4,8,7,5,3]=>1000111=>0111000
[3,1,8,4,6,7,5,2]=>1010011=>0101100
[3,1,7,6,4,8,5,2]=>1011011=>0100100
[7,1,2,4,6,8,5,3]=>1000011=>0111100
[7,1,2,6,8,5,3,4]=>1000110=>0111001
[6,1,2,7,8,5,3,4]=>1000110=>0111001
[6,1,2,7,4,8,5,3]=>1001011=>0110100
[3,1,6,4,7,8,5,2]=>1010011=>0101100
[5,7,1,3,8,4,6,2]=>0100101=>1011010
[5,7,1,8,4,2,6,3]=>0101101=>1010010
[7,1,5,3,2,8,6,4]=>1011011=>0100100
[7,1,4,5,2,8,6,3]=>1001011=>0110100
[4,7,3,1,5,8,6,2]=>0110011=>1001100
[4,8,7,3,1,5,6,2]=>0111001=>1000110
[8,1,7,4,5,2,6,3]=>1010101=>0101010
[8,1,7,5,3,2,6,4]=>1011101=>0100010
[8,3,7,1,2,6,4,5]=>1010010=>0101101
[3,1,2,8,4,7,5,6]=>1001010=>0110101
[3,1,2,8,6,4,5,7]=>1001100=>0110011
[3,1,7,2,6,4,5,8]=>1010100=>0101011
[1,4,2,3,8,6,5,7]=>0100110=>1011001
[1,4,2,3,8,5,7,6]=>0100101=>1011010
[5,8,1,7,2,4,6,3]=>0101001=>1010110
[5,8,1,3,4,7,6,2]=>0100011=>1011100
[3,1,8,6,4,7,5,2]=>1011011=>0100100
[8,1,2,6,7,4,5,3]=>1000101=>0111010
[6,1,2,8,7,3,5,4]=>1001101=>0110010
[1,2,3,5,8,4,7,6]=>0000101=>1111010
[1,2,3,5,8,6,4,7]=>0000110=>1111001
[7,1,2,8,3,6,5,4]=>1001011=>0110100
[7,1,2,8,6,4,5,3]=>1001101=>0110010
[3,1,7,8,4,6,5,2]=>1001011=>0110100
[3,1,8,7,6,4,5,2]=>1011101=>0100010
[8,1,2,7,4,6,5,3]=>1001011=>0110100
[8,1,2,7,3,6,5,4]=>1001011=>0110100
[1,2,3,5,8,7,4,6]=>0000110=>1111001
[1,2,3,6,8,5,4,7]=>0000110=>1111001
[7,8,5,6,3,1,4,2]=>0101101=>1010010
[7,8,5,3,6,1,2,4]=>0110100=>1001011
[7,5,6,3,1,4,2,8]=>1011010=>0100101
[7,5,8,3,1,4,2,6]=>1011010=>0100101
[7,8,5,3,1,4,2,6]=>0111010=>1000101
[7,8,5,3,1,6,2,4]=>0111010=>1000101
[7,8,5,3,1,6,4,2]=>0111011=>1000100
[7,8,5,3,6,1,4,2]=>0110101=>1001010
[7,8,5,3,6,4,1,2]=>0110110=>1001001
[7,8,5,3,4,1,6,2]=>0110101=>1001010
[7,8,5,3,1,4,6,2]=>0111001=>1000110
[7,8,5,3,1,2,6,4]=>0111001=>1000110
[7,5,3,8,1,2,6,4]=>1101001=>0010110
[7,5,8,3,4,1,6,2]=>1010101=>0101010
[7,5,8,3,4,6,1,2]=>1010010=>0101101
[7,5,6,3,4,1,8,2]=>1010101=>0101010
[7,5,6,3,1,4,8,2]=>1011001=>0100110
[7,5,6,3,1,2,8,4]=>1011001=>0100110
[7,5,3,6,1,2,8,4]=>1101001=>0010110
[7,5,3,4,1,2,8,6]=>1101001=>0010110
[7,5,3,1,4,2,6,8]=>1110100=>0001011
[7,5,3,1,4,2,8,6]=>1110101=>0001010
[7,5,3,1,6,2,8,4]=>1110101=>0001010
[7,5,3,1,6,4,8,2]=>1110101=>0001010
[7,5,3,6,1,4,8,2]=>1101001=>0010110
[7,5,3,6,4,1,8,2]=>1101101=>0010010
[7,5,3,6,4,8,1,2]=>1101010=>0010101
[7,5,3,8,4,6,1,2]=>1101010=>0010101
[7,5,3,8,1,4,6,2]=>1101001=>0010110
[7,5,3,1,8,4,6,2]=>1110101=>0001010
[7,5,3,1,8,2,6,4]=>1110101=>0001010
[7,5,3,1,8,2,4,6]=>1110100=>0001011
[7,5,3,1,6,2,4,8]=>1110100=>0001011
[7,5,3,1,6,4,2,8]=>1110110=>0001001
[7,5,3,1,8,4,2,6]=>1110110=>0001001
[7,5,3,1,8,6,2,4]=>1110110=>0001001
[7,5,3,8,1,6,4,2]=>1101011=>0010100
[7,5,3,8,6,1,4,2]=>1101101=>0010010
[7,5,3,8,6,4,1,2]=>1101110=>0010001
[7,5,8,3,6,4,1,2]=>1010110=>0101001
[7,5,8,3,6,1,4,2]=>1010101=>0101010
[7,5,8,3,1,6,4,2]=>1011011=>0100100
[7,5,8,3,1,6,2,4]=>1011010=>0100101
[7,5,3,6,1,4,2,8]=>1101010=>0010101
[7,5,3,6,4,1,2,8]=>1101100=>0010011
[7,5,3,8,4,1,2,6]=>1101100=>0010011
[7,5,8,6,3,1,2,4]=>1011100=>0100011
[7,5,8,6,3,1,4,2]=>1011101=>0100010
[7,5,8,6,3,4,1,2]=>1011010=>0100101
[7,5,6,8,3,1,4,2]=>1001101=>0110010
[7,5,6,3,8,1,2,4]=>1010100=>0101011
[7,5,3,4,1,6,2,8]=>1101010=>0010101
[7,5,3,4,1,8,2,6]=>1101010=>0010101
[7,5,6,3,1,8,2,4]=>1011010=>0100101
[7,5,6,3,1,8,4,2]=>1011011=>0100100
[7,5,6,3,8,1,4,2]=>1010101=>0101010
[7,5,6,3,8,4,1,2]=>1010110=>0101001
[7,5,3,6,8,4,1,2]=>1100110=>0011001
[7,5,3,6,8,1,4,2]=>1100101=>0011010
[7,5,3,6,1,8,4,2]=>1101011=>0010100
[7,5,3,1,6,8,4,2]=>1110011=>0001100
[7,5,3,1,6,8,2,4]=>1110010=>0001101
[7,5,3,1,4,8,2,6]=>1110010=>0001101
[7,5,3,1,4,6,2,8]=>1110010=>0001101
[7,5,3,1,2,6,4,8]=>1110010=>0001101
[7,5,3,1,2,8,4,6]=>1110010=>0001101
[7,5,3,1,2,8,6,4]=>1110011=>0001100
[7,5,3,1,4,8,6,2]=>1110011=>0001100
[7,5,3,4,1,8,6,2]=>1101011=>0010100
[7,5,3,4,8,1,6,2]=>1100101=>0011010
[7,5,3,4,8,6,1,2]=>1100110=>0011001
[7,5,3,4,6,1,8,2]=>1100101=>0011010
[7,5,3,4,1,6,8,2]=>1101001=>0010110
[7,5,3,1,4,6,8,2]=>1110001=>0001110
[7,5,3,1,2,6,8,4]=>1110001=>0001110
[7,5,3,1,2,4,8,6]=>1110001=>0001110
[3,6,2,5,4,1,8,7]=>0101101=>1010010
[3,5,2,8,4,7,6,1]=>0101011=>1010100
[5,4,7,3,2,8,6,1]=>1011011=>0100100
[5,4,8,3,2,7,6,1]=>1011011=>0100100
[6,4,5,3,2,1,8,7]=>1011101=>0100010
[5,3,2,6,4,1,8,7]=>1101101=>0010010
[4,5,8,3,2,7,6,1]=>0011011=>1100100
[4,7,6,3,8,5,2,1]=>0110111=>1001000
[4,8,6,3,7,5,2,1]=>0110111=>1001000
[4,8,5,3,2,7,6,1]=>0111011=>1000100
[5,8,4,3,2,7,6,1]=>0111011=>1000100
[5,3,2,8,4,7,6,1]=>1101011=>0010100
[2,1,5,8,4,7,6,3]=>1001011=>0110100
[5,3,2,7,4,8,6,1]=>1101011=>0010100
[5,7,4,3,2,8,6,1]=>0111011=>1000100
[4,7,5,3,2,8,6,1]=>0111011=>1000100
[4,7,8,3,6,5,2,1]=>0010111=>1101000
[4,6,8,3,7,5,2,1]=>0010111=>1101000
[7,6,4,3,8,5,2,1]=>1110111=>0001000
[7,3,2,6,8,5,4,1]=>1100111=>0011000
[2,1,8,6,7,5,4,3]=>1010111=>0101000
[8,3,2,6,7,5,4,1]=>1100111=>0011000
[8,6,4,3,7,5,2,1]=>1110111=>0001000
[8,5,7,6,4,3,2,1]=>1011111=>0100000
[8,4,5,3,2,7,6,1]=>1011011=>0100100
[8,4,7,3,6,5,2,1]=>1010111=>0101000
[8,4,6,3,7,5,2,1]=>1010111=>0101000
[7,4,6,3,8,5,2,1]=>1010111=>0101000
[3,7,2,6,8,5,4,1]=>0100111=>1011000
[3,8,2,6,7,5,4,1]=>0100111=>1011000
[3,8,2,5,4,7,6,1]=>0101011=>1010100
[3,7,2,8,6,5,4,1]=>0101111=>1010000
[3,6,2,8,7,5,4,1]=>0101111=>1010000
[6,4,7,3,8,5,2,1]=>1010111=>0101000
[6,4,8,3,7,5,2,1]=>1010111=>0101000
[7,4,8,3,6,5,2,1]=>1010111=>0101000
[7,4,5,3,2,8,6,1]=>1011011=>0100100
[7,5,4,3,2,8,6,1]=>1111011=>0000100
[7,3,2,5,4,8,6,1]=>1101011=>0010100
[2,1,7,5,4,8,6,3]=>1011011=>0100100
[7,3,2,8,6,5,4,1]=>1101111=>0010000
[7,8,4,3,6,5,2,1]=>0110111=>1001000
[6,8,5,7,4,3,2,1]=>0101111=>1010000
[6,8,4,3,7,5,2,1]=>0110111=>1001000
[6,3,2,8,7,5,4,1]=>1101111=>0010000
[6,3,2,7,8,5,4,1]=>1100111=>0011000
[6,7,4,3,8,5,2,1]=>0110111=>1001000
[2,3,1,4,5,6,7,8,9]=>01000000=>10111111
[2,3,4,1,5,6,7,8,9]=>00100000=>11011111
[2,3,4,5,1,6,7,8,9]=>00010000=>11101111
[2,3,4,5,6,1,7,8,9]=>00001000=>11110111
[2,3,1,4,5,6,7,8,9,10]=>010000000=>101111111
[2,4,3,1,5,6,7,8,9]=>01100000=>10011111
[2,3,4,1,5,6,7,8,9,10]=>001000000=>110111111
[2,3,5,4,1,6,7,8,9]=>00110000=>11001111
[2,3,4,5,1,6,7,8,9,10]=>000100000=>111011111
[2,3,4,6,5,1,7,8,9]=>00011000=>11100111
[2,3,4,5,6,1,7,8,9,10]=>000010000=>111101111
[2,3,4,5,7,6,1,8,9]=>00001100=>11110011
[2,3,4,5,6,7,1,8,9,10]=>000001000=>111110111
[2,3,4,5,6,8,7,1,9]=>00000110=>11111001
[2,3,4,5,6,7,8,1,9,10]=>000000100=>111111011
[2,3,4,5,6,7,9,8,1]=>00000011=>11111100
[4,6,8,3,5,7,1,2]=>0010010=>1101101
[6,8,1,2,4,5,7,3]=>0100001=>1011110
[3,5,8,2,4,7,1,6]=>0010010=>1101101
[8,3,5,2,4,1,6,7]=>1010100=>0101011
[4,2,5,7,3,6,1,8]=>1001010=>0110101
[4,5,2,8,3,1,6,7]=>0101100=>1010011
[4,2,5,8,3,7,1,6]=>1001010=>0110101
[2,1,6,8,4,7,3,5]=>1001010=>0110101
[1,2,5,8,3,6,7,4]=>0001001=>1110110
[5,3,6,8,4,7,1,2]=>1001010=>0110101
[1,6,5,8,2,4,7,3]=>0101001=>1010110
[3,1,2,6,8,5,7,4]=>1000101=>0111010
[1,4,3,8,2,6,7,5]=>0101001=>1010110
[5,4,8,3,2,1,6,7]=>1011100=>0100011
[5,4,3,7,2,6,1,8]=>1101010=>0010101
[4,3,6,2,7,5,1,8]=>1010110=>0101001
[4,6,3,2,1,8,5,7]=>0111010=>1000101
[4,1,7,3,2,5,8,6]=>1011001=>0100110
[4,3,1,7,8,2,6,5]=>1100101=>0011010
[3,5,1,2,7,8,6,4]=>0100011=>1011100
[7,5,1,4,8,2,6,3]=>1100101=>0011010
[5,4,7,3,8,6,1,2]=>1010110=>0101001
[5,8,4,7,6,3,1,2]=>0101110=>1010001
[5,8,7,1,4,2,6,3]=>0110101=>1001010
[8,3,5,1,2,7,6,4]=>1010011=>0101100
[4,8,3,1,7,2,6,5]=>0110101=>1001010
[1,8,4,3,5,2,7,6]=>0110101=>1001010
[4,6,3,1,5,2,8,7]=>0110101=>1001010
[4,7,3,6,5,2,1,8]=>0101110=>1010001
[5,3,7,6,4,2,1,8]=>1011110=>0100001
[1,6,3,4,2,8,7,5]=>0101011=>1010100
[1,8,3,6,2,7,5,4]=>0101011=>1010100
[1,6,8,7,4,2,5,3]=>0011101=>1100010
[6,4,8,7,5,3,1,2]=>1011110=>0100001
[7,6,4,3,8,5,1,2]=>1110110=>0001001
[1,7,6,2,8,4,5,3]=>0110101=>1001010
[7,1,3,2,6,8,5,4]=>1010011=>0101100
[1,5,3,2,7,4,8,6]=>0110101=>1001010
[6,3,2,1,8,5,4,7]=>1110110=>0001001
[6,5,3,2,7,4,1,8]=>1110110=>0001001
[5,2,6,3,7,4,1,8]=>1010110=>0101001
[2,8,5,3,1,6,4,7]=>0111010=>1000101
[2,1,7,3,8,5,4,6]=>1010110=>0101001
[1,6,2,3,7,8,5,4]=>0100011=>1011100
[1,6,7,2,8,4,5,3]=>0010101=>1101010
[5,7,1,8,2,4,6,3]=>0101001=>1010110
[5,1,2,7,8,3,6,4]=>1000101=>0111010
[2,4,1,7,8,6,3,5]=>0100110=>1011001
[4,2,1,7,3,8,5,6]=>1101010=>0010101
[6,2,8,4,3,1,5,7]=>1011100=>0100011
[7,3,2,1,8,4,5,6]=>1110100=>0001011
[7,8,3,2,5,6,1,4]=>0110010=>1001101
[7,1,8,2,4,5,6,3]=>1010001=>0101110
[8,7,6,1,2,4,5,3]=>1110001=>0001110
[8,3,7,6,2,1,4,5]=>1011100=>0100011
[3,2,8,7,5,1,4,6]=>1011100=>0100011
[8,3,6,5,2,1,4,7]=>1011100=>0100011
[7,6,3,5,2,4,1,8]=>1101010=>0010101
[7,4,6,2,5,3,1,8]=>1010110=>0101001
[8,2,4,1,6,5,3,7]=>1010110=>0101001
[4,2,8,1,7,5,3,6]=>1010110=>0101001
[8,2,4,1,7,6,3,5]=>1010110=>0101001
[8,7,1,5,6,2,4,3]=>1100101=>0011010
[8,5,7,3,6,4,1,2]=>1010110=>0101001
[6,8,3,7,5,4,1,2]=>0101110=>1010001
[8,1,6,7,5,2,4,3]=>1001101=>0110010
[8,1,2,6,4,3,7,5]=>1001101=>0110010
[2,8,1,7,5,4,3,6]=>0101110=>1010001
[2,5,1,8,6,4,3,7]=>0101110=>1010001
[5,7,2,6,4,3,1,8]=>0101110=>1010001
[6,2,7,5,4,3,1,8]=>1011110=>0100001
[2,1,8,6,5,4,3,7]=>1011110=>0100001
[1,2,7,5,4,3,8,6]=>0011101=>1100010
[1,7,2,4,3,8,6,5]=>0101011=>1010100
[1,7,2,8,3,6,5,4]=>0101011=>1010100
[1,7,8,6,5,2,4,3]=>0011101=>1100010
[7,3,8,6,5,4,1,2]=>1011110=>0100001
[1,8,7,6,5,2,4,3]=>0111101=>1000010
[8,1,7,3,2,6,5,4]=>1011011=>0100100
[5,1,4,3,2,8,7,6]=>1011011=>0100100
[8,6,5,3,2,1,7,4]=>1111101=>0000010
[8,6,3,2,1,7,4,5]=>1111010=>0000101
[8,6,5,4,1,7,2,3]=>1111010=>0000101
[8,6,5,1,7,3,2,4]=>1110110=>0001001
[8,6,1,7,4,3,2,5]=>1101110=>0010001
[4,6,3,2,7,5,1,8]=>0110110=>1001001
[1,4,3,7,2,5,8,6]=>0101001=>1010110
[7,4,8,3,1,6,2,5]=>1011010=>0100101
[7,1,5,8,3,2,6,4]=>1001101=>0110010
[5,7,4,1,8,2,6,3]=>0110101=>1001010
[5,7,4,3,1,8,6,2]=>0111011=>1000100
[1,8,7,2,5,4,6,3]=>0110101=>1001010
[1,8,5,3,7,2,6,4]=>0110101=>1001010
[4,3,1,8,7,5,2,6]=>1101110=>0010001
[1,4,8,6,3,5,2,7]=>0011010=>1100101
[7,4,6,3,5,2,1,8]=>1010110=>0101001
[1,3,5,6,8,4,2,7]=>0000110=>1111001
[3,5,4,8,7,1,2,6]=>0101100=>1010011
[3,1,4,6,8,7,2,5]=>1000110=>0111001
[1,6,3,8,7,2,5,4]=>0101101=>1010010
[1,6,2,4,8,7,5,3]=>0100111=>1011000
[8,4,1,6,7,5,3,2]=>1100111=>0011000
[7,1,6,4,8,5,2,3]=>1010110=>0101001
[7,3,6,8,5,1,2,4]=>1001100=>0110011
[1,3,7,2,6,8,4,5]=>0010010=>1101101
[3,6,5,2,8,1,4,7]=>0110100=>1001011
[3,6,5,7,2,4,1,8]=>0101010=>1010101
[4,2,6,3,8,1,5,7]=>1010100=>0101011
[4,2,6,7,3,5,1,8]=>1001010=>0110101
[3,6,2,4,7,5,1,8]=>0100110=>1011001
[3,6,2,4,1,8,5,7]=>0101010=>1010101
[7,3,8,2,1,6,4,5]=>1011010=>0100101
[7,3,5,2,1,8,6,4]=>1011011=>0100100
[8,7,6,4,3,1,5,2]=>1111101=>0000010
[8,7,6,4,1,5,2,3]=>1111010=>0000101
[3,8,7,2,1,4,6,5]=>0111001=>1000110
[3,8,2,7,1,5,4,6]=>0101010=>1010101
[3,6,8,2,1,5,4,7]=>0011010=>1100101
[2,4,8,1,6,5,3,7]=>0010110=>1101001
[4,2,8,1,5,7,3,6]=>1010010=>0101101
[8,5,7,6,1,4,2,3]=>1011010=>0100101
[8,6,1,7,3,5,4,2]=>1101011=>0010100
[8,6,1,7,5,4,2,3]=>1101110=>0010001
[1,6,2,8,7,3,5,4]=>0101101=>1010010
[1,8,2,4,6,7,3,5]=>0100010=>1011101
[2,8,5,4,7,1,3,6]=>0110100=>1001011
[2,1,5,8,6,4,3,7]=>1001110=>0110001
[7,2,5,6,4,3,1,8]=>1001110=>0110001
[1,2,5,7,8,4,3,6]=>0000110=>1111001
[1,2,7,4,8,6,3,5]=>0010110=>1101001
[1,2,7,8,3,6,5,4]=>0001011=>1110100
[7,1,8,6,3,5,4,2]=>1011011=>0100100
[1,8,7,6,3,5,2,4]=>0111010=>1000101
[1,8,7,4,6,3,2,5]=>0110110=>1001001
[7,1,5,8,3,4,6,2]=>1001001=>0110110
[7,1,6,4,2,3,5,8]=>1011000=>0100111
[8,6,2,4,7,3,5,1]=>1100101=>0011010
[8,6,2,4,5,7,3,1]=>1100011=>0011100
[2,7,1,4,5,8,3,6]=>0100010=>1011101
[7,1,6,4,5,2,3,8]=>1010100=>0101011
[7,1,4,5,6,8,2,3]=>1000010=>0111101
[7,1,4,6,5,8,3,2]=>1001011=>0110100
[7,1,2,3,8,5,4,6]=>1000110=>0111001
[7,1,5,4,3,8,2,6]=>1011010=>0100101
[7,1,3,4,2,6,8,5]=>1001001=>0110110
[7,1,5,4,6,2,8,3]=>1010101=>0101010
[7,1,5,6,4,3,8,2]=>1001101=>0110010
[7,1,6,5,4,3,2,8]=>1011110=>0100001
[8,6,2,5,4,3,7,1]=>1101101=>0010010
[2,5,1,7,4,3,6,8]=>0101100=>1010011
[2,5,1,4,7,8,6,3]=>0100011=>1011100
[3,5,1,4,8,6,2,7]=>0100110=>1011001
[3,6,2,4,7,8,1,5]=>0100010=>1011101
[5,6,2,4,8,7,1,3]=>0100110=>1011001
[6,3,8,2,4,7,1,5]=>1010010=>0101101
[6,5,8,7,2,3,1,4]=>1011010=>0100101
[6,5,7,8,2,4,1,3]=>1001010=>0110101
[6,3,4,2,8,5,1,7]=>1010110=>0101001
[3,4,7,2,5,8,1,6]=>0010010=>1101101
[4,6,8,1,3,5,2,7]=>0010010=>1101101
[4,3,8,1,2,7,5,6]=>1010010=>0101101
[3,6,4,1,7,2,5,8]=>0110100=>1001011
[2,8,3,1,5,6,4,7]=>0110010=>1001101
[3,8,7,1,5,4,2,6]=>0110110=>1001001
[4,3,1,7,6,8,2,5]=>1101010=>0010101
[3,4,1,7,5,6,8,2]=>0101001=>1010110
[3,4,1,5,7,6,2,8]=>0100110=>1011001
[3,7,4,1,6,2,8,5]=>0110101=>1001010
[8,4,7,2,5,3,6,1]=>1010101=>0101010
[4,7,8,1,2,3,6,5]=>0010001=>1101110
[2,8,6,1,5,3,7,4]=>0110101=>1001010
[7,6,5,1,3,8,2,4]=>1110010=>0001101
[7,6,5,1,3,4,8,2]=>1110001=>0001110
[7,2,6,4,1,3,8,5]=>1011001=>0100110
[6,7,5,2,1,3,8,4]=>0111001=>1000110
[8,4,5,3,7,2,6,1]=>1010101=>0101010
[4,7,5,2,8,1,6,3]=>0110101=>1001010
[2,6,4,3,1,5,7,8]=>0111000=>1000111
[7,3,8,4,1,5,2,6]=>1011010=>0100101
[7,2,3,4,1,6,5,8]=>1001010=>0110101
[4,2,8,3,6,1,5,7]=>1010100=>0101011
[6,8,5,7,2,1,3,4]=>0101100=>1010011
[4,8,5,2,7,1,3,6]=>0110100=>1001011
[6,3,5,2,1,7,4,8]=>1011010=>0100101
[6,8,5,3,1,4,2,7]=>0111010=>1000101
[3,6,5,4,2,8,1,7]=>0111010=>1000101
[1,6,4,7,2,5,3,8]=>0101010=>1010101
[1,6,4,8,2,5,3,7]=>0101010=>1010101
[1,6,5,8,2,4,3,7]=>0101010=>1010101
[1,6,8,2,4,3,7,5]=>0010101=>1101010
[1,6,2,4,3,7,8,5]=>0101001=>1010110
[1,5,6,2,4,7,3,8]=>0010010=>1101101
[1,5,6,2,4,7,8,3]=>0010001=>1101110
[1,5,8,2,4,7,3,6]=>0010010=>1101101
[1,5,7,2,4,8,3,6]=>0010010=>1101101
[1,6,5,7,2,4,3,8]=>0101010=>1010101
[1,6,7,2,4,3,8,5]=>0010101=>1101010
[1,5,6,7,2,4,8,3]=>0001001=>1110110
[1,5,8,2,4,6,7,3]=>0010001=>1101110
[1,5,7,2,4,6,8,3]=>0010001=>1101110
[1,5,7,8,3,2,4,6]=>0001100=>1110011
[1,5,8,3,2,4,6,7]=>0011000=>1100111
[1,5,6,2,4,8,3,7]=>0010010=>1101101
[1,7,6,2,8,3,4,5]=>0110100=>1001011
[1,7,3,4,2,8,6,5]=>0101011=>1010100
[1,6,2,4,3,8,7,5]=>0101011=>1010100
[1,5,6,2,4,8,7,3]=>0010011=>1101100
[1,5,8,7,3,2,4,6]=>0011100=>1100011
[1,4,2,3,5,8,7,6]=>0100011=>1011100
[1,5,2,3,4,8,7,6]=>0100011=>1011100
[1,6,5,2,3,8,7,4]=>0110011=>1001100
[1,7,4,2,8,6,5,3]=>0110111=>1001000
[1,7,6,5,2,8,4,3]=>0111011=>1000100
[1,6,7,5,2,3,8,4]=>0011001=>1100110
[1,7,5,2,8,4,3,6]=>0110110=>1001001
[1,7,5,6,2,8,3,4]=>0101010=>1010101
[1,5,7,6,2,4,8,3]=>0011001=>1100110
[1,5,8,3,2,4,7,6]=>0011001=>1100110
[1,6,5,2,3,7,4,8]=>0110010=>1001101
[1,6,5,2,3,7,8,4]=>0110001=>1001110
[1,6,8,4,2,3,7,5]=>0011001=>1100110
[1,7,4,6,2,8,3,5]=>0101010=>1010101
[1,7,3,5,2,8,4,6]=>0101010=>1010101
[1,6,8,5,2,3,7,4]=>0011001=>1100110
[1,6,4,2,3,7,8,5]=>0110001=>1001110
[1,6,4,2,3,7,5,8]=>0110010=>1001101
[1,5,8,6,2,4,7,3]=>0011001=>1100110
[1,5,7,3,2,4,8,6]=>0011001=>1100110
[1,7,3,4,2,8,5,6]=>0101010=>1010101
[1,7,4,2,8,5,3,6]=>0110110=>1001001
[1,6,7,4,2,3,8,5]=>0011001=>1100110
[1,6,4,2,3,8,5,7]=>0110010=>1001101
[1,7,6,4,2,8,5,3]=>0111011=>1000100
[1,7,5,2,8,6,4,3]=>0110111=>1001000
[1,6,4,2,3,8,7,5]=>0110011=>1001100
[7,3,5,6,1,4,8,2]=>1001001=>0110110
[3,7,5,6,1,4,8,2]=>0101001=>1010110
[8,2,4,1,6,7,5,3]=>1010011=>0101100
[8,6,1,4,2,7,5,3]=>1101011=>0010100
[3,6,1,4,2,8,5,7]=>0101010=>1010101
[1,6,7,4,3,5,8,2]=>0011001=>1100110
[6,7,1,4,3,5,8,2]=>0101001=>1010110
[7,6,1,4,3,5,8,2]=>1101001=>0010110
[3,5,4,1,6,7,8,2]=>0110001=>1001110
[4,7,1,6,3,5,8,2]=>0101001=>1010110
[3,1,4,7,6,5,8,2]=>1001101=>0110010
[6,1,7,4,3,5,8,2]=>1011001=>0100110
[7,1,6,4,3,5,8,2]=>1011001=>0100110
[1,7,6,4,3,5,8,2]=>0111001=>1000110
[8,1,6,4,2,7,5,3]=>1011011=>0100100
[8,4,1,3,7,2,5,6]=>1100100=>0011011
[4,7,1,3,8,2,5,6]=>0100100=>1011011
[7,4,1,3,8,2,5,6]=>1100100=>0011011
[1,3,6,4,2,8,5,7]=>0011010=>1100101
[4,7,3,1,2,8,5,6]=>0110010=>1001101
[4,7,8,1,2,6,5,3]=>0010011=>1101100
[6,8,1,4,2,7,5,3]=>0101011=>1010100
[1,8,6,4,2,7,5,3]=>0111011=>1000100
[4,8,1,3,7,2,5,6]=>0100100=>1011011
[8,7,1,3,6,2,5,4]=>1100101=>0011010
[6,8,5,7,3,2,1,4]=>0101110=>1010001
[1,8,4,3,7,2,5,6]=>0110100=>1001011
[2,8,3,4,7,6,1,5]=>0100110=>1011001
[3,7,8,4,6,2,1,5]=>0010110=>1101001
[3,7,4,6,8,2,1,5]=>0100110=>1011001
[2,4,3,7,8,6,1,5]=>0100110=>1011001
[1,4,7,3,8,2,5,6]=>0010100=>1101011
[5,7,6,8,3,2,1,4]=>0101110=>1010001
[2,5,3,4,8,6,1,7]=>0100110=>1011001
[3,7,5,4,8,2,1,6]=>0110110=>1001001
[7,1,3,4,2,8,5,6]=>1001010=>0110101
[6,1,4,3,8,2,5,7]=>1010100=>0101011
[4,1,7,3,8,2,5,6]=>1010100=>0101011
[8,1,4,3,7,2,5,6]=>1010100=>0101011
[8,2,3,4,7,6,1,5]=>1000110=>0111001
[4,2,3,7,8,6,1,5]=>1000110=>0111001
[5,2,3,4,8,6,1,7]=>1000110=>0111001
[2,7,5,6,3,8,1,4]=>0101010=>1010101
[5,7,2,6,3,8,1,4]=>0101010=>1010101
[5,7,2,6,8,4,1,3]=>0100110=>1011001
[7,2,5,6,8,4,1,3]=>1000110=>0111001
[4,2,3,8,5,6,1,7]=>1001010=>0110101
[5,2,3,8,7,6,1,4]=>1001110=>0110001
[8,2,3,7,5,6,1,4]=>1001010=>0110101
[6,1,8,3,7,2,5,4]=>1010101=>0101010
[1,7,8,4,2,6,5,3]=>0011011=>1100100
[4,7,1,8,2,5,6,3]=>0101001=>1010110
[3,7,4,8,5,2,1,6]=>0101110=>1010001
[2,4,3,8,5,6,1,7]=>0101010=>1010101
[1,4,8,3,6,2,5,7]=>0010100=>1101011
[7,5,8,6,3,2,1,4]=>1011110=>0100001
[6,5,8,7,3,2,1,4]=>1011110=>0100001
[8,5,7,6,3,2,1,4]=>1011110=>0100001
[2,5,3,8,7,6,1,4]=>0101110=>1010001
[3,7,5,8,6,2,1,4]=>0101110=>1010001
[3,7,8,6,5,2,1,4]=>0011110=>1100001
[1,8,7,3,6,2,5,4]=>0110101=>1001010
[6,8,7,5,3,2,1,4]=>0111110=>1000001
[5,7,6,8,3,4,1,2]=>0101010=>1010101
[3,7,6,8,4,5,1,2]=>0101010=>1010101
[1,5,4,7,6,8,2,3]=>0101010=>1010101
[1,7,4,6,5,8,2,3]=>0101010=>1010101
[3,7,4,6,5,8,1,2]=>0101010=>1010101
[3,5,4,8,6,7,1,2]=>0101010=>1010101
[3,8,4,6,5,7,1,2]=>0101010=>1010101
[3,6,4,7,5,8,1,2]=>0101010=>1010101
[1,6,2,7,5,8,3,4]=>0101010=>1010101
[1,6,4,8,5,7,2,3]=>0101010=>1010101
[1,8,4,6,5,7,2,3]=>0101010=>1010101
[1,5,4,8,6,7,2,3]=>0101010=>1010101
[7,8,1,5,4,6,2,3]=>0101010=>1010101
[7,8,1,5,2,4,3,6]=>0101010=>1010101
[1,8,2,6,5,7,3,4]=>0101010=>1010101
[1,7,2,8,5,6,3,4]=>0101010=>1010101
[1,7,2,6,5,8,3,4]=>0101010=>1010101
[1,5,2,7,6,8,3,4]=>0101010=>1010101
[1,7,6,8,2,5,3,4]=>0101010=>1010101
[1,7,6,8,4,5,2,3]=>0101010=>1010101
[5,7,6,8,1,4,2,3]=>0101010=>1010101
[7,8,5,6,1,3,2,4]=>0101010=>1010101
[5,8,6,7,1,3,2,4]=>0101010=>1010101
[1,3,2,7,6,8,4,5]=>0101010=>1010101
[1,7,6,8,2,4,3,5]=>0101010=>1010101
[7,8,1,3,2,6,4,5]=>0101010=>1010101
[7,8,1,6,2,4,3,5]=>0101010=>1010101
[1,8,6,7,2,4,3,5]=>0101010=>1010101
[7,8,1,4,2,6,3,5]=>0101010=>1010101
[7,8,1,4,2,5,3,6]=>0101010=>1010101
[7,8,2,1,4,3,6,5]=>0110101=>1001010
[7,8,1,2,4,3,5,6]=>0100100=>1011011
[4,3,6,5,8,7,1,2]=>1010110=>0101001
[3,4,6,5,7,8,1,2]=>0010010=>1101101
[3,4,1,5,6,7,8,9,2]=>01000001=>10111110
[3,4,5,1,6,7,8,9,2]=>00100001=>11011110
[3,4,5,6,1,7,8,9,2]=>00010001=>11101110
[3,4,5,6,7,1,8,9,2]=>00001001=>11110110
[3,4,5,6,7,8,1,9,2]=>00000101=>11111010
[3,1,2,5,6,7,8,9,4]=>10000001=>01111110
[3,4,1,5,6,7,8,9,10,2]=>010000001=>101111110
[3,4,1,2,6,7,8,9,5]=>01000001=>10111110
[3,4,5,1,6,7,8,9,10,2]=>001000001=>110111110
[3,4,5,1,2,7,8,9,6]=>00100001=>11011110
[3,4,5,6,1,7,8,9,10,2]=>000100001=>111011110
[3,4,5,6,1,2,8,9,7]=>00010001=>11101110
[3,4,5,6,7,1,8,9,10,2]=>000010001=>111101110
[3,4,5,6,7,1,2,9,8]=>00001001=>11110110
[3,4,5,6,7,8,1,9,10,2]=>000001001=>111110110
[3,4,5,6,7,8,1,2,9]=>00000100=>11111011
[3,4,5,6,7,8,9,1,10,2]=>000000101=>111111010
[1,6,2,3,8,7,4,5]=>0100110=>1011001
[1,7,4,3,2,8,6,5]=>0111011=>1000100
[1,4,7,6,2,5,8,3]=>0011001=>1100110
[1,2,6,5,3,7,4,8]=>0011010=>1100101
[1,2,6,5,3,7,8,4]=>0011001=>1100110
[1,3,7,5,2,6,8,4]=>0011001=>1100110
[1,3,7,4,2,6,8,5]=>0011001=>1100110
[1,2,6,4,3,7,8,5]=>0011001=>1100110
[1,2,6,4,3,7,5,8]=>0011010=>1100101
[1,4,7,3,2,5,8,6]=>0011001=>1100110
[1,4,3,2,5,8,6,7]=>0110010=>1001101
[1,5,3,2,4,8,6,7]=>0110010=>1001101
[1,7,5,3,2,8,6,4]=>0111011=>1000100
[1,5,3,2,4,8,7,6]=>0110011=>1001100
[7,6,5,4,3,1,8,2]=>1111101=>0000010
[6,8,5,4,3,2,1,7]=>0111110=>1000001
[8,7,6,5,4,3,1,9,2]=>11111101=>00000010
[7,9,6,5,4,3,2,1,8]=>01111110=>10000001
[9,8,7,6,5,4,3,1,10,2]=>111111101=>000000010
[1,7,6,5,4,3,9,8,2]=>01111011=>10000100
[7,1,5,4,3,8,6,2]=>1011011=>0100100
[3,6,5,4,8,1,7,2]=>0110101=>1001010
[6,8,1,4,3,2,7,5]=>0101101=>1010010
[2,8,5,4,3,7,1,6]=>0111010=>1000101
[1,9,6,5,4,3,2,8,7]=>01111101=>10000010
[8,10,7,6,5,4,3,2,1,9]=>011111110=>100000001
[10,9,8,7,6,5,4,3,1,11,2]=>1111111101=>0000000010
[1,8,7,6,5,4,3,10,9,2]=>011111011=>100000100
[8,1,6,5,4,3,9,7,2]=>10111011=>01000100
[3,7,6,5,4,9,1,8,2]=>01110101=>10001010
[7,6,1,4,3,8,5,2]=>1101011=>0010100
[4,6,5,8,3,1,7,2]=>0101101=>1010010
[6,8,5,1,3,2,7,4]=>0110101=>1001010
[1,8,2,4,3,7,6,5]=>0101011=>1010100
[7,9,1,5,4,3,2,8,6]=>01011101=>10100010
[3,8,5,4,7,2,1,6]=>0110110=>1001001
[2,9,6,5,4,3,8,1,7]=>01111010=>10000101
[1,10,7,6,5,4,3,2,9,8]=>011111101=>100000010
[9,11,8,7,6,5,4,3,2,1,10]=>0111111110=>1000000001
[11,10,9,8,7,6,5,4,3,1,12,2]=>11111111101=>00000000010
[1,9,8,7,6,5,4,3,11,10,2]=>0111111011=>1000000100
[9,1,7,6,5,4,3,10,8,2]=>101111011=>010000100
[3,8,7,6,5,4,10,1,9,2]=>011110101=>100001010
[8,7,1,5,4,3,9,6,2]=>11011011=>00100100
[1,3,6,5,4,9,8,7,2]=>00110111=>11001000
[4,7,6,5,9,3,1,8,2]=>01101101=>10010010
[7,6,5,1,3,8,4,2]=>1110011=>0001100
[1,6,3,4,8,7,5,2]=>0100111=>1011000
[1,4,5,8,3,7,6,2]=>0001011=>1110100
[6,8,5,4,1,2,7,3]=>0111001=>1000110
[1,8,5,2,3,7,6,4]=>0110011=>1001100
[7,9,6,1,4,3,2,8,5]=>01101101=>10010010
[6,8,2,4,3,7,1,5]=>0101010=>1010101
[1,8,3,4,7,2,6,5]=>0100101=>1011010
[1,9,2,5,4,3,8,7,6]=>01011011=>10100100
[8,10,1,6,5,4,3,2,9,7]=>010111101=>101000010
[7,5,8,4,3,2,1,6]=>1011110=>0100001
[4,8,5,7,3,2,1,6]=>0101110=>1010001
[3,9,6,5,4,8,2,1,7]=>01110110=>10001001
[2,10,7,6,5,4,3,9,1,8]=>011111010=>100000101
[1,11,8,7,6,5,4,3,2,10,9]=>0111111101=>1000000010
[10,12,9,8,7,6,5,4,3,2,1,11]=>01111111110=>10000000001
[5,1,7,6,8,4,3,2]=>1010111=>0101000
[6,4,8,5,2,7,1,3]=>1011010=>0100101
[5,1,8,6,7,4,3,2]=>1010111=>0101000
[8,4,7,5,2,6,1,3]=>1011010=>0100101
[5,4,6,8,2,1,7,3]=>1001101=>0110010
[6,4,5,8,1,2,7,3]=>1001001=>0110110
[7,4,6,5,2,1,8,3]=>1011101=>0100010
[8,4,6,5,2,1,7,3]=>1011101=>0100010
[4,8,7,5,6,1,3,2]=>0110101=>1001010
[2,7,5,1,8,4,3,6]=>0110110=>1001001
[5,1,8,7,4,2,3,6]=>1011100=>0100011
[2,8,6,7,4,3,5,1]=>0101101=>1010010
[3,6,5,2,4,1,8,7]=>0110101=>1001010
[5,2,3,6,4,1,8,7]=>1001101=>0110010
[6,1,4,5,3,2,8,7]=>1001101=>0110010
[3,8,7,1,4,6,5,2]=>0110011=>1001100
[5,7,1,2,4,3,8,6]=>0100101=>1011010
[4,3,7,6,8,2,5,1]=>1010101=>0101010
[5,3,6,8,1,7,2,4]=>1001010=>0110101
[3,2,6,8,5,7,1,4]=>1001010=>0110101
[6,3,7,2,4,8,5,1]=>1010011=>0101100
[7,4,8,6,5,2,1,3]=>1011110=>0100001
[7,1,8,2,5,4,3,6]=>1010110=>0101001
[2,5,3,7,4,1,8,6]=>0101101=>1010010
[3,6,4,7,5,1,8,2]=>0101101=>1010010
[8,4,7,6,2,3,1,5]=>1011010=>0100101
[8,4,7,1,2,5,6,3]=>1010001=>0101110
[4,2,8,7,3,5,6,1]=>1011001=>0100110
[8,1,7,4,2,5,6,3]=>1011001=>0100110
[7,4,3,8,2,5,6,1]=>1101001=>0010110
[6,4,1,5,8,2,7,3]=>1100101=>0011010
[2,5,8,7,3,6,1,4]=>0011010=>1100101
[2,1,5,8,7,4,6,3]=>1001101=>0110010
[8,3,5,6,7,4,1,2]=>1000110=>0111001
[7,4,3,2,8,5,6,1]=>1110101=>0001010
[4,2,7,1,8,5,6,3]=>1010101=>0101010
[4,1,7,2,8,5,6,3]=>1010101=>0101010
[2,4,8,7,3,5,6,1]=>0011001=>1100110
[4,7,8,3,1,5,6,2]=>0011001=>1100110
[3,4,7,2,8,5,6,1]=>0010101=>1101010
[3,7,1,4,8,5,6,2]=>0100101=>1011010
[7,2,3,4,8,5,6,1]=>1000101=>0111010
[6,1,8,5,2,7,4,3]=>1011011=>0100100
[2,1,7,4,5,8,6,3]=>1010011=>0101100
[2,1,8,3,6,7,5,4]=>1010011=>0101100
[8,2,1,6,4,7,5,3]=>1101011=>0010100
[7,8,2,6,4,1,5,3]=>0101101=>1010010
[2,6,3,5,8,7,1,4]=>0100110=>1011001
[7,6,2,1,5,8,4,3]=>1110011=>0001100
[4,5,2,7,6,1,8,3]=>0101101=>1010010
[5,1,6,8,4,7,2,3]=>1001010=>0110101
[3,6,8,7,5,2,1,4]=>0011110=>1100001
[7,4,8,6,5,2,3,1]=>1011101=>0100010
[8,1,6,4,7,3,2,5]=>1010110=>0101001
[7,6,4,1,2,3,8,5]=>1110001=>0001110
[2,6,4,8,5,3,7,1]=>0101101=>1010010
[7,3,5,8,4,2,1,6]=>1001110=>0110001
[3,2,5,8,4,1,7,6]=>1001101=>0110010
[8,4,7,1,5,2,3,6]=>1010100=>0101011
[4,8,7,5,6,1,2,3]=>0110100=>1001011
[6,1,4,8,7,3,5,2]=>1001101=>0110010
[7,2,8,4,3,5,6,1]=>1011001=>0100110
[4,7,8,1,3,5,6,2]=>0010001=>1101110
[8,7,3,4,1,5,6,2]=>1101001=>0010110
[4,8,2,7,3,5,6,1]=>0101001=>1010110
[3,1,8,7,2,5,6,4]=>1011001=>0100110
[3,8,1,7,2,5,6,4]=>0101001=>1010110
[8,2,3,7,1,5,6,4]=>1001001=>0110110
[6,4,8,7,1,3,2,5]=>1011010=>0100101
[2,8,4,6,7,3,1,5]=>0100110=>1011001
[4,3,8,2,7,6,1,5]=>1010110=>0101001
[6,8,4,2,1,3,7,5]=>0111001=>1000110
[7,8,2,4,3,5,6,1]=>0101001=>1010110
[2,8,3,7,1,5,6,4]=>0101001=>1010110
[8,1,2,7,3,5,6,4]=>1001001=>0110110
[6,4,1,3,2,8,5,7]=>1101010=>0010101
[5,3,8,6,2,1,4,7]=>1011100=>0100011
[4,6,5,2,8,3,1,7]=>0110110=>1001001
[4,3,7,5,1,8,2,6]=>1011010=>0100101
[6,8,5,2,7,4,3,1]=>0110111=>1001000
[7,2,5,4,3,8,1,6]=>1011010=>0100101
[3,6,8,1,4,5,2,7]=>0010010=>1101101
[6,8,1,2,4,5,3,7]=>0100010=>1011101
[8,1,6,2,4,5,3,7]=>1010010=>0101101
[3,8,6,1,2,5,4,7]=>0110010=>1001101
[5,8,1,6,2,3,4,7]=>0101000=>1010111
[4,1,6,5,8,2,3,7]=>1010100=>0101011
[4,3,8,6,2,5,1,7]=>1011010=>0100101
[8,3,6,1,4,5,2,7]=>1010010=>0101101
[2,3,6,8,4,5,1,7]=>0001010=>1110101
[2,7,5,4,3,8,1,6]=>0111010=>1000101
[6,3,8,7,4,2,5,1]=>1011101=>0100010
[5,8,4,3,7,6,1,2]=>0110110=>1001001
[8,7,4,3,1,6,2,5]=>1111010=>0000101
[1,7,4,3,8,6,2,5]=>0110110=>1001001
[7,1,5,3,4,8,2,6]=>1010010=>0101101
[2,8,6,1,7,4,5,3]=>0110101=>1001010
[4,8,6,5,7,2,1,3]=>0110110=>1001001
[4,7,6,8,2,1,5,3]=>0101101=>1010010
[6,1,8,7,4,3,5,2]=>1011101=>0100010
[8,5,4,3,1,6,7,2]=>1111001=>0000110
[1,5,8,6,3,4,7,2]=>0011001=>1100110
[2,5,8,6,3,4,7,1]=>0011001=>1100110
[4,1,3,8,5,6,7,2]=>1001001=>0110110
[6,5,8,4,3,1,7,2]=>1011101=>0100010
[4,6,5,2,8,1,7,3]=>0110101=>1001010
[7,2,8,1,3,6,4,5]=>1010010=>0101101
[1,8,5,2,3,6,7,4]=>0110001=>1001110
[1,8,3,2,5,6,7,4]=>0110001=>1001110
[2,8,3,1,5,6,7,4]=>0110001=>1001110
[4,8,3,2,5,6,7,1]=>0110001=>1001110
[8,2,3,1,5,6,7,4]=>1010001=>0101110
[2,1,8,3,5,6,7,4]=>1010001=>0101110
[1,4,8,2,3,6,7,5]=>0010001=>1101110
[3,1,2,7,8,6,4,5]=>1000110=>0111001
[7,5,1,8,2,4,3,6]=>1101010=>0010101
[3,5,8,1,2,4,7,6]=>0010001=>1101110
[4,5,8,1,2,3,7,6]=>0010001=>1101110
[4,2,7,1,8,6,3,5]=>1010110=>0101001
[3,8,4,1,2,6,7,5]=>0110001=>1001110
[5,4,8,2,3,6,7,1]=>1010001=>0101110
[5,8,3,6,7,4,1,2]=>0100110=>1011001
[2,3,1,6,8,4,7,5]=>0100101=>1011010
[2,4,3,7,1,8,5,6]=>0101010=>1010101
[1,4,7,3,2,8,5,6]=>0011010=>1100101
[2,7,1,4,3,8,5,6]=>0101010=>1010101
[2,4,1,8,6,3,7,5]=>0101101=>1010010
[8,4,1,3,6,2,7,5]=>1100101=>0011010
[6,8,5,1,7,2,3,4]=>0110100=>1001011
[7,3,6,5,8,2,1,4]=>1010110=>0101001
[7,6,3,5,8,2,1,4]=>1100110=>0011001
[4,5,8,7,3,6,1,2]=>0011010=>1100101
[3,5,2,8,6,1,7,4]=>0101101=>1010010
[8,2,5,6,1,4,7,3]=>1001001=>0110110
[8,6,5,4,1,2,7,3]=>1111001=>0000110
[2,6,1,8,3,7,5,4]=>0101011=>1010100
[4,7,1,6,2,8,5,3]=>0101011=>1010100
[6,1,5,3,8,7,2,4]=>1010110=>0101001
[2,8,6,3,7,1,5,4]=>0110101=>1001010
[7,6,1,5,8,2,3,4]=>1100100=>0011011
[3,6,8,5,1,2,7,4]=>0011001=>1100110
[6,5,2,4,8,1,7,3]=>1100101=>0011010
[5,1,4,8,2,6,7,3]=>1001001=>0110110
[4,8,2,5,1,6,7,3]=>0101001=>1010110
[3,4,8,5,2,6,7,1]=>0011001=>1100110
[4,2,1,8,5,6,7,3]=>1101001=>0010110
[1,5,4,8,2,6,7,3]=>0101001=>1010110
[7,2,1,5,8,6,3,4]=>1100110=>0011001
[2,8,4,5,1,6,7,3]=>0101001=>1010110
[5,4,8,3,7,6,1,2]=>1010110=>0101001
[3,1,5,8,6,2,7,4]=>1001101=>0110010
[6,3,4,8,5,1,7,2]=>1001101=>0110010
[5,3,4,8,1,6,7,2]=>1001001=>0110110
[7,6,1,2,8,3,5,4]=>1100101=>0011010
[7,5,8,4,1,2,6,3]=>1011001=>0100110
[7,5,8,4,6,1,3,2]=>1010101=>0101010
[6,5,4,8,7,1,3,2]=>1101101=>0010010
[6,5,4,8,1,2,7,3]=>1101001=>0010110
[7,5,1,6,2,3,8,4]=>1101001=>0010110
[7,5,1,6,8,2,4,3]=>1100101=>0011010
[6,5,4,1,8,2,7,3]=>1110101=>0001010
[6,5,4,7,1,2,8,3]=>1101001=>0010110
[6,5,4,7,8,1,3,2]=>1100101=>0011010
[6,5,3,7,1,4,2,8]=>1101010=>0010101
[6,5,3,1,8,4,2,7]=>1110110=>0001001
[7,5,1,4,8,3,2,6]=>1100110=>0011001
[8,1,6,4,7,3,5,2]=>1010101=>0101010
[7,5,1,4,8,3,6,2]=>1100101=>0011010
[6,5,3,7,1,4,8,2]=>1101001=>0010110
[6,4,3,1,5,8,7,2]=>1110011=>0001100
[7,4,1,5,3,8,6,2]=>1101011=>0010100
[8,1,5,4,3,7,6,2]=>1011011=>0100100
[8,1,5,4,3,7,2,6]=>1011010=>0100101
[7,4,1,5,3,8,2,6]=>1101010=>0010101
[7,4,1,5,3,2,6,8]=>1101100=>0010011
[8,1,5,4,3,2,6,7]=>1011100=>0100011
[8,1,6,4,2,5,3,7]=>1011010=>0100101
[6,5,3,1,2,7,4,8]=>1110010=>0001101
[6,5,3,8,1,4,2,7]=>1101010=>0010101
[7,6,8,1,4,3,2,5]=>1010110=>0101001
[8,1,7,2,5,4,3,6]=>1010110=>0101001
[8,1,7,2,5,4,6,3]=>1010101=>0101010
[7,6,1,2,5,4,8,3]=>1100101=>0011010
[6,5,3,8,1,4,7,2]=>1101001=>0010110
[6,5,3,1,2,7,8,4]=>1110001=>0001110
[7,5,1,4,2,6,8,3]=>1101001=>0010110
[8,1,6,4,2,5,7,3]=>1011001=>0100110
[7,4,1,5,3,2,8,6]=>1101101=>0010010
[6,4,3,1,5,2,8,7]=>1110101=>0001010
[6,4,3,1,5,7,2,8]=>1110010=>0001101
[7,4,1,5,3,6,2,8]=>1101010=>0010101
[8,1,5,4,3,6,2,7]=>1011010=>0100101
[8,1,5,4,3,6,7,2]=>1011001=>0100110
[7,4,1,5,3,6,8,2]=>1101001=>0010110
[6,4,3,1,5,7,8,2]=>1110001=>0001110
[6,7,3,8,4,5,1,2]=>0101010=>1010101
[6,7,4,5,1,8,2,3]=>0101010=>1010101
[4,7,5,6,2,3,1,8]=>0101010=>1010101
[4,7,5,6,1,8,2,3]=>0101010=>1010101
[4,7,5,6,3,8,1,2]=>0101010=>1010101
[3,7,5,8,4,6,1,2]=>0101010=>1010101
[4,5,3,8,6,7,1,2]=>0101010=>1010101
[4,8,3,6,5,7,1,2]=>0101010=>1010101
[5,6,4,7,1,8,2,3]=>0101010=>1010101
[5,6,1,7,3,8,2,4]=>0101010=>1010101
[5,6,1,8,2,7,3,4]=>0101010=>1010101
[5,6,1,8,4,7,2,3]=>0101010=>1010101
[4,8,1,6,5,7,2,3]=>0101010=>1010101
[4,5,1,8,6,7,2,3]=>0101010=>1010101
[7,8,4,5,1,6,2,3]=>0101010=>1010101
[4,8,2,3,1,6,5,7]=>0101010=>1010101
[5,6,2,8,1,4,3,7]=>0101010=>1010101
[5,6,3,4,1,8,2,7]=>0101010=>1010101
[3,6,4,5,2,7,1,8]=>0101010=>1010101
[3,6,4,5,1,8,2,7]=>0101010=>1010101
[2,6,4,8,1,5,3,7]=>0101010=>1010101
[2,8,3,6,1,5,4,7]=>0101010=>1010101
[2,8,3,4,1,6,5,7]=>0101010=>1010101
[7,8,2,5,3,4,1,6]=>0101010=>1010101
[7,8,1,5,3,6,2,4]=>0101010=>1010101
[1,5,3,8,6,7,2,4]=>0101010=>1010101
[1,8,3,6,2,7,4,5]=>0101010=>1010101
[1,6,4,8,2,7,3,5]=>0101010=>1010101
[2,6,4,7,3,5,1,8]=>0101010=>1010101
[2,7,3,6,4,5,1,8]=>0101010=>1010101
[1,7,3,6,4,8,2,5]=>0101010=>1010101
[1,7,2,8,4,6,3,5]=>0101010=>1010101
[1,7,5,8,4,6,2,3]=>0101010=>1010101
[1,7,5,8,2,6,3,4]=>0101010=>1010101
[1,7,5,6,3,8,2,4]=>0101010=>1010101
[2,7,5,6,3,4,1,8]=>0101010=>1010101
[6,7,2,5,3,4,1,8]=>0101010=>1010101
[6,7,1,5,3,8,2,4]=>0101010=>1010101
[6,7,5,8,1,4,2,3]=>0101010=>1010101
[5,8,6,7,2,3,1,4]=>0101010=>1010101
[6,7,2,3,1,8,4,5]=>0101010=>1010101
[6,7,2,8,1,4,3,5]=>0101010=>1010101
[3,4,2,7,5,6,1,8]=>0101010=>1010101
[3,4,1,7,5,8,2,6]=>0101010=>1010101
[2,7,5,8,1,4,3,6]=>0101010=>1010101
[2,3,1,7,5,8,4,6]=>0101010=>1010101
[2,3,1,8,4,7,5,6]=>0101010=>1010101
[7,8,2,3,1,6,4,5]=>0101010=>1010101
[7,8,2,6,1,4,3,5]=>0101010=>1010101
[2,8,6,7,1,4,3,5]=>0101010=>1010101
[2,8,1,4,3,7,5,6]=>0101010=>1010101
[3,7,2,5,4,6,1,8]=>0101010=>1010101
[4,5,2,7,3,6,1,8]=>0101010=>1010101
[4,5,1,8,2,7,3,6]=>0101010=>1010101
[3,4,1,8,2,7,5,6]=>0101010=>1010101
[3,4,1,8,6,7,2,5]=>0101010=>1010101
[3,4,2,5,1,8,6,7]=>0101010=>1010101
[3,4,2,8,1,6,5,7]=>0101010=>1010101
[3,8,2,5,1,6,4,7]=>0101010=>1010101
[4,5,2,8,1,6,3,7]=>0101010=>1010101
[4,5,3,6,1,8,2,7]=>0101010=>1010101
[8,6,7,1,4,2,5,3]=>1010101=>0101010
[8,6,3,7,5,1,2,4]=>1101100=>0010011
[7,6,1,8,3,5,2,4]=>1101010=>0010101
[7,6,2,8,3,5,1,4]=>1101010=>0010101
[7,6,2,3,8,5,1,4]=>1100110=>0011001
[8,7,1,5,2,6,3,4]=>1101010=>0010101
[8,7,1,5,2,3,6,4]=>1101001=>0010110
[8,5,2,3,1,7,6,4]=>1101011=>0010100
[8,6,2,3,7,1,5,4]=>1100101=>0011010
[8,6,2,7,3,1,5,4]=>1101101=>0010010
[8,7,2,5,1,6,3,4]=>1101010=>0010101
[8,4,2,1,7,6,3,5]=>1110110=>0001001
[8,5,7,2,1,4,3,6]=>1011010=>0100101
[5,8,7,3,1,4,2,6]=>0111010=>1000101
[5,8,7,3,1,4,6,2]=>0111001=>1000110
[8,5,7,2,1,4,6,3]=>1011001=>0100110
[8,4,2,1,3,7,6,5]=>1110011=>0001100
[8,4,3,1,7,2,6,5]=>1110101=>0001010
[8,6,1,3,7,2,5,4]=>1100101=>0011010
[8,5,1,3,2,7,6,4]=>1101011=>0010100
[6,1,5,8,4,2,7,3]=>1001101=>0110010
[5,2,8,6,4,1,3,7]=>1011100=>0100011
[8,4,7,5,1,6,2,3]=>1011010=>0100101
[8,4,7,5,1,2,3,6]=>1011000=>0100111
[8,7,3,5,1,2,6,4]=>1101001=>0010110
[8,3,2,6,5,1,4,7]=>1101100=>0010011
[4,8,6,3,5,1,2,7]=>0110100=>1001011
[4,8,7,3,1,5,2,6]=>0111010=>1000101
[8,4,7,2,1,5,3,6]=>1011010=>0100101
[8,7,3,1,4,2,6,5]=>1110101=>0001010
[8,7,3,1,2,6,4,5]=>1110010=>0001101
[8,7,3,1,2,4,6,5]=>1110001=>0001110
[8,3,2,1,4,7,6,5]=>1110011=>0001100
[8,3,2,1,7,4,6,5]=>1110101=>0001010
[8,3,2,7,1,5,6,4]=>1101001=>0010110
[8,4,7,2,1,5,6,3]=>1011001=>0100110
[8,7,2,1,6,3,4,5]=>1110100=>0001011
[3,6,5,4,1,2,8,7]=>0111001=>1000110
[3,8,5,6,7,4,1,2]=>0100110=>1011001
[4,7,5,8,6,2,1,3]=>0101110=>1010001
[2,5,7,8,6,3,4,1]=>0001101=>1110010
[4,8,5,7,6,3,1,2]=>0101110=>1010001
[4,6,3,2,1,5,8,7]=>0111001=>1000110
[6,2,1,5,3,4,8,7]=>1101001=>0010110
[5,8,1,3,7,6,4,2]=>0100111=>1011000
[4,7,2,3,6,1,8,5]=>0100101=>1011010
[3,7,4,2,8,1,5,6]=>0110100=>1001011
[4,2,6,8,5,7,3,1]=>1001011=>0110100
[6,4,2,7,3,8,5,1]=>1101011=>0010100
[8,1,6,7,5,3,4,2]=>1001101=>0110010
[2,1,5,8,7,6,3,4]=>1001110=>0110001
[2,1,4,7,6,3,8,5]=>1001101=>0110010
[6,4,7,8,5,3,2,1]=>1001111=>0110000
[4,1,3,7,6,2,8,5]=>1001101=>0110010
[8,5,1,6,3,2,7,4]=>1101101=>0010010
[6,3,7,1,5,2,8,4]=>1010101=>0101010
[3,2,6,8,4,7,5,1]=>1001011=>0110100
[8,4,6,1,3,2,5,7]=>1010100=>0101011
[4,2,8,6,7,3,1,5]=>1010110=>0101001
[7,4,3,8,2,1,5,6]=>1101100=>0010011
[4,7,5,8,1,6,3,2]=>0101011=>1010100
[6,4,3,2,7,8,1,5]=>1110010=>0001101
[4,2,5,1,6,7,8,3]=>1010001=>0101110
[2,4,8,5,7,1,3,6]=>0010100=>1101011
[3,7,1,4,6,8,5,2]=>0100011=>1011100
[7,8,2,5,6,1,4,3]=>0100101=>1011010
[2,4,3,8,7,5,6,1]=>0101101=>1010010
[2,6,7,3,5,1,8,4]=>0010101=>1101010
[7,6,8,4,2,5,3,1]=>1011011=>0100100
[8,5,7,1,6,3,2,4]=>1010110=>0101001
[6,5,7,2,8,4,3,1]=>1010111=>0101000
[3,4,8,6,5,2,1,7]=>0011110=>1100001
[2,7,6,1,4,5,8,3]=>0110001=>1001110
[6,5,8,2,1,7,3,4]=>1011010=>0100101
[7,4,3,5,1,6,8,2]=>1101001=>0010110
[4,1,6,3,5,8,7,2]=>1010011=>0101100
[6,2,5,8,4,3,7,1]=>1001101=>0110010
[8,6,7,1,5,4,3,2]=>1010111=>0101000
[2,1,6,5,8,4,7,3]=>1010101=>0101010
[2,1,6,8,5,4,3,7]=>1001110=>0110001
[4,1,8,5,6,2,3,7]=>1010100=>0101011
[2,6,4,8,7,3,5,1]=>0101101=>1010010
[6,2,8,4,3,5,1,7]=>1011010=>0100101
[4,8,2,7,6,1,3,5]=>0101100=>1010011
[3,1,8,2,7,5,4,6]=>1010110=>0101001
[3,8,1,2,6,7,4,5]=>0100010=>1011101
[5,8,4,3,2,7,1,6]=>0111010=>1000101
[7,4,8,6,3,2,5,1]=>1011101=>0100010
[5,8,4,7,2,1,3,6]=>0101100=>1010011
[2,1,8,4,3,7,5,6]=>1011010=>0100101
[6,3,8,2,4,5,7,1]=>1010001=>0101110
[5,8,4,2,3,6,1,7]=>0110010=>1001101
[5,8,2,4,3,1,6,7]=>0101100=>1010011
[2,8,3,1,6,4,5,7]=>0110100=>1001011
[8,2,1,3,4,7,5,6]=>1100010=>0011101
[1,4,8,2,6,3,5,7]=>0010100=>1101011
[1,2,7,3,5,4,8,6]=>0010101=>1101010
[1,2,3,8,4,5,7,6]=>0001001=>1110110
[1,2,8,3,4,5,7,6]=>0010001=>1101110
[1,3,8,2,6,4,5,7]=>0010100=>1101011
[1,5,7,2,3,6,4,8]=>0010010=>1101101
[1,7,2,3,5,4,8,6]=>0100101=>1011010
[1,3,8,2,4,5,7,6]=>0010001=>1101110
[1,2,3,8,4,6,7,5]=>0001001=>1110110
[1,8,2,3,5,4,6,7]=>0100100=>1011011
[1,7,8,2,3,6,4,5]=>0010010=>1101101
[1,6,7,8,2,3,5,4]=>0001001=>1110110
[1,7,8,2,5,3,6,4]=>0010101=>1101010
[1,7,8,2,4,5,3,6]=>0010010=>1101101
[1,2,8,3,6,4,5,7]=>0010100=>1101011
[1,8,2,3,6,4,5,7]=>0100100=>1011011
[1,2,8,3,5,4,6,7]=>0010100=>1101011
[1,2,7,8,3,6,4,5]=>0001010=>1110101
[1,5,2,7,8,3,6,4]=>0100101=>1011010
[1,3,2,8,4,6,7,5]=>0101001=>1010110
[1,8,2,3,4,6,7,5]=>0100001=>1011110
[1,7,8,2,4,3,6,5]=>0010101=>1101010
[7,6,3,1,5,2,4,8]=>1110100=>0001011
[6,7,3,1,5,2,8,4]=>0110101=>1001010
[6,8,3,1,5,2,7,4]=>0110101=>1001010
[6,8,4,5,1,2,7,3]=>0101001=>1010110
[6,7,4,5,1,2,8,3]=>0101001=>1010110
[7,2,1,6,5,3,4,8]=>1101100=>0010011
[7,3,6,1,5,2,4,8]=>1010100=>0101011
[7,4,6,5,1,2,3,8]=>1011000=>0100111
[6,7,5,4,1,2,8,3]=>0111001=>1000110
[5,8,6,4,1,7,2,3]=>0111010=>1000101
[5,7,6,4,1,8,2,3]=>0111010=>1000101
[5,6,7,4,1,8,2,3]=>0011010=>1100101
[6,5,7,4,1,2,8,3]=>1011001=>0100110
[6,4,7,5,1,2,8,3]=>1011001=>0100110
[6,2,1,7,5,3,8,4]=>1101101=>0010010
[6,3,8,1,5,2,7,4]=>1010101=>0101010
[6,4,8,5,1,2,7,3]=>1011001=>0100110
[6,5,8,4,1,2,7,3]=>1011001=>0100110
[5,6,8,4,1,7,2,3]=>0011010=>1100101
[4,6,8,5,7,1,2,3]=>0010100=>1101011
[4,5,8,6,7,1,2,3]=>0010100=>1101011
[5,4,8,6,1,7,2,3]=>1011010=>0100101
[5,3,8,1,6,7,2,4]=>1010010=>0101101
[5,2,1,8,6,7,3,4]=>1101010=>0010101
[5,2,1,7,6,8,3,4]=>1101010=>0010101
[5,4,7,6,1,8,2,3]=>1011010=>0100101
[4,5,7,6,8,1,2,3]=>0010100=>1101011
[4,6,7,5,8,1,2,3]=>0010100=>1101011
[4,8,6,5,7,1,2,3]=>0110100=>1001011
[4,8,5,6,7,1,2,3]=>0100100=>1011011
[4,7,5,6,8,1,2,3]=>0100100=>1011011
[4,6,5,7,8,1,2,3]=>0100100=>1011011
[5,7,4,6,1,8,2,3]=>0101010=>1010101
[5,8,4,6,1,7,2,3]=>0101010=>1010101
[5,8,3,1,6,7,2,4]=>0110010=>1001101
[5,7,3,1,6,8,2,4]=>0110010=>1001101
[5,6,3,1,7,8,2,4]=>0110010=>1001101
[6,2,1,4,3,8,7,5]=>1101011=>0010100
[5,8,3,1,7,6,2,4]=>0110110=>1001001
[5,7,4,8,1,6,2,3]=>0101010=>1010101
[5,2,1,6,8,7,3,4]=>1100110=>0011001
[5,4,6,8,1,7,2,3]=>1001010=>0110101
[4,5,6,8,7,1,2,3]=>0001100=>1110011
[4,7,5,8,6,1,2,3]=>0101100=>1010011
[4,8,5,7,6,1,2,3]=>0101100=>1010011
[4,8,6,7,5,1,2,3]=>0101100=>1010011
[4,7,6,8,5,1,2,3]=>0101100=>1010011
[4,6,7,8,5,1,2,3]=>0001100=>1110011
[4,5,7,8,6,1,2,3]=>0001100=>1110011
[5,4,7,8,1,6,2,3]=>1001010=>0110101
[5,3,7,1,8,6,2,4]=>1010110=>0101001
[5,2,1,7,8,6,3,4]=>1100110=>0011001
[5,3,8,1,7,6,2,4]=>1010110=>0101001
[5,4,8,7,1,6,2,3]=>1011010=>0100101
[4,6,8,7,5,1,2,3]=>0011100=>1100011
[4,7,8,6,5,1,2,3]=>0011100=>1100011
[4,8,7,6,5,1,2,3]=>0111100=>1000011
[2,5,4,7,3,6,1,8]=>0101010=>1010101
[2,4,6,3,7,5,1,8]=>0010110=>1101001
[4,2,7,3,6,5,1,8]=>1010110=>0101001
[4,2,6,3,1,5,8,7]=>1011001=>0100110
[2,5,3,1,6,4,8,7]=>0110101=>1001010
[2,5,3,7,6,4,1,8]=>0101110=>1010001
[2,6,5,3,7,4,1,8]=>0110110=>1001001
[4,2,7,6,3,5,1,8]=>1011010=>0100101
[2,7,5,3,6,4,1,8]=>0110110=>1001001
[2,6,3,7,5,4,1,8]=>0101110=>1010001
[1,7,5,2,3,8,4,6]=>0110010=>1001101
[2,1,3,7,5,4,8,6]=>1001101=>0110010
[2,3,1,8,6,5,4,7]=>0101110=>1010001
[2,5,3,1,8,6,4,7]=>0110110=>1001001
[4,2,8,3,1,6,5,7]=>1011010=>0100101
[8,3,2,6,4,1,5,7]=>1101100=>0010011
[3,6,8,2,1,4,5,7]=>0011000=>1100111
[1,5,2,8,3,4,7,6]=>0101001=>1010110
[1,2,6,3,8,7,4,5]=>0010110=>1101001
[1,2,8,3,6,4,7,5]=>0010101=>1101010
[1,2,7,6,3,4,8,5]=>0011001=>1100110
[2,1,3,8,7,5,4,6]=>1001110=>0110001
[1,2,3,8,6,4,7,5]=>0001101=>1110010
[1,2,3,7,4,8,6,5]=>0001011=>1110100
[1,2,7,6,3,8,4,5]=>0011010=>1100101
[1,2,3,6,4,8,7,5]=>0001011=>1110100
[1,2,3,7,6,4,8,5]=>0001101=>1110010
[2,6,3,1,8,5,4,7]=>0110110=>1001001
[2,1,3,8,5,4,7,6]=>1001101=>0110010
[7,1,8,4,2,3,5,6]=>1011000=>0100111
[2,1,8,4,3,5,7,6]=>1011001=>0100110
[4,2,6,3,1,8,5,7]=>1011010=>0100101
[5,4,2,8,3,1,6,7]=>1101100=>0010011
[3,5,8,2,4,1,6,7]=>0010100=>1101011
[2,5,4,8,3,1,6,7]=>0101100=>1010011
[4,2,1,8,3,5,7,6]=>1101001=>0010110
[1,8,7,4,2,3,5,6]=>0111000=>1000111
[1,5,2,8,7,3,4,6]=>0101100=>1010011
[1,2,7,3,6,4,8,5]=>0010101=>1101010
[1,2,8,6,3,7,4,5]=>0011010=>1100101
[1,2,7,3,8,6,4,5]=>0010110=>1101001
[1,2,3,8,4,7,6,5]=>0001011=>1110100
[1,2,7,3,4,8,6,5]=>0010011=>1101100
[1,2,6,3,8,4,7,5]=>0010101=>1101010
[1,5,2,3,8,7,4,6]=>0100110=>1011001
[4,2,1,8,3,7,5,6]=>1101010=>0010101
[8,3,2,1,7,4,5,6]=>1110100=>0001011
[1,8,4,2,7,3,5,6]=>0110100=>1001011
[1,2,8,6,3,4,7,5]=>0011001=>1100110
[1,2,7,3,8,4,6,5]=>0010101=>1101010
[1,2,3,8,7,4,6,5]=>0001101=>1110010
[1,2,3,8,7,6,4,5]=>0001110=>1110001
[2,5,3,8,1,6,4,7]=>0101010=>1010101
[2,6,4,7,1,5,3,8]=>0101010=>1010101
[2,6,5,7,1,4,3,8]=>0101010=>1010101
[3,8,5,7,1,2,6,4]=>0101001=>1010110
[3,8,5,7,2,6,4,1]=>0101011=>1010100
[3,4,8,6,2,5,7,1]=>0011001=>1100110
[3,4,8,6,1,2,5,7]=>0011000=>1100111
[2,5,7,1,4,8,6,3]=>0010011=>1101100
[2,4,8,1,5,7,6,3]=>0010011=>1101100
[2,4,3,8,1,6,5,7]=>0101010=>1010101
[2,8,1,7,5,6,4,3]=>0101011=>1010100
[2,3,8,1,6,5,7,4]=>0010101=>1101010
[2,4,8,1,3,5,7,6]=>0010001=>1101110
[3,5,7,6,1,2,4,8]=>0011000=>1100111
[3,5,7,6,2,4,8,1]=>0011001=>1100110
[4,8,6,7,2,3,5,1]=>0101001=>1010110
[4,8,6,7,1,2,3,5]=>0101000=>1010111
[4,8,6,7,1,3,5,2]=>0101001=>1010110
[3,4,8,6,1,5,7,2]=>0011001=>1100110
[3,8,5,7,1,6,4,2]=>0101011=>1010100
[3,2,8,5,6,1,7,4]=>1010101=>0101010
[3,8,5,7,2,1,6,4]=>0101101=>1010010
[3,4,8,6,2,1,5,7]=>0011100=>1100011
[3,5,7,6,2,1,4,8]=>0011100=>1100011
[4,8,6,7,2,1,3,5]=>0101100=>1010011
[4,8,6,7,3,5,2,1]=>0101011=>1010100
[5,8,6,7,3,4,2,1]=>0101011=>1010100
[5,8,6,7,2,1,3,4]=>0101100=>1010011
[5,8,6,7,2,1,4,3]=>0101101=>1010010
[4,8,6,7,2,1,5,3]=>0101101=>1010010
[4,3,1,7,5,2,8,6]=>1101101=>0010010
[4,3,2,8,5,1,7,6]=>1101101=>0010010
[4,3,8,5,1,6,7,2]=>1011001=>0100110
[4,8,6,7,1,5,3,2]=>0101011=>1010100
[5,8,6,7,1,4,3,2]=>0101011=>1010100
[5,8,6,7,2,3,4,1]=>0101001=>1010110
[5,8,6,7,2,4,3,1]=>0101011=>1010100
[5,8,6,7,1,2,4,3]=>0101001=>1010110
[4,2,3,8,5,1,6,7]=>1001100=>0110011
[4,2,8,5,1,7,6,3]=>1011011=>0100100
[3,4,2,8,5,6,1,7]=>0101010=>1010101
[3,2,4,8,6,1,5,7]=>1001100=>0110011
[3,2,5,7,6,1,4,8]=>1001100=>0110011
[4,8,6,7,1,3,2,5]=>0101010=>1010101
[4,8,6,7,1,2,5,3]=>0101001=>1010110
[4,8,6,7,2,5,3,1]=>0101011=>1010100
[4,3,8,5,2,6,7,1]=>1011001=>0100110
[4,3,8,5,1,2,6,7]=>1011000=>0100111
[4,2,6,7,5,1,3,8]=>1001100=>0110011
[3,8,5,7,1,4,2,6]=>0101010=>1010101
[3,8,4,7,1,5,2,6]=>0101010=>1010101
[3,5,2,8,4,6,1,7]=>0101010=>1010101
[3,5,1,7,4,6,2,8]=>0101010=>1010101
[3,8,4,7,2,5,1,6]=>0101010=>1010101
[4,1,3,8,5,2,6,7]=>1001100=>0110011
[4,1,2,6,7,5,3,8]=>1000110=>0111001
[4,2,6,7,5,3,8,1]=>1001101=>0110010
[4,8,6,7,3,2,5,1]=>0101101=>1010010
[4,8,6,7,3,1,2,5]=>0101100=>1010011
[3,1,5,7,6,2,4,8]=>1001100=>0110011
[3,4,1,7,5,6,2,8]=>0101010=>1010101
[4,1,7,5,2,8,6,3]=>1011011=>0100100
[4,1,6,7,5,2,3,8]=>1001100=>0110011
[4,8,6,7,2,3,1,5]=>0101010=>1010101
[5,8,6,7,3,2,4,1]=>0101101=>1010010
[5,8,6,7,4,2,3,1]=>0101101=>1010010
[5,8,6,7,4,1,2,3]=>0101100=>1010011
[5,8,6,7,4,1,3,2]=>0101101=>1010010
[5,8,6,7,3,1,4,2]=>0101101=>1010010
[4,8,6,7,3,1,5,2]=>0101101=>1010010
[4,1,6,7,5,3,8,2]=>1001101=>0110010
[4,1,7,5,3,2,8,6]=>1011101=>0100010
[4,2,8,5,3,1,7,6]=>1011101=>0100010
[4,2,1,6,7,5,3,8]=>1100110=>0011001
[4,8,6,7,3,2,1,5]=>0101110=>1010001
[5,8,6,7,4,2,1,3]=>0101110=>1010001
[5,8,6,7,4,3,1,2]=>0101110=>1010001
[7,3,5,8,1,4,2,6]=>1001010=>0110101
[3,8,7,6,1,4,2,5]=>0111010=>1000101
[5,1,8,3,6,7,2,4]=>1010010=>0101101
[1,4,7,8,5,6,2,3]=>0001010=>1110101
[3,4,7,1,5,8,6,2]=>0010011=>1101100
[3,6,1,4,7,8,5,2]=>0100011=>1011100
[1,6,8,4,7,5,2,3]=>0010110=>1101001
[6,8,1,3,5,7,2,4]=>0100010=>1011101
[7,6,1,4,3,8,2,5]=>1101010=>0010101
[3,8,1,6,5,4,2,7]=>0101110=>1010001
[4,1,3,7,5,8,2,6]=>1001010=>0110101
[6,1,7,3,8,4,2,5]=>1010110=>0101001
[7,1,8,6,3,5,2,4]=>1011010=>0100101
[3,1,7,6,5,8,4,2]=>1011011=>0100100
[8,2,7,6,5,3,4,1]=>1011101=>0100010
[8,4,2,6,7,5,3,1]=>1100111=>0011000
[4,8,1,6,7,5,3,2]=>0100111=>1011000
[7,4,1,6,8,2,5,3]=>1100101=>0011010
[1,3,8,6,2,7,5,4]=>0011011=>1100100
[6,1,3,2,7,8,4,5]=>1010010=>0101101
[1,8,6,2,5,3,4,7]=>0110100=>1001011
[4,7,2,6,8,1,5,3]=>0100101=>1011010
[8,7,3,6,4,5,2,1]=>1101011=>0010100
[5,7,8,6,2,1,4,3]=>0011101=>1100010
[2,7,4,1,6,8,3,5]=>0110010=>1001101
[3,7,2,4,5,1,6,8]=>0100100=>1011011
[1,8,6,4,5,2,3,7]=>0110100=>1001011
[2,8,4,6,5,1,3,7]=>0101100=>1010011
[3,4,1,7,5,2,6,8]=>0101100=>1010011
[7,5,8,6,1,2,4,3]=>1011001=>0100110
[5,6,8,7,3,1,4,2]=>0011101=>1100010
[2,5,4,3,6,8,1,7]=>0110010=>1001101
[3,8,5,4,6,2,1,7]=>0110110=>1001001
[4,8,2,1,3,7,5,6]=>0110010=>1001101
[6,4,1,2,7,5,8,3]=>1100101=>0011010
[4,1,8,3,6,7,5,2]=>1010011=>0101100
[8,3,7,4,5,2,6,1]=>1010101=>0101010
[4,3,7,8,5,1,6,2]=>1001101=>0110010
[5,4,8,2,7,6,1,3]=>1010110=>0101001
[1,2,7,3,6,5,8,4]=>0010101=>1101010
[2,8,7,6,3,4,1,5]=>0111010=>1000101
[5,8,2,6,3,4,1,7]=>0101010=>1010101
[4,1,7,5,8,6,2,3]=>1010110=>0101001
[5,1,7,8,4,3,6,2]=>1001101=>0110010
[8,2,7,5,4,3,6,1]=>1011101=>0100010
[6,3,8,1,4,7,5,2]=>1010011=>0101100
[3,8,4,5,6,1,2,7]=>0100100=>1011011
[1,4,3,5,7,8,2,6]=>0100010=>1011101
[6,5,8,7,1,3,4,2]=>1011001=>0100110
[3,6,7,2,4,8,1,5]=>0010010=>1101101
[1,5,2,7,4,3,8,6]=>0101101=>1010010
[2,8,5,6,4,3,1,7]=>0101110=>1010001
[1,8,6,5,4,3,2,7]=>0111110=>1000001
[6,1,5,2,8,4,7,3]=>1010101=>0101010
[4,6,1,8,5,7,2,3]=>0101010=>1010101
[4,7,1,2,8,5,6,3]=>0100101=>1011010
[1,4,7,2,8,5,6,3]=>0010101=>1101010
[1,7,3,5,8,6,2,4]=>0100110=>1011001
[7,3,5,8,6,1,2,4]=>1001100=>0110011
[3,6,8,1,5,7,2,4]=>0010010=>1101101
[3,4,6,5,8,1,7,2]=>0010101=>1101010
[6,8,1,5,7,2,3,4]=>0100100=>1011011
[7,1,2,5,8,6,3,4]=>1000110=>0111001
[1,7,2,5,8,6,3,4]=>0100110=>1011001
[1,7,6,8,2,3,5,4]=>0101001=>1010110
[7,6,8,1,2,3,5,4]=>1010001=>0101110
[2,7,1,5,8,6,3,4]=>0100110=>1011001
[2,4,7,1,8,5,6,3]=>0010101=>1101010
[4,7,5,8,3,1,6,2]=>0101101=>1010010
[4,7,2,1,8,5,6,3]=>0110101=>1001010
[7,6,8,2,1,3,5,4]=>1011001=>0100110
[1,2,7,6,8,3,5,4]=>0010101=>1101010
[3,7,6,8,2,1,5,4]=>0101101=>1010010
[7,4,2,1,6,8,5,3]=>1110011=>0001100
[6,7,4,1,8,5,3,2]=>0110111=>1001000
[6,7,4,3,1,8,5,2]=>0111011=>1000100
[2,7,4,1,6,8,5,3]=>0110011=>1001100
[2,3,7,6,8,1,5,4]=>0010101=>1101010
[7,4,2,6,8,5,1,3]=>1100110=>0011001
[7,3,2,5,8,6,1,4]=>1100110=>0011001
[3,1,7,6,8,2,5,4]=>1010101=>0101010
[3,7,6,8,1,2,5,4]=>0101001=>1010110
[1,3,7,6,8,2,5,4]=>0010101=>1101010
[1,7,4,2,6,8,5,3]=>0110011=>1001100
[7,4,1,2,6,8,5,3]=>1100011=>0011100
[7,1,4,2,8,5,6,3]=>1010101=>0101010
[7,1,8,2,5,4,6,3]=>1010101=>0101010
[7,3,8,4,6,1,5,2]=>1010101=>0101010
[7,2,8,1,6,4,5,3]=>1010101=>0101010
[7,1,6,8,5,4,2,3]=>1001110=>0110001
[7,1,2,6,8,5,4,3]=>1000111=>0111000
[1,7,2,6,8,5,4,3]=>0100111=>1011000
[1,7,6,8,3,2,5,4]=>0101101=>1010010
[7,6,8,3,1,2,5,4]=>1011001=>0100110
[7,1,5,8,6,3,2,4]=>1001110=>0110001
[7,2,5,8,6,3,1,4]=>1001110=>0110001
[3,6,7,1,8,5,4,2]=>0010111=>1101000
[7,2,6,8,5,4,1,3]=>1001110=>0110001
[7,6,8,2,3,1,5,4]=>1010101=>0101010
[2,7,6,8,3,1,5,4]=>0101101=>1010010
[2,7,1,6,8,5,4,3]=>0100111=>1011000
[6,7,3,1,8,5,4,2]=>0110111=>1001000
[6,7,1,8,5,4,3,2]=>0101111=>1010000
[7,2,1,6,8,5,4,3]=>1100111=>0011000
[7,6,8,3,2,1,5,4]=>1011101=>0100010
[4,7,8,5,6,1,3,2]=>0010101=>1101010
[4,6,5,8,7,1,3,2]=>0101101=>1010010
[5,6,4,8,1,2,7,3]=>0101001=>1010110
[8,1,5,6,7,2,4,3]=>1000101=>0111010
[6,4,5,1,8,2,7,3]=>1010101=>0101010
[5,4,6,7,1,2,8,3]=>1001001=>0110110
[4,3,6,7,2,1,5,8]=>1001100=>0110011
[5,3,6,7,1,4,2,8]=>1001010=>0110101
[8,1,4,6,7,3,2,5]=>1000110=>0111001
[8,1,3,6,7,4,5,2]=>1000101=>0111010
[7,2,1,6,8,4,5,3]=>1100101=>0011010
[5,2,6,7,1,4,8,3]=>1001001=>0110110
[4,2,6,7,3,1,8,5]=>1001101=>0110010
[6,2,4,1,5,8,7,3]=>1010011=>0101100
[7,2,1,5,4,8,6,3]=>1101011=>0010100
[8,1,4,5,3,7,2,6]=>1001010=>0110101
[7,3,1,5,4,8,2,6]=>1101010=>0010101
[6,3,4,1,5,8,2,7]=>1010010=>0101101
[5,3,4,2,1,8,6,7]=>1011010=>0100101
[4,3,5,2,7,1,6,8]=>1010100=>0101011
[5,6,3,8,1,4,2,7]=>0101010=>1010101
[8,1,7,2,4,5,6,3]=>1010001=>0101110
[7,6,1,2,4,5,8,3]=>1100001=>0011110
[4,7,8,2,3,1,6,5]=>0010101=>1101010
[5,6,2,8,1,4,7,3]=>0101001=>1010110
[6,5,2,1,3,7,8,4]=>1110001=>0001110
[7,5,1,3,2,6,8,4]=>1101001=>0010110
[8,1,6,3,2,5,7,4]=>1011001=>0100110
[7,4,1,3,5,2,8,6]=>1100101=>0011010
[5,4,2,3,1,6,8,7]=>1101001=>0010110
[7,3,1,4,5,6,2,8]=>1100010=>0011101
[8,1,4,3,5,6,2,7]=>1010010=>0101101
[6,2,3,1,5,7,8,4]=>1010001=>0101110
[7,8,4,2,1,6,5,3]=>0111011=>1000100
[7,8,4,2,1,5,6,3]=>0111001=>1000110
[6,2,3,4,8,7,1,5]=>1000110=>0111001
[6,2,3,4,7,8,1,5]=>1000010=>0111101
[7,8,3,4,6,2,1,5]=>0100110=>1011001
[7,8,3,6,4,2,1,5]=>0101110=>1010001
[7,8,3,5,6,2,1,4]=>0100110=>1011001
[6,2,3,8,7,5,1,4]=>1001110=>0110001
[6,2,3,7,8,5,1,4]=>1000110=>0111001
[5,2,6,3,8,1,7,4]=>1010101=>0101010
[6,3,2,5,8,7,1,4]=>1100110=>0011001
[6,3,2,8,4,7,1,5]=>1101010=>0010101
[6,4,3,8,7,5,1,2]=>1101110=>0010001
[6,4,3,7,8,5,1,2]=>1100110=>0011001
[6,2,4,1,7,3,5,8]=>1010100=>0101011
[6,3,2,7,4,8,1,5]=>1101010=>0010101
[6,3,2,5,7,8,1,4]=>1100010=>0011101
[5,7,2,3,6,1,8,4]=>0100101=>1011010
[5,8,2,3,6,1,7,4]=>0100101=>1011010
[4,7,5,8,3,2,1,6]=>0101110=>1010001
[4,5,6,8,3,2,1,7]=>0001110=>1110001
[4,6,8,5,3,2,1,7]=>0011110=>1100001
[5,6,1,4,2,3,7,8]=>0101000=>1010111
[5,6,8,4,3,7,1,2]=>0011010=>1100101
[5,6,1,4,2,3,8,7]=>0101001=>1010110
[5,2,8,3,4,1,7,6]=>1010101=>0101010
[4,5,8,6,3,2,1,7]=>0011110=>1100001
[4,6,5,8,3,2,1,7]=>0101110=>1010001
[4,7,5,6,3,2,1,8]=>0101110=>1010001
[6,2,3,4,5,8,1,7]=>1000010=>0111101
[5,1,4,3,6,2,8,7]=>1010101=>0101010
[5,1,4,3,7,2,8,6]=>1010101=>0101010
[5,1,4,3,8,2,7,6]=>1010101=>0101010
[5,6,2,4,1,7,8,3]=>0101001=>1010110
[5,6,2,4,1,8,7,3]=>0101011=>1010100
[5,7,2,4,1,8,6,3]=>0101011=>1010100
[6,1,4,2,8,7,5,3]=>1010111=>0101000
[6,1,4,2,7,8,5,3]=>1010011=>0101100
[5,8,2,4,1,7,6,3]=>0101011=>1010100
[5,2,7,4,1,6,8,3]=>1011001=>0100110
[5,4,1,3,7,2,6,8]=>1100100=>0011011
[5,1,4,3,6,2,7,8]=>1010100=>0101011
[5,8,6,4,3,7,1,2]=>0111010=>1000101
[5,8,1,4,2,3,7,6]=>0101001=>1010110
[5,1,6,3,4,2,7,8]=>1010100=>0101011
[4,8,6,5,3,2,1,7]=>0111110=>1000001
[4,8,5,6,3,2,1,7]=>0101110=>1010001
[5,4,7,8,3,2,1,6]=>1001110=>0110001
[5,4,8,7,3,2,1,6]=>1011110=>0100001
[4,6,8,7,3,2,1,5]=>0011110=>1100001
[4,6,7,8,3,2,1,5]=>0001110=>1110001
[4,7,6,8,3,2,1,5]=>0101110=>1010001
[4,7,8,5,3,2,1,6]=>0011110=>1100001
[5,7,1,3,4,2,6,8]=>0100100=>1011011
[5,1,8,4,2,3,6,7]=>1011000=>0100111
[5,1,7,4,2,3,6,8]=>1011000=>0100111
[5,8,1,3,4,2,6,7]=>0100100=>1011011
[4,8,7,5,3,2,1,6]=>0111110=>1000001
[4,7,8,6,3,2,1,5]=>0011110=>1100001
[4,8,7,6,3,2,1,5]=>0111110=>1000001
[4,8,2,6,3,7,5,1]=>0101011=>1010100
[4,8,2,3,6,7,5,1]=>0100011=>1011100
[4,8,3,1,6,7,5,2]=>0110011=>1001100
[4,3,8,1,6,2,5,7]=>1010100=>0101011
[1,4,8,7,3,5,2,6]=>0011010=>1100101
[4,3,8,7,2,5,1,6]=>1011010=>0100101
[5,8,4,3,7,1,6,2]=>0110101=>1001010
[5,8,1,4,7,2,6,3]=>0100101=>1011010
[5,8,1,7,4,2,3,6]=>0101100=>1010011
[6,8,1,2,4,3,5,7]=>0100100=>1011011
[5,8,7,1,3,4,2,6]=>0110010=>1001101
[4,8,7,6,3,1,2,5]=>0111100=>1000011
[5,8,4,7,3,1,2,6]=>0101100=>1010011
[4,3,8,2,7,5,6,1]=>1010101=>0101010
[1,4,8,3,7,5,6,2]=>0010101=>1101010
[1,4,3,8,2,6,5,7]=>0101010=>1010101
[4,3,2,8,1,6,5,7]=>1101010=>0010101
[4,1,3,8,2,6,5,7]=>1001010=>0110101
[4,1,8,3,7,5,6,2]=>1010101=>0101010
[4,1,8,7,3,5,2,6]=>1011010=>0100101
[3,7,8,1,5,4,2,6]=>0010110=>1101001
[7,3,8,1,5,4,6,2]=>1010101=>0101010
[3,4,8,1,6,2,5,7]=>0010100=>1101011
[3,4,8,7,2,5,1,6]=>0011010=>1100101
[3,4,8,2,7,5,6,1]=>0010101=>1101010
[1,2,4,8,3,6,5,7]=>0001010=>1110101
[1,2,4,3,8,6,5,7]=>0010110=>1101001
[3,4,2,1,8,6,5,7]=>0110110=>1001001
[3,4,1,8,2,6,5,7]=>0101010=>1010101
[3,6,7,8,4,1,2,5]=>0001100=>1110011
[4,1,7,8,5,3,2,6]=>1001110=>0110001
[4,1,2,8,3,6,5,7]=>1001010=>0110101
[1,4,3,2,8,6,5,7]=>0110110=>1001001
[4,2,3,1,8,6,5,7]=>1010110=>0101001
[3,7,6,8,4,2,1,5]=>0101110=>1010001
[4,7,1,8,5,2,3,6]=>0101100=>1010011
[2,6,8,7,4,3,1,5]=>0011110=>1100001
[3,7,8,6,2,4,1,5]=>0011010=>1100101
[3,7,8,2,6,4,5,1]=>0010101=>1101010
[4,2,3,8,1,6,5,7]=>1001010=>0110101
[4,3,1,8,2,6,5,7]=>1101010=>0010101
[1,4,7,8,5,3,2,6]=>0001110=>1110001
[4,3,7,8,5,2,1,6]=>1001110=>0110001
[3,7,2,8,4,6,5,1]=>0101011=>1010100
[4,2,8,6,3,1,5,7]=>1011100=>0100011
[2,6,8,4,7,3,1,5]=>0010110=>1101001
[2,4,8,6,3,1,5,7]=>0011100=>1100011
[7,3,6,8,4,2,1,5]=>1001110=>0110001
[7,6,2,8,3,5,4,1]=>1101011=>0010100
[1,7,3,8,4,6,5,2]=>0101011=>1010100
[1,3,4,8,2,6,5,7]=>0001010=>1110101
[3,2,4,8,1,6,5,7]=>1001010=>0110101
[7,3,8,6,2,4,1,5]=>1011010=>0100101
[7,3,8,2,6,4,5,1]=>1010101=>0101010
[2,4,8,3,6,1,5,7]=>0010100=>1101011
[6,2,8,7,4,3,5,1]=>1011101=>0100010
[7,4,1,8,5,2,6,3]=>1101101=>0010010
[7,3,2,8,4,6,5,1]=>1101011=>0010100
[2,4,3,1,8,6,5,7]=>0110110=>1001001
[1,3,4,2,8,6,5,7]=>0010110=>1101001
[1,3,2,4,8,6,5,7]=>0100110=>1011001
[3,2,1,4,8,6,5,7]=>1100110=>0011001
[3,1,2,4,8,6,5,7]=>1000110=>0111001
[3,1,4,2,8,6,5,7]=>1010110=>0101001
[3,1,4,8,2,6,5,7]=>1001010=>0110101
[7,3,4,8,5,1,6,2]=>1001101=>0110010
[3,7,4,8,5,1,2,6]=>0101100=>1010011
[6,7,2,8,3,5,4,1]=>0101011=>1010100
[2,3,1,4,8,6,5,7]=>0100110=>1011001
[2,1,3,4,8,6,5,7]=>1000110=>0111001
[1,2,3,4,8,6,5,7]=>0000110=>1111001
[4,8,3,6,2,1,5,7]=>0101100=>1010011
[3,5,8,2,6,1,4,7]=>0010100=>1101011
[3,6,5,8,2,4,1,7]=>0101010=>1010101
[5,3,8,7,2,4,6,1]=>1011001=>0100110
[2,8,4,5,7,3,6,1]=>0100101=>1011010
[2,4,5,7,3,8,1,6]=>0001010=>1110101
[6,2,4,5,8,3,1,7]=>1000110=>0111001
[4,8,1,2,5,6,3,7]=>0100010=>1011101
[8,1,3,5,2,6,4,7]=>1001010=>0110101
[5,2,1,6,3,8,4,7]=>1101010=>0010101
[6,2,5,1,8,4,3,7]=>1010110=>0101001
[3,6,1,5,8,4,2,7]=>0100110=>1011001
[6,1,4,5,8,3,2,7]=>1000110=>0111001
[5,6,4,8,1,3,2,7]=>0101010=>1010101
[6,5,4,3,8,2,1,7]=>1110110=>0001001
[5,4,3,7,2,8,1,6]=>1101010=>0010101
[5,8,4,3,7,2,6,1]=>0110101=>1001010
[4,6,8,3,7,2,5,1]=>0010101=>1101010
[7,4,6,3,2,8,1,5]=>1011010=>0100101
[1,4,3,6,2,7,8,5]=>0101001=>1010110
[1,5,4,3,7,2,8,6]=>0110101=>1001010
[4,7,8,5,3,1,2,6]=>0011100=>1100011
[5,7,3,4,1,2,8,6]=>0101001=>1010110
[8,5,4,7,6,2,1,3]=>1101110=>0010001
[8,5,7,4,3,6,1,2]=>1011010=>0100101
[4,3,8,1,6,7,5,2]=>1010011=>0101100
[4,7,8,3,6,1,5,2]=>0010101=>1101010
[5,3,8,6,7,4,1,2]=>1010110=>0101001
[1,3,8,6,4,7,5,2]=>0011011=>1100100
[8,6,2,7,4,1,5,3]=>1101101=>0010010
[7,6,2,1,4,3,8,5]=>1110101=>0001010
[7,6,1,3,4,2,8,5]=>1100101=>0011010
[1,5,7,3,2,6,8,4]=>0011001=>1100110
[1,6,7,3,2,5,8,4]=>0011001=>1100110
[3,2,6,8,5,7,4,1]=>1001011=>0110100
[5,8,2,3,6,7,4,1]=>0100011=>1011100
[7,5,2,3,1,6,8,4]=>1101001=>0010110
[1,6,4,7,2,3,8,5]=>0101001=>1010110
[3,1,7,5,2,8,4,6]=>1011010=>0100101
[2,5,7,4,1,8,3,6]=>0011010=>1100101
[4,2,6,1,7,8,3,5]=>1010010=>0101101
[4,2,7,6,3,8,1,5]=>1011010=>0100101
[6,4,8,7,2,3,5,1]=>1011001=>0100110
[3,2,6,8,7,4,5,1]=>1001101=>0110010
[3,2,7,4,1,6,8,5]=>1011001=>0100110
[6,3,2,1,7,8,4,5]=>1110010=>0001101
[3,7,1,8,4,2,5,6]=>0101100=>1010011
[4,2,1,3,7,5,8,6]=>1100101=>0011010
[8,1,3,7,4,2,6,5]=>1001101=>0110010
[8,4,3,7,6,2,1,5]=>1101110=>0010001
[8,3,5,2,7,6,1,4]=>1010110=>0101001
[3,6,2,8,7,1,5,4]=>0101101=>1010010
[7,3,2,8,1,6,5,4]=>1101011=>0010100
[3,8,7,2,6,5,4,1]=>0110111=>1001000
[4,2,7,8,6,1,5,3]=>1001101=>0110010
[6,8,2,4,7,1,5,3]=>0100101=>1011010
[5,2,1,8,7,3,6,4]=>1101101=>0010010
[8,2,1,6,3,7,5,4]=>1101011=>0010100
[6,8,3,1,7,5,2,4]=>0110110=>1001001
[5,8,1,6,7,2,4,3]=>0100101=>1011010
[6,2,8,1,5,7,4,3]=>1010011=>0101100
[5,7,8,2,6,1,4,3]=>0010101=>1101010
[8,7,2,5,6,4,3,1]=>1100111=>0011000
[8,6,7,5,2,4,3,1]=>1011011=>0100100
[7,2,6,8,1,5,4,3]=>1001011=>0110100
[1,2,7,8,5,6,4,3]=>0001011=>1110100
[7,4,8,1,6,2,5,3]=>1010101=>0101010
[3,7,1,8,2,6,5,4]=>0101011=>1010100
[2,1,7,3,8,6,5,4]=>1010111=>0101000
[8,2,1,7,6,5,4,3]=>1101111=>0010000
[8,1,4,7,6,5,3,2]=>1001111=>0110000
[8,6,7,5,1,4,3,2]=>1011011=>0100100
[7,8,6,5,4,1,3,2]=>0111101=>1000010
[5,8,4,3,2,1,6,7]=>0111100=>1000011
[6,4,7,3,2,1,8,5]=>1011101=>0100010
[5,4,7,3,2,1,6,8]=>1011100=>0100011
[6,5,3,7,2,1,4,8]=>1101100=>0010011
[5,8,3,6,2,1,4,7]=>0101100=>1010011
[6,3,7,8,2,1,4,5]=>1001100=>0110011
[5,3,7,6,2,1,4,8]=>1011100=>0100011
[3,8,7,6,2,1,4,5]=>0111100=>1000011
[5,8,4,2,6,1,3,7]=>0110100=>1001011
[4,8,7,2,5,1,3,6]=>0110100=>1001011
[5,8,3,2,6,1,4,7]=>0110100=>1001011
[4,8,3,2,5,1,7,6]=>0110101=>1001010
[4,3,7,2,5,1,8,6]=>1010101=>0101010
[3,8,7,2,5,1,4,6]=>0110100=>1001011
[6,4,2,7,5,1,3,8]=>1101100=>0010011
[6,3,2,7,5,1,4,8]=>1101100=>0010011
[5,3,2,6,7,1,4,8]=>1100100=>0011011
[3,8,2,6,5,1,4,7]=>0101100=>1010011
[6,2,7,8,5,1,3,4]=>1001100=>0110011
[5,2,7,6,8,1,3,4]=>1010100=>0101011
[4,2,7,6,5,1,3,8]=>1011100=>0100011
[2,8,7,6,5,1,3,4]=>0111100=>1000011
[6,5,4,3,1,7,8,2]=>1111001=>0000110
[6,4,7,3,1,5,8,2]=>1011001=>0100110
[5,4,7,3,1,8,6,2]=>1011011=>0100100
[6,4,3,7,1,5,8,2]=>1101001=>0010110
[5,4,3,6,1,8,7,2]=>1101011=>0010100
[6,3,7,8,1,4,5,2]=>1001001=>0110110
[5,3,7,6,1,4,8,2]=>1011001=>0100110
[4,3,7,6,1,5,8,2]=>1011001=>0100110
[3,8,7,6,1,4,5,2]=>0111001=>1000110
[6,5,4,2,1,7,3,8]=>1111010=>0000101
[6,4,7,2,1,5,3,8]=>1011010=>0100101
[4,8,7,2,1,5,3,6]=>0111010=>1000101
[5,8,3,2,1,4,7,6]=>0111001=>1000110
[4,8,3,2,1,5,7,6]=>0111001=>1000110
[5,3,7,2,1,4,8,6]=>1011001=>0100110
[3,8,7,2,1,4,5,6]=>0111000=>1000111
[6,5,2,7,1,4,3,8]=>1101010=>0010101
[5,8,2,6,1,4,3,7]=>0101010=>1010101
[6,4,2,7,1,5,3,8]=>1101010=>0010101
[5,4,2,6,1,8,3,7]=>1101010=>0010101
[4,3,2,6,1,5,8,7]=>1101001=>0010110
[6,2,7,8,1,4,3,5]=>1001010=>0110101
[4,2,7,6,1,5,3,8]=>1011010=>0100101
[3,2,7,6,1,4,5,8]=>1011000=>0100111
[6,5,4,1,8,7,3,2]=>1110111=>0001000
[5,8,4,1,6,7,3,2]=>0110011=>1001100
[6,4,7,1,5,8,3,2]=>1010011=>0101100
[5,4,7,1,6,8,3,2]=>1010011=>0101100
[4,8,7,1,5,6,3,2]=>0110011=>1001100
[5,4,3,1,6,8,7,2]=>1110011=>0001100
[4,8,3,1,5,6,7,2]=>0110001=>1001110
[3,8,7,1,5,4,6,2]=>0110101=>1001010
[5,8,2,1,6,4,3,7]=>0110110=>1001001
[6,3,2,1,5,4,8,7]=>1110101=>0001010
[5,3,2,1,6,4,8,7]=>1110101=>0001010
[3,8,2,1,5,4,6,7]=>0110100=>1001011
[6,2,7,1,5,4,3,8]=>1010110=>0101001
[5,2,7,1,6,4,3,8]=>1010110=>0101001
