Identifier
Images
=>
[1]=>=>
[1,2]=>0=>0
[2,1]=>1=>1
[1,2,3]=>00=>00
[1,3,2]=>01=>10
[2,1,3]=>10=>01
[2,3,1]=>01=>10
[3,1,2]=>01=>10
[3,2,1]=>11=>11
[1,2,3,4]=>000=>000
[1,2,4,3]=>001=>100
[1,3,2,4]=>010=>010
[1,3,4,2]=>001=>100
[1,4,2,3]=>001=>100
[1,4,3,2]=>011=>110
[2,1,3,4]=>100=>001
[2,1,4,3]=>101=>101
[2,3,1,4]=>010=>010
[2,3,4,1]=>001=>100
[2,4,1,3]=>001=>100
[2,4,3,1]=>011=>110
[3,1,2,4]=>010=>010
[3,1,4,2]=>011=>110
[3,2,1,4]=>110=>011
[3,2,4,1]=>011=>110
[3,4,1,2]=>001=>100
[3,4,2,1]=>101=>101
[4,1,2,3]=>001=>100
[4,1,3,2]=>011=>110
[4,2,1,3]=>101=>101
[4,2,3,1]=>011=>110
[4,3,1,2]=>011=>110
[4,3,2,1]=>111=>111
[1,2,3,4,5]=>0000=>0000
[1,2,3,5,4]=>0001=>1000
[1,2,4,3,5]=>0010=>0100
[1,2,4,5,3]=>0001=>1000
[1,2,5,3,4]=>0001=>1000
[1,2,5,4,3]=>0011=>1100
[1,3,2,4,5]=>0100=>0010
[1,3,2,5,4]=>0101=>1010
[1,3,4,2,5]=>0010=>0100
[1,3,4,5,2]=>0001=>1000
[1,3,5,2,4]=>0001=>1000
[1,3,5,4,2]=>0011=>1100
[1,4,2,3,5]=>0010=>0100
[1,4,2,5,3]=>0011=>1100
[1,4,3,2,5]=>0110=>0110
[1,4,3,5,2]=>0011=>1100
[1,4,5,2,3]=>0001=>1000
[1,4,5,3,2]=>0101=>1010
[1,5,2,3,4]=>0001=>1000
[1,5,2,4,3]=>0011=>1100
[1,5,3,2,4]=>0101=>1010
[1,5,3,4,2]=>0011=>1100
[1,5,4,2,3]=>0011=>1100
[1,5,4,3,2]=>0111=>1110
[2,1,3,4,5]=>1000=>0001
[2,1,3,5,4]=>1001=>1001
[2,1,4,3,5]=>1010=>0101
[2,1,4,5,3]=>1001=>1001
[2,1,5,3,4]=>1001=>1001
[2,1,5,4,3]=>1011=>1101
[2,3,1,4,5]=>0100=>0010
[2,3,1,5,4]=>0101=>1010
[2,3,4,1,5]=>0010=>0100
[2,3,4,5,1]=>0001=>1000
[2,3,5,1,4]=>0001=>1000
[2,3,5,4,1]=>0011=>1100
[2,4,1,3,5]=>0010=>0100
[2,4,1,5,3]=>0011=>1100
[2,4,3,1,5]=>0110=>0110
[2,4,3,5,1]=>0011=>1100
[2,4,5,1,3]=>0001=>1000
[2,4,5,3,1]=>0101=>1010
[2,5,1,3,4]=>0001=>1000
[2,5,1,4,3]=>0011=>1100
[2,5,3,1,4]=>0101=>1010
[2,5,3,4,1]=>0011=>1100
[2,5,4,1,3]=>0011=>1100
[2,5,4,3,1]=>0111=>1110
[3,1,2,4,5]=>0100=>0010
[3,1,2,5,4]=>0101=>1010
[3,1,4,2,5]=>0110=>0110
[3,1,4,5,2]=>0101=>1010
[3,1,5,2,4]=>0101=>1010
[3,1,5,4,2]=>0111=>1110
[3,2,1,4,5]=>1100=>0011
[3,2,1,5,4]=>1101=>1011
[3,2,4,1,5]=>0110=>0110
[3,2,4,5,1]=>0101=>1010
[3,2,5,1,4]=>0101=>1010
[3,2,5,4,1]=>0111=>1110
[3,4,1,2,5]=>0010=>0100
[3,4,1,5,2]=>0011=>1100
[3,4,2,1,5]=>1010=>0101
[3,4,2,5,1]=>0011=>1100
[3,4,5,1,2]=>0001=>1000
[3,4,5,2,1]=>1001=>1001
[3,5,1,2,4]=>0001=>1000
[3,5,1,4,2]=>0011=>1100
[3,5,2,1,4]=>1001=>1001
[3,5,2,4,1]=>0011=>1100
[3,5,4,1,2]=>0011=>1100
[3,5,4,2,1]=>1011=>1101
[4,1,2,3,5]=>0010=>0100
[4,1,2,5,3]=>0011=>1100
[4,1,3,2,5]=>0110=>0110
[4,1,3,5,2]=>0011=>1100
[4,1,5,2,3]=>0011=>1100
[4,1,5,3,2]=>0111=>1110
[4,2,1,3,5]=>1010=>0101
[4,2,1,5,3]=>1011=>1101
[4,2,3,1,5]=>0110=>0110
[4,2,3,5,1]=>0011=>1100
[4,2,5,1,3]=>0011=>1100
[4,2,5,3,1]=>0111=>1110
[4,3,1,2,5]=>0110=>0110
[4,3,1,5,2]=>0111=>1110
[4,3,2,1,5]=>1110=>0111
[4,3,2,5,1]=>0111=>1110
[4,3,5,1,2]=>0011=>1100
[4,3,5,2,1]=>1011=>1101
[4,5,1,2,3]=>0001=>1000
[4,5,1,3,2]=>0101=>1010
[4,5,2,1,3]=>1001=>1001
[4,5,2,3,1]=>0101=>1010
[4,5,3,1,2]=>0101=>1010
[4,5,3,2,1]=>1101=>1011
[5,1,2,3,4]=>0001=>1000
[5,1,2,4,3]=>0011=>1100
[5,1,3,2,4]=>0101=>1010
[5,1,3,4,2]=>0011=>1100
[5,1,4,2,3]=>0011=>1100
[5,1,4,3,2]=>0111=>1110
[5,2,1,3,4]=>1001=>1001
[5,2,1,4,3]=>1011=>1101
[5,2,3,1,4]=>0101=>1010
[5,2,3,4,1]=>0011=>1100
[5,2,4,1,3]=>0011=>1100
[5,2,4,3,1]=>0111=>1110
[5,3,1,2,4]=>0101=>1010
[5,3,1,4,2]=>0111=>1110
[5,3,2,1,4]=>1101=>1011
[5,3,2,4,1]=>0111=>1110
[5,3,4,1,2]=>0011=>1100
[5,3,4,2,1]=>1011=>1101
[5,4,1,2,3]=>0011=>1100
[5,4,1,3,2]=>0111=>1110
[5,4,2,1,3]=>1011=>1101
[5,4,2,3,1]=>0111=>1110
[5,4,3,1,2]=>0111=>1110
[5,4,3,2,1]=>1111=>1111
[1,2,3,4,5,6]=>00000=>00000
[1,2,3,4,6,5]=>00001=>10000
[1,2,3,5,4,6]=>00010=>01000
[1,2,3,5,6,4]=>00001=>10000
[1,2,3,6,4,5]=>00001=>10000
[1,2,3,6,5,4]=>00011=>11000
[1,2,4,3,5,6]=>00100=>00100
[1,2,4,3,6,5]=>00101=>10100
[1,2,4,5,3,6]=>00010=>01000
[1,2,4,5,6,3]=>00001=>10000
[1,2,4,6,3,5]=>00001=>10000
[1,2,4,6,5,3]=>00011=>11000
[1,2,5,3,4,6]=>00010=>01000
[1,2,5,3,6,4]=>00011=>11000
[1,2,5,4,3,6]=>00110=>01100
[1,2,5,4,6,3]=>00011=>11000
[1,2,5,6,3,4]=>00001=>10000
[1,2,5,6,4,3]=>00101=>10100
[1,2,6,3,4,5]=>00001=>10000
[1,2,6,3,5,4]=>00011=>11000
[1,2,6,4,3,5]=>00101=>10100
[1,2,6,4,5,3]=>00011=>11000
[1,2,6,5,3,4]=>00011=>11000
[1,2,6,5,4,3]=>00111=>11100
[1,3,2,4,5,6]=>01000=>00010
[1,3,2,4,6,5]=>01001=>10010
[1,3,2,5,4,6]=>01010=>01010
[1,3,2,5,6,4]=>01001=>10010
[1,3,2,6,4,5]=>01001=>10010
[1,3,2,6,5,4]=>01011=>11010
[1,3,4,2,5,6]=>00100=>00100
[1,3,4,2,6,5]=>00101=>10100
[1,3,4,5,2,6]=>00010=>01000
[1,3,4,5,6,2]=>00001=>10000
[1,3,4,6,2,5]=>00001=>10000
[1,3,4,6,5,2]=>00011=>11000
[1,3,5,2,4,6]=>00010=>01000
[1,3,5,2,6,4]=>00011=>11000
[1,3,5,4,2,6]=>00110=>01100
[1,3,5,4,6,2]=>00011=>11000
[1,3,5,6,2,4]=>00001=>10000
[1,3,5,6,4,2]=>00101=>10100
[1,3,6,2,4,5]=>00001=>10000
[1,3,6,2,5,4]=>00011=>11000
[1,3,6,4,2,5]=>00101=>10100
[1,3,6,4,5,2]=>00011=>11000
[1,3,6,5,2,4]=>00011=>11000
[1,3,6,5,4,2]=>00111=>11100
[1,4,2,3,5,6]=>00100=>00100
[1,4,2,3,6,5]=>00101=>10100
[1,4,2,5,3,6]=>00110=>01100
[1,4,2,5,6,3]=>00101=>10100
[1,4,2,6,3,5]=>00101=>10100
[1,4,2,6,5,3]=>00111=>11100
[1,4,3,2,5,6]=>01100=>00110
[1,4,3,2,6,5]=>01101=>10110
[1,4,3,5,2,6]=>00110=>01100
[1,4,3,5,6,2]=>00101=>10100
[1,4,3,6,2,5]=>00101=>10100
[1,4,3,6,5,2]=>00111=>11100
[1,4,5,2,3,6]=>00010=>01000
[1,4,5,2,6,3]=>00011=>11000
[1,4,5,3,2,6]=>01010=>01010
[1,4,5,3,6,2]=>00011=>11000
[1,4,5,6,2,3]=>00001=>10000
[1,4,5,6,3,2]=>01001=>10010
[1,4,6,2,3,5]=>00001=>10000
[1,4,6,2,5,3]=>00011=>11000
[1,4,6,3,2,5]=>01001=>10010
[1,4,6,3,5,2]=>00011=>11000
[1,4,6,5,2,3]=>00011=>11000
[1,4,6,5,3,2]=>01011=>11010
[1,5,2,3,4,6]=>00010=>01000
[1,5,2,3,6,4]=>00011=>11000
[1,5,2,4,3,6]=>00110=>01100
[1,5,2,4,6,3]=>00011=>11000
[1,5,2,6,3,4]=>00011=>11000
[1,5,2,6,4,3]=>00111=>11100
[1,5,3,2,4,6]=>01010=>01010
[1,5,3,2,6,4]=>01011=>11010
[1,5,3,4,2,6]=>00110=>01100
[1,5,3,4,6,2]=>00011=>11000
[1,5,3,6,2,4]=>00011=>11000
[1,5,3,6,4,2]=>00111=>11100
[1,5,4,2,3,6]=>00110=>01100
[1,5,4,2,6,3]=>00111=>11100
[1,5,4,3,2,6]=>01110=>01110
[1,5,4,3,6,2]=>00111=>11100
[1,5,4,6,2,3]=>00011=>11000
[1,5,4,6,3,2]=>01011=>11010
[1,5,6,2,3,4]=>00001=>10000
[1,5,6,2,4,3]=>00101=>10100
[1,5,6,3,2,4]=>01001=>10010
[1,5,6,3,4,2]=>00101=>10100
[1,5,6,4,2,3]=>00101=>10100
[1,5,6,4,3,2]=>01101=>10110
[1,6,2,3,4,5]=>00001=>10000
[1,6,2,3,5,4]=>00011=>11000
[1,6,2,4,3,5]=>00101=>10100
[1,6,2,4,5,3]=>00011=>11000
[1,6,2,5,3,4]=>00011=>11000
[1,6,2,5,4,3]=>00111=>11100
[1,6,3,2,4,5]=>01001=>10010
[1,6,3,2,5,4]=>01011=>11010
[1,6,3,4,2,5]=>00101=>10100
[1,6,3,4,5,2]=>00011=>11000
[1,6,3,5,2,4]=>00011=>11000
[1,6,3,5,4,2]=>00111=>11100
[1,6,4,2,3,5]=>00101=>10100
[1,6,4,2,5,3]=>00111=>11100
[1,6,4,3,2,5]=>01101=>10110
[1,6,4,3,5,2]=>00111=>11100
[1,6,4,5,2,3]=>00011=>11000
[1,6,4,5,3,2]=>01011=>11010
[1,6,5,2,3,4]=>00011=>11000
[1,6,5,2,4,3]=>00111=>11100
[1,6,5,3,2,4]=>01011=>11010
[1,6,5,3,4,2]=>00111=>11100
[1,6,5,4,2,3]=>00111=>11100
[1,6,5,4,3,2]=>01111=>11110
[2,1,3,4,5,6]=>10000=>00001
[2,1,3,4,6,5]=>10001=>10001
[2,1,3,5,4,6]=>10010=>01001
[2,1,3,5,6,4]=>10001=>10001
[2,1,3,6,4,5]=>10001=>10001
[2,1,3,6,5,4]=>10011=>11001
[2,1,4,3,5,6]=>10100=>00101
[2,1,4,3,6,5]=>10101=>10101
[2,1,4,5,3,6]=>10010=>01001
[2,1,4,5,6,3]=>10001=>10001
[2,1,4,6,3,5]=>10001=>10001
[2,1,4,6,5,3]=>10011=>11001
[2,1,5,3,4,6]=>10010=>01001
[2,1,5,3,6,4]=>10011=>11001
[2,1,5,4,3,6]=>10110=>01101
[2,1,5,4,6,3]=>10011=>11001
[2,1,5,6,3,4]=>10001=>10001
[2,1,5,6,4,3]=>10101=>10101
[2,1,6,3,4,5]=>10001=>10001
[2,1,6,3,5,4]=>10011=>11001
[2,1,6,4,3,5]=>10101=>10101
[2,1,6,4,5,3]=>10011=>11001
[2,1,6,5,3,4]=>10011=>11001
[2,1,6,5,4,3]=>10111=>11101
[2,3,1,4,5,6]=>01000=>00010
[2,3,1,4,6,5]=>01001=>10010
[2,3,1,5,4,6]=>01010=>01010
[2,3,1,5,6,4]=>01001=>10010
[2,3,1,6,4,5]=>01001=>10010
[2,3,1,6,5,4]=>01011=>11010
[2,3,4,1,5,6]=>00100=>00100
[2,3,4,1,6,5]=>00101=>10100
[2,3,4,5,1,6]=>00010=>01000
[2,3,4,5,6,1]=>00001=>10000
[2,3,4,6,1,5]=>00001=>10000
[2,3,4,6,5,1]=>00011=>11000
[2,3,5,1,4,6]=>00010=>01000
[2,3,5,1,6,4]=>00011=>11000
[2,3,5,4,1,6]=>00110=>01100
[2,3,5,4,6,1]=>00011=>11000
[2,3,5,6,1,4]=>00001=>10000
[2,3,5,6,4,1]=>00101=>10100
[2,3,6,1,4,5]=>00001=>10000
[2,3,6,1,5,4]=>00011=>11000
[2,3,6,4,1,5]=>00101=>10100
[2,3,6,4,5,1]=>00011=>11000
[2,3,6,5,1,4]=>00011=>11000
[2,3,6,5,4,1]=>00111=>11100
[2,4,1,3,5,6]=>00100=>00100
[2,4,1,3,6,5]=>00101=>10100
[2,4,1,5,3,6]=>00110=>01100
[2,4,1,5,6,3]=>00101=>10100
[2,4,1,6,3,5]=>00101=>10100
[2,4,1,6,5,3]=>00111=>11100
[2,4,3,1,5,6]=>01100=>00110
[2,4,3,1,6,5]=>01101=>10110
[2,4,3,5,1,6]=>00110=>01100
[2,4,3,5,6,1]=>00101=>10100
[2,4,3,6,1,5]=>00101=>10100
[2,4,3,6,5,1]=>00111=>11100
[2,4,5,1,3,6]=>00010=>01000
[2,4,5,1,6,3]=>00011=>11000
[2,4,5,3,1,6]=>01010=>01010
[2,4,5,3,6,1]=>00011=>11000
[2,4,5,6,1,3]=>00001=>10000
[2,4,5,6,3,1]=>01001=>10010
[2,4,6,1,3,5]=>00001=>10000
[2,4,6,1,5,3]=>00011=>11000
[2,4,6,3,1,5]=>01001=>10010
[2,4,6,3,5,1]=>00011=>11000
[2,4,6,5,1,3]=>00011=>11000
[2,4,6,5,3,1]=>01011=>11010
[2,5,1,3,4,6]=>00010=>01000
[2,5,1,3,6,4]=>00011=>11000
[2,5,1,4,3,6]=>00110=>01100
[2,5,1,4,6,3]=>00011=>11000
[2,5,1,6,3,4]=>00011=>11000
[2,5,1,6,4,3]=>00111=>11100
[2,5,3,1,4,6]=>01010=>01010
[2,5,3,1,6,4]=>01011=>11010
[2,5,3,4,1,6]=>00110=>01100
[2,5,3,4,6,1]=>00011=>11000
[2,5,3,6,1,4]=>00011=>11000
[2,5,3,6,4,1]=>00111=>11100
[2,5,4,1,3,6]=>00110=>01100
[2,5,4,1,6,3]=>00111=>11100
[2,5,4,3,1,6]=>01110=>01110
[2,5,4,3,6,1]=>00111=>11100
[2,5,4,6,1,3]=>00011=>11000
[2,5,4,6,3,1]=>01011=>11010
[2,5,6,1,3,4]=>00001=>10000
[2,5,6,1,4,3]=>00101=>10100
[2,5,6,3,1,4]=>01001=>10010
[2,5,6,3,4,1]=>00101=>10100
[2,5,6,4,1,3]=>00101=>10100
[2,5,6,4,3,1]=>01101=>10110
[2,6,1,3,4,5]=>00001=>10000
[2,6,1,3,5,4]=>00011=>11000
[2,6,1,4,3,5]=>00101=>10100
[2,6,1,4,5,3]=>00011=>11000
[2,6,1,5,3,4]=>00011=>11000
[2,6,1,5,4,3]=>00111=>11100
[2,6,3,1,4,5]=>01001=>10010
[2,6,3,1,5,4]=>01011=>11010
[2,6,3,4,1,5]=>00101=>10100
[2,6,3,4,5,1]=>00011=>11000
[2,6,3,5,1,4]=>00011=>11000
[2,6,3,5,4,1]=>00111=>11100
[2,6,4,1,3,5]=>00101=>10100
[2,6,4,1,5,3]=>00111=>11100
[2,6,4,3,1,5]=>01101=>10110
[2,6,4,3,5,1]=>00111=>11100
[2,6,4,5,1,3]=>00011=>11000
[2,6,4,5,3,1]=>01011=>11010
[2,6,5,1,3,4]=>00011=>11000
[2,6,5,1,4,3]=>00111=>11100
[2,6,5,3,1,4]=>01011=>11010
[2,6,5,3,4,1]=>00111=>11100
[2,6,5,4,1,3]=>00111=>11100
[2,6,5,4,3,1]=>01111=>11110
[3,1,2,4,5,6]=>01000=>00010
[3,1,2,4,6,5]=>01001=>10010
[3,1,2,5,4,6]=>01010=>01010
[3,1,2,5,6,4]=>01001=>10010
[3,1,2,6,4,5]=>01001=>10010
[3,1,2,6,5,4]=>01011=>11010
[3,1,4,2,5,6]=>01100=>00110
[3,1,4,2,6,5]=>01101=>10110
[3,1,4,5,2,6]=>01010=>01010
[3,1,4,5,6,2]=>01001=>10010
[3,1,4,6,2,5]=>01001=>10010
[3,1,4,6,5,2]=>01011=>11010
[3,1,5,2,4,6]=>01010=>01010
[3,1,5,2,6,4]=>01011=>11010
[3,1,5,4,2,6]=>01110=>01110
[3,1,5,4,6,2]=>01011=>11010
[3,1,5,6,2,4]=>01001=>10010
[3,1,5,6,4,2]=>01101=>10110
[3,1,6,2,4,5]=>01001=>10010
[3,1,6,2,5,4]=>01011=>11010
[3,1,6,4,2,5]=>01101=>10110
[3,1,6,4,5,2]=>01011=>11010
[3,1,6,5,2,4]=>01011=>11010
[3,1,6,5,4,2]=>01111=>11110
[3,2,1,4,5,6]=>11000=>00011
[3,2,1,4,6,5]=>11001=>10011
[3,2,1,5,4,6]=>11010=>01011
[3,2,1,5,6,4]=>11001=>10011
[3,2,1,6,4,5]=>11001=>10011
[3,2,1,6,5,4]=>11011=>11011
[3,2,4,1,5,6]=>01100=>00110
[3,2,4,1,6,5]=>01101=>10110
[3,2,4,5,1,6]=>01010=>01010
[3,2,4,5,6,1]=>01001=>10010
[3,2,4,6,1,5]=>01001=>10010
[3,2,4,6,5,1]=>01011=>11010
[3,2,5,1,4,6]=>01010=>01010
[3,2,5,1,6,4]=>01011=>11010
[3,2,5,4,1,6]=>01110=>01110
[3,2,5,4,6,1]=>01011=>11010
[3,2,5,6,1,4]=>01001=>10010
[3,2,5,6,4,1]=>01101=>10110
[3,2,6,1,4,5]=>01001=>10010
[3,2,6,1,5,4]=>01011=>11010
[3,2,6,4,1,5]=>01101=>10110
[3,2,6,4,5,1]=>01011=>11010
[3,2,6,5,1,4]=>01011=>11010
[3,2,6,5,4,1]=>01111=>11110
[3,4,1,2,5,6]=>00100=>00100
[3,4,1,2,6,5]=>00101=>10100
[3,4,1,5,2,6]=>00110=>01100
[3,4,1,5,6,2]=>00101=>10100
[3,4,1,6,2,5]=>00101=>10100
[3,4,1,6,5,2]=>00111=>11100
[3,4,2,1,5,6]=>10100=>00101
[3,4,2,1,6,5]=>10101=>10101
[3,4,2,5,1,6]=>00110=>01100
[3,4,2,5,6,1]=>00101=>10100
[3,4,2,6,1,5]=>00101=>10100
[3,4,2,6,5,1]=>00111=>11100
[3,4,5,1,2,6]=>00010=>01000
[3,4,5,1,6,2]=>00011=>11000
[3,4,5,2,1,6]=>10010=>01001
[3,4,5,2,6,1]=>00011=>11000
[3,4,5,6,1,2]=>00001=>10000
[3,4,5,6,2,1]=>10001=>10001
[3,4,6,1,2,5]=>00001=>10000
[3,4,6,1,5,2]=>00011=>11000
[3,4,6,2,1,5]=>10001=>10001
[3,4,6,2,5,1]=>00011=>11000
[3,4,6,5,1,2]=>00011=>11000
[3,4,6,5,2,1]=>10011=>11001
[3,5,1,2,4,6]=>00010=>01000
[3,5,1,2,6,4]=>00011=>11000
[3,5,1,4,2,6]=>00110=>01100
[3,5,1,4,6,2]=>00011=>11000
[3,5,1,6,2,4]=>00011=>11000
[3,5,1,6,4,2]=>00111=>11100
[3,5,2,1,4,6]=>10010=>01001
[3,5,2,1,6,4]=>10011=>11001
[3,5,2,4,1,6]=>00110=>01100
[3,5,2,4,6,1]=>00011=>11000
[3,5,2,6,1,4]=>00011=>11000
[3,5,2,6,4,1]=>00111=>11100
[3,5,4,1,2,6]=>00110=>01100
[3,5,4,1,6,2]=>00111=>11100
[3,5,4,2,1,6]=>10110=>01101
[3,5,4,2,6,1]=>00111=>11100
[3,5,4,6,1,2]=>00011=>11000
[3,5,4,6,2,1]=>10011=>11001
[3,5,6,1,2,4]=>00001=>10000
[3,5,6,1,4,2]=>00101=>10100
[3,5,6,2,1,4]=>10001=>10001
[3,5,6,2,4,1]=>00101=>10100
[3,5,6,4,1,2]=>00101=>10100
[3,5,6,4,2,1]=>10101=>10101
[3,6,1,2,4,5]=>00001=>10000
[3,6,1,2,5,4]=>00011=>11000
[3,6,1,4,2,5]=>00101=>10100
[3,6,1,4,5,2]=>00011=>11000
[3,6,1,5,2,4]=>00011=>11000
[3,6,1,5,4,2]=>00111=>11100
[3,6,2,1,4,5]=>10001=>10001
[3,6,2,1,5,4]=>10011=>11001
[3,6,2,4,1,5]=>00101=>10100
[3,6,2,4,5,1]=>00011=>11000
[3,6,2,5,1,4]=>00011=>11000
[3,6,2,5,4,1]=>00111=>11100
[3,6,4,1,2,5]=>00101=>10100
[3,6,4,1,5,2]=>00111=>11100
[3,6,4,2,1,5]=>10101=>10101
[3,6,4,2,5,1]=>00111=>11100
[3,6,4,5,1,2]=>00011=>11000
[3,6,4,5,2,1]=>10011=>11001
[3,6,5,1,2,4]=>00011=>11000
[3,6,5,1,4,2]=>00111=>11100
[3,6,5,2,1,4]=>10011=>11001
[3,6,5,2,4,1]=>00111=>11100
[3,6,5,4,1,2]=>00111=>11100
[3,6,5,4,2,1]=>10111=>11101
[4,1,2,3,5,6]=>00100=>00100
[4,1,2,3,6,5]=>00101=>10100
[4,1,2,5,3,6]=>00110=>01100
[4,1,2,5,6,3]=>00101=>10100
[4,1,2,6,3,5]=>00101=>10100
[4,1,2,6,5,3]=>00111=>11100
[4,1,3,2,5,6]=>01100=>00110
[4,1,3,2,6,5]=>01101=>10110
[4,1,3,5,2,6]=>00110=>01100
[4,1,3,5,6,2]=>00101=>10100
[4,1,3,6,2,5]=>00101=>10100
[4,1,3,6,5,2]=>00111=>11100
[4,1,5,2,3,6]=>00110=>01100
[4,1,5,2,6,3]=>00111=>11100
[4,1,5,3,2,6]=>01110=>01110
[4,1,5,3,6,2]=>00111=>11100
[4,1,5,6,2,3]=>00101=>10100
[4,1,5,6,3,2]=>01101=>10110
[4,1,6,2,3,5]=>00101=>10100
[4,1,6,2,5,3]=>00111=>11100
[4,1,6,3,2,5]=>01101=>10110
[4,1,6,3,5,2]=>00111=>11100
[4,1,6,5,2,3]=>00111=>11100
[4,1,6,5,3,2]=>01111=>11110
[4,2,1,3,5,6]=>10100=>00101
[4,2,1,3,6,5]=>10101=>10101
[4,2,1,5,3,6]=>10110=>01101
[4,2,1,5,6,3]=>10101=>10101
[4,2,1,6,3,5]=>10101=>10101
[4,2,1,6,5,3]=>10111=>11101
[4,2,3,1,5,6]=>01100=>00110
[4,2,3,1,6,5]=>01101=>10110
[4,2,3,5,1,6]=>00110=>01100
[4,2,3,5,6,1]=>00101=>10100
[4,2,3,6,1,5]=>00101=>10100
[4,2,3,6,5,1]=>00111=>11100
[4,2,5,1,3,6]=>00110=>01100
[4,2,5,1,6,3]=>00111=>11100
[4,2,5,3,1,6]=>01110=>01110
[4,2,5,3,6,1]=>00111=>11100
[4,2,5,6,1,3]=>00101=>10100
[4,2,5,6,3,1]=>01101=>10110
[4,2,6,1,3,5]=>00101=>10100
[4,2,6,1,5,3]=>00111=>11100
[4,2,6,3,1,5]=>01101=>10110
[4,2,6,3,5,1]=>00111=>11100
[4,2,6,5,1,3]=>00111=>11100
[4,2,6,5,3,1]=>01111=>11110
[4,3,1,2,5,6]=>01100=>00110
[4,3,1,2,6,5]=>01101=>10110
[4,3,1,5,2,6]=>01110=>01110
[4,3,1,5,6,2]=>01101=>10110
[4,3,1,6,2,5]=>01101=>10110
[4,3,1,6,5,2]=>01111=>11110
[4,3,2,1,5,6]=>11100=>00111
[4,3,2,1,6,5]=>11101=>10111
[4,3,2,5,1,6]=>01110=>01110
[4,3,2,5,6,1]=>01101=>10110
[4,3,2,6,1,5]=>01101=>10110
[4,3,2,6,5,1]=>01111=>11110
[4,3,5,1,2,6]=>00110=>01100
[4,3,5,1,6,2]=>00111=>11100
[4,3,5,2,1,6]=>10110=>01101
[4,3,5,2,6,1]=>00111=>11100
[4,3,5,6,1,2]=>00101=>10100
[4,3,5,6,2,1]=>10101=>10101
[4,3,6,1,2,5]=>00101=>10100
[4,3,6,1,5,2]=>00111=>11100
[4,3,6,2,1,5]=>10101=>10101
[4,3,6,2,5,1]=>00111=>11100
[4,3,6,5,1,2]=>00111=>11100
[4,3,6,5,2,1]=>10111=>11101
[4,5,1,2,3,6]=>00010=>01000
[4,5,1,2,6,3]=>00011=>11000
[4,5,1,3,2,6]=>01010=>01010
[4,5,1,3,6,2]=>00011=>11000
[4,5,1,6,2,3]=>00011=>11000
[4,5,1,6,3,2]=>01011=>11010
[4,5,2,1,3,6]=>10010=>01001
[4,5,2,1,6,3]=>10011=>11001
[4,5,2,3,1,6]=>01010=>01010
[4,5,2,3,6,1]=>00011=>11000
[4,5,2,6,1,3]=>00011=>11000
[4,5,2,6,3,1]=>01011=>11010
[4,5,3,1,2,6]=>01010=>01010
[4,5,3,1,6,2]=>01011=>11010
[4,5,3,2,1,6]=>11010=>01011
[4,5,3,2,6,1]=>01011=>11010
[4,5,3,6,1,2]=>00011=>11000
[4,5,3,6,2,1]=>10011=>11001
[4,5,6,1,2,3]=>00001=>10000
[4,5,6,1,3,2]=>01001=>10010
[4,5,6,2,1,3]=>10001=>10001
[4,5,6,2,3,1]=>01001=>10010
[4,5,6,3,1,2]=>01001=>10010
[4,5,6,3,2,1]=>11001=>10011
[4,6,1,2,3,5]=>00001=>10000
[4,6,1,2,5,3]=>00011=>11000
[4,6,1,3,2,5]=>01001=>10010
[4,6,1,3,5,2]=>00011=>11000
[4,6,1,5,2,3]=>00011=>11000
[4,6,1,5,3,2]=>01011=>11010
[4,6,2,1,3,5]=>10001=>10001
[4,6,2,1,5,3]=>10011=>11001
[4,6,2,3,1,5]=>01001=>10010
[4,6,2,3,5,1]=>00011=>11000
[4,6,2,5,1,3]=>00011=>11000
[4,6,2,5,3,1]=>01011=>11010
[4,6,3,1,2,5]=>01001=>10010
[4,6,3,1,5,2]=>01011=>11010
[4,6,3,2,1,5]=>11001=>10011
[4,6,3,2,5,1]=>01011=>11010
[4,6,3,5,1,2]=>00011=>11000
[4,6,3,5,2,1]=>10011=>11001
[4,6,5,1,2,3]=>00011=>11000
[4,6,5,1,3,2]=>01011=>11010
[4,6,5,2,1,3]=>10011=>11001
[4,6,5,2,3,1]=>01011=>11010
[4,6,5,3,1,2]=>01011=>11010
[4,6,5,3,2,1]=>11011=>11011
[5,1,2,3,4,6]=>00010=>01000
[5,1,2,3,6,4]=>00011=>11000
[5,1,2,4,3,6]=>00110=>01100
[5,1,2,4,6,3]=>00011=>11000
[5,1,2,6,3,4]=>00011=>11000
[5,1,2,6,4,3]=>00111=>11100
[5,1,3,2,4,6]=>01010=>01010
[5,1,3,2,6,4]=>01011=>11010
[5,1,3,4,2,6]=>00110=>01100
[5,1,3,4,6,2]=>00011=>11000
[5,1,3,6,2,4]=>00011=>11000
[5,1,3,6,4,2]=>00111=>11100
[5,1,4,2,3,6]=>00110=>01100
[5,1,4,2,6,3]=>00111=>11100
[5,1,4,3,2,6]=>01110=>01110
[5,1,4,3,6,2]=>00111=>11100
[5,1,4,6,2,3]=>00011=>11000
[5,1,4,6,3,2]=>01011=>11010
[5,1,6,2,3,4]=>00011=>11000
[5,1,6,2,4,3]=>00111=>11100
[5,1,6,3,2,4]=>01011=>11010
[5,1,6,3,4,2]=>00111=>11100
[5,1,6,4,2,3]=>00111=>11100
[5,1,6,4,3,2]=>01111=>11110
[5,2,1,3,4,6]=>10010=>01001
[5,2,1,3,6,4]=>10011=>11001
[5,2,1,4,3,6]=>10110=>01101
[5,2,1,4,6,3]=>10011=>11001
[5,2,1,6,3,4]=>10011=>11001
[5,2,1,6,4,3]=>10111=>11101
[5,2,3,1,4,6]=>01010=>01010
[5,2,3,1,6,4]=>01011=>11010
[5,2,3,4,1,6]=>00110=>01100
[5,2,3,4,6,1]=>00011=>11000
[5,2,3,6,1,4]=>00011=>11000
[5,2,3,6,4,1]=>00111=>11100
[5,2,4,1,3,6]=>00110=>01100
[5,2,4,1,6,3]=>00111=>11100
[5,2,4,3,1,6]=>01110=>01110
[5,2,4,3,6,1]=>00111=>11100
[5,2,4,6,1,3]=>00011=>11000
[5,2,4,6,3,1]=>01011=>11010
[5,2,6,1,3,4]=>00011=>11000
[5,2,6,1,4,3]=>00111=>11100
[5,2,6,3,1,4]=>01011=>11010
[5,2,6,3,4,1]=>00111=>11100
[5,2,6,4,1,3]=>00111=>11100
[5,2,6,4,3,1]=>01111=>11110
[5,3,1,2,4,6]=>01010=>01010
[5,3,1,2,6,4]=>01011=>11010
[5,3,1,4,2,6]=>01110=>01110
[5,3,1,4,6,2]=>01011=>11010
[5,3,1,6,2,4]=>01011=>11010
[5,3,1,6,4,2]=>01111=>11110
[5,3,2,1,4,6]=>11010=>01011
[5,3,2,1,6,4]=>11011=>11011
[5,3,2,4,1,6]=>01110=>01110
[5,3,2,4,6,1]=>01011=>11010
[5,3,2,6,1,4]=>01011=>11010
[5,3,2,6,4,1]=>01111=>11110
[5,3,4,1,2,6]=>00110=>01100
[5,3,4,1,6,2]=>00111=>11100
[5,3,4,2,1,6]=>10110=>01101
[5,3,4,2,6,1]=>00111=>11100
[5,3,4,6,1,2]=>00011=>11000
[5,3,4,6,2,1]=>10011=>11001
[5,3,6,1,2,4]=>00011=>11000
[5,3,6,1,4,2]=>00111=>11100
[5,3,6,2,1,4]=>10011=>11001
[5,3,6,2,4,1]=>00111=>11100
[5,3,6,4,1,2]=>00111=>11100
[5,3,6,4,2,1]=>10111=>11101
[5,4,1,2,3,6]=>00110=>01100
[5,4,1,2,6,3]=>00111=>11100
[5,4,1,3,2,6]=>01110=>01110
[5,4,1,3,6,2]=>00111=>11100
[5,4,1,6,2,3]=>00111=>11100
[5,4,1,6,3,2]=>01111=>11110
[5,4,2,1,3,6]=>10110=>01101
[5,4,2,1,6,3]=>10111=>11101
[5,4,2,3,1,6]=>01110=>01110
[5,4,2,3,6,1]=>00111=>11100
[5,4,2,6,1,3]=>00111=>11100
[5,4,2,6,3,1]=>01111=>11110
[5,4,3,1,2,6]=>01110=>01110
[5,4,3,1,6,2]=>01111=>11110
[5,4,3,2,1,6]=>11110=>01111
[5,4,3,2,6,1]=>01111=>11110
[5,4,3,6,1,2]=>00111=>11100
[5,4,3,6,2,1]=>10111=>11101
[5,4,6,1,2,3]=>00011=>11000
[5,4,6,1,3,2]=>01011=>11010
[5,4,6,2,1,3]=>10011=>11001
[5,4,6,2,3,1]=>01011=>11010
[5,4,6,3,1,2]=>01011=>11010
[5,4,6,3,2,1]=>11011=>11011
[5,6,1,2,3,4]=>00001=>10000
[5,6,1,2,4,3]=>00101=>10100
[5,6,1,3,2,4]=>01001=>10010
[5,6,1,3,4,2]=>00101=>10100
[5,6,1,4,2,3]=>00101=>10100
[5,6,1,4,3,2]=>01101=>10110
[5,6,2,1,3,4]=>10001=>10001
[5,6,2,1,4,3]=>10101=>10101
[5,6,2,3,1,4]=>01001=>10010
[5,6,2,3,4,1]=>00101=>10100
[5,6,2,4,1,3]=>00101=>10100
[5,6,2,4,3,1]=>01101=>10110
[5,6,3,1,2,4]=>01001=>10010
[5,6,3,1,4,2]=>01101=>10110
[5,6,3,2,1,4]=>11001=>10011
[5,6,3,2,4,1]=>01101=>10110
[5,6,3,4,1,2]=>00101=>10100
[5,6,3,4,2,1]=>10101=>10101
[5,6,4,1,2,3]=>00101=>10100
[5,6,4,1,3,2]=>01101=>10110
[5,6,4,2,1,3]=>10101=>10101
[5,6,4,2,3,1]=>01101=>10110
[5,6,4,3,1,2]=>01101=>10110
[5,6,4,3,2,1]=>11101=>10111
[6,1,2,3,4,5]=>00001=>10000
[6,1,2,3,5,4]=>00011=>11000
[6,1,2,4,3,5]=>00101=>10100
[6,1,2,4,5,3]=>00011=>11000
[6,1,2,5,3,4]=>00011=>11000
[6,1,2,5,4,3]=>00111=>11100
[6,1,3,2,4,5]=>01001=>10010
[6,1,3,2,5,4]=>01011=>11010
[6,1,3,4,2,5]=>00101=>10100
[6,1,3,4,5,2]=>00011=>11000
[6,1,3,5,2,4]=>00011=>11000
[6,1,3,5,4,2]=>00111=>11100
[6,1,4,2,3,5]=>00101=>10100
[6,1,4,2,5,3]=>00111=>11100
[6,1,4,3,2,5]=>01101=>10110
[6,1,4,3,5,2]=>00111=>11100
[6,1,4,5,2,3]=>00011=>11000
[6,1,4,5,3,2]=>01011=>11010
[6,1,5,2,3,4]=>00011=>11000
[6,1,5,2,4,3]=>00111=>11100
[6,1,5,3,2,4]=>01011=>11010
[6,1,5,3,4,2]=>00111=>11100
[6,1,5,4,2,3]=>00111=>11100
[6,1,5,4,3,2]=>01111=>11110
[6,2,1,3,4,5]=>10001=>10001
[6,2,1,3,5,4]=>10011=>11001
[6,2,1,4,3,5]=>10101=>10101
[6,2,1,4,5,3]=>10011=>11001
[6,2,1,5,3,4]=>10011=>11001
[6,2,1,5,4,3]=>10111=>11101
[6,2,3,1,4,5]=>01001=>10010
[6,2,3,1,5,4]=>01011=>11010
[6,2,3,4,1,5]=>00101=>10100
[6,2,3,4,5,1]=>00011=>11000
[6,2,3,5,1,4]=>00011=>11000
[6,2,3,5,4,1]=>00111=>11100
[6,2,4,1,3,5]=>00101=>10100
[6,2,4,1,5,3]=>00111=>11100
[6,2,4,3,1,5]=>01101=>10110
[6,2,4,3,5,1]=>00111=>11100
[6,2,4,5,1,3]=>00011=>11000
[6,2,4,5,3,1]=>01011=>11010
[6,2,5,1,3,4]=>00011=>11000
[6,2,5,1,4,3]=>00111=>11100
[6,2,5,3,1,4]=>01011=>11010
[6,2,5,3,4,1]=>00111=>11100
[6,2,5,4,1,3]=>00111=>11100
[6,2,5,4,3,1]=>01111=>11110
[6,3,1,2,4,5]=>01001=>10010
[6,3,1,2,5,4]=>01011=>11010
[6,3,1,4,2,5]=>01101=>10110
[6,3,1,4,5,2]=>01011=>11010
[6,3,1,5,2,4]=>01011=>11010
[6,3,1,5,4,2]=>01111=>11110
[6,3,2,1,4,5]=>11001=>10011
[6,3,2,1,5,4]=>11011=>11011
[6,3,2,4,1,5]=>01101=>10110
[6,3,2,4,5,1]=>01011=>11010
[6,3,2,5,1,4]=>01011=>11010
[6,3,2,5,4,1]=>01111=>11110
[6,3,4,1,2,5]=>00101=>10100
[6,3,4,1,5,2]=>00111=>11100
[6,3,4,2,1,5]=>10101=>10101
[6,3,4,2,5,1]=>00111=>11100
[6,3,4,5,1,2]=>00011=>11000
[6,3,4,5,2,1]=>10011=>11001
[6,3,5,1,2,4]=>00011=>11000
[6,3,5,1,4,2]=>00111=>11100
[6,3,5,2,1,4]=>10011=>11001
[6,3,5,2,4,1]=>00111=>11100
[6,3,5,4,1,2]=>00111=>11100
[6,3,5,4,2,1]=>10111=>11101
[6,4,1,2,3,5]=>00101=>10100
[6,4,1,2,5,3]=>00111=>11100
[6,4,1,3,2,5]=>01101=>10110
[6,4,1,3,5,2]=>00111=>11100
[6,4,1,5,2,3]=>00111=>11100
[6,4,1,5,3,2]=>01111=>11110
[6,4,2,1,3,5]=>10101=>10101
[6,4,2,1,5,3]=>10111=>11101
[6,4,2,3,1,5]=>01101=>10110
[6,4,2,3,5,1]=>00111=>11100
[6,4,2,5,1,3]=>00111=>11100
[6,4,2,5,3,1]=>01111=>11110
[6,4,3,1,2,5]=>01101=>10110
[6,4,3,1,5,2]=>01111=>11110
[6,4,3,2,1,5]=>11101=>10111
[6,4,3,2,5,1]=>01111=>11110
[6,4,3,5,1,2]=>00111=>11100
[6,4,3,5,2,1]=>10111=>11101
[6,4,5,1,2,3]=>00011=>11000
[6,4,5,1,3,2]=>01011=>11010
[6,4,5,2,1,3]=>10011=>11001
[6,4,5,2,3,1]=>01011=>11010
[6,4,5,3,1,2]=>01011=>11010
[6,4,5,3,2,1]=>11011=>11011
[6,5,1,2,3,4]=>00011=>11000
[6,5,1,2,4,3]=>00111=>11100
[6,5,1,3,2,4]=>01011=>11010
[6,5,1,3,4,2]=>00111=>11100
[6,5,1,4,2,3]=>00111=>11100
[6,5,1,4,3,2]=>01111=>11110
[6,5,2,1,3,4]=>10011=>11001
[6,5,2,1,4,3]=>10111=>11101
[6,5,2,3,1,4]=>01011=>11010
[6,5,2,3,4,1]=>00111=>11100
[6,5,2,4,1,3]=>00111=>11100
[6,5,2,4,3,1]=>01111=>11110
[6,5,3,1,2,4]=>01011=>11010
[6,5,3,1,4,2]=>01111=>11110
[6,5,3,2,1,4]=>11011=>11011
[6,5,3,2,4,1]=>01111=>11110
[6,5,3,4,1,2]=>00111=>11100
[6,5,3,4,2,1]=>10111=>11101
[6,5,4,1,2,3]=>00111=>11100
[6,5,4,1,3,2]=>01111=>11110
[6,5,4,2,1,3]=>10111=>11101
[6,5,4,2,3,1]=>01111=>11110
[6,5,4,3,1,2]=>01111=>11110
[6,5,4,3,2,1]=>11111=>11111
[1,2,3,4,5,6,7]=>000000=>000000
[1,2,3,4,5,7,6]=>000001=>100000
[1,2,3,4,6,5,7]=>000010=>010000
[1,2,3,4,6,7,5]=>000001=>100000
[1,2,3,4,7,5,6]=>000001=>100000
[1,2,3,4,7,6,5]=>000011=>110000
[1,2,3,5,4,6,7]=>000100=>001000
[1,2,3,5,4,7,6]=>000101=>101000
[1,2,3,5,6,4,7]=>000010=>010000
[1,2,3,5,6,7,4]=>000001=>100000
[1,2,3,5,7,4,6]=>000001=>100000
[1,2,3,5,7,6,4]=>000011=>110000
[1,2,3,6,4,5,7]=>000010=>010000
[1,2,3,6,4,7,5]=>000011=>110000
[1,2,3,6,5,4,7]=>000110=>011000
[1,2,3,6,5,7,4]=>000011=>110000
[1,2,3,6,7,4,5]=>000001=>100000
[1,2,3,6,7,5,4]=>000101=>101000
[1,2,3,7,4,5,6]=>000001=>100000
[1,2,3,7,4,6,5]=>000011=>110000
[1,2,3,7,5,4,6]=>000101=>101000
[1,2,3,7,5,6,4]=>000011=>110000
[1,2,3,7,6,4,5]=>000011=>110000
[1,2,3,7,6,5,4]=>000111=>111000
[1,2,4,3,5,6,7]=>001000=>000100
[1,2,4,3,5,7,6]=>001001=>100100
[1,2,4,3,6,5,7]=>001010=>010100
[1,2,4,3,6,7,5]=>001001=>100100
[1,2,4,3,7,5,6]=>001001=>100100
[1,2,4,3,7,6,5]=>001011=>110100
[1,2,4,5,3,6,7]=>000100=>001000
[1,2,4,5,3,7,6]=>000101=>101000
[1,2,4,5,6,3,7]=>000010=>010000
[1,2,4,5,6,7,3]=>000001=>100000
[1,2,4,5,7,3,6]=>000001=>100000
[1,2,4,5,7,6,3]=>000011=>110000
[1,2,4,6,3,5,7]=>000010=>010000
[1,2,4,6,3,7,5]=>000011=>110000
[1,2,4,6,5,3,7]=>000110=>011000
[1,2,4,6,5,7,3]=>000011=>110000
[1,2,4,6,7,3,5]=>000001=>100000
[1,2,4,6,7,5,3]=>000101=>101000
[1,2,4,7,3,5,6]=>000001=>100000
[1,2,4,7,3,6,5]=>000011=>110000
[1,2,4,7,5,3,6]=>000101=>101000
[1,2,4,7,5,6,3]=>000011=>110000
[1,2,4,7,6,3,5]=>000011=>110000
[1,2,4,7,6,5,3]=>000111=>111000
[1,2,5,3,4,6,7]=>000100=>001000
[1,2,5,3,4,7,6]=>000101=>101000
[1,2,5,3,6,4,7]=>000110=>011000
[1,2,5,3,6,7,4]=>000101=>101000
[1,2,5,3,7,4,6]=>000101=>101000
[1,2,5,3,7,6,4]=>000111=>111000
[1,2,5,4,3,6,7]=>001100=>001100
[1,2,5,4,3,7,6]=>001101=>101100
[1,2,5,4,6,3,7]=>000110=>011000
[1,2,5,4,6,7,3]=>000101=>101000
[1,2,5,4,7,3,6]=>000101=>101000
[1,2,5,4,7,6,3]=>000111=>111000
[1,2,5,6,3,4,7]=>000010=>010000
[1,2,5,6,3,7,4]=>000011=>110000
[1,2,5,6,4,3,7]=>001010=>010100
[1,2,5,6,4,7,3]=>000011=>110000
[1,2,5,6,7,3,4]=>000001=>100000
[1,2,5,6,7,4,3]=>001001=>100100
[1,2,5,7,3,4,6]=>000001=>100000
[1,2,5,7,3,6,4]=>000011=>110000
[1,2,5,7,4,3,6]=>001001=>100100
[1,2,5,7,4,6,3]=>000011=>110000
[1,2,5,7,6,3,4]=>000011=>110000
[1,2,5,7,6,4,3]=>001011=>110100
[1,2,6,3,4,5,7]=>000010=>010000
[1,2,6,3,4,7,5]=>000011=>110000
[1,2,6,3,5,4,7]=>000110=>011000
[1,2,6,3,5,7,4]=>000011=>110000
[1,2,6,3,7,4,5]=>000011=>110000
[1,2,6,3,7,5,4]=>000111=>111000
[1,2,6,4,3,5,7]=>001010=>010100
[1,2,6,4,3,7,5]=>001011=>110100
[1,2,6,4,5,3,7]=>000110=>011000
[1,2,6,4,5,7,3]=>000011=>110000
[1,2,6,4,7,3,5]=>000011=>110000
[1,2,6,4,7,5,3]=>000111=>111000
[1,2,6,5,3,4,7]=>000110=>011000
[1,2,6,5,3,7,4]=>000111=>111000
[1,2,6,5,4,3,7]=>001110=>011100
[1,2,6,5,4,7,3]=>000111=>111000
[1,2,6,5,7,3,4]=>000011=>110000
[1,2,6,5,7,4,3]=>001011=>110100
[1,2,6,7,3,4,5]=>000001=>100000
[1,2,6,7,3,5,4]=>000101=>101000
[1,2,6,7,4,3,5]=>001001=>100100
[1,2,6,7,4,5,3]=>000101=>101000
[1,2,6,7,5,3,4]=>000101=>101000
[1,2,6,7,5,4,3]=>001101=>101100
[1,2,7,3,4,5,6]=>000001=>100000
[1,2,7,3,4,6,5]=>000011=>110000
[1,2,7,3,5,4,6]=>000101=>101000
[1,2,7,3,5,6,4]=>000011=>110000
[1,2,7,3,6,4,5]=>000011=>110000
[1,2,7,3,6,5,4]=>000111=>111000
[1,2,7,4,3,5,6]=>001001=>100100
[1,2,7,4,3,6,5]=>001011=>110100
[1,2,7,4,5,3,6]=>000101=>101000
[1,2,7,4,5,6,3]=>000011=>110000
[1,2,7,4,6,3,5]=>000011=>110000
[1,2,7,4,6,5,3]=>000111=>111000
[1,2,7,5,3,4,6]=>000101=>101000
[1,2,7,5,3,6,4]=>000111=>111000
[1,2,7,5,4,3,6]=>001101=>101100
[1,2,7,5,4,6,3]=>000111=>111000
[1,2,7,5,6,3,4]=>000011=>110000
[1,2,7,5,6,4,3]=>001011=>110100
[1,2,7,6,3,4,5]=>000011=>110000
[1,2,7,6,3,5,4]=>000111=>111000
[1,2,7,6,4,3,5]=>001011=>110100
[1,2,7,6,4,5,3]=>000111=>111000
[1,2,7,6,5,3,4]=>000111=>111000
[1,2,7,6,5,4,3]=>001111=>111100
[1,3,2,4,5,6,7]=>010000=>000010
[1,3,2,4,5,7,6]=>010001=>100010
[1,3,2,4,6,5,7]=>010010=>010010
[1,3,2,4,6,7,5]=>010001=>100010
[1,3,2,4,7,5,6]=>010001=>100010
[1,3,2,4,7,6,5]=>010011=>110010
[1,3,2,5,4,6,7]=>010100=>001010
[1,3,2,5,4,7,6]=>010101=>101010
[1,3,2,5,6,4,7]=>010010=>010010
[1,3,2,5,6,7,4]=>010001=>100010
[1,3,2,5,7,4,6]=>010001=>100010
[1,3,2,5,7,6,4]=>010011=>110010
[1,3,2,6,4,5,7]=>010010=>010010
[1,3,2,6,4,7,5]=>010011=>110010
[1,3,2,6,5,4,7]=>010110=>011010
[1,3,2,6,5,7,4]=>010011=>110010
[1,3,2,6,7,4,5]=>010001=>100010
[1,3,2,6,7,5,4]=>010101=>101010
[1,3,2,7,4,5,6]=>010001=>100010
[1,3,2,7,4,6,5]=>010011=>110010
[1,3,2,7,5,4,6]=>010101=>101010
[1,3,2,7,5,6,4]=>010011=>110010
[1,3,2,7,6,4,5]=>010011=>110010
[1,3,2,7,6,5,4]=>010111=>111010
[1,3,4,2,5,6,7]=>001000=>000100
[1,3,4,2,5,7,6]=>001001=>100100
[1,3,4,2,6,5,7]=>001010=>010100
[1,3,4,2,6,7,5]=>001001=>100100
[1,3,4,2,7,5,6]=>001001=>100100
[1,3,4,2,7,6,5]=>001011=>110100
[1,3,4,5,2,6,7]=>000100=>001000
[1,3,4,5,2,7,6]=>000101=>101000
[1,3,4,5,6,2,7]=>000010=>010000
[1,3,4,5,6,7,2]=>000001=>100000
[1,3,4,5,7,2,6]=>000001=>100000
[1,3,4,5,7,6,2]=>000011=>110000
[1,3,4,6,2,5,7]=>000010=>010000
[1,3,4,6,2,7,5]=>000011=>110000
[1,3,4,6,5,2,7]=>000110=>011000
[1,3,4,6,5,7,2]=>000011=>110000
[1,3,4,6,7,2,5]=>000001=>100000
[1,3,4,6,7,5,2]=>000101=>101000
[1,3,4,7,2,5,6]=>000001=>100000
[1,3,4,7,2,6,5]=>000011=>110000
[1,3,4,7,5,2,6]=>000101=>101000
[1,3,4,7,5,6,2]=>000011=>110000
[1,3,4,7,6,2,5]=>000011=>110000
[1,3,4,7,6,5,2]=>000111=>111000
[1,3,5,2,4,6,7]=>000100=>001000
[1,3,5,2,4,7,6]=>000101=>101000
[1,3,5,2,6,4,7]=>000110=>011000
[1,3,5,2,6,7,4]=>000101=>101000
[1,3,5,2,7,4,6]=>000101=>101000
[1,3,5,2,7,6,4]=>000111=>111000
[1,3,5,4,2,6,7]=>001100=>001100
[1,3,5,4,2,7,6]=>001101=>101100
[1,3,5,4,6,2,7]=>000110=>011000
[1,3,5,4,6,7,2]=>000101=>101000
[1,3,5,4,7,2,6]=>000101=>101000
[1,3,5,4,7,6,2]=>000111=>111000
[1,3,5,6,2,4,7]=>000010=>010000
[1,3,5,6,2,7,4]=>000011=>110000
[1,3,5,6,4,2,7]=>001010=>010100
[1,3,5,6,4,7,2]=>000011=>110000
[1,3,5,6,7,2,4]=>000001=>100000
[1,3,5,6,7,4,2]=>001001=>100100
[1,3,5,7,2,4,6]=>000001=>100000
[1,3,5,7,2,6,4]=>000011=>110000
[1,3,5,7,4,2,6]=>001001=>100100
[1,3,5,7,4,6,2]=>000011=>110000
[1,3,5,7,6,2,4]=>000011=>110000
[1,3,5,7,6,4,2]=>001011=>110100
[1,3,6,2,4,5,7]=>000010=>010000
[1,3,6,2,4,7,5]=>000011=>110000
[1,3,6,2,5,4,7]=>000110=>011000
[1,3,6,2,5,7,4]=>000011=>110000
[1,3,6,2,7,4,5]=>000011=>110000
[1,3,6,2,7,5,4]=>000111=>111000
[1,3,6,4,2,5,7]=>001010=>010100
[1,3,6,4,2,7,5]=>001011=>110100
[1,3,6,4,5,2,7]=>000110=>011000
[1,3,6,4,5,7,2]=>000011=>110000
[1,3,6,4,7,2,5]=>000011=>110000
[1,3,6,4,7,5,2]=>000111=>111000
[1,3,6,5,2,4,7]=>000110=>011000
[1,3,6,5,2,7,4]=>000111=>111000
[1,3,6,5,4,2,7]=>001110=>011100
[1,3,6,5,4,7,2]=>000111=>111000
[1,3,6,5,7,2,4]=>000011=>110000
[1,3,6,5,7,4,2]=>001011=>110100
[1,3,6,7,2,4,5]=>000001=>100000
[1,3,6,7,2,5,4]=>000101=>101000
[1,3,6,7,4,2,5]=>001001=>100100
[1,3,6,7,4,5,2]=>000101=>101000
[1,3,6,7,5,2,4]=>000101=>101000
[1,3,6,7,5,4,2]=>001101=>101100
[1,3,7,2,4,5,6]=>000001=>100000
[1,3,7,2,4,6,5]=>000011=>110000
[1,3,7,2,5,4,6]=>000101=>101000
[1,3,7,2,5,6,4]=>000011=>110000
[1,3,7,2,6,4,5]=>000011=>110000
[1,3,7,2,6,5,4]=>000111=>111000
[1,3,7,4,2,5,6]=>001001=>100100
[1,3,7,4,2,6,5]=>001011=>110100
[1,3,7,4,5,2,6]=>000101=>101000
[1,3,7,4,5,6,2]=>000011=>110000
[1,3,7,4,6,2,5]=>000011=>110000
[1,3,7,4,6,5,2]=>000111=>111000
[1,3,7,5,2,4,6]=>000101=>101000
[1,3,7,5,2,6,4]=>000111=>111000
[1,3,7,5,4,2,6]=>001101=>101100
[1,3,7,5,4,6,2]=>000111=>111000
[1,3,7,5,6,2,4]=>000011=>110000
[1,3,7,5,6,4,2]=>001011=>110100
[1,3,7,6,2,4,5]=>000011=>110000
[1,3,7,6,2,5,4]=>000111=>111000
[1,3,7,6,4,2,5]=>001011=>110100
[1,3,7,6,4,5,2]=>000111=>111000
[1,3,7,6,5,2,4]=>000111=>111000
[1,3,7,6,5,4,2]=>001111=>111100
[1,4,2,3,5,6,7]=>001000=>000100
[1,4,2,3,5,7,6]=>001001=>100100
[1,4,2,3,6,5,7]=>001010=>010100
[1,4,2,3,6,7,5]=>001001=>100100
[1,4,2,3,7,5,6]=>001001=>100100
[1,4,2,3,7,6,5]=>001011=>110100
[1,4,2,5,3,6,7]=>001100=>001100
[1,4,2,5,3,7,6]=>001101=>101100
[1,4,2,5,6,3,7]=>001010=>010100
[1,4,2,5,6,7,3]=>001001=>100100
[1,4,2,5,7,3,6]=>001001=>100100
[1,4,2,5,7,6,3]=>001011=>110100
[1,4,2,6,3,5,7]=>001010=>010100
[1,4,2,6,3,7,5]=>001011=>110100
[1,4,2,6,5,3,7]=>001110=>011100
[1,4,2,6,5,7,3]=>001011=>110100
[1,4,2,6,7,3,5]=>001001=>100100
[1,4,2,6,7,5,3]=>001101=>101100
[1,4,2,7,3,5,6]=>001001=>100100
[1,4,2,7,3,6,5]=>001011=>110100
[1,4,2,7,5,3,6]=>001101=>101100
[1,4,2,7,5,6,3]=>001011=>110100
[1,4,2,7,6,3,5]=>001011=>110100
[1,4,2,7,6,5,3]=>001111=>111100
[1,4,3,2,5,6,7]=>011000=>000110
[1,4,3,2,5,7,6]=>011001=>100110
[1,4,3,2,6,5,7]=>011010=>010110
[1,4,3,2,6,7,5]=>011001=>100110
[1,4,3,2,7,5,6]=>011001=>100110
[1,4,3,2,7,6,5]=>011011=>110110
[1,4,3,5,2,6,7]=>001100=>001100
[1,4,3,5,2,7,6]=>001101=>101100
[1,4,3,5,6,2,7]=>001010=>010100
[1,4,3,5,6,7,2]=>001001=>100100
[1,4,3,5,7,2,6]=>001001=>100100
[1,4,3,5,7,6,2]=>001011=>110100
[1,4,3,6,2,5,7]=>001010=>010100
[1,4,3,6,2,7,5]=>001011=>110100
[1,4,3,6,5,2,7]=>001110=>011100
[1,4,3,6,5,7,2]=>001011=>110100
[1,4,3,6,7,2,5]=>001001=>100100
[1,4,3,6,7,5,2]=>001101=>101100
[1,4,3,7,2,5,6]=>001001=>100100
[1,4,3,7,2,6,5]=>001011=>110100
[1,4,3,7,5,2,6]=>001101=>101100
[1,4,3,7,5,6,2]=>001011=>110100
[1,4,3,7,6,2,5]=>001011=>110100
[1,4,3,7,6,5,2]=>001111=>111100
[1,4,5,2,3,6,7]=>000100=>001000
[1,4,5,2,3,7,6]=>000101=>101000
[1,4,5,2,6,3,7]=>000110=>011000
[1,4,5,2,6,7,3]=>000101=>101000
[1,4,5,2,7,3,6]=>000101=>101000
[1,4,5,2,7,6,3]=>000111=>111000
[1,4,5,3,2,6,7]=>010100=>001010
[1,4,5,3,2,7,6]=>010101=>101010
[1,4,5,3,6,2,7]=>000110=>011000
[1,4,5,3,6,7,2]=>000101=>101000
[1,4,5,3,7,2,6]=>000101=>101000
[1,4,5,3,7,6,2]=>000111=>111000
[1,4,5,6,2,3,7]=>000010=>010000
[1,4,5,6,2,7,3]=>000011=>110000
[1,4,5,6,3,2,7]=>010010=>010010
[1,4,5,6,3,7,2]=>000011=>110000
[1,4,5,6,7,2,3]=>000001=>100000
[1,4,5,6,7,3,2]=>010001=>100010
[1,4,5,7,2,3,6]=>000001=>100000
[1,4,5,7,2,6,3]=>000011=>110000
[1,4,5,7,3,2,6]=>010001=>100010
[1,4,5,7,3,6,2]=>000011=>110000
[1,4,5,7,6,2,3]=>000011=>110000
[1,4,5,7,6,3,2]=>010011=>110010
[1,4,6,2,3,5,7]=>000010=>010000
[1,4,6,2,3,7,5]=>000011=>110000
[1,4,6,2,5,3,7]=>000110=>011000
[1,4,6,2,5,7,3]=>000011=>110000
[1,4,6,2,7,3,5]=>000011=>110000
[1,4,6,2,7,5,3]=>000111=>111000
[1,4,6,3,2,5,7]=>010010=>010010
[1,4,6,3,2,7,5]=>010011=>110010
[1,4,6,3,5,2,7]=>000110=>011000
[1,4,6,3,5,7,2]=>000011=>110000
[1,4,6,3,7,2,5]=>000011=>110000
[1,4,6,3,7,5,2]=>000111=>111000
[1,4,6,5,2,3,7]=>000110=>011000
[1,4,6,5,2,7,3]=>000111=>111000
[1,4,6,5,3,2,7]=>010110=>011010
[1,4,6,5,3,7,2]=>000111=>111000
[1,4,6,5,7,2,3]=>000011=>110000
[1,4,6,5,7,3,2]=>010011=>110010
[1,4,6,7,2,3,5]=>000001=>100000
[1,4,6,7,2,5,3]=>000101=>101000
[1,4,6,7,3,2,5]=>010001=>100010
[1,4,6,7,3,5,2]=>000101=>101000
[1,4,6,7,5,2,3]=>000101=>101000
[1,4,6,7,5,3,2]=>010101=>101010
[1,4,7,2,3,5,6]=>000001=>100000
[1,4,7,2,3,6,5]=>000011=>110000
[1,4,7,2,5,3,6]=>000101=>101000
[1,4,7,2,5,6,3]=>000011=>110000
[1,4,7,2,6,3,5]=>000011=>110000
[1,4,7,2,6,5,3]=>000111=>111000
[1,4,7,3,2,5,6]=>010001=>100010
[1,4,7,3,2,6,5]=>010011=>110010
[1,4,7,3,5,2,6]=>000101=>101000
[1,4,7,3,5,6,2]=>000011=>110000
[1,4,7,3,6,2,5]=>000011=>110000
[1,4,7,3,6,5,2]=>000111=>111000
[1,4,7,5,2,3,6]=>000101=>101000
[1,4,7,5,2,6,3]=>000111=>111000
[1,4,7,5,3,2,6]=>010101=>101010
[1,4,7,5,3,6,2]=>000111=>111000
[1,4,7,5,6,2,3]=>000011=>110000
[1,4,7,5,6,3,2]=>010011=>110010
[1,4,7,6,2,3,5]=>000011=>110000
[1,4,7,6,2,5,3]=>000111=>111000
[1,4,7,6,3,2,5]=>010011=>110010
[1,4,7,6,3,5,2]=>000111=>111000
[1,4,7,6,5,2,3]=>000111=>111000
[1,4,7,6,5,3,2]=>010111=>111010
[1,5,2,3,4,6,7]=>000100=>001000
[1,5,2,3,4,7,6]=>000101=>101000
[1,5,2,3,6,4,7]=>000110=>011000
[1,5,2,3,6,7,4]=>000101=>101000
[1,5,2,3,7,4,6]=>000101=>101000
[1,5,2,3,7,6,4]=>000111=>111000
[1,5,2,4,3,6,7]=>001100=>001100
[1,5,2,4,3,7,6]=>001101=>101100
[1,5,2,4,6,3,7]=>000110=>011000
[1,5,2,4,6,7,3]=>000101=>101000
[1,5,2,4,7,3,6]=>000101=>101000
[1,5,2,4,7,6,3]=>000111=>111000
[1,5,2,6,3,4,7]=>000110=>011000
[1,5,2,6,3,7,4]=>000111=>111000
[1,5,2,6,4,3,7]=>001110=>011100
[1,5,2,6,4,7,3]=>000111=>111000
[1,5,2,6,7,3,4]=>000101=>101000
[1,5,2,6,7,4,3]=>001101=>101100
[1,5,2,7,3,4,6]=>000101=>101000
[1,5,2,7,3,6,4]=>000111=>111000
[1,5,2,7,4,3,6]=>001101=>101100
[1,5,2,7,4,6,3]=>000111=>111000
[1,5,2,7,6,3,4]=>000111=>111000
[1,5,2,7,6,4,3]=>001111=>111100
[1,5,3,2,4,6,7]=>010100=>001010
[1,5,3,2,4,7,6]=>010101=>101010
[1,5,3,2,6,4,7]=>010110=>011010
[1,5,3,2,6,7,4]=>010101=>101010
[1,5,3,2,7,4,6]=>010101=>101010
[1,5,3,2,7,6,4]=>010111=>111010
[1,5,3,4,2,6,7]=>001100=>001100
[1,5,3,4,2,7,6]=>001101=>101100
[1,5,3,4,6,2,7]=>000110=>011000
[1,5,3,4,6,7,2]=>000101=>101000
[1,5,3,4,7,2,6]=>000101=>101000
[1,5,3,4,7,6,2]=>000111=>111000
[1,5,3,6,2,4,7]=>000110=>011000
[1,5,3,6,2,7,4]=>000111=>111000
[1,5,3,6,4,2,7]=>001110=>011100
[1,5,3,6,4,7,2]=>000111=>111000
[1,5,3,6,7,2,4]=>000101=>101000
[1,5,3,6,7,4,2]=>001101=>101100
[1,5,3,7,2,4,6]=>000101=>101000
[1,5,3,7,2,6,4]=>000111=>111000
[1,5,3,7,4,2,6]=>001101=>101100
[1,5,3,7,4,6,2]=>000111=>111000
[1,5,3,7,6,2,4]=>000111=>111000
[1,5,3,7,6,4,2]=>001111=>111100
[1,5,4,2,3,6,7]=>001100=>001100
[1,5,4,2,3,7,6]=>001101=>101100
[1,5,4,2,6,3,7]=>001110=>011100
[1,5,4,2,6,7,3]=>001101=>101100
[1,5,4,2,7,3,6]=>001101=>101100
[1,5,4,2,7,6,3]=>001111=>111100
[1,5,4,3,2,6,7]=>011100=>001110
[1,5,4,3,2,7,6]=>011101=>101110
[1,5,4,3,6,2,7]=>001110=>011100
[1,5,4,3,6,7,2]=>001101=>101100
[1,5,4,3,7,2,6]=>001101=>101100
[1,5,4,3,7,6,2]=>001111=>111100
[1,5,4,6,2,3,7]=>000110=>011000
[1,5,4,6,2,7,3]=>000111=>111000
[1,5,4,6,3,2,7]=>010110=>011010
[1,5,4,6,3,7,2]=>000111=>111000
[1,5,4,6,7,2,3]=>000101=>101000
[1,5,4,6,7,3,2]=>010101=>101010
[1,5,4,7,2,3,6]=>000101=>101000
[1,5,4,7,2,6,3]=>000111=>111000
[1,5,4,7,3,2,6]=>010101=>101010
[1,5,4,7,3,6,2]=>000111=>111000
[1,5,4,7,6,2,3]=>000111=>111000
[1,5,4,7,6,3,2]=>010111=>111010
[1,5,6,2,3,4,7]=>000010=>010000
[1,5,6,2,3,7,4]=>000011=>110000
[1,5,6,2,4,3,7]=>001010=>010100
[1,5,6,2,4,7,3]=>000011=>110000
[1,5,6,2,7,3,4]=>000011=>110000
[1,5,6,2,7,4,3]=>001011=>110100
[1,5,6,3,2,4,7]=>010010=>010010
[1,5,6,3,2,7,4]=>010011=>110010
[1,5,6,3,4,2,7]=>001010=>010100
[1,5,6,3,4,7,2]=>000011=>110000
[1,5,6,3,7,2,4]=>000011=>110000
[1,5,6,3,7,4,2]=>001011=>110100
[1,5,6,4,2,3,7]=>001010=>010100
[1,5,6,4,2,7,3]=>001011=>110100
[1,5,6,4,3,2,7]=>011010=>010110
[1,5,6,4,3,7,2]=>001011=>110100
[1,5,6,4,7,2,3]=>000011=>110000
[1,5,6,4,7,3,2]=>010011=>110010
[1,5,6,7,2,3,4]=>000001=>100000
[1,5,6,7,2,4,3]=>001001=>100100
[1,5,6,7,3,2,4]=>010001=>100010
[1,5,6,7,3,4,2]=>001001=>100100
[1,5,6,7,4,2,3]=>001001=>100100
[1,5,6,7,4,3,2]=>011001=>100110
[1,5,7,2,3,4,6]=>000001=>100000
[1,5,7,2,3,6,4]=>000011=>110000
[1,5,7,2,4,3,6]=>001001=>100100
[1,5,7,2,4,6,3]=>000011=>110000
[1,5,7,2,6,3,4]=>000011=>110000
[1,5,7,2,6,4,3]=>001011=>110100
[1,5,7,3,2,4,6]=>010001=>100010
[1,5,7,3,2,6,4]=>010011=>110010
[1,5,7,3,4,2,6]=>001001=>100100
[1,5,7,3,4,6,2]=>000011=>110000
[1,5,7,3,6,2,4]=>000011=>110000
[1,5,7,3,6,4,2]=>001011=>110100
[1,5,7,4,2,3,6]=>001001=>100100
[1,5,7,4,2,6,3]=>001011=>110100
[1,5,7,4,3,2,6]=>011001=>100110
[1,5,7,4,3,6,2]=>001011=>110100
[1,5,7,4,6,2,3]=>000011=>110000
[1,5,7,4,6,3,2]=>010011=>110010
[1,5,7,6,2,3,4]=>000011=>110000
[1,5,7,6,2,4,3]=>001011=>110100
[1,5,7,6,3,2,4]=>010011=>110010
[1,5,7,6,3,4,2]=>001011=>110100
[1,5,7,6,4,2,3]=>001011=>110100
[1,5,7,6,4,3,2]=>011011=>110110
[1,6,2,3,4,5,7]=>000010=>010000
[1,6,2,3,4,7,5]=>000011=>110000
[1,6,2,3,5,4,7]=>000110=>011000
[1,6,2,3,5,7,4]=>000011=>110000
[1,6,2,3,7,4,5]=>000011=>110000
[1,6,2,3,7,5,4]=>000111=>111000
[1,6,2,4,3,5,7]=>001010=>010100
[1,6,2,4,3,7,5]=>001011=>110100
[1,6,2,4,5,3,7]=>000110=>011000
[1,6,2,4,5,7,3]=>000011=>110000
[1,6,2,4,7,3,5]=>000011=>110000
[1,6,2,4,7,5,3]=>000111=>111000
[1,6,2,5,3,4,7]=>000110=>011000
[1,6,2,5,3,7,4]=>000111=>111000
[1,6,2,5,4,3,7]=>001110=>011100
[1,6,2,5,4,7,3]=>000111=>111000
[1,6,2,5,7,3,4]=>000011=>110000
[1,6,2,5,7,4,3]=>001011=>110100
[1,6,2,7,3,4,5]=>000011=>110000
[1,6,2,7,3,5,4]=>000111=>111000
[1,6,2,7,4,3,5]=>001011=>110100
[1,6,2,7,4,5,3]=>000111=>111000
[1,6,2,7,5,3,4]=>000111=>111000
[1,6,2,7,5,4,3]=>001111=>111100
[1,6,3,2,4,5,7]=>010010=>010010
[1,6,3,2,4,7,5]=>010011=>110010
[1,6,3,2,5,4,7]=>010110=>011010
[1,6,3,2,5,7,4]=>010011=>110010
[1,6,3,2,7,4,5]=>010011=>110010
[1,6,3,2,7,5,4]=>010111=>111010
[1,6,3,4,2,5,7]=>001010=>010100
[1,6,3,4,2,7,5]=>001011=>110100
[1,6,3,4,5,2,7]=>000110=>011000
[1,6,3,4,5,7,2]=>000011=>110000
[1,6,3,4,7,2,5]=>000011=>110000
[1,6,3,4,7,5,2]=>000111=>111000
[1,6,3,5,2,4,7]=>000110=>011000
[1,6,3,5,2,7,4]=>000111=>111000
[1,6,3,5,4,2,7]=>001110=>011100
[1,6,3,5,4,7,2]=>000111=>111000
[1,6,3,5,7,2,4]=>000011=>110000
[1,6,3,5,7,4,2]=>001011=>110100
[1,6,3,7,2,4,5]=>000011=>110000
[1,6,3,7,2,5,4]=>000111=>111000
[1,6,3,7,4,2,5]=>001011=>110100
[1,6,3,7,4,5,2]=>000111=>111000
[1,6,3,7,5,2,4]=>000111=>111000
[1,6,3,7,5,4,2]=>001111=>111100
[1,6,4,2,3,5,7]=>001010=>010100
[1,6,4,2,3,7,5]=>001011=>110100
[1,6,4,2,5,3,7]=>001110=>011100
[1,6,4,2,5,7,3]=>001011=>110100
[1,6,4,2,7,3,5]=>001011=>110100
[1,6,4,2,7,5,3]=>001111=>111100
[1,6,4,3,2,5,7]=>011010=>010110
[1,6,4,3,2,7,5]=>011011=>110110
[1,6,4,3,5,2,7]=>001110=>011100
[1,6,4,3,5,7,2]=>001011=>110100
[1,6,4,3,7,2,5]=>001011=>110100
[1,6,4,3,7,5,2]=>001111=>111100
[1,6,4,5,2,3,7]=>000110=>011000
[1,6,4,5,2,7,3]=>000111=>111000
[1,6,4,5,3,2,7]=>010110=>011010
[1,6,4,5,3,7,2]=>000111=>111000
[1,6,4,5,7,2,3]=>000011=>110000
[1,6,4,5,7,3,2]=>010011=>110010
[1,6,4,7,2,3,5]=>000011=>110000
[1,6,4,7,2,5,3]=>000111=>111000
[1,6,4,7,3,2,5]=>010011=>110010
[1,6,4,7,3,5,2]=>000111=>111000
[1,6,4,7,5,2,3]=>000111=>111000
[1,6,4,7,5,3,2]=>010111=>111010
[1,6,5,2,3,4,7]=>000110=>011000
[1,6,5,2,3,7,4]=>000111=>111000
[1,6,5,2,4,3,7]=>001110=>011100
[1,6,5,2,4,7,3]=>000111=>111000
[1,6,5,2,7,3,4]=>000111=>111000
[1,6,5,2,7,4,3]=>001111=>111100
[1,6,5,3,2,4,7]=>010110=>011010
[1,6,5,3,2,7,4]=>010111=>111010
[1,6,5,3,4,2,7]=>001110=>011100
[1,6,5,3,4,7,2]=>000111=>111000
[1,6,5,3,7,2,4]=>000111=>111000
[1,6,5,3,7,4,2]=>001111=>111100
[1,6,5,4,2,3,7]=>001110=>011100
[1,6,5,4,2,7,3]=>001111=>111100
[1,6,5,4,3,2,7]=>011110=>011110
[1,6,5,4,3,7,2]=>001111=>111100
[1,6,5,4,7,2,3]=>000111=>111000
[1,6,5,4,7,3,2]=>010111=>111010
[1,6,5,7,2,3,4]=>000011=>110000
[1,6,5,7,2,4,3]=>001011=>110100
[1,6,5,7,3,2,4]=>010011=>110010
[1,6,5,7,3,4,2]=>001011=>110100
[1,6,5,7,4,2,3]=>001011=>110100
[1,6,5,7,4,3,2]=>011011=>110110
[1,6,7,2,3,4,5]=>000001=>100000
[1,6,7,2,3,5,4]=>000101=>101000
[1,6,7,2,4,3,5]=>001001=>100100
[1,6,7,2,4,5,3]=>000101=>101000
[1,6,7,2,5,3,4]=>000101=>101000
[1,6,7,2,5,4,3]=>001101=>101100
[1,6,7,3,2,4,5]=>010001=>100010
[1,6,7,3,2,5,4]=>010101=>101010
[1,6,7,3,4,2,5]=>001001=>100100
[1,6,7,3,4,5,2]=>000101=>101000
[1,6,7,3,5,2,4]=>000101=>101000
[1,6,7,3,5,4,2]=>001101=>101100
[1,6,7,4,2,3,5]=>001001=>100100
[1,6,7,4,2,5,3]=>001101=>101100
[1,6,7,4,3,2,5]=>011001=>100110
[1,6,7,4,3,5,2]=>001101=>101100
[1,6,7,4,5,2,3]=>000101=>101000
[1,6,7,4,5,3,2]=>010101=>101010
[1,6,7,5,2,3,4]=>000101=>101000
[1,6,7,5,2,4,3]=>001101=>101100
[1,6,7,5,3,2,4]=>010101=>101010
[1,6,7,5,3,4,2]=>001101=>101100
[1,6,7,5,4,2,3]=>001101=>101100
[1,6,7,5,4,3,2]=>011101=>101110
[1,7,2,3,4,5,6]=>000001=>100000
[1,7,2,3,4,6,5]=>000011=>110000
[1,7,2,3,5,4,6]=>000101=>101000
[1,7,2,3,5,6,4]=>000011=>110000
[1,7,2,3,6,4,5]=>000011=>110000
[1,7,2,3,6,5,4]=>000111=>111000
[1,7,2,4,3,5,6]=>001001=>100100
[1,7,2,4,3,6,5]=>001011=>110100
[1,7,2,4,5,3,6]=>000101=>101000
[1,7,2,4,5,6,3]=>000011=>110000
[1,7,2,4,6,3,5]=>000011=>110000
[1,7,2,4,6,5,3]=>000111=>111000
[1,7,2,5,3,4,6]=>000101=>101000
[1,7,2,5,3,6,4]=>000111=>111000
[1,7,2,5,4,3,6]=>001101=>101100
[1,7,2,5,4,6,3]=>000111=>111000
[1,7,2,5,6,3,4]=>000011=>110000
[1,7,2,5,6,4,3]=>001011=>110100
[1,7,2,6,3,4,5]=>000011=>110000
[1,7,2,6,3,5,4]=>000111=>111000
[1,7,2,6,4,3,5]=>001011=>110100
[1,7,2,6,4,5,3]=>000111=>111000
[1,7,2,6,5,3,4]=>000111=>111000
[1,7,2,6,5,4,3]=>001111=>111100
[1,7,3,2,4,5,6]=>010001=>100010
[1,7,3,2,4,6,5]=>010011=>110010
[1,7,3,2,5,4,6]=>010101=>101010
[1,7,3,2,5,6,4]=>010011=>110010
[1,7,3,2,6,4,5]=>010011=>110010
[1,7,3,2,6,5,4]=>010111=>111010
[1,7,3,4,2,5,6]=>001001=>100100
[1,7,3,4,2,6,5]=>001011=>110100
[1,7,3,4,5,2,6]=>000101=>101000
[1,7,3,4,5,6,2]=>000011=>110000
[1,7,3,4,6,2,5]=>000011=>110000
[1,7,3,4,6,5,2]=>000111=>111000
[1,7,3,5,2,4,6]=>000101=>101000
[1,7,3,5,2,6,4]=>000111=>111000
[1,7,3,5,4,2,6]=>001101=>101100
[1,7,3,5,4,6,2]=>000111=>111000
[1,7,3,5,6,2,4]=>000011=>110000
[1,7,3,5,6,4,2]=>001011=>110100
[1,7,3,6,2,4,5]=>000011=>110000
[1,7,3,6,2,5,4]=>000111=>111000
[1,7,3,6,4,2,5]=>001011=>110100
[1,7,3,6,4,5,2]=>000111=>111000
[1,7,3,6,5,2,4]=>000111=>111000
[1,7,3,6,5,4,2]=>001111=>111100
[1,7,4,2,3,5,6]=>001001=>100100
[1,7,4,2,3,6,5]=>001011=>110100
[1,7,4,2,5,3,6]=>001101=>101100
[1,7,4,2,5,6,3]=>001011=>110100
[1,7,4,2,6,3,5]=>001011=>110100
[1,7,4,2,6,5,3]=>001111=>111100
[1,7,4,3,2,5,6]=>011001=>100110
[1,7,4,3,2,6,5]=>011011=>110110
[1,7,4,3,5,2,6]=>001101=>101100
[1,7,4,3,5,6,2]=>001011=>110100
[1,7,4,3,6,2,5]=>001011=>110100
[1,7,4,3,6,5,2]=>001111=>111100
[1,7,4,5,2,3,6]=>000101=>101000
[1,7,4,5,2,6,3]=>000111=>111000
[1,7,4,5,3,2,6]=>010101=>101010
[1,7,4,5,3,6,2]=>000111=>111000
[1,7,4,5,6,2,3]=>000011=>110000
[1,7,4,5,6,3,2]=>010011=>110010
[1,7,4,6,2,3,5]=>000011=>110000
[1,7,4,6,2,5,3]=>000111=>111000
[1,7,4,6,3,2,5]=>010011=>110010
[1,7,4,6,3,5,2]=>000111=>111000
[1,7,4,6,5,2,3]=>000111=>111000
[1,7,4,6,5,3,2]=>010111=>111010
[1,7,5,2,3,4,6]=>000101=>101000
[1,7,5,2,3,6,4]=>000111=>111000
[1,7,5,2,4,3,6]=>001101=>101100
[1,7,5,2,4,6,3]=>000111=>111000
[1,7,5,2,6,3,4]=>000111=>111000
[1,7,5,2,6,4,3]=>001111=>111100
[1,7,5,3,2,4,6]=>010101=>101010
[1,7,5,3,2,6,4]=>010111=>111010
[1,7,5,3,4,2,6]=>001101=>101100
[1,7,5,3,4,6,2]=>000111=>111000
[1,7,5,3,6,2,4]=>000111=>111000
[1,7,5,3,6,4,2]=>001111=>111100
[1,7,5,4,2,3,6]=>001101=>101100
[1,7,5,4,2,6,3]=>001111=>111100
[1,7,5,4,3,2,6]=>011101=>101110
[1,7,5,4,3,6,2]=>001111=>111100
[1,7,5,4,6,2,3]=>000111=>111000
[1,7,5,4,6,3,2]=>010111=>111010
[1,7,5,6,2,3,4]=>000011=>110000
[1,7,5,6,2,4,3]=>001011=>110100
[1,7,5,6,3,2,4]=>010011=>110010
[1,7,5,6,3,4,2]=>001011=>110100
[1,7,5,6,4,2,3]=>001011=>110100
[1,7,5,6,4,3,2]=>011011=>110110
[1,7,6,2,3,4,5]=>000011=>110000
[1,7,6,2,3,5,4]=>000111=>111000
[1,7,6,2,4,3,5]=>001011=>110100
[1,7,6,2,4,5,3]=>000111=>111000
[1,7,6,2,5,3,4]=>000111=>111000
[1,7,6,2,5,4,3]=>001111=>111100
[1,7,6,3,2,4,5]=>010011=>110010
[1,7,6,3,2,5,4]=>010111=>111010
[1,7,6,3,4,2,5]=>001011=>110100
[1,7,6,3,4,5,2]=>000111=>111000
[1,7,6,3,5,2,4]=>000111=>111000
[1,7,6,3,5,4,2]=>001111=>111100
[1,7,6,4,2,3,5]=>001011=>110100
[1,7,6,4,2,5,3]=>001111=>111100
[1,7,6,4,3,2,5]=>011011=>110110
[1,7,6,4,3,5,2]=>001111=>111100
[1,7,6,4,5,2,3]=>000111=>111000
[1,7,6,4,5,3,2]=>010111=>111010
[1,7,6,5,2,3,4]=>000111=>111000
[1,7,6,5,2,4,3]=>001111=>111100
[1,7,6,5,3,2,4]=>010111=>111010
[1,7,6,5,3,4,2]=>001111=>111100
[1,7,6,5,4,2,3]=>001111=>111100
[1,7,6,5,4,3,2]=>011111=>111110
[2,1,3,4,5,6,7]=>100000=>000001
[2,1,3,4,5,7,6]=>100001=>100001
[2,1,3,4,6,5,7]=>100010=>010001
[2,1,3,4,6,7,5]=>100001=>100001
[2,1,3,4,7,5,6]=>100001=>100001
[2,1,3,4,7,6,5]=>100011=>110001
[2,1,3,5,4,6,7]=>100100=>001001
[2,1,3,5,4,7,6]=>100101=>101001
[2,1,3,5,6,4,7]=>100010=>010001
[2,1,3,5,6,7,4]=>100001=>100001
[2,1,3,5,7,4,6]=>100001=>100001
[2,1,3,5,7,6,4]=>100011=>110001
[2,1,3,6,4,5,7]=>100010=>010001
[2,1,3,6,4,7,5]=>100011=>110001
[2,1,3,6,5,4,7]=>100110=>011001
[2,1,3,6,5,7,4]=>100011=>110001
[2,1,3,6,7,4,5]=>100001=>100001
[2,1,3,6,7,5,4]=>100101=>101001
[2,1,3,7,4,5,6]=>100001=>100001
[2,1,3,7,4,6,5]=>100011=>110001
[2,1,3,7,5,4,6]=>100101=>101001
[2,1,3,7,5,6,4]=>100011=>110001
[2,1,3,7,6,4,5]=>100011=>110001
[2,1,3,7,6,5,4]=>100111=>111001
[2,1,4,3,5,6,7]=>101000=>000101
[2,1,4,3,5,7,6]=>101001=>100101
[2,1,4,3,6,5,7]=>101010=>010101
[2,1,4,3,6,7,5]=>101001=>100101
[2,1,4,3,7,5,6]=>101001=>100101
[2,1,4,3,7,6,5]=>101011=>110101
[2,1,4,5,3,6,7]=>100100=>001001
[2,1,4,5,3,7,6]=>100101=>101001
[2,1,4,5,6,3,7]=>100010=>010001
[2,1,4,5,6,7,3]=>100001=>100001
[2,1,4,5,7,3,6]=>100001=>100001
[2,1,4,5,7,6,3]=>100011=>110001
[2,1,4,6,3,5,7]=>100010=>010001
[2,1,4,6,3,7,5]=>100011=>110001
[2,1,4,6,5,3,7]=>100110=>011001
[2,1,4,6,5,7,3]=>100011=>110001
[2,1,4,6,7,3,5]=>100001=>100001
[2,1,4,6,7,5,3]=>100101=>101001
[2,1,4,7,3,5,6]=>100001=>100001
[2,1,4,7,3,6,5]=>100011=>110001
[2,1,4,7,5,3,6]=>100101=>101001
[2,1,4,7,5,6,3]=>100011=>110001
[2,1,4,7,6,3,5]=>100011=>110001
[2,1,4,7,6,5,3]=>100111=>111001
[2,1,5,3,4,6,7]=>100100=>001001
[2,1,5,3,4,7,6]=>100101=>101001
[2,1,5,3,6,4,7]=>100110=>011001
[2,1,5,3,6,7,4]=>100101=>101001
[2,1,5,3,7,4,6]=>100101=>101001
[2,1,5,3,7,6,4]=>100111=>111001
[2,1,5,4,3,6,7]=>101100=>001101
[2,1,5,4,3,7,6]=>101101=>101101
[2,1,5,4,6,3,7]=>100110=>011001
[2,1,5,4,6,7,3]=>100101=>101001
[2,1,5,4,7,3,6]=>100101=>101001
[2,1,5,4,7,6,3]=>100111=>111001
[2,1,5,6,3,4,7]=>100010=>010001
[2,1,5,6,3,7,4]=>100011=>110001
[2,1,5,6,4,3,7]=>101010=>010101
[2,1,5,6,4,7,3]=>100011=>110001
[2,1,5,6,7,3,4]=>100001=>100001
[2,1,5,6,7,4,3]=>101001=>100101
[2,1,5,7,3,4,6]=>100001=>100001
[2,1,5,7,3,6,4]=>100011=>110001
[2,1,5,7,4,3,6]=>101001=>100101
[2,1,5,7,4,6,3]=>100011=>110001
[2,1,5,7,6,3,4]=>100011=>110001
[2,1,5,7,6,4,3]=>101011=>110101
[2,1,6,3,4,5,7]=>100010=>010001
[2,1,6,3,4,7,5]=>100011=>110001
[2,1,6,3,5,4,7]=>100110=>011001
[2,1,6,3,5,7,4]=>100011=>110001
[2,1,6,3,7,4,5]=>100011=>110001
[2,1,6,3,7,5,4]=>100111=>111001
[2,1,6,4,3,5,7]=>101010=>010101
[2,1,6,4,3,7,5]=>101011=>110101
[2,1,6,4,5,3,7]=>100110=>011001
[2,1,6,4,5,7,3]=>100011=>110001
[2,1,6,4,7,3,5]=>100011=>110001
[2,1,6,4,7,5,3]=>100111=>111001
[2,1,6,5,3,4,7]=>100110=>011001
[2,1,6,5,3,7,4]=>100111=>111001
[2,1,6,5,4,3,7]=>101110=>011101
[2,1,6,5,4,7,3]=>100111=>111001
[2,1,6,5,7,3,4]=>100011=>110001
[2,1,6,5,7,4,3]=>101011=>110101
[2,1,6,7,3,4,5]=>100001=>100001
[2,1,6,7,3,5,4]=>100101=>101001
[2,1,6,7,4,3,5]=>101001=>100101
[2,1,6,7,4,5,3]=>100101=>101001
[2,1,6,7,5,3,4]=>100101=>101001
[2,1,6,7,5,4,3]=>101101=>101101
[2,1,7,3,4,5,6]=>100001=>100001
[2,1,7,3,4,6,5]=>100011=>110001
[2,1,7,3,5,4,6]=>100101=>101001
[2,1,7,3,5,6,4]=>100011=>110001
[2,1,7,3,6,4,5]=>100011=>110001
[2,1,7,3,6,5,4]=>100111=>111001
[2,1,7,4,3,5,6]=>101001=>100101
[2,1,7,4,3,6,5]=>101011=>110101
[2,1,7,4,5,3,6]=>100101=>101001
[2,1,7,4,5,6,3]=>100011=>110001
[2,1,7,4,6,3,5]=>100011=>110001
[2,1,7,4,6,5,3]=>100111=>111001
[2,1,7,5,3,4,6]=>100101=>101001
[2,1,7,5,3,6,4]=>100111=>111001
[2,1,7,5,4,3,6]=>101101=>101101
[2,1,7,5,4,6,3]=>100111=>111001
[2,1,7,5,6,3,4]=>100011=>110001
[2,1,7,5,6,4,3]=>101011=>110101
[2,1,7,6,3,4,5]=>100011=>110001
[2,1,7,6,3,5,4]=>100111=>111001
[2,1,7,6,4,3,5]=>101011=>110101
[2,1,7,6,4,5,3]=>100111=>111001
[2,1,7,6,5,3,4]=>100111=>111001
[2,1,7,6,5,4,3]=>101111=>111101
[2,3,1,4,5,6,7]=>010000=>000010
[2,3,1,4,5,7,6]=>010001=>100010
[2,3,1,4,6,5,7]=>010010=>010010
[2,3,1,4,6,7,5]=>010001=>100010
[2,3,1,4,7,5,6]=>010001=>100010
[2,3,1,4,7,6,5]=>010011=>110010
[2,3,1,5,4,6,7]=>010100=>001010
[2,3,1,5,4,7,6]=>010101=>101010
[2,3,1,5,6,4,7]=>010010=>010010
[2,3,1,5,6,7,4]=>010001=>100010
[2,3,1,5,7,4,6]=>010001=>100010
[2,3,1,5,7,6,4]=>010011=>110010
[2,3,1,6,4,5,7]=>010010=>010010
[2,3,1,6,4,7,5]=>010011=>110010
[2,3,1,6,5,4,7]=>010110=>011010
[2,3,1,6,5,7,4]=>010011=>110010
[2,3,1,6,7,4,5]=>010001=>100010
[2,3,1,6,7,5,4]=>010101=>101010
[2,3,1,7,4,5,6]=>010001=>100010
[2,3,1,7,4,6,5]=>010011=>110010
[2,3,1,7,5,4,6]=>010101=>101010
[2,3,1,7,5,6,4]=>010011=>110010
[2,3,1,7,6,4,5]=>010011=>110010
[2,3,1,7,6,5,4]=>010111=>111010
[2,3,4,1,5,6,7]=>001000=>000100
[2,3,4,1,5,7,6]=>001001=>100100
[2,3,4,1,6,5,7]=>001010=>010100
[2,3,4,1,6,7,5]=>001001=>100100
[2,3,4,1,7,5,6]=>001001=>100100
[2,3,4,1,7,6,5]=>001011=>110100
[2,3,4,5,1,6,7]=>000100=>001000
[2,3,4,5,1,7,6]=>000101=>101000
[2,3,4,5,6,1,7]=>000010=>010000
[2,3,4,5,6,7,1]=>000001=>100000
[2,3,4,5,7,1,6]=>000001=>100000
[2,3,4,5,7,6,1]=>000011=>110000
[2,3,4,6,1,5,7]=>000010=>010000
[2,3,4,6,1,7,5]=>000011=>110000
[2,3,4,6,5,1,7]=>000110=>011000
[2,3,4,6,5,7,1]=>000011=>110000
[2,3,4,6,7,1,5]=>000001=>100000
[2,3,4,6,7,5,1]=>000101=>101000
[2,3,4,7,1,5,6]=>000001=>100000
[2,3,4,7,1,6,5]=>000011=>110000
[2,3,4,7,5,1,6]=>000101=>101000
[2,3,4,7,5,6,1]=>000011=>110000
[2,3,4,7,6,1,5]=>000011=>110000
[2,3,4,7,6,5,1]=>000111=>111000
[2,3,5,1,4,6,7]=>000100=>001000
[2,3,5,1,4,7,6]=>000101=>101000
[2,3,5,1,6,4,7]=>000110=>011000
[2,3,5,1,6,7,4]=>000101=>101000
[2,3,5,1,7,4,6]=>000101=>101000
[2,3,5,1,7,6,4]=>000111=>111000
[2,3,5,4,1,6,7]=>001100=>001100
[2,3,5,4,1,7,6]=>001101=>101100
[2,3,5,4,6,1,7]=>000110=>011000
[2,3,5,4,6,7,1]=>000101=>101000
[2,3,5,4,7,1,6]=>000101=>101000
[2,3,5,4,7,6,1]=>000111=>111000
[2,3,5,6,1,4,7]=>000010=>010000
[2,3,5,6,1,7,4]=>000011=>110000
[2,3,5,6,4,1,7]=>001010=>010100
[2,3,5,6,4,7,1]=>000011=>110000
[2,3,5,6,7,1,4]=>000001=>100000
[2,3,5,6,7,4,1]=>001001=>100100
[2,3,5,7,1,4,6]=>000001=>100000
[2,3,5,7,1,6,4]=>000011=>110000
[2,3,5,7,4,1,6]=>001001=>100100
[2,3,5,7,4,6,1]=>000011=>110000
[2,3,5,7,6,1,4]=>000011=>110000
[2,3,5,7,6,4,1]=>001011=>110100
[2,3,6,1,4,5,7]=>000010=>010000
[2,3,6,1,4,7,5]=>000011=>110000
[2,3,6,1,5,4,7]=>000110=>011000
[2,3,6,1,5,7,4]=>000011=>110000
[2,3,6,1,7,4,5]=>000011=>110000
[2,3,6,1,7,5,4]=>000111=>111000
[2,3,6,4,1,5,7]=>001010=>010100
[2,3,6,4,1,7,5]=>001011=>110100
[2,3,6,4,5,1,7]=>000110=>011000
[2,3,6,4,5,7,1]=>000011=>110000
[2,3,6,4,7,1,5]=>000011=>110000
[2,3,6,4,7,5,1]=>000111=>111000
[2,3,6,5,1,4,7]=>000110=>011000
[2,3,6,5,1,7,4]=>000111=>111000
[2,3,6,5,4,1,7]=>001110=>011100
[2,3,6,5,4,7,1]=>000111=>111000
[2,3,6,5,7,1,4]=>000011=>110000
[2,3,6,5,7,4,1]=>001011=>110100
[2,3,6,7,1,4,5]=>000001=>100000
[2,3,6,7,1,5,4]=>000101=>101000
[2,3,6,7,4,1,5]=>001001=>100100
[2,3,6,7,4,5,1]=>000101=>101000
[2,3,6,7,5,1,4]=>000101=>101000
[2,3,6,7,5,4,1]=>001101=>101100
[2,3,7,1,4,5,6]=>000001=>100000
[2,3,7,1,4,6,5]=>000011=>110000
[2,3,7,1,5,4,6]=>000101=>101000
[2,3,7,1,5,6,4]=>000011=>110000
[2,3,7,1,6,4,5]=>000011=>110000
[2,3,7,1,6,5,4]=>000111=>111000
[2,3,7,4,1,5,6]=>001001=>100100
[2,3,7,4,1,6,5]=>001011=>110100
[2,3,7,4,5,1,6]=>000101=>101000
[2,3,7,4,5,6,1]=>000011=>110000
[2,3,7,4,6,1,5]=>000011=>110000
[2,3,7,4,6,5,1]=>000111=>111000
[2,3,7,5,1,4,6]=>000101=>101000
[2,3,7,5,1,6,4]=>000111=>111000
[2,3,7,5,4,1,6]=>001101=>101100
[2,3,7,5,4,6,1]=>000111=>111000
[2,3,7,5,6,1,4]=>000011=>110000
[2,3,7,5,6,4,1]=>001011=>110100
[2,3,7,6,1,4,5]=>000011=>110000
[2,3,7,6,1,5,4]=>000111=>111000
[2,3,7,6,4,1,5]=>001011=>110100
[2,3,7,6,4,5,1]=>000111=>111000
[2,3,7,6,5,1,4]=>000111=>111000
[2,3,7,6,5,4,1]=>001111=>111100
[2,4,1,3,5,6,7]=>001000=>000100
[2,4,1,3,5,7,6]=>001001=>100100
[2,4,1,3,6,5,7]=>001010=>010100
[2,4,1,3,6,7,5]=>001001=>100100
[2,4,1,3,7,5,6]=>001001=>100100
[2,4,1,3,7,6,5]=>001011=>110100
[2,4,1,5,3,6,7]=>001100=>001100
[2,4,1,5,3,7,6]=>001101=>101100
[2,4,1,5,6,3,7]=>001010=>010100
[2,4,1,5,6,7,3]=>001001=>100100
[2,4,1,5,7,3,6]=>001001=>100100
[2,4,1,5,7,6,3]=>001011=>110100
[2,4,1,6,3,5,7]=>001010=>010100
[2,4,1,6,3,7,5]=>001011=>110100
[2,4,1,6,5,3,7]=>001110=>011100
[2,4,1,6,5,7,3]=>001011=>110100
[2,4,1,6,7,3,5]=>001001=>100100
[2,4,1,6,7,5,3]=>001101=>101100
[2,4,1,7,3,5,6]=>001001=>100100
[2,4,1,7,3,6,5]=>001011=>110100
[2,4,1,7,5,3,6]=>001101=>101100
[2,4,1,7,5,6,3]=>001011=>110100
[2,4,1,7,6,3,5]=>001011=>110100
[2,4,1,7,6,5,3]=>001111=>111100
[2,4,3,1,5,6,7]=>011000=>000110
[2,4,3,1,5,7,6]=>011001=>100110
[2,4,3,1,6,5,7]=>011010=>010110
[2,4,3,1,6,7,5]=>011001=>100110
[2,4,3,1,7,5,6]=>011001=>100110
[2,4,3,1,7,6,5]=>011011=>110110
[2,4,3,5,1,6,7]=>001100=>001100
[2,4,3,5,1,7,6]=>001101=>101100
[2,4,3,5,6,1,7]=>001010=>010100
[2,4,3,5,6,7,1]=>001001=>100100
[2,4,3,5,7,1,6]=>001001=>100100
[2,4,3,5,7,6,1]=>001011=>110100
[2,4,3,6,1,5,7]=>001010=>010100
[2,4,3,6,1,7,5]=>001011=>110100
[2,4,3,6,5,1,7]=>001110=>011100
[2,4,3,6,5,7,1]=>001011=>110100
[2,4,3,6,7,1,5]=>001001=>100100
[2,4,3,6,7,5,1]=>001101=>101100
[2,4,3,7,1,5,6]=>001001=>100100
[2,4,3,7,1,6,5]=>001011=>110100
[2,4,3,7,5,1,6]=>001101=>101100
[2,4,3,7,5,6,1]=>001011=>110100
[2,4,3,7,6,1,5]=>001011=>110100
[2,4,3,7,6,5,1]=>001111=>111100
[2,4,5,1,3,6,7]=>000100=>001000
[2,4,5,1,3,7,6]=>000101=>101000
[2,4,5,1,6,3,7]=>000110=>011000
[2,4,5,1,6,7,3]=>000101=>101000
[2,4,5,1,7,3,6]=>000101=>101000
[2,4,5,1,7,6,3]=>000111=>111000
[2,4,5,3,1,6,7]=>010100=>001010
[2,4,5,3,1,7,6]=>010101=>101010
[2,4,5,3,6,1,7]=>000110=>011000
[2,4,5,3,6,7,1]=>000101=>101000
[2,4,5,3,7,1,6]=>000101=>101000
[2,4,5,3,7,6,1]=>000111=>111000
[2,4,5,6,1,3,7]=>000010=>010000
[2,4,5,6,1,7,3]=>000011=>110000
[2,4,5,6,3,1,7]=>010010=>010010
[2,4,5,6,3,7,1]=>000011=>110000
[2,4,5,6,7,1,3]=>000001=>100000
[2,4,5,6,7,3,1]=>010001=>100010
[2,4,5,7,1,3,6]=>000001=>100000
[2,4,5,7,1,6,3]=>000011=>110000
[2,4,5,7,3,1,6]=>010001=>100010
[2,4,5,7,3,6,1]=>000011=>110000
[2,4,5,7,6,1,3]=>000011=>110000
[2,4,5,7,6,3,1]=>010011=>110010
[2,4,6,1,3,5,7]=>000010=>010000
[2,4,6,1,3,7,5]=>000011=>110000
[2,4,6,1,5,3,7]=>000110=>011000
[2,4,6,1,5,7,3]=>000011=>110000
[2,4,6,1,7,3,5]=>000011=>110000
[2,4,6,1,7,5,3]=>000111=>111000
[2,4,6,3,1,5,7]=>010010=>010010
[2,4,6,3,1,7,5]=>010011=>110010
[2,4,6,3,5,1,7]=>000110=>011000
[2,4,6,3,5,7,1]=>000011=>110000
[2,4,6,3,7,1,5]=>000011=>110000
[2,4,6,3,7,5,1]=>000111=>111000
[2,4,6,5,1,3,7]=>000110=>011000
[2,4,6,5,1,7,3]=>000111=>111000
[2,4,6,5,3,1,7]=>010110=>011010
[2,4,6,5,3,7,1]=>000111=>111000
[2,4,6,5,7,1,3]=>000011=>110000
[2,4,6,5,7,3,1]=>010011=>110010
[2,4,6,7,1,3,5]=>000001=>100000
[2,4,6,7,1,5,3]=>000101=>101000
[2,4,6,7,3,1,5]=>010001=>100010
[2,4,6,7,3,5,1]=>000101=>101000
[2,4,6,7,5,1,3]=>000101=>101000
[2,4,6,7,5,3,1]=>010101=>101010
[2,4,7,1,3,5,6]=>000001=>100000
[2,4,7,1,3,6,5]=>000011=>110000
[2,4,7,1,5,3,6]=>000101=>101000
[2,4,7,1,5,6,3]=>000011=>110000
[2,4,7,1,6,3,5]=>000011=>110000
[2,4,7,1,6,5,3]=>000111=>111000
[2,4,7,3,1,5,6]=>010001=>100010
[2,4,7,3,1,6,5]=>010011=>110010
[2,4,7,3,5,1,6]=>000101=>101000
[2,4,7,3,5,6,1]=>000011=>110000
[2,4,7,3,6,1,5]=>000011=>110000
[2,4,7,3,6,5,1]=>000111=>111000
[2,4,7,5,1,3,6]=>000101=>101000
[2,4,7,5,1,6,3]=>000111=>111000
[2,4,7,5,3,1,6]=>010101=>101010
[2,4,7,5,3,6,1]=>000111=>111000
[2,4,7,5,6,1,3]=>000011=>110000
[2,4,7,5,6,3,1]=>010011=>110010
[2,4,7,6,1,3,5]=>000011=>110000
[2,4,7,6,1,5,3]=>000111=>111000
[2,4,7,6,3,1,5]=>010011=>110010
[2,4,7,6,3,5,1]=>000111=>111000
[2,4,7,6,5,1,3]=>000111=>111000
[2,4,7,6,5,3,1]=>010111=>111010
[2,5,1,3,4,6,7]=>000100=>001000
[2,5,1,3,4,7,6]=>000101=>101000
[2,5,1,3,6,4,7]=>000110=>011000
[2,5,1,3,6,7,4]=>000101=>101000
[2,5,1,3,7,4,6]=>000101=>101000
[2,5,1,3,7,6,4]=>000111=>111000
[2,5,1,4,3,6,7]=>001100=>001100
[2,5,1,4,3,7,6]=>001101=>101100
[2,5,1,4,6,3,7]=>000110=>011000
[2,5,1,4,6,7,3]=>000101=>101000
[2,5,1,4,7,3,6]=>000101=>101000
[2,5,1,4,7,6,3]=>000111=>111000
[2,5,1,6,3,4,7]=>000110=>011000
[2,5,1,6,3,7,4]=>000111=>111000
[2,5,1,6,4,3,7]=>001110=>011100
[2,5,1,6,4,7,3]=>000111=>111000
[2,5,1,6,7,3,4]=>000101=>101000
[2,5,1,6,7,4,3]=>001101=>101100
[2,5,1,7,3,4,6]=>000101=>101000
[2,5,1,7,3,6,4]=>000111=>111000
[2,5,1,7,4,3,6]=>001101=>101100
[2,5,1,7,4,6,3]=>000111=>111000
[2,5,1,7,6,3,4]=>000111=>111000
[2,5,1,7,6,4,3]=>001111=>111100
[2,5,3,1,4,6,7]=>010100=>001010
[2,5,3,1,4,7,6]=>010101=>101010
[2,5,3,1,6,4,7]=>010110=>011010
[2,5,3,1,6,7,4]=>010101=>101010
[2,5,3,1,7,4,6]=>010101=>101010
[2,5,3,1,7,6,4]=>010111=>111010
[2,5,3,4,1,6,7]=>001100=>001100
[2,5,3,4,1,7,6]=>001101=>101100
[2,5,3,4,6,1,7]=>000110=>011000
[2,5,3,4,6,7,1]=>000101=>101000
[2,5,3,4,7,1,6]=>000101=>101000
[2,5,3,4,7,6,1]=>000111=>111000
[2,5,3,6,1,4,7]=>000110=>011000
[2,5,3,6,1,7,4]=>000111=>111000
[2,5,3,6,4,1,7]=>001110=>011100
[2,5,3,6,4,7,1]=>000111=>111000
[2,5,3,6,7,1,4]=>000101=>101000
[2,5,3,6,7,4,1]=>001101=>101100
[2,5,3,7,1,4,6]=>000101=>101000
[2,5,3,7,1,6,4]=>000111=>111000
[2,5,3,7,4,1,6]=>001101=>101100
[2,5,3,7,4,6,1]=>000111=>111000
[2,5,3,7,6,1,4]=>000111=>111000
[2,5,3,7,6,4,1]=>001111=>111100
[2,5,4,1,3,6,7]=>001100=>001100
[2,5,4,1,3,7,6]=>001101=>101100
[2,5,4,1,6,3,7]=>001110=>011100
[2,5,4,1,6,7,3]=>001101=>101100
[2,5,4,1,7,3,6]=>001101=>101100
[2,5,4,1,7,6,3]=>001111=>111100
[2,5,4,3,1,6,7]=>011100=>001110
[2,5,4,3,1,7,6]=>011101=>101110
[2,5,4,3,6,1,7]=>001110=>011100
[2,5,4,3,6,7,1]=>001101=>101100
[2,5,4,3,7,1,6]=>001101=>101100
[2,5,4,3,7,6,1]=>001111=>111100
[2,5,4,6,1,3,7]=>000110=>011000
[2,5,4,6,1,7,3]=>000111=>111000
[2,5,4,6,3,1,7]=>010110=>011010
[2,5,4,6,3,7,1]=>000111=>111000
[2,5,4,6,7,1,3]=>000101=>101000
[2,5,4,6,7,3,1]=>010101=>101010
[2,5,4,7,1,3,6]=>000101=>101000
[2,5,4,7,1,6,3]=>000111=>111000
[2,5,4,7,3,1,6]=>010101=>101010
[2,5,4,7,3,6,1]=>000111=>111000
[2,5,4,7,6,1,3]=>000111=>111000
[2,5,4,7,6,3,1]=>010111=>111010
[2,5,6,1,3,4,7]=>000010=>010000
[2,5,6,1,3,7,4]=>000011=>110000
[2,5,6,1,4,3,7]=>001010=>010100
[2,5,6,1,4,7,3]=>000011=>110000
[2,5,6,1,7,3,4]=>000011=>110000
[2,5,6,1,7,4,3]=>001011=>110100
[2,5,6,3,1,4,7]=>010010=>010010
[2,5,6,3,1,7,4]=>010011=>110010
[2,5,6,3,4,1,7]=>001010=>010100
[2,5,6,3,4,7,1]=>000011=>110000
[2,5,6,3,7,1,4]=>000011=>110000
[2,5,6,3,7,4,1]=>001011=>110100
[2,5,6,4,1,3,7]=>001010=>010100
[2,5,6,4,1,7,3]=>001011=>110100
[2,5,6,4,3,1,7]=>011010=>010110
[2,5,6,4,3,7,1]=>001011=>110100
[2,5,6,4,7,1,3]=>000011=>110000
[2,5,6,4,7,3,1]=>010011=>110010
[2,5,6,7,1,3,4]=>000001=>100000
[2,5,6,7,1,4,3]=>001001=>100100
[2,5,6,7,3,1,4]=>010001=>100010
[2,5,6,7,3,4,1]=>001001=>100100
[2,5,6,7,4,1,3]=>001001=>100100
[2,5,6,7,4,3,1]=>011001=>100110
[2,5,7,1,3,4,6]=>000001=>100000
[2,5,7,1,3,6,4]=>000011=>110000
[2,5,7,1,4,3,6]=>001001=>100100
[2,5,7,1,4,6,3]=>000011=>110000
[2,5,7,1,6,3,4]=>000011=>110000
[2,5,7,1,6,4,3]=>001011=>110100
[2,5,7,3,1,4,6]=>010001=>100010
[2,5,7,3,1,6,4]=>010011=>110010
[2,5,7,3,4,1,6]=>001001=>100100
[2,5,7,3,4,6,1]=>000011=>110000
[2,5,7,3,6,1,4]=>000011=>110000
[2,5,7,3,6,4,1]=>001011=>110100
[2,5,7,4,1,3,6]=>001001=>100100
[2,5,7,4,1,6,3]=>001011=>110100
[2,5,7,4,3,1,6]=>011001=>100110
[2,5,7,4,3,6,1]=>001011=>110100
[2,5,7,4,6,1,3]=>000011=>110000
[2,5,7,4,6,3,1]=>010011=>110010
[2,5,7,6,1,3,4]=>000011=>110000
[2,5,7,6,1,4,3]=>001011=>110100
[2,5,7,6,3,1,4]=>010011=>110010
[2,5,7,6,3,4,1]=>001011=>110100
[2,5,7,6,4,1,3]=>001011=>110100
[2,5,7,6,4,3,1]=>011011=>110110
[2,6,1,3,4,5,7]=>000010=>010000
[2,6,1,3,4,7,5]=>000011=>110000
[2,6,1,3,5,4,7]=>000110=>011000
[2,6,1,3,5,7,4]=>000011=>110000
[2,6,1,3,7,4,5]=>000011=>110000
[2,6,1,3,7,5,4]=>000111=>111000
[2,6,1,4,3,5,7]=>001010=>010100
[2,6,1,4,3,7,5]=>001011=>110100
[2,6,1,4,5,3,7]=>000110=>011000
[2,6,1,4,5,7,3]=>000011=>110000
[2,6,1,4,7,3,5]=>000011=>110000
[2,6,1,4,7,5,3]=>000111=>111000
[2,6,1,5,3,4,7]=>000110=>011000
[2,6,1,5,3,7,4]=>000111=>111000
[2,6,1,5,4,3,7]=>001110=>011100
[2,6,1,5,4,7,3]=>000111=>111000
[2,6,1,5,7,3,4]=>000011=>110000
[2,6,1,5,7,4,3]=>001011=>110100
[2,6,1,7,3,4,5]=>000011=>110000
[2,6,1,7,3,5,4]=>000111=>111000
[2,6,1,7,4,3,5]=>001011=>110100
[2,6,1,7,4,5,3]=>000111=>111000
[2,6,1,7,5,3,4]=>000111=>111000
[2,6,1,7,5,4,3]=>001111=>111100
[2,6,3,1,4,5,7]=>010010=>010010
[2,6,3,1,4,7,5]=>010011=>110010
[2,6,3,1,5,4,7]=>010110=>011010
[2,6,3,1,5,7,4]=>010011=>110010
[2,6,3,1,7,4,5]=>010011=>110010
[2,6,3,1,7,5,4]=>010111=>111010
[2,6,3,4,1,5,7]=>001010=>010100
[2,6,3,4,1,7,5]=>001011=>110100
[2,6,3,4,5,1,7]=>000110=>011000
[2,6,3,4,5,7,1]=>000011=>110000
[2,6,3,4,7,1,5]=>000011=>110000
[2,6,3,4,7,5,1]=>000111=>111000
[2,6,3,5,1,4,7]=>000110=>011000
[2,6,3,5,1,7,4]=>000111=>111000
[2,6,3,5,4,1,7]=>001110=>011100
[2,6,3,5,4,7,1]=>000111=>111000
[2,6,3,5,7,1,4]=>000011=>110000
[2,6,3,5,7,4,1]=>001011=>110100
[2,6,3,7,1,4,5]=>000011=>110000
[2,6,3,7,1,5,4]=>000111=>111000
[2,6,3,7,4,1,5]=>001011=>110100
[2,6,3,7,4,5,1]=>000111=>111000
[2,6,3,7,5,1,4]=>000111=>111000
[2,6,3,7,5,4,1]=>001111=>111100
[2,6,4,1,3,5,7]=>001010=>010100
[2,6,4,1,3,7,5]=>001011=>110100
[2,6,4,1,5,3,7]=>001110=>011100
[2,6,4,1,5,7,3]=>001011=>110100
[2,6,4,1,7,3,5]=>001011=>110100
[2,6,4,1,7,5,3]=>001111=>111100
[2,6,4,3,1,5,7]=>011010=>010110
[2,6,4,3,1,7,5]=>011011=>110110
[2,6,4,3,5,1,7]=>001110=>011100
[2,6,4,3,5,7,1]=>001011=>110100
[2,6,4,3,7,1,5]=>001011=>110100
[2,6,4,3,7,5,1]=>001111=>111100
[2,6,4,5,1,3,7]=>000110=>011000
[2,6,4,5,1,7,3]=>000111=>111000
[2,6,4,5,3,1,7]=>010110=>011010
[2,6,4,5,3,7,1]=>000111=>111000
[2,6,4,5,7,1,3]=>000011=>110000
[2,6,4,5,7,3,1]=>010011=>110010
[2,6,4,7,1,3,5]=>000011=>110000
[2,6,4,7,1,5,3]=>000111=>111000
[2,6,4,7,3,1,5]=>010011=>110010
[2,6,4,7,3,5,1]=>000111=>111000
[2,6,4,7,5,1,3]=>000111=>111000
[2,6,4,7,5,3,1]=>010111=>111010
[2,6,5,1,3,4,7]=>000110=>011000
[2,6,5,1,3,7,4]=>000111=>111000
[2,6,5,1,4,3,7]=>001110=>011100
[2,6,5,1,4,7,3]=>000111=>111000
[2,6,5,1,7,3,4]=>000111=>111000
[2,6,5,1,7,4,3]=>001111=>111100
[2,6,5,3,1,4,7]=>010110=>011010
[2,6,5,3,1,7,4]=>010111=>111010
[2,6,5,3,4,1,7]=>001110=>011100
[2,6,5,3,4,7,1]=>000111=>111000
[2,6,5,3,7,1,4]=>000111=>111000
[2,6,5,3,7,4,1]=>001111=>111100
[2,6,5,4,1,3,7]=>001110=>011100
[2,6,5,4,1,7,3]=>001111=>111100
[2,6,5,4,3,1,7]=>011110=>011110
[2,6,5,4,3,7,1]=>001111=>111100
[2,6,5,4,7,1,3]=>000111=>111000
[2,6,5,4,7,3,1]=>010111=>111010
[2,6,5,7,1,3,4]=>000011=>110000
[2,6,5,7,1,4,3]=>001011=>110100
[2,6,5,7,3,1,4]=>010011=>110010
[2,6,5,7,3,4,1]=>001011=>110100
[2,6,5,7,4,1,3]=>001011=>110100
[2,6,5,7,4,3,1]=>011011=>110110
[2,6,7,1,3,4,5]=>000001=>100000
[2,6,7,1,3,5,4]=>000101=>101000
[2,6,7,1,4,3,5]=>001001=>100100
[2,6,7,1,4,5,3]=>000101=>101000
[2,6,7,1,5,3,4]=>000101=>101000
[2,6,7,1,5,4,3]=>001101=>101100
[2,6,7,3,1,4,5]=>010001=>100010
[2,6,7,3,1,5,4]=>010101=>101010
[2,6,7,3,4,1,5]=>001001=>100100
[2,6,7,3,4,5,1]=>000101=>101000
[2,6,7,3,5,1,4]=>000101=>101000
[2,6,7,3,5,4,1]=>001101=>101100
[2,6,7,4,1,3,5]=>001001=>100100
[2,6,7,4,1,5,3]=>001101=>101100
[2,6,7,4,3,1,5]=>011001=>100110
[2,6,7,4,3,5,1]=>001101=>101100
[2,6,7,4,5,1,3]=>000101=>101000
[2,6,7,4,5,3,1]=>010101=>101010
[2,6,7,5,1,3,4]=>000101=>101000
[2,6,7,5,1,4,3]=>001101=>101100
[2,6,7,5,3,1,4]=>010101=>101010
[2,6,7,5,3,4,1]=>001101=>101100
[2,6,7,5,4,1,3]=>001101=>101100
[2,6,7,5,4,3,1]=>011101=>101110
[2,7,1,3,4,5,6]=>000001=>100000
[2,7,1,3,4,6,5]=>000011=>110000
[2,7,1,3,5,4,6]=>000101=>101000
[2,7,1,3,5,6,4]=>000011=>110000
[2,7,1,3,6,4,5]=>000011=>110000
[2,7,1,3,6,5,4]=>000111=>111000
[2,7,1,4,3,5,6]=>001001=>100100
[2,7,1,4,3,6,5]=>001011=>110100
[2,7,1,4,5,3,6]=>000101=>101000
[2,7,1,4,5,6,3]=>000011=>110000
[2,7,1,4,6,3,5]=>000011=>110000
[2,7,1,4,6,5,3]=>000111=>111000
[2,7,1,5,3,4,6]=>000101=>101000
[2,7,1,5,3,6,4]=>000111=>111000
[2,7,1,5,4,3,6]=>001101=>101100
[2,7,1,5,4,6,3]=>000111=>111000
[2,7,1,5,6,3,4]=>000011=>110000
[2,7,1,5,6,4,3]=>001011=>110100
[2,7,1,6,3,4,5]=>000011=>110000
[2,7,1,6,3,5,4]=>000111=>111000
[2,7,1,6,4,3,5]=>001011=>110100
[2,7,1,6,4,5,3]=>000111=>111000
[2,7,1,6,5,3,4]=>000111=>111000
[2,7,1,6,5,4,3]=>001111=>111100
[2,7,3,1,4,5,6]=>010001=>100010
[2,7,3,1,4,6,5]=>010011=>110010
[2,7,3,1,5,4,6]=>010101=>101010
[2,7,3,1,5,6,4]=>010011=>110010
[2,7,3,1,6,4,5]=>010011=>110010
[2,7,3,1,6,5,4]=>010111=>111010
[2,7,3,4,1,5,6]=>001001=>100100
[2,7,3,4,1,6,5]=>001011=>110100
[2,7,3,4,5,1,6]=>000101=>101000
[2,7,3,4,5,6,1]=>000011=>110000
[2,7,3,4,6,1,5]=>000011=>110000
[2,7,3,4,6,5,1]=>000111=>111000
[2,7,3,5,1,4,6]=>000101=>101000
[2,7,3,5,1,6,4]=>000111=>111000
[2,7,3,5,4,1,6]=>001101=>101100
[2,7,3,5,4,6,1]=>000111=>111000
[2,7,3,5,6,1,4]=>000011=>110000
[2,7,3,5,6,4,1]=>001011=>110100
[2,7,3,6,1,4,5]=>000011=>110000
[2,7,3,6,1,5,4]=>000111=>111000
[2,7,3,6,4,1,5]=>001011=>110100
[2,7,3,6,4,5,1]=>000111=>111000
[2,7,3,6,5,1,4]=>000111=>111000
[2,7,3,6,5,4,1]=>001111=>111100
[2,7,4,1,3,5,6]=>001001=>100100
[2,7,4,1,3,6,5]=>001011=>110100
[2,7,4,1,5,3,6]=>001101=>101100
[2,7,4,1,5,6,3]=>001011=>110100
[2,7,4,1,6,3,5]=>001011=>110100
[2,7,4,1,6,5,3]=>001111=>111100
[2,7,4,3,1,5,6]=>011001=>100110
[2,7,4,3,1,6,5]=>011011=>110110
[2,7,4,3,5,1,6]=>001101=>101100
[2,7,4,3,5,6,1]=>001011=>110100
[2,7,4,3,6,1,5]=>001011=>110100
[2,7,4,3,6,5,1]=>001111=>111100
[2,7,4,5,1,3,6]=>000101=>101000
[2,7,4,5,1,6,3]=>000111=>111000
[2,7,4,5,3,1,6]=>010101=>101010
[2,7,4,5,3,6,1]=>000111=>111000
[2,7,4,5,6,1,3]=>000011=>110000
[2,7,4,5,6,3,1]=>010011=>110010
[2,7,4,6,1,3,5]=>000011=>110000
[2,7,4,6,1,5,3]=>000111=>111000
[2,7,4,6,3,1,5]=>010011=>110010
[2,7,4,6,3,5,1]=>000111=>111000
[2,7,4,6,5,1,3]=>000111=>111000
[2,7,4,6,5,3,1]=>010111=>111010
[2,7,5,1,3,4,6]=>000101=>101000
[2,7,5,1,3,6,4]=>000111=>111000
[2,7,5,1,4,3,6]=>001101=>101100
[2,7,5,1,4,6,3]=>000111=>111000
[2,7,5,1,6,3,4]=>000111=>111000
[2,7,5,1,6,4,3]=>001111=>111100
[2,7,5,3,1,4,6]=>010101=>101010
[2,7,5,3,1,6,4]=>010111=>111010
[2,7,5,3,4,1,6]=>001101=>101100
[2,7,5,3,4,6,1]=>000111=>111000
[2,7,5,3,6,1,4]=>000111=>111000
[2,7,5,3,6,4,1]=>001111=>111100
[2,7,5,4,1,3,6]=>001101=>101100
[2,7,5,4,1,6,3]=>001111=>111100
[2,7,5,4,3,1,6]=>011101=>101110
[2,7,5,4,3,6,1]=>001111=>111100
[2,7,5,4,6,1,3]=>000111=>111000
[2,7,5,4,6,3,1]=>010111=>111010
[2,7,5,6,1,3,4]=>000011=>110000
[2,7,5,6,1,4,3]=>001011=>110100
[2,7,5,6,3,1,4]=>010011=>110010
[2,7,5,6,3,4,1]=>001011=>110100
[2,7,5,6,4,1,3]=>001011=>110100
[2,7,5,6,4,3,1]=>011011=>110110
[2,7,6,1,3,4,5]=>000011=>110000
[2,7,6,1,3,5,4]=>000111=>111000
[2,7,6,1,4,3,5]=>001011=>110100
[2,7,6,1,4,5,3]=>000111=>111000
[2,7,6,1,5,3,4]=>000111=>111000
[2,7,6,1,5,4,3]=>001111=>111100
[2,7,6,3,1,4,5]=>010011=>110010
[2,7,6,3,1,5,4]=>010111=>111010
[2,7,6,3,4,1,5]=>001011=>110100
[2,7,6,3,4,5,1]=>000111=>111000
[2,7,6,3,5,1,4]=>000111=>111000
[2,7,6,3,5,4,1]=>001111=>111100
[2,7,6,4,1,3,5]=>001011=>110100
[2,7,6,4,1,5,3]=>001111=>111100
[2,7,6,4,3,1,5]=>011011=>110110
[2,7,6,4,3,5,1]=>001111=>111100
[2,7,6,4,5,1,3]=>000111=>111000
[2,7,6,4,5,3,1]=>010111=>111010
[2,7,6,5,1,3,4]=>000111=>111000
[2,7,6,5,1,4,3]=>001111=>111100
[2,7,6,5,3,1,4]=>010111=>111010
[2,7,6,5,3,4,1]=>001111=>111100
[2,7,6,5,4,1,3]=>001111=>111100
[2,7,6,5,4,3,1]=>011111=>111110
[3,1,2,4,5,6,7]=>010000=>000010
[3,1,2,4,5,7,6]=>010001=>100010
[3,1,2,4,6,5,7]=>010010=>010010
[3,1,2,4,6,7,5]=>010001=>100010
[3,1,2,4,7,5,6]=>010001=>100010
[3,1,2,4,7,6,5]=>010011=>110010
[3,1,2,5,4,6,7]=>010100=>001010
[3,1,2,5,4,7,6]=>010101=>101010
[3,1,2,5,6,4,7]=>010010=>010010
[3,1,2,5,6,7,4]=>010001=>100010
[3,1,2,5,7,4,6]=>010001=>100010
[3,1,2,5,7,6,4]=>010011=>110010
[3,1,2,6,4,5,7]=>010010=>010010
[3,1,2,6,4,7,5]=>010011=>110010
[3,1,2,6,5,4,7]=>010110=>011010
[3,1,2,6,5,7,4]=>010011=>110010
[3,1,2,6,7,4,5]=>010001=>100010
[3,1,2,6,7,5,4]=>010101=>101010
[3,1,2,7,4,5,6]=>010001=>100010
[3,1,2,7,4,6,5]=>010011=>110010
[3,1,2,7,5,4,6]=>010101=>101010
[3,1,2,7,5,6,4]=>010011=>110010
[3,1,2,7,6,4,5]=>010011=>110010
[3,1,2,7,6,5,4]=>010111=>111010
[3,1,4,2,5,6,7]=>011000=>000110
[3,1,4,2,5,7,6]=>011001=>100110
[3,1,4,2,6,5,7]=>011010=>010110
[3,1,4,2,6,7,5]=>011001=>100110
[3,1,4,2,7,5,6]=>011001=>100110
[3,1,4,2,7,6,5]=>011011=>110110
[3,1,4,5,2,6,7]=>010100=>001010
[3,1,4,5,2,7,6]=>010101=>101010
[3,1,4,5,6,2,7]=>010010=>010010
[3,1,4,5,6,7,2]=>010001=>100010
[3,1,4,5,7,2,6]=>010001=>100010
[3,1,4,5,7,6,2]=>010011=>110010
[3,1,4,6,2,5,7]=>010010=>010010
[3,1,4,6,2,7,5]=>010011=>110010
[3,1,4,6,5,2,7]=>010110=>011010
[3,1,4,6,5,7,2]=>010011=>110010
[3,1,4,6,7,2,5]=>010001=>100010
[3,1,4,6,7,5,2]=>010101=>101010
[3,1,4,7,2,5,6]=>010001=>100010
[3,1,4,7,2,6,5]=>010011=>110010
[3,1,4,7,5,2,6]=>010101=>101010
[3,1,4,7,5,6,2]=>010011=>110010
[3,1,4,7,6,2,5]=>010011=>110010
[3,1,4,7,6,5,2]=>010111=>111010
[3,1,5,2,4,6,7]=>010100=>001010
[3,1,5,2,4,7,6]=>010101=>101010
[3,1,5,2,6,4,7]=>010110=>011010
[3,1,5,2,6,7,4]=>010101=>101010
[3,1,5,2,7,4,6]=>010101=>101010
[3,1,5,2,7,6,4]=>010111=>111010
[3,1,5,4,2,6,7]=>011100=>001110
[3,1,5,4,2,7,6]=>011101=>101110
[3,1,5,4,6,2,7]=>010110=>011010
[3,1,5,4,6,7,2]=>010101=>101010
[3,1,5,4,7,2,6]=>010101=>101010
[3,1,5,4,7,6,2]=>010111=>111010
[3,1,5,6,2,4,7]=>010010=>010010
[3,1,5,6,2,7,4]=>010011=>110010
[3,1,5,6,4,2,7]=>011010=>010110
[3,1,5,6,4,7,2]=>010011=>110010
[3,1,5,6,7,2,4]=>010001=>100010
[3,1,5,6,7,4,2]=>011001=>100110
[3,1,5,7,2,4,6]=>010001=>100010
[3,1,5,7,2,6,4]=>010011=>110010
[3,1,5,7,4,2,6]=>011001=>100110
[3,1,5,7,4,6,2]=>010011=>110010
[3,1,5,7,6,2,4]=>010011=>110010
[3,1,5,7,6,4,2]=>011011=>110110
[3,1,6,2,4,5,7]=>010010=>010010
[3,1,6,2,4,7,5]=>010011=>110010
[3,1,6,2,5,4,7]=>010110=>011010
[3,1,6,2,5,7,4]=>010011=>110010
[3,1,6,2,7,4,5]=>010011=>110010
[3,1,6,2,7,5,4]=>010111=>111010
[3,1,6,4,2,5,7]=>011010=>010110
[3,1,6,4,2,7,5]=>011011=>110110
[3,1,6,4,5,2,7]=>010110=>011010
[3,1,6,4,5,7,2]=>010011=>110010
[3,1,6,4,7,2,5]=>010011=>110010
[3,1,6,4,7,5,2]=>010111=>111010
[3,1,6,5,2,4,7]=>010110=>011010
[3,1,6,5,2,7,4]=>010111=>111010
[3,1,6,5,4,2,7]=>011110=>011110
[3,1,6,5,4,7,2]=>010111=>111010
[3,1,6,5,7,2,4]=>010011=>110010
[3,1,6,5,7,4,2]=>011011=>110110
[3,1,6,7,2,4,5]=>010001=>100010
[3,1,6,7,2,5,4]=>010101=>101010
[3,1,6,7,4,2,5]=>011001=>100110
[3,1,6,7,4,5,2]=>010101=>101010
[3,1,6,7,5,2,4]=>010101=>101010
[3,1,6,7,5,4,2]=>011101=>101110
[3,1,7,2,4,5,6]=>010001=>100010
[3,1,7,2,4,6,5]=>010011=>110010
[3,1,7,2,5,4,6]=>010101=>101010
[3,1,7,2,5,6,4]=>010011=>110010
[3,1,7,2,6,4,5]=>010011=>110010
[3,1,7,2,6,5,4]=>010111=>111010
[3,1,7,4,2,5,6]=>011001=>100110
[3,1,7,4,2,6,5]=>011011=>110110
[3,1,7,4,5,2,6]=>010101=>101010
[3,1,7,4,5,6,2]=>010011=>110010
[3,1,7,4,6,2,5]=>010011=>110010
[3,1,7,4,6,5,2]=>010111=>111010
[3,1,7,5,2,4,6]=>010101=>101010
[3,1,7,5,2,6,4]=>010111=>111010
[3,1,7,5,4,2,6]=>011101=>101110
[3,1,7,5,4,6,2]=>010111=>111010
[3,1,7,5,6,2,4]=>010011=>110010
[3,1,7,5,6,4,2]=>011011=>110110
[3,1,7,6,2,4,5]=>010011=>110010
[3,1,7,6,2,5,4]=>010111=>111010
[3,1,7,6,4,2,5]=>011011=>110110
[3,1,7,6,4,5,2]=>010111=>111010
[3,1,7,6,5,2,4]=>010111=>111010
[3,1,7,6,5,4,2]=>011111=>111110
[3,2,1,4,5,6,7]=>110000=>000011
[3,2,1,4,5,7,6]=>110001=>100011
[3,2,1,4,6,5,7]=>110010=>010011
[3,2,1,4,6,7,5]=>110001=>100011
[3,2,1,4,7,5,6]=>110001=>100011
[3,2,1,4,7,6,5]=>110011=>110011
[3,2,1,5,4,6,7]=>110100=>001011
[3,2,1,5,4,7,6]=>110101=>101011
[3,2,1,5,6,4,7]=>110010=>010011
[3,2,1,5,6,7,4]=>110001=>100011
[3,2,1,5,7,4,6]=>110001=>100011
[3,2,1,5,7,6,4]=>110011=>110011
[3,2,1,6,4,5,7]=>110010=>010011
[3,2,1,6,4,7,5]=>110011=>110011
[3,2,1,6,5,4,7]=>110110=>011011
[3,2,1,6,5,7,4]=>110011=>110011
[3,2,1,6,7,4,5]=>110001=>100011
[3,2,1,6,7,5,4]=>110101=>101011
[3,2,1,7,4,5,6]=>110001=>100011
[3,2,1,7,4,6,5]=>110011=>110011
[3,2,1,7,5,4,6]=>110101=>101011
[3,2,1,7,5,6,4]=>110011=>110011
[3,2,1,7,6,4,5]=>110011=>110011
[3,2,1,7,6,5,4]=>110111=>111011
[3,2,4,1,5,6,7]=>011000=>000110
[3,2,4,1,5,7,6]=>011001=>100110
[3,2,4,1,6,5,7]=>011010=>010110
[3,2,4,1,6,7,5]=>011001=>100110
[3,2,4,1,7,5,6]=>011001=>100110
[3,2,4,1,7,6,5]=>011011=>110110
[3,2,4,5,1,6,7]=>010100=>001010
[3,2,4,5,1,7,6]=>010101=>101010
[3,2,4,5,6,1,7]=>010010=>010010
[3,2,4,5,6,7,1]=>010001=>100010
[3,2,4,5,7,1,6]=>010001=>100010
[3,2,4,5,7,6,1]=>010011=>110010
[3,2,4,6,1,5,7]=>010010=>010010
[3,2,4,6,1,7,5]=>010011=>110010
[3,2,4,6,5,1,7]=>010110=>011010
[3,2,4,6,5,7,1]=>010011=>110010
[3,2,4,6,7,1,5]=>010001=>100010
[3,2,4,6,7,5,1]=>010101=>101010
[3,2,4,7,1,5,6]=>010001=>100010
[3,2,4,7,1,6,5]=>010011=>110010
[3,2,4,7,5,1,6]=>010101=>101010
[3,2,4,7,5,6,1]=>010011=>110010
[3,2,4,7,6,1,5]=>010011=>110010
[3,2,4,7,6,5,1]=>010111=>111010
[3,2,5,1,4,6,7]=>010100=>001010
[3,2,5,1,4,7,6]=>010101=>101010
[3,2,5,1,6,4,7]=>010110=>011010
[3,2,5,1,6,7,4]=>010101=>101010
[3,2,5,1,7,4,6]=>010101=>101010
[3,2,5,1,7,6,4]=>010111=>111010
[3,2,5,4,1,6,7]=>011100=>001110
[3,2,5,4,1,7,6]=>011101=>101110
[3,2,5,4,6,1,7]=>010110=>011010
[3,2,5,4,6,7,1]=>010101=>101010
[3,2,5,4,7,1,6]=>010101=>101010
[3,2,5,4,7,6,1]=>010111=>111010
[3,2,5,6,1,4,7]=>010010=>010010
[3,2,5,6,1,7,4]=>010011=>110010
[3,2,5,6,4,1,7]=>011010=>010110
[3,2,5,6,4,7,1]=>010011=>110010
[3,2,5,6,7,1,4]=>010001=>100010
[3,2,5,6,7,4,1]=>011001=>100110
[3,2,5,7,1,4,6]=>010001=>100010
[3,2,5,7,1,6,4]=>010011=>110010
[3,2,5,7,4,1,6]=>011001=>100110
[3,2,5,7,4,6,1]=>010011=>110010
[3,2,5,7,6,1,4]=>010011=>110010
[3,2,5,7,6,4,1]=>011011=>110110
[3,2,6,1,4,5,7]=>010010=>010010
[3,2,6,1,4,7,5]=>010011=>110010
[3,2,6,1,5,4,7]=>010110=>011010
[3,2,6,1,5,7,4]=>010011=>110010
[3,2,6,1,7,4,5]=>010011=>110010
[3,2,6,1,7,5,4]=>010111=>111010
[3,2,6,4,1,5,7]=>011010=>010110
[3,2,6,4,1,7,5]=>011011=>110110
[3,2,6,4,5,1,7]=>010110=>011010
[3,2,6,4,5,7,1]=>010011=>110010
[3,2,6,4,7,1,5]=>010011=>110010
[3,2,6,4,7,5,1]=>010111=>111010
[3,2,6,5,1,4,7]=>010110=>011010
[3,2,6,5,1,7,4]=>010111=>111010
[3,2,6,5,4,1,7]=>011110=>011110
[3,2,6,5,4,7,1]=>010111=>111010
[3,2,6,5,7,1,4]=>010011=>110010
[3,2,6,5,7,4,1]=>011011=>110110
[3,2,6,7,1,4,5]=>010001=>100010
[3,2,6,7,1,5,4]=>010101=>101010
[3,2,6,7,4,1,5]=>011001=>100110
[3,2,6,7,4,5,1]=>010101=>101010
[3,2,6,7,5,1,4]=>010101=>101010
[3,2,6,7,5,4,1]=>011101=>101110
[3,2,7,1,4,5,6]=>010001=>100010
[3,2,7,1,4,6,5]=>010011=>110010
[3,2,7,1,5,4,6]=>010101=>101010
[3,2,7,1,5,6,4]=>010011=>110010
[3,2,7,1,6,4,5]=>010011=>110010
[3,2,7,1,6,5,4]=>010111=>111010
[3,2,7,4,1,5,6]=>011001=>100110
[3,2,7,4,1,6,5]=>011011=>110110
[3,2,7,4,5,1,6]=>010101=>101010
[3,2,7,4,5,6,1]=>010011=>110010
[3,2,7,4,6,1,5]=>010011=>110010
[3,2,7,4,6,5,1]=>010111=>111010
[3,2,7,5,1,4,6]=>010101=>101010
[3,2,7,5,1,6,4]=>010111=>111010
[3,2,7,5,4,1,6]=>011101=>101110
[3,2,7,5,4,6,1]=>010111=>111010
[3,2,7,5,6,1,4]=>010011=>110010
[3,2,7,5,6,4,1]=>011011=>110110
[3,2,7,6,1,4,5]=>010011=>110010
[3,2,7,6,1,5,4]=>010111=>111010
[3,2,7,6,4,1,5]=>011011=>110110
[3,2,7,6,4,5,1]=>010111=>111010
[3,2,7,6,5,1,4]=>010111=>111010
[3,2,7,6,5,4,1]=>011111=>111110
[3,4,1,2,5,6,7]=>001000=>000100
[3,4,1,2,5,7,6]=>001001=>100100
[3,4,1,2,6,5,7]=>001010=>010100
[3,4,1,2,6,7,5]=>001001=>100100
[3,4,1,2,7,5,6]=>001001=>100100
[3,4,1,2,7,6,5]=>001011=>110100
[3,4,1,5,2,6,7]=>001100=>001100
[3,4,1,5,2,7,6]=>001101=>101100
[3,4,1,5,6,2,7]=>001010=>010100
[3,4,1,5,6,7,2]=>001001=>100100
[3,4,1,5,7,2,6]=>001001=>100100
[3,4,1,5,7,6,2]=>001011=>110100
[3,4,1,6,2,5,7]=>001010=>010100
[3,4,1,6,2,7,5]=>001011=>110100
[3,4,1,6,5,2,7]=>001110=>011100
[3,4,1,6,5,7,2]=>001011=>110100
[3,4,1,6,7,2,5]=>001001=>100100
[3,4,1,6,7,5,2]=>001101=>101100
[3,4,1,7,2,5,6]=>001001=>100100
[3,4,1,7,2,6,5]=>001011=>110100
[3,4,1,7,5,2,6]=>001101=>101100
[3,4,1,7,5,6,2]=>001011=>110100
[3,4,1,7,6,2,5]=>001011=>110100
[3,4,1,7,6,5,2]=>001111=>111100
[3,4,2,1,5,6,7]=>101000=>000101
[3,4,2,1,5,7,6]=>101001=>100101
[3,4,2,1,6,5,7]=>101010=>010101
[3,4,2,1,6,7,5]=>101001=>100101
[3,4,2,1,7,5,6]=>101001=>100101
[3,4,2,1,7,6,5]=>101011=>110101
[3,4,2,5,1,6,7]=>001100=>001100
[3,4,2,5,1,7,6]=>001101=>101100
[3,4,2,5,6,1,7]=>001010=>010100
[3,4,2,5,6,7,1]=>001001=>100100
[3,4,2,5,7,1,6]=>001001=>100100
[3,4,2,5,7,6,1]=>001011=>110100
[3,4,2,6,1,5,7]=>001010=>010100
[3,4,2,6,1,7,5]=>001011=>110100
[3,4,2,6,5,1,7]=>001110=>011100
[3,4,2,6,5,7,1]=>001011=>110100
[3,4,2,6,7,1,5]=>001001=>100100
[3,4,2,6,7,5,1]=>001101=>101100
[3,4,2,7,1,5,6]=>001001=>100100
[3,4,2,7,1,6,5]=>001011=>110100
[3,4,2,7,5,1,6]=>001101=>101100
[3,4,2,7,5,6,1]=>001011=>110100
[3,4,2,7,6,1,5]=>001011=>110100
[3,4,2,7,6,5,1]=>001111=>111100
[3,4,5,1,2,6,7]=>000100=>001000
[3,4,5,1,2,7,6]=>000101=>101000
[3,4,5,1,6,2,7]=>000110=>011000
[3,4,5,1,6,7,2]=>000101=>101000
[3,4,5,1,7,2,6]=>000101=>101000
[3,4,5,1,7,6,2]=>000111=>111000
[3,4,5,2,1,6,7]=>100100=>001001
[3,4,5,2,1,7,6]=>100101=>101001
[3,4,5,2,6,1,7]=>000110=>011000
[3,4,5,2,6,7,1]=>000101=>101000
[3,4,5,2,7,1,6]=>000101=>101000
[3,4,5,2,7,6,1]=>000111=>111000
[3,4,5,6,1,2,7]=>000010=>010000
[3,4,5,6,1,7,2]=>000011=>110000
[3,4,5,6,2,1,7]=>100010=>010001
[3,4,5,6,2,7,1]=>000011=>110000
[3,4,5,6,7,1,2]=>000001=>100000
[3,4,5,6,7,2,1]=>100001=>100001
[3,4,5,7,1,2,6]=>000001=>100000
[3,4,5,7,1,6,2]=>000011=>110000
[3,4,5,7,2,1,6]=>100001=>100001
[3,4,5,7,2,6,1]=>000011=>110000
[3,4,5,7,6,1,2]=>000011=>110000
[3,4,5,7,6,2,1]=>100011=>110001
[3,4,6,1,2,5,7]=>000010=>010000
[3,4,6,1,2,7,5]=>000011=>110000
[3,4,6,1,5,2,7]=>000110=>011000
[3,4,6,1,5,7,2]=>000011=>110000
[3,4,6,1,7,2,5]=>000011=>110000
[3,4,6,1,7,5,2]=>000111=>111000
[3,4,6,2,1,5,7]=>100010=>010001
[3,4,6,2,1,7,5]=>100011=>110001
[3,4,6,2,5,1,7]=>000110=>011000
[3,4,6,2,5,7,1]=>000011=>110000
[3,4,6,2,7,1,5]=>000011=>110000
[3,4,6,2,7,5,1]=>000111=>111000
[3,4,6,5,1,2,7]=>000110=>011000
[3,4,6,5,1,7,2]=>000111=>111000
[3,4,6,5,2,1,7]=>100110=>011001
[3,4,6,5,2,7,1]=>000111=>111000
[3,4,6,5,7,1,2]=>000011=>110000
[3,4,6,5,7,2,1]=>100011=>110001
[3,4,6,7,1,2,5]=>000001=>100000
[3,4,6,7,1,5,2]=>000101=>101000
[3,4,6,7,2,1,5]=>100001=>100001
[3,4,6,7,2,5,1]=>000101=>101000
[3,4,6,7,5,1,2]=>000101=>101000
[3,4,6,7,5,2,1]=>100101=>101001
[3,4,7,1,2,5,6]=>000001=>100000
[3,4,7,1,2,6,5]=>000011=>110000
[3,4,7,1,5,2,6]=>000101=>101000
[3,4,7,1,5,6,2]=>000011=>110000
[3,4,7,1,6,2,5]=>000011=>110000
[3,4,7,1,6,5,2]=>000111=>111000
[3,4,7,2,1,5,6]=>100001=>100001
[3,4,7,2,1,6,5]=>100011=>110001
[3,4,7,2,5,1,6]=>000101=>101000
[3,4,7,2,5,6,1]=>000011=>110000
[3,4,7,2,6,1,5]=>000011=>110000
[3,4,7,2,6,5,1]=>000111=>111000
[3,4,7,5,1,2,6]=>000101=>101000
[3,4,7,5,1,6,2]=>000111=>111000
[3,4,7,5,2,1,6]=>100101=>101001
[3,4,7,5,2,6,1]=>000111=>111000
[3,4,7,5,6,1,2]=>000011=>110000
[3,4,7,5,6,2,1]=>100011=>110001
[3,4,7,6,1,2,5]=>000011=>110000
[3,4,7,6,1,5,2]=>000111=>111000
[3,4,7,6,2,1,5]=>100011=>110001
[3,4,7,6,2,5,1]=>000111=>111000
[3,4,7,6,5,1,2]=>000111=>111000
[3,4,7,6,5,2,1]=>100111=>111001
[3,5,1,2,4,6,7]=>000100=>001000
[3,5,1,2,4,7,6]=>000101=>101000
[3,5,1,2,6,4,7]=>000110=>011000
[3,5,1,2,6,7,4]=>000101=>101000
[3,5,1,2,7,4,6]=>000101=>101000
[3,5,1,2,7,6,4]=>000111=>111000
[3,5,1,4,2,6,7]=>001100=>001100
[3,5,1,4,2,7,6]=>001101=>101100
[3,5,1,4,6,2,7]=>000110=>011000
[3,5,1,4,6,7,2]=>000101=>101000
[3,5,1,4,7,2,6]=>000101=>101000
[3,5,1,4,7,6,2]=>000111=>111000
[3,5,1,6,2,4,7]=>000110=>011000
[3,5,1,6,2,7,4]=>000111=>111000
[3,5,1,6,4,2,7]=>001110=>011100
[3,5,1,6,4,7,2]=>000111=>111000
[3,5,1,6,7,2,4]=>000101=>101000
[3,5,1,6,7,4,2]=>001101=>101100
[3,5,1,7,2,4,6]=>000101=>101000
[3,5,1,7,2,6,4]=>000111=>111000
[3,5,1,7,4,2,6]=>001101=>101100
[3,5,1,7,4,6,2]=>000111=>111000
[3,5,1,7,6,2,4]=>000111=>111000
[3,5,1,7,6,4,2]=>001111=>111100
[3,5,2,1,4,6,7]=>100100=>001001
[3,5,2,1,4,7,6]=>100101=>101001
[3,5,2,1,6,4,7]=>100110=>011001
[3,5,2,1,6,7,4]=>100101=>101001
[3,5,2,1,7,4,6]=>100101=>101001
[3,5,2,1,7,6,4]=>100111=>111001
[3,5,2,4,1,6,7]=>001100=>001100
[3,5,2,4,1,7,6]=>001101=>101100
[3,5,2,4,6,1,7]=>000110=>011000
[3,5,2,4,6,7,1]=>000101=>101000
[3,5,2,4,7,1,6]=>000101=>101000
[3,5,2,4,7,6,1]=>000111=>111000
[3,5,2,6,1,4,7]=>000110=>011000
[3,5,2,6,1,7,4]=>000111=>111000
[3,5,2,6,4,1,7]=>001110=>011100
[3,5,2,6,4,7,1]=>000111=>111000
[3,5,2,6,7,1,4]=>000101=>101000
[3,5,2,6,7,4,1]=>001101=>101100
[3,5,2,7,1,4,6]=>000101=>101000
[3,5,2,7,1,6,4]=>000111=>111000
[3,5,2,7,4,1,6]=>001101=>101100
[3,5,2,7,4,6,1]=>000111=>111000
[3,5,2,7,6,1,4]=>000111=>111000
[3,5,2,7,6,4,1]=>001111=>111100
[3,5,4,1,2,6,7]=>001100=>001100
[3,5,4,1,2,7,6]=>001101=>101100
[3,5,4,1,6,2,7]=>001110=>011100
[3,5,4,1,6,7,2]=>001101=>101100
[3,5,4,1,7,2,6]=>001101=>101100
[3,5,4,1,7,6,2]=>001111=>111100
[3,5,4,2,1,6,7]=>101100=>001101
[3,5,4,2,1,7,6]=>101101=>101101
[3,5,4,2,6,1,7]=>001110=>011100
[3,5,4,2,6,7,1]=>001101=>101100
[3,5,4,2,7,1,6]=>001101=>101100
[3,5,4,2,7,6,1]=>001111=>111100
[3,5,4,6,1,2,7]=>000110=>011000
[3,5,4,6,1,7,2]=>000111=>111000
[3,5,4,6,2,1,7]=>100110=>011001
[3,5,4,6,2,7,1]=>000111=>111000
[3,5,4,6,7,1,2]=>000101=>101000
[3,5,4,6,7,2,1]=>100101=>101001
[3,5,4,7,1,2,6]=>000101=>101000
[3,5,4,7,1,6,2]=>000111=>111000
[3,5,4,7,2,1,6]=>100101=>101001
[3,5,4,7,2,6,1]=>000111=>111000
[3,5,4,7,6,1,2]=>000111=>111000
[3,5,4,7,6,2,1]=>100111=>111001
[3,5,6,1,2,4,7]=>000010=>010000
[3,5,6,1,2,7,4]=>000011=>110000
[3,5,6,1,4,2,7]=>001010=>010100
[3,5,6,1,4,7,2]=>000011=>110000
[3,5,6,1,7,2,4]=>000011=>110000
[3,5,6,1,7,4,2]=>001011=>110100
[3,5,6,2,1,4,7]=>100010=>010001
[3,5,6,2,1,7,4]=>100011=>110001
[3,5,6,2,4,1,7]=>001010=>010100
[3,5,6,2,4,7,1]=>000011=>110000
[3,5,6,2,7,1,4]=>000011=>110000
[3,5,6,2,7,4,1]=>001011=>110100
[3,5,6,4,1,2,7]=>001010=>010100
[3,5,6,4,1,7,2]=>001011=>110100
[3,5,6,4,2,1,7]=>101010=>010101
[3,5,6,4,2,7,1]=>001011=>110100
[3,5,6,4,7,1,2]=>000011=>110000
[3,5,6,4,7,2,1]=>100011=>110001
[3,5,6,7,1,2,4]=>000001=>100000
[3,5,6,7,1,4,2]=>001001=>100100
[3,5,6,7,2,1,4]=>100001=>100001
[3,5,6,7,2,4,1]=>001001=>100100
[3,5,6,7,4,1,2]=>001001=>100100
[3,5,6,7,4,2,1]=>101001=>100101
[3,5,7,1,2,4,6]=>000001=>100000
[3,5,7,1,2,6,4]=>000011=>110000
[3,5,7,1,4,2,6]=>001001=>100100
[3,5,7,1,4,6,2]=>000011=>110000
[3,5,7,1,6,2,4]=>000011=>110000
[3,5,7,1,6,4,2]=>001011=>110100
[3,5,7,2,1,4,6]=>100001=>100001
[3,5,7,2,1,6,4]=>100011=>110001
[3,5,7,2,4,1,6]=>001001=>100100
[3,5,7,2,4,6,1]=>000011=>110000
[3,5,7,2,6,1,4]=>000011=>110000
[3,5,7,2,6,4,1]=>001011=>110100
[3,5,7,4,1,2,6]=>001001=>100100
[3,5,7,4,1,6,2]=>001011=>110100
[3,5,7,4,2,1,6]=>101001=>100101
[3,5,7,4,2,6,1]=>001011=>110100
[3,5,7,4,6,1,2]=>000011=>110000
[3,5,7,4,6,2,1]=>100011=>110001
[3,5,7,6,1,2,4]=>000011=>110000
[3,5,7,6,1,4,2]=>001011=>110100
[3,5,7,6,2,1,4]=>100011=>110001
[3,5,7,6,2,4,1]=>001011=>110100
[3,5,7,6,4,1,2]=>001011=>110100
[3,5,7,6,4,2,1]=>101011=>110101
[3,6,1,2,4,5,7]=>000010=>010000
[3,6,1,2,4,7,5]=>000011=>110000
[3,6,1,2,5,4,7]=>000110=>011000
[3,6,1,2,5,7,4]=>000011=>110000
[3,6,1,2,7,4,5]=>000011=>110000
[3,6,1,2,7,5,4]=>000111=>111000
[3,6,1,4,2,5,7]=>001010=>010100
[3,6,1,4,2,7,5]=>001011=>110100
[3,6,1,4,5,2,7]=>000110=>011000
[3,6,1,4,5,7,2]=>000011=>110000
[3,6,1,4,7,2,5]=>000011=>110000
[3,6,1,4,7,5,2]=>000111=>111000
[3,6,1,5,2,4,7]=>000110=>011000
[3,6,1,5,2,7,4]=>000111=>111000
[3,6,1,5,4,2,7]=>001110=>011100
[3,6,1,5,4,7,2]=>000111=>111000
[3,6,1,5,7,2,4]=>000011=>110000
[3,6,1,5,7,4,2]=>001011=>110100
[3,6,1,7,2,4,5]=>000011=>110000
[3,6,1,7,2,5,4]=>000111=>111000
[3,6,1,7,4,2,5]=>001011=>110100
[3,6,1,7,4,5,2]=>000111=>111000
[3,6,1,7,5,2,4]=>000111=>111000
[3,6,1,7,5,4,2]=>001111=>111100
[3,6,2,1,4,5,7]=>100010=>010001
[3,6,2,1,4,7,5]=>100011=>110001
[3,6,2,1,5,4,7]=>100110=>011001
[3,6,2,1,5,7,4]=>100011=>110001
[3,6,2,1,7,4,5]=>100011=>110001
[3,6,2,1,7,5,4]=>100111=>111001
[3,6,2,4,1,5,7]=>001010=>010100
[3,6,2,4,1,7,5]=>001011=>110100
[3,6,2,4,5,1,7]=>000110=>011000
[3,6,2,4,5,7,1]=>000011=>110000
[3,6,2,4,7,1,5]=>000011=>110000
[3,6,2,4,7,5,1]=>000111=>111000
[3,6,2,5,1,4,7]=>000110=>011000
[3,6,2,5,1,7,4]=>000111=>111000
[3,6,2,5,4,1,7]=>001110=>011100
[3,6,2,5,4,7,1]=>000111=>111000
[3,6,2,5,7,1,4]=>000011=>110000
[3,6,2,5,7,4,1]=>001011=>110100
[3,6,2,7,1,4,5]=>000011=>110000
[3,6,2,7,1,5,4]=>000111=>111000
[3,6,2,7,4,1,5]=>001011=>110100
[3,6,2,7,4,5,1]=>000111=>111000
[3,6,2,7,5,1,4]=>000111=>111000
[3,6,2,7,5,4,1]=>001111=>111100
[3,6,4,1,2,5,7]=>001010=>010100
[3,6,4,1,2,7,5]=>001011=>110100
[3,6,4,1,5,2,7]=>001110=>011100
[3,6,4,1,5,7,2]=>001011=>110100
[3,6,4,1,7,2,5]=>001011=>110100
[3,6,4,1,7,5,2]=>001111=>111100
[3,6,4,2,1,5,7]=>101010=>010101
[3,6,4,2,1,7,5]=>101011=>110101
[3,6,4,2,5,1,7]=>001110=>011100
[3,6,4,2,5,7,1]=>001011=>110100
[3,6,4,2,7,1,5]=>001011=>110100
[3,6,4,2,7,5,1]=>001111=>111100
[3,6,4,5,1,2,7]=>000110=>011000
[3,6,4,5,1,7,2]=>000111=>111000
[3,6,4,5,2,1,7]=>100110=>011001
[3,6,4,5,2,7,1]=>000111=>111000
[3,6,4,5,7,1,2]=>000011=>110000
[3,6,4,5,7,2,1]=>100011=>110001
[3,6,4,7,1,2,5]=>000011=>110000
[3,6,4,7,1,5,2]=>000111=>111000
[3,6,4,7,2,1,5]=>100011=>110001
[3,6,4,7,2,5,1]=>000111=>111000
[3,6,4,7,5,1,2]=>000111=>111000
[3,6,4,7,5,2,1]=>100111=>111001
[3,6,5,1,2,4,7]=>000110=>011000
[3,6,5,1,2,7,4]=>000111=>111000
[3,6,5,1,4,2,7]=>001110=>011100
[3,6,5,1,4,7,2]=>000111=>111000
[3,6,5,1,7,2,4]=>000111=>111000
[3,6,5,1,7,4,2]=>001111=>111100
[3,6,5,2,1,4,7]=>100110=>011001
[3,6,5,2,1,7,4]=>100111=>111001
[3,6,5,2,4,1,7]=>001110=>011100
[3,6,5,2,4,7,1]=>000111=>111000
[3,6,5,2,7,1,4]=>000111=>111000
[3,6,5,2,7,4,1]=>001111=>111100
[3,6,5,4,1,2,7]=>001110=>011100
[3,6,5,4,1,7,2]=>001111=>111100
[3,6,5,4,2,1,7]=>101110=>011101
[3,6,5,4,2,7,1]=>001111=>111100
[3,6,5,4,7,1,2]=>000111=>111000
[3,6,5,4,7,2,1]=>100111=>111001
[3,6,5,7,1,2,4]=>000011=>110000
[3,6,5,7,1,4,2]=>001011=>110100
[3,6,5,7,2,1,4]=>100011=>110001
[3,6,5,7,2,4,1]=>001011=>110100
[3,6,5,7,4,1,2]=>001011=>110100
[3,6,5,7,4,2,1]=>101011=>110101
[3,6,7,1,2,4,5]=>000001=>100000
[3,6,7,1,2,5,4]=>000101=>101000
[3,6,7,1,4,2,5]=>001001=>100100
[3,6,7,1,4,5,2]=>000101=>101000
[3,6,7,1,5,2,4]=>000101=>101000
[3,6,7,1,5,4,2]=>001101=>101100
[3,6,7,2,1,4,5]=>100001=>100001
[3,6,7,2,1,5,4]=>100101=>101001
[3,6,7,2,4,1,5]=>001001=>100100
[3,6,7,2,4,5,1]=>000101=>101000
[3,6,7,2,5,1,4]=>000101=>101000
[3,6,7,2,5,4,1]=>001101=>101100
[3,6,7,4,1,2,5]=>001001=>100100
[3,6,7,4,1,5,2]=>001101=>101100
[3,6,7,4,2,1,5]=>101001=>100101
[3,6,7,4,2,5,1]=>001101=>101100
[3,6,7,4,5,1,2]=>000101=>101000
[3,6,7,4,5,2,1]=>100101=>101001
[3,6,7,5,1,2,4]=>000101=>101000
[3,6,7,5,1,4,2]=>001101=>101100
[3,6,7,5,2,1,4]=>100101=>101001
[3,6,7,5,2,4,1]=>001101=>101100
[3,6,7,5,4,1,2]=>001101=>101100
[3,6,7,5,4,2,1]=>101101=>101101
[3,7,1,2,4,5,6]=>000001=>100000
[3,7,1,2,4,6,5]=>000011=>110000
[3,7,1,2,5,4,6]=>000101=>101000
[3,7,1,2,5,6,4]=>000011=>110000
[3,7,1,2,6,4,5]=>000011=>110000
[3,7,1,2,6,5,4]=>000111=>111000
[3,7,1,4,2,5,6]=>001001=>100100
[3,7,1,4,2,6,5]=>001011=>110100
[3,7,1,4,5,2,6]=>000101=>101000
[3,7,1,4,5,6,2]=>000011=>110000
[3,7,1,4,6,2,5]=>000011=>110000
[3,7,1,4,6,5,2]=>000111=>111000
[3,7,1,5,2,4,6]=>000101=>101000
[3,7,1,5,2,6,4]=>000111=>111000
[3,7,1,5,4,2,6]=>001101=>101100
[3,7,1,5,4,6,2]=>000111=>111000
[3,7,1,5,6,2,4]=>000011=>110000
[3,7,1,5,6,4,2]=>001011=>110100
[3,7,1,6,2,4,5]=>000011=>110000
[3,7,1,6,2,5,4]=>000111=>111000
[3,7,1,6,4,2,5]=>001011=>110100
[3,7,1,6,4,5,2]=>000111=>111000
[3,7,1,6,5,2,4]=>000111=>111000
[3,7,1,6,5,4,2]=>001111=>111100
[3,7,2,1,4,5,6]=>100001=>100001
[3,7,2,1,4,6,5]=>100011=>110001
[3,7,2,1,5,4,6]=>100101=>101001
[3,7,2,1,5,6,4]=>100011=>110001
[3,7,2,1,6,4,5]=>100011=>110001
[3,7,2,1,6,5,4]=>100111=>111001
[3,7,2,4,1,5,6]=>001001=>100100
[3,7,2,4,1,6,5]=>001011=>110100
[3,7,2,4,5,1,6]=>000101=>101000
[3,7,2,4,5,6,1]=>000011=>110000
[3,7,2,4,6,1,5]=>000011=>110000
[3,7,2,4,6,5,1]=>000111=>111000
[3,7,2,5,1,4,6]=>000101=>101000
[3,7,2,5,1,6,4]=>000111=>111000
[3,7,2,5,4,1,6]=>001101=>101100
[3,7,2,5,4,6,1]=>000111=>111000
[3,7,2,5,6,1,4]=>000011=>110000
[3,7,2,5,6,4,1]=>001011=>110100
[3,7,2,6,1,4,5]=>000011=>110000
[3,7,2,6,1,5,4]=>000111=>111000
[3,7,2,6,4,1,5]=>001011=>110100
[3,7,2,6,4,5,1]=>000111=>111000
[3,7,2,6,5,1,4]=>000111=>111000
[3,7,2,6,5,4,1]=>001111=>111100
[3,7,4,1,2,5,6]=>001001=>100100
[3,7,4,1,2,6,5]=>001011=>110100
[3,7,4,1,5,2,6]=>001101=>101100
[3,7,4,1,5,6,2]=>001011=>110100
[3,7,4,1,6,2,5]=>001011=>110100
[3,7,4,1,6,5,2]=>001111=>111100
[3,7,4,2,1,5,6]=>101001=>100101
[3,7,4,2,1,6,5]=>101011=>110101
[3,7,4,2,5,1,6]=>001101=>101100
[3,7,4,2,5,6,1]=>001011=>110100
[3,7,4,2,6,1,5]=>001011=>110100
[3,7,4,2,6,5,1]=>001111=>111100
[3,7,4,5,1,2,6]=>000101=>101000
[3,7,4,5,1,6,2]=>000111=>111000
[3,7,4,5,2,1,6]=>100101=>101001
[3,7,4,5,2,6,1]=>000111=>111000
[3,7,4,5,6,1,2]=>000011=>110000
[3,7,4,5,6,2,1]=>100011=>110001
[3,7,4,6,1,2,5]=>000011=>110000
[3,7,4,6,1,5,2]=>000111=>111000
[3,7,4,6,2,1,5]=>100011=>110001
[3,7,4,6,2,5,1]=>000111=>111000
[3,7,4,6,5,1,2]=>000111=>111000
[3,7,4,6,5,2,1]=>100111=>111001
[3,7,5,1,2,4,6]=>000101=>101000
[3,7,5,1,2,6,4]=>000111=>111000
[3,7,5,1,4,2,6]=>001101=>101100
[3,7,5,1,4,6,2]=>000111=>111000
[3,7,5,1,6,2,4]=>000111=>111000
[3,7,5,1,6,4,2]=>001111=>111100
[3,7,5,2,1,4,6]=>100101=>101001
[3,7,5,2,1,6,4]=>100111=>111001
[3,7,5,2,4,1,6]=>001101=>101100
[3,7,5,2,4,6,1]=>000111=>111000
[3,7,5,2,6,1,4]=>000111=>111000
[3,7,5,2,6,4,1]=>001111=>111100
[3,7,5,4,1,2,6]=>001101=>101100
[3,7,5,4,1,6,2]=>001111=>111100
[3,7,5,4,2,1,6]=>101101=>101101
[3,7,5,4,2,6,1]=>001111=>111100
[3,7,5,4,6,1,2]=>000111=>111000
[3,7,5,4,6,2,1]=>100111=>111001
[3,7,5,6,1,2,4]=>000011=>110000
[3,7,5,6,1,4,2]=>001011=>110100
[3,7,5,6,2,1,4]=>100011=>110001
[3,7,5,6,2,4,1]=>001011=>110100
[3,7,5,6,4,1,2]=>001011=>110100
[3,7,5,6,4,2,1]=>101011=>110101
[3,7,6,1,2,4,5]=>000011=>110000
[3,7,6,1,2,5,4]=>000111=>111000
[3,7,6,1,4,2,5]=>001011=>110100
[3,7,6,1,4,5,2]=>000111=>111000
[3,7,6,1,5,2,4]=>000111=>111000
[3,7,6,1,5,4,2]=>001111=>111100
[3,7,6,2,1,4,5]=>100011=>110001
[3,7,6,2,1,5,4]=>100111=>111001
[3,7,6,2,4,1,5]=>001011=>110100
[3,7,6,2,4,5,1]=>000111=>111000
[3,7,6,2,5,1,4]=>000111=>111000
[3,7,6,2,5,4,1]=>001111=>111100
[3,7,6,4,1,2,5]=>001011=>110100
[3,7,6,4,1,5,2]=>001111=>111100
[3,7,6,4,2,1,5]=>101011=>110101
[3,7,6,4,2,5,1]=>001111=>111100
[3,7,6,4,5,1,2]=>000111=>111000
[3,7,6,4,5,2,1]=>100111=>111001
[3,7,6,5,1,2,4]=>000111=>111000
[3,7,6,5,1,4,2]=>001111=>111100
[3,7,6,5,2,1,4]=>100111=>111001
[3,7,6,5,2,4,1]=>001111=>111100
[3,7,6,5,4,1,2]=>001111=>111100
[3,7,6,5,4,2,1]=>101111=>111101
[4,1,2,3,5,6,7]=>001000=>000100
[4,1,2,3,5,7,6]=>001001=>100100
[4,1,2,3,6,5,7]=>001010=>010100
[4,1,2,3,6,7,5]=>001001=>100100
[4,1,2,3,7,5,6]=>001001=>100100
[4,1,2,3,7,6,5]=>001011=>110100
[4,1,2,5,3,6,7]=>001100=>001100
[4,1,2,5,3,7,6]=>001101=>101100
[4,1,2,5,6,3,7]=>001010=>010100
[4,1,2,5,6,7,3]=>001001=>100100
[4,1,2,5,7,3,6]=>001001=>100100
[4,1,2,5,7,6,3]=>001011=>110100
[4,1,2,6,3,5,7]=>001010=>010100
[4,1,2,6,3,7,5]=>001011=>110100
[4,1,2,6,5,3,7]=>001110=>011100
[4,1,2,6,5,7,3]=>001011=>110100
[4,1,2,6,7,3,5]=>001001=>100100
[4,1,2,6,7,5,3]=>001101=>101100
[4,1,2,7,3,5,6]=>001001=>100100
[4,1,2,7,3,6,5]=>001011=>110100
[4,1,2,7,5,3,6]=>001101=>101100
[4,1,2,7,5,6,3]=>001011=>110100
[4,1,2,7,6,3,5]=>001011=>110100
[4,1,2,7,6,5,3]=>001111=>111100
[4,1,3,2,5,6,7]=>011000=>000110
[4,1,3,2,5,7,6]=>011001=>100110
[4,1,3,2,6,5,7]=>011010=>010110
[4,1,3,2,6,7,5]=>011001=>100110
[4,1,3,2,7,5,6]=>011001=>100110
[4,1,3,2,7,6,5]=>011011=>110110
[4,1,3,5,2,6,7]=>001100=>001100
[4,1,3,5,2,7,6]=>001101=>101100
[4,1,3,5,6,2,7]=>001010=>010100
[4,1,3,5,6,7,2]=>001001=>100100
[4,1,3,5,7,2,6]=>001001=>100100
[4,1,3,5,7,6,2]=>001011=>110100
[4,1,3,6,2,5,7]=>001010=>010100
[4,1,3,6,2,7,5]=>001011=>110100
[4,1,3,6,5,2,7]=>001110=>011100
[4,1,3,6,5,7,2]=>001011=>110100
[4,1,3,6,7,2,5]=>001001=>100100
[4,1,3,6,7,5,2]=>001101=>101100
[4,1,3,7,2,5,6]=>001001=>100100
[4,1,3,7,2,6,5]=>001011=>110100
[4,1,3,7,5,2,6]=>001101=>101100
[4,1,3,7,5,6,2]=>001011=>110100
[4,1,3,7,6,2,5]=>001011=>110100
[4,1,3,7,6,5,2]=>001111=>111100
[4,1,5,2,3,6,7]=>001100=>001100
[4,1,5,2,3,7,6]=>001101=>101100
[4,1,5,2,6,3,7]=>001110=>011100
[4,1,5,2,6,7,3]=>001101=>101100
[4,1,5,2,7,3,6]=>001101=>101100
[4,1,5,2,7,6,3]=>001111=>111100
[4,1,5,3,2,6,7]=>011100=>001110
[4,1,5,3,2,7,6]=>011101=>101110
[4,1,5,3,6,2,7]=>001110=>011100
[4,1,5,3,6,7,2]=>001101=>101100
[4,1,5,3,7,2,6]=>001101=>101100
[4,1,5,3,7,6,2]=>001111=>111100
[4,1,5,6,2,3,7]=>001010=>010100
[4,1,5,6,2,7,3]=>001011=>110100
[4,1,5,6,3,2,7]=>011010=>010110
[4,1,5,6,3,7,2]=>001011=>110100
[4,1,5,6,7,2,3]=>001001=>100100
[4,1,5,6,7,3,2]=>011001=>100110
[4,1,5,7,2,3,6]=>001001=>100100
[4,1,5,7,2,6,3]=>001011=>110100
[4,1,5,7,3,2,6]=>011001=>100110
[4,1,5,7,3,6,2]=>001011=>110100
[4,1,5,7,6,2,3]=>001011=>110100
[4,1,5,7,6,3,2]=>011011=>110110
[4,1,6,2,3,5,7]=>001010=>010100
[4,1,6,2,3,7,5]=>001011=>110100
[4,1,6,2,5,3,7]=>001110=>011100
[4,1,6,2,5,7,3]=>001011=>110100
[4,1,6,2,7,3,5]=>001011=>110100
[4,1,6,2,7,5,3]=>001111=>111100
[4,1,6,3,2,5,7]=>011010=>010110
[4,1,6,3,2,7,5]=>011011=>110110
[4,1,6,3,5,2,7]=>001110=>011100
[4,1,6,3,5,7,2]=>001011=>110100
[4,1,6,3,7,2,5]=>001011=>110100
[4,1,6,3,7,5,2]=>001111=>111100
[4,1,6,5,2,3,7]=>001110=>011100
[4,1,6,5,2,7,3]=>001111=>111100
[4,1,6,5,3,2,7]=>011110=>011110
[4,1,6,5,3,7,2]=>001111=>111100
[4,1,6,5,7,2,3]=>001011=>110100
[4,1,6,5,7,3,2]=>011011=>110110
[4,1,6,7,2,3,5]=>001001=>100100
[4,1,6,7,2,5,3]=>001101=>101100
[4,1,6,7,3,2,5]=>011001=>100110
[4,1,6,7,3,5,2]=>001101=>101100
[4,1,6,7,5,2,3]=>001101=>101100
[4,1,6,7,5,3,2]=>011101=>101110
[4,1,7,2,3,5,6]=>001001=>100100
[4,1,7,2,3,6,5]=>001011=>110100
[4,1,7,2,5,3,6]=>001101=>101100
[4,1,7,2,5,6,3]=>001011=>110100
[4,1,7,2,6,3,5]=>001011=>110100
[4,1,7,2,6,5,3]=>001111=>111100
[4,1,7,3,2,5,6]=>011001=>100110
[4,1,7,3,2,6,5]=>011011=>110110
[4,1,7,3,5,2,6]=>001101=>101100
[4,1,7,3,5,6,2]=>001011=>110100
[4,1,7,3,6,2,5]=>001011=>110100
[4,1,7,3,6,5,2]=>001111=>111100
[4,1,7,5,2,3,6]=>001101=>101100
[4,1,7,5,2,6,3]=>001111=>111100
[4,1,7,5,3,2,6]=>011101=>101110
[4,1,7,5,3,6,2]=>001111=>111100
[4,1,7,5,6,2,3]=>001011=>110100
[4,1,7,5,6,3,2]=>011011=>110110
[4,1,7,6,2,3,5]=>001011=>110100
[4,1,7,6,2,5,3]=>001111=>111100
[4,1,7,6,3,2,5]=>011011=>110110
[4,1,7,6,3,5,2]=>001111=>111100
[4,1,7,6,5,2,3]=>001111=>111100
[4,1,7,6,5,3,2]=>011111=>111110
[4,2,1,3,5,6,7]=>101000=>000101
[4,2,1,3,5,7,6]=>101001=>100101
[4,2,1,3,6,5,7]=>101010=>010101
[4,2,1,3,6,7,5]=>101001=>100101
[4,2,1,3,7,5,6]=>101001=>100101
[4,2,1,3,7,6,5]=>101011=>110101
[4,2,1,5,3,6,7]=>101100=>001101
[4,2,1,5,3,7,6]=>101101=>101101
[4,2,1,5,6,3,7]=>101010=>010101
[4,2,1,5,6,7,3]=>101001=>100101
[4,2,1,5,7,3,6]=>101001=>100101
[4,2,1,5,7,6,3]=>101011=>110101
[4,2,1,6,3,5,7]=>101010=>010101
[4,2,1,6,3,7,5]=>101011=>110101
[4,2,1,6,5,3,7]=>101110=>011101
[4,2,1,6,5,7,3]=>101011=>110101
[4,2,1,6,7,3,5]=>101001=>100101
[4,2,1,6,7,5,3]=>101101=>101101
[4,2,1,7,3,5,6]=>101001=>100101
[4,2,1,7,3,6,5]=>101011=>110101
[4,2,1,7,5,3,6]=>101101=>101101
[4,2,1,7,5,6,3]=>101011=>110101
[4,2,1,7,6,3,5]=>101011=>110101
[4,2,1,7,6,5,3]=>101111=>111101
[4,2,3,1,5,6,7]=>011000=>000110
[4,2,3,1,5,7,6]=>011001=>100110
[4,2,3,1,6,5,7]=>011010=>010110
[4,2,3,1,6,7,5]=>011001=>100110
[4,2,3,1,7,5,6]=>011001=>100110
[4,2,3,1,7,6,5]=>011011=>110110
[4,2,3,5,1,6,7]=>001100=>001100
[4,2,3,5,1,7,6]=>001101=>101100
[4,2,3,5,6,1,7]=>001010=>010100
[4,2,3,5,6,7,1]=>001001=>100100
[4,2,3,5,7,1,6]=>001001=>100100
[4,2,3,5,7,6,1]=>001011=>110100
[4,2,3,6,1,5,7]=>001010=>010100
[4,2,3,6,1,7,5]=>001011=>110100
[4,2,3,6,5,1,7]=>001110=>011100
[4,2,3,6,5,7,1]=>001011=>110100
[4,2,3,6,7,1,5]=>001001=>100100
[4,2,3,6,7,5,1]=>001101=>101100
[4,2,3,7,1,5,6]=>001001=>100100
[4,2,3,7,1,6,5]=>001011=>110100
[4,2,3,7,5,1,6]=>001101=>101100
[4,2,3,7,5,6,1]=>001011=>110100
[4,2,3,7,6,1,5]=>001011=>110100
[4,2,3,7,6,5,1]=>001111=>111100
[4,2,5,1,3,6,7]=>001100=>001100
[4,2,5,1,3,7,6]=>001101=>101100
[4,2,5,1,6,3,7]=>001110=>011100
[4,2,5,1,6,7,3]=>001101=>101100
[4,2,5,1,7,3,6]=>001101=>101100
[4,2,5,1,7,6,3]=>001111=>111100
[4,2,5,3,1,6,7]=>011100=>001110
[4,2,5,3,1,7,6]=>011101=>101110
[4,2,5,3,6,1,7]=>001110=>011100
[4,2,5,3,6,7,1]=>001101=>101100
[4,2,5,3,7,1,6]=>001101=>101100
[4,2,5,3,7,6,1]=>001111=>111100
[4,2,5,6,1,3,7]=>001010=>010100
[4,2,5,6,1,7,3]=>001011=>110100
[4,2,5,6,3,1,7]=>011010=>010110
[4,2,5,6,3,7,1]=>001011=>110100
[4,2,5,6,7,1,3]=>001001=>100100
[4,2,5,6,7,3,1]=>011001=>100110
[4,2,5,7,1,3,6]=>001001=>100100
[4,2,5,7,1,6,3]=>001011=>110100
[4,2,5,7,3,1,6]=>011001=>100110
[4,2,5,7,3,6,1]=>001011=>110100
[4,2,5,7,6,1,3]=>001011=>110100
[4,2,5,7,6,3,1]=>011011=>110110
[4,2,6,1,3,5,7]=>001010=>010100
[4,2,6,1,3,7,5]=>001011=>110100
[4,2,6,1,5,3,7]=>001110=>011100
[4,2,6,1,5,7,3]=>001011=>110100
[4,2,6,1,7,3,5]=>001011=>110100
[4,2,6,1,7,5,3]=>001111=>111100
[4,2,6,3,1,5,7]=>011010=>010110
[4,2,6,3,1,7,5]=>011011=>110110
[4,2,6,3,5,1,7]=>001110=>011100
[4,2,6,3,5,7,1]=>001011=>110100
[4,2,6,3,7,1,5]=>001011=>110100
[4,2,6,3,7,5,1]=>001111=>111100
[4,2,6,5,1,3,7]=>001110=>011100
[4,2,6,5,1,7,3]=>001111=>111100
[4,2,6,5,3,1,7]=>011110=>011110
[4,2,6,5,3,7,1]=>001111=>111100
[4,2,6,5,7,1,3]=>001011=>110100
[4,2,6,5,7,3,1]=>011011=>110110
[4,2,6,7,1,3,5]=>001001=>100100
[4,2,6,7,1,5,3]=>001101=>101100
[4,2,6,7,3,1,5]=>011001=>100110
[4,2,6,7,3,5,1]=>001101=>101100
[4,2,6,7,5,1,3]=>001101=>101100
[4,2,6,7,5,3,1]=>011101=>101110
[4,2,7,1,3,5,6]=>001001=>100100
[4,2,7,1,3,6,5]=>001011=>110100
[4,2,7,1,5,3,6]=>001101=>101100
[4,2,7,1,5,6,3]=>001011=>110100
[4,2,7,1,6,3,5]=>001011=>110100
[4,2,7,1,6,5,3]=>001111=>111100
[4,2,7,3,1,5,6]=>011001=>100110
[4,2,7,3,1,6,5]=>011011=>110110
[4,2,7,3,5,1,6]=>001101=>101100
[4,2,7,3,5,6,1]=>001011=>110100
[4,2,7,3,6,1,5]=>001011=>110100
[4,2,7,3,6,5,1]=>001111=>111100
[4,2,7,5,1,3,6]=>001101=>101100
[4,2,7,5,1,6,3]=>001111=>111100
[4,2,7,5,3,1,6]=>011101=>101110
[4,2,7,5,3,6,1]=>001111=>111100
[4,2,7,5,6,1,3]=>001011=>110100
[4,2,7,5,6,3,1]=>011011=>110110
[4,2,7,6,1,3,5]=>001011=>110100
[4,2,7,6,1,5,3]=>001111=>111100
[4,2,7,6,3,1,5]=>011011=>110110
[4,2,7,6,3,5,1]=>001111=>111100
[4,2,7,6,5,1,3]=>001111=>111100
[4,2,7,6,5,3,1]=>011111=>111110
[4,3,1,2,5,6,7]=>011000=>000110
[4,3,1,2,5,7,6]=>011001=>100110
[4,3,1,2,6,5,7]=>011010=>010110
[4,3,1,2,6,7,5]=>011001=>100110
[4,3,1,2,7,5,6]=>011001=>100110
[4,3,1,2,7,6,5]=>011011=>110110
[4,3,1,5,2,6,7]=>011100=>001110
[4,3,1,5,2,7,6]=>011101=>101110
[4,3,1,5,6,2,7]=>011010=>010110
[4,3,1,5,6,7,2]=>011001=>100110
[4,3,1,5,7,2,6]=>011001=>100110
[4,3,1,5,7,6,2]=>011011=>110110
[4,3,1,6,2,5,7]=>011010=>010110
[4,3,1,6,2,7,5]=>011011=>110110
[4,3,1,6,5,2,7]=>011110=>011110
[4,3,1,6,5,7,2]=>011011=>110110
[4,3,1,6,7,2,5]=>011001=>100110
[4,3,1,6,7,5,2]=>011101=>101110
[4,3,1,7,2,5,6]=>011001=>100110
[4,3,1,7,2,6,5]=>011011=>110110
[4,3,1,7,5,2,6]=>011101=>101110
[4,3,1,7,5,6,2]=>011011=>110110
[4,3,1,7,6,2,5]=>011011=>110110
[4,3,1,7,6,5,2]=>011111=>111110
[4,3,2,1,5,6,7]=>111000=>000111
[4,3,2,1,5,7,6]=>111001=>100111
[4,3,2,1,6,5,7]=>111010=>010111
[4,3,2,1,6,7,5]=>111001=>100111
[4,3,2,1,7,5,6]=>111001=>100111
[4,3,2,1,7,6,5]=>111011=>110111
[4,3,2,5,1,6,7]=>011100=>001110
[4,3,2,5,1,7,6]=>011101=>101110
[4,3,2,5,6,1,7]=>011010=>010110
[4,3,2,5,6,7,1]=>011001=>100110
[4,3,2,5,7,1,6]=>011001=>100110
[4,3,2,5,7,6,1]=>011011=>110110
[4,3,2,6,1,5,7]=>011010=>010110
[4,3,2,6,1,7,5]=>011011=>110110
[4,3,2,6,5,1,7]=>011110=>011110
[4,3,2,6,5,7,1]=>011011=>110110
[4,3,2,6,7,1,5]=>011001=>100110
[4,3,2,6,7,5,1]=>011101=>101110
[4,3,2,7,1,5,6]=>011001=>100110
[4,3,2,7,1,6,5]=>011011=>110110
[4,3,2,7,5,1,6]=>011101=>101110
[4,3,2,7,5,6,1]=>011011=>110110
[4,3,2,7,6,1,5]=>011011=>110110
[4,3,2,7,6,5,1]=>011111=>111110
[4,3,5,1,2,6,7]=>001100=>001100
[4,3,5,1,2,7,6]=>001101=>101100
[4,3,5,1,6,2,7]=>001110=>011100
[4,3,5,1,6,7,2]=>001101=>101100
[4,3,5,1,7,2,6]=>001101=>101100
[4,3,5,1,7,6,2]=>001111=>111100
[4,3,5,2,1,6,7]=>101100=>001101
[4,3,5,2,1,7,6]=>101101=>101101
[4,3,5,2,6,1,7]=>001110=>011100
[4,3,5,2,6,7,1]=>001101=>101100
[4,3,5,2,7,1,6]=>001101=>101100
[4,3,5,2,7,6,1]=>001111=>111100
[4,3,5,6,1,2,7]=>001010=>010100
[4,3,5,6,1,7,2]=>001011=>110100
[4,3,5,6,2,1,7]=>101010=>010101
[4,3,5,6,2,7,1]=>001011=>110100
[4,3,5,6,7,1,2]=>001001=>100100
[4,3,5,6,7,2,1]=>101001=>100101
[4,3,5,7,1,2,6]=>001001=>100100
[4,3,5,7,1,6,2]=>001011=>110100
[4,3,5,7,2,1,6]=>101001=>100101
[4,3,5,7,2,6,1]=>001011=>110100
[4,3,5,7,6,1,2]=>001011=>110100
[4,3,5,7,6,2,1]=>101011=>110101
[4,3,6,1,2,5,7]=>001010=>010100
[4,3,6,1,2,7,5]=>001011=>110100
[4,3,6,1,5,2,7]=>001110=>011100
[4,3,6,1,5,7,2]=>001011=>110100
[4,3,6,1,7,2,5]=>001011=>110100
[4,3,6,1,7,5,2]=>001111=>111100
[4,3,6,2,1,5,7]=>101010=>010101
[4,3,6,2,1,7,5]=>101011=>110101
[4,3,6,2,5,1,7]=>001110=>011100
[4,3,6,2,5,7,1]=>001011=>110100
[4,3,6,2,7,1,5]=>001011=>110100
[4,3,6,2,7,5,1]=>001111=>111100
[4,3,6,5,1,2,7]=>001110=>011100
[4,3,6,5,1,7,2]=>001111=>111100
[4,3,6,5,2,1,7]=>101110=>011101
[4,3,6,5,2,7,1]=>001111=>111100
[4,3,6,5,7,1,2]=>001011=>110100
[4,3,6,5,7,2,1]=>101011=>110101
[4,3,6,7,1,2,5]=>001001=>100100
[4,3,6,7,1,5,2]=>001101=>101100
[4,3,6,7,2,1,5]=>101001=>100101
[4,3,6,7,2,5,1]=>001101=>101100
[4,3,6,7,5,1,2]=>001101=>101100
[4,3,6,7,5,2,1]=>101101=>101101
[4,3,7,1,2,5,6]=>001001=>100100
[4,3,7,1,2,6,5]=>001011=>110100
[4,3,7,1,5,2,6]=>001101=>101100
[4,3,7,1,5,6,2]=>001011=>110100
[4,3,7,1,6,2,5]=>001011=>110100
[4,3,7,1,6,5,2]=>001111=>111100
[4,3,7,2,1,5,6]=>101001=>100101
[4,3,7,2,1,6,5]=>101011=>110101
[4,3,7,2,5,1,6]=>001101=>101100
[4,3,7,2,5,6,1]=>001011=>110100
[4,3,7,2,6,1,5]=>001011=>110100
[4,3,7,2,6,5,1]=>001111=>111100
[4,3,7,5,1,2,6]=>001101=>101100
[4,3,7,5,1,6,2]=>001111=>111100
[4,3,7,5,2,1,6]=>101101=>101101
[4,3,7,5,2,6,1]=>001111=>111100
[4,3,7,5,6,1,2]=>001011=>110100
[4,3,7,5,6,2,1]=>101011=>110101
[4,3,7,6,1,2,5]=>001011=>110100
[4,3,7,6,1,5,2]=>001111=>111100
[4,3,7,6,2,1,5]=>101011=>110101
[4,3,7,6,2,5,1]=>001111=>111100
[4,3,7,6,5,1,2]=>001111=>111100
[4,3,7,6,5,2,1]=>101111=>111101
[4,5,1,2,3,6,7]=>000100=>001000
[4,5,1,2,3,7,6]=>000101=>101000
[4,5,1,2,6,3,7]=>000110=>011000
[4,5,1,2,6,7,3]=>000101=>101000
[4,5,1,2,7,3,6]=>000101=>101000
[4,5,1,2,7,6,3]=>000111=>111000
[4,5,1,3,2,6,7]=>010100=>001010
[4,5,1,3,2,7,6]=>010101=>101010
[4,5,1,3,6,2,7]=>000110=>011000
[4,5,1,3,6,7,2]=>000101=>101000
[4,5,1,3,7,2,6]=>000101=>101000
[4,5,1,3,7,6,2]=>000111=>111000
[4,5,1,6,2,3,7]=>000110=>011000
[4,5,1,6,2,7,3]=>000111=>111000
[4,5,1,6,3,2,7]=>010110=>011010
[4,5,1,6,3,7,2]=>000111=>111000
[4,5,1,6,7,2,3]=>000101=>101000
[4,5,1,6,7,3,2]=>010101=>101010
[4,5,1,7,2,3,6]=>000101=>101000
[4,5,1,7,2,6,3]=>000111=>111000
[4,5,1,7,3,2,6]=>010101=>101010
[4,5,1,7,3,6,2]=>000111=>111000
[4,5,1,7,6,2,3]=>000111=>111000
[4,5,1,7,6,3,2]=>010111=>111010
[4,5,2,1,3,6,7]=>100100=>001001
[4,5,2,1,3,7,6]=>100101=>101001
[4,5,2,1,6,3,7]=>100110=>011001
[4,5,2,1,6,7,3]=>100101=>101001
[4,5,2,1,7,3,6]=>100101=>101001
[4,5,2,1,7,6,3]=>100111=>111001
[4,5,2,3,1,6,7]=>010100=>001010
[4,5,2,3,1,7,6]=>010101=>101010
[4,5,2,3,6,1,7]=>000110=>011000
[4,5,2,3,6,7,1]=>000101=>101000
[4,5,2,3,7,1,6]=>000101=>101000
[4,5,2,3,7,6,1]=>000111=>111000
[4,5,2,6,1,3,7]=>000110=>011000
[4,5,2,6,1,7,3]=>000111=>111000
[4,5,2,6,3,1,7]=>010110=>011010
[4,5,2,6,3,7,1]=>000111=>111000
[4,5,2,6,7,1,3]=>000101=>101000
[4,5,2,6,7,3,1]=>010101=>101010
[4,5,2,7,1,3,6]=>000101=>101000
[4,5,2,7,1,6,3]=>000111=>111000
[4,5,2,7,3,1,6]=>010101=>101010
[4,5,2,7,3,6,1]=>000111=>111000
[4,5,2,7,6,1,3]=>000111=>111000
[4,5,2,7,6,3,1]=>010111=>111010
[4,5,3,1,2,6,7]=>010100=>001010
[4,5,3,1,2,7,6]=>010101=>101010
[4,5,3,1,6,2,7]=>010110=>011010
[4,5,3,1,6,7,2]=>010101=>101010
[4,5,3,1,7,2,6]=>010101=>101010
[4,5,3,1,7,6,2]=>010111=>111010
[4,5,3,2,1,6,7]=>110100=>001011
[4,5,3,2,1,7,6]=>110101=>101011
[4,5,3,2,6,1,7]=>010110=>011010
[4,5,3,2,6,7,1]=>010101=>101010
[4,5,3,2,7,1,6]=>010101=>101010
[4,5,3,2,7,6,1]=>010111=>111010
[4,5,3,6,1,2,7]=>000110=>011000
[4,5,3,6,1,7,2]=>000111=>111000
[4,5,3,6,2,1,7]=>100110=>011001
[4,5,3,6,2,7,1]=>000111=>111000
[4,5,3,6,7,1,2]=>000101=>101000
[4,5,3,6,7,2,1]=>100101=>101001
[4,5,3,7,1,2,6]=>000101=>101000
[4,5,3,7,1,6,2]=>000111=>111000
[4,5,3,7,2,1,6]=>100101=>101001
[4,5,3,7,2,6,1]=>000111=>111000
[4,5,3,7,6,1,2]=>000111=>111000
[4,5,3,7,6,2,1]=>100111=>111001
[4,5,6,1,2,3,7]=>000010=>010000
[4,5,6,1,2,7,3]=>000011=>110000
[4,5,6,1,3,2,7]=>010010=>010010
[4,5,6,1,3,7,2]=>000011=>110000
[4,5,6,1,7,2,3]=>000011=>110000
[4,5,6,1,7,3,2]=>010011=>110010
[4,5,6,2,1,3,7]=>100010=>010001
[4,5,6,2,1,7,3]=>100011=>110001
[4,5,6,2,3,1,7]=>010010=>010010
[4,5,6,2,3,7,1]=>000011=>110000
[4,5,6,2,7,1,3]=>000011=>110000
[4,5,6,2,7,3,1]=>010011=>110010
[4,5,6,3,1,2,7]=>010010=>010010
[4,5,6,3,1,7,2]=>010011=>110010
[4,5,6,3,2,1,7]=>110010=>010011
[4,5,6,3,2,7,1]=>010011=>110010
[4,5,6,3,7,1,2]=>000011=>110000
[4,5,6,3,7,2,1]=>100011=>110001
[4,5,6,7,1,2,3]=>000001=>100000
[4,5,6,7,1,3,2]=>010001=>100010
[4,5,6,7,2,1,3]=>100001=>100001
[4,5,6,7,2,3,1]=>010001=>100010
[4,5,6,7,3,1,2]=>010001=>100010
[4,5,6,7,3,2,1]=>110001=>100011
[4,5,7,1,2,3,6]=>000001=>100000
[4,5,7,1,2,6,3]=>000011=>110000
[4,5,7,1,3,2,6]=>010001=>100010
[4,5,7,1,3,6,2]=>000011=>110000
[4,5,7,1,6,2,3]=>000011=>110000
[4,5,7,1,6,3,2]=>010011=>110010
[4,5,7,2,1,3,6]=>100001=>100001
[4,5,7,2,1,6,3]=>100011=>110001
[4,5,7,2,3,1,6]=>010001=>100010
[4,5,7,2,3,6,1]=>000011=>110000
[4,5,7,2,6,1,3]=>000011=>110000
[4,5,7,2,6,3,1]=>010011=>110010
[4,5,7,3,1,2,6]=>010001=>100010
[4,5,7,3,1,6,2]=>010011=>110010
[4,5,7,3,2,1,6]=>110001=>100011
[4,5,7,3,2,6,1]=>010011=>110010
[4,5,7,3,6,1,2]=>000011=>110000
[4,5,7,3,6,2,1]=>100011=>110001
[4,5,7,6,1,2,3]=>000011=>110000
[4,5,7,6,1,3,2]=>010011=>110010
[4,5,7,6,2,1,3]=>100011=>110001
[4,5,7,6,2,3,1]=>010011=>110010
[4,5,7,6,3,1,2]=>010011=>110010
[4,5,7,6,3,2,1]=>110011=>110011
[4,6,1,2,3,5,7]=>000010=>010000
[4,6,1,2,3,7,5]=>000011=>110000
[4,6,1,2,5,3,7]=>000110=>011000
[4,6,1,2,5,7,3]=>000011=>110000
[4,6,1,2,7,3,5]=>000011=>110000
[4,6,1,2,7,5,3]=>000111=>111000
[4,6,1,3,2,5,7]=>010010=>010010
[4,6,1,3,2,7,5]=>010011=>110010
[4,6,1,3,5,2,7]=>000110=>011000
[4,6,1,3,5,7,2]=>000011=>110000
[4,6,1,3,7,2,5]=>000011=>110000
[4,6,1,3,7,5,2]=>000111=>111000
[4,6,1,5,2,3,7]=>000110=>011000
[4,6,1,5,2,7,3]=>000111=>111000
[4,6,1,5,3,2,7]=>010110=>011010
[4,6,1,5,3,7,2]=>000111=>111000
[4,6,1,5,7,2,3]=>000011=>110000
[4,6,1,5,7,3,2]=>010011=>110010
[4,6,1,7,2,3,5]=>000011=>110000
[4,6,1,7,2,5,3]=>000111=>111000
[4,6,1,7,3,2,5]=>010011=>110010
[4,6,1,7,3,5,2]=>000111=>111000
[4,6,1,7,5,2,3]=>000111=>111000
[4,6,1,7,5,3,2]=>010111=>111010
[4,6,2,1,3,5,7]=>100010=>010001
[4,6,2,1,3,7,5]=>100011=>110001
[4,6,2,1,5,3,7]=>100110=>011001
[4,6,2,1,5,7,3]=>100011=>110001
[4,6,2,1,7,3,5]=>100011=>110001
[4,6,2,1,7,5,3]=>100111=>111001
[4,6,2,3,1,5,7]=>010010=>010010
[4,6,2,3,1,7,5]=>010011=>110010
[4,6,2,3,5,1,7]=>000110=>011000
[4,6,2,3,5,7,1]=>000011=>110000
[4,6,2,3,7,1,5]=>000011=>110000
[4,6,2,3,7,5,1]=>000111=>111000
[4,6,2,5,1,3,7]=>000110=>011000
[4,6,2,5,1,7,3]=>000111=>111000
[4,6,2,5,3,1,7]=>010110=>011010
[4,6,2,5,3,7,1]=>000111=>111000
[4,6,2,5,7,1,3]=>000011=>110000
[4,6,2,5,7,3,1]=>010011=>110010
[4,6,2,7,1,3,5]=>000011=>110000
[4,6,2,7,1,5,3]=>000111=>111000
[4,6,2,7,3,1,5]=>010011=>110010
[4,6,2,7,3,5,1]=>000111=>111000
[4,6,2,7,5,1,3]=>000111=>111000
[4,6,2,7,5,3,1]=>010111=>111010
[4,6,3,1,2,5,7]=>010010=>010010
[4,6,3,1,2,7,5]=>010011=>110010
[4,6,3,1,5,2,7]=>010110=>011010
[4,6,3,1,5,7,2]=>010011=>110010
[4,6,3,1,7,2,5]=>010011=>110010
[4,6,3,1,7,5,2]=>010111=>111010
[4,6,3,2,1,5,7]=>110010=>010011
[4,6,3,2,1,7,5]=>110011=>110011
[4,6,3,2,5,1,7]=>010110=>011010
[4,6,3,2,5,7,1]=>010011=>110010
[4,6,3,2,7,1,5]=>010011=>110010
[4,6,3,2,7,5,1]=>010111=>111010
[4,6,3,5,1,2,7]=>000110=>011000
[4,6,3,5,1,7,2]=>000111=>111000
[4,6,3,5,2,1,7]=>100110=>011001
[4,6,3,5,2,7,1]=>000111=>111000
[4,6,3,5,7,1,2]=>000011=>110000
[4,6,3,5,7,2,1]=>100011=>110001
[4,6,3,7,1,2,5]=>000011=>110000
[4,6,3,7,1,5,2]=>000111=>111000
[4,6,3,7,2,1,5]=>100011=>110001
[4,6,3,7,2,5,1]=>000111=>111000
[4,6,3,7,5,1,2]=>000111=>111000
[4,6,3,7,5,2,1]=>100111=>111001
[4,6,5,1,2,3,7]=>000110=>011000
[4,6,5,1,2,7,3]=>000111=>111000
[4,6,5,1,3,2,7]=>010110=>011010
[4,6,5,1,3,7,2]=>000111=>111000
[4,6,5,1,7,2,3]=>000111=>111000
[4,6,5,1,7,3,2]=>010111=>111010
[4,6,5,2,1,3,7]=>100110=>011001
[4,6,5,2,1,7,3]=>100111=>111001
[4,6,5,2,3,1,7]=>010110=>011010
[4,6,5,2,3,7,1]=>000111=>111000
[4,6,5,2,7,1,3]=>000111=>111000
[4,6,5,2,7,3,1]=>010111=>111010
[4,6,5,3,1,2,7]=>010110=>011010
[4,6,5,3,1,7,2]=>010111=>111010
[4,6,5,3,2,1,7]=>110110=>011011
[4,6,5,3,2,7,1]=>010111=>111010
[4,6,5,3,7,1,2]=>000111=>111000
[4,6,5,3,7,2,1]=>100111=>111001
[4,6,5,7,1,2,3]=>000011=>110000
[4,6,5,7,1,3,2]=>010011=>110010
[4,6,5,7,2,1,3]=>100011=>110001
[4,6,5,7,2,3,1]=>010011=>110010
[4,6,5,7,3,1,2]=>010011=>110010
[4,6,5,7,3,2,1]=>110011=>110011
[4,6,7,1,2,3,5]=>000001=>100000
[4,6,7,1,2,5,3]=>000101=>101000
[4,6,7,1,3,2,5]=>010001=>100010
[4,6,7,1,3,5,2]=>000101=>101000
[4,6,7,1,5,2,3]=>000101=>101000
[4,6,7,1,5,3,2]=>010101=>101010
[4,6,7,2,1,3,5]=>100001=>100001
[4,6,7,2,1,5,3]=>100101=>101001
[4,6,7,2,3,1,5]=>010001=>100010
[4,6,7,2,3,5,1]=>000101=>101000
[4,6,7,2,5,1,3]=>000101=>101000
[4,6,7,2,5,3,1]=>010101=>101010
[4,6,7,3,1,2,5]=>010001=>100010
[4,6,7,3,1,5,2]=>010101=>101010
[4,6,7,3,2,1,5]=>110001=>100011
[4,6,7,3,2,5,1]=>010101=>101010
[4,6,7,3,5,1,2]=>000101=>101000
[4,6,7,3,5,2,1]=>100101=>101001
[4,6,7,5,1,2,3]=>000101=>101000
[4,6,7,5,1,3,2]=>010101=>101010
[4,6,7,5,2,1,3]=>100101=>101001
[4,6,7,5,2,3,1]=>010101=>101010
[4,6,7,5,3,1,2]=>010101=>101010
[4,6,7,5,3,2,1]=>110101=>101011
[4,7,1,2,3,5,6]=>000001=>100000
[4,7,1,2,3,6,5]=>000011=>110000
[4,7,1,2,5,3,6]=>000101=>101000
[4,7,1,2,5,6,3]=>000011=>110000
[4,7,1,2,6,3,5]=>000011=>110000
[4,7,1,2,6,5,3]=>000111=>111000
[4,7,1,3,2,5,6]=>010001=>100010
[4,7,1,3,2,6,5]=>010011=>110010
[4,7,1,3,5,2,6]=>000101=>101000
[4,7,1,3,5,6,2]=>000011=>110000
[4,7,1,3,6,2,5]=>000011=>110000
[4,7,1,3,6,5,2]=>000111=>111000
[4,7,1,5,2,3,6]=>000101=>101000
[4,7,1,5,2,6,3]=>000111=>111000
[4,7,1,5,3,2,6]=>010101=>101010
[4,7,1,5,3,6,2]=>000111=>111000
[4,7,1,5,6,2,3]=>000011=>110000
[4,7,1,5,6,3,2]=>010011=>110010
[4,7,1,6,2,3,5]=>000011=>110000
[4,7,1,6,2,5,3]=>000111=>111000
[4,7,1,6,3,2,5]=>010011=>110010
[4,7,1,6,3,5,2]=>000111=>111000
[4,7,1,6,5,2,3]=>000111=>111000
[4,7,1,6,5,3,2]=>010111=>111010
[4,7,2,1,3,5,6]=>100001=>100001
[4,7,2,1,3,6,5]=>100011=>110001
[4,7,2,1,5,3,6]=>100101=>101001
[4,7,2,1,5,6,3]=>100011=>110001
[4,7,2,1,6,3,5]=>100011=>110001
[4,7,2,1,6,5,3]=>100111=>111001
[4,7,2,3,1,5,6]=>010001=>100010
[4,7,2,3,1,6,5]=>010011=>110010
[4,7,2,3,5,1,6]=>000101=>101000
[4,7,2,3,5,6,1]=>000011=>110000
[4,7,2,3,6,1,5]=>000011=>110000
[4,7,2,3,6,5,1]=>000111=>111000
[4,7,2,5,1,3,6]=>000101=>101000
[4,7,2,5,1,6,3]=>000111=>111000
[4,7,2,5,3,1,6]=>010101=>101010
[4,7,2,5,3,6,1]=>000111=>111000
[4,7,2,5,6,1,3]=>000011=>110000
[4,7,2,5,6,3,1]=>010011=>110010
[4,7,2,6,1,3,5]=>000011=>110000
[4,7,2,6,1,5,3]=>000111=>111000
[4,7,2,6,3,1,5]=>010011=>110010
[4,7,2,6,3,5,1]=>000111=>111000
[4,7,2,6,5,1,3]=>000111=>111000
[4,7,2,6,5,3,1]=>010111=>111010
[4,7,3,1,2,5,6]=>010001=>100010
[4,7,3,1,2,6,5]=>010011=>110010
[4,7,3,1,5,2,6]=>010101=>101010
[4,7,3,1,5,6,2]=>010011=>110010
[4,7,3,1,6,2,5]=>010011=>110010
[4,7,3,1,6,5,2]=>010111=>111010
[4,7,3,2,1,5,6]=>110001=>100011
[4,7,3,2,1,6,5]=>110011=>110011
[4,7,3,2,5,1,6]=>010101=>101010
[4,7,3,2,5,6,1]=>010011=>110010
[4,7,3,2,6,1,5]=>010011=>110010
[4,7,3,2,6,5,1]=>010111=>111010
[4,7,3,5,1,2,6]=>000101=>101000
[4,7,3,5,1,6,2]=>000111=>111000
[4,7,3,5,2,1,6]=>100101=>101001
[4,7,3,5,2,6,1]=>000111=>111000
[4,7,3,5,6,1,2]=>000011=>110000
[4,7,3,5,6,2,1]=>100011=>110001
[4,7,3,6,1,2,5]=>000011=>110000
[4,7,3,6,1,5,2]=>000111=>111000
[4,7,3,6,2,1,5]=>100011=>110001
[4,7,3,6,2,5,1]=>000111=>111000
[4,7,3,6,5,1,2]=>000111=>111000
[4,7,3,6,5,2,1]=>100111=>111001
[4,7,5,1,2,3,6]=>000101=>101000
[4,7,5,1,2,6,3]=>000111=>111000
[4,7,5,1,3,2,6]=>010101=>101010
[4,7,5,1,3,6,2]=>000111=>111000
[4,7,5,1,6,2,3]=>000111=>111000
[4,7,5,1,6,3,2]=>010111=>111010
[4,7,5,2,1,3,6]=>100101=>101001
[4,7,5,2,1,6,3]=>100111=>111001
[4,7,5,2,3,1,6]=>010101=>101010
[4,7,5,2,3,6,1]=>000111=>111000
[4,7,5,2,6,1,3]=>000111=>111000
[4,7,5,2,6,3,1]=>010111=>111010
[4,7,5,3,1,2,6]=>010101=>101010
[4,7,5,3,1,6,2]=>010111=>111010
[4,7,5,3,2,1,6]=>110101=>101011
[4,7,5,3,2,6,1]=>010111=>111010
[4,7,5,3,6,1,2]=>000111=>111000
[4,7,5,3,6,2,1]=>100111=>111001
[4,7,5,6,1,2,3]=>000011=>110000
[4,7,5,6,1,3,2]=>010011=>110010
[4,7,5,6,2,1,3]=>100011=>110001
[4,7,5,6,2,3,1]=>010011=>110010
[4,7,5,6,3,1,2]=>010011=>110010
[4,7,5,6,3,2,1]=>110011=>110011
[4,7,6,1,2,3,5]=>000011=>110000
[4,7,6,1,2,5,3]=>000111=>111000
[4,7,6,1,3,2,5]=>010011=>110010
[4,7,6,1,3,5,2]=>000111=>111000
[4,7,6,1,5,2,3]=>000111=>111000
[4,7,6,1,5,3,2]=>010111=>111010
[4,7,6,2,1,3,5]=>100011=>110001
[4,7,6,2,1,5,3]=>100111=>111001
[4,7,6,2,3,1,5]=>010011=>110010
[4,7,6,2,3,5,1]=>000111=>111000
[4,7,6,2,5,1,3]=>000111=>111000
[4,7,6,2,5,3,1]=>010111=>111010
[4,7,6,3,1,2,5]=>010011=>110010
[4,7,6,3,1,5,2]=>010111=>111010
[4,7,6,3,2,1,5]=>110011=>110011
[4,7,6,3,2,5,1]=>010111=>111010
[4,7,6,3,5,1,2]=>000111=>111000
[4,7,6,3,5,2,1]=>100111=>111001
[4,7,6,5,1,2,3]=>000111=>111000
[4,7,6,5,1,3,2]=>010111=>111010
[4,7,6,5,2,1,3]=>100111=>111001
[4,7,6,5,2,3,1]=>010111=>111010
[4,7,6,5,3,1,2]=>010111=>111010
[4,7,6,5,3,2,1]=>110111=>111011
[5,1,2,3,4,6,7]=>000100=>001000
[5,1,2,3,4,7,6]=>000101=>101000
[5,1,2,3,6,4,7]=>000110=>011000
[5,1,2,3,6,7,4]=>000101=>101000
[5,1,2,3,7,4,6]=>000101=>101000
[5,1,2,3,7,6,4]=>000111=>111000
[5,1,2,4,3,6,7]=>001100=>001100
[5,1,2,4,3,7,6]=>001101=>101100
[5,1,2,4,6,3,7]=>000110=>011000
[5,1,2,4,6,7,3]=>000101=>101000
[5,1,2,4,7,3,6]=>000101=>101000
[5,1,2,4,7,6,3]=>000111=>111000
[5,1,2,6,3,4,7]=>000110=>011000
[5,1,2,6,3,7,4]=>000111=>111000
[5,1,2,6,4,3,7]=>001110=>011100
[5,1,2,6,4,7,3]=>000111=>111000
[5,1,2,6,7,3,4]=>000101=>101000
[5,1,2,6,7,4,3]=>001101=>101100
[5,1,2,7,3,4,6]=>000101=>101000
[5,1,2,7,3,6,4]=>000111=>111000
[5,1,2,7,4,3,6]=>001101=>101100
[5,1,2,7,4,6,3]=>000111=>111000
[5,1,2,7,6,3,4]=>000111=>111000
[5,1,2,7,6,4,3]=>001111=>111100
[5,1,3,2,4,6,7]=>010100=>001010
[5,1,3,2,4,7,6]=>010101=>101010
[5,1,3,2,6,4,7]=>010110=>011010
[5,1,3,2,6,7,4]=>010101=>101010
[5,1,3,2,7,4,6]=>010101=>101010
[5,1,3,2,7,6,4]=>010111=>111010
[5,1,3,4,2,6,7]=>001100=>001100
[5,1,3,4,2,7,6]=>001101=>101100
[5,1,3,4,6,2,7]=>000110=>011000
[5,1,3,4,6,7,2]=>000101=>101000
[5,1,3,4,7,2,6]=>000101=>101000
[5,1,3,4,7,6,2]=>000111=>111000
[5,1,3,6,2,4,7]=>000110=>011000
[5,1,3,6,2,7,4]=>000111=>111000
[5,1,3,6,4,2,7]=>001110=>011100
[5,1,3,6,4,7,2]=>000111=>111000
[5,1,3,6,7,2,4]=>000101=>101000
[5,1,3,6,7,4,2]=>001101=>101100
[5,1,3,7,2,4,6]=>000101=>101000
[5,1,3,7,2,6,4]=>000111=>111000
[5,1,3,7,4,2,6]=>001101=>101100
[5,1,3,7,4,6,2]=>000111=>111000
[5,1,3,7,6,2,4]=>000111=>111000
[5,1,3,7,6,4,2]=>001111=>111100
[5,1,4,2,3,6,7]=>001100=>001100
[5,1,4,2,3,7,6]=>001101=>101100
[5,1,4,2,6,3,7]=>001110=>011100
[5,1,4,2,6,7,3]=>001101=>101100
[5,1,4,2,7,3,6]=>001101=>101100
[5,1,4,2,7,6,3]=>001111=>111100
[5,1,4,3,2,6,7]=>011100=>001110
[5,1,4,3,2,7,6]=>011101=>101110
[5,1,4,3,6,2,7]=>001110=>011100
[5,1,4,3,6,7,2]=>001101=>101100
[5,1,4,3,7,2,6]=>001101=>101100
[5,1,4,3,7,6,2]=>001111=>111100
[5,1,4,6,2,3,7]=>000110=>011000
[5,1,4,6,2,7,3]=>000111=>111000
[5,1,4,6,3,2,7]=>010110=>011010
[5,1,4,6,3,7,2]=>000111=>111000
[5,1,4,6,7,2,3]=>000101=>101000
[5,1,4,6,7,3,2]=>010101=>101010
[5,1,4,7,2,3,6]=>000101=>101000
[5,1,4,7,2,6,3]=>000111=>111000
[5,1,4,7,3,2,6]=>010101=>101010
[5,1,4,7,3,6,2]=>000111=>111000
[5,1,4,7,6,2,3]=>000111=>111000
[5,1,4,7,6,3,2]=>010111=>111010
[5,1,6,2,3,4,7]=>000110=>011000
[5,1,6,2,3,7,4]=>000111=>111000
[5,1,6,2,4,3,7]=>001110=>011100
[5,1,6,2,4,7,3]=>000111=>111000
[5,1,6,2,7,3,4]=>000111=>111000
[5,1,6,2,7,4,3]=>001111=>111100
[5,1,6,3,2,4,7]=>010110=>011010
[5,1,6,3,2,7,4]=>010111=>111010
[5,1,6,3,4,2,7]=>001110=>011100
[5,1,6,3,4,7,2]=>000111=>111000
[5,1,6,3,7,2,4]=>000111=>111000
[5,1,6,3,7,4,2]=>001111=>111100
[5,1,6,4,2,3,7]=>001110=>011100
[5,1,6,4,2,7,3]=>001111=>111100
[5,1,6,4,3,2,7]=>011110=>011110
[5,1,6,4,3,7,2]=>001111=>111100
[5,1,6,4,7,2,3]=>000111=>111000
[5,1,6,4,7,3,2]=>010111=>111010
[5,1,6,7,2,3,4]=>000101=>101000
[5,1,6,7,2,4,3]=>001101=>101100
[5,1,6,7,3,2,4]=>010101=>101010
[5,1,6,7,3,4,2]=>001101=>101100
[5,1,6,7,4,2,3]=>001101=>101100
[5,1,6,7,4,3,2]=>011101=>101110
[5,1,7,2,3,4,6]=>000101=>101000
[5,1,7,2,3,6,4]=>000111=>111000
[5,1,7,2,4,3,6]=>001101=>101100
[5,1,7,2,4,6,3]=>000111=>111000
[5,1,7,2,6,3,4]=>000111=>111000
[5,1,7,2,6,4,3]=>001111=>111100
[5,1,7,3,2,4,6]=>010101=>101010
[5,1,7,3,2,6,4]=>010111=>111010
[5,1,7,3,4,2,6]=>001101=>101100
[5,1,7,3,4,6,2]=>000111=>111000
[5,1,7,3,6,2,4]=>000111=>111000
[5,1,7,3,6,4,2]=>001111=>111100
[5,1,7,4,2,3,6]=>001101=>101100
[5,1,7,4,2,6,3]=>001111=>111100
[5,1,7,4,3,2,6]=>011101=>101110
[5,1,7,4,3,6,2]=>001111=>111100
[5,1,7,4,6,2,3]=>000111=>111000
[5,1,7,4,6,3,2]=>010111=>111010
[5,1,7,6,2,3,4]=>000111=>111000
[5,1,7,6,2,4,3]=>001111=>111100
[5,1,7,6,3,2,4]=>010111=>111010
[5,1,7,6,3,4,2]=>001111=>111100
[5,1,7,6,4,2,3]=>001111=>111100
[5,1,7,6,4,3,2]=>011111=>111110
[5,2,1,3,4,6,7]=>100100=>001001
[5,2,1,3,4,7,6]=>100101=>101001
[5,2,1,3,6,4,7]=>100110=>011001
[5,2,1,3,6,7,4]=>100101=>101001
[5,2,1,3,7,4,6]=>100101=>101001
[5,2,1,3,7,6,4]=>100111=>111001
[5,2,1,4,3,6,7]=>101100=>001101
[5,2,1,4,3,7,6]=>101101=>101101
[5,2,1,4,6,3,7]=>100110=>011001
[5,2,1,4,6,7,3]=>100101=>101001
[5,2,1,4,7,3,6]=>100101=>101001
[5,2,1,4,7,6,3]=>100111=>111001
[5,2,1,6,3,4,7]=>100110=>011001
[5,2,1,6,3,7,4]=>100111=>111001
[5,2,1,6,4,3,7]=>101110=>011101
[5,2,1,6,4,7,3]=>100111=>111001
[5,2,1,6,7,3,4]=>100101=>101001
[5,2,1,6,7,4,3]=>101101=>101101
[5,2,1,7,3,4,6]=>100101=>101001
[5,2,1,7,3,6,4]=>100111=>111001
[5,2,1,7,4,3,6]=>101101=>101101
[5,2,1,7,4,6,3]=>100111=>111001
[5,2,1,7,6,3,4]=>100111=>111001
[5,2,1,7,6,4,3]=>101111=>111101
[5,2,3,1,4,6,7]=>010100=>001010
[5,2,3,1,4,7,6]=>010101=>101010
[5,2,3,1,6,4,7]=>010110=>011010
[5,2,3,1,6,7,4]=>010101=>101010
[5,2,3,1,7,4,6]=>010101=>101010
[5,2,3,1,7,6,4]=>010111=>111010
[5,2,3,4,1,6,7]=>001100=>001100
[5,2,3,4,1,7,6]=>001101=>101100
[5,2,3,4,6,1,7]=>000110=>011000
[5,2,3,4,6,7,1]=>000101=>101000
[5,2,3,4,7,1,6]=>000101=>101000
[5,2,3,4,7,6,1]=>000111=>111000
[5,2,3,6,1,4,7]=>000110=>011000
[5,2,3,6,1,7,4]=>000111=>111000
[5,2,3,6,4,1,7]=>001110=>011100
[5,2,3,6,4,7,1]=>000111=>111000
[5,2,3,6,7,1,4]=>000101=>101000
[5,2,3,6,7,4,1]=>001101=>101100
[5,2,3,7,1,4,6]=>000101=>101000
[5,2,3,7,1,6,4]=>000111=>111000
[5,2,3,7,4,1,6]=>001101=>101100
[5,2,3,7,4,6,1]=>000111=>111000
[5,2,3,7,6,1,4]=>000111=>111000
[5,2,3,7,6,4,1]=>001111=>111100
[5,2,4,1,3,6,7]=>001100=>001100
[5,2,4,1,3,7,6]=>001101=>101100
[5,2,4,1,6,3,7]=>001110=>011100
[5,2,4,1,6,7,3]=>001101=>101100
[5,2,4,1,7,3,6]=>001101=>101100
[5,2,4,1,7,6,3]=>001111=>111100
[5,2,4,3,1,6,7]=>011100=>001110
[5,2,4,3,1,7,6]=>011101=>101110
[5,2,4,3,6,1,7]=>001110=>011100
[5,2,4,3,6,7,1]=>001101=>101100
[5,2,4,3,7,1,6]=>001101=>101100
[5,2,4,3,7,6,1]=>001111=>111100
[5,2,4,6,1,3,7]=>000110=>011000
[5,2,4,6,1,7,3]=>000111=>111000
[5,2,4,6,3,1,7]=>010110=>011010
[5,2,4,6,3,7,1]=>000111=>111000
[5,2,4,6,7,1,3]=>000101=>101000
[5,2,4,6,7,3,1]=>010101=>101010
[5,2,4,7,1,3,6]=>000101=>101000
[5,2,4,7,1,6,3]=>000111=>111000
[5,2,4,7,3,1,6]=>010101=>101010
[5,2,4,7,3,6,1]=>000111=>111000
[5,2,4,7,6,1,3]=>000111=>111000
[5,2,4,7,6,3,1]=>010111=>111010
[5,2,6,1,3,4,7]=>000110=>011000
[5,2,6,1,3,7,4]=>000111=>111000
[5,2,6,1,4,3,7]=>001110=>011100
[5,2,6,1,4,7,3]=>000111=>111000
[5,2,6,1,7,3,4]=>000111=>111000
[5,2,6,1,7,4,3]=>001111=>111100
[5,2,6,3,1,4,7]=>010110=>011010
[5,2,6,3,1,7,4]=>010111=>111010
[5,2,6,3,4,1,7]=>001110=>011100
[5,2,6,3,4,7,1]=>000111=>111000
[5,2,6,3,7,1,4]=>000111=>111000
[5,2,6,3,7,4,1]=>001111=>111100
[5,2,6,4,1,3,7]=>001110=>011100
[5,2,6,4,1,7,3]=>001111=>111100
[5,2,6,4,3,1,7]=>011110=>011110
[5,2,6,4,3,7,1]=>001111=>111100
[5,2,6,4,7,1,3]=>000111=>111000
[5,2,6,4,7,3,1]=>010111=>111010
[5,2,6,7,1,3,4]=>000101=>101000
[5,2,6,7,1,4,3]=>001101=>101100
[5,2,6,7,3,1,4]=>010101=>101010
[5,2,6,7,3,4,1]=>001101=>101100
[5,2,6,7,4,1,3]=>001101=>101100
[5,2,6,7,4,3,1]=>011101=>101110
[5,2,7,1,3,4,6]=>000101=>101000
[5,2,7,1,3,6,4]=>000111=>111000
[5,2,7,1,4,3,6]=>001101=>101100
[5,2,7,1,4,6,3]=>000111=>111000
[5,2,7,1,6,3,4]=>000111=>111000
[5,2,7,1,6,4,3]=>001111=>111100
[5,2,7,3,1,4,6]=>010101=>101010
[5,2,7,3,1,6,4]=>010111=>111010
[5,2,7,3,4,1,6]=>001101=>101100
[5,2,7,3,4,6,1]=>000111=>111000
[5,2,7,3,6,1,4]=>000111=>111000
[5,2,7,3,6,4,1]=>001111=>111100
[5,2,7,4,1,3,6]=>001101=>101100
[5,2,7,4,1,6,3]=>001111=>111100
[5,2,7,4,3,1,6]=>011101=>101110
[5,2,7,4,3,6,1]=>001111=>111100
[5,2,7,4,6,1,3]=>000111=>111000
[5,2,7,4,6,3,1]=>010111=>111010
[5,2,7,6,1,3,4]=>000111=>111000
[5,2,7,6,1,4,3]=>001111=>111100
[5,2,7,6,3,1,4]=>010111=>111010
[5,2,7,6,3,4,1]=>001111=>111100
[5,2,7,6,4,1,3]=>001111=>111100
[5,2,7,6,4,3,1]=>011111=>111110
[5,3,1,2,4,6,7]=>010100=>001010
[5,3,1,2,4,7,6]=>010101=>101010
[5,3,1,2,6,4,7]=>010110=>011010
[5,3,1,2,6,7,4]=>010101=>101010
[5,3,1,2,7,4,6]=>010101=>101010
[5,3,1,2,7,6,4]=>010111=>111010
[5,3,1,4,2,6,7]=>011100=>001110
[5,3,1,4,2,7,6]=>011101=>101110
[5,3,1,4,6,2,7]=>010110=>011010
[5,3,1,4,6,7,2]=>010101=>101010
[5,3,1,4,7,2,6]=>010101=>101010
[5,3,1,4,7,6,2]=>010111=>111010
[5,3,1,6,2,4,7]=>010110=>011010
[5,3,1,6,2,7,4]=>010111=>111010
[5,3,1,6,4,2,7]=>011110=>011110
[5,3,1,6,4,7,2]=>010111=>111010
[5,3,1,6,7,2,4]=>010101=>101010
[5,3,1,6,7,4,2]=>011101=>101110
[5,3,1,7,2,4,6]=>010101=>101010
[5,3,1,7,2,6,4]=>010111=>111010
[5,3,1,7,4,2,6]=>011101=>101110
[5,3,1,7,4,6,2]=>010111=>111010
[5,3,1,7,6,2,4]=>010111=>111010
[5,3,1,7,6,4,2]=>011111=>111110
[5,3,2,1,4,6,7]=>110100=>001011
[5,3,2,1,4,7,6]=>110101=>101011
[5,3,2,1,6,4,7]=>110110=>011011
[5,3,2,1,6,7,4]=>110101=>101011
[5,3,2,1,7,4,6]=>110101=>101011
[5,3,2,1,7,6,4]=>110111=>111011
[5,3,2,4,1,6,7]=>011100=>001110
[5,3,2,4,1,7,6]=>011101=>101110
[5,3,2,4,6,1,7]=>010110=>011010
[5,3,2,4,6,7,1]=>010101=>101010
[5,3,2,4,7,1,6]=>010101=>101010
[5,3,2,4,7,6,1]=>010111=>111010
[5,3,2,6,1,4,7]=>010110=>011010
[5,3,2,6,1,7,4]=>010111=>111010
[5,3,2,6,4,1,7]=>011110=>011110
[5,3,2,6,4,7,1]=>010111=>111010
[5,3,2,6,7,1,4]=>010101=>101010
[5,3,2,6,7,4,1]=>011101=>101110
[5,3,2,7,1,4,6]=>010101=>101010
[5,3,2,7,1,6,4]=>010111=>111010
[5,3,2,7,4,1,6]=>011101=>101110
[5,3,2,7,4,6,1]=>010111=>111010
[5,3,2,7,6,1,4]=>010111=>111010
[5,3,2,7,6,4,1]=>011111=>111110
[5,3,4,1,2,6,7]=>001100=>001100
[5,3,4,1,2,7,6]=>001101=>101100
[5,3,4,1,6,2,7]=>001110=>011100
[5,3,4,1,6,7,2]=>001101=>101100
[5,3,4,1,7,2,6]=>001101=>101100
[5,3,4,1,7,6,2]=>001111=>111100
[5,3,4,2,1,6,7]=>101100=>001101
[5,3,4,2,1,7,6]=>101101=>101101
[5,3,4,2,6,1,7]=>001110=>011100
[5,3,4,2,6,7,1]=>001101=>101100
[5,3,4,2,7,1,6]=>001101=>101100
[5,3,4,2,7,6,1]=>001111=>111100
[5,3,4,6,1,2,7]=>000110=>011000
[5,3,4,6,1,7,2]=>000111=>111000
[5,3,4,6,2,1,7]=>100110=>011001
[5,3,4,6,2,7,1]=>000111=>111000
[5,3,4,6,7,1,2]=>000101=>101000
[5,3,4,6,7,2,1]=>100101=>101001
[5,3,4,7,1,2,6]=>000101=>101000
[5,3,4,7,1,6,2]=>000111=>111000
[5,3,4,7,2,1,6]=>100101=>101001
[5,3,4,7,2,6,1]=>000111=>111000
[5,3,4,7,6,1,2]=>000111=>111000
[5,3,4,7,6,2,1]=>100111=>111001
[5,3,6,1,2,4,7]=>000110=>011000
[5,3,6,1,2,7,4]=>000111=>111000
[5,3,6,1,4,2,7]=>001110=>011100
[5,3,6,1,4,7,2]=>000111=>111000
[5,3,6,1,7,2,4]=>000111=>111000
[5,3,6,1,7,4,2]=>001111=>111100
[5,3,6,2,1,4,7]=>100110=>011001
[5,3,6,2,1,7,4]=>100111=>111001
[5,3,6,2,4,1,7]=>001110=>011100
[5,3,6,2,4,7,1]=>000111=>111000
[5,3,6,2,7,1,4]=>000111=>111000
[5,3,6,2,7,4,1]=>001111=>111100
[5,3,6,4,1,2,7]=>001110=>011100
[5,3,6,4,1,7,2]=>001111=>111100
[5,3,6,4,2,1,7]=>101110=>011101
[5,3,6,4,2,7,1]=>001111=>111100
[5,3,6,4,7,1,2]=>000111=>111000
[5,3,6,4,7,2,1]=>100111=>111001
[5,3,6,7,1,2,4]=>000101=>101000
[5,3,6,7,1,4,2]=>001101=>101100
[5,3,6,7,2,1,4]=>100101=>101001
[5,3,6,7,2,4,1]=>001101=>101100
[5,3,6,7,4,1,2]=>001101=>101100
[5,3,6,7,4,2,1]=>101101=>101101
[5,3,7,1,2,4,6]=>000101=>101000
[5,3,7,1,2,6,4]=>000111=>111000
[5,3,7,1,4,2,6]=>001101=>101100
[5,3,7,1,4,6,2]=>000111=>111000
[5,3,7,1,6,2,4]=>000111=>111000
[5,3,7,1,6,4,2]=>001111=>111100
[5,3,7,2,1,4,6]=>100101=>101001
[5,3,7,2,1,6,4]=>100111=>111001
[5,3,7,2,4,1,6]=>001101=>101100
[5,3,7,2,4,6,1]=>000111=>111000
[5,3,7,2,6,1,4]=>000111=>111000
[5,3,7,2,6,4,1]=>001111=>111100
[5,3,7,4,1,2,6]=>001101=>101100
[5,3,7,4,1,6,2]=>001111=>111100
[5,3,7,4,2,1,6]=>101101=>101101
[5,3,7,4,2,6,1]=>001111=>111100
[5,3,7,4,6,1,2]=>000111=>111000
[5,3,7,4,6,2,1]=>100111=>111001
[5,3,7,6,1,2,4]=>000111=>111000
[5,3,7,6,1,4,2]=>001111=>111100
[5,3,7,6,2,1,4]=>100111=>111001
[5,3,7,6,2,4,1]=>001111=>111100
[5,3,7,6,4,1,2]=>001111=>111100
[5,3,7,6,4,2,1]=>101111=>111101
[5,4,1,2,3,6,7]=>001100=>001100
[5,4,1,2,3,7,6]=>001101=>101100
[5,4,1,2,6,3,7]=>001110=>011100
[5,4,1,2,6,7,3]=>001101=>101100
[5,4,1,2,7,3,6]=>001101=>101100
[5,4,1,2,7,6,3]=>001111=>111100
[5,4,1,3,2,6,7]=>011100=>001110
[5,4,1,3,2,7,6]=>011101=>101110
[5,4,1,3,6,2,7]=>001110=>011100
[5,4,1,3,6,7,2]=>001101=>101100
[5,4,1,3,7,2,6]=>001101=>101100
[5,4,1,3,7,6,2]=>001111=>111100
[5,4,1,6,2,3,7]=>001110=>011100
[5,4,1,6,2,7,3]=>001111=>111100
[5,4,1,6,3,2,7]=>011110=>011110
[5,4,1,6,3,7,2]=>001111=>111100
[5,4,1,6,7,2,3]=>001101=>101100
[5,4,1,6,7,3,2]=>011101=>101110
[5,4,1,7,2,3,6]=>001101=>101100
[5,4,1,7,2,6,3]=>001111=>111100
[5,4,1,7,3,2,6]=>011101=>101110
[5,4,1,7,3,6,2]=>001111=>111100
[5,4,1,7,6,2,3]=>001111=>111100
[5,4,1,7,6,3,2]=>011111=>111110
[5,4,2,1,3,6,7]=>101100=>001101
[5,4,2,1,3,7,6]=>101101=>101101
[5,4,2,1,6,3,7]=>101110=>011101
[5,4,2,1,6,7,3]=>101101=>101101
[5,4,2,1,7,3,6]=>101101=>101101
[5,4,2,1,7,6,3]=>101111=>111101
[5,4,2,3,1,6,7]=>011100=>001110
[5,4,2,3,1,7,6]=>011101=>101110
[5,4,2,3,6,1,7]=>001110=>011100
[5,4,2,3,6,7,1]=>001101=>101100
[5,4,2,3,7,1,6]=>001101=>101100
[5,4,2,3,7,6,1]=>001111=>111100
[5,4,2,6,1,3,7]=>001110=>011100
[5,4,2,6,1,7,3]=>001111=>111100
[5,4,2,6,3,1,7]=>011110=>011110
[5,4,2,6,3,7,1]=>001111=>111100
[5,4,2,6,7,1,3]=>001101=>101100
[5,4,2,6,7,3,1]=>011101=>101110
[5,4,2,7,1,3,6]=>001101=>101100
[5,4,2,7,1,6,3]=>001111=>111100
[5,4,2,7,3,1,6]=>011101=>101110
[5,4,2,7,3,6,1]=>001111=>111100
[5,4,2,7,6,1,3]=>001111=>111100
[5,4,2,7,6,3,1]=>011111=>111110
[5,4,3,1,2,6,7]=>011100=>001110
[5,4,3,1,2,7,6]=>011101=>101110
[5,4,3,1,6,2,7]=>011110=>011110
[5,4,3,1,6,7,2]=>011101=>101110
[5,4,3,1,7,2,6]=>011101=>101110
[5,4,3,1,7,6,2]=>011111=>111110
[5,4,3,2,1,6,7]=>111100=>001111
[5,4,3,2,1,7,6]=>111101=>101111
[5,4,3,2,6,1,7]=>011110=>011110
[5,4,3,2,6,7,1]=>011101=>101110
[5,4,3,2,7,1,6]=>011101=>101110
[5,4,3,2,7,6,1]=>011111=>111110
[5,4,3,6,1,2,7]=>001110=>011100
[5,4,3,6,1,7,2]=>001111=>111100
[5,4,3,6,2,1,7]=>101110=>011101
[5,4,3,6,2,7,1]=>001111=>111100
[5,4,3,6,7,1,2]=>001101=>101100
[5,4,3,6,7,2,1]=>101101=>101101
[5,4,3,7,1,2,6]=>001101=>101100
[5,4,3,7,1,6,2]=>001111=>111100
[5,4,3,7,2,1,6]=>101101=>101101
[5,4,3,7,2,6,1]=>001111=>111100
[5,4,3,7,6,1,2]=>001111=>111100
[5,4,3,7,6,2,1]=>101111=>111101
[5,4,6,1,2,3,7]=>000110=>011000
[5,4,6,1,2,7,3]=>000111=>111000
[5,4,6,1,3,2,7]=>010110=>011010
[5,4,6,1,3,7,2]=>000111=>111000
[5,4,6,1,7,2,3]=>000111=>111000
[5,4,6,1,7,3,2]=>010111=>111010
[5,4,6,2,1,3,7]=>100110=>011001
[5,4,6,2,1,7,3]=>100111=>111001
[5,4,6,2,3,1,7]=>010110=>011010
[5,4,6,2,3,7,1]=>000111=>111000
[5,4,6,2,7,1,3]=>000111=>111000
[5,4,6,2,7,3,1]=>010111=>111010
[5,4,6,3,1,2,7]=>010110=>011010
[5,4,6,3,1,7,2]=>010111=>111010
[5,4,6,3,2,1,7]=>110110=>011011
[5,4,6,3,2,7,1]=>010111=>111010
[5,4,6,3,7,1,2]=>000111=>111000
[5,4,6,3,7,2,1]=>100111=>111001
[5,4,6,7,1,2,3]=>000101=>101000
[5,4,6,7,1,3,2]=>010101=>101010
[5,4,6,7,2,1,3]=>100101=>101001
[5,4,6,7,2,3,1]=>010101=>101010
[5,4,6,7,3,1,2]=>010101=>101010
[5,4,6,7,3,2,1]=>110101=>101011
[5,4,7,1,2,3,6]=>000101=>101000
[5,4,7,1,2,6,3]=>000111=>111000
[5,4,7,1,3,2,6]=>010101=>101010
[5,4,7,1,3,6,2]=>000111=>111000
[5,4,7,1,6,2,3]=>000111=>111000
[5,4,7,1,6,3,2]=>010111=>111010
[5,4,7,2,1,3,6]=>100101=>101001
[5,4,7,2,1,6,3]=>100111=>111001
[5,4,7,2,3,1,6]=>010101=>101010
[5,4,7,2,3,6,1]=>000111=>111000
[5,4,7,2,6,1,3]=>000111=>111000
[5,4,7,2,6,3,1]=>010111=>111010
[5,4,7,3,1,2,6]=>010101=>101010
[5,4,7,3,1,6,2]=>010111=>111010
[5,4,7,3,2,1,6]=>110101=>101011
[5,4,7,3,2,6,1]=>010111=>111010
[5,4,7,3,6,1,2]=>000111=>111000
[5,4,7,3,6,2,1]=>100111=>111001
[5,4,7,6,1,2,3]=>000111=>111000
[5,4,7,6,1,3,2]=>010111=>111010
[5,4,7,6,2,1,3]=>100111=>111001
[5,4,7,6,2,3,1]=>010111=>111010
[5,4,7,6,3,1,2]=>010111=>111010
[5,4,7,6,3,2,1]=>110111=>111011
[5,6,1,2,3,4,7]=>000010=>010000
[5,6,1,2,3,7,4]=>000011=>110000
[5,6,1,2,4,3,7]=>001010=>010100
[5,6,1,2,4,7,3]=>000011=>110000
[5,6,1,2,7,3,4]=>000011=>110000
[5,6,1,2,7,4,3]=>001011=>110100
[5,6,1,3,2,4,7]=>010010=>010010
[5,6,1,3,2,7,4]=>010011=>110010
[5,6,1,3,4,2,7]=>001010=>010100
[5,6,1,3,4,7,2]=>000011=>110000
[5,6,1,3,7,2,4]=>000011=>110000
[5,6,1,3,7,4,2]=>001011=>110100
[5,6,1,4,2,3,7]=>001010=>010100
[5,6,1,4,2,7,3]=>001011=>110100
[5,6,1,4,3,2,7]=>011010=>010110
[5,6,1,4,3,7,2]=>001011=>110100
[5,6,1,4,7,2,3]=>000011=>110000
[5,6,1,4,7,3,2]=>010011=>110010
[5,6,1,7,2,3,4]=>000011=>110000
[5,6,1,7,2,4,3]=>001011=>110100
[5,6,1,7,3,2,4]=>010011=>110010
[5,6,1,7,3,4,2]=>001011=>110100
[5,6,1,7,4,2,3]=>001011=>110100
[5,6,1,7,4,3,2]=>011011=>110110
[5,6,2,1,3,4,7]=>100010=>010001
[5,6,2,1,3,7,4]=>100011=>110001
[5,6,2,1,4,3,7]=>101010=>010101
[5,6,2,1,4,7,3]=>100011=>110001
[5,6,2,1,7,3,4]=>100011=>110001
[5,6,2,1,7,4,3]=>101011=>110101
[5,6,2,3,1,4,7]=>010010=>010010
[5,6,2,3,1,7,4]=>010011=>110010
[5,6,2,3,4,1,7]=>001010=>010100
[5,6,2,3,4,7,1]=>000011=>110000
[5,6,2,3,7,1,4]=>000011=>110000
[5,6,2,3,7,4,1]=>001011=>110100
[5,6,2,4,1,3,7]=>001010=>010100
[5,6,2,4,1,7,3]=>001011=>110100
[5,6,2,4,3,1,7]=>011010=>010110
[5,6,2,4,3,7,1]=>001011=>110100
[5,6,2,4,7,1,3]=>000011=>110000
[5,6,2,4,7,3,1]=>010011=>110010
[5,6,2,7,1,3,4]=>000011=>110000
[5,6,2,7,1,4,3]=>001011=>110100
[5,6,2,7,3,1,4]=>010011=>110010
[5,6,2,7,3,4,1]=>001011=>110100
[5,6,2,7,4,1,3]=>001011=>110100
[5,6,2,7,4,3,1]=>011011=>110110
[5,6,3,1,2,4,7]=>010010=>010010
[5,6,3,1,2,7,4]=>010011=>110010
[5,6,3,1,4,2,7]=>011010=>010110
[5,6,3,1,4,7,2]=>010011=>110010
[5,6,3,1,7,2,4]=>010011=>110010
[5,6,3,1,7,4,2]=>011011=>110110
[5,6,3,2,1,4,7]=>110010=>010011
[5,6,3,2,1,7,4]=>110011=>110011
[5,6,3,2,4,1,7]=>011010=>010110
[5,6,3,2,4,7,1]=>010011=>110010
[5,6,3,2,7,1,4]=>010011=>110010
[5,6,3,2,7,4,1]=>011011=>110110
[5,6,3,4,1,2,7]=>001010=>010100
[5,6,3,4,1,7,2]=>001011=>110100
[5,6,3,4,2,1,7]=>101010=>010101
[5,6,3,4,2,7,1]=>001011=>110100
[5,6,3,4,7,1,2]=>000011=>110000
[5,6,3,4,7,2,1]=>100011=>110001
[5,6,3,7,1,2,4]=>000011=>110000
[5,6,3,7,1,4,2]=>001011=>110100
[5,6,3,7,2,1,4]=>100011=>110001
[5,6,3,7,2,4,1]=>001011=>110100
[5,6,3,7,4,1,2]=>001011=>110100
[5,6,3,7,4,2,1]=>101011=>110101
[5,6,4,1,2,3,7]=>001010=>010100
[5,6,4,1,2,7,3]=>001011=>110100
[5,6,4,1,3,2,7]=>011010=>010110
[5,6,4,1,3,7,2]=>001011=>110100
[5,6,4,1,7,2,3]=>001011=>110100
[5,6,4,1,7,3,2]=>011011=>110110
[5,6,4,2,1,3,7]=>101010=>010101
[5,6,4,2,1,7,3]=>101011=>110101
[5,6,4,2,3,1,7]=>011010=>010110
[5,6,4,2,3,7,1]=>001011=>110100
[5,6,4,2,7,1,3]=>001011=>110100
[5,6,4,2,7,3,1]=>011011=>110110
[5,6,4,3,1,2,7]=>011010=>010110
[5,6,4,3,1,7,2]=>011011=>110110
[5,6,4,3,2,1,7]=>111010=>010111
[5,6,4,3,2,7,1]=>011011=>110110
[5,6,4,3,7,1,2]=>001011=>110100
[5,6,4,3,7,2,1]=>101011=>110101
[5,6,4,7,1,2,3]=>000011=>110000
[5,6,4,7,1,3,2]=>010011=>110010
[5,6,4,7,2,1,3]=>100011=>110001
[5,6,4,7,2,3,1]=>010011=>110010
[5,6,4,7,3,1,2]=>010011=>110010
[5,6,4,7,3,2,1]=>110011=>110011
[5,6,7,1,2,3,4]=>000001=>100000
[5,6,7,1,2,4,3]=>001001=>100100
[5,6,7,1,3,2,4]=>010001=>100010
[5,6,7,1,3,4,2]=>001001=>100100
[5,6,7,1,4,2,3]=>001001=>100100
[5,6,7,1,4,3,2]=>011001=>100110
[5,6,7,2,1,3,4]=>100001=>100001
[5,6,7,2,1,4,3]=>101001=>100101
[5,6,7,2,3,1,4]=>010001=>100010
[5,6,7,2,3,4,1]=>001001=>100100
[5,6,7,2,4,1,3]=>001001=>100100
[5,6,7,2,4,3,1]=>011001=>100110
[5,6,7,3,1,2,4]=>010001=>100010
[5,6,7,3,1,4,2]=>011001=>100110
[5,6,7,3,2,1,4]=>110001=>100011
[5,6,7,3,2,4,1]=>011001=>100110
[5,6,7,3,4,1,2]=>001001=>100100
[5,6,7,3,4,2,1]=>101001=>100101
[5,6,7,4,1,2,3]=>001001=>100100
[5,6,7,4,1,3,2]=>011001=>100110
[5,6,7,4,2,1,3]=>101001=>100101
[5,6,7,4,2,3,1]=>011001=>100110
[5,6,7,4,3,1,2]=>011001=>100110
[5,6,7,4,3,2,1]=>111001=>100111
[5,7,1,2,3,4,6]=>000001=>100000
[5,7,1,2,3,6,4]=>000011=>110000
[5,7,1,2,4,3,6]=>001001=>100100
[5,7,1,2,4,6,3]=>000011=>110000
[5,7,1,2,6,3,4]=>000011=>110000
[5,7,1,2,6,4,3]=>001011=>110100
[5,7,1,3,2,4,6]=>010001=>100010
[5,7,1,3,2,6,4]=>010011=>110010
[5,7,1,3,4,2,6]=>001001=>100100
[5,7,1,3,4,6,2]=>000011=>110000
[5,7,1,3,6,2,4]=>000011=>110000
[5,7,1,3,6,4,2]=>001011=>110100
[5,7,1,4,2,3,6]=>001001=>100100
[5,7,1,4,2,6,3]=>001011=>110100
[5,7,1,4,3,2,6]=>011001=>100110
[5,7,1,4,3,6,2]=>001011=>110100
[5,7,1,4,6,2,3]=>000011=>110000
[5,7,1,4,6,3,2]=>010011=>110010
[5,7,1,6,2,3,4]=>000011=>110000
[5,7,1,6,2,4,3]=>001011=>110100
[5,7,1,6,3,2,4]=>010011=>110010
[5,7,1,6,3,4,2]=>001011=>110100
[5,7,1,6,4,2,3]=>001011=>110100
[5,7,1,6,4,3,2]=>011011=>110110
[5,7,2,1,3,4,6]=>100001=>100001
[5,7,2,1,3,6,4]=>100011=>110001
[5,7,2,1,4,3,6]=>101001=>100101
[5,7,2,1,4,6,3]=>100011=>110001
[5,7,2,1,6,3,4]=>100011=>110001
[5,7,2,1,6,4,3]=>101011=>110101
[5,7,2,3,1,4,6]=>010001=>100010
[5,7,2,3,1,6,4]=>010011=>110010
[5,7,2,3,4,1,6]=>001001=>100100
[5,7,2,3,4,6,1]=>000011=>110000
[5,7,2,3,6,1,4]=>000011=>110000
[5,7,2,3,6,4,1]=>001011=>110100
[5,7,2,4,1,3,6]=>001001=>100100
[5,7,2,4,1,6,3]=>001011=>110100
[5,7,2,4,3,1,6]=>011001=>100110
[5,7,2,4,3,6,1]=>001011=>110100
[5,7,2,4,6,1,3]=>000011=>110000
[5,7,2,4,6,3,1]=>010011=>110010
[5,7,2,6,1,3,4]=>000011=>110000
[5,7,2,6,1,4,3]=>001011=>110100
[5,7,2,6,3,1,4]=>010011=>110010
[5,7,2,6,3,4,1]=>001011=>110100
[5,7,2,6,4,1,3]=>001011=>110100
[5,7,2,6,4,3,1]=>011011=>110110
[5,7,3,1,2,4,6]=>010001=>100010
[5,7,3,1,2,6,4]=>010011=>110010
[5,7,3,1,4,2,6]=>011001=>100110
[5,7,3,1,4,6,2]=>010011=>110010
[5,7,3,1,6,2,4]=>010011=>110010
[5,7,3,1,6,4,2]=>011011=>110110
[5,7,3,2,1,4,6]=>110001=>100011
[5,7,3,2,1,6,4]=>110011=>110011
[5,7,3,2,4,1,6]=>011001=>100110
[5,7,3,2,4,6,1]=>010011=>110010
[5,7,3,2,6,1,4]=>010011=>110010
[5,7,3,2,6,4,1]=>011011=>110110
[5,7,3,4,1,2,6]=>001001=>100100
[5,7,3,4,1,6,2]=>001011=>110100
[5,7,3,4,2,1,6]=>101001=>100101
[5,7,3,4,2,6,1]=>001011=>110100
[5,7,3,4,6,1,2]=>000011=>110000
[5,7,3,4,6,2,1]=>100011=>110001
[5,7,3,6,1,2,4]=>000011=>110000
[5,7,3,6,1,4,2]=>001011=>110100
[5,7,3,6,2,1,4]=>100011=>110001
[5,7,3,6,2,4,1]=>001011=>110100
[5,7,3,6,4,1,2]=>001011=>110100
[5,7,3,6,4,2,1]=>101011=>110101
[5,7,4,1,2,3,6]=>001001=>100100
[5,7,4,1,2,6,3]=>001011=>110100
[5,7,4,1,3,2,6]=>011001=>100110
[5,7,4,1,3,6,2]=>001011=>110100
[5,7,4,1,6,2,3]=>001011=>110100
[5,7,4,1,6,3,2]=>011011=>110110
[5,7,4,2,1,3,6]=>101001=>100101
[5,7,4,2,1,6,3]=>101011=>110101
[5,7,4,2,3,1,6]=>011001=>100110
[5,7,4,2,3,6,1]=>001011=>110100
[5,7,4,2,6,1,3]=>001011=>110100
[5,7,4,2,6,3,1]=>011011=>110110
[5,7,4,3,1,2,6]=>011001=>100110
[5,7,4,3,1,6,2]=>011011=>110110
[5,7,4,3,2,1,6]=>111001=>100111
[5,7,4,3,2,6,1]=>011011=>110110
[5,7,4,3,6,1,2]=>001011=>110100
[5,7,4,3,6,2,1]=>101011=>110101
[5,7,4,6,1,2,3]=>000011=>110000
[5,7,4,6,1,3,2]=>010011=>110010
[5,7,4,6,2,1,3]=>100011=>110001
[5,7,4,6,2,3,1]=>010011=>110010
[5,7,4,6,3,1,2]=>010011=>110010
[5,7,4,6,3,2,1]=>110011=>110011
[5,7,6,1,2,3,4]=>000011=>110000
[5,7,6,1,2,4,3]=>001011=>110100
[5,7,6,1,3,2,4]=>010011=>110010
[5,7,6,1,3,4,2]=>001011=>110100
[5,7,6,1,4,2,3]=>001011=>110100
[5,7,6,1,4,3,2]=>011011=>110110
[5,7,6,2,1,3,4]=>100011=>110001
[5,7,6,2,1,4,3]=>101011=>110101
[5,7,6,2,3,1,4]=>010011=>110010
[5,7,6,2,3,4,1]=>001011=>110100
[5,7,6,2,4,1,3]=>001011=>110100
[5,7,6,2,4,3,1]=>011011=>110110
[5,7,6,3,1,2,4]=>010011=>110010
[5,7,6,3,1,4,2]=>011011=>110110
[5,7,6,3,2,1,4]=>110011=>110011
[5,7,6,3,2,4,1]=>011011=>110110
[5,7,6,3,4,1,2]=>001011=>110100
[5,7,6,3,4,2,1]=>101011=>110101
[5,7,6,4,1,2,3]=>001011=>110100
[5,7,6,4,1,3,2]=>011011=>110110
[5,7,6,4,2,1,3]=>101011=>110101
[5,7,6,4,2,3,1]=>011011=>110110
[5,7,6,4,3,1,2]=>011011=>110110
[5,7,6,4,3,2,1]=>111011=>110111
[6,1,2,3,4,5,7]=>000010=>010000
[6,1,2,3,4,7,5]=>000011=>110000
[6,1,2,3,5,4,7]=>000110=>011000
[6,1,2,3,5,7,4]=>000011=>110000
[6,1,2,3,7,4,5]=>000011=>110000
[6,1,2,3,7,5,4]=>000111=>111000
[6,1,2,4,3,5,7]=>001010=>010100
[6,1,2,4,3,7,5]=>001011=>110100
[6,1,2,4,5,3,7]=>000110=>011000
[6,1,2,4,5,7,3]=>000011=>110000
[6,1,2,4,7,3,5]=>000011=>110000
[6,1,2,4,7,5,3]=>000111=>111000
[6,1,2,5,3,4,7]=>000110=>011000
[6,1,2,5,3,7,4]=>000111=>111000
[6,1,2,5,4,3,7]=>001110=>011100
[6,1,2,5,4,7,3]=>000111=>111000
[6,1,2,5,7,3,4]=>000011=>110000
[6,1,2,5,7,4,3]=>001011=>110100
[6,1,2,7,3,4,5]=>000011=>110000
[6,1,2,7,3,5,4]=>000111=>111000
[6,1,2,7,4,3,5]=>001011=>110100
[6,1,2,7,4,5,3]=>000111=>111000
[6,1,2,7,5,3,4]=>000111=>111000
[6,1,2,7,5,4,3]=>001111=>111100
[6,1,3,2,4,5,7]=>010010=>010010
[6,1,3,2,4,7,5]=>010011=>110010
[6,1,3,2,5,4,7]=>010110=>011010
[6,1,3,2,5,7,4]=>010011=>110010
[6,1,3,2,7,4,5]=>010011=>110010
[6,1,3,2,7,5,4]=>010111=>111010
[6,1,3,4,2,5,7]=>001010=>010100
[6,1,3,4,2,7,5]=>001011=>110100
[6,1,3,4,5,2,7]=>000110=>011000
[6,1,3,4,5,7,2]=>000011=>110000
[6,1,3,4,7,2,5]=>000011=>110000
[6,1,3,4,7,5,2]=>000111=>111000
[6,1,3,5,2,4,7]=>000110=>011000
[6,1,3,5,2,7,4]=>000111=>111000
[6,1,3,5,4,2,7]=>001110=>011100
[6,1,3,5,4,7,2]=>000111=>111000
[6,1,3,5,7,2,4]=>000011=>110000
[6,1,3,5,7,4,2]=>001011=>110100
[6,1,3,7,2,4,5]=>000011=>110000
[6,1,3,7,2,5,4]=>000111=>111000
[6,1,3,7,4,2,5]=>001011=>110100
[6,1,3,7,4,5,2]=>000111=>111000
[6,1,3,7,5,2,4]=>000111=>111000
[6,1,3,7,5,4,2]=>001111=>111100
[6,1,4,2,3,5,7]=>001010=>010100
[6,1,4,2,3,7,5]=>001011=>110100
[6,1,4,2,5,3,7]=>001110=>011100
[6,1,4,2,5,7,3]=>001011=>110100
[6,1,4,2,7,3,5]=>001011=>110100
[6,1,4,2,7,5,3]=>001111=>111100
[6,1,4,3,2,5,7]=>011010=>010110
[6,1,4,3,2,7,5]=>011011=>110110
[6,1,4,3,5,2,7]=>001110=>011100
[6,1,4,3,5,7,2]=>001011=>110100
[6,1,4,3,7,2,5]=>001011=>110100
[6,1,4,3,7,5,2]=>001111=>111100
[6,1,4,5,2,3,7]=>000110=>011000
[6,1,4,5,2,7,3]=>000111=>111000
[6,1,4,5,3,2,7]=>010110=>011010
[6,1,4,5,3,7,2]=>000111=>111000
[6,1,4,5,7,2,3]=>000011=>110000
[6,1,4,5,7,3,2]=>010011=>110010
[6,1,4,7,2,3,5]=>000011=>110000
[6,1,4,7,2,5,3]=>000111=>111000
[6,1,4,7,3,2,5]=>010011=>110010
[6,1,4,7,3,5,2]=>000111=>111000
[6,1,4,7,5,2,3]=>000111=>111000
[6,1,4,7,5,3,2]=>010111=>111010
[6,1,5,2,3,4,7]=>000110=>011000
[6,1,5,2,3,7,4]=>000111=>111000
[6,1,5,2,4,3,7]=>001110=>011100
[6,1,5,2,4,7,3]=>000111=>111000
[6,1,5,2,7,3,4]=>000111=>111000
[6,1,5,2,7,4,3]=>001111=>111100
[6,1,5,3,2,4,7]=>010110=>011010
[6,1,5,3,2,7,4]=>010111=>111010
[6,1,5,3,4,2,7]=>001110=>011100
[6,1,5,3,4,7,2]=>000111=>111000
[6,1,5,3,7,2,4]=>000111=>111000
[6,1,5,3,7,4,2]=>001111=>111100
[6,1,5,4,2,3,7]=>001110=>011100
[6,1,5,4,2,7,3]=>001111=>111100
[6,1,5,4,3,2,7]=>011110=>011110
[6,1,5,4,3,7,2]=>001111=>111100
[6,1,5,4,7,2,3]=>000111=>111000
[6,1,5,4,7,3,2]=>010111=>111010
[6,1,5,7,2,3,4]=>000011=>110000
[6,1,5,7,2,4,3]=>001011=>110100
[6,1,5,7,3,2,4]=>010011=>110010
[6,1,5,7,3,4,2]=>001011=>110100
[6,1,5,7,4,2,3]=>001011=>110100
[6,1,5,7,4,3,2]=>011011=>110110
[6,1,7,2,3,4,5]=>000011=>110000
[6,1,7,2,3,5,4]=>000111=>111000
[6,1,7,2,4,3,5]=>001011=>110100
[6,1,7,2,4,5,3]=>000111=>111000
[6,1,7,2,5,3,4]=>000111=>111000
[6,1,7,2,5,4,3]=>001111=>111100
[6,1,7,3,2,4,5]=>010011=>110010
[6,1,7,3,2,5,4]=>010111=>111010
[6,1,7,3,4,2,5]=>001011=>110100
[6,1,7,3,4,5,2]=>000111=>111000
[6,1,7,3,5,2,4]=>000111=>111000
[6,1,7,3,5,4,2]=>001111=>111100
[6,1,7,4,2,3,5]=>001011=>110100
[6,1,7,4,2,5,3]=>001111=>111100
[6,1,7,4,3,2,5]=>011011=>110110
[6,1,7,4,3,5,2]=>001111=>111100
[6,1,7,4,5,2,3]=>000111=>111000
[6,1,7,4,5,3,2]=>010111=>111010
[6,1,7,5,2,3,4]=>000111=>111000
[6,1,7,5,2,4,3]=>001111=>111100
[6,1,7,5,3,2,4]=>010111=>111010
[6,1,7,5,3,4,2]=>001111=>111100
[6,1,7,5,4,2,3]=>001111=>111100
[6,1,7,5,4,3,2]=>011111=>111110
[6,2,1,3,4,5,7]=>100010=>010001
[6,2,1,3,4,7,5]=>100011=>110001
[6,2,1,3,5,4,7]=>100110=>011001
[6,2,1,3,5,7,4]=>100011=>110001
[6,2,1,3,7,4,5]=>100011=>110001
[6,2,1,3,7,5,4]=>100111=>111001
[6,2,1,4,3,5,7]=>101010=>010101
[6,2,1,4,3,7,5]=>101011=>110101
[6,2,1,4,5,3,7]=>100110=>011001
[6,2,1,4,5,7,3]=>100011=>110001
[6,2,1,4,7,3,5]=>100011=>110001
[6,2,1,4,7,5,3]=>100111=>111001
[6,2,1,5,3,4,7]=>100110=>011001
[6,2,1,5,3,7,4]=>100111=>111001
[6,2,1,5,4,3,7]=>101110=>011101
[6,2,1,5,4,7,3]=>100111=>111001
[6,2,1,5,7,3,4]=>100011=>110001
[6,2,1,5,7,4,3]=>101011=>110101
[6,2,1,7,3,4,5]=>100011=>110001
[6,2,1,7,3,5,4]=>100111=>111001
[6,2,1,7,4,3,5]=>101011=>110101
[6,2,1,7,4,5,3]=>100111=>111001
[6,2,1,7,5,3,4]=>100111=>111001
[6,2,1,7,5,4,3]=>101111=>111101
[6,2,3,1,4,5,7]=>010010=>010010
[6,2,3,1,4,7,5]=>010011=>110010
[6,2,3,1,5,4,7]=>010110=>011010
[6,2,3,1,5,7,4]=>010011=>110010
[6,2,3,1,7,4,5]=>010011=>110010
[6,2,3,1,7,5,4]=>010111=>111010
[6,2,3,4,1,5,7]=>001010=>010100
[6,2,3,4,1,7,5]=>001011=>110100
[6,2,3,4,5,1,7]=>000110=>011000
[6,2,3,4,5,7,1]=>000011=>110000
[6,2,3,4,7,1,5]=>000011=>110000
[6,2,3,4,7,5,1]=>000111=>111000
[6,2,3,5,1,4,7]=>000110=>011000
[6,2,3,5,1,7,4]=>000111=>111000
[6,2,3,5,4,1,7]=>001110=>011100
[6,2,3,5,4,7,1]=>000111=>111000
[6,2,3,5,7,1,4]=>000011=>110000
[6,2,3,5,7,4,1]=>001011=>110100
[6,2,3,7,1,4,5]=>000011=>110000
[6,2,3,7,1,5,4]=>000111=>111000
[6,2,3,7,4,1,5]=>001011=>110100
[6,2,3,7,4,5,1]=>000111=>111000
[6,2,3,7,5,1,4]=>000111=>111000
[6,2,3,7,5,4,1]=>001111=>111100
[6,2,4,1,3,5,7]=>001010=>010100
[6,2,4,1,3,7,5]=>001011=>110100
[6,2,4,1,5,3,7]=>001110=>011100
[6,2,4,1,5,7,3]=>001011=>110100
[6,2,4,1,7,3,5]=>001011=>110100
[6,2,4,1,7,5,3]=>001111=>111100
[6,2,4,3,1,5,7]=>011010=>010110
[6,2,4,3,1,7,5]=>011011=>110110
[6,2,4,3,5,1,7]=>001110=>011100
[6,2,4,3,5,7,1]=>001011=>110100
[6,2,4,3,7,1,5]=>001011=>110100
[6,2,4,3,7,5,1]=>001111=>111100
[6,2,4,5,1,3,7]=>000110=>011000
[6,2,4,5,1,7,3]=>000111=>111000
[6,2,4,5,3,1,7]=>010110=>011010
[6,2,4,5,3,7,1]=>000111=>111000
[6,2,4,5,7,1,3]=>000011=>110000
[6,2,4,5,7,3,1]=>010011=>110010
[6,2,4,7,1,3,5]=>000011=>110000
[6,2,4,7,1,5,3]=>000111=>111000
[6,2,4,7,3,1,5]=>010011=>110010
[6,2,4,7,3,5,1]=>000111=>111000
[6,2,4,7,5,1,3]=>000111=>111000
[6,2,4,7,5,3,1]=>010111=>111010
[6,2,5,1,3,4,7]=>000110=>011000
[6,2,5,1,3,7,4]=>000111=>111000
[6,2,5,1,4,3,7]=>001110=>011100
[6,2,5,1,4,7,3]=>000111=>111000
[6,2,5,1,7,3,4]=>000111=>111000
[6,2,5,1,7,4,3]=>001111=>111100
[6,2,5,3,1,4,7]=>010110=>011010
[6,2,5,3,1,7,4]=>010111=>111010
[6,2,5,3,4,1,7]=>001110=>011100
[6,2,5,3,4,7,1]=>000111=>111000
[6,2,5,3,7,1,4]=>000111=>111000
[6,2,5,3,7,4,1]=>001111=>111100
[6,2,5,4,1,3,7]=>001110=>011100
[6,2,5,4,1,7,3]=>001111=>111100
[6,2,5,4,3,1,7]=>011110=>011110
[6,2,5,4,3,7,1]=>001111=>111100
[6,2,5,4,7,1,3]=>000111=>111000
[6,2,5,4,7,3,1]=>010111=>111010
[6,2,5,7,1,3,4]=>000011=>110000
[6,2,5,7,1,4,3]=>001011=>110100
[6,2,5,7,3,1,4]=>010011=>110010
[6,2,5,7,3,4,1]=>001011=>110100
[6,2,5,7,4,1,3]=>001011=>110100
[6,2,5,7,4,3,1]=>011011=>110110
[6,2,7,1,3,4,5]=>000011=>110000
[6,2,7,1,3,5,4]=>000111=>111000
[6,2,7,1,4,3,5]=>001011=>110100
[6,2,7,1,4,5,3]=>000111=>111000
[6,2,7,1,5,3,4]=>000111=>111000
[6,2,7,1,5,4,3]=>001111=>111100
[6,2,7,3,1,4,5]=>010011=>110010
[6,2,7,3,1,5,4]=>010111=>111010
[6,2,7,3,4,1,5]=>001011=>110100
[6,2,7,3,4,5,1]=>000111=>111000
[6,2,7,3,5,1,4]=>000111=>111000
[6,2,7,3,5,4,1]=>001111=>111100
[6,2,7,4,1,3,5]=>001011=>110100
[6,2,7,4,1,5,3]=>001111=>111100
[6,2,7,4,3,1,5]=>011011=>110110
[6,2,7,4,3,5,1]=>001111=>111100
[6,2,7,4,5,1,3]=>000111=>111000
[6,2,7,4,5,3,1]=>010111=>111010
[6,2,7,5,1,3,4]=>000111=>111000
[6,2,7,5,1,4,3]=>001111=>111100
[6,2,7,5,3,1,4]=>010111=>111010
[6,2,7,5,3,4,1]=>001111=>111100
[6,2,7,5,4,1,3]=>001111=>111100
[6,2,7,5,4,3,1]=>011111=>111110
[6,3,1,2,4,5,7]=>010010=>010010
[6,3,1,2,4,7,5]=>010011=>110010
[6,3,1,2,5,4,7]=>010110=>011010
[6,3,1,2,5,7,4]=>010011=>110010
[6,3,1,2,7,4,5]=>010011=>110010
[6,3,1,2,7,5,4]=>010111=>111010
[6,3,1,4,2,5,7]=>011010=>010110
[6,3,1,4,2,7,5]=>011011=>110110
[6,3,1,4,5,2,7]=>010110=>011010
[6,3,1,4,5,7,2]=>010011=>110010
[6,3,1,4,7,2,5]=>010011=>110010
[6,3,1,4,7,5,2]=>010111=>111010
[6,3,1,5,2,4,7]=>010110=>011010
[6,3,1,5,2,7,4]=>010111=>111010
[6,3,1,5,4,2,7]=>011110=>011110
[6,3,1,5,4,7,2]=>010111=>111010
[6,3,1,5,7,2,4]=>010011=>110010
[6,3,1,5,7,4,2]=>011011=>110110
[6,3,1,7,2,4,5]=>010011=>110010
[6,3,1,7,2,5,4]=>010111=>111010
[6,3,1,7,4,2,5]=>011011=>110110
[6,3,1,7,4,5,2]=>010111=>111010
[6,3,1,7,5,2,4]=>010111=>111010
[6,3,1,7,5,4,2]=>011111=>111110
[6,3,2,1,4,5,7]=>110010=>010011
[6,3,2,1,4,7,5]=>110011=>110011
[6,3,2,1,5,4,7]=>110110=>011011
[6,3,2,1,5,7,4]=>110011=>110011
[6,3,2,1,7,4,5]=>110011=>110011
[6,3,2,1,7,5,4]=>110111=>111011
[6,3,2,4,1,5,7]=>011010=>010110
[6,3,2,4,1,7,5]=>011011=>110110
[6,3,2,4,5,1,7]=>010110=>011010
[6,3,2,4,5,7,1]=>010011=>110010
[6,3,2,4,7,1,5]=>010011=>110010
[6,3,2,4,7,5,1]=>010111=>111010
[6,3,2,5,1,4,7]=>010110=>011010
[6,3,2,5,1,7,4]=>010111=>111010
[6,3,2,5,4,1,7]=>011110=>011110
[6,3,2,5,4,7,1]=>010111=>111010
[6,3,2,5,7,1,4]=>010011=>110010
[6,3,2,5,7,4,1]=>011011=>110110
[6,3,2,7,1,4,5]=>010011=>110010
[6,3,2,7,1,5,4]=>010111=>111010
[6,3,2,7,4,1,5]=>011011=>110110
[6,3,2,7,4,5,1]=>010111=>111010
[6,3,2,7,5,1,4]=>010111=>111010
[6,3,2,7,5,4,1]=>011111=>111110
[6,3,4,1,2,5,7]=>001010=>010100
[6,3,4,1,2,7,5]=>001011=>110100
[6,3,4,1,5,2,7]=>001110=>011100
[6,3,4,1,5,7,2]=>001011=>110100
[6,3,4,1,7,2,5]=>001011=>110100
[6,3,4,1,7,5,2]=>001111=>111100
[6,3,4,2,1,5,7]=>101010=>010101
[6,3,4,2,1,7,5]=>101011=>110101
[6,3,4,2,5,1,7]=>001110=>011100
[6,3,4,2,5,7,1]=>001011=>110100
[6,3,4,2,7,1,5]=>001011=>110100
[6,3,4,2,7,5,1]=>001111=>111100
[6,3,4,5,1,2,7]=>000110=>011000
[6,3,4,5,1,7,2]=>000111=>111000
[6,3,4,5,2,1,7]=>100110=>011001
[6,3,4,5,2,7,1]=>000111=>111000
[6,3,4,5,7,1,2]=>000011=>110000
[6,3,4,5,7,2,1]=>100011=>110001
[6,3,4,7,1,2,5]=>000011=>110000
[6,3,4,7,1,5,2]=>000111=>111000
[6,3,4,7,2,1,5]=>100011=>110001
[6,3,4,7,2,5,1]=>000111=>111000
[6,3,4,7,5,1,2]=>000111=>111000
[6,3,4,7,5,2,1]=>100111=>111001
[6,3,5,1,2,4,7]=>000110=>011000
[6,3,5,1,2,7,4]=>000111=>111000
[6,3,5,1,4,2,7]=>001110=>011100
[6,3,5,1,4,7,2]=>000111=>111000
[6,3,5,1,7,2,4]=>000111=>111000
[6,3,5,1,7,4,2]=>001111=>111100
[6,3,5,2,1,4,7]=>100110=>011001
[6,3,5,2,1,7,4]=>100111=>111001
[6,3,5,2,4,1,7]=>001110=>011100
[6,3,5,2,4,7,1]=>000111=>111000
[6,3,5,2,7,1,4]=>000111=>111000
[6,3,5,2,7,4,1]=>001111=>111100
[6,3,5,4,1,2,7]=>001110=>011100
[6,3,5,4,1,7,2]=>001111=>111100
[6,3,5,4,2,1,7]=>101110=>011101
[6,3,5,4,2,7,1]=>001111=>111100
[6,3,5,4,7,1,2]=>000111=>111000
[6,3,5,4,7,2,1]=>100111=>111001
[6,3,5,7,1,2,4]=>000011=>110000
[6,3,5,7,1,4,2]=>001011=>110100
[6,3,5,7,2,1,4]=>100011=>110001
[6,3,5,7,2,4,1]=>001011=>110100
[6,3,5,7,4,1,2]=>001011=>110100
[6,3,5,7,4,2,1]=>101011=>110101
[6,3,7,1,2,4,5]=>000011=>110000
[6,3,7,1,2,5,4]=>000111=>111000
[6,3,7,1,4,2,5]=>001011=>110100
[6,3,7,1,4,5,2]=>000111=>111000
[6,3,7,1,5,2,4]=>000111=>111000
[6,3,7,1,5,4,2]=>001111=>111100
[6,3,7,2,1,4,5]=>100011=>110001
[6,3,7,2,1,5,4]=>100111=>111001
[6,3,7,2,4,1,5]=>001011=>110100
[6,3,7,2,4,5,1]=>000111=>111000
[6,3,7,2,5,1,4]=>000111=>111000
[6,3,7,2,5,4,1]=>001111=>111100
[6,3,7,4,1,2,5]=>001011=>110100
[6,3,7,4,1,5,2]=>001111=>111100
[6,3,7,4,2,1,5]=>101011=>110101
[6,3,7,4,2,5,1]=>001111=>111100
[6,3,7,4,5,1,2]=>000111=>111000
[6,3,7,4,5,2,1]=>100111=>111001
[6,3,7,5,1,2,4]=>000111=>111000
[6,3,7,5,1,4,2]=>001111=>111100
[6,3,7,5,2,1,4]=>100111=>111001
[6,3,7,5,2,4,1]=>001111=>111100
[6,3,7,5,4,1,2]=>001111=>111100
[6,3,7,5,4,2,1]=>101111=>111101
[6,4,1,2,3,5,7]=>001010=>010100
[6,4,1,2,3,7,5]=>001011=>110100
[6,4,1,2,5,3,7]=>001110=>011100
[6,4,1,2,5,7,3]=>001011=>110100
[6,4,1,2,7,3,5]=>001011=>110100
[6,4,1,2,7,5,3]=>001111=>111100
[6,4,1,3,2,5,7]=>011010=>010110
[6,4,1,3,2,7,5]=>011011=>110110
[6,4,1,3,5,2,7]=>001110=>011100
[6,4,1,3,5,7,2]=>001011=>110100
[6,4,1,3,7,2,5]=>001011=>110100
[6,4,1,3,7,5,2]=>001111=>111100
[6,4,1,5,2,3,7]=>001110=>011100
[6,4,1,5,2,7,3]=>001111=>111100
[6,4,1,5,3,2,7]=>011110=>011110
[6,4,1,5,3,7,2]=>001111=>111100
[6,4,1,5,7,2,3]=>001011=>110100
[6,4,1,5,7,3,2]=>011011=>110110
[6,4,1,7,2,3,5]=>001011=>110100
[6,4,1,7,2,5,3]=>001111=>111100
[6,4,1,7,3,2,5]=>011011=>110110
[6,4,1,7,3,5,2]=>001111=>111100
[6,4,1,7,5,2,3]=>001111=>111100
[6,4,1,7,5,3,2]=>011111=>111110
[6,4,2,1,3,5,7]=>101010=>010101
[6,4,2,1,3,7,5]=>101011=>110101
[6,4,2,1,5,3,7]=>101110=>011101
[6,4,2,1,5,7,3]=>101011=>110101
[6,4,2,1,7,3,5]=>101011=>110101
[6,4,2,1,7,5,3]=>101111=>111101
[6,4,2,3,1,5,7]=>011010=>010110
[6,4,2,3,1,7,5]=>011011=>110110
[6,4,2,3,5,1,7]=>001110=>011100
[6,4,2,3,5,7,1]=>001011=>110100
[6,4,2,3,7,1,5]=>001011=>110100
[6,4,2,3,7,5,1]=>001111=>111100
[6,4,2,5,1,3,7]=>001110=>011100
[6,4,2,5,1,7,3]=>001111=>111100
[6,4,2,5,3,1,7]=>011110=>011110
[6,4,2,5,3,7,1]=>001111=>111100
[6,4,2,5,7,1,3]=>001011=>110100
[6,4,2,5,7,3,1]=>011011=>110110
[6,4,2,7,1,3,5]=>001011=>110100
[6,4,2,7,1,5,3]=>001111=>111100
[6,4,2,7,3,1,5]=>011011=>110110
[6,4,2,7,3,5,1]=>001111=>111100
[6,4,2,7,5,1,3]=>001111=>111100
[6,4,2,7,5,3,1]=>011111=>111110
[6,4,3,1,2,5,7]=>011010=>010110
[6,4,3,1,2,7,5]=>011011=>110110
[6,4,3,1,5,2,7]=>011110=>011110
[6,4,3,1,5,7,2]=>011011=>110110
[6,4,3,1,7,2,5]=>011011=>110110
[6,4,3,1,7,5,2]=>011111=>111110
[6,4,3,2,1,5,7]=>111010=>010111
[6,4,3,2,1,7,5]=>111011=>110111
[6,4,3,2,5,1,7]=>011110=>011110
[6,4,3,2,5,7,1]=>011011=>110110
[6,4,3,2,7,1,5]=>011011=>110110
[6,4,3,2,7,5,1]=>011111=>111110
[6,4,3,5,1,2,7]=>001110=>011100
[6,4,3,5,1,7,2]=>001111=>111100
[6,4,3,5,2,1,7]=>101110=>011101
[6,4,3,5,2,7,1]=>001111=>111100
[6,4,3,5,7,1,2]=>001011=>110100
[6,4,3,5,7,2,1]=>101011=>110101
[6,4,3,7,1,2,5]=>001011=>110100
[6,4,3,7,1,5,2]=>001111=>111100
[6,4,3,7,2,1,5]=>101011=>110101
[6,4,3,7,2,5,1]=>001111=>111100
[6,4,3,7,5,1,2]=>001111=>111100
[6,4,3,7,5,2,1]=>101111=>111101
[6,4,5,1,2,3,7]=>000110=>011000
[6,4,5,1,2,7,3]=>000111=>111000
[6,4,5,1,3,2,7]=>010110=>011010
[6,4,5,1,3,7,2]=>000111=>111000
[6,4,5,1,7,2,3]=>000111=>111000
[6,4,5,1,7,3,2]=>010111=>111010
[6,4,5,2,1,3,7]=>100110=>011001
[6,4,5,2,1,7,3]=>100111=>111001
[6,4,5,2,3,1,7]=>010110=>011010
[6,4,5,2,3,7,1]=>000111=>111000
[6,4,5,2,7,1,3]=>000111=>111000
[6,4,5,2,7,3,1]=>010111=>111010
[6,4,5,3,1,2,7]=>010110=>011010
[6,4,5,3,1,7,2]=>010111=>111010
[6,4,5,3,2,1,7]=>110110=>011011
[6,4,5,3,2,7,1]=>010111=>111010
[6,4,5,3,7,1,2]=>000111=>111000
[6,4,5,3,7,2,1]=>100111=>111001
[6,4,5,7,1,2,3]=>000011=>110000
[6,4,5,7,1,3,2]=>010011=>110010
[6,4,5,7,2,1,3]=>100011=>110001
[6,4,5,7,2,3,1]=>010011=>110010
[6,4,5,7,3,1,2]=>010011=>110010
[6,4,5,7,3,2,1]=>110011=>110011
[6,4,7,1,2,3,5]=>000011=>110000
[6,4,7,1,2,5,3]=>000111=>111000
[6,4,7,1,3,2,5]=>010011=>110010
[6,4,7,1,3,5,2]=>000111=>111000
[6,4,7,1,5,2,3]=>000111=>111000
[6,4,7,1,5,3,2]=>010111=>111010
[6,4,7,2,1,3,5]=>100011=>110001
[6,4,7,2,1,5,3]=>100111=>111001
[6,4,7,2,3,1,5]=>010011=>110010
[6,4,7,2,3,5,1]=>000111=>111000
[6,4,7,2,5,1,3]=>000111=>111000
[6,4,7,2,5,3,1]=>010111=>111010
[6,4,7,3,1,2,5]=>010011=>110010
[6,4,7,3,1,5,2]=>010111=>111010
[6,4,7,3,2,1,5]=>110011=>110011
[6,4,7,3,2,5,1]=>010111=>111010
[6,4,7,3,5,1,2]=>000111=>111000
[6,4,7,3,5,2,1]=>100111=>111001
[6,4,7,5,1,2,3]=>000111=>111000
[6,4,7,5,1,3,2]=>010111=>111010
[6,4,7,5,2,1,3]=>100111=>111001
[6,4,7,5,2,3,1]=>010111=>111010
[6,4,7,5,3,1,2]=>010111=>111010
[6,4,7,5,3,2,1]=>110111=>111011
[6,5,1,2,3,4,7]=>000110=>011000
[6,5,1,2,3,7,4]=>000111=>111000
[6,5,1,2,4,3,7]=>001110=>011100
[6,5,1,2,4,7,3]=>000111=>111000
[6,5,1,2,7,3,4]=>000111=>111000
[6,5,1,2,7,4,3]=>001111=>111100
[6,5,1,3,2,4,7]=>010110=>011010
[6,5,1,3,2,7,4]=>010111=>111010
[6,5,1,3,4,2,7]=>001110=>011100
[6,5,1,3,4,7,2]=>000111=>111000
[6,5,1,3,7,2,4]=>000111=>111000
[6,5,1,3,7,4,2]=>001111=>111100
[6,5,1,4,2,3,7]=>001110=>011100
[6,5,1,4,2,7,3]=>001111=>111100
[6,5,1,4,3,2,7]=>011110=>011110
[6,5,1,4,3,7,2]=>001111=>111100
[6,5,1,4,7,2,3]=>000111=>111000
[6,5,1,4,7,3,2]=>010111=>111010
[6,5,1,7,2,3,4]=>000111=>111000
[6,5,1,7,2,4,3]=>001111=>111100
[6,5,1,7,3,2,4]=>010111=>111010
[6,5,1,7,3,4,2]=>001111=>111100
[6,5,1,7,4,2,3]=>001111=>111100
[6,5,1,7,4,3,2]=>011111=>111110
[6,5,2,1,3,4,7]=>100110=>011001
[6,5,2,1,3,7,4]=>100111=>111001
[6,5,2,1,4,3,7]=>101110=>011101
[6,5,2,1,4,7,3]=>100111=>111001
[6,5,2,1,7,3,4]=>100111=>111001
[6,5,2,1,7,4,3]=>101111=>111101
[6,5,2,3,1,4,7]=>010110=>011010
[6,5,2,3,1,7,4]=>010111=>111010
[6,5,2,3,4,1,7]=>001110=>011100
[6,5,2,3,4,7,1]=>000111=>111000
[6,5,2,3,7,1,4]=>000111=>111000
[6,5,2,3,7,4,1]=>001111=>111100
[6,5,2,4,1,3,7]=>001110=>011100
[6,5,2,4,1,7,3]=>001111=>111100
[6,5,2,4,3,1,7]=>011110=>011110
[6,5,2,4,3,7,1]=>001111=>111100
[6,5,2,4,7,1,3]=>000111=>111000
[6,5,2,4,7,3,1]=>010111=>111010
[6,5,2,7,1,3,4]=>000111=>111000
[6,5,2,7,1,4,3]=>001111=>111100
[6,5,2,7,3,1,4]=>010111=>111010
[6,5,2,7,3,4,1]=>001111=>111100
[6,5,2,7,4,1,3]=>001111=>111100
[6,5,2,7,4,3,1]=>011111=>111110
[6,5,3,1,2,4,7]=>010110=>011010
[6,5,3,1,2,7,4]=>010111=>111010
[6,5,3,1,4,2,7]=>011110=>011110
[6,5,3,1,4,7,2]=>010111=>111010
[6,5,3,1,7,2,4]=>010111=>111010
[6,5,3,1,7,4,2]=>011111=>111110
[6,5,3,2,1,4,7]=>110110=>011011
[6,5,3,2,1,7,4]=>110111=>111011
[6,5,3,2,4,1,7]=>011110=>011110
[6,5,3,2,4,7,1]=>010111=>111010
[6,5,3,2,7,1,4]=>010111=>111010
[6,5,3,2,7,4,1]=>011111=>111110
[6,5,3,4,1,2,7]=>001110=>011100
[6,5,3,4,1,7,2]=>001111=>111100
[6,5,3,4,2,1,7]=>101110=>011101
[6,5,3,4,2,7,1]=>001111=>111100
[6,5,3,4,7,1,2]=>000111=>111000
[6,5,3,4,7,2,1]=>100111=>111001
[6,5,3,7,1,2,4]=>000111=>111000
[6,5,3,7,1,4,2]=>001111=>111100
[6,5,3,7,2,1,4]=>100111=>111001
[6,5,3,7,2,4,1]=>001111=>111100
[6,5,3,7,4,1,2]=>001111=>111100
[6,5,3,7,4,2,1]=>101111=>111101
[6,5,4,1,2,3,7]=>001110=>011100
[6,5,4,1,2,7,3]=>001111=>111100
[6,5,4,1,3,2,7]=>011110=>011110
[6,5,4,1,3,7,2]=>001111=>111100
[6,5,4,1,7,2,3]=>001111=>111100
[6,5,4,1,7,3,2]=>011111=>111110
[6,5,4,2,1,3,7]=>101110=>011101
[6,5,4,2,1,7,3]=>101111=>111101
[6,5,4,2,3,1,7]=>011110=>011110
[6,5,4,2,3,7,1]=>001111=>111100
[6,5,4,2,7,1,3]=>001111=>111100
[6,5,4,2,7,3,1]=>011111=>111110
[6,5,4,3,1,2,7]=>011110=>011110
[6,5,4,3,1,7,2]=>011111=>111110
[6,5,4,3,2,1,7]=>111110=>011111
[6,5,4,3,2,7,1]=>011111=>111110
[6,5,4,3,7,1,2]=>001111=>111100
[6,5,4,3,7,2,1]=>101111=>111101
[6,5,4,7,1,2,3]=>000111=>111000
[6,5,4,7,1,3,2]=>010111=>111010
[6,5,4,7,2,1,3]=>100111=>111001
[6,5,4,7,2,3,1]=>010111=>111010
[6,5,4,7,3,1,2]=>010111=>111010
[6,5,4,7,3,2,1]=>110111=>111011
[6,5,7,1,2,3,4]=>000011=>110000
[6,5,7,1,2,4,3]=>001011=>110100
[6,5,7,1,3,2,4]=>010011=>110010
[6,5,7,1,3,4,2]=>001011=>110100
[6,5,7,1,4,2,3]=>001011=>110100
[6,5,7,1,4,3,2]=>011011=>110110
[6,5,7,2,1,3,4]=>100011=>110001
[6,5,7,2,1,4,3]=>101011=>110101
[6,5,7,2,3,1,4]=>010011=>110010
[6,5,7,2,3,4,1]=>001011=>110100
[6,5,7,2,4,1,3]=>001011=>110100
[6,5,7,2,4,3,1]=>011011=>110110
[6,5,7,3,1,2,4]=>010011=>110010
[6,5,7,3,1,4,2]=>011011=>110110
[6,5,7,3,2,1,4]=>110011=>110011
[6,5,7,3,2,4,1]=>011011=>110110
[6,5,7,3,4,1,2]=>001011=>110100
[6,5,7,3,4,2,1]=>101011=>110101
[6,5,7,4,1,2,3]=>001011=>110100
[6,5,7,4,1,3,2]=>011011=>110110
[6,5,7,4,2,1,3]=>101011=>110101
[6,5,7,4,2,3,1]=>011011=>110110
[6,5,7,4,3,1,2]=>011011=>110110
[6,5,7,4,3,2,1]=>111011=>110111
[6,7,1,2,3,4,5]=>000001=>100000
[6,7,1,2,3,5,4]=>000101=>101000
[6,7,1,2,4,3,5]=>001001=>100100
[6,7,1,2,4,5,3]=>000101=>101000
[6,7,1,2,5,3,4]=>000101=>101000
[6,7,1,2,5,4,3]=>001101=>101100
[6,7,1,3,2,4,5]=>010001=>100010
[6,7,1,3,2,5,4]=>010101=>101010
[6,7,1,3,4,2,5]=>001001=>100100
[6,7,1,3,4,5,2]=>000101=>101000
[6,7,1,3,5,2,4]=>000101=>101000
[6,7,1,3,5,4,2]=>001101=>101100
[6,7,1,4,2,3,5]=>001001=>100100
[6,7,1,4,2,5,3]=>001101=>101100
[6,7,1,4,3,2,5]=>011001=>100110
[6,7,1,4,3,5,2]=>001101=>101100
[6,7,1,4,5,2,3]=>000101=>101000
[6,7,1,4,5,3,2]=>010101=>101010
[6,7,1,5,2,3,4]=>000101=>101000
[6,7,1,5,2,4,3]=>001101=>101100
[6,7,1,5,3,2,4]=>010101=>101010
[6,7,1,5,3,4,2]=>001101=>101100
[6,7,1,5,4,2,3]=>001101=>101100
[6,7,1,5,4,3,2]=>011101=>101110
[6,7,2,1,3,4,5]=>100001=>100001
[6,7,2,1,3,5,4]=>100101=>101001
[6,7,2,1,4,3,5]=>101001=>100101
[6,7,2,1,4,5,3]=>100101=>101001
[6,7,2,1,5,3,4]=>100101=>101001
[6,7,2,1,5,4,3]=>101101=>101101
[6,7,2,3,1,4,5]=>010001=>100010
[6,7,2,3,1,5,4]=>010101=>101010
[6,7,2,3,4,1,5]=>001001=>100100
[6,7,2,3,4,5,1]=>000101=>101000
[6,7,2,3,5,1,4]=>000101=>101000
[6,7,2,3,5,4,1]=>001101=>101100
[6,7,2,4,1,3,5]=>001001=>100100
[6,7,2,4,1,5,3]=>001101=>101100
[6,7,2,4,3,1,5]=>011001=>100110
[6,7,2,4,3,5,1]=>001101=>101100
[6,7,2,4,5,1,3]=>000101=>101000
[6,7,2,4,5,3,1]=>010101=>101010
[6,7,2,5,1,3,4]=>000101=>101000
[6,7,2,5,1,4,3]=>001101=>101100
[6,7,2,5,3,1,4]=>010101=>101010
[6,7,2,5,3,4,1]=>001101=>101100
[6,7,2,5,4,1,3]=>001101=>101100
[6,7,2,5,4,3,1]=>011101=>101110
[6,7,3,1,2,4,5]=>010001=>100010
[6,7,3,1,2,5,4]=>010101=>101010
[6,7,3,1,4,2,5]=>011001=>100110
[6,7,3,1,4,5,2]=>010101=>101010
[6,7,3,1,5,2,4]=>010101=>101010
[6,7,3,1,5,4,2]=>011101=>101110
[6,7,3,2,1,4,5]=>110001=>100011
[6,7,3,2,1,5,4]=>110101=>101011
[6,7,3,2,4,1,5]=>011001=>100110
[6,7,3,2,4,5,1]=>010101=>101010
[6,7,3,2,5,1,4]=>010101=>101010
[6,7,3,2,5,4,1]=>011101=>101110
[6,7,3,4,1,2,5]=>001001=>100100
[6,7,3,4,1,5,2]=>001101=>101100
[6,7,3,4,2,1,5]=>101001=>100101
[6,7,3,4,2,5,1]=>001101=>101100
[6,7,3,4,5,1,2]=>000101=>101000
[6,7,3,4,5,2,1]=>100101=>101001
[6,7,3,5,1,2,4]=>000101=>101000
[6,7,3,5,1,4,2]=>001101=>101100
[6,7,3,5,2,1,4]=>100101=>101001
[6,7,3,5,2,4,1]=>001101=>101100
[6,7,3,5,4,1,2]=>001101=>101100
[6,7,3,5,4,2,1]=>101101=>101101
[6,7,4,1,2,3,5]=>001001=>100100
[6,7,4,1,2,5,3]=>001101=>101100
[6,7,4,1,3,2,5]=>011001=>100110
[6,7,4,1,3,5,2]=>001101=>101100
[6,7,4,1,5,2,3]=>001101=>101100
[6,7,4,1,5,3,2]=>011101=>101110
[6,7,4,2,1,3,5]=>101001=>100101
[6,7,4,2,1,5,3]=>101101=>101101
[6,7,4,2,3,1,5]=>011001=>100110
[6,7,4,2,3,5,1]=>001101=>101100
[6,7,4,2,5,1,3]=>001101=>101100
[6,7,4,2,5,3,1]=>011101=>101110
[6,7,4,3,1,2,5]=>011001=>100110
[6,7,4,3,1,5,2]=>011101=>101110
[6,7,4,3,2,1,5]=>111001=>100111
[6,7,4,3,2,5,1]=>011101=>101110
[6,7,4,3,5,1,2]=>001101=>101100
[6,7,4,3,5,2,1]=>101101=>101101
[6,7,4,5,1,2,3]=>000101=>101000
[6,7,4,5,1,3,2]=>010101=>101010
[6,7,4,5,2,1,3]=>100101=>101001
[6,7,4,5,2,3,1]=>010101=>101010
[6,7,4,5,3,1,2]=>010101=>101010
[6,7,4,5,3,2,1]=>110101=>101011
[6,7,5,1,2,3,4]=>000101=>101000
[6,7,5,1,2,4,3]=>001101=>101100
[6,7,5,1,3,2,4]=>010101=>101010
[6,7,5,1,3,4,2]=>001101=>101100
[6,7,5,1,4,2,3]=>001101=>101100
[6,7,5,1,4,3,2]=>011101=>101110
[6,7,5,2,1,3,4]=>100101=>101001
[6,7,5,2,1,4,3]=>101101=>101101
[6,7,5,2,3,1,4]=>010101=>101010
[6,7,5,2,3,4,1]=>001101=>101100
[6,7,5,2,4,1,3]=>001101=>101100
[6,7,5,2,4,3,1]=>011101=>101110
[6,7,5,3,1,2,4]=>010101=>101010
[6,7,5,3,1,4,2]=>011101=>101110
[6,7,5,3,2,1,4]=>110101=>101011
[6,7,5,3,2,4,1]=>011101=>101110
[6,7,5,3,4,1,2]=>001101=>101100
[6,7,5,3,4,2,1]=>101101=>101101
[6,7,5,4,1,2,3]=>001101=>101100
[6,7,5,4,1,3,2]=>011101=>101110
[6,7,5,4,2,1,3]=>101101=>101101
[6,7,5,4,2,3,1]=>011101=>101110
[6,7,5,4,3,1,2]=>011101=>101110
[6,7,5,4,3,2,1]=>111101=>101111
[7,1,2,3,4,5,6]=>000001=>100000
[7,1,2,3,4,6,5]=>000011=>110000
[7,1,2,3,5,4,6]=>000101=>101000
[7,1,2,3,5,6,4]=>000011=>110000
[7,1,2,3,6,4,5]=>000011=>110000
[7,1,2,3,6,5,4]=>000111=>111000
[7,1,2,4,3,5,6]=>001001=>100100
[7,1,2,4,3,6,5]=>001011=>110100
[7,1,2,4,5,3,6]=>000101=>101000
[7,1,2,4,5,6,3]=>000011=>110000
[7,1,2,4,6,3,5]=>000011=>110000
[7,1,2,4,6,5,3]=>000111=>111000
[7,1,2,5,3,4,6]=>000101=>101000
[7,1,2,5,3,6,4]=>000111=>111000
[7,1,2,5,4,3,6]=>001101=>101100
[7,1,2,5,4,6,3]=>000111=>111000
[7,1,2,5,6,3,4]=>000011=>110000
[7,1,2,5,6,4,3]=>001011=>110100
[7,1,2,6,3,4,5]=>000011=>110000
[7,1,2,6,3,5,4]=>000111=>111000
[7,1,2,6,4,3,5]=>001011=>110100
[7,1,2,6,4,5,3]=>000111=>111000
[7,1,2,6,5,3,4]=>000111=>111000
[7,1,2,6,5,4,3]=>001111=>111100
[7,1,3,2,4,5,6]=>010001=>100010
[7,1,3,2,4,6,5]=>010011=>110010
[7,1,3,2,5,4,6]=>010101=>101010
[7,1,3,2,5,6,4]=>010011=>110010
[7,1,3,2,6,4,5]=>010011=>110010
[7,1,3,2,6,5,4]=>010111=>111010
[7,1,3,4,2,5,6]=>001001=>100100
[7,1,3,4,2,6,5]=>001011=>110100
[7,1,3,4,5,2,6]=>000101=>101000
[7,1,3,4,5,6,2]=>000011=>110000
[7,1,3,4,6,2,5]=>000011=>110000
[7,1,3,4,6,5,2]=>000111=>111000
[7,1,3,5,2,4,6]=>000101=>101000
[7,1,3,5,2,6,4]=>000111=>111000
[7,1,3,5,4,2,6]=>001101=>101100
[7,1,3,5,4,6,2]=>000111=>111000
[7,1,3,5,6,2,4]=>000011=>110000
[7,1,3,5,6,4,2]=>001011=>110100
[7,1,3,6,2,4,5]=>000011=>110000
[7,1,3,6,2,5,4]=>000111=>111000
[7,1,3,6,4,2,5]=>001011=>110100
[7,1,3,6,4,5,2]=>000111=>111000
[7,1,3,6,5,2,4]=>000111=>111000
[7,1,3,6,5,4,2]=>001111=>111100
[7,1,4,2,3,5,6]=>001001=>100100
[7,1,4,2,3,6,5]=>001011=>110100
[7,1,4,2,5,3,6]=>001101=>101100
[7,1,4,2,5,6,3]=>001011=>110100
[7,1,4,2,6,3,5]=>001011=>110100
[7,1,4,2,6,5,3]=>001111=>111100
[7,1,4,3,2,5,6]=>011001=>100110
[7,1,4,3,2,6,5]=>011011=>110110
[7,1,4,3,5,2,6]=>001101=>101100
[7,1,4,3,5,6,2]=>001011=>110100
[7,1,4,3,6,2,5]=>001011=>110100
[7,1,4,3,6,5,2]=>001111=>111100
[7,1,4,5,2,3,6]=>000101=>101000
[7,1,4,5,2,6,3]=>000111=>111000
[7,1,4,5,3,2,6]=>010101=>101010
[7,1,4,5,3,6,2]=>000111=>111000
[7,1,4,5,6,2,3]=>000011=>110000
[7,1,4,5,6,3,2]=>010011=>110010
[7,1,4,6,2,3,5]=>000011=>110000
[7,1,4,6,2,5,3]=>000111=>111000
[7,1,4,6,3,2,5]=>010011=>110010
[7,1,4,6,3,5,2]=>000111=>111000
[7,1,4,6,5,2,3]=>000111=>111000
[7,1,4,6,5,3,2]=>010111=>111010
[7,1,5,2,3,4,6]=>000101=>101000
[7,1,5,2,3,6,4]=>000111=>111000
[7,1,5,2,4,3,6]=>001101=>101100
[7,1,5,2,4,6,3]=>000111=>111000
[7,1,5,2,6,3,4]=>000111=>111000
[7,1,5,2,6,4,3]=>001111=>111100
[7,1,5,3,2,4,6]=>010101=>101010
[7,1,5,3,2,6,4]=>010111=>111010
[7,1,5,3,4,2,6]=>001101=>101100
[7,1,5,3,4,6,2]=>000111=>111000
[7,1,5,3,6,2,4]=>000111=>111000
[7,1,5,3,6,4,2]=>001111=>111100
[7,1,5,4,2,3,6]=>001101=>101100
[7,1,5,4,2,6,3]=>001111=>111100
[7,1,5,4,3,2,6]=>011101=>101110
[7,1,5,4,3,6,2]=>001111=>111100
[7,1,5,4,6,2,3]=>000111=>111000
[7,1,5,4,6,3,2]=>010111=>111010
[7,1,5,6,2,3,4]=>000011=>110000
[7,1,5,6,2,4,3]=>001011=>110100
[7,1,5,6,3,2,4]=>010011=>110010
[7,1,5,6,3,4,2]=>001011=>110100
[7,1,5,6,4,2,3]=>001011=>110100
[7,1,5,6,4,3,2]=>011011=>110110
[7,1,6,2,3,4,5]=>000011=>110000
[7,1,6,2,3,5,4]=>000111=>111000
[7,1,6,2,4,3,5]=>001011=>110100
[7,1,6,2,4,5,3]=>000111=>111000
[7,1,6,2,5,3,4]=>000111=>111000
[7,1,6,2,5,4,3]=>001111=>111100
[7,1,6,3,2,4,5]=>010011=>110010
[7,1,6,3,2,5,4]=>010111=>111010
[7,1,6,3,4,2,5]=>001011=>110100
[7,1,6,3,4,5,2]=>000111=>111000
[7,1,6,3,5,2,4]=>000111=>111000
[7,1,6,3,5,4,2]=>001111=>111100
[7,1,6,4,2,3,5]=>001011=>110100
[7,1,6,4,2,5,3]=>001111=>111100
[7,1,6,4,3,2,5]=>011011=>110110
[7,1,6,4,3,5,2]=>001111=>111100
[7,1,6,4,5,2,3]=>000111=>111000
[7,1,6,4,5,3,2]=>010111=>111010
[7,1,6,5,2,3,4]=>000111=>111000
[7,1,6,5,2,4,3]=>001111=>111100
[7,1,6,5,3,2,4]=>010111=>111010
[7,1,6,5,3,4,2]=>001111=>111100
[7,1,6,5,4,2,3]=>001111=>111100
[7,1,6,5,4,3,2]=>011111=>111110
[7,2,1,3,4,5,6]=>100001=>100001
[7,2,1,3,4,6,5]=>100011=>110001
[7,2,1,3,5,4,6]=>100101=>101001
[7,2,1,3,5,6,4]=>100011=>110001
[7,2,1,3,6,4,5]=>100011=>110001
[7,2,1,3,6,5,4]=>100111=>111001
[7,2,1,4,3,5,6]=>101001=>100101
[7,2,1,4,3,6,5]=>101011=>110101
[7,2,1,4,5,3,6]=>100101=>101001
[7,2,1,4,5,6,3]=>100011=>110001
[7,2,1,4,6,3,5]=>100011=>110001
[7,2,1,4,6,5,3]=>100111=>111001
[7,2,1,5,3,4,6]=>100101=>101001
[7,2,1,5,3,6,4]=>100111=>111001
[7,2,1,5,4,3,6]=>101101=>101101
[7,2,1,5,4,6,3]=>100111=>111001
[7,2,1,5,6,3,4]=>100011=>110001
[7,2,1,5,6,4,3]=>101011=>110101
[7,2,1,6,3,4,5]=>100011=>110001
[7,2,1,6,3,5,4]=>100111=>111001
[7,2,1,6,4,3,5]=>101011=>110101
[7,2,1,6,4,5,3]=>100111=>111001
[7,2,1,6,5,3,4]=>100111=>111001
[7,2,1,6,5,4,3]=>101111=>111101
[7,2,3,1,4,5,6]=>010001=>100010
[7,2,3,1,4,6,5]=>010011=>110010
[7,2,3,1,5,4,6]=>010101=>101010
[7,2,3,1,5,6,4]=>010011=>110010
[7,2,3,1,6,4,5]=>010011=>110010
[7,2,3,1,6,5,4]=>010111=>111010
[7,2,3,4,1,5,6]=>001001=>100100
[7,2,3,4,1,6,5]=>001011=>110100
[7,2,3,4,5,1,6]=>000101=>101000
[7,2,3,4,5,6,1]=>000011=>110000
[7,2,3,4,6,1,5]=>000011=>110000
[7,2,3,4,6,5,1]=>000111=>111000
[7,2,3,5,1,4,6]=>000101=>101000
[7,2,3,5,1,6,4]=>000111=>111000
[7,2,3,5,4,1,6]=>001101=>101100
[7,2,3,5,4,6,1]=>000111=>111000
[7,2,3,5,6,1,4]=>000011=>110000
[7,2,3,5,6,4,1]=>001011=>110100
[7,2,3,6,1,4,5]=>000011=>110000
[7,2,3,6,1,5,4]=>000111=>111000
[7,2,3,6,4,1,5]=>001011=>110100
[7,2,3,6,4,5,1]=>000111=>111000
[7,2,3,6,5,1,4]=>000111=>111000
[7,2,3,6,5,4,1]=>001111=>111100
[7,2,4,1,3,5,6]=>001001=>100100
[7,2,4,1,3,6,5]=>001011=>110100
[7,2,4,1,5,3,6]=>001101=>101100
[7,2,4,1,5,6,3]=>001011=>110100
[7,2,4,1,6,3,5]=>001011=>110100
[7,2,4,1,6,5,3]=>001111=>111100
[7,2,4,3,1,5,6]=>011001=>100110
[7,2,4,3,1,6,5]=>011011=>110110
[7,2,4,3,5,1,6]=>001101=>101100
[7,2,4,3,5,6,1]=>001011=>110100
[7,2,4,3,6,1,5]=>001011=>110100
[7,2,4,3,6,5,1]=>001111=>111100
[7,2,4,5,1,3,6]=>000101=>101000
[7,2,4,5,1,6,3]=>000111=>111000
[7,2,4,5,3,1,6]=>010101=>101010
[7,2,4,5,3,6,1]=>000111=>111000
[7,2,4,5,6,1,3]=>000011=>110000
[7,2,4,5,6,3,1]=>010011=>110010
[7,2,4,6,1,3,5]=>000011=>110000
[7,2,4,6,1,5,3]=>000111=>111000
[7,2,4,6,3,1,5]=>010011=>110010
[7,2,4,6,3,5,1]=>000111=>111000
[7,2,4,6,5,1,3]=>000111=>111000
[7,2,4,6,5,3,1]=>010111=>111010
[7,2,5,1,3,4,6]=>000101=>101000
[7,2,5,1,3,6,4]=>000111=>111000
[7,2,5,1,4,3,6]=>001101=>101100
[7,2,5,1,4,6,3]=>000111=>111000
[7,2,5,1,6,3,4]=>000111=>111000
[7,2,5,1,6,4,3]=>001111=>111100
[7,2,5,3,1,4,6]=>010101=>101010
[7,2,5,3,1,6,4]=>010111=>111010
[7,2,5,3,4,1,6]=>001101=>101100
[7,2,5,3,4,6,1]=>000111=>111000
[7,2,5,3,6,1,4]=>000111=>111000
[7,2,5,3,6,4,1]=>001111=>111100
[7,2,5,4,1,3,6]=>001101=>101100
[7,2,5,4,1,6,3]=>001111=>111100
[7,2,5,4,3,1,6]=>011101=>101110
[7,2,5,4,3,6,1]=>001111=>111100
[7,2,5,4,6,1,3]=>000111=>111000
[7,2,5,4,6,3,1]=>010111=>111010
[7,2,5,6,1,3,4]=>000011=>110000
[7,2,5,6,1,4,3]=>001011=>110100
[7,2,5,6,3,1,4]=>010011=>110010
[7,2,5,6,3,4,1]=>001011=>110100
[7,2,5,6,4,1,3]=>001011=>110100
[7,2,5,6,4,3,1]=>011011=>110110
[7,2,6,1,3,4,5]=>000011=>110000
[7,2,6,1,3,5,4]=>000111=>111000
[7,2,6,1,4,3,5]=>001011=>110100
[7,2,6,1,4,5,3]=>000111=>111000
[7,2,6,1,5,3,4]=>000111=>111000
[7,2,6,1,5,4,3]=>001111=>111100
[7,2,6,3,1,4,5]=>010011=>110010
[7,2,6,3,1,5,4]=>010111=>111010
[7,2,6,3,4,1,5]=>001011=>110100
[7,2,6,3,4,5,1]=>000111=>111000
[7,2,6,3,5,1,4]=>000111=>111000
[7,2,6,3,5,4,1]=>001111=>111100
[7,2,6,4,1,3,5]=>001011=>110100
[7,2,6,4,1,5,3]=>001111=>111100
[7,2,6,4,3,1,5]=>011011=>110110
[7,2,6,4,3,5,1]=>001111=>111100
[7,2,6,4,5,1,3]=>000111=>111000
[7,2,6,4,5,3,1]=>010111=>111010
[7,2,6,5,1,3,4]=>000111=>111000
[7,2,6,5,1,4,3]=>001111=>111100
[7,2,6,5,3,1,4]=>010111=>111010
[7,2,6,5,3,4,1]=>001111=>111100
[7,2,6,5,4,1,3]=>001111=>111100
[7,2,6,5,4,3,1]=>011111=>111110
[7,3,1,2,4,5,6]=>010001=>100010
[7,3,1,2,4,6,5]=>010011=>110010
[7,3,1,2,5,4,6]=>010101=>101010
[7,3,1,2,5,6,4]=>010011=>110010
[7,3,1,2,6,4,5]=>010011=>110010
[7,3,1,2,6,5,4]=>010111=>111010
[7,3,1,4,2,5,6]=>011001=>100110
[7,3,1,4,2,6,5]=>011011=>110110
[7,3,1,4,5,2,6]=>010101=>101010
[7,3,1,4,5,6,2]=>010011=>110010
[7,3,1,4,6,2,5]=>010011=>110010
[7,3,1,4,6,5,2]=>010111=>111010
[7,3,1,5,2,4,6]=>010101=>101010
[7,3,1,5,2,6,4]=>010111=>111010
[7,3,1,5,4,2,6]=>011101=>101110
[7,3,1,5,4,6,2]=>010111=>111010
[7,3,1,5,6,2,4]=>010011=>110010
[7,3,1,5,6,4,2]=>011011=>110110
[7,3,1,6,2,4,5]=>010011=>110010
[7,3,1,6,2,5,4]=>010111=>111010
[7,3,1,6,4,2,5]=>011011=>110110
[7,3,1,6,4,5,2]=>010111=>111010
[7,3,1,6,5,2,4]=>010111=>111010
[7,3,1,6,5,4,2]=>011111=>111110
[7,3,2,1,4,5,6]=>110001=>100011
[7,3,2,1,4,6,5]=>110011=>110011
[7,3,2,1,5,4,6]=>110101=>101011
[7,3,2,1,5,6,4]=>110011=>110011
[7,3,2,1,6,4,5]=>110011=>110011
[7,3,2,1,6,5,4]=>110111=>111011
[7,3,2,4,1,5,6]=>011001=>100110
[7,3,2,4,1,6,5]=>011011=>110110
[7,3,2,4,5,1,6]=>010101=>101010
[7,3,2,4,5,6,1]=>010011=>110010
[7,3,2,4,6,1,5]=>010011=>110010
[7,3,2,4,6,5,1]=>010111=>111010
[7,3,2,5,1,4,6]=>010101=>101010
[7,3,2,5,1,6,4]=>010111=>111010
[7,3,2,5,4,1,6]=>011101=>101110
[7,3,2,5,4,6,1]=>010111=>111010
[7,3,2,5,6,1,4]=>010011=>110010
[7,3,2,5,6,4,1]=>011011=>110110
[7,3,2,6,1,4,5]=>010011=>110010
[7,3,2,6,1,5,4]=>010111=>111010
[7,3,2,6,4,1,5]=>011011=>110110
[7,3,2,6,4,5,1]=>010111=>111010
[7,3,2,6,5,1,4]=>010111=>111010
[7,3,2,6,5,4,1]=>011111=>111110
[7,3,4,1,2,5,6]=>001001=>100100
[7,3,4,1,2,6,5]=>001011=>110100
[7,3,4,1,5,2,6]=>001101=>101100
[7,3,4,1,5,6,2]=>001011=>110100
[7,3,4,1,6,2,5]=>001011=>110100
[7,3,4,1,6,5,2]=>001111=>111100
[7,3,4,2,1,5,6]=>101001=>100101
[7,3,4,2,1,6,5]=>101011=>110101
[7,3,4,2,5,1,6]=>001101=>101100
[7,3,4,2,5,6,1]=>001011=>110100
[7,3,4,2,6,1,5]=>001011=>110100
[7,3,4,2,6,5,1]=>001111=>111100
[7,3,4,5,1,2,6]=>000101=>101000
[7,3,4,5,1,6,2]=>000111=>111000
[7,3,4,5,2,1,6]=>100101=>101001
[7,3,4,5,2,6,1]=>000111=>111000
[7,3,4,5,6,1,2]=>000011=>110000
[7,3,4,5,6,2,1]=>100011=>110001
[7,3,4,6,1,2,5]=>000011=>110000
[7,3,4,6,1,5,2]=>000111=>111000
[7,3,4,6,2,1,5]=>100011=>110001
[7,3,4,6,2,5,1]=>000111=>111000
[7,3,4,6,5,1,2]=>000111=>111000
[7,3,4,6,5,2,1]=>100111=>111001
[7,3,5,1,2,4,6]=>000101=>101000
[7,3,5,1,2,6,4]=>000111=>111000
[7,3,5,1,4,2,6]=>001101=>101100
[7,3,5,1,4,6,2]=>000111=>111000
[7,3,5,1,6,2,4]=>000111=>111000
[7,3,5,1,6,4,2]=>001111=>111100
[7,3,5,2,1,4,6]=>100101=>101001
[7,3,5,2,1,6,4]=>100111=>111001
[7,3,5,2,4,1,6]=>001101=>101100
[7,3,5,2,4,6,1]=>000111=>111000
[7,3,5,2,6,1,4]=>000111=>111000
[7,3,5,2,6,4,1]=>001111=>111100
[7,3,5,4,1,2,6]=>001101=>101100
[7,3,5,4,1,6,2]=>001111=>111100
[7,3,5,4,2,1,6]=>101101=>101101
[7,3,5,4,2,6,1]=>001111=>111100
[7,3,5,4,6,1,2]=>000111=>111000
[7,3,5,4,6,2,1]=>100111=>111001
[7,3,5,6,1,2,4]=>000011=>110000
[7,3,5,6,1,4,2]=>001011=>110100
[7,3,5,6,2,1,4]=>100011=>110001
[7,3,5,6,2,4,1]=>001011=>110100
[7,3,5,6,4,1,2]=>001011=>110100
[7,3,5,6,4,2,1]=>101011=>110101
[7,3,6,1,2,4,5]=>000011=>110000
[7,3,6,1,2,5,4]=>000111=>111000
[7,3,6,1,4,2,5]=>001011=>110100
[7,3,6,1,4,5,2]=>000111=>111000
[7,3,6,1,5,2,4]=>000111=>111000
[7,3,6,1,5,4,2]=>001111=>111100
[7,3,6,2,1,4,5]=>100011=>110001
[7,3,6,2,1,5,4]=>100111=>111001
[7,3,6,2,4,1,5]=>001011=>110100
[7,3,6,2,4,5,1]=>000111=>111000
[7,3,6,2,5,1,4]=>000111=>111000
[7,3,6,2,5,4,1]=>001111=>111100
[7,3,6,4,1,2,5]=>001011=>110100
[7,3,6,4,1,5,2]=>001111=>111100
[7,3,6,4,2,1,5]=>101011=>110101
[7,3,6,4,2,5,1]=>001111=>111100
[7,3,6,4,5,1,2]=>000111=>111000
[7,3,6,4,5,2,1]=>100111=>111001
[7,3,6,5,1,2,4]=>000111=>111000
[7,3,6,5,1,4,2]=>001111=>111100
[7,3,6,5,2,1,4]=>100111=>111001
[7,3,6,5,2,4,1]=>001111=>111100
[7,3,6,5,4,1,2]=>001111=>111100
[7,3,6,5,4,2,1]=>101111=>111101
[7,4,1,2,3,5,6]=>001001=>100100
[7,4,1,2,3,6,5]=>001011=>110100
[7,4,1,2,5,3,6]=>001101=>101100
[7,4,1,2,5,6,3]=>001011=>110100
[7,4,1,2,6,3,5]=>001011=>110100
[7,4,1,2,6,5,3]=>001111=>111100
[7,4,1,3,2,5,6]=>011001=>100110
[7,4,1,3,2,6,5]=>011011=>110110
[7,4,1,3,5,2,6]=>001101=>101100
[7,4,1,3,5,6,2]=>001011=>110100
[7,4,1,3,6,2,5]=>001011=>110100
[7,4,1,3,6,5,2]=>001111=>111100
[7,4,1,5,2,3,6]=>001101=>101100
[7,4,1,5,2,6,3]=>001111=>111100
[7,4,1,5,3,2,6]=>011101=>101110
[7,4,1,5,3,6,2]=>001111=>111100
[7,4,1,5,6,2,3]=>001011=>110100
[7,4,1,5,6,3,2]=>011011=>110110
[7,4,1,6,2,3,5]=>001011=>110100
[7,4,1,6,2,5,3]=>001111=>111100
[7,4,1,6,3,2,5]=>011011=>110110
[7,4,1,6,3,5,2]=>001111=>111100
[7,4,1,6,5,2,3]=>001111=>111100
[7,4,1,6,5,3,2]=>011111=>111110
[7,4,2,1,3,5,6]=>101001=>100101
[7,4,2,1,3,6,5]=>101011=>110101
[7,4,2,1,5,3,6]=>101101=>101101
[7,4,2,1,5,6,3]=>101011=>110101
[7,4,2,1,6,3,5]=>101011=>110101
[7,4,2,1,6,5,3]=>101111=>111101
[7,4,2,3,1,5,6]=>011001=>100110
[7,4,2,3,1,6,5]=>011011=>110110
[7,4,2,3,5,1,6]=>001101=>101100
[7,4,2,3,5,6,1]=>001011=>110100
[7,4,2,3,6,1,5]=>001011=>110100
[7,4,2,3,6,5,1]=>001111=>111100
[7,4,2,5,1,3,6]=>001101=>101100
[7,4,2,5,1,6,3]=>001111=>111100
[7,4,2,5,3,1,6]=>011101=>101110
[7,4,2,5,3,6,1]=>001111=>111100
[7,4,2,5,6,1,3]=>001011=>110100
[7,4,2,5,6,3,1]=>011011=>110110
[7,4,2,6,1,3,5]=>001011=>110100
[7,4,2,6,1,5,3]=>001111=>111100
[7,4,2,6,3,1,5]=>011011=>110110
[7,4,2,6,3,5,1]=>001111=>111100
[7,4,2,6,5,1,3]=>001111=>111100
[7,4,2,6,5,3,1]=>011111=>111110
[7,4,3,1,2,5,6]=>011001=>100110
[7,4,3,1,2,6,5]=>011011=>110110
[7,4,3,1,5,2,6]=>011101=>101110
[7,4,3,1,5,6,2]=>011011=>110110
[7,4,3,1,6,2,5]=>011011=>110110
[7,4,3,1,6,5,2]=>011111=>111110
[7,4,3,2,1,5,6]=>111001=>100111
[7,4,3,2,1,6,5]=>111011=>110111
[7,4,3,2,5,1,6]=>011101=>101110
[7,4,3,2,5,6,1]=>011011=>110110
[7,4,3,2,6,1,5]=>011011=>110110
[7,4,3,2,6,5,1]=>011111=>111110
[7,4,3,5,1,2,6]=>001101=>101100
[7,4,3,5,1,6,2]=>001111=>111100
[7,4,3,5,2,1,6]=>101101=>101101
[7,4,3,5,2,6,1]=>001111=>111100
[7,4,3,5,6,1,2]=>001011=>110100
[7,4,3,5,6,2,1]=>101011=>110101
[7,4,3,6,1,2,5]=>001011=>110100
[7,4,3,6,1,5,2]=>001111=>111100
[7,4,3,6,2,1,5]=>101011=>110101
[7,4,3,6,2,5,1]=>001111=>111100
[7,4,3,6,5,1,2]=>001111=>111100
[7,4,3,6,5,2,1]=>101111=>111101
[7,4,5,1,2,3,6]=>000101=>101000
[7,4,5,1,2,6,3]=>000111=>111000
[7,4,5,1,3,2,6]=>010101=>101010
[7,4,5,1,3,6,2]=>000111=>111000
[7,4,5,1,6,2,3]=>000111=>111000
[7,4,5,1,6,3,2]=>010111=>111010
[7,4,5,2,1,3,6]=>100101=>101001
[7,4,5,2,1,6,3]=>100111=>111001
[7,4,5,2,3,1,6]=>010101=>101010
[7,4,5,2,3,6,1]=>000111=>111000
[7,4,5,2,6,1,3]=>000111=>111000
[7,4,5,2,6,3,1]=>010111=>111010
[7,4,5,3,1,2,6]=>010101=>101010
[7,4,5,3,1,6,2]=>010111=>111010
[7,4,5,3,2,1,6]=>110101=>101011
[7,4,5,3,2,6,1]=>010111=>111010
[7,4,5,3,6,1,2]=>000111=>111000
[7,4,5,3,6,2,1]=>100111=>111001
[7,4,5,6,1,2,3]=>000011=>110000
[7,4,5,6,1,3,2]=>010011=>110010
[7,4,5,6,2,1,3]=>100011=>110001
[7,4,5,6,2,3,1]=>010011=>110010
[7,4,5,6,3,1,2]=>010011=>110010
[7,4,5,6,3,2,1]=>110011=>110011
[7,4,6,1,2,3,5]=>000011=>110000
[7,4,6,1,2,5,3]=>000111=>111000
[7,4,6,1,3,2,5]=>010011=>110010
[7,4,6,1,3,5,2]=>000111=>111000
[7,4,6,1,5,2,3]=>000111=>111000
[7,4,6,1,5,3,2]=>010111=>111010
[7,4,6,2,1,3,5]=>100011=>110001
[7,4,6,2,1,5,3]=>100111=>111001
[7,4,6,2,3,1,5]=>010011=>110010
[7,4,6,2,3,5,1]=>000111=>111000
[7,4,6,2,5,1,3]=>000111=>111000
[7,4,6,2,5,3,1]=>010111=>111010
[7,4,6,3,1,2,5]=>010011=>110010
[7,4,6,3,1,5,2]=>010111=>111010
[7,4,6,3,2,1,5]=>110011=>110011
[7,4,6,3,2,5,1]=>010111=>111010
[7,4,6,3,5,1,2]=>000111=>111000
[7,4,6,3,5,2,1]=>100111=>111001
[7,4,6,5,1,2,3]=>000111=>111000
[7,4,6,5,1,3,2]=>010111=>111010
[7,4,6,5,2,1,3]=>100111=>111001
[7,4,6,5,2,3,1]=>010111=>111010
[7,4,6,5,3,1,2]=>010111=>111010
[7,4,6,5,3,2,1]=>110111=>111011
[7,5,1,2,3,4,6]=>000101=>101000
[7,5,1,2,3,6,4]=>000111=>111000
[7,5,1,2,4,3,6]=>001101=>101100
[7,5,1,2,4,6,3]=>000111=>111000
[7,5,1,2,6,3,4]=>000111=>111000
[7,5,1,2,6,4,3]=>001111=>111100
[7,5,1,3,2,4,6]=>010101=>101010
[7,5,1,3,2,6,4]=>010111=>111010
[7,5,1,3,4,2,6]=>001101=>101100
[7,5,1,3,4,6,2]=>000111=>111000
[7,5,1,3,6,2,4]=>000111=>111000
[7,5,1,3,6,4,2]=>001111=>111100
[7,5,1,4,2,3,6]=>001101=>101100
[7,5,1,4,2,6,3]=>001111=>111100
[7,5,1,4,3,2,6]=>011101=>101110
[7,5,1,4,3,6,2]=>001111=>111100
[7,5,1,4,6,2,3]=>000111=>111000
[7,5,1,4,6,3,2]=>010111=>111010
[7,5,1,6,2,3,4]=>000111=>111000
[7,5,1,6,2,4,3]=>001111=>111100
[7,5,1,6,3,2,4]=>010111=>111010
[7,5,1,6,3,4,2]=>001111=>111100
[7,5,1,6,4,2,3]=>001111=>111100
[7,5,1,6,4,3,2]=>011111=>111110
[7,5,2,1,3,4,6]=>100101=>101001
[7,5,2,1,3,6,4]=>100111=>111001
[7,5,2,1,4,3,6]=>101101=>101101
[7,5,2,1,4,6,3]=>100111=>111001
[7,5,2,1,6,3,4]=>100111=>111001
[7,5,2,1,6,4,3]=>101111=>111101
[7,5,2,3,1,4,6]=>010101=>101010
[7,5,2,3,1,6,4]=>010111=>111010
[7,5,2,3,4,1,6]=>001101=>101100
[7,5,2,3,4,6,1]=>000111=>111000
[7,5,2,3,6,1,4]=>000111=>111000
[7,5,2,3,6,4,1]=>001111=>111100
[7,5,2,4,1,3,6]=>001101=>101100
[7,5,2,4,1,6,3]=>001111=>111100
[7,5,2,4,3,1,6]=>011101=>101110
[7,5,2,4,3,6,1]=>001111=>111100
[7,5,2,4,6,1,3]=>000111=>111000
[7,5,2,4,6,3,1]=>010111=>111010
[7,5,2,6,1,3,4]=>000111=>111000
[7,5,2,6,1,4,3]=>001111=>111100
[7,5,2,6,3,1,4]=>010111=>111010
[7,5,2,6,3,4,1]=>001111=>111100
[7,5,2,6,4,1,3]=>001111=>111100
[7,5,2,6,4,3,1]=>011111=>111110
[7,5,3,1,2,4,6]=>010101=>101010
[7,5,3,1,2,6,4]=>010111=>111010
[7,5,3,1,4,2,6]=>011101=>101110
[7,5,3,1,4,6,2]=>010111=>111010
[7,5,3,1,6,2,4]=>010111=>111010
[7,5,3,1,6,4,2]=>011111=>111110
[7,5,3,2,1,4,6]=>110101=>101011
[7,5,3,2,1,6,4]=>110111=>111011
[7,5,3,2,4,1,6]=>011101=>101110
[7,5,3,2,4,6,1]=>010111=>111010
[7,5,3,2,6,1,4]=>010111=>111010
[7,5,3,2,6,4,1]=>011111=>111110
[7,5,3,4,1,2,6]=>001101=>101100
[7,5,3,4,1,6,2]=>001111=>111100
[7,5,3,4,2,1,6]=>101101=>101101
[7,5,3,4,2,6,1]=>001111=>111100
[7,5,3,4,6,1,2]=>000111=>111000
[7,5,3,4,6,2,1]=>100111=>111001
[7,5,3,6,1,2,4]=>000111=>111000
[7,5,3,6,1,4,2]=>001111=>111100
[7,5,3,6,2,1,4]=>100111=>111001
[7,5,3,6,2,4,1]=>001111=>111100
[7,5,3,6,4,1,2]=>001111=>111100
[7,5,3,6,4,2,1]=>101111=>111101
[7,5,4,1,2,3,6]=>001101=>101100
[7,5,4,1,2,6,3]=>001111=>111100
[7,5,4,1,3,2,6]=>011101=>101110
[7,5,4,1,3,6,2]=>001111=>111100
[7,5,4,1,6,2,3]=>001111=>111100
[7,5,4,1,6,3,2]=>011111=>111110
[7,5,4,2,1,3,6]=>101101=>101101
[7,5,4,2,1,6,3]=>101111=>111101
[7,5,4,2,3,1,6]=>011101=>101110
[7,5,4,2,3,6,1]=>001111=>111100
[7,5,4,2,6,1,3]=>001111=>111100
[7,5,4,2,6,3,1]=>011111=>111110
[7,5,4,3,1,2,6]=>011101=>101110
[7,5,4,3,1,6,2]=>011111=>111110
[7,5,4,3,2,1,6]=>111101=>101111
[7,5,4,3,2,6,1]=>011111=>111110
[7,5,4,3,6,1,2]=>001111=>111100
[7,5,4,3,6,2,1]=>101111=>111101
[7,5,4,6,1,2,3]=>000111=>111000
[7,5,4,6,1,3,2]=>010111=>111010
[7,5,4,6,2,1,3]=>100111=>111001
[7,5,4,6,2,3,1]=>010111=>111010
[7,5,4,6,3,1,2]=>010111=>111010
[7,5,4,6,3,2,1]=>110111=>111011
[7,5,6,1,2,3,4]=>000011=>110000
[7,5,6,1,2,4,3]=>001011=>110100
[7,5,6,1,3,2,4]=>010011=>110010
[7,5,6,1,3,4,2]=>001011=>110100
[7,5,6,1,4,2,3]=>001011=>110100
[7,5,6,1,4,3,2]=>011011=>110110
[7,5,6,2,1,3,4]=>100011=>110001
[7,5,6,2,1,4,3]=>101011=>110101
[7,5,6,2,3,1,4]=>010011=>110010
[7,5,6,2,3,4,1]=>001011=>110100
[7,5,6,2,4,1,3]=>001011=>110100
[7,5,6,2,4,3,1]=>011011=>110110
[7,5,6,3,1,2,4]=>010011=>110010
[7,5,6,3,1,4,2]=>011011=>110110
[7,5,6,3,2,1,4]=>110011=>110011
[7,5,6,3,2,4,1]=>011011=>110110
[7,5,6,3,4,1,2]=>001011=>110100
[7,5,6,3,4,2,1]=>101011=>110101
[7,5,6,4,1,2,3]=>001011=>110100
[7,5,6,4,1,3,2]=>011011=>110110
[7,5,6,4,2,1,3]=>101011=>110101
[7,5,6,4,2,3,1]=>011011=>110110
[7,5,6,4,3,1,2]=>011011=>110110
[7,5,6,4,3,2,1]=>111011=>110111
[7,6,1,2,3,4,5]=>000011=>110000
[7,6,1,2,3,5,4]=>000111=>111000
[7,6,1,2,4,3,5]=>001011=>110100
[7,6,1,2,4,5,3]=>000111=>111000
[7,6,1,2,5,3,4]=>000111=>111000
[7,6,1,2,5,4,3]=>001111=>111100
[7,6,1,3,2,4,5]=>010011=>110010
[7,6,1,3,2,5,4]=>010111=>111010
[7,6,1,3,4,2,5]=>001011=>110100
[7,6,1,3,4,5,2]=>000111=>111000
[7,6,1,3,5,2,4]=>000111=>111000
[7,6,1,3,5,4,2]=>001111=>111100
[7,6,1,4,2,3,5]=>001011=>110100
[7,6,1,4,2,5,3]=>001111=>111100
[7,6,1,4,3,2,5]=>011011=>110110
[7,6,1,4,3,5,2]=>001111=>111100
[7,6,1,4,5,2,3]=>000111=>111000
[7,6,1,4,5,3,2]=>010111=>111010
[7,6,1,5,2,3,4]=>000111=>111000
[7,6,1,5,2,4,3]=>001111=>111100
[7,6,1,5,3,2,4]=>010111=>111010
[7,6,1,5,3,4,2]=>001111=>111100
[7,6,1,5,4,2,3]=>001111=>111100
[7,6,1,5,4,3,2]=>011111=>111110
[7,6,2,1,3,4,5]=>100011=>110001
[7,6,2,1,3,5,4]=>100111=>111001
[7,6,2,1,4,3,5]=>101011=>110101
[7,6,2,1,4,5,3]=>100111=>111001
[7,6,2,1,5,3,4]=>100111=>111001
[7,6,2,1,5,4,3]=>101111=>111101
[7,6,2,3,1,4,5]=>010011=>110010
[7,6,2,3,1,5,4]=>010111=>111010
[7,6,2,3,4,1,5]=>001011=>110100
[7,6,2,3,4,5,1]=>000111=>111000
[7,6,2,3,5,1,4]=>000111=>111000
[7,6,2,3,5,4,1]=>001111=>111100
[7,6,2,4,1,3,5]=>001011=>110100
[7,6,2,4,1,5,3]=>001111=>111100
[7,6,2,4,3,1,5]=>011011=>110110
[7,6,2,4,3,5,1]=>001111=>111100
[7,6,2,4,5,1,3]=>000111=>111000
[7,6,2,4,5,3,1]=>010111=>111010
[7,6,2,5,1,3,4]=>000111=>111000
[7,6,2,5,1,4,3]=>001111=>111100
[7,6,2,5,3,1,4]=>010111=>111010
[7,6,2,5,3,4,1]=>001111=>111100
[7,6,2,5,4,1,3]=>001111=>111100
[7,6,2,5,4,3,1]=>011111=>111110
[7,6,3,1,2,4,5]=>010011=>110010
[7,6,3,1,2,5,4]=>010111=>111010
[7,6,3,1,4,2,5]=>011011=>110110
[7,6,3,1,4,5,2]=>010111=>111010
[7,6,3,1,5,2,4]=>010111=>111010
[7,6,3,1,5,4,2]=>011111=>111110
[7,6,3,2,1,4,5]=>110011=>110011
[7,6,3,2,1,5,4]=>110111=>111011
[7,6,3,2,4,1,5]=>011011=>110110
[7,6,3,2,4,5,1]=>010111=>111010
[7,6,3,2,5,1,4]=>010111=>111010
[7,6,3,2,5,4,1]=>011111=>111110
[7,6,3,4,1,2,5]=>001011=>110100
[7,6,3,4,1,5,2]=>001111=>111100
[7,6,3,4,2,1,5]=>101011=>110101
[7,6,3,4,2,5,1]=>001111=>111100
[7,6,3,4,5,1,2]=>000111=>111000
[7,6,3,4,5,2,1]=>100111=>111001
[7,6,3,5,1,2,4]=>000111=>111000
[7,6,3,5,1,4,2]=>001111=>111100
[7,6,3,5,2,1,4]=>100111=>111001
[7,6,3,5,2,4,1]=>001111=>111100
[7,6,3,5,4,1,2]=>001111=>111100
[7,6,3,5,4,2,1]=>101111=>111101
[7,6,4,1,2,3,5]=>001011=>110100
[7,6,4,1,2,5,3]=>001111=>111100
[7,6,4,1,3,2,5]=>011011=>110110
[7,6,4,1,3,5,2]=>001111=>111100
[7,6,4,1,5,2,3]=>001111=>111100
[7,6,4,1,5,3,2]=>011111=>111110
[7,6,4,2,1,3,5]=>101011=>110101
[7,6,4,2,1,5,3]=>101111=>111101
[7,6,4,2,3,1,5]=>011011=>110110
[7,6,4,2,3,5,1]=>001111=>111100
[7,6,4,2,5,1,3]=>001111=>111100
[7,6,4,2,5,3,1]=>011111=>111110
[7,6,4,3,1,2,5]=>011011=>110110
[7,6,4,3,1,5,2]=>011111=>111110
[7,6,4,3,2,1,5]=>111011=>110111
[7,6,4,3,2,5,1]=>011111=>111110
[7,6,4,3,5,1,2]=>001111=>111100
[7,6,4,3,5,2,1]=>101111=>111101
[7,6,4,5,1,2,3]=>000111=>111000
[7,6,4,5,1,3,2]=>010111=>111010
[7,6,4,5,2,1,3]=>100111=>111001
[7,6,4,5,2,3,1]=>010111=>111010
[7,6,4,5,3,1,2]=>010111=>111010
[7,6,4,5,3,2,1]=>110111=>111011
[7,6,5,1,2,3,4]=>000111=>111000
[7,6,5,1,2,4,3]=>001111=>111100
[7,6,5,1,3,2,4]=>010111=>111010
[7,6,5,1,3,4,2]=>001111=>111100
[7,6,5,1,4,2,3]=>001111=>111100
[7,6,5,1,4,3,2]=>011111=>111110
[7,6,5,2,1,3,4]=>100111=>111001
[7,6,5,2,1,4,3]=>101111=>111101
[7,6,5,2,3,1,4]=>010111=>111010
[7,6,5,2,3,4,1]=>001111=>111100
[7,6,5,2,4,1,3]=>001111=>111100
[7,6,5,2,4,3,1]=>011111=>111110
[7,6,5,3,1,2,4]=>010111=>111010
[7,6,5,3,1,4,2]=>011111=>111110
[7,6,5,3,2,1,4]=>110111=>111011
[7,6,5,3,2,4,1]=>011111=>111110
[7,6,5,3,4,1,2]=>001111=>111100
[7,6,5,3,4,2,1]=>101111=>111101
[7,6,5,4,1,2,3]=>001111=>111100
[7,6,5,4,1,3,2]=>011111=>111110
[7,6,5,4,2,1,3]=>101111=>111101
[7,6,5,4,2,3,1]=>011111=>111110
[7,6,5,4,3,1,2]=>011111=>111110
[7,6,5,4,3,2,1]=>111111=>111111
[8,7,6,5,4,3,2,1]=>1111111=>1111111
[7,8,6,5,4,3,2,1]=>1111101=>1011111
[8,6,7,5,4,3,2,1]=>1111011=>1101111
[7,6,8,5,4,3,2,1]=>1111011=>1101111
[6,7,8,5,4,3,2,1]=>1111001=>1001111
[8,7,5,6,4,3,2,1]=>1110111=>1110111
[7,8,5,6,4,3,2,1]=>1110101=>1010111
[8,6,5,7,4,3,2,1]=>1110111=>1110111
[8,5,6,7,4,3,2,1]=>1110011=>1100111
[7,6,5,8,4,3,2,1]=>1110111=>1110111
[6,7,5,8,4,3,2,1]=>1110011=>1100111
[7,5,6,8,4,3,2,1]=>1110011=>1100111
[6,5,7,8,4,3,2,1]=>1110101=>1010111
[5,6,7,8,4,3,2,1]=>1110001=>1000111
[8,7,6,4,5,3,2,1]=>1101111=>1111011
[7,8,6,4,5,3,2,1]=>1101101=>1011011
[8,6,7,4,5,3,2,1]=>1101011=>1101011
[7,6,8,4,5,3,2,1]=>1101011=>1101011
[6,7,8,4,5,3,2,1]=>1101001=>1001011
[8,7,5,4,6,3,2,1]=>1101111=>1111011
[8,7,4,5,6,3,2,1]=>1100111=>1110011
[8,6,5,4,7,3,2,1]=>1101111=>1111011
[8,5,6,4,7,3,2,1]=>1100111=>1110011
[8,6,4,5,7,3,2,1]=>1100111=>1110011
[8,5,4,6,7,3,2,1]=>1101011=>1101011
[8,4,5,6,7,3,2,1]=>1100011=>1100011
[7,6,5,4,8,3,2,1]=>1101111=>1111011
[6,7,5,4,8,3,2,1]=>1101011=>1101011
[7,5,6,4,8,3,2,1]=>1100111=>1110011
[6,5,7,4,8,3,2,1]=>1100111=>1110011
[5,6,7,4,8,3,2,1]=>1100011=>1100011
[7,6,4,5,8,3,2,1]=>1100111=>1110011
[6,7,4,5,8,3,2,1]=>1100011=>1100011
[7,5,4,6,8,3,2,1]=>1101011=>1101011
[7,4,5,6,8,3,2,1]=>1100011=>1100011
[6,5,4,7,8,3,2,1]=>1101101=>1011011
[5,6,4,7,8,3,2,1]=>1100101=>1010011
[6,4,5,7,8,3,2,1]=>1100101=>1010011
[5,4,6,7,8,3,2,1]=>1101001=>1001011
[4,5,6,7,8,3,2,1]=>1100001=>1000011
[8,7,6,5,3,4,2,1]=>1011111=>1111101
[7,8,6,5,3,4,2,1]=>1011101=>1011101
[8,6,7,5,3,4,2,1]=>1011011=>1101101
[7,6,8,5,3,4,2,1]=>1011011=>1101101
[8,7,5,6,3,4,2,1]=>1010111=>1110101
[7,8,5,6,3,4,2,1]=>1010101=>1010101
[8,5,6,7,3,4,2,1]=>1010011=>1100101
[7,6,5,8,3,4,2,1]=>1010111=>1110101
[6,7,5,8,3,4,2,1]=>1010011=>1100101
[6,5,7,8,3,4,2,1]=>1010101=>1010101
[5,6,7,8,3,4,2,1]=>1010001=>1000101
[8,7,6,4,3,5,2,1]=>1011111=>1111101
[7,8,6,4,3,5,2,1]=>1011101=>1011101
[8,6,7,4,3,5,2,1]=>1011011=>1101101
[7,6,8,4,3,5,2,1]=>1011011=>1101101
[6,7,8,4,3,5,2,1]=>1011001=>1001101
[8,7,6,3,4,5,2,1]=>1001111=>1111001
[7,8,6,3,4,5,2,1]=>1001101=>1011001
[8,6,7,3,4,5,2,1]=>1001011=>1101001
[7,6,8,3,4,5,2,1]=>1001011=>1101001
[6,7,8,3,4,5,2,1]=>1001001=>1001001
[8,7,5,4,3,6,2,1]=>1011111=>1111101
[7,8,5,4,3,6,2,1]=>1011101=>1011101
[8,7,4,5,3,6,2,1]=>1001111=>1111001
[8,7,5,3,4,6,2,1]=>1001111=>1111001
[7,8,5,3,4,6,2,1]=>1001101=>1011001
[8,7,4,3,5,6,2,1]=>1010111=>1110101
[8,7,3,4,5,6,2,1]=>1000111=>1110001
[7,8,3,4,5,6,2,1]=>1000101=>1010001
[8,6,5,4,3,7,2,1]=>1011111=>1111101
[8,6,4,5,3,7,2,1]=>1001111=>1111001
[8,6,4,3,5,7,2,1]=>1010111=>1110101
[8,5,4,3,6,7,2,1]=>1011011=>1101101
[8,5,3,4,6,7,2,1]=>1001011=>1101001
[8,4,3,5,6,7,2,1]=>1010011=>1100101
[8,3,4,5,6,7,2,1]=>1000011=>1100001
[7,6,5,4,3,8,2,1]=>1011111=>1111101
[6,7,5,4,3,8,2,1]=>1011011=>1101101
[7,5,6,4,3,8,2,1]=>1010111=>1110101
[6,5,7,4,3,8,2,1]=>1010111=>1110101
[5,6,7,4,3,8,2,1]=>1010011=>1100101
[6,7,4,5,3,8,2,1]=>1001011=>1101001
[7,5,4,6,3,8,2,1]=>1001111=>1111001
[7,4,5,6,3,8,2,1]=>1000111=>1110001
[6,5,4,7,3,8,2,1]=>1001111=>1111001
[6,4,5,7,3,8,2,1]=>1000111=>1110001
[5,4,6,7,3,8,2,1]=>1001011=>1101001
[4,5,6,7,3,8,2,1]=>1000011=>1100001
[7,6,5,3,4,8,2,1]=>1001111=>1111001
[7,6,4,3,5,8,2,1]=>1010111=>1110101
[7,6,3,4,5,8,2,1]=>1000111=>1110001
[7,5,4,3,6,8,2,1]=>1011011=>1101101
[7,5,3,4,6,8,2,1]=>1001011=>1101001
[7,3,4,5,6,8,2,1]=>1000011=>1100001
[6,5,4,3,7,8,2,1]=>1011101=>1011101
[4,5,6,3,7,8,2,1]=>1000101=>1010001
[6,5,3,4,7,8,2,1]=>1001101=>1011001
[6,3,4,5,7,8,2,1]=>1000101=>1010001
[5,4,3,6,7,8,2,1]=>1011001=>1001101
[5,3,4,6,7,8,2,1]=>1001001=>1001001
[4,3,5,6,7,8,2,1]=>1010001=>1000101
[3,4,5,6,7,8,2,1]=>1000001=>1000001
[8,7,6,5,4,2,3,1]=>0111111=>1111110
[7,8,6,5,4,2,3,1]=>0111101=>1011110
[8,6,7,5,4,2,3,1]=>0111011=>1101110
[7,6,8,5,4,2,3,1]=>0111011=>1101110
[8,7,5,6,4,2,3,1]=>0110111=>1110110
[8,6,5,7,4,2,3,1]=>0110111=>1110110
[8,5,6,7,4,2,3,1]=>0110011=>1100110
[7,6,5,8,4,2,3,1]=>0110111=>1110110
[6,7,5,8,4,2,3,1]=>0110011=>1100110
[7,5,6,8,4,2,3,1]=>0110011=>1100110
[5,6,7,8,4,2,3,1]=>0110001=>1000110
[8,7,6,4,5,2,3,1]=>0101111=>1111010
[8,6,7,4,5,2,3,1]=>0101011=>1101010
[7,6,8,4,5,2,3,1]=>0101011=>1101010
[6,7,8,4,5,2,3,1]=>0101001=>1001010
[8,7,5,4,6,2,3,1]=>0101111=>1111010
[8,7,4,5,6,2,3,1]=>0100111=>1110010
[7,8,4,5,6,2,3,1]=>0100101=>1010010
[8,6,5,4,7,2,3,1]=>0101111=>1111010
[8,5,6,4,7,2,3,1]=>0100111=>1110010
[8,6,4,5,7,2,3,1]=>0100111=>1110010
[8,4,5,6,7,2,3,1]=>0100011=>1100010
[7,6,5,4,8,2,3,1]=>0101111=>1111010
[7,5,6,4,8,2,3,1]=>0100111=>1110010
[6,5,7,4,8,2,3,1]=>0100111=>1110010
[6,7,4,5,8,2,3,1]=>0100011=>1100010
[4,5,6,7,8,2,3,1]=>0100001=>1000010
[8,7,6,5,3,2,4,1]=>0111111=>1111110
[7,8,6,5,3,2,4,1]=>0111101=>1011110
[8,6,7,5,3,2,4,1]=>0111011=>1101110
[7,6,8,5,3,2,4,1]=>0111011=>1101110
[6,7,8,5,3,2,4,1]=>0111001=>1001110
[8,7,5,6,3,2,4,1]=>0110111=>1110110
[8,6,5,7,3,2,4,1]=>0110111=>1110110
[8,5,6,7,3,2,4,1]=>0110011=>1100110
[7,6,5,8,3,2,4,1]=>0110111=>1110110
[6,7,5,8,3,2,4,1]=>0110011=>1100110
[5,6,7,8,3,2,4,1]=>0110001=>1000110
[8,7,6,5,2,3,4,1]=>0011111=>1111100
[8,6,7,5,2,3,4,1]=>0011011=>1101100
[7,6,8,5,2,3,4,1]=>0011011=>1101100
[6,7,8,5,2,3,4,1]=>0011001=>1001100
[8,7,5,6,2,3,4,1]=>0010111=>1110100
[7,8,5,6,2,3,4,1]=>0010101=>1010100
[8,6,5,7,2,3,4,1]=>0010111=>1110100
[8,5,6,7,2,3,4,1]=>0010011=>1100100
[7,6,5,8,2,3,4,1]=>0010111=>1110100
[6,7,5,8,2,3,4,1]=>0010011=>1100100
[6,5,7,8,2,3,4,1]=>0010101=>1010100
[5,6,7,8,2,3,4,1]=>0010001=>1000100
[8,7,6,4,3,2,5,1]=>0111111=>1111110
[7,8,6,4,3,2,5,1]=>0111101=>1011110
[8,6,7,4,3,2,5,1]=>0111011=>1101110
[7,6,8,4,3,2,5,1]=>0111011=>1101110
[6,7,8,4,3,2,5,1]=>0111001=>1001110
[8,7,6,3,4,2,5,1]=>0011111=>1111100
[7,8,6,3,4,2,5,1]=>0011101=>1011100
[8,6,7,3,4,2,5,1]=>0011011=>1101100
[7,6,8,3,4,2,5,1]=>0011011=>1101100
[6,7,8,3,4,2,5,1]=>0011001=>1001100
[8,7,6,4,2,3,5,1]=>0011111=>1111100
[8,6,7,4,2,3,5,1]=>0011011=>1101100
[7,6,8,4,2,3,5,1]=>0011011=>1101100
[6,7,8,4,2,3,5,1]=>0011001=>1001100
[8,7,6,3,2,4,5,1]=>0101111=>1111010
[7,8,6,3,2,4,5,1]=>0101101=>1011010
[8,6,7,3,2,4,5,1]=>0101011=>1101010
[6,7,8,3,2,4,5,1]=>0101001=>1001010
[8,7,6,2,3,4,5,1]=>0001111=>1111000
[7,8,6,2,3,4,5,1]=>0001101=>1011000
[8,6,7,2,3,4,5,1]=>0001011=>1101000
[7,6,8,2,3,4,5,1]=>0001011=>1101000
[6,7,8,2,3,4,5,1]=>0001001=>1001000
[8,7,5,4,3,2,6,1]=>0111111=>1111110
[7,8,5,4,3,2,6,1]=>0111101=>1011110
[8,7,5,3,4,2,6,1]=>0011111=>1111100
[7,8,5,3,4,2,6,1]=>0011101=>1011100
[8,7,4,3,5,2,6,1]=>0011111=>1111100
[7,8,4,3,5,2,6,1]=>0011101=>1011100
[8,7,5,4,2,3,6,1]=>0011111=>1111100
[8,7,5,3,2,4,6,1]=>0101111=>1111010
[8,7,4,3,2,5,6,1]=>0110111=>1110110
[7,8,4,3,2,5,6,1]=>0110101=>1010110
[7,8,3,4,2,5,6,1]=>0010101=>1010100
[7,8,4,2,3,5,6,1]=>0010101=>1010100
[7,8,3,2,4,5,6,1]=>0100101=>1010010
[8,7,2,3,4,5,6,1]=>0000111=>1110000
[7,8,2,3,4,5,6,1]=>0000101=>1010000
[8,6,5,4,3,2,7,1]=>0111111=>1111110
[8,5,6,4,3,2,7,1]=>0110111=>1110110
[8,6,4,5,3,2,7,1]=>0101111=>1111010
[8,5,4,6,3,2,7,1]=>0101111=>1111010
[8,6,5,3,4,2,7,1]=>0011111=>1111100
[8,5,6,3,4,2,7,1]=>0010111=>1110100
[8,6,4,3,5,2,7,1]=>0011111=>1111100
[8,6,3,4,5,2,7,1]=>0001111=>1111000
[8,5,4,3,6,2,7,1]=>0011111=>1111100
[8,4,5,3,6,2,7,1]=>0001111=>1111000
[8,4,3,5,6,2,7,1]=>0010111=>1110100
[8,3,4,5,6,2,7,1]=>0000111=>1110000
[8,6,5,4,2,3,7,1]=>0011111=>1111100
[8,5,6,4,2,3,7,1]=>0010111=>1110100
[8,6,4,5,2,3,7,1]=>0001111=>1111000
[8,6,5,3,2,4,7,1]=>0101111=>1111010
[8,6,4,3,2,5,7,1]=>0110111=>1110110
[8,6,4,2,3,5,7,1]=>0010111=>1110100
[8,5,4,3,2,6,7,1]=>0111011=>1101110
[8,4,5,3,2,6,7,1]=>0101011=>1101010
[8,5,3,4,2,6,7,1]=>0011011=>1101100
[8,3,4,5,2,6,7,1]=>0001011=>1101000
[8,5,4,2,3,6,7,1]=>0011011=>1101100
[8,4,5,2,3,6,7,1]=>0001011=>1101000
[8,5,2,3,4,6,7,1]=>0001011=>1101000
[8,4,3,2,5,6,7,1]=>0110011=>1100110
[8,3,4,2,5,6,7,1]=>0010011=>1100100
[8,4,2,3,5,6,7,1]=>0010011=>1100100
[8,3,2,4,5,6,7,1]=>0100011=>1100010
[8,2,3,4,5,6,7,1]=>0000011=>1100000
[7,6,5,4,3,2,8,1]=>0111111=>1111110
[6,7,5,4,3,2,8,1]=>0111011=>1101110
[7,5,6,4,3,2,8,1]=>0110111=>1110110
[6,5,7,4,3,2,8,1]=>0110111=>1110110
[5,6,7,4,3,2,8,1]=>0110011=>1100110
[7,6,4,5,3,2,8,1]=>0101111=>1111010
[6,7,4,5,3,2,8,1]=>0101011=>1101010
[7,4,5,6,3,2,8,1]=>0100111=>1110010
[6,5,4,7,3,2,8,1]=>0101111=>1111010
[6,4,5,7,3,2,8,1]=>0100111=>1110010
[4,5,6,7,3,2,8,1]=>0100011=>1100010
[7,6,5,3,4,2,8,1]=>0011111=>1111100
[7,5,6,3,4,2,8,1]=>0010111=>1110100
[6,5,7,3,4,2,8,1]=>0010111=>1110100
[5,6,7,3,4,2,8,1]=>0010011=>1100100
[7,6,4,3,5,2,8,1]=>0011111=>1111100
[7,6,3,4,5,2,8,1]=>0001111=>1111000
[7,5,4,3,6,2,8,1]=>0011111=>1111100
[7,4,5,3,6,2,8,1]=>0001111=>1111000
[7,5,3,4,6,2,8,1]=>0001111=>1111000
[7,3,4,5,6,2,8,1]=>0000111=>1110000
[6,5,4,3,7,2,8,1]=>0011111=>1111100
[6,4,5,3,7,2,8,1]=>0001111=>1111000
[5,4,6,3,7,2,8,1]=>0001111=>1111000
[4,5,6,3,7,2,8,1]=>0000111=>1110000
[6,5,3,4,7,2,8,1]=>0001111=>1111000
[5,6,3,4,7,2,8,1]=>0000111=>1110000
[6,4,3,5,7,2,8,1]=>0010111=>1110100
[6,3,4,5,7,2,8,1]=>0000111=>1110000
[5,4,3,6,7,2,8,1]=>0011011=>1101100
[4,5,3,6,7,2,8,1]=>0001011=>1101000
[4,3,5,6,7,2,8,1]=>0010011=>1100100
[3,4,5,6,7,2,8,1]=>0000011=>1100000
[7,6,5,4,2,3,8,1]=>0011111=>1111100
[6,7,5,4,2,3,8,1]=>0011011=>1101100
[7,5,6,4,2,3,8,1]=>0010111=>1110100
[6,5,7,4,2,3,8,1]=>0010111=>1110100
[5,6,7,4,2,3,8,1]=>0010011=>1100100
[7,6,4,5,2,3,8,1]=>0001111=>1111000
[6,7,4,5,2,3,8,1]=>0001011=>1101000
[7,5,4,6,2,3,8,1]=>0001111=>1111000
[7,4,5,6,2,3,8,1]=>0000111=>1110000
[6,5,4,7,2,3,8,1]=>0001111=>1111000
[5,6,4,7,2,3,8,1]=>0000111=>1110000
[6,4,5,7,2,3,8,1]=>0000111=>1110000
[5,4,6,7,2,3,8,1]=>0001011=>1101000
[4,5,6,7,2,3,8,1]=>0000011=>1100000
[7,6,5,3,2,4,8,1]=>0101111=>1111010
[6,7,5,3,2,4,8,1]=>0101011=>1101010
[6,5,7,3,2,4,8,1]=>0100111=>1110010
[7,6,5,2,3,4,8,1]=>0001111=>1111000
[7,5,6,2,3,4,8,1]=>0000111=>1110000
[5,6,7,2,3,4,8,1]=>0000011=>1100000
[6,7,4,3,2,5,8,1]=>0110011=>1100110
[7,6,4,2,3,5,8,1]=>0010111=>1110100
[7,6,3,2,4,5,8,1]=>0100111=>1110010
[6,7,3,2,4,5,8,1]=>0100011=>1100010
[7,6,2,3,4,5,8,1]=>0000111=>1110000
[6,7,2,3,4,5,8,1]=>0000011=>1100000
[7,5,4,3,2,6,8,1]=>0111011=>1101110
[7,4,3,5,2,6,8,1]=>0011011=>1101100
[7,5,4,2,3,6,8,1]=>0011011=>1101100
[7,4,5,2,3,6,8,1]=>0001011=>1101000
[7,5,3,2,4,6,8,1]=>0101011=>1101010
[7,5,2,3,4,6,8,1]=>0001011=>1101000
[7,4,3,2,5,6,8,1]=>0110011=>1100110
[7,4,2,3,5,6,8,1]=>0010011=>1100100
[7,3,2,4,5,6,8,1]=>0100011=>1100010
[7,2,3,4,5,6,8,1]=>0000011=>1100000
[6,5,4,3,2,7,8,1]=>0111101=>1011110
[5,4,6,3,2,7,8,1]=>0101101=>1011010
[4,5,6,3,2,7,8,1]=>0100101=>1010010
[6,5,3,4,2,7,8,1]=>0011101=>1011100
[6,3,4,5,2,7,8,1]=>0001101=>1011000
[5,4,3,6,2,7,8,1]=>0011101=>1011100
[4,3,5,6,2,7,8,1]=>0010101=>1010100
[3,4,5,6,2,7,8,1]=>0000101=>1010000
[6,5,4,2,3,7,8,1]=>0011101=>1011100
[5,6,4,2,3,7,8,1]=>0010101=>1010100
[6,4,5,2,3,7,8,1]=>0001101=>1011000
[5,4,6,2,3,7,8,1]=>0001101=>1011000
[4,5,6,2,3,7,8,1]=>0000101=>1010000
[6,5,3,2,4,7,8,1]=>0101101=>1011010
[6,5,2,3,4,7,8,1]=>0001101=>1011000
[6,2,3,4,5,7,8,1]=>0000101=>1010000
[5,4,3,2,6,7,8,1]=>0111001=>1001110
[4,5,3,2,6,7,8,1]=>0101001=>1001010
[5,3,4,2,6,7,8,1]=>0011001=>1001100
[4,3,5,2,6,7,8,1]=>0011001=>1001100
[3,4,5,2,6,7,8,1]=>0001001=>1001000
[5,4,2,3,6,7,8,1]=>0011001=>1001100
[4,5,2,3,6,7,8,1]=>0001001=>1001000
[5,3,2,4,6,7,8,1]=>0101001=>1001010
[5,2,3,4,6,7,8,1]=>0001001=>1001000
[4,3,2,5,6,7,8,1]=>0110001=>1000110
[3,4,2,5,6,7,8,1]=>0010001=>1000100
[4,2,3,5,6,7,8,1]=>0010001=>1000100
[3,2,4,5,6,7,8,1]=>0100001=>1000010
[2,3,4,5,6,7,8,1]=>0000001=>1000000
[8,7,6,5,4,3,1,2]=>0111111=>1111110
[7,8,6,5,4,3,1,2]=>0111101=>1011110
[8,6,7,5,4,3,1,2]=>0111011=>1101110
[7,6,8,5,4,3,1,2]=>0111011=>1101110
[6,7,8,5,4,3,1,2]=>0111001=>1001110
[8,7,5,6,4,3,1,2]=>0110111=>1110110
[7,8,5,6,4,3,1,2]=>0110101=>1010110
[8,6,5,7,4,3,1,2]=>0110111=>1110110
[7,6,5,8,4,3,1,2]=>0110111=>1110110
[6,7,5,8,4,3,1,2]=>0110011=>1100110
[7,5,6,8,4,3,1,2]=>0110011=>1100110
[6,5,7,8,4,3,1,2]=>0110101=>1010110
[5,6,7,8,4,3,1,2]=>0110001=>1000110
[8,7,6,4,5,3,1,2]=>0101111=>1111010
[7,8,6,4,5,3,1,2]=>0101101=>1011010
[8,6,7,4,5,3,1,2]=>0101011=>1101010
[6,7,8,4,5,3,1,2]=>0101001=>1001010
[8,7,5,4,6,3,1,2]=>0101111=>1111010
[7,8,4,5,6,3,1,2]=>0100101=>1010010
[8,5,6,4,7,3,1,2]=>0100111=>1110010
[8,6,4,5,7,3,1,2]=>0100111=>1110010
[8,5,4,6,7,3,1,2]=>0101011=>1101010
[7,6,5,4,8,3,1,2]=>0101111=>1111010
[7,5,6,4,8,3,1,2]=>0100111=>1110010
[6,5,7,4,8,3,1,2]=>0100111=>1110010
[7,6,4,5,8,3,1,2]=>0100111=>1110010
[6,7,4,5,8,3,1,2]=>0100011=>1100010
[6,5,4,7,8,3,1,2]=>0101101=>1011010
[5,6,4,7,8,3,1,2]=>0100101=>1010010
[5,4,6,7,8,3,1,2]=>0101001=>1001010
[4,5,6,7,8,3,1,2]=>0100001=>1000010
[8,7,6,5,3,4,1,2]=>0011111=>1111100
[7,8,6,5,3,4,1,2]=>0011101=>1011100
[7,6,8,5,3,4,1,2]=>0011011=>1101100
[6,7,8,5,3,4,1,2]=>0011001=>1001100
[8,7,5,6,3,4,1,2]=>0010111=>1110100
[7,8,5,6,3,4,1,2]=>0010101=>1010100
[8,6,5,7,3,4,1,2]=>0010111=>1110100
[8,5,6,7,3,4,1,2]=>0010011=>1100100
[7,6,5,8,3,4,1,2]=>0010111=>1110100
[6,7,5,8,3,4,1,2]=>0010011=>1100100
[7,5,6,8,3,4,1,2]=>0010011=>1100100
[6,5,7,8,3,4,1,2]=>0010101=>1010100
[5,6,7,8,3,4,1,2]=>0010001=>1000100
[6,7,8,4,3,5,1,2]=>0011001=>1001100
[8,7,6,3,4,5,1,2]=>0001111=>1111000
[7,8,6,3,4,5,1,2]=>0001101=>1011000
[8,6,7,3,4,5,1,2]=>0001011=>1101000
[6,7,8,3,4,5,1,2]=>0001001=>1001000
[7,8,5,4,3,6,1,2]=>0011101=>1011100
[8,7,4,5,3,6,1,2]=>0001111=>1111000
[7,8,4,5,3,6,1,2]=>0001101=>1011000
[7,8,5,3,4,6,1,2]=>0001101=>1011000
[8,7,4,3,5,6,1,2]=>0010111=>1110100
[7,8,4,3,5,6,1,2]=>0010101=>1010100
[8,7,3,4,5,6,1,2]=>0000111=>1110000
[7,8,3,4,5,6,1,2]=>0000101=>1010000
[8,6,5,4,3,7,1,2]=>0011111=>1111100
[8,5,4,6,3,7,1,2]=>0001111=>1111000
[8,5,4,3,6,7,1,2]=>0011011=>1101100
[8,5,3,4,6,7,1,2]=>0001011=>1101000
[8,4,3,5,6,7,1,2]=>0010011=>1100100
[8,3,4,5,6,7,1,2]=>0000011=>1100000
[7,6,5,4,3,8,1,2]=>0011111=>1111100
[7,5,6,4,3,8,1,2]=>0010111=>1110100
[6,5,7,4,3,8,1,2]=>0010111=>1110100
[5,6,7,4,3,8,1,2]=>0010011=>1100100
[6,7,4,5,3,8,1,2]=>0001011=>1101000
[7,5,4,6,3,8,1,2]=>0001111=>1111000
[6,5,4,7,3,8,1,2]=>0001111=>1111000
[5,6,4,7,3,8,1,2]=>0000111=>1110000
[5,4,6,7,3,8,1,2]=>0001011=>1101000
[4,5,6,7,3,8,1,2]=>0000011=>1100000
[7,6,5,3,4,8,1,2]=>0001111=>1111000
[7,5,6,3,4,8,1,2]=>0000111=>1110000
[5,6,7,3,4,8,1,2]=>0000011=>1100000
[7,6,4,3,5,8,1,2]=>0010111=>1110100
[7,6,3,4,5,8,1,2]=>0000111=>1110000
[7,5,4,3,6,8,1,2]=>0011011=>1101100
[7,4,5,3,6,8,1,2]=>0001011=>1101000
[7,5,3,4,6,8,1,2]=>0001011=>1101000
[7,3,4,5,6,8,1,2]=>0000011=>1100000
[6,5,4,3,7,8,1,2]=>0011101=>1011100
[5,6,4,3,7,8,1,2]=>0010101=>1010100
[5,4,6,3,7,8,1,2]=>0001101=>1011000
[4,5,6,3,7,8,1,2]=>0000101=>1010000
[6,5,3,4,7,8,1,2]=>0001101=>1011000
[5,6,3,4,7,8,1,2]=>0000101=>1010000
[6,4,3,5,7,8,1,2]=>0010101=>1010100
[6,3,4,5,7,8,1,2]=>0000101=>1010000
[5,4,3,6,7,8,1,2]=>0011001=>1001100
[4,5,3,6,7,8,1,2]=>0001001=>1001000
[5,3,4,6,7,8,1,2]=>0001001=>1001000
[4,3,5,6,7,8,1,2]=>0010001=>1000100
[3,4,5,6,7,8,1,2]=>0000001=>1000000
[8,7,6,5,4,2,1,3]=>1011111=>1111101
[7,8,6,5,4,2,1,3]=>1011101=>1011101
[8,6,7,5,4,2,1,3]=>1011011=>1101101
[7,6,8,5,4,2,1,3]=>1011011=>1101101
[6,7,8,5,4,2,1,3]=>1011001=>1001101
[8,7,5,6,4,2,1,3]=>1010111=>1110101
[7,8,5,6,4,2,1,3]=>1010101=>1010101
[8,6,5,7,4,2,1,3]=>1010111=>1110101
[7,6,5,8,4,2,1,3]=>1010111=>1110101
[6,7,5,8,4,2,1,3]=>1010011=>1100101
[7,5,6,8,4,2,1,3]=>1010011=>1100101
[6,5,7,8,4,2,1,3]=>1010101=>1010101
[5,6,7,8,4,2,1,3]=>1010001=>1000101
[8,7,6,4,5,2,1,3]=>1001111=>1111001
[8,6,7,4,5,2,1,3]=>1001011=>1101001
[7,6,8,4,5,2,1,3]=>1001011=>1101001
[8,7,4,5,6,2,1,3]=>1000111=>1110001
[8,6,5,4,7,2,1,3]=>1001111=>1111001
[8,6,4,5,7,2,1,3]=>1000111=>1110001
[8,4,5,6,7,2,1,3]=>1000011=>1100001
[7,6,5,4,8,2,1,3]=>1001111=>1111001
[6,7,5,4,8,2,1,3]=>1001011=>1101001
[7,5,6,4,8,2,1,3]=>1000111=>1110001
[6,5,7,4,8,2,1,3]=>1000111=>1110001
[5,6,7,4,8,2,1,3]=>1000011=>1100001
[7,6,4,5,8,2,1,3]=>1000111=>1110001
[7,4,5,6,8,2,1,3]=>1000011=>1100001
[5,4,6,7,8,2,1,3]=>1001001=>1001001
[4,5,6,7,8,2,1,3]=>1000001=>1000001
[8,7,6,5,4,1,2,3]=>0011111=>1111100
[7,8,6,5,4,1,2,3]=>0011101=>1011100
[7,6,8,5,4,1,2,3]=>0011011=>1101100
[6,7,8,5,4,1,2,3]=>0011001=>1001100
[7,8,5,6,4,1,2,3]=>0010101=>1010100
[8,6,5,7,4,1,2,3]=>0010111=>1110100
[8,5,6,7,4,1,2,3]=>0010011=>1100100
[7,6,5,8,4,1,2,3]=>0010111=>1110100
[6,7,5,8,4,1,2,3]=>0010011=>1100100
[7,5,6,8,4,1,2,3]=>0010011=>1100100
[6,5,7,8,4,1,2,3]=>0010101=>1010100
[5,6,7,8,4,1,2,3]=>0010001=>1000100
[8,7,6,4,5,1,2,3]=>0001111=>1111000
[8,6,7,4,5,1,2,3]=>0001011=>1101000
[6,7,8,4,5,1,2,3]=>0001001=>1001000
[8,7,5,4,6,1,2,3]=>0001111=>1111000
[7,8,5,4,6,1,2,3]=>0001101=>1011000
[8,7,4,5,6,1,2,3]=>0000111=>1110000
[7,8,4,5,6,1,2,3]=>0000101=>1010000
[8,6,5,4,7,1,2,3]=>0001111=>1111000
[8,5,6,4,7,1,2,3]=>0000111=>1110000
[8,6,4,5,7,1,2,3]=>0000111=>1110000
[8,5,4,6,7,1,2,3]=>0001011=>1101000
[8,4,5,6,7,1,2,3]=>0000011=>1100000
[7,6,5,4,8,1,2,3]=>0001111=>1111000
[6,7,5,4,8,1,2,3]=>0001011=>1101000
[7,5,6,4,8,1,2,3]=>0000111=>1110000
[6,5,7,4,8,1,2,3]=>0000111=>1110000
[5,6,7,4,8,1,2,3]=>0000011=>1100000
[7,6,4,5,8,1,2,3]=>0000111=>1110000
[6,7,4,5,8,1,2,3]=>0000011=>1100000
[7,5,4,6,8,1,2,3]=>0001011=>1101000
[7,4,5,6,8,1,2,3]=>0000011=>1100000
[6,5,4,7,8,1,2,3]=>0001101=>1011000
[5,6,4,7,8,1,2,3]=>0000101=>1010000
[6,4,5,7,8,1,2,3]=>0000101=>1010000
[5,4,6,7,8,1,2,3]=>0001001=>1001000
[4,5,6,7,8,1,2,3]=>0000001=>1000000
[8,7,6,5,3,2,1,4]=>1101111=>1111011
[7,8,6,5,3,2,1,4]=>1101101=>1011011
[8,6,7,5,3,2,1,4]=>1101011=>1101011
[7,6,8,5,3,2,1,4]=>1101011=>1101011
[6,7,8,5,3,2,1,4]=>1101001=>1001011
[8,7,5,6,3,2,1,4]=>1100111=>1110011
[7,8,5,6,3,2,1,4]=>1100101=>1010011
[8,6,5,7,3,2,1,4]=>1100111=>1110011
[8,5,6,7,3,2,1,4]=>1100011=>1100011
[7,6,5,8,3,2,1,4]=>1100111=>1110011
[6,7,5,8,3,2,1,4]=>1100011=>1100011
[7,5,6,8,3,2,1,4]=>1100011=>1100011
[6,5,7,8,3,2,1,4]=>1100101=>1010011
[5,6,7,8,3,2,1,4]=>1100001=>1000011
[8,7,6,5,2,3,1,4]=>0101111=>1111010
[7,8,6,5,2,3,1,4]=>0101101=>1011010
[8,6,7,5,2,3,1,4]=>0101011=>1101010
[7,6,8,5,2,3,1,4]=>0101011=>1101010
[6,7,8,5,2,3,1,4]=>0101001=>1001010
[8,7,5,6,2,3,1,4]=>0100111=>1110010
[7,8,5,6,2,3,1,4]=>0100101=>1010010
[8,6,5,7,2,3,1,4]=>0100111=>1110010
[8,5,6,7,2,3,1,4]=>0100011=>1100010
[7,6,5,8,2,3,1,4]=>0100111=>1110010
[6,7,5,8,2,3,1,4]=>0100011=>1100010
[7,5,6,8,2,3,1,4]=>0100011=>1100010
[6,5,7,8,2,3,1,4]=>0100101=>1010010
[5,6,7,8,2,3,1,4]=>0100001=>1000010
[8,7,6,5,3,1,2,4]=>0101111=>1111010
[7,8,6,5,3,1,2,4]=>0101101=>1011010
[8,6,7,5,3,1,2,4]=>0101011=>1101010
[7,6,8,5,3,1,2,4]=>0101011=>1101010
[8,7,5,6,3,1,2,4]=>0100111=>1110010
[7,8,5,6,3,1,2,4]=>0100101=>1010010
[8,6,5,7,3,1,2,4]=>0100111=>1110010
[7,6,5,8,3,1,2,4]=>0100111=>1110010
[6,7,5,8,3,1,2,4]=>0100011=>1100010
[7,5,6,8,3,1,2,4]=>0100011=>1100010
[6,5,7,8,3,1,2,4]=>0100101=>1010010
[5,6,7,8,3,1,2,4]=>0100001=>1000010
[8,7,6,5,2,1,3,4]=>1001111=>1111001
[7,8,6,5,2,1,3,4]=>1001101=>1011001
[7,6,8,5,2,1,3,4]=>1001011=>1101001
[6,7,8,5,2,1,3,4]=>1001001=>1001001
[8,7,5,6,2,1,3,4]=>1000111=>1110001
[7,8,5,6,2,1,3,4]=>1000101=>1010001
[8,6,5,7,2,1,3,4]=>1000111=>1110001
[8,5,6,7,2,1,3,4]=>1000011=>1100001
[7,6,5,8,2,1,3,4]=>1000111=>1110001
[6,7,5,8,2,1,3,4]=>1000011=>1100001
[7,5,6,8,2,1,3,4]=>1000011=>1100001
[6,5,7,8,2,1,3,4]=>1000101=>1010001
[5,6,7,8,2,1,3,4]=>1000001=>1000001
[8,7,6,5,1,2,3,4]=>0001111=>1111000
[7,8,6,5,1,2,3,4]=>0001101=>1011000
[8,6,7,5,1,2,3,4]=>0001011=>1101000
[7,6,8,5,1,2,3,4]=>0001011=>1101000
[6,7,8,5,1,2,3,4]=>0001001=>1001000
[8,7,5,6,1,2,3,4]=>0000111=>1110000
[7,8,5,6,1,2,3,4]=>0000101=>1010000
[8,6,5,7,1,2,3,4]=>0000111=>1110000
[8,5,6,7,1,2,3,4]=>0000011=>1100000
[7,6,5,8,1,2,3,4]=>0000111=>1110000
[6,7,5,8,1,2,3,4]=>0000011=>1100000
[7,5,6,8,1,2,3,4]=>0000011=>1100000
[6,5,7,8,1,2,3,4]=>0000101=>1010000
[5,6,7,8,1,2,3,4]=>0000001=>1000000
[8,7,6,4,3,2,1,5]=>1110111=>1110111
[7,8,6,4,3,2,1,5]=>1110101=>1010111
[8,6,7,4,3,2,1,5]=>1110011=>1100111
[7,6,8,4,3,2,1,5]=>1110011=>1100111
[6,7,8,4,3,2,1,5]=>1110001=>1000111
[8,7,6,3,4,2,1,5]=>1010111=>1110101
[7,8,6,3,4,2,1,5]=>1010101=>1010101
[6,7,8,3,4,2,1,5]=>1010001=>1000101
[8,7,6,4,2,3,1,5]=>0110111=>1110110
[8,6,7,4,2,3,1,5]=>0110011=>1100110
[7,6,8,4,2,3,1,5]=>0110011=>1100110
[6,7,8,4,2,3,1,5]=>0110001=>1000110
[8,7,6,3,2,4,1,5]=>0110111=>1110110
[8,6,7,3,2,4,1,5]=>0110011=>1100110
[6,7,8,3,2,4,1,5]=>0110001=>1000110
[8,7,6,2,3,4,1,5]=>0010111=>1110100
[8,6,7,2,3,4,1,5]=>0010011=>1100100
[7,6,8,2,3,4,1,5]=>0010011=>1100100
[6,7,8,2,3,4,1,5]=>0010001=>1000100
[8,7,6,4,3,1,2,5]=>0110111=>1110110
[6,7,8,4,3,1,2,5]=>0110001=>1000110
[8,7,6,3,4,1,2,5]=>0010111=>1110100
[7,8,6,3,4,1,2,5]=>0010101=>1010100
[8,6,7,3,4,1,2,5]=>0010011=>1100100
[6,7,8,3,4,1,2,5]=>0010001=>1000100
[8,7,6,4,2,1,3,5]=>1010111=>1110101
[7,8,6,4,2,1,3,5]=>1010101=>1010101
[8,6,7,4,2,1,3,5]=>1010011=>1100101
[6,7,8,4,2,1,3,5]=>1010001=>1000101
[8,7,6,4,1,2,3,5]=>0010111=>1110100
[7,8,6,4,1,2,3,5]=>0010101=>1010100
[7,6,8,4,1,2,3,5]=>0010011=>1100100
[6,7,8,4,1,2,3,5]=>0010001=>1000100
[8,7,6,3,2,1,4,5]=>1100111=>1110011
[7,8,6,3,2,1,4,5]=>1100101=>1010011
[8,6,7,3,2,1,4,5]=>1100011=>1100011
[7,6,8,3,2,1,4,5]=>1100011=>1100011
[6,7,8,3,2,1,4,5]=>1100001=>1000011
[8,7,6,2,3,1,4,5]=>0100111=>1110010
[7,8,6,2,3,1,4,5]=>0100101=>1010010
[8,6,7,2,3,1,4,5]=>0100011=>1100010
[7,6,8,2,3,1,4,5]=>0100011=>1100010
[6,7,8,2,3,1,4,5]=>0100001=>1000010
[8,7,6,3,1,2,4,5]=>0100111=>1110010
[7,8,6,3,1,2,4,5]=>0100101=>1010010
[8,6,7,3,1,2,4,5]=>0100011=>1100010
[7,6,8,3,1,2,4,5]=>0100011=>1100010
[6,7,8,3,1,2,4,5]=>0100001=>1000010
[8,7,6,2,1,3,4,5]=>1000111=>1110001
[7,8,6,2,1,3,4,5]=>1000101=>1010001
[8,6,7,2,1,3,4,5]=>1000011=>1100001
[6,7,8,2,1,3,4,5]=>1000001=>1000001
[8,7,6,1,2,3,4,5]=>0000111=>1110000
[7,8,6,1,2,3,4,5]=>0000101=>1010000
[8,6,7,1,2,3,4,5]=>0000011=>1100000
[7,6,8,1,2,3,4,5]=>0000011=>1100000
[6,7,8,1,2,3,4,5]=>0000001=>1000000
[8,7,5,4,3,2,1,6]=>1111011=>1101111
[7,8,5,4,3,2,1,6]=>1111001=>1001111
[8,7,4,5,3,2,1,6]=>1101011=>1101011
[7,8,4,5,3,2,1,6]=>1101001=>1001011
[8,7,5,3,4,2,1,6]=>1011011=>1101101
[8,7,4,3,5,2,1,6]=>1011011=>1101101
[8,7,3,4,5,2,1,6]=>1001011=>1101001
[7,8,3,4,5,2,1,6]=>1001001=>1001001
[8,7,4,5,2,3,1,6]=>0101011=>1101010
[7,8,4,5,2,3,1,6]=>0101001=>1001010
[8,7,5,3,2,4,1,6]=>0111011=>1101110
[7,8,5,2,3,4,1,6]=>0011001=>1001100
[8,7,4,3,2,5,1,6]=>0111011=>1101110
[7,8,4,3,2,5,1,6]=>0111001=>1001110
[8,7,3,4,2,5,1,6]=>0011011=>1101100
[7,8,3,4,2,5,1,6]=>0011001=>1001100
[8,7,2,3,4,5,1,6]=>0001011=>1101000
[7,8,2,3,4,5,1,6]=>0001001=>1001000
[8,7,5,4,3,1,2,6]=>0111011=>1101110
[7,8,5,4,3,1,2,6]=>0111001=>1001110
[8,7,5,3,4,1,2,6]=>0011011=>1101100
[7,8,5,3,4,1,2,6]=>0011001=>1001100
[8,7,3,4,5,1,2,6]=>0001011=>1101000
[7,8,3,4,5,1,2,6]=>0001001=>1001000
[7,8,5,4,2,1,3,6]=>1011001=>1001101
[8,7,5,4,1,2,3,6]=>0011011=>1101100
[7,8,5,4,1,2,3,6]=>0011001=>1001100
[8,7,4,5,1,2,3,6]=>0001011=>1101000
[7,8,4,5,1,2,3,6]=>0001001=>1001000
[8,7,5,3,2,1,4,6]=>1101011=>1101011
[7,8,5,3,2,1,4,6]=>1101001=>1001011
[8,7,5,2,3,1,4,6]=>0101011=>1101010
[8,7,5,3,1,2,4,6]=>0101011=>1101010
[7,8,5,3,1,2,4,6]=>0101001=>1001010
[8,7,5,2,1,3,4,6]=>1001011=>1101001
[7,8,5,2,1,3,4,6]=>1001001=>1001001
[8,7,5,1,2,3,4,6]=>0001011=>1101000
[7,8,5,1,2,3,4,6]=>0001001=>1001000
[8,7,4,3,2,1,5,6]=>1110011=>1100111
[7,8,4,3,2,1,5,6]=>1110001=>1000111
[8,7,3,4,2,1,5,6]=>1010011=>1100101
[7,8,3,4,2,1,5,6]=>1010001=>1000101
[7,8,4,2,3,1,5,6]=>0110001=>1000110
[8,7,3,2,4,1,5,6]=>0110011=>1100110
[7,8,3,2,4,1,5,6]=>0110001=>1000110
[8,7,2,3,4,1,5,6]=>0010011=>1100100
[7,8,2,3,4,1,5,6]=>0010001=>1000100
[7,8,4,3,1,2,5,6]=>0110001=>1000110
[8,7,3,4,1,2,5,6]=>0010011=>1100100
[7,8,3,4,1,2,5,6]=>0010001=>1000100
[8,7,4,2,1,3,5,6]=>1010011=>1100101
[7,8,4,2,1,3,5,6]=>1010001=>1000101
[8,7,4,1,2,3,5,6]=>0010011=>1100100
[7,8,4,1,2,3,5,6]=>0010001=>1000100
[8,7,3,2,1,4,5,6]=>1100011=>1100011
[7,8,3,2,1,4,5,6]=>1100001=>1000011
[8,7,2,3,1,4,5,6]=>0100011=>1100010
[7,8,2,3,1,4,5,6]=>0100001=>1000010
[7,8,3,1,2,4,5,6]=>0100001=>1000010
[8,7,2,1,3,4,5,6]=>1000011=>1100001
[7,8,2,1,3,4,5,6]=>1000001=>1000001
[8,7,1,2,3,4,5,6]=>0000011=>1100000
[7,8,1,2,3,4,5,6]=>0000001=>1000000
[8,6,5,4,3,2,1,7]=>1111101=>1011111
[8,5,6,4,3,2,1,7]=>1110101=>1010111
[8,6,4,5,3,2,1,7]=>1101101=>1011011
[8,5,4,6,3,2,1,7]=>1101101=>1011011
[8,4,5,6,3,2,1,7]=>1100101=>1010011
[8,6,5,3,4,2,1,7]=>1011101=>1011101
[8,5,6,3,4,2,1,7]=>1010101=>1010101
[8,6,4,3,5,2,1,7]=>1011101=>1011101
[8,4,5,3,6,2,1,7]=>1001101=>1011001
[8,4,3,5,6,2,1,7]=>1010101=>1010101
[8,3,4,5,6,2,1,7]=>1000101=>1010001
[8,6,5,4,2,3,1,7]=>0111101=>1011110
[8,5,6,4,2,3,1,7]=>0110101=>1010110
[8,6,4,5,2,3,1,7]=>0101101=>1011010
[8,4,5,6,2,3,1,7]=>0100101=>1010010
[8,6,5,3,2,4,1,7]=>0111101=>1011110
[8,6,5,2,3,4,1,7]=>0011101=>1011100
[8,5,6,2,3,4,1,7]=>0010101=>1010100
[8,6,4,3,2,5,1,7]=>0111101=>1011110
[8,6,4,2,3,5,1,7]=>0011101=>1011100
[8,6,3,2,4,5,1,7]=>0101101=>1011010
[8,5,4,3,2,6,1,7]=>0111101=>1011110
[8,4,3,5,2,6,1,7]=>0011101=>1011100
[8,5,4,2,3,6,1,7]=>0011101=>1011100
[8,4,5,2,3,6,1,7]=>0001101=>1011000
[8,5,3,2,4,6,1,7]=>0101101=>1011010
[8,5,2,3,4,6,1,7]=>0001101=>1011000
[8,3,4,2,5,6,1,7]=>0010101=>1010100
[8,3,2,4,5,6,1,7]=>0100101=>1010010
[8,2,3,4,5,6,1,7]=>0000101=>1010000
[8,6,5,4,3,1,2,7]=>0111101=>1011110
[8,6,4,5,3,1,2,7]=>0101101=>1011010
[8,6,5,3,4,1,2,7]=>0011101=>1011100
[8,5,6,3,4,1,2,7]=>0010101=>1010100
[8,6,3,4,5,1,2,7]=>0001101=>1011000
[8,5,4,3,6,1,2,7]=>0011101=>1011100
[8,4,5,3,6,1,2,7]=>0001101=>1011000
[8,5,3,4,6,1,2,7]=>0001101=>1011000
[8,4,3,5,6,1,2,7]=>0010101=>1010100
[8,3,4,5,6,1,2,7]=>0000101=>1010000
[8,6,5,4,2,1,3,7]=>1011101=>1011101
[8,5,6,4,2,1,3,7]=>1010101=>1010101
[8,6,4,5,2,1,3,7]=>1001101=>1011001
[8,4,5,6,2,1,3,7]=>1000101=>1010001
[8,6,5,4,1,2,3,7]=>0011101=>1011100
[8,5,6,4,1,2,3,7]=>0010101=>1010100
[8,6,4,5,1,2,3,7]=>0001101=>1011000
[8,4,5,6,1,2,3,7]=>0000101=>1010000
[8,6,5,3,2,1,4,7]=>1101101=>1011011
[8,5,6,3,2,1,4,7]=>1100101=>1010011
[8,6,5,2,3,1,4,7]=>0101101=>1011010
[8,5,6,2,3,1,4,7]=>0100101=>1010010
[8,5,6,3,1,2,4,7]=>0100101=>1010010
[8,6,5,2,1,3,4,7]=>1001101=>1011001
[8,5,6,2,1,3,4,7]=>1000101=>1010001
[8,6,5,1,2,3,4,7]=>0001101=>1011000
[8,5,6,1,2,3,4,7]=>0000101=>1010000
[8,6,4,3,2,1,5,7]=>1110101=>1010111
[8,6,3,4,2,1,5,7]=>1010101=>1010101
[8,6,4,2,3,1,5,7]=>0110101=>1010110
[8,6,3,2,4,1,5,7]=>0110101=>1010110
[8,6,2,3,4,1,5,7]=>0010101=>1010100
[8,6,4,3,1,2,5,7]=>0110101=>1010110
[8,6,3,4,1,2,5,7]=>0010101=>1010100
[8,6,4,2,1,3,5,7]=>1010101=>1010101
[8,6,3,2,1,4,5,7]=>1100101=>1010011
[8,6,1,2,3,4,5,7]=>0000101=>1010000
[8,5,4,3,2,1,6,7]=>1111001=>1001111
[8,4,5,3,2,1,6,7]=>1101001=>1001011
[8,4,3,5,2,1,6,7]=>1011001=>1001101
[8,3,4,5,2,1,6,7]=>1001001=>1001001
[8,4,5,2,3,1,6,7]=>0101001=>1001010
[8,5,2,3,4,1,6,7]=>0011001=>1001100
[8,4,2,3,5,1,6,7]=>0011001=>1001100
[8,2,3,4,5,1,6,7]=>0001001=>1001000
[8,5,3,4,1,2,6,7]=>0011001=>1001100
[8,3,4,5,1,2,6,7]=>0001001=>1001000
[8,5,4,2,1,3,6,7]=>1011001=>1001101
[8,5,4,1,2,3,6,7]=>0011001=>1001100
[8,4,5,1,2,3,6,7]=>0001001=>1001000
[8,5,3,2,1,4,6,7]=>1101001=>1001011
[8,5,3,1,2,4,6,7]=>0101001=>1001010
[8,5,2,1,3,4,6,7]=>1001001=>1001001
[8,5,1,2,3,4,6,7]=>0001001=>1001000
[8,4,3,2,1,5,6,7]=>1110001=>1000111
[8,3,4,2,1,5,6,7]=>1010001=>1000101
[8,4,2,3,1,5,6,7]=>0110001=>1000110
[8,2,3,4,1,5,6,7]=>0010001=>1000100
[8,3,4,1,2,5,6,7]=>0010001=>1000100
[8,4,2,1,3,5,6,7]=>1010001=>1000101
[8,4,1,2,3,5,6,7]=>0010001=>1000100
[8,3,2,1,4,5,6,7]=>1100001=>1000011
[8,2,3,1,4,5,6,7]=>0100001=>1000010
[8,3,1,2,4,5,6,7]=>0100001=>1000010
[8,2,1,3,4,5,6,7]=>1000001=>1000001
[8,1,2,3,4,5,6,7]=>0000001=>1000000
[7,6,5,4,3,2,1,8]=>1111110=>0111111
[6,7,5,4,3,2,1,8]=>1111010=>0101111
[7,5,6,4,3,2,1,8]=>1110110=>0110111
[6,5,7,4,3,2,1,8]=>1110110=>0110111
[5,6,7,4,3,2,1,8]=>1110010=>0100111
[7,6,4,5,3,2,1,8]=>1101110=>0111011
[6,7,4,5,3,2,1,8]=>1101010=>0101011
[7,5,4,6,3,2,1,8]=>1101110=>0111011
[7,4,5,6,3,2,1,8]=>1100110=>0110011
[6,5,4,7,3,2,1,8]=>1101110=>0111011
[5,6,4,7,3,2,1,8]=>1100110=>0110011
[5,4,6,7,3,2,1,8]=>1101010=>0101011
[4,5,6,7,3,2,1,8]=>1100010=>0100011
[7,6,5,3,4,2,1,8]=>1011110=>0111101
[6,7,5,3,4,2,1,8]=>1011010=>0101101
[7,5,6,3,4,2,1,8]=>1010110=>0110101
[6,5,7,3,4,2,1,8]=>1010110=>0110101
[5,6,7,3,4,2,1,8]=>1010010=>0100101
[7,6,4,3,5,2,1,8]=>1011110=>0111101
[6,7,4,3,5,2,1,8]=>1011010=>0101101
[7,6,3,4,5,2,1,8]=>1001110=>0111001
[7,5,4,3,6,2,1,8]=>1011110=>0111101
[7,4,5,3,6,2,1,8]=>1001110=>0111001
[7,3,4,5,6,2,1,8]=>1000110=>0110001
[6,5,4,3,7,2,1,8]=>1011110=>0111101
[5,6,4,3,7,2,1,8]=>1010110=>0110101
[5,4,6,3,7,2,1,8]=>1001110=>0111001
[5,4,3,6,7,2,1,8]=>1011010=>0101101
[3,4,5,6,7,2,1,8]=>1000010=>0100001
[7,6,5,4,2,3,1,8]=>0111110=>0111110
[6,7,5,4,2,3,1,8]=>0111010=>0101110
[7,5,6,4,2,3,1,8]=>0110110=>0110110
[5,6,7,4,2,3,1,8]=>0110010=>0100110
[7,6,4,5,2,3,1,8]=>0101110=>0111010
[6,7,4,5,2,3,1,8]=>0101010=>0101010
[7,5,4,6,2,3,1,8]=>0101110=>0111010
[7,4,5,6,2,3,1,8]=>0100110=>0110010
[6,5,4,7,2,3,1,8]=>0101110=>0111010
[5,6,4,7,2,3,1,8]=>0100110=>0110010
[5,4,6,7,2,3,1,8]=>0101010=>0101010
[4,5,6,7,2,3,1,8]=>0100010=>0100010
[7,6,5,3,2,4,1,8]=>0111110=>0111110
[6,5,7,3,2,4,1,8]=>0110110=>0110110
[5,6,7,3,2,4,1,8]=>0110010=>0100110
[7,6,5,2,3,4,1,8]=>0011110=>0111100
[6,7,5,2,3,4,1,8]=>0011010=>0101100
[7,5,6,2,3,4,1,8]=>0010110=>0110100
[6,5,7,2,3,4,1,8]=>0010110=>0110100
[5,6,7,2,3,4,1,8]=>0010010=>0100100
[7,6,4,3,2,5,1,8]=>0111110=>0111110
[6,7,4,3,2,5,1,8]=>0111010=>0101110
[6,7,3,4,2,5,1,8]=>0011010=>0101100
[7,6,4,2,3,5,1,8]=>0011110=>0111100
[6,7,4,2,3,5,1,8]=>0011010=>0101100
[7,6,3,2,4,5,1,8]=>0101110=>0111010
[6,7,3,2,4,5,1,8]=>0101010=>0101010
[7,6,2,3,4,5,1,8]=>0001110=>0111000
[6,7,2,3,4,5,1,8]=>0001010=>0101000
[7,5,4,3,2,6,1,8]=>0111110=>0111110
[7,4,5,3,2,6,1,8]=>0101110=>0111010
[7,5,3,4,2,6,1,8]=>0011110=>0111100
[7,4,3,5,2,6,1,8]=>0011110=>0111100
[7,5,4,2,3,6,1,8]=>0011110=>0111100
[7,4,5,2,3,6,1,8]=>0001110=>0111000
[7,5,3,2,4,6,1,8]=>0101110=>0111010
[7,2,3,4,5,6,1,8]=>0000110=>0110000
[6,5,4,3,2,7,1,8]=>0111110=>0111110
[5,6,4,3,2,7,1,8]=>0110110=>0110110
[5,4,6,3,2,7,1,8]=>0101110=>0111010
[5,6,3,4,2,7,1,8]=>0010110=>0110100
[6,3,4,5,2,7,1,8]=>0001110=>0111000
[5,4,3,6,2,7,1,8]=>0011110=>0111100
[4,5,3,6,2,7,1,8]=>0001110=>0111000
[5,3,4,6,2,7,1,8]=>0001110=>0111000
[4,3,5,6,2,7,1,8]=>0010110=>0110100
[3,4,5,6,2,7,1,8]=>0000110=>0110000
[5,4,6,2,3,7,1,8]=>0001110=>0111000
[6,5,3,2,4,7,1,8]=>0101110=>0111010
[6,3,2,4,5,7,1,8]=>0100110=>0110010
[6,2,3,4,5,7,1,8]=>0000110=>0110000
[5,4,3,2,6,7,1,8]=>0111010=>0101110
[3,4,5,2,6,7,1,8]=>0001010=>0101000
[5,4,2,3,6,7,1,8]=>0011010=>0101100
[4,5,2,3,6,7,1,8]=>0001010=>0101000
[5,2,3,4,6,7,1,8]=>0001010=>0101000
[4,3,2,5,6,7,1,8]=>0110010=>0100110
[3,4,2,5,6,7,1,8]=>0010010=>0100100
[4,2,3,5,6,7,1,8]=>0010010=>0100100
[3,2,4,5,6,7,1,8]=>0100010=>0100010
[2,3,4,5,6,7,1,8]=>0000010=>0100000
[7,6,5,4,3,1,2,8]=>0111110=>0111110
[6,7,5,4,3,1,2,8]=>0111010=>0101110
[7,5,6,4,3,1,2,8]=>0110110=>0110110
[7,6,4,5,3,1,2,8]=>0101110=>0111010
[7,4,5,6,3,1,2,8]=>0100110=>0110010
[5,4,6,7,3,1,2,8]=>0101010=>0101010
[4,5,6,7,3,1,2,8]=>0100010=>0100010
[7,6,5,3,4,1,2,8]=>0011110=>0111100
[7,5,6,3,4,1,2,8]=>0010110=>0110100
[6,5,7,3,4,1,2,8]=>0010110=>0110100
[6,7,3,4,5,1,2,8]=>0001010=>0101000
[7,5,3,4,6,1,2,8]=>0001110=>0111000
[6,5,4,3,7,1,2,8]=>0011110=>0111100
[6,4,5,3,7,1,2,8]=>0001110=>0111000
[5,6,3,4,7,1,2,8]=>0000110=>0110000
[6,4,3,5,7,1,2,8]=>0010110=>0110100
[6,3,4,5,7,1,2,8]=>0000110=>0110000
[4,3,5,6,7,1,2,8]=>0010010=>0100100
[3,4,5,6,7,1,2,8]=>0000010=>0100000
[7,6,5,4,2,1,3,8]=>1011110=>0111101
[6,5,7,4,2,1,3,8]=>1010110=>0110101
[7,6,4,5,2,1,3,8]=>1001110=>0111001
[7,5,4,6,2,1,3,8]=>1001110=>0111001
[7,4,5,6,2,1,3,8]=>1000110=>0110001
[5,4,6,7,2,1,3,8]=>1001010=>0101001
[4,5,6,7,2,1,3,8]=>1000010=>0100001
[7,6,5,4,1,2,3,8]=>0011110=>0111100
[7,5,6,4,1,2,3,8]=>0010110=>0110100
[5,6,7,4,1,2,3,8]=>0010010=>0100100
[7,6,4,5,1,2,3,8]=>0001110=>0111000
[7,5,4,6,1,2,3,8]=>0001110=>0111000
[7,4,5,6,1,2,3,8]=>0000110=>0110000
[5,6,4,7,1,2,3,8]=>0000110=>0110000
[5,4,6,7,1,2,3,8]=>0001010=>0101000
[4,5,6,7,1,2,3,8]=>0000010=>0100000
[7,6,5,3,2,1,4,8]=>1101110=>0111011
[7,6,5,2,3,1,4,8]=>0101110=>0111010
[6,7,5,2,3,1,4,8]=>0101010=>0101010
[7,5,6,2,3,1,4,8]=>0100110=>0110010
[6,5,7,2,3,1,4,8]=>0100110=>0110010
[5,6,7,2,3,1,4,8]=>0100010=>0100010
[7,5,6,3,1,2,4,8]=>0100110=>0110010
[5,6,7,3,1,2,4,8]=>0100010=>0100010
[7,6,5,2,1,3,4,8]=>1001110=>0111001
[6,7,5,2,1,3,4,8]=>1001010=>0101001
[7,5,6,2,1,3,4,8]=>1000110=>0110001
[5,6,7,2,1,3,4,8]=>1000010=>0100001
[7,6,5,1,2,3,4,8]=>0001110=>0111000
[6,7,5,1,2,3,4,8]=>0001010=>0101000
[7,5,6,1,2,3,4,8]=>0000110=>0110000
[6,5,7,1,2,3,4,8]=>0000110=>0110000
[5,6,7,1,2,3,4,8]=>0000010=>0100000
[7,6,4,3,2,1,5,8]=>1110110=>0110111
[6,7,4,3,2,1,5,8]=>1110010=>0100111
[7,6,3,4,2,1,5,8]=>1010110=>0110101
[6,7,3,4,2,1,5,8]=>1010010=>0100101
[7,6,4,2,3,1,5,8]=>0110110=>0110110
[7,6,3,2,4,1,5,8]=>0110110=>0110110
[6,7,3,2,4,1,5,8]=>0110010=>0100110
[7,6,2,3,4,1,5,8]=>0010110=>0110100
[6,7,2,3,4,1,5,8]=>0010010=>0100100
[7,6,4,3,1,2,5,8]=>0110110=>0110110
[6,7,3,4,1,2,5,8]=>0010010=>0100100
[7,6,4,2,1,3,5,8]=>1010110=>0110101
[7,6,3,2,1,4,5,8]=>1100110=>0110011
[6,7,3,2,1,4,5,8]=>1100010=>0100011
[7,6,2,3,1,4,5,8]=>0100110=>0110010
[6,7,2,3,1,4,5,8]=>0100010=>0100010
[6,7,3,1,2,4,5,8]=>0100010=>0100010
[7,6,1,2,3,4,5,8]=>0000110=>0110000
[6,7,1,2,3,4,5,8]=>0000010=>0100000
[7,5,4,3,2,1,6,8]=>1111010=>0101111
[7,4,5,3,2,1,6,8]=>1101010=>0101011
[7,4,3,5,2,1,6,8]=>1011010=>0101101
[7,3,4,5,2,1,6,8]=>1001010=>0101001
[7,5,4,2,3,1,6,8]=>0111010=>0101110
[7,5,3,2,4,1,6,8]=>0111010=>0101110
[7,5,2,3,4,1,6,8]=>0011010=>0101100
[7,4,2,3,5,1,6,8]=>0011010=>0101100
[7,2,3,4,5,1,6,8]=>0001010=>0101000
[7,5,4,3,1,2,6,8]=>0111010=>0101110
[7,5,3,4,1,2,6,8]=>0011010=>0101100
[7,4,5,2,1,3,6,8]=>1001010=>0101001
[7,4,5,1,2,3,6,8]=>0001010=>0101000
[7,5,3,2,1,4,6,8]=>1101010=>0101011
[7,5,2,3,1,4,6,8]=>0101010=>0101010
[7,5,3,1,2,4,6,8]=>0101010=>0101010
[7,5,1,2,3,4,6,8]=>0001010=>0101000
[7,4,3,2,1,5,6,8]=>1110010=>0100111
[7,2,3,4,1,5,6,8]=>0010010=>0100100
[7,4,3,1,2,5,6,8]=>0110010=>0100110
[7,3,4,1,2,5,6,8]=>0010010=>0100100
[7,4,1,2,3,5,6,8]=>0010010=>0100100
[7,3,2,1,4,5,6,8]=>1100010=>0100011
[7,2,3,1,4,5,6,8]=>0100010=>0100010
[7,3,1,2,4,5,6,8]=>0100010=>0100010
[7,2,1,3,4,5,6,8]=>1000010=>0100001
[7,1,2,3,4,5,6,8]=>0000010=>0100000
[6,5,4,3,2,1,7,8]=>1111100=>0011111
[5,6,4,3,2,1,7,8]=>1110100=>0010111
[5,4,6,3,2,1,7,8]=>1101100=>0011011
[4,5,6,3,2,1,7,8]=>1100100=>0010011
[6,5,3,4,2,1,7,8]=>1011100=>0011101
[5,6,3,4,2,1,7,8]=>1010100=>0010101
[5,4,3,6,2,1,7,8]=>1011100=>0011101
[3,4,5,6,2,1,7,8]=>1000100=>0010001
[5,4,6,2,3,1,7,8]=>0101100=>0011010
[5,6,3,2,4,1,7,8]=>0110100=>0010110
[6,5,2,3,4,1,7,8]=>0011100=>0011100
[5,6,2,3,4,1,7,8]=>0010100=>0010100
[6,4,3,2,5,1,7,8]=>0111100=>0011110
[6,2,3,4,5,1,7,8]=>0001100=>0011000
[5,4,3,2,6,1,7,8]=>0111100=>0011110
[4,5,3,2,6,1,7,8]=>0101100=>0011010
[4,3,5,2,6,1,7,8]=>0011100=>0011100
[3,4,5,2,6,1,7,8]=>0001100=>0011000
[5,3,2,4,6,1,7,8]=>0101100=>0011010
[5,2,3,4,6,1,7,8]=>0001100=>0011000
[4,3,2,5,6,1,7,8]=>0110100=>0010110
[3,4,2,5,6,1,7,8]=>0010100=>0010100
[4,2,3,5,6,1,7,8]=>0010100=>0010100
[3,2,4,5,6,1,7,8]=>0100100=>0010010
[2,3,4,5,6,1,7,8]=>0000100=>0010000
[6,5,4,3,1,2,7,8]=>0111100=>0011110
[5,6,4,3,1,2,7,8]=>0110100=>0010110
[6,4,5,3,1,2,7,8]=>0101100=>0011010
[5,4,6,3,1,2,7,8]=>0101100=>0011010
[5,6,3,4,1,2,7,8]=>0010100=>0010100
[6,4,3,5,1,2,7,8]=>0011100=>0011100
[5,4,3,6,1,2,7,8]=>0011100=>0011100
[4,3,5,6,1,2,7,8]=>0010100=>0010100
[3,4,5,6,1,2,7,8]=>0000100=>0010000
[6,5,4,2,1,3,7,8]=>1011100=>0011101
[5,6,4,2,1,3,7,8]=>1010100=>0010101
[6,4,5,2,1,3,7,8]=>1001100=>0011001
[5,4,6,2,1,3,7,8]=>1001100=>0011001
[4,5,6,2,1,3,7,8]=>1000100=>0010001
[6,5,4,1,2,3,7,8]=>0011100=>0011100
[4,5,6,1,2,3,7,8]=>0000100=>0010000
[6,5,3,2,1,4,7,8]=>1101100=>0011011
[5,6,3,2,1,4,7,8]=>1100100=>0010011
[5,6,2,1,3,4,7,8]=>1000100=>0010001
[6,4,3,2,1,5,7,8]=>1110100=>0010111
[6,3,4,2,1,5,7,8]=>1010100=>0010101
[6,4,3,1,2,5,7,8]=>0110100=>0010110
[6,4,2,1,3,5,7,8]=>1010100=>0010101
[6,4,1,2,3,5,7,8]=>0010100=>0010100
[6,3,2,1,4,5,7,8]=>1100100=>0010011
[6,2,3,1,4,5,7,8]=>0100100=>0010010
[6,3,1,2,4,5,7,8]=>0100100=>0010010
[6,2,1,3,4,5,7,8]=>1000100=>0010001
[6,1,2,3,4,5,7,8]=>0000100=>0010000
[5,4,3,2,1,6,7,8]=>1111000=>0001111
[4,5,3,2,1,6,7,8]=>1101000=>0001011
[5,3,4,2,1,6,7,8]=>1011000=>0001101
[4,3,5,2,1,6,7,8]=>1011000=>0001101
[3,4,5,2,1,6,7,8]=>1001000=>0001001
[5,4,2,3,1,6,7,8]=>0111000=>0001110
[4,5,2,3,1,6,7,8]=>0101000=>0001010
[5,3,2,4,1,6,7,8]=>0111000=>0001110
[5,2,3,4,1,6,7,8]=>0011000=>0001100
[4,3,2,5,1,6,7,8]=>0111000=>0001110
[3,4,2,5,1,6,7,8]=>0011000=>0001100
[4,2,3,5,1,6,7,8]=>0011000=>0001100
[3,2,4,5,1,6,7,8]=>0101000=>0001010
[2,3,4,5,1,6,7,8]=>0001000=>0001000
[5,4,3,1,2,6,7,8]=>0111000=>0001110
[5,3,4,1,2,6,7,8]=>0011000=>0001100
[4,3,5,1,2,6,7,8]=>0011000=>0001100
[3,4,5,1,2,6,7,8]=>0001000=>0001000
[5,4,2,1,3,6,7,8]=>1011000=>0001101
[4,5,2,1,3,6,7,8]=>1001000=>0001001
[5,4,1,2,3,6,7,8]=>0011000=>0001100
[4,5,1,2,3,6,7,8]=>0001000=>0001000
[5,3,2,1,4,6,7,8]=>1101000=>0001011
[5,2,3,1,4,6,7,8]=>0101000=>0001010
[5,3,1,2,4,6,7,8]=>0101000=>0001010
[5,2,1,3,4,6,7,8]=>1001000=>0001001
[5,1,2,3,4,6,7,8]=>0001000=>0001000
[4,3,2,1,5,6,7,8]=>1110000=>0000111
[3,4,2,1,5,6,7,8]=>1010000=>0000101
[4,2,3,1,5,6,7,8]=>0110000=>0000110
[3,2,4,1,5,6,7,8]=>0110000=>0000110
[2,3,4,1,5,6,7,8]=>0010000=>0000100
[4,3,1,2,5,6,7,8]=>0110000=>0000110
[3,4,1,2,5,6,7,8]=>0010000=>0000100
[4,2,1,3,5,6,7,8]=>1010000=>0000101
[4,1,2,3,5,6,7,8]=>0010000=>0000100
[3,2,1,4,5,6,7,8]=>1100000=>0000011
[2,3,1,4,5,6,7,8]=>0100000=>0000010
[3,1,2,4,5,6,7,8]=>0100000=>0000010
[2,1,3,4,5,6,7,8]=>1000000=>0000001
[1,2,3,4,5,6,7,8]=>0000000=>0000000
[6,8,7,5,4,3,2,1]=>1111011=>1101111
[5,8,7,6,4,3,2,1]=>1110111=>1110111
[5,7,8,6,4,3,2,1]=>1110101=>1010111
[6,5,8,7,4,3,2,1]=>1110111=>1110111
[5,6,8,7,4,3,2,1]=>1110011=>1100111
[5,7,6,8,4,3,2,1]=>1110011=>1100111
[4,8,7,6,5,3,2,1]=>1101111=>1111011
[4,7,8,6,5,3,2,1]=>1101101=>1011011
[4,6,8,7,5,3,2,1]=>1101011=>1101011
[4,7,6,8,5,3,2,1]=>1101011=>1101011
[4,6,7,8,5,3,2,1]=>1101001=>1001011
[5,4,7,8,6,3,2,1]=>1101101=>1011011
[4,5,8,7,6,3,2,1]=>1100111=>1110011
[4,5,7,8,6,3,2,1]=>1100101=>1010011
[6,5,4,8,7,3,2,1]=>1101111=>1111011
[5,6,4,8,7,3,2,1]=>1100111=>1110011
[4,6,5,8,7,3,2,1]=>1100111=>1110011
[4,5,6,8,7,3,2,1]=>1100011=>1100011
[5,7,6,4,8,3,2,1]=>1100111=>1110011
[4,7,6,5,8,3,2,1]=>1100111=>1110011
[4,6,7,5,8,3,2,1]=>1100011=>1100011
[5,4,7,6,8,3,2,1]=>1101011=>1101011
[4,5,7,6,8,3,2,1]=>1100011=>1100011
[4,6,5,7,8,3,2,1]=>1100101=>1010011
[3,8,7,6,5,4,2,1]=>1011111=>1111101
[3,7,8,6,5,4,2,1]=>1011101=>1011101
[3,6,8,7,5,4,2,1]=>1011011=>1101101
[3,7,6,8,5,4,2,1]=>1011011=>1101101
[3,5,8,7,6,4,2,1]=>1010111=>1110101
[3,5,7,8,6,4,2,1]=>1010101=>1010101
[3,5,6,8,7,4,2,1]=>1010011=>1100101
[3,7,6,5,8,4,2,1]=>1010111=>1110101
[3,6,7,5,8,4,2,1]=>1010011=>1100101
[3,5,7,6,8,4,2,1]=>1010011=>1100101
[3,5,6,7,8,4,2,1]=>1010001=>1000101
[4,3,8,7,6,5,2,1]=>1011111=>1111101
[4,3,7,8,6,5,2,1]=>1011101=>1011101
[4,3,6,7,8,5,2,1]=>1011001=>1001101
[3,4,8,7,6,5,2,1]=>1001111=>1111001
[3,4,6,7,8,5,2,1]=>1001001=>1001001
[5,4,3,8,7,6,2,1]=>1011111=>1111101
[5,4,3,7,8,6,2,1]=>1011101=>1011101
[4,5,3,7,8,6,2,1]=>1001101=>1011001
[3,5,4,7,8,6,2,1]=>1001101=>1011001
[4,3,5,7,8,6,2,1]=>1010101=>1010101
[3,4,5,8,7,6,2,1]=>1000111=>1110001
[3,4,5,7,8,6,2,1]=>1000101=>1010001
[6,5,4,3,8,7,2,1]=>1011111=>1111101
[5,6,4,3,8,7,2,1]=>1010111=>1110101
[4,5,6,3,8,7,2,1]=>1000111=>1110001
[3,6,5,4,8,7,2,1]=>1001111=>1111001
[4,3,6,5,8,7,2,1]=>1010111=>1110101
[5,4,3,6,8,7,2,1]=>1011011=>1101101
[4,5,3,6,8,7,2,1]=>1001011=>1101001
[4,3,5,6,8,7,2,1]=>1010011=>1100101
[3,4,5,6,8,7,2,1]=>1000011=>1100001
[5,7,6,4,3,8,2,1]=>1010111=>1110101
[4,7,6,5,3,8,2,1]=>1001111=>1111001
[5,4,7,6,3,8,2,1]=>1001111=>1111001
[3,7,6,5,4,8,2,1]=>1001111=>1111001
[3,5,7,6,4,8,2,1]=>1000111=>1110001
[3,5,6,7,4,8,2,1]=>1000011=>1100001
[4,3,7,6,5,8,2,1]=>1010111=>1110101
[3,4,7,6,5,8,2,1]=>1000111=>1110001
[3,4,6,7,5,8,2,1]=>1000011=>1100001
[4,5,3,7,6,8,2,1]=>1001011=>1101001
[3,5,4,7,6,8,2,1]=>1001011=>1101001
[4,3,5,7,6,8,2,1]=>1010011=>1100101
[3,4,5,7,6,8,2,1]=>1000011=>1100001
[3,6,5,4,7,8,2,1]=>1001101=>1011001
[3,5,6,4,7,8,2,1]=>1000101=>1010001
[4,3,6,5,7,8,2,1]=>1010101=>1010101
[3,4,6,5,7,8,2,1]=>1000101=>1010001
[3,5,4,6,7,8,2,1]=>1001001=>1001001
[2,8,7,6,5,4,3,1]=>0111111=>1111110
[2,7,8,6,5,4,3,1]=>0111101=>1011110
[2,6,8,7,5,4,3,1]=>0111011=>1101110
[2,7,6,8,5,4,3,1]=>0111011=>1101110
[2,6,7,8,5,4,3,1]=>0111001=>1001110
[2,5,8,7,6,4,3,1]=>0110111=>1110110
[2,6,7,5,8,4,3,1]=>0110011=>1100110
[2,6,5,7,8,4,3,1]=>0110101=>1010110
[2,5,6,7,8,4,3,1]=>0110001=>1000110
[2,4,8,7,6,5,3,1]=>0101111=>1111010
[2,4,7,8,6,5,3,1]=>0101101=>1011010
[2,4,6,8,7,5,3,1]=>0101011=>1101010
[2,4,6,7,8,5,3,1]=>0101001=>1001010
[2,5,4,8,7,6,3,1]=>0101111=>1111010
[2,5,4,7,8,6,3,1]=>0101101=>1011010
[2,4,5,7,8,6,3,1]=>0100101=>1010010
[2,6,5,4,8,7,3,1]=>0101111=>1111010
[2,5,6,4,8,7,3,1]=>0100111=>1110010
[2,4,6,5,8,7,3,1]=>0100111=>1110010
[2,4,5,6,8,7,3,1]=>0100011=>1100010
[2,7,6,5,4,8,3,1]=>0101111=>1111010
[2,6,7,5,4,8,3,1]=>0101011=>1101010
[2,5,6,7,4,8,3,1]=>0100011=>1100010
[2,4,7,6,5,8,3,1]=>0100111=>1110010
[2,4,6,7,5,8,3,1]=>0100011=>1100010
[2,5,4,7,6,8,3,1]=>0101011=>1101010
[2,6,5,4,7,8,3,1]=>0101101=>1011010
[2,5,6,4,7,8,3,1]=>0100101=>1010010
[2,4,6,5,7,8,3,1]=>0100101=>1010010
[2,5,4,6,7,8,3,1]=>0101001=>1001010
[2,4,5,6,7,8,3,1]=>0100001=>1000010
[3,2,8,7,6,5,4,1]=>0111111=>1111110
[3,2,7,8,6,5,4,1]=>0111101=>1011110
[3,2,6,8,7,5,4,1]=>0111011=>1101110
[3,2,5,7,8,6,4,1]=>0110101=>1010110
[3,2,6,5,8,7,4,1]=>0110111=>1110110
[3,2,5,7,6,8,4,1]=>0110011=>1100110
[3,2,5,6,7,8,4,1]=>0110001=>1000110
[2,3,8,7,6,5,4,1]=>0011111=>1111100
[2,3,6,7,8,5,4,1]=>0011001=>1001100
[2,3,5,8,7,6,4,1]=>0010111=>1110100
[2,3,5,7,8,6,4,1]=>0010101=>1010100
[2,3,6,5,8,7,4,1]=>0010111=>1110100
[2,3,5,6,8,7,4,1]=>0010011=>1100100
[2,3,7,6,5,8,4,1]=>0010111=>1110100
[2,3,5,7,6,8,4,1]=>0010011=>1100100
[2,3,5,6,7,8,4,1]=>0010001=>1000100
[4,3,2,8,7,6,5,1]=>0111111=>1111110
[4,3,2,7,8,6,5,1]=>0111101=>1011110
[4,3,2,6,8,7,5,1]=>0111011=>1101110
[3,4,2,8,7,6,5,1]=>0011111=>1111100
[3,4,2,7,8,6,5,1]=>0011101=>1011100
[2,4,3,8,7,6,5,1]=>0011111=>1111100
[2,4,3,6,8,7,5,1]=>0011011=>1101100
[2,4,3,6,7,8,5,1]=>0011001=>1001100
[3,2,4,8,7,6,5,1]=>0101111=>1111010
[3,2,4,7,8,6,5,1]=>0101101=>1011010
[2,3,4,8,7,6,5,1]=>0001111=>1111000
[2,3,4,7,8,6,5,1]=>0001101=>1011000
[2,3,4,6,8,7,5,1]=>0001011=>1101000
[2,3,4,7,6,8,5,1]=>0001011=>1101000
[2,3,4,6,7,8,5,1]=>0001001=>1001000
[5,4,3,2,8,7,6,1]=>0111111=>1111110
[5,4,3,2,7,8,6,1]=>0111101=>1011110
[4,5,3,2,8,7,6,1]=>0101111=>1111010
[3,5,4,2,7,8,6,1]=>0011101=>1011100
[4,3,5,2,8,7,6,1]=>0011111=>1111100
[3,4,5,2,7,8,6,1]=>0001101=>1011000
[2,5,4,3,8,7,6,1]=>0011111=>1111100
[2,5,4,3,7,8,6,1]=>0011101=>1011100
[2,4,5,3,8,7,6,1]=>0001111=>1111000
[2,4,5,3,7,8,6,1]=>0001101=>1011000
[3,2,5,4,7,8,6,1]=>0101101=>1011010
[2,3,5,4,8,7,6,1]=>0001111=>1111000
[2,3,5,4,7,8,6,1]=>0001101=>1011000
[4,3,2,5,8,7,6,1]=>0110111=>1110110
[4,3,2,5,7,8,6,1]=>0110101=>1010110
[3,4,2,5,8,7,6,1]=>0010111=>1110100
[3,4,2,5,7,8,6,1]=>0010101=>1010100
[2,4,3,5,8,7,6,1]=>0010111=>1110100
[3,2,4,5,7,8,6,1]=>0100101=>1010010
[2,3,4,5,8,7,6,1]=>0000111=>1110000
[2,3,4,5,7,8,6,1]=>0000101=>1010000
[6,5,4,3,2,8,7,1]=>0111111=>1111110
[4,6,5,3,2,8,7,1]=>0101111=>1111010
[5,4,6,3,2,8,7,1]=>0101111=>1111010
[4,5,6,3,2,8,7,1]=>0100111=>1110010
[3,6,5,4,2,8,7,1]=>0011111=>1111100
[3,5,6,4,2,8,7,1]=>0010111=>1110100
[4,3,6,5,2,8,7,1]=>0011111=>1111100
[5,4,3,6,2,8,7,1]=>0011111=>1111100
[4,5,3,6,2,8,7,1]=>0001111=>1111000
[3,5,4,6,2,8,7,1]=>0001111=>1111000
[3,4,5,6,2,8,7,1]=>0000111=>1110000
[2,6,5,4,3,8,7,1]=>0011111=>1111100
[2,4,6,5,3,8,7,1]=>0001111=>1111000
[2,4,5,6,3,8,7,1]=>0000111=>1110000
[3,2,6,5,4,8,7,1]=>0101111=>1111010
[2,3,5,6,4,8,7,1]=>0000111=>1110000
[4,3,2,6,5,8,7,1]=>0110111=>1110110
[3,4,2,6,5,8,7,1]=>0010111=>1110100
[2,4,3,6,5,8,7,1]=>0010111=>1110100
[3,2,4,6,5,8,7,1]=>0100111=>1110010
[2,3,4,6,5,8,7,1]=>0000111=>1110000
[5,4,3,2,6,8,7,1]=>0111011=>1101110
[4,5,3,2,6,8,7,1]=>0101011=>1101010
[2,5,4,3,6,8,7,1]=>0011011=>1101100
[2,4,5,3,6,8,7,1]=>0001011=>1101000
[3,2,5,4,6,8,7,1]=>0101011=>1101010
[4,3,2,5,6,8,7,1]=>0110011=>1100110
[3,4,2,5,6,8,7,1]=>0010011=>1100100
[2,4,3,5,6,8,7,1]=>0010011=>1100100
[3,2,4,5,6,8,7,1]=>0100011=>1100010
[2,3,4,5,6,8,7,1]=>0000011=>1100000
[5,7,6,4,3,2,8,1]=>0110111=>1110110
[4,7,6,5,3,2,8,1]=>0101111=>1111010
[4,6,7,5,3,2,8,1]=>0101011=>1101010
[4,6,5,7,3,2,8,1]=>0100111=>1110010
[3,5,7,6,4,2,8,1]=>0010111=>1110100
[3,5,6,7,4,2,8,1]=>0010011=>1100100
[4,3,7,6,5,2,8,1]=>0011111=>1111100
[4,3,6,7,5,2,8,1]=>0011011=>1101100
[3,4,7,6,5,2,8,1]=>0001111=>1111000
[3,4,6,7,5,2,8,1]=>0001011=>1101000
[5,4,3,7,6,2,8,1]=>0011111=>1111100
[4,5,3,7,6,2,8,1]=>0001111=>1111000
[3,5,4,7,6,2,8,1]=>0001111=>1111000
[3,4,5,7,6,2,8,1]=>0000111=>1110000
[4,6,5,3,7,2,8,1]=>0001111=>1111000
[3,6,5,4,7,2,8,1]=>0001111=>1111000
[3,5,6,4,7,2,8,1]=>0000111=>1110000
[4,3,6,5,7,2,8,1]=>0010111=>1110100
[3,4,6,5,7,2,8,1]=>0000111=>1110000
[3,5,4,6,7,2,8,1]=>0001011=>1101000
[2,7,6,5,4,3,8,1]=>0011111=>1111100
[2,6,5,7,4,3,8,1]=>0010111=>1110100
[2,5,6,7,4,3,8,1]=>0010011=>1100100
[2,4,6,7,5,3,8,1]=>0001011=>1101000
[2,5,4,7,6,3,8,1]=>0001111=>1111000
[2,4,6,5,7,3,8,1]=>0000111=>1110000
[2,5,4,6,7,3,8,1]=>0001011=>1101000
[2,4,5,6,7,3,8,1]=>0000011=>1100000
[3,2,7,6,5,4,8,1]=>0101111=>1111010
[3,2,6,7,5,4,8,1]=>0101011=>1101010
[3,2,5,7,6,4,8,1]=>0100111=>1110010
[3,2,6,5,7,4,8,1]=>0100111=>1110010
[3,2,5,6,7,4,8,1]=>0100011=>1100010
[2,3,7,6,5,4,8,1]=>0001111=>1111000
[2,3,5,7,6,4,8,1]=>0000111=>1110000
[2,3,5,6,7,4,8,1]=>0000011=>1100000
[4,3,2,7,6,5,8,1]=>0110111=>1110110
[4,3,2,6,7,5,8,1]=>0110011=>1100110
[3,4,2,7,6,5,8,1]=>0010111=>1110100
[3,4,2,6,7,5,8,1]=>0010011=>1100100
[2,4,3,7,6,5,8,1]=>0010111=>1110100
[2,4,3,6,7,5,8,1]=>0010011=>1100100
[3,2,4,7,6,5,8,1]=>0100111=>1110010
[2,3,4,7,6,5,8,1]=>0000111=>1110000
[2,3,4,6,7,5,8,1]=>0000011=>1100000
[5,4,3,2,7,6,8,1]=>0111011=>1101110
[3,5,4,2,7,6,8,1]=>0011011=>1101100
[4,3,5,2,7,6,8,1]=>0011011=>1101100
[3,4,5,2,7,6,8,1]=>0001011=>1101000
[2,5,4,3,7,6,8,1]=>0011011=>1101100
[3,2,5,4,7,6,8,1]=>0101011=>1101010
[2,3,5,4,7,6,8,1]=>0001011=>1101000
[4,3,2,5,7,6,8,1]=>0110011=>1100110
[3,4,2,5,7,6,8,1]=>0010011=>1100100
[2,4,3,5,7,6,8,1]=>0010011=>1100100
[3,2,4,5,7,6,8,1]=>0100011=>1100010
[2,3,4,5,7,6,8,1]=>0000011=>1100000
[3,6,5,4,2,7,8,1]=>0011101=>1011100
[3,5,6,4,2,7,8,1]=>0010101=>1010100
[3,4,6,5,2,7,8,1]=>0001101=>1011000
[3,5,4,6,2,7,8,1]=>0001101=>1011000
[2,6,5,4,3,7,8,1]=>0011101=>1011100
[2,5,6,4,3,7,8,1]=>0010101=>1010100
[2,4,6,5,3,7,8,1]=>0001101=>1011000
[2,5,4,6,3,7,8,1]=>0001101=>1011000
[2,4,5,6,3,7,8,1]=>0000101=>1010000
[3,2,5,6,4,7,8,1]=>0100101=>1010010
[2,3,6,5,4,7,8,1]=>0001101=>1011000
[2,3,5,6,4,7,8,1]=>0000101=>1010000
[4,3,2,6,5,7,8,1]=>0110101=>1010110
[3,4,2,6,5,7,8,1]=>0010101=>1010100
[2,4,3,6,5,7,8,1]=>0010101=>1010100
[2,3,4,6,5,7,8,1]=>0000101=>1010000
[3,5,4,2,6,7,8,1]=>0011001=>1001100
[2,5,4,3,6,7,8,1]=>0011001=>1001100
[2,4,5,3,6,7,8,1]=>0001001=>1001000
[3,2,5,4,6,7,8,1]=>0101001=>1001010
[2,3,5,4,6,7,8,1]=>0001001=>1001000
[2,4,3,5,6,7,8,1]=>0010001=>1000100
[1,8,7,6,5,4,3,2]=>0111111=>1111110
[1,7,8,6,5,4,3,2]=>0111101=>1011110
[1,6,8,7,5,4,3,2]=>0111011=>1101110
[1,7,6,8,5,4,3,2]=>0111011=>1101110
[1,6,7,8,5,4,3,2]=>0111001=>1001110
[1,5,8,7,6,4,3,2]=>0110111=>1110110
[1,6,5,8,7,4,3,2]=>0110111=>1110110
[1,7,6,5,8,4,3,2]=>0110111=>1110110
[1,6,7,5,8,4,3,2]=>0110011=>1100110
[1,5,7,6,8,4,3,2]=>0110011=>1100110
[1,6,5,7,8,4,3,2]=>0110101=>1010110
[1,5,6,7,8,4,3,2]=>0110001=>1000110
[1,4,8,7,6,5,3,2]=>0101111=>1111010
[1,4,7,8,6,5,3,2]=>0101101=>1011010
[1,4,6,8,7,5,3,2]=>0101011=>1101010
[1,4,6,7,8,5,3,2]=>0101001=>1001010
[1,5,4,7,8,6,3,2]=>0101101=>1011010
[1,4,5,8,7,6,3,2]=>0100111=>1110010
[1,4,5,7,8,6,3,2]=>0100101=>1010010
[1,6,5,4,8,7,3,2]=>0101111=>1111010
[1,4,6,5,8,7,3,2]=>0100111=>1110010
[1,5,4,6,8,7,3,2]=>0101011=>1101010
[1,7,6,5,4,8,3,2]=>0101111=>1111010
[1,4,7,6,5,8,3,2]=>0100111=>1110010
[1,4,6,7,5,8,3,2]=>0100011=>1100010
[1,6,5,4,7,8,3,2]=>0101101=>1011010
[1,5,6,4,7,8,3,2]=>0100101=>1010010
[1,5,4,6,7,8,3,2]=>0101001=>1001010
[1,4,5,6,7,8,3,2]=>0100001=>1000010
[1,3,8,7,6,5,4,2]=>0011111=>1111100
[1,3,7,8,6,5,4,2]=>0011101=>1011100
[1,3,6,8,7,5,4,2]=>0011011=>1101100
[1,3,6,7,8,5,4,2]=>0011001=>1001100
[1,3,5,8,7,6,4,2]=>0010111=>1110100
[1,3,5,7,8,6,4,2]=>0010101=>1010100
[1,3,5,6,8,7,4,2]=>0010011=>1100100
[1,3,6,7,5,8,4,2]=>0010011=>1100100
[1,3,5,7,6,8,4,2]=>0010011=>1100100
[1,3,6,5,7,8,4,2]=>0010101=>1010100
[1,3,5,6,7,8,4,2]=>0010001=>1000100
[1,4,3,8,7,6,5,2]=>0011111=>1111100
[1,4,3,7,8,6,5,2]=>0011101=>1011100
[1,4,3,6,8,7,5,2]=>0011011=>1101100
[1,4,3,7,6,8,5,2]=>0011011=>1101100
[1,4,3,6,7,8,5,2]=>0011001=>1001100
[1,3,4,8,7,6,5,2]=>0001111=>1111000
[1,3,4,7,6,8,5,2]=>0001011=>1101000
[1,3,4,6,7,8,5,2]=>0001001=>1001000
[1,5,4,3,8,7,6,2]=>0011111=>1111100
[1,4,5,3,8,7,6,2]=>0001111=>1111000
[1,4,5,3,7,8,6,2]=>0001101=>1011000
[1,3,5,4,8,7,6,2]=>0001111=>1111000
[1,3,5,4,7,8,6,2]=>0001101=>1011000
[1,4,3,5,8,7,6,2]=>0010111=>1110100
[1,4,3,5,7,8,6,2]=>0010101=>1010100
[1,3,4,5,8,7,6,2]=>0000111=>1110000
[1,3,4,5,7,8,6,2]=>0000101=>1010000
[1,6,5,4,3,8,7,2]=>0011111=>1111100
[1,5,6,4,3,8,7,2]=>0010111=>1110100
[1,4,6,5,3,8,7,2]=>0001111=>1111000
[1,4,5,6,3,8,7,2]=>0000111=>1110000
[1,3,6,5,4,8,7,2]=>0001111=>1111000
[1,4,3,6,5,8,7,2]=>0010111=>1110100
[1,5,4,3,6,8,7,2]=>0011011=>1101100
[1,4,5,3,6,8,7,2]=>0001011=>1101000
[1,3,4,5,6,8,7,2]=>0000011=>1100000
[1,7,6,5,4,3,8,2]=>0011111=>1111100
[1,6,7,5,4,3,8,2]=>0011011=>1101100
[1,6,5,7,4,3,8,2]=>0010111=>1110100
[1,5,6,7,4,3,8,2]=>0010011=>1100100
[1,4,6,7,5,3,8,2]=>0001011=>1101000
[1,5,6,4,7,3,8,2]=>0000111=>1110000
[1,4,6,5,7,3,8,2]=>0000111=>1110000
[1,5,4,6,7,3,8,2]=>0001011=>1101000
[1,4,5,6,7,3,8,2]=>0000011=>1100000
[1,3,5,7,6,4,8,2]=>0000111=>1110000
[1,3,6,5,7,4,8,2]=>0000111=>1110000
[1,3,5,6,7,4,8,2]=>0000011=>1100000
[1,4,3,6,7,5,8,2]=>0010011=>1100100
[1,3,4,7,6,5,8,2]=>0000111=>1110000
[1,3,4,6,7,5,8,2]=>0000011=>1100000
[1,3,5,4,7,6,8,2]=>0001011=>1101000
[1,3,4,5,7,6,8,2]=>0000011=>1100000
[1,6,5,4,3,7,8,2]=>0011101=>1011100
[1,5,4,6,3,7,8,2]=>0001101=>1011000
[1,3,5,6,4,7,8,2]=>0000101=>1010000
[1,4,3,6,5,7,8,2]=>0010101=>1010100
[1,3,4,6,5,7,8,2]=>0000101=>1010000
[1,5,4,3,6,7,8,2]=>0011001=>1001100
[1,4,5,3,6,7,8,2]=>0001001=>1001000
[1,3,5,4,6,7,8,2]=>0001001=>1001000
[1,4,3,5,6,7,8,2]=>0010001=>1000100
[1,3,4,5,6,7,8,2]=>0000001=>1000000
[2,1,8,7,6,5,4,3]=>1011111=>1111101
[2,1,7,8,6,5,4,3]=>1011101=>1011101
[2,1,6,8,7,5,4,3]=>1011011=>1101101
[2,1,7,6,8,5,4,3]=>1011011=>1101101
[2,1,6,7,8,5,4,3]=>1011001=>1001101
[2,1,5,8,7,6,4,3]=>1010111=>1110101
[2,1,5,7,8,6,4,3]=>1010101=>1010101
[2,1,6,5,8,7,4,3]=>1010111=>1110101
[2,1,5,6,8,7,4,3]=>1010011=>1100101
[2,1,7,6,5,8,4,3]=>1010111=>1110101
[2,1,6,7,5,8,4,3]=>1010011=>1100101
[2,1,5,7,6,8,4,3]=>1010011=>1100101
[2,1,6,5,7,8,4,3]=>1010101=>1010101
[2,1,5,6,7,8,4,3]=>1010001=>1000101
[2,1,4,8,7,6,5,3]=>1001111=>1111001
[2,1,4,7,8,6,5,3]=>1001101=>1011001
[2,1,4,6,8,7,5,3]=>1001011=>1101001
[2,1,4,7,6,8,5,3]=>1001011=>1101001
[2,1,4,6,7,8,5,3]=>1001001=>1001001
[2,1,5,4,8,7,6,3]=>1001111=>1111001
[2,1,5,4,7,8,6,3]=>1001101=>1011001
[2,1,4,5,8,7,6,3]=>1000111=>1110001
[2,1,4,5,7,8,6,3]=>1000101=>1010001
[2,1,6,5,4,8,7,3]=>1001111=>1111001
[2,1,5,6,4,8,7,3]=>1000111=>1110001
[2,1,4,6,5,8,7,3]=>1000111=>1110001
[2,1,5,4,6,8,7,3]=>1001011=>1101001
[2,1,4,5,6,8,7,3]=>1000011=>1100001
[2,1,7,6,5,4,8,3]=>1001111=>1111001
[2,1,6,7,5,4,8,3]=>1001011=>1101001
[2,1,5,7,6,4,8,3]=>1000111=>1110001
[2,1,6,5,7,4,8,3]=>1000111=>1110001
[2,1,5,6,7,4,8,3]=>1000011=>1100001
[2,1,4,7,6,5,8,3]=>1000111=>1110001
[2,1,4,6,7,5,8,3]=>1000011=>1100001
[2,1,5,4,7,6,8,3]=>1001011=>1101001
[2,1,5,6,4,7,8,3]=>1000101=>1010001
[2,1,5,4,6,7,8,3]=>1001001=>1001001
[2,1,4,5,6,7,8,3]=>1000001=>1000001
[1,2,8,7,6,5,4,3]=>0011111=>1111100
[1,2,7,8,6,5,4,3]=>0011101=>1011100
[1,2,7,6,8,5,4,3]=>0011011=>1101100
[1,2,6,7,8,5,4,3]=>0011001=>1001100
[1,2,5,8,7,6,4,3]=>0010111=>1110100
[1,2,6,5,8,7,4,3]=>0010111=>1110100
[1,2,5,6,8,7,4,3]=>0010011=>1100100
[1,2,7,6,5,8,4,3]=>0010111=>1110100
[1,2,5,7,6,8,4,3]=>0010011=>1100100
[1,2,6,5,7,8,4,3]=>0010101=>1010100
[1,2,5,6,7,8,4,3]=>0010001=>1000100
[1,2,4,8,7,6,5,3]=>0001111=>1111000
[1,2,4,7,8,6,5,3]=>0001101=>1011000
[1,2,4,6,8,7,5,3]=>0001011=>1101000
[1,2,4,7,6,8,5,3]=>0001011=>1101000
[1,2,4,6,7,8,5,3]=>0001001=>1001000
[1,2,5,4,8,7,6,3]=>0001111=>1111000
[1,2,5,4,7,8,6,3]=>0001101=>1011000
[1,2,4,5,8,7,6,3]=>0000111=>1110000
[1,2,4,5,7,8,6,3]=>0000101=>1010000
[1,2,6,5,4,8,7,3]=>0001111=>1111000
[1,2,4,6,5,8,7,3]=>0000111=>1110000
[1,2,5,4,6,8,7,3]=>0001011=>1101000
[1,2,4,5,6,8,7,3]=>0000011=>1100000
[1,2,7,6,5,4,8,3]=>0001111=>1111000
[1,2,5,7,6,4,8,3]=>0000111=>1110000
[1,2,5,6,7,4,8,3]=>0000011=>1100000
[1,2,4,7,6,5,8,3]=>0000111=>1110000
[1,2,5,4,7,6,8,3]=>0001011=>1101000
[1,2,6,5,4,7,8,3]=>0001101=>1011000
[1,2,5,6,4,7,8,3]=>0000101=>1010000
[1,2,4,6,5,7,8,3]=>0000101=>1010000
[1,2,5,4,6,7,8,3]=>0001001=>1001000
[1,2,4,5,6,7,8,3]=>0000001=>1000000
[3,2,1,8,7,6,5,4]=>1101111=>1111011
[3,2,1,7,8,6,5,4]=>1101101=>1011011
[3,2,1,6,8,7,5,4]=>1101011=>1101011
[3,2,1,7,6,8,5,4]=>1101011=>1101011
[3,2,1,6,7,8,5,4]=>1101001=>1001011
[3,2,1,5,8,7,6,4]=>1100111=>1110011
[3,2,1,5,7,8,6,4]=>1100101=>1010011
[3,2,1,6,5,8,7,4]=>1100111=>1110011
[3,2,1,5,6,8,7,4]=>1100011=>1100011
[3,2,1,7,6,5,8,4]=>1100111=>1110011
[3,2,1,6,7,5,8,4]=>1100011=>1100011
[3,2,1,5,7,6,8,4]=>1100011=>1100011
[3,2,1,6,5,7,8,4]=>1100101=>1010011
[3,2,1,5,6,7,8,4]=>1100001=>1000011
[2,3,1,8,7,6,5,4]=>0101111=>1111010
[2,3,1,7,8,6,5,4]=>0101101=>1011010
[2,3,1,6,8,7,5,4]=>0101011=>1101010
[2,3,1,7,6,8,5,4]=>0101011=>1101010
[2,3,1,6,7,8,5,4]=>0101001=>1001010
[2,3,1,5,7,8,6,4]=>0100101=>1010010
[2,3,1,6,5,8,7,4]=>0100111=>1110010
[2,3,1,7,6,5,8,4]=>0100111=>1110010
[2,3,1,6,7,5,8,4]=>0100011=>1100010
[2,3,1,5,7,6,8,4]=>0100011=>1100010
[2,3,1,5,6,7,8,4]=>0100001=>1000010
[1,3,2,8,7,6,5,4]=>0101111=>1111010
[1,3,2,6,8,7,5,4]=>0101011=>1101010
[1,3,2,7,6,8,5,4]=>0101011=>1101010
[1,3,2,6,7,8,5,4]=>0101001=>1001010
[1,3,2,5,8,7,6,4]=>0100111=>1110010
[1,3,2,5,7,8,6,4]=>0100101=>1010010
[1,3,2,6,5,8,7,4]=>0100111=>1110010
[1,3,2,5,6,8,7,4]=>0100011=>1100010
[1,3,2,7,6,5,8,4]=>0100111=>1110010
[1,3,2,6,7,5,8,4]=>0100011=>1100010
[1,3,2,5,7,6,8,4]=>0100011=>1100010
[1,3,2,6,5,7,8,4]=>0100101=>1010010
[1,3,2,5,6,7,8,4]=>0100001=>1000010
[2,1,3,8,7,6,5,4]=>1001111=>1111001
[2,1,3,7,8,6,5,4]=>1001101=>1011001
[2,1,3,6,8,7,5,4]=>1001011=>1101001
[2,1,3,6,7,8,5,4]=>1001001=>1001001
[2,1,3,6,5,8,7,4]=>1000111=>1110001
[2,1,3,5,7,6,8,4]=>1000011=>1100001
[2,1,3,5,6,7,8,4]=>1000001=>1000001
[1,2,3,8,7,6,5,4]=>0001111=>1111000
[1,2,3,7,8,6,5,4]=>0001101=>1011000
[1,2,3,6,8,7,5,4]=>0001011=>1101000
[1,2,3,7,6,8,5,4]=>0001011=>1101000
[1,2,3,6,7,8,5,4]=>0001001=>1001000
[1,2,3,5,8,7,6,4]=>0000111=>1110000
[1,2,3,5,7,8,6,4]=>0000101=>1010000
[1,2,3,6,5,8,7,4]=>0000111=>1110000
[1,2,3,5,6,8,7,4]=>0000011=>1100000
[1,2,3,7,6,5,8,4]=>0000111=>1110000
[1,2,3,6,7,5,8,4]=>0000011=>1100000
[1,2,3,5,7,6,8,4]=>0000011=>1100000
[1,2,3,6,5,7,8,4]=>0000101=>1010000
[1,2,3,5,6,7,8,4]=>0000001=>1000000
[4,3,2,1,8,7,6,5]=>1110111=>1110111
[4,3,2,1,7,8,6,5]=>1110101=>1010111
[4,3,2,1,6,8,7,5]=>1110011=>1100111
[4,3,2,1,7,6,8,5]=>1110011=>1100111
[4,3,2,1,6,7,8,5]=>1110001=>1000111
[3,4,2,1,8,7,6,5]=>1010111=>1110101
[3,4,2,1,7,8,6,5]=>1010101=>1010101
[3,4,2,1,6,8,7,5]=>1010011=>1100101
[3,4,2,1,7,6,8,5]=>1010011=>1100101
[3,4,2,1,6,7,8,5]=>1010001=>1000101
[2,4,3,1,8,7,6,5]=>0110111=>1110110
[2,4,3,1,7,8,6,5]=>0110101=>1010110
[2,4,3,1,6,8,7,5]=>0110011=>1100110
[2,4,3,1,7,6,8,5]=>0110011=>1100110
[2,4,3,1,6,7,8,5]=>0110001=>1000110
[3,2,4,1,8,7,6,5]=>0110111=>1110110
[3,2,4,1,7,8,6,5]=>0110101=>1010110
[3,2,4,1,6,8,7,5]=>0110011=>1100110
[3,2,4,1,7,6,8,5]=>0110011=>1100110
[3,2,4,1,6,7,8,5]=>0110001=>1000110
[2,3,4,1,8,7,6,5]=>0010111=>1110100
[2,3,4,1,7,8,6,5]=>0010101=>1010100
[2,3,4,1,6,8,7,5]=>0010011=>1100100
[2,3,4,1,7,6,8,5]=>0010011=>1100100
[2,3,4,1,6,7,8,5]=>0010001=>1000100
[1,4,3,2,8,7,6,5]=>0110111=>1110110
[1,4,3,2,6,8,7,5]=>0110011=>1100110
[1,4,3,2,7,6,8,5]=>0110011=>1100110
[1,4,3,2,6,7,8,5]=>0110001=>1000110
[1,3,4,2,8,7,6,5]=>0010111=>1110100
[1,3,4,2,7,8,6,5]=>0010101=>1010100
[1,3,4,2,6,8,7,5]=>0010011=>1100100
[1,3,4,2,7,6,8,5]=>0010011=>1100100
[1,3,4,2,6,7,8,5]=>0010001=>1000100
[2,1,4,3,8,7,6,5]=>1010111=>1110101
[2,1,4,3,7,8,6,5]=>1010101=>1010101
[2,1,4,3,6,8,7,5]=>1010011=>1100101
[2,1,4,3,7,6,8,5]=>1010011=>1100101
[2,1,4,3,6,7,8,5]=>1010001=>1000101
[1,2,4,3,8,7,6,5]=>0010111=>1110100
[1,2,4,3,7,8,6,5]=>0010101=>1010100
[1,2,4,3,6,8,7,5]=>0010011=>1100100
[1,2,4,3,7,6,8,5]=>0010011=>1100100
[1,2,4,3,6,7,8,5]=>0010001=>1000100
[3,2,1,4,8,7,6,5]=>1100111=>1110011
[3,2,1,4,7,8,6,5]=>1100101=>1010011
[3,2,1,4,6,8,7,5]=>1100011=>1100011
[3,2,1,4,7,6,8,5]=>1100011=>1100011
[3,2,1,4,6,7,8,5]=>1100001=>1000011
[2,3,1,4,8,7,6,5]=>0100111=>1110010
[2,3,1,4,7,8,6,5]=>0100101=>1010010
[2,3,1,4,7,6,8,5]=>0100011=>1100010
[2,3,1,4,6,7,8,5]=>0100001=>1000010
[1,3,2,4,8,7,6,5]=>0100111=>1110010
[1,3,2,4,6,8,7,5]=>0100011=>1100010
[1,3,2,4,7,6,8,5]=>0100011=>1100010
[1,3,2,4,6,7,8,5]=>0100001=>1000010
[2,1,3,4,8,7,6,5]=>1000111=>1110001
[2,1,3,4,7,8,6,5]=>1000101=>1010001
[2,1,3,4,7,6,8,5]=>1000011=>1100001
[2,1,3,4,6,7,8,5]=>1000001=>1000001
[1,2,3,4,8,7,6,5]=>0000111=>1110000
[1,2,3,4,7,8,6,5]=>0000101=>1010000
[1,2,3,4,6,8,7,5]=>0000011=>1100000
[1,2,3,4,7,6,8,5]=>0000011=>1100000
[1,2,3,4,6,7,8,5]=>0000001=>1000000
[5,4,3,2,1,8,7,6]=>1111011=>1101111
[5,4,3,2,1,7,8,6]=>1111001=>1001111
[4,5,3,2,1,8,7,6]=>1101011=>1101011
[3,5,4,2,1,8,7,6]=>1011011=>1101101
[3,5,4,2,1,7,8,6]=>1011001=>1001101
[4,3,5,2,1,8,7,6]=>1011011=>1101101
[3,4,5,2,1,8,7,6]=>1001011=>1101001
[3,4,5,2,1,7,8,6]=>1001001=>1001001
[2,5,4,3,1,8,7,6]=>0111011=>1101110
[2,5,4,3,1,7,8,6]=>0111001=>1001110
[2,4,5,3,1,8,7,6]=>0101011=>1101010
[2,4,5,3,1,7,8,6]=>0101001=>1001010
[3,2,5,4,1,8,7,6]=>0111011=>1101110
[3,2,5,4,1,7,8,6]=>0111001=>1001110
[2,3,5,4,1,8,7,6]=>0011011=>1101100
[4,3,2,5,1,8,7,6]=>0111011=>1101110
[4,3,2,5,1,7,8,6]=>0111001=>1001110
[3,4,2,5,1,8,7,6]=>0011011=>1101100
[3,4,2,5,1,7,8,6]=>0011001=>1001100
[2,4,3,5,1,8,7,6]=>0011011=>1101100
[2,4,3,5,1,7,8,6]=>0011001=>1001100
[3,2,4,5,1,8,7,6]=>0101011=>1101010
[2,3,4,5,1,8,7,6]=>0001011=>1101000
[2,3,4,5,1,7,8,6]=>0001001=>1001000
[1,5,4,3,2,8,7,6]=>0111011=>1101110
[1,5,4,3,2,7,8,6]=>0111001=>1001110
[1,4,5,3,2,8,7,6]=>0101011=>1101010
[1,4,5,3,2,7,8,6]=>0101001=>1001010
[1,3,5,4,2,7,8,6]=>0011001=>1001100
[1,4,3,5,2,8,7,6]=>0011011=>1101100
[1,4,3,5,2,7,8,6]=>0011001=>1001100
[1,3,4,5,2,8,7,6]=>0001011=>1101000
[1,3,4,5,2,7,8,6]=>0001001=>1001000
[2,1,5,4,3,8,7,6]=>1011011=>1101101
[2,1,4,5,3,8,7,6]=>1001011=>1101001
[1,2,5,4,3,8,7,6]=>0011011=>1101100
[1,2,5,4,3,7,8,6]=>0011001=>1001100
[1,2,4,5,3,8,7,6]=>0001011=>1101000
[1,2,4,5,3,7,8,6]=>0001001=>1001000
[1,3,2,5,4,8,7,6]=>0101011=>1101010
[1,3,2,5,4,7,8,6]=>0101001=>1001010
[2,1,3,5,4,8,7,6]=>1001011=>1101001
[2,1,3,5,4,7,8,6]=>1001001=>1001001
[1,2,3,5,4,8,7,6]=>0001011=>1101000
[1,2,3,5,4,7,8,6]=>0001001=>1001000
[4,3,2,1,5,8,7,6]=>1110011=>1100111
[4,3,2,1,5,7,8,6]=>1110001=>1000111
[3,4,2,1,5,8,7,6]=>1010011=>1100101
[2,4,3,1,5,8,7,6]=>0110011=>1100110
[3,2,4,1,5,8,7,6]=>0110011=>1100110
[3,2,4,1,5,7,8,6]=>0110001=>1000110
[2,3,4,1,5,8,7,6]=>0010011=>1100100
[2,3,4,1,5,7,8,6]=>0010001=>1000100
[1,4,3,2,5,8,7,6]=>0110011=>1100110
[1,4,3,2,5,7,8,6]=>0110001=>1000110
[1,3,4,2,5,8,7,6]=>0010011=>1100100
[1,3,4,2,5,7,8,6]=>0010001=>1000100
[2,1,4,3,5,8,7,6]=>1010011=>1100101
[2,1,4,3,5,7,8,6]=>1010001=>1000101
[1,2,4,3,5,8,7,6]=>0010011=>1100100
[1,2,4,3,5,7,8,6]=>0010001=>1000100
[3,2,1,4,5,8,7,6]=>1100011=>1100011
[3,2,1,4,5,7,8,6]=>1100001=>1000011
[2,3,1,4,5,7,8,6]=>0100001=>1000010
[1,3,2,4,5,8,7,6]=>0100011=>1100010
[1,3,2,4,5,7,8,6]=>0100001=>1000010
[2,1,3,4,5,8,7,6]=>1000011=>1100001
[2,1,3,4,5,7,8,6]=>1000001=>1000001
[1,2,3,4,5,8,7,6]=>0000011=>1100000
[1,2,3,4,5,7,8,6]=>0000001=>1000000
[6,5,4,3,2,1,8,7]=>1111101=>1011111
[5,6,4,3,2,1,8,7]=>1110101=>1010111
[4,6,5,3,2,1,8,7]=>1101101=>1011011
[5,4,6,3,2,1,8,7]=>1101101=>1011011
[4,5,6,3,2,1,8,7]=>1100101=>1010011
[3,6,5,4,2,1,8,7]=>1011101=>1011101
[3,5,6,4,2,1,8,7]=>1010101=>1010101
[4,3,6,5,2,1,8,7]=>1011101=>1011101
[3,4,6,5,2,1,8,7]=>1001101=>1011001
[5,4,3,6,2,1,8,7]=>1011101=>1011101
[4,5,3,6,2,1,8,7]=>1001101=>1011001
[4,3,5,6,2,1,8,7]=>1010101=>1010101
[3,4,5,6,2,1,8,7]=>1000101=>1010001
[2,6,5,4,3,1,8,7]=>0111101=>1011110
[2,5,6,4,3,1,8,7]=>0110101=>1010110
[2,4,6,5,3,1,8,7]=>0101101=>1011010
[3,2,6,5,4,1,8,7]=>0111101=>1011110
[3,2,5,6,4,1,8,7]=>0110101=>1010110
[2,3,6,5,4,1,8,7]=>0011101=>1011100
[2,3,5,6,4,1,8,7]=>0010101=>1010100
[4,3,2,6,5,1,8,7]=>0111101=>1011110
[3,4,2,6,5,1,8,7]=>0011101=>1011100
[2,4,3,6,5,1,8,7]=>0011101=>1011100
[5,4,3,2,6,1,8,7]=>0111101=>1011110
[4,5,3,2,6,1,8,7]=>0101101=>1011010
[3,5,4,2,6,1,8,7]=>0011101=>1011100
[4,3,5,2,6,1,8,7]=>0011101=>1011100
[3,4,5,2,6,1,8,7]=>0001101=>1011000
[2,5,4,3,6,1,8,7]=>0011101=>1011100
[2,4,5,3,6,1,8,7]=>0001101=>1011000
[3,2,5,4,6,1,8,7]=>0101101=>1011010
[4,3,2,5,6,1,8,7]=>0110101=>1010110
[3,4,2,5,6,1,8,7]=>0010101=>1010100
[2,4,3,5,6,1,8,7]=>0010101=>1010100
[2,3,4,5,6,1,8,7]=>0000101=>1010000
[1,6,5,4,3,2,8,7]=>0111101=>1011110
[1,5,6,4,3,2,8,7]=>0110101=>1010110
[1,5,4,6,3,2,8,7]=>0101101=>1011010
[1,3,6,5,4,2,8,7]=>0011101=>1011100
[1,3,4,5,6,2,8,7]=>0000101=>1010000
[2,1,6,5,4,3,8,7]=>1011101=>1011101
[2,1,5,6,4,3,8,7]=>1010101=>1010101
[2,1,4,6,5,3,8,7]=>1001101=>1011001
[2,1,5,4,6,3,8,7]=>1001101=>1011001
[2,1,4,5,6,3,8,7]=>1000101=>1010001
[1,2,4,5,6,3,8,7]=>0000101=>1010000
[3,2,1,6,5,4,8,7]=>1101101=>1011011
[2,3,1,6,5,4,8,7]=>0101101=>1011010
[1,3,2,6,5,4,8,7]=>0101101=>1011010
[1,3,2,5,6,4,8,7]=>0100101=>1010010
[2,1,3,6,5,4,8,7]=>1001101=>1011001
[2,1,3,5,6,4,8,7]=>1000101=>1010001
[1,2,3,6,5,4,8,7]=>0001101=>1011000
[1,2,3,5,6,4,8,7]=>0000101=>1010000
[4,3,2,1,6,5,8,7]=>1110101=>1010111
[3,4,2,1,6,5,8,7]=>1010101=>1010101
[2,4,3,1,6,5,8,7]=>0110101=>1010110
[3,2,4,1,6,5,8,7]=>0110101=>1010110
[2,3,4,1,6,5,8,7]=>0010101=>1010100
[1,3,4,2,6,5,8,7]=>0010101=>1010100
[2,1,4,3,6,5,8,7]=>1010101=>1010101
[1,2,4,3,6,5,8,7]=>0010101=>1010100
[2,3,1,4,6,5,8,7]=>0100101=>1010010
[1,3,2,4,6,5,8,7]=>0100101=>1010010
[2,1,3,4,6,5,8,7]=>1000101=>1010001
[1,2,3,4,6,5,8,7]=>0000101=>1010000
[5,4,3,2,1,6,8,7]=>1111001=>1001111
[4,5,3,2,1,6,8,7]=>1101001=>1001011
[3,5,4,2,1,6,8,7]=>1011001=>1001101
[4,3,5,2,1,6,8,7]=>1011001=>1001101
[3,4,5,2,1,6,8,7]=>1001001=>1001001
[2,5,4,3,1,6,8,7]=>0111001=>1001110
[2,4,5,3,1,6,8,7]=>0101001=>1001010
[3,2,5,4,1,6,8,7]=>0111001=>1001110
[2,3,5,4,1,6,8,7]=>0011001=>1001100
[2,4,3,5,1,6,8,7]=>0011001=>1001100
[2,3,4,5,1,6,8,7]=>0001001=>1001000
[1,4,5,3,2,6,8,7]=>0101001=>1001010
[1,3,5,4,2,6,8,7]=>0011001=>1001100
[1,3,4,5,2,6,8,7]=>0001001=>1001000
[2,1,5,4,3,6,8,7]=>1011001=>1001101
[2,1,4,5,3,6,8,7]=>1001001=>1001001
[1,2,5,4,3,6,8,7]=>0011001=>1001100
[2,1,3,5,4,6,8,7]=>1001001=>1001001
[1,2,3,5,4,6,8,7]=>0001001=>1001000
[4,3,2,1,5,6,8,7]=>1110001=>1000111
[3,4,2,1,5,6,8,7]=>1010001=>1000101
[3,2,4,1,5,6,8,7]=>0110001=>1000110
[2,3,4,1,5,6,8,7]=>0010001=>1000100
[1,4,3,2,5,6,8,7]=>0110001=>1000110
[1,3,4,2,5,6,8,7]=>0010001=>1000100
[2,1,4,3,5,6,8,7]=>1010001=>1000101
[1,2,4,3,5,6,8,7]=>0010001=>1000100
[3,2,1,4,5,6,8,7]=>1100001=>1000011
[2,3,1,4,5,6,8,7]=>0100001=>1000010
[1,3,2,4,5,6,8,7]=>0100001=>1000010
[2,1,3,4,5,6,8,7]=>1000001=>1000001
[1,2,3,4,5,6,8,7]=>0000001=>1000000
[5,7,6,4,3,2,1,8]=>1110110=>0110111
[4,7,6,5,3,2,1,8]=>1101110=>0111011
[4,6,7,5,3,2,1,8]=>1101010=>0101011
[5,4,7,6,3,2,1,8]=>1101110=>0111011
[4,5,7,6,3,2,1,8]=>1100110=>0110011
[4,6,5,7,3,2,1,8]=>1100110=>0110011
[3,5,7,6,4,2,1,8]=>1010110=>0110101
[3,5,6,7,4,2,1,8]=>1010010=>0100101
[4,3,7,6,5,2,1,8]=>1011110=>0111101
[3,4,7,6,5,2,1,8]=>1001110=>0111001
[5,4,3,7,6,2,1,8]=>1011110=>0111101
[4,5,3,7,6,2,1,8]=>1001110=>0111001
[3,5,4,7,6,2,1,8]=>1001110=>0111001
[4,3,5,7,6,2,1,8]=>1010110=>0110101
[3,6,5,4,7,2,1,8]=>1001110=>0111001
[3,5,6,4,7,2,1,8]=>1000110=>0110001
[4,3,6,5,7,2,1,8]=>1010110=>0110101
[2,7,6,5,4,3,1,8]=>0111110=>0111110
[2,6,7,5,4,3,1,8]=>0111010=>0101110
[2,5,7,6,4,3,1,8]=>0110110=>0110110
[2,5,6,7,4,3,1,8]=>0110010=>0100110
[2,4,6,7,5,3,1,8]=>0101010=>0101010
[2,5,4,7,6,3,1,8]=>0101110=>0111010
[2,5,6,4,7,3,1,8]=>0100110=>0110010
[2,5,4,6,7,3,1,8]=>0101010=>0101010
[2,4,5,6,7,3,1,8]=>0100010=>0100010
[3,2,7,6,5,4,1,8]=>0111110=>0111110
[3,2,6,7,5,4,1,8]=>0111010=>0101110
[3,2,5,7,6,4,1,8]=>0110110=>0110110
[3,2,6,5,7,4,1,8]=>0110110=>0110110
[3,2,5,6,7,4,1,8]=>0110010=>0100110
[2,3,7,6,5,4,1,8]=>0011110=>0111100
[2,3,6,7,5,4,1,8]=>0011010=>0101100
[2,3,5,7,6,4,1,8]=>0010110=>0110100
[2,3,6,5,7,4,1,8]=>0010110=>0110100
[2,3,5,6,7,4,1,8]=>0010010=>0100100
[4,3,2,6,7,5,1,8]=>0111010=>0101110
[3,4,2,7,6,5,1,8]=>0011110=>0111100
[3,4,2,6,7,5,1,8]=>0011010=>0101100
[3,2,4,6,7,5,1,8]=>0101010=>0101010
[2,3,4,7,6,5,1,8]=>0001110=>0111000
[2,3,4,6,7,5,1,8]=>0001010=>0101000
[5,4,3,2,7,6,1,8]=>0111110=>0111110
[4,5,3,2,7,6,1,8]=>0101110=>0111010
[3,5,4,2,7,6,1,8]=>0011110=>0111100
[4,3,5,2,7,6,1,8]=>0011110=>0111100
[3,4,5,2,7,6,1,8]=>0001110=>0111000
[3,2,5,4,7,6,1,8]=>0101110=>0111010
[4,3,2,5,7,6,1,8]=>0110110=>0110110
[3,4,2,5,7,6,1,8]=>0010110=>0110100
[2,3,4,5,7,6,1,8]=>0000110=>0110000
[3,6,5,4,2,7,1,8]=>0011110=>0111100
[3,5,6,4,2,7,1,8]=>0010110=>0110100
[3,4,6,5,2,7,1,8]=>0001110=>0111000
[3,5,4,6,2,7,1,8]=>0001110=>0111000
[2,5,4,6,3,7,1,8]=>0001110=>0111000
[3,2,6,5,4,7,1,8]=>0101110=>0111010
[2,3,5,6,4,7,1,8]=>0000110=>0110000
[4,3,2,6,5,7,1,8]=>0110110=>0110110
[3,4,2,6,5,7,1,8]=>0010110=>0110100
[2,4,3,6,5,7,1,8]=>0010110=>0110100
[2,3,4,6,5,7,1,8]=>0000110=>0110000
[3,5,4,2,6,7,1,8]=>0011010=>0101100
[2,5,4,3,6,7,1,8]=>0011010=>0101100
[2,4,5,3,6,7,1,8]=>0001010=>0101000
[2,3,5,4,6,7,1,8]=>0001010=>0101000
[1,7,6,5,4,3,2,8]=>0111110=>0111110
[1,6,7,5,4,3,2,8]=>0111010=>0101110
[1,6,5,7,4,3,2,8]=>0110110=>0110110
[1,5,6,7,4,3,2,8]=>0110010=>0100110
[1,4,7,6,5,3,2,8]=>0101110=>0111010
[1,4,6,7,5,3,2,8]=>0101010=>0101010
[1,5,4,7,6,3,2,8]=>0101110=>0111010
[1,5,6,4,7,3,2,8]=>0100110=>0110010
[1,4,6,5,7,3,2,8]=>0100110=>0110010
[1,5,4,6,7,3,2,8]=>0101010=>0101010
[1,4,5,6,7,3,2,8]=>0100010=>0100010
[1,3,7,6,5,4,2,8]=>0011110=>0111100
[1,3,6,7,5,4,2,8]=>0011010=>0101100
[1,3,5,7,6,4,2,8]=>0010110=>0110100
[1,3,6,5,7,4,2,8]=>0010110=>0110100
[1,3,5,6,7,4,2,8]=>0010010=>0100100
[1,3,4,6,7,5,2,8]=>0001010=>0101000
[1,3,5,4,7,6,2,8]=>0001110=>0111000
[1,4,3,5,7,6,2,8]=>0010110=>0110100
[1,3,4,5,7,6,2,8]=>0000110=>0110000
[1,5,4,6,3,7,2,8]=>0001110=>0111000
[1,4,5,6,3,7,2,8]=>0000110=>0110000
[1,3,6,5,4,7,2,8]=>0001110=>0111000
[1,3,5,6,4,7,2,8]=>0000110=>0110000
[1,4,3,6,5,7,2,8]=>0010110=>0110100
[1,3,4,6,5,7,2,8]=>0000110=>0110000
[1,5,4,3,6,7,2,8]=>0011010=>0101100
[1,4,5,3,6,7,2,8]=>0001010=>0101000
[1,3,5,4,6,7,2,8]=>0001010=>0101000
[1,3,4,5,6,7,2,8]=>0000010=>0100000
[2,1,7,6,5,4,3,8]=>1011110=>0111101
[2,1,6,7,5,4,3,8]=>1011010=>0101101
[2,1,5,6,7,4,3,8]=>1010010=>0100101
[2,1,4,6,7,5,3,8]=>1001010=>0101001
[2,1,5,4,6,7,3,8]=>1001010=>0101001
[2,1,4,5,6,7,3,8]=>1000010=>0100001
[1,2,7,6,5,4,3,8]=>0011110=>0111100
[1,2,6,7,5,4,3,8]=>0011010=>0101100
[1,2,5,7,6,4,3,8]=>0010110=>0110100
[1,2,5,6,7,4,3,8]=>0010010=>0100100
[1,2,4,6,7,5,3,8]=>0001010=>0101000
[1,2,5,6,4,7,3,8]=>0000110=>0110000
[1,2,5,4,6,7,3,8]=>0001010=>0101000
[1,2,4,5,6,7,3,8]=>0000010=>0100000
[3,2,1,7,6,5,4,8]=>1101110=>0111011
[3,2,1,6,7,5,4,8]=>1101010=>0101011
[3,2,1,5,7,6,4,8]=>1100110=>0110011
[3,2,1,6,5,7,4,8]=>1100110=>0110011
[3,2,1,5,6,7,4,8]=>1100010=>0100011
[2,3,1,6,7,5,4,8]=>0101010=>0101010
[2,3,1,6,5,7,4,8]=>0100110=>0110010
[2,3,1,5,6,7,4,8]=>0100010=>0100010
[1,3,2,7,6,5,4,8]=>0101110=>0111010
[1,3,2,6,7,5,4,8]=>0101010=>0101010
[1,3,2,5,7,6,4,8]=>0100110=>0110010
[1,3,2,6,5,7,4,8]=>0100110=>0110010
[1,3,2,5,6,7,4,8]=>0100010=>0100010
[2,1,3,6,7,5,4,8]=>1001010=>0101001
[1,2,3,7,6,5,4,8]=>0001110=>0111000
[1,2,3,6,7,5,4,8]=>0001010=>0101000
[1,2,3,5,7,6,4,8]=>0000110=>0110000
[1,2,3,6,5,7,4,8]=>0000110=>0110000
[1,2,3,5,6,7,4,8]=>0000010=>0100000
[4,3,2,1,7,6,5,8]=>1110110=>0110111
[4,3,2,1,6,7,5,8]=>1110010=>0100111
[3,2,4,1,7,6,5,8]=>0110110=>0110110
[3,2,4,1,6,7,5,8]=>0110010=>0100110
[2,3,4,1,7,6,5,8]=>0010110=>0110100
[2,3,4,1,6,7,5,8]=>0010010=>0100100
[1,4,3,2,7,6,5,8]=>0110110=>0110110
[1,4,3,2,6,7,5,8]=>0110010=>0100110
[1,3,4,2,6,7,5,8]=>0010010=>0100100
[2,1,4,3,6,7,5,8]=>1010010=>0100101
[1,2,4,3,6,7,5,8]=>0010010=>0100100
[3,2,1,4,7,6,5,8]=>1100110=>0110011
[2,3,1,4,6,7,5,8]=>0100010=>0100010
[1,3,2,4,7,6,5,8]=>0100110=>0110010
[2,1,3,4,6,7,5,8]=>1000010=>0100001
[1,2,3,4,7,6,5,8]=>0000110=>0110000
[1,2,3,4,6,7,5,8]=>0000010=>0100000
[5,4,3,2,1,7,6,8]=>1111010=>0101111
[4,5,3,2,1,7,6,8]=>1101010=>0101011
[3,5,4,2,1,7,6,8]=>1011010=>0101101
[3,4,5,2,1,7,6,8]=>1001010=>0101001
[2,5,4,3,1,7,6,8]=>0111010=>0101110
[2,4,5,3,1,7,6,8]=>0101010=>0101010
[3,2,5,4,1,7,6,8]=>0111010=>0101110
[2,3,5,4,1,7,6,8]=>0011010=>0101100
[3,4,2,5,1,7,6,8]=>0011010=>0101100
[2,4,3,5,1,7,6,8]=>0011010=>0101100
[2,3,4,5,1,7,6,8]=>0001010=>0101000
[1,5,4,3,2,7,6,8]=>0111010=>0101110
[1,4,5,3,2,7,6,8]=>0101010=>0101010
[1,3,5,4,2,7,6,8]=>0011010=>0101100
[1,4,3,5,2,7,6,8]=>0011010=>0101100
[1,3,4,5,2,7,6,8]=>0001010=>0101000
[2,1,5,4,3,7,6,8]=>1011010=>0101101
[1,2,4,5,3,7,6,8]=>0001010=>0101000
[3,2,1,5,4,7,6,8]=>1101010=>0101011
[2,3,1,5,4,7,6,8]=>0101010=>0101010
[1,3,2,5,4,7,6,8]=>0101010=>0101010
[1,2,3,5,4,7,6,8]=>0001010=>0101000
[4,3,2,1,5,7,6,8]=>1110010=>0100111
[3,2,4,1,5,7,6,8]=>0110010=>0100110
[2,3,4,1,5,7,6,8]=>0010010=>0100100
[1,4,3,2,5,7,6,8]=>0110010=>0100110
[1,3,4,2,5,7,6,8]=>0010010=>0100100
[1,2,4,3,5,7,6,8]=>0010010=>0100100
[3,2,1,4,5,7,6,8]=>1100010=>0100011
[2,3,1,4,5,7,6,8]=>0100010=>0100010
[1,3,2,4,5,7,6,8]=>0100010=>0100010
[2,1,3,4,5,7,6,8]=>1000010=>0100001
[1,2,3,4,5,7,6,8]=>0000010=>0100000
[3,6,5,4,2,1,7,8]=>1011100=>0011101
[4,3,6,5,2,1,7,8]=>1011100=>0011101
[2,4,6,5,3,1,7,8]=>0101100=>0011010
[2,4,5,6,3,1,7,8]=>0100100=>0010010
[2,3,6,5,4,1,7,8]=>0011100=>0011100
[2,3,5,6,4,1,7,8]=>0010100=>0010100
[4,3,2,6,5,1,7,8]=>0111100=>0011110
[2,4,3,6,5,1,7,8]=>0011100=>0011100
[2,3,4,6,5,1,7,8]=>0001100=>0011000
[3,5,4,2,6,1,7,8]=>0011100=>0011100
[2,3,5,4,6,1,7,8]=>0001100=>0011000
[1,6,5,4,3,2,7,8]=>0111100=>0011110
[1,5,6,4,3,2,7,8]=>0110100=>0010110
[1,4,6,5,3,2,7,8]=>0101100=>0011010
[1,5,4,6,3,2,7,8]=>0101100=>0011010
[1,4,5,6,3,2,7,8]=>0100100=>0010010
[1,3,5,6,4,2,7,8]=>0010100=>0010100
[1,4,3,6,5,2,7,8]=>0011100=>0011100
[1,5,4,3,6,2,7,8]=>0011100=>0011100
[1,4,5,3,6,2,7,8]=>0001100=>0011000
[1,3,5,4,6,2,7,8]=>0001100=>0011000
[1,4,3,5,6,2,7,8]=>0010100=>0010100
[1,3,4,5,6,2,7,8]=>0000100=>0010000
[2,1,5,6,4,3,7,8]=>1010100=>0010101
[2,1,4,6,5,3,7,8]=>1001100=>0011001
[1,2,6,5,4,3,7,8]=>0011100=>0011100
[1,2,5,6,4,3,7,8]=>0010100=>0010100
[1,2,4,6,5,3,7,8]=>0001100=>0011000
[1,2,4,5,6,3,7,8]=>0000100=>0010000
[3,2,1,6,5,4,7,8]=>1101100=>0011011
[3,2,1,5,6,4,7,8]=>1100100=>0010011
[2,3,1,6,5,4,7,8]=>0101100=>0011010
[2,3,1,5,6,4,7,8]=>0100100=>0010010
[1,3,2,6,5,4,7,8]=>0101100=>0011010
[1,3,2,5,6,4,7,8]=>0100100=>0010010
[1,2,3,6,5,4,7,8]=>0001100=>0011000
[1,2,3,5,6,4,7,8]=>0000100=>0010000
[4,3,2,1,6,5,7,8]=>1110100=>0010111
[2,4,3,1,6,5,7,8]=>0110100=>0010110
[3,2,4,1,6,5,7,8]=>0110100=>0010110
[2,3,4,1,6,5,7,8]=>0010100=>0010100
[2,1,4,3,6,5,7,8]=>1010100=>0010101
[1,2,4,3,6,5,7,8]=>0010100=>0010100
[1,3,2,4,6,5,7,8]=>0100100=>0010010
[2,1,3,4,6,5,7,8]=>1000100=>0010001
[1,2,3,4,6,5,7,8]=>0000100=>0010000
[3,5,4,2,1,6,7,8]=>1011000=>0001101
[2,5,4,3,1,6,7,8]=>0111000=>0001110
[2,4,5,3,1,6,7,8]=>0101000=>0001010
[3,2,5,4,1,6,7,8]=>0111000=>0001110
[2,3,5,4,1,6,7,8]=>0011000=>0001100
[2,4,3,5,1,6,7,8]=>0011000=>0001100
[1,5,4,3,2,6,7,8]=>0111000=>0001110
[1,4,5,3,2,6,7,8]=>0101000=>0001010
[1,3,5,4,2,6,7,8]=>0011000=>0001100
[1,3,4,5,2,6,7,8]=>0001000=>0001000
[2,1,5,4,3,6,7,8]=>1011000=>0001101
[2,1,4,5,3,6,7,8]=>1001000=>0001001
[1,2,5,4,3,6,7,8]=>0011000=>0001100
[3,2,1,5,4,6,7,8]=>1101000=>0001011
[2,3,1,5,4,6,7,8]=>0101000=>0001010
[1,3,2,5,4,6,7,8]=>0101000=>0001010
[2,1,3,5,4,6,7,8]=>1001000=>0001001
[1,2,3,5,4,6,7,8]=>0001000=>0001000
[2,4,3,1,5,6,7,8]=>0110000=>0000110
[1,4,3,2,5,6,7,8]=>0110000=>0000110
[1,3,4,2,5,6,7,8]=>0010000=>0000100
[2,1,4,3,5,6,7,8]=>1010000=>0000101
[1,2,4,3,5,6,7,8]=>0010000=>0000100
[1,3,2,4,5,6,7,8]=>0100000=>0000010
[1,2,3,4,8,6,7,5]=>0000011=>1100000
[1,2,3,5,8,6,7,4]=>0000011=>1100000
[1,2,3,7,5,6,4,8]=>0000110=>0110000
[1,2,3,7,5,6,8,4]=>0000011=>1100000
[1,2,3,8,5,6,7,4]=>0000011=>1100000
[1,2,3,8,5,7,6,4]=>0000111=>1110000
[1,2,3,8,6,5,7,4]=>0000111=>1110000
[1,2,3,8,6,7,5,4]=>0001011=>1101000
[1,2,4,3,8,6,7,5]=>0010011=>1100100
[1,2,4,5,8,6,7,3]=>0000011=>1100000
[1,2,4,7,5,6,8,3]=>0000011=>1100000
[1,2,4,8,5,6,7,3]=>0000011=>1100000
[1,2,4,8,6,5,7,3]=>0000111=>1110000
[1,2,5,4,8,6,7,3]=>0001011=>1101000
[1,2,6,4,5,3,7,8]=>0001100=>0011000
[1,2,6,4,5,7,8,3]=>0000101=>1010000
[1,2,6,4,5,8,7,3]=>0000111=>1110000
[1,2,7,4,5,6,8,3]=>0000011=>1100000
[1,2,8,4,5,6,7,3]=>0000011=>1100000
[1,2,8,4,6,7,5,3]=>0001011=>1101000
[1,2,8,4,7,6,5,3]=>0001111=>1111000
[1,2,7,5,4,6,3,8]=>0001110=>0111000
[1,2,7,5,4,6,8,3]=>0001011=>1101000
[1,2,8,5,4,6,7,3]=>0001011=>1101000
[1,2,8,5,4,7,6,3]=>0001111=>1111000
[1,2,8,5,6,4,7,3]=>0000111=>1110000
[1,2,8,5,6,7,4,3]=>0010011=>1100100
[1,2,8,6,5,4,7,3]=>0001111=>1111000
[1,2,8,6,5,7,4,3]=>0010111=>1110100
[1,2,8,7,5,6,4,3]=>0010111=>1110100
[1,3,2,4,8,6,7,5]=>0100011=>1100010
[1,3,2,7,5,6,8,4]=>0100011=>1100010
[1,3,2,8,5,7,6,4]=>0100111=>1110010
[1,3,2,8,6,5,7,4]=>0100111=>1110010
[1,3,2,8,6,7,5,4]=>0101011=>1101010
[1,3,4,2,8,6,7,5]=>0010011=>1100100
[1,3,4,5,8,6,7,2]=>0000011=>1100000
[1,3,4,8,5,6,7,2]=>0000011=>1100000
[1,3,4,8,6,5,7,2]=>0000111=>1110000
[1,3,4,8,6,7,5,2]=>0001011=>1101000
[1,3,6,4,5,2,8,7]=>0001101=>1011000
[1,3,6,4,5,7,2,8]=>0000110=>0110000
[1,3,6,4,5,7,8,2]=>0000101=>1010000
[1,3,6,4,5,8,7,2]=>0000111=>1110000
[1,3,7,4,5,6,2,8]=>0000110=>0110000
[1,3,7,4,5,6,8,2]=>0000011=>1100000
[1,3,8,4,5,6,7,2]=>0000011=>1100000
[1,3,8,4,6,5,7,2]=>0000111=>1110000
[1,3,8,4,6,7,5,2]=>0001011=>1101000
[1,3,8,5,4,6,7,2]=>0001011=>1101000
[1,3,8,5,4,7,6,2]=>0001111=>1111000
[1,3,8,5,6,7,4,2]=>0010011=>1100100
[1,3,8,5,7,6,4,2]=>0010111=>1110100
[1,3,8,6,5,7,4,2]=>0010111=>1110100
[1,3,8,7,5,6,4,2]=>0010111=>1110100
[1,4,3,2,8,6,7,5]=>0110011=>1100110
[1,4,3,5,8,6,7,2]=>0010011=>1100100
[1,4,3,8,5,6,7,2]=>0010011=>1100100
[1,4,3,8,5,7,6,2]=>0010111=>1110100
[1,4,3,8,6,5,7,2]=>0010111=>1110100
[1,4,3,8,6,7,5,2]=>0011011=>1101100
[1,5,3,4,2,6,7,8]=>0011000=>0001100
[1,5,3,4,2,7,8,6]=>0011001=>1001100
[1,5,3,4,2,8,7,6]=>0011011=>1101100
[1,5,3,4,6,2,7,8]=>0001100=>0011000
[1,5,3,4,6,2,8,7]=>0001101=>1011000
[1,5,3,4,6,7,2,8]=>0001010=>0101000
[1,5,3,4,6,7,8,2]=>0001001=>1001000
[1,5,3,4,7,6,2,8]=>0001110=>0111000
[1,5,3,4,8,6,7,2]=>0001011=>1101000
[1,6,3,4,5,2,7,8]=>0001100=>0011000
[1,6,3,4,5,8,7,2]=>0000111=>1110000
[1,7,3,4,5,6,2,8]=>0000110=>0110000
[1,7,3,4,5,6,8,2]=>0000011=>1100000
[1,8,3,4,5,6,7,2]=>0000011=>1100000
[1,8,3,4,6,7,5,2]=>0001011=>1101000
[1,8,3,4,7,6,5,2]=>0001111=>1111000
[1,6,3,5,4,2,7,8]=>0011100=>0011100
[1,6,3,5,4,8,7,2]=>0001111=>1111000
[1,7,3,5,4,6,2,8]=>0001110=>0111000
[1,8,3,5,4,6,7,2]=>0001011=>1101000
[1,8,3,5,4,7,6,2]=>0001111=>1111000
[1,8,3,5,6,4,7,2]=>0000111=>1110000
[1,8,3,5,6,7,4,2]=>0010011=>1100100
[1,8,3,5,7,6,4,2]=>0010111=>1110100
[1,7,3,6,5,4,2,8]=>0011110=>0111100
[1,7,3,6,5,4,8,2]=>0001111=>1111000
[1,8,3,6,5,4,7,2]=>0001111=>1111000
[1,8,3,7,5,6,4,2]=>0010111=>1110100
[1,8,3,7,6,5,4,2]=>0011111=>1111100
[1,6,4,3,5,2,7,8]=>0011100=>0011100
[1,6,4,3,5,8,7,2]=>0010111=>1110100
[1,8,4,3,5,6,7,2]=>0010011=>1100100
[1,8,4,3,5,7,6,2]=>0010111=>1110100
[1,7,4,3,6,5,8,2]=>0010111=>1110100
[1,8,4,3,6,5,7,2]=>0010111=>1110100
[1,8,4,3,6,7,5,2]=>0011011=>1101100
[1,6,4,5,3,2,7,8]=>0101100=>0011010
[1,6,4,5,3,2,8,7]=>0101101=>1011010
[1,6,4,5,3,8,7,2]=>0001111=>1111000
[1,7,4,5,3,6,8,2]=>0001011=>1101000
[1,8,4,5,3,6,7,2]=>0001011=>1101000
[1,7,4,5,6,3,2,8]=>0100110=>0110010
[1,7,4,5,6,3,8,2]=>0000111=>1110000
[1,8,4,5,6,3,7,2]=>0000111=>1110000
[1,8,4,5,6,7,3,2]=>0100011=>1100010
[1,7,4,6,5,3,2,8]=>0101110=>0111010
[1,8,4,6,5,3,7,2]=>0001111=>1111000
[1,8,4,6,5,7,3,2]=>0100111=>1110010
[1,8,4,7,6,5,3,2]=>0101111=>1111010
[1,7,5,4,3,6,2,8]=>0011110=>0111100
[1,7,5,4,3,6,8,2]=>0011011=>1101100
[1,8,5,4,3,6,7,2]=>0011011=>1101100
[1,8,5,4,3,7,6,2]=>0011111=>1111100
[1,8,5,4,6,3,7,2]=>0001111=>1111000
[1,8,5,4,6,7,3,2]=>0101011=>1101010
[1,8,5,4,7,6,3,2]=>0101111=>1111010
[1,7,6,4,5,3,2,8]=>0101110=>0111010
[1,8,6,4,5,3,7,2]=>0001111=>1111000
[1,8,6,4,5,7,3,2]=>0100111=>1110010
[1,8,7,4,5,6,3,2]=>0100111=>1110010
[1,8,7,4,6,5,3,2]=>0101111=>1111010
[1,8,6,5,4,3,7,2]=>0011111=>1111100
[1,8,6,5,4,7,3,2]=>0101111=>1111010
[1,8,7,5,4,6,3,2]=>0101111=>1111010
[1,8,7,5,6,4,3,2]=>0110111=>1110110
[2,1,3,4,8,6,7,5]=>1000011=>1100001
[2,1,3,5,8,6,7,4]=>1000011=>1100001
[2,1,3,8,5,6,7,4]=>1000011=>1100001
[2,1,3,8,5,7,6,4]=>1000111=>1110001
[2,1,3,8,6,5,7,4]=>1000111=>1110001
[2,1,3,8,6,7,5,4]=>1001011=>1101001
[2,1,4,3,8,6,7,5]=>1010011=>1100101
[2,1,4,5,8,6,7,3]=>1000011=>1100001
[2,1,4,8,5,6,7,3]=>1000011=>1100001
[2,1,4,8,5,7,6,3]=>1000111=>1110001
[2,1,4,8,6,5,7,3]=>1000111=>1110001
[2,1,4,8,6,7,5,3]=>1001011=>1101001
[2,1,6,4,5,3,8,7]=>1001101=>1011001
[2,1,6,4,5,7,8,3]=>1000101=>1010001
[2,1,6,4,5,8,7,3]=>1000111=>1110001
[2,1,8,4,5,6,7,3]=>1000011=>1100001
[2,1,8,4,5,7,6,3]=>1000111=>1110001
[2,1,7,4,6,5,8,3]=>1000111=>1110001
[2,1,8,4,6,5,7,3]=>1000111=>1110001
[2,1,8,4,6,7,5,3]=>1001011=>1101001
[2,1,8,4,7,6,5,3]=>1001111=>1111001
[2,1,7,5,4,6,8,3]=>1001011=>1101001
[2,1,8,5,4,6,7,3]=>1001011=>1101001
[2,1,8,5,4,7,6,3]=>1001111=>1111001
[2,1,7,5,6,4,8,3]=>1000111=>1110001
[2,1,8,5,6,7,4,3]=>1010011=>1100101
[2,1,8,5,7,6,4,3]=>1010111=>1110101
[2,1,8,6,5,4,7,3]=>1001111=>1111001
[2,1,8,6,5,7,4,3]=>1010111=>1110101
[2,1,8,7,5,6,4,3]=>1010111=>1110101
[2,3,1,5,8,6,7,4]=>0100011=>1100010
[2,3,1,7,5,6,4,8]=>0100110=>0110010
[2,3,1,8,5,6,7,4]=>0100011=>1100010
[2,3,1,8,6,7,5,4]=>0101011=>1101010
[2,3,4,1,8,6,7,5]=>0010011=>1100100
[2,3,4,5,8,6,7,1]=>0000011=>1100000
[2,3,4,7,5,6,1,8]=>0000110=>0110000
[2,3,4,7,5,6,8,1]=>0000011=>1100000
[2,3,4,8,5,6,7,1]=>0000011=>1100000
[2,3,4,8,5,7,6,1]=>0000111=>1110000
[2,3,4,8,6,5,7,1]=>0000111=>1110000
[2,3,4,8,6,7,5,1]=>0001011=>1101000
[2,3,5,4,8,6,7,1]=>0001011=>1101000
[2,3,6,4,5,1,7,8]=>0001100=>0011000
[2,3,6,4,5,1,8,7]=>0001101=>1011000
[2,3,6,4,5,7,8,1]=>0000101=>1010000
[2,3,6,4,5,8,7,1]=>0000111=>1110000
[2,3,7,4,5,6,8,1]=>0000011=>1100000
[2,3,8,4,5,6,7,1]=>0000011=>1100000
[2,3,7,4,6,5,8,1]=>0000111=>1110000
[2,3,8,4,6,7,5,1]=>0001011=>1101000
[2,3,7,5,4,6,1,8]=>0001110=>0111000
[2,3,7,5,4,6,8,1]=>0001011=>1101000
[2,3,8,5,4,6,7,1]=>0001011=>1101000
[2,3,7,5,6,4,1,8]=>0010110=>0110100
[2,3,7,5,6,4,8,1]=>0000111=>1110000
[2,3,8,5,6,4,7,1]=>0000111=>1110000
[2,3,8,5,6,7,4,1]=>0010011=>1100100
[2,3,8,5,7,6,4,1]=>0010111=>1110100
[2,3,8,6,5,4,7,1]=>0001111=>1111000
[2,4,3,1,8,6,7,5]=>0110011=>1100110
[2,4,3,5,8,6,7,1]=>0010011=>1100100
[2,4,3,7,5,6,8,1]=>0010011=>1100100
[2,4,3,8,5,6,7,1]=>0010011=>1100100
[2,4,3,8,5,7,6,1]=>0010111=>1110100
[2,4,3,8,6,5,7,1]=>0010111=>1110100
[2,4,3,8,6,7,5,1]=>0011011=>1101100
[2,5,3,4,1,6,7,8]=>0011000=>0001100
[2,5,3,4,1,8,7,6]=>0011011=>1101100
[2,5,3,4,6,7,1,8]=>0001010=>0101000
[2,5,3,4,6,7,8,1]=>0001001=>1001000
[2,5,3,4,6,8,7,1]=>0001011=>1101000
[2,5,3,4,7,6,8,1]=>0001011=>1101000
[2,5,3,4,8,6,7,1]=>0001011=>1101000
[2,5,3,4,8,7,6,1]=>0001111=>1111000
[2,6,3,4,5,1,7,8]=>0001100=>0011000
[2,6,3,4,5,7,8,1]=>0000101=>1010000
[2,6,3,4,5,8,7,1]=>0000111=>1110000
[2,7,3,4,5,6,1,8]=>0000110=>0110000
[2,8,3,4,5,6,7,1]=>0000011=>1100000
[2,8,3,4,5,7,6,1]=>0000111=>1110000
[2,6,3,5,4,1,7,8]=>0011100=>0011100
[2,6,3,5,4,1,8,7]=>0011101=>1011100
[2,6,3,5,4,7,8,1]=>0001101=>1011000
[2,6,3,5,4,8,7,1]=>0001111=>1111000
[2,7,3,5,4,6,8,1]=>0001011=>1101000
[2,8,3,5,4,7,6,1]=>0001111=>1111000
[2,7,3,5,6,4,8,1]=>0000111=>1110000
[2,8,3,5,6,7,4,1]=>0010011=>1100100
[2,8,3,5,7,6,4,1]=>0010111=>1110100
[2,7,3,6,5,4,1,8]=>0011110=>0111100
[2,8,3,7,5,6,4,1]=>0010111=>1110100
[2,8,3,7,6,5,4,1]=>0011111=>1111100
[2,5,4,3,8,6,7,1]=>0011011=>1101100
[2,6,4,3,5,1,8,7]=>0011101=>1011100
[2,6,4,3,5,7,8,1]=>0010101=>1010100
[2,6,4,3,5,8,7,1]=>0010111=>1110100
[2,7,4,3,5,6,8,1]=>0010011=>1100100
[2,8,4,3,5,6,7,1]=>0010011=>1100100
[2,8,4,3,5,7,6,1]=>0010111=>1110100
[2,7,4,3,6,5,8,1]=>0010111=>1110100
[2,8,4,3,6,5,7,1]=>0010111=>1110100
[2,8,4,3,6,7,5,1]=>0011011=>1101100
[2,8,4,3,7,6,5,1]=>0011111=>1111100
[2,6,4,5,3,1,7,8]=>0101100=>0011010
[2,6,4,5,3,1,8,7]=>0101101=>1011010
[2,6,4,5,3,7,8,1]=>0001101=>1011000
[2,6,4,5,3,8,7,1]=>0001111=>1111000
[2,8,4,5,3,6,7,1]=>0001011=>1101000
[2,7,4,5,6,3,1,8]=>0100110=>0110010
[2,7,4,5,6,3,8,1]=>0000111=>1110000
[2,8,4,5,6,3,7,1]=>0000111=>1110000
[2,8,4,5,6,7,3,1]=>0100011=>1100010
[2,7,4,6,5,3,1,8]=>0101110=>0111010
[2,7,4,6,5,3,8,1]=>0001111=>1111000
[2,8,4,6,5,3,7,1]=>0001111=>1111000
[2,8,4,7,6,5,3,1]=>0101111=>1111010
[2,7,5,4,3,6,8,1]=>0011011=>1101100
[2,8,5,4,3,6,7,1]=>0011011=>1101100
[2,8,5,4,3,7,6,1]=>0011111=>1111100
[2,7,5,4,6,3,8,1]=>0001111=>1111000
[2,8,5,4,6,7,3,1]=>0101011=>1101010
[2,8,5,4,7,6,3,1]=>0101111=>1111010
[2,7,6,4,5,3,8,1]=>0001111=>1111000
[2,8,7,4,5,6,3,1]=>0100111=>1110010
[2,8,7,4,6,5,3,1]=>0101111=>1111010
[2,8,7,5,4,6,3,1]=>0101111=>1111010
[2,8,7,5,6,4,3,1]=>0110111=>1110110
[3,2,1,4,8,6,7,5]=>1100011=>1100011
[3,2,1,5,8,6,7,4]=>1100011=>1100011
[3,2,1,7,5,6,4,8]=>1100110=>0110011
[3,2,1,7,5,6,8,4]=>1100011=>1100011
[3,2,1,8,5,6,7,4]=>1100011=>1100011
[3,2,1,8,5,7,6,4]=>1100111=>1110011
[3,2,1,8,6,5,7,4]=>1100111=>1110011
[3,2,1,8,6,7,5,4]=>1101011=>1101011
[3,2,4,1,8,6,7,5]=>0110011=>1100110
[3,2,4,5,8,6,7,1]=>0100011=>1100010
[3,2,4,7,5,6,8,1]=>0100011=>1100010
[3,2,4,8,5,6,7,1]=>0100011=>1100010
[3,2,4,8,6,7,5,1]=>0101011=>1101010
[3,2,5,4,8,6,7,1]=>0101011=>1101010
[3,2,6,4,5,7,1,8]=>0100110=>0110010
[3,2,7,4,5,6,1,8]=>0100110=>0110010
[3,2,8,4,5,6,7,1]=>0100011=>1100010
[3,2,7,4,6,5,1,8]=>0101110=>0111010
[3,2,7,4,6,5,8,1]=>0100111=>1110010
[3,2,7,5,4,6,1,8]=>0101110=>0111010
[3,2,8,5,4,6,7,1]=>0101011=>1101010
[3,2,8,5,4,7,6,1]=>0101111=>1111010
[3,2,7,5,6,4,1,8]=>0110110=>0110110
[3,2,7,5,6,4,8,1]=>0100111=>1110010
[3,2,8,5,7,6,4,1]=>0110111=>1110110
[3,2,8,6,5,7,4,1]=>0110111=>1110110
[3,2,8,7,5,6,4,1]=>0110111=>1110110
[4,2,3,1,5,7,6,8]=>0110010=>0100110
[4,2,3,1,5,7,8,6]=>0110001=>1000110
[4,2,3,1,5,8,7,6]=>0110011=>1100110
[4,2,3,1,6,5,7,8]=>0110100=>0010110
[4,2,3,1,6,5,8,7]=>0110101=>1010110
[4,2,3,1,6,7,8,5]=>0110001=>1000110
[4,2,3,1,6,8,7,5]=>0110011=>1100110
[4,2,3,1,7,6,5,8]=>0110110=>0110110
[4,2,3,1,7,6,8,5]=>0110011=>1100110
[4,2,3,1,8,6,7,5]=>0110011=>1100110
[4,2,3,1,8,7,6,5]=>0110111=>1110110
[4,2,3,5,1,6,8,7]=>0011001=>1001100
[4,2,3,5,1,7,8,6]=>0011001=>1001100
[4,2,3,5,1,8,7,6]=>0011011=>1101100
[4,2,3,5,6,1,8,7]=>0010101=>1010100
[4,2,3,5,6,8,7,1]=>0010011=>1100100
[4,2,3,5,7,6,1,8]=>0010110=>0110100
[4,2,3,5,8,7,6,1]=>0010111=>1110100
[4,2,3,6,5,1,7,8]=>0011100=>0011100
[4,2,3,6,5,1,8,7]=>0011101=>1011100
[4,2,3,6,5,8,7,1]=>0010111=>1110100
[4,2,3,7,5,6,1,8]=>0010110=>0110100
[4,2,3,7,5,6,8,1]=>0010011=>1100100
[4,2,3,8,5,6,7,1]=>0010011=>1100100
[4,2,3,8,5,7,6,1]=>0010111=>1110100
[4,2,3,7,6,5,8,1]=>0010111=>1110100
[4,2,3,8,6,7,5,1]=>0011011=>1101100
[4,2,3,8,7,6,5,1]=>0011111=>1111100
[5,2,3,4,1,6,8,7]=>0011001=>1001100
[5,2,3,4,1,7,8,6]=>0011001=>1001100
[5,2,3,4,1,8,7,6]=>0011011=>1101100
[5,2,3,4,6,1,8,7]=>0001101=>1011000
[5,2,3,4,7,6,1,8]=>0001110=>0111000
[5,2,3,4,8,6,7,1]=>0001011=>1101000
[5,2,3,4,8,7,6,1]=>0001111=>1111000
[6,2,3,4,5,1,8,7]=>0001101=>1011000
[6,2,3,4,5,8,7,1]=>0000111=>1110000
[8,2,3,4,5,7,6,1]=>0000111=>1110000
[7,2,3,4,6,5,1,8]=>0001110=>0111000
[8,2,3,4,7,6,5,1]=>0001111=>1111000
[6,2,3,5,4,1,7,8]=>0011100=>0011100
[6,2,3,5,4,1,8,7]=>0011101=>1011100
[6,2,3,5,4,7,1,8]=>0001110=>0111000
[6,2,3,5,4,7,8,1]=>0001101=>1011000
[7,2,3,5,4,6,1,8]=>0001110=>0111000
[8,2,3,5,4,6,7,1]=>0001011=>1101000
[8,2,3,5,4,7,6,1]=>0001111=>1111000
[7,2,3,5,6,4,1,8]=>0010110=>0110100
[8,2,3,5,6,7,4,1]=>0010011=>1100100
[8,2,3,5,7,6,4,1]=>0010111=>1110100
[7,2,3,6,5,4,1,8]=>0011110=>0111100
[8,2,3,6,5,4,7,1]=>0001111=>1111000
[8,2,3,7,5,6,4,1]=>0010111=>1110100
[8,2,3,7,6,5,4,1]=>0011111=>1111100
[5,2,4,3,1,6,7,8]=>0111000=>0001110
[5,2,4,3,1,6,8,7]=>0111001=>1001110
[5,2,4,3,1,7,6,8]=>0111010=>0101110
[5,2,4,3,1,8,7,6]=>0111011=>1101110
[5,2,4,3,6,1,7,8]=>0011100=>0011100
[5,2,4,3,6,1,8,7]=>0011101=>1011100
[5,2,4,3,6,7,1,8]=>0011010=>0101100
[5,2,4,3,7,6,1,8]=>0011110=>0111100
[5,2,4,3,7,6,8,1]=>0011011=>1101100
[5,2,4,3,8,7,6,1]=>0011111=>1111100
[6,2,4,3,5,1,8,7]=>0011101=>1011100
[7,2,4,3,6,5,1,8]=>0011110=>0111100
[7,2,4,3,6,5,8,1]=>0010111=>1110100
[8,2,4,3,6,5,7,1]=>0010111=>1110100
[8,2,4,3,6,7,5,1]=>0011011=>1101100
[8,2,4,3,7,6,5,1]=>0011111=>1111100
[6,2,4,5,3,1,7,8]=>0101100=>0011010
[6,2,4,5,3,1,8,7]=>0101101=>1011010
[6,2,4,5,3,8,7,1]=>0001111=>1111000
[7,2,4,5,3,6,1,8]=>0001110=>0111000
[7,2,4,5,3,6,8,1]=>0001011=>1101000
[8,2,4,5,3,7,6,1]=>0001111=>1111000
[8,2,4,5,6,3,7,1]=>0000111=>1110000
[8,2,4,5,6,7,3,1]=>0100011=>1100010
[8,2,4,5,7,6,3,1]=>0100111=>1110010
[7,2,4,6,5,3,1,8]=>0101110=>0111010
[7,2,4,6,5,3,8,1]=>0001111=>1111000
[8,2,4,7,5,6,3,1]=>0100111=>1110010
[8,2,4,7,6,5,3,1]=>0101111=>1111010
[6,2,5,4,3,1,7,8]=>0111100=>0011110
[6,2,5,4,3,1,8,7]=>0111101=>1011110
[6,2,5,4,3,7,1,8]=>0011110=>0111100
[6,2,5,4,3,7,8,1]=>0011101=>1011100
[7,2,5,4,3,6,1,8]=>0011110=>0111100
[8,2,5,4,3,6,7,1]=>0011011=>1101100
[8,2,5,4,3,7,6,1]=>0011111=>1111100
[7,2,5,4,6,3,8,1]=>0001111=>1111000
[8,2,5,4,7,6,3,1]=>0101111=>1111010
[7,2,6,4,5,3,1,8]=>0101110=>0111010
[7,2,6,4,5,3,8,1]=>0001111=>1111000
[8,2,6,4,5,3,7,1]=>0001111=>1111000
[8,2,6,4,5,7,3,1]=>0100111=>1110010
[8,2,7,4,5,6,3,1]=>0100111=>1110010
[8,2,7,4,6,5,3,1]=>0101111=>1111010
[7,2,6,5,4,3,1,8]=>0111110=>0111110
[7,2,6,5,4,3,8,1]=>0011111=>1111100
[8,2,6,5,4,3,7,1]=>0011111=>1111100
[8,2,6,5,4,7,3,1]=>0101111=>1111010
[8,2,7,5,4,6,3,1]=>0101111=>1111010
[8,2,7,5,6,4,3,1]=>0110111=>1110110
[8,2,7,6,5,4,3,1]=>0111111=>1111110
[4,3,2,1,8,6,7,5]=>1110011=>1100111
[4,3,2,7,5,6,8,1]=>0110011=>1100110
[4,3,2,8,5,6,7,1]=>0110011=>1100110
[4,3,2,8,5,7,6,1]=>0110111=>1110110
[4,3,2,8,6,7,5,1]=>0111011=>1101110
[5,3,2,4,1,6,8,7]=>0111001=>1001110
[5,3,2,4,1,7,6,8]=>0111010=>0101110
[5,3,2,4,1,8,7,6]=>0111011=>1101110
[5,3,2,4,6,1,8,7]=>0101101=>1011010
[5,3,2,4,7,6,1,8]=>0101110=>0111010
[8,3,2,4,6,5,7,1]=>0100111=>1110010
[8,3,2,4,6,7,5,1]=>0101011=>1101010
[8,3,2,4,7,6,5,1]=>0101111=>1111010
[6,3,2,5,4,1,7,8]=>0111100=>0011110
[6,3,2,5,4,1,8,7]=>0111101=>1011110
[6,3,2,5,4,7,1,8]=>0101110=>0111010
[6,3,2,5,4,7,8,1]=>0101101=>1011010
[6,3,2,5,4,8,7,1]=>0101111=>1111010
[7,3,2,5,4,6,1,8]=>0101110=>0111010
[8,3,2,5,4,7,6,1]=>0101111=>1111010
[7,3,2,5,6,4,8,1]=>0100111=>1110010
[8,3,2,5,6,4,7,1]=>0100111=>1110010
[8,3,2,5,6,7,4,1]=>0110011=>1100110
[8,3,2,5,7,6,4,1]=>0110111=>1110110
[8,3,2,6,5,7,4,1]=>0110111=>1110110
[8,3,2,7,5,6,4,1]=>0110111=>1110110
[8,3,2,7,6,5,4,1]=>0111111=>1111110
[5,3,4,2,1,6,8,7]=>1011001=>1001101
[5,3,4,2,1,7,8,6]=>1011001=>1001101
[5,3,4,2,1,8,7,6]=>1011011=>1101101
[5,3,4,2,7,6,1,8]=>0011110=>0111100
[7,3,4,2,6,5,1,8]=>0011110=>0111100
[7,3,4,2,6,5,8,1]=>0010111=>1110100
[8,3,4,2,6,5,7,1]=>0010111=>1110100
[6,3,4,5,2,1,8,7]=>1001101=>1011001
[6,3,4,5,2,8,7,1]=>0001111=>1111000
[8,3,4,5,2,7,6,1]=>0001111=>1111000
[8,3,4,5,7,6,2,1]=>1000111=>1110001
[7,3,4,6,5,2,1,8]=>1001110=>0111001
[8,3,4,7,6,5,2,1]=>1001111=>1111001
[6,3,5,4,2,1,8,7]=>1011101=>1011101
[6,3,5,4,2,7,1,8]=>0011110=>0111100
[6,3,5,4,2,7,8,1]=>0011101=>1011100
[6,3,5,4,2,8,7,1]=>0011111=>1111100
[7,3,5,4,2,6,1,8]=>0011110=>0111100
[8,3,5,4,2,6,7,1]=>0011011=>1101100
[8,3,5,4,2,7,6,1]=>0011111=>1111100
[7,3,5,4,6,2,1,8]=>1001110=>0111001
[7,3,5,4,6,2,8,1]=>0001111=>1111000
[8,3,5,4,6,7,2,1]=>1001011=>1101001
[8,3,5,4,7,6,2,1]=>1001111=>1111001
[7,3,6,4,5,2,1,8]=>1001110=>0111001
[8,3,6,4,5,2,7,1]=>0001111=>1111000
[8,3,6,4,5,7,2,1]=>1000111=>1110001
[8,3,7,4,5,6,2,1]=>1000111=>1110001
[8,3,7,4,6,5,2,1]=>1001111=>1111001
[7,3,6,5,4,2,1,8]=>1011110=>0111101
[7,3,6,5,4,2,8,1]=>0011111=>1111100
[8,3,6,5,4,2,7,1]=>0011111=>1111100
[8,3,6,5,4,7,2,1]=>1001111=>1111001
[8,3,7,5,4,6,2,1]=>1001111=>1111001
[8,3,7,5,6,4,2,1]=>1010111=>1110101
[8,3,7,6,5,4,2,1]=>1011111=>1111101
[5,4,3,2,8,6,7,1]=>0111011=>1101110
[6,4,3,2,5,1,8,7]=>0111101=>1011110
[6,4,3,2,5,8,7,1]=>0110111=>1110110
[8,4,3,2,5,7,6,1]=>0110111=>1110110
[7,4,3,2,6,5,1,8]=>0111110=>0111110
[7,4,3,2,6,5,8,1]=>0110111=>1110110
[8,4,3,2,6,5,7,1]=>0110111=>1110110
[8,4,3,2,6,7,5,1]=>0111011=>1101110
[8,4,3,2,7,6,5,1]=>0111111=>1111110
[6,4,3,5,2,1,8,7]=>1011101=>1011101
[8,4,3,5,2,7,6,1]=>0011111=>1111100
[8,4,3,5,7,6,2,1]=>1010111=>1110101
[7,4,3,6,5,2,1,8]=>1011110=>0111101
[7,4,3,6,5,2,8,1]=>0011111=>1111100
[8,4,3,7,5,6,2,1]=>1010111=>1110101
[8,4,3,7,6,5,2,1]=>1011111=>1111101
[6,5,3,4,2,1,8,7]=>1011101=>1011101
[8,5,3,4,2,7,6,1]=>0011111=>1111100
[8,5,3,4,7,6,2,1]=>1001111=>1111001
[8,7,3,4,6,5,2,1]=>1001111=>1111001
[7,6,3,5,4,2,1,8]=>1011110=>0111101
[7,6,3,5,4,2,8,1]=>0011111=>1111100
[8,6,3,5,4,2,7,1]=>0011111=>1111100
[8,6,3,5,4,7,2,1]=>1001111=>1111001
[8,7,3,5,4,6,2,1]=>1001111=>1111001
[8,7,3,5,6,4,2,1]=>1010111=>1110101
[8,7,3,6,5,4,2,1]=>1011111=>1111101
[8,5,4,3,2,7,6,1]=>0111111=>1111110
[8,5,4,3,7,6,2,1]=>1011111=>1111101
[8,7,4,3,6,5,2,1]=>1011111=>1111101
[8,7,4,6,5,3,2,1]=>1101111=>1111011
[2,4,1,3,6,5,8,7]=>0010101=>1010100
[2,1,4,6,3,5,8,7]=>1000101=>1010001
[2,4,1,6,3,5,8,7]=>0010101=>1010100
[2,4,6,1,3,5,8,7]=>0000101=>1010000
[2,1,4,3,6,8,5,7]=>1010001=>1000101
[2,4,1,3,6,8,5,7]=>0010001=>1000100
[2,1,4,6,3,8,5,7]=>1000101=>1010001
[2,4,1,6,3,8,5,7]=>0010101=>1010100
[2,4,6,1,3,8,5,7]=>0000101=>1010000
[2,1,4,6,8,3,5,7]=>1000001=>1000001
[2,4,1,6,8,3,5,7]=>0010001=>1000100
[2,4,6,1,8,3,5,7]=>0000101=>1010000
[2,4,6,8,1,3,5,7]=>0000001=>1000000
[2,4,1,3,6,5,7,8]=>0010100=>0010100
[2,1,4,6,3,5,7,8]=>1000100=>0010001
[2,4,1,6,3,5,7,8]=>0010100=>0010100
[2,4,6,1,3,5,7,8]=>0000100=>0010000
[2,1,4,6,3,7,5,8]=>1000110=>0110001
[2,4,1,6,3,7,5,8]=>0010110=>0110100
[2,4,6,1,3,7,5,8]=>0000110=>0110000
[2,1,4,6,7,3,5,8]=>1000010=>0100001
[2,4,1,6,7,3,5,8]=>0010010=>0100100
[2,4,6,7,1,3,5,8]=>0000010=>0100000
[2,4,1,3,6,7,8,5]=>0010001=>1000100
[2,1,4,6,3,7,8,5]=>1000101=>1010001
[2,4,1,6,3,7,8,5]=>0010101=>1010100
[2,4,6,1,3,7,8,5]=>0000101=>1010000
[2,1,4,6,7,3,8,5]=>1000011=>1100001
[2,4,1,6,7,3,8,5]=>0010011=>1100100
[2,4,6,1,7,3,8,5]=>0000111=>1110000
[2,4,6,7,1,3,8,5]=>0000011=>1100000
[2,1,4,6,7,8,3,5]=>1000001=>1000001
[2,4,1,6,7,8,3,5]=>0010001=>1000100
[2,4,6,1,7,8,3,5]=>0000101=>1010000
[2,4,6,7,1,8,3,5]=>0000011=>1100000
[2,4,6,7,8,1,3,5]=>0000001=>1000000
[2,1,4,3,7,5,8,6]=>1010011=>1100101
[2,4,1,3,7,5,8,6]=>0010011=>1100100
[2,1,4,7,3,5,8,6]=>1000011=>1100001
[2,4,1,7,3,5,8,6]=>0010011=>1100100
[2,4,7,1,3,5,8,6]=>0000011=>1100000
[2,1,4,3,7,8,5,6]=>1010001=>1000101
[2,4,1,3,7,8,5,6]=>0010001=>1000100
[2,4,1,7,3,8,5,6]=>0010011=>1100100
[2,4,7,1,3,8,5,6]=>0000011=>1100000
[2,1,4,7,8,3,5,6]=>1000001=>1000001
[2,4,1,7,8,3,5,6]=>0010001=>1000100
[2,4,7,1,8,3,5,6]=>0000011=>1100000
[2,4,7,8,1,3,5,6]=>0000001=>1000000
[2,4,1,5,3,7,6,8]=>0011010=>0101100
[2,4,5,1,3,7,6,8]=>0001010=>0101000
[2,4,5,1,7,3,6,8]=>0001010=>0101000
[2,4,1,3,5,7,8,6]=>0010001=>1000100
[2,4,1,5,3,7,8,6]=>0011001=>1001100
[2,4,5,1,3,7,8,6]=>0001001=>1001000
[2,1,4,5,7,3,8,6]=>1000011=>1100001
[2,4,1,5,7,3,8,6]=>0010011=>1100100
[2,4,5,1,7,3,8,6]=>0001011=>1101000
[2,4,5,7,1,3,8,6]=>0000011=>1100000
[2,1,4,5,7,8,3,6]=>1000001=>1000001
[2,4,5,1,7,8,3,6]=>0001001=>1001000
[2,4,5,7,1,8,3,6]=>0000011=>1100000
[2,4,5,7,8,1,3,6]=>0000001=>1000000
[2,1,4,3,8,5,6,7]=>1010001=>1000101
[2,4,1,3,8,5,6,7]=>0010001=>1000100
[2,1,4,8,3,5,6,7]=>1000001=>1000001
[2,4,1,8,3,5,6,7]=>0010001=>1000100
[2,4,8,1,3,5,6,7]=>0000001=>1000000
[2,1,4,3,5,8,6,7]=>1010001=>1000101
[2,4,1,5,3,8,6,7]=>0011001=>1001100
[2,1,4,5,8,3,6,7]=>1000001=>1000001
[2,4,1,5,8,3,6,7]=>0010001=>1000100
[2,4,5,1,8,3,6,7]=>0001001=>1001000
[2,4,5,8,1,3,6,7]=>0000001=>1000000
[2,4,1,5,3,6,8,7]=>0011001=>1001100
[2,4,1,5,6,3,8,7]=>0010101=>1010100
[2,4,5,1,6,3,8,7]=>0001101=>1011000
[2,4,5,6,1,3,8,7]=>0000101=>1010000
[2,1,4,5,6,8,3,7]=>1000001=>1000001
[2,4,1,5,6,8,3,7]=>0010001=>1000100
[2,4,5,1,6,8,3,7]=>0001001=>1001000
[2,4,5,6,1,8,3,7]=>0000101=>1010000
[2,4,5,6,8,1,3,7]=>0000001=>1000000
[2,4,1,3,5,6,7,8]=>0010000=>0000100
[2,4,1,5,3,6,7,8]=>0011000=>0001100
[2,4,5,1,3,6,7,8]=>0001000=>0001000
[2,4,1,5,6,3,7,8]=>0010100=>0010100
[2,4,5,1,6,3,7,8]=>0001100=>0011000
[2,4,5,6,1,3,7,8]=>0000100=>0010000
[2,4,1,5,6,7,3,8]=>0010010=>0100100
[2,4,5,1,6,7,3,8]=>0001010=>0101000
[2,4,5,6,1,7,3,8]=>0000110=>0110000
[2,4,5,6,7,1,3,8]=>0000010=>0100000
[2,4,1,5,6,7,8,3]=>0010001=>1000100
[2,4,5,1,6,7,8,3]=>0001001=>1001000
[2,4,5,6,1,7,8,3]=>0000101=>1010000
[2,4,5,6,7,1,8,3]=>0000011=>1100000
[2,4,5,6,7,8,1,3]=>0000001=>1000000
[2,1,5,3,6,4,8,7]=>1001101=>1011001
[2,5,1,3,6,4,8,7]=>0001101=>1011000
[2,1,5,6,3,4,8,7]=>1000101=>1010001
[2,5,1,6,3,4,8,7]=>0001101=>1011000
[2,5,6,1,3,4,8,7]=>0000101=>1010000
[2,1,5,3,6,8,4,7]=>1001001=>1001001
[2,5,1,3,6,8,4,7]=>0001001=>1001000
[2,5,1,6,3,8,4,7]=>0001101=>1011000
[2,5,6,1,3,8,4,7]=>0000101=>1010000
[2,1,5,6,8,3,4,7]=>1000001=>1000001
[2,5,1,6,8,3,4,7]=>0001001=>1001000
[2,5,6,8,1,3,4,7]=>0000001=>1000000
[2,5,1,3,6,4,7,8]=>0001100=>0011000
[2,1,5,6,3,4,7,8]=>1000100=>0010001
[2,5,1,6,3,4,7,8]=>0001100=>0011000
[2,1,5,3,6,7,4,8]=>1001010=>0101001
[2,1,5,6,3,7,4,8]=>1000110=>0110001
[2,5,1,6,3,7,4,8]=>0001110=>0111000
[2,5,6,1,3,7,4,8]=>0000110=>0110000
[2,1,5,6,7,3,4,8]=>1000010=>0100001
[2,5,1,6,7,3,4,8]=>0001010=>0101000
[2,5,6,1,7,3,4,8]=>0000110=>0110000
[2,1,5,3,6,7,8,4]=>1001001=>1001001
[2,5,1,3,6,7,8,4]=>0001001=>1001000
[2,1,5,6,3,7,8,4]=>1000101=>1010001
[2,5,1,6,3,7,8,4]=>0001101=>1011000
[2,5,6,1,3,7,8,4]=>0000101=>1010000
[2,1,5,6,7,3,8,4]=>1000011=>1100001
[2,5,1,6,7,3,8,4]=>0001011=>1101000
[2,5,6,7,1,3,8,4]=>0000011=>1100000
[2,1,5,6,7,8,3,4]=>1000001=>1000001
[2,5,1,6,7,8,3,4]=>0001001=>1001000
[2,5,6,1,7,8,3,4]=>0000101=>1010000
[2,5,6,7,1,8,3,4]=>0000011=>1100000
[2,5,6,7,8,1,3,4]=>0000001=>1000000
[2,1,5,3,7,4,8,6]=>1001011=>1101001
[2,5,1,3,7,4,8,6]=>0001011=>1101000
[2,1,5,7,3,4,8,6]=>1000011=>1100001
[2,5,1,7,3,4,8,6]=>0001011=>1101000
[2,5,7,1,3,4,8,6]=>0000011=>1100000
[2,1,5,3,7,8,4,6]=>1001001=>1001001
[2,5,1,3,7,8,4,6]=>0001001=>1001000
[2,1,5,7,3,8,4,6]=>1000011=>1100001
[2,5,1,7,3,8,4,6]=>0001011=>1101000
[2,5,7,1,3,8,4,6]=>0000011=>1100000
[2,1,5,7,8,3,4,6]=>1000001=>1000001
[2,5,1,7,8,3,4,6]=>0001001=>1001000
[2,5,7,1,8,3,4,6]=>0000011=>1100000
[2,5,7,8,1,3,4,6]=>0000001=>1000000
[2,5,1,3,7,4,6,8]=>0001010=>0101000
[2,1,5,7,3,4,6,8]=>1000010=>0100001
[2,3,5,1,4,7,6,8]=>0001010=>0101000
[2,3,5,7,1,4,6,8]=>0000010=>0100000
[2,3,5,1,7,4,8,6]=>0001011=>1101000
[2,3,5,7,1,4,8,6]=>0000011=>1100000
[2,3,1,5,7,8,4,6]=>0100001=>1000010
[2,3,5,7,1,8,4,6]=>0000011=>1100000
[2,3,5,7,8,1,4,6]=>0000001=>1000000
[2,1,5,3,8,4,6,7]=>1001001=>1001001
[2,5,1,3,8,4,6,7]=>0001001=>1001000
[2,1,5,8,3,4,6,7]=>1000001=>1000001
[2,5,1,8,3,4,6,7]=>0001001=>1001000
[2,5,8,1,3,4,6,7]=>0000001=>1000000
[2,3,5,1,4,8,6,7]=>0001001=>1001000
[2,1,3,5,8,4,6,7]=>1000001=>1000001
[2,3,5,1,8,4,6,7]=>0001001=>1001000
[2,3,5,8,1,4,6,7]=>0000001=>1000000
[2,1,5,3,4,6,8,7]=>1001001=>1001001
[2,3,5,1,6,4,8,7]=>0001101=>1011000
[2,3,5,6,1,4,8,7]=>0000101=>1010000
[2,1,3,5,6,8,4,7]=>1000001=>1000001
[2,3,1,5,6,8,4,7]=>0100001=>1000010
[2,3,5,1,6,8,4,7]=>0001001=>1001000
[2,3,5,6,1,8,4,7]=>0000101=>1010000
[2,3,5,6,8,1,4,7]=>0000001=>1000000
[2,1,5,3,4,6,7,8]=>1001000=>0001001
[2,5,1,3,4,6,7,8]=>0001000=>0001000
[2,3,5,1,4,6,7,8]=>0001000=>0001000
[2,3,5,1,6,4,7,8]=>0001100=>0011000
[2,3,5,6,1,4,7,8]=>0000100=>0010000
[2,3,5,6,1,7,4,8]=>0000110=>0110000
[2,3,5,6,7,1,4,8]=>0000010=>0100000
[2,3,5,1,6,7,8,4]=>0001001=>1001000
[2,3,5,6,1,7,8,4]=>0000101=>1010000
[2,3,5,6,7,1,8,4]=>0000011=>1100000
[2,3,5,6,7,8,1,4]=>0000001=>1000000
[2,1,6,3,7,4,8,5]=>1000111=>1110001
[2,6,1,3,7,4,8,5]=>0000111=>1110000
[2,1,6,7,3,4,8,5]=>1000011=>1100001
[2,6,1,7,3,4,8,5]=>0000111=>1110000
[2,6,7,1,3,4,8,5]=>0000011=>1100000
[2,1,6,3,7,8,4,5]=>1000101=>1010001
[2,6,1,3,7,8,4,5]=>0000101=>1010000
[2,1,6,7,3,8,4,5]=>1000011=>1100001
[2,6,1,7,3,8,4,5]=>0000111=>1110000
[2,6,7,1,3,8,4,5]=>0000011=>1100000
[2,1,6,7,8,3,4,5]=>1000001=>1000001
[2,6,1,7,8,3,4,5]=>0000101=>1010000
[2,6,7,1,8,3,4,5]=>0000011=>1100000
[2,6,7,8,1,3,4,5]=>0000001=>1000000
[2,1,6,3,7,4,5,8]=>1000110=>0110001
[2,6,1,7,3,4,5,8]=>0000110=>0110000
[2,6,7,1,3,4,5,8]=>0000010=>0100000
[2,6,1,3,4,7,5,8]=>0000110=>0110000
[2,3,1,6,4,7,5,8]=>0100110=>0110010
[2,3,6,1,4,7,5,8]=>0000110=>0110000
[2,3,6,7,1,4,5,8]=>0000010=>0100000
[2,1,6,3,4,7,8,5]=>1000101=>1010001
[2,6,1,3,4,7,8,5]=>0000101=>1010000
[2,3,6,1,4,7,8,5]=>0000101=>1010000
[2,1,3,6,7,4,8,5]=>1000011=>1100001
[2,3,6,7,1,4,8,5]=>0000011=>1100000
[2,1,3,6,7,8,4,5]=>1000001=>1000001
[2,3,1,6,7,8,4,5]=>0100001=>1000010
[2,3,6,1,7,8,4,5]=>0000101=>1010000
[2,3,6,7,1,8,4,5]=>0000011=>1100000
[2,3,6,7,8,1,4,5]=>0000001=>1000000
[2,1,6,3,8,4,5,7]=>1000101=>1010001
[2,6,1,3,8,4,5,7]=>0000101=>1010000
[2,1,6,8,3,4,5,7]=>1000001=>1000001
[2,6,1,8,3,4,5,7]=>0000101=>1010000
[2,6,8,1,3,4,5,7]=>0000001=>1000000
[2,1,6,3,4,8,5,7]=>1000101=>1010001
[2,6,1,3,4,8,5,7]=>0000101=>1010000
[2,3,1,6,4,8,5,7]=>0100101=>1010010
[2,3,6,1,4,8,5,7]=>0000101=>1010000
[2,3,1,6,8,4,5,7]=>0100001=>1000010
[2,3,6,1,8,4,5,7]=>0000101=>1010000
[2,3,6,8,1,4,5,7]=>0000001=>1000000
[2,1,6,3,4,5,8,7]=>1000101=>1010001
[2,6,1,3,4,5,8,7]=>0000101=>1010000
[2,1,3,6,4,5,8,7]=>1000101=>1010001
[2,3,6,1,4,5,8,7]=>0000101=>1010000
[2,3,4,1,6,8,5,7]=>0010001=>1000100
[2,3,4,6,1,8,5,7]=>0000101=>1010000
[2,3,4,6,8,1,5,7]=>0000001=>1000000
[2,6,1,3,4,5,7,8]=>0000100=>0010000
[2,1,3,6,4,5,7,8]=>1000100=>0010001
[2,3,1,6,4,5,7,8]=>0100100=>0010010
[2,3,6,1,4,5,7,8]=>0000100=>0010000
[2,3,4,6,1,5,7,8]=>0000100=>0010000
[2,3,4,6,1,7,5,8]=>0000110=>0110000
[2,3,4,6,7,1,5,8]=>0000010=>0100000
[2,3,4,6,1,7,8,5]=>0000101=>1010000
[2,3,4,6,7,8,1,5]=>0000001=>1000000
[2,1,7,3,8,4,5,6]=>1000011=>1100001
[2,7,1,3,8,4,5,6]=>0000011=>1100000
[2,1,7,8,3,4,5,6]=>1000001=>1000001
[2,7,1,8,3,4,5,6]=>0000011=>1100000
[2,7,8,1,3,4,5,6]=>0000001=>1000000
[2,1,7,3,4,8,5,6]=>1000011=>1100001
[2,7,1,3,4,8,5,6]=>0000011=>1100000
[2,1,3,7,4,8,5,6]=>1000011=>1100001
[2,3,1,7,4,8,5,6]=>0100011=>1100010
[2,3,7,1,4,8,5,6]=>0000011=>1100000
[2,1,3,7,8,4,5,6]=>1000001=>1000001
[2,3,1,7,8,4,5,6]=>0100001=>1000010
[2,3,7,8,1,4,5,6]=>0000001=>1000000
[2,1,7,3,4,5,8,6]=>1000011=>1100001
[2,7,1,3,4,5,8,6]=>0000011=>1100000
[2,3,1,7,4,5,8,6]=>0100011=>1100010
[2,3,7,1,4,5,8,6]=>0000011=>1100000
[2,1,3,4,7,5,8,6]=>1000011=>1100001
[2,3,4,1,7,5,8,6]=>0010011=>1100100
[2,3,4,7,1,5,8,6]=>0000011=>1100000
[2,1,3,4,7,8,5,6]=>1000001=>1000001
[2,3,1,4,7,8,5,6]=>0100001=>1000010
[2,3,4,1,7,8,5,6]=>0010001=>1000100
[2,3,4,7,1,8,5,6]=>0000011=>1100000
[2,3,4,7,8,1,5,6]=>0000001=>1000000
[2,1,7,3,4,5,6,8]=>1000010=>0100001
[2,7,1,3,4,5,6,8]=>0000010=>0100000
[2,3,7,1,4,5,6,8]=>0000010=>0100000
[2,1,3,4,7,5,6,8]=>1000010=>0100001
[2,3,1,4,7,5,6,8]=>0100010=>0100010
[2,3,4,1,7,5,6,8]=>0010010=>0100100
[2,3,4,7,1,5,6,8]=>0000010=>0100000
[2,3,4,5,7,1,6,8]=>0000010=>0100000
[2,3,4,5,7,1,8,6]=>0000011=>1100000
[2,3,4,5,7,8,1,6]=>0000001=>1000000
[2,1,8,3,4,5,6,7]=>1000001=>1000001
[2,8,1,3,4,5,6,7]=>0000001=>1000000
[2,1,3,8,4,5,6,7]=>1000001=>1000001
[2,3,1,8,4,5,6,7]=>0100001=>1000010
[2,3,8,1,4,5,6,7]=>0000001=>1000000
[2,1,3,4,8,5,6,7]=>1000001=>1000001
[2,3,1,4,8,5,6,7]=>0100001=>1000010
[2,3,4,1,8,5,6,7]=>0010001=>1000100
[2,3,4,8,1,5,6,7]=>0000001=>1000000
[2,1,3,4,5,8,6,7]=>1000001=>1000001
[2,3,1,4,5,8,6,7]=>0100001=>1000010
[2,3,4,1,5,8,6,7]=>0010001=>1000100
[2,3,4,5,1,8,6,7]=>0001001=>1001000
[2,3,4,5,8,1,6,7]=>0000001=>1000000
[2,3,4,5,6,8,1,7]=>0000001=>1000000
[3,1,4,2,6,5,8,7]=>0110101=>1010110
[3,4,1,2,6,5,8,7]=>0010101=>1010100
[3,1,4,6,2,5,8,7]=>0100101=>1010010
[3,4,1,6,2,5,8,7]=>0010101=>1010100
[3,4,6,1,2,5,8,7]=>0000101=>1010000
[3,1,4,2,6,8,5,7]=>0110001=>1000110
[3,4,1,2,6,8,5,7]=>0010001=>1000100
[3,1,4,6,2,8,5,7]=>0100101=>1010010
[3,4,1,6,2,8,5,7]=>0010101=>1010100
[3,1,4,6,8,2,5,7]=>0100001=>1000010
[3,4,1,6,8,2,5,7]=>0010001=>1000100
[3,4,6,8,1,2,5,7]=>0000001=>1000000
[3,1,4,2,6,5,7,8]=>0110100=>0010110
[3,4,1,2,6,5,7,8]=>0010100=>0010100
[3,1,4,2,6,7,5,8]=>0110010=>0100110
[3,4,1,2,6,7,5,8]=>0010010=>0100100
[3,4,1,6,2,7,5,8]=>0010110=>0110100
[3,4,6,1,2,7,5,8]=>0000110=>0110000
[3,4,1,6,7,2,5,8]=>0010010=>0100100
[3,4,6,7,1,2,5,8]=>0000010=>0100000
[3,1,4,2,6,7,8,5]=>0110001=>1000110
[3,4,1,2,6,7,8,5]=>0010001=>1000100
[3,1,4,6,2,7,8,5]=>0100101=>1010010
[3,4,1,6,2,7,8,5]=>0010101=>1010100
[3,4,6,1,2,7,8,5]=>0000101=>1010000
[3,1,4,6,7,2,8,5]=>0100011=>1100010
[3,4,1,6,7,2,8,5]=>0010011=>1100100
[3,4,6,1,7,2,8,5]=>0000111=>1110000
[3,4,6,7,1,2,8,5]=>0000011=>1100000
[3,1,4,6,7,8,2,5]=>0100001=>1000010
[3,4,1,6,7,8,2,5]=>0010001=>1000100
[3,4,6,1,7,8,2,5]=>0000101=>1010000
[3,4,6,7,1,8,2,5]=>0000011=>1100000
[3,4,6,7,8,1,2,5]=>0000001=>1000000
[3,1,4,2,7,5,8,6]=>0110011=>1100110
[3,4,1,2,7,5,8,6]=>0010011=>1100100
[3,1,4,7,2,5,8,6]=>0100011=>1100010
[3,4,1,7,2,5,8,6]=>0010011=>1100100
[3,4,7,1,2,5,8,6]=>0000011=>1100000
[3,1,4,2,7,8,5,6]=>0110001=>1000110
[3,4,1,2,7,8,5,6]=>0010001=>1000100
[3,1,4,7,2,8,5,6]=>0100011=>1100010
[3,4,7,1,8,2,5,6]=>0000011=>1100000
[3,4,7,8,1,2,5,6]=>0000001=>1000000
[3,1,4,2,7,5,6,8]=>0110010=>0100110
[3,4,1,2,7,5,6,8]=>0010010=>0100100
[3,4,1,2,5,7,6,8]=>0010010=>0100100
[3,1,4,5,2,7,6,8]=>0101010=>0101010
[3,4,1,5,2,7,6,8]=>0011010=>0101100
[3,4,1,5,7,2,6,8]=>0010010=>0100100
[3,4,5,1,7,2,6,8]=>0001010=>0101000
[3,4,5,7,1,2,6,8]=>0000010=>0100000
[3,1,4,2,5,7,8,6]=>0110001=>1000110
[3,4,1,2,5,7,8,6]=>0010001=>1000100
[3,1,4,5,2,7,8,6]=>0101001=>1001010
[3,4,5,1,2,7,8,6]=>0001001=>1001000
[3,1,4,5,7,2,8,6]=>0100011=>1100010
[3,4,1,5,7,2,8,6]=>0010011=>1100100
[3,4,5,7,1,2,8,6]=>0000011=>1100000
[3,1,4,5,7,8,2,6]=>0100001=>1000010
[3,4,1,5,7,8,2,6]=>0010001=>1000100
[3,4,5,1,7,8,2,6]=>0001001=>1001000
[3,4,5,7,1,8,2,6]=>0000011=>1100000
[3,4,5,7,8,1,2,6]=>0000001=>1000000
[3,1,4,2,8,5,6,7]=>0110001=>1000110
[3,4,1,2,8,5,6,7]=>0010001=>1000100
[3,1,4,8,2,5,6,7]=>0100001=>1000010
[3,4,1,8,2,5,6,7]=>0010001=>1000100
[3,4,8,1,2,5,6,7]=>0000001=>1000000
[3,1,4,2,5,8,6,7]=>0110001=>1000110
[3,4,1,2,5,8,6,7]=>0010001=>1000100
[3,4,1,5,2,8,6,7]=>0011001=>1001100
[3,4,5,1,2,8,6,7]=>0001001=>1001000
[3,1,4,5,8,2,6,7]=>0100001=>1000010
[3,4,1,5,8,2,6,7]=>0010001=>1000100
[3,4,5,8,1,2,6,7]=>0000001=>1000000
[3,4,1,2,5,6,8,7]=>0010001=>1000100
[3,4,5,1,2,6,8,7]=>0001001=>1001000
[3,1,4,5,6,2,8,7]=>0100101=>1010010
[3,4,1,5,6,2,8,7]=>0010101=>1010100
[3,4,5,1,6,2,8,7]=>0001101=>1011000
[3,4,5,6,1,2,8,7]=>0000101=>1010000
[3,1,4,5,6,8,2,7]=>0100001=>1000010
[3,4,1,5,6,8,2,7]=>0010001=>1000100
[3,4,5,6,1,8,2,7]=>0000101=>1010000
[3,4,5,6,8,1,2,7]=>0000001=>1000000
[3,1,4,2,5,6,7,8]=>0110000=>0000110
[3,1,4,5,2,6,7,8]=>0101000=>0001010
[3,4,1,5,2,6,7,8]=>0011000=>0001100
[3,1,4,5,6,2,7,8]=>0100100=>0010010
[3,4,1,5,6,2,7,8]=>0010100=>0010100
[3,4,5,1,6,2,7,8]=>0001100=>0011000
[3,1,4,5,6,7,2,8]=>0100010=>0100010
[3,4,1,5,6,7,2,8]=>0010010=>0100100
[3,4,5,1,6,7,2,8]=>0001010=>0101000
[3,4,5,6,1,7,2,8]=>0000110=>0110000
[3,1,4,5,6,7,8,2]=>0100001=>1000010
[3,4,1,5,6,7,8,2]=>0010001=>1000100
[3,4,5,1,6,7,8,2]=>0001001=>1001000
[3,4,5,6,1,7,8,2]=>0000101=>1010000
[3,4,5,6,7,1,8,2]=>0000011=>1100000
[3,1,5,2,6,4,8,7]=>0101101=>1011010
[3,5,1,2,6,4,8,7]=>0001101=>1011000
[3,1,5,6,2,4,8,7]=>0100101=>1010010
[3,5,1,6,2,4,8,7]=>0001101=>1011000
[3,5,6,1,2,4,8,7]=>0000101=>1010000
[3,1,5,2,6,8,4,7]=>0101001=>1001010
[3,5,1,2,6,8,4,7]=>0001001=>1001000
[3,1,5,6,2,8,4,7]=>0100101=>1010010
[3,5,6,1,2,8,4,7]=>0000101=>1010000
[3,1,5,6,8,2,4,7]=>0100001=>1000010
[3,5,1,6,8,2,4,7]=>0001001=>1001000
[3,5,6,1,8,2,4,7]=>0000101=>1010000
[3,5,6,8,1,2,4,7]=>0000001=>1000000
[3,1,5,6,2,4,7,8]=>0100100=>0010010
[3,5,1,6,2,4,7,8]=>0001100=>0011000
[3,5,6,1,2,4,7,8]=>0000100=>0010000
[3,5,1,2,6,7,4,8]=>0001010=>0101000
[3,5,1,6,2,7,4,8]=>0001110=>0111000
[3,5,6,1,2,7,4,8]=>0000110=>0110000
[3,5,1,6,7,2,4,8]=>0001010=>0101000
[3,5,6,1,7,2,4,8]=>0000110=>0110000
[3,5,6,7,1,2,4,8]=>0000010=>0100000
[3,1,5,2,6,7,8,4]=>0101001=>1001010
[3,5,1,2,6,7,8,4]=>0001001=>1001000
[3,1,5,6,2,7,8,4]=>0100101=>1010010
[3,5,1,6,2,7,8,4]=>0001101=>1011000
[3,5,6,1,2,7,8,4]=>0000101=>1010000
[3,1,5,6,7,2,8,4]=>0100011=>1100010
[3,5,1,6,7,2,8,4]=>0001011=>1101000
[3,5,6,1,7,2,8,4]=>0000111=>1110000
[3,5,6,7,1,2,8,4]=>0000011=>1100000
[3,1,5,6,7,8,2,4]=>0100001=>1000010
[3,5,1,6,7,8,2,4]=>0001001=>1001000
[3,5,6,1,7,8,2,4]=>0000101=>1010000
[3,5,6,7,1,8,2,4]=>0000011=>1100000
[3,5,6,7,8,1,2,4]=>0000001=>1000000
[3,1,5,2,7,4,8,6]=>0101011=>1101010
[3,5,1,2,7,4,8,6]=>0001011=>1101000
[3,1,5,7,2,4,8,6]=>0100011=>1100010
[3,5,1,7,2,4,8,6]=>0001011=>1101000
[3,5,7,1,2,4,8,6]=>0000011=>1100000
[3,1,5,2,7,8,4,6]=>0101001=>1001010
[3,5,1,2,7,8,4,6]=>0001001=>1001000
[3,1,5,7,2,8,4,6]=>0100011=>1100010
[3,5,1,7,2,8,4,6]=>0001011=>1101000
[3,5,7,1,2,8,4,6]=>0000011=>1100000
[3,1,5,7,8,2,4,6]=>0100001=>1000010
[3,5,1,7,8,2,4,6]=>0001001=>1001000
[3,5,7,8,1,2,4,6]=>0000001=>1000000
[3,1,5,2,7,4,6,8]=>0101010=>0101010
[3,5,1,2,7,4,6,8]=>0001010=>0101000
[3,1,5,7,2,4,6,8]=>0100010=>0100010
[3,5,1,7,2,4,6,8]=>0001010=>0101000
[3,5,7,1,2,4,6,8]=>0000010=>0100000
[3,1,5,2,4,7,6,8]=>0101010=>0101010
[3,5,1,2,4,7,6,8]=>0001010=>0101000
[3,1,2,5,4,7,6,8]=>0101010=>0101010
[1,3,5,2,4,7,6,8]=>0001010=>0101000
[3,1,2,5,7,4,6,8]=>0100010=>0100010
[1,3,2,5,7,4,6,8]=>0100010=>0100010
[1,3,5,2,7,4,6,8]=>0001010=>0101000
[1,3,5,7,2,4,6,8]=>0000010=>0100000
[3,1,5,2,4,7,8,6]=>0101001=>1001010
[3,5,1,2,4,7,8,6]=>0001001=>1001000
[1,3,5,2,4,7,8,6]=>0001001=>1001000
[3,1,2,5,7,4,8,6]=>0100011=>1100010
[1,3,2,5,7,4,8,6]=>0100011=>1100010
[1,3,5,2,7,4,8,6]=>0001011=>1101000
[1,3,5,7,2,4,8,6]=>0000011=>1100000
[3,1,2,5,7,8,4,6]=>0100001=>1000010
[1,3,2,5,7,8,4,6]=>0100001=>1000010
[1,3,5,2,7,8,4,6]=>0001001=>1001000
[1,3,5,7,2,8,4,6]=>0000011=>1100000
[1,3,5,7,8,2,4,6]=>0000001=>1000000
[3,1,5,2,8,4,6,7]=>0101001=>1001010
[3,5,1,2,8,4,6,7]=>0001001=>1001000
[3,1,5,8,2,4,6,7]=>0100001=>1000010
[3,5,1,8,2,4,6,7]=>0001001=>1001000
[3,1,5,2,4,8,6,7]=>0101001=>1001010
[3,5,1,2,4,8,6,7]=>0001001=>1001000
[1,3,2,5,4,8,6,7]=>0101001=>1001010
[1,3,5,2,4,8,6,7]=>0001001=>1001000
[3,1,2,5,8,4,6,7]=>0100001=>1000010
[1,3,2,5,8,4,6,7]=>0100001=>1000010
[1,3,5,2,8,4,6,7]=>0001001=>1001000
[1,3,5,8,2,4,6,7]=>0000001=>1000000
[3,1,5,2,4,6,8,7]=>0101001=>1001010
[3,5,1,2,4,6,8,7]=>0001001=>1001000
[3,1,2,5,4,6,8,7]=>0101001=>1001010
[1,3,5,2,4,6,8,7]=>0001001=>1001000
[1,3,5,2,6,4,8,7]=>0001101=>1011000
[1,3,5,6,2,4,8,7]=>0000101=>1010000
[3,1,2,5,6,8,4,7]=>0100001=>1000010
[1,3,5,2,6,8,4,7]=>0001001=>1001000
[1,3,5,6,2,8,4,7]=>0000101=>1010000
[1,3,5,6,8,2,4,7]=>0000001=>1000000
[3,1,5,2,4,6,7,8]=>0101000=>0001010
[3,5,1,2,4,6,7,8]=>0001000=>0001000
[1,3,5,2,4,6,7,8]=>0001000=>0001000
[3,1,2,5,6,4,7,8]=>0100100=>0010010
[1,3,5,2,6,4,7,8]=>0001100=>0011000
[1,3,5,6,2,4,7,8]=>0000100=>0010000
[3,1,2,5,6,7,4,8]=>0100010=>0100010
[1,3,5,2,6,7,4,8]=>0001010=>0101000
[1,3,5,6,2,7,4,8]=>0000110=>0110000
[1,3,5,6,7,2,4,8]=>0000010=>0100000
[3,1,2,5,6,7,8,4]=>0100001=>1000010
[1,3,5,2,6,7,8,4]=>0001001=>1001000
[1,3,5,6,2,7,8,4]=>0000101=>1010000
[1,3,5,6,7,2,8,4]=>0000011=>1100000
[1,3,5,6,7,8,2,4]=>0000001=>1000000
[3,1,6,2,7,4,8,5]=>0100111=>1110010
[3,6,1,2,7,4,8,5]=>0000111=>1110000
[3,6,1,7,2,4,8,5]=>0000111=>1110000
[3,6,7,1,2,4,8,5]=>0000011=>1100000
[3,6,1,2,7,8,4,5]=>0000101=>1010000
[3,1,6,7,2,8,4,5]=>0100011=>1100010
[3,6,1,7,2,8,4,5]=>0000111=>1110000
[3,6,7,1,2,8,4,5]=>0000011=>1100000
[3,6,1,7,8,2,4,5]=>0000101=>1010000
[3,6,7,8,1,2,4,5]=>0000001=>1000000
[3,1,6,2,7,4,5,8]=>0100110=>0110010
[3,1,6,7,2,4,5,8]=>0100010=>0100010
[3,6,7,1,2,4,5,8]=>0000010=>0100000
[3,1,6,2,4,7,5,8]=>0100110=>0110010
[3,6,1,2,4,7,5,8]=>0000110=>0110000
[3,1,2,6,4,7,5,8]=>0100110=>0110010
[1,3,2,6,4,7,5,8]=>0100110=>0110010
[1,3,6,2,4,7,5,8]=>0000110=>0110000
[1,3,2,6,7,4,5,8]=>0100010=>0100010
[1,3,6,2,7,4,5,8]=>0000110=>0110000
[3,1,6,2,4,7,8,5]=>0100101=>1010010
[3,6,1,2,4,7,8,5]=>0000101=>1010000
[3,1,2,6,4,7,8,5]=>0100101=>1010010
[1,3,2,6,4,7,8,5]=>0100101=>1010010
[1,3,6,2,4,7,8,5]=>0000101=>1010000
[3,1,2,6,7,4,8,5]=>0100011=>1100010
[1,3,2,6,7,4,8,5]=>0100011=>1100010
[1,3,6,2,7,4,8,5]=>0000111=>1110000
[1,3,6,7,2,4,8,5]=>0000011=>1100000
[3,1,2,6,7,8,4,5]=>0100001=>1000010
[1,3,2,6,7,8,4,5]=>0100001=>1000010
[1,3,6,2,7,8,4,5]=>0000101=>1010000
[1,3,6,7,8,2,4,5]=>0000001=>1000000
[3,1,6,2,8,4,5,7]=>0100101=>1010010
[3,6,1,2,8,4,5,7]=>0000101=>1010000
[3,1,6,8,2,4,5,7]=>0100001=>1000010
[3,6,1,8,2,4,5,7]=>0000101=>1010000
[3,6,8,1,2,4,5,7]=>0000001=>1000000
[3,1,6,2,4,8,5,7]=>0100101=>1010010
[3,6,1,2,4,8,5,7]=>0000101=>1010000
[1,3,2,6,4,8,5,7]=>0100101=>1010010
[1,3,6,2,4,8,5,7]=>0000101=>1010000
[3,1,2,6,8,4,5,7]=>0100001=>1000010
[1,3,2,6,8,4,5,7]=>0100001=>1000010
[3,1,6,2,4,5,8,7]=>0100101=>1010010
[3,6,1,2,4,5,8,7]=>0000101=>1010000
[3,1,2,6,4,5,8,7]=>0100101=>1010010
[1,3,6,2,4,5,8,7]=>0000101=>1010000
[3,1,2,4,6,5,8,7]=>0100101=>1010010
[1,3,4,6,2,5,8,7]=>0000101=>1010000
[3,1,2,4,6,8,5,7]=>0100001=>1000010
[1,3,2,4,6,8,5,7]=>0100001=>1000010
[1,3,4,6,8,2,5,7]=>0000001=>1000000
[3,1,6,2,4,5,7,8]=>0100100=>0010010
[3,6,1,2,4,5,7,8]=>0000100=>0010000
[1,3,2,6,4,5,7,8]=>0100100=>0010010
[1,3,6,2,4,5,7,8]=>0000100=>0010000
[1,3,4,6,2,5,7,8]=>0000100=>0010000
[3,1,2,4,6,7,5,8]=>0100010=>0100010
[1,3,4,6,2,7,5,8]=>0000110=>0110000
[1,3,4,6,7,2,5,8]=>0000010=>0100000
[3,1,2,4,6,7,8,5]=>0100001=>1000010
[1,3,4,6,7,2,8,5]=>0000011=>1100000
[1,3,4,6,7,8,2,5]=>0000001=>1000000
[3,1,7,2,8,4,5,6]=>0100011=>1100010
[3,7,1,2,8,4,5,6]=>0000011=>1100000
[3,1,7,8,2,4,5,6]=>0100001=>1000010
[3,7,1,8,2,4,5,6]=>0000011=>1100000
[3,7,8,1,2,4,5,6]=>0000001=>1000000
[3,7,1,2,4,8,5,6]=>0000011=>1100000
[3,1,2,7,4,8,5,6]=>0100011=>1100010
[1,3,2,7,4,8,5,6]=>0100011=>1100010
[1,3,7,2,4,8,5,6]=>0000011=>1100000
[3,1,2,7,8,4,5,6]=>0100001=>1000010
[1,3,7,2,8,4,5,6]=>0000011=>1100000
[1,3,7,8,2,4,5,6]=>0000001=>1000000
[3,1,7,2,4,5,8,6]=>0100011=>1100010
[3,7,1,2,4,5,8,6]=>0000011=>1100000
[1,3,7,2,4,5,8,6]=>0000011=>1100000
[3,1,2,4,7,5,8,6]=>0100011=>1100010
[1,3,2,4,7,5,8,6]=>0100011=>1100010
[1,3,4,2,7,5,8,6]=>0010011=>1100100
[1,3,4,7,2,5,8,6]=>0000011=>1100000
[3,1,2,4,7,8,5,6]=>0100001=>1000010
[1,3,2,4,7,8,5,6]=>0100001=>1000010
[1,3,4,2,7,8,5,6]=>0010001=>1000100
[1,3,4,7,8,2,5,6]=>0000001=>1000000
[3,1,7,2,4,5,6,8]=>0100010=>0100010
[3,7,1,2,4,5,6,8]=>0000010=>0100000
[3,1,2,7,4,5,6,8]=>0100010=>0100010
[1,3,2,7,4,5,6,8]=>0100010=>0100010
[1,3,7,2,4,5,6,8]=>0000010=>0100000
[3,1,2,4,7,5,6,8]=>0100010=>0100010
[1,3,4,7,2,5,6,8]=>0000010=>0100000
[3,1,2,4,5,7,6,8]=>0100010=>0100010
[1,3,4,5,7,2,6,8]=>0000010=>0100000
[3,1,2,4,5,7,8,6]=>0100001=>1000010
[1,3,4,5,7,2,8,6]=>0000011=>1100000
[1,3,4,5,7,8,2,6]=>0000001=>1000000
[3,1,8,2,4,5,6,7]=>0100001=>1000010
[3,8,1,2,4,5,6,7]=>0000001=>1000000
[3,1,2,8,4,5,6,7]=>0100001=>1000010
[1,3,2,8,4,5,6,7]=>0100001=>1000010
[1,3,8,2,4,5,6,7]=>0000001=>1000000
[3,1,2,4,8,5,6,7]=>0100001=>1000010
[1,3,2,4,8,5,6,7]=>0100001=>1000010
[1,3,4,2,8,5,6,7]=>0010001=>1000100
[1,3,4,8,2,5,6,7]=>0000001=>1000000
[3,1,2,4,5,8,6,7]=>0100001=>1000010
[1,3,2,4,5,8,6,7]=>0100001=>1000010
[1,3,4,2,5,8,6,7]=>0010001=>1000100
[1,3,4,5,2,8,6,7]=>0001001=>1001000
[1,3,4,5,8,2,6,7]=>0000001=>1000000
[3,1,2,4,5,6,8,7]=>0100001=>1000010
[1,3,4,5,6,8,2,7]=>0000001=>1000000
[4,1,5,2,6,3,8,7]=>0011101=>1011100
[4,5,1,2,6,3,8,7]=>0001101=>1011000
[4,1,5,6,2,3,8,7]=>0010101=>1010100
[4,5,1,6,2,3,8,7]=>0001101=>1011000
[4,5,6,1,2,3,8,7]=>0000101=>1010000
[4,1,5,2,6,8,3,7]=>0011001=>1001100
[4,5,1,2,6,8,3,7]=>0001001=>1001000
[4,1,5,6,2,8,3,7]=>0010101=>1010100
[4,5,1,6,2,8,3,7]=>0001101=>1011000
[4,5,6,1,2,8,3,7]=>0000101=>1010000
[4,1,5,6,8,2,3,7]=>0010001=>1000100
[4,5,1,6,8,2,3,7]=>0001001=>1001000
[4,5,6,1,8,2,3,7]=>0000101=>1010000
[4,5,6,8,1,2,3,7]=>0000001=>1000000
[4,1,5,2,6,3,7,8]=>0011100=>0011100
[4,1,5,6,2,3,7,8]=>0010100=>0010100
[4,5,1,6,2,3,7,8]=>0001100=>0011000
[4,5,1,2,6,7,3,8]=>0001010=>0101000
[4,5,1,6,2,7,3,8]=>0001110=>0111000
[4,5,6,1,2,7,3,8]=>0000110=>0110000
[4,1,5,6,7,2,3,8]=>0010010=>0100100
[4,5,1,6,7,2,3,8]=>0001010=>0101000
[4,5,6,1,7,2,3,8]=>0000110=>0110000
[4,1,5,2,6,7,8,3]=>0011001=>1001100
[4,5,1,2,6,7,8,3]=>0001001=>1001000
[4,5,1,6,2,7,8,3]=>0001101=>1011000
[4,5,6,1,2,7,8,3]=>0000101=>1010000
[4,1,5,6,7,2,8,3]=>0010011=>1100100
[4,5,1,6,7,2,8,3]=>0001011=>1101000
[4,5,6,1,7,2,8,3]=>0000111=>1110000
[4,5,6,7,1,2,8,3]=>0000011=>1100000
[4,1,5,6,7,8,2,3]=>0010001=>1000100
[4,5,1,6,7,8,2,3]=>0001001=>1001000
[4,5,6,1,7,8,2,3]=>0000101=>1010000
[4,5,6,7,1,8,2,3]=>0000011=>1100000
[4,1,5,2,7,3,8,6]=>0011011=>1101100
[4,5,1,2,7,3,8,6]=>0001011=>1101000
[4,5,1,7,2,3,8,6]=>0001011=>1101000
[4,5,7,1,2,3,8,6]=>0000011=>1100000
[4,1,5,2,7,8,3,6]=>0011001=>1001100
[4,5,1,2,7,8,3,6]=>0001001=>1001000
[4,1,5,7,2,8,3,6]=>0010011=>1100100
[4,5,1,7,2,8,3,6]=>0001011=>1101000
[4,5,7,1,2,8,3,6]=>0000011=>1100000
[4,5,1,7,8,2,3,6]=>0001001=>1001000
[4,5,7,8,1,2,3,6]=>0000001=>1000000
[4,1,5,2,7,3,6,8]=>0011010=>0101100
[4,5,1,2,7,3,6,8]=>0001010=>0101000
[4,1,5,7,2,3,6,8]=>0010010=>0100100
[4,5,1,7,2,3,6,8]=>0001010=>0101000
[4,1,5,2,3,7,6,8]=>0011010=>0101100
[4,5,1,2,3,7,6,8]=>0001010=>0101000
[4,1,2,5,3,7,6,8]=>0011010=>0101100
[1,4,2,5,3,7,6,8]=>0011010=>0101100
[1,4,5,2,3,7,6,8]=>0001010=>0101000
[4,1,2,5,7,3,6,8]=>0010010=>0100100
[1,4,2,5,7,3,6,8]=>0010010=>0100100
[1,4,5,2,7,3,6,8]=>0001010=>0101000
[1,4,5,7,2,3,6,8]=>0000010=>0100000
[4,1,5,2,3,7,8,6]=>0011001=>1001100
[4,1,2,5,3,7,8,6]=>0011001=>1001100
[1,4,2,5,3,7,8,6]=>0011001=>1001100
[1,4,5,2,3,7,8,6]=>0001001=>1001000
[4,1,2,5,7,3,8,6]=>0010011=>1100100
[1,4,2,5,7,3,8,6]=>0010011=>1100100
[1,4,5,2,7,3,8,6]=>0001011=>1101000
[1,4,5,7,2,3,8,6]=>0000011=>1100000
[4,1,2,5,7,8,3,6]=>0010001=>1000100
[1,4,2,5,7,8,3,6]=>0010001=>1000100
[1,4,5,2,7,8,3,6]=>0001001=>1001000
[1,4,5,7,8,2,3,6]=>0000001=>1000000
[4,1,5,2,8,3,6,7]=>0011001=>1001100
[4,5,1,2,8,3,6,7]=>0001001=>1001000
[4,1,5,8,2,3,6,7]=>0010001=>1000100
[4,5,1,8,2,3,6,7]=>0001001=>1001000
[4,5,8,1,2,3,6,7]=>0000001=>1000000
[4,1,5,2,3,8,6,7]=>0011001=>1001100
[4,5,1,2,3,8,6,7]=>0001001=>1001000
[4,1,2,5,3,8,6,7]=>0011001=>1001100
[1,4,2,5,3,8,6,7]=>0011001=>1001100
[1,4,5,2,3,8,6,7]=>0001001=>1001000
[4,1,2,5,8,3,6,7]=>0010001=>1000100
[1,4,2,5,8,3,6,7]=>0010001=>1000100
[1,4,5,2,8,3,6,7]=>0001001=>1001000
[1,4,5,8,2,3,6,7]=>0000001=>1000000
[1,4,2,5,3,6,8,7]=>0011001=>1001100
[4,1,2,5,6,3,8,7]=>0010101=>1010100
[1,4,5,2,6,3,8,7]=>0001101=>1011000
[1,4,5,6,2,3,8,7]=>0000101=>1010000
[4,1,2,5,6,8,3,7]=>0010001=>1000100
[1,4,2,5,6,8,3,7]=>0010001=>1000100
[1,4,5,2,6,8,3,7]=>0001001=>1001000
[1,4,5,6,2,8,3,7]=>0000101=>1010000
[1,4,5,6,8,2,3,7]=>0000001=>1000000
[4,1,5,2,3,6,7,8]=>0011000=>0001100
[4,1,2,5,3,6,7,8]=>0011000=>0001100
[1,4,2,5,3,6,7,8]=>0011000=>0001100
[1,4,5,2,3,6,7,8]=>0001000=>0001000
[4,1,2,5,6,3,7,8]=>0010100=>0010100
[1,4,5,2,6,3,7,8]=>0001100=>0011000
[1,4,5,6,2,3,7,8]=>0000100=>0010000
[4,1,2,5,6,7,3,8]=>0010010=>0100100
[1,4,2,5,6,7,3,8]=>0010010=>0100100
[1,4,5,2,6,7,3,8]=>0001010=>0101000
[1,4,5,6,2,7,3,8]=>0000110=>0110000
[1,4,5,6,7,2,3,8]=>0000010=>0100000
[4,1,2,5,6,7,8,3]=>0010001=>1000100
[1,4,2,5,6,7,8,3]=>0010001=>1000100
[1,4,5,2,6,7,8,3]=>0001001=>1001000
[1,4,5,6,2,7,8,3]=>0000101=>1010000
[1,4,5,6,7,2,8,3]=>0000011=>1100000
[1,4,5,6,7,8,2,3]=>0000001=>1000000
[4,1,6,2,7,3,8,5]=>0010111=>1110100
[4,1,6,7,2,3,8,5]=>0010011=>1100100
[4,6,1,7,2,3,8,5]=>0000111=>1110000
[4,6,7,1,2,3,8,5]=>0000011=>1100000
[4,6,1,2,7,8,3,5]=>0000101=>1010000
[4,1,6,7,2,8,3,5]=>0010011=>1100100
[4,6,1,7,2,8,3,5]=>0000111=>1110000
[4,1,6,7,8,2,3,5]=>0010001=>1000100
[4,6,1,7,8,2,3,5]=>0000101=>1010000
[4,6,7,1,8,2,3,5]=>0000011=>1100000
[4,6,7,8,1,2,3,5]=>0000001=>1000000
[4,1,6,2,7,3,5,8]=>0010110=>0110100
[4,6,1,2,7,3,5,8]=>0000110=>0110000
[4,1,6,7,2,3,5,8]=>0010010=>0100100
[4,6,1,7,2,3,5,8]=>0000110=>0110000
[4,6,7,1,2,3,5,8]=>0000010=>0100000
[4,1,6,2,3,7,5,8]=>0010110=>0110100
[4,6,1,2,3,7,5,8]=>0000110=>0110000
[4,1,2,6,3,7,5,8]=>0010110=>0110100
[1,4,2,6,3,7,5,8]=>0010110=>0110100
[4,1,2,6,7,3,5,8]=>0010010=>0100100
[1,4,2,6,7,3,5,8]=>0010010=>0100100
[1,4,6,2,7,3,5,8]=>0000110=>0110000
[1,4,6,7,2,3,5,8]=>0000010=>0100000
[4,1,6,2,3,7,8,5]=>0010101=>1010100
[4,1,2,6,3,7,8,5]=>0010101=>1010100
[1,4,6,2,3,7,8,5]=>0000101=>1010000
[4,1,2,6,7,3,8,5]=>0010011=>1100100
[1,4,6,2,7,3,8,5]=>0000111=>1110000
[1,4,6,7,2,3,8,5]=>0000011=>1100000
[1,4,2,6,7,8,3,5]=>0010001=>1000100
[1,4,6,2,7,8,3,5]=>0000101=>1010000
[1,4,6,7,2,8,3,5]=>0000011=>1100000
[1,4,6,7,8,2,3,5]=>0000001=>1000000
[4,1,6,2,8,3,5,7]=>0010101=>1010100
[4,6,1,2,8,3,5,7]=>0000101=>1010000
[4,1,6,8,2,3,5,7]=>0010001=>1000100
[4,6,1,8,2,3,5,7]=>0000101=>1010000
[4,6,8,1,2,3,5,7]=>0000001=>1000000
[4,1,6,2,3,8,5,7]=>0010101=>1010100
[4,6,1,2,3,8,5,7]=>0000101=>1010000
[4,1,2,6,3,8,5,7]=>0010101=>1010100
[1,4,2,6,3,8,5,7]=>0010101=>1010100
[1,4,6,2,3,8,5,7]=>0000101=>1010000
[1,4,2,6,8,3,5,7]=>0010001=>1000100
[1,4,6,2,8,3,5,7]=>0000101=>1010000
[1,4,6,8,2,3,5,7]=>0000001=>1000000
[4,1,6,2,3,5,8,7]=>0010101=>1010100
[4,6,1,2,3,5,8,7]=>0000101=>1010000
[4,1,2,6,3,5,8,7]=>0010101=>1010100
[1,4,2,6,3,5,8,7]=>0010101=>1010100
[1,4,6,2,3,5,8,7]=>0000101=>1010000
[4,1,2,3,6,5,8,7]=>0010101=>1010100
[1,4,2,3,6,5,8,7]=>0010101=>1010100
[1,2,4,6,3,5,8,7]=>0000101=>1010000
[4,1,2,3,6,8,5,7]=>0010001=>1000100
[1,2,4,3,6,8,5,7]=>0010001=>1000100
[1,2,4,6,3,8,5,7]=>0000101=>1010000
[1,2,4,6,8,3,5,7]=>0000001=>1000000
[4,1,6,2,3,5,7,8]=>0010100=>0010100
[4,6,1,2,3,5,7,8]=>0000100=>0010000
[4,1,2,6,3,5,7,8]=>0010100=>0010100
[1,4,2,6,3,5,7,8]=>0010100=>0010100
[1,4,6,2,3,5,7,8]=>0000100=>0010000
[4,1,2,3,6,5,7,8]=>0010100=>0010100
[1,4,2,3,6,5,7,8]=>0010100=>0010100
[1,2,4,6,3,5,7,8]=>0000100=>0010000
[4,1,2,3,6,7,5,8]=>0010010=>0100100
[1,4,2,3,6,7,5,8]=>0010010=>0100100
[1,2,4,6,7,3,5,8]=>0000010=>0100000
[4,1,2,3,6,7,8,5]=>0010001=>1000100
[1,4,2,3,6,7,8,5]=>0010001=>1000100
[1,2,4,6,3,7,8,5]=>0000101=>1010000
[1,2,4,6,7,3,8,5]=>0000011=>1100000
[1,2,4,6,7,8,3,5]=>0000001=>1000000
[4,1,7,2,8,3,5,6]=>0010011=>1100100
[4,7,1,2,8,3,5,6]=>0000011=>1100000
[4,1,7,8,2,3,5,6]=>0010001=>1000100
[4,7,1,8,2,3,5,6]=>0000011=>1100000
[4,7,8,1,2,3,5,6]=>0000001=>1000000
[4,1,7,2,3,8,5,6]=>0010011=>1100100
[4,7,1,2,3,8,5,6]=>0000011=>1100000
[1,4,2,7,3,8,5,6]=>0010011=>1100100
[1,4,7,2,3,8,5,6]=>0000011=>1100000
[4,1,2,7,8,3,5,6]=>0010001=>1000100
[1,4,2,7,8,3,5,6]=>0010001=>1000100
[1,4,7,2,8,3,5,6]=>0000011=>1100000
[1,4,7,8,2,3,5,6]=>0000001=>1000000
[4,1,7,2,3,5,8,6]=>0010011=>1100100
[4,7,1,2,3,5,8,6]=>0000011=>1100000
[4,1,2,7,3,5,8,6]=>0010011=>1100100
[1,4,2,7,3,5,8,6]=>0010011=>1100100
[1,4,7,2,3,5,8,6]=>0000011=>1100000
[4,1,2,3,7,5,8,6]=>0010011=>1100100
[1,4,2,3,7,5,8,6]=>0010011=>1100100
[1,2,4,3,7,5,8,6]=>0010011=>1100100
[1,2,4,7,3,5,8,6]=>0000011=>1100000
[4,1,2,3,7,8,5,6]=>0010001=>1000100
[1,4,2,3,7,8,5,6]=>0010001=>1000100
[1,2,4,3,7,8,5,6]=>0010001=>1000100
[1,2,4,7,3,8,5,6]=>0000011=>1100000
[1,2,4,7,8,3,5,6]=>0000001=>1000000
[4,1,7,2,3,5,6,8]=>0010010=>0100100
[4,7,1,2,3,5,6,8]=>0000010=>0100000
[4,1,2,7,3,5,6,8]=>0010010=>0100100
[1,4,2,7,3,5,6,8]=>0010010=>0100100
[1,4,7,2,3,5,6,8]=>0000010=>0100000
[4,1,2,3,7,5,6,8]=>0010010=>0100100
[1,4,2,3,7,5,6,8]=>0010010=>0100100
[1,2,4,3,7,5,6,8]=>0010010=>0100100
[1,2,4,7,3,5,6,8]=>0000010=>0100000
[4,1,2,3,5,7,6,8]=>0010010=>0100100
[1,4,2,3,5,7,6,8]=>0010010=>0100100
[1,2,4,5,7,3,6,8]=>0000010=>0100000
[4,1,2,3,5,7,8,6]=>0010001=>1000100
[1,4,2,3,5,7,8,6]=>0010001=>1000100
[1,2,4,5,7,3,8,6]=>0000011=>1100000
[1,2,4,5,7,8,3,6]=>0000001=>1000000
[4,1,8,2,3,5,6,7]=>0010001=>1000100
[4,8,1,2,3,5,6,7]=>0000001=>1000000
[4,1,2,8,3,5,6,7]=>0010001=>1000100
[1,4,2,8,3,5,6,7]=>0010001=>1000100
[1,4,8,2,3,5,6,7]=>0000001=>1000000
[4,1,2,3,8,5,6,7]=>0010001=>1000100
[1,4,2,3,8,5,6,7]=>0010001=>1000100
[1,2,4,3,8,5,6,7]=>0010001=>1000100
[1,2,4,8,3,5,6,7]=>0000001=>1000000
[4,1,2,3,5,8,6,7]=>0010001=>1000100
[1,4,2,3,5,8,6,7]=>0010001=>1000100
[1,2,4,3,5,8,6,7]=>0010001=>1000100
[1,2,4,5,3,8,6,7]=>0001001=>1001000
[1,2,4,5,8,3,6,7]=>0000001=>1000000
[4,1,2,3,5,6,8,7]=>0010001=>1000100
[1,4,2,3,5,6,8,7]=>0010001=>1000100
[1,2,4,5,6,8,3,7]=>0000001=>1000000
[1,4,2,3,5,6,7,8]=>0010000=>0000100
[5,1,6,2,7,3,8,4]=>0001111=>1111000
[5,6,1,2,7,3,8,4]=>0000111=>1110000
[5,1,6,7,2,3,8,4]=>0001011=>1101000
[5,6,1,7,2,3,8,4]=>0000111=>1110000
[5,6,7,1,2,3,8,4]=>0000011=>1100000
[5,1,6,2,7,8,3,4]=>0001101=>1011000
[5,6,1,2,7,8,3,4]=>0000101=>1010000
[5,1,6,7,2,8,3,4]=>0001011=>1101000
[5,6,1,7,2,8,3,4]=>0000111=>1110000
[5,6,7,1,2,8,3,4]=>0000011=>1100000
[5,1,6,7,8,2,3,4]=>0001001=>1001000
[5,6,1,7,8,2,3,4]=>0000101=>1010000
[5,6,7,1,8,2,3,4]=>0000011=>1100000
[5,1,6,2,7,3,4,8]=>0001110=>0111000
[5,6,1,2,7,3,4,8]=>0000110=>0110000
[5,6,1,7,2,3,4,8]=>0000110=>0110000
[5,1,6,2,3,7,4,8]=>0001110=>0111000
[5,1,2,6,3,7,4,8]=>0001110=>0111000
[1,5,2,6,3,7,4,8]=>0001110=>0111000
[5,1,2,6,7,3,4,8]=>0001010=>0101000
[1,5,2,6,7,3,4,8]=>0001010=>0101000
[1,5,6,2,7,3,4,8]=>0000110=>0110000
[1,5,6,7,2,3,4,8]=>0000010=>0100000
[5,1,6,2,3,7,8,4]=>0001101=>1011000
[5,6,1,2,3,7,8,4]=>0000101=>1010000
[5,1,2,6,3,7,8,4]=>0001101=>1011000
[1,5,2,6,3,7,8,4]=>0001101=>1011000
[1,5,6,2,3,7,8,4]=>0000101=>1010000
[5,1,2,6,7,3,8,4]=>0001011=>1101000
[1,5,6,7,2,3,8,4]=>0000011=>1100000
[5,1,2,6,7,8,3,4]=>0001001=>1001000
[1,5,2,6,7,8,3,4]=>0001001=>1001000
[1,5,6,2,7,8,3,4]=>0000101=>1010000
[1,5,6,7,2,8,3,4]=>0000011=>1100000
[1,5,6,7,8,2,3,4]=>0000001=>1000000
[5,1,6,2,8,3,4,7]=>0001101=>1011000
[5,6,1,2,8,3,4,7]=>0000101=>1010000
[5,6,1,8,2,3,4,7]=>0000101=>1010000
[5,6,8,1,2,3,4,7]=>0000001=>1000000
[5,1,6,2,3,8,4,7]=>0001101=>1011000
[5,6,1,2,3,8,4,7]=>0000101=>1010000
[5,1,2,6,3,8,4,7]=>0001101=>1011000
[1,5,2,6,3,8,4,7]=>0001101=>1011000
[1,5,6,2,3,8,4,7]=>0000101=>1010000
[5,1,2,6,8,3,4,7]=>0001001=>1001000
[1,5,2,6,8,3,4,7]=>0001001=>1001000
[1,5,6,2,8,3,4,7]=>0000101=>1010000
[1,5,6,8,2,3,4,7]=>0000001=>1000000
[5,1,6,2,3,4,8,7]=>0001101=>1011000
[5,6,1,2,3,4,8,7]=>0000101=>1010000
[5,1,2,6,3,4,8,7]=>0001101=>1011000
[1,5,2,6,3,4,8,7]=>0001101=>1011000
[1,5,6,2,3,4,8,7]=>0000101=>1010000
[1,5,2,3,6,4,8,7]=>0001101=>1011000
[1,2,5,3,6,4,8,7]=>0001101=>1011000
[1,2,5,6,3,4,8,7]=>0000101=>1010000
[5,1,2,3,6,8,4,7]=>0001001=>1001000
[1,5,2,3,6,8,4,7]=>0001001=>1001000
[1,2,5,6,3,8,4,7]=>0000101=>1010000
[1,2,5,6,8,3,4,7]=>0000001=>1000000
[5,1,6,2,3,4,7,8]=>0001100=>0011000
[5,1,2,6,3,4,7,8]=>0001100=>0011000
[1,5,2,6,3,4,7,8]=>0001100=>0011000
[1,5,6,2,3,4,7,8]=>0000100=>0010000
[5,1,2,3,6,4,7,8]=>0001100=>0011000
[1,5,2,3,6,4,7,8]=>0001100=>0011000
[1,2,5,3,6,4,7,8]=>0001100=>0011000
[1,2,5,6,3,4,7,8]=>0000100=>0010000
[5,1,2,3,6,7,4,8]=>0001010=>0101000
[1,5,2,3,6,7,4,8]=>0001010=>0101000
[1,2,5,3,6,7,4,8]=>0001010=>0101000
[1,2,5,6,3,7,4,8]=>0000110=>0110000
[5,1,2,3,6,7,8,4]=>0001001=>1001000
[1,5,2,3,6,7,8,4]=>0001001=>1001000
[1,2,5,3,6,7,8,4]=>0001001=>1001000
[1,2,5,6,3,7,8,4]=>0000101=>1010000
[1,2,5,6,7,3,8,4]=>0000011=>1100000
[1,2,5,6,7,8,3,4]=>0000001=>1000000
[5,1,7,2,8,3,4,6]=>0001011=>1101000
[5,7,1,2,8,3,4,6]=>0000011=>1100000
[5,1,7,8,2,3,4,6]=>0001001=>1001000
[5,7,1,8,2,3,4,6]=>0000011=>1100000
[5,7,8,1,2,3,4,6]=>0000001=>1000000
[5,1,7,2,3,8,4,6]=>0001011=>1101000
[5,7,1,2,3,8,4,6]=>0000011=>1100000
[5,1,2,7,3,8,4,6]=>0001011=>1101000
[1,5,2,7,3,8,4,6]=>0001011=>1101000
[1,5,7,2,3,8,4,6]=>0000011=>1100000
[5,1,2,7,8,3,4,6]=>0001001=>1001000
[1,5,2,7,8,3,4,6]=>0001001=>1001000
[1,5,7,2,8,3,4,6]=>0000011=>1100000
[1,5,7,8,2,3,4,6]=>0000001=>1000000
[5,1,7,2,3,4,8,6]=>0001011=>1101000
[5,7,1,2,3,4,8,6]=>0000011=>1100000
[5,1,2,7,3,4,8,6]=>0001011=>1101000
[1,5,2,7,3,4,8,6]=>0001011=>1101000
[1,5,7,2,3,4,8,6]=>0000011=>1100000
[5,1,2,3,7,4,8,6]=>0001011=>1101000
[1,5,2,3,7,4,8,6]=>0001011=>1101000
[1,2,5,3,7,4,8,6]=>0001011=>1101000
[1,2,5,7,3,4,8,6]=>0000011=>1100000
[5,1,2,3,7,8,4,6]=>0001001=>1001000
[1,5,2,3,7,8,4,6]=>0001001=>1001000
[1,2,5,3,7,8,4,6]=>0001001=>1001000
[1,2,5,7,3,8,4,6]=>0000011=>1100000
[1,2,5,7,8,3,4,6]=>0000001=>1000000
[5,1,7,2,3,4,6,8]=>0001010=>0101000
[5,7,1,2,3,4,6,8]=>0000010=>0100000
[5,1,2,7,3,4,6,8]=>0001010=>0101000
[1,5,2,7,3,4,6,8]=>0001010=>0101000
[1,5,7,2,3,4,6,8]=>0000010=>0100000
[5,1,2,3,7,4,6,8]=>0001010=>0101000
[1,5,2,3,7,4,6,8]=>0001010=>0101000
[1,2,5,3,7,4,6,8]=>0001010=>0101000
[1,2,5,7,3,4,6,8]=>0000010=>0100000
[1,5,2,3,4,7,6,8]=>0001010=>0101000
[1,2,5,3,4,7,6,8]=>0001010=>0101000
[1,2,3,5,7,4,6,8]=>0000010=>0100000
[5,1,2,3,4,7,8,6]=>0001001=>1001000
[1,5,2,3,4,7,8,6]=>0001001=>1001000
[1,2,5,3,4,7,8,6]=>0001001=>1001000
[1,2,3,5,7,4,8,6]=>0000011=>1100000
[1,2,3,5,7,8,4,6]=>0000001=>1000000
[5,1,8,2,3,4,6,7]=>0001001=>1001000
[5,8,1,2,3,4,6,7]=>0000001=>1000000
[5,1,2,8,3,4,6,7]=>0001001=>1001000
[1,5,2,8,3,4,6,7]=>0001001=>1001000
[1,5,8,2,3,4,6,7]=>0000001=>1000000
[5,1,2,3,8,4,6,7]=>0001001=>1001000
[1,5,2,3,8,4,6,7]=>0001001=>1001000
[1,2,5,3,8,4,6,7]=>0001001=>1001000
[1,2,5,8,3,4,6,7]=>0000001=>1000000
[5,1,2,3,4,8,6,7]=>0001001=>1001000
[1,5,2,3,4,8,6,7]=>0001001=>1001000
[1,2,5,3,4,8,6,7]=>0001001=>1001000
[1,2,3,5,4,8,6,7]=>0001001=>1001000
[1,2,3,5,8,4,6,7]=>0000001=>1000000
[5,1,2,3,4,6,8,7]=>0001001=>1001000
[1,5,2,3,4,6,8,7]=>0001001=>1001000
[1,2,5,3,4,6,8,7]=>0001001=>1001000
[1,2,3,5,6,8,4,7]=>0000001=>1000000
[1,5,2,3,4,6,7,8]=>0001000=>0001000
[1,2,5,3,4,6,7,8]=>0001000=>0001000
[6,1,7,2,8,3,4,5]=>0000111=>1110000
[6,7,1,2,8,3,4,5]=>0000011=>1100000
[6,1,7,8,2,3,4,5]=>0000101=>1010000
[6,7,1,8,2,3,4,5]=>0000011=>1100000
[6,1,7,2,3,8,4,5]=>0000111=>1110000
[6,7,1,2,3,8,4,5]=>0000011=>1100000
[6,1,2,7,3,8,4,5]=>0000111=>1110000
[1,6,2,7,3,8,4,5]=>0000111=>1110000
[1,6,7,2,3,8,4,5]=>0000011=>1100000
[6,1,2,7,8,3,4,5]=>0000101=>1010000
[1,6,2,7,8,3,4,5]=>0000101=>1010000
[1,6,7,2,8,3,4,5]=>0000011=>1100000
[1,6,7,8,2,3,4,5]=>0000001=>1000000
[6,1,7,2,3,4,8,5]=>0000111=>1110000
[6,7,1,2,3,4,8,5]=>0000011=>1100000
[6,1,2,7,3,4,8,5]=>0000111=>1110000
[1,6,2,7,3,4,8,5]=>0000111=>1110000
[1,6,7,2,3,4,8,5]=>0000011=>1100000
[6,1,2,3,7,4,8,5]=>0000111=>1110000
[1,6,2,3,7,4,8,5]=>0000111=>1110000
[1,2,6,3,7,4,8,5]=>0000111=>1110000
[1,2,6,7,3,4,8,5]=>0000011=>1100000
[6,1,2,3,7,8,4,5]=>0000101=>1010000
[1,6,2,3,7,8,4,5]=>0000101=>1010000
[1,2,6,3,7,8,4,5]=>0000101=>1010000
[1,2,6,7,3,8,4,5]=>0000011=>1100000
[1,2,6,7,8,3,4,5]=>0000001=>1000000
[6,1,7,2,3,4,5,8]=>0000110=>0110000
[6,1,2,7,3,4,5,8]=>0000110=>0110000
[1,6,2,7,3,4,5,8]=>0000110=>0110000
[1,6,7,2,3,4,5,8]=>0000010=>0100000
[6,1,2,3,7,4,5,8]=>0000110=>0110000
[1,6,2,3,7,4,5,8]=>0000110=>0110000
[1,2,6,3,7,4,5,8]=>0000110=>0110000
[1,2,6,7,3,4,5,8]=>0000010=>0100000
[6,1,2,3,4,7,5,8]=>0000110=>0110000
[1,6,2,3,4,7,5,8]=>0000110=>0110000
[1,2,6,3,4,7,5,8]=>0000110=>0110000
[1,2,3,6,4,7,5,8]=>0000110=>0110000
[1,2,3,6,7,4,5,8]=>0000010=>0100000
[6,1,2,3,4,7,8,5]=>0000101=>1010000
[1,6,2,3,4,7,8,5]=>0000101=>1010000
[1,2,6,3,4,7,8,5]=>0000101=>1010000
[1,2,3,6,4,7,8,5]=>0000101=>1010000
[1,2,3,6,7,4,8,5]=>0000011=>1100000
[1,2,3,6,7,8,4,5]=>0000001=>1000000
[6,1,8,2,3,4,5,7]=>0000101=>1010000
[6,8,1,2,3,4,5,7]=>0000001=>1000000
[6,1,2,8,3,4,5,7]=>0000101=>1010000
[1,6,2,8,3,4,5,7]=>0000101=>1010000
[1,6,8,2,3,4,5,7]=>0000001=>1000000
[6,1,2,3,8,4,5,7]=>0000101=>1010000
[1,6,2,3,8,4,5,7]=>0000101=>1010000
[1,2,6,3,8,4,5,7]=>0000101=>1010000
[1,2,6,8,3,4,5,7]=>0000001=>1000000
[6,1,2,3,4,8,5,7]=>0000101=>1010000
[1,6,2,3,4,8,5,7]=>0000101=>1010000
[1,2,6,3,4,8,5,7]=>0000101=>1010000
[1,2,3,6,4,8,5,7]=>0000101=>1010000
[1,2,3,6,8,4,5,7]=>0000001=>1000000
[6,1,2,3,4,5,8,7]=>0000101=>1010000
[1,6,2,3,4,5,8,7]=>0000101=>1010000
[1,2,6,3,4,5,8,7]=>0000101=>1010000
[1,2,3,6,4,5,8,7]=>0000101=>1010000
[1,2,3,4,6,8,5,7]=>0000001=>1000000
[1,6,2,3,4,5,7,8]=>0000100=>0010000
[1,2,6,3,4,5,7,8]=>0000100=>0010000
[1,2,3,6,4,5,7,8]=>0000100=>0010000
[7,1,8,2,3,4,5,6]=>0000011=>1100000
[7,1,2,8,3,4,5,6]=>0000011=>1100000
[1,7,2,8,3,4,5,6]=>0000011=>1100000
[1,7,8,2,3,4,5,6]=>0000001=>1000000
[7,1,2,3,8,4,5,6]=>0000011=>1100000
[1,7,2,3,8,4,5,6]=>0000011=>1100000
[1,2,7,3,8,4,5,6]=>0000011=>1100000
[1,2,7,8,3,4,5,6]=>0000001=>1000000
[7,1,2,3,4,8,5,6]=>0000011=>1100000
[1,7,2,3,4,8,5,6]=>0000011=>1100000
[1,2,7,3,4,8,5,6]=>0000011=>1100000
[1,2,3,7,4,8,5,6]=>0000011=>1100000
[1,2,3,7,8,4,5,6]=>0000001=>1000000
[7,1,2,3,4,5,8,6]=>0000011=>1100000
[1,7,2,3,4,5,8,6]=>0000011=>1100000
[1,2,7,3,4,5,8,6]=>0000011=>1100000
[1,2,3,7,4,5,8,6]=>0000011=>1100000
[1,2,3,4,7,5,8,6]=>0000011=>1100000
[1,2,3,4,7,8,5,6]=>0000001=>1000000
[1,7,2,3,4,5,6,8]=>0000010=>0100000
[1,2,7,3,4,5,6,8]=>0000010=>0100000
[1,2,3,7,4,5,6,8]=>0000010=>0100000
[1,2,3,4,7,5,6,8]=>0000010=>0100000
[1,8,2,3,4,5,6,7]=>0000001=>1000000
[1,2,8,3,4,5,6,7]=>0000001=>1000000
[1,2,3,8,4,5,6,7]=>0000001=>1000000
[1,2,3,4,8,5,6,7]=>0000001=>1000000
[1,2,3,4,5,8,6,7]=>0000001=>1000000
[5,3,2,6,1,4,8,7]=>0101101=>1011010
[7,3,2,5,4,8,1,6]=>0101011=>1101010
[8,4,5,2,3,7,6,1]=>0001111=>1111000
[7,4,5,2,3,8,1,6]=>0001011=>1101000
[6,4,5,2,3,1,8,7]=>0101101=>1011010
[5,4,6,2,1,3,8,7]=>1001101=>1011001
[3,6,1,5,4,2,8,7]=>0011101=>1011100
[4,6,5,1,3,2,8,7]=>0101101=>1011010
[5,6,4,3,1,2,8,7]=>0110101=>1010110
[7,5,4,3,2,8,1,6]=>0111011=>1101110
[8,6,4,3,7,2,5,1]=>0011111=>1111100
[7,6,4,3,8,2,1,5]=>1010111=>1110101
[6,7,4,3,8,1,2,5]=>0010011=>1100100
[5,7,4,3,1,8,2,6]=>0110011=>1100110
[4,7,5,1,3,8,2,6]=>0001011=>1101000
[3,7,1,5,4,8,2,6]=>0001011=>1101000
[2,1,7,5,4,8,3,6]=>1001011=>1101001
[3,8,1,5,4,7,6,2]=>0001111=>1111000
[4,8,5,1,3,7,6,2]=>0001111=>1111000
[5,8,4,3,1,7,6,2]=>0110111=>1110110
[6,8,4,3,7,1,5,2]=>0011011=>1101100
[7,8,4,3,6,5,1,2]=>0011101=>1011100
[6,8,5,7,3,1,4,2]=>0110011=>1100110
[5,8,6,7,1,3,4,2]=>0010011=>1100100
[4,8,6,1,7,3,5,2]=>0001111=>1111000
[3,8,1,6,7,4,5,2]=>0001011=>1101000
[2,1,8,6,7,4,5,3]=>1001011=>1101001
[2,1,7,6,8,4,3,5]=>1010011=>1100101
[3,7,1,6,8,4,2,5]=>0010011=>1100100
[4,7,6,1,8,3,2,5]=>0100111=>1110010
[5,7,6,8,1,3,2,4]=>0100011=>1100010
[5,4,7,2,1,8,3,6]=>1001011=>1101001
[6,4,7,2,8,1,3,5]=>0000111=>1110000
[7,4,6,2,8,3,1,5]=>0100111=>1110010
[8,4,6,2,7,3,5,1]=>0001111=>1111000
[8,3,2,6,7,4,5,1]=>0101011=>1101010
[7,3,2,6,8,4,1,5]=>0110011=>1100110
[6,3,2,7,8,1,4,5]=>0100101=>1010010
[5,3,2,7,1,8,4,6]=>0101011=>1101010
[4,3,2,1,7,8,5,6]=>1110001=>1000111
[3,4,1,2,8,7,6,5]=>0010111=>1110100
[5,3,2,8,1,7,6,4]=>0101111=>1111010
[6,3,2,8,7,1,5,4]=>0101111=>1111010
[7,3,2,8,6,5,1,4]=>0101111=>1111010
[8,4,7,2,6,5,3,1]=>0101111=>1111010
[7,4,8,2,6,5,1,3]=>0001111=>1111000
[6,4,8,2,7,1,5,3]=>0001111=>1111000
[5,4,8,2,1,7,6,3]=>1001111=>1111001
[4,5,8,1,2,7,6,3]=>0000111=>1110000
[3,5,1,8,2,7,6,4]=>0001111=>1111000
[2,1,5,8,3,7,6,4]=>1000111=>1110001
[2,1,6,8,7,3,5,4]=>1001011=>1101001
[3,6,1,8,7,2,5,4]=>0001111=>1111000
[4,6,8,1,7,2,5,3]=>0001011=>1101000
[5,6,8,7,1,2,4,3]=>0010011=>1100100
[6,5,8,7,2,1,4,3]=>1010111=>1110101
[7,5,8,6,2,4,1,3]=>0010111=>1110100
[8,5,7,6,2,4,3,1]=>0110111=>1110110
[5,7,8,6,1,4,2,3]=>0010101=>1010100
[4,7,8,1,6,5,2,3]=>0001101=>1011000
[3,7,1,8,6,5,2,4]=>0001111=>1111000