[4,2,7,1,5,6,3,8]=>1010010=>0101101
[3,2,7,1,5,4,6,8]=>1010100=>0101011
[2,8,7,1,5,4,3,6]=>0110110=>1001001
[6,5,1,7,8,4,3,2]=>1100111=>0011000
[5,8,1,6,7,4,3,2]=>0100111=>1011000
[6,4,1,7,5,8,3,2]=>1101011=>0010100
[5,4,1,6,7,8,3,2]=>1100011=>0011100
[4,8,1,6,5,7,3,2]=>0101011=>1010100
[6,3,1,7,5,4,8,2]=>1101101=>0010010
[5,3,1,6,7,4,8,2]=>1100101=>0011010
[4,3,1,6,5,7,8,2]=>1101001=>0010110
[3,8,1,6,5,4,7,2]=>0101101=>1010010
[5,2,1,6,7,4,3,8]=>1100110=>0011001
[4,2,1,6,5,7,3,8]=>1101010=>0010101
[2,8,1,6,5,4,3,7]=>0101110=>1010001
[6,1,7,8,5,4,3,2]=>1001111=>0110000
[4,1,7,6,5,8,3,2]=>1011011=>0100100
[3,1,7,6,5,4,8,2]=>1011101=>0100010
[4,5,8,1,2,6,3,7]=>0010010=>1101101
[1,4,5,7,2,6,3,8]=>0001010=>1110101
[1,7,3,5,6,2,4,8]=>0100100=>1011011
[8,1,3,5,7,2,4,6]=>1000100=>0111011
[3,6,8,1,7,2,4,5]=>0010100=>1101011
[3,4,5,6,8,1,7,2]=>0000101=>1111010
[4,5,8,2,6,7,1,3]=>0010010=>1101101
[8,2,3,5,6,7,1,4]=>1000010=>0111101
[1,7,2,3,5,4,6,8]=>0100100=>1011011
[8,1,2,3,5,4,6,7]=>1000100=>0111011
[2,7,8,1,3,5,4,6]=>0010010=>1101101
[2,7,8,3,5,6,1,4]=>0010010=>1101101
[2,4,5,7,8,1,6,3]=>0000101=>1111010
[4,5,8,1,7,6,3,2]=>0010111=>1101000
[4,5,8,7,2,1,6,3]=>0011101=>1100010
[8,7,3,5,6,2,1,4]=>1100110=>0011001
[8,7,2,1,3,5,4,6]=>1110010=>0001101
[3,6,8,7,2,1,5,4]=>0011101=>1100010
[8,6,4,1,7,5,3,2]=>1110111=>0001000
[7,6,4,3,1,8,5,2]=>1111011=>0000100
[2,3,6,7,8,1,5,4]=>0000101=>1111010
[3,6,8,1,2,5,4,7]=>0010010=>1101101
[1,3,6,7,2,5,4,8]=>0001010=>1110101
[7,4,1,8,5,2,3,6]=>1101100=>0010011
[7,1,4,2,8,3,6,5]=>1010101=>0101010
[7,1,8,2,5,3,6,4]=>1010101=>0101010
[8,1,7,5,4,2,3,6]=>1011100=>0100011
[1,7,2,6,5,4,3,8]=>0101110=>1010001
[1,7,6,3,2,5,4,8]=>0111010=>1000101
[8,6,3,1,2,5,4,7]=>1110010=>0001101
[8,1,7,6,3,2,4,5]=>1011100=>0100011
[8,2,5,7,6,3,1,4]=>1001110=>0110001
[3,6,8,1,7,5,4,2]=>0010111=>1101000
[8,2,6,7,5,4,1,3]=>1001110=>0110001
[2,7,8,6,3,1,5,4]=>0011101=>1100010
[2,7,8,1,6,5,4,3]=>0010111=>1101000
[7,3,1,8,6,5,4,2]=>1101111=>0010000
[8,7,2,1,6,5,4,3]=>1110111=>0001000
[8,7,6,3,2,1,5,4]=>1111101=>0000010
[2,1,8,6,3,7,4,5]=>1011010=>0100101
[8,6,1,5,2,7,4,3]=>1101011=>0010100
[8,5,1,7,4,2,6,3]=>1101101=>0010010
[2,1,7,5,4,3,8,6]=>1011101=>0100010
[2,1,7,8,3,6,5,4]=>1001011=>0110100
[2,1,4,8,5,7,3,6]=>1001010=>0110101
[8,5,3,1,6,2,4,7]=>1110100=>0001011
[6,4,1,5,2,3,8,7]=>1101001=>0010110
[8,3,7,5,2,6,1,4]=>1011010=>0100101
[5,3,7,4,6,8,1,2]=>1010010=>0101101
[5,8,3,7,6,2,1,4]=>0101110=>1010001
[4,2,6,3,8,5,1,7]=>1010110=>0101001
[5,8,2,1,7,6,4,3]=>0110111=>1001000
[8,3,2,4,1,7,5,6]=>1101010=>0010101
[7,8,3,1,5,4,6,2]=>0110101=>1001010
[7,2,8,1,4,6,5,3]=>1010011=>0101100
[6,2,3,1,4,5,8,7]=>1010001=>0101110
[6,8,1,4,5,3,2,7]=>0100110=>1011001
[8,2,6,1,4,7,3,5]=>1010010=>0101101
[8,3,5,6,1,7,4,2]=>1001011=>0110100
[6,3,5,4,1,2,8,7]=>1011001=>0100110
[8,7,3,6,5,1,4,2]=>1101101=>0010010
[2,7,4,3,6,1,8,5]=>0110101=>1001010
[3,4,7,2,8,1,5,6]=>0010100=>1101011
[4,2,3,5,8,1,6,7]=>1000100=>0111011
[3,8,4,7,1,6,5,2]=>0101011=>1010100
[3,2,4,6,1,5,8,7]=>1001001=>0110110
[8,3,4,5,7,6,1,2]=>1000110=>0111001
[3,2,4,5,6,8,1,7]=>1000010=>0111101
[5,6,8,1,4,2,7,3]=>0010101=>1101010
[1,5,7,8,4,6,2,3]=>0001010=>1110101
[1,3,5,7,8,6,2,4]=>0000110=>1111001
[3,5,7,8,6,1,2,4]=>0001100=>1110011
[3,5,1,6,8,2,7,4]=>0100101=>1011010
[3,1,5,6,8,2,7,4]=>1000101=>0111010
[2,3,5,6,8,1,7,4]=>0000101=>1111010
[5,6,4,8,2,1,7,3]=>0101101=>1010010
[5,1,6,3,8,4,7,2]=>1010101=>0101010
[2,5,1,6,8,3,7,4]=>0100101=>1011010
[5,1,2,6,8,3,7,4]=>1000101=>0111010
[5,7,1,8,6,2,3,4]=>0101100=>1010011
[1,5,2,7,8,6,3,4]=>0100110=>1011001
[1,6,7,5,2,8,3,4]=>0011010=>1100101
[6,1,7,5,2,8,3,4]=>1011010=>0100101
[2,6,7,5,1,8,3,4]=>0011010=>1100101
[5,7,2,8,6,1,3,4]=>0101100=>1010011
[3,5,7,8,6,2,1,4]=>0001110=>1110001
[5,1,7,8,6,3,4,2]=>1001101=>0110010
[5,1,3,7,8,6,4,2]=>1000111=>0111000
[5,2,7,8,4,6,1,3]=>1001010=>0110101
[3,2,5,7,8,6,1,4]=>1000110=>0111001
[6,2,7,5,1,8,3,4]=>1011010=>0100101
[1,2,6,7,5,8,3,4]=>0001010=>1110101
[6,2,7,5,4,1,8,3]=>1011101=>0100010
[6,7,5,2,4,1,8,3]=>0110101=>1001010
[6,7,2,5,3,8,1,4]=>0101010=>1010101
[6,7,4,5,2,1,8,3]=>0101101=>1010010
[5,1,7,8,6,4,3,2]=>1001111=>0110000
[2,5,7,8,6,3,1,4]=>0001110=>1110001
[5,1,7,8,6,3,2,4]=>1001110=>0110001
[6,3,7,5,1,8,2,4]=>1011010=>0100101
[1,6,7,5,3,8,2,4]=>0011010=>1100101
[1,6,7,5,4,2,8,3]=>0011101=>1100010
[6,7,5,1,4,2,8,3]=>0110101=>1001010
[5,7,8,6,4,1,2,3]=>0011100=>1100011
[4,1,7,2,6,5,8,3]=>1010101=>0101010
[2,4,7,1,5,6,8,3]=>0010001=>1101110
[6,7,4,1,5,2,8,3]=>0110101=>1001010
[1,6,7,4,5,2,8,3]=>0010101=>1101010
[1,6,3,7,5,8,2,4]=>0101010=>1010101
[6,3,1,7,5,8,2,4]=>1101010=>0010101
[2,5,3,7,8,6,1,4]=>0100110=>1011001
[6,7,5,4,2,1,8,3]=>0111101=>1000010
[6,3,2,7,5,8,1,4]=>1101010=>0010101
[6,7,4,2,5,1,8,3]=>0110101=>1001010
[6,2,7,4,5,1,8,3]=>1010101=>0101010
[6,2,3,7,5,8,1,4]=>1001010=>0110101
[4,5,1,6,3,2,8,7]=>0101101=>1010010
[7,5,1,6,3,8,2,4]=>1101010=>0010101
[7,5,1,6,3,8,4,2]=>1101011=>0010100
[2,7,6,1,3,8,4,5]=>0110010=>1001101
[2,7,6,1,3,8,5,4]=>0110011=>1001100
[7,3,5,1,8,2,6,4]=>1010101=>0101010
[7,3,5,1,8,2,4,6]=>1010100=>0101011
[3,7,5,1,8,6,2,4]=>0110110=>1001001
[2,6,7,1,5,8,3,4]=>0010010=>1101101
[2,6,7,4,1,8,3,5]=>0011010=>1100101
[2,1,6,7,3,8,5,4]=>1001011=>0110100
[2,6,7,4,1,8,5,3]=>0011011=>1100100
[2,6,7,1,5,8,4,3]=>0010011=>1101100
[3,6,5,1,8,4,7,2]=>0110101=>1001010
[3,6,5,1,8,4,2,7]=>0110110=>1001001
[3,7,5,4,8,1,6,2]=>0110101=>1001010
[3,7,5,4,8,1,2,6]=>0110100=>1001011
[4,6,1,5,8,7,3,2]=>0100111=>1011000
[4,6,1,5,8,7,2,3]=>0100110=>1011001
[4,6,1,5,8,2,7,3]=>0100101=>1011010
[7,5,1,6,2,8,3,4]=>1101010=>0010101
[7,5,1,6,2,8,4,3]=>1101011=>0010100
[4,6,1,5,8,2,3,7]=>0100100=>1011011
[4,7,1,5,8,3,6,2]=>0100101=>1011010
[2,3,4,7,8,1,6,5]=>0000101=>1111010
[6,8,5,4,3,2,7,1]=>0111101=>1000010
[10,11,9,8,7,6,5,4,3,2,1]=>0111111111=>1000000000
[7,9,6,5,4,3,2,8,1]=>01111101=>10000010
[8,9,6,5,4,3,2,1,7]=>01111110=>10000001
[6,8,5,4,3,7,2,1]=>0111011=>1000100
[5,8,4,3,2,1,7,6]=>0111101=>1000010
[6,5,4,3,1,8,7,2]=>1111011=>0000100
[8,7,6,5,4,3,9,1,2]=>11111010=>00000101
[8,7,5,4,3,1,6,2]=>1111101=>0000010
[9,7,6,5,4,3,1,8,2]=>11111101=>00000010
[11,10,9,8,7,6,5,4,3,1,2]=>1111111110=>0000000001
[8,3,4,6,2,1,5,7]=>1001100=>0110011
[3,5,6,2,1,8,4,7]=>0011010=>1100101
[3,5,2,6,8,4,1,7]=>0100110=>1011001
[7,5,3,2,8,4,1,6]=>1110110=>0001001
[7,5,3,2,8,4,6,1]=>1110101=>0001010
[2,4,5,7,3,8,6,1]=>0001011=>1110100
[4,2,5,6,8,3,1,7]=>1000110=>0111001
[4,2,8,1,5,6,3,7]=>1010010=>0101101
[2,5,6,1,8,4,3,7]=>0010110=>1101001
[5,3,6,8,1,4,2,7]=>1001010=>0110101
[4,5,6,8,1,3,2,7]=>0001010=>1110101
[1,4,5,6,8,3,2,7]=>0000110=>1111001
[4,5,6,3,8,2,1,7]=>0010110=>1101001
[4,5,3,7,2,8,6,1]=>0101011=>1010100
[6,4,7,3,2,8,5,1]=>1011011=>0100100
[6,1,4,7,3,2,8,5]=>1001101=>0110010
[1,7,8,4,5,3,2,6]=>0010110=>1101001
[5,1,7,3,8,4,2,6]=>1010110=>0101001
[2,5,1,7,4,3,8,6]=>0101101=>1010010
[2,5,7,4,1,8,6,3]=>0011011=>1100100
[5,3,7,1,4,8,6,2]=>1010011=>0101100
[6,4,3,1,7,8,5,2]=>1110011=>0001100
[6,4,1,7,3,8,5,2]=>1101011=>0010100
[5,6,3,7,8,4,2,1]=>0100111=>1011000
[5,1,6,3,7,8,4,2]=>1010011=>0101100
[5,6,1,3,7,8,4,2]=>0100011=>1011100
[5,6,1,7,8,3,4,2]=>0100101=>1011010
[1,6,3,7,4,8,5,2]=>0101011=>1010100
[6,7,2,4,1,8,5,3]=>0101011=>1010100
[6,7,2,1,4,3,8,5]=>0110101=>1001010
[6,4,7,3,1,2,8,5]=>1011001=>0100110
[5,6,3,1,2,7,8,4]=>0110001=>1001110
[5,6,1,3,2,7,8,4]=>0101001=>1010110
[5,6,3,2,1,7,8,4]=>0111001=>1000110
[2,5,6,3,7,8,4,1]=>0010011=>1101100
[2,5,6,3,1,7,8,4]=>0011001=>1100110
[2,6,4,7,3,1,8,5]=>0101101=>1010010
[6,3,7,2,8,4,5,1]=>1010101=>0101010
[6,3,7,2,8,4,1,5]=>1010110=>0101001
[6,3,2,7,1,8,4,5]=>1101010=>0010101
[7,5,3,2,1,8,4,6]=>1111010=>0000101
[7,3,8,4,2,1,5,6]=>1011100=>0100011
[4,7,2,1,3,8,6,5]=>0110011=>1001100
[1,3,7,8,6,4,2,5]=>0001110=>1110001
[7,3,8,4,6,2,1,5]=>1010110=>0101001
[5,7,3,8,2,1,6,4]=>0101101=>1010010
[6,3,7,8,5,2,1,4]=>1001110=>0110001
[4,6,2,7,8,5,3,1]=>0100111=>1011000
[4,6,2,1,7,8,5,3]=>0110011=>1001100
[7,4,5,8,1,2,6,3]=>1001001=>0110110
[2,5,1,7,3,8,6,4]=>0101011=>1010100
[6,7,2,1,3,8,5,4]=>0110011=>1001100
[5,1,6,7,8,2,4,3]=>1000101=>0111010
[6,3,7,1,8,5,2,4]=>1010110=>0101001
[6,2,1,7,3,8,5,4]=>1101011=>0010100
[6,2,7,1,8,5,4,3]=>1010111=>0101000
[6,3,1,7,8,5,4,2]=>1100111=>0011000
[4,1,3,6,8,2,5,7]=>1000100=>0111011
[4,2,3,6,8,1,5,7]=>1000100=>0111011
[5,3,2,1,8,4,7,6]=>1110101=>0001010
[3,6,5,8,2,1,7,4]=>0101101=>1010010
[4,5,2,1,3,8,7,6]=>0110011=>1001100
[3,2,6,4,5,8,1,7]=>1010010=>0101101
[2,4,6,5,8,1,3,7]=>0010100=>1101011
[1,6,2,4,5,8,3,7]=>0100010=>1011101
[5,3,2,1,6,8,4,7]=>1110010=>0001101
[6,2,4,5,8,1,3,7]=>1000100=>0111011
[1,3,4,6,5,8,2,7]=>0001010=>1110101
[1,6,3,4,5,8,2,7]=>0100010=>1011101
[3,4,1,8,5,2,7,6]=>0101101=>1010010
[2,8,4,1,7,6,3,5]=>0110110=>1001001
[8,1,4,2,7,3,6,5]=>1010101=>0101010
[1,5,3,2,8,7,4,6]=>0110110=>1001001
[8,2,1,7,5,3,4,6]=>1101100=>0010011
[1,7,6,4,5,8,3,2]=>0110011=>1001100
[5,8,7,4,1,2,6,3]=>0111001=>1000110
[5,8,7,4,6,2,1,3]=>0110110=>1001001
[3,4,2,5,8,6,7,1]=>0100101=>1011010
[4,1,3,5,6,8,7,2]=>1000011=>0111100
[2,4,8,6,7,1,3,5]=>0010100=>1101011
[4,3,6,2,8,1,7,5]=>1010101=>0101010
[3,7,4,8,2,1,6,5]=>0101101=>1010010
[2,3,5,8,6,7,1,4]=>0001010=>1110101
[3,2,5,6,8,7,1,4]=>1000110=>0111001
[2,1,8,5,6,7,3,4]=>1010010=>0101101
[1,2,8,3,5,6,7,4]=>0010001=>1101110
[4,2,3,7,1,8,6,5]=>1001011=>0110100
[3,2,6,4,8,1,7,5]=>1010101=>0101010
[8,2,1,6,7,3,4,5]=>1100100=>0011011
[2,7,8,5,4,1,3,6]=>0011100=>1100011
[1,7,5,3,8,4,2,6]=>0110110=>1001001
[4,7,5,3,1,2,8,6]=>0111001=>1000110
[7,2,4,8,5,3,1,6]=>1001110=>0110001
[4,8,3,1,2,7,6,5]=>0110011=>1001100
[3,5,2,7,4,1,8,6]=>0101101=>1010010
[8,4,2,3,7,1,5,6]=>1100100=>0011011
[2,8,4,7,1,3,5,6]=>0101000=>1010111
[8,2,4,6,7,1,3,5]=>1000100=>0111011
[4,8,2,3,6,7,1,5]=>0100010=>1011101
[3,5,2,7,6,1,8,4]=>0101101=>1010010
[1,6,3,2,5,8,7,4]=>0110011=>1001100
[5,8,3,2,1,6,7,4]=>0111001=>1000110
[5,8,7,3,4,6,2,1]=>0110011=>1001100
[5,8,2,7,4,1,6,3]=>0101101=>1010010
[5,1,4,2,8,7,6,3]=>1010111=>0101000
[4,7,6,5,8,2,1,3]=>0110110=>1001001
[5,3,7,1,6,2,8,4]=>1010101=>0101010
[5,2,6,8,7,1,3,4]=>1001100=>0110011
[6,3,2,1,8,5,7,4]=>1110101=>0001010
[2,7,5,4,1,8,6,3]=>0111011=>1000100
[4,2,5,6,8,7,1,3]=>1000110=>0111001
[1,8,4,2,5,6,7,3]=>0110001=>1001110
[3,8,4,1,5,6,7,2]=>0110001=>1001110
[4,2,8,5,6,7,1,3]=>1010010=>0101101
[5,2,4,7,1,8,6,3]=>1001011=>0110100
[5,3,4,7,1,8,6,2]=>1001011=>0110100
[8,6,4,1,3,2,5,7]=>1110100=>0001011
[8,1,3,6,5,2,4,7]=>1001100=>0110011
[8,1,4,3,6,5,2,7]=>1010110=>0101001
[3,6,5,2,1,8,7,4]=>0111011=>1000100
[8,3,2,4,6,5,1,7]=>1100110=>0011001
[8,4,2,1,6,5,3,7]=>1110110=>0001001
[8,4,1,2,6,5,3,7]=>1100110=>0011001
[8,6,4,2,1,5,3,7]=>1111010=>0000101
[8,3,6,4,1,5,2,7]=>1011010=>0100101
[8,2,6,3,4,5,1,7]=>1010010=>0101101
[1,3,4,8,5,7,2,6]=>0001010=>1110101
[5,8,4,7,6,2,3,1]=>0101101=>1010010
[1,3,4,7,5,8,2,6]=>0001010=>1110101
[1,3,5,2,4,8,7,6]=>0010011=>1101100
[2,6,5,1,3,8,7,4]=>0110011=>1001100
[4,7,1,6,5,8,3,2]=>0101011=>1010100
[5,4,8,7,6,3,1,2]=>1011110=>0100001
[2,8,5,1,4,7,6,3]=>0110011=>1001100
[4,3,1,5,8,6,7,2]=>1100101=>0011010
[4,1,3,5,8,6,7,2]=>1000101=>0111010
[6,5,3,8,4,7,1,2]=>1101010=>0010101
[5,4,2,1,6,8,7,3]=>1110011=>0001100
[6,8,4,3,2,7,1,5]=>0111010=>1000101
[3,4,7,8,2,1,6,5]=>0001101=>1110010
[5,1,3,2,8,6,7,4]=>1010101=>0101010
[5,3,1,2,8,6,7,4]=>1100101=>0011010
[5,2,3,1,6,8,7,4]=>1010011=>0101100
[5,3,2,1,8,6,7,4]=>1110101=>0001010
[5,2,1,3,6,8,7,4]=>1100011=>0011100
[2,4,7,3,8,1,6,5]=>0010101=>1101010
[6,3,8,2,7,4,1,5]=>1010110=>0101001
[8,2,1,3,6,4,7,5]=>1100101=>0011010
[3,5,1,7,8,4,2,6]=>0100110=>1011001
[2,7,4,5,8,3,1,6]=>0100110=>1011001
[1,8,4,3,7,2,6,5]=>0110101=>1001010
[3,4,8,7,2,1,6,5]=>0011101=>1100010
[5,4,7,8,3,6,2,1]=>1001011=>0110100
[6,4,3,8,7,2,1,5]=>1101110=>0010001
[6,3,8,7,4,1,2,5]=>1011100=>0100011
[3,5,7,2,4,8,1,6]=>0010010=>1101101
[8,4,7,2,3,1,5,6]=>1010100=>0101011
[8,4,7,1,3,2,5,6]=>1010100=>0101011
[8,4,7,2,1,3,5,6]=>1011000=>0100111
[8,6,4,2,1,3,7,5]=>1111001=>0000110
[8,6,4,1,3,2,7,5]=>1110101=>0001010
[8,6,4,2,3,1,7,5]=>1110101=>0001010
[3,5,7,2,6,1,8,4]=>0010101=>1101010
[6,1,3,8,5,7,2,4]=>1001010=>0110101
[5,8,3,2,6,7,1,4]=>0110010=>1001101
[4,8,5,3,6,2,7,1]=>0110101=>1001010
[2,8,1,5,4,7,6,3]=>0101011=>1010100
[1,5,8,7,4,6,2,3]=>0011010=>1100101
[2,1,7,6,4,5,8,3]=>1011001=>0100110
[1,7,2,4,6,5,8,3]=>0100101=>1011010
[3,5,1,7,6,8,2,4]=>0101010=>1010101
[5,8,2,6,1,3,7,4]=>0101001=>1010110
[6,3,5,8,7,2,1,4]=>1001110=>0110001
[2,5,7,8,4,1,6,3]=>0001101=>1110010
[4,2,8,1,5,6,7,3]=>1010001=>0101110
[4,1,5,2,6,8,7,3]=>1010011=>0101100
[3,4,5,1,6,8,7,2]=>0010011=>1101100
[4,2,8,5,1,6,7,3]=>1011001=>0100110
[4,1,8,5,2,6,7,3]=>1011001=>0100110
[2,7,1,8,5,4,6,3]=>0101101=>1010010
[5,8,6,2,1,3,7,4]=>0111001=>1000110
[8,2,4,1,5,6,7,3]=>1010001=>0101110
[4,6,3,5,8,1,7,2]=>0100101=>1011010
[1,7,8,3,5,4,6,2]=>0010101=>1101010
[3,4,5,1,8,6,7,2]=>0010101=>1101010
[3,8,1,4,5,6,7,2]=>0100001=>1011110
[3,4,5,6,8,2,1,7]=>0000110=>1111001
[3,4,5,7,1,8,6,2]=>0001011=>1110100
[3,4,5,7,8,2,6,1]=>0000101=>1111010
[3,4,6,2,8,5,1,7]=>0010110=>1101001
[3,4,6,8,1,5,2,7]=>0001010=>1110101
[3,4,7,2,1,8,6,5]=>0011011=>1100100
[3,4,7,8,1,5,6,2]=>0001001=>1110110
[3,4,8,2,1,5,6,7]=>0011000=>1100111
[3,5,2,6,7,8,1,4]=>0100010=>1011101
[3,5,2,7,8,4,6,1]=>0100101=>1011010
[3,5,2,8,4,1,6,7]=>0101100=>1010011
[3,5,6,2,8,4,1,7]=>0010110=>1101001
[3,5,6,8,4,1,2,7]=>0001100=>1110011
[3,5,7,2,4,8,6,1]=>0010011=>1101100
[3,5,7,2,8,4,6,1]=>0010101=>1101010
[3,5,7,8,4,1,6,2]=>0001101=>1110010
[3,6,2,1,7,8,5,4]=>0110011=>1001100
[3,6,2,1,8,5,4,7]=>0110110=>1001001
[3,6,7,2,4,8,5,1]=>0010011=>1101100
[3,6,7,2,8,5,4,1]=>0010111=>1101000
[3,6,7,8,4,5,1,2]=>0001010=>1110101
[3,6,8,2,4,5,1,7]=>0010010=>1101101
[3,7,2,1,4,8,6,5]=>0110011=>1001100
[3,7,2,1,8,5,6,4]=>0110101=>1001010
[3,7,2,8,4,5,6,1]=>0101001=>1010110
[3,7,8,2,4,5,6,1]=>0010001=>1101110
[3,8,2,1,4,5,6,7]=>0110000=>1001111
[4,1,5,6,7,8,3,2]=>1000011=>0111100
[4,1,5,7,3,8,6,2]=>1001011=>0110100
[4,1,6,3,7,8,5,2]=>1010011=>0101100
[4,1,6,3,8,5,2,7]=>1010110=>0101001
[4,1,6,7,3,8,5,2]=>1001011=>0110100
[4,1,6,7,8,5,2,3]=>1000110=>0111001
[4,1,6,8,3,5,2,7]=>1001010=>0110101
[4,1,7,3,2,8,6,5]=>1011011=>0100100
[4,1,7,8,3,5,6,2]=>1001001=>0110110
[4,1,8,3,2,5,6,7]=>1011000=>0100111
[4,5,2,6,7,8,3,1]=>0100011=>1011100
[4,5,2,6,8,1,3,7]=>0100100=>1011011
[4,5,6,3,8,1,2,7]=>0010100=>1101011
[4,5,6,8,3,1,2,7]=>0001100=>1110011
[4,5,7,3,8,1,6,2]=>0010101=>1101010
[4,5,8,3,2,1,6,7]=>0011100=>1100011
[4,6,2,3,7,8,5,1]=>0100011=>1011100
[4,6,2,3,8,5,1,7]=>0100110=>1011001
[4,6,2,7,3,8,5,1]=>0101011=>1010100
[4,6,2,7,8,5,1,3]=>0100110=>1011001
[4,6,7,3,2,8,5,1]=>0011011=>1100100
[4,6,8,3,2,5,1,7]=>0011010=>1100101
[4,7,2,3,1,8,6,5]=>0101011=>1010100
[4,7,2,8,3,5,6,1]=>0101001=>1010110
[4,7,8,3,2,5,6,1]=>0011001=>1100110
[4,8,2,3,1,5,6,7]=>0101000=>1010111
[5,1,2,6,8,4,3,7]=>1000110=>0111001
[5,1,2,7,4,8,6,3]=>1001011=>0110100
[5,1,2,7,8,4,6,3]=>1000101=>0111010
[5,1,2,8,4,3,6,7]=>1001100=>0110011
[5,1,6,3,8,4,2,7]=>1010110=>0101001
[5,1,6,7,4,8,2,3]=>1001010=>0110101
[5,1,6,7,8,4,2,3]=>1000110=>0111001
[5,1,8,3,4,2,6,7]=>1010100=>0101011
[5,6,2,3,8,4,1,7]=>0100110=>1011001
[5,6,2,7,8,4,1,3]=>0100110=>1011001
[5,6,8,3,4,2,1,7]=>0010110=>1101001
[5,7,2,3,4,8,6,1]=>0100011=>1011100
[5,7,2,3,8,4,6,1]=>0100101=>1011010
[5,7,8,3,4,2,6,1]=>0010101=>1101010
[5,8,2,3,4,1,6,7]=>0100100=>1011011
[6,1,2,3,7,8,5,4]=>1000011=>0111100
[6,1,2,3,8,5,4,7]=>1000110=>0111001
[6,1,2,7,8,5,4,3]=>1000111=>0111000
[6,1,2,8,4,5,3,7]=>1001010=>0110101
[6,1,7,3,4,8,5,2]=>1010011=>0101100
[6,1,7,3,8,5,4,2]=>1010111=>0101000
[6,1,7,8,4,5,3,2]=>1001011=>0110100
[6,1,8,3,4,5,2,7]=>1010010=>0101101
[6,7,2,3,8,5,4,1]=>0100111=>1011000
[6,7,2,8,4,5,3,1]=>0101011=>1010100
[6,8,2,3,4,5,1,7]=>0100010=>1011101
[7,1,2,3,4,8,6,5]=>1000011=>0111100
[7,1,2,8,4,5,6,3]=>1001001=>0110110
[7,1,8,3,4,5,6,2]=>1010001=>0101110
[6,4,1,8,2,3,7,5]=>1101001=>0010110
[5,8,1,2,4,3,7,6]=>0100101=>1011010
[1,3,5,7,2,6,4,8]=>0001010=>1110101
[3,5,8,6,1,2,4,7]=>0011000=>1100111
[3,1,6,8,2,4,7,5]=>1001001=>0110110
[3,6,2,8,1,5,7,4]=>0101001=>1010110
[2,6,1,3,8,4,7,5]=>0100101=>1011010
[1,7,5,2,3,4,6,8]=>0110000=>1001111
[2,7,5,1,3,8,4,6]=>0110010=>1001101
[8,2,5,7,4,6,1,3]=>1001010=>0110101
[8,2,1,3,7,6,4,5]=>1100110=>0011001
[8,2,5,1,3,7,4,6]=>1010010=>0101101
[8,2,7,5,3,1,6,4]=>1011101=>0100010
[8,2,6,5,4,7,1,3]=>1011010=>0100101
[7,6,5,2,4,8,1,3]=>1110010=>0001101
[7,8,2,5,3,1,6,4]=>0101101=>1010010
[7,1,8,6,3,2,4,5]=>1011100=>0100011
[6,8,1,5,3,2,4,7]=>0101100=>1010011
[1,6,7,5,3,2,4,8]=>0011100=>1100011
[6,5,1,2,4,8,3,7]=>1100010=>0011101
[7,8,1,6,4,2,3,5]=>0101100=>1010011
[8,4,1,2,5,6,3,7]=>1100010=>0011101
[1,7,3,6,5,2,4,8]=>0101100=>1010011
[8,1,3,7,2,6,4,5]=>1001010=>0110101
[7,3,2,6,5,1,8,4]=>1101101=>0010010
[7,8,4,2,5,6,1,3]=>0110010=>1001101
[8,2,7,4,5,6,1,3]=>1010010=>0101101
[8,2,3,6,5,1,7,4]=>1001101=>0110010
[7,9,8,6,5,4,3,2,1]=>01111111=>10000000
[6,9,8,7,5,4,3,2,1]=>01111111=>10000000
[5,9,8,7,6,4,3,2,1]=>01111111=>10000000
[4,9,8,7,6,5,3,2,1]=>01111111=>10000000
[3,9,8,7,6,5,4,2,1]=>01111111=>10000000
[2,9,8,7,6,5,4,3,1]=>01111111=>10000000
[8,10,9,7,6,5,4,3,2,1]=>011111111=>100000000
[6,9,7,8,5,4,3,2,1]=>01011111=>10100000
[7,10,9,8,6,5,4,3,2,1]=>011111111=>100000000
[4,8,6,5,7,3,2,1]=>0110111=>1001000
[5,9,8,6,7,4,3,2,1]=>01101111=>10010000
[6,10,9,8,7,5,4,3,2,1]=>011111111=>100000000
[3,8,7,5,4,6,2,1]=>0111011=>1000100
[4,8,5,6,7,3,2,1]=>0100111=>1011000
[4,9,8,7,5,6,3,2,1]=>01110111=>10001000
[5,10,9,8,7,6,4,3,2,1]=>011111111=>100000000
[2,8,7,6,4,3,5,1]=>0111101=>1000010
[3,8,7,4,5,6,2,1]=>0110011=>1001100
[3,9,8,7,6,4,5,2,1]=>01111011=>10000100
[4,10,9,8,7,6,5,3,2,1]=>011111111=>100000000
[1,8,7,6,5,3,2,4]=>0111110=>1000001
[2,8,7,6,3,4,5,1]=>0111001=>1000110
[2,9,8,7,6,5,3,4,1]=>01111101=>10000010
[3,10,9,8,7,6,5,4,2,1]=>011111111=>100000000
[1,8,7,6,5,2,3,4]=>0111100=>1000011
[1,9,8,7,6,5,4,2,3]=>01111110=>10000001
[2,10,9,8,7,6,5,4,3,1]=>011111111=>100000000
[7,2,8,6,5,4,1,3]=>1011110=>0100001
[7,2,8,5,4,6,1,3]=>1011010=>0100101
[6,3,2,8,5,1,7,4]=>1101101=>0010010
[8,4,7,2,5,6,3,1]=>1010011=>0101100
[6,8,5,4,3,1,7,2]=>0111101=>1000010
[5,8,6,4,1,3,7,2]=>0111001=>1000110
[4,8,6,1,5,3,7,2]=>0110101=>1001010
[3,6,1,8,5,2,7,4]=>0101101=>1010010
[3,4,1,2,8,6,7,5]=>0100101=>1011010
[6,8,3,5,4,1,7,2]=>0101101=>1010010
[7,2,5,8,3,6,1,4]=>1001010=>0110101
[1,7,5,6,3,4,2,8]=>0101010=>1010101
[7,2,6,8,5,3,1,4]=>1001110=>0110001
[7,6,3,8,5,2,1,4]=>1101110=>0010001
[7,2,6,4,8,3,1,5]=>1010110=>0101001
[1,5,7,4,2,6,3,8]=>0011010=>1100101
[4,2,3,1,7,8,5,6]=>1010010=>0101101
[5,2,8,4,1,7,6,3]=>1011011=>0100100
[8,6,3,4,7,2,5,1]=>1100101=>0011010
[6,8,3,4,5,1,7,2]=>0100101=>1011010
[1,6,3,2,5,8,4,7]=>0110010=>1001101
[8,3,2,1,5,4,7,6]=>1110101=>0001010
[6,3,7,1,5,8,4,2]=>1010011=>0101100
[2,5,1,8,4,3,7,6]=>0101101=>1010010
[6,2,5,4,8,1,3,7]=>1010100=>0101011
[4,3,1,6,5,8,2,7]=>1101010=>0010101
[1,3,5,4,6,8,2,7]=>0010010=>1101101
[6,1,3,4,5,8,2,7]=>1000010=>0111101
[8,3,4,1,5,2,7,6]=>1010101=>0101010
[7,5,4,2,6,8,3,1]=>1110011=>0001100
[8,2,6,4,1,7,3,5]=>1011010=>0100101
[7,3,8,4,5,2,1,6]=>1010110=>0101001
[7,2,5,1,8,4,3,6]=>1010110=>0101001
[1,7,3,2,5,4,8,6]=>0110101=>1001010
[8,7,2,1,5,3,4,6]=>1110100=>0001011
[3,6,1,5,8,7,4,2]=>0100111=>1011000
[8,3,6,4,5,1,7,2]=>1010101=>0101010
[5,4,6,8,1,2,7,3]=>1001001=>0110110
[6,4,7,2,3,5,8,1]=>1010001=>0101110
[6,8,4,1,3,5,7,2]=>0110001=>1001110
[3,4,7,8,6,2,5,1]=>0001101=>1110010
[4,1,3,5,7,8,6,2]=>1000011=>0111100
[6,5,1,8,4,7,3,2]=>1101011=>0010100
[5,3,1,8,4,7,6,2]=>1101011=>0010100
[8,2,7,4,6,1,3,5]=>1010100=>0101011
[4,7,3,2,8,1,6,5]=>0110101=>1001010
[6,3,1,4,7,2,8,5]=>1100101=>0011010
[8,7,3,6,1,5,2,4]=>1101010=>0010101
[7,4,3,6,8,2,5,1]=>1100101=>0011010
[2,4,7,3,8,5,6,1]=>0010101=>1101010
[2,8,6,1,5,7,3,4]=>0110010=>1001101
[7,8,2,5,4,3,1,6]=>0101110=>1010001
[1,8,3,4,2,7,6,5]=>0101011=>1010100
[8,5,3,7,4,2,6,1]=>1101101=>0010010
[5,7,3,2,4,1,8,6]=>0110101=>1001010
[2,8,3,4,7,1,5,6]=>0100100=>1011011
[4,1,3,6,7,8,2,5]=>1000010=>0111101
[1,7,6,3,2,5,8,4]=>0111001=>1000110
[3,8,1,5,6,2,7,4]=>0100101=>1011010
[8,2,5,6,1,7,4,3]=>1001011=>0110100
[7,1,5,2,8,6,4,3]=>1010111=>0101000
[6,5,4,8,7,2,1,3]=>1101110=>0010001
[1,8,6,4,5,2,7,3]=>0110101=>1001010
[1,8,5,3,6,2,7,4]=>0110101=>1001010
[3,6,2,1,7,5,8,4]=>0110101=>1001010
[2,5,4,1,8,7,6,3]=>0110111=>1001000
[4,7,2,6,5,8,1,3]=>0101010=>1010101
[6,8,1,4,2,7,3,5]=>0101010=>1010101
[6,3,4,7,1,8,2,5]=>1001010=>0110101
[3,4,7,8,2,5,6,1]=>0001001=>1110110
[1,8,2,4,5,6,7,3]=>0100001=>1011110
[5,2,4,1,6,8,7,3]=>1010011=>0101100
[3,2,5,7,6,1,8,4]=>1001101=>0110010
[4,3,5,6,1,8,7,2]=>1001011=>0110100
[5,3,4,1,7,6,8,2]=>1010101=>0101010
[3,1,4,6,5,7,8,2]=>1001001=>0110110
[1,4,7,3,5,6,8,2]=>0010001=>1101110
[1,3,2,7,5,8,6,4]=>0101011=>1010100
[1,4,2,5,8,3,7,6]=>0100101=>1011010
[4,1,2,6,8,5,3,7]=>1000110=>0111001
[1,5,2,4,8,7,6,3]=>0100111=>1011000
[1,2,6,4,8,7,5,3]=>0010111=>1101000
[1,2,7,4,8,6,5,3]=>0010111=>1101000
[1,3,2,7,5,8,4,6]=>0101010=>1010101
[1,3,2,8,5,7,4,6]=>0101010=>1010101
[1,5,2,4,8,7,3,6]=>0100110=>1011001
[1,2,6,4,8,7,3,5]=>0010110=>1101001
[1,2,7,8,5,6,3,4]=>0001010=>1110101
[1,3,8,2,6,7,4,5]=>0010010=>1101101
[1,6,7,8,2,5,3,4]=>0001010=>1110101
[1,5,7,8,2,3,6,4]=>0001001=>1110110
[1,5,2,7,8,4,6,3]=>0100101=>1011010
[1,3,6,2,4,8,7,5]=>0010011=>1101100
[1,6,7,3,4,8,5,2]=>0010011=>1101100
[1,5,3,7,4,8,6,2]=>0101011=>1010100
[2,8,4,1,5,3,7,6]=>0110101=>1001010
[3,8,4,1,5,7,2,6]=>0110010=>1001101
[1,3,8,4,2,7,6,5]=>0011011=>1100100
[1,2,8,4,7,3,6,5]=>0010101=>1101010
[1,2,7,4,8,3,6,5]=>0010101=>1101010
[1,2,6,4,8,3,7,5]=>0010101=>1101010
[1,5,2,4,8,3,7,6]=>0100101=>1011010
[1,8,3,5,2,7,4,6]=>0101010=>1010101
[1,3,8,6,2,7,4,5]=>0011010=>1100101
[1,4,8,6,7,2,3,5]=>0010100=>1101011
[1,2,6,8,5,3,7,4]=>0001101=>1110010
[1,2,7,8,6,3,5,4]=>0001101=>1110010
[1,6,7,8,5,2,3,4]=>0001100=>1110011
[1,5,7,8,6,2,3,4]=>0001100=>1110011
[1,4,7,6,8,2,3,5]=>0010100=>1101011
[1,3,7,6,2,8,4,5]=>0011010=>1100101
[2,3,8,7,4,1,6,5]=>0011101=>1100010
[1,2,5,8,7,6,3,4]=>0001110=>1110001
[1,2,6,8,7,5,3,4]=>0001110=>1110001
[1,2,7,8,6,5,3,4]=>0001110=>1110001
[5,2,6,7,3,4,8,1]=>1001001=>0110110
[5,2,4,7,6,3,8,1]=>1001101=>0110010
[5,6,2,1,7,8,3,4]=>0110010=>1001101
[5,6,2,1,4,8,7,3]=>0110011=>1001100
[2,6,1,4,5,8,7,3]=>0100011=>1011100
[5,4,2,7,6,3,8,1]=>1101101=>0010010
[2,3,7,6,4,5,8,1]=>0011001=>1100110
[2,6,1,7,5,8,3,4]=>0101010=>1010101
[2,6,1,7,4,8,5,3]=>0101011=>1010100
[5,1,2,7,8,4,3,6]=>1000110=>0111001
[2,6,1,7,4,8,3,5]=>0101010=>1010101
[3,6,4,1,7,8,2,5]=>0110010=>1001101
[5,4,6,1,3,8,7,2]=>1010011=>0101100
[3,6,4,1,5,8,7,2]=>0110011=>1001100
[2,6,1,5,4,8,7,3]=>0101011=>1010100
[2,6,1,4,7,8,5,3]=>0100011=>1011100
[5,1,2,4,8,6,7,3]=>1000101=>0111010
[5,1,2,4,8,7,3,6]=>1000110=>0111001
[5,1,2,4,8,7,6,3]=>1000111=>0111000
[1,2,3,8,5,4,7,6]=>0001101=>1110010
[4,3,1,2,8,5,7,6]=>1100101=>0011010
[2,1,5,3,8,6,4,7]=>1010110=>0101001
[1,2,3,8,5,6,4,7]=>0001010=>1110101
[1,2,3,8,6,4,5,7]=>0001100=>1110011
[1,2,3,8,6,5,4,7]=>0001110=>1110001
[1,2,3,8,5,4,6,7]=>0001100=>1110011
[2,6,1,5,4,8,3,7]=>0101010=>1010101
[5,1,2,4,8,6,3,7]=>1000110=>0111001
[5,1,2,4,8,3,7,6]=>1000101=>0111010
[5,6,3,1,4,8,2,7]=>0110010=>1001101
[2,5,4,3,1,8,6,7]=>0111010=>1000101
[5,4,6,3,1,8,7,2]=>1011011=>0100100
[3,6,4,5,1,8,7,2]=>0101011=>1010100
[3,6,5,4,1,8,7,2]=>0111011=>1000100
[5,2,6,1,7,8,4,3]=>1010011=>0101100
[5,1,6,2,8,7,3,4]=>1010110=>0101001
[2,1,3,7,8,6,4,5]=>1000110=>0111001
[2,1,3,7,8,5,6,4]=>1000101=>0111010
[5,2,4,1,7,8,6,3]=>1010011=>0101100
[4,3,1,2,8,6,7,5]=>1100101=>0011010
[5,1,4,2,8,6,7,3]=>1010101=>0101010
[2,1,3,6,8,5,7,4]=>1000101=>0111010
[1,2,3,8,6,7,4,5]=>0001010=>1110101
[1,2,3,8,7,5,4,6]=>0001110=>1110001
[1,2,3,8,7,4,5,6]=>0001100=>1110011
[1,2,3,8,5,7,4,6]=>0001010=>1110101
[2,1,3,6,8,7,4,5]=>1000110=>0111001
[5,4,1,2,8,7,6,3]=>1100111=>0011000
[3,1,6,2,8,7,5,4]=>1010111=>0101000
[1,2,3,4,5,9,6,7,8]=>00000100=>11111011
[1,2,3,4,9,5,6,7,8]=>00001000=>11110111
[1,2,3,9,4,5,6,7,8]=>00010000=>11101111
[1,2,9,3,4,5,6,7,8]=>00100000=>11011111
[1,2,3,4,5,6,7,10,8,9]=>000000010=>111111101
[1,2,3,4,5,9,7,6,8]=>00000110=>11111001
[1,2,3,4,5,6,10,7,8,9]=>000000100=>111111011
[1,2,3,4,9,6,5,7,8]=>00001100=>11110011
[1,2,3,4,5,10,6,7,8,9]=>000001000=>111110111
[1,2,8,4,5,3,6,7]=>0010100=>1101011
[1,2,3,9,5,4,6,7,8]=>00011000=>11100111
[1,2,3,4,10,5,6,7,8,9]=>000010000=>111101111
[1,8,3,4,2,5,6,7]=>0101000=>1010111
[1,2,9,4,3,5,6,7,8]=>00110000=>11001111
[1,2,3,10,4,5,6,7,8,9]=>000100000=>111011111
[1,8,4,3,2,5,6,7]=>0111000=>1000111
[1,9,3,2,4,5,6,7,8]=>01100000=>10011111
[1,2,10,3,4,5,6,7,8,9]=>001000000=>110111111
[8,4,7,6,5,3,2,1]=>1011111=>0100000
[8,4,7,5,6,3,2,1]=>1010111=>0101000
[8,5,7,4,6,3,2,1]=>1010111=>0101000
[8,7,6,3,5,4,2,1]=>1110111=>0001000
[8,6,7,3,5,4,2,1]=>1010111=>0101000
[8,5,7,3,6,4,2,1]=>1010111=>0101000
[8,1,7,4,6,5,3,2]=>1010111=>0101000
[8,1,7,3,6,5,4,2]=>1010111=>0101000
[8,2,7,3,6,5,4,1]=>1010111=>0101000
[8,3,7,2,6,5,4,1]=>1010111=>0101000
[8,5,7,2,6,4,3,1]=>1010111=>0101000
[8,6,7,2,5,4,3,1]=>1010111=>0101000
[8,7,6,2,5,4,3,1]=>1110111=>0001000
[8,4,7,1,6,5,3,2]=>1010111=>0101000
[8,3,7,1,6,5,4,2]=>1010111=>0101000
[8,2,7,1,6,5,4,3]=>1010111=>0101000
[8,1,7,2,6,5,4,3]=>1010111=>0101000
[8,7,6,2,5,3,4,1]=>1110101=>0001010
[8,1,7,6,5,3,4,2]=>1011101=>0100010
[8,3,7,6,5,2,4,1]=>1011101=>0100010
[8,4,7,6,5,2,3,1]=>1011101=>0100010
[8,5,7,6,4,2,3,1]=>1011101=>0100010
[8,6,7,5,4,1,3,2]=>1011101=>0100010
[8,5,7,6,4,1,3,2]=>1011101=>0100010
[8,3,7,6,5,1,4,2]=>1011101=>0100010
[8,7,6,4,5,1,3,2]=>1110101=>0001010
[8,7,6,2,5,1,4,3]=>1110101=>0001010
[8,7,6,1,5,2,4,3]=>1110101=>0001010
[6,8,1,3,2,5,4,7]=>0101010=>1010101
[6,8,1,4,2,5,3,7]=>0101010=>1010101
[7,8,3,6,1,4,2,5]=>0101010=>1010101
[7,8,2,5,3,6,1,4]=>0101010=>1010101
[7,8,2,5,1,4,3,6]=>0101010=>1010101
[7,8,1,4,3,6,2,5]=>0101010=>1010101
[5,8,1,4,3,7,2,6]=>0101010=>1010101
[6,8,2,5,1,4,3,7]=>0101010=>1010101
[6,8,2,5,3,7,1,4]=>0101010=>1010101
[6,8,2,5,4,7,1,3]=>0101010=>1010101
[2,5,4,7,6,8,1,3]=>0101010=>1010101
[2,5,3,7,6,8,1,4]=>0101010=>1010101
[2,5,1,4,3,7,6,8]=>0101010=>1010101
[2,6,1,4,3,7,5,8]=>0101010=>1010101
[2,6,5,8,1,4,3,7]=>0101010=>1010101
[2,6,1,5,3,7,4,8]=>0101010=>1010101
[2,6,3,7,4,8,1,5]=>0101010=>1010101
[2,6,4,7,5,8,1,3]=>0101010=>1010101
[5,8,3,6,4,7,1,2]=>0101010=>1010101
[5,8,2,6,4,7,1,3]=>0101010=>1010101
[4,8,2,6,3,7,1,5]=>0101010=>1010101
[4,8,1,5,3,7,2,6]=>0101010=>1010101
[4,8,1,5,2,6,3,7]=>0101010=>1010101
[4,8,3,7,1,5,2,6]=>0101010=>1010101
[6,8,3,7,1,4,2,5]=>0101010=>1010101
[5,8,1,3,2,6,4,7]=>0101010=>1010101
[5,8,4,7,1,3,2,6]=>0101010=>1010101
[6,8,4,7,1,3,2,5]=>0101010=>1010101
[6,8,5,7,1,3,2,4]=>0101010=>1010101
[5,7,6,8,2,4,1,3]=>0101010=>1010101
[4,7,6,8,1,3,2,5]=>0101010=>1010101
[4,7,5,8,1,3,2,6]=>0101010=>1010101
[4,7,1,3,2,6,5,8]=>0101010=>1010101
[3,7,1,4,2,6,5,8]=>0101010=>1010101
[3,7,5,8,1,4,2,6]=>0101010=>1010101
[3,7,6,8,1,4,2,5]=>0101010=>1010101
[3,7,6,8,2,5,1,4]=>0101010=>1010101
[4,7,6,8,2,5,1,3]=>0101010=>1010101
[4,7,5,8,3,6,1,2]=>0101010=>1010101
[4,7,5,8,2,6,1,3]=>0101010=>1010101
[3,7,5,8,2,6,1,4]=>0101010=>1010101
[3,7,4,8,2,6,1,5]=>0101010=>1010101
[3,7,4,8,1,5,2,6]=>0101010=>1010101
[3,7,1,5,2,6,4,8]=>0101010=>1010101
[3,7,2,6,1,5,4,8]=>0101010=>1010101
[3,7,2,6,5,8,1,4]=>0101010=>1010101
[4,7,3,6,5,8,1,2]=>0101010=>1010101
[3,6,5,8,4,7,1,2]=>0101010=>1010101
[2,6,5,8,4,7,1,3]=>0101010=>1010101
[2,6,5,8,3,7,1,4]=>0101010=>1010101
[2,6,3,7,1,5,4,8]=>0101010=>1010101
[7,6,4,2,8,5,3,1]=>1110111=>0001000
[7,6,4,3,8,2,5,1]=>1110101=>0001010
[7,6,4,8,5,2,3,1]=>1101101=>0010010
[6,8,4,3,7,2,1,5]=>0110110=>1001001
[6,7,4,3,5,1,8,2]=>0110101=>1001010
[6,7,3,5,4,8,2,1]=>0101011=>1010100
[6,8,3,7,5,2,4,1]=>0101101=>1010010
[7,6,8,3,5,2,4,1]=>1010101=>0101010
[7,6,3,5,8,2,4,1]=>1100101=>0011010
[7,6,3,5,2,4,8,1]=>1101001=>0010110
[7,6,4,2,5,1,8,3]=>1110101=>0001010
[7,6,2,8,4,1,5,3]=>1101101=>0010010
[7,6,3,8,2,4,1,5]=>1101010=>0010101
[7,6,3,4,8,2,5,1]=>1100101=>0011010
[6,8,3,7,4,5,2,1]=>0101011=>1010100
[6,7,3,5,8,4,2,1]=>0100111=>1011000
[5,7,8,3,6,2,1,4]=>0010110=>1101001
[5,8,3,6,7,2,1,4]=>0100110=>1011001
[6,3,4,8,7,2,5,1]=>1001101=>0110010
[6,3,8,4,7,2,1,5]=>1010110=>0101001
[6,2,8,4,1,7,5,3]=>1011011=>0100100
[6,2,7,4,1,5,3,8]=>1011010=>0100101
[6,3,4,7,5,8,2,1]=>1001011=>0110100
[6,3,5,7,8,4,2,1]=>1000111=>0111000
[5,7,3,6,8,2,1,4]=>0100110=>1011001
[5,6,8,3,7,2,1,4]=>0010110=>1101001
[5,6,7,3,4,1,8,2]=>0010101=>1101010
[4,6,7,8,3,5,2,1]=>0001011=>1110100
[4,6,8,3,5,7,2,1]=>0010011=>1101100
[4,7,3,5,6,8,2,1]=>0100011=>1011100
[4,7,3,5,8,2,6,1]=>0100101=>1011010
[5,3,4,7,8,2,1,6]=>1000110=>0111001
[5,3,8,2,4,1,6,7]=>1010100=>0101011
[5,3,4,8,2,6,1,7]=>1001010=>0110101
[4,8,3,6,2,5,7,1]=>0101001=>1010110
[4,8,3,5,7,2,6,1]=>0100101=>1011010
[4,8,3,5,6,7,2,1]=>0100011=>1011100
[4,7,8,3,5,6,2,1]=>0010011=>1101100
[4,7,8,3,6,2,5,1]=>0010101=>1101010
[4,8,3,6,7,2,5,1]=>0100101=>1011010
[4,8,3,7,2,5,6,1]=>0101001=>1010110
[5,3,4,8,2,7,6,1]=>1001011=>0110100
[5,3,8,2,4,1,7,6]=>1010101=>0101010
[5,2,8,4,1,7,3,6]=>1011010=>0100101
[6,4,2,5,1,8,7,3]=>1101011=>0010100
[6,4,3,5,8,2,1,7]=>1100110=>0011001
[6,3,5,8,7,2,4,1]=>1001101=>0110010
[5,8,3,7,2,6,4,1]=>0101011=>1010100
[5,7,3,4,8,2,1,6]=>0100110=>1011001
[5,8,4,2,3,1,6,7]=>0110100=>1001011
[5,8,4,2,3,1,7,6]=>0110101=>1001010
[6,4,5,3,8,2,1,7]=>1010110=>0101001
[6,4,8,5,3,7,2,1]=>1011011=>0100100
[6,4,3,8,5,7,2,1]=>1101011=>0010100
[6,4,2,8,5,3,1,7]=>1101110=>0010001
[6,4,2,7,3,1,8,5]=>1101101=>0010010
[6,4,3,7,8,5,2,1]=>1100111=>0011000
[6,4,5,3,7,1,8,2]=>1010101=>0101010
[5,7,4,2,3,1,6,8]=>0110100=>1001011
[5,6,3,7,1,8,2,4]=>0101010=>1010101
[5,6,3,4,7,1,8,2]=>0100101=>1011010
[5,6,3,4,8,2,1,7]=>0100110=>1011001
[6,3,5,7,4,8,2,1]=>1001011=>0110100
[6,3,5,4,7,8,2,1]=>1010011=>0101100
[6,4,3,5,7,1,8,2]=>1100101=>0011010
[6,4,2,5,1,7,3,8]=>1101010=>0010101
[5,3,7,2,4,1,6,8]=>1010100=>0101011
[5,3,4,7,2,6,1,8]=>1001010=>0110101
[4,7,3,6,2,5,8,1]=>0101001=>1010110
[4,7,3,6,8,2,5,1]=>0100101=>1011010
[4,6,7,3,5,8,2,1]=>0010011=>1101100
[4,5,7,8,3,6,2,1]=>0001011=>1110100
[4,5,8,3,6,7,2,1]=>0010011=>1101100
[4,5,8,3,7,2,6,1]=>0010101=>1101010
[5,3,4,6,8,2,1,7]=>1000110=>0111001
[5,3,6,8,2,1,4,7]=>1001100=>0110011
[5,3,6,7,1,8,2,4]=>1001010=>0110101
[5,3,4,6,7,1,8,2]=>1000101=>0111010
[4,6,3,5,7,8,2,1]=>0100011=>1011100
[4,5,7,3,6,8,2,1]=>0010011=>1101100
[4,5,6,8,3,7,2,1]=>0001011=>1110100
[5,7,4,8,6,3,2,1]=>0101111=>1010000
[3,2,6,5,1,8,7,4]=>1011011=>0100100
[3,5,6,7,2,8,4,1]=>0001011=>1110100
[7,6,9,8,5,4,3,2,1]=>10111111=>01000000
[6,5,4,9,8,7,3,2,1]=>11011111=>00100000
[6,8,5,9,7,4,3,2,1]=>01011111=>10100000
[6,7,8,9,5,4,3,2,1]=>00011111=>11100000
[5,4,3,2,9,8,7,6,1]=>11101111=>00010000
[5,8,4,3,9,7,6,2,1]=>01101111=>10010000
[5,4,7,6,9,8,3,2,1]=>10101111=>01010000
[5,7,8,4,9,6,3,2,1]=>00101111=>11010000
[5,6,7,8,9,4,3,2,1]=>00001111=>11110000
[4,8,3,2,1,9,7,6,5]=>01110111=>10001000
[4,3,7,6,2,9,8,5,1]=>10110111=>01001000
[4,7,8,3,2,9,6,5,1]=>00110111=>11001000
[4,6,3,8,5,9,7,2,1]=>01010111=>10101000
[4,6,7,8,3,9,5,2,1]=>00010111=>11101000
[4,5,6,7,8,9,3,2,1]=>00000111=>11111000
[3,2,1,6,5,4,9,8,7]=>11011011=>00100100
[3,6,2,8,5,1,9,7,4]=>01011011=>10100100
[3,6,7,8,2,1,9,5,4]=>00011011=>11100100
[3,2,5,4,7,6,9,8,1]=>10101011=>01010100
[3,5,7,2,8,4,9,6,1]=>00101011=>11010100
[3,5,6,7,8,2,9,4,1]=>00001011=>11110100
[3,4,5,6,7,8,9,2,1]=>00000011=>11111100
[2,4,6,7,1,8,3,9,5]=>00010101=>11101010
[2,4,5,6,7,8,1,9,3]=>00000101=>11111010
[8,7,10,9,6,5,4,3,2,1]=>101111111=>010000000
[8,9,10,7,6,5,4,3,2,1]=>001111111=>110000000
[7,6,5,10,9,8,4,3,2,1]=>110111111=>001000000
[7,9,6,10,8,5,4,3,2,1]=>010111111=>101000000
[7,8,9,10,6,5,4,3,2,1]=>000111111=>111000000
[6,5,4,3,10,9,8,7,2,1]=>111011111=>000100000
[6,9,5,4,10,8,7,3,2,1]=>011011111=>100100000
[6,5,8,7,10,9,4,3,2,1]=>101011111=>010100000
[6,8,9,5,10,7,4,3,2,1]=>001011111=>110100000
[5,4,3,2,1,10,9,8,7,6]=>111101111=>000010000
[5,9,4,3,2,10,8,7,6,1]=>011101111=>100010000
[5,4,8,7,3,10,9,6,2,1]=>101101111=>010010000
[5,8,9,4,3,10,7,6,2,1]=>001101111=>110010000
[5,7,4,9,6,10,8,3,2,1]=>010101111=>101010000
[5,6,7,8,9,10,4,3,2,1]=>000001111=>111110000
[4,3,8,7,2,1,10,9,6,5]=>101110111=>010001000
[4,8,9,3,2,1,10,7,6,5]=>001110111=>110001000
[4,3,2,7,6,5,10,9,8,1]=>110110111=>001001000
[4,7,3,9,6,2,10,8,5,1]=>010110111=>101001000
[4,7,8,9,3,2,10,6,5,1]=>000110111=>111001000
[4,3,6,5,8,7,10,9,2,1]=>101010111=>010101000
[4,6,7,8,9,3,10,5,2,1]=>000010111=>111101000
[4,5,6,7,8,9,10,3,2,1]=>000000111=>111111000
[3,6,2,1,9,5,4,10,8,7]=>011011011=>100100100
[3,2,6,5,8,7,1,10,9,4]=>101011011=>010100100
[3,6,8,2,9,5,1,10,7,4]=>001011011=>110100100
[3,6,7,8,9,2,1,10,5,4]=>000011011=>111100100
[3,5,7,8,2,9,4,10,6,1]=>000101011=>111010100
[3,5,6,7,8,9,2,10,4,1]=>000001011=>111110100
[3,4,5,6,7,8,9,10,2,1]=>000000011=>111111100
[2,4,6,1,8,3,9,5,10,7]=>001010101=>110101010
[2,4,6,7,8,1,9,3,10,5]=>000010101=>111101010
[2,4,5,6,7,8,9,1,10,3]=>000000101=>111111010
[1,6,2,5,3,4,8,7]=>0101001=>1010110
[1,3,8,2,4,6,5,7]=>0010010=>1101101
[1,7,2,3,6,4,8,5]=>0100101=>1011010
[1,6,8,2,5,3,7,4]=>0010101=>1101010
[1,8,2,5,3,4,7,6]=>0101001=>1010110
[1,8,2,3,6,4,7,5]=>0100101=>1011010
[1,3,5,2,8,4,7,6]=>0010101=>1101010
[1,2,7,3,5,4,6,8]=>0010100=>1101011
[1,8,2,7,3,4,6,5]=>0101001=>1010110
[1,5,8,2,3,7,4,6]=>0010010=>1101101
[1,6,8,2,3,5,4,7]=>0010010=>1101101
[5,3,6,1,2,4,8,7]=>1010001=>0101110
[7,1,5,8,4,2,3,6]=>1001100=>0110011
[8,1,5,7,4,2,3,6]=>1001100=>0110011
[7,1,4,5,8,2,3,6]=>1000100=>0111011
[7,4,1,6,2,8,3,5]=>1101010=>0010101
[8,4,1,7,2,6,3,5]=>1101010=>0010101
[8,1,4,7,5,2,3,6]=>1001100=>0110011
[8,1,5,4,7,2,3,6]=>1010100=>0101011
[2,1,7,5,8,3,4,6]=>1010100=>0101011
[7,1,5,4,8,2,3,6]=>1010100=>0101011
[7,1,4,8,5,2,3,6]=>1001100=>0110011
[6,4,1,7,2,3,8,5]=>1101001=>0010110
[7,8,3,1,2,4,6,5]=>0110001=>1001110
[8,7,1,6,4,2,3,5]=>1101100=>0010011
[8,6,1,7,4,2,3,5]=>1101100=>0010011
[7,6,1,8,4,2,3,5]=>1101100=>0010011
[7,3,8,1,2,4,6,5]=>1010001=>0101110
[8,3,7,1,2,4,6,5]=>1010001=>0101110
[8,3,6,1,2,4,7,5]=>1010001=>0101110
[8,3,7,5,1,2,4,6]=>1011000=>0100111
[7,3,6,1,2,4,8,5]=>1010001=>0101110
[6,7,1,8,4,2,3,5]=>0101100=>1010011
[6,8,1,7,4,2,3,5]=>0101100=>1010011
[7,1,8,5,4,2,3,6]=>1011100=>0100011
[7,1,8,4,5,2,3,6]=>1010100=>0101011
[2,1,7,8,5,3,4,6]=>1001100=>0110011
[7,6,3,1,2,4,8,5]=>1110001=>0001110
[6,1,2,3,8,7,5,4]=>1000111=>0111000
[6,8,1,4,2,3,7,5]=>0101001=>1010110
[6,8,3,1,2,7,4,5]=>0110010=>1001101
[6,7,3,1,2,8,4,5]=>0110010=>1001101
[6,7,1,4,2,3,8,5]=>0101001=>1010110
[4,3,6,8,5,7,1,2]=>1001010=>0110101
[6,1,2,5,4,8,3,7]=>1001010=>0110101
[3,2,8,5,4,1,7,6]=>1011101=>0100010
[7,8,2,1,4,6,3,5]=>0110010=>1001101
[7,2,1,5,8,3,4,6]=>1100100=>0011011
[2,4,8,5,1,3,6,7]=>0011000=>1100111
[3,5,6,1,8,4,2,7]=>0010110=>1101001
[1,3,6,8,7,4,2,5]=>0001110=>1110001
[1,2,8,5,7,3,4,6]=>0010100=>1101011
[2,6,1,5,8,3,4,7]=>0100100=>1011011
[5,7,1,6,8,4,3,2]=>0100111=>1011000
[4,8,1,2,5,7,3,6]=>0100010=>1011101
[8,4,6,2,5,7,3,1]=>1010011=>0101100
[8,3,6,4,7,2,5,1]=>1010101=>0101010
[3,8,1,4,7,2,5,6]=>0100100=>1011011
[1,7,8,4,6,2,5,3]=>0010101=>1101010
[3,7,4,8,5,1,6,2]=>0101101=>1010010
[3,7,1,6,5,4,8,2]=>0101101=>1010010
[2,7,3,1,5,8,4,6]=>0110010=>1001101
[2,7,4,6,8,1,3,5]=>0100100=>1011011
[2,7,5,8,6,4,1,3]=>0101110=>1010001
[8,2,6,7,5,4,3,1]=>1001111=>0110000
[3,8,7,1,6,4,5,2]=>0110101=>1001010
[3,6,8,2,7,4,1,5]=>0010110=>1101001
[1,5,2,8,7,4,6,3]=>0101101=>1010010
[3,4,2,7,8,1,6,5]=>0100101=>1011010
[4,1,3,7,5,6,8,2]=>1001001=>0110110
[6,3,8,1,7,4,2,5]=>1010110=>0101001
[6,5,8,7,1,4,2,3]=>1011010=>0100101
[4,1,7,3,8,5,2,6]=>1010110=>0101001
[3,6,1,4,5,8,2,7]=>0100010=>1011101
[1,6,7,4,5,3,8,2]=>0010101=>1101010
[6,1,7,3,5,4,8,2]=>1010101=>0101010
[6,3,1,2,5,8,4,7]=>1100010=>0011101
[1,4,7,2,8,5,3,6]=>0010110=>1101001
[5,6,8,7,2,4,1,3]=>0011010=>1100101
[6,8,5,7,1,2,4,3]=>0101001=>1010110
[2,8,4,1,7,5,6,3]=>0110101=>1001010
[8,2,4,3,7,5,6,1]=>1010101=>0101010
[6,8,2,1,5,7,3,4]=>0110010=>1001101
[7,2,8,4,1,6,3,5]=>1011010=>0100101
[1,2,4,8,6,5,3,7]=>0001110=>1110001
[7,1,5,6,8,4,3,2]=>1000111=>0111000
[2,7,8,1,4,6,3,5]=>0010010=>1101101
[4,8,2,5,7,1,6,3]=>0100101=>1011010
[4,1,6,8,5,3,7,2]=>1001101=>0110010
[5,2,6,4,8,3,1,7]=>1010110=>0101001
[6,7,1,3,4,5,8,2]=>0100001=>1011110
[1,7,3,2,4,8,5,6]=>0110010=>1001101
[1,3,6,5,2,8,4,7]=>0011010=>1100101
[7,1,6,5,3,4,8,2]=>1011001=>0100110
[6,3,4,2,8,7,5,1]=>1010111=>0101000
[4,3,8,7,5,2,6,1]=>1011101=>0100010
[6,8,7,4,2,3,5,1]=>0111001=>1000110
[3,6,4,5,2,8,7,1]=>0101011=>1010100
[8,6,1,3,5,4,2,7]=>1100110=>0011001
[5,3,8,6,1,2,4,7]=>1011000=>0100111
[2,5,6,3,4,8,7,1]=>0010011=>1101100
[2,5,3,6,8,7,4,1]=>0100111=>1011000
[4,8,7,3,5,2,6,1]=>0110101=>1001010
[3,8,7,2,6,4,5,1]=>0110101=>1001010
[6,3,5,4,8,7,2,1]=>1010111=>0101000
[4,3,8,6,1,5,2,7]=>1011010=>0100101
[4,7,6,2,5,3,8,1]=>0110101=>1001010
[7,5,2,6,8,1,4,3]=>1100101=>0011010
[8,5,2,7,1,4,3,6]=>1101010=>0010101
[1,8,5,3,6,2,4,7]=>0110100=>1001011
[5,1,7,2,4,3,8,6]=>1010101=>0101010
[1,5,3,4,8,6,2,7]=>0100110=>1011001
[5,4,1,3,8,6,2,7]=>1100110=>0011001
[5,1,8,6,3,4,2,7]=>1011010=>0100101
[4,5,2,8,3,7,6,1]=>0101011=>1010100
[8,2,3,7,6,4,5,1]=>1001101=>0110010
[5,8,2,4,7,6,3,1]=>0100111=>1011000
[6,8,2,5,3,4,7,1]=>0101001=>1010110
[7,2,5,6,4,8,1,3]=>1001010=>0110101
[1,6,7,4,8,2,3,5]=>0010100=>1101011
[7,1,3,5,8,2,6,4]=>1000101=>0111010
[8,2,1,3,5,6,7,4]=>1100001=>0011110
[6,3,1,4,7,5,8,2]=>1100101=>0011010
[4,1,3,8,2,6,7,5]=>1001001=>0110110
[2,8,3,6,7,5,4,1]=>0100111=>1011000
[3,1,7,2,8,5,4,6]=>1010110=>0101001
[3,6,1,4,7,2,8,5]=>0100101=>1011010
[1,5,8,4,7,2,3,6]=>0010100=>1101011
[7,1,3,6,2,8,4,5]=>1001010=>0110101
[6,2,7,4,5,8,1,3]=>1010010=>0101101
[2,1,8,4,5,7,3,6]=>1010010=>0101101
[1,8,5,7,3,2,4,6]=>0101100=>1010011
[2,1,8,5,4,3,6,7]=>1011100=>0100011
[2,7,4,1,5,3,8,6]=>0110101=>1001010
[7,4,8,6,2,3,1,5]=>1011010=>0100101
[2,7,1,4,6,3,8,5]=>0100101=>1011010
[4,7,5,6,8,1,3,2]=>0100101=>1011010
[7,1,3,2,8,5,4,6]=>1010110=>0101001
[2,8,5,4,1,3,6,7]=>0111000=>1000111
[5,1,7,4,2,3,8,6]=>1011001=>0100110
[3,8,6,5,1,4,2,7]=>0111010=>1000101
[1,3,4,8,6,5,2,7]=>0001110=>1110001
[4,1,8,6,5,3,2,7]=>1011110=>0100001
[4,8,5,2,7,3,6,1]=>0110101=>1001010
[7,2,8,5,3,6,4,1]=>1011011=>0100100
[5,2,8,4,3,7,6,1]=>1011011=>0100100
[8,4,7,5,2,3,6,1]=>1011001=>0100110
[7,5,2,8,4,6,1,3]=>1101010=>0010101
[5,7,4,3,6,2,8,1]=>0110101=>1001010
[6,7,5,1,2,8,3,4]=>0110010=>1001101
[5,2,6,8,3,4,7,1]=>1001001=>0110110
[7,6,2,4,5,8,3,1]=>1100011=>0011100
[3,6,8,4,7,2,5,1]=>0010101=>1101010
[7,6,3,8,4,2,5,1]=>1101101=>0010010
[2,6,3,8,4,7,5,1]=>0101011=>1010100
[7,2,3,6,5,8,4,1]=>1001011=>0110100
[6,2,7,5,8,3,1,4]=>1010110=>0101001
[2,8,3,6,4,5,7,1]=>0101001=>1010110
[2,1,5,6,8,3,7,4]=>1000101=>0111010
[5,8,1,2,6,4,7,3]=>0100101=>1011010
[1,6,8,3,2,7,4,5]=>0011010=>1100101
[6,5,7,2,8,4,1,3]=>1010110=>0101001
[7,5,1,2,8,4,6,3]=>1100101=>0011010
[5,4,8,3,6,2,7,1]=>1010101=>0101010
[5,8,2,7,4,3,6,1]=>0101101=>1010010
[6,4,5,8,2,7,3,1]=>1001011=>0110100
[5,7,3,6,4,8,2,1]=>0101011=>1010100
[1,5,6,4,8,2,7,3]=>0010101=>1101010
[3,1,5,6,4,8,7,2]=>1001011=>0110100
[1,3,6,2,5,7,8,4]=>0010001=>1101110
[1,4,6,3,5,7,8,2]=>0010001=>1101110
[3,5,1,6,4,7,8,2]=>0101001=>1010110
[3,6,1,4,2,7,8,5]=>0101001=>1010110
[2,4,6,3,1,7,8,5]=>0011001=>1100110
[1,3,6,5,2,7,8,4]=>0011001=>1100110
[1,2,6,4,3,8,5,7]=>0011010=>1100101
[1,2,6,3,5,8,7,4]=>0010011=>1101100
[2,3,5,1,8,4,7,6]=>0010101=>1101010
[2,3,6,1,8,5,4,7]=>0010110=>1101001
[1,2,7,4,6,8,3,5]=>0010010=>1101101
[2,3,7,5,1,8,4,6]=>0011010=>1100101
[4,7,2,5,3,8,6,1]=>0101011=>1010100
[3,1,7,5,4,8,6,2]=>1011011=>0100100
[1,2,7,6,4,8,5,3]=>0011011=>1100100
[1,2,7,3,6,8,5,4]=>0010011=>1101100
[2,3,6,1,8,5,7,4]=>0010101=>1101010
[3,1,5,4,8,7,6,2]=>1010111=>0101000
[1,2,5,8,4,7,3,6]=>0001010=>1110101
[1,2,6,8,5,4,7,3]=>0001101=>1110010
[1,3,6,8,5,2,7,4]=>0001101=>1110010
[3,5,7,4,8,2,1,6]=>0010110=>1101001
[2,4,7,6,8,3,1,5]=>0010110=>1101001
[1,4,6,8,3,5,2,7]=>0001010=>1110101
[1,3,6,8,5,2,4,7]=>0001100=>1110011
[1,2,6,8,5,4,3,7]=>0001110=>1110001
[1,2,5,8,4,3,7,6]=>0001101=>1110010
[1,3,5,8,2,4,7,6]=>0001001=>1110110
[1,3,6,8,2,5,4,7]=>0001010=>1110101
[1,4,6,8,3,2,5,7]=>0001100=>1110011
[3,5,7,4,8,1,2,6]=>0010100=>1101011
[4,6,1,7,5,8,2,3]=>0101010=>1010101
[2,3,6,7,5,8,1,4]=>0001010=>1110101
[1,3,7,5,6,8,2,4]=>0010010=>1101101
[2,3,6,5,8,1,7,4]=>0010101=>1101010
[3,4,6,2,8,1,7,5]=>0010101=>1101010
[3,5,4,6,8,2,1,7]=>0100110=>1011001
[3,5,4,6,8,1,2,7]=>0100100=>1011011
[1,2,4,7,5,8,3,6]=>0001010=>1110101
[1,2,6,7,4,8,3,5]=>0001010=>1110101
[3,6,4,7,1,8,5,2]=>0101011=>1010100
[1,2,6,7,3,8,5,4]=>0001011=>1110100
[1,2,5,7,3,8,6,4]=>0001011=>1110100
[3,1,5,7,6,8,4,2]=>1001011=>0110100
[3,5,4,6,8,2,7,1]=>0100101=>1011010
[4,2,6,1,8,7,5,3]=>1010111=>0101000
[3,1,6,5,8,7,4,2]=>1010111=>0101000
[2,3,6,5,8,7,1,4]=>0010110=>1101001
[1,2,7,4,6,8,5,3]=>0010011=>1101100
[1,2,7,5,6,8,4,3]=>0010011=>1101100
[3,1,6,7,5,8,4,2]=>1001011=>0110100
[4,6,2,7,5,8,3,1]=>0101011=>1010100
[3,5,7,4,8,2,6,1]=>0010101=>1101010
[2,4,7,6,8,3,5,1]=>0010101=>1101010
[1,4,6,8,3,5,7,2]=>0001001=>1110110
[1,3,6,8,2,5,7,4]=>0001001=>1110110
[1,3,5,8,2,7,4,6]=>0001010=>1110101
[1,2,5,8,4,7,6,3]=>0001011=>1110100
[1,2,4,8,7,3,6,5]=>0001101=>1110010
[1,2,5,8,7,4,3,6]=>0001110=>1110001
[1,3,5,8,7,2,4,6]=>0001100=>1110011
[2,3,7,6,8,5,1,4]=>0010110=>1101001
[5,7,1,2,8,6,4,3]=>0100111=>1011000
[3,1,7,6,8,5,4,2]=>1010111=>0101000
[1,2,6,8,5,7,4,3]=>0001011=>1110100
[1,2,5,8,7,4,6,3]=>0001101=>1110010
[1,2,4,8,7,6,3,5]=>0001110=>1110001
[6,4,5,7,2,8,1,3]=>1001010=>0110101
[5,3,4,7,2,8,1,6]=>1001010=>0110101
[3,2,7,4,6,8,1,5]=>1010010=>0101101
[5,3,6,2,7,1,4,8]=>1010100=>0101011
[2,6,3,4,7,1,5,8]=>0100100=>1011011
[2,7,3,4,5,8,1,6]=>0100010=>1011101
[3,7,4,5,6,8,1,2]=>0100010=>1011101
[2,5,7,3,6,8,1,4]=>0010010=>1101101
[4,7,6,2,3,8,1,5]=>0110010=>1001101
[7,3,5,2,4,8,1,6]=>1010010=>0101101
[7,6,2,4,5,8,1,3]=>1100010=>0011101
[6,5,2,3,4,8,1,7]=>1100010=>0011101
[5,3,1,2,8,4,7,6]=>1100101=>0011010
[6,5,2,3,7,1,4,8]=>1100100=>0011011
[5,2,1,7,3,4,6,8]=>1101000=>0010111
[5,2,1,8,3,4,6,7]=>1101000=>0010111
[6,3,2,8,4,5,7,1]=>1101001=>0010110
[7,3,1,2,8,4,6,5]=>1100101=>0011010
[6,4,1,3,8,5,7,2]=>1100101=>0011010
[6,2,3,1,8,4,7,5]=>1010101=>0101010
[8,3,5,2,7,1,4,6]=>1010100=>0101011
[8,6,2,4,7,1,5,3]=>1100101=>0011010
[8,5,2,3,6,1,4,7]=>1100100=>0011011
[8,2,1,7,3,4,5,6]=>1101000=>0010111
[8,6,3,7,2,4,5,1]=>1101001=>0010110
[7,1,6,2,3,4,5,8]=>1010000=>0101111
[8,2,7,3,4,5,6,1]=>1010001=>0101110
[8,1,6,2,3,4,5,7]=>1010000=>0101111
[8,1,7,3,4,5,6,2]=>1010001=>0101110
[8,6,1,7,2,4,5,3]=>1101001=>0010110
[8,1,5,7,2,3,6,4]=>1001001=>0110110
[1,7,5,8,2,3,6,4]=>0101001=>1010110
[7,2,1,8,3,4,5,6]=>1101000=>0010111
[7,3,8,2,4,5,6,1]=>1010001=>0101110
[7,2,8,3,4,5,6,1]=>1010001=>0101110
[1,7,8,3,4,5,6,2]=>0010001=>1101110
[1,4,5,8,3,6,7,2]=>0001001=>1110110
[2,5,7,1,8,3,6,4]=>0010101=>1101010
[6,2,7,1,8,4,5,3]=>1010101=>0101010
[4,7,1,3,8,5,6,2]=>0100101=>1011010
[1,6,2,8,4,5,7,3]=>0101001=>1010110
[4,1,3,6,8,2,7,5]=>1000101=>0111010
[5,3,4,6,8,2,7,1]=>1000101=>0111010
[4,6,3,8,7,1,2,5]=>0101100=>1010011
[6,4,5,8,7,1,2,3]=>1001100=>0110011
[5,3,4,8,7,1,2,6]=>1001100=>0110011
[3,2,8,7,1,4,6,5]=>1011001=>0100110
[3,1,8,7,2,4,6,5]=>1011001=>0100110
[5,3,7,6,1,2,4,8]=>1011000=>0100111
[1,8,3,7,2,4,5,6]=>0101000=>1010111
[3,8,1,7,2,4,5,6]=>0101000=>1010111
[6,8,2,3,5,1,4,7]=>0100100=>1011011
[4,7,8,2,6,1,3,5]=>0010100=>1101011
[6,2,8,7,1,4,5,3]=>1011001=>0100110
[3,8,7,1,4,5,6,2]=>0110001=>1001110
[2,8,6,1,3,4,5,7]=>0110000=>1001111
[2,7,6,1,3,4,5,8]=>0110000=>1001111
[1,7,6,2,3,4,5,8]=>0110000=>1001111
[1,8,6,2,3,4,5,7]=>0110000=>1001111
[2,8,7,3,4,5,6,1]=>0110001=>1001110
[3,8,7,2,4,5,6,1]=>0110001=>1001110
[7,8,3,6,2,4,5,1]=>0101001=>1010110
[1,5,8,7,2,3,6,4]=>0011001=>1100110
[8,7,6,1,3,4,5,2]=>1110001=>0001110
[3,6,2,4,7,1,8,5]=>0100101=>1011010
[3,4,7,2,5,1,8,6]=>0010101=>1101010
[2,1,6,4,8,5,3,7]=>1010110=>0101001
[4,1,8,5,3,2,7,6]=>1011101=>0100010
[3,6,2,5,7,1,4,8]=>0100100=>1011011
[1,2,8,3,7,5,4,6]=>0010110=>1101001
[6,1,3,2,8,5,4,7]=>1010110=>0101001
[5,6,1,2,8,4,3,7]=>0100110=>1011001
[1,6,3,8,7,4,2,5]=>0101110=>1010001
[4,3,8,1,2,6,7,5]=>1010001=>0101110
[7,8,10,9,5,6,3,4,1,2]=>001101010=>110010101
[9,10,5,6,8,7,3,4,1,2]=>010011010=>101100101
[5,8,10,6,9,7,3,4,1,2]=>001011010=>110100101
[5,6,7,10,9,8,3,4,1,2]=>000111010=>111000101
[9,10,7,8,3,4,6,5,1,2]=>010100110=>101011001
[7,8,10,9,3,4,6,5,1,2]=>001100110=>110011001
[9,10,3,6,8,4,7,5,1,2]=>010010110=>101101001
[3,8,10,6,9,4,7,5,1,2]=>001010110=>110101001
[3,6,7,10,9,4,8,5,1,2]=>000110110=>111001001
[9,10,3,4,5,8,7,6,1,2]=>010001110=>101110001
[3,8,10,4,5,9,7,6,1,2]=>001001110=>110110001
[3,4,7,10,5,9,8,6,1,2]=>000101110=>111010001
[3,4,5,6,10,9,8,7,1,2]=>000011110=>111100001
[9,10,7,8,5,6,1,2,4,3]=>010101001=>101010110
[7,8,10,9,5,6,1,2,4,3]=>001101001=>110010110
[9,10,5,6,8,7,1,2,4,3]=>010011001=>101100110
[5,8,10,6,9,7,1,2,4,3]=>001011001=>110100110
[5,6,7,10,9,8,1,2,4,3]=>000111001=>111000110
[9,10,7,8,1,4,6,2,5,3]=>010100101=>101011010
[7,8,10,9,1,4,6,2,5,3]=>001100101=>110011010
[9,10,1,6,8,4,7,2,5,3]=>010010101=>101101010
[1,8,10,6,9,4,7,2,5,3]=>001010101=>110101010
[1,6,7,10,9,4,8,2,5,3]=>000110101=>111001010
[9,10,1,4,5,8,7,2,6,3]=>010001101=>101110010
[1,8,10,4,5,9,7,2,6,3]=>001001101=>110110010
[1,4,7,10,5,9,8,2,6,3]=>000101101=>111010010
[1,4,5,6,10,9,8,2,7,3]=>000011101=>111100010
[9,10,7,8,1,2,3,6,5,4]=>010100011=>101011100
[7,8,10,9,1,2,3,6,5,4]=>001100011=>110011100
[9,10,1,6,8,2,3,7,5,4]=>010010011=>101101100
[1,8,10,6,9,2,3,7,5,4]=>001010011=>110101100
[1,6,7,10,9,2,3,8,5,4]=>000110011=>111001100
[9,10,1,2,5,8,3,7,6,4]=>010001011=>101110100
[1,8,10,2,5,9,3,7,6,4]=>001001011=>110110100
[1,2,7,10,5,9,3,8,6,4]=>000101011=>111010100
[1,2,5,6,10,9,3,8,7,4]=>000011011=>111100100
[9,10,1,2,3,4,8,7,6,5]=>010000111=>101111000
[1,8,10,2,3,4,9,7,6,5]=>001000111=>110111000
[1,2,7,10,3,4,9,8,6,5]=>000100111=>111011000
[1,2,3,6,10,4,9,8,7,5]=>000010111=>111101000
[1,2,3,4,5,10,9,8,7,6]=>000001111=>111110000
[11,12,9,10,7,8,5,6,3,4,1,2]=>01010101010=>10101010101
[11,12,5,8,10,6,9,7,3,4,1,2]=>01001011010=>10110100101
[5,8,9,12,11,6,10,7,3,4,1,2]=>00011011010=>11100100101
[5,10,12,6,7,11,9,8,3,4,1,2]=>00100111010=>11011000101
[5,6,9,12,7,11,10,8,3,4,1,2]=>00010111010=>11101000101
[5,6,7,8,12,11,10,9,3,4,1,2]=>00001111010=>11110000101
[11,12,9,10,3,6,8,4,7,5,1,2]=>01010010110=>10101101001
[3,8,9,12,11,6,10,4,7,5,1,2]=>00011010110=>11100101001
[3,6,9,12,7,11,10,4,8,5,1,2]=>00010110110=>11101001001
[3,6,7,8,12,11,10,4,9,5,1,2]=>00001110110=>11110001001
[9,10,12,11,3,4,5,8,7,6,1,2]=>00110001110=>11001110001
[11,12,3,8,10,4,5,9,7,6,1,2]=>01001001110=>10110110001
[3,10,12,8,11,4,5,9,7,6,1,2]=>00101001110=>11010110001
[3,8,9,12,11,4,5,10,7,6,1,2]=>00011001110=>11100110001
[3,10,12,4,7,11,5,9,8,6,1,2]=>00100101110=>11011010001
[3,4,9,12,7,11,5,10,8,6,1,2]=>00010101110=>11101010001
[3,4,7,8,12,11,5,10,9,6,1,2]=>00001101110=>11110010001
[3,4,9,12,5,6,11,10,8,7,1,2]=>00010011110=>11101100001
[3,4,5,8,12,6,11,10,9,7,1,2]=>00001011110=>11110100001
[3,4,5,6,7,12,11,10,9,8,1,2]=>00000111110=>11111000001
[7,8,9,12,11,10,5,6,1,2,4,3]=>00011101001=>11100010110
[9,10,12,11,5,6,8,7,1,2,4,3]=>00110011001=>11001100110
[11,12,5,8,10,6,9,7,1,2,4,3]=>01001011001=>10110100110
[5,10,12,8,11,6,9,7,1,2,4,3]=>00101011001=>11010100110
[5,8,9,12,11,6,10,7,1,2,4,3]=>00011011001=>11100100110
[5,10,12,6,7,11,9,8,1,2,4,3]=>00100111001=>11011000110
[5,6,9,12,7,11,10,8,1,2,4,3]=>00010111001=>11101000110
[9,10,12,11,7,8,1,4,6,2,5,3]=>00110100101=>11001011010
[7,10,12,8,11,9,1,4,6,2,5,3]=>00101100101=>11010011010
[7,8,9,12,11,10,1,4,6,2,5,3]=>00011100101=>11100011010
[9,10,12,11,1,6,8,4,7,2,5,3]=>00110010101=>11001101010
[1,10,12,8,11,6,9,4,7,2,5,3]=>00101010101=>11010101010
[1,8,9,12,11,6,10,4,7,2,5,3]=>00011010101=>11100101010
[1,10,12,6,7,11,9,4,8,2,5,3]=>00100110101=>11011001010
[1,6,9,12,7,11,10,4,8,2,5,3]=>00010110101=>11101001010
[1,6,7,8,12,11,10,4,9,2,5,3]=>00001110101=>11110001010
[1,10,12,8,11,4,5,9,7,2,6,3]=>00101001101=>11010110010
[1,8,9,12,11,4,5,10,7,2,6,3]=>00011001101=>11100110010
[1,10,12,4,7,11,5,9,8,2,6,3]=>00100101101=>11011010010
[1,4,9,12,7,11,5,10,8,2,6,3]=>00010101101=>11101010010
[1,4,7,8,12,11,5,10,9,2,6,3]=>00001101101=>11110010010
[11,12,1,4,5,6,10,9,8,2,7,3]=>01000011101=>10111100010
[1,10,12,4,5,6,11,9,8,2,7,3]=>00100011101=>11011100010
[1,4,9,12,5,6,11,10,8,2,7,3]=>00010011101=>11101100010
[1,4,5,8,12,6,11,10,9,2,7,3]=>00001011101=>11110100010
[1,4,5,6,7,12,11,10,9,2,8,3]=>00000111101=>11111000010
[11,12,7,8,10,9,1,2,3,6,5,4]=>01001100011=>10110011100
[1,10,12,8,11,6,9,2,3,7,5,4]=>00101010011=>11010101100
[1,8,9,12,11,6,10,2,3,7,5,4]=>00011010011=>11100101100
[11,12,1,6,7,10,9,2,3,8,5,4]=>01000110011=>10111001100
[1,10,12,6,7,11,9,2,3,8,5,4]=>00100110011=>11011001100
[1,6,9,12,7,11,10,2,3,8,5,4]=>00010110011=>11101001100
[1,6,7,8,12,11,10,2,3,9,5,4]=>00001110011=>11110001100
[9,10,12,11,1,2,5,8,3,7,6,4]=>00110001011=>11001110100
[1,10,12,8,11,2,5,9,3,7,6,4]=>00101001011=>11010110100
[1,8,9,12,11,2,5,10,3,7,6,4]=>00011001011=>11100110100
[1,10,12,2,7,11,5,9,3,8,6,4]=>00100101011=>11011010100
[1,2,9,12,7,11,5,10,3,8,6,4]=>00010101011=>11101010100
[1,2,7,8,12,11,5,10,3,9,6,4]=>00001101011=>11110010100
[1,10,12,2,5,6,11,9,3,8,7,4]=>00100011011=>11011100100
[1,2,9,12,5,6,11,10,3,8,7,4]=>00010011011=>11101100100
[1,2,5,8,12,6,11,10,3,9,7,4]=>00001011011=>11110100100
[1,2,5,6,7,12,11,10,3,9,8,4]=>00000111011=>11111000100
[9,10,12,11,1,2,3,4,8,7,6,5]=>00110000111=>11001111000
[1,10,12,8,11,2,3,4,9,7,6,5]=>00101000111=>11010111000
[1,8,9,12,11,2,3,4,10,7,6,5]=>00011000111=>11100111000
[1,10,12,2,7,11,3,4,9,8,6,5]=>00100100111=>11011011000
[1,2,9,12,7,11,3,4,10,8,6,5]=>00010100111=>11101011000
[1,2,7,8,12,11,3,4,10,9,6,5]=>00001100111=>11110011000
[1,10,12,2,3,6,11,4,9,8,7,5]=>00100010111=>11011101000
[1,2,9,12,3,6,11,4,10,8,7,5]=>00010010111=>11101101000
[1,2,3,8,12,6,11,4,10,9,7,5]=>00001010111=>11110101000
[1,2,3,6,7,12,11,4,10,9,8,5]=>00000110111=>11111001000
[1,10,12,2,3,4,5,11,9,8,7,6]=>00100001111=>11011110000
[1,2,9,12,3,4,5,11,10,8,7,6]=>00010001111=>11101110000
[1,2,3,8,12,4,5,11,10,9,7,6]=>00001001111=>11110110000
[1,2,3,4,7,12,5,11,10,9,8,6]=>00000101111=>11111010000
[1,2,3,4,5,6,12,11,10,9,8,7]=>00000011111=>11111100000
[3,1,2,4,5,6,7,8,9]=>10000000=>01111111
[2,4,1,3,5,6,7,8,9]=>01000000=>10111111
[2,3,5,1,4,6,7,8,9]=>00100000=>11011111
[2,3,4,6,1,5,7,8,9]=>00010000=>11101111
[2,3,4,5,7,1,6,8,9]=>00001000=>11110111
[2,3,4,5,6,8,1,7,9]=>00000100=>11111011
[3,6,8,7,1,2,5,4]=>0011001=>1100110
[6,2,8,5,4,7,1,3]=>1011010=>0100101
[6,5,7,2,4,8,1,3]=>1010010=>0101101
[3,4,1,6,5,8,7,2]=>0101011=>1010100
[3,5,1,2,4,8,7,6]=>0100011=>1011100
[3,7,5,2,1,4,6,8]=>0111000=>1000111
[3,8,5,2,7,4,1,6]=>0110110=>1001001
[5,2,8,4,7,3,1,6]=>1010110=>0101001
[5,2,7,4,1,3,6,8]=>1011000=>0100111
[4,3,5,1,2,8,7,6]=>1010011=>0101100
[3,1,4,6,2,8,7,5]=>1001011=>0110100
[1,4,6,5,2,8,7,3]=>0011011=>1100100
[3,4,5,6,1,8,7,2]=>0001011=>1110100
[3,4,5,8,7,2,1,6]=>0001110=>1110001
[1,4,7,2,6,3,5,8]=>0010100=>1101011
[8,4,7,5,2,1,6,3]=>1011101=>0100010
[8,1,4,7,2,3,6,5]=>1001001=>0110110
[1,8,5,7,3,4,6,2]=>0101001=>1010110
[6,3,5,1,7,4,2,8]=>1010110=>0101001
[6,1,4,8,7,3,2,5]=>1001110=>0110001
[6,4,8,5,7,1,2,3]=>1010100=>0101011
[5,4,8,1,6,3,2,7]=>1010110=>0101001
[1,4,8,6,3,7,2,5]=>0011010=>1100101
[5,4,7,6,3,8,1,2]=>1011010=>0100101
[4,6,3,7,5,8,1,2]=>0101010=>1010101
[4,1,3,5,8,6,2,7]=>1000110=>0111001
[5,7,4,3,8,1,2,6]=>0110100=>1001011
[1,4,8,3,7,6,5,2]=>0010111=>1101000
[4,3,8,2,1,6,5,7]=>1011010=>0100101
[3,8,4,2,7,1,5,6]=>0110100=>1001011
[3,1,2,5,7,6,4,8]=>1000110=>0111001
[1,8,2,7,6,5,4,3]=>0101111=>1010000
[3,8,1,6,7,5,4,2]=>0100111=>1011000
[3,7,2,6,8,5,1,4]=>0100110=>1011001
[7,2,3,8,5,6,1,4]=>1001010=>0110101
[8,2,1,7,5,6,4,3]=>1101011=>0010100
[8,1,3,6,5,7,4,2]=>1001011=>0110100
[8,2,4,3,6,1,5,7]=>1010100=>0101011
[1,7,8,5,4,3,6,2]=>0011101=>1100010
[1,8,4,5,3,2,6,7]=>0101100=>1010011
[7,8,5,4,3,1,6,2]=>0111101=>1000010
[7,1,6,3,4,2,5,8]=>1010100=>0101011
[6,8,7,1,4,2,5,3]=>0110101=>1001010
[3,6,1,4,2,7,5,8]=>0101010=>1010101
[3,4,1,8,5,7,6,2]=>0101011=>1010100
[3,6,5,1,2,8,4,7]=>0110010=>1001101
[3,8,5,6,7,2,1,4]=>0100110=>1011001
[8,1,7,6,2,4,3,5]=>1011010=>0100101
[8,5,6,1,4,2,3,7]=>1010100=>0101011
[8,6,5,4,7,1,3,2]=>1110101=>0001010
[1,6,4,5,7,2,3,8]=>0100100=>1011011
[8,3,6,1,7,2,4,5]=>1010100=>0101011
[1,8,6,5,7,3,4,2]=>0110101=>1001010
[1,7,5,3,6,8,4,2]=>0110011=>1001100
[7,4,1,6,5,8,3,2]=>1101011=>0010100
[4,1,5,8,7,6,3,2]=>1001111=>0110000
[1,2,5,8,6,7,3,4]=>0001010=>1110101
[4,2,1,5,8,7,3,6]=>1100110=>0011001
[5,2,4,6,1,7,3,8]=>1001010=>0110101
[1,5,3,6,8,7,4,2]=>0100111=>1011000
[3,5,4,6,1,8,2,7]=>0101010=>1010101
[3,1,5,7,6,8,2,4]=>1001010=>0110101
[1,4,5,6,8,7,2,3]=>0000110=>1111001
[1,4,6,3,7,2,8,5]=>0010101=>1101010
[1,7,3,6,5,2,8,4]=>0101101=>1010010
[8,6,2,5,4,1,7,3]=>1101101=>0010010
[3,7,2,6,5,4,1,8]=>0101110=>1010001
[7,6,2,5,4,3,1,8]=>1101110=>0010001
[4,7,5,2,6,3,1,8]=>0110110=>1001001
[3,2,6,4,7,5,1,8]=>1010110=>0101001
[6,2,3,7,5,4,1,8]=>1001110=>0110001
[1,3,4,7,6,2,8,5]=>0001101=>1110010
[2,8,3,6,1,7,5,4]=>0101011=>1010100
[8,7,2,5,1,6,4,3]=>1101011=>0010100
[3,8,2,6,5,1,7,4]=>0101101=>1010010
[7,8,2,5,4,1,6,3]=>0101101=>1010010
[4,8,5,2,6,1,7,3]=>0110101=>1001010
[4,5,1,3,7,2,8,6]=>0100101=>1011010
[6,1,3,7,5,2,8,4]=>1001101=>0110010
[7,1,3,6,2,8,5,4]=>1001011=>0110100
[8,1,3,6,2,7,5,4]=>1001011=>0110100
[1,2,4,7,3,8,6,5]=>0001011=>1110100
[7,1,8,2,6,5,4,3]=>1010111=>0101000
[3,1,8,6,2,7,5,4]=>1011011=>0100100
[4,1,7,8,2,6,5,3]=>1001011=>0110100
[5,6,1,8,2,7,4,3]=>0101011=>1010100
[4,2,7,8,1,6,5,3]=>1001011=>0110100
[3,2,8,6,1,7,5,4]=>1011011=>0100100
[7,2,8,1,6,5,4,3]=>1010111=>0101000
[1,8,7,2,6,5,4,3]=>0110111=>1001000
[2,8,7,1,6,5,4,3]=>0110111=>1001000
[3,8,7,1,6,5,4,2]=>0110111=>1001000
[4,8,7,5,1,6,3,2]=>0111011=>1000100
[6,7,8,5,1,4,3,2]=>0011011=>1100100
[5,6,3,8,4,1,7,2]=>0101101=>1010010
[7,3,8,5,4,1,6,2]=>1011101=>0100010
[3,4,8,6,5,1,7,2]=>0011101=>1100010
[8,3,7,5,1,6,4,2]=>1011011=>0100100
[1,4,8,6,2,7,5,3]=>0011011=>1100100
[8,4,6,7,1,5,3,2]=>1001011=>0110100
[5,6,4,7,8,1,3,2]=>0100101=>1011010
[3,4,6,5,1,2,8,7]=>0011001=>1100110
[7,3,5,1,2,8,6,4]=>1010011=>0101100
[1,4,6,2,3,8,7,5]=>0010011=>1101100
[1,3,2,7,4,8,6,5]=>0101011=>1010100
[7,2,1,6,3,8,5,4]=>1101011=>0010100
[2,3,1,7,6,4,8,5]=>0101101=>1010010
[4,5,2,1,7,3,8,6]=>0110101=>1001010
[5,6,7,1,2,8,4,3]=>0010011=>1101100
[4,7,5,1,2,8,6,3]=>0110011=>1001100
[3,7,1,6,2,8,5,4]=>0101011=>1010100
[7,6,1,2,8,5,4,3]=>1100111=>0011000
[2,7,1,3,8,6,5,4]=>0100111=>1011000
[8,6,1,2,7,5,4,3]=>1100111=>0011000
[1,7,2,3,8,6,5,4]=>0100111=>1011000
[8,7,1,2,6,5,4,3]=>1100111=>0011000
[7,8,1,2,6,5,4,3]=>0100111=>1011000
[3,8,1,6,2,7,5,4]=>0101011=>1010100
[4,8,5,1,2,7,6,3]=>0110011=>1001100
[5,6,8,1,2,7,4,3]=>0010011=>1101100
[2,1,3,7,4,8,6,5]=>1001011=>0110100
[4,2,7,3,6,8,1,5]=>1010010=>0101101
[5,3,6,4,2,8,1,7]=>1011010=>0100101
[4,1,5,3,8,2,7,6]=>1010101=>0101010
[5,2,6,4,7,3,1,8]=>1010110=>0101001
[2,6,3,4,7,5,1,8]=>0100110=>1011001
[2,6,3,5,4,8,1,7]=>0101010=>1010101
[2,7,4,3,5,8,1,6]=>0110010=>1001101
[7,3,6,4,2,8,1,5]=>1011010=>0100101
[7,6,4,5,2,8,1,3]=>1101010=>0010101
[5,4,3,1,8,2,7,6]=>1110101=>0001010
[6,5,4,2,7,3,1,8]=>1110110=>0001001
[5,4,1,7,2,6,3,8]=>1101010=>0010101
[5,4,1,8,3,2,6,7]=>1101100=>0010011
[6,5,2,8,3,4,7,1]=>1101001=>0010110
[7,4,2,1,8,3,6,5]=>1110101=>0001010
[6,5,3,4,8,2,7,1]=>1100101=>0011010
[6,1,5,3,8,2,7,4]=>1010101=>0101010
[4,6,3,1,8,2,7,5]=>0110101=>1001010
[5,8,4,2,7,3,1,6]=>0110110=>1001001
[8,2,6,4,7,3,1,5]=>1010110=>0101001
[8,6,2,5,7,4,1,3]=>1100110=>0011001
[8,5,3,2,6,4,1,7]=>1110110=>0001001
[8,3,1,7,2,5,4,6]=>1101010=>0010101
[7,5,2,6,4,3,1,8]=>1101110=>0010001
[7,1,6,2,5,4,3,8]=>1010110=>0101001
[8,1,7,3,5,6,4,2]=>1010011=>0101100
[8,6,1,7,4,5,2,3]=>1101010=>0010101
[8,1,3,7,2,6,5,4]=>1001011=>0110100
[1,7,6,8,3,2,4,5]=>0101100=>1010011
[7,1,5,8,4,2,6,3]=>1001101=>0110010
[7,3,8,4,5,2,6,1]=>1010101=>0101010
[7,2,8,5,3,4,6,1]=>1011001=>0100110
[6,1,8,4,3,2,5,7]=>1011100=>0100011
[6,1,7,4,2,5,3,8]=>1011010=>0100101
[1,2,7,3,4,6,5,8]=>0010010=>1101101
[1,7,8,4,3,5,6,2]=>0011001=>1100110
[1,6,2,8,3,5,7,4]=>0101001=>1010110
[2,6,1,7,3,5,4,8]=>0101010=>1010101