[2,1,7,8,6,5,3,4]=>1001101=>1011001
[3,8,1,7,6,5,4,2]=>0011111=>1111100
[4,8,7,1,6,5,3,2]=>0101111=>1111010
[5,8,7,6,1,4,3,2]=>0110111=>1110110
[6,8,7,5,4,1,3,2]=>0111011=>1101110
[2,1,4,3,6,5,8,7,10,9]=>101010101=>101010101
[3,4,1,2,6,5,8,7,10,9]=>001010101=>101010100
[4,3,2,1,6,5,8,7,10,9]=>111010101=>101010111
[6,3,2,5,4,1,8,7,10,9]=>011110101=>101011110
[8,3,2,5,4,7,6,1,10,9]=>010111101=>101111010
[10,3,2,5,4,7,6,9,8,1]=>010101111=>111101010
[4,5,6,1,2,3,8,7,10,9]=>000010101=>101010000
[3,5,1,6,2,4,8,7,10,9]=>000110101=>101011000
[2,1,5,6,3,4,8,7,10,9]=>100010101=>101010001
[2,1,6,5,4,3,8,7,10,9]=>101110101=>101011101
[6,5,4,3,2,1,8,7,10,9]=>111110101=>101011111
[8,5,4,3,2,7,6,1,10,9]=>011111101=>101111110
[10,5,4,3,2,7,6,9,8,1]=>011101111=>111101110
[2,1,8,5,4,7,6,3,10,9]=>100111101=>101111001
[8,7,4,3,6,5,2,1,10,9]=>101111101=>101111101
[10,7,4,3,6,5,2,9,8,1]=>001111111=>111111100
[2,1,10,5,4,7,6,9,8,3]=>100101111=>111101001
[10,9,4,3,6,5,8,7,2,1]=>101011111=>111110101
[8,9,5,6,3,4,10,1,2,7]=>000010011=>110010000
[5,6,7,8,1,2,3,4,10,9]=>000000101=>101000000
[4,6,7,1,8,2,3,5,10,9]=>000001101=>101100000
[3,6,1,7,8,2,4,5,10,9]=>000010101=>101010000
[2,1,6,7,8,3,4,5,10,9]=>100000101=>101000001
[2,1,5,7,3,8,4,6,10,9]=>100001101=>101100001
[3,5,1,7,2,8,4,6,10,9]=>000101101=>101101000
[4,5,7,1,2,8,3,6,10,9]=>000001101=>101100000
[3,4,1,2,7,8,5,6,10,9]=>001000101=>101000100
[2,1,4,3,7,8,5,6,10,9]=>101000101=>101000101
[2,1,4,3,8,7,6,5,10,9]=>101011101=>101110101
[4,3,2,1,8,7,6,5,10,9]=>111011101=>101110111
[8,3,2,7,6,5,4,1,10,9]=>011111101=>101111110
[10,3,2,7,6,5,4,9,8,1]=>010111111=>111111010
[2,1,8,7,6,5,4,3,10,9]=>101111101=>101111101
[8,7,6,5,4,3,2,1,10,9]=>111111101=>101111111
[9,7,6,5,4,3,2,10,1,8]=>011111011=>110111110
[10,7,6,5,4,3,2,9,8,1]=>011111111=>111111110
[2,1,10,7,6,5,4,9,8,3]=>100111111=>111111001
[10,9,6,5,4,3,8,7,2,1]=>101111111=>111111101
[2,1,4,3,10,7,6,9,8,5]=>101001111=>111100101
[4,3,2,1,10,7,6,9,8,5]=>111001111=>111100111
[10,3,2,9,6,5,8,7,4,1]=>011011111=>111110110
[2,1,10,9,6,5,8,7,4,3]=>101011111=>111110101
[10,9,8,5,4,7,6,3,2,1]=>110111111=>111111011
[10,8,9,6,7,4,5,2,3,1]=>010101011=>110101010
[2,1,7,8,9,10,3,4,5,6]=>100000001=>100000001
[3,7,1,8,9,10,2,4,5,6]=>000001001=>100100000
[4,7,8,1,9,10,2,3,5,6]=>000000101=>101000000
[5,7,8,9,1,10,2,3,4,6]=>000000011=>110000000
[6,7,8,9,10,1,2,3,4,5]=>000000001=>100000000
[5,6,8,9,1,2,10,3,4,7]=>000000011=>110000000
[4,6,8,1,9,2,10,3,5,7]=>000000111=>111000000
[3,6,1,8,9,2,10,4,5,7]=>000010011=>110010000
[2,1,6,8,9,3,10,4,5,7]=>100000011=>110000001
[2,1,5,8,3,9,10,4,6,7]=>100000101=>101000001
[3,5,1,8,2,9,10,4,6,7]=>000100101=>101001000
[4,5,8,1,2,9,10,3,6,7]=>000000101=>101000000
[7,3,2,8,9,10,1,4,5,6]=>010001001=>100100010
[3,4,1,2,8,9,10,5,6,7]=>001000001=>100000100
[2,1,4,3,8,9,10,5,6,7]=>101000001=>100000101
[2,1,4,3,7,9,5,10,6,8]=>101000011=>110000101
[3,4,1,2,7,9,5,10,6,8]=>001000011=>110000100
[4,5,7,1,2,9,3,10,6,8]=>000001011=>110100000
[3,5,1,7,2,9,4,10,6,8]=>000101011=>110101000
[2,1,5,7,3,9,4,10,6,8]=>100001011=>110100001
[2,1,6,7,9,3,4,10,5,8]=>100000011=>110000001
[3,6,1,7,9,2,4,10,5,8]=>000010011=>110010000
[4,6,7,1,9,2,3,10,5,8]=>000001011=>110100000
[5,6,7,9,1,2,3,10,4,8]=>000000011=>110000000
[8,5,4,3,2,9,10,1,6,7]=>011100101=>101001110
[2,1,5,6,3,4,9,10,7,8]=>100010001=>100010001
[3,5,1,6,2,4,9,10,7,8]=>000110001=>100011000
[4,5,6,1,2,3,9,10,7,8]=>000010001=>100010000
[3,4,1,2,6,5,9,10,7,8]=>001010001=>100010100
[2,1,4,3,6,5,9,10,7,8]=>101010001=>100010101
[2,1,4,3,6,5,10,9,8,7]=>101010111=>111010101
[4,3,2,1,6,5,10,9,8,7]=>111010111=>111010111
[6,3,2,5,4,1,10,9,8,7]=>011110111=>111011110
[10,3,2,5,4,9,8,7,6,1]=>010111111=>111111010
[2,1,6,5,4,3,10,9,8,7]=>101110111=>111011101
[6,5,4,3,2,1,10,9,8,7]=>111110111=>111011111
[10,5,4,3,2,9,8,7,6,1]=>011111111=>111111110
[2,1,10,5,4,9,8,7,6,3]=>100111111=>111111001
[10,9,4,3,8,7,6,5,2,1]=>101111111=>111111101
[9,7,5,10,3,8,2,6,1,4]=>000011111=>111110000
[2,1,4,3,10,9,8,7,6,5]=>101011111=>111110101
[4,3,2,1,10,9,8,7,6,5]=>111011111=>111110111
[10,3,2,9,8,7,6,5,4,1]=>011111111=>111111110
[2,1,10,9,8,7,6,5,4,3]=>101111111=>111111101
[9,10,8,7,6,5,4,3,1,2]=>011111101=>101111110
[10,9,8,7,6,5,4,3,2,1]=>111111111=>111111111
[3,2,5,1,4,6,7,8]=>0101000=>0001010
[4,2,5,1,3,6,7,8]=>0011000=>0001100
[5,2,4,1,3,6,7,8]=>0011000=>0001100
[3,2,6,1,4,5,7,8]=>0100100=>0010010
[4,2,6,1,3,5,7,8]=>0010100=>0010100
[5,3,6,1,2,4,7,8]=>0001100=>0011000
[6,2,4,1,3,5,7,8]=>0010100=>0010100
[6,3,5,1,2,4,7,8]=>0001100=>0011000
[5,2,7,1,3,4,6,8]=>0001010=>0101000
[5,3,7,1,2,4,6,8]=>0001010=>0101000
[5,4,7,1,2,3,6,8]=>0001010=>0101000
[6,2,7,1,3,4,5,8]=>0000110=>0110000
[6,3,7,1,2,4,5,8]=>0000110=>0110000
[6,4,7,1,2,3,5,8]=>0000110=>0110000
[7,3,5,1,2,4,6,8]=>0001010=>0101000
[7,3,6,1,2,4,5,8]=>0000110=>0110000
[7,4,6,1,2,3,5,8]=>0000110=>0110000
[3,2,8,1,4,5,6,7]=>0100001=>1000010
[4,2,8,1,3,5,6,7]=>0010001=>1000100
[5,2,8,1,3,4,6,7]=>0001001=>1001000
[5,4,8,1,2,3,6,7]=>0001001=>1001000
[6,2,8,1,3,4,5,7]=>0000101=>1010000
[6,3,8,1,2,4,5,7]=>0000101=>1010000
[6,4,8,1,2,3,5,7]=>0000101=>1010000
[6,5,8,1,2,3,4,7]=>0000101=>1010000
[7,2,8,1,3,4,5,6]=>0000011=>1100000
[7,3,8,1,2,4,5,6]=>0000011=>1100000
[7,4,8,1,2,3,5,6]=>0000011=>1100000
[7,5,8,1,2,3,4,6]=>0000011=>1100000
[8,2,4,1,3,5,6,7]=>0010001=>1000100
[8,3,5,1,2,4,6,7]=>0001001=>1001000
[8,3,6,1,2,4,5,7]=>0000101=>1010000
[8,3,7,1,2,4,5,6]=>0000011=>1100000
[8,4,7,1,2,3,5,6]=>0000011=>1100000
[8,5,7,1,2,3,4,6]=>0000011=>1100000
[3,2,5,7,1,4,6,8]=>0100010=>0100010
[4,2,5,7,1,3,6,8]=>0010010=>0100100
[4,3,5,7,1,2,6,8]=>0010010=>0100100
[5,2,4,7,1,3,6,8]=>0001010=>0101000
[5,3,4,7,1,2,6,8]=>0001010=>0101000
[4,2,6,7,1,3,5,8]=>0010010=>0100100
[5,2,6,7,1,3,4,8]=>0001010=>0101000
[5,3,6,7,1,2,4,8]=>0001010=>0101000
[6,2,5,7,1,3,4,8]=>0000110=>0110000
[6,3,5,7,1,2,4,8]=>0000110=>0110000
[7,2,4,6,1,3,5,8]=>0000110=>0110000
[7,3,4,6,1,2,5,8]=>0000110=>0110000
[7,3,5,6,1,2,4,8]=>0000110=>0110000
[3,2,5,8,1,4,6,7]=>0100001=>1000010
[4,2,5,8,1,3,6,7]=>0010001=>1000100
[4,3,5,8,1,2,6,7]=>0010001=>1000100
[5,2,4,8,1,3,6,7]=>0001001=>1001000
[3,2,6,8,1,4,5,7]=>0100001=>1000010
[4,2,6,8,1,3,5,7]=>0010001=>1000100
[4,3,6,8,1,2,5,7]=>0010001=>1000100
[5,2,6,8,1,3,4,7]=>0001001=>1001000
[6,2,4,8,1,3,5,7]=>0000101=>1010000
[6,2,5,8,1,3,4,7]=>0000101=>1010000
[6,3,5,8,1,2,4,7]=>0000101=>1010000
[6,4,5,8,1,2,3,7]=>0000101=>1010000
[3,2,7,8,1,4,5,6]=>0100001=>1000010
[4,3,7,8,1,2,5,6]=>0010001=>1000100
[5,3,7,8,1,2,4,6]=>0001001=>1001000
[5,4,7,8,1,2,3,6]=>0001001=>1001000
[6,2,7,8,1,3,4,5]=>0000101=>1010000
[6,3,7,8,1,2,4,5]=>0000101=>1010000
[6,4,7,8,1,2,3,5]=>0000101=>1010000
[7,2,4,8,1,3,5,6]=>0000011=>1100000
[7,3,4,8,1,2,5,6]=>0000011=>1100000
[7,3,5,8,1,2,4,6]=>0000011=>1100000
[7,4,5,8,1,2,3,6]=>0000011=>1100000
[7,4,6,8,1,2,3,5]=>0000011=>1100000
[8,2,4,6,1,3,5,7]=>0000101=>1010000
[8,3,4,6,1,2,5,7]=>0000101=>1010000
[8,2,5,6,1,3,4,7]=>0000101=>1010000
[8,3,5,6,1,2,4,7]=>0000101=>1010000
[8,2,4,7,1,3,5,6]=>0000011=>1100000
[8,2,5,7,1,3,4,6]=>0000011=>1100000
[8,3,5,7,1,2,4,6]=>0000011=>1100000
[8,2,6,7,1,3,4,5]=>0000011=>1100000
[8,4,6,7,1,2,3,5]=>0000011=>1100000
[3,6,2,5,1,4,7,8]=>0001100=>0011000
[4,6,2,5,1,3,7,8]=>0001100=>0011000
[4,6,3,5,1,2,7,8]=>0001100=>0011000
[5,6,2,4,1,3,7,8]=>0010100=>0010100
[3,7,2,5,1,4,6,8]=>0001010=>0101000
[4,7,3,5,1,2,6,8]=>0001010=>0101000
[5,7,2,4,1,3,6,8]=>0010010=>0100100
[5,7,3,4,1,2,6,8]=>0010010=>0100100
[3,7,2,6,1,4,5,8]=>0000110=>0110000
[4,7,3,6,1,2,5,8]=>0000110=>0110000
[5,7,2,6,1,3,4,8]=>0000110=>0110000
[5,7,3,6,1,2,4,8]=>0000110=>0110000
[6,7,2,5,1,3,4,8]=>0001010=>0101000
[4,8,2,5,1,3,6,7]=>0001001=>1001000
[5,8,3,4,1,2,6,7]=>0010001=>1000100
[3,8,2,6,1,4,5,7]=>0000101=>1010000
[4,8,2,6,1,3,5,7]=>0000101=>1010000
[5,8,3,6,1,2,4,7]=>0000101=>1010000
[5,8,4,6,1,2,3,7]=>0000101=>1010000
[6,8,2,4,1,3,5,7]=>0010001=>1000100
[6,8,3,4,1,2,5,7]=>0010001=>1000100
[6,8,3,5,1,2,4,7]=>0001001=>1001000
[6,8,4,5,1,2,3,7]=>0001001=>1001000
[3,8,2,7,1,4,5,6]=>0000011=>1100000
[4,8,2,7,1,3,5,6]=>0000011=>1100000
[4,8,3,7,1,2,5,6]=>0000011=>1100000
[5,8,2,7,1,3,4,6]=>0000011=>1100000
[5,8,3,7,1,2,4,6]=>0000011=>1100000
[5,8,4,7,1,2,3,6]=>0000011=>1100000
[6,8,2,7,1,3,4,5]=>0000011=>1100000
[6,8,3,7,1,2,4,5]=>0000011=>1100000
[6,8,5,7,1,2,3,4]=>0000011=>1100000
[7,8,2,4,1,3,5,6]=>0010001=>1000100
[7,8,2,5,1,3,4,6]=>0001001=>1001000
[7,8,3,5,1,2,4,6]=>0001001=>1001000
[7,8,4,6,1,2,3,5]=>0000101=>1010000
[4,3,2,6,1,5,7,8]=>0110100=>0010110
[5,3,2,6,1,4,7,8]=>0101100=>0011010
[5,4,2,6,1,3,7,8]=>0011100=>0011100
[6,3,2,5,1,4,7,8]=>0101100=>0011010
[6,4,2,5,1,3,7,8]=>0011100=>0011100
[6,5,2,4,1,3,7,8]=>0011100=>0011100
[4,3,2,7,1,5,6,8]=>0110010=>0100110
[5,3,2,7,1,4,6,8]=>0101010=>0101010
[5,4,3,7,1,2,6,8]=>0011010=>0101100
[6,3,2,7,1,4,5,8]=>0100110=>0110010
[6,4,2,7,1,3,5,8]=>0010110=>0110100
[6,4,3,7,1,2,5,8]=>0010110=>0110100
[6,5,2,7,1,3,4,8]=>0001110=>0111000
[6,5,3,7,1,2,4,8]=>0001110=>0111000
[7,3,2,5,1,4,6,8]=>0101010=>0101010
[7,4,2,5,1,3,6,8]=>0011010=>0101100
[7,3,2,6,1,4,5,8]=>0100110=>0110010
[7,4,2,6,1,3,5,8]=>0010110=>0110100
[7,4,3,6,1,2,5,8]=>0010110=>0110100
[7,5,2,6,1,3,4,8]=>0001110=>0111000
[7,5,3,6,1,2,4,8]=>0001110=>0111000
[7,6,3,5,1,2,4,8]=>0001110=>0111000
[4,3,2,8,1,5,6,7]=>0110001=>1000110
[5,3,2,8,1,4,6,7]=>0101001=>1001010
[5,4,3,8,1,2,6,7]=>0011001=>1001100
[6,3,2,8,1,4,5,7]=>0100101=>1010010
[6,4,2,8,1,3,5,7]=>0010101=>1010100
[6,4,3,8,1,2,5,7]=>0010101=>1010100
[6,5,2,8,1,3,4,7]=>0001101=>1011000
[6,5,3,8,1,2,4,7]=>0001101=>1011000
[6,5,4,8,1,2,3,7]=>0001101=>1011000
[7,3,2,8,1,4,5,6]=>0100011=>1100010
[7,4,2,8,1,3,5,6]=>0010011=>1100100
[7,4,3,8,1,2,5,6]=>0010011=>1100100
[7,5,3,8,1,2,4,6]=>0001011=>1101000
[7,5,4,8,1,2,3,6]=>0001011=>1101000
[7,6,2,8,1,3,4,5]=>0000111=>1110000
[8,3,2,5,1,4,6,7]=>0101001=>1001010
[8,4,2,5,1,3,6,7]=>0011001=>1001100
[8,3,2,6,1,4,5,7]=>0100101=>1010010
[8,4,2,6,1,3,5,7]=>0010101=>1010100
[8,5,3,6,1,2,4,7]=>0001101=>1011000
[8,6,2,4,1,3,5,7]=>0010101=>1010100
[8,6,2,5,1,3,4,7]=>0001101=>1011000
[8,3,2,7,1,4,5,6]=>0100011=>1100010
[8,4,2,7,1,3,5,6]=>0010011=>1100100
[8,4,3,7,1,2,5,6]=>0010011=>1100100
[8,5,2,7,1,3,4,6]=>0001011=>1101000
[8,5,3,7,1,2,4,6]=>0001011=>1101000
[8,5,4,7,1,2,3,6]=>0001011=>1101000
[8,6,3,7,1,2,4,5]=>0000111=>1110000
[8,7,2,4,1,3,5,6]=>0010011=>1100100
[8,7,2,5,1,3,4,6]=>0001011=>1101000
[8,7,3,5,1,2,4,6]=>0001011=>1101000
[8,7,2,6,1,3,4,5]=>0000111=>1110000
[8,7,3,6,1,2,4,5]=>0000111=>1110000
[8,7,4,6,1,2,3,5]=>0000111=>1110000
[3,6,2,5,8,1,4,7]=>0000101=>1010000
[4,6,3,5,8,1,2,7]=>0000101=>1010000
[5,6,2,4,8,1,3,7]=>0000101=>1010000
[4,7,2,5,8,1,3,6]=>0000011=>1100000
[4,7,3,5,8,1,2,6]=>0000011=>1100000
[5,7,2,4,8,1,3,6]=>0000011=>1100000
[5,7,3,4,8,1,2,6]=>0000011=>1100000
[3,7,2,6,8,1,4,5]=>0000011=>1100000
[4,7,3,6,8,1,2,5]=>0000011=>1100000
[5,7,2,6,8,1,3,4]=>0000011=>1100000
[5,7,4,6,8,1,2,3]=>0000011=>1100000
[6,7,3,4,8,1,2,5]=>0000011=>1100000
[6,7,3,5,8,1,2,4]=>0000011=>1100000
[3,8,2,5,7,1,4,6]=>0000011=>1100000
[4,8,2,5,7,1,3,6]=>0000011=>1100000
[4,8,3,5,7,1,2,6]=>0000011=>1100000
[5,8,2,4,7,1,3,6]=>0000011=>1100000
[3,8,2,6,7,1,4,5]=>0000011=>1100000
[4,8,3,6,7,1,2,5]=>0000011=>1100000
[5,8,2,6,7,1,3,4]=>0000011=>1100000
[5,8,3,6,7,1,2,4]=>0000011=>1100000
[5,8,4,6,7,1,2,3]=>0000011=>1100000
[6,8,2,5,7,1,3,4]=>0000011=>1100000
[6,8,3,5,7,1,2,4]=>0000011=>1100000
[6,8,4,5,7,1,2,3]=>0000011=>1100000
[7,8,2,4,6,1,3,5]=>0000101=>1010000
[7,8,3,4,6,1,2,5]=>0000101=>1010000
[7,8,2,5,6,1,3,4]=>0000101=>1010000
[7,8,3,5,6,1,2,4]=>0000101=>1010000
[4,3,2,6,8,1,5,7]=>0110001=>1000110
[5,3,2,6,8,1,4,7]=>0101001=>1001010
[5,4,2,6,8,1,3,7]=>0011001=>1001100
[5,4,3,6,8,1,2,7]=>0011001=>1001100
[6,3,2,5,8,1,4,7]=>0100101=>1010010
[6,4,3,5,8,1,2,7]=>0010101=>1010100
[6,5,2,4,8,1,3,7]=>0001101=>1011000
[4,3,2,7,8,1,5,6]=>0110001=>1000110
[5,3,2,7,8,1,4,6]=>0101001=>1001010
[5,4,2,7,8,1,3,6]=>0011001=>1001100
[5,4,3,7,8,1,2,6]=>0011001=>1001100
[6,4,2,7,8,1,3,5]=>0010101=>1010100
[6,4,3,7,8,1,2,5]=>0010101=>1010100
[6,5,2,7,8,1,3,4]=>0001101=>1011000
[7,4,2,5,8,1,3,6]=>0010011=>1100100
[7,4,3,5,8,1,2,6]=>0010011=>1100100
[7,5,3,4,8,1,2,6]=>0001011=>1101000
[7,3,2,6,8,1,4,5]=>0100011=>1100010
[7,5,2,6,8,1,3,4]=>0001011=>1101000
[7,5,3,6,8,1,2,4]=>0001011=>1101000
[7,6,2,4,8,1,3,5]=>0000111=>1110000
[7,6,3,5,8,1,2,4]=>0000111=>1110000
[8,3,2,5,7,1,4,6]=>0100011=>1100010
[8,4,2,5,7,1,3,6]=>0010011=>1100100
[8,5,2,4,7,1,3,6]=>0001011=>1101000
[8,3,2,6,7,1,4,5]=>0100011=>1100010
[8,4,2,6,7,1,3,5]=>0010011=>1100100
[8,5,2,6,7,1,3,4]=>0001011=>1101000
[8,5,3,6,7,1,2,4]=>0001011=>1101000
[8,6,2,4,7,1,3,5]=>0000111=>1110000
[8,6,2,5,7,1,3,4]=>0000111=>1110000
[8,6,3,5,7,1,2,4]=>0000111=>1110000
[8,7,2,4,6,1,3,5]=>0000111=>1110000
[8,7,3,4,6,1,2,5]=>0000111=>1110000
[8,7,2,5,6,1,3,4]=>0000111=>1110000
[8,7,3,5,6,1,2,4]=>0000111=>1110000
[4,3,7,2,6,1,5,8]=>0010110=>0110100
[5,3,7,2,6,1,4,8]=>0001110=>0111000
[5,4,7,2,6,1,3,8]=>0001110=>0111000
[6,3,7,2,5,1,4,8]=>0001110=>0111000
[6,4,7,2,5,1,3,8]=>0001110=>0111000
[6,4,7,3,5,1,2,8]=>0001110=>0111000
[7,3,6,2,5,1,4,8]=>0001110=>0111000
[4,3,8,2,6,1,5,7]=>0010101=>1010100
[5,3,8,2,6,1,4,7]=>0001101=>1011000
[5,4,8,2,6,1,3,7]=>0001101=>1011000
[5,4,8,3,6,1,2,7]=>0001101=>1011000
[6,3,8,2,5,1,4,7]=>0001101=>1011000
[6,4,8,2,5,1,3,7]=>0001101=>1011000
[6,4,8,3,5,1,2,7]=>0001101=>1011000
[6,5,8,2,4,1,3,7]=>0010101=>1010100
[6,5,8,3,4,1,2,7]=>0010101=>1010100
[4,3,8,2,7,1,5,6]=>0010011=>1100100
[5,3,8,2,7,1,4,6]=>0001011=>1101000
[5,4,8,2,7,1,3,6]=>0001011=>1101000
[5,4,8,3,7,1,2,6]=>0001011=>1101000
[6,3,8,2,7,1,4,5]=>0000111=>1110000
[6,4,8,2,7,1,3,5]=>0000111=>1110000
[6,4,8,3,7,1,2,5]=>0000111=>1110000
[6,5,8,2,7,1,3,4]=>0000111=>1110000
[7,3,8,2,5,1,4,6]=>0001011=>1101000
[7,4,8,3,5,1,2,6]=>0001011=>1101000
[7,5,8,2,4,1,3,6]=>0010011=>1100100
[7,5,8,3,4,1,2,6]=>0010011=>1100100
[7,3,8,2,6,1,4,5]=>0000111=>1110000
[7,4,8,2,6,1,3,5]=>0000111=>1110000
[7,5,8,2,6,1,3,4]=>0000111=>1110000
[7,5,8,3,6,1,2,4]=>0000111=>1110000
[7,5,8,4,6,1,2,3]=>0000111=>1110000
[7,6,8,2,5,1,3,4]=>0001011=>1101000
[7,6,8,3,5,1,2,4]=>0001011=>1101000
[8,3,6,2,5,1,4,7]=>0001101=>1011000
[8,4,6,2,5,1,3,7]=>0001101=>1011000
[8,5,6,2,4,1,3,7]=>0010101=>1010100
[8,3,7,2,5,1,4,6]=>0001011=>1101000
[8,4,7,3,5,1,2,6]=>0001011=>1101000
[8,5,7,2,4,1,3,6]=>0010011=>1100100
[8,3,7,2,6,1,4,5]=>0000111=>1110000
[8,4,7,2,6,1,3,5]=>0000111=>1110000
[8,4,7,3,6,1,2,5]=>0000111=>1110000
[8,5,7,2,6,1,3,4]=>0000111=>1110000
[8,6,7,2,4,1,3,5]=>0010011=>1100100
[8,6,7,2,5,1,3,4]=>0001011=>1101000
[8,6,7,3,5,1,2,4]=>0001011=>1101000
[5,4,3,2,7,1,6,8]=>0111010=>0101110
[6,4,3,2,7,1,5,8]=>0110110=>0110110
[6,5,3,2,7,1,4,8]=>0101110=>0111010
[6,5,4,2,7,1,3,8]=>0011110=>0111100
[7,5,3,2,6,1,4,8]=>0101110=>0111010
[7,5,4,2,6,1,3,8]=>0011110=>0111100
[7,6,3,2,5,1,4,8]=>0101110=>0111010
[5,4,3,2,8,1,6,7]=>0111001=>1001110
[6,5,3,2,8,1,4,7]=>0101101=>1011010
[6,5,4,2,8,1,3,7]=>0011101=>1011100
[6,5,4,3,8,1,2,7]=>0011101=>1011100
[7,5,3,2,8,1,4,6]=>0101011=>1101010
[7,5,4,2,8,1,3,6]=>0011011=>1101100
[7,6,3,2,8,1,4,5]=>0100111=>1110010
[7,6,4,3,8,1,2,5]=>0010111=>1110100
[7,6,5,2,8,1,3,4]=>0001111=>1111000
[7,6,5,3,8,1,2,4]=>0001111=>1111000
[8,5,3,2,6,1,4,7]=>0101101=>1011010
[8,5,4,2,6,1,3,7]=>0011101=>1011100
[8,6,4,2,5,1,3,7]=>0011101=>1011100
[8,6,5,2,4,1,3,7]=>0011101=>1011100
[8,5,3,2,7,1,4,6]=>0101011=>1101010
[8,6,3,2,7,1,4,5]=>0100111=>1110010
[8,6,4,2,7,1,3,5]=>0010111=>1110100
[8,6,4,3,7,1,2,5]=>0010111=>1110100
[8,6,5,3,7,1,2,4]=>0001111=>1111000
[8,7,3,2,6,1,4,5]=>0100111=>1110010
[8,7,4,2,6,1,3,5]=>0010111=>1110100
[8,7,4,3,6,1,2,5]=>0010111=>1110100
[8,7,5,2,6,1,3,4]=>0001111=>1111000
[8,7,5,3,6,1,2,4]=>0001111=>1111000
[8,7,6,2,4,1,3,5]=>0010111=>1110100
[8,7,6,2,5,1,3,4]=>0001111=>1111000
[8,7,6,3,5,1,2,4]=>0001111=>1111000
[4,8,3,7,2,6,1,5]=>0000111=>1110000
[5,8,3,7,2,6,1,4]=>0000111=>1110000
[5,8,4,7,2,6,1,3]=>0000111=>1110000
[5,8,4,7,3,6,1,2]=>0000111=>1110000
[6,8,3,7,2,5,1,4]=>0001011=>1101000
[6,8,4,7,2,5,1,3]=>0001011=>1101000
[6,8,4,7,3,5,1,2]=>0001011=>1101000
[6,8,5,7,2,4,1,3]=>0010011=>1100100
[6,8,5,7,3,4,1,2]=>0010011=>1100100
[7,8,3,6,2,5,1,4]=>0001101=>1011000
[7,8,4,6,2,5,1,3]=>0001101=>1011000
[7,8,4,6,3,5,1,2]=>0001101=>1011000
[7,8,5,6,2,4,1,3]=>0010101=>1010100
[5,4,3,8,2,7,1,6]=>0011011=>1101100
[6,4,3,8,2,7,1,5]=>0010111=>1110100
[6,5,3,8,2,7,1,4]=>0001111=>1111000
[6,5,4,8,2,7,1,3]=>0001111=>1111000
[6,5,4,8,3,7,1,2]=>0001111=>1111000
[7,4,3,8,2,6,1,5]=>0010111=>1110100
[7,5,3,8,2,6,1,4]=>0001111=>1111000
[7,5,4,8,2,6,1,3]=>0001111=>1111000
[7,6,3,8,2,5,1,4]=>0001111=>1111000
[7,6,4,8,2,5,1,3]=>0001111=>1111000
[7,6,5,8,2,4,1,3]=>0010111=>1110100
[8,4,3,7,2,6,1,5]=>0010111=>1110100
[8,5,3,7,2,6,1,4]=>0001111=>1111000
[8,5,4,7,2,6,1,3]=>0001111=>1111000
[8,5,4,7,3,6,1,2]=>0001111=>1111000
[8,6,3,7,2,5,1,4]=>0001111=>1111000
[8,6,4,7,2,5,1,3]=>0001111=>1111000
[8,6,4,7,3,5,1,2]=>0001111=>1111000
[8,6,5,7,2,4,1,3]=>0010111=>1110100
[8,7,3,6,2,5,1,4]=>0001111=>1111000
[8,7,4,6,2,5,1,3]=>0001111=>1111000
[8,7,4,6,3,5,1,2]=>0001111=>1111000
[8,7,5,6,2,4,1,3]=>0010111=>1110100
[6,5,4,3,2,8,1,7]=>0111101=>1011110
[7,6,4,3,2,8,1,5]=>0110111=>1110110
[7,6,5,4,2,8,1,3]=>0011111=>1111100
[8,5,4,3,2,7,1,6]=>0111011=>1101110
[8,6,4,3,2,7,1,5]=>0110111=>1110110
[8,6,5,3,2,7,1,4]=>0101111=>1111010
[8,6,5,4,2,7,1,3]=>0011111=>1111100
[8,7,4,3,2,6,1,5]=>0110111=>1110110
[8,7,5,3,2,6,1,4]=>0101111=>1111010
[8,7,5,4,2,6,1,3]=>0011111=>1111100
[8,7,6,3,2,5,1,4]=>0101111=>1111010
[8,7,6,4,2,5,1,3]=>0011111=>1111100
[8,7,6,5,2,4,1,3]=>0011111=>1111100
[8,1,2,3,4,7,5,6]=>0000011=>1100000
[8,1,2,3,6,4,5,7]=>0000101=>1010000
[8,1,2,3,7,4,5,6]=>0000011=>1100000
[7,1,2,3,6,4,8,5]=>0000111=>1110000
[5,1,2,3,8,7,4,6]=>0001011=>1101000
[8,1,2,3,6,7,4,5]=>0000011=>1100000
[4,1,2,8,3,7,5,6]=>0010011=>1100100
[8,1,2,5,3,4,6,7]=>0001001=>1001000
[7,1,2,5,3,4,8,6]=>0001011=>1101000
[8,1,2,6,3,4,5,7]=>0000101=>1010000
[7,1,2,6,3,4,8,5]=>0000111=>1110000
[6,1,2,5,3,8,4,7]=>0001101=>1011000
[8,1,2,5,3,7,4,6]=>0001011=>1101000
[8,1,2,6,3,7,4,5]=>0000111=>1110000
[6,1,2,5,3,7,8,4]=>0001101=>1011000
[4,1,2,8,6,3,5,7]=>0010101=>1010100
[4,1,2,8,7,3,5,6]=>0010011=>1100100
[4,1,2,7,6,3,8,5]=>0010111=>1110100
[8,1,2,5,6,3,4,7]=>0000101=>1010000
[8,1,2,5,7,3,4,6]=>0000011=>1100000
[8,1,2,7,6,3,4,5]=>0000111=>1110000
[7,1,2,5,6,3,8,4]=>0000111=>1110000
[4,1,2,5,8,7,3,6]=>0010011=>1100100
[4,1,2,8,6,7,3,5]=>0010011=>1100100
[8,1,2,5,6,7,3,4]=>0000011=>1100000
[3,1,8,2,4,7,5,6]=>0100011=>1100010
[3,1,8,2,6,4,5,7]=>0100101=>1010010
[3,1,8,2,7,4,5,6]=>0100011=>1100010
[3,1,7,2,6,4,8,5]=>0100111=>1110010
[3,1,5,2,8,7,4,6]=>0101011=>1101010
[3,1,8,2,6,7,4,5]=>0100011=>1100010
[8,1,4,2,3,5,6,7]=>0010001=>1000100
[7,1,4,2,3,5,8,6]=>0010011=>1100100
[6,1,4,2,3,8,5,7]=>0010101=>1010100
[8,1,4,2,3,7,5,6]=>0010011=>1100100
[6,1,4,2,3,7,8,5]=>0010101=>1010100
[8,1,5,2,3,4,6,7]=>0001001=>1001000
[7,1,5,2,3,4,8,6]=>0001011=>1101000
[8,1,7,2,3,4,5,6]=>0000011=>1100000
[6,1,5,2,3,8,4,7]=>0001101=>1011000
[8,1,5,2,3,7,4,6]=>0001011=>1101000
[6,1,8,2,3,7,4,5]=>0000111=>1110000
[6,1,5,2,3,7,8,4]=>0001101=>1011000
[5,1,4,2,8,3,6,7]=>0011001=>1001100
[5,1,4,2,7,3,8,6]=>0011011=>1101100
[8,1,4,2,6,3,5,7]=>0010101=>1010100
[8,1,4,2,7,3,5,6]=>0010011=>1100100
[7,1,4,2,6,3,8,5]=>0010111=>1110100
[8,1,5,2,6,3,4,7]=>0001101=>1011000
[8,1,5,2,7,3,4,6]=>0001011=>1101000
[7,1,8,2,6,3,4,5]=>0000111=>1110000
[7,1,5,2,6,3,8,4]=>0001111=>1111000
[5,1,4,2,6,8,3,7]=>0011001=>1001100
[5,1,4,2,8,7,3,6]=>0011011=>1101100
[8,1,4,2,6,7,3,5]=>0010011=>1100100
[8,1,5,2,6,7,3,4]=>0001011=>1101000
[5,1,4,2,6,7,8,3]=>0011001=>1001100
[3,1,4,8,2,7,5,6]=>0100011=>1100010
[3,1,8,5,2,4,6,7]=>0101001=>1001010
[3,1,7,5,2,4,8,6]=>0101011=>1101010
[3,1,8,6,2,4,5,7]=>0100101=>1010010
[3,1,7,6,2,4,8,5]=>0100111=>1110010
[3,1,6,5,2,8,4,7]=>0101101=>1011010
[3,1,8,5,2,7,4,6]=>0101011=>1101010
[3,1,8,6,2,7,4,5]=>0100111=>1110010
[3,1,6,5,2,7,8,4]=>0101101=>1011010
[8,1,4,5,2,3,6,7]=>0001001=>1001000
[7,1,4,5,2,3,8,6]=>0001011=>1101000
[8,1,4,6,2,3,5,7]=>0000101=>1010000
[7,1,4,8,2,3,5,6]=>0000011=>1100000
[7,1,4,6,2,3,8,5]=>0000111=>1110000
[8,1,6,5,2,3,4,7]=>0001101=>1011000
[7,1,8,5,2,3,4,6]=>0001011=>1101000
[7,1,8,6,2,3,4,5]=>0000111=>1110000
[7,1,6,5,2,3,8,4]=>0001111=>1111000
[6,1,4,5,2,8,3,7]=>0001101=>1011000
[8,1,4,5,2,7,3,6]=>0001011=>1101000
[8,1,4,6,2,7,3,5]=>0000111=>1110000
[8,1,6,5,2,7,3,4]=>0001111=>1111000
[6,1,4,5,2,7,8,3]=>0001101=>1011000
[3,1,4,8,6,2,5,7]=>0100101=>1010010
[3,1,4,8,7,2,5,6]=>0100011=>1100010
[3,1,4,7,6,2,8,5]=>0100111=>1110010
[3,1,8,5,6,2,4,7]=>0100101=>1010010
[3,1,8,5,7,2,4,6]=>0100011=>1100010
[3,1,8,7,6,2,4,5]=>0100111=>1110010
[3,1,7,5,6,2,8,4]=>0100111=>1110010
[8,1,4,5,6,2,3,7]=>0000101=>1010000
[8,1,4,5,7,2,3,6]=>0000011=>1100000
[8,1,4,7,6,2,3,5]=>0000111=>1110000
[8,1,7,5,6,2,3,4]=>0000111=>1110000
[7,1,4,5,6,2,8,3]=>0000111=>1110000
[3,1,4,5,8,7,2,6]=>0100011=>1100010
[3,1,4,8,6,7,2,5]=>0100011=>1100010
[3,1,8,5,6,7,2,4]=>0100011=>1100010
[8,1,4,5,6,7,2,3]=>0000011=>1100000
[2,8,1,3,4,7,5,6]=>0000011=>1100000
[2,8,1,3,6,4,5,7]=>0000101=>1010000
[2,8,1,3,7,4,5,6]=>0000011=>1100000
[2,7,1,3,6,4,8,5]=>0000111=>1110000
[2,5,1,3,8,7,4,6]=>0001011=>1101000
[2,8,1,3,6,7,4,5]=>0000011=>1100000
[2,4,1,8,3,7,5,6]=>0010011=>1100100
[2,8,1,5,3,4,6,7]=>0001001=>1001000
[2,7,1,5,3,4,8,6]=>0001011=>1101000
[2,8,1,6,3,4,5,7]=>0000101=>1010000
[2,7,1,6,3,4,8,5]=>0000111=>1110000
[2,6,1,5,3,8,4,7]=>0001101=>1011000
[2,8,1,5,3,7,4,6]=>0001011=>1101000
[2,6,1,5,3,7,8,4]=>0001101=>1011000
[2,4,1,8,6,3,5,7]=>0010101=>1010100
[2,4,1,8,7,3,5,6]=>0010011=>1100100
[2,4,1,7,6,3,8,5]=>0010111=>1110100
[2,8,1,5,6,3,4,7]=>0000101=>1010000
[2,8,1,5,7,3,4,6]=>0000011=>1100000
[2,8,1,7,6,3,4,5]=>0000111=>1110000
[2,7,1,5,6,3,8,4]=>0000111=>1110000
[2,4,1,5,8,7,3,6]=>0010011=>1100100
[2,4,1,8,6,7,3,5]=>0010011=>1100100
[2,8,1,5,6,7,3,4]=>0000011=>1100000
[7,3,1,2,4,5,8,6]=>0100011=>1100010
[6,3,1,2,4,8,5,7]=>0100101=>1010010
[8,3,1,2,4,7,5,6]=>0100011=>1100010
[6,3,1,2,4,7,8,5]=>0100101=>1010010
[5,3,1,2,8,4,6,7]=>0101001=>1001010
[5,3,1,2,7,4,8,6]=>0101011=>1101010
[8,3,1,2,6,4,5,7]=>0100101=>1010010
[8,3,1,2,7,4,5,6]=>0100011=>1100010
[7,3,1,2,6,4,8,5]=>0100111=>1110010
[5,3,1,2,6,8,4,7]=>0101001=>1001010
[5,3,1,2,8,7,4,6]=>0101011=>1101010
[8,3,1,2,6,7,4,5]=>0100011=>1100010
[5,3,1,2,6,7,8,4]=>0101001=>1001010
[7,4,1,2,3,5,8,6]=>0010011=>1100100
[6,4,1,2,3,8,5,7]=>0010101=>1010100
[8,4,1,2,3,7,5,6]=>0010011=>1100100
[6,4,1,2,3,7,8,5]=>0010101=>1010100
[7,6,1,2,3,4,8,5]=>0000111=>1110000
[5,8,1,2,3,7,4,6]=>0000011=>1100000
[8,6,1,2,3,7,4,5]=>0000111=>1110000
[5,4,1,2,8,3,6,7]=>0011001=>1001100
[5,4,1,2,7,3,8,6]=>0011011=>1101100
[8,4,1,2,6,3,5,7]=>0010101=>1010100
[8,4,1,2,7,3,5,6]=>0010011=>1100100
[7,4,1,2,6,3,8,5]=>0010111=>1110100
[5,8,1,2,6,3,4,7]=>0000101=>1010000
[5,8,1,2,7,3,4,6]=>0000011=>1100000
[8,7,1,2,6,3,4,5]=>0000111=>1110000
[5,7,1,2,6,3,8,4]=>0000111=>1110000
[5,4,1,2,6,8,3,7]=>0011001=>1001100
[5,4,1,2,8,7,3,6]=>0011011=>1101100
[8,4,1,2,6,7,3,5]=>0010011=>1100100
[5,8,1,2,6,7,3,4]=>0000011=>1100000
[5,4,1,2,6,7,8,3]=>0011001=>1001100
[4,3,1,8,2,5,6,7]=>0110001=>1000110
[4,3,1,7,2,5,8,6]=>0110011=>1100110
[4,3,1,6,2,8,5,7]=>0110101=>1010110
[4,3,1,8,2,7,5,6]=>0110011=>1100110
[4,3,1,6,2,7,8,5]=>0110101=>1010110
[8,3,1,5,2,4,6,7]=>0101001=>1001010
[7,3,1,5,2,4,8,6]=>0101011=>1101010
[8,3,1,6,2,4,5,7]=>0100101=>1010010
[7,3,1,8,2,4,5,6]=>0100011=>1100010
[7,3,1,6,2,4,8,5]=>0100111=>1110010
[6,3,1,5,2,8,4,7]=>0101101=>1011010
[8,3,1,5,2,7,4,6]=>0101011=>1101010
[8,3,1,6,2,7,4,5]=>0100111=>1110010
[6,3,1,5,2,7,8,4]=>0101101=>1011010
[8,4,1,5,2,3,6,7]=>0011001=>1001100
[7,4,1,5,2,3,8,6]=>0011011=>1101100
[8,4,1,6,2,3,5,7]=>0010101=>1010100
[7,4,1,8,2,3,5,6]=>0010011=>1100100
[7,4,1,6,2,3,8,5]=>0010111=>1110100
[6,8,1,5,2,3,4,7]=>0001001=>1001000
[8,7,1,5,2,3,4,6]=>0001011=>1101000
[8,7,1,6,2,3,4,5]=>0000111=>1110000
[6,7,1,5,2,3,8,4]=>0001011=>1101000
[6,4,1,5,2,8,3,7]=>0011101=>1011100
[8,4,1,5,2,7,3,6]=>0011011=>1101100
[8,4,1,6,2,7,3,5]=>0010111=>1110100
[6,8,1,5,2,7,3,4]=>0001011=>1101000
[6,4,1,5,2,7,8,3]=>0011101=>1011100
[4,3,1,5,8,2,6,7]=>0110001=>1000110
[4,3,1,5,7,2,8,6]=>0110011=>1100110
[4,3,1,8,6,2,5,7]=>0110101=>1010110
[4,3,1,8,7,2,5,6]=>0110011=>1100110
[4,3,1,7,6,2,8,5]=>0110111=>1110110
[8,3,1,5,6,2,4,7]=>0100101=>1010010
[8,3,1,5,7,2,4,6]=>0100011=>1100010
[8,3,1,7,6,2,4,5]=>0100111=>1110010
[7,3,1,5,6,2,8,4]=>0100111=>1110010
[8,4,1,5,6,2,3,7]=>0010101=>1010100
[8,4,1,5,7,2,3,6]=>0010011=>1100100
[8,4,1,7,6,2,3,5]=>0010111=>1110100
[7,8,1,5,6,2,3,4]=>0000101=>1010000
[7,4,1,5,6,2,8,3]=>0010111=>1110100
[4,3,1,5,6,8,2,7]=>0110001=>1000110
[4,3,1,5,8,7,2,6]=>0110011=>1100110
[4,3,1,8,6,7,2,5]=>0110011=>1100110
[8,3,1,5,6,7,2,4]=>0100011=>1100010
[8,4,1,5,6,7,2,3]=>0010011=>1100100
[4,3,1,5,6,7,8,2]=>0110001=>1000110
[2,3,8,1,4,7,5,6]=>0000011=>1100000
[2,3,8,1,6,4,5,7]=>0000101=>1010000
[2,3,8,1,7,4,5,6]=>0000011=>1100000
[2,3,7,1,6,4,8,5]=>0000111=>1110000
[2,3,5,1,8,7,4,6]=>0001011=>1101000
[2,3,8,1,6,7,4,5]=>0000011=>1100000
[2,8,4,1,3,5,6,7]=>0010001=>1000100
[2,7,4,1,3,5,8,6]=>0010011=>1100100
[2,6,4,1,3,8,5,7]=>0010101=>1010100
[2,8,4,1,3,7,5,6]=>0010011=>1100100
[2,6,4,1,3,7,8,5]=>0010101=>1010100
[2,8,5,1,3,4,6,7]=>0001001=>1001000
[2,7,5,1,3,4,8,6]=>0001011=>1101000
[2,8,7,1,3,4,5,6]=>0000011=>1100000
[2,6,5,1,3,8,4,7]=>0001101=>1011000
[2,8,5,1,3,7,4,6]=>0001011=>1101000
[2,6,8,1,3,7,4,5]=>0000011=>1100000
[2,6,5,1,3,7,8,4]=>0001101=>1011000
[2,5,4,1,8,3,6,7]=>0011001=>1001100
[2,5,4,1,7,3,8,6]=>0011011=>1101100
[2,8,4,1,6,3,5,7]=>0010101=>1010100
[2,8,4,1,7,3,5,6]=>0010011=>1100100
[2,7,4,1,6,3,8,5]=>0010111=>1110100
[2,8,5,1,6,3,4,7]=>0001101=>1011000
[2,8,5,1,7,3,4,6]=>0001011=>1101000
[2,7,8,1,6,3,4,5]=>0000101=>1010000
[2,7,5,1,6,3,8,4]=>0001111=>1111000
[2,5,4,1,6,8,3,7]=>0011001=>1001100
[2,5,4,1,8,7,3,6]=>0011011=>1101100
[2,8,4,1,6,7,3,5]=>0010011=>1100100
[2,8,5,1,6,7,3,4]=>0001011=>1101000
[2,5,4,1,6,7,8,3]=>0011001=>1001100
[7,3,4,1,2,5,8,6]=>0010011=>1100100
[6,3,4,1,2,8,5,7]=>0010101=>1010100
[8,3,4,1,2,7,5,6]=>0010011=>1100100
[6,3,4,1,2,7,8,5]=>0010101=>1010100
[7,3,5,1,2,4,8,6]=>0001011=>1101000
[6,3,7,1,2,4,8,5]=>0000111=>1110000
[6,3,5,1,2,8,4,7]=>0001101=>1011000
[8,3,5,1,2,7,4,6]=>0001011=>1101000
[6,3,8,1,2,7,4,5]=>0000111=>1110000
[6,3,5,1,2,7,8,4]=>0001101=>1011000
[7,5,4,1,2,3,8,6]=>0011011=>1101100
[6,8,4,1,2,3,5,7]=>0010001=>1000100
[6,7,4,1,2,3,8,5]=>0010011=>1100100
[6,8,5,1,2,3,4,7]=>0001001=>1001000
[6,7,5,1,2,3,8,4]=>0001011=>1101000
[6,5,4,1,2,8,3,7]=>0011101=>1011100
[8,5,4,1,2,7,3,6]=>0011011=>1101100
[6,8,4,1,2,7,3,5]=>0010011=>1100100
[6,8,5,1,2,7,3,4]=>0001011=>1101000
[6,5,4,1,2,7,8,3]=>0011101=>1011100
[5,3,4,1,8,2,6,7]=>0011001=>1001100
[5,3,4,1,7,2,8,6]=>0011011=>1101100
[8,3,4,1,6,2,5,7]=>0010101=>1010100
[8,3,4,1,7,2,5,6]=>0010011=>1100100
[7,3,4,1,6,2,8,5]=>0010111=>1110100
[8,3,5,1,6,2,4,7]=>0001101=>1011000
[8,3,5,1,7,2,4,6]=>0001011=>1101000
[7,3,8,1,6,2,4,5]=>0000111=>1110000
[7,3,5,1,6,2,8,4]=>0001111=>1111000
[8,5,4,1,6,2,3,7]=>0011101=>1011100
[8,5,4,1,7,2,3,6]=>0011011=>1101100
[7,8,4,1,6,2,3,5]=>0010101=>1010100
[7,8,5,1,6,2,3,4]=>0001101=>1011000
[7,5,4,1,6,2,8,3]=>0011111=>1111100
[5,3,4,1,6,8,2,7]=>0011001=>1001100
[5,3,4,1,8,7,2,6]=>0011011=>1101100
[8,3,4,1,6,7,2,5]=>0010011=>1100100
[8,3,5,1,6,7,2,4]=>0001011=>1101000
[8,5,4,1,6,7,2,3]=>0011011=>1101100
[5,3,4,1,6,7,8,2]=>0011001=>1001100
[2,3,4,8,1,7,5,6]=>0000011=>1100000
[2,3,8,5,1,4,6,7]=>0001001=>1001000
[2,3,7,5,1,4,8,6]=>0001011=>1101000
[2,3,8,6,1,4,5,7]=>0000101=>1010000
[2,3,7,6,1,4,8,5]=>0000111=>1110000
[2,3,6,5,1,8,4,7]=>0001101=>1011000
[2,3,8,5,1,7,4,6]=>0001011=>1101000
[2,3,8,6,1,7,4,5]=>0000111=>1110000
[2,3,6,5,1,7,8,4]=>0001101=>1011000
[2,8,4,5,1,3,6,7]=>0001001=>1001000
[2,7,4,5,1,3,8,6]=>0001011=>1101000
[2,8,4,6,1,3,5,7]=>0000101=>1010000
[2,7,4,8,1,3,5,6]=>0000011=>1100000
[2,7,4,6,1,3,8,5]=>0000111=>1110000
[2,8,6,5,1,3,4,7]=>0001101=>1011000
[2,7,8,5,1,3,4,6]=>0001001=>1001000
[2,7,8,6,1,3,4,5]=>0000101=>1010000
[2,7,6,5,1,3,8,4]=>0001111=>1111000
[2,6,4,5,1,8,3,7]=>0001101=>1011000
[2,8,4,5,1,7,3,6]=>0001011=>1101000
[2,8,4,6,1,7,3,5]=>0000111=>1110000
[2,8,6,5,1,7,3,4]=>0001111=>1111000
[2,6,4,5,1,7,8,3]=>0001101=>1011000
[7,3,4,5,1,2,8,6]=>0001011=>1101000
[7,3,4,6,1,2,8,5]=>0000111=>1110000
[8,3,6,5,1,2,4,7]=>0001101=>1011000
[7,3,8,5,1,2,4,6]=>0001011=>1101000
[7,3,8,6,1,2,4,5]=>0000111=>1110000
[7,3,6,5,1,2,8,4]=>0001111=>1111000
[7,6,4,5,1,2,8,3]=>0001111=>1111000
[6,3,4,5,1,8,2,7]=>0001101=>1011000
[8,3,4,5,1,7,2,6]=>0001011=>1101000
[8,3,4,6,1,7,2,5]=>0000111=>1110000
[8,3,6,5,1,7,2,4]=>0001111=>1111000
[8,6,4,5,1,7,2,3]=>0001111=>1111000
[6,3,4,5,1,7,8,2]=>0001101=>1011000
[2,3,4,8,6,1,5,7]=>0000101=>1010000
[2,3,4,8,7,1,5,6]=>0000011=>1100000
[2,3,4,7,6,1,8,5]=>0000111=>1110000
[2,3,8,5,6,1,4,7]=>0000101=>1010000
[2,3,8,5,7,1,4,6]=>0000011=>1100000
[2,3,8,7,6,1,4,5]=>0000111=>1110000
[2,3,7,5,6,1,8,4]=>0000111=>1110000
[2,8,4,5,6,1,3,7]=>0000101=>1010000
[2,8,4,5,7,1,3,6]=>0000011=>1100000
[2,8,4,7,6,1,3,5]=>0000111=>1110000
[2,8,7,5,6,1,3,4]=>0000111=>1110000
[2,7,4,5,6,1,8,3]=>0000111=>1110000
[8,3,4,5,7,1,2,6]=>0000011=>1100000
[8,3,4,7,6,1,2,5]=>0000111=>1110000
[8,3,7,5,6,1,2,4]=>0000111=>1110000
[7,3,4,5,6,1,8,2]=>0000111=>1110000
[2,3,4,5,8,7,1,6]=>0000011=>1100000
[2,3,4,8,6,7,1,5]=>0000011=>1100000
[2,3,8,5,6,7,1,4]=>0000011=>1100000
[2,8,4,5,6,7,1,3]=>0000011=>1100000
[9,1,2,3,4,5,6,7,8]=>00000001=>10000000
[8,1,2,3,4,5,6,9,7]=>00000011=>11000000
[7,1,2,3,4,5,9,6,8]=>00000101=>10100000
[9,1,2,3,4,5,8,6,7]=>00000011=>11000000
[7,1,2,3,4,5,8,9,6]=>00000101=>10100000
[6,1,2,3,4,9,5,7,8]=>00001001=>10010000
[6,1,2,3,4,8,5,9,7]=>00001011=>11010000
[9,1,2,3,4,7,5,6,8]=>00000101=>10100000
[9,1,2,3,4,8,5,6,7]=>00000011=>11000000
[8,1,2,3,4,7,5,9,6]=>00000111=>11100000
[6,1,2,3,4,7,9,5,8]=>00001001=>10010000
[6,1,2,3,4,9,8,5,7]=>00001011=>11010000
[9,1,2,3,4,7,8,5,6]=>00000011=>11000000
[6,1,2,3,4,7,8,9,5]=>00001001=>10010000
[5,1,2,3,9,4,6,7,8]=>00010001=>10001000
[5,1,2,3,8,4,6,9,7]=>00010011=>11001000
[9,1,2,3,6,4,5,7,8]=>00001001=>10010000
[8,1,2,3,9,4,5,6,7]=>00000011=>11000000
[5,1,2,3,9,8,4,6,7]=>00010011=>11001000
[9,1,2,3,6,8,4,5,7]=>00000011=>11000000
[5,1,2,3,6,9,8,4,7]=>00010011=>11001000
[5,1,2,3,6,7,8,9,4]=>00010001=>10001000
[4,1,2,8,3,5,6,9,7]=>00100011=>11000100
[4,1,2,9,3,5,8,6,7]=>00100011=>11000100
[4,1,2,9,3,8,5,6,7]=>00100011=>11000100
[9,1,2,5,3,4,6,7,8]=>00010001=>10001000
[9,1,2,8,3,4,5,6,7]=>00000011=>11000000
[7,1,2,8,3,4,5,9,6]=>00000111=>11100000
[4,1,2,5,9,3,6,7,8]=>00100001=>10000100
[4,1,2,8,9,3,5,6,7]=>00100001=>10000100
[8,1,2,5,9,3,4,6,7]=>00000011=>11000000
[8,1,2,9,6,3,4,5,7]=>00001011=>11010000
[4,1,2,5,9,8,3,6,7]=>00100011=>11000100
[9,1,2,8,6,7,3,4,5]=>00000111=>11100000
[4,1,2,5,6,7,9,3,8]=>00100001=>10000100
[4,1,2,9,6,7,8,3,5]=>00100011=>11000100
[9,1,2,5,6,7,8,3,4]=>00000011=>11000000
[4,1,2,5,6,7,8,9,3]=>00100001=>10000100
[3,1,9,2,4,5,6,7,8]=>01000001=>10000010
[3,1,8,2,4,5,6,9,7]=>01000011=>11000010
[3,1,9,2,4,5,8,6,7]=>01000011=>11000010
[3,1,5,2,7,4,9,6,8]=>01010101=>10101010
[8,1,4,2,3,5,6,9,7]=>00100011=>11000100
[9,1,4,2,3,5,8,6,7]=>00100011=>11000100
[6,1,4,2,3,7,8,9,5]=>00101001=>10010100
[9,1,8,2,3,4,5,6,7]=>00000011=>11000000
[8,1,7,2,3,4,5,9,6]=>00000111=>11100000
[3,1,4,9,2,5,6,7,8]=>01000001=>10000010
[3,1,4,9,2,5,8,6,7]=>01000011=>11000010
[3,1,9,8,2,4,5,6,7]=>01000011=>11000010
[9,1,4,5,2,3,6,7,8]=>00010001=>10001000
[7,1,4,5,2,3,8,9,6]=>00010101=>10101000
[7,1,4,9,2,3,5,6,8]=>00000101=>10100000
[9,1,4,8,2,3,5,6,7]=>00000011=>11000000
[9,1,6,5,2,3,4,7,8]=>00011001=>10011000
[7,1,9,6,2,3,4,5,8]=>00001101=>10110000
[9,1,8,6,2,3,4,5,7]=>00001011=>11010000
[7,1,8,9,2,3,4,5,6]=>00000101=>10100000
[3,1,4,8,9,2,5,6,7]=>01000001=>10000010
[3,1,8,9,7,2,4,5,6]=>01000101=>10100010
[8,1,4,5,6,2,3,9,7]=>00001011=>11010000
[8,1,4,9,7,2,3,5,6]=>00000111=>11100000
[8,1,9,5,6,2,3,4,7]=>00001011=>11010000
[8,1,9,7,6,2,3,4,5]=>00001111=>11110000
[7,1,4,5,6,2,8,9,3]=>00001101=>10110000
[3,1,4,5,6,9,2,7,8]=>01000001=>10000010
[3,1,4,5,6,8,2,9,7]=>01000011=>11000010
[3,1,4,9,8,7,2,5,6]=>01000111=>11100010
[3,1,9,8,6,7,2,4,5]=>01000111=>11100010
[9,1,4,5,6,7,2,3,8]=>00000101=>10100000
[9,1,4,8,6,7,2,3,5]=>00000111=>11100000
[9,1,8,5,6,7,2,3,4]=>00000111=>11100000
[8,1,4,5,6,7,2,9,3]=>00000111=>11100000
[3,1,4,5,6,7,9,2,8]=>01000001=>10000010
[3,1,4,9,6,7,8,2,5]=>01000011=>11000010
[3,1,9,5,6,7,8,2,4]=>01000011=>11000010
[9,1,4,5,6,7,8,2,3]=>00000011=>11000000
[3,1,4,5,6,7,8,9,2]=>01000001=>10000010
[2,9,1,3,4,5,6,7,8]=>00000001=>10000000
[2,8,1,3,4,5,6,9,7]=>00000011=>11000000
[2,7,1,3,4,5,9,6,8]=>00000101=>10100000
[2,9,1,3,4,5,8,6,7]=>00000011=>11000000
[2,7,1,3,4,5,8,9,6]=>00000101=>10100000
[2,6,1,3,4,9,5,7,8]=>00001001=>10010000
[2,9,1,3,4,8,5,6,7]=>00000011=>11000000
[2,8,1,3,9,4,5,6,7]=>00000011=>11000000
[2,9,1,3,8,7,4,5,6]=>00000111=>11100000
[2,9,1,3,6,7,8,4,5]=>00000011=>11000000
[2,5,1,3,6,7,8,9,4]=>00010001=>10001000
[2,4,1,6,3,8,5,9,7]=>00101011=>11010100
[2,9,1,8,3,4,5,6,7]=>00000011=>11000000
[2,7,1,6,3,4,8,9,5]=>00001101=>10110000
[2,6,1,5,3,7,8,9,4]=>00011001=>10011000
[2,4,1,5,9,3,6,7,8]=>00100001=>10000100
[2,4,1,8,9,3,5,6,7]=>00100001=>10000100
[2,8,1,9,7,3,4,5,6]=>00000111=>11100000
[2,9,1,8,6,7,3,4,5]=>00000111=>11100000
[2,4,1,5,6,7,9,3,8]=>00100001=>10000100
[2,4,1,5,6,9,8,3,7]=>00100011=>11000100
[2,9,1,5,6,7,8,3,4]=>00000011=>11000000
[2,4,1,5,6,7,8,9,3]=>00100001=>10000100
[9,3,1,2,4,5,6,7,8]=>01000001=>10000010
[8,3,1,2,4,5,6,9,7]=>01000011=>11000010
[9,3,1,2,4,5,8,6,7]=>01000011=>11000010
[6,3,1,2,4,7,8,9,5]=>01001001=>10010010
[9,3,1,2,6,7,8,4,5]=>01000011=>11000010
[5,3,1,2,6,7,8,9,4]=>01010001=>10001010
[9,4,1,2,3,5,6,7,8]=>00100001=>10000100
[7,4,1,2,3,5,8,9,6]=>00100101=>10100100
[6,4,1,2,3,7,8,9,5]=>00101001=>10010100
[5,9,1,2,3,4,6,7,8]=>00000001=>10000000
[5,8,1,2,3,4,6,9,7]=>00000011=>11000000
[5,7,1,2,3,4,8,9,6]=>00000101=>10100000
[9,6,1,2,3,4,5,7,8]=>00001001=>10010000
[8,6,1,2,3,4,5,9,7]=>00001011=>11010000
[9,7,1,2,3,4,5,6,8]=>00000101=>10100000
[8,9,1,2,3,4,5,6,7]=>00000001=>10000000
[8,7,1,2,3,4,5,9,6]=>00000111=>11100000
[7,6,1,2,3,4,9,5,8]=>00001101=>10110000
[9,6,1,2,3,4,8,5,7]=>00001011=>11010000
[9,7,1,2,3,4,8,5,6]=>00000111=>11100000
[7,6,1,2,3,4,8,9,5]=>00001101=>10110000
[5,6,1,2,3,9,4,7,8]=>00001001=>10010000
[5,9,1,2,3,8,4,6,7]=>00000011=>11000000
[9,6,1,2,3,7,4,5,8]=>00001101=>10110000
[9,8,1,2,3,7,4,5,6]=>00000111=>11100000
[8,6,1,2,3,7,4,9,5]=>00001111=>11110000
[5,6,1,2,3,7,9,4,8]=>00001001=>10010000
[9,6,1,2,3,7,8,4,5]=>00001011=>11010000
[5,6,1,2,3,7,8,9,4]=>00001001=>10010000
[5,4,1,2,9,3,6,7,8]=>00110001=>10001100
[8,4,1,2,9,3,5,6,7]=>00100011=>11000100
[5,9,1,2,6,3,4,7,8]=>00001001=>10010000
[5,8,1,2,9,3,4,6,7]=>00000011=>11000000
[9,7,1,2,6,3,8,4,5]=>00001111=>11110000
[5,4,1,2,6,9,3,7,8]=>00110001=>10001100
[9,8,1,2,6,7,3,4,5]=>00000111=>11100000
[5,4,1,2,6,7,9,3,8]=>00110001=>10001100
[5,4,1,2,6,7,8,9,3]=>00110001=>10001100
[4,3,1,9,2,5,6,7,8]=>01100001=>10000110
[9,3,1,8,2,4,5,6,7]=>01000011=>11000010
[9,4,1,5,2,3,6,7,8]=>00110001=>10001100
[9,4,1,8,2,3,5,6,7]=>00100011=>11000100
[6,9,1,5,2,3,4,7,8]=>00010001=>10001000
[9,7,1,6,2,3,4,5,8]=>00001101=>10110000
[8,7,1,9,2,3,4,5,6]=>00000111=>11100000
[8,7,1,6,2,3,4,9,5]=>00001111=>11110000
[9,4,1,6,2,8,3,5,7]=>00101011=>11010100
[9,8,1,6,2,7,3,4,5]=>00001111=>11110000
[4,3,1,5,9,2,6,7,8]=>01100001=>10000110
[9,8,1,7,6,2,3,4,5]=>00001111=>11110000
[4,3,1,5,6,8,2,9,7]=>01100011=>11000110
[4,3,1,5,9,8,2,6,7]=>01100011=>11000110
[4,3,1,5,8,7,2,9,6]=>01100111=>11100110
[8,9,1,5,6,7,2,3,4]=>00000101=>10100000
[4,3,1,5,6,7,9,2,8]=>01100001=>10000110
[4,3,1,5,6,9,8,2,7]=>01100011=>11000110
[9,3,1,5,6,7,8,2,4]=>01000011=>11000010
[9,4,1,5,6,7,8,2,3]=>00100011=>11000100
[4,3,1,5,6,7,8,9,2]=>01100001=>10000110
[2,3,9,1,4,5,6,7,8]=>00000001=>10000000
[2,3,8,1,4,5,6,9,7]=>00000011=>11000000
[2,3,9,1,4,5,8,6,7]=>00000011=>11000000
[2,3,9,1,4,7,8,5,6]=>00000011=>11000000
[2,3,9,1,8,7,4,5,6]=>00000111=>11100000
[2,3,8,1,6,7,4,9,5]=>00000111=>11100000
[2,3,5,1,6,7,9,4,8]=>00010001=>10001000
[2,3,9,1,6,7,8,4,5]=>00000011=>11000000
[2,3,5,1,6,7,8,9,4]=>00010001=>10001000
[2,9,4,1,3,5,6,7,8]=>00100001=>10000100
[2,6,4,1,3,7,8,9,5]=>00101001=>10010100
[2,9,5,1,3,4,6,7,8]=>00010001=>10001000
[2,6,9,1,3,4,5,7,8]=>00000001=>10000000
[2,9,7,1,3,4,5,6,8]=>00000101=>10100000
[2,9,8,1,3,4,5,6,7]=>00000011=>11000000
[2,6,7,1,3,4,8,9,5]=>00000101=>10100000
[2,9,4,1,6,3,5,7,8]=>00101001=>10010100
[2,8,4,1,9,3,5,6,7]=>00100011=>11000100
[2,9,4,1,6,3,8,5,7]=>00101011=>11010100
[2,9,8,1,7,3,4,5,6]=>00000111=>11100000
[2,9,5,1,6,7,8,3,4]=>00010011=>11001000
[9,3,4,1,2,5,6,7,8]=>00100001=>10000100
[6,3,4,1,2,7,8,9,5]=>00101001=>10010100
[9,3,7,1,2,4,5,6,8]=>00000101=>10100000
[9,3,8,1,2,4,5,6,7]=>00000011=>11000000
[9,5,4,1,2,3,6,7,8]=>00110001=>10001100
[8,5,4,1,2,3,6,9,7]=>00110011=>11001100
[6,9,4,1,2,3,5,7,8]=>00100001=>10000100
[6,8,4,1,2,3,5,9,7]=>00100011=>11000100
[9,7,4,1,2,3,5,6,8]=>00100101=>10100100
[9,8,4,1,2,3,5,6,7]=>00100011=>11000100
[6,9,5,1,2,3,4,7,8]=>00010001=>10001000
[6,8,5,1,2,3,4,9,7]=>00010011=>11001000
[8,7,5,1,2,3,4,9,6]=>00010111=>11101000
[6,7,9,1,2,3,4,5,8]=>00000001=>10000000
[6,9,8,1,2,3,4,5,7]=>00000011=>11000000
[9,7,8,1,2,3,4,5,6]=>00000011=>11000000
[6,7,8,1,2,3,4,9,5]=>00000011=>11000000
[6,5,4,1,2,8,3,9,7]=>00111011=>11011100
[9,8,5,1,7,2,3,4,6]=>00010111=>11101000
[7,8,9,1,6,2,3,4,5]=>00001001=>10010000
[7,8,5,1,6,2,3,9,4]=>00011011=>11011000
[5,3,4,1,6,8,2,9,7]=>00110011=>11001100
[9,3,4,1,8,7,2,5,6]=>00100111=>11100100
[8,3,4,1,6,7,2,9,5]=>00100111=>11100100
[9,5,4,1,8,7,2,3,6]=>00110111=>11101100
[8,5,4,1,6,7,2,9,3]=>00110111=>11101100
[5,3,4,1,9,7,8,2,6]=>00110011=>11001100
[9,3,5,1,6,7,8,2,4]=>00010011=>11001000
[9,5,4,1,6,7,8,2,3]=>00110011=>11001100
[5,3,4,1,6,7,8,9,2]=>00110001=>10001100
[2,3,4,9,1,5,6,7,8]=>00000001=>10000000
[2,3,4,9,1,5,8,6,7]=>00000011=>11000000
[2,3,4,9,1,7,8,5,6]=>00000011=>11000000
[2,3,4,6,1,7,8,9,5]=>00001001=>10010000
[2,3,9,5,1,4,6,7,8]=>00010001=>10001000
[2,3,9,6,1,4,5,7,8]=>00001001=>10010000
[2,3,7,9,1,4,5,6,8]=>00000001=>10000000
[2,3,9,8,1,4,5,6,7]=>00000011=>11000000
[2,3,9,5,1,7,4,6,8]=>00010101=>10101000
[2,3,9,6,1,7,8,4,5]=>00001011=>11010000
[2,9,4,5,1,3,6,7,8]=>00010001=>10001000
[2,7,4,5,1,3,8,9,6]=>00010101=>10101000
[2,9,8,6,1,3,4,5,7]=>00001011=>11010000
[2,7,8,9,1,3,4,5,6]=>00000001=>10000000
[2,8,9,6,1,7,3,4,5]=>00001101=>10110000
[2,9,6,5,1,7,8,3,4]=>00011011=>11011000
[7,3,4,5,1,2,8,9,6]=>00010101=>10101000
[9,3,4,8,1,2,5,6,7]=>00000011=>11000000
[7,3,4,8,1,2,5,9,6]=>00000111=>11100000
[7,3,8,9,1,2,4,5,6]=>00000101=>10100000
[9,8,4,5,1,2,3,6,7]=>00010011=>11001000
[7,8,4,6,1,2,3,9,5]=>00001011=>11010000
[9,8,6,5,1,2,3,4,7]=>00011011=>11011000
[7,8,9,6,1,2,3,4,5]=>00001001=>10010000
[7,8,6,5,1,2,3,9,4]=>00011011=>11011000
[8,3,9,6,1,7,2,4,5]=>00001111=>11110000
[8,3,6,5,1,7,2,9,4]=>00011111=>11111000
[8,6,4,5,1,7,2,9,3]=>00011111=>11111000
[6,3,4,5,1,7,9,2,8]=>00011001=>10011000
[6,3,4,5,1,9,8,2,7]=>00011011=>11011000
[9,3,4,6,1,7,8,2,5]=>00001011=>11010000
[6,3,4,5,1,7,8,9,2]=>00011001=>10011000
[2,3,4,5,9,1,6,7,8]=>00000001=>10000000
[2,3,4,5,8,1,6,9,7]=>00000011=>11000000
[2,3,4,5,9,1,8,6,7]=>00000011=>11000000
[2,3,4,5,7,1,8,9,6]=>00000101=>10100000
[2,3,4,9,6,1,5,7,8]=>00001001=>10010000
[2,3,4,9,7,1,5,6,8]=>00000101=>10100000
[2,3,4,9,6,1,8,5,7]=>00001011=>11010000
[2,3,4,9,7,1,8,5,6]=>00000111=>11100000
[2,3,9,5,6,1,4,7,8]=>00001001=>10010000
[2,3,8,5,6,1,4,9,7]=>00001011=>11010000
[2,3,9,5,6,1,8,4,7]=>00001011=>11010000
[2,8,4,5,6,1,3,9,7]=>00001011=>11010000
[2,8,9,5,7,1,3,4,6]=>00000101=>10100000
[2,8,9,7,6,1,3,4,5]=>00001101=>10110000
[2,9,7,5,6,1,8,3,4]=>00001111=>11110000
[8,3,4,5,6,1,2,9,7]=>00001011=>11010000
[8,3,4,7,6,1,2,9,5]=>00001111=>11110000
[8,3,9,7,6,1,2,4,5]=>00001111=>11110000
[8,3,7,5,6,1,2,9,4]=>00001111=>11110000
[9,7,4,5,6,1,2,3,8]=>00001101=>10110000
[8,9,4,5,6,1,2,3,7]=>00001001=>10010000
[8,9,7,5,6,1,2,3,4]=>00001101=>10110000
[8,7,4,5,6,1,2,9,3]=>00001111=>11110000
[7,3,4,5,6,1,9,2,8]=>00001101=>10110000
[9,3,4,5,6,1,8,2,7]=>00001011=>11010000
[9,3,7,5,6,1,8,2,4]=>00001111=>11110000
[7,3,4,5,6,1,8,9,2]=>00001101=>10110000
[2,3,4,5,6,9,1,7,8]=>00000001=>10000000
[2,3,4,5,6,8,1,9,7]=>00000011=>11000000
[2,3,4,5,9,7,1,6,8]=>00000101=>10100000
[2,3,4,5,9,8,1,6,7]=>00000011=>11000000
[2,3,4,9,6,7,1,5,8]=>00000101=>10100000
[2,3,9,5,6,7,1,4,8]=>00000101=>10100000
[2,3,9,5,6,8,1,4,7]=>00000011=>11000000
[2,9,4,5,6,7,1,3,8]=>00000101=>10100000
[2,9,4,5,6,8,1,3,7]=>00000011=>11000000
[2,9,4,5,8,7,1,3,6]=>00000111=>11100000
[2,9,4,8,6,7,1,3,5]=>00000111=>11100000
[2,9,8,5,6,7,1,3,4]=>00000111=>11100000
[2,8,4,5,6,7,1,9,3]=>00000111=>11100000
[9,3,4,5,6,7,1,2,8]=>00000101=>10100000
[9,3,4,5,6,8,1,2,7]=>00000011=>11000000
[9,8,4,5,6,7,1,2,3]=>00000111=>11100000
[8,3,4,5,6,7,1,9,2]=>00000111=>11100000
[2,3,4,5,6,7,9,1,8]=>00000001=>10000000
[2,3,4,5,6,9,8,1,7]=>00000011=>11000000
[2,3,4,5,9,7,8,1,6]=>00000011=>11000000
[2,3,4,9,6,7,8,1,5]=>00000011=>11000000
[2,3,9,5,6,7,8,1,4]=>00000011=>11000000
[2,9,4,5,6,7,8,1,3]=>00000011=>11000000
[9,3,4,5,6,7,8,1,2]=>00000011=>11000000
[2,3,4,5,6,7,8,9,1]=>00000001=>10000000
[]=>=>
[3,5,2,6,1,4,8,7]=>0001101=>1011000
[3,5,2,6,4,1,8,7]=>0011101=>1011100
[3,5,2,7,4,8,1,6]=>0001011=>1101000
[3,5,2,7,4,8,6,1]=>0001111=>1111000
[4,5,7,2,3,8,6,1]=>0000111=>1110000
[4,5,7,2,3,8,1,6]=>0000011=>1100000
[4,5,6,2,3,1,8,7]=>0100101=>1010010
[4,5,6,2,1,3,8,7]=>1000101=>1010001
[3,5,1,6,4,2,8,7]=>0011101=>1011100
[4,5,6,1,3,2,8,7]=>0100101=>1010010
[4,5,6,3,1,2,8,7]=>0100101=>1010010
[4,5,7,3,2,8,1,6]=>0100011=>1100010
[4,5,7,3,2,8,6,1]=>0100111=>1110010
[4,6,7,3,8,2,5,1]=>0001011=>1101000
[4,6,7,3,8,2,1,5]=>1000011=>1100001
[4,6,7,3,8,1,2,5]=>0000011=>1100000
[4,5,7,3,1,8,2,6]=>0100011=>1100010
[4,5,7,1,3,8,2,6]=>0000011=>1100000
[3,5,1,7,4,8,2,6]=>0001011=>1101000
[2,1,5,7,4,8,3,6]=>1000011=>1100001
[2,1,5,7,4,8,6,3]=>1000111=>1110001
[3,5,1,7,4,8,6,2]=>0001111=>1111000
[4,5,7,1,3,8,6,2]=>0000111=>1110000
[4,5,7,3,1,8,6,2]=>0100111=>1110010
[4,6,7,3,8,1,5,2]=>0001011=>1101000
[4,6,7,3,8,5,1,2]=>0001011=>1101000
[4,6,7,3,8,5,2,1]=>1001011=>1101001
[5,6,7,8,3,1,4,2]=>0110001=>1000110
[5,6,7,8,1,3,4,2]=>0010001=>1000100
[4,6,7,1,8,3,5,2]=>0001011=>1101000
[3,6,1,7,8,4,5,2]=>0001101=>1011000
[2,1,6,7,8,4,5,3]=>1001001=>1001001
[2,1,6,7,8,4,3,5]=>1010001=>1000101
[3,6,1,7,8,4,2,5]=>0010101=>1010100
[4,6,7,1,8,3,2,5]=>0100011=>1100010
[5,6,7,8,1,3,2,4]=>0100001=>1000010
[4,5,7,2,1,8,3,6]=>1000011=>1100001
[4,6,7,2,8,1,3,5]=>0000011=>1100000
[4,6,7,2,8,3,1,5]=>0100011=>1100010
[4,6,7,2,8,3,5,1]=>0001011=>1101000
[3,6,2,7,8,4,5,1]=>0001101=>1011000
[3,6,2,7,8,4,1,5]=>0010101=>1010100
[3,6,2,7,8,1,4,5]=>0000101=>1010000
[3,5,2,7,1,8,4,6]=>0001011=>1101000
[3,4,2,1,7,8,5,6]=>1010001=>1000101
[3,4,1,2,7,8,6,5]=>0010101=>1010100
[3,5,2,7,1,8,6,4]=>0001111=>1111000
[3,6,2,7,8,1,5,4]=>0001101=>1011000
[3,6,2,7,8,5,1,4]=>0001101=>1011000
[3,6,2,7,8,5,4,1]=>0011101=>1011100
[4,6,7,2,8,5,3,1]=>0101011=>1101010
[4,6,7,2,8,5,1,3]=>0001011=>1101000
[4,6,7,2,8,1,5,3]=>0001011=>1101000
[4,5,7,2,1,8,6,3]=>1000111=>1110001
[4,5,7,1,2,8,6,3]=>0000111=>1110000
[3,5,1,7,2,8,6,4]=>0001111=>1111000
[2,1,5,7,3,8,6,4]=>1000111=>1110001
[2,1,6,7,8,3,5,4]=>1001001=>1001001
[3,6,1,7,8,2,5,4]=>0001101=>1011000
[4,6,7,1,8,2,5,3]=>0001011=>1101000
[5,6,7,8,1,2,4,3]=>0010001=>1000100
[5,6,7,8,2,1,4,3]=>1010001=>1000101
[5,6,7,8,2,4,1,3]=>0010001=>1000100
[5,6,7,8,2,4,3,1]=>0110001=>1000110
[5,6,7,8,1,4,2,3]=>0010001=>1000100
[4,6,7,1,8,5,2,3]=>0001011=>1101000
[3,6,1,7,8,5,2,4]=>0001101=>1011000
[2,1,6,7,8,5,3,4]=>1001001=>1001001
[3,6,1,7,8,5,4,2]=>0011101=>1011100
[4,6,7,1,8,5,3,2]=>0101011=>1101010
[5,6,7,8,1,4,3,2]=>0110001=>1000110
[5,6,7,8,4,1,3,2]=>0110001=>1000110
[3,4,2,1,6,5,8,7,10,9]=>101010101=>101010101
[3,5,2,6,4,1,8,7,10,9]=>001110101=>101011100
[3,5,2,7,4,8,6,1,10,9]=>000111101=>101111000
[3,5,2,7,4,9,6,10,8,1]=>000101111=>111101000
[2,1,5,6,4,3,8,7,10,9]=>101010101=>101010101
[4,5,6,3,2,1,8,7,10,9]=>110010101=>101010011
[4,5,7,3,2,8,6,1,10,9]=>010011101=>101110010
[4,5,7,3,2,9,6,10,8,1]=>010001111=>111100010
[2,1,5,7,4,8,6,3,10,9]=>100011101=>101110001
[4,6,7,3,8,5,2,1,10,9]=>100101101=>101101001
[4,6,7,3,9,5,2,10,8,1]=>000101111=>111101000
[2,1,5,7,4,9,6,10,8,3]=>100001111=>111100001
[4,6,8,3,9,5,10,7,2,1]=>100001111=>111100001
[2,1,4,3,7,8,6,5,10,9]=>101010101=>101010101
[3,4,2,1,7,8,6,5,10,9]=>101010101=>101010101
[3,6,2,7,8,5,4,1,10,9]=>001110101=>101011100
[3,6,2,7,9,5,4,10,8,1]=>000110111=>111011000
[2,1,6,7,8,5,4,3,10,9]=>101100101=>101001101
[5,6,7,8,4,3,2,1,10,9]=>111000101=>101000111
[5,6,7,9,4,3,2,10,8,1]=>011000111=>111000110
[2,1,6,7,9,5,4,10,8,3]=>100100111=>111001001
[5,6,8,9,4,3,10,7,2,1]=>101001011=>110100101
[2,1,4,3,7,9,6,10,8,5]=>101000111=>111000101
[3,4,2,1,7,9,6,10,8,5]=>101000111=>111000101
[3,6,2,8,9,5,10,7,4,1]=>001011011=>110110100
[2,1,6,8,9,5,10,7,4,3]=>101001011=>110100101
[5,7,8,9,4,10,6,3,2,1]=>110010011=>110010011
[6,7,8,9,10,4,5,3,2,1]=>110100001=>100001011
[6,7,8,9,10,1,4,5,3,2]=>010100001=>100001010
[6,7,8,9,10,1,4,5,2,3]=>000100001=>100001000
[6,7,8,9,10,4,5,2,3,1]=>010100001=>100001010
[6,7,8,9,10,4,3,2,1,5]=>111000001=>100000111
[6,7,8,9,10,3,4,5,2,1]=>100100001=>100001001
[6,7,8,9,10,3,4,5,1,2]=>000100001=>100001000
[6,7,8,9,10,1,3,4,5,2]=>000100001=>100001000
[6,7,8,9,10,3,4,1,2,5]=>001000001=>100000100
[6,7,8,9,10,3,4,2,1,5]=>101000001=>100000101
[6,7,8,9,10,2,3,4,1,5]=>001000001=>100000100
[6,7,8,9,10,2,3,4,5,1]=>000100001=>100001000
[2,1,4,3,6,5,9,10,8,7]=>101010101=>101010101
[3,4,2,1,6,5,9,10,8,7]=>101010101=>101010101
[3,5,2,6,4,1,9,10,8,7]=>001110101=>101011100
[3,5,2,8,4,9,10,7,6,1]=>000111101=>101111000
[2,1,5,6,4,3,9,10,8,7]=>101010101=>101010101
[4,5,6,3,2,1,9,10,8,7]=>110010101=>101010011
[4,5,8,3,2,9,10,7,6,1]=>010011101=>101110010
[2,1,5,8,4,9,10,7,6,3]=>100011101=>101110001
[4,7,8,3,9,10,6,5,2,1]=>100110101=>101011001
[2,1,4,3,8,9,10,7,6,5]=>101011001=>100110101
[3,4,2,1,8,9,10,7,6,5]=>101011001=>100110101
[3,7,2,8,9,10,6,5,4,1]=>001111001=>100111100
[2,1,7,8,9,10,6,5,4,3]=>101110001=>100011101
[6,7,8,9,10,1,5,4,3,2]=>011100001=>100001110
[6,7,8,9,10,5,4,3,2,1]=>111100001=>100001111
[6,5,8,7,3,4,1,2]=>0010111=>1110100
[3,6,7,4,5,8,1,2]=>0000011=>1100000
[2,6,7,4,5,1,8,3]=>0001011=>1101000
[1,6,7,4,5,2,3,8]=>0001010=>0101000
[1,5,4,7,6,2,3,8]=>0001110=>0111000
[2,5,4,7,6,1,8,3]=>0001111=>1111000
[3,5,4,7,6,8,1,2]=>0001011=>1101000
[4,5,3,7,8,6,1,2]=>0001101=>1011000
[5,4,3,8,7,6,1,2]=>0011111=>1111100
[6,4,8,3,7,5,1,2]=>0001111=>1111000
[6,3,8,4,5,7,1,2]=>0000111=>1110000
[5,3,4,8,6,7,1,2]=>0001011=>1101000
[4,3,5,6,8,7,1,2]=>0010011=>1100100
[3,2,5,6,1,8,7,4]=>0100111=>1110010
[4,2,5,6,8,1,7,3]=>0010011=>1100100
[5,2,4,8,6,1,7,3]=>0001111=>1111000
[6,2,8,4,5,1,7,3]=>0001111=>1111000
[7,8,2,4,5,1,6,3]=>0001101=>1011000
[7,8,1,4,5,2,3,6]=>0001001=>1001000
[6,1,8,4,5,2,3,7]=>0001101=>1011000
[5,1,4,8,6,2,3,7]=>0001101=>1011000
[4,1,3,2,8,6,5,7]=>0110101=>1010110
[5,1,3,8,2,6,4,7]=>0001101=>1011000
[6,1,8,3,2,5,4,7]=>0101101=>1011010
[7,8,1,3,2,5,4,6]=>0101001=>1001010
[7,8,2,3,1,5,6,4]=>0100101=>1010010
[6,2,8,3,1,5,7,4]=>0100111=>1110010
[5,2,3,8,1,6,7,4]=>0001011=>1101000
[6,3,8,2,1,7,5,4]=>1001111=>1111001
[7,8,3,2,1,6,5,4]=>1101101=>1011011
[7,8,4,2,6,1,5,3]=>0011101=>1011100
[5,4,2,8,7,1,6,3]=>0011111=>1111100
[4,5,2,7,8,1,6,3]=>0001101=>1011000
[2,5,3,7,1,6,8,4]=>0001011=>1101000
[1,5,3,7,2,6,4,8]=>0001110=>0111000
[1,6,7,3,2,5,4,8]=>0101010=>0101010
[2,6,7,3,1,5,8,4]=>0100011=>1100010
[3,6,7,2,1,8,5,4]=>1001011=>1101001
[7,8,5,6,2,1,4,3]=>1010101=>1010101
[6,5,8,7,1,2,3,4]=>0000111=>1110000
[5,4,1,8,7,2,3,6]=>0011011=>1101100
[6,4,8,1,7,2,3,5]=>0000111=>1110000
[7,8,3,1,2,6,4,5]=>0100101=>1010010
[5,3,1,8,2,7,4,6]=>0101011=>1101010
[4,3,1,2,8,7,5,6]=>0110011=>1100110
[4,2,1,3,8,5,7,6]=>1010011=>1100101
[5,2,1,8,3,4,7,6]=>1001011=>1101001
[6,2,8,1,3,4,7,5]=>0000111=>1110000
[7,8,2,1,3,4,6,5]=>1000101=>1010001
[4,3,1,2,6,5,8,7]=>0110101=>1010110
[5,3,1,6,2,4,8,7]=>0101101=>1011010
[6,3,1,5,2,4,8,7]=>0101101=>1011010
[7,3,1,5,2,8,4,6]=>0101011=>1101010
[8,4,5,1,2,7,3,6]=>0001011=>1101000
[7,4,5,1,2,8,3,6]=>0001011=>1101000
[6,4,5,1,2,3,8,7]=>0001101=>1011000
[5,4,6,1,2,3,8,7]=>0001101=>1011000
[2,1,6,5,3,4,8,7]=>1001101=>1011001
[3,6,1,5,2,4,8,7]=>0001101=>1011000
[4,6,5,1,2,3,8,7]=>0001101=>1011000
[5,6,4,1,2,3,8,7]=>0010101=>1010100
[6,5,4,1,2,3,8,7]=>0011101=>1011100
[7,5,4,1,2,8,3,6]=>0011011=>1101100
[8,6,4,1,7,2,3,5]=>0010111=>1110100
[7,6,4,1,8,2,3,5]=>0010111=>1110100
[6,7,4,1,8,2,3,5]=>0010011=>1100100
[5,7,4,1,2,8,3,6]=>0010011=>1100100
[4,7,5,1,2,8,3,6]=>0001011=>1101000
[3,7,1,5,2,8,4,6]=>0001011=>1101000
[2,1,7,5,3,8,4,6]=>1001011=>1101001
[2,1,8,5,3,7,4,6]=>1001011=>1101001
[3,8,1,5,2,7,4,6]=>0001011=>1101000
[4,8,5,1,2,7,3,6]=>0001011=>1101000
[5,8,4,1,2,7,3,6]=>0010011=>1100100
[6,8,4,1,7,2,3,5]=>0010011=>1100100
[8,7,4,1,6,2,3,5]=>0010111=>1110100
[5,8,6,7,1,2,3,4]=>0000011=>1100000
[4,8,6,1,7,2,3,5]=>0000111=>1110000
[3,8,1,6,7,2,4,5]=>0000011=>1100000
[2,1,8,6,7,3,4,5]=>1000011=>1100001
[2,1,7,6,8,3,4,5]=>1000011=>1100001
[3,7,1,6,8,2,4,5]=>0000011=>1100000
[4,7,6,1,8,2,3,5]=>0000111=>1110000
[5,7,6,8,1,2,3,4]=>0000011=>1100000
[5,4,7,1,2,8,3,6]=>0001011=>1101000
[6,4,7,1,8,2,3,5]=>0000111=>1110000
[7,4,6,1,8,2,3,5]=>0000111=>1110000
[8,4,6,1,7,2,3,5]=>0000111=>1110000
[8,3,1,6,7,2,4,5]=>0100011=>1100010
[7,3,1,6,8,2,4,5]=>0100011=>1100010
[6,3,1,7,8,2,4,5]=>0100101=>1010010
[5,3,1,7,2,8,4,6]=>0101011=>1101010
[4,3,1,2,7,8,5,6]=>0110001=>1000110
[2,1,4,3,8,7,5,6]=>1010011=>1100101
[3,4,1,2,8,7,5,6]=>0010011=>1100100
[6,3,1,8,7,2,4,5]=>0100111=>1110010
[7,3,1,8,6,2,4,5]=>0100111=>1110010
[8,4,7,1,6,2,3,5]=>0000111=>1110000
[7,4,8,1,6,2,3,5]=>0000111=>1110000
[5,4,8,1,2,7,3,6]=>0001011=>1101000
[4,5,8,1,2,7,3,6]=>0000011=>1100000
[3,5,1,8,2,7,4,6]=>0001011=>1101000
[2,1,5,8,3,7,4,6]=>1000011=>1100001
[2,1,6,8,7,3,4,5]=>1000011=>1100001
[3,6,1,8,7,2,4,5]=>0000111=>1110000
[4,6,8,1,7,2,3,5]=>0000011=>1100000
[5,6,8,7,1,2,3,4]=>0000011=>1100000
[7,5,8,6,1,2,3,4]=>0000111=>1110000
[8,5,7,6,1,2,3,4]=>0000111=>1110000
[5,7,8,6,1,2,3,4]=>0000101=>1010000
[4,7,8,1,6,2,3,5]=>0000101=>1010000
[3,7,1,8,6,2,4,5]=>0000111=>1110000
[2,1,7,8,6,3,4,5]=>1000101=>1010001
[2,1,8,7,6,3,4,5]=>1000111=>1110001
[3,8,1,7,6,2,4,5]=>0000111=>1110000
[4,8,7,1,6,2,3,5]=>0000111=>1110000
[5,8,7,6,1,2,3,4]=>0000111=>1110000
[6,8,7,5,1,2,3,4]=>0001011=>1101000
[6,4,7,3,8,5,1,2]=>0001111=>1111000
[6,4,7,3,5,8,1,2]=>0000111=>1110000
[6,4,7,2,5,1,8,3]=>0001111=>1111000
[5,4,2,7,6,1,3,8]=>0011110=>0111100
[5,4,2,7,6,1,8,3]=>0011111=>1111100
[5,4,3,7,6,8,1,2]=>0011011=>1101100
[5,4,3,7,8,6,1,2]=>0011101=>1011100
[6,4,8,3,5,7,1,2]=>0000111=>1110000
[5,4,3,8,6,7,1,2]=>0011011=>1101100
[5,4,3,6,8,7,1,2]=>0011011=>1101100
[5,4,2,6,7,1,8,3]=>0011011=>1101100
[5,4,2,6,7,1,3,8]=>0011010=>0101100
[5,3,2,6,1,7,4,8]=>0101110=>0111010
[5,3,2,6,1,7,8,4]=>0101101=>1011010
[5,3,2,6,1,8,7,4]=>0101111=>1111010
[5,4,2,6,8,1,7,3]=>0011011=>1101100
[5,4,2,8,6,1,7,3]=>0011111=>1111100
[6,4,8,2,5,1,7,3]=>0001111=>1111000
[7,8,4,2,5,1,6,3]=>0011101=>1011100
[7,8,4,2,5,1,3,6]=>0011001=>1001100
[5,4,2,8,6,1,3,7]=>0011101=>1011100
[5,3,2,6,1,8,4,7]=>0101101=>1011010
[4,3,2,1,6,8,5,7]=>1110001=>1000111
[4,3,2,1,8,6,5,7]=>1110101=>1010111
[5,3,2,8,1,6,4,7]=>0101101=>1011010
[6,3,8,2,1,5,4,7]=>1001101=>1011001
[7,8,3,2,1,5,4,6]=>1101001=>1001011
[7,8,3,2,1,5,6,4]=>1100101=>1010011
[6,3,8,2,1,5,7,4]=>1000111=>1110001
[5,3,2,8,1,6,7,4]=>0101011=>1101010
[5,4,2,7,8,1,6,3]=>0011101=>1011100
[5,3,2,7,1,8,6,4]=>0101111=>1111010
[5,3,2,7,1,6,8,4]=>0101011=>1101010
[5,3,2,7,1,6,4,8]=>0101110=>0111010
[6,3,7,2,1,5,4,8]=>1001110=>0111001
[6,3,7,2,1,5,8,4]=>1000111=>1110001
[6,3,7,2,1,8,5,4]=>1001111=>1111001
[6,4,7,2,8,1,5,3]=>0001111=>1111000
[6,5,7,8,2,1,4,3]=>1010101=>1010101
[6,5,8,7,2,1,3,4]=>1000111=>1110001
[6,3,7,2,1,8,4,5]=>1000111=>1110001
[6,3,7,2,1,4,8,5]=>1000111=>1110001
[6,3,7,2,1,4,5,8]=>1000110=>0110001
[5,3,2,7,1,4,8,6]=>0101011=>1101010
[5,4,2,8,7,1,3,6]=>0011011=>1101100
[7,8,4,2,6,1,3,5]=>0010101=>1010100
[7,8,3,2,1,6,4,5]=>1100101=>1010011
[6,3,8,2,1,7,4,5]=>1000111=>1110001
[5,3,2,8,1,7,4,6]=>0101011=>1101010
[4,3,2,1,8,7,5,6]=>1110011=>1100111
[4,3,2,1,7,5,8,6]=>1110011=>1100111
[4,3,2,1,7,5,6,8]=>1110010=>0100111
[4,3,2,1,8,5,7,6]=>1110011=>1100111
[5,3,2,8,1,4,7,6]=>0101011=>1101010
[6,3,8,2,1,4,7,5]=>1000111=>1110001
[7,8,3,2,1,4,6,5]=>1100101=>1010011
[6,3,8,2,1,4,5,7]=>1000101=>1010001
[4,3,2,1,8,5,6,7]=>1110001=>1000111
[4,3,2,1,5,8,6,7]=>1110001=>1000111
[7,8,5,6,1,2,4,3]=>0010101=>1010100
[7,8,4,1,6,2,5,3]=>0011101=>1011100
[7,8,1,4,6,2,5,3]=>0001101=>1011000
[6,1,8,4,7,2,5,3]=>0001111=>1111000
[1,6,8,4,7,2,5,3]=>0001011=>1101000
[1,6,8,3,2,7,5,4]=>0101011=>1101010
[6,1,8,3,2,7,5,4]=>0101111=>1111010
[7,8,1,3,2,6,5,4]=>0101101=>1011010
[7,8,3,1,2,6,5,4]=>0101101=>1011010
[7,8,3,4,6,5,1,2]=>0001101=>1011000
[7,8,2,4,6,1,5,3]=>0001101=>1011000
[7,8,2,3,1,6,5,4]=>0101101=>1011010
[7,8,2,1,3,6,5,4]=>1001101=>1011001
[7,8,1,2,3,6,5,4]=>0001101=>1011000
[6,1,8,2,3,7,5,4]=>0001111=>1111000
[1,6,8,2,3,7,5,4]=>0001011=>1101000
[1,5,2,8,3,7,6,4]=>0001111=>1111000
[5,1,2,8,3,7,6,4]=>0001111=>1111000
[5,2,1,8,3,7,6,4]=>1001111=>1111001
[6,2,8,1,3,7,5,4]=>0001111=>1111000
[6,2,8,3,1,7,5,4]=>0101111=>1111010
[6,2,8,4,7,1,5,3]=>0001111=>1111000
[6,3,8,4,7,5,1,2]=>0001111=>1111000
[3,6,8,4,7,5,1,2]=>0001011=>1101000
[2,6,8,4,7,1,5,3]=>0001011=>1101000
[2,6,8,3,1,7,5,4]=>0101011=>1101010
[2,6,8,1,3,7,5,4]=>0001011=>1101000
[2,5,1,8,3,7,6,4]=>0001111=>1111000
[1,2,5,8,3,7,6,4]=>0000111=>1110000
[2,4,1,3,8,7,6,5]=>0010111=>1110100
[2,5,3,8,1,7,6,4]=>0001111=>1111000
[2,5,4,8,7,1,6,3]=>0001111=>1111000
[3,5,4,8,7,6,1,2]=>0001111=>1111000
[5,3,4,8,7,6,1,2]=>0001111=>1111000
[5,2,4,8,7,1,6,3]=>0001111=>1111000
[5,2,3,8,1,7,6,4]=>0001111=>1111000
[4,2,1,3,8,7,6,5]=>1010111=>1110101
[4,1,2,3,8,7,6,5]=>0010111=>1110100
[1,4,2,3,8,7,6,5]=>0010111=>1110100
[4,1,3,2,8,7,6,5]=>0110111=>1110110
[4,3,1,2,8,7,6,5]=>0110111=>1110110
[6,3,8,1,2,7,5,4]=>0001111=>1111000
[5,3,1,8,2,7,6,4]=>0101111=>1111010
[5,1,3,8,2,7,6,4]=>0001111=>1111000
[1,5,3,8,2,7,6,4]=>0001111=>1111000
[1,5,4,8,7,2,6,3]=>0001111=>1111000
[5,1,4,8,7,2,6,3]=>0001111=>1111000
[5,4,1,8,7,2,6,3]=>0011111=>1111100
[6,4,8,1,7,2,5,3]=>0001111=>1111000
[6,5,8,7,1,2,4,3]=>0010111=>1110100
[5,6,8,7,3,4,1,2]=>0010011=>1100100
[5,6,8,7,2,1,4,3]=>1010011=>1100101
[4,5,1,8,7,2,6,3]=>0001111=>1111000
[4,1,5,8,7,2,6,3]=>0010111=>1110100
[1,4,5,8,7,2,6,3]=>0000111=>1110000
[1,3,5,8,2,7,6,4]=>0000111=>1110000
[3,1,5,8,2,7,6,4]=>0100111=>1110010
[3,6,8,1,2,7,5,4]=>0001011=>1101000
[3,6,8,2,1,7,5,4]=>1001011=>1101001
[4,6,8,2,7,1,5,3]=>0001011=>1101000
[4,6,8,3,7,5,1,2]=>0001011=>1101000
[4,5,3,8,7,6,1,2]=>0001111=>1111000
[4,5,2,8,7,1,6,3]=>0001111=>1111000
[3,5,2,8,1,7,6,4]=>0001111=>1111000
[3,1,4,2,8,7,6,5]=>0110111=>1110110
[3,1,2,4,8,7,6,5]=>0100111=>1110010
[3,2,5,8,1,7,6,4]=>0100111=>1110010
[4,2,5,8,7,1,6,3]=>0010111=>1110100
[4,3,5,8,7,6,1,2]=>0010111=>1110100
[3,4,5,8,7,6,1,2]=>0000111=>1110000
[2,4,5,8,7,1,6,3]=>0000111=>1110000
[2,3,5,8,1,7,6,4]=>0000111=>1110000
[4,1,3,2,6,5,8,7]=>0110101=>1010110
[5,1,3,2,6,4,8,7]=>0101101=>1011010
[6,1,3,2,5,4,8,7]=>0101101=>1011010
[7,1,3,2,5,4,8,6]=>0101011=>1101010
[8,1,3,2,5,4,7,6]=>0101011=>1101010
[8,1,4,2,5,3,7,6]=>0011011=>1101100
[7,1,4,2,5,3,8,6]=>0011011=>1101100
[6,1,4,2,5,3,8,7]=>0011101=>1011100
[5,1,4,2,6,3,8,7]=>0011101=>1011100
[2,1,6,3,5,4,8,7]=>1001101=>1011001
[3,1,6,2,5,4,8,7]=>0101101=>1011010
[4,1,6,2,5,3,8,7]=>0011101=>1011100
[6,2,5,1,4,3,8,7]=>0011101=>1011100
[5,2,6,1,4,3,8,7]=>0011101=>1011100
[5,2,7,1,4,3,8,6]=>0011011=>1101100
[5,2,8,1,4,3,7,6]=>0011011=>1101100
[6,2,8,1,4,3,7,5]=>0010111=>1110100
[6,2,7,1,4,3,8,5]=>0010111=>1110100
[7,2,6,1,4,3,8,5]=>0010111=>1110100
[7,2,5,1,4,3,8,6]=>0011011=>1101100
[4,1,7,2,5,3,8,6]=>0011011=>1101100
[3,1,7,2,5,4,8,6]=>0101011=>1101010
[2,1,7,3,5,4,8,6]=>1001011=>1101001
[2,1,8,3,5,4,7,6]=>1001011=>1101001
[3,1,8,2,5,4,7,6]=>0101011=>1101010
[4,1,8,2,5,3,7,6]=>0011011=>1101100
[8,2,5,1,4,3,7,6]=>0011011=>1101100
[8,2,6,1,4,3,7,5]=>0010111=>1110100
[7,1,4,3,8,2,6,5]=>0010111=>1110100
[8,1,4,3,7,2,6,5]=>0010111=>1110100
[8,1,5,3,7,2,6,4]=>0001111=>1111000
[7,1,5,3,8,2,6,4]=>0001111=>1111000
[8,2,6,1,5,3,7,4]=>0001111=>1111000
[5,1,8,2,6,3,7,4]=>0001111=>1111000
[4,1,8,2,6,3,7,5]=>0010111=>1110100
[3,1,8,2,6,4,7,5]=>0100111=>1110010
[2,1,8,3,6,4,7,5]=>1000111=>1110001
[2,1,7,3,6,4,8,5]=>1000111=>1110001
[4,1,7,2,6,3,8,5]=>0010111=>1110100
[5,1,7,2,6,3,8,4]=>0001111=>1111000
[7,2,6,1,5,3,8,4]=>0001111=>1111000
[6,2,7,1,5,3,8,4]=>0001111=>1111000
[6,2,8,1,5,3,7,4]=>0001111=>1111000
[8,1,5,2,6,3,7,4]=>0001111=>1111000
[6,1,5,2,7,3,8,4]=>0001111=>1111000
[6,1,4,2,7,3,8,5]=>0010111=>1110100
[8,1,4,2,6,3,7,5]=>0010111=>1110100
[8,1,3,2,6,4,7,5]=>0100111=>1110010
[7,1,3,2,6,4,8,5]=>0100111=>1110010
[6,1,3,2,7,4,8,5]=>0100111=>1110010
[5,1,3,2,7,4,8,6]=>0101011=>1101010
[4,1,3,2,7,5,8,6]=>0110011=>1100110
[2,1,4,3,8,5,7,6]=>1010011=>1100101
[3,1,4,2,8,5,7,6]=>0110011=>1100110
[4,1,3,2,8,5,7,6]=>0110011=>1100110
[5,1,3,2,8,4,7,6]=>0101011=>1101010
[6,1,3,2,8,4,7,5]=>0100111=>1110010
[8,4,7,1,3,2,6,5]=>0100111=>1110010
[7,4,8,1,3,2,6,5]=>0100111=>1110010
[7,3,8,1,4,2,6,5]=>0010111=>1110100
[8,3,7,1,4,2,6,5]=>0010111=>1110100
[6,1,4,2,8,3,7,5]=>0010111=>1110100
[5,1,4,2,8,3,7,6]=>0011011=>1101100
[4,1,5,2,8,3,7,6]=>0011011=>1101100
[3,1,5,2,8,4,7,6]=>0101011=>1101010
[2,1,5,3,8,4,7,6]=>1001011=>1101001
[2,1,6,3,8,4,7,5]=>1000111=>1110001
[3,1,6,2,8,4,7,5]=>0100111=>1110010
[4,1,6,2,8,3,7,5]=>0010111=>1110100
[5,1,6,2,8,3,7,4]=>0001111=>1111000
[6,1,5,2,8,3,7,4]=>0001111=>1111000
[8,3,7,1,5,2,6,4]=>0001111=>1111000
[7,3,8,1,5,2,6,4]=>0001111=>1111000
[6,2,7,3,8,1,5,4]=>0001111=>1111000
[6,2,8,3,7,1,5,4]=>0001111=>1111000
[8,3,7,2,6,1,5,4]=>0001111=>1111000
[5,1,8,3,7,2,6,4]=>0001111=>1111000
[4,1,8,3,7,2,6,5]=>0010111=>1110100
[3,1,8,4,7,2,6,5]=>0100111=>1110010
[2,1,8,4,7,3,6,5]=>1000111=>1110001
[2,1,7,4,8,3,6,5]=>1000111=>1110001
[3,1,7,4,8,2,6,5]=>0100111=>1110010
[4,1,7,3,8,2,6,5]=>0010111=>1110100
[5,1,7,3,8,2,6,4]=>0001111=>1111000
[7,3,8,2,6,1,5,4]=>0001111=>1111000
[8,2,6,3,7,1,5,4]=>0001111=>1111000
[7,2,6,3,8,1,5,4]=>0001111=>1111000
[3,4,2,6,8,1,5,7]=>0010001=>1000100
[5,3,6,2,8,1,4,7]=>0001101=>1011000
[5,3,6,2,4,8,1,7]=>0001101=>1011000
[5,7,3,8,2,4,1,6]=>0010011=>1100100
[5,7,3,8,2,4,6,1]=>0000111=>1110000
[7,4,2,5,8,3,6,1]=>0010111=>1110100
[7,4,2,5,8,3,1,6]=>0110011=>1100110
[4,5,2,6,3,8,1,7]=>0001101=>1011000
[4,5,2,1,6,8,3,7]=>1001001=>1001001
[5,3,1,6,8,2,4,7]=>0101001=>1001010
[5,6,2,8,1,3,4,7]=>0000101=>1010000
[3,5,6,1,4,8,2,7]=>0000101=>1010000
[4,1,5,6,3,8,2,7]=>0010101=>1010100
[4,5,1,6,3,8,2,7]=>0001101=>1011000
[4,5,6,3,2,8,1,7]=>0100101=>1010010
[7,4,5,3,8,2,1,6]=>1001011=>1101001
[7,4,5,3,8,2,6,1]=>0001111=>1111000
[6,7,4,8,3,2,5,1]=>0101011=>1101010
[6,7,4,8,3,2,1,5]=>1100011=>1100011
[6,7,4,1,8,3,2,5]=>0110011=>1100110
[7,4,5,3,1,8,2,6]=>0101011=>1101010
[4,7,1,5,8,3,2,6]=>0100011=>1100010
[5,3,7,8,1,4,2,6]=>0011001=>1001100
[7,5,8,2,4,6,1,3]=>0000111=>1110000
[7,3,5,8,1,4,6,2]=>0000111=>1110000
[4,5,1,7,8,3,6,2]=>0001101=>1011000
[7,4,1,5,8,3,6,2]=>0010111=>1110100
[6,7,4,3,8,1,5,2]=>0011011=>1101100
[6,7,4,8,3,1,5,2]=>0101011=>1101010
[6,7,4,8,3,5,2,1]=>1001011=>1101001
[5,6,7,3,8,4,2,1]=>1010011=>1100101
[5,6,7,3,1,8,4,2]=>0110011=>1100110
[5,6,1,7,3,8,4,2]=>0010111=>1110100
[5,1,6,7,3,8,4,2]=>0011011=>1101100
[6,4,7,1,8,3,5,2]=>0001111=>1111000
[6,7,8,3,1,4,5,2]=>0101001=>1001010
[6,7,2,8,4,5,1,3]=>0001011=>1101000
[6,7,2,8,4,1,3,5]=>0010011=>1100100
[6,1,7,4,8,3,2,5]=>0100111=>1110010
[5,1,6,7,3,2,8,4]=>0101011=>1101010
[5,6,1,7,3,2,8,4]=>0100111=>1110010
[5,6,7,3,2,1,8,4]=>1100011=>1100011
[5,6,7,3,2,8,4,1]=>0110011=>1100110
[5,6,2,7,3,8,4,1]=>0010111=>1110100
[5,6,2,7,3,1,8,4]=>0100111=>1110010
[5,6,2,1,7,3,8,4]=>1000111=>1110001
[6,1,7,4,2,8,3,5]=>0010111=>1110100
[6,7,2,1,8,3,4,5]=>1000011=>1100001
[7,5,8,2,1,3,4,6]=>1000011=>1100001
[5,7,3,1,8,2,4,6]=>0100011=>1100010
[4,7,1,5,2,8,3,6]=>0001011=>1101000
[7,4,2,5,1,8,3,6]=>0011011=>1101100
[6,7,4,2,1,8,3,5]=>1010011=>1100101
[6,7,4,2,8,3,1,5]=>0110011=>1100110
[6,7,4,2,8,3,5,1]=>0011011=>1101100
[3,6,7,2,8,4,5,1]=>0001011=>1101000
[3,6,7,2,8,4,1,5]=>0010011=>1100100
[3,6,7,2,1,8,4,5]=>1000011=>1100001
[5,7,3,8,2,1,4,6]=>1000011=>1100001
[3,4,7,8,2,1,5,6]=>1000001=>1000001
[3,7,8,1,4,6,2,5]=>0000101=>1010000
[3,4,7,8,2,6,1,5]=>0000101=>1010000
[5,7,3,8,2,6,1,4]=>0000111=>1110000
[3,6,7,2,8,5,1,4]=>0001011=>1101000
[3,6,7,8,5,2,1,4]=>1001001=>1001001
[3,6,7,8,5,2,4,1]=>0011001=>1001100
[6,4,7,8,2,5,3,1]=>0101101=>1011010
[6,4,7,8,2,1,5,3]=>1001101=>1011001
[4,1,5,7,8,2,6,3]=>0010101=>1010100
[5,3,7,8,1,6,2,4]=>0001101=>1011000
[6,7,2,8,5,1,3,4]=>0001011=>1101000
[6,4,1,7,8,2,5,3]=>0011101=>1011100
[5,1,6,2,7,8,4,3]=>0011101=>1011100
[5,6,2,1,7,8,4,3]=>1010101=>1010101
[5,6,2,7,1,8,4,3]=>0010111=>1110100
[5,6,2,7,8,4,3,1]=>0110101=>1010110
[5,6,7,2,8,4,3,1]=>0110011=>1100110
[5,6,7,2,1,8,4,3]=>1010011=>1100101
[5,6,1,7,2,8,4,3]=>0010111=>1110100
[5,1,6,7,2,8,4,3]=>0011011=>1101100
[6,4,7,1,8,2,5,3]=>0001111=>1111000
[3,6,7,1,8,5,2,4]=>0001011=>1101000
[6,7,8,5,2,4,1,3]=>0011001=>1001100
[6,7,8,3,5,1,4,2]=>0011001=>1001100
[4,6,7,8,1,5,3,2]=>0101001=>1001010
[5,1,6,7,8,4,3,2]=>0111001=>1001110
[5,6,1,7,8,4,3,2]=>0110101=>1010110
[5,6,7,1,8,4,3,2]=>0110011=>1100110
[8,6,1,3,4,2,5,7]=>0010101=>1010100
[8,3,2,5,1,6,4,7]=>0101101=>1011010
[8,5,3,6,2,4,1,7]=>0011101=>1011100
[5,3,2,7,4,1,8,6]=>0111011=>1101110
[7,5,3,8,2,4,6,1]=>0001111=>1111000
[7,2,4,5,8,3,6,1]=>0000111=>1110000
[2,4,5,3,7,1,8,6]=>0001011=>1101000
[8,2,4,5,6,3,1,7]=>0100101=>1010010
[8,2,4,5,6,1,3,7]=>0000101=>1010000
[8,1,2,4,5,6,3,7]=>0000101=>1010000
[8,2,5,1,3,6,4,7]=>0001101=>1011000
[8,5,6,2,1,4,3,7]=>1010101=>1010101
[8,5,3,6,4,1,2,7]=>0011101=>1011100
[8,4,1,5,6,3,2,7]=>0110101=>1010110
[8,1,4,5,6,3,2,7]=>0100101=>1010010
[4,5,3,7,2,1,8,6]=>1001011=>1101001
[7,4,5,8,3,2,6,1]=>0100111=>1110010
[4,3,6,7,2,8,5,1]=>0011011=>1101100
[4,3,6,7,2,8,1,5]=>0010011=>1100100
[1,4,3,6,7,2,8,5]=>0010011=>1100100
[4,5,3,7,1,8,2,6]=>0001011=>1101000
[4,1,5,3,7,2,8,6]=>0011011=>1101100
[5,3,4,7,1,2,8,6]=>0001011=>1101000
[7,5,8,2,1,4,6,3]=>1000111=>1110001
[7,5,3,8,4,1,6,2]=>0011111=>1111100
[7,4,5,8,3,6,1,2]=>0000111=>1110000
[4,3,6,7,8,1,5,2]=>0011001=>1001100
[1,6,4,7,8,3,5,2]=>0001101=>1011000
[6,4,7,8,3,5,2,1]=>1001101=>1011001
[3,5,6,7,8,4,1,2]=>0010001=>1000100
[3,1,5,6,7,8,4,2]=>0110001=>1000110
[4,6,1,7,8,3,5,2]=>0001101=>1011000
[3,6,7,1,4,8,5,2]=>0001011=>1101000
[6,2,4,1,7,8,5,3]=>0011101=>1011100
[2,6,7,1,4,8,3,5]=>0000011=>1100000
[4,3,6,7,8,1,2,5]=>0010001=>1000100
[1,5,3,6,7,8,2,4]=>0001001=>1001000
[3,5,6,7,8,2,1,4]=>1000001=>1000001
[3,5,6,7,8,2,4,1]=>0010001=>1000100
[5,2,7,1,3,8,4,6]=>0001011=>1101000
[5,3,1,7,8,2,4,6]=>0101001=>1001010
[4,5,2,7,8,1,3,6]=>0001001=>1001000
[4,2,6,7,8,3,1,5]=>0110001=>1000110
[4,2,6,7,8,3,5,1]=>0011001=>1001100
[3,6,2,7,4,8,5,1]=>0001111=>1111000
[3,6,2,7,4,8,1,5]=>0000111=>1110000
[3,2,1,6,4,7,8,5]=>1100101=>1010011
[3,7,4,2,1,5,8,6]=>1010011=>1100101
[1,7,3,4,2,5,8,6]=>0010011=>1100100
[4,7,2,1,3,5,8,6]=>1000011=>1100001
[7,8,4,2,1,3,6,5]=>1010101=>1010101
[7,8,1,3,4,2,6,5]=>0010101=>1010100
[7,8,3,4,2,1,6,5]=>1010101=>1010101
[6,3,2,7,1,8,5,4]=>0101111=>1111010
[3,6,2,7,1,8,5,4]=>0001111=>1111000
[6,7,3,8,2,5,4,1]=>0011011=>1101100
[6,4,7,8,5,2,3,1]=>0101101=>1011010
[2,6,4,7,8,1,5,3]=>0001101=>1011000
[4,6,2,7,8,1,5,3]=>0001101=>1011000
[7,4,5,8,6,2,1,3]=>1000111=>1110001
[7,4,1,5,8,6,2,3]=>0010111=>1110100
[7,5,3,8,6,1,2,4]=>0001111=>1111000
[7,5,8,2,1,6,3,4]=>1000111=>1110001
[6,2,7,1,3,8,5,4]=>0001111=>1111000
[6,3,1,7,8,2,5,4]=>0101101=>1011010
[4,6,1,7,8,5,2,3]=>0001101=>1011000
[5,1,2,6,7,8,4,3]=>0011001=>1001100
[5,2,6,7,8,4,1,3]=>0011001=>1001100
[5,2,6,7,8,4,3,1]=>0111001=>1001110
[2,5,6,7,8,4,1,3]=>0010001=>1000100
[1,5,2,6,7,8,4,3]=>0011001=>1001100
[1,6,4,7,8,5,2,3]=>0001101=>1011000
[2,6,7,1,3,8,5,4]=>0001011=>1101000
[6,7,8,2,1,5,4,3]=>1011001=>1001101
[6,7,3,8,5,1,4,2]=>0011011=>1101100
[6,4,7,8,5,3,1,2]=>0101101=>1011010
[4,5,2,3,7,6,1,8]=>0001110=>0111000
[6,4,3,7,2,5,1,8]=>0011110=>0111100
[8,4,3,6,5,1,2,7]=>0011101=>1011100
[1,5,6,3,4,8,7,2]=>0000111=>1110000
[4,6,2,7,3,5,1,8]=>0001110=>0111000
[3,2,6,7,4,5,1,8]=>0101010=>0101010
[4,7,2,6,5,3,1,8]=>0101110=>0111010
[5,7,6,2,4,3,1,8]=>0110110=>0110110
[1,7,5,4,8,3,6,2]=>0001111=>1111000
[8,7,5,4,1,3,2,6]=>0111011=>1101110
[6,8,5,4,2,1,3,7]=>1011001=>1001101
[5,8,6,2,4,1,3,7]=>0010101=>1010100
[4,8,2,6,5,1,3,7]=>0001101=>1011000
[3,2,8,6,5,1,4,7]=>0101101=>1011010
[4,1,2,6,5,8,7,3]=>0010111=>1110100
[5,1,6,2,4,8,7,3]=>0001111=>1111000
[6,1,5,4,2,8,7,3]=>0011111=>1111100
[7,1,5,4,8,2,6,3]=>0001111=>1111000
[8,1,5,4,7,6,2,3]=>0001111=>1111000
[1,8,6,7,4,5,3,2]=>0101011=>1101010
[8,1,6,7,4,5,2,3]=>0001011=>1101000
[7,1,6,8,4,2,5,3]=>0011011=>1101100
[6,1,7,8,2,4,5,3]=>0001101=>1011000
[5,1,7,2,8,4,6,3]=>0001111=>1111000
[4,1,2,7,8,5,6,3]=>0010101=>1010100
[3,2,1,7,8,5,6,4]=>1100101=>1010011
[3,2,8,7,1,5,4,6]=>0101011=>1101010
[4,8,2,7,1,5,3,6]=>0001011=>1101000
[5,8,7,2,1,4,3,6]=>1010011=>1100101
[6,8,7,1,2,4,3,5]=>0010011=>1100100
[7,8,6,1,4,2,3,5]=>0010101=>1010100
[8,7,6,1,4,3,2,5]=>0110111=>1110110
[1,7,6,8,4,3,5,2]=>0011011=>1101100
[1,6,7,8,3,4,5,2]=>0001001=>1001000
[8,6,7,1,3,4,2,5]=>0010011=>1100100
[7,6,8,1,3,2,4,5]=>0100011=>1100010
[5,7,8,2,1,3,4,6]=>1000001=>1000001
[4,7,2,8,1,3,5,6]=>0000011=>1100000
[3,2,6,8,4,1,5,7]=>0110001=>1000110
[4,6,2,8,3,1,5,7]=>0100101=>1010010
[5,6,8,2,3,1,4,7]=>0100001=>1000010
[6,5,8,3,2,1,4,7]=>1100101=>1010011
[7,5,8,3,1,2,4,6]=>0100011=>1100010
[8,5,7,3,1,4,2,6]=>0110011=>1100110
[1,5,7,3,8,4,6,2]=>0000111=>1110000
[1,4,3,7,8,5,6,2]=>0010101=>1010100
[8,4,3,7,1,5,2,6]=>0011011=>1101100
[6,4,3,8,2,1,5,7]=>1010101=>1010101
[4,5,2,3,8,1,6,7]=>0001001=>1001000
[3,2,5,4,8,1,6,7]=>0101001=>1001010
[4,5,2,3,1,8,7,6]=>0101011=>1101010
[6,4,3,1,2,8,7,5]=>0110111=>1110110
[7,4,3,1,8,2,6,5]=>0110111=>1110110
[8,4,3,1,7,6,2,5]=>0110111=>1110110
[1,5,8,3,7,6,4,2]=>0010111=>1110100
[8,5,1,3,7,6,2,4]=>0001111=>1111000
[7,5,1,3,8,2,6,4]=>0001111=>1111000
[6,5,1,3,2,8,7,4]=>0101111=>1111010
[5,6,1,2,3,8,7,4]=>0000111=>1110000
[4,6,2,1,3,8,7,5]=>1000111=>1110001
[3,2,6,1,4,8,7,5]=>0100111=>1110010
[3,2,7,1,8,4,6,5]=>0100111=>1110010
[4,7,2,1,8,3,6,5]=>1000111=>1110001
[5,7,1,2,8,3,6,4]=>0000111=>1110000
[6,7,1,8,2,3,5,4]=>0001011=>1101000
[7,6,1,8,3,2,5,4]=>0101111=>1111010
[8,6,1,7,3,5,2,4]=>0001111=>1111000
[1,6,8,7,3,5,4,2]=>0011011=>1101100
[1,7,8,6,5,3,4,2]=>0011101=>1011100
[8,7,1,6,5,3,2,4]=>0101111=>1111010
[7,8,1,6,5,2,3,4]=>0001101=>1011000
[6,8,1,7,2,5,3,4]=>0001011=>1101000
[5,8,1,2,7,6,3,4]=>0000111=>1110000
[4,8,2,1,7,6,3,5]=>1000111=>1110001
[3,2,8,1,7,6,4,5]=>0100111=>1110010
[4,1,2,8,7,6,5,3]=>0011111=>1111100
[5,1,8,2,7,6,4,3]=>0011111=>1111100
[6,1,8,7,2,5,4,3]=>0011111=>1111100
[7,1,8,6,5,2,4,3]=>0011111=>1111100
[8,1,7,6,5,4,2,3]=>0011111=>1111100
[3,1,2,6,5,8,7,4]=>0100111=>1110010
[3,1,6,2,4,8,7,5]=>0100111=>1110010
[3,1,5,2,4,8,7,6]=>0101011=>1101010
[4,5,1,2,3,8,7,6]=>0001011=>1101000
[4,6,1,2,3,8,7,5]=>0000111=>1110000
[1,6,5,3,4,8,7,2]=>0001111=>1111000
[6,1,5,2,4,8,7,3]=>0001111=>1111000
[6,5,1,2,3,8,7,4]=>0001111=>1111000
[6,4,1,2,3,8,7,5]=>0010111=>1110100
[5,4,1,2,3,8,7,6]=>0011011=>1101100
[5,4,1,2,7,3,6,8]=>0011010=>0101100
[6,4,1,7,2,3,5,8]=>0010110=>0110100
[6,4,1,8,2,3,5,7]=>0010101=>1010100
[7,4,1,2,8,3,6,5]=>0010111=>1110100
[7,5,1,2,8,3,6,4]=>0001111=>1111000
[7,1,5,2,8,4,6,3]=>0001111=>1111000
[1,7,5,3,8,4,6,2]=>0001111=>1111000
[1,8,5,3,7,4,6,2]=>0001111=>1111000
[8,1,5,2,7,4,6,3]=>0001111=>1111000
[8,5,1,2,7,3,6,4]=>0001111=>1111000
[8,4,1,2,7,3,6,5]=>0010111=>1110100
[8,4,1,7,2,3,5,6]=>0010011=>1100100
[7,4,1,6,2,3,5,8]=>0010110=>0110100
[8,6,1,7,2,3,5,4]=>0001111=>1111000
[8,1,6,7,2,4,5,3]=>0001011=>1101000
[1,8,6,7,3,4,5,2]=>0001011=>1101000
[1,7,6,8,3,4,5,2]=>0001011=>1101000
[7,1,6,8,2,4,5,3]=>0001011=>1101000
[7,6,1,8,2,3,5,4]=>0001111=>1111000
[4,7,1,2,8,3,6,5]=>0000111=>1110000
[3,1,7,2,8,4,6,5]=>0100111=>1110010
[3,1,2,7,8,5,6,4]=>0100101=>1010010
[1,4,3,8,7,5,6,2]=>0010111=>1110100
[4,1,2,8,7,5,6,3]=>0010111=>1110100
[3,1,2,8,7,5,6,4]=>0100111=>1110010
[3,1,8,2,7,4,6,5]=>0100111=>1110010
[3,1,8,7,2,4,5,6]=>0100011=>1100010
[3,1,7,6,2,4,5,8]=>0100110=>0110010
[4,7,1,6,2,3,5,8]=>0000110=>0110000
[4,8,1,6,2,3,5,7]=>0000101=>1010000
[4,8,1,7,2,3,5,6]=>0000011=>1100000
[4,8,1,2,7,3,6,5]=>0000111=>1110000
[5,8,1,2,7,3,6,4]=>0000111=>1110000
[5,1,8,2,7,4,6,3]=>0001111=>1111000
[1,5,8,3,7,4,6,2]=>0000111=>1110000
[1,6,8,7,3,4,5,2]=>0001011=>1101000
[6,1,8,7,2,4,5,3]=>0001111=>1111000
[6,8,1,7,2,3,5,4]=>0001011=>1101000
[6,8,7,1,2,3,4,5]=>0000011=>1100000
[5,8,7,1,2,3,4,6]=>0000011=>1100000
[5,8,6,1,2,3,4,7]=>0000101=>1010000
[5,7,6,1,2,3,4,8]=>0000110=>0110000
[7,8,1,6,2,3,5,4]=>0001101=>1011000
[7,1,8,6,2,4,5,3]=>0001111=>1111000
[1,7,8,6,3,4,5,2]=>0001101=>1011000
[1,8,7,6,3,4,5,2]=>0001111=>1111000
[8,1,7,6,2,4,5,3]=>0001111=>1111000
[8,7,1,6,2,3,5,4]=>0001111=>1111000
[3,2,5,1,6,4,8,7]=>0101101=>1011010
[3,2,5,4,7,1,8,6]=>0101011=>1101010
[4,2,5,3,7,6,8,1]=>0011011=>1101100
[4,2,5,3,7,1,8,6]=>0011011=>1101100
[4,2,5,3,6,1,8,7]=>0011101=>1011100
[4,2,5,1,6,3,8,7]=>0011101=>1011100
[3,1,5,4,6,2,8,7]=>0101101=>1011010
[4,1,5,3,6,2,8,7]=>0011101=>1011100
[4,3,5,1,6,2,8,7]=>0011101=>1011100
[4,3,5,2,7,1,8,6]=>0011011=>1101100
[4,3,6,2,7,5,8,1]=>0010111=>1110100
[4,3,6,2,7,1,8,5]=>0010111=>1110100
[4,3,6,1,7,2,8,5]=>0010111=>1110100
[4,3,5,1,7,2,8,6]=>0011011=>1101100
[3,1,5,4,7,2,8,6]=>0101011=>1101010
[2,1,5,4,7,3,8,6]=>1001011=>1101001
[3,1,5,4,7,6,8,2]=>0101011=>1101010
[4,1,5,3,7,6,8,2]=>0011011=>1101100
[4,3,5,1,7,6,8,2]=>0011011=>1101100
[4,3,6,1,7,5,8,2]=>0010111=>1110100
[4,3,6,5,7,1,8,2]=>0010111=>1110100
[5,3,6,4,7,2,8,1]=>0001111=>1111000
[5,3,6,4,7,1,8,2]=>0001111=>1111000
[5,3,6,1,7,4,8,2]=>0001111=>1111000
[5,1,6,3,7,4,8,2]=>0001111=>1111000
[4,1,6,3,7,5,8,2]=>0010111=>1110100
[3,1,6,4,7,5,8,2]=>0100111=>1110010
[2,1,6,4,7,5,8,3]=>1000111=>1110001
[2,1,6,4,7,3,8,5]=>1000111=>1110001
[3,1,6,4,7,2,8,5]=>0100111=>1110010
[4,1,6,3,7,2,8,5]=>0010111=>1110100
[5,1,6,3,7,2,8,4]=>0001111=>1111000
[5,3,6,1,7,2,8,4]=>0001111=>1111000
[5,3,6,2,7,1,8,4]=>0001111=>1111000
[5,3,6,2,7,4,8,1]=>0001111=>1111000
[5,2,6,3,7,4,8,1]=>0001111=>1111000
[5,2,6,3,7,1,8,4]=>0001111=>1111000
[5,2,6,1,7,3,8,4]=>0001111=>1111000
[4,2,5,1,7,3,8,6]=>0011011=>1101100
[4,2,6,1,7,3,8,5]=>0010111=>1110100
[4,2,6,3,7,1,8,5]=>0010111=>1110100
[4,2,6,3,7,5,8,1]=>0010111=>1110100
[3,2,6,4,7,5,8,1]=>0100111=>1110010
[3,2,6,4,7,1,8,5]=>0100111=>1110010
[3,2,6,1,7,4,8,5]=>0100111=>1110010
[3,2,5,1,7,4,8,6]=>0101011=>1101010
[3,2,4,1,7,5,8,6]=>0110011=>1100110
[3,1,4,2,7,6,8,5]=>0110011=>1100110
[3,2,5,1,7,6,8,4]=>0101011=>1101010
[3,2,6,1,7,5,8,4]=>0100111=>1110010
[3,2,6,5,7,1,8,4]=>0100111=>1110010
[4,2,6,5,7,3,8,1]=>0010111=>1110100
[4,2,6,5,7,1,8,3]=>0010111=>1110100
[4,2,6,1,7,5,8,3]=>0010111=>1110100
[4,2,5,1,7,6,8,3]=>0011011=>1101100
[4,1,5,2,7,6,8,3]=>0011011=>1101100
[3,1,5,2,7,6,8,4]=>0101011=>1101010
[2,1,5,3,7,6,8,4]=>1001011=>1101001
[2,1,6,3,7,5,8,4]=>1000111=>1110001
[3,1,6,2,7,5,8,4]=>0100111=>1110010
[4,1,6,2,7,5,8,3]=>0010111=>1110100
[5,1,6,2,7,4,8,3]=>0001111=>1111000
[5,2,6,1,7,4,8,3]=>0001111=>1111000
[5,2,6,4,7,1,8,3]=>0001111=>1111000
[5,2,6,4,7,3,8,1]=>0001111=>1111000
[5,4,6,2,7,3,8,1]=>0001111=>1111000
[5,4,6,2,7,1,8,3]=>0001111=>1111000
[5,4,6,1,7,2,8,3]=>0001111=>1111000
[5,1,6,4,7,2,8,3]=>0001111=>1111000
[4,1,6,5,7,2,8,3]=>0010111=>1110100
[3,1,6,5,7,2,8,4]=>0100111=>1110010
[2,1,6,5,7,3,8,4]=>1000111=>1110001
[3,1,6,5,7,4,8,2]=>0100111=>1110010
[4,1,6,5,7,3,8,2]=>0010111=>1110100
[5,1,6,4,7,3,8,2]=>0001111=>1111000
[5,4,6,1,7,3,8,2]=>0001111=>1111000
[5,4,6,3,7,1,8,2]=>0001111=>1111000
[8,3,5,2,1,6,4,7]=>1001101=>1011001
[8,6,3,5,2,4,1,7]=>0011101=>1011100
[3,7,5,2,4,1,8,6]=>0011011=>1101100
[8,3,7,5,2,4,6,1]=>0001111=>1111000
[8,2,4,5,7,3,6,1]=>0000111=>1110000
[2,4,5,7,3,1,8,6]=>0100011=>1100010
[8,2,4,6,5,3,1,7]=>0101101=>1011010
[8,2,5,4,6,1,3,7]=>0001101=>1011000
[8,6,3,5,1,4,2,7]=>0011101=>1011100
[8,6,1,4,5,3,2,7]=>0101101=>1011010
[8,1,5,6,4,3,2,7]=>0110101=>1010110
[5,7,4,3,2,1,8,6]=>1110011=>1100111
[8,5,7,4,3,2,6,1]=>0110111=>1110110
[4,6,8,3,2,7,5,1]=>0101011=>1101010
[4,7,6,3,2,8,1,5]=>0100111=>1110010
[1,4,6,7,3,2,8,5]=>0100011=>1100010
[5,4,7,3,1,8,2,6]=>0101011=>1101010
[1,7,4,5,3,2,8,6]=>0101011=>1101010
[3,7,5,1,4,2,8,6]=>0011011=>1101100
[5,7,4,2,1,3,8,6]=>1010011=>1100101
[8,5,7,4,2,1,6,3]=>1010111=>1110101
[8,3,7,5,1,4,6,2]=>0001111=>1111000
[8,4,1,7,5,3,6,2]=>0011111=>1111100
[4,6,3,8,7,1,5,2]=>0001111=>1111000
[1,7,4,8,6,3,5,2]=>0001111=>1111000
[8,4,7,6,3,5,2,1]=>1001111=>1111001
[3,6,5,8,7,4,1,2]=>0010111=>1110100
[3,1,5,8,6,7,4,2]=>0110011=>1100110
[4,8,1,6,7,3,5,2]=>0001011=>1101000
[3,6,4,1,8,7,5,2]=>0011111=>1111100
[8,2,6,1,4,7,5,3]=>0001111=>1111000
[2,7,6,8,1,4,3,5]=>0010011=>1100100
[3,7,1,6,4,8,2,5]=>0000111=>1110000
[1,7,3,5,6,8,2,4]=>0000011=>1100000
[1,3,6,7,5,8,2,4]=>0000011=>1100000
[3,7,6,5,8,2,1,4]=>1000111=>1110001
[3,6,8,5,7,2,4,1]=>0010011=>1100100
[2,3,5,7,6,8,1,4]=>0000011=>1100000
[2,1,6,5,7,8,3,4]=>1000101=>1010001
[4,2,7,6,8,3,1,5]=>0110011=>1100110
[4,2,6,8,7,3,5,1]=>0011011=>1101100
[3,8,2,4,6,7,5,1]=>0001011=>1101000
[3,7,2,6,4,8,1,5]=>0000111=>1110000
[3,2,6,1,4,7,8,5]=>0100101=>1010010
[5,3,7,2,1,8,4,6]=>1001011=>1101001
[4,7,3,2,1,5,8,6]=>1100011=>1100011
[8,7,6,1,3,4,2,5]=>0010111=>1110100
[8,5,7,3,2,1,6,4]=>1100111=>1110011
[8,3,6,7,2,1,5,4]=>1001011=>1101001
[3,7,8,6,2,1,5,4]=>1001101=>1011001
[8,7,6,3,5,2,4,1]=>0011111=>1111100
[2,7,4,8,1,6,5,3]=>0001111=>1111000
[4,6,8,2,1,7,5,3]=>1001011=>1101001
[8,4,1,5,7,2,6,3]=>0010111=>1110100
[8,5,3,7,1,6,2,4]=>0001111=>1111000
[8,5,7,2,1,3,6,4]=>1000111=>1110001
[8,2,6,7,1,3,5,4]=>0001011=>1101000
[8,3,6,1,7,5,2,4]=>0001111=>1111000
[4,6,1,8,7,2,5,3]=>0001111=>1111000
[8,1,2,5,6,7,4,3]=>0010011=>1100100
[8,2,6,5,7,4,1,3]=>0010111=>1110100
[2,1,7,8,5,6,4,3]=>1010101=>1010101
[8,2,5,7,6,4,3,1]=>0110111=>1110110
[2,7,6,8,5,4,1,3]=>0011011=>1101100
[1,7,2,5,8,6,4,3]=>0010111=>1110100
[1,7,4,8,2,6,5,3]=>0001111=>1111000
[3,7,8,1,6,5,2,4]=>0001101=>1011000
[2,7,8,6,1,3,5,4]=>0001101=>1011000
[8,7,6,3,5,1,4,2]=>0011111=>1111100
[8,4,7,6,5,1,3,2]=>0101111=>1111010
[8,7,1,5,6,4,3,2]=>0110111=>1110110
[8,1,6,7,5,4,3,2]=>0111011=>1101110
[6,5,3,1,2,4,8,7]=>0101101=>1011010
[4,6,3,5,1,2,8,7]=>0001101=>1011000
[8,5,3,7,2,1,4,6]=>1001011=>1101001
[6,8,1,4,5,7,3,2]=>0100011=>1100010
[8,7,2,4,5,1,3,6]=>0001011=>1101000
[3,6,2,4,5,1,8,7]=>0001101=>1011000
[2,6,1,4,5,3,8,7]=>0001101=>1011000
[6,1,2,4,5,3,8,7]=>0001101=>1011000
[5,6,3,2,1,4,8,7]=>1100101=>1010011
[5,4,3,6,1,2,8,7]=>0011101=>1011100
[6,3,1,4,5,2,8,7]=>0101101=>1011010
[3,1,6,4,5,2,8,7]=>0101101=>1011010
[8,3,7,4,5,1,2,6]=>0001011=>1101000
[5,8,7,4,2,6,3,1]=>0110111=>1110110
[2,8,7,4,1,6,3,5]=>0010111=>1110100
[8,1,7,4,2,6,3,5]=>0010111=>1110100
[3,7,8,4,5,1,2,6]=>0001001=>1001000
[2,1,8,7,5,3,4,6]=>1001011=>1101001
[2,1,6,8,5,7,3,4]=>1000011=>1100001
[5,6,3,8,1,7,2,4]=>0000111=>1110000
[7,6,1,4,5,8,3,2]=>0100111=>1110010
[3,7,6,4,5,8,2,1]=>1000111=>1110001
[8,5,7,4,1,6,3,2]=>0110111=>1110110
[5,1,8,4,7,6,2,3]=>0001111=>1111000
[2,5,8,4,7,6,1,3]=>0000111=>1110000
[2,4,8,3,5,6,7,1]=>0000011=>1100000
[4,1,8,3,5,6,7,2]=>0010011=>1100100
[3,8,4,2,5,6,7,1]=>0010011=>1100100
[8,4,1,3,5,6,7,2]=>0010011=>1100100
[7,5,8,4,3,6,1,2]=>0010111=>1110100
[6,5,3,8,4,1,7,2]=>0011111=>1111100
[2,1,5,8,4,6,7,3]=>1000011=>1100001
[2,1,4,8,3,6,7,5]=>1000011=>1100001
[6,4,3,8,2,1,7,5]=>1010111=>1110101
[7,3,8,4,2,6,1,5]=>0010111=>1110100
[8,3,1,2,5,6,7,4]=>0100011=>1100010
[3,1,8,2,5,6,7,4]=>0100011=>1100010
[2,3,8,1,5,6,7,4]=>0000011=>1100000
[4,3,8,2,5,6,7,1]=>0010011=>1100100
[4,8,2,3,5,6,7,1]=>0000011=>1100000
[3,8,2,1,5,6,7,4]=>1000011=>1100001
[2,8,1,3,5,6,7,4]=>0000011=>1100000
[8,1,2,3,5,6,7,4]=>0000011=>1100000
[7,8,2,4,3,6,1,5]=>0010101=>1010100
[6,8,3,2,4,1,7,5]=>0110011=>1100110
[2,1,8,3,4,6,7,5]=>1000011=>1100001
[2,1,7,8,5,4,3,6]=>1011001=>1001101
[5,7,3,8,1,4,2,6]=>0010011=>1100100
[7,1,8,4,5,3,2,6]=>0101011=>1101010
[2,7,8,4,5,3,1,6]=>0101001=>1001010
[8,7,1,4,3,6,2,5]=>0010111=>1110100
[3,8,7,4,2,6,1,5]=>0010111=>1110100
[5,7,8,4,3,6,2,1]=>1010101=>1010101
[5,6,3,8,4,2,7,1]=>0010111=>1110100
[4,8,3,6,2,1,7,5]=>1000111=>1110001
[8,6,3,1,4,2,7,5]=>0110111=>1110110
[7,5,3,8,2,4,1,6]=>0011011=>1101100
[2,4,3,1,8,5,7,6]=>0110011=>1100110
[4,1,3,2,6,8,7,5]=>0110011=>1100110
[7,5,3,6,2,8,1,4]=>0001111=>1111000
[8,6,3,5,1,2,7,4]=>0001111=>1111000
[5,8,3,2,6,1,7,4]=>0100111=>1110010
[4,5,3,8,6,2,7,1]=>0001111=>1111000
[3,5,8,4,7,6,2,1]=>1000111=>1110001
[5,8,2,4,7,6,1,3]=>0000111=>1110000
[8,7,5,4,1,6,2,3]=>0011111=>1111100
[2,7,6,4,5,8,1,3]=>0000111=>1110000
[7,1,6,4,5,8,2,3]=>0000111=>1110000
[5,7,3,6,1,8,2,4]=>0000111=>1110000
[2,1,7,6,5,8,3,4]=>1000111=>1110001
[2,1,8,5,3,6,7,4]=>1001011=>1101001
[6,8,3,5,2,1,7,4]=>1001011=>1101001
[7,8,5,4,2,6,1,3]=>0011101=>1011100
[8,1,4,2,5,6,7,3]=>0010011=>1100100
[2,8,4,1,5,6,7,3]=>0010011=>1100100
[4,8,1,2,5,6,7,3]=>0000011=>1100000
[3,4,8,1,5,6,7,2]=>0000011=>1100000
[3,4,2,8,5,6,7,1]=>0010011=>1100100
[2,4,1,8,5,6,7,3]=>0010011=>1100100
[4,1,2,8,5,6,7,3]=>0010011=>1100100
[8,4,2,1,5,6,7,3]=>1010011=>1100101
[7,5,2,4,8,6,1,3]=>0001111=>1111000
[6,5,3,2,8,1,7,4]=>0101111=>1111010
[2,1,5,3,8,6,7,4]=>1001011=>1101001
[6,4,3,5,8,1,7,2]=>0010111=>1110100
[7,3,5,4,8,6,1,2]=>0001111=>1111000
[8,3,4,1,5,6,7,2]=>0010011=>1100100
[4,3,1,8,5,6,7,2]=>0110011=>1100110
[3,1,4,8,5,6,7,2]=>0100011=>1100010
[6,5,3,7,2,8,4,1]=>0011111=>1111100
[6,3,7,4,5,8,2,1]=>1000111=>1110001
[6,7,2,4,5,8,3,1]=>0100011=>1100010
[5,1,7,4,8,6,3,2]=>0101111=>1111010
[2,5,7,4,8,6,3,1]=>0100111=>1110010
[5,6,3,7,1,8,4,2]=>0010111=>1110100
[3,8,7,4,5,2,1,6]=>1001011=>1101001
[3,7,5,4,8,6,2,1]=>1001111=>1111001
[5,7,1,4,8,6,2,3]=>0000111=>1110000
[5,6,3,1,8,2,7,4]=>0100111=>1110010
[4,6,3,5,8,2,7,1]=>0000111=>1110000
[4,6,3,8,1,2,7,5]=>0000111=>1110000
[3,7,8,4,1,6,2,5]=>0010101=>1010100
[3,2,5,1,6,8,4,7]=>0101001=>1001010
[3,6,2,5,4,8,1,7]=>0001101=>1011000
[3,5,2,4,7,1,8,6]=>0001011=>1101000
[3,5,8,2,4,7,6,1]=>0000111=>1110000
[4,2,5,8,3,7,6,1]=>0010111=>1110100
[4,2,6,5,3,8,1,7]=>0011101=>1011100
[5,4,2,1,6,8,3,7]=>1011001=>1001101
[6,3,5,1,4,8,2,7]=>0001101=>1011000
[4,6,1,5,3,8,2,7]=>0001101=>1011000
[5,1,6,4,3,8,2,7]=>0011101=>1011100
[5,4,3,2,7,1,8,6]=>0111011=>1101110
[5,4,3,8,2,7,6,1]=>0011111=>1111100
[4,3,6,2,8,7,5,1]=>0011111=>1111100
[4,3,7,6,2,1,8,5]=>1010111=>1110101
[6,4,3,1,7,2,8,5]=>0110111=>1110110
[7,5,4,3,1,8,2,6]=>0111011=>1101110
[1,4,7,5,8,3,2,6]=>0100011=>1100010
[7,1,3,5,8,4,2,6]=>0010011=>1100100
[7,2,5,8,4,1,3,6]=>0010011=>1100100
[2,8,5,7,4,6,1,3]=>0000111=>1110000
[3,5,8,7,1,4,6,2]=>0000111=>1110000
[1,4,5,8,7,3,6,2]=>0000111=>1110000
[1,5,4,8,7,3,6,2]=>0001111=>1111000
[6,4,3,8,1,7,5,2]=>0011111=>1111100
[4,3,7,1,8,6,5,2]=>0011111=>1111100
[4,8,3,7,6,5,2,1]=>1001111=>1111001
[5,3,8,7,6,4,2,1]=>1011111=>1111101
[7,5,3,1,8,6,4,2]=>0111111=>1111110
[1,8,6,5,3,7,4,2]=>0011111=>1111100
[1,5,8,6,3,7,4,2]=>0010111=>1110100
[4,6,1,8,7,3,5,2]=>0001111=>1111000
[6,8,7,3,1,4,5,2]=>0101011=>1101010
[6,2,8,7,4,5,1,3]=>0001111=>1111000
[7,6,2,8,4,1,3,5]=>0010111=>1110100
[7,3,1,6,8,4,2,5]=>0110011=>1100110
[1,7,6,4,8,3,2,5]=>0100111=>1110010
[5,7,1,6,3,2,8,4]=>0100111=>1110010
[6,1,7,5,3,2,8,4]=>0101111=>1111010
[7,6,5,3,2,1,8,4]=>1101111=>1111011
[6,5,3,2,8,7,4,1]=>0111111=>1111110
[5,2,6,3,8,7,4,1]=>0011111=>1111100
[5,2,7,6,3,1,8,4]=>0101111=>1111010
[6,5,2,1,7,3,8,4]=>1001111=>1111001
[5,2,7,4,1,8,3,6]=>0011011=>1101100
[4,7,2,6,3,1,8,5]=>0100111=>1110010
[2,4,8,6,3,7,5,1]=>0001111=>1111000
[3,8,6,2,4,7,5,1]=>0001111=>1111000
[7,3,6,2,4,1,8,5]=>0010111=>1110100
[3,6,7,2,1,4,8,5]=>1000011=>1100001
[4,3,7,8,2,1,5,6]=>1010001=>1000101
[8,3,7,1,4,6,2,5]=>0000111=>1110000
[3,8,2,5,7,1,6,4]=>0000111=>1110000
[8,3,6,2,7,1,5,4]=>0001111=>1111000
[7,8,3,6,2,1,5,4]=>1001101=>1011001
[8,7,3,6,2,5,4,1]=>0011111=>1111100
[4,7,8,2,1,6,5,3]=>1001101=>1011001
[4,2,6,8,1,7,5,3]=>0011011=>1101100
[5,4,8,2,7,1,6,3]=>0001111=>1111000
[4,8,1,5,7,2,6,3]=>0000111=>1110000
[5,8,3,7,1,6,2,4]=>0000111=>1110000
[5,8,7,2,6,1,3,4]=>0000111=>1110000
[8,6,2,7,5,1,3,4]=>0001111=>1111000
[3,6,8,1,7,5,2,4]=>0001011=>1101000
[5,1,6,8,2,7,4,3]=>0011011=>1101100
[6,5,2,8,1,7,4,3]=>0011111=>1111100
[5,2,7,1,8,6,4,3]=>0011111=>1111100
[5,8,2,7,6,4,3,1]=>0110111=>1110110
[6,2,8,7,5,4,3,1]=>0111111=>1111110
[7,6,2,1,8,5,4,3]=>1011111=>1111101
[6,1,7,2,8,5,4,3]=>0011111=>1111100
[7,5,1,8,2,6,4,3]=>0011111=>1111100
[4,7,1,8,6,2,5,3]=>0001111=>1111000
[7,8,3,1,6,5,2,4]=>0101101=>1011010
[8,7,4,6,1,5,3,2]=>0101111=>1111010
[8,5,7,1,6,4,3,2]=>0110111=>1110110
[6,8,1,7,5,4,3,2]=>0111011=>1101110
[7,1,8,6,5,4,3,2]=>0111111=>1111110
[5,4,2,3,7,6,1,8]=>0011110=>0111100
[6,4,2,7,3,5,1,8]=>0011110=>0111100
[7,4,2,6,3,5,1,8]=>0011110=>0111100
[8,4,2,6,3,1,5,7]=>0110101=>1010110
[3,2,7,6,4,5,1,8]=>0101110=>0111010
[4,7,2,6,3,5,1,8]=>0001110=>0111000
[5,7,6,2,3,4,1,8]=>0010110=>0110100
[1,6,5,2,3,8,4,7]=>0001101=>1011000
[1,7,5,2,8,3,4,6]=>0001011=>1101000
[6,8,5,2,3,1,4,7]=>0101001=>1001010
[5,8,6,2,3,1,4,7]=>0100101=>1010010
[4,8,2,6,3,1,5,7]=>0100101=>1010010
[3,2,8,6,4,1,5,7]=>0110101=>1010110
[3,2,1,6,4,8,5,7]=>1100101=>1010011
[7,1,5,2,8,3,4,6]=>0001011=>1101000
[1,8,5,2,7,3,4,6]=>0001011=>1101000
[1,8,6,7,2,3,4,5]=>0000011=>1100000
[8,1,6,7,2,3,4,5]=>0000011=>1100000
[7,1,6,8,2,3,4,5]=>0000011=>1100000
[3,2,1,7,8,4,5,6]=>1100001=>1000011
[3,2,8,7,1,4,5,6]=>0100011=>1100010
[5,8,7,2,1,3,4,6]=>1000011=>1100001
[1,7,6,8,2,3,4,5]=>0000011=>1100000
[6,5,8,2,3,1,4,7]=>0100101=>1010010
[8,5,7,2,1,3,4,6]=>1000011=>1100001
[6,4,2,8,3,1,5,7]=>0110101=>1010110
[5,4,2,3,8,1,6,7]=>0011001=>1001100
[3,2,5,4,1,8,6,7]=>0111001=>1001110
[4,5,2,3,1,8,6,7]=>0101001=>1001010
[5,4,2,3,1,8,6,7]=>0111001=>1001110
[6,4,2,1,3,8,5,7]=>1010101=>1010101
[7,4,2,1,8,3,5,6]=>1010011=>1100101
[8,4,2,1,7,3,5,6]=>1010011=>1100101
[1,4,2,8,7,3,5,6]=>0010011=>1100100
[1,5,8,2,7,3,4,6]=>0000011=>1100000
[8,5,1,2,7,3,4,6]=>0001011=>1101000
[7,5,1,2,8,3,4,6]=>0001011=>1101000
[6,5,1,2,3,8,4,7]=>0001101=>1011000
[4,6,2,1,3,8,5,7]=>1000101=>1010001
[3,2,6,1,4,8,5,7]=>0100101=>1010010
[3,2,7,1,8,4,5,6]=>0100011=>1100010
[4,7,2,1,8,3,5,6]=>1000011=>1100001
[7,6,1,8,2,3,4,5]=>0000111=>1110000
[8,6,1,7,2,3,4,5]=>0000111=>1110000
[1,6,8,7,2,3,4,5]=>0000011=>1100000
[1,7,8,6,2,3,4,5]=>0000101=>1010000
[7,8,1,6,2,3,4,5]=>0000101=>1010000
[6,8,1,7,2,3,4,5]=>0000011=>1100000
[4,8,2,1,7,3,5,6]=>1000011=>1100001
[3,2,8,1,7,4,5,6]=>0100011=>1100010
[3,2,1,8,7,4,5,6]=>1100011=>1100011
[5,1,8,2,7,3,4,6]=>0001011=>1101000
[6,1,8,7,2,3,4,5]=>0000111=>1110000
[8,1,7,6,2,3,4,5]=>0000111=>1110000
[1,8,7,6,2,3,4,5]=>0000111=>1110000
[6,3,5,1,2,4,8,7]=>0001101=>1011000
[4,3,5,6,1,2,8,7]=>0010101=>1010100
[8,3,7,5,2,1,4,6]=>1001011=>1101001
[6,3,7,5,1,8,4,2]=>0011111=>1111100
[6,5,2,7,1,8,3,4]=>0001111=>1111000
[8,5,2,7,4,1,3,6]=>0011011=>1101100
[2,6,1,5,4,3,8,7]=>0011101=>1011100
[6,4,3,5,1,2,8,7]=>0011101=>1011100
[5,3,1,4,6,2,8,7]=>0101101=>1011010
[3,1,4,6,5,2,8,7]=>0101101=>1011010
[5,7,4,6,2,8,3,1]=>0100111=>1110010
[8,1,4,7,2,6,3,5]=>0000111=>1110000
[3,4,7,8,5,2,1,6]=>1001001=>1001001
[2,1,8,5,7,3,4,6]=>1000011=>1100001
[8,6,3,5,1,7,4,2]=>0011111=>1111100
[5,8,2,4,6,7,3,1]=>0100011=>1100010
[3,4,8,6,5,7,1,2]=>0000111=>1110000
[7,5,4,8,1,6,3,2]=>0101111=>1111010
[5,1,4,6,8,2,7,3]=>0001011=>1101000
[2,5,4,6,7,1,8,3]=>0001011=>1101000
[2,4,6,3,7,5,8,1]=>0000111=>1110000
[4,1,6,3,8,5,7,2]=>0010111=>1110100
[3,7,4,2,8,6,5,1]=>0011111=>1111100
[7,4,1,3,5,8,6,2]=>0010111=>1110100
[6,5,8,4,1,7,3,2]=>0110111=>1110110
[8,5,3,7,4,1,6,2]=>0011111=>1111100
[2,1,4,8,3,7,6,5]=>1000111=>1110001
[7,4,3,8,2,1,6,5]=>1010111=>1110101
[6,3,7,4,1,8,2,5]=>0010111=>1110100
[8,3,1,2,5,7,6,4]=>0100111=>1110010
[3,1,8,2,7,6,5,4]=>0101111=>1111010
[2,3,8,1,6,7,5,4]=>0001011=>1101000
[4,3,7,2,6,8,5,1]=>0011011=>1101100
[4,7,2,3,8,5,6,1]=>0000111=>1110000
[3,8,2,1,7,5,6,4]=>1000111=>1110001
[2,8,1,3,6,5,7,4]=>0000111=>1110000
[2,7,8,5,4,3,1,6]=>0111001=>1001110
[8,7,1,6,3,4,2,5]=>0010111=>1110100
[3,8,6,7,2,4,1,5]=>0010011=>1100100
[5,3,8,7,4,2,6,1]=>0011111=>1111100
[4,3,8,7,2,1,6,5]=>1010111=>1110101
[8,3,6,1,4,2,7,5]=>0010111=>1110100
[7,3,5,8,2,4,1,6]=>0010011=>1100100
[2,3,4,1,8,5,7,6]=>0010011=>1100100
[4,1,3,2,6,7,8,5]=>0110001=>1000110
[8,3,5,6,2,7,1,4]=>0000111=>1110000
[5,3,6,1,8,7,2,4]=>0001111=>1111000
[5,6,2,8,7,4,1,3]=>0010111=>1110100
[7,8,5,6,1,4,2,3]=>0010101=>1010100
[2,8,6,5,4,7,1,3]=>0001111=>1111000
[8,1,6,4,5,7,2,3]=>0000111=>1110000
[5,8,3,6,1,7,2,4]=>0000111=>1110000
[2,1,8,6,5,7,3,4]=>1000111=>1110001
[2,1,7,5,3,6,8,4]=>1001011=>1101001
[6,7,3,5,2,1,8,4]=>1001011=>1101001
[7,1,4,2,5,6,8,3]=>0010011=>1100100
[2,7,4,1,6,5,8,3]=>0010111=>1110100
[4,6,1,2,8,7,3,5]=>0000111=>1110000
[2,4,1,5,8,7,6,3]=>0010111=>1110100
[4,1,2,5,8,6,7,3]=>0010011=>1100100
[6,4,2,1,5,8,7,3]=>1010111=>1110101
[8,5,2,4,6,1,7,3]=>0001111=>1111000
[7,5,3,2,6,8,1,4]=>0101011=>1101010
[2,1,5,3,6,8,7,4]=>1001011=>1101001
[7,3,5,4,6,1,8,2]=>0001111=>1111000
[6,3,4,1,5,7,8,2]=>0010101=>1010100
[4,3,1,5,7,6,8,2]=>0110011=>1100110
[3,1,4,5,6,8,7,2]=>0100011=>1100010
[4,5,2,6,3,1,8,7]=>0101101=>1011010
[6,5,2,1,4,3,8,7]=>1011101=>1011101
[6,5,2,7,4,8,3,1]=>0101111=>1111010
[8,5,2,7,4,1,6,3]=>0011111=>1111100
[8,3,7,5,2,1,6,4]=>1001111=>1111001
[6,3,7,5,2,8,4,1]=>0011111=>1111100
[3,1,6,5,4,2,8,7]=>0111101=>1011110
[5,6,3,2,4,1,8,7]=>0110101=>1010110
[3,6,2,4,1,5,8,7]=>0010101=>1010100
[2,6,1,3,5,4,8,7]=>0001101=>1011000
[6,7,2,3,4,8,5,1]=>0001011=>1101000
[8,7,2,3,4,1,6,5]=>0010111=>1110100
[5,1,7,3,8,4,6,2]=>0001111=>1111000
[2,5,7,3,8,6,4,1]=>0010111=>1110100
[7,6,1,3,5,8,4,2]=>0010111=>1110100
[3,6,7,4,1,8,5,2]=>0011011=>1101100
[5,6,3,7,4,8,1,2]=>0000111=>1110000
[2,1,6,7,4,8,5,3]=>1001011=>1101001
[2,1,8,7,4,3,6,5]=>1010111=>1110101
[5,8,3,7,4,2,6,1]=>0010111=>1110100
[3,8,7,4,1,2,6,5]=>0010111=>1110100
[7,8,1,3,5,2,6,4]=>0001101=>1011000
[5,8,7,3,2,6,1,4]=>0100111=>1110010
[2,8,6,3,1,5,7,4]=>0100111=>1110010
[8,1,6,3,2,5,4,7]=>0101101=>1011010
[2,8,4,1,6,3,7,5]=>0010111=>1110100
[4,8,1,2,7,6,3,5]=>0000111=>1110000
[3,8,4,2,5,7,1,6]=>0010011=>1100100
[6,8,3,5,2,7,4,1]=>0011011=>1101100
[2,1,5,3,8,7,6,4]=>1001111=>1111001
[6,5,3,2,8,7,1,4]=>0101111=>1111010
[7,5,2,4,8,1,6,3]=>0001111=>1111000
[3,4,2,8,5,7,6,1]=>0010111=>1110100
[2,4,1,8,7,6,5,3]=>0011111=>1111100
[8,4,2,1,7,5,3,6]=>1011011=>1101101
[4,3,1,8,6,7,5,2]=>0111011=>1101110
[3,1,4,8,6,5,7,2]=>0100111=>1110010
[7,1,6,5,4,8,2,3]=>0001111=>1111000
[3,7,5,6,8,4,2,1]=>1010011=>1100101
[5,7,1,6,8,2,4,3]=>0010011=>1100100
[8,6,2,5,1,7,4,3]=>0011111=>1111100
[5,6,2,1,8,7,3,4]=>1000111=>1110001
[4,6,2,5,8,3,7,1]=>0000111=>1110000
[7,5,2,6,3,8,1,4]=>0001111=>1111000
[4,1,2,3,6,8,7,5]=>0010011=>1100100
[2,4,3,1,8,5,6,7]=>0110001=>1000110
[7,5,2,8,3,4,6,1]=>0001111=>1111000
[5,6,2,8,4,3,1,7]=>0110101=>1010110
[4,7,2,8,1,5,3,6]=>0001011=>1101000
[8,7,2,1,4,5,6,3]=>1000111=>1110001
[3,6,8,7,1,5,4,2]=>0011011=>1101100
[5,7,8,6,3,4,1,2]=>0010101=>1010100
[7,1,8,5,4,3,6,2]=>0011111=>1111100
[2,7,8,4,5,3,6,1]=>0001101=>1011000
[5,7,3,8,1,4,6,2]=>0000111=>1110000
[2,1,7,8,5,4,6,3]=>1001101=>1011001
[2,1,5,8,4,6,3,7]=>1000101=>1010001
[6,5,3,8,4,1,2,7]=>0011101=>1011100
[7,5,8,4,3,6,2,1]=>1010111=>1110101
[2,4,8,3,5,6,1,7]=>0000101=>1010000
[4,1,8,3,6,5,2,7]=>0011101=>1011100
[3,4,8,1,7,2,5,6]=>0000011=>1100000
[8,4,1,3,7,2,6,5]=>0010111=>1110100
[3,1,8,2,4,7,6,5]=>0100111=>1110010
[2,3,8,1,4,6,7,5]=>0000011=>1100000
[4,3,8,2,5,1,7,6]=>0011011=>1101100
[6,3,8,4,2,5,7,1]=>0010111=>1110100
[7,4,3,8,2,5,1,6]=>0011011=>1101100
[2,1,4,8,3,5,7,6]=>1000011=>1100001
[6,8,2,4,3,5,1,7]=>0011001=>1001100
[4,8,2,3,5,1,6,7]=>0001001=>1001000
[3,8,2,1,4,6,5,7]=>1000101=>1010001
[2,8,1,3,4,5,7,6]=>0000011=>1100000
[2,8,4,1,6,5,3,7]=>0011101=>1011100
[2,8,4,1,6,5,7,3]=>0010111=>1110100
[2,8,7,6,1,4,3,5]=>0010111=>1110100
[2,8,5,6,7,4,3,1]=>0110011=>1100110
[7,5,8,6,1,4,2,3]=>0010111=>1110100
[3,5,7,6,1,4,2,8]=>0010110=>0110100
[3,5,7,2,4,1,6,8]=>0010010=>0100100
[7,5,8,2,4,1,6,3]=>0010111=>1110100
[2,8,5,3,4,7,6,1]=>0001111=>1111000
[2,8,5,3,4,1,7,6]=>0011011=>1101100
[2,8,5,3,4,1,6,7]=>0011001=>1001100
[2,8,7,6,1,4,5,3]=>0001111=>1111000
[2,8,5,3,6,1,7,4]=>0001111=>1111000
[2,8,5,6,7,4,1,3]=>0010011=>1100100
[2,8,5,3,4,7,1,6]=>0001011=>1101000
[2,8,5,3,4,6,1,7]=>0001101=>1011000
[2,8,5,3,4,6,7,1]=>0001011=>1101000
[3,5,7,2,4,6,1,8]=>0000110=>0110000
[6,5,2,7,3,1,4,8]=>0101110=>0111010
[6,5,2,8,3,1,7,4]=>0101111=>1111010
[6,5,2,8,3,1,4,7]=>0101101=>1011010
[7,5,8,2,4,6,3,1]=>0100111=>1110010
[7,5,8,6,1,4,3,2]=>0110111=>1110110
[6,5,8,2,1,3,7,4]=>1000111=>1110001
[3,5,6,2,1,8,7,4]=>1000111=>1110001
[3,5,7,6,1,4,8,2]=>0000111=>1110000
[3,5,7,2,4,1,8,6]=>0010011=>1100100
[3,5,7,2,4,6,8,1]=>0000011=>1100000
[6,5,2,7,3,1,8,4]=>0101111=>1111010
[4,5,2,6,3,1,7,8]=>0101100=>0011010
[4,1,2,3,7,6,8,5]=>0010011=>1100100
[6,5,2,7,3,4,8,1]=>0001111=>1111000
[5,1,6,7,4,3,8,2]=>0011011=>1101100
[5,1,2,6,4,8,7,3]=>0001111=>1111000
[5,1,2,8,6,4,7,3]=>0001111=>1111000
[5,1,6,8,7,3,4,2]=>0011011=>1101100
[6,5,2,8,3,7,4,1]=>0011111=>1111100
[4,1,2,3,8,7,5,6]=>0010011=>1100100
[4,1,2,3,8,6,5,7]=>0010101=>1010100
[4,1,2,3,8,6,7,5]=>0010011=>1100100
[4,1,2,3,7,6,5,8]=>0010110=>0110100
[4,1,2,3,8,5,7,6]=>0010011=>1100100
[7,1,6,8,4,3,5,2]=>0011011=>1101100
[6,1,2,8,4,5,7,3]=>0000111=>1110000
[5,6,8,2,3,1,7,4]=>0100011=>1100010
[6,5,8,2,4,3,1,7]=>0110101=>1010110
[6,5,8,2,4,3,7,1]=>0010111=>1110100
[7,5,2,8,3,4,1,6]=>0011011=>1101100
[6,5,2,8,3,7,1,4]=>0001111=>1111000
[6,5,2,7,3,4,1,8]=>0011110=>0111100
[5,1,6,7,4,3,2,8]=>0111010=>0101110
[5,1,6,8,7,3,2,4]=>0101011=>1101010
[7,1,6,8,4,3,2,5]=>0110011=>1100110
[5,7,8,6,3,4,2,1]=>1010101=>1010101
[4,1,8,3,6,5,7,2]=>0010111=>1110100
[4,1,8,3,6,2,7,5]=>0010111=>1110100
[3,1,4,8,6,2,7,5]=>0100111=>1110010
[3,1,4,8,6,5,2,7]=>0101101=>1011010
[7,1,6,5,8,3,2,4]=>0100111=>1110010
[4,1,6,7,8,3,2,5]=>0110001=>1000110
[4,1,6,5,7,3,2,8]=>0110110=>0110110
[4,5,2,6,3,7,1,8]=>0001110=>0111000
[4,5,2,7,3,8,1,6]=>0001011=>1101000
[3,5,6,2,4,8,7,1]=>0000111=>1110000
[3,5,6,2,4,8,1,7]=>0000101=>1010000
[3,7,5,6,8,4,1,2]=>0010011=>1100100
[3,6,5,2,8,1,7,4]=>0001111=>1111000
[6,1,2,5,8,4,7,3]=>0000111=>1110000
[7,1,6,5,8,3,4,2]=>0010111=>1110100
[7,5,2,6,3,8,4,1]=>0011111=>1111100
[4,1,2,3,5,8,7,6]=>0010011=>1100100
[4,1,2,3,7,8,6,5]=>0010101=>1010100
[4,5,2,7,3,8,6,1]=>0001111=>1111000
[4,1,6,7,8,3,5,2]=>0011001=>1001100
[4,1,2,6,8,5,7,3]=>0010011=>1100100
[4,1,2,5,6,8,7,3]=>0010011=>1100100
[4,5,2,6,3,7,8,1]=>0001101=>1011000
[7,8,5,6,1,4,3,2]=>0110101=>1010110
[7,8,4,2,1,5,3,6]=>1011001=>1001101
[7,8,2,1,6,5,3,4]=>1001101=>1011001
[6,4,1,2,5,7,3,8]=>0010110=>0110100
[2,4,8,1,5,7,3,6]=>0000011=>1100000
[4,3,8,1,7,2,5,6]=>0010011=>1100100
[6,3,1,4,7,2,5,8]=>0100110=>0110010
[7,8,3,4,5,1,6,2]=>0001101=>1011000
[7,8,3,5,4,2,1,6]=>1011001=>1001101
[7,8,4,1,2,3,6,5]=>0010101=>1010100
[7,8,3,6,5,4,1,2]=>0011101=>1011100
[7,8,2,1,5,3,4,6]=>1001001=>1001001
[7,8,2,6,4,1,3,5]=>0010101=>1010100
[7,8,2,5,6,4,1,3]=>0010101=>1010100
[7,8,1,6,5,4,3,2]=>0111101=>1011110
[6,2,1,7,5,4,3,8]=>1011110=>0111101
[2,1,8,7,5,4,3,6]=>1011011=>1101101
[1,3,8,2,6,4,7,5]=>0000111=>1110000
[5,3,7,1,6,4,8,2]=>0001111=>1111000
[5,3,6,2,7,4,1,8]=>0011110=>0111100
[6,1,2,5,8,7,4,3]=>0010111=>1110100
[6,3,1,8,4,2,7,5]=>0110111=>1110110
[6,4,2,1,5,3,8,7]=>1011101=>1011101
[6,4,3,7,5,8,1,2]=>0010111=>1110100
[4,3,8,7,5,6,1,2]=>0010111=>1110100
[2,4,7,1,5,3,6,8]=>0001010=>0101000
[1,3,7,6,4,2,8,5]=>0010111=>1110100
[2,1,7,5,6,8,4,3]=>1010011=>1100101
[3,7,2,8,6,4,1,5]=>0010111=>1110100
[3,8,1,7,6,4,5,2]=>0001111=>1111000
[1,8,5,7,3,6,4,2]=>0010111=>1110100
[2,7,5,8,3,6,1,4]=>0000111=>1110000
[1,5,6,8,2,4,7,3]=>0000011=>1100000
[2,6,8,5,3,1,4,7]=>0101001=>1001010
[2,6,1,4,7,3,5,8]=>0000110=>0110000
[5,6,7,3,8,4,1,2]=>0010011=>1100100
[5,2,8,1,4,7,3,6]=>0001011=>1101000
[4,6,7,5,2,1,3,8]=>1001010=>0101001
[4,5,6,7,2,8,1,3]=>0000011=>1100000
[4,5,7,6,1,8,3,2]=>0100111=>1110010
[1,5,8,6,2,7,3,4]=>0000111=>1110000
[1,6,5,8,3,2,7,4]=>0100111=>1110010
[4,6,5,7,1,2,8,3]=>0000111=>1110000
[4,7,5,6,3,1,8,2]=>0100111=>1110010
[5,1,6,3,4,2,8,7]=>0011101=>1011100
[5,7,1,4,2,3,8,6]=>0010011=>1100100
[5,7,6,4,3,8,1,2]=>0010111=>1110100
[6,3,4,5,8,7,1,2]=>0000111=>1110000
[6,2,4,1,8,3,7,5]=>0010111=>1110100
[6,2,3,5,4,8,1,7]=>0001101=>1011000
[6,1,3,4,5,8,7,2]=>0000111=>1110000
[5,1,4,2,7,6,8,3]=>0011011=>1101100
[1,6,2,4,7,8,3,5]=>0000101=>1010000
[5,7,2,4,1,6,3,8]=>0010110=>0110100
[6,1,4,2,8,5,3,7]=>0011101=>1011100
[6,7,5,8,1,4,3,2]=>0110011=>1100110
[5,8,7,6,3,4,1,2]=>0010111=>1110100
[5,8,7,6,2,3,1,4]=>0100111=>1110010
[4,1,7,2,6,5,3,8]=>0011110=>0111100
[4,8,2,1,5,6,3,7]=>1000101=>1010001
[4,2,7,8,1,6,3,5]=>0010101=>1010100
[2,1,8,7,6,5,3,4]=>1001111=>1111001
[3,1,4,7,8,2,6,5]=>0100101=>1010010
[3,1,7,4,5,6,8,2]=>0100011=>1100010
[4,2,7,1,6,3,8,5]=>0010111=>1110100
[4,3,7,5,6,8,1,2]=>0010011=>1100100
[4,8,6,3,5,7,1,2]=>0000111=>1110000
[4,8,1,2,5,3,7,6]=>0001011=>1101000
[3,8,6,5,2,4,1,7]=>0011101=>1011100
[3,8,5,6,1,4,7,2]=>0000111=>1110000
[5,3,7,8,2,1,6,4]=>1001101=>1011001
[5,2,8,7,1,6,4,3]=>0011111=>1111100
[1,6,8,7,5,2,4,3]=>0011011=>1101100
[3,6,7,8,5,1,4,2]=>0011001=>1001100
[3,7,6,8,5,2,1,4]=>1001011=>1101001
[3,7,8,5,1,2,4,6]=>0001001=>1001000
[3,7,1,6,4,2,5,8]=>0010110=>0110100
[4,1,8,6,2,3,5,7]=>0010101=>1010100
[4,7,8,6,3,5,1,2]=>0001101=>1011000
[3,8,7,6,5,4,1,2]=>0011111=>1111100
[2,1,7,6,5,3,4,8]=>1001110=>0111001
[2,8,1,6,4,5,3,7]=>0001101=>1011000
[2,8,7,5,1,4,3,6]=>0011011=>1101100
[2,8,6,7,5,1,3,4]=>0001011=>1101000
[2,7,8,6,5,4,1,3]=>0011101=>1011100
[6,3,1,2,7,4,8,5]=>0100111=>1110010
[6,4,2,7,1,3,8,5]=>0010111=>1110100
[7,4,2,5,1,3,8,6]=>0011011=>1101100
[7,5,3,6,1,8,2,4]=>0001111=>1111000
[8,5,3,6,1,7,2,4]=>0001111=>1111000
[8,3,6,2,4,7,1,5]=>0000111=>1110000
[7,3,6,2,4,8,1,5]=>0000111=>1110000
[4,3,7,1,2,5,8,6]=>0010011=>1100100
[3,6,2,7,1,4,8,5]=>0000111=>1110000
[5,3,6,7,1,2,8,4]=>0001011=>1101000
[6,3,7,4,1,2,8,5]=>0010111=>1110100
[4,7,1,5,2,3,8,6]=>0001011=>1101000
[3,7,5,1,2,4,8,6]=>0001011=>1101000
[7,6,4,2,3,8,1,5]=>0010111=>1110100
[8,6,4,2,3,7,1,5]=>0010111=>1110100
[4,7,6,3,8,1,2,5]=>0000111=>1110000
[5,7,4,2,3,8,1,6]=>0010011=>1100100
[3,7,6,1,4,8,2,5]=>0000111=>1110000
[5,7,2,6,1,8,3,4]=>0000111=>1110000
[6,4,7,5,2,8,1,3]=>0001111=>1111000
[7,4,8,5,2,6,1,3]=>0001111=>1111000
[5,8,2,6,3,7,1,4]=>0000111=>1110000
[3,8,6,1,2,7,4,5]=>0000111=>1110000
[3,8,6,2,4,7,1,5]=>0000111=>1110000
[6,8,4,3,7,1,2,5]=>0010011=>1100100
[6,8,5,3,7,1,2,4]=>0001011=>1101000
[3,8,5,7,1,2,4,6]=>0000011=>1100000
[2,8,5,7,1,3,4,6]=>0000011=>1100000
[4,8,6,2,7,1,3,5]=>0000111=>1110000
[7,3,8,5,6,1,2,4]=>0000111=>1110000
[6,3,7,5,8,1,2,4]=>0000111=>1110000
[2,7,6,4,8,1,3,5]=>0000111=>1110000
[2,6,5,8,1,3,4,7]=>0000101=>1010000
[3,6,5,8,1,2,4,7]=>0000101=>1010000
[2,5,7,4,8,1,3,6]=>0000011=>1100000
[5,4,6,7,2,8,1,3]=>0001011=>1101000
[4,6,3,7,1,8,2,5]=>0000111=>1110000
[3,5,7,1,4,8,2,6]=>0000011=>1100000
[5,3,7,2,4,8,1,6]=>0001011=>1101000
[5,4,7,3,8,1,2,6]=>0001011=>1101000
[7,4,6,3,8,1,2,5]=>0000111=>1110000
[8,4,6,3,7,1,2,5]=>0000111=>1110000
[8,4,1,6,7,2,3,5]=>0010011=>1100100
[7,4,1,6,8,2,3,5]=>0010011=>1100100
[5,4,1,7,8,2,3,6]=>0011001=>1001100
[6,5,3,7,1,8,2,4]=>0001111=>1111000
[6,5,1,2,7,8,3,4]=>0001101=>1011000
[5,3,6,4,7,8,1,2]=>0001101=>1011000
[6,3,7,4,8,5,1,2]=>0001111=>1111000
[4,7,1,5,8,6,2,3]=>0000111=>1110000
[7,5,1,2,8,6,3,4]=>0001111=>1111000
[7,5,3,8,1,6,2,4]=>0001111=>1111000
[7,4,1,8,6,2,3,5]=>0010111=>1110100
[7,6,1,8,5,2,3,4]=>0001111=>1111000
[8,6,1,7,5,2,3,4]=>0001111=>1111000
[5,7,2,8,1,6,3,4]=>0000111=>1110000
[6,4,7,8,2,5,1,3]=>0001101=>1011000
[6,3,7,8,5,1,2,4]=>0001101=>1011000
[3,6,8,2,7,1,4,5]=>0000011=>1100000
[2,4,8,7,1,3,5,6]=>0000011=>1100000
[4,3,8,7,1,2,5,6]=>0010011=>1100100
[5,3,8,7,1,2,4,6]=>0001011=>1101000
[8,3,7,6,1,2,4,5]=>0000111=>1110000
[8,4,7,6,1,2,3,5]=>0000111=>1110000
[5,4,8,7,1,2,3,6]=>0001011=>1101000
[3,5,8,7,1,2,4,6]=>0000011=>1100000
[2,5,8,7,1,3,4,6]=>0000011=>1100000
[4,6,8,2,7,1,3,5]=>0000011=>1100000
[4,7,1,8,6,2,3,5]=>0000111=>1110000
[7,5,8,6,4,1,2,3]=>0010111=>1110100
[6,8,4,7,5,1,2,3]=>0001011=>1101000
[5,8,7,1,6,2,3,4]=>0000111=>1110000
[2,8,7,6,1,3,4,5]=>0000111=>1110000
[3,8,7,6,1,2,4,5]=>0000111=>1110000
[4,8,7,6,1,2,3,5]=>0000111=>1110000
[5,6,3,1,4,2,8,7]=>0110101=>1010110
[7,5,3,8,2,1,6,4]=>1001111=>1111001
[3,8,7,4,5,1,6,2]=>0001111=>1111000
[6,7,1,4,5,8,2,3]=>0000011=>1100000
[2,1,7,8,5,3,6,4]=>1001101=>1011001
[5,7,3,8,1,2,6,4]=>0000111=>1110000
[8,7,1,4,5,3,2,6]=>0101011=>1101010
[2,7,8,4,1,6,5,3]=>0011101=>1011100
[7,1,8,4,2,6,5,3]=>0011111=>1111100
[7,5,1,4,8,6,3,2]=>0101111=>1111010
[6,5,3,1,8,4,7,2]=>0101111=>1111010
[6,4,3,8,1,5,7,2]=>0010111=>1110100
[8,6,3,1,2,5,7,4]=>0100111=>1110010
[8,7,1,4,2,6,5,3]=>0011111=>1111100
[7,3,8,4,1,6,5,2]=>0011111=>1111100
[2,3,4,5,6,7,8,1,9]=>00000010=>01000000
[2,3,4,5,6,8,9,1,7]=>00000001=>10000000
[2,3,4,5,7,8,9,1,6]=>00000001=>10000000
[2,3,4,6,7,8,9,1,5]=>00000001=>10000000
[2,3,5,6,7,8,9,1,4]=>00000001=>10000000
[2,4,5,6,7,8,9,1,3]=>00000001=>10000000
[3,4,5,6,7,8,9,1,2]=>00000001=>10000000
[2,3,4,5,6,7,8,9,10,1]=>000000001=>100000000
[2,3,4,5,6,7,8,9,1,10]=>000000010=>010000000
[2,3,4,5,6,7,1,8,9]=>00000100=>00100000
[2,3,4,5,6,7,8,10,1,9]=>000000001=>100000000
[2,3,4,5,6,1,9,7,8]=>00001001=>10010000
[2,3,4,5,6,7,9,10,1,8]=>000000001=>100000000
[2,3,4,5,1,8,9,6,7]=>00010001=>10001000
[2,3,4,5,6,8,9,10,1,7]=>000000001=>100000000
[2,3,4,1,7,8,9,5,6]=>00100001=>10000100
[2,3,4,5,7,8,9,10,1,6]=>000000001=>100000000
[2,3,1,6,7,8,9,4,5]=>01000001=>10000010
[2,3,4,6,7,8,9,10,1,5]=>000000001=>100000000
[2,1,5,6,7,8,9,3,4]=>10000001=>10000001
[2,3,5,6,7,8,9,10,1,4]=>000000001=>100000000
[1,4,5,6,7,8,9,2,3]=>00000001=>10000000
[2,4,5,6,7,8,9,10,1,3]=>000000001=>100000000
[3,4,5,6,7,8,9,10,1,2]=>000000001=>100000000
[3,6,4,5,7,2,8,1]=>0000111=>1110000
[5,3,2,7,4,6,8,1]=>0101011=>1101010
[7,5,3,6,2,4,8,1]=>0001111=>1111000
[6,3,2,5,1,8,4,7]=>0101101=>1011010
[8,5,3,6,2,7,1,4]=>0001111=>1111000
[8,2,6,3,4,7,1,5]=>0000111=>1110000
[7,2,6,3,4,5,8,1]=>0000111=>1110000
[6,2,7,3,4,5,8,1]=>0000111=>1110000
[3,6,2,7,4,5,8,1]=>0000111=>1110000
[4,2,5,7,3,6,8,1]=>0010011=>1100100
[5,4,7,6,2,3,8,1]=>0001111=>1111000
[6,7,3,5,2,4,8,1]=>0001011=>1101000
[3,7,6,2,4,5,8,1]=>0000111=>1110000
[2,7,6,3,4,5,8,1]=>0000111=>1110000
[6,5,3,1,2,8,4,7]=>0101101=>1011010
[8,6,5,2,3,7,1,4]=>0001111=>1111000
[8,5,2,1,7,3,4,6]=>1001011=>1101001
[7,5,2,1,8,3,4,6]=>1001011=>1101001
[1,6,3,2,8,4,5,7]=>0100101=>1010010
[5,7,3,1,2,8,4,6]=>0100011=>1100010
[5,6,2,3,1,8,4,7]=>0100101=>1010010
[4,2,6,5,1,8,3,7]=>0011101=>1011100
[5,4,8,6,2,7,1,3]=>0001111=>1111000
[6,8,3,5,2,7,1,4]=>0001011=>1101000
[7,8,5,2,3,6,1,4]=>0001101=>1011000
[6,8,2,1,7,3,4,5]=>1000011=>1100001
[1,8,6,3,7,2,4,5]=>0000111=>1110000
[1,8,2,7,3,4,5,6]=>0000011=>1100000
[2,8,1,7,3,4,5,6]=>0000011=>1100000
[3,8,6,1,7,2,4,5]=>0000111=>1110000
[4,8,1,5,7,2,3,6]=>0000011=>1100000
[4,2,8,3,7,1,5,6]=>0010011=>1100100
[4,1,7,5,8,2,3,6]=>0010011=>1100100
[1,7,3,8,2,4,5,6]=>0000011=>1100000
[8,1,2,7,3,4,5,6]=>0000011=>1100000
[4,2,5,7,1,8,3,6]=>0010011=>1100100
[3,6,2,7,1,8,4,5]=>0000111=>1110000
[6,3,7,1,2,8,4,5]=>0000111=>1110000
[7,2,6,1,8,3,4,5]=>0000111=>1110000
[8,2,6,1,7,3,4,5]=>0000111=>1110000
[7,3,1,5,8,2,4,6]=>0100011=>1100010
[3,2,1,5,8,4,6,7]=>1100001=>1000011
[5,4,1,3,6,8,2,7]=>0011001=>1001100
[1,5,3,4,6,8,2,7]=>0001001=>1001000
[4,3,5,1,6,8,2,7]=>0011001=>1001100
[5,4,6,3,8,7,1,2]=>0001111=>1111000
[3,6,4,5,8,7,1,2]=>0000111=>1110000
[6,5,3,4,8,7,1,2]=>0001111=>1111000
[5,3,2,8,7,1,4,6]=>0101011=>1101010
[5,3,1,8,7,2,4,6]=>0101011=>1101010
[8,5,3,7,6,1,2,4]=>0001111=>1111000
[6,1,8,3,7,2,4,5]=>0000111=>1110000
[6,3,8,1,7,2,4,5]=>0000111=>1110000
[7,6,8,2,3,5,1,4]=>0001011=>1101000
[3,7,8,2,4,6,1,5]=>0000101=>1010000
[6,7,3,8,2,5,1,4]=>0001011=>1101000
[5,4,7,8,2,6,1,3]=>0001101=>1011000
[4,2,5,8,7,1,3,6]=>0010011=>1100100
[3,6,2,8,7,1,4,5]=>0000111=>1110000
[3,7,8,1,6,2,4,5]=>0000101=>1010000
[2,3,8,7,1,4,5,6]=>0000011=>1100000
[7,2,8,6,1,3,4,5]=>0000111=>1110000
[2,1,8,7,3,4,5,6]=>1000011=>1100001
[8,2,7,6,1,3,4,5]=>0000111=>1110000
[1,2,8,7,3,4,5,6]=>0000011=>1100000
[1,3,8,7,2,4,5,6]=>0000011=>1100000
[1,7,8,3,6,2,4,5]=>0000101=>1010000
[4,1,5,8,7,2,3,6]=>0010011=>1100100
[5,4,8,7,6,1,2,3]=>0001111=>1111000
[6,8,3,7,5,1,2,4]=>0001011=>1101000
[7,8,6,2,5,1,3,4]=>0001101=>1011000
[8,1,6,7,3,2,5,4]=>0101011=>1101010
[8,1,6,7,3,2,4,5]=>0100011=>1100010
[8,1,5,3,7,2,4,6]=>0001011=>1101000
[8,1,5,3,6,2,4,7]=>0001101=>1011000
[7,5,1,3,6,2,4,8]=>0001110=>0111000
[7,5,8,3,6,2,4,1]=>0010111=>1110100
[7,4,8,3,2,6,5,1]=>0101111=>1111010
[7,4,1,3,2,6,5,8]=>0110110=>0110110
[8,1,4,3,2,6,5,7]=>0110101=>1010110
[8,1,4,3,2,7,5,6]=>0110011=>1100110
[8,1,4,3,2,7,6,5]=>0110111=>1110110
[8,1,5,4,6,7,2,3]=>0001011=>1101000
[8,1,5,3,6,2,7,4]=>0001111=>1111000
[8,1,4,3,2,6,7,5]=>0110011=>1100110
[8,1,4,3,2,5,7,6]=>0110011=>1100110
[8,1,4,3,2,5,6,7]=>0110001=>1000110
[7,4,1,3,2,5,6,8]=>0110010=>0100110
[7,4,8,3,2,5,6,1]=>0100111=>1110010
[6,4,3,8,2,5,7,1]=>0010111=>1110100
[6,4,3,1,2,5,8,7]=>0110101=>1010110
[7,4,1,3,2,5,8,6]=>0110011=>1100110
[7,4,1,3,2,6,8,5]=>0110011=>1100110
[7,5,1,3,6,2,8,4]=>0001111=>1111000
[7,5,1,4,6,8,2,3]=>0001011=>1101000
[7,5,8,3,6,2,1,4]=>1000111=>1110001
[7,4,8,3,2,6,1,5]=>0100111=>1110010
[7,4,8,3,2,5,1,6]=>0101011=>1101010
[6,4,3,8,2,5,1,7]=>0011101=>1011100
[6,4,3,7,2,5,8,1]=>0010111=>1110100
[5,4,3,2,8,6,1,7]=>0111101=>1011110
[5,4,3,2,8,7,1,6]=>0111011=>1101110
[6,5,3,8,7,2,1,4]=>1001111=>1111001
[6,5,4,8,7,1,2,3]=>0001111=>1111000
[6,5,4,1,7,8,2,3]=>0011101=>1011100
[6,5,3,1,7,2,8,4]=>0101111=>1111010
[6,4,3,1,2,7,8,5]=>0110101=>1010110
[5,4,3,2,1,8,6,7]=>1111001=>1001111
[6,5,3,1,8,2,7,4]=>0101111=>1111010
[6,5,4,1,8,7,2,3]=>0011111=>1111100
[7,5,1,4,8,6,2,3]=>0001111=>1111000
[7,4,1,3,2,8,6,5]=>0110111=>1110110
[7,4,1,3,2,8,5,6]=>0110011=>1100110
[6,4,3,1,2,8,5,7]=>0110101=>1010110
[6,4,3,1,2,7,5,8]=>0110110=>0110110
[6,4,3,8,2,7,5,1]=>0011111=>1111100
[6,5,3,8,7,2,4,1]=>0011111=>1111100
[6,5,3,1,7,2,4,8]=>0101110=>0111010
[6,5,3,1,8,2,4,7]=>0101101=>1011010
[7,5,1,3,8,2,4,6]=>0001011=>1101000
[7,6,1,8,3,2,4,5]=>0100111=>1110010
[7,6,1,8,4,5,2,3]=>0001111=>1111000
[7,6,8,1,4,5,2,3]=>0001011=>1101000
[7,6,8,1,3,2,5,4]=>0101011=>1101010
[6,5,3,7,8,2,4,1]=>0011101=>1011100
[6,4,3,7,2,8,5,1]=>0011111=>1111100
[6,4,3,7,2,1,5,8]=>1010110=>0110101
[7,4,8,3,2,1,5,6]=>1100011=>1100011
[7,4,8,3,2,1,6,5]=>1100111=>1110011
[7,5,8,3,1,2,6,4]=>0100111=>1110010
[7,5,8,4,1,6,2,3]=>0010111=>1110100
[6,5,4,8,1,7,2,3]=>0001111=>1111000
[6,5,3,8,1,2,7,4]=>0001111=>1111000
[5,4,3,2,8,1,7,6]=>0111011=>1101110
[6,4,3,7,2,1,8,5]=>1010111=>1110101
[6,5,3,7,1,2,8,4]=>0001111=>1111000
[6,5,4,7,1,8,2,3]=>0001111=>1111000
[6,5,3,7,8,2,1,4]=>1001101=>1011001
[6,4,3,7,2,8,1,5]=>0010111=>1110100
[5,4,3,2,7,8,1,6]=>0111001=>1001110
[5,4,3,2,6,8,1,7]=>0111001=>1001110
[5,6,2,1,3,4,8,7]=>1000101=>1010001
[5,8,2,7,4,1,3,6]=>0010011=>1100100
[5,3,7,8,2,1,4,6]=>1001001=>1001001
[7,6,1,2,5,8,3,4]=>0000111=>1110000
[2,1,7,8,4,3,5,6]=>1010001=>1000101
[8,3,7,4,1,5,6,2]=>0010111=>1110100
[7,8,1,2,5,4,6,3]=>0001101=>1011000
[2,6,8,3,1,4,7,5]=>0100011=>1100010
[6,1,8,3,2,4,5,7]=>0100101=>1010010
[8,4,1,3,7,6,2,5]=>0010111=>1110100
[5,8,7,4,2,1,6,3]=>1010111=>1110101
[7,5,1,6,8,3,4,2]=>0011011=>1101100
[6,5,2,1,8,7,4,3]=>1011111=>1111101
[4,7,2,8,1,3,6,5]=>0000111=>1110000
[7,3,8,6,1,2,5,4]=>0001111=>1111000
[3,4,7,1,8,2,6,5]=>0000111=>1110000
[1,8,2,4,3,5,6,7]=>0010001=>1000100
[1,7,2,4,3,5,6,8]=>0010010=>0100100
[1,6,2,4,3,5,7,8]=>0010100=>0010100
[1,5,2,4,3,6,7,8]=>0011000=>0001100
[1,6,2,5,3,4,7,8]=>0001100=>0011000
[1,7,2,5,3,4,6,8]=>0001010=>0101000
[1,8,2,5,3,4,6,7]=>0001001=>1001000
[1,8,2,6,3,4,5,7]=>0000101=>1010000
[1,7,2,6,3,4,5,8]=>0000110=>0110000
[1,8,2,7,3,5,4,6]=>0001011=>1101000
[1,7,2,8,3,5,4,6]=>0001011=>1101000
[1,6,2,8,3,5,4,7]=>0001101=>1011000
[1,5,2,8,3,6,4,7]=>0001101=>1011000
[1,4,2,8,3,6,5,7]=>0010101=>1010100
[1,3,2,8,4,6,5,7]=>0100101=>1010010
[1,2,3,8,4,6,5,7]=>0000101=>1010000
[1,2,3,7,4,6,5,8]=>0000110=>0110000
[1,3,2,7,4,6,5,8]=>0100110=>0110010
[1,4,2,7,3,6,5,8]=>0010110=>0110100
[1,5,2,7,3,6,4,8]=>0001110=>0111000
[1,6,2,7,3,5,4,8]=>0001110=>0111000
[1,7,2,6,3,5,4,8]=>0001110=>0111000
[1,8,2,6,3,5,4,7]=>0001101=>1011000
[1,8,2,5,3,6,4,7]=>0001101=>1011000
[1,7,2,5,3,6,4,8]=>0001110=>0111000
[1,6,2,5,3,7,4,8]=>0001110=>0111000
[1,5,2,4,3,7,6,8]=>0011010=>0101100
[1,6,2,4,3,7,5,8]=>0010110=>0110100
[1,7,2,4,3,6,5,8]=>0010110=>0110100
[1,8,2,4,3,6,5,7]=>0010101=>1010100
[1,8,2,3,4,6,5,7]=>0000101=>1010000
[1,7,2,3,4,6,5,8]=>0000110=>0110000
[1,8,2,3,4,7,5,6]=>0000011=>1100000
[1,8,2,4,3,7,5,6]=>0010011=>1100100
[1,7,2,4,3,8,5,6]=>0010011=>1100100
[1,6,2,4,3,8,5,7]=>0010101=>1010100
[1,5,2,4,3,8,6,7]=>0011001=>1001100
[1,6,2,5,3,8,4,7]=>0001101=>1011000
[1,7,2,5,3,8,4,6]=>0001011=>1101000
[1,8,2,5,3,7,4,6]=>0001011=>1101000
[1,8,2,6,3,7,4,5]=>0000111=>1110000
[1,7,2,6,3,8,4,5]=>0000111=>1110000
[1,2,3,8,4,7,5,6]=>0000011=>1100000
[1,3,2,8,4,7,5,6]=>0100011=>1100010
[1,4,2,8,3,7,5,6]=>0010011=>1100100
[1,5,2,8,3,7,4,6]=>0001011=>1101000
[1,6,2,8,3,7,4,5]=>0000111=>1110000
[1,7,2,8,3,6,4,5]=>0000111=>1110000
[1,8,2,7,3,6,4,5]=>0000111=>1110000
[4,6,3,7,2,5,1,8]=>0001110=>0111000
[4,6,3,7,5,2,1,8]=>1001110=>0111001
[4,6,3,8,5,1,7,2]=>0001111=>1111000
[4,6,3,8,5,1,2,7]=>0001101=>1011000
[5,6,8,3,4,1,2,7]=>0010001=>1000100
[5,6,8,3,4,1,7,2]=>0010011=>1100100
[4,6,2,7,5,3,1,8]=>0101110=>0111010
[5,6,7,2,4,3,1,8]=>0110010=>0100110
[5,6,8,4,3,1,7,2]=>0110011=>1100110
[5,6,8,4,3,1,2,7]=>0110001=>1000110
[5,7,8,4,1,6,2,3]=>0010101=>1010100
[5,7,8,4,1,6,3,2]=>0110101=>1010110
[5,7,8,4,1,3,6,2]=>0010101=>1010100
[5,6,8,4,2,1,7,3]=>1010011=>1100101
[5,6,8,2,4,1,7,3]=>0010011=>1100100
[4,6,2,8,5,1,7,3]=>0001111=>1111000
[3,2,6,8,5,1,7,4]=>0101011=>1101010
[3,2,6,8,5,1,4,7]=>0101001=>1001010
[4,6,2,8,5,1,3,7]=>0001101=>1011000
[5,6,8,2,4,1,3,7]=>0010001=>1000100
[5,6,8,4,2,1,3,7]=>1010001=>1000101
[5,7,8,4,1,3,2,6]=>0110001=>1000110
[5,7,8,4,1,2,6,3]=>0010101=>1010100
[5,7,8,4,1,2,3,6]=>0010001=>1000100
[6,7,8,1,5,2,3,4]=>0001001=>1001000
[6,7,8,1,5,2,4,3]=>0011001=>1001100
[6,7,8,1,5,3,2,4]=>0101001=>1001010
[6,7,8,1,3,5,2,4]=>0001001=>1001000
[5,7,8,2,1,6,3,4]=>1000101=>1010001
[4,7,2,8,1,6,3,5]=>0000111=>1110000
[3,2,7,8,1,6,4,5]=>0100101=>1010010
[3,2,7,8,1,6,5,4]=>0101101=>1011010
[4,7,2,8,1,6,5,3]=>0001111=>1111000
[5,7,8,2,1,6,4,3]=>1010101=>1010101
[6,7,8,1,3,5,4,2]=>0011001=>1001100
[6,7,8,1,5,3,4,2]=>0011001=>1001100
[6,7,8,1,5,4,3,2]=>0111001=>1001110
[6,7,8,1,5,4,2,3]=>0011001=>1001100
[6,7,8,1,4,5,2,3]=>0001001=>1001000
[6,7,8,1,4,5,3,2]=>0101001=>1001010
[6,7,8,1,4,3,5,2]=>0011001=>1001100
[6,7,8,1,3,4,5,2]=>0001001=>1001000
[5,7,8,2,1,4,6,3]=>1000101=>1010001
[4,7,2,8,1,5,6,3]=>0000111=>1110000
[3,2,7,8,1,5,6,4]=>0100101=>1010010
[3,2,6,8,4,1,7,5]=>0110011=>1100110
[4,6,2,8,3,1,7,5]=>0100111=>1110010
[5,6,8,3,2,1,7,4]=>1100011=>1100011
[5,7,8,3,1,4,6,2]=>0100101=>1010010
[5,7,8,3,1,6,4,2]=>0110101=>1010110
[5,7,8,3,1,6,2,4]=>0100101=>1010010
[4,7,3,8,1,6,2,5]=>0000111=>1110000
[4,7,3,8,1,6,5,2]=>0001111=>1111000
[4,7,3,8,1,5,6,2]=>0000111=>1110000
[4,6,3,8,2,1,7,5]=>1000111=>1110001
[4,5,3,2,8,1,7,6]=>0101011=>1101010
[4,5,2,3,8,1,7,6]=>0001011=>1101000
[3,2,5,4,8,1,7,6]=>0101011=>1101010
[4,5,3,2,8,1,6,7]=>0101001=>1001010
[4,6,3,8,2,1,5,7]=>1000101=>1010001
[4,7,3,8,1,5,2,6]=>0001011=>1101000
[4,7,3,8,1,2,6,5]=>0000111=>1110000
[4,7,3,8,1,2,5,6]=>0000011=>1100000
[5,7,8,3,1,2,4,6]=>0100001=>1000010
[5,7,8,3,1,2,6,4]=>0100101=>1010010
[5,7,8,3,1,4,2,6]=>0110001=>1000110
[5,6,8,3,2,1,4,7]=>1100001=>1000011
[3,2,7,8,1,5,4,6]=>0101001=>1001010
[5,7,8,2,1,4,3,6]=>1010001=>1000101
[6,7,8,1,3,4,2,5]=>0010001=>1000100
[6,7,8,1,4,3,2,5]=>0110001=>1000110
[6,7,8,1,4,2,5,3]=>0011001=>1001100
[6,7,8,1,4,2,3,5]=>0010001=>1000100
[6,7,8,1,2,5,3,4]=>0001001=>1001000
[6,7,8,1,2,5,4,3]=>0011001=>1001100
[6,7,8,1,2,4,5,3]=>0001001=>1001000
[6,7,8,1,3,2,5,4]=>0101001=>1001010
[5,7,8,2,1,3,6,4]=>1000101=>1010001
[3,2,7,8,1,4,6,5]=>0100101=>1010010
[6,7,8,1,3,2,4,5]=>0100001=>1000010
[6,7,8,1,2,4,3,5]=>0010001=>1000100
[6,7,8,1,2,3,5,4]=>0001001=>1001000
[7,2,8,5,1,6,4,3]=>0011111=>1111100
[1,3,7,5,2,6,4,8]=>0001110=>0111000
[1,3,7,5,4,2,6,8]=>0011010=>0101100
[7,2,8,5,4,1,6,3]=>0011111=>1111100
[2,8,5,4,3,1,7,6]=>0111011=>1101110
[2,8,4,5,6,1,7,3]=>0000111=>1110000
[2,8,6,5,7,3,1,4]=>0100111=>1110010
[2,8,4,5,3,7,1,6]=>0001011=>1101000
[2,8,4,3,5,6,1,7]=>0010101=>1010100
[7,2,8,4,5,6,1,3]=>0000111=>1110000
[1,6,3,7,5,2,4,8]=>0001110=>0111000
[6,2,3,8,5,1,7,4]=>0001111=>1111000
[6,3,2,8,5,1,4,7]=>0101101=>1011010
[7,4,8,2,5,6,3,1]=>0100111=>1110010
[7,4,8,5,2,1,3,6]=>1001011=>1101001
[6,4,8,5,1,3,7,2]=>0001111=>1111000
[6,3,7,5,2,1,8,4]=>1001111=>1111001
[4,3,7,5,1,2,8,6]=>0011011=>1101100
[4,3,7,1,5,6,8,2]=>0010011=>1100100
[3,6,1,7,5,2,8,4]=>0001111=>1111000
[3,4,1,2,7,6,8,5]=>0010011=>1100100
[3,4,2,1,7,5,8,6]=>1010011=>1100101
[3,6,5,7,1,4,8,2]=>0000111=>1110000
[6,5,2,7,4,1,8,3]=>0011111=>1111100
[3,5,2,6,4,8,7,1]=>0001111=>1111000
[5,3,1,8,6,4,7,2]=>0101111=>1111010
[5,6,1,8,7,2,4,3]=>0010111=>1110100
[6,3,5,8,2,7,4,1]=>0010111=>1110100
[6,5,8,4,2,3,7,1]=>0010111=>1110100
[6,2,5,8,3,7,1,4]=>0000111=>1110000
[1,6,5,7,3,4,2,8]=>0010110=>0110100
[1,5,2,7,4,6,3,8]=>0001110=>0111000
[5,2,1,8,7,6,3,4]=>1001111=>1111001
[7,1,3,8,4,6,2,5]=>0000111=>1110000
[2,3,4,8,6,1,7,5]=>0000111=>1110000
[2,3,4,8,6,5,1,7]=>0001101=>1011000
[2,7,3,5,8,6,1,4]=>0000111=>1110000
[3,2,4,7,8,6,1,5]=>0100101=>1010010
[1,5,4,6,2,7,3,8]=>0001110=>0111000
[5,2,4,7,1,8,3,6]=>0001011=>1101000
[5,3,6,4,1,8,7,2]=>0011111=>1111100
[5,3,6,1,4,8,2,7]=>0001101=>1011000
[7,3,5,6,8,4,2,1]=>1010011=>1100101
[6,3,5,1,8,2,7,4]=>0001111=>1111000
[2,6,1,5,8,4,7,3]=>0000111=>1110000
[2,7,6,5,8,3,4,1]=>0010111=>1110100
[5,7,1,6,3,8,4,2]=>0010111=>1110100
[3,2,4,1,7,8,5,6]=>0110001=>1000110
[3,1,4,2,7,8,6,5]=>0110101=>1010110
[5,1,4,7,2,8,6,3]=>0001111=>1111000
[3,6,4,7,8,2,5,1]=>0001101=>1011000
[3,1,4,6,8,5,7,2]=>0100011=>1100010
[6,3,4,5,7,1,8,2]=>0000111=>1110000
[2,5,4,6,1,7,8,3]=>0001101=>1011000
[7,2,1,4,3,6,5,8]=>1010110=>0110101
[7,3,4,1,2,6,5,8]=>0010110=>0110100
[7,4,3,2,1,6,5,8]=>1110110=>0110111
[7,6,3,2,5,4,1,8]=>0111110=>0111110
[6,7,3,2,5,4,8,1]=>0101011=>1101010
[1,8,3,2,5,4,7,6]=>0101011=>1101010
[1,8,4,5,2,3,7,6]=>0001011=>1101000
[7,3,5,1,6,2,4,8]=>0001110=>0111000
[7,2,1,5,6,3,4,8]=>1000110=>0110001
[7,2,1,6,5,4,3,8]=>1011110=>0111101
[7,3,6,1,5,4,2,8]=>0011110=>0111100
[7,4,6,5,1,3,2,8]=>0101110=>0111010
[1,8,5,4,3,2,7,6]=>0111011=>1101110
[1,8,6,4,3,7,2,5]=>0010111=>1110100
[6,5,7,4,3,1,8,2]=>0110111=>1110110
[6,4,7,5,1,3,8,2]=>0001111=>1111000
[6,3,7,1,5,4,8,2]=>0001111=>1111000
[6,2,1,7,5,4,8,3]=>1001111=>1111001
[3,2,1,8,5,4,7,6]=>1101011=>1101011
[2,3,8,1,5,4,7,6]=>0001011=>1101000
[2,4,8,5,1,3,7,6]=>0001011=>1101000
[2,5,8,4,3,1,7,6]=>0110011=>1100110
[2,6,8,4,3,7,1,5]=>0010011=>1100100
[2,7,8,4,3,6,5,1]=>0011101=>1011100
[1,8,7,4,3,6,5,2]=>0011111=>1111100
[1,8,7,5,6,3,4,2]=>0010111=>1110100
[2,7,8,5,6,3,4,1]=>0010101=>1010100
[2,6,8,5,7,3,1,4]=>0100011=>1100010
[2,5,8,6,7,1,3,4]=>0000011=>1100000
[2,4,8,6,1,7,3,5]=>0000111=>1110000
[3,2,1,8,6,7,4,5]=>1100011=>1100011
[5,2,1,7,6,8,4,3]=>1011011=>1101101
[5,3,7,1,6,8,4,2]=>0011011=>1101100
[5,4,7,6,1,8,3,2]=>0101111=>1111010
[4,5,7,6,8,1,3,2]=>0100011=>1100010
[4,6,7,5,8,3,1,2]=>0100011=>1100010
[1,8,6,5,7,3,2,4]=>0100111=>1110010
[1,8,5,6,7,2,3,4]=>0000011=>1100000
[4,7,5,6,8,2,3,1]=>0100011=>1100010
[4,6,5,7,8,2,1,3]=>1000101=>1010001
[5,4,6,7,1,8,2,3]=>0001011=>1101000
[5,3,6,1,7,8,2,4]=>0001101=>1011000
[5,2,1,6,7,8,3,4]=>1001001=>1001001
[6,2,1,5,7,3,8,4]=>1000111=>1110001
[6,3,5,1,7,2,8,4]=>0001111=>1111000
[6,4,5,7,1,2,8,3]=>0000111=>1110000
[6,5,4,7,2,1,8,3]=>1001111=>1111001
[5,6,4,7,2,8,1,3]=>0000111=>1110000
[1,8,4,6,2,7,3,5]=>0000111=>1110000
[1,8,3,2,6,7,4,5]=>0100011=>1100010
[5,7,3,2,6,8,4,1]=>0110011=>1100110
[5,6,3,2,7,8,1,4]=>0100101=>1010010
[6,5,3,2,7,1,8,4]=>0101111=>1111010
[6,4,3,2,1,7,8,5]=>1110101=>1010111
[6,2,1,4,3,7,8,5]=>1010101=>1010101
[5,2,1,4,3,8,7,6]=>1011011=>1101101
[5,3,4,1,2,8,7,6]=>0011011=>1101100
[4,6,3,2,8,7,1,5]=>0100111=>1110010
[4,7,3,2,8,6,5,1]=>0101111=>1111010
[1,8,3,2,7,6,5,4]=>0101111=>1111010
[1,8,4,7,2,6,5,3]=>0001111=>1111000
[3,7,4,8,2,6,5,1]=>0001111=>1111000
[3,6,4,8,2,7,1,5]=>0000111=>1110000
[3,5,4,8,2,1,7,6]=>1001011=>1101001
[3,4,5,8,1,2,7,6]=>0000011=>1100000
[4,3,5,1,8,2,7,6]=>0011011=>1101100
[4,2,1,5,8,3,7,6]=>1010011=>1100101
[4,2,1,6,8,7,3,5]=>1010011=>1100101
[4,3,6,1,8,7,2,5]=>0010111=>1110100
[3,4,6,8,1,7,2,5]=>0000011=>1100000
[3,5,6,8,7,1,2,4]=>0000011=>1100000
[3,6,5,8,7,2,1,4]=>1000111=>1110001
[3,7,5,8,6,2,4,1]=>0010111=>1110100
[1,8,5,7,6,2,4,3]=>0010111=>1110100
[1,8,6,7,5,4,2,3]=>0011011=>1101100
[3,6,7,8,5,4,1,2]=>0011001=>1001100
[3,5,7,8,6,1,4,2]=>0010101=>1010100
[3,4,7,8,1,6,5,2]=>0001101=>1011000
[4,2,1,7,8,6,5,3]=>1011101=>1011101
[2,3,8,1,7,6,5,4]=>0001111=>1111000
[2,4,8,7,1,6,5,3]=>0001111=>1111000
[2,5,8,7,6,1,4,3]=>0010111=>1110100
[2,6,8,7,5,4,1,3]=>0011011=>1101100
[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101=>10101010101
[2,1,4,3,6,5,8,7,12,11,10,9]=>10101010111=>11101010101
[2,1,4,3,6,5,10,9,8,7,12,11]=>10101011101=>10111010101
[2,1,4,3,6,5,12,9,8,11,10,7]=>10101001111=>11110010101
[2,1,4,3,6,5,12,11,10,9,8,7]=>10101011111=>11111010101
[2,1,4,3,8,7,6,5,10,9,12,11]=>10101110101=>10101110101
[2,1,4,3,8,7,6,5,12,11,10,9]=>10101110111=>11101110101
[2,1,4,3,10,7,6,9,8,5,12,11]=>10100111101=>10111100101
[2,1,4,3,12,7,6,9,8,11,10,5]=>10100101111=>11110100101
[2,1,4,3,12,7,6,11,10,9,8,5]=>10100111111=>11111100101
[2,1,4,3,10,9,8,7,6,5,12,11]=>10101111101=>10111110101
[2,1,4,3,12,9,8,7,6,11,10,5]=>10100111111=>11111100101
[2,1,4,3,12,11,8,7,10,9,6,5]=>10101011111=>11111010101
[2,1,4,3,12,11,10,9,8,7,6,5]=>10101111111=>11111110101
[2,1,6,5,4,3,8,7,10,9,12,11]=>10111010101=>10101011101
[2,1,6,5,4,3,8,7,12,11,10,9]=>10111010111=>11101011101
[2,1,6,5,4,3,10,9,8,7,12,11]=>10111011101=>10111011101
[2,1,6,5,4,3,12,9,8,11,10,7]=>10111001111=>11110011101
[2,1,6,5,4,3,12,11,10,9,8,7]=>10111011111=>11111011101
[2,1,8,5,4,7,6,3,10,9,12,11]=>10011110101=>10101111001
[2,1,8,5,4,7,6,3,12,11,10,9]=>10011110111=>11101111001
[2,1,10,5,4,7,6,9,8,3,12,11]=>10010111101=>10111101001
[2,1,12,5,4,7,6,9,8,11,10,3]=>10010101111=>11110101001
[2,1,12,5,4,7,6,11,10,9,8,3]=>10010111111=>11111101001
[2,1,10,5,4,9,8,7,6,3,12,11]=>10011111101=>10111111001
[2,1,12,5,4,9,8,7,6,11,10,3]=>10010111111=>11111101001
[2,1,12,5,4,11,8,7,10,9,6,3]=>10011011111=>11111011001
[2,1,12,5,4,11,10,9,8,7,6,3]=>10011111111=>11111111001
[2,1,8,7,6,5,4,3,10,9,12,11]=>10111110101=>10101111101
[2,1,8,7,6,5,4,3,12,11,10,9]=>10111110111=>11101111101
[2,1,10,7,6,5,4,9,8,3,12,11]=>10011111101=>10111111001
[2,1,12,7,6,5,4,9,8,11,10,3]=>10011101111=>11110111001
[2,1,12,7,6,5,4,11,10,9,8,3]=>10011111111=>11111111001
[2,1,10,9,6,5,8,7,4,3,12,11]=>10101111101=>10111110101
[2,1,12,9,6,5,8,7,4,11,10,3]=>10001111111=>11111110001
[2,1,12,11,6,5,8,7,10,9,4,3]=>10101011111=>11111010101
[2,1,12,11,6,5,10,9,8,7,4,3]=>10101111111=>11111110101
[2,1,10,9,8,7,6,5,4,3,12,11]=>10111111101=>10111111101
[2,1,12,9,8,7,6,5,4,11,10,3]=>10011111111=>11111111001
[2,1,12,11,8,7,6,5,10,9,4,3]=>10101111111=>11111110101
[2,1,12,11,10,7,6,9,8,5,4,3]=>10110111111=>11111101101
[2,1,12,11,10,9,8,7,6,5,4,3]=>10111111111=>11111111101
[4,3,2,1,6,5,8,7,10,9,12,11]=>11101010101=>10101010111
[4,3,2,1,6,5,8,7,12,11,10,9]=>11101010111=>11101010111
[4,3,2,1,6,5,10,9,8,7,12,11]=>11101011101=>10111010111
[4,3,2,1,6,5,12,9,8,11,10,7]=>11101001111=>11110010111
[4,3,2,1,6,5,12,11,10,9,8,7]=>11101011111=>11111010111
[4,3,2,1,8,7,6,5,10,9,12,11]=>11101110101=>10101110111
[4,3,2,1,8,7,6,5,12,11,10,9]=>11101110111=>11101110111
[4,3,2,1,10,7,6,9,8,5,12,11]=>11100111101=>10111100111
[4,3,2,1,12,7,6,9,8,11,10,5]=>11100101111=>11110100111
[4,3,2,1,12,7,6,11,10,9,8,5]=>11100111111=>11111100111
[4,3,2,1,10,9,8,7,6,5,12,11]=>11101111101=>10111110111
[4,3,2,1,12,9,8,7,6,11,10,5]=>11100111111=>11111100111
[4,3,2,1,12,11,8,7,10,9,6,5]=>11101011111=>11111010111
[4,3,2,1,12,11,10,9,8,7,6,5]=>11101111111=>11111110111
[6,3,2,5,4,1,8,7,10,9,12,11]=>01111010101=>10101011110
[6,3,2,5,4,1,8,7,12,11,10,9]=>01111010111=>11101011110
[6,3,2,5,4,1,10,9,8,7,12,11]=>01111011101=>10111011110
[6,3,2,5,4,1,12,9,8,11,10,7]=>01111001111=>11110011110
[6,3,2,5,4,1,12,11,10,9,8,7]=>01111011111=>11111011110
[8,3,2,5,4,7,6,1,10,9,12,11]=>01011110101=>10101111010
[8,3,2,5,4,7,6,1,12,11,10,9]=>01011110111=>11101111010
[10,3,2,5,4,7,6,9,8,1,12,11]=>01010111101=>10111101010
[12,3,2,5,4,7,6,9,8,11,10,1]=>01010101111=>11110101010
[12,3,2,5,4,7,6,11,10,9,8,1]=>01010111111=>11111101010
[10,3,2,5,4,9,8,7,6,1,12,11]=>01011111101=>10111111010
[12,3,2,5,4,9,8,7,6,11,10,1]=>01010111111=>11111101010
[12,3,2,5,4,11,8,7,10,9,6,1]=>01011011111=>11111011010
[12,3,2,5,4,11,10,9,8,7,6,1]=>01011111111=>11111111010
[8,3,2,7,6,5,4,1,10,9,12,11]=>01111110101=>10101111110
[8,3,2,7,6,5,4,1,12,11,10,9]=>01111110111=>11101111110
[10,3,2,7,6,5,4,9,8,1,12,11]=>01011111101=>10111111010
[12,3,2,7,6,5,4,9,8,11,10,1]=>01011101111=>11110111010
[12,3,2,7,6,5,4,11,10,9,8,1]=>01011111111=>11111111010
[10,3,2,9,6,5,8,7,4,1,12,11]=>01101111101=>10111110110
[12,3,2,9,6,5,8,7,4,11,10,1]=>01001111111=>11111110010
[12,3,2,11,6,5,8,7,10,9,4,1]=>01101011111=>11111010110
[12,3,2,11,6,5,10,9,8,7,4,1]=>01101111111=>11111110110
[10,3,2,9,8,7,6,5,4,1,12,11]=>01111111101=>10111111110
[12,3,2,9,8,7,6,5,4,11,10,1]=>01011111111=>11111111010
[12,3,2,11,8,7,6,5,10,9,4,1]=>01101111111=>11111110110
[12,3,2,11,10,7,6,9,8,5,4,1]=>01110111111=>11111101110
[12,3,2,11,10,9,8,7,6,5,4,1]=>01111111111=>11111111110
[6,5,4,3,2,1,8,7,10,9,12,11]=>11111010101=>10101011111
[6,5,4,3,2,1,8,7,12,11,10,9]=>11111010111=>11101011111
[6,5,4,3,2,1,10,9,8,7,12,11]=>11111011101=>10111011111
[6,5,4,3,2,1,12,9,8,11,10,7]=>11111001111=>11110011111
[6,5,4,3,2,1,12,11,10,9,8,7]=>11111011111=>11111011111
[8,5,4,3,2,7,6,1,10,9,12,11]=>01111110101=>10101111110
[8,5,4,3,2,7,6,1,12,11,10,9]=>01111110111=>11101111110
[10,5,4,3,2,7,6,9,8,1,12,11]=>01110111101=>10111101110
[12,5,4,3,2,7,6,9,8,11,10,1]=>01110101111=>11110101110
[12,5,4,3,2,7,6,11,10,9,8,1]=>01110111111=>11111101110
[10,5,4,3,2,9,8,7,6,1,12,11]=>01111111101=>10111111110
[12,5,4,3,2,9,8,7,6,11,10,1]=>01110111111=>11111101110
[12,5,4,3,2,11,8,7,10,9,6,1]=>01111011111=>11111011110
[12,5,4,3,2,11,10,9,8,7,6,1]=>01111111111=>11111111110
[8,7,4,3,6,5,2,1,10,9,12,11]=>10111110101=>10101111101
[8,7,4,3,6,5,2,1,12,11,10,9]=>10111110111=>11101111101
[10,7,4,3,6,5,2,9,8,1,12,11]=>00111111101=>10111111100
[12,7,4,3,6,5,2,9,8,11,10,1]=>00111101111=>11110111100
[12,7,4,3,6,5,2,11,10,9,8,1]=>00111111111=>11111111100
[10,9,4,3,6,5,8,7,2,1,12,11]=>10101111101=>10111110101
[12,9,4,3,6,5,8,7,2,11,10,1]=>00101111111=>11111110100
[12,11,4,3,6,5,8,7,10,9,2,1]=>10101011111=>11111010101
[12,11,4,3,6,5,10,9,8,7,2,1]=>10101111111=>11111110101
[10,9,4,3,8,7,6,5,2,1,12,11]=>10111111101=>10111111101
[12,9,4,3,8,7,6,5,2,11,10,1]=>00111111111=>11111111100
[12,11,4,3,8,7,6,5,10,9,2,1]=>10101111111=>11111110101
[12,11,4,3,10,7,6,9,8,5,2,1]=>10110111111=>11111101101
[12,11,4,3,10,9,8,7,6,5,2,1]=>10111111111=>11111111101
[8,7,6,5,4,3,2,1,10,9,12,11]=>11111110101=>10101111111
[8,7,6,5,4,3,2,1,12,11,10,9]=>11111110111=>11101111111
[10,7,6,5,4,3,2,9,8,1,12,11]=>01111111101=>10111111110
[12,7,6,5,4,3,2,9,8,11,10,1]=>01111101111=>11110111110
[12,7,6,5,4,3,2,11,10,9,8,1]=>01111111111=>11111111110
[10,9,6,5,4,3,8,7,2,1,12,11]=>10111111101=>10111111101
[12,9,6,5,4,3,8,7,2,11,10,1]=>00111111111=>11111111100
[12,11,6,5,4,3,8,7,10,9,2,1]=>10111011111=>11111011101
[12,11,6,5,4,3,10,9,8,7,2,1]=>10111111111=>11111111101
[10,9,8,5,4,7,6,3,2,1,12,11]=>11011111101=>10111111011
[12,9,8,5,4,7,6,3,2,11,10,1]=>01011111111=>11111111010
[12,11,8,5,4,7,6,3,10,9,2,1]=>10011111111=>11111111001
[12,11,10,5,4,7,6,9,8,3,2,1]=>11010111111=>11111101011
[12,11,10,5,4,9,8,7,6,3,2,1]=>11011111111=>11111111011
[10,9,8,7,6,5,4,3,2,1,12,11]=>11111111101=>10111111111
[12,9,8,7,6,5,4,3,2,11,10,1]=>01111111111=>11111111110
[12,11,8,7,6,5,4,3,10,9,2,1]=>10111111111=>11111111101
[12,11,10,7,6,5,4,9,8,3,2,1]=>11011111111=>11111111011
[12,11,10,9,6,5,8,7,4,3,2,1]=>11101111111=>11111110111
[12,11,10,9,8,7,6,5,4,3,2,1]=>11111111111=>11111111111
[7,4,6,1,8,3,5,2]=>0001111=>1111000
[8,3,5,1,7,4,6,2]=>0001111=>1111000
[8,3,4,1,7,5,6,2]=>0010111=>1110100
[4,8,3,1,7,5,6,2]=>0100111=>1110010
[4,6,2,1,7,5,8,3]=>1000111=>1110001
[1,4,6,2,7,5,8,3]=>0000111=>1110000
[1,7,5,2,6,8,4,3]=>0011011=>1101100
[7,5,2,1,6,8,4,3]=>1011011=>1101101
[6,8,4,3,1,7,5,2]=>0111011=>1101110
[3,6,8,4,1,7,5,2]=>0011011=>1101100
[3,6,7,5,1,8,4,2]=>0011011=>1101100
[7,5,6,1,8,3,4,2]=>0010111=>1110100
[3,4,6,5,7,1,8,2]=>0000111=>1110000
[4,7,5,6,1,8,3,2]=>0100111=>1110010
[6,7,5,1,8,4,3,2]=>0111011=>1101110
[6,8,4,1,7,5,3,2]=>0111011=>1101110
[6,7,5,3,1,8,4,2]=>0111011=>1101110
[8,4,2,1,6,7,5,3]=>1011011=>1101101
[1,8,4,2,6,7,5,3]=>0011011=>1101100
[1,5,3,2,7,6,8,4]=>0101011=>1101010
[5,3,2,1,7,6,8,4]=>1101011=>1101011
[2,5,3,1,7,6,8,4]=>0101011=>1101010
[2,8,4,1,6,7,5,3]=>0011011=>1101100
[2,7,5,1,6,8,4,3]=>0011011=>1101100
[2,4,6,1,7,5,8,3]=>0000111=>1110000
[4,7,1,6,5,8,2,3]=>0000111=>1110000
[4,8,2,6,5,7,1,3]=>0000111=>1110000
[4,6,1,2,7,5,8,3]=>0000111=>1110000
[7,5,1,2,6,8,4,3]=>0011011=>1101100
[8,4,1,2,6,7,5,3]=>0011011=>1101100
[5,3,1,2,7,6,8,4]=>0101011=>1101010
[1,2,5,3,7,6,8,4]=>0001011=>1101000
[4,3,1,2,7,6,8,5]=>0110011=>1100110
[3,5,1,2,7,6,8,4]=>0001011=>1101000
[6,7,1,5,8,2,3,4]=>0000011=>1100000
[2,7,6,1,5,8,3,4]=>0000111=>1110000
[2,3,5,1,7,6,8,4]=>0001011=>1101000
[7,6,1,5,8,3,2,4]=>0100111=>1110010
[3,6,7,1,5,8,2,4]=>0000011=>1100000
[7,1,6,5,8,2,4,3]=>0010111=>1110100
[7,5,1,6,8,4,2,3]=>0011011=>1101100
[8,4,1,6,7,5,2,3]=>0011011=>1101100
[5,2,3,1,7,6,8,4]=>0101011=>1101010
[3,5,2,1,7,6,8,4]=>1001011=>1101001
[1,3,5,2,7,6,8,4]=>0001011=>1101000
[1,7,6,2,5,8,3,4]=>0000111=>1110000
[7,6,2,1,5,8,3,4]=>1000111=>1110001
[8,3,1,5,7,6,2,4]=>0100111=>1110010
[6,2,4,1,7,5,8,3]=>0010111=>1110100
[6,2,5,1,7,4,8,3]=>0001111=>1111000
[7,1,6,4,8,2,5,3]=>0001111=>1111000
[8,2,6,4,7,1,5,3]=>0001111=>1111000
[6,1,5,2,7,4,8,3]=>0001111=>1111000
[7,6,2,5,8,3,1,4]=>0100111=>1110010
[8,3,5,7,6,2,1,4]=>1000111=>1110001
[1,8,3,5,7,6,2,4]=>0000111=>1110000
[1,5,2,3,7,6,8,4]=>0001011=>1101000
[5,2,1,3,7,6,8,4]=>1001011=>1101001
[7,5,2,6,8,4,1,3]=>0011011=>1101100
[8,4,2,6,7,5,1,3]=>0011011=>1101100
[6,1,4,2,7,5,8,3]=>0010111=>1110100
[8,2,6,5,7,1,4,3]=>0010111=>1110100
[3,6,8,2,5,7,1,4]=>0000011=>1100000
[8,3,2,5,7,6,1,4]=>0100111=>1110010
[5,1,3,2,7,6,8,4]=>0101011=>1101010
[4,1,3,2,7,6,8,5]=>0110011=>1100110
[4,2,1,3,7,6,8,5]=>1010011=>1100101
[1,4,2,3,7,6,8,5]=>0010011=>1100100
[2,4,1,3,7,6,8,5]=>0010011=>1100100
[2,5,1,3,7,6,8,4]=>0001011=>1101000
[2,8,3,5,7,6,1,4]=>0000111=>1110000
[6,8,2,3,5,7,1,4]=>0000011=>1100000
[6,7,1,3,5,8,2,4]=>0000011=>1100000
[8,3,5,7,6,1,2,4]=>0000111=>1110000
[5,1,2,3,7,6,8,4]=>0001011=>1101000
[3,1,2,4,7,6,8,5]=>0100011=>1100010
[10,8,9,5,6,7,1,2,3,4]=>000001011=>110100000
[10,8,9,4,5,6,1,2,3,7]=>000010011=>110010000
[10,7,8,5,6,9,1,2,3,4]=>000000111=>111000000
[10,7,8,4,5,9,1,2,3,6]=>000000111=>111000000
[10,6,7,4,5,8,1,2,3,9]=>000001101=>101100000
[10,7,8,3,4,9,1,2,5,6]=>000000111=>111000000
[10,6,7,3,4,8,1,2,5,9]=>000001101=>101100000
[9,8,10,5,6,7,1,2,3,4]=>000001011=>110100000
[9,8,10,4,5,6,1,2,3,7]=>000010011=>110010000
[9,7,10,5,6,8,1,2,3,4]=>000000111=>111000000
[9,7,10,4,5,8,1,2,3,6]=>000000111=>111000000
[9,6,10,4,5,7,1,2,3,8]=>000001011=>110100000
[9,7,10,3,4,8,1,2,5,6]=>000000111=>111000000
[9,6,10,3,4,7,1,2,5,8]=>000001011=>110100000
[8,7,9,5,6,10,1,2,3,4]=>000000111=>111000000
[8,7,9,4,5,10,1,2,3,6]=>000000111=>111000000
[8,6,9,4,5,10,1,2,3,7]=>000000111=>111000000
[7,6,8,4,5,9,1,2,3,10]=>000001110=>011100000
[8,7,9,3,4,10,1,2,5,6]=>000000111=>111000000
[8,6,9,3,4,10,1,2,5,7]=>000000111=>111000000
[7,6,8,3,4,9,1,2,5,10]=>000001110=>011100000
[9,6,10,5,7,8,1,2,3,4]=>000000111=>111000000
[9,6,10,4,7,8,1,2,3,5]=>000000111=>111000000
[9,5,10,4,6,7,1,2,3,8]=>000001011=>110100000
[9,6,10,3,7,8,1,2,4,5]=>000000111=>111000000
[9,5,10,3,6,7,1,2,4,8]=>000001011=>110100000
[8,6,9,5,7,10,1,2,3,4]=>000000111=>111000000
[8,6,9,4,7,10,1,2,3,5]=>000000111=>111000000
[8,5,9,4,6,10,1,2,3,7]=>000000111=>111000000
[7,5,8,4,6,9,1,2,3,10]=>000001110=>011100000
[8,6,9,3,7,10,1,2,4,5]=>000000111=>111000000
[8,5,9,3,6,10,1,2,4,7]=>000000111=>111000000
[7,5,8,3,6,9,1,2,4,10]=>000001110=>011100000
[8,4,9,3,5,10,1,2,6,7]=>000000111=>111000000
[7,4,8,3,5,9,1,2,6,10]=>000001110=>011100000
[9,6,10,2,7,8,1,3,4,5]=>000000111=>111000000
[9,5,10,2,6,7,1,3,4,8]=>000001011=>110100000
[8,6,9,2,7,10,1,3,4,5]=>000000111=>111000000
[8,5,9,2,6,10,1,3,4,7]=>000000111=>111000000
[7,5,8,2,6,9,1,3,4,10]=>000001110=>011100000
[8,4,9,2,5,10,1,3,6,7]=>000000111=>111000000
[7,4,8,2,5,9,1,3,6,10]=>000001110=>011100000
[8,1,2,4,3,6,5,7]=>0010101=>1010100
[8,1,3,5,6,2,7,4]=>0000111=>1110000
[8,1,3,4,2,6,7,5]=>0010011=>1100100
[8,1,3,2,4,5,7,6]=>0100011=>1100010
[2,7,8,3,4,5,6,1]=>0000101=>1010000
[2,6,3,8,4,5,7,1]=>0000111=>1110000
[6,3,2,1,4,5,8,7]=>1100101=>1010011
[7,3,1,4,2,6,8,5]=>0110011=>1100110
[7,4,1,5,6,8,2,3]=>0010011=>1100100
[4,7,8,5,6,1,2,3]=>0000101=>1010000
[3,7,8,5,6,2,1,4]=>1000101=>1010001
[3,7,8,4,2,6,1,5]=>0010101=>1010100
[3,7,8,2,4,5,1,6]=>0001001=>1001000
[3,6,2,8,4,5,1,7]=>0001101=>1011000
[2,3,6,7,4,5,8,1]=>0000011=>1100000
[3,5,2,4,8,6,1,7]=>0001101=>1011000
[3,5,4,2,8,7,1,6]=>0011011=>1101100
[4,6,5,8,7,1,2,3]=>0000111=>1110000
[6,4,5,1,7,8,2,3]=>0001101=>1011000
[7,4,1,2,3,8,5,6]=>0010011=>1100100
[6,2,4,1,3,7,5,8]=>0010110=>0110100
[2,6,4,8,3,7,5,1]=>0001111=>1111000
[2,6,5,8,7,3,4,1]=>0010111=>1110100
[6,2,5,1,7,3,4,8]=>0001110=>0111000
[6,5,2,1,8,3,4,7]=>1001101=>1011001
[2,5,6,7,8,3,4,1]=>0010001=>1000100
[2,4,6,7,3,8,5,1]=>0001011=>1101000
[4,2,6,7,3,1,5,8]=>0110010=>0100110
[4,7,8,2,3,1,5,6]=>0100001=>1000010
[4,7,8,3,2,1,6,5]=>1100101=>1010011
[5,6,4,8,1,7,2,3]=>0000111=>1110000
[5,6,3,8,1,2,7,4]=>0000111=>1110000
[4,2,5,3,7,1,6,8]=>0011010=>0101100
[4,3,6,7,2,1,8,5]=>1010011=>1100101
[3,4,6,7,2,8,1,5]=>0000011=>1100000
[3,4,5,2,7,8,1,6]=>0001001=>1001000
[3,4,2,5,6,8,1,7]=>0010001=>1000100
[5,2,7,8,6,4,1,3]=>0011101=>1011100
[5,1,2,7,8,6,4,3]=>0011101=>1011100
[4,7,1,8,6,5,2,3]=>0001111=>1111000
[4,7,1,2,8,6,5,3]=>0001111=>1111000
[4,6,8,1,2,7,5,3]=>0001011=>1101000
[6,8,7,1,5,3,2,4]=>0101011=>1101010
[6,8,7,3,5,1,2,4]=>0001011=>1101000
[7,8,1,6,3,5,2,4]=>0001101=>1011000
[7,8,1,3,6,5,2,4]=>0001101=>1011000
[7,8,3,6,5,2,1,4]=>1001101=>1011001
[4,7,2,8,6,1,5,3]=>0001111=>1111000
[1,7,3,4,8,6,5,2]=>0001111=>1111000
[4,2,7,1,8,6,5,3]=>0011111=>1111100
[7,8,2,3,6,5,1,4]=>0001101=>1011000
[8,5,7,1,6,2,3,4]=>0000111=>1110000
[8,5,7,1,2,6,3,4]=>0000111=>1110000
[6,8,2,7,1,3,5,4]=>0001011=>1101000
[6,8,7,2,5,3,1,4]=>0101011=>1101010
[6,2,4,8,7,1,5,3]=>0001111=>1111000
[1,6,8,3,7,4,5,2]=>0001011=>1101000
[1,6,8,3,4,7,5,2]=>0001011=>1101000
[6,2,4,8,1,7,5,3]=>0001111=>1111000
[6,8,7,2,3,5,1,4]=>0001011=>1101000
[6,8,2,1,7,3,5,4]=>1001011=>1101001
[8,5,7,2,1,6,3,4]=>1000111=>1110001
[8,5,7,1,2,3,6,4]=>0000111=>1110000
[8,7,6,2,1,4,3,5]=>1010111=>1110101
[8,5,7,2,3,1,6,4]=>0100111=>1110010
[5,8,4,2,7,1,6,3]=>0010111=>1110100
[1,8,7,5,3,4,6,2]=>0001111=>1111000
[1,8,7,3,5,4,6,2]=>0001111=>1111000
[8,2,5,4,7,1,6,3]=>0001111=>1111000
[8,5,2,7,3,1,6,4]=>0101111=>1111010
[8,7,6,2,4,3,1,5]=>0110111=>1110110
[8,7,6,1,2,4,3,5]=>0010111=>1110100
[8,7,6,1,4,2,3,5]=>0010111=>1110100
[8,7,6,4,1,3,2,5]=>0110111=>1110110
[5,8,4,7,2,1,6,3]=>1000111=>1110001
[1,8,7,5,4,3,6,2]=>0011111=>1111100
[1,6,8,4,3,7,5,2]=>0011011=>1101100
[6,8,7,3,2,5,1,4]=>0101011=>1101010
[6,8,1,7,3,2,5,4]=>0101011=>1101010
[8,5,7,3,1,6,2,4]=>0100111=>1110010
[8,5,7,1,3,2,6,4]=>0100111=>1110010
[8,5,7,3,1,2,6,4]=>0100111=>1110010
[5,8,4,7,1,2,6,3]=>0000111=>1110000
[5,8,4,1,7,2,6,3]=>0010111=>1110100
[5,8,4,7,1,6,2,3]=>0000111=>1110000
[8,1,2,6,5,7,4,3]=>0010111=>1110100
[8,2,5,6,7,4,1,3]=>0010011=>1100100
[4,8,5,7,1,6,2,3]=>0000111=>1110000
[4,8,5,7,1,2,6,3]=>0000111=>1110000
[4,8,5,1,7,2,6,3]=>0001111=>1111000
[8,5,3,1,7,2,6,4]=>0101111=>1111010
[8,5,3,7,1,2,6,4]=>0001111=>1111000
[6,8,1,3,7,2,5,4]=>0001011=>1101000
[4,6,2,8,1,7,5,3]=>0001111=>1111000
[1,6,4,8,3,7,5,2]=>0001111=>1111000
[1,8,7,4,5,3,6,2]=>0001111=>1111000
[4,8,5,7,2,1,6,3]=>1000111=>1110001
[8,5,3,7,2,1,6,4]=>1001111=>1111001
[8,7,6,3,1,4,2,5]=>0110111=>1110110
[8,7,6,1,3,2,4,5]=>0100111=>1110010
[8,5,3,2,7,1,6,4]=>0101111=>1111010
[4,8,5,2,7,1,6,3]=>0001111=>1111000
[1,8,7,4,3,5,6,2]=>0010111=>1110100
[1,8,7,3,4,5,6,2]=>0000111=>1110000
[8,2,4,5,7,1,6,3]=>0000111=>1110000
[8,5,2,3,7,1,6,4]=>0001111=>1111000
[6,3,1,5,4,2,8,7]=>0111101=>1011110
[8,3,1,5,2,7,6,4]=>0101111=>1111010
[8,5,4,2,1,7,3,6]=>1011011=>1101101
[8,5,4,2,1,7,6,3]=>1011111=>1111101
[6,5,4,2,1,3,8,7]=>1011101=>1011101
[6,5,4,2,3,1,8,7]=>0111101=>1011110
[6,3,2,5,1,4,8,7]=>0101101=>1011010
[6,5,4,3,1,2,8,7]=>0111101=>1011110
[6,5,4,1,3,2,8,7]=>0111101=>1011110
[8,5,4,1,2,7,6,3]=>0011111=>1111100
[8,7,4,1,6,3,2,5]=>0110111=>1110110
[8,7,4,1,6,3,5,2]=>0011111=>1111100
[8,7,4,1,6,5,3,2]=>0111111=>1111110
[8,5,4,1,3,7,6,2]=>0011111=>1111100
[8,5,4,3,1,7,6,2]=>0111111=>1111110
[8,3,2,5,1,7,6,4]=>0101111=>1111010
[2,1,8,5,3,7,6,4]=>1001111=>1111001
[8,3,2,5,1,7,4,6]=>0101011=>1101010
[8,5,4,3,1,7,2,6]=>0111011=>1101110
[8,5,4,1,3,7,2,6]=>0011011=>1101100
[8,7,4,1,6,5,2,3]=>0011111=>1111100
[8,7,4,1,6,2,5,3]=>0011111=>1111100
[8,7,6,5,2,1,4,3]=>1011111=>1111101
[8,7,4,3,6,2,1,5]=>1010111=>1110101
[8,3,2,7,6,4,1,5]=>0110111=>1110110
[2,1,8,7,6,4,3,5]=>1010111=>1110101
[2,1,8,7,6,4,5,3]=>1001111=>1111001
[8,3,2,7,6,4,5,1]=>0101111=>1111010
[8,7,4,3,6,2,5,1]=>0011111=>1111100
[8,7,6,5,2,4,3,1]=>0111111=>1111110
[8,5,4,2,3,7,6,1]=>0011111=>1111100
[8,7,4,2,6,5,3,1]=>0111111=>1111110
[8,7,4,2,6,3,5,1]=>0011111=>1111100
[8,7,4,2,6,3,1,5]=>0110111=>1110110
[8,3,1,7,6,4,2,5]=>0110111=>1110110
[8,3,1,7,6,4,5,2]=>0101111=>1111010
[8,3,1,7,6,5,4,2]=>0111111=>1111110
[8,3,1,5,4,7,6,2]=>0101111=>1111010
[8,3,1,5,4,7,2,6]=>0101011=>1101010
[8,3,1,7,6,5,2,4]=>0101111=>1111010
[8,3,1,7,6,2,5,4]=>0101111=>1111010
[8,7,4,2,6,1,5,3]=>0011111=>1111100
[8,7,4,2,6,5,1,3]=>0011111=>1111100
[8,5,4,2,3,7,1,6]=>0011011=>1101100
[8,3,2,5,4,7,1,6]=>0101011=>1101010
[2,1,8,5,4,7,3,6]=>1001011=>1101001
[8,3,2,7,6,5,1,4]=>0101111=>1111010
[8,7,4,3,6,5,1,2]=>0011111=>1111100
[8,7,6,5,3,1,4,2]=>0111111=>1111110
[8,7,6,5,1,3,2,4]=>0101111=>1111010
[8,7,6,5,1,3,4,2]=>0011111=>1111100
[8,7,6,5,1,4,3,2]=>0111111=>1111110
[8,7,6,5,4,1,3,2]=>0111111=>1111110
[8,7,4,3,6,1,5,2]=>0011111=>1111100
[8,3,2,7,6,1,5,4]=>0101111=>1111010
[2,1,8,7,6,3,5,4]=>1001111=>1111001
[8,3,2,7,6,1,4,5]=>0100111=>1110010
[8,7,6,5,1,4,2,3]=>0011111=>1111100
[8,7,6,5,1,2,4,3]=>0011111=>1111100
[7,3,5,1,8,4,6,2]=>0001111=>1111000
[7,3,4,1,8,5,6,2]=>0010111=>1110100
[4,5,6,2,1,8,7,3]=>1000111=>1110001
[1,6,5,2,7,4,3,8]=>0011110=>0111100
[7,4,3,1,8,6,5,2]=>0111111=>1111110
[7,6,5,1,8,4,3,2]=>0111111=>1111110
[7,6,4,1,8,5,3,2]=>0111111=>1111110
[6,4,2,1,8,7,5,3]=>1011111=>1111101
[1,6,4,2,7,5,3,8]=>0011110=>0111100
[1,5,3,2,7,6,4,8]=>0101110=>0111010
[5,3,2,1,8,7,6,4]=>1101111=>1111011
[2,5,3,1,7,8,6,4]=>0101101=>1011010
[2,6,4,1,7,8,5,3]=>0011101=>1011100
[2,6,5,1,7,8,4,3]=>0011101=>1011100
[4,5,7,1,6,8,2,3]=>0000011=>1100000
[6,5,1,2,8,4,3,7]=>0011101=>1011100
[6,4,1,2,8,5,3,7]=>0011101=>1011100
[5,3,1,2,8,6,4,7]=>0101101=>1011010
[4,3,1,2,8,6,5,7]=>0110101=>1010110
[6,1,2,5,8,3,4,7]=>0000101=>1010000
[7,1,3,4,8,2,5,6]=>0000011=>1100000
[7,1,5,6,8,2,3,4]=>0000011=>1100000
[2,6,1,5,7,8,3,4]=>0000101=>1010000
[7,4,1,6,8,5,2,3]=>0011011=>1101100
[5,2,3,1,8,6,7,4]=>0101011=>1101010
[3,5,2,1,6,8,7,4]=>1001011=>1101001
[1,6,2,5,7,3,4,8]=>0000110=>0110000
[6,2,1,5,8,7,3,4]=>1000111=>1110001
[7,3,1,5,8,6,2,4]=>0100111=>1110010
[6,2,4,1,8,5,7,3]=>0010111=>1110100
[6,2,5,1,8,4,7,3]=>0001111=>1111000
[7,3,1,4,8,6,2,5]=>0100111=>1110010
[6,2,1,4,8,7,3,5]=>1000111=>1110001
[1,6,2,4,7,3,5,8]=>0000110=>0110000
[5,2,1,3,8,7,4,6]=>1001011=>1101001
[7,4,1,3,8,5,2,6]=>0011011=>1101100
[7,5,1,3,8,4,2,6]=>0011011=>1101100
[3,6,7,1,4,8,2,5]=>0000011=>1100000
[7,6,1,4,8,3,2,5]=>0100111=>1110010
[4,2,1,3,8,7,5,6]=>1010011=>1100101
[2,6,1,4,7,8,3,5]=>0000101=>1010000
[7,1,4,6,8,2,3,5]=>0000011=>1100000
[7,1,3,5,8,2,4,6]=>0000011=>1100000
[6,1,2,4,8,3,5,7]=>0000101=>1010000
[7,4,5,2,3,1,8,6]=>0101011=>1101010
[8,6,7,3,5,2,4,1]=>0011011=>1101100
[6,3,5,2,4,1,8,7]=>0011101=>1011100
[4,1,6,3,5,2,8,7]=>0011101=>1011100
[5,2,6,3,4,1,8,7]=>0011101=>1011100
[5,2,7,3,4,1,8,6]=>0011011=>1101100
[5,2,8,6,7,3,4,1]=>0011011=>1101100
[6,2,8,5,7,3,4,1]=>0010111=>1110100
[6,2,7,3,4,1,8,5]=>0010111=>1110100
[4,1,7,3,5,2,8,6]=>0011011=>1101100
[3,1,7,4,5,2,8,6]=>0101011=>1101010
[3,1,8,6,7,4,5,2]=>0101011=>1101010
[4,1,8,6,7,3,5,2]=>0011011=>1101100
[8,6,7,3,4,1,5,2]=>0011011=>1101100
[8,5,7,3,4,1,6,2]=>0010111=>1110100
[8,5,6,2,7,3,4,1]=>0010111=>1110100
[8,4,7,3,5,1,6,2]=>0001111=>1111000
[5,1,8,4,7,3,6,2]=>0001111=>1111000
[4,1,8,5,7,3,6,2]=>0010111=>1110100
[2,1,8,5,7,4,6,3]=>1000111=>1110001
[2,1,7,4,6,3,8,5]=>1000111=>1110001
[4,1,7,3,6,2,8,5]=>0010111=>1110100
[5,1,7,3,6,2,8,4]=>0001111=>1111000
[6,2,7,3,5,1,8,4]=>0001111=>1111000
[6,2,8,4,7,3,5,1]=>0001111=>1111000
[8,4,7,3,6,2,5,1]=>0001111=>1111000
[7,3,6,2,5,1,8,4]=>0001111=>1111000
[6,2,5,1,7,3,8,4]=>0001111=>1111000
[5,2,4,1,7,3,8,6]=>0011011=>1101100
[6,2,4,1,7,3,8,5]=>0010111=>1110100
[8,5,7,3,6,2,4,1]=>0010111=>1110100
[8,5,7,4,6,2,3,1]=>0100111=>1110010
[4,2,3,1,7,5,8,6]=>0110011=>1100110
[3,1,4,2,8,6,7,5]=>0110011=>1100110
[8,5,6,2,3,1,7,4]=>0100111=>1110010
[7,4,8,5,6,2,3,1]=>0100111=>1110010
[7,3,8,5,6,2,4,1]=>0010111=>1110100
[8,5,6,2,4,1,7,3]=>0010111=>1110100
[3,1,5,2,8,6,7,4]=>0101011=>1101010
[2,1,6,3,8,5,7,4]=>1000111=>1110001
[3,1,6,2,8,5,7,4]=>0100111=>1110010
[4,1,6,2,8,5,7,3]=>0010111=>1110100
[5,1,6,2,8,4,7,3]=>0001111=>1111000
[8,4,6,2,5,1,7,3]=>0001111=>1111000
[7,3,8,4,6,2,5,1]=>0001111=>1111000
[6,2,7,3,8,4,5,1]=>0001111=>1111000
[8,4,5,1,6,2,7,3]=>0001111=>1111000
[5,1,8,4,6,2,7,3]=>0001111=>1111000
[4,1,8,5,6,2,7,3]=>0010111=>1110100
[3,1,8,5,6,2,7,4]=>0100111=>1110010
[2,1,7,4,8,5,6,3]=>1000111=>1110001
[4,1,7,3,8,5,6,2]=>0010111=>1110100
[7,3,8,4,5,1,6,2]=>0001111=>1111000
[8,4,5,1,7,3,6,2]=>0001111=>1111000
[7,3,6,2,8,4,5,1]=>0001111=>1111000
[7,8,5,6,1,3,4,2]=>0010101=>1010100
[7,8,1,3,6,2,5,4]=>0001101=>1011000
[1,3,8,4,7,2,5,6]=>0000011=>1100000
[3,6,1,4,7,2,5,8]=>0000110=>0110000
[4,6,1,2,5,7,3,8]=>0000110=>0110000
[1,4,8,2,5,7,3,6]=>0000011=>1100000
[7,8,2,4,5,6,1,3]=>0000101=>1010000
[7,8,1,5,4,6,3,2]=>0101101=>1011010
[7,8,2,1,6,3,4,5]=>1000101=>1010001
[7,8,3,5,6,4,1,2]=>0010101=>1010100
[7,8,1,4,2,3,6,5]=>0010101=>1010100
[7,8,5,1,4,2,6,3]=>0011101=>1011100
[7,8,4,5,3,1,6,2]=>0101101=>1011010
[1,5,8,4,3,2,7,6]=>0110011=>1100110
[5,6,1,4,3,2,7,8]=>0110100=>0010110
[2,6,4,8,3,7,1,5]=>0000111=>1110000
[1,4,6,8,3,7,5,2]=>0001011=>1101000
[2,4,8,5,3,1,6,7]=>0101001=>1001010
[2,5,8,1,4,7,6,3]=>0000111=>1110000
[3,5,8,4,7,6,1,2]=>0000111=>1110000
[1,6,2,4,7,3,8,5]=>0000111=>1110000
[5,6,2,1,4,7,8,3]=>1000101=>1010001
[4,6,2,5,3,1,8,7]=>0101101=>1011010
[4,7,5,1,3,6,8,2]=>0001011=>1101000
[7,5,3,6,2,4,1,8]=>0011110=>0111100
[5,7,3,6,1,4,8,2]=>0000111=>1110000
[5,3,6,7,2,1,8,4]=>1001011=>1101001
[6,1,7,5,2,4,8,3]=>0001111=>1111000
[6,3,1,2,4,5,8,7]=>0100101=>1010010
[1,4,7,2,5,3,8,6]=>0001011=>1101000
[4,6,7,8,3,5,1,2]=>0001001=>1001000
[3,6,1,8,4,2,5,7]=>0010101=>1010100
[1,6,7,5,8,2,4,3]=>0010011=>1100100
[3,5,6,7,8,1,4,2]=>0010001=>1000100
[3,6,5,7,8,2,1,4]=>1000101=>1010001
[5,2,7,6,1,4,3,8]=>0011110=>0111100
[2,5,7,6,8,1,3,4]=>0000011=>1100000
[2,7,5,6,8,4,1,3]=>0010011=>1100100
[2,1,6,8,4,5,3,7]=>1001001=>1001001
[2,7,1,8,5,3,4,6]=>0001011=>1101000
[3,7,6,8,5,4,1,2]=>0011011=>1101100
[4,3,8,5,6,7,1,2]=>0010011=>1100100
[4,2,8,1,6,3,7,5]=>0010111=>1110100
[3,1,8,5,4,6,7,2]=>0101011=>1101010
[3,2,8,4,5,6,1,7]=>0100101=>1010010
[3,4,2,8,6,1,7,5]=>0010111=>1110100
[3,4,7,1,5,2,6,8]=>0001010=>0101000
[4,3,7,8,1,2,6,5]=>0010101=>1010100
[1,7,3,8,5,2,6,4]=>0001111=>1111000
[4,1,8,3,6,2,5,7]=>0010101=>1010100
[5,7,8,6,3,2,1,4]=>1100101=>1010011
[5,7,8,6,1,3,4,2]=>0010101=>1010100
[7,6,5,8,1,3,4,2]=>0010111=>1110100
[1,6,4,3,8,2,5,7]=>0010101=>1010100
[7,1,3,4,8,2,6,5]=>0000111=>1110000
[3,6,5,4,1,2,7,8]=>0011100=>0011100
[2,4,5,1,7,8,6,3]=>0001101=>1011000
[2,6,3,4,5,8,1,7]=>0000101=>1010000
[2,6,4,1,8,3,7,5]=>0010111=>1110100
[7,3,6,4,8,5,1,2]=>0001111=>1111000
[7,2,1,4,8,3,5,6]=>1000011=>1100001
[7,1,6,5,3,8,4,2]=>0011111=>1111100
[7,2,5,6,3,8,1,4]=>0000111=>1110000
[6,5,2,7,1,8,4,3]=>0011111=>1111100
[5,6,2,7,3,1,4,8]=>0100110=>0110010
[5,6,7,4,2,8,1,3]=>0010011=>1100100
[5,7,6,4,1,8,3,2]=>0110111=>1110110
[6,7,1,5,2,8,3,4]=>0001011=>1101000
[1,7,5,2,4,8,3,6]=>0001011=>1101000
[6,1,5,2,8,3,4,7]=>0001101=>1011000
[6,7,5,3,8,4,1,2]=>0011011=>1101100
[1,6,5,4,2,3,8,7]=>0011101=>1011100
[7,1,5,3,4,2,8,6]=>0011011=>1101100
[7,6,1,5,3,2,8,4]=>0101111=>1111010
[7,5,6,4,1,2,8,3]=>0010111=>1110100
[6,7,5,4,3,1,8,2]=>0111011=>1101110
[7,5,2,4,3,1,6,8]=>0111010=>0101110
[7,4,6,1,2,5,3,8]=>0001110=>0111000
[7,1,4,2,5,3,6,8]=>0011010=>0101100
[6,8,1,4,2,5,7,3]=>0010011=>1100100
[1,6,4,2,5,7,3,8]=>0010110=>0110100
[1,6,3,7,5,4,2,8]=>0011110=>0111100
[6,8,1,3,7,5,4,2]=>0011011=>1101100
[7,1,3,5,6,4,2,8]=>0010110=>0110100
[7,3,1,6,4,5,2,8]=>0101110=>0111010
[7,4,2,6,5,1,3,8]=>0011110=>0111100
[7,4,6,3,1,5,2,8]=>0101110=>0111010
[7,2,4,1,5,3,6,8]=>0011010=>0101100
[7,2,3,5,4,1,6,8]=>0011010=>0101100
[6,8,1,2,3,4,7,5]=>0000011=>1100000
[1,5,7,2,3,8,6,4]=>0000111=>1110000
[5,1,8,2,3,6,7,4]=>0001011=>1101000
[5,8,2,3,7,6,4,1]=>0010111=>1110100
[6,2,8,1,3,7,4,5]=>0000111=>1110000
[6,8,2,3,5,4,7,1]=>0001011=>1101000
[6,8,2,4,1,5,7,3]=>0010011=>1100100
[6,8,3,1,2,4,7,5]=>0100011=>1100010
[2,6,4,1,5,7,3,8]=>0010110=>0110100
[2,6,3,5,7,1,4,8]=>0000110=>0110000
[2,5,1,7,8,3,6,4]=>0001101=>1011000
[2,5,3,6,8,4,7,1]=>0001011=>1101000
[2,1,4,7,8,5,6,3]=>1000101=>1010001
[2,4,7,6,8,5,1,3]=>0001011=>1101000
[2,5,3,7,6,1,8,4]=>0001111=>1111000
[2,5,7,8,1,4,6,3]=>0000101=>1010000
[3,5,7,4,1,6,2,8]=>0010110=>0110100
[5,3,4,1,8,6,7,2]=>0011011=>1101100
[5,2,8,4,6,1,7,3]=>0001111=>1111000
[5,2,1,8,6,3,7,4]=>1001111=>1111001
[4,2,8,6,5,3,7,1]=>0011111=>1111100
[4,2,8,5,7,6,3,1]=>0110111=>1110110
[1,4,2,7,5,8,6,3]=>0010111=>1110100
[4,1,8,6,7,5,3,2]=>0111011=>1101110
[5,3,8,7,6,2,4,1]=>0011111=>1111100
[5,8,4,7,6,2,1,3]=>1000111=>1110001
[5,8,7,4,3,6,1,2]=>0010111=>1110100
[6,4,8,3,1,7,2,5]=>0100111=>1110010
[6,4,2,8,7,1,3,5]=>0010111=>1110100
[6,3,8,7,2,5,1,4]=>0001111=>1111000
[5,8,3,7,1,6,4,2]=>0010111=>1110100
[5,1,3,8,6,7,2,4]=>0001011=>1101000
[1,5,3,7,8,6,2,4]=>0001101=>1011000
[1,5,7,6,4,2,8,3]=>0010111=>1110100
[5,8,7,4,1,6,2,3]=>0010111=>1110100
[6,4,8,1,2,7,3,5]=>0000111=>1110000
[6,8,5,1,2,3,7,4]=>0001011=>1101000
[6,8,5,2,4,3,7,1]=>0011011=>1101100
[6,8,5,3,1,2,7,4]=>0101011=>1101010
[4,5,1,2,7,6,3,8]=>0001110=>0111000
[4,5,1,2,6,8,7,3]=>0001011=>1101000
[3,5,6,1,8,4,7,2]=>0000111=>1110000
[3,5,7,1,2,8,6,4]=>0000111=>1110000
[3,6,2,7,5,1,4,8]=>0001110=>0111000
[4,2,6,1,7,3,5,8]=>0010110=>0110100
[4,6,3,1,2,7,5,8]=>0100110=>0110010
[4,5,3,1,7,6,2,8]=>0101110=>0111010
[4,2,5,7,1,6,3,8]=>0010110=>0110100
[3,5,2,7,8,1,6,4]=>0001101=>1011000
[3,1,4,7,5,6,2,8]=>0100110=>0110010
[3,4,6,5,8,7,1,2]=>0000111=>1110000
[3,1,4,5,8,6,7,2]=>0100011=>1100010
[3,4,6,8,5,2,7,1]=>0001011=>1101000
[3,5,6,2,8,4,7,1]=>0000111=>1110000
[4,2,5,6,1,8,7,3]=>0010111=>1110100
[4,5,3,1,6,8,7,2]=>0101011=>1101010
[2,1,7,5,8,6,4,3]=>1010111=>1110101
[1,2,7,5,3,8,6,4]=>0001111=>1111000
[4,1,2,7,3,8,6,5]=>0010111=>1110100
[6,4,1,7,5,2,3,8]=>0011110=>0111100
[6,1,3,7,5,2,4,8]=>0001110=>0111000
[3,1,2,6,8,5,4,7]=>0101001=>1001010
[3,7,1,2,5,4,8,6]=>0001011=>1101000
[1,3,7,2,4,8,6,5]=>0000111=>1110000
[2,4,1,7,8,6,5,3]=>0011101=>1011100
[3,4,7,5,1,8,6,2]=>0001111=>1111000
[2,7,4,1,5,8,6,3]=>0010111=>1110100
[2,3,7,1,5,8,6,4]=>0000111=>1110000
[5,2,8,1,3,7,4,6]=>0001011=>1101000
[2,1,6,8,3,4,7,5]=>1000011=>1100001
[2,6,8,3,1,5,7,4]=>0100011=>1100010
[2,8,6,4,1,5,7,3]=>0010111=>1110100
[3,6,4,8,5,1,7,2]=>0001111=>1111000
[6,3,7,4,5,1,8,2]=>0001111=>1111000
[2,6,3,7,5,8,1,4]=>0000111=>1110000
[5,2,1,7,8,3,4,6]=>1001001=>1001001
[4,7,2,3,6,8,1,5]=>0000011=>1100000
[5,2,7,3,6,8,1,4]=>0001011=>1101000
[5,7,4,6,2,8,1,3]=>0000111=>1110000
[5,7,3,4,6,1,8,2]=>0000111=>1110000
[5,3,8,4,6,1,7,2]=>0001111=>1111000
[8,5,2,4,1,6,7,3]=>0011011=>1101100
[8,2,3,5,1,6,7,4]=>0001011=>1101000
[4,2,8,3,6,7,1,5]=>0010011=>1100100
[2,4,8,1,7,3,5,6]=>0000011=>1100000
[8,4,1,3,6,2,5,7]=>0010101=>1010100
[4,8,3,1,7,2,5,6]=>0100011=>1100010
[5,2,8,4,7,1,6,3]=>0001111=>1111000
[5,8,4,7,3,1,6,2]=>0100111=>1110010
[4,6,8,3,1,7,5,2]=>0101011=>1101010
[6,3,8,2,7,1,5,4]=>0001111=>1111000
[6,3,1,8,2,4,7,5]=>0100111=>1110010
[5,3,8,1,2,6,4,7]=>0001101=>1011000
[5,7,4,1,6,2,3,8]=>0010110=>0110100
[8,5,4,1,2,6,3,7]=>0011101=>1011100
[5,1,8,4,2,7,3,6]=>0011011=>1101100
[1,6,2,8,5,3,7,4]=>0001111=>1111000
[6,8,5,3,1,7,4,2]=>0111011=>1101110
[8,4,5,1,2,6,3,7]=>0001101=>1011000
[5,6,3,7,1,2,4,8]=>0000110=>0110000
[1,6,3,7,2,8,4,5]=>0000111=>1110000
[6,3,2,7,8,5,1,4]=>0101101=>1011010
[4,5,7,8,3,1,6,2]=>0100101=>1010010
[4,7,2,5,8,1,6,3]=>0000111=>1110000
[8,1,3,4,6,2,5,7]=>0000101=>1010000
[3,8,2,4,6,7,1,5]=>0000011=>1100000
[3,5,6,8,2,7,1,4]=>0000011=>1100000
[2,4,5,6,8,1,7,3]=>0000011=>1100000
[4,8,3,5,6,1,7,2]=>0000111=>1110000
[5,6,2,3,7,8,1,4]=>0000101=>1010000
[5,8,7,3,4,1,2,6]=>0010011=>1100100
[6,8,7,3,4,1,2,5]=>0010011=>1100100
[6,8,4,7,1,5,3,2]=>0101011=>1101010
[6,8,4,7,2,5,3,1]=>0101011=>1101010
[5,4,8,7,2,6,3,1]=>0101111=>1111010
[5,4,8,7,1,6,3,2]=>0101111=>1111010
[5,3,8,7,6,1,2,4]=>0001111=>1111000
[4,3,8,7,6,1,2,5]=>0010111=>1110100
[4,8,3,7,5,1,2,6]=>0001011=>1101000
[8,3,4,6,5,1,2,7]=>0001101=>1011000
[3,8,4,7,5,1,2,6]=>0001011=>1101000
[3,4,8,7,6,1,2,5]=>0000111=>1110000
[3,5,8,7,6,1,2,4]=>0000111=>1110000
[4,5,8,7,6,1,2,3]=>0000111=>1110000
[4,5,8,7,1,6,3,2]=>0100111=>1110010
[4,5,8,7,2,6,3,1]=>0100111=>1110010
[3,5,8,2,7,6,4,1]=>0010111=>1110100
[3,5,8,1,7,6,4,2]=>0010111=>1110100
[2,5,8,1,7,6,4,3]=>0010111=>1110100
[2,5,8,7,1,6,3,4]=>0000111=>1110000
[2,4,8,7,1,6,3,5]=>0000111=>1110000
[2,8,4,7,1,5,3,6]=>0001011=>1101000
[8,2,4,6,1,5,3,7]=>0001101=>1011000
[8,1,4,6,2,5,3,7]=>0001101=>1011000
[1,8,4,7,2,5,3,6]=>0001011=>1101000
[1,4,8,7,2,6,3,5]=>0000111=>1110000
[1,5,8,7,2,6,3,4]=>0000111=>1110000
[1,5,8,2,7,6,4,3]=>0010111=>1110100
[2,5,8,3,7,6,4,1]=>0010111=>1110100
[1,4,2,8,7,6,5,3]=>0011111=>1111100
[1,3,8,2,7,6,4,5]=>0000111=>1110000
[1,8,3,2,7,5,4,6]=>0101011=>1101010
[8,1,3,2,6,5,4,7]=>0101101=>1011010
[8,2,3,1,6,5,4,7]=>0101101=>1011010
[2,8,3,1,7,5,4,6]=>0101011=>1101010
[2,3,8,1,7,6,4,5]=>0000111=>1110000
[3,4,1,8,7,6,5,2]=>0011111=>1111100
[4,3,1,8,7,6,5,2]=>0111111=>1111110
[4,2,1,8,7,6,5,3]=>1011111=>1111101
[3,8,2,1,7,5,4,6]=>1001011=>1101001
[8,3,2,1,6,5,4,7]=>1101101=>1011011
[8,4,2,6,1,5,3,7]=>0011101=>1011100
[4,2,8,7,1,6,3,5]=>0010111=>1110100
[5,2,8,7,1,6,3,4]=>0001111=>1111000
[5,2,8,1,7,6,4,3]=>0011111=>1111100
[5,3,8,1,7,6,4,2]=>0011111=>1111100
[5,3,8,2,7,6,4,1]=>0011111=>1111100
[6,8,3,2,7,5,4,1]=>0111011=>1101110
[6,8,3,1,7,5,4,2]=>0111011=>1101110
[6,8,2,1,7,5,4,3]=>1011011=>1101101
[6,8,2,7,1,5,3,4]=>0001011=>1101000
[6,8,7,2,1,4,3,5]=>1010011=>1100101
[8,5,6,1,2,4,3,7]=>0010101=>1010100
[5,8,7,1,2,4,3,6]=>0010011=>1100100
[6,8,1,2,7,5,4,3]=>0011011=>1101100
[6,8,2,3,7,5,4,1]=>0011011=>1101100
[5,2,8,3,7,6,4,1]=>0011111=>1111100
[5,1,8,3,7,6,4,2]=>0011111=>1111100
[5,1,8,7,2,6,3,4]=>0001111=>1111000
[4,1,8,7,2,6,3,5]=>0010111=>1110100
[4,8,1,7,2,5,3,6]=>0001011=>1101000
[8,4,1,6,2,5,3,7]=>0011101=>1011100
[8,3,1,2,6,5,4,7]=>0101101=>1011010
[3,8,1,2,7,5,4,6]=>0001011=>1101000
[3,1,8,2,7,6,4,5]=>0100111=>1110010
[3,1,2,8,7,6,5,4]=>0101111=>1111010
[4,1,3,8,7,6,5,2]=>0011111=>1111100
[3,1,4,8,7,6,5,2]=>0101111=>1111010
[2,1,8,3,7,6,4,5]=>1000111=>1110001
[2,8,1,3,7,5,4,6]=>0001011=>1101000
[8,2,1,3,6,5,4,7]=>1001101=>1011001
[8,1,2,3,6,5,4,7]=>0001101=>1011000
[1,8,2,3,7,5,4,6]=>0001011=>1101000
[1,2,8,3,7,6,4,5]=>0000111=>1110000
[1,4,3,6,8,2,5,7]=>0010001=>1000100
[3,1,6,2,5,8,4,7]=>0100101=>1010010
[3,5,1,8,2,4,7,6]=>0001011=>1101000
[1,4,5,2,8,3,7,6]=>0001011=>1101000
[1,4,2,6,5,8,3,7]=>0010101=>1010100
[1,5,4,2,6,8,3,7]=>0011001=>1001100
[3,1,6,5,8,2,4,7]=>0100101=>1010010
[1,6,4,2,5,8,3,7]=>0010101=>1010100
[1,5,2,6,4,8,3,7]=>0001101=>1011000
[1,2,6,5,4,8,3,7]=>0001101=>1011000
[1,2,5,4,7,3,8,6]=>0001011=>1101000
[4,1,2,6,3,8,7,5]=>0010111=>1110100
[7,1,5,4,2,8,3,6]=>0011011=>1101100
[1,4,7,5,2,8,3,6]=>0001011=>1101000
[7,1,3,5,2,8,4,6]=>0001011=>1101000
[7,2,5,1,8,3,4,6]=>0001011=>1101000
[1,4,5,2,8,7,3,6]=>0001011=>1101000
[1,6,4,2,8,3,7,5]=>0010111=>1110100
[1,4,2,8,3,7,6,5]=>0010111=>1110100
[1,2,5,3,8,7,6,4]=>0001111=>1111000
[1,2,8,6,5,3,7,4]=>0001111=>1111000
[1,5,2,8,6,3,7,4]=>0001111=>1111000
[1,6,4,2,8,7,3,5]=>0010111=>1110100
[6,2,1,8,7,3,4,5]=>1000111=>1110001
[7,6,2,1,8,3,4,5]=>1000111=>1110001
[7,3,1,6,2,8,4,5]=>0100111=>1110010
[1,7,6,4,2,8,3,5]=>0010111=>1110100
[1,7,5,2,6,3,8,4]=>0001111=>1111000
[1,6,2,7,5,3,8,4]=>0001111=>1111000
[1,2,7,6,5,3,8,4]=>0001111=>1111000
[1,2,6,5,3,8,7,4]=>0001111=>1111000
[1,5,2,6,3,8,7,4]=>0001111=>1111000
[1,5,2,7,6,3,8,4]=>0001111=>1111000
[1,6,5,2,7,3,8,4]=>0001111=>1111000
[1,5,7,4,2,8,3,6]=>0010011=>1100100
[4,1,2,8,6,3,7,5]=>0010111=>1110100
[3,1,8,6,2,4,7,5]=>0100111=>1110010
[4,3,7,1,8,2,5,6]=>0010011=>1100100
[8,3,1,6,2,4,7,5]=>0100111=>1110010
[7,1,8,3,2,4,6,5]=>0100111=>1110010
[1,8,7,3,2,4,6,5]=>0100111=>1110010
[1,4,2,8,7,3,6,5]=>0010111=>1110100
[1,7,4,2,8,3,6,5]=>0010111=>1110100
[8,1,5,4,2,7,3,6]=>0011011=>1101100
[1,4,8,5,2,7,3,6]=>0001011=>1101000
[8,5,3,1,7,2,4,6]=>0101011=>1101010
[8,6,2,1,7,3,4,5]=>1000111=>1110001
[1,8,6,4,2,7,3,5]=>0010111=>1110100
[1,8,5,2,6,3,7,4]=>0001111=>1111000
[1,5,2,7,3,8,6,4]=>0001111=>1111000
[1,2,8,5,3,7,6,4]=>0001111=>1111000
[1,2,6,3,8,7,5,4]=>0001111=>1111000
[1,2,7,6,3,8,5,4]=>0001111=>1111000
[1,6,2,7,3,8,5,4]=>0001111=>1111000
[1,7,2,8,5,3,6,4]=>0001111=>1111000
[1,7,4,2,8,6,3,5]=>0010111=>1110100
[7,1,8,3,2,6,4,5]=>0100111=>1110010
[7,2,1,8,6,3,4,5]=>1000111=>1110001
[1,8,7,3,2,6,4,5]=>0100111=>1110010
[1,4,2,8,7,6,3,5]=>0010111=>1110100
[1,2,8,7,5,3,6,4]=>0001111=>1111000
[1,2,8,6,3,7,5,4]=>0001111=>1111000
[1,2,7,3,8,6,5,4]=>0001111=>1111000
[4,1,7,3,6,5,8,2]=>0010111=>1110100
[5,1,8,7,6,2,4,3]=>0011111=>1111100
[8,1,7,6,3,4,5,2]=>0001111=>1111000
[5,7,8,6,2,4,1,3]=>0010101=>1010100
[5,7,1,6,2,4,3,8]=>0010110=>0110100
[6,4,1,5,2,7,3,8]=>0011110=>0111100
[8,1,4,5,3,7,6,2]=>0001111=>1111000
[6,1,4,5,3,8,7,2]=>0001111=>1111000
[6,1,4,5,3,7,8,2]=>0001101=>1011000
[5,1,7,8,6,2,4,3]=>0011101=>1011100
[6,1,4,8,3,5,7,2]=>0000111=>1110000
[7,1,8,6,3,4,5,2]=>0001111=>1111000
[7,1,4,5,3,8,6,2]=>0001111=>1111000
[7,1,4,5,3,6,8,2]=>0001011=>1101000
[8,1,4,5,3,6,7,2]=>0001011=>1101000
[7,4,1,5,2,6,3,8]=>0011110=>0111100
[6,3,5,7,2,1,4,8]=>1000110=>0110001
[6,3,5,8,2,1,7,4]=>1000111=>1110001
[6,3,5,7,2,1,8,4]=>1000111=>1110001
[8,4,5,7,3,6,1,2]=>0000111=>1110000
[6,4,5,8,3,7,2,1]=>1000111=>1110001
[5,8,7,6,2,4,1,3]=>0010111=>1110100
[5,4,8,6,3,1,7,2]=>0101111=>1111010
[5,4,1,8,2,3,7,6]=>0011011=>1101100
[5,8,1,6,2,4,3,7]=>0010101=>1010100
[8,4,1,5,2,6,3,7]=>0011101=>1011100
[6,3,5,8,2,1,4,7]=>1000101=>1010001
[2,3,4,1,8,6,5,7]=>0010101=>1010100
[8,3,5,6,2,1,4,7]=>1000101=>1010001
[2,3,8,5,1,4,7,6]=>0001011=>1101000
[2,3,8,6,1,5,7,4]=>0000111=>1110000
[2,8,6,7,1,3,5,4]=>0001011=>1101000
[8,3,5,7,2,1,6,4]=>1000111=>1110001
[2,3,8,5,6,1,7,4]=>0000111=>1110000
[7,4,5,6,3,1,8,2]=>0100111=>1110010
[8,4,5,6,3,1,7,2]=>0100111=>1110010
[7,3,5,6,2,8,1,4]=>0000111=>1110000
[7,3,5,8,2,1,6,4]=>1000111=>1110001
[7,3,5,6,2,1,4,8]=>1000110=>0110001
[2,7,6,5,1,3,4,8]=>0001110=>0111000
[2,7,6,8,1,3,5,4]=>0001011=>1101000
[2,7,6,5,8,3,1,4]=>0100111=>1110010
[8,7,5,6,1,4,2,3]=>0010111=>1110100
[2,6,4,1,8,5,7,3]=>0010111=>1110100
[2,6,1,3,8,5,7,4]=>0000111=>1110000
[2,7,1,3,6,5,8,4]=>0000111=>1110000
[2,7,6,8,4,3,1,5]=>0110011=>1100110
[2,7,6,1,8,3,4,5]=>0000111=>1110000
[2,7,6,1,4,3,5,8]=>0010110=>0110100
[7,3,5,1,2,8,4,6]=>0001011=>1101000
[8,4,1,5,2,3,7,6]=>0011011=>1101100
[7,8,1,6,3,4,2,5]=>0010101=>1010100
[6,4,1,8,3,2,7,5]=>0110111=>1110110
[2,3,8,6,4,1,7,5]=>0010111=>1110100
[2,8,6,7,4,3,1,5]=>0110011=>1100110
[8,3,5,7,2,4,1,6]=>0010011=>1100100
[2,3,4,1,8,7,5,6]=>0010011=>1100100
[2,8,6,1,7,3,4,5]=>0000111=>1110000
[2,3,8,1,6,4,7,5]=>0000111=>1110000
[2,3,8,1,4,5,7,6]=>0000011=>1100000
[2,8,6,1,4,3,5,7]=>0010101=>1010100
[1,2,3,4,5,6,7,9,8]=>00000001=>10000000
[2,1,3,4,5,6,7,8,9]=>10000000=>00000001
[1,2,3,4,5,6,7,8,10,9]=>000000001=>100000000
[2,1,3,4,5,6,7,8,9,10]=>100000000=>000000001
[1,2,3,4,5,6,7,8,9,11,10]=>0000000001=>1000000000
[9,1,2,3,4,5,6,7,10,8]=>000000011=>110000000
[1,8,2,3,4,5,6,9,7]=>00000011=>11000000
[7,1,2,3,4,5,6,9,8]=>00000101=>10100000
[2,1,9,3,4,5,6,7,8]=>10000001=>10000001
[2,8,1,3,4,5,6,7,9]=>00000010=>01000000
[2,10,1,3,4,5,6,7,8,9]=>000000001=>100000000
[2,1,3,4,5,6,7,8,9,10,11]=>1000000000=>0000000001
[8,4,3,6,5,1,7,2]=>0011111=>1111100
[8,5,6,3,4,1,7,2]=>0010111=>1110100
[8,6,5,4,3,1,7,2]=>0111111=>1111110
[1,7,6,5,4,2,3,8]=>0011110=>0111100
[1,8,6,5,2,7,3,4]=>0001111=>1111000
[8,7,5,4,1,6,3,2]=>0111111=>1111110
[7,8,5,4,1,3,6,2]=>0011101=>1011100
[6,8,5,4,2,1,7,3]=>1011011=>1101101
[5,8,6,2,4,1,7,3]=>0010111=>1110100
[4,8,2,6,5,1,7,3]=>0001111=>1111000
[3,2,8,6,5,1,7,4]=>0101111=>1111010
[3,2,1,7,6,4,5,8]=>1100110=>0110011
[4,1,3,7,6,2,5,8]=>0010110=>0110100
[5,1,7,3,6,2,4,8]=>0001110=>0111000
[6,1,7,5,3,2,4,8]=>0101110=>0111010
[7,1,6,5,2,4,3,8]=>0011110=>0111100
[8,1,6,5,2,3,7,4]=>0001111=>1111000
[1,2,7,6,3,4,5,8]=>0000110=>0110000
[1,2,8,3,7,4,5,6]=>0000011=>1100000
[8,1,7,2,6,3,5,4]=>0001111=>1111000
[7,1,8,2,6,4,3,5]=>0010111=>1110100
[6,1,8,2,4,7,3,5]=>0000111=>1110000
[5,1,8,3,2,7,4,6]=>0101011=>1101010
[4,1,3,8,2,7,5,6]=>0010011=>1100100
[3,2,1,8,4,7,5,6]=>1100011=>1100011
[3,2,8,7,1,6,5,4]=>0101111=>1111010
[4,8,2,7,1,6,5,3]=>0001111=>1111000
[5,8,7,2,1,6,4,3]=>1010111=>1110101
[6,8,7,1,3,5,4,2]=>0011011=>1101100
[7,8,6,1,5,3,4,2]=>0011101=>1011100
[8,7,6,1,5,4,3,2]=>0111111=>1111110
[1,8,7,2,6,5,3,4]=>0001111=>1111000
[1,7,8,2,5,6,3,4]=>0000101=>1010000
[8,6,7,1,4,5,3,2]=>0101011=>1101010
[7,6,8,1,4,3,5,2]=>0011011=>1101100
[6,5,8,3,2,1,7,4]=>1100111=>1110011
[7,5,8,3,1,4,6,2]=>0100111=>1110010
[8,5,7,3,1,6,4,2]=>0110111=>1110110
[1,6,8,4,2,7,3,5]=>0010011=>1100100
[1,5,4,8,2,7,3,6]=>0001011=>1101000
[8,4,3,7,1,6,5,2]=>0011111=>1111100
[7,4,3,8,1,5,6,2]=>0010111=>1110100
[6,4,3,1,5,2,7,8]=>0111100=>0011110
[7,4,3,1,2,6,5,8]=>0110110=>0110110
[8,4,3,1,2,5,7,6]=>0110011=>1100110
[1,5,4,2,3,6,7,8]=>0011000=>0001100
[8,5,1,4,2,3,7,6]=>0011011=>1101100
[7,5,1,4,2,6,3,8]=>0011110=>0111100
[6,5,1,4,3,2,7,8]=>0111100=>0011110
[5,6,1,3,4,2,7,8]=>0010100=>0010100
[4,6,2,1,5,3,7,8]=>1001100=>0011001
[3,2,6,1,5,4,7,8]=>0101100=>0011010
[3,2,7,1,4,6,5,8]=>0100110=>0110010
[4,7,2,1,3,6,5,8]=>1000110=>0110001
[5,7,1,3,2,6,4,8]=>0100110=>0110010
[6,7,1,2,4,5,3,8]=>0001010=>0101000
[7,6,1,2,5,4,3,8]=>0011110=>0111100
[8,6,1,2,5,3,7,4]=>0001111=>1111000
[1,7,2,3,6,4,5,8]=>0000110=>0110000
[8,7,1,2,3,6,5,4]=>0001111=>1111000
[7,8,1,2,3,5,6,4]=>0000101=>1010000
[6,8,1,2,4,3,7,5]=>0010011=>1100100
[5,8,1,3,2,4,7,6]=>0100011=>1100010
[4,8,2,1,3,5,7,6]=>1000011=>1100001
[3,2,8,1,4,5,7,6]=>0100011=>1100010
[4,1,3,2,5,6,7,8]=>0110000=>0000110
[5,1,2,4,3,6,7,8]=>0011000=>0001100
[6,1,2,3,5,4,7,8]=>0001100=>0011000
[7,1,2,3,4,6,5,8]=>0000110=>0110000
[8,1,2,3,4,5,7,6]=>0000011=>1100000
[6,7,3,8,5,1,2,4]=>0001011=>1101000
[6,7,4,5,1,8,3,2]=>0101011=>1101010
[5,4,7,6,8,1,2,3]=>0001011=>1101000
[5,3,7,8,6,1,2,4]=>0001101=>1011000
[3,8,4,5,7,1,2,6]=>0000011=>1100000
[3,4,8,6,7,1,2,5]=>0000011=>1100000
[4,5,6,7,1,8,3,2]=>0100011=>1100010
[3,5,6,2,7,4,8,1]=>0000111=>1110000
[3,5,6,1,7,8,4,2]=>0010101=>1010100
[2,5,6,1,8,7,4,3]=>0010111=>1110100
[2,5,6,8,1,7,3,4]=>0000011=>1100000
[8,2,4,5,1,6,3,7]=>0001101=>1011000
[1,4,8,6,2,3,7,5]=>0000111=>1110000
[1,5,6,8,2,3,7,4]=>0000011=>1100000
[1,5,6,2,8,4,7,3]=>0000111=>1110000
[2,5,6,3,4,7,8,1]=>0000101=>1010000
[1,4,2,6,8,5,7,3]=>0010011=>1100100
[8,1,3,2,5,4,6,7]=>0101001=>1001010
[8,2,3,1,5,6,4,7]=>0100101=>1010010
[2,8,3,1,5,7,4,6]=>0100011=>1100010
[2,4,1,6,8,7,5,3]=>0011011=>1101100
[3,4,1,6,7,8,5,2]=>0011001=>1001100
[4,3,1,7,6,8,5,2]=>0111011=>1101110
[5,2,7,8,1,6,3,4]=>0001101=>1011000
[5,3,7,2,6,4,8,1]=>0001111=>1111000
[6,7,3,1,5,8,4,2]=>0110011=>1100110
[6,7,2,1,8,5,4,3]=>1011011=>1101101
[6,7,2,8,1,5,3,4]=>0001011=>1101000
[6,7,8,2,1,4,3,5]=>1010001=>1000101
[6,7,1,2,8,4,5,3]=>0001011=>1101000
[6,7,1,3,4,8,5,2]=>0001011=>1101000
[5,2,7,3,4,6,8,1]=>0001011=>1101000
[5,1,7,3,4,8,6,2]=>0001111=>1111000
[5,1,7,8,2,3,6,4]=>0001101=>1011000
[4,1,8,7,2,3,6,5]=>0010111=>1110100
[3,8,1,2,7,4,5,6]=>0000011=>1100000
[4,1,3,7,5,8,6,2]=>0010111=>1110100
[3,1,4,5,7,8,6,2]=>0100101=>1010010
[2,1,8,3,4,7,6,5]=>1000111=>1110001
[8,2,1,3,4,6,5,7]=>1000101=>1010001
[1,8,2,3,4,5,7,6]=>0000011=>1100000
[1,2,8,3,4,6,7,5]=>0000011=>1100000
[4,2,1,6,5,8,7,3]=>1010111=>1110101
[5,2,6,1,4,8,7,3]=>0001111=>1111000
[5,2,6,4,1,8,7,3]=>0011111=>1111100
[5,2,7,4,8,1,6,3]=>0001111=>1111000
[5,2,7,4,8,6,1,3]=>0001111=>1111000
[5,7,2,3,8,6,1,4]=>0000111=>1110000
[5,7,2,3,8,1,6,4]=>0000111=>1110000
[5,6,2,3,1,8,7,4]=>0100111=>1110010
[5,6,2,1,3,8,7,4]=>1000111=>1110001
[5,1,6,4,2,8,7,3]=>0011111=>1111100
[5,6,1,3,2,8,7,4]=>0100111=>1110010
[5,6,3,1,2,8,7,4]=>0100111=>1110010
[5,6,3,2,1,8,7,4]=>1100111=>1110011
[5,7,3,2,8,1,6,4]=>0100111=>1110010
[5,7,3,2,8,6,1,4]=>0100111=>1110010
[6,7,3,8,2,1,5,4]=>1001011=>1101001
[6,7,3,8,1,2,5,4]=>0001011=>1101000
[5,7,3,1,8,2,6,4]=>0100111=>1110010
[5,7,1,3,8,2,6,4]=>0000111=>1110000
[5,1,7,4,8,2,6,3]=>0001111=>1111000
[1,5,7,4,8,3,6,2]=>0000111=>1110000
[1,5,7,4,8,6,3,2]=>0100111=>1110010
[5,1,7,4,8,6,2,3]=>0001111=>1111000
[5,7,1,3,8,6,2,4]=>0000111=>1110000
[5,7,3,1,8,6,2,4]=>0100111=>1110010
[6,7,3,8,1,5,2,4]=>0001011=>1101000
[6,7,3,8,5,2,1,4]=>1001011=>1101001
[6,7,8,3,1,4,2,5]=>0110001=>1000110
[6,7,1,8,3,5,2,4]=>0001011=>1101000
[6,1,7,8,4,5,2,3]=>0001101=>1011000
[1,6,7,8,4,5,3,2]=>0101001=>1001010
[1,6,7,8,4,3,5,2]=>0011001=>1001100
[6,1,7,8,4,2,5,3]=>0011101=>1011100
[6,7,1,8,3,2,5,4]=>0101011=>1101010
[5,7,2,1,8,3,6,4]=>1000111=>1110001
[6,7,2,8,1,3,5,4]=>0001011=>1101000
[6,7,2,8,3,1,5,4]=>0101011=>1101010
[6,7,2,8,3,5,1,4]=>0001011=>1101000
[6,2,7,8,4,5,1,3]=>0001101=>1011000
[6,2,7,8,4,1,5,3]=>0011101=>1011100
[6,2,7,8,1,4,5,3]=>0001101=>1011000
[5,2,7,1,8,4,6,3]=>0001111=>1111000
[4,2,1,7,8,5,6,3]=>1010101=>1010101
[4,1,2,7,8,6,5,3]=>0011101=>1011100
[6,2,7,8,1,5,4,3]=>0011101=>1011100
[6,2,7,8,5,1,4,3]=>0011101=>1011100
[6,2,7,8,5,4,1,3]=>0011101=>1011100
[6,7,2,8,5,3,1,4]=>0101011=>1101010
[5,7,2,1,8,6,3,4]=>1000111=>1110001
[5,7,1,2,8,6,3,4]=>0000111=>1110000
[5,1,7,2,8,6,4,3]=>0011111=>1111100
[1,5,7,3,8,6,4,2]=>0010111=>1110100
[1,6,7,8,3,5,4,2]=>0011001=>1001100
[6,1,7,8,2,5,4,3]=>0011101=>1011100
[6,7,1,8,2,5,3,4]=>0001011=>1101000
[6,7,8,2,4,1,3,5]=>0010001=>1000100
[6,7,8,2,4,3,1,5]=>0110001=>1000110
[6,7,1,8,5,2,3,4]=>0001011=>1101000
[6,1,7,8,5,2,4,3]=>0011101=>1011100
[1,6,7,8,5,3,4,2]=>0011001=>1001100
[6,1,7,8,5,4,2,3]=>0011101=>1011100
[6,7,1,8,5,3,2,4]=>0101011=>1101010
[6,7,8,4,1,3,2,5]=>0110001=>1000110
[6,3,8,5,2,7,4,1]=>0011111=>1111100
[6,5,2,8,4,7,3,1]=>0101111=>1111010
[6,3,4,5,8,7,2,1]=>1000111=>1110001
[3,8,4,7,5,2,1,6]=>1001011=>1101001
[5,8,1,4,7,2,3,6]=>0000011=>1100000
[5,6,1,4,8,7,3,2]=>0100111=>1110010
[3,6,4,8,5,7,1,2]=>0000111=>1110000
[5,1,4,8,6,3,7,2]=>0001111=>1111000
[3,4,7,1,8,6,5,2]=>0001111=>1111000
[6,3,8,4,2,7,1,5]=>0010111=>1110100
[3,6,8,7,1,4,2,5]=>0010011=>1100100
[5,3,7,1,6,8,2,4]=>0001011=>1101000
[4,3,8,5,6,7,2,1]=>1010011=>1100101
[5,8,1,7,6,2,4,3]=>0010111=>1110100
[4,6,1,2,7,8,5,3]=>0001101=>1011000
[3,6,4,2,8,7,5,1]=>0011111=>1111100
[6,3,7,5,2,8,1,4]=>0001111=>1111000
[6,5,2,7,4,8,1,3]=>0001111=>1111000
[5,7,1,4,8,3,2,6]=>0100011=>1100010
[7,8,3,5,1,4,6,2]=>0001101=>1011000
[5,8,1,4,6,7,2,3]=>0000011=>1100000
[6,5,8,4,3,7,2,1]=>1010111=>1110101
[6,3,7,4,2,8,5,1]=>0011111=>1111100
[8,7,1,6,2,4,5,3]=>0001111=>1111000
[3,8,6,7,1,4,5,2]=>0001011=>1101000
[5,3,8,7,4,1,2,6]=>0011011=>1101100
[4,3,8,7,1,5,6,2]=>0010111=>1110100
[8,3,6,1,2,5,7,4]=>0000111=>1110000
[5,6,1,8,7,3,2,4]=>0100111=>1110010
[5,4,2,7,3,6,8,1]=>0011011=>1101100
[7,5,3,6,4,2,8,1]=>0011111=>1111100
[6,4,1,5,3,8,2,7]=>0011101=>1011100
[8,5,2,6,4,7,3,1]=>0101111=>1111010
[8,2,6,3,4,7,5,1]=>0001111=>1111000
[7,2,6,3,5,4,8,1]=>0001111=>1111000
[6,2,7,4,3,5,8,1]=>0010111=>1110100
[5,7,3,6,4,2,8,1]=>0010111=>1110100
[3,7,6,4,5,2,8,1]=>0001111=>1111000
[2,7,6,5,3,4,8,1]=>0001111=>1111000
[6,5,4,3,1,8,2,7]=>0111101=>1011110
[8,6,5,4,2,7,3,1]=>0111111=>1111110
[8,5,4,1,7,2,6,3]=>0011111=>1111100
[7,5,4,1,8,3,2,6]=>0111011=>1101110
[1,6,5,2,8,3,4,7]=>0001101=>1011000
[5,7,4,2,1,8,3,6]=>1010011=>1100101
[1,6,5,3,4,8,2,7]=>0001101=>1011000
[5,4,6,3,1,8,2,7]=>0101101=>1011010
[6,5,8,4,2,7,3,1]=>0110111=>1110110
[5,8,2,6,4,7,3,1]=>0100111=>1110010
[3,8,6,2,5,7,4,1]=>0010111=>1110100
[7,8,5,3,2,6,4,1]=>0111101=>1011110
[6,8,3,1,7,2,5,4]=>0101011=>1101010
[1,8,6,3,7,5,2,4]=>0001111=>1111000
[8,7,5,2,6,4,3,1]=>0111111=>1111110
[8,7,1,6,2,5,4,3]=>0011111=>1111100
[7,8,1,6,3,2,5,4]=>0101101=>1011010
[2,8,1,7,3,5,6,4]=>0000111=>1110000
[3,8,6,1,7,4,5,2]=>0001111=>1111000
[4,8,1,3,7,2,6,5]=>0000111=>1110000
[4,2,8,5,7,3,6,1]=>0010111=>1110100
[5,1,7,6,8,3,2,4]=>0101011=>1101010
[3,7,1,5,8,4,2,6]=>0010011=>1100100
[6,7,3,1,8,4,2,5]=>0110011=>1100110
[1,7,3,8,4,5,2,6]=>0001011=>1101000
[1,7,2,8,5,3,4,6]=>0001011=>1101000
[7,6,1,8,4,3,2,5]=>0110111=>1110110
[8,6,1,7,4,2,5,3]=>0011111=>1111100
[8,1,2,7,3,4,6,5]=>0000111=>1110000
[7,1,2,8,3,5,4,6]=>0001011=>1101000
[7,2,6,1,8,4,3,5]=>0010111=>1110100
[8,2,6,1,7,3,5,4]=>0001111=>1111000
[8,3,1,4,7,5,6,2]=>0100111=>1110010
[7,3,1,5,8,4,2,6]=>0110011=>1100110
[4,2,1,5,8,3,6,7]=>1010001=>1000101
[5,4,2,7,1,8,3,6]=>0011011=>1101100
[5,4,3,1,6,8,2,7]=>0111001=>1001110
[4,7,5,6,8,3,2,1]=>1100011=>1100011
[6,5,4,8,2,7,3,1]=>0101111=>1111010
[6,5,2,8,7,3,4,1]=>0011111=>1111100
[6,5,1,8,7,4,2,3]=>0011111=>1111100
[8,6,4,7,5,3,2,1]=>1101111=>1111011
[5,1,8,3,7,6,2,4]=>0001111=>1111000
[5,4,8,1,7,2,6,3]=>0001111=>1111000
[7,5,8,3,2,6,4,1]=>0110111=>1110110
[3,6,8,2,4,7,5,1]=>0001011=>1101000
[5,7,3,8,2,6,4,1]=>0010111=>1110100
[5,4,6,8,2,7,3,1]=>0101011=>1101010
[5,2,6,8,7,3,4,1]=>0011011=>1101100
[4,7,2,8,6,3,5,1]=>0001111=>1111000
[3,6,8,1,7,2,5,4]=>0001011=>1101000
[2,3,8,7,4,5,6,1]=>0000111=>1110000
[7,2,8,6,4,3,5,1]=>0011111=>1111100
[2,1,8,7,5,6,3,4]=>1000111=>1110001
[8,2,7,6,3,5,4,1]=>0011111=>1111100
[8,1,7,6,5,2,4,3]=>0011111=>1111100
[7,1,8,6,5,3,2,4]=>0101111=>1111010
[1,2,8,7,6,3,4,5]=>0000111=>1110000
[1,3,8,7,4,6,2,5]=>0000111=>1110000
[1,5,8,3,7,6,2,4]=>0000111=>1110000
[5,1,6,8,7,4,2,3]=>0011011=>1101100
[6,8,4,7,5,3,2,1]=>1101011=>1101011
[6,8,7,2,5,4,3,1]=>0111011=>1101110
[3,8,7,6,4,5,2,1]=>1001111=>1111001
[2,8,7,6,5,3,4,1]=>0011111=>1111100
[1,8,7,6,5,4,2,3]=>0011111=>1111100
[5,8,6,7,3,4,1,2]=>0010011=>1100100
[4,8,6,7,3,5,1,2]=>0001011=>1101000
[3,8,6,7,4,5,1,2]=>0001011=>1101000
[2,8,6,7,4,5,1,3]=>0001011=>1101000
[1,8,6,7,4,5,2,3]=>0001011=>1101000
[1,8,5,7,4,6,2,3]=>0000111=>1110000
[3,8,5,7,4,6,1,2]=>0000111=>1110000
[4,8,5,7,3,6,1,2]=>0000111=>1110000
[7,8,3,6,4,5,1,2]=>0001101=>1011000
[6,8,3,7,4,5,1,2]=>0001011=>1101000
[5,8,3,7,4,6,1,2]=>0000111=>1110000
[3,7,4,8,5,6,1,2]=>0000111=>1110000
[4,7,3,8,5,6,1,2]=>0000111=>1110000
[4,7,2,8,5,6,1,3]=>0000111=>1110000
[4,7,1,8,5,6,2,3]=>0000111=>1110000
[3,7,1,8,5,6,2,4]=>0000111=>1110000
[3,7,2,8,5,6,1,4]=>0000111=>1110000
[2,7,3,8,5,6,1,4]=>0000111=>1110000
[2,7,4,8,5,6,1,3]=>0000111=>1110000
[5,8,2,7,4,6,1,3]=>0000111=>1110000
[6,8,2,7,4,5,1,3]=>0001011=>1101000
[7,8,2,6,4,5,1,3]=>0001101=>1011000
[7,8,1,6,4,5,2,3]=>0001101=>1011000
[6,8,1,7,4,5,2,3]=>0001011=>1101000
[5,8,1,7,4,6,2,3]=>0000111=>1110000
[1,7,4,8,5,6,2,3]=>0000111=>1110000
[1,7,3,8,5,6,2,4]=>0000111=>1110000
[2,8,5,6,1,7,3,4]=>0000111=>1110000
[1,8,5,6,2,7,3,4]=>0000111=>1110000
[1,7,3,8,4,6,2,5]=>0000111=>1110000
[4,8,1,7,3,6,2,5]=>0000111=>1110000
[5,8,1,7,3,6,2,4]=>0000111=>1110000
[6,8,1,7,3,5,2,4]=>0001011=>1101000
[7,8,2,6,3,5,1,4]=>0001101=>1011000
[6,8,2,7,3,5,1,4]=>0001011=>1101000
[5,8,2,7,3,6,1,4]=>0000111=>1110000
[4,8,2,7,3,6,1,5]=>0000111=>1110000
[2,7,3,8,4,6,1,5]=>0000111=>1110000
[3,7,2,8,4,6,1,5]=>0000111=>1110000
[3,7,1,8,4,6,2,5]=>0000111=>1110000
[1,8,4,7,3,6,2,5]=>0000111=>1110000
[2,8,4,7,3,6,1,5]=>0000111=>1110000
[3,8,4,7,2,6,1,5]=>0000111=>1110000
[4,8,5,7,2,6,1,3]=>0000111=>1110000
[3,8,5,7,2,6,1,4]=>0000111=>1110000
[2,8,5,7,3,6,1,4]=>0000111=>1110000
[1,8,5,7,3,6,2,4]=>0000111=>1110000
[1,8,6,7,3,5,2,4]=>0001011=>1101000
[2,8,6,7,3,5,1,4]=>0001011=>1101000
[3,8,6,7,2,5,1,4]=>0001011=>1101000
[4,8,6,7,2,5,1,3]=>0001011=>1101000
[5,8,6,7,2,4,1,3]=>0010011=>1100100
[6,8,5,7,1,4,2,3]=>0010011=>1100100
[5,8,6,7,1,4,2,3]=>0010011=>1100100
[4,8,6,7,1,5,2,3]=>0001011=>1101000
[3,8,6,7,1,5,2,4]=>0001011=>1101000
[1,5,2,8,6,7,3,4]=>0001011=>1101000
[2,5,1,8,6,7,3,4]=>0001011=>1101000
[2,6,1,8,5,7,3,4]=>0000111=>1110000
[1,6,2,8,5,7,3,4]=>0000111=>1110000
[3,8,5,7,1,6,2,4]=>0000111=>1110000
[6,8,4,7,1,5,2,3]=>0001011=>1101000
[7,8,4,6,1,5,2,3]=>0001101=>1011000
[7,8,3,6,1,5,2,4]=>0001101=>1011000
[6,8,3,7,1,5,2,4]=>0001011=>1101000
[4,8,3,7,1,6,2,5]=>0000111=>1110000
[3,8,4,7,1,6,2,5]=>0000111=>1110000
[1,6,2,8,4,7,3,5]=>0000111=>1110000
[2,6,1,8,4,7,3,5]=>0000111=>1110000
[3,7,2,6,1,8,4,5]=>0000111=>1110000
[3,7,1,6,2,8,4,5]=>0000111=>1110000
[4,8,1,6,2,7,3,5]=>0000111=>1110000
[5,8,1,6,2,7,3,4]=>0000111=>1110000
[7,8,1,5,2,6,3,4]=>0001101=>1011000
[7,8,2,5,1,6,3,4]=>0001101=>1011000
[6,8,2,5,1,7,3,4]=>0001011=>1101000
[5,8,2,6,1,7,3,4]=>0000111=>1110000
[4,8,2,6,1,7,3,5]=>0000111=>1110000
[1,7,3,6,2,8,4,5]=>0000111=>1110000
[2,7,3,6,1,8,4,5]=>0000111=>1110000
[1,2,3,4,5,6,7,8,9]=>00000000=>00000000
[1,2,3,4,5,6,8,9,7]=>00000001=>10000000
[1,2,3,4,5,7,8,9,6]=>00000001=>10000000
[1,2,3,4,6,7,8,9,5]=>00000001=>10000000
[1,2,3,5,6,7,8,9,4]=>00000001=>10000000
[1,2,4,5,6,7,8,9,3]=>00000001=>10000000
[1,3,4,5,6,7,8,9,2]=>00000001=>10000000
[1,2,3,4,5,6,7,8,9,10]=>000000000=>000000000
[1,2,3,4,5,6,9,8,7]=>00000011=>11000000
[1,2,3,4,5,6,7,9,10,8]=>000000001=>100000000
[1,2,3,4,5,8,7,9,6]=>00000011=>11000000
[1,2,3,4,5,6,8,9,10,7]=>000000001=>100000000
[1,2,3,4,7,6,8,9,5]=>00000101=>10100000
[1,2,3,4,5,7,8,9,10,6]=>000000001=>100000000
[1,2,3,6,5,7,8,9,4]=>00001001=>10010000
[1,2,3,4,6,7,8,9,10,5]=>000000001=>100000000
[1,2,5,4,6,7,8,9,3]=>00010001=>10001000
[1,2,3,5,6,7,8,9,10,4]=>000000001=>100000000
[1,4,3,5,6,7,8,9,2]=>00100001=>10000100
[1,2,4,5,6,7,8,9,10,3]=>000000001=>100000000
[3,2,4,5,6,7,8,9,1]=>01000001=>10000010
[1,3,4,5,6,7,8,9,10,2]=>000000001=>100000000
[6,7,4,8,3,5,1,2]=>0001011=>1101000
[6,7,4,5,2,8,1,3]=>0001011=>1101000
[5,7,4,6,2,3,1,8]=>0100110=>0110010
[5,7,4,6,3,8,1,2]=>0000111=>1110000
[5,7,4,8,3,6,1,2]=>0000111=>1110000
[6,8,4,5,3,7,1,2]=>0001011=>1101000
[5,8,4,6,3,7,1,2]=>0000111=>1110000
[5,6,4,8,3,7,1,2]=>0000111=>1110000
[5,6,3,7,2,4,1,8]=>0010110=>0110100
[5,6,3,7,2,8,1,4]=>0000111=>1110000
[5,6,3,8,2,7,1,4]=>0000111=>1110000
[5,6,4,8,2,7,1,3]=>0000111=>1110000
[5,8,4,6,2,7,1,3]=>0000111=>1110000
[6,8,4,5,2,7,1,3]=>0001011=>1101000
[7,8,4,5,2,6,1,3]=>0001101=>1011000
[6,8,4,5,2,3,1,7]=>0101001=>1001010
[5,8,4,6,2,3,1,7]=>0100101=>1010010
[5,6,4,8,2,3,1,7]=>0100101=>1010010
[5,6,3,8,2,4,1,7]=>0010101=>1010100
[5,6,3,4,2,8,1,7]=>0010101=>1010100
[4,6,3,5,2,7,1,8]=>0001110=>0111000
[4,6,3,5,2,8,1,7]=>0001101=>1011000
[4,6,3,8,2,5,1,7]=>0001101=>1011000
[4,8,3,6,2,5,1,7]=>0001101=>1011000
[5,8,3,6,2,4,1,7]=>0010101=>1010100
[6,8,3,5,2,4,1,7]=>0011001=>1001100
[7,8,3,5,2,4,1,6]=>0011001=>1001100
[7,8,3,5,2,6,1,4]=>0001101=>1011000
[5,8,3,6,2,7,1,4]=>0000111=>1110000
[4,8,3,6,2,7,1,5]=>0000111=>1110000
[4,6,3,8,2,7,1,5]=>0000111=>1110000
[4,6,3,7,2,8,1,5]=>0000111=>1110000
[4,7,3,6,2,5,1,8]=>0001110=>0111000
[4,7,3,6,2,8,1,5]=>0000111=>1110000
[4,7,3,8,2,6,1,5]=>0000111=>1110000
[5,7,4,8,2,6,1,3]=>0000111=>1110000
[5,7,3,6,2,8,1,4]=>0000111=>1110000
[5,7,3,6,2,4,1,8]=>0010110=>0110100
[6,7,3,5,2,4,1,8]=>0011010=>0101100
[6,7,3,5,2,8,1,4]=>0001011=>1101000
[6,7,4,8,2,5,1,3]=>0001011=>1101000
[6,7,5,8,2,4,1,3]=>0010011=>1100100
[6,8,5,7,2,3,1,4]=>0100011=>1100010
[6,7,4,8,2,3,1,5]=>0100011=>1100010
[6,7,3,8,2,4,1,5]=>0010011=>1100100
[6,7,3,4,2,8,1,5]=>0010011=>1100100
[5,7,3,4,2,6,1,8]=>0010110=>0110100
[5,7,3,4,2,8,1,6]=>0010011=>1100100
[5,7,4,8,2,3,1,6]=>0100011=>1100010
[5,8,4,7,2,3,1,6]=>0100011=>1100010
[6,8,4,7,2,3,1,5]=>0100011=>1100010
[7,8,4,6,2,3,1,5]=>0100101=>1010010
[7,8,3,6,2,4,1,5]=>0010101=>1010100
[6,8,3,7,2,4,1,5]=>0010011=>1100100
[5,8,3,7,2,4,1,6]=>0010011=>1100100
[4,8,3,7,2,5,1,6]=>0001011=>1101000
[4,7,3,8,2,5,1,6]=>0001011=>1101000
[4,7,3,5,2,8,1,6]=>0001011=>1101000
[4,7,3,5,2,6,1,8]=>0001110=>0111000
[4,5,3,7,2,6,1,8]=>0001110=>0111000
[4,5,3,7,2,8,1,6]=>0001011=>1101000
[4,5,3,8,2,7,1,6]=>0001011=>1101000
[4,8,3,5,2,7,1,6]=>0001011=>1101000
[5,8,3,4,2,7,1,6]=>0010011=>1100100
[6,8,3,4,2,7,1,5]=>0010011=>1100100
[7,8,3,4,2,6,1,5]=>0010101=>1010100
[6,8,3,4,2,5,1,7]=>0011001=>1001100
[5,8,3,4,2,6,1,7]=>0010101=>1010100
[4,8,3,5,2,6,1,7]=>0001101=>1011000
[4,5,3,8,2,6,1,7]=>0001101=>1011000
[4,5,3,6,2,8,1,7]=>0001101=>1011000
[4,7,5,2,1,8,3,6]=>1001011=>1101001
[4,8,5,2,1,7,6,3]=>1001111=>1111001
[4,6,5,2,1,3,8,7]=>1001101=>1011001
[5,6,4,2,3,1,8,7]=>0110101=>1010110
[6,4,5,3,1,2,8,7]=>0101101=>1011010
[5,4,6,1,3,2,8,7]=>0101101=>1011010
[4,6,8,1,7,3,2,5]=>0100011=>1100010
[4,7,8,1,6,3,5,2]=>0001101=>1011000
[7,4,8,1,6,5,3,2]=>0101111=>1111010
[5,4,8,1,3,7,6,2]=>0001111=>1111000
[8,4,5,3,1,7,6,2]=>0101111=>1111010
[5,4,7,1,3,8,2,6]=>0001011=>1101000
[6,4,8,1,7,5,2,3]=>0001111=>1111000
[5,6,8,7,2,1,3,4]=>1000011=>1100001
[8,5,7,6,4,2,1,3]=>1010111=>1110101
[8,4,6,3,7,2,1,5]=>1000111=>1110001
[6,3,2,8,7,4,1,5]=>0110111=>1110110
[2,1,6,8,7,4,3,5]=>1010011=>1100101
[2,1,7,8,6,4,5,3]=>1001101=>1011001
[7,3,2,8,6,4,5,1]=>0101111=>1111010
[7,6,8,5,2,4,3,1]=>0111011=>1101110
[5,7,8,6,2,3,1,4]=>0100101=>1010010
[5,8,7,6,3,2,1,4]=>1100111=>1110011
[6,8,7,5,3,2,4,1]=>0111011=>1101110
[5,8,4,2,3,7,6,1]=>0010111=>1110100
[7,8,4,2,6,5,3,1]=>0111101=>1011110
[4,8,7,2,6,3,5,1]=>0001111=>1111000
[4,8,6,2,7,3,1,5]=>0100111=>1110010
[3,6,1,8,7,4,2,5]=>0010111=>1110100
[3,7,1,8,6,4,5,2]=>0001111=>1111000
[3,8,1,6,7,5,2,4]=>0001011=>1101000
[3,7,1,6,8,2,5,4]=>0001011=>1101000
[4,7,6,2,8,1,3,5]=>0000111=>1110000
[6,7,4,2,8,1,5,3]=>0011011=>1101100
[6,8,4,2,7,5,1,3]=>0011011=>1101100
[2,1,8,6,7,5,3,4]=>1001011=>1101001
[8,3,2,6,7,5,1,4]=>0101011=>1101010
[8,6,4,3,7,5,1,2]=>0011111=>1111100
[5,8,6,7,3,1,2,4]=>0100011=>1100010
[6,7,5,8,1,3,4,2]=>0010011=>1100100
[7,6,5,8,1,4,3,2]=>0110111=>1110110
[8,6,5,7,4,1,3,2]=>0110111=>1110110
[7,6,4,3,8,1,5,2]=>0011111=>1111100
[7,3,2,6,8,1,5,4]=>0101011=>1101010
[2,1,7,6,8,3,5,4]=>1001011=>1101001
[7,5,6,8,1,4,2,3]=>0010011=>1100100
[6,5,7,8,1,2,4,3]=>0010101=>1010100
[8,1,3,7,4,6,5,2]=>0001111=>1111000
[5,2,8,7,4,6,1,3]=>0001111=>1111000
[1,6,2,5,4,7,3,8]=>0001110=>0111000
[6,2,7,5,4,8,3,1]=>0101111=>1111010
[8,1,3,5,4,7,6,2]=>0001111=>1111000
[6,1,5,4,3,8,7,2]=>0011111=>1111100
[6,1,8,3,4,5,7,2]=>0000111=>1110000
[7,1,5,3,4,8,6,2]=>0001111=>1111000
[7,1,4,3,5,6,8,2]=>0010011=>1100100
[8,1,3,4,5,6,7,2]=>0000011=>1100000
[1,7,2,4,5,6,3,8]=>0000110=>0110000
[6,3,2,7,5,1,8,4]=>0101111=>1111010
[8,4,7,2,5,6,1,3]=>0000111=>1110000
[6,5,8,2,4,7,3,1]=>0100111=>1110010
[8,5,2,1,4,3,7,6]=>1011011=>1101101
[6,5,2,8,4,1,3,7]=>0011101=>1011100
[5,6,2,1,4,8,3,7]=>1000101=>1010001
[3,6,1,8,5,2,4,7]=>0001101=>1011000
[1,2,6,3,5,4,7,8]=>0001100=>0011000
[3,4,1,2,8,6,5,7]=>0010101=>1010100
[4,3,1,2,6,8,5,7]=>0110001=>1000110
[5,8,1,6,3,2,4,7]=>0100101=>1010010
[6,3,8,5,2,1,4,7]=>1001101=>1011001
[8,3,1,5,2,4,7,6]=>0101011=>1101010
[3,8,2,6,1,5,7,4]=>0000111=>1110000
[3,8,6,7,2,1,5,4]=>1001011=>1101001
[8,5,6,4,2,1,7,3]=>1010111=>1110101
[7,2,5,8,3,1,6,4]=>0100111=>1110010
[1,7,5,6,3,2,4,8]=>0100110=>0110010
[6,1,2,3,8,5,7,4]=>0000111=>1110000
[7,1,2,3,6,5,8,4]=>0000111=>1110000
[7,2,1,3,8,6,4,5]=>1000111=>1110001
[1,5,7,3,2,4,6,8]=>0100010=>0100010
[5,2,7,3,1,8,4,6]=>0101011=>1101010
[5,8,2,4,1,3,7,6]=>0010011=>1100100
[8,7,2,6,3,4,1,5]=>0010111=>1110100
[4,8,1,6,3,2,7,5]=>0100111=>1110010
[3,1,8,6,4,2,7,5]=>0110111=>1110110
[8,1,6,7,4,3,2,5]=>0110011=>1100110
[3,5,8,7,2,4,1,6]=>0010011=>1100100
[4,2,1,3,7,8,5,6]=>1010001=>1000101
[2,4,1,3,8,7,5,6]=>0010011=>1100100
[2,5,8,3,1,7,4,6]=>0100011=>1100010
[8,6,1,3,7,2,4,5]=>0000111=>1110000
[2,8,1,3,6,4,7,5]=>0000111=>1110000
[6,8,2,3,4,1,5,7]=>0010001=>1000100
[5,1,8,3,2,4,6,7]=>0101001=>1001010
[9,8,7,6,5,4,3,2,1]=>11111111=>11111111
[8,9,7,6,5,4,3,2,1]=>11111101=>10111111
[8,7,9,6,5,4,3,2,1]=>11111011=>11011111
[8,7,6,9,5,4,3,2,1]=>11110111=>11101111
[8,7,6,5,9,4,3,2,1]=>11101111=>11110111
[8,7,6,5,4,9,3,2,1]=>11011111=>11111011
[8,7,6,5,4,3,9,2,1]=>10111111=>11111101
[8,7,6,5,4,3,2,9,1]=>01111111=>11111110
[8,7,6,5,4,3,2,1,9]=>11111110=>01111111
[9,10,8,7,6,5,4,3,2,1]=>111111101=>101111111
[7,8,9,6,5,4,3,2,1]=>11111001=>10011111
[9,8,10,7,6,5,4,3,2,1]=>111111011=>110111111
[8,6,7,9,5,4,3,2,1]=>11110011=>11001111
[9,8,7,10,6,5,4,3,2,1]=>111110111=>111011111
[8,7,5,6,9,4,3,2,1]=>11100111=>11100111
[9,8,7,6,10,5,4,3,2,1]=>111101111=>111101111
[8,7,6,4,5,9,3,2,1]=>11001111=>11110011
[9,8,7,6,5,10,4,3,2,1]=>111011111=>111110111
[8,7,6,5,3,4,9,2,1]=>10011111=>11111001
[9,8,7,6,5,4,10,3,2,1]=>110111111=>111111011
[8,7,6,5,4,2,3,9,1]=>00111111=>11111100
[9,8,7,6,5,4,3,10,2,1]=>101111111=>111111101
[8,7,6,5,4,3,1,2,9]=>01111110=>01111110
[9,8,7,6,5,4,3,2,10,1]=>011111111=>111111110
[9,8,7,6,5,4,3,2,1,10]=>111111110=>011111111
[1,4,2,7,8,6,3,5]=>0010101=>1010100
[1,6,2,4,8,5,3,7]=>0001101=>1011000
[1,6,2,4,7,5,3,8]=>0001110=>0111000
[1,7,3,8,5,2,4,6]=>0001011=>1101000
[1,7,3,2,8,6,4,5]=>0100111=>1110010
[4,2,5,7,8,6,1,3]=>0010101=>1010100
[7,2,3,1,8,5,6,4]=>0100111=>1110010
[8,2,5,1,7,3,4,6]=>0001011=>1101000
[6,2,1,8,3,4,7,5]=>1000111=>1110001
[6,2,8,3,5,1,7,4]=>0001111=>1111000
[6,2,4,8,5,7,1,3]=>0000111=>1110000
[1,3,6,4,8,5,7,2]=>0000111=>1110000
[1,3,6,4,7,5,8,2]=>0000111=>1110000
[6,2,4,7,5,8,1,3]=>0000111=>1110000
[6,2,1,3,7,8,4,5]=>1000101=>1010001
[7,8,2,1,4,3,5,6]=>1010001=>1000101
[7,6,4,2,3,1,8,5]=>0110111=>1110110
[5,7,2,3,1,6,8,4]=>0100011=>1100010
[7,5,4,2,6,8,1,3]=>0011011=>1101100
[1,7,5,3,4,6,8,2]=>0001011=>1101000
[8,2,5,4,6,7,1,3]=>0001011=>1101000
[5,2,6,3,1,8,7,4]=>0101111=>1111010
[8,2,6,4,3,1,7,5]=>0110111=>1110110
[8,2,7,4,1,3,5,6]=>0010011=>1100100
[1,2,8,4,3,5,6,7]=>0010001=>1000100
[1,7,4,2,3,5,6,8]=>0010010=>0100100
[6,8,4,1,3,2,5,7]=>0110001=>1000110
[1,8,7,4,3,2,5,6]=>0110011=>1100110
[1,6,3,8,2,4,7,5]=>0000111=>1110000
[5,3,8,1,2,7,4,6]=>0001011=>1101000
[5,1,8,3,2,6,4,7]=>0101101=>1011010
[5,7,3,1,2,6,4,8]=>0100110=>0110010
[1,7,5,4,2,6,3,8]=>0011110=>0111100
[1,5,8,2,4,6,3,7]=>0000101=>1010000
[1,5,8,4,2,7,3,6]=>0010011=>1100100
[1,4,6,2,8,3,7,5]=>0000111=>1110000
[5,3,1,6,7,2,4,8]=>0101010=>0101010
[5,3,6,1,2,8,4,7]=>0001101=>1011000
[1,6,3,2,7,8,4,5]=>0100101=>1010010
[1,7,4,5,3,8,6,2]=>0001111=>1111000
[6,3,4,1,2,5,8,7]=>0010101=>1010100
[6,3,1,4,2,7,5,8]=>0110110=>0110110
[1,8,3,2,4,5,6,7]=>0100001=>1000010
[8,6,3,2,4,1,7,5]=>0110111=>1110110
[8,5,3,2,6,7,1,4]=>0101011=>1101010
[4,5,2,6,8,1,7,3]=>0001011=>1101000
[4,2,5,6,7,8,1,3]=>0010001=>1000100
[5,2,3,6,7,1,8,4]=>0001011=>1101000
[6,2,3,4,1,7,8,5]=>0010101=>1010100
[7,2,3,1,4,5,8,6]=>0100011=>1100010
[8,6,1,4,3,2,5,7]=>0110101=>1010110
[8,3,1,6,5,2,4,7]=>0101101=>1011010
[3,7,5,1,8,2,4,6]=>0001011=>1101000
[4,1,5,2,8,7,3,6]=>0011011=>1101100
[8,1,2,4,6,5,3,7]=>0001101=>1011000
[8,1,2,5,4,6,3,7]=>0001101=>1011000
[8,2,6,5,1,3,4,7]=>0001101=>1011000
[8,3,1,6,2,5,4,7]=>0101101=>1011010
[8,1,2,6,4,5,3,7]=>0001101=>1011000
[8,1,2,5,6,4,3,7]=>0010101=>1010100
[8,1,2,6,5,4,3,7]=>0011101=>1011100
[1,7,5,4,2,8,3,6]=>0011011=>1101100
[5,1,4,8,2,7,3,6]=>0001011=>1101000
[1,4,6,8,2,7,3,5]=>0000011=>1100000
[1,4,7,6,2,8,3,5]=>0000111=>1110000
[5,1,4,7,2,8,3,6]=>0001011=>1101000
[1,7,4,5,2,8,3,6]=>0001011=>1101000
[3,7,5,1,2,8,4,6]=>0001011=>1101000
[5,7,2,8,1,3,4,6]=>0000011=>1100000
[5,2,8,7,1,3,4,6]=>0001011=>1101000
[4,1,5,8,2,7,3,6]=>0010011=>1100100
[1,4,6,2,8,7,3,5]=>0000111=>1110000
[1,4,2,8,6,7,3,5]=>0010011=>1100100
[3,1,2,6,4,8,7,5]=>0100111=>1110010
[2,1,7,6,3,4,8,5]=>1000111=>1110001
[3,1,2,7,4,6,8,5]=>0100011=>1100010
[1,4,7,2,6,8,3,5]=>0000011=>1100000
[1,2,3,6,8,5,7,4]=>0000011=>1100000
[5,1,4,2,7,8,3,6]=>0011001=>1001100
[1,4,2,7,6,8,3,5]=>0010011=>1100100
[1,4,2,6,8,7,3,5]=>0010011=>1100100
[3,1,2,8,4,6,7,5]=>0100011=>1100010
[3,1,2,7,6,4,8,5]=>0100111=>1110010
[5,3,7,1,8,2,4,6]=>0001011=>1101000
[1,7,4,3,2,5,8,6]=>0110011=>1100110
[4,8,7,2,1,3,5,6]=>1000011=>1100001
[1,8,7,3,4,2,5,6]=>0010011=>1100100
[3,1,7,8,2,6,4,5]=>0100101=>1010010
[1,4,2,7,8,3,6,5]=>0010101=>1010100
[5,2,8,1,3,4,7,6]=>0001011=>1101000
[2,1,8,6,3,4,7,5]=>1000111=>1110001
[1,4,2,6,8,3,7,5]=>0010011=>1100100
[1,2,3,7,8,5,6,4]=>0000101=>1010000
[1,2,3,7,5,8,6,4]=>0000111=>1110000
[1,4,2,7,3,8,6,5]=>0010111=>1110100
[3,1,7,2,8,6,4,5]=>0100111=>1110010
[2,1,7,8,3,4,6,5]=>1000101=>1010001
[1,2,3,8,7,5,6,4]=>0000111=>1110000
[10,1,2,3,4,5,6,7,8,9]=>000000001=>100000000
[10,1,2,3,4,5,6,9,7,8]=>000000011=>110000000
[10,1,2,3,4,5,9,6,7,8]=>000000011=>110000000
[9,1,2,3,4,10,5,6,7,8]=>000000011=>110000000
[10,1,2,3,9,4,5,6,7,8]=>000000011=>110000000
[10,1,2,9,3,4,5,6,7,8]=>000000011=>110000000
[9,1,10,2,3,4,5,6,7,8]=>000000011=>110000000
[10,9,1,2,3,4,5,6,7,8]=>000000011=>110000000
[11,1,2,3,4,5,6,7,8,9,10]=>0000000001=>1000000000
[10,1,2,3,4,5,6,7,8,11,9]=>0000000011=>1100000000
[8,1,2,3,4,5,6,9,10,7]=>000000101=>101000000
[11,1,2,3,4,5,6,7,10,8,9]=>0000000011=>1100000000
[7,1,2,3,4,5,10,9,6,8]=>000001011=>110100000
[11,1,2,3,4,5,6,10,7,8,9]=>0000000011=>1100000000
[6,1,2,3,4,10,9,5,7,8]=>000010011=>110010000
[10,1,2,3,4,5,11,6,7,8,9]=>0000000011=>1100000000
[5,1,2,3,9,10,4,6,7,8]=>000100001=>100001000
[11,1,2,3,4,10,5,6,7,8,9]=>0000000011=>1100000000
[4,1,2,10,9,3,5,6,7,8]=>001000011=>110000100
[11,1,2,3,10,4,5,6,7,8,9]=>0000000011=>1100000000
[3,1,10,9,2,4,5,6,7,8]=>010000011=>110000010
[10,1,2,11,3,4,5,6,7,8,9]=>0000000011=>1100000000
[2,9,10,1,3,4,5,6,7,8]=>000000001=>100000000
[11,1,10,2,3,4,5,6,7,8,9]=>0000000011=>1100000000
[11,10,1,2,3,4,5,6,7,8,9]=>0000000011=>1100000000
[4,7,8,5,6,2,1,3]=>1000101=>1010001
[5,7,8,4,2,6,1,3]=>0010101=>1010100
[6,7,8,4,2,5,1,3]=>0011001=>1001100
[8,6,3,7,2,1,5,4]=>1001111=>1111001
[7,6,3,8,2,1,5,4]=>1001111=>1111001
[6,7,8,3,2,1,5,4]=>1101001=>1001011
[5,7,8,3,2,1,6,4]=>1100101=>1010011
[2,7,8,4,3,5,6,1]=>0010101=>1010100
[3,7,8,4,2,5,1,6]=>0011001=>1001100
[4,7,8,3,2,1,5,6]=>1100001=>1000011
[5,7,8,3,2,1,4,6]=>1100001=>1000011
[7,6,3,8,2,1,4,5]=>1000111=>1110001
[8,6,3,7,2,1,4,5]=>1000111=>1110001
[5,6,3,8,2,1,4,7]=>1000101=>1010001
[3,6,4,8,2,5,1,7]=>0001101=>1011000
[2,6,4,8,3,5,7,1]=>0000111=>1110000
[2,6,4,7,3,5,8,1]=>0000111=>1110000
[3,6,4,7,2,5,1,8]=>0001110=>0111000
[4,6,3,7,2,1,5,8]=>1000110=>0110001
[5,6,3,7,2,1,4,8]=>1000110=>0110001
[8,4,3,2,1,6,5,7]=>1110101=>1010111
[6,4,3,2,1,7,5,8]=>1110110=>0110111
[4,5,3,2,7,1,6,8]=>0101010=>0101010
[3,5,4,2,8,6,1,7]=>0011101=>1011100
[6,4,3,2,1,8,5,7]=>1110101=>1010111
[7,4,3,2,1,8,5,6]=>1110011=>1100111
[8,4,3,2,1,7,5,6]=>1110011=>1100111
[8,4,3,2,1,7,6,5]=>1110111=>1110111
[7,4,3,2,1,8,6,5]=>1110111=>1110111
[6,4,3,2,1,8,7,5]=>1110111=>1110111
[5,6,3,8,2,1,7,4]=>1000111=>1110001
[7,5,3,2,8,1,6,4]=>0101111=>1111010
[8,5,4,2,7,6,1,3]=>0011111=>1111100
[7,5,4,2,8,6,1,3]=>0011111=>1111100
[6,5,4,2,8,7,1,3]=>0011111=>1111100
[4,6,5,8,7,2,1,3]=>1000111=>1110001
[2,6,5,7,8,3,4,1]=>0010101=>1010100
[6,5,4,2,7,8,1,3]=>0011101=>1011100
[8,5,4,2,6,7,1,3]=>0011011=>1101100
[8,5,3,2,6,1,7,4]=>0101111=>1111010
[7,5,3,2,6,1,8,4]=>0101111=>1111010
[5,6,3,7,2,1,8,4]=>1000111=>1110001
[4,6,3,7,2,1,8,5]=>1000111=>1110001
[3,6,4,7,2,8,1,5]=>0000111=>1110000
[2,6,4,7,3,8,5,1]=>0001111=>1111000
[3,5,4,2,7,8,1,6]=>0011001=>1001100
[4,5,3,2,7,1,8,6]=>0101011=>1101010
[7,4,3,2,1,6,8,5]=>1110011=>1100111
[8,4,3,2,1,6,7,5]=>1110011=>1100111
[8,4,3,2,1,5,7,6]=>1110011=>1100111
[7,4,3,2,1,5,8,6]=>1110011=>1100111
[6,4,3,2,1,5,8,7]=>1110101=>1010111
[3,5,4,2,6,8,1,7]=>0011001=>1001100
[5,6,3,4,1,2,8,7]=>0010101=>1010100
[8,5,3,7,2,6,4,1]=>0011111=>1111100
[8,5,7,4,2,6,3,1]=>0110111=>1110110
[7,5,8,4,2,6,1,3]=>0010111=>1110100
[2,1,7,8,5,6,3,4]=>1000101=>1010001
[6,8,3,7,5,1,4,2]=>0011011=>1101100
[5,7,3,8,1,6,2,4]=>0000111=>1110000
[3,2,6,4,8,5,1,7]=>0101101=>1011010
[3,2,5,8,4,6,1,7]=>0100101=>1010010
[3,5,2,4,1,7,6,8]=>0011010=>0101100
[4,2,1,5,7,3,6,8]=>1010010=>0100101
[4,5,2,3,7,1,6,8]=>0001010=>0101000
[4,2,5,3,8,1,6,7]=>0011001=>1001100
[4,2,5,8,3,1,6,7]=>0110001=>1000110
[3,1,5,4,2,8,6,7]=>0111001=>1001110
[4,1,5,3,8,2,6,7]=>0011001=>1001100
[4,1,5,8,3,2,6,7]=>0110001=>1000110
[4,3,8,5,2,1,6,7]=>1011001=>1001101
[4,7,3,5,2,1,6,8]=>1001010=>0101001
[4,3,2,7,5,1,6,8]=>0111010=>0101110
[4,3,6,2,5,1,7,8]=>0011100=>0011100
[4,6,3,2,5,1,7,8]=>0101100=>0011010
[4,6,7,1,3,2,5,8]=>0100010=>0100010
[4,5,1,7,3,2,6,8]=>0101010=>0101010
[4,5,1,3,7,2,6,8]=>0001010=>0101000
[3,5,1,4,2,7,6,8]=>0011010=>0101100
[2,5,1,4,3,7,8,6]=>0011001=>1001100
[5,2,1,4,3,7,8,6]=>1011001=>1001101
[5,3,1,4,2,7,6,8]=>0111010=>0101110
[4,3,1,5,7,2,6,8]=>0110010=>0100110
[4,3,1,7,5,2,6,8]=>0111010=>0101110
[4,3,6,1,5,2,7,8]=>0011100=>0011100
[4,6,3,1,5,2,7,8]=>0101100=>0011010
[5,3,6,4,1,2,7,8]=>0011100=>0011100
[4,3,6,1,7,2,5,8]=>0010110=>0110100
[6,3,4,1,2,7,5,8]=>0010110=>0110100
[6,2,4,1,3,7,8,5]=>0010101=>1010100
[3,6,4,1,2,7,5,8]=>0010110=>0110100
[4,6,3,1,7,2,5,8]=>0100110=>0110010
[5,3,6,2,1,4,7,8]=>1001100=>0011001
[5,6,2,7,1,3,4,8]=>0000110=>0110000
[4,5,2,7,3,1,6,8]=>0101010=>0101010
[4,6,7,2,3,1,5,8]=>0100010=>0100010
[4,6,2,1,7,3,5,8]=>1000110=>0110001
[3,2,6,1,4,7,5,8]=>0100110=>0110010
[3,6,2,1,4,7,5,8]=>1000110=>0110001
[3,6,7,2,4,5,1,8]=>0001010=>0101000
[3,5,2,7,4,6,1,8]=>0001110=>0111000
[3,7,2,4,8,5,1,6]=>0001011=>1101000
[7,2,1,4,6,3,8,5]=>1000111=>1110001
[7,3,1,4,6,8,2,5]=>0100011=>1100010
[3,2,6,1,5,7,4,8]=>0100110=>0110010
[3,6,2,1,5,7,4,8]=>1000110=>0110001
[6,3,2,1,5,7,4,8]=>1100110=>0110011
[6,4,2,1,5,3,7,8]=>1011100=>0011101
[4,2,6,1,5,3,7,8]=>0011100=>0011100
[4,2,1,7,5,3,6,8]=>1011010=>0101101
[7,4,1,5,6,2,3,8]=>0010110=>0110100
[7,3,1,5,2,6,4,8]=>0101110=>0111010
[7,2,1,5,3,6,8,4]=>1001011=>1101001
[6,2,5,1,3,7,8,4]=>0001101=>1011000
[6,3,5,1,2,7,4,8]=>0001110=>0111000
[6,4,5,1,7,2,3,8]=>0001110=>0111000
[5,2,6,4,1,3,7,8]=>0011100=>0011100
[4,6,5,1,7,2,3,8]=>0001110=>0111000
[3,6,5,1,2,7,4,8]=>0001110=>0111000
[6,5,2,1,4,7,8,3]=>1001101=>1011001
[6,5,3,1,4,7,2,8]=>0101110=>0111010
[2,3,1,8,5,4,7,6]=>0101011=>1101010
[2,4,1,5,8,3,7,6]=>0010011=>1100100
[2,4,1,5,3,8,7,6]=>0011011=>1101100
[3,4,5,1,2,8,7,6]=>0001011=>1101000
[3,4,5,1,8,2,7,6]=>0001011=>1101000
[1,8,4,5,3,2,7,6]=>0101011=>1101010
[2,4,8,5,3,1,7,6]=>0101011=>1101010
[3,4,5,8,2,1,7,6]=>1000011=>1100001
[3,4,5,2,8,1,7,6]=>0001011=>1101000
[3,4,6,2,1,7,8,5]=>1000101=>1010001
[3,4,6,2,1,7,5,8]=>1000110=>0110001
[3,5,6,2,7,1,4,8]=>0000110=>0110000
[3,5,6,2,7,1,8,4]=>0000111=>1110000
[3,5,6,2,7,8,1,4]=>0000101=>1010000
[3,4,6,2,8,7,1,5]=>0000111=>1110000
[3,4,6,8,2,7,1,5]=>0000011=>1100000
[2,4,8,6,3,7,1,5]=>0000111=>1110000
[1,8,4,6,3,7,2,5]=>0000111=>1110000
[1,8,4,6,3,7,5,2]=>0001111=>1111000
[3,4,6,8,2,7,5,1]=>0001011=>1101000
[3,4,6,2,8,7,5,1]=>0001111=>1111000
[3,5,6,2,7,8,4,1]=>0010101=>1010100
[3,5,6,2,7,4,1,8]=>0010110=>0110100
[4,5,6,7,2,8,3,1]=>0100011=>1100010
[3,5,6,8,7,2,4,1]=>0010011=>1100100
[2,5,8,6,7,3,4,1]=>0010011=>1100100
[1,8,5,6,7,3,4,2]=>0010011=>1100100
[1,8,5,6,7,3,2,4]=>0100011=>1100010
[2,5,8,6,7,3,1,4]=>0100011=>1100010
[3,5,6,8,7,2,1,4]=>1000011=>1100001
[4,5,6,7,2,1,8,3]=>1000011=>1100001
[3,4,6,1,8,7,2,5]=>0000111=>1110000
[2,4,1,6,8,7,3,5]=>0010011=>1100100
[2,3,1,8,6,7,4,5]=>0100011=>1100010
[1,8,3,2,6,7,5,4]=>0101011=>1101010
[2,5,1,6,7,8,4,3]=>0011001=>1001100
[2,5,1,6,7,4,8,3]=>0001011=>1101000
[2,5,1,6,7,4,3,8]=>0011010=>0101100
[3,5,6,1,7,4,2,8]=>0010110=>0110100
[3,5,6,1,7,4,8,2]=>0000111=>1110000
[3,4,6,1,8,7,5,2]=>0001111=>1111000
[3,4,6,8,1,7,5,2]=>0001011=>1101000
[2,4,8,6,1,7,5,3]=>0001111=>1111000
[1,8,4,6,2,7,5,3]=>0001111=>1111000
[1,8,5,6,7,2,4,3]=>0010011=>1100100
[2,5,8,6,7,1,4,3]=>0010011=>1100100
[3,5,6,8,7,1,4,2]=>0010011=>1100100
[4,5,6,7,8,1,3,2]=>0100001=>1000010
[4,5,6,7,1,3,8,2]=>0000011=>1100000
[4,5,6,7,1,3,2,8]=>0100010=>0100010
[4,5,6,7,3,1,8,2]=>0100011=>1100010
[3,5,6,8,7,4,1,2]=>0010011=>1100100
[2,5,8,6,7,4,1,3]=>0010011=>1100100
[1,8,5,6,7,4,2,3]=>0010011=>1100100
[1,8,5,6,7,4,3,2]=>0110011=>1100110
[2,5,8,6,7,4,3,1]=>0110011=>1100110
[8,2,5,3,7,1,6,4]=>0001111=>1111000
[8,2,4,3,7,1,6,5]=>0010111=>1110100
[5,8,2,4,3,7,1,6]=>0010011=>1100100
[4,2,5,6,1,8,3,7]=>0010101=>1010100
[4,2,5,6,1,7,3,8]=>0010110=>0110100
[6,1,5,7,3,2,4,8]=>0100110=>0110010
[6,1,5,8,3,2,4,7]=>0100101=>1010010
[3,8,2,4,7,1,5,6]=>0000011=>1100000
[3,6,8,2,4,7,1,5]=>0000011=>1100000
[4,3,5,6,7,1,8,2]=>0010011=>1100100
[3,7,1,5,6,8,2,4]=>0000011=>1100000
[3,7,1,5,8,2,4,6]=>0000011=>1100000
[8,3,2,4,6,1,5,7]=>0100101=>1010010
[7,3,2,4,6,1,5,8]=>0100110=>0110010
[3,2,5,1,7,4,6,8]=>0101010=>0101010
[3,2,5,1,8,4,6,7]=>0101001=>1001010
[3,2,5,1,7,8,4,6]=>0101001=>1001010
[7,8,3,2,4,6,1,5]=>0100101=>1010010
[6,1,5,7,8,3,2,4]=>0100101=>1010010
[4,2,5,6,1,7,8,3]=>0010101=>1010100
[5,7,6,1,8,3,4,2]=>0010111=>1110100
[5,8,6,1,7,3,4,2]=>0010111=>1110100
[6,1,5,8,7,3,2,4]=>0100111=>1110010
[8,7,3,2,4,6,1,5]=>0100111=>1110010
[3,2,5,1,8,7,4,6]=>0101011=>1101010
[3,2,5,1,6,4,7,8]=>0101100=>0011010
[3,2,4,1,8,7,5,6]=>0110011=>1100110
[3,2,5,1,6,8,7,4]=>0101011=>1101010
[3,8,6,5,1,7,4,2]=>0011111=>1111100
[3,7,6,5,1,8,4,2]=>0011111=>1111100
[6,5,1,7,8,4,2,3]=>0011101=>1011100
[3,2,5,1,6,7,8,4]=>0101001=>1001010
[3,2,4,1,8,5,6,7]=>0110001=>1000110
[3,2,4,1,7,5,6,8]=>0110010=>0100110
[3,2,4,1,6,8,5,7]=>0110001=>1000110
[3,2,4,1,8,5,7,6]=>0110011=>1100110
[8,3,2,4,7,6,1,5]=>0100111=>1110010
[3,2,5,1,8,4,7,6]=>0101011=>1101010
[3,2,5,1,6,7,4,8]=>0101010=>0101010
[6,5,1,7,4,2,3,8]=>0011110=>0111100
[6,5,1,8,4,2,3,7]=>0011101=>1011100
[8,4,2,3,7,5,1,6]=>0011011=>1101100
[4,2,6,1,8,3,7,5]=>0010111=>1110100
[5,2,6,1,8,3,7,4]=>0001111=>1111000
[8,4,6,1,7,3,5,2]=>0001111=>1111000
[5,2,6,1,8,4,7,3]=>0001111=>1111000
[7,4,2,3,8,5,1,6]=>0011011=>1101100
[8,5,1,6,4,2,3,7]=>0011101=>1011100
[7,5,1,6,4,2,3,8]=>0011110=>0111100
[3,2,5,1,7,6,4,8]=>0101110=>0111010
[3,2,5,1,8,6,4,7]=>0101101=>1011010
[7,3,2,4,8,6,1,5]=>0100111=>1110010
[8,6,1,5,7,3,2,4]=>0100111=>1110010
[4,2,6,1,8,5,7,3]=>0010111=>1110100
[8,5,6,1,7,3,4,2]=>0010111=>1110100
[3,6,8,5,1,7,4,2]=>0011011=>1101100
[8,5,1,6,7,4,2,3]=>0011011=>1101100
[3,2,5,1,8,6,7,4]=>0101011=>1101010
[3,2,4,1,8,6,5,7]=>0110101=>1010110
[3,2,4,1,5,8,6,7]=>0110001=>1000110
[3,2,5,1,7,8,6,4]=>0101101=>1011010
[7,8,5,1,6,4,2,3]=>0011101=>1011100
[3,8,5,1,7,6,4,2]=>0011111=>1111100
[3,7,5,1,8,6,4,2]=>0011111=>1111100
[8,7,5,1,6,4,2,3]=>0011111=>1111100
[3,2,5,1,8,7,6,4]=>0101111=>1111010
[6,5,7,3,1,8,4,2]=>0110111=>1110110
[4,6,3,7,1,8,5,2]=>0001111=>1111000
[4,6,3,7,5,1,8,2]=>0001111=>1111000
[4,2,6,1,7,5,3,8]=>0011110=>0111100
[2,5,7,4,1,6,3,8]=>0010110=>0110100
[2,5,7,4,1,6,8,3]=>0010011=>1100100
[5,4,7,3,6,1,8,2]=>0001111=>1111000
[5,4,7,8,3,1,6,2]=>0101101=>1011010
[4,3,7,5,1,8,6,2]=>0011111=>1111100
[6,4,3,8,5,1,7,2]=>0011111=>1111100
[5,8,4,3,6,1,7,2]=>0010111=>1110100
[5,4,8,3,6,1,7,2]=>0001111=>1111000
[5,4,3,6,7,1,8,2]=>0011011=>1101100
[2,5,4,6,1,7,3,8]=>0001110=>0111000
[3,2,5,8,1,6,7,4]=>0100011=>1100010
[2,5,4,6,8,1,7,3]=>0001011=>1101000
[5,2,8,4,1,6,7,3]=>0011011=>1101100
[4,6,2,1,8,5,7,3]=>1000111=>1110001
[2,4,1,7,5,8,6,3]=>0010111=>1110100
[2,4,1,7,5,3,8,6]=>0011011=>1101100
[2,6,4,1,8,5,3,7]=>0011101=>1011100
[5,4,8,2,1,6,3,7]=>1001101=>1011001
[2,5,8,4,1,6,3,7]=>0010101=>1010100
[3,2,5,6,1,8,4,7]=>0100101=>1010010
[4,8,3,2,6,1,5,7]=>0100101=>1010010
[3,5,2,8,1,6,4,7]=>0001101=>1011000
[3,2,1,6,8,5,4,7]=>1101001=>1001011
[3,2,7,1,5,4,8,6]=>0101011=>1101010
[3,2,7,1,5,8,6,4]=>0100111=>1110010
[3,8,2,5,1,6,7,4]=>0001011=>1101000
[4,8,3,2,6,7,1,5]=>0100011=>1100010
[4,3,8,2,6,7,1,5]=>0010011=>1100100
[4,3,2,6,7,8,1,5]=>0110001=>1000110
[4,3,2,6,7,1,5,8]=>0110010=>0100110
[4,3,7,2,6,8,1,5]=>0010011=>1100100
[4,3,7,8,2,6,1,5]=>0010101=>1010100
[2,5,7,4,8,1,6,3]=>0000111=>1110000
[3,2,5,7,8,1,6,4]=>0100101=>1010010
[3,2,5,7,1,6,8,4]=>0100011=>1100010
[3,2,5,7,1,6,4,8]=>0100110=>0110010
[6,3,2,7,1,5,4,8]=>0101110=>0111010
[6,3,2,7,1,5,8,4]=>0100111=>1110010
[6,3,2,7,8,1,5,4]=>0101101=>1011010
[4,2,6,1,7,8,5,3]=>0011101=>1011100
[6,5,2,1,7,8,4,3]=>1011101=>1011101
[2,1,7,5,3,8,6,4]=>1001111=>1111001
[6,2,1,8,5,3,7,4]=>1001111=>1111001
[6,3,2,7,1,4,8,5]=>0100111=>1110010
[6,3,2,1,4,7,8,5]=>1100101=>1010011
[6,3,2,1,4,7,5,8]=>1100110=>0110011
[3,5,2,1,7,4,6,8]=>1001010=>0101001
[3,5,2,1,7,8,4,6]=>1001001=>1001001
[5,8,4,2,1,7,3,6]=>1010011=>1100101
[4,6,2,1,8,3,7,5]=>1000111=>1110001
[2,4,1,7,3,8,6,5]=>0010111=>1110100
[3,2,7,1,4,8,6,5]=>0100111=>1110010
[3,5,8,2,1,7,4,6]=>1000011=>1100001
[4,8,3,7,2,1,5,6]=>1000011=>1100001
[4,3,7,2,8,1,5,6]=>0010011=>1100100
[4,3,7,2,1,5,6,8]=>1010010=>0100101
[4,8,3,2,7,1,5,6]=>0100011=>1100010
[3,5,2,8,1,7,4,6]=>0001011=>1101000
[6,3,2,8,1,4,7,5]=>0100111=>1110010
[3,2,1,4,7,5,8,6]=>1100011=>1100011
[5,3,2,1,8,4,6,7]=>1101001=>1001011
[4,8,3,2,1,5,6,7]=>1100001=>1000011
[4,3,8,2,1,5,6,7]=>1010001=>1000101
[1,9,8,7,6,5,4,3,2]=>01111111=>11111110
[8,7,6,4,5,3,2,1,9]=>11011110=>01111011
[1,9,8,7,5,6,4,3,2]=>01101111=>11110110
[1,10,9,8,7,6,5,4,3,2]=>011111111=>111111110
[10,9,8,7,6,5,4,3,2,1,11]=>1111111110=>0111111111
[9,8,7,5,6,4,3,2,1,10]=>111011110=>011110111
[8,7,5,4,6,3,2,1,9]=>11011110=>01111011
[8,7,4,6,5,3,2,1,9]=>11011110=>01111011
[1,9,8,6,5,7,4,3,2]=>01101111=>11110110
[1,9,8,5,7,6,4,3,2]=>01101111=>11110110
[1,10,9,8,6,7,5,4,3,2]=>011101111=>111101110
[1,11,10,9,8,7,6,5,4,3,2]=>0111111111=>1111111110
[6,2,3,1,5,4,8,7]=>0101101=>1011010
[8,4,5,2,3,1,7,6]=>0101011=>1101010
[8,6,7,2,5,3,4,1]=>0011011=>1101100
[8,2,5,3,4,1,7,6]=>0011011=>1101100
[6,2,5,3,4,1,8,7]=>0011101=>1011100
[6,1,5,2,4,3,8,7]=>0011101=>1011100
[6,4,5,1,3,2,8,7]=>0101101=>1011010
[6,1,5,3,4,2,8,7]=>0011101=>1011100
[6,3,5,1,4,2,8,7]=>0011101=>1011100
[8,3,5,2,4,1,7,6]=>0011011=>1101100
[8,3,7,5,6,2,4,1]=>0010111=>1110100
[8,3,7,2,4,1,6,5]=>0010111=>1110100
[8,3,5,1,4,2,7,6]=>0011011=>1101100
[8,1,5,3,4,2,7,6]=>0011011=>1101100
[8,4,5,1,3,2,7,6]=>0101011=>1101010
[2,1,8,4,5,3,7,6]=>1001011=>1101001
[8,6,7,4,5,1,3,2]=>0101011=>1101010
[8,6,7,1,5,3,4,2]=>0011011=>1101100
[8,6,7,3,5,1,4,2]=>0011011=>1101100
[8,3,7,5,6,1,4,2]=>0010111=>1110100
[8,5,7,3,6,1,4,2]=>0010111=>1110100
[8,3,7,4,6,2,5,1]=>0001111=>1111000
[8,3,7,4,6,1,5,2]=>0001111=>1111000
[8,3,7,1,6,4,5,2]=>0001111=>1111000
[8,1,7,3,6,4,5,2]=>0001111=>1111000
[8,1,7,5,6,3,4,2]=>0010111=>1110100
[8,4,7,5,6,1,3,2]=>0100111=>1110010
[2,1,8,4,7,5,6,3]=>1000111=>1110001
[8,1,7,3,4,2,6,5]=>0010111=>1110100
[8,1,7,3,6,2,5,4]=>0001111=>1111000
[8,3,7,1,6,2,5,4]=>0001111=>1111000
[8,3,7,2,6,4,5,1]=>0001111=>1111000
[8,2,7,3,6,4,5,1]=>0001111=>1111000
[8,2,7,3,6,1,5,4]=>0001111=>1111000
[8,2,7,1,6,3,5,4]=>0001111=>1111000
[8,1,7,2,4,3,6,5]=>0010111=>1110100
[8,1,3,2,7,4,6,5]=>0100111=>1110010
[2,1,8,3,7,4,6,5]=>1000111=>1110001
[8,1,5,2,4,3,7,6]=>0011011=>1101100
[8,2,7,1,4,3,6,5]=>0010111=>1110100
[8,2,7,3,4,1,6,5]=>0010111=>1110100
[8,2,7,5,6,3,4,1]=>0010111=>1110100
[8,4,7,5,6,2,3,1]=>0100111=>1110010
[8,4,7,2,3,1,6,5]=>0100111=>1110010
[8,2,3,1,7,4,6,5]=>0100111=>1110010
[8,2,3,1,5,4,7,6]=>0101011=>1101010
[4,2,3,1,8,5,7,6]=>0110011=>1100110
[4,1,3,2,8,6,7,5]=>0110011=>1100110
[8,6,7,2,3,1,5,4]=>0101011=>1101010
[8,2,3,1,7,5,6,4]=>0100111=>1110010
[8,5,7,2,6,3,4,1]=>0010111=>1110100
[8,5,7,2,6,1,4,3]=>0010111=>1110100
[8,2,7,5,6,1,4,3]=>0010111=>1110100
[8,6,7,2,5,1,4,3]=>0011011=>1101100
[8,6,7,1,5,2,4,3]=>0011011=>1101100
[8,6,7,1,3,2,5,4]=>0101011=>1101010
[2,1,8,6,7,3,5,4]=>1001011=>1101001
[2,1,8,3,7,5,6,4]=>1000111=>1110001
[8,1,3,2,7,5,6,4]=>0100111=>1110010
[8,1,7,5,6,2,4,3]=>0010111=>1110100
[8,1,7,2,6,4,5,3]=>0001111=>1111000
[8,2,7,1,6,4,5,3]=>0001111=>1111000
[8,2,7,4,6,1,5,3]=>0001111=>1111000
[8,2,7,4,6,3,5,1]=>0001111=>1111000
[8,4,7,2,6,3,5,1]=>0001111=>1111000
[8,4,7,2,6,1,5,3]=>0001111=>1111000
[8,4,7,1,6,2,5,3]=>0001111=>1111000
[8,1,7,4,6,2,5,3]=>0001111=>1111000
[8,5,7,1,6,2,4,3]=>0010111=>1110100
[2,1,8,5,7,3,6,4]=>1000111=>1110001
[8,5,7,4,6,1,3,2]=>0100111=>1110010
[8,5,7,1,6,3,4,2]=>0010111=>1110100
[8,1,7,4,6,3,5,2]=>0001111=>1111000
[8,4,7,1,6,3,5,2]=>0001111=>1111000
[8,4,7,3,6,1,5,2]=>0001111=>1111000
[2,4,8,3,6,1,7,5]=>0000111=>1110000
[6,5,8,1,3,2,7,4]=>0100111=>1110010
[4,5,8,6,3,2,7,1]=>0100111=>1110010
[6,5,8,7,3,1,2,4]=>0100111=>1110010
[1,5,8,7,3,6,2,4]=>0000111=>1110000
[1,7,2,8,4,6,5,3]=>0001111=>1111000
[6,7,2,8,4,1,5,3]=>0011011=>1101100
[3,6,2,8,4,5,7,1]=>0000111=>1110000
[2,6,1,8,4,5,7,3]=>0000111=>1110000
[2,8,4,6,1,5,7,3]=>0000111=>1110000
[6,3,1,8,4,5,7,2]=>0100111=>1110010
[3,1,6,8,4,5,7,2]=>0100011=>1100010
[2,3,6,8,4,5,7,1]=>0000011=>1100000
[6,3,7,8,4,1,5,2]=>0011101=>1011100
[1,3,7,8,4,6,5,2]=>0001101=>1011000
[1,5,7,8,2,4,6,3]=>0000101=>1010000
[5,1,7,8,2,4,6,3]=>0001101=>1011000
[3,6,7,8,4,2,5,1]=>0011001=>1001100
[7,6,1,8,4,2,5,3]=>0011111=>1111100
[5,6,8,7,3,2,1,4]=>1100011=>1100011
[2,8,3,7,1,6,5,4]=>0001111=>1111000
[5,2,8,7,3,6,1,4]=>0001111=>1111000
[7,2,1,8,4,6,5,3]=>1001111=>1111001
[3,2,7,8,4,6,5,1]=>0101101=>1011010
[5,2,7,8,1,4,6,3]=>0001101=>1011000
[1,2,7,8,5,4,6,3]=>0001101=>1011000
[4,2,1,3,8,5,6,7]=>1010001=>1000101
[7,2,5,8,3,4,6,1]=>0000111=>1110000
[6,2,8,5,4,3,1,7]=>0111101=>1011110
[2,8,3,5,4,1,6,7]=>0011001=>1001100
[2,8,4,5,3,1,6,7]=>0101001=>1001010
[6,4,8,5,2,3,1,7]=>0101101=>1011010
[7,3,5,8,2,4,6,1]=>0000111=>1110000
[4,3,1,2,8,5,6,7]=>0110001=>1000110
[3,4,2,1,8,5,6,7]=>1010001=>1000101
[2,7,6,8,4,3,5,1]=>0011011=>1101100
[5,7,1,8,3,4,6,2]=>0000111=>1110000
[3,7,5,8,1,4,6,2]=>0000111=>1110000
[1,7,5,8,3,4,6,2]=>0000111=>1110000
[1,6,8,5,4,3,2,7]=>0111001=>1001110
[4,6,8,5,1,3,2,7]=>0101001=>1001010
[5,6,8,1,4,3,2,7]=>0110001=>1000110
[7,5,8,6,3,4,2,1]=>1010111=>1110101
[2,4,8,3,6,5,1,7]=>0001101=>1011000
[2,8,4,1,5,6,3,7]=>0010101=>1010100
[4,1,8,3,5,6,2,7]=>0010101=>1010100
[5,6,8,4,1,3,2,7]=>0110001=>1000110
[4,6,8,1,5,3,2,7]=>0101001=>1001010
[1,6,8,4,5,3,2,7]=>0101001=>1001010
[1,7,3,8,5,4,6,2]=>0001111=>1111000
[3,7,1,8,5,4,6,2]=>0001111=>1111000
[2,7,3,8,4,6,5,1]=>0001111=>1111000
[7,1,3,8,4,6,5,2]=>0001111=>1111000
[5,7,8,4,3,6,1,2]=>0010101=>1010100
[2,8,7,4,1,6,5,3]=>0011111=>1111100
[2,8,5,4,3,1,6,7]=>0111001=>1001110
[6,5,8,4,2,3,1,7]=>0110101=>1010110
[4,1,3,2,8,5,6,7]=>0110001=>1000110
[1,4,3,2,8,5,6,7]=>0110001=>1000110
[7,3,2,8,5,4,6,1]=>0101111=>1111010
[6,4,8,2,5,3,1,7]=>0101101=>1011010
[2,8,4,3,5,1,6,7]=>0011001=>1001100
[2,8,3,4,5,1,6,7]=>0001001=>1001000
[6,2,8,4,5,3,1,7]=>0101101=>1011010
[7,2,3,8,5,4,6,1]=>0001111=>1111000
[4,2,3,1,8,5,6,7]=>0110001=>1000110
[3,2,1,4,8,5,6,7]=>1100001=>1000011
[5,1,3,2,4,8,6,7]=>0101001=>1001010
[2,8,1,5,3,4,7,6]=>0001011=>1101000
[1,2,8,4,5,3,7,6]=>0001011=>1101000
[1,4,2,8,5,3,6,7]=>0011001=>1001100
[1,8,4,2,5,3,6,7]=>0011001=>1001100
[8,1,5,3,2,4,6,7]=>0101001=>1001010
[3,8,1,5,2,4,6,7]=>0001001=>1001000
[3,5,1,4,8,2,6,7]=>0001001=>1001000
[1,5,2,8,4,3,6,7]=>0011001=>1001100
[1,2,8,5,4,3,6,7]=>0011001=>1001100
[1,2,5,4,3,8,6,7]=>0011001=>1001100
[1,2,4,8,5,3,7,6]=>0001011=>1101000
[1,2,7,4,8,5,3,6]=>0001011=>1101000
[1,5,2,7,8,4,3,6]=>0011001=>1001100
[5,1,2,7,4,8,3,6]=>0001011=>1101000
[8,3,5,1,4,7,2,6]=>0001011=>1101000
[2,8,1,5,4,7,3,6]=>0001011=>1101000
[1,2,8,5,7,4,3,6]=>0010011=>1100100
[1,2,4,8,7,5,3,6]=>0001011=>1101000
[2,8,1,4,3,7,6,5]=>0010111=>1110100
[6,1,2,8,7,4,3,5]=>0010111=>1110100
[6,4,1,2,8,7,3,5]=>0010111=>1110100
[3,6,4,8,1,7,2,5]=>0000111=>1110000
[7,6,1,4,2,8,3,5]=>0010111=>1110100
[7,1,6,2,8,4,3,5]=>0010111=>1110100
[1,6,7,2,8,4,3,5]=>0010011=>1100100
[6,7,1,4,2,8,3,5]=>0010011=>1100100
[6,3,7,1,4,8,2,5]=>0000111=>1110000
[3,7,8,1,5,2,4,6]=>0001001=>1001000
[7,1,2,8,5,3,4,6]=>0001011=>1101000
[1,7,2,8,4,5,3,6]=>0001011=>1101000
[1,4,2,7,8,5,3,6]=>0011001=>1001100
[6,1,2,8,4,3,7,5]=>0010111=>1110100
[6,4,1,2,8,3,7,5]=>0010111=>1110100
[7,6,1,3,2,4,8,5]=>0100111=>1110010
[6,7,1,3,2,4,8,5]=>0100011=>1100010
[1,2,7,3,5,8,4,6]=>0000011=>1100000
[1,2,7,5,8,3,4,6]=>0000011=>1100000
[5,8,1,3,7,2,4,6]=>0000011=>1100000
[1,2,5,8,7,3,4,6]=>0000011=>1100000
[1,2,5,8,3,7,4,6]=>0000011=>1100000
[2,8,1,7,3,5,4,6]=>0001011=>1101000
[8,6,1,3,2,4,7,5]=>0100111=>1110010
[4,2,8,1,7,3,6,5]=>0010111=>1110100
[2,8,1,7,4,3,6,5]=>0010111=>1110100
[7,1,2,8,4,3,6,5]=>0010111=>1110100
[1,2,8,4,7,5,3,6]=>0001011=>1101000
[1,2,8,7,4,5,3,6]=>0001011=>1101000
[2,8,1,7,5,3,4,6]=>0001011=>1101000
[8,3,7,1,5,2,4,6]=>0001011=>1101000
[3,8,6,1,4,7,2,5]=>0000111=>1110000
[8,6,1,4,2,7,3,5]=>0010111=>1110100
[8,1,6,2,7,4,3,5]=>0010111=>1110100
[7,1,2,8,6,4,3,5]=>0010111=>1110100
[7,4,1,2,8,6,3,5]=>0010111=>1110100
[3,7,4,8,1,6,2,5]=>0000111=>1110000
[3,4,8,7,1,6,2,5]=>0000111=>1110000
[4,2,8,1,7,6,3,5]=>0010111=>1110100
[2,8,1,7,6,4,3,5]=>0010111=>1110100
[7,8,3,4,1,5,2,6]=>0011001=>1001100
[7,8,3,4,1,6,2,5]=>0010101=>1010100
[6,8,3,4,1,7,2,5]=>0010011=>1100100
[6,7,3,4,1,8,2,5]=>0010011=>1100100
[5,7,3,4,1,8,2,6]=>0010011=>1100100
[5,8,3,4,1,7,2,6]=>0010011=>1100100
[5,8,3,4,1,6,2,7]=>0010101=>1010100
[6,8,3,4,1,5,2,7]=>0011001=>1001100
[6,7,3,4,1,5,2,8]=>0011010=>0101100
[5,7,3,4,1,6,2,8]=>0010110=>0110100
[5,6,2,8,3,4,1,7]=>0010101=>1010100
[5,6,2,7,3,4,1,8]=>0010110=>0110100
[4,6,2,8,3,5,1,7]=>0001101=>1011000
[4,7,3,5,1,6,2,8]=>0001110=>0111000
[4,8,3,5,1,6,2,7]=>0001101=>1011000
[4,8,3,5,1,7,2,6]=>0001011=>1101000
[4,7,3,5,1,8,2,6]=>0001011=>1101000
[5,6,2,3,1,7,4,8]=>0100110=>0110010
[5,6,2,4,1,8,3,7]=>0010101=>1010100
[5,6,2,4,1,7,3,8]=>0010110=>0110100
[4,6,2,5,1,7,3,8]=>0001110=>0111000
[4,6,2,5,1,8,3,7]=>0001101=>1011000
[4,5,1,8,3,7,2,6]=>0001011=>1101000
[4,5,1,7,3,8,2,6]=>0001011=>1101000
[4,6,2,7,3,8,1,5]=>0000111=>1110000
[5,6,2,7,3,8,1,4]=>0000111=>1110000
[5,6,2,7,4,8,1,3]=>0000111=>1110000
[5,6,3,8,4,7,1,2]=>0000111=>1110000
[5,6,2,8,4,7,1,3]=>0000111=>1110000
[5,6,2,8,3,7,1,4]=>0000111=>1110000
[4,6,2,8,3,7,1,5]=>0000111=>1110000
[4,5,1,7,3,6,2,8]=>0001110=>0111000
[4,5,1,8,3,6,2,7]=>0001101=>1011000
[9,2,1,3,4,5,6,7,8]=>10000001=>10000001
[10,2,1,3,4,5,6,7,8,9]=>100000001=>100000001
[9,2,3,1,4,5,6,7,8]=>01000001=>10000010
[4,2,3,5,6,7,8,9,1]=>00100001=>10000100
[3,4,2,5,6,7,8,9,1]=>00100001=>10000100
[3,2,4,5,6,7,8,9,10,1]=>010000001=>100000010
[2,3,4,5,6,7,8,9,10,11,1]=>0000000001=>1000000000
[6,5,3,2,1,4,8,7]=>1101101=>1011011
[4,6,3,5,2,1,8,7]=>1001101=>1011001
[8,7,3,5,2,4,1,6]=>0011011=>1101100
[6,8,2,4,5,7,3,1]=>0100011=>1100010
[8,7,2,4,5,3,1,6]=>0101011=>1101010
[3,6,1,4,5,2,8,7]=>0001101=>1011000
[8,3,7,4,5,2,1,6]=>1001011=>1101001
[6,3,8,4,5,7,2,1]=>1000111=>1110001
[5,8,7,4,3,6,2,1]=>1010111=>1110101
[2,8,7,4,3,6,1,5]=>0010111=>1110100
[8,1,7,4,3,6,2,5]=>0010111=>1110100
[8,7,3,5,1,4,2,6]=>0011011=>1101100
[2,1,6,8,5,7,4,3]=>1010011=>1100101
[6,8,3,5,1,7,4,2]=>0011011=>1101100
[5,1,8,4,7,6,3,2]=>0101111=>1111010
[2,5,8,4,7,6,3,1]=>0100111=>1110010
[4,3,8,1,5,6,7,2]=>0010011=>1100100
[4,8,1,3,5,6,7,2]=>0000011=>1100000
[5,8,7,4,1,6,3,2]=>0110111=>1110110
[5,8,3,6,1,4,7,2]=>0000111=>1110000
[4,8,3,6,1,2,7,5]=>0000111=>1110000
[3,8,7,4,1,6,2,5]=>0010111=>1110100
[3,8,1,2,5,6,7,4]=>0000011=>1100000
[8,7,1,4,2,6,3,5]=>0010111=>1110100
[8,6,3,1,2,4,7,5]=>0100111=>1110010
[8,1,7,4,5,2,3,6]=>0001011=>1101000
[2,8,7,4,5,1,3,6]=>0001011=>1101000
[8,7,2,4,1,6,3,5]=>0010111=>1110100
[5,8,3,6,2,4,7,1]=>0000111=>1110000
[8,6,3,2,1,4,7,5]=>1100111=>1110011
[8,7,3,5,2,1,4,6]=>1001011=>1101001
[5,8,3,6,2,1,7,4]=>1000111=>1110001
[5,8,7,4,2,6,1,3]=>0010111=>1110100
[2,6,8,4,5,7,1,3]=>0000011=>1100000
[6,1,8,4,5,7,2,3]=>0000111=>1110000
[6,8,3,5,1,7,2,4]=>0001011=>1101000
[2,1,5,8,3,6,7,4]=>1000011=>1100001
[5,8,3,6,1,2,7,4]=>0000111=>1110000
[4,1,8,2,5,6,7,3]=>0010011=>1100100
[2,4,8,1,5,6,7,3]=>0000011=>1100000
[4,8,2,1,5,6,7,3]=>1000011=>1100001
[3,4,8,2,5,6,7,1]=>0000011=>1100000
[5,8,1,4,7,6,2,3]=>0000111=>1110000
[5,8,3,1,6,2,7,4]=>0100111=>1110010
[4,5,3,8,6,1,7,2]=>0001111=>1111000
[3,4,1,8,5,6,7,2]=>0010011=>1100100
[2,4,6,8,10,1,3,5,7,9]=>000000001=>100000000
[2,4,6,9,10,1,3,5,7,8]=>000000001=>100000000
[2,4,7,8,10,1,3,5,6,9]=>000000001=>100000000
[2,4,7,9,10,1,3,5,6,8]=>000000001=>100000000
[2,4,8,9,10,1,3,5,6,7]=>000000001=>100000000
[2,5,6,8,10,1,3,4,7,9]=>000000001=>100000000
[2,5,6,9,10,1,3,4,7,8]=>000000001=>100000000
[2,5,7,8,10,1,3,4,6,9]=>000000001=>100000000
[2,5,7,9,10,1,3,4,6,8]=>000000001=>100000000
[2,5,8,9,10,1,3,4,6,7]=>000000001=>100000000
[2,6,7,8,10,1,3,4,5,9]=>000000001=>100000000
[2,6,7,9,10,1,3,4,5,8]=>000000001=>100000000
[2,6,8,9,10,1,3,4,5,7]=>000000001=>100000000
[2,7,8,9,10,1,3,4,5,6]=>000000001=>100000000
[3,4,6,8,10,1,2,5,7,9]=>000000001=>100000000
[3,4,6,9,10,1,2,5,7,8]=>000000001=>100000000
[3,4,7,8,10,1,2,5,6,9]=>000000001=>100000000
[3,4,7,9,10,1,2,5,6,8]=>000000001=>100000000
[3,4,8,9,10,1,2,5,6,7]=>000000001=>100000000
[3,5,6,8,10,1,2,4,7,9]=>000000001=>100000000
[3,5,6,9,10,1,2,4,7,8]=>000000001=>100000000
[3,5,7,8,10,1,2,4,6,9]=>000000001=>100000000
[3,5,7,9,10,1,2,4,6,8]=>000000001=>100000000
[3,5,8,9,10,1,2,4,6,7]=>000000001=>100000000
[3,6,7,8,10,1,2,4,5,9]=>000000001=>100000000
[3,6,7,9,10,1,2,4,5,8]=>000000001=>100000000
[3,6,8,9,10,1,2,4,5,7]=>000000001=>100000000
[3,7,8,9,10,1,2,4,5,6]=>000000001=>100000000
[4,5,6,8,10,1,2,3,7,9]=>000000001=>100000000
[4,5,6,9,10,1,2,3,7,8]=>000000001=>100000000
[4,5,7,8,10,1,2,3,6,9]=>000000001=>100000000
[4,5,7,9,10,1,2,3,6,8]=>000000001=>100000000
[4,5,8,9,10,1,2,3,6,7]=>000000001=>100000000
[4,6,7,8,10,1,2,3,5,9]=>000000001=>100000000
[4,6,7,9,10,1,2,3,5,8]=>000000001=>100000000
[4,6,8,9,10,1,2,3,5,7]=>000000001=>100000000
[4,7,8,9,10,1,2,3,5,6]=>000000001=>100000000
[5,6,7,8,10,1,2,3,4,9]=>000000001=>100000000
[5,6,7,9,10,1,2,3,4,8]=>000000001=>100000000
[5,6,8,9,10,1,2,3,4,7]=>000000001=>100000000
[5,7,8,9,10,1,2,3,4,6]=>000000001=>100000000
[2,4,6,8,10,12,1,3,5,7,9,11]=>00000000001=>10000000000
[2,4,6,8,11,12,1,3,5,7,9,10]=>00000000001=>10000000000
[2,4,6,9,10,12,1,3,5,7,8,11]=>00000000001=>10000000000
[2,4,6,9,11,12,1,3,5,7,8,10]=>00000000001=>10000000000
[2,4,6,10,11,12,1,3,5,7,8,9]=>00000000001=>10000000000
[2,4,7,8,10,12,1,3,5,6,9,11]=>00000000001=>10000000000
[2,4,7,8,11,12,1,3,5,6,9,10]=>00000000001=>10000000000
[2,4,7,9,10,12,1,3,5,6,8,11]=>00000000001=>10000000000
[2,4,7,9,11,12,1,3,5,6,8,10]=>00000000001=>10000000000
[2,4,7,10,11,12,1,3,5,6,8,9]=>00000000001=>10000000000
[2,4,8,9,10,12,1,3,5,6,7,11]=>00000000001=>10000000000
[2,4,8,9,11,12,1,3,5,6,7,10]=>00000000001=>10000000000
[2,4,8,10,11,12,1,3,5,6,7,9]=>00000000001=>10000000000
[2,4,9,10,11,12,1,3,5,6,7,8]=>00000000001=>10000000000
[2,5,6,8,10,12,1,3,4,7,9,11]=>00000000001=>10000000000
[2,5,6,8,11,12,1,3,4,7,9,10]=>00000000001=>10000000000
[2,5,6,9,10,12,1,3,4,7,8,11]=>00000000001=>10000000000
[2,5,6,9,11,12,1,3,4,7,8,10]=>00000000001=>10000000000
[2,5,6,10,11,12,1,3,4,7,8,9]=>00000000001=>10000000000
[2,5,7,8,10,12,1,3,4,6,9,11]=>00000000001=>10000000000
[2,5,7,8,11,12,1,3,4,6,9,10]=>00000000001=>10000000000
[2,5,7,9,10,12,1,3,4,6,8,11]=>00000000001=>10000000000
[2,5,7,9,11,12,1,3,4,6,8,10]=>00000000001=>10000000000
[2,5,7,10,11,12,1,3,4,6,8,9]=>00000000001=>10000000000
[2,5,8,9,10,12,1,3,4,6,7,11]=>00000000001=>10000000000
[2,5,8,9,11,12,1,3,4,6,7,10]=>00000000001=>10000000000
[2,5,8,10,11,12,1,3,4,6,7,9]=>00000000001=>10000000000
[2,5,9,10,11,12,1,3,4,6,7,8]=>00000000001=>10000000000
[2,6,7,8,10,12,1,3,4,5,9,11]=>00000000001=>10000000000
[2,6,7,8,11,12,1,3,4,5,9,10]=>00000000001=>10000000000
[2,6,7,9,10,12,1,3,4,5,8,11]=>00000000001=>10000000000
[2,6,7,9,11,12,1,3,4,5,8,10]=>00000000001=>10000000000
[2,6,7,10,11,12,1,3,4,5,8,9]=>00000000001=>10000000000
[2,6,8,9,10,12,1,3,4,5,7,11]=>00000000001=>10000000000
[2,6,8,9,11,12,1,3,4,5,7,10]=>00000000001=>10000000000
[2,6,8,10,11,12,1,3,4,5,7,9]=>00000000001=>10000000000
[2,6,9,10,11,12,1,3,4,5,7,8]=>00000000001=>10000000000
[2,7,8,9,10,12,1,3,4,5,6,11]=>00000000001=>10000000000
[2,7,8,9,11,12,1,3,4,5,6,10]=>00000000001=>10000000000
[2,7,8,10,11,12,1,3,4,5,6,9]=>00000000001=>10000000000
[2,7,9,10,11,12,1,3,4,5,6,8]=>00000000001=>10000000000
[2,8,9,10,11,12,1,3,4,5,6,7]=>00000000001=>10000000000
[3,4,6,8,10,12,1,2,5,7,9,11]=>00000000001=>10000000000
[3,4,6,8,11,12,1,2,5,7,9,10]=>00000000001=>10000000000
[3,4,6,9,10,12,1,2,5,7,8,11]=>00000000001=>10000000000
[3,4,6,9,11,12,1,2,5,7,8,10]=>00000000001=>10000000000
[3,4,6,10,11,12,1,2,5,7,8,9]=>00000000001=>10000000000
[3,4,7,8,10,12,1,2,5,6,9,11]=>00000000001=>10000000000
[3,4,7,8,11,12,1,2,5,6,9,10]=>00000000001=>10000000000
[3,4,7,9,10,12,1,2,5,6,8,11]=>00000000001=>10000000000
[3,4,7,9,11,12,1,2,5,6,8,10]=>00000000001=>10000000000
[3,4,7,10,11,12,1,2,5,6,8,9]=>00000000001=>10000000000
[3,4,8,9,10,12,1,2,5,6,7,11]=>00000000001=>10000000000
[3,4,8,9,11,12,1,2,5,6,7,10]=>00000000001=>10000000000
[3,4,8,10,11,12,1,2,5,6,7,9]=>00000000001=>10000000000
[3,4,9,10,11,12,1,2,5,6,7,8]=>00000000001=>10000000000
[3,5,6,8,10,12,1,2,4,7,9,11]=>00000000001=>10000000000
[3,5,6,8,11,12,1,2,4,7,9,10]=>00000000001=>10000000000
[3,5,6,9,10,12,1,2,4,7,8,11]=>00000000001=>10000000000
[3,5,6,9,11,12,1,2,4,7,8,10]=>00000000001=>10000000000
[3,5,6,10,11,12,1,2,4,7,8,9]=>00000000001=>10000000000
[3,5,7,8,10,12,1,2,4,6,9,11]=>00000000001=>10000000000
[3,5,7,8,11,12,1,2,4,6,9,10]=>00000000001=>10000000000
[3,5,7,9,10,12,1,2,4,6,8,11]=>00000000001=>10000000000
[3,5,7,9,11,12,1,2,4,6,8,10]=>00000000001=>10000000000
[3,5,7,10,11,12,1,2,4,6,8,9]=>00000000001=>10000000000
[3,5,8,9,10,12,1,2,4,6,7,11]=>00000000001=>10000000000
[3,5,8,9,11,12,1,2,4,6,7,10]=>00000000001=>10000000000
[3,5,8,10,11,12,1,2,4,6,7,9]=>00000000001=>10000000000
[3,5,9,10,11,12,1,2,4,6,7,8]=>00000000001=>10000000000
[3,6,7,8,10,12,1,2,4,5,9,11]=>00000000001=>10000000000
[3,6,7,8,11,12,1,2,4,5,9,10]=>00000000001=>10000000000
[3,6,7,9,10,12,1,2,4,5,8,11]=>00000000001=>10000000000
[3,6,7,9,11,12,1,2,4,5,8,10]=>00000000001=>10000000000
[3,6,7,10,11,12,1,2,4,5,8,9]=>00000000001=>10000000000
[3,6,8,9,10,12,1,2,4,5,7,11]=>00000000001=>10000000000
[3,6,8,9,11,12,1,2,4,5,7,10]=>00000000001=>10000000000
[3,6,8,10,11,12,1,2,4,5,7,9]=>00000000001=>10000000000
[3,6,9,10,11,12,1,2,4,5,7,8]=>00000000001=>10000000000
[3,7,8,9,10,12,1,2,4,5,6,11]=>00000000001=>10000000000
[3,7,8,9,11,12,1,2,4,5,6,10]=>00000000001=>10000000000
[3,7,8,10,11,12,1,2,4,5,6,9]=>00000000001=>10000000000
[3,7,9,10,11,12,1,2,4,5,6,8]=>00000000001=>10000000000
[3,8,9,10,11,12,1,2,4,5,6,7]=>00000000001=>10000000000
[4,5,6,8,10,12,1,2,3,7,9,11]=>00000000001=>10000000000
[4,5,6,8,11,12,1,2,3,7,9,10]=>00000000001=>10000000000
[4,5,6,9,10,12,1,2,3,7,8,11]=>00000000001=>10000000000
[4,5,6,9,11,12,1,2,3,7,8,10]=>00000000001=>10000000000
[4,5,6,10,11,12,1,2,3,7,8,9]=>00000000001=>10000000000
[4,5,7,8,10,12,1,2,3,6,9,11]=>00000000001=>10000000000
[4,5,7,8,11,12,1,2,3,6,9,10]=>00000000001=>10000000000
[4,5,7,9,10,12,1,2,3,6,8,11]=>00000000001=>10000000000
[4,5,7,9,11,12,1,2,3,6,8,10]=>00000000001=>10000000000
[4,5,7,10,11,12,1,2,3,6,8,9]=>00000000001=>10000000000
[4,5,8,9,10,12,1,2,3,6,7,11]=>00000000001=>10000000000
[4,5,8,9,11,12,1,2,3,6,7,10]=>00000000001=>10000000000
[4,5,8,10,11,12,1,2,3,6,7,9]=>00000000001=>10000000000
[4,5,9,10,11,12,1,2,3,6,7,8]=>00000000001=>10000000000
[4,6,7,8,10,12,1,2,3,5,9,11]=>00000000001=>10000000000
[4,6,7,8,11,12,1,2,3,5,9,10]=>00000000001=>10000000000
[4,6,7,9,10,12,1,2,3,5,8,11]=>00000000001=>10000000000
[4,6,7,9,11,12,1,2,3,5,8,10]=>00000000001=>10000000000
[4,6,7,10,11,12,1,2,3,5,8,9]=>00000000001=>10000000000
[4,6,8,9,10,12,1,2,3,5,7,11]=>00000000001=>10000000000
[4,6,8,9,11,12,1,2,3,5,7,10]=>00000000001=>10000000000
[4,6,8,10,11,12,1,2,3,5,7,9]=>00000000001=>10000000000
[4,6,9,10,11,12,1,2,3,5,7,8]=>00000000001=>10000000000
[4,7,8,9,10,12,1,2,3,5,6,11]=>00000000001=>10000000000
[4,7,8,9,11,12,1,2,3,5,6,10]=>00000000001=>10000000000
[4,7,8,10,11,12,1,2,3,5,6,9]=>00000000001=>10000000000
[4,7,9,10,11,12,1,2,3,5,6,8]=>00000000001=>10000000000
[4,8,9,10,11,12,1,2,3,5,6,7]=>00000000001=>10000000000
[5,6,7,8,10,12,1,2,3,4,9,11]=>00000000001=>10000000000
[5,6,7,8,11,12,1,2,3,4,9,10]=>00000000001=>10000000000
[5,6,7,9,10,12,1,2,3,4,8,11]=>00000000001=>10000000000
[5,6,7,9,11,12,1,2,3,4,8,10]=>00000000001=>10000000000
[5,6,7,10,11,12,1,2,3,4,8,9]=>00000000001=>10000000000
[5,6,8,9,10,12,1,2,3,4,7,11]=>00000000001=>10000000000
[5,6,8,9,11,12,1,2,3,4,7,10]=>00000000001=>10000000000
[5,6,8,10,11,12,1,2,3,4,7,9]=>00000000001=>10000000000
[5,6,9,10,11,12,1,2,3,4,7,8]=>00000000001=>10000000000
[5,7,8,9,10,12,1,2,3,4,6,11]=>00000000001=>10000000000
[5,7,8,9,11,12,1,2,3,4,6,10]=>00000000001=>10000000000
[5,7,8,10,11,12,1,2,3,4,6,9]=>00000000001=>10000000000
[5,7,9,10,11,12,1,2,3,4,6,8]=>00000000001=>10000000000
[5,8,9,10,11,12,1,2,3,4,6,7]=>00000000001=>10000000000
[6,7,8,9,10,12,1,2,3,4,5,11]=>00000000001=>10000000000
[6,7,8,9,11,12,1,2,3,4,5,10]=>00000000001=>10000000000
[6,7,8,10,11,12,1,2,3,4,5,9]=>00000000001=>10000000000
[6,7,9,10,11,12,1,2,3,4,5,8]=>00000000001=>10000000000
[6,8,9,10,11,12,1,2,3,4,5,7]=>00000000001=>10000000000
[7,8,9,10,11,12,1,2,3,4,5,6]=>00000000001=>10000000000
[4,5,7,6,2,3,8,1]=>0000111=>1110000
[3,5,7,2,6,4,8,1]=>0000111=>1110000
[2,5,7,3,6,4,8,1]=>0000111=>1110000
[1,5,7,3,6,8,4,2]=>0010011=>1100100
[8,4,3,7,6,1,5,2]=>0011111=>1111100
[6,7,2,3,5,4,8,1]=>0001011=>1101000
[5,2,7,3,6,4,8,1]=>0001111=>1111000
[8,3,4,7,6,1,5,2]=>0001111=>1111000
[8,2,4,7,1,6,5,3]=>0001111=>1111000
[3,1,4,7,6,8,5,2]=>0101011=>1101010
[4,1,3,7,6,8,5,2]=>0011011=>1101100
[5,1,7,3,6,8,4,2]=>0011011=>1101100
[6,7,1,3,5,8,4,2]=>0010011=>1100100
[5,8,7,3,6,1,4,2]=>0010111=>1110100
[4,8,3,7,6,1,5,2]=>0001111=>1111000
[3,8,4,7,6,1,5,2]=>0001111=>1111000
[2,8,4,7,1,6,5,3]=>0001111=>1111000
[8,1,4,7,2,6,5,3]=>0001111=>1111000
[8,1,3,2,7,6,5,4]=>0101111=>1111010
[2,8,3,1,7,6,5,4]=>0101111=>1111010
[3,8,2,1,7,6,5,4]=>1001111=>1111001
[6,7,1,2,8,5,4,3]=>0011011=>1101100
[8,2,3,1,7,6,5,4]=>0101111=>1111010
[8,3,2,1,7,6,5,4]=>1101111=>1111011
[3,4,1,7,6,8,5,2]=>0011011=>1101100
[1,4,2,7,8,6,5,3]=>0011101=>1011100
[8,4,2,7,1,6,5,3]=>0011111=>1111100
[8,5,7,2,1,6,4,3]=>1010111=>1110101
[1,5,7,2,8,6,4,3]=>0010111=>1110100
[2,5,7,1,8,6,4,3]=>0010111=>1110100
[3,5,7,1,6,8,4,2]=>0010011=>1100100
[6,7,4,5,8,1,3,2]=>0100011=>1100010
[5,4,7,6,8,1,3,2]=>0101011=>1101010
[2,5,7,8,1,6,4,3]=>0010101=>1010100
[1,5,7,8,2,6,4,3]=>0010101=>1010100
[8,5,7,1,2,6,4,3]=>0010111=>1110100
[8,4,1,7,2,6,5,3]=>0011111=>1111100
[1,4,8,7,2,6,5,3]=>0001111=>1111000
[3,4,8,7,6,1,5,2]=>0001111=>1111000
[4,3,8,7,6,1,5,2]=>0011111=>1111100
[5,3,7,8,6,1,4,2]=>0011101=>1011100
[6,7,2,8,1,5,4,3]=>0011011=>1101100
[5,2,7,8,1,6,4,3]=>0011101=>1011100
[4,2,8,7,1,6,5,3]=>0011111=>1111100
[3,2,8,1,7,6,5,4]=>0101111=>1111010
[1,3,8,2,7,6,5,4]=>0001111=>1111000
[8,3,1,2,7,6,5,4]=>0101111=>1111010
[8,2,1,3,7,6,5,4]=>1001111=>1111001
[1,2,8,3,7,6,5,4]=>0001111=>1111000
[2,1,8,3,7,6,5,4]=>1001111=>1111001
[4,1,8,7,2,6,5,3]=>0011111=>1111100
[5,1,7,8,2,6,4,3]=>0011101=>1011100
[6,7,1,8,2,5,4,3]=>0011011=>1101100
[5,8,7,1,2,6,4,3]=>0010111=>1110100
[4,8,1,7,2,6,5,3]=>0001111=>1111000
[3,8,1,2,7,6,5,4]=>0001111=>1111000
[2,8,1,3,7,6,5,4]=>0001111=>1111000
[1,8,2,3,7,6,5,4]=>0001111=>1111000
[8,1,2,3,7,6,5,4]=>0001111=>1111000
[3,1,4,5,6,7,8,9,10,2]=>010000001=>100000010
[2,3,4,5,6,7,8,9,11,1,10]=>0000000001=>1000000000
[10,3,4,5,6,7,8,1,2,9]=>000000101=>101000000
[10,1,4,5,6,7,8,9,2,3]=>000000011=>110000000
[3,1,4,5,6,7,8,9,10,11,2]=>0100000001=>1000000010
[2,3,4,5,6,7,8,9,10,12,1,11]=>00000000001=>10000000000
[11,3,4,5,6,7,8,9,1,2,10]=>0000000101=>1010000000
[2,10,4,5,6,7,8,1,3,9]=>000000101=>101000000
[8,3,4,5,6,7,1,10,2,9]=>000001101=>101100000
[3,1,10,5,6,7,8,9,2,4]=>010000011=>110000010
[9,1,4,5,6,7,8,2,10,3]=>000000111=>111000000
[11,1,4,5,6,7,8,9,10,2,3]=>0000000011=>1100000000
[3,1,4,5,6,7,8,9,10,11,12,2]=>01000000001=>10000000010
[6,7,1,8,4,5,2,3]=>0001011=>1101000
[3,7,1,5,8,2,6,4]=>0000111=>1110000
[2,7,1,5,8,3,6,4]=>0000111=>1110000
[2,6,5,1,8,3,7,4]=>0001111=>1111000
[3,6,5,1,8,2,7,4]=>0001111=>1111000
[4,6,5,1,8,7,2,3]=>0001111=>1111000
[5,6,4,1,8,7,2,3]=>0010111=>1110100
[8,1,4,5,7,6,2,3]=>0000111=>1110000
[6,4,5,1,8,7,2,3]=>0001111=>1111000
[5,4,6,1,8,7,2,3]=>0001111=>1111000
[4,5,6,1,8,7,2,3]=>0000111=>1110000
[3,5,6,1,8,2,7,4]=>0000111=>1110000
[2,5,6,1,8,3,7,4]=>0000111=>1110000
[2,4,6,1,3,8,7,5]=>0000111=>1110000
[3,4,6,1,2,8,7,5]=>0000111=>1110000
[4,3,6,1,2,8,7,5]=>0010111=>1110100
[5,3,6,1,8,2,7,4]=>0001111=>1111000
[7,3,1,5,8,2,6,4]=>0100111=>1110010
[8,1,3,5,7,2,6,4]=>0000111=>1110000
[8,1,2,5,7,3,6,4]=>0000111=>1110000
[7,2,1,5,8,3,6,4]=>1000111=>1110001
[6,2,5,1,8,3,7,4]=>0001111=>1111000
[4,2,6,1,3,8,7,5]=>0010111=>1110100
[2,3,6,1,4,8,7,5]=>0000111=>1110000
[4,2,5,3,1,8,7,6]=>0111011=>1101110
[6,2,4,1,3,8,7,5]=>0010111=>1110100
[7,2,1,4,3,8,6,5]=>1010111=>1110101
[8,1,2,4,3,7,6,5]=>0010111=>1110100
[8,1,3,4,2,7,6,5]=>0010111=>1110100
[7,3,1,4,2,8,6,5]=>0110111=>1110110
[6,3,4,1,2,8,7,5]=>0010111=>1110100
[4,6,3,1,2,8,7,5]=>0100111=>1110010
[3,6,4,1,2,8,7,5]=>0010111=>1110100
[2,6,4,1,3,8,7,5]=>0010111=>1110100
[2,7,1,4,3,8,6,5]=>0010111=>1110100
[3,7,1,4,2,8,6,5]=>0010111=>1110100
[4,7,1,3,2,8,6,5]=>0100111=>1110010
[8,1,6,7,2,3,5,4]=>0001011=>1101000
[4,7,1,2,3,8,6,5]=>0000111=>1110000
[3,7,1,2,4,8,6,5]=>0000111=>1110000
[2,7,1,3,4,8,6,5]=>0000111=>1110000
[2,6,3,1,4,8,7,5]=>0100111=>1110010
[3,6,2,1,4,8,7,5]=>1000111=>1110001
[5,6,2,1,8,3,7,4]=>1000111=>1110001
[6,5,2,1,8,3,7,4]=>1001111=>1111001
[8,1,5,2,7,3,6,4]=>0001111=>1111000
[8,1,4,2,3,7,6,5]=>0010111=>1110100
[7,4,1,2,3,8,6,5]=>0010111=>1110100
[6,4,2,1,3,8,7,5]=>1010111=>1110101
[5,4,2,3,1,8,7,6]=>0111011=>1101110
[3,5,2,4,1,8,7,6]=>0011011=>1101100
[6,3,2,1,4,8,7,5]=>1100111=>1110011
[7,3,1,2,4,8,6,5]=>0100111=>1110010
[8,1,3,2,4,7,6,5]=>0100111=>1110010
[8,1,2,3,4,7,6,5]=>0000111=>1110000
[7,2,1,3,4,8,6,5]=>1000111=>1110001
[6,2,3,1,4,8,7,5]=>0100111=>1110010
[2,4,3,6,1,5,8,7]=>0010101=>1010100
[2,4,3,6,5,8,1,7]=>0010101=>1010100
[2,4,6,3,5,8,7,1]=>0000111=>1110000
[2,4,6,3,5,8,1,7]=>0000101=>1010000
[2,4,6,3,5,1,8,7]=>0001101=>1011000
[2,4,6,3,1,5,8,7]=>0100101=>1010010
[2,4,1,6,5,3,8,7]=>0011101=>1011100
[2,4,6,1,5,3,8,7]=>0001101=>1011000
[4,2,6,5,3,1,8,7]=>0111101=>1011110
[4,2,6,5,1,3,8,7]=>0011101=>1011100
[4,2,6,5,1,8,7,3]=>0011111=>1111100
[4,2,6,5,8,1,7,3]=>0010111=>1110100
[4,2,6,5,8,1,3,7]=>0010101=>1010100
[4,2,6,5,8,3,1,7]=>0110101=>1010110
[2,4,6,1,5,8,3,7]=>0000101=>1010000
[2,4,1,6,5,8,3,7]=>0010101=>1010100
[2,1,4,6,5,8,3,7]=>1000101=>1010001
[2,4,1,6,5,8,7,3]=>0010111=>1110100
[2,4,6,1,5,8,7,3]=>0000111=>1110000
[4,2,6,5,3,8,7,1]=>0011111=>1111100
[4,2,6,5,8,3,7,1]=>0010111=>1110100
[2,6,4,3,8,7,1,5]=>0010111=>1110100
[2,6,4,3,8,7,5,1]=>0011111=>1111100
[4,2,6,8,5,3,7,1]=>0011011=>1101100
[2,4,6,8,1,5,7,3]=>0000011=>1100000
[2,4,6,1,8,5,7,3]=>0000111=>1110000
[2,4,1,6,8,5,7,3]=>0010011=>1100100
[2,1,4,6,8,5,7,3]=>1000011=>1100001
[2,1,4,6,8,5,3,7]=>1001001=>1001001
[2,4,1,6,8,5,3,7]=>0011001=>1001100
[2,4,6,1,8,5,3,7]=>0001101=>1011000
[2,4,6,8,1,5,3,7]=>0001001=>1001000
[4,2,6,8,5,3,1,7]=>0111001=>1001110
[4,2,6,8,5,1,3,7]=>0011001=>1001100
[4,2,6,8,5,1,7,3]=>0011011=>1101100
[2,4,6,8,3,5,7,1]=>0000011=>1100000
[2,4,6,8,3,5,1,7]=>0001001=>1001000
[2,4,6,8,3,1,5,7]=>0100001=>1000010
[2,4,6,3,1,8,5,7]=>0100101=>1010010
[2,4,6,3,8,1,5,7]=>0000101=>1010000
[2,4,6,3,8,5,1,7]=>0001101=>1011000
[2,4,6,3,8,5,7,1]=>0000111=>1110000
[2,4,3,6,8,5,7,1]=>0010011=>1100100
[2,4,3,6,8,5,1,7]=>0011001=>1001100
[2,4,3,6,8,1,5,7]=>0010001=>1000100
[2,4,3,6,1,8,5,7]=>0010101=>1010100
[2,4,3,1,6,8,5,7]=>0110001=>1000110
[2,4,1,3,6,8,7,5]=>0010011=>1100100
[2,4,3,6,1,8,7,5]=>0010111=>1110100
[2,4,3,6,8,1,7,5]=>0010011=>1100100
[4,6,5,2,8,7,3,1]=>0101111=>1111010
[4,6,5,2,8,7,1,3]=>0001111=>1111000
[4,6,2,5,8,7,1,3]=>0000111=>1110000
[4,6,2,5,8,7,3,1]=>0100111=>1110010
[2,4,6,3,8,1,7,5]=>0000111=>1110000
[2,4,6,3,1,8,7,5]=>0100111=>1110010
[2,4,1,6,3,8,7,5]=>0010111=>1110100
[2,1,4,6,3,8,7,5]=>1000111=>1110001
[2,1,4,6,8,3,7,5]=>1000011=>1100001
[2,4,1,6,8,3,7,5]=>0010011=>1100100
[2,4,6,1,8,3,7,5]=>0000111=>1110000
[2,4,6,8,1,3,7,5]=>0000011=>1100000
[2,4,6,8,3,1,7,5]=>0100011=>1100010
[4,6,2,8,5,7,3,1]=>0100111=>1110010
[4,6,2,8,5,7,1,3]=>0000111=>1110000
[6,2,4,8,7,1,3,5]=>0000111=>1110000
[6,4,2,8,7,5,3,1]=>0111111=>1111110
[2,6,4,8,1,7,5,3]=>0001111=>1111000
[2,6,4,1,8,7,5,3]=>0011111=>1111100
[2,6,1,4,8,7,5,3]=>0001111=>1111000
[2,1,6,4,8,7,5,3]=>1001111=>1111001
[2,1,6,4,8,7,3,5]=>1000111=>1110001
[2,6,1,4,8,7,3,5]=>0000111=>1110000
[2,6,4,1,8,7,3,5]=>0010111=>1110100
[2,6,4,8,1,7,3,5]=>0000111=>1110000
[6,4,2,8,7,5,1,3]=>0011111=>1111100
[6,2,4,8,7,3,5,1]=>0001111=>1111000
[6,2,4,8,7,3,1,5]=>0100111=>1110010
[1,6,4,7,3,8,2,5]=>0000111=>1110000
[1,3,7,4,5,8,2,6]=>0000011=>1100000
[5,2,4,7,3,6,8,1]=>0001011=>1101000
[1,7,6,3,4,8,2,5]=>0000111=>1110000
[8,1,6,3,7,2,4,5]=>0000111=>1110000
[7,1,6,3,8,2,4,5]=>0000111=>1110000
[1,2,7,4,8,3,5,6]=>0000011=>1100000
[6,1,7,3,4,8,2,5]=>0000111=>1110000
[2,1,7,4,5,8,3,6]=>1000011=>1100001
[5,1,4,7,3,8,2,6]=>0001011=>1101000
[4,3,1,7,5,8,2,6]=>0110011=>1100110
[2,8,6,3,7,1,4,5]=>0000111=>1110000
[6,8,1,3,7,2,4,5]=>0000011=>1100000
[5,8,2,1,7,3,4,6]=>1000011=>1100001
[5,7,2,1,8,3,4,6]=>1000011=>1100001
[6,7,1,3,8,2,4,5]=>0000011=>1100000
[5,1,2,4,8,3,6,7]=>0001001=>1001000
[4,3,6,1,5,8,2,7]=>0010101=>1010100
[2,6,1,4,5,8,3,7]=>0000101=>1010000
[6,5,1,3,4,8,2,7]=>0001101=>1011000
[1,6,2,4,8,3,5,7]=>0000101=>1010000
[8,5,1,3,7,2,4,6]=>0001011=>1101000
[1,5,3,2,8,4,6,7]=>0101001=>1001010
[6,4,2,1,5,8,3,7]=>1010101=>1010101
[2,5,3,4,1,8,6,7]=>0011001=>1001100
[4,3,5,2,1,8,6,7]=>1011001=>1001101
[2,6,4,8,7,1,3,5]=>0000111=>1110000
[1,6,4,8,7,2,3,5]=>0000111=>1110000
[2,7,8,3,6,1,4,5]=>0000101=>1010000
[4,3,2,8,7,1,5,6]=>0110011=>1100110
[5,2,4,8,7,1,3,6]=>0001011=>1101000
[6,2,8,3,7,1,4,5]=>0000111=>1110000
[5,1,4,8,7,2,3,6]=>0001011=>1101000
[4,8,2,5,1,3,7,6]=>0001011=>1101000
[4,7,2,5,1,3,8,6]=>0001011=>1101000
[3,7,2,1,5,4,8,6]=>1001011=>1101001
[3,8,2,1,5,4,7,6]=>1001011=>1101001
[8,3,2,1,5,4,6,7]=>1101001=>1001011
[8,3,2,1,6,4,5,7]=>1100101=>1010011
[8,4,2,5,1,6,3,7]=>0011101=>1011100
[8,3,2,1,5,6,4,7]=>1100101=>1010011
[8,3,2,1,4,6,5,7]=>1100101=>1010011
[3,8,2,1,4,5,7,6]=>1000011=>1100001
[3,7,2,1,4,5,8,6]=>1000011=>1100001
[3,2,7,1,4,6,8,5]=>0100011=>1100010
[3,2,8,1,4,6,7,5]=>0100011=>1100010
[3,2,8,1,4,7,6,5]=>0100111=>1110010
[3,8,2,1,4,7,5,6]=>1000011=>1100001
[3,8,2,1,5,7,4,6]=>1000011=>1100001
[4,8,2,5,1,7,3,6]=>0001011=>1101000
[4,7,2,5,1,8,3,6]=>0001011=>1101000
[3,7,2,1,5,8,4,6]=>1000011=>1100001
[3,7,2,1,4,8,5,6]=>1000011=>1100001
[3,2,1,7,5,8,6,4]=>1100111=>1110011
[3,2,7,1,6,8,4,5]=>0100011=>1100010
[4,2,7,6,1,8,3,5]=>0010111=>1110100
[4,3,7,6,8,1,2,5]=>0010011=>1100100
[4,3,8,6,7,1,2,5]=>0010011=>1100100
[4,2,8,6,1,7,3,5]=>0010111=>1110100
[3,2,8,1,6,7,4,5]=>0100011=>1100010
[3,2,1,8,7,5,6,4]=>1100111=>1110011
[3,8,2,1,7,4,5,6]=>1000011=>1100001
[3,2,8,1,7,4,6,5]=>0100111=>1110010
[3,2,8,1,6,4,7,5]=>0100111=>1110010
[3,2,7,1,6,4,8,5]=>0100111=>1110010
[4,2,7,6,1,3,8,5]=>0010111=>1110100
[4,2,8,6,1,3,7,5]=>0010111=>1110100
[4,2,8,7,1,3,6,5]=>0010111=>1110100
[5,7,8,3,4,1,2,6]=>0010001=>1000100
[4,2,7,8,1,3,6,5]=>0010101=>1010100
[4,2,6,8,1,3,7,5]=>0010011=>1100100
[4,2,6,7,1,3,8,5]=>0010011=>1100100
[3,2,6,1,8,4,7,5]=>0100111=>1110010
[3,7,2,1,8,4,5,6]=>1000011=>1100001
[3,7,2,1,8,5,4,6]=>1001011=>1101001
[4,7,3,8,5,1,2,6]=>0001011=>1101000
[4,3,7,8,6,1,2,5]=>0010101=>1010100
[3,2,7,1,8,6,4,5]=>0100111=>1110010
[3,2,1,6,8,5,7,4]=>1100011=>1100011
[3,2,6,1,8,7,4,5]=>0100111=>1110010
[4,2,6,8,1,7,3,5]=>0010011=>1100100
[4,3,6,8,7,1,2,5]=>0010011=>1100100
[4,2,6,7,1,8,3,5]=>0010011=>1100100
[3,2,6,1,7,8,4,5]=>0100101=>1010010
[3,4,6,8,7,5,1,2]=>0001011=>1101000
[5,3,6,4,8,7,1,2]=>0001111=>1111000
[1,4,6,2,7,8,5,3]=>0001101=>1011000
[3,1,8,5,4,2,6,7]=>0111001=>1001110
[1,2,7,5,4,8,6,3]=>0001111=>1111000
[6,3,7,5,4,8,1,2]=>0001111=>1111000
[7,3,8,5,4,6,1,2]=>0001111=>1111000
[3,8,7,5,4,6,1,2]=>0001111=>1111000
[4,3,6,7,8,5,1,2]=>0011001=>1001100
[4,5,6,3,8,7,1,2]=>0000111=>1110000
[3,6,8,5,4,7,1,2]=>0001011=>1101000
[6,8,3,5,4,7,1,2]=>0001011=>1101000
[7,6,3,5,4,8,1,2]=>0001111=>1111000
[1,6,2,5,4,8,7,3]=>0001111=>1111000
[7,1,2,5,8,3,6,4]=>0000111=>1110000
[1,8,2,5,7,3,6,4]=>0000111=>1110000
[6,2,1,5,4,8,7,3]=>1001111=>1111001
[4,1,6,2,8,7,5,3]=>0011111=>1111100
[7,8,1,2,4,6,5,3]=>0001101=>1011000
[7,8,3,1,4,2,6,5]=>0110101=>1010110
[4,3,6,1,8,2,7,5]=>0010111=>1110100
[2,3,8,5,4,1,6,7]=>0011001=>1001100
[4,8,1,5,2,3,7,6]=>0001011=>1101000
[7,5,1,6,4,3,2,8]=>0111110=>0111110
[5,8,1,6,4,3,2,7]=>0110101=>1010110
[6,1,5,7,4,3,2,8]=>0110110=>0110110
[1,5,8,6,4,3,2,7]=>0110101=>1010110
[3,4,6,1,5,8,2,7]=>0000101=>1010000
[7,8,4,1,5,3,2,6]=>0111001=>1001110
[7,8,5,1,6,3,2,4]=>0101101=>1011010
[2,6,1,5,7,3,8,4]=>0000111=>1110000
[1,6,8,7,4,3,2,5]=>0110011=>1100110
[6,8,1,7,4,3,2,5]=>0110011=>1100110
[5,6,1,7,4,3,2,8]=>0110110=>0110110
[5,1,7,6,4,3,2,8]=>0111110=>0111110
[6,1,7,8,4,3,2,5]=>0110101=>1010110
[7,1,8,6,4,3,2,5]=>0110111=>1110110
[1,8,7,6,4,3,2,5]=>0110111=>1110110
[2,1,7,5,6,3,8,4]=>1000111=>1110001
[3,1,6,7,5,8,2,4]=>0100011=>1100010
[7,8,1,6,5,3,2,4]=>0101101=>1011010
[7,8,2,1,4,5,6,3]=>1000101=>1010001
[2,8,1,5,4,6,7,3]=>0001011=>1101000
[7,2,1,5,4,6,8,3]=>1001011=>1101001
[1,2,8,5,6,3,7,4]=>0000111=>1110000
[6,1,2,5,7,3,8,4]=>0000111=>1110000
[4,2,1,5,6,3,7,8]=>1010100=>0010101
[4,3,6,1,5,7,2,8]=>0010110=>0110100
[5,1,6,3,7,8,2,4]=>0001101=>1011000
[1,3,6,8,5,7,2,4]=>0000011=>1100000
[2,4,6,3,7,1,8,5]=>0000111=>1110000
[1,3,6,4,8,7,2,5]=>0000111=>1110000
[4,1,6,7,3,8,2,5]=>0010011=>1100100
[5,4,6,1,3,7,2,8]=>0001110=>0111000
[6,4,1,5,2,3,7,8]=>0011100=>0011100
[4,1,7,5,2,3,8,6]=>0011011=>1101100
[1,2,4,5,8,3,7,6]=>0000011=>1100000
[7,2,3,5,4,1,8,6]=>0011011=>1101100
[2,8,3,5,4,1,7,6]=>0011011=>1101100
[4,2,6,3,8,1,7,5]=>0010111=>1110100
[7,8,2,3,4,1,6,5]=>0010101=>1010100
[7,8,1,4,6,3,2,5]=>0100101=>1010010
[3,1,6,4,7,8,2,5]=>0100101=>1010010
[1,8,5,7,4,3,2,6]=>0110011=>1100110
[7,1,5,8,4,3,2,6]=>0110011=>1100110
[5,1,8,7,4,3,2,6]=>0111011=>1101110
[6,5,1,8,4,3,2,7]=>0111101=>1011110
[6,5,7,1,4,3,2,8]=>0110110=>0110110
[7,5,8,1,4,3,2,6]=>0110011=>1100110
[5,8,7,1,4,3,2,6]=>0110011=>1100110
[1,5,7,8,4,3,2,6]=>0110001=>1000110
[2,4,7,5,1,3,8,6]=>0001011=>1101000
[7,8,4,6,1,3,2,5]=>0100101=>1010010
[7,8,5,4,1,3,2,6]=>0111001=>1001110
[3,5,6,4,1,8,2,7]=>0010101=>1010100
[2,6,4,5,1,3,8,7]=>0001101=>1011000
[1,6,5,8,4,3,2,7]=>0110101=>1010110
[6,8,5,1,4,3,2,7]=>0111001=>1001110
[7,6,5,1,4,3,2,8]=>0111110=>0111110
[1,2,3,4,5,6,9,7,8]=>00000001=>10000000
[1,2,3,4,5,8,6,9,7]=>00000011=>11000000
[1,2,3,4,7,5,8,9,6]=>00000101=>10100000
[1,2,3,6,4,7,8,9,5]=>00001001=>10010000
[1,2,5,3,6,7,8,9,4]=>00010001=>10001000
[1,4,2,5,6,7,8,9,3]=>00100001=>10000100
[9,8,1,2,3,4,5,6,7]=>00000011=>11000000
[7,8,9,1,2,3,4,5,6]=>00000001=>10000000
[9,8,7,1,2,3,4,5,6]=>00000111=>11100000
[6,7,8,9,1,2,3,4,5]=>00000001=>10000000
[9,6,7,8,1,2,3,4,5]=>00000011=>11000000
[8,9,6,7,1,2,3,4,5]=>00000101=>10100000
[9,8,6,7,1,2,3,4,5]=>00000111=>11100000
[9,8,7,6,1,2,3,4,5]=>00001111=>11110000
[9,5,6,7,8,1,2,3,4]=>00000011=>11000000
[8,9,5,6,7,1,2,3,4]=>00000101=>10100000
[9,8,5,6,7,1,2,3,4]=>00000111=>11100000
[9,7,8,5,6,1,2,3,4]=>00001011=>11010000
[9,8,7,5,6,1,2,3,4]=>00001111=>11110000
[9,8,7,6,5,1,2,3,4]=>00011111=>11111000
[7,8,9,4,5,6,1,2,3]=>00001001=>10010000
[9,7,8,4,5,6,1,2,3]=>00001011=>11010000
[9,8,7,4,5,6,1,2,3]=>00001111=>11110000
[8,9,6,7,4,5,1,2,3]=>00010101=>10101000
[9,8,6,7,4,5,1,2,3]=>00010111=>11101000
[9,8,7,6,4,5,1,2,3]=>00011111=>11111000
[9,8,7,6,5,4,1,2,3]=>00111111=>11111100
[9,7,8,5,6,3,4,1,2]=>00101011=>11010100
[9,8,7,5,6,3,4,1,2]=>00101111=>11110100
[9,8,7,6,5,3,4,1,2]=>00111111=>11111100
[9,8,7,6,5,4,3,1,2]=>01111111=>11111110
[9,10,1,2,3,4,5,6,7,8]=>000000001=>100000000
[8,9,10,1,2,3,4,5,6,7]=>000000001=>100000000
[10,8,9,1,2,3,4,5,6,7]=>000000011=>110000000
[10,9,8,1,2,3,4,5,6,7]=>000000111=>111000000
[7,8,9,10,1,2,3,4,5,6]=>000000001=>100000000
[10,7,8,9,1,2,3,4,5,6]=>000000011=>110000000
[9,10,7,8,1,2,3,4,5,6]=>000000101=>101000000
[10,9,7,8,1,2,3,4,5,6]=>000000111=>111000000
[10,9,8,7,1,2,3,4,5,6]=>000001111=>111100000
[10,6,7,8,9,1,2,3,4,5]=>000000011=>110000000
[9,10,6,7,8,1,2,3,4,5]=>000000101=>101000000
[10,9,6,7,8,1,2,3,4,5]=>000000111=>111000000
[10,8,9,6,7,1,2,3,4,5]=>000001011=>110100000
[10,9,8,6,7,1,2,3,4,5]=>000001111=>111100000
[10,9,8,7,6,1,2,3,4,5]=>000011111=>111110000
[9,10,5,6,7,8,1,2,3,4]=>000000101=>101000000
[10,9,5,6,7,8,1,2,3,4]=>000000111=>111000000
[8,9,10,5,6,7,1,2,3,4]=>000001001=>100100000
[10,9,8,5,6,7,1,2,3,4]=>000001111=>111100000
[9,10,7,8,5,6,1,2,3,4]=>000010101=>101010000
[10,9,7,8,5,6,1,2,3,4]=>000010111=>111010000
[10,9,8,7,5,6,1,2,3,4]=>000011111=>111110000
[10,9,8,7,6,5,1,2,3,4]=>000111111=>111111000
[10,7,8,9,4,5,6,1,2,3]=>000010011=>110010000
[9,10,7,8,4,5,6,1,2,3]=>000010101=>101010000
[10,9,7,8,4,5,6,1,2,3]=>000010111=>111010000
[10,9,8,7,4,5,6,1,2,3]=>000011111=>111110000
[10,8,9,6,7,4,5,1,2,3]=>000101011=>110101000
[10,9,8,6,7,4,5,1,2,3]=>000101111=>111101000
[10,9,8,7,6,4,5,1,2,3]=>000111111=>111111000
[10,9,8,7,6,5,4,1,2,3]=>001111111=>111111100
[9,10,7,8,5,6,3,4,1,2]=>001010101=>101010100
[10,9,7,8,5,6,3,4,1,2]=>001010111=>111010100
[10,9,8,7,5,6,3,4,1,2]=>001011111=>111110100
[10,9,8,7,6,5,3,4,1,2]=>001111111=>111111100
[10,9,8,7,6,5,4,3,1,2]=>011111111=>111111110
[3,4,6,2,7,1,5,8]=>0000110=>0110000
[3,6,2,5,4,1,7,8]=>0011100=>0011100
[3,2,7,5,4,1,6,8]=>0111010=>0101110
[4,3,6,2,8,1,5,7]=>0010101=>1010100
[6,1,2,5,4,7,8,3]=>0001101=>1011000
[6,2,4,5,1,3,7,8]=>0001100=>0011000
[4,2,8,5,1,3,7,6]=>0011011=>1101100
[4,3,6,8,1,7,2,5]=>0010011=>1100100
[5,3,6,4,1,7,2,8]=>0011110=>0111100
[6,2,1,5,8,3,7,4]=>1000111=>1110001
[1,6,7,4,8,3,5,2]=>0001011=>1101000
[1,4,6,3,7,5,8,2]=>0000111=>1110000
[4,6,7,2,5,8,1,3]=>0000011=>1100000
[2,4,6,1,7,5,3,8]=>0001110=>0111000
[2,7,5,4,1,6,3,8]=>0011110=>0111100
[7,5,4,6,2,8,1,3]=>0001111=>1111000
[1,7,5,4,3,8,6,2]=>0011111=>1111100
[1,4,6,3,5,8,7,2]=>0000111=>1110000
[1,5,8,4,3,6,7,2]=>0010011=>1100100
[5,4,6,2,7,8,1,3]=>0001101=>1011000
[2,5,4,1,6,7,3,8]=>0011010=>0101100
[5,6,3,2,7,1,4,8]=>0100110=>0110010
[5,6,3,2,7,1,8,4]=>0100111=>1110010
[8,5,6,3,2,7,1,4]=>0100111=>1110010
[5,4,6,2,8,1,7,3]=>0001111=>1111000
[2,4,1,7,8,5,3,6]=>0011001=>1001100
[2,5,4,1,6,3,8,7]=>0011101=>1011100
[5,6,3,2,1,8,4,7]=>1100101=>1010011
[3,5,2,1,6,4,7,8]=>1001100=>0011001
[6,8,4,3,2,1,5,7]=>1110001=>1000111
[5,3,8,2,1,6,4,7]=>1001101=>1011001
[3,7,5,8,2,1,4,6]=>1000011=>1100001
[7,3,2,8,5,1,6,4]=>0101111=>1111010
[8,4,6,3,2,1,7,5]=>1100111=>1110011
[8,6,4,3,2,1,7,5]=>1110111=>1110111
[7,6,4,3,2,1,8,5]=>1110111=>1110111
[7,8,4,3,2,1,6,5]=>1110101=>1010111
[5,4,7,2,1,8,6,3]=>1001111=>1111001
[7,5,8,3,2,6,1,4]=>0100111=>1110010
[5,7,3,2,1,6,8,4]=>1100011=>1100011
[5,7,3,2,1,6,4,8]=>1100110=>0110011
[6,3,7,2,5,1,8,4]=>0001111=>1111000
[6,7,8,3,5,2,1,4]=>1001001=>1001001
[6,2,5,7,8,4,1,3]=>0010101=>1010100
[2,1,5,7,8,6,3,4]=>1000101=>1010001
[3,6,7,2,8,1,4,5]=>0000011=>1100000
[6,3,7,2,8,1,4,5]=>0000111=>1110000
[3,2,6,1,7,4,5,8]=>0100110=>0110010
[3,5,2,1,4,7,6,8]=>1001010=>0101001
[7,3,5,2,1,8,4,6]=>1001011=>1101001
[2,5,4,1,3,7,8,6]=>0011001=>1001100
[2,5,8,4,1,3,7,6]=>0010011=>1100100
[2,4,1,7,8,3,6,5]=>0010101=>1010100
[3,7,2,8,6,1,4,5]=>0000111=>1110000
[3,6,8,2,1,7,4,5]=>1000011=>1100001
[5,3,8,2,1,4,7,6]=>1001011=>1101001
[4,8,7,3,2,1,5,6]=>1100011=>1100011
[4,7,3,2,1,5,6,8]=>1100010=>0100011
[8,4,7,3,2,1,5,6]=>1100011=>1100011
[8,3,5,2,1,4,7,6]=>1001011=>1101001
[7,3,2,8,6,1,4,5]=>0100111=>1110010
[3,5,2,1,4,6,8,7]=>1001001=>1001001
[7,8,6,5,4,3,2,1,9]=>11111010=>01011111
[1,8,9,7,6,5,4,3,2]=>01111101=>10111110
[8,9,7,6,5,4,3,2,1,10]=>111111010=>010111111
[7,6,8,5,4,3,2,1,9]=>11110110=>01101111
[6,8,7,5,4,3,2,1,9]=>11110110=>01101111
[1,8,7,9,6,5,4,3,2]=>01111011=>11011110
[1,7,9,8,6,5,4,3,2]=>01111011=>11011110
[1,9,10,8,7,6,5,4,3,2]=>011111101=>101111110
[7,8,3,5,4,6,1,2]=>0001101=>1011000
[8,6,3,7,5,2,4,1]=>0011111=>1111100
[5,4,1,6,3,2,8,7]=>0111101=>1011110
[5,4,1,6,2,3,8,7]=>0011101=>1011100
[5,7,1,6,2,8,3,4]=>0000111=>1110000
[5,7,1,6,2,8,4,3]=>0010111=>1110100
[2,7,6,5,1,8,3,4]=>0001111=>1111000
[2,7,6,5,1,8,4,3]=>0011111=>1111100
[2,3,6,5,1,4,8,7]=>0001101=>1011000
[2,3,6,4,1,5,8,7]=>0010101=>1010100
[2,3,6,1,5,4,8,7]=>0001101=>1011000
[2,7,6,1,4,8,5,3]=>0001111=>1111000
[2,7,6,1,4,8,3,5]=>0000111=>1110000
[7,3,5,1,8,4,2,6]=>0011011=>1101100
[7,3,5,1,8,6,4,2]=>0011111=>1111100
[2,7,6,1,5,8,4,3]=>0010111=>1110100
[2,7,6,4,1,8,5,3]=>0011111=>1111100
[2,1,7,6,3,8,5,4]=>1001111=>1111001
[2,1,7,6,3,8,4,5]=>1000111=>1110001
[5,7,3,6,2,8,4,1]=>0010111=>1110100
[2,7,6,4,1,8,3,5]=>0010111=>1110100
[7,3,5,1,8,6,2,4]=>0001111=>1111000
[6,3,5,1,8,2,4,7]=>0001101=>1011000
[2,3,4,8,7,6,1,5]=>0000111=>1110000
[2,3,4,8,5,7,1,6]=>0000011=>1100000
[7,3,5,4,8,1,2,6]=>0001011=>1101000
[6,4,3,5,8,7,2,1]=>1010111=>1110101
[2,1,4,5,8,7,3,6]=>1000011=>1100001
[6,4,3,5,8,7,1,2]=>0010111=>1110100
[7,3,5,4,8,1,6,2]=>0001111=>1111000
[2,3,4,8,7,5,6,1]=>0000111=>1110000
[2,3,4,8,7,5,1,6]=>0001011=>1101000
[2,7,6,5,4,8,1,3]=>0001111=>1111000
[7,3,5,6,8,4,1,2]=>0010011=>1100100
[7,3,5,6,8,1,4,2]=>0010011=>1100100
[7,3,5,6,8,1,2,4]=>0000011=>1100000
[6,4,1,5,8,7,2,3]=>0010111=>1110100
[6,4,1,5,8,7,3,2]=>0110111=>1110110
[6,4,1,5,8,3,7,2]=>0010111=>1110100
[5,7,1,6,3,8,2,4]=>0000111=>1110000
[6,4,1,5,8,3,2,7]=>0110101=>1010110
[7,4,1,5,8,2,3,6]=>0010011=>1100100
[7,4,1,5,8,2,6,3]=>0010111=>1110100
[6,3,5,7,8,2,1,4]=>1000101=>1010001
[6,3,5,7,8,2,4,1]=>0010101=>1010100
[2,7,6,4,5,8,3,1]=>0100111=>1110010
[5,7,3,6,1,8,4,2]=>0010111=>1110100
[2,1,4,5,8,6,3,7]=>1000101=>1010001
[7,3,5,4,8,6,2,1]=>1001111=>1111001
[2,3,4,8,5,6,1,7]=>0000101=>1010000
[2,3,4,8,7,1,6,5]=>0000111=>1110000
[2,3,4,8,1,7,6,5]=>0000111=>1110000
[2,3,4,8,1,6,7,5]=>0000011=>1100000
[2,3,4,8,5,1,7,6]=>0001011=>1101000
[6,3,5,4,8,2,7,1]=>0001111=>1111000
[7,4,3,5,8,2,1,6]=>1010011=>1100101
[2,1,4,5,8,3,7,6]=>1000011=>1100001
[7,4,3,5,8,2,6,1]=>0010111=>1110100
[6,3,5,4,8,2,1,7]=>1001101=>1011001
[2,3,4,8,5,1,6,7]=>0001001=>1001000
[2,3,4,8,1,6,5,7]=>0000101=>1010000
[2,3,4,8,1,5,7,6]=>0000011=>1100000
[7,8,2,6,1,5,3,4]=>0001101=>1011000
[7,8,1,6,2,5,3,4]=>0001101=>1011000
[1,8,6,7,2,5,3,4]=>0001011=>1101000
[1,8,5,7,2,6,3,4]=>0000111=>1110000
[5,8,1,7,2,6,3,4]=>0000111=>1110000
[5,8,2,7,1,6,3,4]=>0000111=>1110000
[2,8,6,7,1,5,3,4]=>0001011=>1101000
[2,8,5,7,1,6,3,4]=>0000111=>1110000
[2,8,1,7,5,6,3,4]=>0000111=>1110000
[1,8,2,7,5,6,3,4]=>0000111=>1110000
[1,8,2,7,4,6,3,5]=>0000111=>1110000
[2,8,1,7,4,6,3,5]=>0000111=>1110000
[2,8,4,7,1,6,3,5]=>0000111=>1110000
[4,8,2,7,1,6,3,5]=>0000111=>1110000
[4,8,1,7,2,6,3,5]=>0000111=>1110000
[1,8,4,7,2,6,3,5]=>0000111=>1110000
[4,8,1,7,5,6,2,3]=>0000111=>1110000
[1,8,4,7,5,6,2,3]=>0000111=>1110000
[1,8,3,7,5,6,2,4]=>0000111=>1110000
[3,8,1,7,5,6,2,4]=>0000111=>1110000
[3,8,1,7,4,6,2,5]=>0000111=>1110000
[1,8,3,7,4,6,2,5]=>0000111=>1110000
[1,8,3,7,2,6,4,5]=>0000111=>1110000
[3,8,1,7,2,6,4,5]=>0000111=>1110000
[3,8,2,7,1,6,4,5]=>0000111=>1110000
[3,8,2,7,4,6,1,5]=>0000111=>1110000
[3,8,2,7,5,6,1,4]=>0000111=>1110000
[4,8,2,7,5,6,1,3]=>0000111=>1110000
[4,8,3,7,5,6,1,2]=>0000111=>1110000
[3,8,4,7,5,6,1,2]=>0000111=>1110000
[2,8,4,7,5,6,1,3]=>0000111=>1110000
[2,8,3,7,5,6,1,4]=>0000111=>1110000
[2,8,3,7,4,6,1,5]=>0000111=>1110000
[2,8,3,7,1,6,4,5]=>0000111=>1110000
[2,8,1,7,3,6,4,5]=>0000111=>1110000
[7,5,2,8,6,4,1,3]=>0011111=>1111100
[7,5,1,8,6,2,3,4]=>0001111=>1111000
[7,4,8,6,1,5,2,3]=>0001111=>1111000
[7,1,8,4,5,2,6,3]=>0001111=>1111000
[6,8,1,7,4,2,5,3]=>0011011=>1101100
[1,6,7,4,2,8,5,3]=>0011011=>1101100
[1,6,7,3,8,5,2,4]=>0001011=>1101000
[7,1,8,3,5,6,2,4]=>0000111=>1110000
[7,3,8,6,2,5,1,4]=>0001111=>1111000
[7,4,2,8,6,1,3,5]=>0010111=>1110100
[7,3,1,8,4,2,5,6]=>0110011=>1100110
[7,2,8,4,1,5,3,6]=>0011011=>1101100
[7,2,8,3,5,1,6,4]=>0001111=>1111000
[7,2,8,3,4,6,1,5]=>0000111=>1110000
[1,5,7,8,2,6,3,4]=>0000101=>1010000
[6,2,3,8,5,7,4,1]=>0010111=>1110100
[6,2,4,8,5,3,1,7]=>0101101=>1011010
[6,3,1,4,8,5,2,7]=>0101101=>1011010
[2,6,3,7,8,5,4,1]=>0011101=>1011100
[2,6,3,7,8,4,5,1]=>0001101=>1011000
[2,4,7,3,5,6,8,1]=>0000011=>1100000
[2,4,7,3,6,8,5,1]=>0001011=>1101000
[2,5,3,7,8,1,6,4]=>0001101=>1011000
[3,1,5,4,7,8,2,6]=>0101001=>1001010
[5,3,1,4,8,2,6,7]=>0101001=>1001010
[5,2,4,8,6,1,3,7]=>0001101=>1011000
[5,2,3,8,4,6,7,1]=>0001011=>1101000
[4,8,2,3,6,1,7,5]=>0000111=>1110000
[4,8,2,3,5,7,1,6]=>0000011=>1100000
[1,4,7,8,3,6,2,5]=>0000101=>1010000
[4,8,1,3,6,7,2,5]=>0000011=>1100000
[5,3,8,2,4,7,1,6]=>0001011=>1101000
[5,4,3,8,1,2,7,6]=>0011011=>1101100
[6,4,2,8,1,3,7,5]=>0010111=>1110100
[6,3,8,2,5,1,7,4]=>0001111=>1111000
[6,3,8,1,4,7,2,5]=>0000111=>1110000
[5,8,1,3,6,2,7,4]=>0000111=>1110000
[1,5,7,4,2,6,8,3]=>0010011=>1100100
[5,8,1,4,2,6,3,7]=>0010101=>1010100
[5,8,4,1,2,7,6,3]=>0010111=>1110100
[6,5,1,2,8,7,3,4]=>0001111=>1111000
[6,5,3,1,4,2,8,7]=>0111101=>1011110
[5,3,1,6,4,2,7,8]=>0111100=>0011110
[5,2,6,4,1,7,3,8]=>0011110=>0111100
[4,6,1,7,5,2,8,3]=>0001111=>1111000
[4,5,1,7,2,6,3,8]=>0001110=>0111000
[3,5,6,1,2,8,7,4]=>0000111=>1110000
[3,5,7,1,8,6,2,4]=>0000111=>1110000
[3,6,2,7,5,1,8,4]=>0001111=>1111000
[4,2,5,7,1,8,6,3]=>0010111=>1110100
[3,4,7,2,8,6,1,5]=>0000111=>1110000
[3,4,5,8,2,7,1,6]=>0000011=>1100000
[3,4,6,2,8,1,5,7]=>0000101=>1010000
[3,5,2,6,8,1,7,4]=>0001011=>1101000
[4,2,5,6,1,3,8,7]=>0010101=>1010100
[4,3,1,2,5,6,8,7]=>0110001=>1000110
[5,3,6,8,4,7,2,1]=>1001011=>1101001
[3,7,2,5,4,8,6,1]=>0001111=>1111000
[8,4,2,5,7,3,6,1]=>0010111=>1110100
[4,7,2,5,8,3,6,1]=>0000111=>1110000
[5,2,6,8,4,3,7,1]=>0011011=>1101100
[3,1,6,5,4,8,2,7]=>0101101=>1011010
[4,1,6,5,8,3,2,7]=>0110101=>1010110
[5,1,6,8,4,3,2,7]=>0111001=>1001110
[8,5,4,7,6,3,2,1]=>1101111=>1111011
[5,7,1,8,4,3,2,6]=>0110011=>1100110
[2,7,1,5,4,3,8,6]=>0011011=>1101100
[8,2,1,5,4,3,7,6]=>1011011=>1101101
[8,4,1,5,7,3,2,6]=>0110011=>1100110
[8,5,6,7,1,3,2,4]=>0100011=>1100010
[8,4,6,1,7,3,2,5]=>0100111=>1110010
[8,3,6,1,4,7,2,5]=>0000111=>1110000
[2,7,6,1,4,3,8,5]=>0010111=>1110100
[6,7,8,5,1,3,2,4]=>0101001=>1001010
[5,7,6,8,2,3,4,1]=>0010011=>1100100
[5,7,2,8,4,3,6,1]=>0010111=>1110100
[6,7,8,2,4,3,5,1]=>0011001=>1001100
[4,7,6,2,8,3,5,1]=>0001111=>1111000
[8,3,6,2,4,7,5,1]=>0001111=>1111000
[3,7,6,2,4,8,5,1]=>0001111=>1111000
[5,7,3,8,4,6,2,1]=>1000111=>1110001
[4,7,3,5,8,6,2,1]=>1000111=>1110001
[8,7,2,1,4,3,6,5]=>1010111=>1110101
[8,7,3,1,4,6,2,5]=>0100111=>1110010
[8,7,6,3,2,5,4,1]=>0111111=>1111110
[8,7,3,5,1,6,2,4]=>0001111=>1111000
[8,7,2,5,1,3,6,4]=>0001111=>1111000
[8,2,6,5,1,3,7,4]=>0001111=>1111000
[8,4,6,5,7,1,2,3]=>0000111=>1110000
[5,7,6,8,4,1,2,3]=>0010011=>1100100
[4,7,6,5,8,1,2,3]=>0000111=>1110000
[3,7,6,5,1,8,2,4]=>0001111=>1111000
[8,1,2,3,4,5,6,7,9]=>00000010=>01000000
[1,9,2,3,4,5,6,7,8]=>00000001=>10000000
[9,1,2,3,4,5,6,7,8,10]=>000000010=>010000000
[7,8,1,2,3,4,5,6,9]=>00000010=>01000000
[1,8,9,2,3,4,5,6,7]=>00000001=>10000000
[1,10,2,3,4,5,6,7,8,9]=>000000001=>100000000
[10,1,2,3,4,5,6,7,8,9,11]=>0000000010=>0100000000
[8,9,1,2,3,4,5,6,7,10]=>000000010=>010000000
[7,1,8,2,3,4,5,6,9]=>00000110=>01100000
[6,8,1,2,3,4,5,7,9]=>00000010=>01000000
[1,8,2,9,3,4,5,6,7]=>00000011=>11000000
[1,7,9,2,3,4,5,6,8]=>00000001=>10000000
[1,9,10,2,3,4,5,6,7,8]=>000000001=>100000000
[1,11,2,3,4,5,6,7,8,9,10]=>0000000001=>1000000000
[3,6,4,8,7,5,1,2]=>0001111=>1111000
[5,6,4,3,8,7,1,2]=>0010111=>1110100
[1,6,2,4,7,8,5,3]=>0001101=>1011000
[3,6,2,4,8,1,5,7]=>0000101=>1010000
[3,4,7,2,8,1,6,5]=>0000111=>1110000
[1,4,7,2,5,8,6,3]=>0000111=>1110000
[7,3,8,4,5,6,1,2]=>0000111=>1110000
[3,5,6,4,8,7,1,2]=>0000111=>1110000
[4,6,8,5,3,7,1,2]=>0001011=>1101000
[6,8,5,3,4,7,1,2]=>0001011=>1101000
[1,6,5,4,2,8,7,3]=>0011111=>1111100
[1,8,5,2,7,3,6,4]=>0001111=>1111000
[4,2,7,5,1,8,6,3]=>0011111=>1111100
[7,8,1,4,2,6,5,3]=>0011101=>1011100
[1,3,6,4,8,2,5,7]=>0000101=>1010000
[4,1,7,5,3,2,6,8]=>0111010=>0101110
[6,5,1,3,4,2,8,7]=>0011101=>1011100
[4,8,5,3,1,7,2,6]=>0101011=>1101010
[7,4,5,3,2,8,1,6]=>0101011=>1101010
[5,8,3,6,1,4,2,7]=>0010101=>1010100
[2,5,8,6,4,1,3,7]=>0010101=>1010100
[1,4,6,2,5,8,3,7]=>0000101=>1010000
[3,6,2,5,8,1,7,4]=>0000111=>1110000
[1,6,8,7,4,2,3,5]=>0010011=>1100100
[6,1,7,8,2,4,3,5]=>0010101=>1010100
[7,1,8,6,3,4,2,5]=>0010111=>1110100
[7,2,1,4,5,6,8,3]=>1000011=>1100001
[1,2,8,3,6,5,7,4]=>0000111=>1110000
[6,1,3,2,7,5,8,4]=>0100111=>1110010
[1,6,3,8,5,7,2,4]=>0000111=>1110000
[2,6,4,1,7,5,8,3]=>0010111=>1110100
[7,6,5,8,1,4,2,3]=>0010111=>1110100
[5,8,6,7,3,2,1,4]=>1100011=>1100011
[1,6,4,3,7,2,8,5]=>0010111=>1110100
[2,6,3,4,8,7,1,5]=>0000111=>1110000
[7,1,3,4,5,2,8,6]=>0001011=>1101000
[1,8,3,5,4,2,7,6]=>0011011=>1101100
[4,1,6,3,8,2,7,5]=>0010111=>1110100
[7,8,2,4,6,3,1,5]=>0100101=>1010010
[3,2,6,4,7,8,1,5]=>0100101=>1010010
[2,8,5,7,4,3,1,6]=>0110011=>1100110
[7,2,5,8,3,4,1,6]=>0010011=>1100100
[5,3,8,7,1,2,6,4]=>0001111=>1111000
[6,5,3,8,2,1,7,4]=>1001111=>1111001
[7,5,8,4,1,2,3,6]=>0010011=>1100100
[5,8,7,4,1,3,2,6]=>0110011=>1100110
[3,5,7,8,4,1,2,6]=>0010001=>1000100
[1,4,7,5,3,8,2,6]=>0001011=>1101000
[2,4,6,7,3,1,8,5]=>0100011=>1100010
[7,8,4,6,3,1,2,5]=>0100101=>1010010
[2,6,4,5,3,8,1,7]=>0001101=>1011000
[3,6,5,8,4,2,1,7]=>1010101=>1010101
[5,6,8,4,2,3,1,7]=>0110001=>1000110
[6,8,5,4,3,1,2,7]=>0111001=>1001110
[6,1,4,2,8,5,7,3]=>0010111=>1110100
[4,8,6,5,3,2,7,1]=>0101111=>1111010
[8,6,5,1,2,4,7,3]=>0001111=>1111000
[6,7,5,8,2,1,4,3]=>1010011=>1100101
[1,7,5,8,2,6,4,3]=>0010111=>1110100
[1,3,8,5,7,6,2,4]=>0000111=>1110000
[6,3,8,5,7,1,2,4]=>0000111=>1110000
[8,3,1,5,6,2,7,4]=>0100111=>1110010
[6,8,5,2,1,4,7,3]=>1001011=>1101001
[3,8,2,5,6,1,7,4]=>0000111=>1110000
[2,8,1,5,6,3,7,4]=>0000111=>1110000
[8,1,2,5,6,3,7,4]=>0000111=>1110000
[1,8,2,5,7,6,3,4]=>0000111=>1110000
[5,1,8,6,2,7,3,4]=>0001111=>1111000
[2,5,8,6,1,7,3,4]=>0000111=>1110000
[8,6,1,5,7,2,3,4]=>0000111=>1110000
[3,8,6,5,7,1,2,4]=>0000111=>1110000
[7,6,5,8,1,2,4,3]=>0010111=>1110100
[5,1,7,6,8,4,2,3]=>0011011=>1101100
[5,1,3,7,8,6,2,4]=>0001101=>1011000
[7,2,5,8,1,6,4,3]=>0010111=>1110100
[3,2,8,5,7,6,1,4]=>0100111=>1110010
[8,2,1,5,7,6,3,4]=>1000111=>1110001
[5,2,8,6,1,7,3,4]=>0001111=>1111000
[1,2,8,6,5,7,3,4]=>0000111=>1110000
[4,2,1,3,6,7,8,5]=>1010001=>1000101
[8,2,5,6,3,7,1,4]=>0000111=>1110000
[7,2,6,5,4,1,8,3]=>0011111=>1111100
[6,1,3,5,4,7,8,2]=>0001101=>1011000
[6,1,5,3,4,7,8,2]=>0001101=>1011000
[7,5,6,2,4,1,8,3]=>0010111=>1110100
[8,5,2,6,3,7,1,4]=>0001111=>1111000
[4,3,1,2,6,7,8,5]=>0110001=>1000110
[8,1,6,5,7,3,2,4]=>0100111=>1110010
[3,5,8,6,2,7,1,4]=>0000111=>1110000
[5,8,1,6,3,7,2,4]=>0000111=>1110000
[1,8,5,6,3,7,2,4]=>0000111=>1110000
[1,7,6,5,4,2,8,3]=>0011111=>1111100
[5,7,6,1,4,2,8,3]=>0010111=>1110100
[7,1,4,2,6,5,8,3]=>0010111=>1110100
[4,1,7,3,5,6,8,2]=>0010011=>1100100
[2,7,4,1,5,6,8,3]=>0010011=>1100100
[5,7,6,4,1,2,8,3]=>0010111=>1110100
[4,7,6,1,5,2,8,3]=>0001111=>1111000
[1,7,6,4,5,2,8,3]=>0001111=>1111000
[1,8,3,6,5,7,2,4]=>0000111=>1110000
[3,8,1,6,5,7,2,4]=>0000111=>1110000
[8,1,3,5,7,6,2,4]=>0000111=>1110000
[7,8,5,4,1,6,2,3]=>0011101=>1011100
[6,1,5,4,3,7,8,2]=>0011101=>1011100
[7,5,6,4,2,1,8,3]=>1010111=>1110101
[8,3,2,6,5,7,1,4]=>0100111=>1110010
[7,4,6,2,5,1,8,3]=>0001111=>1111000
[6,1,4,3,5,7,8,2]=>0010101=>1010100
[6,1,3,4,5,7,8,2]=>0000101=>1010000
[7,2,6,4,5,1,8,3]=>0001111=>1111000
[8,2,3,6,5,7,1,4]=>0000111=>1110000
[5,4,7,3,6,8,1,2]=>0001011=>1101000
[3,4,7,8,5,6,1,2]=>0000101=>1010000
[3,4,7,2,5,1,6,8]=>0001010=>0101000
[1,4,7,2,5,8,3,6]=>0000011=>1100000
[3,6,2,4,7,1,5,8]=>0000110=>0110000
[6,8,3,4,5,7,1,2]=>0000011=>1100000
[4,3,6,7,5,8,1,2]=>0010011=>1100100
[6,3,7,5,8,4,1,2]=>0010111=>1110100
[7,3,8,6,4,5,1,2]=>0001111=>1111000
[3,2,7,6,5,1,4,8]=>0101110=>0111010
[1,2,7,6,5,8,3,4]=>0000111=>1110000
[4,8,2,6,1,5,3,7]=>0001101=>1011000
[2,3,8,6,4,1,5,7]=>0010101=>1010100
[4,3,6,2,5,1,8,7]=>0011101=>1011100
[7,8,3,2,5,1,4,6]=>0101001=>1001010
[7,8,1,2,5,6,3,4]=>0000101=>1010000
[4,1,6,2,5,7,3,8]=>0010110=>0110100
[6,1,2,5,8,7,3,4]=>0000111=>1110000
[2,1,8,6,4,7,3,5]=>1000111=>1110001
[7,1,3,6,8,4,2,5]=>0010011=>1100100
[1,8,3,6,7,4,5,2]=>0001011=>1101000
[7,1,5,8,3,6,2,4]=>0000111=>1110000
[5,1,8,7,2,3,6,4]=>0001111=>1111000
[6,1,5,7,4,2,8,3]=>0010111=>1110100
[3,1,6,4,7,2,5,8]=>0100110=>0110010
[2,4,7,5,1,8,3,6]=>0001011=>1101000
[6,5,7,1,4,2,3,8]=>0010110=>0110100
[5,6,8,1,3,2,4,7]=>0100001=>1000010
[6,8,5,1,3,4,2,7]=>0011001=>1001100
[2,8,3,4,5,1,7,6]=>0001011=>1101000
[6,2,4,3,1,5,7,8]=>0110100=>0010110
[4,2,8,3,1,7,5,6]=>0110011=>1100110
[1,3,7,4,8,2,5,6]=>0000011=>1100000
[5,3,7,4,1,6,2,8]=>0011110=>0111100
[2,4,7,3,6,1,8,5]=>0000111=>1110000
[5,8,7,6,3,1,2,4]=>0100111=>1110010
[7,5,6,8,1,4,3,2]=>0110011=>1100110
[2,4,7,1,6,5,3,8]=>0001110=>0111000
[1,2,7,8,5,4,3,6]=>0011001=>1001100
[6,3,1,2,8,4,5,7]=>0100101=>1010010
[4,2,1,3,6,5,8,7]=>1010101=>1010101
[2,8,1,4,5,6,3,7]=>0000101=>1010000
[7,2,1,5,4,6,3,8]=>1001110=>0111001
[4,2,6,1,8,5,3,7]=>0011101=>1011100
[7,8,2,1,4,5,3,6]=>1001001=>1001001
[7,8,4,1,5,3,6,2]=>0011101=>1011100
[3,4,6,1,5,8,7,2]=>0000111=>1110000
[7,5,1,6,4,3,8,2]=>0011111=>1111100
[5,8,1,6,3,4,7,2]=>0000111=>1110000
[6,5,1,8,2,7,4,3]=>0011111=>1111100
[6,8,1,7,5,2,3,4]=>0001011=>1101000
[7,6,1,8,5,3,2,4]=>0101111=>1111010
[5,6,1,7,4,8,2,3]=>0000111=>1110000
[3,6,1,5,7,4,2,8]=>0010110=>0110100
[2,5,6,1,7,4,8,3]=>0000111=>1110000
[3,1,7,5,6,4,8,2]=>0100111=>1110010
[5,1,7,6,4,8,3,2]=>0101111=>1111010
[6,1,7,8,5,3,4,2]=>0011101=>1011100
[7,1,8,6,5,4,2,3]=>0011111=>1111100
[2,6,5,7,3,4,8,1]=>0000111=>1110000
[1,6,4,7,5,8,2,3]=>0000111=>1110000
[8,5,3,6,2,7,4,1]=>0011111=>1111100
[1,3,7,4,6,8,2,5]=>0000011=>1100000
[4,7,5,6,3,2,8,1]=>0100111=>1110010
[1,7,6,5,4,8,2,3]=>0001111=>1111000
[8,1,6,5,7,2,4,3]=>0010111=>1110100
[1,2,7,6,8,3,4,5]=>0000011=>1100000
[6,1,7,5,3,8,2,4]=>0001111=>1111000
[2,1,7,5,6,8,3,4]=>1000011=>1100001
[5,4,1,7,6,8,2,3]=>0011011=>1101100
[4,8,5,6,2,7,3,1]=>0100111=>1110010
[3,8,6,4,2,7,5,1]=>0011111=>1111100
[7,8,5,2,4,6,3,1]=>0101101=>1011010
[2,8,6,3,7,4,5,1]=>0001111=>1111000
[7,8,1,6,2,4,5,3]=>0001101=>1011000
[6,8,1,4,7,2,5,3]=>0001011=>1101000
[3,8,4,1,7,2,6,5]=>0010111=>1110100
[5,4,7,1,8,3,2,6]=>0101011=>1101010
[3,7,4,1,8,5,2,6]=>0011011=>1101100
[6,7,1,4,8,3,2,5]=>0100011=>1100010
[2,7,1,8,4,5,3,6]=>0001011=>1101000
[6,1,2,8,4,3,5,7]=>0010101=>1010100
[6,5,1,4,3,8,2,7]=>0011101=>1011100
[1,6,2,5,8,3,4,7]=>0000101=>1010000
[8,5,1,3,7,2,6,4]=>0001111=>1111000
[8,4,2,1,7,3,6,5]=>1010111=>1110101
[7,4,2,1,8,5,3,6]=>1011011=>1101101
[1,5,4,2,8,3,6,7]=>0011001=>1001100
[6,4,3,1,5,8,2,7]=>0110101=>1010110
[3,7,6,8,4,5,2,1]=>1001011=>1101001
[2,7,6,8,5,3,4,1]=>0011011=>1101100
[1,7,6,8,5,4,2,3]=>0011011=>1101100
[1,4,8,6,7,5,2,3]=>0001011=>1101000
[2,4,8,6,7,3,5,1]=>0001011=>1101000
[7,3,8,5,4,6,2,1]=>1001111=>1111001
[3,4,8,5,6,7,2,1]=>1000011=>1100001
[6,3,5,8,4,7,2,1]=>1000111=>1110001
[5,4,3,8,6,7,2,1]=>1011011=>1101101
[5,4,2,8,7,3,6,1]=>0011111=>1111100
[6,2,5,8,7,3,4,1]=>0010111=>1110100
[3,2,8,5,7,4,6,1]=>0100111=>1110010
[1,3,8,7,5,6,2,4]=>0000111=>1110000
[2,1,8,7,4,6,3,5]=>1000111=>1110001
[3,1,8,5,7,6,2,4]=>0100111=>1110010
[6,1,5,8,7,4,2,3]=>0010111=>1110100
[5,4,1,8,7,6,2,3]=>0011111=>1111100
[5,8,6,7,4,3,2,1]=>1110011=>1100111
[4,8,7,5,6,3,2,1]=>1100111=>1110011
[4,2,1,6,3,5,8,7]=>1010101=>1010101
[6,2,1,4,3,5,8,7]=>1010101=>1010101
[6,2,1,4,3,8,5,7]=>1010101=>1010101
[8,2,1,4,3,6,5,7]=>1010101=>1010101
[8,2,4,1,3,6,5,7]=>0010101=>1010100
[6,2,4,1,3,8,5,7]=>0010101=>1010100
[6,2,4,1,3,5,8,7]=>0010101=>1010100
[4,2,6,1,3,5,8,7]=>0010101=>1010100
[2,1,6,4,3,5,8,7]=>1010101=>1010101
[2,6,1,4,3,5,8,7]=>0010101=>1010100
[2,6,4,1,3,5,8,7]=>0010101=>1010100
[4,6,2,1,3,5,8,7]=>1000101=>1010001
[6,4,2,1,3,5,8,7]=>1010101=>1010101
[8,4,2,1,3,6,5,7]=>1010101=>1010101
[8,4,2,1,6,3,5,7]=>1010101=>1010101
[6,4,2,1,8,3,5,7]=>1010101=>1010101
[4,6,2,1,8,3,5,7]=>1000101=>1010001
[2,6,1,4,3,8,5,7]=>0010101=>1010100
[2,1,6,4,3,8,5,7]=>1010101=>1010101
[2,1,8,4,3,6,5,7]=>1010101=>1010101
[2,8,1,4,3,6,5,7]=>0010101=>1010100
[2,8,4,1,3,6,5,7]=>0010101=>1010100
[4,8,2,1,3,6,5,7]=>1000101=>1010001
[4,8,2,1,6,3,5,7]=>1000101=>1010001
[6,8,2,1,4,3,5,7]=>1010001=>1000101
[8,6,2,1,4,3,5,7]=>1010101=>1010101
[2,8,1,4,6,3,5,7]=>0000101=>1010000
[2,1,8,4,6,3,5,7]=>1000101=>1010001
[2,1,6,4,8,3,5,7]=>1000101=>1010001
[2,6,1,4,8,3,5,7]=>0000101=>1010000
[2,6,4,1,8,3,5,7]=>0010101=>1010100
[2,6,4,8,1,3,5,7]=>0000101=>1010000
[4,6,2,8,1,3,5,7]=>0000101=>1010000
[4,2,6,1,3,8,5,7]=>0010101=>1010100
[4,2,6,1,8,3,5,7]=>0010101=>1010100
[6,2,4,1,8,3,5,7]=>0010101=>1010100
[8,2,4,1,6,3,5,7]=>0010101=>1010100
[8,2,1,4,6,3,5,7]=>1000101=>1010001
[6,2,1,4,8,3,5,7]=>1000101=>1010001
[4,2,1,6,8,3,5,7]=>1010001=>1000101
[4,2,1,6,3,8,5,7]=>1010101=>1010101
[4,2,1,3,6,8,5,7]=>1010001=>1000101
[2,1,4,3,8,6,5,7]=>1010101=>1010101
[2,4,1,3,8,6,5,7]=>0010101=>1010100
[4,2,1,3,8,6,5,7]=>1010101=>1010101
[4,2,1,8,3,6,5,7]=>1010101=>1010101
[4,2,1,8,6,3,5,7]=>1010101=>1010101
[6,2,1,8,4,3,5,7]=>1010101=>1010101
[8,2,1,6,4,3,5,7]=>1010101=>1010101
[8,2,6,1,4,3,5,7]=>0010101=>1010100
[6,2,8,1,4,3,5,7]=>0010101=>1010100
[4,2,8,1,6,3,5,7]=>0010101=>1010100
[4,2,8,1,3,6,5,7]=>0010101=>1010100
[2,4,8,1,3,6,5,7]=>0000101=>1010000
[2,4,1,8,3,6,5,7]=>0010101=>1010100
[2,1,4,8,3,6,5,7]=>1000101=>1010001
[2,1,4,8,6,3,5,7]=>1000101=>1010001
[2,4,8,1,6,3,5,7]=>0000101=>1010000
[2,4,8,6,1,3,5,7]=>0000101=>1010000
[4,2,8,6,1,3,5,7]=>0010101=>1010100
[6,2,8,4,1,3,5,7]=>0010101=>1010100
[8,2,6,4,1,3,5,7]=>0010101=>1010100
[8,4,6,2,1,3,5,7]=>1000101=>1010001
[6,4,8,2,1,3,5,7]=>1000101=>1010001
[4,6,8,2,1,3,5,7]=>1000001=>1000001
[2,6,8,4,1,3,5,7]=>0010001=>1000100
[2,6,8,1,4,3,5,7]=>0010001=>1000100
[2,6,1,8,4,3,5,7]=>0010101=>1010100
[2,1,6,8,4,3,5,7]=>1010001=>1000101
[2,1,8,6,4,3,5,7]=>1010101=>1010101
[2,8,1,6,4,3,5,7]=>0010101=>1010100
[2,8,6,4,1,3,5,7]=>0010101=>1010100
[4,8,6,2,1,3,5,7]=>1000101=>1010001
[6,8,4,2,1,3,5,7]=>1010001=>1000101
[3,2,6,1,5,4,8,7]=>0101101=>1011010
[5,2,4,3,8,1,7,6]=>0011011=>1101100
[6,2,4,1,5,3,8,7]=>0011101=>1011100
[4,3,6,1,5,2,8,7]=>0011101=>1011100
[4,3,5,2,8,1,7,6]=>0011011=>1101100
[4,3,7,2,6,5,8,1]=>0010111=>1110100
[4,3,8,2,6,1,7,5]=>0010111=>1110100
[4,3,8,1,7,2,6,5]=>0010111=>1110100
[4,3,8,1,5,2,7,6]=>0011011=>1101100
[5,1,8,3,4,2,7,6]=>0011011=>1101100
[5,4,8,1,3,2,7,6]=>0101011=>1101010
[2,1,5,4,8,3,7,6]=>1001011=>1101001
[5,1,7,6,8,3,4,2]=>0011011=>1101100
[4,3,7,6,8,1,5,2]=>0011011=>1101100
[4,3,7,1,8,5,6,2]=>0010111=>1110100
[4,3,6,5,8,1,7,2]=>0010111=>1110100
[6,3,5,4,7,2,8,1]=>0001111=>1111000
[6,3,5,4,8,1,7,2]=>0001111=>1111000
[7,1,6,3,8,4,5,2]=>0001111=>1111000
[7,4,6,5,8,1,3,2]=>0100111=>1110010
[2,1,8,4,6,3,7,5]=>1000111=>1110001
[8,4,6,1,3,2,7,5]=>0100111=>1110010
[8,1,6,3,4,2,7,5]=>0010111=>1110100
[8,1,6,3,7,2,5,4]=>0001111=>1111000
[8,3,5,1,7,2,6,4]=>0001111=>1111000
[8,3,5,2,6,1,7,4]=>0001111=>1111000
[7,3,5,2,6,4,8,1]=>0001111=>1111000
[8,2,6,3,5,1,7,4]=>0001111=>1111000
[8,2,7,1,5,3,6,4]=>0001111=>1111000
[8,2,4,1,5,3,7,6]=>0011011=>1101100
[8,2,4,1,7,3,6,5]=>0010111=>1110100
[8,2,4,3,6,1,7,5]=>0010111=>1110100
[3,2,8,4,6,1,7,5]=>0100111=>1110010
[3,2,8,1,5,4,7,6]=>0101011=>1101010
[3,2,7,6,8,1,5,4]=>0101011=>1101010
[3,2,7,1,8,5,6,4]=>0100111=>1110010
[3,2,6,5,8,1,7,4]=>0100111=>1110010
[6,5,7,2,4,3,8,1]=>0010111=>1110100
[6,5,8,2,4,1,7,3]=>0010111=>1110100
[7,2,4,1,8,5,6,3]=>0010111=>1110100
[7,6,8,2,4,1,5,3]=>0011011=>1101100
[7,6,8,1,5,2,4,3]=>0011011=>1101100
[2,1,7,3,8,5,6,4]=>1000111=>1110001
[7,1,3,2,8,5,6,4]=>0100111=>1110010
[7,1,8,5,6,2,4,3]=>0010111=>1110100
[7,1,8,2,6,4,5,3]=>0001111=>1111000
[7,2,8,1,5,4,6,3]=>0001111=>1111000
[6,2,7,4,5,3,8,1]=>0001111=>1111000
[5,4,7,2,6,3,8,1]=>0001111=>1111000
[5,4,8,2,6,1,7,3]=>0001111=>1111000
[6,5,8,1,7,2,4,3]=>0010111=>1110100
[2,1,6,5,8,3,7,4]=>1000111=>1110001
[6,5,7,4,8,1,3,2]=>0100111=>1110010
[6,5,7,1,8,3,4,2]=>0010111=>1110100
[6,1,7,4,8,3,5,2]=>0001111=>1111000
[5,4,7,1,8,3,6,2]=>0001111=>1111000
[5,4,6,3,8,1,7,2]=>0001111=>1111000
[2,1,4,3,6,5,8,7,11,12,10,9]=>10101010101=>10101010101
[2,1,4,3,6,5,9,10,8,7,12,11]=>10101010101=>10101010101
[2,1,4,3,6,5,9,11,8,12,10,7]=>10101000111=>11100010101
[2,1,4,3,6,5,10,11,12,9,8,7]=>10101011001=>10011010101
[2,1,4,3,7,8,6,5,10,9,12,11]=>10101010101=>10101010101
[2,1,4,3,7,8,6,5,11,12,10,9]=>10101010101=>10101010101
[2,1,4,3,7,9,6,10,8,5,12,11]=>10100011101=>10111000101
[2,1,4,3,7,9,6,11,8,12,10,5]=>10100001111=>11110000101
[2,1,4,3,7,10,6,11,12,9,8,5]=>10100011101=>10111000101
[2,1,4,3,8,9,10,7,6,5,12,11]=>10101100101=>10100110101
[2,1,4,3,8,9,11,7,6,12,10,5]=>10100100111=>11100100101
[2,1,4,3,8,10,11,7,12,9,6,5]=>10101001011=>11010010101
[2,1,4,3,9,10,11,12,8,7,6,5]=>10101110001=>10001110101
[2,1,5,6,4,3,8,7,10,9,12,11]=>10101010101=>10101010101
[2,1,5,6,4,3,8,7,11,12,10,9]=>10101010101=>10101010101
[2,1,5,6,4,3,9,10,8,7,12,11]=>10101010101=>10101010101
[2,1,5,6,4,3,9,11,8,12,10,7]=>10101000111=>11100010101
[2,1,5,6,4,3,10,11,12,9,8,7]=>10101011001=>10011010101
[2,1,5,7,4,8,6,3,10,9,12,11]=>10001110101=>10101110001
[2,1,5,7,4,8,6,3,11,12,10,9]=>10001110101=>10101110001
[2,1,5,7,4,9,6,10,8,3,12,11]=>10000111101=>10111100001
[2,1,5,7,4,9,6,11,8,12,10,3]=>10000101111=>11110100001
[2,1,5,7,4,10,6,11,12,9,8,3]=>10000111101=>10111100001
[2,1,5,8,4,9,10,7,6,3,12,11]=>10001110101=>10101110001
[2,1,5,8,4,9,11,7,6,12,10,3]=>10000110111=>11101100001
[2,1,5,8,4,10,11,7,12,9,6,3]=>10001011011=>11011010001
[2,1,5,9,4,10,11,12,8,7,6,3]=>10001111001=>10011110001
[2,1,6,7,8,5,4,3,10,9,12,11]=>10110010101=>10101001101
[2,1,6,7,8,5,4,3,11,12,10,9]=>10110010101=>10101001101
[2,1,6,7,9,5,4,10,8,3,12,11]=>10010011101=>10111001001
[2,1,6,7,9,5,4,11,8,12,10,3]=>10010001111=>11110001001
[2,1,6,7,10,5,4,11,12,9,8,3]=>10010011101=>10111001001
[2,1,6,8,9,5,10,7,4,3,12,11]=>10100101101=>10110100101
[2,1,6,8,9,5,11,7,4,12,10,3]=>10000101111=>11110100001
[2,1,6,8,10,5,11,7,12,9,4,3]=>10100001111=>11110000101
[2,1,6,9,10,5,11,12,8,7,4,3]=>10100110101=>10101100101
[2,1,7,8,9,10,6,5,4,3,12,11]=>10111000101=>10100011101
[2,1,7,8,9,11,6,5,4,12,10,3]=>10011000111=>11100011001
[2,1,7,8,10,11,6,5,12,9,4,3]=>10101001011=>11010010101
[2,1,7,9,10,11,6,12,8,5,4,3]=>10110010011=>11001001101
[2,1,8,9,10,11,12,7,6,5,4,3]=>10111100001=>10000111101
[3,4,2,1,6,5,8,7,10,9,12,11]=>10101010101=>10101010101
[3,4,2,1,6,5,8,7,11,12,10,9]=>10101010101=>10101010101
[3,4,2,1,6,5,9,10,8,7,12,11]=>10101010101=>10101010101
[3,4,2,1,6,5,9,11,8,12,10,7]=>10101000111=>11100010101
[3,4,2,1,6,5,10,11,12,9,8,7]=>10101011001=>10011010101
[3,4,2,1,7,8,6,5,10,9,12,11]=>10101010101=>10101010101
[3,4,2,1,7,8,6,5,11,12,10,9]=>10101010101=>10101010101
[3,4,2,1,7,9,6,10,8,5,12,11]=>10100011101=>10111000101
[3,4,2,1,7,9,6,11,8,12,10,5]=>10100001111=>11110000101
[3,4,2,1,7,10,6,11,12,9,8,5]=>10100011101=>10111000101
[3,4,2,1,8,9,10,7,6,5,12,11]=>10101100101=>10100110101
[3,4,2,1,8,9,11,7,6,12,10,5]=>10100100111=>11100100101
[3,4,2,1,8,10,11,7,12,9,6,5]=>10101001011=>11010010101
[3,4,2,1,9,10,11,12,8,7,6,5]=>10101110001=>10001110101
[3,5,2,6,4,1,8,7,10,9,12,11]=>00111010101=>10101011100
[3,5,2,6,4,1,8,7,11,12,10,9]=>00111010101=>10101011100
[3,5,2,6,4,1,9,10,8,7,12,11]=>00111010101=>10101011100
[3,5,2,6,4,1,9,11,8,12,10,7]=>00111000111=>11100011100
[3,5,2,6,4,1,10,11,12,9,8,7]=>00111011001=>10011011100
[3,5,2,7,4,8,6,1,10,9,12,11]=>00011110101=>10101111000
[3,5,2,7,4,8,6,1,11,12,10,9]=>00011110101=>10101111000
[3,5,2,7,4,9,6,10,8,1,12,11]=>00010111101=>10111101000
[3,5,2,7,4,9,6,11,8,12,10,1]=>00010101111=>11110101000
[3,5,2,7,4,10,6,11,12,9,8,1]=>00010111101=>10111101000
[3,5,2,8,4,9,10,7,6,1,12,11]=>00011110101=>10101111000
[3,5,2,8,4,9,11,7,6,12,10,1]=>00010110111=>11101101000
[3,5,2,8,4,10,11,7,12,9,6,1]=>00011011011=>11011011000
[3,5,2,9,4,10,11,12,8,7,6,1]=>00011111001=>10011111000
[3,6,2,7,8,5,4,1,10,9,12,11]=>00111010101=>10101011100
[3,6,2,7,8,5,4,1,11,12,10,9]=>00111010101=>10101011100
[3,6,2,7,9,5,4,10,8,1,12,11]=>00011011101=>10111011000
[3,6,2,7,9,5,4,11,8,12,10,1]=>00011001111=>11110011000
[3,6,2,7,10,5,4,11,12,9,8,1]=>00011011101=>10111011000
[3,6,2,8,9,5,10,7,4,1,12,11]=>00101101101=>10110110100
[3,6,2,8,9,5,11,7,4,12,10,1]=>00001101111=>11110110000
[3,6,2,8,10,5,11,7,12,9,4,1]=>00101001111=>11110010100
[3,6,2,9,10,5,11,12,8,7,4,1]=>00101110101=>10101110100
[3,7,2,8,9,10,6,5,4,1,12,11]=>00111100101=>10100111100
[3,7,2,8,9,11,6,5,4,12,10,1]=>00011100111=>11100111000
[3,7,2,8,10,11,6,5,12,9,4,1]=>00101101011=>11010110100
[3,7,2,9,10,11,6,12,8,5,4,1]=>00110110011=>11001101100
[3,8,2,9,10,11,12,7,6,5,4,1]=>00111110001=>10001111100
[4,5,6,3,2,1,8,7,10,9,12,11]=>11001010101=>10101010011
[4,5,6,3,2,1,8,7,11,12,10,9]=>11001010101=>10101010011
[4,5,6,3,2,1,9,10,8,7,12,11]=>11001010101=>10101010011
[4,5,6,3,2,1,9,11,8,12,10,7]=>11001000111=>11100010011
[4,5,6,3,2,1,10,11,12,9,8,7]=>11001011001=>10011010011
[4,5,7,3,2,8,6,1,10,9,12,11]=>01001110101=>10101110010
[4,5,7,3,2,8,6,1,11,12,10,9]=>01001110101=>10101110010
[4,5,7,3,2,9,6,10,8,1,12,11]=>01000111101=>10111100010
[4,5,7,3,2,9,6,11,8,12,10,1]=>01000101111=>11110100010
[4,5,7,3,2,10,6,11,12,9,8,1]=>01000111101=>10111100010
[4,5,8,3,2,9,10,7,6,1,12,11]=>01001110101=>10101110010
[4,5,8,3,2,9,11,7,6,12,10,1]=>01000110111=>11101100010
[4,5,8,3,2,10,11,7,12,9,6,1]=>01001011011=>11011010010
[4,5,9,3,2,10,11,12,8,7,6,1]=>01001111001=>10011110010
[4,6,7,3,8,5,2,1,10,9,12,11]=>10010110101=>10101101001
[4,6,7,3,8,5,2,1,11,12,10,9]=>10010110101=>10101101001
[4,6,7,3,9,5,2,10,8,1,12,11]=>00010111101=>10111101000
[4,6,7,3,9,5,2,11,8,12,10,1]=>00010101111=>11110101000
[4,6,7,3,10,5,2,11,12,9,8,1]=>00010111101=>10111101000
[4,6,8,3,9,5,10,7,2,1,12,11]=>10000111101=>10111100001
[4,6,8,3,9,5,11,7,2,12,10,1]=>00000111111=>11111100000
[4,6,8,3,10,5,11,7,12,9,2,1]=>10000011111=>11111000001
[4,6,9,3,10,5,11,12,8,7,2,1]=>10000111101=>10111100001
[4,7,8,3,9,10,6,5,2,1,12,11]=>10011010101=>10101011001
[4,7,8,3,9,11,6,5,2,12,10,1]=>00011010111=>11101011000
[4,7,8,3,10,11,6,5,12,9,2,1]=>10001011011=>11011010001
[4,7,9,3,10,11,6,12,8,5,2,1]=>10010011011=>11011001001
[4,8,9,3,10,11,12,7,6,5,2,1]=>10011101001=>10010111001
[5,6,7,8,4,3,2,1,10,9,12,11]=>11100010101=>10101000111
[5,6,7,8,4,3,2,1,11,12,10,9]=>11100010101=>10101000111
[5,6,7,9,4,3,2,10,8,1,12,11]=>01100011101=>10111000110
[5,6,7,9,4,3,2,11,8,12,10,1]=>01100001111=>11110000110
[5,6,7,10,4,3,2,11,12,9,8,1]=>01100011101=>10111000110
[5,6,8,9,4,3,10,7,2,1,12,11]=>10100101101=>10110100101
[5,6,8,9,4,3,11,7,2,12,10,1]=>00100101111=>11110100100
[5,6,8,10,4,3,11,7,12,9,2,1]=>10100001111=>11110000101
[5,6,9,10,4,3,11,12,8,7,2,1]=>10100110101=>10101100101
[5,7,8,9,4,10,6,3,2,1,12,11]=>11001001101=>10110010011
[5,7,8,9,4,11,6,3,2,12,10,1]=>01001001111=>11110010010
[5,7,8,10,4,11,6,3,12,9,2,1]=>10001001111=>11110010001
[5,7,9,10,4,11,6,12,8,3,2,1]=>11000010111=>11101000011
[5,8,9,10,4,11,12,7,6,3,2,1]=>11001100101=>10100110011
[6,7,8,9,10,5,4,3,2,1,12,11]=>11110000101=>10100001111
[6,7,8,9,11,5,4,3,2,12,10,1]=>01110000111=>11100001110
[6,7,8,10,11,5,4,3,12,9,2,1]=>10110001011=>11010001101
[6,7,9,10,11,5,4,12,8,3,2,1]=>11010010011=>11001001011
[6,8,9,10,11,5,12,7,4,3,2,1]=>11100100011=>11000100111
[7,8,9,10,11,12,6,5,4,3,2,1]=>11111000001=>10000011111
[2,8,3,1,5,4,6,7]=>0101001=>1001010
[2,5,3,4,7,1,8,6]=>0001011=>1101000
[2,4,8,3,5,7,6,1]=>0000111=>1110000
[4,2,5,3,1,8,6,7]=>0111001=>1001110
[4,2,1,8,5,3,6,7]=>1011001=>1001101
[5,4,1,3,8,2,6,7]=>0011001=>1001100
[5,1,4,8,3,2,6,7]=>0101001=>1001010
[1,5,8,4,3,2,6,7]=>0110001=>1000110
[1,8,5,4,3,2,6,7]=>0111001=>1001110
[1,7,4,3,8,5,2,6]=>0011011=>1101100
[1,5,7,3,8,4,2,6]=>0010011=>1100100
[5,1,4,7,8,3,2,6]=>0101001=>1001010
[4,8,1,5,7,3,6,2]=>0000111=>1110000
[8,1,5,3,7,4,6,2]=>0001111=>1111000
[3,8,4,7,6,5,2,1]=>1001111=>1111001
[1,6,8,5,3,7,4,2]=>0011011=>1101100
[6,8,1,7,4,3,5,2]=>0011011=>1101100
[6,4,8,1,7,3,5,2]=>0001111=>1111000
[6,4,8,7,1,5,2,3]=>0001111=>1111000
[7,6,4,1,3,8,2,5]=>0010111=>1110100
[1,7,5,6,3,2,8,4]=>0100111=>1110010
[4,2,1,7,8,5,3,6]=>1011001=>1001101
[2,7,4,6,3,1,8,5]=>0100111=>1110010
[2,6,8,4,3,7,5,1]=>0011011=>1101100
[6,2,4,8,3,7,5,1]=>0001111=>1111000
[7,2,6,3,4,1,8,5]=>0010111=>1110100
[2,6,7,3,1,4,8,5]=>0100011=>1100010
[2,7,1,8,3,5,4,6]=>0001011=>1101000
[2,1,7,3,5,8,4,6]=>1000011=>1100001
[8,7,1,3,6,2,4,5]=>0000111=>1110000
[8,2,1,7,3,5,6,4]=>1000111=>1110001
[7,8,2,6,3,1,5,4]=>0101101=>1011010
[8,7,2,6,3,5,4,1]=>0011111=>1111100
[1,2,8,7,4,5,6,3]=>0000111=>1110000
[8,3,7,1,5,6,2,4]=>0000111=>1110000
[8,6,1,2,7,5,3,4]=>0001111=>1111000
[8,1,6,2,7,4,5,3]=>0001111=>1111000
[1,8,5,2,6,7,4,3]=>0011011=>1101100
[5,2,1,8,6,7,4,3]=>1011011=>1101101
[2,8,5,7,6,4,3,1]=>0110111=>1110110
[1,7,8,5,2,6,4,3]=>0011101=>1011100
[7,8,1,6,4,2,5,3]=>0011101=>1011100
[7,8,6,1,5,3,2,4]=>0101101=>1011010
[7,3,8,6,1,5,2,4]=>0001111=>1111000
[8,7,6,1,5,3,4,2]=>0011111=>1111100
[8,7,1,6,4,5,3,2]=>0101111=>1111010
[8,1,7,5,6,4,3,2]=>0110111=>1110110
[1,8,6,7,5,4,3,2]=>0111011=>1101110
[6,3,5,2,1,4,8,7]=>1001101=>1011001
[6,3,5,7,2,8,4,1]=>0010111=>1110100
[8,5,2,7,4,3,1,6]=>0111011=>1101110
[4,5,3,6,1,2,8,7]=>0001101=>1011000
[3,5,1,4,6,2,8,7]=>0001101=>1011000
[8,3,4,5,7,2,1,6]=>1000011=>1100001
[5,7,4,6,3,8,2,1]=>1000111=>1110001
[2,8,4,6,3,7,1,5]=>0000111=>1110000
[8,1,4,7,3,6,2,5]=>0000111=>1110000
[8,3,4,7,5,1,2,6]=>0001011=>1101000
[8,5,1,4,7,3,2,6]=>0101011=>1101010
[8,5,3,7,1,4,2,6]=>0011011=>1101100
[2,1,8,5,7,4,3,6]=>1010011=>1100101
[6,5,3,7,1,8,4,2]=>0011111=>1111100
[6,5,1,4,7,8,3,2]=>0101101=>1011010
[6,3,4,7,5,8,1,2]=>0000111=>1110000
[5,1,4,6,8,3,7,2]=>0001011=>1101000
[4,7,1,3,5,8,6,2]=>0000111=>1110000
[4,8,3,7,1,2,6,5]=>0000111=>1110000
[3,8,6,4,1,7,2,5]=>0010111=>1110100
[3,8,1,2,5,7,6,4]=>0000111=>1110000
[2,8,7,5,4,1,3,6]=>0011011=>1101100
[8,7,2,6,4,1,3,5]=>0010111=>1110100
[3,8,6,7,4,2,1,5]=>1010011=>1100101
[5,7,6,8,4,2,3,1]=>0110011=>1100110
[5,3,7,8,2,4,6,1]=>0001101=>1011000
[8,3,6,2,1,4,7,5]=>1000111=>1110001
[5,3,7,6,2,1,8,4]=>1001111=>1111001
[5,3,6,2,8,7,1,4]=>0001111=>1111000
[5,7,8,6,4,2,1,3]=>1010101=>1010101
[2,6,7,5,4,8,1,3]=>0001011=>1101000
[6,1,7,4,5,8,2,3]=>0000111=>1110000
[6,7,3,5,1,8,2,4]=>0001011=>1101000
[2,1,6,7,5,8,3,4]=>1000011=>1100001
[2,1,5,7,3,6,8,4]=>1000011=>1100001
[5,7,3,6,1,2,8,4]=>0000111=>1110000
[4,1,7,2,5,6,8,3]=>0010011=>1100100
[2,4,7,1,6,5,8,3]=>0000111=>1110000
[4,6,2,1,8,7,5,3]=>1001111=>1111001
[3,4,6,2,7,8,5,1]=>0001101=>1011000
[4,6,1,2,5,8,7,3]=>0000111=>1110000
[5,6,1,4,8,2,7,3]=>0000111=>1110000
[5,6,3,1,8,7,2,4]=>0100111=>1110010
[3,5,6,4,7,1,8,2]=>0000111=>1110000
[3,4,6,1,5,7,8,2]=>0000101=>1010000
[3,4,1,5,7,6,8,2]=>0010011=>1100100
[3,8,2,7,1,6,5,4]=>0001111=>1111000
[3,8,2,7,6,1,5,4]=>0001111=>1111000
[3,8,2,7,6,5,1,4]=>0001111=>1111000
[3,8,2,7,6,5,4,1]=>0011111=>1111100
[4,8,7,2,6,5,3,1]=>0101111=>1111010
[4,8,7,2,6,5,1,3]=>0001111=>1111000
[4,8,7,2,6,1,5,3]=>0001111=>1111000
[4,8,7,2,1,6,5,3]=>1001111=>1111001
[4,8,7,3,1,6,5,2]=>0101111=>1111010
[4,8,7,3,2,1,6,5]=>1100111=>1110011
[4,8,7,3,2,6,1,5]=>0100111=>1110010
[4,8,7,3,2,6,5,1]=>0101111=>1111010
[4,8,7,3,6,2,5,1]=>0001111=>1111000
[4,8,7,3,6,2,1,5]=>1000111=>1110001
[4,8,7,3,6,1,5,2]=>0001111=>1111000
[4,8,7,3,6,5,1,2]=>0001111=>1111000
[4,8,7,3,6,5,2,1]=>1001111=>1111001
[5,8,7,6,3,4,2,1]=>1010111=>1110101
[5,8,7,6,3,1,4,2]=>0110111=>1110110
[5,8,7,6,3,2,4,1]=>0110111=>1110110
[5,8,7,6,2,4,3,1]=>0110111=>1110110
[5,8,7,6,2,1,4,3]=>1010111=>1110101
[5,8,7,6,4,2,3,1]=>0110111=>1110110
[5,8,7,6,4,2,1,3]=>1010111=>1110101
[5,8,7,6,4,1,3,2]=>0110111=>1110110
[5,8,7,6,4,3,1,2]=>0110111=>1110110
[7,3,4,2,1,6,5,8]=>1010110=>0110101
[7,3,5,2,6,1,4,8]=>0001110=>0111000
[7,3,5,2,6,4,1,8]=>0011110=>0111100
[6,3,5,2,7,4,8,1]=>0001111=>1111000
[7,2,1,5,6,4,3,8]=>1010110=>0110101
[7,3,5,1,6,4,2,8]=>0011110=>0111100
[7,4,5,6,1,3,2,8]=>0100110=>0110010
[1,4,5,7,3,2,8,6]=>0100011=>1100010
[1,4,6,7,3,8,2,5]=>0000011=>1100000
[6,4,5,7,3,1,8,2]=>0100111=>1110010
[6,4,5,7,1,3,8,2]=>0000111=>1110000
[6,3,5,1,7,4,8,2]=>0001111=>1111000
[6,2,1,5,7,4,8,3]=>1000111=>1110001
[3,2,1,5,7,4,8,6]=>1100011=>1100011
[2,4,6,7,3,8,1,5]=>0000011=>1100000
[1,4,6,7,3,8,5,2]=>0001011=>1101000
[1,5,6,7,8,3,4,2]=>0010001=>1000100
[2,5,6,7,8,3,1,4]=>0100001=>1000010
[3,2,1,6,7,8,4,5]=>1100001=>1000011
[5,2,1,6,7,8,4,3]=>1011001=>1001101
[5,3,6,1,7,8,4,2]=>0011101=>1011100
[5,4,6,7,1,8,3,2]=>0101011=>1101010
[1,5,6,7,8,3,2,4]=>0100001=>1000010
[6,4,5,7,2,1,8,3]=>1000111=>1110001
[5,4,6,7,2,8,3,1]=>0101011=>1101010
[5,3,6,2,7,8,4,1]=>0011101=>1011100
[5,3,6,2,7,8,1,4]=>0001101=>1011000
[6,3,5,2,7,1,8,4]=>0001111=>1111000
[6,3,4,2,1,7,8,5]=>1010101=>1010101
[5,3,4,1,2,7,8,6]=>0011001=>1001100
[4,3,6,2,7,8,1,5]=>0010101=>1010100
[4,3,6,2,7,8,5,1]=>0011101=>1011100
[1,3,6,2,7,8,5,4]=>0001101=>1011000
[1,4,6,7,2,8,5,3]=>0001011=>1101000
[3,4,6,7,2,8,5,1]=>0001011=>1101000
[3,4,5,7,2,1,8,6]=>1000011=>1100001
[4,2,1,5,7,3,8,6]=>1010011=>1100101
[4,2,1,6,7,8,3,5]=>1010001=>1000101
[4,3,6,1,7,8,2,5]=>0010101=>1010100
[1,5,6,7,8,2,4,3]=>0010001=>1000100
[1,5,6,7,8,4,2,3]=>0010001=>1000100
[3,4,6,7,1,8,5,2]=>0001011=>1101000
[4,3,6,1,7,8,5,2]=>0011101=>1011100
[4,2,1,6,7,8,5,3]=>1011001=>1001101
[2,3,6,1,7,8,5,4]=>0001101=>1011000
[2,4,6,7,1,8,5,3]=>0001011=>1101000
[2,5,6,7,8,1,4,3]=>0010001=>1000100
[2,1,4,3,6,5,8,7,9]=>10101010=>01010101
[2,4,1,3,6,5,8,7,9]=>00101010=>01010100
[2,4,1,6,3,5,8,7,9]=>00101010=>01010100
[2,4,1,6,3,8,5,7,9]=>00101010=>01010100
[2,4,1,6,3,7,5,9,8]=>00101101=>10110100
[2,4,1,5,3,7,6,9,8]=>00110101=>10101100
[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]=>001010101=>101010100
[2,4,6,1,3,5,8,7,9]=>00001010=>01010000
[2,4,1,6,3,5,8,7,10,9]=>001010101=>101010100
[2,4,1,6,8,3,5,7,9]=>00100010=>01000100
[2,4,1,6,3,8,5,7,10,9]=>001010101=>101010100
[2,4,1,6,3,8,9,5,7]=>00101001=>10010100
[2,4,1,6,3,8,5,10,7,9]=>001010101=>101010100
[2,4,1,6,3,7,5,8,9]=>00101100=>00110100
[2,4,1,6,3,8,5,9,7,10]=>001010110=>011010100
[2,4,1,5,3,8,6,9,7]=>00110011=>11001100
[2,4,1,6,3,7,5,9,8,10]=>001011010=>010110100
[2,3,1,6,4,7,5,9,8]=>01001101=>10110010
[2,4,1,5,3,7,6,9,8,10]=>001101010=>010101100
[1,4,2,5,3,7,6,9,8]=>00110101=>10101100
[2,3,1,5,4,7,6,9,8,10]=>010101010=>010101010
[1,3,2,5,4,7,6,9,8,10]=>010101010=>010101010
[7,1,2,3,4,5,6,8,9]=>00000100=>00100000
[1,4,3,6,2,5,7,8]=>0010100=>0010100
[1,4,3,7,2,5,6,8]=>0010010=>0100100
[1,4,3,7,6,8,2,5]=>0010011=>1100100
[1,4,3,7,5,8,2,6]=>0010011=>1100100
[1,4,3,7,2,6,5,8]=>0010110=>0110100
[1,5,3,7,4,8,2,6]=>0001011=>1101000
[1,3,2,6,5,8,4,7]=>0100101=>1010010
[1,5,4,8,2,6,3,7]=>0001101=>1011000
[1,5,4,8,3,7,2,6]=>0001011=>1101000
[1,2,3,6,5,8,4,7]=>0000101=>1010000
[6,8,2,4,5,7,1,3]=>0000011=>1100000
[3,7,8,4,5,2,6,1]=>0001101=>1011000
[7,8,1,4,5,3,6,2]=>0001101=>1011000
[3,8,7,4,1,6,5,2]=>0011111=>1111100
[4,8,3,6,1,5,7,2]=>0000111=>1110000
[5,8,3,1,6,4,7,2]=>0100111=>1110010
[5,8,1,4,7,6,3,2]=>0100111=>1110010
[7,5,1,8,6,2,4,3]=>0011111=>1111100
[7,4,1,8,2,6,3,5]=>0010111=>1110100
[7,1,8,4,2,6,3,5]=>0010111=>1110100
[1,6,3,8,5,2,4,7]=>0001101=>1011000
[6,1,3,8,5,2,4,7]=>0001101=>1011000
[7,1,8,3,6,2,5,4]=>0001111=>1111000
[7,3,1,8,4,2,6,5]=>0110111=>1110110
[7,2,8,4,1,6,5,3]=>0011111=>1111100
[7,2,8,3,6,5,1,4]=>0001111=>1111000
[7,2,8,3,6,1,5,4]=>0001111=>1111000
[7,1,8,2,3,6,5,4]=>0001111=>1111000
[6,1,2,8,3,5,4,7]=>0001101=>1011000
[1,5,2,3,8,4,7,6]=>0001011=>1101000
[5,1,2,3,8,4,7,6]=>0001011=>1101000
[5,2,3,8,1,4,7,6]=>0001011=>1101000
[6,2,8,1,3,5,4,7]=>0001101=>1011000
[6,2,4,1,8,7,3,5]=>0010111=>1110100
[6,3,1,4,2,8,5,7]=>0110101=>1010110
[3,1,6,4,2,8,5,7]=>0110101=>1010110
[2,6,3,8,7,1,5,4]=>0001111=>1111000
[2,6,3,8,5,1,4,7]=>0001101=>1011000
[2,5,1,8,3,4,7,6]=>0001011=>1101000
[2,5,1,3,8,4,7,6]=>0001011=>1101000
[1,2,5,3,8,4,7,6]=>0001011=>1101000
[1,2,4,8,3,7,6,5]=>0000111=>1110000
[2,4,8,1,3,7,6,5]=>0000111=>1110000
[2,4,8,3,7,1,6,5]=>0000111=>1110000
[2,4,8,3,7,6,1,5]=>0000111=>1110000
[2,5,3,8,1,7,4,6]=>0001011=>1101000
[2,5,4,1,3,8,7,6]=>0011011=>1101100
[3,1,5,4,8,2,7,6]=>0101011=>1101010
[5,3,1,4,8,2,7,6]=>0101011=>1101010
[5,2,3,8,4,7,1,6]=>0001011=>1101000
[4,8,2,3,7,6,1,5]=>0000111=>1110000
[4,8,2,3,7,1,6,5]=>0000111=>1110000
[4,8,1,2,3,7,6,5]=>0000111=>1110000
[1,4,8,2,3,7,6,5]=>0000111=>1110000
[1,4,8,3,7,2,6,5]=>0000111=>1110000
[6,3,8,1,5,2,4,7]=>0001101=>1011000
[5,3,8,1,2,4,7,6]=>0001011=>1101000
[5,1,3,8,2,4,7,6]=>0001011=>1101000
[1,5,3,8,2,4,7,6]=>0001011=>1101000
[1,5,4,8,2,7,6,3]=>0001111=>1111000
[5,1,4,8,2,7,6,3]=>0001111=>1111000
[5,4,8,1,2,7,6,3]=>0001111=>1111000
[6,5,1,2,8,7,4,3]=>0011111=>1111100
[5,3,1,6,4,2,8,7]=>0111101=>1011110
[5,1,6,2,8,7,4,3]=>0011111=>1111100
[4,1,5,8,2,7,6,3]=>0010111=>1110100
[4,1,2,5,8,7,6,3]=>0010111=>1110100
[1,4,2,5,8,7,6,3]=>0010111=>1110100
[1,3,5,2,8,7,4,6]=>0001011=>1101000
[3,5,1,2,8,7,4,6]=>0001011=>1101000
[3,6,2,8,7,5,1,4]=>0001111=>1111000
[4,2,6,1,8,7,3,5]=>0010111=>1110100
[4,3,1,5,8,2,7,6]=>0110011=>1100110
[3,5,2,8,7,1,4,6]=>0001011=>1101000
[3,4,8,7,2,6,1,5]=>0000111=>1110000
[3,4,8,7,1,2,6,5]=>0000111=>1110000
[3,4,8,1,7,2,6,5]=>0000111=>1110000
[1,3,4,8,7,2,6,5]=>0000111=>1110000
[1,3,4,8,2,7,6,5]=>0000111=>1110000
[3,4,8,1,2,7,6,5]=>0000111=>1110000
[3,4,8,2,7,1,6,5]=>0000111=>1110000
[3,4,8,2,7,6,1,5]=>0000111=>1110000
[4,2,5,8,1,7,6,3]=>0010111=>1110100
[4,3,1,2,5,8,7,6]=>0110011=>1100110
[3,1,4,2,5,8,7,6]=>0110011=>1100110
[2,3,5,1,8,7,6,4]=>0001111=>1111000
[7,8,2,1,5,3,6,4]=>1001101=>1011001
[6,4,1,2,7,3,5,8]=>0010110=>0110100
[2,3,7,5,4,1,8,6]=>0011011=>1101100
[6,3,1,5,4,2,7,8]=>0111100=>0011110
[7,8,1,5,4,2,6,3]=>0011101=>1011100
[7,8,3,5,4,1,6,2]=>0011101=>1011100
[7,8,2,5,4,1,3,6]=>0011001=>1001100
[7,8,2,5,4,6,1,3]=>0001101=>1011000
[6,2,1,5,4,7,3,8]=>1001110=>0111001
[5,3,6,1,4,7,8,2]=>0001101=>1011000
[5,3,6,2,4,7,1,8]=>0001110=>0111000
[6,4,2,1,7,3,8,5]=>1010111=>1110101
[4,3,7,5,8,6,1,2]=>0010111=>1110100
[4,2,7,1,8,3,6,5]=>0010111=>1110100
[3,2,6,7,4,8,1,5]=>0100011=>1100010
[3,1,6,7,4,8,5,2]=>0101011=>1101010
[1,7,6,5,3,8,4,2]=>0011111=>1111100
[2,7,6,5,3,8,1,4]=>0001111=>1111000
[1,7,6,5,2,4,8,3]=>0001111=>1111000
[2,7,6,5,3,1,4,8]=>0101110=>0111010
[2,7,1,4,8,3,5,6]=>0000011=>1100000
[3,7,6,4,8,5,1,2]=>0001111=>1111000
[5,7,6,3,8,4,1,2]=>0010111=>1110100
[5,1,6,2,4,8,3,7]=>0001101=>1011000
[4,7,6,5,2,1,3,8]=>1001110=>0111001
[4,7,6,5,2,8,1,3]=>0001111=>1111000
[4,7,6,5,1,8,3,2]=>0101111=>1111010
[1,7,6,5,2,8,3,4]=>0001111=>1111000
[1,7,6,5,3,2,8,4]=>0101111=>1111010
[4,7,6,5,1,2,8,3]=>0001111=>1111000
[4,7,6,5,3,1,8,2]=>0101111=>1111010
[6,1,3,5,4,8,7,2]=>0001111=>1111000
[5,2,6,3,4,1,7,8]=>0011100=>0011100
[5,1,6,2,4,7,8,3]=>0001101=>1011000
[1,2,6,3,4,8,7,5]=>0000111=>1110000
[1,7,2,4,8,3,6,5]=>0000111=>1110000
[6,1,4,2,8,3,5,7]=>0010101=>1010100
[4,1,8,2,6,3,5,7]=>0010101=>1010100
[4,7,2,1,5,3,6,8]=>1001010=>0101001
[4,7,1,6,2,3,8,5]=>0000111=>1110000
[1,7,2,6,8,3,5,4]=>0001011=>1101000
[1,2,6,7,4,8,5,3]=>0001011=>1101000
[3,1,6,7,4,2,8,5]=>0110011=>1100110
[3,2,8,5,4,6,1,7]=>0101101=>1011010
[4,7,6,3,5,8,1,2]=>0000111=>1110000
[4,7,1,2,5,3,8,6]=>0001011=>1101000
[3,7,6,5,2,4,1,8]=>0011110=>0111100
[3,7,6,5,1,4,8,2]=>0001111=>1111000
[3,7,6,5,2,1,8,4]=>1001111=>1111001
[1,7,6,5,8,2,4,3]=>0010111=>1110100
[3,7,6,5,8,1,4,2]=>0010111=>1110100
[3,7,6,5,1,2,4,8]=>0001110=>0111000
[3,1,6,8,4,2,5,7]=>0110001=>1000110
[4,7,6,8,3,5,1,2]=>0001011=>1101000
[2,7,6,5,1,4,3,8]=>0011110=>0111100
[2,7,6,5,8,1,3,4]=>0000111=>1110000
[2,7,6,5,8,4,1,3]=>0010111=>1110100
[6,3,2,1,7,4,8,5]=>1100111=>1110011
[4,2,1,7,3,5,8,6]=>1010011=>1100101
[7,3,1,5,4,2,8,6]=>0111011=>1101110
[8,4,1,5,2,7,6,3]=>0011111=>1111100
[8,2,5,1,3,7,6,4]=>0001111=>1111000
[4,3,7,2,1,5,8,6]=>1010011=>1100101
[6,3,7,4,2,1,8,5]=>1010111=>1110101
[4,7,2,5,3,1,8,6]=>0101011=>1101010
[2,7,5,4,1,3,8,6]=>0011011=>1101100
[7,5,4,3,2,1,8,6]=>1111011=>1101111
[8,5,3,2,1,7,6,4]=>1101111=>1111011
[6,5,2,1,8,4,3,7]=>1011101=>1011101
[4,6,3,2,8,1,5,7]=>0100101=>1010010
[5,7,4,3,2,8,1,6]=>0110011=>1100110
[1,7,6,2,4,8,3,5]=>0000111=>1110000
[2,7,3,6,4,8,1,5]=>0000111=>1110000
[6,2,7,5,3,8,1,4]=>0001111=>1111000
[7,1,8,5,3,6,4,2]=>0011111=>1111100
[5,8,1,6,2,7,4,3]=>0010111=>1110100
[1,8,6,2,3,7,5,4]=>0001111=>1111000
[1,8,6,3,2,7,5,4]=>0101111=>1111010
[5,8,3,2,7,1,6,4]=>0100111=>1110010
[8,7,3,1,6,5,4,2]=>0111111=>1111110
[8,7,2,6,1,5,4,3]=>0011111=>1111100
[1,8,5,7,4,3,6,2]=>0010111=>1110100
[1,8,5,7,2,4,6,3]=>0000111=>1110000
[3,8,6,1,7,2,5,4]=>0001111=>1111000
[5,8,4,6,7,1,3,2]=>0100011=>1100010
[7,2,8,5,6,1,4,3]=>0010111=>1110100
[6,3,7,5,8,2,1,4]=>1000111=>1110001
[3,7,2,6,8,4,1,5]=>0010011=>1100100
[3,6,5,8,1,4,2,7]=>0010101=>1010100
[2,6,5,8,4,1,3,7]=>0010101=>1010100
[6,5,4,8,3,2,1,7]=>1101101=>1011011
[8,4,3,7,2,1,6,5]=>1010111=>1110101
[8,2,4,7,1,3,6,5]=>0000111=>1110000
[6,2,5,8,1,4,3,7]=>0010101=>1010100
[4,3,6,8,2,1,5,7]=>1010001=>1000101
[6,3,5,1,8,4,2,7]=>0011101=>1011100
[8,4,1,5,7,3,6,2]=>0010111=>1110100
[6,4,2,5,8,3,1,7]=>0110101=>1010110
[5,4,1,6,8,2,3,7]=>0011001=>1001100
[6,5,2,1,7,8,3,4]=>1001101=>1011001
[6,3,7,4,8,5,2,1]=>1001111=>1111001
[4,7,2,5,8,6,3,1]=>0100111=>1110010
[6,3,1,8,4,7,5,2]=>0101111=>1111010
[6,4,2,8,7,3,5,1]=>0011111=>1111100
[6,5,3,8,7,4,1,2]=>0011111=>1111100
[8,5,3,7,6,4,2,1]=>1011111=>1111101
[5,4,8,1,7,6,2,3]=>0001111=>1111000
[5,2,8,1,7,3,6,4]=>0001111=>1111000
[6,4,8,2,1,7,5,3]=>1001111=>1111001
[3,6,8,1,4,7,5,2]=>0001011=>1101000
[5,7,3,8,1,6,4,2]=>0010111=>1110100
[6,4,7,8,1,5,3,2]=>0101101=>1011010
[6,3,7,8,5,2,4,1]=>0011101=>1011100
[2,5,8,7,1,3,6,4]=>0000111=>1110000
[5,3,8,7,2,1,6,4]=>1001111=>1111001
[8,3,7,6,1,5,4,2]=>0011111=>1111100
[8,2,7,6,5,1,4,3]=>0011111=>1111100
[4,3,8,7,6,2,1,5]=>1010111=>1110101
[2,4,8,7,6,1,3,5]=>0000111=>1110000
[3,5,8,7,2,6,1,4]=>0000111=>1110000
[4,7,3,8,6,5,1,2]=>0001111=>1111000
[7,5,8,6,4,3,2,1]=>1110111=>1110111
[5,8,7,3,6,4,2,1]=>1010111=>1110101
[4,8,7,6,2,5,3,1]=>0101111=>1111010
[3,8,7,6,5,1,4,2]=>0011111=>1111100
[2,8,7,6,5,4,1,3]=>0011111=>1111100
[3,4,1,2,5,6,7,8,9]=>00100000=>00000100
[3,2,1,4,5,6,7,8,9]=>11000000=>00000011
[4,5,6,1,2,3,7,8,9]=>00001000=>00010000
[4,2,5,1,3,6,7,8,9]=>00110000=>00001100
[4,3,2,1,5,6,7,8,9]=>11100000=>00000111
[5,6,7,8,1,2,3,4,9]=>00000010=>01000000
[5,2,6,7,1,3,4,8,9]=>00010100=>00101000
[5,6,3,4,1,2,7,8,9]=>00101000=>00010100
[5,3,2,6,1,4,7,8,9]=>01011000=>00011010
[5,4,3,2,1,6,7,8,9]=>11110000=>00001111
[6,2,7,8,9,1,3,4,5]=>00001001=>10010000
[6,7,3,4,8,1,2,5,9]=>00000110=>01100000
[6,3,2,7,8,1,4,5,9]=>01001010=>01010010
[6,4,7,2,5,1,3,8,9]=>00011100=>00111000
[6,4,3,2,7,1,5,8,9]=>01101100=>00110110
[6,5,4,3,2,1,7,8,9]=>11111000=>00011111
[7,4,8,2,5,9,1,3,6]=>00000111=>11100000
[7,4,3,2,8,9,1,5,6]=>01100101=>10100110
[7,8,5,6,3,4,1,2,9]=>00101010=>01010100
[7,5,3,8,2,6,1,4,9]=>00011110=>01111000
[7,5,4,3,2,8,1,6,9]=>01110110=>01101110
[7,6,5,4,3,2,1,8,9]=>11111100=>00111111
[8,6,9,4,7,2,5,1,3]=>00010111=>11101000
[8,6,4,3,9,2,7,1,5]=>00101111=>11110100
[8,6,5,4,3,2,9,1,7]=>01111011=>11011110
[3,4,1,2,5,6,7,8,9,10]=>001000000=>000000100
[3,2,1,4,5,6,7,8,9,10]=>110000000=>000000011
[4,5,6,1,2,3,7,8,9,10]=>000010000=>000010000
[4,2,5,1,3,6,7,8,9,10]=>001100000=>000001100
[4,3,2,1,5,6,7,8,9,10]=>111000000=>000000111
[5,6,7,8,1,2,3,4,9,10]=>000000100=>001000000
[5,2,6,7,1,3,4,8,9,10]=>000101000=>000101000
[5,6,3,4,1,2,7,8,9,10]=>001010000=>000010100
[5,3,2,6,1,4,7,8,9,10]=>010110000=>000011010
[5,4,3,2,1,6,7,8,9,10]=>111100000=>000001111
[6,2,7,8,9,1,3,4,5,10]=>000010010=>010010000
[6,7,3,4,8,1,2,5,9,10]=>000001100=>001100000
[6,3,2,7,8,1,4,5,9,10]=>010010100=>001010010
[6,4,7,2,5,1,3,8,9,10]=>000111000=>000111000
[6,4,3,2,7,1,5,8,9,10]=>011011000=>000110110
[6,5,4,3,2,1,7,8,9,10]=>111110000=>000011111
[7,8,3,4,9,10,1,2,5,6]=>000000101=>101000000
[7,8,9,4,5,6,1,2,3,10]=>000010010=>010010000
[7,4,3,2,8,9,1,5,6,10]=>011001010=>010100110
[7,8,5,6,3,4,1,2,9,10]=>001010100=>001010100
[7,5,3,8,2,6,1,4,9,10]=>000111100=>001111000
[7,5,4,3,2,8,1,6,9,10]=>011101100=>001101110
[7,6,5,4,3,2,1,8,9,10]=>111111000=>000111111
[8,5,9,10,2,6,7,1,3,4]=>000001101=>101100000
[8,5,3,9,2,6,10,1,4,7]=>000100111=>111001000
[8,6,9,4,7,2,5,1,3,10]=>000101110=>011101000
[8,6,4,3,9,2,7,1,5,10]=>001011110=>011110100
[8,6,5,4,3,2,9,1,7,10]=>011110110=>011011110
[8,7,6,5,4,3,2,1,9,10]=>111111100=>001111111
[9,7,5,4,3,10,2,8,1,6]=>001101111=>111101100
[3,6,5,1,2,4,8,7]=>0001101=>1011000
[3,7,5,8,2,4,1,6]=>0010011=>1100100
[3,8,5,7,2,4,1,6]=>0010011=>1100100
[5,1,7,8,4,3,2,6]=>0111001=>1001110
[5,1,2,6,4,3,8,7]=>0011101=>1011100
[6,1,2,5,4,3,8,7]=>0011101=>1011100
[5,1,2,4,6,3,8,7]=>0001101=>1011000
[4,1,2,6,5,3,8,7]=>0011101=>1011100
[4,1,5,7,8,3,2,6]=>0110001=>1000110
[4,1,5,8,7,3,2,6]=>0110011=>1100110
[4,7,1,8,3,6,2,5]=>0000111=>1110000
[4,1,7,8,5,2,3,6]=>0011001=>1001100
[5,1,7,4,8,2,3,6]=>0001011=>1101000
[7,5,3,8,1,4,2,6]=>0011011=>1101100
[2,1,5,8,7,3,4,6]=>1000011=>1100001
[5,1,8,4,7,2,3,6]=>0001011=>1101000
[4,1,8,7,5,2,3,6]=>0011011=>1101100
[4,7,1,6,3,2,8,5]=>0100111=>1110010
[6,1,2,3,7,5,8,4]=>0000111=>1110000
[7,1,2,3,8,6,5,4]=>0001111=>1111000
[7,1,2,3,5,8,6,4]=>0000111=>1110000
[6,8,1,4,3,7,2,5]=>0010011=>1100100
[8,7,3,2,4,1,6,5]=>0110111=>1110110
[2,1,7,3,4,8,6,5]=>1000111=>1110001
[7,8,3,2,4,1,6,5]=>0110101=>1010110
[6,7,1,4,3,8,2,5]=>0010011=>1100100
[8,1,2,3,5,7,6,4]=>0000111=>1110000
[8,1,2,3,6,7,5,4]=>0001011=>1101000
[7,1,2,3,6,8,5,4]=>0001011=>1101000
[7,1,2,3,8,5,6,4]=>0000111=>1110000
[8,1,2,3,7,5,6,4]=>0000111=>1110000
[8,1,2,3,6,5,7,4]=>0000111=>1110000
[7,1,8,5,4,3,2,6]=>0111011=>1101110
[7,8,2,6,3,4,1,5]=>0010101=>1010100
[6,8,2,7,3,4,1,5]=>0010011=>1100100
[6,7,2,8,3,4,1,5]=>0010011=>1100100
[3,8,7,1,4,2,6,5]=>0010111=>1110100
[3,7,8,1,4,2,6,5]=>0010101=>1010100
[3,6,8,1,4,2,7,5]=>0010011=>1100100
[3,5,7,8,2,4,1,6]=>0010001=>1000100
[3,6,7,1,4,2,8,5]=>0010011=>1100100
[7,6,2,8,3,1,4,5]=>0100111=>1110010
[8,6,2,7,3,1,4,5]=>0100111=>1110010
[8,1,7,5,4,3,2,6]=>0111011=>1101110
[8,1,7,4,5,3,2,6]=>0101011=>1101010
[5,8,3,7,1,4,2,6]=>0010011=>1100100
[2,1,7,3,4,6,8,5]=>1000011=>1100001
[6,7,3,2,4,1,8,5]=>0110011=>1100110
[8,7,2,4,3,6,1,5]=>0010111=>1110100
[7,1,2,3,5,6,8,4]=>0000011=>1100000
[6,1,2,3,8,7,4,5]=>0000111=>1110000
[5,1,2,3,7,8,6,4]=>0001101=>1011000
[5,1,2,3,8,7,6,4]=>0001111=>1111000
[5,1,2,3,8,6,7,4]=>0001011=>1101000
[6,1,2,3,5,8,7,4]=>0000111=>1110000
[8,6,2,4,3,1,7,5]=>0110111=>1110110
[7,6,3,2,4,8,1,5]=>0100111=>1110010
[2,1,6,3,4,8,7,5]=>1000111=>1110001
[8,6,3,2,4,7,1,5]=>0100111=>1110010
[7,6,2,4,3,1,8,5]=>0110111=>1110110
[6,1,2,3,5,7,8,4]=>0000101=>1010000
[5,1,2,3,6,8,7,4]=>0001011=>1101000
[7,8,1,2,6,3,5,4]=>0001101=>1011000
[1,4,8,2,7,3,5,6]=>0000011=>1100000
[1,2,8,5,4,7,3,6]=>0001011=>1101000
[1,3,8,5,4,2,7,6]=>0011011=>1101100
[2,3,6,8,4,7,1,5]=>0000011=>1100000
[1,3,6,8,4,7,5,2]=>0001011=>1101000
[2,4,8,1,7,3,6,5]=>0000111=>1110000
[3,4,8,5,7,6,1,2]=>0000111=>1110000
[1,2,6,8,4,5,7,3]=>0000011=>1100000
[7,5,1,2,4,3,6,8]=>0011010=>0101100
[7,4,6,1,5,2,3,8]=>0001110=>0111000
[7,1,4,2,6,3,5,8]=>0010110=>0110100
[6,8,1,4,7,2,3,5]=>0000011=>1100000
[1,6,4,2,8,3,5,7]=>0010101=>1010100
[1,6,3,8,5,4,2,7]=>0011101=>1011100
[6,8,1,7,3,5,4,2]=>0011011=>1101100
[7,1,3,6,5,4,2,8]=>0011110=>0111100
[7,3,1,6,5,4,2,8]=>0111110=>0111110
[7,2,1,4,6,3,5,8]=>1000110=>0110001
[7,2,3,6,5,1,4,8]=>0001110=>0111000
[7,1,2,3,6,5,4,8]=>0001110=>0111000
[6,8,1,2,7,3,5,4]=>0001011=>1101000
[1,6,2,3,8,5,4,7]=>0001101=>1011000
[1,5,8,2,7,6,3,4]=>0000111=>1110000
[5,1,8,2,7,6,3,4]=>0001111=>1111000
[5,8,2,7,6,3,4,1]=>0010111=>1110100
[6,2,8,1,7,3,5,4]=>0001111=>1111000
[6,8,2,1,7,4,3,5]=>1010011=>1100101
[3,6,4,1,2,8,5,7]=>0010101=>1010100
[2,1,6,3,8,5,4,7]=>1001101=>1011001
[2,5,1,8,7,6,3,4]=>0001111=>1111000
[2,5,3,8,7,4,6,1]=>0001111=>1111000
[1,2,5,3,8,7,4,6]=>0001011=>1101000
[2,4,8,7,6,5,1,3]=>0001111=>1111000
[2,5,3,8,7,1,6,4]=>0001111=>1111000
[2,5,8,4,1,7,6,3]=>0010111=>1110100
[3,5,8,7,1,4,2,6]=>0010011=>1100100
[5,3,8,4,1,7,6,2]=>0011111=>1111100
[4,2,8,7,6,3,5,1]=>0011111=>1111100
[4,2,8,7,6,5,3,1]=>0111111=>1111110
[4,1,8,7,6,5,3,2]=>0111111=>1111110
[4,3,8,7,6,5,1,2]=>0011111=>1111100
[6,3,1,8,7,2,5,4]=>0101111=>1111010
[5,8,3,7,6,1,4,2]=>0010111=>1110100
[5,1,3,8,7,6,2,4]=>0001111=>1111000
[1,5,3,8,7,6,2,4]=>0001111=>1111000
[1,5,8,4,7,2,6,3]=>0000111=>1110000
[5,1,8,4,7,2,6,3]=>0001111=>1111000
[5,8,7,4,6,1,2,3]=>0000111=>1110000
[6,8,5,1,2,4,7,3]=>0001011=>1101000
[5,6,3,1,2,4,8,7]=>0100101=>1010010
[5,6,2,4,3,1,8,7]=>0110101=>1010110
[5,6,1,2,4,3,8,7]=>0010101=>1010100
[4,5,8,1,7,2,3,6]=>0000011=>1100000
[4,5,8,1,7,2,6,3]=>0000111=>1110000
[1,3,2,5,8,7,4,6]=>0100011=>1100010
[3,5,1,8,7,4,6,2]=>0001111=>1111000
[3,5,1,8,7,2,6,4]=>0001111=>1111000
[4,3,6,1,2,8,5,7]=>0010101=>1010100
[4,5,8,3,1,7,2,6]=>0100011=>1100010
[4,5,2,8,7,1,3,6]=>0001011=>1101000
[3,2,5,8,7,1,6,4]=>0100111=>1110010
[3,4,8,7,6,2,1,5]=>1000111=>1110001
[3,1,4,8,7,6,2,5]=>0100111=>1110010
[3,4,8,7,6,5,1,2]=>0001111=>1111000
[1,3,4,8,7,6,2,5]=>0000111=>1110000
[3,4,8,7,6,2,5,1]=>0001111=>1111000
[3,2,5,8,7,4,6,1]=>0100111=>1110010
[4,5,8,3,1,7,6,2]=>0100111=>1110010
[2,1,3,5,8,7,4,6]=>1000011=>1100001
[1,2,7,5,8,6,4,3]=>0010111=>1110100
[7,1,4,8,2,6,5,3]=>0001111=>1111000
[6,8,1,3,7,5,2,4]=>0001011=>1101000
[3,7,8,1,2,6,5,4]=>0001101=>1011000
[1,3,7,8,2,6,5,4]=>0001101=>1011000
[2,3,7,8,1,6,5,4]=>0001101=>1011000
[2,7,8,1,3,6,5,4]=>0001101=>1011000
[8,1,2,6,7,3,5,4]=>0001011=>1101000
[8,1,2,6,7,5,3,4]=>0001011=>1101000
[8,2,5,7,1,3,6,4]=>0000111=>1110000
[2,8,1,6,7,3,5,4]=>0001011=>1101000
[2,6,8,3,7,1,5,4]=>0001011=>1101000
[2,8,6,4,7,1,5,3]=>0001111=>1111000
[6,8,3,4,1,7,5,2]=>0011011=>1101100
[6,8,3,7,4,1,5,2]=>0011011=>1101100
[2,6,8,3,7,5,1,4]=>0001011=>1101000
[2,8,1,6,7,5,3,4]=>0001011=>1101000
[8,2,5,7,1,6,3,4]=>0000111=>1110000
[8,4,7,2,3,6,1,5]=>0000111=>1110000
[8,5,7,4,2,6,1,3]=>0010111=>1110100
[8,3,5,7,4,1,6,2]=>0010111=>1110100
[8,5,2,4,7,1,6,3]=>0001111=>1111000
[8,2,3,5,7,1,6,4]=>0000111=>1110000
[8,2,4,7,3,6,1,5]=>0000111=>1110000
[8,2,7,1,4,6,3,5]=>0000111=>1110000
[8,7,1,2,4,6,3,5]=>0000111=>1110000
[8,7,1,4,6,2,3,5]=>0000111=>1110000
[8,4,7,1,3,6,2,5]=>0000111=>1110000
[1,6,8,3,7,2,5,4]=>0001011=>1101000
[8,3,5,7,1,2,6,4]=>0000111=>1110000
[5,8,7,1,3,6,2,4]=>0000111=>1110000
[8,5,4,7,1,6,2,3]=>0001111=>1111000
[8,5,4,7,1,2,6,3]=>0001111=>1111000
[8,5,1,4,7,2,6,3]=>0001111=>1111000
[1,4,6,8,2,7,5,3]=>0001011=>1101000
[1,6,5,8,2,7,4,3]=>0010111=>1110100
[8,5,6,3,1,7,4,2]=>0110111=>1110110
[5,6,2,8,1,7,4,3]=>0010111=>1110100
[1,8,4,5,7,2,6,3]=>0000111=>1110000
[5,8,7,3,6,1,2,4]=>0000111=>1110000
[8,3,5,7,1,6,2,4]=>0000111=>1110000
[1,6,8,3,7,5,2,4]=>0001011=>1101000
[6,3,8,2,7,5,1,4]=>0001111=>1111000
[6,8,4,2,7,1,5,3]=>0011011=>1101100
[8,6,4,7,3,1,5,2]=>0101111=>1111010
[8,4,5,7,3,1,6,2]=>0100111=>1110010
[8,4,2,5,7,1,6,3]=>0010111=>1110100
[8,3,4,7,2,6,1,5]=>0000111=>1110000
[8,7,1,3,4,6,2,5]=>0000111=>1110000
[8,3,7,2,4,6,1,5]=>0000111=>1110000
[2,8,4,5,7,1,6,3]=>0000111=>1110000
[8,7,3,4,5,1,6,2]=>0001111=>1111000
[8,7,4,5,2,6,1,3]=>0001111=>1111000
[5,8,7,2,3,6,1,4]=>0000111=>1110000
[8,7,2,3,4,6,1,5]=>0000111=>1110000
[8,7,2,3,6,1,4,5]=>0000111=>1110000
[1,3,2,8,5,4,7,6]=>0101011=>1101010
[4,2,8,5,3,7,1,6]=>0011011=>1101100
[5,2,1,8,4,3,7,6]=>1011011=>1101101
[6,2,8,4,3,7,5,1]=>0011111=>1111100
[7,2,8,4,3,1,6,5]=>0110111=>1110110
[7,3,4,8,2,1,6,5]=>1000111=>1110001
[6,3,4,8,2,7,5,1]=>0001111=>1111000
[5,3,4,1,8,2,7,6]=>0011011=>1101100
[8,1,4,5,2,3,7,6]=>0001011=>1101000
[8,1,5,4,3,2,7,6]=>0111011=>1101110
[3,5,4,2,8,1,7,6]=>0011011=>1101100
[4,5,3,2,8,7,1,6]=>0101011=>1101010
[6,4,3,2,8,7,5,1]=>0111111=>1111110
[6,5,3,2,1,7,8,4]=>1101101=>1011011
[5,6,3,2,7,8,4,1]=>0110101=>1010110
[4,1,6,3,2,7,8,5]=>0110101=>1010110
[3,6,4,2,7,8,1,5]=>0010101=>1010100
[8,1,6,4,3,7,2,5]=>0010111=>1110100
[8,1,7,4,3,6,5,2]=>0011111=>1111100
[2,7,4,1,3,6,5,8]=>0010110=>0110100
[3,7,4,2,6,1,5,8]=>0010110=>0110100
[4,1,7,3,2,6,5,8]=>0110110=>0110110
[5,7,3,2,6,4,8,1]=>0100111=>1110010
[6,7,3,2,5,4,1,8]=>0111010=>0101110
[7,6,3,2,1,5,4,8]=>1101110=>0111011
[4,7,5,6,2,3,8,1]=>0000111=>1110000
[3,1,7,5,6,2,4,8]=>0100110=>0110010
[2,7,5,6,1,3,4,8]=>0000110=>0110000
[2,6,5,7,1,3,8,4]=>0000111=>1110000
[4,6,5,7,2,8,1,3]=>0000111=>1110000
[5,6,4,7,2,8,3,1]=>0100111=>1110010
[6,5,4,1,7,2,8,3]=>0011111=>1111100
[7,5,4,6,2,1,8,3]=>1001111=>1111001
[6,4,5,7,1,8,2,3]=>0000111=>1110000
[5,4,6,1,7,8,2,3]=>0001101=>1011000
[8,1,5,6,7,2,3,4]=>0000011=>1100000
[2,1,4,6,8,7,3,5]=>1000011=>1100001
[3,4,6,8,7,1,2,5]=>0000011=>1100000
[4,3,1,6,8,7,2,5]=>0110011=>1100110
[5,3,6,8,7,2,4,1]=>0011011=>1101100
[6,3,5,1,8,7,2,4]=>0001111=>1111000
[7,3,5,8,6,2,1,4]=>1000111=>1110001
[7,2,8,5,6,3,1,4]=>0100111=>1110010
[6,2,8,5,1,7,3,4]=>0001111=>1111000
[4,2,1,8,6,7,3,5]=>1010011=>1100101
[1,3,2,8,6,7,4,5]=>0100011=>1100010
[2,3,8,6,7,1,4,5]=>0000011=>1100000
[8,1,3,2,6,7,4,5]=>0100011=>1100010
[2,3,8,7,1,6,5,4]=>0001111=>1111000
[4,2,8,7,6,1,5,3]=>0011111=>1111100
[5,2,8,7,6,4,1,3]=>0011111=>1111100
[7,2,1,8,6,5,4,3]=>1011111=>1111101
[7,3,6,1,8,5,4,2]=>0011111=>1111100
[6,3,7,8,5,4,2,1]=>1011101=>1011101
[5,3,7,8,6,4,1,2]=>0011101=>1011100
[4,3,1,7,8,6,5,2]=>0111101=>1011110
[3,4,7,8,6,1,5,2]=>0001101=>1011000
[8,1,5,7,6,2,4,3]=>0010111=>1110100
[3,5,7,6,8,1,4,2]=>0010011=>1100100
[4,5,7,6,8,3,1,2]=>0100011=>1100010
[5,4,1,7,6,8,3,2]=>0111011=>1101110
[6,4,7,5,8,3,2,1]=>1100111=>1110011
[7,4,6,5,1,8,3,2]=>0101111=>1111010
[7,5,6,4,3,1,8,2]=>0110111=>1110110
[6,5,1,7,4,3,8,2]=>0011111=>1111100
[4,6,7,5,3,8,1,2]=>0001011=>1101000
[3,6,7,5,1,4,8,2]=>0001011=>1101000
[8,1,6,7,5,4,2,3]=>0011011=>1101100
[8,1,7,6,5,4,3,2]=>0111111=>1111110
[2,7,6,1,5,4,3,8]=>0011110=>0111100
[3,7,6,5,1,4,2,8]=>0011110=>0111100
[4,7,6,5,3,1,2,8]=>0101110=>0111010
[8,6,4,3,1,5,7,2]=>0110111=>1110110
[8,6,4,1,5,2,7,3]=>0011111=>1111100
[8,6,5,1,3,2,7,4]=>0101111=>1111010
[8,6,3,1,7,2,4,5]=>0100111=>1110010
[8,7,3,1,5,2,4,6]=>0101011=>1101010
[5,3,1,7,2,4,6,8]=>0101010=>0101010
[8,7,1,2,4,5,3,6]=>0001011=>1101000
[8,6,1,2,4,7,3,5]=>0000111=>1110000
[8,5,1,2,6,7,3,4]=>0001011=>1101000
[8,5,1,6,4,2,7,3]=>0011111=>1111100
[8,5,1,3,6,4,7,2]=>0001111=>1111000
[8,6,1,5,3,4,7,2]=>0001111=>1111000
[8,6,1,5,2,4,7,3]=>0001111=>1111000
[8,6,1,2,5,7,3,4]=>0000111=>1110000
[8,6,1,2,7,4,3,5]=>0010111=>1110100
[8,7,1,2,5,4,3,6]=>0011011=>1101100
[5,1,4,2,3,8,6,7]=>0011001=>1001100
[5,1,4,2,7,3,6,8]=>0011010=>0101100
[7,1,5,8,2,6,3,4]=>0000111=>1110000
[5,7,8,1,2,4,6,3]=>0000101=>1010000
[5,7,8,1,3,4,6,2]=>0000101=>1010000
[5,8,1,7,3,4,6,2]=>0000111=>1110000
[8,1,5,7,2,4,6,3]=>0000111=>1110000
[8,4,1,2,7,6,3,5]=>0010111=>1110100
[1,4,2,3,8,7,5,6]=>0010011=>1100100
[1,4,2,7,6,3,5,8]=>0010110=>0110100
[6,1,2,8,7,5,3,4]=>0001111=>1111000
[6,1,2,4,8,7,5,3]=>0001111=>1111000
[3,1,8,4,6,7,5,2]=>0101011=>1101010
[3,1,7,6,4,8,5,2]=>0101111=>1111010
[7,1,2,4,6,8,5,3]=>0001011=>1101000
[7,1,2,6,8,5,3,4]=>0001011=>1101000
[6,1,2,7,8,5,3,4]=>0001101=>1011000
[6,1,2,7,4,8,5,3]=>0001111=>1111000
[3,1,6,4,7,8,5,2]=>0101101=>1011010
[5,7,1,3,8,4,6,2]=>0000111=>1110000
[5,7,1,8,4,2,6,3]=>0010111=>1110100
[7,1,5,3,2,8,6,4]=>0101111=>1111010
[7,1,4,5,2,8,6,3]=>0001111=>1111000
[4,7,3,1,5,8,6,2]=>0100111=>1110010
[4,8,7,3,1,5,6,2]=>0100111=>1110010
[8,1,7,4,5,2,6,3]=>0001111=>1111000
[8,1,7,5,3,2,6,4]=>0101111=>1111010
[8,3,7,1,2,6,4,5]=>0000111=>1110000
[3,1,2,8,4,7,5,6]=>0100011=>1100010
[3,1,2,8,6,4,5,7]=>0100101=>1010010
[3,1,7,2,6,4,5,8]=>0100110=>0110010
[1,4,2,3,8,6,5,7]=>0010101=>1010100
[1,4,2,3,8,5,7,6]=>0010011=>1100100
[5,8,1,7,2,4,6,3]=>0000111=>1110000
[5,8,1,3,4,7,6,2]=>0000111=>1110000
[3,1,8,6,4,7,5,2]=>0101111=>1111010
[8,1,2,6,7,4,5,3]=>0001011=>1101000
[6,1,2,8,7,3,5,4]=>0001111=>1111000
[1,2,3,5,8,4,7,6]=>0000011=>1100000
[1,2,3,5,8,6,4,7]=>0000101=>1010000
[7,1,2,8,3,6,5,4]=>0001111=>1111000
[7,1,2,8,6,4,5,3]=>0001111=>1111000
[3,1,7,8,4,6,5,2]=>0101101=>1011010
[3,1,8,7,6,4,5,2]=>0101111=>1111010
[8,1,2,7,4,6,5,3]=>0001111=>1111000
[8,1,2,7,3,6,5,4]=>0001111=>1111000
[1,2,3,5,8,7,4,6]=>0000011=>1100000
[1,2,3,6,8,5,4,7]=>0001001=>1001000
[7,8,5,6,3,1,4,2]=>0110101=>1010110
[7,8,5,3,6,1,2,4]=>0001101=>1011000
[7,5,6,3,1,4,2,8]=>0110110=>0110110
[7,5,8,3,1,4,2,6]=>0110011=>1100110
[7,8,5,3,1,4,2,6]=>0111001=>1001110
[7,8,5,3,1,6,2,4]=>0101101=>1011010
[7,8,5,3,1,6,4,2]=>0111101=>1011110
[7,8,5,3,6,1,4,2]=>0011101=>1011100
[7,8,5,3,6,4,1,2]=>0011101=>1011100
[7,8,5,3,4,1,6,2]=>0011101=>1011100
[7,8,5,3,1,4,6,2]=>0101101=>1011010
[7,8,5,3,1,2,6,4]=>0101101=>1011010
[7,5,3,8,1,2,6,4]=>0001111=>1111000
[7,5,8,3,4,1,6,2]=>0010111=>1110100
[7,5,8,3,4,6,1,2]=>0000111=>1110000
[7,5,6,3,4,1,8,2]=>0010111=>1110100
[7,5,6,3,1,4,8,2]=>0100111=>1110010
[7,5,6,3,1,2,8,4]=>0100111=>1110010
[7,5,3,6,1,2,8,4]=>0001111=>1111000
[7,5,3,4,1,2,8,6]=>0011011=>1101100
[7,5,3,1,4,2,6,8]=>0111010=>0101110
[7,5,3,1,4,2,8,6]=>0111011=>1101110
[7,5,3,1,6,2,8,4]=>0101111=>1111010
[7,5,3,1,6,4,8,2]=>0101111=>1111010
[7,5,3,6,1,4,8,2]=>0001111=>1111000
[7,5,3,6,4,1,8,2]=>0011111=>1111100
[7,5,3,6,4,8,1,2]=>0001111=>1111000
[7,5,3,8,4,6,1,2]=>0001111=>1111000
[7,5,3,8,1,4,6,2]=>0001111=>1111000
[7,5,3,1,8,4,6,2]=>0101111=>1111010
[7,5,3,1,8,2,6,4]=>0101111=>1111010
[7,5,3,1,8,2,4,6]=>0101011=>1101010
[7,5,3,1,6,2,4,8]=>0101110=>0111010
[7,5,3,1,6,4,2,8]=>0111110=>0111110
[7,5,3,1,8,4,2,6]=>0111011=>1101110
[7,5,3,1,8,6,2,4]=>0101111=>1111010
[7,5,3,8,1,6,4,2]=>0011111=>1111100
[7,5,3,8,6,1,4,2]=>0011111=>1111100
[7,5,3,8,6,4,1,2]=>0011111=>1111100
[7,5,8,3,6,4,1,2]=>0010111=>1110100
[7,5,8,3,6,1,4,2]=>0010111=>1110100
[7,5,8,3,1,6,4,2]=>0110111=>1110110
[7,5,8,3,1,6,2,4]=>0100111=>1110010
[7,5,3,6,1,4,2,8]=>0011110=>0111100
[7,5,3,6,4,1,2,8]=>0011110=>0111100
[7,5,3,8,4,1,2,6]=>0011011=>1101100
[7,5,8,6,3,1,2,4]=>0100111=>1110010
[7,5,8,6,3,1,4,2]=>0110111=>1110110
[7,5,8,6,3,4,1,2]=>0010111=>1110100
[7,5,6,8,3,1,4,2]=>0110011=>1100110
[7,5,6,3,8,1,2,4]=>0000111=>1110000
[7,5,3,4,1,6,2,8]=>0011110=>0111100
[7,5,3,4,1,8,2,6]=>0011011=>1101100
[7,5,6,3,1,8,2,4]=>0100111=>1110010
[7,5,6,3,1,8,4,2]=>0110111=>1110110
[7,5,6,3,8,1,4,2]=>0010111=>1110100
[7,5,6,3,8,4,1,2]=>0010111=>1110100
[7,5,3,6,8,4,1,2]=>0011011=>1101100
[7,5,3,6,8,1,4,2]=>0011011=>1101100
[7,5,3,6,1,8,4,2]=>0011111=>1111100
[7,5,3,1,6,8,4,2]=>0111011=>1101110
[7,5,3,1,6,8,2,4]=>0101011=>1101010
[7,5,3,1,4,8,2,6]=>0101011=>1101010
[7,5,3,1,4,6,2,8]=>0101110=>0111010
[7,5,3,1,2,6,4,8]=>0101110=>0111010
[7,5,3,1,2,8,4,6]=>0101011=>1101010
[7,5,3,1,2,8,6,4]=>0101111=>1111010
[7,5,3,1,4,8,6,2]=>0101111=>1111010
[7,5,3,4,1,8,6,2]=>0011111=>1111100
[7,5,3,4,8,1,6,2]=>0001111=>1111000
[7,5,3,4,8,6,1,2]=>0001111=>1111000
[7,5,3,4,6,1,8,2]=>0001111=>1111000
[7,5,3,4,1,6,8,2]=>0011011=>1101100
[7,5,3,1,4,6,8,2]=>0101011=>1101010
[7,5,3,1,2,6,8,4]=>0101011=>1101010
[7,5,3,1,2,4,8,6]=>0101011=>1101010
[3,6,2,5,4,1,8,7]=>0011101=>1011100
[3,5,2,8,4,7,6,1]=>0001111=>1111000
[5,4,7,3,2,8,6,1]=>0101111=>1111010
[5,4,8,3,2,7,6,1]=>0101111=>1111010
[6,4,5,3,2,1,8,7]=>1101101=>1011011
[5,3,2,6,4,1,8,7]=>0111101=>1011110
[4,5,8,3,2,7,6,1]=>0100111=>1110010
[4,7,6,3,8,5,2,1]=>1001111=>1111001
[4,8,6,3,7,5,2,1]=>1001111=>1111001
[4,8,5,3,2,7,6,1]=>0101111=>1111010
[5,8,4,3,2,7,6,1]=>0110111=>1110110
[5,3,2,8,4,7,6,1]=>0101111=>1111010
[2,1,5,8,4,7,6,3]=>1000111=>1110001
[5,3,2,7,4,8,6,1]=>0101111=>1111010
[5,7,4,3,2,8,6,1]=>0110111=>1110110
[4,7,5,3,2,8,6,1]=>0101111=>1111010
[4,7,8,3,6,5,2,1]=>1001101=>1011001
[4,6,8,3,7,5,2,1]=>1001011=>1101001
[7,6,4,3,8,5,2,1]=>1011111=>1111101
[7,3,2,6,8,5,4,1]=>0111011=>1101110
[2,1,8,6,7,5,4,3]=>1011011=>1101101
[8,3,2,6,7,5,4,1]=>0111011=>1101110
[8,6,4,3,7,5,2,1]=>1011111=>1111101
[8,5,7,6,4,3,2,1]=>1110111=>1110111
[8,4,5,3,2,7,6,1]=>0101111=>1111010
[8,4,7,3,6,5,2,1]=>1001111=>1111001
[8,4,6,3,7,5,2,1]=>1001111=>1111001
[7,4,6,3,8,5,2,1]=>1001111=>1111001
[3,7,2,6,8,5,4,1]=>0011011=>1101100
[3,8,2,6,7,5,4,1]=>0011011=>1101100
[3,8,2,5,4,7,6,1]=>0001111=>1111000
[3,7,2,8,6,5,4,1]=>0011111=>1111100
[3,6,2,8,7,5,4,1]=>0011111=>1111100
[6,4,7,3,8,5,2,1]=>1001111=>1111001
[6,4,8,3,7,5,2,1]=>1001111=>1111001
[7,4,8,3,6,5,2,1]=>1001111=>1111001
[7,4,5,3,2,8,6,1]=>0101111=>1111010
[7,5,4,3,2,8,6,1]=>0111111=>1111110
[7,3,2,5,4,8,6,1]=>0101111=>1111010
[2,1,7,5,4,8,6,3]=>1001111=>1111001
[7,3,2,8,6,5,4,1]=>0111111=>1111110
[7,8,4,3,6,5,2,1]=>1011101=>1011101
[6,8,5,7,4,3,2,1]=>1110011=>1100111
[6,8,4,3,7,5,2,1]=>1011011=>1101101
[6,3,2,8,7,5,4,1]=>0111111=>1111110
[6,3,2,7,8,5,4,1]=>0111101=>1011110
[6,7,4,3,8,5,2,1]=>1011011=>1101101
[2,3,1,4,5,6,7,8,9]=>01000000=>00000010
[2,3,4,1,5,6,7,8,9]=>00100000=>00000100
[2,3,4,5,1,6,7,8,9]=>00010000=>00001000
[2,3,4,5,6,1,7,8,9]=>00001000=>00010000
[2,3,1,4,5,6,7,8,9,10]=>010000000=>000000010
[2,4,3,1,5,6,7,8,9]=>01100000=>00000110
[2,3,4,1,5,6,7,8,9,10]=>001000000=>000000100
[2,3,5,4,1,6,7,8,9]=>00110000=>00001100
[2,3,4,5,1,6,7,8,9,10]=>000100000=>000001000
[2,3,4,6,5,1,7,8,9]=>00011000=>00011000
[2,3,4,5,6,1,7,8,9,10]=>000010000=>000010000
[2,3,4,5,7,6,1,8,9]=>00001100=>00110000
[2,3,4,5,6,7,1,8,9,10]=>000001000=>000100000
[2,3,4,5,6,8,7,1,9]=>00000110=>01100000
[2,3,4,5,6,7,8,1,9,10]=>000000100=>001000000
[2,3,4,5,6,7,9,8,1]=>00000011=>11000000
[4,6,8,3,5,7,1,2]=>0000011=>1100000
[6,8,1,2,4,5,7,3]=>0000011=>1100000
[3,5,8,2,4,7,1,6]=>0000011=>1100000
[8,3,5,2,4,1,6,7]=>0011001=>1001100
[4,2,5,7,3,6,1,8]=>0010110=>0110100
[4,5,2,8,3,1,6,7]=>0101001=>1001010
[4,2,5,8,3,7,1,6]=>0010011=>1100100
[2,1,6,8,4,7,3,5]=>1000011=>1100001
[1,2,5,8,3,6,7,4]=>0000011=>1100000
[5,3,6,8,4,7,1,2]=>0001011=>1101000
[1,6,5,8,2,4,7,3]=>0000111=>1110000
[3,1,2,6,8,5,7,4]=>0100011=>1100010
[1,4,3,8,2,6,7,5]=>0010011=>1100100
[5,4,8,3,2,1,6,7]=>1101001=>1001011
[5,4,3,7,2,6,1,8]=>0011110=>0111100
[4,3,6,2,7,5,1,8]=>0011110=>0111100
[4,6,3,2,1,8,5,7]=>1100101=>1010011
[4,1,7,3,2,5,8,6]=>0110011=>1100110
[4,3,1,7,8,2,6,5]=>0110101=>1010110
[3,5,1,2,7,8,6,4]=>0001101=>1011000
[7,5,1,4,8,2,6,3]=>0001111=>1111000
[5,4,7,3,8,6,1,2]=>0001111=>1111000
[5,8,4,7,6,3,1,2]=>0100111=>1110010
[5,8,7,1,4,2,6,3]=>0010111=>1110100
[8,3,5,1,2,7,6,4]=>0001111=>1111000
[4,8,3,1,7,2,6,5]=>0100111=>1110010
[1,8,4,3,5,2,7,6]=>0011011=>1101100
[4,6,3,1,5,2,8,7]=>0101101=>1011010
[4,7,3,6,5,2,1,8]=>1001110=>0111001
[5,3,7,6,4,2,1,8]=>1011110=>0111101
[1,6,3,4,2,8,7,5]=>0010111=>1110100
[1,8,3,6,2,7,5,4]=>0001111=>1111000
[1,6,8,7,4,2,5,3]=>0011011=>1101100
[6,4,8,7,5,3,1,2]=>0101111=>1111010
[7,6,4,3,8,5,1,2]=>0011111=>1111100
[1,7,6,2,8,4,5,3]=>0001111=>1111000
[7,1,3,2,6,8,5,4]=>0101011=>1101010
[1,5,3,2,7,4,8,6]=>0101011=>1101010
[6,3,2,1,8,5,4,7]=>1101101=>1011011
[6,5,3,2,7,4,1,8]=>0111110=>0111110
[5,2,6,3,7,4,1,8]=>0011110=>0111100
[2,8,5,3,1,6,4,7]=>0101101=>1011010
[2,1,7,3,8,5,4,6]=>1001011=>1101001
[1,6,2,3,7,8,5,4]=>0001101=>1011000
[1,6,7,2,8,4,5,3]=>0001011=>1101000
[5,7,1,8,2,4,6,3]=>0000111=>1110000
[5,1,2,7,8,3,6,4]=>0001101=>1011000
[2,4,1,7,8,6,3,5]=>0010101=>1010100
[4,2,1,7,3,8,5,6]=>1010011=>1100101
[6,2,8,4,3,1,5,7]=>0110101=>1010110
[7,3,2,1,8,4,5,6]=>1100011=>1100011
[7,8,3,2,5,6,1,4]=>0100101=>1010010
[7,1,8,2,4,5,6,3]=>0000111=>1110000
[8,7,6,1,2,4,5,3]=>0001111=>1111000
[8,3,7,6,2,1,4,5]=>1000111=>1110001
[3,2,8,7,5,1,4,6]=>0101011=>1101010
[8,3,6,5,2,1,4,7]=>1001101=>1011001
[7,6,3,5,2,4,1,8]=>0011110=>0111100
[7,4,6,2,5,3,1,8]=>0101110=>0111010
[8,2,4,1,6,5,3,7]=>0011101=>1011100
[4,2,8,1,7,5,3,6]=>0011011=>1101100
[8,2,4,1,7,6,3,5]=>0010111=>1110100
[8,7,1,5,6,2,4,3]=>0010111=>1110100
[8,5,7,3,6,4,1,2]=>0010111=>1110100
[6,8,3,7,5,4,1,2]=>0011011=>1101100
[8,1,6,7,5,2,4,3]=>0011011=>1101100
[8,1,2,6,4,3,7,5]=>0010111=>1110100
[2,8,1,7,5,4,3,6]=>0011011=>1101100
[2,5,1,8,6,4,3,7]=>0011101=>1011100
[5,7,2,6,4,3,1,8]=>0110110=>0110110
[6,2,7,5,4,3,1,8]=>0111110=>0111110
[2,1,8,6,5,4,3,7]=>1011101=>1011101
[1,2,7,5,4,3,8,6]=>0011011=>1101100
[1,7,2,4,3,8,6,5]=>0010111=>1110100
[1,7,2,8,3,6,5,4]=>0001111=>1111000
[1,7,8,6,5,2,4,3]=>0011101=>1011100
[7,3,8,6,5,4,1,2]=>0011111=>1111100
[1,8,7,6,5,2,4,3]=>0011111=>1111100
[8,1,7,3,2,6,5,4]=>0101111=>1111010
[5,1,4,3,2,8,7,6]=>0111011=>1101110
[8,6,5,3,2,1,7,4]=>1101111=>1111011
[8,6,3,2,1,7,4,5]=>1100111=>1110011
[8,6,5,4,1,7,2,3]=>0011111=>1111100
[8,6,5,1,7,3,2,4]=>0101111=>1111010
[8,6,1,7,4,3,2,5]=>0110111=>1110110
[4,6,3,2,7,5,1,8]=>0101110=>0111010
[1,4,3,7,2,5,8,6]=>0010011=>1100100
[7,4,8,3,1,6,2,5]=>0100111=>1110010
[7,1,5,8,3,2,6,4]=>0100111=>1110010
[5,7,4,1,8,2,6,3]=>0010111=>1110100
[5,7,4,3,1,8,6,2]=>0110111=>1110110
[1,8,7,2,5,4,6,3]=>0001111=>1111000
[1,8,5,3,7,2,6,4]=>0001111=>1111000
[4,3,1,8,7,5,2,6]=>0111011=>1101110
[1,4,8,6,3,5,2,7]=>0001101=>1011000
[7,4,6,3,5,2,1,8]=>1001110=>0111001
[1,3,5,6,8,4,2,7]=>0010001=>1000100
[3,5,4,8,7,1,2,6]=>0001011=>1101000
[3,1,4,6,8,7,2,5]=>0100011=>1100010
[1,6,3,8,7,2,5,4]=>0001111=>1111000
[1,6,2,4,8,7,5,3]=>0001111=>1111000
[8,4,1,6,7,5,3,2]=>0111011=>1101110
[7,1,6,4,8,5,2,3]=>0001111=>1111000
[7,3,6,8,5,1,2,4]=>0001011=>1101000
[1,3,7,2,6,8,4,5]=>0000011=>1100000
[3,6,5,2,8,1,4,7]=>0001101=>1011000
[3,6,5,7,2,4,1,8]=>0010110=>0110100
[4,2,6,3,8,1,5,7]=>0010101=>1010100
[4,2,6,7,3,5,1,8]=>0011010=>0101100
[3,6,2,4,7,5,1,8]=>0001110=>0111000
[3,6,2,4,1,8,5,7]=>0010101=>1010100
[7,3,8,2,1,6,4,5]=>1000111=>1110001
[7,3,5,2,1,8,6,4]=>1001111=>1111001
[8,7,6,4,3,1,5,2]=>0111111=>1111110
[8,7,6,4,1,5,2,3]=>0011111=>1111100
[3,8,7,2,1,4,6,5]=>1000111=>1110001
[3,8,2,7,1,5,4,6]=>0001011=>1101000
[3,6,8,2,1,5,4,7]=>1001001=>1001001
[2,4,8,1,6,5,3,7]=>0001101=>1011000
[4,2,8,1,5,7,3,6]=>0010011=>1100100
[8,5,7,6,1,4,2,3]=>0010111=>1110100
[8,6,1,7,3,5,4,2]=>0011111=>1111100
[8,6,1,7,5,4,2,3]=>0011111=>1111100
[1,6,2,8,7,3,5,4]=>0001111=>1111000
[1,8,2,4,6,7,3,5]=>0000011=>1100000
[2,8,5,4,7,1,3,6]=>0001011=>1101000
[2,1,5,8,6,4,3,7]=>1010101=>1010101
[7,2,5,6,4,3,1,8]=>0110110=>0110110
[1,2,5,7,8,4,3,6]=>0010001=>1000100
[1,2,7,4,8,6,3,5]=>0000111=>1110000
[1,2,7,8,3,6,5,4]=>0001101=>1011000
[7,1,8,6,3,5,4,2]=>0011111=>1111100
[1,8,7,6,3,5,2,4]=>0001111=>1111000
[1,8,7,4,6,3,2,5]=>0100111=>1110010
[7,1,5,8,3,4,6,2]=>0000111=>1110000
[7,1,6,4,2,3,5,8]=>0010110=>0110100
[8,6,2,4,7,3,5,1]=>0001111=>1111000
[8,6,2,4,5,7,3,1]=>0100111=>1110010
[2,7,1,4,5,8,3,6]=>0000011=>1100000
[7,1,6,4,5,2,3,8]=>0001110=>0111000
[7,1,4,5,6,8,2,3]=>0000011=>1100000
[7,1,4,6,5,8,3,2]=>0100111=>1110010
[7,1,2,3,8,5,4,6]=>0001011=>1101000
[7,1,5,4,3,8,2,6]=>0011011=>1101100
[7,1,3,4,2,6,8,5]=>0010011=>1100100
[7,1,5,4,6,2,8,3]=>0001111=>1111000
[7,1,5,6,4,3,8,2]=>0010111=>1110100
[7,1,6,5,4,3,2,8]=>0111110=>0111110
[8,6,2,5,4,3,7,1]=>0011111=>1111100
[2,5,1,7,4,3,6,8]=>0011010=>0101100
[2,5,1,4,7,8,6,3]=>0001101=>1011000
[3,5,1,4,8,6,2,7]=>0001101=>1011000
[3,6,2,4,7,8,1,5]=>0000101=>1010000
[5,6,2,4,8,7,1,3]=>0000111=>1110000
[6,3,8,2,4,7,1,5]=>0000111=>1110000
[6,5,8,7,2,3,1,4]=>0100111=>1110010
[6,5,7,8,2,4,1,3]=>0010101=>1010100
[6,3,4,2,8,5,1,7]=>0011101=>1011100
[3,4,7,2,5,8,1,6]=>0000011=>1100000
[4,6,8,1,3,5,2,7]=>0001001=>1001000
[4,3,8,1,2,7,5,6]=>0010011=>1100100
[3,6,4,1,7,2,5,8]=>0010110=>0110100
[2,8,3,1,5,6,4,7]=>0100101=>1010010
[3,8,7,1,5,4,2,6]=>0011011=>1101100
[4,3,1,7,6,8,2,5]=>0110011=>1100110
[3,4,1,7,5,6,8,2]=>0010011=>1100100
[3,4,1,5,7,6,2,8]=>0010110=>0110100
[3,7,4,1,6,2,8,5]=>0010111=>1110100
[8,4,7,2,5,3,6,1]=>0001111=>1111000
[4,7,8,1,2,3,6,5]=>0000101=>1010000
[2,8,6,1,5,3,7,4]=>0001111=>1111000
[7,6,5,1,3,8,2,4]=>0001111=>1111000
[7,6,5,1,3,4,8,2]=>0001111=>1111000
[7,2,6,4,1,3,8,5]=>0010111=>1110100
[6,7,5,2,1,3,8,4]=>1001011=>1101001
[8,4,5,3,7,2,6,1]=>0001111=>1111000
[4,7,5,2,8,1,6,3]=>0001111=>1111000
[2,6,4,3,1,5,7,8]=>0110100=>0010110
[7,3,8,4,1,5,2,6]=>0011011=>1101100
[7,2,3,4,1,6,5,8]=>0010110=>0110100
[4,2,8,3,6,1,5,7]=>0010101=>1010100
[6,8,5,7,2,1,3,4]=>1000011=>1100001
[4,8,5,2,7,1,3,6]=>0001011=>1101000
[6,3,5,2,1,7,4,8]=>1001110=>0111001
[6,8,5,3,1,4,2,7]=>0111001=>1001110
[3,6,5,4,2,8,1,7]=>0011101=>1011100
[1,6,4,7,2,5,3,8]=>0001110=>0111000
[1,6,4,8,2,5,3,7]=>0001101=>1011000
[1,6,5,8,2,4,3,7]=>0010101=>1010100
[1,6,8,2,4,3,7,5]=>0010011=>1100100
[1,6,2,4,3,7,8,5]=>0010101=>1010100
[1,5,6,2,4,7,3,8]=>0000110=>0110000
[1,5,6,2,4,7,8,3]=>0000101=>1010000
[1,5,8,2,4,7,3,6]=>0000011=>1100000
[1,5,7,2,4,8,3,6]=>0000011=>1100000
[1,6,5,7,2,4,3,8]=>0010110=>0110100
[1,6,7,2,4,3,8,5]=>0010011=>1100100
[1,5,6,7,2,4,8,3]=>0000011=>1100000
[1,5,8,2,4,6,7,3]=>0000011=>1100000
[1,5,7,2,4,6,8,3]=>0000011=>1100000
[1,5,7,8,3,2,4,6]=>0100001=>1000010
[1,5,8,3,2,4,6,7]=>0100001=>1000010
[1,5,6,2,4,8,3,7]=>0000101=>1010000
[1,7,6,2,8,3,4,5]=>0000111=>1110000
[1,7,3,4,2,8,6,5]=>0010111=>1110100
[1,6,2,4,3,8,7,5]=>0010111=>1110100
[1,5,6,2,4,8,7,3]=>0000111=>1110000
[1,5,8,7,3,2,4,6]=>0100011=>1100010
[1,4,2,3,5,8,7,6]=>0010011=>1100100
[1,5,2,3,4,8,7,6]=>0001011=>1101000
[1,6,5,2,3,8,7,4]=>0001111=>1111000
[1,7,4,2,8,6,5,3]=>0011111=>1111100
[1,7,6,5,2,8,4,3]=>0011111=>1111100
[1,6,7,5,2,3,8,4]=>0001011=>1101000
[1,7,5,2,8,4,3,6]=>0011011=>1101100
[1,7,5,6,2,8,3,4]=>0000111=>1110000
[1,5,7,6,2,4,8,3]=>0000111=>1110000
[1,5,8,3,2,4,7,6]=>0100011=>1100010
[1,6,5,2,3,7,4,8]=>0001110=>0111000
[1,6,5,2,3,7,8,4]=>0001101=>1011000
[1,6,8,4,2,3,7,5]=>0010011=>1100100
[1,7,4,6,2,8,3,5]=>0000111=>1110000
[1,7,3,5,2,8,4,6]=>0001011=>1101000
[1,6,8,5,2,3,7,4]=>0001011=>1101000
[1,6,4,2,3,7,8,5]=>0010101=>1010100
[1,6,4,2,3,7,5,8]=>0010110=>0110100
[1,5,8,6,2,4,7,3]=>0000111=>1110000
[1,5,7,3,2,4,8,6]=>0100011=>1100010
[1,7,3,4,2,8,5,6]=>0010011=>1100100
[1,7,4,2,8,5,3,6]=>0011011=>1101100
[1,6,7,4,2,3,8,5]=>0010011=>1100100
[1,6,4,2,3,8,5,7]=>0010101=>1010100
[1,7,6,4,2,8,5,3]=>0011111=>1111100
[1,7,5,2,8,6,4,3]=>0011111=>1111100
[1,6,4,2,3,8,7,5]=>0010111=>1110100
[7,3,5,6,1,4,8,2]=>0000111=>1110000
[3,7,5,6,1,4,8,2]=>0000111=>1110000
[8,2,4,1,6,7,5,3]=>0011011=>1101100
[8,6,1,4,2,7,5,3]=>0011111=>1111100
[3,6,1,4,2,8,5,7]=>0010101=>1010100
[1,6,7,4,3,5,8,2]=>0010011=>1100100
[6,7,1,4,3,5,8,2]=>0010011=>1100100
[7,6,1,4,3,5,8,2]=>0010111=>1110100
[3,5,4,1,6,7,8,2]=>0011001=>1001100
[4,7,1,6,3,5,8,2]=>0000111=>1110000
[3,1,4,7,6,5,8,2]=>0100111=>1110010
[6,1,7,4,3,5,8,2]=>0010111=>1110100
[7,1,6,4,3,5,8,2]=>0010111=>1110100
[1,7,6,4,3,5,8,2]=>0010111=>1110100
[8,1,6,4,2,7,5,3]=>0011111=>1111100
[8,4,1,3,7,2,5,6]=>0010011=>1100100
[4,7,1,3,8,2,5,6]=>0000011=>1100000
[7,4,1,3,8,2,5,6]=>0010011=>1100100
[1,3,6,4,2,8,5,7]=>0010101=>1010100
[4,7,3,1,2,8,5,6]=>0100011=>1100010
[4,7,8,1,2,6,5,3]=>0001101=>1011000
[6,8,1,4,2,7,5,3]=>0011011=>1101100
[1,8,6,4,2,7,5,3]=>0011111=>1111100
[4,8,1,3,7,2,5,6]=>0000011=>1100000
[8,7,1,3,6,2,5,4]=>0001111=>1111000
[6,8,5,7,3,2,1,4]=>1100011=>1100011
[1,8,4,3,7,2,5,6]=>0010011=>1100100
[2,8,3,4,7,6,1,5]=>0000111=>1110000
[3,7,8,4,6,2,1,5]=>1000101=>1010001
[3,7,4,6,8,2,1,5]=>1000011=>1100001
[2,4,3,7,8,6,1,5]=>0010101=>1010100
[1,4,7,3,8,2,5,6]=>0000011=>1100000
[5,7,6,8,3,2,1,4]=>1100011=>1100011
[2,5,3,4,8,6,1,7]=>0001101=>1011000
[3,7,5,4,8,2,1,6]=>1001011=>1101001
[7,1,3,4,2,8,5,6]=>0010011=>1100100
[6,1,4,3,8,2,5,7]=>0010101=>1010100
[4,1,7,3,8,2,5,6]=>0010011=>1100100
[8,1,4,3,7,2,5,6]=>0010011=>1100100
[8,2,3,4,7,6,1,5]=>0000111=>1110000
[4,2,3,7,8,6,1,5]=>0010101=>1010100
[5,2,3,4,8,6,1,7]=>0001101=>1011000
[2,7,5,6,3,8,1,4]=>0000111=>1110000
[5,7,2,6,3,8,1,4]=>0000111=>1110000
[5,7,2,6,8,4,1,3]=>0010011=>1100100
[7,2,5,6,8,4,1,3]=>0010011=>1100100
[4,2,3,8,5,6,1,7]=>0010101=>1010100
[5,2,3,8,7,6,1,4]=>0001111=>1111000
[8,2,3,7,5,6,1,4]=>0000111=>1110000
[6,1,8,3,7,2,5,4]=>0001111=>1111000
[1,7,8,4,2,6,5,3]=>0011101=>1011100
[4,7,1,8,2,5,6,3]=>0000111=>1110000
[3,7,4,8,5,2,1,6]=>1001011=>1101001
[2,4,3,8,5,6,1,7]=>0010101=>1010100
[1,4,8,3,6,2,5,7]=>0000101=>1010000
[7,5,8,6,3,2,1,4]=>1100111=>1110011
[6,5,8,7,3,2,1,4]=>1100111=>1110011
[8,5,7,6,3,2,1,4]=>1100111=>1110011
[2,5,3,8,7,6,1,4]=>0001111=>1111000
[3,7,5,8,6,2,1,4]=>1000111=>1110001
[3,7,8,6,5,2,1,4]=>1001101=>1011001
[1,8,7,3,6,2,5,4]=>0001111=>1111000
[6,8,7,5,3,2,1,4]=>1101011=>1101011
[5,7,6,8,3,4,1,2]=>0010011=>1100100
[3,7,6,8,4,5,1,2]=>0001011=>1101000
[1,5,4,7,6,8,2,3]=>0001011=>1101000
[1,7,4,6,5,8,2,3]=>0000111=>1110000
[3,7,4,6,5,8,1,2]=>0000111=>1110000
[3,5,4,8,6,7,1,2]=>0001011=>1101000
[3,8,4,6,5,7,1,2]=>0000111=>1110000
[3,6,4,7,5,8,1,2]=>0000111=>1110000
[1,6,2,7,5,8,3,4]=>0000111=>1110000
[1,6,4,8,5,7,2,3]=>0000111=>1110000
[1,8,4,6,5,7,2,3]=>0000111=>1110000
[1,5,4,8,6,7,2,3]=>0001011=>1101000
[7,8,1,5,4,6,2,3]=>0001101=>1011000
[7,8,1,5,2,4,3,6]=>0011001=>1001100
[1,8,2,6,5,7,3,4]=>0000111=>1110000
[1,7,2,8,5,6,3,4]=>0000111=>1110000
[1,7,2,6,5,8,3,4]=>0000111=>1110000
[1,5,2,7,6,8,3,4]=>0001011=>1101000
[1,7,6,8,2,5,3,4]=>0001011=>1101000
[1,7,6,8,4,5,2,3]=>0001011=>1101000
[5,7,6,8,1,4,2,3]=>0010011=>1100100
[7,8,5,6,1,3,2,4]=>0100101=>1010010
[5,8,6,7,1,3,2,4]=>0100011=>1100010
[1,3,2,7,6,8,4,5]=>0100011=>1100010
[1,7,6,8,2,4,3,5]=>0010011=>1100100
[7,8,1,3,2,6,4,5]=>0100101=>1010010
[7,8,1,6,2,4,3,5]=>0010101=>1010100
[1,8,6,7,2,4,3,5]=>0010011=>1100100
[7,8,1,4,2,6,3,5]=>0010101=>1010100
[7,8,1,4,2,5,3,6]=>0011001=>1001100
[7,8,2,1,4,3,6,5]=>1010101=>1010101
[7,8,1,2,4,3,5,6]=>0010001=>1000100
[4,3,6,5,8,7,1,2]=>0010111=>1110100
[3,4,6,5,7,8,1,2]=>0000101=>1010000
[3,4,1,5,6,7,8,9,2]=>00100001=>10000100
[3,4,5,1,6,7,8,9,2]=>00010001=>10001000
[3,4,5,6,1,7,8,9,2]=>00001001=>10010000
[3,4,5,6,7,1,8,9,2]=>00000101=>10100000
[3,4,5,6,7,8,1,9,2]=>00000011=>11000000
[3,1,2,5,6,7,8,9,4]=>01000001=>10000010
[3,4,1,5,6,7,8,9,10,2]=>001000001=>100000100
[3,4,1,2,6,7,8,9,5]=>00100001=>10000100
[3,4,5,1,6,7,8,9,10,2]=>000100001=>100001000
[3,4,5,1,2,7,8,9,6]=>00010001=>10001000
[3,4,5,6,1,7,8,9,10,2]=>000010001=>100010000
[3,4,5,6,1,2,8,9,7]=>00001001=>10010000
[3,4,5,6,7,1,8,9,10,2]=>000001001=>100100000
[3,4,5,6,7,1,2,9,8]=>00000101=>10100000
[3,4,5,6,7,8,1,9,10,2]=>000000101=>101000000
[3,4,5,6,7,8,1,2,9]=>00000010=>01000000
[3,4,5,6,7,8,9,1,10,2]=>000000011=>110000000
[1,6,2,3,8,7,4,5]=>0000111=>1110000
[1,7,4,3,2,8,6,5]=>0110111=>1110110
[1,4,7,6,2,5,8,3]=>0000111=>1110000
[1,2,6,5,3,7,4,8]=>0001110=>0111000
[1,2,6,5,3,7,8,4]=>0001101=>1011000
[1,3,7,5,2,6,8,4]=>0001011=>1101000
[1,3,7,4,2,6,8,5]=>0010011=>1100100
[1,2,6,4,3,7,8,5]=>0010101=>1010100
[1,2,6,4,3,7,5,8]=>0010110=>0110100
[1,4,7,3,2,5,8,6]=>0100011=>1100010
[1,4,3,2,5,8,6,7]=>0110001=>1000110
[1,5,3,2,4,8,6,7]=>0101001=>1001010
[1,7,5,3,2,8,6,4]=>0101111=>1111010
[1,5,3,2,4,8,7,6]=>0101011=>1101010
[7,6,5,4,3,1,8,2]=>0111111=>1111110
[6,8,5,4,3,2,1,7]=>1111001=>1001111
[8,7,6,5,4,3,1,9,2]=>01111111=>11111110
[7,9,6,5,4,3,2,1,8]=>11111001=>10011111
[9,8,7,6,5,4,3,1,10,2]=>011111111=>111111110
[1,7,6,5,4,3,9,8,2]=>00111111=>11111100
[7,1,5,4,3,8,6,2]=>0011111=>1111100
[3,6,5,4,8,1,7,2]=>0001111=>1111000
[6,8,1,4,3,2,7,5]=>0110011=>1100110
[2,8,5,4,3,7,1,6]=>0011011=>1101100
[1,9,6,5,4,3,2,8,7]=>01111011=>11011110
[8,10,7,6,5,4,3,2,1,9]=>111111001=>100111111
[10,9,8,7,6,5,4,3,1,11,2]=>0111111111=>1111111110
[1,8,7,6,5,4,3,10,9,2]=>001111111=>111111100
[8,1,6,5,4,3,9,7,2]=>00111111=>11111100
[3,7,6,5,4,9,1,8,2]=>00011111=>11111000
[7,6,1,4,3,8,5,2]=>0011111=>1111100
[4,6,5,8,3,1,7,2]=>0100111=>1110010
[6,8,5,1,3,2,7,4]=>0101011=>1101010
[1,8,2,4,3,7,6,5]=>0010111=>1110100
[7,9,1,5,4,3,2,8,6]=>01110011=>11001110
[3,8,5,4,7,2,1,6]=>1001011=>1101001
[2,9,6,5,4,3,8,1,7]=>00111011=>11011100
[1,10,7,6,5,4,3,2,9,8]=>011111011=>110111110
[9,11,8,7,6,5,4,3,2,1,10]=>1111111001=>1001111111
[11,10,9,8,7,6,5,4,3,1,12,2]=>01111111111=>11111111110
[1,9,8,7,6,5,4,3,11,10,2]=>0011111111=>1111111100
[9,1,7,6,5,4,3,10,8,2]=>001111111=>111111100
[3,8,7,6,5,4,10,1,9,2]=>000111111=>111111000
[8,7,1,5,4,3,9,6,2]=>00111111=>11111100
[1,3,6,5,4,9,8,7,2]=>00011111=>11111000
[4,7,6,5,9,3,1,8,2]=>01001111=>11110010
[7,6,5,1,3,8,4,2]=>0011111=>1111100
[1,6,3,4,8,7,5,2]=>0001111=>1111000
[1,4,5,8,3,7,6,2]=>0000111=>1110000
[6,8,5,4,1,2,7,3]=>0011011=>1101100
[1,8,5,2,3,7,6,4]=>0001111=>1111000
[7,9,6,1,4,3,2,8,5]=>01101011=>11010110
[6,8,2,4,3,7,1,5]=>0010011=>1100100
[1,8,3,4,7,2,6,5]=>0000111=>1110000
[1,9,2,5,4,3,8,7,6]=>00110111=>11101100
[8,10,1,6,5,4,3,2,9,7]=>011110011=>110011110
[7,5,8,4,3,2,1,6]=>1110011=>1100111
[4,8,5,7,3,2,1,6]=>1100011=>1100011
[3,9,6,5,4,8,2,1,7]=>10011011=>11011001
[2,10,7,6,5,4,3,9,1,8]=>001111011=>110111100
[1,11,8,7,6,5,4,3,2,10,9]=>0111111011=>1101111110
[10,12,9,8,7,6,5,4,3,2,1,11]=>11111111001=>10011111111
[5,1,7,6,8,4,3,2]=>0111011=>1101110
[6,4,8,5,2,7,1,3]=>0001111=>1111000
[5,1,8,6,7,4,3,2]=>0111011=>1101110
[8,4,7,5,2,6,1,3]=>0001111=>1111000
[5,4,6,8,2,1,7,3]=>1001011=>1101001
[6,4,5,8,1,2,7,3]=>0000111=>1110000
[7,4,6,5,2,1,8,3]=>1001111=>1111001
[8,4,6,5,2,1,7,3]=>1001111=>1111001
[4,8,7,5,6,1,3,2]=>0100111=>1110010
[2,7,5,1,8,4,3,6]=>0011011=>1101100
[5,1,8,7,4,2,3,6]=>0011011=>1101100
[2,8,6,7,4,3,5,1]=>0011011=>1101100
[3,6,5,2,4,1,8,7]=>0011101=>1011100
[5,2,3,6,4,1,8,7]=>0011101=>1011100
[6,1,4,5,3,2,8,7]=>0101101=>1011010
[3,8,7,1,4,6,5,2]=>0001111=>1111000
[5,7,1,2,4,3,8,6]=>0010011=>1100100
[4,3,7,6,8,2,5,1]=>0011011=>1101100
[5,3,6,8,1,7,2,4]=>0001011=>1101000
[3,2,6,8,5,7,1,4]=>0100011=>1100010
[6,3,7,2,4,8,5,1]=>0001111=>1111000
[7,4,8,6,5,2,1,3]=>1001111=>1111001
[7,1,8,2,5,4,3,6]=>0011011=>1101100
[2,5,3,7,4,1,8,6]=>0011011=>1101100
[3,6,4,7,5,1,8,2]=>0001111=>1111000
[8,4,7,6,2,3,1,5]=>0100111=>1110010
[8,4,7,1,2,5,6,3]=>0000111=>1110000
[4,2,8,7,3,5,6,1]=>0010111=>1110100
[8,1,7,4,2,5,6,3]=>0010111=>1110100
[7,4,3,8,2,5,6,1]=>0010111=>1110100
[6,4,1,5,8,2,7,3]=>0010111=>1110100
[2,5,8,7,3,6,1,4]=>0000111=>1110000
[2,1,5,8,7,4,6,3]=>1000111=>1110001
[8,3,5,6,7,4,1,2]=>0010011=>1100100
[7,4,3,2,8,5,6,1]=>0110111=>1110110
[4,2,7,1,8,5,6,3]=>0010111=>1110100
[4,1,7,2,8,5,6,3]=>0010111=>1110100
[2,4,8,7,3,5,6,1]=>0000111=>1110000
[4,7,8,3,1,5,6,2]=>0100101=>1010010
[3,4,7,2,8,5,6,1]=>0000111=>1110000
[3,7,1,4,8,5,6,2]=>0000111=>1110000
[7,2,3,4,8,5,6,1]=>0000111=>1110000
[6,1,8,5,2,7,4,3]=>0011111=>1111100
[2,1,7,4,5,8,6,3]=>1000111=>1110001
[2,1,8,3,6,7,5,4]=>1001011=>1101001
[8,2,1,6,4,7,5,3]=>1001111=>1111001
[7,8,2,6,4,1,5,3]=>0011101=>1011100
[2,6,3,5,8,7,1,4]=>0000111=>1110000
[7,6,2,1,5,8,4,3]=>1010111=>1110101
[4,5,2,7,6,1,8,3]=>0001111=>1111000
[5,1,6,8,4,7,2,3]=>0001011=>1101000
[3,6,8,7,5,2,1,4]=>1001011=>1101001
[7,4,8,6,5,2,3,1]=>0101111=>1111010
[8,1,6,4,7,3,2,5]=>0100111=>1110010
[7,6,4,1,2,3,8,5]=>0010111=>1110100
[2,6,4,8,5,3,7,1]=>0001111=>1111000
[7,3,5,8,4,2,1,6]=>1010011=>1100101
[3,2,5,8,4,1,7,6]=>0110011=>1100110
[8,4,7,1,5,2,3,6]=>0001011=>1101000
[4,8,7,5,6,1,2,3]=>0000111=>1110000
[6,1,4,8,7,3,5,2]=>0001111=>1111000
[7,2,8,4,3,5,6,1]=>0010111=>1110100
[4,7,8,1,3,5,6,2]=>0000101=>1010000
[8,7,3,4,1,5,6,2]=>0010111=>1110100
[4,8,2,7,3,5,6,1]=>0000111=>1110000
[3,1,8,7,2,5,6,4]=>0100111=>1110010
[3,8,1,7,2,5,6,4]=>0000111=>1110000
[8,2,3,7,1,5,6,4]=>0000111=>1110000
[6,4,8,7,1,3,2,5]=>0100111=>1110010
[2,8,4,6,7,3,1,5]=>0100011=>1100010
[4,3,8,2,7,6,1,5]=>0010111=>1110100
[6,8,4,2,1,3,7,5]=>1010011=>1100101
[7,8,2,4,3,5,6,1]=>0010101=>1010100
[2,8,3,7,1,5,6,4]=>0000111=>1110000
[8,1,2,7,3,5,6,4]=>0000111=>1110000
[6,4,1,3,2,8,5,7]=>0110101=>1010110
[5,3,8,6,2,1,4,7]=>1001101=>1011001
[4,6,5,2,8,3,1,7]=>0101101=>1011010
[4,3,7,5,1,8,2,6]=>0011011=>1101100
[6,8,5,2,7,4,3,1]=>0111011=>1101110
[7,2,5,4,3,8,1,6]=>0011011=>1101100
[3,6,8,1,4,5,2,7]=>0001001=>1001000
[6,8,1,2,4,5,3,7]=>0001001=>1001000
[8,1,6,2,4,5,3,7]=>0001101=>1011000
[3,8,6,1,2,5,4,7]=>0001101=>1011000
[5,8,1,6,2,3,4,7]=>0000101=>1010000
[4,1,6,5,8,2,3,7]=>0010101=>1010100
[4,3,8,6,2,5,1,7]=>0011101=>1011100
[8,3,6,1,4,5,2,7]=>0001101=>1011000
[2,3,6,8,4,5,1,7]=>0001001=>1001000
[2,7,5,4,3,8,1,6]=>0011011=>1101100
[6,3,8,7,4,2,5,1]=>0011111=>1111100
[5,8,4,3,7,6,1,2]=>0010111=>1110100
[8,7,4,3,1,6,2,5]=>0110111=>1110110
[1,7,4,3,8,6,2,5]=>0010111=>1110100
[7,1,5,3,4,8,2,6]=>0001011=>1101000
[2,8,6,1,7,4,5,3]=>0001111=>1111000
[4,8,6,5,7,2,1,3]=>1000111=>1110001
[4,7,6,8,2,1,5,3]=>1001011=>1101001
[6,1,8,7,4,3,5,2]=>0011111=>1111100
[8,5,4,3,1,6,7,2]=>0111011=>1101110
[1,5,8,6,3,4,7,2]=>0000111=>1110000
[2,5,8,6,3,4,7,1]=>0000111=>1110000
[4,1,3,8,5,6,7,2]=>0010011=>1100100
[6,5,8,4,3,1,7,2]=>0110111=>1110110
[4,6,5,2,8,1,7,3]=>0001111=>1111000
[7,2,8,1,3,6,4,5]=>0000111=>1110000
[1,8,5,2,3,6,7,4]=>0001011=>1101000
[1,8,3,2,5,6,7,4]=>0100011=>1100010
[2,8,3,1,5,6,7,4]=>0100011=>1100010
[4,8,3,2,5,6,7,1]=>0100011=>1100010
[8,2,3,1,5,6,7,4]=>0100011=>1100010
[2,1,8,3,5,6,7,4]=>1000011=>1100001
[1,4,8,2,3,6,7,5]=>0000011=>1100000
[3,1,2,7,8,6,4,5]=>0100101=>1010010
[7,5,1,8,2,4,3,6]=>0011011=>1101100
[3,5,8,1,2,4,7,6]=>0000011=>1100000
[4,5,8,1,2,3,7,6]=>0000011=>1100000
[4,2,7,1,8,6,3,5]=>0010111=>1110100
[3,8,4,1,2,6,7,5]=>0010011=>1100100
[5,4,8,2,3,6,7,1]=>0001011=>1101000
[5,8,3,6,7,4,1,2]=>0010011=>1100100
[2,3,1,6,8,4,7,5]=>0100011=>1100010
[2,4,3,7,1,8,5,6]=>0010011=>1100100
[1,4,7,3,2,8,5,6]=>0100011=>1100010
[2,7,1,4,3,8,5,6]=>0010011=>1100100
[2,4,1,8,6,3,7,5]=>0010111=>1110100
[8,4,1,3,6,2,7,5]=>0010111=>1110100
[6,8,5,1,7,2,3,4]=>0001011=>1101000
[7,3,6,5,8,2,1,4]=>1000111=>1110001
[7,6,3,5,8,2,1,4]=>1000111=>1110001
[4,5,8,7,3,6,1,2]=>0000111=>1110000
[3,5,2,8,6,1,7,4]=>0001111=>1111000
[8,2,5,6,1,4,7,3]=>0000111=>1110000
[8,6,5,4,1,2,7,3]=>0011111=>1111100
[2,6,1,8,3,7,5,4]=>0001111=>1111000
[4,7,1,6,2,8,5,3]=>0001111=>1111000
[6,1,5,3,8,7,2,4]=>0001111=>1111000
[2,8,6,3,7,1,5,4]=>0001111=>1111000
[7,6,1,5,8,2,3,4]=>0000111=>1110000
[3,6,8,5,1,2,7,4]=>0001011=>1101000
[6,5,2,4,8,1,7,3]=>0001111=>1111000
[5,1,4,8,2,6,7,3]=>0001011=>1101000
[4,8,2,5,1,6,7,3]=>0001011=>1101000
[3,4,8,5,2,6,7,1]=>0001011=>1101000
[4,2,1,8,5,6,7,3]=>1010011=>1100101
[1,5,4,8,2,6,7,3]=>0001011=>1101000
[7,2,1,5,8,6,3,4]=>1000111=>1110001
[2,8,4,5,1,6,7,3]=>0001011=>1101000
[5,4,8,3,7,6,1,2]=>0001111=>1111000
[3,1,5,8,6,2,7,4]=>0100111=>1110010
[6,3,4,8,5,1,7,2]=>0001111=>1111000
[5,3,4,8,1,6,7,2]=>0001011=>1101000
[7,6,1,2,8,3,5,4]=>0001111=>1111000
[7,5,8,4,1,2,6,3]=>0010111=>1110100
[7,5,8,4,6,1,3,2]=>0100111=>1110010
[6,5,4,8,7,1,3,2]=>0101111=>1111010
[6,5,4,8,1,2,7,3]=>0001111=>1111000
[7,5,1,6,2,3,8,4]=>0001111=>1111000
[7,5,1,6,8,2,4,3]=>0011011=>1101100
[6,5,4,1,8,2,7,3]=>0011111=>1111100
[6,5,4,7,1,2,8,3]=>0001111=>1111000
[6,5,4,7,8,1,3,2]=>0101101=>1011010
[6,5,3,7,1,4,2,8]=>0011110=>0111100
[6,5,3,1,8,4,2,7]=>0111101=>1011110
[7,5,1,4,8,3,2,6]=>0101011=>1101010
[8,1,6,4,7,3,5,2]=>0001111=>1111000
[7,5,1,4,8,3,6,2]=>0001111=>1111000
[6,5,3,7,1,4,8,2]=>0001111=>1111000
[6,4,3,1,5,8,7,2]=>0110111=>1110110
[7,4,1,5,3,8,6,2]=>0011111=>1111100
[8,1,5,4,3,7,6,2]=>0011111=>1111100
[8,1,5,4,3,7,2,6]=>0011011=>1101100
[7,4,1,5,3,8,2,6]=>0011011=>1101100
[7,4,1,5,3,2,6,8]=>0111010=>0101110
[8,1,5,4,3,2,6,7]=>0111001=>1001110
[8,1,6,4,2,5,3,7]=>0011101=>1011100
[6,5,3,1,2,7,4,8]=>0101110=>0111010
[6,5,3,8,1,4,2,7]=>0011101=>1011100
[7,6,8,1,4,3,2,5]=>0110011=>1100110
[8,1,7,2,5,4,3,6]=>0011011=>1101100
[8,1,7,2,5,4,6,3]=>0001111=>1111000
[7,6,1,2,5,4,8,3]=>0001111=>1111000
[6,5,3,8,1,4,7,2]=>0001111=>1111000
[6,5,3,1,2,7,8,4]=>0101101=>1011010
[7,5,1,4,2,6,8,3]=>0011011=>1101100
[8,1,6,4,2,5,7,3]=>0010111=>1110100
[7,4,1,5,3,2,8,6]=>0111011=>1101110
[6,4,3,1,5,2,8,7]=>0111101=>1011110
[6,4,3,1,5,7,2,8]=>0110110=>0110110
[7,4,1,5,3,6,2,8]=>0011110=>0111100
[8,1,5,4,3,6,2,7]=>0011101=>1011100
[8,1,5,4,3,6,7,2]=>0011011=>1101100
[7,4,1,5,3,6,8,2]=>0011011=>1101100
[6,4,3,1,5,7,8,2]=>0110101=>1010110
[6,7,3,8,4,5,1,2]=>0001011=>1101000
[6,7,4,5,1,8,2,3]=>0001011=>1101000
[4,7,5,6,2,3,1,8]=>0100110=>0110010
[4,7,5,6,1,8,2,3]=>0000111=>1110000
[4,7,5,6,3,8,1,2]=>0000111=>1110000
[3,7,5,8,4,6,1,2]=>0000111=>1110000
[4,5,3,8,6,7,1,2]=>0001011=>1101000
[4,8,3,6,5,7,1,2]=>0000111=>1110000
[5,6,4,7,1,8,2,3]=>0000111=>1110000
[5,6,1,7,3,8,2,4]=>0000111=>1110000
[5,6,1,8,2,7,3,4]=>0000111=>1110000
[5,6,1,8,4,7,2,3]=>0000111=>1110000
[4,8,1,6,5,7,2,3]=>0000111=>1110000
[4,5,1,8,6,7,2,3]=>0001011=>1101000
[7,8,4,5,1,6,2,3]=>0001101=>1011000
[4,8,2,3,1,6,5,7]=>0100101=>1010010
[5,6,2,8,1,4,3,7]=>0010101=>1010100
[5,6,3,4,1,8,2,7]=>0010101=>1010100
[3,6,4,5,2,7,1,8]=>0001110=>0111000
[3,6,4,5,1,8,2,7]=>0001101=>1011000
[2,6,4,8,1,5,3,7]=>0001101=>1011000
[2,8,3,6,1,5,4,7]=>0001101=>1011000
[2,8,3,4,1,6,5,7]=>0010101=>1010100
[7,8,2,5,3,4,1,6]=>0011001=>1001100
[7,8,1,5,3,6,2,4]=>0001101=>1011000
[1,5,3,8,6,7,2,4]=>0001011=>1101000
[1,8,3,6,2,7,4,5]=>0000111=>1110000
[1,6,4,8,2,7,3,5]=>0000111=>1110000
[2,6,4,7,3,5,1,8]=>0001110=>0111000
[2,7,3,6,4,5,1,8]=>0001110=>0111000
[1,7,3,6,4,8,2,5]=>0000111=>1110000
[1,7,2,8,4,6,3,5]=>0000111=>1110000
[1,7,5,8,4,6,2,3]=>0000111=>1110000
[1,7,5,8,2,6,3,4]=>0000111=>1110000
[1,7,5,6,3,8,2,4]=>0000111=>1110000
[2,7,5,6,3,4,1,8]=>0010110=>0110100
[6,7,2,5,3,4,1,8]=>0011010=>0101100
[6,7,1,5,3,8,2,4]=>0001011=>1101000
[6,7,5,8,1,4,2,3]=>0010011=>1100100
[5,8,6,7,2,3,1,4]=>0100011=>1100010
[6,7,2,3,1,8,4,5]=>0100011=>1100010
[6,7,2,8,1,4,3,5]=>0010011=>1100100
[3,4,2,7,5,6,1,8]=>0010110=>0110100
[3,4,1,7,5,8,2,6]=>0010011=>1100100
[2,7,5,8,1,4,3,6]=>0010011=>1100100
[2,3,1,7,5,8,4,6]=>0100011=>1100010
[2,3,1,8,4,7,5,6]=>0100011=>1100010
[7,8,2,3,1,6,4,5]=>0100101=>1010010
[7,8,2,6,1,4,3,5]=>0010101=>1010100
[2,8,6,7,1,4,3,5]=>0010011=>1100100
[2,8,1,4,3,7,5,6]=>0010011=>1100100
[3,7,2,5,4,6,1,8]=>0001110=>0111000
[4,5,2,7,3,6,1,8]=>0001110=>0111000
[4,5,1,8,2,7,3,6]=>0001011=>1101000
[3,4,1,8,2,7,5,6]=>0010011=>1100100
[3,4,1,8,6,7,2,5]=>0010011=>1100100
[3,4,2,5,1,8,6,7]=>0011001=>1001100
[3,4,2,8,1,6,5,7]=>0010101=>1010100
[3,8,2,5,1,6,4,7]=>0001101=>1011000
[4,5,2,8,1,6,3,7]=>0001101=>1011000
[4,5,3,6,1,8,2,7]=>0001101=>1011000
[7,1,5,8,4,6,2,3]=>0000111=>1110000
[8,6,7,1,4,2,5,3]=>0011011=>1101100
[8,6,3,7,5,1,2,4]=>0001111=>1111000
[8,6,1,7,3,2,5,4]=>0101111=>1111010
[7,6,1,8,3,5,2,4]=>0001111=>1111000
[7,6,1,3,8,5,2,4]=>0001111=>1111000
[7,6,8,2,4,5,1,3]=>0001011=>1101000
[7,6,2,8,3,5,1,4]=>0001111=>1111000
[7,6,2,3,8,5,1,4]=>0001111=>1111000
[8,7,1,5,2,6,3,4]=>0001111=>1111000
[8,7,1,5,2,3,6,4]=>0001111=>1111000
[8,5,2,3,1,7,6,4]=>0101111=>1111010
[8,6,2,3,7,1,5,4]=>0001111=>1111000
[8,6,2,7,3,1,5,4]=>0101111=>1111010
[8,6,7,2,4,1,5,3]=>0011011=>1101100
[6,8,7,3,4,1,5,2]=>0011011=>1101100
[8,7,2,5,1,6,3,4]=>0001111=>1111000
[8,7,2,1,4,6,3,5]=>1000111=>1110001
[8,4,2,1,7,6,3,5]=>1010111=>1110101
[8,5,2,7,1,6,3,4]=>0001111=>1111000
[8,5,7,2,1,4,3,6]=>1010011=>1100101
[5,8,7,3,1,4,2,6]=>0110011=>1100110
[5,8,7,3,1,4,6,2]=>0100111=>1110010
[8,5,7,2,1,4,6,3]=>1000111=>1110001
[8,5,2,7,1,3,6,4]=>0001111=>1111000
[8,4,2,1,3,7,6,5]=>1010111=>1110101
[8,7,4,1,2,3,6,5]=>0010111=>1110100
[8,7,4,1,2,6,3,5]=>0010111=>1110100
[8,4,3,1,7,2,6,5]=>0110111=>1110110
[8,4,3,1,2,7,6,5]=>0110111=>1110110
[8,6,1,3,7,2,5,4]=>0001111=>1111000
[8,5,1,3,2,7,6,4]=>0101111=>1111010
[8,5,7,4,1,6,2,3]=>0010111=>1110100
[8,5,7,4,1,2,6,3]=>0010111=>1110100
[8,1,5,4,2,7,6,3]=>0011111=>1111100
[8,1,6,4,7,2,5,3]=>0001111=>1111000
[6,1,5,8,4,2,7,3]=>0010111=>1110100
[5,8,3,6,4,1,2,7]=>0010101=>1010100
[5,2,8,6,4,1,3,7]=>0011101=>1011100
[8,4,7,5,1,6,2,3]=>0001111=>1111000
[8,4,7,5,1,2,6,3]=>0001111=>1111000
[8,4,7,5,1,2,3,6]=>0001011=>1101000
[8,7,3,5,1,2,6,4]=>0001111=>1111000
[8,3,2,6,5,1,4,7]=>0101101=>1011010
[4,8,6,3,5,1,2,7]=>0001101=>1011000
[4,8,7,3,1,5,2,6]=>0101011=>1101010
[8,4,7,2,1,5,3,6]=>1001011=>1101001
[8,3,2,7,1,5,4,6]=>0101011=>1101010
[8,3,2,1,7,6,4,5]=>1100111=>1110011
[8,7,3,1,4,2,6,5]=>0110111=>1110110
[8,7,3,1,6,2,4,5]=>0100111=>1110010
[8,7,3,1,2,6,4,5]=>0100111=>1110010
[8,7,3,1,2,4,6,5]=>0100111=>1110010
[8,3,2,1,4,7,6,5]=>1100111=>1110011
[8,3,2,1,7,4,6,5]=>1100111=>1110011
[8,3,2,7,1,5,6,4]=>0100111=>1110010
[8,4,7,2,1,5,6,3]=>1000111=>1110001
[3,8,7,4,1,2,5,6]=>0010011=>1100100
[8,7,2,1,6,3,4,5]=>1000111=>1110001
[8,7,2,1,3,6,4,5]=>1000111=>1110001
[8,7,2,1,3,4,6,5]=>1000111=>1110001
[3,6,5,4,1,2,8,7]=>0011101=>1011100
[3,8,5,6,7,4,1,2]=>0010011=>1100100
[4,7,5,8,6,2,1,3]=>1000111=>1110001
[2,5,7,8,6,3,4,1]=>0010101=>1010100
[4,8,5,7,6,3,1,2]=>0100111=>1110010
[4,6,3,2,1,5,8,7]=>1100101=>1010011
[6,2,1,5,3,4,8,7]=>1001101=>1011001
[5,8,1,3,7,6,4,2]=>0010111=>1110100
[4,7,2,3,6,1,8,5]=>0000111=>1110000
[3,7,4,2,8,1,5,6]=>0010011=>1100100
[4,2,6,8,5,7,3,1]=>0110011=>1100110
[6,4,2,7,3,8,5,1]=>0011111=>1111100
[8,1,6,7,5,3,4,2]=>0011011=>1101100
[2,1,5,8,7,6,3,4]=>1000111=>1110001
[2,1,4,7,6,3,8,5]=>1000111=>1110001
[6,4,7,8,5,3,2,1]=>1101101=>1011011
[4,1,3,7,6,2,8,5]=>0010111=>1110100
[8,5,1,6,3,2,7,4]=>0101111=>1111010
[6,3,7,1,5,2,8,4]=>0001111=>1111000
[3,2,6,8,4,7,5,1]=>0101011=>1101010
[8,4,6,1,3,2,5,7]=>0100101=>1010010
[4,2,8,6,7,3,1,5]=>0110011=>1100110
[7,4,3,8,2,1,5,6]=>1010011=>1100101
[4,7,5,8,1,6,3,2]=>0100111=>1110010
[6,4,3,2,7,8,1,5]=>0110101=>1010110
[4,2,5,1,6,7,8,3]=>0011001=>1001100
[2,4,8,5,7,1,3,6]=>0000011=>1100000
[3,7,1,4,6,8,5,2]=>0001011=>1101000
[7,8,2,5,6,1,4,3]=>0010101=>1010100
[2,4,3,8,7,5,6,1]=>0010111=>1110100
[2,6,7,3,5,1,8,4]=>0001011=>1101000
[7,6,8,4,2,5,3,1]=>0111011=>1101110
[8,5,7,1,6,3,2,4]=>0100111=>1110010
[6,5,7,2,8,4,3,1]=>0110111=>1110110
[3,4,8,6,5,2,1,7]=>1001101=>1011001
[2,7,6,1,4,5,8,3]=>0000111=>1110000
[6,5,8,2,1,7,3,4]=>1000111=>1110001
[7,4,3,5,1,6,8,2]=>0011011=>1101100
[4,1,6,3,5,8,7,2]=>0010111=>1110100
[6,2,5,8,4,3,7,1]=>0010111=>1110100
[8,6,7,1,5,4,3,2]=>0111011=>1101110
[2,1,6,5,8,4,7,3]=>1000111=>1110001
[2,1,6,8,5,4,3,7]=>1011001=>1001101
[4,1,8,5,6,2,3,7]=>0010101=>1010100
[2,6,4,8,7,3,5,1]=>0001111=>1111000
[6,2,8,4,3,5,1,7]=>0011101=>1011100
[4,8,2,7,6,1,3,5]=>0000111=>1110000
[3,1,8,2,7,5,4,6]=>0101011=>1101010
[3,8,1,2,6,7,4,5]=>0000011=>1100000
[5,8,4,3,2,7,1,6]=>0110011=>1100110
[7,4,8,6,3,2,5,1]=>0101111=>1111010
[5,8,4,7,2,1,3,6]=>1000011=>1100001
[2,1,8,4,3,7,5,6]=>1010011=>1100101
[6,3,8,2,4,5,7,1]=>0000111=>1110000
[5,8,4,2,3,6,1,7]=>0010101=>1010100
[5,8,2,4,3,1,6,7]=>0110001=>1000110
[2,8,3,1,6,4,5,7]=>0100101=>1010010
[8,2,1,3,4,7,5,6]=>1000011=>1100001
[1,4,8,2,6,3,5,7]=>0000101=>1010000
[1,2,7,3,5,4,8,6]=>0001011=>1101000
[1,2,3,8,4,5,7,6]=>0000011=>1100000
[1,2,8,3,4,5,7,6]=>0000011=>1100000
[1,3,8,2,6,4,5,7]=>0000101=>1010000
[1,5,7,2,3,6,4,8]=>0000110=>0110000
[1,7,2,3,5,4,8,6]=>0001011=>1101000
[1,3,8,2,4,5,7,6]=>0000011=>1100000
[1,2,3,8,4,6,7,5]=>0000011=>1100000
[1,8,2,3,5,4,6,7]=>0001001=>1001000
[1,7,8,2,3,6,4,5]=>0000101=>1010000
[1,6,7,8,2,3,5,4]=>0001001=>1001000
[1,7,8,2,5,3,6,4]=>0001101=>1011000
[1,7,8,2,4,5,3,6]=>0001001=>1001000
[1,2,8,3,6,4,5,7]=>0000101=>1010000
[1,8,2,3,6,4,5,7]=>0000101=>1010000
[1,2,8,3,5,4,6,7]=>0001001=>1001000
[1,2,7,8,3,6,4,5]=>0000101=>1010000
[1,5,2,7,8,3,6,4]=>0001101=>1011000
[1,3,2,8,4,6,7,5]=>0100011=>1100010
[1,8,2,3,4,6,7,5]=>0000011=>1100000
[1,7,8,2,4,3,6,5]=>0010101=>1010100
[7,6,3,1,5,2,4,8]=>0101110=>0111010
[6,7,3,1,5,2,8,4]=>0101011=>1101010
[6,8,3,1,5,2,7,4]=>0101011=>1101010
[6,8,4,5,1,2,7,3]=>0001011=>1101000
[6,7,4,5,1,2,8,3]=>0001011=>1101000
[7,2,1,6,5,3,4,8]=>1001110=>0111001
[7,3,6,1,5,2,4,8]=>0001110=>0111000
[7,4,6,5,1,2,3,8]=>0001110=>0111000
[6,7,5,4,1,2,8,3]=>0011011=>1101100
[5,8,6,4,1,7,2,3]=>0010111=>1110100
[5,7,6,4,1,8,2,3]=>0010111=>1110100
[5,6,7,4,1,8,2,3]=>0010011=>1100100
[6,5,7,4,1,2,8,3]=>0010111=>1110100
[6,4,7,5,1,2,8,3]=>0001111=>1111000
[6,2,1,7,5,3,8,4]=>1001111=>1111001
[6,3,8,1,5,2,7,4]=>0001111=>1111000
[6,4,8,5,1,2,7,3]=>0001111=>1111000
[6,5,8,4,1,2,7,3]=>0010111=>1110100
[5,6,8,4,1,7,2,3]=>0010011=>1100100
[4,6,8,5,7,1,2,3]=>0000011=>1100000
[4,5,8,6,7,1,2,3]=>0000011=>1100000
[5,4,8,6,1,7,2,3]=>0001111=>1111000
[5,3,8,1,6,7,2,4]=>0001011=>1101000
[5,2,1,8,6,7,3,4]=>1001011=>1101001
[5,2,1,7,6,8,3,4]=>1001011=>1101001
[5,4,7,6,1,8,2,3]=>0001111=>1111000
[4,5,7,6,8,1,2,3]=>0000011=>1100000
[4,6,7,5,8,1,2,3]=>0000011=>1100000
[4,8,6,5,7,1,2,3]=>0000111=>1110000
[4,8,5,6,7,1,2,3]=>0000011=>1100000
[4,7,5,6,8,1,2,3]=>0000011=>1100000
[4,6,5,7,8,1,2,3]=>0000101=>1010000
[5,7,4,6,1,8,2,3]=>0000111=>1110000
[5,8,4,6,1,7,2,3]=>0000111=>1110000
[5,8,3,1,6,7,2,4]=>0100011=>1100010
[5,7,3,1,6,8,2,4]=>0100011=>1100010
[5,6,3,1,7,8,2,4]=>0100101=>1010010
[6,2,1,4,3,8,7,5]=>1010111=>1110101
[5,8,3,1,7,6,2,4]=>0100111=>1110010