[3,1,5,8,4,2,6,7]=>1001100=>0110011
[4,3,1,6,8,2,7,5]=>1100101=>0011010
[5,7,4,8,3,2,1,6]=>0101110=>1010001
[5,4,8,2,7,3,1,6]=>1010110=>0101001
[5,2,8,7,3,4,1,6]=>1011010=>0100101
[6,4,7,5,3,2,1,8]=>1011110=>0100001
[1,8,3,7,6,2,4,5]=>0101100=>1010011
[5,8,3,2,6,4,1,7]=>0110110=>1001001
[6,8,2,4,7,5,1,3]=>0100110=>1011001
[7,3,8,2,6,4,1,5]=>1010110=>0101001
[4,6,8,2,7,3,1,5]=>0010110=>1101001
[2,6,8,7,3,4,1,5]=>0011010=>1100101
[7,2,8,6,3,5,1,4]=>1011010=>0100101
[6,8,1,7,2,5,4,3]=>0101011=>1010100
[3,8,7,4,5,6,1,2]=>0110010=>1001101
[2,8,6,4,3,5,1,7]=>0111010=>1000101
[2,7,6,3,5,4,1,8]=>0110110=>1001001
[1,7,6,5,2,4,3,8]=>0111010=>1000101
[1,8,6,5,3,2,4,7]=>0111100=>1000011
[3,8,7,4,6,2,5,1]=>0110101=>1001010
[5,8,3,7,6,2,4,1]=>0101101=>1010010
[7,1,8,6,5,2,3,4]=>1011100=>0100011
[8,4,7,5,3,2,1,6]=>1011110=>0100001
[8,7,2,5,4,3,1,6]=>1101110=>0010001
[6,8,3,2,5,4,7,1]=>0110101=>1001010
[6,8,4,5,2,3,7,1]=>0101001=>1010110
[1,5,7,8,4,3,6,2]=>0001101=>1110010
[6,3,8,1,5,4,7,2]=>1010101=>0101010
[6,2,1,8,5,4,7,3]=>1101101=>0010010
[2,6,3,1,7,5,4,8]=>0110110=>1001001
[2,6,5,7,4,1,3,8]=>0101100=>1010011
[2,5,6,8,4,3,7,1]=>0001101=>1110010
[2,4,7,5,8,1,6,3]=>0010101=>1101010
[2,5,4,7,1,8,6,3]=>0101011=>1010100
[5,2,1,8,7,6,4,3]=>1101111=>0010000
[4,8,5,7,6,1,3,2]=>0101101=>1010010
[4,8,6,7,5,3,1,2]=>0101110=>1010001
[4,8,7,5,6,2,3,1]=>0110101=>1001010
[6,5,4,8,2,1,7,3]=>1101101=>0010010
[5,8,4,7,2,6,3,1]=>0101011=>1010100
[1,5,7,4,8,2,6,3]=>0010101=>1101010
[1,5,7,3,2,8,6,4]=>0011011=>1100100
[5,8,3,2,7,6,4,1]=>0110111=>1001000
[5,2,1,4,3,6,7,8]=>1101000=>0010111
[3,5,7,4,2,6,1,8]=>0011010=>1100101
[3,6,4,5,1,2,7,8]=>0101000=>1010111
[4,2,1,6,5,3,7,8]=>1101100=>0010011
[4,2,1,5,7,6,3,8]=>1100110=>0011001
[4,3,5,1,7,6,2,8]=>1010110=>0101001
[3,5,4,7,1,6,2,8]=>0101010=>1010101
[3,4,7,5,6,1,2,8]=>0010100=>1101011
[3,4,5,8,6,7,1,2]=>0001010=>1110101
[3,5,4,6,1,8,7,2]=>0101011=>1010100
[4,3,5,1,6,8,7,2]=>1010011=>0101100
[4,2,1,5,6,8,7,3]=>1100011=>0011100
[4,3,2,1,7,6,5,9,8,10]=>111011010=>000100101
[7,3,2,1,6,5,4,9,8,10]=>111011010=>000100101
[4,3,2,1,9,6,5,8,7,10]=>111011010=>000100101
[6,3,2,1,9,5,4,8,7,10]=>111011010=>000100101
[9,3,2,1,8,5,4,7,6,10]=>111011010=>000100101
[6,5,2,1,9,4,3,8,7,10]=>111011010=>000100101
[9,5,2,1,8,4,3,7,6,10]=>111011010=>000100101
[4,3,2,1,7,6,5,10,8,9]=>111011010=>000100101
[7,3,2,1,6,5,4,10,8,9]=>111011010=>000100101
[4,3,2,1,8,6,5,10,7,9]=>111011010=>000100101
[6,3,2,1,8,5,4,10,7,9]=>111011010=>000100101
[8,3,2,1,7,5,4,10,6,9]=>111011010=>000100101
[6,5,2,1,8,4,3,10,7,9]=>111011010=>000100101
[8,5,2,1,7,4,3,10,6,9]=>111011010=>000100101
[4,3,2,1,10,6,5,9,7,8]=>111011010=>000100101
[6,3,2,1,10,5,4,9,7,8]=>111011010=>000100101
[7,3,2,1,10,5,4,9,6,8]=>111011010=>000100101
[10,3,2,1,9,5,4,8,6,7]=>111011010=>000100101
[6,5,2,1,10,4,3,9,7,8]=>111011010=>000100101
[7,5,2,1,10,4,3,9,6,8]=>111011010=>000100101
[10,5,2,1,9,4,3,8,6,7]=>111011010=>000100101
[4,3,2,1,8,7,5,10,6,9]=>111011010=>000100101
[5,3,2,1,8,7,4,10,6,9]=>111011010=>000100101
[8,3,2,1,7,6,4,10,5,9]=>111011010=>000100101
[5,4,2,1,8,7,3,10,6,9]=>111011010=>000100101
[8,4,2,1,7,6,3,10,5,9]=>111011010=>000100101
[4,3,2,1,10,7,5,9,6,8]=>111011010=>000100101
[5,3,2,1,10,7,4,9,6,8]=>111011010=>000100101
[7,3,2,1,10,6,4,9,5,8]=>111011010=>000100101
[10,3,2,1,9,6,4,8,5,7]=>111011010=>000100101
[5,4,2,1,10,7,3,9,6,8]=>111011010=>000100101
[7,4,2,1,10,6,3,9,5,8]=>111011010=>000100101
[10,4,2,1,9,6,3,8,5,7]=>111011010=>000100101
[7,6,2,1,10,5,3,9,4,8]=>111011010=>000100101
[10,6,2,1,9,5,3,8,4,7]=>111011010=>000100101
[5,4,3,1,8,7,2,10,6,9]=>111011010=>000100101
[8,4,3,1,7,6,2,10,5,9]=>111011010=>000100101
[5,4,3,1,10,7,2,9,6,8]=>111011010=>000100101
[7,4,3,1,10,6,2,9,5,8]=>111011010=>000100101
[10,4,3,1,9,6,2,8,5,7]=>111011010=>000100101
[7,6,3,1,10,5,2,9,4,8]=>111011010=>000100101
[10,6,3,1,9,5,2,8,4,7]=>111011010=>000100101
[2,1,4,3,6,5,10,9,7,8]=>101010110=>010101001
[2,1,4,3,8,7,5,6,10,9]=>101011001=>010100110
[2,1,4,3,10,7,5,9,6,8]=>101011010=>010100101
[2,1,4,3,10,9,8,5,6,7]=>101011100=>010100011
[2,1,6,5,3,4,8,7,10,9]=>101100101=>010011010
[2,1,6,5,3,4,10,9,7,8]=>101100110=>010011001
[2,1,8,5,3,7,4,6,10,9]=>101101001=>010010110
[2,1,10,5,3,7,4,9,6,8]=>101101010=>010010101
[2,1,10,5,3,9,8,4,6,7]=>101101100=>010010011
[2,1,8,7,6,3,4,5,10,9]=>101110001=>010001110
[2,1,10,7,6,3,4,9,5,8]=>101110010=>010001101
[2,1,10,9,6,3,8,4,5,7]=>101110100=>010001011
[2,1,10,9,8,7,3,4,5,6]=>101111000=>010000111
[4,3,1,2,6,5,8,7,10,9]=>110010101=>001101010
[4,3,1,2,6,5,10,9,7,8]=>110010110=>001101001
[4,3,1,2,8,7,5,6,10,9]=>110011001=>001100110
[4,3,1,2,10,7,5,9,6,8]=>110011010=>001100101
[4,3,1,2,10,9,8,5,6,7]=>110011100=>001100011
[6,3,1,5,2,4,8,7,10,9]=>110100101=>001011010
[6,3,1,5,2,4,10,9,7,8]=>110100110=>001011001
[8,3,1,5,2,7,4,6,10,9]=>110101001=>001010110
[10,3,1,5,2,7,4,9,6,8]=>110101010=>001010101
[10,3,1,5,2,9,8,4,6,7]=>110101100=>001010011
[8,3,1,7,6,2,4,5,10,9]=>110110001=>001001110
[10,3,1,7,6,2,4,9,5,8]=>110110010=>001001101
[10,3,1,9,6,2,8,4,5,7]=>110110100=>001001011
[10,3,1,9,8,7,2,4,5,6]=>110111000=>001000111
[6,5,4,1,2,3,8,7,10,9]=>111000101=>000111010
[6,5,4,1,2,3,10,9,7,8]=>111000110=>000111001
[8,5,4,1,2,7,3,6,10,9]=>111001001=>000110110
[10,5,4,1,2,7,3,9,6,8]=>111001010=>000110101
[10,5,4,1,2,9,8,3,6,7]=>111001100=>000110011
[8,7,4,1,6,2,3,5,10,9]=>111010001=>000101110
[10,7,4,1,6,2,3,9,5,8]=>111010010=>000101101
[10,9,4,1,6,2,8,3,5,7]=>111010100=>000101011
[10,9,4,1,8,7,2,3,5,6]=>111011000=>000100111
[8,7,6,5,1,2,3,4,10,9]=>111100001=>000011110
[10,7,6,5,1,2,3,9,4,8]=>111100010=>000011101
[10,9,6,5,1,2,8,3,4,7]=>111100100=>000011011
[10,9,8,5,1,7,2,3,4,6]=>111101000=>000010111
[2,1,4,3,6,5,8,7,12,11,9,10]=>10101010110=>01010101001
[2,1,4,3,6,5,10,9,7,8,12,11]=>10101011001=>01010100110
[2,1,4,3,6,5,12,9,7,11,8,10]=>10101011010=>01010100101
[2,1,4,3,6,5,12,11,10,7,8,9]=>10101011100=>01010100011
[2,1,4,3,8,7,5,6,10,9,12,11]=>10101100101=>01010011010
[2,1,4,3,8,7,5,6,12,11,9,10]=>10101100110=>01010011001
[2,1,4,3,10,7,5,9,6,8,12,11]=>10101101001=>01010010110
[2,1,4,3,12,7,5,9,6,11,8,10]=>10101101010=>01010010101
[2,1,4,3,12,7,5,11,10,6,8,9]=>10101101100=>01010010011
[2,1,4,3,10,9,8,5,6,7,12,11]=>10101110001=>01010001110
[2,1,4,3,12,9,8,5,6,11,7,10]=>10101110010=>01010001101
[2,1,4,3,12,11,8,5,10,6,7,9]=>10101110100=>01010001011
[2,1,4,3,12,11,10,9,5,6,7,8]=>10101111000=>01010000111
[2,1,6,5,3,4,8,7,10,9,12,11]=>10110010101=>01001101010
[2,1,6,5,3,4,8,7,12,11,9,10]=>10110010110=>01001101001
[2,1,6,5,3,4,10,9,7,8,12,11]=>10110011001=>01001100110
[2,1,6,5,3,4,12,9,7,11,8,10]=>10110011010=>01001100101
[2,1,6,5,3,4,12,11,10,7,8,9]=>10110011100=>01001100011
[2,1,8,5,3,7,4,6,10,9,12,11]=>10110100101=>01001011010
[2,1,8,5,3,7,4,6,12,11,9,10]=>10110100110=>01001011001
[2,1,10,5,3,7,4,9,6,8,12,11]=>10110101001=>01001010110
[2,1,12,5,3,7,4,9,6,11,8,10]=>10110101010=>01001010101
[2,1,12,5,3,7,4,11,10,6,8,9]=>10110101100=>01001010011
[2,1,10,5,3,9,8,4,6,7,12,11]=>10110110001=>01001001110
[2,1,12,5,3,9,8,4,6,11,7,10]=>10110110010=>01001001101
[2,1,12,5,3,11,8,4,10,6,7,9]=>10110110100=>01001001011
[2,1,12,5,3,11,10,9,4,6,7,8]=>10110111000=>01001000111
[2,1,8,7,6,3,4,5,10,9,12,11]=>10111000101=>01000111010
[2,1,8,7,6,3,4,5,12,11,9,10]=>10111000110=>01000111001
[2,1,10,7,6,3,4,9,5,8,12,11]=>10111001001=>01000110110
[2,1,12,7,6,3,4,9,5,11,8,10]=>10111001010=>01000110101
[2,1,12,7,6,3,4,11,10,5,8,9]=>10111001100=>01000110011
[2,1,10,9,6,3,8,4,5,7,12,11]=>10111010001=>01000101110
[2,1,12,9,6,3,8,4,5,11,7,10]=>10111010010=>01000101101
[2,1,12,11,6,3,8,4,10,5,7,9]=>10111010100=>01000101011
[2,1,12,11,6,3,10,9,4,5,7,8]=>10111011000=>01000100111
[2,1,10,9,8,7,3,4,5,6,12,11]=>10111100001=>01000011110
[2,1,12,9,8,7,3,4,5,11,6,10]=>10111100010=>01000011101
[2,1,12,11,8,7,3,4,10,5,6,9]=>10111100100=>01000011011
[2,1,12,11,10,7,3,9,4,5,6,8]=>10111101000=>01000010111
[2,1,12,11,10,9,8,3,4,5,6,7]=>10111110000=>01000001111
[4,3,1,2,6,5,8,7,10,9,12,11]=>11001010101=>00110101010
[4,3,1,2,6,5,8,7,12,11,9,10]=>11001010110=>00110101001
[4,3,1,2,6,5,10,9,7,8,12,11]=>11001011001=>00110100110
[4,3,1,2,6,5,12,9,7,11,8,10]=>11001011010=>00110100101
[4,3,1,2,6,5,12,11,10,7,8,9]=>11001011100=>00110100011
[4,3,1,2,8,7,5,6,10,9,12,11]=>11001100101=>00110011010
[4,3,1,2,8,7,5,6,12,11,9,10]=>11001100110=>00110011001
[4,3,1,2,10,7,5,9,6,8,12,11]=>11001101001=>00110010110
[4,3,1,2,12,7,5,9,6,11,8,10]=>11001101010=>00110010101
[4,3,1,2,12,7,5,11,10,6,8,9]=>11001101100=>00110010011
[4,3,1,2,10,9,8,5,6,7,12,11]=>11001110001=>00110001110
[4,3,1,2,12,9,8,5,6,11,7,10]=>11001110010=>00110001101
[4,3,1,2,12,11,8,5,10,6,7,9]=>11001110100=>00110001011
[4,3,1,2,12,11,10,9,5,6,7,8]=>11001111000=>00110000111
[6,3,1,5,2,4,8,7,10,9,12,11]=>11010010101=>00101101010
[6,3,1,5,2,4,8,7,12,11,9,10]=>11010010110=>00101101001
[6,3,1,5,2,4,10,9,7,8,12,11]=>11010011001=>00101100110
[6,3,1,5,2,4,12,9,7,11,8,10]=>11010011010=>00101100101
[6,3,1,5,2,4,12,11,10,7,8,9]=>11010011100=>00101100011
[8,3,1,5,2,7,4,6,10,9,12,11]=>11010100101=>00101011010
[8,3,1,5,2,7,4,6,12,11,9,10]=>11010100110=>00101011001
[10,3,1,5,2,7,4,9,6,8,12,11]=>11010101001=>00101010110
[12,3,1,5,2,7,4,9,6,11,8,10]=>11010101010=>00101010101
[12,3,1,5,2,7,4,11,10,6,8,9]=>11010101100=>00101010011
[10,3,1,5,2,9,8,4,6,7,12,11]=>11010110001=>00101001110
[12,3,1,5,2,9,8,4,6,11,7,10]=>11010110010=>00101001101
[12,3,1,5,2,11,8,4,10,6,7,9]=>11010110100=>00101001011
[12,3,1,5,2,11,10,9,4,6,7,8]=>11010111000=>00101000111
[8,3,1,7,6,2,4,5,10,9,12,11]=>11011000101=>00100111010
[8,3,1,7,6,2,4,5,12,11,9,10]=>11011000110=>00100111001
[10,3,1,7,6,2,4,9,5,8,12,11]=>11011001001=>00100110110
[12,3,1,7,6,2,4,9,5,11,8,10]=>11011001010=>00100110101
[12,3,1,7,6,2,4,11,10,5,8,9]=>11011001100=>00100110011
[10,3,1,9,6,2,8,4,5,7,12,11]=>11011010001=>00100101110
[12,3,1,9,6,2,8,4,5,11,7,10]=>11011010010=>00100101101
[12,3,1,11,6,2,8,4,10,5,7,9]=>11011010100=>00100101011
[12,3,1,11,6,2,10,9,4,5,7,8]=>11011011000=>00100100111
[10,3,1,9,8,7,2,4,5,6,12,11]=>11011100001=>00100011110
[12,3,1,9,8,7,2,4,5,11,6,10]=>11011100010=>00100011101
[12,3,1,11,8,7,2,4,10,5,6,9]=>11011100100=>00100011011
[12,3,1,11,10,7,2,9,4,5,6,8]=>11011101000=>00100010111
[12,3,1,11,10,9,8,2,4,5,6,7]=>11011110000=>00100001111
[6,5,4,1,2,3,8,7,10,9,12,11]=>11100010101=>00011101010
[6,5,4,1,2,3,8,7,12,11,9,10]=>11100010110=>00011101001
[6,5,4,1,2,3,10,9,7,8,12,11]=>11100011001=>00011100110
[6,5,4,1,2,3,12,9,7,11,8,10]=>11100011010=>00011100101
[6,5,4,1,2,3,12,11,10,7,8,9]=>11100011100=>00011100011
[8,5,4,1,2,7,3,6,10,9,12,11]=>11100100101=>00011011010
[8,5,4,1,2,7,3,6,12,11,9,10]=>11100100110=>00011011001
[10,5,4,1,2,7,3,9,6,8,12,11]=>11100101001=>00011010110
[12,5,4,1,2,7,3,9,6,11,8,10]=>11100101010=>00011010101
[12,5,4,1,2,7,3,11,10,6,8,9]=>11100101100=>00011010011
[10,5,4,1,2,9,8,3,6,7,12,11]=>11100110001=>00011001110
[12,5,4,1,2,9,8,3,6,11,7,10]=>11100110010=>00011001101
[12,5,4,1,2,11,8,3,10,6,7,9]=>11100110100=>00011001011
[12,5,4,1,2,11,10,9,3,6,7,8]=>11100111000=>00011000111
[8,7,4,1,6,2,3,5,10,9,12,11]=>11101000101=>00010111010
[8,7,4,1,6,2,3,5,12,11,9,10]=>11101000110=>00010111001
[10,7,4,1,6,2,3,9,5,8,12,11]=>11101001001=>00010110110
[12,7,4,1,6,2,3,9,5,11,8,10]=>11101001010=>00010110101
[12,7,4,1,6,2,3,11,10,5,8,9]=>11101001100=>00010110011
[10,9,4,1,6,2,8,3,5,7,12,11]=>11101010001=>00010101110
[12,9,4,1,6,2,8,3,5,11,7,10]=>11101010010=>00010101101
[12,11,4,1,6,2,8,3,10,5,7,9]=>11101010100=>00010101011
[12,11,4,1,6,2,10,9,3,5,7,8]=>11101011000=>00010100111
[10,9,4,1,8,7,2,3,5,6,12,11]=>11101100001=>00010011110
[12,9,4,1,8,7,2,3,5,11,6,10]=>11101100010=>00010011101
[12,11,4,1,8,7,2,3,10,5,6,9]=>11101100100=>00010011011
[12,11,4,1,10,7,2,9,3,5,6,8]=>11101101000=>00010010111
[12,11,4,1,10,9,8,2,3,5,6,7]=>11101110000=>00010001111
[8,7,6,5,1,2,3,4,10,9,12,11]=>11110000101=>00001111010
[8,7,6,5,1,2,3,4,12,11,9,10]=>11110000110=>00001111001
[10,7,6,5,1,2,3,9,4,8,12,11]=>11110001001=>00001110110
[12,7,6,5,1,2,3,9,4,11,8,10]=>11110001010=>00001110101
[12,7,6,5,1,2,3,11,10,4,8,9]=>11110001100=>00001110011
[10,9,6,5,1,2,8,3,4,7,12,11]=>11110010001=>00001101110
[12,9,6,5,1,2,8,3,4,11,7,10]=>11110010010=>00001101101
[12,11,6,5,1,2,8,3,10,4,7,9]=>11110010100=>00001101011
[12,11,6,5,1,2,10,9,3,4,7,8]=>11110011000=>00001100111
[10,9,8,5,1,7,2,3,4,6,12,11]=>11110100001=>00001011110
[12,9,8,5,1,7,2,3,4,11,6,10]=>11110100010=>00001011101
[12,11,8,5,1,7,2,3,10,4,6,9]=>11110100100=>00001011011
[12,11,10,5,1,7,2,9,3,4,6,8]=>11110101000=>00001010111
[12,11,10,5,1,9,8,2,3,4,6,7]=>11110110000=>00001001111
[10,9,8,7,6,1,2,3,4,5,12,11]=>11111000001=>00000111110
[12,9,8,7,6,1,2,3,4,11,5,10]=>11111000010=>00000111101
[12,11,8,7,6,1,2,3,10,4,5,9]=>11111000100=>00000111011
[12,11,10,7,6,1,2,9,3,4,5,8]=>11111001000=>00000110111
[12,11,10,9,6,1,8,2,3,4,5,7]=>11111010000=>00000101111
[12,11,10,9,8,7,1,2,3,4,5,6]=>11111100000=>00000011111
[7,6,5,4,3,2,9,1,8]=>11111010=>00000101
[6,5,4,3,9,2,8,1,7]=>11101010=>00010101
[6,5,4,3,2,8,1,7,9]=>11110100=>00001011
[5,4,9,3,8,2,7,1,6]=>10101010=>01010101
[5,4,3,8,2,7,1,6,9]=>11010100=>00101011
[5,4,3,2,7,9,1,6,8]=>11100100=>00011011
[5,4,3,2,7,1,6,8,9]=>11101000=>00010111
[4,8,3,7,2,6,1,5,9]=>01010100=>10101011
[4,3,7,2,6,9,1,5,8]=>10100100=>01011011
[4,3,7,2,6,1,5,8,9]=>10101000=>01010111
[4,3,2,6,8,1,5,7,9]=>11001000=>00110111
[4,3,2,6,1,5,7,8,9]=>11010000=>00101111
[3,6,9,2,5,8,1,4,7]=>00100100=>11011011
[3,6,2,5,8,1,4,7,9]=>01001000=>10110111
[3,6,2,5,1,4,7,8,9]=>01010000=>10101111
[3,2,5,7,9,1,4,6,8]=>10001000=>01110111
[3,2,5,7,1,4,6,8,9]=>10010000=>01101111
[3,2,5,1,4,6,7,8,9]=>10100000=>01011111
[2,4,6,8,1,3,5,7,9]=>00010000=>11101111
[2,4,6,1,3,5,7,8,9]=>00100000=>11011111
[8,7,6,5,4,3,2,10,1,9]=>111111010=>000000101
[7,6,5,4,3,10,2,9,1,8]=>111101010=>000010101
[7,6,5,4,3,2,9,1,8,10]=>111110100=>000001011
[6,5,4,10,3,9,2,8,1,7]=>110101010=>001010101
[6,5,4,3,9,2,8,1,7,10]=>111010100=>000101011
[6,5,4,3,2,8,10,1,7,9]=>111100100=>000011011
[6,5,4,3,2,8,1,7,9,10]=>111101000=>000010111
[5,10,4,9,3,8,2,7,1,6]=>010101010=>101010101
[5,4,9,3,8,2,7,1,6,10]=>101010100=>010101011
[5,4,3,8,2,7,10,1,6,9]=>110100100=>001011011
[5,4,3,8,2,7,1,6,9,10]=>110101000=>001010111
[5,4,3,2,7,9,1,6,8,10]=>111001000=>000110111
[5,4,3,2,7,1,6,8,9,10]=>111010000=>000101111
[4,8,3,7,2,6,10,1,5,9]=>010100100=>101011011
[4,8,3,7,2,6,1,5,9,10]=>010101000=>101010111
[4,3,7,10,2,6,9,1,5,8]=>100100100=>011011011
[4,3,7,2,6,9,1,5,8,10]=>101001000=>010110111
[4,3,7,2,6,1,5,8,9,10]=>101010000=>010101111
[4,3,2,6,8,10,1,5,7,9]=>110001000=>001110111
[4,3,2,6,8,1,5,7,9,10]=>110010000=>001101111
[4,3,2,6,1,5,7,8,9,10]=>110100000=>001011111
[3,6,9,2,5,8,1,4,7,10]=>001001000=>110110111
[3,6,2,5,8,10,1,4,7,9]=>010001000=>101110111
[3,6,2,5,8,1,4,7,9,10]=>010010000=>101101111
[3,6,2,5,1,4,7,8,9,10]=>010100000=>101011111
[3,2,5,7,9,1,4,6,8,10]=>100010000=>011101111
[3,2,5,7,1,4,6,8,9,10]=>100100000=>011011111
[3,2,5,1,4,6,7,8,9,10]=>101000000=>010111111
[2,4,6,8,1,3,5,7,9,10]=>000100000=>111011111
[2,4,6,1,3,5,7,8,9,10]=>001000000=>110111111
[2,4,1,3,5,6,7,8,9,10]=>010000000=>101111111
[2,1,7,3,8,4,6,5]=>1010101=>0101010
[4,1,8,2,7,3,6,5]=>1010101=>0101010
[4,1,7,2,8,3,6,5]=>1010101=>0101010
[7,1,3,2,8,4,6,5]=>1010101=>0101010
[7,1,8,2,4,3,6,5]=>1010101=>0101010
[8,1,7,2,5,3,6,4]=>1010101=>0101010
[7,1,5,2,8,3,6,4]=>1010101=>0101010
[5,1,7,2,8,3,6,4]=>1010101=>0101010
[5,1,8,2,7,3,6,4]=>1010101=>0101010
[5,1,8,2,4,3,7,6]=>1010101=>0101010
[8,1,6,2,4,3,7,5]=>1010101=>0101010
[6,1,8,2,4,3,7,5]=>1010101=>0101010
[6,1,8,2,5,3,7,4]=>1010101=>0101010
[8,1,6,2,5,3,7,4]=>1010101=>0101010
[8,1,6,2,7,3,5,4]=>1010101=>0101010
[6,1,8,2,7,3,5,4]=>1010101=>0101010
[6,1,7,2,8,3,5,4]=>1010101=>0101010
[6,1,7,2,5,3,8,4]=>1010101=>0101010
[6,1,7,2,4,3,8,5]=>1010101=>0101010
[5,1,6,2,4,3,8,7]=>1010101=>0101010
[7,1,5,2,4,3,8,6]=>1010101=>0101010
[7,1,6,2,4,3,8,5]=>1010101=>0101010
[7,1,6,2,5,3,8,4]=>1010101=>0101010
[7,1,6,2,8,3,5,4]=>1010101=>0101010
[7,1,8,2,6,3,5,4]=>1010101=>0101010
[1,8,2,7,5,4,6,3]=>0101101=>1010010
[1,8,2,7,4,3,5,6]=>0101100=>1010011
[1,8,6,4,7,2,3,5]=>0110100=>1001011
[1,8,4,2,6,3,5,7]=>0110100=>1001011
[7,4,8,1,5,2,3,6]=>1010100=>0101011
[4,1,7,2,6,3,5,8]=>1010100=>0101011
[5,1,7,4,3,6,2,8]=>1011010=>0100101
[7,5,8,3,2,4,1,6]=>1011010=>0100101
[1,8,5,4,3,6,2,7]=>0111010=>1000101
[1,8,5,4,3,7,2,6]=>0111010=>1000101
[1,8,5,4,7,2,6,3]=>0110101=>1001010
[1,8,4,2,5,3,7,6]=>0110101=>1001010
[1,8,5,4,2,6,7,3]=>0111001=>1000110
[7,4,8,2,1,3,5,6]=>1011000=>0100111
[4,1,7,3,2,5,6,8]=>1011000=>0100111
[7,5,4,8,2,3,6,1]=>1101001=>0010110
[7,3,8,1,5,6,2,4]=>1010010=>0101101
[3,1,7,2,6,8,4,5]=>1010010=>0101101
[5,1,7,4,2,6,8,3]=>1011001=>0100110
[4,1,6,3,2,5,8,7]=>1011001=>0100110
[4,3,1,6,2,5,7,8]=>1101000=>0010111
[6,5,4,3,7,1,8,2]=>1110101=>0001010
[6,3,2,8,5,7,1,4]=>1101010=>0010101
[6,5,4,3,8,2,7,1]=>1110101=>0001010
[6,5,4,3,8,7,1,2]=>1110110=>0001001
[7,6,3,8,5,4,1,2]=>1101110=>0010001
[5,4,8,2,1,7,3,6]=>1011010=>0100101
[6,4,2,8,5,1,3,7]=>1101100=>0010011
[7,6,4,8,5,1,2,3]=>1101100=>0010011
[7,2,8,6,3,1,4,5]=>1011100=>0100011
[7,2,8,6,1,5,3,4]=>1011010=>0100101
[2,1,7,8,3,6,4,5]=>1001010=>0110101
[6,4,1,7,8,2,3,5]=>1100100=>0011011
[4,2,1,6,7,3,5,8]=>1100100=>0011011
[4,3,1,5,2,7,6,8]=>1101010=>0010101
[5,4,2,7,3,8,1,6]=>1101010=>0010101
[4,1,5,3,2,8,6,7]=>1011010=>0100101
[3,1,6,2,8,7,4,5]=>1010110=>0101001
[6,3,1,7,8,5,2,4]=>1100110=>0011001
[6,5,4,1,7,8,3,2]=>1110011=>0001100
[5,4,3,1,6,7,2,8]=>1110010=>0001101
[6,5,4,2,7,8,3,1]=>1110011=>0001100
[5,4,2,6,3,8,7,1]=>1101011=>0010100
[4,3,1,5,2,6,8,7]=>1101001=>0010110
[5,4,2,1,6,7,8,3]=>1110001=>0001110
[5,4,3,1,6,7,8,2]=>1110001=>0001110
[6,3,8,1,2,5,7,4]=>1010001=>0101110
[3,6,7,1,2,5,8,4]=>0010001=>1101110
[7,8,3,1,2,5,6,4]=>0110001=>1001110
[7,8,1,3,2,4,6,5]=>0101001=>1010110
[7,8,2,1,3,5,4,6]=>0110010=>1001101
[5,2,3,7,1,8,6,4]=>1001011=>0110100
[2,5,3,6,1,8,7,4]=>0101011=>1010100
[2,6,7,3,1,8,4,5]=>0011010=>1100101
[2,6,7,1,3,5,4,8]=>0010010=>1101101
[6,2,8,3,1,7,4,5]=>1011010=>0100101
[3,2,5,7,1,8,4,6]=>1001010=>0110101
[4,3,1,2,7,8,6,5]=>1100011=>0011100
[5,1,2,7,3,6,4,8]=>1001010=>0110101
[5,1,4,7,8,2,3,6]=>1000100=>0111011
[5,3,4,7,8,6,1,2]=>1000110=>0111001
[3,5,4,6,8,7,1,2]=>0100110=>1011001
[1,5,4,6,8,2,3,7]=>0100100=>1011011
[1,6,7,3,2,4,8,5]=>0011001=>1100110
[1,5,3,6,2,7,8,4]=>0101001=>1010110
[5,1,3,7,2,6,8,4]=>1001001=>0110110
[5,2,4,7,8,1,6,3]=>1000101=>0111010
[4,2,5,7,6,1,8,3]=>1001101=>0110010
[4,5,2,8,6,1,7,3]=>0101101=>1010010
[5,3,1,8,2,6,7,4]=>1101001=>0010110
[6,1,8,3,2,4,7,5]=>1011001=>0100110
[4,3,5,7,6,8,1,2]=>1001010=>0110101
[4,1,5,7,6,2,3,8]=>1001100=>0110011
[4,5,1,8,6,2,3,7]=>0101100=>1010011
[5,2,1,8,3,6,4,7]=>1101010=>0010101
[3,4,2,1,8,7,5,6]=>0110110=>1001001
[7,6,5,4,2,1,8,3]=>1111101=>0000010
[7,6,5,4,8,1,3,2]=>1110101=>0001010
[8,7,6,5,4,2,1,9,3]=>11111101=>00000010
[7,6,5,8,2,1,4,3]=>1101101=>0010010
[8,7,6,5,3,2,1,9,4]=>11111101=>00000010
[8,7,6,4,3,2,1,9,5]=>11111101=>00000010
[8,7,5,4,3,2,1,9,6]=>11111101=>00000010
[8,5,4,3,2,1,7,6]=>1111101=>0000010
[8,6,5,4,3,2,1,9,7]=>11111101=>00000010
[7,6,5,4,3,2,1,9,8]=>11111101=>00000010
[7,6,5,4,1,8,3,2]=>1111011=>0000100
[8,7,6,5,4,9,1,3,2]=>11110101=>00001010
[9,8,7,6,5,4,2,1,10,3]=>111111101=>000000010
[7,6,5,2,8,1,4,3]=>1110101=>0001010
[8,7,6,5,9,2,1,4,3]=>11101101=>00010010
[9,8,7,6,5,3,2,1,10,4]=>111111101=>000000010
[7,6,5,8,4,1,3,2]=>1101101=>0010010
[8,7,6,9,3,2,1,5,4]=>11011101=>00100010
[9,8,7,6,4,3,2,1,10,5]=>111111101=>000000010
[7,6,8,5,2,1,4,3]=>1011101=>0100010
[8,7,9,4,3,2,1,6,5]=>10111101=>01000010
[9,8,7,5,4,3,2,1,10,6]=>111111101=>000000010
[7,8,6,3,2,1,5,4]=>0111101=>1000010
[8,9,5,4,3,2,1,7,6]=>01111101=>10000010
[9,8,6,5,4,3,2,1,10,7]=>111111101=>000000010
[8,7,4,3,2,1,6,5]=>1111101=>0000010
[9,6,5,4,3,2,1,8,7]=>11111101=>00000010
[9,7,6,5,4,3,2,1,10,8]=>111111101=>000000010
[7,8,9,10,4,5,6,2,3,1]=>000100101=>111011010
[7,8,9,4,5,6,10,2,3,1]=>001000101=>110111010
[7,8,9,10,4,5,2,3,6,1]=>000101001=>111010110
[7,8,9,4,5,10,2,3,6,1]=>001001001=>110110110
[7,8,9,4,5,2,3,6,10,1]=>001010001=>110101110
[7,8,4,5,9,10,2,3,6,1]=>010001001=>101110110
[7,8,4,5,9,2,3,6,10,1]=>010010001=>101101110
[7,8,9,10,4,5,6,2,1,3]=>000100110=>111011001
[7,8,9,4,5,6,10,2,1,3]=>001000110=>110111001
[7,8,9,10,4,5,2,6,1,3]=>000101010=>111010101
[7,8,9,4,5,10,2,6,1,3]=>001001010=>110110101
[7,8,9,4,5,2,6,10,1,3]=>001010010=>110101101
[7,8,4,5,9,10,2,6,1,3]=>010001010=>101110101
[7,8,4,5,9,2,6,10,1,3]=>010010010=>101101101
[7,8,9,10,4,5,2,1,3,6]=>000101100=>111010011
[7,8,9,4,5,10,2,1,3,6]=>001001100=>110110011
[7,8,9,4,5,2,10,1,3,6]=>001010100=>110101011
[7,8,9,4,5,2,1,3,6,10]=>001011000=>110100111
[7,8,4,5,9,10,2,1,3,6]=>010001100=>101110011
[7,8,4,5,9,2,10,1,3,6]=>010010100=>101101011
[7,8,4,5,9,2,1,3,6,10]=>010011000=>101100111
[7,8,9,10,4,2,5,6,1,3]=>000110010=>111001101
[7,8,9,4,10,2,5,6,1,3]=>001010010=>110101101
[7,8,9,4,2,5,6,10,1,3]=>001100010=>110011101
[7,8,4,9,10,2,5,6,1,3]=>010010010=>101101101
[7,8,4,9,2,5,6,10,1,3]=>010100010=>101011101
[7,8,9,10,4,2,5,1,3,6]=>000110100=>111001011
[7,8,9,4,10,2,5,1,3,6]=>001010100=>110101011
[7,8,9,4,2,5,10,1,3,6]=>001100100=>110011011
[7,8,9,4,2,5,1,3,6,10]=>001101000=>110010111
[7,8,4,9,10,2,5,1,3,6]=>010010100=>101101011
[7,8,4,9,2,5,10,1,3,6]=>010100100=>101011011
[7,8,4,9,2,5,1,3,6,10]=>010101000=>101010111
[7,8,4,2,5,9,10,1,3,6]=>011000100=>100111011
[7,8,4,2,5,9,1,3,6,10]=>011001000=>100110111
[7,4,8,9,10,2,5,6,1,3]=>100010010=>011101101
[7,4,8,9,2,5,6,10,1,3]=>100100010=>011011101
[7,4,8,9,10,2,5,1,3,6]=>100010100=>011101011
[7,4,8,9,2,5,10,1,3,6]=>100100100=>011011011
[7,4,8,9,2,5,1,3,6,10]=>100101000=>011010111
[7,4,8,2,5,9,10,1,3,6]=>101000100=>010111011
[7,8,2,4,5,1,3,6]=>0100100=>1011011
[4,6,7,2,5,1,3,8]=>0010100=>1101011
[7,8,1,3,2,4,5,6]=>0101000=>1010111
[7,8,4,1,5,2,3,6]=>0110100=>1001011
[3,6,7,2,1,4,5,8]=>0011000=>1100111
[5,2,3,6,1,4,7,8]=>1001000=>0110111
[2,5,3,6,1,4,7,8]=>0101000=>1010111
[2,6,7,3,1,4,5,8]=>0011000=>1100111
[4,6,7,1,5,2,3,8]=>0010100=>1101011
[4,6,7,3,5,8,1,2]=>0010010=>1101101
[6,4,7,1,5,2,3,8]=>1010100=>0101011
[6,2,7,3,1,4,5,8]=>1011000=>0100111
[3,2,5,6,1,4,7,8]=>1001000=>0110111
[3,5,2,6,1,4,7,8]=>0101000=>1010111
[5,1,4,6,7,2,3,8]=>1000100=>0111011
[3,5,4,6,7,8,1,2]=>0100010=>1011101
[1,5,4,6,7,2,3,8]=>0100100=>1011011
[1,6,7,3,2,4,5,8]=>0011000=>1100111
[1,5,3,6,2,4,7,8]=>0101000=>1010111
[5,1,3,6,2,4,7,8]=>1001000=>0110111
[5,2,4,6,7,1,3,8]=>1000100=>0111011
[2,5,4,6,7,1,3,8]=>0100100=>1011011
[2,6,7,4,5,1,3,8]=>0010100=>1101011
[6,2,7,4,5,1,3,8]=>1010100=>0101011
[4,2,5,6,7,1,3,8]=>1000100=>0111011
[4,5,2,6,7,1,3,8]=>0100100=>1011011
[5,3,1,6,2,4,7,8]=>1101000=>0010111
[6,1,7,3,2,4,5,8]=>1011000=>0100111
[6,1,7,4,5,2,3,8]=>1010100=>0101011
[6,3,7,4,5,8,1,2]=>1010010=>0101101
[5,4,1,6,7,2,3,8]=>1100100=>0011011
[5,2,1,6,3,4,7,8]=>1101000=>0010111
[7,3,2,5,4,1,6,8]=>1101100=>0010011
[7,3,5,4,2,1,6,8]=>1011100=>0100011
[7,3,5,2,4,1,6,8]=>1010100=>0101011
[7,6,5,2,1,4,3,8]=>1111010=>0000101
[1,3,6,7,5,2,8,4]=>0001101=>1110010
[7,3,4,1,6,2,5,8]=>1010100=>0101011
[7,3,4,1,6,5,2,8]=>1010110=>0101001
[7,3,4,1,5,6,2,8]=>1010010=>0101101
[7,3,2,5,1,6,4,8]=>1101010=>0010101
[7,6,5,4,1,3,2,8]=>1111010=>0000101
[7,3,4,1,5,2,6,8]=>1010100=>0101011
[1,3,6,7,2,5,8,4]=>0001001=>1110110
[1,7,4,6,2,8,5,3]=>0101011=>1010100
[4,3,1,7,2,6,8,5]=>1101001=>0010110
[5,6,1,4,7,3,8,2]=>0100101=>1011010
[5,3,2,1,7,4,8,6]=>1110101=>0001010
[1,3,4,5,8,7,2,6]=>0000110=>1111001
[6,3,4,5,8,1,7,2]=>1000101=>0111010
[2,4,5,1,6,8,7,3]=>0010011=>1101100
[3,1,2,5,6,8,7,4]=>1000011=>0111100
[4,3,2,5,6,8,1,7]=>1100010=>0011101
[3,7,5,4,6,8,1,2]=>0110010=>1001101
[3,1,4,6,5,8,2,7]=>1001010=>0110101
[2,3,4,5,8,6,1,7]=>0000110=>1111001
[2,3,4,5,8,1,7,6]=>0000101=>1111010
[3,1,4,6,5,8,7,2]=>1001011=>0110100
[3,7,5,4,6,8,2,1]=>0110011=>1001100
[5,6,1,4,7,2,8,3]=>0100101=>1011010
[4,3,1,7,5,6,8,2]=>1101001=>0010110
[4,3,1,7,6,5,8,2]=>1101101=>0010010
[3,1,4,6,7,8,5,2]=>1000011=>0111100
[1,4,5,2,6,8,7,3]=>0010011=>1101100
[3,7,5,2,6,8,1,4]=>0110010=>1001101
[3,7,5,2,6,8,4,1]=>0110011=>1001100
[5,6,1,2,7,4,8,3]=>0100101=>1011010
[6,3,5,2,4,7,8,1]=>1010001=>0101110
[5,3,2,1,4,7,8,6]=>1110001=>0001110
[5,3,1,4,2,7,8,6]=>1101001=>0010110
[5,3,1,2,4,7,8,6]=>1100001=>0011110
[7,1,5,2,6,8,4,3]=>1010011=>0101100
[7,1,5,2,6,8,3,4]=>1010010=>0101101
[1,7,4,6,5,8,3,2]=>0101011=>1010100
[2,7,4,6,1,8,3,5]=>0101010=>1010101
[2,7,4,6,1,8,5,3]=>0101011=>1010100
[2,3,6,7,1,5,8,4]=>0001001=>1110110
[2,3,6,7,5,1,8,4]=>0001101=>1110010
[4,3,2,6,7,1,8,5]=>1100101=>0011010
[7,3,2,5,6,8,1,4]=>1100010=>0011101
[7,1,5,4,6,8,2,3]=>1010010=>0101101
[2,7,4,6,5,8,1,3]=>0101010=>1010101
[7,3,4,5,8,6,1,2]=>1000110=>0111001
[7,3,4,5,8,1,6,2]=>1000101=>0111010
[7,3,4,5,8,1,2,6]=>1000100=>0111011
[1,3,4,5,8,6,2,7]=>0000110=>1111001
[1,3,4,5,8,2,7,6]=>0000101=>1111010
[6,3,4,5,8,2,1,7]=>1000110=>0111001
[6,3,4,5,8,2,7,1]=>1000101=>0111010
[7,3,4,5,8,6,2,1]=>1000111=>0111000
[2,7,4,6,5,8,3,1]=>0101011=>1010100
[7,1,5,4,6,8,3,2]=>1010011=>0101100
[7,3,2,5,6,8,4,1]=>1100011=>0011100
[5,7,4,6,1,8,3,2]=>0101011=>1010100
[6,3,4,5,8,1,2,7]=>1000100=>0111011
[7,3,4,5,8,2,1,6]=>1000110=>0111001
[7,3,4,5,8,2,6,1]=>1000101=>0111010
[4,7,6,1,8,2,5,3]=>0110101=>1001010
[4,8,6,1,7,5,2,3]=>0110110=>1001001
[4,7,8,2,6,1,5,3]=>0010101=>1101010
[7,6,4,2,8,3,5,1]=>1110101=>0001010
[8,6,4,2,7,5,3,1]=>1110111=>0001000
[8,4,7,3,6,5,1,2]=>1010110=>0101001
[8,4,6,1,7,5,3,2]=>1010111=>0101000
[6,4,7,1,8,3,2,5]=>1010110=>0101001
[7,4,8,3,6,1,5,2]=>1010101=>0101010
[7,8,4,3,6,2,5,1]=>0110101=>1001010
[8,10,7,9,5,6,3,4,1,2]=>010101010=>101010101
[9,10,6,8,5,7,3,4,1,2]=>010101010=>101010101
[8,10,6,9,5,7,3,4,1,2]=>010101010=>101010101
[7,10,6,9,5,8,3,4,1,2]=>010101010=>101010101
[9,10,7,8,4,6,3,5,1,2]=>010101010=>101010101
[8,10,7,9,4,6,3,5,1,2]=>010101010=>101010101
[9,10,6,8,4,7,3,5,1,2]=>010101010=>101010101
[8,10,6,9,4,7,3,5,1,2]=>010101010=>101010101
[7,10,6,9,4,8,3,5,1,2]=>010101010=>101010101
[9,10,5,8,4,7,3,6,1,2]=>010101010=>101010101
[8,10,5,9,4,7,3,6,1,2]=>010101010=>101010101
[7,10,5,9,4,8,3,6,1,2]=>010101010=>101010101
[6,10,5,9,4,8,3,7,1,2]=>010101010=>101010101
[9,10,7,8,5,6,2,4,1,3]=>010101010=>101010101
[8,10,7,9,5,6,2,4,1,3]=>010101010=>101010101
[9,10,6,8,5,7,2,4,1,3]=>010101010=>101010101
[8,10,6,9,5,7,2,4,1,3]=>010101010=>101010101
[7,10,6,9,5,8,2,4,1,3]=>010101010=>101010101
[9,10,7,8,4,6,2,5,1,3]=>010101010=>101010101
[8,10,7,9,4,6,2,5,1,3]=>010101010=>101010101
[9,10,6,8,4,7,2,5,1,3]=>010101010=>101010101
[8,10,6,9,4,7,2,5,1,3]=>010101010=>101010101
[7,10,6,9,4,8,2,5,1,3]=>010101010=>101010101
[9,10,5,8,4,7,2,6,1,3]=>010101010=>101010101
[8,10,5,9,4,7,2,6,1,3]=>010101010=>101010101
[7,10,5,9,4,8,2,6,1,3]=>010101010=>101010101
[6,10,5,9,4,8,2,7,1,3]=>010101010=>101010101
[9,10,7,8,3,6,2,5,1,4]=>010101010=>101010101
[8,10,7,9,3,6,2,5,1,4]=>010101010=>101010101
[9,10,6,8,3,7,2,5,1,4]=>010101010=>101010101
[8,10,6,9,3,7,2,5,1,4]=>010101010=>101010101
[7,10,6,9,3,8,2,5,1,4]=>010101010=>101010101
[9,10,5,8,3,7,2,6,1,4]=>010101010=>101010101
[8,10,5,9,3,7,2,6,1,4]=>010101010=>101010101
[7,10,5,9,3,8,2,6,1,4]=>010101010=>101010101
[6,10,5,9,3,8,2,7,1,4]=>010101010=>101010101
[9,10,4,8,3,7,2,6,1,5]=>010101010=>101010101
[8,10,4,9,3,7,2,6,1,5]=>010101010=>101010101
[7,10,4,9,3,8,2,6,1,5]=>010101010=>101010101
[6,10,4,9,3,8,2,7,1,5]=>010101010=>101010101
[10,12,9,11,7,8,5,6,3,4,1,2]=>01010101010=>10101010101
[11,12,8,10,7,9,5,6,3,4,1,2]=>01010101010=>10101010101
[10,12,8,11,7,9,5,6,3,4,1,2]=>01010101010=>10101010101
[9,12,8,11,7,10,5,6,3,4,1,2]=>01010101010=>10101010101
[11,12,9,10,6,8,5,7,3,4,1,2]=>01010101010=>10101010101
[10,12,9,11,6,8,5,7,3,4,1,2]=>01010101010=>10101010101
[11,12,8,10,6,9,5,7,3,4,1,2]=>01010101010=>10101010101
[10,12,8,11,6,9,5,7,3,4,1,2]=>01010101010=>10101010101
[9,12,8,11,6,10,5,7,3,4,1,2]=>01010101010=>10101010101
[11,12,7,10,6,9,5,8,3,4,1,2]=>01010101010=>10101010101
[10,12,7,11,6,9,5,8,3,4,1,2]=>01010101010=>10101010101
[9,12,7,11,6,10,5,8,3,4,1,2]=>01010101010=>10101010101
[8,12,7,11,6,10,5,9,3,4,1,2]=>01010101010=>10101010101
[11,12,9,10,7,8,4,6,3,5,1,2]=>01010101010=>10101010101
[10,12,9,11,7,8,4,6,3,5,1,2]=>01010101010=>10101010101
[11,12,8,10,7,9,4,6,3,5,1,2]=>01010101010=>10101010101
[10,12,8,11,7,9,4,6,3,5,1,2]=>01010101010=>10101010101
[9,12,8,11,7,10,4,6,3,5,1,2]=>01010101010=>10101010101
[11,12,9,10,6,8,4,7,3,5,1,2]=>01010101010=>10101010101
[10,12,9,11,6,8,4,7,3,5,1,2]=>01010101010=>10101010101
[11,12,8,10,6,9,4,7,3,5,1,2]=>01010101010=>10101010101
[10,12,8,11,6,9,4,7,3,5,1,2]=>01010101010=>10101010101
[9,12,8,11,6,10,4,7,3,5,1,2]=>01010101010=>10101010101
[11,12,7,10,6,9,4,8,3,5,1,2]=>01010101010=>10101010101
[10,12,7,11,6,9,4,8,3,5,1,2]=>01010101010=>10101010101
[9,12,7,11,6,10,4,8,3,5,1,2]=>01010101010=>10101010101
[8,12,7,11,6,10,4,9,3,5,1,2]=>01010101010=>10101010101
[11,12,9,10,5,8,4,7,3,6,1,2]=>01010101010=>10101010101
[10,12,9,11,5,8,4,7,3,6,1,2]=>01010101010=>10101010101
[11,12,8,10,5,9,4,7,3,6,1,2]=>01010101010=>10101010101
[10,12,8,11,5,9,4,7,3,6,1,2]=>01010101010=>10101010101
[9,12,8,11,5,10,4,7,3,6,1,2]=>01010101010=>10101010101
[11,12,7,10,5,9,4,8,3,6,1,2]=>01010101010=>10101010101
[10,12,7,11,5,9,4,8,3,6,1,2]=>01010101010=>10101010101
[9,12,7,11,5,10,4,8,3,6,1,2]=>01010101010=>10101010101
[8,12,7,11,5,10,4,9,3,6,1,2]=>01010101010=>10101010101
[11,12,6,10,5,9,4,8,3,7,1,2]=>01010101010=>10101010101
[10,12,6,11,5,9,4,8,3,7,1,2]=>01010101010=>10101010101
[9,12,6,11,5,10,4,8,3,7,1,2]=>01010101010=>10101010101
[8,12,6,11,5,10,4,9,3,7,1,2]=>01010101010=>10101010101
[7,12,6,11,5,10,4,9,3,8,1,2]=>01010101010=>10101010101
[11,12,9,10,7,8,5,6,2,4,1,3]=>01010101010=>10101010101
[10,12,9,11,7,8,5,6,2,4,1,3]=>01010101010=>10101010101
[11,12,8,10,7,9,5,6,2,4,1,3]=>01010101010=>10101010101
[10,12,8,11,7,9,5,6,2,4,1,3]=>01010101010=>10101010101
[9,12,8,11,7,10,5,6,2,4,1,3]=>01010101010=>10101010101
[11,12,9,10,6,8,5,7,2,4,1,3]=>01010101010=>10101010101
[10,12,9,11,6,8,5,7,2,4,1,3]=>01010101010=>10101010101
[11,12,8,10,6,9,5,7,2,4,1,3]=>01010101010=>10101010101
[10,12,8,11,6,9,5,7,2,4,1,3]=>01010101010=>10101010101
[9,12,8,11,6,10,5,7,2,4,1,3]=>01010101010=>10101010101
[11,12,7,10,6,9,5,8,2,4,1,3]=>01010101010=>10101010101
[10,12,7,11,6,9,5,8,2,4,1,3]=>01010101010=>10101010101
[9,12,7,11,6,10,5,8,2,4,1,3]=>01010101010=>10101010101
[8,12,7,11,6,10,5,9,2,4,1,3]=>01010101010=>10101010101
[11,12,9,10,7,8,4,6,2,5,1,3]=>01010101010=>10101010101
[10,12,9,11,7,8,4,6,2,5,1,3]=>01010101010=>10101010101
[11,12,8,10,7,9,4,6,2,5,1,3]=>01010101010=>10101010101
[10,12,8,11,7,9,4,6,2,5,1,3]=>01010101010=>10101010101
[9,12,8,11,7,10,4,6,2,5,1,3]=>01010101010=>10101010101
[11,12,9,10,6,8,4,7,2,5,1,3]=>01010101010=>10101010101
[10,12,9,11,6,8,4,7,2,5,1,3]=>01010101010=>10101010101
[11,12,8,10,6,9,4,7,2,5,1,3]=>01010101010=>10101010101
[10,12,8,11,6,9,4,7,2,5,1,3]=>01010101010=>10101010101
[9,12,8,11,6,10,4,7,2,5,1,3]=>01010101010=>10101010101
[11,12,7,10,6,9,4,8,2,5,1,3]=>01010101010=>10101010101
[10,12,7,11,6,9,4,8,2,5,1,3]=>01010101010=>10101010101
[9,12,7,11,6,10,4,8,2,5,1,3]=>01010101010=>10101010101
[8,12,7,11,6,10,4,9,2,5,1,3]=>01010101010=>10101010101
[11,12,9,10,5,8,4,7,2,6,1,3]=>01010101010=>10101010101
[10,12,9,11,5,8,4,7,2,6,1,3]=>01010101010=>10101010101
[11,12,8,10,5,9,4,7,2,6,1,3]=>01010101010=>10101010101
[10,12,8,11,5,9,4,7,2,6,1,3]=>01010101010=>10101010101
[9,12,8,11,5,10,4,7,2,6,1,3]=>01010101010=>10101010101
[11,12,7,10,5,9,4,8,2,6,1,3]=>01010101010=>10101010101
[10,12,7,11,5,9,4,8,2,6,1,3]=>01010101010=>10101010101
[9,12,7,11,5,10,4,8,2,6,1,3]=>01010101010=>10101010101
[8,12,7,11,5,10,4,9,2,6,1,3]=>01010101010=>10101010101
[11,12,6,10,5,9,4,8,2,7,1,3]=>01010101010=>10101010101
[10,12,6,11,5,9,4,8,2,7,1,3]=>01010101010=>10101010101
[9,12,6,11,5,10,4,8,2,7,1,3]=>01010101010=>10101010101
[8,12,6,11,5,10,4,9,2,7,1,3]=>01010101010=>10101010101
[7,12,6,11,5,10,4,9,2,8,1,3]=>01010101010=>10101010101
[11,12,9,10,7,8,3,6,2,5,1,4]=>01010101010=>10101010101
[10,12,9,11,7,8,3,6,2,5,1,4]=>01010101010=>10101010101
[11,12,8,10,7,9,3,6,2,5,1,4]=>01010101010=>10101010101
[10,12,8,11,7,9,3,6,2,5,1,4]=>01010101010=>10101010101
[9,12,8,11,7,10,3,6,2,5,1,4]=>01010101010=>10101010101
[11,12,9,10,6,8,3,7,2,5,1,4]=>01010101010=>10101010101
[10,12,9,11,6,8,3,7,2,5,1,4]=>01010101010=>10101010101
[11,12,8,10,6,9,3,7,2,5,1,4]=>01010101010=>10101010101
[10,12,8,11,6,9,3,7,2,5,1,4]=>01010101010=>10101010101
[9,12,8,11,6,10,3,7,2,5,1,4]=>01010101010=>10101010101
[11,12,7,10,6,9,3,8,2,5,1,4]=>01010101010=>10101010101
[10,12,7,11,6,9,3,8,2,5,1,4]=>01010101010=>10101010101
[9,12,7,11,6,10,3,8,2,5,1,4]=>01010101010=>10101010101
[8,12,7,11,6,10,3,9,2,5,1,4]=>01010101010=>10101010101
[11,12,9,10,5,8,3,7,2,6,1,4]=>01010101010=>10101010101
[10,12,9,11,5,8,3,7,2,6,1,4]=>01010101010=>10101010101
[11,12,8,10,5,9,3,7,2,6,1,4]=>01010101010=>10101010101
[10,12,8,11,5,9,3,7,2,6,1,4]=>01010101010=>10101010101
[9,12,8,11,5,10,3,7,2,6,1,4]=>01010101010=>10101010101
[11,12,7,10,5,9,3,8,2,6,1,4]=>01010101010=>10101010101
[10,12,7,11,5,9,3,8,2,6,1,4]=>01010101010=>10101010101
[9,12,7,11,5,10,3,8,2,6,1,4]=>01010101010=>10101010101
[8,12,7,11,5,10,3,9,2,6,1,4]=>01010101010=>10101010101
[11,12,6,10,5,9,3,8,2,7,1,4]=>01010101010=>10101010101
[10,12,6,11,5,9,3,8,2,7,1,4]=>01010101010=>10101010101
[9,12,6,11,5,10,3,8,2,7,1,4]=>01010101010=>10101010101
[8,12,6,11,5,10,3,9,2,7,1,4]=>01010101010=>10101010101
[7,12,6,11,5,10,3,9,2,8,1,4]=>01010101010=>10101010101
[11,12,9,10,4,8,3,7,2,6,1,5]=>01010101010=>10101010101
[10,12,9,11,4,8,3,7,2,6,1,5]=>01010101010=>10101010101
[11,12,8,10,4,9,3,7,2,6,1,5]=>01010101010=>10101010101
[10,12,8,11,4,9,3,7,2,6,1,5]=>01010101010=>10101010101
[9,12,8,11,4,10,3,7,2,6,1,5]=>01010101010=>10101010101
[11,12,7,10,4,9,3,8,2,6,1,5]=>01010101010=>10101010101
[10,12,7,11,4,9,3,8,2,6,1,5]=>01010101010=>10101010101
[9,12,7,11,4,10,3,8,2,6,1,5]=>01010101010=>10101010101
[8,12,7,11,4,10,3,9,2,6,1,5]=>01010101010=>10101010101
[11,12,6,10,4,9,3,8,2,7,1,5]=>01010101010=>10101010101
[10,12,6,11,4,9,3,8,2,7,1,5]=>01010101010=>10101010101
[9,12,6,11,4,10,3,8,2,7,1,5]=>01010101010=>10101010101
[8,12,6,11,4,10,3,9,2,7,1,5]=>01010101010=>10101010101
[7,12,6,11,4,10,3,9,2,8,1,5]=>01010101010=>10101010101
[11,12,5,10,4,9,3,8,2,7,1,6]=>01010101010=>10101010101
[10,12,5,11,4,9,3,8,2,7,1,6]=>01010101010=>10101010101
[9,12,5,11,4,10,3,8,2,7,1,6]=>01010101010=>10101010101
[8,12,5,11,4,10,3,9,2,7,1,6]=>01010101010=>10101010101
[7,12,5,11,4,10,3,9,2,8,1,6]=>01010101010=>10101010101
[6,12,5,11,4,10,3,9,2,8,1,7]=>01010101010=>10101010101
[2,1,7,3,5,8,6,4]=>1010011=>0101100
[4,2,1,8,3,6,7,5]=>1101001=>0010110
[2,1,8,6,3,5,7,4]=>1011001=>0100110
[6,2,1,7,3,5,8,4]=>1101001=>0010110
[2,7,3,1,4,8,5,6]=>0110010=>1001101
[3,2,1,5,7,8,4,6]=>1100010=>0011101
[2,1,7,3,6,8,4,5]=>1010010=>0101101
[2,7,3,1,5,6,8,4]=>0110001=>1001110
[4,3,7,5,6,1,8,2]=>1010101=>0101010
[4,3,6,8,5,1,7,2]=>1001101=>0110010
[2,6,1,8,3,5,7,4]=>0101001=>1010110
[2,1,6,8,3,7,4,5]=>1001010=>0110101
[2,1,8,3,5,7,4,6]=>1010010=>0101101
[3,2,1,5,6,8,4,7]=>1100010=>0011101
[3,2,1,5,7,4,6,8]=>1100100=>0011011
[8,2,4,1,7,5,6,3]=>1010101=>0101010
[3,8,4,7,5,1,6,2]=>0101101=>1010010
[8,4,3,6,1,7,5,2]=>1101011=>0010100
[8,2,1,7,3,5,4,6]=>1101010=>0010101
[5,8,6,3,1,7,4,2]=>0111011=>1000100
[2,4,7,1,8,5,3,6]=>0010110=>1101001
[2,4,8,5,1,6,3,7]=>0011010=>1100101
[6,2,1,7,3,4,8,5]=>1101001=>0010110
[6,2,1,7,8,3,5,4]=>1100101=>0011010
[2,1,8,3,6,4,5,7]=>1010100=>0101011
[3,2,1,6,7,4,5,8]=>1100100=>0011011
[3,2,1,6,8,4,5,7]=>1100100=>0011011
[2,1,8,3,7,4,5,6]=>1010100=>0101011
[2,1,8,3,6,7,4,5]=>1010010=>0101101
[2,4,8,5,1,6,7,3]=>0011001=>1100110
[3,2,1,8,4,5,6,7]=>1101000=>0010111
[1,6,8,3,7,2,4,5]=>0010100=>1101011
[3,8,1,5,7,2,4,6]=>0100100=>1011011
[1,2,6,8,4,7,3,5]=>0001010=>1110101
[6,1,5,8,2,4,7,3]=>1001001=>0110110
[1,2,4,8,3,6,7,5]=>0001001=>1110110
[4,1,2,7,8,3,6,5]=>1000101=>0111010
[3,5,7,4,8,6,1,2]=>0010110=>1101001
[5,3,8,4,7,6,1,2]=>1010110=>0101001
[8,7,1,2,5,4,6,3]=>1100101=>0011010
[5,8,1,2,3,7,6,4]=>0100011=>1011100
[1,2,8,4,3,5,7,6]=>0011001=>1100110
[1,2,5,3,7,6,4,8]=>0010110=>1101001
[6,1,2,8,7,4,5,3]=>1001101=>0110010
[7,1,6,2,8,4,5,3]=>1010101=>0101010
[1,2,6,3,8,5,4,7]=>0010110=>1101001
[1,2,8,5,3,6,4,7]=>0011010=>1100101
[1,2,7,3,8,5,4,6]=>0010110=>1101001
[4,1,2,7,8,6,3,5]=>1000110=>0111001
[1,6,2,8,4,3,5,7]=>0101100=>1010011
[1,6,4,2,7,3,5,8]=>0110100=>1001011
[1,8,6,3,2,4,5,7]=>0111000=>1000111
[1,7,3,2,8,4,5,6]=>0110100=>1001011
[3,1,7,8,6,2,4,5]=>1001100=>0110011
[1,8,7,2,4,5,6,3]=>0110001=>1001110
[1,8,7,3,5,6,2,4]=>0110010=>1001101
[1,3,2,8,7,4,5,6]=>0101100=>1010011
[1,8,3,2,6,4,5,7]=>0110100=>1001011
[1,7,6,3,2,4,5,8]=>0111000=>1000111
[1,2,8,4,3,7,5,6]=>0011010=>1100101
[8,5,1,7,2,4,6,3]=>1101001=>0010110
[5,3,8,7,4,6,1,2]=>1011010=>0100101
[3,8,6,4,7,5,1,2]=>0110110=>1001001
[6,1,8,2,7,4,5,3]=>1010101=>0101010
[1,2,5,3,8,6,4,7]=>0010110=>1101001
[1,2,7,5,3,6,4,8]=>0011010=>1100101
[1,2,6,3,7,5,4,8]=>0010110=>1101001
[1,2,3,7,5,4,8,6]=>0001101=>1110010
[3,7,4,8,6,5,1,2]=>0101110=>1010001
[1,8,2,7,6,4,5,3]=>0101101=>1010010
[2,9,8,7,6,5,4,1,3]=>01111110=>10000001
[2,8,7,6,5,1,4,3]=>0111101=>1000010
[7,1,6,3,2,5,4,8]=>1011010=>0100101
[2,7,6,3,1,5,8,4]=>0111001=>1000110
[1,8,4,3,6,5,2,7]=>0110110=>1001001
[1,8,4,6,5,3,2,7]=>0101110=>1010001
[7,4,2,1,6,5,3,8]=>1110110=>0001001
[7,6,1,4,3,5,2,8]=>1101010=>0010101
[7,4,1,3,5,2,6,8]=>1100100=>0011011
[7,3,1,2,4,6,5,8]=>1100010=>0011101
[1,8,6,3,4,5,2,7]=>0110010=>1001101
[1,8,6,7,4,2,5,3]=>0101101=>1010010
[3,6,2,1,4,8,5,7]=>0110010=>1001101
[3,1,7,2,4,6,8,5]=>1010001=>0101110
[3,4,7,1,5,2,8,6]=>0010101=>1101010
[3,6,7,4,1,5,8,2]=>0011001=>1100110
[4,3,2,7,1,5,8,6]=>1101001=>0010110
[3,1,2,8,6,5,4,7]=>1001110=>0110001
[5,4,8,6,1,2,3,7]=>1011000=>0100111
[5,6,8,7,4,3,1,2]=>0011110=>1100001
[1,8,2,7,4,3,6,5]=>0101101=>1010010
[6,5,8,2,3,7,1,4]=>1010010=>0101101
[6,4,8,5,3,1,7,2]=>1011101=>0100010
[5,7,8,6,1,3,2,4]=>0011010=>1100101
[2,4,8,1,6,3,7,5]=>0010101=>1101010
[3,1,2,8,6,4,7,5]=>1001101=>0110010
[5,3,2,6,4,8,1,7]=>1101010=>0010101
[4,1,6,3,5,8,2,7]=>1010010=>0101101
[2,4,5,3,8,6,1,7]=>0010110=>1101001
[1,8,5,3,2,7,6,4]=>0111011=>1000100
[1,8,4,5,2,6,7,3]=>0101001=>1010110
[4,1,2,7,6,5,8,3]=>1001101=>0110010
[2,4,1,6,7,8,5,3]=>0100011=>1011100
[1,8,4,3,6,2,7,5]=>0110101=>1001010
[5,6,7,3,2,8,1,4]=>0011010=>1100101
[2,5,7,3,6,8,4,1]=>0010011=>1101100
[5,3,2,1,4,8,6,7]=>1110010=>0001101
[5,3,1,4,2,8,6,7]=>1101010=>0010101
[7,6,1,3,8,5,4,2]=>1100111=>0011000
[3,4,7,8,1,2,6,5]=>0001001=>1110110
[3,6,7,8,1,4,5,2]=>0001001=>1110110
[3,6,2,8,1,5,4,7]=>0101010=>1010101
[2,3,6,8,5,1,4,7]=>0001100=>1110011
[3,1,6,4,8,2,5,7]=>1010100=>0101011
[7,3,2,6,8,5,1,4]=>1100110=>0011001
[7,3,5,8,4,6,1,2]=>1001010=>0110101
[7,5,2,8,4,1,6,3]=>1101101=>0010010
[7,4,5,8,2,1,3,6]=>1001100=>0110011
[1,8,5,2,4,6,3,7]=>0110010=>1001101
[1,8,4,2,3,5,7,6]=>0110001=>1001110
[6,4,2,8,3,5,1,7]=>1101010=>0010101
[6,3,4,8,2,5,7,1]=>1001001=>0110110
[7,5,4,8,3,6,2,1]=>1101011=>0010100
[2,7,4,8,5,3,6,1]=>0101101=>1010010
[7,1,5,4,8,3,6,2]=>1010101=>0101010
[7,3,2,5,8,4,6,1]=>1100101=>0011010
[8,4,6,3,7,2,5,1]=>1010101=>0101010
[7,4,6,3,8,5,1,2]=>1010110=>0101001
[2,5,6,8,3,4,1,7]=>0001010=>1110101
[8,4,6,2,7,5,3,1]=>1010111=>0101000
[8,5,6,7,2,4,3,1]=>1001011=>0110100
[2,5,6,8,4,3,1,7]=>0001110=>1110001
[2,5,7,8,4,1,3,6]=>0001100=>1110011
[6,5,7,8,4,1,3,2]=>1001101=>0110010
[7,5,6,8,2,4,1,3]=>1001010=>0110101
[7,4,6,2,8,5,1,3]=>1010110=>0101001
[4,3,2,6,8,5,1,7]=>1100110=>0011001
[3,5,6,8,2,4,1,7]=>0001010=>1110101
[3,5,6,8,4,2,1,7]=>0001110=>1110001
[2,6,7,8,1,4,5,3]=>0001001=>1110110
[3,6,7,8,1,4,2,5]=>0001010=>1110101
[3,5,7,8,2,1,4,6]=>0001100=>1110011
[2,6,7,8,1,4,3,5]=>0001010=>1110101
[6,5,7,8,3,1,4,2]=>1001101=>0110010
[2,5,7,8,3,1,4,6]=>0001100=>1110011
[2,4,7,3,8,1,5,6]=>0010100=>1101011
[6,4,7,3,8,1,5,2]=>1010101=>0101010
[6,4,7,3,8,1,2,5]=>1010100=>0101011
[7,4,6,3,8,2,1,5]=>1010110=>0101001
[6,3,2,5,4,8,1,7]=>1101010=>0010101
[6,4,5,2,3,8,1,7]=>1010010=>0101101
[6,4,5,3,2,8,1,7]=>1011010=>0100101
[5,4,6,3,8,2,1,7]=>1010110=>0101001
[5,4,7,3,8,1,6,2]=>1010101=>0101010
[2,5,7,8,3,1,6,4]=>0001101=>1110010
[4,5,7,8,3,1,2,6]=>0001100=>1110011
[4,5,6,8,2,3,1,7]=>0001010=>1110101
[5,4,6,2,8,3,1,7]=>1010110=>0101001
[5,3,2,6,8,4,1,7]=>1100110=>0011001
[5,4,7,2,8,1,3,6]=>1010100=>0101011
[4,5,7,8,2,1,3,6]=>0001100=>1110011
[4,6,7,8,1,3,2,5]=>0001010=>1110101
[4,6,7,8,1,3,5,2]=>0001001=>1110110
[2,6,7,8,1,3,5,4]=>0001001=>1110110
[2,6,7,8,1,5,3,4]=>0001010=>1110101
[4,6,7,8,1,5,2,3]=>0001010=>1110101
[4,6,7,8,1,2,5,3]=>0001001=>1110110
[4,5,7,8,2,1,6,3]=>0001101=>1110010
[5,4,7,2,8,1,6,3]=>1010101=>0101010
[5,3,2,7,8,1,6,4]=>1100101=>0011010
[4,3,2,7,8,1,6,5]=>1100101=>0011010
[3,5,7,8,2,1,6,4]=>0001101=>1110010
[3,6,7,8,1,2,5,4]=>0001001=>1110110
[3,6,7,8,1,5,2,4]=>0001010=>1110101
[3,6,7,8,1,5,4,2]=>0001011=>1110100
[2,6,7,8,1,5,4,3]=>0001011=>1110100
[2,3,4,5,6,7,8,9,10,1,11]=>0000000010=>1111111101
[3,4,5,6,7,8,9,1,2,10]=>000000100=>111111011
[2,4,5,6,7,8,1,3,9]=>00000100=>11111011
[3,4,5,6,7,1,8,2,9]=>00001010=>11110101
[1,3,5,6,7,8,9,2,4]=>00000010=>11111101
[1,4,5,6,7,8,2,9,3]=>00000101=>11111010
[1,4,5,6,7,8,9,10,2,3]=>000000010=>111111101
[1,3,4,5,6,7,8,9,10,11,2]=>0000000001=>1111111110
[4,2,7,1,5,3,8,6]=>1010101=>0101010
[4,2,8,6,1,5,3,7]=>1011010=>0100101
[3,2,6,7,5,1,4,8]=>1001100=>0110011
[2,7,1,3,5,4,8,6]=>0100101=>1011010
[4,7,2,1,5,8,6,3]=>0110011=>1001100
[7,2,1,3,5,8,6,4]=>1100011=>0011100
[2,3,6,4,7,1,5,8]=>0010100=>1101011
[1,3,4,8,2,7,5,6]=>0001010=>1110101
[3,1,4,8,2,6,7,5]=>1001001=>0110110
[8,3,1,6,2,5,7,4]=>1101001=>0010110
[4,8,6,2,1,5,7,3]=>0111001=>1000110
[4,8,3,6,5,1,7,2]=>0101101=>1010010
[6,4,7,3,5,1,8,2]=>1010101=>0101010
[6,4,7,5,1,8,2,3]=>1011010=>0100101
[3,6,1,7,5,8,2,4]=>0101010=>1010101
[7,3,5,1,6,8,2,4]=>1010010=>0101101
[4,7,3,5,6,1,8,2]=>0100101=>1011010
[3,4,6,8,5,1,7,2]=>0001101=>1110010
[4,6,8,2,1,5,7,3]=>0011001=>1100110
[6,8,2,1,3,5,7,4]=>0110001=>1001110
[1,8,2,3,5,7,4,6]=>0100010=>1011101
[2,7,3,6,1,4,5,8]=>0101000=>1010111
[2,6,1,3,5,8,4,7]=>0100010=>1011101
[7,3,2,5,6,1,4,8]=>1100100=>0011011
[4,7,5,2,6,1,3,8]=>0110100=>1001011
[4,6,2,8,1,5,3,7]=>0101010=>1010101
[8,4,1,2,7,5,3,6]=>1100110=>0011001
[4,5,6,2,7,1,3,8]=>0010100=>1101011
[8,5,1,2,6,3,4,7]=>1100100=>0011011
[1,6,2,7,4,8,3,5]=>0101010=>1010101
[6,2,1,7,8,5,3,4]=>1100110=>0011001
[6,7,3,8,4,1,5,2]=>0101101=>1010010
[2,7,8,4,1,5,6,3]=>0011001=>1100110
[2,7,1,8,5,6,3,4]=>0101010=>1010101
[8,2,5,1,6,7,3,4]=>1010010=>0101101
[8,2,4,5,1,6,7,3]=>1001001=>0110110
[3,8,4,5,6,1,7,2]=>0100101=>1011010
[4,5,8,3,6,7,1,2]=>0010010=>1101101
[4,5,8,3,7,6,1,2]=>0010110=>1101001
[4,2,8,3,7,1,6,5]=>1010101=>0101010
[7,2,3,4,8,1,6,5]=>1000101=>0111010
[7,2,3,4,8,1,5,6]=>1000100=>0111011
[7,6,3,4,8,5,1,2]=>1100110=>0011001
[7,6,3,5,8,4,1,2]=>1100110=>0011001
[7,6,3,8,4,5,1,2]=>1101010=>0010101
[7,2,3,8,5,1,4,6]=>1001100=>0110011
[7,2,3,8,5,1,6,4]=>1001101=>0110010
[2,6,4,8,1,5,7,3]=>0101001=>1010110
[7,2,3,8,4,1,5,6]=>1001100=>0110011
[7,2,3,5,8,1,4,6]=>1000100=>0111011
[7,8,2,3,6,1,4,5]=>0100100=>1011011
[7,8,2,3,6,1,5,4]=>0100101=>1011010
[4,2,6,3,7,1,5,8]=>1010100=>0101011
[7,2,3,5,8,1,6,4]=>1000101=>0111010
[7,2,3,8,4,1,6,5]=>1001101=>0110010
[2,6,4,8,1,3,7,5]=>0101001=>1010110
[3,6,4,8,1,7,5,2]=>0101011=>1010100
[7,6,5,1,2,3,8,4]=>1110001=>0001110
[7,6,5,1,4,2,8,3]=>1110101=>0001010
[2,6,4,5,1,8,7,3]=>0101011=>1010100
[3,5,6,4,1,2,7,8]=>0011000=>1100111
[7,8,5,4,1,2,6,3]=>0111001=>1000110
[3,5,6,4,1,2,8,7]=>0011001=>1100110
[7,6,5,1,4,2,3,8]=>1110100=>0001011
[7,6,5,1,2,4,3,8]=>1110010=>0001101
[7,6,5,1,2,4,8,3]=>1110001=>0001110
[7,6,5,1,3,2,8,4]=>1110101=>0001010
[7,6,5,1,3,2,4,8]=>1110100=>0001011
[7,6,5,1,3,4,2,8]=>1110010=>0001101
[7,2,3,4,5,1,8,6]=>1000101=>0111010
[2,6,4,3,1,5,8,7]=>0111001=>1000110
[2,6,4,3,1,8,5,7]=>0111010=>1000101
[2,6,4,3,1,8,7,5]=>0111011=>1000100
[3,5,8,4,1,2,7,6]=>0011001=>1100110
[3,5,8,4,1,2,6,7]=>0011000=>1100111
[3,5,8,4,1,6,2,7]=>0011010=>1100101
[4,2,8,3,6,1,7,5]=>1010101=>0101010
[3,5,8,4,1,6,7,2]=>0011001=>1100110
[2,5,8,4,1,7,3,6]=>0011010=>1100101
[3,6,4,2,1,7,8,5]=>0111001=>1000110
[3,6,4,2,1,7,5,8]=>0111010=>1000101
[3,5,6,4,1,8,7,2]=>0011011=>1100100
[2,6,4,5,1,3,7,8]=>0101000=>1010111
[7,6,5,1,4,3,8,2]=>1110101=>0001010
[7,6,5,1,2,8,4,3]=>1110011=>0001100
[7,6,5,1,2,8,3,4]=>1110010=>0001101
[7,6,5,1,8,2,4,3]=>1110101=>0001010
[7,6,5,1,8,2,3,4]=>1110100=>0001011
[7,6,5,1,8,3,2,4]=>1110110=>0001001
[7,6,5,1,4,8,2,3]=>1110010=>0001101
[3,6,4,5,1,7,2,8]=>0101010=>1010101
[2,5,6,4,1,7,8,3]=>0011001=>1100110
[7,8,5,4,1,6,3,2]=>0111011=>1000100
[2,5,6,4,1,7,3,8]=>0011010=>1100101
[3,6,4,5,1,7,8,2]=>0101001=>1010110
[7,6,5,1,4,8,3,2]=>1110011=>0001100
[7,6,5,1,8,3,4,2]=>1110101=>0001010
[7,6,5,1,8,4,2,3]=>1110110=>0001001
[4,1,7,6,2,8,5,3]=>1011011=>0100100
[7,8,6,2,1,3,5,4]=>0111001=>1000110
[3,7,6,1,2,8,4,5]=>0110010=>1001101
[2,6,5,3,1,4,8,7]=>0111001=>1000110
[4,6,1,5,3,2,8,7]=>0101101=>1010010
[3,6,1,4,2,5,8,7]=>0101001=>1010110
[2,6,4,5,7,8,1,3]=>0100010=>1011101
[8,7,1,6,5,2,4,3]=>1101101=>0010010
[7,2,5,6,8,1,3,4]=>1000100=>0111011
[6,1,3,4,2,8,7,5]=>1001011=>0110100
[2,4,5,6,1,8,7,3]=>0001011=>1110100
[8,4,1,6,5,7,3,2]=>1101011=>0010100
[2,8,3,4,7,5,1,6]=>0100110=>1011001
[6,8,2,7,4,3,5,1]=>0101101=>1010010
[4,7,8,5,1,6,3,2]=>0011011=>1100100
[8,2,6,4,7,3,5,1]=>1010101=>0101010
[4,8,6,1,7,3,2,5]=>0110110=>1001001
[8,7,3,2,1,5,4,6]=>1111010=>0000101
[3,8,5,1,7,2,4,6]=>0110100=>1001011
[6,8,7,1,3,2,4,5]=>0110100=>1001011
[2,5,1,8,7,4,6,3]=>0101101=>1010010
[3,7,1,8,4,5,6,2]=>0101001=>1010110
[6,2,3,8,4,7,5,1]=>1001011=>0110100
[8,6,4,3,1,7,2,5]=>1111010=>0000101
[8,3,7,4,6,1,2,5]=>1010100=>0101011
[7,1,3,8,6,4,5,2]=>1001101=>0110010
[2,3,5,8,6,7,4,1]=>0001011=>1110100
[7,4,2,1,8,6,5,3]=>1110111=>0001000
[4,6,7,2,5,8,3,1]=>0010011=>1101100
[7,6,2,5,3,8,1,4]=>1101010=>0010101
[6,2,1,3,4,8,7,5]=>1100011=>0011100
[6,5,4,2,8,3,1,7]=>1110110=>0001001
[5,4,3,1,8,7,2,6]=>1110110=>0001001
[6,1,4,3,8,5,2,7]=>1010110=>0101001
[4,7,6,2,8,1,5,3]=>0110101=>1001010
[6,4,5,1,7,8,3,2]=>1010011=>0101100
[4,2,3,1,7,8,6,5]=>1010011=>0101100
[3,4,2,1,8,6,7,5]=>0110101=>1001010
[2,7,6,8,1,5,3,4]=>0101010=>1010101
[6,4,5,8,3,1,2,7]=>1001100=>0110011
[8,1,3,2,5,6,7,4]=>1010001=>0101110
[3,6,8,1,5,2,4,7]=>0010100=>1101011
[3,2,8,7,4,5,1,6]=>1011010=>0100101
[6,3,8,5,7,4,2,1]=>1010111=>0101000
[7,4,6,8,5,1,2,3]=>1001100=>0110011
[2,1,4,8,7,5,3,6]=>1001110=>0110001
[2,1,6,8,3,7,5,4]=>1001011=>0110100
[3,6,8,2,4,1,5,7]=>0010100=>1101011
[6,2,8,1,7,5,4,3]=>1010111=>0101000
[2,6,5,4,8,1,3,7]=>0110100=>1001011
[6,5,3,4,8,1,7,2]=>1100101=>0011010
[8,4,3,2,5,1,7,6]=>1110101=>0001010
[4,2,8,1,5,3,6,7]=>1010100=>0101011
[5,1,8,2,6,4,3,7]=>1010110=>0101001
[7,4,8,6,2,1,3,5]=>1011100=>0100011
[4,6,2,8,3,7,5,1]=>0101011=>1010100
[2,1,5,8,3,6,4,7]=>1001010=>0110101
[2,8,5,3,6,7,1,4]=>0110010=>1001101
[7,8,5,6,4,1,3,2]=>0101101=>1010010
[5,8,4,1,6,3,7,2]=>0110101=>1001010
[4,8,1,3,5,7,6,2]=>0100011=>1011100
[3,8,1,4,5,6,2,7]=>0100010=>1011101
[9,7,8,5,6,3,1,4,2]=>10101101=>01010010
[9,7,8,5,3,6,1,4,2]=>10110101=>01001010
[9,7,5,8,3,6,1,4,2]=>11010101=>00101010
[7,9,5,8,3,6,1,4,2]=>01010101=>10101010
[7,6,8,3,5,1,4,2]=>1010101=>0101010
[8,9,5,7,3,6,1,4,2]=>01010101=>10101010
[8,9,6,7,3,5,1,4,2]=>01010101=>10101010
[8,9,6,7,4,5,1,3,2]=>01010101=>10101010
[8,9,6,7,4,5,2,3,1]=>01010101=>10101010
[9,10,7,8,5,6,3,1,4,2]=>010101101=>101010010
[9,7,8,5,3,1,6,4,2]=>10111011=>01000100
[9,10,7,8,5,3,6,1,4,2]=>010110101=>101001010
[9,7,5,3,8,6,1,4,2]=>11101101=>00010010
[9,10,7,5,8,3,6,1,4,2]=>011010101=>100101010
[7,5,9,8,3,6,1,4,2]=>10110101=>01001010
[9,7,10,5,8,3,6,1,4,2]=>101010101=>010101010
[7,8,6,3,5,1,4,2]=>0110101=>1001010
[5,3,8,7,6,1,4,2]=>1011101=>0100010
[9,8,5,7,3,6,1,4,2]=>11010101=>00101010
[10,7,9,5,8,3,6,1,4,2]=>101010101=>010101010
[7,9,6,8,3,5,1,4,2]=>01010101=>10101010
[10,8,9,5,7,3,6,1,4,2]=>101010101=>010101010
[6,5,8,4,7,1,3,2]=>1010101=>0101010
[8,9,5,7,4,6,1,3,2]=>01010101=>10101010
[10,8,9,6,7,3,5,1,4,2]=>101010101=>010101010
[8,9,6,7,3,5,2,4,1]=>01010101=>10101010
[10,8,9,6,7,4,5,1,3,2]=>101010101=>010101010
[6,7,4,2,5,3,1,8]=>0110110=>1001001
[7,6,4,8,3,1,5,2]=>1101101=>0010010
[7,4,8,5,6,1,3,2]=>1010101=>0101010
[7,4,2,5,6,3,1,8]=>1100110=>0011001
[4,2,7,5,6,3,1,8]=>1010110=>0101001
[3,4,7,5,6,2,1,8]=>0010110=>1101001
[4,7,3,5,6,2,1,8]=>0100110=>1011001
[3,7,2,5,6,4,1,8]=>0100110=>1011001
[7,8,3,5,6,1,4,2]=>0100101=>1011010
[1,6,8,5,2,7,4,3]=>0011011=>1100100
[6,2,8,5,1,7,4,3]=>1011011=>0100100
[6,7,4,8,2,1,5,3]=>0101101=>1010010
[3,2,7,8,6,1,5,4]=>1001101=>0110010
[6,8,4,1,2,3,7,5]=>0110001=>1001110
[4,1,8,5,6,3,2,7]=>1010110=>0101001
[1,8,2,5,6,4,3,7]=>0100110=>1011001
[6,1,8,5,3,7,4,2]=>1011011=>0100100
[3,8,1,5,2,7,6,4]=>0101011=>1010100
[8,2,1,5,3,7,6,4]=>1101011=>0010100
[1,5,2,4,6,7,8,3]=>0100001=>1011110
[4,1,5,3,6,7,8,2]=>1010001=>0101110
[8,1,6,5,3,7,2,4]=>1011010=>0100101
[7,1,4,6,3,2,8,5]=>1001101=>0110010
[3,2,6,4,1,7,8,5]=>1011001=>0100110
[7,6,4,3,1,2,8,5]=>1111001=>0000110
[8,6,3,5,1,7,2,4]=>1101010=>0010101
[4,5,3,1,6,7,8,2]=>0110001=>1001110
[3,5,2,1,6,7,8,4]=>0110001=>1001110
[5,2,3,1,6,7,8,4]=>1010001=>0101110
[1,5,3,2,6,7,8,4]=>0110001=>1001110
[8,4,6,5,1,7,2,3]=>1011010=>0100101
[7,5,4,6,1,2,8,3]=>1101001=>0010110
[3,2,5,6,1,7,8,4]=>1001001=>0110110
[3,2,8,7,6,1,4,5]=>1011100=>0100011
[6,8,4,7,2,1,3,5]=>0101100=>1010011
[3,8,7,5,6,1,2,4]=>0110100=>1001011
[8,2,7,5,6,1,3,4]=>1010100=>0101011
[4,8,6,5,1,7,3,2]=>0111011=>1000100
[1,7,4,6,2,3,8,5]=>0101001=>1010110
[7,6,4,2,1,5,8,3]=>1111001=>0000110
[5,7,4,6,1,3,8,2]=>0101001=>1010110
[8,6,4,7,3,1,2,5]=>1101100=>0010011
[5,2,4,3,7,1,8,6]=>1010101=>0101010
[3,5,4,2,7,1,8,6]=>0110101=>1001010
[8,6,4,1,3,5,2,7]=>1110010=>0001101
[6,7,4,1,5,3,8,2]=>0110101=>1001010
[7,5,4,1,2,6,8,3]=>1110001=>0001110
[1,7,4,2,3,6,8,5]=>0110001=>1001110
[1,8,2,5,3,7,6,4]=>0101011=>1010100
[6,8,1,5,4,7,3,2]=>0101011=>1010100
[8,2,1,5,6,4,3,7]=>1100110=>0011001
[3,8,1,5,6,4,2,7]=>0100110=>1011001
[6,8,4,1,2,5,3,7]=>0110010=>1001101
[3,2,8,1,6,5,4,7]=>1010110=>0101001
[3,2,6,1,5,7,8,4]=>1010001=>0101110
[7,6,4,1,5,2,8,3]=>1110101=>0001010
[8,6,1,5,4,7,2,3]=>1101010=>0010101
[3,5,1,4,6,7,8,2]=>0100001=>1011110
[5,2,1,4,6,7,8,3]=>1100001=>0011110
[5,4,1,3,6,7,8,2]=>1100001=>0011110
[8,4,1,5,3,7,2,6]=>1101010=>0010101
[7,5,4,1,3,2,8,6]=>1110101=>0001010
[3,2,5,1,4,7,8,6]=>1010001=>0101110
[7,1,4,3,5,2,8,6]=>1010101=>0101010
[8,1,3,5,4,7,2,6]=>1001010=>0110101
[5,1,3,4,6,7,8,2]=>1000001=>0111110
[3,1,8,2,5,7,4,6]=>1010010=>0101101
[8,3,2,6,1,4,7,5]=>1101001=>0010110
[2,8,1,6,4,3,7,5]=>0101101=>1010010
[2,6,1,3,8,7,5,4]=>0100111=>1011000
[2,5,7,1,3,8,6,4]=>0010011=>1101100
[2,6,8,1,5,7,4,3]=>0010011=>1101100
[2,7,1,5,8,4,6,3]=>0100101=>1011010
[2,7,1,6,4,8,3,5]=>0101010=>1010101
[2,7,1,6,5,3,8,4]=>0101101=>1010010
[2,8,1,7,6,5,4,3]=>0101111=>1010000
[8,3,2,7,1,6,5,4]=>1101011=>0010100
[4,1,8,7,3,2,6,5]=>1011101=>0100010
[4,1,7,2,8,6,5,3]=>1010111=>0101000
[3,7,1,8,6,5,4,2]=>0101111=>1010000
[3,7,6,1,4,2,5,8]=>0110100=>1001011
[3,7,5,1,4,6,8,2]=>0110001=>1001110
[3,6,8,5,1,4,7,2]=>0011001=>1100110
[7,3,5,8,2,1,4,6]=>1001100=>0110011
[7,3,6,2,1,4,5,8]=>1011000=>0100111
[7,3,6,2,1,5,4,8]=>1011010=>0100101
[7,4,2,8,1,6,5,3]=>1101011=>0010100
[8,7,5,3,2,1,6,4]=>1111101=>0000010
[7,5,2,6,3,1,4,8]=>1101100=>0010011
[7,4,6,2,1,8,3,5]=>1011010=>0100101
[6,8,4,5,2,1,7,3]=>0101101=>1010010
[4,6,8,5,1,7,3,2]=>0011011=>1100100
[4,7,5,1,3,8,6,2]=>0110011=>1001100
[4,7,6,1,5,3,2,8]=>0110110=>1001001
[5,1,7,6,3,8,2,4]=>1011010=>0100101
[5,1,7,6,4,2,8,3]=>1011101=>0100010
[5,1,8,7,6,4,3,2]=>1011111=>0100000
[8,5,2,1,7,6,4,3]=>1110111=>0001000
[8,5,2,1,6,3,7,4]=>1110101=>0001010
[5,1,8,6,3,2,7,4]=>1011101=>0100010
[3,6,1,7,4,8,2,5]=>0101010=>1010101
[4,1,8,6,3,7,2,5]=>1011010=>0100101
[8,4,2,5,7,3,1,6]=>1100110=>0011001
[3,4,6,8,5,7,1,2]=>0001010=>1110101
[5,4,8,2,7,3,6,1]=>1010101=>0101010
[5,4,8,7,3,6,1,2]=>1011010=>0100101
[8,5,4,7,3,6,2,1]=>1101011=>0010100
[6,4,3,8,7,1,2,5]=>1101100=>0010011
[6,3,7,2,4,8,1,5]=>1010010=>0101101
[5,6,8,4,2,7,3,1]=>0011011=>1100100
[5,7,4,2,8,1,3,6]=>0110100=>1001011
[6,5,2,7,1,3,8,4]=>1101001=>0010110
[8,6,5,4,2,1,7,3]=>1111101=>0000010
[6,4,7,3,1,8,2,5]=>1011010=>0100101
[5,7,4,3,8,6,1,2]=>0110110=>1001001
[7,5,8,4,6,3,2,1]=>1010111=>0101000
[7,6,4,8,3,5,2,1]=>1101011=>0010100
[7,6,5,3,8,2,4,1]=>1110101=>0001010
[6,5,4,3,2,1,9,8,7]=>11111011=>00000100
[6,5,4,3,2,1,8,7,9]=>11111010=>00000101
[5,4,3,2,1,9,8,7,6]=>11110111=>00001000
[5,4,3,2,1,8,7,6,9]=>11110110=>00001001
[5,4,3,2,1,7,6,9,8]=>11110101=>00001010
[5,4,3,2,1,7,6,8,9]=>11110100=>00001011
[4,3,2,1,8,7,6,5,9]=>11101110=>00010001
[4,3,2,1,7,6,5,9,8]=>11101101=>00010010
[4,3,2,1,7,6,5,8,9]=>11101100=>00010011
[4,3,2,1,6,5,8,7,9]=>11101010=>00010101
[4,3,2,1,6,5,7,8,9]=>11101000=>00010111
[3,2,1,6,5,4,8,7,9]=>11011010=>00100101
[3,2,1,6,5,4,7,8,9]=>11011000=>00100111
[3,2,1,5,4,7,6,9,8]=>11010101=>00101010
[3,2,1,5,4,7,6,8,9]=>11010100=>00101011
[3,2,1,5,4,6,7,8,9]=>11010000=>00101111
[2,1,4,3,6,5,7,8,9]=>10101000=>01010111
[2,1,4,3,5,6,7,8,9]=>10100000=>01011111
[7,6,5,4,3,2,1,10,9,8]=>111111011=>000000100
[7,6,5,4,3,2,1,9,8,10]=>111111010=>000000101
[6,5,4,3,2,1,9,8,7,10]=>111110110=>000001001
[6,5,4,3,2,1,8,7,9,10]=>111110100=>000001011
[5,4,3,2,1,9,8,7,6,10]=>111101110=>000010001
[5,4,3,2,1,8,7,6,10,9]=>111101101=>000010010
[5,4,3,2,1,8,7,6,9,10]=>111101100=>000010011
[5,4,3,2,1,7,6,9,8,10]=>111101010=>000010101
[5,4,3,2,1,7,6,8,9,10]=>111101000=>000010111
[4,3,2,1,8,7,6,5,9,10]=>111011100=>000100011
[4,3,2,1,7,6,5,10,9,8]=>111011011=>000100100
[4,3,2,1,7,6,5,8,9,10]=>111011000=>000100111
[4,3,2,1,6,5,8,7,9,10]=>111010100=>000101011
[4,3,2,1,6,5,7,8,9,10]=>111010000=>000101111
[3,2,1,6,5,4,9,8,7,10]=>110110110=>001001001
[3,2,1,6,5,4,8,7,10,9]=>110110101=>001001010
[3,2,1,6,5,4,8,7,9,10]=>110110100=>001001011
[3,2,1,6,5,4,7,8,9,10]=>110110000=>001001111
[3,2,1,5,4,7,6,9,8,10]=>110101010=>001010101
[3,2,1,5,4,7,6,8,9,10]=>110101000=>001010111
[3,2,1,5,4,6,7,8,9,10]=>110100000=>001011111
[2,1,4,3,6,5,8,7,9,10]=>101010100=>010101011
[2,1,4,3,6,5,7,8,9,10]=>101010000=>010101111
[2,1,4,3,5,6,7,8,9,10]=>101000000=>010111111
[5,6,3,7,4,2,1,8]=>0101110=>1010001
[7,6,3,8,5,1,4,2]=>1101101=>0010010
[6,4,8,1,3,2,5,7]=>1010100=>0101011
[7,4,8,6,3,1,5,2]=>1011101=>0100010
[4,2,7,6,5,3,1,8]=>1011110=>0100001
[3,7,2,4,6,5,1,8]=>0100110=>1011001
[8,1,3,4,5,2,6,7]=>1000100=>0111011
[1,6,8,4,2,5,3,7]=>0011010=>1100101
[6,2,8,4,1,5,7,3]=>1011001=>0100110
[6,7,4,8,5,1,2,3]=>0101100=>1010011
[3,2,7,8,5,1,6,4]=>1001101=>0110010
[3,2,8,1,5,4,6,7]=>1010100=>0101011
[6,1,4,8,5,3,7,2]=>1001101=>0110010
[1,4,8,5,2,6,7,3]=>0011001=>1100110
[6,1,8,4,3,7,2,5]=>1011010=>0100101
[3,7,1,4,2,5,8,6]=>0101001=>1010110
[7,2,1,4,3,5,6,8]=>1101000=>0010111
[4,1,5,3,6,8,2,7]=>1010010=>0101101
[6,1,8,5,3,2,7,4]=>1011101=>0100010
[7,1,4,6,3,8,5,2]=>1001011=>0110100
[3,2,6,4,1,8,7,5]=>1011011=>0100100
[7,6,4,3,1,8,2,5]=>1111010=>0000101
[3,5,2,1,8,7,6,4]=>0110111=>1001000
[1,5,3,2,8,6,4,7]=>0110110=>1001001
[5,4,2,1,7,8,6,3]=>1110011=>0001100
[8,2,7,6,5,1,3,4]=>1011100=>0100011
[8,6,2,7,1,4,5,3]=>1101001=>0010110
[1,7,3,6,2,8,5,4]=>0101011=>1010100
[7,6,3,2,1,8,5,4]=>1111011=>0000100
[8,6,3,7,4,1,2,5]=>1101100=>0010011
[5,2,3,4,7,1,8,6]=>1000101=>0111010
[8,6,3,1,4,5,7,2]=>1110001=>0001110
[6,7,3,1,5,4,2,8]=>0110110=>1001001
[5,8,3,1,2,4,7,6]=>0110001=>1001110
[8,1,3,2,4,5,6,7]=>1010000=>0101111
[8,4,1,7,2,3,6,5]=>1101001=>0010110
[8,2,1,6,5,4,7,3]=>1101101=>0010010
[3,8,1,5,6,4,7,2]=>0100101=>1011010
[6,8,4,1,2,5,7,3]=>0110001=>1001110
[3,2,8,1,6,5,7,4]=>1010101=>0101010
[7,6,4,1,5,2,3,8]=>1110100=>0001011
[8,6,1,5,4,7,3,2]=>1101011=>0010100
[3,5,1,4,6,7,2,8]=>0100010=>1011101
[5,2,1,4,7,6,3,8]=>1100110=>0011001
[4,5,8,2,1,3,7,6]=>0011001=>1100110
[5,8,2,3,1,4,6,7]=>0101000=>1010111
[4,2,1,3,5,8,7,6]=>1100011=>0011100
[5,4,1,3,6,2,8,7]=>1100101=>0011010
[8,5,4,1,3,6,2,7]=>1110010=>0001101
[3,2,5,1,4,6,8,7]=>1010001=>0101110
[8,1,4,3,5,6,7,2]=>1010001=>0101110
[7,1,3,5,4,6,2,8]=>1001010=>0110101
[5,1,3,4,6,2,7,8]=>1000100=>0111011
[4,1,3,2,5,7,6,8]=>1010010=>0101101
[3,1,4,2,6,5,8,7,9]=>10101010=>01010101