[5,7,4,8,1,6,2,3]=>0000111=>1110000
[5,2,1,6,8,7,3,4]=>1001011=>1101001
[5,4,6,8,1,7,2,3]=>0001011=>1101000
[4,5,6,8,7,1,2,3]=>0000011=>1100000
[4,7,5,8,6,1,2,3]=>0000111=>1110000
[4,8,5,7,6,1,2,3]=>0000111=>1110000
[4,8,6,7,5,1,2,3]=>0001011=>1101000
[4,7,6,8,5,1,2,3]=>0001011=>1101000
[4,6,7,8,5,1,2,3]=>0001001=>1001000
[4,5,7,8,6,1,2,3]=>0000101=>1010000
[5,4,7,8,1,6,2,3]=>0001101=>1011000
[5,3,7,1,8,6,2,4]=>0001111=>1111000
[5,2,1,7,8,6,3,4]=>1001101=>1011001
[5,3,8,1,7,6,2,4]=>0001111=>1111000
[5,4,8,7,1,6,2,3]=>0001111=>1111000
[4,6,8,7,5,1,2,3]=>0001011=>1101000
[4,7,8,6,5,1,2,3]=>0001101=>1011000
[4,8,7,6,5,1,2,3]=>0001111=>1111000
[2,5,4,7,3,6,1,8]=>0001110=>0111000
[2,4,6,3,7,5,1,8]=>0001110=>0111000
[4,2,7,3,6,5,1,8]=>0011110=>0111100
[4,2,6,3,1,5,8,7]=>0110101=>1010110
[2,5,3,1,6,4,8,7]=>0101101=>1011010
[2,5,3,7,6,4,1,8]=>0011110=>0111100
[2,6,5,3,7,4,1,8]=>0011110=>0111100
[4,2,7,6,3,5,1,8]=>0011110=>0111100
[2,7,5,3,6,4,1,8]=>0011110=>0111100
[2,6,3,7,5,4,1,8]=>0011110=>0111100
[1,7,5,2,3,8,4,6]=>0001011=>1101000
[2,1,3,7,5,4,8,6]=>1001011=>1101001
[2,3,1,8,6,5,4,7]=>0101101=>1011010
[2,5,3,1,8,6,4,7]=>0101101=>1011010
[4,2,8,3,1,6,5,7]=>0110101=>1010110
[8,3,2,6,4,1,5,7]=>0110101=>1010110
[3,6,8,2,1,4,5,7]=>1000001=>1000001
[1,5,2,8,3,4,7,6]=>0001011=>1101000
[1,2,6,3,8,7,4,5]=>0000111=>1110000
[1,2,8,3,6,4,7,5]=>0000111=>1110000
[1,2,7,6,3,4,8,5]=>0000111=>1110000
[2,1,3,8,7,5,4,6]=>1001011=>1101001
[1,2,3,8,6,4,7,5]=>0000111=>1110000
[1,2,3,7,4,8,6,5]=>0000111=>1110000
[1,2,7,6,3,8,4,5]=>0000111=>1110000
[1,2,3,6,4,8,7,5]=>0000111=>1110000
[1,2,3,7,6,4,8,5]=>0000111=>1110000
[2,6,3,1,8,5,4,7]=>0101101=>1011010
[2,1,3,8,5,4,7,6]=>1001011=>1101001
[7,1,8,4,2,3,5,6]=>0010011=>1100100
[2,1,8,4,3,5,7,6]=>1010011=>1100101
[4,2,6,3,1,8,5,7]=>0110101=>1010110
[5,4,2,8,3,1,6,7]=>0111001=>1001110
[3,5,8,2,4,1,6,7]=>0010001=>1000100
[2,5,4,8,3,1,6,7]=>0101001=>1001010
[4,2,1,8,3,5,7,6]=>1010011=>1100101
[1,8,7,4,2,3,5,6]=>0010011=>1100100
[1,5,2,8,7,3,4,6]=>0001011=>1101000
[1,2,7,3,6,4,8,5]=>0000111=>1110000
[1,2,8,6,3,7,4,5]=>0000111=>1110000
[1,2,7,3,8,6,4,5]=>0000111=>1110000
[1,2,3,8,4,7,6,5]=>0000111=>1110000
[1,2,7,3,4,8,6,5]=>0000111=>1110000
[1,2,6,3,8,4,7,5]=>0000111=>1110000
[1,5,2,3,8,7,4,6]=>0001011=>1101000
[4,2,1,8,3,7,5,6]=>1010011=>1100101
[8,3,2,1,7,4,5,6]=>1100011=>1100011
[1,8,4,2,7,3,5,6]=>0010011=>1100100
[1,2,8,6,3,4,7,5]=>0000111=>1110000
[1,2,7,3,8,4,6,5]=>0000111=>1110000
[1,2,3,8,7,4,6,5]=>0000111=>1110000
[1,2,3,8,7,6,4,5]=>0000111=>1110000
[2,5,3,8,1,6,4,7]=>0001101=>1011000
[2,6,4,7,1,5,3,8]=>0001110=>0111000
[2,6,5,7,1,4,3,8]=>0010110=>0110100
[3,8,5,7,1,2,6,4]=>0000111=>1110000
[3,8,5,7,2,6,4,1]=>0010111=>1110100
[3,4,8,6,2,5,7,1]=>0000111=>1110000
[3,4,8,6,1,2,5,7]=>0000101=>1010000
[2,5,7,1,4,8,6,3]=>0000111=>1110000
[2,4,8,1,5,7,6,3]=>0000111=>1110000
[2,4,3,8,1,6,5,7]=>0010101=>1010100
[2,8,1,7,5,6,4,3]=>0010111=>1110100
[2,3,8,1,6,5,7,4]=>0000111=>1110000
[2,4,8,1,3,5,7,6]=>0000011=>1100000
[3,5,7,6,1,2,4,8]=>0000110=>0110000
[3,5,7,6,2,4,8,1]=>0000111=>1110000
[4,8,6,7,2,3,5,1]=>0001011=>1101000
[4,8,6,7,1,2,3,5]=>0000011=>1100000
[4,8,6,7,1,3,5,2]=>0001011=>1101000
[3,4,8,6,1,5,7,2]=>0000111=>1110000
[3,8,5,7,1,6,4,2]=>0010111=>1110100
[3,2,8,5,6,1,7,4]=>0100111=>1110010
[3,8,5,7,2,1,6,4]=>1000111=>1110001
[3,4,8,6,2,1,5,7]=>1000101=>1010001
[3,5,7,6,2,1,4,8]=>1000110=>0110001
[4,8,6,7,2,1,3,5]=>1000011=>1100001
[4,8,6,7,3,5,2,1]=>1001011=>1101001
[5,8,6,7,3,4,2,1]=>1010011=>1100101
[5,8,6,7,2,1,3,4]=>1000011=>1100001
[5,8,6,7,2,1,4,3]=>1010011=>1100101
[4,8,6,7,2,1,5,3]=>1001011=>1101001
[4,3,1,7,5,2,8,6]=>0111011=>1101110
[4,3,2,8,5,1,7,6]=>0111011=>1101110
[4,3,8,5,1,6,7,2]=>0011011=>1101100
[4,8,6,7,1,5,3,2]=>0101011=>1101010
[5,8,6,7,1,4,3,2]=>0110011=>1100110
[5,8,6,7,2,3,4,1]=>0010011=>1100100
[5,8,6,7,2,4,3,1]=>0110011=>1100110
[5,8,6,7,1,2,4,3]=>0010011=>1100100
[4,2,3,8,5,1,6,7]=>0011001=>1001100
[4,2,8,5,1,7,6,3]=>0011111=>1111100
[3,4,2,8,5,6,1,7]=>0010101=>1010100
[3,2,4,8,6,1,5,7]=>0100101=>1010010
[3,2,5,7,6,1,4,8]=>0100110=>0110010
[4,8,6,7,1,3,2,5]=>0100011=>1100010
[4,8,6,7,1,2,5,3]=>0001011=>1101000
[4,8,6,7,2,5,3,1]=>0101011=>1101010
[4,3,8,5,2,6,7,1]=>0011011=>1101100
[4,3,8,5,1,2,6,7]=>0011001=>1001100
[4,2,6,7,5,1,3,8]=>0011010=>0101100
[3,8,5,7,1,4,2,6]=>0010011=>1100100
[3,8,4,7,1,5,2,6]=>0001011=>1101000
[3,5,2,8,4,6,1,7]=>0001101=>1011000
[3,5,1,7,4,6,2,8]=>0001110=>0111000
[3,8,4,7,2,5,1,6]=>0001011=>1101000
[4,1,3,8,5,2,6,7]=>0011001=>1001100
[4,1,2,6,7,5,3,8]=>0011010=>0101100
[4,2,6,7,5,3,8,1]=>0011011=>1101100
[4,8,6,7,3,2,5,1]=>0101011=>1101010
[4,8,6,7,3,1,2,5]=>0100011=>1100010
[3,1,5,7,6,2,4,8]=>0100110=>0110010
[3,4,1,7,5,6,2,8]=>0010110=>0110100
[4,1,7,5,2,8,6,3]=>0011111=>1111100
[4,1,6,7,5,2,3,8]=>0011010=>0101100
[4,8,6,7,2,3,1,5]=>0100011=>1100010
[5,8,6,7,3,2,4,1]=>0110011=>1100110
[5,8,6,7,4,2,3,1]=>0110011=>1100110
[5,8,6,7,4,1,2,3]=>0010011=>1100100
[5,8,6,7,4,1,3,2]=>0110011=>1100110
[5,8,6,7,3,1,4,2]=>0110011=>1100110
[4,8,6,7,3,1,5,2]=>0101011=>1101010
[4,1,6,7,5,3,8,2]=>0011011=>1101100
[4,1,7,5,3,2,8,6]=>0111011=>1101110
[4,2,8,5,3,1,7,6]=>0111011=>1101110
[4,2,1,6,7,5,3,8]=>1011010=>0101101
[4,8,6,7,3,2,1,5]=>1100011=>1100011
[5,8,6,7,4,2,1,3]=>1010011=>1100101
[5,8,6,7,4,3,1,2]=>0110011=>1100110
[7,3,5,8,1,4,2,6]=>0010011=>1100100
[3,8,7,6,1,4,2,5]=>0010111=>1110100
[5,1,8,3,6,7,2,4]=>0001011=>1101000
[1,4,7,8,5,6,2,3]=>0000101=>1010000
[3,4,7,1,5,8,6,2]=>0000111=>1110000
[3,6,1,4,7,8,5,2]=>0001101=>1011000
[1,6,8,4,7,5,2,3]=>0001011=>1101000
[6,8,1,3,5,7,2,4]=>0000011=>1100000
[7,6,1,4,3,8,2,5]=>0010111=>1110100
[3,8,1,6,5,4,2,7]=>0011101=>1011100
[4,1,3,7,5,8,2,6]=>0010011=>1100100
[6,1,7,3,8,4,2,5]=>0010111=>1110100
[7,1,8,6,3,5,2,4]=>0001111=>1111000
[3,1,7,6,5,8,4,2]=>0110111=>1110110
[8,2,7,6,5,3,4,1]=>0011111=>1111100
[8,4,2,6,7,5,3,1]=>0111011=>1101110
[4,8,1,6,7,5,3,2]=>0101011=>1101010
[7,4,1,6,8,2,5,3]=>0011011=>1101100
[1,3,8,6,2,7,5,4]=>0001111=>1111000
[6,1,3,2,7,8,4,5]=>0100101=>1010010
[1,8,6,2,5,3,4,7]=>0001101=>1011000
[4,7,2,6,8,1,5,3]=>0001011=>1101000
[8,7,3,6,4,5,2,1]=>1001111=>1111001
[5,7,8,6,2,1,4,3]=>1010101=>1010101
[2,7,4,1,6,8,3,5]=>0010011=>1100100
[3,7,2,4,5,1,6,8]=>0001010=>0101000
[1,8,6,4,5,2,3,7]=>0001101=>1011000
[2,8,4,6,5,1,3,7]=>0001101=>1011000
[3,4,1,7,5,2,6,8]=>0011010=>0101100
[7,5,8,6,1,2,4,3]=>0010111=>1110100
[5,6,8,7,3,1,4,2]=>0110011=>1100110
[2,5,4,3,6,8,1,7]=>0011001=>1001100
[3,8,5,4,6,2,1,7]=>1001101=>1011001
[4,8,2,1,3,7,5,6]=>1000011=>1100001
[6,4,1,2,7,5,8,3]=>0010111=>1110100
[4,1,8,3,6,7,5,2]=>0011011=>1101100
[8,3,7,4,5,2,6,1]=>0001111=>1111000
[4,3,7,8,5,1,6,2]=>0011101=>1011100
[5,4,8,2,7,6,1,3]=>0001111=>1111000
[1,2,7,3,6,5,8,4]=>0000111=>1110000
[2,8,7,6,3,4,1,5]=>0010111=>1110100
[5,8,2,6,3,4,1,7]=>0010101=>1010100
[4,1,7,5,8,6,2,3]=>0010111=>1110100
[5,1,7,8,4,3,6,2]=>0011101=>1011100
[8,2,7,5,4,3,6,1]=>0011111=>1111100
[6,3,8,1,4,7,5,2]=>0001111=>1111000
[3,8,4,5,6,1,2,7]=>0000101=>1010000
[1,4,3,5,7,8,2,6]=>0010001=>1000100
[6,5,8,7,1,3,4,2]=>0010111=>1110100
[3,6,7,2,4,8,1,5]=>0000011=>1100000
[1,5,2,7,4,3,8,6]=>0011011=>1101100
[2,8,5,6,4,3,1,7]=>0110101=>1010110
[1,8,6,5,4,3,2,7]=>0111101=>1011110
[6,1,5,2,8,4,7,3]=>0001111=>1111000
[4,6,1,8,5,7,2,3]=>0000111=>1110000
[4,7,1,2,8,5,6,3]=>0000111=>1110000
[1,4,7,2,8,5,6,3]=>0000111=>1110000
[1,7,3,5,8,6,2,4]=>0000111=>1110000
[7,3,5,8,6,1,2,4]=>0000111=>1110000
[3,6,8,1,5,7,2,4]=>0000011=>1100000
[3,4,6,5,8,1,7,2]=>0000111=>1110000
[6,8,1,5,7,2,3,4]=>0000011=>1100000
[7,1,2,5,8,6,3,4]=>0000111=>1110000
[1,7,2,5,8,6,3,4]=>0000111=>1110000
[1,7,6,8,2,3,5,4]=>0001011=>1101000
[7,6,8,1,2,3,5,4]=>0001011=>1101000
[2,7,1,5,8,6,3,4]=>0000111=>1110000
[2,4,7,1,8,5,6,3]=>0000111=>1110000
[4,7,5,8,3,1,6,2]=>0100111=>1110010
[4,7,2,1,8,5,6,3]=>1000111=>1110001
[7,6,8,2,1,3,5,4]=>1001011=>1101001
[1,2,7,6,8,3,5,4]=>0001011=>1101000
[3,7,6,8,2,1,5,4]=>1001011=>1101001
[7,4,2,1,6,8,5,3]=>1011011=>1101101
[6,7,4,1,8,5,3,2]=>0111011=>1101110
[6,7,4,3,1,8,5,2]=>0111011=>1101110
[2,7,4,1,6,8,5,3]=>0011011=>1101100
[2,3,7,6,8,1,5,4]=>0001011=>1101000
[7,4,2,6,8,5,1,3]=>0011011=>1101100
[7,3,2,5,8,6,1,4]=>0100111=>1110010
[3,1,7,6,8,2,5,4]=>0101011=>1101010
[3,7,6,8,1,2,5,4]=>0001011=>1101000
[1,3,7,6,8,2,5,4]=>0001011=>1101000
[1,7,4,2,6,8,5,3]=>0011011=>1101100
[7,4,1,2,6,8,5,3]=>0011011=>1101100
[7,1,4,2,8,5,6,3]=>0010111=>1110100
[7,1,8,2,5,4,6,3]=>0001111=>1111000
[7,3,8,4,6,1,5,2]=>0001111=>1111000
[7,2,8,1,6,4,5,3]=>0001111=>1111000
[7,1,6,8,5,4,2,3]=>0011011=>1101100
[7,1,2,6,8,5,4,3]=>0011011=>1101100
[1,7,2,6,8,5,4,3]=>0011011=>1101100
[1,7,6,8,3,2,5,4]=>0101011=>1101010
[7,6,8,3,1,2,5,4]=>0101011=>1101010
[7,1,5,8,6,3,2,4]=>0100111=>1110010
[7,2,5,8,6,3,1,4]=>0100111=>1110010
[3,6,7,1,8,5,4,2]=>0011011=>1101100
[7,2,6,8,5,4,1,3]=>0011011=>1101100
[7,6,8,2,3,1,5,4]=>0101011=>1101010
[2,7,6,8,3,1,5,4]=>0101011=>1101010
[2,7,1,6,8,5,4,3]=>0011011=>1101100
[6,7,3,1,8,5,4,2]=>0111011=>1101110
[6,7,1,8,5,4,3,2]=>0111011=>1101110
[7,2,1,6,8,5,4,3]=>1011011=>1101101
[7,6,8,3,2,1,5,4]=>1101011=>1101011
[4,7,8,5,6,1,3,2]=>0100101=>1010010
[4,6,5,8,7,1,3,2]=>0100111=>1110010
[5,6,4,8,1,2,7,3]=>0000111=>1110000
[8,1,5,6,7,2,4,3]=>0010011=>1100100
[6,4,5,1,8,2,7,3]=>0001111=>1111000
[5,4,6,7,1,2,8,3]=>0001011=>1101000
[4,3,6,7,2,1,5,8]=>1010010=>0100101
[5,3,6,7,1,4,2,8]=>0011010=>0101100
[8,1,4,6,7,3,2,5]=>0100011=>1100010
[8,1,3,6,7,4,5,2]=>0001011=>1101000
[7,2,1,6,8,4,5,3]=>1001011=>1101001
[5,2,6,7,1,4,8,3]=>0001011=>1101000
[4,2,6,7,3,1,8,5]=>0110011=>1100110
[6,2,4,1,5,8,7,3]=>0010111=>1110100
[7,2,1,5,4,8,6,3]=>1001111=>1111001
[8,1,4,5,3,7,2,6]=>0001011=>1101000
[7,3,1,5,4,8,2,6]=>0101011=>1101010
[6,3,4,1,5,8,2,7]=>0010101=>1010100
[5,3,4,2,1,8,6,7]=>1011001=>1001101
[4,3,5,2,7,1,6,8]=>0011010=>0101100
[5,6,3,8,1,4,2,7]=>0010101=>1010100
[8,1,7,2,4,5,6,3]=>0000111=>1110000
[7,6,1,2,4,5,8,3]=>0000111=>1110000
[4,7,8,2,3,1,6,5]=>0100101=>1010010
[5,6,2,8,1,4,7,3]=>0000111=>1110000
[6,5,2,1,3,7,8,4]=>1001101=>1011001
[7,5,1,3,2,6,8,4]=>0101011=>1101010
[8,1,6,3,2,5,7,4]=>0100111=>1110010
[7,4,1,3,5,2,8,6]=>0011011=>1101100
[5,4,2,3,1,6,8,7]=>0111001=>1001110
[7,3,1,4,5,6,2,8]=>0100110=>0110010
[8,1,4,3,5,6,2,7]=>0010101=>1010100
[6,2,3,1,5,7,8,4]=>0100101=>1010010
[7,8,4,2,1,6,5,3]=>1011101=>1011101
[7,8,4,2,1,5,6,3]=>1010101=>1010101
[6,2,3,4,8,7,1,5]=>0000111=>1110000
[6,2,3,4,7,8,1,5]=>0000101=>1010000
[7,8,3,4,6,2,1,5]=>1000101=>1010001
[7,8,3,6,4,2,1,5]=>1010101=>1010101
[7,8,3,5,6,2,1,4]=>1000101=>1010001
[6,2,3,8,7,5,1,4]=>0001111=>1111000
[6,2,3,7,8,5,1,4]=>0001101=>1011000
[5,2,6,3,8,1,7,4]=>0001111=>1111000
[6,3,2,5,8,7,1,4]=>0100111=>1110010
[6,3,2,8,4,7,1,5]=>0100111=>1110010
[6,4,3,8,7,5,1,2]=>0011111=>1111100
[6,4,3,7,8,5,1,2]=>0011101=>1011100
[6,2,4,1,7,3,5,8]=>0010110=>0110100
[6,3,2,7,4,8,1,5]=>0100111=>1110010
[6,3,2,5,7,8,1,4]=>0100101=>1010010
[5,7,2,3,6,1,8,4]=>0000111=>1110000
[5,8,2,3,6,1,7,4]=>0000111=>1110000
[4,7,5,8,3,2,1,6]=>1100011=>1100011
[4,5,6,8,3,2,1,7]=>1100001=>1000011
[4,6,8,5,3,2,1,7]=>1101001=>1001011
[5,6,1,4,2,3,7,8]=>0010100=>0010100
[5,6,8,4,3,7,1,2]=>0010011=>1100100
[5,6,1,4,2,3,8,7]=>0010101=>1010100
[5,2,8,3,4,1,7,6]=>0011011=>1101100
[4,5,8,6,3,2,1,7]=>1100101=>1010011
[4,6,5,8,3,2,1,7]=>1100101=>1010011
[4,7,5,6,3,2,1,8]=>1100110=>0110011
[6,2,3,4,5,8,1,7]=>0000101=>1010000
[5,1,4,3,6,2,8,7]=>0011101=>1011100
[5,1,4,3,7,2,8,6]=>0011011=>1101100
[5,1,4,3,8,2,7,6]=>0011011=>1101100
[5,6,2,4,1,7,8,3]=>0010101=>1010100
[5,6,2,4,1,8,7,3]=>0010111=>1110100
[5,7,2,4,1,8,6,3]=>0010111=>1110100
[6,1,4,2,8,7,5,3]=>0011111=>1111100
[6,1,4,2,7,8,5,3]=>0011101=>1011100
[5,8,2,4,1,7,6,3]=>0010111=>1110100
[5,2,7,4,1,6,8,3]=>0011011=>1101100
[5,4,1,3,7,2,6,8]=>0011010=>0101100
[5,1,4,3,6,2,7,8]=>0011100=>0011100
[5,8,6,4,3,7,1,2]=>0010111=>1110100
[5,8,1,4,2,3,7,6]=>0010011=>1100100
[5,1,6,3,4,2,7,8]=>0011100=>0011100
[4,8,6,5,3,2,1,7]=>1101101=>1011011
[4,8,5,6,3,2,1,7]=>1100101=>1010011
[5,4,7,8,3,2,1,6]=>1101001=>1001011
[5,4,8,7,3,2,1,6]=>1101011=>1101011
[4,6,8,7,3,2,1,5]=>1100011=>1100011
[4,6,7,8,3,2,1,5]=>1100001=>1000011
[4,7,6,8,3,2,1,5]=>1100011=>1100011
[4,7,8,5,3,2,1,6]=>1101001=>1001011
[5,7,1,3,4,2,6,8]=>0010010=>0100100
[5,1,8,4,2,3,6,7]=>0011001=>1001100
[5,1,7,4,2,3,6,8]=>0011010=>0101100
[5,8,1,3,4,2,6,7]=>0010001=>1000100
[4,8,7,5,3,2,1,6]=>1101011=>1101011
[4,7,8,6,3,2,1,5]=>1100101=>1010011
[4,8,7,6,3,2,1,5]=>1100111=>1110011
[4,8,2,6,3,7,5,1]=>0001111=>1111000
[4,8,2,3,6,7,5,1]=>0001011=>1101000
[4,8,3,1,6,7,5,2]=>0101011=>1101010
[4,3,8,1,6,2,5,7]=>0010101=>1010100
[1,4,8,7,3,5,2,6]=>0001011=>1101000
[4,3,8,7,2,5,1,6]=>0011011=>1101100
[5,8,4,3,7,1,6,2]=>0010111=>1110100
[5,8,1,4,7,2,6,3]=>0000111=>1110000
[5,8,1,7,4,2,3,6]=>0010011=>1100100
[6,8,1,2,4,3,5,7]=>0010001=>1000100
[5,8,7,1,3,4,2,6]=>0010011=>1100100
[4,8,7,6,3,1,2,5]=>0100111=>1110010
[5,8,4,7,3,1,2,6]=>0100011=>1100010
[4,3,8,2,7,5,6,1]=>0010111=>1110100
[1,4,8,3,7,5,6,2]=>0000111=>1110000
[1,4,3,8,2,6,5,7]=>0010101=>1010100
[4,3,2,8,1,6,5,7]=>0110101=>1010110
[4,1,3,8,2,6,5,7]=>0010101=>1010100
[4,1,8,3,7,5,6,2]=>0010111=>1110100
[4,1,8,7,3,5,2,6]=>0011011=>1101100
[3,7,8,1,5,4,2,6]=>0011001=>1001100
[7,3,8,1,5,4,6,2]=>0001111=>1111000
[3,4,8,1,6,2,5,7]=>0000101=>1010000
[3,4,8,7,2,5,1,6]=>0001011=>1101000
[3,4,8,2,7,5,6,1]=>0000111=>1110000
[1,2,4,8,3,6,5,7]=>0000101=>1010000
[1,2,4,3,8,6,5,7]=>0010101=>1010100
[3,4,2,1,8,6,5,7]=>1010101=>1010101
[3,4,1,8,2,6,5,7]=>0010101=>1010100
[3,6,7,8,4,1,2,5]=>0010001=>1000100
[4,1,7,8,5,3,2,6]=>0111001=>1001110
[4,1,2,8,3,6,5,7]=>0010101=>1010100
[1,4,3,2,8,6,5,7]=>0110101=>1010110
[4,2,3,1,8,6,5,7]=>0110101=>1010110
[3,7,6,8,4,2,1,5]=>1010011=>1100101
[4,7,1,8,5,2,3,6]=>0001011=>1101000
[2,6,8,7,4,3,1,5]=>0110011=>1100110
[3,7,8,6,2,4,1,5]=>0010101=>1010100
[3,7,8,2,6,4,5,1]=>0001101=>1011000
[4,2,3,8,1,6,5,7]=>0010101=>1010100
[4,3,1,8,2,6,5,7]=>0110101=>1010110
[1,4,7,8,5,3,2,6]=>0101001=>1001010
[4,3,7,8,5,2,1,6]=>1011001=>1001101
[3,7,2,8,4,6,5,1]=>0001111=>1111000
[4,2,8,6,3,1,5,7]=>0110101=>1010110
[2,6,8,4,7,3,1,5]=>0100011=>1100010
[2,4,8,6,3,1,5,7]=>0100101=>1010010
[7,3,6,8,4,2,1,5]=>1010011=>1100101
[7,6,2,8,3,5,4,1]=>0011111=>1111100
[1,7,3,8,4,6,5,2]=>0001111=>1111000
[1,3,4,8,2,6,5,7]=>0000101=>1010000
[3,2,4,8,1,6,5,7]=>0100101=>1010010
[7,3,8,6,2,4,1,5]=>0010111=>1110100
[7,3,8,2,6,4,5,1]=>0001111=>1111000
[2,4,8,3,6,1,5,7]=>0000101=>1010000
[6,2,8,7,4,3,5,1]=>0011111=>1111100
[7,4,1,8,5,2,6,3]=>0011111=>1111100
[7,3,2,8,4,6,5,1]=>0101111=>1111010
[2,4,3,1,8,6,5,7]=>0110101=>1010110
[1,3,4,2,8,6,5,7]=>0010101=>1010100
[1,3,2,4,8,6,5,7]=>0100101=>1010010
[3,2,1,4,8,6,5,7]=>1100101=>1010011
[3,1,2,4,8,6,5,7]=>0100101=>1010010
[3,1,4,2,8,6,5,7]=>0110101=>1010110
[3,1,4,8,2,6,5,7]=>0100101=>1010010
[7,3,4,8,5,1,6,2]=>0001111=>1111000
[3,7,4,8,5,1,2,6]=>0001011=>1101000
[6,7,2,8,3,5,4,1]=>0011011=>1101100
[2,3,1,4,8,6,5,7]=>0100101=>1010010
[2,1,3,4,8,6,5,7]=>1000101=>1010001
[1,2,3,4,8,6,5,7]=>0000101=>1010000
[4,8,3,6,2,1,5,7]=>1000101=>1010001
[3,5,8,2,6,1,4,7]=>0000101=>1010000
[3,6,5,8,2,4,1,7]=>0010101=>1010100
[5,3,8,7,2,4,6,1]=>0001111=>1111000
[2,8,4,5,7,3,6,1]=>0000111=>1110000
[2,4,5,7,3,8,1,6]=>0000011=>1100000
[6,2,4,5,8,3,1,7]=>0100101=>1010010
[4,8,1,2,5,6,3,7]=>0000101=>1010000
[8,1,3,5,2,6,4,7]=>0001101=>1011000
[5,2,1,6,3,8,4,7]=>1001101=>1011001
[6,2,5,1,8,4,3,7]=>0011101=>1011100
[3,6,1,5,8,4,2,7]=>0010101=>1010100
[6,1,4,5,8,3,2,7]=>0100101=>1010010
[5,6,4,8,1,3,2,7]=>0100101=>1010010
[6,5,4,3,8,2,1,7]=>1011101=>1011101
[5,4,3,7,2,8,1,6]=>0011011=>1101100
[5,8,4,3,7,2,6,1]=>0010111=>1110100
[4,6,8,3,7,2,5,1]=>0001011=>1101000
[7,4,6,3,2,8,1,5]=>0100111=>1110010
[1,4,3,6,2,7,8,5]=>0010101=>1010100
[1,5,4,3,7,2,8,6]=>0011011=>1101100
[4,7,8,5,3,1,2,6]=>0101001=>1001010
[5,7,3,4,1,2,8,6]=>0010011=>1100100
[8,5,4,7,6,2,1,3]=>1001111=>1111001
[8,5,7,4,3,6,1,2]=>0010111=>1110100
[4,3,8,1,6,7,5,2]=>0011011=>1101100
[4,7,8,3,6,1,5,2]=>0001101=>1011000
[5,3,8,6,7,4,1,2]=>0011011=>1101100
[1,3,8,6,4,7,5,2]=>0001111=>1111000
[8,6,2,7,4,1,5,3]=>0011111=>1111100
[7,6,2,1,4,3,8,5]=>1010111=>1110101
[7,6,1,3,4,2,8,5]=>0010111=>1110100
[1,5,7,3,2,6,8,4]=>0100011=>1100010
[1,6,7,3,2,5,8,4]=>0100011=>1100010
[3,2,6,8,5,7,4,1]=>0110011=>1100110
[5,8,2,3,6,7,4,1]=>0010011=>1100100
[7,5,2,3,1,6,8,4]=>0101011=>1101010
[1,6,4,7,2,3,8,5]=>0000111=>1110000
[3,1,7,5,2,8,4,6]=>0101011=>1101010
[2,5,7,4,1,8,3,6]=>0010011=>1100100
[4,2,6,1,7,8,3,5]=>0010101=>1010100
[4,2,7,6,3,8,1,5]=>0010111=>1110100
[6,4,8,7,2,3,5,1]=>0001111=>1111000
[3,2,6,8,7,4,5,1]=>0101011=>1101010
[3,2,7,4,1,6,8,5]=>0110011=>1100110
[6,3,2,1,7,8,4,5]=>1100101=>1010011
[3,7,1,8,4,2,5,6]=>0010011=>1100100
[4,2,1,3,7,5,8,6]=>1010011=>1100101
[8,1,3,7,4,2,6,5]=>0010111=>1110100
[8,4,3,7,6,2,1,5]=>1010111=>1110101
[8,3,5,2,7,6,1,4]=>0001111=>1111000
[3,6,2,8,7,1,5,4]=>0001111=>1111000
[7,3,2,8,1,6,5,4]=>0101111=>1111010
[3,8,7,2,6,5,4,1]=>0011111=>1111100
[4,2,7,8,6,1,5,3]=>0011101=>1011100
[6,8,2,4,7,1,5,3]=>0001011=>1101000
[5,2,1,8,7,3,6,4]=>1001111=>1111001
[8,2,1,6,3,7,5,4]=>1001111=>1111001
[6,8,3,1,7,5,2,4]=>0101011=>1101010
[5,8,1,6,7,2,4,3]=>0010011=>1100100
[6,2,8,1,5,7,4,3]=>0010111=>1110100
[5,7,8,2,6,1,4,3]=>0010101=>1010100
[8,7,2,5,6,4,3,1]=>0110111=>1110110
[8,6,7,5,2,4,3,1]=>0111011=>1101110
[7,2,6,8,1,5,4,3]=>0011011=>1101100
[1,2,7,8,5,6,4,3]=>0010101=>1010100
[7,4,8,1,6,2,5,3]=>0001111=>1111000
[3,7,1,8,2,6,5,4]=>0001111=>1111000
[2,1,7,3,8,6,5,4]=>1001111=>1111001
[8,2,1,7,6,5,4,3]=>1011111=>1111101
[8,1,4,7,6,5,3,2]=>0101111=>1111010
[8,6,7,5,1,4,3,2]=>0111011=>1101110
[7,8,6,5,4,1,3,2]=>0111101=>1011110
[5,8,4,3,2,1,6,7]=>1110001=>1000111
[6,4,7,3,2,1,8,5]=>1100111=>1110011
[5,4,7,3,2,1,6,8]=>1101010=>0101011
[6,5,3,7,2,1,4,8]=>1001110=>0111001
[5,8,3,6,2,1,4,7]=>1000101=>1010001
[6,3,7,8,2,1,4,5]=>1000101=>1010001
[5,3,7,6,2,1,4,8]=>1001110=>0111001
[3,8,7,6,2,1,4,5]=>1000111=>1110001
[5,8,4,2,6,1,3,7]=>0010101=>1010100
[4,8,7,2,5,1,3,6]=>0001011=>1101000
[5,8,3,2,6,1,4,7]=>0100101=>1010010
[4,8,3,2,5,1,7,6]=>0101011=>1101010
[4,3,7,2,5,1,8,6]=>0011011=>1101100
[3,8,7,2,5,1,4,6]=>0001011=>1101000
[6,4,2,7,5,1,3,8]=>0011110=>0111100
[6,3,2,7,5,1,4,8]=>0101110=>0111010
[5,3,2,6,7,1,4,8]=>0101010=>0101010
[3,8,2,6,5,1,4,7]=>0001101=>1011000
[6,2,7,8,5,1,3,4]=>0001101=>1011000
[5,2,7,6,8,1,3,4]=>0001011=>1101000
[4,2,7,6,5,1,3,8]=>0011110=>0111100
[2,8,7,6,5,1,3,4]=>0001111=>1111000
[6,5,4,3,1,7,8,2]=>0111101=>1011110
[6,4,7,3,1,5,8,2]=>0100111=>1110010
[5,4,7,3,1,8,6,2]=>0101111=>1111010
[6,4,3,7,1,5,8,2]=>0010111=>1110100
[5,4,3,6,1,8,7,2]=>0011111=>1111100
[6,3,7,8,1,4,5,2]=>0001101=>1011000
[5,3,7,6,1,4,8,2]=>0001111=>1111000
[4,3,7,6,1,5,8,2]=>0010111=>1110100
[3,8,7,6,1,4,5,2]=>0001111=>1111000
[6,5,4,2,1,7,3,8]=>1011110=>0111101
[6,4,7,2,1,5,3,8]=>1001110=>0111001
[4,8,7,2,1,5,3,6]=>1001011=>1101001
[5,8,3,2,1,4,7,6]=>1100011=>1100011
[4,8,3,2,1,5,7,6]=>1100011=>1100011
[5,3,7,2,1,4,8,6]=>1001011=>1101001
[3,8,7,2,1,4,5,6]=>1000011=>1100001
[6,5,2,7,1,4,3,8]=>0011110=>0111100
[5,8,2,6,1,4,3,7]=>0010101=>1010100
[6,4,2,7,1,5,3,8]=>0011110=>0111100
[5,4,2,6,1,8,3,7]=>0011101=>1011100
[4,3,2,6,1,5,8,7]=>0110101=>1010110
[6,2,7,8,1,4,3,5]=>0010101=>1010100
[4,2,7,6,1,5,3,8]=>0011110=>0111100
[3,2,7,6,1,4,5,8]=>0100110=>0110010
[6,5,4,1,8,7,3,2]=>0111111=>1111110
[5,8,4,1,6,7,3,2]=>0110011=>1100110
[6,4,7,1,5,8,3,2]=>0100111=>1110010
[5,4,7,1,6,8,3,2]=>0101011=>1101010
[4,8,7,1,5,6,3,2]=>0100111=>1110010
[5,4,3,1,6,8,7,2]=>0111011=>1101110
[4,8,3,1,5,6,7,2]=>0100011=>1100010
[3,8,7,1,5,4,6,2]=>0001111=>1111000
[5,8,2,1,6,4,3,7]=>1010101=>1010101
[6,3,2,1,5,4,8,7]=>1101101=>1011011
[5,3,2,1,6,4,8,7]=>1101101=>1011011
[3,8,2,1,5,4,6,7]=>1001001=>1001001
[6,2,7,1,5,4,3,8]=>0011110=>0111100
[5,2,7,1,6,4,3,8]=>0011110=>0111100
[4,2,7,1,5,6,3,8]=>0010110=>0110100
[3,2,7,1,5,4,6,8]=>0101010=>0101010
[2,8,7,1,5,4,3,6]=>0011011=>1101100
[6,5,1,7,8,4,3,2]=>0111101=>1011110
[5,8,1,6,7,4,3,2]=>0110011=>1100110
[6,4,1,7,5,8,3,2]=>0110111=>1110110
[5,4,1,6,7,8,3,2]=>0111001=>1001110
[4,8,1,6,5,7,3,2]=>0100111=>1110010
[6,3,1,7,5,4,8,2]=>0101111=>1111010
[5,3,1,6,7,4,8,2]=>0101011=>1101010
[4,3,1,6,5,7,8,2]=>0110101=>1010110
[3,8,1,6,5,4,7,2]=>0001111=>1111000
[5,2,1,6,7,4,3,8]=>1011010=>0101101
[4,2,1,6,5,7,3,8]=>1010110=>0110101
[2,8,1,6,5,4,3,7]=>0011101=>1011100
[6,1,7,8,5,4,3,2]=>0111101=>1011110
[4,1,7,6,5,8,3,2]=>0110111=>1110110
[3,1,7,6,5,4,8,2]=>0101111=>1111010
[4,5,8,1,2,6,3,7]=>0000101=>1010000
[1,4,5,7,2,6,3,8]=>0000110=>0110000
[1,7,3,5,6,2,4,8]=>0000110=>0110000
[8,1,3,5,7,2,4,6]=>0000011=>1100000
[3,6,8,1,7,2,4,5]=>0000011=>1100000
[3,4,5,6,8,1,7,2]=>0000011=>1100000
[4,5,8,2,6,7,1,3]=>0000011=>1100000
[8,2,3,5,6,7,1,4]=>0000011=>1100000
[1,7,2,3,5,4,6,8]=>0001010=>0101000
[8,1,2,3,5,4,6,7]=>0001001=>1001000
[2,7,8,1,3,5,4,6]=>0001001=>1001000
[2,7,8,3,5,6,1,4]=>0000101=>1010000
[2,4,5,7,8,1,6,3]=>0000101=>1010000
[4,5,8,1,7,6,3,2]=>0100111=>1110010
[4,5,8,7,2,1,6,3]=>1000111=>1110001
[8,7,3,5,6,2,1,4]=>1000111=>1110001
[8,7,2,1,3,5,4,6]=>1001011=>1101001
[3,6,8,7,2,1,5,4]=>1001011=>1101001
[8,6,4,1,7,5,3,2]=>0111111=>1111110
[7,6,4,3,1,8,5,2]=>0111111=>1111110
[2,3,6,7,8,1,5,4]=>0001001=>1001000
[3,6,8,1,2,5,4,7]=>0001001=>1001000
[1,3,6,7,2,5,4,8]=>0001010=>0101000
[7,4,1,8,5,2,3,6]=>0011011=>1101100
[7,1,4,2,8,3,6,5]=>0010111=>1110100
[7,1,8,2,5,3,6,4]=>0001111=>1111000
[8,1,7,5,4,2,3,6]=>0011011=>1101100
[1,7,2,6,5,4,3,8]=>0011110=>0111100
[1,7,6,3,2,5,4,8]=>0101110=>0111010
[8,6,3,1,2,5,4,7]=>0101101=>1011010
[8,1,7,6,3,2,4,5]=>0100111=>1110010
[8,2,5,7,6,3,1,4]=>0100111=>1110010
[3,6,8,1,7,5,4,2]=>0011011=>1101100
[8,2,6,7,5,4,1,3]=>0011011=>1101100
[2,7,8,6,3,1,5,4]=>0101101=>1011010
[2,7,8,1,6,5,4,3]=>0011101=>1011100
[7,3,1,8,6,5,4,2]=>0111111=>1111110
[8,7,2,1,6,5,4,3]=>1011111=>1111101
[8,7,6,3,2,1,5,4]=>1101111=>1111011
[2,1,8,6,3,7,4,5]=>1000111=>1110001
[8,6,1,5,2,7,4,3]=>0011111=>1111100
[8,5,1,7,4,2,6,3]=>0011111=>1111100
[2,1,7,5,4,3,8,6]=>1011011=>1101101
[2,1,7,8,3,6,5,4]=>1001101=>1011001
[2,1,4,8,5,7,3,6]=>1000011=>1100001
[8,5,3,1,6,2,4,7]=>0101101=>1011010
[6,4,1,5,2,3,8,7]=>0011101=>1011100
[8,3,7,5,2,6,1,4]=>0001111=>1111000
[5,3,7,4,6,8,1,2]=>0001011=>1101000
[5,8,3,7,6,2,1,4]=>1000111=>1110001
[4,2,6,3,8,5,1,7]=>0011101=>1011100
[3,8,2,4,7,5,1,6]=>0001011=>1101000
[5,8,2,1,7,6,4,3]=>1010111=>1110101
[8,3,2,4,1,7,5,6]=>0110011=>1100110
[7,8,3,1,5,4,6,2]=>0101101=>1011010
[7,2,8,1,4,6,5,3]=>0001111=>1111000
[6,2,3,1,4,5,8,7]=>0100101=>1010010
[5,6,1,4,3,2,8,7]=>0110101=>1010110
[5,7,1,8,3,6,2,4]=>0000111=>1110000
[6,8,1,4,5,3,2,7]=>0101001=>1001010
[8,2,6,1,4,7,3,5]=>0000111=>1110000
[8,3,5,6,1,7,4,2]=>0010111=>1110100
[6,3,5,4,1,2,8,7]=>0011101=>1011100
[8,7,3,6,5,1,4,2]=>0011111=>1111100
[2,7,4,3,6,1,8,5]=>0010111=>1110100
[3,4,7,2,8,1,5,6]=>0000011=>1100000
[4,2,3,5,8,1,6,7]=>0010001=>1000100
[3,8,4,7,1,6,5,2]=>0001111=>1111000
[3,2,4,6,1,5,8,7]=>0100101=>1010010
[8,3,4,5,7,6,1,2]=>0000111=>1110000
[3,2,4,5,6,8,1,7]=>0100001=>1000010
[5,6,8,1,4,2,7,3]=>0010011=>1100100
[1,5,7,8,4,6,2,3]=>0000101=>1010000
[1,3,5,7,8,6,2,4]=>0000101=>1010000
[3,5,7,8,6,1,2,4]=>0000101=>1010000
[3,5,1,6,8,2,7,4]=>0001011=>1101000
[3,1,5,6,8,2,7,4]=>0100011=>1100010
[2,3,5,6,8,1,7,4]=>0000011=>1100000
[5,6,4,8,2,1,7,3]=>1000111=>1110001
[5,1,6,3,8,4,7,2]=>0001111=>1111000
[2,5,1,6,8,3,7,4]=>0001011=>1101000
[5,1,2,6,8,3,7,4]=>0001011=>1101000
[5,7,1,8,6,2,3,4]=>0000111=>1110000
[1,5,2,7,8,6,3,4]=>0001101=>1011000
[1,6,7,5,2,8,3,4]=>0001011=>1101000
[6,1,7,5,2,8,3,4]=>0001111=>1111000
[2,6,7,5,1,8,3,4]=>0001011=>1101000
[5,7,2,8,6,1,3,4]=>0000111=>1110000
[3,5,7,8,6,2,1,4]=>1000101=>1010001
[5,1,7,8,6,3,4,2]=>0011101=>1011100
[5,1,3,7,8,6,4,2]=>0011101=>1011100
[5,2,7,8,4,6,1,3]=>0001101=>1011000
[3,2,5,7,8,6,1,4]=>0100101=>1010010
[6,2,7,5,1,8,3,4]=>0001111=>1111000
[1,2,6,7,5,8,3,4]=>0000011=>1100000
[6,2,7,5,4,1,8,3]=>0011111=>1111100
[6,7,5,2,4,1,8,3]=>0011011=>1101100
[6,7,2,5,3,8,1,4]=>0001011=>1101000
[6,7,4,5,2,1,8,3]=>1001011=>1101001
[5,1,7,8,6,4,3,2]=>0111101=>1011110
[2,5,7,8,6,3,1,4]=>0100101=>1010010
[5,1,7,8,6,3,2,4]=>0101101=>1011010
[6,3,7,5,1,8,2,4]=>0001111=>1111000
[1,6,7,5,3,8,2,4]=>0001011=>1101000
[1,6,7,5,4,2,8,3]=>0011011=>1101100
[6,7,5,1,4,2,8,3]=>0011011=>1101100
[5,7,8,6,4,1,2,3]=>0010101=>1010100
[4,1,7,2,6,5,8,3]=>0010111=>1110100
[2,4,7,1,5,6,8,3]=>0000011=>1100000
[6,7,4,1,5,2,8,3]=>0011011=>1101100
[1,6,7,4,5,2,8,3]=>0001011=>1101000
[1,6,3,7,5,8,2,4]=>0000111=>1110000
[6,3,1,7,5,8,2,4]=>0100111=>1110010
[2,5,3,7,8,6,1,4]=>0001101=>1011000
[6,7,5,4,2,1,8,3]=>1011011=>1101101
[6,3,2,7,5,8,1,4]=>0100111=>1110010
[6,7,4,2,5,1,8,3]=>0011011=>1101100
[6,2,7,4,5,1,8,3]=>0001111=>1111000
[6,2,3,7,5,8,1,4]=>0000111=>1110000
[4,5,1,6,3,2,8,7]=>0101101=>1011010
[7,5,1,6,3,8,2,4]=>0001111=>1111000
[7,5,1,6,3,8,4,2]=>0011111=>1111100
[2,7,6,1,3,8,4,5]=>0000111=>1110000
[2,7,6,1,3,8,5,4]=>0001111=>1111000
[7,3,5,1,8,2,6,4]=>0001111=>1111000
[7,3,5,1,8,2,4,6]=>0001011=>1101000
[3,7,5,1,8,6,2,4]=>0001111=>1111000
[2,6,7,1,5,8,3,4]=>0000011=>1100000
[2,6,7,4,1,8,3,5]=>0010011=>1100100
[2,1,6,7,3,8,5,4]=>1001011=>1101001
[2,6,7,4,1,8,5,3]=>0011011=>1101100
[2,6,7,1,5,8,4,3]=>0010011=>1100100
[3,6,5,1,8,4,7,2]=>0001111=>1111000
[3,6,5,1,8,4,2,7]=>0011101=>1011100
[3,7,5,4,8,1,6,2]=>0001111=>1111000
[3,7,5,4,8,1,2,6]=>0001011=>1101000
[4,6,1,5,8,7,3,2]=>0100111=>1110010
[4,6,1,5,8,7,2,3]=>0000111=>1110000
[4,6,1,5,8,2,7,3]=>0000111=>1110000
[7,5,1,6,2,8,3,4]=>0001111=>1111000
[7,5,1,6,2,8,4,3]=>0011111=>1111100
[4,6,1,5,8,2,3,7]=>0000101=>1010000
[4,7,1,5,8,3,6,2]=>0000111=>1110000
[2,3,4,7,8,1,6,5]=>0000101=>1010000
[6,8,5,4,3,2,7,1]=>0111011=>1101110
[10,11,9,8,7,6,5,4,3,2,1]=>1111111101=>1011111111
[7,9,6,5,4,3,2,8,1]=>01111011=>11011110
[8,9,6,5,4,3,2,1,7]=>11111001=>10011111
[6,8,5,4,3,7,2,1]=>1011011=>1101101
[5,8,4,3,2,1,7,6]=>1110011=>1100111
[6,5,4,3,1,8,7,2]=>0111111=>1111110
[8,7,6,5,4,3,9,1,2]=>00111111=>11111100
[8,7,5,4,3,1,6,2]=>0111111=>1111110
[9,7,6,5,4,3,1,8,2]=>01111111=>11111110
[11,10,9,8,7,6,5,4,3,1,2]=>0111111111=>1111111110
[8,3,4,6,2,1,5,7]=>1000101=>1010001
[3,5,6,2,1,8,4,7]=>1000101=>1010001
[3,5,2,6,8,4,1,7]=>0011001=>1001100
[7,5,3,2,8,4,1,6]=>0111011=>1101110
[7,5,3,2,8,4,6,1]=>0101111=>1111010
[2,4,5,7,3,8,6,1]=>0000111=>1110000
[4,2,5,6,8,3,1,7]=>0110001=>1000110
[4,2,8,1,5,6,3,7]=>0010101=>1010100
[2,5,6,1,8,4,3,7]=>0010101=>1010100
[5,3,6,8,1,4,2,7]=>0011001=>1001100
[4,5,6,8,1,3,2,7]=>0100001=>1000010
[1,4,5,6,8,3,2,7]=>0100001=>1000010
[4,5,6,3,8,2,1,7]=>1000101=>1010001
[4,5,3,7,2,8,6,1]=>0001111=>1111000
[6,4,7,3,2,8,5,1]=>0101111=>1111010
[6,1,4,7,3,2,8,5]=>0100111=>1110010
[1,7,8,4,5,3,2,6]=>0101001=>1001010
[5,1,7,3,8,4,2,6]=>0011011=>1101100
[2,5,1,7,4,3,8,6]=>0011011=>1101100
[2,5,7,4,1,8,6,3]=>0010111=>1110100
[5,3,7,1,4,8,6,2]=>0001111=>1111000
[6,4,3,1,7,8,5,2]=>0111101=>1011110
[6,4,1,7,3,8,5,2]=>0011111=>1111100
[5,6,3,7,8,4,2,1]=>1010101=>1010101
[5,1,6,3,7,8,4,2]=>0011101=>1011100
[5,6,1,3,7,8,4,2]=>0010101=>1010100
[5,6,1,7,8,3,4,2]=>0010101=>1010100
[1,6,3,7,4,8,5,2]=>0001111=>1111000
[6,7,2,4,1,8,5,3]=>0011011=>1101100
[6,7,2,1,4,3,8,5]=>1010011=>1100101
[6,4,7,3,1,2,8,5]=>0100111=>1110010
[5,6,3,1,2,7,8,4]=>0100101=>1010010
[5,6,1,3,2,7,8,4]=>0100101=>1010010
[5,6,3,2,1,7,8,4]=>1100101=>1010011
[2,5,6,3,7,8,4,1]=>0010101=>1010100
[2,5,6,3,1,7,8,4]=>0100101=>1010010
[2,6,4,7,3,1,8,5]=>0100111=>1110010
[6,3,7,2,8,4,5,1]=>0001111=>1111000
[6,3,7,2,8,4,1,5]=>0010111=>1110100
[6,3,2,7,1,8,4,5]=>0100111=>1110010
[7,5,3,2,1,8,4,6]=>1101011=>1101011
[7,3,8,4,2,1,5,6]=>1010011=>1100101
[4,7,2,1,3,8,6,5]=>1000111=>1110001
[1,3,7,8,6,4,2,5]=>0010101=>1010100
[7,3,8,4,6,2,1,5]=>1000111=>1110001
[5,7,3,8,2,1,6,4]=>1000111=>1110001
[6,3,7,8,5,2,1,4]=>1001101=>1011001
[4,6,2,7,8,5,3,1]=>0101101=>1011010
[4,6,2,1,7,8,5,3]=>1001101=>1011001
[7,4,5,8,1,2,6,3]=>0000111=>1110000
[2,5,1,7,3,8,6,4]=>0001111=>1111000
[6,7,2,1,3,8,5,4]=>1001011=>1101001
[5,1,6,7,8,2,4,3]=>0011001=>1001100
[6,3,7,1,8,5,2,4]=>0001111=>1111000
[6,2,1,7,3,8,5,4]=>1001111=>1111001
[6,2,7,1,8,5,4,3]=>0011111=>1111100
[6,3,1,7,8,5,4,2]=>0111101=>1011110
[4,1,3,6,8,2,5,7]=>0010001=>1000100
[4,2,3,6,8,1,5,7]=>0010001=>1000100
[5,3,2,1,8,4,7,6]=>1101011=>1101011
[3,6,5,8,2,1,7,4]=>1000111=>1110001
[4,5,2,1,3,8,7,6]=>1001011=>1101001
[3,2,6,4,5,8,1,7]=>0100101=>1010010
[2,4,6,5,8,1,3,7]=>0000101=>1010000
[1,6,2,4,5,8,3,7]=>0000101=>1010000
[5,3,2,1,6,8,4,7]=>1101001=>1001011
[6,2,4,5,8,1,3,7]=>0000101=>1010000
[1,3,4,6,5,8,2,7]=>0000101=>1010000
[1,6,3,4,5,8,2,7]=>0000101=>1010000
[3,4,1,8,5,2,7,6]=>0011011=>1101100
[2,8,4,1,7,6,3,5]=>0010111=>1110100
[8,1,4,2,7,3,6,5]=>0010111=>1110100
[1,5,3,2,8,7,4,6]=>0101011=>1101010
[8,2,1,7,5,3,4,6]=>1001011=>1101001
[1,7,6,4,5,8,3,2]=>0100111=>1110010
[5,8,7,4,1,2,6,3]=>0010111=>1110100
[5,8,7,4,6,2,1,3]=>1000111=>1110001
[3,4,2,5,8,6,7,1]=>0010011=>1100100
[4,1,3,5,6,8,7,2]=>0010011=>1100100
[2,4,8,6,7,1,3,5]=>0000011=>1100000
[4,3,6,2,8,1,7,5]=>0010111=>1110100
[3,7,4,8,2,1,6,5]=>1000111=>1110001
[2,3,5,8,6,7,1,4]=>0000011=>1100000
[3,2,5,6,8,7,1,4]=>0100011=>1100010
[2,1,8,5,6,7,3,4]=>1000011=>1100001
[1,2,8,3,5,6,7,4]=>0000011=>1100000
[4,2,3,7,1,8,6,5]=>0010111=>1110100
[3,2,6,4,8,1,7,5]=>0100111=>1110010
[8,2,1,6,7,3,4,5]=>1000011=>1100001
[2,7,8,5,4,1,3,6]=>0011001=>1001100
[1,7,5,3,8,4,2,6]=>0011011=>1101100
[4,7,5,3,1,2,8,6]=>0101011=>1101010
[7,2,4,8,5,3,1,6]=>0101011=>1101010
[4,8,3,1,2,7,6,5]=>0100111=>1110010
[3,5,2,7,4,1,8,6]=>0011011=>1101100
[8,4,2,3,7,1,5,6]=>0010011=>1100100
[2,8,4,7,1,3,5,6]=>0000011=>1100000
[8,2,4,6,7,1,3,5]=>0000011=>1100000
[4,8,2,3,6,7,1,5]=>0000011=>1100000
[3,5,2,7,6,1,8,4]=>0001111=>1111000
[1,6,3,2,5,8,7,4]=>0100111=>1110010
[5,8,3,2,1,6,7,4]=>1100011=>1100011
[5,8,7,3,4,6,2,1]=>1000111=>1110001
[5,8,2,7,4,1,6,3]=>0010111=>1110100
[5,1,4,2,8,7,6,3]=>0011111=>1111100
[4,7,6,5,8,2,1,3]=>1000111=>1110001
[5,3,7,1,6,2,8,4]=>0001111=>1111000
[5,2,6,8,7,1,3,4]=>0001011=>1101000
[6,3,2,1,8,5,7,4]=>1100111=>1110011
[2,7,5,4,1,8,6,3]=>0011111=>1111100
[4,2,5,6,8,7,1,3]=>0010011=>1100100
[1,8,4,2,5,6,7,3]=>0010011=>1100100
[3,8,4,1,5,6,7,2]=>0010011=>1100100
[4,2,8,5,6,7,1,3]=>0010011=>1100100
[5,2,4,7,1,8,6,3]=>0001111=>1111000
[5,3,4,7,1,8,6,2]=>0001111=>1111000
[8,6,4,1,3,2,5,7]=>0110101=>1010110
[8,1,3,6,5,2,4,7]=>0001101=>1011000
[8,1,4,3,6,5,2,7]=>0011101=>1011100
[3,6,5,2,1,8,7,4]=>1001111=>1111001
[8,3,2,4,6,5,1,7]=>0101101=>1011010
[8,4,2,1,6,5,3,7]=>1011101=>1011101
[8,4,1,2,6,5,3,7]=>0011101=>1011100
[8,6,4,2,1,5,3,7]=>1011101=>1011101
[8,3,6,4,1,5,2,7]=>0011101=>1011100
[8,2,6,3,4,5,1,7]=>0001101=>1011000
[1,3,4,8,5,7,2,6]=>0000011=>1100000
[5,8,4,7,6,2,3,1]=>0100111=>1110010
[1,3,4,7,5,8,2,6]=>0000011=>1100000
[1,3,5,2,4,8,7,6]=>0001011=>1101000
[2,6,5,1,3,8,7,4]=>0001111=>1111000
[4,7,1,6,5,8,3,2]=>0100111=>1110010
[5,4,8,7,6,3,1,2]=>0101111=>1111010
[2,8,5,1,4,7,6,3]=>0001111=>1111000
[4,3,1,5,8,6,7,2]=>0110011=>1100110
[4,1,3,5,8,6,7,2]=>0010011=>1100100
[6,5,3,8,4,7,1,2]=>0001111=>1111000
[5,4,2,1,6,8,7,3]=>1011011=>1101101
[6,8,4,3,2,7,1,5]=>0110011=>1100110
[3,4,7,8,2,1,6,5]=>1000101=>1010001
[5,1,3,2,8,6,7,4]=>0101011=>1101010
[5,3,1,2,8,6,7,4]=>0101011=>1101010
[5,2,3,1,6,8,7,4]=>0101011=>1101010
[5,3,2,1,8,6,7,4]=>1101011=>1101011
[5,2,1,3,6,8,7,4]=>1001011=>1101001
[2,4,7,3,8,1,6,5]=>0000111=>1110000
[6,3,8,2,7,4,1,5]=>0010111=>1110100
[8,2,1,3,6,4,7,5]=>1000111=>1110001
[3,5,1,7,8,4,2,6]=>0011001=>1001100
[2,7,4,5,8,3,1,6]=>0100011=>1100010
[1,8,4,3,7,2,6,5]=>0010111=>1110100
[3,4,8,7,2,1,6,5]=>1000111=>1110001
[5,4,7,8,3,6,2,1]=>1001101=>1011001
[6,4,3,8,7,2,1,5]=>1010111=>1110101
[6,3,8,7,4,1,2,5]=>0010111=>1110100
[3,5,7,2,4,8,1,6]=>0000011=>1100000
[8,4,7,2,3,1,5,6]=>0100011=>1100010
[8,4,7,1,3,2,5,6]=>0100011=>1100010
[8,4,7,2,1,3,5,6]=>1000011=>1100001
[8,6,4,2,1,3,7,5]=>1010111=>1110101
[8,6,4,1,3,2,7,5]=>0110111=>1110110
[8,6,4,2,3,1,7,5]=>0110111=>1110110
[3,5,7,2,6,1,8,4]=>0000111=>1110000
[6,1,3,8,5,7,2,4]=>0000111=>1110000
[5,8,3,2,6,7,1,4]=>0100011=>1100010
[4,8,5,3,6,2,7,1]=>0001111=>1111000
[2,8,1,5,4,7,6,3]=>0001111=>1111000
[1,5,8,7,4,6,2,3]=>0000111=>1110000
[2,1,7,6,4,5,8,3]=>1000111=>1110001
[1,7,2,4,6,5,8,3]=>0000111=>1110000
[3,5,1,7,6,8,2,4]=>0001011=>1101000
[5,8,2,6,1,3,7,4]=>0000111=>1110000
[6,3,5,8,7,2,1,4]=>1000111=>1110001
[2,5,7,8,4,1,6,3]=>0010101=>1010100
[4,2,8,1,5,6,7,3]=>0010011=>1100100
[4,1,5,2,6,8,7,3]=>0011011=>1101100
[3,4,5,1,6,8,7,2]=>0001011=>1101000
[4,2,8,5,1,6,7,3]=>0011011=>1101100
[4,1,8,5,2,6,7,3]=>0011011=>1101100
[2,7,1,8,5,4,6,3]=>0001111=>1111000
[5,8,6,2,1,3,7,4]=>1000111=>1110001
[8,2,4,1,5,6,7,3]=>0010011=>1100100
[4,6,3,5,8,1,7,2]=>0000111=>1110000
[1,7,8,3,5,4,6,2]=>0001101=>1011000
[3,4,5,1,8,6,7,2]=>0001011=>1101000
[3,8,1,4,5,6,7,2]=>0000011=>1100000
[3,4,5,6,8,2,1,7]=>1000001=>1000001
[3,4,5,7,1,8,6,2]=>0000111=>1110000
[3,4,5,7,8,2,6,1]=>0000101=>1010000
[3,4,6,2,8,5,1,7]=>0001101=>1011000
[3,4,6,8,1,5,2,7]=>0001001=>1001000
[3,4,7,2,1,8,6,5]=>1000111=>1110001
[3,4,7,8,1,5,6,2]=>0000101=>1010000
[3,4,8,2,1,5,6,7]=>1000001=>1000001
[3,5,2,6,7,8,1,4]=>0001001=>1001000
[3,5,2,7,8,4,6,1]=>0001101=>1011000
[3,5,2,8,4,1,6,7]=>0011001=>1001100
[3,5,6,2,8,4,1,7]=>0010101=>1010100
[3,5,6,8,4,1,2,7]=>0010001=>1000100
[3,5,7,2,4,8,6,1]=>0000111=>1110000
[3,5,7,2,8,4,6,1]=>0000111=>1110000
[3,5,7,8,4,1,6,2]=>0010101=>1010100
[3,6,2,1,7,8,5,4]=>1001101=>1011001
[3,6,2,1,8,5,4,7]=>1001101=>1011001
[3,6,7,2,4,8,5,1]=>0001011=>1101000
[3,6,7,2,8,5,4,1]=>0011011=>1101100
[3,6,7,8,4,5,1,2]=>0001001=>1001000
[3,6,8,2,4,5,1,7]=>0001001=>1001000
[3,7,2,1,4,8,6,5]=>1000111=>1110001
[3,7,2,1,8,5,6,4]=>1000111=>1110001
[3,7,2,8,4,5,6,1]=>0000111=>1110000
[3,7,8,2,4,5,6,1]=>0000101=>1010000
[3,8,2,1,4,5,6,7]=>1000001=>1000001
[4,1,5,6,7,8,3,2]=>0110001=>1000110
[4,1,5,7,3,8,6,2]=>0010111=>1110100
[4,1,6,3,7,8,5,2]=>0011101=>1011100
[4,1,6,3,8,5,2,7]=>0011101=>1011100
[4,1,6,7,3,8,5,2]=>0011011=>1101100
[4,1,6,7,8,5,2,3]=>0011001=>1001100
[4,1,6,8,3,5,2,7]=>0011001=>1001100
[4,1,7,3,2,8,6,5]=>0110111=>1110110
[4,1,7,8,3,5,6,2]=>0010101=>1010100
[4,1,8,3,2,5,6,7]=>0110001=>1000110
[4,5,2,6,7,8,3,1]=>0101001=>1001010
[4,5,2,6,8,1,3,7]=>0001001=>1001000
[4,5,6,3,8,1,2,7]=>0000101=>1010000
[4,5,6,8,3,1,2,7]=>0100001=>1000010
[4,5,7,3,8,1,6,2]=>0000111=>1110000
[4,5,8,3,2,1,6,7]=>1100001=>1000011
[4,6,2,3,7,8,5,1]=>0001101=>1011000
[4,6,2,3,8,5,1,7]=>0001101=>1011000
[4,6,2,7,3,8,5,1]=>0001111=>1111000
[4,6,2,7,8,5,1,3]=>0001101=>1011000
[4,6,7,3,2,8,5,1]=>0101011=>1101010
[4,6,8,3,2,5,1,7]=>0101001=>1001010
[4,7,2,3,1,8,6,5]=>0100111=>1110010
[4,7,2,8,3,5,6,1]=>0000111=>1110000
[4,7,8,3,2,5,6,1]=>0100101=>1010010
[4,8,2,3,1,5,6,7]=>0100001=>1000010
[5,1,2,6,8,4,3,7]=>0011001=>1001100
[5,1,2,7,4,8,6,3]=>0001111=>1111000
[5,1,2,7,8,4,6,3]=>0001101=>1011000
[5,1,2,8,4,3,6,7]=>0011001=>1001100
[5,1,6,3,8,4,2,7]=>0011101=>1011100
[5,1,6,7,4,8,2,3]=>0001011=>1101000
[5,1,6,7,8,4,2,3]=>0011001=>1001100
[5,1,8,3,4,2,6,7]=>0011001=>1001100
[5,6,2,3,8,4,1,7]=>0010101=>1010100
[5,6,2,7,8,4,1,3]=>0010101=>1010100
[5,6,8,3,4,2,1,7]=>1010001=>1000101
[5,7,2,3,4,8,6,1]=>0000111=>1110000
[5,7,2,3,8,4,6,1]=>0000111=>1110000
[5,7,8,3,4,2,6,1]=>0010101=>1010100
[5,8,2,3,4,1,6,7]=>0010001=>1000100
[6,1,2,3,7,8,5,4]=>0001101=>1011000
[6,1,2,3,8,5,4,7]=>0001101=>1011000
[6,1,2,7,8,5,4,3]=>0011101=>1011100
[6,1,2,8,4,5,3,7]=>0001101=>1011000
[6,1,7,3,4,8,5,2]=>0001111=>1111000
[6,1,7,3,8,5,4,2]=>0011111=>1111100
[6,1,7,8,4,5,3,2]=>0101101=>1011010
[6,1,8,3,4,5,2,7]=>0001101=>1011000
[6,7,2,3,8,5,4,1]=>0011011=>1101100
[6,7,2,8,4,5,3,1]=>0101011=>1101010
[6,8,2,3,4,5,1,7]=>0001001=>1001000
[7,1,2,3,4,8,6,5]=>0000111=>1110000
[7,1,2,8,4,5,6,3]=>0000111=>1110000
[7,1,8,3,4,5,6,2]=>0000111=>1110000
[6,4,1,8,2,3,7,5]=>0010111=>1110100
[5,8,1,2,4,3,7,6]=>0010011=>1100100
[1,3,5,7,2,6,4,8]=>0000110=>0110000
[3,5,8,6,1,2,4,7]=>0000101=>1010000
[3,1,6,8,2,4,7,5]=>0100011=>1100010
[3,6,2,8,1,5,7,4]=>0000111=>1110000
[2,6,1,3,8,4,7,5]=>0000111=>1110000
[1,7,5,2,3,4,6,8]=>0001010=>0101000
[2,7,5,1,3,8,4,6]=>0001011=>1101000
[8,2,5,7,4,6,1,3]=>0000111=>1110000
[8,2,1,3,7,6,4,5]=>1000111=>1110001
[8,2,5,1,3,7,4,6]=>0001011=>1101000
[8,2,7,5,3,1,6,4]=>0101111=>1111010
[8,2,6,5,4,7,1,3]=>0001111=>1111000
[7,6,5,2,4,8,1,3]=>0001111=>1111000
[7,8,2,5,3,1,6,4]=>0101101=>1011010
[7,1,8,6,3,2,4,5]=>0100111=>1110010
[6,8,1,5,3,2,4,7]=>0101001=>1001010
[1,6,7,5,3,2,4,8]=>0101010=>0101010
[6,5,1,2,4,8,3,7]=>0001101=>1011000
[7,8,1,6,4,2,3,5]=>0010101=>1010100
[8,4,1,2,5,6,3,7]=>0010101=>1010100
[1,7,3,6,5,2,4,8]=>0001110=>0111000
[8,1,3,7,2,6,4,5]=>0000111=>1110000
[7,3,2,6,5,1,8,4]=>0101111=>1111010
[7,8,4,2,5,6,1,3]=>0010101=>1010100
[8,2,7,4,5,6,1,3]=>0000111=>1110000
[8,2,3,6,5,1,7,4]=>0001111=>1111000
[7,9,8,6,5,4,3,2,1]=>11111011=>11011111
[6,9,8,7,5,4,3,2,1]=>11110111=>11101111
[5,9,8,7,6,4,3,2,1]=>11101111=>11110111
[4,9,8,7,6,5,3,2,1]=>11011111=>11111011
[3,9,8,7,6,5,4,2,1]=>10111111=>11111101
[2,9,8,7,6,5,4,3,1]=>01111111=>11111110
[8,10,9,7,6,5,4,3,2,1]=>111111011=>110111111
[6,9,7,8,5,4,3,2,1]=>11110011=>11001111
[7,10,9,8,6,5,4,3,2,1]=>111110111=>111011111
[4,8,6,5,7,3,2,1]=>1100111=>1110011
[5,9,8,6,7,4,3,2,1]=>11100111=>11100111
[6,10,9,8,7,5,4,3,2,1]=>111101111=>111101111
[3,8,7,5,4,6,2,1]=>1001111=>1111001
[4,8,5,6,7,3,2,1]=>1100011=>1100011
[4,9,8,7,5,6,3,2,1]=>11001111=>11110011
[5,10,9,8,7,6,4,3,2,1]=>111011111=>111110111
[2,8,7,6,4,3,5,1]=>0011111=>1111100
[3,8,7,4,5,6,2,1]=>1000111=>1110001
[3,9,8,7,6,4,5,2,1]=>10011111=>11111001
[4,10,9,8,7,6,5,3,2,1]=>110111111=>111111011
[1,8,7,6,5,3,2,4]=>0101111=>1111010
[2,8,7,6,3,4,5,1]=>0001111=>1111000
[2,9,8,7,6,5,3,4,1]=>00111111=>11111100
[3,10,9,8,7,6,5,4,2,1]=>101111111=>111111101
[1,8,7,6,5,2,3,4]=>0001111=>1111000
[1,9,8,7,6,5,4,2,3]=>00111111=>11111100
[2,10,9,8,7,6,5,4,3,1]=>011111111=>111111110
[7,2,8,6,5,4,1,3]=>0011111=>1111100
[7,2,8,5,4,6,1,3]=>0001111=>1111000
[6,3,2,8,5,1,7,4]=>0101111=>1111010
[8,4,7,2,5,6,3,1]=>0100111=>1110010
[6,8,5,4,3,1,7,2]=>0111011=>1101110
[5,8,6,4,1,3,7,2]=>0010111=>1110100
[4,8,6,1,5,3,7,2]=>0001111=>1111000
[3,6,1,8,5,2,7,4]=>0001111=>1111000
[3,4,1,2,8,6,7,5]=>0010011=>1100100
[6,8,3,5,4,1,7,2]=>0011011=>1101100
[7,2,5,8,3,6,1,4]=>0000111=>1110000
[1,7,5,6,3,4,2,8]=>0010110=>0110100
[7,2,6,8,5,3,1,4]=>0101011=>1101010
[7,6,3,8,5,2,1,4]=>1001111=>1111001
[7,2,6,4,8,3,1,5]=>0100111=>1110010
[1,5,7,4,2,6,3,8]=>0010110=>0110100
[4,2,3,1,7,8,5,6]=>0110001=>1000110
[5,2,8,4,1,7,6,3]=>0011111=>1111100
[8,6,3,4,7,2,5,1]=>0001111=>1111000
[6,8,3,4,5,1,7,2]=>0001011=>1101000
[1,6,3,2,5,8,4,7]=>0100101=>1010010
[8,3,2,1,5,4,7,6]=>1101011=>1101011
[6,3,7,1,5,8,4,2]=>0010111=>1110100
[2,5,1,8,4,3,7,6]=>0011011=>1101100
[6,2,5,4,8,1,3,7]=>0001101=>1011000
[4,3,1,6,5,8,2,7]=>0110101=>1010110
[1,3,5,4,6,8,2,7]=>0001001=>1001000
[6,1,3,4,5,8,2,7]=>0000101=>1010000
[8,3,4,1,5,2,7,6]=>0011011=>1101100
[7,5,4,2,6,8,3,1]=>0111011=>1101110
[8,2,6,4,1,7,3,5]=>0010111=>1110100
[7,3,8,4,5,2,1,6]=>1001011=>1101001
[7,2,5,1,8,4,3,6]=>0011011=>1101100
[1,7,3,2,5,4,8,6]=>0101011=>1101010
[8,7,2,1,5,3,4,6]=>1001011=>1101001
[3,6,1,5,8,7,4,2]=>0010111=>1110100
[8,3,6,4,5,1,7,2]=>0001111=>1111000
[5,4,6,8,1,2,7,3]=>0001011=>1101000
[6,4,7,2,3,5,8,1]=>0000111=>1110000
[6,8,4,1,3,5,7,2]=>0010011=>1100100
[3,4,7,8,6,2,5,1]=>0001101=>1011000
[4,1,3,5,7,8,6,2]=>0010101=>1010100
[6,5,1,8,4,7,3,2]=>0101111=>1111010
[5,3,1,8,4,7,6,2]=>0101111=>1111010
[8,2,7,4,6,1,3,5]=>0000111=>1110000
[4,7,3,2,8,1,6,5]=>0100111=>1110010
[6,3,1,4,7,2,8,5]=>0100111=>1110010
[8,7,3,6,1,5,2,4]=>0001111=>1111000
[7,4,3,6,8,2,5,1]=>0011011=>1101100
[2,4,7,3,8,5,6,1]=>0000111=>1110000
[2,8,6,1,5,7,3,4]=>0000111=>1110000
[7,8,2,5,4,3,1,6]=>0111001=>1001110
[1,8,3,4,2,7,6,5]=>0010111=>1110100
[8,5,3,7,4,2,6,1]=>0011111=>1111100
[5,7,3,2,4,1,8,6]=>0110011=>1100110
[2,8,3,4,7,1,5,6]=>0000011=>1100000
[4,1,3,6,7,8,2,5]=>0010001=>1000100
[1,7,6,3,2,5,8,4]=>0100111=>1110010
[3,8,1,5,6,2,7,4]=>0000111=>1110000
[8,2,5,6,1,7,4,3]=>0010111=>1110100
[7,1,5,2,8,6,4,3]=>0011111=>1111100
[6,5,4,8,7,2,1,3]=>1001111=>1111001
[1,8,6,4,5,2,7,3]=>0001111=>1111000
[1,8,5,3,6,2,7,4]=>0001111=>1111000
[3,6,2,1,7,5,8,4]=>1000111=>1110001
[2,5,4,1,8,7,6,3]=>0011111=>1111100
[4,7,2,6,5,8,1,3]=>0000111=>1110000
[6,8,1,4,2,7,3,5]=>0010011=>1100100
[6,3,4,7,1,8,2,5]=>0000111=>1110000
[3,4,7,8,2,5,6,1]=>0000101=>1010000
[1,8,2,4,5,6,7,3]=>0000011=>1100000
[5,2,4,1,6,8,7,3]=>0011011=>1101100
[3,2,5,7,6,1,8,4]=>0100111=>1110010
[4,3,5,6,1,8,7,2]=>0010111=>1110100
[5,3,4,1,7,6,8,2]=>0011011=>1101100
[3,1,4,6,5,7,8,2]=>0100101=>1010010
[1,4,7,3,5,6,8,2]=>0000011=>1100000
[5,1,3,6,4,8,7,2]=>0001111=>1111000
[1,3,2,7,5,8,6,4]=>0100111=>1110010
[1,4,2,5,8,3,7,6]=>0010011=>1100100
[1,4,2,7,8,5,6,3]=>0010101=>1010100
[5,1,2,6,8,4,7,3]=>0001011=>1101000
[3,1,2,6,5,8,4,7]=>0100101=>1010010
[4,1,2,6,8,5,3,7]=>0011001=>1001100
[1,5,2,4,8,7,6,3]=>0001111=>1111000
[1,2,6,4,8,7,5,3]=>0001111=>1111000
[1,2,7,4,8,6,5,3]=>0001111=>1111000
[1,3,2,7,5,8,4,6]=>0100011=>1100010
[2,3,1,7,5,4,8,6]=>0101011=>1101010
[1,3,2,8,5,7,4,6]=>0100011=>1100010
[1,4,2,5,8,7,3,6]=>0010011=>1100100
[1,5,2,4,8,7,3,6]=>0001011=>1101000
[1,2,6,4,8,7,3,5]=>0000111=>1110000
[1,2,7,8,5,6,3,4]=>0000101=>1010000
[1,2,6,8,5,7,3,4]=>0000011=>1100000
[1,5,6,8,2,7,3,4]=>0000011=>1100000
[1,3,8,2,6,7,4,5]=>0000011=>1100000
[1,4,7,2,8,6,3,5]=>0000111=>1110000
[1,6,7,8,2,5,3,4]=>0001001=>1001000
[1,2,6,8,3,7,5,4]=>0001011=>1101000
[1,5,7,8,2,3,6,4]=>0000101=>1010000
[1,5,2,7,8,4,6,3]=>0001101=>1011000
[1,4,7,2,8,3,6,5]=>0000111=>1110000
[1,3,6,2,4,8,7,5]=>0000111=>1110000
[1,6,7,3,4,8,5,2]=>0001011=>1101000
[1,5,3,7,4,8,6,2]=>0001111=>1111000
[2,8,4,1,5,3,7,6]=>0011011=>1101100
[3,8,4,1,5,7,2,6]=>0010011=>1100100
[1,3,6,4,2,8,7,5]=>0010111=>1110100
[1,3,7,4,2,8,6,5]=>0010111=>1110100
[1,3,8,4,2,7,6,5]=>0010111=>1110100
[1,2,8,4,7,3,6,5]=>0000111=>1110000
[1,2,7,4,8,3,6,5]=>0000111=>1110000
[1,2,6,4,8,3,7,5]=>0000111=>1110000
[1,5,2,4,8,3,7,6]=>0001011=>1101000
[1,8,4,5,7,2,3,6]=>0000011=>1100000
[1,8,3,5,2,7,4,6]=>0001011=>1101000
[2,8,3,5,1,4,7,6]=>0001011=>1101000
[2,3,8,6,1,4,7,5]=>0000111=>1110000
[1,3,8,6,2,7,4,5]=>0000111=>1110000
[1,4,8,6,7,2,3,5]=>0000011=>1100000
[1,5,6,8,7,2,3,4]=>0000011=>1100000
[1,2,6,8,5,3,7,4]=>0001011=>1101000
[1,2,7,8,5,3,6,4]=>0001101=>1011000
[1,2,5,8,7,3,6,4]=>0000111=>1110000
[1,2,6,8,7,3,5,4]=>0001011=>1101000
[1,2,7,8,6,3,5,4]=>0001101=>1011000
[1,6,7,8,5,2,3,4]=>0001001=>1001000
[1,5,7,8,6,2,3,4]=>0000101=>1010000
[1,4,7,6,8,2,3,5]=>0000011=>1100000
[1,3,7,6,2,8,4,5]=>0000111=>1110000
[2,3,8,7,4,1,6,5]=>0010111=>1110100
[1,2,8,4,7,6,3,5]=>0000111=>1110000
[1,2,5,8,7,6,3,4]=>0000111=>1110000
[1,2,6,8,7,5,3,4]=>0001011=>1101000
[1,2,7,8,6,5,3,4]=>0001101=>1011000
[5,2,6,7,3,4,8,1]=>0001011=>1101000
[5,2,4,7,6,3,8,1]=>0001111=>1111000
[5,6,2,1,7,8,3,4]=>1000101=>1010001
[5,6,2,1,4,8,7,3]=>1000111=>1110001
[2,6,1,4,5,8,7,3]=>0000111=>1110000
[5,4,2,7,6,3,8,1]=>0011111=>1111100
[2,3,7,6,4,5,8,1]=>0000111=>1110000
[2,6,1,7,5,8,3,4]=>0000111=>1110000
[2,6,1,7,4,8,5,3]=>0001111=>1111000
[5,1,2,7,8,4,3,6]=>0011001=>1001100
[2,6,1,7,4,8,3,5]=>0000111=>1110000
[3,6,4,1,7,8,2,5]=>0010101=>1010100
[5,4,6,1,3,8,7,2]=>0001111=>1111000
[3,6,4,1,5,8,7,2]=>0010111=>1110100
[2,6,1,5,4,8,7,3]=>0001111=>1111000
[2,6,1,4,7,8,5,3]=>0001101=>1011000
[5,1,2,4,8,6,7,3]=>0001011=>1101000
[5,1,2,4,8,7,3,6]=>0001011=>1101000
[5,1,2,4,8,7,6,3]=>0001111=>1111000
[1,2,3,8,5,4,7,6]=>0001011=>1101000
[4,3,1,2,8,5,7,6]=>0110011=>1100110
[2,1,5,3,8,6,4,7]=>1001101=>1011001
[1,2,3,8,5,6,4,7]=>0000101=>1010000
[1,2,3,8,6,4,5,7]=>0000101=>1010000
[1,2,3,8,6,5,4,7]=>0001101=>1011000
[1,2,3,8,5,4,6,7]=>0001001=>1001000
[2,6,1,5,4,8,3,7]=>0001101=>1011000
[5,1,2,4,8,6,3,7]=>0001101=>1011000
[5,1,2,4,8,3,7,6]=>0001011=>1101000
[5,6,3,1,4,8,2,7]=>0100101=>1010010
[2,5,4,3,1,8,6,7]=>0111001=>1001110
[5,4,6,3,1,8,7,2]=>0101111=>1111010
[3,6,4,5,1,8,7,2]=>0001111=>1111000
[3,6,5,4,1,8,7,2]=>0011111=>1111100
[5,2,6,1,7,8,4,3]=>0011101=>1011100
[5,1,6,2,8,7,3,4]=>0001111=>1111000
[2,1,3,7,8,6,4,5]=>1000101=>1010001
[2,1,3,7,8,5,6,4]=>1000101=>1010001
[5,2,4,1,7,8,6,3]=>0011101=>1011100
[4,3,1,2,8,6,7,5]=>0110011=>1100110
[5,1,4,2,8,6,7,3]=>0011011=>1101100
[2,1,3,6,8,5,7,4]=>1000011=>1100001
[1,2,3,8,6,7,4,5]=>0000011=>1100000
[1,2,3,8,7,5,4,6]=>0001011=>1101000
[1,2,3,8,7,4,5,6]=>0000011=>1100000
[1,2,3,8,5,7,4,6]=>0000011=>1100000
[2,1,3,6,8,7,4,5]=>1000011=>1100001
[5,4,1,2,8,7,6,3]=>0011111=>1111100
[3,1,6,2,8,7,5,4]=>0101111=>1111010
[1,2,3,4,5,9,6,7,8]=>00000001=>10000000
[1,2,3,4,9,5,6,7,8]=>00000001=>10000000
[1,2,3,9,4,5,6,7,8]=>00000001=>10000000
[1,2,9,3,4,5,6,7,8]=>00000001=>10000000
[1,2,3,4,5,6,7,10,8,9]=>000000001=>100000000
[1,2,3,4,5,9,7,6,8]=>00000101=>10100000
[1,2,3,4,5,6,10,7,8,9]=>000000001=>100000000
[1,2,3,4,9,6,5,7,8]=>00001001=>10010000
[1,2,3,4,5,10,6,7,8,9]=>000000001=>100000000
[1,2,8,4,5,3,6,7]=>0001001=>1001000
[1,2,3,9,5,4,6,7,8]=>00010001=>10001000
[1,2,3,4,10,5,6,7,8,9]=>000000001=>100000000
[1,8,3,4,2,5,6,7]=>0010001=>1000100
[1,2,9,4,3,5,6,7,8]=>00100001=>10000100
[1,2,3,10,4,5,6,7,8,9]=>000000001=>100000000
[1,8,4,3,2,5,6,7]=>0110001=>1000110
[1,9,3,2,4,5,6,7,8]=>01000001=>10000010
[1,2,10,3,4,5,6,7,8,9]=>000000001=>100000000
[8,4,7,6,5,3,2,1]=>1101111=>1111011
[8,4,7,5,6,3,2,1]=>1100111=>1110011
[8,5,7,4,6,3,2,1]=>1100111=>1110011
[8,7,6,3,5,4,2,1]=>1011111=>1111101
[8,6,7,3,5,4,2,1]=>1011011=>1101101
[8,5,7,3,6,4,2,1]=>1010111=>1110101
[8,1,7,4,6,5,3,2]=>0101111=>1111010
[8,1,7,3,6,5,4,2]=>0011111=>1111100
[8,2,7,3,6,5,4,1]=>0011111=>1111100
[8,3,7,2,6,5,4,1]=>0011111=>1111100
[8,5,7,2,6,4,3,1]=>0110111=>1110110
[8,6,7,2,5,4,3,1]=>0111011=>1101110
[8,7,6,2,5,4,3,1]=>0111111=>1111110
[8,4,7,1,6,5,3,2]=>0101111=>1111010
[8,3,7,1,6,5,4,2]=>0011111=>1111100
[8,2,7,1,6,5,4,3]=>0011111=>1111100
[8,1,7,2,6,5,4,3]=>0011111=>1111100
[8,7,6,2,5,3,4,1]=>0011111=>1111100
[8,1,7,6,5,3,4,2]=>0011111=>1111100
[8,3,7,6,5,2,4,1]=>0011111=>1111100
[8,4,7,6,5,2,3,1]=>0101111=>1111010
[8,5,7,6,4,2,3,1]=>0110111=>1110110
[8,6,7,5,4,1,3,2]=>0111011=>1101110
[8,5,7,6,4,1,3,2]=>0110111=>1110110
[8,3,7,6,5,1,4,2]=>0011111=>1111100
[8,7,6,4,5,1,3,2]=>0101111=>1111010
[8,7,6,2,5,1,4,3]=>0011111=>1111100
[8,7,6,1,5,2,4,3]=>0011111=>1111100
[6,8,1,3,2,5,4,7]=>0101001=>1001010
[6,8,1,4,2,5,3,7]=>0011001=>1001100
[7,8,3,6,1,4,2,5]=>0010101=>1010100
[7,8,2,5,3,6,1,4]=>0001101=>1011000
[7,8,2,5,1,4,3,6]=>0011001=>1001100
[7,8,1,4,3,6,2,5]=>0010101=>1010100
[5,8,1,4,3,7,2,6]=>0010011=>1100100
[6,8,2,5,1,4,3,7]=>0011001=>1001100
[6,8,2,5,3,7,1,4]=>0001011=>1101000
[6,8,2,5,4,7,1,3]=>0001011=>1101000
[2,5,4,7,6,8,1,3]=>0001011=>1101000
[2,5,3,7,6,8,1,4]=>0001011=>1101000
[2,5,1,4,3,7,6,8]=>0011010=>0101100
[2,6,1,4,3,7,5,8]=>0010110=>0110100
[2,6,5,8,1,4,3,7]=>0010101=>1010100
[2,6,1,5,3,7,4,8]=>0001110=>0111000
[2,6,3,7,4,8,1,5]=>0000111=>1110000
[2,6,4,7,5,8,1,3]=>0000111=>1110000
[5,8,3,6,4,7,1,2]=>0000111=>1110000
[5,8,2,6,4,7,1,3]=>0000111=>1110000
[4,8,2,6,3,7,1,5]=>0000111=>1110000
[4,8,1,5,3,7,2,6]=>0001011=>1101000
[4,8,1,5,2,6,3,7]=>0001101=>1011000
[4,8,3,7,1,5,2,6]=>0001011=>1101000
[6,8,3,7,1,4,2,5]=>0010011=>1100100
[5,8,1,3,2,6,4,7]=>0100101=>1010010
[5,8,4,7,1,3,2,6]=>0100011=>1100010
[6,8,4,7,1,3,2,5]=>0100011=>1100010
[6,8,5,7,1,3,2,4]=>0100011=>1100010
[5,7,6,8,2,4,1,3]=>0010011=>1100100
[4,7,6,8,1,3,2,5]=>0100011=>1100010
[4,7,5,8,1,3,2,6]=>0100011=>1100010
[4,7,1,3,2,6,5,8]=>0100110=>0110010
[3,7,1,4,2,6,5,8]=>0010110=>0110100
[3,7,5,8,1,4,2,6]=>0010011=>1100100
[3,7,6,8,1,4,2,5]=>0010011=>1100100
[3,7,6,8,2,5,1,4]=>0001011=>1101000
[4,7,6,8,2,5,1,3]=>0001011=>1101000
[4,7,5,8,3,6,1,2]=>0000111=>1110000
[4,7,5,8,2,6,1,3]=>0000111=>1110000
[3,7,5,8,2,6,1,4]=>0000111=>1110000
[3,7,4,8,2,6,1,5]=>0000111=>1110000
[3,7,4,8,1,5,2,6]=>0001011=>1101000
[3,7,1,5,2,6,4,8]=>0001110=>0111000
[3,7,2,6,1,5,4,8]=>0001110=>0111000
[3,7,2,6,5,8,1,4]=>0000111=>1110000
[4,7,3,6,5,8,1,2]=>0000111=>1110000
[3,6,5,8,4,7,1,2]=>0000111=>1110000
[2,6,5,8,4,7,1,3]=>0000111=>1110000
[2,6,5,8,3,7,1,4]=>0000111=>1110000
[2,6,3,7,1,5,4,8]=>0001110=>0111000
[7,6,4,2,8,5,3,1]=>0111111=>1111110
[7,6,4,3,8,2,5,1]=>0011111=>1111100
[7,6,4,8,5,2,3,1]=>0101111=>1111010
[6,8,4,3,7,2,1,5]=>1010011=>1100101
[6,7,4,3,5,1,8,2]=>0011011=>1101100
[6,7,3,5,4,8,2,1]=>1001011=>1101001
[6,8,3,7,5,2,4,1]=>0011011=>1101100
[7,6,8,3,5,2,4,1]=>0011011=>1101100
[7,6,3,5,8,2,4,1]=>0010111=>1110100
[7,6,3,5,2,4,8,1]=>0001111=>1111000
[7,6,4,2,5,1,8,3]=>0011111=>1111100
[7,6,2,8,4,1,5,3]=>0011111=>1111100
[7,6,3,8,2,4,1,5]=>0010111=>1110100
[7,6,3,4,8,2,5,1]=>0001111=>1111000
[6,8,3,7,4,5,2,1]=>1001011=>1101001
[6,7,3,5,8,4,2,1]=>1010011=>1100101
[5,7,8,3,6,2,1,4]=>1000101=>1010001
[5,8,3,6,7,2,1,4]=>1000011=>1100001
[6,3,4,8,7,2,5,1]=>0001111=>1111000
[6,3,8,4,7,2,1,5]=>1000111=>1110001
[6,2,8,4,1,7,5,3]=>0011111=>1111100
[6,2,7,4,1,5,3,8]=>0011110=>0111100
[6,3,4,7,5,8,2,1]=>1000111=>1110001
[6,3,5,7,8,4,2,1]=>1010101=>1010101
[5,7,3,6,8,2,1,4]=>1000011=>1100001
[5,6,8,3,7,2,1,4]=>1000011=>1100001
[5,6,7,3,4,1,8,2]=>0010011=>1100100
[4,6,7,8,3,5,2,1]=>1001001=>1001001
[4,6,8,3,5,7,2,1]=>1000011=>1100001
[4,7,3,5,6,8,2,1]=>1000011=>1100001
[4,7,3,5,8,2,6,1]=>0000111=>1110000
[5,3,4,7,8,2,1,6]=>1001001=>1001001
[5,3,8,2,4,1,6,7]=>0011001=>1001100
[5,3,4,8,2,6,1,7]=>0001101=>1011000
[4,8,3,6,2,5,7,1]=>0000111=>1110000
[4,8,3,5,7,2,6,1]=>0000111=>1110000
[4,8,3,5,6,7,2,1]=>1000011=>1100001
[4,7,8,3,5,6,2,1]=>1000101=>1010001
[4,7,8,3,6,2,5,1]=>0001101=>1011000
[4,8,3,6,7,2,5,1]=>0001011=>1101000
[4,8,3,7,2,5,6,1]=>0000111=>1110000
[5,3,4,8,2,7,6,1]=>0001111=>1111000
[5,3,8,2,4,1,7,6]=>0011011=>1101100
[5,2,8,4,1,7,3,6]=>0011011=>1101100
[6,4,2,5,1,8,7,3]=>0011111=>1111100
[6,4,3,5,8,2,1,7]=>1010101=>1010101
[6,3,5,8,7,2,4,1]=>0010111=>1110100
[5,8,3,7,2,6,4,1]=>0010111=>1110100
[5,7,3,4,8,2,1,6]=>1000011=>1100001
[5,8,4,2,3,1,6,7]=>0110001=>1000110
[5,8,4,2,3,1,7,6]=>0110011=>1100110
[6,4,5,3,8,2,1,7]=>1001101=>1011001
[6,4,8,5,3,7,2,1]=>1001111=>1111001
[6,4,3,8,5,7,2,1]=>1010111=>1110101
[6,4,2,8,5,3,1,7]=>0111101=>1011110
[6,4,2,7,3,1,8,5]=>0110111=>1110110
[6,4,3,7,8,5,2,1]=>1011101=>1011101
[6,4,5,3,7,1,8,2]=>0001111=>1111000
[5,7,4,2,3,1,6,8]=>0110010=>0100110
[5,6,3,7,1,8,2,4]=>0000111=>1110000
[5,6,3,4,7,1,8,2]=>0000111=>1110000
[5,6,3,4,8,2,1,7]=>1000101=>1010001
[6,3,5,7,4,8,2,1]=>1000111=>1110001
[6,3,5,4,7,8,2,1]=>1001101=>1011001
[6,4,3,5,7,1,8,2]=>0010111=>1110100
[6,4,2,5,1,7,3,8]=>0011110=>0111100
[5,3,7,2,4,1,6,8]=>0011010=>0101100
[5,3,4,7,2,6,1,8]=>0001110=>0111000
[4,7,3,6,2,5,8,1]=>0000111=>1110000
[4,7,3,6,8,2,5,1]=>0001011=>1101000
[4,6,7,3,5,8,2,1]=>1000011=>1100001
[4,5,7,8,3,6,2,1]=>1000101=>1010001
[4,5,8,3,6,7,2,1]=>1000011=>1100001
[4,5,8,3,7,2,6,1]=>0000111=>1110000
[5,3,4,6,8,2,1,7]=>1001001=>1001001
[5,3,6,8,2,1,4,7]=>1001001=>1001001
[5,3,6,7,1,8,2,4]=>0001011=>1101000
[5,3,4,6,7,1,8,2]=>0001011=>1101000
[4,6,3,5,7,8,2,1]=>1000101=>1010001
[4,5,7,3,6,8,2,1]=>1000011=>1100001
[4,5,6,8,3,7,2,1]=>1000011=>1100001
[5,7,4,8,6,3,2,1]=>1100111=>1110011
[3,2,6,5,1,8,7,4]=>0101111=>1111010
[3,5,6,7,2,8,4,1]=>0010011=>1100100
[7,6,9,8,5,4,3,2,1]=>11110111=>11101111
[6,5,4,9,8,7,3,2,1]=>11011111=>11111011
[6,8,5,9,7,4,3,2,1]=>11100111=>11100111
[6,7,8,9,5,4,3,2,1]=>11110001=>10001111
[5,4,3,2,9,8,7,6,1]=>01111111=>11111110
[5,8,4,3,9,7,6,2,1]=>10101111=>11110101
[5,4,7,6,9,8,3,2,1]=>11010111=>11101011
[5,7,8,4,9,6,3,2,1]=>11001011=>11010011
[5,6,7,8,9,4,3,2,1]=>11100001=>10000111
[4,8,3,2,1,9,7,6,5]=>11001111=>11110011
[4,3,7,6,2,9,8,5,1]=>00111111=>11111100
[4,7,8,3,2,9,6,5,1]=>01011011=>11011010
[4,6,3,8,5,9,7,2,1]=>10001111=>11110001
[4,6,7,8,3,9,5,2,1]=>10010011=>11001001
[4,5,6,7,8,9,3,2,1]=>11000001=>10000011
[3,2,1,6,5,4,9,8,7]=>11011011=>11011011
[3,6,2,8,5,1,9,7,4]=>00011111=>11111000
[3,6,7,8,2,1,9,5,4]=>10010011=>11001001
[3,2,5,4,7,6,9,8,1]=>01010111=>11101010
[3,5,7,2,8,4,9,6,1]=>00001111=>11110000
[3,5,6,7,8,2,9,4,1]=>00100011=>11000100
[3,4,5,6,7,8,9,2,1]=>10000001=>10000001
[2,4,6,7,1,8,3,9,5]=>00000111=>11100000
[2,4,5,6,7,8,1,9,3]=>00000011=>11000000
[8,7,10,9,6,5,4,3,2,1]=>111110111=>111011111
[8,9,10,7,6,5,4,3,2,1]=>111111001=>100111111
[7,6,5,10,9,8,4,3,2,1]=>111011111=>111110111
[7,9,6,10,8,5,4,3,2,1]=>111100111=>111001111
[7,8,9,10,6,5,4,3,2,1]=>111110001=>100011111
[6,5,4,3,10,9,8,7,2,1]=>101111111=>111111101
[6,9,5,4,10,8,7,3,2,1]=>110101111=>111101011
[6,5,8,7,10,9,4,3,2,1]=>111010111=>111010111
[6,8,9,5,10,7,4,3,2,1]=>111001011=>110100111
[5,4,3,2,1,10,9,8,7,6]=>111101111=>111101111
[5,9,4,3,2,10,8,7,6,1]=>011011111=>111110110
[5,4,8,7,3,10,9,6,2,1]=>100111111=>111111001
[5,8,9,4,3,10,7,6,2,1]=>101011011=>110110101
[5,7,4,9,6,10,8,3,2,1]=>110001111=>111100011
[5,6,7,8,9,10,4,3,2,1]=>111000001=>100000111
[4,3,8,7,2,1,10,9,6,5]=>101011111=>111110101
[4,8,9,3,2,1,10,7,6,5]=>110011011=>110110011
[4,3,2,7,6,5,10,9,8,1]=>011011111=>111110110
[4,7,3,9,6,2,10,8,5,1]=>000111111=>111111000
[4,7,8,9,3,2,10,6,5,1]=>010110011=>110011010
[4,3,6,5,8,7,10,9,2,1]=>101010111=>111010101
[4,6,7,8,9,3,10,5,2,1]=>100100011=>110001001
[4,5,6,7,8,9,10,3,2,1]=>110000001=>100000011
[3,6,2,1,9,5,4,10,8,7]=>100110111=>111011001
[3,2,6,5,8,7,1,10,9,4]=>010011111=>111110010
[3,6,8,2,9,5,1,10,7,4]=>000101111=>111101000
[3,6,7,8,9,2,1,10,5,4]=>100100011=>110001001
[3,5,7,8,2,9,4,10,6,1]=>000010111=>111010000
[3,5,6,7,8,9,2,10,4,1]=>001000011=>110000100
[3,4,5,6,7,8,9,10,2,1]=>100000001=>100000001
[2,4,6,1,8,3,9,5,10,7]=>000010111=>111010000
[2,4,6,7,8,1,9,3,10,5]=>000000111=>111000000
[2,4,5,6,7,8,9,1,10,3]=>000000011=>110000000
[1,6,2,5,3,4,8,7]=>0001101=>1011000
[1,3,8,2,4,6,5,7]=>0000101=>1010000
[1,7,2,3,6,4,8,5]=>0000111=>1110000
[1,6,8,2,5,3,7,4]=>0001011=>1101000
[1,8,2,5,3,4,7,6]=>0001011=>1101000
[1,8,2,3,6,4,7,5]=>0000111=>1110000
[1,3,5,2,8,4,7,6]=>0001011=>1101000
[1,2,7,3,5,4,6,8]=>0001010=>0101000
[1,8,2,7,3,4,6,5]=>0000111=>1110000
[1,5,8,2,3,7,4,6]=>0000011=>1100000
[1,6,8,2,3,5,4,7]=>0001001=>1001000
[5,3,6,1,2,4,8,7]=>0001101=>1011000
[7,1,5,8,4,2,3,6]=>0010011=>1100100
[8,1,5,7,4,2,3,6]=>0010011=>1100100
[7,1,4,5,8,2,3,6]=>0000011=>1100000
[7,4,1,6,2,8,3,5]=>0010111=>1110100
[8,4,1,7,2,6,3,5]=>0010111=>1110100
[8,1,4,7,5,2,3,6]=>0001011=>1101000
[8,1,5,4,7,2,3,6]=>0001011=>1101000
[2,1,7,5,8,3,4,6]=>1000011=>1100001
[7,1,5,4,8,2,3,6]=>0001011=>1101000
[7,1,4,8,5,2,3,6]=>0001011=>1101000
[6,4,1,7,2,3,8,5]=>0010111=>1110100
[7,8,3,1,2,4,6,5]=>0100101=>1010010
[8,7,1,6,4,2,3,5]=>0010111=>1110100
[8,6,1,7,4,2,3,5]=>0010111=>1110100
[7,6,1,8,4,2,3,5]=>0010111=>1110100
[7,3,8,1,2,4,6,5]=>0000111=>1110000
[8,3,7,1,2,4,6,5]=>0000111=>1110000
[8,3,6,1,2,4,7,5]=>0000111=>1110000
[8,3,7,5,1,2,4,6]=>0001011=>1101000
[7,3,6,1,2,4,8,5]=>0000111=>1110000
[6,7,1,8,4,2,3,5]=>0010011=>1100100
[6,8,1,7,4,2,3,5]=>0010011=>1100100
[7,1,8,5,4,2,3,6]=>0011011=>1101100
[7,1,8,4,5,2,3,6]=>0001011=>1101000
[2,1,7,8,5,3,4,6]=>1001001=>1001001
[7,6,3,1,2,4,8,5]=>0100111=>1110010
[6,1,2,3,8,7,5,4]=>0001111=>1111000
[6,8,1,4,2,3,7,5]=>0010011=>1100100
[6,8,3,1,2,7,4,5]=>0100011=>1100010
[6,7,3,1,2,8,4,5]=>0100011=>1100010
[6,7,1,4,2,3,8,5]=>0010011=>1100100
[4,3,6,8,5,7,1,2]=>0010011=>1100100
[6,1,2,5,4,8,3,7]=>0001101=>1011000
[3,2,8,5,4,1,7,6]=>0111011=>1101110
[7,8,2,1,4,6,3,5]=>1000101=>1010001
[7,2,1,5,8,3,4,6]=>1000011=>1100001
[2,4,8,5,1,3,6,7]=>0001001=>1001000
[3,5,6,1,8,4,2,7]=>0010101=>1010100
[1,3,6,8,7,4,2,5]=>0010011=>1100100
[1,2,8,5,7,3,4,6]=>0000011=>1100000
[2,6,1,5,8,3,4,7]=>0000101=>1010000
[5,7,1,6,8,4,3,2]=>0110011=>1100110
[4,8,1,2,5,7,3,6]=>0000011=>1100000
[8,4,6,2,5,7,3,1]=>0100111=>1110010
[8,3,6,4,7,2,5,1]=>0001111=>1111000
[3,8,1,4,7,2,5,6]=>0000011=>1100000
[1,7,8,4,6,2,5,3]=>0001101=>1011000
[3,7,4,8,5,1,6,2]=>0001111=>1111000
[3,7,1,6,5,4,8,2]=>0001111=>1111000
[2,7,3,1,5,8,4,6]=>0100011=>1100010
[2,7,4,6,8,1,3,5]=>0000011=>1100000
[2,7,5,8,6,4,1,3]=>0010111=>1110100
[8,2,6,7,5,4,3,1]=>0111011=>1101110
[3,8,7,1,6,4,5,2]=>0001111=>1111000
[3,6,8,2,7,4,1,5]=>0010011=>1100100
[1,5,2,8,7,4,6,3]=>0001111=>1111000
[3,4,2,7,8,1,6,5]=>0010101=>1010100
[4,1,3,7,5,6,8,2]=>0010011=>1100100
[6,3,8,1,7,4,2,5]=>0010111=>1110100
[6,5,8,7,1,4,2,3]=>0010111=>1110100
[4,1,7,3,8,5,2,6]=>0011011=>1101100
[3,6,1,4,5,8,2,7]=>0000101=>1010000
[1,6,7,4,5,3,8,2]=>0001011=>1101000
[6,1,7,3,5,4,8,2]=>0001111=>1111000
[6,3,1,2,5,8,4,7]=>0100101=>1010010
[1,4,7,2,8,5,3,6]=>0001011=>1101000
[5,6,8,7,2,4,1,3]=>0010011=>1100100
[6,8,5,7,1,2,4,3]=>0010011=>1100100
[2,8,4,1,7,5,6,3]=>0010111=>1110100
[8,2,4,3,7,5,6,1]=>0010111=>1110100
[6,8,2,1,5,7,3,4]=>1000011=>1100001
[7,2,8,4,1,6,3,5]=>0010111=>1110100
[1,2,4,8,6,5,3,7]=>0001101=>1011000
[7,1,5,6,8,4,3,2]=>0110011=>1100110
[2,7,8,1,4,6,3,5]=>0000101=>1010000
[4,8,2,5,7,1,6,3]=>0000111=>1110000
[4,1,6,8,5,3,7,2]=>0011011=>1101100
[5,2,6,4,8,3,1,7]=>0101101=>1011010
[6,7,1,3,4,5,8,2]=>0000011=>1100000
[1,7,3,2,4,8,5,6]=>0100011=>1100010
[1,3,6,5,2,8,4,7]=>0001101=>1011000
[7,1,6,5,3,4,8,2]=>0001111=>1111000
[6,3,4,2,8,7,5,1]=>0011111=>1111100
[4,3,8,7,5,2,6,1]=>0011111=>1111100
[6,8,7,4,2,3,5,1]=>0011011=>1101100
[3,6,4,5,2,8,7,1]=>0001111=>1111000
[8,6,1,3,5,4,2,7]=>0011101=>1011100
[5,3,8,6,1,2,4,7]=>0001101=>1011000
[2,5,6,3,4,8,7,1]=>0000111=>1110000
[2,5,3,6,8,7,4,1]=>0011011=>1101100
[4,8,7,3,5,2,6,1]=>0001111=>1111000
[3,8,7,2,6,4,5,1]=>0001111=>1111000
[6,3,5,4,8,7,2,1]=>1001111=>1111001
[4,3,8,6,1,5,2,7]=>0011101=>1011100
[4,7,6,2,5,3,8,1]=>0001111=>1111000
[7,5,2,6,8,1,4,3]=>0011011=>1101100
[8,5,2,7,1,4,3,6]=>0011011=>1101100
[1,8,5,3,6,2,4,7]=>0001101=>1011000
[5,1,7,2,4,3,8,6]=>0011011=>1101100
[1,5,3,4,8,6,2,7]=>0001101=>1011000
[5,4,1,3,8,6,2,7]=>0011101=>1011100
[5,1,8,6,3,4,2,7]=>0011101=>1011100
[4,5,2,8,3,7,6,1]=>0001111=>1111000
[8,2,3,7,6,4,5,1]=>0001111=>1111000
[5,8,2,4,7,6,3,1]=>0100111=>1110010
[6,8,2,5,3,4,7,1]=>0001011=>1101000
[7,2,5,6,4,8,1,3]=>0000111=>1110000
[1,6,7,4,8,2,3,5]=>0000011=>1100000
[7,1,3,5,8,2,6,4]=>0000111=>1110000
[8,2,1,3,5,6,7,4]=>1000011=>1100001
[6,3,1,4,7,5,8,2]=>0100111=>1110010
[4,1,3,8,2,6,7,5]=>0010011=>1100100
[2,8,3,6,7,5,4,1]=>0011011=>1101100
[3,1,7,2,8,5,4,6]=>0101011=>1101010
[3,6,1,4,7,2,8,5]=>0000111=>1110000
[1,5,8,4,7,2,3,6]=>0000011=>1100000
[7,1,3,6,2,8,4,5]=>0000111=>1110000
[6,2,7,4,5,8,1,3]=>0000111=>1110000
[2,1,8,4,5,7,3,6]=>1000011=>1100001
[1,8,5,7,3,2,4,6]=>0100011=>1100010
[2,1,8,5,4,3,6,7]=>1011001=>1001101
[2,7,4,1,5,3,8,6]=>0011011=>1101100
[7,4,8,6,2,3,1,5]=>0100111=>1110010
[2,7,1,4,6,3,8,5]=>0000111=>1110000
[4,7,5,6,8,1,3,2]=>0100011=>1100010
[7,1,3,2,8,5,4,6]=>0101011=>1101010
[2,8,5,4,1,3,6,7]=>0011001=>1001100
[5,1,7,4,2,3,8,6]=>0011011=>1101100
[3,8,6,5,1,4,2,7]=>0011101=>1011100
[1,3,4,8,6,5,2,7]=>0001101=>1011000
[4,1,8,6,5,3,2,7]=>0111101=>1011110
[4,8,5,2,7,3,6,1]=>0001111=>1111000
[7,2,8,5,3,6,4,1]=>0011111=>1111100
[5,2,8,4,3,7,6,1]=>0011111=>1111100
[8,4,7,5,2,3,6,1]=>0001111=>1111000
[7,5,2,8,4,6,1,3]=>0001111=>1111000
[5,7,4,3,6,2,8,1]=>0010111=>1110100
[6,7,5,1,2,8,3,4]=>0001011=>1101000
[5,2,6,8,3,4,7,1]=>0001011=>1101000
[7,6,2,4,5,8,3,1]=>0100111=>1110010
[3,6,8,4,7,2,5,1]=>0001011=>1101000
[7,6,3,8,4,2,5,1]=>0011111=>1111100
[2,6,3,8,4,7,5,1]=>0001111=>1111000
[7,2,3,6,5,8,4,1]=>0010111=>1110100
[6,2,7,5,8,3,1,4]=>0100111=>1110010
[2,8,3,6,4,5,7,1]=>0000111=>1110000
[2,1,5,6,8,3,7,4]=>1000011=>1100001
[5,8,1,2,6,4,7,3]=>0000111=>1110000
[1,6,8,3,2,7,4,5]=>0100011=>1100010
[6,5,7,2,8,4,1,3]=>0010111=>1110100
[7,5,1,2,8,4,6,3]=>0001111=>1111000
[5,4,8,3,6,2,7,1]=>0001111=>1111000
[5,8,2,7,4,3,6,1]=>0010111=>1110100
[6,4,5,8,2,7,3,1]=>0100111=>1110010
[5,7,3,6,4,8,2,1]=>1000111=>1110001
[1,5,6,4,8,2,7,3]=>0000111=>1110000
[3,1,5,6,4,8,7,2]=>0100111=>1110010
[1,3,6,2,5,7,8,4]=>0000101=>1010000
[1,4,6,3,5,7,8,2]=>0000101=>1010000
[3,5,1,6,4,7,8,2]=>0001101=>1011000
[3,6,1,4,2,7,8,5]=>0010101=>1010100
[2,4,6,3,1,7,8,5]=>0100101=>1010010
[1,3,6,5,2,7,8,4]=>0001101=>1011000
[1,2,6,4,3,8,5,7]=>0010101=>1010100
[1,2,6,3,5,8,7,4]=>0000111=>1110000
[2,3,5,1,8,4,7,6]=>0001011=>1101000
[2,3,6,1,8,5,4,7]=>0001101=>1011000
[1,2,7,4,6,8,3,5]=>0000011=>1100000
[2,3,7,5,1,8,4,6]=>0001011=>1101000
[4,7,2,5,3,8,6,1]=>0001111=>1111000
[3,1,7,5,4,8,6,2]=>0101111=>1111010
[1,2,7,6,4,8,5,3]=>0001111=>1111000
[1,2,7,3,6,8,5,4]=>0001011=>1101000
[2,3,6,1,8,5,7,4]=>0000111=>1110000
[3,1,5,4,8,7,6,2]=>0101111=>1111010
[1,2,5,8,4,7,3,6]=>0000011=>1100000
[1,2,6,8,5,4,7,3]=>0001011=>1101000
[1,3,6,8,5,2,7,4]=>0001011=>1101000
[3,5,7,4,8,2,1,6]=>1000011=>1100001
[2,4,7,6,8,3,1,5]=>0100011=>1100010
[1,4,6,8,3,5,2,7]=>0001001=>1001000
[1,3,6,8,5,2,4,7]=>0001001=>1001000
[1,2,6,8,5,4,3,7]=>0011001=>1001100
[1,2,5,8,4,3,7,6]=>0010011=>1100100
[1,3,5,8,2,4,7,6]=>0000011=>1100000
[1,3,6,8,2,5,4,7]=>0001001=>1001000
[1,4,6,8,3,2,5,7]=>0100001=>1000010
[3,5,7,4,8,1,2,6]=>0000011=>1100000
[4,6,1,7,5,8,2,3]=>0000111=>1110000
[2,3,6,7,5,8,1,4]=>0000011=>1100000
[1,3,7,5,6,8,2,4]=>0000011=>1100000
[2,3,6,5,8,1,7,4]=>0000111=>1110000
[3,4,6,2,8,1,7,5]=>0000111=>1110000
[3,5,4,6,8,2,1,7]=>1001001=>1001001
[3,5,4,6,8,1,2,7]=>0001001=>1001000
[1,2,4,7,5,8,3,6]=>0000011=>1100000
[1,2,6,7,4,8,3,5]=>0000011=>1100000
[3,6,4,7,1,8,5,2]=>0001111=>1111000
[1,2,6,7,3,8,5,4]=>0001011=>1101000
[1,2,5,7,3,8,6,4]=>0000111=>1110000
[3,1,5,7,6,8,4,2]=>0110011=>1100110
[3,5,4,6,8,2,7,1]=>0001011=>1101000
[4,2,6,1,8,7,5,3]=>0011111=>1111100
[3,1,6,5,8,7,4,2]=>0110111=>1110110
[2,3,6,5,8,7,1,4]=>0000111=>1110000
[1,2,7,4,6,8,5,3]=>0001011=>1101000
[1,2,7,5,6,8,4,3]=>0010011=>1100100
[3,1,6,7,5,8,4,2]=>0110011=>1100110
[4,6,2,7,5,8,3,1]=>0100111=>1110010
[3,5,7,4,8,2,6,1]=>0000111=>1110000
[2,4,7,6,8,3,5,1]=>0001011=>1101000
[1,4,6,8,3,5,7,2]=>0000011=>1100000
[1,3,6,8,2,5,7,4]=>0000011=>1100000
[1,3,5,8,2,7,4,6]=>0000011=>1100000
[1,2,5,8,4,7,6,3]=>0000111=>1110000
[1,2,4,8,7,3,6,5]=>0000111=>1110000
[1,2,5,8,7,4,3,6]=>0010011=>1100100
[1,3,5,8,7,2,4,6]=>0000011=>1100000
[2,3,7,6,8,5,1,4]=>0001011=>1101000
[5,7,1,2,8,6,4,3]=>0010111=>1110100
[3,1,7,6,8,5,4,2]=>0111011=>1101110
[1,2,6,8,5,7,4,3]=>0010011=>1100100
[1,2,5,8,7,4,6,3]=>0000111=>1110000
[1,2,4,8,7,6,3,5]=>0000111=>1110000
[6,4,5,7,2,8,1,3]=>0000111=>1110000
[5,3,4,7,2,8,1,6]=>0001011=>1101000
[3,2,7,4,6,8,1,5]=>0100011=>1100010
[5,3,6,2,7,1,4,8]=>0001110=>0111000
[2,6,3,4,7,1,5,8]=>0000110=>0110000
[2,7,3,4,5,8,1,6]=>0000011=>1100000
[3,7,4,5,6,8,1,2]=>0000011=>1100000
[2,5,7,3,6,8,1,4]=>0000011=>1100000
[4,7,6,2,3,8,1,5]=>0000111=>1110000
[7,3,5,2,4,8,1,6]=>0001011=>1101000
[7,6,2,4,5,8,1,3]=>0000111=>1110000
[6,5,2,3,4,8,1,7]=>0001101=>1011000
[5,3,1,2,8,4,7,6]=>0101011=>1101010
[6,5,2,3,7,1,4,8]=>0001110=>0111000
[5,2,1,7,3,4,6,8]=>1001010=>0101001
[5,2,1,8,3,4,6,7]=>1001001=>1001001
[6,3,2,8,4,5,7,1]=>0100111=>1110010
[7,3,1,2,8,4,6,5]=>0100111=>1110010
[6,4,1,3,8,5,7,2]=>0010111=>1110100
[6,2,3,1,8,4,7,5]=>0100111=>1110010
[8,3,5,2,7,1,4,6]=>0001011=>1101000
[8,6,2,4,7,1,5,3]=>0001111=>1111000
[8,5,2,3,6,1,4,7]=>0001101=>1011000
[8,2,1,7,3,4,5,6]=>1000011=>1100001
[8,6,3,7,2,4,5,1]=>0001111=>1111000
[7,1,6,2,3,4,5,8]=>0000110=>0110000
[8,2,7,3,4,5,6,1]=>0000111=>1110000
[8,1,6,2,3,4,5,7]=>0000101=>1010000
[8,1,7,3,4,5,6,2]=>0000111=>1110000
[8,6,1,7,2,4,5,3]=>0001111=>1111000
[8,1,5,7,2,3,6,4]=>0000111=>1110000
[1,7,5,8,2,3,6,4]=>0000111=>1110000
[7,2,1,8,3,4,5,6]=>1000011=>1100001
[7,3,8,2,4,5,6,1]=>0000111=>1110000
[7,2,8,3,4,5,6,1]=>0000111=>1110000
[1,7,8,3,4,5,6,2]=>0000101=>1010000
[1,4,5,8,3,6,7,2]=>0000011=>1100000
[2,5,7,1,8,3,6,4]=>0000111=>1110000
[6,2,7,1,8,4,5,3]=>0001111=>1111000
[4,7,1,3,8,5,6,2]=>0000111=>1110000
[1,6,2,8,4,5,7,3]=>0000111=>1110000
[4,1,3,6,8,2,7,5]=>0010011=>1100100
[5,3,4,6,8,2,7,1]=>0001011=>1101000
[4,6,3,8,7,1,2,5]=>0000111=>1110000
[6,4,5,8,7,1,2,3]=>0000111=>1110000
[5,3,4,8,7,1,2,6]=>0001011=>1101000
[3,2,8,7,1,4,6,5]=>0100111=>1110010
[3,1,8,7,2,4,6,5]=>0100111=>1110010
[5,3,7,6,1,2,4,8]=>0001110=>0111000
[1,8,3,7,2,4,5,6]=>0000011=>1100000
[3,8,1,7,2,4,5,6]=>0000011=>1100000
[6,8,2,3,5,1,4,7]=>0001001=>1001000
[4,7,8,2,6,1,3,5]=>0000101=>1010000
[6,2,8,7,1,4,5,3]=>0001111=>1111000
[3,8,7,1,4,5,6,2]=>0000111=>1110000
[2,8,6,1,3,4,5,7]=>0000101=>1010000
[2,7,6,1,3,4,5,8]=>0000110=>0110000
[1,7,6,2,3,4,5,8]=>0000110=>0110000
[1,8,6,2,3,4,5,7]=>0000101=>1010000
[2,8,7,3,4,5,6,1]=>0000111=>1110000
[3,8,7,2,4,5,6,1]=>0000111=>1110000
[7,8,3,6,2,4,5,1]=>0001101=>1011000
[1,5,8,7,2,3,6,4]=>0000111=>1110000
[8,7,6,1,3,4,5,2]=>0001111=>1111000
[3,6,2,4,7,1,8,5]=>0000111=>1110000
[3,4,7,2,5,1,8,6]=>0001011=>1101000
[2,1,6,4,8,5,3,7]=>1001101=>1011001
[4,1,8,5,3,2,7,6]=>0111011=>1101110
[3,6,2,5,7,1,4,8]=>0000110=>0110000
[1,2,8,3,7,5,4,6]=>0001011=>1101000
[6,1,3,2,8,5,4,7]=>0101101=>1011010
[5,6,1,2,8,4,3,7]=>0010101=>1010100
[1,6,3,8,7,4,2,5]=>0010111=>1110100
[4,3,8,1,2,6,7,5]=>0010011=>1100100
[7,8,10,9,5,6,3,4,1,2]=>001010011=>110010100
[9,10,5,6,8,7,3,4,1,2]=>001001101=>101100100
[5,8,10,6,9,7,3,4,1,2]=>001001011=>110100100
[5,6,7,10,9,8,3,4,1,2]=>001000111=>111000100
[9,10,7,8,3,4,6,5,1,2]=>000110101=>101011000
[7,8,10,9,3,4,6,5,1,2]=>000110011=>110011000
[9,10,3,6,8,4,7,5,1,2]=>000101101=>101101000
[3,8,10,6,9,4,7,5,1,2]=>000101011=>110101000
[3,6,7,10,9,4,8,5,1,2]=>000100111=>111001000
[9,10,3,4,5,8,7,6,1,2]=>000011101=>101110000
[3,8,10,4,5,9,7,6,1,2]=>000011011=>110110000
[3,4,7,10,5,9,8,6,1,2]=>000010111=>111010000
[3,4,5,6,10,9,8,7,1,2]=>000001111=>111100000
[9,10,7,8,5,6,1,2,4,3]=>001010101=>101010100
[7,8,10,9,5,6,1,2,4,3]=>001010011=>110010100
[9,10,5,6,8,7,1,2,4,3]=>001001101=>101100100
[5,8,10,6,9,7,1,2,4,3]=>001001011=>110100100
[5,6,7,10,9,8,1,2,4,3]=>001000111=>111000100
[9,10,7,8,1,4,6,2,5,3]=>000110101=>101011000
[7,8,10,9,1,4,6,2,5,3]=>000110011=>110011000
[9,10,1,6,8,4,7,2,5,3]=>000101101=>101101000
[1,8,10,6,9,4,7,2,5,3]=>000101011=>110101000
[1,6,7,10,9,4,8,2,5,3]=>000100111=>111001000
[9,10,1,4,5,8,7,2,6,3]=>000011101=>101110000
[1,8,10,4,5,9,7,2,6,3]=>000011011=>110110000
[1,4,7,10,5,9,8,2,6,3]=>000010111=>111010000
[1,4,5,6,10,9,8,2,7,3]=>000001111=>111100000
[9,10,7,8,1,2,3,6,5,4]=>000110101=>101011000
[7,8,10,9,1,2,3,6,5,4]=>000110011=>110011000
[9,10,1,6,8,2,3,7,5,4]=>000101101=>101101000
[1,8,10,6,9,2,3,7,5,4]=>000101011=>110101000
[1,6,7,10,9,2,3,8,5,4]=>000100111=>111001000
[9,10,1,2,5,8,3,7,6,4]=>000011101=>101110000
[1,8,10,2,5,9,3,7,6,4]=>000011011=>110110000
[1,2,7,10,5,9,3,8,6,4]=>000010111=>111010000
[1,2,5,6,10,9,3,8,7,4]=>000001111=>111100000
[9,10,1,2,3,4,8,7,6,5]=>000011101=>101110000
[1,8,10,2,3,4,9,7,6,5]=>000011011=>110110000
[1,2,7,10,3,4,9,8,6,5]=>000010111=>111010000
[1,2,3,6,10,4,9,8,7,5]=>000001111=>111100000
[1,2,3,4,5,10,9,8,7,6]=>000001111=>111100000
[11,12,9,10,7,8,5,6,3,4,1,2]=>00101010101=>10101010100
[9,10,12,11,7,8,5,6,3,4,1,2]=>00101010011=>11001010100
[11,12,7,8,10,9,5,6,3,4,1,2]=>00101001101=>10110010100
[7,10,12,8,11,9,5,6,3,4,1,2]=>00101001011=>11010010100
[7,8,9,12,11,10,5,6,3,4,1,2]=>00101000111=>11100010100
[11,12,9,10,5,6,8,7,3,4,1,2]=>00100110101=>10101100100
[9,10,12,11,5,6,8,7,3,4,1,2]=>00100110011=>11001100100
[11,12,5,8,10,6,9,7,3,4,1,2]=>00100101101=>10110100100
[5,10,12,8,11,6,9,7,3,4,1,2]=>00100101011=>11010100100
[5,8,9,12,11,6,10,7,3,4,1,2]=>00100100111=>11100100100
[11,12,5,6,7,10,9,8,3,4,1,2]=>00100011101=>10111000100
[5,10,12,6,7,11,9,8,3,4,1,2]=>00100011011=>11011000100
[5,6,9,12,7,11,10,8,3,4,1,2]=>00100010111=>11101000100
[5,6,7,8,12,11,10,9,3,4,1,2]=>00100001111=>11110000100
[11,12,9,10,7,8,3,4,6,5,1,2]=>00011010101=>10101011000
[9,10,12,11,7,8,3,4,6,5,1,2]=>00011010011=>11001011000
[11,12,7,8,10,9,3,4,6,5,1,2]=>00011001101=>10110011000
[7,10,12,8,11,9,3,4,6,5,1,2]=>00011001011=>11010011000
[7,8,9,12,11,10,3,4,6,5,1,2]=>00011000111=>11100011000
[11,12,9,10,3,6,8,4,7,5,1,2]=>00010110101=>10101101000
[9,10,12,11,3,6,8,4,7,5,1,2]=>00010110011=>11001101000
[11,12,3,8,10,6,9,4,7,5,1,2]=>00010101101=>10110101000
[3,10,12,8,11,6,9,4,7,5,1,2]=>00010101011=>11010101000
[3,8,9,12,11,6,10,4,7,5,1,2]=>00010100111=>11100101000
[11,12,3,6,7,10,9,4,8,5,1,2]=>00010011101=>10111001000
[3,10,12,6,7,11,9,4,8,5,1,2]=>00010011011=>11011001000
[3,6,9,12,7,11,10,4,8,5,1,2]=>00010010111=>11101001000
[3,6,7,8,12,11,10,4,9,5,1,2]=>00010001111=>11110001000
[11,12,9,10,3,4,5,8,7,6,1,2]=>00001110101=>10101110000
[9,10,12,11,3,4,5,8,7,6,1,2]=>00001110011=>11001110000
[11,12,3,8,10,4,5,9,7,6,1,2]=>00001101101=>10110110000
[3,10,12,8,11,4,5,9,7,6,1,2]=>00001101011=>11010110000
[3,8,9,12,11,4,5,10,7,6,1,2]=>00001100111=>11100110000
[11,12,3,4,7,10,5,9,8,6,1,2]=>00001011101=>10111010000
[3,10,12,4,7,11,5,9,8,6,1,2]=>00001011011=>11011010000
[3,4,9,12,7,11,5,10,8,6,1,2]=>00001010111=>11101010000
[3,4,7,8,12,11,5,10,9,6,1,2]=>00001001111=>11110010000
[11,12,3,4,5,6,10,9,8,7,1,2]=>00000111101=>10111100000
[3,10,12,4,5,6,11,9,8,7,1,2]=>00000111011=>11011100000
[3,4,9,12,5,6,11,10,8,7,1,2]=>00000110111=>11101100000
[3,4,5,8,12,6,11,10,9,7,1,2]=>00000101111=>11110100000
[3,4,5,6,7,12,11,10,9,8,1,2]=>00000011111=>11111000000
[11,12,9,10,7,8,5,6,1,2,4,3]=>00101010101=>10101010100
[9,10,12,11,7,8,5,6,1,2,4,3]=>00101010011=>11001010100
[11,12,7,8,10,9,5,6,1,2,4,3]=>00101001101=>10110010100
[7,10,12,8,11,9,5,6,1,2,4,3]=>00101001011=>11010010100
[7,8,9,12,11,10,5,6,1,2,4,3]=>00101000111=>11100010100
[11,12,9,10,5,6,8,7,1,2,4,3]=>00100110101=>10101100100
[9,10,12,11,5,6,8,7,1,2,4,3]=>00100110011=>11001100100
[11,12,5,8,10,6,9,7,1,2,4,3]=>00100101101=>10110100100
[5,10,12,8,11,6,9,7,1,2,4,3]=>00100101011=>11010100100
[5,8,9,12,11,6,10,7,1,2,4,3]=>00100100111=>11100100100
[11,12,5,6,7,10,9,8,1,2,4,3]=>00100011101=>10111000100
[5,10,12,6,7,11,9,8,1,2,4,3]=>00100011011=>11011000100
[5,6,9,12,7,11,10,8,1,2,4,3]=>00100010111=>11101000100
[5,6,7,8,12,11,10,9,1,2,4,3]=>00100001111=>11110000100
[11,12,9,10,7,8,1,4,6,2,5,3]=>00011010101=>10101011000
[9,10,12,11,7,8,1,4,6,2,5,3]=>00011010011=>11001011000
[11,12,7,8,10,9,1,4,6,2,5,3]=>00011001101=>10110011000
[7,10,12,8,11,9,1,4,6,2,5,3]=>00011001011=>11010011000
[7,8,9,12,11,10,1,4,6,2,5,3]=>00011000111=>11100011000
[11,12,9,10,1,6,8,4,7,2,5,3]=>00010110101=>10101101000
[9,10,12,11,1,6,8,4,7,2,5,3]=>00010110011=>11001101000
[11,12,1,8,10,6,9,4,7,2,5,3]=>00010101101=>10110101000
[1,10,12,8,11,6,9,4,7,2,5,3]=>00010101011=>11010101000
[1,8,9,12,11,6,10,4,7,2,5,3]=>00010100111=>11100101000
[11,12,1,6,7,10,9,4,8,2,5,3]=>00010011101=>10111001000
[1,10,12,6,7,11,9,4,8,2,5,3]=>00010011011=>11011001000
[1,6,9,12,7,11,10,4,8,2,5,3]=>00010010111=>11101001000
[1,6,7,8,12,11,10,4,9,2,5,3]=>00010001111=>11110001000
[11,12,9,10,1,4,5,8,7,2,6,3]=>00001110101=>10101110000
[9,10,12,11,1,4,5,8,7,2,6,3]=>00001110011=>11001110000
[11,12,1,8,10,4,5,9,7,2,6,3]=>00001101101=>10110110000
[1,10,12,8,11,4,5,9,7,2,6,3]=>00001101011=>11010110000
[1,8,9,12,11,4,5,10,7,2,6,3]=>00001100111=>11100110000
[11,12,1,4,7,10,5,9,8,2,6,3]=>00001011101=>10111010000
[1,10,12,4,7,11,5,9,8,2,6,3]=>00001011011=>11011010000
[1,4,9,12,7,11,5,10,8,2,6,3]=>00001010111=>11101010000
[1,4,7,8,12,11,5,10,9,2,6,3]=>00001001111=>11110010000
[11,12,1,4,5,6,10,9,8,2,7,3]=>00000111101=>10111100000
[1,10,12,4,5,6,11,9,8,2,7,3]=>00000111011=>11011100000
[1,4,9,12,5,6,11,10,8,2,7,3]=>00000110111=>11101100000
[1,4,5,8,12,6,11,10,9,2,7,3]=>00000101111=>11110100000
[1,4,5,6,7,12,11,10,9,2,8,3]=>00000011111=>11111000000
[11,12,9,10,7,8,1,2,3,6,5,4]=>00011010101=>10101011000
[9,10,12,11,7,8,1,2,3,6,5,4]=>00011010011=>11001011000
[11,12,7,8,10,9,1,2,3,6,5,4]=>00011001101=>10110011000
[7,10,12,8,11,9,1,2,3,6,5,4]=>00011001011=>11010011000
[7,8,9,12,11,10,1,2,3,6,5,4]=>00011000111=>11100011000
[11,12,9,10,1,6,8,2,3,7,5,4]=>00010110101=>10101101000
[9,10,12,11,1,6,8,2,3,7,5,4]=>00010110011=>11001101000
[11,12,1,8,10,6,9,2,3,7,5,4]=>00010101101=>10110101000
[1,10,12,8,11,6,9,2,3,7,5,4]=>00010101011=>11010101000
[1,8,9,12,11,6,10,2,3,7,5,4]=>00010100111=>11100101000
[11,12,1,6,7,10,9,2,3,8,5,4]=>00010011101=>10111001000
[1,10,12,6,7,11,9,2,3,8,5,4]=>00010011011=>11011001000
[1,6,9,12,7,11,10,2,3,8,5,4]=>00010010111=>11101001000
[1,6,7,8,12,11,10,2,3,9,5,4]=>00010001111=>11110001000
[11,12,9,10,1,2,5,8,3,7,6,4]=>00001110101=>10101110000
[9,10,12,11,1,2,5,8,3,7,6,4]=>00001110011=>11001110000
[11,12,1,8,10,2,5,9,3,7,6,4]=>00001101101=>10110110000
[1,10,12,8,11,2,5,9,3,7,6,4]=>00001101011=>11010110000
[1,8,9,12,11,2,5,10,3,7,6,4]=>00001100111=>11100110000
[11,12,1,2,7,10,5,9,3,8,6,4]=>00001011101=>10111010000
[1,10,12,2,7,11,5,9,3,8,6,4]=>00001011011=>11011010000
[1,2,9,12,7,11,5,10,3,8,6,4]=>00001010111=>11101010000
[1,2,7,8,12,11,5,10,3,9,6,4]=>00001001111=>11110010000
[11,12,1,2,5,6,10,9,3,8,7,4]=>00000111101=>10111100000
[1,10,12,2,5,6,11,9,3,8,7,4]=>00000111011=>11011100000
[1,2,9,12,5,6,11,10,3,8,7,4]=>00000110111=>11101100000
[1,2,5,8,12,6,11,10,3,9,7,4]=>00000101111=>11110100000
[1,2,5,6,7,12,11,10,3,9,8,4]=>00000011111=>11111000000
[11,12,9,10,1,2,3,4,8,7,6,5]=>00001110101=>10101110000
[9,10,12,11,1,2,3,4,8,7,6,5]=>00001110011=>11001110000
[11,12,1,8,10,2,3,4,9,7,6,5]=>00001101101=>10110110000
[1,10,12,8,11,2,3,4,9,7,6,5]=>00001101011=>11010110000
[1,8,9,12,11,2,3,4,10,7,6,5]=>00001100111=>11100110000
[11,12,1,2,7,10,3,4,9,8,6,5]=>00001011101=>10111010000
[1,10,12,2,7,11,3,4,9,8,6,5]=>00001011011=>11011010000
[1,2,9,12,7,11,3,4,10,8,6,5]=>00001010111=>11101010000
[1,2,7,8,12,11,3,4,10,9,6,5]=>00001001111=>11110010000
[11,12,1,2,3,6,10,4,9,8,7,5]=>00000111101=>10111100000
[1,10,12,2,3,6,11,4,9,8,7,5]=>00000111011=>11011100000
[1,2,9,12,3,6,11,4,10,8,7,5]=>00000110111=>11101100000
[1,2,3,8,12,6,11,4,10,9,7,5]=>00000101111=>11110100000
[1,2,3,6,7,12,11,4,10,9,8,5]=>00000011111=>11111000000
[11,12,1,2,3,4,5,10,9,8,7,6]=>00000111101=>10111100000
[1,10,12,2,3,4,5,11,9,8,7,6]=>00000111011=>11011100000
[1,2,9,12,3,4,5,11,10,8,7,6]=>00000110111=>11101100000
[1,2,3,8,12,4,5,11,10,9,7,6]=>00000101111=>11110100000
[1,2,3,4,7,12,5,11,10,9,8,6]=>00000011111=>11111000000
[1,2,3,4,5,6,12,11,10,9,8,7]=>00000011111=>11111000000
[3,1,2,4,5,6,7,8,9]=>01000000=>00000010
[2,4,1,3,5,6,7,8,9]=>00100000=>00000100
[2,3,5,1,4,6,7,8,9]=>00010000=>00001000
[2,3,4,6,1,5,7,8,9]=>00001000=>00010000
[2,3,4,5,7,1,6,8,9]=>00000100=>00100000
[2,3,4,5,6,8,1,7,9]=>00000010=>01000000
[3,6,8,7,1,2,5,4]=>0001011=>1101000
[6,2,8,5,4,7,1,3]=>0001111=>1111000
[6,5,7,2,4,8,1,3]=>0000111=>1110000
[3,4,1,6,5,8,7,2]=>0010111=>1110100
[3,5,1,2,4,8,7,6]=>0001011=>1101000
[3,7,5,2,1,4,6,8]=>1001010=>0101001
[3,8,5,2,7,4,1,6]=>0011011=>1101100
[5,2,8,4,7,3,1,6]=>0101011=>1101010
[5,2,7,4,1,3,6,8]=>0011010=>0101100
[4,3,5,1,2,8,7,6]=>0011011=>1101100
[3,1,4,6,2,8,7,5]=>0100111=>1110010
[1,4,6,5,2,8,7,3]=>0001111=>1111000
[3,4,5,6,1,8,7,2]=>0000111=>1110000
[3,4,5,8,7,2,1,6]=>1000011=>1100001
[1,4,7,2,6,3,5,8]=>0000110=>0110000
[8,4,7,5,2,1,6,3]=>1001111=>1111001
[8,1,4,7,2,3,6,5]=>0000111=>1110000
[1,8,5,7,3,4,6,2]=>0000111=>1110000
[6,3,5,1,7,4,2,8]=>0011110=>0111100
[6,1,4,8,7,3,2,5]=>0100111=>1110010
[6,4,8,5,7,1,2,3]=>0000111=>1110000
[5,4,8,1,6,3,2,7]=>0101101=>1011010
[1,4,8,6,3,7,2,5]=>0000111=>1110000
[5,4,7,6,3,8,1,2]=>0001111=>1111000
[4,6,3,7,5,8,1,2]=>0000111=>1110000
[4,1,3,5,8,6,2,7]=>0010101=>1010100
[5,7,4,3,8,1,2,6]=>0010011=>1100100
[1,4,8,3,7,6,5,2]=>0001111=>1111000
[4,3,8,2,1,6,5,7]=>1010101=>1010101
[3,8,4,2,7,1,5,6]=>0010011=>1100100
[3,1,2,5,7,6,4,8]=>0100110=>0110010
[1,8,2,7,6,5,4,3]=>0011111=>1111100
[3,8,1,6,7,5,4,2]=>0011011=>1101100
[3,7,2,6,8,5,1,4]=>0001011=>1101000
[7,2,3,8,5,6,1,4]=>0000111=>1110000
[8,2,1,7,5,6,4,3]=>1010111=>1110101
[8,1,3,6,5,7,4,2]=>0010111=>1110100
[8,2,4,3,6,1,5,7]=>0010101=>1010100
[1,7,8,5,4,3,6,2]=>0011101=>1011100
[1,8,4,5,3,2,6,7]=>0101001=>1001010
[7,8,5,4,3,1,6,2]=>0111101=>1011110
[7,1,6,3,4,2,5,8]=>0010110=>0110100
[6,8,7,1,4,2,5,3]=>0011011=>1101100
[3,6,1,4,2,7,5,8]=>0010110=>0110100
[3,4,1,8,5,7,6,2]=>0010111=>1110100
[3,6,5,1,2,8,4,7]=>0001101=>1011000
[3,8,5,6,7,2,1,4]=>1000011=>1100001
[8,1,7,6,2,4,3,5]=>0010111=>1110100
[8,5,6,1,4,2,3,7]=>0010101=>1010100
[8,6,5,4,7,1,3,2]=>0101111=>1111010
[1,6,4,5,7,2,3,8]=>0000110=>0110000
[8,3,6,1,7,2,4,5]=>0000111=>1110000
[1,8,6,5,7,3,4,2]=>0010111=>1110100
[1,7,5,3,6,8,4,2]=>0011011=>1101100
[7,4,1,6,5,8,3,2]=>0110111=>1110110
[4,1,5,8,7,6,3,2]=>0110111=>1110110
[1,2,5,8,6,7,3,4]=>0000011=>1100000
[4,2,1,5,8,7,3,6]=>1010011=>1100101
[5,2,4,6,1,7,3,8]=>0001110=>0111000
[1,5,3,6,8,7,4,2]=>0011011=>1101100
[3,5,4,6,1,8,2,7]=>0001101=>1011000
[3,1,5,7,6,8,2,4]=>0100011=>1100010
[1,4,5,6,8,7,2,3]=>0000011=>1100000
[1,4,6,3,7,2,8,5]=>0000111=>1110000
[1,7,3,6,5,2,8,4]=>0001111=>1111000
[8,6,2,5,4,1,7,3]=>0011111=>1111100
[3,7,2,6,5,4,1,8]=>0011110=>0111100
[7,6,2,5,4,3,1,8]=>0111110=>0111110
[4,7,5,2,6,3,1,8]=>0101110=>0111010
[3,2,6,4,7,5,1,8]=>0101110=>0111010
[6,2,3,7,5,4,1,8]=>0011110=>0111100
[1,3,4,7,6,2,8,5]=>0000111=>1110000
[2,8,3,6,1,7,5,4]=>0001111=>1111000
[8,7,2,5,1,6,4,3]=>0011111=>1111100
[3,8,2,6,5,1,7,4]=>0001111=>1111000
[7,8,2,5,4,1,6,3]=>0011101=>1011100
[4,8,5,2,6,1,7,3]=>0001111=>1111000
[4,5,1,3,7,2,8,6]=>0001011=>1101000
[6,1,3,7,5,2,8,4]=>0001111=>1111000
[7,1,3,6,2,8,5,4]=>0001111=>1111000
[8,1,3,6,2,7,5,4]=>0001111=>1111000
[1,2,4,7,3,8,6,5]=>0000111=>1110000
[7,1,8,2,6,5,4,3]=>0011111=>1111100
[3,1,8,6,2,7,5,4]=>0101111=>1111010
[4,1,7,8,2,6,5,3]=>0011101=>1011100
[5,6,1,8,2,7,4,3]=>0010111=>1110100
[4,2,7,8,1,6,5,3]=>0011101=>1011100
[3,2,8,6,1,7,5,4]=>0101111=>1111010
[7,2,8,1,6,5,4,3]=>0011111=>1111100
[1,8,7,2,6,5,4,3]=>0011111=>1111100
[2,8,7,1,6,5,4,3]=>0011111=>1111100
[3,8,7,1,6,5,4,2]=>0011111=>1111100
[4,8,7,5,1,6,3,2]=>0101111=>1111010
[6,7,8,5,1,4,3,2]=>0111001=>1001110
[5,6,3,8,4,1,7,2]=>0010111=>1110100
[7,3,8,5,4,1,6,2]=>0011111=>1111100
[3,4,8,6,5,1,7,2]=>0001111=>1111000
[8,3,7,5,1,6,4,2]=>0011111=>1111100
[1,4,8,6,2,7,5,3]=>0001111=>1111000
[8,4,6,7,1,5,3,2]=>0101011=>1101010
[5,6,4,7,8,1,3,2]=>0100101=>1010010
[3,4,6,5,1,2,8,7]=>0001101=>1011000
[7,3,5,1,2,8,6,4]=>0001111=>1111000
[1,4,6,2,3,8,7,5]=>0000111=>1110000
[1,3,2,7,4,8,6,5]=>0100111=>1110010
[7,2,1,6,3,8,5,4]=>1001111=>1111001
[2,3,1,7,6,4,8,5]=>0100111=>1110010
[4,5,2,1,7,3,8,6]=>1001011=>1101001
[5,6,7,1,2,8,4,3]=>0010011=>1100100
[4,7,5,1,2,8,6,3]=>0001111=>1111000
[3,7,1,6,2,8,5,4]=>0001111=>1111000
[7,6,1,2,8,5,4,3]=>0011111=>1111100
[2,7,1,3,8,6,5,4]=>0001111=>1111000
[8,6,1,2,7,5,4,3]=>0011111=>1111100
[1,7,2,3,8,6,5,4]=>0001111=>1111000
[8,7,1,2,6,5,4,3]=>0011111=>1111100
[7,8,1,2,6,5,4,3]=>0011101=>1011100
[3,8,1,6,2,7,5,4]=>0001111=>1111000
[4,8,5,1,2,7,6,3]=>0001111=>1111000
[5,6,8,1,2,7,4,3]=>0010011=>1100100
[2,1,3,7,4,8,6,5]=>1000111=>1110001
[4,2,7,3,6,8,1,5]=>0010011=>1100100
[5,3,6,4,2,8,1,7]=>0011101=>1011100
[4,1,5,3,8,2,7,6]=>0011011=>1101100
[5,2,6,4,7,3,1,8]=>0101110=>0111010
[2,6,3,4,7,5,1,8]=>0001110=>0111000
[2,6,3,5,4,8,1,7]=>0001101=>1011000
[2,7,4,3,5,8,1,6]=>0010011=>1100100
[7,3,6,4,2,8,1,5]=>0010111=>1110100
[7,6,4,5,2,8,1,3]=>0001111=>1111000
[5,4,3,1,8,2,7,6]=>0111011=>1101110
[6,5,4,2,7,3,1,8]=>0111110=>0111110
[5,4,1,7,2,6,3,8]=>0011110=>0111100
[5,4,1,8,3,2,6,7]=>0111001=>1001110
[6,5,2,8,3,4,7,1]=>0001111=>1111000
[7,4,2,1,8,3,6,5]=>1010111=>1110101
[6,5,3,4,8,2,7,1]=>0001111=>1111000
[6,1,5,3,8,2,7,4]=>0001111=>1111000
[4,6,3,1,8,2,7,5]=>0100111=>1110010
[5,8,4,2,7,3,1,6]=>0110011=>1100110
[8,2,6,4,7,3,1,5]=>0100111=>1110010
[8,6,2,5,7,4,1,3]=>0010111=>1110100
[8,5,3,2,6,4,1,7]=>0111101=>1011110
[8,3,1,7,2,5,4,6]=>0101011=>1101010
[7,5,2,6,4,3,1,8]=>0111110=>0111110
[7,1,6,2,5,4,3,8]=>0011110=>0111100
[8,1,7,3,5,6,4,2]=>0010111=>1110100
[8,6,1,7,4,5,2,3]=>0001111=>1111000
[8,1,3,7,2,6,5,4]=>0001111=>1111000
[1,7,6,8,3,2,4,5]=>0100011=>1100010
[7,1,5,8,4,2,6,3]=>0010111=>1110100
[7,3,8,4,5,2,6,1]=>0001111=>1111000
[7,2,8,5,3,4,6,1]=>0001111=>1111000
[6,1,8,4,3,2,5,7]=>0110101=>1010110
[6,1,7,4,2,5,3,8]=>0011110=>0111100
[1,2,7,3,4,6,5,8]=>0000110=>0110000
[1,7,8,4,3,5,6,2]=>0010101=>1010100
[1,6,2,8,3,5,7,4]=>0000111=>1110000
[2,6,1,7,3,5,4,8]=>0001110=>0111000
[3,1,5,8,4,2,6,7]=>0110001=>1000110
[4,3,1,6,8,2,7,5]=>0110011=>1100110
[5,7,4,8,3,2,1,6]=>1100011=>1100011
[5,4,8,2,7,3,1,6]=>0101011=>1101010
[5,2,8,7,3,4,1,6]=>0011011=>1101100
[6,4,7,5,3,2,1,8]=>1101110=>0111011
[1,8,3,7,6,2,4,5]=>0000111=>1110000
[5,8,3,2,6,4,1,7]=>0110101=>1010110
[6,8,2,4,7,5,1,3]=>0001011=>1101000
[7,3,8,2,6,4,1,5]=>0010111=>1110100
[4,6,8,2,7,3,1,5]=>0100011=>1100010
[2,6,8,7,3,4,1,5]=>0010011=>1100100
[7,2,8,6,3,5,1,4]=>0001111=>1111000
[6,8,1,7,2,5,4,3]=>0011011=>1101100
[3,8,7,4,5,6,1,2]=>0000111=>1110000
[2,8,6,4,3,5,1,7]=>0011101=>1011100
[2,7,6,3,5,4,1,8]=>0011110=>0111100
[1,7,6,5,2,4,3,8]=>0011110=>0111100
[1,8,6,5,3,2,4,7]=>0101101=>1011010
[3,8,7,4,6,2,5,1]=>0001111=>1111000
[5,8,3,7,6,2,4,1]=>0010111=>1110100
[7,1,8,6,5,2,3,4]=>0001111=>1111000
[8,4,7,5,3,2,1,6]=>1101011=>1101011
[8,7,2,5,4,3,1,6]=>0111011=>1101110
[6,8,3,2,5,4,7,1]=>0101011=>1101010
[6,8,4,5,2,3,7,1]=>0001011=>1101000
[1,5,7,8,4,3,6,2]=>0010101=>1010100
[6,3,8,1,5,4,7,2]=>0001111=>1111000
[6,2,1,8,5,4,7,3]=>1001111=>1111001
[2,6,3,1,7,5,4,8]=>0101110=>0111010
[2,6,5,7,4,1,3,8]=>0010110=>0110100
[2,5,6,8,4,3,7,1]=>0010011=>1100100
[2,4,7,5,8,1,6,3]=>0000111=>1110000
[2,5,4,7,1,8,6,3]=>0001111=>1111000
[5,2,1,8,7,6,4,3]=>1011111=>1111101
[4,8,5,7,6,1,3,2]=>0100111=>1110010
[4,8,6,7,5,3,1,2]=>0101011=>1101010
[4,8,7,5,6,2,3,1]=>0100111=>1110010
[6,5,4,8,2,1,7,3]=>1001111=>1111001
[5,8,4,7,2,6,3,1]=>0100111=>1110010
[1,5,7,4,8,2,6,3]=>0000111=>1110000
[1,5,7,3,2,8,6,4]=>0100111=>1110010
[5,8,3,2,7,6,4,1]=>0110111=>1110110
[5,2,1,4,3,6,7,8]=>1011000=>0001101
[3,5,7,4,2,6,1,8]=>0010110=>0110100
[3,6,4,5,1,2,7,8]=>0001100=>0011000
[4,2,1,6,5,3,7,8]=>1011100=>0011101
[4,2,1,5,7,6,3,8]=>1010110=>0110101
[4,3,5,1,7,6,2,8]=>0011110=>0111100
[3,5,4,7,1,6,2,8]=>0001110=>0111000
[3,4,7,5,6,1,2,8]=>0000110=>0110000
[3,4,5,8,6,7,1,2]=>0000011=>1100000
[3,5,4,6,1,8,7,2]=>0001111=>1111000
[4,3,5,1,6,8,7,2]=>0011011=>1101100
[4,2,1,5,6,8,7,3]=>1010011=>1100101
[4,3,2,1,7,6,5,9,8,10]=>111011010=>010110111
[7,3,2,1,6,5,4,9,8,10]=>110111010=>010111011
[4,3,2,1,9,6,5,8,7,10]=>111010110=>011010111
[6,3,2,1,9,5,4,8,7,10]=>110110110=>011011011
[9,3,2,1,8,5,4,7,6,10]=>110101110=>011101011
[6,5,2,1,9,4,3,8,7,10]=>101110110=>011011101
[9,5,2,1,8,4,3,7,6,10]=>101101110=>011101101
[4,3,2,1,7,6,5,10,8,9]=>111011001=>100110111
[7,3,2,1,6,5,4,10,8,9]=>110111001=>100111011
[4,3,2,1,8,6,5,10,7,9]=>111010101=>101010111
[6,3,2,1,8,5,4,10,7,9]=>110110101=>101011011
[8,3,2,1,7,5,4,10,6,9]=>110101101=>101101011
[6,5,2,1,8,4,3,10,7,9]=>101110101=>101011101
[8,5,2,1,7,4,3,10,6,9]=>101101101=>101101101
[4,3,2,1,10,6,5,9,7,8]=>111010011=>110010111
[6,3,2,1,10,5,4,9,7,8]=>110110011=>110011011
[7,3,2,1,10,5,4,9,6,8]=>110101011=>110101011
[10,3,2,1,9,5,4,8,6,7]=>110100111=>111001011
[6,5,2,1,10,4,3,9,7,8]=>101110011=>110011101
[7,5,2,1,10,4,3,9,6,8]=>101101011=>110101101
[10,5,2,1,9,4,3,8,6,7]=>101100111=>111001101
[4,3,2,1,8,7,5,10,6,9]=>111001101=>101100111
[5,3,2,1,8,7,4,10,6,9]=>110101101=>101101011
[8,3,2,1,7,6,4,10,5,9]=>110011101=>101110011
[5,4,2,1,8,7,3,10,6,9]=>101101101=>101101101
[8,4,2,1,7,6,3,10,5,9]=>101011101=>101110101
[4,3,2,1,10,7,5,9,6,8]=>111001011=>110100111
[5,3,2,1,10,7,4,9,6,8]=>110101011=>110101011
[7,3,2,1,10,6,4,9,5,8]=>110011011=>110110011
[10,3,2,1,9,6,4,8,5,7]=>110010111=>111010011
[5,4,2,1,10,7,3,9,6,8]=>101101011=>110101101
[7,4,2,1,10,6,3,9,5,8]=>101011011=>110110101
[10,4,2,1,9,6,3,8,5,7]=>101010111=>111010101
[7,6,2,1,10,5,3,9,4,8]=>100111011=>110111001
[10,6,2,1,9,5,3,8,4,7]=>100110111=>111011001
[5,4,3,1,8,7,2,10,6,9]=>011101101=>101101110
[8,4,3,1,7,6,2,10,5,9]=>011011101=>101110110
[5,4,3,1,10,7,2,9,6,8]=>011101011=>110101110
[7,4,3,1,10,6,2,9,5,8]=>011011011=>110110110
[10,4,3,1,9,6,2,8,5,7]=>011010111=>111010110
[7,6,3,1,10,5,2,9,4,8]=>010111011=>110111010
[10,6,3,1,9,5,2,8,4,7]=>010110111=>111011010
[2,1,4,3,6,5,10,9,7,8]=>101010011=>110010101
[2,1,4,3,8,7,5,6,10,9]=>101001101=>101100101
[2,1,4,3,10,7,5,9,6,8]=>101001011=>110100101
[2,1,4,3,10,9,8,5,6,7]=>101000111=>111000101
[2,1,6,5,3,4,8,7,10,9]=>100110101=>101011001
[2,1,6,5,3,4,10,9,7,8]=>100110011=>110011001
[2,1,8,5,3,7,4,6,10,9]=>100101101=>101101001
[2,1,10,5,3,7,4,9,6,8]=>100101011=>110101001
[2,1,10,5,3,9,8,4,6,7]=>100100111=>111001001
[2,1,8,7,6,3,4,5,10,9]=>100011101=>101110001
[2,1,10,7,6,3,4,9,5,8]=>100011011=>110110001
[2,1,10,9,6,3,8,4,5,7]=>100010111=>111010001
[2,1,10,9,8,7,3,4,5,6]=>100001111=>111100001
[4,3,1,2,6,5,8,7,10,9]=>011010101=>101010110
[4,3,1,2,6,5,10,9,7,8]=>011010011=>110010110
[4,3,1,2,8,7,5,6,10,9]=>011001101=>101100110
[4,3,1,2,10,7,5,9,6,8]=>011001011=>110100110
[4,3,1,2,10,9,8,5,6,7]=>011000111=>111000110
[6,3,1,5,2,4,8,7,10,9]=>010110101=>101011010
[6,3,1,5,2,4,10,9,7,8]=>010110011=>110011010
[8,3,1,5,2,7,4,6,10,9]=>010101101=>101101010
[10,3,1,5,2,7,4,9,6,8]=>010101011=>110101010
[10,3,1,5,2,9,8,4,6,7]=>010100111=>111001010
[8,3,1,7,6,2,4,5,10,9]=>010011101=>101110010
[10,3,1,7,6,2,4,9,5,8]=>010011011=>110110010
[10,3,1,9,6,2,8,4,5,7]=>010010111=>111010010
[10,3,1,9,8,7,2,4,5,6]=>010001111=>111100010
[6,5,4,1,2,3,8,7,10,9]=>001110101=>101011100
[6,5,4,1,2,3,10,9,7,8]=>001110011=>110011100
[8,5,4,1,2,7,3,6,10,9]=>001101101=>101101100
[10,5,4,1,2,7,3,9,6,8]=>001101011=>110101100
[10,5,4,1,2,9,8,3,6,7]=>001100111=>111001100
[8,7,4,1,6,2,3,5,10,9]=>001011101=>101110100
[10,7,4,1,6,2,3,9,5,8]=>001011011=>110110100
[10,9,4,1,6,2,8,3,5,7]=>001010111=>111010100
[10,9,4,1,8,7,2,3,5,6]=>001001111=>111100100
[8,7,6,5,1,2,3,4,10,9]=>000111101=>101111000
[10,7,6,5,1,2,3,9,4,8]=>000111011=>110111000
[10,9,6,5,1,2,8,3,4,7]=>000110111=>111011000
[10,9,8,5,1,7,2,3,4,6]=>000101111=>111101000
[2,1,4,3,6,5,8,7,12,11,9,10]=>10101010011=>11001010101
[2,1,4,3,6,5,10,9,7,8,12,11]=>10101001101=>10110010101
[2,1,4,3,6,5,12,9,7,11,8,10]=>10101001011=>11010010101
[2,1,4,3,6,5,12,11,10,7,8,9]=>10101000111=>11100010101
[2,1,4,3,8,7,5,6,10,9,12,11]=>10100110101=>10101100101
[2,1,4,3,8,7,5,6,12,11,9,10]=>10100110011=>11001100101
[2,1,4,3,10,7,5,9,6,8,12,11]=>10100101101=>10110100101
[2,1,4,3,12,7,5,9,6,11,8,10]=>10100101011=>11010100101
[2,1,4,3,12,7,5,11,10,6,8,9]=>10100100111=>11100100101
[2,1,4,3,10,9,8,5,6,7,12,11]=>10100011101=>10111000101
[2,1,4,3,12,9,8,5,6,11,7,10]=>10100011011=>11011000101
[2,1,4,3,12,11,8,5,10,6,7,9]=>10100010111=>11101000101
[2,1,4,3,12,11,10,9,5,6,7,8]=>10100001111=>11110000101
[2,1,6,5,3,4,8,7,10,9,12,11]=>10011010101=>10101011001
[2,1,6,5,3,4,8,7,12,11,9,10]=>10011010011=>11001011001
[2,1,6,5,3,4,10,9,7,8,12,11]=>10011001101=>10110011001
[2,1,6,5,3,4,12,9,7,11,8,10]=>10011001011=>11010011001
[2,1,6,5,3,4,12,11,10,7,8,9]=>10011000111=>11100011001
[2,1,8,5,3,7,4,6,10,9,12,11]=>10010110101=>10101101001
[2,1,8,5,3,7,4,6,12,11,9,10]=>10010110011=>11001101001
[2,1,10,5,3,7,4,9,6,8,12,11]=>10010101101=>10110101001
[2,1,12,5,3,7,4,9,6,11,8,10]=>10010101011=>11010101001
[2,1,12,5,3,7,4,11,10,6,8,9]=>10010100111=>11100101001
[2,1,10,5,3,9,8,4,6,7,12,11]=>10010011101=>10111001001
[2,1,12,5,3,9,8,4,6,11,7,10]=>10010011011=>11011001001
[2,1,12,5,3,11,8,4,10,6,7,9]=>10010010111=>11101001001
[2,1,12,5,3,11,10,9,4,6,7,8]=>10010001111=>11110001001
[2,1,8,7,6,3,4,5,10,9,12,11]=>10001110101=>10101110001
[2,1,8,7,6,3,4,5,12,11,9,10]=>10001110011=>11001110001
[2,1,10,7,6,3,4,9,5,8,12,11]=>10001101101=>10110110001
[2,1,12,7,6,3,4,9,5,11,8,10]=>10001101011=>11010110001
[2,1,12,7,6,3,4,11,10,5,8,9]=>10001100111=>11100110001
[2,1,10,9,6,3,8,4,5,7,12,11]=>10001011101=>10111010001
[2,1,12,9,6,3,8,4,5,11,7,10]=>10001011011=>11011010001
[2,1,12,11,6,3,8,4,10,5,7,9]=>10001010111=>11101010001
[2,1,12,11,6,3,10,9,4,5,7,8]=>10001001111=>11110010001
[2,1,10,9,8,7,3,4,5,6,12,11]=>10000111101=>10111100001
[2,1,12,9,8,7,3,4,5,11,6,10]=>10000111011=>11011100001
[2,1,12,11,8,7,3,4,10,5,6,9]=>10000110111=>11101100001
[2,1,12,11,10,7,3,9,4,5,6,8]=>10000101111=>11110100001
[2,1,12,11,10,9,8,3,4,5,6,7]=>10000011111=>11111000001
[4,3,1,2,6,5,8,7,10,9,12,11]=>01101010101=>10101010110
[4,3,1,2,6,5,8,7,12,11,9,10]=>01101010011=>11001010110
[4,3,1,2,6,5,10,9,7,8,12,11]=>01101001101=>10110010110
[4,3,1,2,6,5,12,9,7,11,8,10]=>01101001011=>11010010110
[4,3,1,2,6,5,12,11,10,7,8,9]=>01101000111=>11100010110
[4,3,1,2,8,7,5,6,10,9,12,11]=>01100110101=>10101100110
[4,3,1,2,8,7,5,6,12,11,9,10]=>01100110011=>11001100110
[4,3,1,2,10,7,5,9,6,8,12,11]=>01100101101=>10110100110
[4,3,1,2,12,7,5,9,6,11,8,10]=>01100101011=>11010100110
[4,3,1,2,12,7,5,11,10,6,8,9]=>01100100111=>11100100110
[4,3,1,2,10,9,8,5,6,7,12,11]=>01100011101=>10111000110
[4,3,1,2,12,9,8,5,6,11,7,10]=>01100011011=>11011000110
[4,3,1,2,12,11,8,5,10,6,7,9]=>01100010111=>11101000110
[4,3,1,2,12,11,10,9,5,6,7,8]=>01100001111=>11110000110
[6,3,1,5,2,4,8,7,10,9,12,11]=>01011010101=>10101011010
[6,3,1,5,2,4,8,7,12,11,9,10]=>01011010011=>11001011010
[6,3,1,5,2,4,10,9,7,8,12,11]=>01011001101=>10110011010
[6,3,1,5,2,4,12,9,7,11,8,10]=>01011001011=>11010011010
[6,3,1,5,2,4,12,11,10,7,8,9]=>01011000111=>11100011010
[8,3,1,5,2,7,4,6,10,9,12,11]=>01010110101=>10101101010
[8,3,1,5,2,7,4,6,12,11,9,10]=>01010110011=>11001101010
[10,3,1,5,2,7,4,9,6,8,12,11]=>01010101101=>10110101010
[12,3,1,5,2,7,4,9,6,11,8,10]=>01010101011=>11010101010
[12,3,1,5,2,7,4,11,10,6,8,9]=>01010100111=>11100101010
[10,3,1,5,2,9,8,4,6,7,12,11]=>01010011101=>10111001010
[12,3,1,5,2,9,8,4,6,11,7,10]=>01010011011=>11011001010
[12,3,1,5,2,11,8,4,10,6,7,9]=>01010010111=>11101001010
[12,3,1,5,2,11,10,9,4,6,7,8]=>01010001111=>11110001010
[8,3,1,7,6,2,4,5,10,9,12,11]=>01001110101=>10101110010
[8,3,1,7,6,2,4,5,12,11,9,10]=>01001110011=>11001110010
[10,3,1,7,6,2,4,9,5,8,12,11]=>01001101101=>10110110010
[12,3,1,7,6,2,4,9,5,11,8,10]=>01001101011=>11010110010
[12,3,1,7,6,2,4,11,10,5,8,9]=>01001100111=>11100110010
[10,3,1,9,6,2,8,4,5,7,12,11]=>01001011101=>10111010010
[12,3,1,9,6,2,8,4,5,11,7,10]=>01001011011=>11011010010
[12,3,1,11,6,2,8,4,10,5,7,9]=>01001010111=>11101010010
[12,3,1,11,6,2,10,9,4,5,7,8]=>01001001111=>11110010010
[10,3,1,9,8,7,2,4,5,6,12,11]=>01000111101=>10111100010
[12,3,1,9,8,7,2,4,5,11,6,10]=>01000111011=>11011100010
[12,3,1,11,8,7,2,4,10,5,6,9]=>01000110111=>11101100010
[12,3,1,11,10,7,2,9,4,5,6,8]=>01000101111=>11110100010
[12,3,1,11,10,9,8,2,4,5,6,7]=>01000011111=>11111000010
[6,5,4,1,2,3,8,7,10,9,12,11]=>00111010101=>10101011100
[6,5,4,1,2,3,8,7,12,11,9,10]=>00111010011=>11001011100
[6,5,4,1,2,3,10,9,7,8,12,11]=>00111001101=>10110011100
[6,5,4,1,2,3,12,9,7,11,8,10]=>00111001011=>11010011100
[6,5,4,1,2,3,12,11,10,7,8,9]=>00111000111=>11100011100
[8,5,4,1,2,7,3,6,10,9,12,11]=>00110110101=>10101101100
[8,5,4,1,2,7,3,6,12,11,9,10]=>00110110011=>11001101100
[10,5,4,1,2,7,3,9,6,8,12,11]=>00110101101=>10110101100
[12,5,4,1,2,7,3,9,6,11,8,10]=>00110101011=>11010101100
[12,5,4,1,2,7,3,11,10,6,8,9]=>00110100111=>11100101100
[10,5,4,1,2,9,8,3,6,7,12,11]=>00110011101=>10111001100
[12,5,4,1,2,9,8,3,6,11,7,10]=>00110011011=>11011001100
[12,5,4,1,2,11,8,3,10,6,7,9]=>00110010111=>11101001100
[12,5,4,1,2,11,10,9,3,6,7,8]=>00110001111=>11110001100
[8,7,4,1,6,2,3,5,10,9,12,11]=>00101110101=>10101110100
[8,7,4,1,6,2,3,5,12,11,9,10]=>00101110011=>11001110100
[10,7,4,1,6,2,3,9,5,8,12,11]=>00101101101=>10110110100
[12,7,4,1,6,2,3,9,5,11,8,10]=>00101101011=>11010110100
[12,7,4,1,6,2,3,11,10,5,8,9]=>00101100111=>11100110100
[10,9,4,1,6,2,8,3,5,7,12,11]=>00101011101=>10111010100
[12,9,4,1,6,2,8,3,5,11,7,10]=>00101011011=>11011010100
[12,11,4,1,6,2,8,3,10,5,7,9]=>00101010111=>11101010100
[12,11,4,1,6,2,10,9,3,5,7,8]=>00101001111=>11110010100
[10,9,4,1,8,7,2,3,5,6,12,11]=>00100111101=>10111100100
[12,9,4,1,8,7,2,3,5,11,6,10]=>00100111011=>11011100100
[12,11,4,1,8,7,2,3,10,5,6,9]=>00100110111=>11101100100
[12,11,4,1,10,7,2,9,3,5,6,8]=>00100101111=>11110100100
[12,11,4,1,10,9,8,2,3,5,6,7]=>00100011111=>11111000100
[8,7,6,5,1,2,3,4,10,9,12,11]=>00011110101=>10101111000
[8,7,6,5,1,2,3,4,12,11,9,10]=>00011110011=>11001111000
[10,7,6,5,1,2,3,9,4,8,12,11]=>00011101101=>10110111000
[12,7,6,5,1,2,3,9,4,11,8,10]=>00011101011=>11010111000
[12,7,6,5,1,2,3,11,10,4,8,9]=>00011100111=>11100111000
[10,9,6,5,1,2,8,3,4,7,12,11]=>00011011101=>10111011000
[12,9,6,5,1,2,8,3,4,11,7,10]=>00011011011=>11011011000
[12,11,6,5,1,2,8,3,10,4,7,9]=>00011010111=>11101011000
[12,11,6,5,1,2,10,9,3,4,7,8]=>00011001111=>11110011000
[10,9,8,5,1,7,2,3,4,6,12,11]=>00010111101=>10111101000
[12,9,8,5,1,7,2,3,4,11,6,10]=>00010111011=>11011101000
[12,11,8,5,1,7,2,3,10,4,6,9]=>00010110111=>11101101000
[12,11,10,5,1,7,2,9,3,4,6,8]=>00010101111=>11110101000
[12,11,10,5,1,9,8,2,3,4,6,7]=>00010011111=>11111001000
[10,9,8,7,6,1,2,3,4,5,12,11]=>00001111101=>10111110000
[12,9,8,7,6,1,2,3,4,11,5,10]=>00001111011=>11011110000
[12,11,8,7,6,1,2,3,10,4,5,9]=>00001110111=>11101110000
[12,11,10,7,6,1,2,9,3,4,5,8]=>00001101111=>11110110000
[12,11,10,9,6,1,8,2,3,4,5,7]=>00001011111=>11111010000
[12,11,10,9,8,7,1,2,3,4,5,6]=>00000111111=>11111100000
[7,6,5,4,3,2,9,1,8]=>01111101=>10111110
[6,5,4,3,9,2,8,1,7]=>00111011=>11011100
[6,5,4,3,2,8,1,7,9]=>01111010=>01011110
[5,4,9,3,8,2,7,1,6]=>00010111=>11101000
[5,4,3,8,2,7,1,6,9]=>00110110=>01101100
[5,4,3,2,7,9,1,6,8]=>01110001=>10001110
[5,4,3,2,7,1,6,8,9]=>01110100=>00101110
[4,8,3,7,2,6,1,5,9]=>00001110=>01110000
[4,3,7,2,6,9,1,5,8]=>00100101=>10100100
[4,3,7,2,6,1,5,8,9]=>00101100=>00110100
[4,3,2,6,8,1,5,7,9]=>01100010=>01000110
[4,3,2,6,1,5,7,8,9]=>01101000=>00010110
[3,6,9,2,5,8,1,4,7]=>00000011=>11000000
[3,6,2,5,8,1,4,7,9]=>00001010=>01010000
[3,6,2,5,1,4,7,8,9]=>00011000=>00011000
[3,2,5,7,9,1,4,6,8]=>01000001=>10000010
[3,2,5,7,1,4,6,8,9]=>01000100=>00100010
[3,2,5,1,4,6,7,8,9]=>01010000=>00001010
[2,4,6,8,1,3,5,7,9]=>00000010=>01000000
[2,4,6,1,3,5,7,8,9]=>00001000=>00010000
[8,7,6,5,4,3,2,10,1,9]=>011111101=>101111110
[7,6,5,4,3,10,2,9,1,8]=>001111011=>110111100
[7,6,5,4,3,2,9,1,8,10]=>011111010=>010111110
[6,5,4,10,3,9,2,8,1,7]=>000110111=>111011000
[6,5,4,3,9,2,8,1,7,10]=>001110110=>011011100
[6,5,4,3,2,8,10,1,7,9]=>011110001=>100011110
[6,5,4,3,2,8,1,7,9,10]=>011110100=>001011110
[5,10,4,9,3,8,2,7,1,6]=>000001111=>111100000
[5,4,9,3,8,2,7,1,6,10]=>000101110=>011101000
[5,4,3,8,2,7,10,1,6,9]=>001100101=>101001100
[5,4,3,8,2,7,1,6,9,10]=>001101100=>001101100
[5,4,3,2,7,9,1,6,8,10]=>011100010=>010001110
[5,4,3,2,7,1,6,8,9,10]=>011101000=>000101110
[4,8,3,7,2,6,10,1,5,9]=>000001101=>101100000
[4,8,3,7,2,6,1,5,9,10]=>000011100=>001110000
[4,3,7,10,2,6,9,1,5,8]=>001000011=>110000100
[4,3,7,2,6,9,1,5,8,10]=>001001010=>010100100
[4,3,7,2,6,1,5,8,9,10]=>001011000=>000110100
[4,3,2,6,8,10,1,5,7,9]=>011000001=>100000110
[4,3,2,6,8,1,5,7,9,10]=>011000100=>001000110
[4,3,2,6,1,5,7,8,9,10]=>011010000=>000010110
[3,6,9,2,5,8,1,4,7,10]=>000000110=>011000000
[3,6,2,5,8,10,1,4,7,9]=>000010001=>100010000
[3,6,2,5,8,1,4,7,9,10]=>000010100=>001010000
[3,6,2,5,1,4,7,8,9,10]=>000110000=>000011000
[3,2,5,7,9,1,4,6,8,10]=>010000010=>010000010
[3,2,5,7,1,4,6,8,9,10]=>010001000=>000100010
[3,2,5,1,4,6,7,8,9,10]=>010100000=>000001010
[2,4,6,8,1,3,5,7,9,10]=>000000100=>001000000
[2,4,6,1,3,5,7,8,9,10]=>000010000=>000010000
[2,4,1,3,5,6,7,8,9,10]=>001000000=>000000100
[2,1,7,3,8,4,6,5]=>1000111=>1110001
[4,1,7,2,8,3,6,5]=>0010111=>1110100
[7,1,8,2,4,3,6,5]=>0010111=>1110100
[7,1,5,2,8,3,6,4]=>0001111=>1111000
[5,1,7,2,8,3,6,4]=>0001111=>1111000
[8,1,6,2,5,3,7,4]=>0001111=>1111000
[6,1,7,2,8,3,5,4]=>0001111=>1111000
[5,1,6,2,4,3,8,7]=>0011101=>1011100
[1,8,2,7,5,4,6,3]=>0001111=>1111000
[1,8,2,7,4,3,5,6]=>0010011=>1100100
[1,8,6,4,7,2,3,5]=>0000111=>1110000
[1,8,4,2,6,3,5,7]=>0010101=>1010100
[7,4,8,1,5,2,3,6]=>0001011=>1101000
[4,1,7,2,6,3,5,8]=>0010110=>0110100
[5,1,7,4,3,6,2,8]=>0011110=>0111100
[7,5,8,3,2,4,1,6]=>0110011=>1100110
[1,8,5,4,3,6,2,7]=>0011101=>1011100
[1,8,5,4,3,7,2,6]=>0011011=>1101100
[1,8,5,4,7,2,6,3]=>0001111=>1111000
[1,8,4,2,5,3,7,6]=>0011011=>1101100
[1,8,5,4,2,6,7,3]=>0011011=>1101100
[7,4,8,2,1,3,5,6]=>1000011=>1100001
[4,1,7,3,2,5,6,8]=>0110010=>0100110
[7,5,4,8,2,3,6,1]=>0001111=>1111000
[6,4,8,2,1,3,7,5]=>1000111=>1110001
[7,3,8,1,5,6,2,4]=>0000111=>1110000
[3,1,7,2,6,8,4,5]=>0100011=>1100010
[5,1,7,4,2,6,8,3]=>0011011=>1101100
[4,1,6,3,2,5,8,7]=>0110101=>1010110
[5,4,3,7,1,2,8,6]=>0011011=>1101100
[4,3,1,6,2,5,7,8]=>0110100=>0010110
[6,5,4,3,7,1,8,2]=>0011111=>1111100
[5,4,2,7,1,6,8,3]=>0011011=>1101100
[6,5,1,7,3,8,2,4]=>0001111=>1111000
[6,3,2,8,5,7,1,4]=>0100111=>1110010
[6,5,4,2,8,3,7,1]=>0011111=>1111100
[6,5,4,3,8,2,7,1]=>0011111=>1111100
[6,5,4,3,8,7,1,2]=>0011111=>1111100
[7,5,4,8,6,1,3,2]=>0101111=>1111010
[7,6,3,8,5,4,1,2]=>0011111=>1111100
[6,3,8,1,7,5,2,4]=>0001111=>1111000
[6,5,8,3,1,7,4,2]=>0110111=>1110110
[5,4,8,2,1,7,3,6]=>1001011=>1101001
[5,4,3,8,1,6,2,7]=>0011101=>1011100
[5,4,3,7,1,6,2,8]=>0011110=>0111100
[6,4,2,8,5,1,3,7]=>0011101=>1011100
[7,6,4,8,5,1,2,3]=>0001111=>1111000
[7,2,8,6,3,1,4,5]=>0100111=>1110010
[7,2,8,6,1,5,3,4]=>0001111=>1111000
[2,1,7,8,3,6,4,5]=>1000101=>1010001
[6,4,1,7,8,2,3,5]=>0010101=>1010100
[4,2,1,6,7,3,5,8]=>1010010=>0100101
[4,3,1,5,2,7,6,8]=>0111010=>0101110
[5,4,2,7,3,8,1,6]=>0011011=>1101100
[4,1,5,3,2,8,6,7]=>0111001=>1001110
[3,1,6,2,8,7,4,5]=>0100111=>1110010
[6,3,1,7,8,5,2,4]=>0101101=>1011010
[5,4,1,7,8,2,6,3]=>0011101=>1011100
[5,4,2,6,1,8,7,3]=>0011111=>1111100
[6,5,4,1,7,8,3,2]=>0111101=>1011110
[5,4,3,1,6,7,2,8]=>0111010=>0101110
[6,5,4,2,7,8,3,1]=>0111101=>1011110
[5,4,2,6,3,8,7,1]=>0011111=>1111100
[4,3,1,5,2,6,8,7]=>0111001=>1001110
[5,4,2,1,6,7,8,3]=>1011001=>1001101
[5,4,3,1,6,7,8,2]=>0111001=>1001110
[6,3,8,1,2,5,7,4]=>0000111=>1110000
[3,6,7,1,2,5,8,4]=>0000011=>1100000
[7,8,3,1,2,5,6,4]=>0100101=>1010010
[7,8,1,3,2,4,6,5]=>0100101=>1010010
[7,8,2,1,3,5,4,6]=>1001001=>1001001
[5,2,3,7,1,8,6,4]=>0001111=>1111000
[2,5,3,6,1,8,7,4]=>0001111=>1111000
[2,6,7,3,1,8,4,5]=>0100011=>1100010
[2,6,7,1,3,5,4,8]=>0001010=>0101000
[6,2,8,3,1,7,4,5]=>0100111=>1110010
[3,2,5,7,1,8,4,6]=>0100011=>1100010
[4,3,1,2,7,8,6,5]=>0110101=>1010110
[5,1,2,7,3,6,4,8]=>0001110=>0111000
[5,1,4,7,8,2,3,6]=>0001001=>1001000
[5,3,4,7,8,6,1,2]=>0001101=>1011000
[3,5,4,6,8,7,1,2]=>0001011=>1101000
[1,5,4,6,8,2,3,7]=>0001001=>1001000
[1,6,7,3,2,4,8,5]=>0100011=>1100010
[1,5,3,6,2,7,8,4]=>0001101=>1011000
[5,1,3,7,2,6,8,4]=>0001011=>1101000
[5,2,4,7,8,1,6,3]=>0001101=>1011000
[4,2,5,7,6,1,8,3]=>0010111=>1110100
[4,5,2,8,6,1,7,3]=>0001111=>1111000
[5,3,1,8,2,6,7,4]=>0101011=>1101010
[6,1,8,3,2,4,7,5]=>0100111=>1110010
[4,3,5,7,6,8,1,2]=>0010011=>1100100
[4,1,5,7,6,2,3,8]=>0010110=>0110100
[4,5,1,8,6,2,3,7]=>0001101=>1011000
[5,2,1,8,3,6,4,7]=>1001101=>1011001
[3,4,2,1,8,7,5,6]=>1010011=>1100101
[7,6,5,4,2,1,8,3]=>1011111=>1111101
[7,6,5,4,8,1,3,2]=>0101111=>1111010
[8,7,6,5,4,2,1,9,3]=>10111111=>11111101
[7,6,5,8,2,1,4,3]=>1010111=>1110101
[8,7,6,5,3,2,1,9,4]=>11011111=>11111011
[8,7,6,4,3,2,1,9,5]=>11101111=>11110111
[8,7,5,4,3,2,1,9,6]=>11110111=>11101111
[8,5,4,3,2,1,7,6]=>1111011=>1101111
[8,6,5,4,3,2,1,9,7]=>11111011=>11011111
[7,6,5,4,3,2,1,9,8]=>11111101=>10111111
[7,6,5,4,1,8,3,2]=>0111111=>1111110
[8,7,6,5,4,9,1,3,2]=>01011111=>11111010
[9,8,7,6,5,4,2,1,10,3]=>101111111=>111111101
[7,6,5,2,8,1,4,3]=>0011111=>1111100
[8,7,6,5,9,2,1,4,3]=>10101111=>11110101
[9,8,7,6,5,3,2,1,10,4]=>110111111=>111111011
[7,6,5,8,4,1,3,2]=>0110111=>1110110
[8,7,6,9,3,2,1,5,4]=>11010111=>11101011
[9,8,7,6,4,3,2,1,10,5]=>111011111=>111110111
[7,6,8,5,2,1,4,3]=>1011011=>1101101
[8,7,9,4,3,2,1,6,5]=>11101011=>11010111
[9,8,7,5,4,3,2,1,10,6]=>111101111=>111101111
[7,8,6,3,2,1,5,4]=>1101101=>1011011
[8,9,5,4,3,2,1,7,6]=>11110101=>10101111
[9,8,6,5,4,3,2,1,10,7]=>111110111=>111011111
[8,7,4,3,2,1,6,5]=>1110111=>1110111
[9,6,5,4,3,2,1,8,7]=>11111011=>11011111
[9,7,6,5,4,3,2,1,10,8]=>111111011=>110111111
[7,8,9,10,4,5,6,2,3,1]=>010010001=>100010010
[7,8,9,4,5,6,10,2,3,1]=>010000011=>110000010
[7,8,9,10,4,5,2,3,6,1]=>000110001=>100011000
[7,8,9,4,5,10,2,3,6,1]=>000010011=>110010000
[7,8,9,4,5,2,3,6,10,1]=>000100011=>110001000
[7,8,4,5,9,10,2,3,6,1]=>000010101=>101010000
[7,8,4,5,9,2,3,6,10,1]=>000000111=>111000000
[7,8,9,10,4,5,6,2,1,3]=>100010001=>100010001
[7,8,9,4,5,6,10,2,1,3]=>100000011=>110000001
[7,8,9,10,4,5,2,6,1,3]=>000110001=>100011000
[7,8,9,4,5,10,2,6,1,3]=>000010011=>110010000
[7,8,9,4,5,2,6,10,1,3]=>000100011=>110001000
[7,8,4,5,9,10,2,6,1,3]=>000010101=>101010000
[7,8,4,5,9,2,6,10,1,3]=>000000111=>111000000
[7,8,9,10,4,5,2,1,3,6]=>100100001=>100001001
[7,8,9,4,5,10,2,1,3,6]=>100000011=>110000001
[7,8,9,4,5,2,10,1,3,6]=>000100011=>110001000
[7,8,9,4,5,2,1,3,6,10]=>100100010=>010001001
[7,8,4,5,9,10,2,1,3,6]=>100000101=>101000001
[7,8,4,5,9,2,10,1,3,6]=>000000111=>111000000
[7,8,4,5,9,2,1,3,6,10]=>100000110=>011000001
[7,8,9,10,4,2,5,6,1,3]=>001010001=>100010100
[7,8,9,4,10,2,5,6,1,3]=>000010011=>110010000
[7,8,9,4,2,5,6,10,1,3]=>001000011=>110000100
[7,8,4,9,10,2,5,6,1,3]=>000010101=>101010000
[7,8,4,9,2,5,6,10,1,3]=>000000111=>111000000
[7,8,9,10,4,2,5,1,3,6]=>001100001=>100001100
[7,8,9,4,10,2,5,1,3,6]=>000100011=>110001000
[7,8,9,4,2,5,10,1,3,6]=>001000011=>110000100
[7,8,9,4,2,5,1,3,6,10]=>001100010=>010001100
[7,8,4,9,10,2,5,1,3,6]=>000100101=>101001000
[7,8,4,9,2,5,10,1,3,6]=>000000111=>111000000
[7,8,4,9,2,5,1,3,6,10]=>000100110=>011001000
[7,8,4,2,5,9,10,1,3,6]=>001000101=>101000100
[7,8,4,2,5,9,1,3,6,10]=>001000110=>011000100
[7,4,8,9,10,2,5,6,1,3]=>000011001=>100110000
[7,4,8,9,2,5,6,10,1,3]=>000001011=>110100000
[7,4,8,9,10,2,5,1,3,6]=>000101001=>100101000
[7,4,8,9,2,5,10,1,3,6]=>000001011=>110100000
[7,4,8,9,2,5,1,3,6,10]=>000101010=>010101000
[7,4,8,2,5,9,10,1,3,6]=>000001101=>101100000
[7,8,2,4,5,1,3,6]=>0001001=>1001000
[4,6,7,2,5,1,3,8]=>0001010=>0101000
[7,8,1,3,2,4,5,6]=>0100001=>1000010
[7,8,4,1,5,2,3,6]=>0011001=>1001100
[3,6,7,2,1,4,5,8]=>1000010=>0100001
[5,2,3,6,1,4,7,8]=>0001100=>0011000
[2,5,3,6,1,4,7,8]=>0001100=>0011000
[2,6,7,3,1,4,5,8]=>0100010=>0100010
[4,6,7,1,5,2,3,8]=>0001010=>0101000
[4,6,7,3,5,8,1,2]=>0000011=>1100000
[6,4,7,1,5,2,3,8]=>0001110=>0111000
[6,2,7,3,1,4,5,8]=>0100110=>0110010
[3,2,5,6,1,4,7,8]=>0100100=>0010010
[3,5,2,6,1,4,7,8]=>0001100=>0011000
[5,1,4,6,7,2,3,8]=>0001010=>0101000
[3,5,4,6,7,8,1,2]=>0001001=>1001000
[1,5,4,6,7,2,3,8]=>0001010=>0101000
[1,6,7,3,2,4,5,8]=>0100010=>0100010
[1,5,3,6,2,4,7,8]=>0001100=>0011000
[5,1,3,6,2,4,7,8]=>0001100=>0011000
[5,2,4,6,7,1,3,8]=>0001010=>0101000
[2,5,4,6,7,1,3,8]=>0001010=>0101000
[2,6,7,4,5,1,3,8]=>0001010=>0101000
[6,2,7,4,5,1,3,8]=>0001110=>0111000
[4,2,5,6,7,1,3,8]=>0010010=>0100100
[4,5,2,6,7,1,3,8]=>0001010=>0101000
[5,3,1,6,2,4,7,8]=>0101100=>0011010
[6,1,7,3,2,4,5,8]=>0100110=>0110010
[6,1,7,4,5,2,3,8]=>0001110=>0111000
[6,3,7,4,5,8,1,2]=>0000111=>1110000
[5,4,1,6,7,2,3,8]=>0011010=>0101100
[5,2,1,6,3,4,7,8]=>1001100=>0011001
[7,3,2,5,4,1,6,8]=>0111010=>0101110
[7,3,5,4,2,1,6,8]=>1011010=>0101101
[7,3,5,2,4,1,6,8]=>0011010=>0101100
[7,6,5,2,1,4,3,8]=>1011110=>0111101
[1,3,6,7,5,2,8,4]=>0001011=>1101000
[7,3,4,1,6,2,5,8]=>0010110=>0110100
[7,3,4,1,6,5,2,8]=>0011110=>0111100
[7,3,4,1,5,6,2,8]=>0010110=>0110100
[7,3,2,5,1,6,4,8]=>0101110=>0111010
[7,6,5,4,1,3,2,8]=>0111110=>0111110
[7,3,4,1,5,2,6,8]=>0011010=>0101100
[1,3,6,7,2,5,8,4]=>0000011=>1100000
[1,7,4,6,2,8,5,3]=>0001111=>1111000
[4,3,1,7,2,6,8,5]=>0110011=>1100110
[5,6,1,4,7,3,8,2]=>0000111=>1110000
[5,3,2,1,7,4,8,6]=>1101011=>1101011
[1,3,4,5,8,7,2,6]=>0000011=>1100000
[6,3,4,5,8,1,7,2]=>0000111=>1110000
[2,4,5,1,6,8,7,3]=>0001011=>1101000
[3,1,2,5,6,8,7,4]=>0100011=>1100010
[4,3,2,5,6,8,1,7]=>0110001=>1000110
[3,7,5,4,6,8,1,2]=>0001011=>1101000
[3,1,4,6,5,8,2,7]=>0100101=>1010010
[2,3,4,5,8,6,1,7]=>0000101=>1010000
[2,3,4,5,8,1,7,6]=>0000011=>1100000
[3,1,4,6,5,8,7,2]=>0100111=>1110010
[3,7,5,4,6,8,2,1]=>1001011=>1101001
[5,6,1,4,7,2,8,3]=>0000111=>1110000
[4,3,1,7,5,6,8,2]=>0110011=>1100110
[4,3,1,7,6,5,8,2]=>0110111=>1110110
[3,1,4,6,7,8,5,2]=>0101001=>1001010
[1,4,5,2,6,8,7,3]=>0001011=>1101000
[3,7,5,2,6,8,1,4]=>0001011=>1101000
[3,7,5,2,6,8,4,1]=>0011011=>1101100
[5,6,1,2,7,4,8,3]=>0000111=>1110000
[6,3,5,2,4,7,8,1]=>0001101=>1011000
[5,3,2,1,4,7,8,6]=>1101001=>1001011
[5,3,1,4,2,7,8,6]=>0111001=>1001110
[5,3,1,2,4,7,8,6]=>0101001=>1001010
[7,1,5,2,6,8,4,3]=>0011011=>1101100
[7,1,5,2,6,8,3,4]=>0001011=>1101000
[1,7,4,6,5,8,3,2]=>0100111=>1110010
[2,7,4,6,1,8,3,5]=>0000111=>1110000
[2,7,4,6,1,8,5,3]=>0001111=>1111000
[2,3,6,7,1,5,8,4]=>0000011=>1100000
[2,3,6,7,5,1,8,4]=>0001011=>1101000
[4,3,2,6,7,1,8,5]=>0110011=>1100110
[7,3,2,5,6,8,1,4]=>0100011=>1100010
[7,1,5,4,6,8,2,3]=>0001011=>1101000
[2,7,4,6,5,8,1,3]=>0000111=>1110000
[7,3,4,5,8,6,1,2]=>0000111=>1110000
[7,3,4,5,8,1,6,2]=>0000111=>1110000
[7,3,4,5,8,1,2,6]=>0000011=>1100000
[1,3,4,5,8,6,2,7]=>0000101=>1010000
[1,3,4,5,8,2,7,6]=>0000011=>1100000
[6,3,4,5,8,2,1,7]=>1000101=>1010001
[6,3,4,5,8,2,7,1]=>0000111=>1110000
[7,3,4,5,8,6,2,1]=>1000111=>1110001
[2,7,4,6,5,8,3,1]=>0100111=>1110010
[7,1,5,4,6,8,3,2]=>0101011=>1101010
[7,3,2,5,6,8,4,1]=>0110011=>1100110
[5,7,4,6,1,8,3,2]=>0100111=>1110010
[6,3,4,5,8,1,2,7]=>0000101=>1010000
[7,3,4,5,8,2,1,6]=>1000011=>1100001
[7,3,4,5,8,2,6,1]=>0000111=>1110000
[4,7,6,1,8,2,5,3]=>0001111=>1111000
[4,8,6,1,7,5,2,3]=>0001111=>1111000
[4,7,8,2,6,1,5,3]=>0001101=>1011000
[7,6,4,2,8,3,5,1]=>0011111=>1111100
[8,6,4,2,7,5,3,1]=>0111111=>1111110
[8,4,7,3,6,5,1,2]=>0001111=>1111000
[8,4,6,1,7,5,3,2]=>0101111=>1111010
[6,4,7,1,8,3,2,5]=>0100111=>1110010
[7,4,8,3,6,1,5,2]=>0001111=>1111000
[7,8,4,3,6,2,5,1]=>0011101=>1011100
[8,10,7,9,5,6,3,4,1,2]=>001010011=>110010100
[9,10,6,8,5,7,3,4,1,2]=>001001101=>101100100
[8,10,6,9,5,7,3,4,1,2]=>001001011=>110100100
[7,10,6,9,5,8,3,4,1,2]=>001000111=>111000100
[9,10,7,8,4,6,3,5,1,2]=>000110101=>101011000
[8,10,7,9,4,6,3,5,1,2]=>000110011=>110011000
[9,10,6,8,4,7,3,5,1,2]=>000101101=>101101000
[8,10,6,9,4,7,3,5,1,2]=>000101011=>110101000
[7,10,6,9,4,8,3,5,1,2]=>000100111=>111001000
[9,10,5,8,4,7,3,6,1,2]=>000011101=>101110000
[8,10,5,9,4,7,3,6,1,2]=>000011011=>110110000
[7,10,5,9,4,8,3,6,1,2]=>000010111=>111010000
[6,10,5,9,4,8,3,7,1,2]=>000001111=>111100000
[9,10,7,8,5,6,2,4,1,3]=>001010101=>101010100
[8,10,7,9,5,6,2,4,1,3]=>001010011=>110010100
[9,10,6,8,5,7,2,4,1,3]=>001001101=>101100100
[8,10,6,9,5,7,2,4,1,3]=>001001011=>110100100
[7,10,6,9,5,8,2,4,1,3]=>001000111=>111000100
[9,10,7,8,4,6,2,5,1,3]=>000110101=>101011000
[8,10,7,9,4,6,2,5,1,3]=>000110011=>110011000
[9,10,6,8,4,7,2,5,1,3]=>000101101=>101101000
[8,10,6,9,4,7,2,5,1,3]=>000101011=>110101000
[7,10,6,9,4,8,2,5,1,3]=>000100111=>111001000
[9,10,5,8,4,7,2,6,1,3]=>000011101=>101110000
[8,10,5,9,4,7,2,6,1,3]=>000011011=>110110000
[7,10,5,9,4,8,2,6,1,3]=>000010111=>111010000
[6,10,5,9,4,8,2,7,1,3]=>000001111=>111100000
[9,10,7,8,3,6,2,5,1,4]=>000110101=>101011000
[8,10,7,9,3,6,2,5,1,4]=>000110011=>110011000
[9,10,6,8,3,7,2,5,1,4]=>000101101=>101101000
[8,10,6,9,3,7,2,5,1,4]=>000101011=>110101000
[7,10,6,9,3,8,2,5,1,4]=>000100111=>111001000
[9,10,5,8,3,7,2,6,1,4]=>000011101=>101110000
[8,10,5,9,3,7,2,6,1,4]=>000011011=>110110000
[7,10,5,9,3,8,2,6,1,4]=>000010111=>111010000
[6,10,5,9,3,8,2,7,1,4]=>000001111=>111100000
[9,10,4,8,3,7,2,6,1,5]=>000011101=>101110000
[8,10,4,9,3,7,2,6,1,5]=>000011011=>110110000
[7,10,4,9,3,8,2,6,1,5]=>000010111=>111010000
[6,10,4,9,3,8,2,7,1,5]=>000001111=>111100000
[10,12,9,11,7,8,5,6,3,4,1,2]=>00101010011=>11001010100
[11,12,8,10,7,9,5,6,3,4,1,2]=>00101001101=>10110010100
[10,12,8,11,7,9,5,6,3,4,1,2]=>00101001011=>11010010100
[9,12,8,11,7,10,5,6,3,4,1,2]=>00101000111=>11100010100
[11,12,9,10,6,8,5,7,3,4,1,2]=>00100110101=>10101100100
[10,12,9,11,6,8,5,7,3,4,1,2]=>00100110011=>11001100100
[11,12,8,10,6,9,5,7,3,4,1,2]=>00100101101=>10110100100
[10,12,8,11,6,9,5,7,3,4,1,2]=>00100101011=>11010100100
[9,12,8,11,6,10,5,7,3,4,1,2]=>00100100111=>11100100100
[11,12,7,10,6,9,5,8,3,4,1,2]=>00100011101=>10111000100
[10,12,7,11,6,9,5,8,3,4,1,2]=>00100011011=>11011000100
[9,12,7,11,6,10,5,8,3,4,1,2]=>00100010111=>11101000100
[8,12,7,11,6,10,5,9,3,4,1,2]=>00100001111=>11110000100
[11,12,9,10,7,8,4,6,3,5,1,2]=>00011010101=>10101011000
[10,12,9,11,7,8,4,6,3,5,1,2]=>00011010011=>11001011000
[11,12,8,10,7,9,4,6,3,5,1,2]=>00011001101=>10110011000
[10,12,8,11,7,9,4,6,3,5,1,2]=>00011001011=>11010011000
[9,12,8,11,7,10,4,6,3,5,1,2]=>00011000111=>11100011000
[11,12,9,10,6,8,4,7,3,5,1,2]=>00010110101=>10101101000
[10,12,9,11,6,8,4,7,3,5,1,2]=>00010110011=>11001101000
[11,12,8,10,6,9,4,7,3,5,1,2]=>00010101101=>10110101000
[10,12,8,11,6,9,4,7,3,5,1,2]=>00010101011=>11010101000
[9,12,8,11,6,10,4,7,3,5,1,2]=>00010100111=>11100101000
[11,12,7,10,6,9,4,8,3,5,1,2]=>00010011101=>10111001000
[10,12,7,11,6,9,4,8,3,5,1,2]=>00010011011=>11011001000
[9,12,7,11,6,10,4,8,3,5,1,2]=>00010010111=>11101001000
[8,12,7,11,6,10,4,9,3,5,1,2]=>00010001111=>11110001000
[11,12,9,10,5,8,4,7,3,6,1,2]=>00001110101=>10101110000
[10,12,9,11,5,8,4,7,3,6,1,2]=>00001110011=>11001110000
[11,12,8,10,5,9,4,7,3,6,1,2]=>00001101101=>10110110000
[10,12,8,11,5,9,4,7,3,6,1,2]=>00001101011=>11010110000
[9,12,8,11,5,10,4,7,3,6,1,2]=>00001100111=>11100110000
[11,12,7,10,5,9,4,8,3,6,1,2]=>00001011101=>10111010000
[10,12,7,11,5,9,4,8,3,6,1,2]=>00001011011=>11011010000
[9,12,7,11,5,10,4,8,3,6,1,2]=>00001010111=>11101010000
[8,12,7,11,5,10,4,9,3,6,1,2]=>00001001111=>11110010000
[11,12,6,10,5,9,4,8,3,7,1,2]=>00000111101=>10111100000
[10,12,6,11,5,9,4,8,3,7,1,2]=>00000111011=>11011100000
[9,12,6,11,5,10,4,8,3,7,1,2]=>00000110111=>11101100000
[8,12,6,11,5,10,4,9,3,7,1,2]=>00000101111=>11110100000
[7,12,6,11,5,10,4,9,3,8,1,2]=>00000011111=>11111000000
[11,12,9,10,7,8,5,6,2,4,1,3]=>00101010101=>10101010100
[10,12,9,11,7,8,5,6,2,4,1,3]=>00101010011=>11001010100
[11,12,8,10,7,9,5,6,2,4,1,3]=>00101001101=>10110010100
[10,12,8,11,7,9,5,6,2,4,1,3]=>00101001011=>11010010100
[9,12,8,11,7,10,5,6,2,4,1,3]=>00101000111=>11100010100
[11,12,9,10,6,8,5,7,2,4,1,3]=>00100110101=>10101100100
[10,12,9,11,6,8,5,7,2,4,1,3]=>00100110011=>11001100100
[11,12,8,10,6,9,5,7,2,4,1,3]=>00100101101=>10110100100
[10,12,8,11,6,9,5,7,2,4,1,3]=>00100101011=>11010100100
[9,12,8,11,6,10,5,7,2,4,1,3]=>00100100111=>11100100100
[11,12,7,10,6,9,5,8,2,4,1,3]=>00100011101=>10111000100
[10,12,7,11,6,9,5,8,2,4,1,3]=>00100011011=>11011000100
[9,12,7,11,6,10,5,8,2,4,1,3]=>00100010111=>11101000100
[8,12,7,11,6,10,5,9,2,4,1,3]=>00100001111=>11110000100
[11,12,9,10,7,8,4,6,2,5,1,3]=>00011010101=>10101011000
[10,12,9,11,7,8,4,6,2,5,1,3]=>00011010011=>11001011000
[11,12,8,10,7,9,4,6,2,5,1,3]=>00011001101=>10110011000
[10,12,8,11,7,9,4,6,2,5,1,3]=>00011001011=>11010011000
[9,12,8,11,7,10,4,6,2,5,1,3]=>00011000111=>11100011000
[11,12,9,10,6,8,4,7,2,5,1,3]=>00010110101=>10101101000
[10,12,9,11,6,8,4,7,2,5,1,3]=>00010110011=>11001101000
[11,12,8,10,6,9,4,7,2,5,1,3]=>00010101101=>10110101000
[10,12,8,11,6,9,4,7,2,5,1,3]=>00010101011=>11010101000
[9,12,8,11,6,10,4,7,2,5,1,3]=>00010100111=>11100101000
[11,12,7,10,6,9,4,8,2,5,1,3]=>00010011101=>10111001000
[10,12,7,11,6,9,4,8,2,5,1,3]=>00010011011=>11011001000
[9,12,7,11,6,10,4,8,2,5,1,3]=>00010010111=>11101001000
[8,12,7,11,6,10,4,9,2,5,1,3]=>00010001111=>11110001000
[11,12,9,10,5,8,4,7,2,6,1,3]=>00001110101=>10101110000
[10,12,9,11,5,8,4,7,2,6,1,3]=>00001110011=>11001110000
[11,12,8,10,5,9,4,7,2,6,1,3]=>00001101101=>10110110000
[10,12,8,11,5,9,4,7,2,6,1,3]=>00001101011=>11010110000
[9,12,8,11,5,10,4,7,2,6,1,3]=>00001100111=>11100110000
[11,12,7,10,5,9,4,8,2,6,1,3]=>00001011101=>10111010000
[10,12,7,11,5,9,4,8,2,6,1,3]=>00001011011=>11011010000
[9,12,7,11,5,10,4,8,2,6,1,3]=>00001010111=>11101010000
[8,12,7,11,5,10,4,9,2,6,1,3]=>00001001111=>11110010000
[11,12,6,10,5,9,4,8,2,7,1,3]=>00000111101=>10111100000
[10,12,6,11,5,9,4,8,2,7,1,3]=>00000111011=>11011100000
[9,12,6,11,5,10,4,8,2,7,1,3]=>00000110111=>11101100000
[8,12,6,11,5,10,4,9,2,7,1,3]=>00000101111=>11110100000
[7,12,6,11,5,10,4,9,2,8,1,3]=>00000011111=>11111000000
[11,12,9,10,7,8,3,6,2,5,1,4]=>00011010101=>10101011000
[10,12,9,11,7,8,3,6,2,5,1,4]=>00011010011=>11001011000
[11,12,8,10,7,9,3,6,2,5,1,4]=>00011001101=>10110011000
[10,12,8,11,7,9,3,6,2,5,1,4]=>00011001011=>11010011000
[9,12,8,11,7,10,3,6,2,5,1,4]=>00011000111=>11100011000
[11,12,9,10,6,8,3,7,2,5,1,4]=>00010110101=>10101101000
[10,12,9,11,6,8,3,7,2,5,1,4]=>00010110011=>11001101000
[11,12,8,10,6,9,3,7,2,5,1,4]=>00010101101=>10110101000
[10,12,8,11,6,9,3,7,2,5,1,4]=>00010101011=>11010101000
[9,12,8,11,6,10,3,7,2,5,1,4]=>00010100111=>11100101000
[11,12,7,10,6,9,3,8,2,5,1,4]=>00010011101=>10111001000
[10,12,7,11,6,9,3,8,2,5,1,4]=>00010011011=>11011001000
[9,12,7,11,6,10,3,8,2,5,1,4]=>00010010111=>11101001000
[8,12,7,11,6,10,3,9,2,5,1,4]=>00010001111=>11110001000
[11,12,9,10,5,8,3,7,2,6,1,4]=>00001110101=>10101110000
[10,12,9,11,5,8,3,7,2,6,1,4]=>00001110011=>11001110000
[11,12,8,10,5,9,3,7,2,6,1,4]=>00001101101=>10110110000
[10,12,8,11,5,9,3,7,2,6,1,4]=>00001101011=>11010110000
[9,12,8,11,5,10,3,7,2,6,1,4]=>00001100111=>11100110000
[11,12,7,10,5,9,3,8,2,6,1,4]=>00001011101=>10111010000
[10,12,7,11,5,9,3,8,2,6,1,4]=>00001011011=>11011010000
[9,12,7,11,5,10,3,8,2,6,1,4]=>00001010111=>11101010000
[8,12,7,11,5,10,3,9,2,6,1,4]=>00001001111=>11110010000
[11,12,6,10,5,9,3,8,2,7,1,4]=>00000111101=>10111100000
[10,12,6,11,5,9,3,8,2,7,1,4]=>00000111011=>11011100000
[9,12,6,11,5,10,3,8,2,7,1,4]=>00000110111=>11101100000
[8,12,6,11,5,10,3,9,2,7,1,4]=>00000101111=>11110100000
[7,12,6,11,5,10,3,9,2,8,1,4]=>00000011111=>11111000000
[11,12,9,10,4,8,3,7,2,6,1,5]=>00001110101=>10101110000
[10,12,9,11,4,8,3,7,2,6,1,5]=>00001110011=>11001110000
[11,12,8,10,4,9,3,7,2,6,1,5]=>00001101101=>10110110000
[10,12,8,11,4,9,3,7,2,6,1,5]=>00001101011=>11010110000
[9,12,8,11,4,10,3,7,2,6,1,5]=>00001100111=>11100110000
[11,12,7,10,4,9,3,8,2,6,1,5]=>00001011101=>10111010000
[10,12,7,11,4,9,3,8,2,6,1,5]=>00001011011=>11011010000
[9,12,7,11,4,10,3,8,2,6,1,5]=>00001010111=>11101010000
[8,12,7,11,4,10,3,9,2,6,1,5]=>00001001111=>11110010000
[11,12,6,10,4,9,3,8,2,7,1,5]=>00000111101=>10111100000
[10,12,6,11,4,9,3,8,2,7,1,5]=>00000111011=>11011100000
[9,12,6,11,4,10,3,8,2,7,1,5]=>00000110111=>11101100000
[8,12,6,11,4,10,3,9,2,7,1,5]=>00000101111=>11110100000
[7,12,6,11,4,10,3,9,2,8,1,5]=>00000011111=>11111000000
[11,12,5,10,4,9,3,8,2,7,1,6]=>00000111101=>10111100000
[10,12,5,11,4,9,3,8,2,7,1,6]=>00000111011=>11011100000
[9,12,5,11,4,10,3,8,2,7,1,6]=>00000110111=>11101100000
[8,12,5,11,4,10,3,9,2,7,1,6]=>00000101111=>11110100000
[7,12,5,11,4,10,3,9,2,8,1,6]=>00000011111=>11111000000
[6,12,5,11,4,10,3,9,2,8,1,7]=>00000011111=>11111000000
[6,2,1,7,3,5,4,8]=>1001110=>0111001
[2,1,8,6,3,5,4,7]=>1001101=>1011001
[2,1,7,3,5,8,6,4]=>1000111=>1110001
[2,7,3,1,5,4,6,8]=>0101010=>0101010
[2,6,3,1,4,8,5,7]=>0100101=>1010010
[4,2,1,8,3,6,7,5]=>1010011=>1100101
[2,1,8,6,3,5,7,4]=>1000111=>1110001
[6,2,1,7,3,5,8,4]=>1000111=>1110001
[2,7,3,1,4,8,5,6]=>0100011=>1100010
[3,2,1,6,4,5,7,8]=>1100100=>0010011
[3,2,1,5,7,8,4,6]=>1100001=>1000011
[2,1,7,3,6,8,4,5]=>1000011=>1100001
[2,7,3,1,5,6,8,4]=>0100011=>1100010
[2,4,7,5,1,6,8,3]=>0001011=>1101000
[4,3,7,5,6,1,8,2]=>0010111=>1110100
[4,3,6,8,5,1,7,2]=>0011011=>1101100
[2,6,1,8,3,5,7,4]=>0000111=>1110000
[2,1,6,8,3,7,4,5]=>1000011=>1100001
[2,1,8,3,5,7,4,6]=>1000011=>1100001
[3,2,1,5,6,8,4,7]=>1100001=>1000011
[3,2,1,5,7,4,6,8]=>1100010=>0100011
[2,1,7,3,6,4,5,8]=>1000110=>0110001
[2,1,6,3,5,8,4,7]=>1000101=>1010001
[8,2,4,1,7,5,6,3]=>0010111=>1110100
[3,8,4,7,5,1,6,2]=>0001111=>1111000
[8,4,3,6,1,7,5,2]=>0011111=>1111100
[8,2,1,7,3,5,4,6]=>1001011=>1101001
[2,6,1,8,3,5,4,7]=>0001101=>1011000
[2,7,3,1,5,6,4,8]=>0100110=>0110010
[2,4,7,5,1,6,3,8]=>0001110=>0111000
[8,2,4,1,7,5,3,6]=>0011011=>1101100
[5,8,6,3,1,7,4,2]=>0110111=>1110110
[2,4,7,1,8,5,3,6]=>0001011=>1101000
[2,4,8,5,1,6,3,7]=>0001101=>1011000
[6,2,1,7,3,4,8,5]=>1000111=>1110001
[6,2,1,7,8,3,5,4]=>1001101=>1011001
[2,7,1,8,3,5,6,4]=>0000111=>1110000
[2,1,8,3,6,4,5,7]=>1000101=>1010001
[3,2,1,6,7,4,5,8]=>1100010=>0100011
[3,2,1,7,4,5,6,8]=>1100010=>0100011
[3,2,1,6,8,4,5,7]=>1100001=>1000011
[2,1,8,3,7,4,5,6]=>1000011=>1100001
[2,1,8,3,6,7,4,5]=>1000011=>1100001
[2,4,8,5,1,6,7,3]=>0001011=>1101000
[4,3,8,5,6,1,7,2]=>0010111=>1110100
[3,2,1,8,4,5,6,7]=>1100001=>1000011
[1,6,8,3,7,2,4,5]=>0000011=>1100000
[3,8,1,5,7,2,4,6]=>0000011=>1100000
[1,2,6,8,4,7,3,5]=>0000011=>1100000
[6,1,5,8,2,4,7,3]=>0000111=>1110000
[1,2,4,8,3,6,7,5]=>0000011=>1100000
[4,1,2,7,8,3,6,5]=>0010101=>1010100
[3,5,7,4,8,6,1,2]=>0000111=>1110000
[5,3,8,4,7,6,1,2]=>0001111=>1111000
[8,7,1,2,5,4,6,3]=>0001111=>1111000
[5,8,1,2,3,7,6,4]=>0000111=>1110000
[1,2,8,4,3,5,7,6]=>0010011=>1100100
[1,2,5,3,7,6,4,8]=>0001110=>0111000
[6,1,2,8,7,4,5,3]=>0001111=>1111000
[7,1,6,2,8,4,5,3]=>0001111=>1111000
[1,2,6,3,8,5,4,7]=>0001101=>1011000
[1,2,8,5,3,6,4,7]=>0001101=>1011000
[1,2,7,3,8,5,4,6]=>0001011=>1101000
[4,1,2,7,8,6,3,5]=>0010101=>1010100
[1,6,2,8,4,3,5,7]=>0010101=>1010100
[1,6,4,2,7,3,5,8]=>0010110=>0110100
[1,8,6,3,2,4,5,7]=>0100101=>1010010
[1,7,3,2,8,4,5,6]=>0100011=>1100010
[3,1,7,8,6,2,4,5]=>0100101=>1010010
[1,8,7,2,4,5,6,3]=>0000111=>1110000
[1,8,7,3,5,6,2,4]=>0000111=>1110000
[1,3,2,8,7,4,5,6]=>0100011=>1100010
[1,8,3,2,6,4,5,7]=>0100101=>1010010
[1,7,6,3,2,4,5,8]=>0100110=>0110010
[1,2,8,4,3,7,5,6]=>0010011=>1100100
[8,5,1,7,2,4,6,3]=>0001111=>1111000
[5,3,8,7,4,6,1,2]=>0001111=>1111000
[3,8,6,4,7,5,1,2]=>0001111=>1111000
[6,1,8,2,7,4,5,3]=>0001111=>1111000
[1,2,5,3,8,6,4,7]=>0001101=>1011000
[1,2,7,5,3,6,4,8]=>0001110=>0111000
[1,2,6,3,7,5,4,8]=>0001110=>0111000
[1,2,3,7,5,4,8,6]=>0001011=>1101000
[3,7,4,8,6,5,1,2]=>0001111=>1111000
[1,8,2,7,6,4,5,3]=>0001111=>1111000
[2,9,8,7,6,5,4,1,3]=>00111111=>11111100
[2,8,7,6,5,1,4,3]=>0011111=>1111100
[7,1,6,3,2,5,4,8]=>0101110=>0111010
[2,7,6,3,1,5,8,4]=>0100111=>1110010
[1,8,4,3,6,5,2,7]=>0011101=>1011100
[1,8,4,6,5,3,2,7]=>0101101=>1011010
[7,4,2,1,6,5,3,8]=>1011110=>0111101
[7,6,1,4,3,5,2,8]=>0011110=>0111100
[7,4,1,3,5,2,6,8]=>0011010=>0101100
[7,3,1,2,4,6,5,8]=>0100110=>0110010
[1,8,6,3,4,5,2,7]=>0001101=>1011000
[1,8,6,7,4,2,5,3]=>0011011=>1101100
[3,6,2,1,4,8,5,7]=>1000101=>1010001
[3,1,7,2,4,6,8,5]=>0100011=>1100010
[3,4,7,1,5,2,8,6]=>0001011=>1101000
[3,6,7,4,1,5,8,2]=>0010011=>1100100
[4,3,2,7,1,5,8,6]=>0110011=>1100110
[3,1,2,8,6,5,4,7]=>0101101=>1011010
[5,4,8,6,1,2,3,7]=>0001101=>1011000
[5,6,8,7,4,3,1,2]=>0110011=>1100110
[1,8,2,7,4,3,6,5]=>0010111=>1110100
[6,5,8,2,3,7,1,4]=>0000111=>1110000
[6,4,8,5,3,1,7,2]=>0101111=>1111010
[5,7,8,6,1,3,2,4]=>0100101=>1010010
[2,4,8,1,6,3,7,5]=>0000111=>1110000
[3,1,2,8,6,4,7,5]=>0100111=>1110010
[5,3,2,6,4,8,1,7]=>0101101=>1011010
[4,1,6,3,5,8,2,7]=>0010101=>1010100
[2,4,5,3,8,6,1,7]=>0001101=>1011000
[1,8,5,3,2,7,6,4]=>0101111=>1111010
[1,8,4,5,2,6,7,3]=>0001011=>1101000
[4,1,2,7,6,5,8,3]=>0010111=>1110100
[2,4,1,6,7,8,5,3]=>0011001=>1001100
[1,8,4,3,6,2,7,5]=>0010111=>1110100
[5,6,7,3,2,8,1,4]=>0100011=>1100010
[2,5,7,3,6,8,4,1]=>0010011=>1100100
[5,3,2,1,4,8,6,7]=>1101001=>1001011
[5,3,1,4,2,8,6,7]=>0111001=>1001110
[7,6,1,3,8,5,4,2]=>0011111=>1111100
[3,4,7,8,1,2,6,5]=>0000101=>1010000
[3,6,7,8,1,4,5,2]=>0001001=>1001000
[3,6,2,8,1,5,4,7]=>0001101=>1011000
[2,3,6,8,5,1,4,7]=>0001001=>1001000
[3,1,6,4,8,2,5,7]=>0100101=>1010010
[7,3,2,6,8,5,1,4]=>0101011=>1101010
[7,3,5,8,4,6,1,2]=>0000111=>1110000
[7,5,2,8,4,1,6,3]=>0011111=>1111100
[7,4,5,8,2,1,3,6]=>1000011=>1100001
[1,8,5,2,4,6,3,7]=>0001101=>1011000
[1,8,4,2,3,5,7,6]=>0010011=>1100100
[6,4,2,8,3,5,1,7]=>0011101=>1011100
[6,3,4,8,2,5,7,1]=>0000111=>1110000
[7,5,4,8,3,6,2,1]=>1001111=>1111001
[2,7,4,8,5,3,6,1]=>0001111=>1111000
[7,1,5,4,8,3,6,2]=>0001111=>1111000
[7,3,2,5,8,4,6,1]=>0100111=>1110010
[8,4,6,3,7,2,5,1]=>0001111=>1111000
[7,4,6,3,8,5,1,2]=>0001111=>1111000
[2,5,6,8,3,4,1,7]=>0010001=>1000100
[8,4,6,2,7,5,3,1]=>0101111=>1111010
[8,5,6,7,2,4,3,1]=>0110011=>1100110
[2,5,6,8,4,3,1,7]=>0110001=>1000110
[2,5,7,8,4,1,3,6]=>0010001=>1000100
[6,5,7,8,4,1,3,2]=>0110101=>1010110
[7,5,6,8,2,4,1,3]=>0010011=>1100100
[7,4,6,2,8,5,1,3]=>0001111=>1111000
[4,3,2,6,8,5,1,7]=>0111001=>1001110
[3,5,6,8,2,4,1,7]=>0010001=>1000100
[3,5,6,8,4,2,1,7]=>1010001=>1000101
[2,6,7,8,1,4,5,3]=>0001001=>1001000
[3,6,7,8,1,4,2,5]=>0010001=>1000100
[3,5,7,8,2,1,4,6]=>1000001=>1000001
[2,6,7,8,1,4,3,5]=>0010001=>1000100
[6,5,7,8,3,1,4,2]=>0110101=>1010110
[2,5,7,8,3,1,4,6]=>0100001=>1000010
[2,4,7,3,8,1,5,6]=>0000011=>1100000
[6,4,7,3,8,1,5,2]=>0001111=>1111000
[6,4,7,3,8,1,2,5]=>0000111=>1110000
[7,4,6,3,8,2,1,5]=>1000111=>1110001
[6,3,2,5,4,8,1,7]=>0101101=>1011010
[6,4,5,2,3,8,1,7]=>0001101=>1011000
[6,4,5,3,2,8,1,7]=>0101101=>1011010
[5,4,6,3,8,2,1,7]=>1001101=>1011001
[5,4,7,3,8,1,6,2]=>0001111=>1111000
[2,5,7,8,3,1,6,4]=>0100101=>1010010
[4,5,7,8,3,1,2,6]=>0100001=>1000010
[4,5,6,8,2,3,1,7]=>0100001=>1000010
[5,4,6,2,8,3,1,7]=>0101101=>1011010
[5,3,2,6,8,4,1,7]=>0111001=>1001110
[5,4,7,2,8,1,3,6]=>0001011=>1101000
[4,5,7,8,2,1,3,6]=>1000001=>1000001
[4,6,7,8,1,3,2,5]=>0100001=>1000010
[4,6,7,8,1,3,5,2]=>0001001=>1001000
[2,6,7,8,1,3,5,4]=>0001001=>1001000
[2,6,7,8,1,5,3,4]=>0001001=>1001000
[4,6,7,8,1,5,2,3]=>0001001=>1001000
[4,6,7,8,1,2,5,3]=>0001001=>1001000
[4,5,7,8,2,1,6,3]=>1000101=>1010001
[5,4,7,2,8,1,6,3]=>0001111=>1111000
[5,3,2,7,8,1,6,4]=>0101101=>1011010
[4,3,2,7,8,1,6,5]=>0110101=>1010110
[3,5,7,8,2,1,6,4]=>1000101=>1010001
[3,6,7,8,1,2,5,4]=>0001001=>1001000
[3,6,7,8,1,5,2,4]=>0001001=>1001000
[3,6,7,8,1,5,4,2]=>0011001=>1001100
[2,6,7,8,1,5,4,3]=>0011001=>1001100
[2,3,4,5,6,7,8,9,10,1,11]=>0000000010=>0100000000
[3,4,5,6,7,8,9,1,2,10]=>000000010=>010000000
[2,4,5,6,7,8,1,3,9]=>00000010=>01000000
[3,4,5,6,7,1,8,2,9]=>00000110=>01100000
[1,3,5,6,7,8,9,2,4]=>00000001=>10000000
[1,4,5,6,7,8,2,9,3]=>00000011=>11000000
[1,4,5,6,7,8,9,10,2,3]=>000000001=>100000000
[1,3,4,5,6,7,8,9,10,11,2]=>0000000001=>1000000000
[4,2,7,1,5,3,8,6]=>0011011=>1101100
[4,2,8,6,1,5,3,7]=>0011101=>1011100
[3,2,6,7,5,1,4,8]=>0101010=>0101010
[2,7,1,3,5,4,8,6]=>0001011=>1101000
[4,7,2,1,5,8,6,3]=>1000111=>1110001
[7,2,1,3,5,8,6,4]=>1000111=>1110001
[2,3,6,4,7,1,5,8]=>0000110=>0110000
[1,3,4,8,2,7,5,6]=>0000011=>1100000
[3,1,4,8,2,6,7,5]=>0100011=>1100010
[8,3,1,6,2,5,7,4]=>0100111=>1110010
[4,8,6,2,1,5,7,3]=>1000111=>1110001
[4,8,3,6,5,1,7,2]=>0001111=>1111000
[6,4,7,3,5,1,8,2]=>0001111=>1111000
[6,4,7,5,1,8,2,3]=>0001111=>1111000
[3,6,1,7,5,8,2,4]=>0000111=>1110000
[7,3,5,1,6,8,2,4]=>0001011=>1101000
[4,7,3,5,6,1,8,2]=>0000111=>1110000
[3,4,6,8,5,1,7,2]=>0001011=>1101000
[4,6,8,2,1,5,7,3]=>1000011=>1100001
[6,8,2,1,3,5,7,4]=>1000011=>1100001
[1,8,2,3,5,7,4,6]=>0000011=>1100000
[2,7,3,6,1,4,5,8]=>0000110=>0110000
[2,6,1,3,5,8,4,7]=>0000101=>1010000
[7,3,2,5,6,1,4,8]=>0100110=>0110010
[4,7,5,2,6,1,3,8]=>0001110=>0111000
[4,6,2,8,1,5,3,7]=>0001101=>1011000
[8,4,1,2,7,5,3,6]=>0011011=>1101100
[4,5,6,2,7,1,3,8]=>0000110=>0110000
[8,5,1,2,6,3,4,7]=>0001101=>1011000
[1,6,2,7,4,8,3,5]=>0000111=>1110000
[6,2,1,7,8,5,3,4]=>1001101=>1011001
[6,7,3,8,4,1,5,2]=>0011011=>1101100
[2,7,8,4,1,5,6,3]=>0010101=>1010100
[2,7,1,8,5,6,3,4]=>0000111=>1110000
[8,2,5,1,6,7,3,4]=>0001011=>1101000
[8,2,4,5,1,6,7,3]=>0001011=>1101000
[3,8,4,5,6,1,7,2]=>0000111=>1110000
[4,5,8,3,6,7,1,2]=>0000011=>1100000
[4,5,8,3,7,6,1,2]=>0000111=>1110000
[4,2,8,3,7,1,6,5]=>0010111=>1110100
[7,2,3,4,8,1,6,5]=>0000111=>1110000
[7,2,3,4,8,1,5,6]=>0000011=>1100000
[7,6,3,4,8,5,1,2]=>0001111=>1111000
[7,6,3,5,8,4,1,2]=>0010111=>1110100
[7,6,3,8,4,5,1,2]=>0001111=>1111000
[7,2,3,8,5,1,4,6]=>0001011=>1101000
[7,2,3,8,5,1,6,4]=>0001111=>1111000
[2,6,4,8,1,5,7,3]=>0000111=>1110000
[7,2,3,8,4,1,5,6]=>0010011=>1100100
[7,2,3,5,8,1,4,6]=>0000011=>1100000
[7,8,2,3,6,1,4,5]=>0000101=>1010000
[7,8,2,3,6,1,5,4]=>0001101=>1011000
[4,2,6,3,7,1,5,8]=>0010110=>0110100
[7,2,3,5,8,1,6,4]=>0000111=>1110000
[7,2,3,8,4,1,6,5]=>0010111=>1110100
[2,6,4,8,1,3,7,5]=>0000111=>1110000
[3,6,4,8,1,7,5,2]=>0001111=>1111000
[7,6,5,1,2,3,8,4]=>0001111=>1111000
[7,6,5,1,4,2,8,3]=>0011111=>1111100
[2,6,4,5,1,8,7,3]=>0001111=>1111000
[3,5,6,4,1,2,7,8]=>0010100=>0010100
[7,8,5,4,1,2,6,3]=>0011101=>1011100
[3,5,6,4,1,2,8,7]=>0010101=>1010100
[7,6,5,1,4,2,3,8]=>0011110=>0111100
[7,6,5,1,2,4,3,8]=>0011110=>0111100
[7,6,5,1,2,4,8,3]=>0001111=>1111000
[7,6,5,1,3,2,8,4]=>0101111=>1111010
[7,6,5,1,3,2,4,8]=>0101110=>0111010
[7,6,5,1,3,4,2,8]=>0011110=>0111100
[7,2,3,4,5,1,8,6]=>0001011=>1101000
[2,6,4,3,1,5,8,7]=>0110101=>1010110
[2,6,4,3,1,8,5,7]=>0110101=>1010110
[2,6,4,3,1,8,7,5]=>0110111=>1110110
[3,5,8,4,1,2,7,6]=>0010011=>1100100
[3,5,8,4,1,2,6,7]=>0010001=>1000100
[3,5,8,4,1,6,2,7]=>0010101=>1010100
[4,2,8,3,6,1,7,5]=>0010111=>1110100
[3,5,8,4,1,6,7,2]=>0010011=>1100100
[2,5,8,4,1,7,3,6]=>0010011=>1100100
[3,6,4,2,1,7,8,5]=>1010101=>1010101
[3,6,4,2,1,7,5,8]=>1010110=>0110101
[3,5,6,4,1,8,7,2]=>0010111=>1110100
[2,6,4,5,1,3,7,8]=>0001100=>0011000
[7,6,5,1,4,3,8,2]=>0011111=>1111100
[7,6,5,1,2,8,4,3]=>0011111=>1111100
[7,6,5,1,2,8,3,4]=>0001111=>1111000
[7,6,5,1,8,2,4,3]=>0011111=>1111100
[7,6,5,1,8,2,3,4]=>0001111=>1111000
[7,6,5,1,8,3,2,4]=>0101111=>1111010
[7,6,5,1,4,8,2,3]=>0001111=>1111000
[3,6,4,5,1,7,2,8]=>0001110=>0111000
[2,5,6,4,1,7,8,3]=>0010101=>1010100
[7,8,5,4,1,6,3,2]=>0111101=>1011110
[2,5,6,4,1,7,3,8]=>0010110=>0110100
[3,6,4,5,1,7,8,2]=>0001101=>1011000
[7,6,5,1,4,8,3,2]=>0101111=>1111010
[7,6,5,1,8,3,4,2]=>0011111=>1111100
[7,6,5,1,8,4,2,3]=>0011111=>1111100
[4,1,7,6,2,8,5,3]=>0011111=>1111100
[7,8,6,2,1,3,5,4]=>1001101=>1011001
[3,7,6,1,2,8,4,5]=>0000111=>1110000
[2,6,5,3,1,4,8,7]=>0101101=>1011010
[4,6,1,5,3,2,8,7]=>0101101=>1011010
[3,6,1,4,2,5,8,7]=>0010101=>1010100
[2,6,4,5,7,8,1,3]=>0000101=>1010000
[8,7,1,6,5,2,4,3]=>0011111=>1111100
[7,2,5,6,8,1,3,4]=>0000011=>1100000
[6,1,3,4,2,8,7,5]=>0010111=>1110100
[2,4,5,6,1,8,7,3]=>0000111=>1110000
[8,4,1,6,5,7,3,2]=>0110111=>1110110
[2,8,3,4,7,5,1,6]=>0001011=>1101000
[6,8,2,7,4,3,5,1]=>0011011=>1101100
[4,7,8,5,1,6,3,2]=>0101101=>1011010
[8,2,6,4,7,3,5,1]=>0001111=>1111000
[4,8,6,1,7,3,2,5]=>0100111=>1110010
[8,7,3,2,1,5,4,6]=>1101011=>1101011
[3,8,5,1,7,2,4,6]=>0001011=>1101000
[6,8,7,1,3,2,4,5]=>0100011=>1100010
[2,5,1,8,7,4,6,3]=>0001111=>1111000
[3,7,1,8,4,5,6,2]=>0000111=>1110000
[6,2,3,8,4,7,5,1]=>0001111=>1111000
[8,6,4,3,1,7,2,5]=>0110111=>1110110
[8,3,7,4,6,1,2,5]=>0000111=>1110000
[7,1,3,8,6,4,5,2]=>0001111=>1111000
[2,3,5,8,6,7,4,1]=>0010011=>1100100
[7,4,2,1,8,6,5,3]=>1011111=>1111101
[4,6,7,2,5,8,3,1]=>0100011=>1100010
[7,6,2,5,3,8,1,4]=>0001111=>1111000
[6,2,1,3,4,8,7,5]=>1000111=>1110001
[6,5,4,2,8,3,1,7]=>0111101=>1011110
[5,4,3,1,8,7,2,6]=>0111011=>1101110
[6,1,4,3,8,5,2,7]=>0011101=>1011100
[4,7,6,2,8,1,5,3]=>0001111=>1111000
[6,4,5,1,7,8,3,2]=>0101101=>1011010
[4,2,3,1,7,8,6,5]=>0110101=>1010110
[3,4,2,1,8,6,7,5]=>1010011=>1100101
[2,7,6,8,1,5,3,4]=>0001011=>1101000
[6,4,5,8,3,1,2,7]=>0100101=>1010010
[8,1,3,2,5,6,7,4]=>0100011=>1100010
[3,6,8,1,5,2,4,7]=>0001001=>1001000
[3,2,8,7,4,5,1,6]=>0101011=>1101010
[6,3,8,5,7,4,2,1]=>1010111=>1110101
[7,4,6,8,5,1,2,3]=>0001011=>1101000
[2,1,4,8,7,5,3,6]=>1001011=>1101001
[2,1,6,8,3,7,5,4]=>1001011=>1101001
[3,6,8,2,4,1,5,7]=>0010001=>1000100
[6,2,8,1,7,5,4,3]=>0011111=>1111100
[2,6,5,4,8,1,3,7]=>0001101=>1011000
[6,5,3,4,8,1,7,2]=>0001111=>1111000
[8,4,3,2,5,1,7,6]=>0111011=>1101110
[4,2,8,1,5,3,6,7]=>0011001=>1001100
[5,1,8,2,6,4,3,7]=>0011101=>1011100
[7,4,8,6,2,1,3,5]=>1000111=>1110001
[4,6,2,8,3,7,5,1]=>0001111=>1111000
[2,1,5,8,3,6,4,7]=>1000101=>1010001
[2,8,5,3,6,7,1,4]=>0001011=>1101000
[7,8,5,6,4,1,3,2]=>0110101=>1010110
[5,8,4,1,6,3,7,2]=>0010111=>1110100
[4,8,1,3,5,7,6,2]=>0000111=>1110000
[3,8,1,4,5,6,2,7]=>0000101=>1010000
[9,7,8,5,6,3,1,4,2]=>01101011=>11010110
[9,7,8,5,3,6,1,4,2]=>00111011=>11011100
[9,7,5,8,3,6,1,4,2]=>00101111=>11110100
[7,9,5,8,3,6,1,4,2]=>00101011=>11010100
[7,6,8,3,5,1,4,2]=>0011011=>1101100
[8,9,5,7,3,6,1,4,2]=>00101101=>10110100
[8,9,6,7,3,5,1,4,2]=>00110101=>10101100
[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]=>011010101=>101010110
[9,7,8,5,3,1,6,4,2]=>01111011=>11011110
[9,10,7,8,5,3,6,1,4,2]=>001110101=>101011100
[9,7,5,3,8,6,1,4,2]=>00111111=>11111100
[9,10,7,5,8,3,6,1,4,2]=>001011101=>101110100
[7,5,9,8,3,6,1,4,2]=>00101111=>11110100
[9,7,10,5,8,3,6,1,4,2]=>001010111=>111010100
[7,8,6,3,5,1,4,2]=>0011101=>1011100
[5,3,8,7,6,1,4,2]=>0011111=>1111100
[9,8,5,7,3,6,1,4,2]=>00101111=>11110100
[10,7,9,5,8,3,6,1,4,2]=>001010111=>111010100
[7,9,6,8,3,5,1,4,2]=>00110011=>11001100
[10,8,9,5,7,3,6,1,4,2]=>001011011=>110110100
[6,5,8,4,7,1,3,2]=>0100111=>1110010
[8,9,5,7,4,6,1,3,2]=>01001101=>10110010
[10,8,9,6,7,3,5,1,4,2]=>001101011=>110101100
[8,9,6,7,3,5,2,4,1]=>00110101=>10101100
[10,8,9,6,7,4,5,1,3,2]=>010101011=>110101010
[6,7,4,2,5,3,1,8]=>0111010=>0101110
[7,6,4,8,3,1,5,2]=>0101111=>1111010
[7,4,8,5,6,1,3,2]=>0100111=>1110010
[7,4,2,5,6,3,1,8]=>0110110=>0110110
[4,2,7,5,6,3,1,8]=>0110110=>0110110
[3,4,7,5,6,2,1,8]=>1000110=>0110001
[4,7,3,5,6,2,1,8]=>1000110=>0110001
[3,7,2,5,6,4,1,8]=>0010110=>0110100
[7,8,3,5,6,1,4,2]=>0010101=>1010100
[1,6,8,5,2,7,4,3]=>0011011=>1101100
[6,2,8,5,1,7,4,3]=>0011111=>1111100
[6,7,4,8,2,1,5,3]=>1001011=>1101001
[3,2,7,8,6,1,5,4]=>0101101=>1011010
[6,8,4,1,2,3,7,5]=>0010011=>1100100
[4,1,8,5,6,3,2,7]=>0110101=>1010110
[1,8,2,5,6,4,3,7]=>0010101=>1010100
[6,1,8,5,3,7,4,2]=>0011111=>1111100
[3,8,1,5,2,7,6,4]=>0001111=>1111000
[8,2,1,5,3,7,6,4]=>1001111=>1111001
[1,5,2,4,6,7,8,3]=>0001001=>1001000
[4,1,5,3,6,7,8,2]=>0011001=>1001100
[8,1,6,5,3,7,2,4]=>0001111=>1111000
[7,1,4,6,3,2,8,5]=>0100111=>1110010
[3,2,6,4,1,7,8,5]=>0110101=>1010110
[7,6,4,3,1,2,8,5]=>0110111=>1110110
[8,6,3,5,1,7,2,4]=>0001111=>1111000
[4,5,3,1,6,7,8,2]=>0101001=>1001010
[3,5,2,1,6,7,8,4]=>1001001=>1001001
[5,2,3,1,6,7,8,4]=>0101001=>1001010
[1,5,3,2,6,7,8,4]=>0101001=>1001010
[8,4,6,5,1,7,2,3]=>0001111=>1111000
[7,5,4,6,1,2,8,3]=>0001111=>1111000
[3,2,5,6,1,7,8,4]=>0100101=>1010010
[3,2,8,7,6,1,4,5]=>0100111=>1110010
[6,8,4,7,2,1,3,5]=>1000011=>1100001
[3,8,7,5,6,1,2,4]=>0000111=>1110000
[8,2,7,5,6,1,3,4]=>0000111=>1110000
[4,8,6,5,1,7,3,2]=>0101111=>1111010
[1,7,4,6,2,3,8,5]=>0000111=>1110000
[7,6,4,2,1,5,8,3]=>1010111=>1110101
[5,7,4,6,1,3,8,2]=>0000111=>1110000
[8,6,4,7,3,1,2,5]=>0100111=>1110010
[5,2,4,3,7,1,8,6]=>0011011=>1101100
[3,5,4,2,7,1,8,6]=>0011011=>1101100
[8,6,4,1,3,5,2,7]=>0011101=>1011100
[6,7,4,1,5,3,8,2]=>0011011=>1101100
[7,5,4,1,2,6,8,3]=>0011011=>1101100
[1,7,4,2,3,6,8,5]=>0010011=>1100100
[1,8,2,5,3,7,6,4]=>0001111=>1111000
[6,8,1,5,4,7,3,2]=>0101011=>1101010
[8,2,1,5,6,4,3,7]=>1010101=>1010101
[3,8,1,5,6,4,2,7]=>0010101=>1010100
[6,8,4,1,2,5,3,7]=>0011001=>1001100
[3,2,8,1,6,5,4,7]=>0101101=>1011010
[3,2,6,1,5,7,8,4]=>0100101=>1010010
[7,6,4,1,5,2,8,3]=>0011111=>1111100
[8,6,1,5,4,7,2,3]=>0001111=>1111000
[3,5,1,4,6,7,8,2]=>0001001=>1001000
[5,2,1,4,6,7,8,3]=>1001001=>1001001
[5,4,1,3,6,7,8,2]=>0011001=>1001100
[8,4,1,5,3,7,2,6]=>0011011=>1101100
[7,5,4,1,3,2,8,6]=>0111011=>1101110
[3,2,5,1,4,7,8,6]=>0101001=>1001010
[7,1,4,3,5,2,8,6]=>0011011=>1101100
[8,1,3,5,4,7,2,6]=>0001011=>1101000
[5,1,3,4,6,7,8,2]=>0001001=>1001000
[3,1,8,2,5,7,4,6]=>0100011=>1100010
[8,3,2,6,1,4,7,5]=>0100111=>1110010
[2,8,1,6,4,3,7,5]=>0010111=>1110100
[2,6,1,3,8,7,5,4]=>0001111=>1111000
[2,5,7,1,3,8,6,4]=>0000111=>1110000
[2,6,8,1,5,7,4,3]=>0010011=>1100100
[2,7,1,5,8,4,6,3]=>0000111=>1110000
[2,7,1,6,4,8,3,5]=>0000111=>1110000
[2,7,1,6,5,3,8,4]=>0001111=>1111000
[2,8,1,7,6,5,4,3]=>0011111=>1111100
[8,3,2,7,1,6,5,4]=>0101111=>1111010
[4,1,8,7,3,2,6,5]=>0110111=>1110110
[4,1,7,2,8,6,5,3]=>0011111=>1111100
[3,7,1,8,6,5,4,2]=>0011111=>1111100
[3,7,6,1,4,2,5,8]=>0010110=>0110100
[3,7,5,1,4,6,8,2]=>0001011=>1101000
[3,6,8,5,1,4,7,2]=>0001011=>1101000
[7,3,5,8,2,1,4,6]=>1000011=>1100001
[7,3,6,2,1,4,5,8]=>1000110=>0110001
[7,3,6,2,1,5,4,8]=>1001110=>0111001
[7,4,2,8,1,6,5,3]=>0011111=>1111100
[8,7,5,3,2,1,6,4]=>1101111=>1111011
[7,5,2,6,3,1,4,8]=>0101110=>0111010
[7,4,6,2,1,8,3,5]=>1000111=>1110001
[6,8,4,5,2,1,7,3]=>1001011=>1101001
[4,6,8,5,1,7,3,2]=>0101011=>1101010
[4,7,5,1,3,8,6,2]=>0001111=>1111000
[4,7,6,1,5,3,2,8]=>0101110=>0111010
[5,1,7,6,3,8,2,4]=>0001111=>1111000
[5,1,7,6,4,2,8,3]=>0011111=>1111100
[5,1,8,7,6,4,3,2]=>0111111=>1111110
[8,5,2,1,7,6,4,3]=>1011111=>1111101
[8,5,2,1,6,3,7,4]=>1001111=>1111001
[5,1,8,6,3,2,7,4]=>0101111=>1111010
[3,6,1,7,4,8,2,5]=>0000111=>1110000
[4,1,8,6,3,7,2,5]=>0010111=>1110100
[8,4,2,5,7,3,1,6]=>0110011=>1100110
[3,4,6,8,5,7,1,2]=>0000011=>1100000
[5,4,8,2,7,3,6,1]=>0001111=>1111000
[5,4,8,7,3,6,1,2]=>0001111=>1111000
[8,5,4,7,3,6,2,1]=>1001111=>1111001
[6,4,3,8,7,1,2,5]=>0010111=>1110100
[6,3,7,2,4,8,1,5]=>0000111=>1110000
[5,6,8,4,2,7,3,1]=>0110011=>1100110
[5,7,4,2,8,1,3,6]=>0010011=>1100100
[6,5,2,7,1,3,8,4]=>0001111=>1111000
[8,6,5,4,2,1,7,3]=>1011111=>1111101
[6,4,7,3,1,8,2,5]=>0100111=>1110010
[5,7,4,3,8,6,1,2]=>0010111=>1110100
[7,5,8,4,6,3,2,1]=>1100111=>1110011
[7,6,4,8,3,5,2,1]=>1001111=>1111001
[7,6,5,3,8,2,4,1]=>0011111=>1111100
[6,5,4,3,2,1,9,8,7]=>11111011=>11011111
[6,5,4,3,2,1,8,7,9]=>11111010=>01011111
[5,4,3,2,1,9,8,7,6]=>11110111=>11101111
[5,4,3,2,1,8,7,6,9]=>11110110=>01101111
[5,4,3,2,1,7,6,9,8]=>11110101=>10101111
[5,4,3,2,1,7,6,8,9]=>11110100=>00101111
[4,3,2,1,8,7,6,5,9]=>11101110=>01110111
[4,3,2,1,7,6,5,9,8]=>11101101=>10110111
[4,3,2,1,7,6,5,8,9]=>11101100=>00110111
[4,3,2,1,6,5,8,7,9]=>11101010=>01010111
[4,3,2,1,6,5,7,8,9]=>11101000=>00010111
[3,2,1,6,5,4,8,7,9]=>11011010=>01011011
[3,2,1,6,5,4,7,8,9]=>11011000=>00011011
[3,2,1,5,4,7,6,9,8]=>11010101=>10101011
[3,2,1,5,4,7,6,8,9]=>11010100=>00101011
[3,2,1,5,4,6,7,8,9]=>11010000=>00001011
[2,1,4,3,6,5,7,8,9]=>10101000=>00010101
[2,1,4,3,5,6,7,8,9]=>10100000=>00000101
[7,6,5,4,3,2,1,10,9,8]=>111111011=>110111111
[7,6,5,4,3,2,1,9,8,10]=>111111010=>010111111
[6,5,4,3,2,1,9,8,7,10]=>111110110=>011011111
[6,5,4,3,2,1,8,7,9,10]=>111110100=>001011111
[5,4,3,2,1,9,8,7,6,10]=>111101110=>011101111
[5,4,3,2,1,8,7,6,10,9]=>111101101=>101101111
[5,4,3,2,1,8,7,6,9,10]=>111101100=>001101111
[5,4,3,2,1,7,6,9,8,10]=>111101010=>010101111
[5,4,3,2,1,7,6,8,9,10]=>111101000=>000101111
[4,3,2,1,8,7,6,5,9,10]=>111011100=>001110111
[4,3,2,1,7,6,5,10,9,8]=>111011011=>110110111
[4,3,2,1,7,6,5,8,9,10]=>111011000=>000110111
[4,3,2,1,6,5,8,7,9,10]=>111010100=>001010111
[4,3,2,1,6,5,7,8,9,10]=>111010000=>000010111
[3,2,1,6,5,4,9,8,7,10]=>110110110=>011011011
[3,2,1,6,5,4,8,7,10,9]=>110110101=>101011011
[3,2,1,6,5,4,8,7,9,10]=>110110100=>001011011
[3,2,1,6,5,4,7,8,9,10]=>110110000=>000011011
[3,2,1,5,4,7,6,9,8,10]=>110101010=>010101011
[3,2,1,5,4,7,6,8,9,10]=>110101000=>000101011
[3,2,1,5,4,6,7,8,9,10]=>110100000=>000001011
[2,1,4,3,6,5,8,7,9,10]=>101010100=>001010101
[2,1,4,3,6,5,7,8,9,10]=>101010000=>000010101
[2,1,4,3,5,6,7,8,9,10]=>101000000=>000000101
[5,6,3,7,4,2,1,8]=>1010110=>0110101
[7,6,3,8,5,1,4,2]=>0011111=>1111100
[6,4,8,1,3,2,5,7]=>0100101=>1010010
[7,4,8,6,3,1,5,2]=>0101111=>1111010
[4,2,7,6,5,3,1,8]=>0111110=>0111110
[3,7,2,4,6,5,1,8]=>0001110=>0111000
[8,1,3,4,5,2,6,7]=>0001001=>1001000
[1,6,8,4,2,5,3,7]=>0011001=>1001100
[6,2,8,4,1,5,7,3]=>0010111=>1110100
[6,7,4,8,5,1,2,3]=>0001011=>1101000
[3,2,7,8,5,1,6,4]=>0101101=>1011010
[3,2,8,1,5,4,6,7]=>0101001=>1001010
[6,1,4,8,5,3,7,2]=>0001111=>1111000
[1,4,8,5,2,6,7,3]=>0001011=>1101000
[6,1,8,4,3,7,2,5]=>0010111=>1110100
[3,7,1,4,2,5,8,6]=>0010011=>1100100
[7,2,1,4,3,5,6,8]=>1010010=>0100101
[4,1,5,3,6,8,2,7]=>0011001=>1001100
[6,1,8,5,3,2,7,4]=>0101111=>1111010
[7,1,4,6,3,8,5,2]=>0001111=>1111000
[3,2,6,4,1,8,7,5]=>0110111=>1110110
[7,6,4,3,1,8,2,5]=>0110111=>1110110
[3,5,2,1,8,7,6,4]=>1001111=>1111001
[1,5,3,2,8,6,4,7]=>0101101=>1011010
[5,4,2,1,7,8,6,3]=>1011101=>1011101
[8,2,7,6,5,1,3,4]=>0001111=>1111000
[8,6,2,7,1,4,5,3]=>0001111=>1111000
[1,7,3,6,2,8,5,4]=>0001111=>1111000
[7,6,3,2,1,8,5,4]=>1101111=>1111011
[8,6,3,7,4,1,2,5]=>0010111=>1110100
[5,2,3,4,7,1,8,6]=>0001011=>1101000
[8,6,3,1,4,5,7,2]=>0100111=>1110010
[6,7,3,1,5,4,2,8]=>0111010=>0101110
[5,8,3,1,2,4,7,6]=>0100011=>1100010
[8,1,3,2,4,5,6,7]=>0100001=>1000010
[8,4,1,7,2,3,6,5]=>0010111=>1110100
[8,2,1,6,5,4,7,3]=>1001111=>1111001
[3,8,1,5,6,4,7,2]=>0000111=>1110000
[6,8,4,1,2,5,7,3]=>0010011=>1100100
[3,2,8,1,6,5,7,4]=>0100111=>1110010
[7,6,4,1,5,2,3,8]=>0011110=>0111100
[8,6,1,5,4,7,3,2]=>0101111=>1111010
[3,5,1,4,6,7,2,8]=>0001010=>0101000
[5,2,1,4,7,6,3,8]=>1001110=>0111001
[4,5,8,2,1,3,7,6]=>1000011=>1100001
[5,8,2,3,1,4,6,7]=>0100001=>1000010
[4,2,1,3,5,8,7,6]=>1010011=>1100101
[5,4,1,3,6,2,8,7]=>0011101=>1011100
[8,5,4,1,3,6,2,7]=>0011101=>1011100
[3,2,5,1,4,6,8,7]=>0101001=>1001010
[8,1,4,3,5,6,7,2]=>0010011=>1100100
[7,1,3,5,4,6,2,8]=>0001110=>0111000
[5,1,3,4,6,2,7,8]=>0001100=>0011000
[4,1,3,2,5,7,6,8]=>0110010=>0100110
[3,1,4,2,6,5,8,7,9]=>01101010=>01010110
[3,1,5,2,6,4,8,7,9]=>01011010=>01011010
[3,1,5,2,7,4,8,6,9]=>01010110=>01101010
[3,1,5,2,7,4,6,9,8]=>01010101=>10101010
[3,1,5,2,4,7,6,9,8]=>01010101=>10101010
[3,1,2,5,4,7,6,9,8]=>01010101=>10101010
[3,1,4,2,6,5,8,7,10,9]=>011010101=>101010110
[4,1,5,2,6,3,8,7,9]=>00111010=>01011100
[3,1,5,2,6,4,8,7,10,9]=>010110101=>101011010
[3,1,6,2,7,4,8,5,9]=>01001110=>01110010
[3,1,5,2,7,4,8,6,10,9]=>010101101=>101101010
[3,1,5,2,8,4,9,6,7]=>01010011=>11001010
[3,1,5,2,7,4,9,6,10,8]=>010101011=>110101010
[3,1,5,2,7,4,6,8,9]=>01010100=>00101010
[3,1,5,2,7,4,9,6,8,10]=>010101010=>010101010
[3,1,5,2,4,7,9,6,8]=>01010001=>10001010
[3,1,5,2,7,4,6,9,8,10]=>010101010=>010101010
[3,1,2,5,7,4,6,9,8]=>01000101=>10100010
[3,1,5,2,4,7,6,9,8,10]=>010101010=>010101010
[1,3,5,2,4,7,6,9,8]=>00010101=>10101000
[3,1,2,5,4,7,6,9,8,10]=>010101010=>010101010
[6,8,2,4,5,1,3,7]=>0001001=>1001000
[3,6,7,2,5,1,4,8]=>0001010=>0101000
[4,6,7,3,1,5,2,8]=>0101010=>0101010
[5,8,1,2,4,7,3,6]=>0000011=>1100000
[6,8,1,3,5,2,7,4]=>0001011=>1101000
[6,8,3,1,4,5,7,2]=>0100011=>1100010
[7,5,1,8,2,3,6,4]=>0001111=>1111000
[6,1,8,2,3,4,7,5]=>0000111=>1110000
[5,3,8,4,2,6,7,1]=>0011011=>1101100
[5,1,8,4,6,3,7,2]=>0001111=>1111000
[4,1,8,3,5,7,2,6]=>0010011=>1100100
[3,4,7,2,6,1,8,5]=>0000111=>1110000
[4,5,7,3,2,6,8,1]=>0100011=>1100010
[4,5,7,2,3,6,8,1]=>0000011=>1100000
[2,6,3,4,7,5,8,1]=>0000111=>1110000
[3,6,4,2,7,5,8,1]=>0010111=>1110100
[4,5,2,7,1,6,8,3]=>0001011=>1101000
[3,4,1,6,5,8,2,7]=>0010101=>1010100
[4,1,2,8,5,7,3,6]=>0010011=>1100100
[5,1,4,8,6,2,7,3]=>0001111=>1111000
[7,3,1,4,8,5,6,2]=>0100111=>1110010
[5,6,3,1,7,4,2,8]=>0110110=>0110110
[7,3,4,1,8,5,2,6]=>0011011=>1101100
[6,4,2,8,7,1,5,3]=>0011111=>1111100
[7,2,4,8,1,5,3,6]=>0001011=>1101000
[2,6,3,7,5,1,4,8]=>0001110=>0111000
[7,1,3,8,5,2,4,6]=>0001011=>1101000
[1,5,3,7,8,2,4,6]=>0001001=>1001000
[3,2,6,7,1,8,4,5]=>0100011=>1100010
[4,6,3,1,7,8,5,2]=>0101101=>1011010
[5,3,1,6,7,8,4,2]=>0111001=>1001110
[4,1,6,2,7,8,5,3]=>0011101=>1011100
[2,1,3,4,8,7,5,6]=>1000011=>1100001
[4,5,6,7,8,9,1,2,3]=>00000001=>10000000
[4,5,6,7,8,9,2,3,1]=>01000001=>10000010
[5,6,7,8,9,1,2,3,4]=>00000001=>10000000
[5,6,7,8,9,2,3,4,1]=>00100001=>10000100
[5,6,7,8,9,3,4,1,2]=>00100001=>10000100
[5,6,7,8,9,3,4,2,1]=>10100001=>10000101
[6,7,8,9,2,3,4,5,1]=>00010001=>10001000
[6,7,8,9,3,4,5,1,2]=>00010001=>10001000
[6,7,8,9,3,4,5,2,1]=>10010001=>10001001
[6,7,8,9,4,5,2,3,1]=>01010001=>10001010
[6,7,8,9,4,5,3,2,1]=>11010001=>10001011
[7,8,9,4,5,6,2,3,1]=>01001001=>10010010
[7,8,9,4,5,6,3,2,1]=>11001001=>10010011
[7,8,9,5,6,3,4,1,2]=>00101001=>10010100
[7,8,9,5,6,3,4,2,1]=>10101001=>10010101
[7,8,9,5,6,4,3,2,1]=>11101001=>10010111
[8,9,6,7,4,5,3,2,1]=>11010101=>10101011
[8,9,6,7,5,4,3,2,1]=>11110101=>10101111
[4,5,6,7,8,9,10,1,2,3]=>000000001=>100000000
[4,5,6,7,8,9,10,2,3,1]=>010000001=>100000010
[5,6,7,8,9,10,1,2,3,4]=>000000001=>100000000
[5,6,7,8,9,10,2,3,4,1]=>001000001=>100000100
[5,6,7,8,9,10,3,4,1,2]=>001000001=>100000100
[5,6,7,8,9,10,3,4,2,1]=>101000001=>100000101
[7,8,9,10,3,4,5,6,1,2]=>000010001=>100010000
[7,8,9,10,3,4,5,6,2,1]=>100010001=>100010001
[7,8,9,10,4,5,6,1,2,3]=>000010001=>100010000
[7,8,9,10,4,5,6,3,2,1]=>110010001=>100010011
[7,8,9,10,5,6,3,4,1,2]=>001010001=>100010100
[7,8,9,10,5,6,3,4,2,1]=>101010001=>100010101
[7,8,9,10,5,6,4,3,2,1]=>111010001=>100010111
[8,9,10,5,6,7,2,3,4,1]=>001001001=>100100100
[8,9,10,5,6,7,3,4,1,2]=>001001001=>100100100
[8,9,10,5,6,7,3,4,2,1]=>101001001=>100100101
[8,9,10,5,6,7,4,3,2,1]=>111001001=>100100111
[8,9,10,6,7,4,5,2,3,1]=>010101001=>100101010
[8,9,10,6,7,4,5,3,2,1]=>110101001=>100101011
[8,9,10,6,7,5,4,3,2,1]=>111101001=>100101111
[9,10,7,8,5,6,3,4,2,1]=>101010101=>101010101
[9,10,7,8,5,6,4,3,2,1]=>111010101=>101010111
[9,10,7,8,6,5,4,3,2,1]=>111110101=>101011111
[4,8,3,7,6,5,1,2]=>0001111=>1111000
[6,3,8,7,5,4,1,2]=>0011111=>1111100
[5,3,8,7,6,4,1,2]=>0011111=>1111100
[2,8,7,6,1,5,4,3]=>0011111=>1111100
[5,2,8,7,6,1,4,3]=>0011111=>1111100
[6,2,8,7,5,1,4,3]=>0011111=>1111100
[7,8,2,6,5,1,4,3]=>0011101=>1011100
[6,1,8,7,5,4,3,2]=>0111111=>1111110
[3,1,8,7,6,5,4,2]=>0111111=>1111110
[7,8,2,6,1,5,4,3]=>0011101=>1011100
[6,2,8,7,1,5,4,3]=>0011111=>1111100
[4,2,8,1,7,6,5,3]=>0011111=>1111100
[4,8,2,7,6,1,5,3]=>0001111=>1111000
[3,8,7,2,1,6,5,4]=>1001111=>1111001
[6,5,8,7,1,4,3,2]=>0110111=>1110110
[4,8,1,7,6,5,3,2]=>0101111=>1111010
[5,4,1,8,7,6,3,2]=>0111111=>1111110
[6,4,8,1,7,5,3,2]=>0101111=>1111010
[7,8,4,1,6,5,3,2]=>0111101=>1011110
[7,8,3,1,6,5,4,2]=>0111101=>1011110
[6,3,8,1,7,5,4,2]=>0011111=>1111100
[5,3,1,8,7,6,4,2]=>0111111=>1111110
[7,8,2,1,6,5,4,3]=>1011101=>1011101
[6,5,3,1,8,7,4,2]=>0111111=>1111110
[6,4,3,1,8,7,5,2]=>0111111=>1111110
[5,4,3,1,8,7,6,2]=>0111111=>1111110
[7,5,2,1,8,6,4,3]=>1011111=>1111101
[5,4,2,1,8,7,6,3]=>1011111=>1111101
[7,3,2,1,8,6,5,4]=>1101111=>1111011
[6,3,2,1,8,7,5,4]=>1101111=>1111011
[9,7,5,3,1,10,8,6,4,2]=>011111111=>111111110
[8,7,5,3,1,10,9,6,4,2]=>011111111=>111111110
[9,6,5,3,1,10,8,7,4,2]=>011111111=>111111110
[8,6,5,3,1,10,9,7,4,2]=>011111111=>111111110
[7,6,5,3,1,10,9,8,4,2]=>011111111=>111111110
[9,7,4,3,1,10,8,6,5,2]=>011111111=>111111110
[8,7,4,3,1,10,9,6,5,2]=>011111111=>111111110
[9,6,4,3,1,10,8,7,5,2]=>011111111=>111111110
[8,6,4,3,1,10,9,7,5,2]=>011111111=>111111110
[7,6,4,3,1,10,9,8,5,2]=>011111111=>111111110
[9,5,4,3,1,10,8,7,6,2]=>011111111=>111111110
[8,5,4,3,1,10,9,7,6,2]=>011111111=>111111110
[7,5,4,3,1,10,9,8,6,2]=>011111111=>111111110
[6,5,4,3,1,10,9,8,7,2]=>011111111=>111111110
[9,7,5,2,1,10,8,6,4,3]=>101111111=>111111101
[8,7,5,2,1,10,9,6,4,3]=>101111111=>111111101
[9,6,5,2,1,10,8,7,4,3]=>101111111=>111111101
[8,6,5,2,1,10,9,7,4,3]=>101111111=>111111101
[7,6,5,2,1,10,9,8,4,3]=>101111111=>111111101
[9,7,4,2,1,10,8,6,5,3]=>101111111=>111111101
[8,7,4,2,1,10,9,6,5,3]=>101111111=>111111101
[9,6,4,2,1,10,8,7,5,3]=>101111111=>111111101
[8,6,4,2,1,10,9,7,5,3]=>101111111=>111111101
[7,6,4,2,1,10,9,8,5,3]=>101111111=>111111101
[9,5,4,2,1,10,8,7,6,3]=>101111111=>111111101
[8,5,4,2,1,10,9,7,6,3]=>101111111=>111111101
[7,5,4,2,1,10,9,8,6,3]=>101111111=>111111101
[6,5,4,2,1,10,9,8,7,3]=>101111111=>111111101
[9,7,3,2,1,10,8,6,5,4]=>110111111=>111111011
[8,7,3,2,1,10,9,6,5,4]=>110111111=>111111011
[9,6,3,2,1,10,8,7,5,4]=>110111111=>111111011
[8,6,3,2,1,10,9,7,5,4]=>110111111=>111111011
[7,6,3,2,1,10,9,8,5,4]=>110111111=>111111011
[9,5,3,2,1,10,8,7,6,4]=>110111111=>111111011
[8,5,3,2,1,10,9,7,6,4]=>110111111=>111111011
[7,5,3,2,1,10,9,8,6,4]=>110111111=>111111011
[6,5,3,2,1,10,9,8,7,4]=>110111111=>111111011
[9,4,3,2,1,10,8,7,6,5]=>111011111=>111110111
[8,4,3,2,1,10,9,7,6,5]=>111011111=>111110111
[7,4,3,2,1,10,9,8,6,5]=>111011111=>111110111
[6,4,3,2,1,10,9,8,7,5]=>111011111=>111110111
[11,9,7,5,3,1,12,10,8,6,4,2]=>01111111111=>11111111110
[10,9,7,5,3,1,12,11,8,6,4,2]=>01111111111=>11111111110
[11,8,7,5,3,1,12,10,9,6,4,2]=>01111111111=>11111111110
[10,8,7,5,3,1,12,11,9,6,4,2]=>01111111111=>11111111110
[9,8,7,5,3,1,12,11,10,6,4,2]=>01111111111=>11111111110
[11,9,6,5,3,1,12,10,8,7,4,2]=>01111111111=>11111111110
[10,9,6,5,3,1,12,11,8,7,4,2]=>01111111111=>11111111110
[11,8,6,5,3,1,12,10,9,7,4,2]=>01111111111=>11111111110
[10,8,6,5,3,1,12,11,9,7,4,2]=>01111111111=>11111111110
[9,8,6,5,3,1,12,11,10,7,4,2]=>01111111111=>11111111110
[11,7,6,5,3,1,12,10,9,8,4,2]=>01111111111=>11111111110
[10,7,6,5,3,1,12,11,9,8,4,2]=>01111111111=>11111111110
[9,7,6,5,3,1,12,11,10,8,4,2]=>01111111111=>11111111110
[8,7,6,5,3,1,12,11,10,9,4,2]=>01111111111=>11111111110
[11,9,7,4,3,1,12,10,8,6,5,2]=>01111111111=>11111111110
[10,9,7,4,3,1,12,11,8,6,5,2]=>01111111111=>11111111110
[11,8,7,4,3,1,12,10,9,6,5,2]=>01111111111=>11111111110
[10,8,7,4,3,1,12,11,9,6,5,2]=>01111111111=>11111111110
[9,8,7,4,3,1,12,11,10,6,5,2]=>01111111111=>11111111110
[11,9,6,4,3,1,12,10,8,7,5,2]=>01111111111=>11111111110
[10,9,6,4,3,1,12,11,8,7,5,2]=>01111111111=>11111111110
[11,8,6,4,3,1,12,10,9,7,5,2]=>01111111111=>11111111110
[10,8,6,4,3,1,12,11,9,7,5,2]=>01111111111=>11111111110
[9,8,6,4,3,1,12,11,10,7,5,2]=>01111111111=>11111111110
[11,7,6,4,3,1,12,10,9,8,5,2]=>01111111111=>11111111110
[10,7,6,4,3,1,12,11,9,8,5,2]=>01111111111=>11111111110
[9,7,6,4,3,1,12,11,10,8,5,2]=>01111111111=>11111111110
[8,7,6,4,3,1,12,11,10,9,5,2]=>01111111111=>11111111110
[11,9,5,4,3,1,12,10,8,7,6,2]=>01111111111=>11111111110
[10,9,5,4,3,1,12,11,8,7,6,2]=>01111111111=>11111111110
[11,8,5,4,3,1,12,10,9,7,6,2]=>01111111111=>11111111110
[10,8,5,4,3,1,12,11,9,7,6,2]=>01111111111=>11111111110
[9,8,5,4,3,1,12,11,10,7,6,2]=>01111111111=>11111111110
[11,7,5,4,3,1,12,10,9,8,6,2]=>01111111111=>11111111110
[10,7,5,4,3,1,12,11,9,8,6,2]=>01111111111=>11111111110
[9,7,5,4,3,1,12,11,10,8,6,2]=>01111111111=>11111111110
[8,7,5,4,3,1,12,11,10,9,6,2]=>01111111111=>11111111110
[11,6,5,4,3,1,12,10,9,8,7,2]=>01111111111=>11111111110
[10,6,5,4,3,1,12,11,9,8,7,2]=>01111111111=>11111111110
[9,6,5,4,3,1,12,11,10,8,7,2]=>01111111111=>11111111110
[8,6,5,4,3,1,12,11,10,9,7,2]=>01111111111=>11111111110
[7,6,5,4,3,1,12,11,10,9,8,2]=>01111111111=>11111111110
[11,9,7,5,2,1,12,10,8,6,4,3]=>10111111111=>11111111101
[10,9,7,5,2,1,12,11,8,6,4,3]=>10111111111=>11111111101
[11,8,7,5,2,1,12,10,9,6,4,3]=>10111111111=>11111111101
[10,8,7,5,2,1,12,11,9,6,4,3]=>10111111111=>11111111101
[9,8,7,5,2,1,12,11,10,6,4,3]=>10111111111=>11111111101
[11,9,6,5,2,1,12,10,8,7,4,3]=>10111111111=>11111111101
[10,9,6,5,2,1,12,11,8,7,4,3]=>10111111111=>11111111101
[11,8,6,5,2,1,12,10,9,7,4,3]=>10111111111=>11111111101
[10,8,6,5,2,1,12,11,9,7,4,3]=>10111111111=>11111111101
[9,8,6,5,2,1,12,11,10,7,4,3]=>10111111111=>11111111101
[11,7,6,5,2,1,12,10,9,8,4,3]=>10111111111=>11111111101
[10,7,6,5,2,1,12,11,9,8,4,3]=>10111111111=>11111111101
[9,7,6,5,2,1,12,11,10,8,4,3]=>10111111111=>11111111101
[8,7,6,5,2,1,12,11,10,9,4,3]=>10111111111=>11111111101
[11,9,7,4,2,1,12,10,8,6,5,3]=>10111111111=>11111111101
[10,9,7,4,2,1,12,11,8,6,5,3]=>10111111111=>11111111101
[11,8,7,4,2,1,12,10,9,6,5,3]=>10111111111=>11111111101
[10,8,7,4,2,1,12,11,9,6,5,3]=>10111111111=>11111111101
[9,8,7,4,2,1,12,11,10,6,5,3]=>10111111111=>11111111101
[11,9,6,4,2,1,12,10,8,7,5,3]=>10111111111=>11111111101
[10,9,6,4,2,1,12,11,8,7,5,3]=>10111111111=>11111111101
[11,8,6,4,2,1,12,10,9,7,5,3]=>10111111111=>11111111101
[10,8,6,4,2,1,12,11,9,7,5,3]=>10111111111=>11111111101
[9,8,6,4,2,1,12,11,10,7,5,3]=>10111111111=>11111111101
[11,7,6,4,2,1,12,10,9,8,5,3]=>10111111111=>11111111101
[10,7,6,4,2,1,12,11,9,8,5,3]=>10111111111=>11111111101
[9,7,6,4,2,1,12,11,10,8,5,3]=>10111111111=>11111111101
[8,7,6,4,2,1,12,11,10,9,5,3]=>10111111111=>11111111101
[11,9,5,4,2,1,12,10,8,7,6,3]=>10111111111=>11111111101
[10,9,5,4,2,1,12,11,8,7,6,3]=>10111111111=>11111111101
[11,8,5,4,2,1,12,10,9,7,6,3]=>10111111111=>11111111101
[10,8,5,4,2,1,12,11,9,7,6,3]=>10111111111=>11111111101
[9,8,5,4,2,1,12,11,10,7,6,3]=>10111111111=>11111111101
[11,7,5,4,2,1,12,10,9,8,6,3]=>10111111111=>11111111101
[10,7,5,4,2,1,12,11,9,8,6,3]=>10111111111=>11111111101
[9,7,5,4,2,1,12,11,10,8,6,3]=>10111111111=>11111111101
[8,7,5,4,2,1,12,11,10,9,6,3]=>10111111111=>11111111101
[11,6,5,4,2,1,12,10,9,8,7,3]=>10111111111=>11111111101
[10,6,5,4,2,1,12,11,9,8,7,3]=>10111111111=>11111111101
[9,6,5,4,2,1,12,11,10,8,7,3]=>10111111111=>11111111101
[8,6,5,4,2,1,12,11,10,9,7,3]=>10111111111=>11111111101
[7,6,5,4,2,1,12,11,10,9,8,3]=>10111111111=>11111111101
[11,9,7,3,2,1,12,10,8,6,5,4]=>11011111111=>11111111011
[10,9,7,3,2,1,12,11,8,6,5,4]=>11011111111=>11111111011
[11,8,7,3,2,1,12,10,9,6,5,4]=>11011111111=>11111111011
[10,8,7,3,2,1,12,11,9,6,5,4]=>11011111111=>11111111011
[9,8,7,3,2,1,12,11,10,6,5,4]=>11011111111=>11111111011
[11,9,6,3,2,1,12,10,8,7,5,4]=>11011111111=>11111111011
[10,9,6,3,2,1,12,11,8,7,5,4]=>11011111111=>11111111011
[11,8,6,3,2,1,12,10,9,7,5,4]=>11011111111=>11111111011
[10,8,6,3,2,1,12,11,9,7,5,4]=>11011111111=>11111111011
[9,8,6,3,2,1,12,11,10,7,5,4]=>11011111111=>11111111011
[11,7,6,3,2,1,12,10,9,8,5,4]=>11011111111=>11111111011
[10,7,6,3,2,1,12,11,9,8,5,4]=>11011111111=>11111111011
[9,7,6,3,2,1,12,11,10,8,5,4]=>11011111111=>11111111011
[8,7,6,3,2,1,12,11,10,9,5,4]=>11011111111=>11111111011
[11,9,5,3,2,1,12,10,8,7,6,4]=>11011111111=>11111111011
[10,9,5,3,2,1,12,11,8,7,6,4]=>11011111111=>11111111011
[11,8,5,3,2,1,12,10,9,7,6,4]=>11011111111=>11111111011
[10,8,5,3,2,1,12,11,9,7,6,4]=>11011111111=>11111111011
[9,8,5,3,2,1,12,11,10,7,6,4]=>11011111111=>11111111011
[11,7,5,3,2,1,12,10,9,8,6,4]=>11011111111=>11111111011
[10,7,5,3,2,1,12,11,9,8,6,4]=>11011111111=>11111111011
[9,7,5,3,2,1,12,11,10,8,6,4]=>11011111111=>11111111011
[8,7,5,3,2,1,12,11,10,9,6,4]=>11011111111=>11111111011
[11,6,5,3,2,1,12,10,9,8,7,4]=>11011111111=>11111111011
[10,6,5,3,2,1,12,11,9,8,7,4]=>11011111111=>11111111011
[9,6,5,3,2,1,12,11,10,8,7,4]=>11011111111=>11111111011
[8,6,5,3,2,1,12,11,10,9,7,4]=>11011111111=>11111111011
[7,6,5,3,2,1,12,11,10,9,8,4]=>11011111111=>11111111011
[11,9,4,3,2,1,12,10,8,7,6,5]=>11101111111=>11111110111
[10,9,4,3,2,1,12,11,8,7,6,5]=>11101111111=>11111110111
[11,8,4,3,2,1,12,10,9,7,6,5]=>11101111111=>11111110111
[10,8,4,3,2,1,12,11,9,7,6,5]=>11101111111=>11111110111
[9,8,4,3,2,1,12,11,10,7,6,5]=>11101111111=>11111110111
[11,7,4,3,2,1,12,10,9,8,6,5]=>11101111111=>11111110111
[10,7,4,3,2,1,12,11,9,8,6,5]=>11101111111=>11111110111
[9,7,4,3,2,1,12,11,10,8,6,5]=>11101111111=>11111110111
[8,7,4,3,2,1,12,11,10,9,6,5]=>11101111111=>11111110111
[11,6,4,3,2,1,12,10,9,8,7,5]=>11101111111=>11111110111
[10,6,4,3,2,1,12,11,9,8,7,5]=>11101111111=>11111110111
[9,6,4,3,2,1,12,11,10,8,7,5]=>11101111111=>11111110111
[8,6,4,3,2,1,12,11,10,9,7,5]=>11101111111=>11111110111
[7,6,4,3,2,1,12,11,10,9,8,5]=>11101111111=>11111110111
[11,5,4,3,2,1,12,10,9,8,7,6]=>11110111111=>11111101111
[10,5,4,3,2,1,12,11,9,8,7,6]=>11110111111=>11111101111
[9,5,4,3,2,1,12,11,10,8,7,6]=>11110111111=>11111101111
[8,5,4,3,2,1,12,11,10,9,7,6]=>11110111111=>11111101111
[7,5,4,3,2,1,12,11,10,9,8,6]=>11110111111=>11111101111
[6,1,4,2,3,5,8,7]=>0010101=>1010100
[8,6,1,4,2,3,5,7]=>0010101=>1010100
[6,8,1,4,2,3,5,7]=>0010001=>1000100
[8,1,4,2,3,6,5,7]=>0010101=>1010100
[4,1,8,2,3,6,5,7]=>0010101=>1010100
[8,2,3,6,1,4,5,7]=>0000101=>1010000
[6,2,3,8,1,4,5,7]=>0000101=>1010000
[4,6,2,3,8,1,5,7]=>0000101=>1010000
[4,8,2,3,6,1,5,7]=>0000101=>1010000
[8,2,3,6,4,1,5,7]=>0010101=>1010100
[8,4,3,6,2,1,5,7]=>1010101=>1010101
[6,2,3,8,4,1,5,7]=>0010101=>1010100
[8,4,2,3,6,1,5,7]=>0010101=>1010100
[6,4,2,3,8,1,5,7]=>0010101=>1010100
[2,6,4,3,8,1,5,7]=>0010101=>1010100
[2,8,4,3,6,1,5,7]=>0010101=>1010100
[2,6,3,8,4,1,5,7]=>0010101=>1010100
[6,3,8,4,2,1,5,7]=>1010101=>1010101
[2,6,3,8,1,4,5,7]=>0000101=>1010000
[2,8,3,6,1,4,5,7]=>0000101=>1010000
[8,3,6,4,2,1,5,7]=>1010101=>1010101
[2,8,3,6,4,1,5,7]=>0010101=>1010100
[8,3,6,2,4,1,5,7]=>0010101=>1010100
[8,3,6,2,1,4,5,7]=>1000101=>1010001
[6,2,1,3,8,4,5,7]=>1000101=>1010001
[8,2,1,3,6,4,5,7]=>1000101=>1010001
[6,3,8,2,4,1,5,7]=>0010101=>1010100
[6,2,4,3,8,1,5,7]=>0010101=>1010100
[3,6,4,7,8,5,1,2]=>0001101=>1011000
[1,6,4,2,7,5,8,3]=>0010111=>1110100
[3,6,4,2,7,1,5,8]=>0010110=>0110100
[1,4,7,2,5,6,8,3]=>0000011=>1100000
[6,4,8,5,3,7,1,2]=>0001111=>1111000
[1,6,5,4,2,7,8,3]=>0011101=>1011100
[4,2,5,3,6,1,7,8]=>0011100=>0011100
[7,1,5,3,6,2,8,4]=>0001111=>1111000
[1,6,5,2,4,8,7,3]=>0001111=>1111000
[1,4,6,2,8,5,7,3]=>0000111=>1110000
[7,8,1,4,2,5,6,3]=>0010101=>1010100
[3,4,8,5,2,1,6,7]=>1001001=>1001001
[4,8,5,3,1,6,2,7]=>0101101=>1011010
[6,1,3,5,8,2,7,4]=>0000111=>1110000
[6,1,8,7,4,2,3,5]=>0010111=>1110100
[1,2,8,5,7,3,6,4]=>0000111=>1110000
[1,3,6,8,7,5,2,4]=>0001011=>1101000
[1,8,2,5,4,7,6,3]=>0001111=>1111000
[7,1,2,4,5,8,6,3]=>0000111=>1110000
[1,2,7,3,5,8,6,4]=>0000111=>1110000
[6,1,3,2,5,7,8,4]=>0100101=>1010010
[4,6,2,1,7,5,3,8]=>1001110=>0111001
[1,6,3,7,8,5,2,4]=>0001101=>1011000
[4,6,2,3,7,8,1,5]=>0000101=>1010000
[4,6,3,7,1,2,8,5]=>0000111=>1110000
[4,2,1,3,5,7,8,6]=>1010001=>1000101
[7,3,2,4,5,1,8,6]=>0101011=>1101010
[3,8,2,5,4,1,7,6]=>0011011=>1101100
[7,8,4,2,6,3,1,5]=>0110101=>1010110
[4,2,6,3,8,7,1,5]=>0010111=>1110100
[5,8,2,7,4,3,1,6]=>0110011=>1100110
[4,3,8,5,1,7,2,6]=>0011011=>1101100
[4,3,6,8,1,2,7,5]=>0010011=>1100100
[6,4,3,5,2,8,1,7]=>0011101=>1011100
[6,5,3,8,4,2,1,7]=>1011101=>1011101
[6,1,7,2,8,3,9,4,10,5]=>000011111=>111110000
[6,1,7,2,8,3,9,10,4,5]=>000011101=>101110000
[6,1,7,2,8,9,3,4,10,5]=>000011011=>110110000
[6,1,7,2,8,9,3,10,4,5]=>000011011=>110110000
[6,1,7,2,8,9,10,3,4,5]=>000011001=>100110000
[6,1,7,8,2,3,9,4,10,5]=>000010111=>111010000
[6,1,7,8,2,3,9,10,4,5]=>000010101=>101010000
[6,1,7,8,2,9,3,4,10,5]=>000010111=>111010000
[6,1,7,8,2,9,3,10,4,5]=>000010111=>111010000
[6,1,7,8,2,9,10,3,4,5]=>000010101=>101010000
[6,1,7,8,9,2,3,4,10,5]=>000010011=>110010000
[6,1,7,8,9,2,3,10,4,5]=>000010011=>110010000
[6,1,7,8,9,2,10,3,4,5]=>000010011=>110010000
[6,1,7,8,9,10,2,3,4,5]=>000010001=>100010000
[6,7,1,2,8,3,9,4,10,5]=>000001111=>111100000
[6,7,1,2,8,3,9,10,4,5]=>000001101=>101100000
[6,7,1,2,8,9,3,4,10,5]=>000001011=>110100000
[6,7,1,2,8,9,3,10,4,5]=>000001011=>110100000
[6,7,1,2,8,9,10,3,4,5]=>000001001=>100100000
[6,7,1,8,2,3,9,4,10,5]=>000001111=>111100000
[6,7,1,8,2,3,9,10,4,5]=>000001101=>101100000
[6,7,1,8,2,9,3,4,10,5]=>000001111=>111100000
[6,7,1,8,2,9,3,10,4,5]=>000001111=>111100000
[6,7,1,8,2,9,10,3,4,5]=>000001101=>101100000
[6,7,1,8,9,2,3,4,10,5]=>000001011=>110100000
[6,7,1,8,9,2,3,10,4,5]=>000001011=>110100000
[6,7,1,8,9,2,10,3,4,5]=>000001011=>110100000
[6,7,1,8,9,10,2,3,4,5]=>000001001=>100100000
[6,7,8,1,2,3,9,4,10,5]=>000000111=>111000000
[6,7,8,1,2,3,9,10,4,5]=>000000101=>101000000
[6,7,8,1,2,9,3,4,10,5]=>000000111=>111000000
[6,7,8,1,2,9,3,10,4,5]=>000000111=>111000000
[6,7,8,1,2,9,10,3,4,5]=>000000101=>101000000
[6,7,8,1,9,2,3,4,10,5]=>000000111=>111000000
[6,7,8,1,9,2,3,10,4,5]=>000000111=>111000000
[6,7,8,1,9,2,10,3,4,5]=>000000111=>111000000
[6,7,8,1,9,10,2,3,4,5]=>000000101=>101000000
[6,7,8,9,1,2,3,4,10,5]=>000000011=>110000000
[6,7,8,9,1,2,3,10,4,5]=>000000011=>110000000
[6,7,8,9,1,2,10,3,4,5]=>000000011=>110000000
[6,7,8,9,1,10,2,3,4,5]=>000000011=>110000000
[7,1,8,2,9,3,10,4,11,5,12,6]=>00000111111=>11111100000
[7,1,8,2,9,3,10,4,11,12,5,6]=>00000111101=>10111100000
[7,1,8,2,9,3,10,11,4,5,12,6]=>00000111011=>11011100000
[7,1,8,2,9,3,10,11,4,12,5,6]=>00000111011=>11011100000
[7,1,8,2,9,3,10,11,12,4,5,6]=>00000111001=>10011100000
[7,1,8,2,9,10,3,4,11,5,12,6]=>00000110111=>11101100000
[7,1,8,2,9,10,3,4,11,12,5,6]=>00000110101=>10101100000
[7,1,8,2,9,10,3,11,4,5,12,6]=>00000110111=>11101100000
[7,1,8,2,9,10,3,11,4,12,5,6]=>00000110111=>11101100000
[7,1,8,2,9,10,3,11,12,4,5,6]=>00000110101=>10101100000
[7,1,8,2,9,10,11,3,4,5,12,6]=>00000110011=>11001100000
[7,1,8,2,9,10,11,3,4,12,5,6]=>00000110011=>11001100000
[7,1,8,2,9,10,11,3,12,4,5,6]=>00000110011=>11001100000
[7,1,8,2,9,10,11,12,3,4,5,6]=>00000110001=>10001100000
[7,1,8,9,2,3,10,4,11,5,12,6]=>00000101111=>11110100000
[7,1,8,9,2,3,10,4,11,12,5,6]=>00000101101=>10110100000
[7,1,8,9,2,3,10,11,4,5,12,6]=>00000101011=>11010100000
[7,1,8,9,2,3,10,11,4,12,5,6]=>00000101011=>11010100000
[7,1,8,9,2,3,10,11,12,4,5,6]=>00000101001=>10010100000
[7,1,8,9,2,10,3,4,11,5,12,6]=>00000101111=>11110100000
[7,1,8,9,2,10,3,4,11,12,5,6]=>00000101101=>10110100000
[7,1,8,9,2,10,3,11,4,5,12,6]=>00000101111=>11110100000
[7,1,8,9,2,10,3,11,4,12,5,6]=>00000101111=>11110100000
[7,1,8,9,2,10,3,11,12,4,5,6]=>00000101101=>10110100000
[7,1,8,9,2,10,11,3,4,5,12,6]=>00000101011=>11010100000
[7,1,8,9,2,10,11,3,4,12,5,6]=>00000101011=>11010100000
[7,1,8,9,2,10,11,3,12,4,5,6]=>00000101011=>11010100000
[7,1,8,9,2,10,11,12,3,4,5,6]=>00000101001=>10010100000
[7,1,8,9,10,2,3,4,11,5,12,6]=>00000100111=>11100100000
[7,1,8,9,10,2,3,4,11,12,5,6]=>00000100101=>10100100000
[7,1,8,9,10,2,3,11,4,5,12,6]=>00000100111=>11100100000
[7,1,8,9,10,2,3,11,4,12,5,6]=>00000100111=>11100100000
[7,1,8,9,10,2,3,11,12,4,5,6]=>00000100101=>10100100000
[7,1,8,9,10,2,11,3,4,5,12,6]=>00000100111=>11100100000
[7,1,8,9,10,2,11,3,4,12,5,6]=>00000100111=>11100100000
[7,1,8,9,10,2,11,3,12,4,5,6]=>00000100111=>11100100000
[7,1,8,9,10,2,11,12,3,4,5,6]=>00000100101=>10100100000
[7,1,8,9,10,11,2,3,4,5,12,6]=>00000100011=>11000100000
[7,1,8,9,10,11,2,3,4,12,5,6]=>00000100011=>11000100000
[7,1,8,9,10,11,2,3,12,4,5,6]=>00000100011=>11000100000
[7,1,8,9,10,11,2,12,3,4,5,6]=>00000100011=>11000100000
[7,1,8,9,10,11,12,2,3,4,5,6]=>00000100001=>10000100000
[7,8,1,2,9,3,10,4,11,5,12,6]=>00000011111=>11111000000
[7,8,1,2,9,3,10,4,11,12,5,6]=>00000011101=>10111000000
[7,8,1,2,9,3,10,11,4,5,12,6]=>00000011011=>11011000000
[7,8,1,2,9,3,10,11,4,12,5,6]=>00000011011=>11011000000
[7,8,1,2,9,3,10,11,12,4,5,6]=>00000011001=>10011000000
[7,8,1,2,9,10,3,4,11,5,12,6]=>00000010111=>11101000000
[7,8,1,2,9,10,3,4,11,12,5,6]=>00000010101=>10101000000
[7,8,1,2,9,10,3,11,4,5,12,6]=>00000010111=>11101000000
[7,8,1,2,9,10,3,11,4,12,5,6]=>00000010111=>11101000000
[7,8,1,2,9,10,3,11,12,4,5,6]=>00000010101=>10101000000
[7,8,1,2,9,10,11,3,4,5,12,6]=>00000010011=>11001000000
[7,8,1,2,9,10,11,3,4,12,5,6]=>00000010011=>11001000000
[7,8,1,2,9,10,11,3,12,4,5,6]=>00000010011=>11001000000
[7,8,1,2,9,10,11,12,3,4,5,6]=>00000010001=>10001000000
[7,8,1,9,2,3,10,4,11,5,12,6]=>00000011111=>11111000000
[7,8,1,9,2,3,10,4,11,12,5,6]=>00000011101=>10111000000
[7,8,1,9,2,3,10,11,4,5,12,6]=>00000011011=>11011000000
[7,8,1,9,2,3,10,11,4,12,5,6]=>00000011011=>11011000000
[7,8,1,9,2,3,10,11,12,4,5,6]=>00000011001=>10011000000
[7,8,1,9,2,10,3,4,11,5,12,6]=>00000011111=>11111000000
[7,8,1,9,2,10,3,4,11,12,5,6]=>00000011101=>10111000000
[7,8,1,9,2,10,3,11,4,5,12,6]=>00000011111=>11111000000
[7,8,1,9,2,10,3,11,4,12,5,6]=>00000011111=>11111000000
[7,8,1,9,2,10,3,11,12,4,5,6]=>00000011101=>10111000000
[7,8,1,9,2,10,11,3,4,5,12,6]=>00000011011=>11011000000
[7,8,1,9,2,10,11,3,4,12,5,6]=>00000011011=>11011000000
[7,8,1,9,2,10,11,3,12,4,5,6]=>00000011011=>11011000000
[7,8,1,9,2,10,11,12,3,4,5,6]=>00000011001=>10011000000
[7,8,1,9,10,2,3,4,11,5,12,6]=>00000010111=>11101000000
[7,8,1,9,10,2,3,4,11,12,5,6]=>00000010101=>10101000000
[7,8,1,9,10,2,3,11,4,5,12,6]=>00000010111=>11101000000
[7,8,1,9,10,2,3,11,4,12,5,6]=>00000010111=>11101000000
[7,8,1,9,10,2,3,11,12,4,5,6]=>00000010101=>10101000000
[7,8,1,9,10,2,11,3,4,5,12,6]=>00000010111=>11101000000
[7,8,1,9,10,2,11,3,4,12,5,6]=>00000010111=>11101000000
[7,8,1,9,10,2,11,3,12,4,5,6]=>00000010111=>11101000000
[7,8,1,9,10,2,11,12,3,4,5,6]=>00000010101=>10101000000
[7,8,1,9,10,11,2,3,4,5,12,6]=>00000010011=>11001000000