[3,1,5,2,6,4,8,7,9]=>10101010=>01010101
[3,1,5,2,7,4,8,6,9]=>10101010=>01010101
[3,1,5,2,7,4,6,9,8]=>10101001=>01010110
[3,1,5,2,4,7,6,9,8]=>10100101=>01011010
[3,1,2,5,4,7,6,9,8]=>10010101=>01101010
[3,1,4,2,6,5,8,7,10,9]=>101010101=>010101010
[4,1,5,2,6,3,8,7,9]=>10101010=>01010101
[3,1,5,2,6,4,8,7,10,9]=>101010101=>010101010
[3,1,6,2,7,4,8,5,9]=>10101010=>01010101
[3,1,5,2,7,4,8,6,10,9]=>101010101=>010101010
[3,1,5,2,8,4,9,6,7]=>10101010=>01010101
[3,1,5,2,7,4,9,6,10,8]=>101010101=>010101010
[3,1,5,2,7,4,6,8,9]=>10101000=>01010111
[3,1,5,2,7,4,9,6,8,10]=>101010100=>010101011
[3,1,5,2,4,7,9,6,8]=>10100010=>01011101
[3,1,5,2,7,4,6,9,8,10]=>101010010=>010101101
[3,1,2,5,7,4,6,9,8]=>10001001=>01110110
[3,1,5,2,4,7,6,9,8,10]=>101001010=>010110101
[1,3,5,2,4,7,6,9,8]=>00100101=>11011010
[3,1,2,5,4,7,6,9,8,10]=>100101010=>011010101
[6,8,2,4,5,1,3,7]=>0100100=>1011011
[4,6,7,3,1,5,2,8]=>0011010=>1100101
[5,8,1,2,4,7,3,6]=>0100010=>1011101
[6,8,1,3,5,2,7,4]=>0100101=>1011010
[6,8,3,1,4,5,7,2]=>0110001=>1001110
[7,5,1,8,2,3,6,4]=>1101001=>0010110
[5,3,8,4,2,6,7,1]=>1011001=>0100110
[4,1,8,3,5,7,2,6]=>1010010=>0101101
[3,4,7,2,6,1,8,5]=>0010101=>1101010
[4,5,7,2,3,6,8,1]=>0010001=>1101110
[2,6,3,4,7,5,8,1]=>0100101=>1011010
[4,5,2,7,1,6,8,3]=>0101001=>1010110
[3,4,1,6,5,8,2,7]=>0101010=>1010101
[7,3,1,4,8,5,6,2]=>1100101=>0011010
[5,6,3,1,7,4,2,8]=>0110110=>1001001
[7,3,4,1,8,5,2,6]=>1010110=>0101001
[6,4,2,8,7,1,5,3]=>1101101=>0010010
[7,2,4,8,1,5,3,6]=>1001010=>0110101
[4,6,3,1,7,8,5,2]=>0110011=>1001100
[5,3,1,6,7,8,4,2]=>1100011=>0011100
[4,1,6,2,7,8,5,3]=>1010011=>0101100
[2,1,3,4,8,7,5,6]=>1000110=>0111001
[4,5,6,7,8,9,1,2,3]=>00000100=>11111011
[4,5,6,7,8,9,2,3,1]=>00000101=>11111010
[5,6,7,8,9,1,2,3,4]=>00001000=>11110111
[6,7,8,9,2,3,4,5,1]=>00010001=>11101110
[8,9,6,7,5,4,3,2,1]=>01011111=>10100000
[4,5,6,7,8,9,10,1,2,3]=>000000100=>111111011
[4,5,6,7,8,9,10,2,3,1]=>000000101=>111111010
[5,6,7,8,9,10,1,2,3,4]=>000001000=>111110111
[5,6,7,8,9,10,3,4,1,2]=>000001010=>111110101
[7,8,9,10,3,4,5,6,1,2]=>000100010=>111011101
[7,8,9,10,5,6,3,4,1,2]=>000101010=>111010101
[8,9,10,5,6,7,2,3,4,1]=>001001001=>110110110
[4,8,3,7,6,5,1,2]=>0101110=>1010001
[6,3,8,7,5,4,1,2]=>1011110=>0100001
[5,3,8,7,6,4,1,2]=>1011110=>0100001
[2,8,7,6,1,5,4,3]=>0111011=>1000100
[5,2,8,7,6,1,4,3]=>1011101=>0100010
[6,2,8,7,5,1,4,3]=>1011101=>0100010
[7,8,2,6,5,1,4,3]=>0101101=>1010010
[6,1,8,7,5,4,3,2]=>1011111=>0100000
[3,1,8,7,6,5,4,2]=>1011111=>0100000
[7,8,2,6,1,5,4,3]=>0101011=>1010100
[6,2,8,7,1,5,4,3]=>1011011=>0100100
[4,2,8,1,7,6,5,3]=>1010111=>0101000
[4,8,2,7,6,1,5,3]=>0101101=>1010010
[3,8,7,2,1,6,5,4]=>0111011=>1000100
[6,5,8,7,1,4,3,2]=>1011011=>0100100
[4,8,1,7,6,5,3,2]=>0101111=>1010000
[5,4,1,8,7,6,3,2]=>1101111=>0010000
[6,4,8,1,7,5,3,2]=>1010111=>0101000
[7,8,4,1,6,5,3,2]=>0110111=>1001000
[7,8,3,1,6,5,4,2]=>0110111=>1001000
[6,3,8,1,7,5,4,2]=>1010111=>0101000
[5,3,1,8,7,6,4,2]=>1101111=>0010000
[7,8,2,1,6,5,4,3]=>0110111=>1001000
[6,5,3,1,8,7,4,2]=>1110111=>0001000
[6,4,3,1,8,7,5,2]=>1110111=>0001000
[5,4,3,1,8,7,6,2]=>1110111=>0001000
[7,5,2,1,8,6,4,3]=>1110111=>0001000
[5,4,2,1,8,7,6,3]=>1110111=>0001000
[7,3,2,1,8,6,5,4]=>1110111=>0001000
[6,3,2,1,8,7,5,4]=>1110111=>0001000
[9,7,5,3,1,10,8,6,4,2]=>111101111=>000010000
[8,7,5,3,1,10,9,6,4,2]=>111101111=>000010000
[9,6,5,3,1,10,8,7,4,2]=>111101111=>000010000
[8,6,5,3,1,10,9,7,4,2]=>111101111=>000010000
[7,6,5,3,1,10,9,8,4,2]=>111101111=>000010000
[9,7,4,3,1,10,8,6,5,2]=>111101111=>000010000
[8,7,4,3,1,10,9,6,5,2]=>111101111=>000010000
[9,6,4,3,1,10,8,7,5,2]=>111101111=>000010000
[8,6,4,3,1,10,9,7,5,2]=>111101111=>000010000
[7,6,4,3,1,10,9,8,5,2]=>111101111=>000010000
[9,5,4,3,1,10,8,7,6,2]=>111101111=>000010000
[8,5,4,3,1,10,9,7,6,2]=>111101111=>000010000
[7,5,4,3,1,10,9,8,6,2]=>111101111=>000010000
[6,5,4,3,1,10,9,8,7,2]=>111101111=>000010000
[9,7,5,2,1,10,8,6,4,3]=>111101111=>000010000
[8,7,5,2,1,10,9,6,4,3]=>111101111=>000010000
[9,6,5,2,1,10,8,7,4,3]=>111101111=>000010000
[8,6,5,2,1,10,9,7,4,3]=>111101111=>000010000
[7,6,5,2,1,10,9,8,4,3]=>111101111=>000010000
[9,7,4,2,1,10,8,6,5,3]=>111101111=>000010000
[8,7,4,2,1,10,9,6,5,3]=>111101111=>000010000
[9,6,4,2,1,10,8,7,5,3]=>111101111=>000010000
[8,6,4,2,1,10,9,7,5,3]=>111101111=>000010000
[7,6,4,2,1,10,9,8,5,3]=>111101111=>000010000
[9,5,4,2,1,10,8,7,6,3]=>111101111=>000010000
[8,5,4,2,1,10,9,7,6,3]=>111101111=>000010000
[7,5,4,2,1,10,9,8,6,3]=>111101111=>000010000
[6,5,4,2,1,10,9,8,7,3]=>111101111=>000010000
[9,7,3,2,1,10,8,6,5,4]=>111101111=>000010000
[8,7,3,2,1,10,9,6,5,4]=>111101111=>000010000
[9,6,3,2,1,10,8,7,5,4]=>111101111=>000010000
[8,6,3,2,1,10,9,7,5,4]=>111101111=>000010000
[7,6,3,2,1,10,9,8,5,4]=>111101111=>000010000
[9,5,3,2,1,10,8,7,6,4]=>111101111=>000010000
[8,5,3,2,1,10,9,7,6,4]=>111101111=>000010000
[7,5,3,2,1,10,9,8,6,4]=>111101111=>000010000
[6,5,3,2,1,10,9,8,7,4]=>111101111=>000010000
[9,4,3,2,1,10,8,7,6,5]=>111101111=>000010000
[8,4,3,2,1,10,9,7,6,5]=>111101111=>000010000
[7,4,3,2,1,10,9,8,6,5]=>111101111=>000010000
[6,4,3,2,1,10,9,8,7,5]=>111101111=>000010000
[11,9,7,5,3,1,12,10,8,6,4,2]=>11111011111=>00000100000
[10,9,7,5,3,1,12,11,8,6,4,2]=>11111011111=>00000100000
[11,8,7,5,3,1,12,10,9,6,4,2]=>11111011111=>00000100000
[10,8,7,5,3,1,12,11,9,6,4,2]=>11111011111=>00000100000
[9,8,7,5,3,1,12,11,10,6,4,2]=>11111011111=>00000100000
[11,9,6,5,3,1,12,10,8,7,4,2]=>11111011111=>00000100000
[10,9,6,5,3,1,12,11,8,7,4,2]=>11111011111=>00000100000
[11,8,6,5,3,1,12,10,9,7,4,2]=>11111011111=>00000100000
[10,8,6,5,3,1,12,11,9,7,4,2]=>11111011111=>00000100000
[9,8,6,5,3,1,12,11,10,7,4,2]=>11111011111=>00000100000
[11,7,6,5,3,1,12,10,9,8,4,2]=>11111011111=>00000100000
[10,7,6,5,3,1,12,11,9,8,4,2]=>11111011111=>00000100000
[9,7,6,5,3,1,12,11,10,8,4,2]=>11111011111=>00000100000
[8,7,6,5,3,1,12,11,10,9,4,2]=>11111011111=>00000100000
[11,9,7,4,3,1,12,10,8,6,5,2]=>11111011111=>00000100000
[10,9,7,4,3,1,12,11,8,6,5,2]=>11111011111=>00000100000
[11,8,7,4,3,1,12,10,9,6,5,2]=>11111011111=>00000100000
[10,8,7,4,3,1,12,11,9,6,5,2]=>11111011111=>00000100000
[9,8,7,4,3,1,12,11,10,6,5,2]=>11111011111=>00000100000
[11,9,6,4,3,1,12,10,8,7,5,2]=>11111011111=>00000100000
[10,9,6,4,3,1,12,11,8,7,5,2]=>11111011111=>00000100000
[11,8,6,4,3,1,12,10,9,7,5,2]=>11111011111=>00000100000
[10,8,6,4,3,1,12,11,9,7,5,2]=>11111011111=>00000100000
[9,8,6,4,3,1,12,11,10,7,5,2]=>11111011111=>00000100000
[11,7,6,4,3,1,12,10,9,8,5,2]=>11111011111=>00000100000
[10,7,6,4,3,1,12,11,9,8,5,2]=>11111011111=>00000100000
[9,7,6,4,3,1,12,11,10,8,5,2]=>11111011111=>00000100000
[8,7,6,4,3,1,12,11,10,9,5,2]=>11111011111=>00000100000
[11,9,5,4,3,1,12,10,8,7,6,2]=>11111011111=>00000100000
[10,9,5,4,3,1,12,11,8,7,6,2]=>11111011111=>00000100000
[11,8,5,4,3,1,12,10,9,7,6,2]=>11111011111=>00000100000
[10,8,5,4,3,1,12,11,9,7,6,2]=>11111011111=>00000100000
[9,8,5,4,3,1,12,11,10,7,6,2]=>11111011111=>00000100000
[11,7,5,4,3,1,12,10,9,8,6,2]=>11111011111=>00000100000
[10,7,5,4,3,1,12,11,9,8,6,2]=>11111011111=>00000100000
[9,7,5,4,3,1,12,11,10,8,6,2]=>11111011111=>00000100000
[8,7,5,4,3,1,12,11,10,9,6,2]=>11111011111=>00000100000
[11,6,5,4,3,1,12,10,9,8,7,2]=>11111011111=>00000100000
[10,6,5,4,3,1,12,11,9,8,7,2]=>11111011111=>00000100000
[9,6,5,4,3,1,12,11,10,8,7,2]=>11111011111=>00000100000
[8,6,5,4,3,1,12,11,10,9,7,2]=>11111011111=>00000100000
[7,6,5,4,3,1,12,11,10,9,8,2]=>11111011111=>00000100000
[11,9,7,5,2,1,12,10,8,6,4,3]=>11111011111=>00000100000
[10,9,7,5,2,1,12,11,8,6,4,3]=>11111011111=>00000100000
[11,8,7,5,2,1,12,10,9,6,4,3]=>11111011111=>00000100000
[10,8,7,5,2,1,12,11,9,6,4,3]=>11111011111=>00000100000
[9,8,7,5,2,1,12,11,10,6,4,3]=>11111011111=>00000100000
[11,9,6,5,2,1,12,10,8,7,4,3]=>11111011111=>00000100000
[10,9,6,5,2,1,12,11,8,7,4,3]=>11111011111=>00000100000
[11,8,6,5,2,1,12,10,9,7,4,3]=>11111011111=>00000100000
[10,8,6,5,2,1,12,11,9,7,4,3]=>11111011111=>00000100000
[9,8,6,5,2,1,12,11,10,7,4,3]=>11111011111=>00000100000
[11,7,6,5,2,1,12,10,9,8,4,3]=>11111011111=>00000100000
[10,7,6,5,2,1,12,11,9,8,4,3]=>11111011111=>00000100000
[9,7,6,5,2,1,12,11,10,8,4,3]=>11111011111=>00000100000
[8,7,6,5,2,1,12,11,10,9,4,3]=>11111011111=>00000100000
[11,9,7,4,2,1,12,10,8,6,5,3]=>11111011111=>00000100000
[10,9,7,4,2,1,12,11,8,6,5,3]=>11111011111=>00000100000
[11,8,7,4,2,1,12,10,9,6,5,3]=>11111011111=>00000100000
[10,8,7,4,2,1,12,11,9,6,5,3]=>11111011111=>00000100000
[9,8,7,4,2,1,12,11,10,6,5,3]=>11111011111=>00000100000
[11,9,6,4,2,1,12,10,8,7,5,3]=>11111011111=>00000100000
[10,9,6,4,2,1,12,11,8,7,5,3]=>11111011111=>00000100000
[11,8,6,4,2,1,12,10,9,7,5,3]=>11111011111=>00000100000
[10,8,6,4,2,1,12,11,9,7,5,3]=>11111011111=>00000100000
[9,8,6,4,2,1,12,11,10,7,5,3]=>11111011111=>00000100000
[11,7,6,4,2,1,12,10,9,8,5,3]=>11111011111=>00000100000
[10,7,6,4,2,1,12,11,9,8,5,3]=>11111011111=>00000100000
[9,7,6,4,2,1,12,11,10,8,5,3]=>11111011111=>00000100000
[8,7,6,4,2,1,12,11,10,9,5,3]=>11111011111=>00000100000
[11,9,5,4,2,1,12,10,8,7,6,3]=>11111011111=>00000100000
[10,9,5,4,2,1,12,11,8,7,6,3]=>11111011111=>00000100000
[11,8,5,4,2,1,12,10,9,7,6,3]=>11111011111=>00000100000
[10,8,5,4,2,1,12,11,9,7,6,3]=>11111011111=>00000100000
[9,8,5,4,2,1,12,11,10,7,6,3]=>11111011111=>00000100000
[11,7,5,4,2,1,12,10,9,8,6,3]=>11111011111=>00000100000
[10,7,5,4,2,1,12,11,9,8,6,3]=>11111011111=>00000100000
[9,7,5,4,2,1,12,11,10,8,6,3]=>11111011111=>00000100000
[8,7,5,4,2,1,12,11,10,9,6,3]=>11111011111=>00000100000
[11,6,5,4,2,1,12,10,9,8,7,3]=>11111011111=>00000100000
[10,6,5,4,2,1,12,11,9,8,7,3]=>11111011111=>00000100000
[9,6,5,4,2,1,12,11,10,8,7,3]=>11111011111=>00000100000
[8,6,5,4,2,1,12,11,10,9,7,3]=>11111011111=>00000100000
[7,6,5,4,2,1,12,11,10,9,8,3]=>11111011111=>00000100000
[11,9,7,3,2,1,12,10,8,6,5,4]=>11111011111=>00000100000
[10,9,7,3,2,1,12,11,8,6,5,4]=>11111011111=>00000100000
[11,8,7,3,2,1,12,10,9,6,5,4]=>11111011111=>00000100000
[10,8,7,3,2,1,12,11,9,6,5,4]=>11111011111=>00000100000
[9,8,7,3,2,1,12,11,10,6,5,4]=>11111011111=>00000100000
[11,9,6,3,2,1,12,10,8,7,5,4]=>11111011111=>00000100000
[10,9,6,3,2,1,12,11,8,7,5,4]=>11111011111=>00000100000
[11,8,6,3,2,1,12,10,9,7,5,4]=>11111011111=>00000100000
[10,8,6,3,2,1,12,11,9,7,5,4]=>11111011111=>00000100000
[9,8,6,3,2,1,12,11,10,7,5,4]=>11111011111=>00000100000
[11,7,6,3,2,1,12,10,9,8,5,4]=>11111011111=>00000100000
[10,7,6,3,2,1,12,11,9,8,5,4]=>11111011111=>00000100000
[9,7,6,3,2,1,12,11,10,8,5,4]=>11111011111=>00000100000
[8,7,6,3,2,1,12,11,10,9,5,4]=>11111011111=>00000100000
[11,9,5,3,2,1,12,10,8,7,6,4]=>11111011111=>00000100000
[10,9,5,3,2,1,12,11,8,7,6,4]=>11111011111=>00000100000
[11,8,5,3,2,1,12,10,9,7,6,4]=>11111011111=>00000100000
[10,8,5,3,2,1,12,11,9,7,6,4]=>11111011111=>00000100000
[9,8,5,3,2,1,12,11,10,7,6,4]=>11111011111=>00000100000
[11,7,5,3,2,1,12,10,9,8,6,4]=>11111011111=>00000100000
[10,7,5,3,2,1,12,11,9,8,6,4]=>11111011111=>00000100000
[9,7,5,3,2,1,12,11,10,8,6,4]=>11111011111=>00000100000
[8,7,5,3,2,1,12,11,10,9,6,4]=>11111011111=>00000100000
[11,6,5,3,2,1,12,10,9,8,7,4]=>11111011111=>00000100000
[10,6,5,3,2,1,12,11,9,8,7,4]=>11111011111=>00000100000
[9,6,5,3,2,1,12,11,10,8,7,4]=>11111011111=>00000100000
[8,6,5,3,2,1,12,11,10,9,7,4]=>11111011111=>00000100000
[7,6,5,3,2,1,12,11,10,9,8,4]=>11111011111=>00000100000
[11,9,4,3,2,1,12,10,8,7,6,5]=>11111011111=>00000100000
[10,9,4,3,2,1,12,11,8,7,6,5]=>11111011111=>00000100000
[11,8,4,3,2,1,12,10,9,7,6,5]=>11111011111=>00000100000
[10,8,4,3,2,1,12,11,9,7,6,5]=>11111011111=>00000100000
[9,8,4,3,2,1,12,11,10,7,6,5]=>11111011111=>00000100000
[11,7,4,3,2,1,12,10,9,8,6,5]=>11111011111=>00000100000
[10,7,4,3,2,1,12,11,9,8,6,5]=>11111011111=>00000100000
[9,7,4,3,2,1,12,11,10,8,6,5]=>11111011111=>00000100000
[8,7,4,3,2,1,12,11,10,9,6,5]=>11111011111=>00000100000
[11,6,4,3,2,1,12,10,9,8,7,5]=>11111011111=>00000100000
[10,6,4,3,2,1,12,11,9,8,7,5]=>11111011111=>00000100000
[9,6,4,3,2,1,12,11,10,8,7,5]=>11111011111=>00000100000
[8,6,4,3,2,1,12,11,10,9,7,5]=>11111011111=>00000100000
[7,6,4,3,2,1,12,11,10,9,8,5]=>11111011111=>00000100000
[11,5,4,3,2,1,12,10,9,8,7,6]=>11111011111=>00000100000
[10,5,4,3,2,1,12,11,9,8,7,6]=>11111011111=>00000100000
[9,5,4,3,2,1,12,11,10,8,7,6]=>11111011111=>00000100000
[8,5,4,3,2,1,12,11,10,9,7,6]=>11111011111=>00000100000
[7,5,4,3,2,1,12,11,10,9,8,6]=>11111011111=>00000100000
[6,1,4,2,3,5,8,7]=>1010001=>0101110
[8,6,1,4,2,3,5,7]=>1101000=>0010111
[6,8,1,4,2,3,5,7]=>0101000=>1010111
[8,1,4,2,3,6,5,7]=>1010010=>0101101
[4,1,8,2,3,6,5,7]=>1010010=>0101101
[8,2,3,6,1,4,5,7]=>1001000=>0110111
[6,2,3,8,1,4,5,7]=>1001000=>0110111
[4,6,2,3,8,1,5,7]=>0100100=>1011011
[4,8,2,3,6,1,5,7]=>0100100=>1011011
[8,2,3,6,4,1,5,7]=>1001100=>0110011
[8,4,3,6,2,1,5,7]=>1101100=>0010011
[6,2,3,8,4,1,5,7]=>1001100=>0110011
[8,4,2,3,6,1,5,7]=>1100100=>0011011
[6,4,2,3,8,1,5,7]=>1100100=>0011011
[2,6,4,3,8,1,5,7]=>0110100=>1001011
[2,8,4,3,6,1,5,7]=>0110100=>1001011
[2,6,3,8,4,1,5,7]=>0101100=>1010011
[6,3,8,4,2,1,5,7]=>1011100=>0100011
[2,6,3,8,1,4,5,7]=>0101000=>1010111
[2,8,3,6,1,4,5,7]=>0101000=>1010111
[8,3,6,4,2,1,5,7]=>1011100=>0100011
[2,8,3,6,4,1,5,7]=>0101100=>1010011
[8,3,6,2,4,1,5,7]=>1010100=>0101011
[8,3,6,2,1,4,5,7]=>1011000=>0100111
[6,2,1,3,8,4,5,7]=>1100100=>0011011
[8,2,1,3,6,4,5,7]=>1100100=>0011011
[6,3,8,2,4,1,5,7]=>1010100=>0101011
[6,2,4,3,8,1,5,7]=>1010100=>0101011
[3,6,4,7,8,5,1,2]=>0100110=>1011001
[1,6,4,2,7,5,8,3]=>0110101=>1001010
[3,6,4,2,7,1,5,8]=>0110100=>1001011
[1,4,7,2,5,6,8,3]=>0010001=>1101110
[6,4,8,5,3,7,1,2]=>1011010=>0100101
[1,6,5,4,2,7,8,3]=>0111001=>1000110
[4,2,5,3,6,1,7,8]=>1010100=>0101011
[7,1,5,3,6,2,8,4]=>1010101=>0101010
[1,6,5,2,4,8,7,3]=>0110011=>1001100
[1,4,6,2,8,5,7,3]=>0010101=>1101010
[7,8,1,4,2,5,6,3]=>0101001=>1010110
[3,4,8,5,2,1,6,7]=>0011100=>1100011
[4,8,5,3,1,6,2,7]=>0111010=>1000101
[6,1,3,5,8,2,7,4]=>1000101=>0111010
[6,1,8,7,4,2,3,5]=>1011100=>0100011
[1,2,8,5,7,3,6,4]=>0010101=>1101010
[1,3,6,8,7,5,2,4]=>0001110=>1110001
[1,8,2,5,4,7,6,3]=>0101011=>1010100
[7,1,2,4,5,8,6,3]=>1000011=>0111100
[1,2,7,3,5,8,6,4]=>0010011=>1101100
[6,1,3,2,5,7,8,4]=>1010001=>0101110
[4,6,2,1,7,5,3,8]=>0110110=>1001001
[1,6,3,7,8,5,2,4]=>0100110=>1011001
[4,6,2,3,7,8,1,5]=>0100010=>1011101
[4,6,3,7,1,2,8,5]=>0101001=>1010110
[4,2,1,3,5,7,8,6]=>1100001=>0011110
[7,3,2,4,5,1,8,6]=>1100101=>0011010
[3,8,2,5,4,1,7,6]=>0101101=>1010010
[7,8,4,2,6,3,1,5]=>0110110=>1001001
[4,2,6,3,8,7,1,5]=>1010110=>0101001
[5,8,2,7,4,3,1,6]=>0101110=>1010001
[4,3,8,5,1,7,2,6]=>1011010=>0100101
[4,3,6,8,1,2,7,5]=>1001001=>0110110
[6,4,3,5,2,8,1,7]=>1101010=>0010101
[6,5,3,8,4,2,1,7]=>1101110=>0010001
[6,1,7,2,8,3,9,4,10,5]=>101010101=>010101010
[6,1,7,8,9,10,2,3,4,5]=>100001000=>011110111
[7,1,8,2,9,3,10,4,11,5,12,6]=>10101010101=>01010101010
[3,8,1,7,5,6,4,2]=>0101011=>1010100
[8,2,5,7,3,6,4,1]=>1001011=>0110100
[1,8,6,7,5,3,4,2]=>0101101=>1010010
[8,2,6,7,5,3,4,1]=>1001101=>0110010
[1,5,8,7,2,6,4,3]=>0011011=>1100100
[5,4,8,6,2,3,7,1]=>1011001=>0100110
[2,7,6,1,3,5,4,8]=>0110010=>1001101
[6,4,1,8,2,5,7,3]=>1101001=>0010110
[2,8,6,1,3,5,4,7]=>0110010=>1001101
[4,1,3,6,5,8,7,2]=>1001011=>0110100
[2,1,6,3,5,8,7,4]=>1010011=>0101100
[2,4,1,3,8,5,7,6]=>0100101=>1011010
[2,4,1,3,5,8,7,6]=>0100011=>1011100
[2,6,1,3,5,8,7,4]=>0100011=>1011100
[4,6,1,3,5,8,7,2]=>0100011=>1011100
[6,1,4,3,5,8,7,2]=>1010011=>0101100
[6,4,1,3,5,8,7,2]=>1100011=>0011100
[6,2,1,3,5,8,7,4]=>1100011=>0011100
[4,2,1,3,6,5,7,8]=>1100100=>0011011
[4,2,1,6,3,5,7,8]=>1101000=>0010111
[6,2,1,8,3,5,7,4]=>1101001=>0010110
[6,2,1,3,8,5,7,4]=>1100101=>0011010
[6,1,4,3,8,5,7,2]=>1010101=>0101010
[1,6,4,3,8,5,7,2]=>0110101=>1001010
[8,1,4,3,6,5,7,2]=>1010101=>0101010
[8,4,1,3,6,5,7,2]=>1100101=>0011010
[8,2,1,3,6,5,7,4]=>1100101=>0011010
[8,2,1,6,3,5,7,4]=>1101001=>0010110
[8,2,1,4,3,5,7,6]=>1101001=>0010110
[6,2,1,4,3,5,7,8]=>1101000=>0010111
[8,2,4,1,3,5,7,6]=>1010001=>0101110
[8,2,6,1,3,5,7,4]=>1010001=>0101110
[8,4,6,1,3,5,7,2]=>1010001=>0101110
[8,4,1,6,3,5,7,2]=>1101001=>0010110
[8,1,4,6,3,5,7,2]=>1001001=>0110110
[1,8,4,6,3,5,7,2]=>0101001=>1010110
[1,6,4,8,3,5,7,2]=>0101001=>1010110
[6,4,1,8,3,5,7,2]=>1101001=>0010110
[6,4,8,1,3,5,7,2]=>1010001=>0101110
[6,2,8,1,3,5,7,4]=>1010001=>0101110
[4,2,8,1,3,5,7,6]=>1010001=>0101110
[2,6,8,1,3,5,7,4]=>0010001=>1101110
[4,6,8,1,3,5,7,2]=>0010001=>1101110
[4,6,1,8,3,5,7,2]=>0101001=>1010110
[4,1,6,8,3,5,7,2]=>1001001=>0110110
[1,4,6,3,8,5,7,2]=>0010101=>1101010
[4,6,1,3,8,5,7,2]=>0100101=>1011010
[2,4,1,8,3,5,7,6]=>0101001=>1010110
[2,1,6,8,3,5,7,4]=>1001001=>0110110
[4,1,3,6,8,5,7,2]=>1000101=>0111010
[1,4,3,6,8,5,7,2]=>0100101=>1011010
[4,1,3,8,6,5,7,2]=>1001101=>0110010
[2,1,8,3,6,5,7,4]=>1010101=>0101010
[2,1,6,4,3,5,7,8]=>1011000=>0100111
[2,6,1,4,3,5,7,8]=>0101000=>1010111
[2,8,1,4,3,5,7,6]=>0101001=>1010110
[2,8,1,6,3,5,7,4]=>0101001=>1010110
[4,8,1,3,6,5,7,2]=>0100101=>1011010
[1,4,8,3,6,5,7,2]=>0010101=>1101010
[1,4,8,6,3,5,7,2]=>0011001=>1100110
[4,1,8,6,3,5,7,2]=>1011001=>0100110
[4,8,1,6,3,5,7,2]=>0101001=>1010110
[4,8,6,1,3,5,7,2]=>0110001=>1001110
[2,8,6,1,3,5,7,4]=>0110001=>1001110
[2,8,4,1,3,5,7,6]=>0110001=>1001110
[2,6,4,1,3,5,7,8]=>0110000=>1001111
[4,6,2,1,3,5,7,8]=>0110000=>1001111
[6,8,1,4,3,5,7,2]=>0101001=>1010110
[6,1,8,4,3,5,7,2]=>1011001=>0100110
[1,6,8,4,3,5,7,2]=>0011001=>1100110
[1,8,6,4,3,5,7,2]=>0111001=>1000110
[8,1,6,4,3,5,7,2]=>1011001=>0100110
[8,6,1,4,3,5,7,2]=>1101001=>0010110
[8,6,4,1,3,5,7,2]=>1110001=>0001110
[8,6,2,1,3,5,7,4]=>1110001=>0001110
[8,4,2,1,3,5,7,6]=>1110001=>0001110
[7,8,6,5,2,1,4,3]=>0111101=>1000010
[5,7,4,1,8,6,3,2]=>0110111=>1001000
[5,6,4,2,8,3,7,1]=>0110101=>1001010
[5,6,4,2,7,3,1,8]=>0110110=>1001001
[5,7,1,4,6,3,2,8]=>0100110=>1011001
[5,8,1,4,6,3,7,2]=>0100101=>1011010
[3,6,7,4,5,8,2,1]=>0010011=>1101100
[3,5,7,4,6,8,2,1]=>0010011=>1101100
[6,8,4,1,7,2,5,3]=>0110101=>1001010
[5,4,6,1,7,8,3,2]=>1010011=>0101100
[5,6,4,1,8,7,3,2]=>0110111=>1001000
[3,5,8,4,6,7,2,1]=>0010011=>1101100
[3,6,8,4,5,7,2,1]=>0010011=>1101100
[3,7,8,4,5,6,2,1]=>0010011=>1101100
[6,8,1,4,5,3,7,2]=>0100101=>1011010
[6,7,1,4,5,3,2,8]=>0100110=>1011001
[3,7,1,5,4,6,2,8]=>0101010=>1010101
[3,8,1,5,4,6,7,2]=>0101001=>1010110
[3,7,1,5,4,6,8,2]=>0101001=>1010110
[6,7,1,4,5,3,8,2]=>0100101=>1011010
[5,7,1,4,6,3,8,2]=>0100101=>1011010
[5,6,4,2,7,3,8,1]=>0110101=>1001010
[5,4,7,2,8,3,1,6]=>1010110=>0101001
[5,4,7,2,8,3,6,1]=>1010101=>0101010
[5,6,4,2,8,3,1,7]=>0110110=>1001001
[5,8,1,4,6,3,2,7]=>0100110=>1011001
[3,8,1,5,4,6,2,7]=>0101010=>1010101
[3,6,1,5,4,2,7,8]=>0101100=>1010011
[3,6,1,5,4,8,2,7]=>0101010=>1010101
[6,8,3,1,4,2,5,7]=>0110100=>1001011
[7,3,8,1,4,2,5,6]=>1010100=>0101011
[6,7,3,1,4,2,8,5]=>0110101=>1001010
[3,6,1,5,4,7,8,2]=>0101001=>1010110
[3,4,1,2,7,6,5,8]=>0100110=>1011001
[3,4,1,2,6,8,7,5]=>0100011=>1011100
[6,8,3,1,4,7,2,5]=>0110010=>1001101
[6,4,7,2,8,5,1,3]=>1010110=>0101001
[5,8,1,4,7,3,2,6]=>0100110=>1011001
[7,8,1,4,5,3,2,6]=>0100110=>1011001
[3,8,1,5,4,7,2,6]=>0101010=>1010101
[3,6,1,5,4,8,7,2]=>0101011=>1010100
[3,6,1,5,4,7,2,8]=>0101010=>1010101
[6,7,3,1,4,2,5,8]=>0110100=>1001011
[6,8,3,1,4,2,7,5]=>0110101=>1001010
[7,8,3,1,4,6,2,5]=>0110010=>1001101
[7,8,4,2,6,5,1,3]=>0110110=>1001001
[6,5,8,7,3,4,2,1]=>1011011=>0100100
[7,8,3,1,4,6,5,2]=>0110011=>1001100
[6,7,3,1,4,5,2,8]=>0110010=>1001101
[3,7,1,5,4,2,6,8]=>0101100=>1010011
[3,8,1,5,4,2,7,6]=>0101101=>1010010
[5,8,1,4,7,3,6,2]=>0100101=>1011010
[6,8,4,2,7,5,3,1]=>0110111=>1001000
[6,4,7,2,8,5,3,1]=>1010111=>0101000
[6,3,7,1,4,8,5,2]=>1010011=>0101100
[6,8,3,1,4,7,5,2]=>0110011=>1001100
[3,7,1,5,4,8,6,2]=>0101011=>1010100
[3,4,1,2,8,5,7,6]=>0100101=>1011010
[3,4,1,2,5,8,7,6]=>0100011=>1011100
[3,7,1,5,4,2,8,6]=>0101101=>1010010
[6,7,3,1,4,5,8,2]=>0110001=>1001110
[7,3,8,1,4,5,2,6]=>1010010=>0101101
[7,3,8,1,4,5,6,2]=>1010001=>0101110
[6,8,3,1,4,5,2,7]=>0110010=>1001101
[3,8,1,5,4,2,6,7]=>0101100=>1010011
[9,8,7,6,5,4,2,1,3]=>11111110=>00000001
[9,8,7,6,5,3,2,1,4]=>11111110=>00000001
[8,7,6,3,5,2,1,4]=>1110110=>0001001
[9,8,7,6,4,3,2,1,5]=>11111110=>00000001
[8,7,4,6,3,2,1,5]=>1101110=>0010001
[9,8,7,5,4,3,2,1,6]=>11111110=>00000001
[8,5,7,4,3,2,1,6]=>1011110=>0100001
[9,8,6,5,4,3,2,1,7]=>11111110=>00000001
[9,7,6,5,4,3,2,1,8]=>11111110=>00000001
[9,8,7,6,5,4,1,3,2]=>11111101=>00000010
[10,9,8,7,6,5,4,2,1,3]=>111111110=>000000001
[9,8,7,6,5,2,4,1,3]=>11111010=>00000101
[10,9,8,7,6,5,3,2,1,4]=>111111110=>000000001
[9,8,7,6,3,5,2,1,4]=>11110110=>00001001
[10,9,8,7,6,4,3,2,1,5]=>111111110=>000000001
[8,7,6,2,5,4,1,3]=>1110110=>0001001
[9,8,7,4,6,3,2,1,5]=>11101110=>00010001
[10,9,8,7,5,4,3,2,1,6]=>111111110=>000000001
[8,5,4,7,3,2,1,6]=>1101110=>0010001
[8,7,3,6,5,2,1,4]=>1101110=>0010001
[9,8,5,7,4,3,2,1,6]=>11011110=>00100001
[10,9,8,6,5,4,3,2,1,7]=>111111110=>000000001
[6,5,8,4,3,2,1,7]=>1011110=>0100001
[8,4,7,6,3,2,1,5]=>1011110=>0100001
[9,6,8,5,4,3,2,1,7]=>10111110=>01000001
[10,9,7,6,5,4,3,2,1,8]=>111111110=>000000001
[5,8,7,4,3,2,1,6]=>0111110=>1000001
[10,8,7,6,5,4,3,2,1,9]=>111111110=>000000001
[5,8,6,2,3,4,7,1]=>0110001=>1001110
[4,5,2,7,3,1,8,6]=>0101101=>1010010
[4,8,2,6,3,5,7,1]=>0101001=>1010110
[4,3,7,8,6,5,1,2]=>1001110=>0110001
[4,1,7,2,5,8,6,3]=>1010011=>0101100
[7,8,2,1,5,6,4,3]=>0110011=>1001100
[1,6,2,5,8,4,3,7]=>0100110=>1011001
[2,1,8,7,4,5,3,6]=>1011010=>0100101
[7,3,1,6,8,5,2,4]=>1100110=>0011001
[1,5,8,6,2,3,7,4]=>0011001=>1100110
[2,4,8,3,1,6,5,7]=>0011010=>1100101
[5,2,7,1,8,6,3,4]=>1010110=>0101001
[2,6,1,3,8,7,4,5]=>0100110=>1011001
[6,5,2,8,1,7,3,4]=>1101010=>0010101
[2,8,3,5,1,7,4,6]=>0101010=>1010101
[5,4,3,8,7,1,6,2]=>1101101=>0010010
[8,5,4,3,7,2,6,1]=>1110101=>0001010
[8,3,7,4,2,6,5,1]=>1011011=>0100100
[2,8,6,5,1,7,4,3]=>0111011=>1000100
[6,3,2,8,4,1,7,5]=>1101101=>0010010
[2,8,3,4,1,7,5,6]=>0101010=>1010101
[5,4,2,8,3,1,7,6]=>1101101=>0010010
[2,8,4,3,1,7,6,5]=>0111011=>1000100
[2,8,5,3,1,7,6,4]=>0111011=>1000100
[2,8,6,4,1,7,5,3]=>0111011=>1000100
[3,8,7,5,1,6,4,2]=>0111011=>1000100
[8,3,7,5,2,6,4,1]=>1011011=>0100100
[8,4,7,6,2,5,3,1]=>1011011=>0100100
[4,8,7,6,1,5,3,2]=>0111011=>1000100
[7,4,8,6,2,1,5,3]=>1011101=>0100010
[7,3,8,5,2,1,6,4]=>1011101=>0100010
[7,3,8,4,2,1,6,5]=>1011101=>0100010
[7,5,4,3,8,2,1,6]=>1110110=>0001001
[3,7,8,4,1,2,6,5]=>0011001=>1100110
[3,7,8,5,1,2,6,4]=>0011001=>1100110
[4,7,8,6,1,2,5,3]=>0011001=>1100110
[8,7,4,6,3,5,2,1]=>1101011=>0010100
[5,7,8,6,1,2,4,3]=>0011001=>1100110
[6,4,7,8,3,1,2,5]=>1001100=>0110011
[7,3,4,8,2,1,5,6]=>1001100=>0110011
[7,6,4,8,3,2,1,5]=>1101110=>0010001
[7,5,8,6,2,1,4,3]=>1011101=>0100010
[6,5,8,7,3,1,4,2]=>1011101=>0100010
[2,4,8,3,1,5,7,6]=>0011001=>1100110
[6,3,2,4,8,1,5,7]=>1100100=>0011011
[2,3,8,4,1,6,7,5]=>0011001=>1100110
[2,3,8,5,1,6,7,4]=>0011001=>1100110
[6,4,8,7,3,1,5,2]=>1011101=>0100010
[8,6,4,7,3,2,5,1]=>1101101=>0010010
[8,3,4,7,2,5,6,1]=>1001001=>0110110
[3,4,8,7,1,5,6,2]=>0011001=>1100110
[2,4,8,6,1,5,7,3]=>0011001=>1100110
[2,5,8,6,1,4,7,3]=>0011001=>1100110
[8,3,5,7,2,4,6,1]=>1001001=>0110110
[8,4,6,7,2,3,5,1]=>1001001=>0110110
[4,6,8,7,1,3,5,2]=>0011001=>1100110
[2,6,8,5,1,3,7,4]=>0011001=>1100110
[2,6,8,4,1,3,7,5]=>0011001=>1100110
[2,5,8,3,1,4,7,6]=>0011001=>1100110
[5,6,8,7,1,3,4,2]=>0011001=>1100110
[7,4,6,8,2,1,3,5]=>1001100=>0110011
[2,3,5,4,1,8,6,7]=>0011010=>1100101
[2,3,6,4,8,1,5,7]=>0010100=>1101011
[1,8,4,6,3,5,2,7]=>0101010=>1010101
[5,4,8,6,2,1,3,7]=>1011100=>0100011
[2,3,6,8,1,5,4,7]=>0001010=>1110101
[2,5,6,1,4,7,8,3]=>0010001=>1101110
[2,5,6,1,4,7,3,8]=>0010010=>1101101
[7,3,5,1,6,8,4,2]=>1010011=>0101100
[2,7,6,1,8,5,4,3]=>0110111=>1001000
[2,7,6,8,1,4,5,3]=>0101001=>1010110
[1,8,7,6,3,2,5,4]=>0111101=>1000010
[1,8,7,6,3,2,4,5]=>0111100=>1000011
[5,7,8,6,2,3,4,1]=>0011001=>1100110
[2,7,6,1,8,5,3,4]=>0110110=>1001001
[6,3,5,1,7,2,4,8]=>1010100=>0101011
[2,3,4,7,6,1,5,8]=>0001100=>1110011
[7,3,5,8,4,1,2,6]=>1001100=>0110011
[1,8,4,5,2,7,3,6]=>0101010=>1010101
[1,8,4,5,2,7,6,3]=>0101011=>1010100
[7,3,5,8,4,1,6,2]=>1001101=>0110010
[2,7,6,4,8,5,1,3]=>0110110=>1001001
[7,3,5,4,6,8,1,2]=>1010010=>0101101
[6,3,5,4,7,1,8,2]=>1010101=>0101010
[6,3,5,4,7,1,2,8]=>1010100=>0101011
[3,4,1,5,6,8,7,2]=>0100011=>1011100
[3,7,1,6,8,5,2,4]=>0100110=>1011001
[2,3,1,8,6,4,7,5]=>0101101=>1010010
[1,8,4,3,6,2,5,7]=>0110100=>1001011
[2,3,1,8,6,4,5,7]=>0101100=>1010011
[3,7,1,6,8,5,4,2]=>0100111=>1011000
[6,3,5,4,7,2,1,8]=>1010110=>0101001
[7,3,5,4,6,8,2,1]=>1010011=>0101100
[2,7,6,4,8,5,3,1]=>0110111=>1001000
[1,8,4,5,2,6,3,7]=>0101010=>1010101
[6,4,8,5,3,1,2,7]=>1011100=>0100011
[7,3,5,8,4,6,2,1]=>1001011=>0110100
[2,3,4,6,5,8,1,7]=>0001010=>1110101
[2,3,4,7,5,1,8,6]=>0001101=>1110010
[2,3,4,7,5,1,6,8]=>0001100=>1110011
[2,3,4,7,1,6,5,8]=>0001010=>1110101
[2,3,4,7,1,6,8,5]=>0001001=>1110110
[2,3,4,6,1,8,7,5]=>0001011=>1110100
[6,3,5,8,4,2,7,1]=>1001101=>0110010
[7,4,8,5,3,2,1,6]=>1011110=>0100001
[1,8,4,5,2,3,6,7]=>0101000=>1010111
[7,4,8,5,3,2,6,1]=>1011101=>0100010
[6,3,5,8,4,2,1,7]=>1001110=>0110001
[5,2,4,6,8,3,7,1]=>1000101=>0111010
[1,5,7,4,6,3,2,8]=>0010110=>1101001
[5,2,8,4,6,3,7,1]=>1010101=>0101010
[3,8,5,4,6,7,2,1]=>0110011=>1001100
[6,8,3,4,5,7,2,1]=>0100011=>1011100
[2,5,7,4,6,3,8,1]=>0010101=>1101010
[5,4,1,7,8,3,2,6]=>1100110=>0011001
[5,4,2,7,8,3,6,1]=>1100101=>0011010
[5,1,4,6,8,3,2,7]=>1000110=>0111001
[5,1,8,4,6,3,2,7]=>1010110=>0101001
[8,1,6,4,5,3,2,7]=>1010110=>0101001
[8,1,3,5,4,6,2,7]=>1001010=>0110101
[8,1,6,2,4,3,5,7]=>1010100=>0101011
[8,7,1,2,4,3,5,6]=>1100100=>0011011
[1,7,6,2,4,3,5,8]=>0110100=>1001011
[8,7,3,2,4,6,5,1]=>1110011=>0001100
[8,2,6,3,4,5,7,1]=>1010001=>0101110
[1,7,6,3,4,5,2,8]=>0110010=>1001101
[1,7,2,5,4,3,6,8]=>0101100=>1010011
[8,7,2,4,5,3,6,1]=>1100101=>0011010
[5,8,2,4,7,3,6,1]=>0100101=>1011010
[6,8,3,2,4,7,5,1]=>0110011=>1001100
[8,7,1,3,4,5,2,6]=>1100010=>0011101
[8,1,6,3,4,5,2,7]=>1010010=>0101101
[8,1,2,5,4,3,6,7]=>1001100=>0110011
[3,4,8,7,5,2,6,1]=>0011101=>1100010
[3,2,8,6,1,5,4,7]=>1011010=>0100101
[8,6,1,2,4,3,5,7]=>1100100=>0011011
[8,7,3,6,4,2,5,1]=>1101101=>0010010
[3,8,7,2,5,4,6,1]=>0110101=>1001010
[8,7,2,4,5,6,3,1]=>1100011=>0011100
[5,3,6,2,4,8,7,1]=>1010011=>0101100
[3,5,2,8,6,1,4,7]=>0101100=>1010011
[3,7,2,5,1,4,8,6]=>0101001=>1010110
[5,1,8,6,2,3,4,7]=>1011000=>0100111
[2,5,4,1,8,6,3,7]=>0110110=>1001001
[3,7,6,1,8,2,5,4]=>0110101=>1001010
[7,6,3,1,8,2,4,5]=>1110100=>0001011
[8,2,3,6,1,4,7,5]=>1001001=>0110110
[1,8,2,6,3,4,7,5]=>0101001=>1010110
[8,1,3,6,4,7,2,5]=>1001010=>0110101
[7,1,3,6,4,8,2,5]=>1001010=>0110101
[8,2,1,3,5,7,4,6]=>1100010=>0011101
[8,2,6,3,1,4,7,5]=>1011001=>0100110
[7,5,4,1,3,8,2,6]=>1110010=>0001101
[2,7,5,8,3,4,1,6]=>0101010=>1010101
[7,3,8,5,4,1,2,6]=>1011100=>0100011
[7,2,3,6,1,4,8,5]=>1001001=>0110110
[1,3,7,2,5,8,4,6]=>0010010=>1101101
[1,7,2,3,5,8,4,6]=>0100010=>1011101
[7,4,8,1,3,6,2,5]=>1010010=>0101101
[8,1,2,3,5,7,4,6]=>1000010=>0111101
[7,1,2,3,5,8,4,6]=>1000010=>0111101
[8,6,1,4,7,3,2,5]=>1100110=>0011001
[2,6,3,7,1,4,8,5]=>0101001=>1010110
[2,6,3,8,1,4,7,5]=>0101001=>1010110
[7,5,4,8,1,3,2,6]=>1101010=>0010101
[8,5,4,7,1,3,2,6]=>1101010=>0010101
[2,3,1,8,5,4,6,7]=>0101100=>1010011
[8,6,5,1,3,4,2,7]=>1110010=>0001101
[8,5,1,7,6,3,4,2]=>1101101=>0010010
[3,4,7,6,1,8,5,2]=>0011011=>1100100
[3,5,2,6,7,1,8,4]=>0100101=>1011010
[3,2,8,4,7,5,1,6]=>1010110=>0101001
[8,4,7,5,1,3,2,6]=>1011010=>0100101
[3,8,1,6,5,2,7,4]=>0101101=>1010010
[6,1,2,8,3,4,7,5]=>1001001=>0110110
[6,8,3,1,7,2,4,5]=>0110100=>1001011
[3,7,2,5,6,1,8,4]=>0100101=>1011010
[6,8,4,2,5,1,7,3]=>0110101=>1001010
[2,7,5,3,8,4,1,6]=>0110110=>1001001
[8,3,1,4,7,2,6,5]=>1100101=>0011010
[8,3,2,1,5,7,4,6]=>1110010=>0001101
[2,8,3,6,4,7,1,5]=>0101010=>1010101
[7,3,6,4,8,1,2,5]=>1010100=>0101011
[8,3,6,4,7,1,2,5]=>1010100=>0101011
[1,2,8,3,5,7,4,6]=>0010010=>1101101
[1,8,3,2,5,7,4,6]=>0110010=>1001101
[6,5,1,7,4,2,8,3]=>1101101=>0010010
[7,3,6,4,8,2,1,5]=>1010110=>0101001
[4,6,1,7,3,5,2,8]=>0101010=>1010101
[5,6,1,7,3,4,2,8]=>0101010=>1010101
[6,1,7,3,4,2,8,5]=>1010101=>0101010
[7,3,8,1,6,5,2,4]=>1010110=>0101001
[8,3,7,1,6,5,2,4]=>1010110=>0101001
[5,1,7,4,2,8,6,3]=>1011011=>0100100
[2,8,1,7,6,5,3,4]=>0101110=>1010001
[4,2,8,6,5,1,7,3]=>1011101=>0100010
[6,4,2,8,5,1,7,3]=>1101101=>0010010
[8,6,4,7,1,5,2,3]=>1101010=>0010101
[7,6,4,8,1,5,2,3]=>1101010=>0010101
[5,1,6,4,2,3,8,7]=>1011001=>0100110
[4,2,3,8,7,5,1,6]=>1001110=>0110001
[3,8,7,1,6,5,2,4]=>0110110=>1001001
[2,4,3,8,1,6,7,5]=>0101001=>1010110
[2,4,3,7,1,6,8,5]=>0101001=>1010110
[4,2,3,7,8,5,1,6]=>1000110=>0111001
[5,1,6,4,2,3,7,8]=>1011000=>0100111
[6,4,7,8,1,5,2,3]=>1001010=>0110101
[8,7,4,6,1,5,2,3]=>1101010=>0010101
[6,5,7,8,1,4,2,3]=>1001010=>0110101
[4,7,8,6,1,5,2,3]=>0011010=>1100101
[3,2,4,7,8,1,5,6]=>1000100=>0111011
[3,2,4,8,7,1,5,6]=>1001100=>0110011
[4,8,7,6,1,5,2,3]=>0111010=>1000101
[5,8,7,6,1,4,2,3]=>0111010=>1000101
[8,6,5,7,1,4,2,3]=>1101010=>0010101
[5,1,6,7,4,2,3,8]=>1001100=>0110011
[6,7,4,8,1,5,2,3]=>0101010=>1010101
[8,4,7,6,1,5,2,3]=>1011010=>0100101
[8,3,2,4,7,1,5,6]=>1100100=>0011011
[7,3,2,4,8,1,5,6]=>1100100=>0011011
[2,5,3,7,1,6,4,8]=>0101010=>1010101
[8,4,6,7,1,5,2,3]=>1001010=>0110101
[7,4,6,8,1,5,2,3]=>1001010=>0110101
[5,1,6,8,4,2,3,7]=>1001100=>0110011
[4,2,3,7,5,1,6,8]=>1001100=>0110011
[3,7,5,8,1,6,2,4]=>0101010=>1010101
[2,4,3,7,1,6,5,8]=>0101010=>1010101
[2,4,7,1,5,8,6,3]=>0010011=>1101100
[3,2,4,7,6,1,5,8]=>1001100=>0110011
[4,7,6,8,1,5,2,3]=>0101010=>1010101
[8,5,6,7,1,4,2,3]=>1001010=>0110101
[8,6,7,5,1,4,2,3]=>1011010=>0100101
[7,6,8,5,1,4,2,3]=>1011010=>0100101
[6,8,7,5,1,4,2,3]=>0111010=>1000101
[5,6,8,7,1,4,2,3]=>0011010=>1100101
[4,6,8,7,1,5,2,3]=>0011010=>1100101
[2,4,6,7,1,5,8,3]=>0001001=>1110110
[3,2,4,6,1,5,7,8]=>1001000=>0110111
[6,7,8,5,1,4,2,3]=>0011010=>1100101
[7,8,6,5,1,4,2,3]=>0111010=>1000101
[3,1,7,5,4,2,8,6]=>1011101=>0100010
[2,1,8,5,4,6,3,7]=>1011010=>0100101
[4,1,8,5,2,3,6,7]=>1011000=>0100111
[5,4,1,3,6,7,2,8]=>1100010=>0011101
[8,4,1,2,6,3,7,5]=>1100101=>0011010
[8,2,7,1,5,3,4,6]=>1010100=>0101011
[3,2,7,1,5,8,4,6]=>1010010=>0101101
[6,3,7,1,5,4,2,8]=>1010110=>0101001
[7,3,8,1,5,4,2,6]=>1010110=>0101001
[7,1,5,3,8,4,2,6]=>1010110=>0101001
[4,5,1,3,6,8,2,7]=>0100010=>1011101
[3,6,8,1,5,4,2,7]=>0010110=>1101001
[6,8,3,1,5,4,2,7]=>0110110=>1001001
[7,6,3,1,5,4,2,8]=>1110110=>0001001
[3,6,2,1,5,8,4,7]=>0110010=>1001101
[8,6,2,1,5,3,4,7]=>1110100=>0001011
[4,8,2,1,7,5,3,6]=>0110110=>1001001
[2,3,8,1,5,7,4,6]=>0010010=>1101101
[7,1,3,2,8,6,4,5]=>1010110=>0101001
[7,1,6,2,8,3,4,5]=>1010100=>0101011
[4,7,1,2,6,3,8,5]=>0100101=>1011010
[2,7,8,1,5,3,4,6]=>0010100=>1101011
[6,7,2,1,5,3,4,8]=>0110100=>1001011
[4,7,2,1,8,5,3,6]=>0110110=>1001001
[8,7,2,1,4,5,3,6]=>1110010=>0001101
[8,7,5,6,1,4,3,2]=>1101011=>0010100
[5,7,8,6,1,4,3,2]=>0011011=>1100100
[2,7,4,1,6,5,3,8]=>0110110=>1001001
[3,7,1,4,5,6,8,2]=>0100001=>1011110
[7,1,6,4,5,8,3,2]=>1010011=>0101100
[3,5,1,4,7,6,8,2]=>0100101=>1011010
[2,6,4,1,7,5,3,8]=>0110110=>1001001
[5,6,8,7,1,4,3,2]=>0011011=>1100100
[6,8,5,7,1,4,3,2]=>0101011=>1010100
[8,6,5,7,1,4,3,2]=>1101011=>0010100
[8,5,7,6,1,4,3,2]=>1011011=>0100100
[6,5,7,8,1,4,3,2]=>1001011=>0110100
[7,2,3,1,5,6,4,8]=>1010010=>0101101
[4,2,8,1,6,5,3,7]=>1010110=>0101001
[6,2,4,1,8,5,3,7]=>1010110=>0101001
[8,3,1,4,5,6,7,2]=>1100001=>0011110
[5,3,1,4,8,6,7,2]=>1100101=>0011010
[7,5,1,6,3,4,8,2]=>1101001=>0010110
[7,1,5,8,4,3,6,2]=>1001101=>0110010
[5,8,1,6,4,3,7,2]=>0101101=>1010010
[5,3,1,8,4,6,7,2]=>1101001=>0010110
[8,3,1,5,4,6,7,2]=>1101001=>0010110
[8,2,6,1,4,5,3,7]=>1010010=>0101101
[6,2,8,1,4,5,3,7]=>1010010=>0101101
[7,2,6,1,5,3,4,8]=>1010100=>0101011
[2,8,6,1,5,3,4,7]=>0110100=>1001011
[4,2,1,5,6,3,8,7]=>1100101=>0011010
[7,1,2,5,8,3,4,6]=>1000100=>0111011
[7,1,4,5,6,8,3,2]=>1000011=>0111100
[8,5,6,7,1,4,3,2]=>1001011=>0110100
[7,6,8,5,1,4,3,2]=>1011011=>0100100
[6,8,7,5,1,4,3,2]=>0111011=>1000100
[2,6,7,1,4,5,3,8]=>0010010=>1101101
[3,5,1,7,4,6,8,2]=>0101001=>1010110
[7,1,5,6,4,8,3,2]=>1001011=>0110100
[7,1,6,5,4,8,3,2]=>1011011=>0100100
[2,7,6,1,4,5,3,8]=>0110010=>1001101
[5,7,6,8,1,4,3,2]=>0101011=>1010100
[7,8,6,5,1,4,3,2]=>0111011=>1000100
[4,3,1,6,5,8,7,2]=>1101011=>0010100
[5,3,1,2,4,8,7,6]=>1100011=>0011100
[5,3,6,2,1,8,7,4]=>1011011=>0100100
[5,3,7,2,1,4,6,8]=>1011000=>0100111
[5,3,7,2,8,4,1,6]=>1010110=>0101001
[7,2,4,5,8,3,1,6]=>1000110=>0111001
[7,2,4,5,1,3,6,8]=>1001000=>0110111
[6,2,4,5,1,8,7,3]=>1001011=>0110100
[3,1,4,5,2,8,7,6]=>1001011=>0110100
[1,6,4,5,2,8,7,3]=>0101011=>1010100
[3,7,4,5,1,2,6,8]=>0101000=>1010111
[3,7,4,5,8,2,1,6]=>0100110=>1011001
[1,7,4,2,6,3,5,8]=>0110100=>1001011
[8,7,4,5,2,1,6,3]=>1101101=>0010010
[6,3,7,1,8,4,2,5]=>1010110=>0101001
[5,7,4,1,6,3,2,8]=>0110110=>1001001
[1,7,4,8,6,3,2,5]=>0101110=>1010001
[5,7,4,8,6,3,1,2]=>0101110=>1010001
[4,8,3,5,6,7,1,2]=>0100010=>1011101
[1,8,3,5,6,7,2,4]=>0100010=>1011101
[4,8,1,5,6,7,2,3]=>0100010=>1011101
[4,1,3,5,6,7,2,8]=>1000010=>0111101
[5,8,4,3,6,1,2,7]=>0110100=>1001011
[5,3,8,4,1,7,2,6]=>1011010=>0100101
[1,5,8,4,6,7,3,2]=>0010011=>1101100
[1,4,8,3,6,7,5,2]=>0010011=>1101100
[4,3,8,2,1,7,5,6]=>1011010=>0100101
[3,8,4,2,6,1,5,7]=>0110100=>1001011
[1,8,2,5,6,7,4,3]=>0100011=>1011100
[3,8,1,5,6,7,4,2]=>0100011=>1011100
[3,8,2,5,6,7,1,4]=>0100010=>1011101
[8,2,1,5,6,7,4,3]=>1100011=>0011100
[8,1,3,5,6,7,4,2]=>1000011=>0111100
[7,1,4,3,6,2,5,8]=>1010100=>0101011
[7,8,4,3,6,2,1,5]=>0110110=>1001001
[4,3,1,8,5,7,6,2]=>1101011=>0010100
[4,3,1,6,8,7,5,2]=>1100111=>0011000
[6,3,1,8,2,7,4,5]=>1101010=>0010101
[6,3,5,8,2,7,1,4]=>1001010=>0110101
[7,5,4,8,6,2,1,3]=>1101110=>0010001
[7,1,4,8,6,2,3,5]=>1001100=>0110011
[7,5,4,1,6,2,3,8]=>1110100=>0001011
[7,6,4,5,8,1,3,2]=>1100101=>0011010
[1,6,4,5,8,2,3,7]=>0100100=>1011011
[7,3,6,1,8,2,4,5]=>1010100=>0101011
[1,7,6,5,8,3,4,2]=>0110101=>1001010
[1,8,5,3,6,7,4,2]=>0110011=>1001100
[8,3,5,2,1,7,4,6]=>1011010=>0100101
[8,4,1,5,6,7,3,2]=>1100011=>0011100
[8,4,2,5,6,7,1,3]=>1100010=>0011101
[4,1,8,5,6,7,3,2]=>1010011=>0101100
[1,2,8,5,6,7,3,4]=>0010010=>1101101
[4,2,1,5,6,7,3,8]=>1100010=>0011101
[1,5,3,8,6,7,4,2]=>0101011=>1010100
[1,4,5,8,6,7,3,2]=>0001011=>1110100
[4,3,5,8,1,7,2,6]=>1001010=>0110101
[3,5,4,8,6,1,2,7]=>0101100=>1010011
[1,4,8,5,6,7,2,3]=>0010010=>1101101
[3,4,8,5,6,7,1,2]=>0010010=>1101101
[2,7,1,5,6,3,4,8]=>0100100=>1011011
[2,7,1,4,3,6,5,8]=>0101010=>1010101
[4,3,7,2,5,6,8,1]=>1010001=>0101110
[2,6,3,1,4,5,8,7]=>0110001=>1001110
[3,7,1,4,2,6,8,5]=>0101001=>1010110
[3,7,1,5,6,2,8,4]=>0100101=>1011010
[4,7,1,5,6,8,2,3]=>0100010=>1011101
[8,5,2,6,7,3,1,4]=>1100110=>0011001
[8,4,2,6,3,7,1,5]=>1101010=>0010101
[8,4,2,3,5,7,1,6]=>1100010=>0011101
[4,7,3,2,5,6,1,8]=>0110010=>1001101
[5,3,4,6,2,8,1,7]=>1001010=>0110101
[5,3,7,4,2,8,1,6]=>1011010=>0100101
[6,4,7,2,3,8,1,5]=>1010010=>0101101
[6,5,7,2,8,3,1,4]=>1010110=>0101001
[5,3,7,2,4,8,6,1]=>1010011=>0101100
[2,6,5,1,8,3,4,7]=>0110100=>1001011
[8,7,6,1,4,5,2,3]=>1110010=>0001101
[8,7,6,1,3,2,5,4]=>1110101=>0001010
[8,7,2,4,3,1,6,5]=>1101101=>0010010
[8,7,4,5,1,6,2,3]=>1101010=>0010101
[8,5,6,4,1,7,2,3]=>1011010=>0100101
[8,5,6,3,1,2,7,4]=>1011001=>0100110
[8,4,6,2,3,1,7,5]=>1010101=>0101010
[8,3,5,4,2,1,7,6]=>1011101=>0100010
[5,7,3,4,2,1,8,6]=>0101101=>1010010
[6,7,4,2,3,1,8,5]=>0110101=>1001010
[6,7,5,3,1,2,8,4]=>0111001=>1000110
[6,7,5,4,1,8,2,3]=>0111010=>1000101
[10,3,1,2,4,5,6,7,8,9]=>110000000=>001111111
[10,4,1,2,3,5,6,7,8,9]=>110000000=>001111111
[5,10,1,2,3,4,6,7,8,9]=>010000000=>101111111
[10,6,1,2,3,4,5,7,8,9]=>110000000=>001111111
[10,7,1,2,3,4,5,6,8,9]=>110000000=>001111111
[8,10,1,2,3,4,5,6,7,9]=>010000000=>101111111
[2,11,1,3,4,5,6,7,8,9,10]=>0100000000=>1011111111
[2,3,10,1,4,5,6,7,8,9]=>001000000=>110111111
[11,3,1,2,4,5,6,7,8,9,10]=>1100000000=>0011111111
[4,3,1,10,2,5,6,7,8,9]=>110100000=>001011111
[11,4,1,2,3,5,6,7,8,9,10]=>1100000000=>0011111111
[5,4,1,2,10,3,6,7,8,9]=>110010000=>001101111
[5,11,1,2,3,4,6,7,8,9,10]=>0100000000=>1011111111
[5,6,1,2,3,10,4,7,8,9]=>010001000=>101110111
[11,6,1,2,3,4,5,7,8,9,10]=>1100000000=>0011111111
[7,6,1,2,3,4,10,5,8,9]=>110000100=>001111011
[11,7,1,2,3,4,5,6,8,9,10]=>1100000000=>0011111111
[8,7,1,2,3,4,5,10,6,9]=>110000010=>001111101
[8,11,1,2,3,4,5,6,7,9,10]=>0100000000=>1011111111
[8,9,1,2,3,4,5,6,10,7]=>010000001=>101111110
[11,9,1,2,3,4,5,6,7,8,10]=>1100000000=>0011111111
[6,2,4,3,8,7,5,1]=>1010111=>0101000
[7,3,5,4,1,8,6,2]=>1011011=>0100100
[5,2,7,1,3,4,8,6]=>1010001=>0101110
[2,6,5,7,3,1,4,8]=>0101100=>1010011
[2,6,5,7,3,1,8,4]=>0101101=>1010010
[6,3,1,4,7,8,5,2]=>1100011=>0011100
[6,8,2,1,3,4,5,7]=>0110000=>1001111
[3,7,1,8,4,5,2,6]=>0101010=>1010101
[6,3,2,4,7,5,8,1]=>1100101=>0011010
[6,3,2,4,7,5,1,8]=>1100110=>0011001
[4,2,1,6,3,7,5,8]=>1101010=>0010101
[4,2,1,6,3,7,8,5]=>1101001=>0010110
[7,4,3,5,8,6,1,2]=>1100110=>0011001
[2,7,6,8,3,1,4,5]=>0101100=>1010011
[7,4,3,5,8,6,2,1]=>1100111=>0011000
[4,2,1,7,3,8,6,5]=>1101011=>0010100
[4,2,1,3,7,8,6,5]=>1100011=>0011100
[5,8,1,7,4,3,6,2]=>0101101=>1010010
[5,8,1,7,4,3,2,6]=>0101110=>1010001
[3,7,8,6,2,1,4,5]=>0011100=>1100011
[4,2,1,8,3,5,6,7]=>1101000=>0010111
[4,2,1,3,6,7,5,8]=>1100010=>0011101
[4,2,1,3,7,5,6,8]=>1100100=>0011011
[4,2,1,3,6,8,7,5]=>1100011=>0011100
[7,3,2,4,8,6,5,1]=>1100111=>0011000
[4,2,1,6,3,8,7,5]=>1101011=>0010100
[4,2,1,7,3,5,6,8]=>1101000=>0010111
[3,6,7,5,2,1,4,8]=>0011100=>1100011
[3,6,7,5,2,1,8,4]=>0011101=>1100010
[7,3,4,2,6,8,5,1]=>1010011=>0101100
[4,8,6,2,7,3,5,1]=>0110101=>1001010
[7,3,4,2,6,8,1,5]=>1010010=>0101101
[3,6,7,5,2,4,8,1]=>0011001=>1100110
[3,6,7,5,2,4,1,8]=>0011010=>1100101
[4,2,1,7,3,6,5,8]=>1101010=>0010101
[4,2,1,7,3,6,8,5]=>1101001=>0010110
[3,7,6,8,4,2,5,1]=>0101101=>1010010
[5,8,1,7,4,2,6,3]=>0101101=>1010010
[3,7,8,6,2,4,5,1]=>0011001=>1100110
[4,2,1,3,8,6,7,5]=>1100101=>0011010
[4,2,1,3,7,6,5,8]=>1100110=>0011001
[4,2,1,3,5,7,6,8]=>1100010=>0011101
[4,2,1,3,5,8,6,7]=>1100010=>0011101
[4,8,1,7,3,6,5,2]=>0101011=>1010100
[4,7,8,6,3,5,2,1]=>0011011=>1100100
[4,2,1,8,3,7,6,5]=>1101011=>0010100
[4,2,1,3,5,6,8,7]=>1100001=>0011110
[7,8,2,4,1,3,6,5]=>0101001=>1010110
[2,6,1,5,4,7,8,3]=>0101001=>1010110
[4,6,3,5,8,7,1,2]=>0100110=>1011001
[3,5,6,1,4,8,7,2]=>0010011=>1101100
[2,3,6,8,4,1,5,7]=>0001100=>1110011
[2,7,5,1,8,3,4,6]=>0110100=>1001011
[4,7,5,2,1,3,6,8]=>0111000=>1000111
[3,5,6,2,4,1,7,8]=>0010100=>1101011
[2,5,6,1,4,8,3,7]=>0010010=>1101101
[6,7,8,4,1,5,3,2]=>0011011=>1100100
[7,1,6,8,4,5,3,2]=>1001011=>0110100
[7,4,6,5,2,8,1,3]=>1011010=>0100101
[7,1,5,6,4,2,3,8]=>1001100=>0110011
[5,7,4,6,8,1,3,2]=>0100101=>1011010
[5,7,8,1,4,6,3,2]=>0010011=>1101100
[8,1,5,7,4,6,3,2]=>1001011=>0110100
[1,8,4,6,7,5,3,2]=>0100111=>1011000
[6,1,8,4,7,5,3,2]=>1010111=>0101000
[4,5,8,6,1,7,3,2]=>0011011=>1100100
[4,8,5,1,6,7,3,2]=>0110011=>1001100
[8,1,4,5,6,7,3,2]=>1000011=>0111100
[5,6,7,1,4,2,3,8]=>0010100=>1101011
[8,4,2,6,1,5,7,3]=>1101001=>0010110
[4,8,5,2,1,6,7,3]=>0111001=>1000110
[5,1,8,4,2,6,3,7]=>1011010=>0100101
[1,8,4,6,2,5,3,7]=>0101010=>1010101
[6,1,5,2,3,4,7,8]=>1010000=>0101111
[8,3,1,4,6,2,5,7]=>1100100=>0011011
[3,1,8,2,5,6,4,7]=>1010010=>0101101
[3,5,1,8,2,6,4,7]=>0101010=>1010101
[3,5,1,2,8,4,7,6]=>0100101=>1011010
[2,3,5,8,6,1,7,4]=>0001101=>1110010
[8,2,4,3,6,7,1,5]=>1010010=>0101101
[3,2,8,5,7,1,6,4]=>1010101=>0101010
[3,6,2,8,5,1,7,4]=>0101101=>1010010
[6,2,1,8,4,7,5,3]=>1101011=>0010100
[2,8,7,1,4,6,5,3]=>0110011=>1001100
[8,2,7,1,5,4,6,3]=>1010101=>0101010
[7,2,5,3,6,8,1,4]=>1010010=>0101101
[7,3,1,5,6,2,4,8]=>1100100=>0011011
[3,7,5,1,6,2,4,8]=>0110100=>1001011
[2,7,3,6,5,8,1,4]=>0101010=>1010101
[8,7,2,4,1,6,5,3]=>1101011=>0010100
[1,8,7,2,3,6,5,4]=>0110011=>1001100
[1,7,8,2,6,4,3,5]=>0010110=>1101001
[1,7,3,8,2,6,4,5]=>0101010=>1010101
[1,2,7,3,6,4,5,8]=>0010100=>1101011
[7,1,5,8,3,2,4,6]=>1001100=>0110011
[1,6,2,8,4,3,7,5]=>0101101=>1010010
[1,3,8,7,2,4,6,5]=>0011001=>1100110
[1,8,3,7,2,5,4,6]=>0101010=>1010101
[8,1,4,7,3,2,5,6]=>1001100=>0110011
[4,7,8,1,3,2,5,6]=>0010100=>1101011
[7,1,4,2,3,5,6,8]=>1010000=>0101111
[8,2,1,4,7,3,5,6]=>1100100=>0011011
[2,1,3,8,4,6,7,5]=>1001001=>0110110
[1,2,3,4,8,5,7,6]=>0000101=>1111010
[2,4,7,5,6,8,3,1]=>0010011=>1101100
[2,4,8,7,5,6,3,1]=>0011011=>1100100
[2,5,3,8,4,7,6,1]=>0101011=>1010100
[2,8,5,7,3,6,4,1]=>0101011=>1010100
[3,1,8,5,2,7,6,4]=>1011011=>0100100
[2,8,6,3,4,5,7,1]=>0110001=>1001110
[2,5,7,3,4,8,6,1]=>0010011=>1101100
[8,3,7,6,1,4,5,2]=>1011001=>0100110
[3,1,7,8,2,5,6,4]=>1001001=>0110110
[7,3,8,5,1,6,4,2]=>1011011=>0100100
[7,5,1,2,3,4,8,6]=>1100001=>0011110
[4,8,1,5,2,7,3,6]=>0101010=>1010101
[4,1,2,5,3,8,7,6]=>1001011=>0110100
[4,3,6,8,7,5,1,2]=>1001110=>0110001
[5,4,1,8,2,7,6,3]=>1101011=>0010100
[6,4,8,1,2,5,3,7]=>1010010=>0101101
[6,7,3,1,4,8,5,2]=>0110011=>1001100
[5,4,1,6,8,2,7,3]=>1100101=>0011010
[5,4,7,1,2,8,6,3]=>1010011=>0101100
[6,7,4,1,2,8,3,5]=>0110010=>1001101
[6,5,1,2,3,7,8,4]=>1100001=>0011110
[6,5,1,2,3,4,8,7]=>1100001=>0011110
[6,7,4,1,2,5,3,8]=>0110010=>1001101
[2,4,6,3,5,7,1,8]=>0010010=>1101101
[1,4,6,3,7,2,5,8]=>0010100=>1101011
[8,6,2,5,3,1,7,4]=>1101101=>0010010
[8,2,3,4,5,1,7,6]=>1000101=>0111010
[1,8,3,4,2,7,5,6]=>0101010=>1010101
[2,8,3,4,1,6,7,5]=>0101001=>1010110
[8,7,2,3,1,6,5,4]=>1101011=>0010100
[3,8,2,4,6,1,7,5]=>0100101=>1011010
[7,8,2,4,3,1,6,5]=>0101101=>1010010
[4,5,8,2,3,1,7,6]=>0010101=>1101010
[5,1,4,3,7,2,6,8]=>1010100=>0101011
[6,1,3,5,7,2,4,8]=>1000100=>0111011
[2,1,4,7,5,3,6,8]=>1001100=>0110011
[7,1,3,6,2,5,4,8]=>1001010=>0110101
[8,1,3,6,2,4,7,5]=>1001001=>0110110
[2,1,8,3,7,5,4,6]=>1010110=>0101001
[7,1,8,2,5,6,3,4]=>1010010=>0101101
[6,1,5,8,2,7,3,4]=>1001010=>0110101
[4,5,2,8,1,6,7,3]=>0101001=>1010110
[6,2,5,8,1,4,7,3]=>1001001=>0110110
[3,2,8,5,1,6,7,4]=>1011001=>0100110
[8,2,7,1,4,6,5,3]=>1010011=>0101100
[1,3,8,2,5,7,4,6]=>0010010=>1101101
[2,8,7,1,6,4,5,3]=>0110101=>1001010
[3,8,7,1,5,6,4,2]=>0110011=>1001100
[3,4,8,5,6,1,7,2]=>0010101=>1101010
[8,3,7,4,1,6,5,2]=>1011011=>0100100
[1,4,8,6,2,7,3,5]=>0011010=>1100101
[8,4,5,7,1,6,3,2]=>1001011=>0110100
[3,5,6,8,4,1,7,2]=>0001101=>1110010
[6,2,3,1,5,4,7,8]=>1010100=>0101011
[7,2,3,1,4,6,5,8]=>1010010=>0101101
[8,2,3,1,4,5,7,6]=>1010001=>0101110
[8,5,1,3,2,4,7,6]=>1101001=>0010110
[7,5,1,3,2,6,4,8]=>1101010=>0010101
[2,6,1,4,5,3,7,8]=>0100100=>1011011
[3,6,4,1,5,2,7,8]=>0110100=>1001011
[4,5,6,1,3,2,7,8]=>0010100=>1101011
[4,5,7,1,2,6,3,8]=>0010010=>1101101
[3,7,4,1,2,6,5,8]=>0110010=>1001101
[6,7,1,4,2,5,3,8]=>0101010=>1010101
[2,7,1,3,5,6,4,8]=>0100010=>1011101
[8,6,1,2,4,3,7,5]=>1100101=>0011010
[2,8,1,3,4,6,7,5]=>0100001=>1011110
[7,8,1,2,5,3,6,4]=>0100101=>1011010
[3,8,4,1,2,5,7,6]=>0110001=>1001110
[1,2,6,7,5,3,8,4]=>0001101=>1110010
[1,7,5,3,2,8,4,6]=>0111010=>1000101
[1,6,7,5,3,8,4,2]=>0011011=>1100100
[1,6,5,7,2,3,8,4]=>0101001=>1010110
[1,3,8,2,6,5,7,4]=>0010101=>1101010
[1,2,5,7,6,3,4,8]=>0001100=>1110011
[1,3,4,8,2,5,7,6]=>0001001=>1110110
[1,5,7,6,2,3,4,8]=>0011000=>1100111
[1,5,3,8,2,6,4,7]=>0101010=>1010101
[1,4,8,3,2,5,7,6]=>0011001=>1100110
[1,4,8,3,5,7,6,2]=>0010011=>1101100
[1,2,4,8,3,5,7,6]=>0001001=>1110110
[1,3,8,4,2,6,7,5]=>0011001=>1100110
[1,4,8,2,3,5,7,6]=>0010001=>1101110
[6,5,7,3,8,2,4,1]=>1010101=>0101010
[4,2,6,7,5,8,3,1]=>1001011=>0110100
[6,7,5,2,1,8,4,3]=>0111011=>1000100
[3,4,8,7,5,2,1,6]=>0011110=>1100001
[1,7,5,2,8,4,6,3]=>0110101=>1001010
[5,6,8,3,1,7,2,4]=>0011010=>1100101
[6,1,4,8,3,2,7,5]=>1001101=>0110010
[3,4,7,1,8,6,2,5]=>0010110=>1101001
[3,4,6,8,2,1,5,7]=>0001100=>1110011
[3,8,2,5,6,1,4,7]=>0100100=>1011011
[3,5,2,8,6,4,1,7]=>0101110=>1010001
[4,2,5,7,3,8,6,1]=>1001011=>0110100
[7,4,2,5,3,8,1,6]=>1101010=>0010101
[3,1,2,8,5,6,4,7]=>1001010=>0110101
[5,2,1,6,8,3,4,7]=>1100100=>0011011
[5,2,6,8,4,1,3,7]=>1001100=>0110011
[1,5,6,8,3,4,2,7]=>0001010=>1110101
[4,5,8,1,6,3,2,7]=>0010110=>1101001
[4,5,1,6,8,3,2,7]=>0100110=>1011001
[4,5,7,3,8,2,6,1]=>0010101=>1101010
[6,4,3,7,8,2,5,1]=>1100101=>0011010
[6,4,3,1,7,8,2,5]=>1110010=>0001101
[4,5,3,1,7,8,2,6]=>0110010=>1001101
[7,1,3,5,4,8,2,6]=>1001010=>0110101
[7,5,2,8,1,4,3,6]=>1101010=>0010101
[5,7,3,8,4,6,1,2]=>0101010=>1010101
[1,4,5,7,3,8,6,2]=>0001011=>1110100
[4,6,3,7,8,5,2,1]=>0100111=>1011000
[5,3,6,7,8,4,2,1]=>1000111=>0111000
[1,5,3,6,7,8,4,2]=>0100011=>1011100
[4,6,1,7,3,8,5,2]=>0101011=>1010100
[6,3,7,1,8,4,5,2]=>1010101=>0101010
[6,7,2,4,8,1,5,3]=>0100101=>1011010
[2,6,1,4,7,3,8,5]=>0100101=>1011010
[3,2,5,6,7,8,1,4]=>1000010=>0111101
[5,2,3,6,7,8,4,1]=>1000011=>0111100
[6,7,1,3,2,8,4,5]=>0101010=>1010101
[6,2,7,1,3,4,8,5]=>1010001=>0101110
[5,2,1,7,3,8,4,6]=>1101010=>0010101
[6,4,2,7,1,8,3,5]=>1101010=>0010101
[4,2,6,3,7,8,1,5]=>1010010=>0101101
[4,2,6,3,7,8,5,1]=>1010011=>0101100
[6,7,3,8,2,4,5,1]=>0101001=>1010110
[3,6,2,7,4,1,8,5]=>0101101=>1010010
[6,7,3,2,1,4,8,5]=>0111001=>1000110
[7,1,8,3,4,2,5,6]=>1010100=>0101011
[7,2,4,1,8,3,5,6]=>1010100=>0101011
[7,2,4,8,6,1,3,5]=>1001100=>0110011
[7,3,4,8,6,2,1,5]=>1001110=>0110001
[3,5,7,2,1,8,6,4]=>0011011=>1100100
[6,7,8,3,2,5,1,4]=>0011010=>1100101
[6,3,7,8,2,5,4,1]=>1001011=>0110100
[2,6,7,4,8,5,3,1]=>0010111=>1101000
[6,2,4,7,1,8,5,3]=>1001011=>0110100
[4,6,2,7,1,8,5,3]=>0101011=>1010100
[1,7,4,8,5,2,6,3]=>0101101=>1010010
[1,3,7,8,5,2,6,4]=>0001101=>1110010
[2,5,7,8,1,6,3,4]=>0001010=>1110101
[6,3,7,1,8,2,5,4]=>1010101=>0101010
[1,6,4,7,8,2,5,3]=>0100101=>1011010
[2,5,6,1,7,8,4,3]=>0010011=>1101100
[5,6,1,2,7,8,4,3]=>0100011=>1011100
[6,7,2,1,8,5,3,4]=>0110110=>1001001
[6,7,2,8,5,4,1,3]=>0101110=>1010001
[1,6,7,4,8,5,3,2]=>0010111=>1101000
[1,8,2,4,6,3,5,7]=>0100100=>1011011
[1,5,7,4,3,6,2,8]=>0011010=>1100101
[1,8,4,5,3,6,2,7]=>0101010=>1010101
[1,8,5,3,4,7,2,6]=>0110010=>1001101
[1,8,2,4,6,3,7,5]=>0100101=>1011010
[1,8,2,5,4,6,7,3]=>0101001=>1010110
[3,6,2,7,1,4,5,8]=>0101000=>1010111
[1,4,7,5,2,6,8,3]=>0011001=>1100110
[4,6,5,3,7,1,8,2]=>0110101=>1001010
[4,2,3,8,6,7,1,5]=>1001010=>0110101
[5,2,4,8,1,3,7,6]=>1001001=>0110110
[6,2,5,4,8,3,7,1]=>1010101=>0101010
[6,4,3,5,8,2,7,1]=>1100101=>0011010
[5,2,3,4,8,1,6,7]=>1000100=>0111011
[3,5,2,4,7,1,6,8]=>0100100=>1011011
[5,3,4,8,1,6,2,7]=>1001010=>0110101
[4,5,3,7,1,6,2,8]=>0101010=>1010101
[6,2,4,8,5,1,3,7]=>1001100=>0110011
[7,6,3,8,5,1,2,4]=>1101100=>0010011
[4,2,6,7,3,8,1,5]=>1001010=>0110101
[1,5,7,4,2,8,6,3]=>0011011=>1100100
[1,3,7,2,8,6,4,5]=>0010110=>1101001
[1,4,3,7,8,6,2,5]=>0100110=>1011001
[1,5,3,6,8,2,7,4]=>0100101=>1011010
[4,3,6,5,7,8,1,2]=>1010010=>0101101
[4,2,3,5,6,8,1,7]=>1000010=>0111101
[4,2,6,7,3,8,5,1]=>1001011=>0110100
[3,2,5,6,8,1,7,4]=>1000101=>0111010
[6,4,5,2,3,8,7,1]=>1010011=>0101100
[8,4,6,7,5,2,3,1]=>1001101=>0110010
[4,6,5,2,3,1,8,7]=>0110101=>1001010
[6,4,2,5,3,1,8,7]=>1101101=>0010010
[6,4,2,5,3,8,7,1]=>1101011=>0010100
[8,6,4,7,5,2,3,1]=>1101101=>0010010
[8,6,2,7,4,5,3,1]=>1101011=>0010100
[6,4,2,5,8,7,3,1]=>1100111=>0011000
[4,6,2,5,3,8,7,1]=>0101011=>1010100
[4,6,5,2,3,8,7,1]=>0110011=>1001100
[6,8,7,4,5,2,3,1]=>0110101=>1001010
[4,8,6,7,5,2,3,1]=>0101101=>1010010
[6,8,4,7,5,2,3,1]=>0101101=>1010010
[6,8,2,7,4,5,3,1]=>0101011=>1010100
[8,6,4,7,2,5,3,1]=>1101011=>0010100
[8,6,2,4,7,5,3,1]=>1100111=>0011000
[6,8,2,4,7,5,3,1]=>0100111=>1011000
[4,8,2,6,7,5,3,1]=>0100111=>1011000
[2,8,4,6,7,5,3,1]=>0100111=>1011000
[2,8,6,7,4,5,3,1]=>0101011=>1010100
[6,8,7,2,4,5,3,1]=>0110011=>1001100
[2,6,4,5,8,7,3,1]=>0100111=>1011000
[2,6,4,8,7,5,3,1]=>0101111=>1010000
[4,6,2,8,7,5,3,1]=>0101111=>1010000
[8,2,4,6,7,5,3,1]=>1000111=>0111000
[6,2,4,8,7,5,3,1]=>1001111=>0110000
[4,2,6,8,7,5,3,1]=>1001111=>0110000
[4,2,6,5,8,7,3,1]=>1010111=>0101000
[6,2,4,5,8,7,3,1]=>1000111=>0111000
[8,2,6,7,4,5,3,1]=>1001011=>0110100
[8,6,7,2,4,5,3,1]=>1010011=>0101100
[6,4,5,2,8,7,3,1]=>1010111=>0101000
[4,2,3,6,8,7,5,1]=>1000111=>0111000
[6,4,5,8,7,2,3,1]=>1001101=>0110010
[8,6,7,4,2,5,3,1]=>1011011=>0100100
[8,4,6,7,2,5,3,1]=>1001011=>0110100
[6,4,8,7,2,5,3,1]=>1011011=>0100100
[6,2,8,7,4,5,3,1]=>1011011=>0100100
[6,4,8,7,5,2,3,1]=>1011101=>0100010
[4,6,8,7,5,2,3,1]=>0011101=>1100010
[4,6,5,8,7,2,3,1]=>0101101=>1010010
[2,1,6,8,7,4,5,3]=>1001101=>0110010
[2,6,8,7,4,5,3,1]=>0011011=>1100100
[2,4,8,6,7,5,3,1]=>0010111=>1101000
[4,2,8,6,7,5,3,1]=>1010111=>0101000
[6,2,8,4,7,5,3,1]=>1010111=>0101000
[8,2,6,4,7,5,3,1]=>1010111=>0101000
[6,4,8,2,7,5,3,1]=>1010111=>0101000
[4,6,8,2,7,5,3,1]=>0010111=>1101000
[2,6,8,4,7,5,3,1]=>0010111=>1101000
[4,6,8,7,2,5,3,1]=>0011011=>1100100
[4,6,5,8,2,7,3,1]=>0101011=>1010100
[2,1,6,8,4,7,5,3]=>1001011=>0110100
[2,1,8,6,4,7,5,3]=>1011011=>0100100
[6,8,7,4,2,5,3,1]=>0111011=>1000100
[2,8,6,4,7,5,3,1]=>0110111=>1001000
[4,8,6,2,7,5,3,1]=>0110111=>1001000
[9,8,7,3,6,2,5,1,4]=>11101010=>00010101
[9,8,7,6,3,5,1,2,4]=>11110100=>00001011
[9,4,8,3,7,2,6,1,5]=>10101010=>01010101
[9,8,4,7,3,6,1,2,5]=>11010100=>00101011
[9,8,7,2,4,6,1,3,5]=>11100100=>00011011
[9,8,7,4,6,1,2,3,5]=>11101000=>00010111
[5,9,4,8,3,7,1,2,6]=>01010100=>10101011
[9,5,8,2,4,7,1,3,6]=>10100100=>01011011
[9,5,8,4,7,1,2,3,6]=>10101000=>01010111
[9,8,3,5,7,1,2,4,6]=>11001000=>00110111
[9,8,5,7,1,2,3,4,6]=>11010000=>00101111
[6,9,3,5,8,1,2,4,7]=>01001000=>10110111
[6,9,5,8,1,2,3,4,7]=>01010000=>10101111
[9,2,4,6,8,1,3,5,7]=>10001000=>01110111
[9,4,6,8,1,2,3,5,7]=>10010000=>01101111
[9,6,8,1,2,3,4,5,7]=>10100000=>01011111
[3,5,7,9,1,2,4,6,8]=>00010000=>11101111
[5,7,9,1,2,3,4,6,8]=>00100000=>11011111
[7,9,1,2,3,4,5,6,8]=>01000000=>10111111
[10,9,8,7,6,5,2,4,1,3]=>111111010=>000000101
[10,9,8,7,3,6,2,5,1,4]=>111101010=>000010101
[10,9,8,7,6,3,5,1,2,4]=>111110100=>000001011
[10,9,4,8,3,7,2,6,1,5]=>110101010=>001010101
[10,9,8,4,7,3,6,1,2,5]=>111010100=>000101011
[10,9,8,7,2,4,6,1,3,5]=>111100100=>000011011
[10,9,8,7,4,6,1,2,3,5]=>111101000=>000010111
[10,5,9,4,8,3,7,1,2,6]=>101010100=>010101011
[10,9,5,8,2,4,7,1,3,6]=>110100100=>001011011
[10,9,5,8,4,7,1,2,3,6]=>110101000=>001010111
[10,9,8,3,5,7,1,2,4,6]=>111001000=>000110111
[10,9,8,5,7,1,2,3,4,6]=>111010000=>000101111
[6,10,5,9,2,4,8,1,3,7]=>010100100=>101011011
[6,10,5,9,4,8,1,2,3,7]=>010101000=>101010111
[10,3,6,9,2,5,8,1,4,7]=>100100100=>011011011
[10,6,9,3,5,8,1,2,4,7]=>101001000=>010110111
[10,6,9,5,8,1,2,3,4,7]=>101010000=>010101111
[10,9,2,4,6,8,1,3,5,7]=>110001000=>001110111
[10,9,4,6,8,1,2,3,5,7]=>110010000=>001101111
[10,9,6,8,1,2,3,4,5,7]=>110100000=>001011111
[4,7,10,3,6,9,1,2,5,8]=>001001000=>110110111
[7,10,2,4,6,9,1,3,5,8]=>010001000=>101110111
[7,10,4,6,9,1,2,3,5,8]=>010010000=>101101111
[7,10,6,9,1,2,3,4,5,8]=>010100000=>101011111
[10,3,5,7,9,1,2,4,6,8]=>100010000=>011101111
[10,5,7,9,1,2,3,4,6,8]=>100100000=>011011111
[10,7,9,1,2,3,4,5,6,8]=>101000000=>010111111
[4,6,8,10,1,2,3,5,7,9]=>000100000=>111011111
[6,8,10,1,2,3,4,5,7,9]=>001000000=>110111111
[4,2,5,6,3,8,1,7]=>1001010=>0110101
[6,2,5,7,4,8,3,1]=>1001011=>0110100
[8,5,2,1,4,7,6,3]=>1110011=>0001100
[6,7,3,2,5,8,4,1]=>0110011=>1001100
[3,2,6,4,8,1,5,7]=>1010100=>0101011
[2,3,6,4,7,8,5,1]=>0010011=>1101100
[7,5,1,8,3,4,6,2]=>1101001=>0010110
[5,7,8,2,6,3,4,1]=>0010101=>1101010
[7,1,6,3,5,8,4,2]=>1010011=>0101100
[6,3,1,7,8,4,5,2]=>1100101=>0011010
[5,3,6,7,4,1,8,2]=>1001101=>0110010
[7,3,1,2,5,8,6,4]=>1100011=>0011100
[1,6,3,5,2,4,8,7]=>0101001=>1010110
[3,4,8,2,7,5,1,6]=>0010110=>1101001
[6,3,2,8,5,7,4,1]=>1101011=>0010100
[3,8,4,7,2,5,6,1]=>0101001=>1010110
[2,4,8,1,5,3,7,6]=>0010101=>1101010
[3,4,8,1,6,2,7,5]=>0010101=>1101010
[1,8,4,6,7,3,5,2]=>0100101=>1011010
[8,1,6,3,4,5,7,2]=>1010001=>0101110
[7,6,5,4,1,2,8,3]=>1111001=>0000110
[5,7,6,8,3,4,2,1]=>0101011=>1010100
[2,8,1,6,5,7,4,3]=>0101011=>1010100
[4,6,8,2,5,3,7,1]=>0010101=>1101010
[5,2,3,7,6,1,8,4]=>1001101=>0110010
[8,1,2,4,6,7,3,5]=>1000010=>0111101
[5,2,3,7,4,8,6,1]=>1001011=>0110100
[5,2,6,8,4,3,1,7]=>1001110=>0110001
[7,8,1,5,4,3,6,2]=>0101101=>1010010
[7,2,4,8,5,3,6,1]=>1001101=>0110010
[3,7,5,1,8,4,6,2]=>0110101=>1001010
[2,7,8,5,4,6,1,3]=>0011010=>1100101
[5,7,4,3,8,6,2,1]=>0110111=>1001000
[4,8,1,6,3,5,2,7]=>0101010=>1010101
[8,3,1,7,4,2,5,6]=>1101100=>0010011
[3,1,8,2,4,5,7,6]=>1010001=>0101110
[8,1,3,7,6,2,4,5]=>1001100=>0110011
[2,3,6,8,7,1,4,5]=>0001100=>1110011
[4,3,2,8,5,7,1,6]=>1101010=>0010101
[3,6,4,2,8,5,7,1]=>0110101=>1001010
[4,7,3,2,5,1,8,6]=>0110101=>1001010
[3,2,4,7,5,8,6,1]=>1001011=>0110100
[4,2,3,8,6,5,1,7]=>1001110=>0110001
[2,4,3,5,1,8,6,7]=>0101010=>1010101
[3,2,8,1,4,6,5,7]=>1010010=>0101101
[3,7,8,5,6,1,2,4]=>0010100=>1101011
[3,6,1,8,4,7,2,5]=>0101010=>1010101
[3,1,6,8,4,7,2,5]=>1001010=>0110101
[4,1,6,8,3,2,7,5]=>1001101=>0110010
[4,6,1,8,3,2,7,5]=>0101101=>1010010
[4,7,8,1,3,2,6,5]=>0010101=>1101010
[4,7,8,3,1,2,6,5]=>0011001=>1100110
[2,7,8,3,4,6,5,1]=>0010011=>1101100
[4,7,8,2,1,3,6,5]=>0011001=>1100110
[4,6,1,8,2,3,7,5]=>0101001=>1010110
[4,1,6,8,2,3,7,5]=>1001001=>0110110
[4,5,1,2,8,3,7,6]=>0100101=>1011010
[4,5,2,1,8,3,7,6]=>0110101=>1001010
[4,6,2,8,1,3,7,5]=>0101001=>1010110
[3,6,2,8,4,7,1,5]=>0101010=>1010101
[2,3,6,8,4,7,5,1]=>0001011=>1110100
[3,2,6,8,4,7,1,5]=>1001010=>0110101
[4,2,6,8,3,1,7,5]=>1001101=>0110010
[4,2,5,1,8,3,7,6]=>1010101=>0101010
[4,1,2,5,8,3,7,6]=>1000101=>0111010
[5,1,2,4,3,8,7,6]=>1001011=>0110100
[5,2,4,1,3,8,7,6]=>1010011=>0101100
[4,2,5,3,8,1,7,6]=>1010101=>0101010
[3,2,5,4,8,7,1,6]=>1010110=>0101001
[3,5,2,4,8,7,1,6]=>0100110=>1011001
[5,4,2,1,3,8,7,6]=>1110011=>0001100
[5,1,4,2,3,8,7,6]=>1010011=>0101100
[5,4,1,3,2,8,7,6]=>1101011=>0010100
[5,4,3,1,2,8,7,6]=>1110011=>0001100
[4,5,3,1,8,2,7,6]=>0110101=>1001010
[4,5,1,3,8,2,7,6]=>0100101=>1011010
[3,1,5,4,8,7,2,6]=>1010110=>0101001
[3,5,1,4,8,7,2,6]=>0100110=>1011001
[3,5,4,1,8,7,2,6]=>0110110=>1001001
[3,6,5,8,7,1,2,4]=>0101100=>1010011
[2,5,6,8,7,3,4,1]=>0001101=>1110010
[3,4,5,1,8,7,2,6]=>0010110=>1101001
[3,4,1,5,8,7,2,6]=>0100110=>1011001
[4,1,3,5,8,2,7,6]=>1000101=>0111010
[4,3,6,8,2,1,7,5]=>1001101=>0110010
[2,4,6,8,3,7,5,1]=>0001011=>1110100
[3,4,5,2,8,7,1,6]=>0010110=>1101001
[5,3,1,4,2,8,7,6]=>1101011=>0010100
[5,1,3,4,2,8,7,6]=>1001011=>0110100
[5,1,3,2,4,8,7,6]=>1010011=>0101100
[5,3,2,1,4,8,7,6]=>1110011=>0001100
[4,3,2,5,8,1,7,6]=>1100101=>0011010
[3,4,2,5,8,7,1,6]=>0100110=>1011001
[3,2,4,5,8,7,1,6]=>1000110=>0111001
[4,2,3,5,8,1,7,6]=>1000101=>0111010
[5,2,3,1,4,8,7,6]=>1010011=>0101100
[5,2,1,3,4,8,7,6]=>1100011=>0011100
[5,1,2,3,4,8,7,6]=>1000011=>0111100
[8,6,2,5,4,1,3,7]=>1101100=>0010011
[6,5,7,4,2,8,3,1]=>1011011=>0100100
[6,7,5,3,8,2,4,1]=>0110101=>1001010
[8,2,1,6,3,4,5,7]=>1101000=>0010111
[8,3,5,6,2,4,1,7]=>1001010=>0110101
[8,6,2,1,3,5,4,7]=>1110010=>0001101
[8,1,2,3,4,6,5,7]=>1000010=>0111101
[6,2,3,7,8,4,5,1]=>1000101=>0111010
[7,5,8,2,6,3,4,1]=>1010101=>0101010
[7,3,1,6,5,8,4,2]=>1101011=>0010100
[1,5,6,7,3,4,8,2]=>0001001=>1110110
[6,7,8,2,1,4,5,3]=>0011001=>1100110
[8,4,7,6,2,1,3,5]=>1011100=>0100011
[5,3,8,4,7,2,6,1]=>1010101=>0101010
[8,1,3,7,6,4,2,5]=>1001110=>0110001
[5,3,1,7,8,6,2,4]=>1100110=>0011001
[3,5,8,2,7,1,6,4]=>0010101=>1101010
[6,2,8,5,3,1,7,4]=>1011101=>0100010
[8,2,6,4,7,1,3,5]=>1010100=>0101011
[3,4,2,8,5,1,7,6]=>0101101=>1010010
[3,8,6,5,2,1,7,4]=>0111101=>1000010
[8,3,7,4,2,5,6,1]=>1011001=>0100110
[4,8,5,7,2,1,3,6]=>0101100=>1010011
[3,4,1,8,2,6,7,5]=>0101001=>1010110
[8,4,6,3,7,1,5,2]=>1010101=>0101010
[6,8,3,4,1,5,7,2]=>0101001=>1010110
[5,1,7,6,2,8,4,3]=>1011011=>0100100
[6,8,2,5,7,4,1,3]=>0100110=>1011001
[2,8,5,6,7,1,3,4]=>0100100=>1011011
[2,5,7,6,3,1,8,4]=>0011101=>1100010
[4,2,8,3,1,5,6,7]=>1011000=>0100111
[2,5,7,3,8,4,6,1]=>0010101=>1101010
[4,2,7,1,8,5,3,6]=>1010110=>0101001
[4,2,1,8,7,5,6,3]=>1101101=>0010010
[8,3,6,7,1,5,4,2]=>1001011=>0110100
[1,3,7,5,8,6,4,2]=>0010111=>1101000
[5,7,8,4,3,1,6,2]=>0011101=>1100010
[2,7,4,5,8,3,6,1]=>0100101=>1011010
[3,5,7,1,4,8,6,2]=>0010011=>1101100
[7,2,8,5,1,4,6,3]=>1011001=>0100110
[1,6,5,3,8,4,2,7]=>0110110=>1001001
[5,7,4,8,3,6,2,1]=>0101011=>1010100
[4,8,6,1,3,5,2,7]=>0110010=>1001101
[1,8,3,2,4,7,5,6]=>0110010=>1001101
[8,4,3,2,5,7,1,6]=>1110010=>0001101
[3,6,4,8,2,5,7,1]=>0101001=>1010110
[4,3,7,2,5,8,1,6]=>1010010=>0101101
[3,2,4,7,8,5,6,1]=>1000101=>0111010
[2,6,4,3,8,5,1,7]=>0110110=>1001001
[3,8,2,1,6,4,5,7]=>0110100=>1001011
[8,2,1,3,4,5,7,6]=>1100001=>0011110
[4,6,8,3,2,1,5,7]=>0011100=>1100011
[3,2,6,8,5,4,1,7]=>1001110=>0110001
[7,3,8,2,5,4,1,6]=>1010110=>0101001
[4,2,5,3,8,7,6,1]=>1010111=>0101000
[4,8,2,6,5,3,1,7]=>0101110=>1010001
[2,6,8,5,4,1,3,7]=>0011100=>1100011
[3,1,8,6,5,4,2,7]=>1011110=>0100001
[5,4,8,7,3,2,6,1]=>1011101=>0100010
[6,4,8,3,7,2,5,1]=>1010101=>0101010
[4,7,3,6,2,1,8,5]=>0101101=>1010010
[5,4,3,7,1,8,2,6]=>1101010=>0010101
[7,3,8,5,1,4,2,6]=>1011010=>0100101
[5,4,8,7,6,2,1,3]=>1011110=>0100001
[3,8,1,5,7,4,6,2]=>0100101=>1011010
[4,8,5,7,3,1,6,2]=>0101101=>1010010
[1,5,4,8,3,7,6,2]=>0101011=>1010100
[4,8,3,6,7,1,5,2]=>0100101=>1011010
[4,7,8,3,1,6,5,2]=>0011011=>1100100
[8,7,5,3,6,4,2,1]=>1110111=>0001000
[4,6,1,3,8,7,5,2]=>0100111=>1011000
[6,8,2,1,7,4,5,3]=>0110101=>1001010
[3,7,1,6,4,2,8,5]=>0101101=>1010010
[3,1,2,7,5,6,8,4]=>1001001=>0110110
[3,6,1,2,7,5,8,4]=>0100101=>1011010
[3,7,6,2,5,8,1,4]=>0110010=>1001101
[3,6,2,5,8,7,4,1]=>0100111=>1011000
[8,5,2,3,6,7,4,1]=>1100011=>0011100
[4,7,2,6,3,8,1,5]=>0101010=>1010101
[6,3,2,4,8,7,5,1]=>1100111=>0011000
[3,7,2,4,6,1,8,5]=>0100101=>1011010
[5,3,7,2,8,1,4,6]=>1010100=>0101011
[6,3,2,8,7,5,1,4]=>1101110=>0010001
[7,3,8,2,6,5,1,4]=>1010110=>0101001
[6,4,8,7,2,5,1,3]=>1011010=>0100101
[2,5,4,8,1,7,6,3]=>0101011=>1010100
[5,2,8,1,7,6,3,4]=>1010110=>0101001
[6,2,1,3,8,7,5,4]=>1100111=>0011000
[3,6,1,8,7,5,2,4]=>0101110=>1010001
[5,6,1,2,8,7,4,3]=>0100111=>1011000
[7,5,2,8,1,6,4,3]=>1101011=>0010100
[2,7,6,8,1,5,4,3]=>0101011=>1010100
[7,8,5,1,6,2,4,3]=>0110101=>1001010
[7,4,8,6,1,2,5,3]=>1011001=>0100110
[7,2,1,8,3,6,5,4]=>1101011=>0010100
[5,8,7,1,6,4,3,2]=>0110111=>1001000
[7,6,5,4,3,2,9,8,1]=>11111011=>00000100
[11,9,8,7,6,5,4,3,2,1,10]=>1111111110=>0000000001
[10,7,6,5,4,3,2,1,9,8]=>111111101=>000000010
[9,6,5,4,3,2,8,1,7]=>11111010=>00000101
[9,7,5,4,3,2,1,8,6]=>11111101=>00000010
[8,5,4,3,7,2,1,6]=>1110110=>0001001
[6,5,4,8,3,2,7,1]=>1101101=>0010010
[7,6,5,4,3,9,2,8,1]=>11110101=>00001010
[7,6,4,3,2,8,5,1]=>1111011=>0000100
[8,6,5,4,3,2,9,7,1]=>11111011=>00000100
[8,7,6,5,4,3,2,10,9,1]=>111111011=>000000100
[10,9,8,7,6,5,4,3,2,11,1]=>1111111101=>0000000010
[7,3,1,4,8,2,5,6]=>1100100=>0011011
[7,4,1,2,5,8,3,6]=>1100010=>0011101
[6,7,4,2,5,1,3,8]=>0110100=>1001011
[5,7,2,4,6,8,1,3]=>0100010=>1011101
[4,7,5,1,6,2,8,3]=>0110101=>1001010
[5,7,4,6,3,1,8,2]=>0101101=>1010010
[7,5,1,4,3,2,8,6]=>1101101=>0010010
[8,6,4,2,3,7,5,1]=>1110011=>0001100
[6,4,7,1,3,8,5,2]=>1010011=>0101100
[5,4,2,7,3,1,6,8]=>1101100=>0010011
[4,5,1,2,7,6,8,3]=>0100101=>1011010
[5,4,6,8,3,1,2,7]=>1001100=>0110011
[6,4,8,1,3,7,2,5]=>1010010=>0101101
[4,6,1,3,8,5,2,7]=>0100110=>1011001
[1,3,8,4,5,7,2,6]=>0010010=>1101101
[2,6,7,4,5,3,1,8]=>0010110=>1101001
[2,6,8,4,3,5,1,7]=>0011010=>1100101
[1,3,7,4,2,8,5,6]=>0011010=>1100101
[4,6,1,3,7,2,5,8]=>0100100=>1011011
[7,5,8,6,2,1,3,4]=>1011100=>0100011
[2,8,1,3,6,5,4,7]=>0100110=>1011001
[2,8,7,3,5,4,1,6]=>0110110=>1001001
[3,4,2,6,8,7,1,5]=>0100110=>1011001
[7,4,2,3,6,1,8,5]=>1100101=>0011010
[8,4,2,3,6,5,7,1]=>1100101=>0011010
[7,3,8,4,1,2,6,5]=>1011001=>0100110
[6,8,3,2,7,1,5,4]=>0110101=>1001010
[2,8,5,6,3,7,1,4]=>0101010=>1010101
[7,4,2,5,8,1,6,3]=>1100101=>0011010
[2,7,8,3,4,5,1,6]=>0010010=>1101101
[3,7,1,2,4,6,5,8]=>0100010=>1011101
[7,5,6,8,2,1,4,3]=>1001101=>0110010
[3,1,6,5,2,7,4,8]=>1011010=>0100101
[2,8,6,5,3,4,1,7]=>0111010=>1000101
[1,7,2,3,5,6,8,4]=>0100001=>1011110
[3,7,4,2,1,5,6,8]=>0111000=>1000111
[3,4,6,2,8,5,7,1]=>0010101=>1101010
[4,2,1,7,5,8,3,6]=>1101010=>0010101
[4,7,2,6,5,1,3,8]=>0101100=>1010011
[3,7,4,1,2,5,8,6]=>0110001=>1001110
[4,7,1,6,5,2,8,3]=>0101101=>1010010
[4,7,3,6,5,1,8,2]=>0101101=>1010010
[4,3,7,1,6,8,5,2]=>1010011=>0101100
[4,2,1,7,5,6,8,3]=>1101001=>0010110
[3,2,4,8,6,7,1,5]=>1001010=>0110101
[4,2,6,8,7,3,1,5]=>1001110=>0110001
[3,4,6,1,8,5,2,7]=>0010110=>1101001
[4,1,6,7,5,8,2,3]=>1001010=>0110101
[4,3,6,7,5,1,2,8]=>1001100=>0110011
[4,3,7,1,6,8,2,5]=>1010010=>0101101
[4,3,7,5,6,8,2,1]=>1010011=>0101100
[4,1,7,3,6,5,2,8]=>1010110=>0101001
[2,8,7,4,5,3,1,6]=>0110110=>1001001
[2,8,7,4,3,5,1,6]=>0111010=>1000101
[3,8,1,4,2,6,5,7]=>0101010=>1010101
[4,1,7,3,6,2,5,8]=>1010100=>0101011
[5,8,7,6,1,2,4,3]=>0111001=>1000110
[5,8,7,6,2,1,3,4]=>0111100=>1000011
[4,1,7,2,6,8,5,3]=>1010011=>0101100
[4,2,7,3,6,1,8,5]=>1010101=>0101010
[4,2,7,3,6,5,8,1]=>1010101=>0101010
[3,8,2,4,5,6,7,1]=>0100001=>1011110
[3,8,2,4,1,6,7,5]=>0101001=>1010110
[3,8,5,6,2,4,1,7]=>0101010=>1010101
[2,8,6,5,3,7,1,4]=>0111010=>1000101
[3,8,6,5,1,4,7,2]=>0111001=>1000110
[3,8,2,1,4,6,7,5]=>0110001=>1001110
[3,8,2,5,4,6,7,1]=>0101001=>1010110
[4,2,7,5,6,3,8,1]=>1010101=>0101010
[4,2,7,5,6,1,8,3]=>1010101=>0101010
[4,2,6,7,5,3,1,8]=>1001110=>0110001
[3,2,6,1,4,5,8,7]=>1010001=>0101110
[2,8,7,3,4,5,1,6]=>0110010=>1001101
[3,8,1,2,4,6,5,7]=>0100010=>1011101
[5,8,7,6,1,3,4,2]=>0111001=>1000110
[5,8,7,6,2,3,4,1]=>0111001=>1000110
[4,1,7,5,6,2,3,8]=>1010100=>0101011
[3,8,1,5,2,6,4,7]=>0101010=>1010101
[2,8,7,5,3,4,1,6]=>0111010=>1000101
[2,8,7,5,4,3,1,6]=>0111110=>1000001
[4,1,7,5,6,3,2,8]=>1010110=>0101001
[5,8,7,6,1,3,2,4]=>0111010=>1000101
[5,8,7,6,4,1,2,3]=>0111100=>1000011
[5,4,2,3,7,6,8,1]=>1100101=>0011010
[7,4,3,5,2,8,1,6]=>1101010=>0010101
[8,4,3,7,5,1,6,2]=>1101101=>0010010
[8,4,7,2,5,1,6,3]=>1010101=>0101010
[7,4,6,2,3,5,8,1]=>1010001=>0101110
[5,1,7,2,4,6,8,3]=>1010001=>0101110
[4,5,7,1,2,6,8,3]=>0010001=>1101110
[5,4,1,7,3,6,8,2]=>1101001=>0010110
[3,6,4,7,5,2,8,1]=>0101101=>1010010
[3,4,7,6,2,5,8,1]=>0011001=>1100110
[4,7,5,6,1,3,8,2]=>0101001=>1010110
[5,7,6,4,3,1,8,2]=>0111101=>1000010
[5,7,6,3,1,4,8,2]=>0111001=>1000110
[7,5,2,3,4,8,1,6]=>1100010=>0011101
[8,7,5,3,4,1,6,2]=>1110101=>0001010
[6,7,1,3,8,4,2,5]=>0100110=>1011001
[7,6,1,3,4,8,5,2]=>1100011=>0011100
[3,6,5,2,7,8,1,4]=>0110010=>1001101
[3,2,8,6,7,1,4,5]=>1010100=>0101011
[4,8,3,6,5,2,1,7]=>0101110=>1010001
[1,8,6,5,4,2,3,7]=>0111100=>1000011
[1,8,7,2,3,5,4,6]=>0110010=>1001101
[1,8,7,2,5,3,4,6]=>0110100=>1001011
[3,6,8,5,1,2,4,7]=>0011000=>1100111
[3,7,5,1,8,2,6,4]=>0110101=>1001010
[7,1,2,8,3,5,6,4]=>1001001=>0110110
[6,1,7,8,2,5,3,4]=>1001010=>0110101
[6,7,5,2,8,1,4,3]=>0110101=>1001010
[7,1,4,5,8,6,2,3]=>1000110=>0111001
[5,7,6,4,2,8,1,3]=>0111010=>1000101
[7,5,6,1,2,8,4,3]=>1010011=>0101100
[4,1,3,7,8,6,2,5]=>1000110=>0111001
[5,1,4,3,6,8,7,2]=>1010011=>0101100
[4,5,7,6,8,2,1,3]=>0010110=>1101001
[5,7,6,8,4,2,1,3]=>0101110=>1010001
[5,1,6,8,4,2,7,3]=>1001101=>0110010
[7,4,8,2,3,6,5,1]=>1010011=>0101100
[5,6,8,4,7,3,2,1]=>0010111=>1101000
[6,4,7,8,5,2,1,3]=>1001110=>0110001
[3,6,4,8,5,1,2,7]=>0101100=>1010011
[3,7,4,8,1,2,5,6]=>0101000=>1010111
[7,4,3,8,2,6,5,1]=>1101011=>0010100
[7,6,8,3,2,5,4,1]=>1011011=>0100100
[8,7,1,3,5,4,6,2]=>1100101=>0011010
[7,1,8,3,4,2,6,5]=>1010101=>0101010
[7,6,8,3,1,4,5,2]=>1011001=>0100110
[3,1,4,8,2,5,7,6]=>1001001=>0110110
[4,8,5,2,1,3,6,7]=>0111000=>1000111
[5,8,2,6,3,1,4,7]=>0101100=>1010011
[6,8,2,3,7,4,1,5]=>0100110=>1011001
[7,8,2,3,4,6,5,1]=>0100011=>1011100
[8,1,7,2,4,5,3,6]=>1010010=>0101101
[8,1,3,6,2,5,4,7]=>1001010=>0110101
[7,2,1,6,3,5,4,8]=>1101010=>0010101
[2,7,1,6,3,5,4,8]=>0101010=>1010101
[2,7,1,5,4,3,6,8]=>0101100=>1010011
[7,2,1,5,4,3,6,8]=>1101100=>0010011
[8,1,3,5,4,2,6,7]=>1001100=>0110011
[8,1,5,3,4,2,6,7]=>1010100=>0101011
[8,1,5,6,2,3,7,4]=>1001001=>0110110
[8,1,4,5,3,2,6,7]=>1001100=>0110011
[8,1,4,3,5,2,6,7]=>1010100=>0101011
[7,2,1,4,5,3,6,8]=>1100100=>0011011
[2,7,1,4,5,3,6,8]=>0100100=>1011011
[2,6,3,1,5,4,7,8]=>0110100=>1001011
[6,3,2,1,5,4,7,8]=>1110100=>0001011
[7,3,1,4,5,2,6,8]=>1100100=>0011011
[7,3,1,5,4,2,6,8]=>1101100=>0010011
[7,3,1,6,2,5,4,8]=>1101010=>0010101
[3,7,1,6,2,5,4,8]=>0101010=>1010101
[3,7,1,4,5,2,6,8]=>0100100=>1011011
[3,6,2,1,5,4,7,8]=>0110100=>1001011
[2,3,6,1,5,4,7,8]=>0010100=>1101011
[3,5,2,4,1,6,7,8]=>0101000=>1010111
[6,3,4,1,5,2,7,8]=>1010100=>0101011
[6,2,4,1,5,3,7,8]=>1010100=>0101011
[2,6,4,1,5,3,7,8]=>0110100=>1001011
[2,6,5,1,3,7,4,8]=>0110010=>1001101
[6,2,5,1,3,7,4,8]=>1010010=>0101101
[6,5,2,1,3,7,4,8]=>1110010=>0001101
[7,6,1,2,4,5,3,8]=>1100010=>0011101
[6,7,1,2,8,3,5,4]=>0100101=>1011010
[6,7,1,2,5,4,3,8]=>0100110=>1011001
[5,6,2,1,3,7,4,8]=>0110010=>1001101
[5,2,6,1,3,7,4,8]=>1010010=>0101101
[2,4,6,1,5,3,7,8]=>0010100=>1101011
[4,7,1,3,5,2,6,8]=>0100100=>1011011
[4,7,1,5,3,2,6,8]=>0101100=>1010011
[5,7,1,4,2,6,3,8]=>0101010=>1010101
[5,7,1,6,2,3,8,4]=>0101001=>1010110
[5,6,3,1,2,7,4,8]=>0110010=>1001101
[4,2,5,3,1,6,7,8]=>1011000=>0100111
[5,3,6,1,2,7,4,8]=>1010010=>0101101
[3,4,6,1,5,2,7,8]=>0010100=>1101011
[6,5,1,8,7,3,4,2]=>1101101=>0010010
[8,2,7,5,4,1,3,6]=>1011100=>0100011
[6,8,5,2,3,4,1,7]=>0110010=>1001101
[2,6,8,7,1,5,3,4]=>0011010=>1100101
[8,5,6,2,7,1,4,3]=>1010101=>0101010
[6,5,1,2,7,8,4,3]=>1100011=>0011100
[4,7,6,1,5,3,8,2]=>0110101=>1001010
[5,7,6,4,1,3,8,2]=>0111001=>1000110
[7,6,2,4,5,3,8,1]=>1100101=>0011010
[6,1,7,5,3,8,4,2]=>1011011=>0100100
[8,6,7,5,3,1,4,2]=>1011101=>0100010
[8,5,2,7,1,6,4,3]=>1101011=>0010100
[7,6,1,5,3,8,4,2]=>1101011=>0010100
[5,6,2,4,7,8,1,3]=>0100010=>1011101
[3,4,6,1,7,8,5,2]=>0010011=>1101100
[3,4,8,6,7,1,5,2]=>0010101=>1101010
[4,8,5,6,7,2,3,1]=>0100101=>1011010
[5,8,6,4,1,2,7,3]=>0111001=>1000110
[5,8,6,1,7,2,4,3]=>0110101=>1001010
[5,8,7,3,2,6,4,1]=>0111011=>1000100
[5,8,1,7,2,6,4,3]=>0101011=>1010100
[8,1,5,7,2,6,4,3]=>1001011=>0110100
[8,1,7,2,5,6,3,4]=>1010010=>0101101
[6,8,7,2,5,1,3,4]=>0110100=>1001011
[5,8,7,2,1,6,3,4]=>0111010=>1000101
[4,8,1,5,2,6,7,3]=>0101001=>1010110
[3,7,8,5,1,6,2,4]=>0011010=>1100101
[6,5,2,7,8,1,4,3]=>1100101=>0011010
[7,1,2,8,5,6,3,4]=>1001010=>0110101
[8,7,2,1,5,6,3,4]=>1110010=>0001101
[8,6,7,1,5,2,3,4]=>1010100=>0101011
[6,1,7,8,5,2,3,4]=>1001100=>0110011
[7,5,6,2,1,8,4,3]=>1011011=>0100100
[8,7,5,2,1,6,4,3]=>1111011=>0000100
[7,1,3,5,8,6,2,4]=>1000110=>0111001
[5,1,3,4,6,8,7,2]=>1000011=>0111100
[4,5,3,6,8,2,7,1]=>0100101=>1011010
[5,6,3,4,8,1,7,2]=>0100101=>1011010
[4,6,7,8,5,1,3,2]=>0001101=>1110010
[8,4,3,1,2,6,7,5]=>1110001=>0001110
[8,5,1,6,3,4,7,2]=>1101001=>0010110
[5,1,8,6,3,4,7,2]=>1011001=>0100110
[4,6,8,1,5,3,7,2]=>0010101=>1101010
[6,4,5,8,3,2,7,1]=>1001101=>0110010
[3,6,4,8,7,1,5,2]=>0101101=>1010010
[6,5,8,1,3,4,7,2]=>1010001=>0101110
[5,6,8,3,1,2,7,4]=>0011001=>1100110
[6,1,8,3,5,2,7,4]=>1010101=>0101010
[7,6,8,3,5,2,1,4]=>1010110=>0101001
[8,6,1,3,5,2,7,4]=>1100101=>0011010
[8,7,1,3,5,6,2,4]=>1100010=>0011101
[6,7,8,3,5,1,2,4]=>0010100=>1101011
[3,4,8,1,2,6,7,5]=>0010001=>1101110
[5,8,2,4,3,6,7,1]=>0101001=>1010110
[5,8,2,3,1,6,7,4]=>0101001=>1010110
[6,8,2,3,5,1,7,4]=>0100101=>1011010
[7,8,2,3,5,6,1,4]=>0100010=>1011101
[8,6,5,1,4,3,7,2]=>1110101=>0001010
[2,4,8,6,1,3,7,5]=>0011001=>1100110
[6,7,1,8,4,3,5,2]=>0101101=>1010010
[2,7,8,6,1,4,3,5]=>0011010=>1100101
[2,7,3,8,1,6,4,5]=>0101010=>1010101
[7,5,1,8,2,4,6,3]=>1101001=>0010110
[2,7,8,4,1,6,3,5]=>0011010=>1100101
[2,6,5,4,1,3,8,7]=>0111001=>1000110
[4,1,7,6,3,8,2,5]=>1011010=>0100101
[4,8,2,5,7,6,3,1]=>0100111=>1011000
[3,4,6,5,1,8,2,7]=>0011010=>1100101
[2,6,5,3,4,1,8,7]=>0110101=>1001010
[4,6,1,5,2,3,8,7]=>0101001=>1010110
[6,2,3,5,1,4,8,7]=>1001001=>0110110
[2,6,7,5,1,8,4,3]=>0011011=>1100100
[8,6,1,2,5,3,4,7]=>1100100=>0011011
[6,2,5,1,8,3,4,7]=>1010100=>0101011
[7,6,5,2,8,3,4,1]=>1110101=>0001010
[2,6,3,5,1,8,7,4]=>0101011=>1010100
[2,4,7,6,5,8,1,3]=>0011010=>1100101
[2,1,4,8,7,6,3,5]=>1001110=>0110001
[7,4,6,8,5,3,2,1]=>1001111=>0110000
[8,1,3,5,7,4,6,2]=>1000101=>0111010
[3,2,8,7,5,1,6,4]=>1011101=>0100010
[4,8,5,1,6,7,2,3]=>0110010=>1001101
[3,8,5,1,6,7,2,4]=>0110010=>1001101
[7,8,6,1,3,5,2,4]=>0110010=>1001101
[5,6,7,2,8,1,3,4]=>0010100=>1101011
[2,5,1,8,6,7,4,3]=>0101011=>1010100
[3,5,1,8,6,7,4,2]=>0101011=>1010100
[5,2,3,8,6,7,4,1]=>1001011=>0110100
[8,3,5,4,6,7,1,2]=>1010010=>0101101
[5,1,3,8,6,7,4,2]=>1001011=>0110100
[3,2,5,8,6,7,4,1]=>1001011=>0110100
[6,2,1,5,3,8,7,4]=>1101011=>0010100
[5,6,3,2,8,1,4,7]=>0110100=>1001011
[8,1,6,3,5,2,7,4]=>1010101=>0101010
[8,7,6,2,5,3,1,4]=>1110110=>0001001
[4,7,6,8,3,2,5,1]=>0101101=>1010010
[2,7,5,8,1,3,4,6]=>0101000=>1010111
[7,6,2,8,5,1,4,3]=>1101101=>0010010
[8,1,3,7,5,2,6,4]=>1001101=>0110010
[3,4,8,7,5,1,6,2]=>0011101=>1100010
[6,3,8,1,4,2,5,7]=>1010100=>0101011
[6,3,8,5,7,4,1,2]=>1010110=>0101001
[7,4,6,8,5,1,3,2]=>1001101=>0110010
[2,1,4,8,7,5,6,3]=>1001101=>0110010
[7,1,5,8,2,6,4,3]=>1001011=>0110100
[3,6,8,2,4,1,7,5]=>0010101=>1101010
[4,5,8,2,6,7,3,1]=>0010011=>1101100
[5,2,8,1,6,7,3,4]=>1010010=>0101101
[2,5,8,4,6,7,3,1]=>0010011=>1101100
[5,8,3,4,6,7,2,1]=>0100011=>1011100
[8,4,3,2,6,7,1,5]=>1110010=>0001101
[4,2,8,1,6,7,3,5]=>1010010=>0101101
[2,4,8,1,6,7,3,5]=>0010010=>1101101
[5,1,8,2,6,7,3,4]=>1010010=>0101101
[3,4,8,7,2,1,5,6]=>0011100=>1100011
[7,8,5,3,6,4,2,1]=>0110111=>1001000
[2,8,5,7,4,1,3,6]=>0101100=>1010011
[5,8,4,1,6,7,2,3]=>0110010=>1001101
[3,8,1,4,6,7,2,5]=>0100010=>1011101
[8,2,3,4,6,7,1,5]=>1000010=>0111101
[6,2,7,3,8,4,1,5]=>1010110=>0101001
[7,4,3,2,8,5,1,6]=>1110110=>0001001
[8,3,6,2,5,4,1,7]=>1010110=>0101001
[5,4,8,3,2,6,1,7]=>1011010=>0100101
[3,5,8,2,4,6,1,7]=>0010010=>1101101
[6,4,7,8,2,3,1,5]=>1001010=>0110101
[4,8,6,2,5,3,1,7]=>0110110=>1001001
[1,6,4,3,2,8,7,5]=>0111011=>1000100
[1,5,3,2,8,4,7,6]=>0110101=>1001010
[5,7,4,3,1,2,6,8]=>0111000=>1000111
[2,8,7,3,5,1,4,6]=>0110100=>1001011
[6,1,2,7,3,8,5,4]=>1001011=>0110100
[5,1,3,2,8,7,4,6]=>1010110=>0101001
[1,8,3,7,2,6,5,4]=>0101011=>1010100
[5,1,4,8,3,7,2,6]=>1001010=>0110101
[2,1,6,8,5,4,7,3]=>1001101=>0110010
[8,3,1,6,7,2,5,4]=>1100101=>0011010
[3,7,6,1,5,2,4,8]=>0110100=>1001011
[1,5,4,8,3,2,7,6]=>0101101=>1010010
[7,3,6,1,2,5,4,8]=>1010010=>0101101
[5,4,7,1,3,2,6,8]=>1010100=>0101011
[5,7,2,3,8,1,4,6]=>0100100=>1011011
[6,4,7,5,8,1,2,3]=>1010100=>0101011
[7,4,8,5,1,6,3,2]=>1011011=>0100100
[8,6,4,2,1,7,5,3]=>1111011=>0000100
[7,4,2,1,5,8,6,3]=>1110011=>0001100
[7,6,4,1,8,5,2,3]=>1110110=>0001001
[1,6,4,8,7,5,3,2]=>0101111=>1010000
[6,3,1,2,8,4,7,5]=>1100101=>0011010
[6,8,4,1,2,7,5,3]=>0110011=>1001100
[3,6,1,8,2,4,7,5]=>0101001=>1010110
[1,3,8,7,6,2,5,4]=>0011101=>1100010
[5,4,1,8,7,3,2,6]=>1101110=>0010001
[3,5,1,8,7,2,4,6]=>0101100=>1010011
[5,8,4,1,7,6,2,3]=>0110110=>1001001
[8,6,1,7,5,4,3,2]=>1101111=>0010000
[7,1,5,8,6,4,3,2]=>1001111=>0110000
[4,1,8,7,6,2,5,3]=>1011101=>0100010
[3,1,8,7,6,5,2,4]=>1011110=>0100001
[1,6,4,5,2,3,7,8]=>0101000=>1010111
[1,7,4,5,2,3,6,8]=>0101000=>1010111
[1,7,3,5,2,4,6,8]=>0101000=>1010111
[1,6,3,5,2,4,7,8]=>0101000=>1010111
[1,6,3,4,2,5,7,8]=>0101000=>1010111
[1,7,3,4,2,5,6,8]=>0101000=>1010111
[1,8,6,7,3,4,2,5]=>0101010=>1010101
[1,8,5,7,3,4,2,6]=>0101010=>1010101
[1,7,3,4,2,6,5,8]=>0101010=>1010101
[1,5,2,8,4,7,3,6]=>0101010=>1010101
[1,4,2,8,5,7,3,6]=>0101010=>1010101
[1,7,3,5,2,6,4,8]=>0101010=>1010101
[1,8,4,7,3,5,2,6]=>0101010=>1010101
[1,7,3,6,2,5,4,8]=>0101010=>1010101
[1,7,3,6,2,4,5,8]=>0101000=>1010111
[1,7,4,6,2,3,5,8]=>0101000=>1010111
[1,8,5,6,2,3,4,7]=>0101000=>1010111
[1,8,5,6,2,4,3,7]=>0101010=>1010101
[1,3,2,8,5,6,4,7]=>0101010=>1010101
[1,4,2,8,5,6,3,7]=>0101010=>1010101
[1,5,2,8,4,6,3,7]=>0101010=>1010101
[1,6,2,8,4,5,3,7]=>0101010=>1010101
[9,1,2,3,5,4,6,7,8]=>10001000=>01110111
[8,1,2,4,5,3,6,7]=>1000100=>0111011
[2,3,4,6,5,7,8,9,1]=>00010001=>11101110
[10,1,2,3,4,6,5,7,8,9]=>100001000=>011110111
[9,1,2,3,5,6,4,7,8]=>10000100=>01111011
[2,3,4,7,5,6,8,9,1]=>00010001=>11101110
[2,3,4,6,7,5,8,9,1]=>00001001=>11110110
[2,3,4,5,7,6,8,9,10,1]=>000010001=>111101110
[9,10,5,6,7,8,3,4,1,2]=>010001010=>101110101
[5,8,9,6,7,10,3,4,1,2]=>001001010=>110110101
[9,10,7,8,3,4,5,6,1,2]=>010100010=>101011101
[9,10,3,6,7,4,5,8,1,2]=>010010010=>101101101
[3,8,9,6,7,4,5,10,1,2]=>001010010=>110101101
[3,6,7,8,9,4,5,10,1,2]=>000010010=>111101101
[9,10,3,4,5,6,7,8,1,2]=>010000010=>101111101
[3,8,9,4,5,6,7,10,1,2]=>001000010=>110111101
[3,4,7,8,5,6,9,10,1,2]=>000100010=>111011101
[7,8,9,10,5,6,1,2,3,4]=>000101000=>111010111
[5,8,9,6,7,10,1,2,3,4]=>001001000=>110110111
[9,10,7,8,1,4,5,2,3,6]=>010100100=>101011011
[7,8,9,10,1,4,5,2,3,6]=>000100100=>111011011
[9,10,1,6,7,4,5,2,3,8]=>010010100=>101101011
[1,8,9,6,7,4,5,2,3,10]=>001010100=>110101011
[1,6,7,8,9,4,5,2,3,10]=>000010100=>111101011
[9,10,1,4,5,6,7,2,3,8]=>010000100=>101111011
[1,8,9,4,5,6,7,2,3,10]=>001000100=>110111011
[1,4,7,8,5,6,9,2,3,10]=>000100100=>111011011
[1,4,5,6,7,8,9,2,3,10]=>000000100=>111111011
[9,10,1,6,7,2,3,4,5,8]=>010010000=>101101111
[1,8,9,6,7,2,3,4,5,10]=>001010000=>110101111
[1,6,7,8,9,2,3,4,5,10]=>000010000=>111101111
[9,10,1,2,5,6,3,4,7,8]=>010001000=>101110111
[1,8,9,2,5,6,3,4,7,10]=>001001000=>110110111
[1,2,7,8,5,6,3,4,9,10]=>000101000=>111010111
[1,2,5,6,7,8,3,4,9,10]=>000001000=>111110111
[1,8,9,2,3,4,5,6,7,10]=>001000000=>110111111
[1,2,7,8,3,4,5,6,9,10]=>000100000=>111011111
[1,2,3,6,7,4,5,8,9,10]=>000010000=>111101111
[9,10,11,12,7,8,5,6,3,4,1,2]=>00010101010=>11101010101
[11,12,7,8,9,10,5,6,3,4,1,2]=>01000101010=>10111010101
[7,8,9,10,11,12,5,6,3,4,1,2]=>00000101010=>11111010101
[11,12,9,10,5,6,7,8,3,4,1,2]=>01010001010=>10101110101
[9,10,11,12,5,6,7,8,3,4,1,2]=>00010001010=>11101110101
[5,8,9,10,11,6,7,12,3,4,1,2]=>00001001010=>11110110101
[11,12,5,6,7,8,9,10,3,4,1,2]=>01000001010=>10111110101
[5,6,9,10,7,8,11,12,3,4,1,2]=>00010001010=>11101110101
[5,6,7,8,9,10,11,12,3,4,1,2]=>00000001010=>11111110101
[11,12,9,10,7,8,3,4,5,6,1,2]=>01010100010=>10101011101
[9,10,11,12,7,8,3,4,5,6,1,2]=>00010100010=>11101011101
[11,12,7,8,9,10,3,4,5,6,1,2]=>01000100010=>10111011101
[7,8,9,10,11,12,3,4,5,6,1,2]=>00000100010=>11111011101
[9,10,11,12,3,6,7,4,5,8,1,2]=>00010010010=>11101101101
[3,8,9,10,11,6,7,4,5,12,1,2]=>00001010010=>11110101101
[3,6,9,10,7,8,11,4,5,12,1,2]=>00010010010=>11101101101
[3,6,7,8,9,10,11,4,5,12,1,2]=>00000010010=>11111101101
[11,12,9,10,3,4,5,6,7,8,1,2]=>01010000010=>10101111101
[9,10,11,12,3,4,5,6,7,8,1,2]=>00010000010=>11101111101
[3,8,9,10,11,4,5,6,7,12,1,2]=>00001000010=>11110111101
[11,12,3,4,7,8,5,6,9,10,1,2]=>01000100010=>10111011101
[3,4,9,10,7,8,5,6,11,12,1,2]=>00010100010=>11101011101
[3,4,7,8,9,10,5,6,11,12,1,2]=>00000100010=>11111011101
[11,12,3,4,5,6,7,8,9,10,1,2]=>01000000010=>10111111101
[3,10,11,4,5,6,7,8,9,12,1,2]=>00100000010=>11011111101
[3,4,9,10,5,6,7,8,11,12,1,2]=>00010000010=>11101111101
[3,4,5,8,9,6,7,10,11,12,1,2]=>00001000010=>11110111101
[3,4,5,6,7,8,9,10,11,12,1,2]=>00000000010=>11111111101
[11,12,9,10,7,8,5,6,1,2,3,4]=>01010101000=>10101010111
[9,10,11,12,7,8,5,6,1,2,3,4]=>00010101000=>11101010111
[11,12,7,8,9,10,5,6,1,2,3,4]=>01000101000=>10111010111
[7,10,11,8,9,12,5,6,1,2,3,4]=>00100101000=>11011010111
[7,8,9,10,11,12,5,6,1,2,3,4]=>00000101000=>11111010111
[11,12,9,10,5,6,7,8,1,2,3,4]=>01010001000=>10101110111
[9,10,11,12,5,6,7,8,1,2,3,4]=>00010001000=>11101110111
[11,12,5,8,9,6,7,10,1,2,3,4]=>01001001000=>10110110111
[5,10,11,8,9,6,7,12,1,2,3,4]=>00101001000=>11010110111
[5,8,9,10,11,6,7,12,1,2,3,4]=>00001001000=>11110110111
[11,12,5,6,7,8,9,10,1,2,3,4]=>01000001000=>10111110111
[5,10,11,6,7,8,9,12,1,2,3,4]=>00100001000=>11011110111
[5,6,9,10,7,8,11,12,1,2,3,4]=>00010001000=>11101110111
[5,6,7,8,9,10,11,12,1,2,3,4]=>00000001000=>11111110111
[9,10,11,12,7,8,1,4,5,2,3,6]=>00010100100=>11101011011
[7,8,9,10,11,12,1,4,5,2,3,6]=>00000100100=>11111011011
[9,10,11,12,1,6,7,4,5,2,3,8]=>00010010100=>11101101011
[1,10,11,8,9,6,7,4,5,2,3,12]=>00101010100=>11010101011
[1,8,9,10,11,6,7,4,5,2,3,12]=>00001010100=>11110101011
[1,6,9,10,7,8,11,4,5,2,3,12]=>00010010100=>11101101011
[1,6,7,8,9,10,11,4,5,2,3,12]=>00000010100=>11111101011
[9,10,11,12,1,4,5,6,7,2,3,8]=>00010000100=>11101111011
[1,8,9,10,11,4,5,6,7,2,3,12]=>00001000100=>11110111011
[1,4,9,10,7,8,5,6,11,2,3,12]=>00010100100=>11101011011
[1,4,7,8,9,10,5,6,11,2,3,12]=>00000100100=>11111011011
[11,12,1,4,5,6,7,8,9,2,3,10]=>01000000100=>10111111011
[1,4,9,10,5,6,7,8,11,2,3,12]=>00010000100=>11101111011
[1,4,5,8,9,6,7,10,11,2,3,12]=>00001000100=>11110111011
[1,4,5,6,7,8,9,10,11,2,3,12]=>00000000100=>11111111011
[11,12,9,10,7,8,1,2,3,4,5,6]=>01010100000=>10101011111
[9,10,11,12,7,8,1,2,3,4,5,6]=>00010100000=>11101011111
[11,12,7,8,9,10,1,2,3,4,5,6]=>01000100000=>10111011111
[7,10,11,8,9,12,1,2,3,4,5,6]=>00100100000=>11011011111
[11,12,9,10,1,6,7,2,3,4,5,8]=>01010010000=>10101101111
[9,10,11,12,1,6,7,2,3,4,5,8]=>00010010000=>11101101111
[11,12,1,8,9,6,7,2,3,4,5,10]=>01001010000=>10110101111
[1,10,11,8,9,6,7,2,3,4,5,12]=>00101010000=>11010101111
[11,12,1,6,7,8,9,2,3,4,5,10]=>01000010000=>10111101111
[1,10,11,6,7,8,9,2,3,4,5,12]=>00100010000=>11011101111
[1,6,9,10,7,8,11,2,3,4,5,12]=>00010010000=>11101101111
[1,6,7,8,9,10,11,2,3,4,5,12]=>00000010000=>11111101111
[11,12,9,10,1,2,5,6,3,4,7,8]=>01010001000=>10101110111
[9,10,11,12,1,2,5,6,3,4,7,8]=>00010001000=>11101110111
[11,12,1,8,9,2,5,6,3,4,7,10]=>01001001000=>10110110111
[1,10,11,8,9,2,5,6,3,4,7,12]=>00101001000=>11010110111
[1,8,9,10,11,2,5,6,3,4,7,12]=>00001001000=>11110110111
[11,12,1,2,7,8,5,6,3,4,9,10]=>01000101000=>10111010111
[1,10,11,2,7,8,5,6,3,4,9,12]=>00100101000=>11011010111
[1,2,9,10,7,8,5,6,3,4,11,12]=>00010101000=>11101010111
[1,2,7,8,9,10,5,6,3,4,11,12]=>00000101000=>11111010111
[11,12,1,2,5,6,7,8,3,4,9,10]=>01000001000=>10111110111
[1,10,11,2,5,6,7,8,3,4,9,12]=>00100001000=>11011110111
[1,2,9,10,5,6,7,8,3,4,11,12]=>00010001000=>11101110111
[1,2,5,8,9,6,7,10,3,4,11,12]=>00001001000=>11110110111
[1,2,5,6,7,8,9,10,3,4,11,12]=>00000001000=>11111110111
[11,12,9,10,1,2,3,4,5,6,7,8]=>01010000000=>10101111111
[9,10,11,12,1,2,3,4,5,6,7,8]=>00010000000=>11101111111
[11,12,1,8,9,2,3,4,5,6,7,10]=>01001000000=>10110111111
[1,10,11,8,9,2,3,4,5,6,7,12]=>00101000000=>11010111111
[1,8,9,10,11,2,3,4,5,6,7,12]=>00001000000=>11110111111
[11,12,1,2,7,8,3,4,5,6,9,10]=>01000100000=>10111011111
[1,10,11,2,7,8,3,4,5,6,9,12]=>00100100000=>11011011111
[1,2,9,10,7,8,3,4,5,6,11,12]=>00010100000=>11101011111
[1,2,7,8,9,10,3,4,5,6,11,12]=>00000100000=>11111011111
[11,12,1,2,3,6,7,4,5,8,9,10]=>01000010000=>10111101111
[1,10,11,2,3,6,7,4,5,8,9,12]=>00100010000=>11011101111
[1,2,9,10,3,6,7,4,5,8,11,12]=>00010010000=>11101101111
[1,2,3,6,7,8,9,4,5,10,11,12]=>00000010000=>11111101111
[11,12,1,2,3,4,5,6,7,8,9,10]=>01000000000=>10111111111
[1,10,11,2,3,4,5,6,7,8,9,12]=>00100000000=>11011111111
[1,2,9,10,3,4,5,6,7,8,11,12]=>00010000000=>11101111111
[1,2,3,8,9,4,5,6,7,10,11,12]=>00001000000=>11110111111
[1,2,3,4,7,8,5,6,9,10,11,12]=>00000100000=>11111011111
[1,2,3,4,5,6,7,8,9,10,11,12]=>00000000000=>11111111111
[8,6,4,7,2,1,3,5]=>1101100=>0010011
[8,4,6,2,3,5,1,7]=>1010010=>0101101
[5,4,8,2,3,6,1,7]=>1010010=>0101101
[3,8,6,2,4,5,1,7]=>0110010=>1001101
[1,7,6,4,8,2,3,5]=>0110100=>1001011
[5,8,7,4,1,2,3,6]=>0111000=>1000111
[6,8,5,3,4,1,2,7]=>0110100=>1001011
[6,8,3,7,2,1,4,5]=>0101100=>1010011
[6,1,3,7,4,8,2,5]=>1001010=>0110101
[7,1,6,4,8,2,3,5]=>1010100=>0101011
[1,8,5,7,2,3,4,6]=>0101000=>1010111
[6,1,5,8,2,3,4,7]=>1001000=>0110111
[6,1,5,7,8,2,3,4]=>1000100=>0111011
[3,8,7,5,1,2,4,6]=>0111000=>1000111
[3,7,6,1,2,4,5,8]=>0110000=>1001111
[4,7,6,1,2,3,5,8]=>0110000=>1001111
[1,6,5,8,2,3,4,7]=>0101000=>1010111
[8,5,7,4,1,2,3,6]=>1011000=>0100111
[8,6,2,3,1,7,4,5]=>1101010=>0010101
[8,6,4,1,2,7,3,5]=>1110010=>0001101
[1,7,2,8,6,3,4,5]=>0101100=>1010011
[7,5,8,1,3,6,2,4]=>1010010=>0101101
[5,4,1,8,2,3,6,7]=>1101000=>0010111
[1,4,8,7,2,3,5,6]=>0011000=>1100111
[1,5,8,7,2,3,4,6]=>0011000=>1100111
[5,7,1,3,8,2,4,6]=>0100100=>1011011
[7,1,5,8,6,2,3,4]=>1001100=>0110011
[6,1,8,2,7,3,4,5]=>1010100=>0101011
[4,1,8,7,2,3,5,6]=>1011000=>0100111
[5,1,8,7,2,3,4,6]=>1011000=>0100111
[1,8,7,6,4,5,3,2]=>0111011=>1000100
[9,8,7,6,4,5,3,2,1,10]=>111101110=>000010001
[8,7,6,4,3,5,2,1,9]=>11110110=>00001001
[8,7,6,3,5,4,2,1,9]=>11101110=>00010001
[1,9,8,7,5,4,6,3,2]=>01111011=>10000100
[1,8,7,3,6,5,4,2]=>0110111=>1001000
[1,9,8,7,4,6,5,3,2]=>01110111=>10001000
[1,10,9,8,7,5,6,4,3,2]=>011110111=>100001000
[7,1,5,8,3,4,2,6]=>1001010=>0110101
[7,1,4,3,2,5,6,8]=>1011000=>0100111
[6,4,2,3,8,5,7,1]=>1100101=>0011010
[6,4,2,7,5,8,3,1]=>1101011=>0010100
[2,4,1,7,5,8,3,6]=>0101010=>1010101
[7,1,4,6,5,2,3,8]=>1001100=>0110011
[7,1,4,6,5,8,2,3]=>1001010=>0110101
[7,1,4,6,3,8,2,5]=>1001010=>0110101
[7,1,4,3,2,5,8,6]=>1011001=>0100110
[7,1,4,6,5,2,8,3]=>1001101=>0110010
[7,1,4,6,5,3,8,2]=>1001101=>0110010
[7,1,4,6,5,3,2,8]=>1001110=>0110001
[6,4,2,7,5,3,8,1]=>1101101=>0010010
[3,4,7,2,6,8,5,1]=>0010011=>1101100
[3,4,7,1,6,8,2,5]=>0010010=>1101101
[3,4,7,1,6,8,5,2]=>0010011=>1101100
[2,4,1,7,5,3,6,8]=>0101100=>1010011
[3,4,1,7,8,6,2,5]=>0100110=>1011001
[6,4,2,3,8,5,1,7]=>1100110=>0011001
[6,4,2,7,5,8,1,3]=>1101010=>0010101
[6,4,2,7,5,3,1,8]=>1101110=>0010001
[3,4,7,2,6,8,1,5]=>0010010=>1101101
[5,4,7,3,6,8,2,1]=>1010011=>0101100
[3,4,7,2,6,5,1,8]=>0010110=>1101001
[4,8,3,2,5,6,1,7]=>0110010=>1001101
[4,8,7,3,5,1,2,6]=>0110100=>1001011
[4,8,7,1,3,5,2,6]=>0110010=>1001101
[4,8,3,1,2,6,5,7]=>0110010=>1001101
[3,4,7,1,6,2,5,8]=>0010100=>1101011
[3,4,7,1,6,2,8,5]=>0010101=>1101010
[3,4,7,2,6,5,8,1]=>0010101=>1101010
[4,8,3,1,2,6,7,5]=>0110001=>1001110
[5,8,1,6,3,4,2,7]=>0101010=>1010101
[6,8,5,1,3,7,2,4]=>0110010=>1001101
[6,8,5,1,3,4,7,2]=>0110001=>1001110
[5,8,3,4,2,6,7,1]=>0101001=>1010110
[5,4,7,3,6,2,8,1]=>1010101=>0101010
[5,4,7,2,6,1,8,3]=>1010101=>0101010
[6,4,3,7,5,1,2,8]=>1101100=>0010011
[6,4,3,7,5,1,8,2]=>1101101=>0010010
[6,2,4,3,1,5,8,7]=>1011001=>0100110
[3,8,7,4,1,5,2,6]=>0111010=>1000101
[2,4,7,3,6,1,5,8]=>0010100=>1101011
[5,8,3,2,1,6,4,7]=>0111010=>1000101
[5,8,7,4,3,1,2,6]=>0111100=>1000011
[5,4,7,3,6,2,1,8]=>1010110=>0101001
[7,3,8,2,1,6,5,4]=>1011011=>0100100
[7,4,3,8,5,2,1,6]=>1101110=>0010001
[6,5,2,8,4,3,1,7]=>1101110=>0010001
[4,3,2,8,6,5,1,7]=>1101110=>0010001
[4,3,8,7,5,1,6,2]=>1011101=>0100010
[3,2,5,8,6,1,4,7]=>1001100=>0110011
[8,4,3,7,5,2,6,1]=>1101101=>0010010
[4,3,7,8,5,1,2,6]=>1001100=>0110011
[5,3,7,8,4,1,2,6]=>1001100=>0110011
[6,2,5,8,3,1,4,7]=>1001100=>0110011
[6,2,4,8,3,1,5,7]=>1001100=>0110011
[5,2,3,8,4,1,6,7]=>1001100=>0110011
[5,3,8,7,4,1,6,2]=>1011101=>0100010
[5,3,2,8,6,4,1,7]=>1101110=>0010001
[7,5,3,8,4,2,1,6]=>1101110=>0010001
[8,7,5,3,6,2,4,1]=>1110101=>0001010
[8,6,5,3,7,2,4,1]=>1110101=>0001010
[7,5,4,3,8,2,6,1]=>1110101=>0001010
[6,4,5,3,8,2,7,1]=>1010101=>0101010
[7,4,6,3,8,2,5,1]=>1010101=>0101010
[7,5,6,3,8,2,4,1]=>1010101=>0101010
[8,5,6,3,7,2,4,1]=>1010101=>0101010
[7,4,6,3,5,2,8,1]=>1010101=>0101010
[8,4,6,3,5,2,7,1]=>1010101=>0101010
[8,4,7,3,5,2,6,1]=>1010101=>0101010
[8,5,7,3,4,2,6,1]=>1010101=>0101010
[7,5,8,4,3,2,6,1]=>1011101=>0100010
[6,5,8,4,3,2,7,1]=>1011101=>0100010
[6,5,8,3,4,2,7,1]=>1010101=>0101010
[7,5,8,3,4,2,6,1]=>1010101=>0101010
[7,5,8,4,6,2,3,1]=>1010101=>0101010
[7,4,8,3,6,2,5,1]=>1010101=>0101010
[7,4,8,3,5,2,6,1]=>1010101=>0101010
[6,4,8,3,5,2,7,1]=>1010101=>0101010
[6,4,7,3,5,2,8,1]=>1010101=>0101010
[5,4,8,3,7,2,6,1]=>1010101=>0101010
[6,5,8,3,7,2,4,1]=>1010101=>0101010
[6,5,8,4,7,2,3,1]=>1010101=>0101010
[6,5,8,4,7,3,2,1]=>1010111=>0101000
[6,4,7,3,8,2,5,1]=>1010101=>0101010
[5,4,7,3,8,2,6,1]=>1010101=>0101010
[5,4,6,3,8,2,7,1]=>1010101=>0101010
[5,3,6,2,4,7,8,1]=>1010001=>0101110
[5,3,6,1,4,8,7,2]=>1010011=>0101100
[5,3,7,2,4,6,8,1]=>1010001=>0101110
[4,3,1,5,6,8,7,2]=>1100011=>0011100
[4,2,1,5,8,6,3,7]=>1100110=>0011001
[4,2,1,5,8,6,7,3]=>1100101=>0011010
[4,2,1,5,8,7,6,3]=>1100111=>0011000
[4,3,1,5,7,8,6,2]=>1100011=>0011100
[4,3,1,7,5,8,6,2]=>1101011=>0010100
[6,7,3,1,4,8,2,5]=>0110010=>1001101
[5,3,7,1,4,8,2,6]=>1010010=>0101101
[4,3,1,5,7,8,2,6]=>1100010=>0011101
[3,2,1,8,5,4,6,7]=>1101100=>0010011
[3,2,1,8,5,7,4,6]=>1101010=>0010101
[3,2,1,8,7,5,4,6]=>1101110=>0010001
[5,2,7,1,8,4,3,6]=>1010110=>0101001
[6,7,2,1,8,4,3,5]=>0110110=>1001001
[6,7,2,1,8,4,5,3]=>0110101=>1001010
[3,2,1,8,5,6,4,7]=>1101010=>0010101
[3,2,1,8,6,5,4,7]=>1101110=>0010001
[4,3,1,6,7,8,5,2]=>1100011=>0011100
[4,2,1,6,8,7,5,3]=>1100111=>0011000
[4,2,1,6,8,5,7,3]=>1100101=>0011010
[4,2,1,6,8,5,3,7]=>1100110=>0011001
[5,2,6,1,8,4,3,7]=>1010110=>0101001
[5,2,6,1,8,7,4,3]=>1010111=>0101000
[5,2,6,1,8,7,3,4]=>1010110=>0101001
[5,2,6,1,8,3,4,7]=>1010100=>0101011
[4,2,1,6,8,3,7,5]=>1100101=>0011010
[4,3,1,6,7,8,2,5]=>1100010=>0011101
[6,7,3,1,5,8,2,4]=>0110010=>1001101
[4,2,1,7,8,6,3,5]=>1100110=>0011001
[3,2,1,8,7,6,4,5]=>1101110=>0010001
[3,2,1,8,6,4,7,5]=>1101101=>0010010
[3,2,1,8,6,4,5,7]=>1101100=>0010011
[3,2,1,8,4,6,5,7]=>1101010=>0010101
[3,2,1,8,4,6,7,5]=>1101001=>0010110
[3,2,1,8,4,7,6,5]=>1101011=>0010100
[3,2,1,8,7,4,6,5]=>1101101=>0010010
[4,2,1,7,8,3,6,5]=>1100101=>0011010
[5,2,7,1,8,3,6,4]=>1010101=>0101010
[6,7,2,1,8,3,5,4]=>0110101=>1001010
[5,2,7,1,8,3,4,6]=>1010100=>0101011
[4,2,1,7,8,3,5,6]=>1100100=>0011011
[3,2,1,8,4,5,7,6]=>1101001=>0010110
[7,5,2,8,6,3,4,1]=>1101101=>0010010
[7,4,8,6,2,5,3,1]=>1011011=>0100100
[7,3,8,6,2,4,5,1]=>1011001=>0100110
[7,4,3,1,8,2,5,6]=>1110100=>0001011
[7,4,2,8,5,6,1,3]=>1101010=>0010101
[7,3,8,5,2,4,6,1]=>1011001=>0100110
[7,3,8,4,5,6,2,1]=>1010011=>0101100
[6,3,8,2,4,5,1,7]=>1010010=>0101101
[6,3,8,2,5,7,4,1]=>1010011=>0101100
[6,4,3,8,1,5,2,7]=>1101010=>0010101
[6,3,7,8,2,4,1,5]=>1001010=>0110101
[5,6,7,3,8,2,4,1]=>0010101=>1101010
[5,4,7,2,6,8,1,3]=>1010010=>0101101
[5,3,8,2,4,6,7,1]=>1010001=>0101110
[6,3,8,2,4,7,5,1]=>1010011=>0101100
[5,7,4,2,6,8,1,3]=>0110010=>1001101
[6,4,8,2,7,5,1,3]=>1010110=>0101001
[6,5,3,1,4,2,7,8]=>1110100=>0001011
[5,7,4,2,6,1,3,8]=>0110100=>1001011
[5,6,4,2,3,8,1,7]=>0110010=>1001101
[5,6,3,7,8,2,4,1]=>0100101=>1011010
[5,6,3,8,2,4,7,1]=>0101001=>1010110
[6,3,7,2,4,5,1,8]=>1010010=>0101101
[6,3,7,2,5,8,4,1]=>1010011=>0101100
[5,3,6,8,2,4,7,1]=>1001001=>0110110
[5,4,6,2,3,8,1,7]=>1010010=>0101101
[5,3,6,7,8,2,4,1]=>1000101=>0111010
[3,6,4,2,1,5,8,7]=>0111001=>1000110
[3,5,8,6,4,2,1,7]=>0011110=>1100001
[5,8,6,3,4,2,1,7]=>0110110=>1001001
[5,6,3,4,2,1,8,7]=>0101101=>1010010
[6,3,4,2,1,5,8,7]=>1011001=>0100110
[5,6,4,2,1,3,8,7]=>0111001=>1000110
[2,5,4,1,7,8,6,3]=>0110011=>1001100
[2,7,8,5,4,1,6,3]=>0011101=>1100010
[2,8,5,4,1,6,3,7]=>0111010=>1000101
[2,6,3,8,5,4,1,7]=>0101110=>1010001
[2,8,6,3,5,4,1,7]=>0110110=>1001001
[5,8,6,4,2,1,3,7]=>0111100=>1000011
[4,2,1,5,7,8,6,3]=>1100011=>0011100
[2,7,8,6,3,5,4,1]=>0011011=>1100100
[4,3,8,5,7,6,2,1]=>1010111=>0101000
[7,6,2,1,8,4,3,5]=>1110110=>0001001
[2,1,8,5,6,4,3,7]=>1010110=>0101001
[4,2,1,8,5,6,3,7]=>1101010=>0010101
[8,4,2,1,5,6,3,7]=>1110010=>0001101
[2,5,6,3,8,4,1,7]=>0010110=>1101001
[6,3,4,2,1,8,5,7]=>1011010=>0100101
[3,7,8,5,6,4,2,1]=>0010111=>1101000
[3,8,5,6,4,2,1,7]=>0101110=>1010001
[3,6,4,2,1,8,5,7]=>0111010=>1000101
[3,8,6,4,2,1,5,7]=>0111100=>1000011
[3,7,8,6,4,2,1,5]=>0011110=>1100001
[8,5,3,7,6,2,4,1]=>1101101=>0010010
[7,6,2,4,1,8,5,3]=>1101011=>0010100
[8,5,4,1,7,6,2,3]=>1110110=>0001001
[7,6,2,3,8,5,4,1]=>1100111=>0011000
[2,1,7,8,6,4,3,5]=>1001110=>0110001
[2,1,6,4,3,7,8,5]=>1011001=>0100110
[6,4,2,1,3,7,8,5]=>1110001=>0001110
[6,3,7,8,4,2,1,5]=>1001110=>0110001
[7,8,4,2,1,6,3,5]=>0111010=>1000101
[5,7,6,2,3,8,4,1]=>0110011=>1001100
[2,6,1,8,4,3,7,5]=>0101101=>1010010
[2,6,1,7,5,8,4,3]=>0101011=>1010100
[8,4,2,3,7,5,6,1]=>1100101=>0011010
[8,5,7,6,2,1,4,3]=>1011101=>0100010
[4,8,5,7,6,2,1,3]=>0101110=>1010001
[4,7,6,2,1,3,8,5]=>0111001=>1000110
[7,5,6,1,8,4,2,3]=>1010110=>0101001
[2,7,5,8,4,3,6,1]=>0101101=>1010010
[2,8,4,3,6,1,7,5]=>0110101=>1001010
[6,4,7,8,3,2,1,5]=>1001110=>0110001
[7,6,5,8,4,3,2,1,9]=>11011110=>00100001
[7,6,5,4,9,3,2,1,8]=>11101110=>00010001
[7,6,5,4,3,8,2,1,9]=>11110110=>00001001
[7,6,5,4,3,2,8,1,9]=>11111010=>00000101
[6,9,8,5,4,3,2,1,7]=>01111110=>10000001
[8,7,9,6,5,4,3,2,1,10]=>101111110=>010000001
[7,5,8,9,4,3,2,1,6]=>10011110=>01100001
[8,7,6,9,5,4,3,2,1,10]=>110111110=>001000001
[6,4,3,7,5,2,1,8]=>1101110=>0010001
[7,6,4,8,9,3,2,1,5]=>11001110=>00110001
[8,7,6,5,10,4,3,2,1,9]=>111011110=>000100001
[6,5,3,2,8,4,1,7]=>1110110=>0001001
[7,6,5,3,9,8,2,1,4]=>11101110=>00010001
[8,7,6,5,4,9,3,2,1,10]=>111101110=>000010001
[6,5,2,7,8,4,1,3]=>1100110=>0011001
[7,6,5,4,2,8,9,1,3]=>11110010=>00001101
[8,7,6,5,4,3,9,2,1,10]=>111110110=>000001001
[7,6,5,4,3,1,8,9,2]=>11111001=>00000110
[7,10,9,6,5,4,3,2,1,8]=>011111110=>100000001
[9,8,10,7,6,5,4,3,2,1,11]=>1011111110=>0100000001
[6,5,8,7,4,3,2,1,9]=>10111110=>01000001
[8,6,9,10,5,4,3,2,1,7]=>100111110=>011000001
[9,8,7,10,6,5,4,3,2,1,11]=>1101111110=>0010000001
[7,5,4,8,6,3,2,1,9]=>11011110=>00100001
[5,9,8,7,4,3,2,1,6]=>01111110=>10000001
[8,7,5,9,10,4,3,2,1,6]=>110011110=>001100001
[9,8,7,6,11,5,4,3,2,1,10]=>1110111110=>0001000001
[6,4,3,2,5,8,1,7]=>1110010=>0001101
[7,6,4,3,9,5,2,1,8]=>11101110=>00010001
[7,4,8,9,6,3,2,1,5]=>10011110=>01100001
[8,7,6,4,10,9,3,2,1,5]=>111011110=>000100001
[9,8,7,6,5,10,4,3,2,1,11]=>1111011110=>0000100001
[6,3,7,2,5,4,1,8]=>1010110=>0101001
[7,6,5,3,2,8,4,1,9]=>11110110=>00001001
[7,6,3,8,9,5,2,1,4]=>11001110=>00110001
[8,7,6,5,3,9,10,2,1,4]=>111100110=>000011001
[9,8,7,6,5,4,10,3,2,1,11]=>1111101110=>0000010001
[7,6,5,4,2,1,8,3,9]=>11111010=>00000101
[6,3,2,7,5,4,1,8]=>1101110=>0010001
[7,6,5,2,9,8,4,1,3]=>11101110=>00010001
[8,7,6,5,4,2,9,10,1,3]=>111110010=>000001101
[9,8,7,6,5,4,3,11,2,1,10]=>1111110110=>0000001001
[7,6,5,4,1,8,9,3,2]=>11110011=>00001100
[8,7,6,5,4,3,1,10,9,2]=>111111011=>000000100
[9,8,7,6,5,4,3,2,10,1,11]=>1111111010=>0000000101
[9,8,7,6,5,4,3,2,1,10,11]=>1111111100=>0000000011
[8,4,2,6,3,1,7,5]=>1101101=>0010010
[1,5,3,7,4,2,8,6]=>0101101=>1010010
[1,6,7,3,4,2,8,5]=>0010101=>1101010
[8,6,5,2,3,1,7,4]=>1110101=>0001010
[1,7,6,3,4,2,8,5]=>0110101=>1001010
[1,8,6,3,2,5,7,4]=>0111001=>1000110
[8,7,5,2,1,4,6,3]=>1111001=>0000110
[7,8,5,2,1,4,6,3]=>0111001=>1000110
[6,8,5,2,3,1,7,4]=>0110101=>1001010
[5,8,6,2,3,1,7,4]=>0110101=>1001010
[4,8,2,6,3,1,7,5]=>0101101=>1010010
[3,2,8,6,4,1,7,5]=>1011101=>0100010
[3,2,1,7,5,4,8,6]=>1101101=>0010010
[4,1,3,7,5,2,8,6]=>1001101=>0110010
[5,1,7,3,4,2,8,6]=>1010101=>0101010
[7,1,6,3,2,5,8,4]=>1011001=>0100110
[1,2,7,4,3,6,8,5]=>0011001=>1100110
[6,1,8,2,4,5,7,3]=>1010001=>0101110
[5,1,8,3,2,6,7,4]=>1011001=>0100110
[3,2,8,7,1,5,6,4]=>1011001=>0100110
[4,8,2,7,1,5,6,3]=>0101001=>1010110
[5,8,7,2,1,4,6,3]=>0111001=>1000110
[6,8,7,1,3,4,5,2]=>0110001=>1001110
[7,8,6,1,3,4,5,2]=>0110001=>1001110
[1,7,8,2,4,5,6,3]=>0010001=>1101110
[8,6,7,1,3,4,5,2]=>1010001=>0101110
[7,6,8,1,3,4,5,2]=>1010001=>0101110
[6,5,8,2,3,1,7,4]=>1010101=>0101010
[1,6,8,3,2,5,7,4]=>0011001=>1100110
[1,5,3,8,2,6,7,4]=>0101001=>1010110
[8,4,2,7,1,5,6,3]=>1101001=>0010110
[7,4,2,8,1,5,6,3]=>1101001=>0010110
[6,4,2,8,3,1,7,5]=>1101101=>0010010
[5,4,2,3,8,1,7,6]=>1100101=>0011010
[4,5,2,3,1,6,8,7]=>0101001=>1010110
[7,4,2,1,3,6,8,5]=>1110001=>0001110
[8,4,2,1,3,6,7,5]=>1110001=>0001110
[1,5,3,2,4,7,8,6]=>0110001=>1001110
[8,5,1,3,2,6,7,4]=>1101001=>0010110
[5,6,1,3,4,2,8,7]=>0100101=>1011010
[4,6,2,1,5,3,8,7]=>0110101=>1001010
[4,7,2,1,3,6,8,5]=>0110001=>1001110
[5,7,1,3,2,6,8,4]=>0101001=>1010110
[6,7,1,2,4,5,8,3]=>0100001=>1011110
[8,6,1,2,4,5,7,3]=>1100001=>0011110
[1,8,2,3,5,6,7,4]=>0100001=>1011110
[8,7,1,2,4,5,6,3]=>1100001=>0011110
[7,8,1,2,4,5,6,3]=>0100001=>1011110
[5,8,1,3,2,6,7,4]=>0101001=>1010110
[4,8,2,1,3,6,7,5]=>0110001=>1001110
[4,1,3,2,5,7,8,6]=>1010001=>0101110
[5,1,2,4,3,7,8,6]=>1001001=>0110110
[5,4,8,1,2,3,7,6]=>1010001=>0101110
[1,4,7,6,3,2,5,8]=>0011100=>1100011
[4,8,3,2,7,6,1,5]=>0110110=>1001001
[4,3,8,2,7,1,6,5]=>1010101=>0101010
[1,4,7,3,6,2,5,8]=>0010100=>1101011
[4,3,2,8,1,7,6,5]=>1101011=>0010100
[4,1,8,3,7,2,5,6]=>1010100=>0101011
[4,1,8,7,3,2,5,6]=>1011100=>0100011
[4,7,8,1,2,5,3,6]=>0010010=>1101101
[3,4,7,6,2,1,8,5]=>0011101=>1100010
[3,4,2,7,1,6,8,5]=>0101001=>1010110
[2,3,6,7,4,1,8,5]=>0001101=>1110010
[2,6,3,4,7,8,1,5]=>0100010=>1011101
[2,6,7,8,3,4,1,5]=>0001010=>1110101
[3,1,7,8,4,2,5,6]=>1001100=>0110011
[4,1,3,2,8,7,5,6]=>1010110=>0101001
[3,7,8,2,6,4,1,5]=>0010110=>1101001
[4,2,3,8,1,6,7,5]=>1001001=>0110110
[4,3,1,8,2,5,7,6]=>1101001=>0010110
[1,3,6,7,4,2,5,8]=>0001100=>1110011
[3,2,7,8,4,1,6,5]=>1001101=>0110010
[4,2,8,6,3,1,7,5]=>1011101=>0100010
[3,7,2,4,8,6,1,5]=>0100110=>1011001
[3,2,7,4,8,1,6,5]=>1010101=>0101010
[1,3,6,4,7,2,5,8]=>0010100=>1101011
[3,2,4,7,1,8,6,5]=>1001011=>0110100
[3,7,4,2,6,8,1,5]=>0110010=>1001101
[3,7,4,6,2,8,1,5]=>0101010=>1010101
[4,7,1,5,8,2,3,6]=>0100100=>1011011
[3,7,6,4,8,2,1,5]=>0110110=>1001001
[3,1,7,4,8,2,5,6]=>1010100=>0101011
[2,6,7,3,8,4,1,5]=>0010110=>1101001
[2,3,6,4,7,1,8,5]=>0010101=>1101010
[8,7,5,2,6,3,4,1]=>1110101=>0001010
[8,6,5,2,7,3,4,1]=>1110101=>0001010
[7,4,8,5,6,3,2,1]=>1010111=>0101000
[3,4,6,7,8,5,1,2]=>0000110=>1111001
[1,2,6,4,7,5,8,3]=>0010101=>1101010
[3,1,7,5,4,2,6,8]=>1011100=>0100011
[6,3,8,5,4,7,1,2]=>1011010=>0100101
[1,6,2,5,4,7,8,3]=>0101001=>1010110
[1,8,2,5,6,3,7,4]=>0100101=>1011010
[1,2,6,4,8,5,7,3]=>0010101=>1101010
[7,8,3,1,4,2,5,6]=>0110100=>1001011
[4,8,1,5,2,3,6,7]=>0101000=>1010111
[7,4,1,5,2,3,6,8]=>1101000=>0010111
[5,6,1,8,4,3,2,7]=>0101110=>1010001
[5,1,8,6,4,3,2,7]=>1011110=>0100001
[5,1,6,3,8,7,2,4]=>1010110=>0101001
[6,1,2,5,8,3,7,4]=>1000101=>0111010
[6,1,8,7,4,3,2,5]=>1011110=>0100001
[7,1,2,5,4,8,6,3]=>1001011=>0110100
[1,2,7,5,8,3,6,4]=>0010101=>1101010
[4,1,6,3,7,5,2,8]=>1010110=>0101001
[1,3,6,7,8,5,2,4]=>0000110=>1111001
[1,2,6,4,7,8,5,3]=>0010011=>1101100
[4,1,6,3,7,8,2,5]=>1010010=>0101101
[3,1,6,4,8,2,7,5]=>1010101=>0101010
[7,8,4,1,6,3,2,5]=>0110110=>1001001
[4,1,6,3,8,7,2,5]=>1010110=>0101001
[7,5,1,8,4,3,2,6]=>1101110=>0010001
[6,5,1,7,4,3,2,8]=>1101110=>0010001
[4,1,8,5,2,3,7,6]=>1011001=>0100110
[4,1,6,8,3,7,2,5]=>1001010=>0110101
[5,4,6,1,3,8,2,7]=>1010010=>0101101
[6,5,8,1,4,3,2,7]=>1010110=>0101001
[1,3,5,7,6,8,2,4]=>0001010=>1110101
[1,3,5,7,6,2,8,4]=>0001101=>1110010
[1,3,5,7,2,6,8,4]=>0001001=>1110110
[1,3,5,2,7,6,4,8]=>0010110=>1101001
[1,3,5,7,6,2,4,8]=>0001100=>1110011
[1,3,5,7,4,6,8,2]=>0001001=>1110110
[1,3,5,7,4,6,2,8]=>0001010=>1110101
[1,3,5,7,4,2,6,8]=>0001100=>1110011
[1,3,5,4,7,2,6,8]=>0010100=>1101011
[1,3,5,4,7,8,2,6]=>0010010=>1101101
[1,3,5,4,7,2,8,6]=>0010101=>1101010
[1,3,5,7,4,2,8,6]=>0001101=>1110010
[1,3,5,7,4,8,2,6]=>0001010=>1110101
[1,3,5,7,4,8,6,2]=>0001011=>1110100
[1,3,5,7,8,4,6,2]=>0000101=>1111010
[1,3,5,7,8,4,2,6]=>0000110=>1111001
[1,3,5,2,7,8,6,4]=>0010011=>1101100
[1,3,5,7,2,8,6,4]=>0001011=>1110100
[1,3,5,7,8,2,6,4]=>0000101=>1111010
[1,6,3,2,7,4,8,5]=>0110101=>1001010
[3,5,1,6,2,8,7,4]=>0101011=>1010100
[1,3,7,2,5,4,8,6]=>0010101=>1101010
[1,3,7,5,2,4,8,6]=>0011001=>1100110
[2,5,7,4,3,8,1,6]=>0011010=>1100101
[2,5,3,7,4,8,1,6]=>0101010=>1010101
[2,4,7,3,1,8,6,5]=>0011011=>1100100
[1,4,7,3,8,2,6,5]=>0010101=>1101010
[3,2,6,7,8,1,5,4]=>1000101=>0111010
[3,5,2,7,8,4,1,6]=>0100110=>1011001
[1,5,7,4,8,3,2,6]=>0010110=>1101001
[4,6,2,1,7,8,3,5]=>0110010=>1001101
[3,5,2,6,8,4,7,1]=>0100101=>1011010
[2,5,7,4,3,8,6,1]=>0011011=>1100100
[1,5,7,2,4,8,6,3]=>0010011=>1101100
[4,6,3,7,2,8,5,1]=>0101011=>1010100
[1,4,7,3,8,6,2,5]=>0010110=>1101001
[5,1,6,8,2,4,3,7]=>1001010=>0110101
[5,3,7,8,2,4,1,6]=>1001010=>0110101
[8,5,3,7,2,4,1,6]=>1101010=>0010101
[8,2,4,7,3,1,5,6]=>1001100=>0110011
[2,4,7,8,3,1,5,6]=>0001100=>1110011
[6,3,1,5,8,2,4,7]=>1100100=>0011011
[6,5,3,4,2,8,1,7]=>1101010=>0010101
[5,2,4,3,8,1,6,7]=>1010100=>0101011
[3,2,4,8,1,5,6,7]=>1001000=>0110111
[3,2,4,6,8,1,5,7]=>1000100=>0111011
[8,1,5,7,3,2,4,6]=>1001100=>0110011
[8,4,6,7,2,3,1,5]=>1001010=>0110101
[4,6,7,8,2,3,1,5]=>0001010=>1110101
[7,4,6,8,2,3,1,5]=>1001010=>0110101
[7,2,4,8,3,1,5,6]=>1001100=>0110011
[5,3,8,7,2,4,1,6]=>1011010=>0100101
[2,4,8,7,3,1,5,6]=>0011100=>1100011
[4,6,8,7,2,3,1,5]=>0011010=>1100101
[8,7,4,6,2,3,1,5]=>1101010=>0010101
[5,6,8,7,2,3,1,4]=>0011010=>1100101
[6,4,8,7,2,3,1,5]=>1011010=>0100101
[3,1,7,4,2,8,6,5]=>1011011=>0100100
[3,2,8,4,1,7,6,5]=>1011011=>0100100
[7,6,4,8,2,3,1,5]=>1101010=>0010101
[5,7,6,8,2,3,1,4]=>0101010=>1010101
[4,7,6,8,2,3,1,5]=>0101010=>1010101
[8,6,4,7,2,3,1,5]=>1101010=>0010101
[8,2,3,7,4,1,6,5]=>1001101=>0110010
[2,3,7,8,4,1,6,5]=>0001101=>1110010
[3,7,4,8,2,5,1,6]=>0101010=>1010101
[2,3,7,4,1,6,8,5]=>0011001=>1100110
[8,1,6,4,2,3,7,5]=>1011001=>0100110
[4,7,8,6,2,3,1,5]=>0011010=>1100101
[2,4,7,3,1,5,8,6]=>0011001=>1100110
[6,3,1,7,4,2,8,5]=>1101101=>0010010
[8,5,7,6,2,3,1,4]=>1011010=>0100101
[7,5,8,6,2,3,1,4]=>1011010=>0100101
[7,1,6,4,2,3,8,5]=>1011001=>0100110
[3,1,7,6,4,2,8,5]=>1011101=>0100010
[4,8,7,6,2,3,1,5]=>0111010=>1000101
[6,8,7,5,2,3,1,4]=>0111010=>1000101
[4,3,6,1,5,8,7,2]=>1010011=>0101100
[4,3,6,5,1,8,7,2]=>1011011=>0100100
[4,6,3,5,1,8,7,2]=>0101011=>1010100
[4,6,3,1,5,8,7,2]=>0110011=>1001100
[4,1,6,5,3,8,7,2]=>1011011=>0100100
[4,6,1,5,3,8,7,2]=>0101011=>1010100
[2,6,5,3,1,8,7,4]=>0111011=>1000100
[2,6,5,1,8,7,3,4]=>0110110=>1001001
[2,6,5,8,1,7,3,4]=>0101010=>1010101
[2,6,5,8,1,3,7,4]=>0101001=>1010110
[2,6,5,8,3,1,7,4]=>0101101=>1010010
[2,6,5,3,8,1,7,4]=>0110101=>1001010
[4,6,1,5,8,3,7,2]=>0100101=>1011010
[4,1,6,5,8,3,7,2]=>1010101=>0101010
[1,4,6,5,8,3,7,2]=>0010101=>1101010
[4,1,6,5,8,7,3,2]=>1010111=>0101000
[2,6,5,3,8,7,1,4]=>0110110=>1001001
[6,4,3,8,7,1,5,2]=>1101101=>0010010
[6,4,8,3,7,1,5,2]=>1010101=>0101010
[2,6,8,5,3,7,1,4]=>0011010=>1100101
[4,6,8,1,5,7,3,2]=>0010011=>1101100
[4,6,1,8,5,7,3,2]=>0101011=>1010100
[4,1,6,8,5,7,3,2]=>1001011=>0110100
[1,4,6,8,5,7,3,2]=>0001011=>1110100
[1,4,6,8,5,3,7,2]=>0001101=>1110010
[4,6,1,8,5,3,7,2]=>0101101=>1010010
[2,6,8,5,3,1,7,4]=>0011101=>1100010
[2,6,8,5,1,7,3,4]=>0011010=>1100101
[4,6,8,3,5,1,7,2]=>0010101=>1101010
[4,6,8,3,1,5,7,2]=>0011001=>1100110
[4,6,3,1,8,5,7,2]=>0110101=>1001010
[4,6,3,8,1,5,7,2]=>0101001=>1010110
[4,6,3,8,5,7,1,2]=>0101010=>1010101
[4,3,6,8,1,5,7,2]=>1001001=>0110110
[4,3,6,1,8,5,7,2]=>1010101=>0101010
[4,3,1,6,8,5,7,2]=>1100101=>0011010
[4,1,3,6,8,7,5,2]=>1000111=>0111000
[4,3,6,1,8,7,5,2]=>1010111=>0101000
[4,3,6,8,1,7,5,2]=>1001011=>0110100
[6,5,2,8,7,3,1,4]=>1101110=>0010001
[6,5,2,8,7,1,3,4]=>1101100=>0010011
[6,2,5,8,7,1,3,4]=>1001100=>0110011
[6,2,5,8,7,3,1,4]=>1001110=>0110001
[4,6,3,8,1,7,5,2]=>0101011=>1010100
[4,6,3,1,8,7,5,2]=>0110111=>1001000
[4,1,6,3,8,7,5,2]=>1010111=>0101000
[1,4,6,3,8,7,5,2]=>0010111=>1101000
[4,1,6,8,3,7,5,2]=>1001011=>0110100
[4,6,1,8,3,7,5,2]=>0101011=>1010100
[4,6,8,1,3,7,5,2]=>0010011=>1101100
[6,2,8,5,7,3,1,4]=>1010110=>0101001
[6,2,8,5,7,1,3,4]=>1010100=>0101011
[2,4,8,7,1,5,3,6]=>0011010=>1100101
[4,2,8,7,5,3,1,6]=>1011110=>0100001
[6,4,1,8,7,5,3,2]=>1101111=>0010000
[6,1,4,8,7,5,3,2]=>1001111=>0110000
[1,6,4,8,7,3,5,2]=>0101101=>1010010
[6,4,1,8,7,3,5,2]=>1101101=>0010010
[4,2,8,7,5,1,3,6]=>1011100=>0100011
[2,4,8,7,3,5,1,6]=>0011010=>1100101
[2,3,4,5,6,8,9,7,1]=>00000011=>11111100
[2,3,4,7,1,8,6,5]=>0001011=>1110100
[2,3,4,5,7,8,9,6,1]=>00000011=>11111100
[2,3,5,6,7,8,9,4,1]=>00000011=>11111100
[2,4,5,6,7,8,9,3,1]=>00000011=>11111100
[2,3,4,5,6,7,9,10,8,1]=>000000011=>111111100
[2,3,4,7,8,5,6,1]=>0000101=>1111010
[2,3,4,5,8,1,9,7,6]=>00001011=>11110100
[2,3,4,5,6,8,9,10,7,1]=>000000011=>111111100
[2,3,6,7,4,8,5,1]=>0001011=>1110100
[2,3,4,7,1,8,9,6,5]=>00010011=>11101100
[2,5,6,3,7,8,1,4]=>0010010=>1101101
[2,3,7,1,4,8,6,5]=>0010011=>1101100
[2,3,6,1,7,8,9,4,5]=>00100010=>11011101
[2,3,4,6,7,8,9,10,5,1]=>000000011=>111111100
[2,6,1,3,7,8,5,4]=>0100011=>1011100
[2,5,1,6,7,8,9,4,3]=>01000011=>10111100
[2,3,5,6,7,8,9,10,4,1]=>000000011=>111111100
[4,1,5,6,7,8,9,3,2]=>10000011=>01111100
[2,3,4,5,6,7,10,1,8,9]=>000000100=>111111011
[2,3,4,5,6,7,8,10,11,9,1]=>0000000011=>1111111100
[2,3,4,5,8,9,6,7,1]=>00000101=>11111010
[2,3,4,5,6,9,1,10,8,7]=>000001011=>111110100
[2,3,4,5,6,7,9,10,11,8,1]=>0000000011=>1111111100
[2,3,4,7,8,5,9,6,1]=>00001011=>11110100
[2,3,4,5,8,1,9,10,7,6]=>000010011=>111101100
[2,3,4,5,6,8,9,10,11,1,7]=>0000000010=>1111111101
[2,5,6,7,4,8,1,3]=>0001010=>1110101
[2,3,6,7,4,8,9,1,5]=>00010010=>11101101
[2,3,4,8,1,5,9,7,6]=>00010011=>11101100
[2,3,4,7,1,8,9,10,5,6]=>000100010=>111011101
[2,3,4,5,7,8,9,10,11,6,1]=>0000000011=>1111111100
[2,5,6,3,7,8,9,4,1]=>00100011=>11011100
[2,3,7,8,4,5,6,1]=>0001001=>1110110
[2,3,7,1,4,8,9,6,5]=>00100011=>11011100
[2,3,6,1,7,8,9,10,5,4]=>001000011=>110111100
[2,3,4,6,7,8,9,10,11,5,1]=>0000000011=>1111111100
[4,5,2,6,7,8,9,3,1]=>01000011=>10111100
[2,6,7,3,4,8,5,1]=>0010011=>1101100
[2,6,1,3,7,8,9,4,5]=>01000010=>10111101
[2,5,1,6,7,8,9,10,4,3]=>010000011=>101111100
[2,3,5,6,7,8,9,10,11,1,4]=>0000000010=>1111111101
[5,1,2,6,7,8,9,4,3]=>10000011=>01111100
[4,1,5,6,7,8,9,10,2,3]=>100000010=>011111101
[2,4,5,6,7,8,9,10,11,3,1]=>0000000011=>1111111100
[3,4,5,6,7,8,9,10,11,2,1]=>0000000011=>1111111100
[1,5,3,2,6,4,7,8]=>0110100=>1001011
[1,5,3,2,6,7,4,8]=>0110010=>1001101
[1,7,3,2,8,5,4,6]=>0110110=>1001001
[1,7,3,2,5,8,4,6]=>0110010=>1001101
[1,3,2,7,5,4,8,6]=>0101101=>1010010
[6,5,2,4,3,7,1,8]=>1101010=>0010101
[6,4,2,5,3,7,1,8]=>1101010=>0010101
[5,4,7,6,2,3,1,8]=>1011010=>0100101
[3,6,4,8,2,1,5,7]=>0101100=>1010011
[1,6,2,8,5,3,4,7]=>0101100=>1010011
[4,6,2,3,7,5,1,8]=>0100110=>1011001
[4,7,2,3,6,5,1,8]=>0100110=>1011001
[4,7,2,3,5,6,1,8]=>0100010=>1011101
[5,3,2,7,4,6,1,8]=>1101010=>0010101
[5,3,2,6,4,7,1,8]=>1101010=>0010101
[4,6,2,3,5,7,1,8]=>0100010=>1011101
[3,5,2,1,6,8,4,7]=>0110010=>1001101
[1,5,2,6,8,4,3,7]=>0100110=>1011001
[1,5,7,2,8,4,3,6]=>0010110=>1101001
[3,5,2,1,8,6,4,7]=>0110110=>1001001
[3,6,8,4,2,1,5,7]=>0011100=>1100011
[4,3,2,6,1,8,5,7]=>1101010=>0010101
[1,5,8,2,7,4,3,6]=>0010110=>1101001
[1,7,2,3,4,8,6,5]=>0100011=>1011100
[6,8,2,3,4,1,7,5]=>0100101=>1011010
[4,1,8,2,3,5,7,6]=>1010001=>0101110
[2,3,1,8,4,5,7,6]=>0101001=>1010110
[7,3,2,1,4,5,8,6]=>1110001=>0001110
[7,8,1,4,3,5,2,6]=>0101010=>1010101
[7,1,2,3,4,6,8,5]=>1000001=>0111110
[6,1,2,3,4,8,7,5]=>1000011=>0111100
[1,8,2,3,4,7,6,5]=>0100011=>1011100
[8,1,2,3,4,6,7,5]=>1000001=>0111110
[2,8,1,3,5,4,7,6]=>0100101=>1011010
[8,7,1,4,3,5,2,6]=>1101010=>0010101
[8,3,2,1,4,5,7,6]=>1110001=>0001110
[3,8,2,1,5,6,4,7]=>0110010=>1001101
[3,8,2,1,6,5,4,7]=>0110110=>1001001
[1,7,8,3,5,4,2,6]=>0010110=>1101001
[7,4,1,8,3,5,2,6]=>1101010=>0010101
[8,4,1,7,3,5,2,6]=>1101010=>0010101
[3,8,4,6,2,1,5,7]=>0101100=>1010011
[8,4,2,5,3,1,6,7]=>1101100=>0010011
[8,5,2,4,3,1,6,7]=>1101100=>0010011
[8,3,2,5,4,1,6,7]=>1101100=>0010011
[4,3,2,5,1,8,6,7]=>1101010=>0010101
[3,5,2,4,1,8,6,7]=>0101010=>1010101
[2,4,7,8,1,5,3,6]=>0001010=>1110101
[1,8,7,3,5,4,2,6]=>0110110=>1001001
[5,1,8,2,7,4,3,6]=>1010110=>0101001
[5,1,7,2,8,4,3,6]=>1010110=>0101001
[6,1,2,8,5,3,4,7]=>1001100=>0110011
[6,3,2,1,8,4,5,7]=>1110100=>0001011
[7,3,2,8,4,5,1,6]=>1101010=>0010101
[2,7,8,4,3,5,1,6]=>0011010=>1100101
[7,1,8,3,5,4,2,6]=>1010110=>0101001
[7,8,2,3,4,6,1,5]=>0100010=>1011101
[6,7,1,3,4,8,2,5]=>0100010=>1011101
[6,8,1,3,4,7,2,5]=>0100010=>1011101
[1,7,2,3,4,6,8,5]=>0100001=>1011110
[1,6,2,3,4,8,7,5]=>0100011=>1011100
[7,6,2,3,4,1,8,5]=>1100101=>0011010
[8,6,2,3,4,1,7,5]=>1100101=>0011010
[8,1,7,3,5,4,2,6]=>1010110=>0101001
[8,3,2,7,4,5,1,6]=>1101010=>0010101
[6,7,2,3,4,1,8,5]=>0100101=>1011010
[7,6,2,3,4,8,1,5]=>1100010=>0011101
[8,6,2,3,4,7,1,5]=>1100010=>0011101
[6,3,4,8,7,5,1,2]=>1001110=>0110001
[4,8,7,3,5,6,1,2]=>0110010=>1001101
[4,8,7,5,3,6,1,2]=>0111010=>1000101
[5,8,7,3,4,6,1,2]=>0110010=>1001101
[5,8,4,2,1,6,7,3]=>0111001=>1000110
[5,8,4,1,2,6,7,3]=>0110001=>1001110
[5,3,7,2,6,1,8,4]=>1010101=>0101010
[5,2,8,1,6,3,7,4]=>1010101=>0101010
[5,8,2,1,4,7,6,3]=>0110011=>1001100
[4,8,2,5,1,7,6,3]=>0101011=>1010100
[7,8,4,1,2,6,5,3]=>0110011=>1001100
[4,8,1,5,2,7,6,3]=>0101011=>1010100
[5,8,1,2,4,7,6,3]=>0100011=>1011100
[5,2,8,3,6,7,1,4]=>1010010=>0101101
[3,8,7,6,2,4,1,5]=>0111010=>1000101
[2,8,7,6,4,1,3,5]=>0111100=>1000011
[7,8,2,6,5,1,3,4]=>0101100=>1010011
[1,8,7,6,4,2,3,5]=>0111100=>1000011
[2,8,7,6,3,1,4,5]=>0111100=>1000011
[1,8,7,6,2,4,3,5]=>0111010=>1000101
[1,8,7,6,3,4,2,5]=>0111010=>1000101
[2,8,1,4,5,6,7,3]=>0100001=>1011110
[2,1,7,3,6,5,8,4]=>1010101=>0101010
[3,1,7,2,6,5,8,4]=>1010101=>0101010
[3,2,7,1,6,5,8,4]=>1010101=>0101010
[6,1,2,8,5,7,3,4]=>1001010=>0110101
[6,2,1,8,5,7,3,4]=>1101010=>0010101
[6,3,1,8,5,7,2,4]=>1101010=>0010101
[6,4,2,1,7,5,8,3]=>1110101=>0001010
[6,1,3,8,5,2,7,4]=>1001101=>0110010
[2,3,7,1,6,8,5,4]=>0010011=>1101100
[1,3,7,2,6,8,5,4]=>0010011=>1101100
[7,8,2,6,5,3,1,4]=>0101110=>1010001
[3,2,6,7,5,8,1,4]=>1001010=>0110101
[1,2,7,5,6,3,8,4]=>0010101=>1101010
[2,8,7,6,4,3,1,5]=>0111110=>1000001
[3,8,7,6,1,2,5,4]=>0111001=>1000110
[3,8,7,6,2,1,5,4]=>0111101=>1000010
[4,8,7,6,2,1,3,5]=>0111100=>1000011
[4,8,7,6,1,3,2,5]=>0111010=>1000101
[3,8,7,6,4,1,2,5]=>0111100=>1000011
[7,8,3,6,5,1,2,4]=>0101100=>1010011
[2,3,7,5,6,8,1,4]=>0010010=>1101101
[3,8,7,6,4,2,1,5]=>0111110=>1000001
[5,1,4,6,8,2,3,7]=>1000100=>0111011
[1,7,6,3,5,4,8,2]=>0110101=>1001010
[4,3,7,2,6,5,1,8]=>1010110=>0101001
[3,4,6,1,5,7,2,8]=>0010010=>1101101
[1,6,8,5,7,3,4,2]=>0010101=>1101010
[2,4,1,5,8,6,3,7]=>0100110=>1011001
[4,6,1,2,5,8,3,7]=>0100010=>1011101
[5,6,7,2,1,4,8,3]=>0011001=>1100110
[7,8,6,5,1,2,4,3]=>0111001=>1000110
[1,3,6,5,7,8,2,4]=>0010010=>1101101
[7,4,8,5,3,1,6,2]=>1011101=>0100010
[6,8,5,2,4,1,7,3]=>0110101=>1001010
[2,3,1,6,8,5,7,4]=>0100101=>1011010
[7,3,2,5,1,4,8,6]=>1101001=>0010110
[7,1,4,2,3,6,8,5]=>1010001=>0101110
[1,5,8,3,4,6,7,2]=>0010001=>1101110
[8,3,1,2,4,7,6,5]=>1100011=>0011100
[2,3,8,1,6,5,4,7]=>0010110=>1101001
[8,1,4,7,2,5,3,6]=>1001010=>0110101
[3,5,2,4,1,7,8,6]=>0101001=>1010110
[3,4,7,8,6,2,1,5]=>0001110=>1110001
[3,4,8,6,2,7,1,5]=>0011010=>1100101
[5,8,2,1,6,7,3,4]=>0110010=>1001101
[5,7,2,8,6,4,3,1]=>0101111=>1010000
[6,1,2,7,5,3,8,4]=>1001101=>0110010
[7,3,2,8,6,4,1,5]=>1101110=>0010001
[2,7,8,4,6,3,1,5]=>0010110=>1101001
[1,4,5,7,2,6,8,3]=>0001001=>1110110
[7,3,5,2,6,1,8,4]=>1010101=>0101010
[8,5,2,3,6,1,7,4]=>1100101=>0011010
[8,1,6,3,5,7,2,4]=>1010010=>0101101
[2,8,6,4,3,7,1,5]=>0111010=>1000101
[8,3,2,6,4,7,1,5]=>1101010=>0010101
[2,3,8,7,6,5,1,4]=>0011110=>1100001
[1,2,8,7,3,6,5,4]=>0011011=>1100100
[4,2,8,7,3,6,1,5]=>1011010=>0100101
[4,5,8,7,1,2,6,3]=>0011001=>1100110
[1,5,8,7,3,2,6,4]=>0011101=>1100010
[4,5,8,7,3,2,1,6]=>0011110=>1100001
[2,6,8,1,7,5,4,3]=>0010111=>1101000
[3,6,8,4,7,2,1,5]=>0010110=>1101001
[2,5,8,3,7,6,1,4]=>0010110=>1101001
[3,2,8,4,7,6,1,5]=>1010110=>0101001
[1,5,8,3,7,2,6,4]=>0010101=>1101010
[3,5,8,4,7,2,1,6]=>0010110=>1101001
[5,6,8,2,3,7,1,4]=>0010010=>1101101
[1,6,8,4,2,7,5,3]=>0011011=>1100100
[1,5,8,4,2,7,6,3]=>0011011=>1100100
[1,5,8,2,3,7,6,4]=>0010011=>1101100
[2,1,8,4,3,7,6,5]=>1011011=>0100100
[2,5,8,4,3,7,1,6]=>0011010=>1100101
[5,6,8,4,1,2,7,3]=>0011001=>1100110
[5,6,8,1,3,2,7,4]=>0010101=>1101010
[1,6,8,4,3,2,7,5]=>0011101=>1100010
[5,6,8,4,3,2,1,7]=>0011110=>1100001
[7,1,2,8,6,5,4,3]=>1001111=>0110000
[7,1,4,8,6,2,5,3]=>1001101=>0110010
[7,3,1,8,6,2,5,4]=>1101101=>0010010
[7,2,4,8,3,6,1,5]=>1001010=>0110101
[7,1,4,8,3,2,6,5]=>1001101=>0110010
[7,4,5,8,3,2,1,6]=>1001110=>0110001
[1,6,2,8,7,5,4,3]=>0101111=>1010000
[1,6,4,8,7,2,5,3]=>0101101=>1010010
[3,6,4,8,7,2,1,5]=>0101110=>1010001
[3,2,5,8,7,6,1,4]=>1001110=>0110001
[3,2,4,8,7,6,1,5]=>1001110=>0110001
[3,1,5,8,7,2,6,4]=>1001101=>0110010
[3,1,4,8,7,2,6,5]=>1001101=>0110010
[1,6,4,8,2,7,5,3]=>0101011=>1010100
[1,4,5,8,2,7,6,3]=>0001011=>1110100
[2,4,5,8,3,7,1,6]=>0001010=>1110101
[4,6,5,8,1,2,7,3]=>0101001=>1010110
[1,6,4,8,3,2,7,5]=>0101101=>1010010
[1,4,5,8,3,2,7,6]=>0001101=>1110010
[7,6,1,4,8,2,5,3]=>1100101=>0011010
[7,6,1,3,8,2,5,4]=>1100101=>0011010
[7,6,3,4,8,2,1,5]=>1100110=>0011001
[7,2,5,1,8,6,4,3]=>1010111=>0101000
[7,2,5,3,8,6,1,4]=>1010110=>0101001
[7,2,1,4,8,6,5,3]=>1100111=>0011000
[7,2,1,3,8,6,5,4]=>1100111=>0011000
[7,2,3,4,8,6,1,5]=>1000110=>0111001
[7,3,5,4,8,2,1,6]=>1010110=>0101001
[2,6,5,1,8,7,4,3]=>0110111=>1001000
[2,3,5,4,8,7,1,6]=>0010110=>1101001
[1,6,5,4,8,2,7,3]=>0110101=>1001010
[1,6,5,3,8,2,7,4]=>0110101=>1001010
[1,6,3,4,8,2,7,5]=>0100101=>1011010
[1,3,5,4,8,2,7,6]=>0010101=>1101010
[3,6,5,4,8,2,1,7]=>0110110=>1001001
[7,6,5,2,3,8,1,4]=>1110010=>0001101
[7,6,1,4,2,8,5,3]=>1101011=>0010100
[7,6,1,2,3,8,5,4]=>1100011=>0011100
[7,6,2,4,3,8,1,5]=>1101010=>0010101
[7,1,5,4,2,8,6,3]=>1011011=>0100100
[7,1,5,2,3,8,6,4]=>1010011=>0101100
[7,1,2,4,3,8,6,5]=>1001011=>0110100
[2,6,5,4,3,8,1,7]=>0111010=>1000101
[7,6,1,4,3,2,8,5]=>1101101=>0010010
[7,1,5,4,3,2,8,6]=>1011101=>0100010
[3,4,2,6,7,8,1,5]=>0100010=>1011101
[3,1,4,2,6,8,7,5]=>1010011=>0101100
[8,3,4,2,6,1,7,5]=>1010101=>0101010
[2,6,7,3,5,4,1,8]=>0010110=>1101001
[2,7,8,3,5,4,1,6]=>0010110=>1101001
[2,6,8,3,5,4,1,7]=>0010110=>1101001
[4,7,1,2,8,5,3,6]=>0100110=>1011001
[4,8,1,2,7,5,3,6]=>0100110=>1011001
[2,1,6,3,7,5,4,8]=>1010110=>0101001
[2,7,1,3,6,8,4,5]=>0100010=>1011101
[6,7,3,2,8,1,4,5]=>0110100=>1001011
[7,3,4,2,6,1,8,5]=>1010101=>0101010
[7,4,1,2,8,5,3,6]=>1100110=>0011001
[8,7,4,2,1,5,3,6]=>1111010=>0000101
[7,4,1,2,6,5,3,8]=>1100110=>0011001
[7,4,3,1,5,6,8,2]=>1110001=>0001110
[6,7,4,1,5,8,3,2]=>0110011=>1001100
[4,7,5,1,6,8,3,2]=>0110011=>1001100
[4,5,3,1,7,6,8,2]=>0110101=>1001010
[4,6,1,2,7,5,3,8]=>0100110=>1011001
[2,7,1,3,6,5,4,8]=>0100110=>1011001
[4,1,8,2,6,5,3,7]=>1010110=>0101001
[4,6,1,2,8,5,3,7]=>0100110=>1011001
[8,4,3,1,5,6,7,2]=>1110001=>0001110
[4,5,3,1,8,6,7,2]=>0110101=>1001010
[4,8,5,6,3,1,7,2]=>0101101=>1010010
[5,1,3,4,8,6,7,2]=>1000101=>0111010
[5,4,3,8,1,6,7,2]=>1101001=>0010110
[8,5,3,4,1,6,7,2]=>1101001=>0010110
[6,4,8,2,1,5,3,7]=>1011010=>0100101
[6,7,3,2,5,1,4,8]=>0110100=>1001011
[6,8,3,2,5,1,4,7]=>0110100=>1001011
[5,7,1,4,6,8,3,2]=>0100011=>1011100
[5,1,3,4,7,6,8,2]=>1000101=>0111010
[6,1,4,2,7,5,3,8]=>1010110=>0101001
[5,4,3,7,1,6,8,2]=>1101001=>0010110
[6,7,5,4,1,8,3,2]=>0111011=>1000100
[7,6,4,2,1,5,3,8]=>1111010=>0000101
[8,2,7,6,5,4,1,3]=>1011110=>0100001
[7,2,8,6,5,4,3,1]=>1011111=>0100000
[8,1,9,7,6,5,4,3,2]=>10111111=>01000000
[2,10,9,8,7,6,5,4,1,3]=>011111110=>100000001
[9,2,8,7,6,5,4,1,3]=>10111110=>01000001
[3,9,8,7,6,5,4,1,2]=>01111110=>10000001
[8,7,2,6,5,4,1,3]=>1101110=>0010001
[3,2,8,7,6,5,1,4]=>1011110=>0100001
[4,8,7,6,5,3,1,2]=>0111110=>1000001
[7,8,6,1,5,4,3,2]=>0110111=>1001000
[8,9,1,7,6,5,4,3,2]=>01011111=>10100000
[7,3,8,6,5,4,2,1]=>1011111=>0100000
[8,2,9,7,6,5,4,3,1]=>10111111=>01000000
[9,1,10,8,7,6,5,4,3,2]=>101111111=>010000000
[4,8,5,7,6,3,2,1]=>0101111=>1010000
[3,8,7,4,6,5,2,1]=>0110111=>1001000
[2,8,7,6,3,5,4,1]=>0111011=>1000100
[8,5,6,1,3,2,4,7]=>1010100=>0101011
[8,6,1,5,3,2,4,7]=>1101100=>0010011
[7,8,1,5,3,2,4,6]=>0101100=>1010011
[8,1,7,5,3,2,4,6]=>1011100=>0100011
[8,6,1,4,5,2,3,7]=>1100100=>0011011
[8,6,3,1,5,2,4,7]=>1110100=>0001011
[8,4,6,1,5,2,3,7]=>1010100=>0101011
[8,6,2,1,5,4,3,7]=>1110110=>0001001
[8,5,2,6,1,4,3,7]=>1101010=>0010101
[8,5,2,1,7,4,3,6]=>1110110=>0001001
[7,8,2,1,5,4,3,6]=>0110110=>1001001
[7,8,3,1,5,2,4,6]=>0110100=>1001011
[8,2,7,5,1,3,4,6]=>1011000=>0100111
[8,4,1,7,5,2,3,6]=>1101100=>0010011
[8,2,7,1,5,4,3,6]=>1010110=>0101001
[8,2,6,1,7,4,3,5]=>1010110=>0101001
[8,1,7,4,3,2,6,5]=>1011101=>0100010
[8,1,5,7,3,2,6,4]=>1001101=>0110010
[5,7,8,1,3,2,6,4]=>0010101=>1101010
[8,2,6,1,5,7,3,4]=>1010010=>0101101
[5,8,1,6,7,2,3,4]=>0100100=>1011011
[5,7,6,1,8,2,3,4]=>0110100=>1001011
[6,7,2,5,1,8,3,4]=>0101010=>1010101
[7,5,1,6,8,2,3,4]=>1100100=>0011011
[6,5,7,1,8,2,3,4]=>1010100=>0101011
[6,7,3,8,1,2,4,5]=>0101000=>1010111
[7,5,4,1,8,2,3,6]=>1110100=>0001011
[7,6,1,4,8,2,3,5]=>1100100=>0011011
[8,1,6,4,7,2,3,5]=>1010100=>0101011
[7,5,8,1,3,2,4,6]=>1010100=>0101011
[7,8,4,1,3,2,5,6]=>0110100=>1001011
[8,3,7,4,1,2,5,6]=>1011000=>0100111
[8,5,1,7,3,2,4,6]=>1101100=>0010011
[6,8,1,7,3,2,4,5]=>0101100=>1010011
[7,1,8,4,3,6,2,5]=>1011010=>0100101
[7,3,1,8,6,4,2,5]=>1101110=>0010001
[8,3,1,7,4,6,2,5]=>1101010=>0010101
[8,4,5,1,7,2,3,6]=>1010100=>0101011
[5,6,8,1,7,2,3,4]=>0010100=>1101011
[6,5,8,1,2,7,3,4]=>1010010=>0101101
[7,3,1,8,5,6,2,4]=>1101010=>0010101
[6,2,7,8,3,1,5,4]=>1001101=>0110010
[5,8,1,7,3,2,6,4]=>0101101=>1010010
[8,4,1,7,3,2,6,5]=>1101101=>0010010
[8,3,4,7,1,2,6,5]=>1001001=>0110110
[8,2,7,4,1,3,6,5]=>1011001=>0100110
[7,4,8,2,1,3,6,5]=>1011001=>0100110
[7,4,3,8,1,2,6,5]=>1101001=>0010110
[8,2,3,6,7,1,5,4]=>1000101=>0111010
[2,6,8,7,1,5,4,3]=>0011011=>1100100
[7,8,5,2,3,6,4,1]=>0110011=>1001100
[8,7,5,2,3,1,6,4]=>1110101=>0001010
[6,8,5,2,3,4,7,1]=>0110001=>1001110
[3,5,2,6,8,1,4,7]=>0100100=>1011011
[3,5,2,4,6,8,1,7]=>0100010=>1011101
[2,4,5,7,3,6,8,1]=>0001001=>1110110
[2,4,5,3,6,8,1,7]=>0010010=>1101101
[5,2,4,6,8,1,3,7]=>1000100=>0111011
[5,1,3,4,6,8,2,7]=>1000010=>0111101
[4,3,5,2,6,8,1,7]=>1010010=>0101101
[4,3,5,7,2,8,1,6]=>1001010=>0110101
[4,3,5,7,2,6,8,1]=>1001001=>0110110
[4,6,3,7,2,5,8,1]=>0101001=>1010110
[4,6,3,1,7,8,2,5]=>0110010=>1001101
[4,3,5,1,7,8,2,6]=>1010010=>0101101
[5,7,1,3,4,8,2,6]=>0100010=>1011101
[5,7,1,3,4,6,8,2]=>0100001=>1011110
[4,5,7,1,3,6,8,2]=>0010001=>1101110
[4,3,6,7,1,5,8,2]=>1001001=>0110110
[4,6,3,5,1,7,8,2]=>0101001=>1010110
[4,6,3,5,7,2,8,1]=>0100101=>1011010
[3,5,6,4,1,7,8,2]=>0011001=>1100110
[3,1,5,6,7,4,8,2]=>1000101=>0111010
[5,1,6,7,3,4,8,2]=>1001001=>0110110
[6,4,7,1,3,5,8,2]=>1010001=>0101110
[1,6,7,3,4,5,8,2]=>0010001=>1101110
[2,6,7,4,5,8,1,3]=>0010010=>1101101
[2,6,7,4,8,1,3,5]=>0010100=>1101011
[5,3,6,1,2,7,8,4]=>1010001=>0101110
[3,5,2,6,1,7,8,4]=>0101001=>1010110