[7,8,1,9,10,11,2,3,4,12,5,6]=>00000010011=>11001000000
[7,8,1,9,10,11,2,3,12,4,5,6]=>00000010011=>11001000000
[7,8,1,9,10,11,2,12,3,4,5,6]=>00000010011=>11001000000
[7,8,1,9,10,11,12,2,3,4,5,6]=>00000010001=>10001000000
[7,8,9,1,2,3,10,4,11,5,12,6]=>00000001111=>11110000000
[7,8,9,1,2,3,10,4,11,12,5,6]=>00000001101=>10110000000
[7,8,9,1,2,3,10,11,4,5,12,6]=>00000001011=>11010000000
[7,8,9,1,2,3,10,11,4,12,5,6]=>00000001011=>11010000000
[7,8,9,1,2,3,10,11,12,4,5,6]=>00000001001=>10010000000
[7,8,9,1,2,10,3,4,11,5,12,6]=>00000001111=>11110000000
[7,8,9,1,2,10,3,4,11,12,5,6]=>00000001101=>10110000000
[7,8,9,1,2,10,3,11,4,5,12,6]=>00000001111=>11110000000
[7,8,9,1,2,10,3,11,4,12,5,6]=>00000001111=>11110000000
[7,8,9,1,2,10,3,11,12,4,5,6]=>00000001101=>10110000000
[7,8,9,1,2,10,11,3,4,5,12,6]=>00000001011=>11010000000
[7,8,9,1,2,10,11,3,4,12,5,6]=>00000001011=>11010000000
[7,8,9,1,2,10,11,3,12,4,5,6]=>00000001011=>11010000000
[7,8,9,1,2,10,11,12,3,4,5,6]=>00000001001=>10010000000
[7,8,9,1,10,2,3,4,11,5,12,6]=>00000001111=>11110000000
[7,8,9,1,10,2,3,4,11,12,5,6]=>00000001101=>10110000000
[7,8,9,1,10,2,3,11,4,5,12,6]=>00000001111=>11110000000
[7,8,9,1,10,2,3,11,4,12,5,6]=>00000001111=>11110000000
[7,8,9,1,10,2,3,11,12,4,5,6]=>00000001101=>10110000000
[7,8,9,1,10,2,11,3,4,5,12,6]=>00000001111=>11110000000
[7,8,9,1,10,2,11,3,4,12,5,6]=>00000001111=>11110000000
[7,8,9,1,10,2,11,3,12,4,5,6]=>00000001111=>11110000000
[7,8,9,1,10,2,11,12,3,4,5,6]=>00000001101=>10110000000
[7,8,9,1,10,11,2,3,4,5,12,6]=>00000001011=>11010000000
[7,8,9,1,10,11,2,3,4,12,5,6]=>00000001011=>11010000000
[7,8,9,1,10,11,2,3,12,4,5,6]=>00000001011=>11010000000
[7,8,9,1,10,11,2,12,3,4,5,6]=>00000001011=>11010000000
[7,8,9,1,10,11,12,2,3,4,5,6]=>00000001001=>10010000000
[7,8,9,10,1,2,3,4,11,5,12,6]=>00000000111=>11100000000
[7,8,9,10,1,2,3,4,11,12,5,6]=>00000000101=>10100000000
[7,8,9,10,1,2,3,11,4,5,12,6]=>00000000111=>11100000000
[7,8,9,10,1,2,3,11,4,12,5,6]=>00000000111=>11100000000
[7,8,9,10,1,2,3,11,12,4,5,6]=>00000000101=>10100000000
[7,8,9,10,1,2,11,3,4,5,12,6]=>00000000111=>11100000000
[7,8,9,10,1,2,11,3,4,12,5,6]=>00000000111=>11100000000
[7,8,9,10,1,2,11,3,12,4,5,6]=>00000000111=>11100000000
[7,8,9,10,1,2,11,12,3,4,5,6]=>00000000101=>10100000000
[7,8,9,10,1,11,2,3,4,5,12,6]=>00000000111=>11100000000
[7,8,9,10,1,11,2,3,4,12,5,6]=>00000000111=>11100000000
[7,8,9,10,1,11,2,3,12,4,5,6]=>00000000111=>11100000000
[7,8,9,10,1,11,2,12,3,4,5,6]=>00000000111=>11100000000
[7,8,9,10,1,11,12,2,3,4,5,6]=>00000000101=>10100000000
[7,8,9,10,11,1,2,3,4,5,12,6]=>00000000011=>11000000000
[7,8,9,10,11,1,2,3,4,12,5,6]=>00000000011=>11000000000
[7,8,9,10,11,1,2,3,12,4,5,6]=>00000000011=>11000000000
[7,8,9,10,11,1,2,12,3,4,5,6]=>00000000011=>11000000000
[7,8,9,10,11,1,12,2,3,4,5,6]=>00000000011=>11000000000
[3,8,1,7,5,6,4,2]=>0010111=>1110100
[8,2,5,7,3,6,4,1]=>0010111=>1110100
[1,8,6,7,5,3,4,2]=>0011011=>1101100
[8,2,6,7,5,3,4,1]=>0011011=>1101100
[1,5,8,7,2,6,4,3]=>0010111=>1110100
[5,4,8,6,2,3,7,1]=>0001111=>1111000
[2,7,6,1,3,5,4,8]=>0001110=>0111000
[6,4,1,8,2,5,7,3]=>0010111=>1110100
[2,8,6,1,3,5,4,7]=>0001101=>1011000
[4,1,3,6,5,8,7,2]=>0010111=>1110100
[2,1,6,3,5,8,7,4]=>1000111=>1110001
[2,4,1,3,8,5,7,6]=>0010011=>1100100
[2,4,1,3,5,8,7,6]=>0010011=>1100100
[2,6,1,3,5,8,7,4]=>0000111=>1110000
[4,6,1,3,5,8,7,2]=>0000111=>1110000
[6,1,4,3,5,8,7,2]=>0010111=>1110100
[6,4,1,3,5,8,7,2]=>0010111=>1110100
[6,2,1,3,5,8,7,4]=>1000111=>1110001
[4,2,1,3,6,5,7,8]=>1010100=>0010101
[4,2,1,6,3,5,7,8]=>1010100=>0010101
[6,2,1,8,3,5,7,4]=>1000111=>1110001
[6,2,1,3,8,5,7,4]=>1000111=>1110001
[6,1,4,3,8,5,7,2]=>0010111=>1110100
[1,6,4,3,8,5,7,2]=>0010111=>1110100
[8,1,4,3,6,5,7,2]=>0010111=>1110100
[8,4,1,3,6,5,7,2]=>0010111=>1110100
[8,2,1,3,6,5,7,4]=>1000111=>1110001
[8,2,1,6,3,5,7,4]=>1000111=>1110001
[8,2,1,4,3,5,7,6]=>1010011=>1100101
[6,2,1,4,3,5,7,8]=>1010100=>0010101
[8,2,4,1,3,5,7,6]=>0010011=>1100100
[8,2,6,1,3,5,7,4]=>0000111=>1110000
[8,4,6,1,3,5,7,2]=>0000111=>1110000
[8,4,1,6,3,5,7,2]=>0010111=>1110100
[8,1,4,6,3,5,7,2]=>0000111=>1110000
[1,8,4,6,3,5,7,2]=>0000111=>1110000
[1,6,4,8,3,5,7,2]=>0000111=>1110000
[6,4,1,8,3,5,7,2]=>0010111=>1110100
[6,4,8,1,3,5,7,2]=>0000111=>1110000
[6,2,8,1,3,5,7,4]=>0000111=>1110000
[4,2,8,1,3,5,7,6]=>0010011=>1100100
[2,6,8,1,3,5,7,4]=>0000011=>1100000
[4,6,8,1,3,5,7,2]=>0000011=>1100000
[4,6,1,8,3,5,7,2]=>0000111=>1110000
[4,1,6,8,3,5,7,2]=>0010011=>1100100
[1,4,6,3,8,5,7,2]=>0000111=>1110000
[4,6,1,3,8,5,7,2]=>0000111=>1110000
[2,4,1,8,3,5,7,6]=>0010011=>1100100
[2,1,6,8,3,5,7,4]=>1000011=>1100001
[4,1,3,6,8,5,7,2]=>0010011=>1100100
[1,4,3,6,8,5,7,2]=>0010011=>1100100
[4,1,3,8,6,5,7,2]=>0010111=>1110100
[2,1,8,3,6,5,7,4]=>1000111=>1110001
[2,1,6,4,3,5,7,8]=>1010100=>0010101
[2,6,1,4,3,5,7,8]=>0010100=>0010100
[2,8,1,4,3,5,7,6]=>0010011=>1100100
[2,8,1,6,3,5,7,4]=>0000111=>1110000
[4,8,1,3,6,5,7,2]=>0000111=>1110000
[1,4,8,3,6,5,7,2]=>0000111=>1110000
[1,4,8,6,3,5,7,2]=>0000111=>1110000
[4,1,8,6,3,5,7,2]=>0010111=>1110100
[4,8,1,6,3,5,7,2]=>0000111=>1110000
[4,8,6,1,3,5,7,2]=>0000111=>1110000
[2,8,6,1,3,5,7,4]=>0000111=>1110000
[2,8,4,1,3,5,7,6]=>0010011=>1100100
[2,6,4,1,3,5,7,8]=>0010100=>0010100
[4,6,2,1,3,5,7,8]=>1000100=>0010001
[6,8,1,4,3,5,7,2]=>0010011=>1100100
[6,1,8,4,3,5,7,2]=>0010111=>1110100
[1,6,8,4,3,5,7,2]=>0010011=>1100100
[1,8,6,4,3,5,7,2]=>0010111=>1110100
[8,1,6,4,3,5,7,2]=>0010111=>1110100
[8,6,1,4,3,5,7,2]=>0010111=>1110100
[8,6,4,1,3,5,7,2]=>0010111=>1110100
[8,6,2,1,3,5,7,4]=>1000111=>1110001
[8,4,2,1,3,5,7,6]=>1010011=>1100101
[7,8,6,5,2,1,4,3]=>1011101=>1011101
[5,7,4,1,8,6,3,2]=>0110111=>1110110
[5,6,4,2,8,3,7,1]=>0010111=>1110100
[5,6,4,2,7,3,1,8]=>0110110=>0110110
[5,7,1,4,6,3,2,8]=>0100110=>0110010
[5,8,1,4,6,3,7,2]=>0000111=>1110000
[3,6,7,4,5,8,2,1]=>1000011=>1100001
[3,5,7,4,6,8,2,1]=>1000011=>1100001
[6,8,4,1,7,2,5,3]=>0011011=>1101100
[5,4,6,1,7,8,3,2]=>0101101=>1011010
[5,6,4,1,8,7,3,2]=>0110111=>1110110
[3,5,8,4,6,7,2,1]=>1000011=>1100001
[3,6,8,4,5,7,2,1]=>1000011=>1100001
[3,7,8,4,5,6,2,1]=>1000101=>1010001
[6,8,1,4,5,3,7,2]=>0001011=>1101000
[6,7,1,4,5,3,2,8]=>0101010=>0101010
[3,7,1,5,4,6,2,8]=>0001110=>0111000
[3,8,1,5,4,6,7,2]=>0001011=>1101000
[3,7,1,5,4,6,8,2]=>0001011=>1101000
[6,7,1,4,5,3,8,2]=>0001011=>1101000
[5,7,1,4,6,3,8,2]=>0000111=>1110000
[5,6,4,2,7,3,8,1]=>0010111=>1110100
[5,4,7,2,8,3,1,6]=>0101011=>1101010
[5,4,7,2,8,3,6,1]=>0001111=>1111000
[5,6,4,2,8,3,1,7]=>0110101=>1010110
[5,8,1,4,6,3,2,7]=>0100101=>1010010
[3,8,1,5,4,6,2,7]=>0001101=>1011000
[3,6,1,5,4,2,7,8]=>0011100=>0011100
[3,6,1,5,4,8,2,7]=>0001101=>1011000
[6,8,3,1,4,2,5,7]=>0110001=>1000110
[7,3,8,1,4,2,5,6]=>0010011=>1100100
[6,7,3,1,4,2,8,5]=>0110011=>1100110
[3,6,1,5,4,7,8,2]=>0001101=>1011000
[3,4,1,2,7,6,5,8]=>0010110=>0110100
[3,4,1,2,6,8,7,5]=>0010011=>1100100
[6,8,3,1,4,7,2,5]=>0100011=>1100010
[6,4,7,2,8,5,1,3]=>0001111=>1111000
[5,8,1,4,7,3,2,6]=>0100011=>1100010
[7,8,1,4,5,3,2,6]=>0101001=>1001010
[3,8,1,5,4,7,2,6]=>0001011=>1101000
[3,6,1,5,4,8,7,2]=>0001111=>1111000
[3,6,1,5,4,7,2,8]=>0001110=>0111000
[6,7,3,1,4,2,5,8]=>0110010=>0100110
[6,8,3,1,4,2,7,5]=>0110011=>1100110
[7,8,3,1,4,6,2,5]=>0100101=>1010010
[7,8,4,2,6,5,1,3]=>0011101=>1011100
[6,5,8,7,3,4,2,1]=>1010111=>1110101
[7,8,3,1,4,6,5,2]=>0101101=>1011010
[6,7,3,1,4,5,2,8]=>0101010=>0101010
[3,7,1,5,4,2,6,8]=>0011010=>0101100
[3,8,1,5,4,2,7,6]=>0011011=>1101100
[5,8,1,4,7,3,6,2]=>0000111=>1110000
[6,8,4,2,7,5,3,1]=>0111011=>1101110
[6,4,7,2,8,5,3,1]=>0101111=>1111010
[6,3,7,1,4,8,5,2]=>0001111=>1111000
[6,8,3,1,4,7,5,2]=>0101011=>1101010
[3,7,1,5,4,8,6,2]=>0001111=>1111000
[3,4,1,2,8,5,7,6]=>0010011=>1100100
[3,4,1,2,5,8,7,6]=>0010011=>1100100
[3,7,1,5,4,2,8,6]=>0011011=>1101100
[6,7,3,1,4,5,8,2]=>0100011=>1100010
[7,3,8,1,4,5,2,6]=>0001011=>1101000
[7,3,8,1,4,5,6,2]=>0000111=>1110000
[6,8,3,1,4,5,2,7]=>0101001=>1001010
[3,8,1,5,4,2,6,7]=>0011001=>1001100
[9,8,7,6,5,4,2,1,3]=>10111111=>11111101
[9,8,7,6,5,3,2,1,4]=>11011111=>11111011
[8,7,6,3,5,2,1,4]=>1001111=>1111001
[9,8,7,6,4,3,2,1,5]=>11101111=>11110111
[8,7,4,6,3,2,1,5]=>1100111=>1110011
[9,8,7,5,4,3,2,1,6]=>11110111=>11101111
[8,5,7,4,3,2,1,6]=>1110011=>1100111
[9,8,6,5,4,3,2,1,7]=>11111011=>11011111
[9,7,6,5,4,3,2,1,8]=>11111101=>10111111
[9,8,7,6,5,4,1,3,2]=>01111111=>11111110
[10,9,8,7,6,5,4,2,1,3]=>101111111=>111111101
[9,8,7,6,5,2,4,1,3]=>00111111=>11111100
[10,9,8,7,6,5,3,2,1,4]=>110111111=>111111011
[9,8,7,6,3,5,2,1,4]=>10011111=>11111001
[10,9,8,7,6,4,3,2,1,5]=>111011111=>111110111
[8,7,6,2,5,4,1,3]=>0011111=>1111100
[9,8,7,4,6,3,2,1,5]=>11001111=>11110011
[10,9,8,7,5,4,3,2,1,6]=>111101111=>111101111
[8,5,4,7,3,2,1,6]=>1101011=>1101011
[8,7,3,6,5,2,1,4]=>1001111=>1111001
[9,8,5,7,4,3,2,1,6]=>11100111=>11100111
[10,9,8,6,5,4,3,2,1,7]=>111110111=>111011111
[6,5,8,4,3,2,1,7]=>1110101=>1010111
[8,4,7,6,3,2,1,5]=>1100111=>1110011
[9,6,8,5,4,3,2,1,7]=>11110011=>11001111
[10,9,7,6,5,4,3,2,1,8]=>111111011=>110111111
[5,8,7,4,3,2,1,6]=>1110011=>1100111
[10,8,7,6,5,4,3,2,1,9]=>111111101=>101111111
[5,8,6,2,3,4,7,1]=>0000111=>1110000
[4,5,2,7,3,1,8,6]=>0101011=>1101010
[4,8,2,6,3,5,7,1]=>0000111=>1110000
[4,3,7,8,6,5,1,2]=>0011101=>1011100
[4,1,7,2,5,8,6,3]=>0010111=>1110100
[7,8,2,1,5,6,4,3]=>1010101=>1010101
[1,6,2,5,8,4,3,7]=>0010101=>1010100
[2,1,8,7,4,5,3,6]=>1001011=>1101001
[7,3,1,6,8,5,2,4]=>0101011=>1101010
[1,5,8,6,2,3,7,4]=>0000111=>1110000
[2,4,8,3,1,6,5,7]=>0100101=>1010010
[5,2,7,1,8,6,3,4]=>0001111=>1111000
[2,6,1,3,8,7,4,5]=>0000111=>1110000
[6,5,2,8,1,7,3,4]=>0001111=>1111000
[2,8,3,5,1,7,4,6]=>0001011=>1101000
[5,4,3,8,7,1,6,2]=>0011111=>1111100
[8,5,4,3,7,2,6,1]=>0011111=>1111100
[8,3,7,4,2,6,5,1]=>0011111=>1111100
[2,8,6,5,1,7,4,3]=>0011111=>1111100
[6,3,2,8,4,1,7,5]=>0110111=>1110110
[2,8,3,4,1,7,5,6]=>0010011=>1100100
[5,4,2,8,3,1,7,6]=>0111011=>1101110
[2,8,4,3,1,7,6,5]=>0110111=>1110110
[2,8,5,3,1,7,6,4]=>0101111=>1111010
[2,8,6,4,1,7,5,3]=>0011111=>1111100
[3,8,7,5,1,6,4,2]=>0011111=>1111100
[8,3,7,5,2,6,4,1]=>0011111=>1111100
[8,4,7,6,2,5,3,1]=>0101111=>1111010
[4,8,7,6,1,5,3,2]=>0101111=>1111010
[7,4,8,6,2,1,5,3]=>1001111=>1111001
[7,3,8,5,2,1,6,4]=>1001111=>1111001
[7,3,8,4,2,1,6,5]=>1010111=>1110101
[7,5,4,3,8,2,1,6]=>1011011=>1101101
[3,7,8,4,1,2,6,5]=>0010101=>1010100
[3,7,8,5,1,2,6,4]=>0001101=>1011000
[4,7,8,6,1,2,5,3]=>0001101=>1011000
[8,7,4,6,3,5,2,1]=>1001111=>1111001
[5,7,8,6,1,2,4,3]=>0010101=>1010100
[6,4,7,8,3,1,2,5]=>0100101=>1010010
[7,3,4,8,2,1,5,6]=>1000011=>1100001
[7,6,4,8,3,2,1,5]=>1100111=>1110011
[7,5,8,6,2,1,4,3]=>1010111=>1110101
[6,5,8,7,3,1,4,2]=>0110111=>1110110
[2,4,8,3,1,5,7,6]=>0100011=>1100010
[6,3,2,4,8,1,5,7]=>0100101=>1010010
[2,3,8,4,1,6,7,5]=>0010011=>1100100
[2,3,8,5,1,6,7,4]=>0001011=>1101000
[6,4,8,7,3,1,5,2]=>0101111=>1111010
[8,6,4,7,3,2,5,1]=>0101111=>1111010
[8,3,4,7,2,5,6,1]=>0000111=>1110000
[3,4,8,7,1,5,6,2]=>0000111=>1110000
[2,4,8,6,1,5,7,3]=>0000111=>1110000
[2,5,8,6,1,4,7,3]=>0000111=>1110000
[8,3,5,7,2,4,6,1]=>0000111=>1110000
[8,4,6,7,2,3,5,1]=>0001011=>1101000
[4,6,8,7,1,3,5,2]=>0001011=>1101000
[2,6,8,5,1,3,7,4]=>0001011=>1101000
[2,6,8,4,1,3,7,5]=>0010011=>1100100
[2,5,8,3,1,4,7,6]=>0100011=>1100010
[5,6,8,7,1,3,4,2]=>0010011=>1100100
[7,4,6,8,2,1,3,5]=>1000011=>1100001
[2,3,5,4,1,8,6,7]=>0011001=>1001100
[2,3,6,4,8,1,5,7]=>0000101=>1010000
[1,8,4,6,3,5,2,7]=>0001101=>1011000
[5,4,8,6,2,1,3,7]=>1001101=>1011001
[2,3,6,8,1,5,4,7]=>0001001=>1001000
[2,5,6,1,4,7,8,3]=>0000101=>1010000
[2,5,6,1,4,7,3,8]=>0000110=>0110000
[7,3,5,1,6,8,4,2]=>0011011=>1101100
[2,7,6,1,8,5,4,3]=>0011111=>1111100
[2,7,6,8,1,4,5,3]=>0001011=>1101000
[1,8,7,6,3,2,5,4]=>0101111=>1111010
[1,8,7,6,3,2,4,5]=>0100111=>1110010
[5,7,8,6,2,3,4,1]=>0010101=>1010100
[2,7,6,1,8,5,3,4]=>0001111=>1111000
[6,3,5,1,7,2,4,8]=>0001110=>0111000
[2,3,4,7,6,1,5,8]=>0000110=>0110000
[7,3,5,8,4,1,2,6]=>0010011=>1100100
[1,8,4,5,2,7,3,6]=>0001011=>1101000
[1,8,4,5,2,7,6,3]=>0001111=>1111000
[7,3,5,8,4,1,6,2]=>0010111=>1110100
[2,7,6,4,8,5,1,3]=>0001111=>1111000
[7,3,5,4,6,8,1,2]=>0001011=>1101000
[6,3,5,4,7,1,8,2]=>0001111=>1111000
[6,3,5,4,7,1,2,8]=>0001110=>0111000
[3,4,1,5,6,8,7,2]=>0010011=>1100100
[3,7,1,6,8,5,2,4]=>0001011=>1101000
[2,3,1,8,6,4,7,5]=>0100111=>1110010
[1,8,4,3,6,2,5,7]=>0010101=>1010100
[2,3,1,8,6,4,5,7]=>0100101=>1010010
[3,7,1,6,8,5,4,2]=>0011011=>1101100
[6,3,5,4,7,2,1,8]=>1001110=>0111001
[7,3,5,4,6,8,2,1]=>1001011=>1101001
[2,7,6,4,8,5,3,1]=>0101111=>1111010
[1,8,4,5,2,6,3,7]=>0001101=>1011000
[6,4,8,5,3,1,2,7]=>0101101=>1011010
[7,3,5,8,4,6,2,1]=>1000111=>1110001
[2,3,4,6,5,8,1,7]=>0000101=>1010000
[2,3,4,7,5,1,8,6]=>0001011=>1101000
[2,3,4,7,5,1,6,8]=>0001010=>0101000
[2,3,4,7,1,6,5,8]=>0000110=>0110000
[2,3,4,7,1,6,8,5]=>0000011=>1100000
[2,3,4,6,1,8,7,5]=>0000111=>1110000
[6,3,5,8,4,2,7,1]=>0010111=>1110100
[7,4,8,5,3,2,1,6]=>1101011=>1101011
[1,8,4,5,2,3,6,7]=>0001001=>1001000
[7,4,8,5,3,2,6,1]=>0101111=>1111010
[6,3,5,8,4,2,1,7]=>1010101=>1010101
[5,2,4,6,8,3,7,1]=>0001011=>1101000
[1,5,7,4,6,3,2,8]=>0100110=>0110010
[5,2,8,4,6,3,7,1]=>0001111=>1111000
[3,8,5,4,6,7,2,1]=>1001011=>1101001
[6,8,3,4,5,7,2,1]=>1000011=>1100001
[2,5,7,4,6,3,8,1]=>0000111=>1110000
[5,4,1,7,8,3,2,6]=>0111001=>1001110
[5,4,2,7,8,3,6,1]=>0011101=>1011100
[5,1,4,6,8,3,2,7]=>0101001=>1001010
[5,1,8,4,6,3,2,7]=>0101101=>1011010
[8,1,6,4,5,3,2,7]=>0101101=>1011010
[8,1,3,5,4,6,2,7]=>0001101=>1011000
[8,1,6,2,4,3,5,7]=>0010101=>1010100
[8,7,1,2,4,3,5,6]=>0010011=>1100100
[1,7,6,2,4,3,5,8]=>0010110=>0110100
[8,7,3,2,4,6,5,1]=>0101111=>1111010
[8,2,6,3,4,5,7,1]=>0000111=>1110000
[1,7,6,3,4,5,2,8]=>0001110=>0111000
[1,7,2,5,4,3,6,8]=>0011010=>0101100
[8,7,2,4,5,3,6,1]=>0001111=>1111000
[5,8,2,4,7,3,6,1]=>0000111=>1110000
[6,8,3,2,4,7,5,1]=>0101011=>1101010
[8,7,1,3,4,5,2,6]=>0001011=>1101000
[8,1,6,3,4,5,2,7]=>0001101=>1011000
[8,1,2,5,4,3,6,7]=>0011001=>1001100
[3,4,8,7,5,2,6,1]=>0001111=>1111000
[3,2,8,6,1,5,4,7]=>0101101=>1011010
[8,6,1,2,4,3,5,7]=>0010101=>1010100
[8,7,3,6,4,2,5,1]=>0011111=>1111100
[3,8,7,2,5,4,6,1]=>0001111=>1111000
[8,7,2,4,5,6,3,1]=>0100111=>1110010
[5,3,6,2,4,8,7,1]=>0001111=>1111000
[3,5,2,8,6,1,4,7]=>0001101=>1011000
[3,7,2,5,1,4,8,6]=>0001011=>1101000
[5,1,8,6,2,3,4,7]=>0001101=>1011000
[2,5,4,1,8,6,3,7]=>0011101=>1011100
[3,7,6,1,8,2,5,4]=>0001111=>1111000
[7,6,3,1,8,2,4,5]=>0100111=>1110010
[8,2,3,6,1,4,7,5]=>0000111=>1110000
[1,8,2,6,3,4,7,5]=>0000111=>1110000
[8,1,3,6,4,7,2,5]=>0000111=>1110000
[7,1,3,6,4,8,2,5]=>0000111=>1110000
[8,2,1,3,5,7,4,6]=>1000011=>1100001
[8,2,6,3,1,4,7,5]=>0100111=>1110010
[7,5,4,1,3,8,2,6]=>0011011=>1101100
[2,7,5,8,3,4,1,6]=>0010011=>1100100
[7,3,8,5,4,1,2,6]=>0011011=>1101100
[7,2,3,6,1,4,8,5]=>0000111=>1110000
[1,3,7,2,5,8,4,6]=>0000011=>1100000
[1,7,2,3,5,8,4,6]=>0000011=>1100000
[7,4,8,1,3,6,2,5]=>0000111=>1110000
[8,1,2,3,5,7,4,6]=>0000011=>1100000
[7,1,2,3,5,8,4,6]=>0000011=>1100000
[8,6,1,4,7,3,2,5]=>0100111=>1110010
[2,6,3,7,1,4,8,5]=>0000111=>1110000
[2,6,3,8,1,4,7,5]=>0000111=>1110000
[7,5,4,8,1,3,2,6]=>0101011=>1101010
[8,5,4,7,1,3,2,6]=>0101011=>1101010
[2,3,1,8,5,4,6,7]=>0101001=>1001010
[8,6,5,1,3,4,2,7]=>0011101=>1011100
[8,5,1,7,6,3,4,2]=>0011111=>1111100
[3,4,7,6,1,8,5,2]=>0001111=>1111000
[3,5,2,6,7,1,8,4]=>0001011=>1101000
[3,2,8,4,7,5,1,6]=>0101011=>1101010
[8,4,7,5,1,3,2,6]=>0101011=>1101010
[3,8,1,6,5,2,7,4]=>0001111=>1111000
[6,1,2,8,3,4,7,5]=>0000111=>1110000
[6,8,3,1,7,2,4,5]=>0100011=>1100010
[3,7,2,5,6,1,8,4]=>0000111=>1110000
[6,8,4,2,5,1,7,3]=>0011011=>1101100
[2,7,5,3,8,4,1,6]=>0011011=>1101100
[8,3,1,4,7,2,6,5]=>0100111=>1110010
[8,3,2,1,5,7,4,6]=>1100011=>1100011
[2,8,3,6,4,7,1,5]=>0000111=>1110000
[7,3,6,4,8,1,2,5]=>0000111=>1110000
[8,3,6,4,7,1,2,5]=>0000111=>1110000
[1,2,8,3,5,7,4,6]=>0000011=>1100000
[1,8,3,2,5,7,4,6]=>0100011=>1100010
[6,5,1,7,4,2,8,3]=>0011111=>1111100
[7,3,6,4,8,2,1,5]=>1000111=>1110001
[4,6,1,7,3,5,2,8]=>0001110=>0111000
[5,6,1,7,3,4,2,8]=>0010110=>0110100
[6,1,7,3,4,2,8,5]=>0010111=>1110100
[7,3,8,1,6,5,2,4]=>0001111=>1111000
[8,3,7,1,6,5,2,4]=>0001111=>1111000
[5,1,7,4,2,8,6,3]=>0011111=>1111100
[2,8,1,7,6,5,3,4]=>0001111=>1111000
[4,2,8,6,5,1,7,3]=>0011111=>1111100
[6,4,2,8,5,1,7,3]=>0011111=>1111100
[8,6,4,7,1,5,2,3]=>0001111=>1111000
[7,6,4,8,1,5,2,3]=>0001111=>1111000
[5,1,6,4,2,3,8,7]=>0011101=>1011100
[4,2,3,8,7,5,1,6]=>0011011=>1101100
[3,8,7,1,6,5,2,4]=>0001111=>1111000
[2,4,3,8,1,6,7,5]=>0010011=>1100100
[2,4,3,7,1,6,8,5]=>0010011=>1100100
[4,2,3,7,8,5,1,6]=>0011001=>1001100
[5,1,6,4,2,3,7,8]=>0011100=>0011100
[6,4,7,8,1,5,2,3]=>0001101=>1011000
[8,7,4,6,1,5,2,3]=>0001111=>1111000
[6,5,7,8,1,4,2,3]=>0010101=>1010100
[4,7,8,6,1,5,2,3]=>0001101=>1011000
[3,2,4,7,8,1,5,6]=>0100001=>1000010
[3,2,4,8,7,1,5,6]=>0100011=>1100010
[4,8,7,6,1,5,2,3]=>0001111=>1111000
[5,8,7,6,1,4,2,3]=>0010111=>1110100
[8,6,5,7,1,4,2,3]=>0010111=>1110100
[5,1,6,7,4,2,3,8]=>0011010=>0101100
[6,7,4,8,1,5,2,3]=>0001011=>1101000
[8,4,7,6,1,5,2,3]=>0001111=>1111000
[8,3,2,4,7,1,5,6]=>0100011=>1100010
[7,3,2,4,8,1,5,6]=>0100011=>1100010
[2,5,3,7,1,6,4,8]=>0001110=>0111000
[8,4,6,7,1,5,2,3]=>0001011=>1101000
[7,4,6,8,1,5,2,3]=>0001011=>1101000
[5,1,6,8,4,2,3,7]=>0011001=>1001100
[4,2,3,7,5,1,6,8]=>0011010=>0101100
[3,7,5,8,1,6,2,4]=>0000111=>1110000
[2,4,3,7,1,6,5,8]=>0010110=>0110100
[2,4,7,1,5,8,6,3]=>0000111=>1110000
[3,2,4,7,6,1,5,8]=>0100110=>0110010
[4,7,6,8,1,5,2,3]=>0001011=>1101000
[8,5,6,7,1,4,2,3]=>0010011=>1100100
[8,6,7,5,1,4,2,3]=>0011011=>1101100
[7,6,8,5,1,4,2,3]=>0011011=>1101100
[6,8,7,5,1,4,2,3]=>0011011=>1101100
[5,6,8,7,1,4,2,3]=>0010011=>1100100
[4,6,8,7,1,5,2,3]=>0001011=>1101000
[2,4,6,7,1,5,8,3]=>0000011=>1100000
[3,2,4,6,1,5,7,8]=>0100100=>0010010
[6,7,8,5,1,4,2,3]=>0011001=>1001100
[7,8,6,5,1,4,2,3]=>0011101=>1011100
[3,1,7,5,4,2,8,6]=>0111011=>1101110
[2,1,8,5,4,6,3,7]=>1001101=>1011001
[4,1,8,5,2,3,6,7]=>0011001=>1001100
[5,4,1,3,6,7,2,8]=>0011010=>0101100
[8,4,1,2,6,3,7,5]=>0010111=>1110100
[8,2,7,1,5,3,4,6]=>0001011=>1101000
[3,2,7,1,5,8,4,6]=>0100011=>1100010
[6,3,7,1,5,4,2,8]=>0011110=>0111100
[7,3,8,1,5,4,2,6]=>0011011=>1101100
[7,1,5,3,8,4,2,6]=>0011011=>1101100
[4,5,1,3,6,8,2,7]=>0001001=>1001000
[3,6,8,1,5,4,2,7]=>0011001=>1001100
[6,8,3,1,5,4,2,7]=>0111001=>1001110
[7,6,3,1,5,4,2,8]=>0111110=>0111110
[3,6,2,1,5,8,4,7]=>1000101=>1010001
[8,6,2,1,5,3,4,7]=>1001101=>1011001
[4,8,2,1,7,5,3,6]=>1001011=>1101001
[2,3,8,1,5,7,4,6]=>0000011=>1100000
[7,1,3,2,8,6,4,5]=>0100111=>1110010
[7,1,6,2,8,3,4,5]=>0000111=>1110000
[4,7,1,2,6,3,8,5]=>0000111=>1110000
[2,7,8,1,5,3,4,6]=>0001001=>1001000
[6,7,2,1,5,3,4,8]=>1001010=>0101001
[4,7,2,1,8,5,3,6]=>1001011=>1101001
[8,7,2,1,4,5,3,6]=>1001011=>1101001
[8,7,5,6,1,4,3,2]=>0110111=>1110110
[5,7,8,6,1,4,3,2]=>0110101=>1010110
[2,7,4,1,6,5,3,8]=>0011110=>0111100
[3,7,1,4,5,6,8,2]=>0000011=>1100000
[7,1,6,4,5,8,3,2]=>0100111=>1110010
[3,5,1,4,7,6,8,2]=>0001011=>1101000
[2,6,4,1,7,5,3,8]=>0011110=>0111100
[5,6,8,7,1,4,3,2]=>0110011=>1100110
[6,8,5,7,1,4,3,2]=>0110011=>1100110
[8,6,5,7,1,4,3,2]=>0110111=>1110110
[8,5,7,6,1,4,3,2]=>0110111=>1110110
[6,5,7,8,1,4,3,2]=>0110101=>1010110
[7,2,3,1,5,6,4,8]=>0100110=>0110010
[4,2,8,1,6,5,3,7]=>0011101=>1011100
[6,2,4,1,8,5,3,7]=>0011101=>1011100
[8,3,1,4,5,6,7,2]=>0100011=>1100010
[5,3,1,4,8,6,7,2]=>0101011=>1101010
[7,5,1,6,3,4,8,2]=>0001111=>1111000
[7,1,5,8,4,3,6,2]=>0010111=>1110100
[5,8,1,6,4,3,7,2]=>0010111=>1110100
[5,3,1,8,4,6,7,2]=>0101011=>1101010
[8,3,1,5,4,6,7,2]=>0101011=>1101010
[8,2,6,1,4,5,3,7]=>0001101=>1011000
[6,2,8,1,4,5,3,7]=>0001101=>1011000
[7,2,6,1,5,3,4,8]=>0001110=>0111000
[2,8,6,1,5,3,4,7]=>0001101=>1011000
[4,2,1,5,6,3,8,7]=>1010101=>1010101
[7,1,2,5,8,3,4,6]=>0000011=>1100000
[7,1,4,5,6,8,3,2]=>0100011=>1100010
[8,5,6,7,1,4,3,2]=>0110011=>1100110
[7,6,8,5,1,4,3,2]=>0111011=>1101110
[6,8,7,5,1,4,3,2]=>0111011=>1101110
[2,6,7,1,4,5,3,8]=>0001010=>0101000
[3,5,1,7,4,6,8,2]=>0001011=>1101000
[7,1,5,6,4,8,3,2]=>0100111=>1110010
[7,1,6,5,4,8,3,2]=>0101111=>1111010
[2,7,6,1,4,5,3,8]=>0001110=>0111000
[5,7,6,8,1,4,3,2]=>0110011=>1100110
[7,8,6,5,1,4,3,2]=>0111101=>1011110
[4,3,1,6,5,8,7,2]=>0110111=>1110110
[5,3,1,2,4,8,7,6]=>0101011=>1101010
[5,3,6,2,1,8,7,4]=>1001111=>1111001
[5,3,7,2,1,4,6,8]=>1001010=>0101001
[5,3,7,2,8,4,1,6]=>0011011=>1101100
[7,2,4,5,8,3,1,6]=>0100011=>1100010
[7,2,4,5,1,3,6,8]=>0001010=>0101000
[6,2,4,5,1,8,7,3]=>0001111=>1111000
[3,1,4,5,2,8,7,6]=>0101011=>1101010
[1,6,4,5,2,8,7,3]=>0001111=>1111000
[3,7,4,5,1,2,6,8]=>0001010=>0101000
[3,7,4,5,8,2,1,6]=>1000011=>1100001
[1,7,4,2,6,3,5,8]=>0010110=>0110100
[8,7,4,5,2,1,6,3]=>1001111=>1111001
[6,3,7,1,8,4,2,5]=>0010111=>1110100
[5,7,4,1,6,3,2,8]=>0110110=>0110110
[1,7,4,8,6,3,2,5]=>0100111=>1110010
[5,7,4,8,6,3,1,2]=>0100111=>1110010
[4,8,3,5,6,7,1,2]=>0000011=>1100000
[1,8,3,5,6,7,2,4]=>0000011=>1100000
[4,8,1,5,6,7,2,3]=>0000011=>1100000
[4,1,3,5,6,7,2,8]=>0010010=>0100100
[5,8,4,3,6,1,2,7]=>0010101=>1010100
[5,3,8,4,1,7,2,6]=>0011011=>1101100
[1,5,8,4,6,7,3,2]=>0100011=>1100010
[1,4,8,3,6,7,5,2]=>0001011=>1101000
[4,3,8,2,1,7,5,6]=>1010011=>1100101
[3,8,4,2,6,1,5,7]=>0010101=>1010100
[1,8,2,5,6,7,4,3]=>0010011=>1100100
[3,8,1,5,6,7,4,2]=>0010011=>1100100
[3,8,2,5,6,7,1,4]=>0000011=>1100000
[8,2,1,5,6,7,4,3]=>1010011=>1100101
[8,1,3,5,6,7,4,2]=>0010011=>1100100
[7,1,4,3,6,2,5,8]=>0010110=>0110100
[7,8,4,3,6,2,1,5]=>1010101=>1010101
[4,3,1,8,5,7,6,2]=>0110111=>1110110
[4,3,1,6,8,7,5,2]=>0111011=>1101110
[6,3,1,8,2,7,4,5]=>0100111=>1110010
[6,3,5,8,2,7,1,4]=>0000111=>1110000
[7,5,4,8,6,2,1,3]=>1001111=>1111001
[7,1,4,8,6,2,3,5]=>0000111=>1110000
[7,5,4,1,6,2,3,8]=>0011110=>0111100
[7,6,4,5,8,1,3,2]=>0100111=>1110010
[1,6,4,5,8,2,3,7]=>0000101=>1010000
[7,3,6,1,8,2,4,5]=>0000111=>1110000
[1,7,6,5,8,3,4,2]=>0010111=>1110100
[1,8,5,3,6,7,4,2]=>0011011=>1101100
[8,3,5,2,1,7,4,6]=>1001011=>1101001
[8,4,1,5,6,7,3,2]=>0110011=>1100110
[8,4,2,5,6,7,1,3]=>0010011=>1100100
[4,1,8,5,6,7,3,2]=>0110011=>1100110
[1,2,8,5,6,7,3,4]=>0000011=>1100000
[4,2,1,5,6,7,3,8]=>1010010=>0100101
[1,5,3,8,6,7,4,2]=>0011011=>1101100
[1,4,5,8,6,7,3,2]=>0100011=>1100010
[4,3,5,8,1,7,2,6]=>0010011=>1100100
[3,5,4,8,6,1,2,7]=>0001101=>1011000
[1,4,8,5,6,7,2,3]=>0000011=>1100000
[3,4,8,5,6,7,1,2]=>0000011=>1100000
[2,7,1,5,6,3,4,8]=>0000110=>0110000
[2,7,1,4,3,6,5,8]=>0010110=>0110100
[4,3,7,2,5,6,8,1]=>0010011=>1100100
[2,6,3,1,4,5,8,7]=>0100101=>1010010
[3,7,1,4,2,6,8,5]=>0010011=>1100100
[3,7,1,5,6,2,8,4]=>0000111=>1110000
[4,7,1,5,6,8,2,3]=>0000011=>1100000
[8,5,2,6,7,3,1,4]=>0101011=>1101010
[8,4,2,6,3,7,1,5]=>0010111=>1110100
[8,4,2,3,5,7,1,6]=>0010011=>1100100
[4,7,3,2,5,6,1,8]=>0100110=>0110010
[5,3,4,6,2,8,1,7]=>0001101=>1011000
[5,3,7,4,2,8,1,6]=>0011011=>1101100
[6,4,7,2,3,8,1,5]=>0000111=>1110000
[6,5,7,2,8,3,1,4]=>0100111=>1110010
[5,3,7,2,4,8,6,1]=>0001111=>1111000
[2,6,5,1,8,3,4,7]=>0001101=>1011000
[8,7,6,1,4,5,2,3]=>0001111=>1111000
[8,7,6,1,3,2,5,4]=>0101111=>1111010
[8,7,2,4,3,1,6,5]=>0110111=>1110110
[8,7,4,5,1,6,2,3]=>0001111=>1111000
[8,5,6,4,1,7,2,3]=>0010111=>1110100
[8,5,6,3,1,2,7,4]=>0100111=>1110010
[8,4,6,2,3,1,7,5]=>0100111=>1110010
[8,3,5,4,2,1,7,6]=>1011011=>1101101
[5,7,3,4,2,1,8,6]=>1010011=>1100101
[6,7,4,2,3,1,8,5]=>0110011=>1100110
[6,7,5,3,1,2,8,4]=>0101011=>1101010
[6,7,5,4,1,8,2,3]=>0011011=>1101100
[10,3,1,2,4,5,6,7,8,9]=>010000001=>100000010
[10,4,1,2,3,5,6,7,8,9]=>001000001=>100000100
[5,10,1,2,3,4,6,7,8,9]=>000000001=>100000000
[10,6,1,2,3,4,5,7,8,9]=>000010001=>100010000
[10,7,1,2,3,4,5,6,8,9]=>000001001=>100100000
[8,10,1,2,3,4,5,6,7,9]=>000000001=>100000000
[2,11,1,3,4,5,6,7,8,9,10]=>0000000001=>1000000000
[2,3,10,1,4,5,6,7,8,9]=>000000001=>100000000
[11,3,1,2,4,5,6,7,8,9,10]=>0100000001=>1000000010
[4,3,1,10,2,5,6,7,8,9]=>011000001=>100000110
[11,4,1,2,3,5,6,7,8,9,10]=>0010000001=>1000000100
[5,4,1,2,10,3,6,7,8,9]=>001100001=>100001100
[5,11,1,2,3,4,6,7,8,9,10]=>0000000001=>1000000000
[5,6,1,2,3,10,4,7,8,9]=>000010001=>100010000
[11,6,1,2,3,4,5,7,8,9,10]=>0000100001=>1000010000
[7,6,1,2,3,4,10,5,8,9]=>000011001=>100110000
[11,7,1,2,3,4,5,6,8,9,10]=>0000010001=>1000100000
[8,7,1,2,3,4,5,10,6,9]=>000001101=>101100000
[8,11,1,2,3,4,5,6,7,9,10]=>0000000001=>1000000000
[8,9,1,2,3,4,5,6,10,7]=>000000011=>110000000
[11,9,1,2,3,4,5,6,7,8,10]=>0000000101=>1010000000
[6,2,4,3,8,7,5,1]=>0011111=>1111100
[7,3,5,4,1,8,6,2]=>0011111=>1111100
[5,2,7,1,3,4,8,6]=>0001011=>1101000
[2,6,5,7,3,1,4,8]=>0100110=>0110010
[2,6,5,7,3,1,8,4]=>0100111=>1110010
[6,3,1,4,7,8,5,2]=>0101101=>1011010
[6,8,2,1,3,4,5,7]=>1000001=>1000001
[3,7,1,8,4,5,2,6]=>0001011=>1101000
[6,3,2,4,7,5,8,1]=>0100111=>1110010
[6,3,2,4,7,5,1,8]=>0101110=>0111010
[4,2,1,6,3,7,5,8]=>1010110=>0110101
[4,2,1,6,3,7,8,5]=>1010101=>1010101
[7,4,3,5,8,6,1,2]=>0010111=>1110100
[2,7,6,8,3,1,4,5]=>0100011=>1100010
[7,4,3,5,8,6,2,1]=>1010111=>1110101
[4,2,1,7,3,8,6,5]=>1010111=>1110101
[4,2,1,3,7,8,6,5]=>1010101=>1010101
[5,8,1,7,4,3,6,2]=>0010111=>1110100
[5,8,1,7,4,3,2,6]=>0110011=>1100110
[3,7,8,6,2,1,4,5]=>1000101=>1010001
[4,2,1,8,3,5,6,7]=>1010001=>1000101
[4,2,1,3,6,7,5,8]=>1010010=>0100101
[4,2,1,3,7,5,6,8]=>1010010=>0100101
[4,2,1,3,6,8,7,5]=>1010011=>1100101
[7,3,2,4,8,6,5,1]=>0101111=>1111010
[4,2,1,6,3,8,7,5]=>1010111=>1110101
[4,2,1,7,3,5,6,8]=>1010010=>0100101
[3,6,7,5,2,1,4,8]=>1001010=>0101001
[3,6,7,5,2,1,8,4]=>1001011=>1101001
[7,3,4,2,6,8,5,1]=>0011011=>1101100
[4,8,6,2,7,3,5,1]=>0001111=>1111000
[7,3,4,2,6,8,1,5]=>0010011=>1100100
[3,6,7,5,2,4,8,1]=>0001011=>1101000
[3,6,7,5,2,4,1,8]=>0011010=>0101100
[4,2,1,7,3,6,5,8]=>1010110=>0110101
[4,2,1,7,3,6,8,5]=>1010011=>1100101
[3,7,6,8,4,2,5,1]=>0011011=>1101100
[5,8,1,7,4,2,6,3]=>0010111=>1110100
[3,7,8,6,2,4,5,1]=>0001101=>1011000
[4,2,1,3,8,6,7,5]=>1010011=>1100101
[4,2,1,3,7,6,5,8]=>1010110=>0110101
[4,2,1,3,5,7,6,8]=>1010010=>0100101
[4,2,1,3,5,8,6,7]=>1010001=>1000101
[4,8,1,7,3,6,5,2]=>0001111=>1111000
[4,7,8,6,3,5,2,1]=>1001101=>1011001
[4,2,1,8,3,7,6,5]=>1010111=>1110101
[4,2,1,3,5,6,8,7]=>1010001=>1000101
[7,8,2,4,1,3,6,5]=>0010101=>1010100
[2,6,1,5,4,7,8,3]=>0001101=>1011000
[4,6,3,5,8,7,1,2]=>0000111=>1110000
[3,5,6,1,4,8,7,2]=>0000111=>1110000
[2,3,6,8,4,1,5,7]=>0010001=>1000100
[2,7,5,1,8,3,4,6]=>0001011=>1101000
[4,7,5,2,1,3,6,8]=>1001010=>0101001
[3,5,6,2,4,1,7,8]=>0010100=>0010100
[2,5,6,1,4,8,3,7]=>0000101=>1010000
[6,7,8,4,1,5,3,2]=>0111001=>1001110
[7,1,6,8,4,5,3,2]=>0101011=>1101010
[7,4,6,5,2,8,1,3]=>0001111=>1111000
[7,1,5,6,4,2,3,8]=>0010110=>0110100
[5,7,4,6,8,1,3,2]=>0100011=>1100010
[5,7,8,1,4,6,3,2]=>0100101=>1010010
[8,1,5,7,4,6,3,2]=>0100111=>1110010
[1,8,4,6,7,5,3,2]=>0101011=>1101010
[6,1,8,4,7,5,3,2]=>0101111=>1111010
[4,5,8,6,1,7,3,2]=>0100111=>1110010
[4,8,5,1,6,7,3,2]=>0101011=>1101010
[8,1,4,5,6,7,3,2]=>0100011=>1100010
[5,6,7,1,4,2,3,8]=>0010010=>0100100
[8,4,2,6,1,5,7,3]=>0010111=>1110100
[4,8,5,2,1,6,7,3]=>1001011=>1101001
[5,1,8,4,2,6,3,7]=>0011101=>1011100
[1,8,4,6,2,5,3,7]=>0001101=>1011000
[6,1,5,2,3,4,7,8]=>0001100=>0011000
[8,3,1,4,6,2,5,7]=>0100101=>1010010
[3,1,8,2,5,6,4,7]=>0100101=>1010010
[3,5,1,8,2,6,4,7]=>0001101=>1011000
[3,5,1,2,8,4,7,6]=>0001011=>1101000
[2,3,5,8,6,1,7,4]=>0000111=>1110000
[8,2,4,3,6,7,1,5]=>0010011=>1100100
[3,2,8,5,7,1,6,4]=>0100111=>1110010
[3,6,2,8,5,1,7,4]=>0001111=>1111000
[6,2,1,8,4,7,5,3]=>1001111=>1111001
[2,8,7,1,4,6,5,3]=>0001111=>1111000
[8,2,7,1,5,4,6,3]=>0001111=>1111000
[7,2,5,3,6,8,1,4]=>0001011=>1101000
[7,3,1,5,6,2,4,8]=>0100110=>0110010
[3,7,5,1,6,2,4,8]=>0001110=>0111000
[2,7,3,6,5,8,1,4]=>0000111=>1110000
[8,7,2,4,1,6,5,3]=>0011111=>1111100
[1,8,7,2,3,6,5,4]=>0001111=>1111000
[1,7,8,2,6,4,3,5]=>0010101=>1010100
[1,7,3,8,2,6,4,5]=>0000111=>1110000
[1,2,7,3,6,4,5,8]=>0000110=>0110000
[7,1,5,8,3,2,4,6]=>0100011=>1100010
[1,6,2,8,4,3,7,5]=>0010111=>1110100
[1,3,8,7,2,4,6,5]=>0000111=>1110000
[1,8,3,7,2,5,4,6]=>0001011=>1101000
[8,1,4,7,3,2,5,6]=>0100011=>1100010
[4,7,8,1,3,2,5,6]=>0100001=>1000010
[7,1,4,2,3,5,6,8]=>0010010=>0100100
[8,2,1,4,7,3,5,6]=>1000011=>1100001
[2,1,3,8,4,6,7,5]=>1000011=>1100001
[1,2,3,4,8,5,7,6]=>0000011=>1100000
[2,4,7,5,6,8,3,1]=>0100011=>1100010
[2,4,8,7,5,6,3,1]=>0100111=>1110010
[2,5,3,8,4,7,6,1]=>0001111=>1111000
[2,8,5,7,3,6,4,1]=>0010111=>1110100
[3,1,8,5,2,7,6,4]=>0101111=>1111010
[2,8,6,3,4,5,7,1]=>0000111=>1110000
[2,5,7,3,4,8,6,1]=>0000111=>1110000
[8,3,7,6,1,4,5,2]=>0001111=>1111000
[3,1,7,8,2,5,6,4]=>0100101=>1010010
[7,3,8,5,1,6,4,2]=>0011111=>1111100
[7,5,1,2,3,4,8,6]=>0001011=>1101000
[4,8,1,5,2,7,3,6]=>0001011=>1101000
[4,1,2,5,3,8,7,6]=>0011011=>1101100
[4,3,6,8,7,5,1,2]=>0011011=>1101100
[5,4,1,8,2,7,6,3]=>0011111=>1111100
[6,4,8,1,2,5,3,7]=>0001101=>1011000
[6,7,3,1,4,8,5,2]=>0101011=>1101010
[5,4,1,6,8,2,7,3]=>0011011=>1101100
[5,4,7,1,2,8,6,3]=>0001111=>1111000
[6,5,1,2,3,7,8,4]=>0001101=>1011000
[6,5,1,2,3,4,8,7]=>0001101=>1011000
[6,7,4,1,2,5,3,8]=>0011010=>0101100
[2,4,6,3,5,7,1,8]=>0000110=>0110000
[1,4,6,3,7,2,5,8]=>0000110=>0110000
[8,6,2,5,3,1,7,4]=>0101111=>1111010
[8,2,3,4,5,1,7,6]=>0001011=>1101000
[1,8,3,4,2,7,5,6]=>0010011=>1100100
[2,8,3,4,1,6,7,5]=>0010011=>1100100
[8,7,2,3,1,6,5,4]=>0101111=>1111010
[3,8,2,4,6,1,7,5]=>0000111=>1110000
[7,8,2,4,3,1,6,5]=>0110101=>1010110
[4,5,8,2,3,1,7,6]=>0100011=>1100010
[5,1,4,3,7,2,6,8]=>0011010=>0101100
[6,1,3,5,7,2,4,8]=>0000110=>0110000
[2,1,4,7,5,3,6,8]=>1001010=>0101001
[7,1,3,6,2,5,4,8]=>0001110=>0111000
[8,1,3,6,2,4,7,5]=>0000111=>1110000
[2,1,8,3,7,5,4,6]=>1001011=>1101001
[7,1,8,2,5,6,3,4]=>0000111=>1110000
[6,1,5,8,2,7,3,4]=>0000111=>1110000
[4,5,2,8,1,6,7,3]=>0001011=>1101000
[6,2,5,8,1,4,7,3]=>0000111=>1110000
[3,2,8,5,1,6,7,4]=>0101011=>1101010
[8,2,7,1,4,6,5,3]=>0001111=>1111000
[1,3,8,2,5,7,4,6]=>0000011=>1100000
[2,8,7,1,6,4,5,3]=>0001111=>1111000
[3,8,7,1,5,6,4,2]=>0010111=>1110100
[3,4,8,5,6,1,7,2]=>0000111=>1110000
[8,3,7,4,1,6,5,2]=>0011111=>1111100
[1,4,8,6,2,7,3,5]=>0000111=>1110000
[8,4,5,7,1,6,3,2]=>0100111=>1110010
[3,5,6,8,4,1,7,2]=>0010011=>1100100
[6,2,3,1,5,4,7,8]=>0101100=>0011010
[7,2,3,1,4,6,5,8]=>0100110=>0110010
[8,2,3,1,4,5,7,6]=>0100011=>1100010
[8,5,1,3,2,4,7,6]=>0101011=>1101010
[7,5,1,3,2,6,4,8]=>0101110=>0111010
[2,6,1,4,5,3,7,8]=>0001100=>0011000
[3,6,4,1,5,2,7,8]=>0011100=>0011100
[4,5,6,1,3,2,7,8]=>0100100=>0010010
[4,5,7,1,2,6,3,8]=>0000110=>0110000
[3,7,4,1,2,6,5,8]=>0010110=>0110100
[6,7,1,4,2,5,3,8]=>0011010=>0101100
[2,7,1,3,5,6,4,8]=>0000110=>0110000
[8,6,1,2,4,3,7,5]=>0010111=>1110100
[2,8,1,3,4,6,7,5]=>0000011=>1100000
[7,8,1,2,5,3,6,4]=>0001101=>1011000
[3,8,4,1,2,5,7,6]=>0010011=>1100100
[1,2,6,7,5,3,8,4]=>0001011=>1101000
[1,7,5,3,2,8,4,6]=>0101011=>1101010
[1,6,7,5,3,8,4,2]=>0011011=>1101100
[1,6,5,7,2,3,8,4]=>0000111=>1110000
[1,3,8,2,6,5,7,4]=>0000111=>1110000
[1,2,5,7,6,3,4,8]=>0000110=>0110000
[1,3,4,8,2,5,7,6]=>0000011=>1100000
[1,5,7,6,2,3,4,8]=>0000110=>0110000
[1,5,3,8,2,6,4,7]=>0001101=>1011000
[1,4,8,3,2,5,7,6]=>0100011=>1100010
[1,4,8,3,5,7,6,2]=>0000111=>1110000
[1,2,4,8,3,5,7,6]=>0000011=>1100000
[1,3,8,4,2,6,7,5]=>0010011=>1100100
[1,4,8,2,3,5,7,6]=>0000011=>1100000
[6,5,7,3,8,2,4,1]=>0010111=>1110100
[4,2,6,7,5,8,3,1]=>0110011=>1100110
[6,7,5,2,1,8,4,3]=>1011011=>1101101
[3,4,8,7,5,2,1,6]=>1001011=>1101001
[1,7,5,2,8,4,6,3]=>0001111=>1111000
[5,6,8,3,1,7,2,4]=>0100011=>1100010
[6,1,4,8,3,2,7,5]=>0100111=>1110010
[3,4,7,1,8,6,2,5]=>0000111=>1110000
[3,4,6,8,2,1,5,7]=>1000001=>1000001
[3,8,2,5,6,1,4,7]=>0000101=>1010000
[3,5,2,8,6,4,1,7]=>0011101=>1011100
[4,2,5,7,3,8,6,1]=>0010111=>1110100
[7,4,2,5,3,8,1,6]=>0011011=>1101100
[3,1,2,8,5,6,4,7]=>0100101=>1010010
[5,2,1,6,8,3,4,7]=>1001001=>1001001
[5,2,6,8,4,1,3,7]=>0011001=>1001100
[1,5,6,8,3,4,2,7]=>0010001=>1000100
[4,5,8,1,6,3,2,7]=>0100101=>1010010
[4,5,1,6,8,3,2,7]=>0101001=>1001010
[4,5,7,3,8,2,6,1]=>0000111=>1110000
[6,4,3,7,8,2,5,1]=>0011101=>1011100
[6,4,3,1,7,8,2,5]=>0110101=>1010110
[4,5,3,1,7,8,2,6]=>0101001=>1001010
[7,1,3,5,4,8,2,6]=>0001011=>1101000
[7,5,2,8,1,4,3,6]=>0011011=>1101100
[5,7,3,8,4,6,1,2]=>0000111=>1110000
[1,4,5,7,3,8,6,2]=>0000111=>1110000
[4,6,3,7,8,5,2,1]=>1001101=>1011001
[5,3,6,7,8,4,2,1]=>1011001=>1001101
[1,5,3,6,7,8,4,2]=>0011001=>1001100
[4,6,1,7,3,8,5,2]=>0001111=>1111000
[6,3,7,1,8,4,5,2]=>0001111=>1111000
[6,7,2,4,8,1,5,3]=>0001011=>1101000
[2,6,1,4,7,3,8,5]=>0000111=>1110000
[3,2,5,6,7,8,1,4]=>0100001=>1000010
[5,2,3,6,7,8,4,1]=>0011001=>1001100
[6,7,1,3,2,8,4,5]=>0100011=>1100010
[6,2,7,1,3,4,8,5]=>0000111=>1110000
[5,2,1,7,3,8,4,6]=>1001011=>1101001
[6,4,2,7,1,8,3,5]=>0010111=>1110100
[4,2,6,3,7,8,1,5]=>0010101=>1010100
[4,2,6,3,7,8,5,1]=>0011101=>1011100
[6,7,3,8,2,4,5,1]=>0001011=>1101000
[3,6,2,7,4,1,8,5]=>0010111=>1110100
[6,7,3,2,1,4,8,5]=>1100011=>1100011
[7,1,8,3,4,2,5,6]=>0010011=>1100100
[7,2,4,1,8,3,5,6]=>0010011=>1100100
[7,2,4,8,6,1,3,5]=>0000111=>1110000
[7,3,4,8,6,2,1,5]=>1000111=>1110001
[3,5,7,2,1,8,6,4]=>1000111=>1110001
[6,7,8,3,2,5,1,4]=>0101001=>1001010
[6,3,7,8,2,5,4,1]=>0011101=>1011100
[2,6,7,4,8,5,3,1]=>0101011=>1101010
[6,2,4,7,1,8,5,3]=>0001111=>1111000
[4,6,2,7,1,8,5,3]=>0001111=>1111000
[1,7,4,8,5,2,6,3]=>0001111=>1111000
[1,3,7,8,5,2,6,4]=>0001101=>1011000
[2,5,7,8,1,6,3,4]=>0000101=>1010000
[6,3,7,1,8,2,5,4]=>0001111=>1111000
[1,6,4,7,8,2,5,3]=>0001101=>1011000
[2,5,6,1,7,8,4,3]=>0010101=>1010100
[5,6,1,2,7,8,4,3]=>0010101=>1010100
[6,7,2,1,8,5,3,4]=>1001011=>1101001
[6,7,2,8,5,4,1,3]=>0011011=>1101100
[1,6,7,4,8,5,3,2]=>0101011=>1101010
[1,8,2,4,6,3,5,7]=>0000101=>1010000
[7,2,8,3,5,1,4,6]=>0001011=>1101000
[1,3,7,4,6,2,5,8]=>0000110=>0110000
[1,5,7,4,3,6,2,8]=>0010110=>0110100
[1,8,4,5,3,6,2,7]=>0001101=>1011000
[1,8,5,3,4,7,2,6]=>0001011=>1101000
[1,8,2,4,6,3,7,5]=>0000111=>1110000
[1,8,2,5,4,6,7,3]=>0001011=>1101000
[3,6,2,7,1,4,5,8]=>0000110=>0110000
[6,3,8,1,2,4,7,5]=>0000111=>1110000
[1,3,7,4,6,2,8,5]=>0000111=>1110000
[1,4,7,5,2,6,8,3]=>0001011=>1101000
[4,5,2,7,1,3,8,6]=>0001011=>1101000
[4,5,2,3,6,1,8,7]=>0001101=>1011000
[4,6,5,3,7,1,8,2]=>0001111=>1111000
[2,5,4,7,1,6,8,3]=>0001011=>1101000
[4,2,3,8,6,7,1,5]=>0010011=>1100100
[6,2,4,8,5,1,7,3]=>0001111=>1111000
[5,2,4,8,1,3,7,6]=>0001011=>1101000
[6,2,5,4,8,3,7,1]=>0001111=>1111000
[6,4,3,5,8,2,7,1]=>0010111=>1110100
[5,2,3,4,8,1,6,7]=>0001001=>1001000
[3,5,2,4,7,1,6,8]=>0001010=>0101000
[5,3,4,8,1,6,2,7]=>0001101=>1011000
[4,5,3,7,1,6,2,8]=>0001110=>0111000
[6,2,4,8,5,1,3,7]=>0001101=>1011000
[7,6,3,8,5,1,2,4]=>0001111=>1111000
[1,4,3,7,8,2,5,6]=>0010001=>1000100
[4,2,6,7,3,8,1,5]=>0010011=>1100100
[1,5,7,4,2,8,6,3]=>0010111=>1110100
[1,3,7,2,8,6,4,5]=>0000111=>1110000
[1,4,3,7,8,6,2,5]=>0010101=>1010100
[1,5,3,6,8,2,7,4]=>0001011=>1101000
[4,5,2,7,1,8,6,3]=>0001111=>1111000
[4,3,6,5,7,8,1,2]=>0010101=>1010100
[4,2,3,5,6,8,1,7]=>0010001=>1000100
[5,2,6,4,7,8,3,1]=>0101101=>1011010
[4,2,6,7,3,8,5,1]=>0011011=>1101100
[3,2,5,6,8,1,7,4]=>0100011=>1100010
[6,4,5,2,3,8,7,1]=>0001111=>1111000
[8,4,6,7,5,2,3,1]=>0101011=>1101010
[4,6,5,2,3,1,8,7]=>0101101=>1011010
[6,4,2,5,3,1,8,7]=>0111101=>1011110
[6,4,2,5,3,8,7,1]=>0011111=>1111100
[8,6,4,7,5,2,3,1]=>0101111=>1111010
[8,6,2,7,4,5,3,1]=>0101111=>1111010
[6,4,2,5,8,7,3,1]=>0110111=>1110110
[4,6,2,5,3,8,7,1]=>0001111=>1111000
[4,6,5,2,3,8,7,1]=>0001111=>1111000
[6,8,7,4,5,2,3,1]=>0101011=>1101010
[4,8,6,7,5,2,3,1]=>0101011=>1101010
[6,8,4,7,5,2,3,1]=>0101011=>1101010
[6,8,2,7,4,5,3,1]=>0101011=>1101010
[8,6,4,7,2,5,3,1]=>0101111=>1111010
[8,6,2,4,7,5,3,1]=>0101111=>1111010
[6,8,2,4,7,5,3,1]=>0101011=>1101010
[4,8,2,6,7,5,3,1]=>0101011=>1101010
[2,8,4,6,7,5,3,1]=>0101011=>1101010
[2,8,6,7,4,5,3,1]=>0101011=>1101010
[6,8,7,2,4,5,3,1]=>0101011=>1101010
[2,6,4,5,8,7,3,1]=>0100111=>1110010
[2,6,4,8,7,5,3,1]=>0101111=>1111010
[4,6,2,8,7,5,3,1]=>0101111=>1111010
[8,2,4,6,7,5,3,1]=>0101011=>1101010
[6,2,4,8,7,5,3,1]=>0101111=>1111010
[4,2,6,8,7,5,3,1]=>0111011=>1101110
[4,2,6,5,8,7,3,1]=>0110111=>1110110
[6,2,4,5,8,7,3,1]=>0100111=>1110010
[8,2,6,7,4,5,3,1]=>0101011=>1101010
[8,6,7,2,4,5,3,1]=>0101011=>1101010
[6,4,5,2,8,7,3,1]=>0101111=>1111010
[4,2,3,6,8,7,5,1]=>0011011=>1101100
[6,4,5,8,7,2,3,1]=>0100111=>1110010
[8,6,7,4,2,5,3,1]=>0111011=>1101110
[8,4,6,7,2,5,3,1]=>0101011=>1101010
[6,4,8,7,2,5,3,1]=>0101111=>1111010
[6,2,8,7,4,5,3,1]=>0101111=>1111010
[6,4,8,7,5,2,3,1]=>0101111=>1111010
[4,6,8,7,5,2,3,1]=>0101011=>1101010
[4,6,5,8,7,2,3,1]=>0100111=>1110010
[2,1,6,8,7,4,5,3]=>1001011=>1101001
[2,6,8,7,4,5,3,1]=>0101011=>1101010
[2,4,8,6,7,5,3,1]=>0101011=>1101010
[4,2,8,6,7,5,3,1]=>0111011=>1101110
[6,2,8,4,7,5,3,1]=>0101111=>1111010
[8,2,6,4,7,5,3,1]=>0101111=>1111010
[6,4,8,2,7,5,3,1]=>0101111=>1111010
[4,6,8,2,7,5,3,1]=>0101011=>1101010
[2,6,8,4,7,5,3,1]=>0101011=>1101010
[4,6,8,7,2,5,3,1]=>0101011=>1101010
[4,6,5,8,2,7,3,1]=>0100111=>1110010
[2,1,6,8,4,7,5,3]=>1001011=>1101001
[2,1,8,6,4,7,5,3]=>1001111=>1111001
[6,8,7,4,2,5,3,1]=>0111011=>1101110
[2,8,6,4,7,5,3,1]=>0101111=>1111010
[4,8,6,2,7,5,3,1]=>0101111=>1111010
[9,8,7,3,6,2,5,1,4]=>00011111=>11111000
[9,8,7,6,3,5,1,2,4]=>00011111=>11111000
[9,4,8,3,7,2,6,1,5]=>00001111=>11110000
[9,8,4,7,3,6,1,2,5]=>00001111=>11110000
[9,8,7,2,4,6,1,3,5]=>00001111=>11110000
[9,8,7,4,6,1,2,3,5]=>00001111=>11110000
[5,9,4,8,3,7,1,2,6]=>00000111=>11100000
[9,5,8,2,4,7,1,3,6]=>00000111=>11100000
[9,5,8,4,7,1,2,3,6]=>00000111=>11100000
[9,8,3,5,7,1,2,4,6]=>00000111=>11100000
[9,8,5,7,1,2,3,4,6]=>00000111=>11100000
[6,9,3,5,8,1,2,4,7]=>00000011=>11000000
[6,9,5,8,1,2,3,4,7]=>00000011=>11000000
[9,2,4,6,8,1,3,5,7]=>00000011=>11000000
[9,4,6,8,1,2,3,5,7]=>00000011=>11000000
[9,6,8,1,2,3,4,5,7]=>00000011=>11000000
[3,5,7,9,1,2,4,6,8]=>00000001=>10000000
[5,7,9,1,2,3,4,6,8]=>00000001=>10000000
[7,9,1,2,3,4,5,6,8]=>00000001=>10000000
[10,9,8,7,6,5,2,4,1,3]=>001111111=>111111100
[10,9,8,7,3,6,2,5,1,4]=>000111111=>111111000
[10,9,8,7,6,3,5,1,2,4]=>000111111=>111111000
[10,9,4,8,3,7,2,6,1,5]=>000011111=>111110000
[10,9,8,4,7,3,6,1,2,5]=>000011111=>111110000
[10,9,8,7,2,4,6,1,3,5]=>000011111=>111110000
[10,9,8,7,4,6,1,2,3,5]=>000011111=>111110000
[10,5,9,4,8,3,7,1,2,6]=>000001111=>111100000
[10,9,5,8,2,4,7,1,3,6]=>000001111=>111100000
[10,9,5,8,4,7,1,2,3,6]=>000001111=>111100000
[10,9,8,3,5,7,1,2,4,6]=>000001111=>111100000
[10,9,8,5,7,1,2,3,4,6]=>000001111=>111100000
[6,10,5,9,2,4,8,1,3,7]=>000000111=>111000000
[6,10,5,9,4,8,1,2,3,7]=>000000111=>111000000
[10,3,6,9,2,5,8,1,4,7]=>000000111=>111000000
[10,6,9,3,5,8,1,2,4,7]=>000000111=>111000000
[10,6,9,5,8,1,2,3,4,7]=>000000111=>111000000
[10,9,2,4,6,8,1,3,5,7]=>000000111=>111000000
[10,9,4,6,8,1,2,3,5,7]=>000000111=>111000000
[10,9,6,8,1,2,3,4,5,7]=>000000111=>111000000
[4,7,10,3,6,9,1,2,5,8]=>000000011=>110000000
[7,10,2,4,6,9,1,3,5,8]=>000000011=>110000000
[7,10,4,6,9,1,2,3,5,8]=>000000011=>110000000
[7,10,6,9,1,2,3,4,5,8]=>000000011=>110000000
[10,3,5,7,9,1,2,4,6,8]=>000000011=>110000000
[10,5,7,9,1,2,3,4,6,8]=>000000011=>110000000
[10,7,9,1,2,3,4,5,6,8]=>000000011=>110000000
[4,6,8,10,1,2,3,5,7,9]=>000000001=>100000000
[6,8,10,1,2,3,4,5,7,9]=>000000001=>100000000
[4,2,5,6,3,8,1,7]=>0010101=>1010100
[6,2,5,7,4,8,3,1]=>0100111=>1110010
[8,5,2,1,4,7,6,3]=>1001111=>1111001
[6,7,3,2,5,8,4,1]=>0110011=>1100110
[3,2,6,4,8,1,5,7]=>0100101=>1010010
[2,3,6,4,7,8,5,1]=>0001101=>1011000
[7,5,1,8,3,4,6,2]=>0001111=>1111000
[5,7,8,2,6,3,4,1]=>0010101=>1010100
[7,1,6,3,5,8,4,2]=>0010111=>1110100
[6,3,1,7,8,4,5,2]=>0101101=>1011010
[5,3,6,7,4,1,8,2]=>0011011=>1101100
[7,3,1,2,5,8,6,4]=>0100111=>1110010
[1,6,3,5,2,4,8,7]=>0001101=>1011000
[3,4,8,2,7,5,1,6]=>0001011=>1101000
[6,3,2,8,5,7,4,1]=>0110111=>1110110
[3,8,4,7,2,5,6,1]=>0000111=>1110000
[2,4,8,1,5,3,7,6]=>0001011=>1101000
[3,4,8,1,6,2,7,5]=>0000111=>1110000
[1,8,4,6,7,3,5,2]=>0001011=>1101000
[8,1,6,3,4,5,7,2]=>0000111=>1110000
[7,6,5,4,1,2,8,3]=>0011111=>1111100
[5,7,6,8,3,4,2,1]=>1010011=>1100101
[2,8,1,6,5,7,4,3]=>0010111=>1110100
[4,6,8,2,5,3,7,1]=>0001011=>1101000
[5,2,3,7,6,1,8,4]=>0001111=>1111000
[8,1,2,4,6,7,3,5]=>0000011=>1100000
[5,2,3,7,4,8,6,1]=>0001111=>1111000
[5,2,6,8,4,3,1,7]=>0111001=>1001110
[7,8,1,5,4,3,6,2]=>0011101=>1011100
[7,2,4,8,5,3,6,1]=>0001111=>1111000
[3,7,5,1,8,4,6,2]=>0001111=>1111000
[2,7,8,5,4,6,1,3]=>0001101=>1011000
[5,7,4,3,8,6,2,1]=>1010111=>1110101
[4,8,1,6,3,5,2,7]=>0001101=>1011000
[8,3,1,7,4,2,5,6]=>0110011=>1100110
[3,1,8,2,4,5,7,6]=>0100011=>1100010
[8,1,3,7,6,2,4,5]=>0000111=>1110000
[2,3,6,8,7,1,4,5]=>0000011=>1100000
[4,3,2,8,5,7,1,6]=>0110011=>1100110
[3,6,4,2,8,5,7,1]=>0010111=>1110100
[4,7,3,2,5,1,8,6]=>0101011=>1101010
[3,2,4,7,5,8,6,1]=>0100111=>1110010
[4,2,3,8,6,5,1,7]=>0011101=>1011100
[2,4,3,5,1,8,6,7]=>0011001=>1001100
[3,2,8,1,4,6,5,7]=>0100101=>1010010
[3,7,8,5,6,1,2,4]=>0000101=>1010000
[3,6,1,8,4,7,2,5]=>0000111=>1110000
[3,1,6,8,4,7,2,5]=>0100011=>1100010
[4,1,6,8,3,2,7,5]=>0110011=>1100110
[4,6,1,8,3,2,7,5]=>0100111=>1110010
[4,7,8,1,3,2,6,5]=>0100101=>1010010
[4,7,8,3,1,2,6,5]=>0100101=>1010010
[2,7,8,3,4,6,5,1]=>0001101=>1011000
[4,7,8,2,1,3,6,5]=>1000101=>1010001
[4,6,1,8,2,3,7,5]=>0000111=>1110000
[4,1,6,8,2,3,7,5]=>0010011=>1100100
[4,5,1,2,8,3,7,6]=>0001011=>1101000
[4,5,2,1,8,3,7,6]=>1001011=>1101001
[4,6,2,8,1,3,7,5]=>0000111=>1110000
[3,6,2,8,4,7,1,5]=>0000111=>1110000
[2,3,6,8,4,7,5,1]=>0001011=>1101000
[3,2,6,8,4,7,1,5]=>0100011=>1100010
[4,2,6,8,3,1,7,5]=>0110011=>1100110
[4,2,5,1,8,3,7,6]=>0011011=>1101100
[4,1,2,5,8,3,7,6]=>0010011=>1100100
[5,1,2,4,3,8,7,6]=>0011011=>1101100
[5,2,4,1,3,8,7,6]=>0011011=>1101100
[4,2,5,3,8,1,7,6]=>0011011=>1101100
[3,2,5,4,8,7,1,6]=>0101011=>1101010
[3,5,2,4,8,7,1,6]=>0001011=>1101000
[5,4,2,1,3,8,7,6]=>1011011=>1101101
[5,1,4,2,3,8,7,6]=>0011011=>1101100
[5,4,1,3,2,8,7,6]=>0111011=>1101110
[5,4,3,1,2,8,7,6]=>0111011=>1101110
[4,5,3,1,8,2,7,6]=>0101011=>1101010
[4,5,1,3,8,2,7,6]=>0001011=>1101000
[3,1,5,4,8,7,2,6]=>0101011=>1101010
[3,5,1,4,8,7,2,6]=>0001011=>1101000
[3,5,4,1,8,7,2,6]=>0011011=>1101100
[3,6,5,8,7,1,2,4]=>0000111=>1110000
[2,5,6,8,7,3,4,1]=>0010011=>1100100
[3,4,5,1,8,7,2,6]=>0001011=>1101000
[3,4,1,5,8,7,2,6]=>0010011=>1100100
[4,1,3,5,8,2,7,6]=>0010011=>1100100
[4,3,6,8,2,1,7,5]=>1010011=>1100101
[2,4,6,8,3,7,5,1]=>0001011=>1101000
[3,4,5,2,8,7,1,6]=>0001011=>1101000
[5,3,1,4,2,8,7,6]=>0111011=>1101110
[5,1,3,4,2,8,7,6]=>0011011=>1101100
[5,1,3,2,4,8,7,6]=>0101011=>1101010
[5,3,2,1,4,8,7,6]=>1101011=>1101011
[4,3,2,5,8,1,7,6]=>0110011=>1100110
[3,4,2,5,8,7,1,6]=>0010011=>1100100
[3,2,4,5,8,7,1,6]=>0100011=>1100010
[4,2,3,5,8,1,7,6]=>0010011=>1100100
[5,2,3,1,4,8,7,6]=>0101011=>1101010
[5,2,1,3,4,8,7,6]=>1001011=>1101001
[5,1,2,3,4,8,7,6]=>0001011=>1101000
[8,6,2,5,4,1,3,7]=>0011101=>1011100
[6,5,7,4,2,8,3,1]=>0110111=>1110110
[6,7,5,3,8,2,4,1]=>0011011=>1101100
[8,2,1,6,3,4,5,7]=>1000101=>1010001
[8,3,5,6,2,4,1,7]=>0010101=>1010100
[8,6,2,1,3,5,4,7]=>1001101=>1011001
[8,1,2,3,4,6,5,7]=>0000101=>1010000
[6,2,3,7,8,4,5,1]=>0001101=>1011000
[7,5,8,2,6,3,4,1]=>0010111=>1110100
[7,3,1,6,5,8,4,2]=>0110111=>1110110
[1,5,6,7,3,4,8,2]=>0000011=>1100000
[6,7,8,2,1,4,5,3]=>1001001=>1001001
[8,4,7,6,2,1,3,5]=>1000111=>1110001
[5,3,8,4,7,2,6,1]=>0001111=>1111000
[8,1,3,7,6,4,2,5]=>0010111=>1110100
[5,3,1,7,8,6,2,4]=>0101101=>1011010
[3,5,8,2,7,1,6,4]=>0000111=>1110000
[6,2,8,5,3,1,7,4]=>0101111=>1111010
[8,2,6,4,7,1,3,5]=>0000111=>1110000
[3,4,2,8,5,1,7,6]=>0011011=>1101100
[3,8,6,5,2,1,7,4]=>1001111=>1111001
[8,3,7,4,2,5,6,1]=>0010111=>1110100
[4,8,5,7,2,1,3,6]=>1000011=>1100001
[3,4,1,8,2,6,7,5]=>0010011=>1100100
[8,4,6,3,7,1,5,2]=>0001111=>1111000
[6,8,3,4,1,5,7,2]=>0010011=>1100100
[5,1,7,6,2,8,4,3]=>0011111=>1111100
[6,8,2,5,7,4,1,3]=>0010011=>1100100
[2,8,5,6,7,1,3,4]=>0000011=>1100000
[2,5,7,6,3,1,8,4]=>0100111=>1110010
[4,2,8,3,1,5,6,7]=>0110001=>1000110
[2,5,7,3,8,4,6,1]=>0000111=>1110000
[4,2,7,1,8,5,3,6]=>0011011=>1101100
[4,2,1,8,7,5,6,3]=>1010111=>1110101
[8,3,6,7,1,5,4,2]=>0011011=>1101100
[1,3,7,5,8,6,4,2]=>0010111=>1110100
[5,7,8,4,3,1,6,2]=>0110101=>1010110
[2,7,4,5,8,3,6,1]=>0000111=>1110000
[3,5,7,1,4,8,6,2]=>0000111=>1110000
[7,2,8,5,1,4,6,3]=>0001111=>1111000
[1,6,5,3,8,4,2,7]=>0011101=>1011100
[5,7,4,8,3,6,2,1]=>1000111=>1110001
[4,8,6,1,3,5,2,7]=>0001101=>1011000
[1,8,3,2,4,7,5,6]=>0100011=>1100010
[8,4,3,2,5,7,1,6]=>0110011=>1100110
[3,6,4,8,2,5,7,1]=>0000111=>1110000
[4,3,7,2,5,8,1,6]=>0010011=>1100100
[3,2,4,7,8,5,6,1]=>0100101=>1010010
[2,6,4,3,8,5,1,7]=>0011101=>1011100
[3,8,2,1,6,4,5,7]=>1000101=>1010001
[8,2,1,3,4,5,7,6]=>1000011=>1100001
[4,6,8,3,2,1,5,7]=>1100001=>1000011
[3,2,6,8,5,4,1,7]=>0111001=>1001110
[7,3,8,2,5,4,1,6]=>0011011=>1101100
[4,2,5,3,8,7,6,1]=>0011111=>1111100
[4,8,2,6,5,3,1,7]=>0101101=>1011010
[2,6,8,5,4,1,3,7]=>0011001=>1001100
[3,1,8,6,5,4,2,7]=>0111101=>1011110
[5,4,8,7,3,2,6,1]=>0101111=>1111010
[6,4,8,3,7,2,5,1]=>0001111=>1111000
[4,7,3,6,2,1,8,5]=>1000111=>1110001
[5,4,3,7,1,8,2,6]=>0011011=>1101100
[7,3,8,5,1,4,2,6]=>0011011=>1101100
[5,4,8,7,6,2,1,3]=>1001111=>1111001
[3,8,1,5,7,4,6,2]=>0000111=>1110000
[4,8,5,7,3,1,6,2]=>0100111=>1110010
[1,5,4,8,3,7,6,2]=>0001111=>1111000
[4,8,3,6,7,1,5,2]=>0001011=>1101000
[4,7,8,3,1,6,5,2]=>0101101=>1011010
[8,7,5,3,6,4,2,1]=>1011111=>1111101
[4,6,1,3,8,7,5,2]=>0001111=>1111000
[6,8,2,1,7,4,5,3]=>1001011=>1101001
[3,7,1,6,4,2,8,5]=>0010111=>1110100
[3,1,2,7,5,6,8,4]=>0100011=>1100010
[3,6,1,2,7,5,8,4]=>0000111=>1110000
[3,7,6,2,5,8,1,4]=>0000111=>1110000
[3,6,2,5,8,7,4,1]=>0010111=>1110100
[8,5,2,3,6,7,4,1]=>0011011=>1101100
[4,7,2,6,3,8,1,5]=>0000111=>1110000
[6,3,2,4,8,7,5,1]=>0101111=>1111010
[3,7,2,4,6,1,8,5]=>0000111=>1110000
[5,3,7,2,8,1,4,6]=>0001011=>1101000
[6,3,2,8,7,5,1,4]=>0101111=>1111010
[7,3,8,2,6,5,1,4]=>0001111=>1111000
[6,4,8,7,2,5,1,3]=>0001111=>1111000
[2,5,4,8,1,7,6,3]=>0001111=>1111000
[5,2,8,1,7,6,3,4]=>0001111=>1111000
[6,2,1,3,8,7,5,4]=>1001111=>1111001
[3,6,1,8,7,5,2,4]=>0001111=>1111000
[5,6,1,2,8,7,4,3]=>0010111=>1110100
[7,5,2,8,1,6,4,3]=>0011111=>1111100
[2,7,6,8,1,5,4,3]=>0011011=>1101100
[7,8,5,1,6,2,4,3]=>0011101=>1011100
[7,4,8,6,1,2,5,3]=>0001111=>1111000
[7,2,1,8,3,6,5,4]=>1001111=>1111001
[5,8,7,1,6,4,3,2]=>0110111=>1110110
[7,6,5,4,3,2,9,8,1]=>01111111=>11111110
[11,9,8,7,6,5,4,3,2,1,10]=>1111111101=>1011111111
[10,7,6,5,4,3,2,1,9,8]=>111111011=>110111111
[9,6,5,4,3,2,8,1,7]=>01111011=>11011110
[9,7,5,4,3,2,1,8,6]=>11110111=>11101111
[8,5,4,3,7,2,1,6]=>1011011=>1101101
[6,5,4,8,3,2,7,1]=>0101111=>1111010
[7,6,5,4,3,9,2,8,1]=>00111111=>11111100
[7,6,4,3,2,8,5,1]=>0111111=>1111110
[8,6,5,4,3,2,9,7,1]=>01111111=>11111110
[8,7,6,5,4,3,2,10,9,1]=>011111111=>111111110
[10,9,8,7,6,5,4,3,2,11,1]=>0111111111=>1111111110
[7,3,1,4,8,2,5,6]=>0100011=>1100010
[7,4,1,2,5,8,3,6]=>0010011=>1100100
[6,7,4,2,5,1,3,8]=>0011010=>0101100
[5,7,2,4,6,8,1,3]=>0000011=>1100000
[4,7,5,1,6,2,8,3]=>0001111=>1111000
[5,7,4,6,3,1,8,2]=>0100111=>1110010
[7,5,1,4,3,2,8,6]=>0111011=>1101110
[8,6,4,2,3,7,5,1]=>0011111=>1111100
[6,4,7,1,3,8,5,2]=>0001111=>1111000
[5,4,2,7,3,1,6,8]=>0111010=>0101110
[4,5,1,2,7,6,8,3]=>0001011=>1101000
[5,4,6,8,3,1,2,7]=>0101001=>1001010
[6,4,8,1,3,7,2,5]=>0000111=>1110000
[4,6,1,3,8,5,2,7]=>0001101=>1011000
[1,3,8,4,5,7,2,6]=>0000011=>1100000
[2,6,7,4,5,3,1,8]=>0101010=>0101010
[2,6,8,4,3,5,1,7]=>0011001=>1001100
[1,3,7,4,2,8,5,6]=>0010011=>1100100
[4,6,1,3,7,2,5,8]=>0000110=>0110000
[7,5,8,6,2,1,3,4]=>1000111=>1110001
[2,8,1,3,6,5,4,7]=>0001101=>1011000
[2,8,7,3,5,4,1,6]=>0011011=>1101100
[3,4,2,6,8,7,1,5]=>0010011=>1100100
[7,4,2,3,6,1,8,5]=>0010111=>1110100
[8,4,2,3,6,5,7,1]=>0010111=>1110100
[7,3,8,4,1,2,6,5]=>0010111=>1110100
[6,8,3,2,7,1,5,4]=>0101011=>1101010
[2,8,5,6,3,7,1,4]=>0000111=>1110000
[7,4,2,5,8,1,6,3]=>0010111=>1110100
[2,7,8,3,4,5,1,6]=>0001001=>1001000
[3,7,1,2,4,6,5,8]=>0000110=>0110000
[7,5,6,8,2,1,4,3]=>1010011=>1100101
[3,1,6,5,2,7,4,8]=>0101110=>0111010
[2,8,6,5,3,4,1,7]=>0011101=>1011100
[1,7,2,3,5,6,8,4]=>0000011=>1100000
[3,7,4,2,1,5,6,8]=>1010010=>0100101
[3,4,6,2,8,5,7,1]=>0000111=>1110000
[4,2,1,7,5,8,3,6]=>1010011=>1100101
[4,7,2,6,5,1,3,8]=>0001110=>0111000
[3,7,4,1,2,5,8,6]=>0010011=>1100100
[4,7,1,6,5,2,8,3]=>0001111=>1111000
[4,7,3,6,5,1,8,2]=>0001111=>1111000
[4,3,7,1,6,8,5,2]=>0011011=>1101100
[4,2,1,7,5,6,8,3]=>1010011=>1100101
[3,2,4,8,6,7,1,5]=>0100011=>1100010
[4,2,6,8,7,3,1,5]=>0110011=>1100110
[3,4,6,1,8,5,2,7]=>0001101=>1011000
[4,1,6,7,5,8,2,3]=>0010011=>1100100
[4,3,6,7,5,1,2,8]=>0011010=>0101100
[4,3,7,1,6,8,2,5]=>0010011=>1100100
[4,3,7,5,6,8,2,1]=>1010011=>1100101
[4,1,7,3,6,5,2,8]=>0011110=>0111100
[2,8,7,4,5,3,1,6]=>0101011=>1101010
[2,8,7,4,3,5,1,6]=>0011011=>1101100
[3,8,1,4,2,6,5,7]=>0010101=>1010100
[4,1,7,3,6,2,5,8]=>0010110=>0110100
[5,8,7,6,1,2,4,3]=>0010111=>1110100
[5,8,7,6,2,1,3,4]=>1000111=>1110001
[4,1,7,2,6,8,5,3]=>0011011=>1101100
[4,2,7,3,6,1,8,5]=>0010111=>1110100
[4,2,7,3,6,5,8,1]=>0010111=>1110100
[3,8,2,4,5,6,7,1]=>0000011=>1100000
[3,8,2,4,1,6,7,5]=>0010011=>1100100
[3,8,5,6,2,4,1,7]=>0010101=>1010100
[2,8,6,5,3,7,1,4]=>0001111=>1111000
[3,8,6,5,1,4,7,2]=>0001111=>1111000
[3,8,2,1,4,6,7,5]=>1000011=>1100001
[3,8,2,5,4,6,7,1]=>0001011=>1101000
[4,2,7,5,6,3,8,1]=>0010111=>1110100
[4,2,7,5,6,1,8,3]=>0010111=>1110100
[4,2,6,7,5,3,1,8]=>0111010=>0101110
[3,2,6,1,4,5,8,7]=>0100101=>1010010
[2,8,7,3,4,5,1,6]=>0001011=>1101000
[3,8,1,2,4,6,5,7]=>0000101=>1010000
[5,8,7,6,1,3,4,2]=>0010111=>1110100
[5,8,7,6,2,3,4,1]=>0010111=>1110100
[4,1,7,5,6,2,3,8]=>0010110=>0110100
[3,8,1,5,2,6,4,7]=>0001101=>1011000
[2,8,7,5,3,4,1,6]=>0011011=>1101100
[2,8,7,5,4,3,1,6]=>0111011=>1101110
[4,1,7,5,6,3,2,8]=>0110110=>0110110
[5,8,7,6,1,3,2,4]=>0100111=>1110010
[5,8,7,6,4,1,2,3]=>0010111=>1110100
[5,4,2,3,7,6,8,1]=>0011011=>1101100
[7,4,3,5,2,8,1,6]=>0011011=>1101100
[8,4,3,7,5,1,6,2]=>0011111=>1111100
[8,4,7,2,5,1,6,3]=>0001111=>1111000
[7,4,6,2,3,5,8,1]=>0000111=>1110000
[5,1,7,2,4,6,8,3]=>0001011=>1101000
[4,5,7,1,2,6,8,3]=>0000011=>1100000
[5,4,1,7,3,6,8,2]=>0011011=>1101100
[3,6,4,7,5,2,8,1]=>0001111=>1111000
[3,4,7,6,2,5,8,1]=>0000111=>1110000
[4,7,5,6,1,3,8,2]=>0000111=>1110000
[5,7,6,4,3,1,8,2]=>0110111=>1110110
[5,7,6,3,1,4,8,2]=>0100111=>1110010
[7,5,2,3,4,8,1,6]=>0001011=>1101000
[8,7,5,3,4,1,6,2]=>0011111=>1111100
[6,7,1,3,8,4,2,5]=>0010011=>1100100
[7,6,1,3,4,8,5,2]=>0001111=>1111000
[3,6,5,2,7,8,1,4]=>0001101=>1011000
[3,2,8,6,7,1,4,5]=>0100011=>1100010
[4,8,3,6,5,2,1,7]=>1001101=>1011001
[1,8,6,5,4,2,3,7]=>0011101=>1011100
[1,8,7,2,3,5,4,6]=>0001011=>1101000
[1,8,7,2,5,3,4,6]=>0001011=>1101000
[3,6,8,5,1,2,4,7]=>0001001=>1001000
[3,7,5,1,8,2,6,4]=>0001111=>1111000
[7,1,2,8,3,5,6,4]=>0000111=>1110000
[6,1,7,8,2,5,3,4]=>0001101=>1011000
[6,7,5,2,8,1,4,3]=>0011011=>1101100
[7,1,4,5,8,6,2,3]=>0000111=>1110000
[5,7,6,4,2,8,1,3]=>0010111=>1110100
[7,5,6,1,2,8,4,3]=>0010111=>1110100
[4,1,3,7,8,6,2,5]=>0010101=>1010100
[5,1,4,3,6,8,7,2]=>0011011=>1101100
[4,5,7,6,8,2,1,3]=>1000011=>1100001
[5,7,6,8,4,2,1,3]=>1010011=>1100101
[5,1,6,8,4,2,7,3]=>0011011=>1101100
[7,4,8,2,3,6,5,1]=>0001111=>1111000
[5,6,8,4,7,3,2,1]=>1100011=>1100011
[6,4,7,8,5,2,1,3]=>1001101=>1011001
[3,6,4,8,5,1,2,7]=>0001101=>1011000
[3,7,4,8,1,2,5,6]=>0000011=>1100000
[7,4,3,8,2,6,5,1]=>0011111=>1111100
[7,6,8,3,2,5,4,1]=>0111011=>1101110
[8,7,1,3,5,4,6,2]=>0001111=>1111000
[7,1,8,3,4,2,6,5]=>0010111=>1110100
[7,6,8,3,1,4,5,2]=>0101011=>1101010
[3,1,4,8,2,5,7,6]=>0100011=>1100010
[4,8,5,2,1,3,6,7]=>1001001=>1001001
[5,8,2,6,3,1,4,7]=>0100101=>1010010
[6,8,2,3,7,4,1,5]=>0010011=>1100100
[7,8,2,3,4,6,5,1]=>0001101=>1011000
[8,1,7,2,4,5,3,6]=>0001011=>1101000
[8,1,3,6,2,5,4,7]=>0001101=>1011000
[7,2,1,6,3,5,4,8]=>1001110=>0111001
[2,7,1,6,3,5,4,8]=>0001110=>0111000
[2,7,1,5,4,3,6,8]=>0011010=>0101100
[7,2,1,5,4,3,6,8]=>1011010=>0101101
[8,1,3,5,4,2,6,7]=>0011001=>1001100
[8,1,5,3,4,2,6,7]=>0011001=>1001100
[8,1,5,6,2,3,7,4]=>0000111=>1110000
[8,1,4,5,3,2,6,7]=>0101001=>1001010
[8,1,4,3,5,2,6,7]=>0011001=>1001100
[7,2,1,4,5,3,6,8]=>1001010=>0101001
[2,7,1,4,5,3,6,8]=>0001010=>0101000
[2,6,3,1,5,4,7,8]=>0101100=>0011010
[6,3,2,1,5,4,7,8]=>1101100=>0011011
[7,3,1,4,5,2,6,8]=>0101010=>0101010
[7,3,1,5,4,2,6,8]=>0111010=>0101110
[7,3,1,6,2,5,4,8]=>0101110=>0111010
[3,7,1,6,2,5,4,8]=>0001110=>0111000
[3,7,1,4,5,2,6,8]=>0001010=>0101000
[3,6,2,1,5,4,7,8]=>1001100=>0011001
[2,3,6,1,5,4,7,8]=>0001100=>0011000
[3,5,2,4,1,6,7,8]=>0011000=>0001100
[6,3,4,1,5,2,7,8]=>0011100=>0011100
[6,2,4,1,5,3,7,8]=>0011100=>0011100
[2,6,4,1,5,3,7,8]=>0011100=>0011100
[2,6,5,1,3,7,4,8]=>0001110=>0111000
[6,2,5,1,3,7,4,8]=>0001110=>0111000
[6,5,2,1,3,7,4,8]=>1001110=>0111001
[7,6,1,2,4,5,3,8]=>0001110=>0111000
[6,7,1,2,8,3,5,4]=>0001011=>1101000
[6,7,1,2,5,4,3,8]=>0011010=>0101100
[5,6,2,1,3,7,4,8]=>1000110=>0110001
[5,2,6,1,3,7,4,8]=>0001110=>0111000
[2,4,6,1,5,3,7,8]=>0001100=>0011000
[4,7,1,3,5,2,6,8]=>0001010=>0101000
[4,7,1,5,3,2,6,8]=>0101010=>0101010
[5,7,1,4,2,6,3,8]=>0010110=>0110100
[5,7,1,6,2,3,8,4]=>0000111=>1110000
[5,6,3,1,2,7,4,8]=>0100110=>0110010
[4,2,5,3,1,6,7,8]=>0111000=>0001110
[5,3,6,1,2,7,4,8]=>0001110=>0111000
[3,4,6,1,5,2,7,8]=>0001100=>0011000
[6,5,1,8,7,3,4,2]=>0011111=>1111100
[8,2,7,5,4,1,3,6]=>0011011=>1101100
[6,8,5,2,3,4,1,7]=>0011001=>1001100
[2,6,8,7,1,5,3,4]=>0001011=>1101000
[8,5,6,2,7,1,4,3]=>0010111=>1110100
[6,5,1,2,7,8,4,3]=>0011101=>1011100
[4,7,6,1,5,3,8,2]=>0001111=>1111000
[5,7,6,4,1,3,8,2]=>0010111=>1110100
[7,6,2,4,5,3,8,1]=>0001111=>1111000
[6,1,7,5,3,8,4,2]=>0011111=>1111100
[8,6,7,5,3,1,4,2]=>0111011=>1101110
[8,5,2,7,1,6,4,3]=>0011111=>1111100
[7,6,1,5,3,8,4,2]=>0011111=>1111100
[5,6,2,4,7,8,1,3]=>0000101=>1010000
[3,4,6,1,7,8,5,2]=>0001101=>1011000
[3,4,8,6,7,1,5,2]=>0001011=>1101000
[4,8,5,6,7,2,3,1]=>0100011=>1100010
[5,8,6,4,1,2,7,3]=>0010111=>1110100
[5,8,6,1,7,2,4,3]=>0010111=>1110100
[5,8,7,3,2,6,4,1]=>0110111=>1110110
[5,8,1,7,2,6,4,3]=>0010111=>1110100
[8,1,5,7,2,6,4,3]=>0010111=>1110100
[8,1,7,2,5,6,3,4]=>0000111=>1110000
[6,8,7,2,5,1,3,4]=>0001011=>1101000
[5,8,7,2,1,6,3,4]=>1000111=>1110001
[4,8,1,5,2,6,7,3]=>0001011=>1101000
[3,7,8,5,1,6,2,4]=>0001101=>1011000
[6,5,2,7,8,1,4,3]=>0011101=>1011100
[7,1,2,8,5,6,3,4]=>0000111=>1110000
[8,7,2,1,5,6,3,4]=>1000111=>1110001
[8,6,7,1,5,2,3,4]=>0001011=>1101000
[6,1,7,8,5,2,3,4]=>0001101=>1011000
[7,5,6,2,1,8,4,3]=>1010111=>1110101
[8,7,5,2,1,6,4,3]=>1011111=>1111101
[7,1,3,5,8,6,2,4]=>0000111=>1110000
[5,1,3,4,6,8,7,2]=>0001011=>1101000
[4,5,3,6,8,2,7,1]=>0001011=>1101000
[5,6,3,4,8,1,7,2]=>0000111=>1110000
[4,6,7,8,5,1,3,2]=>0101001=>1001010
[8,4,3,1,2,6,7,5]=>0110011=>1100110
[8,5,1,6,3,4,7,2]=>0001111=>1111000
[5,1,8,6,3,4,7,2]=>0001111=>1111000
[4,6,8,1,5,3,7,2]=>0001011=>1101000
[6,4,5,8,3,2,7,1]=>0100111=>1110010
[3,6,4,8,7,1,5,2]=>0001111=>1111000
[6,5,8,1,3,4,7,2]=>0000111=>1110000
[5,6,8,3,1,2,7,4]=>0100011=>1100010
[6,1,8,3,5,2,7,4]=>0001111=>1111000
[7,6,8,3,5,2,1,4]=>1001011=>1101001
[8,6,1,3,5,2,7,4]=>0001111=>1111000
[8,7,1,3,5,6,2,4]=>0000111=>1110000
[6,7,8,3,5,1,2,4]=>0001001=>1001000
[3,4,8,1,2,6,7,5]=>0000011=>1100000
[5,8,2,4,3,6,7,1]=>0010011=>1100100
[5,8,2,3,1,6,7,4]=>0100011=>1100010
[6,8,2,3,5,1,7,4]=>0001011=>1101000
[7,8,2,3,5,6,1,4]=>0000101=>1010000
[8,6,5,1,4,3,7,2]=>0011111=>1111100
[2,4,8,6,1,3,7,5]=>0000111=>1110000
[6,7,1,8,4,3,5,2]=>0011011=>1101100
[2,7,8,6,1,4,3,5]=>0010101=>1010100
[2,7,3,8,1,6,4,5]=>0000111=>1110000
[7,5,1,8,2,4,6,3]=>0001111=>1111000
[2,7,8,4,1,6,3,5]=>0010101=>1010100
[2,6,5,4,1,3,8,7]=>0011101=>1011100
[4,1,7,6,3,8,2,5]=>0010111=>1110100
[4,8,2,5,7,6,3,1]=>0100111=>1110010
[3,4,6,5,1,8,2,7]=>0001101=>1011000
[2,6,5,3,4,1,8,7]=>0011101=>1011100
[4,6,1,5,2,3,8,7]=>0001101=>1011000
[6,2,3,5,1,4,8,7]=>0001101=>1011000
[2,6,7,5,1,8,4,3]=>0011011=>1101100
[8,6,1,2,5,3,4,7]=>0001101=>1011000
[6,2,5,1,8,3,4,7]=>0001101=>1011000
[7,6,5,2,8,3,4,1]=>0011111=>1111100
[2,6,3,5,1,8,7,4]=>0001111=>1111000
[2,4,7,6,5,8,1,3]=>0000111=>1110000
[2,1,4,8,7,6,3,5]=>1000111=>1110001
[7,4,6,8,5,3,2,1]=>1101011=>1101011
[8,1,3,5,7,4,6,2]=>0000111=>1110000
[3,2,8,7,5,1,6,4]=>0101111=>1111010
[4,8,5,1,6,7,2,3]=>0001011=>1101000
[3,8,5,1,6,7,2,4]=>0001011=>1101000
[7,8,6,1,3,5,2,4]=>0001101=>1011000
[5,6,7,2,8,1,3,4]=>0000011=>1100000
[2,5,1,8,6,7,4,3]=>0011011=>1101100
[3,5,1,8,6,7,4,2]=>0011011=>1101100
[5,2,3,8,6,7,4,1]=>0011011=>1101100
[8,3,5,4,6,7,1,2]=>0001011=>1101000
[5,1,3,8,6,7,4,2]=>0011011=>1101100
[3,2,5,8,6,7,4,1]=>0110011=>1100110
[6,2,1,5,3,8,7,4]=>1001111=>1111001
[5,6,3,2,8,1,4,7]=>0100101=>1010010
[8,1,6,3,5,2,7,4]=>0001111=>1111000
[8,7,6,2,5,3,1,4]=>0101111=>1111010
[4,7,6,8,3,2,5,1]=>0101011=>1101010
[2,7,5,8,1,3,4,6]=>0000011=>1100000
[7,6,2,8,5,1,4,3]=>0011111=>1111100
[8,1,3,7,5,2,6,4]=>0001111=>1111000
[3,4,8,7,5,1,6,2]=>0001111=>1111000
[6,3,8,1,4,2,5,7]=>0010101=>1010100
[6,3,8,5,7,4,1,2]=>0010111=>1110100
[7,4,6,8,5,1,3,2]=>0101011=>1101010
[2,1,4,8,7,5,6,3]=>1000111=>1110001
[7,1,5,8,2,6,4,3]=>0010111=>1110100
[3,6,8,2,4,1,7,5]=>0010011=>1100100
[4,5,8,2,6,7,3,1]=>0100011=>1100010
[5,2,8,1,6,7,3,4]=>0001011=>1101000
[2,5,8,4,6,7,3,1]=>0100011=>1100010
[5,8,3,4,6,7,2,1]=>1000011=>1100001
[8,4,3,2,6,7,1,5]=>0110011=>1100110
[4,2,8,1,6,7,3,5]=>0010011=>1100100
[2,4,8,1,6,7,3,5]=>0000011=>1100000
[5,1,8,2,6,7,3,4]=>0001011=>1101000
[3,4,8,7,2,1,5,6]=>1000011=>1100001
[7,8,5,3,6,4,2,1]=>1011101=>1011101
[2,8,5,7,4,1,3,6]=>0010011=>1100100
[5,8,4,1,6,7,2,3]=>0010011=>1100100
[3,8,1,4,6,7,2,5]=>0000011=>1100000
[8,2,3,4,6,7,1,5]=>0000011=>1100000
[6,2,7,3,8,4,1,5]=>0010111=>1110100
[7,4,3,2,8,5,1,6]=>0111011=>1101110
[5,3,2,8,4,6,1,7]=>0101101=>1011010
[8,4,2,6,5,3,1,7]=>0111101=>1011110
[7,4,2,5,3,1,6,8]=>0111010=>0101110
[8,3,6,2,5,4,1,7]=>0011101=>1011100
[5,4,8,3,2,6,1,7]=>0101101=>1011010
[3,5,8,2,4,6,1,7]=>0000101=>1010000
[6,4,7,8,2,3,1,5]=>0100101=>1010010
[5,8,3,6,4,2,1,7]=>1010101=>1010101
[4,8,6,2,5,3,1,7]=>0101101=>1011010
[1,6,4,3,2,8,7,5]=>0110111=>1110110
[1,5,3,2,8,4,7,6]=>0101011=>1101010
[5,7,4,3,1,2,6,8]=>0110010=>0100110
[2,8,7,3,5,1,4,6]=>0001011=>1101000
[7,3,8,6,4,1,2,5]=>0010111=>1110100
[6,1,2,7,3,8,5,4]=>0001111=>1111000
[2,1,7,4,3,8,6,5]=>1010111=>1110101
[6,1,4,3,8,2,7,5]=>0010111=>1110100
[5,1,3,2,8,7,4,6]=>0101011=>1101010
[1,8,4,2,7,6,5,3]=>0011111=>1111100
[1,8,3,7,2,6,5,4]=>0001111=>1111000
[5,1,4,8,3,7,2,6]=>0001011=>1101000
[2,1,6,8,5,4,7,3]=>1001011=>1101001
[6,1,5,7,8,2,4,3]=>0010101=>1010100
[8,3,1,6,7,2,5,4]=>0101011=>1101010
[7,4,8,6,1,3,2,5]=>0100111=>1110010
[4,7,6,1,2,5,3,8]=>0001110=>0111000
[3,7,6,1,5,2,4,8]=>0001110=>0111000
[1,5,4,8,3,2,7,6]=>0101011=>1101010
[7,3,6,1,2,5,4,8]=>0001110=>0111000
[5,4,7,1,3,2,6,8]=>0101010=>0101010
[5,7,4,8,2,1,3,6]=>1000011=>1100001
[4,6,8,2,5,1,3,7]=>0001001=>1001000
[7,4,6,2,1,5,3,8]=>1001110=>0111001
[1,2,6,3,8,5,7,4]=>0000111=>1110000
[1,5,2,6,8,4,7,3]=>0001011=>1101000
[5,7,2,3,8,1,4,6]=>0000011=>1100000
[6,4,7,5,8,1,2,3]=>0000111=>1110000
[7,4,8,5,1,6,3,2]=>0101111=>1111010
[5,8,3,6,1,7,4,2]=>0010111=>1110100
[8,6,4,2,1,7,5,3]=>1011111=>1111101
[7,4,2,1,5,8,6,3]=>1010111=>1110101
[7,6,4,1,8,5,2,3]=>0011111=>1111100
[1,6,4,8,7,5,3,2]=>0101111=>1111010
[6,3,1,2,8,4,7,5]=>0100111=>1110010
[7,5,1,3,2,8,6,4]=>0101111=>1111010
[4,7,1,2,5,8,6,3]=>0000111=>1110000
[6,8,4,1,2,7,5,3]=>0011011=>1101100
[7,5,8,1,2,6,4,3]=>0010111=>1110100
[7,4,8,1,6,3,5,2]=>0001111=>1111000
[5,8,2,1,7,3,6,4]=>1000111=>1110001
[3,6,1,8,2,4,7,5]=>0000111=>1110000
[1,3,8,7,6,2,5,4]=>0001111=>1111000
[5,4,1,8,7,3,2,6]=>0111011=>1101110
[3,5,1,8,7,2,4,6]=>0001011=>1101000
[4,6,1,8,3,7,2,5]=>0000111=>1110000
[4,7,1,2,8,6,3,5]=>0000111=>1110000
[5,8,4,1,7,6,2,3]=>0010111=>1110100
[7,6,8,1,5,4,2,3]=>0011011=>1101100
[8,6,1,7,5,4,3,2]=>0111111=>1111110
[7,1,5,8,6,4,3,2]=>0110111=>1110110
[5,1,8,7,3,6,4,2]=>0011111=>1111100
[4,1,8,7,6,2,5,3]=>0011111=>1111100
[3,1,8,7,6,5,2,4]=>0101111=>1111010
[1,6,4,5,2,3,7,8]=>0001100=>0011000
[1,7,4,5,2,3,6,8]=>0001010=>0101000
[1,7,3,5,2,4,6,8]=>0001010=>0101000
[1,6,3,5,2,4,7,8]=>0001100=>0011000
[1,6,3,4,2,5,7,8]=>0010100=>0010100
[1,7,3,4,2,5,6,8]=>0010010=>0100100
[1,8,6,7,3,4,2,5]=>0010011=>1100100
[1,8,5,7,3,4,2,6]=>0010011=>1100100
[1,7,3,4,2,6,5,8]=>0010110=>0110100
[1,5,2,8,4,7,3,6]=>0001011=>1101000
[1,4,2,8,5,7,3,6]=>0010011=>1100100
[1,7,3,5,2,6,4,8]=>0001110=>0111000
[1,8,4,7,3,5,2,6]=>0001011=>1101000
[1,7,3,6,2,5,4,8]=>0001110=>0111000
[1,7,3,6,2,4,5,8]=>0000110=>0110000
[1,7,4,6,2,3,5,8]=>0000110=>0110000
[1,8,5,6,2,3,4,7]=>0000101=>1010000
[1,8,5,6,2,4,3,7]=>0010101=>1010100
[1,3,2,8,5,6,4,7]=>0100101=>1010010
[1,4,2,8,5,6,3,7]=>0010101=>1010100
[1,5,2,8,4,6,3,7]=>0001101=>1011000
[1,6,2,8,4,5,3,7]=>0001101=>1011000
[9,1,2,3,5,4,6,7,8]=>00010001=>10001000
[8,1,2,4,5,3,6,7]=>0001001=>1001000
[2,3,4,6,5,7,8,9,1]=>00001001=>10010000
[10,1,2,3,4,6,5,7,8,9]=>000010001=>100010000
[9,1,2,3,5,6,4,7,8]=>00001001=>10010000
[2,3,4,7,5,6,8,9,1]=>00000101=>10100000
[2,3,4,6,7,5,8,9,1]=>00000101=>10100000
[2,3,4,5,7,6,8,9,10,1]=>000001001=>100100000
[9,10,5,6,7,8,3,4,1,2]=>001000101=>101000100
[5,8,9,6,7,10,3,4,1,2]=>001000011=>110000100
[9,10,7,8,3,4,5,6,1,2]=>000010101=>101010000
[9,10,3,6,7,4,5,8,1,2]=>000001101=>101100000
[3,8,9,6,7,4,5,10,1,2]=>000001011=>110100000
[3,6,7,8,9,4,5,10,1,2]=>000000011=>110000000
[9,10,3,4,5,6,7,8,1,2]=>000000101=>101000000
[3,8,9,4,5,6,7,10,1,2]=>000000011=>110000000
[3,4,7,8,5,6,9,10,1,2]=>000000101=>101000000
[7,8,9,10,5,6,1,2,3,4]=>000010001=>100010000
[5,8,9,6,7,10,1,2,3,4]=>000000011=>110000000
[9,10,7,8,1,4,5,2,3,6]=>000100101=>101001000
[7,8,9,10,1,4,5,2,3,6]=>000100001=>100001000
[9,10,1,6,7,4,5,2,3,8]=>000101001=>100101000
[1,8,9,6,7,4,5,2,3,10]=>000101010=>010101000
[1,6,7,8,9,4,5,2,3,10]=>000100010=>010001000
[9,10,1,4,5,6,7,2,3,8]=>000001001=>100100000
[1,8,9,4,5,6,7,2,3,10]=>000001010=>010100000
[1,4,7,8,5,6,9,2,3,10]=>000000110=>011000000
[1,4,5,6,7,8,9,2,3,10]=>000000010=>010000000
[9,10,1,6,7,2,3,4,5,8]=>000001001=>100100000
[1,8,9,6,7,2,3,4,5,10]=>000001010=>010100000
[1,6,7,8,9,2,3,4,5,10]=>000000010=>010000000
[9,10,1,2,5,6,3,4,7,8]=>000010001=>100010000
[1,8,9,2,5,6,3,4,7,10]=>000010010=>010010000
[1,2,7,8,5,6,3,4,9,10]=>000010100=>001010000
[1,2,5,6,7,8,3,4,9,10]=>000000100=>001000000
[1,8,9,2,3,4,5,6,7,10]=>000000010=>010000000
[1,2,7,8,3,4,5,6,9,10]=>000000100=>001000000
[1,2,3,6,7,4,5,8,9,10]=>000001000=>000100000
[9,10,11,12,7,8,5,6,3,4,1,2]=>00101010001=>10001010100
[11,12,7,8,9,10,5,6,3,4,1,2]=>00101000101=>10100010100
[7,10,11,8,9,12,5,6,3,4,1,2]=>00101000011=>11000010100
[7,8,9,10,11,12,5,6,3,4,1,2]=>00101000001=>10000010100
[11,12,9,10,5,6,7,8,3,4,1,2]=>00100010101=>10101000100
[9,10,11,12,5,6,7,8,3,4,1,2]=>00100010001=>10001000100
[5,10,11,8,9,6,7,12,3,4,1,2]=>00100001011=>11010000100
[5,6,7,8,9,10,11,12,3,4,1,2]=>00100000001=>10000000100
[11,12,9,10,7,8,3,4,5,6,1,2]=>00001010101=>10101010000
[9,10,11,12,7,8,3,4,5,6,1,2]=>00001010001=>10001010000
[11,12,7,8,9,10,3,4,5,6,1,2]=>00001000101=>10100010000
[7,8,9,10,11,12,3,4,5,6,1,2]=>00001000001=>10000010000
[11,12,9,10,3,6,7,4,5,8,1,2]=>00000110101=>10101100000
[9,10,11,12,3,6,7,4,5,8,1,2]=>00000110001=>10001100000
[11,12,3,8,9,6,7,4,5,10,1,2]=>00000101101=>10110100000
[3,10,11,8,9,6,7,4,5,12,1,2]=>00000101011=>11010100000
[3,8,9,10,11,6,7,4,5,12,1,2]=>00000100011=>11000100000
[11,12,3,6,7,8,9,4,5,10,1,2]=>00000001101=>10110000000
[3,10,11,6,7,8,9,4,5,12,1,2]=>00000001011=>11010000000
[3,6,9,10,7,8,11,4,5,12,1,2]=>00000000111=>11100000000
[3,6,7,8,9,10,11,4,5,12,1,2]=>00000000011=>11000000000
[11,12,9,10,3,4,5,6,7,8,1,2]=>00000010101=>10101000000
[9,10,11,12,3,4,5,6,7,8,1,2]=>00000010001=>10001000000
[11,12,3,8,9,4,5,6,7,10,1,2]=>00000001101=>10110000000
[3,10,11,8,9,4,5,6,7,12,1,2]=>00000001011=>11010000000
[3,8,9,10,11,4,5,6,7,12,1,2]=>00000000011=>11000000000
[11,12,3,4,7,8,5,6,9,10,1,2]=>00000010101=>10101000000
[3,10,11,4,7,8,5,6,9,12,1,2]=>00000010011=>11001000000
[3,4,9,10,7,8,5,6,11,12,1,2]=>00000010101=>10101000000
[3,4,7,8,9,10,5,6,11,12,1,2]=>00000000101=>10100000000
[11,12,3,4,5,6,7,8,9,10,1,2]=>00000000101=>10100000000
[3,10,11,4,5,6,7,8,9,12,1,2]=>00000000011=>11000000000
[3,4,9,10,5,6,7,8,11,12,1,2]=>00000000101=>10100000000
[3,4,5,8,9,6,7,10,11,12,1,2]=>00000001001=>10010000000
[3,4,5,6,7,8,9,10,11,12,1,2]=>00000000001=>10000000000
[11,12,9,10,7,8,5,6,1,2,3,4]=>00001010101=>10101010000
[9,10,11,12,7,8,5,6,1,2,3,4]=>00001010001=>10001010000
[11,12,7,8,9,10,5,6,1,2,3,4]=>00001000101=>10100010000
[7,8,9,10,11,12,5,6,1,2,3,4]=>00001000001=>10000010000
[11,12,9,10,5,6,7,8,1,2,3,4]=>00000010101=>10101000000
[9,10,11,12,5,6,7,8,1,2,3,4]=>00000010001=>10001000000
[11,12,5,8,9,6,7,10,1,2,3,4]=>00000001101=>10110000000
[5,10,11,8,9,6,7,12,1,2,3,4]=>00000001011=>11010000000
[5,8,9,10,11,6,7,12,1,2,3,4]=>00000000011=>11000000000
[11,12,5,6,7,8,9,10,1,2,3,4]=>00000000101=>10100000000
[5,10,11,6,7,8,9,12,1,2,3,4]=>00000000011=>11000000000
[5,6,9,10,7,8,11,12,1,2,3,4]=>00000000101=>10100000000
[5,6,7,8,9,10,11,12,1,2,3,4]=>00000000001=>10000000000
[11,12,9,10,7,8,1,4,5,2,3,6]=>00010010101=>10101001000
[9,10,11,12,7,8,1,4,5,2,3,6]=>00010010001=>10001001000
[11,12,7,8,9,10,1,4,5,2,3,6]=>00010000101=>10100001000
[7,10,11,8,9,12,1,4,5,2,3,6]=>00010000011=>11000001000
[11,12,9,10,1,6,7,4,5,2,3,8]=>00010100101=>10100101000
[9,10,11,12,1,6,7,4,5,2,3,8]=>00010100001=>10000101000
[11,12,1,8,9,6,7,4,5,2,3,10]=>00010101001=>10010101000
[1,10,11,8,9,6,7,4,5,2,3,12]=>00010101010=>01010101000
[1,8,9,10,11,6,7,4,5,2,3,12]=>00010100010=>01000101000
[11,12,1,6,7,8,9,4,5,2,3,10]=>00010001001=>10010001000
[1,10,11,6,7,8,9,4,5,2,3,12]=>00010001010=>01010001000
[1,6,7,8,9,10,11,4,5,2,3,12]=>00010000010=>01000001000
[11,12,9,10,1,4,5,6,7,2,3,8]=>00000100101=>10100100000
[9,10,11,12,1,4,5,6,7,2,3,8]=>00000100001=>10000100000
[11,12,1,8,9,4,5,6,7,2,3,10]=>00000101001=>10010100000
[1,10,11,8,9,4,5,6,7,2,3,12]=>00000101010=>01010100000
[1,8,9,10,11,4,5,6,7,2,3,12]=>00000100010=>01000100000
[11,12,1,4,7,8,5,6,9,2,3,10]=>00000011001=>10011000000
[1,10,11,4,7,8,5,6,9,2,3,12]=>00000011010=>01011000000
[1,4,9,10,7,8,5,6,11,2,3,12]=>00000010110=>01101000000
[1,4,7,8,9,10,5,6,11,2,3,12]=>00000000110=>01100000000
[11,12,1,4,5,6,7,8,9,2,3,10]=>00000001001=>10010000000
[1,10,11,4,5,6,7,8,9,2,3,12]=>00000001010=>01010000000
[1,4,9,10,5,6,7,8,11,2,3,12]=>00000000110=>01100000000
[1,4,5,8,9,6,7,10,11,2,3,12]=>00000001010=>01010000000
[1,4,5,6,7,8,9,10,11,2,3,12]=>00000000010=>01000000000
[11,12,9,10,7,8,1,2,3,4,5,6]=>00000010101=>10101000000
[9,10,11,12,7,8,1,2,3,4,5,6]=>00000010001=>10001000000
[11,12,7,8,9,10,1,2,3,4,5,6]=>00000000101=>10100000000
[7,10,11,8,9,12,1,2,3,4,5,6]=>00000000011=>11000000000
[11,12,9,10,1,6,7,2,3,4,5,8]=>00000100101=>10100100000
[9,10,11,12,1,6,7,2,3,4,5,8]=>00000100001=>10000100000
[11,12,1,8,9,6,7,2,3,4,5,10]=>00000101001=>10010100000
[1,10,11,8,9,6,7,2,3,4,5,12]=>00000101010=>01010100000
[1,8,9,10,11,6,7,2,3,4,5,12]=>00000100010=>01000100000
[11,12,1,6,7,8,9,2,3,4,5,10]=>00000001001=>10010000000
[1,10,11,6,7,8,9,2,3,4,5,12]=>00000001010=>01010000000
[1,6,9,10,7,8,11,2,3,4,5,12]=>00000000110=>01100000000
[1,6,7,8,9,10,11,2,3,4,5,12]=>00000000010=>01000000000
[11,12,9,10,1,2,5,6,3,4,7,8]=>00001000101=>10100010000
[9,10,11,12,1,2,5,6,3,4,7,8]=>00001000001=>10000010000
[11,12,1,8,9,2,5,6,3,4,7,10]=>00001001001=>10010010000
[1,10,11,8,9,2,5,6,3,4,7,12]=>00001001010=>01010010000
[1,8,9,10,11,2,5,6,3,4,7,12]=>00001000010=>01000010000
[11,12,1,2,7,8,5,6,3,4,9,10]=>00001010001=>10001010000
[1,10,11,2,7,8,5,6,3,4,9,12]=>00001010010=>01001010000
[1,2,9,10,7,8,5,6,3,4,11,12]=>00001010100=>00101010000
[1,2,7,8,9,10,5,6,3,4,11,12]=>00001000100=>00100010000
[11,12,1,2,5,6,7,8,3,4,9,10]=>00000010001=>10001000000
[1,10,11,2,5,6,7,8,3,4,9,12]=>00000010010=>01001000000
[1,2,9,10,5,6,7,8,3,4,11,12]=>00000010100=>00101000000
[1,2,5,8,9,6,7,10,3,4,11,12]=>00000001100=>00110000000
[1,2,5,6,7,8,9,10,3,4,11,12]=>00000000100=>00100000000
[11,12,9,10,1,2,3,4,5,6,7,8]=>00000000101=>10100000000
[9,10,11,12,1,2,3,4,5,6,7,8]=>00000000001=>10000000000
[11,12,1,8,9,2,3,4,5,6,7,10]=>00000001001=>10010000000
[1,10,11,8,9,2,3,4,5,6,7,12]=>00000001010=>01010000000
[1,8,9,10,11,2,3,4,5,6,7,12]=>00000000010=>01000000000
[11,12,1,2,7,8,3,4,5,6,9,10]=>00000010001=>10001000000
[1,10,11,2,7,8,3,4,5,6,9,12]=>00000010010=>01001000000
[1,2,9,10,7,8,3,4,5,6,11,12]=>00000010100=>00101000000
[1,2,7,8,9,10,3,4,5,6,11,12]=>00000000100=>00100000000
[11,12,1,2,3,6,7,4,5,8,9,10]=>00000100001=>10000100000
[1,10,11,2,3,6,7,4,5,8,9,12]=>00000100010=>01000100000
[1,2,9,10,3,6,7,4,5,8,11,12]=>00000100100=>00100100000
[1,2,3,8,9,6,7,4,5,10,11,12]=>00000101000=>00010100000
[1,2,3,6,7,8,9,4,5,10,11,12]=>00000001000=>00010000000
[11,12,1,2,3,4,5,6,7,8,9,10]=>00000000001=>10000000000
[1,10,11,2,3,4,5,6,7,8,9,12]=>00000000010=>01000000000
[1,2,9,10,3,4,5,6,7,8,11,12]=>00000000100=>00100000000
[1,2,3,8,9,4,5,6,7,10,11,12]=>00000001000=>00010000000
[1,2,3,4,7,8,5,6,9,10,11,12]=>00000010000=>00001000000
[1,2,3,4,5,6,7,8,9,10,11,12]=>00000000000=>00000000000
[8,6,4,7,2,1,3,5]=>1000111=>1110001
[1,6,4,7,2,8,3,5]=>0000111=>1110000
[1,4,7,3,5,8,2,6]=>0000011=>1100000
[8,4,6,2,3,5,1,7]=>0001101=>1011000
[5,4,8,2,3,6,1,7]=>0001101=>1011000
[7,4,8,5,2,3,1,6]=>0101011=>1101010
[3,8,6,2,4,5,1,7]=>0001101=>1011000
[4,8,6,2,3,5,1,7]=>0001101=>1011000
[1,7,5,3,4,8,2,6]=>0001011=>1101000
[1,7,6,4,8,2,3,5]=>0000111=>1110000
[5,8,7,4,1,2,3,6]=>0010011=>1100100
[6,8,5,3,4,1,2,7]=>0011001=>1001100
[6,8,3,7,2,1,4,5]=>1000011=>1100001
[8,5,1,6,3,7,2,4]=>0001111=>1111000
[6,1,3,7,4,8,2,5]=>0000111=>1110000
[4,1,7,3,5,8,2,6]=>0010011=>1100100
[7,1,6,4,8,2,3,5]=>0000111=>1110000
[1,8,5,7,2,3,4,6]=>0000011=>1100000
[6,1,5,8,2,3,4,7]=>0000101=>1010000
[5,1,7,3,8,2,4,6]=>0001011=>1101000
[6,1,5,7,8,2,3,4]=>0000101=>1010000
[7,4,8,6,1,2,3,5]=>0000111=>1110000
[3,8,7,5,1,2,4,6]=>0001011=>1101000
[3,7,6,1,2,4,5,8]=>0000110=>0110000
[4,7,6,1,2,3,5,8]=>0000110=>0110000
[1,6,5,8,2,3,4,7]=>0000101=>1010000
[6,5,8,4,1,2,3,7]=>0010101=>1010100
[8,5,7,4,1,2,3,6]=>0010011=>1100100
[1,5,7,4,8,2,3,6]=>0000011=>1100000
[7,6,4,8,2,1,3,5]=>1000111=>1110001
[7,6,2,3,8,1,4,5]=>0000111=>1110000
[7,4,8,5,1,6,2,3]=>0001111=>1111000
[8,6,2,3,1,7,4,5]=>0100111=>1110010
[8,6,4,1,2,7,3,5]=>0010111=>1110100
[1,7,2,8,6,3,4,5]=>0000111=>1110000
[7,6,1,3,8,2,4,5]=>0000111=>1110000
[7,5,8,1,3,6,2,4]=>0000111=>1110000
[5,4,1,8,2,3,6,7]=>0011001=>1001100
[1,4,8,7,2,3,5,6]=>0000011=>1100000
[1,5,8,7,2,3,4,6]=>0000011=>1100000
[6,5,1,8,2,3,4,7]=>0001101=>1011000
[5,7,1,3,8,2,4,6]=>0000011=>1100000
[7,6,8,1,5,2,3,4]=>0001011=>1101000
[7,1,5,8,6,2,3,4]=>0000111=>1110000
[6,1,8,2,7,3,4,5]=>0000111=>1110000
[4,1,8,7,2,3,5,6]=>0010011=>1100100
[5,1,8,7,2,3,4,6]=>0001011=>1101000
[1,8,7,6,4,5,3,2]=>0101111=>1111010
[9,8,7,6,4,5,3,2,1,10]=>110111110=>011111011
[8,7,6,4,3,5,2,1,9]=>10111110=>01111101
[8,7,6,3,5,4,2,1,9]=>10111110=>01111101
[1,9,8,7,5,4,6,3,2]=>01011111=>11111010
[1,8,7,3,6,5,4,2]=>0011111=>1111100
[1,9,8,7,4,6,5,3,2]=>01011111=>11111010
[1,10,9,8,7,5,6,4,3,2]=>011011111=>111110110
[7,1,5,8,3,4,2,6]=>0010011=>1100100
[7,1,4,3,2,5,6,8]=>0110010=>0100110
[6,4,2,3,8,5,7,1]=>0010111=>1110100
[6,4,2,7,5,8,3,1]=>0110111=>1110110
[2,4,1,7,5,8,3,6]=>0010011=>1100100
[7,1,4,6,5,2,3,8]=>0001110=>0111000
[7,1,4,6,5,8,2,3]=>0000111=>1110000
[7,1,4,6,3,8,2,5]=>0000111=>1110000
[7,1,4,3,2,5,8,6]=>0110011=>1100110
[7,1,4,6,5,2,8,3]=>0001111=>1111000
[7,1,4,6,5,3,8,2]=>0001111=>1111000
[7,1,4,6,5,3,2,8]=>0101110=>0111010
[6,4,2,7,5,3,8,1]=>0011111=>1111100
[3,4,7,2,6,8,5,1]=>0001011=>1101000
[3,4,7,1,6,8,2,5]=>0000011=>1100000
[3,4,7,1,6,8,5,2]=>0001011=>1101000
[2,4,1,7,5,3,6,8]=>0011010=>0101100
[3,4,1,7,8,6,2,5]=>0010101=>1010100
[6,4,2,3,8,5,1,7]=>0011101=>1011100
[6,4,2,7,5,8,1,3]=>0010111=>1110100
[6,4,2,7,5,3,1,8]=>0111110=>0111110
[3,4,7,2,6,8,1,5]=>0000011=>1100000
[5,4,7,3,6,8,2,1]=>1001011=>1101001
[3,4,7,2,6,5,1,8]=>0001110=>0111000
[4,8,3,2,5,6,1,7]=>0100101=>1010010
[4,8,7,3,5,1,2,6]=>0001011=>1101000
[4,8,7,1,3,5,2,6]=>0001011=>1101000
[4,8,3,1,2,6,5,7]=>0100101=>1010010
[3,4,7,1,6,2,5,8]=>0000110=>0110000
[3,4,7,1,6,2,8,5]=>0000111=>1110000
[3,4,7,2,6,5,8,1]=>0000111=>1110000
[4,8,3,1,2,6,7,5]=>0100011=>1100010
[5,8,1,6,3,4,2,7]=>0010101=>1010100
[6,8,5,1,3,7,2,4]=>0001011=>1101000
[6,8,5,1,3,4,7,2]=>0001011=>1101000
[5,8,3,4,2,6,7,1]=>0010011=>1100100
[5,4,7,3,6,2,8,1]=>0001111=>1111000
[5,4,7,2,6,1,8,3]=>0001111=>1111000
[6,4,3,7,5,1,2,8]=>0011110=>0111100
[6,4,3,7,5,1,8,2]=>0011111=>1111100
[6,2,4,3,1,5,8,7]=>0110101=>1010110
[3,8,7,4,1,5,2,6]=>0011011=>1101100
[2,4,7,3,6,1,5,8]=>0000110=>0110000
[5,8,3,2,1,6,4,7]=>1100101=>1010011
[5,8,7,4,3,1,2,6]=>0110011=>1100110
[5,4,7,3,6,2,1,8]=>1001110=>0111001
[7,3,8,2,1,6,5,4]=>1001111=>1111001
[7,4,3,8,5,2,1,6]=>1011011=>1101101
[6,5,2,8,4,3,1,7]=>0111101=>1011110
[4,3,2,8,6,5,1,7]=>0111101=>1011110
[4,3,8,7,5,1,6,2]=>0011111=>1111100
[3,2,5,8,6,1,4,7]=>0100101=>1010010
[8,4,3,7,5,2,6,1]=>0011111=>1111100
[4,3,7,8,5,1,2,6]=>0011001=>1001100
[5,3,7,8,4,1,2,6]=>0011001=>1001100
[6,2,5,8,3,1,4,7]=>0100101=>1010010
[6,2,4,8,3,1,5,7]=>0100101=>1010010
[5,2,3,8,4,1,6,7]=>0011001=>1001100
[5,3,8,7,4,1,6,2]=>0011111=>1111100
[5,3,2,8,6,4,1,7]=>0111101=>1011110
[7,5,3,8,4,2,1,6]=>1011011=>1101101
[8,7,5,3,6,2,4,1]=>0011111=>1111100
[8,6,5,3,7,2,4,1]=>0011111=>1111100
[7,5,4,3,8,2,6,1]=>0011111=>1111100
[6,4,5,3,8,2,7,1]=>0001111=>1111000
[7,4,6,3,8,2,5,1]=>0001111=>1111000
[7,5,6,3,8,2,4,1]=>0010111=>1110100
[8,5,6,3,7,2,4,1]=>0010111=>1110100
[7,4,6,3,5,2,8,1]=>0001111=>1111000
[8,4,6,3,5,2,7,1]=>0001111=>1111000
[8,4,7,3,5,2,6,1]=>0001111=>1111000
[8,5,7,3,4,2,6,1]=>0010111=>1110100
[7,5,8,4,3,2,6,1]=>0110111=>1110110
[6,5,8,4,3,2,7,1]=>0110111=>1110110
[6,5,8,3,4,2,7,1]=>0010111=>1110100
[7,5,8,3,4,2,6,1]=>0010111=>1110100
[7,5,8,4,6,2,3,1]=>0100111=>1110010
[7,4,8,3,6,2,5,1]=>0001111=>1111000
[7,4,8,3,5,2,6,1]=>0001111=>1111000
[6,4,8,3,5,2,7,1]=>0001111=>1111000
[6,4,7,3,5,2,8,1]=>0001111=>1111000
[5,4,8,3,7,2,6,1]=>0001111=>1111000
[6,5,8,3,7,2,4,1]=>0010111=>1110100
[6,5,8,4,7,2,3,1]=>0100111=>1110010
[6,5,8,4,7,3,2,1]=>1100111=>1110011
[6,4,7,3,8,2,5,1]=>0001111=>1111000
[5,4,7,3,8,2,6,1]=>0001111=>1111000
[5,4,6,3,8,2,7,1]=>0001111=>1111000
[5,3,6,2,4,7,8,1]=>0001101=>1011000
[5,3,6,1,4,8,7,2]=>0001111=>1111000
[5,3,7,2,4,6,8,1]=>0001011=>1101000
[4,3,1,5,6,8,7,2]=>0110011=>1100110
[4,2,1,5,8,6,3,7]=>1010101=>1010101
[4,2,1,5,8,6,7,3]=>1010011=>1100101
[4,2,1,5,8,7,6,3]=>1010111=>1110101
[4,3,1,5,7,8,6,2]=>0110101=>1010110
[4,3,1,7,5,8,6,2]=>0110111=>1110110
[6,7,3,1,4,8,2,5]=>0100011=>1100010
[5,3,7,1,4,8,2,6]=>0001011=>1101000
[4,3,1,5,7,8,2,6]=>0110001=>1000110
[3,2,1,8,5,4,6,7]=>1101001=>1001011
[3,2,1,8,5,7,4,6]=>1100011=>1100011
[3,2,1,8,7,5,4,6]=>1101011=>1101011
[5,2,7,1,8,4,3,6]=>0011011=>1101100
[6,7,2,1,8,4,3,5]=>1010011=>1100101
[6,7,2,1,8,4,5,3]=>1001011=>1101001
[3,2,1,8,5,6,4,7]=>1100101=>1010011
[3,2,1,8,6,5,4,7]=>1101101=>1011011
[4,3,1,6,7,8,5,2]=>0111001=>1001110
[4,2,1,6,8,7,5,3]=>1011011=>1101101
[4,2,1,6,8,5,7,3]=>1010011=>1100101
[4,2,1,6,8,5,3,7]=>1011001=>1001101
[5,2,6,1,8,4,3,7]=>0011101=>1011100
[5,2,6,1,8,7,4,3]=>0011111=>1111100
[5,2,6,1,8,7,3,4]=>0001111=>1111000
[5,2,6,1,8,3,4,7]=>0001101=>1011000
[4,2,1,6,8,3,7,5]=>1010011=>1100101
[4,3,1,6,7,8,2,5]=>0110001=>1000110
[6,7,3,1,5,8,2,4]=>0100011=>1100010
[4,2,1,7,8,6,3,5]=>1010101=>1010101
[3,2,1,8,7,6,4,5]=>1100111=>1110011
[3,2,1,8,6,4,7,5]=>1100111=>1110011
[3,2,1,8,6,4,5,7]=>1100101=>1010011
[3,2,1,8,4,6,5,7]=>1100101=>1010011
[3,2,1,8,4,6,7,5]=>1100011=>1100011
[3,2,1,8,4,7,6,5]=>1100111=>1110011
[3,2,1,8,7,4,6,5]=>1100111=>1110011
[4,2,1,7,8,3,6,5]=>1010101=>1010101
[5,2,7,1,8,3,6,4]=>0001111=>1111000
[6,7,2,1,8,3,5,4]=>1001011=>1101001
[5,2,7,1,8,3,4,6]=>0001011=>1101000
[4,2,1,7,8,3,5,6]=>1010001=>1000101
[3,2,1,8,4,5,7,6]=>1100011=>1100011
[7,5,2,8,6,3,4,1]=>0011111=>1111100
[7,4,8,6,2,5,3,1]=>0101111=>1111010
[7,3,8,6,2,4,5,1]=>0001111=>1111000
[7,4,3,1,8,2,5,6]=>0110011=>1100110
[7,4,2,8,5,6,1,3]=>0010111=>1110100
[7,3,8,5,2,4,6,1]=>0001111=>1111000
[7,3,8,4,5,6,2,1]=>1000111=>1110001
[6,3,8,2,4,5,1,7]=>0001101=>1011000
[6,3,8,2,5,7,4,1]=>0010111=>1110100
[6,4,3,8,1,5,2,7]=>0011101=>1011100
[6,3,7,8,2,4,1,5]=>0010101=>1010100
[5,6,7,3,8,2,4,1]=>0010011=>1100100
[5,4,7,2,6,8,1,3]=>0001011=>1101000
[5,3,8,2,4,6,7,1]=>0001011=>1101000
[6,3,8,2,4,7,5,1]=>0001111=>1111000
[5,7,4,2,6,8,1,3]=>0010011=>1100100
[6,4,8,2,7,5,1,3]=>0001111=>1111000
[6,5,3,1,4,2,7,8]=>0111100=>0011110
[5,7,4,2,6,1,3,8]=>0010110=>0110100
[5,6,4,2,3,8,1,7]=>0010101=>1010100
[5,6,3,7,8,2,4,1]=>0010101=>1010100
[5,6,3,8,2,4,7,1]=>0000111=>1110000
[6,3,7,2,4,5,1,8]=>0001110=>0111000
[6,3,7,2,5,8,4,1]=>0010111=>1110100
[5,3,6,8,2,4,7,1]=>0001011=>1101000
[5,4,6,2,3,8,1,7]=>0001101=>1011000
[5,3,6,7,8,2,4,1]=>0011001=>1001100
[3,6,4,2,1,5,8,7]=>1010101=>1010101
[3,5,8,6,4,2,1,7]=>1010101=>1010101
[5,8,6,3,4,2,1,7]=>1010101=>1010101
[5,6,3,4,2,1,8,7]=>1010101=>1010101
[6,3,4,2,1,5,8,7]=>1010101=>1010101
[5,6,4,2,1,3,8,7]=>1010101=>1010101
[2,5,4,1,7,8,6,3]=>0011101=>1011100
[2,7,8,5,4,1,6,3]=>0011101=>1011100
[2,8,5,4,1,6,3,7]=>0011101=>1011100
[2,6,3,8,5,4,1,7]=>0011101=>1011100
[2,8,6,3,5,4,1,7]=>0011101=>1011100
[5,8,6,4,2,1,3,7]=>1010101=>1010101
[4,2,1,5,7,8,6,3]=>1010101=>1010101
[2,7,8,6,3,5,4,1]=>0011101=>1011100
[4,3,8,5,7,6,2,1]=>1010111=>1110101
[7,6,2,1,8,4,3,5]=>1010111=>1110101
[2,1,8,5,6,4,3,7]=>1010101=>1010101
[4,2,1,8,5,6,3,7]=>1010101=>1010101
[8,4,2,1,5,6,3,7]=>1010101=>1010101
[2,5,6,3,8,4,1,7]=>0010101=>1010100
[6,3,4,2,1,8,5,7]=>1010101=>1010101
[3,7,8,5,6,4,2,1]=>1010101=>1010101
[3,8,5,6,4,2,1,7]=>1010101=>1010101
[3,6,4,2,1,8,5,7]=>1010101=>1010101
[3,8,6,4,2,1,5,7]=>1010101=>1010101
[3,7,8,6,4,2,1,5]=>1010101=>1010101
[8,5,3,7,6,2,4,1]=>0011111=>1111100
[7,6,2,4,1,8,5,3]=>0011111=>1111100
[8,5,4,1,7,6,2,3]=>0011111=>1111100
[7,6,2,3,8,5,4,1]=>0011111=>1111100
[2,1,7,8,6,4,3,5]=>1010101=>1010101
[2,1,6,4,3,7,8,5]=>1010101=>1010101
[6,4,2,1,3,7,8,5]=>1010101=>1010101
[6,3,7,8,4,2,1,5]=>1010101=>1010101
[7,8,4,2,1,6,3,5]=>1010101=>1010101
[5,7,6,2,3,8,4,1]=>0010111=>1110100
[2,6,1,8,4,3,7,5]=>0010111=>1110100
[2,6,1,7,5,8,4,3]=>0010111=>1110100
[8,4,2,3,7,5,6,1]=>0010111=>1110100
[8,5,7,6,2,1,4,3]=>1010111=>1110101
[4,8,5,7,6,2,1,3]=>1000111=>1110001
[4,7,6,2,1,3,8,5]=>1000111=>1110001
[7,5,6,1,8,4,2,3]=>0010111=>1110100
[2,7,5,8,4,3,6,1]=>0010111=>1110100
[2,8,4,3,6,1,7,5]=>0010111=>1110100
[6,4,7,8,3,2,1,5]=>1100101=>1010011
[7,6,5,8,4,3,2,1,9]=>11101110=>01110111
[7,6,5,4,9,3,2,1,8]=>11011101=>10111011
[7,6,5,4,3,8,2,1,9]=>10111110=>01111101
[7,6,5,4,3,2,8,1,9]=>01111110=>01111110
[6,9,8,5,4,3,2,1,7]=>11110011=>11001111
[8,7,9,6,5,4,3,2,1,10]=>111110110=>011011111
[7,5,8,9,4,3,2,1,6]=>11100101=>10100111
[8,7,6,9,5,4,3,2,1,10]=>111101110=>011101111
[6,4,3,7,5,2,1,8]=>1011110=>0111101
[7,6,4,8,9,3,2,1,5]=>11001101=>10110011
[8,7,6,5,10,4,3,2,1,9]=>111011101=>101110111
[6,5,3,2,8,4,1,7]=>0111101=>1011110
[7,6,5,3,9,8,2,1,4]=>10011111=>11111001
[8,7,6,5,4,9,3,2,1,10]=>110111110=>011111011
[6,5,2,7,8,4,1,3]=>0011101=>1011100
[7,6,5,4,2,8,9,1,3]=>00111101=>10111100
[8,7,6,5,4,3,9,2,1,10]=>101111110=>011111101
[7,6,5,4,3,1,8,9,2]=>01111101=>10111110
[7,10,9,6,5,4,3,2,1,8]=>111110011=>110011111
[9,8,10,7,6,5,4,3,2,1,11]=>1111110110=>0110111111
[6,5,8,7,4,3,2,1,9]=>11101110=>01110111
[8,6,9,10,5,4,3,2,1,7]=>111100101=>101001111
[9,8,7,10,6,5,4,3,2,1,11]=>1111101110=>0111011111
[7,5,4,8,6,3,2,1,9]=>11011110=>01111011
[5,9,8,7,4,3,2,1,6]=>11100111=>11100111
[8,7,5,9,10,4,3,2,1,6]=>111001101=>101100111
[9,8,7,6,11,5,4,3,2,1,10]=>1111011101=>1011101111
[6,4,3,2,5,8,1,7]=>0110101=>1010110
[7,6,4,3,9,5,2,1,8]=>10111101=>10111101
[7,4,8,9,6,3,2,1,5]=>11001101=>10110011
[8,7,6,4,10,9,3,2,1,5]=>110011111=>111110011
[9,8,7,6,5,10,4,3,2,1,11]=>1110111110=>0111110111
[6,3,7,2,5,4,1,8]=>0011110=>0111100
[7,6,5,3,2,8,4,1,9]=>01111110=>01111110
[7,6,3,8,9,5,2,1,4]=>10011101=>10111001
[8,7,6,5,3,9,10,2,1,4]=>100111101=>101111001
[9,8,7,6,5,4,10,3,2,1,11]=>1101111110=>0111111011
[7,6,5,4,2,1,8,3,9]=>10111110=>01111101
[6,3,2,7,5,4,1,8]=>0111110=>0111110
[7,6,5,2,9,8,4,1,3]=>00111111=>11111100
[8,7,6,5,4,2,9,10,1,3]=>001111101=>101111100
[9,8,7,6,5,4,3,11,2,1,10]=>1011111101=>1011111101
[7,6,5,4,1,8,9,3,2]=>01111101=>10111110
[8,7,6,5,4,3,1,10,9,2]=>011111111=>111111110
[9,8,7,6,5,4,3,2,10,1,11]=>0111111110=>0111111110
[9,8,7,6,5,4,3,2,1,10,11]=>1111111100=>0011111111
[8,4,2,6,3,1,7,5]=>0110111=>1110110
[1,5,3,7,4,2,8,6]=>0011011=>1101100
[1,6,7,3,4,2,8,5]=>0010011=>1100100
[8,6,5,2,3,1,7,4]=>0101111=>1111010
[1,7,6,3,4,2,8,5]=>0010111=>1110100
[1,8,6,3,2,5,7,4]=>0100111=>1110010
[8,7,5,2,1,4,6,3]=>1001111=>1111001
[7,8,5,2,1,4,6,3]=>1001101=>1011001
[6,8,5,2,3,1,7,4]=>0101011=>1101010
[5,8,6,2,3,1,7,4]=>0100111=>1110010
[4,8,2,6,3,1,7,5]=>0100111=>1110010
[3,2,8,6,4,1,7,5]=>0110111=>1110110
[3,2,1,7,5,4,8,6]=>1101011=>1101011
[4,1,3,7,5,2,8,6]=>0011011=>1101100
[5,1,7,3,4,2,8,6]=>0011011=>1101100
[7,1,6,3,2,5,8,4]=>0100111=>1110010
[1,2,7,4,3,6,8,5]=>0010011=>1100100
[6,1,8,2,4,5,7,3]=>0000111=>1110000
[5,1,8,3,2,6,7,4]=>0101011=>1101010
[3,2,8,7,1,5,6,4]=>0100111=>1110010
[4,8,2,7,1,5,6,3]=>0000111=>1110000
[5,8,7,2,1,4,6,3]=>1000111=>1110001
[6,8,7,1,3,4,5,2]=>0001011=>1101000
[7,8,6,1,3,4,5,2]=>0001101=>1011000
[1,7,8,2,4,5,6,3]=>0000101=>1010000
[8,6,7,1,3,4,5,2]=>0001011=>1101000
[7,6,8,1,3,4,5,2]=>0001011=>1101000
[6,5,8,2,3,1,7,4]=>0100111=>1110010
[1,6,8,3,2,5,7,4]=>0100011=>1100010
[1,5,3,8,2,6,7,4]=>0001011=>1101000
[8,4,2,7,1,5,6,3]=>0010111=>1110100
[7,4,2,8,1,5,6,3]=>0010111=>1110100
[6,4,2,8,3,1,7,5]=>0110111=>1110110
[5,4,2,3,8,1,7,6]=>0011011=>1101100
[4,5,2,3,1,6,8,7]=>0101001=>1001010
[7,4,2,1,3,6,8,5]=>1010011=>1100101
[8,4,2,1,3,6,7,5]=>1010011=>1100101
[1,5,3,2,4,7,8,6]=>0101001=>1001010
[8,5,1,3,2,6,7,4]=>0101011=>1101010
[5,6,1,3,4,2,8,7]=>0010101=>1010100
[4,6,2,1,5,3,8,7]=>1001101=>1011001
[4,7,2,1,3,6,8,5]=>1000011=>1100001
[5,7,1,3,2,6,8,4]=>0100011=>1100010
[6,7,1,2,4,5,8,3]=>0000011=>1100000
[8,6,1,2,4,5,7,3]=>0000111=>1110000
[1,8,2,3,5,6,7,4]=>0000011=>1100000
[8,7,1,2,4,5,6,3]=>0000111=>1110000
[7,8,1,2,4,5,6,3]=>0000101=>1010000
[5,8,1,3,2,6,7,4]=>0100011=>1100010
[4,8,2,1,3,6,7,5]=>1000011=>1100001
[4,1,3,2,5,7,8,6]=>0110001=>1000110
[5,1,2,4,3,7,8,6]=>0011001=>1001100
[5,4,8,1,2,3,7,6]=>0001011=>1101000
[1,4,7,6,3,2,5,8]=>0100110=>0110010
[4,8,3,2,7,6,1,5]=>0100111=>1110010
[4,3,8,2,7,1,6,5]=>0010111=>1110100
[1,4,7,3,6,2,5,8]=>0000110=>0110000
[4,3,2,8,1,7,6,5]=>0110111=>1110110
[4,1,8,3,7,2,5,6]=>0010011=>1100100
[4,1,8,7,3,2,5,6]=>0110011=>1100110
[4,7,8,1,2,5,3,6]=>0001001=>1001000
[3,4,7,6,2,1,8,5]=>1000111=>1110001
[3,4,2,7,1,6,8,5]=>0010011=>1100100
[2,3,6,7,4,1,8,5]=>0010011=>1100100
[2,6,3,4,7,8,1,5]=>0000101=>1010000
[2,6,7,8,3,4,1,5]=>0010001=>1000100
[3,1,7,8,4,2,5,6]=>0110001=>1000110
[4,1,3,2,8,7,5,6]=>0110011=>1100110
[3,7,8,2,6,4,1,5]=>0010101=>1010100
[4,2,3,8,1,6,7,5]=>0010011=>1100100
[4,3,1,8,2,5,7,6]=>0110011=>1100110
[1,3,6,7,4,2,5,8]=>0010010=>0100100
[3,2,7,8,4,1,6,5]=>0110101=>1010110
[4,2,8,6,3,1,7,5]=>0110111=>1110110
[3,7,2,4,8,6,1,5]=>0000111=>1110000
[3,2,7,4,8,1,6,5]=>0100111=>1110010
[1,3,6,4,7,2,5,8]=>0000110=>0110000
[3,2,4,7,1,8,6,5]=>0100111=>1110010
[3,7,4,2,6,8,1,5]=>0010011=>1100100
[3,7,4,6,2,8,1,5]=>0000111=>1110000
[4,7,1,5,8,2,3,6]=>0000011=>1100000
[3,7,6,4,8,2,1,5]=>1000111=>1110001
[3,1,7,4,8,2,5,6]=>0100011=>1100010
[2,6,7,3,8,4,1,5]=>0010011=>1100100
[2,3,6,4,7,1,8,5]=>0000111=>1110000
[8,7,5,2,6,3,4,1]=>0011111=>1111100
[8,6,5,2,7,3,4,1]=>0011111=>1111100
[7,4,8,5,6,3,2,1]=>1100111=>1110011
[3,4,6,7,8,5,1,2]=>0001001=>1001000
[1,2,6,4,7,5,8,3]=>0000111=>1110000
[3,1,7,5,4,2,6,8]=>0111010=>0101110
[6,3,8,5,4,7,1,2]=>0001111=>1111000
[1,6,2,5,4,7,8,3]=>0001101=>1011000
[1,8,2,5,6,3,7,4]=>0000111=>1110000
[1,2,6,4,8,5,7,3]=>0000111=>1110000
[7,8,3,1,4,2,5,6]=>0110001=>1000110
[4,8,1,5,2,3,6,7]=>0001001=>1001000
[7,4,1,5,2,3,6,8]=>0011010=>0101100
[5,6,1,8,4,3,2,7]=>0110101=>1010110
[5,1,8,6,4,3,2,7]=>0111101=>1011110
[5,1,6,3,8,7,2,4]=>0001111=>1111000
[6,1,2,5,8,3,7,4]=>0000111=>1110000
[6,1,8,7,4,3,2,5]=>0110111=>1110110
[7,1,2,5,4,8,6,3]=>0001111=>1111000
[1,2,7,5,8,3,6,4]=>0000111=>1110000
[4,1,6,3,7,5,2,8]=>0011110=>0111100
[1,3,6,7,8,5,2,4]=>0001001=>1001000
[1,2,6,4,7,8,5,3]=>0001101=>1011000
[4,1,6,3,7,8,2,5]=>0010101=>1010100
[3,1,6,4,8,2,7,5]=>0100111=>1110010
[7,8,4,1,6,3,2,5]=>0110101=>1010110
[4,1,6,3,8,7,2,5]=>0010111=>1110100
[7,5,1,8,4,3,2,6]=>0111011=>1101110
[6,5,1,7,4,3,2,8]=>0111110=>0111110
[4,1,8,5,2,3,7,6]=>0011011=>1101100
[4,1,6,8,3,7,2,5]=>0010011=>1100100
[5,4,6,1,3,8,2,7]=>0001101=>1011000
[6,5,8,1,4,3,2,7]=>0110101=>1010110
[1,3,5,7,6,8,2,4]=>0000011=>1100000
[1,3,5,7,6,2,8,4]=>0000111=>1110000
[1,3,5,7,2,6,8,4]=>0000011=>1100000
[1,3,5,2,7,6,4,8]=>0001110=>0111000
[1,3,5,7,6,2,4,8]=>0000110=>0110000
[1,3,5,7,4,6,8,2]=>0000011=>1100000
[1,3,5,7,4,6,2,8]=>0000110=>0110000
[1,3,5,7,4,2,6,8]=>0010010=>0100100
[1,3,5,4,7,2,6,8]=>0001010=>0101000
[1,3,5,4,7,8,2,6]=>0001001=>1001000
[1,3,5,4,7,2,8,6]=>0001011=>1101000
[1,3,5,7,4,2,8,6]=>0010011=>1100100
[1,3,5,7,4,8,2,6]=>0000011=>1100000
[1,3,5,7,4,8,6,2]=>0000111=>1110000
[1,3,5,7,8,4,6,2]=>0000101=>1010000
[1,3,5,7,8,4,2,6]=>0010001=>1000100
[1,3,5,2,7,8,6,4]=>0001101=>1011000
[1,3,5,7,2,8,6,4]=>0000111=>1110000
[1,3,5,7,8,2,6,4]=>0000101=>1010000
[1,6,3,2,7,4,8,5]=>0100111=>1110010
[3,5,1,6,2,8,7,4]=>0001111=>1111000
[1,3,7,2,5,4,8,6]=>0001011=>1101000
[2,6,1,7,4,3,8,5]=>0010111=>1110100
[1,4,7,3,5,2,8,6]=>0001011=>1101000
[1,3,7,5,2,4,8,6]=>0001011=>1101000
[2,5,7,4,3,8,1,6]=>0010011=>1100100
[2,5,3,7,4,8,1,6]=>0001011=>1101000
[1,4,7,2,3,8,6,5]=>0000111=>1110000
[2,4,7,3,1,8,6,5]=>0100111=>1110010
[1,4,6,3,8,2,7,5]=>0000111=>1110000
[1,3,5,2,8,7,6,4]=>0001111=>1111000
[1,4,7,3,8,2,6,5]=>0000111=>1110000
[2,5,1,7,8,4,6,3]=>0001101=>1011000
[3,2,6,7,8,1,5,4]=>0101001=>1001010
[4,3,6,7,8,2,1,5]=>1010001=>1000101
[3,5,2,7,8,4,1,6]=>0011001=>1001100
[1,5,7,4,8,3,2,6]=>0100011=>1100010
[2,5,1,6,8,4,7,3]=>0001011=>1101000
[4,6,2,1,7,8,3,5]=>1000101=>1010001
[5,3,6,4,7,8,2,1]=>1001101=>1011001
[3,5,2,6,8,4,7,1]=>0001011=>1101000
[2,5,4,6,8,7,1,3]=>0001011=>1101000
[1,3,6,2,8,7,5,4]=>0001111=>1111000
[1,4,6,3,8,7,2,5]=>0000111=>1110000
[2,5,7,4,3,8,6,1]=>0010111=>1110100
[1,5,7,2,4,8,6,3]=>0000111=>1110000
[4,6,3,7,2,8,5,1]=>0001111=>1111000
[4,3,6,7,8,2,5,1]=>0011001=>1001100
[1,4,7,3,8,6,2,5]=>0000111=>1110000
[2,5,4,7,8,6,1,3]=>0001101=>1011000
[3,2,6,7,8,5,1,4]=>0101001=>1001010
[1,3,7,2,8,6,5,4]=>0001111=>1111000
[5,1,6,8,2,4,3,7]=>0011001=>1001100
[5,3,7,8,2,4,1,6]=>0011001=>1001100
[8,5,3,7,2,4,1,6]=>0011011=>1101100
[8,2,4,7,3,1,5,6]=>0100011=>1100010
[2,4,7,8,3,1,5,6]=>0100001=>1000010
[6,3,1,5,8,2,4,7]=>0100101=>1010010
[6,5,3,4,2,8,1,7]=>0011101=>1011100
[5,2,4,3,8,1,6,7]=>0011001=>1001100
[3,2,4,8,1,5,6,7]=>0100001=>1000010
[3,2,4,6,8,1,5,7]=>0100001=>1000010
[8,1,5,7,3,2,4,6]=>0100011=>1100010
[8,4,6,7,2,3,1,5]=>0100011=>1100010
[4,6,7,8,2,3,1,5]=>0100001=>1000010
[7,4,6,8,2,3,1,5]=>0100011=>1100010
[7,2,4,8,3,1,5,6]=>0100011=>1100010
[5,3,8,7,2,4,1,6]=>0011011=>1101100
[2,4,8,7,3,1,5,6]=>0100011=>1100010
[4,6,8,7,2,3,1,5]=>0100011=>1100010
[8,7,4,6,2,3,1,5]=>0100111=>1110010
[5,6,8,7,2,3,1,4]=>0100011=>1100010
[6,4,8,7,2,3,1,5]=>0100111=>1110010
[3,1,7,4,2,8,6,5]=>0110111=>1110110
[3,2,8,4,1,7,6,5]=>0110111=>1110110
[7,6,4,8,2,3,1,5]=>0100111=>1110010
[5,7,6,8,2,3,1,4]=>0100011=>1100010
[4,7,6,8,2,3,1,5]=>0100011=>1100010
[8,6,4,7,2,3,1,5]=>0100111=>1110010
[8,2,3,7,4,1,6,5]=>0010111=>1110100
[2,3,7,8,4,1,6,5]=>0010101=>1010100
[3,7,4,8,2,5,1,6]=>0001011=>1101000
[2,3,7,4,1,6,8,5]=>0010011=>1100100
[8,1,6,4,2,3,7,5]=>0010111=>1110100
[4,7,8,6,2,3,1,5]=>0100101=>1010010
[2,4,7,3,1,5,8,6]=>0100011=>1100010
[6,3,1,7,4,2,8,5]=>0110111=>1110110
[8,5,7,6,2,3,1,4]=>0100111=>1110010
[7,5,8,6,2,3,1,4]=>0100111=>1110010
[7,1,6,4,2,3,8,5]=>0010111=>1110100
[3,1,7,6,4,2,8,5]=>0110111=>1110110
[4,8,7,6,2,3,1,5]=>0100111=>1110010
[6,8,7,5,2,3,1,4]=>0101011=>1101010
[4,3,6,1,5,8,7,2]=>0010111=>1110100
[4,3,6,5,1,8,7,2]=>0011111=>1111100
[4,6,3,5,1,8,7,2]=>0001111=>1111000
[4,6,3,1,5,8,7,2]=>0100111=>1110010
[4,1,6,5,3,8,7,2]=>0011111=>1111100
[4,6,1,5,3,8,7,2]=>0001111=>1111000
[2,6,5,3,1,8,7,4]=>0101111=>1111010
[2,6,5,1,8,7,3,4]=>0001111=>1111000
[2,6,5,8,1,7,3,4]=>0000111=>1110000
[2,6,5,8,1,3,7,4]=>0000111=>1110000
[2,6,5,8,3,1,7,4]=>0100111=>1110010
[2,6,5,3,8,1,7,4]=>0001111=>1111000
[4,6,1,5,8,3,7,2]=>0000111=>1110000
[4,1,6,5,8,3,7,2]=>0010111=>1110100
[1,4,6,5,8,3,7,2]=>0000111=>1110000
[4,1,6,5,8,7,3,2]=>0110111=>1110110
[2,6,5,3,8,7,1,4]=>0001111=>1111000
[6,4,3,8,7,1,5,2]=>0011111=>1111100
[6,4,8,3,7,1,5,2]=>0001111=>1111000
[2,6,8,5,3,7,1,4]=>0001011=>1101000
[4,6,8,1,5,7,3,2]=>0100011=>1100010
[4,6,1,8,5,7,3,2]=>0100111=>1110010
[4,1,6,8,5,7,3,2]=>0110011=>1100110
[1,4,6,8,5,7,3,2]=>0100011=>1100010
[1,4,6,8,5,3,7,2]=>0001011=>1101000
[4,6,1,8,5,3,7,2]=>0001111=>1111000
[2,6,8,5,3,1,7,4]=>0101011=>1101010
[2,6,8,5,1,7,3,4]=>0001011=>1101000
[4,6,8,3,5,1,7,2]=>0001011=>1101000
[4,6,8,3,1,5,7,2]=>0100011=>1100010
[4,6,3,1,8,5,7,2]=>0100111=>1110010
[4,6,3,8,1,5,7,2]=>0000111=>1110000
[4,6,3,8,5,7,1,2]=>0000111=>1110000
[4,3,6,8,1,5,7,2]=>0010011=>1100100
[4,3,6,1,8,5,7,2]=>0010111=>1110100
[4,3,1,6,8,5,7,2]=>0110011=>1100110
[4,1,3,6,8,7,5,2]=>0011011=>1101100
[4,3,6,1,8,7,5,2]=>0011111=>1111100
[4,3,6,8,1,7,5,2]=>0011011=>1101100
[6,5,2,8,7,3,1,4]=>0101111=>1111010
[6,5,2,8,7,1,3,4]=>0001111=>1111000
[6,2,5,8,7,1,3,4]=>0000111=>1110000
[6,2,5,8,7,3,1,4]=>0100111=>1110010
[4,6,3,8,1,7,5,2]=>0001111=>1111000
[4,6,3,1,8,7,5,2]=>0101111=>1111010
[4,1,6,3,8,7,5,2]=>0011111=>1111100
[1,4,6,3,8,7,5,2]=>0001111=>1111000
[4,1,6,8,3,7,5,2]=>0011011=>1101100
[4,6,1,8,3,7,5,2]=>0001111=>1111000
[4,6,8,1,3,7,5,2]=>0001011=>1101000
[6,2,8,5,7,3,1,4]=>0100111=>1110010
[6,2,8,5,7,1,3,4]=>0000111=>1110000
[2,4,8,7,1,5,3,6]=>0001011=>1101000
[4,2,8,7,5,3,1,6]=>0111011=>1101110
[6,4,1,8,7,5,3,2]=>0111111=>1111110
[6,1,4,8,7,5,3,2]=>0101111=>1111010
[1,6,4,8,7,3,5,2]=>0001111=>1111000
[6,4,1,8,7,3,5,2]=>0011111=>1111100
[4,2,8,7,5,1,3,6]=>0011011=>1101100
[2,4,8,7,3,5,1,6]=>0001011=>1101000
[2,3,4,5,6,8,9,7,1]=>00000101=>10100000
[2,3,4,7,1,8,6,5]=>0000111=>1110000
[2,3,4,5,7,8,9,6,1]=>00001001=>10010000
[2,3,5,6,7,8,9,4,1]=>00100001=>10000100
[2,4,5,6,7,8,9,3,1]=>01000001=>10000010
[2,3,4,5,6,7,9,10,8,1]=>000000101=>101000000
[2,3,4,7,8,5,6,1]=>0000101=>1010000
[2,3,4,5,8,1,9,7,6]=>00000111=>11100000
[2,3,4,5,6,8,9,10,7,1]=>000001001=>100100000
[2,3,6,7,4,8,5,1]=>0001011=>1101000
[2,3,4,7,1,8,9,6,5]=>00001101=>10110000
[2,5,6,3,7,8,1,4]=>0000101=>1010000
[2,3,7,1,4,8,6,5]=>0000111=>1110000
[2,3,6,1,7,8,9,4,5]=>00001001=>10010000
[2,3,4,6,7,8,9,10,5,1]=>000100001=>100001000
[2,6,1,3,7,8,5,4]=>0001101=>1011000
[2,5,1,6,7,8,9,4,3]=>00110001=>10001100
[2,3,5,6,7,8,9,10,4,1]=>001000001=>100000100
[4,1,5,6,7,8,9,3,2]=>01100001=>10000110
[2,3,4,5,6,7,10,1,8,9]=>000000001=>100000000
[2,3,4,5,6,7,8,10,11,9,1]=>0000000101=>1010000000
[2,3,4,5,8,9,6,7,1]=>00000101=>10100000
[2,3,4,5,6,9,1,10,8,7]=>000000111=>111000000
[2,3,4,5,6,7,9,10,11,8,1]=>0000001001=>1001000000
[2,3,4,7,8,5,9,6,1]=>00001011=>11010000
[2,3,4,5,8,1,9,10,7,6]=>000001101=>101100000
[2,3,4,5,6,8,9,10,11,1,7]=>0000000001=>1000000000
[2,5,6,7,4,8,1,3]=>0000011=>1100000
[2,3,6,7,4,8,9,1,5]=>00000101=>10100000
[2,3,4,8,1,5,9,7,6]=>00000111=>11100000
[2,3,4,7,1,8,9,10,5,6]=>000001001=>100100000
[2,3,4,5,7,8,9,10,11,6,1]=>0000100001=>1000010000
[2,5,6,3,7,8,9,4,1]=>00101001=>10010100
[2,3,7,8,4,5,6,1]=>0000101=>1010000
[2,3,7,1,4,8,9,6,5]=>00001101=>10110000
[2,3,6,1,7,8,9,10,5,4]=>000110001=>100011000
[2,3,4,6,7,8,9,10,11,5,1]=>0001000001=>1000001000
[4,5,2,6,7,8,9,3,1]=>01010001=>10001010
[2,6,7,3,4,8,5,1]=>0001011=>1101000
[2,6,1,3,7,8,9,4,5]=>00001001=>10010000
[2,5,1,6,7,8,9,10,4,3]=>001100001=>100001100
[2,3,5,6,7,8,9,10,11,1,4]=>0000000001=>1000000000
[5,1,2,6,7,8,9,4,3]=>00110001=>10001100
[4,1,5,6,7,8,9,10,2,3]=>001000001=>100000100
[2,4,5,6,7,8,9,10,11,3,1]=>0100000001=>1000000010
[3,4,5,6,7,8,9,10,11,2,1]=>1000000001=>1000000001
[1,5,3,2,6,4,7,8]=>0101100=>0011010
[1,5,3,2,6,7,4,8]=>0101010=>0101010
[1,7,3,2,8,5,4,6]=>0101011=>1101010
[1,7,3,2,5,8,4,6]=>0100011=>1100010
[1,3,2,7,5,4,8,6]=>0101011=>1101010
[6,5,2,4,3,7,1,8]=>0011110=>0111100
[6,4,2,5,3,7,1,8]=>0011110=>0111100
[5,4,7,6,2,3,1,8]=>0101110=>0111010
[3,6,4,8,2,1,5,7]=>1000101=>1010001
[1,6,2,8,5,3,4,7]=>0001101=>1011000
[4,6,2,3,7,5,1,8]=>0001110=>0111000
[4,7,2,3,6,5,1,8]=>0001110=>0111000
[4,7,2,3,5,6,1,8]=>0000110=>0110000
[5,3,2,7,4,6,1,8]=>0101110=>0111010
[5,3,2,6,4,7,1,8]=>0101110=>0111010
[4,6,2,3,5,7,1,8]=>0000110=>0110000
[3,5,2,1,6,8,4,7]=>1001001=>1001001
[1,5,2,6,8,4,3,7]=>0011001=>1001100
[1,5,7,2,8,4,3,6]=>0010011=>1100100
[3,5,2,1,8,6,4,7]=>1001101=>1011001
[3,6,8,4,2,1,5,7]=>1010001=>1000101
[4,3,2,6,1,8,5,7]=>0110101=>1010110
[1,5,8,2,7,4,3,6]=>0010011=>1100100
[1,7,2,3,4,8,6,5]=>0000111=>1110000
[6,8,2,3,4,1,7,5]=>0010011=>1100100
[4,1,8,2,3,5,7,6]=>0010011=>1100100
[2,3,1,8,4,5,7,6]=>0100011=>1100010
[7,3,2,1,4,5,8,6]=>1100011=>1100011
[7,8,1,4,3,5,2,6]=>0011001=>1001100
[7,1,2,3,4,6,8,5]=>0000011=>1100000
[6,1,2,3,4,8,7,5]=>0000111=>1110000
[1,8,2,3,4,7,6,5]=>0000111=>1110000
[8,1,2,3,4,6,7,5]=>0000011=>1100000
[2,8,1,3,5,4,7,6]=>0001011=>1101000
[8,7,1,4,3,5,2,6]=>0011011=>1101100
[8,3,2,1,4,5,7,6]=>1100011=>1100011
[3,8,2,1,5,6,4,7]=>1000101=>1010001
[3,8,2,1,6,5,4,7]=>1001101=>1011001
[1,7,8,3,5,4,2,6]=>0011001=>1001100
[7,4,1,8,3,5,2,6]=>0011011=>1101100
[8,4,1,7,3,5,2,6]=>0011011=>1101100
[3,8,4,6,2,1,5,7]=>1000101=>1010001
[8,4,2,5,3,1,6,7]=>0111001=>1001110
[8,5,2,4,3,1,6,7]=>0111001=>1001110
[8,3,2,5,4,1,6,7]=>0111001=>1001110
[4,3,2,5,1,8,6,7]=>0111001=>1001110
[3,5,2,4,1,8,6,7]=>0011001=>1001100
[2,4,7,8,1,5,3,6]=>0001001=>1001000
[1,8,7,3,5,4,2,6]=>0011011=>1101100
[5,1,8,2,7,4,3,6]=>0011011=>1101100
[5,1,7,2,8,4,3,6]=>0011011=>1101100
[6,1,2,8,5,3,4,7]=>0001101=>1011000
[6,3,2,1,8,4,5,7]=>1100101=>1010011
[7,3,2,8,4,5,1,6]=>0101011=>1101010
[2,7,8,4,3,5,1,6]=>0011001=>1001100
[7,1,8,3,5,4,2,6]=>0011011=>1101100
[7,8,2,3,4,6,1,5]=>0000101=>1010000
[6,7,1,3,4,8,2,5]=>0000011=>1100000
[6,8,1,3,4,7,2,5]=>0000011=>1100000
[1,7,2,3,4,6,8,5]=>0000011=>1100000
[1,6,2,3,4,8,7,5]=>0000111=>1110000
[7,6,2,3,4,1,8,5]=>0010111=>1110100
[8,6,2,3,4,1,7,5]=>0010111=>1110100
[8,1,7,3,5,4,2,6]=>0011011=>1101100
[8,3,2,7,4,5,1,6]=>0101011=>1101010
[6,7,2,3,4,1,8,5]=>0010011=>1100100
[7,6,2,3,4,8,1,5]=>0000111=>1110000
[8,6,2,3,4,7,1,5]=>0000111=>1110000
[6,3,4,8,7,5,1,2]=>0001111=>1111000
[4,8,7,3,5,6,1,2]=>0000111=>1110000
[4,8,7,5,3,6,1,2]=>0001111=>1111000
[5,8,7,3,4,6,1,2]=>0000111=>1110000
[5,8,4,2,1,6,7,3]=>1010011=>1100101
[5,8,4,1,2,6,7,3]=>0010011=>1100100
[5,3,7,2,6,1,8,4]=>0001111=>1111000
[5,2,8,1,6,3,7,4]=>0001111=>1111000
[5,8,2,1,4,7,6,3]=>1000111=>1110001
[4,8,2,5,1,7,6,3]=>0001111=>1111000
[7,8,4,1,2,6,5,3]=>0011101=>1011100
[4,8,1,5,2,7,6,3]=>0001111=>1111000
[5,8,1,2,4,7,6,3]=>0000111=>1110000
[5,2,8,3,6,7,1,4]=>0001011=>1101000
[3,8,7,6,2,4,1,5]=>0010111=>1110100
[2,8,7,6,4,1,3,5]=>0010111=>1110100
[7,8,2,6,5,1,3,4]=>0001101=>1011000
[1,8,7,6,4,2,3,5]=>0010111=>1110100
[2,8,7,6,3,1,4,5]=>0100111=>1110010
[1,8,7,6,2,4,3,5]=>0010111=>1110100
[1,8,7,6,3,4,2,5]=>0010111=>1110100
[2,8,1,4,5,6,7,3]=>0000011=>1100000
[2,1,7,3,6,5,8,4]=>1000111=>1110001
[3,1,7,2,6,5,8,4]=>0100111=>1110010
[3,2,7,1,6,5,8,4]=>0100111=>1110010
[6,1,2,8,5,7,3,4]=>0000111=>1110000
[6,2,1,8,5,7,3,4]=>1000111=>1110001
[6,3,1,8,5,7,2,4]=>0100111=>1110010
[6,4,2,1,7,5,8,3]=>1010111=>1110101
[6,1,3,8,5,2,7,4]=>0001111=>1111000
[2,3,7,1,6,8,5,4]=>0001011=>1101000
[1,3,7,2,6,8,5,4]=>0001011=>1101000
[7,8,2,6,5,3,1,4]=>0101101=>1011010
[3,2,6,7,5,8,1,4]=>0100011=>1100010
[1,2,7,5,6,3,8,4]=>0000111=>1110000
[2,8,7,6,4,3,1,5]=>0110111=>1110110
[3,8,7,6,1,2,5,4]=>0001111=>1111000
[3,8,7,6,2,1,5,4]=>1001111=>1111001
[4,8,7,6,2,1,3,5]=>1000111=>1110001
[4,8,7,6,1,3,2,5]=>0100111=>1110010
[3,8,7,6,4,1,2,5]=>0010111=>1110100
[7,8,3,6,5,1,2,4]=>0001101=>1011000
[2,3,7,5,6,8,1,4]=>0000011=>1100000
[3,8,7,6,4,2,1,5]=>1010111=>1110101
[5,1,4,6,8,2,3,7]=>0001001=>1001000
[1,7,6,3,5,4,8,2]=>0001111=>1111000
[4,3,7,2,6,5,1,8]=>0011110=>0111100
[3,4,6,1,5,7,2,8]=>0000110=>0110000
[1,6,8,5,7,3,4,2]=>0010011=>1100100
[2,4,1,5,8,6,3,7]=>0010101=>1010100
[4,6,1,2,5,8,3,7]=>0000101=>1010000
[5,6,7,2,1,4,8,3]=>1000011=>1100001
[7,8,6,5,1,2,4,3]=>0011101=>1011100
[1,3,6,5,7,8,2,4]=>0000101=>1010000
[7,4,8,5,3,1,6,2]=>0101111=>1111010
[6,8,5,2,4,1,7,3]=>0011011=>1101100
[2,3,1,6,8,5,7,4]=>0100011=>1100010
[7,3,2,5,1,4,8,6]=>0101011=>1101010
[7,1,4,2,3,6,8,5]=>0010011=>1100100
[1,5,8,3,4,6,7,2]=>0000011=>1100000
[8,3,1,2,4,7,6,5]=>0100111=>1110010
[2,3,8,1,6,5,4,7]=>0001101=>1011000
[8,1,4,7,2,5,3,6]=>0001011=>1101000
[3,5,2,4,1,7,8,6]=>0011001=>1001100
[3,4,7,8,6,2,1,5]=>1000101=>1010001
[3,4,8,6,2,7,1,5]=>0000111=>1110000
[5,8,2,1,6,7,3,4]=>1000011=>1100001
[5,7,2,8,6,4,3,1]=>0110111=>1110110
[6,1,2,7,5,3,8,4]=>0001111=>1111000
[7,3,2,8,6,4,1,5]=>0110111=>1110110
[2,7,8,4,6,3,1,5]=>0100101=>1010010
[1,4,5,7,2,6,8,3]=>0000011=>1100000
[7,3,5,2,6,1,8,4]=>0001111=>1111000
[8,5,2,3,6,1,7,4]=>0001111=>1111000
[8,1,6,3,5,7,2,4]=>0000111=>1110000
[2,8,6,4,3,7,1,5]=>0010111=>1110100
[8,3,2,6,4,7,1,5]=>0100111=>1110010
[2,3,8,7,6,5,1,4]=>0001111=>1111000
[1,2,8,7,3,6,5,4]=>0001111=>1111000
[4,2,8,7,3,6,1,5]=>0010111=>1110100
[4,5,8,7,1,2,6,3]=>0000111=>1110000
[1,5,8,7,3,2,6,4]=>0100111=>1110010
[4,5,8,7,3,2,1,6]=>1100011=>1100011
[2,6,8,1,7,5,4,3]=>0011011=>1101100
[3,6,8,4,7,2,1,5]=>1000011=>1100001
[2,5,8,3,7,6,1,4]=>0000111=>1110000
[3,2,8,4,7,6,1,5]=>0100111=>1110010
[1,5,8,3,7,2,6,4]=>0000111=>1110000
[3,5,8,4,7,2,1,6]=>1000011=>1100001
[5,6,8,2,3,7,1,4]=>0000011=>1100000
[1,6,8,4,2,7,5,3]=>0011011=>1101100
[1,5,8,4,2,7,6,3]=>0010111=>1110100
[1,5,8,2,3,7,6,4]=>0000111=>1110000
[2,1,8,4,3,7,6,5]=>1010111=>1110101
[2,5,8,4,3,7,1,6]=>0010011=>1100100
[5,6,8,4,1,2,7,3]=>0010011=>1100100
[5,6,8,1,3,2,7,4]=>0100011=>1100010
[1,6,8,4,3,2,7,5]=>0110011=>1100110
[5,6,8,4,3,2,1,7]=>1110001=>1000111
[7,1,2,8,6,5,4,3]=>0011111=>1111100
[7,1,4,8,6,2,5,3]=>0001111=>1111000
[7,3,1,8,6,2,5,4]=>0101111=>1111010
[7,2,4,8,3,6,1,5]=>0000111=>1110000
[7,1,4,8,3,2,6,5]=>0100111=>1110010
[7,4,5,8,3,2,1,6]=>1100011=>1100011
[1,6,2,8,7,5,4,3]=>0011111=>1111100
[1,6,4,8,7,2,5,3]=>0001111=>1111000
[3,6,4,8,7,2,1,5]=>1000111=>1110001
[3,2,5,8,7,6,1,4]=>0100111=>1110010
[3,2,4,8,7,6,1,5]=>0100111=>1110010
[3,1,5,8,7,2,6,4]=>0100111=>1110010
[3,1,4,8,7,2,6,5]=>0100111=>1110010
[1,6,4,8,2,7,5,3]=>0001111=>1111000
[1,4,5,8,2,7,6,3]=>0000111=>1110000
[2,4,5,8,3,7,1,6]=>0000011=>1100000
[4,6,5,8,1,2,7,3]=>0000111=>1110000
[1,6,4,8,3,2,7,5]=>0100111=>1110010
[1,4,5,8,3,2,7,6]=>0100011=>1100010
[7,6,1,4,8,2,5,3]=>0001111=>1111000
[7,6,1,3,8,2,5,4]=>0001111=>1111000
[7,6,3,4,8,2,1,5]=>1000111=>1110001
[7,2,5,1,8,6,4,3]=>0011111=>1111100
[7,2,5,3,8,6,1,4]=>0001111=>1111000
[7,2,1,4,8,6,5,3]=>1001111=>1111001
[7,2,1,3,8,6,5,4]=>1001111=>1111001
[7,2,3,4,8,6,1,5]=>0000111=>1110000
[7,3,5,4,8,2,1,6]=>1001011=>1101001
[2,6,5,1,8,7,4,3]=>0011111=>1111100
[2,3,5,4,8,7,1,6]=>0001011=>1101000
[1,6,5,4,8,2,7,3]=>0001111=>1111000
[1,6,5,3,8,2,7,4]=>0001111=>1111000
[1,6,3,4,8,2,7,5]=>0000111=>1110000
[1,3,5,4,8,2,7,6]=>0001011=>1101000
[3,6,5,4,8,2,1,7]=>1001101=>1011001
[7,6,5,2,3,8,1,4]=>0001111=>1111000
[7,6,1,4,2,8,5,3]=>0011111=>1111100
[7,6,1,2,3,8,5,4]=>0001111=>1111000
[7,6,2,4,3,8,1,5]=>0010111=>1110100
[7,1,5,4,2,8,6,3]=>0011111=>1111100
[7,1,5,2,3,8,6,4]=>0001111=>1111000
[7,1,2,4,3,8,6,5]=>0010111=>1110100
[2,6,5,4,3,8,1,7]=>0011101=>1011100
[7,6,1,4,3,2,8,5]=>0110111=>1110110
[7,1,5,4,3,2,8,6]=>0111011=>1101110
[3,4,2,6,7,8,1,5]=>0010001=>1000100
[3,1,4,2,6,8,7,5]=>0110011=>1100110
[8,3,4,2,6,1,7,5]=>0010111=>1110100
[2,6,7,3,5,4,1,8]=>0011010=>0101100
[2,7,8,3,5,4,1,6]=>0011001=>1001100
[2,6,8,3,5,4,1,7]=>0011001=>1001100
[4,7,1,2,8,5,3,6]=>0001011=>1101000
[4,8,1,2,7,5,3,6]=>0001011=>1101000
[2,1,6,3,7,5,4,8]=>1001110=>0111001
[2,7,1,3,6,8,4,5]=>0000011=>1100000
[6,7,3,2,8,1,4,5]=>0100011=>1100010
[7,3,4,2,6,1,8,5]=>0010111=>1110100
[7,4,1,2,8,5,3,6]=>0011011=>1101100
[8,7,4,2,1,5,3,6]=>1011011=>1101101
[7,4,1,2,6,5,3,8]=>0011110=>0111100
[7,4,3,1,5,6,8,2]=>0110011=>1100110
[6,7,4,1,5,8,3,2]=>0110011=>1100110
[4,7,5,1,6,8,3,2]=>0101011=>1101010
[4,5,3,1,7,6,8,2]=>0101011=>1101010
[4,6,1,2,7,5,3,8]=>0001110=>0111000
[2,7,1,3,6,5,4,8]=>0001110=>0111000
[4,1,8,2,6,5,3,7]=>0011101=>1011100
[4,6,1,2,8,5,3,7]=>0001101=>1011000
[8,4,3,1,5,6,7,2]=>0110011=>1100110
[4,5,3,1,8,6,7,2]=>0101011=>1101010
[4,8,5,6,3,1,7,2]=>0100111=>1110010
[5,1,3,4,8,6,7,2]=>0001011=>1101000
[5,4,3,8,1,6,7,2]=>0011011=>1101100
[8,5,3,4,1,6,7,2]=>0011011=>1101100
[6,4,8,2,1,5,3,7]=>1001101=>1011001
[6,7,3,2,5,1,4,8]=>0101010=>0101010
[6,8,3,2,5,1,4,7]=>0101001=>1001010
[5,7,1,4,6,8,3,2]=>0100011=>1100010
[5,1,3,4,7,6,8,2]=>0001011=>1101000
[6,1,4,2,7,5,3,8]=>0011110=>0111100
[5,4,3,7,1,6,8,2]=>0011011=>1101100
[6,7,5,4,1,8,3,2]=>0111011=>1101110
[7,6,4,2,1,5,3,8]=>1011110=>0111101
[8,2,7,6,5,4,1,3]=>0011111=>1111100
[7,2,8,6,5,4,3,1]=>0111111=>1111110
[8,1,9,7,6,5,4,3,2]=>01111111=>11111110
[2,10,9,8,7,6,5,4,1,3]=>001111111=>111111100
[9,2,8,7,6,5,4,1,3]=>00111111=>11111100
[3,9,8,7,6,5,4,1,2]=>00111111=>11111100
[8,7,2,6,5,4,1,3]=>0011111=>1111100
[3,2,8,7,6,5,1,4]=>0101111=>1111010
[4,8,7,6,5,3,1,2]=>0101111=>1111010
[7,8,6,1,5,4,3,2]=>0111101=>1011110
[8,9,1,7,6,5,4,3,2]=>01111101=>10111110
[7,3,8,6,5,4,2,1]=>1011111=>1111101
[8,2,9,7,6,5,4,3,1]=>01111111=>11111110
[9,1,10,8,7,6,5,4,3,2]=>011111111=>111111110
[4,8,5,7,6,3,2,1]=>1100111=>1110011
[3,8,7,4,6,5,2,1]=>1001111=>1111001
[2,8,7,6,3,5,4,1]=>0011111=>1111100
[8,5,6,1,3,2,4,7]=>0100101=>1010010
[8,6,1,5,3,2,4,7]=>0101101=>1011010
[7,8,1,5,3,2,4,6]=>0101001=>1001010
[8,1,7,5,3,2,4,6]=>0101011=>1101010
[8,6,1,4,5,2,3,7]=>0001101=>1011000
[8,6,3,1,5,2,4,7]=>0101101=>1011010
[8,4,6,1,5,2,3,7]=>0001101=>1011000
[8,6,2,1,5,4,3,7]=>1011101=>1011101
[8,5,2,6,1,4,3,7]=>0011101=>1011100
[8,5,2,1,7,4,3,6]=>1011011=>1101101
[7,8,2,1,5,4,3,6]=>1011001=>1001101
[7,8,3,1,5,2,4,6]=>0101001=>1001010
[8,2,7,5,1,3,4,6]=>0001011=>1101000
[8,4,1,7,5,2,3,6]=>0011011=>1101100
[8,2,7,1,5,4,3,6]=>0011011=>1101100
[8,2,6,1,7,4,3,5]=>0010111=>1110100
[8,1,7,4,3,2,6,5]=>0110111=>1110110
[8,1,5,7,3,2,6,4]=>0100111=>1110010
[5,7,8,1,3,2,6,4]=>0100101=>1010010
[8,2,6,1,5,7,3,4]=>0000111=>1110000
[5,8,1,6,7,2,3,4]=>0000011=>1100000
[5,7,6,1,8,2,3,4]=>0000111=>1110000
[6,7,2,5,1,8,3,4]=>0001011=>1101000
[7,5,1,6,8,2,3,4]=>0001011=>1101000
[6,5,7,1,8,2,3,4]=>0000111=>1110000
[6,7,3,8,1,2,4,5]=>0000011=>1100000
[7,5,4,1,8,2,3,6]=>0011011=>1101100
[7,6,1,4,8,2,3,5]=>0000111=>1110000
[8,1,6,4,7,2,3,5]=>0000111=>1110000
[7,5,8,1,3,2,4,6]=>0100011=>1100010
[7,8,4,1,3,2,5,6]=>0110001=>1000110
[8,3,7,4,1,2,5,6]=>0010011=>1100100
[8,5,1,7,3,2,4,6]=>0101011=>1101010
[6,8,1,7,3,2,4,5]=>0100011=>1100010
[7,1,8,4,3,6,2,5]=>0010111=>1110100
[7,3,1,8,6,4,2,5]=>0110111=>1110110
[8,3,1,7,4,6,2,5]=>0100111=>1110010
[8,4,5,1,7,2,3,6]=>0001011=>1101000
[5,6,8,1,7,2,3,4]=>0000011=>1100000
[6,5,8,1,2,7,3,4]=>0000111=>1110000
[7,3,1,8,5,6,2,4]=>0100111=>1110010
[6,2,7,8,3,1,5,4]=>0101101=>1011010
[5,8,1,7,3,2,6,4]=>0100111=>1110010
[8,4,1,7,3,2,6,5]=>0110111=>1110110
[8,3,4,7,1,2,6,5]=>0000111=>1110000
[8,2,7,4,1,3,6,5]=>0010111=>1110100
[7,4,8,2,1,3,6,5]=>1000111=>1110001
[7,4,3,8,1,2,6,5]=>0010111=>1110100
[8,2,3,6,7,1,5,4]=>0001011=>1101000
[2,6,8,7,1,5,4,3]=>0011011=>1101100
[7,8,5,2,3,6,4,1]=>0011101=>1011100
[8,7,5,2,3,1,6,4]=>0101111=>1111010
[6,8,5,2,3,4,7,1]=>0001011=>1101000
[3,5,2,6,8,1,4,7]=>0001001=>1001000
[3,5,2,4,6,8,1,7]=>0001001=>1001000
[2,4,5,7,3,6,8,1]=>0000011=>1100000
[2,4,5,3,6,8,1,7]=>0001001=>1001000
[5,2,4,6,8,1,3,7]=>0001001=>1001000
[5,1,3,4,6,8,2,7]=>0001001=>1001000
[4,3,5,2,6,8,1,7]=>0011001=>1001100
[4,3,5,7,2,8,1,6]=>0010011=>1100100
[4,3,5,7,2,6,8,1]=>0010011=>1100100
[4,6,3,7,2,5,8,1]=>0000111=>1110000
[4,6,3,1,7,8,2,5]=>0100101=>1010010
[4,3,5,1,7,8,2,6]=>0011001=>1001100
[5,7,1,3,4,8,2,6]=>0000011=>1100000
[5,7,1,3,4,6,8,2]=>0000011=>1100000
[4,5,7,1,3,6,8,2]=>0000011=>1100000
[4,3,6,7,1,5,8,2]=>0010011=>1100100
[4,6,3,5,1,7,8,2]=>0001101=>1011000
[4,6,3,5,7,2,8,1]=>0000111=>1110000
[3,5,6,4,1,7,8,2]=>0010101=>1010100
[3,1,5,6,7,4,8,2]=>0100011=>1100010
[5,1,6,7,3,4,8,2]=>0001011=>1101000
[6,4,7,1,3,5,8,2]=>0000111=>1110000
[1,6,7,3,4,5,8,2]=>0000011=>1100000
[2,6,7,4,5,8,1,3]=>0000011=>1100000
[2,6,7,4,8,1,3,5]=>0000011=>1100000
[5,3,6,1,2,7,8,4]=>0001101=>1011000
[3,5,2,6,1,7,8,4]=>0001101=>1011000
[3,5,2,6,7,4,8,1]=>0001011=>1101000
[5,2,3,6,7,4,8,1]=>0001011=>1101000
[5,2,3,6,1,7,8,4]=>0001101=>1011000
[5,2,6,1,3,7,8,4]=>0001101=>1011000
[4,2,6,7,3,5,8,1]=>0010011=>1100100
[6,3,7,2,4,5,8,1]=>0000111=>1110000
[3,5,7,2,8,1,4,6]=>0000011=>1100000
[3,7,2,4,8,1,5,6]=>0000011=>1100000
[7,2,4,6,8,1,3,5]=>0000011=>1100000
[7,1,3,4,6,8,2,5]=>0000011=>1100000
[3,7,2,4,6,8,1,5]=>0000011=>1100000
[3,5,7,2,6,8,1,4]=>0000011=>1100000
[6,3,7,2,5,8,1,4]=>0000111=>1110000
[6,3,5,7,2,8,1,4]=>0000111=>1110000
[6,3,5,7,2,4,8,1]=>0000111=>1110000
[6,2,4,5,7,3,8,1]=>0000111=>1110000
[6,2,4,5,1,7,8,3]=>0001101=>1011000
[4,7,1,2,5,6,8,3]=>0000011=>1100000
[2,6,7,5,8,1,3,4]=>0000011=>1100000
[4,6,7,1,2,5,8,3]=>0000011=>1100000
[5,6,2,4,7,3,8,1]=>0000111=>1110000
[5,4,2,6,7,3,8,1]=>0011011=>1101100
[5,4,2,6,1,7,8,3]=>0011101=>1011100
[1,5,4,6,2,7,8,3]=>0001101=>1011000
[5,6,4,1,2,7,8,3]=>0010101=>1010100
[6,4,5,1,2,7,8,3]=>0001101=>1011000
[6,3,5,1,7,8,2,4]=>0001101=>1011000
[6,5,7,2,8,1,3,4]=>0000111=>1110000
[6,5,7,1,3,4,8,2]=>0000111=>1110000
[5,6,4,7,1,3,8,2]=>0000111=>1110000
[5,4,6,3,1,7,8,2]=>0101101=>1011010
[7,5,3,2,4,8,1,6]=>0101011=>1101010
[8,4,5,2,6,1,3,7]=>0001101=>1011000
[8,5,4,2,1,6,3,7]=>1011101=>1011101
[8,5,3,4,1,6,2,7]=>0011101=>1011100
[8,4,5,3,1,6,2,7]=>0101101=>1011010
[7,5,4,2,1,8,3,6]=>1011011=>1101101
[7,5,4,2,1,6,8,3]=>1011011=>1101101
[7,4,5,3,1,6,8,2]=>0101011=>1101010
[7,4,3,5,6,1,8,2]=>0010111=>1110100
[5,6,3,7,4,1,8,2]=>0010111=>1110100
[5,6,7,3,1,4,8,2]=>0100011=>1100010
[6,7,3,4,1,5,8,2]=>0010011=>1100100
[6,7,4,2,1,5,8,3]=>1010011=>1100101
[5,6,7,3,1,8,2,4]=>0100011=>1100010
[5,6,3,7,8,1,2,4]=>0000101=>1010000
[5,6,3,7,2,4,8,1]=>0000111=>1110000
[5,6,7,2,3,8,1,4]=>0000011=>1100000
[7,4,5,2,8,1,3,6]=>0001011=>1101000
[6,7,3,2,4,8,1,5]=>0100011=>1100010
[7,6,4,2,1,3,8,5]=>1010111=>1110101
[7,6,3,4,1,2,8,5]=>0010111=>1110100
[7,6,3,2,4,1,8,5]=>0110111=>1110110
[6,7,3,2,5,1,8,4]=>0101011=>1101010
[6,5,3,2,7,8,1,4]=>0101101=>1011010
[6,5,3,2,7,4,8,1]=>0101111=>1111010
[6,4,5,2,7,3,8,1]=>0001111=>1111000
[6,4,5,2,7,8,1,3]=>0001101=>1011000
[7,4,5,2,6,1,8,3]=>0001111=>1111000
[7,4,5,6,1,2,8,3]=>0000111=>1110000
[7,5,6,2,1,3,8,4]=>1000111=>1110001
[6,7,3,5,1,2,8,4]=>0001011=>1101000
[5,6,7,4,1,2,8,3]=>0010011=>1100100
[5,6,7,2,4,1,8,3]=>0010011=>1100100
[5,6,4,2,7,8,1,3]=>0010101=>1010100
[6,5,7,2,1,8,3,4]=>1000111=>1110001
[6,5,7,2,1,4,8,3]=>1000111=>1110001
[5,4,6,7,3,1,8,2]=>0101011=>1101010
[5,7,8,3,6,4,1,2]=>0010101=>1010100
[3,7,8,5,6,4,1,2]=>0010101=>1010100
[3,7,8,5,6,1,4,2]=>0010101=>1010100
[1,7,8,5,6,3,4,2]=>0010101=>1010100
[1,7,5,8,6,3,4,2]=>0010111=>1110100
[3,7,5,8,6,1,4,2]=>0010111=>1110100
[3,7,5,8,6,4,1,2]=>0010111=>1110100
[5,7,3,8,6,4,1,2]=>0010111=>1110100
[7,3,8,5,6,4,1,2]=>0010111=>1110100
[7,3,5,8,6,4,1,2]=>0010111=>1110100
[3,5,7,8,6,4,1,2]=>0010101=>1010100
[1,5,7,8,6,3,4,2]=>0010101=>1010100
[1,5,7,8,3,6,4,2]=>0010101=>1010100
[3,5,7,8,1,6,4,2]=>0010101=>1010100
[5,3,7,8,1,6,4,2]=>0011101=>1011100
[7,3,5,8,6,1,4,2]=>0010111=>1110100
[7,3,8,5,6,1,4,2]=>0010111=>1110100
[7,8,1,5,6,3,4,2]=>0010101=>1010100
[7,1,8,5,6,3,4,2]=>0010111=>1110100
[7,1,5,8,6,3,4,2]=>0010111=>1110100
[5,1,7,8,3,6,4,2]=>0011101=>1011100
[3,1,7,8,5,6,4,2]=>0110101=>1010110
[1,3,7,8,5,6,4,2]=>0010101=>1010100
[3,1,7,5,8,6,4,2]=>0110111=>1110110
[5,1,7,3,8,6,4,2]=>0011111=>1111100
[7,1,5,3,8,6,4,2]=>0011111=>1111100
[7,1,5,8,3,6,4,2]=>0010111=>1110100
[7,8,1,5,3,6,4,2]=>0011101=>1011100
[7,8,3,5,1,6,4,2]=>0011101=>1011100
[7,3,5,8,1,6,4,2]=>0010111=>1110100
[5,3,7,1,8,6,4,2]=>0011111=>1111100
[3,5,7,1,8,6,4,2]=>0010111=>1110100
[1,7,5,3,8,6,4,2]=>0011111=>1111100
[5,7,3,1,8,6,4,2]=>0110111=>1110110
[5,7,3,8,6,1,4,2]=>0010111=>1110100
[3,7,5,8,1,6,4,2]=>0010111=>1110100
[1,7,5,8,3,6,4,2]=>0010111=>1110100
[1,7,8,5,3,6,4,2]=>0011101=>1011100
[3,7,8,5,1,6,4,2]=>0011101=>1011100
[5,7,8,3,6,1,4,2]=>0010101=>1010100
[5,7,8,6,3,1,4,2]=>0110101=>1010110
[7,5,8,6,1,3,4,2]=>0010111=>1110100
[5,7,8,1,6,3,4,2]=>0010101=>1010100
[5,7,8,1,3,6,4,2]=>0010101=>1010100
[3,7,8,1,5,6,4,2]=>0010101=>1010100
[1,7,8,3,5,6,4,2]=>0010101=>1010100
[1,7,3,8,5,6,4,2]=>0010111=>1110100
[3,7,1,8,5,6,4,2]=>0010111=>1110100
[5,7,1,8,3,6,4,2]=>0010111=>1110100
[5,7,1,8,6,3,4,2]=>0010111=>1110100
[7,5,1,8,6,3,4,2]=>0011111=>1111100
[7,5,8,1,6,3,4,2]=>0010111=>1110100
[7,8,5,1,6,3,4,2]=>0011101=>1011100
[7,8,5,1,3,6,4,2]=>0011101=>1011100
[7,5,8,1,3,6,4,2]=>0010111=>1110100
[7,5,1,8,3,6,4,2]=>0011111=>1111100
[7,5,1,3,8,6,4,2]=>0011111=>1111100
[5,7,1,3,8,6,4,2]=>0010111=>1110100
[3,7,1,5,8,6,4,2]=>0010111=>1110100
[1,7,3,5,8,6,4,2]=>0010111=>1110100
[1,5,3,7,8,6,4,2]=>0011101=>1011100
[3,5,1,7,8,6,4,2]=>0011101=>1011100
[5,3,1,7,8,6,4,2]=>0111101=>1011110
[7,3,1,5,8,6,4,2]=>0110111=>1110110
[7,3,1,8,5,6,4,2]=>0110111=>1110110
[7,3,8,1,5,6,4,2]=>0010111=>1110100
[7,8,3,1,5,6,4,2]=>0110101=>1010110
[7,8,1,3,5,6,4,2]=>0010101=>1010100
[7,1,8,3,5,6,4,2]=>0010111=>1110100
[7,1,3,8,5,6,4,2]=>0010111=>1110100
[7,1,3,5,8,6,4,2]=>0010111=>1110100
[3,1,5,7,8,6,4,2]=>0110101=>1010110
[5,7,3,4,6,8,1,2]=>0000011=>1100000
[5,7,3,4,8,6,1,2]=>0000111=>1110000
[5,7,3,4,8,1,6,2]=>0000111=>1110000
[5,7,3,4,1,8,6,2]=>0010111=>1110100
[5,7,3,4,1,6,8,2]=>0010011=>1100100
[5,7,3,4,6,1,2,8]=>0000110=>0110000
[7,3,5,6,1,2,8,4]=>0000111=>1110000
[5,7,3,1,4,6,2,8]=>0100110=>0110010
[5,7,3,1,4,6,8,2]=>0100011=>1100010
[5,7,3,1,4,8,6,2]=>0100111=>1110010
[5,7,3,1,4,8,2,6]=>0100011=>1100010
[5,3,7,4,1,2,8,6]=>0011011=>1101100
[5,3,7,4,1,2,6,8]=>0011010=>0101100
[5,3,7,1,4,2,6,8]=>0011010=>0101100
[5,3,7,1,4,2,8,6]=>0011011=>1101100
[3,7,5,1,2,8,6,4]=>0001111=>1111000
[7,8,3,5,1,2,6,4]=>0001101=>1011000
[7,3,8,5,1,2,6,4]=>0001111=>1111000
[7,3,5,8,1,2,6,4]=>0000111=>1110000
[3,7,5,1,2,6,4,8]=>0001110=>0111000
[3,7,5,1,2,6,8,4]=>0001011=>1101000
[6,1,4,3,5,2,8,7]=>0011101=>1011100
[2,5,7,3,8,4,1,6]=>0010011=>1100100
[5,4,7,8,6,1,3,2]=>0101101=>1011010
[7,5,6,2,8,3,1,4]=>0100111=>1110010
[4,7,2,5,8,3,1,6]=>0100011=>1100010
[6,2,4,5,1,3,8,7]=>0001101=>1011000
[5,1,4,6,3,2,8,7]=>0101101=>1011010
[3,5,6,2,4,1,8,7]=>0010101=>1010100
[3,8,6,7,5,4,1,2]=>0011011=>1101100
[6,2,7,8,3,4,1,5]=>0010101=>1010100
[2,5,3,4,8,1,7,6]=>0001011=>1101000
[8,7,1,2,5,3,4,6]=>0001011=>1101000
[5,1,8,2,3,4,7,6]=>0001011=>1101000
[5,4,7,6,2,8,1,3]=>0001111=>1111000
[3,7,8,1,5,4,6,2]=>0001101=>1011000
[7,1,3,4,6,8,5,2]=>0001011=>1101000
[8,3,6,5,7,1,4,2]=>0010111=>1110100
[5,8,7,1,4,6,2,3]=>0000111=>1110000
[4,7,6,1,8,3,5,2]=>0001111=>1111000
[4,7,2,6,3,8,5,1]=>0001111=>1111000
[2,1,8,4,6,7,3,5]=>1000011=>1100001
[4,7,8,6,3,1,2,5]=>0100101=>1010010
[3,8,1,5,6,7,2,4]=>0000011=>1100000
[6,7,2,4,8,5,3,1]=>0101011=>1101010
[2,8,3,6,7,5,1,4]=>0001011=>1101000
[8,2,1,7,6,3,5,4]=>1001111=>1111001
[3,2,4,5,8,1,7,6]=>0100011=>1100010
[7,4,6,3,2,1,8,5]=>1100111=>1110011
[4,7,3,2,1,8,6,5]=>1100111=>1110011
[6,4,7,5,2,3,8,1]=>0001111=>1111000
[6,4,8,1,7,3,2,5]=>0100111=>1110010
[4,8,7,2,3,1,5,6]=>0100011=>1100010
[4,2,3,1,8,7,5,6]=>0110011=>1100110
[7,6,8,1,3,5,2,4]=>0001011=>1101000
[6,7,5,2,3,1,8,4]=>0101011=>1101010
[4,7,2,6,5,1,8,3]=>0001111=>1111000
[6,4,2,1,8,5,7,3]=>1010111=>1110101
[7,2,1,5,6,8,4,3]=>1010011=>1100101
[8,7,2,6,4,1,5,3]=>0011111=>1111100
[6,7,8,2,5,3,1,4]=>0101001=>1001010
[2,1,7,3,6,8,5,4]=>1001011=>1101001
[2,1,5,7,8,4,6,3]=>1000101=>1010001
[2,5,7,8,3,6,1,4]=>0000101=>1010000
[6,4,1,5,7,2,8,3]=>0010111=>1110100
[7,4,8,1,2,5,6,3]=>0000111=>1110000
[4,2,7,8,6,3,5,1]=>0011101=>1011100
[6,1,7,4,3,2,8,5]=>0110111=>1110110
[6,8,3,4,2,1,7,5]=>1010011=>1100101
[4,2,6,1,5,7,8,3]=>0010101=>1010100
[2,4,6,7,3,5,8,1]=>0000011=>1100000
[6,5,8,3,7,4,1,2]=>0010111=>1110100
[7,1,4,8,3,5,6,2]=>0000111=>1110000
[6,8,7,5,3,4,1,2]=>0011011=>1101100
[4,8,6,3,1,5,7,2]=>0100111=>1110010
[3,4,8,2,5,7,6,1]=>0000111=>1110000
[3,6,8,7,2,5,1,4]=>0001011=>1101000
[3,5,7,2,8,6,1,4]=>0000111=>1110000
[2,5,7,4,8,6,1,3]=>0000111=>1110000
[1,6,3,7,5,2,8,4]=>0001111=>1111000
[2,6,3,7,5,1,8,4]=>0001111=>1111000
[2,6,4,8,7,5,1,3]=>0001111=>1111000
[6,3,7,2,8,5,1,4]=>0001111=>1111000
[3,6,2,5,8,7,1,4]=>0000111=>1110000
[5,2,8,4,7,6,1,3]=>0001111=>1111000
[7,2,4,8,6,5,1,3]=>0001111=>1111000
[6,2,4,8,7,5,1,3]=>0001111=>1111000
[2,4,5,8,7,6,1,3]=>0000111=>1110000
[2,3,5,7,6,1,8,4]=>0000111=>1110000
[1,3,4,6,2,8,7,5]=>0000111=>1110000
[5,2,3,6,1,8,7,4]=>0001111=>1111000
[4,2,7,3,8,1,6,5]=>0010111=>1110100
[2,5,1,4,7,3,8,6]=>0001011=>1101000
[6,1,3,8,7,2,5,4]=>0001111=>1111000
[3,1,5,6,2,8,7,4]=>0100111=>1110010
[1,2,4,6,3,8,7,5]=>0000111=>1110000
[4,1,5,2,8,7,6,3]=>0011111=>1111100
[7,1,4,2,8,6,5,3]=>0011111=>1111100
[5,1,3,7,2,8,6,4]=>0001111=>1111000
[4,1,5,3,2,8,7,6]=>0111011=>1101110
[2,6,1,4,3,8,7,5]=>0010111=>1110100
[3,6,2,4,1,8,7,5]=>0010111=>1110100
[7,2,3,5,1,8,6,4]=>0001111=>1111000
[7,3,4,1,8,6,5,2]=>0011111=>1111100
[6,3,4,1,8,7,5,2]=>0011111=>1111100
[3,4,5,1,8,7,6,2]=>0001111=>1111000
[1,4,5,2,8,7,6,3]=>0001111=>1111000
[1,6,4,2,8,7,5,3]=>0011111=>1111100
[5,6,3,1,8,7,4,2]=>0110111=>1110110
[7,4,2,5,1,8,6,3]=>0011111=>1111100
[5,3,6,2,8,1,7,4]=>0001111=>1111000
[4,6,2,7,5,1,8,3]=>0001111=>1111000
[4,5,2,6,1,8,7,3]=>0001111=>1111000
[1,5,3,6,2,8,7,4]=>0001111=>1111000
[1,5,8,3,2,7,6,4]=>0100111=>1110010
[2,5,8,3,1,7,6,4]=>0100111=>1110010
[4,5,8,2,1,7,6,3]=>1000111=>1110001
[3,6,2,5,1,4,8,7]=>0001101=>1011000
[5,2,8,4,1,3,7,6]=>0011011=>1101100
[2,4,8,7,1,3,6,5]=>0000111=>1110000
[2,5,8,1,3,7,6,4]=>0000111=>1110000
[2,3,8,1,4,7,6,5]=>0000111=>1110000
[1,3,8,2,4,7,6,5]=>0000111=>1110000
[3,4,1,7,2,8,6,5]=>0010111=>1110100
[3,5,2,1,7,4,8,6]=>1001011=>1101001
[6,3,1,7,2,8,5,4]=>0101111=>1111010
[7,5,1,2,8,6,4,3]=>0011111=>1111100
[4,6,1,2,8,7,5,3]=>0001111=>1111000
[1,6,2,3,8,7,5,4]=>0001111=>1111000
[1,5,2,3,8,7,6,4]=>0001111=>1111000
[4,5,1,2,8,7,6,3]=>0001111=>1111000
[6,4,1,2,8,7,5,3]=>0011111=>1111100
[7,4,1,2,8,6,5,3]=>0011111=>1111100
[5,3,1,7,2,8,6,4]=>0101111=>1111010
[5,2,8,1,3,7,6,4]=>0001111=>1111000
[4,1,2,8,3,7,6,5]=>0010111=>1110100
[4,7,5,6,8,3,1,2]=>0100011=>1100010
[8,6,4,7,5,3,1,2]=>0101111=>1111010
[7,5,2,6,4,1,3,8]=>0011110=>0111100
[1,6,3,7,5,8,4,2]=>0010111=>1110100
[1,3,7,4,5,8,6,2]=>0000111=>1110000
[7,2,6,3,4,1,5,8]=>0010110=>0110100
[8,3,7,4,6,5,1,2]=>0001111=>1111000
[6,8,4,7,5,3,1,2]=>0101011=>1101010
[4,8,7,5,6,3,1,2]=>0100111=>1110010
[3,8,7,6,4,5,1,2]=>0001111=>1111000
[1,6,5,2,8,3,7,4]=>0001111=>1111000
[8,6,5,2,1,4,3,7]=>1011101=>1011101
[2,7,6,3,1,4,5,8]=>0100110=>0110010
[6,8,5,3,2,1,4,7]=>1101001=>1001011
[2,7,6,4,5,1,3,8]=>0001110=>0111000
[5,7,2,6,4,1,3,8]=>0010110=>0110100
[6,1,3,7,5,8,4,2]=>0010111=>1110100
[4,1,7,3,6,8,5,2]=>0011011=>1101100
[8,1,6,4,3,7,5,2]=>0011111=>1111100
[2,1,7,4,8,6,3,5]=>1000111=>1110001
[1,8,6,3,7,5,4,2]=>0011111=>1111100
[1,8,2,7,3,6,5,4]=>0001111=>1111000
[2,1,3,8,4,7,5,6]=>1000011=>1100001
[8,1,2,7,4,3,6,5]=>0010111=>1110100
[5,3,1,6,8,4,7,2]=>0101011=>1101010
[6,2,8,7,1,4,3,5]=>0010111=>1110100
[8,7,2,1,5,4,3,6]=>1011011=>1101101
[8,2,3,1,4,6,5,7]=>0100101=>1010010
[2,4,8,3,1,5,6,7]=>0100001=>1000010
[3,4,2,7,1,5,6,8]=>0010010=>0100100
[4,7,3,8,2,1,5,6]=>1000011=>1100001
[5,2,7,3,1,4,6,8]=>0101010=>0101010
[8,3,7,2,1,5,4,6]=>1001011=>1101001
[1,3,7,2,8,4,6,5]=>0000111=>1110000
[1,4,2,5,8,6,7,3]=>0010011=>1100100
[6,5,3,8,2,1,4,7]=>1001101=>1011001
[2,6,4,5,7,1,3,8]=>0000110=>0110000
[5,4,6,2,7,1,3,8]=>0001110=>0111000
[7,6,3,1,8,4,5,2]=>0101111=>1111010
[7,6,2,1,8,5,3,4]=>1001111=>1111001
[1,7,5,8,6,4,3,2]=>0110111=>1110110
[6,5,1,2,8,3,7,4]=>0001111=>1111000
[8,6,1,4,3,7,5,2]=>0011111=>1111100
[6,8,4,1,3,7,5,2]=>0011011=>1101100
[6,5,7,1,3,8,4,2]=>0010111=>1110100
[5,8,3,1,7,4,6,2]=>0100111=>1110010
[8,3,1,7,5,4,6,2]=>0101111=>1111010
[1,3,8,7,4,6,5,2]=>0001111=>1111000
[1,2,8,7,6,3,5,4]=>0001111=>1111000
[8,2,1,7,6,4,3,5]=>1010111=>1110101
[2,3,1,8,7,4,5,6]=>0100011=>1100010
[2,4,1,8,5,7,3,6]=>0010011=>1100100
[5,8,2,1,7,6,3,4]=>1000111=>1110001
[6,2,7,1,8,5,3,4]=>0001111=>1111000
[8,7,1,6,5,4,3,2]=>0111111=>1111110
[7,1,8,3,6,5,4,2]=>0011111=>1111100
[4,1,8,7,5,6,3,2]=>0110111=>1110110
[8,1,2,3,4,5,9,6,7]=>00000011=>11000000
[8,1,2,3,4,9,5,6,7]=>00000011=>11000000
[8,1,2,9,3,4,5,6,7]=>00000011=>11000000
[8,1,9,2,3,4,5,6,7]=>00000011=>11000000
[6,1,2,3,4,5,8,9,7]=>00001001=>10010000
[9,1,2,3,4,5,6,10,7,8]=>000000011=>110000000
[5,1,2,3,4,8,9,6,7]=>00010001=>10001000
[9,1,2,3,4,5,10,6,7,8]=>000000011=>110000000
[4,1,2,3,8,9,5,6,7]=>00100001=>10000100
[3,1,2,8,9,4,5,6,7]=>01000001=>10000010
[9,1,2,3,10,4,5,6,7,8]=>000000011=>110000000
[2,1,8,9,3,4,5,6,7]=>10000001=>10000001
[9,1,2,10,3,4,5,6,7,8]=>000000011=>110000000
[3,5,8,7,2,6,4,1]=>0010111=>1110100
[5,8,2,7,1,6,4,3]=>0010111=>1110100
[2,1,6,4,5,8,3,7]=>1000101=>1010001
[8,6,3,7,5,2,1,4]=>1001111=>1111001
[4,6,3,8,5,2,1,7]=>1001101=>1011001
[4,6,3,7,5,2,8,1]=>0001111=>1111000
[3,5,7,8,2,6,1,4]=>0000101=>1010000
[8,2,3,4,6,1,5,7]=>0000101=>1010000
[7,2,3,4,6,8,5,1]=>0001011=>1101000
[4,2,3,6,1,5,8,7]=>0010101=>1010100
[4,8,3,7,5,1,6,2]=>0001111=>1111000
[5,2,3,4,8,7,1,6]=>0001011=>1101000
[5,2,3,4,6,8,1,7]=>0001001=>1001000
[4,2,8,5,7,6,1,3]=>0010111=>1110100
[3,7,6,4,5,1,8,2]=>0001111=>1111000
[3,8,6,4,5,1,2,7]=>0001101=>1011000
[4,8,3,7,5,2,1,6]=>1001011=>1101001
[8,7,3,6,5,1,2,4]=>0001111=>1111000
[4,2,7,5,8,6,3,1]=>0110111=>1110110
[5,8,1,7,3,6,4,2]=>0010111=>1110100
[5,2,7,8,4,6,3,1]=>0101101=>1011010
[5,2,8,3,7,6,1,4]=>0001111=>1111000
[8,2,7,3,1,6,4,5]=>0100111=>1110010
[6,2,3,4,8,5,1,7]=>0001101=>1011000
[6,2,3,4,1,8,5,7]=>0010101=>1010100
[7,2,3,4,1,8,6,5]=>0010111=>1110100
[7,2,3,4,1,5,8,6]=>0010011=>1100100
[1,2,3,4,8,7,5,6]=>0000011=>1100000
[1,2,8,5,3,4,6,7]=>0001001=>1001000
[1,8,4,2,3,5,6,7]=>0010001=>1000100
[8,6,7,4,1,5,3,2]=>0111011=>1101110
[4,8,6,7,5,1,3,2]=>0101011=>1101010
[7,1,8,4,6,5,2,3]=>0001111=>1111000
[8,7,1,5,4,6,2,3]=>0001111=>1111000
[8,5,7,1,4,6,3,2]=>0100111=>1110010
[6,4,8,5,1,7,3,2]=>0101111=>1111010
[4,8,5,7,1,6,3,2]=>0100111=>1110010
[8,4,7,1,5,6,3,2]=>0100111=>1110010
[8,7,1,4,5,6,3,2]=>0100111=>1110010
[8,7,4,5,6,1,3,2]=>0100111=>1110010
[8,7,5,1,4,6,2,3]=>0001111=>1111000
[8,7,2,5,1,4,6,3]=>0001111=>1111000
[4,8,7,2,5,1,6,3]=>0001111=>1111000
[1,6,4,8,5,2,7,3]=>0001111=>1111000
[8,7,1,4,2,5,6,3]=>0010111=>1110100
[8,7,5,1,2,4,6,3]=>0001111=>1111000
[7,1,8,5,6,2,3,4]=>0000111=>1110000
[3,8,7,1,2,5,6,4]=>0000111=>1110000
[3,5,8,7,1,2,6,4]=>0000111=>1110000
[2,3,8,5,7,1,6,4]=>0000111=>1110000
[3,8,7,1,5,6,2,4]=>0000111=>1110000
[3,5,8,7,1,6,2,4]=>0000111=>1110000
[2,3,8,6,7,5,1,4]=>0001011=>1101000
[3,2,8,6,7,5,1,4]=>0101011=>1101010
[4,1,8,6,2,7,5,3]=>0011111=>1111100
[8,7,4,1,2,6,5,3]=>0011111=>1111100
[1,3,8,6,7,5,2,4]=>0001011=>1101000
[5,7,1,8,2,6,3,4]=>0000111=>1110000
[2,8,7,1,5,6,3,4]=>0000111=>1110000
[8,7,1,5,2,4,6,3]=>0001111=>1111000
[7,1,8,2,4,6,5,3]=>0001111=>1111000
[1,6,2,8,4,7,5,3]=>0001111=>1111000
[1,3,8,5,7,2,6,4]=>0000111=>1110000
[1,8,3,7,2,5,6,4]=>0000111=>1110000
[2,8,7,1,3,5,6,4]=>0000111=>1110000
[5,7,1,8,2,3,6,4]=>0000111=>1110000
[7,1,8,2,3,5,6,4]=>0000111=>1110000
[8,6,3,7,4,1,5,2]=>0011111=>1111100
[4,2,8,6,7,5,1,3]=>0011011=>1101100
[8,4,2,7,5,6,1,3]=>0010111=>1110100
[4,8,3,6,1,7,5,2]=>0001111=>1111000
[8,3,4,7,5,1,6,2]=>0001111=>1111000
[8,3,7,4,5,1,6,2]=>0001111=>1111000
[8,7,4,2,5,6,1,3]=>0010111=>1110100
[8,7,5,1,6,2,3,4]=>0001111=>1111000
[8,7,2,4,1,5,6,3]=>0010111=>1110100
[4,8,6,1,7,2,5,3]=>0001111=>1111000
[4,7,1,8,2,6,5,3]=>0001111=>1111000
[4,2,8,6,7,1,5,3]=>0011011=>1101100
[8,7,4,1,2,5,6,3]=>0010111=>1110100
[8,2,7,1,6,3,4,5]=>0000111=>1110000
[8,2,7,1,3,6,4,5]=>0000111=>1110000
[2,8,3,6,7,1,5,4]=>0001011=>1101000
[8,7,2,1,3,5,6,4]=>1000111=>1110001
[1,8,7,2,3,6,4,5]=>0000111=>1110000
[1,8,7,2,6,3,4,5]=>0000111=>1110000
[8,2,7,3,6,1,4,5]=>0000111=>1110000
[1,8,7,3,6,2,4,5]=>0000111=>1110000
[1,8,2,7,6,3,4,5]=>0000111=>1110000
[8,2,7,4,1,5,6,3]=>0010111=>1110100
[8,2,1,7,5,6,3,4]=>1000111=>1110001
[8,7,3,1,5,6,2,4]=>0100111=>1110010
[2,8,7,3,5,6,1,4]=>0000111=>1110000
[8,3,1,6,7,5,2,4]=>0101011=>1101010
[8,5,2,1,6,7,4,3]=>1011011=>1101101
[1,5,2,8,6,7,4,3]=>0011011=>1101100
[1,2,8,6,7,5,3,4]=>0001011=>1101000
[1,8,3,6,7,5,2,4]=>0001011=>1101000
[8,2,3,6,7,5,1,4]=>0001011=>1101000
[8,3,7,2,5,6,1,4]=>0000111=>1110000
[8,1,3,7,5,6,2,4]=>0000111=>1110000
[8,4,1,2,7,5,6,3]=>0010111=>1110100
[8,1,4,2,6,7,5,3]=>0011011=>1101100
[1,2,8,6,7,3,5,4]=>0001011=>1101000
[8,1,2,7,3,6,4,5]=>0000111=>1110000
[8,1,7,3,6,2,4,5]=>0000111=>1110000
[8,1,7,2,6,3,4,5]=>0000111=>1110000
[8,1,7,2,3,6,4,5]=>0000111=>1110000
[8,1,3,7,2,5,6,4]=>0000111=>1110000
[1,8,3,6,7,2,5,4]=>0001011=>1101000
[1,7,8,2,3,6,5,4]=>0001101=>1011000
[8,3,7,1,2,5,6,4]=>0000111=>1110000
[8,7,1,2,3,6,4,5]=>0000111=>1110000
[2,8,5,7,4,6,3,1]=>0100111=>1110010
[3,1,8,5,7,4,2,6]=>0110011=>1100110
[8,3,5,7,4,2,6,1]=>0010111=>1110100
[8,3,6,2,4,5,7,1]=>0000111=>1110000
[2,8,6,4,3,5,7,1]=>0010111=>1110100
[2,6,8,3,5,4,7,1]=>0001011=>1101000
[2,7,5,8,4,6,3,1]=>0100111=>1110010
[8,4,2,7,6,1,3,5]=>0010111=>1110100
[4,8,1,7,6,3,2,5]=>0100111=>1110010
[4,1,7,6,2,3,5,8]=>0010110=>0110100
[3,7,1,8,6,2,5,4]=>0001111=>1111000
[3,1,7,6,4,5,2,8]=>0101110=>0111010
[3,1,7,5,8,4,2,6]=>0110011=>1100110
[3,1,6,8,7,5,2,4]=>0101011=>1101010
[6,3,8,7,5,2,4,1]=>0011111=>1111100
[7,3,5,8,4,2,6,1]=>0010111=>1110100
[7,3,6,4,2,8,5,1]=>0011111=>1111100
[7,8,3,6,2,5,4,1]=>0011101=>1011100
[7,4,8,2,1,6,3,5]=>1000111=>1110001
[8,7,4,6,3,2,5,1]=>0101111=>1111010
[7,8,5,2,1,4,3,6]=>1011001=>1001101
[7,5,2,3,1,4,8,6]=>0101011=>1101010
[7,4,6,2,3,8,1,5]=>0000111=>1110000
[6,4,2,5,8,3,7,1]=>0010111=>1110100
[4,6,5,8,1,3,2,7]=>0100101=>1010010
[4,7,1,5,3,8,2,6]=>0001011=>1101000
[4,7,8,1,3,6,2,5]=>0000101=>1010000
[5,7,1,3,4,6,2,8]=>0000110=>0110000
[5,7,1,4,2,3,6,8]=>0010010=>0100100
[5,8,1,3,2,4,6,7]=>0100001=>1000010
[4,8,6,1,3,2,7,5]=>0100111=>1110010
[8,4,6,2,1,3,7,5]=>1000111=>1110001
[5,4,8,7,2,3,6,1]=>0001111=>1111000
[5,4,8,7,3,1,2,6]=>0101011=>1101010
[6,8,3,7,2,5,4,1]=>0011011=>1101100
[5,4,6,8,2,3,7,1]=>0001011=>1101000
[5,7,4,2,8,3,6,1]=>0010111=>1110100
[6,4,7,2,1,8,3,5]=>1000111=>1110001
[6,5,3,4,1,2,8,7]=>0011101=>1011100
[6,8,5,4,1,3,2,7]=>0111001=>1001110
[6,4,3,7,1,5,2,8]=>0011110=>0111100
[9,8,7,6,5,2,3,1,4]=>01011111=>11111010
[9,8,7,6,3,4,2,1,5]=>10101111=>11110101
[9,8,7,4,5,3,2,1,6]=>11010111=>11101011
[9,8,5,6,4,3,2,1,7]=>11101011=>11010111
[9,6,7,5,4,3,2,1,8]=>11110101=>10101111
[7,4,2,6,1,5,3,8]=>0011110=>0111100
[7,4,2,5,6,1,3,8]=>0010110=>0110100
[6,4,2,8,1,5,7,3]=>0010111=>1110100
[6,3,7,8,2,5,1,4]=>0001101=>1011000
[7,3,5,6,4,2,1,8]=>1010110=>0110101
[7,4,3,1,5,6,2,8]=>0110110=>0110110
[7,4,5,2,6,1,3,8]=>0001110=>0111000
[5,3,7,2,8,6,4,1]=>0011111=>1111100
[5,3,8,2,6,7,4,1]=>0011011=>1101100
[6,3,8,2,5,4,7,1]=>0001111=>1111000
[6,4,8,2,1,5,7,3]=>1000111=>1110001
[6,4,3,1,8,2,7,5]=>0110111=>1110110
[5,3,7,8,2,6,4,1]=>0011101=>1011100
[4,7,8,5,6,3,2,1]=>1100101=>1010011
[5,3,7,6,8,2,4,1]=>0011011=>1101100
[5,7,8,4,6,2,1,3]=>1000101=>1010001
[5,8,4,3,6,7,1,2]=>0010011=>1100100
[5,8,6,4,7,2,1,3]=>1000111=>1110001
[5,3,8,6,2,7,4,1]=>0011111=>1111100
[4,7,5,8,6,3,2,1]=>1100111=>1110011
[4,8,6,7,5,3,2,1]=>1101011=>1101011
[6,3,8,7,2,4,1,5]=>0010111=>1110100
[5,3,8,7,2,6,4,1]=>0011111=>1111100
[5,3,8,6,7,2,4,1]=>0011011=>1101100
[5,3,7,8,6,2,4,1]=>0011101=>1011100
[5,7,6,4,8,2,1,3]=>1000111=>1110001
[5,8,4,6,7,2,1,3]=>1000011=>1100001
[6,4,2,8,1,7,3,5]=>0010111=>1110100
[6,5,2,4,3,7,8,1]=>0011101=>1011100
[5,4,6,2,8,7,1,3]=>0001111=>1111000
[5,6,3,8,7,2,4,1]=>0010111=>1110100
[6,7,4,3,1,8,2,5]=>0110011=>1100110
[5,7,4,3,6,8,1,2]=>0010011=>1100100
[5,7,3,8,6,2,4,1]=>0010111=>1110100
[4,5,8,6,7,3,2,1]=>1100011=>1100011
[4,6,8,5,7,3,2,1]=>1100011=>1100011
[5,6,8,3,7,2,4,1]=>0010011=>1100100
[5,4,6,8,2,7,1,3]=>0001011=>1101000
[3,6,7,8,2,5,1,4]=>0001001=>1001000
[5,7,8,2,6,4,1,3]=>0010101=>1010100
[3,6,8,5,7,1,4,2]=>0010011=>1100100
[1,7,4,8,6,2,3,5]=>0000111=>1110000
[3,6,2,5,7,8,1,4]=>0000101=>1010000
[5,2,7,4,6,8,1,3]=>0001011=>1101000
[7,2,4,5,8,6,1,3]=>0000111=>1110000
[5,3,6,7,1,8,4,2]=>0011011=>1101100
[4,2,5,6,7,1,8,3]=>0010011=>1100100
[8,2,3,7,5,1,6,4]=>0001111=>1111000
[7,2,6,3,5,1,8,4]=>0001111=>1111000
[8,1,3,6,7,2,4,5]=>0000011=>1100000
[8,1,4,2,5,6,3,7]=>0010101=>1010100
[8,1,4,2,7,5,3,6]=>0011011=>1101100
[6,1,3,8,2,7,4,5]=>0000111=>1110000
[3,6,2,4,1,7,8,5]=>0010101=>1010100
[6,2,7,3,1,5,8,4]=>0100111=>1110010
[6,3,4,1,8,5,7,2]=>0010111=>1110100
[7,3,4,1,5,8,6,2]=>0010111=>1110100
[1,7,5,2,8,6,3,4]=>0001111=>1111000
[3,7,4,1,8,5,6,2]=>0010111=>1110100
[5,6,3,1,7,8,4,2]=>0110101=>1010110
[3,6,4,8,1,5,7,2]=>0000111=>1110000
[1,5,8,4,2,6,3,7]=>0010101=>1010100
[3,5,7,4,1,6,8,2]=>0010011=>1100100
[3,5,7,1,2,6,4,8]=>0000110=>0110000
[4,5,1,8,2,3,7,6]=>0001011=>1101000
[4,7,1,8,2,6,3,5]=>0000111=>1110000
[6,3,1,8,5,2,4,7]=>0101101=>1011010
[3,5,2,1,8,4,6,7]=>1001001=>1001001
[7,5,1,2,3,8,6,4]=>0001111=>1111000
[6,4,1,2,7,3,8,5]=>0010111=>1110100
[5,2,6,1,3,4,8,7]=>0001101=>1011000
[7,8,4,5,1,3,2,6]=>0101001=>1001010
[6,7,1,3,2,5,4,8]=>0101010=>0101010
[6,7,1,4,3,5,2,8]=>0011010=>0101100
[7,8,2,3,1,5,4,6]=>0101001=>1001010
[7,8,2,4,3,5,1,6]=>0011001=>1001100
[7,8,2,4,1,5,3,6]=>0011001=>1001100
[1,4,2,6,5,7,3,8]=>0010110=>0110100
[5,6,1,4,2,7,3,8]=>0010110=>0110100
[6,7,2,4,1,5,3,8]=>0011010=>0101100
[6,7,2,4,3,5,1,8]=>0011010=>0101100
[6,7,2,3,1,5,4,8]=>0101010=>0101010
[6,7,3,5,4,8,1,2]=>0001011=>1101000
[2,4,1,6,5,7,3,8]=>0010110=>0110100
[1,5,2,6,4,7,3,8]=>0001110=>0111000
[2,5,1,6,4,7,3,8]=>0001110=>0111000
[3,6,5,7,4,8,1,2]=>0000111=>1110000
[5,6,2,4,3,7,1,8]=>0010110=>0110100
[4,5,2,6,1,7,3,8]=>0001110=>0111000
[4,5,1,6,3,7,2,8]=>0001110=>0111000
[4,5,3,6,1,7,2,8]=>0001110=>0111000
[5,6,3,4,1,7,2,8]=>0010110=>0110100
[5,6,1,4,3,7,2,8]=>0010110=>0110100
[5,6,1,3,2,7,4,8]=>0100110=>0110010
[5,6,4,7,1,3,2,8]=>0100110=>0110010
[6,7,4,5,1,3,2,8]=>0101010=>0101010
[6,7,5,8,1,3,2,4]=>0100011=>1100010
[4,5,1,3,2,7,6,8]=>0101010=>0101010
[4,6,5,7,1,3,2,8]=>0100110=>0110010
[4,6,1,3,2,7,5,8]=>0100110=>0110010
[1,4,3,6,2,7,5,8]=>0010110=>0110100
[3,4,1,6,5,7,2,8]=>0010110=>0110100
[4,5,2,3,1,7,6,8]=>0101010=>0101010
[4,5,3,7,6,8,1,2]=>0001011=>1101000
[4,6,5,7,3,8,1,2]=>0000111=>1110000
[4,6,5,7,2,3,1,8]=>0100110=>0110010
[3,5,4,6,1,7,2,8]=>0001110=>0111000
[3,5,1,6,4,7,2,8]=>0001110=>0111000
[1,5,3,6,4,7,2,8]=>0001110=>0111000
[1,5,3,6,2,7,4,8]=>0001110=>0111000
[3,5,2,6,1,7,4,8]=>0001110=>0111000
[3,5,2,6,4,7,1,8]=>0001110=>0111000
[3,4,2,6,1,7,5,8]=>0010110=>0110100
[4,6,2,3,1,7,5,8]=>0100110=>0110010
[2,4,3,6,1,7,5,8]=>0010110=>0110100
[2,5,3,6,4,7,1,8]=>0001110=>0111000
[2,5,3,6,1,7,4,8]=>0001110=>0111000
[4,6,2,7,3,5,8,1]=>0000111=>1110000
[3,6,2,7,5,4,8,1]=>0001111=>1111000
[4,6,1,7,3,8,2,5]=>0000111=>1110000
[2,4,7,1,3,8,6,5]=>0000111=>1110000
[5,2,6,7,4,3,8,1]=>0011011=>1101100
[3,5,2,7,6,4,8,1]=>0001111=>1111000
[1,5,7,4,3,8,2,6]=>0010011=>1100100
[2,5,7,3,1,8,6,4]=>0100111=>1110010
[1,5,7,2,8,3,6,4]=>0000111=>1110000
[2,5,7,3,1,8,4,6]=>0100011=>1100010
[1,5,7,3,4,8,2,6]=>0000011=>1100000
[5,2,6,7,1,8,4,3]=>0011011=>1101100
[1,3,7,2,8,5,6,4]=>0000111=>1110000
[2,3,1,5,8,4,7,6]=>0100011=>1100010
[2,1,5,6,8,4,3,7]=>1010001=>1000101
[2,3,1,5,8,6,4,7]=>0100101=>1010010
[2,4,7,3,1,8,5,6]=>0100011=>1100010
[1,3,7,2,8,5,4,6]=>0001011=>1101000
[2,3,1,6,8,5,4,7]=>0101001=>1001010
[4,6,2,7,1,8,3,5]=>0000111=>1110000
[1,5,4,3,6,8,2,7]=>0011001=>1001100
[1,6,4,5,7,8,3,2]=>0100101=>1010010
[2,5,1,7,8,6,3,4]=>0001101=>1011000
[1,3,6,2,8,7,4,5]=>0000111=>1110000
[2,1,5,6,8,4,7,3]=>1000011=>1100001
[2,4,1,7,8,5,6,3]=>0010101=>1010100
[1,3,6,2,8,4,7,5]=>0000111=>1110000
[2,1,5,6,8,7,3,4]=>1000011=>1100001
[3,6,5,2,7,8,4,1]=>0011101=>1011100
[6,2,4,7,5,8,3,1]=>0100111=>1110010
[1,5,7,8,4,2,6,3]=>0010101=>1010100
[3,7,4,1,8,6,2,5]=>0010111=>1110100
[3,4,6,8,5,7,2,1]=>1000011=>1100001
[4,2,5,7,3,1,8,6]=>0110011=>1100110
[4,5,6,2,8,7,3,1]=>0100111=>1110010
[2,5,6,8,1,7,4,3]=>0010011=>1100100
[4,5,6,1,8,7,3,2]=>0100111=>1110010
[4,5,6,3,1,8,7,2]=>0100111=>1110010
[4,3,6,2,1,7,5,8]=>1010110=>0110101
[4,6,3,2,1,7,5,8]=>1100110=>0110011
[4,6,3,1,7,5,2,8]=>0101110=>0111010
[4,5,3,7,6,1,8,2]=>0001111=>1111000
[4,5,1,7,3,8,6,2]=>0001111=>1111000
[2,5,7,1,4,3,8,6]=>0010011=>1100100
[4,3,5,7,6,1,8,2]=>0010111=>1110100
[4,3,6,1,7,5,2,8]=>0011110=>0111100
[4,3,2,6,1,7,5,8]=>0110110=>0110110
[5,3,2,1,6,4,7,8]=>1101100=>0011011
[5,3,1,6,2,7,4,8]=>0101110=>0111010
[5,1,6,3,2,7,4,8]=>0101110=>0111010
[2,6,1,4,7,5,3,8]=>0001110=>0111000
[3,6,1,7,4,2,5,8]=>0010110=>0110100
[4,6,1,7,5,3,2,8]=>0101110=>0111010
[5,1,6,3,7,4,2,8]=>0011110=>0111100
[5,3,6,4,2,1,7,8]=>1011100=>0011101
[5,3,2,6,4,1,7,8]=>0111100=>0011110
[5,2,1,6,3,7,4,8]=>1001110=>0111001
[5,2,6,3,1,7,4,8]=>0101110=>0111010
[4,2,6,3,1,7,8,5]=>0110101=>1010110
[3,6,2,1,7,4,5,8]=>1000110=>0110001
[3,6,2,7,4,1,5,8]=>0010110=>0110100
[3,5,7,2,8,6,4,1]=>0010111=>1110100
[2,4,7,1,3,6,5,8]=>0000110=>0110000
[2,6,1,3,7,5,4,8]=>0001110=>0111000
[3,6,1,7,5,2,4,8]=>0001110=>0111000
[5,1,6,2,7,4,3,8]=>0011110=>0111100
[5,2,6,4,3,1,7,8]=>0111100=>0011110
[5,2,1,6,4,3,7,8]=>1011100=>0011101
[5,4,2,1,6,3,7,8]=>1011100=>0011101
[5,4,2,6,3,1,7,8]=>0111100=>0011110
[5,4,1,6,2,7,3,8]=>0011110=>0111100
[5,1,6,4,2,7,3,8]=>0011110=>0111100
[3,6,1,7,5,4,8,2]=>0001111=>1111000
[2,6,1,5,4,3,7,8]=>0011100=>0011100
[3,1,6,2,5,4,7,8]=>0101100=>0011010
[5,1,6,4,3,2,7,8]=>0111100=>0011110
[5,4,1,6,3,2,7,8]=>0111100=>0011110
[5,4,3,1,6,2,7,8]=>0111100=>0011110
[8,2,1,7,6,5,4,3,9]=>10111110=>01111101
[7,3,1,6,5,4,8,2]=>0101111=>1111010
[7,2,8,1,5,4,3,6]=>0011011=>1101100
[4,2,7,6,5,8,1,3]=>0010111=>1110100
[3,8,2,6,5,4,1,7]=>0011101=>1011100
[3,2,8,7,6,5,4,1,9]=>01111110=>01111110
[10,1,11,9,8,7,6,5,4,3,2]=>0111111111=>1111111110
[9,2,1,8,7,6,5,4,3,10]=>101111110=>011111101
[8,3,1,7,6,5,4,9,2]=>01011111=>11111010
[8,2,9,1,6,5,4,3,7]=>00111011=>11011100
[7,3,2,1,5,4,6,8]=>1101010=>0101011
[7,2,8,6,1,4,3,5]=>0010111=>1110100
[5,2,7,6,8,4,1,3]=>0011011=>1101100
[4,2,8,7,6,5,9,1,3]=>00101111=>11110100
[3,8,7,2,5,4,1,6]=>0011011=>1101100
[3,9,2,7,6,5,4,1,8]=>00111101=>10111100
[3,2,9,8,7,6,5,4,1,10]=>011111110=>011111110
[2,11,10,9,8,7,6,5,4,1,3]=>0011111111=>1111111100
[11,1,12,10,9,8,7,6,5,4,3,2]=>01111111111=>11111111110
[10,2,1,9,8,7,6,5,4,3,11]=>1011111110=>0111111101
[9,3,1,8,7,6,5,4,10,2]=>010111111=>111111010
[9,2,10,1,7,6,5,4,3,8]=>001111011=>110111100
[8,4,1,7,6,5,9,3,2]=>01101111=>11110110
[8,3,2,1,6,5,4,7,9]=>11011010=>01011011
[8,2,9,7,1,5,4,3,6]=>00110111=>11101100
[7,5,1,6,8,4,3,2]=>0111011=>1101110
[7,4,2,1,5,6,3,8]=>1010110=>0110101
[7,2,8,6,5,1,3,4]=>0001111=>1111000
[5,3,2,6,7,4,1,8]=>0111010=>0101110
[5,2,8,7,6,9,4,1,3]=>00110111=>11101100
[4,3,7,2,5,6,1,8]=>0010110=>0110100
[4,3,2,7,6,5,8,1,9]=>01101110=>01110110
[4,2,9,8,7,6,5,10,1,3]=>001011111=>111110100
[3,9,8,2,6,5,4,1,7]=>00111011=>11011100
[3,10,2,8,7,6,5,4,1,9]=>001111101=>101111100
[3,2,10,9,8,7,6,5,4,1,11]=>0111111110=>0111111110
[2,12,11,10,9,8,7,6,5,4,1,3]=>00111111111=>11111111100
[6,7,1,4,3,2,5,8]=>0110010=>0100110
[3,4,2,6,7,1,5,8]=>0010010=>0100100
[3,7,1,6,5,2,4,8]=>0001110=>0111000
[3,5,6,2,4,7,1,8]=>0000110=>0110000
[3,5,8,7,2,4,6,1]=>0000111=>1110000
[1,7,8,2,5,4,3,6]=>0011001=>1001100
[8,7,2,5,4,3,6,1]=>0011111=>1111100
[2,5,6,4,7,1,3,8]=>0000110=>0110000
[4,7,1,6,3,5,2,8]=>0001110=>0111000
[4,5,3,8,7,2,6,1]=>0001111=>1111000
[1,4,5,3,7,8,2,6]=>0001001=>1001000
[1,4,8,2,7,6,3,5]=>0000111=>1110000
[4,7,3,5,1,8,6,2]=>0001111=>1111000
[8,7,3,6,1,5,4,2]=>0011111=>1111100
[2,5,8,7,4,6,1,3]=>0000111=>1110000
[5,4,2,1,7,8,3,6]=>1011001=>1001101
[4,7,8,3,5,2,1,6]=>1001001=>1001001
[4,7,6,2,1,8,3,5]=>1000111=>1110001
[1,4,6,7,3,5,8,2]=>0000011=>1100000
[8,3,6,2,1,7,5,4]=>1001111=>1111001
[8,3,7,6,4,2,1,5]=>1010111=>1110101
[2,3,1,8,4,7,6,5]=>0100111=>1110010
[2,7,4,8,6,5,1,3]=>0001111=>1111000
[8,6,5,1,4,7,3,2]=>0101111=>1111010
[8,5,4,1,7,3,6,2]=>0011111=>1111100
[6,3,7,2,8,5,4,1]=>0011111=>1111100
[1,6,3,8,2,7,5,4]=>0001111=>1111000
[1,7,5,3,8,2,6,4]=>0001111=>1111000
[6,2,7,4,1,8,5,3]=>0011111=>1111100
[8,6,3,2,7,5,1,4]=>0101111=>1111010
[2,7,5,1,3,8,6,4]=>0001111=>1111000
[1,7,6,4,3,8,2,5]=>0010111=>1110100
[3,7,2,4,8,6,5,1]=>0001111=>1111000
[3,4,2,8,7,6,1,5]=>0010111=>1110100
[5,1,4,3,2,7,8,6]=>0111001=>1001110
[3,7,8,5,2,4,1,6]=>0011001=>1001100
[3,7,6,2,4,1,8,5]=>0010111=>1110100
[1,6,8,2,5,7,4,3]=>0010011=>1100100
[6,7,2,5,8,4,3,1]=>0110011=>1100110
[5,2,7,8,4,3,1,6]=>0111001=>1001110
[5,3,1,7,8,4,2,6]=>0111001=>1001110
[2,7,6,4,1,3,8,5]=>0010111=>1110100
[4,1,7,6,3,2,8,5]=>0110111=>1110110
[8,4,2,7,6,3,1,5]=>0110111=>1110110
[6,3,1,7,5,2,8,4]=>0101111=>1111010
[6,2,7,5,3,1,8,4]=>0101111=>1111010
[1,5,8,2,7,4,6,3]=>0000111=>1110000
[5,7,2,8,4,6,3,1]=>0100111=>1110010
[5,7,3,1,8,4,6,2]=>0100111=>1110010
[8,4,7,3,1,6,5,2]=>0101111=>1111010
[2,6,8,5,7,4,1,3]=>0010011=>1100100
[6,5,2,1,7,4,8,3]=>1001111=>1111001
[5,7,4,6,2,1,8,3]=>1000111=>1110001
[5,6,4,8,3,7,2,1]=>1000111=>1110001
[6,7,1,8,3,4,2,5]=>0010011=>1100100
[7,8,3,5,1,4,2,6]=>0011001=>1001100
[5,6,2,7,1,8,3,4]=>0000111=>1110000
[6,7,2,4,3,8,1,5]=>0010011=>1100100
[2,4,3,8,6,7,1,5]=>0010011=>1100100
[1,8,2,7,4,5,3,6]=>0001011=>1101000
[2,5,4,8,3,6,1,7]=>0001101=>1011000
[2,3,1,8,5,6,4,7]=>0100101=>1010010
[3,8,5,6,4,7,1,2]=>0000111=>1110000
[5,7,3,6,4,8,1,2]=>0000111=>1110000
[5,7,2,3,1,6,4,8]=>0100110=>0110010
[5,7,2,4,3,6,1,8]=>0010110=>0110100
[4,6,2,7,1,5,3,8]=>0001110=>0111000
[4,7,1,6,2,5,3,8]=>0001110=>0111000
[4,7,1,5,3,6,2,8]=>0001110=>0111000
[4,6,3,5,1,7,2,8]=>0001110=>0111000
[6,7,3,5,1,4,2,8]=>0011010=>0101100
[5,6,3,7,1,4,2,8]=>0010110=>0110100
[5,7,1,6,3,4,2,8]=>0010110=>0110100
[1,8,5,6,3,4,2,7]=>0010101=>1010100
[1,8,5,6,4,7,2,3]=>0000111=>1110000
[5,7,1,6,4,8,2,3]=>0000111=>1110000
[4,6,5,8,1,7,2,3]=>0000111=>1110000
[3,7,1,4,2,8,5,6]=>0010011=>1100100
[3,5,1,4,2,8,6,7]=>0011001=>1001100
[4,6,5,8,3,7,1,2]=>0000111=>1110000
[4,6,5,8,2,3,1,7]=>0100101=>1010010
[3,4,2,6,5,8,1,7]=>0010101=>1010100
[3,5,4,6,2,8,1,7]=>0001101=>1011000
[1,8,3,5,4,7,2,6]=>0001011=>1101000
[3,4,2,7,1,8,5,6]=>0010011=>1100100
[4,7,2,3,1,8,5,6]=>0100011=>1100010
[2,4,3,8,1,7,5,6]=>0010011=>1100100
[2,5,3,8,4,7,1,6]=>0001011=>1101000
[2,6,3,8,1,7,4,5]=>0000111=>1110000
[2,7,1,8,3,6,4,5]=>0000111=>1110000
[1,2,8,7,4,6,3,5]=>0000111=>1110000
[3,7,4,8,6,1,5,2]=>0001111=>1111000
[4,5,1,8,7,6,2,3]=>0001111=>1111000
[1,5,2,8,7,6,3,4]=>0001111=>1111000
[5,1,2,8,7,6,3,4]=>0001111=>1111000
[4,1,5,8,7,6,2,3]=>0010111=>1110100
[2,3,6,8,7,4,5,1]=>0001011=>1101000
[2,3,7,8,6,4,5,1]=>0001101=>1011000
[4,5,7,8,2,6,3,1]=>0100101=>1010010
[4,5,6,8,2,7,3,1]=>0100011=>1100010
[5,2,6,8,3,7,4,1]=>0011011=>1101100
[3,1,6,8,7,4,5,2]=>0101011=>1101010
[6,1,4,8,7,2,5,3]=>0001111=>1111000
[6,1,8,4,7,3,5,2]=>0001111=>1111000
[5,8,3,4,7,1,6,2]=>0000111=>1110000
[6,8,3,5,7,1,4,2]=>0010011=>1100100
[3,1,7,8,6,4,5,2]=>0101101=>1011010
[5,2,7,8,3,6,4,1]=>0011101=>1011100
[4,6,7,8,2,5,3,1]=>0101001=>1001010
[7,4,5,2,8,6,3,1]=>0101111=>1111010
[7,5,8,4,2,6,3,1]=>0110111=>1110110
[6,8,4,5,2,7,3,1]=>0101011=>1101010
[6,8,2,5,3,7,4,1]=>0011011=>1101100
[6,3,8,4,2,7,5,1]=>0011111=>1111100
[7,2,5,3,8,6,4,1]=>0011111=>1111100
[3,4,7,5,8,6,2,1]=>1000111=>1110001
[3,6,7,4,8,5,2,1]=>1001011=>1101001
[6,7,4,2,8,5,3,1]=>0111011=>1101110
[4,7,5,2,8,6,3,1]=>0101111=>1111010
[2,7,5,3,8,6,4,1]=>0011111=>1111100
[5,6,2,8,3,7,4,1]=>0010111=>1110100
[5,7,8,3,2,6,4,1]=>0110101=>1010110
[5,6,8,3,2,7,4,1]=>0110011=>1100110
[3,6,8,4,2,7,5,1]=>0011011=>1101100
[1,5,8,2,7,3,6,4]=>0000111=>1110000
[5,8,4,7,2,3,6,1]=>0000111=>1110000
[5,6,8,1,3,7,4,2]=>0010011=>1100100
[6,7,4,8,1,5,3,2]=>0101011=>1101010
[5,7,2,8,3,6,4,1]=>0010111=>1110100
[1,7,4,8,6,2,5,3]=>0001111=>1111000
[7,4,2,8,6,1,5,3]=>0011111=>1111100
[6,8,5,3,7,2,4,1]=>0011011=>1101100
[6,8,5,2,3,7,4,1]=>0011011=>1101100
[7,5,3,8,2,6,4,1]=>0011111=>1111100
[7,5,2,3,8,6,4,1]=>0011111=>1111100
[3,7,4,5,8,6,2,1]=>1000111=>1110001
[6,7,3,4,8,5,2,1]=>1001011=>1101001
[3,6,4,7,8,5,2,1]=>1001101=>1011001
[6,4,2,7,8,5,3,1]=>0111101=>1011110
[7,4,2,5,8,6,3,1]=>0110111=>1110110
[6,1,8,3,4,7,5,2]=>0001111=>1111000
[6,8,4,2,5,7,3,1]=>0110011=>1100110
[7,5,8,3,4,6,2,1]=>1000111=>1110001
[7,4,5,8,1,6,3,2]=>0100111=>1110010
[6,3,4,7,8,5,2,1]=>1001101=>1011001
[7,8,2,3,4,5,6,9,1]=>00000011=>11000000
[6,1,7,3,4,5,8,2]=>0000111=>1110000
[5,7,2,3,4,1,8,6]=>0010011=>1100100
[2,7,1,8,4,5,6,3]=>0000111=>1110000
[2,6,8,3,4,5,1,7]=>0001001=>1001000
[2,8,9,3,4,5,6,7,1]=>00000101=>10100000
[8,9,2,3,4,5,6,7,10,1]=>000000011=>110000000
[7,1,8,3,4,5,6,9,2]=>00000111=>11100000
[6,8,2,3,4,5,1,9,7]=>00010011=>11001000
[6,1,2,7,4,5,8,3]=>0000111=>1110000
[4,7,2,3,1,5,8,6]=>0100011=>1100010
[2,7,1,3,8,5,6,4]=>0000111=>1110000
[2,6,7,8,4,5,3,1]=>0101001=>1001010
[2,8,1,9,4,5,6,7,3]=>00000111=>11100000
[2,5,8,3,4,1,6,7]=>0010001=>1000100
[2,7,9,3,4,5,6,1,8]=>00001001=>10010000
[2,9,10,3,4,5,6,7,8,1]=>000000101=>101000000
[11,1,2,3,4,5,6,7,8,9,12,10]=>00000000011=>11000000000
[9,10,2,3,4,5,6,7,8,11,1]=>0000000011=>1100000000
[8,1,9,3,4,5,6,7,10,2]=>000000111=>111000000
[7,9,2,3,4,5,6,1,10,8]=>000010011=>110010000
[7,1,2,8,4,5,6,9,3]=>00000111=>11100000
[6,7,8,3,4,5,2,9,1]=>00010011=>11001000
[5,8,2,3,4,1,6,9,7]=>00100011=>11000100
[5,6,2,7,4,3,8,1]=>0010111=>1110100
[4,6,7,3,2,5,8,1]=>0100011=>1100010
[2,6,7,3,8,5,4,1]=>0011011=>1101100
[2,8,1,3,9,5,6,7,4]=>00000111=>11100000
[2,6,1,8,4,5,3,7]=>0001101=>1011000
[2,5,7,8,4,3,6,1]=>0010101=>1010100
[2,7,8,9,4,5,6,3,1]=>01001001=>10010010
[2,9,1,10,4,5,6,7,8,3]=>000000111=>111000000
[2,6,9,3,4,5,1,7,8]=>00010001=>10001000
[2,8,10,3,4,5,6,7,1,9]=>000001001=>100100000
[2,10,11,3,4,5,6,7,8,9,1]=>0000000101=>1010000000
[2,12,1,3,4,5,6,7,8,9,10,11]=>00000000001=>10000000000
[3,6,8,4,5,7,1,2]=>0000011=>1100000
[1,6,8,4,7,2,3,5]=>0000011=>1100000
[1,4,5,7,8,2,6,3]=>0000101=>1010000
[3,4,5,7,8,6,1,2]=>0000101=>1010000
[3,4,5,7,6,8,1,2]=>0000011=>1100000
[3,6,7,4,8,5,1,2]=>0001011=>1101000
[3,4,5,6,8,7,1,2]=>0000011=>1100000
[1,4,5,8,7,2,3,6]=>0000011=>1100000
[1,2,5,8,3,6,4,7]=>0000101=>1010000
[1,4,5,8,6,2,3,7]=>0000101=>1010000
[7,8,1,4,6,2,3,5]=>0000101=>1010000
[1,6,7,4,8,2,5,3]=>0001011=>1101000
[1,4,5,6,8,2,7,3]=>0000011=>1100000
[1,4,5,8,6,2,7,3]=>0000111=>1110000
[1,2,5,8,3,4,7,6]=>0000011=>1100000
[1,6,7,2,3,5,8,4]=>0000011=>1100000
[7,8,1,2,3,5,4,6]=>0001001=>1001000
[1,6,7,2,3,5,4,8]=>0001010=>0101000
[1,4,5,7,6,2,3,8]=>0000110=>0110000
[1,2,5,7,3,6,4,8]=>0000110=>0110000
[1,2,5,7,3,6,8,4]=>0000011=>1100000
[1,6,8,2,3,5,7,4]=>0000011=>1100000
[1,6,8,4,5,2,3,7]=>0001001=>1001000
[1,6,8,4,5,2,7,3]=>0001011=>1101000
[1,6,8,2,3,4,7,5]=>0000011=>1100000
[1,6,8,2,3,7,4,5]=>0000011=>1100000
[1,4,5,7,6,2,8,3]=>0000111=>1110000
[7,8,1,4,5,2,6,3]=>0001101=>1011000
[7,8,1,2,3,4,6,5]=>0000101=>1010000
[7,8,1,2,3,6,4,5]=>0000101=>1010000
[1,6,7,2,3,8,5,4]=>0001011=>1101000
[1,2,5,6,3,8,7,4]=>0000111=>1110000
[4,2,1,6,5,3,8,7]=>1011101=>1011101
[8,2,4,3,1,6,5,7]=>0110101=>1010110
[6,2,4,3,1,8,7,5]=>0110111=>1110110
[4,2,6,3,5,1,8,7]=>0011101=>1011100
[4,6,2,1,5,8,7,3]=>1000111=>1110001
[4,6,5,2,1,8,7,3]=>1001111=>1111001
[2,1,6,4,3,8,7,5]=>1010111=>1110101
[4,8,2,1,6,7,3,5]=>1000011=>1100001
[6,8,2,1,4,3,7,5]=>1010011=>1100101
[8,6,2,4,3,1,5,7]=>0110101=>1010110
[6,8,2,4,3,1,7,5]=>0110011=>1100110
[6,8,7,2,4,3,1,5]=>0110011=>1100110
[2,1,8,4,6,5,3,7]=>1001101=>1011001
[2,1,6,4,8,5,7,3]=>1000111=>1110001
[4,6,5,2,8,3,7,1]=>0001111=>1111000
[2,6,4,5,8,3,7,1]=>0000111=>1110000
[6,4,2,8,3,5,7,1]=>0010111=>1110100
[8,4,2,6,3,5,1,7]=>0011101=>1011100
[6,2,4,8,5,3,7,1]=>0001111=>1111000
[4,2,6,3,5,8,7,1]=>0010111=>1110100
[4,2,6,3,8,7,5,1]=>0011111=>1111100
[6,2,4,3,8,5,7,1]=>0010111=>1110100
[8,2,4,3,6,5,1,7]=>0011101=>1011100
[8,2,1,4,6,5,3,7]=>1001101=>1011001
[6,2,1,4,8,5,7,3]=>1000111=>1110001
[6,2,1,8,7,4,3,5]=>1010111=>1110101
[6,2,1,8,4,3,7,5]=>1010111=>1110101
[8,4,6,5,2,1,3,7]=>1001101=>1011001
[6,4,8,5,2,1,7,3]=>1001111=>1111001
[6,4,8,5,7,2,1,3]=>1000111=>1110001
[4,6,8,7,5,2,1,3]=>1001011=>1101001
[2,1,4,8,6,7,3,5]=>1000011=>1100001
[2,6,8,7,4,5,1,3]=>0001011=>1101000
[2,4,8,6,7,5,1,3]=>0001011=>1101000
[4,2,8,6,5,7,1,3]=>0010111=>1110100
[8,2,6,4,5,1,3,7]=>0001101=>1011000
[8,4,6,2,1,5,3,7]=>1001101=>1011001
[4,6,8,7,2,1,5,3]=>1001011=>1101001
[4,6,5,8,2,1,7,3]=>1000111=>1110001
[2,1,6,8,4,3,7,5]=>1010011=>1100101
[6,8,7,4,2,1,3,5]=>1010011=>1100101
[2,8,6,4,7,1,3,5]=>0000111=>1110000
[4,8,6,2,1,7,3,5]=>1000111=>1110001
[2,8,5,3,1,4,6,7]=>0101001=>1001010
[2,7,4,8,3,5,1,6]=>0001011=>1101000
[2,7,4,8,3,5,6,1]=>0000111=>1110000
[7,2,8,4,3,5,1,6]=>0011011=>1101100
[8,4,2,1,5,3,6,7]=>1011001=>1001101
[8,5,1,4,2,3,6,7]=>0011001=>1001100
[8,4,1,5,3,2,6,7]=>0111001=>1001110
[6,7,3,8,4,2,5,1]=>0011011=>1101100
[6,7,3,8,4,2,1,5]=>1010011=>1100101
[7,1,8,4,3,5,2,6]=>0011011=>1101100
[1,7,8,4,3,5,2,6]=>0011001=>1001100
[7,1,4,8,3,5,2,6]=>0001011=>1101000
[7,4,8,1,5,6,2,3]=>0000111=>1110000
[7,1,8,4,3,5,6,2]=>0010111=>1110100
[6,7,3,1,8,4,5,2]=>0101011=>1101010
[6,7,3,8,4,5,2,1]=>1001011=>1101001
[6,7,1,4,8,3,5,2]=>0001011=>1101000
[6,7,4,1,3,8,2,5]=>0010011=>1100100
[1,6,7,8,4,3,2,5]=>0110001=>1000110
[7,2,1,8,4,5,3,6]=>1001011=>1101001
[6,2,7,1,8,4,3,5]=>0010111=>1110100
[6,2,7,8,4,3,1,5]=>0110101=>1010110
[6,2,7,8,4,3,5,1]=>0011101=>1011100
[2,6,7,4,8,3,5,1]=>0001011=>1101000
[2,6,7,4,8,3,1,5]=>0100011=>1100010
[7,8,1,3,6,2,4,5]=>0000101=>1010000
[1,2,7,8,6,3,4,5]=>0000101=>1010000
[2,6,7,1,8,5,3,4]=>0001011=>1101000
[2,6,7,8,5,3,1,4]=>0101001=>1001010
[2,6,7,8,5,3,4,1]=>0011001=>1001100
[6,2,7,8,4,5,3,1]=>0101101=>1011010
[7,2,1,8,4,5,6,3]=>1000111=>1110001
[1,7,2,8,4,5,6,3]=>0000111=>1110000
[3,7,8,1,5,6,2,4]=>0000101=>1010000
[6,3,7,8,1,5,2,4]=>0001101=>1011000
[6,7,1,2,8,5,3,4]=>0001011=>1101000
[1,6,7,8,4,2,5,3]=>0011001=>1001100
[3,1,2,7,6,5,8,4]=>0100111=>1110010
[6,1,2,4,7,3,8,5]=>0000111=>1110000
[1,7,5,3,6,4,8,2]=>0001111=>1111000
[5,1,2,6,7,4,8,3]=>0001011=>1101000
[4,1,5,7,3,2,6,8]=>0110010=>0100110
[4,6,1,7,3,2,5,8]=>0100110=>0110010
[4,6,1,8,3,2,5,7]=>0100101=>1010010
[4,7,1,8,3,5,2,6]=>0001011=>1101000
[4,1,7,8,6,2,3,5]=>0010101=>1010100
[1,6,5,7,8,3,4,2]=>0010101=>1010100
[1,6,5,8,7,3,4,2]=>0010111=>1110100
[4,1,8,7,6,2,3,5]=>0010111=>1110100
[4,8,1,7,3,5,2,6]=>0001011=>1101000
[4,8,1,6,3,2,5,7]=>0100101=>1010010
[4,7,1,6,3,2,5,8]=>0100110=>0110010
[6,1,2,3,7,5,4,8]=>0001110=>0111000
[6,8,1,5,3,7,2,4]=>0001011=>1101000
[8,7,5,2,4,1,6,3]=>0011111=>1111100
[1,5,7,3,4,8,6,2]=>0000111=>1110000
[1,5,8,3,4,7,6,2]=>0000111=>1110000
[7,8,5,2,4,1,6,3]=>0011101=>1011100
[7,1,2,3,5,6,4,8]=>0000110=>0110000
[8,1,2,3,5,6,4,7]=>0000101=>1010000
[8,1,2,3,5,4,7,6]=>0001011=>1101000
[7,1,8,4,6,3,2,5]=>0100111=>1110010
[6,8,2,4,3,1,5,7]=>0110001=>1000110
[6,7,2,4,3,1,5,8]=>0110010=>0100110
[3,8,1,2,4,5,7,6]=>0000011=>1100000
[3,7,1,8,6,4,2,5]=>0010111=>1110100
[1,6,4,3,7,5,8,2]=>0010111=>1110100
[3,1,2,6,7,5,8,4]=>0100011=>1100010
[3,8,1,7,6,4,2,5]=>0010111=>1110100
[7,6,2,4,3,1,5,8]=>0110110=>0110110
[8,7,2,4,3,5,1,6]=>0011011=>1101100
[8,1,7,4,6,3,2,5]=>0100111=>1110010
[8,1,7,6,5,3,2,4]=>0101111=>1111010
[1,5,7,3,4,6,8,2]=>0000011=>1100000
[8,7,2,5,3,6,1,4]=>0001111=>1111000
[7,1,2,3,5,4,8,6]=>0001011=>1101000
[6,1,2,3,5,8,4,7]=>0000101=>1010000
[6,1,2,3,5,7,4,8]=>0000110=>0110000
[5,1,2,3,7,6,4,8]=>0001110=>0111000
[5,1,2,3,8,6,4,7]=>0001101=>1011000
[1,5,6,3,4,7,8,2]=>0000101=>1010000
[8,6,5,2,4,7,1,3]=>0001111=>1111000
[7,6,2,5,3,1,8,4]=>0101111=>1111010
[7,4,5,2,3,8,6,1]=>0001111=>1111000
[8,2,3,7,4,5,1,6]=>0001011=>1101000
[8,4,7,3,2,5,1,6]=>0101011=>1101010
[5,4,6,3,1,2,8,7]=>0101101=>1011010
[4,6,2,3,1,5,8,7]=>0100101=>1010010
[7,2,3,4,5,8,6,1]=>0000111=>1110000
[8,2,3,4,5,7,1,6]=>0000011=>1100000
[7,3,4,6,8,5,1,2]=>0001011=>1101000
[4,7,3,2,8,6,1,5]=>0100111=>1110010
[3,7,4,5,1,8,6,2]=>0001111=>1111000
[3,8,2,6,7,4,5,1]=>0001011=>1101000
[4,8,1,5,6,7,3,2]=>0100011=>1100010
[5,8,2,4,6,7,1,3]=>0000011=>1100000
[6,8,1,3,4,2,7,5]=>0010011=>1100100
[5,8,2,4,3,1,7,6]=>0110011=>1100110
[2,1,7,6,8,5,3,4]=>1001011=>1101001
[3,7,6,1,8,5,2,4]=>0001111=>1111000
[4,7,2,3,8,5,1,6]=>0001011=>1101000
[7,1,3,6,4,8,5,2]=>0001111=>1111000
[7,6,1,4,8,5,2,3]=>0001111=>1111000
[6,2,3,7,8,5,4,1]=>0011101=>1011100
[6,2,3,8,4,5,1,7]=>0001101=>1011000
[7,2,3,6,8,4,1,5]=>0010011=>1100100
[8,2,3,5,7,1,4,6]=>0000011=>1100000
[6,4,8,3,5,1,7,2]=>0001111=>1111000
[5,4,8,3,6,7,1,2]=>0001011=>1101000
[3,5,1,8,4,6,7,2]=>0001011=>1101000
[3,6,1,8,4,5,2,7]=>0001101=>1011000
[4,6,8,3,5,2,7,1]=>0001011=>1101000
[5,7,8,3,2,4,1,6]=>0110001=>1000110
[4,8,2,3,5,6,1,7]=>0000101=>1010000
[6,8,2,3,1,4,5,7]=>0100001=>1000010
[5,2,7,4,8,3,1,6]=>0101011=>1101010
[3,7,8,2,1,4,6,5]=>1000101=>1010001
[3,7,5,2,8,4,1,6]=>0011011=>1101100
[6,3,2,4,1,8,7,5]=>0110111=>1110110
[7,2,3,4,8,5,1,6]=>0001011=>1101000
[5,7,3,1,4,2,6,8]=>0110010=>0100110
[3,7,4,1,8,2,5,6]=>0010011=>1100100
[6,3,7,4,8,1,2,5]=>0000111=>1110000
[8,3,7,4,2,6,1,5]=>0010111=>1110100
[3,7,4,1,5,6,2,8]=>0010110=>0110100
[1,8,3,2,4,5,7,6]=>0100011=>1100010
[8,4,1,6,3,7,5,2]=>0011111=>1111100
[8,7,4,2,1,6,3,5]=>1010111=>1110101
[8,3,5,2,7,4,1,6]=>0011011=>1101100
[1,5,3,8,7,6,4,2]=>0011111=>1111100
[7,2,4,8,1,3,6,5]=>0000111=>1110000
[1,2,8,7,5,6,3,4]=>0000111=>1110000
[3,1,8,6,7,5,2,4]=>0101011=>1101010
[1,4,8,6,5,7,2,3]=>0000111=>1110000
[1,6,5,4,8,2,3,7]=>0001101=>1011000
[5,1,6,8,3,4,2,7]=>0011001=>1001100
[6,2,5,1,7,4,3,8]=>0011110=>0111100
[5,2,1,8,7,4,3,6]=>1011011=>1101101
[5,2,6,3,8,1,4,7]=>0001101=>1011000
[5,2,8,3,4,6,1,7]=>0001101=>1011000
[6,2,8,4,3,1,7,5]=>0110111=>1110110
[7,2,8,1,3,6,5,4]=>0001111=>1111000
[7,3,8,1,4,6,2,5]=>0000111=>1110000
[1,7,8,5,4,6,3,2]=>0101101=>1011010
[1,5,8,4,6,3,7,2]=>0000111=>1110000
[5,3,8,4,1,2,7,6]=>0011011=>1101100
[5,8,4,3,6,2,1,7]=>1010101=>1010101
[1,8,3,6,5,2,7,4]=>0001111=>1111000
[1,8,2,4,7,6,5,3]=>0001111=>1111000
[3,8,1,4,6,7,5,2]=>0001011=>1101000
[3,8,2,5,1,7,6,4]=>0001111=>1111000
[4,3,8,2,5,1,6,7]=>0011001=>1001100
[8,2,4,3,5,1,7,6]=>0011011=>1101100
[8,2,1,4,6,5,7,3]=>1000111=>1110001
[8,1,3,4,5,7,6,2]=>0000111=>1110000
[6,1,5,2,4,7,8,3]=>0001101=>1011000
[4,1,8,5,2,7,6,3]=>0011111=>1111100
[4,8,5,1,3,6,2,7]=>0001101=>1011000
[3,6,1,5,7,2,8,4]=>0000111=>1110000
[6,3,1,2,8,5,7,4]=>0100111=>1110010
[4,1,8,2,3,7,5,6]=>0010011=>1100100
[5,3,8,7,2,1,4,6]=>1001011=>1101001
[6,7,3,5,1,4,8,2]=>0001011=>1101000
[6,4,7,5,8,2,3,1]=>0100111=>1110010
[5,7,8,4,2,6,3,1]=>0110101=>1010110
[5,4,7,6,2,8,3,1]=>0101111=>1111010
[5,7,4,1,6,8,3,2]=>0110011=>1100110
[6,8,4,5,7,1,3,2]=>0100011=>1100010
[5,8,4,6,1,7,3,2]=>0100111=>1110010
[5,6,1,4,7,8,3,2]=>0100101=>1010010
[5,6,7,2,4,8,3,1]=>0100011=>1100010
[5,6,3,7,4,8,2,1]=>1000111=>1110001
[5,3,6,7,4,8,2,1]=>1001011=>1101001
[5,3,2,8,6,7,4,1]=>0111011=>1101110
[5,4,8,2,6,7,3,1]=>0101011=>1101010
[5,4,8,6,2,7,3,1]=>0101111=>1111010
[6,4,8,5,7,2,3,1]=>0100111=>1110010
[7,4,8,5,6,2,1,3]=>1000111=>1110001
[4,6,8,5,7,2,3,1]=>0100011=>1100010
[5,6,8,2,4,7,3,1]=>0100011=>1100010
[5,6,3,8,4,7,2,1]=>1000111=>1110001
[4,6,3,5,8,7,2,1]=>1000111=>1110001
[4,6,3,2,8,7,5,1]=>0101111=>1111010
[5,6,3,8,2,7,4,1]=>0010111=>1110100
[3,6,5,8,7,2,4,1]=>0010111=>1110100
[5,3,6,8,2,7,4,1]=>0011011=>1101100
[4,3,7,2,8,6,5,1]=>0011111=>1111100
[5,4,7,2,6,8,3,1]=>0101011=>1101010
[5,3,2,7,6,8,4,1]=>0111011=>1101110
[6,7,3,8,5,2,4,1]=>0011011=>1101100
[6,3,2,7,5,4,8,1]=>0101111=>1111010
[6,4,7,2,5,3,8,1]=>0001111=>1111000
[6,2,7,5,1,4,8,3]=>0001111=>1111000
[2,7,8,5,3,6,1,4]=>0001101=>1011000
[6,3,7,8,4,2,5,1]=>0011101=>1011100
[3,5,7,8,4,6,2,1]=>1000101=>1010001
[5,3,7,8,4,6,2,1]=>1001101=>1011001
[5,7,8,2,4,6,3,1]=>0100101=>1010010
[2,5,8,4,3,7,6,1]=>0010111=>1110100
[2,6,8,4,7,3,5,1]=>0001011=>1101000
[3,7,4,8,6,2,1,5]=>1000111=>1110001
[3,6,4,8,7,2,5,1]=>0001111=>1111000
[3,5,4,8,2,7,6,1]=>0001111=>1111000
[4,3,7,5,8,6,2,1]=>1010111=>1110101
[4,5,7,3,8,6,2,1]=>1000111=>1110001
[3,5,6,8,4,7,2,1]=>1000011=>1100001
[6,3,1,8,7,5,4,2]=>0111111=>1111110
[5,4,8,1,7,6,3,2]=>0101111=>1111010
[5,8,4,1,7,6,3,2]=>0110111=>1110110
[7,5,4,1,8,6,3,2]=>0111111=>1111110
[8,5,4,1,7,6,3,2]=>0111111=>1111110
[1,8,2,5,6,3,4,7]=>0000101=>1010000
[7,2,8,4,5,1,3,6]=>0001011=>1101000
[1,3,7,5,6,2,4,8]=>0000110=>0110000
[1,6,7,4,3,5,2,8]=>0011010=>0101100
[1,8,5,2,3,7,4,6]=>0001011=>1101000
[1,8,2,5,3,6,7,4]=>0001011=>1101000
[2,6,8,4,3,5,7,1]=>0010011=>1100100
[7,5,8,3,2,1,6,4]=>1100111=>1110011
[7,2,8,4,1,5,6,3]=>0010111=>1110100
[7,5,8,1,2,6,3,4]=>0000111=>1110000
[1,6,7,4,3,2,8,5]=>0110011=>1100110
[1,5,2,6,4,7,8,3]=>0001101=>1011000
[1,5,4,6,2,3,7,8]=>0001100=>0011000
[6,2,5,7,1,4,8,3]=>0000111=>1110000
[6,5,4,3,8,1,7,2]=>0011111=>1111100
[7,3,6,8,5,2,4,1]=>0011011=>1101100
[2,7,8,3,6,5,1,4]=>0001101=>1011000
[2,7,8,5,4,6,3,1]=>0101101=>1011010
[2,6,5,8,3,4,1,7]=>0010101=>1010100
[2,6,5,7,3,4,1,8]=>0010110=>0110100
[6,2,5,7,4,1,3,8]=>0010110=>0110100
[6,2,5,8,4,1,3,7]=>0010101=>1010100
[2,7,8,4,6,1,3,5]=>0000101=>1010000
[6,1,2,8,3,7,4,5]=>0000111=>1110000
[6,1,2,8,5,4,7,3]=>0001111=>1111000
[6,2,5,7,8,1,3,4]=>0000101=>1010000
[1,5,4,2,6,7,3,8]=>0011010=>0101100
[2,6,5,7,3,8,1,4]=>0000111=>1110000
[1,6,2,7,5,8,4,3]=>0010111=>1110100
[1,3,2,7,8,5,6,4]=>0100101=>1010010
[1,6,2,4,8,7,3,5]=>0000111=>1110000
[6,5,2,1,8,7,3,4]=>1001111=>1111001
[2,6,5,3,7,8,4,1]=>0011101=>1011100
[6,2,5,3,8,4,7,1]=>0001111=>1111000
[6,5,2,3,8,7,1,4]=>0001111=>1111000
[5,4,1,2,3,8,6,7]=>0011001=>1001100
[5,1,4,2,3,7,8,6]=>0011001=>1001100
[1,5,4,2,6,3,8,7]=>0011101=>1011100
[5,1,6,3,8,2,7,4]=>0001111=>1111000
[9,8,7,6,5,4,3,1,2,10]=>011111110=>011111110
[8,7,6,5,4,2,1,3,9]=>10111110=>01111101
[1,9,8,7,6,5,3,2,4]=>01011111=>11111010
[1,8,7,6,2,5,4,3]=>0011111=>1111100
[1,9,8,7,6,5,2,4,3]=>00111111=>11111100
[1,10,9,8,7,6,5,4,2,3]=>001111111=>111111100
[2,1,9,8,7,6,5,4,3]=>10111111=>11111101
[1,2,9,8,7,6,5,4,3]=>00111111=>11111100
[3,2,1,9,8,7,6,5,4]=>11011111=>11111011
[1,3,2,9,8,7,6,5,4]=>01011111=>11111010
[1,2,3,9,8,7,6,5,4]=>00011111=>11111000
[4,3,2,1,9,8,7,6,5]=>11101111=>11110111
[1,4,3,2,9,8,7,6,5]=>01101111=>11110110
[2,1,4,3,9,8,7,6,5]=>10101111=>11110101
[1,2,4,3,9,8,7,6,5]=>00101111=>11110100
[1,2,3,4,9,8,7,6,5]=>00001111=>11110000
[1,5,4,3,2,9,8,7,6]=>01110111=>11101110
[2,1,5,4,3,9,8,7,6]=>10110111=>11101101
[1,2,5,4,3,9,8,7,6]=>00110111=>11101100
[1,3,2,5,4,9,8,7,6]=>01010111=>11101010
[1,2,3,5,4,9,8,7,6]=>00010111=>11101000
[1,2,3,4,5,9,8,7,6]=>00000111=>11100000
[1,3,2,6,5,4,9,8,7]=>01011011=>11011010
[1,2,3,6,5,4,9,8,7]=>00011011=>11011000
[2,1,4,3,6,5,9,8,7]=>10101011=>11010101
[1,2,4,3,6,5,9,8,7]=>00101011=>11010100
[1,2,3,4,6,5,9,8,7]=>00001011=>11010000
[1,2,3,5,4,7,6,9,8]=>00010101=>10101000
[1,2,3,4,5,7,6,9,8]=>00000101=>10100000
[1,2,10,9,8,7,6,5,4,3]=>001111111=>111111100
[3,2,1,10,9,8,7,6,5,4]=>110111111=>111111011
[1,3,2,10,9,8,7,6,5,4]=>010111111=>111111010
[1,2,3,10,9,8,7,6,5,4]=>000111111=>111111000
[1,4,3,2,10,9,8,7,6,5]=>011011111=>111110110
[1,2,4,3,10,9,8,7,6,5]=>001011111=>111110100
[1,2,3,4,10,9,8,7,6,5]=>000011111=>111110000
[1,5,4,3,2,10,9,8,7,6]=>011101111=>111101110
[2,1,5,4,3,10,9,8,7,6]=>101101111=>111101101
[1,2,5,4,3,10,9,8,7,6]=>001101111=>111101100
[1,3,2,5,4,10,9,8,7,6]=>010101111=>111101010
[1,2,3,5,4,10,9,8,7,6]=>000101111=>111101000
[1,2,6,5,4,3,10,9,8,7]=>001110111=>111011100
[3,2,1,6,5,4,10,9,8,7]=>110110111=>111011011
[1,3,2,6,5,4,10,9,8,7]=>010110111=>111011010
[1,2,3,6,5,4,10,9,8,7]=>000110111=>111011000
[1,2,4,3,6,5,10,9,8,7]=>001010111=>111010100
[1,2,3,4,6,5,10,9,8,7]=>000010111=>111010000
[1,2,3,4,5,6,10,9,8,7]=>000000111=>111000000
[1,4,3,2,7,6,5,10,9,8]=>011011011=>110110110
[2,1,4,3,7,6,5,10,9,8]=>101011011=>110110101
[1,2,4,3,7,6,5,10,9,8]=>001011011=>110110100
[1,2,3,4,7,6,5,10,9,8]=>000011011=>110110000
[1,3,2,5,4,7,6,10,9,8]=>010101011=>110101010
[1,2,3,5,4,7,6,10,9,8]=>000101011=>110101000
[1,2,3,4,5,7,6,10,9,8]=>000001011=>110100000
[1,2,3,4,5,6,7,10,9,8]=>000000011=>110000000
[1,2,4,3,6,5,8,7,10,9]=>001010101=>101010100
[1,2,3,4,6,5,8,7,10,9]=>000010101=>101010000
[1,2,3,4,5,6,8,7,10,9]=>000000101=>101000000
[5,2,7,4,1,6,3,8]=>0011110=>0111100
[4,7,3,1,5,6,2,8]=>0100110=>0110010
[5,8,3,4,1,6,7,2]=>0010011=>1100100
[1,7,8,4,5,6,2,3]=>0000101=>1010000
[1,5,8,4,2,6,7,3]=>0010011=>1100100
[1,6,3,8,5,2,7,4]=>0001111=>1111000
[5,2,3,7,1,6,4,8]=>0001110=>0111000
[6,2,3,7,5,1,4,8]=>0001110=>0111000
[1,7,3,4,8,6,2,5]=>0000111=>1110000
[6,2,3,4,8,1,7,5]=>0000111=>1110000
[8,7,3,2,1,6,5,4]=>1101111=>1111011
[8,7,6,3,1,5,2,4]=>0101111=>1111010
[8,5,1,7,2,3,4,6]=>0001011=>1101000
[9,8,7,6,5,2,1,4,3]=>10111111=>11111101
[9,8,7,3,2,1,6,5,4]=>11011111=>11111011
[9,8,7,6,3,1,5,2,4]=>01011111=>11111010
[9,4,3,2,1,8,7,6,5]=>11101111=>11110111
[9,8,4,3,1,7,6,2,5]=>01101111=>11110110
[9,8,7,2,1,4,3,6,5]=>10101111=>11110101
[9,8,7,4,1,6,2,3,5]=>00101111=>11110100
[5,4,3,1,9,8,7,2,6]=>01110111=>11101110
[9,5,2,1,8,4,3,7,6]=>10110111=>11101101
[9,8,3,1,5,2,7,4,6]=>01010111=>11101010
[6,3,1,9,5,2,8,4,7]=>01011011=>11011010
[6,5,1,9,8,2,3,4,7]=>00011011=>11011000
[9,2,1,4,3,6,5,8,7]=>10101011=>11010101
[9,6,1,8,2,3,4,5,7]=>00001011=>11010000
[5,1,7,2,9,3,4,6,8]=>00010101=>10101000
[7,1,9,2,3,4,5,6,8]=>00000101=>10100000
[10,9,8,7,6,5,2,1,4,3]=>101111111=>111111101
[10,9,8,7,3,2,1,6,5,4]=>110111111=>111111011
[10,9,8,7,6,3,1,5,2,4]=>010111111=>111111010
[10,9,4,3,2,1,8,7,6,5]=>111011111=>111110111
[10,9,8,4,3,1,7,6,2,5]=>011011111=>111110110
[10,9,8,7,2,1,4,3,6,5]=>101011111=>111110101
[10,9,8,7,4,1,6,2,3,5]=>001011111=>111110100
[10,5,4,3,1,9,8,7,2,6]=>011101111=>111101110
[10,9,5,2,1,8,4,3,7,6]=>101101111=>111101101
[10,9,5,4,1,8,7,2,3,6]=>001101111=>111101100
[10,9,8,3,1,5,2,7,4,6]=>010101111=>111101010
[6,5,2,1,10,9,4,3,8,7]=>101110111=>111011101
[6,5,4,1,10,9,8,2,3,7]=>001110111=>111011100
[10,3,2,1,6,5,4,9,8,7]=>110110111=>111011011
[10,6,5,1,9,8,2,3,4,7]=>000110111=>111011000
[10,9,2,1,4,3,6,5,8,7]=>101010111=>111010101
[10,9,6,1,8,2,3,4,5,7]=>000010111=>111010000
[4,3,1,7,6,2,10,9,5,8]=>011011011=>110110110
[7,2,1,10,4,3,6,5,9,8]=>101011011=>110110101
[7,4,1,10,6,2,9,3,5,8]=>001011011=>110110100
[7,6,1,10,9,2,3,4,5,8]=>000011011=>110110000
[10,5,1,7,2,9,3,4,6,8]=>000101011=>110101000
[10,7,1,9,2,3,4,5,6,8]=>000001011=>110100000
[4,1,6,2,8,3,10,5,7,9]=>001010101=>101010100
[6,1,8,2,10,3,4,5,7,9]=>000010101=>101010000
[8,1,10,2,3,4,5,6,7,9]=>000000101=>101000000
[2,4,8,5,3,7,1,6]=>0001011=>1101000
[2,4,1,8,5,3,7,6]=>0011011=>1101100
[2,4,8,6,3,1,7,5]=>0100111=>1110010
[3,4,6,8,2,1,7,5]=>1000011=>1100001
[3,4,1,5,8,2,7,6]=>0010011=>1100100
[8,1,4,5,3,2,7,6]=>0101011=>1101010
[3,4,1,5,2,8,7,6]=>0011011=>1101100
[3,4,6,2,1,8,7,5]=>1000111=>1110001
[3,5,6,2,1,7,8,4]=>1000101=>1010001
[3,4,6,2,7,8,1,5]=>0000101=>1010000
[8,1,4,6,3,7,2,5]=>0000111=>1110000
[8,1,4,6,3,7,5,2]=>0001111=>1111000
[3,5,6,2,1,7,4,8]=>1000110=>0110001
[8,1,5,6,7,3,4,2]=>0010011=>1100100
[8,1,5,6,7,3,2,4]=>0100011=>1100010
[3,4,1,6,8,7,2,5]=>0010011=>1100100
[3,5,6,1,8,7,2,4]=>0000111=>1110000
[2,1,3,8,6,7,4,5]=>1000011=>1100001
[8,1,3,2,6,7,5,4]=>0101011=>1101010
[2,3,8,6,7,1,5,4]=>0001011=>1101000
[2,4,1,8,6,7,5,3]=>0011011=>1101100
[2,5,8,6,1,7,4,3]=>0010111=>1110100
[3,5,6,1,8,7,4,2]=>0010111=>1110100
[3,4,1,6,8,7,5,2]=>0011011=>1101100
[3,4,6,8,7,1,5,2]=>0001011=>1101000
[8,1,4,6,2,7,5,3]=>0001111=>1111000
[3,5,1,6,7,8,4,2]=>0011001=>1001100
[4,5,6,1,7,8,3,2]=>0100101=>1010010
[4,5,6,1,7,3,8,2]=>0000111=>1110000
[3,5,1,6,7,4,8,2]=>0001011=>1101000
[8,1,5,6,7,4,2,3]=>0010011=>1100100
[8,1,5,6,7,4,3,2]=>0110011=>1100110
[3,5,1,6,7,4,2,8]=>0011010=>0101100
[4,5,6,1,7,3,2,8]=>0100110=>0110010
[6,5,8,7,4,3,1,2]=>0110111=>1110110
[6,4,2,7,8,5,1,3]=>0011101=>1011100
[6,1,4,8,7,5,2,3]=>0001111=>1111000
[1,6,4,8,7,5,2,3]=>0001111=>1111000
[1,8,6,2,4,7,3,5]=>0000111=>1110000
[8,1,6,2,4,7,3,5]=>0000111=>1110000
[7,6,2,1,4,8,3,5]=>1000111=>1110001
[6,4,1,7,8,5,2,3]=>0011101=>1011100
[7,6,1,2,4,8,3,5]=>0000111=>1110000
[7,6,1,3,4,8,2,5]=>0000111=>1110000
[8,1,6,3,4,7,2,5]=>0000111=>1110000
[1,8,6,3,4,7,2,5]=>0000111=>1110000
[1,7,2,5,4,8,3,6]=>0001011=>1101000
[7,1,2,5,4,8,3,6]=>0001011=>1101000
[2,7,1,5,4,8,3,6]=>0001011=>1101000
[2,8,6,3,4,7,1,5]=>0000111=>1110000
[2,8,6,1,4,7,3,5]=>0000111=>1110000
[7,2,1,5,4,8,3,6]=>1001011=>1101001
[1,2,7,5,4,8,3,6]=>0001011=>1101000
[3,2,7,5,4,8,1,6]=>0101011=>1101010
[2,5,8,4,7,3,1,6]=>0100011=>1100010
[2,3,7,5,4,8,1,6]=>0001011=>1101000
[6,8,3,2,4,7,1,5]=>0100011=>1100010
[3,7,2,5,4,8,1,6]=>0001011=>1101000
[3,1,7,5,4,8,2,6]=>0101011=>1101010
[1,3,7,5,4,8,2,6]=>0001011=>1101000
[1,5,8,4,7,3,2,6]=>0100011=>1100010
[5,1,8,4,7,3,2,6]=>0101011=>1101010
[5,8,2,4,7,3,1,6]=>0100011=>1100010
[6,8,4,3,7,5,1,2]=>0011011=>1101100
[8,7,5,6,2,1,4,3]=>1010111=>1110101
[8,5,2,4,7,3,1,6]=>0101011=>1101010
[8,1,5,4,7,3,2,6]=>0101011=>1101010
[1,8,5,4,7,3,2,6]=>0101011=>1101010
[1,7,3,5,4,8,2,6]=>0001011=>1101000
[8,6,3,1,4,7,2,5]=>0100111=>1110010
[8,6,4,2,7,5,1,3]=>0011111=>1111100
[8,6,4,1,7,2,5,3]=>0011111=>1111100
[5,3,7,4,6,8,2,1]=>1001011=>1101001
[4,1,3,2,7,8,5,6]=>0110001=>1000110
[1,4,3,2,7,8,5,6]=>0110001=>1000110
[2,4,3,1,7,8,5,6]=>0110001=>1000110
[2,7,3,5,4,8,1,6]=>0001011=>1101000
[2,8,5,4,7,3,1,6]=>0101011=>1101010
[5,7,3,4,6,8,2,1]=>1000011=>1100001
[8,2,5,4,7,3,1,6]=>0101011=>1101010
[7,2,3,5,4,8,1,6]=>0001011=>1101000
[3,2,1,4,7,8,5,6]=>1100001=>1000011
[8,1,7,6,4,3,5,2]=>0011111=>1111100
[8,6,4,5,2,7,1,3]=>0001111=>1111000
[7,1,8,6,4,3,5,2]=>0011111=>1111100
[7,4,2,5,1,6,3,8]=>0011110=>0111100
[7,3,6,5,2,1,4,8]=>1001110=>0111001
[8,3,6,5,2,1,7,4]=>1001111=>1111001
[7,3,6,5,2,1,8,4]=>1001111=>1111001
[7,5,8,6,4,2,1,3]=>1010111=>1110101
[5,4,2,8,1,3,7,6]=>0011011=>1101100
[5,8,2,6,4,1,3,7]=>0010101=>1010100
[6,4,2,5,1,8,3,7]=>0011101=>1011100
[6,3,5,2,1,4,7,8]=>1001100=>0011001
[2,5,8,6,3,1,4,7]=>0100101=>1010010
[2,3,5,8,1,4,7,6]=>0000011=>1100000
[2,3,6,8,1,5,7,4]=>0000011=>1100000
[6,3,8,5,2,7,1,4]=>0001111=>1111000
[6,3,7,5,2,1,4,8]=>1001110=>0111001
[2,5,7,6,3,1,4,8]=>0100110=>0110010
[2,8,7,6,3,1,5,4]=>0101111=>1111010
[2,5,8,7,6,3,1,4]=>0100111=>1110010
[2,4,8,1,6,5,7,3]=>0000111=>1110000
[2,8,7,3,6,1,4,5]=>0000111=>1110000
[7,3,5,2,1,4,6,8]=>1001010=>0101001
[8,4,2,5,1,3,7,6]=>0011011=>1101100
[2,3,6,8,1,4,7,5]=>0000011=>1100000
[2,7,8,6,3,1,4,5]=>0100101=>1010010
[7,3,8,5,2,1,4,6]=>1001011=>1101001
[2,3,6,1,8,4,7,5]=>0000111=>1110000
[2,8,6,3,1,4,5,7]=>0100101=>1010010
[8,3,5,2,1,4,6,7]=>1001001=>1001001
[2,4,8,1,3,7,5,6]=>0000011=>1100000
[2,5,8,1,7,3,6,4]=>0000111=>1110000
[2,8,1,5,7,3,6,4]=>0000111=>1110000
[3,8,6,1,4,7,5,2]=>0001111=>1111000
[2,6,8,1,5,7,3,4]=>0000011=>1100000
[2,7,1,5,8,3,4,6]=>0000011=>1100000
[3,7,5,8,1,2,6,4]=>0000111=>1110000
[7,3,6,1,2,8,4,5]=>0000111=>1110000
[7,4,8,1,6,5,2,3]=>0001111=>1111000
[7,4,5,8,6,1,2,3]=>0000111=>1110000
[6,8,4,5,1,7,2,3]=>0001011=>1101000
[5,1,8,7,6,2,3,4]=>0001111=>1111000
[8,5,1,6,2,7,3,4]=>0001111=>1111000
[4,6,1,8,7,5,2,3]=>0001111=>1111000
[4,5,1,8,7,2,3,6]=>0001011=>1101000
[3,4,8,7,1,2,5,6]=>0000011=>1100000
[6,4,8,7,1,2,5,3]=>0001111=>1111000