[3,5,2,6,7,4,8,1]=>0100101=>1011010
[5,2,3,6,7,4,8,1]=>1000101=>0111010
[5,2,3,6,1,7,8,4]=>1001001=>0110110
[5,2,6,1,3,7,8,4]=>1010001=>0101110
[4,2,6,7,3,5,8,1]=>1001001=>0110110
[6,3,7,2,4,5,8,1]=>1010001=>0101110
[3,5,7,2,8,1,4,6]=>0010100=>1101011
[3,7,2,4,8,1,5,6]=>0100100=>1011011
[7,2,4,6,8,1,3,5]=>1000100=>0111011
[7,1,3,4,6,8,2,5]=>1000010=>0111101
[3,7,2,4,6,8,1,5]=>0100010=>1011101
[3,5,7,2,6,8,1,4]=>0010010=>1101101
[6,3,7,2,5,8,1,4]=>1010010=>0101101
[6,3,5,7,2,8,1,4]=>1001010=>0110101
[6,3,5,7,2,4,8,1]=>1001001=>0110110
[6,2,4,5,7,3,8,1]=>1000101=>0111010
[6,2,4,5,1,7,8,3]=>1001001=>0110110
[4,7,1,2,5,6,8,3]=>0100001=>1011110
[2,6,7,5,8,1,3,4]=>0010100=>1101011
[4,6,7,1,2,5,8,3]=>0010001=>1101110
[5,6,2,4,7,3,8,1]=>0100101=>1011010
[5,4,2,6,7,3,8,1]=>1100101=>0011010
[5,4,2,6,1,7,8,3]=>1101001=>0010110
[1,5,4,6,2,7,8,3]=>0101001=>1010110
[5,6,4,1,2,7,8,3]=>0110001=>1001110
[6,4,5,1,2,7,8,3]=>1010001=>0101110
[6,3,5,1,7,8,2,4]=>1010010=>0101101
[6,5,7,2,8,1,3,4]=>1010100=>0101011
[6,5,7,1,3,4,8,2]=>1010001=>0101110
[5,6,4,7,1,3,8,2]=>0101001=>1010110
[5,4,6,3,1,7,8,2]=>1011001=>0100110
[7,5,3,2,4,8,1,6]=>1110010=>0001101
[8,4,5,2,6,1,3,7]=>1010100=>0101011
[8,5,4,2,1,6,3,7]=>1111010=>0000101
[8,5,3,4,1,6,2,7]=>1101010=>0010101
[8,4,5,3,1,6,2,7]=>1011010=>0100101
[7,5,4,2,1,8,3,6]=>1111010=>0000101
[7,5,4,2,1,6,8,3]=>1111001=>0000110
[7,4,5,3,1,6,8,2]=>1011001=>0100110
[7,4,3,5,6,1,8,2]=>1100101=>0011010
[5,6,3,7,4,1,8,2]=>0101101=>1010010
[5,6,7,3,1,4,8,2]=>0011001=>1100110
[6,7,3,4,1,5,8,2]=>0101001=>1010110
[6,7,4,2,1,5,8,3]=>0111001=>1000110
[5,6,7,3,1,8,2,4]=>0011010=>1100101
[5,6,3,7,8,1,2,4]=>0100100=>1011011
[5,6,3,7,2,4,8,1]=>0101001=>1010110
[5,6,7,2,3,8,1,4]=>0010010=>1101101
[7,4,5,2,8,1,3,6]=>1010100=>0101011
[6,7,3,2,4,8,1,5]=>0110010=>1001101
[7,6,4,2,1,3,8,5]=>1111001=>0000110
[7,6,3,4,1,2,8,5]=>1101001=>0010110
[7,6,3,2,4,1,8,5]=>1110101=>0001010
[6,7,3,2,5,1,8,4]=>0110101=>1001010
[6,5,3,2,7,8,1,4]=>1110010=>0001101
[6,5,3,2,7,4,8,1]=>1110101=>0001010
[6,4,5,2,7,3,8,1]=>1010101=>0101010
[6,4,5,2,7,8,1,3]=>1010010=>0101101
[7,4,5,2,6,1,8,3]=>1010101=>0101010
[7,4,5,6,1,2,8,3]=>1001001=>0110110
[7,5,6,2,1,3,8,4]=>1011001=>0100110
[6,7,3,5,1,2,8,4]=>0101001=>1010110
[5,6,7,4,1,2,8,3]=>0011001=>1100110
[5,6,7,2,4,1,8,3]=>0010101=>1101010
[5,6,4,2,7,8,1,3]=>0110010=>1001101
[6,5,7,2,1,8,3,4]=>1011010=>0100101
[6,5,7,2,1,4,8,3]=>1011001=>0100110
[5,4,6,7,3,1,8,2]=>1001101=>0110010
[5,7,8,3,6,4,1,2]=>0010110=>1101001
[3,7,8,5,6,4,1,2]=>0010110=>1101001
[3,7,8,5,6,1,4,2]=>0010101=>1101010
[1,7,8,5,6,3,4,2]=>0010101=>1101010
[1,7,5,8,6,3,4,2]=>0101101=>1010010
[3,7,5,8,6,1,4,2]=>0101101=>1010010
[3,7,5,8,6,4,1,2]=>0101110=>1010001
[5,7,3,8,6,4,1,2]=>0101110=>1010001
[7,3,8,5,6,4,1,2]=>1010110=>0101001
[7,3,5,8,6,4,1,2]=>1001110=>0110001
[3,5,7,8,6,4,1,2]=>0001110=>1110001
[1,5,7,8,6,3,4,2]=>0001101=>1110010
[1,5,7,8,3,6,4,2]=>0001011=>1110100
[3,5,7,8,1,6,4,2]=>0001011=>1110100
[5,3,7,8,1,6,4,2]=>1001011=>0110100
[7,3,5,8,6,1,4,2]=>1001101=>0110010
[7,3,8,5,6,1,4,2]=>1010101=>0101010
[7,8,1,5,6,3,4,2]=>0100101=>1011010
[7,1,8,5,6,3,4,2]=>1010101=>0101010
[7,1,5,8,6,3,4,2]=>1001101=>0110010
[5,1,7,8,3,6,4,2]=>1001011=>0110100
[3,1,7,8,5,6,4,2]=>1001011=>0110100
[1,3,7,8,5,6,4,2]=>0001011=>1110100
[3,1,7,5,8,6,4,2]=>1010111=>0101000
[5,1,7,3,8,6,4,2]=>1010111=>0101000
[7,1,5,3,8,6,4,2]=>1010111=>0101000
[7,1,5,8,3,6,4,2]=>1001011=>0110100
[7,8,1,5,3,6,4,2]=>0101011=>1010100
[7,8,3,5,1,6,4,2]=>0101011=>1010100
[7,3,5,8,1,6,4,2]=>1001011=>0110100
[5,3,7,1,8,6,4,2]=>1010111=>0101000
[3,5,7,1,8,6,4,2]=>0010111=>1101000
[1,7,5,3,8,6,4,2]=>0110111=>1001000
[5,7,3,1,8,6,4,2]=>0110111=>1001000
[5,7,3,8,6,1,4,2]=>0101101=>1010010
[3,7,5,8,1,6,4,2]=>0101011=>1010100
[1,7,5,8,3,6,4,2]=>0101011=>1010100
[1,7,8,5,3,6,4,2]=>0011011=>1100100
[3,7,8,5,1,6,4,2]=>0011011=>1100100
[5,7,8,3,6,1,4,2]=>0010101=>1101010
[5,7,8,6,3,1,4,2]=>0011101=>1100010
[7,5,8,6,1,3,4,2]=>1011001=>0100110
[5,7,8,1,6,3,4,2]=>0010101=>1101010
[5,7,8,1,3,6,4,2]=>0010011=>1101100
[3,7,8,1,5,6,4,2]=>0010011=>1101100
[1,7,8,3,5,6,4,2]=>0010011=>1101100
[1,7,3,8,5,6,4,2]=>0101011=>1010100
[3,7,1,8,5,6,4,2]=>0101011=>1010100
[5,7,1,8,3,6,4,2]=>0101011=>1010100
[5,7,1,8,6,3,4,2]=>0101101=>1010010
[7,5,1,8,6,3,4,2]=>1101101=>0010010
[7,5,8,1,6,3,4,2]=>1010101=>0101010
[7,8,5,1,6,3,4,2]=>0110101=>1001010
[7,8,5,1,3,6,4,2]=>0110011=>1001100
[7,5,8,1,3,6,4,2]=>1010011=>0101100
[7,5,1,8,3,6,4,2]=>1101011=>0010100
[7,5,1,3,8,6,4,2]=>1100111=>0011000
[5,7,1,3,8,6,4,2]=>0100111=>1011000
[3,7,1,5,8,6,4,2]=>0100111=>1011000
[1,7,3,5,8,6,4,2]=>0100111=>1011000
[1,5,3,7,8,6,4,2]=>0100111=>1011000
[3,5,1,7,8,6,4,2]=>0100111=>1011000
[5,3,1,7,8,6,4,2]=>1100111=>0011000
[7,3,1,5,8,6,4,2]=>1100111=>0011000
[7,3,1,8,5,6,4,2]=>1101011=>0010100
[7,3,8,1,5,6,4,2]=>1010011=>0101100
[7,8,3,1,5,6,4,2]=>0110011=>1001100
[7,8,1,3,5,6,4,2]=>0100011=>1011100
[7,1,8,3,5,6,4,2]=>1010011=>0101100
[7,1,3,8,5,6,4,2]=>1001011=>0110100
[7,1,3,5,8,6,4,2]=>1000111=>0111000
[3,1,5,7,8,6,4,2]=>1000111=>0111000
[5,7,3,4,6,8,1,2]=>0100010=>1011101
[5,7,3,4,8,6,1,2]=>0100110=>1011001
[5,7,3,4,8,1,6,2]=>0100101=>1011010
[5,7,3,4,1,8,6,2]=>0101011=>1010100
[5,7,3,4,1,6,8,2]=>0101001=>1010110
[5,7,3,4,6,1,2,8]=>0100100=>1011011
[7,3,5,6,1,2,8,4]=>1001001=>0110110
[5,7,3,1,4,6,2,8]=>0110010=>1001101
[5,7,3,1,4,6,8,2]=>0110001=>1001110
[5,7,3,1,4,8,6,2]=>0110011=>1001100
[5,7,3,1,4,8,2,6]=>0110010=>1001101
[5,3,7,4,1,2,8,6]=>1011001=>0100110
[5,3,7,4,1,2,6,8]=>1011000=>0100111
[5,3,7,1,4,2,6,8]=>1010100=>0101011
[5,3,7,1,4,2,8,6]=>1010101=>0101010
[3,7,5,1,2,8,6,4]=>0110011=>1001100
[7,8,3,5,1,2,6,4]=>0101001=>1010110
[7,3,8,5,1,2,6,4]=>1011001=>0100110
[7,3,5,8,1,2,6,4]=>1001001=>0110110
[3,7,5,1,2,6,4,8]=>0110010=>1001101
[3,7,5,1,2,6,8,4]=>0110001=>1001110
[6,1,4,3,5,2,8,7]=>1010101=>0101010
[2,5,7,3,8,4,1,6]=>0010110=>1101001
[5,4,7,8,6,1,3,2]=>1001101=>0110010
[7,5,6,2,8,3,1,4]=>1010110=>0101001
[4,7,2,5,8,3,1,6]=>0100110=>1011001
[6,2,4,5,1,3,8,7]=>1001001=>0110110
[5,1,4,6,3,2,8,7]=>1001101=>0110010
[3,5,6,2,4,1,8,7]=>0010101=>1101010
[3,8,6,7,5,4,1,2]=>0101110=>1010001
[6,2,7,8,3,4,1,5]=>1001010=>0110101
[2,5,3,4,8,1,7,6]=>0100101=>1011010
[8,7,1,2,5,3,4,6]=>1100100=>0011011
[5,1,8,2,3,4,7,6]=>1010001=>0101110
[5,4,7,6,2,8,1,3]=>1011010=>0100101
[3,7,8,1,5,4,6,2]=>0010101=>1101010
[7,1,3,4,6,8,5,2]=>1000011=>0111100
[8,3,6,5,7,1,4,2]=>1010101=>0101010
[5,8,7,1,4,6,2,3]=>0110010=>1001101
[4,7,6,1,8,3,5,2]=>0110101=>1001010
[4,7,2,6,3,8,5,1]=>0101011=>1010100
[2,1,8,4,6,7,3,5]=>1010010=>0101101
[4,7,8,6,3,1,2,5]=>0011100=>1100011
[3,8,1,5,6,7,2,4]=>0100010=>1011101
[6,7,2,4,8,5,3,1]=>0100111=>1011000
[2,8,3,6,7,5,1,4]=>0100110=>1011001
[8,2,1,7,6,3,5,4]=>1101101=>0010010
[3,2,4,5,8,1,7,6]=>1000101=>0111010
[7,4,6,3,2,1,8,5]=>1011101=>0100010
[4,7,3,2,1,8,6,5]=>0111011=>1000100
[6,4,7,5,2,3,8,1]=>1011001=>0100110
[6,4,8,1,7,3,2,5]=>1010110=>0101001
[4,8,7,2,3,1,5,6]=>0110100=>1001011
[4,2,3,1,8,7,5,6]=>1010110=>0101001
[7,6,8,1,3,5,2,4]=>1010010=>0101101
[6,7,5,2,3,1,8,4]=>0110101=>1001010
[4,7,2,6,5,1,8,3]=>0101101=>1010010
[6,4,2,1,8,5,7,3]=>1110101=>0001010
[7,2,1,5,6,8,4,3]=>1100011=>0011100
[8,7,2,6,4,1,5,3]=>1101101=>0010010
[6,7,8,2,5,3,1,4]=>0010110=>1101001
[2,1,7,3,6,8,5,4]=>1010011=>0101100
[2,1,5,7,8,4,6,3]=>1000101=>0111010
[2,5,7,8,3,6,1,4]=>0001010=>1110101
[6,4,1,5,7,2,8,3]=>1100101=>0011010
[7,4,8,1,2,5,6,3]=>1010001=>0101110
[4,2,7,8,6,3,5,1]=>1001101=>0110010
[6,1,7,4,3,2,8,5]=>1011101=>0100010
[6,8,3,4,2,1,7,5]=>0101101=>1010010
[4,2,6,1,5,7,8,3]=>1010001=>0101110
[2,4,6,7,3,5,8,1]=>0001001=>1110110
[6,5,8,3,7,4,1,2]=>1010110=>0101001
[7,1,4,8,3,5,6,2]=>1001001=>0110110
[6,8,7,5,3,4,1,2]=>0111010=>1000101
[4,8,6,3,1,5,7,2]=>0111001=>1000110
[3,4,8,2,5,7,6,1]=>0010011=>1101100
[3,5,7,2,8,6,1,4]=>0010110=>1101001
[2,5,7,4,8,6,1,3]=>0010110=>1101001
[2,6,3,7,5,1,8,4]=>0101101=>1010010
[2,6,4,8,7,5,1,3]=>0101110=>1010001
[6,3,7,2,8,5,1,4]=>1010110=>0101001
[3,6,2,5,8,7,1,4]=>0100110=>1011001
[5,2,8,4,7,6,1,3]=>1010110=>0101001
[7,2,4,8,6,5,1,3]=>1001110=>0110001
[6,2,4,8,7,5,1,3]=>1001110=>0110001
[2,4,5,8,7,6,1,3]=>0001110=>1110001
[4,2,7,3,8,1,6,5]=>1010101=>0101010
[2,5,1,4,7,3,8,6]=>0100101=>1011010
[6,1,3,8,7,2,5,4]=>1001101=>0110010
[3,1,5,6,2,8,7,4]=>1001011=>0110100
[4,1,5,2,8,7,6,3]=>1010111=>0101000
[7,1,4,2,8,6,5,3]=>1010111=>0101000
[4,1,5,3,2,8,7,6]=>1011011=>0100100
[7,2,3,5,1,8,6,4]=>1001011=>0110100
[3,4,5,1,8,7,6,2]=>0010111=>1101000
[1,4,5,2,8,7,6,3]=>0010111=>1101000
[1,6,4,2,8,7,5,3]=>0110111=>1001000
[5,6,3,1,8,7,4,2]=>0110111=>1001000
[7,4,2,5,1,8,6,3]=>1101011=>0010100
[5,3,6,2,8,1,7,4]=>1010101=>0101010
[4,6,2,7,5,1,8,3]=>0101101=>1010010
[1,5,3,6,2,8,7,4]=>0101011=>1010100
[1,5,8,3,2,7,6,4]=>0011011=>1100100
[4,5,8,2,1,7,6,3]=>0011011=>1100100
[3,6,2,5,1,4,8,7]=>0101001=>1010110
[5,2,8,4,1,3,7,6]=>1011001=>0100110
[2,4,8,7,1,3,6,5]=>0011001=>1100110
[1,3,8,2,4,7,6,5]=>0010011=>1101100
[6,3,1,7,2,8,5,4]=>1101011=>0010100
[7,5,1,2,8,6,4,3]=>1100111=>0011000
[1,5,2,3,8,7,6,4]=>0100111=>1011000
[4,5,1,2,8,7,6,3]=>0100111=>1011000
[6,4,1,2,8,7,5,3]=>1100111=>0011000
[5,3,1,7,2,8,6,4]=>1101011=>0010100
[5,2,8,1,3,7,6,4]=>1010011=>0101100
[4,7,5,6,8,3,1,2]=>0100110=>1011001
[8,6,4,7,5,3,1,2]=>1101110=>0010001
[1,6,3,7,5,8,4,2]=>0101011=>1010100
[1,3,7,4,5,8,6,2]=>0010011=>1101100
[6,8,4,7,5,3,1,2]=>0101110=>1010001
[4,8,7,5,6,3,1,2]=>0110110=>1001001
[8,6,5,2,1,4,3,7]=>1111010=>0000101
[2,7,6,3,1,4,5,8]=>0111000=>1000111
[2,7,6,4,5,1,3,8]=>0110100=>1001011
[5,7,2,6,4,1,3,8]=>0101100=>1010011
[1,8,2,7,3,6,5,4]=>0101011=>1010100
[2,1,3,8,4,7,5,6]=>1001010=>0110101
[8,1,2,7,4,3,6,5]=>1001101=>0110010
[8,7,2,1,5,4,3,6]=>1110110=>0001001
[2,4,8,3,1,5,6,7]=>0011000=>1100111
[4,7,3,8,2,1,5,6]=>0101100=>1010011
[5,2,7,3,1,4,6,8]=>1011000=>0100111
[8,3,7,2,1,5,4,6]=>1011010=>0100101
[2,6,4,5,7,1,3,8]=>0100100=>1011011
[7,6,3,1,8,4,5,2]=>1110101=>0001010
[1,7,5,8,6,4,3,2]=>0101111=>1010000
[6,5,1,2,8,3,7,4]=>1100101=>0011010
[6,8,4,1,3,7,5,2]=>0110011=>1001100
[5,8,3,1,7,4,6,2]=>0110101=>1001010
[8,3,1,7,5,4,6,2]=>1101101=>0010010
[1,2,8,7,6,3,5,4]=>0011101=>1100010
[2,3,1,8,7,4,5,6]=>0101100=>1010011
[2,4,1,8,5,7,3,6]=>0101010=>1010101
[5,8,2,1,7,6,3,4]=>0110110=>1001001
[6,2,7,1,8,5,3,4]=>1010110=>0101001
[8,7,1,6,5,4,3,2]=>1101111=>0010000
[7,1,8,3,6,5,4,2]=>1010111=>0101000
[8,1,2,3,4,5,9,6,7]=>10000010=>01111101
[8,1,2,3,4,9,5,6,7]=>10000100=>01111011
[8,1,2,9,3,4,5,6,7]=>10010000=>01101111
[8,1,9,2,3,4,5,6,7]=>10100000=>01011111
[6,1,2,3,4,5,8,9,7]=>10000001=>01111110
[9,1,2,3,4,5,6,10,7,8]=>100000010=>011111101
[5,1,2,3,4,8,9,6,7]=>10000010=>01111101
[9,1,2,3,4,5,10,6,7,8]=>100000100=>011111011
[4,1,2,3,8,9,5,6,7]=>10000100=>01111011
[3,1,2,8,9,4,5,6,7]=>10001000=>01110111
[9,1,2,3,10,4,5,6,7,8]=>100010000=>011101111
[2,1,8,9,3,4,5,6,7]=>10010000=>01101111
[9,1,2,10,3,4,5,6,7,8]=>100100000=>011011111
[3,5,8,7,2,6,4,1]=>0011011=>1100100
[5,8,2,7,1,6,4,3]=>0101011=>1010100
[2,1,6,4,5,8,3,7]=>1010010=>0101101
[8,6,3,7,5,2,1,4]=>1101110=>0010001
[4,6,3,8,5,2,1,7]=>0101110=>1010001
[4,6,3,7,5,2,8,1]=>0101101=>1010010
[3,5,7,8,2,6,1,4]=>0001010=>1110101
[7,2,3,4,6,8,5,1]=>1000011=>0111100
[4,2,3,6,1,5,8,7]=>1001001=>0110110
[4,8,3,7,5,1,6,2]=>0101101=>1010010
[5,2,3,4,8,7,1,6]=>1000110=>0111001
[5,2,3,4,6,8,1,7]=>1000010=>0111101
[4,2,8,5,7,6,1,3]=>1010110=>0101001
[3,7,6,4,5,1,8,2]=>0110101=>1001010
[3,8,6,4,5,1,2,7]=>0110100=>1001011
[4,8,3,7,5,2,1,6]=>0101110=>1010001
[8,7,3,6,5,1,2,4]=>1101100=>0010011
[4,2,7,5,8,6,3,1]=>1010111=>0101000
[5,8,1,7,3,6,4,2]=>0101011=>1010100
[5,2,7,8,4,6,3,1]=>1001011=>0110100
[5,2,8,3,7,6,1,4]=>1010110=>0101001
[8,2,7,3,1,6,4,5]=>1011010=>0100101
[6,2,3,4,8,5,1,7]=>1000110=>0111001
[6,2,3,4,1,8,5,7]=>1001010=>0110101
[7,2,3,4,1,8,6,5]=>1001011=>0110100
[7,2,3,4,1,5,8,6]=>1001001=>0110110
[1,2,3,4,8,7,5,6]=>0000110=>1111001
[1,2,8,5,3,4,6,7]=>0011000=>1100111
[1,8,4,2,3,5,6,7]=>0110000=>1001111
[8,6,7,4,1,5,3,2]=>1011011=>0100100
[4,8,6,7,5,1,3,2]=>0101101=>1010010
[7,1,8,4,6,5,2,3]=>1010110=>0101001
[8,7,1,5,4,6,2,3]=>1101010=>0010101
[8,5,7,1,4,6,3,2]=>1010011=>0101100
[6,4,8,5,1,7,3,2]=>1011011=>0100100
[4,8,5,7,1,6,3,2]=>0101011=>1010100
[8,4,7,1,5,6,3,2]=>1010011=>0101100
[8,7,1,4,5,6,3,2]=>1100011=>0011100
[8,7,4,5,6,1,3,2]=>1100101=>0011010
[8,7,5,1,4,6,2,3]=>1110010=>0001101
[8,7,2,5,1,4,6,3]=>1101001=>0010110
[4,8,7,2,5,1,6,3]=>0110101=>1001010
[1,6,4,8,5,2,7,3]=>0101101=>1010010
[8,7,1,4,2,5,6,3]=>1101001=>0010110
[8,7,5,1,2,4,6,3]=>1110001=>0001110
[7,1,8,5,6,2,3,4]=>1010100=>0101011
[3,8,7,1,2,5,6,4]=>0110001=>1001110
[3,5,8,7,1,2,6,4]=>0011001=>1100110
[2,3,8,5,7,1,6,4]=>0010101=>1101010
[3,8,7,1,5,6,2,4]=>0110010=>1001101
[3,5,8,7,1,6,2,4]=>0011010=>1100101
[2,3,8,6,7,5,1,4]=>0010110=>1101001
[3,2,8,6,7,5,1,4]=>1010110=>0101001
[4,1,8,6,2,7,5,3]=>1011011=>0100100
[8,7,4,1,2,6,5,3]=>1110011=>0001100
[1,3,8,6,7,5,2,4]=>0010110=>1101001
[5,7,1,8,2,6,3,4]=>0101010=>1010101
[2,8,7,1,5,6,3,4]=>0110010=>1001101
[8,7,1,5,2,4,6,3]=>1101001=>0010110
[7,1,8,2,4,6,5,3]=>1010011=>0101100
[1,6,2,8,4,7,5,3]=>0101011=>1010100
[1,3,8,5,7,2,6,4]=>0010101=>1101010
[1,8,3,7,2,5,6,4]=>0101001=>1010110
[2,8,7,1,3,5,6,4]=>0110001=>1001110
[5,7,1,8,2,3,6,4]=>0101001=>1010110
[7,1,8,2,3,5,6,4]=>1010001=>0101110
[8,6,3,7,4,1,5,2]=>1101101=>0010010
[4,2,8,6,7,5,1,3]=>1010110=>0101001
[8,4,2,7,5,6,1,3]=>1101010=>0010101
[4,8,3,6,1,7,5,2]=>0101011=>1010100
[8,3,4,7,5,1,6,2]=>1001101=>0110010
[8,3,7,4,5,1,6,2]=>1010101=>0101010
[8,7,4,2,5,6,1,3]=>1110010=>0001101
[8,7,5,1,6,2,3,4]=>1110100=>0001011
[8,7,2,4,1,5,6,3]=>1101001=>0010110
[4,8,6,1,7,2,5,3]=>0110101=>1001010
[4,7,1,8,2,6,5,3]=>0101011=>1010100
[4,2,8,6,7,1,5,3]=>1010101=>0101010
[8,7,4,1,2,5,6,3]=>1110001=>0001110
[8,2,7,1,6,3,4,5]=>1010100=>0101011
[8,2,7,1,3,6,4,5]=>1010010=>0101101
[2,8,3,6,7,1,5,4]=>0100101=>1011010
[8,7,2,1,3,5,6,4]=>1110001=>0001110
[1,8,7,2,3,6,4,5]=>0110010=>1001101
[1,8,7,2,6,3,4,5]=>0110100=>1001011
[8,2,7,3,6,1,4,5]=>1010100=>0101011
[1,8,7,3,6,2,4,5]=>0110100=>1001011
[1,8,2,7,6,3,4,5]=>0101100=>1010011
[8,2,7,4,1,5,6,3]=>1011001=>0100110
[8,2,1,7,5,6,3,4]=>1101010=>0010101
[8,7,3,1,5,6,2,4]=>1110010=>0001101
[2,8,7,3,5,6,1,4]=>0110010=>1001101
[8,3,1,6,7,5,2,4]=>1100110=>0011001
[8,5,2,1,6,7,4,3]=>1110011=>0001100
[1,5,2,8,6,7,4,3]=>0101011=>1010100
[1,2,8,6,7,5,3,4]=>0010110=>1101001
[1,8,3,6,7,5,2,4]=>0100110=>1011001
[8,2,3,6,7,5,1,4]=>1000110=>0111001
[8,3,7,2,5,6,1,4]=>1010010=>0101101
[8,1,3,7,5,6,2,4]=>1001010=>0110101
[8,4,1,2,7,5,6,3]=>1100101=>0011010
[8,1,4,2,6,7,5,3]=>1010011=>0101100
[1,2,8,6,7,3,5,4]=>0010101=>1101010
[8,1,2,7,3,6,4,5]=>1001010=>0110101
[8,1,7,3,6,2,4,5]=>1010100=>0101011
[8,1,7,2,6,3,4,5]=>1010100=>0101011
[8,1,7,2,3,6,4,5]=>1010010=>0101101
[8,1,3,7,2,5,6,4]=>1001001=>0110110
[1,8,3,6,7,2,5,4]=>0100101=>1011010
[1,7,8,2,3,6,5,4]=>0010011=>1101100
[8,3,7,1,2,5,6,4]=>1010001=>0101110
[8,7,1,2,3,6,4,5]=>1100010=>0011101
[2,8,5,7,4,6,3,1]=>0101011=>1010100
[3,1,8,5,7,4,2,6]=>1010110=>0101001
[8,3,5,7,4,2,6,1]=>1001101=>0110010
[8,3,6,2,4,5,7,1]=>1010001=>0101110
[2,8,6,4,3,5,7,1]=>0111001=>1000110
[2,6,8,3,5,4,7,1]=>0010101=>1101010
[2,7,5,8,4,6,3,1]=>0101011=>1010100
[8,4,2,7,6,1,3,5]=>1101100=>0010011
[4,8,1,7,6,3,2,5]=>0101110=>1010001
[4,1,7,6,2,3,5,8]=>1011000=>0100111
[3,7,1,8,6,2,5,4]=>0101101=>1010010
[3,1,7,6,4,5,2,8]=>1011010=>0100101
[3,1,7,5,8,4,2,6]=>1010110=>0101001
[3,1,6,8,7,5,2,4]=>1001110=>0110001
[6,3,8,7,5,2,4,1]=>1011101=>0100010
[7,3,5,8,4,2,6,1]=>1001101=>0110010
[7,3,6,4,2,8,5,1]=>1011011=>0100100
[7,8,3,6,2,5,4,1]=>0101011=>1010100
[7,4,8,2,1,6,3,5]=>1011010=>0100101
[8,7,4,6,3,2,5,1]=>1101101=>0010010
[7,8,5,2,1,4,3,6]=>0111010=>1000101
[7,5,2,3,1,4,8,6]=>1101001=>0010110
[7,4,6,2,3,8,1,5]=>1010010=>0101101
[6,4,2,5,8,3,7,1]=>1100101=>0011010
[4,6,5,8,1,3,2,7]=>0101010=>1010101
[4,7,1,5,3,8,2,6]=>0101010=>1010101
[4,7,8,1,3,6,2,5]=>0010010=>1101101
[5,7,1,3,4,6,2,8]=>0100010=>1011101
[5,7,1,4,2,3,6,8]=>0101000=>1010111
[5,8,1,3,2,4,6,7]=>0101000=>1010111
[4,8,6,1,3,2,7,5]=>0110101=>1001010
[8,4,6,2,1,3,7,5]=>1011001=>0100110
[5,4,8,7,2,3,6,1]=>1011001=>0100110
[5,4,8,7,3,1,2,6]=>1011100=>0100011
[6,8,3,7,2,5,4,1]=>0101011=>1010100
[5,4,6,8,2,3,7,1]=>1001001=>0110110
[5,7,4,2,8,3,6,1]=>0110101=>1001010
[6,4,7,2,1,8,3,5]=>1011010=>0100101
[6,5,3,4,1,2,8,7]=>1101001=>0010110
[6,8,5,4,1,3,2,7]=>0111010=>1000101
[6,4,3,7,1,5,2,8]=>1101010=>0010101
[9,8,7,6,5,2,3,1,4]=>11111010=>00000101
[9,8,7,6,3,4,2,1,5]=>11110110=>00001001
[9,8,7,4,5,3,2,1,6]=>11101110=>00010001
[9,8,5,6,4,3,2,1,7]=>11011110=>00100001
[9,6,7,5,4,3,2,1,8]=>10111110=>01000001
[7,4,2,6,1,5,3,8]=>1101010=>0010101
[7,4,2,5,6,1,3,8]=>1100100=>0011011
[6,4,2,8,1,5,7,3]=>1101001=>0010110
[6,3,7,8,2,5,1,4]=>1001010=>0110101
[7,3,5,6,4,2,1,8]=>1001110=>0110001
[7,4,3,1,5,6,2,8]=>1110010=>0001101
[7,4,5,2,6,1,3,8]=>1010100=>0101011
[5,3,7,2,8,6,4,1]=>1010111=>0101000
[5,3,8,2,6,7,4,1]=>1010011=>0101100
[6,3,8,2,5,4,7,1]=>1010101=>0101010
[6,4,8,2,1,5,7,3]=>1011001=>0100110
[6,4,3,1,8,2,7,5]=>1110101=>0001010
[5,3,7,8,2,6,4,1]=>1001011=>0110100
[4,7,8,5,6,3,2,1]=>0010111=>1101000
[5,3,7,6,8,2,4,1]=>1010101=>0101010
[5,7,8,4,6,2,1,3]=>0010110=>1101001
[5,8,4,3,6,7,1,2]=>0110010=>1001101
[5,8,6,4,7,2,1,3]=>0110110=>1001001
[5,3,8,6,2,7,4,1]=>1011011=>0100100
[4,7,5,8,6,3,2,1]=>0101111=>1010000
[4,8,6,7,5,3,2,1]=>0101111=>1010000
[6,3,8,7,2,4,1,5]=>1011010=>0100101
[5,3,8,7,2,6,4,1]=>1011011=>0100100
[5,3,8,6,7,2,4,1]=>1010101=>0101010
[5,3,7,8,6,2,4,1]=>1001101=>0110010
[5,7,6,4,8,2,1,3]=>0110110=>1001001
[5,8,4,6,7,2,1,3]=>0100110=>1011001
[6,4,2,8,1,7,3,5]=>1101010=>0010101
[6,5,2,4,3,7,8,1]=>1101001=>0010110
[5,4,6,2,8,7,1,3]=>1010110=>0101001
[5,6,3,8,7,2,4,1]=>0101101=>1010010
[6,7,4,3,1,8,2,5]=>0111010=>1000101
[5,7,4,3,6,8,1,2]=>0110010=>1001101
[5,7,3,8,6,2,4,1]=>0101101=>1010010
[4,5,8,6,7,3,2,1]=>0010111=>1101000
[4,6,8,5,7,3,2,1]=>0010111=>1101000
[5,6,8,3,7,2,4,1]=>0010101=>1101010
[5,4,6,8,2,7,1,3]=>1001010=>0110101
[5,7,8,2,6,4,1,3]=>0010110=>1101001
[1,7,4,8,6,2,3,5]=>0101100=>1010011
[3,6,2,5,7,8,1,4]=>0100010=>1011101
[5,2,7,4,6,8,1,3]=>1010010=>0101101
[5,3,6,7,1,8,4,2]=>1001011=>0110100
[4,2,5,6,7,1,8,3]=>1000101=>0111010
[8,1,3,6,7,2,4,5]=>1000100=>0111011
[8,1,4,2,5,6,3,7]=>1010010=>0101101
[8,1,4,2,7,5,3,6]=>1010110=>0101001
[6,1,3,8,2,7,4,5]=>1001010=>0110101
[7,3,4,1,5,8,6,2]=>1010011=>0101100
[1,7,5,2,8,6,3,4]=>0110110=>1001001
[3,7,4,1,8,5,6,2]=>0110101=>1001010
[5,6,3,1,7,8,4,2]=>0110011=>1001100
[3,6,4,8,1,5,7,2]=>0101001=>1010110
[1,5,8,4,2,6,3,7]=>0011010=>1100101
[3,5,7,4,1,6,8,2]=>0011001=>1100110
[3,5,7,1,2,6,4,8]=>0010010=>1101101
[4,5,1,8,2,3,7,6]=>0101001=>1010110
[4,7,1,8,2,6,3,5]=>0101010=>1010101
[7,5,1,2,3,8,6,4]=>1100011=>0011100
[6,4,1,2,7,3,8,5]=>1100101=>0011010
[5,2,6,1,3,4,8,7]=>1010001=>0101110
[7,8,4,5,1,3,2,6]=>0101010=>1010101
[6,7,1,3,2,5,4,8]=>0101010=>1010101
[6,7,1,4,3,5,2,8]=>0101010=>1010101
[7,8,2,3,1,5,4,6]=>0101010=>1010101
[7,8,2,4,3,5,1,6]=>0101010=>1010101
[7,8,2,4,1,5,3,6]=>0101010=>1010101
[1,4,2,6,5,7,3,8]=>0101010=>1010101
[5,6,1,4,2,7,3,8]=>0101010=>1010101
[6,7,2,4,1,5,3,8]=>0101010=>1010101
[6,7,2,4,3,5,1,8]=>0101010=>1010101
[6,7,2,3,1,5,4,8]=>0101010=>1010101
[6,7,3,5,4,8,1,2]=>0101010=>1010101
[2,4,1,6,5,7,3,8]=>0101010=>1010101
[1,5,2,6,4,7,3,8]=>0101010=>1010101
[2,5,1,6,4,7,3,8]=>0101010=>1010101
[3,6,5,7,4,8,1,2]=>0101010=>1010101
[5,6,2,4,3,7,1,8]=>0101010=>1010101
[4,5,2,6,1,7,3,8]=>0101010=>1010101
[4,5,1,6,3,7,2,8]=>0101010=>1010101
[4,5,3,6,1,7,2,8]=>0101010=>1010101
[5,6,3,4,1,7,2,8]=>0101010=>1010101
[5,6,1,4,3,7,2,8]=>0101010=>1010101
[5,6,1,3,2,7,4,8]=>0101010=>1010101
[5,6,4,7,1,3,2,8]=>0101010=>1010101
[6,7,4,5,1,3,2,8]=>0101010=>1010101
[6,7,5,8,1,3,2,4]=>0101010=>1010101
[4,5,1,3,2,7,6,8]=>0101010=>1010101
[4,6,5,7,1,3,2,8]=>0101010=>1010101
[4,6,1,3,2,7,5,8]=>0101010=>1010101
[1,4,3,6,2,7,5,8]=>0101010=>1010101
[3,4,1,6,5,7,2,8]=>0101010=>1010101
[4,5,2,3,1,7,6,8]=>0101010=>1010101
[4,5,3,7,6,8,1,2]=>0101010=>1010101
[4,6,5,7,3,8,1,2]=>0101010=>1010101
[4,6,5,7,2,3,1,8]=>0101010=>1010101
[3,5,4,6,1,7,2,8]=>0101010=>1010101
[3,5,1,6,4,7,2,8]=>0101010=>1010101
[1,5,3,6,4,7,2,8]=>0101010=>1010101
[1,5,3,6,2,7,4,8]=>0101010=>1010101
[3,5,2,6,1,7,4,8]=>0101010=>1010101
[3,5,2,6,4,7,1,8]=>0101010=>1010101
[3,4,2,6,1,7,5,8]=>0101010=>1010101
[4,6,2,3,1,7,5,8]=>0101010=>1010101
[2,4,3,6,1,7,5,8]=>0101010=>1010101
[2,5,3,6,4,7,1,8]=>0101010=>1010101
[2,5,3,6,1,7,4,8]=>0101010=>1010101
[3,6,2,7,5,4,8,1]=>0101101=>1010010
[4,6,1,7,3,8,2,5]=>0101010=>1010101
[5,2,6,7,4,3,8,1]=>1001101=>0110010
[3,5,2,7,6,4,8,1]=>0101101=>1010010
[1,5,7,2,8,3,6,4]=>0010101=>1101010
[2,5,7,3,1,8,4,6]=>0011010=>1100101
[1,3,7,2,8,5,6,4]=>0010101=>1101010
[2,1,5,6,8,4,3,7]=>1000110=>0111001
[1,3,7,2,8,5,4,6]=>0010110=>1101001
[4,6,2,7,1,8,3,5]=>0101010=>1010101
[1,5,4,3,6,8,2,7]=>0110010=>1001101
[1,6,4,5,7,8,3,2]=>0100011=>1011100
[2,1,5,6,8,4,7,3]=>1000101=>0111010
[2,1,5,6,8,7,3,4]=>1000110=>0111001
[3,6,5,2,7,8,4,1]=>0110011=>1001100
[6,2,4,7,5,8,3,1]=>1001011=>0110100
[1,5,7,8,4,2,6,3]=>0001101=>1110010
[3,7,4,1,8,6,2,5]=>0110110=>1001001
[3,4,6,8,5,7,2,1]=>0001011=>1110100
[4,2,5,7,3,1,8,6]=>1001101=>0110010
[4,5,6,2,8,7,3,1]=>0010111=>1101000
[2,5,6,8,1,7,4,3]=>0001011=>1110100
[4,5,6,1,8,7,3,2]=>0010111=>1101000
[4,5,6,3,1,8,7,2]=>0011011=>1100100
[4,3,6,2,1,7,5,8]=>1011010=>0100101
[4,6,3,2,1,7,5,8]=>0111010=>1000101
[4,6,3,1,7,5,2,8]=>0110110=>1001001
[4,5,3,7,6,1,8,2]=>0101101=>1010010
[4,5,1,7,3,8,6,2]=>0101011=>1010100
[2,5,7,1,4,3,8,6]=>0010101=>1101010
[4,3,5,7,6,1,8,2]=>1001101=>0110010
[4,3,6,1,7,5,2,8]=>1010110=>0101001
[4,3,2,6,1,7,5,8]=>1101010=>0010101
[5,3,2,1,6,4,7,8]=>1110100=>0001011
[5,3,1,6,2,7,4,8]=>1101010=>0010101
[5,1,6,3,2,7,4,8]=>1011010=>0100101
[2,6,1,4,7,5,3,8]=>0100110=>1011001
[3,6,1,7,4,2,5,8]=>0101100=>1010011
[4,6,1,7,5,3,2,8]=>0101110=>1010001
[5,1,6,3,7,4,2,8]=>1010110=>0101001
[5,3,6,4,2,1,7,8]=>1011100=>0100011
[5,3,2,6,4,1,7,8]=>1101100=>0010011
[5,2,1,6,3,7,4,8]=>1101010=>0010101
[5,2,6,3,1,7,4,8]=>1011010=>0100101
[4,2,6,3,1,7,8,5]=>1011001=>0100110
[3,6,2,1,7,4,5,8]=>0110100=>1001011
[3,6,2,7,4,1,5,8]=>0101100=>1010011
[3,5,7,2,8,6,4,1]=>0010111=>1101000
[2,4,7,1,3,6,5,8]=>0010010=>1101101
[2,6,1,3,7,5,4,8]=>0100110=>1011001
[3,6,1,7,5,2,4,8]=>0101100=>1010011
[5,1,6,2,7,4,3,8]=>1010110=>0101001
[5,2,6,4,3,1,7,8]=>1011100=>0100011
[5,2,1,6,4,3,7,8]=>1101100=>0010011
[5,4,2,1,6,3,7,8]=>1110100=>0001011
[5,4,2,6,3,1,7,8]=>1101100=>0010011
[5,4,1,6,2,7,3,8]=>1101010=>0010101
[5,1,6,4,2,7,3,8]=>1011010=>0100101
[3,6,1,7,5,4,8,2]=>0101101=>1010010
[2,6,1,5,4,3,7,8]=>0101100=>1010011
[3,1,6,2,5,4,7,8]=>1010100=>0101011
[5,1,6,4,3,2,7,8]=>1011100=>0100011
[5,4,1,6,3,2,7,8]=>1101100=>0010011
[5,4,3,1,6,2,7,8]=>1110100=>0001011
[8,2,1,7,6,5,4,3,9]=>11011110=>00100001
[7,3,1,6,5,4,8,2]=>1101101=>0010010
[7,2,8,1,5,4,3,6]=>1010110=>0101001
[4,2,7,6,5,8,1,3]=>1011010=>0100101
[3,8,2,6,5,4,1,7]=>0101110=>1010001
[3,2,8,7,6,5,4,1,9]=>10111110=>01000001
[10,1,11,9,8,7,6,5,4,3,2]=>1011111111=>0100000000
[9,2,1,8,7,6,5,4,3,10]=>110111110=>001000001
[8,3,1,7,6,5,4,9,2]=>11011101=>00100010
[8,2,9,1,6,5,4,3,7]=>10101110=>01010001
[7,3,2,1,5,4,6,8]=>1110100=>0001011
[7,2,8,6,1,4,3,5]=>1011010=>0100101
[5,2,7,6,8,4,1,3]=>1010110=>0101001
[4,2,8,7,6,5,9,1,3]=>10111010=>01000101
[3,8,7,2,5,4,1,6]=>0110110=>1001001
[3,9,2,7,6,5,4,1,8]=>01011110=>10100001
[3,2,9,8,7,6,5,4,1,10]=>101111110=>010000001
[2,11,10,9,8,7,6,5,4,1,3]=>0111111110=>1000000001
[11,1,12,10,9,8,7,6,5,4,3,2]=>10111111111=>01000000000
[10,2,1,9,8,7,6,5,4,3,11]=>1101111110=>0010000001
[9,3,1,8,7,6,5,4,10,2]=>110111101=>001000010
[9,2,10,1,7,6,5,4,3,8]=>101011110=>010100001
[8,4,1,7,6,5,9,3,2]=>11011011=>00100100
[8,3,2,1,6,5,4,7,9]=>11101100=>00010011
[8,2,9,7,1,5,4,3,6]=>10110110=>01001001
[7,5,1,6,8,4,3,2]=>1100111=>0011000
[7,4,2,1,5,6,3,8]=>1110010=>0001101
[7,2,8,6,5,1,3,4]=>1011100=>0100011
[5,3,2,6,7,4,1,8]=>1100110=>0011001
[5,2,8,7,6,9,4,1,3]=>10110110=>01001001
[4,3,7,2,5,6,1,8]=>1010010=>0101101
[4,3,2,7,6,5,8,1,9]=>11011010=>00100101
[4,2,9,8,7,6,5,10,1,3]=>101111010=>010000101
[3,9,8,2,6,5,4,1,7]=>01101110=>10010001
[3,10,2,8,7,6,5,4,1,9]=>010111110=>101000001
[3,2,10,9,8,7,6,5,4,1,11]=>1011111110=>0100000001
[2,12,11,10,9,8,7,6,5,4,1,3]=>01111111110=>10000000001
[6,7,1,4,3,2,5,8]=>0101100=>1010011
[3,4,2,6,7,1,5,8]=>0100100=>1011011
[3,7,1,6,5,2,4,8]=>0101100=>1010011
[3,5,6,2,4,7,1,8]=>0010010=>1101101
[3,5,8,7,2,4,6,1]=>0011001=>1100110
[1,7,8,2,5,4,3,6]=>0010110=>1101001
[8,7,2,5,4,3,6,1]=>1101101=>0010010
[2,5,6,4,7,1,3,8]=>0010100=>1101011
[4,7,1,6,3,5,2,8]=>0101010=>1010101
[4,5,3,8,7,2,6,1]=>0101101=>1010010
[1,4,5,3,7,8,2,6]=>0010010=>1101101
[1,4,8,2,7,6,3,5]=>0010110=>1101001
[4,7,3,5,1,8,6,2]=>0101011=>1010100
[8,7,3,6,1,5,4,2]=>1101011=>0010100
[2,5,8,7,4,6,1,3]=>0011010=>1100101
[5,4,2,1,7,8,3,6]=>1110010=>0001101
[4,7,8,3,5,2,1,6]=>0010110=>1101001
[4,7,6,2,1,8,3,5]=>0111010=>1000101
[1,4,6,7,3,5,8,2]=>0001001=>1110110
[8,3,6,2,1,7,5,4]=>1011011=>0100100
[8,3,7,6,4,2,1,5]=>1011110=>0100001
[2,3,1,8,4,7,6,5]=>0101011=>1010100
[2,7,4,8,6,5,1,3]=>0101110=>1010001
[8,6,5,1,4,7,3,2]=>1110011=>0001100
[8,5,4,1,7,3,6,2]=>1110101=>0001010
[6,3,7,2,8,5,4,1]=>1010111=>0101000
[1,6,3,8,2,7,5,4]=>0101011=>1010100
[1,7,5,3,8,2,6,4]=>0110101=>1001010
[6,2,7,4,1,8,5,3]=>1011011=>0100100
[8,6,3,2,7,5,1,4]=>1110110=>0001001
[2,7,5,1,3,8,6,4]=>0110011=>1001100
[1,7,6,4,3,8,2,5]=>0111010=>1000101
[3,7,2,4,8,6,5,1]=>0100111=>1011000
[3,4,2,8,7,6,1,5]=>0101110=>1010001
[5,1,4,3,2,7,8,6]=>1011001=>0100110
[3,7,8,5,2,4,1,6]=>0011010=>1100101
[3,7,6,2,4,1,8,5]=>0110101=>1001010
[1,6,8,2,5,7,4,3]=>0010011=>1101100
[6,7,2,5,8,4,3,1]=>0100111=>1011000
[5,2,7,8,4,3,1,6]=>1001110=>0110001
[5,3,1,7,8,4,2,6]=>1100110=>0011001
[2,7,6,4,1,3,8,5]=>0111001=>1000110
[4,1,7,6,3,2,8,5]=>1011101=>0100010
[8,4,2,7,6,3,1,5]=>1101110=>0010001
[6,3,1,7,5,2,8,4]=>1101101=>0010010
[6,2,7,5,3,1,8,4]=>1011101=>0100010
[1,5,8,2,7,4,6,3]=>0010101=>1101010
[5,7,2,8,4,6,3,1]=>0101011=>1010100
[5,7,3,1,8,4,6,2]=>0110101=>1001010
[8,4,7,3,1,6,5,2]=>1011011=>0100100
[2,6,8,5,7,4,1,3]=>0010110=>1101001
[6,5,2,1,7,4,8,3]=>1110101=>0001010
[5,7,4,6,2,1,8,3]=>0101101=>1010010
[5,6,4,8,3,7,2,1]=>0101011=>1010100
[6,7,1,8,3,4,2,5]=>0101010=>1010101
[7,8,3,5,1,4,2,6]=>0101010=>1010101
[5,6,2,7,1,8,3,4]=>0101010=>1010101
[6,7,2,4,3,8,1,5]=>0101010=>1010101
[2,4,3,8,6,7,1,5]=>0101010=>1010101
[1,8,2,7,4,5,3,6]=>0101010=>1010101
[2,5,4,8,3,6,1,7]=>0101010=>1010101
[2,3,1,8,5,6,4,7]=>0101010=>1010101
[3,8,5,6,4,7,1,2]=>0101010=>1010101
[5,7,3,6,4,8,1,2]=>0101010=>1010101
[5,7,2,3,1,6,4,8]=>0101010=>1010101
[5,7,2,4,3,6,1,8]=>0101010=>1010101
[4,6,2,7,1,5,3,8]=>0101010=>1010101
[4,7,1,6,2,5,3,8]=>0101010=>1010101
[4,7,1,5,3,6,2,8]=>0101010=>1010101
[4,6,3,5,1,7,2,8]=>0101010=>1010101
[6,7,3,5,1,4,2,8]=>0101010=>1010101
[5,6,3,7,1,4,2,8]=>0101010=>1010101
[5,7,1,6,3,4,2,8]=>0101010=>1010101
[1,8,5,6,3,4,2,7]=>0101010=>1010101
[1,8,5,6,4,7,2,3]=>0101010=>1010101
[5,7,1,6,4,8,2,3]=>0101010=>1010101
[4,6,5,8,1,7,2,3]=>0101010=>1010101
[3,7,1,4,2,8,5,6]=>0101010=>1010101
[3,5,1,4,2,8,6,7]=>0101010=>1010101
[4,6,5,8,3,7,1,2]=>0101010=>1010101
[4,6,5,8,2,3,1,7]=>0101010=>1010101
[3,4,2,6,5,8,1,7]=>0101010=>1010101
[3,5,4,6,2,8,1,7]=>0101010=>1010101
[1,8,3,5,4,7,2,6]=>0101010=>1010101
[3,4,2,7,1,8,5,6]=>0101010=>1010101
[4,7,2,3,1,8,5,6]=>0101010=>1010101
[2,4,3,8,1,7,5,6]=>0101010=>1010101
[2,5,3,8,4,7,1,6]=>0101010=>1010101
[2,6,3,8,1,7,4,5]=>0101010=>1010101
[2,7,1,8,3,6,4,5]=>0101010=>1010101
[1,2,8,7,4,6,3,5]=>0011010=>1100101
[4,5,1,8,7,6,2,3]=>0101110=>1010001
[4,1,5,8,7,6,2,3]=>1001110=>0110001
[4,5,7,8,2,6,3,1]=>0001011=>1110100
[5,2,6,8,3,7,4,1]=>1001011=>0110100
[3,1,6,8,7,4,5,2]=>1001101=>0110010
[6,1,4,8,7,2,5,3]=>1001101=>0110010
[6,1,8,4,7,3,5,2]=>1010101=>0101010
[4,6,7,8,2,5,3,1]=>0001011=>1110100
[7,4,5,2,8,6,3,1]=>1010111=>0101000
[7,5,8,4,2,6,3,1]=>1011011=>0100100
[6,8,4,5,2,7,3,1]=>0101011=>1010100
[6,8,2,5,3,7,4,1]=>0101011=>1010100
[6,3,8,4,2,7,5,1]=>1011011=>0100100
[7,2,5,3,8,6,4,1]=>1010111=>0101000
[3,4,7,5,8,6,2,1]=>0010111=>1101000
[3,6,7,4,8,5,2,1]=>0010111=>1101000
[6,7,4,2,8,5,3,1]=>0110111=>1001000
[4,7,5,2,8,6,3,1]=>0110111=>1001000
[2,7,5,3,8,6,4,1]=>0110111=>1001000
[5,6,2,8,3,7,4,1]=>0101011=>1010100
[1,5,8,2,7,3,6,4]=>0010101=>1101010
[5,8,4,7,2,3,6,1]=>0101001=>1010110
[6,7,4,8,1,5,3,2]=>0101011=>1010100
[1,7,4,8,6,2,5,3]=>0101101=>1010010
[6,8,5,3,7,2,4,1]=>0110101=>1001010
[6,8,5,2,3,7,4,1]=>0110011=>1001100
[7,5,3,8,2,6,4,1]=>1101011=>0010100
[7,5,2,3,8,6,4,1]=>1100111=>0011000
[3,7,4,5,8,6,2,1]=>0100111=>1011000
[6,7,3,4,8,5,2,1]=>0100111=>1011000
[3,6,4,7,8,5,2,1]=>0100111=>1011000
[6,4,2,7,8,5,3,1]=>1100111=>0011000
[7,4,2,5,8,6,3,1]=>1100111=>0011000
[6,8,4,2,5,7,3,1]=>0110011=>1001100
[7,5,8,3,4,6,2,1]=>1010011=>0101100
[7,4,5,8,1,6,3,2]=>1001011=>0110100
[6,3,4,7,8,5,2,1]=>1000111=>0111000
[7,8,2,3,4,5,6,9,1]=>01000001=>10111110
[6,1,7,3,4,5,8,2]=>1010001=>0101110
[5,7,2,3,4,1,8,6]=>0100101=>1011010
[2,7,1,8,4,5,6,3]=>0101001=>1010110
[2,6,8,3,4,5,1,7]=>0010010=>1101101
[2,8,9,3,4,5,6,7,1]=>00100001=>11011110
[8,9,2,3,4,5,6,7,10,1]=>010000001=>101111110
[7,1,8,3,4,5,6,9,2]=>10100001=>01011110
[6,8,2,3,4,5,1,9,7]=>01000101=>10111010
[6,1,2,7,4,5,8,3]=>1001001=>0110110
[4,7,2,3,1,5,8,6]=>0101001=>1010110
[2,7,1,3,8,5,6,4]=>0100101=>1011010
[2,6,7,8,4,5,3,1]=>0001011=>1110100
[2,8,1,9,4,5,6,7,3]=>01010001=>10101110
[2,5,8,3,4,1,6,7]=>0010100=>1101011
[2,7,9,3,4,5,6,1,8]=>00100010=>11011101
[2,9,10,3,4,5,6,7,8,1]=>001000001=>110111110
[11,1,2,3,4,5,6,7,8,9,12,10]=>10000000001=>01111111110
[9,10,2,3,4,5,6,7,8,11,1]=>0100000001=>1011111110
[8,1,9,3,4,5,6,7,10,2]=>101000001=>010111110
[7,9,2,3,4,5,6,1,10,8]=>010000101=>101111010
[7,1,2,8,4,5,6,9,3]=>10010001=>01101110
[6,7,8,3,4,5,2,9,1]=>00100101=>11011010
[5,8,2,3,4,1,6,9,7]=>01001001=>10110110
[5,6,2,7,4,3,8,1]=>0101101=>1010010
[4,6,7,3,2,5,8,1]=>0011001=>1100110
[2,6,7,3,8,5,4,1]=>0010111=>1101000
[2,8,1,3,9,5,6,7,4]=>01001001=>10110110
[2,6,1,8,4,5,3,7]=>0101010=>1010101
[2,5,7,8,4,3,6,1]=>0001101=>1110010
[2,7,8,9,4,5,6,3,1]=>00010011=>11101100
[2,9,1,10,4,5,6,7,8,3]=>010100001=>101011110
[2,6,9,3,4,5,1,7,8]=>00100100=>11011011
[2,8,10,3,4,5,6,7,1,9]=>001000010=>110111101
[2,10,11,3,4,5,6,7,8,9,1]=>0010000001=>1101111110
[2,12,1,3,4,5,6,7,8,9,10,11]=>01000000000=>10111111111
[3,6,8,4,5,7,1,2]=>0010010=>1101101
[1,6,8,4,7,2,3,5]=>0010100=>1101011
[1,4,5,7,8,2,6,3]=>0000101=>1111010
[3,4,5,7,8,6,1,2]=>0000110=>1111001
[3,4,5,7,6,8,1,2]=>0001010=>1110101
[3,6,7,4,8,5,1,2]=>0010110=>1101001
[3,4,5,6,8,7,1,2]=>0000110=>1111001
[1,4,5,8,7,2,3,6]=>0001100=>1110011
[1,2,5,8,3,6,4,7]=>0001010=>1110101
[1,4,5,8,6,2,3,7]=>0001100=>1110011
[7,8,1,4,6,2,3,5]=>0100100=>1011011
[1,6,7,4,8,2,5,3]=>0010101=>1101010
[1,4,5,6,8,2,7,3]=>0000101=>1111010
[1,4,5,8,6,2,7,3]=>0001101=>1110010
[1,2,5,8,3,4,7,6]=>0001001=>1110110
[1,6,7,2,3,5,8,4]=>0010001=>1101110
[7,8,1,2,3,5,4,6]=>0100010=>1011101
[1,6,7,2,3,5,4,8]=>0010010=>1101101
[1,4,5,7,6,2,3,8]=>0001100=>1110011
[1,2,5,7,3,6,4,8]=>0001010=>1110101
[1,2,5,7,3,6,8,4]=>0001001=>1110110
[1,6,8,2,3,5,7,4]=>0010001=>1101110
[1,6,8,4,5,2,3,7]=>0010100=>1101011
[1,6,8,4,5,2,7,3]=>0010101=>1101010
[1,6,8,2,3,4,7,5]=>0010001=>1101110
[1,6,8,2,3,7,4,5]=>0010010=>1101101
[1,4,5,7,6,2,8,3]=>0001101=>1110010
[7,8,1,4,5,2,6,3]=>0100101=>1011010
[7,8,1,2,3,4,6,5]=>0100001=>1011110
[7,8,1,2,3,6,4,5]=>0100010=>1011101
[1,6,7,2,3,8,5,4]=>0010011=>1101100
[1,2,5,6,3,8,7,4]=>0001011=>1110100
[4,2,1,6,5,3,8,7]=>1101101=>0010010
[8,2,4,3,1,6,5,7]=>1011010=>0100101
[6,2,4,3,1,8,7,5]=>1011011=>0100100
[4,2,6,3,5,1,8,7]=>1010101=>0101010
[4,6,2,1,5,8,7,3]=>0110011=>1001100
[4,6,5,2,1,8,7,3]=>0111011=>1000100
[2,1,6,4,3,8,7,5]=>1011011=>0100100
[4,8,2,1,6,7,3,5]=>0110010=>1001101
[6,8,2,1,4,3,7,5]=>0110101=>1001010
[8,6,2,4,3,1,5,7]=>1101100=>0010011
[6,8,2,4,3,1,7,5]=>0101101=>1010010
[6,8,7,2,4,3,1,5]=>0110110=>1001001
[2,1,8,4,6,5,3,7]=>1010110=>0101001
[2,1,6,4,8,5,7,3]=>1010101=>0101010
[4,6,5,2,8,3,7,1]=>0110101=>1001010
[2,6,4,5,8,3,7,1]=>0100101=>1011010
[6,4,2,8,3,5,7,1]=>1101001=>0010110
[8,4,2,6,3,5,1,7]=>1101010=>0010101
[6,2,4,8,5,3,7,1]=>1001101=>0110010
[4,2,6,3,5,8,7,1]=>1010011=>0101100
[4,2,6,3,8,7,5,1]=>1010111=>0101000
[6,2,4,3,8,5,7,1]=>1010101=>0101010
[8,2,4,3,6,5,1,7]=>1010110=>0101001
[8,2,1,4,6,5,3,7]=>1100110=>0011001
[6,2,1,4,8,5,7,3]=>1100101=>0011010
[6,2,1,8,7,4,3,5]=>1101110=>0010001
[6,2,1,8,4,3,7,5]=>1101101=>0010010
[8,4,6,5,2,1,3,7]=>1011100=>0100011
[6,4,8,5,2,1,7,3]=>1011101=>0100010
[6,4,8,5,7,2,1,3]=>1010110=>0101001
[4,6,8,7,5,2,1,3]=>0011110=>1100001
[2,1,4,8,6,7,3,5]=>1001010=>0110101
[2,6,8,7,4,5,1,3]=>0011010=>1100101
[2,4,8,6,7,5,1,3]=>0010110=>1101001
[4,2,8,6,5,7,1,3]=>1011010=>0100101
[8,2,6,4,5,1,3,7]=>1010100=>0101011
[8,4,6,2,1,5,3,7]=>1011010=>0100101
[4,6,8,7,2,1,5,3]=>0011101=>1100010
[4,6,5,8,2,1,7,3]=>0101101=>1010010
[2,1,6,8,4,3,7,5]=>1001101=>0110010
[6,8,7,4,2,1,3,5]=>0111100=>1000011
[2,8,6,4,7,1,3,5]=>0110100=>1001011
[4,8,6,2,1,7,3,5]=>0111010=>1000101
[2,8,5,3,1,4,6,7]=>0111000=>1000111
[2,7,4,8,3,5,1,6]=>0101010=>1010101
[2,7,4,8,3,5,6,1]=>0101001=>1010110
[7,2,8,4,3,5,1,6]=>1011010=>0100101
[8,4,2,1,5,3,6,7]=>1110100=>0001011
[8,5,1,4,2,3,6,7]=>1101000=>0010111
[8,4,1,5,3,2,6,7]=>1101100=>0010011
[6,7,3,8,4,2,5,1]=>0101101=>1010010
[6,7,3,8,4,2,1,5]=>0101110=>1010001
[7,1,8,4,3,5,2,6]=>1011010=>0100101
[1,7,8,4,3,5,2,6]=>0011010=>1100101
[7,1,4,8,3,5,2,6]=>1001010=>0110101
[7,4,8,1,5,6,2,3]=>1010010=>0101101
[7,1,8,4,3,5,6,2]=>1011001=>0100110
[6,7,3,1,8,4,5,2]=>0110101=>1001010
[6,7,3,8,4,5,2,1]=>0101011=>1010100
[6,7,1,4,8,3,5,2]=>0100101=>1011010
[6,7,4,1,3,8,2,5]=>0110010=>1001101
[1,6,7,8,4,3,2,5]=>0001110=>1110001
[7,2,1,8,4,5,3,6]=>1101010=>0010101
[6,2,7,1,8,4,3,5]=>1010110=>0101001
[6,2,7,8,4,3,1,5]=>1001110=>0110001
[6,2,7,8,4,3,5,1]=>1001101=>0110010
[2,6,7,4,8,3,5,1]=>0010101=>1101010
[2,6,7,4,8,3,1,5]=>0010110=>1101001
[7,8,1,3,6,2,4,5]=>0100100=>1011011
[1,2,7,8,6,3,4,5]=>0001100=>1110011
[2,6,7,1,8,5,3,4]=>0010110=>1101001
[2,6,7,8,5,3,1,4]=>0001110=>1110001
[2,6,7,8,5,3,4,1]=>0001101=>1110010
[6,2,7,8,4,5,3,1]=>1001011=>0110100
[7,2,1,8,4,5,6,3]=>1101001=>0010110
[1,7,2,8,4,5,6,3]=>0101001=>1010110
[3,7,8,1,5,6,2,4]=>0010010=>1101101
[6,3,7,8,1,5,2,4]=>1001010=>0110101
[6,7,1,2,8,5,3,4]=>0100110=>1011001
[1,6,7,8,4,2,5,3]=>0001101=>1110010
[3,1,2,7,6,5,8,4]=>1001101=>0110010
[6,1,2,4,7,3,8,5]=>1000101=>0111010
[1,7,5,3,6,4,8,2]=>0110101=>1001010
[5,1,2,6,7,4,8,3]=>1000101=>0111010
[4,1,5,7,3,2,6,8]=>1001100=>0110011
[4,6,1,7,3,2,5,8]=>0101100=>1010011
[4,6,1,8,3,2,5,7]=>0101100=>1010011
[4,7,1,8,3,5,2,6]=>0101010=>1010101
[4,1,7,8,6,2,3,5]=>1001100=>0110011
[1,6,5,7,8,3,4,2]=>0100101=>1011010
[1,6,5,8,7,3,4,2]=>0101101=>1010010
[4,1,8,7,6,2,3,5]=>1011100=>0100011
[4,8,1,7,3,5,2,6]=>0101010=>1010101
[4,8,1,6,3,2,5,7]=>0101100=>1010011
[4,7,1,6,3,2,5,8]=>0101100=>1010011
[6,1,2,3,7,5,4,8]=>1000110=>0111001
[6,8,1,5,3,7,2,4]=>0101010=>1010101
[8,7,5,2,4,1,6,3]=>1110101=>0001010
[1,5,7,3,4,8,6,2]=>0010011=>1101100
[1,5,8,3,4,7,6,2]=>0010011=>1101100
[7,8,5,2,4,1,6,3]=>0110101=>1001010
[7,1,2,3,5,6,4,8]=>1000010=>0111101
[8,1,2,3,5,6,4,7]=>1000010=>0111101
[8,1,2,3,5,4,7,6]=>1000101=>0111010
[7,1,8,4,6,3,2,5]=>1010110=>0101001
[6,8,2,4,3,1,5,7]=>0101100=>1010011
[6,7,2,4,3,1,5,8]=>0101100=>1010011
[3,8,1,2,4,5,7,6]=>0100001=>1011110
[3,7,1,8,6,4,2,5]=>0101110=>1010001
[1,6,4,3,7,5,8,2]=>0110101=>1001010
[3,1,2,6,7,5,8,4]=>1000101=>0111010
[3,8,1,7,6,4,2,5]=>0101110=>1010001
[7,6,2,4,3,1,5,8]=>1101100=>0010011
[8,7,2,4,3,5,1,6]=>1101010=>0010101
[8,1,7,4,6,3,2,5]=>1010110=>0101001
[8,1,7,6,5,3,2,4]=>1011110=>0100001
[1,5,7,3,4,6,8,2]=>0010001=>1101110
[8,7,2,5,3,6,1,4]=>1101010=>0010101
[7,1,2,3,5,4,8,6]=>1000101=>0111010
[6,1,2,3,5,8,4,7]=>1000010=>0111101
[6,1,2,3,5,7,4,8]=>1000010=>0111101
[5,1,2,3,7,6,4,8]=>1000110=>0111001
[5,1,2,3,8,6,4,7]=>1000110=>0111001
[1,5,6,3,4,7,8,2]=>0010001=>1101110
[8,6,5,2,4,7,1,3]=>1110010=>0001101
[7,6,2,5,3,1,8,4]=>1101101=>0010010
[7,4,5,2,3,8,6,1]=>1010011=>0101100
[8,2,3,7,4,5,1,6]=>1001010=>0110101
[8,4,7,3,2,5,1,6]=>1011010=>0100101
[5,4,6,3,1,2,8,7]=>1011001=>0100110
[4,6,2,3,1,5,8,7]=>0101001=>1010110
[7,2,3,4,5,8,6,1]=>1000011=>0111100
[8,2,3,4,5,7,1,6]=>1000010=>0111101
[7,3,4,6,8,5,1,2]=>1000110=>0111001
[4,7,3,2,8,6,1,5]=>0110110=>1001001
[3,7,4,5,1,8,6,2]=>0101011=>1010100
[3,8,2,6,7,4,5,1]=>0100101=>1011010
[4,8,1,5,6,7,3,2]=>0100011=>1011100
[5,8,2,4,6,7,1,3]=>0100010=>1011101
[6,8,1,3,4,2,7,5]=>0100101=>1011010
[5,8,2,4,3,1,7,6]=>0101101=>1010010
[2,1,7,6,8,5,3,4]=>1010110=>0101001
[3,7,6,1,8,5,2,4]=>0110110=>1001001
[4,7,2,3,8,5,1,6]=>0100110=>1011001
[7,1,3,6,4,8,5,2]=>1001011=>0110100
[7,6,1,4,8,5,2,3]=>1100110=>0011001
[6,2,3,7,8,5,4,1]=>1000111=>0111000
[6,2,3,8,4,5,1,7]=>1001010=>0110101
[7,2,3,6,8,4,1,5]=>1000110=>0111001
[8,2,3,5,7,1,4,6]=>1000100=>0111011
[6,4,8,3,5,1,7,2]=>1010101=>0101010
[5,4,8,3,6,7,1,2]=>1010010=>0101101
[3,5,1,8,4,6,7,2]=>0101001=>1010110
[3,6,1,8,4,5,2,7]=>0101010=>1010101
[4,6,8,3,5,2,7,1]=>0010101=>1101010
[5,7,8,3,2,4,1,6]=>0011010=>1100101
[4,8,2,3,5,6,1,7]=>0100010=>1011101
[6,8,2,3,1,4,5,7]=>0101000=>1010111
[5,2,7,4,8,3,1,6]=>1010110=>0101001
[3,7,8,2,1,4,6,5]=>0011001=>1100110
[3,7,5,2,8,4,1,6]=>0110110=>1001001
[6,3,2,4,1,8,7,5]=>1101011=>0010100
[7,2,3,4,8,5,1,6]=>1000110=>0111001
[5,7,3,1,4,2,6,8]=>0110100=>1001011
[3,7,4,1,8,2,5,6]=>0110100=>1001011
[6,3,7,4,8,1,2,5]=>1010100=>0101011
[8,3,7,4,2,6,1,5]=>1011010=>0100101
[3,7,4,1,5,6,2,8]=>0110010=>1001101
[1,8,3,2,4,5,7,6]=>0110001=>1001110
[8,4,1,6,3,7,5,2]=>1101011=>0010100
[8,7,4,2,1,6,3,5]=>1111010=>0000101
[8,3,5,2,7,4,1,6]=>1010110=>0101001
[1,5,3,8,7,6,4,2]=>0101111=>1010000
[7,2,4,8,1,3,6,5]=>1001001=>0110110
[1,2,8,7,5,6,3,4]=>0011010=>1100101
[3,1,8,6,7,5,2,4]=>1010110=>0101001
[1,4,8,6,5,7,2,3]=>0011010=>1100101
[1,6,5,4,8,2,3,7]=>0110100=>1001011
[5,1,6,8,3,4,2,7]=>1001010=>0110101
[6,2,5,1,7,4,3,8]=>1010110=>0101001
[5,2,1,8,7,4,3,6]=>1101110=>0010001
[5,2,6,3,8,1,4,7]=>1010100=>0101011
[5,2,8,3,4,6,1,7]=>1010010=>0101101
[6,2,8,4,3,1,7,5]=>1011101=>0100010
[7,2,8,1,3,6,5,4]=>1010011=>0101100
[7,3,8,1,4,6,2,5]=>1010010=>0101101
[1,7,8,5,4,6,3,2]=>0011011=>1100100
[1,5,8,4,6,3,7,2]=>0010101=>1101010
[5,3,8,4,1,2,7,6]=>1011001=>0100110
[5,8,4,3,6,2,1,7]=>0110110=>1001001
[1,8,3,6,5,2,7,4]=>0101101=>1010010
[1,8,2,4,7,6,5,3]=>0100111=>1011000
[3,8,1,4,6,7,5,2]=>0100011=>1011100
[3,8,2,5,1,7,6,4]=>0101011=>1010100
[4,3,8,2,5,1,6,7]=>1010100=>0101011
[8,2,4,3,5,1,7,6]=>1010101=>0101010
[8,2,1,4,6,5,7,3]=>1100101=>0011010
[8,1,3,4,5,7,6,2]=>1000011=>0111100
[6,1,5,2,4,7,8,3]=>1010001=>0101110
[4,1,8,5,2,7,6,3]=>1011011=>0100100
[4,8,5,1,3,6,2,7]=>0110010=>1001101
[3,6,1,5,7,2,8,4]=>0100101=>1011010
[6,3,1,2,8,5,7,4]=>1100101=>0011010
[4,1,8,2,3,7,5,6]=>1010010=>0101101
[5,3,8,7,2,1,4,6]=>1011100=>0100011
[6,7,3,5,1,4,8,2]=>0101001=>1010110
[6,4,7,5,8,2,3,1]=>1010101=>0101010
[5,7,8,4,2,6,3,1]=>0011011=>1100100
[5,7,4,1,6,8,3,2]=>0110011=>1001100
[5,8,4,6,1,7,3,2]=>0101011=>1010100
[5,6,1,4,7,8,3,2]=>0100011=>1011100
[5,6,3,7,4,8,2,1]=>0101011=>1010100
[5,3,6,7,4,8,2,1]=>1001011=>0110100
[5,3,2,8,6,7,4,1]=>1101011=>0010100
[5,4,8,2,6,7,3,1]=>1010011=>0101100
[5,4,8,6,2,7,3,1]=>1011011=>0100100
[7,4,8,5,6,2,1,3]=>1010110=>0101001
[5,6,3,8,4,7,2,1]=>0101011=>1010100
[5,6,3,8,2,7,4,1]=>0101011=>1010100
[4,3,7,2,8,6,5,1]=>1010111=>0101000
[6,7,3,8,5,2,4,1]=>0101101=>1010010
[6,2,7,5,1,4,8,3]=>1011001=>0100110
[3,5,7,8,4,6,2,1]=>0001011=>1110100
[5,3,7,8,4,6,2,1]=>1001011=>0110100
[5,7,8,2,4,6,3,1]=>0010011=>1101100
[2,5,8,4,3,7,6,1]=>0011011=>1100100
[3,7,4,8,6,2,1,5]=>0101110=>1010001
[3,6,4,8,7,2,5,1]=>0101101=>1010010
[3,5,4,8,2,7,6,1]=>0101011=>1010100
[4,5,7,3,8,6,2,1]=>0010111=>1101000
[3,5,6,8,4,7,2,1]=>0001011=>1110100
[6,3,1,8,7,5,4,2]=>1101111=>0010000
[5,4,8,1,7,6,3,2]=>1010111=>0101000
[5,8,4,1,7,6,3,2]=>0110111=>1001000
[7,5,4,1,8,6,3,2]=>1110111=>0001000
[8,5,4,1,7,6,3,2]=>1110111=>0001000
[1,8,2,5,6,3,4,7]=>0100100=>1011011
[7,2,8,4,5,1,3,6]=>1010100=>0101011
[1,3,7,5,6,2,4,8]=>0010100=>1101011
[1,6,7,4,3,5,2,8]=>0011010=>1100101
[1,8,5,2,3,7,4,6]=>0110010=>1001101
[1,8,2,5,3,6,7,4]=>0101001=>1010110
[2,6,8,4,3,5,7,1]=>0011001=>1100110
[7,5,8,3,2,1,6,4]=>1011101=>0100010
[7,2,8,4,1,5,6,3]=>1011001=>0100110
[7,5,8,1,2,6,3,4]=>1010010=>0101101
[1,6,7,4,3,2,8,5]=>0011101=>1100010
[1,5,2,6,4,7,8,3]=>0101001=>1010110
[1,5,4,6,2,3,7,8]=>0101000=>1010111
[6,2,5,7,1,4,8,3]=>1001001=>0110110
[6,5,4,3,8,1,7,2]=>1110101=>0001010
[7,3,6,8,5,2,4,1]=>1001101=>0110010
[2,7,8,3,6,5,1,4]=>0010110=>1101001
[2,7,8,5,4,6,3,1]=>0011011=>1100100
[2,6,5,8,3,4,1,7]=>0101010=>1010101
[2,6,5,7,3,4,1,8]=>0101010=>1010101
[6,2,5,7,4,1,3,8]=>1001100=>0110011
[6,2,5,8,4,1,3,7]=>1001100=>0110011
[2,7,8,4,6,1,3,5]=>0010100=>1101011
[6,1,2,8,3,7,4,5]=>1001010=>0110101
[6,1,2,8,5,4,7,3]=>1001101=>0110010
[6,2,5,7,8,1,3,4]=>1000100=>0111011
[1,5,4,2,6,7,3,8]=>0110010=>1001101
[2,6,5,7,3,8,1,4]=>0101010=>1010101
[1,6,2,7,5,8,4,3]=>0101011=>1010100
[1,3,2,7,8,5,6,4]=>0100101=>1011010
[1,6,2,4,8,7,3,5]=>0100110=>1011001
[6,5,2,1,8,7,3,4]=>1110110=>0001001
[2,6,5,3,7,8,4,1]=>0110011=>1001100
[6,2,5,3,8,4,7,1]=>1010101=>0101010
[6,5,2,3,8,7,1,4]=>1100110=>0011001
[5,4,1,2,3,8,6,7]=>1100010=>0011101
[5,1,4,2,3,7,8,6]=>1010001=>0101110
[1,5,4,2,6,3,8,7]=>0110101=>1001010
[5,1,6,3,8,2,7,4]=>1010101=>0101010
[9,8,7,6,5,4,3,1,2,10]=>111111100=>000000011
[8,7,6,5,4,2,1,3,9]=>11111100=>00000011
[1,9,8,7,6,5,3,2,4]=>01111110=>10000001
[1,8,7,6,2,5,4,3]=>0111011=>1000100
[1,9,8,7,6,5,2,4,3]=>01111101=>10000010
[1,10,9,8,7,6,5,4,2,3]=>011111110=>100000001
[2,1,9,8,7,6,5,4,3]=>10111111=>01000000
[1,2,9,8,7,6,5,4,3]=>00111111=>11000000
[3,2,1,9,8,7,6,5,4]=>11011111=>00100000
[1,3,2,9,8,7,6,5,4]=>01011111=>10100000
[1,2,3,9,8,7,6,5,4]=>00011111=>11100000
[4,3,2,1,9,8,7,6,5]=>11101111=>00010000
[1,4,3,2,9,8,7,6,5]=>01101111=>10010000
[2,1,4,3,9,8,7,6,5]=>10101111=>01010000
[1,2,4,3,9,8,7,6,5]=>00101111=>11010000
[1,2,3,4,9,8,7,6,5]=>00001111=>11110000
[1,5,4,3,2,9,8,7,6]=>01110111=>10001000
[2,1,5,4,3,9,8,7,6]=>10110111=>01001000
[1,2,5,4,3,9,8,7,6]=>00110111=>11001000
[1,3,2,5,4,9,8,7,6]=>01010111=>10101000
[1,2,3,5,4,9,8,7,6]=>00010111=>11101000
[1,2,3,4,5,9,8,7,6]=>00000111=>11111000
[1,3,2,6,5,4,9,8,7]=>01011011=>10100100
[1,2,3,6,5,4,9,8,7]=>00011011=>11100100
[2,1,4,3,6,5,9,8,7]=>10101011=>01010100
[1,2,4,3,6,5,9,8,7]=>00101011=>11010100
[1,2,3,4,6,5,9,8,7]=>00001011=>11110100
[1,2,3,5,4,7,6,9,8]=>00010101=>11101010
[1,2,3,4,5,7,6,9,8]=>00000101=>11111010
[1,2,10,9,8,7,6,5,4,3]=>001111111=>110000000
[3,2,1,10,9,8,7,6,5,4]=>110111111=>001000000
[1,3,2,10,9,8,7,6,5,4]=>010111111=>101000000
[1,2,3,10,9,8,7,6,5,4]=>000111111=>111000000
[1,4,3,2,10,9,8,7,6,5]=>011011111=>100100000
[1,2,4,3,10,9,8,7,6,5]=>001011111=>110100000
[1,2,3,4,10,9,8,7,6,5]=>000011111=>111100000
[1,5,4,3,2,10,9,8,7,6]=>011101111=>100010000
[2,1,5,4,3,10,9,8,7,6]=>101101111=>010010000
[1,2,5,4,3,10,9,8,7,6]=>001101111=>110010000
[1,3,2,5,4,10,9,8,7,6]=>010101111=>101010000
[1,2,3,5,4,10,9,8,7,6]=>000101111=>111010000
[1,2,6,5,4,3,10,9,8,7]=>001110111=>110001000
[3,2,1,6,5,4,10,9,8,7]=>110110111=>001001000
[1,3,2,6,5,4,10,9,8,7]=>010110111=>101001000
[1,2,3,6,5,4,10,9,8,7]=>000110111=>111001000
[1,2,4,3,6,5,10,9,8,7]=>001010111=>110101000
[1,2,3,4,6,5,10,9,8,7]=>000010111=>111101000
[1,2,3,4,5,6,10,9,8,7]=>000000111=>111111000
[1,4,3,2,7,6,5,10,9,8]=>011011011=>100100100
[2,1,4,3,7,6,5,10,9,8]=>101011011=>010100100
[1,2,4,3,7,6,5,10,9,8]=>001011011=>110100100
[1,2,3,4,7,6,5,10,9,8]=>000011011=>111100100
[1,3,2,5,4,7,6,10,9,8]=>010101011=>101010100
[1,2,3,5,4,7,6,10,9,8]=>000101011=>111010100
[1,2,3,4,5,7,6,10,9,8]=>000001011=>111110100
[1,2,3,4,5,6,7,10,9,8]=>000000011=>111111100
[1,2,4,3,6,5,8,7,10,9]=>001010101=>110101010
[1,2,3,4,6,5,8,7,10,9]=>000010101=>111101010
[1,2,3,4,5,6,8,7,10,9]=>000000101=>111111010
[5,2,7,4,1,6,3,8]=>1011010=>0100101
[4,7,3,1,5,6,2,8]=>0110010=>1001101
[5,8,3,4,1,6,7,2]=>0101001=>1010110
[1,7,8,4,5,6,2,3]=>0010010=>1101101
[1,5,8,4,2,6,7,3]=>0011001=>1100110
[1,6,3,8,5,2,7,4]=>0101101=>1010010
[6,2,3,7,5,1,4,8]=>1001100=>0110011
[1,7,3,4,8,6,2,5]=>0100110=>1011001
[8,7,3,2,1,6,5,4]=>1111011=>0000100
[8,7,6,3,1,5,2,4]=>1111010=>0000101
[8,5,1,7,2,3,4,6]=>1101000=>0010111
[9,8,7,6,5,2,1,4,3]=>11111101=>00000010
[9,8,7,3,2,1,6,5,4]=>11111011=>00000100
[9,8,7,6,3,1,5,2,4]=>11111010=>00000101
[9,4,3,2,1,8,7,6,5]=>11110111=>00001000
[9,8,4,3,1,7,6,2,5]=>11110110=>00001001
[9,8,7,2,1,4,3,6,5]=>11110101=>00001010
[9,8,7,4,1,6,2,3,5]=>11110100=>00001011
[5,4,3,1,9,8,7,2,6]=>11101110=>00010001
[9,5,2,1,8,4,3,7,6]=>11101101=>00010010
[9,8,3,1,5,2,7,4,6]=>11101010=>00010101
[6,3,1,9,5,2,8,4,7]=>11011010=>00100101
[6,5,1,9,8,2,3,4,7]=>11011000=>00100111
[9,2,1,4,3,6,5,8,7]=>11010101=>00101010
[9,6,1,8,2,3,4,5,7]=>11010000=>00101111
[5,1,7,2,9,3,4,6,8]=>10101000=>01010111
[7,1,9,2,3,4,5,6,8]=>10100000=>01011111
[10,9,8,7,6,5,2,1,4,3]=>111111101=>000000010
[10,9,8,7,3,2,1,6,5,4]=>111111011=>000000100
[10,9,8,7,6,3,1,5,2,4]=>111111010=>000000101
[10,9,4,3,2,1,8,7,6,5]=>111110111=>000001000
[10,9,8,4,3,1,7,6,2,5]=>111110110=>000001001
[10,9,8,7,2,1,4,3,6,5]=>111110101=>000001010
[10,9,8,7,4,1,6,2,3,5]=>111110100=>000001011
[10,5,4,3,1,9,8,7,2,6]=>111101110=>000010001
[10,9,5,2,1,8,4,3,7,6]=>111101101=>000010010
[10,9,5,4,1,8,7,2,3,6]=>111101100=>000010011
[10,9,8,3,1,5,2,7,4,6]=>111101010=>000010101
[6,5,2,1,10,9,4,3,8,7]=>111011101=>000100010
[6,5,4,1,10,9,8,2,3,7]=>111011100=>000100011
[10,3,2,1,6,5,4,9,8,7]=>111011011=>000100100
[10,6,5,1,9,8,2,3,4,7]=>111011000=>000100111
[10,9,2,1,4,3,6,5,8,7]=>111010101=>000101010
[10,9,6,1,8,2,3,4,5,7]=>111010000=>000101111
[4,3,1,7,6,2,10,9,5,8]=>110110110=>001001001
[7,2,1,10,4,3,6,5,9,8]=>110110101=>001001010
[7,4,1,10,6,2,9,3,5,8]=>110110100=>001001011
[7,6,1,10,9,2,3,4,5,8]=>110110000=>001001111
[10,5,1,7,2,9,3,4,6,8]=>110101000=>001010111
[10,7,1,9,2,3,4,5,6,8]=>110100000=>001011111
[4,1,6,2,8,3,10,5,7,9]=>101010100=>010101011
[6,1,8,2,10,3,4,5,7,9]=>101010000=>010101111
[8,1,10,2,3,4,5,6,7,9]=>101000000=>010111111
[2,4,8,5,3,7,1,6]=>0011010=>1100101
[2,4,1,8,5,3,7,6]=>0101101=>1010010
[2,4,8,6,3,1,7,5]=>0011101=>1100010
[3,4,6,8,2,1,7,5]=>0001101=>1110010
[3,4,1,5,8,2,7,6]=>0100101=>1011010
[8,1,4,5,3,2,7,6]=>1001101=>0110010
[3,4,1,5,2,8,7,6]=>0101011=>1010100
[3,4,6,2,1,8,7,5]=>0011011=>1100100
[3,5,6,2,1,7,8,4]=>0011001=>1100110
[3,4,6,2,7,8,1,5]=>0010010=>1101101
[8,1,4,6,3,7,2,5]=>1001010=>0110101
[8,1,4,6,3,7,5,2]=>1001011=>0110100
[3,5,6,2,1,7,4,8]=>0011010=>1100101
[8,1,5,6,7,3,4,2]=>1000101=>0111010
[8,1,5,6,7,3,2,4]=>1000110=>0111001
[3,4,1,6,8,7,2,5]=>0100110=>1011001
[3,5,6,1,8,7,2,4]=>0010110=>1101001
[2,1,3,8,6,7,4,5]=>1001010=>0110101
[8,1,3,2,6,7,5,4]=>1010011=>0101100
[2,3,8,6,7,1,5,4]=>0010101=>1101010
[2,4,1,8,6,7,5,3]=>0101011=>1010100
[2,5,8,6,1,7,4,3]=>0011011=>1100100
[3,5,6,1,8,7,4,2]=>0010111=>1101000
[3,4,1,6,8,7,5,2]=>0100111=>1011000
[3,4,6,8,7,1,5,2]=>0001101=>1110010
[8,1,4,6,2,7,5,3]=>1001011=>0110100
[3,5,1,6,7,8,4,2]=>0100011=>1011100
[4,5,6,1,7,8,3,2]=>0010011=>1101100
[4,5,6,1,7,3,8,2]=>0010101=>1101010
[3,5,1,6,7,4,8,2]=>0100101=>1011010
[8,1,5,6,7,4,2,3]=>1000110=>0111001
[8,1,5,6,7,4,3,2]=>1000111=>0111000
[3,5,1,6,7,4,2,8]=>0100110=>1011001
[4,5,6,1,7,3,2,8]=>0010110=>1101001
[6,5,8,7,4,3,1,2]=>1011110=>0100001
[6,4,2,7,8,5,1,3]=>1100110=>0011001
[6,1,4,8,7,5,2,3]=>1001110=>0110001
[1,6,4,8,7,5,2,3]=>0101110=>1010001
[1,8,6,2,4,7,3,5]=>0110010=>1001101
[8,1,6,2,4,7,3,5]=>1010010=>0101101
[7,6,2,1,4,8,3,5]=>1110010=>0001101
[6,4,1,7,8,5,2,3]=>1100110=>0011001
[7,6,1,2,4,8,3,5]=>1100010=>0011101
[7,6,1,3,4,8,2,5]=>1100010=>0011101
[8,1,6,3,4,7,2,5]=>1010010=>0101101
[1,8,6,3,4,7,2,5]=>0110010=>1001101
[1,7,2,5,4,8,3,6]=>0101010=>1010101
[7,1,2,5,4,8,3,6]=>1001010=>0110101
[2,7,1,5,4,8,3,6]=>0101010=>1010101
[2,8,6,3,4,7,1,5]=>0110010=>1001101
[2,8,6,1,4,7,3,5]=>0110010=>1001101
[7,2,1,5,4,8,3,6]=>1101010=>0010101
[1,2,7,5,4,8,3,6]=>0011010=>1100101
[3,2,7,5,4,8,1,6]=>1011010=>0100101
[2,5,8,4,7,3,1,6]=>0010110=>1101001
[2,3,7,5,4,8,1,6]=>0011010=>1100101
[6,8,3,2,4,7,1,5]=>0110010=>1001101
[3,7,2,5,4,8,1,6]=>0101010=>1010101
[3,1,7,5,4,8,2,6]=>1011010=>0100101
[1,3,7,5,4,8,2,6]=>0011010=>1100101
[1,5,8,4,7,3,2,6]=>0010110=>1101001
[5,1,8,4,7,3,2,6]=>1010110=>0101001
[5,8,2,4,7,3,1,6]=>0100110=>1011001
[6,8,4,3,7,5,1,2]=>0110110=>1001001
[8,7,5,6,2,1,4,3]=>1101101=>0010010
[8,5,2,4,7,3,1,6]=>1100110=>0011001
[8,1,5,4,7,3,2,6]=>1010110=>0101001
[1,8,5,4,7,3,2,6]=>0110110=>1001001
[1,7,3,5,4,8,2,6]=>0101010=>1010101
[8,6,3,1,4,7,2,5]=>1110010=>0001101
[8,6,4,2,7,5,1,3]=>1110110=>0001001
[8,6,4,1,7,2,5,3]=>1110101=>0001010
[5,3,7,4,6,8,2,1]=>1010011=>0101100
[4,1,3,2,7,8,5,6]=>1010010=>0101101
[1,4,3,2,7,8,5,6]=>0110010=>1001101
[2,4,3,1,7,8,5,6]=>0110010=>1001101
[2,7,3,5,4,8,1,6]=>0101010=>1010101
[2,8,5,4,7,3,1,6]=>0110110=>1001001
[5,7,3,4,6,8,2,1]=>0100011=>1011100
[8,2,5,4,7,3,1,6]=>1010110=>0101001
[7,2,3,5,4,8,1,6]=>1001010=>0110101
[3,2,1,4,7,8,5,6]=>1100010=>0011101
[8,1,7,6,4,3,5,2]=>1011101=>0100010
[8,6,4,5,2,7,1,3]=>1101010=>0010101
[7,1,8,6,4,3,5,2]=>1011101=>0100010
[7,4,2,5,1,6,3,8]=>1101010=>0010101
[7,3,6,5,2,1,4,8]=>1011100=>0100011
[8,3,6,5,2,1,7,4]=>1011101=>0100010
[7,3,6,5,2,1,8,4]=>1011101=>0100010
[7,5,8,6,4,2,1,3]=>1011110=>0100001
[5,4,2,8,1,3,7,6]=>1101001=>0010110
[5,8,2,6,4,1,3,7]=>0101100=>1010011
[6,4,2,5,1,8,3,7]=>1101010=>0010101
[6,3,5,2,1,4,7,8]=>1011000=>0100111
[2,5,8,6,3,1,4,7]=>0011100=>1100011
[2,3,5,8,1,4,7,6]=>0001001=>1110110
[2,3,6,8,1,5,7,4]=>0001001=>1110110
[6,3,8,5,2,7,1,4]=>1011010=>0100101
[6,3,7,5,2,1,4,8]=>1011100=>0100011
[2,5,7,6,3,1,4,8]=>0011100=>1100011
[2,8,7,6,3,1,5,4]=>0111101=>1000010
[2,5,8,7,6,3,1,4]=>0011110=>1100001
[2,4,8,1,6,5,7,3]=>0010101=>1101010
[2,8,7,3,6,1,4,5]=>0110100=>1001011
[7,3,5,2,1,4,6,8]=>1011000=>0100111
[8,4,2,5,1,3,7,6]=>1101001=>0010110
[2,3,6,8,1,4,7,5]=>0001001=>1110110
[2,7,8,6,3,1,4,5]=>0011100=>1100011
[7,3,8,5,2,1,4,6]=>1011100=>0100011
[2,3,6,1,8,4,7,5]=>0010101=>1101010
[2,8,6,3,1,4,5,7]=>0111000=>1000111
[8,3,5,2,1,4,6,7]=>1011000=>0100111
[2,4,8,1,3,7,5,6]=>0010010=>1101101
[2,5,8,1,7,3,6,4]=>0010101=>1101010
[3,8,6,1,4,7,5,2]=>0110011=>1001100
[2,7,1,5,8,3,4,6]=>0100100=>1011011
[3,7,5,8,1,2,6,4]=>0101001=>1010110
[7,3,6,1,2,8,4,5]=>1010010=>0101101
[7,4,8,1,6,5,2,3]=>1010110=>0101001
[7,4,5,8,6,1,2,3]=>1001100=>0110011
[6,8,4,5,1,7,2,3]=>0101010=>1010101
[5,1,8,7,6,2,3,4]=>1011100=>0100011
[8,5,1,6,2,7,3,4]=>1101010=>0010101
[4,6,1,8,7,5,2,3]=>0101110=>1010001
[4,5,1,8,7,2,3,6]=>0101100=>1010011
[3,4,8,7,1,2,5,6]=>0011000=>1100111
[6,4,8,7,1,2,5,3]=>1011001=>0100110
[6,5,1,2,7,3,8,4]=>1100101=>0011010
[6,5,1,8,2,7,3,4]=>1101010=>0010101
[6,5,1,7,2,8,3,4]=>1101010=>0010101
[6,5,1,7,2,3,8,4]=>1101001=>0010110
[5,6,8,7,4,1,2,3]=>0011100=>1100011
[6,8,5,7,4,1,2,3]=>0101100=>1010011
[7,3,8,1,5,2,4,6]=>1010100=>0101011
[4,1,7,5,3,6,2,8]=>1011010=>0100101
[1,8,4,2,3,6,7,5]=>0110001=>1001110
[2,5,8,3,4,6,7,1]=>0010001=>1101110
[4,1,7,2,3,6,8,5]=>1010001=>0101110
[4,6,2,1,5,7,8,3]=>0110001=>1001110
[4,5,2,3,1,7,8,6]=>0101001=>1010110
[3,2,6,7,4,1,8,5]=>1001101=>0110010
[5,6,2,7,1,4,8,3]=>0101001=>1010110
[6,2,3,8,1,7,4,5]=>1001010=>0110101
[2,6,8,3,4,7,1,5]=>0010010=>1101101
[4,6,2,7,5,1,3,8]=>0101100=>1010011
[2,6,3,1,8,4,5,7]=>0110100=>1001011
[2,4,3,7,8,1,5,6]=>0100100=>1011011
[5,3,2,7,4,8,1,6]=>1101010=>0010101
[5,1,2,7,6,8,4,3]=>1001011=>0110100
[2,6,3,1,8,7,4,5]=>0110110=>1001001
[3,5,6,4,7,8,1,2]=>0010010=>1101101
[5,3,6,4,2,8,7,1]=>1011011=>0100100
[5,4,2,3,7,8,6,1]=>1100011=>0011100
[4,1,8,2,5,7,3,6]=>1010010=>0101101
[3,1,8,4,7,2,5,6]=>1010100=>0101011
[6,2,3,8,4,1,7,5]=>1001101=>0110010
[2,6,4,1,5,3,8,7]=>0110101=>1001010
[3,2,7,6,4,1,8,5]=>1011101=>0100010
[2,5,4,1,7,6,8,3]=>0110101=>1001010
[6,2,1,4,7,8,3,5]=>1100010=>0011101
[2,6,5,1,7,8,3,4]=>0110010=>1001101
[4,7,5,2,1,6,3,8]=>0111010=>1000101
[4,2,3,7,8,1,6,5]=>1000101=>0111010
[5,8,3,1,7,2,4,6]=>0110100=>1001011
[6,8,3,1,5,2,4,7]=>0110100=>1001011
[4,2,7,1,6,3,5,8]=>1010100=>0101011
[5,1,7,4,2,6,3,8]=>1011010=>0100101
[5,8,2,1,4,7,3,6]=>0110010=>1001101
[6,8,3,2,5,1,7,4]=>0110101=>1001010
[6,8,4,3,1,5,7,2]=>0111001=>1000110
[6,8,4,2,1,5,7,3]=>0111001=>1000110
[6,8,3,2,1,4,5,7]=>0111000=>1000111
[5,1,7,3,2,4,6,8]=>1011000=>0100111
[5,2,1,8,3,6,7,4]=>1101001=>0010110
[4,3,8,1,6,2,7,5]=>1010101=>0101010
[4,2,1,6,5,8,3,7]=>1101010=>0010101
[4,2,1,8,5,7,3,6]=>1101010=>0010101
[6,3,2,1,7,4,5,8]=>1110100=>0001011
[6,4,2,1,7,5,3,8]=>1110110=>0001001
[7,5,2,1,8,6,3,4]=>1110110=>0001001
[5,3,2,7,6,1,4,8]=>1101100=>0010011
[5,3,2,8,6,1,4,7]=>1101100=>0010011
[6,3,2,8,7,1,4,5]=>1101100=>0010011
[4,2,8,1,7,3,5,6]=>1010100=>0101011
[4,3,8,7,2,1,5,6]=>1011100=>0100011
[2,1,5,8,4,7,3,6]=>1001010=>0110101
[4,3,2,5,8,1,6,7]=>1100100=>0011011
[4,3,2,5,7,1,6,8]=>1100100=>0011011
[4,3,1,6,2,7,5,8]=>1101010=>0010101
[5,4,1,7,2,8,6,3]=>1101011=>0010100
[6,5,3,1,7,8,4,2]=>1110011=>0001100
[6,4,2,1,7,8,5,3]=>1110011=>0001100
[3,2,1,4,8,7,5,6]=>1100110=>0011001
[3,2,1,4,6,8,5,7]=>1100010=>0011101
[5,3,2,1,6,7,8,4]=>1110001=>0001110
[8,6,1,4,5,7,2,3]=>1100010=>0011101
[3,8,6,4,5,7,1,2]=>0110010=>1001101
[5,2,8,3,7,4,6,1]=>1010101=>0101010
[6,2,8,5,4,7,3,1]=>1011011=>0100100
[1,8,6,3,7,4,2,5]=>0110110=>1001001
[1,8,6,5,7,2,3,4]=>0110100=>1001011
[5,2,8,4,3,6,7,1]=>1011001=>0100110
[5,4,2,7,3,6,1,8]=>1101010=>0010101
[5,4,2,8,3,6,1,7]=>1101010=>0010101
[6,5,3,8,4,7,2,1]=>1101011=>0010100
[5,2,8,4,3,7,1,6]=>1011010=>0100101
[6,2,8,3,7,4,1,5]=>1010110=>0101001
[5,4,2,7,3,1,8,6]=>1101101=>0010010
[6,4,3,7,1,2,8,5]=>1101001=>0010110
[6,4,3,8,1,2,7,5]=>1101001=>0010110
[7,6,3,8,4,2,1,5]=>1101110=>0010001
[7,2,8,5,1,6,3,4]=>1011010=>0100101
[7,2,8,4,3,1,5,6]=>1011100=>0100011
[7,5,3,8,4,2,6,1]=>1101101=>0010010
[6,4,2,7,3,1,5,8]=>1101100=>0010011
[7,6,4,8,2,3,5,1]=>1101001=>0010110
[7,6,8,1,2,5,3,4]=>1010010=>0101101
[5,3,1,7,8,4,6,2]=>1100101=>0011010
[5,3,2,7,8,4,6,1]=>1100101=>0011010
[5,4,1,6,3,8,7,2]=>1101011=>0010100
[6,5,1,7,8,2,3,4]=>1100100=>0011011
[6,3,1,7,8,4,2,5]=>1100110=>0011001
[5,4,1,7,3,8,2,6]=>1101010=>0010101
[6,3,2,7,8,4,1,5]=>1100110=>0011001
[6,1,5,4,3,2,8,7]=>1011101=>0100010
[8,7,6,1,3,5,2,4]=>1110010=>0001101
[8,1,6,5,7,3,4,2]=>1010101=>0101010
[8,4,1,5,7,6,2,3]=>1100110=>0011001
[7,8,6,2,5,3,1,4]=>0110110=>1001001
[6,1,3,5,2,8,4,7]=>1001010=>0110101
[8,1,3,7,4,2,5,6]=>1001100=>0110011
[4,3,8,7,5,2,1,6]=>1011110=>0100001
[6,7,1,8,5,3,4,2]=>0101101=>1010010
[2,7,6,4,8,3,5,1]=>0110101=>1001010
[6,5,2,7,1,4,8,3]=>1101001=>0010110
[7,4,6,1,3,2,8,5]=>1010101=>0101010
[7,5,2,1,3,8,4,6]=>1110010=>0001101
[8,4,7,6,3,1,5,2]=>1011101=>0100010
[7,4,1,5,6,3,8,2]=>1100101=>0011010
[3,4,7,5,6,1,8,2]=>0010101=>1101010
[2,4,7,5,6,3,8,1]=>0010101=>1101010
[5,4,1,7,6,2,8,3]=>1101101=>0010010
[3,5,6,7,1,4,8,2]=>0001001=>1110110
[2,7,6,1,3,4,8,5]=>0110001=>1001110
[5,7,2,1,6,3,8,4]=>0110101=>1001010
[4,7,2,5,6,3,8,1]=>0100101=>1011010
[8,6,2,5,7,1,4,3]=>1100101=>0011010
[2,7,4,5,3,8,1,6]=>0101010=>1010101
[6,8,7,1,3,2,5,4]=>0110101=>1001010
[2,8,6,5,7,1,4,3]=>0110101=>1001010
[5,8,4,3,2,6,7,1]=>0111001=>1000110
[1,8,5,6,2,4,7,3]=>0101001=>1010110
[8,1,5,6,2,4,7,3]=>1001001=>0110110
[6,4,8,1,3,2,7,5]=>1010101=>0101010
[1,4,5,2,8,6,7,3]=>0010101=>1101010
[2,3,1,7,8,6,4,5]=>0100110=>1011001
[3,5,7,6,2,8,1,4]=>0011010=>1100101
[4,5,6,1,2,8,7,3]=>0010011=>1101100
[5,4,1,2,8,6,7,3]=>1100101=>0011010
[8,4,5,2,1,6,7,3]=>1011001=>0100110
[3,1,2,6,8,4,7,5]=>1000101=>0111010
[5,1,3,2,7,8,4,6]=>1010010=>0101101
[1,5,4,2,7,8,3,6]=>0110010=>1001101
[4,6,7,8,3,1,5,2]=>0001101=>1110010
[7,6,2,8,4,3,1,5]=>1101110=>0010001
[5,2,8,6,3,4,7,1]=>1011001=>0100110
[5,6,8,4,3,2,7,1]=>0011101=>1100010
[5,3,8,1,7,2,4,6]=>1010100=>0101011
[3,6,7,8,4,2,1,5]=>0001110=>1110001
[6,5,1,8,4,3,7,2]=>1101101=>0010010
[6,3,8,4,2,1,7,5]=>1011101=>0100010
[2,5,8,3,1,6,7,4]=>0011001=>1100110
[3,5,8,1,2,6,7,4]=>0010001=>1101110
[3,2,8,1,5,6,7,4]=>1010001=>0101110
[1,5,8,3,2,6,7,4]=>0011001=>1100110
[1,3,8,6,2,4,7,5]=>0011001=>1100110
[3,2,7,8,4,6,1,5]=>1001010=>0110101
[5,1,8,3,4,6,7,2]=>1010001=>0101110