[5,6,8,3,7,1,4,2]=>0010011=>1100100
[6,4,7,1,2,8,5,3]=>0001111=>1111000
[6,5,1,2,7,3,8,4]=>0001111=>1111000
[6,5,1,8,2,7,3,4]=>0001111=>1111000
[6,5,1,8,7,2,3,4]=>0001111=>1111000
[6,5,1,7,2,8,3,4]=>0001111=>1111000
[6,5,1,7,2,3,8,4]=>0001111=>1111000
[5,6,8,7,4,1,2,3]=>0010011=>1100100
[6,8,5,7,4,1,2,3]=>0010011=>1100100
[7,3,8,1,5,2,4,6]=>0001011=>1101000
[4,1,7,5,3,6,2,8]=>0011110=>0111100
[1,8,4,2,3,6,7,5]=>0010011=>1100100
[2,5,8,3,4,6,7,1]=>0000011=>1100000
[4,1,7,2,3,6,8,5]=>0010011=>1100100
[4,6,2,1,5,7,8,3]=>1000101=>1010001
[4,5,2,3,1,7,8,6]=>0101001=>1001010
[3,2,6,7,4,1,8,5]=>0110011=>1100110
[5,6,2,7,1,4,8,3]=>0000111=>1110000
[6,2,3,8,1,7,4,5]=>0000111=>1110000
[2,6,8,3,4,7,1,5]=>0000011=>1100000
[4,6,2,7,5,1,3,8]=>0001110=>0111000
[2,6,3,1,8,4,5,7]=>0100101=>1010010
[2,4,3,7,8,1,5,6]=>0010001=>1000100
[5,3,2,7,4,8,1,6]=>0101011=>1101010
[5,1,2,7,6,8,4,3]=>0011011=>1101100
[2,6,3,1,8,7,4,5]=>0100111=>1110010
[3,5,6,4,7,8,1,2]=>0000101=>1010000
[5,3,6,4,2,8,7,1]=>0011111=>1111100
[5,4,2,3,7,8,6,1]=>0011101=>1011100
[4,1,8,2,5,7,3,6]=>0010011=>1100100
[3,1,8,4,7,2,5,6]=>0100011=>1100010
[6,2,3,8,4,1,7,5]=>0010111=>1110100
[2,6,4,1,5,3,8,7]=>0011101=>1011100
[3,2,7,6,4,1,8,5]=>0110111=>1110110
[2,5,4,1,7,6,8,3]=>0011011=>1101100
[6,2,1,4,7,8,3,5]=>1000101=>1010001
[2,6,5,1,7,8,3,4]=>0001101=>1011000
[4,7,5,2,1,6,3,8]=>1001110=>0111001
[4,2,3,7,8,1,6,5]=>0010101=>1010100
[5,8,3,1,7,2,4,6]=>0100011=>1100010
[6,8,3,1,5,2,4,7]=>0101001=>1001010
[4,2,7,1,6,3,5,8]=>0010110=>0110100
[5,1,7,4,2,6,3,8]=>0011110=>0111100
[6,8,4,2,1,5,3,7]=>1011001=>1001101
[6,8,5,2,1,7,3,4]=>1001011=>1101001
[5,8,2,1,4,7,3,6]=>1000011=>1100001
[6,8,3,2,5,1,7,4]=>0101011=>1101010
[6,8,4,3,1,5,7,2]=>0110011=>1100110
[6,8,4,2,1,5,7,3]=>1010011=>1100101
[6,8,3,2,1,4,5,7]=>1100001=>1000011
[5,1,7,3,2,4,6,8]=>0101010=>0101010
[5,2,1,8,3,6,7,4]=>1001011=>1101001
[4,3,8,1,6,2,7,5]=>0010111=>1110100
[5,4,7,2,1,6,8,3]=>1001011=>1101001
[5,2,1,7,3,4,8,6]=>1001011=>1101001
[6,4,3,1,7,5,8,2]=>0110111=>1110110
[5,3,1,7,2,6,8,4]=>0101011=>1101010
[3,2,1,7,6,4,8,5]=>1100111=>1110011
[4,2,1,6,5,8,3,7]=>1010101=>1010101
[4,2,1,8,5,7,3,6]=>1010011=>1100101
[7,4,3,1,8,5,6,2]=>0110111=>1110110
[7,4,2,1,8,5,6,3]=>1010111=>1110101
[6,3,2,1,7,4,5,8]=>1100110=>0110011
[6,4,2,1,7,5,3,8]=>1011110=>0111101
[7,5,2,1,8,6,3,4]=>1001111=>1111001
[6,1,8,4,2,7,3,5]=>0010111=>1110100
[6,2,1,8,3,7,4,5]=>1000111=>1110001
[5,2,1,7,3,6,4,8]=>1001110=>0111001
[5,3,2,7,6,1,4,8]=>0101110=>0111010
[5,3,2,8,6,1,4,7]=>0101101=>1011010
[6,3,2,8,7,1,4,5]=>0100111=>1110010
[4,2,8,1,7,3,5,6]=>0010011=>1100100
[4,3,8,7,2,1,5,6]=>1010011=>1100101
[2,1,5,8,4,7,3,6]=>1000011=>1100001
[4,3,2,5,8,1,6,7]=>0110001=>1000110
[4,3,2,5,7,1,6,8]=>0110010=>0100110
[4,3,1,6,2,7,5,8]=>0110110=>0110110
[4,3,1,7,2,8,5,6]=>0110011=>1100110
[5,4,1,7,2,8,6,3]=>0011111=>1111100
[6,5,3,1,7,8,4,2]=>0111101=>1011110
[6,4,2,1,7,8,3,5]=>1010101=>1010101
[5,4,2,1,6,7,3,8]=>1011010=>0101101
[5,3,2,1,6,7,4,8]=>1101010=>0101011
[6,4,2,1,7,8,5,3]=>1011101=>1011101
[5,3,2,6,8,1,7,4]=>0101011=>1101010
[3,2,1,4,8,7,5,6]=>1100011=>1100011
[3,2,1,4,6,8,5,7]=>1100001=>1000011
[4,3,2,6,1,7,8,5]=>0110101=>1010110
[5,3,2,1,6,7,8,4]=>1101001=>1001011
[8,6,1,4,5,7,2,3]=>0000111=>1110000
[3,8,6,4,5,7,1,2]=>0000111=>1110000
[5,2,8,3,7,4,6,1]=>0001111=>1111000
[6,2,8,5,4,7,3,1]=>0101111=>1111010
[1,8,6,3,7,4,2,5]=>0010111=>1110100
[1,8,6,5,7,2,3,4]=>0000111=>1110000
[5,2,8,4,3,6,7,1]=>0011011=>1101100
[5,4,2,7,3,6,1,8]=>0011110=>0111100
[5,4,2,8,3,6,1,7]=>0011101=>1011100
[6,5,3,8,4,7,2,1]=>1001111=>1111001
[5,2,8,4,3,7,1,6]=>0011011=>1101100
[6,2,8,3,7,4,1,5]=>0010111=>1110100
[5,4,2,7,3,1,8,6]=>0111011=>1101110
[6,4,3,7,1,2,8,5]=>0010111=>1110100
[6,4,3,8,1,2,7,5]=>0010111=>1110100
[7,6,3,8,4,2,1,5]=>1010111=>1110101
[7,2,8,5,1,6,3,4]=>0001111=>1111000
[7,2,8,4,3,1,5,6]=>0110011=>1100110
[7,5,3,8,4,2,6,1]=>0011111=>1111100
[6,4,2,7,3,1,5,8]=>0110110=>0110110
[7,6,4,8,2,3,5,1]=>0001111=>1111000
[7,6,8,1,2,5,3,4]=>0001011=>1101000
[5,3,1,7,8,4,6,2]=>0101101=>1011010
[5,3,2,7,8,4,6,1]=>0101101=>1011010
[5,4,1,6,3,8,7,2]=>0011111=>1111100
[6,5,1,7,8,2,3,4]=>0001101=>1011000
[6,3,1,7,8,4,2,5]=>0110101=>1010110
[5,4,1,7,3,8,2,6]=>0011011=>1101100
[6,3,2,7,8,4,1,5]=>0110101=>1010110
[6,1,5,4,3,2,8,7]=>0111101=>1011110
[8,7,6,1,3,5,2,4]=>0001111=>1111000
[8,1,6,5,7,3,4,2]=>0010111=>1110100
[8,4,1,5,7,6,2,3]=>0010111=>1110100
[7,8,6,2,5,3,1,4]=>0101101=>1011010
[6,1,3,5,2,8,4,7]=>0001101=>1011000
[8,1,3,7,4,2,5,6]=>0010011=>1100100
[4,3,8,7,5,2,1,6]=>1011011=>1101101
[6,7,1,8,5,3,4,2]=>0011011=>1101100
[2,7,6,4,8,3,5,1]=>0001111=>1111000
[6,5,2,7,1,4,8,3]=>0001111=>1111000
[7,4,6,1,3,2,8,5]=>0100111=>1110010
[7,5,2,1,3,8,4,6]=>1001011=>1101001
[8,4,7,6,3,1,5,2]=>0101111=>1111010
[7,4,1,5,6,3,8,2]=>0010111=>1110100
[3,4,7,5,6,1,8,2]=>0000111=>1110000
[2,4,7,5,6,3,8,1]=>0000111=>1110000
[5,4,1,7,6,2,8,3]=>0011111=>1111100
[3,5,6,7,1,4,8,2]=>0000011=>1100000
[2,7,6,1,3,4,8,5]=>0000111=>1110000
[5,7,2,1,6,3,8,4]=>1000111=>1110001
[4,7,2,5,6,3,8,1]=>0000111=>1110000
[8,6,2,5,7,1,4,3]=>0010111=>1110100
[2,7,4,5,3,8,1,6]=>0001011=>1101000
[6,8,7,1,3,2,5,4]=>0101011=>1101010
[2,8,6,5,7,1,4,3]=>0010111=>1110100
[5,8,4,3,2,6,7,1]=>0110011=>1100110
[1,8,5,6,2,4,7,3]=>0000111=>1110000
[8,1,5,6,2,4,7,3]=>0000111=>1110000
[6,4,8,1,3,2,7,5]=>0100111=>1110010
[1,4,5,2,8,6,7,3]=>0001011=>1101000
[2,3,1,7,8,6,4,5]=>0100101=>1010010
[3,5,7,6,2,8,1,4]=>0000111=>1110000
[4,5,6,1,2,8,7,3]=>0000111=>1110000
[5,4,1,2,8,6,7,3]=>0011011=>1101100
[8,4,5,2,1,6,7,3]=>1001011=>1101001
[3,1,2,6,8,4,7,5]=>0100011=>1100010
[5,1,3,2,7,8,4,6]=>0101001=>1001010
[1,5,4,2,7,8,3,6]=>0011001=>1001100
[4,6,7,8,3,1,5,2]=>0101001=>1001010
[7,6,2,8,4,3,1,5]=>0110111=>1110110
[5,2,8,6,3,4,7,1]=>0001111=>1111000
[5,6,8,4,3,2,7,1]=>0110011=>1100110
[5,3,8,1,7,2,4,6]=>0001011=>1101000
[3,6,7,8,4,2,1,5]=>1010001=>1000101
[6,5,1,8,4,3,7,2]=>0011111=>1111100
[6,3,8,4,2,1,7,5]=>1010111=>1110101
[2,5,8,3,1,6,7,4]=>0100011=>1100010
[3,5,8,1,2,6,7,4]=>0000011=>1100000
[3,2,8,1,5,6,7,4]=>0100011=>1100010
[1,5,8,3,2,6,7,4]=>0100011=>1100010
[1,3,8,6,2,4,7,5]=>0000111=>1110000
[3,2,7,8,4,6,1,5]=>0100101=>1010010
[5,1,8,3,4,6,7,2]=>0001011=>1101000
[4,8,7,2,1,6,3,5]=>1000111=>1110001
[2,8,1,6,3,4,7,5]=>0000111=>1110000
[8,3,4,2,1,6,5,7]=>1010101=>1010101
[6,4,7,2,5,8,1,3]=>0000111=>1110000
[8,4,5,2,6,3,1,7]=>0101101=>1011010
[2,4,5,8,3,6,1,7]=>0000101=>1010000
[3,5,8,1,2,6,4,7]=>0000101=>1010000
[8,6,1,3,5,2,4,7]=>0001101=>1011000
[8,5,1,2,6,4,3,7]=>0011101=>1011100
[5,8,6,1,3,4,2,7]=>0010101=>1010100
[5,8,4,6,1,3,2,7]=>0100101=>1010010
[7,3,4,5,2,8,1,6]=>0001011=>1101000
[5,7,4,3,6,1,8,2]=>0010111=>1110100
[2,6,4,3,7,8,5,1]=>0011101=>1011100
[7,4,1,8,3,2,5,6]=>0110011=>1100110
[6,2,1,7,8,4,5,3]=>1001101=>1011001
[7,6,3,1,5,4,8,2]=>0101111=>1111010
[2,4,6,5,1,7,8,3]=>0001101=>1011000
[1,4,7,5,6,8,2,3]=>0000011=>1100000
[1,4,7,6,5,8,2,3]=>0000111=>1110000
[3,7,5,2,4,6,8,1]=>0001011=>1101000
[5,6,1,7,4,2,8,3]=>0010111=>1110100
[3,7,4,8,1,2,6,5]=>0000111=>1110000
[6,3,5,7,8,1,4,2]=>0010101=>1010100
[3,6,5,7,1,8,4,2]=>0010111=>1110100
[6,4,7,8,2,1,3,5]=>1000101=>1010001
[6,7,3,8,4,1,2,5]=>0010011=>1100100
[2,7,8,3,4,6,1,5]=>0000101=>1010000
[7,5,8,4,1,3,2,6]=>0110011=>1100110
[4,7,5,8,3,1,2,6]=>0100011=>1100010
[3,6,7,4,8,1,2,5]=>0000011=>1100000
[5,7,3,1,6,8,4,2]=>0110011=>1100110
[2,7,3,1,8,6,4,5]=>0100111=>1110010
[2,8,4,3,1,5,7,6]=>0110011=>1100110
[4,8,1,2,3,5,7,6]=>0000011=>1100000
[7,6,8,1,2,4,3,5]=>0010011=>1100100
[7,6,8,5,1,3,2,4]=>0101011=>1101010
[2,8,5,4,6,1,7,3]=>0001111=>1111000
[8,4,5,2,7,6,1,3]=>0001111=>1111000
[8,7,6,4,1,2,5,3]=>0011111=>1111100
[6,7,1,3,5,2,8,4]=>0001011=>1101000
[5,7,2,3,6,8,1,4]=>0000011=>1100000
[8,5,3,2,7,6,1,4]=>0101111=>1111010
[3,4,6,7,5,8,1,2]=>0000011=>1100000
[3,4,5,7,6,1,8,2]=>0000111=>1110000
[2,6,4,5,7,8,3,1]=>0100101=>1010010
[3,8,5,1,6,2,7,4]=>0001111=>1111000
[2,5,1,3,6,8,7,4]=>0001011=>1101000
[5,4,6,1,3,7,8,2]=>0001101=>1011000
[6,3,5,7,1,4,8,2]=>0000111=>1110000
[7,3,4,6,8,1,5,2]=>0001011=>1101000
[7,5,2,8,4,1,3,6]=>0011011=>1101100
[3,7,6,4,1,8,2,5]=>0010111=>1110100
[3,7,8,4,1,5,6,2]=>0010101=>1010100
[8,7,5,4,2,1,6,3]=>1011111=>1111101
[3,5,8,6,7,4,2,1]=>1010011=>1100101
[5,8,1,6,7,3,4,2]=>0010011=>1100100
[6,7,2,5,1,8,4,3]=>0011011=>1101100
[5,8,2,1,6,7,4,3]=>1010011=>1100101
[4,5,2,8,6,3,7,1]=>0001111=>1111000
[3,6,1,2,5,8,4,7]=>0000101=>1010000
[1,4,5,8,2,3,7,6]=>0000011=>1100000
[1,2,6,4,5,8,3,7]=>0000101=>1010000
[1,5,2,4,6,8,3,7]=>0001001=>1001000
[3,6,1,5,8,2,4,7]=>0000101=>1010000
[2,6,5,1,4,8,3,7]=>0001101=>1011000
[5,2,6,1,4,8,3,7]=>0001101=>1011000
[2,5,1,8,4,7,3,6]=>0001011=>1101000
[2,7,1,4,3,6,8,5]=>0010011=>1100100
[1,3,7,5,8,2,4,6]=>0000011=>1100000
[8,2,1,5,7,3,4,6]=>1000011=>1100001
[2,5,4,8,1,3,7,6]=>0001011=>1101000
[2,4,1,3,8,6,7,5]=>0010011=>1100100
[8,4,3,7,1,2,6,5]=>0010111=>1110100
[1,7,3,5,8,2,6,4]=>0000111=>1110000
[1,8,4,2,6,7,3,5]=>0010011=>1100100
[3,1,6,8,7,2,4,5]=>0100011=>1100010
[7,2,1,6,8,3,4,5]=>1000011=>1100001
[3,1,7,6,8,2,4,5]=>0100011=>1100010
[4,1,7,2,6,8,3,5]=>0010011=>1100100
[5,1,7,2,3,6,8,4]=>0001011=>1101000
[7,2,1,6,3,5,8,4]=>1000111=>1110001
[2,6,1,7,3,5,8,4]=>0000111=>1110000
[7,1,2,5,3,6,8,4]=>0001011=>1101000
[5,4,1,2,7,8,3,6]=>0011001=>1001100
[8,1,3,2,4,6,7,5]=>0100011=>1100010
[7,3,1,2,4,6,8,5]=>0100011=>1100010
[1,8,3,4,7,2,5,6]=>0000011=>1100000
[3,5,8,1,2,7,4,6]=>0000011=>1100000
[3,6,8,1,2,4,7,5]=>0000011=>1100000
[4,1,3,8,7,2,6,5]=>0010111=>1110100
[1,3,7,4,8,2,6,5]=>0000111=>1110000
[1,4,6,8,2,3,7,5]=>0000011=>1100000
[3,5,8,1,7,2,4,6]=>0000011=>1100000
[2,6,8,1,7,3,4,5]=>0000011=>1100000
[6,1,5,8,2,3,7,4]=>0000111=>1110000
[1,8,3,2,7,5,6,4]=>0100111=>1110010
[3,1,7,2,8,5,6,4]=>0100111=>1110010
[2,6,7,3,8,1,5,4]=>0001011=>1101000
[8,4,1,7,3,6,2,5]=>0010111=>1110100
[3,7,2,8,6,1,5,4]=>0001111=>1111000
[6,2,3,8,7,1,5,4]=>0001111=>1111000
[5,1,7,8,4,2,6,3]=>0011101=>1011100
[5,1,8,7,4,2,6,3]=>0011111=>1111100
[4,7,2,8,3,6,5,1]=>0001111=>1111000
[4,1,7,8,5,3,6,2]=>0011101=>1011100
[5,1,7,4,8,3,6,2]=>0001111=>1111000
[4,1,8,7,5,3,6,2]=>0011111=>1111100
[4,8,2,7,3,6,5,1]=>0001111=>1111000
[4,7,2,6,3,5,8,1]=>0000111=>1110000
[6,8,2,4,3,7,5,1]=>0011011=>1101100
[6,7,2,4,3,8,5,1]=>0011011=>1101100
[6,8,2,7,3,5,4,1]=>0011011=>1101100
[3,8,7,2,4,1,5,6]=>0010011=>1100100
[3,7,8,2,4,1,5,6]=>0010001=>1000100
[3,6,8,2,4,5,7,1]=>0000011=>1100000
[3,6,7,2,4,5,8,1]=>0000011=>1100000
[6,5,1,4,2,3,8,7]=>0011101=>1011100
[8,6,1,7,2,5,4,3]=>0011111=>1111100
[8,7,6,1,2,3,5,4]=>0001111=>1111000
[5,4,3,1,6,2,8,7]=>0111101=>1011110
[8,3,4,7,1,6,2,5]=>0000111=>1110000
[6,3,4,1,8,5,2,7]=>0011101=>1011100
[3,8,5,2,7,1,6,4]=>0001111=>1111000
[2,8,6,7,5,3,4,1]=>0011011=>1101100
[2,1,8,7,3,6,4,5]=>1000111=>1110001
[3,6,5,8,2,4,7,1]=>0000111=>1110000
[5,2,1,8,7,3,4,6]=>1001011=>1101001
[6,5,2,7,4,3,8,1]=>0011111=>1111100
[4,6,5,2,7,3,8,1]=>0001111=>1111000
[6,2,7,1,8,3,5,4]=>0001111=>1111000
[2,7,5,4,8,3,6,1]=>0001111=>1111000
[8,7,5,1,2,6,4,3]=>0011111=>1111100
[8,4,3,2,7,1,6,5]=>0110111=>1110110
[7,1,6,2,3,8,5,4]=>0001111=>1111000
[4,8,1,3,2,7,5,6]=>0100011=>1100010
[3,8,1,4,7,5,2,6]=>0001011=>1101000
[6,3,8,7,4,5,1,2]=>0001111=>1111000
[6,1,4,8,5,2,3,7]=>0001101=>1011000
[8,5,7,4,6,2,1,3]=>1000111=>1110001
[4,6,7,8,2,3,5,1]=>0001001=>1001000
[8,7,4,6,2,1,5,3]=>1001111=>1111001
[7,6,1,3,5,2,8,4]=>0001111=>1111000
[5,8,3,2,4,6,1,7]=>0100101=>1010010
[8,2,6,5,3,1,7,4]=>0101111=>1111010
[4,8,7,6,5,2,3,1]=>0101111=>1111010
[2,1,8,6,4,3,7,5]=>1010111=>1110101
[2,1,7,6,5,3,8,4]=>1001111=>1111001
[2,7,6,1,3,5,8,4]=>0000111=>1110000
[7,2,5,4,6,1,8,3]=>0001111=>1111000
[4,7,6,1,2,5,8,3]=>0000111=>1110000
[2,4,1,7,6,8,5,3]=>0011011=>1101100
[3,4,1,7,8,5,6,2]=>0010101=>1010100
[7,5,4,3,1,8,6,2]=>0111111=>1111110
[8,5,6,2,7,3,1,4]=>0100111=>1110010
[8,4,2,5,6,1,7,3]=>0010111=>1110100
[6,3,5,4,1,7,8,2]=>0011101=>1011100
[4,1,3,6,7,5,8,2]=>0010011=>1100100
[1,7,5,3,8,2,4,6]=>0001011=>1101000
[1,7,2,4,5,8,3,6]=>0000011=>1100000
[8,2,5,3,1,6,4,7]=>0101101=>1011010
[1,7,4,5,8,3,2,6]=>0100011=>1100010
[2,6,4,7,8,3,5,1]=>0001101=>1011000
[2,6,4,7,8,3,1,5]=>0100101=>1010010
[1,2,6,4,7,8,3,5]=>0000101=>1010000
[2,7,4,5,8,1,3,6]=>0000011=>1100000
[2,7,5,3,1,8,4,6]=>0101011=>1101010
[6,1,4,7,8,3,5,2]=>0001101=>1011000
[3,6,4,7,8,1,5,2]=>0001101=>1011000
[4,3,6,7,1,8,5,2]=>0011011=>1101100
[4,3,6,7,1,8,2,5]=>0010011=>1100100
[3,6,4,7,8,1,2,5]=>0000101=>1010000
[2,3,6,4,1,7,8,5]=>0010101=>1010100
[4,7,2,1,5,3,8,6]=>1001011=>1101001
[3,7,4,5,2,1,8,6]=>1001011=>1101001
[1,3,6,4,7,2,8,5]=>0000111=>1110000
[3,6,4,7,2,8,5,1]=>0001111=>1111000
[5,1,3,4,2,7,8,6]=>0011001=>1001100
[5,4,2,1,3,7,8,6]=>1011001=>1001101
[6,1,7,3,8,2,5,4]=>0001111=>1111000
[1,6,7,3,8,2,5,4]=>0001011=>1101000
[6,1,4,7,8,5,2,3]=>0001101=>1011000
[6,3,2,1,7,8,5,4]=>1101101=>1011011
[6,2,7,3,1,8,5,4]=>0101111=>1111010
[6,2,4,7,8,1,5,3]=>0001101=>1011000
[2,6,7,3,1,8,5,4]=>0101011=>1101010
[8,6,5,1,3,2,4,7]=>0101101=>1011010
[6,4,7,8,3,2,5,1]=>0101101=>1011010
[3,8,4,7,1,2,5,6]=>0000011=>1100000
[8,6,1,2,5,4,3,7]=>0011101=>1011100
[4,8,6,1,5,3,2,7]=>0101101=>1011010
[5,8,6,4,1,3,2,7]=>0110101=>1010110
[8,3,6,4,5,2,1,7]=>1001101=>1011001
[6,8,5,7,4,2,3,1]=>0110011=>1100110
[2,3,8,7,1,6,4,5]=>0000111=>1110000
[4,3,7,8,1,6,2,5]=>0010101=>1010100
[3,5,8,7,4,1,2,6]=>0010011=>1100100
[7,3,8,4,1,2,5,6]=>0010011=>1100100
[4,8,1,2,7,3,5,6]=>0000011=>1100000
[6,8,1,2,7,4,5,3]=>0001011=>1101000
[5,6,8,4,1,3,7,2]=>0010011=>1100100
[8,5,4,7,1,6,3,2]=>0101111=>1111010
[2,5,8,7,3,6,4,1]=>0010111=>1110100
[2,4,8,7,5,6,1,3]=>0000111=>1110000
[3,7,4,8,5,6,2,1]=>1000111=>1110001
[6,4,8,7,5,1,2,3]=>0001111=>1111000
[3,8,5,2,4,6,7,1]=>0001011=>1101000
[5,7,1,8,4,6,2,3]=>0000111=>1110000
[6,3,8,7,2,1,4,5]=>1000111=>1110001
[2,3,7,8,5,6,1,4]=>0000101=>1010000
[3,7,6,8,5,1,2,4]=>0001011=>1101000
[2,6,7,8,5,1,3,4]=>0001001=>1001000
[2,4,7,8,1,6,3,5]=>0000101=>1010000
[5,4,7,8,2,6,3,1]=>0101101=>1011010
[2,8,3,4,1,5,7,6]=>0010011=>1100100
[6,8,3,4,1,2,7,5]=>0010011=>1100100
[6,8,7,1,5,2,3,4]=>0001011=>1101000
[5,8,3,2,7,6,1,4]=>0100111=>1110010
[2,5,3,1,8,6,7,4]=>0101011=>1101010
[4,5,3,2,8,6,7,1]=>0101011=>1101010
[3,5,8,6,1,4,7,2]=>0000111=>1110000
[2,8,5,6,1,4,7,3]=>0000111=>1110000
[4,8,6,1,5,2,7,3]=>0001111=>1111000
[5,8,2,3,7,6,1,4]=>0000111=>1110000
[4,6,8,5,3,2,7,1]=>0101011=>1101010
[2,6,4,8,5,1,7,3]=>0001111=>1111000
[7,6,4,8,5,2,1,3]=>1001111=>1111001
[3,4,8,6,5,2,7,1]=>0001111=>1111000
[3,4,8,7,5,6,2,1]=>1000111=>1110001
[7,5,3,2,8,6,1,4]=>0101111=>1111010
[2,5,1,3,8,6,7,4]=>0001011=>1101000
[4,5,1,2,8,6,7,3]=>0001011=>1101000
[5,4,8,1,3,6,7,2]=>0001011=>1101000
[8,3,5,4,1,6,7,2]=>0011011=>1101100
[7,3,4,8,5,6,1,2]=>0000111=>1110000
[6,1,5,7,2,4,8,3]=>0000111=>1110000
[7,4,5,1,2,3,8,6]=>0001011=>1101000
[7,4,3,1,2,8,5,6]=>0110011=>1100110
[8,4,7,6,2,1,5,3]=>1001111=>1111001
[8,4,6,5,7,1,3,2]=>0100111=>1110010
[7,2,1,4,5,8,3,6]=>1000011=>1100001
[7,4,1,6,3,5,8,2]=>0010111=>1110100
[3,5,7,6,4,1,8,2]=>0010111=>1110100
[4,7,5,2,1,3,8,6]=>1001011=>1101001
[5,7,2,3,6,4,8,1]=>0000111=>1110000
[8,6,2,3,7,1,4,5]=>0000111=>1110000
[5,7,2,4,8,3,6,1]=>0000111=>1110000
[1,7,2,4,8,6,3,5]=>0000111=>1110000
[7,6,1,5,4,8,3,2]=>0101111=>1111010
[4,7,3,2,1,8,5,6]=>1100011=>1100011
[3,1,7,2,5,8,4,6]=>0100011=>1100010
[4,8,7,6,1,2,5,3]=>0001111=>1111000
[7,8,6,1,3,2,5,4]=>0101101=>1011010
[2,8,6,7,4,1,3,5]=>0010011=>1100100
[5,8,6,4,2,3,1,7]=>0110101=>1010110
[2,8,3,1,6,5,4,7]=>0101101=>1011010
[3,8,1,2,5,7,4,6]=>0000011=>1100000
[6,8,5,4,2,7,3,1]=>0111011=>1101110
[6,8,3,1,2,4,5,7]=>0100001=>1000010
[4,6,8,7,3,1,5,2]=>0101011=>1101010
[6,5,3,7,8,4,1,2]=>0011101=>1011100
[4,1,3,8,7,5,6,2]=>0010111=>1110100
[6,2,7,4,8,1,3,5]=>0000111=>1110000
[8,4,5,2,1,6,3,7]=>1001101=>1011001
[4,3,2,6,8,1,7,5]=>0110011=>1100110
[7,1,5,6,3,8,2,4]=>0000111=>1110000
[5,1,2,4,7,8,3,6]=>0001001=>1001000
[3,5,4,2,8,1,6,7]=>0011001=>1001100
[5,1,3,8,4,2,7,6]=>0011011=>1101100
[6,2,8,7,3,5,4,1]=>0011111=>1111100
[7,1,8,4,3,6,5,2]=>0011111=>1111100
[3,6,8,7,4,1,2,5]=>0010011=>1100100
[5,6,8,1,7,3,2,4]=>0100011=>1100010
[3,1,6,8,7,4,2,5]=>0110011=>1100110
[7,4,6,8,2,1,5,3]=>1001011=>1101001
[6,5,8,4,3,1,2,7]=>0110101=>1010110
[2,5,8,3,6,7,4,1]=>0010011=>1100100
[8,5,1,3,7,4,6,2]=>0001111=>1111000
[1,5,8,3,7,4,2,6]=>0010011=>1100100
[3,8,2,7,1,5,6,4]=>0000111=>1110000
[5,8,2,3,6,4,1,7]=>0010101=>1010100
[6,8,2,3,4,7,5,1]=>0001011=>1101000
[7,5,1,8,4,2,6,3]=>0011111=>1111100
[3,6,8,5,2,7,4,1]=>0011011=>1101100
[2,1,6,5,4,8,3,7]=>1001101=>1011001
[2,1,7,8,4,6,5,3]=>1001101=>1011001
[2,1,7,4,3,5,8,6]=>1010011=>1100101
[3,5,7,8,4,6,1,2]=>0000101=>1010000
[7,5,2,8,4,6,3,1]=>0101111=>1111010
[7,8,2,4,3,1,5,6]=>0110001=>1000110
[7,6,3,8,1,5,4,2]=>0011111=>1111100
[7,2,4,1,6,3,8,5]=>0010111=>1110100
[8,4,3,1,7,5,2,6]=>0111011=>1101110
[7,3,1,4,6,8,5,2]=>0101011=>1101010
[4,3,8,7,1,6,5,2]=>0011111=>1111100
[4,7,1,8,5,2,6,3]=>0001111=>1111000
[5,2,4,3,6,8,1,7]=>0011001=>1001100
[3,8,6,5,4,1,2,7]=>0011101=>1011100
[4,7,5,6,3,8,2,1]=>1000111=>1110001
[4,2,7,5,8,3,6,1]=>0010111=>1110100
[5,8,2,7,3,4,6,1]=>0000111=>1110000
[6,7,2,4,5,3,8,1]=>0001011=>1101000
[6,3,2,1,4,8,5,7]=>1100101=>1010011
[6,2,3,1,4,7,8,5]=>0100101=>1010010
[5,2,1,3,6,4,8,7]=>1001101=>1011001
[7,1,8,3,5,4,6,2]=>0001111=>1111000
[7,1,2,4,8,5,6,3]=>0000111=>1110000
[7,2,1,3,4,5,8,6]=>1000011=>1100001
[8,7,3,5,4,2,1,6]=>1011011=>1101101
[8,4,6,5,3,2,1,7]=>1101101=>1011011
[5,1,6,4,3,2,8,7]=>0111101=>1011110
[8,3,7,1,4,6,5,2]=>0001111=>1111000
[2,8,3,6,4,7,5,1]=>0001111=>1111000
[6,2,1,7,5,8,3,4]=>1000111=>1110001
[6,3,8,7,5,2,1,4]=>1001111=>1111001
[6,7,2,1,5,8,4,3]=>1010011=>1100101
[9,1,8,7,6,5,4,3,2]=>01111111=>11111110
[7,6,8,1,5,4,3,2]=>0111011=>1101110
[7,1,9,8,6,5,4,3,2]=>01111111=>11111110
[6,1,9,8,7,5,4,3,2]=>01111111=>11111110
[5,4,8,7,6,1,3,2]=>0101111=>1111010
[5,1,9,8,7,6,4,3,2]=>01111111=>11111110
[4,1,9,8,7,6,5,3,2]=>01111111=>11111110
[3,1,9,8,7,6,5,4,2]=>01111111=>11111110
[10,1,9,8,7,6,5,4,3,2]=>011111111=>111111110
[9,8,1,7,6,5,4,3,2]=>01111111=>11111110
[7,6,1,8,5,4,3,2]=>0111111=>1111110
[8,7,9,1,6,5,4,3,2]=>01111011=>11011110
[8,1,10,9,7,6,5,4,3,2]=>011111111=>111111110
[6,5,8,1,7,4,3,2]=>0110111=>1110110
[7,6,9,8,1,5,4,3,2]=>01110111=>11101110
[7,1,10,9,8,6,5,4,3,2]=>011111111=>111111110
[6,5,9,8,7,1,4,3,2]=>01101111=>11110110
[6,1,10,9,8,7,5,4,3,2]=>011111111=>111111110
[6,5,8,7,4,1,3,2]=>0110111=>1110110
[5,4,9,8,7,6,1,3,2]=>01011111=>11111010
[5,1,10,9,8,7,6,4,3,2]=>011111111=>111111110
[4,3,9,8,7,6,5,1,2]=>00111111=>11111100
[4,1,10,9,8,7,6,5,3,2]=>011111111=>111111110
[3,2,9,8,7,6,5,4,1]=>01111111=>11111110
[3,1,10,9,8,7,6,5,4,2]=>011111111=>111111110
[1,6,4,8,3,2,5,7]=>0100101=>1010010
[1,8,3,5,6,2,4,7]=>0000101=>1010000
[1,4,8,5,6,2,3,7]=>0000101=>1010000
[1,2,8,5,3,7,4,6]=>0001011=>1101000
[6,1,4,8,2,3,5,7]=>0000101=>1010000
[8,7,2,5,6,1,4,3]=>0010111=>1110100
[1,8,2,5,4,7,3,6]=>0001011=>1101000
[5,7,4,1,2,3,8,6]=>0010011=>1100100
[1,7,4,2,5,3,8,6]=>0011011=>1101100
[6,7,4,2,1,3,8,5]=>1010011=>1100101
[6,4,3,8,5,7,1,2]=>0010111=>1110100
[7,4,3,6,2,1,5,8]=>1010110=>0110101
[7,2,5,3,4,1,6,8]=>0011010=>0101100
[8,3,7,4,5,6,1,2]=>0000111=>1110000
[2,7,4,3,1,5,6,8]=>0110010=>0100110
[6,8,4,2,3,1,5,7]=>0110001=>1000110
[3,7,5,2,4,1,6,8]=>0011010=>0101100
[7,1,3,2,8,4,5,6]=>0100011=>1100010
[2,1,7,4,8,3,5,6]=>1000011=>1100001
[5,2,8,6,1,3,4,7]=>0001101=>1011000
[2,8,3,1,4,5,6,7]=>0100001=>1000010
[7,4,8,2,3,1,5,6]=>0100011=>1100010
[4,2,7,3,1,5,6,8]=>0110010=>0100110
[8,3,7,2,1,4,5,6]=>1000011=>1100001
[6,5,2,4,7,1,3,8]=>0001110=>0111000
[6,5,7,4,1,8,2,3]=>0010111=>1110100
[7,6,4,5,1,8,2,3]=>0001111=>1111000
[8,6,4,1,3,7,2,5]=>0010111=>1110100
[6,4,3,1,8,2,5,7]=>0110101=>1010110
[7,4,1,2,8,3,5,6]=>0010011=>1100100
[4,8,1,3,5,7,2,6]=>0000011=>1100000
[7,8,4,1,3,6,2,5]=>0010101=>1010100
[6,5,8,1,3,7,2,4]=>0000111=>1110000
[5,3,6,1,8,2,4,7]=>0001101=>1011000
[4,7,3,1,8,2,5,6]=>0100011=>1100010
[8,3,1,7,2,4,5,6]=>0100011=>1100010
[2,8,1,4,7,3,5,6]=>0000011=>1100000
[3,1,8,5,4,7,6,2]=>0101111=>1111010
[4,1,5,8,3,7,6,2]=>0010111=>1110100
[4,1,5,3,8,7,6,2]=>0011111=>1111100
[4,5,1,8,2,7,6,3]=>0001111=>1111000
[4,8,5,3,1,7,6,2]=>0101111=>1111010
[4,5,2,8,1,7,6,3]=>0001111=>1111000
[4,5,2,1,8,7,6,3]=>1001111=>1111001
[5,6,2,7,8,1,4,3]=>0010101=>1010100
[4,6,2,8,7,1,5,3]=>0001111=>1111000
[4,8,6,3,7,1,5,2]=>0001111=>1111000
[4,8,6,3,7,5,1,2]=>0001111=>1111000
[4,6,8,2,7,5,1,3]=>0001011=>1101000
[4,6,2,8,7,5,1,3]=>0001111=>1111000
[5,6,2,7,4,1,8,3]=>0010111=>1110100
[5,6,7,2,3,1,8,4]=>0100011=>1100010
[5,6,7,2,8,3,1,4]=>0100011=>1100010
[5,6,7,2,1,8,3,4]=>1000011=>1100001
[5,6,7,2,1,3,8,4]=>1000011=>1100001
[5,6,1,7,8,2,4,3]=>0010101=>1010100
[5,6,1,7,2,4,8,3]=>0000111=>1110000
[5,1,6,7,8,3,4,2]=>0011001=>1001100
[4,1,6,8,7,3,5,2]=>0011011=>1101100
[3,1,8,6,7,5,4,2]=>0111011=>1101110
[4,1,6,8,7,5,3,2]=>0111011=>1101110
[5,1,6,7,4,8,3,2]=>0101011=>1101010
[5,6,1,7,8,4,2,3]=>0010101=>1010100
[4,6,8,1,7,5,2,3]=>0001011=>1101000
[4,8,6,1,7,5,3,2]=>0101111=>1111010
[5,6,7,1,8,3,2,4]=>0100011=>1100010
[5,6,7,1,3,8,2,4]=>0000011=>1100000
[5,6,7,1,3,2,8,4]=>0100011=>1100010
[5,6,7,3,1,2,8,4]=>0100011=>1100010
[5,6,7,3,8,1,2,4]=>0000011=>1100000
[5,6,8,7,4,2,1,3]=>1010011=>1100101
[5,6,7,3,8,2,1,4]=>1000011=>1100001
[7,4,6,2,3,5,1,8]=>0001110=>0111000
[1,4,8,6,3,2,5,7]=>0100101=>1010010
[7,4,1,6,3,8,5,2]=>0011111=>1111100
[7,6,3,1,5,8,4,2]=>0110111=>1110110
[6,4,2,5,7,3,1,8]=>0110110=>0110110
[4,2,5,7,6,3,1,8]=>0110110=>0110110
[7,4,5,6,1,8,3,2]=>0100111=>1110010
[4,1,5,8,6,3,2,7]=>0110101=>1010110
[3,2,7,6,1,8,5,4]=>0101111=>1111010
[4,7,5,1,6,8,2,3]=>0001011=>1101000
[8,6,5,1,2,7,4,3]=>0011111=>1111100
[3,2,5,1,4,8,7,6]=>0101011=>1101010
[8,5,4,1,3,2,7,6]=>0111011=>1101110
[1,4,2,3,6,8,7,5]=>0010011=>1100100
[5,4,8,3,7,1,6,2]=>0001111=>1111000
[4,7,1,8,2,5,3,6]=>0001011=>1101000
[6,4,1,8,5,3,7,2]=>0011111=>1111100
[8,4,6,1,3,5,2,7]=>0001101=>1011000
[3,2,5,4,7,8,1,6]=>0101001=>1001010
[5,2,4,3,7,8,1,6]=>0011001=>1001100
[8,1,6,7,2,5,3,4]=>0001011=>1101000
[3,1,7,6,5,8,2,4]=>0100111=>1110010
[1,2,7,5,6,8,3,4]=>0000011=>1100000
[6,1,4,7,2,8,3,5]=>0000111=>1110000
[3,2,1,7,6,8,4,5]=>1100011=>1100011
[3,2,8,6,4,7,1,5]=>0100111=>1110010
[7,8,4,6,3,2,1,5]=>1100101=>1010011
[1,8,6,5,3,7,2,4]=>0001111=>1111000
[8,2,5,3,6,7,1,4]=>0001011=>1101000
[3,8,5,2,7,6,1,4]=>0001111=>1111000
[4,7,5,3,1,8,6,2]=>0101111=>1111010
[4,5,3,6,8,1,7,2]=>0001011=>1101000
[3,5,2,6,1,8,7,4]=>0001111=>1111000
[1,6,3,5,7,2,8,4]=>0000111=>1110000
[1,5,4,6,7,8,2,3]=>0001001=>1001000
[8,4,6,5,7,2,1,3]=>1000111=>1110001
[7,4,5,2,6,8,1,3]=>0001011=>1101000
[5,4,2,6,8,7,1,3]=>0011011=>1101100
[7,8,4,3,1,2,6,5]=>0110101=>1010110
[6,5,1,4,3,2,8,7]=>0111101=>1011110
[2,6,5,1,4,7,3,8]=>0001110=>0111000
[3,6,4,5,2,1,8,7]=>1001101=>1011001
[5,7,4,1,3,8,6,2]=>0010111=>1110100
[7,5,4,2,3,8,1,6]=>0011011=>1101100
[5,2,6,7,3,1,4,8]=>0101010=>0101010
[2,4,3,8,6,1,5,7]=>0010101=>1010100
[7,8,1,3,5,6,2,4]=>0000101=>1010000
[7,8,3,1,5,6,2,4]=>0100101=>1010010
[7,1,3,8,5,6,2,4]=>0000111=>1110000
[1,7,8,3,5,6,2,4]=>0000101=>1010000
[5,1,7,8,3,4,6,2]=>0001101=>1011000
[1,5,7,8,3,4,6,2]=>0000101=>1010000
[3,7,1,5,8,6,2,4]=>0000111=>1110000
[1,3,7,8,2,5,6,4]=>0000101=>1010000
[3,1,7,8,5,2,6,4]=>0101101=>1011010
[1,3,7,5,8,2,6,4]=>0000111=>1110000
[3,1,7,5,8,2,6,4]=>0100111=>1110010
[3,5,7,1,8,4,6,2]=>0000111=>1110000
[3,5,7,8,1,4,6,2]=>0000101=>1010000
[5,3,7,8,4,6,1,2]=>0001101=>1011000
[5,3,7,8,4,1,6,2]=>0011101=>1011100
[5,3,7,8,1,4,6,2]=>0001101=>1011000
[5,3,7,1,8,4,6,2]=>0001111=>1111000
[1,5,3,7,8,4,2,6]=>0011001=>1001100
[5,1,3,7,8,4,2,6]=>0011001=>1001100
[3,6,2,1,4,5,8,7]=>1000101=>1010001
[8,6,2,7,4,5,1,3]=>0001111=>1111000
[5,2,8,1,7,3,4,6]=>0001011=>1101000
[4,2,3,8,1,5,6,7]=>0010001=>1000100
[2,1,5,8,4,3,6,7]=>1010001=>1000101
[5,8,3,2,7,1,4,6]=>0100011=>1100010
[2,6,8,3,7,1,4,5]=>0000011=>1100000
[5,1,8,3,7,2,4,6]=>0001011=>1101000
[5,1,8,4,6,2,3,7]=>0001101=>1011000
[3,1,8,4,2,5,6,7]=>0110001=>1000110
[3,8,4,2,1,5,6,7]=>1010001=>1000101
[3,4,2,8,1,5,6,7]=>0010001=>1000100
[4,8,5,2,6,1,3,7]=>0001101=>1011000
[4,1,7,5,6,2,8,3]=>0010111=>1110100
[5,7,4,3,8,1,6,2]=>0010111=>1110100
[5,7,4,3,8,2,6,1]=>0010111=>1110100
[3,8,4,2,6,7,5,1]=>0011011=>1101100
[3,8,4,1,6,7,5,2]=>0011011=>1101100
[6,1,7,5,2,8,4,3]=>0011111=>1111100
[5,6,4,3,2,8,1,7]=>0110101=>1010110
[2,6,7,5,3,8,4,1]=>0011011=>1101100
[6,7,4,8,2,5,3,1]=>0101011=>1101010
[2,1,6,7,5,3,8,4]=>1001011=>1101001
[3,8,4,2,1,6,7,5]=>1010011=>1100101
[5,7,4,3,8,2,1,6]=>1010011=>1100101
[6,7,4,8,1,2,5,3]=>0001011=>1101000
[6,7,5,8,1,2,4,3]=>0010011=>1100100
[6,7,4,8,3,1,2,5]=>0100011=>1100010
[3,4,8,1,2,5,7,6]=>0000011=>1100000
[6,1,3,4,8,2,5,7]=>0000101=>1010000
[6,2,3,4,8,1,5,7]=>0000101=>1010000
[3,4,8,2,1,5,7,6]=>1000011=>1100001
[6,7,5,8,2,4,3,1]=>0110011=>1100110
[6,7,5,8,3,1,4,2]=>0110011=>1100110
[3,4,8,1,5,7,6,2]=>0000111=>1110000
[2,5,7,6,1,4,8,3]=>0000111=>1110000
[6,7,4,8,2,3,5,1]=>0001011=>1101000
[6,7,4,8,1,3,5,2]=>0001011=>1101000
[2,6,7,5,1,3,8,4]=>0001011=>1101000
[6,3,1,4,8,2,5,7]=>0100101=>1010010
[6,7,4,8,1,3,2,5]=>0100011=>1100010
[6,7,5,8,4,1,3,2]=>0110011=>1100110
[6,7,4,8,2,1,3,5]=>1000011=>1100001
[6,7,4,8,1,2,3,5]=>0000011=>1100000
[1,5,6,3,4,8,2,7]=>0000101=>1010000
[1,4,3,6,5,8,2,7]=>0010101=>1010100
[8,1,3,4,7,2,6,5]=>0000111=>1110000
[5,1,7,3,4,8,2,6]=>0001011=>1101000
[6,7,8,2,3,5,4,1]=>0011001=>1001100
[5,8,6,2,3,7,4,1]=>0010111=>1110100
[2,8,3,4,7,5,6,1]=>0000111=>1110000
[1,8,3,4,7,6,2,5]=>0000111=>1110000
[8,7,2,3,6,5,4,1]=>0011111=>1111100
[3,8,1,7,5,2,6,4]=>0001111=>1111000
[4,8,1,6,7,2,5,3]=>0001011=>1101000
[2,1,3,8,4,6,5,7]=>1000101=>1010001
[8,2,1,7,4,3,6,5]=>1010111=>1110101
[1,3,2,8,5,4,6,7]=>0101001=>1001010
[8,3,1,5,7,2,6,4]=>0100111=>1110010
[8,4,5,1,7,2,6,3]=>0001111=>1111000
[1,5,6,8,7,4,2,3]=>0010011=>1100100
[8,4,5,7,6,3,2,1]=>1100111=>1110011
[1,4,8,5,7,6,2,3]=>0000111=>1110000
[2,4,8,5,7,3,6,1]=>0000111=>1110000
[4,3,8,6,5,7,2,1]=>1010111=>1110101
[6,7,2,8,5,3,4,1]=>0011011=>1101100
[5,2,7,8,6,3,4,1]=>0011101=>1011100
[4,2,8,6,7,3,5,1]=>0011011=>1101100
[3,2,8,7,5,4,6,1]=>0101111=>1111010
[3,1,8,7,5,6,2,4]=>0100111=>1110010
[4,1,8,6,7,5,2,3]=>0011011=>1101100
[5,1,7,8,6,4,2,3]=>0011101=>1011100
[6,7,1,8,5,4,2,3]=>0011011=>1101100
[7,8,3,2,6,1,4,5]=>0100101=>1010010
[3,4,8,2,6,1,7,5]=>0000111=>1110000
[7,8,4,1,5,6,3,2]=>0110101=>1010110
[7,8,1,4,5,6,3,2]=>0100101=>1010010
[7,8,1,2,6,3,4,5]=>0000101=>1010000
[7,8,5,1,4,6,3,2]=>0101101=>1011010
[7,8,4,5,1,6,3,2]=>0101101=>1011010
[5,3,8,4,1,6,7,2]=>0011011=>1101100
[6,2,4,8,1,5,3,7]=>0001101=>1011000
[3,4,8,5,1,6,7,2]=>0001011=>1101000
[3,5,8,1,4,6,7,2]=>0000011=>1100000
[1,4,8,2,6,3,7,5]=>0000111=>1110000
[5,3,8,1,4,6,7,2]=>0001011=>1101000
[4,2,6,8,1,5,3,7]=>0011001=>1001100
[7,4,2,8,1,5,3,6]=>0011011=>1101100
[6,1,7,5,8,4,3,2]=>0110111=>1110110
[6,2,1,8,4,5,3,7]=>1001101=>1011001
[1,2,7,8,5,3,4,6]=>0001001=>1001000
[6,3,7,8,5,4,1,2]=>0011101=>1011100
[6,1,5,7,8,4,3,2]=>0110101=>1010110
[1,7,5,6,8,4,3,2]=>0110011=>1100110
[3,1,8,4,5,6,7,2]=>0100011=>1100010
[2,1,4,8,6,5,3,7]=>1001101=>1011001
[2,4,1,8,6,5,3,7]=>0011101=>1011100
[4,2,1,8,6,5,3,7]=>1011101=>1011101
[3,2,7,8,5,1,4,6]=>0101001=>1001010
[2,3,7,8,5,1,4,6]=>0001001=>1001000
[2,7,3,8,5,1,4,6]=>0001011=>1101000
[3,6,2,8,5,1,4,7]=>0001101=>1011000
[4,1,2,8,7,5,3,6]=>0011011=>1101100
[1,4,2,8,7,5,3,6]=>0011011=>1101100
[7,3,6,8,5,4,1,2]=>0011011=>1101100
[7,2,1,8,5,3,4,6]=>1001011=>1101001
[1,2,6,8,4,5,3,7]=>0001001=>1001000
[7,1,6,5,8,4,3,2]=>0110111=>1110110
[6,5,7,1,8,4,3,2]=>0110111=>1110110
[5,7,6,1,8,4,3,2]=>0110111=>1110110
[6,7,1,5,8,4,3,2]=>0110011=>1100110
[6,7,3,8,5,4,1,2]=>0011011=>1101100
[7,1,2,8,4,5,3,6]=>0001011=>1101000
[7,6,1,5,8,4,3,2]=>0110111=>1110110
[7,5,6,1,8,4,3,2]=>0110111=>1110110
[9,10,7,8,5,6,2,1,3,4]=>100010101=>101010001
[9,10,7,8,4,3,5,6,1,2]=>001010101=>101010100
[9,10,7,8,4,2,5,1,3,6]=>001100101=>101001100
[9,10,7,8,3,2,1,4,5,6]=>110000101=>101000011
[9,10,6,5,7,8,3,4,1,2]=>001010101=>101010100
[9,10,6,5,7,8,2,1,3,4]=>100010101=>101010001
[9,10,6,4,7,3,5,8,1,2]=>000011101=>101110000
[9,10,6,4,7,2,5,1,3,8]=>000111001=>100111000
[9,10,6,3,7,2,1,4,5,8]=>100011001=>100110001
[9,10,5,4,3,6,7,8,1,2]=>001100101=>101001100
[9,10,5,4,2,6,7,1,3,8]=>001101001=>100101100
[9,10,5,3,2,6,1,4,7,8]=>010110001=>100011010
[9,10,4,3,2,1,5,6,7,8]=>111000001=>100000111
[8,7,9,10,5,6,3,4,1,2]=>001010101=>101010100
[8,7,9,10,5,6,2,1,3,4]=>100010101=>101010001
[8,7,9,10,4,3,5,6,1,2]=>001010101=>101010100
[8,7,9,10,4,2,5,1,3,6]=>001100101=>101001100
[8,7,9,10,3,2,1,4,5,6]=>110000101=>101000011
[8,6,9,5,7,10,3,4,1,2]=>001000111=>111000100
[8,6,9,5,7,10,2,1,3,4]=>100000111=>111000001
[8,6,9,4,7,3,5,10,1,2]=>000001111=>111100000
[8,6,9,3,7,2,1,4,5,10]=>100001110=>011100001
[8,5,9,4,3,6,7,10,1,2]=>001000111=>111000100
[8,5,9,4,2,6,7,1,3,10]=>001001110=>011100100
[8,5,9,3,2,6,1,4,7,10]=>010010110=>011010010
[8,4,9,3,2,1,5,6,7,10]=>110000110=>011000011
[7,6,5,8,9,10,3,4,1,2]=>001011001=>100110100
[7,6,5,8,9,10,2,1,3,4]=>100011001=>100110001
[7,6,4,8,9,3,5,10,1,2]=>000011011=>110110000
[7,6,4,8,9,2,5,1,3,10]=>000111010=>010111000
[7,6,3,8,9,2,1,4,5,10]=>100011010=>010110001
[7,5,4,8,3,6,9,10,1,2]=>000101101=>101101000
[7,5,4,8,2,6,9,1,3,10]=>000101110=>011101000
[7,4,3,8,2,1,5,6,9,10]=>101001100=>001100101
[6,5,4,3,7,8,9,10,1,2]=>001110001=>100011100
[6,5,4,2,7,8,9,1,3,10]=>001110010=>010011100
[6,5,3,2,7,8,1,4,9,10]=>010110100=>001011010
[11,12,9,10,7,8,5,6,2,1,3,4]=>10001010101=>10101010001
[11,12,9,10,7,8,4,3,5,6,1,2]=>00101010101=>10101010100
[11,12,9,10,7,8,4,2,5,1,3,6]=>00110010101=>10101001100
[11,12,9,10,7,8,3,2,1,4,5,6]=>11000010101=>10101000011
[11,12,9,10,6,5,7,8,3,4,1,2]=>00101010101=>10101010100
[11,12,9,10,6,5,7,8,2,1,3,4]=>10001010101=>10101010001
[11,12,9,10,6,4,7,3,5,8,1,2]=>00001110101=>10101110000
[11,12,9,10,5,4,3,6,7,8,1,2]=>00110010101=>10101001100
[11,12,9,10,5,3,2,6,1,4,7,8]=>01011000101=>10100011010
[11,12,8,7,9,10,5,6,3,4,1,2]=>00101010101=>10101010100
[11,12,8,7,9,10,5,6,2,1,3,4]=>10001010101=>10101010001
[11,12,8,7,9,10,4,3,5,6,1,2]=>00101010101=>10101010100
[11,12,8,7,9,10,4,2,5,1,3,6]=>00110010101=>10101001100
[11,12,8,7,9,10,3,2,1,4,5,6]=>11000010101=>10101000011
[11,12,8,6,9,5,7,10,3,4,1,2]=>00100011101=>10111000100
[11,12,8,6,9,5,7,10,2,1,3,4]=>10000011101=>10111000001
[11,12,8,6,9,4,7,3,5,10,1,2]=>00000111101=>10111100000
[11,12,8,5,9,4,3,6,7,10,1,2]=>00100011101=>10111000100
[11,12,7,6,4,8,9,3,5,10,1,2]=>00001101101=>10110110000
[11,12,7,5,4,8,3,6,9,10,1,2]=>00010110101=>10101101000
[11,12,6,4,3,2,7,1,5,8,9,10]=>01101100001=>10000110110
[11,12,5,4,3,2,1,6,7,8,9,10]=>11110000001=>10000001111
[10,9,11,12,7,8,5,6,3,4,1,2]=>00101010101=>10101010100
[10,9,11,12,7,8,5,6,2,1,3,4]=>10001010101=>10101010001
[10,9,11,12,7,8,4,3,5,6,1,2]=>00101010101=>10101010100
[10,9,11,12,7,8,4,2,5,1,3,6]=>00110010101=>10101001100
[10,9,11,12,7,8,3,2,1,4,5,6]=>11000010101=>10101000011
[10,9,11,12,6,5,7,8,3,4,1,2]=>00101010101=>10101010100
[10,9,11,12,6,5,7,8,2,1,3,4]=>10001010101=>10101010001
[10,9,11,12,6,4,7,3,5,8,1,2]=>00001110101=>10101110000
[10,9,11,12,5,4,3,6,7,8,1,2]=>00110010101=>10101001100
[10,9,11,12,5,3,2,6,1,4,7,8]=>01011000101=>10100011010
[10,8,11,7,9,12,5,6,3,4,1,2]=>00101000111=>11100010100
[10,8,11,7,9,12,5,6,2,1,3,4]=>10001000111=>11100010001
[10,8,11,7,9,12,4,3,5,6,1,2]=>00101000111=>11100010100
[10,8,11,6,9,5,7,12,3,4,1,2]=>00100001111=>11110000100
[10,8,11,6,9,4,7,3,5,12,1,2]=>00000101111=>11110100000
[10,8,11,6,9,3,7,2,1,4,5,12]=>10000101110=>01110100001
[10,8,11,5,9,4,3,6,7,12,1,2]=>00100001111=>11110000100
[10,8,11,4,9,3,2,1,5,6,7,12]=>11000001110=>01110000011
[10,7,11,6,5,8,9,12,3,4,1,2]=>00101000111=>11100010100
[10,7,11,6,5,8,9,12,2,1,3,4]=>10001000111=>11100010001
[10,7,11,6,4,8,9,3,5,12,1,2]=>00001001111=>11110010000
[10,7,11,6,3,8,9,2,1,4,5,12]=>10001001110=>01110010001
[10,7,11,5,4,8,3,6,9,12,1,2]=>00010010111=>11101001000
[10,7,11,5,3,8,2,6,1,4,9,12]=>00011010110=>01101011000
[9,8,6,10,11,5,7,12,3,4,1,2]=>00100011011=>11011000100
[9,8,6,10,11,4,7,3,5,12,1,2]=>00000111011=>11011100000
[9,8,6,10,11,4,7,2,5,1,3,12]=>00010111010=>01011101000
[9,8,5,10,11,4,3,6,7,12,1,2]=>00100011011=>11011000100
[9,8,5,10,11,3,2,6,1,4,7,12]=>01001011010=>01011010010
[9,7,6,10,5,8,11,12,3,4,1,2]=>00100101101=>10110100100
[9,7,6,10,5,8,11,12,2,1,3,4]=>10000101101=>10110100001
[9,7,6,10,4,8,11,3,5,12,1,2]=>00000101111=>11110100000
[9,7,6,10,3,8,11,2,1,4,5,12]=>10000101110=>01110100001
[9,7,5,10,4,8,3,6,11,12,1,2]=>00000111101=>10111100000
[9,7,5,10,4,8,2,6,11,1,3,12]=>00000111110=>01111100000
[9,7,5,10,3,8,2,6,1,4,11,12]=>00001111100=>00111110000
[9,7,4,10,3,8,2,1,5,6,11,12]=>10000111100=>00111100001
[9,6,5,10,4,3,7,8,11,12,1,2]=>00101001101=>10110010100
[8,7,6,5,9,10,11,12,3,4,1,2]=>00101110001=>10001110100
[8,7,6,5,9,10,11,12,2,1,3,4]=>10001110001=>10001110001
[8,7,6,4,9,10,11,3,5,12,1,2]=>00001110011=>11001110000
[8,7,5,4,9,10,3,6,11,12,1,2]=>00010110101=>10101101000
[8,7,5,4,9,10,2,6,11,1,3,12]=>00010110110=>01101101000
[8,6,5,4,9,3,7,10,11,12,1,2]=>00011011001=>10011011000
[8,6,5,4,9,2,7,10,11,1,3,12]=>00011011010=>01011011000
[8,5,4,3,9,2,1,6,7,10,11,12]=>10110011000=>00011001101
[7,5,4,3,2,8,1,6,9,10,11,12]=>01110110000=>00001101110
[6,5,4,3,2,1,7,8,9,10,11,12]=>11111000000=>00000011111
[7,1,6,5,3,2,4,8]=>0101110=>0111010
[1,8,7,5,3,2,4,6]=>0101011=>1101010
[1,8,7,4,2,5,3,6]=>0011011=>1101100
[8,7,4,2,5,3,6,1]=>0011111=>1111100
[7,1,6,4,2,5,3,8]=>0011110=>0111100
[2,6,5,4,7,1,3,8]=>0001110=>0111000
[7,1,5,3,6,4,2,8]=>0011110=>0111100
[5,3,7,1,6,4,2,8]=>0011110=>0111100
[5,3,6,4,2,7,1,8]=>0011110=>0111100
[1,5,3,8,7,4,2,6]=>0011011=>1101100
[7,4,2,8,6,3,5,1]=>0011111=>1111100
[5,3,6,1,8,7,4,2]=>0011111=>1111100
[6,1,5,3,8,7,4,2]=>0011111=>1111100
[2,8,7,5,4,6,1,3]=>0001111=>1111000
[2,3,1,8,7,5,4,6]=>0101011=>1101010
[5,3,8,7,4,2,1,6]=>1011011=>1101101
[7,4,2,1,8,6,3,5]=>1010111=>1110101
[8,6,3,5,7,4,2,1]=>1010111=>1110101
[1,8,6,3,5,7,4,2]=>0010111=>1110100
[6,3,8,5,2,1,7,4]=>1001111=>1111001
[8,6,3,7,4,2,1,5]=>1010111=>1110101
[2,8,6,4,7,5,1,3]=>0001111=>1111000
[5,1,8,6,3,7,4,2]=>0011111=>1111100
[6,3,7,4,1,8,5,2]=>0011111=>1111100
[8,5,2,6,3,7,4,1]=>0011111=>1111100
[6,1,8,7,4,2,5,3]=>0011111=>1111100
[8,6,3,7,4,2,5,1]=>0011111=>1111100
[1,8,6,3,2,4,7,5]=>0100111=>1110010
[8,6,3,2,4,7,5,1]=>0101111=>1111010
[7,5,1,8,6,3,2,4]=>0101111=>1111010
[6,1,8,7,5,3,2,4]=>0101111=>1111010
[4,3,2,8,7,6,1,5]=>0110111=>1110110
[2,4,5,1,3,8,7,6]=>0001011=>1101000
[7,5,8,6,3,2,4,1]=>0110111=>1110110
[1,7,5,8,6,3,2,4]=>0100111=>1110010
[1,7,4,2,5,8,6,3]=>0010111=>1110100
[8,6,3,1,7,4,2,5]=>0110111=>1110110
[8,7,4,2,5,3,1,6]=>0111011=>1101110
[5,3,1,8,7,4,2,6]=>0111011=>1101110
[4,1,8,7,5,3,2,6]=>0111011=>1101110
[2,8,6,4,1,3,7,5]=>0010111=>1110100
[4,1,8,6,3,2,7,5]=>0110111=>1110110
[7,4,2,8,6,3,1,5]=>0110111=>1110110
[6,3,1,8,5,2,7,4]=>0101111=>1111010
[8,5,2,6,3,1,7,4]=>0101111=>1111010
[7,4,8,5,2,6,3,1]=>0101111=>1111010
[1,8,5,2,7,4,6,3]=>0001111=>1111000
[8,5,2,7,4,6,3,1]=>0101111=>1111010
[7,4,6,3,1,8,5,2]=>0101111=>1111010
[6,3,1,7,4,8,5,2]=>0101111=>1111010
[8,6,3,1,5,7,4,2]=>0110111=>1110110
[4,1,7,5,8,6,3,2]=>0110111=>1110110
[2,3,1,7,5,8,6,4]=>0100111=>1110010
[7,4,8,5,2,1,6,3]=>1001111=>1111001
[8,5,2,1,7,4,6,3]=>1001111=>1111001
[1,7,4,6,3,8,5,2]=>0001111=>1111000
[3,6,5,2,1,4,8,7]=>1001101=>1011001
[3,5,6,2,1,4,8,7]=>1000101=>1010001
[3,5,7,8,1,4,2,6]=>0010001=>1000100
[4,1,8,5,7,3,2,6]=>0110011=>1100110
[4,1,7,5,8,3,2,6]=>0110011=>1100110
[2,1,5,8,7,4,3,6]=>1010011=>1100101
[2,1,5,7,8,4,3,6]=>1010001=>1000101
[5,1,7,4,8,3,2,6]=>0101011=>1101010
[4,7,2,8,3,6,1,5]=>0000111=>1110000
[4,6,2,7,3,1,8,5]=>0100111=>1110010
[3,7,8,2,4,1,6,5]=>0010101=>1010100
[3,8,7,2,4,1,6,5]=>0010111=>1110100
[3,8,6,2,4,1,7,5]=>0010111=>1110100
[1,3,2,7,6,5,10,9,8,4]=>010011111=>111110010
[1,4,3,6,5,2,10,9,8,7]=>001110111=>111011100
[1,4,3,7,6,2,10,9,8,5]=>001011111=>111110100
[1,5,4,7,6,3,10,9,8,2]=>000111111=>111111000
[1,4,3,8,7,2,10,9,6,5]=>001011111=>111110100
[1,5,4,8,7,3,10,9,6,2]=>000111111=>111111000
[2,3,1,6,5,4,10,9,8,7]=>010110111=>111011010
[2,3,1,7,6,5,10,9,8,4]=>010011111=>111110010
[2,4,1,6,5,3,10,9,8,7]=>001110111=>111011100
[2,4,1,7,6,3,10,9,8,5]=>001011111=>111110100
[2,5,1,7,6,4,10,9,8,3]=>000111111=>111111000
[2,4,1,8,7,3,10,9,6,5]=>001011111=>111110100
[2,5,1,8,7,4,10,9,6,3]=>000111111=>111111000
[3,4,2,6,5,1,10,9,8,7]=>001110111=>111011100
[3,4,2,7,6,1,10,9,8,5]=>001011111=>111110100
[3,5,2,7,6,1,10,9,8,4]=>000111111=>111111000
[4,5,3,7,6,2,10,9,8,1]=>000111111=>111111000
[3,4,2,8,7,1,10,9,6,5]=>001011111=>111110100
[3,5,2,8,7,1,10,9,6,4]=>000111111=>111111000
[4,5,3,8,7,2,10,9,6,1]=>000111111=>111111000
[2,5,1,6,4,3,10,9,8,7]=>001110111=>111011100
[2,5,1,7,4,3,10,9,8,6]=>001101111=>111101100
[2,6,1,7,5,4,10,9,8,3]=>000111111=>111111000
[2,5,1,8,4,3,10,9,7,6]=>001101111=>111101100
[2,6,1,8,5,4,10,9,7,3]=>000111111=>111111000
[3,5,2,6,4,1,10,9,8,7]=>001110111=>111011100
[3,5,2,7,4,1,10,9,8,6]=>001101111=>111101100
[3,6,2,7,5,1,10,9,8,4]=>000111111=>111111000
[4,6,3,7,5,2,10,9,8,1]=>000111111=>111111000
[3,5,2,8,4,1,10,9,7,6]=>001101111=>111101100
[3,6,2,8,5,1,10,9,7,4]=>000111111=>111111000
[4,6,3,8,5,2,10,9,7,1]=>000111111=>111111000
[3,7,2,8,6,1,10,9,5,4]=>000111111=>111111000
[4,7,3,8,6,2,10,9,5,1]=>000111111=>111111000
[2,5,1,9,4,3,10,8,7,6]=>001101111=>111101100
[2,6,1,9,5,4,10,8,7,3]=>000111111=>111111000
[3,5,2,9,4,1,10,8,7,6]=>001101111=>111101100
[3,6,2,9,5,1,10,8,7,4]=>000111111=>111111000
[4,6,3,9,5,2,10,8,7,1]=>000111111=>111111000
[3,7,2,9,6,1,10,8,5,4]=>000111111=>111111000
[6,2,8,4,1,7,3,5]=>0010111=>1110100
[7,3,4,8,1,6,2,5]=>0000111=>1110000
[6,3,4,8,1,7,2,5]=>0000111=>1110000
[5,3,4,8,1,2,7,6]=>0001011=>1101000
[4,3,5,8,1,2,7,6]=>0010011=>1100100
[1,8,5,4,2,3,7,6]=>0011011=>1101100
[3,5,4,8,1,2,7,6]=>0001011=>1101000
[4,5,3,8,1,2,7,6]=>0001011=>1101000
[6,4,3,8,1,7,2,5]=>0010111=>1110100
[7,4,3,8,1,6,2,5]=>0010111=>1110100
[6,5,3,8,7,1,2,4]=>0001111=>1111000
[5,6,3,8,7,1,2,4]=>0000111=>1110000
[4,6,3,8,1,7,2,5]=>0000111=>1110000
[2,6,8,4,1,7,3,5]=>0010011=>1100100
[1,8,7,4,2,6,3,5]=>0010111=>1110100
[5,7,3,8,6,1,2,4]=>0000111=>1110000
[3,7,5,8,6,1,2,4]=>0000111=>1110000
[2,7,8,5,6,1,3,4]=>0000101=>1010000
[1,8,7,5,6,2,3,4]=>0000111=>1110000
[2,6,8,5,7,1,3,4]=>0000011=>1100000
[5,3,6,8,7,1,2,4]=>0001011=>1101000
[6,3,5,8,7,1,2,4]=>0000111=>1110000
[7,2,8,5,6,1,3,4]=>0000111=>1110000
[5,2,8,6,7,1,3,4]=>0001011=>1101000
[1,8,3,2,7,6,4,5]=>0100111=>1110010
[5,2,8,7,6,1,3,4]=>0001111=>1111000
[6,2,8,7,5,1,3,4]=>0001111=>1111000
[3,4,7,8,1,6,2,5]=>0000101=>1010000
[1,8,5,7,6,2,3,4]=>0000111=>1110000
[2,5,8,7,6,1,3,4]=>0000111=>1110000
[7,4,6,5,8,1,2,3]=>0000111=>1110000
[3,6,7,8,5,1,2,4]=>0001001=>1001000
[2,6,8,7,5,1,3,4]=>0001011=>1101000
[1,8,6,7,5,2,3,4]=>0001011=>1101000
[2,7,8,6,5,1,3,4]=>0001101=>1011000
[5,7,6,4,8,1,2,3]=>0000111=>1110000
[6,3,8,7,5,1,2,4]=>0001111=>1111000
[2,8,7,4,1,3,5,6]=>0010011=>1100100
[5,4,8,7,1,3,2,6]=>0101011=>1101010
[4,8,6,1,3,2,5,7]=>0100101=>1010010
[5,4,2,7,6,8,1,3]=>0011011=>1101100
[2,8,7,1,4,5,3,6]=>0001011=>1101000
[4,2,1,8,7,3,5,6]=>1010011=>1100101
[5,1,6,3,2,8,7,4]=>0101111=>1111010
[4,6,1,8,7,3,2,5]=>0100111=>1110010
[8,7,2,3,5,4,1,6]=>0011011=>1101100
[5,3,1,4,8,7,2,6]=>0101011=>1101010
[4,3,5,2,8,7,1,6]=>0011011=>1101100
[3,4,2,8,6,1,5,7]=>0010101=>1010100
[3,7,6,8,1,5,2,4]=>0001011=>1101000
[8,1,4,2,3,6,7,5]=>0010011=>1100100
[3,7,2,1,8,6,4,5]=>1000111=>1110001
[2,8,6,1,7,3,5,4]=>0001111=>1111000
[1,7,6,3,5,8,2,4]=>0000111=>1110000
[3,7,5,1,6,8,2,4]=>0001011=>1101000
[3,6,5,8,1,4,7,2]=>0000111=>1110000
[8,1,5,6,4,7,2,3]=>0000111=>1110000
[3,6,7,4,1,8,2,5]=>0010011=>1100100
[1,7,4,6,8,2,5,3]=>0001011=>1101000
[7,5,8,2,6,3,1,4]=>0100111=>1110010
[2,7,1,6,5,4,8,3]=>0001111=>1111000
[7,3,2,6,1,8,5,4]=>0101111=>1111010
[6,4,7,2,3,1,8,5]=>0100111=>1110010
[5,3,1,8,4,6,2,7]=>0101101=>1011010
[3,8,1,6,7,4,2,5]=>0010011=>1100100
[2,7,4,3,6,8,1,5]=>0010011=>1100100
[2,8,4,6,1,5,3,7]=>0001101=>1011000
[8,4,1,6,3,2,5,7]=>0110101=>1010110
[4,7,3,8,5,2,1,6]=>1001011=>1101001
[3,1,7,4,8,5,2,6]=>0101011=>1101010
[7,4,1,6,3,2,8,5]=>0110111=>1110110
[3,8,6,2,7,4,1,5]=>0010111=>1110100
[7,3,1,4,5,2,8,6]=>0101011=>1101010
[6,1,4,8,5,3,2,7]=>0101101=>1011010
[8,1,2,4,6,7,5,3]=>0001011=>1101000
[8,1,3,6,7,5,4,2]=>0011011=>1101100
[7,5,2,3,8,6,1,4]=>0001111=>1111000
[8,6,2,4,1,3,7,5]=>0010111=>1110100
[4,7,5,1,8,6,3,2]=>0101111=>1111010
[4,7,3,2,8,5,6,1]=>0100111=>1110010
[8,4,5,7,6,1,3,2]=>0100111=>1110010
[7,5,8,4,2,3,6,1]=>0010111=>1110100
[3,8,4,6,1,7,5,2]=>0001111=>1111000
[3,7,4,6,5,2,8,1]=>0001111=>1111000
[4,2,7,6,1,5,8,3]=>0010111=>1110100
[8,3,1,4,5,7,6,2]=>0100111=>1110010
[3,5,1,6,8,4,7,2]=>0001011=>1101000
[6,1,5,7,3,8,4,2]=>0010111=>1110100
[5,8,4,7,3,2,6,1]=>0100111=>1110010
[7,2,6,5,8,4,1,3]=>0010111=>1110100
[8,3,2,5,1,6,7,4]=>0101011=>1101010
[2,6,8,3,7,4,1,5]=>0010011=>1100100
[8,1,5,6,4,7,3,2]=>0100111=>1110010
[2,5,8,1,6,4,7,3]=>0000111=>1110000
[7,4,1,8,3,2,6,5]=>0110111=>1110110
[8,3,7,4,2,1,6,5]=>1010111=>1110101
[5,2,6,8,3,1,7,4]=>0101011=>1101010
[3,6,5,8,4,1,7,2]=>0010111=>1110100
[7,3,6,1,8,4,5,2]=>0001111=>1111000
[8,2,7,3,4,6,5,1]=>0001111=>1111000
[7,3,8,2,5,6,4,1]=>0010111=>1110100
[5,7,3,1,6,4,8,2]=>0100111=>1110010
[6,1,3,2,4,8,7,5]=>0100111=>1110010
[8,7,4,2,3,6,1,5]=>0010111=>1110100
[8,7,1,5,4,2,3,6]=>0011011=>1101100
[3,7,1,5,2,8,6,4]=>0001111=>1111000
[8,7,2,5,4,1,3,6]=>0011011=>1101100
[8,7,2,5,3,1,4,6]=>0101011=>1101010
[5,2,8,7,1,4,3,6]=>0011011=>1101100
[7,1,8,6,2,4,3,5]=>0010111=>1110100
[8,1,6,2,7,5,3,4]=>0001111=>1111000
[7,1,6,2,8,5,3,4]=>0001111=>1111000
[6,3,4,1,7,2,8,5]=>0010111=>1110100
[7,2,4,3,5,1,8,6]=>0011011=>1101100
[5,1,7,2,3,8,6,4]=>0001111=>1111000
[8,2,3,5,1,7,6,4]=>0001111=>1111000
[7,6,3,1,4,8,2,5]=>0100111=>1110010
[6,1,8,2,7,5,3,4]=>0001111=>1111000
[7,2,8,1,6,5,3,4]=>0001111=>1111000
[7,2,6,4,3,8,1,5]=>0010111=>1110100
[5,1,7,4,3,8,2,6]=>0011011=>1101100
[5,3,1,7,4,8,2,6]=>0101011=>1101010
[7,4,8,2,1,5,3,6]=>1001011=>1101001
[8,2,4,1,6,3,7,5]=>0010111=>1110100
[8,2,7,5,1,6,4,3]=>0011111=>1111100
[6,1,7,3,2,8,5,4]=>0101111=>1111010
[4,7,2,1,6,3,8,5]=>1000111=>1110001
[6,2,1,5,3,8,4,7]=>1001101=>1011001
[5,3,1,6,2,8,4,7]=>0101101=>1011010
[6,1,5,2,8,4,3,7]=>0011101=>1011100
[7,4,3,8,1,5,2,6]=>0011011=>1101100
[7,4,8,1,5,3,2,6]=>0101011=>1101010
[6,1,5,3,2,8,4,7]=>0101101=>1011010
[6,3,2,8,4,1,5,7]=>0110101=>1010110
[7,3,4,2,8,5,1,6]=>0011011=>1101100
[7,1,6,3,4,2,8,5]=>0010111=>1110100
[8,5,1,3,7,4,2,6]=>0011011=>1101100
[3,8,6,1,5,2,7,4]=>0001111=>1111000
[8,6,1,3,7,5,2,4]=>0001111=>1111000
[4,8,5,6,1,7,3,2]=>0100111=>1110010
[6,7,1,3,8,5,2,4]=>0001011=>1101000
[3,6,7,1,5,2,8,4]=>0001011=>1101000
[7,1,3,8,4,2,6,5]=>0010111=>1110100
[5,6,2,7,1,3,8,4]=>0000111=>1110000
[5,6,2,8,1,3,7,4]=>0000111=>1110000
[6,1,8,3,7,5,2,4]=>0001111=>1111000
[7,4,2,1,5,8,3,6]=>1010011=>1100101
[7,4,1,5,8,3,2,6]=>0110011=>1100110
[7,3,2,6,4,8,1,5]=>0100111=>1110010
[6,4,2,7,3,8,1,5]=>0010111=>1110100
[5,1,8,3,7,4,2,6]=>0011011=>1101100
[7,4,8,3,1,5,2,6]=>0101011=>1101010
[5,2,1,7,4,8,3,6]=>1001011=>1101001
[6,1,8,4,5,2,7,3]=>0001111=>1111000
[7,1,6,4,5,2,8,3]=>0001111=>1111000
[3,5,2,7,1,6,8,4]=>0001011=>1101000
[4,5,7,3,1,6,8,2]=>0100011=>1100010
[4,5,7,2,8,6,1,3]=>0000111=>1110000
[3,5,1,7,2,6,8,4]=>0001011=>1101000
[4,5,7,2,8,1,3,6]=>0000011=>1100000
[4,6,7,2,1,5,8,3]=>1000011=>1100001
[4,6,7,1,3,8,5,2]=>0001011=>1101000
[3,6,1,5,7,8,4,2]=>0010101=>1010100
[4,6,7,1,5,8,3,2]=>0100011=>1100010
[6,1,3,7,4,8,5,2]=>0001111=>1111000
[3,2,1,7,4,8,5,6]=>1100011=>1100011
[4,1,5,2,7,6,3,8]=>0011110=>0111100
[2,5,1,3,7,6,4,8]=>0001110=>0111000
[2,5,1,4,3,8,6,7]=>0011001=>1001100
[3,7,2,1,5,8,6,4]=>1000111=>1110001
[6,2,7,1,4,8,5,3]=>0001111=>1111000
[3,7,4,2,1,8,5,6]=>1010011=>1100101
[7,2,5,3,1,8,6,4]=>0101111=>1111010
[7,5,1,4,2,8,6,3]=>0011111=>1111100
[7,5,4,1,3,8,6,2]=>0011111=>1111100
[5,3,2,1,7,6,4,8]=>1101110=>0111011
[6,3,2,8,1,5,7,4]=>0100111=>1110010
[7,4,3,2,8,1,6,5]=>0110111=>1110110
[7,6,2,4,8,3,5,1]=>0001111=>1111000
[7,3,6,4,8,1,5,2]=>0001111=>1111000
[2,7,5,3,8,1,4,6]=>0001011=>1101000
[1,8,5,3,6,4,2,7]=>0011101=>1011100
[8,6,2,3,7,5,4,1]=>0011111=>1111100
[8,6,3,2,7,5,4,1]=>0111111=>1111110
[8,3,2,7,1,6,4,5]=>0100111=>1110010
[7,2,6,1,5,4,3,8]=>0011110=>0111100
[8,5,7,4,3,6,2,1]=>1010111=>1110101
[8,5,7,2,4,6,3,1]=>0100111=>1110010
[8,4,6,7,1,3,2,5]=>0100011=>1100010
[2,8,5,6,1,4,3,7]=>0010101=>1010100
[7,2,6,8,4,1,5,3]=>0011011=>1101100
[7,6,4,8,3,2,5,1]=>0101111=>1111010
[6,5,8,1,4,2,7,3]=>0010111=>1110100
[6,5,8,4,1,3,7,2]=>0010111=>1110100
[5,4,8,3,2,1,7,6]=>1101011=>1101011
[4,3,7,2,1,6,5,8]=>1010110=>0110101
[2,5,8,1,4,3,7,6]=>0010011=>1100100
[3,6,8,2,1,5,7,4]=>1000011=>1100001
[5,7,4,8,1,3,6,2]=>0000111=>1110000
[5,7,1,4,8,2,6,3]=>0000111=>1110000
[2,7,4,1,8,3,6,5]=>0010111=>1110100
[3,5,1,8,4,2,7,6]=>0011011=>1101100
[4,1,5,7,3,6,2,8]=>0010110=>0110100
[4,2,5,8,3,1,7,6]=>0110011=>1100110
[6,1,2,7,8,3,5,4]=>0001101=>1011000
[5,3,1,8,6,4,2,7]=>0111101=>1011110
[3,1,8,4,7,5,2,6]=>0101011=>1101010
[4,2,8,7,3,5,1,6]=>0011011=>1101100
[4,8,1,7,6,2,3,5]=>0000111=>1110000
[6,8,1,4,7,5,2,3]=>0001011=>1101000
[7,3,8,1,6,4,2,5]=>0010111=>1110100
[4,7,8,1,5,3,2,6]=>0101001=>1001010
[7,1,8,6,2,5,3,4]=>0001111=>1111000
[5,8,7,1,3,6,4,2]=>0010111=>1110100
[3,8,7,2,1,6,4,5]=>1000111=>1110001
[2,8,7,1,6,3,5,4]=>0001111=>1111000
[3,7,6,1,5,4,2,8]=>0011110=>0111100
[4,8,7,6,1,3,5,2]=>0001111=>1111000
[5,8,7,2,6,1,4,3]=>0010111=>1110100
[6,8,1,7,5,2,4,3]=>0011011=>1101100
[7,3,8,6,5,1,2,4]=>0001111=>1111000
[5,7,8,4,3,1,2,6]=>0110001=>1000110
[5,8,6,4,3,2,1,7]=>1110101=>1010111
[8,7,3,6,4,2,1,5]=>1010111=>1110101
[6,1,4,2,5,3,7,8]=>0011100=>0011100
[1,3,7,5,4,2,8,6]=>0011011=>1101100
[6,1,3,5,4,2,7,8]=>0011100=>0011100
[6,1,2,5,4,7,3,8]=>0001110=>0111000
[5,1,6,3,4,7,8,2]=>0001101=>1011000
[5,2,6,3,4,7,1,8]=>0001110=>0111000
[3,4,7,5,8,6,1,2]=>0000111=>1110000
[2,4,7,1,5,3,8,6]=>0001011=>1101000
[2,3,6,7,4,8,1,5]=>0000011=>1100000
[1,3,6,7,4,8,5,2]=>0001011=>1101000
[2,7,6,5,3,1,8,4]=>0101111=>1111010
[5,2,6,1,4,7,8,3]=>0001101=>1011000
[4,7,6,5,2,1,8,3]=>1001111=>1111001
[5,3,6,2,4,1,7,8]=>0011100=>0011100
[5,7,4,2,1,3,6,8]=>1010010=>0100101
[6,3,1,5,4,7,8,2]=>0101101=>1011010
[5,3,6,1,4,2,7,8]=>0011100=>0011100
[1,7,4,2,6,3,8,5]=>0010111=>1110100
[5,7,4,1,2,3,6,8]=>0010010=>0100100
[6,4,1,2,5,3,7,8]=>0011100=>0011100
[4,7,6,3,8,5,1,2]=>0001111=>1111000
[3,7,6,5,2,8,1,4]=>0001111=>1111000
[3,7,6,5,1,2,8,4]=>0001111=>1111000
[4,7,2,6,1,3,8,5]=>0000111=>1110000
[2,7,1,6,8,3,5,4]=>0001011=>1101000
[2,7,6,5,8,1,4,3]=>0010111=>1110100
[9,1,2,3,4,5,6,8,7]=>00000011=>11000000
[10,1,2,3,4,5,6,7,9,8]=>000000011=>110000000
[9,1,2,3,4,5,7,8,6]=>00000011=>11000000
[2,3,4,5,6,9,7,8,1]=>00000011=>11000000
[2,3,4,5,6,7,8,10,9,1]=>000000011=>110000000
[9,2,1,8,7,6,5,4,3]=>10111111=>11111101
[2,11,10,9,8,7,6,5,4,3,1]=>0111111111=>1111111110
[3,2,10,9,8,7,6,5,4,1]=>011111111=>111111110
[3,9,2,8,7,6,5,4,1]=>00111111=>11111100
[4,2,9,8,7,6,5,3,1]=>01111111=>11111110
[5,2,8,7,6,4,3,1]=>0111111=>1111110
[8,2,7,6,1,5,4,3]=>0011111=>1111100
[9,2,8,1,7,6,5,4,3]=>00111111=>11111100
[8,4,1,7,6,5,3,2]=>0111111=>1111110
[9,3,1,8,7,6,5,4,2]=>01111111=>11111110
[10,2,1,9,8,7,6,5,4,3]=>101111111=>111111101
[11,1,10,9,8,7,6,5,4,3,2]=>0111111111=>1111111110
[4,5,6,2,3,8,1,7]=>0000101=>1010000
[4,5,3,2,7,8,1,6]=>0101001=>1001010
[6,5,7,3,8,4,2,1]=>1010111=>1110101
[6,8,7,2,4,3,5,1]=>0011011=>1101100
[3,2,7,4,5,8,1,6]=>0100011=>1100010
[6,8,1,5,2,4,3,7]=>0011001=>1001100
[8,3,4,6,1,5,2,7]=>0001101=>1011000
[2,3,4,7,5,8,1,6]=>0000011=>1100000
[6,3,4,7,8,2,5,1]=>0001101=>1011000
[5,3,7,4,8,6,1,2]=>0001111=>1111000
[8,3,6,4,1,7,2,5]=>0010111=>1110100
[1,3,7,4,8,6,2,5]=>0000111=>1110000
[3,7,8,5,4,1,2,6]=>0011001=>1001100
[5,4,3,1,7,8,2,6]=>0111001=>1001110
[5,7,6,2,8,4,1,3]=>0010111=>1110100
[6,1,7,5,8,3,4,2]=>0010111=>1110100
[7,5,6,4,1,3,8,2]=>0010111=>1110100
[1,5,6,8,4,7,3,2]=>0100011=>1100010
[4,1,3,7,6,5,8,2]=>0010111=>1110100
[3,4,1,7,5,8,6,2]=>0010111=>1110100
[8,5,7,4,3,1,6,2]=>0110111=>1110110
[6,8,5,1,7,2,4,3]=>0011011=>1101100
[8,2,4,1,3,7,6,5]=>0010111=>1110100
[7,8,3,6,2,1,4,5]=>1000101=>1010001
[8,1,7,4,2,3,6,5]=>0010111=>1110100
[1,8,7,2,3,5,6,4]=>0000111=>1110000
[2,8,3,1,6,7,5,4]=>0101011=>1101010
[8,2,3,1,5,7,6,4]=>0100111=>1110010
[3,8,4,1,2,7,6,5]=>0010111=>1110100
[5,4,7,2,3,6,8,1]=>0001011=>1101000
[6,3,2,1,8,4,7,5]=>1100111=>1110011
[2,3,7,4,1,8,5,6]=>0010011=>1100100
[6,4,1,3,2,7,8,5]=>0110101=>1010110
[2,7,8,5,1,3,6,4]=>0001101=>1011000
[8,2,5,6,7,1,3,4]=>0000011=>1100000
[2,8,5,4,7,6,1,3]=>0001111=>1111000
[6,7,1,5,8,2,4,3]=>0010011=>1100100
[4,8,7,6,2,3,5,1]=>0001111=>1111000
[7,8,1,5,3,2,6,4]=>0101101=>1011010
[6,5,7,3,8,2,1,4]=>1000111=>1110001
[8,1,4,7,2,5,6,3]=>0000111=>1110000
[7,3,4,6,1,5,8,2]=>0000111=>1110000
[8,3,4,5,7,1,6,2]=>0000111=>1110000
[4,2,6,8,3,1,5,7]=>0110001=>1000110
[3,7,6,2,4,5,1,8]=>0001110=>0111000
[2,3,6,5,8,1,4,7]=>0000101=>1010000
[2,3,5,8,6,1,4,7]=>0000101=>1010000
[4,2,3,8,6,1,5,7]=>0010101=>1010100
[6,4,1,2,8,3,5,7]=>0010101=>1010100
[1,2,3,7,4,6,8,5]=>0000011=>1100000
[3,2,7,1,4,5,8,6]=>0100011=>1100010
[2,1,5,3,8,7,4,6]=>1001011=>1101001
[5,8,3,2,4,1,6,7]=>0110001=>1000110
[4,2,7,1,8,3,5,6]=>0010011=>1100100
[4,1,8,2,7,3,5,6]=>0010011=>1100100
[1,2,7,5,3,8,4,6]=>0001011=>1101000
[3,2,7,1,4,8,5,6]=>0100011=>1100010
[1,2,3,7,6,8,4,5]=>0000011=>1100000
[1,2,3,6,8,7,4,5]=>0000011=>1100000
[1,2,3,7,8,4,6,5]=>0000101=>1010000
[1,2,3,6,8,4,7,5]=>0000011=>1100000
[1,2,3,7,8,6,4,5]=>0000101=>1010000
[6,2,8,3,7,5,1,4]=>0001111=>1111000
[4,2,8,3,7,5,6,1]=>0010111=>1110100
[7,3,4,8,6,5,1,2]=>0001111=>1111000
[5,3,4,8,7,2,6,1]=>0001111=>1111000
[4,3,5,8,7,2,6,1]=>0010111=>1110100
[4,6,3,8,5,7,2,1]=>1000111=>1110001
[7,5,3,8,6,2,4,1]=>0011111=>1111100
[2,6,8,3,7,4,5,1]=>0001011=>1101000
[1,8,4,3,7,5,6,2]=>0010111=>1110100
[2,5,8,3,7,4,6,1]=>0000111=>1110000
[7,4,3,8,6,2,5,1]=>0011111=>1111100
[3,5,4,8,7,2,6,1]=>0001111=>1111000
[4,5,3,8,6,7,2,1]=>1001011=>1101001
[3,6,7,8,4,5,2,1]=>1001001=>1001001
[2,6,8,5,4,7,3,1]=>0101011=>1101010
[1,8,5,6,4,7,3,2]=>0100111=>1110010
[2,5,8,6,4,7,3,1]=>0100111=>1110010
[7,4,6,5,8,3,2,1]=>1100111=>1110011
[6,3,7,8,4,5,2,1]=>1001101=>1011001
[4,3,7,8,5,6,2,1]=>1010101=>1010101
[5,2,8,6,4,7,3,1]=>0101111=>1111010
[4,2,8,6,5,7,3,1]=>0110111=>1110110
[3,2,8,6,7,4,5,1]=>0101011=>1101010
[2,3,8,7,5,4,6,1]=>0001111=>1111000
[1,8,2,7,4,5,6,3]=>0000111=>1110000
[7,2,8,6,3,4,5,1]=>0001111=>1111000
[6,2,8,4,5,7,3,1]=>0100111=>1110010
[5,2,8,4,6,7,3,1]=>0101011=>1101010
[4,2,8,5,6,7,3,1]=>0110011=>1100110
[4,3,6,8,5,7,2,1]=>1010011=>1100101
[3,4,6,8,7,2,5,1]=>0001011=>1101000
[7,3,5,8,6,2,4,1]=>0010111=>1110100
[1,8,3,5,7,4,6,2]=>0000111=>1110000
[2,7,8,4,5,6,3,1]=>0100101=>1010010
[3,7,5,8,4,6,2,1]=>1000111=>1110001
[5,7,4,6,8,3,2,1]=>1100011=>1100011
[3,6,5,8,4,7,2,1]=>1000111=>1110001
[2,6,8,4,5,7,3,1]=>0100011=>1100010
[4,2,7,1,3,8,5,6]=>0010011=>1100100
[4,2,5,1,3,8,6,7]=>0011001=>1001100
[5,3,6,1,7,2,4,8]=>0001110=>0111000
[3,7,1,2,5,8,6,4]=>0000111=>1110000
[3,7,4,1,2,8,5,6]=>0010011=>1100100
[7,5,1,3,4,8,6,2]=>0001111=>1111000
[7,5,1,2,4,8,6,3]=>0001111=>1111000
[6,4,2,3,7,1,5,8]=>0010110=>0110100
[7,6,3,8,1,2,5,4]=>0001111=>1111000
[7,4,2,3,8,1,6,5]=>0010111=>1110100
[4,7,5,2,8,1,3,6]=>0001011=>1101000
[8,2,6,3,7,1,4,5]=>0000111=>1110000
[8,6,1,2,7,4,5,3]=>0001111=>1111000
[8,4,7,1,2,3,6,5]=>0000111=>1110000
[8,5,7,1,2,4,6,3]=>0000111=>1110000
[8,5,7,1,3,4,6,2]=>0000111=>1110000
[8,6,2,7,1,3,5,4]=>0001111=>1111000
[3,8,5,6,1,2,4,7]=>0000101=>1010000
[3,7,5,8,1,2,4,6]=>0000011=>1100000
[7,6,4,8,1,3,5,2]=>0001111=>1111000
[6,5,8,1,2,4,7,3]=>0000111=>1110000
[3,6,8,1,2,5,7,4]=>0000011=>1100000
[3,7,2,4,8,1,6,5]=>0000111=>1110000
[4,6,3,8,1,2,5,7]=>0000101=>1010000
[4,6,3,7,1,2,5,8]=>0000110=>0110000
[4,1,7,8,2,3,6,5]=>0010101=>1010100
[5,1,2,8,6,3,4,7]=>0001101=>1011000
[5,3,8,1,6,2,4,7]=>0001101=>1011000
[6,1,8,5,2,3,4,7]=>0001101=>1011000
[6,1,7,5,2,3,4,8]=>0001110=>0111000
[6,8,1,3,7,4,5,2]=>0001011=>1101000
[7,2,8,1,6,3,4,5]=>0000111=>1110000
[4,7,8,2,5,1,3,6]=>0001001=>1001000
[6,8,2,7,1,4,5,3]=>0001011=>1101000
[4,8,7,1,3,5,6,2]=>0000111=>1110000
[3,8,7,1,2,4,6,5]=>0000111=>1110000
[4,8,7,1,2,3,6,5]=>0000111=>1110000
[5,8,7,1,2,4,6,3]=>0000111=>1110000
[5,8,7,1,3,4,6,2]=>0000111=>1110000
[7,1,8,6,2,3,5,4]=>0001111=>1111000
[5,8,6,4,1,2,3,7]=>0010101=>1010100
[7,8,4,1,2,5,3,6]=>0011001=>1001100
[7,8,1,2,6,5,3,4]=>0001101=>1011000
[1,4,8,2,7,5,3,6]=>0001011=>1101000
[6,1,3,4,7,2,5,8]=>0000110=>0110000
[7,8,2,1,6,3,5,4]=>1001101=>1011001
[6,1,2,7,5,4,3,8]=>0011110=>0111100
[1,2,8,7,5,4,3,6]=>0011011=>1101100
[5,1,7,3,6,4,8,2]=>0001111=>1111000
[6,2,1,5,7,4,3,8]=>1010110=>0110101
[6,2,3,7,4,1,5,8]=>0010110=>0110100
[3,4,8,7,5,6,1,2]=>0000111=>1110000
[2,3,8,7,4,1,5,6]=>0010011=>1100100
[2,7,3,8,6,4,1,5]=>0010111=>1110100
[1,8,3,7,6,4,5,2]=>0001111=>1111000
[5,2,7,1,4,6,8,3]=>0001011=>1101000
[4,6,7,5,2,1,8,3]=>1001011=>1101001
[6,3,1,4,5,7,8,2]=>0100101=>1010010
[5,3,1,4,6,2,7,8]=>0101100=>0011010
[5,1,2,4,7,6,8,3]=>0001011=>1101000
[5,7,4,1,2,6,3,8]=>0010110=>0110100
[4,8,1,2,6,7,3,5]=>0000011=>1100000
[4,1,7,8,2,6,3,5]=>0010101=>1010100
[1,2,8,7,6,5,3,4]=>0001111=>1111000
[3,1,2,4,6,8,7,5]=>0100011=>1100010
[3,1,8,4,5,7,6,2]=>0100111=>1110010
[3,2,8,5,4,7,1,6]=>0101011=>1101010
[4,2,8,1,5,3,7,6]=>0011011=>1101100
[4,3,8,5,7,6,1,2]=>0010111=>1110100
[4,8,2,1,6,3,7,5]=>1000111=>1110001
[3,8,6,5,2,7,1,4]=>0001111=>1111000
[3,8,5,6,1,7,4,2]=>0010111=>1110100
[3,5,7,8,1,2,6,4]=>0000101=>1010000
[3,7,8,5,2,1,6,4]=>1001101=>1011001
[3,7,2,8,4,1,6,5]=>0010111=>1110100
[2,8,1,7,4,6,5,3]=>0001111=>1111000
[2,8,7,5,1,6,4,3]=>0011111=>1111100
[2,8,6,7,5,1,4,3]=>0011011=>1101100
[5,1,3,4,6,7,2,8]=>0001010=>0101000
[1,3,4,8,7,5,2,6]=>0001011=>1101000
[8,2,4,1,7,3,5,6]=>0010011=>1100100
[8,6,1,4,2,3,7,5]=>0010111=>1110100
[3,6,1,4,2,8,7,5]=>0010111=>1110100
[1,6,8,4,3,7,2,5]=>0010011=>1100100
[3,1,4,7,8,5,2,6]=>0101001=>1001010
[6,1,7,4,3,8,2,5]=>0010111=>1110100
[1,8,7,4,3,6,2,5]=>0010111=>1110100
[7,4,1,3,8,2,6,5]=>0010111=>1110100
[4,8,2,3,1,5,7,6]=>0100011=>1100010
[4,8,6,2,1,3,7,5]=>1000111=>1110001
[2,7,4,1,8,3,5,6]=>0010011=>1100100
[1,7,8,4,2,3,6,5]=>0010101=>1010100
[4,7,1,3,8,2,6,5]=>0000111=>1110000
[8,7,1,3,4,2,6,5]=>0010111=>1110100
[1,7,4,3,6,2,8,5]=>0010111=>1110100
[3,8,6,4,5,2,1,7]=>1001101=>1011001
[3,8,4,6,5,2,1,7]=>1001101=>1011001
[2,4,3,7,5,8,1,6]=>0010011=>1100100
[1,4,7,3,6,2,8,5]=>0000111=>1110000
[1,8,3,4,2,6,7,5]=>0010011=>1100100
[6,4,1,3,7,2,8,5]=>0010111=>1110100
[8,1,4,3,6,2,7,5]=>0010111=>1110100
[4,2,3,8,5,7,1,6]=>0010011=>1100100
[2,8,5,7,3,4,1,6]=>0010011=>1100100
[5,8,2,6,4,3,1,7]=>0110101=>1010110
[7,2,5,8,4,3,1,6]=>0110011=>1100110
[4,2,3,5,8,7,1,6]=>0010011=>1100100
[8,2,3,5,4,7,1,6]=>0001011=>1101000
[6,1,8,3,4,2,7,5]=>0010111=>1110100
[1,8,6,4,2,3,7,5]=>0010111=>1110100
[3,8,4,5,6,2,1,7]=>1000101=>1010001
[2,4,3,5,7,8,1,6]=>0010001=>1000100
[3,8,6,5,4,2,1,7]=>1011101=>1011101
[6,3,1,4,2,8,7,5]=>0110111=>1110110
[7,3,8,1,2,6,4,5]=>0000111=>1110000
[7,1,4,5,3,2,6,8]=>0101010=>0101010
[1,8,4,2,6,5,3,7]=>0011101=>1011100
[5,1,4,8,6,3,2,7]=>0101101=>1011010
[5,3,1,8,4,7,2,6]=>0101011=>1101010
[4,3,8,1,5,7,2,6]=>0010011=>1100100
[6,3,1,2,5,7,4,8]=>0100110=>0110010
[7,1,4,2,6,5,3,8]=>0011110=>0111100
[3,8,4,1,6,5,2,7]=>0011101=>1011100
[7,5,3,6,4,8,2,1]=>1001111=>1111001
[7,3,6,4,5,8,2,1]=>1000111=>1110001
[8,7,2,4,5,1,6,3]=>0001111=>1111000
[7,1,5,4,8,6,3,2]=>0101111=>1111010
[2,7,5,4,8,6,3,1]=>0101111=>1111010
[2,1,8,7,5,3,6,4]=>1001111=>1111001
[5,8,3,7,4,1,6,2]=>0010111=>1110100
[8,1,7,4,2,6,5,3]=>0011111=>1111100
[5,6,3,1,8,4,7,2]=>0100111=>1110010
[5,7,1,4,8,6,3,2]=>0100111=>1110010
[3,5,7,4,8,6,2,1]=>1000111=>1110001
[2,6,7,4,5,8,3,1]=>0100011=>1100010
[6,1,7,4,5,8,3,2]=>0100111=>1110010
[5,3,7,4,8,6,2,1]=>1001111=>1111001
[8,5,3,6,1,4,7,2]=>0001111=>1111000
[5,4,3,6,8,2,7,1]=>0011011=>1101100
[6,5,3,7,4,8,2,1]=>1001111=>1111001
[7,5,8,4,1,6,3,2]=>0110111=>1110110
[2,7,8,4,5,1,6,3]=>0001101=>1011000
[5,7,3,8,4,1,6,2]=>0010111=>1110100
[5,6,3,8,1,4,7,2]=>0000111=>1110000
[8,4,1,2,5,6,7,3]=>0010011=>1100100
[3,7,8,4,1,6,5,2]=>0011101=>1011100
[6,8,3,1,2,5,7,4]=>0100011=>1100010
[8,7,1,4,5,2,6,3]=>0001111=>1111000
[8,7,3,1,5,4,2,6]=>0111011=>1101110
[6,8,2,7,4,3,1,5]=>0110011=>1100110
[6,8,2,3,7,5,1,4]=>0001011=>1101000
[7,6,2,5,4,8,1,3]=>0001111=>1111000
[2,6,5,1,8,4,3,7]=>0011101=>1011100
[5,2,7,3,8,6,1,4]=>0001111=>1111000
[2,4,8,3,1,7,5,6]=>0100011=>1100010
[4,8,3,2,1,7,6,5]=>1100111=>1110011
[6,8,3,7,2,1,5,4]=>1001011=>1101001
[2,7,6,3,8,1,4,5]=>0000111=>1110000
[2,1,5,4,8,7,3,6]=>1001011=>1101001
[3,8,5,4,2,1,7,6]=>1011011=>1101101
[3,2,8,7,5,4,1,6]=>0111011=>1101110
[2,8,6,5,4,3,1,7]=>0111101=>1011110
[5,4,2,6,3,1,8,7]=>0111101=>1011110
[6,5,2,1,3,4,8,7]=>1001101=>1011001
[8,5,2,7,3,1,4,6]=>0101011=>1101010
[7,3,6,5,2,8,4,1]=>0011111=>1111100
[7,6,2,3,4,8,5,1]=>0001111=>1111000
[8,7,5,3,1,4,2,6]=>0111011=>1101110
[7,1,5,3,8,4,6,2]=>0001111=>1111000
[6,7,2,3,5,8,4,1]=>0010011=>1100100
[3,7,6,4,2,8,5,1]=>0011111=>1111100
[2,1,7,6,4,8,5,3]=>1001111=>1111001
[2,1,8,7,4,3,5,6]=>1010011=>1100101
[5,8,3,7,2,1,4,6]=>1000011=>1100001
[3,8,7,4,2,1,5,6]=>1010011=>1100101
[7,8,2,3,5,1,4,6]=>0001001=>1001000
[2,8,6,3,1,4,7,5]=>0100111=>1110010
[8,1,6,3,2,4,5,7]=>0100101=>1010010
[5,7,1,4,8,3,6,2]=>0000111=>1110000
[6,1,7,5,4,8,3,2]=>0101111=>1111010
[6,3,7,5,8,4,2,1]=>1010111=>1110101
[7,6,1,5,8,3,4,2]=>0010111=>1110100
[8,6,7,5,1,3,2,4]=>0101011=>1101010
[8,5,2,6,1,7,3,4]=>0001111=>1111000
[5,4,2,6,8,3,7,1]=>0011011=>1101100
[6,5,2,8,1,4,3,7]=>0011101=>1011100
[7,4,2,8,1,3,6,5]=>0010111=>1110100
[2,7,8,4,5,1,3,6]=>0001001=>1001000
[5,7,3,8,4,1,2,6]=>0010011=>1100100
[2,4,8,1,5,6,3,7]=>0000101=>1010000
[3,4,8,1,5,2,7,6]=>0001011=>1101000
[3,6,8,4,1,2,7,5]=>0010011=>1100100
[4,8,1,2,5,3,6,7]=>0001001=>1001000
[8,1,2,4,3,5,6,7]=>0010001=>1000100
[2,3,4,6,5,7,8,9,10,1]=>000010001=>100010000
[2,3,5,6,4,7,8,9,1]=>00001001=>10010000
[2,3,6,4,5,7,8,9,1]=>00001001=>10010000
[9,1,2,4,5,3,6,7,8]=>00010001=>10001000
[10,1,2,3,5,4,6,7,8,9]=>000100001=>100001000
[5,8,7,4,6,3,2,1]=>1100111=>1110011
[4,8,7,6,3,5,2,1]=>1001111=>1111001
[3,8,7,6,5,2,4,1]=>0011111=>1111100
[7,9,6,8,5,4,3,2,1]=>11110011=>11001111
[5,8,4,7,6,3,2,1]=>1100111=>1110011
[6,9,8,5,7,4,3,2,1]=>11100111=>11100111
[6,8,5,4,7,3,2,1]=>1101011=>1101011
[5,9,8,7,4,6,3,2,1]=>11001111=>11110011
[3,8,7,6,2,5,4,1]=>0011111=>1111100
[4,9,8,7,6,3,5,2,1]=>10011111=>11111001
[4,8,7,6,3,2,5,1]=>0101111=>1111010
[3,9,8,7,6,5,2,4,1]=>00111111=>11111100
[3,8,7,6,5,2,1,4]=>1001111=>1111001
[8,6,9,7,4,5,2,3,1]=>01010111=>11101010
[8,6,9,4,7,5,2,3,1]=>01010111=>11101010
[8,6,9,4,7,2,5,3,1]=>01010111=>11101010
[8,6,9,4,7,3,5,1,2]=>00010111=>11101000
[8,6,9,5,7,3,4,1,2]=>00100111=>11100100
[8,7,9,5,6,3,4,1,2]=>00101011=>11010100
[9,7,10,8,5,6,3,4,1,2]=>001010111=>111010100
[8,6,4,9,7,5,2,3,1]=>01011111=>11111010
[9,7,10,5,8,6,3,4,1,2]=>001010111=>111010100
[8,6,9,4,2,7,5,3,1]=>01110111=>11101110
[9,7,10,5,8,3,6,4,1,2]=>001010111=>111010100
[8,6,9,4,7,2,1,5,3]=>10010111=>11101001
[7,5,8,4,6,3,1,2]=>0100111=>1110010
[8,6,9,4,7,3,5,2,1]=>10010111=>11101001
[9,7,10,5,8,3,6,2,4,1]=>001010111=>111010100
[8,6,9,5,7,2,4,1,3]=>00100111=>11100100
[9,7,10,5,8,4,6,2,3,1]=>010010111=>111010010
[7,6,8,2,5,1,4,3]=>0011011=>1101100
[8,7,9,4,6,3,5,1,2]=>00011011=>11011000
[9,7,10,6,8,4,5,2,3,1]=>010100111=>111001010
[9,6,8,5,7,3,4,1,2]=>00100111=>11100100
[9,8,10,6,7,4,5,2,3,1]=>010101011=>110101010
[3,5,2,4,7,6,1,8]=>0001110=>0111000
[3,5,4,7,2,6,1,8]=>0001110=>0111000
[3,5,4,7,6,1,2,8]=>0001110=>0111000
[3,5,4,7,6,1,8,2]=>0001111=>1111000
[3,5,7,4,6,1,8,2]=>0000111=>1110000
[3,5,7,4,6,1,2,8]=>0000110=>0110000
[3,5,7,4,6,2,1,8]=>1000110=>0110001
[3,2,5,7,4,6,1,8]=>0100110=>0110010
[3,5,2,7,6,4,1,8]=>0011110=>0111100
[3,5,7,2,6,4,1,8]=>0010110=>0110100
[5,3,7,6,2,4,1,8]=>0011110=>0111100
[5,3,7,6,1,2,8,4]=>0001111=>1111000
[5,3,7,6,1,4,2,8]=>0011110=>0111100
[5,3,7,6,4,1,2,8]=>0011110=>0111100
[3,5,7,2,6,1,4,8]=>0000110=>0110000
[3,5,2,7,6,1,4,8]=>0001110=>0111000
[5,3,7,6,4,1,8,2]=>0011111=>1111100
[3,7,5,4,1,8,2,6]=>0011011=>1101100
[3,7,5,4,1,8,6,2]=>0011111=>1111100
[3,7,5,1,4,8,6,2]=>0001111=>1111000
[3,7,5,1,4,8,2,6]=>0001011=>1101000
[3,5,7,1,2,6,8,4]=>0000011=>1100000
[3,5,7,2,1,6,8,4]=>1000011=>1100001
[3,5,2,7,1,6,4,8]=>0001110=>0111000
[3,5,7,2,1,6,4,8]=>1000110=>0110001
[5,3,7,1,6,2,4,8]=>0001110=>0111000
[3,5,7,1,4,6,8,2]=>0000011=>1100000
[3,5,7,1,4,6,2,8]=>0000110=>0110000
[3,5,7,1,4,2,6,8]=>0010010=>0100100
[3,5,7,2,1,4,6,8]=>1000010=>0100001
[3,5,2,7,1,4,6,8]=>0001010=>0101000
[3,2,5,7,4,1,6,8]=>0110010=>0100110
[3,5,2,7,4,1,6,8]=>0011010=>0101100
[3,5,7,4,2,1,6,8]=>1010010=>0100101
[3,5,7,4,1,2,6,8]=>0010010=>0100100
[3,5,4,7,1,6,8,2]=>0001011=>1101000
[3,5,4,7,1,2,6,8]=>0001010=>0101000
[3,5,4,7,2,1,6,8]=>1001010=>0101001
[3,5,4,2,7,1,6,8]=>0011010=>0101100
[3,2,5,4,7,1,6,8]=>0101010=>0101010
[3,5,4,7,2,1,8,6]=>1001011=>1101001
[3,5,4,7,1,2,8,6]=>0001011=>1101000
[5,7,6,3,1,8,4,2]=>0110111=>1110110
[5,7,6,3,1,8,2,4]=>0100111=>1110010
[3,5,7,4,1,2,8,6]=>0010011=>1100100
[3,5,7,4,2,1,8,6]=>1010011=>1100101
[3,2,5,7,4,1,8,6]=>0110011=>1100110
[3,2,5,7,1,4,8,6]=>0100011=>1100010
[3,5,2,7,1,4,8,6]=>0001011=>1101000
[3,5,7,2,1,4,8,6]=>1000011=>1100001
[3,5,7,1,4,2,8,6]=>0010011=>1100100
[3,7,5,2,1,8,6,4]=>1001111=>1111001
[3,7,2,5,1,8,6,4]=>0001111=>1111000
[3,2,7,5,1,8,6,4]=>0101111=>1111010
[3,2,7,5,1,8,4,6]=>0101011=>1101010
[3,7,2,5,1,8,4,6]=>0001011=>1101000
[3,7,5,2,1,8,4,6]=>1001011=>1101001
[6,1,2,5,7,4,8,3]=>0000111=>1110000
[6,3,2,7,4,1,8,5]=>0110111=>1110110
[2,1,7,5,8,4,6,3]=>1000111=>1110001
[2,7,3,6,8,4,1,5]=>0010011=>1100100
[2,1,8,3,4,7,5,6]=>1000011=>1100001
[5,1,7,2,4,8,3,6]=>0001011=>1101000
[3,4,2,6,7,1,8,5]=>0010011=>1100100
[3,5,8,7,2,1,6,4]=>1000111=>1110001
[1,3,4,5,6,7,9,2,8]=>00000001=>10000000
[2,3,4,5,6,7,1,9,8]=>00000101=>10100000
[2,1,4,5,6,7,8,9,3]=>10000001=>10000001
[3,1,4,5,6,7,8,2,9]=>01000010=>01000010
[5,8,3,4,1,7,6,2]=>0010111=>1110100
[5,8,7,2,4,1,6,3]=>0010111=>1110100
[3,8,6,4,1,7,5,2]=>0011111=>1111100
[4,3,5,6,8,1,7,2]=>0010011=>1100100
[3,7,6,4,1,8,5,2]=>0011111=>1111100
[3,7,4,1,8,6,5,2]=>0011111=>1111100
[3,8,4,1,7,6,5,2]=>0011111=>1111100
[3,2,7,6,1,5,4,8]=>0101110=>0111010
[3,2,8,7,6,1,5,4]=>0101111=>1111010
[5,7,8,2,4,1,6,3]=>0010101=>1010100
[4,2,5,8,1,6,7,3]=>0010011=>1100100
[4,2,5,8,1,7,3,6]=>0010011=>1100100
[5,8,2,4,1,6,3,7]=>0010101=>1010100
[8,4,2,6,5,1,3,7]=>0011101=>1011100
[3,2,6,8,1,5,4,7]=>0101001=>1001010
[8,3,2,5,6,1,4,7]=>0100101=>1010010
[3,2,8,6,7,1,5,4]=>0101011=>1101010
[3,2,6,8,7,1,5,4]=>0101011=>1101010
[3,2,6,7,1,5,4,8]=>0101010=>0101010
[8,7,3,2,5,6,1,4]=>0100111=>1110010
[7,2,8,1,5,3,6,4]=>0001111=>1111000
[8,4,2,7,5,1,3,6]=>0011011=>1101100
[7,4,2,8,5,1,3,6]=>0011011=>1101100
[7,2,4,1,8,3,6,5]=>0010111=>1110100
[3,2,8,5,7,1,4,6]=>0100011=>1100010
[2,6,5,7,1,8,3,4]=>0000111=>1110000
[2,5,1,8,7,4,3,6]=>0011011=>1101100
[8,1,4,6,3,5,2,7]=>0001101=>1011000
[8,3,5,4,1,6,2,7]=>0011101=>1011100
[8,6,3,4,1,5,2,7]=>0011101=>1011100
[5,4,7,6,8,2,3,1]=>0101011=>1101010
[4,1,8,2,3,7,6,5]=>0010111=>1110100
[2,1,8,5,3,4,7,6]=>1001011=>1101001
[5,2,4,6,8,7,3,1]=>0101011=>1101010
[1,6,8,3,4,5,7,2]=>0000011=>1100000
[5,7,4,8,6,1,3,2]=>0100111=>1110010
[5,4,2,6,7,8,1,3]=>0011001=>1001100
[6,4,2,7,3,5,8,1]=>0010111=>1110100
[7,4,1,8,3,5,6,2]=>0010111=>1110100
[6,5,4,8,7,3,1,2]=>0101111=>1111010
[8,7,4,2,1,3,6,5]=>1010111=>1110101
[8,7,1,3,2,5,6,4]=>0100111=>1110010
[6,8,2,3,1,7,5,4]=>0101011=>1101010
[7,4,3,2,6,8,5,1]=>0111011=>1101110
[2,7,4,3,8,5,6,1]=>0010111=>1110100
[8,3,7,2,1,5,6,4]=>1000111=>1110001
[5,7,8,2,4,3,1,6]=>0110001=>1000110
[8,4,7,3,2,6,1,5]=>0100111=>1110010
[8,3,1,6,7,4,2,5]=>0110011=>1100110
[3,2,5,7,4,8,1,6]=>0100011=>1100010
[8,2,7,3,4,1,5,6]=>0010011=>1100100
[7,1,6,3,5,8,2,4]=>0000111=>1110000
[2,8,5,6,7,1,4,3]=>0010011=>1100100
[1,5,2,7,8,6,4,3]=>0011101=>1011100
[2,6,8,5,1,4,7,3]=>0001011=>1101000
[1,4,2,8,6,5,7,3]=>0010111=>1110100
[3,5,1,6,8,7,2,4]=>0001011=>1101000
[5,7,6,2,1,3,8,4]=>1000111=>1110001
[2,5,8,7,4,1,6,3]=>0010111=>1110100
[4,1,7,5,2,6,8,3]=>0011011=>1101100
[7,6,2,4,5,1,8,3]=>0001111=>1111000
[7,3,4,2,5,8,6,1]=>0010111=>1110100
[8,7,4,2,5,1,6,3]=>0011111=>1111100
[8,1,4,5,2,6,7,3]=>0001011=>1101000
[5,2,4,8,6,7,1,3]=>0001011=>1101000
[8,5,6,2,1,3,7,4]=>1000111=>1110001
[4,2,1,5,6,7,8,3]=>1010001=>1000101
[3,4,6,5,1,7,8,2]=>0001101=>1011000
[7,3,5,2,4,6,1,8]=>0001110=>0111000
[5,3,7,2,4,6,1,8]=>0001110=>0111000
[3,7,5,2,4,6,1,8]=>0001110=>0111000
[5,7,3,2,4,6,1,8]=>0100110=>0110010
[1,5,3,2,4,7,6,8]=>0101010=>0101010
[1,5,3,2,7,4,6,8]=>0101010=>0101010
[5,7,3,2,1,4,6,8]=>1100010=>0100011
[5,7,3,2,4,1,6,8]=>0110010=>0100110
[3,7,2,5,4,1,6,8]=>0011010=>0101100
[5,1,3,2,4,7,6,8]=>0101010=>0101010
[5,1,3,2,7,4,6,8]=>0101010=>0101010
[7,1,3,2,5,4,6,8]=>0101010=>0101010
[1,7,3,2,5,4,6,8]=>0101010=>0101010
[7,1,3,5,2,4,6,8]=>0001010=>0101000
[5,1,3,7,2,4,6,8]=>0001010=>0101000
[3,2,7,5,1,4,6,8]=>0101010=>0101010
[3,7,5,1,2,4,6,8]=>0001010=>0101000
[5,7,3,1,2,4,6,8]=>0100010=>0100010
[1,5,3,7,2,4,6,8]=>0001010=>0101000
[5,3,2,7,4,1,6,8]=>0111010=>0101110
[5,3,2,4,7,1,6,8]=>0101010=>0101010
[5,3,2,1,4,7,6,8]=>1101010=>0101011
[5,3,2,1,7,4,6,8]=>1101010=>0101011
[1,3,2,7,5,4,6,8]=>0101010=>0101010
[1,3,7,2,5,4,6,8]=>0001010=>0101000
[7,3,1,2,5,4,6,8]=>0101010=>0101010
[5,3,1,2,7,4,6,8]=>0101010=>0101010
[5,3,1,2,4,7,6,8]=>0101010=>0101010
[3,2,5,1,4,7,6,8]=>0101010=>0101010
[7,3,1,5,2,4,6,8]=>0101010=>0101010
[1,3,7,5,2,4,6,8]=>0001010=>0101000
[7,5,1,3,2,4,6,8]=>0101010=>0101010
[5,7,1,3,2,4,6,8]=>0100010=>0100010
[3,7,1,5,2,4,6,8]=>0001010=>0101000
[3,7,1,2,5,4,6,8]=>0001010=>0101000
[3,7,2,1,5,4,6,8]=>1001010=>0101001
[3,2,1,7,5,4,6,8]=>1101010=>0101011
[3,1,2,7,5,4,6,8]=>0101010=>0101010
[3,1,7,2,5,4,6,8]=>0101010=>0101010
[3,1,7,5,2,4,6,8]=>0101010=>0101010
[7,1,5,3,2,4,6,8]=>0101010=>0101010
[1,7,5,3,2,4,6,8]=>0101010=>0101010
[1,2,3,4,5,7,9,6,8]=>00000001=>10000000
[1,2,3,4,6,9,5,7,8]=>00000001=>10000000
[1,2,3,5,9,4,6,7,8]=>00000001=>10000000
[1,2,4,9,3,5,6,7,8]=>00000001=>10000000
[1,3,9,2,4,5,6,7,8]=>00000001=>10000000
[1,9,8,7,6,2,5,4,3]=>00111111=>11111100
[2,9,8,7,1,6,5,4,3]=>00111111=>11111100
[1,9,8,2,7,6,5,4,3]=>00111111=>11111100
[1,9,2,8,7,6,5,4,3]=>00111111=>11111100
[3,9,8,7,6,5,2,1,4]=>10011111=>11111001
[1,10,9,8,7,6,5,2,4,3]=>001111111=>111111100
[4,9,8,7,6,1,2,5,3]=>00011111=>11111000
[1,10,9,8,7,6,2,5,4,3]=>001111111=>111111100
[1,8,7,4,2,6,5,3]=>0011111=>1111100
[5,9,8,7,1,2,6,4,3]=>00101111=>11110100
[2,10,9,8,7,1,6,5,4,3]=>001111111=>111111100
[2,8,5,1,7,6,4,3]=>0011111=>1111100
[6,9,8,2,1,7,5,4,3]=>10110111=>11101101
[1,10,9,8,2,7,6,5,4,3]=>001111111=>111111100
[6,8,5,1,2,7,4,3]=>0011011=>1101100
[7,9,1,2,8,6,5,4,3]=>00111011=>11011100
[1,10,9,2,8,7,6,5,4,3]=>001111111=>111111100
[8,1,2,9,7,6,5,4,3]=>00111111=>11111100
[2,10,1,9,8,7,6,5,4,3]=>001111111=>111111100
[3,10,9,8,7,6,5,2,1,4]=>100111111=>111111001
[1,11,10,9,8,7,6,5,2,4,3]=>0011111111=>1111111100
[1,9,8,7,6,3,2,5,4]=>01011111=>11111010
[4,10,9,8,7,6,1,2,5,3]=>000111111=>111111000
[1,11,10,9,8,7,6,2,5,4,3]=>0011111111=>1111111100
[1,9,8,7,4,2,6,5,3]=>00111111=>11111100
[4,9,8,7,6,3,2,1,5]=>11001111=>11110011
[5,10,9,8,7,1,2,6,4,3]=>001011111=>111110100
[2,11,10,9,8,7,1,6,5,4,3]=>0011111111=>1111111100
[2,8,1,4,7,6,5,3]=>0001111=>1111000
[2,9,8,5,1,7,6,4,3]=>00111111=>11111100
[5,9,8,7,4,1,2,6,3]=>00101111=>11110100
[6,10,9,8,2,1,7,5,4,3]=>101101111=>111101101
[1,11,10,9,8,2,7,6,5,4,3]=>0011111111=>1111111100
[1,9,6,2,8,7,5,4,3]=>00111111=>11111100
[1,8,7,4,3,2,6,5]=>0110111=>1110110
[6,9,8,5,1,2,7,4,3]=>00110111=>11101100
[7,10,9,1,2,8,6,5,4,3]=>001110111=>111011100
[1,11,10,9,2,8,7,6,5,4,3]=>0011111111=>1111111100
[1,7,2,9,8,6,5,4,3]=>00111111=>11111100
[1,8,5,4,2,7,6,3]=>0011111=>1111100
[7,9,6,2,1,8,5,4,3]=>10111011=>11011101
[8,10,1,2,9,7,6,5,4,3]=>001111011=>110111100
[2,11,10,1,9,8,7,6,5,4,3]=>0011111111=>1111111100
[8,7,1,2,9,6,5,4,3]=>00111111=>11111100
[9,2,1,10,8,7,6,5,4,3]=>101111111=>111111101
[1,11,2,10,9,8,7,6,5,4,3]=>0011111111=>1111111100
[1,2,11,10,9,8,7,6,5,4,3]=>0011111111=>1111111100
[7,5,3,4,2,8,1,6]=>0011011=>1101100
[8,5,3,6,2,4,7,1]=>0001111=>1111000
[8,5,6,3,7,4,2,1]=>1010111=>1110101
[8,5,6,2,7,4,3,1]=>0110111=>1110110
[8,7,6,3,4,1,5,2]=>0011111=>1111100
[1,7,2,3,6,8,5,4]=>0001011=>1101000
[3,5,6,4,8,2,7,1]=>0000111=>1110000
[3,5,1,4,8,2,7,6]=>0001011=>1101000
[1,7,5,4,8,2,6,3]=>0001111=>1111000
[3,7,5,1,6,4,8,2]=>0001111=>1111000
[2,7,5,4,8,1,3,6]=>0001011=>1101000
[2,7,5,4,8,6,1,3]=>0001111=>1111000
[1,7,5,4,8,6,3,2]=>0101111=>1111010
[2,5,1,4,8,7,3,6]=>0001011=>1101000
[3,6,4,2,8,7,1,5]=>0010111=>1110100
[3,5,2,4,8,1,6,7]=>0001001=>1001000
[3,5,6,4,8,1,2,7]=>0000101=>1010000
[1,5,6,4,8,7,2,3]=>0000111=>1110000
[3,6,4,1,8,7,2,5]=>0010111=>1110100
[3,6,4,5,8,7,2,1]=>1000111=>1110001
[1,6,4,3,8,5,2,7]=>0011101=>1011100
[7,1,3,4,5,8,2,6]=>0000011=>1100000
[7,6,1,4,5,3,8,2]=>0001111=>1111000
[7,6,1,3,5,4,8,2]=>0001111=>1111000
[7,1,3,2,5,8,4,6]=>0100011=>1100010
[1,6,4,2,8,5,3,7]=>0011101=>1011100
[7,6,5,8,2,4,3,1]=>0110111=>1110110
[7,6,5,8,3,1,4,2]=>0110111=>1110110
[2,6,4,3,8,1,7,5]=>0010111=>1110100
[2,6,4,3,8,5,7,1]=>0010111=>1110100
[7,2,3,1,5,8,6,4]=>0100111=>1110010
[7,1,5,6,3,8,4,2]=>0010111=>1110100
[7,3,6,5,1,4,8,2]=>0001111=>1111000
[7,2,6,5,3,8,1,4]=>0001111=>1111000
[7,2,3,1,4,8,6,5]=>0100111=>1110010
[7,2,3,5,4,8,6,1]=>0001111=>1111000
[2,6,4,5,8,1,7,3]=>0000111=>1110000
[1,5,6,4,8,3,7,2]=>0000111=>1110000
[2,5,6,4,8,3,1,7]=>0100101=>1010010
[3,5,6,1,4,7,8,2]=>0000101=>1010000
[7,6,1,3,4,5,8,2]=>0000111=>1110000
[7,1,3,2,4,8,5,6]=>0100011=>1100010
[7,6,1,5,3,4,8,2]=>0001111=>1111000
[7,6,1,5,4,3,8,2]=>0011111=>1111100
[1,6,4,5,8,3,2,7]=>0100101=>1010010
[7,6,5,8,1,3,2,4]=>0100111=>1110010
[3,4,6,8,7,2,1,5]=>1000011=>1100001
[3,5,6,8,2,1,7,4]=>1000011=>1100001
[4,2,1,5,3,7,8,6]=>1011001=>1001101
[4,2,5,6,3,1,8,7]=>0110101=>1010110
[3,5,6,8,1,7,2,4]=>0000011=>1100000
[4,1,5,6,3,2,8,7]=>0110101=>1010110
[4,5,3,1,7,2,8,6]=>0101011=>1101010
[4,1,3,5,2,7,8,6]=>0011001=>1001100
[2,5,4,7,3,8,6,1]=>0001111=>1111000
[3,5,7,1,8,4,2,6]=>0010011=>1100100
[4,1,5,3,2,7,8,6]=>0111001=>1001110
[4,5,3,7,1,2,8,6]=>0001011=>1101000
[4,3,6,1,2,7,5,8]=>0010110=>0110100
[5,1,3,2,4,6,7,8]=>0101000=>0001010
[3,6,1,7,4,5,2,8]=>0001110=>0111000
[5,1,3,4,2,6,7,8]=>0011000=>0001100
[5,3,1,4,2,6,7,8]=>0111000=>0001110
[4,5,2,3,7,1,8,6]=>0001011=>1101000
[4,2,6,1,3,7,5,8]=>0010110=>0110100
[4,6,2,1,3,7,5,8]=>1000110=>0110001
[3,6,2,1,7,4,8,5]=>1000111=>1110001
[3,1,4,7,6,5,2,8]=>0101110=>0111010
[3,6,2,7,1,5,8,4]=>0000111=>1110000
[4,6,2,7,1,3,5,8]=>0000110=>0110000
[3,5,7,1,8,2,6,4]=>0000111=>1110000
[5,1,4,2,3,6,7,8]=>0011000=>0001100
[3,6,1,7,2,5,8,4]=>0000111=>1110000
[2,6,5,3,4,7,8,1]=>0001101=>1011000
[3,6,1,7,5,4,2,8]=>0011110=>0111100
[5,1,4,3,2,6,7,8]=>0111000=>0001110
[5,4,1,3,2,6,7,8]=>0111000=>0001110
[6,4,2,5,3,8,1,7]=>0011101=>1011100
[4,6,2,3,5,1,8,7]=>0001101=>1011000
[6,2,4,5,1,8,3,7]=>0001101=>1011000
[8,2,6,7,1,4,5,3]=>0001011=>1101000
[8,2,6,7,4,1,5,3]=>0011011=>1101100
[4,6,2,3,5,8,1,7]=>0000101=>1010000
[2,6,4,1,5,8,3,7]=>0010101=>1010100
[2,8,1,6,7,4,5,3]=>0001011=>1101000
[6,8,4,5,7,2,3,1]=>0100011=>1100010
[2,8,6,1,4,7,5,3]=>0001111=>1111000
[2,8,1,6,4,7,5,3]=>0001111=>1111000
[2,6,1,4,8,5,3,7]=>0001101=>1011000
[6,4,5,2,8,3,1,7]=>0101101=>1011010
[4,2,3,6,1,8,5,7]=>0010101=>1010100
[4,2,3,1,6,8,5,7]=>0110001=>1000110
[4,2,3,8,6,1,7,5]=>0010111=>1110100
[6,4,5,8,2,3,7,1]=>0000111=>1110000
[8,6,7,2,4,5,1,3]=>0001011=>1101000
[6,4,8,5,2,3,7,1]=>0001111=>1111000
[4,2,8,3,1,6,7,5]=>0110011=>1100110
[2,4,8,1,3,6,7,5]=>0000011=>1100000
[2,4,1,8,3,6,7,5]=>0010011=>1100100
[2,1,4,8,6,3,7,5]=>1000111=>1110001
[6,4,8,2,5,3,7,1]=>0001111=>1111000
[8,6,2,4,7,5,1,3]=>0001111=>1111000
[4,6,8,2,3,5,7,1]=>0000011=>1100000
[2,6,8,4,1,5,7,3]=>0010011=>1100100
[2,6,8,1,4,5,7,3]=>0000011=>1100000
[2,1,6,8,4,5,7,3]=>1000011=>1100001
[2,8,1,4,6,7,3,5]=>0000011=>1100000
[4,8,6,2,3,7,5,1]=>0001111=>1111000
[8,4,2,6,7,3,1,5]=>0110011=>1100110
[7,6,4,5,1,3,8,2]=>0001111=>1111000
[1,6,7,5,3,4,8,2]=>0001011=>1101000
[7,6,2,3,8,4,1,5]=>0010111=>1110100
[1,6,7,5,8,2,3,4]=>0000011=>1100000
[6,2,5,8,3,4,7,1]=>0000111=>1110000
[6,2,3,8,7,4,1,5]=>0010111=>1110100
[2,4,7,3,5,8,6,1]=>0000111=>1110000
[2,5,3,7,1,8,4,6]=>0001011=>1101000
[5,2,8,3,1,4,6,7]=>0101001=>1001010
[4,8,2,3,6,5,7,1]=>0000111=>1110000
[5,8,1,3,6,4,7,2]=>0000111=>1110000
[5,8,1,4,3,6,2,7]=>0010101=>1010100
[5,8,4,1,3,7,6,2]=>0010111=>1110100
[6,4,5,3,8,1,7,2]=>0001111=>1111000
[4,6,5,3,7,1,2,8]=>0001110=>0111000
[4,5,1,3,6,2,8,7]=>0001101=>1011000
[4,2,6,5,1,7,3,8]=>0011110=>0111100
[4,3,5,7,2,1,6,8]=>1010010=>0100101
[3,4,7,6,8,1,2,5]=>0000011=>1100000
[3,4,6,2,5,8,7,1]=>0000111=>1110000
[3,5,2,4,6,1,8,7]=>0001101=>1011000
[4,2,5,1,6,8,3,7]=>0011001=>1001100
[1,8,2,3,6,5,7,4]=>0000111=>1110000
[4,2,8,3,5,7,1,6]=>0010011=>1100100
[4,3,8,6,5,7,1,2]=>0010111=>1110100
[1,3,7,2,6,5,8,4]=>0000111=>1110000
[1,3,6,4,2,5,8,7]=>0010101=>1010100
[1,5,4,7,3,6,8,2]=>0001011=>1101000
[5,2,3,8,4,1,7,6]=>0011011=>1101100
[7,5,3,4,8,2,1,6]=>1001011=>1101001
[7,2,8,3,4,1,5,6]=>0010011=>1100100
[7,4,3,8,5,2,6,1]=>0011111=>1111100
[4,6,2,7,3,1,5,8]=>0100110=>0110010
[7,6,3,8,2,4,5,1]=>0001111=>1111000
[7,2,8,5,1,3,4,6]=>0001011=>1101000
[1,5,3,7,6,8,4,2]=>0011011=>1101100
[1,6,3,7,8,2,4,5]=>0000101=>1010000
[1,4,3,7,8,5,2,6]=>0011001=>1001100
[4,2,6,5,7,8,3,1]=>0110101=>1010110
[4,2,6,7,5,8,1,3]=>0010011=>1100100
[3,2,4,7,8,5,1,6]=>0101001=>1001010
[3,2,6,7,8,1,4,5]=>0100001=>1000010
[5,1,8,3,6,4,7,2]=>0001111=>1111000
[3,6,8,5,7,2,1,4]=>1000011=>1100001
[5,1,3,8,7,6,4,2]=>0011111=>1111100
[3,8,5,6,1,7,2,4]=>0000111=>1110000
[3,4,8,1,7,6,2,5]=>0000111=>1110000
[4,7,6,8,5,1,3,2]=>0101011=>1101010
[6,7,4,8,5,1,3,2]=>0101011=>1101010
[5,3,6,8,7,1,4,2]=>0011011=>1101100
[1,8,4,6,7,2,5,3]=>0001011=>1101000
[5,2,8,3,7,1,6,4]=>0001111=>1111000
[7,4,5,8,6,1,3,2]=>0100111=>1110010
[4,3,6,8,7,1,5,2]=>0011011=>1101100
[6,4,8,3,1,7,5,2]=>0101111=>1111010
[3,6,5,8,7,1,4,2]=>0010111=>1110100
[5,7,4,8,2,6,3,1]=>0100111=>1110010
[5,6,4,8,2,7,3,1]=>0100111=>1110010
[5,6,8,3,1,7,4,2]=>0110011=>1100110
[4,6,3,8,2,7,5,1]=>0001111=>1111000
[5,3,8,1,7,2,6,4]=>0001111=>1111000
[6,5,8,1,3,7,4,2]=>0010111=>1110100
[6,5,3,8,2,7,4,1]=>0011111=>1111100
[6,4,8,1,3,7,5,2]=>0001111=>1111000
[6,2,8,3,4,7,5,1]=>0001111=>1111000
[7,6,3,1,4,2,5,8]=>0110110=>0110110
[1,5,4,3,7,8,2,6]=>0011001=>1001100
[7,8,4,2,5,3,1,6]=>0111001=>1001110
[4,2,7,8,5,3,1,6]=>0111001=>1001110
[4,2,5,3,1,7,8,6]=>0111001=>1001110
[4,2,8,7,6,3,1,5]=>0110111=>1110110
[4,2,7,6,3,1,5,8]=>0110110=>0110110
[6,3,1,7,5,2,4,8]=>0101110=>0111010
[6,3,1,8,7,5,2,4]=>0101111=>1111010
[8,6,3,1,7,5,2,4]=>0101111=>1111010
[4,2,7,6,3,1,8,5]=>0110111=>1110110
[7,6,3,1,8,4,2,5]=>0110111=>1110110
[7,6,4,2,1,8,3,5]=>1010111=>1110101
[1,8,2,7,6,4,3,5]=>0010111=>1110100
[8,3,5,7,6,4,2,1]=>1010111=>1110101
[8,4,2,5,7,6,3,1]=>0110111=>1110110
[7,5,2,4,8,6,3,1]=>0101111=>1111010
[8,7,5,2,4,6,3,1]=>0101111=>1111010
[7,5,2,4,6,3,1,8]=>0101110=>0111010
[5,2,8,6,3,7,4,1]=>0011111=>1111100
[8,4,7,5,2,6,3,1]=>0101111=>1111010
[8,3,6,4,7,5,2,1]=>1001111=>1111001
[1,8,2,7,5,3,6,4]=>0001111=>1111000
[7,5,2,1,8,3,6,4]=>1001111=>1111001
[7,5,2,6,3,1,8,4]=>0101111=>1111010
[5,2,7,4,1,8,6,3]=>0011111=>1111100
[5,2,8,7,4,1,6,3]=>0011111=>1111100
[8,7,4,1,5,2,6,3]=>0011111=>1111100
[7,4,1,5,2,8,6,3]=>0011111=>1111100
[7,6,3,1,4,2,8,5]=>0110111=>1110110
[7,5,2,8,6,3,1,4]=>0101111=>1111010
[8,7,5,2,6,3,1,4]=>0101111=>1111010
[7,5,2,1,3,6,4,8]=>1001110=>0111001
[8,7,5,2,1,3,6,4]=>1001111=>1111001
[7,5,2,1,3,8,6,4]=>1001111=>1111001
[1,3,7,6,5,8,2,4]=>0000111=>1110000
[8,6,4,7,5,2,1,3]=>1001111=>1111001
[6,4,8,7,5,2,1,3]=>1001111=>1111001
[6,4,7,5,2,1,3,8]=>1001110=>0111001
[6,3,1,4,7,5,2,8]=>0101110=>0111010
[6,3,1,4,8,7,5,2]=>0101111=>1111010
[8,6,3,1,4,7,5,2]=>0101111=>1111010
[8,5,7,6,3,1,4,2]=>0110111=>1110110
[1,8,2,5,7,6,4,3]=>0010111=>1110100
[1,8,2,6,4,7,5,3]=>0001111=>1111000
[7,5,2,1,6,4,8,3]=>1001111=>1111001
[6,3,8,7,4,1,5,2]=>0011111=>1111100
[6,3,7,4,1,5,2,8]=>0011110=>0111100
[7,4,1,6,3,5,2,8]=>0011110=>0111100
[7,4,1,8,6,3,5,2]=>0011111=>1111100
[8,4,6,3,1,7,5,2]=>0101111=>1111010
[6,4,7,5,2,1,8,3]=>1001111=>1111001
[1,6,4,7,5,3,8,2]=>0001111=>1111000
[8,6,3,5,2,7,4,1]=>0011111=>1111100
[6,3,5,2,8,7,4,1]=>0011111=>1111100
[6,3,5,2,7,4,1,8]=>0011110=>0111100
[4,5,7,2,6,3,1,8]=>0100110=>0110010
[3,5,8,4,6,1,7,2]=>0000111=>1110000
[1,4,7,3,5,2,6,8]=>0001010=>0101000
[5,7,4,2,6,3,1,8]=>0110110=>0110110
[4,2,6,3,5,7,1,8]=>0010110=>0110100
[1,4,5,8,2,7,3,6]=>0000011=>1100000
[2,4,5,8,1,6,7,3]=>0000011=>1100000
[8,3,4,7,1,6,5,2]=>0001111=>1111000
[4,2,5,7,8,1,6,3]=>0010101=>1010100
[8,3,4,6,5,1,7,2]=>0001111=>1111000
[4,1,7,3,5,2,6,8]=>0011010=>0101100
[6,1,3,7,4,2,5,8]=>0010110=>0110100
[3,1,6,8,2,7,4,5]=>0100011=>1100010
[6,1,3,8,2,5,4,7]=>0001101=>1011000
[4,8,2,3,1,6,7,5]=>0100011=>1100010
[3,2,6,8,1,5,7,4]=>0100011=>1100010
[8,2,6,1,5,4,7,3]=>0001111=>1111000
[8,6,2,7,1,5,4,3]=>0011111=>1111100
[7,6,8,3,1,5,4,2]=>0111011=>1101110
[5,7,4,2,8,1,6,3]=>0010111=>1110100
[6,3,7,2,8,1,5,4]=>0001111=>1111000
[7,5,2,8,6,1,4,3]=>0011111=>1111100
[2,7,3,8,1,5,6,4]=>0000111=>1110000
[1,6,8,5,2,4,3,7]=>0011001=>1001100
[4,5,7,2,8,1,6,3]=>0000111=>1110000
[4,5,6,8,3,1,7,2]=>0100011=>1100010
[8,4,6,5,3,1,7,2]=>0101111=>1111010
[5,6,4,8,3,1,7,2]=>0100111=>1110010
[3,4,7,1,2,6,5,8]=>0000110=>0110000
[4,8,1,6,2,3,7,5]=>0000111=>1110000
[4,5,3,1,7,2,6,8]=>0101010=>0101010
[4,7,3,1,2,6,5,8]=>0100110=>0110010
[5,2,7,1,3,6,4,8]=>0001110=>0111000
[7,8,1,2,4,3,6,5]=>0010101=>1010100
[8,4,1,6,2,3,7,5]=>0010111=>1110100
[4,8,3,1,2,5,7,6]=>0100011=>1100010
[4,1,3,6,5,7,8,2]=>0010101=>1010100
[6,1,3,4,2,8,5,7]=>0010101=>1010100
[8,1,4,2,5,7,6,3]=>0010111=>1110100
[8,1,4,3,5,7,6,2]=>0010111=>1110100
[5,2,4,1,3,7,8,6]=>0011001=>1001100
[2,6,5,3,1,7,8,4]=>0101101=>1011010
[8,3,2,1,5,7,6,4]=>1100111=>1110011
[1,7,4,3,6,8,2,5]=>0010011=>1100100
[2,7,6,3,1,8,4,5]=>0100111=>1110010
[2,8,4,6,3,7,5,1]=>0001111=>1111000
[8,7,1,3,6,5,4,2]=>0011111=>1111100
[1,8,5,7,4,2,6,3]=>0010111=>1110100
[3,8,6,5,7,1,4,2]=>0010111=>1110100
[4,8,6,2,7,1,5,3]=>0001111=>1111000
[4,7,5,3,8,2,1,6]=>1001011=>1101001
[1,6,5,8,3,4,2,7]=>0010101=>1010100
[6,1,5,3,8,4,2,7]=>0011101=>1011100
[8,1,5,4,7,2,6,3]=>0001111=>1111000
[2,1,4,7,5,8,3,6]=>1000011=>1100001
[6,3,5,8,7,4,1,2]=>0010111=>1110100
[4,7,2,8,5,6,3,1]=>0100111=>1110010
[1,4,8,7,3,5,6,2]=>0000111=>1110000
[8,1,7,6,3,5,4,2]=>0011111=>1111100
[3,6,8,5,7,4,1,2]=>0010011=>1100100
[4,7,6,8,5,3,1,2]=>0101011=>1101010
[5,7,2,8,6,4,1,3]=>0010111=>1110100
[3,8,7,5,6,4,2,1]=>1010111=>1110101
[2,8,7,6,4,5,3,1]=>0101111=>1111010
[1,8,7,6,5,3,4,2]=>0011111=>1111100
[4,6,7,2,5,3,1,8]=>0101010=>0101010
[3,6,7,4,8,1,5,2]=>0001011=>1101000
[3,8,5,7,6,1,4,2]=>0010111=>1110100
[1,4,7,8,2,6,5,3]=>0001101=>1011000
[2,4,7,8,1,6,5,3]=>0001101=>1011000
[4,2,6,8,7,1,5,3]=>0011011=>1101100
[3,1,7,8,2,6,5,4]=>0101101=>1011010
[6,1,3,8,2,7,5,4]=>0001111=>1111000
[5,1,8,4,2,7,6,3]=>0011111=>1111100
[8,2,6,1,7,5,4,3]=>0011111=>1111100
[6,8,3,7,1,5,4,2]=>0011011=>1101100
[2,7,3,8,1,6,5,4]=>0001111=>1111000
[1,7,3,8,2,6,5,4]=>0001111=>1111000
[2,6,8,4,1,7,5,3]=>0011011=>1101100
[4,5,8,6,3,1,7,2]=>0100111=>1110010
[4,6,7,1,2,8,5,3]=>0001011=>1101000
[3,6,1,8,2,7,5,4]=>0001111=>1111000
[5,7,4,1,2,8,6,3]=>0010111=>1110100
[6,3,7,1,2,8,5,4]=>0001111=>1111000
[6,2,1,8,3,7,5,4]=>1001111=>1111001
[8,1,5,6,3,2,4,7]=>0100101=>1010010
[1,7,8,3,5,2,4,6]=>0001001=>1001000
[8,5,3,7,2,4,6,1]=>0001111=>1111000
[1,7,2,4,8,5,3,6]=>0001011=>1101000
[1,7,8,5,4,3,2,6]=>0111001=>1001110
[2,6,8,7,4,3,5,1]=>0011011=>1101100
[1,2,6,7,8,4,3,5]=>0010001=>1000100
[2,7,5,8,4,1,3,6]=>0010011=>1100100
[2,1,7,8,4,5,3,6]=>1001001=>1001001
[3,7,8,2,1,5,4,6]=>1001001=>1001001
[8,5,1,4,7,3,6,2]=>0001111=>1111000
[8,4,7,5,3,6,1,2]=>0001111=>1111000
[8,1,4,6,7,3,5,2]=>0001011=>1101000
[3,5,8,6,7,4,1,2]=>0010011=>1100100
[3,6,8,4,7,1,5,2]=>0001011=>1101000
[4,7,1,3,6,8,2,5]=>0000011=>1100000
[3,7,6,4,8,1,2,5]=>0000111=>1110000
[3,1,7,5,6,8,2,4]=>0100011=>1100010
[2,3,6,5,7,1,8,4]=>0000111=>1110000
[3,7,5,4,2,1,8,6]=>1011011=>1101101
[1,3,6,7,4,2,8,5]=>0010011=>1100100
[3,6,4,8,2,7,5,1]=>0001111=>1111000
[1,4,6,3,2,7,8,5]=>0100101=>1010010
[8,7,1,5,6,3,2,4]=>0100111=>1110010
[8,1,6,7,5,3,2,4]=>0101011=>1101010
[1,7,8,6,5,3,2,4]=>0101101=>1011010
[8,7,2,4,6,5,3,1]=>0101111=>1111010
[1,7,8,2,6,4,5,3]=>0001101=>1011000
[8,7,2,5,4,6,1,3]=>0001111=>1111000
[8,7,2,5,3,1,6,4]=>0101111=>1111010
[8,7,3,2,1,5,6,4]=>1100111=>1110011
[8,2,6,7,3,1,5,4]=>0101011=>1101010
[1,7,2,8,5,6,4,3]=>0010111=>1110100
[2,7,1,8,4,6,5,3]=>0001111=>1111000
[3,7,8,2,1,6,5,4]=>1001101=>1011001
[8,7,6,1,4,5,3,2]=>0101111=>1111010
[4,8,1,2,3,7,5,6]=>0000011=>1100000
[1,8,2,3,6,5,4,7]=>0001101=>1011000
[3,5,8,4,7,2,6,1]=>0000111=>1110000
[1,8,5,4,6,2,3,7]=>0001101=>1011000
[3,8,5,4,6,1,2,7]=>0001101=>1011000
[3,8,5,1,6,4,2,7]=>0011101=>1011100
[2,8,5,4,6,1,3,7]=>0001101=>1011000
[2,8,5,4,6,3,1,7]=>0101101=>1011010
[1,8,5,4,6,3,2,7]=>0101101=>1011010
[2,5,8,4,7,3,6,1]=>0000111=>1110000
[3,6,4,2,7,8,5,1]=>0011101=>1011100
[3,5,4,1,6,2,7,8]=>0011100=>0011100
[4,5,8,1,7,6,2,3]=>0000111=>1110000
[3,5,8,4,7,1,6,2]=>0000111=>1110000
[1,5,8,4,7,3,6,2]=>0000111=>1110000
[3,6,4,1,7,8,5,2]=>0011101=>1011100
[3,6,4,8,7,5,2,1]=>1001111=>1111001
[1,6,4,3,7,8,5,2]=>0011101=>1011100
[7,1,3,4,8,6,5,2]=>0001111=>1111000
[7,6,1,3,8,4,2,5]=>0010111=>1110100
[1,6,4,2,7,8,3,5]=>0010101=>1010100
[2,6,4,3,7,1,8,5]=>0010111=>1110100
[2,6,4,1,7,8,3,5]=>0010101=>1010100
[7,2,3,4,8,6,5,1]=>0001111=>1111000
[7,2,3,1,8,6,4,5]=>0100111=>1110010
[7,2,3,4,1,6,8,5]=>0010011=>1100100
[1,2,4,3,8,5,7,6]=>0010011=>1100100
[7,3,8,6,1,4,2,5]=>0010111=>1110100
[7,2,8,6,3,4,1,5]=>0010111=>1110100
[7,2,3,1,5,6,8,4]=>0100011=>1100010
[7,2,3,8,1,6,5,4]=>0001111=>1111000
[7,2,3,8,5,6,4,1]=>0010111=>1110100
[2,6,4,8,7,1,5,3]=>0001111=>1111000
[1,5,8,4,7,6,2,3]=>0000111=>1110000
[3,5,8,1,6,7,2,4]=>0000011=>1100000
[7,6,1,3,5,8,2,4]=>0000111=>1110000
[7,1,3,2,5,6,8,4]=>0100011=>1100010
[7,1,3,8,2,6,5,4]=>0001111=>1111000
[7,6,1,8,5,4,2,3]=>0011111=>1111100
[3,2,6,5,8,4,7,1]=>0100111=>1110010
[4,3,7,1,6,5,8,2]=>0010111=>1110100
[5,2,6,4,8,3,7,1]=>0001111=>1111000
[5,2,6,4,8,1,7,3]=>0001111=>1111000
[4,3,7,5,8,2,6,1]=>0010111=>1110100
[5,3,7,4,8,2,6,1]=>0001111=>1111000
[5,3,7,4,8,1,6,2]=>0001111=>1111000
[5,4,8,1,6,2,7,3]=>0001111=>1111000
[4,3,7,1,5,2,8,6]=>0011011=>1101100
[4,3,7,1,6,2,8,5]=>0010111=>1110100
[5,4,8,2,6,3,7,1]=>0001111=>1111000
[5,4,8,1,6,3,7,2]=>0001111=>1111000
[4,1,7,5,2,3,6,8]=>0011010=>0101100
[4,1,7,8,6,3,2,5]=>0110101=>1010110
[4,7,2,8,3,5,1,6]=>0001011=>1101000
[1,2,6,8,3,7,4,5]=>0000011=>1100000
[6,8,3,2,1,4,7,5]=>1100011=>1100011
[7,5,8,4,3,1,6,2]=>0110111=>1110110
[6,8,2,4,1,3,7,5]=>0010011=>1100100
[2,8,4,7,6,3,5,1]=>0001111=>1111000
[6,1,2,7,5,8,4,3]=>0010111=>1110100
[4,2,7,3,8,5,6,1]=>0010111=>1110100
[4,5,2,6,8,3,7,1]=>0001011=>1101000
[4,8,3,2,5,7,6,1]=>0100111=>1110010
[7,2,4,3,8,5,6,1]=>0010111=>1110100
[8,4,7,6,2,3,5,1]=>0001111=>1111000
[6,8,4,1,5,3,7,2]=>0011011=>1101100
[8,3,4,7,6,2,5,1]=>0001111=>1111000
[1,8,3,5,2,6,7,4]=>0001011=>1101000
[6,8,3,5,1,4,7,2]=>0001011=>1101000
[6,8,5,4,2,3,7,1]=>0011011=>1101100
[5,8,2,4,3,7,6,1]=>0010111=>1110100
[8,2,1,3,5,6,4,7]=>1000101=>1010001
[8,2,1,3,5,4,7,6]=>1001011=>1101001
[8,2,1,3,4,6,7,5]=>1000011=>1100001
[8,1,3,4,2,6,5,7]=>0010101=>1010100
[8,1,3,4,2,5,7,6]=>0010011=>1100100
[8,1,3,2,5,6,4,7]=>0100101=>1010010
[8,1,2,4,5,3,7,6]=>0001011=>1101000
[8,1,2,4,3,6,7,5]=>0010011=>1100100
[10,2,1,4,3,6,5,8,7,9]=>101010101=>101010101
[10,2,1,4,3,6,5,7,9,8]=>101010011=>110010101
[10,2,1,4,3,5,7,8,6,9]=>101000101=>101000101
[10,2,1,4,3,5,7,6,9,8]=>101001011=>110100101
[10,2,1,4,3,5,6,8,9,7]=>101000011=>110000101
[10,2,1,3,5,6,4,8,7,9]=>100010101=>101010001
[10,2,1,3,5,6,4,7,9,8]=>100010011=>110010001
[10,2,1,3,5,4,7,8,6,9]=>100100101=>101001001
[10,2,1,3,5,4,7,6,9,8]=>100101011=>110101001
[10,2,1,3,5,4,6,8,9,7]=>100100011=>110001001
[10,2,1,3,4,6,7,8,5,9]=>100000101=>101000001
[10,2,1,3,4,6,7,5,9,8]=>100001011=>110100001
[10,2,1,3,4,6,5,8,9,7]=>100010011=>110010001
[10,2,1,3,4,5,7,8,9,6]=>100000011=>110000001
[10,1,3,4,2,6,5,8,7,9]=>001010101=>101010100
[10,1,3,4,2,6,5,7,9,8]=>001010011=>110010100
[10,1,3,4,2,5,7,8,6,9]=>001000101=>101000100
[10,1,3,4,2,5,7,6,9,8]=>001001011=>110100100
[10,1,3,4,2,5,6,8,9,7]=>001000011=>110000100
[10,1,3,2,5,6,4,8,7,9]=>010010101=>101010010
[10,1,3,2,5,6,4,7,9,8]=>010010011=>110010010
[10,1,3,2,5,4,7,8,6,9]=>010100101=>101001010
[10,1,3,2,5,4,7,6,9,8]=>010101011=>110101010
[10,1,3,2,5,4,6,8,9,7]=>010100011=>110001010
[10,1,3,2,4,6,7,8,5,9]=>010000101=>101000010
[10,1,3,2,4,6,7,5,9,8]=>010001011=>110100010
[10,1,3,2,4,6,5,8,9,7]=>010010011=>110010010
[10,1,3,2,4,5,7,8,9,6]=>010000011=>110000010
[10,1,2,4,5,6,3,8,7,9]=>000010101=>101010000
[10,1,2,4,5,6,3,7,9,8]=>000010011=>110010000
[10,1,2,4,5,3,7,8,6,9]=>000100101=>101001000
[10,1,2,4,5,3,7,6,9,8]=>000101011=>110101000
[10,1,2,4,5,3,6,8,9,7]=>000100011=>110001000
[10,1,2,4,3,6,7,8,5,9]=>001000101=>101000100
[10,1,2,4,3,6,7,5,9,8]=>001001011=>110100100
[10,1,2,4,3,6,5,8,9,7]=>001010011=>110010100
[10,1,2,4,3,5,7,8,9,6]=>001000011=>110000100
[10,1,2,3,5,6,7,8,4,9]=>000000101=>101000000
[10,1,2,3,5,6,7,4,9,8]=>000001011=>110100000
[10,1,2,3,5,6,4,8,9,7]=>000010011=>110010000
[10,1,2,3,5,4,7,8,9,6]=>000100011=>110001000
[10,1,2,3,4,6,7,8,9,5]=>000000011=>110000000
[12,2,1,4,3,6,5,8,7,10,9,11]=>10101010101=>10101010101
[12,2,1,4,3,6,5,8,7,9,11,10]=>10101010011=>11001010101
[12,2,1,4,3,6,5,7,9,10,8,11]=>10101000101=>10100010101
[12,2,1,4,3,6,5,7,9,8,11,10]=>10101001011=>11010010101
[12,2,1,4,3,5,7,8,6,10,9,11]=>10100010101=>10101000101
[12,2,1,4,3,5,7,6,9,10,8,11]=>10100100101=>10100100101
[12,2,1,4,3,5,7,6,9,8,11,10]=>10100101011=>11010100101
[12,2,1,4,3,5,6,8,9,10,7,11]=>10100000101=>10100000101
[12,2,1,3,5,6,4,8,7,10,9,11]=>10001010101=>10101010001
[12,2,1,3,5,6,4,7,9,10,8,11]=>10001000101=>10100010001
[12,2,1,3,5,4,7,8,6,10,9,11]=>10010010101=>10101001001
[12,2,1,3,5,4,7,6,9,10,8,11]=>10010100101=>10100101001
[12,2,1,3,5,4,7,6,9,8,11,10]=>10010101011=>11010101001
[12,2,1,3,5,4,6,8,9,10,7,11]=>10010000101=>10100001001
[12,2,1,3,4,6,7,8,5,10,9,11]=>10000010101=>10101000001
[12,2,1,3,4,6,5,8,9,10,7,11]=>10001000101=>10100010001
[12,2,1,3,4,5,7,8,9,10,6,11]=>10000000101=>10100000001
[12,2,1,3,4,5,7,8,9,6,11,10]=>10000001011=>11010000001
[12,1,3,4,2,6,5,8,7,10,9,11]=>00101010101=>10101010100
[12,1,3,4,2,6,5,8,7,9,11,10]=>00101010011=>11001010100
[12,1,3,4,2,6,5,7,9,10,8,11]=>00101000101=>10100010100
[12,1,3,4,2,6,5,7,9,8,11,10]=>00101001011=>11010010100
[12,1,3,4,2,6,5,7,8,10,11,9]=>00101000011=>11000010100
[12,1,3,4,2,5,7,8,6,10,9,11]=>00100010101=>10101000100
[12,1,3,4,2,5,7,6,9,10,8,11]=>00100100101=>10100100100
[12,1,3,4,2,5,7,6,9,8,11,10]=>00100101011=>11010100100
[12,1,3,4,2,5,6,8,9,7,11,10]=>00100001011=>11010000100
[12,1,3,2,5,6,4,8,7,10,9,11]=>01001010101=>10101010010
[12,1,3,2,5,6,4,7,9,10,8,11]=>01001000101=>10100010010
[12,1,3,2,5,4,7,8,6,10,9,11]=>01010010101=>10101001010
[12,1,3,2,5,4,7,6,9,10,8,11]=>01010100101=>10100101010
[12,1,3,2,5,4,7,6,9,8,11,10]=>01010101011=>11010101010
[12,1,3,2,5,4,7,6,8,10,11,9]=>01010100011=>11000101010
[12,1,3,2,4,6,7,5,9,10,8,11]=>01000100101=>10100100010
[12,1,3,2,4,6,7,5,8,10,11,9]=>01000100011=>11000100010
[12,1,3,2,4,6,5,8,9,10,7,11]=>01001000101=>10100010010
[12,1,3,2,4,5,7,8,9,10,6,11]=>01000000101=>10100000010
[12,1,3,2,4,5,7,8,9,6,11,10]=>01000001011=>11010000010
[12,1,3,2,4,5,7,6,9,10,11,8]=>01000100011=>11000100010
[12,1,3,2,4,5,6,8,9,10,11,7]=>01000000011=>11000000010
[12,1,2,4,5,6,3,8,7,10,9,11]=>00001010101=>10101010000
[12,1,2,4,5,6,3,7,9,10,8,11]=>00001000101=>10100010000
[12,1,2,4,5,3,7,8,6,10,9,11]=>00010010101=>10101001000
[12,1,2,4,5,3,7,6,9,10,8,11]=>00010100101=>10100101000
[12,1,2,4,5,3,7,6,9,8,11,10]=>00010101011=>11010101000
[12,1,2,4,5,3,6,8,9,10,7,11]=>00010000101=>10100001000
[12,1,2,4,5,3,6,8,9,7,11,10]=>00010001011=>11010001000
[12,1,2,4,5,3,6,7,9,10,11,8]=>00010000011=>11000001000
[12,1,2,4,3,6,7,8,5,10,9,11]=>00100010101=>10101000100
[12,1,2,4,3,6,7,5,9,10,8,11]=>00100100101=>10100100100
[12,1,2,4,3,6,7,5,9,8,11,10]=>00100101011=>11010100100
[12,1,2,4,3,6,5,8,9,10,7,11]=>00101000101=>10100010100
[12,1,2,4,3,6,5,8,9,7,11,10]=>00101001011=>11010010100
[12,1,2,4,3,6,5,8,7,10,11,9]=>00101010011=>11001010100
[12,1,2,4,3,6,5,7,9,10,11,8]=>00101000011=>11000010100
[12,1,2,4,3,5,7,8,9,6,11,10]=>00100001011=>11010000100
[12,1,2,3,5,6,7,8,4,10,9,11]=>00000010101=>10101000000
[12,1,2,3,5,6,7,8,4,9,11,10]=>00000010011=>11001000000
[12,1,2,3,5,6,7,4,9,10,8,11]=>00000100101=>10100100000
[12,1,2,3,5,6,7,4,9,8,11,10]=>00000101011=>11010100000
[12,1,2,3,5,6,7,4,8,10,11,9]=>00000100011=>11000100000
[12,1,2,3,5,6,4,8,9,10,7,11]=>00001000101=>10100010000
[12,1,2,3,5,4,7,8,9,10,6,11]=>00010000101=>10100001000
[12,1,2,3,5,4,7,8,9,6,11,10]=>00010001011=>11010001000
[12,1,2,3,5,4,6,8,9,10,11,7]=>00010000011=>11000001000
[12,1,2,3,4,6,7,8,9,10,5,11]=>00000000101=>10100000000
[12,1,2,3,4,6,7,8,9,5,11,10]=>00000001011=>11010000000
[12,1,2,3,4,6,7,8,5,10,11,9]=>00000010011=>11001000000
[12,1,2,3,4,6,7,5,9,10,11,8]=>00000100011=>11000100000
[12,1,2,3,4,5,7,8,9,10,11,6]=>00000000011=>11000000000
[6,5,3,8,4,2,7,1]=>0011111=>1111100
[7,4,5,1,6,2,8,3]=>0001111=>1111000
[4,7,3,5,6,2,8,1]=>0000111=>1110000
[6,7,8,4,1,3,5,2]=>0011001=>1001100
[3,1,6,8,4,7,5,2]=>0101011=>1101010
[8,3,6,1,5,7,4,2]=>0010111=>1110100
[3,2,7,5,8,6,1,4]=>0100111=>1110010
[2,5,4,7,8,1,6,3]=>0001101=>1011000
[2,4,6,7,8,1,5,3]=>0001001=>1001000
[2,4,6,8,1,7,5,3]=>0001011=>1101000
[7,4,3,8,6,2,1,5]=>1010111=>1110101
[2,4,7,8,3,5,6,1]=>0000101=>1010000
[3,2,7,6,1,8,4,5]=>0100111=>1110010
[3,2,6,8,1,7,4,5]=>0100011=>1100010
[4,3,6,2,1,8,5,7]=>1010101=>1010101
[3,6,4,2,5,8,1,7]=>0010101=>1010100
[4,6,2,3,7,5,8,1]=>0000111=>1110000
[5,8,4,2,3,6,7,1]=>0010011=>1100100
[8,4,5,3,2,1,7,6]=>1101011=>1101011
[5,8,3,4,2,1,7,6]=>1010011=>1100101
[6,8,4,2,3,7,5,1]=>0011011=>1101100
[6,4,8,3,2,7,1,5]=>0100111=>1110010
[5,8,3,7,2,1,6,4]=>1000111=>1110001
[2,5,6,4,7,1,8,3]=>0000111=>1110000
[2,5,4,8,1,6,7,3]=>0001011=>1101000
[6,4,7,3,8,2,1,5]=>1000111=>1110001
[6,7,4,3,2,1,8,5]=>1110011=>1100111
[8,4,3,7,2,1,5,6]=>1010011=>1100101
[1,2,6,5,8,7,3,4]=>0000111=>1110000
[1,5,2,8,4,6,7,3]=>0001011=>1101000
[1,5,2,7,4,6,8,3]=>0001011=>1101000
[5,1,2,7,3,6,8,4]=>0001011=>1101000
[5,1,2,8,3,6,7,4]=>0001011=>1101000
[5,6,3,4,8,7,2,1]=>1000111=>1110001
[6,5,3,4,8,7,2,1]=>1001111=>1111001
[4,1,2,8,3,6,7,5]=>0010011=>1100100
[4,1,2,7,3,6,8,5]=>0010011=>1100100
[7,5,3,8,4,6,2,1]=>1001111=>1111001
[8,5,3,7,4,6,2,1]=>1001111=>1111001
[5,8,1,2,3,4,7,6]=>0000011=>1100000
[7,1,2,8,3,6,4,5]=>0000111=>1110000
[6,1,8,2,3,5,7,4]=>0000111=>1110000
[6,1,7,2,3,5,8,4]=>0000111=>1110000
[1,6,8,2,4,5,7,3]=>0000011=>1100000
[4,3,8,7,5,6,2,1]=>1010111=>1110101
[1,8,2,7,4,6,5,3]=>0001111=>1111000
[7,1,6,2,3,5,8,4]=>0000111=>1110000
[8,1,6,2,3,5,7,4]=>0000111=>1110000
[8,1,7,2,3,5,6,4]=>0000111=>1110000
[5,8,3,7,4,6,2,1]=>1000111=>1110001
[6,8,7,3,4,5,2,1]=>1001011=>1101001
[1,8,7,2,4,5,3,6]=>0001011=>1101000
[8,7,1,2,3,4,6,5]=>0000111=>1110000
[8,6,1,2,3,4,7,5]=>0000111=>1110000
[8,1,6,2,3,5,4,7]=>0001101=>1011000
[1,7,6,2,4,5,3,8]=>0001110=>0111000
[1,8,7,4,6,3,5,2]=>0001111=>1111000
[6,3,7,5,1,4,8,2]=>0001111=>1111000
[1,8,3,5,7,2,6,4]=>0000111=>1110000
[2,3,4,6,8,5,7,1]=>0000011=>1100000
[2,3,5,7,4,8,6,1]=>0000111=>1110000
[2,4,6,3,7,8,5,1]=>0001101=>1011000
[2,5,7,1,8,6,3,4]=>0000111=>1110000
[8,2,4,5,1,3,7,6]=>0001011=>1101000
[1,3,8,5,2,4,6,7]=>0001001=>1001000
[2,6,7,1,8,4,5,3]=>0001011=>1101000
[5,8,3,1,4,2,6,7]=>0110001=>1000110
[2,4,1,8,5,6,3,7]=>0010101=>1010100
[1,6,2,7,8,5,3,4]=>0001101=>1011000
[3,5,2,6,7,8,4,1]=>0011001=>1001100
[4,5,1,6,7,3,8,2]=>0001011=>1101000
[2,8,4,1,7,5,3,6]=>0011011=>1101100
[8,5,3,1,7,4,2,6]=>0111011=>1101110
[4,2,8,7,1,5,3,6]=>0011011=>1101100
[5,2,6,8,1,7,4,3]=>0011011=>1101100
[5,7,3,2,6,8,1,4]=>0100011=>1100010
[8,4,7,3,1,6,2,5]=>0100111=>1110010
[6,7,1,2,3,5,8,4]=>0000011=>1100000
[3,1,6,7,8,4,2,5]=>0110001=>1000110
[3,1,4,8,5,6,2,7]=>0100101=>1010010
[8,3,1,4,5,7,2,6]=>0100011=>1100010
[1,6,7,8,9,2,3,4,5]=>00000001=>10000000
[6,7,8,9,1,2,3,4,5,10]=>000000010=>010000000
[6,7,8,1,2,3,4,5,9]=>00000010=>01000000
[1,7,8,9,2,3,4,5,6]=>00000001=>10000000
[1,7,8,9,10,2,3,4,5,6]=>000000001=>100000000
[6,7,8,9,10,1,2,3,4,5,11]=>0000000010=>0100000000
[5,6,7,8,9,1,2,3,4,10]=>000000010=>010000000
[5,6,7,1,8,2,3,4,9]=>00000110=>01100000
[4,6,7,8,1,2,3,5,9]=>00000010=>01000000
[1,6,7,8,2,9,3,4,5]=>00000011=>11000000
[1,5,7,8,9,2,3,4,6]=>00000001=>10000000
[1,6,7,8,9,10,2,3,4,5]=>000000001=>100000000
[1,7,8,9,10,11,2,3,4,5,6]=>0000000001=>1000000000
[8,6,2,3,5,1,4,7]=>0001101=>1011000
[8,2,4,5,7,3,1,6]=>0100011=>1100010
[2,6,3,8,7,5,4,1]=>0011111=>1111100
[8,2,3,7,5,4,1,6]=>0011011=>1101100
[8,2,6,3,5,4,1,7]=>0011101=>1011100
[8,6,1,5,2,4,3,7]=>0011101=>1011100
[8,6,2,4,1,5,3,7]=>0011101=>1011100
[8,4,1,6,5,3,2,7]=>0111101=>1011110
[8,3,6,1,5,4,2,7]=>0011101=>1011100
[8,3,2,6,5,4,1,7]=>0111101=>1011110
[8,3,2,5,7,4,1,6]=>0110011=>1100110
[8,3,1,7,5,4,2,6]=>0111011=>1101110
[8,2,7,4,1,5,3,6]=>0011011=>1101100
[6,1,3,8,7,5,4,2]=>0011111=>1111100
[3,6,1,8,7,5,4,2]=>0011111=>1111100
[3,8,1,5,7,6,4,2]=>0010111=>1110100
[3,5,2,8,7,6,4,1]=>0011111=>1111100
[3,4,8,2,7,6,5,1]=>0001111=>1111000
[3,4,8,7,1,6,5,2]=>0001111=>1111000
[8,1,3,5,7,6,4,2]=>0010111=>1110100
[4,1,8,5,7,6,3,2]=>0110111=>1110110
[8,2,7,1,4,5,6,3]=>0000111=>1110000
[8,1,7,3,4,6,2,5]=>0000111=>1110000
[8,3,1,7,2,6,5,4]=>0101111=>1111010
[3,8,2,4,7,6,5,1]=>0001111=>1111000
[2,8,3,7,4,6,5,1]=>0001111=>1111000
[8,2,3,7,1,6,5,4]=>0001111=>1111000
[8,2,7,1,3,6,5,4]=>0001111=>1111000
[8,1,7,2,6,4,3,5]=>0010111=>1110100
[8,1,7,5,2,4,3,6]=>0011011=>1101100
[8,2,3,7,4,6,1,5]=>0000111=>1110000
[2,4,8,5,7,6,3,1]=>0100111=>1110010
[8,2,4,3,7,6,1,5]=>0010111=>1110100
[8,2,7,3,5,1,4,6]=>0001011=>1101000
[8,2,7,4,3,1,5,6]=>0110011=>1100110
[8,2,7,3,1,5,6,4]=>0100111=>1110010
[8,2,1,5,7,6,4,3]=>1010111=>1110101
[6,2,1,8,7,5,4,3]=>1011111=>1111101
[6,1,8,2,7,5,4,3]=>0011111=>1111100
[8,1,7,3,5,2,6,4]=>0001111=>1111000
[8,1,5,2,7,6,4,3]=>0011111=>1111100
[8,1,7,2,4,6,5,3]=>0001111=>1111000
[8,2,4,1,7,6,5,3]=>0011111=>1111100
[4,2,8,3,7,6,5,1]=>0011111=>1111100
[4,8,2,1,7,6,5,3]=>1001111=>1111001
[5,1,8,7,2,6,4,3]=>0011111=>1111100
[5,8,1,3,7,6,2,4]=>0000111=>1110000
[8,2,5,4,1,7,6,3]=>0011111=>1111100
[5,1,4,8,7,6,3,2]=>0101111=>1111010
[8,1,4,3,7,6,5,2]=>0011111=>1111100
[4,8,1,3,7,6,5,2]=>0001111=>1111000
[4,3,8,1,7,6,5,2]=>0011111=>1111100
[5,8,6,3,2,1,7,4]=>1100111=>1110011
[5,7,6,3,2,4,1,8]=>0110110=>0110110
[6,5,7,2,4,3,1,8]=>0110110=>0110110
[5,7,1,3,2,8,6,4]=>0100111=>1110010
[5,8,1,3,2,7,4,6]=>0100011=>1100010
[8,5,1,3,2,4,6,7]=>0101001=>1001010
[7,5,1,3,2,4,8,6]=>0101011=>1101010
[7,5,8,2,1,4,3,6]=>1010011=>1100101
[6,7,1,2,5,4,8,3]=>0001011=>1101000
[6,8,1,2,5,7,4,3]=>0010011=>1100100
[7,1,2,3,8,6,4,5]=>0000111=>1110000
[8,1,6,4,2,3,5,7]=>0010101=>1010100
[1,5,4,8,2,3,7,6]=>0001011=>1101000
[1,7,8,2,3,5,6,4]=>0000101=>1010000
[7,5,8,2,3,1,4,6]=>0100011=>1100010
[7,4,1,2,6,8,3,5]=>0010011=>1100100
[6,2,8,1,5,7,3,4]=>0000111=>1110000
[7,2,5,4,1,8,6,3]=>0011111=>1111100
[7,3,5,4,2,1,8,6]=>1011011=>1101101
[7,3,2,8,5,6,1,4]=>0100111=>1110010
[1,7,4,3,6,8,5,2]=>0011011=>1101100
[4,7,6,5,2,3,8,1]=>0001111=>1111000
[4,7,6,5,1,3,8,2]=>0001111=>1111000
[5,4,6,8,7,2,1,3]=>1001011=>1101001
[6,7,4,2,1,8,5,3]=>1011011=>1101101
[1,7,6,3,2,8,4,5]=>0100111=>1110010
[5,4,2,1,7,3,6,8]=>1011010=>0101101
[6,5,8,2,3,7,4,1]=>0010111=>1110100
[6,5,8,3,4,1,7,2]=>0010111=>1110100
[4,1,2,8,5,3,6,7]=>0011001=>1001100
[3,5,8,2,6,1,7,4]=>0000111=>1110000
[3,7,6,1,5,2,8,4]=>0001111=>1111000
[1,7,6,2,5,8,4,3]=>0010111=>1110100
[1,7,6,5,8,4,2,3]=>0010111=>1110100
[3,7,6,5,8,1,2,4]=>0000111=>1110000
[3,7,6,2,8,4,5,1]=>0001111=>1111000
[4,3,6,8,5,1,2,7]=>0011001=>1001100
[2,7,1,5,8,4,3,6]=>0010011=>1100100
[2,7,6,1,8,4,3,5]=>0010111=>1110100
[7,1,2,6,3,5,4,8]=>0001110=>0111000
[7,2,6,3,4,5,1,8]=>0001110=>0111000
[6,7,8,4,2,5,3,1]=>0111001=>1001110
[6,1,2,5,7,8,4,3]=>0010101=>1010100
[4,1,2,7,8,5,3,6]=>0011001=>1001100
[4,7,3,1,2,6,8,5]=>0100011=>1100010
[3,7,6,1,5,8,2,4]=>0000111=>1110000
[3,8,5,6,4,2,7,1]=>0010111=>1110100
[3,2,6,4,7,8,5,1]=>0101101=>1011010
[4,2,7,5,8,3,1,6]=>0110011=>1100110
[4,2,7,1,3,8,6,5]=>0010111=>1110100
[5,2,1,4,7,8,3,6]=>1001001=>1001001
[5,6,2,7,3,4,8,1]=>0000111=>1110000
[6,1,3,8,5,4,7,2]=>0001111=>1111000
[2,7,6,8,5,1,3,4]=>0001011=>1101000
[2,7,6,8,5,3,1,4]=>0101011=>1101010
[1,5,8,6,4,2,3,7]=>0010101=>1010100
[2,5,8,6,4,1,7,3]=>0010111=>1110100
[1,6,2,3,5,8,7,4]=>0000111=>1110000
[4,7,2,3,1,6,8,5]=>0100011=>1100010
[6,7,3,1,5,4,8,2]=>0101011=>1101010
[7,4,6,2,8,3,5,1]=>0001111=>1111000
[7,3,5,1,4,8,2,6]=>0001011=>1101000
[3,4,6,5,1,2,7,8]=>0001100=>0011000
[7,5,4,3,8,6,2,1]=>1011111=>1111101
[4,3,8,2,6,7,5,1]=>0011011=>1101100
[4,3,8,2,5,7,1,6]=>0010011=>1100100
[4,1,6,2,5,3,7,8]=>0011100=>0011100
[5,1,8,6,4,7,2,3]=>0001111=>1111000
[4,2,6,1,5,3,8,7]=>0011101=>1011100
[6,7,2,3,1,5,8,4]=>0100011=>1100010
[7,5,2,3,8,1,6,4]=>0001111=>1111000
[7,5,2,3,8,4,1,6]=>0011011=>1101100
[4,5,1,7,6,3,8,2]=>0001111=>1111000
[8,6,3,1,4,2,5,7]=>0110101=>1010110
[4,5,1,6,2,8,7,3]=>0001111=>1111000
[4,8,3,6,1,7,2,5]=>0000111=>1110000
[6,2,7,8,3,4,5,1]=>0001101=>1011000
[9,2,3,4,5,6,7,8,1]=>00000011=>11000000
[8,2,3,4,5,6,7,1,9]=>00000110=>01100000
[7,2,3,4,5,6,1,8,9]=>00001100=>00110000
[6,2,3,4,5,1,7,8,9]=>00011000=>00011000
[5,2,3,4,1,6,7,8,9]=>00110000=>00001100
[4,2,3,1,5,6,7,8,9]=>01100000=>00000110
[1,2,4,3,5,6,7,8,9]=>00100000=>00000100
[1,2,4,6,8,9,7,5,3]=>00010101=>10101000
[1,2,4,5,3,6,7,8,9]=>00010000=>00001000
[1,2,4,3,5,6,7,8,9,10]=>001000000=>000000100
[1,2,4,6,8,10,9,7,5,3]=>000101011=>110101000
[1,2,4,6,8,5,7,3]=>0000011=>1100000
[2,1,7,5,8,6,3,4]=>1000111=>1110001
[4,7,3,8,6,5,2,1]=>1001111=>1111001
[3,8,7,4,6,5,1,2]=>0001111=>1111000
[7,3,8,4,6,5,1,2]=>0001111=>1111000
[7,4,3,6,5,8,1,2]=>0010111=>1110100
[4,5,8,7,2,6,1,3]=>0000111=>1110000
[3,8,6,7,5,1,4,2]=>0011011=>1101100
[4,2,7,6,5,8,3,1]=>0110111=>1110110
[4,6,7,8,5,2,3,1]=>0101001=>1001010
[4,5,3,8,2,7,6,1]=>0001111=>1111000
[3,8,5,4,1,7,6,2]=>0011111=>1111100
[6,4,7,2,5,8,3,1]=>0100111=>1110010
[6,3,8,7,5,1,4,2]=>0011111=>1111100
[5,3,6,4,1,2,8,7]=>0011101=>1011100
[6,8,4,3,5,7,1,2]=>0010011=>1100100
[5,2,4,8,7,6,1,3]=>0001111=>1111000
[3,2,4,5,1,8,6,7]=>0101001=>1001010
[4,2,5,1,7,8,3,6]=>0011001=>1001100
[2,5,4,1,3,8,6,7]=>0011001=>1001100
[1,4,5,3,8,2,6,7]=>0001001=>1001000
[5,1,8,2,4,3,6,7]=>0011001=>1001100
[1,5,4,8,2,3,6,7]=>0001001=>1001000
[3,5,1,4,7,8,2,6]=>0001001=>1001000
[4,8,3,1,6,7,2,5]=>0100011=>1100010
[3,4,8,2,6,5,7,1]=>0000111=>1110000
[3,6,2,4,8,7,1,5]=>0000111=>1110000
[4,7,3,2,6,8,1,5]=>0100011=>1100010
[7,3,4,6,8,1,2,5]=>0000011=>1100000
[3,6,7,2,5,8,1,4]=>0000011=>1100000
[1,5,6,8,3,7,2,4]=>0000011=>1100000
[6,1,5,8,3,4,7,2]=>0000111=>1110000
[5,6,8,1,3,4,7,2]=>0000011=>1100000
[2,8,5,6,3,4,7,1]=>0000111=>1110000
[6,8,1,3,5,4,7,2]=>0001011=>1101000
[8,1,6,3,5,4,7,2]=>0001111=>1111000
[1,8,7,3,6,4,5,2]=>0001111=>1111000
[7,1,2,5,8,4,6,3]=>0000111=>1110000
[6,2,4,8,1,7,3,5]=>0000111=>1110000
[3,1,7,8,5,4,6,2]=>0101101=>1011010
[1,6,2,7,4,8,5,3]=>0001111=>1111000
[2,7,1,8,4,3,5,6]=>0010011=>1100100
[6,7,1,8,3,2,4,5]=>0100011=>1100010
[2,7,6,3,5,8,1,4]=>0000111=>1110000
[2,7,5,6,8,1,3,4]=>0000011=>1100000
[6,7,2,8,1,3,4,5]=>0000011=>1100000
[5,1,6,8,7,2,3,4]=>0001011=>1101000
[1,5,7,6,8,2,3,4]=>0000011=>1100000
[7,4,6,8,5,3,1,2]=>0101011=>1101010
[2,1,5,7,8,3,6,4]=>1000101=>1010001
[3,8,6,7,5,1,2,4]=>0001011=>1101000
[4,7,5,8,6,3,1,2]=>0100111=>1110010
[1,6,8,3,2,5,4,7]=>0101001=>1001010
[7,8,5,1,3,2,6,4]=>0101101=>1011010
[2,6,8,1,5,4,7,3]=>0001011=>1101000
[1,5,4,7,6,2,8,3]=>0001111=>1111000
[2,3,7,6,5,1,8,4]=>0001111=>1111000
[6,1,5,8,3,2,7,4]=>0100111=>1110010
[3,1,2,4,8,5,7,6]=>0100011=>1100010
[2,5,8,4,6,3,1,7]=>0100101=>1010010
[7,1,5,4,8,3,2,6]=>0101011=>1101010
[6,4,1,7,5,3,2,8]=>0111110=>0111110
[2,7,6,4,8,1,5,3]=>0001111=>1111000
[7,2,5,4,8,1,6,3]=>0001111=>1111000
[1,7,2,5,3,8,6,4]=>0001111=>1111000
[2,4,1,3,6,8,5,7,9]=>00100010=>01000100
[7,2,3,8,6,1,5,4]=>0001111=>1111000
[7,3,2,5,8,1,6,4]=>0100111=>1110010
[5,3,8,4,1,2,6,7]=>0011001=>1001100
[2,4,8,3,7,1,5,6]=>0000011=>1100000
[5,2,8,4,1,6,3,7]=>0011101=>1011100
[7,6,5,2,1,8,4,3]=>1011111=>1111101
[2,7,5,1,8,3,6,4]=>0001111=>1111000
[5,1,8,7,4,3,6,2]=>0011111=>1111100
[3,8,7,2,4,6,1,5]=>0000111=>1110000
[5,7,1,3,2,4,8,6]=>0100011=>1100010
[4,2,7,6,3,5,8,1]=>0010111=>1110100
[8,4,7,6,3,5,1,2]=>0001111=>1111000
[8,1,7,4,2,3,5,6]=>0010011=>1100100
[6,5,1,3,8,7,4,2]=>0011111=>1111100
[4,7,8,3,2,5,1,6]=>0101001=>1001010
[6,1,8,5,3,7,2,4]=>0001111=>1111000
[5,1,6,8,3,7,4,2]=>0011011=>1101100
[8,6,5,1,7,4,3,2]=>0111111=>1111110
[7,6,4,1,3,5,8,2]=>0010111=>1110100
[8,2,3,7,1,4,5,6]=>0000011=>1100000
[2,8,3,7,1,4,5,6]=>0000011=>1100000
[5,6,2,7,4,3,1,8]=>0110110=>0110110
[8,6,2,7,4,1,3,5]=>0010111=>1110100
[3,7,8,2,6,1,4,5]=>0000101=>1010000
[3,7,8,5,2,1,4,6]=>1001001=>1001001
[6,8,4,7,3,1,5,2]=>0101011=>1101010
[4,8,6,5,1,2,7,3]=>0001111=>1111000
[4,8,6,5,1,2,3,7]=>0001101=>1011000
[3,4,5,1,7,6,8,2]=>0001011=>1101000
[3,8,7,6,5,1,2,4]=>0001111=>1111000
[8,4,6,7,1,2,5,3]=>0001011=>1101000
[5,7,2,6,1,8,4,3]=>0010111=>1110100
[5,7,2,6,1,3,8,4]=>0000111=>1110000
[5,8,2,6,1,4,7,3]=>0000111=>1110000
[3,8,7,5,6,1,4,2]=>0010111=>1110100
[6,8,4,7,2,1,5,3]=>1001011=>1101001
[7,4,6,5,1,3,8,2]=>0001111=>1111000
[1,7,3,4,5,2,8,6]=>0001011=>1101000
[4,8,2,1,3,5,6,7]=>1000001=>1000001
[1,7,2,5,4,3,8,6]=>0011011=>1101100
[2,6,7,3,4,8,1,5]=>0000011=>1100000
[2,1,5,7,4,3,8,6]=>1010011=>1100101
[4,1,8,7,5,6,2,3]=>0010111=>1110100
[1,5,8,7,4,3,6,2]=>0010111=>1110100
[6,4,1,3,8,7,5,2]=>0011111=>1111100
[2,1,7,4,6,8,3,5]=>1000011=>1100001
[1,7,2,4,6,8,3,5]=>0000011=>1100000
[8,6,4,2,7,3,5,1]=>0011111=>1111100
[7,4,6,1,2,3,8,5]=>0000111=>1110000
[1,8,6,2,7,3,5,4]=>0001111=>1111000
[1,7,8,6,2,3,5,4]=>0001101=>1011000
[2,1,8,3,5,7,6,4]=>1000111=>1110001
[3,5,8,1,7,6,2,4]=>0000111=>1110000
[2,8,1,3,6,7,5,4]=>0001011=>1101000
[7,2,4,8,6,1,5,3]=>0001111=>1111000
[2,4,1,5,6,7,8,9,10,3]=>001000001=>100000100
[2,3,4,5,6,7,9,1,10,8]=>000000011=>110000000
[2,3,5,1,6,7,8,9,10,4]=>000100001=>100001000
[2,3,4,5,6,8,1,9,10,7]=>000000101=>101000000
[2,3,4,6,1,7,8,9,10,5]=>000010001=>100010000
[2,3,4,5,7,1,8,9,10,6]=>000001001=>100100000
[4,1,2,5,6,7,8,9,10,3]=>001000001=>100000100
[4,3,1,5,6,7,8,10,2,9]=>011000001=>100000110
[2,4,1,5,6,7,8,9,10,11,3]=>0010000001=>1000000100
[2,6,1,5,3,7,8,9,10,4]=>000110001=>100011000
[2,3,4,5,6,7,8,10,1,11,9]=>0000000011=>1100000000
[5,3,4,1,6,7,9,2,10,8]=>001100011=>110001100
[2,3,5,1,6,7,8,9,10,11,4]=>0001000001=>1000001000
[2,3,8,1,6,7,4,9,10,5]=>000001101=>101100000
[2,3,4,5,6,7,9,1,10,11,8]=>0000000101=>1010000000
[6,3,4,5,1,8,2,9,10,7]=>000110101=>101011000
[2,3,4,6,1,7,8,9,10,11,5]=>0000100001=>1000010000
[2,3,4,10,1,7,8,9,5,6]=>000000011=>110000000
[2,3,4,5,6,8,1,9,10,11,7]=>0000001001=>1001000000
[2,3,4,5,7,1,8,9,10,11,6]=>0000010001=>1000100000
[8,2,1,3,4,5,6,7,9]=>10000010=>01000001
[3,2,4,5,6,7,8,1,9]=>01000010=>01000010
[9,2,1,3,4,5,6,7,8,10]=>100000010=>010000001
[8,3,1,2,4,5,6,7,9]=>01000010=>01000010
[8,2,3,1,4,5,6,7,9]=>01000010=>01000010
[4,2,3,5,6,7,8,1,9]=>00100010=>01000100
[6,4,3,2,8,1,7,5]=>0110111=>1110110
[6,2,4,3,8,1,7,5]=>0010111=>1110100
[5,8,4,3,1,6,7,2]=>0110011=>1100110
[8,7,2,4,6,10,1,3,5,9]=>000001101=>101100000
[2,10,7,9,4,6,8,1,3,5]=>000000111=>111000000
[6,5,2,4,8,10,1,3,7,9]=>000110001=>100011000
[2,8,5,7,4,6,10,1,3,9]=>000001101=>101100000
[10,5,2,4,7,9,6,8,1,3]=>000100111=>111001000
[10,9,2,8,5,7,4,6,1,3]=>000011111=>111110000
[8,7,6,5,2,4,10,1,3,9]=>000111101=>101111000
[10,7,2,6,5,9,4,8,1,3]=>000011111=>111110000
[6,10,5,9,8,7,2,4,1,3]=>001001111=>111100100
[4,10,3,9,2,6,8,1,5,7]=>000000111=>111000000
[4,3,10,7,9,2,6,8,1,5]=>001000111=>111000100
[3,6,2,5,4,8,10,1,7,9]=>000110001=>100011000
[3,6,10,2,5,9,4,8,1,7]=>000000111=>111000000
[3,5,8,2,4,7,6,10,1,9]=>000001101=>101100000
[3,5,7,10,2,4,6,9,8,1]=>000000111=>111000000
[10,9,3,5,8,2,4,7,6,1]=>000011111=>111110000
[8,7,3,6,2,5,4,10,1,9]=>000111101=>101111000
[7,6,3,5,10,2,4,9,8,1]=>000011111=>111110000
[3,6,10,9,8,2,5,7,4,1]=>001001111=>111100100
[10,9,8,7,3,6,2,5,4,1]=>001111111=>111111100
[5,4,3,8,2,7,6,10,1,9]=>001101101=>101101100
[5,4,3,7,10,2,6,9,8,1]=>001100111=>111001100
[5,10,4,9,3,8,2,7,6,1]=>000011111=>111110000
[4,8,3,7,6,5,2,10,1,9]=>000111101=>101111000
[4,7,3,6,5,10,2,9,8,1]=>000011111=>111110000
[4,6,10,3,5,9,8,7,2,1]=>100001111=>111100001
[10,9,4,8,3,7,6,5,2,1]=>100111111=>111111001
[7,6,5,4,3,10,2,9,8,1]=>001111111=>111111100
[6,5,4,10,3,9,8,7,2,1]=>100111111=>111111001
[5,10,4,9,8,7,6,3,2,1]=>110011111=>111110011
[12,11,2,4,6,8,10,1,3,5,7,9]=>00000000111=>11100000000
[10,9,2,4,6,8,12,1,3,5,7,11]=>00000001101=>10110000000
[2,12,9,11,4,6,8,10,1,3,5,7]=>00000000111=>11100000000
[12,11,10,9,2,4,6,8,1,3,5,7]=>00000011111=>11111000000
[8,7,2,4,6,10,12,1,3,5,9,11]=>00000110001=>10001100000
[8,12,7,11,2,4,6,10,1,3,5,9]=>00000000111=>11100000000
[2,10,7,9,4,6,8,12,1,3,5,11]=>00000001101=>10110000000
[2,4,12,7,9,11,6,8,10,1,3,5]=>00000000111=>11100000000
[12,11,2,10,7,9,4,6,8,1,3,5]=>00000011111=>11111000000
[10,9,8,7,2,4,6,12,1,3,5,11]=>00000111101=>10111100000
[12,9,2,8,7,11,4,6,10,1,3,5]=>00000011111=>11111000000
[8,12,7,11,10,9,2,4,6,1,3,5]=>00001001111=>11110010000
[12,11,10,9,8,7,2,4,6,1,3,5]=>00001111111=>11111110000
[6,5,2,4,8,10,12,1,3,7,9,11]=>00011000001=>10000011000
[6,12,5,11,2,4,8,10,1,3,7,9]=>00000000111=>11100000000
[6,10,5,9,2,4,8,12,1,3,7,11]=>00000001101=>10110000000
[6,5,12,9,11,2,4,8,10,1,3,7]=>00001000111=>11100010000
[12,11,6,10,5,9,2,4,8,1,3,7]=>00000011111=>11111000000
[2,8,5,7,4,6,10,12,1,3,9,11]=>00000110001=>10001100000
[2,8,12,5,7,11,4,6,10,1,3,9]=>00000000111=>11100000000
[12,5,7,2,4,6,9,11,8,10,1,3]=>00000100111=>11100100000
[12,5,11,10,2,4,7,9,6,8,1,3]=>00000011111=>11111000000
[10,9,2,8,5,7,4,6,12,1,3,11]=>00000111101=>10111100000
[12,5,9,8,2,4,7,11,6,10,1,3]=>00000011111=>11111000000
[2,12,5,11,8,10,7,9,4,6,1,3]=>00001001111=>11110010000
[12,11,10,9,2,8,5,7,4,6,1,3]=>00001111111=>11111110000
[8,7,6,12,5,11,2,4,10,1,3,9]=>00000110111=>11101100000
[10,7,2,6,5,9,4,8,12,1,3,11]=>00001101101=>10110110000
[7,6,12,5,2,4,9,11,8,10,1,3]=>00010100111=>11100101000
[2,12,7,11,6,10,5,9,4,8,1,3]=>00000011111=>11111000000
[6,10,5,9,8,7,2,4,12,1,3,11]=>00000111101=>10111100000
[2,12,6,9,5,8,7,11,4,10,1,3]=>00000011111=>11111000000
[6,8,12,5,7,11,10,9,2,4,1,3]=>00100001111=>11110000100
[12,11,6,10,5,9,8,7,2,4,1,3]=>00100111111=>11111100100
[10,9,8,7,6,5,2,4,12,1,3,11]=>00011111101=>10111111000
[12,9,8,7,2,6,5,11,4,10,1,3]=>00001111111=>11111110000
[8,7,6,12,5,11,10,9,2,4,1,3]=>00100111111=>11111100100
[7,12,6,11,10,9,8,5,2,4,1,3]=>00110011111=>11111001100
[12,11,10,9,8,7,6,5,2,4,1,3]=>00111111111=>11111111100
[4,3,2,6,8,10,12,1,5,7,9,11]=>01100000001=>10000000110
[4,12,3,11,2,6,8,10,1,5,7,9]=>00000000111=>11100000000
[4,10,3,9,2,6,8,12,1,5,7,11]=>00000001101=>10110000000
[4,3,12,9,11,2,6,8,10,1,5,7]=>00100000111=>11100000100
[12,11,4,10,3,9,2,6,8,1,5,7]=>00000011111=>11111000000
[4,8,3,7,2,6,10,12,1,5,9,11]=>00000110001=>10001100000
[4,8,12,3,7,11,2,6,10,1,5,9]=>00000000111=>11100000000
[4,3,7,9,12,11,2,6,8,10,1,5]=>00100000111=>11100000100
[12,4,11,3,10,7,9,2,6,8,1,5]=>00000011111=>11111000000
[10,9,4,8,3,7,2,6,12,1,5,11]=>00000111101=>10111100000
[12,4,9,3,8,7,11,2,6,10,1,5]=>00000011111=>11111000000
[4,8,12,11,10,3,7,9,2,6,1,5]=>00001001111=>11110010000
[12,11,10,9,4,8,3,7,2,6,1,5]=>00001111111=>11111110000
[3,6,2,5,4,8,10,12,1,7,9,11]=>00011000001=>10000011000
[3,6,12,2,5,11,4,8,10,1,7,9]=>00000000111=>11100000000
[3,6,10,2,5,9,4,8,12,1,7,11]=>00000001101=>10110000000
[3,12,6,2,5,9,11,4,8,10,1,7]=>00001000111=>11100010000
[12,11,3,6,10,2,5,9,4,8,1,7]=>00000011111=>11111000000
[3,5,8,2,4,7,6,10,12,1,9,11]=>00000110001=>10001100000
[3,5,8,12,2,4,7,11,6,10,1,9]=>00000000111=>11100000000
[3,5,7,10,2,4,6,9,8,12,1,11]=>00000001101=>10110000000
[3,5,7,9,12,2,4,6,8,11,10,1]=>00000000111=>11100000000
[12,11,3,5,7,10,2,4,6,9,8,1]=>00000011111=>11111000000
[10,9,3,5,8,2,4,7,6,12,1,11]=>00000111101=>10111100000
[9,8,3,5,7,12,2,4,6,11,10,1]=>00000011111=>11111000000
[3,5,12,11,8,10,2,4,7,9,6,1]=>00001001111=>11110010000
[12,11,10,9,3,5,8,2,4,7,6,1]=>00001111111=>11111110000
[8,7,3,6,12,2,5,11,4,10,1,9]=>00000110111=>11101100000
[7,6,3,5,10,2,4,9,8,12,1,11]=>00001101101=>10110110000
[7,6,3,5,9,12,2,4,8,11,10,1]=>00001100111=>11100110000
[7,12,6,11,3,5,10,2,4,9,8,1]=>00000011111=>11111000000
[3,6,10,9,8,2,5,7,4,12,1,11]=>00000111101=>10111100000
[3,9,6,8,5,7,12,2,4,11,10,1]=>00000011111=>11111000000
[3,2,12,6,8,11,10,5,7,9,4,1]=>01100001111=>11110000110
[12,11,3,6,10,9,8,2,5,7,4,1]=>00100111111=>11111100100
[10,9,8,7,3,6,2,5,4,12,1,11]=>00011111101=>10111111000
[9,8,7,6,3,5,12,2,4,11,10,1]=>00001111111=>11111110000
[8,7,3,6,12,11,10,2,5,9,4,1]=>00100111111=>11111100100
[3,12,7,11,10,9,6,8,2,5,4,1]=>00110011111=>11111001100
[12,11,10,9,8,7,3,6,2,5,4,1]=>00111111111=>11111111100
[6,5,4,3,2,8,10,12,1,7,9,11]=>01111000001=>10000011110
[6,5,4,12,3,11,2,8,10,1,7,9]=>00011000111=>11100011000
[6,5,4,10,3,9,2,8,12,1,7,11]=>00011001101=>10110011000
[5,12,4,11,3,7,10,2,6,9,8,1]=>00000011111=>11111000000
[5,10,4,9,3,8,2,7,6,12,1,11]=>00000111101=>10111100000
[5,9,4,8,3,7,12,2,6,11,10,1]=>00000011111=>11111000000
[12,11,5,10,4,9,3,8,2,7,6,1]=>00001111111=>11111110000
[4,8,3,7,6,12,5,11,2,10,1,9]=>00000110111=>11101100000
[4,7,3,6,5,10,2,9,8,12,1,11]=>00001101101=>10110110000
[4,7,3,6,5,9,12,2,8,11,10,1]=>00001100111=>11100110000
[4,7,12,3,6,11,5,10,2,9,8,1]=>00000011111=>11111000000
[4,6,10,3,5,9,8,7,2,12,1,11]=>00000111101=>10111100000
[4,6,9,3,5,8,7,12,2,11,10,1]=>00000011111=>11111000000
[10,9,4,8,3,7,6,5,2,12,1,11]=>00011111101=>10111111000
[9,8,4,7,3,6,5,12,2,11,10,1]=>00001111111=>11111110000
[12,11,10,9,4,8,3,7,6,5,2,1]=>10011111111=>11111111001
[8,7,6,5,4,12,3,11,2,10,1,9]=>00011110111=>11101111000
[7,6,5,4,3,10,2,9,8,12,1,11]=>00111101101=>10110111100
[7,6,5,12,4,11,3,10,2,9,8,1]=>00001111111=>11111110000
[6,5,4,10,3,9,8,7,2,12,1,11]=>00011111101=>10111111000
[6,5,4,9,3,8,7,12,2,11,10,1]=>00011011111=>11111011000
[5,9,4,8,7,6,3,12,2,11,10,1]=>00001111111=>11111110000
[12,11,5,10,4,9,8,7,6,3,2,1]=>11001111111=>11111110011
[10,9,8,7,6,5,4,3,2,12,1,11]=>01111111101=>10111111110
[9,8,7,6,5,4,3,12,2,11,10,1]=>00111111111=>11111111100
[8,7,6,5,4,12,3,11,10,9,2,1]=>10011111111=>11111111001
[7,6,5,12,4,11,10,9,8,3,2,1]=>11001111111=>11111110011
[6,12,5,11,10,9,8,7,4,3,2,1]=>11100111111=>11111100111
[4,2,8,1,5,7,6,3]=>0010111=>1110100
[6,3,7,2,5,4,8,1]=>0001111=>1111000
[5,4,7,3,2,6,8,1]=>0101011=>1101010
[5,7,2,6,3,4,8,1]=>0000111=>1110000
[3,7,5,4,6,2,8,1]=>0001111=>1111000
[6,8,3,2,1,7,4,5]=>1100011=>1100011
[4,8,1,7,5,3,2,6]=>0101011=>1101010
[5,4,3,7,2,8,6,1]=>0011111=>1111100
[3,6,5,7,2,8,4,1]=>0010111=>1110100
[4,6,5,3,8,2,1,7]=>1001101=>1011001
[2,6,5,8,7,3,1,4]=>0100111=>1110010
[6,3,8,4,1,7,2,5]=>0010111=>1110100
[7,2,8,1,6,4,3,5]=>0010111=>1110100
[3,2,8,7,6,4,1,5]=>0110111=>1110110
[8,2,6,4,3,5,1,7]=>0011101=>1011100
[5,4,2,8,6,3,7,1]=>0011111=>1111100
[2,8,7,5,3,1,4,6]=>0101011=>1101010
[2,5,6,3,1,4,8,7]=>0100101=>1010010
[2,4,7,8,5,3,1,6]=>0101001=>1001010
[6,5,3,2,4,1,8,7]=>0111101=>1011110
[6,5,8,7,3,2,4,1]=>0110111=>1110110
[2,1,4,7,8,5,3,6]=>1001001=>1001001
[8,3,1,6,5,7,4,2]=>0110111=>1110110
[8,5,6,7,3,1,4,2]=>0110011=>1100110
[8,7,5,3,2,6,4,1]=>0111111=>1111110
[8,5,3,1,4,6,7,2]=>0101011=>1101010
[8,5,1,6,4,3,7,2]=>0011111=>1111100
[6,1,4,3,7,8,2,5]=>0010101=>1010100
[6,1,2,7,5,8,3,4]=>0000111=>1110000
[2,7,3,1,4,6,8,5]=>0100011=>1100010
[2,8,3,1,6,5,7,4]=>0100111=>1110010
[3,8,5,6,7,1,2,4]=>0000011=>1100000
[6,5,1,2,8,4,7,3]=>0001111=>1111000
[2,5,8,1,4,6,7,3]=>0000011=>1100000
[2,1,8,7,5,4,6,3]=>1001111=>1111001
[7,8,3,4,1,6,5,2]=>0011101=>1011100
[8,7,3,4,2,6,5,1]=>0011111=>1111100
[8,4,5,2,3,7,1,6]=>0001011=>1101000
[6,4,7,5,2,8,3,1]=>0101111=>1111010
[4,6,3,8,7,5,1,2]=>0001111=>1111000
[2,8,4,1,5,7,6,3]=>0010111=>1110100
[1,8,4,2,5,7,6,3]=>0010111=>1110100
[2,8,5,4,1,7,6,3]=>0011111=>1111100
[2,5,8,3,7,1,6,4]=>0000111=>1110000
[1,8,5,2,4,7,6,3]=>0001111=>1111000
[1,4,6,2,8,7,5,3]=>0001111=>1111000
[7,8,2,4,1,6,5,3]=>0011101=>1011100
[2,4,6,1,8,7,5,3]=>0001111=>1111000
[2,8,4,5,1,7,6,3]=>0001111=>1111000
[3,5,8,2,7,6,1,4]=>0000111=>1110000
[2,1,6,8,7,5,3,4]=>1001011=>1101001
[1,8,2,4,5,7,6,3]=>0000111=>1110000
[1,2,8,3,5,7,6,4]=>0000111=>1110000
[1,3,8,2,5,7,6,4]=>0000111=>1110000
[2,3,8,1,5,7,6,4]=>0000111=>1110000
[2,6,1,8,7,5,3,4]=>0001111=>1111000
[1,6,2,8,7,5,3,4]=>0001111=>1111000
[1,6,3,8,7,5,2,4]=>0001111=>1111000
[2,6,3,8,7,5,1,4]=>0001111=>1111000
[3,2,8,1,5,7,6,4]=>0100111=>1110010
[3,1,8,2,5,7,6,4]=>0100111=>1110010
[2,8,1,4,5,7,6,3]=>0000111=>1110000
[7,8,2,1,4,6,5,3]=>1001101=>1011001
[2,3,6,8,7,5,1,4]=>0001011=>1101000
[3,1,6,8,7,2,5,4]=>0101011=>1101010
[3,8,4,5,1,6,2,7]=>0001101=>1011000
[6,1,4,5,7,2,3,8]=>0000110=>0110000
[8,1,4,7,6,3,2,5]=>0100111=>1110010
[8,3,1,6,4,7,2,5]=>0100111=>1110010
[5,3,8,6,2,7,1,4]=>0001111=>1111000
[8,3,6,1,5,7,2,4]=>0000111=>1110000
[8,4,6,3,1,2,5,7]=>0100101=>1010010
[6,8,1,4,5,2,3,7]=>0001001=>1001000
[1,5,8,4,6,2,3,7]=>0000101=>1010000
[2,1,6,5,3,8,4,7]=>1001101=>1011001
[5,6,8,1,4,2,3,7]=>0010001=>1000100
[5,7,4,8,1,2,3,6]=>0000011=>1100000
[8,2,1,5,3,7,4,6]=>1001011=>1101001
[4,7,8,1,2,6,3,5]=>0000101=>1010000
[8,7,1,5,6,2,3,4]=>0000111=>1110000
[1,6,5,8,7,2,3,4]=>0000111=>1110000
[3,7,1,6,2,4,8,5]=>0000111=>1110000
[5,1,2,7,6,8,3,4]=>0001011=>1101000
[6,1,7,2,5,8,3,4]=>0000111=>1110000
[1,7,6,5,8,2,3,4]=>0000111=>1110000
[1,6,8,5,7,2,3,4]=>0000011=>1100000
[7,5,1,2,6,8,3,4]=>0001011=>1101000
[6,1,5,2,7,8,3,4]=>0001101=>1011000
[1,6,3,8,7,2,4,5]=>0000111=>1110000
[1,7,3,2,4,6,8,5]=>0100011=>1100010
[8,3,1,4,2,5,7,6]=>0110011=>1100110
[3,1,2,7,8,4,6,5]=>0100101=>1010010
[5,1,2,6,8,7,3,4]=>0001011=>1101000
[1,8,6,2,5,7,3,4]=>0000111=>1110000
[5,7,8,1,2,6,3,4]=>0000101=>1010000
[8,1,5,7,6,2,3,4]=>0000111=>1110000
[7,1,6,8,5,2,3,4]=>0001011=>1101000
[3,7,1,2,8,4,6,5]=>0000111=>1110000
[8,3,1,2,7,6,4,5]=>0100111=>1110010
[1,5,8,7,6,2,3,4]=>0000111=>1110000
[7,8,6,1,5,2,3,4]=>0001101=>1011000
[1,9,3,4,5,6,7,8,2]=>00000011=>11000000
[9,2,3,4,5,6,7,8,1,10]=>000000110=>011000000
[1,9,8,4,5,6,7,3,2]=>01000111=>11100010
[1,10,3,4,5,6,7,8,9,2]=>000000011=>110000000
[1,10,9,4,5,6,7,8,3,2]=>010000111=>111000010
[7,8,6,3,1,5,2,4]=>0101101=>1011010
[7,8,1,3,4,5,2,6]=>0001001=>1001000
[1,7,4,8,2,5,3,6]=>0001011=>1101000
[3,8,6,1,4,2,7,5]=>0010111=>1110100
[7,1,8,2,4,6,3,5]=>0000111=>1110000
[7,6,8,4,1,5,3,2]=>0111011=>1101110
[7,3,2,8,1,5,4,6]=>0101011=>1101010
[3,5,4,1,7,2,6,8]=>0011010=>0101100
[6,4,7,3,2,5,1,8]=>0101110=>0111010
[7,6,5,3,8,4,1,2]=>0011111=>1111100
[6,4,5,7,8,1,3,2]=>0100101=>1010010
[3,7,4,1,6,8,5,2]=>0011011=>1101100
[3,1,2,7,6,8,5,4]=>0101011=>1101010
[6,3,2,8,4,5,1,7]=>0101101=>1011010
[6,1,8,3,5,4,2,7]=>0011101=>1011100
[3,8,5,2,4,6,1,7]=>0001101=>1011000
[1,6,4,8,3,5,2,7]=>0001101=>1011000
[1,5,4,8,6,3,7,2]=>0001111=>1111000
[4,8,2,5,3,7,1,6]=>0001011=>1101000
[3,8,4,5,2,6,7,1]=>0001011=>1101000
[4,1,8,6,5,3,7,2]=>0011111=>1111100
[5,7,8,4,6,3,2,1]=>1100101=>1010011
[5,3,2,8,6,4,7,1]=>0101111=>1111010
[6,8,1,2,7,4,3,5]=>0010011=>1100100
[5,8,7,3,6,2,4,1]=>0010111=>1110100
[7,5,2,3,4,8,6,1]=>0001111=>1111000
[7,3,5,4,2,8,6,1]=>0011111=>1111100
[5,6,1,3,2,4,7,8]=>0100100=>0010010
[2,5,1,3,7,8,6,4]=>0001101=>1011000
[4,3,7,2,1,8,6,5]=>1010111=>1110101
[4,6,7,2,1,3,5,8]=>1000010=>0100001
[4,6,2,3,1,5,7,8]=>0100100=>0010010
[3,6,4,2,5,1,7,8]=>0011100=>0011100
[3,1,6,4,7,5,2,8]=>0101110=>0111010
[3,6,2,7,5,4,1,8]=>0011110=>0111100
[2,4,7,5,3,6,1,8]=>0001110=>0111000
[2,5,7,3,4,1,6,8]=>0010010=>0100100
[2,3,5,8,6,4,7,1]=>0000111=>1110000
[2,4,7,3,8,6,5,1]=>0001111=>1111000
[3,4,2,7,5,8,6,1]=>0010111=>1110100
[3,1,5,4,7,8,6,2]=>0101101=>1011010
[4,5,7,2,3,1,8,6]=>0100011=>1100010
[3,7,8,1,4,6,5,2]=>0001101=>1011000
[2,5,8,7,4,1,3,6]=>0010011=>1100100
[2,6,4,7,5,3,8,1]=>0001111=>1111000
[6,2,4,7,1,3,8,5]=>0000111=>1110000
[7,3,5,1,4,2,8,6]=>0011011=>1101100
[5,4,7,1,3,2,8,6]=>0101011=>1101010
[6,1,4,7,5,3,8,2]=>0001111=>1111000
[8,7,4,3,1,5,6,2]=>0110111=>1110110
[8,7,1,4,3,5,6,2]=>0010111=>1110100
[6,1,8,4,7,3,2,5]=>0100111=>1110010
[4,7,3,6,1,2,8,5]=>0000111=>1110000
[5,2,1,7,4,3,8,6]=>1011011=>1101101
[4,7,6,2,3,1,8,5]=>0100111=>1110010
[7,6,8,2,5,3,4,1]=>0011011=>1101100
[2,3,6,1,8,7,5,4]=>0001111=>1111000
[2,6,8,7,5,3,1,4]=>0101011=>1101010
[6,4,1,7,5,2,8,3]=>0011111=>1111100
[5,7,8,2,3,6,1,4]=>0000101=>1010000
[4,8,7,1,2,5,6,3]=>0000111=>1110000
[2,8,7,4,1,5,6,3]=>0010111=>1110100
[8,6,2,1,5,7,4,3]=>1010111=>1110101
[3,8,6,7,5,2,1,4]=>1001011=>1101001
[6,1,3,7,5,8,2,4]=>0000111=>1110000
[4,7,3,1,8,5,6,2]=>0100111=>1110010
[2,6,7,5,3,4,8,1]=>0001011=>1101000
[2,6,4,5,7,3,8,1]=>0000111=>1110000
[6,1,4,5,8,3,7,2]=>0000111=>1110000
[6,1,8,5,3,4,7,2]=>0001111=>1111000
[4,1,5,6,8,3,7,2]=>0010011=>1100100
[6,4,1,8,7,2,5,3]=>0011111=>1111100
[8,1,2,3,4,5,6,7,10,9]=>000000101=>101000000
[1,7,2,3,4,5,6,9,8]=>00000101=>10100000
[6,9,1,2,3,4,5,7,8]=>00000001=>10000000
[1,3,8,5,2,7,4,6]=>0001011=>1101000
[1,3,8,6,7,2,4,5]=>0000011=>1100000
[2,8,3,7,6,1,4,5]=>0000111=>1110000
[4,2,7,8,6,1,3,5]=>0010101=>1010100
[1,3,8,7,6,2,4,5]=>0000111=>1110000
[7,4,6,8,5,2,3,1]=>0101011=>1101010
[7,5,3,6,8,2,1,4]=>1001011=>1101001
[5,2,6,7,8,1,3,4]=>0001001=>1001000
[4,5,6,8,1,2,7,3]=>0000011=>1100000
[3,5,8,6,1,2,7,4]=>0000111=>1110000
[4,2,6,8,7,1,3,5]=>0010011=>1100100
[1,4,6,8,7,2,3,5]=>0000011=>1100000
[4,5,3,8,1,7,2,6]=>0001011=>1101000
[3,5,8,4,1,7,2,6]=>0010011=>1100100
[1,6,5,7,8,2,3,4]=>0000101=>1010000
[5,6,4,8,2,3,7,1]=>0000111=>1110000
[6,5,4,8,1,3,7,2]=>0001111=>1111000
[7,6,4,8,5,1,3,2]=>0101111=>1111010
[7,2,6,5,8,1,3,4]=>0000111=>1110000
[6,3,7,5,2,4,8,1]=>0001111=>1111000
[8,1,2,7,4,5,3,6]=>0001011=>1101000
[2,5,7,4,6,1,3,8]=>0000110=>0110000
[6,1,7,4,5,3,8,2]=>0001111=>1111000
[8,2,7,3,1,5,4,6]=>0101011=>1101010
[2,6,4,8,3,1,7,5]=>0100111=>1110010
[8,1,3,7,5,6,4,2]=>0010111=>1110100
[1,2,5,3,8,6,7,4]=>0001011=>1101000
[4,1,6,5,7,8,2,3]=>0010101=>1010100
[6,1,3,7,4,2,8,5]=>0010111=>1110100
[6,7,2,4,1,3,8,5]=>0010011=>1100100
[7,3,8,4,2,6,5,1]=>0011111=>1111100
[8,5,3,4,2,7,1,6]=>0011011=>1101100
[1,3,8,2,5,6,7,4]=>0000011=>1100000
[1,8,6,7,2,5,4,3]=>0011011=>1101100
[7,6,8,3,5,4,2,1]=>1011011=>1101101
[1,6,7,3,8,5,4,2]=>0011011=>1101100
[8,7,2,4,6,1,5,3]=>0001111=>1111000
[7,8,6,5,2,4,3,1]=>0111101=>1011110
[3,6,7,5,2,8,4,1]=>0011011=>1101100
[5,4,6,7,8,1,3,2]=>0101001=>1001010
[5,3,6,7,8,1,4,2]=>0011001=>1001100
[5,3,7,6,8,4,1,2]=>0011011=>1101100
[7,5,3,2,8,6,4,1]=>0111111=>1111110
[5,4,8,6,7,2,3,1]=>0101011=>1101010
[5,4,8,6,3,1,2,7]=>0101101=>1011010
[4,5,7,3,6,2,8,1]=>0000111=>1110000
[4,5,6,3,8,2,7,1]=>0000111=>1110000
[5,4,8,7,2,1,3,6]=>1001011=>1101001
[2,5,4,7,8,1,3,6]=>0001001=>1001000
[5,3,6,4,8,2,7,1]=>0001111=>1111000
[5,3,7,4,6,2,8,1]=>0001111=>1111000
[8,2,6,3,7,4,5,1]=>0001111=>1111000
[8,2,4,7,3,5,6,1]=>0000111=>1110000
[8,2,6,5,7,3,4,1]=>0010111=>1110100
[4,5,6,2,7,3,8,1]=>0000111=>1110000
[5,4,6,2,8,3,7,1]=>0001111=>1111000
[8,4,6,1,7,2,5,3]=>0001111=>1111000
[5,2,1,6,3,8,7,4]=>1001111=>1111001
[4,5,6,3,7,1,8,2]=>0000111=>1110000
[6,3,2,8,5,4,1,7]=>0111101=>1011110
[4,3,1,5,2,8,6,7]=>0111001=>1001110
[8,5,4,1,3,2,6,7]=>0111001=>1001110
[3,8,4,1,5,2,6,7]=>0011001=>1001100
[2,5,4,3,8,1,6,7]=>0011001=>1001100
[2,5,7,4,3,1,6,8]=>0110010=>0100110
[5,3,4,2,7,1,6,8]=>0011010=>0101100
[3,7,5,4,1,2,6,8]=>0011010=>0101100
[4,2,5,1,3,8,7,6]=>0011011=>1101100
[4,3,5,1,2,7,6,8]=>0011010=>0101100
[5,3,4,1,7,2,6,8]=>0011010=>0101100
[4,1,6,3,5,2,7,8]=>0011100=>0011100
[4,2,1,8,6,3,7,5]=>1010111=>1110101
[3,1,7,2,5,6,4,8]=>0100110=>0110010
[3,7,5,4,2,1,6,8]=>1011010=>0101101
[3,7,2,4,1,6,5,8]=>0010110=>0110100
[7,3,2,1,6,4,5,8]=>1100110=>0110011
[2,8,6,1,7,4,3,5]=>0010111=>1110100
[2,5,4,6,1,3,7,8]=>0001100=>0011000
[2,5,6,4,1,3,7,8]=>0010100=>0010100
[8,5,2,6,1,3,7,4]=>0001111=>1111000
[7,1,5,6,3,2,4,8]=>0100110=>0110010
[7,1,2,5,4,6,3,8]=>0001110=>0111000
[2,4,1,6,5,3,7,8]=>0011100=>0011100
[4,1,2,7,5,6,3,8]=>0010110=>0110100
[7,1,2,6,5,4,3,8]=>0011110=>0111100
[8,2,1,5,6,3,7,4]=>1000111=>1110001
[2,8,5,1,6,4,7,3]=>0001111=>1111000
[6,1,4,5,3,2,7,8]=>0101100=>0011010
[3,1,6,5,4,2,7,8]=>0111100=>0011110
[3,1,4,6,5,2,7,8]=>0101100=>0011010
[6,4,1,5,3,2,8,7]=>0111101=>1011110
[2,1,8,6,3,7,5,4]=>1001111=>1111001
[5,8,3,1,7,6,4,2]=>0110111=>1110110
[7,6,3,2,8,5,1,4]=>0101111=>1111010
[5,6,3,8,7,4,1,2]=>0010111=>1110100
[5,2,6,8,7,4,1,3]=>0011011=>1101100
[4,3,8,5,7,2,6,1]=>0010111=>1110100
[6,3,8,5,4,1,2,7]=>0011101=>1011100
[6,3,8,4,5,1,2,7]=>0001101=>1011000
[5,2,3,1,4,8,6,7]=>0101001=>1001010
[5,4,1,3,2,8,6,7]=>0111001=>1001110
[5,1,3,4,2,8,6,7]=>0011001=>1001100
[5,2,1,4,3,8,6,7]=>1011001=>1001101
[4,2,7,3,8,5,1,6]=>0011011=>1101100
[4,7,3,2,8,5,1,6]=>0101011=>1101010
[5,3,1,2,4,8,6,7]=>0101001=>1001010
[5,4,3,1,2,8,6,7]=>0111001=>1001110
[5,3,4,1,2,8,6,7]=>0011001=>1001100
[5,2,3,4,1,8,6,7]=>0011001=>1001100
[5,1,7,3,4,6,8,2]=>0001011=>1101000
[5,8,7,4,3,1,6,2]=>0110111=>1110110
[6,8,1,3,4,5,7,2]=>0000011=>1100000
[3,5,2,8,1,6,7,4]=>0001011=>1101000
[3,1,7,8,2,5,4,6]=>0101001=>1001010
[6,2,3,7,4,1,8,5]=>0010111=>1110100
[6,3,7,4,1,2,5,8]=>0010110=>0110100
[7,2,6,8,4,3,1,5]=>0110011=>1100110
[3,7,2,8,6,5,1,4]=>0001111=>1111000
[3,6,7,5,1,2,4,8]=>0001010=>0101000
[7,4,5,1,8,2,3,6]=>0001011=>1101000
[7,2,3,1,8,4,5,6]=>0100011=>1100010
[2,1,4,8,3,7,5,6]=>1000011=>1100001
[4,8,1,6,7,3,2,5]=>0100011=>1100010
[1,2,7,8,4,3,6,5]=>0010101=>1010100
[5,8,1,4,3,2,7,6]=>0110011=>1100110
[4,8,1,3,5,6,2,7]=>0000101=>1010000
[5,3,7,8,4,2,6,1]=>0011101=>1011100
[6,3,7,8,2,4,5,1]=>0001101=>1011000
[8,5,2,4,3,1,7,6]=>0111011=>1101110
[7,5,4,2,3,1,8,6]=>0111011=>1101110
[3,5,6,4,8,1,7,2]=>0000111=>1110000
[3,5,4,6,7,1,8,2]=>0001011=>1101000
[1,4,2,6,5,8,7,3]=>0010111=>1110100
[1,3,2,6,4,8,7,5]=>0100111=>1110010
[1,4,2,5,3,8,7,6]=>0011011=>1101100
[1,5,2,6,4,8,7,3]=>0001111=>1111000
[1,6,2,5,3,8,7,4]=>0001111=>1111000
[2,5,1,4,3,8,7,6]=>0011011=>1101100
[1,7,3,5,4,8,6,2]=>0001111=>1111000
[1,8,2,6,3,7,5,4]=>0001111=>1111000
[1,8,3,6,4,7,5,2]=>0001111=>1111000
[1,7,2,6,4,8,5,3]=>0001111=>1111000
[1,7,2,6,3,8,5,4]=>0001111=>1111000
[1,5,2,7,4,8,6,3]=>0001111=>1111000
[1,4,2,8,5,7,6,3]=>0010111=>1110100
[4,8,1,3,2,6,5,7]=>0100101=>1010010
[1,5,3,8,4,7,6,2]=>0001111=>1111000
[1,8,4,7,3,6,5,2]=>0001111=>1111000
[2,6,3,8,1,5,4,7]=>0001101=>1011000
[8,3,1,4,2,6,5,7]=>0110101=>1010110
[4,8,7,3,5,2,1,6]=>1001011=>1101001
[6,8,7,3,5,2,4,1]=>0011011=>1101100
[8,3,5,1,2,6,4,7]=>0001101=>1011000
[8,6,3,1,5,4,2,7]=>0111101=>1011110
[8,6,4,1,5,3,2,7]=>0111101=>1011110
[8,6,5,4,1,3,2,7]=>0111101=>1011110
[5,3,8,7,4,6,2,1]=>1001111=>1111001
[2,3,8,7,4,6,1,5]=>0000111=>1110000
[8,3,5,7,4,1,2,6]=>0010011=>1100100
[4,8,5,3,1,2,7,6]=>0101011=>1101010
[6,8,7,3,1,5,4,2]=>0111011=>1101110
[6,8,5,4,1,3,7,2]=>0011011=>1101100
[2,5,8,7,4,6,3,1]=>0100111=>1110010
[4,8,7,6,5,1,3,2]=>0101111=>1111010
[3,8,7,5,1,6,2,4]=>0001111=>1111000
[2,3,8,7,5,6,1,4]=>0000111=>1110000
[2,8,7,1,3,6,4,5]=>0000111=>1110000
[8,5,4,7,2,1,3,6]=>1001011=>1101001
[6,8,7,3,5,2,1,4]=>1001011=>1101001
[3,5,8,6,4,2,7,1]=>0010111=>1110100
[6,8,4,1,5,2,7,3]=>0011011=>1101100
[6,8,2,1,7,5,3,4]=>1001011=>1101001
[5,8,4,6,1,2,7,3]=>0000111=>1110000
[2,4,8,6,5,1,7,3]=>0001111=>1111000
[4,8,7,6,5,2,1,3]=>1001111=>1111001
[4,8,7,5,1,6,2,3]=>0001111=>1111000
[4,5,2,1,8,6,7,3]=>1001011=>1101001
[4,5,8,3,1,6,7,2]=>0100011=>1100010
[5,7,2,8,4,6,1,3]=>0000111=>1110000
[6,7,3,2,4,8,5,1]=>0101011=>1101010
[7,2,8,6,4,5,1,3]=>0001111=>1111000
[8,7,2,6,5,1,3,4]=>0001111=>1111000
[5,2,7,8,4,1,3,6]=>0011001=>1001100
[2,7,8,6,4,1,3,5]=>0010101=>1010100
[7,6,3,5,2,8,4,1]=>0011111=>1111100
[6,2,7,4,8,5,3,1]=>0101111=>1111010
[8,6,5,1,7,2,4,3]=>0011111=>1111100
[6,8,5,1,7,3,2,4]=>0101011=>1101010
[1,6,8,3,7,4,2,5]=>0010011=>1100100
[5,1,6,3,4,8,2,7]=>0001101=>1011000
[3,5,2,6,4,8,1,7]=>0001101=>1011000
[3,5,2,4,8,1,7,6]=>0001011=>1101000
[6,3,8,2,4,1,7,5]=>0010111=>1110100
[4,6,3,8,7,5,2,1]=>1001111=>1111001
[6,3,8,7,5,4,2,1]=>1011111=>1111101
[6,8,4,2,1,7,5,3]=>1011011=>1101101
[5,2,6,4,3,8,1,7]=>0011101=>1011100
[6,5,3,1,4,8,2,7]=>0101101=>1011010
[3,1,7,8,6,4,2,5]=>0110101=>1010110
[3,8,1,7,6,2,5,4]=>0001111=>1111000
[8,1,7,6,4,2,5,3]=>0011111=>1111100
[7,2,6,3,8,5,4,1]=>0011111=>1111100
[7,3,8,6,4,1,5,2]=>0011111=>1111100
[1,7,5,8,2,4,3,6]=>0010011=>1100100
[6,1,5,2,4,8,3,7]=>0001101=>1011000
[1,5,6,3,8,2,4,7]=>0000101=>1010000
[8,7,1,3,6,5,2,4]=>0001111=>1111000
[2,6,7,4,3,8,5,1]=>0011011=>1101100
[5,2,4,7,3,8,6,1]=>0001111=>1111000
[1,5,8,7,2,4,6,3]=>0000111=>1110000
[1,4,8,7,3,6,5,2]=>0001111=>1111000
[8,3,7,2,5,1,6,4]=>0001111=>1111000
[3,7,2,8,1,5,4,6]=>0001011=>1101000
[3,2,6,1,5,8,4,7]=>0100101=>1010010
[7,2,1,5,8,4,3,6]=>1010011=>1100101
[7,2,8,1,4,3,6,5]=>0010111=>1110100
[1,7,8,3,2,6,5,4]=>0101101=>1011010
[1,7,4,8,3,2,6,5]=>0100111=>1110010
[1,7,5,4,8,3,2,6]=>0101011=>1101010
[6,1,5,4,3,8,2,7]=>0011101=>1011100
[1,7,4,5,6,8,2,3]=>0000011=>1100000
[1,3,4,5,6,7,9,8,2]=>00000011=>11000000
[2,3,4,5,6,7,9,8,1,10]=>000000110=>011000000
[7,3,4,5,6,8,1,2,9]=>00000110=>01100000
[2,3,4,5,7,6,8,1,9]=>00000110=>01100000
[1,8,4,5,6,7,9,2,3]=>00000011=>11000000
[1,3,4,5,6,8,7,9,2]=>00000011=>11000000
[1,3,4,5,6,7,8,10,9,2]=>000000011=>110000000
[1,6,4,2,3,5,7,8]=>0010100=>0010100
[1,8,7,2,3,4,5,6]=>0000011=>1100000
[1,5,8,6,2,3,4,7]=>0000101=>1010000
[1,6,5,7,2,3,4,8]=>0000110=>0110000
[1,7,5,6,2,3,4,8]=>0000110=>0110000
[1,3,2,7,6,4,5,8]=>0100110=>0110010
[1,2,3,7,6,4,5,8]=>0000110=>0110000
[1,5,4,2,3,7,6,8]=>0011010=>0101100
[1,5,4,2,3,8,6,7]=>0011001=>1001100
[1,3,2,8,6,4,5,7]=>0100101=>1010010
[1,7,5,8,2,3,4,6]=>0000011=>1100000
[1,8,7,5,2,3,4,6]=>0001011=>1101000
[2,1,5,8,6,3,7,4]=>1000111=>1110001
[2,5,8,4,6,1,7,3]=>0000111=>1110000
[2,5,3,8,6,1,7,4]=>0001111=>1111000
[2,6,3,5,8,1,7,4]=>0000111=>1110000
[6,3,2,5,8,1,7,4]=>0100111=>1110010
[5,3,2,8,6,1,7,4]=>0101111=>1111010
[5,8,4,6,1,3,7,2]=>0000111=>1110000
[5,3,8,6,1,4,7,2]=>0001111=>1111000
[2,6,5,4,8,1,7,3]=>0001111=>1111000
[8,3,5,7,2,6,4,1]=>0010111=>1110100
[2,4,6,8,5,3,7,1]=>0001011=>1101000
[2,4,8,1,7,6,5,3]=>0001111=>1111000
[4,3,8,1,5,7,6,2]=>0010111=>1110100
[3,8,4,1,5,7,6,2]=>0010111=>1110100
[4,3,6,8,5,2,7,1]=>0011011=>1101100
[8,5,4,7,2,6,3,1]=>0101111=>1111010
[3,6,8,5,4,2,7,1]=>0011011=>1101100
[3,6,4,8,5,2,7,1]=>0001111=>1111000
[3,6,4,1,8,2,7,5]=>0010111=>1110100
[3,6,4,1,5,2,8,7]=>0011101=>1011100
[4,8,6,5,1,3,7,2]=>0001111=>1111000
[2,8,3,5,6,7,1,4]=>0000011=>1100000
[5,6,2,4,7,1,8,3]=>0000111=>1110000
[2,7,5,4,6,1,8,3]=>0001111=>1111000
[2,3,7,4,6,1,8,5]=>0000111=>1110000
[2,6,7,4,1,3,8,5]=>0010011=>1100100
[6,5,7,4,1,3,8,2]=>0010111=>1110100
[2,4,6,3,5,7,8,1]=>0000101=>1010000
[4,1,6,3,5,7,8,2]=>0010101=>1010100
[3,6,4,2,5,7,8,1]=>0010101=>1010100
[2,3,6,1,5,7,8,4]=>0000101=>1010000
[4,3,6,2,5,7,8,1]=>0010101=>1010100
[4,6,1,2,5,7,8,3]=>0000101=>1010000
[2,6,4,1,5,7,8,3]=>0010101=>1010100
[2,4,1,6,5,7,8,3]=>0010101=>1010100
[7,5,4,2,6,1,8,3]=>0011111=>1111100
[4,7,3,1,8,6,5,2]=>0101111=>1111010
[5,6,4,2,7,1,8,3]=>0010111=>1110100
[4,2,7,5,3,1,8,6]=>0111011=>1101110
[5,3,6,4,8,2,1,7]=>1001101=>1011001
[7,3,2,5,4,1,8,6]=>0111011=>1101110
[7,3,2,5,1,8,6,4]=>0101111=>1111010
[4,6,3,8,7,2,1,5]=>1000111=>1110001
[4,7,6,3,8,2,1,5]=>1000111=>1110001
[4,7,3,8,6,2,1,5]=>1000111=>1110001
[5,7,3,2,6,1,8,4]=>0100111=>1110010
[5,7,3,2,6,4,1,8]=>0110110=>0110110
[2,7,5,3,1,8,6,4]=>0101111=>1111010
[7,5,2,8,4,3,1,6]=>0111011=>1101110
[7,3,2,4,1,8,6,5]=>0110111=>1110110
[8,4,3,2,7,5,1,6]=>0111011=>1101110
[4,3,7,5,8,2,1,6]=>1010011=>1100101
[4,3,7,5,2,6,1,8]=>0011110=>0111100
[8,4,5,3,7,2,1,6]=>1001011=>1101001
[4,3,5,2,8,6,1,7]=>0011101=>1011100
[4,5,3,6,8,2,1,7]=>1001001=>1001001
[1,2,3,4,5,9,7,8,6]=>00000011=>11000000
[1,2,3,4,9,6,7,8,5]=>00000011=>11000000
[1,2,3,9,5,6,7,8,4]=>00000011=>11000000
[1,2,9,4,5,6,7,8,3]=>00000011=>11000000
[1,2,3,4,5,6,10,8,9,7]=>000000011=>110000000
[1,2,3,4,9,7,6,8,5]=>00000111=>11100000
[1,2,3,4,5,10,7,8,9,6]=>000000011=>110000000
[1,2,8,6,4,5,7,3]=>0000111=>1110000
[1,2,3,9,6,5,7,8,4]=>00001011=>11010000
[1,2,3,4,10,6,7,8,9,5]=>000000011=>110000000
[1,8,5,3,4,6,7,2]=>0001011=>1101000
[1,2,9,5,4,6,7,8,3]=>00010011=>11001000
[1,2,3,10,5,6,7,8,9,4]=>000000011=>110000000
[1,9,4,3,5,6,7,8,2]=>00100011=>11000100
[1,2,10,4,5,6,7,8,9,3]=>000000011=>110000000
[9,3,2,4,5,6,7,8,1]=>01000011=>11000010
[10,2,3,4,5,6,7,8,9,1]=>000000011=>110000000
[3,5,6,7,8,9,4,2,1]=>10100001=>10000101
[7,8,4,1,6,3,5,2]=>0011101=>1011100
[8,7,5,6,1,3,4,2]=>0010111=>1110100
[1,2,3,5,7,4,6,9,8]=>00000101=>10100000
[1,2,3,6,4,7,5,9,8]=>00001101=>10110000
[1,2,3,4,6,8,5,7,10,9]=>000000101=>101000000
[1,2,3,4,6,8,5,7,9]=>00000010=>01000000
[1,2,3,4,7,5,8,6,9]=>00000110=>01100000
[1,2,3,4,7,5,8,6,10,9]=>000001101=>101100000
[1,2,3,4,6,8,5,7,10,9,11]=>0000001010=>0101000000
[1,2,3,5,7,4,6,9,8,10]=>000001010=>010100000
[1,2,5,7,3,4,6,9,8]=>00000101=>10100000
[1,2,4,5,7,3,6,9,8]=>00000101=>10100000
[1,2,6,3,4,7,5,9,8]=>00001101=>10110000
[1,2,5,6,3,7,4,9,8]=>00001101=>10110000
[1,2,3,6,4,7,5,9,8,10]=>000011010=>010110000
[1,2,3,4,7,5,8,6,10,9,11]=>0000011010=>0101100000
[3,2,6,4,1,8,5,7]=>0110101=>1010110
[2,8,6,5,3,1,4,7]=>0101101=>1011010
[5,4,8,6,2,3,1,7]=>0101101=>1011010
[4,8,7,5,2,3,1,6]=>0101011=>1101010
[5,2,4,7,6,8,3,1]=>0101011=>1101010
[3,4,2,8,7,5,1,6]=>0011011=>1101100
[8,5,7,6,3,2,4,1]=>0110111=>1110110
[6,4,1,8,7,3,2,5]=>0110111=>1110110
[1,8,5,4,2,7,3,6]=>0011011=>1101100
[3,7,6,1,5,8,4,2]=>0010111=>1110100
[3,6,5,8,2,7,4,1]=>0010111=>1110100
[8,3,2,7,4,6,5,1]=>0101111=>1111010
[7,5,8,4,1,3,6,2]=>0010111=>1110100
[7,1,6,2,3,8,4,5]=>0000111=>1110000
[6,4,7,1,3,2,8,5]=>0100111=>1110010
[5,1,3,8,7,2,6,4]=>0001111=>1111000
[8,7,1,6,2,5,3,4]=>0001111=>1111000
[3,8,5,2,4,7,6,1]=>0001111=>1111000
[7,1,5,2,4,8,3,6]=>0001011=>1101000
[3,8,5,1,4,7,2,6]=>0001011=>1101000
[7,2,5,4,1,3,8,6]=>0011011=>1101100
[7,5,8,1,6,3,2,4]=>0100111=>1110010
[7,1,4,8,5,6,2,3]=>0000111=>1110000
[2,3,1,9,4,5,6,7,8]=>01000001=>10000010
[4,9,1,2,3,5,6,7,8]=>00000001=>10000000
[3,9,1,2,4,5,6,7,8]=>00000001=>10000000
[6,8,1,9,2,3,4,5,7]=>00000011=>11000000
[7,10,1,2,3,4,5,6,8,9]=>000000001=>100000000
[6,10,1,2,3,4,5,7,8,9]=>000000001=>100000000
[4,8,1,2,3,9,5,6,7]=>00000011=>11000000
[3,8,1,2,4,5,9,6,7]=>00000011=>11000000
[4,10,1,2,3,5,6,7,8,9]=>000000001=>100000000
[3,10,1,2,4,5,6,7,8,9]=>000000001=>100000000
[1,8,2,3,4,5,6,7,9]=>00000010=>01000000
[7,4,6,1,3,2,5,8]=>0100110=>0110010
[1,4,5,8,6,3,2,7]=>0100101=>1010010
[8,4,5,7,2,6,1,3]=>0000111=>1110000
[4,5,2,6,7,3,1,8]=>0101010=>0101010
[8,1,7,5,3,6,2,4]=>0001111=>1111000
[5,2,6,3,1,7,8,4]=>0101101=>1011010
[4,3,5,1,6,7,8,2]=>0011001=>1001100
[5,7,6,1,2,3,8,4]=>0000111=>1110000
[3,6,7,5,1,2,8,4]=>0001011=>1101000
[1,7,6,8,5,2,4,3]=>0011011=>1101100
[5,7,6,8,1,2,4,3]=>0010011=>1100100
[5,6,3,7,1,4,8,2]=>0000111=>1110000
[5,3,2,1,8,6,4,7]=>1101101=>1011011
[9,8,7,5,6,4,3,2,1]=>11101111=>11110111
[2,1,9,8,6,7,5,4,3]=>10110111=>11101101
[11,10,9,8,7,6,5,4,3,2,1]=>1111111111=>1111111111
[10,9,8,7,5,6,4,3,2,1]=>111011111=>111110111
[9,8,7,5,4,6,3,2,1]=>11011111=>11111011
[9,8,7,4,6,5,3,2,1]=>11011111=>11111011
[2,1,9,8,6,5,7,4,3]=>10101111=>11110101
[2,1,9,8,5,7,6,4,3]=>10101111=>11110101
[2,1,10,9,8,6,7,5,4,3]=>101101111=>111101101
[2,1,11,10,9,8,7,6,5,4,3]=>1011111111=>1111111101
[1,8,7,6,5,4,3,2,9]=>01111110=>01111110
[1,9,8,7,6,5,4,3,2,10]=>011111110=>011111110
[2,1,8,7,6,5,4,3,9]=>10111110=>01111101
[2,8,9,7,6,5,4,3,1]=>01111101=>10111110
[7,8,6,1,4,5,2,3]=>0001101=>1011000
[1,8,5,4,6,7,2,3]=>0001011=>1101000
[6,5,8,3,7,2,1,4]=>1000111=>1110001
[7,8,5,3,6,2,1,4]=>1001101=>1011001
[7,8,5,3,6,2,4,1]=>0011101=>1011100
[7,8,4,3,2,6,5,1]=>0111101=>1011110
[1,8,4,3,2,6,7,5]=>0110011=>1100110
[5,4,3,8,2,1,7,6]=>1011011=>1101101
[6,4,8,3,2,1,7,5]=>1100111=>1110011
[1,8,4,3,2,7,6,5]=>0110111=>1110110
[6,5,8,3,1,2,7,4]=>0100111=>1110010
[1,8,6,7,3,2,4,5]=>0100011=>1100010
[7,8,6,1,3,2,4,5]=>0100101=>1010010
[1,8,4,3,2,7,5,6]=>0110011=>1100110
[5,4,3,8,2,1,6,7]=>1011001=>1001101
[1,8,4,3,2,5,7,6]=>0110011=>1100110
[5,4,3,8,2,6,7,1]=>0011011=>1101100
[4,5,6,7,8,1,2,9,3]=>00000011=>11000000
[4,5,6,7,1,2,8,9,3]=>00000101=>10100000
[4,5,6,1,2,7,8,9,3]=>00001001=>10010000
[4,5,1,2,6,7,8,9,3]=>00010001=>10001000
[8,6,3,2,5,4,7,1]=>0101111=>1111010
[7,2,3,4,5,8,1,6]=>0000011=>1100000
[7,2,8,1,5,3,4,6]=>0001011=>1101000
[4,8,2,5,7,3,1,6]=>0100011=>1100010
[3,8,6,2,7,4,5,1]=>0001111=>1111000
[7,3,6,2,8,1,5,4]=>0001111=>1111000
[8,1,5,2,3,7,6,4]=>0001111=>1111000
[6,4,2,3,7,8,5,1]=>0011101=>1011100
[4,3,6,2,1,8,7,5]=>1010111=>1110101
[3,7,4,5,1,6,2,8]=>0001110=>0111000
[3,6,4,5,8,2,1,7]=>1000101=>1010001
[6,1,4,5,2,8,7,3]=>0001111=>1111000
[7,2,4,5,1,6,3,8]=>0001110=>0111000
[7,5,4,1,6,3,2,8]=>0111110=>0111110
[1,5,4,8,6,3,2,7]=>0101101=>1011010
[7,5,4,8,6,3,1,2]=>0101111=>1111010
[1,8,7,5,3,6,4,2]=>0011111=>1111100
[8,3,7,4,1,6,2,5]=>0010111=>1110100
[8,5,4,1,6,3,2,7]=>0111101=>1011110
[1,7,4,2,6,5,3,8]=>0011110=>0111100
[8,2,1,5,6,7,3,4]=>1000011=>1100001
[6,3,1,8,4,7,2,5]=>0100111=>1110010
[7,1,4,8,6,3,2,5]=>0100111=>1110010
[4,1,8,5,6,7,2,3]=>0010011=>1100100
[5,7,4,8,6,2,1,3]=>1000111=>1110001
[5,3,6,8,2,7,1,4]=>0001011=>1101000
[6,3,7,4,8,2,1,5]=>1000111=>1110001
[5,3,6,1,4,7,2,8]=>0001110=>0111000
[4,3,6,8,2,7,1,5]=>0010011=>1100100
[5,3,7,4,8,2,1,6]=>1001011=>1101001
[5,3,8,4,1,6,2,7]=>0011101=>1011100
[5,3,8,1,4,7,2,6]=>0001011=>1101000
[5,8,4,1,6,3,2,7]=>0110101=>1010110
[7,3,8,4,1,6,2,5]=>0010111=>1110100
[1,5,8,3,6,7,4,2]=>0010011=>1100100
[1,8,2,5,6,7,3,4]=>0000011=>1100000
[7,8,4,1,6,5,2,3]=>0011101=>1011100
[6,3,8,1,5,7,2,4]=>0000111=>1110000
[8,3,1,2,5,7,4,6]=>0100011=>1100010
[8,1,4,2,6,5,3,7]=>0011101=>1011100
[7,8,1,2,3,4,5,9,6]=>00000011=>11000000
[2,8,9,1,3,4,5,6,7]=>00000001=>10000000
[2,8,9,10,1,3,4,5,6,7]=>000000001=>100000000
[7,1,8,2,9,3,4,5,6]=>00000111=>11100000
[6,1,7,2,8,3,9,4,5]=>00001111=>11110000
[5,1,6,2,7,3,8,4,9]=>00011110=>01111000
[8,1,9,2,10,3,4,5,6,7]=>000000111=>111000000
[7,1,8,2,3,9,4,5,6]=>00000111=>11100000
[7,1,8,2,9,3,10,4,5,6]=>000001111=>111100000
[6,1,7,2,8,3,4,9,5]=>00001111=>11110000
[5,1,6,2,7,3,9,4,8]=>00011101=>10111000
[5,1,6,2,7,3,8,4,10,9]=>000111101=>101111000
[4,1,5,2,7,3,8,6,9]=>00110110=>01101100
[4,1,5,2,6,3,8,7,10,9]=>001110101=>101011100
[5,1,3,7,4,8,2,6]=>0001011=>1101000
[5,1,3,4,7,8,2,6]=>0001001=>1001000
[2,5,8,7,4,3,6,1]=>0010111=>1110100
[5,1,7,8,3,4,2,6]=>0011001=>1001100
[2,5,4,8,3,7,6,1]=>0001111=>1111000
[5,6,8,2,3,4,1,7]=>0010001=>1000100
[2,3,5,7,4,6,8,1]=>0000011=>1100000
[4,5,2,3,8,6,1,7]=>0001101=>1011000
[3,7,4,5,8,1,2,6]=>0000011=>1100000
[3,7,8,1,4,5,2,6]=>0001001=>1001000
[5,8,2,1,6,3,4,7]=>1000101=>1010001
[4,8,1,3,7,5,2,6]=>0001011=>1101000
[2,4,7,8,5,3,6,1]=>0001101=>1011000
[5,3,1,4,7,2,8,6]=>0101011=>1101010
[4,3,8,5,1,2,7,6]=>0011011=>1101100
[2,4,7,5,8,3,6,1]=>0000111=>1110000
[4,3,5,8,2,1,7,6]=>1010011=>1100101
[4,8,5,3,7,1,2,6]=>0001011=>1101000
[4,8,5,7,3,1,2,6]=>0100011=>1100010
[4,8,7,5,1,3,2,6]=>0101011=>1101010
[4,2,8,5,1,3,6,7]=>0011001=>1001100
[3,7,8,4,1,5,2,6]=>0011001=>1001100
[3,4,7,5,8,2,1,6]=>1000011=>1100001
[1,8,5,7,2,4,3,6]=>0010011=>1100100
[1,8,5,4,2,3,6,7]=>0011001=>1001100
[1,3,6,8,5,4,2,7]=>0011001=>1001100
[1,6,3,8,2,7,4,5]=>0000111=>1110000
[1,4,2,7,5,8,3,6]=>0010011=>1100100
[1,8,2,3,6,7,5,4]=>0001011=>1101000
[1,3,6,8,2,7,5,4]=>0001011=>1101000
[1,6,5,4,3,8,2,7]=>0011101=>1011100
[1,8,3,4,5,6,2,7]=>0000101=>1010000
[1,8,3,6,2,4,5,7]=>0000101=>1010000
[1,4,5,8,3,6,2,7]=>0000101=>1010000
[1,2,7,8,4,5,3,6]=>0001001=>1001000
[7,6,3,8,5,4,2,1]=>1011111=>1111101
[6,2,8,7,5,4,1,3]=>0011111=>1111100
[6,2,8,4,3,7,1,5]=>0010111=>1110100
[5,2,8,4,3,1,7,6]=>0111011=>1101110
[1,5,7,3,6,2,8,4]=>0000111=>1110000
[1,2,5,4,8,3,7,6]=>0001011=>1101000
[1,4,3,6,8,7,2,5]=>0010011=>1100100
[3,2,5,7,6,8,1,4]=>0100011=>1100010
[5,3,2,6,8,4,7,1]=>0101011=>1101010
[3,1,8,6,4,7,2,5]=>0100111=>1110010
[3,1,6,8,5,4,2,7]=>0111001=>1001110
[5,3,2,8,7,6,4,1]=>0111111=>1111110
[5,3,8,2,7,6,1,4]=>0001111=>1111000
[6,5,4,8,3,7,2,1]=>1001111=>1111001
[4,8,5,1,3,7,2,6]=>0001011=>1101000
[4,3,8,7,2,6,5,1]=>0011111=>1111100
[2,7,5,1,8,4,6,3]=>0001111=>1111000
[7,8,5,2,1,6,4,3]=>1011101=>1011101
[7,6,4,8,1,2,5,3]=>0001111=>1111000
[7,5,4,8,3,2,6,1]=>0101111=>1111010
[8,6,4,7,3,2,1,5]=>1100111=>1110011
[3,8,5,6,2,7,1,4]=>0000111=>1110000
[2,4,5,8,7,3,1,6]=>0100011=>1100010
[2,4,5,8,6,7,1,3]=>0000011=>1100000
[4,3,1,5,6,2,8,7]=>0110101=>1010110
[4,1,5,8,6,7,2,3]=>0010011=>1100100
[4,3,7,6,1,2,8,5]=>0010111=>1110100
[4,7,5,6,1,2,8,3]=>0000111=>1110000
[4,3,7,5,6,2,8,1]=>0010111=>1110100
[4,5,1,8,6,7,3,2]=>0101011=>1101010
[3,4,5,8,6,7,2,1]=>1000011=>1100001
[2,1,5,8,6,7,4,3]=>1010011=>1100101
[3,4,5,8,7,1,2,6]=>0000011=>1100000
[4,7,1,5,6,2,8,3]=>0000111=>1110000
[2,6,4,7,1,3,8,5]=>0000111=>1110000
[5,3,8,6,4,7,2,1]=>1001111=>1111001
[6,4,1,5,7,8,3,2]=>0110101=>1010110
[3,6,4,7,2,1,8,5]=>1000111=>1110001
[3,8,4,6,1,7,2,5]=>0000111=>1110000
[3,8,5,6,4,7,2,1]=>1000111=>1110001
[3,8,4,5,6,7,2,1]=>1000011=>1100001
[3,8,6,5,2,7,4,1]=>0011111=>1111100
[3,8,7,5,2,1,4,6]=>1001011=>1101001
[3,8,6,5,1,7,2,4]=>0001111=>1111000
[6,4,1,7,3,2,8,5]=>0110111=>1110110
[5,1,4,6,7,2,8,3]=>0001011=>1101000
[6,5,4,7,1,3,8,2]=>0001111=>1111000
[2,1,6,5,3,7,8,4]=>1001101=>1011001
[6,1,4,7,2,3,8,5]=>0000111=>1110000
[2,1,3,4,5,6,8,9,7]=>10000001=>10000001
[2,1,3,4,5,6,7,9,8]=>10000001=>10000001
[1,2,3,4,5,6,7,8,10,11,9]=>0000000001=>1000000000
[2,1,3,4,5,6,7,9,10,8]=>100000001=>100000001
[2,3,1,4,5,6,8,9,7]=>01000001=>10000010
[1,3,2,4,5,6,8,9,7]=>01000001=>10000010
[2,3,1,4,5,6,7,9,8]=>01000001=>10000010
[1,3,2,4,5,6,7,9,8]=>01000001=>10000010
[2,1,3,4,5,6,7,8,10,9]=>100000001=>100000001
[1,6,2,5,4,8,3,7]=>0001101=>1011000
[4,1,2,7,5,8,3,6]=>0010011=>1100100
[6,1,3,5,8,2,4,7]=>0000101=>1010000
[5,6,4,3,1,8,2,7]=>0110101=>1010110
[6,2,3,5,8,1,4,7]=>0000101=>1010000
[6,7,2,3,8,4,5,1]=>0001011=>1101000
[6,7,2,1,3,8,4,5]=>1000011=>1100001
[5,7,4,1,8,3,2,6]=>0110011=>1100110
[4,1,7,5,8,3,6,2]=>0010111=>1110100
[6,7,1,3,8,4,5,2]=>0001011=>1101000
[1,6,7,4,3,8,5,2]=>0011011=>1101100
[6,1,7,4,2,8,5,3]=>0011111=>1111100
[2,1,6,7,4,3,8,5]=>1010011=>1100101
[6,7,3,2,1,8,4,5]=>1100011=>1100011
[2,5,7,3,1,4,8,6]=>0100011=>1100010
[6,7,3,2,8,4,5,1]=>0101011=>1101010
[1,2,6,7,4,3,8,5]=>0010011=>1100100
[2,7,1,8,4,6,3,5]=>0000111=>1110000
[2,7,5,8,1,6,3,4]=>0000111=>1110000
[6,7,1,8,4,5,3,2]=>0101011=>1101010
[8,3,7,6,1,2,5,4]=>0001111=>1111000
[8,7,3,4,6,2,5,1]=>0001111=>1111000
[8,2,5,7,1,4,6,3]=>0000111=>1110000
[8,2,4,7,1,5,6,3]=>0000111=>1110000
[8,2,3,4,7,1,5,6]=>0000011=>1100000
[8,7,3,5,6,2,4,1]=>0010111=>1110100
[8,7,4,6,5,2,3,1]=>0101111=>1111010
[8,4,6,7,5,1,2,3]=>0001011=>1101000
[8,4,6,7,5,1,3,2]=>0101011=>1101010
[8,3,5,7,6,1,4,2]=>0010111=>1110100
[8,7,3,6,2,1,5,4]=>1001111=>1111001
[8,7,3,4,6,2,1,5]=>1000111=>1110001
[8,7,4,6,5,2,1,3]=>1001111=>1111001
[8,6,5,2,7,4,3,1]=>0111111=>1111110
[8,4,3,7,6,5,1,2]=>0011111=>1111100
[8,5,6,7,4,1,3,2]=>0110011=>1100110
[8,5,7,6,4,1,2,3]=>0010111=>1110100
[8,4,2,7,5,1,6,3]=>0011111=>1111100
[8,3,4,2,7,5,6,1]=>0010111=>1110100
[8,4,7,6,5,1,2,3]=>0001111=>1111000
[8,3,5,2,7,4,6,1]=>0001111=>1111000
[8,5,2,6,7,4,1,3]=>0011011=>1101100
[8,5,3,7,6,4,1,2]=>0011111=>1111100
[8,6,2,5,7,3,1,4]=>0100111=>1110010
[8,6,2,4,7,3,1,5]=>0100111=>1110010
[8,5,2,3,7,4,1,6]=>0011011=>1101100
[8,5,3,2,7,6,4,1]=>0111111=>1111110
[8,6,1,5,4,3,2,7]=>0111101=>1011110
[2,4,5,8,3,1,6,7]=>0100001=>1000010
[2,7,4,6,1,5,8,3]=>0000111=>1110000
[2,4,3,8,5,1,6,7]=>0011001=>1001100
[7,8,3,2,5,4,6,1]=>0101101=>1011010
[1,5,6,7,3,8,2,4]=>0000011=>1100000
[1,6,5,4,8,3,2,7]=>0101101=>1011010
[1,7,3,5,8,4,6,2]=>0000111=>1110000
[7,2,1,6,4,8,5,3]=>1001111=>1111001
[7,5,8,3,2,4,6,1]=>0100111=>1110010
[3,8,7,2,4,6,5,1]=>0001111=>1111000
[1,3,7,6,4,8,5,2]=>0001111=>1111000
[3,1,8,7,6,4,2,5]=>0110111=>1110110
[3,1,8,7,5,4,2,6]=>0111011=>1101110
[3,1,7,6,5,4,2,8]=>0111110=>0111110
[4,7,1,6,5,3,2,8]=>0101110=>0111010
[4,8,1,6,5,3,2,7]=>0101101=>1011010
[8,4,1,7,6,3,2,5]=>0110111=>1110110
[5,4,1,8,6,3,2,7]=>0111101=>1011110
[5,4,1,7,6,3,2,8]=>0111110=>0111110
[6,4,1,8,5,3,2,7]=>0111101=>1011110
[8,4,1,7,5,3,2,6]=>0111011=>1101110
[7,4,1,6,5,3,2,8]=>0111110=>0111110
[7,5,6,1,4,3,2,8]=>0110110=>0110110
[8,5,6,1,4,3,2,7]=>0110101=>1010110
[8,5,7,1,4,3,2,6]=>0110011=>1100110
[5,7,6,1,4,3,2,8]=>0110110=>0110110
[5,8,6,1,4,3,2,7]=>0110101=>1010110
[6,7,5,1,4,3,2,8]=>0111010=>0101110
[8,7,5,1,4,3,2,6]=>0111011=>1101110
[8,6,5,1,4,3,2,7]=>0111101=>1011110
[8,6,1,7,2,5,3,4]=>0001111=>1111000
[1,8,6,3,4,2,5,7]=>0010101=>1010100
[3,1,6,4,5,8,7,2]=>0100111=>1110010
[3,1,6,4,5,2,7,8]=>0101100=>0011010
[3,1,6,4,5,8,2,7]=>0100101=>1010010
[3,1,6,4,5,7,2,8]=>0100110=>0110010
[4,6,8,7,2,5,1,3]=>0001011=>1101000
[7,6,3,8,4,5,2,1]=>1001111=>1111001
[8,2,7,6,1,4,3,5]=>0010111=>1110100
[5,2,7,8,1,4,3,6]=>0011001=>1001100
[5,6,3,8,4,1,2,7]=>0010101=>1010100
[8,2,7,6,1,4,5,3]=>0001111=>1111000
[5,2,3,4,7,1,6,8]=>0001010=>0101000
[5,2,3,7,1,6,8,4]=>0001011=>1101000
[8,7,5,3,1,6,4,2]=>0111111=>1111110
[1,4,7,8,5,2,3,6]=>0001001=>1001000
[3,2,6,7,4,1,5,8]=>0110010=>0100110
[5,8,3,7,6,4,1,2]=>0010111=>1110100
[6,5,1,7,2,4,8,3]=>0001111=>1111000
[3,6,7,1,4,2,5,8]=>0010010=>0100100
[4,7,5,8,2,1,3,6]=>1000011=>1100001
[8,1,2,7,5,4,3,6]=>0011011=>1101100
[6,5,1,8,3,7,2,4]=>0001111=>1111000
[1,8,7,5,3,2,6,4]=>0101111=>1111010
[7,8,1,5,4,2,3,6]=>0011001=>1001100
[2,7,5,1,4,6,3,8]=>0001110=>0111000
[3,4,6,8,1,5,7,2]=>0000011=>1100000
[6,8,1,7,5,4,2,3]=>0011011=>1101100
[7,6,3,1,2,8,5,4]=>0101111=>1111010
[6,3,5,7,1,4,2,8]=>0010110=>0110100
[5,2,6,7,4,8,1,3]=>0001011=>1101000
[1,7,5,2,6,4,8,3]=>0001111=>1111000
[7,1,3,6,8,2,4,5]=>0000011=>1100000
[1,2,5,7,8,4,6,3]=>0000101=>1010000
[3,1,2,7,5,4,8,6]=>0101011=>1101010
[6,7,4,1,3,2,8,5]=>0110011=>1100110
[1,7,2,8,4,3,5,6]=>0010011=>1100100
[1,6,3,5,7,8,2,4]=>0000101=>1010000
[8,6,1,7,5,2,4,3]=>0011111=>1111100
[7,6,4,1,8,3,2,5]=>0110111=>1110110
[8,4,1,6,5,2,7,3]=>0011111=>1111100
[1,5,3,4,7,8,2,6]=>0001001=>1001000
[4,2,1,5,7,8,3,6]=>1010001=>1000101
[5,4,1,6,7,8,2,3]=>0011001=>1001100
[5,1,4,6,7,8,2,3]=>0001001=>1001000
[4,1,5,3,7,8,2,6]=>0011001=>1001100
[8,1,4,6,5,2,7,3]=>0001111=>1111000
[7,1,5,4,6,3,2,8]=>0101110=>0111010
[8,2,1,6,7,5,4,3]=>1011011=>1101101
[1,2,4,7,6,3,8,5]=>0000111=>1110000
[6,7,4,1,8,5,2,3]=>0011011=>1101100
[8,6,4,1,5,7,3,2]=>0110111=>1110110
[5,2,4,3,7,1,6,8]=>0011010=>0101100
[6,1,5,4,8,3,2,7]=>0101101=>1011010
[1,2,8,7,4,3,6,5]=>0010111=>1110100
[3,2,1,7,5,8,4,6]=>1100011=>1100011
[1,3,6,4,7,8,2,5]=>0000101=>1010000
[4,5,1,3,7,8,2,6]=>0001001=>1001000
[5,2,3,1,7,8,4,6]=>0101001=>1001010
[1,6,4,3,7,8,2,5]=>0010101=>1010100
[7,6,4,3,1,5,2,8]=>0111110=>0111110
[7,5,4,6,1,3,2,8]=>0101110=>0111010
[8,4,6,5,1,2,7,3]=>0001111=>1111000
[1,5,6,3,7,8,2,4]=>0000101=>1010000
[7,1,2,3,4,5,8,9,10,6]=>000001001=>100100000
[6,7,1,2,3,4,8,9,5]=>00000101=>10100000
[6,1,2,3,4,7,8,9,10,5]=>000010001=>100010000
[5,1,2,3,6,7,8,9,10,4]=>000100001=>100001000
[6,8,3,5,7,2,4,1]=>0010011=>1100100
[1,5,2,4,3,8,7,6]=>0011011=>1101100
[8,6,5,7,2,1,4,3]=>1010111=>1110101
[1,6,3,8,4,5,7,2]=>0000111=>1110000
[7,5,4,2,6,3,8,1]=>0011111=>1111100
[7,8,6,5,4,3,2,9,1]=>01111011=>11011110
[9,7,6,5,4,3,1,2,8]=>01111101=>10111110
[2,4,3,5,6,7,8,9,1]=>00100001=>10000100
[2,3,8,4,7,5,6,1]=>0000111=>1110000
[3,7,2,8,6,4,5,1]=>0001111=>1111000
[6,3,7,5,8,2,4,1]=>0010111=>1110100
[4,3,7,8,6,2,5,1]=>0011101=>1011100
[3,8,1,7,5,2,4,6]=>0001011=>1101000
[2,4,7,8,6,1,5,3]=>0001101=>1011000
[2,4,8,5,1,7,3,6]=>0001011=>1101000
[2,8,3,5,1,6,4,7]=>0001101=>1011000
[8,2,4,6,3,7,5,1]=>0001111=>1111000
[4,5,3,8,2,1,7,6]=>1001011=>1101001
[4,8,3,2,5,1,6,7]=>0101001=>1001010
[5,2,7,1,3,8,6,4]=>0001111=>1111000
[4,5,6,7,8,9,2,1,3]=>10000001=>10000001
[5,6,7,8,9,2,1,3,4]=>10000001=>10000001
[6,7,8,9,2,1,3,4,5]=>10000001=>10000001
[7,8,9,2,1,3,4,5,6]=>10000001=>10000001
[8,9,2,1,3,4,5,6,7]=>10000001=>10000001
[1,4,6,2,7,5,3,8]=>0001110=>0111000
[8,2,7,5,1,4,6,3]=>0001111=>1111000
[1,7,4,6,8,3,5,2]=>0001011=>1101000
[8,2,1,4,5,6,7,3]=>1000011=>1100001
[7,3,1,2,5,6,4,8]=>0100110=>0110010
[7,2,4,1,5,8,6,3]=>0010111=>1110100
[7,8,2,1,5,4,6,3]=>1001101=>1011001
[1,4,2,8,6,5,3,7]=>0011101=>1011100
[1,4,8,5,2,6,3,7]=>0001101=>1011000
[1,5,2,4,6,3,8,7]=>0001101=>1011000
[1,8,5,3,2,6,4,7]=>0101101=>1011010
[6,4,1,3,2,5,8,7]=>0110101=>1010110
[5,2,3,7,8,1,6,4]=>0001101=>1011000
[5,2,8,6,3,1,7,4]=>0101111=>1111010
[6,2,3,5,1,8,7,4]=>0001111=>1111000
[7,6,3,4,2,8,1,5]=>0010111=>1110100
[6,2,4,5,7,8,1,3]=>0000101=>1010000
[8,6,3,2,5,7,1,4]=>0100111=>1110010
[6,2,5,3,7,1,8,4]=>0001111=>1111000
[8,5,3,6,7,2,1,4]=>1001011=>1101001
[4,5,7,8,6,2,1,3]=>1000101=>1010001
[1,2,8,4,3,6,7,5]=>0010011=>1100100
[1,8,3,2,4,6,7,5]=>0100011=>1100010
[1,2,7,5,3,4,6,8]=>0001010=>0101000
[1,2,7,4,5,3,8,6]=>0001011=>1101000
[1,7,3,2,6,8,4,5]=>0100011=>1100010
[8,2,7,1,4,3,5,6]=>0010011=>1100100
[7,2,1,3,6,8,4,5]=>1000011=>1100001
[6,2,1,7,8,3,4,5]=>1000101=>1010001
[4,7,8,1,6,5,3,2]=>0101101=>1011010
[3,5,8,6,1,4,2,7]=>0010101=>1010100
[1,8,4,2,7,6,3,5]=>0010111=>1110100
[8,7,2,6,5,4,3,1]=>0111111=>1111110
[7,3,8,1,6,5,4,2]=>0011111=>1111100
[7,3,8,2,6,5,4,1]=>0011111=>1111100
[7,1,3,8,6,5,4,2]=>0011111=>1111100
[8,1,3,7,6,5,4,2]=>0011111=>1111100
[2,4,1,8,7,3,6,5]=>0010111=>1110100
[7,3,8,6,1,5,4,2]=>0011111=>1111100
[3,5,1,7,8,2,6,4]=>0001101=>1011000
[5,4,7,8,2,1,6,3]=>1001101=>1011001
[5,3,6,1,8,4,2,7]=>0011101=>1011100
[6,3,8,7,1,5,4,2]=>0011111=>1111100
[8,6,4,7,1,5,3,2]=>0101111=>1111010
[6,4,7,1,5,3,2,8]=>0101110=>0111010
[3,4,6,2,1,8,5,7]=>1000101=>1010001
[4,5,7,2,1,6,3,8]=>1000110=>0110001
[5,6,4,8,3,2,1,7]=>1100101=>1010011
[5,7,4,8,2,1,6,3]=>1000111=>1110001
[4,7,5,8,2,1,6,3]=>1000111=>1110001
[5,7,4,2,6,3,8,1]=>0010111=>1110100
[5,7,4,1,6,2,8,3]=>0010111=>1110100
[6,8,7,3,1,4,2,5]=>0110011=>1100110
[8,5,6,1,7,3,2,4]=>0100111=>1110010
[4,5,1,6,7,8,3,2]=>0101001=>1001010
[4,5,2,6,1,3,8,7]=>0001101=>1011000
[8,4,6,7,2,5,1,3]=>0001011=>1101000
[3,4,6,7,2,5,8,1]=>0000011=>1100000
[7,1,4,6,8,3,5,2]=>0001011=>1101000
[6,7,1,2,4,8,5,3]=>0001011=>1101000
[1,6,3,4,7,8,5,2]=>0001101=>1011000
[2,3,6,4,7,5,8,1]=>0000111=>1110000
[7,8,1,3,4,5,6,2]=>0000101=>1010000
[1,8,2,6,7,3,4,5]=>0000011=>1100000
[4,7,3,2,8,1,5,6]=>0100011=>1100010
[7,1,2,6,3,8,5,4]=>0001111=>1111000
[8,1,2,6,3,7,5,4]=>0001111=>1111000
[8,1,2,7,6,3,5,4]=>0001111=>1111000
[4,8,7,3,1,6,2,5]=>0100111=>1110010
[4,7,8,3,1,6,2,5]=>0100101=>1010010
[7,4,3,1,6,2,8,5]=>0110111=>1110110
[7,4,3,1,8,6,2,5]=>0110111=>1110110
[3,7,6,2,4,8,1,5]=>0000111=>1110000
[4,3,7,2,8,6,1,5]=>0010111=>1110100
[6,1,2,7,4,3,8,5]=>0010111=>1110100
[5,1,2,6,3,8,7,4]=>0001111=>1111000
[5,1,2,7,3,8,6,4]=>0001111=>1111000
[6,1,2,7,3,5,8,4]=>0000111=>1110000
[8,3,6,2,1,7,4,5]=>1000111=>1110001
[6,1,2,8,3,5,7,4]=>0000111=>1110000
[7,5,3,2,1,8,6,4]=>1101111=>1111011
[4,2,1,5,3,6,7,8]=>1011000=>0001101
[8,6,4,3,2,1,9,7,5]=>11101111=>11110111
[7,5,4,3,2,1,8,6,9]=>11110110=>01101111
[8,6,4,2,1,9,7,5,3]=>10111111=>11111101
[7,5,3,2,1,8,6,4,9]=>11011110=>01111011
[7,4,3,2,1,8,5,9,6]=>11100111=>11100111
[6,4,3,2,1,7,5,8,9]=>11101100=>00110111
[7,5,3,1,8,6,4,2,9]=>01111110=>01111110
[7,4,2,1,8,5,3,9,6]=>10110111=>11101101
[6,4,2,1,7,5,3,8,9]=>10111100=>00111101
[6,3,2,1,7,4,8,5,9]=>11001110=>01110011
[5,3,2,1,6,4,7,8,9]=>11011000=>00011011
[7,4,1,8,5,2,9,6,3]=>00111111=>11111100
[6,3,1,7,4,2,8,5,9]=>01101110=>01110110
[5,3,1,6,4,2,7,8,9]=>01111000=>00011110
[6,2,1,7,3,8,4,9,5]=>10001111=>11110001
[5,2,1,6,3,7,4,8,9]=>10011100=>00111001
[4,2,1,5,3,6,7,8,9]=>10110000=>00001101
[4,1,5,2,6,3,7,8,9]=>00111000=>00011100
[3,1,4,2,5,6,7,8,9]=>01100000=>00000110
[9,7,5,4,3,2,1,10,8,6]=>111101111=>111101111
[8,6,5,4,3,2,1,9,7,10]=>111110110=>011011111
[9,7,5,3,2,1,10,8,6,4]=>110111111=>111111011
[8,6,4,3,2,1,9,7,5,10]=>111011110=>011110111
[8,5,4,3,2,1,9,6,10,7]=>111100111=>111001111
[7,5,4,3,2,1,8,6,9,10]=>111101100=>001101111
[8,6,4,2,1,9,7,5,3,10]=>101111110=>011111101
[8,5,3,2,1,9,6,4,10,7]=>110110111=>111011011
[7,5,3,2,1,8,6,4,9,10]=>110111100=>001111011
[7,4,3,2,1,8,5,9,6,10]=>111001110=>011100111
[6,4,3,2,1,7,5,8,9,10]=>111011000=>000110111
[8,5,3,1,9,6,4,2,10,7]=>011110111=>111011110
[7,5,3,1,8,6,4,2,9,10]=>011111100=>001111110
[8,5,2,1,9,6,3,10,7,4]=>100111111=>111111001
[7,4,2,1,8,5,3,9,6,10]=>101101110=>011101101
[6,4,2,1,7,5,3,8,9,10]=>101111000=>000111101
[7,3,2,1,8,4,9,5,10,6]=>110001111=>111100011
[6,3,2,1,7,4,8,5,9,10]=>110011100=>001110011
[5,3,2,1,6,4,7,8,9,10]=>110110000=>000011011
[7,4,1,8,5,2,9,6,3,10]=>001111110=>011111100
[7,3,1,8,4,2,9,5,10,6]=>011001111=>111100110
[6,3,1,7,4,2,8,5,9,10]=>011011100=>001110110
[5,3,1,6,4,2,7,8,9,10]=>011110000=>000011110
[6,2,1,7,3,8,4,9,5,10]=>100011110=>011110001
[5,2,1,6,3,7,4,8,9,10]=>100111000=>000111001
[4,2,1,5,3,6,7,8,9,10]=>101100000=>000001101
[5,1,6,2,7,3,8,4,9,10]=>000111100=>001111000
[4,1,5,2,6,3,7,8,9,10]=>001110000=>000011100
[3,1,4,2,5,6,7,8,9,10]=>011000000=>000000110
[6,2,5,4,1,8,7,3]=>0011111=>1111100
[4,6,3,2,1,8,7,5]=>1100111=>1110011
[6,5,3,2,1,8,7,4]=>1101111=>1111011
[8,4,3,2,7,6,1,5]=>0110111=>1110110
[1,5,8,4,7,6,3,2]=>0100111=>1110010
[3,2,7,4,8,6,1,5]=>0100111=>1110010
[7,4,3,2,8,6,1,5]=>0110111=>1110110
[6,8,3,7,5,2,1,4]=>1001011=>1101001
[5,7,8,4,3,2,1,6]=>1110001=>1000111
[6,4,3,8,5,2,1,7]=>1011101=>1011101
[8,2,5,4,7,6,1,3]=>0001111=>1111000
[7,2,5,4,8,6,1,3]=>0001111=>1111000
[4,5,3,2,8,6,1,7]=>0101101=>1011010
[3,2,5,4,8,6,1,7]=>0101101=>1011010
[3,2,8,6,5,4,1,7]=>0111101=>1011110
[8,4,3,6,5,2,1,7]=>1011101=>1011101
[8,4,3,7,5,2,1,6]=>1011011=>1101101
[3,2,7,8,5,4,1,6]=>0111001=>1001110
[6,8,7,4,3,2,1,5]=>1110011=>1100111
[3,6,1,4,8,7,2,5]=>0000111=>1110000
[5,8,1,3,7,2,6,4]=>0000111=>1110000
[4,7,5,1,8,2,6,3]=>0001111=>1111000
[6,3,2,1,8,7,4,5]=>1100111=>1110011
[6,2,3,1,8,7,4,5]=>0100111=>1110010
[3,4,7,1,8,5,6,2]=>0000111=>1110000
[3,4,8,1,7,5,6,2]=>0000111=>1110000
[7,2,1,5,8,4,6,3]=>1000111=>1110001
[4,2,8,1,7,5,6,3]=>0010111=>1110100
[8,3,6,4,1,7,5,2]=>0011111=>1111100
[7,3,1,5,2,8,6,4]=>0101111=>1111010
[7,1,6,4,2,8,5,3]=>0011111=>1111100
[3,7,4,1,5,8,6,2]=>0010111=>1110100
[5,8,6,1,2,7,4,3]=>0010111=>1110100
[6,8,1,4,3,7,5,2]=>0011011=>1101100
[6,7,1,4,3,8,5,2]=>0011011=>1101100
[6,8,1,2,4,7,5,3]=>0001011=>1101000
[7,1,6,4,8,3,5,2]=>0001111=>1111000
[8,6,4,1,3,7,5,2]=>0011111=>1111100
[8,5,3,6,1,7,4,2]=>0011111=>1111100
[7,2,1,4,5,8,6,3]=>1000111=>1110001
[8,5,6,1,2,7,4,3]=>0010111=>1110100
[8,6,2,5,4,7,3,1]=>0101111=>1111010
[8,5,7,3,2,4,6,1]=>0100111=>1110010
[8,5,2,1,4,3,6,7]=>1011001=>1001101
[2,8,4,1,3,6,7,5]=>0010011=>1100100
[8,1,2,4,5,6,7,3]=>0000011=>1100000
[6,1,4,3,2,7,8,5]=>0110101=>1010110
[1,8,3,6,7,2,4,5]=>0000011=>1100000
[1,2,8,3,7,4,6,5]=>0000111=>1110000
[1,9,2,3,4,5,6,7,8,10]=>000000010=>010000000
[1,7,2,3,4,5,6,8,9]=>00000100=>00100000
[2,4,1,3,6,5,8,7,10,9,11]=>0010101010=>0101010100
[8,2,6,5,4,3,1,7]=>0111101=>1011110
[8,2,7,6,4,5,3,1]=>0101111=>1111010
[8,7,3,5,4,2,6,1]=>0011111=>1111100
[12,10,9,8,7,6,5,4,3,2,1,11]=>11111111101=>10111111111
[4,2,5,6,7,8,3,1]=>0110001=>1000110
[3,7,8,4,5,1,6,2]=>0001101=>1011000
[3,6,1,5,7,8,2,4]=>0000101=>1010000
[4,6,8,5,2,7,1,3]=>0001011=>1101000
[3,7,8,5,2,6,1,4]=>0001101=>1011000
[3,7,8,5,4,1,6,2]=>0011101=>1011100
[7,8,2,3,5,4,1,6]=>0011001=>1001100
[5,1,3,7,6,4,8,2]=>0001111=>1111000
[4,6,5,2,7,8,1,3]=>0001101=>1011000
[1,6,5,2,3,4,8,7]=>0001101=>1011000
[4,6,5,1,7,3,8,2]=>0001111=>1111000
[5,7,3,1,2,4,8,6]=>0100011=>1100010
[6,3,2,5,1,7,4,8]=>0101110=>0111010
[6,1,2,4,8,5,3,7]=>0001101=>1011000
[6,3,1,7,2,5,8,4]=>0100111=>1110010
[3,7,2,8,5,1,4,6]=>0001011=>1101000
[3,6,5,2,4,7,1,8]=>0001110=>0111000
[3,6,5,8,1,7,2,4]=>0000111=>1110000
[1,2,3,4,5,6,8,7,9]=>00000010=>01000000
[1,2,3,4,5,6,7,9,8,10]=>000000010=>010000000
[1,2,3,4,5,7,6,8,9]=>00000100=>00100000
[9,2,3,4,5,6,7,1,8]=>00000101=>10100000
[1,3,5,8,6,4,7,2]=>0000111=>1110000
[1,3,5,8,6,7,2,4]=>0000011=>1100000
[6,1,7,4,8,5,3,2]=>0101111=>1111010
[5,7,4,1,3,6,8,2]=>0010011=>1100100
[7,4,3,1,6,5,8,2]=>0110111=>1110110
[8,6,1,7,5,3,2,4]=>0101111=>1111010
[7,8,1,4,6,5,3,2]=>0101101=>1011010
[7,8,6,1,4,5,3,2]=>0101101=>1011010
[6,2,7,3,8,5,4,1]=>0011111=>1111100
[1,2,7,5,3,4,8,6]=>0001011=>1101000
[7,2,8,3,6,4,5,1]=>0001111=>1111000
[6,2,7,8,3,1,4,5]=>0100101=>1010010
[1,7,8,2,5,3,4,6]=>0001001=>1001000
[3,7,8,1,2,5,6,4]=>0000101=>1010000
[1,2,8,7,3,4,6,5]=>0000111=>1110000
[8,2,7,4,5,1,6,3]=>0001111=>1111000
[3,8,1,5,7,2,6,4]=>0000111=>1110000
[7,5,4,8,6,1,2,3]=>0001111=>1111000
[7,1,8,6,4,5,2,3]=>0001111=>1111000
[8,7,5,1,4,3,6,2]=>0011111=>1111100
[1,5,7,8,3,4,2,6]=>0010001=>1000100
[6,8,4,3,1,7,2,5]=>0110011=>1100110
[8,4,1,3,7,5,6,2]=>0010111=>1110100
[4,8,1,3,7,5,6,2]=>0000111=>1110000
[1,8,5,7,4,2,3,6]=>0010011=>1100100
[2,1,6,8,5,3,4,7]=>1001001=>1001001
[4,5,1,3,8,6,7,2]=>0001011=>1101000
[1,2,6,8,5,3,4,7]=>0001001=>1001000
[5,6,8,7,3,1,2,4]=>0100011=>1100010
[6,7,5,3,8,1,2,4]=>0001011=>1101000
[6,8,5,7,3,1,2,4]=>0100011=>1100010
[5,7,8,6,3,1,2,4]=>0100101=>1010010
[5,1,4,2,6,8,7,3]=>0011011=>1101100
[6,3,2,4,7,1,8,5]=>0100111=>1110010
[1,5,6,8,4,2,3,7]=>0010001=>1000100
[5,7,8,3,6,1,2,4]=>0000101=>1010000
[1,5,8,6,2,4,3,7]=>0010101=>1010100
[1,5,3,7,2,6,8,4]=>0001011=>1101000
[5,1,8,6,2,4,3,7]=>0011101=>1011100
[5,8,6,3,7,1,2,4]=>0000111=>1110000
[1,5,2,4,8,6,7,3]=>0001011=>1101000
[1,5,4,2,6,8,7,3]=>0011011=>1101100
[5,7,6,3,8,1,2,4]=>0000111=>1110000
[5,7,6,8,3,1,2,4]=>0100011=>1100010
[6,8,7,5,3,1,2,4]=>0101011=>1101010
[1,2,5,3,6,8,7,4]=>0001011=>1101000
[6,8,7,2,1,5,3,4]=>1001011=>1101001
[7,3,6,1,4,8,2,5]=>0000111=>1110000
[7,8,1,6,5,3,4,2]=>0011101=>1011100
[8,7,3,2,1,4,6,5]=>1100111=>1110011
[8,3,5,1,7,4,2,6]=>0011011=>1101100
[3,5,6,8,4,2,7,1]=>0010011=>1100100
[5,8,2,6,4,3,7,1]=>0010111=>1110100
[2,8,6,3,4,1,7,5]=>0010111=>1110100
[1,7,2,3,5,8,6,4]=>0000111=>1110000
[4,6,2,3,5,1,7,8]=>0001100=>0011000
[2,8,3,7,5,1,6,4]=>0001111=>1111000
[6,4,8,7,2,1,5,3]=>1001111=>1111001
[1,8,2,3,7,5,6,4]=>0000111=>1110000
[2,8,4,3,6,7,1,5]=>0010011=>1100100
[7,3,2,5,6,1,8,4]=>0100111=>1110010
[1,6,7,8,2,4,3,5]=>0010001=>1000100
[4,1,2,8,5,3,7,6]=>0011011=>1101100
[3,8,4,2,5,1,7,6]=>0011011=>1101100
[1,8,5,6,4,3,2,7]=>0110101=>1010110
[2,8,3,5,6,4,1,7]=>0010101=>1010100
[4,1,5,7,6,8,2,3]=>0010011=>1100100
[7,6,8,3,2,5,1,4]=>0101011=>1101010
[2,7,8,1,6,4,5,3]=>0001101=>1011000
[2,7,1,4,5,3,8,6]=>0001011=>1101000
[1,5,2,7,4,3,6,8]=>0011010=>0101100
[5,1,3,8,4,6,2,7]=>0001101=>1011000
[6,5,8,7,1,3,2,4]=>0100111=>1110010
[2,7,3,5,1,6,8,4]=>0001011=>1101000
[5,7,6,8,2,1,4,3]=>1010011=>1100101
[1,3,6,5,2,7,4,8]=>0001110=>0111000
[1,2,6,5,3,4,7,8]=>0001100=>0011000
[1,7,2,5,6,8,3,4]=>0000011=>1100000
[1,7,2,4,8,3,5,6]=>0000011=>1100000
[1,6,2,4,5,3,7,8]=>0001100=>0011000
[1,3,2,8,4,5,7,6]=>0100011=>1100010
[1,6,8,2,4,3,5,7]=>0010001=>1000100
[1,6,7,2,5,3,4,8]=>0001010=>0101000
[1,2,8,3,6,7,4,5]=>0000011=>1100000
[1,7,2,5,3,4,8,6]=>0001011=>1101000
[10,3,4,5,6,7,8,9,1,2]=>000000011=>110000000
[9,3,4,5,6,7,8,1,10,2]=>000000111=>111000000
[8,3,4,5,6,7,1,9,10,2]=>000001101=>101100000
[7,3,4,5,6,1,8,9,10,2]=>000011001=>100110000
[6,3,4,5,1,7,8,9,10,2]=>000110001=>100011000
[5,3,4,1,6,7,8,9,10,2]=>001100001=>100001100
[4,3,1,5,6,7,8,9,10,2]=>011000001=>100000110
[11,3,4,5,6,7,8,9,10,1,2]=>0000000011=>1100000000
[10,9,4,5,6,7,8,1,2,3]=>000000111=>111000000
[10,3,4,5,6,7,8,9,1,11,2]=>0000000111=>1110000000
[10,3,8,5,6,7,1,9,2,4]=>000001111=>111100000
[9,3,4,5,6,7,8,1,10,11,2]=>0000001101=>1011000000
[10,3,4,7,6,1,8,9,2,5]=>000011011=>110110000
[8,3,4,5,6,7,1,9,10,11,2]=>0000011001=>1001100000
[10,3,4,5,1,7,8,9,2,6]=>000100011=>110001000
[7,3,4,5,6,1,8,9,10,11,2]=>0000110001=>1000110000
[5,3,4,1,6,10,8,9,2,7]=>001100011=>110001100
[6,3,4,5,1,7,8,9,10,11,2]=>0001100001=>1000011000
[4,3,1,5,6,7,10,9,2,8]=>011000011=>110000110
[5,3,4,1,6,7,8,9,10,11,2]=>0011000001=>1000001100
[3,1,4,5,6,7,8,10,2,9]=>010000001=>100000010
[4,3,1,5,6,7,8,9,10,11,2]=>0110000001=>1000000110
[7,1,5,6,2,3,8,4]=>0000111=>1110000
[8,2,1,4,6,7,3,5]=>1000011=>1100001
[7,2,6,1,3,4,8,5]=>0000111=>1110000
[4,1,3,7,2,5,8,6]=>0010011=>1100100
[6,2,7,5,1,3,8,4]=>0001111=>1111000
[1,7,5,6,2,3,8,4]=>0000111=>1110000
[3,7,6,1,2,4,8,5]=>0000111=>1110000
[8,6,1,3,5,7,2,4]=>0000111=>1110000
[1,7,4,3,8,2,5,6]=>0010011=>1100100
[6,1,5,3,4,8,2,7]=>0001101=>1011000
[3,6,7,5,2,8,1,4]=>0001011=>1101000
[7,8,4,1,5,6,2,3]=>0010101=>1010100
[5,8,1,3,6,7,2,4]=>0000011=>1100000
[2,8,4,3,7,1,5,6]=>0010011=>1100100
[3,8,4,6,7,1,2,5]=>0000011=>1100000
[6,3,8,4,7,1,2,5]=>0000111=>1110000
[1,2,5,4,8,3,6,7]=>0001001=>1001000
[7,1,3,8,2,4,5,6]=>0000011=>1100000
[8,1,3,7,2,4,5,6]=>0000011=>1100000
[3,5,4,7,8,1,2,6]=>0001001=>1001000
[8,3,1,4,7,2,5,6]=>0100011=>1100010
[1,6,4,7,8,2,3,5]=>0000101=>1010000
[5,2,3,6,7,8,1,4]=>0001001=>1001000
[6,2,7,3,8,5,1,4]=>0001111=>1111000
[1,3,7,8,5,6,2,4]=>0000101=>1010000
[8,2,6,7,5,1,3,4]=>0001011=>1101000
[8,1,7,4,6,2,3,5]=>0000111=>1110000
[2,5,8,4,7,1,3,6]=>0000011=>1100000
[4,5,8,7,1,2,3,6]=>0000011=>1100000
[4,1,8,5,7,2,3,6]=>0010011=>1100100
[1,8,7,4,6,2,3,5]=>0000111=>1110000
[2,6,5,4,1,8,3,7]=>0011101=>1011100
[6,2,5,1,4,8,3,7]=>0001101=>1011000
[6,5,4,1,3,8,2,7]=>0011101=>1011100
[6,3,5,4,2,8,1,7]=>0011101=>1011100
[1,3,8,7,4,2,6,5]=>0010111=>1110100
[8,7,4,3,1,5,2,6]=>0111011=>1101110
[8,2,5,1,4,6,7,3]=>0001011=>1101000
[3,8,4,5,1,6,7,2]=>0001011=>1101000
[8,5,4,1,3,6,7,2]=>0011011=>1101100
[8,3,1,7,5,6,4,2]=>0110111=>1110110
[8,4,7,6,5,3,1,2]=>0101111=>1111010
[8,1,4,5,7,6,3,2]=>0100111=>1110010
[2,4,1,8,5,7,6,3]=>0010111=>1110100
[8,2,1,4,7,6,3,5]=>1000111=>1110001
[8,3,1,7,4,2,6,5]=>0110111=>1110110
[8,2,7,3,1,6,5,4]=>0101111=>1111010
[1,8,4,2,3,7,6,5]=>0010111=>1110100
[3,1,2,8,7,4,6,5]=>0100111=>1110010
[8,5,1,2,4,3,7,6]=>0011011=>1101100
[2,8,3,7,4,1,6,5]=>0010111=>1110100
[8,4,5,7,6,2,3,1]=>0100111=>1110010
[2,3,1,8,7,6,4,5]=>0100111=>1110010
[4,2,8,7,3,1,5,6]=>0110011=>1100110
[1,3,4,8,7,2,5,6]=>0000011=>1100000
[8,1,3,4,6,7,2,5]=>0000011=>1100000
[3,4,8,2,6,7,1,5]=>0000011=>1100000
[3,6,8,2,5,1,7,4]=>0001011=>1101000
[3,8,2,5,7,4,6,1]=>0000111=>1110000
[8,4,2,1,7,5,6,3]=>1010111=>1110101
[8,2,7,5,6,4,1,3]=>0010111=>1110100
[6,2,8,5,4,1,7,3]=>0011111=>1111100
[6,8,5,4,1,7,2,3]=>0011011=>1101100
[2,8,1,5,7,6,3,4]=>0000111=>1110000
[3,1,8,2,7,5,6,4]=>0100111=>1110010
[8,5,7,1,6,4,2,3]=>0010111=>1110100
[2,8,4,7,3,6,5,1]=>0001111=>1111000