[4,8,7,2,1,6,3,5]=>0111010=>1000101
[2,8,1,6,3,4,7,5]=>0101001=>1010110
[8,3,4,2,1,6,5,7]=>1011010=>0100101
[6,4,7,2,5,8,1,3]=>1010010=>0101101
[8,4,5,2,6,3,1,7]=>1010110=>0101001
[2,4,5,8,3,6,1,7]=>0001010=>1110101
[3,5,8,1,2,6,4,7]=>0010010=>1101101
[8,6,1,3,5,2,4,7]=>1100100=>0011011
[8,5,1,2,6,4,3,7]=>1100110=>0011001
[5,8,6,1,3,4,2,7]=>0110010=>1001101
[5,8,4,6,1,3,2,7]=>0101010=>1010101
[7,3,4,5,2,8,1,6]=>1001010=>0110101
[5,7,4,3,6,1,8,2]=>0110101=>1001010
[2,6,4,3,7,8,5,1]=>0110011=>1001100
[7,4,1,8,3,2,5,6]=>1101100=>0010011
[6,2,1,7,8,4,5,3]=>1100101=>0011010
[7,6,3,1,5,4,8,2]=>1110101=>0001010
[2,4,6,5,1,7,8,3]=>0011001=>1100110
[1,4,7,5,6,8,2,3]=>0010010=>1101101
[1,4,7,6,5,8,2,3]=>0011010=>1100101
[3,7,5,2,4,6,8,1]=>0110001=>1001110
[5,6,1,7,4,2,8,3]=>0101101=>1010010
[3,7,4,8,1,2,6,5]=>0101001=>1010110
[6,3,5,7,8,1,4,2]=>1000101=>0111010
[3,6,5,7,1,8,4,2]=>0101011=>1010100
[6,4,7,8,2,1,3,5]=>1001100=>0110011
[6,7,3,8,4,1,2,5]=>0101100=>1010011
[2,7,8,3,4,6,1,5]=>0010010=>1101101
[7,5,8,4,1,3,2,6]=>1011010=>0100101
[4,7,5,8,3,1,2,6]=>0101100=>1010011
[3,6,7,4,8,1,2,5]=>0010100=>1101011
[5,7,3,1,6,8,4,2]=>0110011=>1001100
[2,7,3,1,8,6,4,5]=>0110110=>1001001
[2,8,4,3,1,5,7,6]=>0111001=>1000110
[4,8,1,2,3,5,7,6]=>0100001=>1011110
[7,6,8,1,2,4,3,5]=>1010010=>0101101
[7,6,8,5,1,3,2,4]=>1011010=>0100101
[2,8,5,4,6,1,7,3]=>0110101=>1001010
[8,4,5,2,7,6,1,3]=>1010110=>0101001
[8,7,6,4,1,2,5,3]=>1111001=>0000110
[6,7,1,3,5,2,8,4]=>0100101=>1011010
[5,7,2,3,6,8,1,4]=>0100010=>1011101
[8,5,3,2,7,6,1,4]=>1110110=>0001001
[3,4,6,7,5,8,1,2]=>0001010=>1110101
[3,4,5,7,6,1,8,2]=>0001101=>1110010
[2,6,4,5,7,8,3,1]=>0100011=>1011100
[3,8,5,1,6,2,7,4]=>0110101=>1001010
[2,5,1,3,6,8,7,4]=>0100011=>1011100
[5,4,6,1,3,7,8,2]=>1010001=>0101110
[6,3,5,7,1,4,8,2]=>1001001=>0110110
[7,3,4,6,8,1,5,2]=>1000101=>0111010
[7,5,2,8,4,1,3,6]=>1101100=>0010011
[3,7,6,4,1,8,2,5]=>0111010=>1000101
[3,7,8,4,1,5,6,2]=>0011001=>1100110
[8,7,5,4,2,1,6,3]=>1111101=>0000010
[3,5,8,6,7,4,2,1]=>0010111=>1101000
[5,8,1,6,7,3,4,2]=>0100101=>1011010
[6,7,2,5,1,8,4,3]=>0101011=>1010100
[5,8,2,1,6,7,4,3]=>0110011=>1001100
[4,5,2,8,6,3,7,1]=>0101101=>1010010
[3,6,1,2,5,8,4,7]=>0100010=>1011101
[1,4,5,8,2,3,7,6]=>0001001=>1110110
[1,2,6,4,5,8,3,7]=>0010010=>1101101
[1,5,2,4,6,8,3,7]=>0100010=>1011101
[3,6,1,5,8,2,4,7]=>0100100=>1011011
[2,6,5,1,4,8,3,7]=>0110010=>1001101
[5,2,6,1,4,8,3,7]=>1010010=>0101101
[2,5,1,8,4,7,3,6]=>0101010=>1010101
[2,7,1,4,3,6,8,5]=>0101001=>1010110
[1,3,7,5,8,2,4,6]=>0010100=>1101011
[8,2,1,5,7,3,4,6]=>1100100=>0011011
[2,5,4,8,1,3,7,6]=>0101001=>1010110
[2,4,1,3,8,6,7,5]=>0100101=>1011010
[8,4,3,7,1,2,6,5]=>1101001=>0010110
[1,7,3,5,8,2,6,4]=>0100101=>1011010
[1,8,4,2,6,7,3,5]=>0110010=>1001101
[3,1,6,8,7,2,4,5]=>1001100=>0110011
[7,2,1,6,8,3,4,5]=>1100100=>0011011
[3,1,7,6,8,2,4,5]=>1010100=>0101011
[4,1,7,2,6,8,3,5]=>1010010=>0101101
[5,1,7,2,3,6,8,4]=>1010001=>0101110
[7,2,1,6,3,5,8,4]=>1101001=>0010110
[2,6,1,7,3,5,8,4]=>0101001=>1010110
[7,1,2,5,3,6,8,4]=>1001001=>0110110
[5,4,1,2,7,8,3,6]=>1100010=>0011101
[8,1,3,2,4,6,7,5]=>1010001=>0101110
[7,3,1,2,4,6,8,5]=>1100001=>0011110
[1,8,3,4,7,2,5,6]=>0100100=>1011011
[3,5,8,1,2,7,4,6]=>0010010=>1101101
[3,6,8,1,2,4,7,5]=>0010001=>1101110
[4,1,3,8,7,2,6,5]=>1001101=>0110010
[1,3,7,4,8,2,6,5]=>0010101=>1101010
[1,4,6,8,2,3,7,5]=>0001001=>1110110
[3,5,8,1,7,2,4,6]=>0010100=>1101011
[2,6,8,1,7,3,4,5]=>0010100=>1101011
[6,1,5,8,2,3,7,4]=>1001001=>0110110
[1,8,3,2,7,5,6,4]=>0110101=>1001010
[3,1,7,2,8,5,6,4]=>1010101=>0101010
[2,6,7,3,8,1,5,4]=>0010101=>1101010
[8,4,1,7,3,6,2,5]=>1101010=>0010101
[3,7,2,8,6,1,5,4]=>0101101=>1010010
[6,2,3,8,7,1,5,4]=>1001101=>0110010
[5,1,7,8,4,2,6,3]=>1001101=>0110010
[5,1,8,7,4,2,6,3]=>1011101=>0100010
[4,7,2,8,3,6,5,1]=>0101011=>1010100
[4,1,7,8,5,3,6,2]=>1001101=>0110010
[5,1,7,4,8,3,6,2]=>1010101=>0101010
[4,1,8,7,5,3,6,2]=>1011101=>0100010
[4,8,2,7,3,6,5,1]=>0101011=>1010100
[4,7,2,6,3,5,8,1]=>0101001=>1010110
[6,8,2,4,3,7,5,1]=>0101011=>1010100
[6,7,2,4,3,8,5,1]=>0101011=>1010100
[6,8,2,7,3,5,4,1]=>0101011=>1010100
[3,8,7,2,4,1,5,6]=>0110100=>1001011
[3,7,8,2,4,1,5,6]=>0010100=>1101011
[3,6,8,2,4,5,7,1]=>0010001=>1101110
[3,6,7,2,4,5,8,1]=>0010001=>1101110
[6,5,1,4,2,3,8,7]=>1101001=>0010110
[8,6,1,7,2,5,4,3]=>1101011=>0010100
[8,7,6,1,2,3,5,4]=>1110001=>0001110
[5,4,3,1,6,2,8,7]=>1110101=>0001010
[8,3,4,7,1,6,2,5]=>1001010=>0110101
[6,3,4,1,8,5,2,7]=>1010110=>0101001
[3,8,5,2,7,1,6,4]=>0110101=>1001010
[2,8,6,7,5,3,4,1]=>0101101=>1010010
[2,1,8,7,3,6,4,5]=>1011010=>0100101
[3,6,5,8,2,4,7,1]=>0101001=>1010110
[5,2,1,8,7,3,4,6]=>1101100=>0010011
[6,5,2,7,4,3,8,1]=>1101101=>0010010
[4,6,5,2,7,3,8,1]=>0110101=>1001010
[6,2,7,1,8,3,5,4]=>1010101=>0101010
[2,7,5,4,8,3,6,1]=>0110101=>1001010
[8,7,5,1,2,6,4,3]=>1110011=>0001100
[8,4,3,2,7,1,6,5]=>1110101=>0001010
[7,1,6,2,3,8,5,4]=>1010011=>0101100
[4,8,1,3,2,7,5,6]=>0101010=>1010101
[3,8,1,4,7,5,2,6]=>0100110=>1011001
[6,3,8,7,4,5,1,2]=>1011010=>0100101
[6,1,4,8,5,2,3,7]=>1001100=>0110011
[8,5,7,4,6,2,1,3]=>1010110=>0101001
[4,6,7,8,2,3,5,1]=>0001001=>1110110
[8,7,4,6,2,1,5,3]=>1101101=>0010010
[7,6,1,3,5,2,8,4]=>1100101=>0011010
[5,8,3,2,4,6,1,7]=>0110010=>1001101
[8,2,6,5,3,1,7,4]=>1011101=>0100010
[4,8,7,6,5,2,3,1]=>0111101=>1000010
[2,1,8,6,4,3,7,5]=>1011101=>0100010
[2,1,7,6,5,3,8,4]=>1011101=>0100010
[2,7,6,1,3,5,8,4]=>0110001=>1001110
[7,2,5,4,6,1,8,3]=>1010101=>0101010
[4,7,6,1,2,5,8,3]=>0110001=>1001110
[2,4,1,7,6,8,5,3]=>0101011=>1010100
[3,4,1,7,8,5,6,2]=>0100101=>1011010
[7,5,4,3,1,8,6,2]=>1111011=>0000100
[8,5,6,2,7,3,1,4]=>1010110=>0101001
[8,4,2,5,6,1,7,3]=>1100101=>0011010
[6,3,5,4,1,7,8,2]=>1011001=>0100110
[4,1,3,6,7,5,8,2]=>1000101=>0111010
[1,7,5,3,8,2,4,6]=>0110100=>1001011
[1,7,2,4,5,8,3,6]=>0100010=>1011101
[8,2,5,3,1,6,4,7]=>1011010=>0100101
[1,7,4,5,8,3,2,6]=>0100110=>1011001
[2,6,4,7,8,3,5,1]=>0100101=>1011010
[2,6,4,7,8,3,1,5]=>0100110=>1011001
[1,2,6,4,7,8,3,5]=>0010010=>1101101
[2,7,4,5,8,1,3,6]=>0100100=>1011011
[2,7,5,3,1,8,4,6]=>0111010=>1000101
[6,1,4,7,8,3,5,2]=>1000101=>0111010
[3,6,4,7,8,1,5,2]=>0100101=>1011010
[4,3,6,7,1,8,5,2]=>1001011=>0110100
[4,3,6,7,1,8,2,5]=>1001010=>0110101
[3,6,4,7,8,1,2,5]=>0100100=>1011011
[2,3,6,4,1,7,8,5]=>0011001=>1100110
[4,7,2,1,5,3,8,6]=>0110101=>1001010
[3,7,4,5,2,1,8,6]=>0101101=>1010010
[1,3,6,4,7,2,8,5]=>0010101=>1101010
[3,6,4,7,2,8,5,1]=>0101011=>1010100
[5,1,3,4,2,7,8,6]=>1001001=>0110110
[5,4,2,1,3,7,8,6]=>1110001=>0001110
[6,1,7,3,8,2,5,4]=>1010101=>0101010
[1,6,7,3,8,2,5,4]=>0010101=>1101010
[6,1,4,7,8,5,2,3]=>1000110=>0111001
[6,3,2,1,7,8,5,4]=>1110011=>0001100
[6,2,7,3,1,8,5,4]=>1011011=>0100100
[6,2,4,7,8,1,5,3]=>1000101=>0111010
[2,6,7,3,1,8,5,4]=>0011011=>1100100
[8,6,5,1,3,2,4,7]=>1110100=>0001011
[6,4,7,8,3,2,5,1]=>1001101=>0110010
[3,8,4,7,1,2,5,6]=>0101000=>1010111
[8,6,1,2,5,4,3,7]=>1100110=>0011001
[4,8,6,1,5,3,2,7]=>0110110=>1001001
[5,8,6,4,1,3,2,7]=>0111010=>1000101
[8,3,6,4,5,2,1,7]=>1010110=>0101001
[6,8,5,7,4,2,3,1]=>0101101=>1010010
[2,3,8,7,1,6,4,5]=>0011010=>1100101
[4,3,7,8,1,6,2,5]=>1001010=>0110101
[3,5,8,7,4,1,2,6]=>0011100=>1100011
[7,3,8,4,1,2,5,6]=>1011000=>0100111
[4,8,1,2,7,3,5,6]=>0100100=>1011011
[6,8,1,2,7,4,5,3]=>0100101=>1011010
[5,6,8,4,1,3,7,2]=>0011001=>1100110
[8,5,4,7,1,6,3,2]=>1101011=>0010100
[2,5,8,7,3,6,4,1]=>0011011=>1100100
[2,4,8,7,5,6,1,3]=>0011010=>1100101
[3,7,4,8,5,6,2,1]=>0101011=>1010100
[6,4,8,7,5,1,2,3]=>1011100=>0100011
[3,8,5,2,4,6,7,1]=>0110001=>1001110
[5,7,1,8,4,6,2,3]=>0101010=>1010101
[6,3,8,7,2,1,4,5]=>1011100=>0100011
[2,3,7,8,5,6,1,4]=>0001010=>1110101
[3,7,6,8,5,1,2,4]=>0101100=>1010011
[2,6,7,8,5,1,3,4]=>0001100=>1110011
[2,4,7,8,1,6,3,5]=>0001010=>1110101
[5,4,7,8,2,6,3,1]=>1001011=>0110100
[2,8,3,4,1,5,7,6]=>0101001=>1010110
[6,8,3,4,1,2,7,5]=>0101001=>1010110
[6,8,7,1,5,2,3,4]=>0110100=>1001011
[5,8,3,2,7,6,1,4]=>0110110=>1001001
[2,5,3,1,8,6,7,4]=>0110101=>1001010
[4,5,3,2,8,6,7,1]=>0110101=>1001010
[3,5,8,6,1,4,7,2]=>0011001=>1100110
[2,8,5,6,1,4,7,3]=>0101001=>1010110
[4,8,6,1,5,2,7,3]=>0110101=>1001010
[5,8,2,3,7,6,1,4]=>0100110=>1011001
[4,6,8,5,3,2,7,1]=>0011101=>1100010
[2,6,4,8,5,1,7,3]=>0101101=>1010010
[7,6,4,8,5,2,1,3]=>1101110=>0010001
[3,4,8,6,5,2,7,1]=>0011101=>1100010
[3,4,8,7,5,6,2,1]=>0011011=>1100100
[7,5,3,2,8,6,1,4]=>1110110=>0001001
[2,5,1,3,8,6,7,4]=>0100101=>1011010
[4,5,1,2,8,6,7,3]=>0100101=>1011010
[5,4,8,1,3,6,7,2]=>1010001=>0101110
[8,3,5,4,1,6,7,2]=>1011001=>0100110
[7,3,4,8,5,6,1,2]=>1001010=>0110101
[6,1,5,7,2,4,8,3]=>1001001=>0110110
[7,4,5,1,2,3,8,6]=>1010001=>0101110
[7,4,3,1,2,8,5,6]=>1110010=>0001101
[8,4,7,6,2,1,5,3]=>1011101=>0100010
[8,4,6,5,7,1,3,2]=>1010101=>0101010
[7,2,1,4,5,8,3,6]=>1100010=>0011101
[7,4,1,6,3,5,8,2]=>1101001=>0010110
[3,5,7,6,4,1,8,2]=>0011101=>1100010
[4,7,5,2,1,3,8,6]=>0111001=>1000110
[5,7,2,3,6,4,8,1]=>0100101=>1011010
[8,6,2,3,7,1,4,5]=>1100100=>0011011
[5,7,2,4,8,3,6,1]=>0100101=>1011010
[1,7,2,4,8,6,3,5]=>0100110=>1011001
[7,6,1,5,4,8,3,2]=>1101011=>0010100
[4,7,3,2,1,8,5,6]=>0111010=>1000101
[3,1,7,2,5,8,4,6]=>1010010=>0101101
[4,8,7,6,1,2,5,3]=>0111001=>1000110
[7,8,6,1,3,2,5,4]=>0110101=>1001010
[2,8,6,7,4,1,3,5]=>0101100=>1010011
[5,8,6,4,2,3,1,7]=>0111010=>1000101
[2,8,3,1,6,5,4,7]=>0110110=>1001001
[3,8,1,2,5,7,4,6]=>0100010=>1011101
[6,8,5,4,2,7,3,1]=>0111011=>1000100
[6,8,3,1,2,4,5,7]=>0110000=>1001111
[4,6,8,7,3,1,5,2]=>0011101=>1100010
[6,5,3,7,8,4,1,2]=>1100110=>0011001
[4,1,3,8,7,5,6,2]=>1001101=>0110010
[6,2,7,4,8,1,3,5]=>1010100=>0101011
[8,4,5,2,1,6,3,7]=>1011010=>0100101
[4,3,2,6,8,1,7,5]=>1100101=>0011010
[7,1,5,6,3,8,2,4]=>1001010=>0110101
[5,1,2,4,7,8,3,6]=>1000010=>0111101
[3,5,4,2,8,1,6,7]=>0110100=>1001011
[5,1,3,8,4,2,7,6]=>1001101=>0110010
[6,2,8,7,3,5,4,1]=>1011011=>0100100
[7,1,8,4,3,6,5,2]=>1011011=>0100100
[3,6,8,7,4,1,2,5]=>0011100=>1100011
[5,6,8,1,7,3,2,4]=>0010110=>1101001
[3,1,6,8,7,4,2,5]=>1001110=>0110001
[7,4,6,8,2,1,5,3]=>1001101=>0110010
[6,5,8,4,3,1,2,7]=>1011100=>0100011
[2,5,8,3,6,7,4,1]=>0010011=>1101100
[8,5,1,3,7,4,6,2]=>1100101=>0011010
[1,5,8,3,7,4,2,6]=>0010110=>1101001
[3,8,2,7,1,5,6,4]=>0101001=>1010110
[5,8,2,3,6,4,1,7]=>0100110=>1011001
[6,8,2,3,4,7,5,1]=>0100011=>1011100
[7,5,1,8,4,2,6,3]=>1101101=>0010010
[3,6,8,5,2,7,4,1]=>0011011=>1100100
[2,1,6,5,4,8,3,7]=>1011010=>0100101
[2,1,7,8,4,6,5,3]=>1001011=>0110100
[2,1,7,4,3,5,8,6]=>1011001=>0100110
[3,5,7,8,4,6,1,2]=>0001010=>1110101
[7,5,2,8,4,6,3,1]=>1101011=>0010100
[7,8,2,4,3,1,5,6]=>0101100=>1010011
[7,6,3,8,1,5,4,2]=>1101011=>0010100
[8,4,3,1,7,5,2,6]=>1110110=>0001001
[7,3,1,4,6,8,5,2]=>1100011=>0011100
[4,3,8,7,1,6,5,2]=>1011011=>0100100
[4,7,1,8,5,2,6,3]=>0101101=>1010010
[5,2,4,3,6,8,1,7]=>1010010=>0101101
[3,8,6,5,4,1,2,7]=>0111100=>1000011
[4,7,5,6,3,8,2,1]=>0101011=>1010100
[4,2,7,5,8,3,6,1]=>1010101=>0101010
[5,8,2,7,3,4,6,1]=>0101001=>1010110
[6,7,2,4,5,3,8,1]=>0100101=>1011010
[6,3,2,1,4,8,5,7]=>1110010=>0001101
[6,2,3,1,4,7,8,5]=>1010001=>0101110
[5,2,1,3,6,4,8,7]=>1100101=>0011010
[7,1,8,3,5,4,6,2]=>1010101=>0101010
[7,1,2,4,8,5,6,3]=>1000101=>0111010
[7,2,1,3,4,5,8,6]=>1100001=>0011110
[8,7,3,5,4,2,1,6]=>1101110=>0010001
[8,4,6,5,3,2,1,7]=>1011110=>0100001
[5,1,6,4,3,2,8,7]=>1011101=>0100010
[8,3,7,1,4,6,5,2]=>1010011=>0101100
[2,8,3,6,4,7,5,1]=>0101011=>1010100
[6,2,1,7,5,8,3,4]=>1101010=>0010101
[6,3,8,7,5,2,1,4]=>1011110=>0100001
[6,7,2,1,5,8,4,3]=>0110011=>1001100
[9,1,8,7,6,5,4,3,2]=>10111111=>01000000
[7,6,8,1,5,4,3,2]=>1010111=>0101000
[7,1,9,8,6,5,4,3,2]=>10111111=>01000000
[6,1,9,8,7,5,4,3,2]=>10111111=>01000000
[5,4,8,7,6,1,3,2]=>1011101=>0100010
[5,1,9,8,7,6,4,3,2]=>10111111=>01000000
[4,1,9,8,7,6,5,3,2]=>10111111=>01000000
[3,1,9,8,7,6,5,4,2]=>10111111=>01000000
[10,1,9,8,7,6,5,4,3,2]=>101111111=>010000000
[9,8,1,7,6,5,4,3,2]=>11011111=>00100000
[7,6,1,8,5,4,3,2]=>1101111=>0010000
[8,7,9,1,6,5,4,3,2]=>10101111=>01010000
[8,1,10,9,7,6,5,4,3,2]=>101111111=>010000000
[6,5,8,1,7,4,3,2]=>1010111=>0101000
[7,6,9,8,1,5,4,3,2]=>10110111=>01001000
[7,1,10,9,8,6,5,4,3,2]=>101111111=>010000000
[6,5,9,8,7,1,4,3,2]=>10111011=>01000100
[6,1,10,9,8,7,5,4,3,2]=>101111111=>010000000
[6,5,8,7,4,1,3,2]=>1011101=>0100010
[5,4,9,8,7,6,1,3,2]=>10111101=>01000010
[5,1,10,9,8,7,6,4,3,2]=>101111111=>010000000
[4,3,9,8,7,6,5,1,2]=>10111110=>01000001
[4,1,10,9,8,7,6,5,3,2]=>101111111=>010000000
[3,2,9,8,7,6,5,4,1]=>10111111=>01000000
[3,1,10,9,8,7,6,5,4,2]=>101111111=>010000000
[1,6,4,8,3,2,5,7]=>0101100=>1010011
[1,8,3,5,6,2,4,7]=>0100100=>1011011
[1,4,8,5,6,2,3,7]=>0010100=>1101011
[1,2,8,5,3,7,4,6]=>0011010=>1100101
[6,1,4,8,2,3,5,7]=>1001000=>0110111
[8,7,2,5,6,1,4,3]=>1100101=>0011010
[1,8,2,5,4,7,3,6]=>0101010=>1010101
[5,7,4,1,2,3,8,6]=>0110001=>1001110
[1,7,4,2,5,3,8,6]=>0110101=>1001010
[6,7,4,2,1,3,8,5]=>0111001=>1000110
[6,4,3,8,5,7,1,2]=>1101010=>0010101
[7,4,3,6,2,1,5,8]=>1101100=>0010011
[6,8,4,2,3,1,5,7]=>0110100=>1001011
[3,7,5,2,4,1,6,8]=>0110100=>1001011
[5,2,8,6,1,3,4,7]=>1011000=>0100111
[7,4,8,2,3,1,5,6]=>1010100=>0101011
[4,2,7,3,1,5,6,8]=>1011000=>0100111
[7,6,4,5,1,8,2,3]=>1101010=>0010101
[8,6,4,1,3,7,2,5]=>1110010=>0001101
[5,3,6,1,8,2,4,7]=>1010100=>0101011
[3,1,8,5,4,7,6,2]=>1011011=>0100100
[4,1,5,8,3,7,6,2]=>1001011=>0110100
[4,1,5,3,8,7,6,2]=>1010111=>0101000
[4,5,1,8,2,7,6,3]=>0101011=>1010100
[4,8,5,3,1,7,6,2]=>0111011=>1000100
[4,5,2,8,1,7,6,3]=>0101011=>1010100
[4,5,2,1,8,7,6,3]=>0110111=>1001000
[5,6,2,7,8,1,4,3]=>0100101=>1011010
[4,6,2,8,7,1,5,3]=>0101101=>1010010
[4,8,6,3,7,1,5,2]=>0110101=>1001010
[4,8,6,3,7,5,1,2]=>0110110=>1001001
[4,6,8,2,7,5,1,3]=>0010110=>1101001
[4,6,2,8,7,5,1,3]=>0101110=>1010001
[5,6,2,7,4,1,8,3]=>0101101=>1010010
[5,6,7,2,3,1,8,4]=>0010101=>1101010
[5,6,7,2,8,3,1,4]=>0010110=>1101001
[5,6,7,2,1,8,3,4]=>0011010=>1100101
[5,6,7,2,1,3,8,4]=>0011001=>1100110
[5,6,1,7,8,2,4,3]=>0100101=>1011010
[5,6,1,7,2,4,8,3]=>0101001=>1010110
[5,1,6,7,8,3,4,2]=>1000101=>0111010
[4,1,6,8,7,3,5,2]=>1001101=>0110010
[3,1,8,6,7,5,4,2]=>1010111=>0101000
[4,1,6,8,7,5,3,2]=>1001111=>0110000
[5,1,6,7,4,8,3,2]=>1001011=>0110100
[5,6,1,7,8,4,2,3]=>0100110=>1011001
[4,6,8,1,7,5,2,3]=>0010110=>1101001
[4,8,6,1,7,5,3,2]=>0110111=>1001000
[5,6,7,1,8,3,2,4]=>0010110=>1101001
[5,6,7,1,3,8,2,4]=>0010010=>1101101
[5,6,7,1,3,2,8,4]=>0010101=>1101010
[5,6,7,3,1,2,8,4]=>0011001=>1100110
[5,6,7,3,8,1,2,4]=>0010100=>1101011
[5,6,8,7,4,2,1,3]=>0011110=>1100001
[5,6,7,3,8,2,1,4]=>0010110=>1101001
[7,4,6,2,3,5,1,8]=>1010010=>0101101
[1,4,8,6,3,2,5,7]=>0011100=>1100011
[7,4,1,6,3,8,5,2]=>1101011=>0010100
[7,6,3,1,5,8,4,2]=>1110011=>0001100
[6,4,2,5,7,3,1,8]=>1100110=>0011001
[4,2,5,7,6,3,1,8]=>1001110=>0110001
[7,4,5,6,1,8,3,2]=>1001011=>0110100
[4,1,5,8,6,3,2,7]=>1001110=>0110001
[3,2,7,6,1,8,5,4]=>1011011=>0100100
[4,7,5,1,6,8,2,3]=>0110010=>1001101
[8,6,5,1,2,7,4,3]=>1110011=>0001100
[3,2,5,1,4,8,7,6]=>1010011=>0101100
[8,5,4,1,3,2,7,6]=>1110101=>0001010
[1,4,2,3,6,8,7,5]=>0100011=>1011100
[5,4,8,3,7,1,6,2]=>1010101=>0101010
[4,7,1,8,2,5,3,6]=>0101010=>1010101
[6,4,1,8,5,3,7,2]=>1101101=>0010010
[8,4,6,1,3,5,2,7]=>1010010=>0101101
[3,2,5,4,7,8,1,6]=>1010010=>0101101
[5,2,4,3,7,8,1,6]=>1010010=>0101101
[8,1,6,7,2,5,3,4]=>1001010=>0110101
[3,1,7,6,5,8,2,4]=>1011010=>0100101
[1,2,7,5,6,8,3,4]=>0010010=>1101101
[6,1,4,7,2,8,3,5]=>1001010=>0110101
[3,2,1,7,6,8,4,5]=>1101010=>0010101
[3,2,8,6,4,7,1,5]=>1011010=>0100101
[7,8,4,6,3,2,1,5]=>0101110=>1010001
[1,8,6,5,3,7,2,4]=>0111010=>1000101
[8,2,5,3,6,7,1,4]=>1010010=>0101101
[3,8,5,2,7,6,1,4]=>0110110=>1001001
[4,7,5,3,1,8,6,2]=>0111011=>1000100
[4,5,3,6,8,1,7,2]=>0100101=>1011010
[3,5,2,6,1,8,7,4]=>0101011=>1010100
[1,6,3,5,7,2,8,4]=>0100101=>1011010
[1,5,4,6,7,8,2,3]=>0100010=>1011101
[8,4,6,5,7,2,1,3]=>1010110=>0101001
[7,4,5,2,6,8,1,3]=>1010010=>0101101
[5,4,2,6,8,7,1,3]=>1100110=>0011001
[7,8,4,3,1,2,6,5]=>0111001=>1000110
[6,5,1,4,3,2,8,7]=>1101101=>0010010
[2,6,5,1,4,7,3,8]=>0110010=>1001101
[3,6,4,5,2,1,8,7]=>0101101=>1010010
[5,7,4,1,3,8,6,2]=>0110011=>1001100
[7,5,4,2,3,8,1,6]=>1110010=>0001101
[5,2,6,7,3,1,4,8]=>1001100=>0110011
[2,4,3,8,6,1,5,7]=>0101100=>1010011
[7,8,1,3,5,6,2,4]=>0100010=>1011101
[7,8,3,1,5,6,2,4]=>0110010=>1001101
[7,1,3,8,5,6,2,4]=>1001010=>0110101
[1,7,8,3,5,6,2,4]=>0010010=>1101101
[5,1,7,8,3,4,6,2]=>1001001=>0110110
[1,5,7,8,3,4,6,2]=>0001001=>1110110
[3,7,1,5,8,6,2,4]=>0100110=>1011001
[1,3,7,8,2,5,6,4]=>0001001=>1110110
[3,1,7,8,5,2,6,4]=>1001101=>0110010
[1,3,7,5,8,2,6,4]=>0010101=>1101010
[3,1,7,5,8,2,6,4]=>1010101=>0101010
[3,5,7,1,8,4,6,2]=>0010101=>1101010
[3,5,7,8,1,4,6,2]=>0001001=>1110110
[5,3,7,8,4,6,1,2]=>1001010=>0110101
[5,3,7,8,4,1,6,2]=>1001101=>0110010
[5,3,7,8,1,4,6,2]=>1001001=>0110110
[5,3,7,1,8,4,6,2]=>1010101=>0101010
[1,5,3,7,8,4,2,6]=>0100110=>1011001
[5,1,3,7,8,4,2,6]=>1000110=>0111001
[3,6,2,1,4,5,8,7]=>0110001=>1001110
[4,6,2,5,1,3,8,7]=>0101001=>1010110
[6,4,2,5,1,3,8,7]=>1101001=>0010110
[8,6,1,7,3,2,4,5]=>1101100=>0010011
[2,5,8,1,7,3,4,6]=>0010100=>1101011
[6,8,2,7,3,1,4,5]=>0101100=>1010011
[6,8,2,3,7,1,4,5]=>0100100=>1011011
[8,6,2,7,4,5,1,3]=>1101010=>0010101
[5,2,8,1,7,3,4,6]=>1010100=>0101011
[4,2,3,8,1,5,6,7]=>1001000=>0110111
[5,2,8,3,7,1,4,6]=>1010100=>0101011
[5,2,8,4,6,1,3,7]=>1010100=>0101011
[2,1,5,8,4,3,6,7]=>1001100=>0110011
[5,8,3,2,7,1,4,6]=>0110100=>1001011
[4,1,3,8,2,5,6,7]=>1001000=>0110111
[3,5,8,2,7,1,4,6]=>0010100=>1101011
[4,5,8,2,6,1,3,7]=>0010100=>1101011
[2,6,8,3,7,1,4,5]=>0010100=>1101011
[5,1,8,3,7,2,4,6]=>1010100=>0101011
[5,1,8,4,6,2,3,7]=>1010100=>0101011
[5,8,4,1,6,2,3,7]=>0110100=>1001011
[4,5,8,1,6,2,3,7]=>0010100=>1101011
[5,4,8,1,6,2,3,7]=>1010100=>0101011
[4,8,5,1,6,2,3,7]=>0110100=>1001011
[2,1,5,4,8,3,6,7]=>1010100=>0101011
[2,4,3,8,1,5,6,7]=>0101000=>1010111
[3,1,8,4,2,5,6,7]=>1011000=>0100111
[3,8,4,2,1,5,6,7]=>0111000=>1000111
[2,3,8,4,1,5,6,7]=>0011000=>1100111
[3,4,2,8,1,5,6,7]=>0101000=>1010111
[3,8,5,2,7,1,4,6]=>0110100=>1001011
[4,8,5,2,6,1,3,7]=>0110100=>1001011
[2,1,4,8,5,3,6,7]=>1001100=>0110011
[3,2,8,4,1,5,6,7]=>1011000=>0100111
[2,8,4,3,1,5,6,7]=>0111000=>1000111
[4,1,7,5,6,2,8,3]=>1010101=>0101010
[5,7,4,3,8,1,6,2]=>0110101=>1001010
[5,7,4,3,8,2,6,1]=>0110101=>1001010
[3,8,4,2,6,7,5,1]=>0110011=>1001100
[3,8,4,1,6,7,5,2]=>0110011=>1001100
[6,1,7,5,2,8,4,3]=>1011011=>0100100
[5,6,4,3,2,8,1,7]=>0111010=>1000101
[2,6,7,5,3,8,4,1]=>0011011=>1100100
[6,7,4,8,2,5,3,1]=>0101011=>1010100
[2,1,6,7,5,3,8,4]=>1001101=>0110010
[3,8,4,2,1,6,7,5]=>0111001=>1000110
[5,7,4,3,8,2,1,6]=>0110110=>1001001
[6,7,4,8,1,2,5,3]=>0101001=>1010110
[6,7,5,8,1,2,4,3]=>0101001=>1010110
[6,7,4,8,3,1,2,5]=>0101100=>1010011
[3,4,8,1,2,5,7,6]=>0010001=>1101110
[6,1,3,4,8,2,5,7]=>1000100=>0111011
[6,2,3,4,8,1,5,7]=>1000100=>0111011
[3,4,8,2,1,5,7,6]=>0011001=>1100110
[6,7,5,8,2,4,3,1]=>0101011=>1010100
[6,7,5,8,3,1,4,2]=>0101101=>1010010
[3,4,8,1,5,7,6,2]=>0010011=>1101100
[2,5,7,6,1,4,8,3]=>0011001=>1100110
[6,7,4,8,2,3,5,1]=>0101001=>1010110
[6,7,4,8,1,3,5,2]=>0101001=>1010110
[2,6,7,5,1,3,8,4]=>0011001=>1100110
[6,3,1,4,8,2,5,7]=>1100100=>0011011
[6,7,4,8,1,3,2,5]=>0101010=>1010101
[6,7,5,8,4,1,3,2]=>0101101=>1010010
[6,7,4,8,2,1,3,5]=>0101100=>1010011
[6,7,4,8,1,2,3,5]=>0101000=>1010111
[1,5,6,3,4,8,2,7]=>0010010=>1101101
[1,4,3,6,5,8,2,7]=>0101010=>1010101
[8,1,3,4,7,2,6,5]=>1000101=>0111010
[5,1,7,3,4,8,2,6]=>1010010=>0101101
[6,7,8,2,3,5,4,1]=>0010011=>1101100
[5,8,6,2,3,7,4,1]=>0110011=>1001100
[2,8,3,4,7,5,6,1]=>0100101=>1011010
[1,8,3,4,7,6,2,5]=>0100110=>1011001
[8,7,2,3,6,5,4,1]=>1100111=>0011000
[3,8,1,7,5,2,6,4]=>0101101=>1010010
[4,8,1,6,7,2,5,3]=>0100101=>1011010
[2,1,3,8,4,6,5,7]=>1001010=>0110101
[8,2,1,7,4,3,6,5]=>1101101=>0010010
[1,3,2,8,5,4,6,7]=>0101100=>1010011
[8,3,1,5,7,2,6,4]=>1100101=>0011010
[8,4,5,1,7,2,6,3]=>1010101=>0101010
[1,5,6,8,7,4,2,3]=>0001110=>1110001
[8,4,5,7,6,3,2,1]=>1001111=>0110000
[1,4,8,5,7,6,2,3]=>0010110=>1101001
[2,4,8,5,7,3,6,1]=>0010101=>1101010
[4,3,8,6,5,7,2,1]=>1011011=>0100100
[6,7,2,8,5,3,4,1]=>0101101=>1010010
[5,2,7,8,6,3,4,1]=>1001101=>0110010
[4,2,8,6,7,3,5,1]=>1010101=>0101010
[3,2,8,7,5,4,6,1]=>1011101=>0100010
[3,1,8,7,5,6,2,4]=>1011010=>0100101
[4,1,8,6,7,5,2,3]=>1010110=>0101001
[5,1,7,8,6,4,2,3]=>1001110=>0110001
[6,7,1,8,5,4,2,3]=>0101110=>1010001
[7,8,3,2,6,1,4,5]=>0110100=>1001011
[3,4,8,2,6,1,7,5]=>0010101=>1101010
[7,8,4,1,5,6,3,2]=>0110011=>1001100
[7,8,1,4,5,6,3,2]=>0100011=>1011100
[7,8,1,2,6,3,4,5]=>0100100=>1011011
[7,8,5,1,4,6,3,2]=>0110011=>1001100
[7,8,4,5,1,6,3,2]=>0101011=>1010100
[5,3,8,4,1,6,7,2]=>1011001=>0100110
[6,2,4,8,1,5,3,7]=>1001010=>0110101
[3,4,8,5,1,6,7,2]=>0011001=>1100110
[3,5,8,1,4,6,7,2]=>0010001=>1101110
[1,4,8,2,6,3,7,5]=>0010101=>1101010
[5,3,8,1,4,6,7,2]=>1010001=>0101110
[4,2,6,8,1,5,3,7]=>1001010=>0110101
[7,4,2,8,1,5,3,6]=>1101010=>0010101
[6,1,7,5,8,4,3,2]=>1010111=>0101000
[6,2,1,8,4,5,3,7]=>1101010=>0010101
[1,2,7,8,5,3,4,6]=>0001100=>1110011
[6,3,7,8,5,4,1,2]=>1001110=>0110001
[6,1,5,7,8,4,3,2]=>1000111=>0111000
[1,7,5,6,8,4,3,2]=>0100111=>1011000
[3,1,8,4,5,6,7,2]=>1010001=>0101110
[2,1,4,8,6,5,3,7]=>1001110=>0110001
[2,4,1,8,6,5,3,7]=>0101110=>1010001
[4,2,1,8,6,5,3,7]=>1101110=>0010001
[3,2,7,8,5,1,4,6]=>1001100=>0110011
[2,3,7,8,5,1,4,6]=>0001100=>1110011
[2,7,3,8,5,1,4,6]=>0101100=>1010011
[3,6,2,8,5,1,4,7]=>0101100=>1010011
[4,1,2,8,7,5,3,6]=>1001110=>0110001
[1,4,2,8,7,5,3,6]=>0101110=>1010001
[7,3,6,8,5,4,1,2]=>1001110=>0110001
[7,2,1,8,5,3,4,6]=>1101100=>0010011
[1,2,6,8,4,5,3,7]=>0001010=>1110101
[7,1,6,5,8,4,3,2]=>1010111=>0101000
[6,5,7,1,8,4,3,2]=>1010111=>0101000
[5,7,6,1,8,4,3,2]=>0110111=>1001000
[6,7,1,5,8,4,3,2]=>0100111=>1011000
[6,7,3,8,5,4,1,2]=>0101110=>1010001
[7,1,2,8,4,5,3,6]=>1001010=>0110101
[7,6,1,5,8,4,3,2]=>1100111=>0011000
[7,5,6,1,8,4,3,2]=>1010111=>0101000
[9,10,7,8,5,6,2,1,3,4]=>010101100=>101010011
[9,10,7,8,4,3,5,6,1,2]=>010110010=>101001101
[9,10,7,8,4,2,5,1,3,6]=>010110100=>101001011
[9,10,7,8,3,2,1,4,5,6]=>010111000=>101000111
[9,10,6,5,7,8,3,4,1,2]=>011001010=>100110101
[9,10,6,5,7,8,2,1,3,4]=>011001100=>100110011
[9,10,6,4,7,3,5,8,1,2]=>011010010=>100101101
[9,10,6,4,7,2,5,1,3,8]=>011010100=>100101011
[9,10,6,3,7,2,1,4,5,8]=>011011000=>100100111
[9,10,5,4,3,6,7,8,1,2]=>011100010=>100011101
[9,10,5,4,2,6,7,1,3,8]=>011100100=>100011011
[9,10,5,3,2,6,1,4,7,8]=>011101000=>100010111
[9,10,4,3,2,1,5,6,7,8]=>011110000=>100001111
[8,7,9,10,5,6,3,4,1,2]=>100101010=>011010101
[8,7,9,10,5,6,2,1,3,4]=>100101100=>011010011
[8,7,9,10,4,3,5,6,1,2]=>100110010=>011001101
[8,7,9,10,4,2,5,1,3,6]=>100110100=>011001011
[8,7,9,10,3,2,1,4,5,6]=>100111000=>011000111
[8,6,9,5,7,10,3,4,1,2]=>101001010=>010110101
[8,6,9,5,7,10,2,1,3,4]=>101001100=>010110011
[8,6,9,4,7,3,5,10,1,2]=>101010010=>010101101
[8,6,9,3,7,2,1,4,5,10]=>101011000=>010100111
[8,5,9,4,3,6,7,10,1,2]=>101100010=>010011101
[8,5,9,4,2,6,7,1,3,10]=>101100100=>010011011
[8,5,9,3,2,6,1,4,7,10]=>101101000=>010010111
[8,4,9,3,2,1,5,6,7,10]=>101110000=>010001111
[7,6,5,8,9,10,3,4,1,2]=>110001010=>001110101
[7,6,5,8,9,10,2,1,3,4]=>110001100=>001110011
[7,6,4,8,9,3,5,10,1,2]=>110010010=>001101101
[7,6,4,8,9,2,5,1,3,10]=>110010100=>001101011
[7,6,3,8,9,2,1,4,5,10]=>110011000=>001100111
[7,5,4,8,3,6,9,10,1,2]=>110100010=>001011101
[7,5,4,8,2,6,9,1,3,10]=>110100100=>001011011
[7,4,3,8,2,1,5,6,9,10]=>110110000=>001001111
[6,5,4,3,7,8,9,10,1,2]=>111000010=>000111101
[6,5,4,2,7,8,9,1,3,10]=>111000100=>000111011
[6,5,3,2,7,8,1,4,9,10]=>111001000=>000110111
[11,12,9,10,7,8,5,6,2,1,3,4]=>01010101100=>10101010011
[11,12,9,10,7,8,4,2,5,1,3,6]=>01010110100=>10101001011
[11,12,9,10,6,4,7,3,5,8,1,2]=>01011010010=>10100101101
[11,12,9,10,6,4,7,2,5,1,3,8]=>01011010100=>10100101011
[11,12,9,10,6,3,7,2,1,4,5,8]=>01011011000=>10100100111
[11,12,9,10,5,4,2,6,7,1,3,8]=>01011100100=>10100011011
[11,12,9,10,5,3,2,6,1,4,7,8]=>01011101000=>10100010111
[11,12,9,10,4,3,2,1,5,6,7,8]=>01011110000=>10100001111
[11,12,8,6,9,5,7,10,3,4,1,2]=>01101001010=>10010110101
[11,12,8,6,9,4,7,2,5,1,3,10]=>01101010100=>10010101011
[11,12,8,6,9,3,7,2,1,4,5,10]=>01101011000=>10010100111
[11,12,8,5,9,3,2,6,1,4,7,10]=>01101101000=>10010010111
[11,12,8,4,9,3,2,1,5,6,7,10]=>01101110000=>10010001111
[11,12,7,6,5,8,9,10,2,1,3,4]=>01110001100=>10001110011
[11,12,7,6,4,8,9,3,5,10,1,2]=>01110010010=>10001101101
[11,12,7,6,4,8,9,2,5,1,3,10]=>01110010100=>10001101011
[11,12,7,6,3,8,9,2,1,4,5,10]=>01110011000=>10001100111
[11,12,7,5,4,8,2,6,9,1,3,10]=>01110100100=>10001011011
[11,12,7,5,3,8,2,6,1,4,9,10]=>01110101000=>10001010111
[11,12,7,4,3,8,2,1,5,6,9,10]=>01110110000=>10001001111
[11,12,6,5,3,2,7,8,1,4,9,10]=>01111001000=>10000110111
[11,12,5,4,3,2,1,6,7,8,9,10]=>01111100000=>10000011111
[10,9,11,12,7,8,3,2,1,4,5,6]=>10010111000=>01101000111
[10,9,11,12,6,5,7,8,2,1,3,4]=>10011001100=>01100110011
[10,9,11,12,6,4,7,3,5,8,1,2]=>10011010010=>01100101101
[10,9,11,12,6,4,7,2,5,1,3,8]=>10011010100=>01100101011
[10,9,11,12,6,3,7,2,1,4,5,8]=>10011011000=>01100100111
[10,9,11,12,5,4,2,6,7,1,3,8]=>10011100100=>01100011011
[10,9,11,12,5,3,2,6,1,4,7,8]=>10011101000=>01100010111
[10,8,11,7,9,12,5,6,2,1,3,4]=>10100101100=>01011010011
[10,8,11,7,9,12,4,2,5,1,3,6]=>10100110100=>01011001011
[10,8,11,7,9,12,3,2,1,4,5,6]=>10100111000=>01011000111
[10,8,11,6,9,5,7,12,2,1,3,4]=>10101001100=>01010110011
[10,8,11,6,9,4,7,3,5,12,1,2]=>10101010010=>01010101101
[10,8,11,6,9,4,7,2,5,1,3,12]=>10101010100=>01010101011
[10,8,11,6,9,3,7,2,1,4,5,12]=>10101011000=>01010100111
[10,8,11,5,9,4,2,6,7,1,3,12]=>10101100100=>01010011011
[10,8,11,5,9,3,2,6,1,4,7,12]=>10101101000=>01010010111
[10,8,11,4,9,3,2,1,5,6,7,12]=>10101110000=>01010001111
[10,7,11,6,4,8,9,2,5,1,3,12]=>10110010100=>01001101011
[10,7,11,6,3,8,9,2,1,4,5,12]=>10110011000=>01001100111
[10,7,11,5,4,8,2,6,9,1,3,12]=>10110100100=>01001011011
[10,7,11,5,3,8,2,6,1,4,9,12]=>10110101000=>01001010111
[10,7,11,4,3,8,2,1,5,6,9,12]=>10110110000=>01001001111
[10,6,11,5,4,3,7,8,9,12,1,2]=>10111000010=>01000111101
[10,6,11,5,4,2,7,8,9,1,3,12]=>10111000100=>01000111011
[10,6,11,5,3,2,7,8,1,4,9,12]=>10111001000=>01000110111
[10,6,11,4,3,2,7,1,5,8,9,12]=>10111010000=>01000101111
[10,5,11,4,3,2,1,6,7,8,9,12]=>10111100000=>01000011111
[9,8,6,10,11,4,7,2,5,1,3,12]=>11001010100=>00110101011
[9,8,6,10,11,3,7,2,1,4,5,12]=>11001011000=>00110100111
[9,8,5,10,11,4,2,6,7,1,3,12]=>11001100100=>00110011011
[9,8,5,10,11,3,2,6,1,4,7,12]=>11001101000=>00110010111
[9,8,4,10,11,3,2,1,5,6,7,12]=>11001110000=>00110001111
[9,7,6,10,5,8,11,12,2,1,3,4]=>11010001100=>00101110011
[9,7,6,10,4,8,11,2,5,1,3,12]=>11010010100=>00101101011
[9,7,6,10,3,8,11,2,1,4,5,12]=>11010011000=>00101100111
[9,7,5,10,4,8,2,6,11,1,3,12]=>11010100100=>00101011011
[9,7,5,10,3,8,2,6,1,4,11,12]=>11010101000=>00101010111
[9,7,4,10,3,8,2,1,5,6,11,12]=>11010110000=>00101001111
[9,6,5,10,4,2,7,8,11,1,3,12]=>11011000100=>00100111011
[9,6,5,10,3,2,7,8,1,4,11,12]=>11011001000=>00100110111
[9,6,4,10,3,2,7,1,5,8,11,12]=>11011010000=>00100101111
[9,5,4,10,3,2,1,6,7,8,11,12]=>11011100000=>00100011111
[8,7,6,5,9,10,11,12,2,1,3,4]=>11100001100=>00011110011
[8,7,6,4,9,10,11,2,5,1,3,12]=>11100010100=>00011101011
[8,7,6,3,9,10,11,2,1,4,5,12]=>11100011000=>00011100111
[8,7,5,4,9,10,2,6,11,1,3,12]=>11100100100=>00011011011
[8,7,5,3,9,10,2,6,1,4,11,12]=>11100101000=>00011010111
[8,7,4,3,9,10,2,1,5,6,11,12]=>11100110000=>00011001111
[8,6,5,4,9,2,7,10,11,1,3,12]=>11101000100=>00010111011
[8,6,5,3,9,2,7,10,1,4,11,12]=>11101001000=>00010110111
[8,6,4,3,9,2,7,1,5,10,11,12]=>11101010000=>00010101111
[8,5,4,3,9,2,1,6,7,10,11,12]=>11101100000=>00010011111
[7,6,5,4,2,8,9,10,11,1,3,12]=>11110000100=>00001111011
[7,6,5,3,2,8,9,10,1,4,11,12]=>11110001000=>00001110111
[7,6,4,3,2,8,9,1,5,10,11,12]=>11110010000=>00001101111
[7,5,4,3,2,8,1,6,9,10,11,12]=>11110100000=>00001011111
[6,5,4,3,2,1,7,8,9,10,11,12]=>11111000000=>00000111111
[7,1,6,5,3,2,4,8]=>1011100=>0100011
[1,8,7,5,3,2,4,6]=>0111100=>1000011
[1,8,7,4,2,5,3,6]=>0111010=>1000101
[8,7,4,2,5,3,6,1]=>1110101=>0001010
[7,1,6,4,2,5,3,8]=>1011010=>0100101
[2,6,5,4,7,1,3,8]=>0110100=>1001011
[7,1,5,3,6,4,2,8]=>1010110=>0101001
[5,3,7,1,6,4,2,8]=>1010110=>0101001
[5,3,6,4,2,7,1,8]=>1011010=>0100101
[1,5,3,8,7,4,2,6]=>0101110=>1010001
[7,4,2,8,6,3,5,1]=>1101101=>0010010
[5,3,6,1,8,7,4,2]=>1010111=>0101000
[6,1,5,3,8,7,4,2]=>1010111=>0101000
[2,8,7,5,4,6,1,3]=>0111010=>1000101
[2,3,1,8,7,5,4,6]=>0101110=>1010001
[5,3,8,7,4,2,1,6]=>1011110=>0100001
[7,4,2,1,8,6,3,5]=>1110110=>0001001
[8,6,3,5,7,4,2,1]=>1100111=>0011000
[1,8,6,3,5,7,4,2]=>0110011=>1001100
[6,3,8,5,2,1,7,4]=>1011101=>0100010
[8,6,3,7,4,2,1,5]=>1101110=>0010001
[2,8,6,4,7,5,1,3]=>0110110=>1001001
[5,1,8,6,3,7,4,2]=>1011011=>0100100
[6,3,7,4,1,8,5,2]=>1011011=>0100100
[8,5,2,6,3,7,4,1]=>1101011=>0010100
[6,1,8,7,4,2,5,3]=>1011101=>0100010
[8,6,3,7,4,2,5,1]=>1101101=>0010010
[1,8,6,3,2,4,7,5]=>0111001=>1000110
[8,6,3,2,4,7,5,1]=>1110011=>0001100
[7,5,1,8,6,3,2,4]=>1101110=>0010001
[6,1,8,7,5,3,2,4]=>1011110=>0100001
[4,3,2,8,7,6,1,5]=>1101110=>0010001
[2,4,5,1,3,8,7,6]=>0010011=>1101100
[7,5,8,6,3,2,4,1]=>1011101=>0100010
[1,7,5,8,6,3,2,4]=>0101110=>1010001
[1,7,4,2,5,8,6,3]=>0110011=>1001100
[8,6,3,1,7,4,2,5]=>1110110=>0001001
[8,7,4,2,5,3,1,6]=>1110110=>0001001
[5,3,1,8,7,4,2,6]=>1101110=>0010001
[4,1,8,7,5,3,2,6]=>1011110=>0100001
[2,8,6,4,1,3,7,5]=>0111001=>1000110
[4,1,8,6,3,2,7,5]=>1011101=>0100010
[7,4,2,8,6,3,1,5]=>1101110=>0010001
[6,3,1,8,5,2,7,4]=>1101101=>0010010
[8,5,2,6,3,1,7,4]=>1101101=>0010010
[7,4,8,5,2,6,3,1]=>1011011=>0100100
[1,8,5,2,7,4,6,3]=>0110101=>1001010
[8,5,2,7,4,6,3,1]=>1101011=>0010100
[7,4,6,3,1,8,5,2]=>1011011=>0100100
[6,3,1,7,4,8,5,2]=>1101011=>0010100
[8,6,3,1,5,7,4,2]=>1110011=>0001100
[4,1,7,5,8,6,3,2]=>1010111=>0101000
[2,3,1,7,5,8,6,4]=>0101011=>1010100
[7,4,8,5,2,1,6,3]=>1011101=>0100010
[8,5,2,1,7,4,6,3]=>1110101=>0001010
[1,7,4,6,3,8,5,2]=>0101011=>1010100
[3,6,5,2,1,4,8,7]=>0111001=>1000110
[3,5,6,2,1,4,8,7]=>0011001=>1100110
[3,5,7,8,1,4,2,6]=>0001010=>1110101
[4,1,8,5,7,3,2,6]=>1010110=>0101001
[4,1,7,5,8,3,2,6]=>1010110=>0101001
[2,1,5,8,7,4,3,6]=>1001110=>0110001
[2,1,5,7,8,4,3,6]=>1000110=>0111001
[5,1,7,4,8,3,2,6]=>1010110=>0101001
[4,7,2,8,3,6,1,5]=>0101010=>1010101
[4,6,2,7,3,1,8,5]=>0101101=>1010010
[3,7,8,2,4,1,6,5]=>0010101=>1101010
[3,8,7,2,4,1,6,5]=>0110101=>1001010
[3,8,6,2,4,1,7,5]=>0110101=>1001010
[1,3,2,7,6,5,10,9,8,4]=>010110111=>101001000
[1,4,3,6,5,2,10,9,8,7]=>010110111=>101001000
[1,4,3,7,6,2,10,9,8,5]=>010110111=>101001000
[1,5,4,7,6,3,10,9,8,2]=>010110111=>101001000
[1,4,3,8,7,2,10,9,6,5]=>010110111=>101001000
[1,5,4,8,7,3,10,9,6,2]=>010110111=>101001000
[2,3,1,6,5,4,10,9,8,7]=>010110111=>101001000
[2,3,1,7,6,5,10,9,8,4]=>010110111=>101001000
[2,4,1,6,5,3,10,9,8,7]=>010110111=>101001000
[2,4,1,7,6,3,10,9,8,5]=>010110111=>101001000
[2,5,1,7,6,4,10,9,8,3]=>010110111=>101001000
[2,4,1,8,7,3,10,9,6,5]=>010110111=>101001000
[2,5,1,8,7,4,10,9,6,3]=>010110111=>101001000
[3,4,2,6,5,1,10,9,8,7]=>010110111=>101001000
[3,4,2,7,6,1,10,9,8,5]=>010110111=>101001000
[3,5,2,7,6,1,10,9,8,4]=>010110111=>101001000
[4,5,3,7,6,2,10,9,8,1]=>010110111=>101001000
[3,4,2,8,7,1,10,9,6,5]=>010110111=>101001000
[3,5,2,8,7,1,10,9,6,4]=>010110111=>101001000
[4,5,3,8,7,2,10,9,6,1]=>010110111=>101001000
[2,5,1,6,4,3,10,9,8,7]=>010110111=>101001000
[2,5,1,7,4,3,10,9,8,6]=>010110111=>101001000
[2,6,1,7,5,4,10,9,8,3]=>010110111=>101001000
[2,5,1,8,4,3,10,9,7,6]=>010110111=>101001000
[2,6,1,8,5,4,10,9,7,3]=>010110111=>101001000
[3,5,2,6,4,1,10,9,8,7]=>010110111=>101001000
[3,5,2,7,4,1,10,9,8,6]=>010110111=>101001000
[3,6,2,7,5,1,10,9,8,4]=>010110111=>101001000
[4,6,3,7,5,2,10,9,8,1]=>010110111=>101001000
[3,5,2,8,4,1,10,9,7,6]=>010110111=>101001000
[3,6,2,8,5,1,10,9,7,4]=>010110111=>101001000
[4,6,3,8,5,2,10,9,7,1]=>010110111=>101001000
[3,7,2,8,6,1,10,9,5,4]=>010110111=>101001000
[4,7,3,8,6,2,10,9,5,1]=>010110111=>101001000
[2,5,1,9,4,3,10,8,7,6]=>010110111=>101001000
[2,6,1,9,5,4,10,8,7,3]=>010110111=>101001000
[3,5,2,9,4,1,10,8,7,6]=>010110111=>101001000
[3,6,2,9,5,1,10,8,7,4]=>010110111=>101001000
[4,6,3,9,5,2,10,8,7,1]=>010110111=>101001000
[3,7,2,9,6,1,10,8,5,4]=>010110111=>101001000
[6,2,8,4,1,7,3,5]=>1011010=>0100101
[7,3,4,8,1,6,2,5]=>1001010=>0110101
[6,3,4,8,1,7,2,5]=>1001010=>0110101
[5,3,4,8,1,2,7,6]=>1001001=>0110110
[4,3,5,8,1,2,7,6]=>1001001=>0110110
[1,8,5,4,2,3,7,6]=>0111001=>1000110
[3,5,4,8,1,2,7,6]=>0101001=>1010110
[4,5,3,8,1,2,7,6]=>0101001=>1010110
[6,4,3,8,1,7,2,5]=>1101010=>0010101
[7,4,3,8,1,6,2,5]=>1101010=>0010101
[6,5,3,8,7,1,2,4]=>1101100=>0010011
[5,6,3,8,7,1,2,4]=>0101100=>1010011
[4,6,3,8,1,7,2,5]=>0101010=>1010101
[2,6,8,4,1,7,3,5]=>0011010=>1100101
[1,8,7,4,2,6,3,5]=>0111010=>1000101
[5,7,3,8,6,1,2,4]=>0101100=>1010011
[3,7,5,8,6,1,2,4]=>0101100=>1010011
[2,7,8,5,6,1,3,4]=>0010100=>1101011
[1,8,7,5,6,2,3,4]=>0110100=>1001011
[2,6,8,5,7,1,3,4]=>0010100=>1101011
[5,3,6,8,7,1,2,4]=>1001100=>0110011
[6,3,5,8,7,1,2,4]=>1001100=>0110011
[7,2,8,5,6,1,3,4]=>1010100=>0101011
[5,2,8,6,7,1,3,4]=>1010100=>0101011
[1,8,3,2,7,6,4,5]=>0110110=>1001001
[5,2,8,7,6,1,3,4]=>1011100=>0100011
[6,2,8,7,5,1,3,4]=>1011100=>0100011
[3,4,7,8,1,6,2,5]=>0001010=>1110101
[1,8,5,7,6,2,3,4]=>0101100=>1010011
[2,5,8,7,6,1,3,4]=>0011100=>1100011
[7,4,6,5,8,1,2,3]=>1010100=>0101011
[3,6,7,8,5,1,2,4]=>0001100=>1110011
[2,6,8,7,5,1,3,4]=>0011100=>1100011
[1,8,6,7,5,2,3,4]=>0101100=>1010011
[2,7,8,6,5,1,3,4]=>0011100=>1100011
[5,7,6,4,8,1,2,3]=>0110100=>1001011
[6,3,8,7,5,1,2,4]=>1011100=>0100011
[2,8,7,4,1,3,5,6]=>0111000=>1000111
[5,4,8,7,1,3,2,6]=>1011010=>0100101
[4,8,6,1,3,2,5,7]=>0110100=>1001011
[5,4,2,7,6,8,1,3]=>1101010=>0010101
[2,8,7,1,4,5,3,6]=>0110010=>1001101
[4,2,1,8,7,3,5,6]=>1101100=>0010011
[5,1,6,3,2,8,7,4]=>1011011=>0100100
[4,6,1,8,7,3,2,5]=>0101110=>1010001
[8,7,2,3,5,4,1,6]=>1100110=>0011001
[5,3,1,4,8,7,2,6]=>1100110=>0011001
[4,3,5,2,8,7,1,6]=>1010110=>0101001
[3,4,2,8,6,1,5,7]=>0101100=>1010011
[3,7,6,8,1,5,2,4]=>0101010=>1010101
[8,1,4,2,3,6,7,5]=>1010001=>0101110
[3,7,2,1,8,6,4,5]=>0110110=>1001001
[2,8,6,1,7,3,5,4]=>0110101=>1001010
[1,7,6,3,5,8,2,4]=>0110010=>1001101
[3,7,5,1,6,8,2,4]=>0110010=>1001101
[3,6,5,8,1,4,7,2]=>0101001=>1010110
[8,1,5,6,4,7,2,3]=>1001010=>0110101
[3,6,7,4,1,8,2,5]=>0011010=>1100101
[1,7,4,6,8,2,5,3]=>0100101=>1011010
[7,5,8,2,6,3,1,4]=>1010110=>0101001
[2,7,1,6,5,4,8,3]=>0101101=>1010010
[7,3,2,6,1,8,5,4]=>1101011=>0010100
[6,4,7,2,3,1,8,5]=>1010101=>0101010
[5,3,1,8,4,6,2,7]=>1101010=>0010101
[3,8,1,6,7,4,2,5]=>0100110=>1011001
[2,7,4,3,6,8,1,5]=>0110010=>1001101
[2,8,4,6,1,5,3,7]=>0101010=>1010101
[8,4,1,6,3,2,5,7]=>1101100=>0010011
[4,7,3,8,5,2,1,6]=>0101110=>1010001
[3,1,7,4,8,5,2,6]=>1010110=>0101001
[7,4,1,6,3,2,8,5]=>1101101=>0010010
[3,8,6,2,7,4,1,5]=>0110110=>1001001
[7,3,1,4,5,2,8,6]=>1100101=>0011010
[6,1,4,8,5,3,2,7]=>1001110=>0110001
[8,1,2,4,6,7,5,3]=>1000011=>0111100
[8,1,3,6,7,5,4,2]=>1000111=>0111000
[7,5,2,3,8,6,1,4]=>1100110=>0011001
[8,6,2,4,1,3,7,5]=>1101001=>0010110
[4,7,5,1,8,6,3,2]=>0110111=>1001000
[4,7,3,2,8,5,6,1]=>0110101=>1001010
[8,4,5,7,6,1,3,2]=>1001101=>0110010
[7,5,8,4,2,3,6,1]=>1011001=>0100110
[3,8,4,6,1,7,5,2]=>0101011=>1010100
[3,7,4,6,5,2,8,1]=>0101101=>1010010
[4,2,7,6,1,5,8,3]=>1011001=>0100110
[8,3,1,4,5,7,6,2]=>1100011=>0011100
[3,5,1,6,8,4,7,2]=>0100101=>1011010
[6,1,5,7,3,8,4,2]=>1001011=>0110100
[5,8,4,7,3,2,6,1]=>0101101=>1010010
[7,2,6,5,8,4,1,3]=>1010110=>0101001
[8,3,2,5,1,6,7,4]=>1101001=>0010110
[2,6,8,3,7,4,1,5]=>0010110=>1101001
[8,1,5,6,4,7,3,2]=>1001011=>0110100
[2,5,8,1,6,4,7,3]=>0010101=>1101010
[7,4,1,8,3,2,6,5]=>1101101=>0010010
[8,3,7,4,2,1,6,5]=>1011101=>0100010
[5,2,6,8,3,1,7,4]=>1001101=>0110010
[3,6,5,8,4,1,7,2]=>0101101=>1010010
[7,3,6,1,8,4,5,2]=>1010101=>0101010
[8,2,7,3,4,6,5,1]=>1010011=>0101100
[7,3,8,2,5,6,4,1]=>1010011=>0101100
[5,7,3,1,6,4,8,2]=>0110101=>1001010
[6,1,3,2,4,8,7,5]=>1010011=>0101100
[8,7,4,2,3,6,1,5]=>1110010=>0001101
[8,7,1,5,4,2,3,6]=>1101100=>0010011
[3,7,1,5,2,8,6,4]=>0101011=>1010100
[8,7,2,5,4,1,3,6]=>1101100=>0010011
[8,7,2,5,3,1,4,6]=>1101100=>0010011
[5,2,8,7,1,4,3,6]=>1011010=>0100101
[7,1,8,6,2,4,3,5]=>1011010=>0100101
[8,1,6,2,7,5,3,4]=>1010110=>0101001
[7,1,6,2,8,5,3,4]=>1010110=>0101001
[6,3,4,1,7,2,8,5]=>1010101=>0101010
[7,2,4,3,5,1,8,6]=>1010101=>0101010
[5,1,7,2,3,8,6,4]=>1010011=>0101100
[8,2,3,5,1,7,6,4]=>1001011=>0110100
[7,6,3,1,4,8,2,5]=>1110010=>0001101
[6,1,8,2,7,5,3,4]=>1010110=>0101001
[7,2,8,1,6,5,3,4]=>1010110=>0101001
[7,2,6,4,3,8,1,5]=>1011010=>0100101
[5,1,7,4,3,8,2,6]=>1011010=>0100101
[5,3,1,7,4,8,2,6]=>1101010=>0010101
[7,4,8,2,1,5,3,6]=>1011010=>0100101
[8,2,4,1,6,3,7,5]=>1010101=>0101010
[8,2,7,5,1,6,4,3]=>1011011=>0100100
[6,1,7,3,2,8,5,4]=>1011011=>0100100
[4,7,2,1,6,3,8,5]=>0110101=>1001010
[6,2,1,5,3,8,4,7]=>1101010=>0010101
[5,3,1,6,2,8,4,7]=>1101010=>0010101
[6,1,5,2,8,4,3,7]=>1010110=>0101001
[7,4,3,8,1,5,2,6]=>1101010=>0010101
[7,4,8,1,5,3,2,6]=>1010110=>0101001
[6,1,5,3,2,8,4,7]=>1011010=>0100101
[6,3,2,8,4,1,5,7]=>1101100=>0010011
[7,3,4,2,8,5,1,6]=>1010110=>0101001
[7,1,6,3,4,2,8,5]=>1010101=>0101010
[8,5,1,3,7,4,2,6]=>1100110=>0011001
[3,8,6,1,5,2,7,4]=>0110101=>1001010
[8,6,1,3,7,5,2,4]=>1100110=>0011001
[4,8,5,6,1,7,3,2]=>0101011=>1010100
[6,7,1,3,8,5,2,4]=>0100110=>1011001
[3,6,7,1,5,2,8,4]=>0010101=>1101010
[7,1,3,8,4,2,6,5]=>1001101=>0110010
[5,6,2,7,1,3,8,4]=>0101001=>1010110
[5,6,2,8,1,3,7,4]=>0101001=>1010110
[6,1,8,3,7,5,2,4]=>1010110=>0101001
[7,4,2,1,5,8,3,6]=>1110010=>0001101
[7,4,1,5,8,3,2,6]=>1100110=>0011001
[7,3,2,6,4,8,1,5]=>1101010=>0010101
[6,4,2,7,3,8,1,5]=>1101010=>0010101
[5,1,8,3,7,4,2,6]=>1010110=>0101001
[7,4,8,3,1,5,2,6]=>1011010=>0100101
[5,2,1,7,4,8,3,6]=>1101010=>0010101
[6,1,8,4,5,2,7,3]=>1010101=>0101010
[7,1,6,4,5,2,8,3]=>1010101=>0101010
[3,5,2,7,1,6,8,4]=>0101001=>1010110
[4,5,7,3,1,6,8,2]=>0011001=>1100110
[4,5,7,2,8,6,1,3]=>0010110=>1101001
[3,5,1,7,2,6,8,4]=>0101001=>1010110
[4,5,7,2,8,1,3,6]=>0010100=>1101011
[4,6,7,2,1,5,8,3]=>0011001=>1100110
[4,6,7,1,3,8,5,2]=>0010011=>1101100
[3,6,1,5,7,8,4,2]=>0100011=>1011100
[4,6,7,1,5,8,3,2]=>0010011=>1101100
[6,1,3,7,4,8,5,2]=>1001011=>0110100
[3,2,1,7,4,8,5,6]=>1101010=>0010101
[4,1,5,2,7,6,3,8]=>1010110=>0101001
[2,5,1,3,7,6,4,8]=>0100110=>1011001
[2,5,1,4,3,8,6,7]=>0101010=>1010101
[3,7,2,1,5,8,6,4]=>0110011=>1001100
[6,2,7,1,4,8,5,3]=>1010011=>0101100
[3,7,4,2,1,8,5,6]=>0111010=>1000101
[7,2,5,3,1,8,6,4]=>1011011=>0100100
[7,5,1,4,2,8,6,3]=>1101011=>0010100
[7,5,4,1,3,8,6,2]=>1110011=>0001100
[5,3,2,1,7,6,4,8]=>1110110=>0001001
[6,3,2,8,1,5,7,4]=>1101001=>0010110
[7,4,3,2,8,1,6,5]=>1110101=>0001010
[7,6,2,4,8,3,5,1]=>1100101=>0011010
[7,3,6,4,8,1,5,2]=>1010101=>0101010
[2,7,5,3,8,1,4,6]=>0110100=>1001011
[1,8,5,3,6,4,2,7]=>0110110=>1001001
[8,6,2,3,7,5,4,1]=>1100111=>0011000
[8,6,3,2,7,5,4,1]=>1110111=>0001000
[8,3,2,7,1,6,4,5]=>1101010=>0010101
[7,2,6,1,5,4,3,8]=>1010110=>0101001
[8,5,7,4,3,6,2,1]=>1011011=>0100100
[8,5,7,2,4,6,3,1]=>1010011=>0101100
[8,4,6,7,1,3,2,5]=>1001010=>0110101
[2,8,5,6,1,4,3,7]=>0101010=>1010101
[7,2,6,8,4,1,5,3]=>1001101=>0110010
[7,6,4,8,3,2,5,1]=>1101101=>0010010
[6,5,8,1,4,2,7,3]=>1010101=>0101010
[6,5,8,4,1,3,7,2]=>1011001=>0100110
[5,4,8,3,2,1,7,6]=>1011101=>0100010
[4,3,7,2,1,6,5,8]=>1011010=>0100101
[2,5,8,1,4,3,7,6]=>0010101=>1101010
[3,6,8,2,1,5,7,4]=>0011001=>1100110
[5,7,4,8,1,3,6,2]=>0101001=>1010110
[5,7,1,4,8,2,6,3]=>0100101=>1011010
[2,7,4,1,8,3,6,5]=>0110101=>1001010
[3,5,1,8,4,2,7,6]=>0101101=>1010010
[4,1,5,7,3,6,2,8]=>1001010=>0110101
[4,2,5,8,3,1,7,6]=>1001101=>0110010
[6,1,2,7,8,3,5,4]=>1000101=>0111010
[5,3,1,8,6,4,2,7]=>1101110=>0010001
[3,1,8,4,7,5,2,6]=>1010110=>0101001
[4,2,8,7,3,5,1,6]=>1011010=>0100101
[4,8,1,7,6,2,3,5]=>0101100=>1010011
[6,8,1,4,7,5,2,3]=>0100110=>1011001
[7,3,8,1,6,4,2,5]=>1010110=>0101001
[4,7,8,1,5,3,2,6]=>0010110=>1101001
[7,1,8,6,2,5,3,4]=>1011010=>0100101
[5,8,7,1,3,6,4,2]=>0110011=>1001100
[3,8,7,2,1,6,4,5]=>0111010=>1000101
[2,8,7,1,6,3,5,4]=>0110101=>1001010
[3,7,6,1,5,4,2,8]=>0110110=>1001001
[4,8,7,6,1,3,5,2]=>0111001=>1000110
[5,8,7,2,6,1,4,3]=>0110101=>1001010
[6,8,1,7,5,2,4,3]=>0101101=>1010010
[7,3,8,6,5,1,2,4]=>1011100=>0100011
[5,7,8,4,3,1,2,6]=>0011100=>1100011
[5,8,6,4,3,2,1,7]=>0111110=>1000001
[8,7,3,6,4,2,1,5]=>1101110=>0010001
[6,1,4,2,5,3,7,8]=>1010100=>0101011
[1,3,7,5,4,2,8,6]=>0011101=>1100010
[6,1,3,5,4,2,7,8]=>1001100=>0110011
[6,1,2,5,4,7,3,8]=>1001010=>0110101
[5,1,6,3,4,7,8,2]=>1010001=>0101110
[5,2,6,3,4,7,1,8]=>1010010=>0101101
[3,4,7,5,8,6,1,2]=>0010110=>1101001
[2,4,7,1,5,3,8,6]=>0010101=>1101010
[2,3,6,7,4,8,1,5]=>0001010=>1110101
[1,3,6,7,4,8,5,2]=>0001011=>1110100
[2,7,6,5,3,1,8,4]=>0111101=>1000010
[5,2,6,1,4,7,8,3]=>1010001=>0101110
[4,7,6,5,2,1,8,3]=>0111101=>1000010
[5,3,6,2,4,1,7,8]=>1010100=>0101011
[5,7,4,2,1,3,6,8]=>0111000=>1000111
[6,3,1,5,4,7,8,2]=>1101001=>0010110
[5,3,6,1,4,2,7,8]=>1010100=>0101011
[1,7,4,2,6,3,8,5]=>0110101=>1001010
[5,7,4,1,2,3,6,8]=>0110000=>1001111
[6,4,1,2,5,3,7,8]=>1100100=>0011011
[4,7,6,3,8,5,1,2]=>0110110=>1001001
[3,7,6,5,2,8,1,4]=>0111010=>1000101
[3,7,6,5,1,2,8,4]=>0111001=>1000110
[4,7,2,6,1,3,8,5]=>0101001=>1010110
[2,7,1,6,8,3,5,4]=>0100101=>1011010
[2,7,6,5,8,1,4,3]=>0110101=>1001010
[9,1,2,3,4,5,6,8,7]=>10000001=>01111110
[10,1,2,3,4,5,6,7,9,8]=>100000001=>011111110
[9,1,2,3,4,5,7,8,6]=>10000001=>01111110
[2,3,4,5,6,9,7,8,1]=>00000101=>11111010
[2,3,4,5,6,7,8,10,9,1]=>000000011=>111111100
[9,2,1,8,7,6,5,4,3]=>11011111=>00100000
[2,11,10,9,8,7,6,5,4,3,1]=>0111111111=>1000000000
[3,2,10,9,8,7,6,5,4,1]=>101111111=>010000000
[3,9,2,8,7,6,5,4,1]=>01011111=>10100000
[4,2,9,8,7,6,5,3,1]=>10111111=>01000000
[5,2,8,7,6,4,3,1]=>1011111=>0100000
[8,2,7,6,1,5,4,3]=>1011011=>0100100
[9,2,8,1,7,6,5,4,3]=>10101111=>01010000
[8,4,1,7,6,5,3,2]=>1101111=>0010000
[9,3,1,8,7,6,5,4,2]=>11011111=>00100000
[10,2,1,9,8,7,6,5,4,3]=>110111111=>001000000
[11,1,10,9,8,7,6,5,4,3,2]=>1011111111=>0100000000
[4,5,6,2,3,8,1,7]=>0010010=>1101101
[4,5,3,2,7,8,1,6]=>0110010=>1001101
[6,5,7,3,8,4,2,1]=>1010111=>0101000
[6,8,7,2,4,3,5,1]=>0110101=>1001010
[3,2,7,4,5,8,1,6]=>1010010=>0101101
[6,8,1,5,2,4,3,7]=>0101010=>1010101
[8,3,4,6,1,5,2,7]=>1001010=>0110101
[2,3,4,7,5,8,1,6]=>0001010=>1110101
[6,3,4,7,8,2,5,1]=>1000101=>0111010
[5,3,7,4,8,6,1,2]=>1010110=>0101001
[8,3,6,4,1,7,2,5]=>1011010=>0100101
[1,3,7,4,8,6,2,5]=>0010110=>1101001
[3,7,8,5,4,1,2,6]=>0011100=>1100011
[5,4,3,1,7,8,2,6]=>1110010=>0001101
[5,7,6,2,8,4,1,3]=>0110110=>1001001
[6,1,7,5,8,3,4,2]=>1010101=>0101010
[7,5,6,4,1,3,8,2]=>1011001=>0100110
[1,5,6,8,4,7,3,2]=>0001011=>1110100
[4,1,3,7,6,5,8,2]=>1001101=>0110010
[3,4,1,7,5,8,6,2]=>0101011=>1010100
[8,5,7,4,3,1,6,2]=>1011101=>0100010
[6,8,5,1,7,2,4,3]=>0110101=>1001010
[8,2,4,1,3,7,6,5]=>1010011=>0101100
[7,8,3,6,2,1,4,5]=>0101100=>1010011
[8,1,7,4,2,3,6,5]=>1011001=>0100110
[1,8,7,2,3,5,6,4]=>0110001=>1001110
[2,8,3,1,6,7,5,4]=>0110011=>1001100
[8,2,3,1,5,7,6,4]=>1010011=>0101100
[3,8,4,1,2,7,6,5]=>0110011=>1001100
[5,4,7,2,3,6,8,1]=>1010001=>0101110
[6,3,2,1,8,4,7,5]=>1110101=>0001010
[2,3,7,4,1,8,5,6]=>0011010=>1100101
[6,4,1,3,2,7,8,5]=>1101001=>0010110
[2,7,8,5,1,3,6,4]=>0011001=>1100110
[8,2,5,6,7,1,3,4]=>1000100=>0111011
[2,8,5,4,7,6,1,3]=>0110110=>1001001
[6,7,1,5,8,2,4,3]=>0100101=>1011010
[4,8,7,6,2,3,5,1]=>0111001=>1000110
[7,8,1,5,3,2,6,4]=>0101101=>1010010
[6,5,7,3,8,2,1,4]=>1010110=>0101001
[8,1,4,7,2,5,6,3]=>1001001=>0110110
[7,3,4,6,1,5,8,2]=>1001001=>0110110
[8,3,4,5,7,1,6,2]=>1000101=>0111010
[4,2,6,8,3,1,5,7]=>1001100=>0110011
[3,7,6,2,4,5,1,8]=>0110010=>1001101
[2,3,6,5,8,1,4,7]=>0010100=>1101011
[2,3,5,8,6,1,4,7]=>0001100=>1110011
[4,2,3,8,6,1,5,7]=>1001100=>0110011
[6,4,1,2,8,3,5,7]=>1100100=>0011011
[1,2,3,7,4,6,8,5]=>0001001=>1110110
[3,2,7,1,4,5,8,6]=>1010001=>0101110
[2,1,5,3,8,7,4,6]=>1010110=>0101001
[5,8,3,2,4,1,6,7]=>0110100=>1001011
[4,2,7,1,8,3,5,6]=>1010100=>0101011
[4,1,8,2,7,3,5,6]=>1010100=>0101011
[1,2,7,5,3,8,4,6]=>0011010=>1100101
[3,2,7,1,4,8,5,6]=>1010010=>0101101
[1,2,3,7,6,8,4,5]=>0001010=>1110101
[1,2,3,6,8,7,4,5]=>0000110=>1111001
[1,2,3,7,8,4,6,5]=>0000101=>1111010
[1,2,3,6,8,4,7,5]=>0000101=>1111010
[1,2,3,7,8,6,4,5]=>0000110=>1111001
[6,2,8,3,7,5,1,4]=>1010110=>0101001
[4,2,8,3,7,5,6,1]=>1010101=>0101010
[7,3,4,8,6,5,1,2]=>1001110=>0110001
[5,3,4,8,7,2,6,1]=>1001101=>0110010
[4,3,5,8,7,2,6,1]=>1001101=>0110010
[4,6,3,8,5,7,2,1]=>0101011=>1010100
[7,5,3,8,6,2,4,1]=>1101101=>0010010
[2,6,8,3,7,4,5,1]=>0010101=>1101010
[1,8,4,3,7,5,6,2]=>0110101=>1001010
[2,5,8,3,7,4,6,1]=>0010101=>1101010
[7,4,3,8,6,2,5,1]=>1101101=>0010010
[3,5,4,8,7,2,6,1]=>0101101=>1010010
[4,5,3,8,6,7,2,1]=>0101011=>1010100
[3,6,7,8,4,5,2,1]=>0001011=>1110100
[2,6,8,5,4,7,3,1]=>0011011=>1100100
[1,8,5,6,4,7,3,2]=>0101011=>1010100
[2,5,8,6,4,7,3,1]=>0011011=>1100100
[7,4,6,5,8,3,2,1]=>1010111=>0101000
[6,3,7,8,4,5,2,1]=>1001011=>0110100
[4,3,7,8,5,6,2,1]=>1001011=>0110100
[5,2,8,6,4,7,3,1]=>1011011=>0100100
[4,2,8,6,5,7,3,1]=>1011011=>0100100
[3,2,8,6,7,4,5,1]=>1010101=>0101010
[2,3,8,7,5,4,6,1]=>0011101=>1100010
[1,8,2,7,4,5,6,3]=>0101001=>1010110
[7,2,8,6,3,4,5,1]=>1011001=>0100110
[6,2,8,4,5,7,3,1]=>1010011=>0101100
[5,2,8,4,6,7,3,1]=>1010011=>0101100
[4,2,8,5,6,7,3,1]=>1010011=>0101100
[4,3,6,8,5,7,2,1]=>1001011=>0110100
[3,4,6,8,7,2,5,1]=>0001101=>1110010
[7,3,5,8,6,2,4,1]=>1001101=>0110010
[1,8,3,5,7,4,6,2]=>0100101=>1011010
[2,7,8,4,5,6,3,1]=>0010011=>1101100
[3,7,5,8,4,6,2,1]=>0101011=>1010100
[5,7,4,6,8,3,2,1]=>0100111=>1011000
[3,6,5,8,4,7,2,1]=>0101011=>1010100
[2,6,8,4,5,7,3,1]=>0010011=>1101100
[4,2,7,1,3,8,5,6]=>1010010=>0101101
[4,2,5,1,3,8,6,7]=>1010010=>0101101
[5,3,6,1,7,2,4,8]=>1010100=>0101011
[3,7,1,2,5,8,6,4]=>0100011=>1011100
[3,7,4,1,2,8,5,6]=>0110010=>1001101
[7,5,1,3,4,8,6,2]=>1100011=>0011100
[7,5,1,2,4,8,6,3]=>1100011=>0011100
[6,4,2,3,7,1,5,8]=>1100100=>0011011
[7,6,3,8,1,2,5,4]=>1101001=>0010110
[7,4,2,3,8,1,6,5]=>1100101=>0011010
[4,7,5,2,8,1,3,6]=>0110100=>1001011
[8,2,6,3,7,1,4,5]=>1010100=>0101011
[8,6,1,2,7,4,5,3]=>1100101=>0011010
[8,4,7,1,2,3,6,5]=>1010001=>0101110
[8,5,7,1,2,4,6,3]=>1010001=>0101110
[8,5,7,1,3,4,6,2]=>1010001=>0101110
[8,6,2,7,1,3,5,4]=>1101001=>0010110
[3,8,5,6,1,2,4,7]=>0101000=>1010111
[3,7,5,8,1,2,4,6]=>0101000=>1010111
[7,6,4,8,1,3,5,2]=>1101001=>0010110
[6,5,8,1,2,4,7,3]=>1010001=>0101110
[3,6,8,1,2,5,7,4]=>0010001=>1101110
[3,7,2,4,8,1,6,5]=>0100101=>1011010
[4,6,3,8,1,2,5,7]=>0101000=>1010111
[4,6,3,7,1,2,5,8]=>0101000=>1010111
[4,1,7,8,2,3,6,5]=>1001001=>0110110
[5,1,2,8,6,3,4,7]=>1001100=>0110011
[5,3,8,1,6,2,4,7]=>1010100=>0101011
[6,1,8,5,2,3,4,7]=>1011000=>0100111
[6,1,7,5,2,3,4,8]=>1011000=>0100111
[6,8,1,3,7,4,5,2]=>0100101=>1011010
[7,2,8,1,6,3,4,5]=>1010100=>0101011
[4,7,8,2,5,1,3,6]=>0010100=>1101011
[6,8,2,7,1,4,5,3]=>0101001=>1010110
[4,8,7,1,3,5,6,2]=>0110001=>1001110
[3,8,7,1,2,4,6,5]=>0110001=>1001110
[4,8,7,1,2,3,6,5]=>0110001=>1001110
[5,8,7,1,2,4,6,3]=>0110001=>1001110
[5,8,7,1,3,4,6,2]=>0110001=>1001110
[7,1,8,6,2,3,5,4]=>1011001=>0100110
[5,8,6,4,1,2,3,7]=>0111000=>1000111
[7,8,4,1,2,5,3,6]=>0110010=>1001101
[7,8,1,2,6,5,3,4]=>0100110=>1011001
[1,4,8,2,7,5,3,6]=>0010110=>1101001
[6,1,3,4,7,2,5,8]=>1000100=>0111011
[7,8,2,1,6,3,5,4]=>0110101=>1001010
[6,1,2,7,5,4,3,8]=>1001110=>0110001
[1,2,8,7,5,4,3,6]=>0011110=>1100001
[5,1,7,3,6,4,8,2]=>1010101=>0101010
[6,2,1,5,7,4,3,8]=>1100110=>0011001
[6,2,3,7,4,1,5,8]=>1001100=>0110011
[3,4,8,7,5,6,1,2]=>0011010=>1100101
[2,3,8,7,4,1,5,6]=>0011100=>1100011
[2,7,3,8,6,4,1,5]=>0101110=>1010001
[1,8,3,7,6,4,5,2]=>0101101=>1010010
[5,2,7,1,4,6,8,3]=>1010001=>0101110
[4,6,7,5,2,1,8,3]=>0011101=>1100010
[6,3,1,4,5,7,8,2]=>1100001=>0011110
[5,3,1,4,6,2,7,8]=>1100100=>0011011
[5,1,2,4,7,6,8,3]=>1000101=>0111010
[5,7,4,1,2,6,3,8]=>0110010=>1001101
[4,8,1,2,6,7,3,5]=>0100010=>1011101
[4,1,7,8,2,6,3,5]=>1001010=>0110101
[1,2,8,7,6,5,3,4]=>0011110=>1100001
[3,1,2,4,6,8,7,5]=>1000011=>0111100
[3,1,8,4,5,7,6,2]=>1010011=>0101100
[3,2,8,5,4,7,1,6]=>1011010=>0100101
[4,2,8,1,5,3,7,6]=>1010101=>0101010
[4,3,8,5,7,6,1,2]=>1010110=>0101001
[4,8,2,1,6,3,7,5]=>0110101=>1001010
[3,8,6,5,2,7,1,4]=>0111010=>1000101
[3,8,5,6,1,7,4,2]=>0101011=>1010100
[3,5,7,8,1,2,6,4]=>0001001=>1110110
[3,7,8,5,2,1,6,4]=>0011101=>1100010
[3,7,2,8,4,1,6,5]=>0101101=>1010010
[2,8,1,7,4,6,5,3]=>0101011=>1010100
[2,8,7,5,1,6,4,3]=>0111011=>1000100
[2,8,6,7,5,1,4,3]=>0101101=>1010010
[5,1,3,4,6,7,2,8]=>1000010=>0111101
[1,3,4,8,7,5,2,6]=>0001110=>1110001
[8,2,4,1,7,3,5,6]=>1010100=>0101011
[8,6,1,4,2,3,7,5]=>1101001=>0010110
[3,6,1,4,2,8,7,5]=>0101011=>1010100
[1,6,8,4,3,7,2,5]=>0011010=>1100101
[3,1,4,7,8,5,2,6]=>1000110=>0111001
[6,1,7,4,3,8,2,5]=>1011010=>0100101
[1,8,7,4,3,6,2,5]=>0111010=>1000101
[7,4,1,3,8,2,6,5]=>1100101=>0011010
[4,8,2,3,1,5,7,6]=>0101001=>1010110
[4,8,6,2,1,3,7,5]=>0111001=>1000110
[2,7,4,1,8,3,5,6]=>0110100=>1001011
[1,7,8,4,2,3,6,5]=>0011001=>1100110
[4,7,1,3,8,2,6,5]=>0100101=>1011010
[8,7,1,3,4,2,6,5]=>1100101=>0011010
[1,7,4,3,6,2,8,5]=>0110101=>1001010
[3,8,6,4,5,2,1,7]=>0110110=>1001001
[3,8,4,6,5,2,1,7]=>0101110=>1010001
[2,4,3,7,5,8,1,6]=>0101010=>1010101
[1,4,7,3,6,2,8,5]=>0010101=>1101010
[1,8,3,4,2,6,7,5]=>0101001=>1010110
[6,4,1,3,7,2,8,5]=>1100101=>0011010
[8,1,4,3,6,2,7,5]=>1010101=>0101010
[4,2,3,8,5,7,1,6]=>1001010=>0110101
[2,8,5,7,3,4,1,6]=>0101010=>1010101
[5,8,2,6,4,3,1,7]=>0101110=>1010001
[7,2,5,8,4,3,1,6]=>1001110=>0110001
[4,2,3,5,8,7,1,6]=>1000110=>0111001
[8,2,3,5,4,7,1,6]=>1001010=>0110101
[6,1,8,3,4,2,7,5]=>1010101=>0101010
[1,8,6,4,2,3,7,5]=>0111001=>1000110
[3,8,4,5,6,2,1,7]=>0100110=>1011001
[2,4,3,5,7,8,1,6]=>0100010=>1011101
[3,8,6,5,4,2,1,7]=>0111110=>1000001
[6,3,1,4,2,8,7,5]=>1101011=>0010100
[7,3,8,1,2,6,4,5]=>1010010=>0101101
[7,1,4,5,3,2,6,8]=>1001100=>0110011
[1,8,4,2,6,5,3,7]=>0110110=>1001001
[5,1,4,8,6,3,2,7]=>1001110=>0110001
[5,3,1,8,4,7,2,6]=>1101010=>0010101
[4,3,8,1,5,7,2,6]=>1010010=>0101101
[6,3,1,2,5,7,4,8]=>1100010=>0011101
[7,1,4,2,6,5,3,8]=>1010110=>0101001
[3,8,4,1,6,5,2,7]=>0110110=>1001001
[7,5,3,6,4,8,2,1]=>1101011=>0010100
[7,3,6,4,5,8,2,1]=>1010011=>0101100
[8,7,2,4,5,1,6,3]=>1100101=>0011010
[7,1,5,4,8,6,3,2]=>1010111=>0101000
[2,7,5,4,8,6,3,1]=>0110111=>1001000
[2,1,8,7,5,3,6,4]=>1011101=>0100010
[5,8,3,7,4,1,6,2]=>0101101=>1010010
[8,1,7,4,2,6,5,3]=>1011011=>0100100
[5,6,3,1,8,4,7,2]=>0110101=>1001010
[5,7,1,4,8,6,3,2]=>0100111=>1011000
[3,5,7,4,8,6,2,1]=>0010111=>1101000
[2,6,7,4,5,8,3,1]=>0010011=>1101100
[6,1,7,4,5,8,3,2]=>1010011=>0101100
[5,3,7,4,8,6,2,1]=>1010111=>0101000
[8,5,3,6,1,4,7,2]=>1101001=>0010110
[5,4,3,6,8,2,7,1]=>1100101=>0011010
[6,5,3,7,4,8,2,1]=>1101011=>0010100
[7,5,8,4,1,6,3,2]=>1011011=>0100100
[2,7,8,4,5,1,6,3]=>0010101=>1101010
[5,7,3,8,4,1,6,2]=>0101101=>1010010
[5,6,3,8,1,4,7,2]=>0101001=>1010110
[8,4,1,2,5,6,7,3]=>1100001=>0011110
[3,7,8,4,1,6,5,2]=>0011011=>1100100
[6,8,3,1,2,5,7,4]=>0110001=>1001110
[8,7,1,4,5,2,6,3]=>1100101=>0011010
[8,7,3,1,5,4,2,6]=>1110110=>0001001
[3,6,2,1,5,4,8,7]=>0110101=>1001010
[5,4,2,6,1,3,8,7]=>1101001=>0010110
[3,2,6,5,1,4,8,7]=>1011001=>0100110
[2,5,8,1,7,4,3,6]=>0010110=>1101001
[6,8,2,7,4,3,1,5]=>0101110=>1010001
[6,8,2,3,7,5,1,4]=>0100110=>1011001
[7,6,2,5,4,8,1,3]=>1101010=>0010101
[2,6,5,1,8,4,3,7]=>0110110=>1001001
[4,2,7,3,1,8,5,6]=>1011010=>0100101
[4,2,3,7,1,5,8,6]=>1001001=>0110110
[5,2,7,3,8,6,1,4]=>1010110=>0101001
[2,1,5,8,4,3,7,6]=>1001101=>0110010
[5,8,4,2,6,7,1,3]=>0110010=>1001101
[3,2,4,8,1,5,7,6]=>1001001=>0110110
[2,4,8,3,1,7,5,6]=>0011010=>1100101
[4,8,3,2,1,7,6,5]=>0111011=>1000100
[4,1,3,7,2,6,8,5]=>1001001=>0110110
[3,4,8,2,1,6,5,7]=>0011010=>1100101
[6,8,3,7,2,1,5,4]=>0101101=>1010010
[3,5,8,1,7,2,6,4]=>0010101=>1101010
[5,1,7,4,6,8,3,2]=>1010011=>0101100
[7,6,4,8,1,5,3,2]=>1101011=>0010100
[5,3,7,1,8,2,6,4]=>1010101=>0101010
[2,7,6,3,8,1,4,5]=>0110100=>1001011
[2,1,7,6,4,8,3,5]=>1011010=>0100101
[2,1,5,4,8,7,3,6]=>1010110=>0101001
[5,4,8,7,2,6,1,3]=>1011010=>0100101
[2,4,3,8,7,1,5,6]=>0101100=>1010011
[3,4,1,8,6,2,7,5]=>0101101=>1010010
[3,8,5,4,2,1,7,6]=>0111101=>1000010
[4,8,6,5,2,7,1,3]=>0111010=>1000101
[3,2,8,7,5,4,1,6]=>1011110=>0100001
[2,8,6,5,4,3,1,7]=>0111110=>1000001
[5,4,2,6,3,1,8,7]=>1101101=>0010010
[6,5,2,1,3,4,8,7]=>1110001=>0001110
[8,5,2,7,3,1,4,6]=>1101100=>0010011
[7,3,6,5,2,8,4,1]=>1011011=>0100100
[7,6,2,3,4,8,5,1]=>1100011=>0011100
[8,7,5,3,1,4,2,6]=>1111010=>0000101
[7,1,5,3,8,4,6,2]=>1010101=>0101010
[6,7,2,3,5,8,4,1]=>0100011=>1011100
[3,7,6,4,2,8,5,1]=>0111011=>1000100
[2,1,7,6,4,8,5,3]=>1011011=>0100100
[2,1,8,7,4,3,5,6]=>1011100=>0100011
[5,8,3,7,2,1,4,6]=>0101100=>1010011
[3,8,7,4,2,1,5,6]=>0111100=>1000011
[7,8,2,3,5,1,4,6]=>0100100=>1011011
[2,8,6,3,1,4,7,5]=>0111001=>1000110
[8,1,6,3,2,4,5,7]=>1011000=>0100111
[5,7,1,4,8,3,6,2]=>0100101=>1011010
[6,1,7,5,4,8,3,2]=>1011011=>0100100
[6,3,7,5,8,4,2,1]=>1010111=>0101000
[7,6,1,5,8,3,4,2]=>1100101=>0011010
[8,6,7,5,1,3,2,4]=>1011010=>0100101
[8,5,2,6,1,7,3,4]=>1101010=>0010101
[5,4,2,6,8,3,7,1]=>1100101=>0011010
[6,5,2,8,1,4,3,7]=>1101010=>0010101
[7,4,2,8,1,3,6,5]=>1101001=>0010110
[2,7,8,4,5,1,3,6]=>0010100=>1101011
[5,7,3,8,4,1,2,6]=>0101100=>1010011
[2,4,8,1,5,6,3,7]=>0010010=>1101101
[3,4,8,1,5,2,7,6]=>0010101=>1101010
[3,6,8,4,1,2,7,5]=>0011001=>1100110
[4,8,1,2,5,3,6,7]=>0100100=>1011011
[8,1,2,4,3,5,6,7]=>1001000=>0110111
[2,3,4,6,5,7,8,9,10,1]=>000100001=>111011110
[2,3,5,6,4,7,8,9,1]=>00010001=>11101110
[2,3,6,4,5,7,8,9,1]=>00100001=>11011110
[9,1,2,4,5,3,6,7,8]=>10001000=>01110111
[10,1,2,3,5,4,6,7,8,9]=>100010000=>011101111
[5,8,7,4,6,3,2,1]=>0110111=>1001000
[4,8,7,6,3,5,2,1]=>0111011=>1000100
[3,8,7,6,5,2,4,1]=>0111101=>1000010
[7,9,6,8,5,4,3,2,1]=>01011111=>10100000
[5,8,4,7,6,3,2,1]=>0101111=>1010000
[6,9,8,5,7,4,3,2,1]=>01101111=>10010000
[6,8,5,4,7,3,2,1]=>0110111=>1001000
[5,9,8,7,4,6,3,2,1]=>01110111=>10001000
[3,8,7,6,2,5,4,1]=>0111011=>1000100
[4,9,8,7,6,3,5,2,1]=>01111011=>10000100
[4,8,7,6,3,2,5,1]=>0111101=>1000010
[3,9,8,7,6,5,2,4,1]=>01111101=>10000010
[3,8,7,6,5,2,1,4]=>0111110=>1000001
[8,6,9,7,4,5,2,3,1]=>10110101=>01001010
[8,6,9,4,7,5,2,3,1]=>10101101=>01010010
[8,6,9,4,7,2,5,3,1]=>10101011=>01010100
[8,6,9,4,7,3,5,1,2]=>10101010=>01010101
[8,6,9,5,7,3,4,1,2]=>10101010=>01010101
[8,7,9,5,6,3,4,1,2]=>10101010=>01010101
[9,7,10,8,5,6,3,4,1,2]=>101101010=>010010101
[8,6,4,9,7,5,2,3,1]=>11011101=>00100010
[9,7,10,5,8,6,3,4,1,2]=>101011010=>010100101
[8,6,9,4,2,7,5,3,1]=>10110111=>01001000
[9,7,10,5,8,3,6,4,1,2]=>101010110=>010101001
[8,6,9,4,7,2,1,5,3]=>10101101=>01010010
[7,5,8,4,6,3,1,2]=>1010110=>0101001
[8,6,9,4,7,3,5,2,1]=>10101011=>01010100
[9,7,10,5,8,3,6,2,4,1]=>101010101=>010101010
[8,6,9,5,7,2,4,1,3]=>10101010=>01010101
[9,7,10,5,8,4,6,2,3,1]=>101010101=>010101010
[7,6,8,2,5,1,4,3]=>1010101=>0101010
[8,7,9,4,6,3,5,1,2]=>10101010=>01010101
[9,7,10,6,8,4,5,2,3,1]=>101010101=>010101010
[9,6,8,5,7,3,4,1,2]=>10101010=>01010101
[9,8,10,6,7,4,5,2,3,1]=>101010101=>010101010
[3,5,2,4,7,6,1,8]=>0100110=>1011001
[3,5,4,7,2,6,1,8]=>0101010=>1010101
[3,5,4,7,6,1,2,8]=>0101100=>1010011
[3,5,4,7,6,1,8,2]=>0101101=>1010010
[3,5,7,4,6,1,8,2]=>0010101=>1101010
[3,5,7,4,6,1,2,8]=>0010100=>1101011
[3,5,7,4,6,2,1,8]=>0010110=>1101001
[3,2,5,7,4,6,1,8]=>1001010=>0110101
[3,5,2,7,6,4,1,8]=>0101110=>1010001
[3,5,7,2,6,4,1,8]=>0010110=>1101001
[5,3,7,6,2,4,1,8]=>1011010=>0100101
[5,3,7,6,1,2,8,4]=>1011001=>0100110
[5,3,7,6,1,4,2,8]=>1011010=>0100101
[5,3,7,6,4,1,2,8]=>1011100=>0100011
[3,5,7,2,6,1,4,8]=>0010100=>1101011
[3,5,2,7,6,1,4,8]=>0101100=>1010011
[5,3,7,6,4,1,8,2]=>1011101=>0100010
[3,7,5,4,1,8,2,6]=>0111010=>1000101
[3,7,5,4,1,8,6,2]=>0111011=>1000100
[3,7,5,1,4,8,6,2]=>0110011=>1001100
[3,7,5,1,4,8,2,6]=>0110010=>1001101
[3,5,7,1,2,6,8,4]=>0010001=>1101110
[3,5,7,2,1,6,8,4]=>0011001=>1100110
[3,5,2,7,1,6,4,8]=>0101010=>1010101
[3,5,7,2,1,6,4,8]=>0011010=>1100101
[5,3,7,1,6,2,4,8]=>1010100=>0101011
[3,5,7,1,4,6,8,2]=>0010001=>1101110
[3,5,7,1,4,6,2,8]=>0010010=>1101101
[3,5,7,1,4,2,6,8]=>0010100=>1101011
[3,5,7,2,1,4,6,8]=>0011000=>1100111
[3,5,2,7,1,4,6,8]=>0101000=>1010111
[3,2,5,7,4,1,6,8]=>1001100=>0110011
[3,5,2,7,4,1,6,8]=>0101100=>1010011
[3,5,7,4,2,1,6,8]=>0011100=>1100011
[3,5,7,4,1,2,6,8]=>0011000=>1100111
[3,5,4,7,1,6,8,2]=>0101001=>1010110
[3,5,4,7,1,2,6,8]=>0101000=>1010111
[3,5,4,7,2,1,6,8]=>0101100=>1010011
[3,5,4,2,7,1,6,8]=>0110100=>1001011
[3,2,5,4,7,1,6,8]=>1010100=>0101011
[3,5,4,7,2,1,8,6]=>0101101=>1010010
[3,5,4,7,1,2,8,6]=>0101001=>1010110
[5,7,6,3,1,8,4,2]=>0111011=>1000100
[5,7,6,3,1,8,2,4]=>0111010=>1000101
[3,5,7,4,1,2,8,6]=>0011001=>1100110
[3,5,7,4,2,1,8,6]=>0011101=>1100010
[3,2,5,7,4,1,8,6]=>1001101=>0110010
[3,2,5,7,1,4,8,6]=>1001001=>0110110
[3,5,2,7,1,4,8,6]=>0101001=>1010110
[3,5,7,2,1,4,8,6]=>0011001=>1100110
[3,5,7,1,4,2,8,6]=>0010101=>1101010
[3,7,5,2,1,8,6,4]=>0111011=>1000100
[3,7,2,5,1,8,6,4]=>0101011=>1010100
[3,2,7,5,1,8,6,4]=>1011011=>0100100
[3,2,7,5,1,8,4,6]=>1011010=>0100101
[3,7,2,5,1,8,4,6]=>0101010=>1010101
[3,7,5,2,1,8,4,6]=>0111010=>1000101
[6,1,2,5,7,4,8,3]=>1000101=>0111010
[6,3,2,7,4,1,8,5]=>1101101=>0010010
[2,1,7,5,8,4,6,3]=>1010101=>0101010
[2,7,3,6,8,4,1,5]=>0100110=>1011001
[2,1,8,3,4,7,5,6]=>1010010=>0101101
[5,1,7,2,4,8,3,6]=>1010010=>0101101
[3,4,2,6,7,1,8,5]=>0100101=>1011010
[3,5,8,7,2,1,6,4]=>0011101=>1100010
[1,3,4,5,6,7,9,2,8]=>00000010=>11111101
[2,3,4,5,6,7,1,9,8]=>00000101=>11111010
[2,1,4,5,6,7,8,9,3]=>10000001=>01111110
[3,1,4,5,6,7,8,2,9]=>10000010=>01111101
[5,8,3,4,1,7,6,2]=>0101011=>1010100
[5,8,7,2,4,1,6,3]=>0110101=>1001010
[3,8,6,4,1,7,5,2]=>0111011=>1000100
[4,3,5,6,8,1,7,2]=>1000101=>0111010
[3,7,6,4,1,8,5,2]=>0111011=>1000100
[3,7,4,1,8,6,5,2]=>0110111=>1001000
[3,8,4,1,7,6,5,2]=>0110111=>1001000
[3,2,7,6,1,5,4,8]=>1011010=>0100101
[3,2,8,7,6,1,5,4]=>1011101=>0100010
[5,7,8,2,4,1,6,3]=>0010101=>1101010
[4,2,5,8,1,6,7,3]=>1001001=>0110110
[4,2,5,8,1,7,3,6]=>1001010=>0110101
[5,8,2,4,1,6,3,7]=>0101010=>1010101
[8,4,2,6,5,1,3,7]=>1101100=>0010011
[3,2,6,8,1,5,4,7]=>1001010=>0110101
[8,3,2,5,6,1,4,7]=>1100100=>0011011
[3,2,8,6,7,1,5,4]=>1010101=>0101010
[3,2,6,8,7,1,5,4]=>1001101=>0110010
[3,2,6,7,1,5,4,8]=>1001010=>0110101
[8,7,3,2,5,6,1,4]=>1110010=>0001101
[7,2,8,1,5,3,6,4]=>1010101=>0101010
[8,4,2,7,5,1,3,6]=>1101100=>0010011
[7,4,2,8,5,1,3,6]=>1101100=>0010011
[7,2,4,1,8,3,6,5]=>1010101=>0101010
[3,2,8,5,7,1,4,6]=>1010100=>0101011
[2,6,5,7,1,8,3,4]=>0101010=>1010101
[2,5,1,8,7,4,3,6]=>0101110=>1010001
[8,1,4,6,3,5,2,7]=>1001010=>0110101
[8,3,5,4,1,6,2,7]=>1011010=>0100101
[8,6,3,4,1,5,2,7]=>1101010=>0010101
[5,4,7,6,8,2,3,1]=>1010101=>0101010
[4,1,8,2,3,7,6,5]=>1010011=>0101100
[2,1,8,5,3,4,7,6]=>1011001=>0100110
[5,2,4,6,8,7,3,1]=>1000111=>0111000
[1,6,8,3,4,5,7,2]=>0010001=>1101110
[5,7,4,8,6,1,3,2]=>0101101=>1010010
[5,4,2,6,7,8,1,3]=>1100010=>0011101
[6,4,2,7,3,5,8,1]=>1101001=>0010110
[7,4,1,8,3,5,6,2]=>1101001=>0010110
[6,5,4,8,7,3,1,2]=>1101110=>0010001
[8,7,4,2,1,3,6,5]=>1111001=>0000110
[8,7,1,3,2,5,6,4]=>1101001=>0010110
[6,8,2,3,1,7,5,4]=>0101011=>1010100
[7,4,3,2,6,8,5,1]=>1110011=>0001100
[2,7,4,3,8,5,6,1]=>0110101=>1001010
[8,3,7,2,1,5,6,4]=>1011001=>0100110
[5,7,8,2,4,3,1,6]=>0010110=>1101001
[8,4,7,3,2,6,1,5]=>1011010=>0100101
[8,3,1,6,7,4,2,5]=>1100110=>0011001
[3,2,5,7,4,8,1,6]=>1001010=>0110101
[8,2,7,3,4,1,5,6]=>1010100=>0101011
[7,1,6,3,5,8,2,4]=>1010010=>0101101
[2,8,5,6,7,1,4,3]=>0100101=>1011010
[1,5,2,7,8,6,4,3]=>0100111=>1011000
[2,6,8,5,1,4,7,3]=>0011001=>1100110
[1,4,2,8,6,5,7,3]=>0101101=>1010010
[3,5,1,6,8,7,2,4]=>0100110=>1011001
[5,7,6,2,1,3,8,4]=>0111001=>1000110
[2,5,8,7,4,1,6,3]=>0011101=>1100010
[4,1,7,5,2,6,8,3]=>1011001=>0100110
[7,6,2,4,5,1,8,3]=>1100101=>0011010
[7,3,4,2,5,8,6,1]=>1010011=>0101100
[8,7,4,2,5,1,6,3]=>1110101=>0001010
[8,1,4,5,2,6,7,3]=>1001001=>0110110
[5,2,4,8,6,7,1,3]=>1001010=>0110101
[8,5,6,2,1,3,7,4]=>1011001=>0100110
[4,2,1,5,6,7,8,3]=>1100001=>0011110
[3,4,6,5,1,7,8,2]=>0011001=>1100110
[7,3,5,2,4,6,1,8]=>1010010=>0101101
[5,3,7,2,4,6,1,8]=>1010010=>0101101
[3,7,5,2,4,6,1,8]=>0110010=>1001101
[5,7,3,2,4,6,1,8]=>0110010=>1001101
[1,5,3,2,4,7,6,8]=>0110010=>1001101
[1,5,3,2,7,4,6,8]=>0110100=>1001011
[5,7,3,2,1,4,6,8]=>0111000=>1000111
[5,7,3,2,4,1,6,8]=>0110100=>1001011
[3,7,2,5,4,1,6,8]=>0101100=>1010011
[5,1,3,2,4,7,6,8]=>1010010=>0101101
[5,1,3,2,7,4,6,8]=>1010100=>0101011
[7,1,3,2,5,4,6,8]=>1010100=>0101011
[1,7,3,2,5,4,6,8]=>0110100=>1001011
[7,1,3,5,2,4,6,8]=>1001000=>0110111
[5,1,3,7,2,4,6,8]=>1001000=>0110111
[3,2,7,5,1,4,6,8]=>1011000=>0100111
[3,7,5,1,2,4,6,8]=>0110000=>1001111
[5,7,3,1,2,4,6,8]=>0110000=>1001111
[1,5,3,7,2,4,6,8]=>0101000=>1010111
[5,3,2,7,4,1,6,8]=>1101100=>0010011
[5,3,2,4,7,1,6,8]=>1100100=>0011011
[5,3,2,1,4,7,6,8]=>1110010=>0001101
[5,3,2,1,7,4,6,8]=>1110100=>0001011
[1,3,2,7,5,4,6,8]=>0101100=>1010011
[1,3,7,2,5,4,6,8]=>0010100=>1101011
[7,3,1,2,5,4,6,8]=>1100100=>0011011
[5,3,1,2,7,4,6,8]=>1100100=>0011011
[5,3,1,2,4,7,6,8]=>1100010=>0011101
[3,2,5,1,4,7,6,8]=>1010010=>0101101
[7,3,1,5,2,4,6,8]=>1101000=>0010111
[1,3,7,5,2,4,6,8]=>0011000=>1100111
[7,5,1,3,2,4,6,8]=>1101000=>0010111
[5,7,1,3,2,4,6,8]=>0101000=>1010111
[3,7,1,5,2,4,6,8]=>0101000=>1010111
[3,7,1,2,5,4,6,8]=>0100100=>1011011
[3,7,2,1,5,4,6,8]=>0110100=>1001011
[3,2,1,7,5,4,6,8]=>1101100=>0010011
[3,1,2,7,5,4,6,8]=>1001100=>0110011
[3,1,7,2,5,4,6,8]=>1010100=>0101011
[3,1,7,5,2,4,6,8]=>1011000=>0100111
[7,1,5,3,2,4,6,8]=>1011000=>0100111
[1,7,5,3,2,4,6,8]=>0111000=>1000111
[1,2,3,4,5,7,9,6,8]=>00000010=>11111101
[1,2,3,4,6,9,5,7,8]=>00000100=>11111011
[1,2,3,5,9,4,6,7,8]=>00001000=>11110111
[1,2,4,9,3,5,6,7,8]=>00010000=>11101111
[1,3,9,2,4,5,6,7,8]=>00100000=>11011111
[1,9,8,7,6,2,5,4,3]=>01111011=>10000100
[2,9,8,7,1,6,5,4,3]=>01110111=>10001000
[1,9,8,2,7,6,5,4,3]=>01101111=>10010000
[1,9,2,8,7,6,5,4,3]=>01011111=>10100000
[3,9,8,7,6,5,2,1,4]=>01111110=>10000001
[1,10,9,8,7,6,5,2,4,3]=>011111101=>100000010
[4,9,8,7,6,1,2,5,3]=>01111001=>10000110
[1,10,9,8,7,6,2,5,4,3]=>011111011=>100000100
[1,8,7,4,2,6,5,3]=>0111011=>1000100
[5,9,8,7,1,2,6,4,3]=>01110011=>10001100
[2,10,9,8,7,1,6,5,4,3]=>011110111=>100001000
[2,8,5,1,7,6,4,3]=>0110111=>1001000
[6,9,8,2,1,7,5,4,3]=>01110111=>10001000
[1,10,9,8,2,7,6,5,4,3]=>011101111=>100010000
[6,8,5,1,2,7,4,3]=>0110011=>1001100
[7,9,1,2,8,6,5,4,3]=>01001111=>10110000
[1,10,9,2,8,7,6,5,4,3]=>011011111=>100100000
[8,1,2,9,7,6,5,4,3]=>10011111=>01100000
[2,10,1,9,8,7,6,5,4,3]=>010111111=>101000000
[3,10,9,8,7,6,5,2,1,4]=>011111110=>100000001
[1,11,10,9,8,7,6,5,2,4,3]=>0111111101=>1000000010
[1,9,8,7,6,3,2,5,4]=>01111101=>10000010
[4,10,9,8,7,6,1,2,5,3]=>011111001=>100000110
[1,11,10,9,8,7,6,2,5,4,3]=>0111111011=>1000000100
[1,9,8,7,4,2,6,5,3]=>01111011=>10000100
[4,9,8,7,6,3,2,1,5]=>01111110=>10000001
[5,10,9,8,7,1,2,6,4,3]=>011110011=>100001100
[2,11,10,9,8,7,1,6,5,4,3]=>0111110111=>1000001000
[2,8,1,4,7,6,5,3]=>0100111=>1011000
[2,9,8,5,1,7,6,4,3]=>01110111=>10001000
[5,9,8,7,4,1,2,6,3]=>01111001=>10000110
[6,10,9,8,2,1,7,5,4,3]=>011110111=>100001000
[1,11,10,9,8,2,7,6,5,4,3]=>0111101111=>1000010000
[1,9,6,2,8,7,5,4,3]=>01101111=>10010000
[1,8,7,4,3,2,6,5]=>0111101=>1000010
[6,9,8,5,1,2,7,4,3]=>01110011=>10001100
[7,10,9,1,2,8,6,5,4,3]=>011001111=>100110000
[1,11,10,9,2,8,7,6,5,4,3]=>0111011111=>1000100000
[1,7,2,9,8,6,5,4,3]=>01011111=>10100000
[1,8,5,4,2,7,6,3]=>0111011=>1000100
[7,9,6,2,1,8,5,4,3]=>01110111=>10001000
[8,10,1,2,9,7,6,5,4,3]=>010011111=>101100000
[2,11,10,1,9,8,7,6,5,4,3]=>0110111111=>1001000000
[8,7,1,2,9,6,5,4,3]=>11001111=>00110000
[9,2,1,10,8,7,6,5,4,3]=>110111111=>001000000
[1,11,2,10,9,8,7,6,5,4,3]=>0101111111=>1010000000
[1,2,11,10,9,8,7,6,5,4,3]=>0011111111=>1100000000
[7,5,3,4,2,8,1,6]=>1101010=>0010101
[8,5,3,6,2,4,7,1]=>1101001=>0010110
[8,5,6,3,7,4,2,1]=>1010111=>0101000
[8,5,6,2,7,4,3,1]=>1010111=>0101000
[8,7,6,3,4,1,5,2]=>1110101=>0001010
[1,7,2,3,6,8,5,4]=>0100011=>1011100
[3,5,6,4,8,2,7,1]=>0010101=>1101010
[3,5,1,4,8,2,7,6]=>0100101=>1011010
[1,7,5,4,8,2,6,3]=>0110101=>1001010
[3,7,5,1,6,4,8,2]=>0110101=>1001010
[2,7,5,4,8,1,3,6]=>0110100=>1001011
[2,7,5,4,8,6,1,3]=>0110110=>1001001
[1,7,5,4,8,6,3,2]=>0110111=>1001000
[2,5,1,4,8,7,3,6]=>0100110=>1011001
[3,6,4,2,8,7,1,5]=>0110110=>1001001
[3,5,2,4,8,1,6,7]=>0100100=>1011011
[3,5,6,4,8,1,2,7]=>0010100=>1101011
[1,5,6,4,8,7,2,3]=>0010110=>1101001
[3,6,4,1,8,7,2,5]=>0110110=>1001001
[3,6,4,5,8,7,2,1]=>0100111=>1011000
[1,6,4,3,8,5,2,7]=>0110110=>1001001
[7,1,3,4,5,8,2,6]=>1000010=>0111101
[7,6,1,4,5,3,8,2]=>1100101=>0011010
[7,6,1,3,5,4,8,2]=>1100101=>0011010
[7,1,3,2,5,8,4,6]=>1010010=>0101101
[1,6,4,2,8,5,3,7]=>0110110=>1001001
[7,6,5,8,2,4,3,1]=>1101011=>0010100
[7,6,5,8,3,1,4,2]=>1101101=>0010010
[2,6,4,3,8,1,7,5]=>0110101=>1001010
[2,6,4,3,8,5,7,1]=>0110101=>1001010
[7,2,3,1,5,8,6,4]=>1010011=>0101100
[7,1,5,6,3,8,4,2]=>1001011=>0110100
[7,3,6,5,1,4,8,2]=>1011001=>0100110
[7,2,6,5,3,8,1,4]=>1011010=>0100101
[7,2,3,1,4,8,6,5]=>1010011=>0101100
[7,2,3,5,4,8,6,1]=>1001011=>0110100
[2,6,4,5,8,1,7,3]=>0100101=>1011010
[1,5,6,4,8,3,7,2]=>0010101=>1101010
[2,5,6,4,8,3,1,7]=>0010110=>1101001
[3,5,6,1,4,7,8,2]=>0010001=>1101110
[7,6,1,3,4,5,8,2]=>1100001=>0011110
[7,1,3,2,4,8,5,6]=>1010010=>0101101
[7,6,1,5,3,4,8,2]=>1101001=>0010110
[7,6,1,5,4,3,8,2]=>1101101=>0010010
[1,6,4,5,8,3,2,7]=>0100110=>1011001
[7,6,5,8,1,3,2,4]=>1101010=>0010101
[3,4,6,8,7,2,1,5]=>0001110=>1110001
[3,5,6,8,2,1,7,4]=>0001101=>1110010
[4,2,1,5,3,7,8,6]=>1101001=>0010110
[4,2,5,6,3,1,8,7]=>1001101=>0110010
[3,5,6,8,1,7,2,4]=>0001010=>1110101
[4,1,5,6,3,2,8,7]=>1001101=>0110010
[4,5,3,1,7,2,8,6]=>0110101=>1001010
[4,1,3,5,2,7,8,6]=>1001001=>0110110
[2,5,4,7,3,8,6,1]=>0101011=>1010100
[3,5,7,1,8,4,2,6]=>0010110=>1101001
[4,1,5,3,2,7,8,6]=>1011001=>0100110
[4,5,3,7,1,2,8,6]=>0101001=>1010110
[4,3,6,1,2,7,5,8]=>1010010=>0101101
[5,1,3,2,4,6,7,8]=>1010000=>0101111
[3,6,1,7,4,5,2,8]=>0101010=>1010101
[5,1,3,4,2,6,7,8]=>1001000=>0110111
[5,3,1,4,2,6,7,8]=>1101000=>0010111
[4,5,2,3,7,1,8,6]=>0100101=>1011010
[4,2,6,1,3,7,5,8]=>1010010=>0101101
[4,6,2,1,3,7,5,8]=>0110010=>1001101
[3,6,2,1,7,4,8,5]=>0110101=>1001010
[3,1,4,7,6,5,2,8]=>1001110=>0110001
[3,6,2,7,1,5,8,4]=>0101001=>1010110
[4,6,2,7,1,3,5,8]=>0101000=>1010111
[3,5,7,1,8,2,6,4]=>0010101=>1101010
[5,1,4,2,3,6,7,8]=>1010000=>0101111
[3,6,1,7,2,5,8,4]=>0101001=>1010110
[2,6,5,3,4,7,8,1]=>0110001=>1001110
[3,6,1,7,5,4,2,8]=>0101110=>1010001
[5,1,4,3,2,6,7,8]=>1011000=>0100111
[5,4,1,3,2,6,7,8]=>1101000=>0010111
[6,4,2,5,3,8,1,7]=>1101010=>0010101
[4,6,2,3,5,1,8,7]=>0100101=>1011010
[6,2,4,5,1,8,3,7]=>1001010=>0110101
[8,2,6,7,1,4,5,3]=>1001001=>0110110
[8,2,6,7,4,1,5,3]=>1001101=>0110010
[4,6,2,3,5,8,1,7]=>0100010=>1011101
[2,6,4,1,5,8,3,7]=>0110010=>1001101
[2,8,1,6,7,4,5,3]=>0100101=>1011010
[6,8,4,5,7,2,3,1]=>0100101=>1011010
[2,8,6,1,4,7,5,3]=>0110011=>1001100
[2,8,1,6,4,7,5,3]=>0101011=>1010100
[2,6,1,4,8,5,3,7]=>0100110=>1011001
[6,4,5,2,8,3,1,7]=>1010110=>0101001
[4,2,3,6,1,8,5,7]=>1001010=>0110101
[4,2,3,1,6,8,5,7]=>1010010=>0101101
[4,2,3,8,6,1,7,5]=>1001101=>0110010
[6,4,5,8,2,3,7,1]=>1001001=>0110110
[8,6,7,2,4,5,1,3]=>1010010=>0101101
[6,4,8,5,2,3,7,1]=>1011001=>0100110
[4,2,8,3,1,6,7,5]=>1011001=>0100110
[2,4,8,1,3,6,7,5]=>0010001=>1101110
[2,4,1,8,3,6,7,5]=>0101001=>1010110
[2,1,4,8,6,3,7,5]=>1001101=>0110010
[6,4,8,2,5,3,7,1]=>1010101=>0101010
[8,6,2,4,7,5,1,3]=>1100110=>0011001
[4,6,8,2,3,5,7,1]=>0010001=>1101110
[2,6,8,4,1,5,7,3]=>0011001=>1100110
[2,6,8,1,4,5,7,3]=>0010001=>1101110
[2,1,6,8,4,5,7,3]=>1001001=>0110110
[2,8,1,4,6,7,3,5]=>0100010=>1011101
[4,8,6,2,3,7,5,1]=>0110011=>1001100
[8,4,2,6,7,3,1,5]=>1100110=>0011001
[7,6,4,5,1,3,8,2]=>1101001=>0010110
[1,6,7,5,3,4,8,2]=>0011001=>1100110
[7,6,2,3,8,4,1,5]=>1100110=>0011001
[1,6,7,5,8,2,3,4]=>0010100=>1101011
[6,2,5,8,3,4,7,1]=>1001001=>0110110
[6,2,3,8,7,4,1,5]=>1001110=>0110001
[2,4,7,3,5,8,6,1]=>0010011=>1101100
[2,5,3,7,1,8,4,6]=>0101010=>1010101
[5,2,8,3,1,4,6,7]=>1011000=>0100111
[4,8,2,3,6,5,7,1]=>0100101=>1011010
[5,8,1,3,6,4,7,2]=>0100101=>1011010
[5,8,1,4,3,6,2,7]=>0101010=>1010101
[5,8,4,1,3,7,6,2]=>0110011=>1001100
[6,4,5,3,8,1,7,2]=>1010101=>0101010
[4,6,5,3,7,1,2,8]=>0110100=>1001011
[4,5,1,3,6,2,8,7]=>0100101=>1011010
[4,2,6,5,1,7,3,8]=>1011010=>0100101
[4,3,5,7,2,1,6,8]=>1001100=>0110011
[3,4,7,6,8,1,2,5]=>0010100=>1101011
[3,4,6,2,5,8,7,1]=>0010011=>1101100
[3,5,2,4,6,1,8,7]=>0100101=>1011010
[4,2,5,1,6,8,3,7]=>1010010=>0101101
[1,8,2,3,6,5,7,4]=>0100101=>1011010
[4,2,8,3,5,7,1,6]=>1010010=>0101101
[4,3,8,6,5,7,1,2]=>1011010=>0100101
[1,3,7,2,6,5,8,4]=>0010101=>1101010
[1,3,6,4,2,5,8,7]=>0011001=>1100110
[1,5,4,7,3,6,8,2]=>0101001=>1010110
[5,2,3,8,4,1,7,6]=>1001101=>0110010
[7,5,3,4,8,2,1,6]=>1100110=>0011001
[7,2,8,3,4,1,5,6]=>1010100=>0101011
[7,4,3,8,5,2,6,1]=>1101101=>0010010
[4,6,2,7,3,1,5,8]=>0101100=>1010011
[7,6,3,8,2,4,5,1]=>1101001=>0010110
[7,2,8,5,1,3,4,6]=>1011000=>0100111
[1,5,3,7,6,8,4,2]=>0101011=>1010100
[1,6,3,7,8,2,4,5]=>0100100=>1011011
[1,4,3,7,8,5,2,6]=>0100110=>1011001
[4,2,6,5,7,8,3,1]=>1010011=>0101100
[4,2,6,7,5,8,1,3]=>1001010=>0110101
[3,2,4,7,8,5,1,6]=>1000110=>0111001
[3,2,6,7,8,1,4,5]=>1000100=>0111011
[5,1,8,3,6,4,7,2]=>1010101=>0101010
[3,6,8,5,7,2,1,4]=>0010110=>1101001
[5,1,3,8,7,6,4,2]=>1001111=>0110000
[3,8,5,6,1,7,2,4]=>0101010=>1010101
[3,4,8,1,7,6,2,5]=>0010110=>1101001
[4,7,6,8,5,1,3,2]=>0101101=>1010010
[6,7,4,8,5,1,3,2]=>0101101=>1010010
[6,4,8,3,1,7,5,2]=>1011011=>0100100
[3,6,5,8,7,1,4,2]=>0101101=>1010010
[5,7,4,8,2,6,3,1]=>0101011=>1010100
[5,6,4,8,2,7,3,1]=>0101011=>1010100
[6,5,3,8,2,7,4,1]=>1101011=>0010100
[6,4,8,1,3,7,5,2]=>1010011=>0101100
[7,6,3,1,4,2,5,8]=>1110100=>0001011
[1,5,4,3,7,8,2,6]=>0110010=>1001101
[7,8,4,2,5,3,1,6]=>0110110=>1001001
[4,2,7,8,5,3,1,6]=>1001110=>0110001
[4,2,5,3,1,7,8,6]=>1011001=>0100110
[4,2,8,7,6,3,1,5]=>1011110=>0100001
[4,2,7,6,3,1,5,8]=>1011100=>0100011
[6,3,1,7,5,2,4,8]=>1101100=>0010011
[6,3,1,8,7,5,2,4]=>1101110=>0010001
[8,6,3,1,7,5,2,4]=>1110110=>0001001
[4,2,7,6,3,1,8,5]=>1011101=>0100010
[7,6,3,1,8,4,2,5]=>1110110=>0001001
[7,6,4,2,1,8,3,5]=>1111010=>0000101
[1,8,2,7,6,4,3,5]=>0101110=>1010001
[8,3,5,7,6,4,2,1]=>1001111=>0110000
[8,4,2,5,7,6,3,1]=>1100111=>0011000
[7,5,2,4,8,6,3,1]=>1100111=>0011000
[8,7,5,2,4,6,3,1]=>1110011=>0001100
[7,5,2,4,6,3,1,8]=>1100110=>0011001
[5,2,8,6,3,7,4,1]=>1011011=>0100100
[8,4,7,5,2,6,3,1]=>1011011=>0100100
[8,3,6,4,7,5,2,1]=>1010111=>0101000
[1,8,2,7,5,3,6,4]=>0101101=>1010010
[7,5,2,1,8,3,6,4]=>1110101=>0001010
[7,5,2,6,3,1,8,4]=>1101101=>0010010
[5,2,7,4,1,8,6,3]=>1011011=>0100100
[5,2,8,7,4,1,6,3]=>1011101=>0100010
[8,7,4,1,5,2,6,3]=>1110101=>0001010
[7,4,1,5,2,8,6,3]=>1101011=>0010100
[7,6,3,1,4,2,8,5]=>1110101=>0001010
[7,5,2,8,6,3,1,4]=>1101110=>0010001
[8,7,5,2,6,3,1,4]=>1110110=>0001001
[7,5,2,1,3,6,4,8]=>1110010=>0001101
[8,7,5,2,1,3,6,4]=>1111001=>0000110
[7,5,2,1,3,8,6,4]=>1110011=>0001100
[1,3,7,6,5,8,2,4]=>0011010=>1100101
[8,6,4,7,5,2,1,3]=>1101110=>0010001
[6,4,8,7,5,2,1,3]=>1011110=>0100001
[6,4,7,5,2,1,3,8]=>1011100=>0100011
[6,3,1,4,7,5,2,8]=>1100110=>0011001
[6,3,1,4,8,7,5,2]=>1100111=>0011000
[8,6,3,1,4,7,5,2]=>1110011=>0001100
[8,5,7,6,3,1,4,2]=>1011101=>0100010
[1,8,2,5,7,6,4,3]=>0100111=>1011000
[1,8,2,6,4,7,5,3]=>0101011=>1010100
[7,5,2,1,6,4,8,3]=>1110101=>0001010
[6,3,8,7,4,1,5,2]=>1011101=>0100010
[6,3,7,4,1,5,2,8]=>1011010=>0100101
[7,4,1,6,3,5,2,8]=>1101010=>0010101
[7,4,1,8,6,3,5,2]=>1101101=>0010010
[8,4,6,3,1,7,5,2]=>1011011=>0100100
[6,4,7,5,2,1,8,3]=>1011101=>0100010
[1,6,4,7,5,3,8,2]=>0101101=>1010010
[8,6,3,5,2,7,4,1]=>1101011=>0010100
[6,3,5,2,8,7,4,1]=>1010111=>0101000
[6,3,5,2,7,4,1,8]=>1010110=>0101001
[1,4,7,3,5,2,6,8]=>0010100=>1101011
[5,7,4,2,6,3,1,8]=>0110110=>1001001
[4,2,6,3,5,7,1,8]=>1010010=>0101101
[2,4,5,8,1,6,7,3]=>0001001=>1110110
[6,1,3,7,4,2,5,8]=>1001100=>0110011
[3,2,6,8,1,5,7,4]=>1001001=>0110110
[8,2,6,1,5,4,7,3]=>1010101=>0101010
[8,6,2,7,1,5,4,3]=>1101011=>0010100
[7,6,8,3,1,5,4,2]=>1011011=>0100100
[6,3,7,2,8,1,5,4]=>1010101=>0101010
[7,5,2,8,6,1,4,3]=>1101101=>0010010
[2,7,3,8,1,5,6,4]=>0101001=>1010110
[1,6,8,5,2,4,3,7]=>0011010=>1100101
[4,5,7,2,8,1,6,3]=>0010101=>1101010
[8,4,6,5,3,1,7,2]=>1011101=>0100010
[4,5,3,1,7,2,6,8]=>0110100=>1001011
[7,8,1,2,4,3,6,5]=>0100101=>1011010
[8,4,1,6,2,3,7,5]=>1101001=>0010110
[4,1,3,6,5,7,8,2]=>1001001=>0110110
[6,1,3,4,2,8,5,7]=>1001010=>0110101
[8,1,4,2,5,7,6,3]=>1010011=>0101100
[8,1,4,3,5,7,6,2]=>1010011=>0101100
[5,2,4,1,3,7,8,6]=>1010001=>0101110
[2,6,5,3,1,7,8,4]=>0111001=>1000110
[8,3,2,1,5,7,6,4]=>1110011=>0001100
[1,7,4,3,6,8,2,5]=>0110010=>1001101
[2,7,6,3,1,8,4,5]=>0111010=>1000101
[2,8,4,6,3,7,5,1]=>0101011=>1010100
[8,7,1,3,6,5,4,2]=>1100111=>0011000
[1,8,5,7,4,2,6,3]=>0101101=>1010010
[3,8,6,5,7,1,4,2]=>0110101=>1001010
[4,8,6,2,7,1,5,3]=>0110101=>1001010
[4,7,5,3,8,2,1,6]=>0110110=>1001001
[1,6,5,8,3,4,2,7]=>0101010=>1010101
[6,1,5,3,8,4,2,7]=>1010110=>0101001
[8,1,5,4,7,2,6,3]=>1010101=>0101010
[2,1,4,7,5,8,3,6]=>1001010=>0110101
[6,3,5,8,7,4,1,2]=>1001110=>0110001
[4,7,2,8,5,6,3,1]=>0101011=>1010100
[1,4,8,7,3,5,6,2]=>0011001=>1100110
[8,1,7,6,3,5,4,2]=>1011011=>0100100
[3,6,8,5,7,4,1,2]=>0010110=>1101001
[4,7,6,8,5,3,1,2]=>0101110=>1010001
[5,7,2,8,6,4,1,3]=>0101110=>1010001
[3,8,7,5,6,4,2,1]=>0110111=>1001000
[2,8,7,6,4,5,3,1]=>0111011=>1000100
[1,8,7,6,5,3,4,2]=>0111101=>1000010
[4,6,7,2,5,3,1,8]=>0010110=>1101001
[2,4,7,8,1,6,5,3]=>0001011=>1110100
[4,2,6,8,7,1,5,3]=>1001101=>0110010
[5,1,8,4,2,7,6,3]=>1011011=>0100100
[6,8,3,7,1,5,4,2]=>0101011=>1010100
[2,7,3,8,1,6,5,4]=>0101011=>1010100
[2,6,8,4,1,7,5,3]=>0011011=>1100100
[4,6,7,1,2,8,5,3]=>0010011=>1101100
[3,6,1,8,2,7,5,4]=>0101011=>1010100
[5,7,4,1,2,8,6,3]=>0110011=>1001100
[6,3,7,1,2,8,5,4]=>1010011=>0101100
[8,1,5,6,3,2,4,7]=>1001100=>0110011
[1,7,8,3,5,2,4,6]=>0010100=>1101011
[8,5,3,7,2,4,6,1]=>1101001=>0010110
[1,7,2,4,8,5,3,6]=>0100110=>1011001
[1,7,8,5,4,3,2,6]=>0011110=>1100001
[2,6,8,7,4,3,5,1]=>0011101=>1100010
[1,2,6,7,8,4,3,5]=>0000110=>1111001
[2,7,5,8,4,1,3,6]=>0101100=>1010011
[2,1,7,8,4,5,3,6]=>1001010=>0110101
[3,7,8,2,1,5,4,6]=>0011010=>1100101
[8,5,1,4,7,3,6,2]=>1100101=>0011010
[8,4,7,5,3,6,1,2]=>1011010=>0100101
[8,1,4,6,7,3,5,2]=>1000101=>0111010
[3,5,8,6,7,4,1,2]=>0010110=>1101001
[3,6,8,4,7,1,5,2]=>0010101=>1101010
[4,7,1,3,6,8,2,5]=>0100010=>1011101
[3,7,6,4,8,1,2,5]=>0110100=>1001011
[3,1,7,5,6,8,2,4]=>1010010=>0101101
[2,3,6,5,7,1,8,4]=>0010101=>1101010
[3,7,5,4,2,1,8,6]=>0111101=>1000010
[1,3,6,7,4,2,8,5]=>0001101=>1110010
[3,6,4,8,2,7,5,1]=>0101011=>1010100
[1,4,6,3,2,7,8,5]=>0011001=>1100110
[8,7,1,5,6,3,2,4]=>1100110=>0011001
[8,1,6,7,5,3,2,4]=>1001110=>0110001
[1,7,8,6,5,3,2,4]=>0011110=>1100001
[8,7,2,4,6,5,3,1]=>1100111=>0011000
[1,7,8,2,6,4,5,3]=>0010101=>1101010
[8,7,2,5,4,6,1,3]=>1101010=>0010101
[8,7,2,5,3,1,6,4]=>1101101=>0010010
[8,7,3,2,1,5,6,4]=>1111001=>0000110
[8,2,6,7,3,1,5,4]=>1001101=>0110010
[1,7,2,8,5,6,4,3]=>0101011=>1010100
[2,7,1,8,4,6,5,3]=>0101011=>1010100
[3,7,8,2,1,6,5,4]=>0011011=>1100100
[8,7,6,1,4,5,3,2]=>1110011=>0001100
[4,8,1,2,3,7,5,6]=>0100010=>1011101
[1,8,2,3,6,5,4,7]=>0100110=>1011001
[3,5,8,4,7,2,6,1]=>0010101=>1101010
[1,8,5,4,6,2,3,7]=>0110100=>1001011
[3,8,5,4,6,1,2,7]=>0110100=>1001011
[3,8,5,1,6,4,2,7]=>0110110=>1001001
[2,8,5,4,6,1,3,7]=>0110100=>1001011
[2,8,5,4,6,3,1,7]=>0110110=>1001001
[1,8,5,4,6,3,2,7]=>0110110=>1001001
[2,5,8,4,7,3,6,1]=>0010101=>1101010
[3,6,4,2,7,8,5,1]=>0110011=>1001100
[3,5,4,1,6,2,7,8]=>0110100=>1001011
[4,5,8,1,7,6,2,3]=>0010110=>1101001
[3,5,8,4,7,1,6,2]=>0010101=>1101010
[1,5,8,4,7,3,6,2]=>0010101=>1101010
[3,6,4,1,7,8,5,2]=>0110011=>1001100
[3,6,4,8,7,5,2,1]=>0101111=>1010000
[1,6,4,3,7,8,5,2]=>0110011=>1001100
[7,1,3,4,8,6,5,2]=>1000111=>0111000
[7,6,1,3,8,4,2,5]=>1100110=>0011001
[1,6,4,2,7,8,3,5]=>0110010=>1001101
[2,6,4,3,7,1,8,5]=>0110101=>1001010
[2,6,4,1,7,8,3,5]=>0110010=>1001101
[7,2,3,4,8,6,5,1]=>1000111=>0111000
[7,2,3,1,8,6,4,5]=>1010110=>0101001
[7,2,3,4,1,6,8,5]=>1001001=>0110110
[1,2,4,3,8,5,7,6]=>0010101=>1101010
[7,3,8,6,1,4,2,5]=>1011010=>0100101
[7,2,8,6,3,4,1,5]=>1011010=>0100101
[7,2,3,1,5,6,8,4]=>1010001=>0101110
[7,2,3,8,1,6,5,4]=>1001011=>0110100
[7,2,3,8,5,6,4,1]=>1001011=>0110100
[2,6,4,8,7,1,5,3]=>0101101=>1010010
[1,5,8,4,7,6,2,3]=>0010110=>1101001
[3,5,8,1,6,7,2,4]=>0010010=>1101101
[7,6,1,3,5,8,2,4]=>1100010=>0011101
[7,1,3,2,5,6,8,4]=>1010001=>0101110
[7,1,3,8,2,6,5,4]=>1001011=>0110100
[7,6,1,8,5,4,2,3]=>1101110=>0010001
[3,2,6,5,8,4,7,1]=>1010101=>0101010
[4,3,7,1,6,5,8,2]=>1010101=>0101010
[5,2,6,4,8,3,7,1]=>1010101=>0101010
[4,3,7,5,8,2,6,1]=>1010101=>0101010
[5,3,7,4,8,2,6,1]=>1010101=>0101010
[5,3,7,4,8,1,6,2]=>1010101=>0101010
[5,4,8,1,6,2,7,3]=>1010101=>0101010
[4,3,7,1,5,2,8,6]=>1010101=>0101010
[5,4,8,2,6,3,7,1]=>1010101=>0101010
[5,4,8,1,6,3,7,2]=>1010101=>0101010
[4,1,7,5,2,3,6,8]=>1011000=>0100111
[4,1,7,8,6,3,2,5]=>1001110=>0110001
[4,7,2,8,3,5,1,6]=>0101010=>1010101
[6,8,3,2,1,4,7,5]=>0111001=>1000110
[7,2,4,1,6,5,8,3]=>1010101=>0101010
[7,5,8,4,3,1,6,2]=>1011101=>0100010
[6,8,2,4,1,3,7,5]=>0101001=>1010110
[2,8,4,7,6,3,5,1]=>0101101=>1010010
[6,1,2,7,5,8,4,3]=>1001011=>0110100
[4,2,7,3,8,5,6,1]=>1010101=>0101010
[4,5,2,6,8,3,7,1]=>0100101=>1011010
[4,8,3,2,5,7,6,1]=>0110011=>1001100
[7,2,4,3,8,5,6,1]=>1010101=>0101010
[6,8,5,3,4,7,2,1]=>0110011=>1001100
[8,4,7,6,2,3,5,1]=>1011001=>0100110
[6,8,4,1,5,3,7,2]=>0110101=>1001010
[8,3,4,7,6,2,5,1]=>1001101=>0110010
[1,8,3,5,2,6,7,4]=>0101001=>1010110
[6,8,3,5,1,4,7,2]=>0101001=>1010110
[6,8,5,4,2,3,7,1]=>0111001=>1000110
[5,8,2,4,3,7,6,1]=>0101011=>1010100
[8,2,1,3,5,6,4,7]=>1100010=>0011101
[8,2,1,3,5,4,7,6]=>1100101=>0011010
[8,2,1,3,4,6,7,5]=>1100001=>0011110
[8,1,3,4,2,6,5,7]=>1001010=>0110101
[8,1,3,4,2,5,7,6]=>1001001=>0110110
[8,1,3,2,5,6,4,7]=>1010010=>0101101
[8,1,2,4,5,3,7,6]=>1000101=>0111010
[8,1,2,4,3,6,7,5]=>1001001=>0110110
[10,2,1,4,3,6,5,8,7,9]=>110101010=>001010101
[10,2,1,4,3,6,5,7,9,8]=>110101001=>001010110
[10,2,1,4,3,5,7,8,6,9]=>110100010=>001011101
[10,2,1,4,3,5,7,6,9,8]=>110100101=>001011010
[10,2,1,4,3,5,6,8,9,7]=>110100001=>001011110
[10,2,1,3,5,6,4,8,7,9]=>110001010=>001110101
[10,2,1,3,5,6,4,7,9,8]=>110001001=>001110110
[10,2,1,3,5,4,7,8,6,9]=>110010010=>001101101
[10,2,1,3,5,4,7,6,9,8]=>110010101=>001101010
[10,2,1,3,5,4,6,8,9,7]=>110010001=>001101110
[10,2,1,3,4,6,7,8,5,9]=>110000010=>001111101
[10,2,1,3,4,6,7,5,9,8]=>110000101=>001111010
[10,2,1,3,4,6,5,8,9,7]=>110001001=>001110110
[10,2,1,3,4,5,7,8,9,6]=>110000001=>001111110
[10,1,3,4,2,6,5,8,7,9]=>100101010=>011010101
[10,1,3,4,2,6,5,7,9,8]=>100101001=>011010110
[10,1,3,4,2,5,7,8,6,9]=>100100010=>011011101
[10,1,3,4,2,5,7,6,9,8]=>100100101=>011011010
[10,1,3,4,2,5,6,8,9,7]=>100100001=>011011110
[10,1,3,2,5,6,4,8,7,9]=>101001010=>010110101
[10,1,3,2,5,6,4,7,9,8]=>101001001=>010110110
[10,1,3,2,5,4,7,8,6,9]=>101010010=>010101101
[10,1,3,2,5,4,7,6,9,8]=>101010101=>010101010
[10,1,3,2,5,4,6,8,9,7]=>101010001=>010101110
[10,1,3,2,4,6,7,8,5,9]=>101000010=>010111101
[10,1,3,2,4,6,7,5,9,8]=>101000101=>010111010
[10,1,3,2,4,6,5,8,9,7]=>101001001=>010110110
[10,1,3,2,4,5,7,8,9,6]=>101000001=>010111110
[10,1,2,4,5,6,3,8,7,9]=>100001010=>011110101
[10,1,2,4,5,6,3,7,9,8]=>100001001=>011110110
[10,1,2,4,5,3,7,8,6,9]=>100010010=>011101101
[10,1,2,4,5,3,7,6,9,8]=>100010101=>011101010
[10,1,2,4,5,3,6,8,9,7]=>100010001=>011101110
[10,1,2,4,3,6,7,8,5,9]=>100100010=>011011101
[10,1,2,4,3,6,7,5,9,8]=>100100101=>011011010
[10,1,2,4,3,6,5,8,9,7]=>100101001=>011010110
[10,1,2,4,3,5,7,8,9,6]=>100100001=>011011110
[10,1,2,3,5,6,7,8,4,9]=>100000010=>011111101
[10,1,2,3,5,6,7,4,9,8]=>100000101=>011111010
[10,1,2,3,5,6,4,8,9,7]=>100001001=>011110110
[10,1,2,3,5,4,7,8,9,6]=>100010001=>011101110
[10,1,2,3,4,6,7,8,9,5]=>100000001=>011111110
[12,2,1,4,3,6,5,8,7,10,9,11]=>11010101010=>00101010101
[12,2,1,4,3,6,5,8,7,9,11,10]=>11010101001=>00101010110
[12,2,1,4,3,6,5,7,9,8,11,10]=>11010100101=>00101011010
[12,2,1,4,3,6,5,7,8,10,11,9]=>11010100001=>00101011110
[12,2,1,4,3,5,7,6,9,8,11,10]=>11010010101=>00101101010
[12,2,1,4,3,5,6,7,9,10,11,8]=>11010000001=>00101111110
[12,2,1,3,5,6,4,7,8,10,11,9]=>11000100001=>00111011110
[12,2,1,3,5,4,7,6,9,8,11,10]=>11001010101=>00110101010
[12,2,1,3,5,4,6,7,9,10,11,8]=>11001000001=>00110111110
[12,2,1,3,4,6,7,8,5,10,9,11]=>11000001010=>00111110101
[12,2,1,3,4,6,7,8,5,9,11,10]=>11000001001=>00111110110
[12,2,1,3,4,6,7,5,9,10,8,11]=>11000010010=>00111101101
[12,2,1,3,4,6,7,5,9,8,11,10]=>11000010101=>00111101010
[12,2,1,3,4,6,7,5,8,10,11,9]=>11000010001=>00111101110
[12,2,1,3,4,6,5,7,9,10,11,8]=>11000100001=>00111011110
[12,2,1,3,4,5,7,8,9,10,6,11]=>11000000010=>00111111101
[12,2,1,3,4,5,7,8,9,6,11,10]=>11000000101=>00111111010
[12,2,1,3,4,5,7,8,6,10,11,9]=>11000001001=>00111110110
[12,2,1,3,4,5,7,6,9,10,11,8]=>11000010001=>00111101110
[12,2,1,3,4,5,6,8,9,10,11,7]=>11000000001=>00111111110
[12,1,3,4,2,6,5,7,8,10,11,9]=>10010100001=>01101011110
[12,1,3,4,2,5,7,6,9,10,8,11]=>10010010010=>01101101101
[12,1,3,4,2,5,7,6,8,10,11,9]=>10010010001=>01101101110
[12,1,3,4,2,5,6,7,9,10,11,8]=>10010000001=>01101111110
[12,1,3,2,5,6,4,7,8,10,11,9]=>10100100001=>01011011110
[12,1,3,2,5,4,7,6,9,10,8,11]=>10101010010=>01010101101
[12,1,3,2,5,4,7,6,9,8,11,10]=>10101010101=>01010101010
[12,1,3,2,5,4,7,6,8,10,11,9]=>10101010001=>01010101110
[12,1,3,2,5,4,6,7,9,10,11,8]=>10101000001=>01010111110
[12,1,3,2,4,6,5,7,9,10,11,8]=>10100100001=>01011011110
[12,1,3,2,4,5,7,8,9,10,6,11]=>10100000010=>01011111101
[12,1,3,2,4,5,6,8,9,10,11,7]=>10100000001=>01011111110
[12,1,2,4,5,6,3,8,7,10,9,11]=>10000101010=>01111010101
[12,1,2,4,5,6,3,8,7,9,11,10]=>10000101001=>01111010110
[12,1,2,4,5,6,3,7,9,10,8,11]=>10000100010=>01111011101
[12,1,2,4,5,6,3,7,9,8,11,10]=>10000100101=>01111011010
[12,1,2,4,5,3,7,8,6,10,9,11]=>10001001010=>01110110101
[12,1,2,4,5,3,7,8,6,9,11,10]=>10001001001=>01110110110
[12,1,2,4,5,3,7,6,9,10,8,11]=>10001010010=>01110101101
[12,1,2,4,5,3,7,6,9,8,11,10]=>10001010101=>01110101010
[12,1,2,4,5,3,6,8,7,10,11,9]=>10001001001=>01110110110
[12,1,2,4,5,3,6,7,9,10,11,8]=>10001000001=>01110111110
[12,1,2,4,3,6,7,5,9,10,8,11]=>10010010010=>01101101101
[12,1,2,4,3,6,7,5,8,10,11,9]=>10010010001=>01101101110
[12,1,2,4,3,6,5,7,9,10,11,8]=>10010100001=>01101011110
[12,1,2,4,3,5,7,6,9,10,11,8]=>10010010001=>01101101110
[12,1,2,4,3,5,6,8,9,10,11,7]=>10010000001=>01101111110
[12,1,2,3,5,6,7,8,4,10,9,11]=>10000001010=>01111110101
[12,1,2,3,5,6,7,4,9,10,8,11]=>10000010010=>01111101101
[12,1,2,3,5,6,7,4,9,8,11,10]=>10000010101=>01111101010
[12,1,2,3,5,6,7,4,8,10,11,9]=>10000010001=>01111101110
[12,1,2,3,5,6,4,8,9,10,7,11]=>10000100010=>01111011101
[12,1,2,3,5,6,4,8,9,7,11,10]=>10000100101=>01111011010
[12,1,2,3,5,6,4,8,7,10,11,9]=>10000101001=>01111010110
[12,1,2,3,5,4,7,8,6,10,11,9]=>10001001001=>01110110110
[12,1,2,3,5,4,6,8,9,10,11,7]=>10001000001=>01110111110
[12,1,2,3,4,6,7,8,9,10,5,11]=>10000000010=>01111111101
[12,1,2,3,4,6,7,8,9,5,11,10]=>10000000101=>01111111010
[12,1,2,3,4,6,7,5,9,10,11,8]=>10000010001=>01111101110
[12,1,2,3,4,5,7,8,9,10,11,6]=>10000000001=>01111111110
[6,5,3,8,4,2,7,1]=>1101101=>0010010
[7,4,5,1,6,2,8,3]=>1010101=>0101010
[4,7,3,5,6,2,8,1]=>0100101=>1011010
[6,7,8,4,1,3,5,2]=>0011001=>1100110
[3,1,6,8,4,7,5,2]=>1001011=>0110100
[8,3,6,1,5,7,4,2]=>1010011=>0101100
[3,2,7,5,8,6,1,4]=>1010110=>0101001
[2,5,4,7,8,1,6,3]=>0100101=>1011010
[2,4,6,7,8,1,5,3]=>0000101=>1111010
[2,4,6,8,1,7,5,3]=>0001011=>1110100
[7,4,3,8,6,2,1,5]=>1101110=>0010001
[2,4,7,8,3,5,6,1]=>0001001=>1110110
[3,2,7,6,1,8,4,5]=>1011010=>0100101
[3,2,6,8,1,7,4,5]=>1001010=>0110101
[4,3,6,2,1,8,5,7]=>1011010=>0100101
[3,6,4,2,5,8,1,7]=>0110010=>1001101
[4,6,2,3,7,5,8,1]=>0100101=>1011010
[5,8,4,2,3,6,7,1]=>0110001=>1001110
[8,4,5,3,2,1,7,6]=>1011101=>0100010
[5,8,3,4,2,1,7,6]=>0101101=>1010010
[6,8,4,2,3,7,5,1]=>0110011=>1001100
[6,4,8,3,2,7,1,5]=>1011010=>0100101
[5,8,3,7,2,1,6,4]=>0101101=>1010010
[2,5,6,4,7,1,8,3]=>0010101=>1101010
[2,5,4,8,1,6,7,3]=>0101001=>1010110
[6,4,7,3,8,2,1,5]=>1010110=>0101001
[6,7,4,3,2,1,8,5]=>0111101=>1000010
[8,4,3,7,2,1,5,6]=>1101100=>0010011
[1,2,6,5,8,7,3,4]=>0010110=>1101001
[1,5,2,8,4,6,7,3]=>0101001=>1010110
[1,5,2,7,4,6,8,3]=>0101001=>1010110
[5,1,2,7,3,6,8,4]=>1001001=>0110110
[5,1,2,8,3,6,7,4]=>1001001=>0110110
[5,6,3,4,8,7,2,1]=>0100111=>1011000
[6,5,3,4,8,7,2,1]=>1100111=>0011000
[4,1,2,8,3,6,7,5]=>1001001=>0110110
[4,1,2,7,3,6,8,5]=>1001001=>0110110
[7,5,3,8,4,6,2,1]=>1101011=>0010100
[8,5,3,7,4,6,2,1]=>1101011=>0010100
[5,8,1,2,3,4,7,6]=>0100001=>1011110
[7,1,2,8,3,6,4,5]=>1001010=>0110101
[6,1,8,2,3,5,7,4]=>1010001=>0101110
[6,1,7,2,3,5,8,4]=>1010001=>0101110
[1,6,8,2,4,5,7,3]=>0010001=>1101110
[4,3,8,7,5,6,2,1]=>1011011=>0100100
[1,8,2,7,4,6,5,3]=>0101011=>1010100
[7,1,6,2,3,5,8,4]=>1010001=>0101110
[8,1,6,2,3,5,7,4]=>1010001=>0101110
[8,1,7,2,3,5,6,4]=>1010001=>0101110
[5,8,3,7,4,6,2,1]=>0101011=>1010100
[6,8,7,3,4,5,2,1]=>0110011=>1001100
[1,8,7,2,4,5,3,6]=>0110010=>1001101
[8,7,1,2,3,4,6,5]=>1100001=>0011110
[8,6,1,2,3,4,7,5]=>1100001=>0011110
[8,1,6,2,3,5,4,7]=>1010010=>0101101
[1,7,6,2,4,5,3,8]=>0110010=>1001101
[1,8,7,4,6,3,5,2]=>0110101=>1001010
[6,3,7,5,1,4,8,2]=>1011001=>0100110
[1,8,3,5,7,2,6,4]=>0100101=>1011010
[2,3,4,6,8,5,7,1]=>0000101=>1111010
[2,3,5,7,4,8,6,1]=>0001011=>1110100
[2,4,6,3,7,8,5,1]=>0010011=>1101100
[2,5,7,1,8,6,3,4]=>0010110=>1101001
[1,3,8,5,2,4,6,7]=>0011000=>1100111
[2,6,7,1,8,4,5,3]=>0010101=>1101010
[5,8,3,1,4,2,6,7]=>0110100=>1001011
[3,8,4,2,6,7,1,5]=>0110010=>1001101
[2,4,1,8,5,6,3,7]=>0101010=>1010101
[1,6,2,7,8,5,3,4]=>0100110=>1011001
[3,5,2,6,7,8,4,1]=>0100011=>1011100
[4,5,1,6,7,3,8,2]=>0100101=>1011010
[2,8,4,1,7,5,3,6]=>0110110=>1001001
[8,5,3,1,7,4,2,6]=>1110110=>0001001
[4,2,8,7,1,5,3,6]=>1011010=>0100101
[5,2,6,8,1,7,4,3]=>1001011=>0110100
[5,7,3,2,6,8,1,4]=>0110010=>1001101
[8,4,7,3,1,6,2,5]=>1011010=>0100101
[6,7,1,2,3,5,8,4]=>0100001=>1011110
[3,1,6,7,8,4,2,5]=>1000110=>0111001
[3,1,4,8,5,6,2,7]=>1001010=>0110101
[8,3,1,4,5,7,2,6]=>1100010=>0011101
[1,6,7,8,9,2,3,4,5]=>00001000=>11110111
[6,7,8,9,1,2,3,4,5,10]=>000100000=>111011111
[6,7,8,1,2,3,4,5,9]=>00100000=>11011111
[1,7,8,9,2,3,4,5,6]=>00010000=>11101111
[1,7,8,9,10,2,3,4,5,6]=>000010000=>111101111
[6,7,8,9,10,1,2,3,4,5,11]=>0000100000=>1111011111
[5,6,7,8,9,1,2,3,4,10]=>000010000=>111101111
[5,6,7,1,8,2,3,4,9]=>00101000=>11010111
[4,6,7,8,1,2,3,5,9]=>00010000=>11101111
[1,6,7,8,2,9,3,4,5]=>00010100=>11101011
[1,5,7,8,9,2,3,4,6]=>00001000=>11110111
[1,6,7,8,9,10,2,3,4,5]=>000001000=>111110111
[1,7,8,9,10,11,2,3,4,5,6]=>0000010000=>1111101111
[8,6,2,3,5,1,4,7]=>1100100=>0011011
[8,2,4,5,7,3,1,6]=>1000110=>0111001
[2,6,3,8,7,5,4,1]=>0101111=>1010000
[8,2,3,7,5,4,1,6]=>1001110=>0110001
[8,2,6,3,5,4,1,7]=>1010110=>0101001
[8,6,1,5,2,4,3,7]=>1101010=>0010101
[8,6,2,4,1,5,3,7]=>1101010=>0010101
[8,4,1,6,5,3,2,7]=>1101110=>0010001
[8,3,6,1,5,4,2,7]=>1010110=>0101001
[8,3,2,6,5,4,1,7]=>1101110=>0010001
[8,3,2,5,7,4,1,6]=>1100110=>0011001
[8,3,1,7,5,4,2,6]=>1101110=>0010001
[8,2,7,4,1,5,3,6]=>1011010=>0100101
[6,1,3,8,7,5,4,2]=>1001111=>0110000
[3,6,1,8,7,5,4,2]=>0101111=>1010000
[3,8,1,5,7,6,4,2]=>0100111=>1011000
[3,5,2,8,7,6,4,1]=>0101111=>1010000
[3,4,8,2,7,6,5,1]=>0010111=>1101000
[3,4,8,7,1,6,5,2]=>0011011=>1100100
[8,1,3,5,7,6,4,2]=>1000111=>0111000
[4,1,8,5,7,6,3,2]=>1010111=>0101000
[8,2,7,1,4,5,6,3]=>1010001=>0101110
[8,1,7,3,4,6,2,5]=>1010010=>0101101
[8,3,1,7,2,6,5,4]=>1101011=>0010100
[3,8,2,4,7,6,5,1]=>0100111=>1011000
[2,8,3,7,4,6,5,1]=>0101011=>1010100
[8,2,3,7,1,6,5,4]=>1001011=>0110100
[8,2,7,1,3,6,5,4]=>1010011=>0101100
[8,1,7,2,6,4,3,5]=>1010110=>0101001
[8,1,7,5,2,4,3,6]=>1011010=>0100101
[8,2,3,7,4,6,1,5]=>1001010=>0110101
[2,4,8,5,7,6,3,1]=>0010111=>1101000
[8,2,4,3,7,6,1,5]=>1010110=>0101001
[8,2,7,3,5,1,4,6]=>1010100=>0101011
[8,2,7,4,3,1,5,6]=>1011100=>0100011
[8,2,7,3,1,5,6,4]=>1011001=>0100110
[8,2,1,5,7,6,4,3]=>1100111=>0011000
[6,2,1,8,7,5,4,3]=>1101111=>0010000
[6,1,8,2,7,5,4,3]=>1010111=>0101000
[8,1,7,3,5,2,6,4]=>1010101=>0101010
[8,1,5,2,7,6,4,3]=>1010111=>0101000
[8,1,7,2,4,6,5,3]=>1010011=>0101100
[8,2,4,1,7,6,5,3]=>1010111=>0101000
[4,2,8,3,7,6,5,1]=>1010111=>0101000
[4,8,2,1,7,6,5,3]=>0110111=>1001000
[5,1,8,7,2,6,4,3]=>1011011=>0100100
[5,8,1,3,7,6,2,4]=>0100110=>1011001
[8,2,5,4,1,7,6,3]=>1011011=>0100100
[5,1,4,8,7,6,3,2]=>1001111=>0110000
[8,1,4,3,7,6,5,2]=>1010111=>0101000
[4,8,1,3,7,6,5,2]=>0100111=>1011000
[4,3,8,1,7,6,5,2]=>1010111=>0101000
[5,8,6,3,2,1,7,4]=>0111101=>1000010
[5,7,6,3,2,4,1,8]=>0111010=>1000101
[6,5,7,2,4,3,1,8]=>1010110=>0101001
[5,7,1,3,2,8,6,4]=>0101011=>1010100
[5,8,1,3,2,7,4,6]=>0101010=>1010101
[8,5,1,3,2,4,6,7]=>1101000=>0010111
[7,5,1,3,2,4,8,6]=>1101001=>0010110
[7,5,8,2,1,4,3,6]=>1011010=>0100101
[6,7,1,2,5,4,8,3]=>0100101=>1011010
[6,8,1,2,5,7,4,3]=>0100011=>1011100
[7,1,2,3,8,6,4,5]=>1000110=>0111001
[8,1,6,4,2,3,5,7]=>1011000=>0100111
[1,5,4,8,2,3,7,6]=>0101001=>1010110
[1,7,8,2,3,5,6,4]=>0010001=>1101110
[7,5,8,2,3,1,4,6]=>1010100=>0101011
[7,4,1,2,6,8,3,5]=>1100010=>0011101
[6,2,8,1,5,7,3,4]=>1010010=>0101101
[7,2,5,4,1,8,6,3]=>1011011=>0100100
[7,3,5,4,2,1,8,6]=>1011101=>0100010
[7,3,2,8,5,6,1,4]=>1101010=>0010101
[1,7,4,3,6,8,5,2]=>0110011=>1001100
[4,7,6,5,2,3,8,1]=>0111001=>1000110
[5,4,6,8,7,2,1,3]=>1001110=>0110001
[6,7,4,2,1,8,5,3]=>0111011=>1000100
[1,7,6,3,2,8,4,5]=>0111010=>1000101
[6,5,8,1,7,3,4,2]=>1010101=>0101010
[6,5,8,2,3,7,4,1]=>1010011=>0101100
[6,5,8,3,4,1,7,2]=>1010101=>0101010
[4,1,2,8,5,3,6,7]=>1001100=>0110011
[3,5,8,2,6,1,7,4]=>0010101=>1101010
[3,7,6,1,5,2,8,4]=>0110101=>1001010
[1,7,6,2,5,8,4,3]=>0110011=>1001100
[1,7,6,5,8,4,2,3]=>0110110=>1001001
[3,7,6,2,8,4,5,1]=>0110101=>1001010
[4,3,6,8,5,1,2,7]=>1001100=>0110011
[2,7,1,5,8,4,3,6]=>0100110=>1011001
[2,7,6,1,8,4,3,5]=>0110110=>1001001
[7,1,2,6,3,5,4,8]=>1001010=>0110101
[7,2,6,3,4,5,1,8]=>1010010=>0101101
[6,1,2,5,7,8,4,3]=>1000011=>0111100
[4,1,2,7,8,5,3,6]=>1000110=>0111001
[4,7,3,1,2,6,8,5]=>0110001=>1001110
[3,7,6,1,5,8,2,4]=>0110010=>1001101
[3,8,5,6,4,2,7,1]=>0101101=>1010010
[3,2,6,4,7,8,5,1]=>1010011=>0101100
[4,2,7,5,8,3,1,6]=>1010110=>0101001
[4,2,7,1,3,8,6,5]=>1010011=>0101100
[5,2,1,4,7,8,3,6]=>1100010=>0011101
[5,6,2,7,3,4,8,1]=>0101001=>1010110
[6,1,3,8,5,4,7,2]=>1001101=>0110010
[2,7,6,8,5,1,3,4]=>0101100=>1010011
[2,7,6,8,5,3,1,4]=>0101110=>1010001
[1,5,8,6,4,2,3,7]=>0011100=>1100011
[2,5,8,6,4,1,7,3]=>0011101=>1100010
[1,6,2,3,5,8,7,4]=>0100011=>1011100
[4,7,2,3,1,6,8,5]=>0101001=>1010110
[6,7,3,1,5,4,8,2]=>0110101=>1001010
[7,4,6,2,8,3,5,1]=>1010101=>0101010
[7,3,5,1,4,8,2,6]=>1010010=>0101101
[3,4,6,5,1,2,7,8]=>0011000=>1100111
[7,5,4,3,8,6,2,1]=>1110111=>0001000
[4,3,8,2,6,7,5,1]=>1010011=>0101100
[4,3,8,2,5,7,1,6]=>1010010=>0101101
[4,1,6,2,5,3,7,8]=>1010100=>0101011
[5,1,8,6,4,7,2,3]=>1011010=>0100101
[4,2,6,1,5,3,8,7]=>1010101=>0101010
[6,7,2,3,1,5,8,4]=>0101001=>1010110
[7,5,2,3,8,1,6,4]=>1100101=>0011010
[7,5,2,3,8,4,1,6]=>1100110=>0011001
[4,5,1,7,6,3,8,2]=>0101101=>1010010
[8,1,7,5,2,3,4,6]=>1011000=>0100111
[8,6,3,1,4,2,5,7]=>1110100=>0001011
[4,5,1,6,2,8,7,3]=>0101011=>1010100
[4,8,3,6,1,7,2,5]=>0101010=>1010101
[6,2,7,8,3,4,5,1]=>1001001=>0110110
[9,2,3,4,5,6,7,8,1]=>10000001=>01111110
[8,2,3,4,5,6,7,1,9]=>10000010=>01111101
[7,2,3,4,5,6,1,8,9]=>10000100=>01111011
[6,2,3,4,5,1,7,8,9]=>10001000=>01110111
[5,2,3,4,1,6,7,8,9]=>10010000=>01101111
[4,2,3,1,5,6,7,8,9]=>10100000=>01011111
[1,2,4,3,5,6,7,8,9]=>00100000=>11011111
[1,2,4,6,8,9,7,5,3]=>00000111=>11111000
[1,2,4,5,3,6,7,8,9]=>00010000=>11101111
[1,2,4,3,5,6,7,8,9,10]=>001000000=>110111111
[1,2,4,6,8,10,9,7,5,3]=>000001111=>111110000
[1,2,4,6,8,5,7,3]=>0000101=>1111010
[2,1,7,5,8,6,3,4]=>1010110=>0101001
[4,7,3,8,6,5,2,1]=>0101111=>1010000
[3,8,7,4,6,5,1,2]=>0110110=>1001001
[7,3,8,4,6,5,1,2]=>1010110=>0101001
[7,4,3,6,5,8,1,2]=>1101010=>0010101
[4,5,8,7,2,6,1,3]=>0011010=>1100101
[3,8,6,7,5,1,4,2]=>0101101=>1010010
[4,2,7,6,5,8,3,1]=>1011011=>0100100
[4,6,7,8,5,2,3,1]=>0001101=>1110010
[4,5,3,8,2,7,6,1]=>0101011=>1010100
[3,8,5,4,1,7,6,2]=>0111011=>1000100
[6,4,7,2,5,8,3,1]=>1010011=>0101100
[6,3,8,7,5,1,4,2]=>1011101=>0100010
[5,3,6,4,1,2,8,7]=>1011001=>0100110
[6,8,4,3,5,7,1,2]=>0110010=>1001101
[5,2,4,8,7,6,1,3]=>1001110=>0110001
[4,2,5,1,7,8,3,6]=>1010010=>0101101
[2,5,4,1,3,8,6,7]=>0110010=>1001101
[1,4,5,3,8,2,6,7]=>0010100=>1101011
[5,1,8,2,4,3,6,7]=>1010100=>0101011
[1,5,4,8,2,3,6,7]=>0101000=>1010111
[3,5,1,4,7,8,2,6]=>0100010=>1011101
[4,8,3,1,6,7,2,5]=>0110010=>1001101
[3,4,8,2,6,5,7,1]=>0010101=>1101010
[3,6,2,4,8,7,1,5]=>0100110=>1011001
[4,7,3,2,6,8,1,5]=>0110010=>1001101
[7,3,4,6,8,1,2,5]=>1000100=>0111011
[3,6,7,2,5,8,1,4]=>0010010=>1101101
[1,5,6,8,3,7,2,4]=>0001010=>1110101
[6,1,5,8,3,4,7,2]=>1001001=>0110110
[5,6,8,1,3,4,7,2]=>0010001=>1101110
[2,8,5,6,3,4,7,1]=>0101001=>1010110
[6,8,1,3,5,4,7,2]=>0100101=>1011010
[8,1,6,3,5,4,7,2]=>1010101=>0101010
[1,8,7,3,6,4,5,2]=>0110101=>1001010
[7,1,2,5,8,4,6,3]=>1000101=>0111010
[6,2,4,8,1,7,3,5]=>1001010=>0110101
[3,1,7,8,5,4,6,2]=>1001101=>0110010
[1,6,2,7,4,8,5,3]=>0101011=>1010100
[2,7,1,8,4,3,5,6]=>0101100=>1010011
[6,7,1,8,3,2,4,5]=>0101100=>1010011
[2,7,6,3,5,8,1,4]=>0110010=>1001101
[2,7,5,6,8,1,3,4]=>0100100=>1011011
[6,7,2,8,1,3,4,5]=>0101000=>1010111
[5,1,6,8,7,2,3,4]=>1001100=>0110011
[1,5,7,6,8,2,3,4]=>0010100=>1101011
[7,4,6,8,5,3,1,2]=>1001110=>0110001
[2,1,5,7,8,3,6,4]=>1000101=>0111010
[3,8,6,7,5,1,2,4]=>0101100=>1010011
[4,7,5,8,6,3,1,2]=>0101110=>1010001
[1,6,8,3,2,5,4,7]=>0011010=>1100101
[7,8,5,1,3,2,6,4]=>0110101=>1001010
[2,6,8,1,5,4,7,3]=>0010101=>1101010
[1,5,4,7,6,2,8,3]=>0101101=>1010010
[2,3,7,6,5,1,8,4]=>0011101=>1100010
[6,1,5,8,3,2,7,4]=>1001101=>0110010
[3,1,2,4,8,5,7,6]=>1000101=>0111010
[2,5,8,4,6,3,1,7]=>0010110=>1101001
[7,1,5,4,8,3,2,6]=>1010110=>0101001
[6,4,1,7,5,3,2,8]=>1101110=>0010001
[2,7,6,4,8,1,5,3]=>0110101=>1001010
[7,2,5,4,8,1,6,3]=>1010101=>0101010
[1,7,2,5,3,8,6,4]=>0101011=>1010100
[2,4,1,3,6,8,5,7,9]=>01000100=>10111011
[7,2,3,8,6,1,5,4]=>1001101=>0110010
[5,3,8,4,1,2,6,7]=>1011000=>0100111
[2,4,8,3,7,1,5,6]=>0010100=>1101011
[5,2,8,4,1,6,3,7]=>1011010=>0100101
[7,6,5,2,1,8,4,3]=>1111011=>0000100
[2,7,5,1,8,3,6,4]=>0110101=>1001010
[5,1,8,7,4,3,6,2]=>1011101=>0100010
[3,8,7,2,4,6,1,5]=>0110010=>1001101
[5,7,1,3,2,4,8,6]=>0101001=>1010110
[4,2,7,6,3,5,8,1]=>1011001=>0100110
[8,4,7,6,3,5,1,2]=>1011010=>0100101
[8,1,7,4,2,3,5,6]=>1011000=>0100111
[6,5,1,3,8,7,4,2]=>1100111=>0011000
[4,7,8,3,2,5,1,6]=>0011010=>1100101
[6,1,8,5,3,7,2,4]=>1011010=>0100101
[5,1,6,8,3,7,4,2]=>1001011=>0110100
[8,6,5,1,7,4,3,2]=>1110111=>0001000
[7,6,4,1,3,5,8,2]=>1110001=>0001110
[8,2,3,7,1,4,5,6]=>1001000=>0110111
[2,8,3,7,1,4,5,6]=>0101000=>1010111
[5,6,2,7,4,3,1,8]=>0101110=>1010001
[8,6,2,7,4,1,3,5]=>1101100=>0010011
[3,7,8,2,6,1,4,5]=>0010100=>1101011
[3,7,8,5,2,1,4,6]=>0011100=>1100011
[6,8,4,7,3,1,5,2]=>0101101=>1010010
[4,8,6,5,1,2,7,3]=>0111001=>1000110
[4,8,6,5,1,2,3,7]=>0111000=>1000111
[3,4,5,1,7,6,8,2]=>0010101=>1101010
[3,8,7,6,5,1,2,4]=>0111100=>1000011
[8,4,6,7,1,2,5,3]=>1001001=>0110110
[5,7,2,6,1,8,4,3]=>0101011=>1010100
[5,7,2,6,1,3,8,4]=>0101001=>1010110
[5,8,2,6,1,4,7,3]=>0101001=>1010110
[3,8,7,5,6,1,4,2]=>0110101=>1001010
[6,8,4,7,2,1,5,3]=>0101101=>1010010
[1,7,3,4,5,2,8,6]=>0100101=>1011010
[4,8,2,1,3,5,6,7]=>0110000=>1001111
[1,7,2,5,4,3,8,6]=>0101101=>1010010
[2,6,7,3,4,8,1,5]=>0010010=>1101101
[2,1,5,7,4,3,8,6]=>1001101=>0110010
[4,1,8,7,5,6,2,3]=>1011010=>0100101
[1,5,8,7,4,3,6,2]=>0011101=>1100010
[6,4,1,3,8,7,5,2]=>1100111=>0011000
[2,1,7,4,6,8,3,5]=>1010010=>0101101
[1,7,2,4,6,8,3,5]=>0100010=>1011101
[8,6,4,2,7,3,5,1]=>1110101=>0001010
[7,4,6,1,2,3,8,5]=>1010001=>0101110
[1,8,6,2,7,3,5,4]=>0110101=>1001010
[1,7,8,6,2,3,5,4]=>0011001=>1100110
[2,1,8,3,5,7,6,4]=>1010011=>0101100
[3,5,8,1,7,6,2,4]=>0010110=>1101001
[2,8,1,3,6,7,5,4]=>0100011=>1011100
[7,2,4,8,6,1,5,3]=>1001101=>0110010
[2,4,1,5,6,7,8,9,10,3]=>010000001=>101111110
[2,3,4,5,6,7,9,1,10,8]=>000000101=>111111010
[2,3,5,1,6,7,8,9,10,4]=>001000001=>110111110
[2,3,4,5,6,8,1,9,10,7]=>000001001=>111110110
[2,3,4,6,1,7,8,9,10,5]=>000100001=>111011110
[2,3,4,5,7,1,8,9,10,6]=>000010001=>111101110
[4,1,2,5,6,7,8,9,10,3]=>100000001=>011111110
[4,3,1,5,6,7,8,10,2,9]=>110000010=>001111101
[2,4,1,5,6,7,8,9,10,11,3]=>0100000001=>1011111110
[2,6,1,5,3,7,8,9,10,4]=>010100001=>101011110
[2,3,4,5,6,7,8,10,1,11,9]=>0000000101=>1111111010
[5,3,4,1,6,7,9,2,10,8]=>101000101=>010111010
[2,3,5,1,6,7,8,9,10,11,4]=>0010000001=>1101111110
[2,3,8,1,6,7,4,9,10,5]=>001001001=>110110110
[2,3,4,5,6,7,9,1,10,11,8]=>0000001001=>1111110110
[6,3,4,5,1,8,2,9,10,7]=>100101001=>011010110
[2,3,4,6,1,7,8,9,10,11,5]=>0001000001=>1110111110
[2,3,4,10,1,7,8,9,5,6]=>000100010=>111011101
[2,3,4,5,6,8,1,9,10,11,7]=>0000010001=>1111101110
[2,3,4,5,7,1,8,9,10,11,6]=>0000100001=>1111011110
[8,2,1,3,4,5,6,7,9]=>11000000=>00111111
[3,2,4,5,6,7,8,1,9]=>10000010=>01111101
[9,2,1,3,4,5,6,7,8,10]=>110000000=>001111111
[8,3,1,2,4,5,6,7,9]=>11000000=>00111111
[8,2,3,1,4,5,6,7,9]=>10100000=>01011111
[4,2,3,5,6,7,8,1,9]=>10000010=>01111101
[6,4,3,2,8,1,7,5]=>1110101=>0001010
[6,2,4,3,8,1,7,5]=>1010101=>0101010
[5,8,4,3,1,6,7,2]=>0111001=>1000110
[8,7,2,4,6,10,1,3,5,9]=>110001000=>001110111
[2,10,7,9,4,6,8,1,3,5]=>010100100=>101011011
[6,5,2,4,8,10,1,3,7,9]=>110001000=>001110111
[2,8,5,7,4,6,10,1,3,9]=>010100100=>101011011
[10,5,2,4,7,9,6,8,1,3]=>110001010=>001110101
[10,9,2,8,5,7,4,6,1,3]=>110101010=>001010101
[8,7,6,5,2,4,10,1,3,9]=>111100100=>000011011
[10,7,2,6,5,9,4,8,1,3]=>110101010=>001010101
[6,10,5,9,8,7,2,4,1,3]=>010111010=>101000101
[4,10,3,9,2,6,8,1,5,7]=>010100100=>101011011
[4,3,10,7,9,2,6,8,1,5]=>101010010=>010101101
[3,6,2,5,4,8,10,1,7,9]=>010100100=>101011011
[3,6,10,2,5,9,4,8,1,7]=>001001010=>110110101
[3,5,8,2,4,7,6,10,1,9]=>001001010=>110110101
[3,5,7,10,2,4,6,9,8,1]=>000100011=>111011100
[10,9,3,5,8,2,4,7,6,1]=>110010011=>001101100
[8,7,3,6,2,5,4,10,1,9]=>110101010=>001010101
[7,6,3,5,10,2,4,9,8,1]=>110010011=>001101100
[3,6,10,9,8,2,5,7,4,1]=>001110011=>110001100
[10,9,8,7,3,6,2,5,4,1]=>111101011=>000010100
[5,4,3,8,2,7,6,10,1,9]=>110101010=>001010101
[5,4,3,7,10,2,6,9,8,1]=>110010011=>001101100
[5,10,4,9,3,8,2,7,6,1]=>010101011=>101010100
[4,8,3,7,6,5,2,10,1,9]=>010111010=>101000101
[4,7,3,6,5,10,2,9,8,1]=>010101011=>101010100
[4,6,10,3,5,9,8,7,2,1]=>001001111=>110110000
[10,9,4,8,3,7,6,5,2,1]=>110101111=>001010000
[7,6,5,4,3,10,2,9,8,1]=>111101011=>000010100
[6,5,4,10,3,9,8,7,2,1]=>110101111=>001010000
[5,10,4,9,8,7,6,3,2,1]=>010111111=>101000000
[12,11,2,4,6,8,10,1,3,5,7,9]=>11000010000=>00111101111
[10,9,2,4,6,8,12,1,3,5,7,11]=>11000010000=>00111101111
[2,12,9,11,4,6,8,10,1,3,5,7]=>01010001000=>10101110111
[12,11,10,9,2,4,6,8,1,3,5,7]=>11110001000=>00001110111
[8,7,2,4,6,10,12,1,3,5,9,11]=>11000010000=>00111101111
[8,12,7,11,2,4,6,10,1,3,5,9]=>01010001000=>10101110111
[2,10,7,9,4,6,8,12,1,3,5,11]=>01010001000=>10101110111
[12,11,2,10,7,9,4,6,8,1,3,5]=>11010100100=>00101011011
[10,9,8,7,2,4,6,12,1,3,5,11]=>11110001000=>00001110111
[12,9,2,8,7,11,4,6,10,1,3,5]=>11010100100=>00101011011
[8,12,7,11,10,9,2,4,6,1,3,5]=>01011100100=>10100011011
[12,11,10,9,8,7,2,4,6,1,3,5]=>11111100100=>00000011011
[6,5,2,4,8,10,12,1,3,7,9,11]=>11000010000=>00111101111
[6,12,5,11,2,4,8,10,1,3,7,9]=>01010001000=>10101110111
[6,10,5,9,2,4,8,12,1,3,7,11]=>01010001000=>10101110111
[6,5,12,9,11,2,4,8,10,1,3,7]=>10101000100=>01010111011
[12,11,6,10,5,9,2,4,8,1,3,7]=>11010100100=>00101011011
[2,8,5,7,4,6,10,12,1,3,9,11]=>01010001000=>10101110111
[10,9,2,8,5,7,4,6,12,1,3,11]=>11010100100=>00101011011
[2,12,5,11,8,10,7,9,4,6,1,3]=>01010101010=>10101010101
[12,11,10,9,2,8,5,7,4,6,1,3]=>11110101010=>00001010101
[8,7,6,5,2,4,10,12,1,3,9,11]=>11110001000=>00001110111
[8,7,6,12,5,11,2,4,10,1,3,9]=>11010100100=>00101011011
[10,7,2,6,5,9,4,8,12,1,3,11]=>11010100100=>00101011011
[2,12,7,11,6,10,5,9,4,8,1,3]=>01010101010=>10101010101
[6,10,5,9,8,7,2,4,12,1,3,11]=>01011100100=>10100011011
[2,12,6,9,5,8,7,11,4,10,1,3]=>01010101010=>10101010101
[6,8,12,5,7,11,10,9,2,4,1,3]=>00100111010=>11011000101
[10,9,8,7,6,5,2,4,12,1,3,11]=>11111100100=>00000011011
[12,9,8,7,2,6,5,11,4,10,1,3]=>11110101010=>00001010101
[12,11,10,9,8,7,6,5,2,4,1,3]=>11111111010=>00000000101
[4,3,2,6,8,10,12,1,5,7,9,11]=>11000010000=>00111101111
[4,12,3,11,2,6,8,10,1,5,7,9]=>01010001000=>10101110111
[4,10,3,9,2,6,8,12,1,5,7,11]=>01010001000=>10101110111
[4,3,12,9,11,2,6,8,10,1,5,7]=>10101000100=>01010111011
[12,11,4,10,3,9,2,6,8,1,5,7]=>11010100100=>00101011011
[4,8,3,7,2,6,10,12,1,5,9,11]=>01010001000=>10101110111
[4,3,10,7,9,2,6,8,12,1,5,11]=>10101000100=>01010111011
[12,4,11,3,10,7,9,2,6,8,1,5]=>10101010010=>01010101101
[10,9,4,8,3,7,2,6,12,1,5,11]=>11010100100=>00101011011
[12,4,9,3,8,7,11,2,6,10,1,5]=>10101010010=>01010101101
[12,11,10,9,4,8,3,7,2,6,1,5]=>11110101010=>00001010101
[3,6,2,5,4,8,10,12,1,7,9,11]=>01010001000=>10101110111
[3,5,8,12,2,4,7,11,6,10,1,9]=>00010001010=>11101110101
[3,5,7,10,2,4,6,9,8,12,1,11]=>00010001010=>11101110101
[3,5,7,9,12,2,4,6,8,11,10,1]=>00001000011=>11110111100
[12,11,10,9,3,5,8,2,4,7,6,1]=>11110010011=>00001101100
[8,7,3,6,2,5,4,10,12,1,9,11]=>11010100100=>00101011011
[3,2,12,6,8,11,10,5,7,9,4,1]=>10100110011=>01011001100
[10,9,8,7,3,6,2,5,4,12,1,11]=>11110101010=>00001010101
[9,8,7,6,3,5,12,2,4,11,10,1]=>11110010011=>00001101100
[12,11,10,9,8,7,3,6,2,5,4,1]=>11111101011=>00000010100
[6,5,4,3,2,8,10,12,1,7,9,11]=>11110001000=>00001110111
[6,5,4,12,3,11,2,8,10,1,7,9]=>11010100100=>00101011011
[6,5,4,10,3,9,2,8,12,1,7,11]=>11010100100=>00101011011
[6,12,5,4,3,9,11,2,8,10,1,7]=>01110010010=>10001101101
[5,4,3,8,2,7,6,10,12,1,9,11]=>11010100100=>00101011011
[5,10,4,9,3,8,2,7,6,12,1,11]=>01010101010=>10101010101
[12,11,5,4,3,8,10,2,7,9,6,1]=>11110010011=>00001101100
[4,8,3,7,6,5,2,10,12,1,9,11]=>01011100100=>10100011011
[4,8,3,7,6,12,5,11,2,10,1,9]=>01010101010=>10101010101
[4,7,3,6,5,10,2,9,8,12,1,11]=>01010101010=>10101010101
[4,7,12,3,6,11,5,10,2,9,8,1]=>00100101011=>11011010100
[4,6,10,3,5,9,8,7,2,12,1,11]=>00100111010=>11011000101
[4,6,9,3,5,8,7,12,2,11,10,1]=>00100101011=>11011010100
[4,6,8,12,3,5,7,11,10,9,2,1]=>00010001111=>11101110000
[12,11,10,9,4,8,3,7,6,5,2,1]=>11110101111=>00001010000
[8,7,6,5,4,3,2,10,12,1,9,11]=>11111100100=>00000011011
[8,7,6,5,4,12,3,11,2,10,1,9]=>11110101010=>00001010101
[7,6,5,4,3,10,2,9,8,12,1,11]=>11110101010=>00001010101
[7,6,5,4,3,9,12,2,8,11,10,1]=>11110010011=>00001101100
[6,12,5,11,4,10,3,9,8,7,2,1]=>01010101111=>10101010000
[5,8,4,7,6,12,3,11,10,9,2,1]=>01010101111=>10101010000
[5,7,12,4,6,11,10,9,8,3,2,1]=>00100111111=>11011000000
[12,11,5,10,4,9,8,7,6,3,2,1]=>11010111111=>00101000000
[10,9,8,7,6,5,4,3,2,12,1,11]=>11111111010=>00000000101
[9,8,7,6,5,4,3,12,2,11,10,1]=>11111101011=>00000010100
[8,7,6,5,4,12,3,11,10,9,2,1]=>11110101111=>00001010000
[7,6,5,12,4,11,10,9,8,3,2,1]=>11010111111=>00101000000
[6,12,5,11,10,9,8,7,4,3,2,1]=>01011111111=>10100000000
[4,2,8,1,5,7,6,3]=>1010011=>0101100
[6,3,7,2,5,4,8,1]=>1010101=>0101010
[5,4,7,3,2,6,8,1]=>1011001=>0100110
[5,7,2,6,3,4,8,1]=>0101001=>1010110
[3,7,5,4,6,2,8,1]=>0110101=>1001010
[6,8,3,2,1,7,4,5]=>0111010=>1000101
[4,8,1,7,5,3,2,6]=>0101110=>1010001
[5,4,3,7,2,8,6,1]=>1101011=>0010100
[3,6,5,7,2,8,4,1]=>0101011=>1010100
[4,6,5,3,8,2,1,7]=>0110110=>1001001
[2,6,5,8,7,3,1,4]=>0101110=>1010001
[6,3,8,4,1,7,2,5]=>1011010=>0100101
[7,2,8,1,6,4,3,5]=>1010110=>0101001
[3,2,8,7,6,4,1,5]=>1011110=>0100001
[8,2,6,4,3,5,1,7]=>1011010=>0100101
[5,4,2,8,6,3,7,1]=>1101101=>0010010
[2,8,7,5,3,1,4,6]=>0111100=>1000011
[2,5,6,3,1,4,8,7]=>0011001=>1100110
[2,4,7,8,5,3,1,6]=>0001110=>1110001
[6,5,3,2,4,1,8,7]=>1110101=>0001010
[6,5,8,7,3,2,4,1]=>1011101=>0100010
[2,1,4,7,8,5,3,6]=>1000110=>0111001
[8,5,6,7,3,1,4,2]=>1001101=>0110010
[8,7,5,3,2,6,4,1]=>1111011=>0000100
[8,5,3,1,4,6,7,2]=>1110001=>0001110
[8,5,1,6,4,3,7,2]=>1101101=>0010010
[6,1,4,3,7,8,2,5]=>1010010=>0101101
[6,1,2,7,5,8,3,4]=>1001010=>0110101
[2,7,3,1,4,6,8,5]=>0110001=>1001110
[2,8,3,1,6,5,7,4]=>0110101=>1001010
[3,8,5,6,7,1,2,4]=>0100100=>1011011
[2,5,8,1,4,6,7,3]=>0010001=>1101110
[2,1,8,7,5,4,6,3]=>1011101=>0100010
[7,8,3,4,1,6,5,2]=>0101011=>1010100
[8,7,3,4,2,6,5,1]=>1101011=>0010100
[8,4,5,2,3,7,1,6]=>1010010=>0101101
[4,7,2,8,6,3,1,5]=>0101110=>1010001
[4,7,5,2,3,8,1,6]=>0110010=>1001101
[6,4,7,5,2,8,3,1]=>1011011=>0100100
[7,5,1,3,6,4,8,2]=>1100101=>0011010
[6,5,2,3,7,8,4,1]=>1100011=>0011100
[7,2,6,3,1,5,8,4]=>1011001=>0100110
[4,6,3,8,7,5,1,2]=>0101110=>1010001
[2,8,4,1,5,7,6,3]=>0110011=>1001100
[1,8,4,2,5,7,6,3]=>0110011=>1001100
[2,8,5,4,1,7,6,3]=>0111011=>1000100
[2,5,8,3,7,1,6,4]=>0010101=>1101010
[1,8,5,2,4,7,6,3]=>0110011=>1001100
[1,4,6,2,8,7,5,3]=>0010111=>1101000
[7,8,2,4,1,6,5,3]=>0101011=>1010100
[2,4,6,1,8,7,5,3]=>0010111=>1101000
[2,8,4,5,1,7,6,3]=>0101011=>1010100
[3,5,8,2,7,6,1,4]=>0010110=>1101001
[2,1,6,8,7,5,3,4]=>1001110=>0110001
[1,8,2,4,5,7,6,3]=>0100011=>1011100
[1,2,8,3,5,7,6,4]=>0010011=>1101100
[1,3,8,2,5,7,6,4]=>0010011=>1101100
[2,3,8,1,5,7,6,4]=>0010011=>1101100
[2,6,1,8,7,5,3,4]=>0101110=>1010001
[1,6,2,8,7,5,3,4]=>0101110=>1010001
[1,6,3,8,7,5,2,4]=>0101110=>1010001
[2,6,3,8,7,5,1,4]=>0101110=>1010001
[3,2,8,1,5,7,6,4]=>1010011=>0101100
[3,1,8,2,5,7,6,4]=>1010011=>0101100
[2,8,1,4,5,7,6,3]=>0100011=>1011100
[7,8,2,1,4,6,5,3]=>0110011=>1001100
[2,3,6,8,7,5,1,4]=>0001110=>1110001
[3,1,6,8,7,2,5,4]=>1001101=>0110010
[3,8,4,5,1,6,2,7]=>0101010=>1010101
[6,1,4,5,7,2,3,8]=>1000100=>0111011
[8,1,4,7,6,3,2,5]=>1001110=>0110001
[8,3,1,6,4,7,2,5]=>1101010=>0010101
[5,3,8,6,2,7,1,4]=>1011010=>0100101
[8,3,6,1,5,7,2,4]=>1010010=>0101101
[8,4,6,3,1,2,5,7]=>1011000=>0100111
[6,8,1,4,5,2,3,7]=>0100100=>1011011
[1,5,8,4,6,2,3,7]=>0010100=>1101011
[2,1,6,5,3,8,4,7]=>1011010=>0100101
[5,6,8,1,4,2,3,7]=>0010100=>1101011
[5,7,4,8,1,2,3,6]=>0101000=>1010111
[8,2,1,5,3,7,4,6]=>1101010=>0010101
[4,7,8,1,2,6,3,5]=>0010010=>1101101
[8,7,1,5,6,2,3,4]=>1100100=>0011011
[1,6,5,8,7,2,3,4]=>0101100=>1010011
[3,7,1,6,2,4,8,5]=>0101001=>1010110
[5,1,2,7,6,8,3,4]=>1001010=>0110101
[6,1,7,2,5,8,3,4]=>1010010=>0101101
[1,7,6,5,8,2,3,4]=>0110100=>1001011
[1,6,8,5,7,2,3,4]=>0010100=>1101011
[7,5,1,2,6,8,3,4]=>1100010=>0011101
[6,1,5,2,7,8,3,4]=>1010010=>0101101
[1,6,3,8,7,2,4,5]=>0101100=>1010011
[1,7,3,2,4,6,8,5]=>0110001=>1001110
[8,3,1,4,2,5,7,6]=>1101001=>0010110
[3,1,2,7,8,4,6,5]=>1000101=>0111010
[5,1,2,6,8,7,3,4]=>1000110=>0111001
[1,8,6,2,5,7,3,4]=>0110010=>1001101
[5,7,8,1,2,6,3,4]=>0010010=>1101101
[8,1,5,7,6,2,3,4]=>1001100=>0110011
[7,1,6,8,5,2,3,4]=>1001100=>0110011
[3,7,1,2,8,4,6,5]=>0100101=>1011010
[8,3,1,2,7,6,4,5]=>1100110=>0011001
[1,5,8,7,6,2,3,4]=>0011100=>1100011
[7,8,6,1,5,2,3,4]=>0110100=>1001011
[1,9,3,4,5,6,7,8,2]=>01000001=>10111110
[9,2,3,4,5,6,7,8,1,10]=>100000010=>011111101
[1,9,8,4,5,6,7,3,2]=>01100011=>10011100
[1,10,3,4,5,6,7,8,9,2]=>010000001=>101111110
[1,10,9,4,5,6,7,8,3,2]=>011000011=>100111100
[7,8,6,3,1,5,2,4]=>0111010=>1000101
[7,8,1,3,4,5,2,6]=>0100010=>1011101
[1,7,4,8,2,5,3,6]=>0101010=>1010101
[3,8,6,1,4,2,7,5]=>0110101=>1001010
[7,1,8,2,4,6,3,5]=>1010010=>0101101
[7,6,8,4,1,5,3,2]=>1011011=>0100100
[7,3,2,8,1,5,4,6]=>1101010=>0010101
[3,5,4,1,7,2,6,8]=>0110100=>1001011
[6,4,7,3,2,5,1,8]=>1011010=>0100101
[7,6,5,3,8,4,1,2]=>1110110=>0001001
[6,4,5,7,8,1,3,2]=>1000101=>0111010
[3,7,4,1,6,8,5,2]=>0110011=>1001100
[3,1,2,7,6,8,5,4]=>1001011=>0110100
[6,3,2,8,4,5,1,7]=>1101010=>0010101
[6,1,8,3,5,4,2,7]=>1010110=>0101001
[3,8,5,2,4,6,1,7]=>0110010=>1001101
[1,6,4,8,3,5,2,7]=>0101010=>1010101
[1,5,4,8,6,3,7,2]=>0101101=>1010010
[4,8,2,5,3,7,1,6]=>0101010=>1010101
[3,8,4,5,2,6,7,1]=>0101001=>1010110
[4,1,8,6,5,3,7,2]=>1011101=>0100010
[5,7,8,4,6,3,2,1]=>0010111=>1101000
[5,3,2,8,6,4,7,1]=>1101101=>0010010
[6,8,1,2,7,4,3,5]=>0100110=>1011001
[5,8,7,3,6,2,4,1]=>0110101=>1001010
[7,5,2,3,4,8,6,1]=>1100011=>0011100
[7,3,5,4,2,8,6,1]=>1011011=>0100100
[5,6,1,3,2,4,7,8]=>0101000=>1010111
[2,5,1,3,7,8,6,4]=>0100011=>1011100
[4,3,7,2,1,8,6,5]=>1011011=>0100100
[4,6,7,2,1,3,5,8]=>0011000=>1100111
[4,6,2,3,1,5,7,8]=>0101000=>1010111
[3,6,4,2,5,1,7,8]=>0110100=>1001011
[3,1,6,4,7,5,2,8]=>1010110=>0101001
[3,6,2,7,5,4,1,8]=>0101110=>1010001
[2,4,7,5,3,6,1,8]=>0011010=>1100101
[2,5,7,3,4,1,6,8]=>0010100=>1101011
[2,3,5,8,6,4,7,1]=>0001101=>1110010
[2,4,7,3,8,6,5,1]=>0010111=>1101000
[3,4,2,7,5,8,6,1]=>0101011=>1010100
[3,1,5,4,7,8,6,2]=>1010011=>0101100
[4,5,7,2,3,1,8,6]=>0010101=>1101010
[3,7,8,1,4,6,5,2]=>0010011=>1101100
[2,5,8,7,4,1,3,6]=>0011100=>1100011
[2,6,4,7,5,3,8,1]=>0101101=>1010010
[6,2,4,7,1,3,8,5]=>1001001=>0110110
[7,3,5,1,4,2,8,6]=>1010101=>0101010
[5,4,7,1,3,2,8,6]=>1010101=>0101010
[6,1,4,7,5,3,8,2]=>1001101=>0110010
[8,7,4,3,1,5,6,2]=>1111001=>0000110
[8,7,1,4,3,5,6,2]=>1101001=>0010110
[6,1,8,4,7,3,2,5]=>1010110=>0101001
[4,7,3,6,1,2,8,5]=>0101001=>1010110
[5,2,1,7,4,3,8,6]=>1101101=>0010010
[4,7,6,2,3,1,8,5]=>0110101=>1001010
[7,6,8,2,5,3,4,1]=>1010101=>0101010
[2,3,6,1,8,7,5,4]=>0010111=>1101000
[2,6,8,7,5,3,1,4]=>0011110=>1100001
[6,4,1,7,5,2,8,3]=>1101101=>0010010
[5,7,8,2,3,6,1,4]=>0010010=>1101101
[4,8,7,1,2,5,6,3]=>0110001=>1001110
[2,8,7,4,1,5,6,3]=>0111001=>1000110
[8,6,2,1,5,7,4,3]=>1110011=>0001100
[3,8,6,7,5,2,1,4]=>0101110=>1010001
[6,1,3,7,5,8,2,4]=>1001010=>0110101
[4,7,3,1,8,5,6,2]=>0110101=>1001010
[2,6,7,5,3,4,8,1]=>0011001=>1100110
[2,6,4,5,7,3,8,1]=>0100101=>1011010
[6,1,4,5,8,3,7,2]=>1000101=>0111010
[6,1,8,5,3,4,7,2]=>1011001=>0100110
[4,1,5,6,8,3,7,2]=>1000101=>0111010
[6,4,1,8,7,2,5,3]=>1101101=>0010010
[8,1,2,3,4,5,6,7,10,9]=>100000001=>011111110
[1,7,2,3,4,5,6,9,8]=>01000001=>10111110
[1,3,8,5,2,7,4,6]=>0011010=>1100101
[1,3,8,6,7,2,4,5]=>0010100=>1101011
[2,8,3,7,6,1,4,5]=>0101100=>1010011
[4,2,7,8,6,1,3,5]=>1001100=>0110011
[1,3,8,7,6,2,4,5]=>0011100=>1100011
[7,4,6,8,5,2,3,1]=>1001101=>0110010
[7,5,3,6,8,2,1,4]=>1100110=>0011001
[5,2,6,7,8,1,3,4]=>1000100=>0111011
[4,5,6,8,1,2,7,3]=>0001001=>1110110
[3,5,8,6,1,2,7,4]=>0011001=>1100110
[4,2,6,8,7,1,3,5]=>1001100=>0110011
[1,4,6,8,7,2,3,5]=>0001100=>1110011
[4,5,3,8,1,7,2,6]=>0101010=>1010101
[3,5,8,4,1,7,2,6]=>0011010=>1100101
[1,6,5,7,8,2,3,4]=>0100100=>1011011
[5,6,4,8,2,3,7,1]=>0101001=>1010110
[6,5,4,8,1,3,7,2]=>1101001=>0010110
[7,6,4,8,5,1,3,2]=>1101101=>0010010
[7,2,6,5,8,1,3,4]=>1010100=>0101011
[6,3,7,5,2,4,8,1]=>1011001=>0100110
[8,1,2,7,4,5,3,6]=>1001010=>0110101
[2,5,7,4,6,1,3,8]=>0010100=>1101011
[6,1,7,4,5,3,8,2]=>1010101=>0101010
[8,2,7,3,1,5,4,6]=>1011010=>0100101
[2,6,4,8,3,1,7,5]=>0101101=>1010010
[8,1,3,7,5,6,4,2]=>1001011=>0110100
[1,2,5,3,8,6,7,4]=>0010101=>1101010
[4,1,6,5,7,8,2,3]=>1010010=>0101101
[6,1,3,7,4,2,8,5]=>1001101=>0110010
[6,7,2,4,1,3,8,5]=>0101001=>1010110
[7,3,8,4,2,6,5,1]=>1011011=>0100100
[8,5,3,4,2,7,1,6]=>1101010=>0010101
[1,3,8,2,5,6,7,4]=>0010001=>1101110
[1,8,6,7,2,5,4,3]=>0101011=>1010100
[7,6,8,3,5,4,2,1]=>1010111=>0101000
[1,6,7,3,8,5,4,2]=>0010111=>1101000
[8,7,2,4,6,1,5,3]=>1100101=>0011010
[7,8,6,5,2,4,3,1]=>0111011=>1000100
[3,6,7,5,2,8,4,1]=>0011011=>1100100
[5,4,6,7,8,1,3,2]=>1000101=>0111010
[5,3,6,7,8,1,4,2]=>1000101=>0111010
[5,3,7,6,8,4,1,2]=>1010110=>0101001
[7,5,3,2,8,6,4,1]=>1110111=>0001000
[5,4,8,6,7,2,3,1]=>1010101=>0101010
[5,4,8,6,3,1,2,7]=>1011100=>0100011
[4,5,7,3,6,2,8,1]=>0010101=>1101010
[4,5,6,3,8,2,7,1]=>0010101=>1101010
[5,4,8,7,2,1,3,6]=>1011100=>0100011
[2,5,4,7,8,1,3,6]=>0100100=>1011011
[5,3,6,4,8,2,7,1]=>1010101=>0101010
[5,3,7,4,6,2,8,1]=>1010101=>0101010
[8,2,6,3,7,4,5,1]=>1010101=>0101010
[8,2,4,7,3,5,6,1]=>1001001=>0110110
[8,2,6,5,7,3,4,1]=>1010101=>0101010
[4,5,6,2,7,3,8,1]=>0010101=>1101010
[5,4,6,2,8,3,7,1]=>1010101=>0101010
[8,4,6,1,7,2,5,3]=>1010101=>0101010
[5,2,1,6,3,8,7,4]=>1101011=>0010100
[4,5,6,3,7,1,8,2]=>0010101=>1101010
[6,3,2,8,5,4,1,7]=>1101110=>0010001
[4,3,1,5,2,8,6,7]=>1101010=>0010101
[8,5,4,1,3,2,6,7]=>1110100=>0001011
[3,8,4,1,5,2,6,7]=>0110100=>1001011
[2,5,4,3,8,1,6,7]=>0110100=>1001011
[2,5,7,4,3,1,6,8]=>0011100=>1100011
[5,3,4,2,7,1,6,8]=>1010100=>0101011
[3,7,5,4,1,2,6,8]=>0111000=>1000111
[4,2,5,1,3,8,7,6]=>1010011=>0101100
[4,3,5,1,2,7,6,8]=>1010010=>0101101
[5,3,4,1,7,2,6,8]=>1010100=>0101011
[4,1,6,3,5,2,7,8]=>1010100=>0101011
[4,2,1,8,6,3,7,5]=>1101101=>0010010
[3,1,7,2,5,6,4,8]=>1010010=>0101101
[3,7,5,4,2,1,6,8]=>0111100=>1000011
[3,7,2,4,1,6,5,8]=>0101010=>1010101
[7,3,2,1,6,4,5,8]=>1110100=>0001011
[2,8,6,1,7,4,3,5]=>0110110=>1001001
[2,5,4,6,1,3,7,8]=>0101000=>1010111
[2,5,6,4,1,3,7,8]=>0011000=>1100111
[8,5,2,6,1,3,7,4]=>1101001=>0010110
[7,1,5,6,3,2,4,8]=>1001100=>0110011
[7,1,2,5,4,6,3,8]=>1001010=>0110101
[2,4,1,6,5,3,7,8]=>0101100=>1010011
[4,1,2,7,5,6,3,8]=>1001010=>0110101
[7,1,2,6,5,4,3,8]=>1001110=>0110001
[8,2,1,5,6,3,7,4]=>1100101=>0011010
[6,1,4,5,3,2,7,8]=>1001100=>0110011
[3,1,6,5,4,2,7,8]=>1011100=>0100011
[3,1,4,6,5,2,7,8]=>1001100=>0110011
[6,4,1,5,3,2,8,7]=>1101101=>0010010
[2,1,8,6,3,7,5,4]=>1011011=>0100100
[5,8,3,1,7,6,4,2]=>0110111=>1001000
[7,6,3,2,8,5,1,4]=>11101