[8,4,7,2,1,6,5,3]=>1001111=>1111001
[1,8,4,7,6,5,2,3]=>0001111=>1111000
[3,5,8,1,7,4,6,2]=>0000111=>1110000
[8,4,7,1,3,6,5,2]=>0001111=>1111000
[8,2,3,4,5,6,9,1,7]=>00000011=>11000000
[8,2,3,9,5,6,7,1,4]=>00000111=>11100000
[8,2,9,4,5,6,7,1,3]=>00000111=>11100000
[8,9,3,4,5,6,7,1,2]=>00000101=>10100000
[9,2,3,4,5,6,7,10,1,8]=>000000011=>110000000
[4,2,3,1,9,8,7,6,5]=>01101111=>11110110
[3,2,1,9,8,6,7,5,4]=>11010111=>11101011
[9,2,10,4,5,6,7,8,1,3]=>000000111=>111000000
[2,3,4,7,6,8,1,5]=>0000011=>1100000
[3,8,1,2,5,6,4,7]=>0000101=>1010000
[3,7,1,2,5,6,4,8]=>0000110=>0110000
[8,5,2,1,4,6,7,3]=>1001011=>1101001
[4,8,1,6,5,2,7,3]=>0001111=>1111000
[4,2,6,3,8,5,7,1]=>0010111=>1110100
[4,5,2,6,7,1,8,3]=>0001011=>1101000
[2,7,4,1,6,3,5,8]=>0010110=>0110100
[8,3,5,4,2,7,1,6]=>0011011=>1101100
[2,8,6,4,7,3,1,5]=>0100111=>1110010
[3,1,8,6,5,2,7,4]=>0101111=>1111010
[8,3,1,5,2,6,7,4]=>0101011=>1101010
[3,8,2,4,1,5,7,6]=>0010011=>1100100
[5,8,3,2,4,1,7,6]=>0110011=>1100110
[7,2,6,8,4,3,5,1]=>0011011=>1101100
[6,5,3,2,4,8,1,7]=>0101101=>1011010
[5,2,4,6,1,3,8,7]=>0001101=>1011000
[7,2,3,4,6,8,1,5]=>0000011=>1100000
[8,3,4,6,7,5,1,2]=>0001011=>1101000
[3,7,4,6,8,2,5,1]=>0001011=>1101000
[3,7,5,2,8,6,1,4]=>0001111=>1111000
[8,4,6,5,2,7,3,1]=>0101111=>1111010
[8,6,2,3,5,1,7,4]=>0001111=>1111000
[7,2,4,5,6,8,1,3]=>0000011=>1100000
[7,1,3,5,6,2,8,4]=>0000111=>1110000
[5,3,6,1,4,2,8,7]=>0011101=>1011100
[5,7,2,1,4,3,8,6]=>1010011=>1100101
[7,1,8,3,5,2,4,6]=>0001011=>1101000
[7,2,4,8,1,5,6,3]=>0000111=>1110000
[7,1,8,4,2,5,6,3]=>0010111=>1110100
[6,4,2,5,8,1,7,3]=>0010111=>1110100
[2,1,7,5,8,3,6,4]=>1000111=>1110001
[7,3,8,5,6,2,1,4]=>1000111=>1110001
[2,7,4,8,1,5,6,3]=>0000111=>1110000
[7,4,8,3,1,5,6,2]=>0100111=>1110010
[6,1,5,8,3,7,4,2]=>0010111=>1110100
[2,6,3,5,8,7,4,1]=>0010111=>1110100
[8,6,5,3,7,2,1,4]=>1001111=>1111001
[4,8,5,3,7,2,1,6]=>1001011=>1101001
[7,4,8,6,5,3,2,1]=>1101111=>1111011
[7,4,8,5,6,3,1,2]=>0100111=>1110010
[7,8,4,1,3,5,6,2]=>0010101=>1010100
[7,8,3,4,1,5,6,2]=>0010101=>1010100
[7,3,1,8,2,5,6,4]=>0100111=>1110010
[7,2,3,8,1,5,6,4]=>0000111=>1110000
[6,4,8,7,3,2,1,5]=>1100111=>1110011
[2,7,4,8,6,3,1,5]=>0100111=>1110010
[6,4,8,2,3,1,7,5]=>0100111=>1110010
[7,2,1,8,3,5,6,4]=>1000111=>1110001
[5,1,6,3,8,2,4,7]=>0001101=>1011000
[3,6,5,1,4,8,7,2]=>0001111=>1111000
[7,3,6,2,8,4,1,5]=>0010111=>1110100
[6,5,1,8,4,7,2,3]=>0001111=>1111000
[7,5,4,8,1,6,2,3]=>0001111=>1111000
[4,3,5,8,7,1,2,6]=>0010011=>1100100
[3,5,6,8,1,4,2,7]=>0010001=>1000100
[4,3,5,8,2,1,6,7]=>1010001=>1000101
[6,4,7,2,3,1,5,8]=>0100110=>0110010
[6,8,1,5,4,2,7,3]=>0011011=>1101100
[7,8,6,3,1,4,2,5]=>0110101=>1010110
[7,8,6,3,5,1,2,4]=>0001101=>1011000
[7,2,8,5,4,6,3,1]=>0101111=>1111010
[6,1,8,4,7,2,3,5]=>0000111=>1110000
[5,6,4,3,7,1,8,2]=>0010111=>1110100
[6,5,3,7,2,4,8,1]=>0001111=>1111000
[5,6,2,8,4,3,7,1]=>0010111=>1110100
[4,1,2,6,8,3,7,5]=>0010011=>1100100
[7,1,3,6,5,8,4,2]=>0010111=>1110100
[5,7,4,3,6,8,2,1]=>1010011=>1100101
[4,6,2,7,8,3,5,1]=>0001101=>1011000
[5,1,2,4,6,7,8,3]=>0001001=>1001000
[4,6,3,5,2,8,7,1]=>0001111=>1111000
[5,6,3,4,8,2,7,1]=>0000111=>1110000
[5,2,6,4,1,7,8,3]=>0011101=>1011100
[5,8,4,6,3,2,7,1]=>0100111=>1110010
[5,4,3,8,6,2,7,1]=>0011111=>1111100
[5,7,8,2,4,3,6,1]=>0010101=>1010100
[5,6,2,4,8,3,7,1]=>0000111=>1110000
[6,4,7,8,2,3,5,1]=>0001101=>1011000
[3,7,5,2,4,8,1,6]=>0001011=>1101000
[4,7,5,2,3,8,6,1]=>0001111=>1111000
[6,4,7,3,2,5,8,1]=>0100111=>1110010
[5,7,3,2,8,4,6,1]=>0100111=>1110010
[5,3,7,2,8,4,6,1]=>0001111=>1111000
[4,3,7,2,5,8,6,1]=>0010111=>1110100
[4,7,3,2,5,8,6,1]=>0100111=>1110010
[4,7,3,2,6,8,5,1]=>0101011=>1101010
[7,5,3,2,6,4,8,1]=>0101111=>1111010
[8,5,2,6,7,3,4,1]=>0011011=>1101100
[8,4,2,6,3,7,5,1]=>0011111=>1111100
[7,4,6,2,3,8,5,1]=>0001111=>1111000
[7,5,6,2,8,3,4,1]=>0010111=>1110100
[5,7,6,2,8,3,4,1]=>0010111=>1110100
[4,7,6,2,3,8,5,1]=>0001111=>1111000
[7,6,3,2,5,8,1,4]=>0100111=>1110010
[7,6,4,2,5,8,3,1]=>0110111=>1110110
[2,10,4,5,6,7,8,9,1,3]=>000000011=>110000000
[9,8,4,5,6,7,1,2,10,3]=>000001111=>111100000
[2,10,9,5,6,7,8,1,3,4]=>000000111=>111000000
[2,11,4,5,6,7,8,9,10,1,3]=>0000000011=>1100000000
[11,3,4,5,6,7,8,9,10,1,12,2]=>00000000111=>11100000000
[10,9,4,5,6,7,8,1,2,11,3]=>0000001111=>1111000000
[9,3,8,5,6,7,1,2,10,4]=>000001111=>111100000
[9,7,4,5,6,1,8,2,10,3]=>000011111=>111110000
[2,10,4,9,6,7,8,1,3,5]=>000000111=>111000000
[2,10,8,5,6,7,1,9,3,4]=>000001111=>111100000
[2,11,10,5,6,7,8,9,1,3,4]=>0000000111=>1110000000
[2,12,4,5,6,7,8,9,10,11,1,3]=>00000000011=>11000000000
[6,3,8,5,4,7,2,1]=>1001111=>1111001
[1,3,2,4,5,6,7,8,9]=>01000000=>00000010
[1,4,2,3,5,6,7,8,9]=>00100000=>00000100
[1,3,2,4,5,6,7,8,9,10]=>010000000=>000000010
[2,4,6,3,8,7,5,1]=>0001111=>1111000
[2,4,6,1,8,7,3,5]=>0000111=>1110000
[2,4,3,6,8,7,1,5]=>0010011=>1100100
[2,4,6,3,8,7,1,5]=>0000111=>1110000
[2,4,6,5,8,7,1,3]=>0000111=>1110000
[2,4,6,8,5,7,3,1]=>0100011=>1100010
[2,4,6,8,5,7,1,3]=>0000011=>1100000
[2,4,6,8,3,7,1,5]=>0000011=>1100000
[2,4,6,8,1,7,3,5]=>0000011=>1100000
[2,4,6,5,1,8,7,3]=>0001111=>1111000
[2,4,6,5,8,3,7,1]=>0000111=>1110000
[2,4,6,5,8,1,7,3]=>0000111=>1110000
[2,4,6,8,5,1,7,3]=>0001011=>1101000
[2,4,6,8,7,3,5,1]=>0001011=>1101000
[2,4,6,8,7,1,5,3]=>0001011=>1101000
[2,4,6,8,7,1,3,5]=>0000011=>1100000
[2,4,6,8,5,1,3,7]=>0001001=>1001000
[2,4,6,5,1,8,3,7]=>0001101=>1011000
[2,4,6,5,1,3,8,7]=>0001101=>1011000
[2,4,6,5,3,8,1,7]=>0001101=>1011000
[2,4,6,5,8,3,1,7]=>0100101=>1010010
[2,4,6,8,5,3,1,7]=>0101001=>1001010
[2,4,6,8,7,3,1,5]=>0100011=>1100010
[2,4,6,8,7,5,1,3]=>0001011=>1101000
[4,8,7,5,2,1,3,6]=>1001011=>1101001
[6,1,4,7,5,8,2,3]=>0000111=>1110000
[1,8,6,5,3,2,7,4]=>0101111=>1111010
[1,6,3,5,8,2,4,7]=>0000101=>1010000
[4,6,1,7,8,5,3,2]=>0101101=>1011010
[6,1,2,7,8,4,5,3]=>0001101=>1011000
[6,1,3,2,7,8,5,4]=>0101101=>1011010
[5,6,3,1,7,4,8,2]=>0100111=>1110010
[4,8,3,7,1,6,5,2]=>0001111=>1111000
[8,7,2,6,5,1,4,3]=>0011111=>1111100
[5,8,3,2,1,7,6,4]=>1100111=>1110011
[5,4,3,8,1,7,6,2]=>0011111=>1111100
[6,5,3,8,7,1,4,2]=>0011111=>1111100
[4,3,8,2,7,6,5,1]=>0011111=>1111100
[4,8,2,7,6,5,3,1]=>0101111=>1111010
[7,8,2,6,5,4,1,3]=>0011101=>1011100
[3,8,7,6,2,5,1,4]=>0001111=>1111000
[4,8,3,7,2,1,6,5]=>1000111=>1110001
[8,6,3,1,7,5,4,2]=>0111111=>1111110
[8,6,3,7,1,5,4,2]=>0011111=>1111100
[4,8,3,7,6,2,5,1]=>0001111=>1111000
[5,8,2,7,6,4,1,3]=>0010111=>1110100
[8,4,2,1,7,6,5,3]=>1011111=>1111101
[1,6,4,2,5,3,7,8]=>0011100=>0011100
[1,8,6,2,7,3,4,5]=>0000111=>1110000
[1,6,3,2,4,5,7,8]=>0100100=>0010010
[1,5,2,6,4,3,7,8]=>0011100=>0011100
[1,5,2,4,6,3,7,8]=>0001100=>0011000
[1,8,6,2,3,7,4,5]=>0000111=>1110000
[1,5,2,8,6,3,4,7]=>0001101=>1011000
[1,3,6,8,2,7,4,5]=>0000011=>1100000
[1,4,3,8,2,5,6,7]=>0010001=>1000100
[1,7,2,3,8,5,4,6]=>0001011=>1101000
[1,3,8,4,2,5,6,7]=>0010001=>1000100
[1,6,2,8,5,4,3,7]=>0011101=>1011100
[1,7,2,3,8,6,4,5]=>0000111=>1110000
[1,5,3,8,2,7,4,6]=>0001011=>1101000
[1,4,8,2,5,6,3,7]=>0000101=>1010000
[1,5,7,3,2,8,4,6]=>0100011=>1100010
[1,2,7,3,6,8,4,5]=>0000011=>1100000
[1,7,2,3,6,8,4,5]=>0000011=>1100000
[1,4,8,3,2,5,6,7]=>0100001=>1000010
[1,7,2,5,8,3,4,6]=>0000011=>1100000
[8,2,3,4,5,6,7,9,1]=>00000011=>11000000
[7,2,3,4,5,6,9,8,1]=>00000111=>11100000
[6,2,3,4,5,9,7,8,1]=>00001011=>11010000
[5,2,3,4,9,6,7,8,1]=>00010011=>11001000
[4,2,3,9,5,6,7,8,1]=>00100011=>11000100
[3,2,9,4,5,6,7,8,1]=>01000011=>11000010
[2,9,3,4,5,6,7,8,1]=>00000011=>11000000
[9,2,3,4,5,6,7,8,10,1]=>000000011=>110000000
[6,2,3,4,5,1,8,9,7]=>00011001=>10011000
[8,2,3,4,5,6,7,10,9,1]=>000000111=>111000000
[5,2,3,4,1,7,9,8,6]=>00110011=>11001100
[7,2,3,4,5,6,10,8,9,1]=>000001011=>110100000
[6,2,3,5,8,1,7,4]=>0000111=>1110000
[4,2,3,1,6,9,7,8,5]=>01100011=>11000110
[6,2,3,4,5,10,7,8,9,1]=>000010011=>110010000
[5,2,4,8,1,6,7,3]=>0001011=>1101000
[3,2,1,5,9,6,7,8,4]=>11000011=>11000011
[5,2,3,4,10,6,7,8,9,1]=>000100011=>110001000
[2,1,4,9,5,6,7,8,3]=>10000011=>11000001
[4,2,3,10,5,6,7,8,9,1]=>001000011=>110000100
[1,3,9,4,5,6,7,8,2]=>00000011=>11000000
[3,2,10,4,5,6,7,8,9,1]=>010000011=>110000010
[2,10,3,4,5,6,7,8,9,1]=>000000011=>110000000
[2,3,5,6,4,7,8,1,9]=>00001010=>01010000
[1,3,4,6,7,5,8,9,2]=>00000101=>10100000
[2,3,4,6,7,5,8,9,1,10]=>000001010=>010100000
[2,3,6,5,7,4,8,1,9]=>00001110=>01110000
[2,3,5,6,7,1,8,4,9]=>00000110=>01100000
[2,6,4,5,7,3,1,8]=>0100110=>0110010
[2,5,6,3,4,7,1,8]=>0000110=>0110000
[1,3,7,5,6,8,4,2]=>0010011=>1100100
[1,3,6,7,4,5,8,2]=>0000011=>1100000
[1,3,4,7,6,8,5,9,2]=>00000111=>11100000
[1,3,4,6,7,8,2,9,5]=>00000011=>11000000
[1,3,4,5,7,8,6,9,10,2]=>000000101=>101000000
[1,5,6,3,4,2,7,8]=>0010100=>0010100
[1,5,6,3,4,7,2,8]=>0000110=>0110000
[1,5,3,6,4,2,7,8]=>0011100=>0011100
[1,7,5,6,8,3,4,2]=>0010011=>1100100
[1,7,5,6,3,8,4,2]=>0010111=>1110100
[1,3,7,5,2,8,6,4]=>0001111=>1111000
[1,3,7,2,5,8,6,4]=>0000111=>1110000
[1,5,3,7,4,6,2,8]=>0001110=>0111000
[1,5,3,7,6,4,2,8]=>0011110=>0111100
[1,5,3,6,7,4,2,8]=>0011010=>0101100
[1,5,6,3,7,4,2,8]=>0010110=>0110100
[1,5,7,6,3,4,8,2]=>0000111=>1110000
[1,5,7,3,6,4,8,2]=>0000111=>1110000
[1,3,7,2,5,6,8,4]=>0000011=>1100000
[1,3,7,5,6,2,8,4]=>0000111=>1110000
[2,5,7,4,1,3,8,6]=>0010011=>1100100
[6,7,3,1,8,5,2,4]=>0101011=>1101010
[6,3,1,5,8,7,2,4]=>0100111=>1110010
[8,3,5,1,7,6,2,4]=>0001111=>1111000
[4,6,3,5,8,2,1,7]=>1000101=>1010001
[7,2,4,8,6,3,1,5]=>0100111=>1110010
[2,3,6,4,1,8,7,5]=>0010111=>1110100
[7,4,5,2,1,8,6,3]=>1001111=>1111001
[4,7,5,2,1,8,6,3]=>1001111=>1111001
[8,5,3,6,2,1,7,4]=>1001111=>1111001
[4,5,7,3,1,2,8,6]=>0100011=>1100010
[4,5,1,8,3,2,7,6]=>0101011=>1101010
[5,7,4,6,3,2,1,8]=>1100110=>0110011
[3,6,1,2,4,8,7,5]=>0000111=>1110000
[2,5,3,8,4,1,7,6]=>0011011=>1101100
[8,6,2,3,1,7,5,4]=>0101111=>1111010
[7,5,2,3,1,8,6,4]=>0101111=>1111010
[6,3,1,2,4,8,7,5]=>0100111=>1110010
[4,7,5,2,3,6,1,8]=>0001110=>0111000
[3,6,8,4,5,1,2,7]=>0001001=>1001000
[5,2,3,7,6,4,1,8]=>0011110=>0111100
[6,2,7,3,5,4,1,8]=>0011110=>0111100
[7,2,6,5,3,4,1,8]=>0011110=>0111100
[8,2,6,5,4,1,3,7]=>0011101=>1011100
[6,2,8,4,5,1,3,7]=>0001101=>1011000
[2,3,1,7,8,5,6,4]=>0100101=>1010010
[7,2,8,5,1,4,3,6]=>0011011=>1101100
[8,6,7,1,4,2,3,5]=>0010011=>1100100
[6,8,7,1,4,3,2,5]=>0110011=>1100110
[6,8,2,5,3,1,4,7]=>0101001=>1001010
[3,7,8,5,1,4,2,6]=>0011001=>1001100
[4,8,7,3,1,2,5,6]=>0100011=>1100010
[4,8,6,2,3,1,5,7]=>0100101=>1010010
[3,8,5,4,2,1,6,7]=>1011001=>1001101
[4,5,3,8,2,1,6,7]=>1001001=>1001001
[3,7,4,1,8,2,6,5]=>0010111=>1110100
[3,8,4,1,7,6,2,5]=>0010111=>1110100
[3,7,2,1,8,4,6,5]=>1000111=>1110001
[8,7,1,6,5,2,3,4]=>0001111=>1111000
[8,5,1,2,7,6,3,4]=>0001111=>1111000
[3,8,2,1,7,6,4,5]=>1000111=>1110001
[3,5,7,8,2,4,6,1]=>0000101=>1010000
[7,8,2,5,4,3,6,1]=>0011101=>1011100
[4,5,3,7,8,2,6,1]=>0001101=>1011000
[1,5,4,7,3,6,2,8]=>0001110=>0111000
[1,7,3,6,8,4,5,2]=>0001011=>1101000
[4,6,8,2,7,3,5,1]=>0001011=>1101000
[4,7,6,3,5,1,8,2]=>0001111=>1111000
[7,8,3,6,1,5,4,2]=>0011101=>1011100
[2,5,7,8,4,6,1,3]=>0000101=>1010000
[3,7,5,6,2,1,4,8]=>1000110=>0110001
[6,2,1,7,4,5,3,8]=>1001110=>0111001
[1,2,6,4,7,5,3,8]=>0001110=>0111000
[7,5,6,3,8,4,2,1]=>1010111=>1110101
[8,5,4,2,1,6,7,3]=>1011011=>1101101
[2,6,8,4,7,5,1,3]=>0001011=>1101000
[6,7,5,1,4,8,3,2]=>0101011=>1101010
[7,4,1,6,5,3,8,2]=>0011111=>1111100
[5,8,2,7,3,6,4,1]=>0010111=>1110100
[1,6,5,7,3,8,4,2]=>0010111=>1110100
[1,5,6,8,4,2,7,3]=>0010011=>1100100
[7,5,4,1,8,2,6,3]=>0011111=>1111100
[6,4,1,8,2,7,5,3]=>0011111=>1111100
[7,8,5,3,2,6,1,4]=>0101101=>1011010
[8,2,5,1,7,6,4,3]=>0011111=>1111100
[6,7,4,3,8,2,5,1]=>0011011=>1101100
[3,4,2,7,8,6,1,5]=>0010101=>1010100
[7,8,6,1,4,3,2,5]=>0110101=>1010110
[2,4,7,8,6,1,3,5]=>0000101=>1010000
[3,7,8,6,5,2,4,1]=>0011101=>1011100
[4,5,2,7,8,6,3,1]=>0101101=>1011010
[4,6,2,5,3,1,7,8]=>0101100=>0011010
[4,1,5,6,3,2,7,8]=>0110100=>0010110
[2,6,7,5,4,1,3,8]=>0011010=>0101100
[4,1,6,7,5,3,2,8]=>0111010=>0101110
[6,7,4,3,1,5,2,8]=>0111010=>0101110
[1,7,5,6,4,3,2,8]=>0110110=>0110110
[7,6,5,3,1,8,4,2]=>0111111=>1111110
[7,8,6,4,3,1,5,2]=>0111101=>1011110
[4,1,7,8,6,5,3,2]=>0111101=>1011110
[6,8,5,3,7,2,1,4]=>1001011=>1101001
[4,7,1,5,8,2,6,3]=>0000111=>1110000
[3,7,6,2,1,8,4,5]=>1000111=>1110001
[2,7,5,8,3,6,4,1]=>0010111=>1110100
[7,4,8,2,6,5,3,1]=>0101111=>1111010
[7,5,4,8,2,6,3,1]=>0101111=>1111010
[4,3,8,1,6,5,2,7]=>0011101=>1011100
[2,3,6,5,7,8,1,4]=>0000101=>1010000
[8,3,4,1,2,6,7,5]=>0010011=>1100100
[7,3,4,8,5,2,1,6]=>1001011=>1101001
[7,3,8,4,1,5,6,2]=>0010111=>1110100
[7,2,4,5,1,8,3,6]=>0001011=>1101000
[7,3,1,2,8,5,6,4]=>0100111=>1110010
[4,8,2,3,5,7,6,1]=>0000111=>1110000
[4,5,2,3,8,6,7,1]=>0001011=>1101000
[6,7,4,8,5,3,2,1]=>1101011=>1101011
[4,3,5,6,1,7,8,2]=>0010101=>1010100
[3,5,2,6,4,7,8,1]=>0001101=>1011000
[4,1,2,8,5,7,6,3]=>0010111=>1110100
[3,1,5,6,4,7,8,2]=>0100101=>1010010
[3,1,4,6,7,5,8,2]=>0100011=>1100010
[2,6,4,5,8,1,3,7]=>0000101=>1010000
[6,4,1,3,5,8,2,7]=>0010101=>1010100
[3,4,1,7,2,6,8,5]=>0010011=>1100100
[2,4,7,5,8,1,3,6]=>0000011=>1100000
[3,1,6,4,8,7,5,2]=>0101111=>1111010
[3,7,6,2,1,5,8,4]=>1000111=>1110001
[4,2,6,1,3,7,8,5]=>0010101=>1010100
[8,5,4,2,7,6,3,1]=>0111111=>1111110
[2,8,4,6,7,1,3,5]=>0000011=>1100000
[5,8,2,1,4,6,7,3]=>1000011=>1100001
[8,4,6,1,2,5,7,3]=>0000111=>1110000
[3,7,8,4,2,6,5,1]=>0011101=>1011100
[5,6,2,8,7,1,3,4]=>0000111=>1110000
[7,1,3,8,4,5,6,2]=>0000111=>1110000
[7,8,1,4,3,5,6,2]=>0010101=>1010100
[3,6,7,2,8,1,5,4]=>0001011=>1101000
[2,6,7,1,3,5,8,4]=>0000011=>1100000
[3,6,7,1,8,2,5,4]=>0001011=>1101000
[3,4,1,8,7,2,6,5]=>0010111=>1110100
[3,1,5,7,2,8,6,4]=>0100111=>1110010
[3,8,1,4,7,2,6,5]=>0000111=>1110000
[4,8,1,3,2,7,6,5]=>0100111=>1110010
[4,1,8,3,2,7,6,5]=>0110111=>1110110
[4,3,8,1,2,7,6,5]=>0010111=>1110100
[4,3,8,2,1,7,6,5]=>1010111=>1110101
[3,8,4,2,7,1,6,5]=>0010111=>1110100
[2,8,4,3,7,6,1,5]=>0010111=>1110100
[3,8,2,4,7,1,6,5]=>0000111=>1110000
[3,2,4,8,7,1,6,5]=>0100111=>1110010
[3,2,5,7,1,8,6,4]=>0100111=>1110010
[4,2,8,3,1,7,6,5]=>0110111=>1110110
[4,8,2,1,3,7,6,5]=>1000111=>1110001
[4,2,8,1,3,7,6,5]=>0010111=>1110100
[2,3,4,6,8,7,1,5]=>0000011=>1100000
[5,6,4,7,1,2,8,3]=>0000111=>1110000
[4,6,7,5,8,2,3,1]=>0100011=>1100010
[3,2,7,6,8,1,4,5]=>0100011=>1100010
[4,5,1,7,6,8,2,3]=>0001011=>1101000
[6,7,2,8,3,1,4,5]=>0100011=>1100010
[7,6,3,1,2,8,4,5]=>0100111=>1110010
[6,2,7,8,4,1,3,5]=>0010101=>1010100
[6,3,7,8,4,1,2,5]=>0010101=>1010100
[7,8,5,2,4,1,3,6]=>0011001=>1001100
[7,6,2,3,1,8,4,5]=>0100111=>1110010
[4,2,5,1,3,7,8,6]=>0011001=>1001100
[3,5,1,4,2,7,8,6]=>0011001=>1001100
[3,4,1,7,8,5,2,6]=>0011001=>1001100
[4,1,3,7,8,5,2,6]=>0011001=>1001100
[4,3,1,8,5,2,7,6]=>0111011=>1101110
[3,1,8,5,4,2,7,6]=>0111011=>1101110
[7,6,3,5,8,4,2,1]=>1010111=>1110101
[4,5,1,3,2,7,8,6]=>0101001=>1001010
[5,1,3,2,4,7,8,6]=>0101001=>1001010
[2,3,7,8,5,4,1,6]=>0011001=>1001100
[8,3,5,6,1,7,2,4]=>0000111=>1110000
[4,5,8,1,2,6,7,3]=>0000011=>1100000
[5,3,6,7,8,2,1,4]=>1001001=>1001001
[1,3,4,8,6,2,7,5]=>0000111=>1110000
[3,8,2,5,4,1,6,7]=>0011001=>1001100
[8,4,5,2,6,1,7,3]=>0001111=>1111000
[4,6,8,2,3,7,5,1]=>0001011=>1101000
[4,5,7,2,3,6,1,8]=>0000110=>0110000
[2,7,3,4,1,5,6,8]=>0010010=>0100100
[6,7,2,3,4,8,1,5]=>0000011=>1100000
[3,5,2,4,6,7,8,1]=>0001001=>1001000
[4,2,6,3,5,7,8,1]=>0010101=>1010100
[2,3,4,5,6,1,8,7,9]=>00001010=>01010000
[2,3,4,5,1,7,6,8,9]=>00010100=>00101000
[2,3,4,1,6,5,7,8,9]=>00101000=>00010100
[2,3,1,5,4,6,7,8,9]=>01010000=>00001010
[1,4,8,5,6,2,7,3]=>0000111=>1110000
[2,4,8,5,6,1,7,3]=>0000111=>1110000
[6,3,5,8,4,7,1,2]=>0000111=>1110000
[2,8,7,4,5,1,6,3]=>0001111=>1111000
[1,3,8,5,2,6,7,4]=>0001011=>1101000
[7,2,8,4,5,1,6,3]=>0001111=>1111000
[6,2,3,5,1,7,8,4]=>0001101=>1011000
[8,6,2,4,1,5,7,3]=>0010111=>1110100
[1,6,4,3,2,7,8,5]=>0110101=>1010110
[8,5,3,2,1,6,7,4]=>1101011=>1101011
[1,7,5,2,3,6,8,4]=>0001011=>1101000
[7,1,5,2,3,6,8,4]=>0001011=>1101000
[8,1,2,5,3,6,7,4]=>0001011=>1101000
[8,4,1,6,3,7,2,5]=>0010111=>1110100
[6,7,5,3,8,2,1,4]=>1001011=>1101001
[5,2,6,8,3,7,1,4]=>0001011=>1101000
[4,2,5,8,6,7,1,3]=>0010011=>1100100
[5,8,6,3,4,1,7,2]=>0010111=>1110100
[3,7,2,4,1,8,6,5]=>0010111=>1110100
[2,4,7,8,5,1,3,6]=>0001001=>1001000
[2,5,3,8,4,1,6,7]=>0011001=>1001100
[5,7,6,8,1,3,4,2]=>0010011=>1100100
[3,1,7,4,5,6,2,8]=>0100110=>0110010
[2,4,8,3,5,7,1,6]=>0000011=>1100000
[8,1,7,2,4,3,5,6]=>0010011=>1100100
[1,3,8,2,4,7,5,6]=>0000011=>1100000
[1,3,7,2,4,6,5,8]=>0000110=>0110000
[1,7,3,2,4,6,5,8]=>0100110=>0110010
[1,8,3,7,4,2,5,6]=>0010011=>1100100
[8,7,3,1,4,2,5,6]=>0110011=>1100110
[2,8,4,3,5,7,1,6]=>0010011=>1100100
[3,2,8,7,4,1,5,6]=>0110011=>1100110
[3,2,1,7,4,6,5,8]=>1100110=>0110011
[3,2,6,5,1,7,8,4]=>0101101=>1011010
[5,3,2,6,7,1,8,4]=>0101011=>1101010
[3,2,8,6,7,4,1,5]=>0110011=>1100110
[8,4,6,2,7,3,1,5]=>0100111=>1110010
[4,3,8,6,7,2,1,5]=>1010011=>1100101
[4,3,6,2,8,7,1,5]=>0010111=>1110100
[3,8,4,7,6,5,1,2]=>0001111=>1111000
[7,8,4,2,6,3,5,1]=>0011101=>1011100
[3,2,7,8,6,4,5,1]=>0101101=>1011010
[3,2,7,5,6,8,4,1]=>0110011=>1100110
[5,7,8,6,3,2,4,1]=>0110101=>1010110
[6,5,4,2,1,7,8,3]=>1011101=>1011101
[5,4,2,1,7,6,3,8]=>1011110=>0111101
[4,1,6,5,2,7,8,3]=>0011101=>1011100
[5,4,1,6,7,2,8,3]=>0011011=>1101100
[6,8,5,3,1,7,2,4]=>0101011=>1101010
[5,2,6,3,8,7,1,4]=>0001111=>1111000
[8,6,1,7,3,4,2,5]=>0010111=>1110100
[1,8,3,6,7,4,2,5]=>0010011=>1100100
[1,6,3,5,2,7,8,4]=>0001101=>1011000
[1,5,7,3,2,6,4,8]=>0100110=>0110010
[5,1,3,7,2,6,4,8]=>0001110=>0111000
[8,1,6,7,2,4,3,5]=>0010011=>1100100
[6,1,4,8,2,7,3,5]=>0000111=>1110000
[6,2,4,8,3,7,1,5]=>0000111=>1110000
[8,7,2,6,3,5,1,4]=>0001111=>1111000
[8,1,7,6,5,2,3,4]=>0001111=>1111000
[7,1,5,6,8,2,4,3]=>0010011=>1100100
[6,7,1,5,2,4,8,3]=>0001011=>1101000
[7,6,1,5,2,4,3,8]=>0011110=>0111100
[7,1,6,3,5,4,2,8]=>0011110=>0111100
[1,6,7,3,5,4,8,2]=>0001011=>1101000
[1,7,3,5,6,8,4,2]=>0010011=>1100100
[1,7,8,3,6,4,5,2]=>0001101=>1011000
[1,8,7,6,4,5,2,3]=>0001111=>1111000
[8,2,7,4,6,5,1,3]=>0001111=>1111000
[2,8,5,7,6,4,1,3]=>0010111=>1110100
[7,4,5,1,6,8,3,2]=>0101011=>1101010
[4,1,7,5,6,8,3,2]=>0110011=>1100110
[5,6,7,4,3,1,8,2]=>0110011=>1100110
[6,7,8,5,3,1,4,2]=>0111001=>1001110
[1,4,6,2,5,3,7,8]=>0001100=>0011000
[1,6,3,2,5,4,7,8]=>0101100=>0011010
[1,6,8,2,5,4,7,3]=>0001011=>1101000
[1,5,4,2,6,3,7,8]=>0011100=>0011100
[1,2,6,4,3,5,7,8]=>0010100=>0010100
[1,6,8,2,7,5,4,3]=>0011011=>1101100
[1,7,4,3,2,6,8,5]=>0110011=>1100110
[1,5,4,7,2,6,8,3]=>0001011=>1101000
[1,3,7,6,2,8,5,4]=>0001111=>1111000
[1,7,6,2,8,4,3,5]=>0010111=>1110100
[1,5,2,8,4,3,7,6]=>0011011=>1101100
[1,2,8,4,3,6,5,7]=>0010101=>1010100
[1,2,8,5,6,3,4,7]=>0000101=>1010000
[1,7,3,5,2,8,6,4]=>0001111=>1111000
[1,6,7,2,5,8,4,3]=>0010011=>1100100
[1,5,8,3,2,7,4,6]=>0100011=>1100010
[1,4,5,8,2,6,3,7]=>0000101=>1010000
[1,7,6,4,8,2,5,3]=>0001111=>1111000
[1,4,8,6,5,2,7,3]=>0001111=>1111000
[1,3,8,2,6,5,4,7]=>0001101=>1011000
[1,7,6,3,8,2,4,5]=>0000111=>1110000
[1,5,2,7,6,4,8,3]=>0001111=>1111000
[1,2,4,3,8,7,5,6]=>0010011=>1100100
[1,4,3,8,7,2,5,6]=>0010011=>1100100
[1,3,8,6,2,4,5,7]=>0000101=>1010000
[1,3,8,5,4,2,6,7]=>0011001=>1001100
[1,7,2,4,8,6,5,3]=>0001111=>1111000
[1,6,5,3,2,8,7,4]=>0101111=>1111010
[1,3,2,8,7,5,4,6]=>0101011=>1101010
[1,2,8,6,5,4,3,7]=>0011101=>1011100
[8,1,3,4,6,5,2,7]=>0001101=>1011000
[8,3,1,4,6,5,2,7]=>0101101=>1011010
[5,8,3,1,2,6,4,7]=>0100101=>1010010
[4,8,1,7,5,2,3,6]=>0001011=>1101000
[4,8,1,7,5,2,6,3]=>0001111=>1111000
[8,5,1,4,2,6,3,7]=>0011101=>1011100
[8,4,1,3,5,6,2,7]=>0010101=>1010100
[8,5,3,2,1,6,4,7]=>1101101=>1011011
[8,1,5,4,2,6,3,7]=>0011101=>1011100
[8,5,2,4,1,6,3,7]=>0011101=>1011100
[4,8,7,1,5,2,6,3]=>0001111=>1111000
[4,8,7,1,5,2,3,6]=>0001011=>1101000
[7,6,8,4,1,3,2,5]=>0110011=>1100110
[7,6,8,4,1,3,5,2]=>0011011=>1101100
[3,8,7,5,4,1,2,6]=>0011011=>1101100
[4,8,2,7,5,1,3,6]=>0001011=>1101000
[7,6,8,4,1,5,2,3]=>0011011=>1101100
[8,7,6,1,5,2,3,4]=>0001111=>1111000
[7,1,4,8,6,3,5,2]=>0001111=>1111000
[8,1,6,5,3,4,7,2]=>0001111=>1111000
[8,6,2,5,3,4,7,1]=>0001111=>1111000
[8,6,5,1,3,4,7,2]=>0001111=>1111000
[8,7,5,1,3,6,2,4]=>0001111=>1111000
[8,7,1,5,3,6,2,4]=>0001111=>1111000
[8,6,1,3,5,4,7,2]=>0001111=>1111000
[7,1,4,8,3,6,5,2]=>0001111=>1111000
[7,8,5,2,4,3,6,1]=>0011101=>1011100
[7,3,8,2,5,4,6,1]=>0001111=>1111000
[8,4,2,5,3,7,6,1]=>0011111=>1111100
[4,8,1,5,3,7,6,2]=>0001111=>1111000
[7,4,8,2,6,3,5,1]=>0001111=>1111000
[7,4,8,2,6,3,1,5]=>0100111=>1110010
[8,7,3,1,6,4,2,5]=>0110111=>1110110
[8,7,3,1,6,4,5,2]=>0101111=>1111010
[8,7,3,1,4,6,5,2]=>0101111=>1111010
[8,4,3,2,7,5,6,1]=>0110111=>1110110
[6,4,1,7,8,5,3,2]=>0111101=>1011110
[7,6,3,4,1,8,5,2]=>0011111=>1111100
[8,7,3,1,6,2,5,4]=>0101111=>1111010
[7,8,6,4,2,5,1,3]=>0011101=>1011100
[7,8,2,4,6,5,1,3]=>0001101=>1011000
[8,1,7,3,5,6,2,4]=>0000111=>1110000
[8,7,5,2,4,6,1,3]=>0001111=>1111000
[8,1,7,5,4,6,2,3]=>0001111=>1111000
[8,7,3,2,6,1,5,4]=>0101111=>1111010
[1,8,6,4,2,9,7,5,3]=>00111111=>11111100
[8,4,6,7,5,3,2,1]=>1101011=>1101011
[1,4,8,6,7,5,3,2]=>0101011=>1101010
[7,6,2,5,8,4,3,1]=>0110111=>1110110
[1,7,3,6,8,5,4,2]=>0011011=>1101100
[8,6,2,5,7,4,3,1]=>0110111=>1110110
[7,1,3,6,8,5,4,2]=>0011011=>1101100
[1,8,3,6,7,5,4,2]=>0011011=>1101100
[8,1,7,6,4,5,3,2]=>0101111=>1111010
[7,1,8,6,4,5,3,2]=>0101111=>1111010
[1,6,2,7,4,5,3,8]=>0001110=>0111000
[1,8,2,6,4,3,5,7]=>0010101=>1010100
[1,7,2,6,4,3,5,8]=>0010110=>0110100
[1,7,2,5,4,6,3,8]=>0001110=>0111000
[6,5,7,2,8,3,4,1]=>0010111=>1110100
[6,2,7,5,8,1,4,3]=>0010111=>1110100
[6,7,2,5,8,1,4,3]=>0010011=>1100100
[6,5,7,3,8,1,4,2]=>0010111=>1110100
[6,3,7,4,8,2,5,1]=>0001111=>1111000
[6,3,7,4,8,1,5,2]=>0001111=>1111000
[6,2,7,4,8,1,5,3]=>0001111=>1111000
[8,7,6,4,2,5,3,1]=>0111111=>1111110
[8,7,4,6,2,3,5,1]=>0001111=>1111000
[6,8,4,5,7,3,2,1]=>1100011=>1100011
[6,7,5,1,4,3,8,2]=>0011011=>1101100
[7,8,5,1,4,3,6,2]=>0011101=>1011100
[2,7,6,8,3,5,1,4]=>0001011=>1101000
[7,2,1,5,3,8,6,4]=>1001111=>1111001
[5,8,2,7,6,1,3,4]=>0000111=>1110000
[5,1,8,7,3,4,2,6]=>0011011=>1101100
[8,2,3,6,7,1,4,5]=>0000011=>1100000
[4,2,3,1,5,8,6,7]=>0110001=>1000110
[6,3,5,1,2,4,7,8,9]=>00011000=>00011000
[8,6,5,4,3,2,1,7,9]=>11111010=>01011111
[3,1,2,4,5,6,7,8,9,10]=>010000000=>000000010
[6,3,5,1,2,4,7,8,9,10]=>000110000=>000011000
[9,7,6,5,4,3,2,1,8,10]=>111111010=>010111111
[10,8,6,9,4,7,2,5,1,3]=>000101111=>111101000
[2,4,8,7,5,3,1,6]=>0101011=>1101010
[2,6,8,7,5,3,4,1]=>0011011=>1101100
[2,6,5,1,4,3,8,7]=>0011101=>1011100
[6,5,1,2,4,3,8,7]=>0011101=>1011100
[4,6,5,3,1,2,8,7]=>0101101=>1011010
[4,8,7,5,3,1,2,6]=>0101011=>1101010
[4,6,8,7,5,3,1,2]=>0101011=>1101010
[6,8,7,5,3,1,4,2]=>0111011=>1101110
[8,7,5,6,3,1,4,2]=>0110111=>1110110
[8,7,3,4,6,5,1,2]=>0001111=>1111000
[2,1,4,8,7,3,6,5]=>1000111=>1110001
[4,8,7,3,1,2,6,5]=>0100111=>1110010
[8,7,3,4,1,2,6,5]=>0010111=>1110100
[8,7,3,1,6,5,2,4]=>0101111=>1111010
[8,7,3,2,6,5,1,4]=>0101111=>1111010
[2,8,7,3,4,6,5,1]=>0001111=>1111000
[2,8,7,3,6,5,1,4]=>0001111=>1111000
[2,8,7,1,6,5,3,4]=>0001111=>1111000
[8,7,1,2,6,5,3,4]=>0001111=>1111000
[8,7,1,2,4,3,6,5]=>0010111=>1110100
[2,1,8,7,3,4,6,5]=>1000111=>1110001
[8,7,5,1,2,4,3,6]=>0011011=>1101100
[2,8,7,1,4,3,6,5]=>0010111=>1110100
[2,8,7,3,4,1,6,5]=>0010111=>1110100
[2,8,7,5,6,3,4,1]=>0010111=>1110100
[2,4,8,7,3,1,6,5]=>0100111=>1110010
[2,8,7,3,1,4,6,5]=>0100111=>1110010
[2,4,3,1,8,7,5,6]=>0110011=>1100110
[4,3,1,2,6,8,7,5]=>0110011=>1100110
[2,8,7,5,6,3,1,4]=>0100111=>1110010
[2,8,7,5,3,1,6,4]=>0101111=>1111010
[2,8,7,5,3,6,4,1]=>0011111=>1111100
[2,8,7,5,6,1,4,3]=>0010111=>1110100
[2,6,8,7,5,1,4,3]=>0011011=>1101100
[6,8,7,5,1,2,4,3]=>0011011=>1101100
[8,7,5,6,1,2,4,3]=>0010111=>1110100
[8,7,1,2,4,6,5,3]=>0001111=>1111000
[2,4,8,7,3,6,5,1]=>0001111=>1111000
[8,7,2,4,3,6,5,1]=>0011111=>1111100
[4,8,7,1,2,6,5,3]=>0001111=>1111000
[8,7,5,3,1,2,6,4]=>0101111=>1111010
[8,7,5,3,6,4,1,2]=>0011111=>1111100
[8,7,1,4,3,6,5,2]=>0011111=>1111100
[8,7,3,4,1,6,5,2]=>0011111=>1111100
[11,2,3,4,5,6,7,8,9,10,1]=>0000000011=>1100000000
[10,3,2,4,5,6,7,8,9,1]=>010000011=>110000010
[9,4,3,2,5,6,7,8,1]=>01100011=>11000110
[8,1,2,3,4,5,7,6,9]=>00000110=>01100000
[7,1,2,3,5,4,6,8]=>0001010=>0101000
[1,9,2,3,4,5,6,8,7]=>00000011=>11000000
[9,1,2,3,4,5,6,8,7,10]=>000000110=>011000000
[8,1,2,3,4,7,6,5,9]=>00001110=>01110000
[8,1,2,3,4,6,5,7,9]=>00001010=>01010000
[7,1,2,6,4,5,3,8]=>0001110=>0111000
[7,1,2,4,3,5,6,8]=>0010010=>0100100
[1,9,2,3,4,5,8,7,6]=>00000111=>11100000
[1,9,2,3,4,5,7,6,8]=>00000101=>10100000
[1,10,2,3,4,5,6,7,9,8]=>000000011=>110000000
[4,7,3,6,5,1,2,8]=>0001110=>0111000
[7,5,4,2,8,3,1,6]=>0111011=>1101110
[8,3,6,1,5,2,4,7]=>0001101=>1011000
[3,1,6,8,5,7,2,4]=>0100011=>1100010
[5,7,2,1,8,4,6,3]=>1000111=>1110001
[7,2,8,6,4,3,1,5]=>0110111=>1110110
[6,3,8,7,4,2,1,5]=>1010111=>1110101
[7,6,3,2,8,4,1,5]=>0110111=>1110110
[8,6,1,3,2,4,5,7]=>0100101=>1010010
[5,8,3,7,4,2,1,6]=>1010011=>1100101
[4,1,7,3,5,8,6,2]=>0010111=>1110100
[8,4,7,3,5,2,1,6]=>1001011=>1101001
[5,4,8,1,3,2,6,7]=>0101001=>1001010
[4,5,8,2,1,3,6,7]=>1000001=>1000001
[8,1,3,5,2,4,6,7]=>0001001=>1001000
[1,8,3,5,7,2,4,6]=>0000011=>1100000
[1,7,3,8,6,2,4,5]=>0000111=>1110000
[8,6,2,1,3,7,5,4]=>1001111=>1111001
[8,1,4,2,7,6,3,5]=>0010111=>1110100
[1,3,4,5,6,7,8,2,9]=>00000010=>01000000
[1,3,4,5,6,7,8,10,2,9]=>000000001=>100000000
[2,1,4,5,6,7,9,3,8]=>10000001=>10000001
[2,1,4,5,6,7,8,3,9]=>10000010=>01000001
[1,3,4,5,6,7,8,9,2,10]=>000000010=>010000000
[1,5,7,3,6,8,2,4]=>0000011=>1100000
[8,4,6,2,5,7,1,3]=>0000111=>1110000
[1,3,4,7,6,8,2,5]=>0000011=>1100000
[8,1,3,6,7,4,2,5]=>0010011=>1100100
[1,2,4,7,8,5,3,6]=>0001001=>1001000
[3,1,4,7,6,8,2,5]=>0100011=>1100010
[4,1,3,7,6,8,2,5]=>0010011=>1100100
[5,1,7,3,6,8,2,4]=>0001011=>1101000
[6,7,8,2,4,5,1,3]=>0001001=>1001000
[5,8,6,2,4,7,1,3]=>0000111=>1110000
[3,8,2,6,5,7,1,4]=>0000111=>1110000
[2,8,3,6,7,4,1,5]=>0010011=>1100100
[8,7,2,5,6,3,1,4]=>0100111=>1110010
[8,7,1,6,4,3,2,5]=>0110111=>1110110
[1,8,2,7,5,4,3,6]=>0011011=>1101100
[3,8,1,7,5,4,2,6]=>0011011=>1101100
[5,8,6,1,7,3,2,4]=>0100111=>1110010
[6,7,1,2,8,4,3,5]=>0010011=>1100100
[2,1,3,8,6,5,4,7]=>1001101=>1011001
[8,2,1,7,5,4,3,6]=>1011011=>1101101
[1,3,2,8,6,5,4,7]=>0101101=>1011010
[3,4,1,7,6,8,2,5]=>0010011=>1100100
[2,5,7,1,8,4,3,6]=>0010011=>1100100
[3,5,7,1,6,8,2,4]=>0000011=>1100000
[4,5,7,6,1,8,2,3]=>0000111=>1110000
[5,4,7,6,8,3,1,2]=>0101011=>1101010
[1,5,7,8,6,3,2,4]=>0100101=>1010010
[8,4,6,7,5,2,1,3]=>1001011=>1101001
[8,3,7,5,6,2,1,4]=>1000111=>1110001
[1,4,8,6,7,3,2,5]=>0100011=>1100010
[2,4,8,6,7,3,1,5]=>0100011=>1100010
[5,2,7,8,6,3,1,4]=>0101101=>1011010
[2,3,8,7,5,4,1,6]=>0011011=>1101100
[1,3,8,7,5,4,2,6]=>0011011=>1101100
[8,2,7,6,4,3,1,5]=>0110111=>1110110
[8,1,7,6,4,3,2,5]=>0110111=>1110110
[4,1,8,6,7,3,2,5]=>0110011=>1100110
[4,8,7,5,6,2,1,3]=>1000111=>1110001
[5,6,8,1,7,4,3,2]=>0110011=>1100110
[1,6,9,8,7,5,4,3,2]=>01110111=>11101110
[1,4,9,8,7,6,5,3,2]=>01011111=>11111010
[1,3,9,8,7,6,5,4,2]=>00111111=>11111100
[8,7,1,9,6,5,4,3,2]=>01111111=>11111110
[1,8,10,9,7,6,5,4,3,2]=>011111011=>110111110
[6,7,9,1,8,5,4,3,2]=>01110011=>11001110
[1,7,10,9,8,6,5,4,3,2]=>011110111=>111011110
[5,6,9,8,1,7,4,3,2]=>01100111=>11100110
[4,1,8,7,3,6,5,2]=>0011111=>1111100
[5,6,8,4,1,7,3,2]=>0110011=>1100110
[5,4,9,8,7,1,6,3,2]=>01011111=>11111010
[1,5,10,9,8,7,6,4,3,2]=>011011111=>111110110
[4,5,8,7,3,1,6,2]=>0100111=>1110010
[3,4,9,8,7,6,1,5,2]=>00011111=>11111000
[1,4,10,9,8,7,6,5,3,2]=>010111111=>111111010
[2,3,9,8,7,6,5,1,4]=>00011111=>11111000
[9,8,1,10,7,6,5,4,3,2]=>011111111=>111111110
[1,9,11,10,8,7,6,5,4,3,2]=>0111111011=>1101111110
[1,7,6,9,8,5,4,3,2]=>01110111=>11101110
[7,8,10,1,9,6,5,4,3,2]=>011110011=>110011110
[1,8,11,10,9,7,6,5,4,3,2]=>0111110111=>1110111110
[1,6,9,5,8,7,4,3,2]=>01100111=>11100110
[8,7,6,1,9,5,4,3,2]=>01111111=>11111110
[6,7,10,9,1,8,5,4,3,2]=>011100111=>111001110
[7,1,11,10,9,8,6,5,4,3,2]=>0111111111=>1111111110
[3,1,8,4,7,6,5,2]=>0101111=>1111010
[5,1,9,8,4,7,6,3,2]=>01011111=>11111010
[6,7,9,5,1,8,4,3,2]=>01110011=>11001110
[6,5,10,9,8,1,7,4,3,2]=>011011111=>111110110
[1,6,11,10,9,8,7,5,4,3,2]=>0111011111=>1111101110
[1,4,9,8,7,3,6,5,2]=>00011111=>11111000
[5,6,9,8,4,1,7,3,2]=>01100111=>11100110
[4,5,10,9,8,7,1,6,3,2]=>010011111=>111110010
[1,5,11,10,9,8,7,6,4,3,2]=>0110111111=>1111110110
[1,3,9,8,7,6,2,5,4]=>00011111=>11111000
[1,5,8,4,3,7,6,2]=>0010111=>1110100
[5,4,9,8,7,3,1,6,2]=>01011111=>11111010
[3,4,10,9,8,7,6,1,5,2]=>000111111=>111111000
[4,1,11,10,9,8,7,6,5,3,2]=>0111111111=>1111111110
[3,4,9,8,7,6,2,1,5]=>10001111=>11110001
[3,2,10,9,8,7,6,5,1,4]=>010111111=>111111010
[1,3,11,10,9,8,7,6,5,4,2]=>0011111111=>1111111100
[8,1,7,2,5,6,4,3]=>0010111=>1110100
[8,1,3,5,2,7,6,4]=>0001111=>1111000
[2,7,1,5,4,8,6,3]=>0001111=>1111000
[8,6,2,4,3,7,5,1]=>0011111=>1111100
[2,4,1,6,7,5,8,3]=>0010011=>1100100
[8,1,4,5,6,3,7,2]=>0000111=>1110000
[8,1,4,5,6,2,7,3]=>0000111=>1110000
[8,1,4,7,6,2,5,3]=>0001111=>1111000
[2,5,1,7,8,6,4,3]=>0011101=>1011100
[3,5,6,2,8,7,4,1]=>0010111=>1110100
[2,4,5,1,7,6,3,8]=>0001110=>0111000
[7,3,1,5,6,4,2,8]=>0110110=>0110110
[8,3,2,5,6,7,1,4]=>0100011=>1100010
[8,4,5,3,7,6,2,1]=>1001111=>1111001
[3,4,5,6,2,8,1,7]=>0000101=>1010000
[3,7,4,2,8,5,1,6]=>0011011=>1101100
[7,3,4,1,6,8,2,5]=>0010011=>1100100
[2,6,3,1,4,7,5,8]=>0100110=>0110010
[7,2,1,6,3,4,8,5]=>1000111=>1110001
[7,3,4,1,6,5,8,2]=>0010111=>1110100
[3,7,4,2,5,8,6,1]=>0010111=>1110100
[2,3,5,1,4,8,7,6]=>0001011=>1101000
[2,7,1,3,6,8,5,4]=>0001011=>1101000
[2,7,1,3,8,4,6,5]=>0000111=>1110000
[3,8,7,1,6,2,5,4]=>0001111=>1111000
[3,8,7,1,4,5,2,6]=>0001011=>1101000
[3,7,4,2,1,8,6,5]=>1010111=>1110101
[4,8,5,7,2,6,3,1]=>0100111=>1110010
[8,4,5,7,3,2,6,1]=>0100111=>1110010
[8,3,7,2,4,1,5,6]=>0010011=>1100100
[8,6,7,2,1,4,3,5]=>1010011=>1100101
[8,3,7,5,1,2,6,4]=>0001111=>1111000
[7,3,4,6,2,1,5,8]=>1000110=>0110001
[3,7,4,6,1,5,2,8]=>0001110=>0111000
[3,4,7,6,1,2,8,5]=>0000111=>1110000
[4,5,8,7,6,1,3,2]=>0100111=>1110010
[8,6,3,7,5,1,4,2]=>0011111=>1111100
[8,7,3,5,6,1,4,2]=>0010111=>1110100
[7,6,3,8,1,4,5,2]=>0001111=>1111000
[8,5,2,7,6,1,3,4]=>0001111=>1111000
[8,7,3,1,4,5,2,6]=>0101011=>1101010
[6,4,7,2,1,5,8,3]=>1000111=>1110001
[8,4,2,5,1,6,7,3]=>0011011=>1101100
[8,5,3,1,6,4,7,2]=>0101111=>1111010
[8,7,3,1,4,5,6,2]=>0100111=>1110010
[8,7,4,1,5,6,2,3]=>0010111=>1110100
[8,6,4,1,7,5,2,3]=>0011111=>1111100
[8,6,3,1,7,4,5,2]=>0101111=>1111010
[8,5,3,1,6,7,4,2]=>0111011=>1101110
[8,5,3,7,1,6,4,2]=>0011111=>1111100
[7,6,3,8,1,4,2,5]=>0010111=>1110100
[7,4,8,2,6,1,5,3]=>0001111=>1111000
[6,4,7,3,1,5,2,8]=>0101110=>0111010
[8,5,3,1,6,4,2,7]=>0111101=>1011110
[8,7,4,1,5,2,3,6]=>0011011=>1101100
[8,7,5,1,2,6,3,4]=>0001111=>1111000
[8,6,4,1,2,7,5,3]=>0011111=>1111100
[8,7,4,1,2,5,3,6]=>0011011=>1101100
[8,7,5,1,2,3,6,4]=>0001111=>1111000
[6,5,3,7,4,2,1,8]=>1011110=>0111101
[1,6,3,8,4,2,5,7]=>0010101=>1010100
[4,7,2,5,3,6,1,8]=>0001110=>0111000
[1,8,3,4,5,2,6,7]=>0001001=>1001000
[1,8,6,4,2,5,3,7]=>0011101=>1011100
[8,2,6,4,1,5,7,3]=>0010111=>1110100
[7,8,3,4,6,1,5,2]=>0001101=>1011000
[4,8,7,5,3,1,6,2]=>0101111=>1111010
[6,1,4,8,3,2,5,7]=>0100101=>1010010
[4,1,8,5,3,2,6,7]=>0111001=>1001110
[8,1,6,4,2,7,3,5]=>0010111=>1110100
[3,1,7,4,2,5,8,6]=>0110011=>1100110
[1,2,7,4,3,5,6,8]=>0010010=>0100100
[6,1,8,5,2,4,3,7]=>0011101=>1011100
[6,8,2,5,1,4,7,3]=>0001011=>1101000
[4,5,2,1,6,8,7,3]=>1001011=>1101001
[7,2,8,6,5,1,4,3]=>0011111=>1111100
[7,4,8,6,1,5,3,2]=>0101111=>1111010
[8,7,2,6,1,4,5,3]=>0001111=>1111000
[1,7,8,6,2,4,3,5]=>0010101=>1010100
[7,6,3,1,2,5,4,8]=>0101110=>0111010
[8,5,3,1,2,4,7,6]=>0101011=>1101010
[8,2,1,6,5,3,4,7]=>1001101=>1011001
[3,8,1,5,6,2,4,7]=>0000101=>1010000
[6,8,4,1,5,2,3,7]=>0011001=>1001100
[3,2,8,1,6,4,5,7]=>0100101=>1010010
[5,2,1,3,7,6,4,8]=>1001110=>0111001
[5,4,1,2,8,3,7,6]=>0011011=>1101100
[5,8,4,1,2,3,7,6]=>0010011=>1100100
[7,1,2,5,3,4,6,8]=>0001010=>0101000
[1,6,7,3,2,8,4,5]=>0100011=>1100010
[1,8,6,3,2,7,4,5]=>0100111=>1110010
[1,5,3,7,2,8,4,6]=>0001011=>1101000
[1,4,6,2,8,5,3,7]=>0001101=>1011000
[1,5,6,2,8,4,3,7]=>0010101=>1010100
[2,4,6,3,1,7,5,8]=>0100110=>0110010
[3,4,8,6,5,7,2,1]=>1000111=>1110001
[1,2,5,7,4,3,6,8]=>0010010=>0100100
[1,2,5,7,4,6,8,3]=>0000011=>1100000
[1,2,4,7,6,8,3,5]=>0000011=>1100000
[3,5,8,6,1,7,2,4]=>0000111=>1110000
[2,3,6,8,1,7,4,5]=>0000011=>1100000
[2,3,7,1,8,6,4,5]=>0000111=>1110000
[2,6,1,7,8,5,3,4]=>0001101=>1011000
[2,4,8,5,6,7,1,3]=>0000011=>1100000
[1,4,8,5,6,7,3,2]=>0100011=>1100010
[3,2,1,6,8,4,7,5]=>1100011=>1100011
[4,8,3,1,6,5,7,2]=>0100111=>1110010
[1,6,8,5,4,2,7,3]=>0011011=>1101100
[6,5,8,4,2,1,7,3]=>1010111=>1110101
[1,7,8,6,5,4,2,3]=>0011101=>1011100
[6,8,7,4,5,1,3,2]=>0101011=>1101010
[6,1,3,5,4,2,8,7]=>0011101=>1011100
[2,1,5,8,6,4,7,3]=>1000111=>1110001
[4,2,8,5,6,3,7,1]=>0010111=>1110100
[5,7,2,3,4,6,8,1]=>0000011=>1100000
[1,8,7,3,2,5,6,4]=>0100111=>1110010
[5,7,1,2,3,8,6,4]=>0000111=>1110000
[7,8,6,2,4,1,5,3]=>0011101=>1011100
[7,2,8,4,6,1,5,3]=>0001111=>1111000
[7,4,6,2,8,1,5,3]=>0001111=>1111000
[7,1,5,8,2,3,6,4]=>0000111=>1110000
[7,6,4,8,2,1,5,3]=>1001111=>1111001
[6,1,8,4,2,3,5,7]=>0010101=>1010100
[7,3,6,2,1,8,5,4]=>1001111=>1111001
[1,8,6,4,2,5,7,3]=>0010111=>1110100
[5,6,2,1,8,4,7,3]=>1000111=>1110001
[2,8,1,6,5,7,3,4]=>0000111=>1110000
[5,1,6,4,3,8,7,2]=>0011111=>1111100
[5,4,6,8,1,3,7,2]=>0001011=>1101000
[3,7,1,6,4,5,8,2]=>0000111=>1110000
[3,5,2,1,4,6,7,8]=>1001000=>0001001
[1,3,8,7,5,4,6,2]=>0001111=>1111000
[9,3,4,2,5,6,7,8,1]=>00100011=>11000100
[1,2,3,4,5,7,9,8,6]=>00000011=>11000000
[1,2,3,4,6,7,9,8,5]=>00000011=>11000000
[1,2,3,4,6,8,9,7,5]=>00000101=>10100000
[1,2,3,4,6,9,8,7,5]=>00000111=>11100000
[1,2,3,5,6,7,9,8,4]=>00000011=>11000000
[1,2,3,5,6,8,9,7,4]=>00000101=>10100000
[1,2,3,5,6,9,8,7,4]=>00000111=>11100000
[1,2,3,5,7,9,8,6,4]=>00001011=>11010000
[1,2,3,5,9,8,7,6,4]=>00001111=>11110000
[1,2,4,5,7,8,9,6,3]=>00001001=>10010000
[1,2,4,5,7,9,8,6,3]=>00001011=>11010000
[1,2,4,5,9,8,7,6,3]=>00001111=>11110000
[1,2,4,6,9,8,7,5,3]=>00010111=>11101000
[1,2,4,9,8,7,6,5,3]=>00011111=>11111000
[1,3,5,7,9,8,6,4,2]=>00101011=>11010100
[1,3,5,9,8,7,6,4,2]=>00101111=>11110100
[1,2,3,4,5,6,8,10,9,7]=>000000011=>110000000
[1,2,3,4,5,7,8,10,9,6]=>000000011=>110000000
[1,2,3,4,5,7,9,10,8,6]=>000000101=>101000000
[1,2,3,4,5,7,10,9,8,6]=>000000111=>111000000
[1,2,3,4,6,7,8,10,9,5]=>000000011=>110000000
[1,2,3,4,6,7,9,10,8,5]=>000000101=>101000000
[1,2,3,4,6,7,10,9,8,5]=>000000111=>111000000
[1,2,3,4,6,8,10,9,7,5]=>000001011=>110100000
[1,2,3,4,6,10,9,8,7,5]=>000001111=>111100000
[1,2,3,5,6,7,9,10,8,4]=>000000101=>101000000
[1,2,3,5,6,7,10,9,8,4]=>000000111=>111000000
[1,2,3,5,6,8,9,10,7,4]=>000001001=>100100000
[1,2,3,5,6,8,10,9,7,4]=>000001011=>110100000
[1,2,3,5,6,10,9,8,7,4]=>000001111=>111100000
[1,2,3,5,7,9,10,8,6,4]=>000010101=>101010000
[1,2,3,5,7,10,9,8,6,4]=>000010111=>111010000
[1,2,3,5,10,9,8,7,6,4]=>000011111=>111110000
[1,2,4,5,7,8,10,9,6,3]=>000010011=>110010000
[1,2,4,5,7,9,10,8,6,3]=>000010101=>101010000
[1,2,4,5,7,10,9,8,6,3]=>000010111=>111010000
[1,2,4,5,10,9,8,7,6,3]=>000011111=>111110000
[1,2,4,6,10,9,8,7,5,3]=>000101111=>111101000
[1,2,4,10,9,8,7,6,5,3]=>000111111=>111111000
[1,3,5,7,9,10,8,6,4,2]=>001010101=>101010100
[1,3,5,7,10,9,8,6,4,2]=>001010111=>111010100
[1,3,5,10,9,8,7,6,4,2]=>001011111=>111110100
[1,3,10,9,8,7,6,5,4,2]=>001111111=>111111100
[6,7,3,4,8,5,1,2]=>0001011=>1101000
[7,4,1,8,2,5,6,3]=>0010111=>1110100
[3,1,7,2,5,6,8,4]=>0100011=>1100010
[4,1,5,7,3,2,8,6]=>0110011=>1100110
[6,4,1,7,2,8,5,3]=>0011111=>1111100
[7,3,1,6,2,8,5,4]=>0101111=>1111010
[4,8,2,5,3,1,6,7]=>0101001=>1001010
[5,1,3,4,8,2,6,7]=>0001001=>1001000
[6,1,4,5,7,8,2,3]=>0000101=>1010000
[6,3,4,7,1,8,5,2]=>0001111=>1111000
[7,8,5,1,3,4,6,2]=>0001101=>1011000
[7,1,3,4,5,6,8,2]=>0000011=>1100000
[8,5,2,7,6,3,1,4]=>0101111=>1111010
[1,8,3,5,6,2,7,4]=>0000111=>1110000
[8,3,2,5,6,1,7,4]=>0100111=>1110010
[4,2,5,1,6,8,7,3]=>0011011=>1101100
[5,4,2,7,8,6,1,3]=>0011101=>1011100
[6,8,7,2,1,3,4,5]=>1000011=>1100001
[3,7,6,8,5,2,4,1]=>0011011=>1101100
[1,7,8,5,2,6,3,4]=>0001101=>1011000
[7,6,1,2,5,3,8,4]=>0001111=>1111000
[5,8,7,2,6,3,4,1]=>0010111=>1110100
[7,6,2,4,8,1,5,3]=>0001111=>1111000
[1,5,7,3,8,6,2,4]=>0000111=>1110000
[6,7,5,1,8,2,3,4]=>0001011=>1101000
[7,6,1,2,4,3,8,5]=>0010111=>1110100
[6,7,2,1,5,3,8,4]=>1001011=>1101001
[4,3,2,8,7,1,6,5]=>0110111=>1110110
[4,8,3,2,7,1,6,5]=>0100111=>1110010
[4,8,3,1,7,6,5,2]=>0101111=>1111010
[5,3,8,7,1,6,4,2]=>0011111=>1111100
[5,8,7,3,1,6,4,2]=>0110111=>1110110
[5,3,8,2,1,7,6,4]=>1001111=>1111001
[3,8,7,2,6,5,1,4]=>0001111=>1111000
[7,4,1,8,6,5,3,2]=>0111111=>1111110
[5,4,2,8,1,7,6,3]=>0011111=>1111100
[5,8,4,2,1,7,6,3]=>1010111=>1110101
[5,8,4,7,1,6,3,2]=>0100111=>1110010
[5,4,8,3,1,7,6,2]=>0101111=>1111010
[8,5,6,1,4,7,2,3]=>0000111=>1110000
[6,7,4,1,2,5,8,3]=>0010011=>1100100
[1,6,7,4,2,5,8,3]=>0010011=>1100100
[3,6,7,5,8,1,2,4]=>0000011=>1100000
[1,6,7,5,8,3,2,4]=>0100011=>1100010
[3,8,6,5,7,4,1,2]=>0010111=>1110100
[8,1,6,5,7,4,3,2]=>0110111=>1110110
[5,2,1,6,8,4,7,3]=>1001011=>1101001
[6,5,8,7,4,2,3,1]=>0110111=>1110110
[6,8,5,7,4,2,1,3]=>1010011=>1100101
[3,6,7,5,8,2,1,4]=>1000011=>1100001
[4,7,5,3,8,1,2,6]=>0001011=>1101000
[4,7,5,3,6,1,2,8]=>0001110=>0111000
[4,7,5,3,1,6,2,8]=>0101110=>0111010
[2,7,5,3,6,4,8,1]=>0001111=>1111000
[4,7,5,3,8,1,6,2]=>0001111=>1111000
[2,7,5,8,6,3,4,1]=>0010111=>1110100
[2,7,5,6,8,3,4,1]=>0010011=>1100100
[2,7,5,6,8,3,1,4]=>0100011=>1100010
[4,7,5,3,6,8,1,2]=>0001011=>1101000
[2,7,5,6,3,8,4,1]=>0010111=>1110100
[2,7,5,3,6,8,1,4]=>0001011=>1101000
[8,7,5,3,1,4,6,2]=>0101111=>1111010
[2,7,5,3,1,4,8,6]=>0101011=>1101010
[2,7,5,3,4,8,6,1]=>0001111=>1111000
[5,7,6,2,8,3,1,4]=>0100111=>1110010
[5,1,6,3,2,4,8,7]=>0101101=>1011010
[5,7,6,1,8,3,2,4]=>0100111=>1110010
[3,8,7,2,1,5,4,6]=>1001011=>1101001
[6,1,7,2,8,4,3,5]=>0010111=>1110100
[4,8,5,6,7,3,1,2]=>0100011=>1100010
[3,7,6,2,8,5,1,4]=>0001111=>1111000
[6,1,7,3,8,5,2,4]=>0001111=>1111000
[7,1,8,3,2,5,4,6]=>0101011=>1101010
[2,7,8,3,1,5,4,6]=>0101001=>1001010
[4,8,5,6,7,2,1,3]=>1000011=>1100001
[5,8,6,2,7,4,1,3]=>0010111=>1110100
[2,4,6,7,8,5,1,3]=>0001001=>1001000
[2,4,6,7,8,3,1,5]=>0100001=>1000010
[4,7,6,2,8,5,1,3]=>0001111=>1111000
[5,8,7,3,2,4,1,6]=>0110011=>1100110
[4,6,5,8,7,3,1,2]=>0100111=>1110010
[8,3,1,7,2,6,4,5]=>0100111=>1110010
[4,5,1,2,8,7,3,6]=>0001011=>1101000
[5,6,1,2,8,3,7,4]=>0000111=>1110000
[5,8,7,1,6,2,4,3]=>0010111=>1110100
[8,4,5,1,7,6,2,3]=>0001111=>1111000
[6,3,1,4,8,2,7,5]=>0100111=>1110010
[8,5,6,1,7,2,4,3]=>0010111=>1110100
[7,5,6,1,3,8,4,2]=>0010111=>1110100
[5,7,6,1,3,8,4,2]=>0010111=>1110100
[6,7,1,4,2,8,5,3]=>0011011=>1101100
[2,1,6,4,8,3,7,5]=>1000111=>1110001
[7,4,5,1,3,8,6,2]=>0001111=>1111000
[1,5,7,8,4,2,3,6]=>0010001=>1000100
[1,3,6,4,2,5,7,8]=>0010100=>0010100
[1,4,5,7,8,3,6,2]=>0000101=>1010000
[1,5,7,8,3,6,2,4]=>0000101=>1010000
[1,5,7,8,2,4,3,6]=>0010001=>1000100
[6,8,4,7,3,2,1,5]=>1100011=>1100011
[6,8,5,4,2,7,1,3]=>0011011=>1101100
[1,8,4,6,3,2,7,5]=>0100111=>1110010
[6,4,8,5,3,2,1,7]=>1101101=>1011011
[3,5,6,1,4,2,7,8]=>0010100=>0010100
[1,6,3,8,4,2,7,5]=>0010111=>1110100
[7,1,3,2,4,6,8,5]=>0100011=>1100010
[2,6,5,7,8,3,1,4]=>0100101=>1010010
[4,1,8,2,6,7,5,3]=>0011011=>1101100
[3,6,7,8,2,1,4,5]=>1000001=>1000001
[2,5,7,1,6,3,4,8]=>0000110=>0110000
[4,2,8,3,6,5,1,7]=>0011101=>1011100
[6,3,8,7,2,4,5,1]=>0001111=>1111000
[7,6,1,8,2,4,5,3]=>0001111=>1111000
[2,5,6,3,4,8,1,7]=>0000101=>1010000
[5,2,4,7,8,6,1,3]=>0001101=>1011000
[7,2,1,3,4,8,5,6]=>1000011=>1100001
[2,4,5,7,1,8,6,3]=>0000111=>1110000
[8,1,6,2,3,4,7,5]=>0000111=>1110000
[6,1,4,2,5,7,8,3]=>0010101=>1010100
[6,5,1,2,3,7,8,9,4]=>00011001=>10011000
[1,6,7,2,4,3,5,8]=>0010010=>0100100
[1,8,3,4,5,2,7,6]=>0001011=>1101000
[1,8,3,6,4,7,2,5]=>0000111=>1110000
[1,4,7,2,5,6,3,8]=>0000110=>0110000
[7,3,5,8,2,6,1,4]=>0000111=>1110000
[3,4,8,6,7,2,1,5]=>1000011=>1100001
[3,4,8,2,5,1,7,6]=>0001011=>1101000
[1,7,2,5,8,4,3,6]=>0010011=>1100100
[1,4,6,7,8,3,5,2]=>0001001=>1001000
[4,1,5,3,6,8,7,2]=>0011011=>1101100
[5,8,7,4,6,2,3,1]=>0100111=>1110010
[6,8,7,1,5,3,4,2]=>0011011=>1101100
[2,7,8,4,6,5,1,3]=>0001101=>1011000
[3,7,8,5,4,6,2,1]=>1001101=>1011001
[4,8,7,5,2,6,3,1]=>0101111=>1111010
[2,8,7,4,6,1,5,3]=>0001111=>1111000
[4,8,7,2,5,6,3,1]=>0100111=>1110010
[4,7,8,5,3,6,2,1]=>1001101=>1011001
[6,4,8,1,5,7,3,2]=>0100111=>1110010
[1,6,8,3,5,2,7,4]=>0001011=>1101000
[4,5,8,6,3,7,2,1]=>1000111=>1110001
[2,6,7,8,4,5,1,3]=>0001001=>1001000
[6,1,2,8,4,7,5,3]=>0001111=>1111000
[4,7,1,8,5,6,3,2]=>0100111=>1110010
[5,7,1,8,2,6,4,3]=>0010111=>1110100
[7,2,1,8,6,4,5,3]=>1001111=>1111001
[5,3,8,4,7,6,2,1]=>1001111=>1111001
[2,5,8,1,7,4,6,3]=>0000111=>1110000
[4,5,8,3,7,6,2,1]=>1000111=>1110001
[1,7,2,8,6,4,5,3]=>0001111=>1111000
[3,5,7,8,1,6,2,4]=>0000101=>1010000
[2,4,7,8,5,6,1,3]=>0000101=>1010000
[4,1,7,8,5,6,3,2]=>0110101=>1010110
[3,5,8,6,4,7,2,1]=>1000111=>1110001
[2,4,8,5,7,6,1,3]=>0000111=>1110000
[2,6,3,8,5,1,7,4]=>0001111=>1111000
[4,1,5,8,6,7,3,2]=>0110011=>1100110
[5,3,4,7,6,1,2,8]=>0001110=>0111000
[6,2,1,4,8,3,7,5]=>1000111=>1110001
[2,8,5,4,1,3,7,6]=>0011011=>1101100
[4,2,8,7,1,3,5,6]=>0010011=>1100100
[5,4,6,3,1,7,2,8]=>0101110=>0111010
[4,3,6,5,1,8,2,7]=>0011101=>1011100
[1,5,6,8,7,3,2,4]=>0100011=>1100010
[1,4,8,3,6,5,2,7]=>0001101=>1011000
[1,3,8,6,4,7,2,5]=>0000111=>1110000
[1,2,8,6,4,3,7,5]=>0010111=>1110100
[6,5,1,8,7,3,2,4]=>0101111=>1111010
[4,1,7,6,8,3,2,5]=>0110011=>1100110
[1,8,4,7,6,2,3,5]=>0000111=>1110000
[8,3,2,6,1,7,4,5]=>0100111=>1110010
[1,6,3,7,4,5,2,8]=>0001110=>0111000
[2,6,3,7,4,8,5,1]=>0001111=>1111000
[4,6,1,7,8,2,5,3]=>0001101=>1011000
[7,2,3,8,4,5,6,1]=>0000111=>1110000
[5,2,6,7,8,3,4,1]=>0011001=>1001100
[6,5,8,1,2,7,4,3]=>0010111=>1110100
[6,5,1,8,7,2,4,3]=>0011111=>1111100
[5,8,4,3,7,2,1,6]=>1010011=>1100101
[6,1,2,8,7,3,4,5]=>0000111=>1110000
[7,3,2,8,4,6,1,5]=>0100111=>1110010
[4,5,1,7,6,2,8,3]=>0001111=>1111000
[1,5,2,7,6,3,4,8]=>0001110=>0111000
[7,2,6,8,3,5,4,1]=>0011011=>1101100
[4,8,1,7,6,2,5,3]=>0001111=>1111000
[7,2,8,6,5,3,4,1]=>0011111=>1111100
[4,1,8,7,6,5,2,3]=>0011111=>1111100
[7,6,5,2,8,4,3,1]=>0111111=>1111110
[6,5,1,8,7,4,3,2]=>0111111=>1111110
[7,5,1,8,6,4,3,2]=>0111111=>1111110
[8,5,1,7,6,4,3,2]=>0111111=>1111110
[8,5,3,7,6,1,4,2]=>0011111=>1111100
[3,8,7,6,1,5,4,2]=>0011111=>1111100
[10,9,1,2,3,4,5,6,7,11,8]=>0000000111=>1110000000
[9,1,8,2,3,4,5,6,10,7]=>000000111=>111000000
[9,7,1,2,3,4,5,6,10,8]=>000001011=>110100000
[2,10,1,9,3,4,5,6,7,8]=>000000011=>110000000
[2,10,8,1,3,4,5,6,7,9]=>000000101=>101000000
[2,11,10,1,3,4,5,6,7,8,9]=>0000000011=>1100000000
[8,3,7,5,4,1,6,2]=>0011111=>1111100
[4,5,3,1,8,7,2,6]=>0101011=>1101010
[3,4,8,1,5,2,6,7]=>0001001=>1001000
[8,6,5,7,1,3,2,4]=>0100111=>1110010
[1,5,8,6,2,7,4,3]=>0010111=>1110100
[3,1,8,5,7,2,6,4]=>0100111=>1110010
[6,8,5,3,4,2,1,7]=>1011001=>1001101
[8,5,2,6,4,3,1,7]=>0111101=>1011110
[8,6,4,5,2,1,7,3]=>1001111=>1111001
[8,5,2,6,1,4,7,3]=>0001111=>1111000
[2,7,5,8,1,4,6,3]=>0000111=>1110000
[3,2,6,7,1,8,5,4]=>0101011=>1101010
[3,4,6,7,8,2,1,5]=>1000001=>1000001
[3,2,6,7,8,4,1,5]=>0110001=>1000110
[6,2,7,4,8,5,1,3]=>0001111=>1111000
[6,7,1,3,8,5,4,2]=>0011011=>1101100
[6,7,1,8,5,2,4,3]=>0011011=>1101100
[1,2,6,7,8,5,3,4]=>0001001=>1001000
[1,6,7,4,8,3,2,5]=>0100011=>1100010
[1,4,6,7,8,3,2,5]=>0100001=>1000010
[6,1,2,4,5,3,7,8]=>0001100=>0011000
[8,1,7,3,2,6,4,5]=>0100111=>1110010
[4,1,3,2,5,6,7,8,9]=>01100000=>00000110
[6,1,2,4,5,3,7,8,9]=>00011000=>00011000
[5,4,1,2,3,6,7,8,9]=>00110000=>00001100
[8,1,2,3,5,6,7,4,9]=>00000110=>01100000
[4,1,6,3,5,2,7,8,9]=>00111000=>00011100
[8,1,7,3,2,6,4,5,9]=>01001110=>01110010
[5,7,1,6,2,4,3,8,9]=>00101100=>00110100
[7,3,4,6,1,2,5,8,9]=>00001100=>00110000
[6,1,2,9,4,5,7,8,3]=>00001011=>11010000
[4,1,6,3,8,5,7,2,9]=>00101110=>01110100
[6,8,5,1,7,2,3,4,9]=>00010110=>01101000
[8,3,4,5,7,1,2,6,9]=>00000110=>01100000
[5,7,1,9,2,8,4,6,3]=>00001111=>11110000
[7,9,4,6,1,8,2,3,5]=>00001011=>11010000
[4,1,3,2,5,6,7,8,9,10]=>011000000=>000000110
[6,1,2,4,5,3,7,8,9,10]=>000110000=>000011000
[5,4,1,2,3,6,7,8,9,10]=>001100000=>000001100
[8,1,2,3,5,6,7,4,9,10]=>000001100=>001100000
[4,1,6,3,5,2,7,8,9,10]=>001110000=>000011100
[8,1,7,3,2,6,4,5,9,10]=>010011100=>001110010
[5,7,1,6,2,4,3,8,9,10]=>001011000=>000110100
[7,3,4,6,1,2,5,8,9,10]=>000011000=>000110000
[6,1,2,9,4,5,7,8,3,10]=>000010110=>011010000
[4,1,6,3,8,5,7,2,9,10]=>001011100=>001110100
[6,8,5,1,7,2,3,4,9,10]=>000101100=>001101000
[8,3,4,5,7,1,2,6,9,10]=>000001100=>001100000
[10,1,6,3,9,5,2,8,4,7]=>000110111=>111011000
[5,7,1,9,2,8,4,6,3,10]=>000011110=>011110000
[7,9,4,6,1,8,2,3,5,10]=>000010110=>011010000
[9,3,4,5,6,8,1,2,7,10]=>000000110=>011000000
[4,1,6,3,8,5,10,7,9,2]=>001010111=>111010100
[6,8,10,1,7,2,9,3,5,4]=>000101011=>110101000
[8,10,4,5,7,1,9,2,3,6]=>000001011=>110100000
[10,3,4,5,6,7,9,1,2,8]=>000000011=>110000000
[8,7,2,1,5,4,6,3]=>1001111=>1111001
[2,7,4,8,6,5,3,1]=>0101111=>1111010
[7,6,5,2,4,1,8,3]=>0011111=>1111100
[7,6,4,3,1,5,8,2]=>0110111=>1110110
[6,1,8,7,2,3,5,4]=>0001111=>1111000
[8,6,1,2,7,3,4,5]=>0000111=>1110000
[3,6,8,2,7,1,5,4]=>0001011=>1101000
[2,8,6,1,4,5,7,3]=>0000111=>1110000
[6,8,7,2,5,4,1,3]=>0011011=>1101100
[3,5,7,9,1,2,4,6,8,10]=>000000010=>010000000
[4,1,2,3,5,6,7,8,9,10]=>001000000=>000000100
[5,1,2,3,4,6,7,8,9,10]=>000100000=>000001000
[8,1,2,3,4,5,6,7,9,10]=>000000100=>001000000
[7,1,2,3,4,5,6,8,9,10]=>000001000=>000100000
[6,1,2,3,4,5,7,8,9,10]=>000010000=>000010000
[3,1,2,4,5,6,7,8,9,10,11,12]=>01000000000=>00000000010
[3,2,6,4,8,7,5,1]=>0101111=>1111010
[4,7,2,8,6,5,1,3]=>0001111=>1111000
[4,7,1,8,6,5,3,2]=>0101111=>1111010
[2,7,4,8,3,6,1,5]=>0000111=>1110000
[4,7,3,8,6,1,5,2]=>0001111=>1111000
[4,3,6,8,7,2,5,1]=>0011011=>1101100
[4,3,8,2,5,7,6,1]=>0010111=>1110100
[4,1,2,6,8,7,5,3]=>0011011=>1101100
[3,1,6,4,8,7,2,5]=>0100111=>1110010
[4,1,6,8,7,5,2,3]=>0011011=>1101100
[3,8,1,4,5,7,2,6]=>0000011=>1100000
[3,8,1,4,2,5,7,6]=>0010011=>1100100
[4,1,8,3,5,2,7,6]=>0011011=>1101100
[3,8,1,2,5,4,7,6]=>0001011=>1101000
[4,2,3,6,8,7,1,5]=>0010011=>1100100
[4,2,8,3,5,1,7,6]=>0011011=>1101100
[4,2,8,3,5,7,6,1]=>0010111=>1110100
[3,8,2,4,5,7,6,1]=>0000111=>1110000
[3,8,2,5,1,4,7,6]=>0001011=>1101000
[4,2,8,5,7,1,3,6]=>0010011=>1100100
[3,8,1,5,2,4,7,6]=>0001011=>1101000
[7,5,6,4,1,3,2,8]=>0110110=>0110110
[7,8,6,4,1,3,2,5]=>0110101=>1010110
[7,1,4,2,5,6,3,8]=>0010110=>0110100
[7,3,2,1,4,6,5,8]=>1100110=>0110011
[7,6,1,4,3,2,5,8]=>0110110=>0110110
[7,4,1,3,5,6,2,8]=>0010110=>0110100
[2,7,1,3,5,6,8,4]=>0000011=>1100000
[3,6,2,1,5,8,7,4]=>1000111=>1110001
[2,3,6,1,5,8,7,4]=>0000111=>1110000
[3,4,7,1,5,6,8,2]=>0000011=>1100000
[3,6,7,4,1,2,8,5]=>0010011=>1100100
[4,3,2,7,1,6,8,5]=>0110011=>1100110
[7,3,2,8,1,6,4,5]=>0100111=>1110010
[7,4,8,1,5,6,3,2]=>0100111=>1110010
[2,6,8,1,5,3,7,4]=>0001011=>1101000
[6,8,2,1,5,3,7,4]=>1001011=>1101001
[4,8,2,5,3,6,7,1]=>0001011=>1101000
[4,5,8,2,3,6,7,1]=>0000011=>1100000
[2,4,8,5,3,6,7,1]=>0001011=>1101000
[5,3,2,6,4,8,7,1]=>0101111=>1111010
[2,4,5,3,8,6,7,1]=>0001011=>1101000
[4,3,5,2,8,6,7,1]=>0011011=>1101100
[4,8,5,3,2,6,7,1]=>0101011=>1101010
[3,5,4,2,8,6,7,1]=>0011011=>1101100
[4,1,2,7,5,6,8,3]=>0010011=>1100100
[5,6,7,4,2,8,3,1]=>0110011=>1100110
[2,5,7,4,6,8,3,1]=>0100011=>1100010
[7,5,2,4,3,8,6,1]=>0011111=>1111100
[6,8,1,2,5,4,7,3]=>0001011=>1101000
[6,4,1,8,5,2,7,3]=>0011111=>1111100
[2,6,1,8,5,4,7,3]=>0001111=>1111000
[7,1,2,8,5,6,4,3]=>0010111=>1110100
[4,3,2,6,8,5,7,1]=>0110011=>1100110
[3,7,6,4,8,5,2,1]=>1001111=>1111001
[3,1,6,8,5,4,7,2]=>0101011=>1101010
[2,3,5,8,4,6,7,1]=>0000011=>1100000
[3,5,2,8,4,6,7,1]=>0001011=>1101000
[3,4,5,8,2,6,7,1]=>0000011=>1100000
[5,4,2,8,3,6,7,1]=>0011011=>1101100
[5,3,4,8,2,6,7,1]=>0001011=>1101000
[2,5,4,8,3,6,7,1]=>0001011=>1101000
[6,3,2,5,8,4,7,1]=>0100111=>1110010
[6,1,8,3,5,4,7,2]=>0001111=>1111000
[5,4,8,3,2,6,7,1]=>0101011=>1101010
[5,8,2,3,4,6,7,1]=>0000011=>1100000
[6,2,1,7,8,5,4,3]=>1011101=>1011101
[3,4,5,2,7,1,6,8]=>0001010=>0101000
[7,5,6,1,2,3,8,4]=>0000111=>1110000
[1,5,7,6,3,2,8,4]=>0100111=>1110010
[8,4,6,7,3,2,5,1]=>0101011=>1101010
[8,4,6,2,3,1,5,7]=>0100101=>1010010
[7,5,2,1,4,3,8,6]=>1011011=>1101101
[3,1,7,8,5,4,2,6]=>0111001=>1001110
[3,4,5,2,1,8,6,7]=>1001001=>1001001
[7,6,4,8,3,1,2,5]=>0100111=>1110010
[7,4,8,5,6,1,2,3]=>0000111=>1110000
[6,2,8,5,1,3,4,7]=>0001101=>1011000
[3,2,7,8,6,1,4,5]=>0100101=>1010010
[6,8,2,5,1,3,7,4]=>0001011=>1101000
[6,7,4,2,1,5,3,8]=>1011010=>0101101
[5,7,4,1,3,6,2,8]=>0010110=>0110100
[4,2,7,5,1,8,3,6]=>0011011=>1101100
[4,1,6,5,3,8,2,7]=>0011101=>1011100
[1,5,4,6,3,8,2,7]=>0001101=>1011000
[1,8,6,4,7,3,2,5]=>0100111=>1110010
[4,7,1,8,6,3,5,2]=>0001111=>1111000
[5,4,8,1,7,3,6,2]=>0001111=>1111000
[4,3,8,6,2,1,7,5]=>1010111=>1110101
[8,3,6,2,4,1,7,5]=>0010111=>1110100
[7,8,3,2,4,6,5,1]=>0101101=>1011010
[7,2,8,5,3,1,6,4]=>0101111=>1111010
[2,5,4,8,7,3,6,1]=>0001111=>1111000
[6,4,2,8,7,3,1,5]=>0110111=>1110110
[3,6,8,1,7,4,2,5]=>0010011=>1100100
[7,8,6,3,1,4,5,2]=>0101101=>1011010
[3,8,6,1,7,5,2,4]=>0001111=>1111000
[2,7,5,4,8,3,1,6]=>0101011=>1101010
[6,8,7,5,2,1,3,4]=>1001011=>1101001
[7,6,2,8,5,1,3,4]=>0001111=>1111000
[1,5,7,6,2,8,4,3]=>0010111=>1110100
[1,6,5,2,7,8,4,3]=>0011101=>1011100
[4,7,8,5,6,2,3,1]=>0100101=>1010010
[2,7,8,5,6,1,4,3]=>0010101=>1010100
[6,7,8,4,2,1,5,3]=>1011001=>1001101
[4,7,8,1,2,5,6,3]=>0000101=>1010000
[8,6,4,1,2,5,7,3]=>0010111=>1110100
[6,1,4,7,2,5,8,3]=>0000111=>1110000
[6,7,8,3,5,4,2,1]=>1011001=>1001101
[6,7,8,2,1,5,3,4]=>1001001=>1001001
[5,6,3,2,7,4,1,8]=>0110110=>0110110
[2,6,4,3,7,5,8,1]=>0010111=>1110100
[7,2,3,6,1,8,4,5]=>0000111=>1110000
[3,4,6,5,7,1,2,8]=>0000110=>0110000
[7,6,2,3,5,4,8,1]=>0001111=>1111000
[8,5,2,4,3,6,1,7]=>0011101=>1011100
[8,5,7,2,4,1,6,3]=>0010111=>1110100
[2,6,7,5,8,1,4,3]=>0010011=>1100100
[7,4,8,2,1,5,6,3]=>1000111=>1110001
[2,3,6,7,8,5,1,4]=>0001001=>1001000
[8,3,7,1,6,4,2,5]=>0010111=>1110100
[8,2,1,7,6,5,3,4]=>1001111=>1111001
[5,7,4,1,6,8,2,3]=>0010011=>1100100
[6,5,1,2,8,3,4,7]=>0001101=>1011000
[5,6,8,1,3,7,2,4]=>0000011=>1100000
[3,7,4,8,6,1,2,5]=>0000111=>1110000
[1,6,8,5,3,2,4,7]=>0101001=>1001010
[5,8,1,6,7,4,2,3]=>0010011=>1100100
[7,2,8,4,6,1,3,5]=>0000111=>1110000
[6,2,7,4,3,8,1,5]=>0010111=>1110100
[1,7,8,4,6,2,3,5]=>0000101=>1010000
[7,1,8,4,6,2,3,5]=>0000111=>1110000
[8,1,6,5,4,7,2,3]=>0001111=>1111000
[4,1,6,8,7,3,2,5]=>0110011=>1100110
[5,1,4,6,7,3,8,2]=>0001011=>1101000
[7,1,3,4,6,2,8,5]=>0000111=>1110000
[3,4,1,6,2,5,8,7,9]=>00101010=>01010100
[3,4,1,2,6,5,8,7,9]=>00101010=>01010100
[2,4,1,6,3,5,8,7,10,9,11]=>0010101010=>0101010100
[3,4,1,6,2,5,8,7,10,9]=>001010101=>101010100
[3,5,1,6,2,4,8,7,9]=>00011010=>01011000
[2,5,1,6,3,4,8,7,9]=>00011010=>01011000
[3,5,1,2,6,4,8,7,9]=>00011010=>01011000
[2,5,1,3,6,4,8,7,9]=>00011010=>01011000
[8,7,1,4,6,3,2,5]=>0100111=>1110010
[6,5,2,8,4,7,1,3]=>0001111=>1111000
[1,4,7,5,8,6,3,2]=>0100111=>1110010
[6,1,8,3,4,7,2,5]=>0000111=>1110000
[1,8,6,3,5,2,7,4]=>0001111=>1111000
[7,8,1,3,5,4,2,6]=>0011001=>1001100
[4,7,1,6,8,3,5,2]=>0001011=>1101000
[3,6,5,2,8,4,1,7]=>0011101=>1011100
[8,2,5,6,3,1,7,4]=>0100111=>1110010
[7,1,8,4,2,5,3,6]=>0011011=>1101100
[1,4,8,7,5,2,6,3]=>0001111=>1111000
[1,5,6,4,2,3,7,8]=>0010100=>0010100
[5,7,3,6,8,4,2,1]=>1010011=>1100101
[5,8,7,4,2,1,3,6]=>1010011=>1100101
[3,1,5,2,7,8,6,4]=>0101101=>1011010
[1,8,7,3,2,5,4,6]=>0101011=>1101010
[1,2,5,4,8,7,3,6]=>0001011=>1101000
[1,2,4,8,6,3,5,7]=>0000101=>1010000
[1,5,2,4,7,3,8,6]=>0001011=>1101000
[8,6,3,5,7,4,1,2]=>0010111=>1110100
[8,5,3,2,1,4,7,6]=>1101011=>1101011
[1,2,7,6,8,4,3,5]=>0010011=>1100100
[1,6,3,2,5,7,8,4]=>0100101=>1010010
[1,7,3,4,2,6,8,5]=>0010011=>1100100
[1,6,3,5,8,4,2,7]=>0010101=>1010100
[1,5,6,3,2,8,4,7]=>0100101=>1010010
[1,2,5,8,4,6,3,7]=>0000101=>1010000
[1,5,3,2,7,8,4,6]=>0101001=>1001010
[4,1,8,6,2,3,7,5]=>0010111=>1110100
[7,5,8,6,2,3,4,1]=>0010111=>1110100
[1,7,6,4,3,8,5,2]=>0011111=>1111100
[1,8,5,7,6,3,2,4]=>0100111=>1110010
[1,4,7,3,6,8,5,2]=>0001011=>1101000
[1,6,3,5,7,8,4,2]=>0010101=>1010100
[1,5,6,3,2,7,8,4]=>0100101=>1010010
[1,2,7,6,8,4,5,3]=>0001011=>1101000
[1,8,4,7,5,3,2,6]=>0101011=>1101010
[6,8,5,2,1,7,4,3]=>1011011=>1101101
[1,2,6,8,4,3,7,5]=>0010011=>1100100
[5,3,7,2,6,4,1,8]=>0011110=>0111100
[5,3,8,2,6,1,7,4]=>0001111=>1111000
[7,6,2,5,3,4,1,8]=>0011110=>0111100
[7,6,2,4,5,3,1,8]=>0101110=>0111010
[7,6,2,4,3,5,1,8]=>0011110=>0111100
[7,6,2,3,5,4,1,8]=>0011110=>0111100
[8,4,2,7,1,6,3,5]=>0010111=>1110100
[8,7,6,1,5,3,2,4]=>0101111=>1111010
[8,7,6,1,4,3,5,2]=>0011111=>1111100
[8,7,6,1,3,5,4,2]=>0011111=>1111100
[8,7,6,1,5,4,2,3]=>0011111=>1111100
[8,6,2,7,1,5,3,4]=>0001111=>1111000
[5,3,7,2,8,1,6,4]=>0001111=>1111000
[8,3,5,4,2,1,6,7]=>1011001=>1001101
[7,8,4,3,1,5,2,6]=>0111001=>1001110
[8,6,3,7,1,5,2,4]=>0001111=>1111000
[8,7,6,1,2,5,3,4]=>0001111=>1111000
[8,7,6,1,2,5,4,3]=>0011111=>1111100
[8,7,6,1,4,2,5,3]=>0011111=>1111100
[4,7,5,8,6,1,3,2]=>0100111=>1110010
[6,5,7,3,8,4,1,2]=>0010111=>1110100
[8,7,5,4,1,2,6,3]=>0011111=>1111100
[8,6,7,1,5,3,2,4]=>0101011=>1101010
[7,5,6,1,3,4,2,8]=>0010110=>0110100
[5,7,8,1,3,4,2,6]=>0010001=>1000100
[7,8,5,1,3,4,2,6]=>0011001=>1001100
[5,7,8,3,4,6,1,2]=>0000101=>1010000
[7,5,1,3,4,2,6,8]=>0011010=>0101100
[5,7,1,3,4,2,8,6]=>0010011=>1100100
[7,3,5,6,4,8,1,2]=>0000111=>1110000
[1,7,3,8,2,5,6,4]=>0000111=>1110000
[1,5,3,7,8,4,6,2]=>0001101=>1011000
[1,5,7,3,8,2,6,4]=>0000111=>1110000
[7,1,5,3,6,2,4,8]=>0001110=>0111000
[1,7,3,5,8,4,2,6]=>0010011=>1100100
[1,3,7,5,8,6,2,4]=>0000111=>1110000
[1,7,8,5,3,6,2,4]=>0001101=>1011000
[1,7,5,8,3,4,2,6]=>0010011=>1100100
[7,1,5,6,3,4,2,8]=>0010110=>0110100
[7,3,5,6,4,1,2,8]=>0010110=>0110100
[3,7,5,8,4,1,2,6]=>0010011=>1100100
[7,5,6,8,1,3,4,2]=>0010011=>1100100
[5,3,4,7,8,1,2,6]=>0001001=>1001000
[5,3,7,6,8,1,2,4]=>0001011=>1101000
[3,7,1,2,5,8,4,6]=>0000011=>1100000
[3,1,2,7,5,8,4,6]=>0100011=>1100010
[3,1,2,5,7,8,6,4]=>0100101=>1010010
[7,3,1,5,4,6,2,8]=>0101110=>0111010
[7,3,5,1,2,6,4,8]=>0001110=>0111000
[3,7,1,2,8,5,6,4]=>0000111=>1110000
[5,3,1,7,4,6,8,2]=>0101011=>1101010
[5,3,7,1,2,6,8,4]=>0001011=>1101000
[7,4,8,3,5,6,1,2]=>0000111=>1110000
[2,4,7,3,5,6,1,8]=>0000110=>0110000
[5,7,6,4,2,3,1,8]=>0110110=>0110110
[7,4,8,2,5,6,1,3]=>0000111=>1110000
[5,8,2,4,6,1,3,7]=>0000101=>1010000
[6,1,4,8,5,2,7,3]=>0001111=>1111000
[3,4,5,8,1,6,7,2]=>0000011=>1100000
[6,8,7,4,2,1,5,3]=>1011011=>1101101
[5,6,8,4,7,3,1,2]=>0100011=>1100010
[3,1,6,8,5,2,7,4]=>0101011=>1101010
[2,3,8,1,5,6,4,7]=>0000101=>1010000
[5,4,8,1,2,6,7,3]=>0001011=>1101000
[5,1,8,2,4,6,7,3]=>0001011=>1101000
[4,1,8,2,3,6,7,5]=>0010011=>1100100
[5,2,3,8,1,7,4,6]=>0001011=>1101000
[2,3,5,7,1,6,4,8]=>0000110=>0110000
[1,5,3,8,2,4,6,7]=>0001001=>1001000
[8,6,2,7,5,1,4,3]=>0011111=>1111100
[2,7,1,8,6,3,5,4]=>0001111=>1111000
[5,7,6,1,3,2,8,4]=>0100111=>1110010
[3,5,4,6,1,7,8,2]=>0001101=>1011000
[8,1,5,4,6,3,7,2]=>0001111=>1111000
[2,7,1,5,6,4,3,8]=>0010110=>0110100
[8,4,6,3,1,7,2,5]=>0100111=>1110010
[8,4,2,5,6,3,7,1]=>0010111=>1110100
[8,6,2,7,5,4,3,1]=>0111111=>1111110
[5,4,7,2,8,6,1,3]=>0001111=>1111000
[3,5,6,4,1,7,2,8]=>0010110=>0110100
[2,5,6,1,7,4,3,8]=>0010110=>0110100
[2,7,1,8,6,5,4,3]=>0011111=>1111100
[3,7,6,1,8,5,4,2]=>0011111=>1111100
[8,6,4,2,1,3,5,7,9]=>10101010=>01010101
[8,6,2,1,4,3,5,7,9]=>10101010=>01010101
[8,4,2,1,6,3,5,7,9]=>10101010=>01010101
[6,4,2,1,8,3,5,7,9]=>10101010=>01010101
[8,6,4,2,9,1,3,5,7]=>00101011=>11010100
[9,6,4,2,7,1,3,5,8]=>00101101=>10110100
[9,7,4,2,5,1,3,6,8]=>00110101=>10101100
[9,7,5,2,3,1,4,6,8]=>01010101=>10101010
[9,7,5,3,1,2,4,6,8]=>01010101=>10101010
[10,8,6,4,2,1,3,5,7,9]=>101010101=>101010101
[10,8,6,2,1,4,3,5,7,9]=>101010101=>101010101
[8,2,1,4,3,6,5,7,9]=>10101010=>01010101
[10,8,4,2,1,6,3,5,7,9]=>101010101=>101010101
[4,2,1,6,3,5,8,7,9]=>10101010=>01010101
[10,6,4,2,1,8,3,5,7,9]=>101010101=>101010101
[6,4,2,1,8,3,5,9,7]=>10101011=>11010101
[8,6,4,2,1,10,3,5,7,9]=>101010101=>101010101
[6,4,2,7,1,3,5,8,9]=>00101100=>00110100
[8,6,4,2,9,1,3,5,7,10]=>001010110=>011010100
[6,2,8,3,1,4,5,7]=>0100101=>1010010
[8,9,4,2,5,1,3,6,7]=>00110001=>10001100
[9,6,4,2,7,1,3,5,8,10]=>001011010=>010110100
[2,7,8,3,1,4,5,6]=>0100001=>1000010
[9,6,7,2,3,1,4,5,8]=>01000101=>10100010
[9,7,4,2,5,1,3,6,8,10]=>001101010=>010101100
[9,7,4,5,1,2,3,6,8]=>00010101=>10101000
[9,7,5,2,3,1,4,6,8,10]=>010101010=>010101010
[9,7,5,3,1,2,4,6,8,10]=>010101010=>010101010
[1,5,3,2,8,6,7,4]=>0101011=>1101010
[1,8,5,3,2,6,7,4]=>0101011=>1101010
[1,7,8,5,6,3,2,4]=>0100101=>1010010
[1,5,6,7,3,2,8,4]=>0100011=>1100010
[1,7,5,2,3,4,8,6]=>0001011=>1101000
[1,7,5,2,4,8,6,3]=>0001111=>1111000
[1,6,7,8,3,2,4,5]=>0100001=>1000010
[1,4,8,6,2,3,5,7]=>0000101=>1010000
[1,8,4,5,6,7,2,3]=>0000011=>1100000
[1,2,8,6,3,4,5,7]=>0000101=>1010000
[1,2,8,6,3,5,7,4]=>0000111=>1110000
[1,2,7,8,4,3,5,6]=>0010001=>1000100
[1,8,6,7,4,2,3,5]=>0010011=>1100100
[1,6,7,8,4,2,3,5]=>0010001=>1000100
[1,6,7,8,3,4,2,5]=>0010001=>1000100
[1,7,8,4,2,3,5,6]=>0010001=>1000100
[1,7,3,5,6,2,8,4]=>0000111=>1110000
[1,7,8,3,4,2,5,6]=>0010001=>1000100
[1,2,3,7,8,5,4,6]=>0001001=>1001000
[1,2,7,4,6,3,8,5]=>0000111=>1110000
[1,7,4,5,2,3,8,6]=>0001011=>1101000
[1,7,8,4,5,2,3,6]=>0001001=>1001000
[1,7,8,3,4,5,2,6]=>0001001=>1001000
[1,2,8,4,5,6,3,7]=>0000101=>1010000
[1,8,4,5,6,2,3,7]=>0000101=>1010000
[5,8,2,7,3,4,1,6]=>0010011=>1100100
[6,8,7,2,3,4,1,5]=>0010011=>1100100
[3,8,7,5,2,6,1,4]=>0001111=>1111000
[4,8,7,3,2,5,1,6]=>0101011=>1101010
[5,3,8,1,6,7,4,2]=>0011011=>1101100
[5,8,2,1,3,7,6,4]=>1000111=>1110001
[5,1,8,2,6,4,7,3]=>0001111=>1111000
[5,1,8,3,6,7,4,2]=>0011011=>1101100
[3,1,8,4,6,2,7,5]=>0100111=>1110010
[8,4,1,6,5,2,3,7]=>0011101=>1011100
[1,8,7,6,4,3,5,2]=>0011111=>1111100
[6,1,8,7,5,3,4,2]=>0011111=>1111100
[6,8,7,3,2,4,1,5]=>0110011=>1100110
[2,3,7,5,6,8,4,1]=>0010011=>1100100
[3,2,4,7,5,8,1,6]=>0100011=>1100010
[2,8,7,6,4,5,1,3]=>0001111=>1111000
[4,8,7,6,3,1,5,2]=>0101111=>1111010
[3,5,2,4,7,6,8,1]=>0001011=>1101000
[5,3,2,6,4,7,8,1]=>0101101=>1011010
[5,3,2,6,7,4,8,1]=>0101011=>1101010
[5,3,2,7,6,4,8,1]=>0101111=>1111010
[7,3,5,2,8,4,6,1]=>0001111=>1111000
[3,5,2,7,4,6,8,1]=>0001011=>1101000
[3,2,5,7,4,6,8,1]=>0100011=>1100010
[3,2,7,5,4,8,6,1]=>0101111=>1111010
[3,7,5,2,4,8,6,1]=>0001111=>1111000
[2,3,7,5,4,8,6,1]=>0001111=>1111000
[8,3,5,1,6,4,7,2]=>0001111=>1111000
[8,4,5,6,1,3,7,2]=>0000111=>1110000
[3,4,7,6,8,2,5,1]=>0001011=>1101000
[5,2,8,4,1,3,6,7]=>0011001=>1001100
[3,8,5,2,1,4,6,7]=>1001001=>1001001
[7,6,4,1,8,2,5,3]=>0011111=>1111100
[7,5,4,2,1,6,3,8]=>1011110=>0111101
[8,1,6,7,3,4,2,5]=>0010011=>1100100
[8,2,1,6,7,4,3,5]=>1010011=>1100101
[5,2,8,6,3,7,1,4]=>0001111=>1111000
[7,6,8,1,2,5,4,3]=>0011011=>1101100
[1,2,9,3,4,5,6,8,7]=>00000011=>11000000
[1,2,3,8,4,5,9,6,7]=>00000011=>11000000
[1,2,3,4,9,5,6,8,7]=>00000011=>11000000
[2,1,3,4,8,5,7,6]=>1000011=>1100001
[1,2,3,4,5,9,6,8,7]=>00000011=>11000000
[7,1,2,3,4,8,5,9,6]=>00000111=>11100000
[6,9,1,2,3,4,8,5,7]=>00000011=>11000000
[1,2,10,3,4,5,6,7,9,8]=>000000011=>110000000
[5,1,9,2,3,4,8,6,7]=>00010011=>11001000
[1,2,3,9,4,5,6,10,7,8]=>000000011=>110000000
[4,1,2,3,5,8,6,9,7]=>00100011=>11000100
[1,2,3,4,10,5,6,7,9,8]=>000000011=>110000000
[3,1,2,4,9,5,8,6,7]=>01000011=>11000010
[1,2,3,4,5,10,6,7,9,8]=>000000011=>110000000
[2,1,3,4,5,9,6,8,7]=>10000011=>11000001
[1,2,3,4,5,6,9,10,7,8]=>000000001=>100000000
[10,1,2,3,4,5,6,7,11,8,9]=>0000000011=>1100000000
[8,1,2,3,4,5,9,6,10,7]=>000000111=>111000000
[1,11,2,3,4,5,6,7,8,10,9]=>0000000011=>1100000000
[1,7,2,3,4,5,9,8,6]=>00000111=>11100000
[7,10,1,2,3,4,5,9,6,8]=>000000011=>110000000
[1,2,11,3,4,5,6,7,8,10,9]=>0000000011=>1100000000
[1,6,2,3,4,5,9,8,7]=>00001011=>11010000
[6,1,2,3,7,4,8,9,5]=>00001101=>10110000
[6,1,10,2,3,4,5,9,7,8]=>000010011=>110010000
[1,2,3,10,4,5,6,7,11,8,9]=>0000000011=>1100000000
[5,7,1,2,6,8,3,4]=>0000011=>1100000
[1,2,3,8,5,4,6,9,7]=>00010011=>11001000
[5,9,1,2,6,3,4,8,7]=>00001011=>11010000
[5,1,2,3,4,6,9,7,10,8]=>000100011=>110001000
[1,2,3,4,11,5,6,7,8,10,9]=>0000000011=>1100000000
[1,4,2,3,5,6,9,8,7]=>00100011=>11000100
[1,5,2,3,6,8,7,4]=>0001011=>1101000
[4,1,9,5,2,3,6,8,7]=>00110011=>11001100
[4,1,2,3,10,5,6,9,7,8]=>001000011=>110000100
[1,2,3,4,5,11,6,7,8,10,9]=>0000000011=>1100000000
[1,3,2,4,5,6,9,8,7]=>01000011=>11000010
[3,4,1,2,5,6,8,9,7]=>00100001=>10000100
[3,1,2,4,5,10,6,9,7,8]=>010000011=>110000010
[1,2,3,4,5,6,10,7,11,8,9]=>0000000011=>1100000000
[2,3,1,4,9,5,6,8,7]=>01000011=>11000010
[1,2,3,4,5,6,7,11,8,10,9]=>0000000011=>1100000000
[1,2,3,4,5,6,7,8,11,10,9]=>0000000011=>1100000000
[3,5,7,4,1,8,2,6]=>0010011=>1100100
[8,6,4,7,5,1,2,3]=>0001111=>1111000
[8,6,4,1,2,5,3,7]=>0011101=>1011100
[2,8,4,3,1,6,5,7]=>0110101=>1010110
[3,8,4,6,1,5,2,7]=>0001101=>1011000
[8,3,5,6,1,4,7,2]=>0000111=>1110000
[6,8,7,3,5,4,2,1]=>1011011=>1101101
[3,1,2,8,5,7,4,6]=>0100011=>1100010
[8,1,2,3,4,6,9,5,7]=>00000011=>11000000
[8,1,2,4,6,9,3,5,7]=>00000011=>11000000
[6,1,2,3,4,5,9,8,7]=>00001011=>11010000
[5,1,2,3,4,8,6,9,7]=>00010011=>11001000
[4,1,2,3,9,6,8,5,7]=>00100011=>11000100
[9,1,2,3,4,5,7,10,6,8]=>000000011=>110000000
[7,3,1,2,5,8,4,6]=>0100011=>1100010
[3,1,2,8,4,6,9,5,7]=>01000011=>11000010
[8,3,5,7,2,1,4,6]=>1000011=>1100001
[2,1,3,8,5,7,4,6]=>1000011=>1100001
[2,1,9,4,6,8,3,5,7]=>10000011=>11000001
[9,1,2,3,5,7,10,4,6,8]=>000000011=>110000000
[1,8,2,4,6,9,3,5,7]=>00000011=>11000000
[9,1,3,5,7,10,2,4,6,8]=>000000011=>110000000
[7,3,1,2,8,4,5,6]=>0100011=>1100010
[2,1,4,7,6,3,5,8]=>1000110=>0110001
[7,2,4,5,3,8,1,6]=>0001011=>1101000
[8,4,2,5,6,7,3,1]=>0110011=>1100110
[5,4,1,6,3,7,8,2]=>0011101=>1011100
[4,5,1,3,6,7,8,2]=>0001001=>1001000
[5,1,7,6,3,4,8,2]=>0001111=>1111000
[6,1,7,5,4,8,2,3]=>0001111=>1111000
[3,7,2,1,6,8,4,5]=>1000011=>1100001
[1,5,8,2,4,7,6,3]=>0000111=>1110000
[5,8,1,6,4,7,3,2]=>0100111=>1110010
[3,8,6,5,7,2,4,1]=>0010111=>1110100
[6,8,1,4,7,3,5,2]=>0001011=>1101000
[1,6,8,2,7,4,5,3]=>0001011=>1101000
[5,7,2,1,8,4,3,6]=>1010011=>1100101
[5,7,1,6,8,3,2,4]=>0100011=>1100010
[5,6,2,1,8,3,4,7]=>1000101=>1010001
[6,4,1,7,3,8,2,5]=>0010111=>1110100
[8,2,5,6,7,1,4,3]=>0010011=>1100100
[7,2,4,6,8,3,1,5]=>0100011=>1100010
[6,2,4,7,8,1,3,5]=>0000101=>1010000
[6,1,4,3,2,8,5,7]=>0110101=>1010110
[2,7,4,8,6,1,5,3]=>0001111=>1111000
[2,4,8,6,5,7,3,1]=>0100111=>1110010
[3,7,8,6,4,2,5,1]=>0011101=>1011100
[6,2,8,4,7,5,1,3]=>0001111=>1111000
[4,5,7,3,6,8,1,2]=>0000011=>1100000
[3,4,7,8,6,5,1,2]=>0001101=>1011000
[1,4,7,2,6,8,5,3]=>0001011=>1101000
[2,3,7,6,5,1,4,8]=>0001110=>0111000
[3,2,7,6,4,1,5,8]=>0110110=>0110110
[6,2,3,5,7,1,4,8]=>0000110=>0110000
[7,8,1,2,5,6,4,3]=>0010101=>1010100
[7,1,3,6,8,5,2,4]=>0001011=>1101000
[4,2,8,5,1,6,3,7]=>0011101=>1011100
[6,5,8,1,4,2,3,7]=>0010101=>1010100
[3,8,2,4,5,1,6,7]=>0001001=>1001000
[3,6,2,4,1,5,7,8]=>0010100=>0010100
[2,3,8,4,1,6,5,7]=>0010101=>1010100
[4,5,7,3,1,6,2,8]=>0100110=>0110010
[2,3,1,4,8,5,7,6]=>0100011=>1100010
[4,2,6,1,5,8,7,3]=>0010111=>1110100
[7,5,1,8,4,3,6,2]=>0011111=>1111100
[3,1,8,5,7,6,4,2]=>0110111=>1110110
[5,1,8,7,4,6,3,2]=>0101111=>1111010
[2,4,8,7,5,1,3,6]=>0001011=>1101000
[3,5,7,6,1,8,4,2]=>0010111=>1110100
[3,5,7,6,2,8,4,1]=>0010111=>1110100
[1,5,3,2,8,7,6,4]=>0101111=>1111010
[6,1,4,3,8,7,5,2]=>0011111=>1111100
[6,3,1,8,7,4,2,5]=>0110111=>1110110
[5,3,6,2,8,7,4,1]=>0011111=>1111100
[6,3,5,2,1,8,7,4]=>1001111=>1111001
[2,8,4,1,3,7,6,5]=>0010111=>1110100
[3,8,1,4,7,6,5,2]=>0001111=>1111000
[6,2,3,8,7,5,4,1]=>0011111=>1111100
[4,1,3,5,8,7,6,2]=>0010111=>1110100
[3,4,7,5,8,1,2,6]=>0000011=>1100000
[2,7,8,3,4,1,5,6]=>0010001=>1000100
[2,8,6,7,5,4,3,1]=>0111011=>1101110
[7,2,6,8,1,4,3,5]=>0010011=>1100100
[5,3,6,2,8,4,7,1]=>0001111=>1111000
[8,1,6,3,7,4,5,2]=>0001111=>1111000
[2,4,3,7,1,8,6,5]=>0010111=>1110100
[2,6,5,7,3,8,4,1]=>0010111=>1110100
[6,8,2,7,4,1,5,3]=>0011011=>1101100
[6,1,7,8,5,3,2,4]=>0101101=>1011010
[2,6,5,4,7,1,8,3]=>0001111=>1111000
[5,8,3,4,6,1,7,2]=>0000111=>1110000
[6,1,7,4,2,5,8,3]=>0010111=>1110100
[6,8,7,1,5,4,2,3]=>0011011=>1101100
[4,8,3,1,5,7,6,2]=>0100111=>1110010
[5,3,8,2,7,1,6,4]=>0001111=>1111000
[8,3,4,5,2,7,1,6]=>0001011=>1101000
[8,2,6,7,1,5,3,4]=>0001011=>1101000
[7,1,5,2,6,3,4,8]=>0001110=>0111000
[3,7,1,5,2,6,8,4]=>0001011=>1101000
[6,7,1,8,3,4,5,2]=>0001011=>1101000
[3,7,1,6,8,4,5,2]=>0001011=>1101000
[3,8,5,2,6,7,1,4]=>0001011=>1101000
[3,6,5,2,7,1,4,8]=>0001110=>0111000
[6,8,3,4,7,1,5,2]=>0001011=>1101000
[3,7,1,6,5,2,8,4]=>0001111=>1111000
[8,3,5,2,7,1,6,4]=>0001111=>1111000
[7,1,8,4,6,3,5,2]=>0001111=>1111000
[3,8,6,4,7,1,5,2]=>0001111=>1111000
[3,7,1,4,8,6,5,2]=>0001111=>1111000
[3,7,1,4,5,2,8,6]=>0001011=>1101000
[2,3,7,6,5,8,1,4]=>0000111=>1110000
[4,3,5,6,7,8,9,1,2]=>00100001=>10000100
[6,7,8,5,4,3,2,1,9]=>11110010=>01001111
[6,5,7,8,4,3,2,1,9]=>11101010=>01010111
[6,5,4,7,8,3,2,1,9]=>11011010=>01011011
[6,5,4,3,7,8,2,1,9]=>10111010=>01011101
[6,5,4,3,2,7,8,1,9]=>01111010=>01011110
[7,8,9,5,4,3,2,1,6]=>11110001=>10001111
[7,8,9,6,5,4,3,2,1,10]=>111110010=>010011111
[6,7,8,9,4,3,2,1,5]=>11100001=>10000111
[7,6,8,9,5,4,3,2,1,10]=>111101010=>010101111
[6,5,7,8,9,3,2,1,4]=>11001001=>10010011
[7,6,5,8,9,4,3,2,1,10]=>111011010=>010110111
[6,5,4,7,8,9,2,1,3]=>10011001=>10011001
[7,6,5,4,8,9,3,2,1,10]=>110111010=>010111011
[6,5,4,3,7,8,9,1,2]=>00111001=>10011100
[7,6,5,4,3,8,9,2,1,10]=>101111010=>010111101
[6,5,4,3,2,7,8,9,1]=>01111001=>10011110
[7,6,5,4,3,2,8,9,1,10]=>011111010=>010111110
[2,1,4,3,6,5,8,7,11,12,9,10]=>10101010001=>10001010101
[2,1,4,3,6,5,9,10,7,8,12,11]=>10101000101=>10100010101
[2,1,4,3,6,5,10,11,12,7,8,9]=>10101000001=>10000010101
[2,1,4,3,7,8,5,6,10,9,12,11]=>10100010101=>10101000101
[2,1,4,3,7,8,5,6,11,12,9,10]=>10100010001=>10001000101
[2,1,4,3,7,10,5,11,12,6,8,9]=>10100000101=>10100000101
[2,1,4,3,8,9,10,5,6,7,12,11]=>10100000101=>10100000101
[2,1,4,3,9,10,11,12,5,6,7,8]=>10100000001=>10000000101
[2,1,5,6,3,4,8,7,10,9,12,11]=>10001010101=>10101010001
[2,1,5,6,3,4,8,7,11,12,9,10]=>10001010001=>10001010001
[2,1,5,6,3,4,9,10,7,8,12,11]=>10001000101=>10100010001
[2,1,5,6,3,4,10,11,12,7,8,9]=>10001000001=>10000010001
[2,1,5,7,3,9,4,10,6,8,12,11]=>10000101101=>10110100001
[2,1,5,8,3,9,10,4,6,7,12,11]=>10000010101=>10101000001
[2,1,5,9,3,10,11,12,4,6,7,8]=>10000001001=>10010000001
[2,1,6,7,8,3,4,5,10,9,12,11]=>10000010101=>10101000001
[2,1,6,7,8,3,4,5,11,12,9,10]=>10000010001=>10001000001
[2,1,6,7,9,3,4,10,5,8,12,11]=>10000001101=>10110000001
[2,1,6,7,9,3,4,11,5,12,8,10]=>10000001011=>11010000001
[2,1,6,7,10,3,4,11,12,5,8,9]=>10000000101=>10100000001
[2,1,6,8,9,3,10,4,5,7,12,11]=>10000001101=>10110000001
[2,1,6,8,9,3,11,4,5,12,7,10]=>10000001011=>11010000001
[2,1,6,8,10,3,11,4,12,5,7,9]=>10000000111=>11100000001
[2,1,6,9,10,3,11,12,4,5,7,8]=>10000000101=>10100000001
[2,1,7,8,9,10,3,4,5,6,12,11]=>10000000101=>10100000001
[2,1,8,9,10,11,12,3,4,5,6,7]=>10000000001=>10000000001
[3,4,1,2,6,5,8,7,10,9,12,11]=>00101010101=>10101010100
[3,4,1,2,6,5,8,7,11,12,9,10]=>00101010001=>10001010100
[3,4,1,2,6,5,9,10,7,8,12,11]=>00101000101=>10100010100
[3,4,1,2,6,5,9,11,7,12,8,10]=>00101000011=>11000010100
[3,4,1,2,6,5,10,11,12,7,8,9]=>00101000001=>10000010100
[3,4,1,2,7,8,5,6,10,9,12,11]=>00100010101=>10101000100
[3,4,1,2,7,8,5,6,11,12,9,10]=>00100010001=>10001000100
[3,4,1,2,7,9,5,11,6,12,8,10]=>00100001011=>11010000100
[3,4,1,2,9,10,11,12,5,6,7,8]=>00100000001=>10000000100
[3,5,1,6,2,4,8,7,10,9,12,11]=>00011010101=>10101011000
[3,5,1,6,2,4,10,11,12,7,8,9]=>00011000001=>10000011000
[3,5,1,7,2,8,4,6,10,9,12,11]=>00010110101=>10101101000
[3,5,1,7,2,9,4,10,6,8,12,11]=>00010101101=>10110101000
[3,5,1,7,2,9,4,11,6,12,8,10]=>00010101011=>11010101000
[3,5,1,7,2,10,4,11,12,6,8,9]=>00010100101=>10100101000
[3,5,1,8,2,9,10,4,6,7,12,11]=>00010010101=>10101001000
[3,5,1,9,2,10,11,12,4,6,7,8]=>00010001001=>10010001000
[3,6,1,7,8,2,4,5,10,9,12,11]=>00001010101=>10101010000
[3,6,1,7,8,2,4,5,11,12,9,10]=>00001010001=>10001010000
[3,6,1,7,10,2,4,11,12,5,8,9]=>00001000101=>10100010000
[3,6,1,8,10,2,11,4,12,5,7,9]=>00001000111=>11100010000
[3,6,1,9,10,2,11,12,4,5,7,8]=>00001000101=>10100010000
[3,7,1,8,9,10,2,4,5,6,12,11]=>00000100101=>10100100000
[3,7,1,8,9,11,2,4,5,12,6,10]=>00000100011=>11000100000
[3,7,1,8,10,11,2,4,12,5,6,9]=>00000100011=>11000100000
[3,7,1,9,10,11,2,12,4,5,6,8]=>00000100011=>11000100000
[3,8,1,9,10,11,12,2,4,5,6,7]=>00000010001=>10001000000
[4,5,6,1,2,3,8,7,10,9,12,11]=>00001010101=>10101010000
[4,5,6,1,2,3,8,7,11,12,9,10]=>00001010001=>10001010000
[4,5,6,1,2,3,9,10,7,8,12,11]=>00001000101=>10100010000
[4,5,6,1,2,3,10,11,12,7,8,9]=>00001000001=>10000010000
[4,5,7,1,2,8,3,6,10,9,12,11]=>00000110101=>10101100000
[4,5,7,1,2,8,3,6,11,12,9,10]=>00000110001=>10001100000
[4,5,7,1,2,9,3,10,6,8,12,11]=>00000101101=>10110100000
[4,5,7,1,2,9,3,11,6,12,8,10]=>00000101011=>11010100000
[4,5,7,1,2,10,3,11,12,6,8,9]=>00000100101=>10100100000
[4,5,8,1,2,9,10,3,6,7,12,11]=>00000010101=>10101000000
[4,5,8,1,2,9,11,3,6,12,7,10]=>00000010011=>11001000000
[4,5,8,1,2,10,11,3,12,6,7,9]=>00000010011=>11001000000
[4,5,9,1,2,10,11,12,3,6,7,8]=>00000001001=>10010000000
[4,6,7,1,8,2,3,5,10,9,12,11]=>00000110101=>10101100000
[4,6,7,1,8,2,3,5,11,12,9,10]=>00000110001=>10001100000
[4,6,7,1,9,2,3,10,5,8,12,11]=>00000101101=>10110100000
[4,6,7,1,9,2,3,11,5,12,8,10]=>00000101011=>11010100000
[4,6,7,1,10,2,3,11,12,5,8,9]=>00000100101=>10100100000
[4,6,8,1,9,2,10,3,5,7,12,11]=>00000011101=>10111000000
[4,6,8,1,9,2,11,3,5,12,7,10]=>00000011011=>11011000000
[4,6,8,1,10,2,11,3,12,5,7,9]=>00000010111=>11101000000
[4,6,9,1,10,2,11,12,3,5,7,8]=>00000001101=>10110000000
[4,7,8,1,9,10,2,3,5,6,12,11]=>00000010101=>10101000000
[4,7,8,1,9,11,2,3,5,12,6,10]=>00000010011=>11001000000
[4,7,8,1,10,11,2,3,12,5,6,9]=>00000010011=>11001000000
[4,7,9,1,10,11,2,12,3,5,6,8]=>00000001011=>11010000000
[4,8,9,1,10,11,12,2,3,5,6,7]=>00000001001=>10010000000
[5,6,7,8,1,2,3,4,10,9,12,11]=>00000010101=>10101000000
[5,6,7,8,1,2,3,4,11,12,9,10]=>00000010001=>10001000000
[5,6,7,9,1,2,3,10,4,8,12,11]=>00000001101=>10110000000
[5,6,7,9,1,2,3,11,4,12,8,10]=>00000001011=>11010000000
[5,6,7,10,1,2,3,11,12,4,8,9]=>00000000101=>10100000000
[5,6,8,9,1,2,10,3,4,7,12,11]=>00000001101=>10110000000
[5,6,8,9,1,2,11,3,4,12,7,10]=>00000001011=>11010000000
[5,6,8,10,1,2,11,3,12,4,7,9]=>00000000111=>11100000000
[5,6,9,10,1,2,11,12,3,4,7,8]=>00000000101=>10100000000
[5,7,8,9,1,10,2,3,4,6,12,11]=>00000001101=>10110000000
[5,7,8,9,1,11,2,3,4,12,6,10]=>00000001011=>11010000000
[5,7,8,10,1,11,2,3,12,4,6,9]=>00000000111=>11100000000
[5,7,9,10,1,11,2,12,3,4,6,8]=>00000000111=>11100000000
[5,8,9,10,1,11,12,2,3,4,6,7]=>00000000101=>10100000000
[6,7,8,9,10,1,2,3,4,5,12,11]=>00000000101=>10100000000
[6,7,8,9,11,1,2,3,4,12,5,10]=>00000000011=>11000000000
[6,7,8,10,11,1,2,3,12,4,5,9]=>00000000011=>11000000000
[6,7,9,10,11,1,2,12,3,4,5,8]=>00000000011=>11000000000
[6,8,9,10,11,1,12,2,3,4,5,7]=>00000000011=>11000000000
[3,5,7,6,8,2,1,4]=>1000011=>1100001
[4,2,5,3,7,6,1,8]=>0011110=>0111100
[6,2,4,3,7,5,1,8]=>0011110=>0111100
[1,3,6,4,7,5,2,8]=>0001110=>0111000
[8,2,5,3,6,4,1,7]=>0011101=>1011100
[7,2,5,3,6,4,1,8]=>0011110=>0111100
[6,2,5,3,7,4,1,8]=>0011110=>0111100
[4,2,6,3,7,5,1,8]=>0011110=>0111100
[5,2,7,3,6,4,1,8]=>0011110=>0111100
[7,3,6,2,5,4,1,8]=>0011110=>0111100
[6,3,8,2,5,4,1,7]=>0011101=>1011100
[7,3,1,4,6,5,2,8]=>0101110=>0111010
[8,3,7,2,5,4,1,6]=>0011011=>1101100
[5,2,8,3,6,4,1,7]=>0011101=>1011100
[3,2,8,4,6,5,1,7]=>0101101=>1011010
[1,4,7,3,6,5,2,8]=>0001110=>0111000
[8,2,5,4,1,6,3,7]=>0011101=>1011100
[8,2,6,4,1,5,3,7]=>0011101=>1011100
[1,4,8,3,7,5,2,6]=>0001011=>1101000
[6,2,1,4,8,5,3,7]=>1001101=>1011001
[5,2,1,4,8,6,3,7]=>1001101=>1011001
[3,2,1,5,8,6,4,7]=>1100101=>1010011
[4,2,8,3,7,5,1,6]=>0011011=>1101100
[5,2,8,3,7,4,1,6]=>0011011=>1101100
[8,3,7,2,6,4,1,5]=>0010111=>1110100
[7,3,1,4,8,5,2,6]=>0101011=>1101010
[1,3,7,4,8,5,2,6]=>0001011=>1101000
[8,2,6,3,7,4,1,5]=>0010111=>1110100
[7,2,6,3,8,4,1,5]=>0010111=>1110100
[5,2,7,3,8,4,1,6]=>0011011=>1101100
[3,2,7,4,8,5,1,6]=>0101011=>1101010
[5,2,6,3,8,4,1,7]=>0011101=>1011100
[6,2,5,3,8,4,1,7]=>0011101=>1011100
[7,2,5,3,8,4,1,6]=>0011011=>1101100
[8,2,5,3,7,4,1,6]=>0011011=>1101100
[1,3,6,4,8,5,2,7]=>0001101=>1011000
[1,3,5,4,8,6,2,7]=>0001101=>1011000
[8,2,4,3,7,5,1,6]=>0011011=>1101100
[7,2,4,3,8,5,1,6]=>0011011=>1101100
[6,2,4,3,8,5,1,7]=>0011101=>1011100
[5,2,4,3,8,6,1,7]=>0011101=>1011100
[4,2,5,3,8,6,1,7]=>0011101=>1011100
[4,2,5,3,1,7,6,8]=>0111010=>0101110
[6,2,4,3,1,7,5,8]=>0110110=>0110110
[7,2,4,3,1,6,5,8]=>0110110=>0110110
[8,5,1,3,6,4,2,7]=>0011101=>1011100
[8,4,1,3,6,5,2,7]=>0011101=>1011100
[1,5,2,4,7,6,3,8]=>0001110=>0111000
[7,2,5,3,1,6,4,8]=>0101110=>0111010
[6,2,5,3,1,7,4,8]=>0101110=>0111010
[4,2,6,3,1,7,5,8]=>0110110=>0110110
[3,2,6,4,1,7,5,8]=>0110110=>0110110
[3,2,7,4,1,6,5,8]=>0110110=>0110110
[4,2,7,3,1,6,5,8]=>0110110=>0110110
[5,2,7,3,1,6,4,8]=>0101110=>0111010
[6,2,7,3,1,5,4,8]=>0101110=>0111010
[7,2,6,3,1,5,4,8]=>0101110=>0111010
[1,5,2,4,8,6,3,7]=>0001101=>1011000
[8,4,1,3,7,5,2,6]=>0011011=>1101100
[6,2,1,5,3,7,4,8]=>1001110=>0111001
[3,2,1,6,4,7,5,8]=>1100110=>0110011
[3,2,8,5,1,6,4,7]=>0101101=>1011010
[6,2,8,4,1,5,3,7]=>0011101=>1011100
[8,3,7,4,1,5,2,6]=>0011011=>1101100
[7,1,3,2,5,6,4,8]=>0100110=>0110010
[6,3,5,2,4,8,1,7]=>0001101=>1011000
[1,5,2,8,7,4,3,6]=>0011011=>1101100
[5,7,2,8,1,4,3,6]=>0010011=>1100100
[5,8,2,7,1,4,3,6]=>0010011=>1100100
[4,8,3,1,5,2,7,6]=>0101011=>1101010
[7,1,5,3,2,6,8,4]=>0101011=>1101010
[3,1,5,7,8,6,2,4]=>0100101=>1010010
[8,7,6,5,3,2,1,4,9]=>11011110=>01111011
[8,7,6,4,3,2,1,5,9]=>11101110=>01110111
[8,7,5,4,3,2,1,6,9]=>11110110=>01101111
[8,7,6,5,4,1,2,3,9]=>00111110=>01111100
[9,8,7,6,5,4,2,1,3,10]=>101111110=>011111101
[8,7,6,5,2,3,1,4,9]=>01011110=>01111010
[9,8,7,6,5,3,2,1,4,10]=>110111110=>011111011
[8,7,6,3,4,2,1,5,9]=>10101110=>01110101
[9,8,7,6,4,3,2,1,5,10]=>111011110=>011110111
[8,7,4,5,3,2,1,6,9]=>11010110=>01101011
[9,8,7,5,4,3,2,1,6,10]=>111101110=>011101111
[8,5,6,4,3,2,1,7,9]=>11101010=>01010111
[9,8,6,5,4,3,2,1,7,10]=>111110110=>011011111
[6,7,5,4,3,2,1,8,9]=>11110100=>00101111
[8,6,2,3,1,5,7,4]=>0100111=>1110010
[2,5,1,7,4,8,6,3]=>0001111=>1111000
[8,6,7,3,5,2,1,4]=>1001011=>1101001
[1,4,2,7,3,6,8,5]=>0010011=>1100100
[3,2,1,7,8,5,4,6]=>1101001=>1001011
[7,3,4,2,1,5,8,6]=>1010011=>1100101
[1,7,6,3,2,4,8,5]=>0100111=>1110010
[2,1,6,4,7,8,5,3]=>1001101=>1011001
[1,6,3,2,4,7,8,5]=>0100101=>1010010
[1,2,3,7,5,8,4,6]=>0000011=>1100000
[1,8,5,3,2,4,7,6]=>0101011=>1101010
[4,7,8,1,5,6,2,3]=>0000101=>1010000
[3,6,7,1,8,4,2,5]=>0010011=>1100100
[1,3,7,6,2,4,5,8]=>0000110=>0110000
[2,7,3,8,4,5,6,1]=>0000111=>1110000
[7,1,4,3,8,5,6,2]=>0010111=>1110100
[5,6,2,7,8,3,4,1]=>0010101=>1010100
[7,4,1,8,5,6,2,3]=>0010111=>1110100
[7,2,5,8,1,6,3,4]=>0000111=>1110000
[6,4,8,1,5,7,2,3]=>0000111=>1110000
[2,7,4,1,3,6,8,5]=>0010011=>1100100
[5,2,1,8,4,6,7,3]=>1001011=>1101001
[6,2,1,4,7,5,8,3]=>1000111=>1110001
[6,8,7,9,5,4,3,2,1]=>11110011=>11001111
[5,8,7,6,9,4,3,2,1]=>11100111=>11100111
[4,8,7,6,5,9,3,2,1]=>11001111=>11110011
[3,8,7,6,5,4,9,2,1]=>10011111=>11111001
[2,8,7,6,5,4,3,9,1]=>00111111=>11111100
[1,2,8,4,6,3,5,7]=>0000101=>1010000
[2,6,1,5,4,7,3,8]=>0001110=>0111000
[1,2,8,5,4,6,3,7]=>0001101=>1011000
[1,3,6,8,4,5,7,2]=>0000011=>1100000
[1,2,8,4,6,3,7,5]=>0000111=>1110000
[4,6,3,5,7,8,1,2]=>0000101=>1010000
[2,7,6,5,1,4,8,3]=>0001111=>1111000
[2,7,4,8,1,3,6,5]=>0000111=>1110000
[2,3,6,8,4,1,7,5]=>0010011=>1100100
[1,2,6,8,4,7,5,3]=>0001011=>1101000
[1,7,2,8,6,3,5,4]=>0001111=>1111000
[2,3,8,5,4,7,1,6]=>0001011=>1101000
[1,2,8,4,7,3,5,6]=>0000011=>1100000
[2,6,1,4,8,3,7,5]=>0000111=>1110000
[3,7,6,5,2,1,4,8]=>1001110=>0111001
[2,5,6,1,4,8,7,3]=>0000111=>1110000
[8,4,2,3,7,1,6,5]=>0010111=>1110100
[5,2,4,8,7,3,1,6]=>0101011=>1101010
[8,3,2,6,7,4,1,5]=>0110011=>1100110
[3,2,4,6,7,8,1,5]=>0100001=>1000010
[5,2,6,8,1,3,7,4]=>0001011=>1101000
[4,8,1,6,3,7,5,2]=>0001111=>1111000
[7,1,5,2,6,4,3,8]=>0011110=>0111100
[8,3,5,2,6,1,4,7]=>0001101=>1011000
[1,8,5,6,2,7,4,3]=>0010111=>1110100
[8,3,2,4,6,7,1,5]=>0100011=>1100010
[4,2,7,6,1,8,5,3]=>0011111=>1111100
[7,2,4,8,6,3,5,1]=>0001111=>1111000
[7,3,2,1,8,5,4,6]=>1101011=>1101011
[7,3,2,1,6,4,8,5]=>1100111=>1110011
[3,6,5,2,1,8,4,7]=>1001101=>1011001
[6,7,2,4,3,5,8,1]=>0010011=>1100100
[4,5,3,7,2,1,6,8]=>1001010=>0101001
[4,3,8,2,1,5,7,6]=>1010011=>1100101
[4,3,2,8,1,6,7,5]=>0110011=>1100110
[4,5,8,3,2,7,1,6]=>0100011=>1100010
[6,8,5,2,7,3,4,1]=>0011011=>1101100
[5,4,7,8,2,3,6,1]=>0001101=>1011000
[4,3,8,2,1,6,7,5]=>1010011=>1100101
[1,9,2,4,5,6,7,8,3]=>00000011=>11000000
[9,1,3,4,5,6,7,8,2]=>00000011=>11000000
[3,5,7,4,6,2,8,1]=>0000111=>1110000
[5,3,7,6,2,4,8,1]=>0001111=>1111000
[4,6,7,2,5,3,8,1]=>0001011=>1101000
[6,4,7,8,3,1,5,2]=>0101101=>1011010
[8,4,7,3,1,5,6,2]=>0100111=>1110010
[5,8,1,7,6,4,2,3]=>0010111=>1110100
[5,6,7,1,8,3,4,2]=>0010011=>1100100
[7,1,8,6,2,5,4,3]=>0011111=>1111100
[8,5,1,7,6,4,2,3]=>0011111=>1111100
[1,5,8,2,6,4,7,3]=>0000111=>1110000
[1,5,7,4,6,8,3,2]=>0100011=>1100010
[1,4,7,5,6,8,3,2]=>0100011=>1100010
[5,6,7,4,8,1,3,2]=>0100011=>1100010
[8,1,2,6,4,5,7,3]=>0000111=>1110000
[4,8,1,7,2,5,6,3]=>0000111=>1110000
[2,6,7,1,5,4,8,3]=>0001011=>1101000
[3,2,7,6,5,8,1,4]=>0100111=>1110010
[1,7,3,4,5,8,2,6]=>0000011=>1100000
[7,1,8,4,5,6,3,2]=>0100111=>1110010
[10,1,3,4,5,6,7,8,9,2]=>000000011=>110000000
[1,2,3,4,5,6,7,8,11,9,10]=>0000000001=>1000000000
[1,8,3,4,5,6,9,2,7]=>00000011=>11000000
[8,2,3,4,5,1,9,7,6]=>00010111=>11101000
[1,2,7,4,5,8,3,6]=>0000011=>1100000
[8,1,9,4,5,6,7,3,2]=>01000111=>11100010
[7,9,3,4,5,6,1,8,2]=>00001011=>11010000
[11,1,3,4,5,6,7,8,9,10,2]=>0000000011=>1100000000
[1,2,3,4,5,6,7,8,9,12,10,11]=>00000000001=>10000000000
[10,2,3,4,5,6,7,8,11,1,9]=>0000000011=>1100000000
[1,9,3,4,5,6,7,10,2,8]=>000000011=>110000000
[9,2,3,4,5,6,1,10,8,7]=>000010111=>111010000
[1,2,8,4,5,6,9,3,7]=>00000011=>11000000
[7,8,3,4,5,2,9,1,6]=>00010011=>11001000
[8,2,3,4,1,6,9,7,5]=>00100111=>11100100
[6,7,3,2,5,8,1,4]=>0100011=>1100010
[8,1,3,9,5,6,7,4,2]=>00100111=>11100100
[6,1,8,4,5,3,7,2]=>0001111=>1111000
[7,8,9,4,5,6,3,1,2]=>01001001=>10010010
[9,1,10,4,5,6,7,8,3,2]=>010000111=>111000010
[6,9,3,4,5,1,7,8,2]=>00010011=>11001000
[8,10,3,4,5,6,7,1,9,2]=>000001011=>110100000
[10,11,3,4,5,6,7,8,9,1,2]=>0000000101=>1010000000
[12,1,3,4,5,6,7,8,9,10,11,2]=>00000000011=>11000000000
[4,6,2,5,1,8,7,3]=>0001111=>1111000
[5,1,4,6,2,8,7,3]=>0001111=>1111000
[7,3,5,2,1,6,8,4]=>1001011=>1101001
[8,5,1,2,6,3,7,4]=>0001111=>1111000
[1,5,8,7,4,6,3,2]=>0100111=>1110010
[5,7,2,1,3,6,8,4]=>1000011=>1100001
[3,7,2,6,8,1,5,4]=>0001011=>1101000
[7,4,8,6,5,1,3,2]=>0101111=>1111010
[2,7,6,8,5,1,4,3]=>0011011=>1101100
[1,6,4,5,7,3,8,2]=>0000111=>1110000
[1,5,4,7,8,6,2,3]=>0001101=>1011000
[7,3,1,6,8,2,5,4]=>0101011=>1101010
[7,1,6,8,5,2,4,3]=>0011011=>1101100
[3,5,8,7,6,4,1,2]=>0010111=>1110100
[1,5,7,8,6,2,4,3]=>0010101=>1010100
[3,6,2,1,4,7,8,5]=>1000101=>1010001
[6,8,2,7,5,4,3,1]=>0111011=>1101110
[5,8,1,7,6,4,3,2]=>0110111=>1110110
[10,6,1,2,3,4,9,5,7,8]=>000010011=>110010000
[10,7,1,2,3,4,9,5,6,8]=>000001011=>110100000
[9,10,1,2,3,4,8,5,6,7]=>000000101=>101000000
[10,1,5,2,3,4,6,7,8,9]=>000100001=>100001000
[10,1,2,5,3,4,6,7,8,9]=>000100001=>100001000
[5,1,2,3,10,4,6,7,8,9]=>000100001=>100001000
[7,1,2,3,4,5,11,6,8,9,10]=>0000010001=>1000100000
[7,6,1,2,3,4,10,9,5,8]=>000011011=>110110000
[11,1,2,3,4,5,8,6,7,9,10]=>0000001001=>1001000000
[9,7,1,2,3,4,8,5,10,6]=>000001111=>111100000
[11,1,2,3,4,5,9,6,7,8,10]=>0000000101=>1010000000
[5,9,1,2,3,4,6,7,10,8]=>000000011=>110000000
[10,8,4,9,1,2,3,5,6,7]=>000000111=>111000000
[11,10,5,1,2,3,4,6,7,8,9]=>0001000011=>1100001000
[2,10,1,5,3,4,6,7,8,9]=>000100001=>100001000
[11,10,1,5,2,3,4,6,7,8,9]=>0001000011=>1100001000
[3,1,5,2,10,4,6,7,8,9]=>010100001=>100001010
[5,11,1,2,10,3,4,6,7,8,9]=>0000000011=>1100000000
[4,1,2,10,3,5,6,7,8,9]=>001000001=>100000100
[5,11,1,2,3,10,4,6,7,8,9]=>0000000011=>1100000000
[4,1,5,6,7,8,9,2,3]=>00100001=>10000100
[2,3,4,5,6,7,8,10,11,1,9]=>0000000001=>1000000000
[2,3,4,5,8,9,1,6,7]=>00000001=>10000000
[2,3,6,7,1,8,9,4,5]=>00000101=>10100000
[2,4,5,6,7,8,9,10,11,1,3]=>0000000001=>1000000000
[3,4,5,6,7,8,9,10,11,1,2]=>0000000001=>1000000000
[8,6,3,2,1,5,4,7]=>1101101=>1011011
[8,5,3,2,4,1,7,6]=>0111011=>1101110
[7,5,2,4,3,6,8,1]=>0011011=>1101100
[8,5,1,4,6,3,2,7]=>0101101=>1011010
[8,5,1,6,3,4,2,7]=>0011101=>1011100
[8,4,3,6,1,5,2,7]=>0011101=>1011100
[8,4,3,5,2,1,7,6]=>1011011=>1101101
[6,4,3,2,8,7,1,5]=>0110111=>1110110
[8,5,1,4,3,7,2,6]=>0011011=>1101100
[8,5,4,2,1,3,7,6]=>1011011=>1101101
[4,7,3,6,1,8,5,2]=>0001111=>1111000
[7,6,2,4,1,5,8,3]=>0010111=>1110100
[8,1,6,3,7,4,2,5]=>0010111=>1110100
[5,3,8,2,6,7,1,4]=>0001011=>1101000
[8,2,5,1,7,6,3,4]=>0001111=>1111000
[8,2,4,6,3,7,1,5]=>0000111=>1110000
[7,2,6,4,3,5,8,1]=>0010111=>1110100
[7,3,6,2,4,5,8,1]=>0000111=>1110000
[8,3,7,2,1,4,6,5]=>1000111=>1110001
[7,6,4,1,3,2,8,5]=>0110111=>1110110
[7,3,8,2,1,5,6,4]=>1000111=>1110001
[6,2,5,7,4,3,8,1]=>0010111=>1110100
[6,2,5,4,8,7,1,3]=>0001111=>1111000
[7,2,4,8,5,1,6,3]=>0001111=>1111000
[4,2,7,6,8,5,1,3]=>0011011=>1101100
[7,1,6,2,8,5,4,3]=>0011111=>1111100
[7,1,6,3,8,5,2,4]=>0001111=>1111000
[7,2,6,8,1,3,5,4]=>0001011=>1101000
[7,2,8,5,1,3,6,4]=>0001111=>1111000
[7,1,8,5,3,2,6,4]=>0101111=>1111010
[7,1,8,2,5,6,4,3]=>0010111=>1110100
[6,1,5,8,7,2,4,3]=>0010111=>1110100
[6,1,5,7,4,8,3,2]=>0100111=>1110010
[6,1,5,7,8,3,4,2]=>0010101=>1010100
[4,6,7,3,1,8,5,2]=>0101011=>1101010
[4,2,6,3,1,8,7,5]=>0110111=>1110110
[6,1,4,2,5,8,7,3]=>0010111=>1110100
[1,5,3,8,4,6,2,7]=>0001101=>1011000
[7,2,3,5,8,4,1,6]=>0010011=>1100100
[7,6,4,2,8,5,1,3]=>0011111=>1111100
[1,7,6,4,8,5,3,2]=>0101111=>1111010
[8,7,4,2,1,5,6,3]=>1010111=>1110101
[8,2,3,5,1,4,6,7]=>0001001=>1001000
[8,7,4,1,3,2,6,5]=>0110111=>1110110
[7,1,4,8,3,6,2,5]=>0000111=>1110000
[4,1,8,5,7,6,2,3]=>0010111=>1110100
[3,7,5,8,4,2,1,6]=>1010011=>1100101
[6,1,5,8,3,4,2,7]=>0010101=>1010100
[6,7,5,1,3,2,4,8]=>0101010=>0101010
[5,2,6,1,7,3,4,8]=>0001110=>0111000
[4,2,6,8,3,7,1,5]=>0010011=>1100100
[6,8,5,1,4,2,3,7]=>0011001=>1001100
[7,8,4,5,1,3,6,2]=>0001101=>1011000
[1,7,8,5,3,4,6,2]=>0001101=>1011000
[1,5,8,3,6,4,7,2]=>0000111=>1110000
[6,3,8,1,4,2,7,5]=>0010111=>1110100
[4,8,1,5,6,3,7,2]=>0000111=>1110000
[1,8,2,6,5,3,7,4]=>0001111=>1111000
[3,8,1,7,2,6,5,4]=>0001111=>1111000
[7,3,8,1,2,6,5,4]=>0001111=>1111000
[8,1,4,2,3,5,7,6]=>0010011=>1100100
[8,1,2,4,6,5,7,3]=>0000111=>1110000
[5,1,8,3,7,4,6,2]=>0001111=>1111000
[8,3,7,1,5,4,6,2]=>0001111=>1111000
[8,4,7,1,5,3,6,2]=>0001111=>1111000
[7,2,5,3,4,6,1,8]=>0001110=>0111000
[7,6,4,2,5,3,1,8]=>0111110=>0111110
[5,8,4,3,6,2,7,1]=>0010111=>1110100
[1,7,2,6,3,4,8,5]=>0000111=>1110000
[7,5,1,6,3,2,4,8]=>0101110=>0111010
[7,1,2,6,3,4,5,8]=>0000110=>0110000
[7,2,5,1,6,3,4,8]=>0001110=>0111000
[7,3,1,4,6,2,5,8]=>0100110=>0110010
[7,1,6,5,4,2,3,8]=>0011110=>0111100
[5,8,4,3,1,7,2,6]=>0110011=>1100110
[3,6,8,5,2,4,7,1]=>0001011=>1101000
[5,7,8,4,3,2,6,1]=>0110101=>1010110
[1,3,8,4,7,2,6,5]=>0000111=>1110000
[3,2,1,4,5,8,6,7]=>1100001=>1000011
[6,7,1,3,2,8,5,4]=>0101011=>1101010
[1,5,3,2,6,8,4,7]=>0101001=>1001010
[5,4,3,1,7,2,8,6]=>0111011=>1101110
[3,7,6,5,8,2,4,1]=>0010111=>1110100
[5,7,4,2,8,6,1,3]=>0010111=>1110100
[5,4,3,7,8,2,6,1]=>0011101=>1011100
[3,8,5,7,6,2,4,1]=>0010111=>1110100
[1,3,6,8,7,2,5,4]=>0001011=>1101000
[5,8,7,1,4,2,3,6]=>0010011=>1100100
[2,6,3,7,1,4,5,8]=>0000110=>0110000
[6,5,1,2,4,7,8,3]=>0001101=>1011000
[7,6,8,4,3,1,5,2]=>0111011=>1101110
[1,7,6,5,3,2,4,8]=>0101110=>0111010
[2,7,6,5,4,1,3,8]=>0011110=>0111100
[6,2,3,5,8,4,1,7]=>0010101=>1010100
[4,7,6,1,5,8,3,2]=>0100111=>1110010
[9,8,7,6,5,4,2,3,1]=>01111111=>11111110
[2,3,9,8,7,6,5,4,1]=>00111111=>11111100
[9,1,3,2,4,5,6,7,8]=>01000001=>10000010
[6,8,7,1,5,4,3,2]=>0111011=>1101110
[8,7,4,6,5,1,3,2]=>0101111=>1111010
[9,8,7,1,6,5,4,3,2]=>01111111=>11111110
[9,8,7,6,1,5,4,3,2]=>01111111=>11111110
[9,8,7,6,5,1,4,3,2]=>01111111=>11111110
[9,10,1,8,7,6,5,4,3,2]=>011111101=>101111110
[10,9,1,8,7,6,5,4,3,2]=>011111111=>111111110
[10,9,8,1,7,6,5,4,3,2]=>011111111=>111111110
[10,9,8,7,1,6,5,4,3,2]=>011111111=>111111110
[10,9,8,7,6,1,5,4,3,2]=>011111111=>111111110
[10,9,8,7,6,5,1,4,3,2]=>011111111=>111111110
[10,9,8,7,6,5,4,1,3,2]=>011111111=>111111110
[3,5,2,4,7,6,9,8,1]=>00010111=>11101000
[2,4,3,6,5,8,7,1,9]=>00101110=>01110100
[3,2,5,4,7,6,9,8,1,10]=>010101110=>011101010
[2,4,3,6,5,8,7,10,9,1]=>001010111=>111010100
[7,2,6,1,5,8,3,4]=>0000111=>1110000
[4,7,3,8,6,2,5,1]=>0001111=>1111000
[4,7,3,6,8,2,1,5]=>1000011=>1100001
[5,4,7,3,8,2,1,6]=>1001011=>1101001
[8,7,2,4,6,3,5,1]=>0001111=>1111000
[4,3,5,7,2,6,1,8]=>0010110=>0110100
[1,7,2,8,5,4,3,6]=>0011011=>1101100
[5,4,8,3,6,2,1,7]=>1001101=>1011001
[6,8,2,5,7,1,4,3]=>0010011=>1100100
[3,8,6,2,7,5,1,4]=>0001111=>1111000
[5,8,4,2,7,3,6,1]=>0010111=>1110100
[8,2,7,3,4,5,1,6]=>0001011=>1101000
[8,1,5,2,4,6,3,7]=>0001101=>1011000
[8,6,1,3,4,5,7,2]=>0000111=>1110000
[8,5,1,2,4,6,7,3]=>0001011=>1101000
[2,6,8,7,3,4,5,1]=>0001011=>1101000
[1,7,8,5,6,4,2,3]=>0010101=>1010100
[8,3,1,2,4,6,7,5]=>0100011=>1100010
[3,1,7,5,8,2,4,6]=>0100011=>1100010
[8,1,3,2,4,6,5,7]=>0100101=>1010010
[8,1,5,6,4,2,3,7]=>0010101=>1010100
[8,1,6,5,4,3,2,7]=>0111101=>1011110
[2,6,8,1,5,4,3,7]=>0011001=>1001100
[5,2,1,7,6,3,8,4]=>1001111=>1111001
[3,5,8,2,1,4,7,6]=>1000011=>1100001
[4,2,8,5,3,7,6,1]=>0011111=>1111100
[4,2,7,5,3,8,6,1]=>0011111=>1111100
[6,4,5,1,8,3,2,7]=>0101101=>1011010
[5,4,7,8,3,1,2,6]=>0101001=>1001010
[4,5,8,1,3,7,2,6]=>0000011=>1100000
[1,5,3,6,8,7,2,4]=>0001011=>1101000
[7,6,2,8,1,4,3,5]=>0010111=>1110100
[4,7,2,6,8,3,5,1]=>0001011=>1101000
[6,3,2,8,7,4,5,1]=>0101111=>1111010
[7,4,3,8,5,6,2,1]=>1010111=>1110101
[3,1,5,8,7,6,2,4]=>0100111=>1110010
[8,2,1,6,5,7,3,4]=>1000111=>1110001
[3,1,8,6,5,7,2,4]=>0100111=>1110010
[1,2,7,6,4,5,8,3]=>0000111=>1110000
[7,2,6,5,1,8,3,4]=>0001111=>1111000
[4,2,8,5,6,3,1,7]=>0110101=>1010110
[4,7,3,2,5,1,6,8]=>0101010=>0101010
[4,2,5,3,8,7,1,6]=>0011011=>1101100
[7,2,5,3,8,4,6,1]=>0001111=>1111000
[3,6,8,1,7,4,5,2]=>0001011=>1101000
[8,7,3,2,5,4,6,1]=>0101111=>1111010
[7,5,6,1,8,3,2,4]=>0100111=>1110010
[4,5,6,2,7,3,1,8]=>0100110=>0110010
[5,3,4,7,1,6,2,8]=>0001110=>0111000
[3,5,1,4,6,8,2,7]=>0001001=>1001000
[8,5,7,4,2,1,3,6]=>1010011=>1100101
[2,3,7,4,1,8,6,5]=>0010111=>1110100
[2,4,5,1,8,6,3,7]=>0001101=>1011000
[2,4,1,6,7,5,3,8]=>0011010=>0101100
[6,3,7,1,5,2,4,8]=>0001110=>0111000
[4,1,3,7,8,2,6,5]=>0010101=>1010100
[7,1,4,8,6,5,2,3]=>0001111=>1111000
[8,3,4,2,1,7,5,6]=>1010011=>1100101
[1,4,5,3,8,6,7,2]=>0001011=>1101000
[4,6,2,7,5,8,1,3]=>0000111=>1110000
[7,3,2,5,1,8,4,6]=>0101011=>1101010
[7,8,1,4,2,3,5,6]=>0010001=>1000100
[6,5,2,4,8,7,1,3]=>0001111=>1111000
[8,5,2,4,1,3,7,6]=>0011011=>1101100
[5,1,2,4,3,6,8,7]=>0011001=>1001100
[5,2,1,4,3,7,6,8]=>1011010=>0101101
[8,6,2,7,5,3,1,4]=>0101111=>1111010
[6,2,1,5,8,3,4,7]=>1000101=>1010001
[2,3,8,7,1,5,4,6]=>0001011=>1101000
[4,3,8,1,5,2,6,7]=>0011001=>1001100
[4,1,3,6,7,2,8,5]=>0010011=>1100100
[7,1,4,5,8,2,6,3]=>0000111=>1110000
[6,1,3,2,4,5,8,7]=>0100101=>1010010
[3,5,1,2,4,7,6,9,8]=>00010101=>10101000
[7,8,1,6,5,2,4,3]=>0011101=>1011100
[7,4,8,6,5,1,2,3]=>0001111=>1111000
[3,7,8,6,5,1,2,4]=>0001101=>1011000
[8,4,5,7,2,6,3,1]=>0100111=>1110010
[4,5,8,2,7,3,1,6]=>0100011=>1100010
[6,5,8,2,7,3,1,4]=>0100111=>1110010
[6,4,8,2,7,3,1,5]=>0100111=>1110010
[7,8,1,3,6,4,2,5]=>0010101=>1010100
[4,3,8,2,7,5,1,6]=>0011011=>1101100
[4,5,7,8,3,2,1,6]=>1100001=>1000011
[5,7,3,4,2,6,8,1]=>0010011=>1100100
[5,7,4,2,3,6,8,1]=>0010011=>1100100
[5,4,7,3,2,8,1,6]=>0101011=>1101010
[6,8,3,2,4,5,1,7]=>0101001=>1001010
[5,8,3,4,6,1,2,7]=>0000101=>1010000
[6,4,3,8,5,1,2,7]=>0011101=>1011100
[6,4,8,2,3,5,1,7]=>0001101=>1011000
[5,4,6,8,2,3,1,7]=>0101001=>1001010
[5,6,8,4,1,2,3,7]=>0010001=>1000100
[6,4,8,5,1,2,3,7]=>0001101=>1011000
[7,4,8,3,1,2,5,6]=>0100011=>1100010
[5,7,8,2,3,1,4,6]=>0100001=>1000010
[5,4,7,8,2,1,3,6]=>1001001=>1001001
[5,8,6,3,1,2,4,7]=>0100101=>1010010
[6,8,5,2,1,3,4,7]=>1001001=>1001001
[5,6,1,3,2,4,8,7]=>0100101=>1010010
[8,1,5,4,6,2,7,3]=>0001111=>1111000
[4,3,8,1,2,5,7,6]=>0010011=>1100100
[4,6,3,2,8,5,7,1]=>0100111=>1110010
[5,3,7,2,1,8,6,4]=>1001111=>1111001
[7,4,3,2,5,1,8,6]=>0111011=>1101110
[3,6,8,5,2,1,7,4]=>1001011=>1101001
[6,1,5,4,7,2,8,3]=>0001111=>1111000
[1,3,6,5,8,2,7,4]=>0000111=>1110000
[5,4,8,3,2,7,1,6]=>0101011=>1101010
[5,4,3,7,2,1,6,8]=>1011010=>0101101
[5,4,3,7,8,2,1,6]=>1011001=>1001101
[3,4,5,6,7,8,2,9,1]=>00000011=>11000000
[3,4,5,6,7,8,9,2,10,1]=>000000011=>110000000
[1,4,5,6,7,8,3,9,2]=>00000011=>11000000
[3,4,5,6,7,2,1,9,8]=>10000101=>10100001
[2,1,5,6,7,8,9,4,3]=>10100001=>10000101
[2,4,5,6,7,8,3,1,9]=>01000010=>01000010
[2,4,5,6,7,8,9,10,3,1]=>010000001=>100000010
[1,4,8,6,3,2,7,5]=>0100111=>1110010
[4,1,8,6,2,5,7,3]=>0010111=>1110100
[6,7,2,5,3,8,4,1]=>0011011=>1101100
[6,3,4,8,1,2,7,5]=>0000111=>1110000
[6,2,8,1,7,4,5,3]=>0001111=>1111000
[2,6,3,1,5,8,7,4]=>0100111=>1110010
[7,1,3,2,6,5,8,4]=>0100111=>1110010
[8,7,6,4,5,3,2,9,1]=>01011111=>11111010
[2,9,8,7,5,6,4,3,1]=>01101111=>11110110
[6,1,3,5,8,7,4,2]=>0010111=>1110100
[3,5,8,7,4,6,2,1]=>1000111=>1110001
[6,8,5,7,3,4,2,1]=>1010011=>1100101
[5,3,6,8,4,2,1,7]=>1011001=>1001101
[5,1,6,8,4,7,3,2]=>0101011=>1101010
[6,2,8,3,4,1,5,7]=>0010101=>1010100
[2,4,1,8,7,6,3,5]=>0010111=>1110100
[1,3,5,8,4,7,2,6]=>0000011=>1100000
[2,3,8,7,5,1,6,4]=>0001111=>1111000
[8,5,4,7,6,1,3,2]=>0101111=>1111010
[5,8,7,2,4,1,3,6]=>0010011=>1100100
[4,1,3,5,6,2,8,7]=>0010101=>1010100
[6,3,8,5,1,7,4,2]=>0011111=>1111100
[8,2,4,6,1,3,7,5]=>0000111=>1110000
[6,4,8,7,3,5,2,1]=>1001111=>1111001
[8,2,3,5,6,1,4,7]=>0000101=>1010000
[4,3,5,6,8,2,7,1]=>0010011=>1100100
[8,2,3,4,6,1,7,5]=>0000111=>1110000
[1,7,4,3,5,2,8,6]=>0011011=>1101100
[2,7,4,3,8,1,5,6]=>0010011=>1100100
[3,8,2,7,6,4,1,5]=>0010111=>1110100
[5,3,6,2,1,8,4,7]=>1001101=>1011001
[4,3,8,6,2,7,1,5]=>0010111=>1110100
[8,2,1,4,6,3,7,5]=>1000111=>1110001
[3,1,6,8,2,7,5,4]=>0101011=>1101010
[5,3,8,6,7,2,1,4]=>1001011=>1101001
[5,8,7,2,4,6,1,3]=>0000111=>1110000
[1,5,2,8,7,6,4,3]=>0011111=>1111100
[2,7,1,4,6,5,3,8]=>0001110=>0111000
[4,7,1,2,6,5,8,3]=>0000111=>1110000
[4,2,5,6,8,7,3,1]=>0110011=>1100110
[6,5,8,3,7,4,2,1]=>1010111=>1110101
[8,2,5,1,6,3,7,4]=>0001111=>1111000
[8,3,4,5,1,6,7,2]=>0001011=>1101000
[7,8,1,5,6,3,2,4]=>0100101=>1010010
[1,7,8,3,2,5,4,6]=>0101001=>1001010
[7,8,1,3,2,5,6,4]=>0100101=>1010010
[7,8,1,3,5,4,6,2]=>0001101=>1011000
[7,8,1,3,5,2,4,6]=>0001001=>1001000
[1,3,7,8,5,2,4,6]=>0001001=>1001000
[1,7,8,3,5,2,6,4]=>0001101=>1011000
[1,7,8,3,2,5,6,4]=>0100101=>1010010
[3,7,8,5,4,6,1,2]=>0001101=>1011000
[3,5,7,6,4,8,1,2]=>0000111=>1110000
[1,3,7,8,5,4,6,2]=>0001101=>1011000
[1,3,7,8,5,4,2,6]=>0011001=>1001100
[1,3,7,8,2,5,4,6]=>0001001=>1001000
[1,3,2,7,8,5,4,6]=>0101001=>1001010
[1,5,7,6,8,3,2,4]=>0100011=>1100010
[3,5,4,7,8,6,1,2]=>0001101=>1011000
[3,5,7,6,8,4,1,2]=>0010011=>1100100
[1,5,7,6,8,3,4,2]=>0010011=>1100100
[3,5,7,4,6,8,1,2]=>0000011=>1100000
[6,5,8,4,3,7,1,2]=>0010111=>1110100
[6,7,3,1,5,2,4,8]=>0101010=>0101010
[5,2,4,1,8,3,6,7]=>0011001=>1001100
[2,1,7,4,3,8,5,6]=>1010011=>1100101
[7,2,3,8,5,4,1,6]=>0011011=>1101100
[4,1,5,7,6,3,8,2]=>0010111=>1110100
[3,2,5,4,7,6,1,10,8,9]=>010111001=>100111010
[3,2,5,4,9,8,6,7,1,10]=>010101110=>011101010
[3,2,5,4,1,8,6,10,7,9]=>011100101=>101001110
[3,2,5,4,1,10,9,6,7,8]=>011100011=>110001110
[3,2,7,6,4,5,9,8,1,10]=>010011110=>011110010
[3,2,7,6,4,5,1,10,8,9]=>010111001=>100111010
[3,2,9,6,4,8,5,7,1,10]=>010011110=>011110010
[3,2,1,6,4,8,5,10,7,9]=>110010101=>101010011
[3,2,1,6,4,10,9,5,7,8]=>110010011=>110010011
[3,2,9,8,7,4,5,6,1,10]=>010011110=>011110010
[3,2,1,8,7,4,5,10,6,9]=>110001101=>101100011
[3,2,1,10,7,4,9,5,6,8]=>110001011=>110100011
[3,2,1,10,9,8,4,5,6,7]=>110000111=>111000011
[5,4,2,3,7,6,9,8,1,10]=>001101110=>011101100
[5,4,2,3,7,6,1,10,8,9]=>001111001=>100111100
[5,4,2,3,9,8,6,7,1,10]=>001101110=>011101100
[5,4,2,3,1,8,6,10,7,9]=>011100101=>101001110
[5,4,2,3,1,10,9,6,7,8]=>011100011=>110001110
[7,4,2,6,3,5,9,8,1,10]=>001011110=>011110100
[7,4,2,6,3,5,1,10,8,9]=>001111001=>100111100
[9,4,2,6,3,8,5,7,1,10]=>001011110=>011110100
[1,4,2,6,3,8,5,10,7,9]=>001010101=>101010100
[1,4,2,6,3,10,9,5,7,8]=>001010011=>110010100
[9,4,2,8,7,3,5,6,1,10]=>001011110=>011110100
[1,4,2,8,7,3,5,10,6,9]=>001001101=>101100100
[1,4,2,10,7,3,9,5,6,8]=>001001011=>110100100
[1,4,2,10,9,8,3,5,6,7]=>001000111=>111000100
[7,6,5,2,3,4,9,8,1,10]=>000111110=>011111000
[7,6,5,2,3,4,1,10,8,9]=>001111001=>100111100
[9,6,5,2,3,8,4,7,1,10]=>000111110=>011111000
[1,6,5,2,3,8,4,10,7,9]=>000110101=>101011000
[1,6,5,2,3,10,9,4,7,8]=>000110011=>110011000
[9,8,5,2,7,3,4,6,1,10]=>000111110=>011111000
[1,8,5,2,7,3,4,10,6,9]=>000101101=>101101000
[1,10,5,2,7,3,9,4,6,8]=>000101011=>110101000
[1,10,5,2,9,8,3,4,6,7]=>000100111=>111001000
[9,8,7,6,2,3,4,5,1,10]=>000111110=>011111000
[1,8,7,6,2,3,4,10,5,9]=>000011101=>101110000
[1,10,7,6,2,3,9,4,5,8]=>000011011=>110110000
[1,10,9,6,2,8,3,4,5,7]=>000010111=>111010000
[1,10,9,8,7,2,3,4,5,6]=>000001111=>111100000
[3,2,5,4,7,6,9,8,11,10,1,12]=>01010101110=>01110101010
[3,2,5,4,7,6,11,10,8,9,1,12]=>01010101110=>01110101010
[3,2,5,4,1,12,9,6,11,7,8,10]=>01110001011=>11010001110
[3,2,5,4,1,12,11,10,6,7,8,9]=>01110000111=>11100001110
[3,2,7,6,4,5,9,8,11,10,1,12]=>01001101110=>01110110010
[3,2,7,6,4,5,9,8,1,12,10,11]=>01001111001=>10011110010
[3,2,7,6,4,5,11,10,8,9,1,12]=>01001101110=>01110110010
[3,2,9,6,4,8,5,7,1,12,10,11]=>01001111001=>10011110010
[3,2,1,6,4,8,5,10,7,12,9,11]=>11001010101=>10101010011
[3,2,1,6,4,10,9,5,7,12,8,11]=>11001001101=>10110010011
[3,2,1,6,4,12,11,10,5,7,8,9]=>11001000111=>11100010011
[3,2,9,8,7,4,5,6,11,10,1,12]=>01000111110=>01111100010
[3,2,9,8,7,4,5,6,1,12,10,11]=>01001111001=>10011110010
[3,2,11,8,7,4,5,10,6,9,1,12]=>01000111110=>01111100010
[3,2,11,10,7,4,9,5,6,8,1,12]=>01000111110=>01111100010
[3,2,11,10,9,8,4,5,6,7,1,12]=>01000111110=>01111100010
[3,2,1,10,9,8,4,5,6,12,7,11]=>11000011101=>10111000011
[3,2,1,12,11,8,4,10,5,6,7,9]=>11000010111=>11101000011
[3,2,1,12,11,10,9,4,5,6,7,8]=>11000001111=>11110000011
[5,4,2,3,7,6,9,8,11,10,1,12]=>00110101110=>01110101100
[5,4,2,3,7,6,9,8,1,12,10,11]=>00110111001=>10011101100
[5,4,2,3,7,6,11,10,8,9,1,12]=>00110101110=>01110101100
[5,4,2,3,7,6,1,10,8,12,9,11]=>00111100101=>10100111100
[5,4,2,3,9,8,6,7,1,12,10,11]=>00110111001=>10011101100
[5,4,2,3,1,12,9,6,11,7,8,10]=>01110001011=>11010001110
[5,4,2,3,1,12,11,10,6,7,8,9]=>01110000111=>11100001110
[7,4,2,6,3,5,9,8,11,10,1,12]=>00101101110=>01110110100
[7,4,2,6,3,5,11,10,8,9,1,12]=>00101101110=>01110110100
[7,4,2,6,3,5,1,10,8,12,9,11]=>00111100101=>10100111100
[1,4,2,6,3,8,5,10,7,12,9,11]=>00101010101=>10101010100
[1,4,2,6,3,8,5,12,11,7,9,10]=>00101010011=>11001010100
[1,4,2,6,3,10,9,5,7,12,8,11]=>00101001101=>10110010100
[1,4,2,6,3,12,9,5,11,7,8,10]=>00101001011=>11010010100
[1,4,2,6,3,12,11,10,5,7,8,9]=>00101000111=>11100010100
[1,4,2,8,7,3,5,10,6,12,9,11]=>00100110101=>10101100100
[1,4,2,8,7,3,5,12,11,6,9,10]=>00100110011=>11001100100
[1,4,2,10,7,3,9,5,6,12,8,11]=>00100101101=>10110100100
[1,4,2,12,7,3,9,5,11,6,8,10]=>00100101011=>11010100100
[1,4,2,12,7,3,11,10,5,6,8,9]=>00100100111=>11100100100
[1,4,2,10,9,8,3,5,6,12,7,11]=>00100011101=>10111000100
[1,4,2,12,9,8,3,5,11,6,7,10]=>00100011011=>11011000100
[1,4,2,12,11,8,3,10,5,6,7,9]=>00100010111=>11101000100
[1,4,2,12,11,10,9,3,5,6,7,8]=>00100001111=>11110000100
[7,6,5,2,3,4,9,8,11,10,1,12]=>00011101110=>01110111000
[7,6,5,2,3,4,9,8,1,12,10,11]=>00011111001=>10011111000
[7,6,5,2,3,4,11,10,8,9,1,12]=>00011101110=>01110111000
[7,6,5,2,3,4,1,10,8,12,9,11]=>00111100101=>10100111100
[9,6,5,2,3,8,4,7,11,10,1,12]=>00011011110=>01111011000
[9,6,5,2,3,8,4,7,1,12,10,11]=>00011111001=>10011111000
[11,6,5,2,3,8,4,10,7,9,1,12]=>00011011110=>01111011000
[1,6,5,2,3,8,4,10,7,12,9,11]=>00011010101=>10101011000
[1,6,5,2,3,8,4,12,11,7,9,10]=>00011010011=>11001011000
[11,6,5,2,3,10,9,4,7,8,1,12]=>00011011110=>01111011000
[1,6,5,2,3,10,9,4,7,12,8,11]=>00011001101=>10110011000
[1,6,5,2,3,12,9,4,11,7,8,10]=>00011001011=>11010011000
[1,6,5,2,3,12,11,10,4,7,8,9]=>00011000111=>11100011000
[9,8,5,2,7,3,4,6,11,10,1,12]=>00010111110=>01111101000
[9,8,5,2,7,3,4,6,1,12,10,11]=>00011111001=>10011111000
[11,8,5,2,7,3,4,10,6,9,1,12]=>00010111110=>01111101000
[1,8,5,2,7,3,4,10,6,12,9,11]=>00010110101=>10101101000
[1,8,5,2,7,3,4,12,11,6,9,10]=>00010110011=>11001101000
[11,10,5,2,7,3,9,4,6,8,1,12]=>00010111110=>01111101000
[1,10,5,2,7,3,9,4,6,12,8,11]=>00010101101=>10110101000
[1,12,5,2,7,3,9,4,11,6,8,10]=>00010101011=>11010101000
[1,12,5,2,7,3,11,10,4,6,8,9]=>00010100111=>11100101000
[11,10,5,2,9,8,3,4,6,7,1,12]=>00010111110=>01111101000
[1,10,5,2,9,8,3,4,6,12,7,11]=>00010011101=>10111001000
[1,12,5,2,9,8,3,4,11,6,7,10]=>00010011011=>11011001000
[1,12,5,2,11,8,3,10,4,6,7,9]=>00010010111=>11101001000
[1,12,5,2,11,10,9,3,4,6,7,8]=>00010001111=>11110001000
[9,8,7,6,2,3,4,5,11,10,1,12]=>00001111110=>01111110000
[9,8,7,6,2,3,4,5,1,12,10,11]=>00011111001=>10011111000
[11,8,7,6,2,3,4,10,5,9,1,12]=>00001111110=>01111110000
[1,8,7,6,2,3,4,10,5,12,9,11]=>00001110101=>10101110000
[1,8,7,6,2,3,4,12,11,5,9,10]=>00001110011=>11001110000
[11,10,7,6,2,3,9,4,5,8,1,12]=>00001111110=>01111110000
[1,10,7,6,2,3,9,4,5,12,8,11]=>00001101101=>10110110000
[1,12,7,6,2,3,9,4,11,5,8,10]=>00001101011=>11010110000
[1,12,7,6,2,3,11,10,4,5,8,9]=>00001100111=>11100110000
[11,10,9,6,2,8,3,4,5,7,1,12]=>00001111110=>01111110000
[1,10,9,6,2,8,3,4,5,12,7,11]=>00001011101=>10111010000
[1,12,9,6,2,8,3,4,11,5,7,10]=>00001011011=>11011010000
[1,12,11,6,2,8,3,10,4,5,7,9]=>00001010111=>11101010000
[1,12,11,6,2,10,9,3,4,5,7,8]=>00001001111=>11110010000
[11,10,9,8,7,2,3,4,5,6,1,12]=>00001111110=>01111110000
[1,10,9,8,7,2,3,4,5,12,6,11]=>00000111101=>10111100000
[1,12,9,8,7,2,3,4,11,5,6,10]=>00000111011=>11011100000
[1,12,11,8,7,2,3,10,4,5,6,9]=>00000110111=>11101100000
[1,12,11,10,7,2,9,3,4,5,6,8]=>00000101111=>11110100000
[1,12,11,10,9,8,2,3,4,5,6,7]=>00000011111=>11111000000
[1,4,8,2,3,6,5,7]=>0000101=>1010000
[1,4,6,7,3,5,2,8]=>0001010=>0101000
[1,4,8,2,6,7,5,3]=>0001011=>1101000
[1,7,3,2,4,5,6,8]=>0100010=>0100010
[1,7,3,2,4,5,8,6]=>0100011=>1100010
[1,6,4,3,2,5,7,8]=>0110100=>0010110
[4,2,6,5,3,1,7,8]=>0111100=>0011110
[5,2,1,6,8,7,4,3]=>1011011=>1101101
[1,3,5,8,6,2,7,4]=>0000111=>1110000
[2,3,8,4,1,7,6,5]=>0010111=>1110100
[3,7,8,5,4,2,6,1]=>0011101=>1011100
[8,3,2,7,5,6,1,4]=>0100111=>1110010
[1,3,8,5,7,4,2,6]=>0010011=>1100100
[1,2,3,7,5,4,6,8]=>0001010=>0101000
[1,4,2,8,6,3,5,7]=>0010101=>1010100
[2,8,6,3,5,7,4,1]=>0010111=>1110100
[6,1,8,2,5,3,4,7]=>0001101=>1011000
[3,8,6,4,2,7,1,5]=>0010111=>1110100
[1,5,4,2,3,6,8,7]=>0011001=>1001100
[6,1,5,2,3,4,8,7]=>0001101=>1011000
[6,5,2,1,7,3,4,8]=>1001110=>0111001
[3,1,2,4,8,6,7,5]=>0100011=>1100010
[3,1,2,5,8,7,4,6]=>0100011=>1100010
[6,5,2,1,8,4,7,3]=>1001111=>1111001
[5,6,2,4,3,8,1,7]=>0010101=>1010100
[3,7,5,2,8,1,4,6]=>0001011=>1101000
[5,1,4,7,3,2,8,6]=>0101011=>1101010
[4,1,5,8,6,2,3,7]=>0010101=>1010100
[5,4,8,6,3,7,1,2]=>0001111=>1111000
[6,5,2,3,1,8,7,4]=>0101111=>1111010
[6,4,7,5,3,8,1,2]=>0001111=>1111000
[5,7,4,8,3,1,6,2]=>0100111=>1110010
[3,1,4,7,5,2,8,6]=>0101011=>1101010
[4,3,5,1,8,7,2,6]=>0011011=>1101100
[2,5,3,6,1,8,4,7]=>0001101=>1011000
[2,5,6,8,3,1,7,4]=>0100011=>1100010
[7,1,4,5,3,6,2,8]=>0001110=>0111000
[1,7,2,4,5,3,6,8]=>0001010=>0101000
[1,7,4,5,3,2,6,8]=>0101010=>0101010
[1,6,4,7,3,5,2,8]=>0001110=>0111000
[3,5,6,4,8,2,1,7]=>1000101=>1010001
[1,6,4,7,5,2,3,8]=>0001110=>0111000
[1,5,2,6,7,4,3,8]=>0011010=>0101100
[8,5,6,1,4,3,7,2]=>0010111=>1110100
[2,5,4,7,8,3,1,6]=>0101001=>1001010
[6,4,5,8,2,3,1,7]=>0100101=>1010010
[8,6,1,3,2,5,7,4]=>0100111=>1110010
[7,5,8,1,4,6,3,2]=>0100111=>1110010
[4,2,6,7,8,1,5,3]=>0011001=>1001100
[3,4,6,7,8,1,5,2]=>0001001=>1001000
[4,7,3,8,5,1,6,2]=>0001111=>1111000
[4,3,2,7,5,8,1,6]=>0110011=>1100110
[4,8,5,3,2,6,1,7]=>0101101=>1011010
[2,8,4,5,3,6,1,7]=>0001101=>1011000
[8,1,5,3,2,4,7,6]=>0101011=>1101010
[7,8,4,1,3,6,5,2]=>0011101=>1011100
[8,6,1,3,2,7,4,5]=>0100111=>1110010
[7,3,8,2,4,1,6,5]=>0010111=>1110100
[6,2,3,7,8,1,5,4]=>0001101=>1011000
[6,3,7,8,1,5,4,2]=>0011101=>1011100
[2,6,3,7,8,1,5,4]=>0001101=>1011000
[7,5,8,1,6,4,2,3]=>0010111=>1110100
[8,1,4,3,7,5,6,2]=>0010111=>1110100
[1,4,8,5,3,2,6,7]=>0101001=>1001010
[8,2,7,6,4,1,5,3]=>0011111=>1111100
[2,7,4,3,8,5,1,6]=>0011011=>1101100
[6,8,2,7,3,1,5,4]=>0101011=>1101010
[8,2,6,3,4,1,7,5]=>0010111=>1110100
[6,1,2,8,5,3,7,4]=>0001111=>1111000
[4,1,5,8,3,6,7,2]=>0010011=>1100100
[7,5,2,8,1,6,3,4]=>0001111=>1111000
[4,8,5,7,1,3,2,6]=>0100011=>1100010
[3,4,7,2,1,5,8,6]=>1000011=>1100001
[4,8,2,7,1,3,6,5]=>0000111=>1110000
[5,2,1,8,7,4,6,3]=>1001111=>1111001
[8,2,1,7,4,6,3,5]=>1000111=>1110001
[4,2,5,8,3,6,7,1]=>0010011=>1100100
[5,1,6,8,3,2,7,4]=>0101011=>1101010
[4,1,5,6,8,2,7,3]=>0010011=>1100100
[5,7,8,2,4,1,3,6]=>0010001=>1000100
[4,5,2,8,7,3,1,6]=>0101011=>1101010
[4,8,5,3,1,6,7,2]=>0101011=>1101010
[6,2,3,1,7,8,5,4]=>0101101=>1011010
[5,2,3,6,8,4,7,1]=>0001011=>1101000
[6,2,1,7,8,4,3,5]=>1010101=>1010101
[5,2,1,3,8,4,7,6]=>1001011=>1101001
[5,2,7,8,4,1,6,3]=>0011101=>1011100
[6,2,7,8,3,5,4,1]=>0011101=>1011100
[5,2,8,6,4,1,7,3]=>0011111=>1111100
[5,1,2,8,4,3,7,6]=>0011011=>1101100
[6,7,8,3,2,5,4,1]=>0111001=>1001110
[5,7,2,6,4,8,1,3]=>0000111=>1110000
[6,2,3,4,7,8,5,1]=>0001101=>1011000
[7,2,1,8,4,3,5,6]=>1010011=>1100101
[6,2,1,3,7,5,8,4]=>1000111=>1110001
[6,8,7,3,4,5,1,2]=>0001011=>1101000
[6,2,3,7,8,1,4,5]=>0000101=>1010000
[7,4,3,2,5,8,1,6]=>0110011=>1100110
[7,2,4,3,5,8,1,6]=>0010011=>1100100
[1,7,6,4,2,3,5,8]=>0010110=>0110100
[1,3,2,5,8,6,4,7]=>0100101=>1010010
[6,1,4,7,2,8,5,3]=>0001111=>1111000
[1,7,5,8,4,2,3,6]=>0010011=>1100100
[1,6,7,2,4,8,5,3]=>0001011=>1101000
[5,7,2,4,3,6,8,1]=>0010011=>1100100
[5,7,3,4,6,2,8,1]=>0000111=>1110000
[2,8,3,6,1,7,4,5]=>0000111=>1110000
[4,3,1,8,5,2,6,7]=>0111001=>1001110
[1,8,4,5,6,2,7,3]=>0000111=>1110000
[7,3,8,2,1,4,5,6]=>1000011=>1100001
[8,2,5,3,1,7,4,6]=>0101011=>1101010
[6,3,5,8,1,7,4,2]=>0010111=>1110100
[3,5,4,8,6,1,7,2]=>0001111=>1111000
[7,5,2,3,8,4,6,1]=>0001111=>1111000
[2,7,5,1,4,8,3,6]=>0001011=>1101000
[5,7,6,1,2,8,3,4]=>0000111=>1110000
[7,4,6,5,1,8,2,3]=>0001111=>1111000
[7,1,3,2,6,8,4,5]=>0100011=>1100010
[4,3,5,2,8,1,6,7]=>0011001=>1001100
[1,7,3,8,2,4,6,5]=>0000111=>1110000
[2,7,4,8,5,3,1,6]=>0101011=>1101010
[6,1,3,8,4,2,7,5]=>0010111=>1110100
[5,4,1,8,6,2,7,3]=>0011111=>1111100
[5,4,6,8,1,3,2,7]=>0101001=>1001010
[3,6,1,5,8,4,7,2]=>0000111=>1110000
[6,4,8,3,5,7,2,1]=>1000111=>1110001
[3,5,8,2,4,1,7,6]=>0010011=>1100100
[7,2,8,4,1,3,6,5]=>0010111=>1110100
[5,8,1,2,4,3,6,7]=>0010001=>1000100
[8,4,3,5,7,2,6,1]=>0010111=>1110100
[4,1,5,2,3,8,7,6]=>0011011=>1101100
[6,3,5,8,2,4,7,1]=>0000111=>1110000
[2,8,7,1,4,6,3,5]=>0000111=>1110000
[1,8,5,3,7,4,2,6]=>0011011=>1101100
[7,5,6,2,8,4,3,1]=>0110111=>1110110
[5,7,6,2,8,1,4,3]=>0010111=>1110100
[6,3,8,1,2,5,4,7]=>0001101=>1011000
[7,6,4,8,5,3,2,1]=>1101111=>1111011
[7,6,5,3,8,4,2,1]=>1011111=>1111101
[7,6,5,4,2,8,3,1]=>0111111=>1111110
[8,6,9,7,5,4,3,2,1]=>11110111=>11101111
[7,5,4,8,6,3,2,1]=>1101111=>1111011
[8,7,5,9,6,4,3,2,1]=>11101111=>11110111
[8,7,6,4,9,5,3,2,1]=>11011111=>11111011
[7,6,5,3,2,8,4,1]=>0111111=>1111110
[8,7,6,5,3,9,4,2,1]=>10111111=>11111101
[8,7,6,5,4,2,9,3,1]=>01111111=>11111110
[3,2,5,4,7,6,1,10,9,8]=>010111011=>110111010
[3,2,5,4,9,8,7,6,1,10]=>010111110=>011111010
[3,2,5,4,1,8,7,10,9,6]=>011100111=>111001110
[3,2,5,4,1,10,9,8,7,6]=>011101111=>111101110
[3,2,7,6,5,4,9,8,1,10]=>010111110=>011111010
[3,2,7,6,5,4,1,10,9,8]=>011111011=>110111110
[3,2,9,6,5,8,7,4,1,10]=>011011110=>011110110
[3,2,1,6,5,8,7,10,9,4]=>110010111=>111010011
[3,2,1,6,5,10,9,8,7,4]=>110011111=>111110011
[3,2,1,8,7,6,5,10,9,4]=>110011111=>111110011
[3,2,1,10,7,6,9,8,5,4]=>110101111=>111101011
[5,4,3,2,7,6,9,8,1,10]=>011101110=>011101110
[5,4,3,2,7,6,1,10,9,8]=>011111011=>110111110
[5,4,3,2,9,8,7,6,1,10]=>011111110=>011111110
[5,4,3,2,1,8,7,10,9,6]=>111100111=>111001111
[7,4,3,6,5,2,9,8,1,10]=>001111110=>011111100
[7,4,3,6,5,2,1,10,9,8]=>101111011=>110111101
[9,4,3,6,5,8,7,2,1,10]=>101011110=>011110101
[1,4,3,6,5,8,7,10,9,2]=>001010111=>111010100
[1,4,3,6,5,10,9,8,7,2]=>001011111=>111110100
[9,4,3,8,7,6,5,2,1,10]=>101111110=>011111101
[1,4,3,8,7,6,5,10,9,2]=>001011111=>111110100
[1,4,3,10,7,6,9,8,5,2]=>001101111=>111101100
[1,4,3,10,9,8,7,6,5,2]=>001111111=>111111100
[7,6,5,4,3,2,9,8,1,10]=>011111110=>011111110
[9,6,5,4,3,8,7,2,1,10]=>101111110=>011111101
[1,6,5,4,3,8,7,10,9,2]=>001110111=>111011100
[1,6,5,4,3,10,9,8,7,2]=>001111111=>111111100
[9,8,5,4,7,6,3,2,1,10]=>110111110=>011111011
[1,8,5,4,7,6,3,10,9,2]=>000111111=>111111000
[1,10,5,4,7,6,9,8,3,2]=>010101111=>111101010
[1,10,5,4,9,8,7,6,3,2]=>010111111=>111111010
[1,10,7,6,5,4,9,8,3,2]=>010111111=>111111010
[1,10,9,6,5,8,7,4,3,2]=>011011111=>111110110
[3,2,5,4,7,6,9,8,1,12,11,10]=>01010111011=>11011101010
[3,2,5,4,7,6,1,12,11,10,9,8]=>01011101111=>11110111010
[3,2,5,4,9,8,7,6,1,12,11,10]=>01011111011=>11011111010
[3,2,5,4,11,8,7,10,9,6,1,12]=>01011011110=>01111011010
[3,2,5,4,1,8,7,10,9,12,11,6]=>01110010111=>11101001110
[3,2,5,4,11,10,9,8,7,6,1,12]=>01011111110=>01111111010
[3,2,5,4,1,12,9,8,11,10,7,6]=>01110101111=>11110101110
[3,2,5,4,1,12,11,10,9,8,7,6]=>01110111111=>11111101110
[3,2,7,6,5,4,9,8,11,10,1,12]=>01011101110=>01110111010
[3,2,7,6,5,4,9,8,1,12,11,10]=>01011111011=>11011111010
[3,2,7,6,5,4,11,10,9,8,1,12]=>01011111110=>01111111010
[3,2,7,6,5,4,1,12,11,10,9,8]=>01111101111=>11110111110
[3,2,9,6,5,8,7,4,1,12,11,10]=>01101111011=>11011110110
[3,2,11,6,5,8,7,10,9,4,1,12]=>01101011110=>01111010110
[3,2,11,6,5,10,9,8,7,4,1,12]=>01101111110=>01111110110
[3,2,1,6,5,12,11,10,9,8,7,4]=>11001111111=>11111110011
[3,2,9,8,7,6,5,4,11,10,1,12]=>01011111110=>01111111010
[3,2,9,8,7,6,5,4,1,12,11,10]=>01111111011=>11011111110
[3,2,11,8,7,6,5,10,9,4,1,12]=>01101111110=>01111110110
[3,2,1,8,7,6,5,10,9,12,11,4]=>11001110111=>11101110011
[3,2,1,8,7,6,5,12,11,10,9,4]=>11001111111=>11111110011
[3,2,11,10,7,6,9,8,5,4,1,12]=>01110111110=>01111101110
[3,2,1,10,7,6,9,8,5,12,11,4]=>11000111111=>11111100011
[3,2,1,12,7,6,9,8,11,10,5,4]=>11010101111=>11110101011
[3,2,1,12,7,6,11,10,9,8,5,4]=>11010111111=>11111101011
[3,2,11,10,9,8,7,6,5,4,1,12]=>01111111110=>01111111110
[3,2,1,10,9,8,7,6,5,12,11,4]=>11001111111=>11111110011
[3,2,1,12,9,8,7,6,11,10,5,4]=>11010111111=>11111101011
[3,2,1,12,11,8,7,10,9,6,5,4]=>11011011111=>11111011011
[3,2,1,12,11,10,9,8,7,6,5,4]=>11011111111=>11111111011
[5,4,3,2,7,6,9,8,11,10,1,12]=>01110101110=>01110101110
[5,4,3,2,7,6,9,8,1,12,11,10]=>01110111011=>11011101110
[5,4,3,2,7,6,11,10,9,8,1,12]=>01110111110=>01111101110
[5,4,3,2,7,6,1,12,11,10,9,8]=>01111101111=>11110111110
[5,4,3,2,9,8,7,6,11,10,1,12]=>01110111110=>01111101110
[5,4,3,2,9,8,7,6,1,12,11,10]=>01111111011=>11011111110
[5,4,3,2,11,8,7,10,9,6,1,12]=>01111011110=>01111011110
[5,4,3,2,1,8,7,10,9,12,11,6]=>11110010111=>11101001111
[5,4,3,2,1,8,7,12,11,10,9,6]=>11110011111=>11111001111
[5,4,3,2,11,10,9,8,7,6,1,12]=>01111111110=>01111111110
[5,4,3,2,1,10,9,8,7,12,11,6]=>11110011111=>11111001111
[5,4,3,2,1,12,9,8,11,10,7,6]=>11110101111=>11110101111
[5,4,3,2,1,12,11,10,9,8,7,6]=>11110111111=>11111101111
[7,4,3,6,5,2,9,8,11,10,1,12]=>00111101110=>01110111100
[7,4,3,6,5,2,11,10,9,8,1,12]=>00111111110=>01111111100
[7,4,3,6,5,2,1,10,9,12,11,8]=>10111100111=>11100111101
[7,4,3,6,5,2,1,12,11,10,9,8]=>10111101111=>11110111101
[9,4,3,6,5,8,7,2,11,10,1,12]=>00101111110=>01111110100
[9,4,3,6,5,8,7,2,1,12,11,10]=>10101111011=>11011110101
[11,4,3,6,5,8,7,10,9,2,1,12]=>10101011110=>01111010101
[1,4,3,6,5,8,7,10,9,12,11,2]=>00101010111=>11101010100
[1,4,3,6,5,8,7,12,11,10,9,2]=>00101011111=>11111010100
[11,4,3,6,5,10,9,8,7,2,1,12]=>10101111110=>01111110101
[1,4,3,6,5,10,9,8,7,12,11,2]=>00101011111=>11111010100
[1,4,3,6,5,12,11,10,9,8,7,2]=>00101111111=>11111110100
[9,4,3,8,7,6,5,2,11,10,1,12]=>00111111110=>01111111100
[9,4,3,8,7,6,5,2,1,12,11,10]=>10111111011=>11011111101
[11,4,3,8,7,6,5,10,9,2,1,12]=>10101111110=>01111110101
[1,4,3,8,7,6,5,10,9,12,11,2]=>00101110111=>11101110100
[1,4,3,8,7,6,5,12,11,10,9,2]=>00101111111=>11111110100
[11,4,3,10,7,6,9,8,5,2,1,12]=>10110111110=>01111101101
[1,4,3,10,7,6,9,8,5,12,11,2]=>00100111111=>11111100100
[1,4,3,12,7,6,11,10,9,8,5,2]=>00110111111=>11111101100
[11,4,3,10,9,8,7,6,5,2,1,12]=>10111111110=>01111111101
[1,4,3,10,9,8,7,6,5,12,11,2]=>00101111111=>11111110100
[1,4,3,12,9,8,7,6,11,10,5,2]=>00110111111=>11111101100
[1,4,3,12,11,8,7,10,9,6,5,2]=>00111011111=>11111011100
[1,4,3,12,11,10,9,8,7,6,5,2]=>00111111111=>11111111100
[7,6,5,4,3,2,9,8,11,10,1,12]=>01111101110=>01110111110
[7,6,5,4,3,2,9,8,1,12,11,10]=>01111111011=>11011111110
[7,6,5,4,3,2,11,10,9,8,1,12]=>01111111110=>01111111110
[7,6,5,4,3,2,1,10,9,12,11,8]=>11111100111=>11100111111
[7,6,5,4,3,2,1,12,11,10,9,8]=>11111101111=>11110111111
[9,6,5,4,3,8,7,2,11,10,1,12]=>00111111110=>01111111100
[9,6,5,4,3,8,7,2,1,12,11,10]=>10111111011=>11011111101
[11,6,5,4,3,8,7,10,9,2,1,12]=>10111011110=>01111011101
[1,6,5,4,3,8,7,10,9,12,11,2]=>00111010111=>11101011100
[1,6,5,4,3,8,7,12,11,10,9,2]=>00111011111=>11111011100
[11,6,5,4,3,10,9,8,7,2,1,12]=>10111111110=>01111111101
[1,6,5,4,3,10,9,8,7,12,11,2]=>00111011111=>11111011100
[1,6,5,4,3,12,9,8,11,10,7,2]=>00111101111=>11110111100
[1,6,5,4,3,12,11,10,9,8,7,2]=>00111111111=>11111111100
[9,8,5,4,7,6,3,2,11,10,1,12]=>01011111110=>01111111010
[9,8,5,4,7,6,3,2,1,12,11,10]=>11011111011=>11011111011
[11,8,5,4,7,6,3,10,9,2,1,12]=>10011111110=>01111111001
[1,8,5,4,7,6,3,10,9,12,11,2]=>00011110111=>11101111000
[1,8,5,4,7,6,3,12,11,10,9,2]=>00011111111=>11111111000
[11,10,5,4,7,6,9,8,3,2,1,12]=>11010111110=>01111101011
[1,10,5,4,7,6,9,8,3,12,11,2]=>00010111111=>11111101000
[1,12,5,4,7,6,9,8,11,10,3,2]=>01010101111=>11110101010
[1,12,5,4,7,6,11,10,9,8,3,2]=>01010111111=>11111101010
[11,10,5,4,9,8,7,6,3,2,1,12]=>11011111110=>01111111011
[1,10,5,4,9,8,7,6,3,12,11,2]=>00011111111=>11111111000
[1,12,5,4,9,8,7,6,11,10,3,2]=>01010111111=>11111101010
[1,12,5,4,11,8,7,10,9,6,3,2]=>01011011111=>11111011010
[1,12,5,4,11,10,9,8,7,6,3,2]=>01011111111=>11111111010
[9,8,7,6,5,4,3,2,11,10,1,12]=>01111111110=>01111111110
[9,8,7,6,5,4,3,2,1,12,11,10]=>11111111011=>11011111111
[11,8,7,6,5,4,3,10,9,2,1,12]=>10111111110=>01111111101
[1,8,7,6,5,4,3,10,9,12,11,2]=>00111110111=>11101111100
[1,8,7,6,5,4,3,12,11,10,9,2]=>00111111111=>11111111100
[11,10,7,6,5,4,9,8,3,2,1,12]=>11011111110=>01111111011
[1,10,7,6,5,4,9,8,3,12,11,2]=>00011111111=>11111111000
[1,12,7,6,5,4,9,8,11,10,3,2]=>01011101111=>11110111010
[1,12,7,6,5,4,11,10,9,8,3,2]=>01011111111=>11111111010
[11,10,9,6,5,8,7,4,3,2,1,12]=>11101111110=>01111110111
[1,10,9,6,5,8,7,4,3,12,11,2]=>00101111111=>11111110100
[1,12,9,6,5,8,7,4,11,10,3,2]=>01001111111=>11111110010
[1,12,11,6,5,8,7,10,9,4,3,2]=>01101011111=>11111010110
[1,12,11,6,5,10,9,8,7,4,3,2]=>01101111111=>11111110110
[11,10,9,8,7,6,5,4,3,2,1,12]=>11111111110=>01111111111
[1,10,9,8,7,6,5,4,3,12,11,2]=>00111111111=>11111111100
[1,12,9,8,7,6,5,4,11,10,3,2]=>01011111111=>11111111010
[1,12,11,8,7,6,5,10,9,4,3,2]=>01101111111=>11111110110
[1,12,11,10,7,6,9,8,5,4,3,2]=>01110111111=>11111101110
[1,12,11,10,9,8,7,6,5,4,3,2]=>01111111111=>11111111110
[1,5,7,2,4,3,6,8]=>0010010=>0100100
[1,6,5,3,2,4,7,8]=>0101100=>0011010
[1,7,2,4,6,5,3,8]=>0001110=>0111000
[1,4,7,2,6,5,3,8]=>0001110=>0111000
[1,2,6,8,7,4,3,5]=>0010011=>1100100
[1,2,7,4,3,5,8,6]=>0010011=>1100100
[1,6,2,8,7,4,3,5]=>0010111=>1110100
[1,7,4,2,3,5,8,6]=>0010011=>1100100
[1,8,5,2,3,6,4,7]=>0001101=>1011000
[1,7,4,8,5,2,3,6]=>0001011=>1101000
[1,4,7,5,2,8,6,3]=>0001111=>1111000
[1,6,3,7,4,2,8,5]=>0010111=>1110100
[1,8,5,2,7,4,3,6]=>0011011=>1101100
[1,4,8,7,5,3,2,6]=>0101011=>1101010
[1,2,5,8,6,3,7,4]=>0000111=>1110000
[1,2,4,7,5,8,6,3]=>0000111=>1110000
[1,5,8,7,6,2,4,3]=>0010111=>1110100
[1,3,5,8,7,6,2,4]=>0000111=>1110000
[1,5,2,4,3,6,8,7]=>0011001=>1001100
[1,6,8,7,5,3,2,4]=>0101011=>1101010
[1,2,5,7,4,3,8,6]=>0010011=>1100100
[1,5,3,2,6,8,7,4]=>0101011=>1101010
[1,4,2,6,8,7,5,3]=>0011011=>1101100
[1,5,8,6,3,2,7,4]=>0100111=>1110010
[1,8,5,2,6,3,4,7]=>0001101=>1011000
[1,7,4,6,3,2,8,5]=>0100111=>1110010
[1,6,3,2,8,5,4,7]=>0101101=>1011010
[1,3,8,6,4,2,5,7]=>0010101=>1010100
[1,5,7,4,2,3,8,6]=>0010011=>1100100
[6,3,7,5,4,2,8,1]=>0011111=>1111100
[7,5,2,6,3,4,8,1]=>0001111=>1111000
[3,8,2,7,5,4,1,6]=>0011011=>1101100
[5,4,8,6,7,1,2,3]=>0001011=>1101000
[2,7,3,6,8,5,4,1]=>0011011=>1101100
[3,7,2,8,1,6,4,5]=>0000111=>1110000
[8,5,2,4,6,7,3,1]=>0101011=>1101010
[2,5,8,7,1,4,3,6]=>0010011=>1100100
[3,4,6,5,8,2,7,1]=>0000111=>1110000
[5,2,4,1,6,7,8,3]=>0011001=>1001100
[4,2,7,1,6,8,3,5]=>0010011=>1100100
[5,2,8,6,4,7,1,3]=>0001111=>1111000
[6,1,3,4,7,2,8,5]=>0000111=>1110000
[8,4,7,2,5,3,1,6]=>0101011=>1101010
[8,3,4,5,2,1,7,6]=>1001011=>1101001
[8,6,1,4,7,3,5,2]=>0001111=>1111000
[5,3,6,7,2,8,4,1]=>0011011=>1101100
[5,3,6,7,2,4,8,1]=>0001011=>1101000
[8,6,4,2,7,1,5,3]=>0011111=>1111100
[8,6,1,4,7,5,2,3]=>0001111=>1111000
[1,5,8,2,6,7,4,3]=>0010011=>1100100
[7,1,3,6,5,2,8,4]=>0001111=>1111000
[8,2,1,4,5,7,6,3]=>1000111=>1110001
[1,4,7,5,2,3,8,6]=>0001011=>1101000
[6,1,7,5,4,2,8,3]=>0011111=>1111100
[2,7,3,6,5,1,8,4]=>0001111=>1111000
[8,6,5,1,3,7,4,2]=>0011111=>1111100
[5,7,6,2,4,8,1,3]=>0000111=>1110000
[3,7,5,6,4,8,1,2]=>0000111=>1110000
[7,6,8,1,3,5,4,2]=>0011011=>1101100
[2,8,4,6,1,7,5,3]=>0001111=>1111000
[2,8,6,4,7,3,5,1]=>0001111=>1111000
[8,7,1,4,6,5,3,2]=>0101111=>1111010
[3,5,8,6,7,1,4,2]=>0010011=>1100100
[1,2,4,6,8,5,3,7]=>0001001=>1001000
[3,1,5,8,6,2,4,7]=>0100101=>1010010
[2,5,4,6,8,1,3,7]=>0001001=>1001000
[6,5,2,4,7,8,1,3]=>0001101=>1011000
[7,2,5,8,6,4,1,3]=>0010111=>1110100
[5,2,8,3,4,7,6,1]=>0001111=>1111000
[2,4,3,8,7,1,6,5]=>0010111=>1110100
[1,5,8,7,4,2,6,3]=>0010111=>1110100
[6,8,7,5,4,3,1,2]=>0111011=>1101110
[5,6,4,7,3,8,2,9,1]=>00001111=>11110000
[5,6,4,7,3,9,2,8,1]=>00001111=>11110000
[5,3,4,8,6,2,7,1]=>0001111=>1111000
[5,4,6,3,7,2,8,1,9]=>00011110=>01111000
[6,5,7,4,8,3,9,2,10,1]=>000011111=>111110000
[6,5,7,4,8,3,10,2,9,1]=>000011111=>111110000
[3,4,5,8,6,2,7,1]=>0000111=>1110000
[5,6,4,7,3,8,2,9,1,10]=>000011110=>011110000
[5,4,2,3,6,1,8,7]=>0011101=>1011100
[5,1,7,4,3,6,8,2]=>0011011=>1101100
[4,3,7,6,8,2,1,5]=>1010011=>1100101
[8,1,4,7,2,3,5,6]=>0000011=>1100000
[6,1,8,5,2,7,3,4]=>0001111=>1111000
[8,7,2,6,3,1,4,5]=>0100111=>1110010
[8,7,1,6,4,5,2,3]=>0001111=>1111000
[5,4,1,3,7,2,8,6]=>0011011=>1101100
[8,3,4,7,6,2,1,5]=>1000111=>1110001
[3,1,8,7,5,2,4,6]=>0101011=>1101010
[6,5,8,7,2,4,3,1]=>0110111=>1110110
[4,3,6,5,8,2,1,7]=>1010101=>1010101
[7,6,3,2,8,5,4,1]=>0111111=>1111110
[3,2,6,8,7,1,4,5]=>0100011=>1100010
[4,3,7,1,8,5,2,6]=>0011011=>1101100
[3,2,8,5,6,7,1,4]=>0100011=>1100010
[8,3,2,1,4,7,5,6]=>1100011=>1100011
[4,7,3,1,8,5,2,6]=>0101011=>1101010
[7,5,1,4,2,3,6,8]=>0011010=>0101100
[7,8,6,1,2,4,5,3]=>0001101=>1011000
[1,5,3,4,7,8,6,2]=>0001101=>1011000
[5,1,2,4,7,8,6,3]=>0001101=>1011000
[5,1,7,8,6,2,3,4]=>0001101=>1011000
[8,5,1,6,7,2,3,4]=>0001011=>1101000
[7,5,1,2,4,6,8,3]=>0001011=>1101000
[6,1,5,2,7,3,4,8]=>0001110=>0111000
[7,1,2,6,4,5,8,3]=>0000111=>1110000
[1,7,3,6,4,5,8,2]=>0000111=>1110000
[1,8,3,6,4,5,7,2]=>0000111=>1110000
[8,1,6,2,7,3,4,5]=>0000111=>1110000
[7,1,6,2,5,3,4,8]=>0001110=>0111000
[8,1,6,2,5,3,4,7]=>0001101=>1011000
[8,1,7,2,5,3,4,6]=>0001011=>1101000
[8,1,2,7,4,5,6,3]=>0000111=>1110000
[1,8,3,7,4,5,6,2]=>0000111=>1110000
[8,1,6,7,5,2,3,4]=>0001011=>1101000
[7,3,1,2,6,4,5,8]=>0100110=>0110010
[3,1,2,8,5,6,7,4]=>0100011=>1100010
[6,3,1,2,7,4,5,8]=>0100110=>0110010
[6,1,7,4,2,3,5,8]=>0010110=>0110100
[1,7,3,4,6,8,5,2]=>0001011=>1101000
[1,7,3,8,4,5,6,2]=>0000111=>1110000
[7,1,8,2,5,3,4,6]=>0001011=>1101000
[6,1,7,2,5,3,4,8]=>0001110=>0111000
[5,1,7,2,6,3,4,8]=>0001110=>0111000
[5,1,8,2,6,3,4,7]=>0001101=>1011000
[1,6,3,7,4,5,8,2]=>0000111=>1110000
[2,4,7,3,5,1,6,8]=>0001010=>0101000
[2,4,8,6,3,5,1,7]=>0001101=>1011000
[2,3,7,5,4,1,6,8]=>0011010=>0101100
[3,4,6,2,1,5,8,7]=>1000101=>1010001
[3,4,7,2,1,6,5,8]=>1000110=>0110001
[2,6,8,3,5,1,4,7]=>0001001=>1001000
[2,3,6,1,5,8,4,7]=>0000101=>1010000
[2,3,7,1,6,5,8,4]=>0000111=>1110000
[2,4,7,1,3,6,8,5]=>0000011=>1100000
[5,4,7,8,1,3,2,6]=>0101001=>1001010
[2,5,7,1,4,6,3,8]=>0000110=>0110000
[2,4,7,1,6,3,5,8]=>0000110=>0110000
[2,3,7,1,6,5,4,8]=>0001110=>0111000
[2,5,7,1,4,3,6,8]=>0010010=>0100100
[2,5,7,3,1,4,6,8]=>0100010=>0100010
[3,4,7,2,1,6,8,5]=>1000011=>1100001
[4,6,3,7,1,5,2,8]=>0001110=>0111000
[5,7,3,2,8,1,4,6]=>0100011=>1100010
[2,6,5,7,1,8,4,3]=>0010111=>1110100
[3,6,8,5,4,1,7,2]=>0011011=>1101100
[5,4,7,8,1,3,6,2]=>0001101=>1011000
[2,5,7,1,4,6,8,3]=>0000011=>1100000
[2,4,7,1,6,3,8,5]=>0000111=>1110000
[2,4,7,1,6,8,3,5]=>0000011=>1100000
[2,4,8,3,1,7,6,5]=>0100111=>1110010
[1,8,3,4,5,6,7,9,2]=>00000011=>11000000
[7,2,3,4,5,6,1,9,8]=>00001101=>10110000
[2,1,9,4,5,6,7,8,3]=>10000011=>11000001
[2,8,3,4,5,6,7,1,9]=>00000110=>01100000
[8,6,5,1,2,4,3,7]=>0011101=>1011100
[7,6,1,4,2,3,5,8]=>0010110=>0110100
[6,5,1,4,8,3,2,7]=>0101101=>1011010
[8,7,1,4,3,2,5,6]=>0110011=>1100110
[8,7,5,1,4,2,3,6]=>0011011=>1101100
[8,4,1,2,5,3,6,7]=>0011001=>1001100
[8,7,5,1,4,2,6,3]=>0011111=>1111100
[8,6,1,4,2,5,3,7]=>0011101=>1011100
[8,7,1,4,3,2,6,5]=>0110111=>1110110
[8,7,6,3,1,5,4,2]=>0111111=>1111110
[2,8,3,7,4,5,6,1]=>0000111=>1110000
[8,7,5,2,4,3,6,1]=>0011111=>1111100
[2,9,1,8,7,6,5,4,3]=>00111111=>11111100
[2,9,8,1,7,6,5,4,3]=>00111111=>11111100
[4,2,5,7,3,1,6,8]=>0110010=>0100110
[8,2,4,5,3,1,6,7]=>0101001=>1001010
[8,4,5,1,3,2,6,7]=>0101001=>1001010
[4,3,7,5,2,1,6,8]=>1011010=>0101101
[1,6,7,4,3,2,5,8]=>0110010=>0100110
[1,4,5,7,3,2,6,8]=>0100010=>0100010
[3,5,1,4,7,2,6,8]=>0001010=>0101000
[2,5,1,4,7,8,3,6]=>0001001=>1001000
[4,3,7,1,5,2,6,8]=>0011010=>0101100
[3,5,1,6,4,2,7,8]=>0011100=>0011100
[6,4,3,1,7,2,5,8]=>0110110=>0110110
[6,2,7,4,3,1,5,8]=>0110110=>0110110
[2,6,4,1,7,3,5,8]=>0010110=>0110100
[6,3,2,7,4,5,1,8]=>0101110=>0111010
[7,2,4,1,3,6,8,5]=>0010011=>1100100
[6,3,2,5,7,1,4,8]=>0100110=>0110010
[3,2,6,5,7,1,4,8]=>0100110=>0110010
[1,7,3,2,5,6,4,8]=>0100110=>0110010
[2,1,7,3,5,6,8,4]=>1000011=>1100001
[2,1,6,3,5,7,8,4]=>1000101=>1010001
[1,6,3,2,5,7,4,8]=>0100110=>0110010
[1,4,6,5,2,7,3,8]=>0001110=>0111000
[5,6,2,1,4,3,7,8]=>1010100=>0010101
[2,5,1,6,4,3,7,8]=>0011100=>0011100
[2,5,4,1,6,3,7,8]=>0011100=>0011100
[4,6,1,5,2,7,3,8]=>0001110=>0111000
[1,6,5,3,7,2,4,8]=>0001110=>0111000
[1,2,5,4,7,3,6,8]=>0001010=>0101000
[1,2,5,3,4,8,7,6]=>0001011=>1101000
[5,2,7,6,1,8,4,3]=>0011111=>1111100
[5,8,2,6,1,7,4,3]=>0010111=>1110100
[1,7,8,2,4,6,5,3]=>0001101=>1011000
[1,5,8,3,6,2,7,4]=>0000111=>1110000
[6,8,7,1,4,5,2,3]=>0001011=>1101000
[1,2,6,4,7,3,8,5]=>0000111=>1110000
[1,2,7,8,3,5,6,4]=>0000101=>1010000
[4,8,7,6,2,1,5,3]=>1001111=>1111001
[2,7,4,5,8,1,6,3]=>0000111=>1110000
[2,6,1,8,5,4,3,7]=>0011101=>1011100
[5,8,6,2,3,4,1,7]=>0010101=>1010100
[5,8,6,2,1,4,3,7]=>1010101=>1010101
[4,5,8,6,2,1,3,7]=>1000101=>1010001
[6,4,7,5,8,2,1,3]=>1000111=>1110001
[6,3,7,4,2,5,8,1]=>0010111=>1110100
[6,2,1,5,8,4,3,7]=>1010101=>1010101
[7,5,6,2,4,3,8,1]=>0010111=>1110100
[4,6,2,5,7,3,8,1]=>0000111=>1110000
[4,2,8,5,3,6,1,7]=>0011101=>1011100
[8,1,7,4,5,6,2,3]=>0000111=>1110000
[2,1,7,8,4,5,6,3]=>1000101=>1010001
[8,2,1,4,3,7,6,5]=>1010111=>1110101
[7,6,5,3,1,2,8,4]=>0101111=>1111010
[5,4,1,6,2,8,3,7]=>0011101=>1011100
[6,2,3,1,7,8,4,5]=>0100101=>1010010
[3,1,8,6,7,2,4,5]=>0100011=>1100010
[4,2,5,1,8,6,7,3]=>0011011=>1101100
[4,5,3,7,1,6,8,2]=>0001011=>1101000
[4,2,8,5,3,6,7,1]=>0011011=>1101100
[2,8,6,3,5,4,7,1]=>0001111=>1111000
[3,5,2,8,6,4,7,1]=>0001111=>1111000
[7,3,5,1,6,4,8,2]=>0001111=>1111000
[5,1,4,7,2,6,8,3]=>0001011=>1101000
[1,8,2,5,6,4,7,3]=>0000111=>1110000
[2,7,1,4,8,5,6,3]=>0000111=>1110000
[2,8,4,6,1,3,7,5]=>0000111=>1110000
[8,4,6,2,5,3,7,1]=>0001111=>1111000
[8,3,7,6,2,1,5,4]=>1001111=>1111001
[8,5,2,7,6,1,4,3]=>0011111=>1111100
[5,8,2,7,6,1,4,3]=>0010111=>1110100
[8,3,7,6,2,5,1,4]=>0001111=>1111000
[7,3,8,6,5,1,4,2]=>0011111=>1111100
[9,8,7,6,1,2,3,4,5,10]=>000011110=>011110000
[2,6,3,7,5,4,8,1]=>0001111=>1111000
[5,4,7,1,3,8,6,2]=>0001111=>1111000
[2,8,5,1,4,7,3,6]=>0001011=>1101000
[8,1,4,2,5,7,3,6]=>0010011=>1100100
[7,2,6,5,8,4,3,1]=>0110111=>1110110
[3,4,8,5,6,2,7,1]=>0000111=>1110000
[5,8,2,3,4,6,1,7]=>0000101=>1010000
[6,1,3,4,2,5,7,8]=>0010100=>0010100
[1,5,6,3,2,4,7,8]=>0100100=>0010010
[6,3,5,2,4,1,7,8]=>0011100=>0011100
[7,8,3,5,2,4,6,1]=>0001101=>1011000
[2,4,5,7,3,6,1,8]=>0000110=>0110000
[2,5,3,1,6,4,7,8]=>0101100=>0011010
[6,5,1,3,4,2,7,8]=>0011100=>0011100
[5,7,4,3,2,6,1,8]=>0110110=>0110110
[6,8,7,4,3,5,1,2]=>0011011=>1101100
[2,6,7,8,4,3,5,1]=>0011001=>1001100
[1,7,8,4,5,3,6,2]=>0001101=>1011000
[7,1,8,5,3,4,6,2]=>0001111=>1111000
[5,7,4,2,1,6,3,8]=>1010110=>0110101
[5,1,4,7,3,6,2,8]=>0001110=>0111000
[7,4,8,6,3,5,2,1]=>1001111=>1111001
[4,7,6,3,5,2,1,8]=>1001110=>0111001
[1,6,5,8,7,4,2,3]=>0010111=>1110100
[6,1,3,8,7,5,2,4]=>0001111=>1111000
[7,6,2,1,8,3,5,4]=>1001111=>1111001
[7,1,3,6,8,2,5,4]=>0001011=>1101000
[1,7,5,6,8,2,4,3]=>0010011=>1100100
[3,6,7,5,8,2,4,1]=>0010011=>1100100
[1,7,4,5,2,8,6,3]=>0001111=>1111000
[7,5,4,2,1,8,6,3]=>1011111=>1111101
[3,6,7,4,2,8,5,1]=>0011011=>1101100
[4,6,3,2,7,8,5,1]=>0101101=>1011010
[7,6,1,3,4,2,5,8]=>0010110=>0110100
[7,8,2,6,4,5,3,1]=>0101101=>1011010
[7,2,5,4,6,1,3,8]=>0001110=>0111000
[7,1,2,4,5,6,3,8]=>0000110=>0110000
[7,3,2,1,5,6,4,8]=>1100110=>0110011
[3,6,2,1,7,5,4,8]=>1001110=>0111001
[2,6,7,3,1,5,4,8]=>0101010=>0101010
[2,1,6,4,7,5,3,8]=>1001110=>0111001
[7,2,8,5,6,4,3,1]=>0110111=>1110110
[7,6,8,5,4,1,3,2]=>0111011=>1101110
[7,1,8,4,6,5,3,2]=>0101111=>1111010
[7,8,6,3,1,5,4,2]=>0111101=>1011110
[7,6,1,4,5,3,2,8]=>0101110=>0111010
[7,1,5,6,4,3,2,8]=>0110110=>0110110
[4,1,3,8,6,2,7,5]=>0010111=>1110100
[5,1,2,8,4,6,7,3]=>0001011=>1101000
[5,6,3,2,8,1,7,4]=>0100111=>1110010
[8,2,6,3,1,5,7,4]=>0100111=>1110010
[8,2,5,6,7,4,3,1]=>0110011=>1100110
[8,2,5,3,4,7,6,1]=>0001111=>1111000
[7,5,3,2,4,1,8,6]=>0111011=>1101110
[7,1,2,3,6,8,4,5]=>0000011=>1100000
[6,7,2,8,3,4,5,1]=>0001011=>1101000
[3,1,8,4,6,5,7,2]=>0100111=>1110010
[6,1,2,3,8,4,7,5]=>0000111=>1110000
[8,1,6,7,4,2,3,5]=>0010011=>1100100
[8,1,6,4,5,2,3,7]=>0001101=>1011000
[8,6,4,7,2,3,5,1]=>0001111=>1111000
[8,6,4,1,2,3,7,5]=>0010111=>1110100
[8,6,1,4,2,5,7,3]=>0010111=>1110100
[8,6,7,4,2,5,1,3]=>0011011=>1101100
[8,6,4,2,5,3,7,1]=>0011111=>1111100
[8,6,4,2,5,3,1,7]=>0111101=>1011110
[8,6,4,2,7,3,1,5]=>0110111=>1110110
[8,6,4,1,5,7,2,3]=>0010111=>1110100
[8,6,4,2,1,5,7,3]=>1010111=>1110101
[8,6,4,2,1,7,3,5]=>1010111=>1110101
[8,6,1,4,7,2,5,3]=>0001111=>1111000
[8,6,4,1,5,2,3,7]=>0011101=>1011100
[8,6,7,1,4,5,2,3]=>0001011=>1101000
[8,6,4,5,2,7,3,1]=>0101111=>1111010
[8,6,7,4,2,1,5,3]=>1011011=>1101101
[8,6,4,7,2,1,5,3]=>1001111=>1111001
[8,6,4,2,5,7,3,1]=>0110111=>1110110
[8,6,4,2,5,1,7,3]=>0011111=>1111100
[8,6,4,2,5,7,1,3]=>0010111=>1110100
[3,4,7,5,8,2,6,1]=>0000111=>1110000
[8,7,1,4,6,5,2,3]=>0001111=>1111000
[8,3,7,6,4,5,1,2]=>0001111=>1111000
[5,3,8,6,4,1,7,2]=>0011111=>1111100
[8,10,1,2,3,4,5,9,6,7]=>000000011=>110000000
[10,8,1,9,2,3,4,5,6,7]=>000000111=>111000000
[8,7,1,2,3,4,5,9,10,6]=>000001101=>101100000
[10,11,1,9,2,3,4,5,6,7,8]=>0000000101=>1010000000
[6,1,2,3,4,5,7,8,9]=>00001000=>00010000
[5,1,2,3,4,6,7,8,9]=>00010000=>00001000
[4,1,2,3,5,6,7,8,9]=>00100000=>00000100
[2,10,1,5,6,7,8,9,3,4]=>000000011=>110000000
[2,3,4,5,6,7,8,9,10,11,12,1]=>00000000001=>10000000000
[7,4,5,1,2,8,6,3]=>0001111=>1111000
[6,4,7,1,8,5,2,3]=>0001111=>1111000
[5,7,4,2,3,8,6,1]=>0010111=>1110100
[3,8,2,5,1,7,4,6]=>0001011=>1101000
[5,8,4,2,3,7,1,6]=>0010011=>1100100
[4,8,5,2,1,7,3,6]=>1001011=>1101001
[8,5,7,6,1,2,4,3]=>0010111=>1110100
[6,8,7,5,2,4,1,3]=>0011011=>1101100
[5,7,6,8,4,1,3,2]=>0110011=>1100110
[7,3,1,6,8,5,4,2]=>0111011=>1101110
[5,3,1,7,4,8,6,2]=>0101111=>1111010
[7,3,1,8,6,4,5,2]=>0101111=>1111010
[8,6,4,1,7,3,2,5]=>0110111=>1110110
[4,6,8,3,7,1,2,5]=>0000011=>1100000
[3,5,2,8,4,7,1,6]=>0001011=>1101000
[6,4,8,3,7,2,1,5]=>1000111=>1110001
[3,6,2,8,7,4,1,5]=>0010111=>1110100
[6,8,4,2,7,3,1,5]=>0110011=>1100110
[9,8,2,3,4,5,6,7,1]=>00000111=>11100000
[8,9,2,3,4,5,6,7,1]=>00000101=>10100000
[9,8,7,6,4,5,3,2,1]=>11011111=>11111011
[5,6,7,9,8,4,3,2,1]=>11100011=>11000111
[5,6,7,8,9,1,4,3,2]=>01100001=>10000110
[10,9,2,3,4,5,6,7,8,1]=>000000111=>111000000
[3,4,7,8,5,1,2,6]=>0001001=>1001000
[4,7,3,2,5,6,8,1]=>0100011=>1100010
[3,2,7,6,4,5,8,1]=>0100111=>1110010
[1,7,3,6,8,4,2,5]=>0010011=>1100100
[2,3,6,5,1,8,7,4]=>0001111=>1111000
[8,3,1,2,6,4,7,5]=>0100111=>1110010
[1,7,8,2,4,3,5,6]=>0010001=>1000100
[3,6,4,7,1,2,8,5]=>0000111=>1110000
[5,7,4,8,1,3,2,6]=>0100011=>1100010
[4,3,7,8,1,5,2,6]=>0011001=>1001100
[8,5,4,2,6,1,7,3]=>0011111=>1111100
[3,2,6,8,7,4,1,5]=>0110011=>1100110
[2,3,7,5,1,8,6,4]=>0001111=>1111000
[6,3,1,2,8,7,4,5]=>0100111=>1110010
[5,2,1,3,8,7,6,4]=>1001111=>1111001
[7,2,1,5,3,8,4,6]=>1001011=>1101001
[1,5,8,2,4,3,6,7]=>0010001=>1000100
[4,3,6,8,1,5,2,7]=>0011001=>1001100
[5,4,6,8,3,1,7,2]=>0101011=>1101010
[3,6,8,4,5,1,7,2]=>0001011=>1101000
[8,6,1,7,2,4,3,5]=>0010111=>1110100
[7,3,1,2,8,6,4,5]=>0100111=>1110010
[2,3,7,6,1,8,5,4]=>0001111=>1111000
[3,2,7,8,6,4,1,5]=>0110101=>1010110
[6,2,8,3,1,4,7,5]=>0100111=>1110010
[3,1,2,8,7,4,5,6]=>0100011=>1100010
[2,1,3,8,7,4,6,5]=>1000111=>1110001
[2,1,3,8,7,4,5,6]=>1000011=>1100001
[1,6,8,3,2,4,7,5]=>0100011=>1100010
[8,5,1,7,2,4,3,6]=>0011011=>1101100
[8,4,1,7,3,2,5,6]=>0110011=>1100110
[8,3,1,6,2,7,5,4]=>0101111=>1111010
[1,3,2,8,7,6,4,5]=>0100111=>1110010
[2,1,3,8,7,6,4,5]=>1000111=>1110001
[2,4,3,1,6,5,8,7,10,9]=>011010101=>101010110
[1,6,3,7,2,5,4,8]=>0001110=>0111000
[1,7,2,4,6,3,5,8]=>0000110=>0110000
[5,7,2,8,4,1,3,6]=>0010011=>1100100
[5,6,2,8,4,1,3,7]=>0010101=>1010100
[2,4,8,3,1,6,7,5]=>0100011=>1100010
[3,5,8,4,2,1,6,7]=>1010001=>1000101
[2,5,8,3,1,4,6,7]=>0100001=>1000010
[2,8,1,3,5,7,4,6]=>0000011=>1100000
[5,4,7,8,3,2,6,1]=>0101101=>1011010
[3,4,8,5,7,1,2,6]=>0000011=>1100000
[3,6,8,2,5,1,4,7]=>0001001=>1001000
[3,6,8,7,2,5,4,1]=>0011011=>1101100
[3,4,6,5,8,2,1,7]=>1000101=>1010001
[2,4,6,7,8,3,5,1]=>0001001=>1001000
[1,4,2,5,7,6,3,8]=>0010110=>0110100
[1,4,2,6,8,5,3,7]=>0011001=>1001100
[1,2,6,8,3,5,4,7]=>0001001=>1001000
[1,6,8,3,5,4,2,7]=>0011001=>1001100
[1,5,3,2,4,6,8,7]=>0101001=>1001010
[1,5,8,7,6,3,2,4]=>0100111=>1110010
[1,5,7,6,3,2,4,8]=>0100110=>0110010
[1,6,3,2,4,7,5,8]=>0100110=>0110010
[1,6,3,2,4,8,7,5]=>0100111=>1110010
[1,2,7,6,4,3,5,8]=>0010110=>0110100
[1,8,7,5,2,4,6,3]=>0001111=>1111000
[1,7,5,2,4,6,3,8]=>0001110=>0111000
[1,7,4,2,5,3,6,8]=>0011010=>0101100
[1,8,4,7,5,2,6,3]=>0001111=>1111000
[1,7,5,2,3,6,4,8]=>0001110=>0111000
[1,7,5,2,6,3,4,8]=>0001110=>0111000
[1,6,3,7,4,2,5,8]=>0010110=>0110100
[1,6,3,2,7,5,4,8]=>0101110=>0111010
[1,4,7,5,2,6,3,8]=>0001110=>0111000
[1,3,6,4,8,7,5,2]=>0001111=>1111000
[1,3,7,6,4,2,5,8]=>0010110=>0110100
[1,3,2,4,8,5,7,6]=>0100011=>1100010
[1,3,8,7,5,2,4,6]=>0001011=>1101000
[1,4,6,3,2,7,5,8]=>0100110=>0110010
[1,4,6,3,2,8,7,5]=>0100111=>1110010
[1,5,7,6,4,2,3,8]=>0010110=>0110100
[1,6,3,2,8,4,7,5]=>0100111=>1110010
[1,6,3,5,2,7,4,8]=>0001110=>0111000
[1,6,3,5,2,8,7,4]=>0001111=>1111000
[1,8,3,7,5,2,4,6]=>0001011=>1101000
[7,8,4,9,5,2,10,6,3,1]=>010110111=>111011010
[6,4,7,1,5,3,8,2]=>0001111=>1111000
[5,3,8,2,6,4,7,1]=>0001111=>1111000
[4,3,8,2,6,5,7,1]=>0010111=>1110100
[2,6,1,8,3,4,7,5]=>0000111=>1110000
[5,7,1,4,8,2,3,6]=>0000011=>1100000
[6,5,7,1,4,3,8,2]=>0010111=>1110100
[4,8,3,5,7,6,1,2]=>0000111=>1110000
[5,7,6,1,2,4,8,3]=>0000111=>1110000
[4,8,3,5,7,6,2,1]=>1000111=>1110001
[1,3,4,2,8,5,7,6]=>0010011=>1100100
[5,7,6,2,4,8,3,1]=>0100111=>1110010
[6,7,5,2,3,8,4,1]=>0011011=>1101100
[6,7,5,3,8,4,2,1]=>1011011=>1101101
[3,2,1,4,8,5,7,6]=>1100011=>1100011
[7,3,1,4,2,6,5,8]=>0110110=>0110110
[7,4,1,6,2,5,3,8]=>0011110=>0111100
[5,4,1,8,2,6,3,7]=>0011101=>1011100
[5,3,1,8,2,6,4,7]=>0101101=>1011010
[4,7,1,5,2,6,3,8]=>0001110=>0111000
[6,5,1,4,2,7,3,8]=>0011110=>0111100
[1,8,7,3,4,5,2,6]=>0001011=>1101000
[1,8,9,3,4,5,6,7,2]=>00000101=>10100000
[1,8,7,4,5,2,3,6]=>0001011=>1101000
[1,2,6,8,7,3,4,5]=>0000011=>1100000
[1,3,7,8,4,5,6,2]=>0000101=>1010000
[1,3,4,5,6,7,8,9,10,11,12,2]=>00000000001=>10000000000
[8,4,2,3,1,6,5,7]=>0110101=>1010110
[4,8,6,2,3,1,7,5]=>0100111=>1110010
[6,4,2,1,8,5,3,7]=>1011101=>1011101
[4,2,6,1,5,8,3,7]=>0010101=>1010100
[6,4,2,3,5,8,1,7]=>0010101=>1010100
[2,8,6,4,5,1,7,3]=>0001111=>1111000
[8,2,4,6,7,1,5,3]=>0001011=>1101000
[2,6,3,1,7,4,8,5]=>0100111=>1110010
[6,5,1,8,3,2,7,4]=>0101111=>1111010
[1,4,3,7,2,8,6,5]=>0010111=>1110100
[1,8,7,4,5,3,2,6]=>0101011=>1101010
[2,8,3,1,4,5,7,6]=>0100011=>1100010
[6,1,7,2,8,4,5,3]=>0001111=>1111000
[8,3,2,1,5,6,7,4]=>1100011=>1100011
[3,2,6,7,8,4,5,1]=>0101001=>1001010
[1,7,4,6,3,8,2,5]=>0000111=>1110000
[5,6,4,1,3,8,2,7]=>0010101=>1010100
[4,5,3,1,8,7,6,2]=>0101111=>1111010
[6,3,4,2,7,8,5,1]=>0011101=>1011100
[8,7,4,5,1,6,3,2]=>0101111=>1111010
[6,2,7,8,1,3,5,4]=>0001101=>1011000
[5,1,8,4,3,7,2,6]=>0011011=>1101100
[7,2,8,1,4,5,6,3]=>0000111=>1110000
[1,4,8,2,5,6,7,3]=>0000011=>1100000
[2,1,4,3,6,5,8,10,9,7]=>101010011=>110010101
[2,1,4,3,6,8,7,5,10,9]=>101001101=>101100101
[2,1,4,3,8,10,7,9,5,6]=>101000011=>110000101
[2,1,4,3,6,7,10,8,9,5]=>101000011=>110000101
[2,1,4,6,5,3,8,7,10,9]=>100110101=>101011001
[2,1,4,6,5,3,8,10,9,7]=>100110011=>110011001
[2,1,6,8,5,7,3,4,10,9]=>100001101=>101100001
[2,1,8,7,5,10,4,9,3,6]=>100001111=>111100001
[2,1,6,7,5,10,8,4,9,3]=>100001111=>111100001
[2,1,4,5,8,6,7,3,10,9]=>100001101=>101100001
[2,1,8,5,10,6,7,9,3,4]=>100000111=>111000001
[2,1,4,7,10,6,9,8,3,5]=>100000111=>111000001
[2,1,4,5,6,10,7,8,9,3]=>100000011=>110000001
[2,4,3,1,6,5,8,10,9,7]=>011010011=>110010110
[2,4,3,1,6,8,7,5,10,9]=>011001101=>101100110
[2,4,3,1,8,10,7,9,5,6]=>011000011=>110000110
[2,4,3,1,6,7,10,8,9,5]=>011000011=>110000110
[4,6,3,5,1,2,8,7,10,9]=>000110101=>101011000
[4,6,3,5,1,2,8,10,9,7]=>000110011=>110011000
[6,5,3,8,2,7,1,4,10,9]=>000111101=>101111000
[8,5,3,7,2,10,4,9,1,6]=>000101111=>111101000
[6,5,3,7,2,10,8,4,9,1]=>000111111=>111111000
[4,5,3,8,6,2,7,1,10,9]=>000111101=>101111000
[8,6,3,5,10,2,7,9,1,4]=>000010111=>111010000
[4,7,3,6,10,1,9,8,2,5]=>000001111=>111100000
[4,5,3,6,10,7,1,8,9,2]=>000101011=>110101000
[2,3,6,4,5,1,8,7,10,9]=>000110101=>101011000
[2,3,6,4,5,1,8,10,9,7]=>000110011=>110011000
[6,3,8,4,5,7,1,2,10,9]=>000011101=>101110000
[8,3,7,4,5,10,2,9,1,6]=>000001111=>111100000
[6,3,7,4,5,10,8,2,9,1]=>000011111=>111110000
[2,5,8,4,7,6,1,3,10,9]=>000011101=>101110000
[8,5,10,4,7,6,2,9,1,3]=>000011111=>111110000
[2,7,10,4,8,6,9,5,1,3]=>000100111=>111001000
[2,5,6,4,10,8,7,3,9,1]=>000011111=>111110000
[2,3,4,8,5,6,7,1,10,9]=>000001101=>101100000
[8,3,4,10,5,6,7,9,1,2]=>000000111=>111000000
[2,7,4,10,5,6,9,8,1,3]=>000001111=>111100000
[2,3,6,10,5,9,7,8,1,4]=>000000111=>111000000
[2,3,4,5,10,6,7,8,9,1]=>000000011=>110000000
[2,1,4,3,6,5,8,7,10,12,11,9]=>10101010011=>11001010101
[2,1,4,3,6,5,8,10,9,7,12,11]=>10101001101=>10110010101
[2,1,4,3,6,8,7,5,10,9,12,11]=>10100110101=>10101100101
[2,1,4,3,6,8,7,5,10,12,11,9]=>10100110011=>11001100101
[2,1,4,3,10,9,7,12,6,11,5,8]=>10100001111=>11110000101
[2,1,4,3,8,9,7,12,10,6,11,5]=>10100001111=>11110000101
[2,1,4,6,5,3,8,7,10,9,12,11]=>10011010101=>10101011001
[2,1,4,6,5,3,8,7,10,12,11,9]=>10011010011=>11001011001
[2,1,4,6,5,3,8,10,9,7,12,11]=>10011001101=>10110011001
[2,1,8,7,5,10,4,9,3,6,12,11]=>10000111101=>10111100001
[2,1,10,7,5,9,4,12,6,11,3,8]=>10000101111=>11110100001
[2,1,6,7,5,10,8,4,9,3,12,11]=>10000111101=>10111100001
[2,1,10,8,5,7,12,4,9,11,3,6]=>10000010111=>11101000001
[2,1,8,5,10,6,7,9,3,4,12,11]=>10000011101=>10111000001
[2,1,8,5,9,6,7,12,10,4,11,3]=>10000011111=>11111000001
[2,1,4,7,10,6,9,8,3,5,12,11]=>10000011101=>10111000001
[2,1,10,7,12,6,9,8,4,11,3,5]=>10000011111=>11111000001
[2,1,4,7,8,6,12,10,9,5,11,3]=>10000011111=>11111000001
[2,1,4,5,6,10,7,8,9,3,12,11]=>10000001101=>10110000001
[2,1,10,5,6,12,7,8,9,11,3,4]=>10000000111=>11100000001
[2,1,4,5,8,12,7,11,9,10,3,6]=>10000000111=>11100000001
[2,4,3,1,6,5,8,7,10,9,12,11]=>01101010101=>10101010110
[2,4,3,1,6,5,8,7,10,12,11,9]=>01101010011=>11001010110
[2,4,3,1,6,5,8,10,9,7,12,11]=>01101001101=>10110010110
[2,4,3,1,6,8,7,5,10,9,12,11]=>01100110101=>10101100110
[2,4,3,1,6,8,7,5,10,12,11,9]=>01100110011=>11001100110
[2,4,3,1,10,9,7,12,6,11,5,8]=>01100001111=>11110000110
[2,4,3,1,8,9,7,12,10,6,11,5]=>01100001111=>11110000110
[4,6,3,5,1,2,8,7,10,9,12,11]=>00011010101=>10101011000
[4,6,3,5,1,2,8,7,10,12,11,9]=>00011010011=>11001011000
[4,6,3,5,1,2,8,10,9,7,12,11]=>00011001101=>10110011000
[6,5,3,8,2,7,1,4,10,9,12,11]=>00011110101=>10101111000
[6,5,3,8,2,7,1,4,10,12,11,9]=>00011110011=>11001111000
[8,5,3,7,2,10,4,9,1,6,12,11]=>00010111101=>10111101000
[10,5,3,7,2,9,4,12,6,11,1,8]=>00010101111=>11110101000
[8,5,3,7,2,9,4,12,10,6,11,1]=>00010111111=>11111101000
[6,5,3,7,2,10,8,4,9,1,12,11]=>00011111101=>10111111000
[10,5,3,8,2,7,12,4,9,11,1,6]=>00010010111=>11101001000
[6,5,3,9,2,8,12,1,11,10,4,7]=>00011001111=>11110011000
[6,5,3,7,2,8,12,9,1,10,11,4]=>00011101011=>11010111000
[4,5,3,8,6,2,7,1,10,9,12,11]=>00011110101=>10101111000
[4,5,3,8,6,2,7,1,10,12,11,9]=>00011110011=>11001111000
[8,6,3,5,10,2,7,9,1,4,12,11]=>00001011101=>10111010000
[10,6,3,5,9,2,7,12,4,11,1,8]=>00001001111=>11110010000
[8,6,3,5,9,2,7,12,10,4,11,1]=>00001011111=>11111010000
[4,7,3,6,10,1,9,8,2,5,12,11]=>00000111101=>10111100000
[10,6,3,7,12,2,9,8,4,11,1,5]=>00001011111=>11111010000
[4,9,3,6,12,1,10,8,11,7,2,5]=>00000101111=>11110100000
[4,7,3,6,8,1,12,10,9,5,11,2]=>00000111111=>11111100000
[4,5,3,6,10,7,1,8,9,2,12,11]=>00010101101=>10110101000
[10,7,3,5,6,12,2,8,9,11,1,4]=>00000100111=>11100100000
[4,9,3,7,6,12,1,8,11,10,2,5]=>00000101111=>11110100000
[4,5,3,8,7,12,2,11,9,10,1,6]=>00010010111=>11101001000
[2,3,6,4,5,1,8,7,10,9,12,11]=>00011010101=>10101011000
[2,3,6,4,5,1,8,7,10,12,11,9]=>00011010011=>11001011000
[2,3,6,4,5,1,8,10,9,7,12,11]=>00011001101=>10110011000
[6,3,8,4,5,7,1,2,10,9,12,11]=>00001110101=>10101110000
[6,3,8,4,5,7,1,2,10,12,11,9]=>00001110011=>11001110000
[8,3,7,4,5,10,2,9,1,6,12,11]=>00000111101=>10111100000
[10,3,7,4,5,9,2,12,6,11,1,8]=>00000101111=>11110100000
[8,3,7,4,5,9,2,12,10,6,11,1]=>00000111111=>11111100000
[6,3,7,4,5,10,8,2,9,1,12,11]=>00001111101=>10111110000
[10,3,8,4,5,7,12,2,9,11,1,6]=>00000010111=>11101000000
[6,3,9,4,5,8,12,1,11,10,2,7]=>00001001111=>11110010000
[6,3,7,4,5,8,12,9,1,10,11,2]=>00001101011=>11010110000
[2,5,8,4,7,6,1,3,10,9,12,11]=>00001110101=>10101110000
[2,5,8,4,7,6,1,3,10,12,11,9]=>00001110011=>11001110000
[8,5,10,4,7,6,2,9,1,3,12,11]=>00001111101=>10111110000
[10,5,9,4,7,6,2,12,3,11,1,8]=>00001101111=>11110110000
[8,5,9,4,7,6,2,12,10,3,11,1]=>00001111111=>11111110000
[2,7,10,4,8,6,9,5,1,3,12,11]=>00010011101=>10111001000
[10,7,12,4,8,6,9,5,2,11,1,3]=>00010011111=>11111001000
[2,9,8,4,12,6,10,3,11,7,1,5]=>00000111111=>11111100000
[2,7,8,4,12,6,9,10,1,3,11,5]=>00000010111=>11101000000
[2,5,6,4,10,8,7,3,9,1,12,11]=>00001111101=>10111110000
[10,5,6,4,12,8,7,3,9,11,1,2]=>00001110111=>11101110000
[2,9,8,4,6,12,7,3,11,10,1,5]=>00000111111=>11111100000
[2,5,8,4,12,9,7,11,6,10,3,1]=>01000011111=>11111000010
[2,5,6,4,7,12,9,8,1,10,11,3]=>00001011011=>11011010000
[2,3,4,8,5,6,7,1,10,9,12,11]=>00000110101=>10101100000
[2,3,4,8,5,6,7,1,10,12,11,9]=>00000110011=>11001100000
[8,3,4,10,5,6,7,9,1,2,12,11]=>00000011101=>10111000000
[10,3,4,9,5,6,7,12,2,11,1,8]=>00000001111=>11110000000
[8,3,4,9,5,6,7,12,10,2,11,1]=>00000011111=>11111000000
[2,7,4,10,5,6,9,8,1,3,12,11]=>00000111101=>10111100000
[10,7,4,12,5,6,9,8,2,11,1,3]=>00000111111=>11111100000
[2,9,4,12,5,6,10,8,11,7,1,3]=>00000101111=>11110100000
[2,7,4,8,5,6,12,10,9,3,11,1]=>00000111111=>11111100000
[2,3,6,10,5,9,7,8,1,4,12,11]=>00000011101=>10111000000
[10,3,6,12,5,9,7,8,2,11,1,4]=>00000011111=>11111000000
[2,9,6,12,5,11,7,8,10,1,3,4]=>00000001111=>11110000000
[2,3,8,12,5,10,7,11,9,6,1,4]=>00001001111=>11110010000
[2,3,6,7,5,12,10,8,9,4,11,1]=>00000101111=>11110100000
[2,3,4,5,10,6,7,8,9,1,12,11]=>00000001101=>10110000000
[10,3,4,5,12,6,7,8,9,11,1,2]=>00000000111=>11100000000
[2,9,4,5,12,6,7,8,11,10,1,3]=>00000001111=>11110000000
[2,3,8,5,12,6,7,11,9,10,1,4]=>00000010111=>11101000000
[2,3,4,7,12,6,11,8,9,10,1,5]=>00000000111=>11100000000
[2,3,4,5,6,12,7,8,9,10,11,1]=>00000000011=>11000000000
[8,1,6,7,2,5,4,3]=>0011011=>1101100
[7,5,2,3,6,8,4,1]=>0011011=>1101100
[8,1,4,6,5,3,2,7]=>0101101=>1011010
[8,1,4,7,6,5,2,3]=>0001111=>1111000
[8,1,2,7,6,5,4,3]=>0011111=>1111100
[4,5,8,1,6,7,2,3]=>0000011=>1100000
[3,2,8,6,1,5,7,4]=>0100111=>1110010
[3,7,2,5,8,4,6,1]=>0000111=>1110000
[6,7,8,4,1,5,2,3]=>0011001=>1001100
[6,2,8,3,5,1,4,7]=>0001101=>1011000
[6,2,7,4,5,3,1,8]=>0101110=>0111010
[6,8,2,5,3,4,1,7]=>0011001=>1001100
[6,8,7,5,4,1,2,3]=>0011011=>1101100
[7,4,5,6,1,8,2,3]=>0000111=>1110000
[6,3,5,2,8,1,7,4]=>0001111=>1111000
[6,1,8,7,4,5,2,3]=>0001111=>1111000
[4,8,7,1,6,3,2,5]=>0100111=>1110010
[4,8,2,7,5,3,6,1]=>0001111=>1111000
[1,3,2,6,8,7,4,5]=>0100011=>1100010
[1,3,8,2,5,4,6,7]=>0001001=>1001000
[1,6,2,5,8,7,3,4]=>0000111=>1110000
[1,6,8,7,2,3,5,4]=>0001011=>1101000
[1,6,8,7,2,5,3,4]=>0001011=>1101000
[1,5,2,4,8,3,6,7]=>0001001=>1001000
[1,2,4,5,8,6,3,7]=>0000101=>1010000
[1,2,8,3,5,4,7,6]=>0001011=>1101000
[1,3,8,2,5,4,7,6]=>0001011=>1101000
[1,6,7,5,2,4,8,3]=>0001011=>1101000
[1,5,6,4,7,2,3,8]=>0000110=>0110000
[1,7,4,2,5,8,3,6]=>0010011=>1100100
[1,6,4,3,7,5,2,8]=>0011110=>0111100
[1,6,5,4,7,2,3,8]=>0001110=>0111000
[1,7,3,2,6,4,8,5]=>0100111=>1110010
[1,5,8,2,3,6,7,4]=>0000011=>1100000
[1,3,2,6,8,5,4,7]=>0101001=>1001010
[1,6,3,2,7,4,5,8]=>0100110=>0110010
[1,7,8,5,4,2,3,6]=>0011001=>1001100
[1,8,4,2,3,6,5,7]=>0010101=>1010100
[1,4,2,7,5,3,8,6]=>0011011=>1101100
[1,5,7,6,2,4,3,8]=>0010110=>0110100
[1,8,4,7,3,2,6,5]=>0100111=>1110010
[1,3,8,4,2,6,5,7]=>0010101=>1010100
[1,7,4,2,6,5,8,3]=>0010111=>1110100
[1,6,5,8,3,7,4,2]=>0010111=>1110100
[1,7,4,8,3,2,5,6]=>0100011=>1100010
[1,4,8,3,2,7,5,6]=>0100011=>1100010
[1,8,3,6,4,5,2,7]=>0001101=>1011000
[1,6,4,7,3,2,8,5]=>0100111=>1110010
[8,2,3,7,4,5,6,1]=>0000111=>1110000
[8,5,7,2,3,6,4,1]=>0010111=>1110100
[7,5,2,1,6,8,3,4]=>1001011=>1101001
[7,6,1,5,4,8,2,3]=>0001111=>1111000
[7,6,3,2,1,8,4,5]=>1100111=>1110011
[2,8,7,3,4,6,1,5]=>0000111=>1110000
[6,5,1,3,7,2,8,4]=>0001111=>1111000
[8,1,7,3,4,5,2,6]=>0001011=>1101000
[7,1,8,3,4,5,2,6]=>0001011=>1101000
[6,8,7,3,4,2,1,5]=>1010011=>1100101
[3,8,7,1,2,4,5,6]=>0000011=>1100000
[1,8,5,3,4,6,2,7]=>0001101=>1011000
[7,1,6,5,4,3,8,2]=>0011111=>1111100
[7,1,3,6,4,5,8,2]=>0000111=>1110000
[7,1,5,3,6,4,8,2]=>0001111=>1111000
[6,1,5,3,7,8,2,4]=>0001101=>1011000
[5,8,7,1,2,6,3,4]=>0000111=>1110000
[6,8,2,3,4,7,1,5]=>0000011=>1100000
[5,1,7,3,8,6,2,4]=>0001111=>1111000
[6,1,3,2,4,7,8,5]=>0100101=>1010010
[6,2,1,3,4,7,8,5]=>1000101=>1010001
[3,4,5,6,1,8,9,2,7]=>00001001=>10010000
[3,4,5,6,8,1,9,2,7]=>00000011=>11000000
[3,4,5,6,8,9,1,2,7]=>00000001=>10000000
[2,4,5,1,6,7,8,9,3]=>00010001=>10001000
[2,3,4,1,6,7,8,9,5]=>00100001=>10000100
[2,3,4,5,6,1,8,9,10,7]=>000010001=>100010000
[3,4,5,6,1,2,9,7,8]=>00001001=>10010000
[3,4,5,6,8,1,2,7,9]=>00000010=>01000000
[2,3,4,5,6,8,9,1,10,7]=>000000011=>110000000
[3,4,5,1,6,7,8,2,9]=>00010010=>01001000
[5,6,1,7,8,9,2,3,4]=>00001001=>10010000
[4,5,6,1,7,8,9,10,2,3]=>000010001=>100010000
[1,3,5,2,6,7,8,9,4]=>00010001=>10001000
[3,5,6,1,7,8,9,10,2,4]=>000010001=>100010000
[2,1,4,3,6,7,8,9,5]=>10100001=>10000101
[3,4,6,1,7,8,9,10,2,5]=>000010001=>100010000
[2,3,1,5,6,7,8,9,4]=>01000001=>10000010
[3,4,5,1,7,8,9,10,2,6]=>000100001=>100001000
[3,2,5,8,7,4,1,6]=>0110011=>1100110
[4,2,5,8,7,3,1,6]=>0110011=>1100110
[8,3,4,1,6,5,2,7]=>0011101=>1011100
[3,4,8,5,7,2,1,6]=>1000011=>1100001
[3,6,4,8,5,7,2,1]=>1000111=>1110001
[5,8,4,7,3,6,2,1]=>1000111=>1110001
[4,2,8,7,3,1,6,5]=>0110111=>1110110
[6,5,8,2,1,7,4,3]=>1010111=>1110101
[6,1,4,3,8,7,2,5]=>0010111=>1110100
[5,1,3,2,6,8,7,4]=>0101011=>1101010
[6,1,3,8,7,2,4,5]=>0000111=>1110000
[1,2,8,4,5,7,3,6]=>0000011=>1100000
[4,2,1,8,7,6,3,5]=>1010111=>1110101
[3,2,5,8,7,1,4,6]=>0100011=>1100010
[5,6,3,8,7,2,1,4]=>1000111=>1110001
[2,5,8,4,7,1,6,3]=>0000111=>1110000
[1,6,2,4,8,5,7,3]=>0000111=>1110000
[3,1,6,5,8,7,2,4]=>0100111=>1110010
[4,8,5,3,6,7,1,2]=>0001011=>1101000
[1,8,5,3,4,7,6,2]=>0001111=>1111000
[2,7,1,3,6,4,5,8]=>0000110=>0110000
[8,1,7,3,5,4,6,2]=>0001111=>1111000
[1,8,6,3,2,5,4,7]=>0101101=>1011010
[3,2,4,8,5,7,1,6]=>0100011=>1100010
[8,1,2,4,7,5,6,3]=>0000111=>1110000
[6,4,5,8,3,1,7,2]=>0100111=>1110010
[8,6,2,1,5,7,3,4]=>1000111=>1110001
[4,6,2,8,5,3,7,1]=>0001111=>1111000
[8,7,2,4,1,5,3,6]=>0011011=>1101100
[7,5,3,4,8,6,2,1]=>1001111=>1111001
[2,8,3,1,4,6,7,5]=>0100011=>1100010
[4,3,6,5,1,2,7,8]=>0011100=>0011100
[5,8,3,7,6,4,2,1]=>1010111=>1110101
[1,3,8,7,6,5,2,4]=>0001111=>1111000
[4,8,7,2,6,3,1,5]=>0100111=>1110010
[1,8,7,2,6,3,5,4]=>0001111=>1111000
[8,7,2,1,4,3,5,6]=>1010011=>1100101
[2,8,7,1,6,3,4,5]=>0000111=>1110000
[4,2,8,7,6,5,1,3]=>0011111=>1111100
[8,4,2,7,6,5,3,1]=>0111111=>1111110
[6,8,7,5,2,4,3,1]=>0111011=>1101110
[1,2,5,7,4,8,6,3]=>0000111=>1110000
[6,2,1,8,7,5,3,4]=>1001111=>1111001
[6,3,8,7,4,5,2,1]=>1001111=>1111001
[2,8,3,4,1,5,6,7]=>0010001=>1000100
[1,3,7,5,4,8,6,2]=>0001111=>1111000
[4,5,6,3,1,8,2,7]=>0100101=>1010010
[5,2,1,4,3,6,8,7]=>1011001=>1001101
[1,5,6,3,8,4,2,7]=>0010101=>1010100
[2,6,5,3,8,4,1,7]=>0011101=>1011100
[5,7,3,8,4,2,6,1]=>0010111=>1110100
[5,3,6,2,8,4,1,7]=>0011101=>1011100
[2,3,6,5,4,8,1,7]=>0001101=>1011000
[3,7,5,4,8,2,6,1]=>0001111=>1111000
[5,3,7,1,2,8,4,6]=>0001011=>1101000
[6,3,8,7,2,5,4,1]=>0011111=>1111100
[2,8,7,6,1,5,3,4]=>0001111=>1111000
[9,7,8,5,4,3,2,1,6]=>11110011=>11001111
[1,2,3,4,6,5,7,8,9]=>00001000=>00010000
[1,2,3,5,4,6,7,8,9]=>00010000=>00001000
[6,8,4,1,7,5,2,3]=>0011011=>1101100
[8,1,4,6,7,5,2,3]=>0001011=>1101000
[2,6,8,1,4,7,5,3]=>0001011=>1101000
[6,4,8,1,2,7,5,3]=>0001111=>1111000
[8,1,4,6,7,2,5,3]=>0001011=>1101000
[8,2,1,6,7,4,5,3]=>1001011=>1101001
[8,2,6,1,7,4,5,3]=>0001111=>1111000
[4,2,8,1,6,7,5,3]=>0011011=>1101100
[8,1,2,6,4,7,5,3]=>0001111=>1111000
[8,4,1,6,2,7,5,3]=>0011111=>1111100
[4,8,1,2,6,7,5,3]=>0001011=>1101000
[4,8,2,1,6,7,5,3]=>1001011=>1101001
[8,1,6,2,4,7,5,3]=>0001111=>1111000
[8,2,4,6,1,7,5,3]=>0001111=>1111000
[2,1,4,3,6,5,8,9,10,7]=>101010001=>100010101
[2,1,4,3,6,7,8,5,10,9]=>101000101=>101000101
[2,1,4,3,8,7,9,10,5,6]=>101000101=>101000101
[2,1,4,3,6,7,8,9,10,5]=>101000001=>100000101
[2,1,4,5,6,3,8,7,10,9]=>100010101=>101010001
[2,1,4,5,6,3,8,9,10,7]=>100010001=>100010001
[2,1,6,5,7,8,3,4,10,9]=>100010101=>101010001
[2,1,8,5,9,7,3,10,6,4]=>100011111=>111110001
[2,1,6,5,7,8,9,10,3,4]=>100010001=>100010001
[2,1,4,5,6,7,8,3,10,9]=>100000101=>101000001
[2,1,8,5,6,7,9,10,3,4]=>100000101=>101000001
[2,1,4,7,6,8,9,3,10,5]=>100001011=>110100001
[2,1,4,5,6,7,8,9,10,3]=>100000001=>100000001
[2,3,4,1,6,5,8,7,10,9]=>001010101=>101010100
[2,3,4,1,6,5,8,9,10,7]=>001010001=>100010100
[2,3,4,1,6,7,8,5,10,9]=>001000101=>101000100
[2,3,4,1,8,7,9,10,5,6]=>001000101=>101000100
[2,3,4,1,6,7,8,9,10,5]=>001000001=>100000100
[4,3,5,6,1,2,8,7,10,9]=>001010101=>101010100
[4,3,5,6,1,2,8,9,10,7]=>001010001=>100010100
[6,3,7,5,1,8,4,2,10,9]=>001111101=>101111100
[8,3,9,5,1,7,4,10,6,2]=>000111111=>111111000
[6,3,7,5,1,8,9,10,4,2]=>001111001=>100111100
[4,3,5,6,7,8,1,2,10,9]=>001000101=>101000100
[8,3,9,5,6,7,1,10,4,2]=>001001111=>111100100
[4,3,7,8,6,10,9,2,5,1]=>001100111=>111001100
[4,3,5,6,7,8,9,10,1,2]=>001000001=>100000100
[2,3,4,5,6,1,8,7,10,9]=>000010101=>101010000
[6,3,4,5,7,8,1,2,10,9]=>000010101=>101010000
[8,3,4,5,9,7,1,10,6,2]=>000011111=>111110000
[6,3,4,5,7,8,9,10,1,2]=>000010001=>100010000
[2,5,4,6,7,1,8,3,10,9]=>000101101=>101101000
[8,5,4,6,7,1,9,10,3,2]=>010101101=>101101010
[2,7,4,8,6,1,9,5,10,3]=>000011111=>111110000
[2,5,4,6,7,8,9,1,10,3]=>000100011=>110001000
[2,3,4,5,6,7,8,1,10,9]=>000000101=>101000000
[8,3,4,5,6,7,9,10,1,2]=>000000101=>101000000
[2,7,4,5,6,8,9,1,10,3]=>000001011=>110100000
[2,3,6,5,7,8,1,9,10,4]=>000010101=>101010000
[2,1,4,3,6,5,8,7,10,11,12,9]=>10101010001=>10001010101
[2,1,4,3,6,5,8,9,10,7,12,11]=>10101000101=>10100010101
[2,1,4,3,6,5,10,9,11,12,7,8]=>10101000101=>10100010101
[2,1,4,3,6,5,8,9,10,11,12,7]=>10101000001=>10000010101
[2,1,4,3,6,7,8,5,10,9,12,11]=>10100010101=>10101000101
[2,1,4,3,6,7,8,5,10,11,12,9]=>10100010001=>10001000101
[2,1,4,3,8,7,9,10,5,6,12,11]=>10100010101=>10101000101
[2,1,4,3,8,7,9,10,11,12,5,6]=>10100010001=>10001000101
[2,1,4,3,6,7,8,9,10,5,12,11]=>10100000101=>10100000101
[2,1,4,3,10,7,8,9,11,12,5,6]=>10100000101=>10100000101
[2,1,4,3,6,7,8,9,10,11,12,5]=>10100000001=>10000000101
[2,1,4,5,6,3,8,7,10,9,12,11]=>10001010101=>10101010001
[2,1,4,5,6,3,8,7,10,11,12,9]=>10001010001=>10001010001
[2,1,4,5,6,3,8,9,10,7,12,11]=>10001000101=>10100010001
[2,1,4,5,6,3,10,9,11,12,7,8]=>10001000101=>10100010001
[2,1,4,5,6,3,8,9,10,11,12,7]=>10001000001=>10000010001
[2,1,6,5,7,8,3,4,10,9,12,11]=>10001010101=>10101010001
[2,1,6,5,7,8,3,4,10,11,12,9]=>10001010001=>10001010001
[2,1,8,5,9,7,3,10,6,4,12,11]=>10001111101=>10111110001
[2,1,8,5,9,7,3,10,11,12,6,4]=>10001111001=>10011110001
[2,1,6,5,7,8,9,10,3,4,12,11]=>10001000101=>10100010001
[2,1,10,5,11,7,8,9,3,12,6,4]=>10001001111=>11110010001
[2,1,6,5,9,10,8,12,11,4,7,3]=>10001100111=>11100110001
[2,1,6,5,7,8,9,10,11,12,3,4]=>10001000001=>10000010001
[2,1,4,5,6,7,8,3,10,9,12,11]=>10000010101=>10101000001
[2,1,4,5,6,7,8,3,10,11,12,9]=>10000010001=>10001000001
[2,1,8,5,6,7,9,10,3,4,12,11]=>10000010101=>10101000001
[2,1,10,5,6,7,11,9,3,12,8,4]=>10000011111=>11111000001
[2,1,8,5,6,7,9,10,11,12,3,4]=>10000010001=>10001000001
[2,1,4,7,6,8,9,3,10,5,12,11]=>10000101101=>10110100001
[2,1,10,7,6,8,9,3,11,12,5,4]=>10010101101=>10110101001
[2,1,4,9,6,10,8,3,11,7,12,5]=>10000011111=>11111000001
[2,1,4,5,6,7,8,9,10,3,12,11]=>10000000101=>10100000001
[2,1,10,5,6,7,8,9,11,12,3,4]=>10000000101=>10100000001
[2,1,4,9,6,7,8,10,11,3,12,5]=>10000001011=>11010000001
[2,1,4,5,8,7,9,10,3,11,12,6]=>10000010101=>10101000001
[2,1,4,5,6,7,8,9,10,11,12,3]=>10000000001=>10000000001
[2,3,4,1,6,5,8,7,10,9,12,11]=>00101010101=>10101010100
[2,3,4,1,6,5,8,7,10,11,12,9]=>00101010001=>10001010100
[2,3,4,1,6,5,8,9,10,7,12,11]=>00101000101=>10100010100
[2,3,4,1,6,5,10,9,11,12,7,8]=>00101000101=>10100010100
[2,3,4,1,6,5,8,9,10,11,12,7]=>00101000001=>10000010100
[2,3,4,1,6,7,8,5,10,9,12,11]=>00100010101=>10101000100
[2,3,4,1,6,7,8,5,10,11,12,9]=>00100010001=>10001000100
[2,3,4,1,8,7,9,10,5,6,12,11]=>00100010101=>10101000100
[2,3,4,1,10,7,11,9,5,12,8,6]=>00100011111=>11111000100
[2,3,4,1,8,7,9,10,11,12,5,6]=>00100010001=>10001000100
[2,3,4,1,6,9,8,10,11,5,12,7]=>00100001011=>11010000100
[2,3,4,1,6,7,8,9,10,11,12,5]=>00100000001=>10000000100
[4,3,5,6,1,2,8,7,10,9,12,11]=>00101010101=>10101010100
[4,3,5,6,1,2,8,7,10,11,12,9]=>00101010001=>10001010100
[4,3,5,6,1,2,8,9,10,7,12,11]=>00101000101=>10100010100
[4,3,5,6,1,2,10,9,11,12,7,8]=>00101000101=>10100010100
[4,3,5,6,1,2,8,9,10,11,12,7]=>00101000001=>10000010100
[6,3,7,5,1,8,4,2,10,11,12,9]=>00111110001=>10001111100
[8,3,9,5,1,7,4,10,6,2,12,11]=>00011111101=>10111111000
[10,3,11,5,1,7,4,9,6,12,8,2]=>00010111111=>11111101000
[8,3,9,5,1,7,4,10,11,12,6,2]=>00011111001=>10011111000
[6,3,7,5,1,8,9,10,4,2,12,11]=>00111100101=>10100111100
[10,3,11,5,1,7,8,9,4,12,6,2]=>00011001111=>11110011000
[6,3,9,5,2,10,8,12,11,4,7,1]=>00011101111=>11110111000
[4,3,5,6,7,8,1,2,10,9,12,11]=>00100010101=>10101000100
[4,3,5,6,7,8,1,2,10,11,12,9]=>00100010001=>10001000100
[8,3,9,5,6,7,1,10,4,2,12,11]=>00100111101=>10111100100
[10,3,11,5,6,7,1,9,4,12,8,2]=>00000111111=>11111100000
[4,3,7,8,6,10,9,2,5,1,12,11]=>00110011101=>10111001100
[4,3,9,10,6,12,8,2,11,7,5,1]=>00110110111=>11101101100
[10,3,11,5,6,7,8,9,1,12,4,2]=>00100001111=>11110000100
[4,3,5,8,9,7,12,10,1,11,6,2]=>00101001111=>11110010100
[4,3,5,6,7,8,9,10,11,12,1,2]=>00100000001=>10000000100
[2,3,4,5,6,1,8,7,10,9,12,11]=>00001010101=>10101010000
[2,3,4,5,6,1,8,7,10,11,12,9]=>00001010001=>10001010000
[2,3,4,5,6,1,8,9,10,7,12,11]=>00001000101=>10100010000
[2,3,4,5,6,1,10,9,11,12,7,8]=>00001000101=>10100010000
[2,3,4,5,6,1,8,9,10,11,12,7]=>00001000001=>10000010000
[6,3,4,5,7,8,1,2,10,9,12,11]=>00001010101=>10101010000
[6,3,4,5,7,8,1,2,10,11,12,9]=>00001010001=>10001010000
[8,3,4,5,9,7,1,10,6,2,12,11]=>00001111101=>10111110000
[10,3,4,5,11,7,1,9,6,12,8,2]=>00000111111=>11111100000
[6,3,4,5,7,8,9,10,1,2,12,11]=>00001000101=>10100010000
[10,3,4,5,11,7,8,9,1,12,6,2]=>00001001111=>11110010000
[6,3,4,5,9,10,8,12,11,2,7,1]=>00001100111=>11100110000
[6,3,4,5,7,8,9,10,11,12,1,2]=>00001000001=>10000010000
[2,5,4,6,7,1,8,3,10,9,12,11]=>00010110101=>10101101000
[8,5,4,6,7,1,9,10,3,2,12,11]=>01010110101=>10101101010
[10,5,4,6,7,1,11,9,3,12,8,2]=>00010111111=>11111101000
[8,5,4,6,7,1,9,10,11,12,3,2]=>01010110001=>10001101010
[2,7,4,8,6,1,9,5,10,3,12,11]=>00001111101=>10111110000
[2,9,4,10,6,1,8,5,11,7,12,3]=>00001011111=>11111010000
[2,7,4,8,6,1,9,10,11,5,12,3]=>00001110011=>11001110000
[2,9,4,10,6,7,8,1,11,5,12,3]=>00000011111=>11111000000
[2,5,4,8,9,7,11,10,3,6,12,1]=>00010001111=>11110001000
[2,5,4,6,7,8,9,10,11,1,12,3]=>00010000011=>11000001000
[2,3,4,5,6,7,8,1,10,9,12,11]=>00000010101=>10101000000
[2,3,4,5,6,7,8,1,10,11,12,9]=>00000010001=>10001000000
[8,3,4,5,6,7,9,10,1,2,12,11]=>00000010101=>10101000000
[10,3,4,5,6,7,11,9,1,12,8,2]=>00000011111=>11111000000
[8,3,4,5,6,7,9,10,11,12,1,2]=>00000010001=>10001000000
[2,7,4,5,6,8,9,1,10,3,12,11]=>00000101101=>10110100000
[2,9,4,5,6,10,8,1,11,7,12,3]=>00000011111=>11111000000
[2,7,4,5,6,8,9,10,11,1,12,3]=>00000100011=>11000100000
[2,3,6,5,7,8,1,9,10,4,12,11]=>00001010101=>10101010000
[10,3,6,5,7,8,1,9,11,12,4,2]=>00101010101=>10101010100
[2,9,6,5,7,8,1,10,11,4,12,3]=>00001011011=>11011010000
[2,3,8,5,9,7,1,10,6,11,12,4]=>00000111101=>10111100000
[2,3,6,5,7,8,9,10,1,11,12,4]=>00001000101=>10100010000
[2,3,4,5,6,7,8,9,10,1,12,11]=>00000000101=>10100000000
[10,3,4,5,6,7,8,9,11,12,1,2]=>00000000101=>10100000000
[2,9,4,5,6,7,8,10,11,1,12,3]=>00000001011=>11010000000
[2,3,8,5,6,7,9,10,1,11,12,4]=>00000010101=>10101000000
[2,3,4,7,6,8,9,1,10,11,12,5]=>00000101001=>10010100000
[5,4,7,6,3,1,2,8]=>0101110=>0111010
[3,6,4,8,1,5,2,7]=>0001101=>1011000
[3,6,8,4,1,5,2,7]=>0011001=>1001100
[8,7,1,4,2,3,5,6]=>0010011=>1100100
[3,8,6,4,1,5,2,7]=>0011101=>1011100
[8,2,6,5,7,1,3,4]=>0000111=>1110000
[4,6,1,3,2,8,7,5]=>0100111=>1110010
[7,1,4,8,2,3,6,5]=>0000111=>1110000
[4,5,3,6,7,1,8,2]=>0001011=>1101000
[1,4,7,8,3,5,2,6]=>0001001=>1001000
[4,6,1,3,5,2,8,7]=>0001101=>1011000
[2,5,1,4,8,3,7,6]=>0001011=>1101000
[6,1,2,5,4,8,7,3]=>0001111=>1111000
[8,4,1,7,3,5,6,2]=>0010111=>1110100
[8,4,1,2,5,7,3,6]=>0010011=>1100100
[2,4,5,6,8,3,1,7]=>0100001=>1000010
[3,4,5,8,6,2,1,7]=>1000101=>1010001
[4,5,1,8,6,3,7,2]=>0001111=>1111000
[1,8,2,3,4,5,9,6,7]=>00000011=>11000000
[1,3,4,5,6,8,9,2,7]=>00000001=>10000000
[8,3,7,2,1,6,5,4]=>1001111=>1111001
[8,4,7,6,2,5,1,3]=>0001111=>1111000
[8,4,7,3,6,2,1,5]=>1000111=>1110001
[3,8,7,5,6,4,1,2]=>0010111=>1110100
[3,8,7,5,6,2,1,4]=>1000111=>1110001
[3,8,7,5,6,2,4,1]=>0010111=>1110100
[2,8,7,5,6,4,1,3]=>0010111=>1110100
[4,5,2,3,6,7,8,9,1]=>00010001=>10001000
[4,3,2,5,6,7,8,9,1]=>01100001=>10000110
[5,6,7,2,3,4,8,9,1]=>00000101=>10100000
[5,3,6,2,4,7,8,9,1]=>00011001=>10011000
[5,4,3,2,6,7,8,9,1]=>01110001=>10001110
[6,3,7,8,2,4,5,9,1]=>00001011=>11010000
[6,7,4,5,2,3,8,9,1]=>00010101=>10101000
[6,4,3,7,2,5,8,9,1]=>00101101=>10110100
[7,8,4,5,9,2,3,6,1]=>00001011=>11010000
[7,4,3,8,9,2,5,6,1]=>00101101=>10110100
[7,5,8,3,6,2,4,9,1]=>00001111=>11110000
[7,5,4,3,8,2,6,9,1]=>00110111=>11101100
[7,6,5,4,3,2,8,9,1]=>01111101=>10111110
[8,6,4,9,3,7,2,5,1]=>00011111=>11111000
[8,6,5,4,3,9,2,7,1]=>00111111=>11111100
[4,5,2,3,6,7,8,9,10,1]=>000100001=>100001000
[4,3,2,5,6,7,8,9,10,1]=>011000001=>100000110
[5,6,7,2,3,4,8,9,10,1]=>000001001=>100100000
[5,3,6,2,4,7,8,9,10,1]=>000110001=>100011000
[5,4,3,2,6,7,8,9,10,1]=>011100001=>100001110
[6,7,8,9,2,3,4,5,10,1]=>000000011=>110000000
[6,3,7,8,2,4,5,9,10,1]=>000010101=>101010000
[6,7,4,5,2,3,8,9,10,1]=>000101001=>100101000
[6,4,3,7,2,5,8,9,10,1]=>001011001=>100110100
[6,5,4,3,2,7,8,9,10,1]=>011110001=>100011110
[7,8,9,10,1,3,4,5,6,2]=>000010001=>100010000
[7,3,8,9,10,2,4,5,6,1]=>000011001=>100110000
[7,4,3,8,9,2,5,6,10,1]=>001001011=>110100100
[7,5,8,3,6,2,4,9,10,1]=>000011101=>101110000
[7,5,4,3,8,2,6,9,10,1]=>001101101=>101101100
[7,6,5,4,3,2,8,9,10,1]=>011111001=>100111110
[8,5,9,3,6,10,2,4,7,1]=>000001111=>111100000
[8,5,4,3,9,10,2,6,7,1]=>001101101=>101101100
[8,9,6,7,4,5,2,3,10,1]=>000101011=>110101000
[8,6,4,9,3,7,2,5,10,1]=>000011111=>111110000
[8,6,5,4,3,9,2,7,10,1]=>001110111=>111011100
[8,7,6,5,4,3,2,9,10,1]=>011111101=>101111110
[9,7,5,4,10,3,8,2,6,1]=>000111111=>111111000
[9,7,6,5,4,3,10,2,8,1]=>001111111=>111111100
[10,1,9,2,8,3,7,4,6,5]=>000011111=>111110000
[1,5,6,3,8,2,7,4]=>0000111=>1110000
[2,6,3,8,4,7,1,5]=>0000111=>1110000
[2,6,3,5,7,8,1,4]=>0000101=>1010000
[1,5,6,3,7,2,8,4]=>0000111=>1110000
[1,7,5,3,6,2,8,4]=>0001111=>1111000
[1,5,7,3,4,2,8,6]=>0010011=>1100100
[1,5,8,3,4,2,7,6]=>0010011=>1100100
[1,4,5,3,7,2,8,6]=>0001011=>1101000
[1,4,5,3,8,2,7,6]=>0001011=>1101000
[6,5,1,4,2,7,8,3]=>0011101=>1011100
[6,5,1,4,2,8,7,3]=>0011111=>1111100
[1,7,5,4,2,8,6,3]=>0011111=>1111100
[5,1,6,8,3,7,2,4]=>0001011=>1101000
[1,2,3,4,5,6,7,8,9,10,11]=>0000000000=>0000000000
[1,4,3,6,5,10,9,7,8,2]=>001010111=>111010100
[1,4,3,8,7,5,6,10,9,2]=>001001111=>111100100
[1,4,3,10,7,5,9,6,8,2]=>001001111=>111100100
[1,4,3,10,9,8,5,6,7,2]=>001001111=>111100100
[1,6,5,3,4,8,7,10,9,2]=>000110111=>111011000
[1,6,5,3,4,10,9,7,8,2]=>000110111=>111011000
[1,8,5,3,7,4,6,10,9,2]=>000101111=>111101000
[1,10,5,3,7,4,9,6,8,2]=>000101111=>111101000
[1,10,5,3,9,8,4,6,7,2]=>000101111=>111101000
[1,8,7,6,3,4,5,10,9,2]=>000011111=>111110000
[1,10,7,6,3,4,9,5,8,2]=>000011111=>111110000
[1,10,9,6,3,8,4,5,7,2]=>000011111=>111110000
[1,10,9,8,7,3,4,5,6,2]=>000011111=>111110000
[3,1,2,6,5,8,7,10,9,4]=>010010111=>111010010
[3,1,2,6,5,10,9,7,8,4]=>010010111=>111010010
[3,1,2,8,7,5,6,10,9,4]=>010001111=>111100010
[3,1,2,10,7,5,9,6,8,4]=>010001111=>111100010
[3,1,2,10,9,8,5,6,7,4]=>010001111=>111100010
[3,1,5,2,4,8,7,10,9,6]=>010100111=>111001010
[3,1,5,2,4,10,9,7,8,6]=>010100111=>111001010
[3,1,5,2,7,4,6,10,9,8]=>010101011=>110101010
[3,1,5,2,9,8,4,6,7,10]=>010100110=>011001010
[3,1,7,6,2,4,5,10,9,8]=>010011011=>110110010
[3,1,7,6,2,4,9,5,8,10]=>010011010=>010110010
[3,1,9,6,2,8,4,5,7,10]=>010010110=>011010010
[3,1,9,8,7,2,4,5,6,10]=>010001110=>011100010
[5,4,1,2,3,8,7,10,9,6]=>001100111=>111001100
[5,4,1,2,3,10,9,7,8,6]=>001100111=>111001100
[5,4,1,2,7,3,6,10,9,8]=>001101011=>110101100
[5,4,1,2,7,3,9,6,8,10]=>001101010=>010101100
[5,4,1,2,9,8,3,6,7,10]=>001100110=>011001100
[7,4,1,6,2,3,5,10,9,8]=>001011011=>110110100
[7,4,1,6,2,3,9,5,8,10]=>001011010=>010110100
[9,4,1,6,2,8,3,5,7,10]=>001010110=>011010100
[9,4,1,8,7,2,3,5,6,10]=>001001110=>011100100
[7,6,5,1,2,3,4,10,9,8]=>000111011=>110111000
[7,6,5,1,2,3,9,4,8,10]=>000111010=>010111000
[9,6,5,1,2,8,3,4,7,10]=>000110110=>011011000
[9,8,5,1,7,2,3,4,6,10]=>000101110=>011101000
[1,4,3,6,5,8,7,12,11,9,10,2]=>00101010111=>11101010100
[1,4,3,6,5,10,9,7,8,12,11,2]=>00101001111=>11110010100
[1,4,3,6,5,12,9,7,11,8,10,2]=>00101001111=>11110010100
[1,4,3,6,5,12,11,10,7,8,9,2]=>00101001111=>11110010100
[1,4,3,8,7,5,6,10,9,12,11,2]=>00100110111=>11101100100
[1,4,3,8,7,5,6,12,11,9,10,2]=>00100110111=>11101100100
[1,4,3,10,7,5,9,6,8,12,11,2]=>00100101111=>11110100100
[1,4,3,12,7,5,9,6,11,8,10,2]=>00100101111=>11110100100
[1,4,3,12,7,5,11,10,6,8,9,2]=>00100101111=>11110100100
[1,4,3,10,9,8,5,6,7,12,11,2]=>00100011111=>11111000100
[1,4,3,12,9,8,5,6,11,7,10,2]=>00100011111=>11111000100
[1,4,3,12,11,8,5,10,6,7,9,2]=>00100011111=>11111000100
[1,4,3,12,11,10,9,5,6,7,8,2]=>00100011111=>11111000100
[1,6,5,3,4,8,7,10,9,12,11,2]=>00011010111=>11101011000
[1,6,5,3,4,8,7,12,11,9,10,2]=>00011010111=>11101011000
[1,6,5,3,4,10,9,7,8,12,11,2]=>00011001111=>11110011000
[1,6,5,3,4,12,9,7,11,8,10,2]=>00011001111=>11110011000
[1,6,5,3,4,12,11,10,7,8,9,2]=>00011001111=>11110011000
[1,8,5,3,7,4,6,10,9,12,11,2]=>00010110111=>11101101000
[1,8,5,3,7,4,6,12,11,9,10,2]=>00010110111=>11101101000
[1,10,5,3,7,4,9,6,8,12,11,2]=>00010101111=>11110101000
[1,12,5,3,7,4,9,6,11,8,10,2]=>00010101111=>11110101000
[1,12,5,3,7,4,11,10,6,8,9,2]=>00010101111=>11110101000
[1,10,5,3,9,8,4,6,7,12,11,2]=>00010011111=>11111001000
[1,12,5,3,9,8,4,6,11,7,10,2]=>00010011111=>11111001000
[1,12,5,3,11,8,4,10,6,7,9,2]=>00010011111=>11111001000
[1,12,5,3,11,10,9,4,6,7,8,2]=>00010011111=>11111001000
[1,8,7,6,3,4,5,10,9,12,11,2]=>00001110111=>11101110000
[1,8,7,6,3,4,5,12,11,9,10,2]=>00001110111=>11101110000
[1,10,7,6,3,4,9,5,8,12,11,2]=>00001101111=>11110110000
[1,12,7,6,3,4,9,5,11,8,10,2]=>00001101111=>11110110000
[1,12,7,6,3,4,11,10,5,8,9,2]=>00001101111=>11110110000
[1,10,9,6,3,8,4,5,7,12,11,2]=>00001011111=>11111010000
[1,12,9,6,3,8,4,5,11,7,10,2]=>00001011111=>11111010000
[1,12,11,6,3,8,4,10,5,7,9,2]=>00001011111=>11111010000
[1,12,11,6,3,10,9,4,5,7,8,2]=>00001011111=>11111010000
[1,10,9,8,7,3,4,5,6,12,11,2]=>00000111111=>11111100000
[1,12,9,8,7,3,4,5,11,6,10,2]=>00000111111=>11111100000
[1,12,11,8,7,3,4,10,5,6,9,2]=>00000111111=>11111100000
[1,12,11,10,7,3,9,4,5,6,8,2]=>00000111111=>11111100000
[1,12,11,10,9,8,3,4,5,6,7,2]=>00000111111=>11111100000
[3,1,2,6,5,8,7,10,9,12,11,4]=>01001010111=>11101010010
[3,1,2,6,5,8,7,12,11,9,10,4]=>01001010111=>11101010010
[3,1,2,6,5,10,9,7,8,12,11,4]=>01001001111=>11110010010
[3,1,2,6,5,12,9,7,11,8,10,4]=>01001001111=>11110010010
[3,1,2,6,5,12,11,10,7,8,9,4]=>01001001111=>11110010010
[3,1,2,8,7,5,6,10,9,12,11,4]=>01000110111=>11101100010
[3,1,2,8,7,5,6,12,11,9,10,4]=>01000110111=>11101100010
[3,1,2,10,7,5,9,6,8,12,11,4]=>01000101111=>11110100010
[3,1,2,12,7,5,9,6,11,8,10,4]=>01000101111=>11110100010
[3,1,2,12,7,5,11,10,6,8,9,4]=>01000101111=>11110100010
[3,1,2,10,9,8,5,6,7,12,11,4]=>01000011111=>11111000010
[3,1,2,12,9,8,5,6,11,7,10,4]=>01000011111=>11111000010
[3,1,2,12,11,8,5,10,6,7,9,4]=>01000011111=>11111000010
[3,1,2,12,11,10,9,5,6,7,8,4]=>01000011111=>11111000010
[3,1,5,2,4,8,7,10,9,12,11,6]=>01010010111=>11101001010
[3,1,5,2,4,8,7,12,11,9,10,6]=>01010010111=>11101001010
[3,1,5,2,4,10,9,7,8,12,11,6]=>01010001111=>11110001010
[3,1,5,2,4,12,9,7,11,8,10,6]=>01010001111=>11110001010
[3,1,5,2,4,12,11,10,7,8,9,6]=>01010001111=>11110001010
[3,1,5,2,7,4,6,10,9,12,11,8]=>01010100111=>11100101010
[3,1,5,2,7,4,6,12,11,9,10,8]=>01010100111=>11100101010
[3,1,5,2,7,4,9,6,8,12,11,10]=>01010101011=>11010101010
[3,1,5,2,7,4,9,6,11,8,10,12]=>01010101010=>01010101010
[3,1,5,2,7,4,11,10,6,8,9,12]=>01010100110=>01100101010
[3,1,5,2,9,8,4,6,7,12,11,10]=>01010011011=>11011001010
[3,1,7,6,2,4,5,10,9,12,11,8]=>01001100111=>11100110010
[3,1,7,6,2,4,5,12,11,9,10,8]=>01001100111=>11100110010
[3,1,7,6,2,4,9,5,8,12,11,10]=>01001101011=>11010110010
[3,1,7,6,2,4,9,5,11,8,10,12]=>01001101010=>01010110010
[3,1,9,6,2,8,4,5,7,12,11,10]=>01001011011=>11011010010
[3,1,9,6,2,8,4,5,11,7,10,12]=>01001011010=>01011010010
[3,1,11,6,2,8,4,10,5,7,9,12]=>01001010110=>01101010010
[3,1,9,8,7,2,4,5,6,12,11,10]=>01000111011=>11011100010
[3,1,9,8,7,2,4,5,11,6,10,12]=>01000111010=>01011100010
[3,1,11,10,7,2,9,4,5,6,8,12]=>01000101110=>01110100010
[5,4,1,2,3,8,7,10,9,12,11,6]=>00110010111=>11101001100
[5,4,1,2,3,8,7,12,11,9,10,6]=>00110010111=>11101001100
[5,4,1,2,3,10,9,7,8,12,11,6]=>00110001111=>11110001100
[5,4,1,2,3,12,9,7,11,8,10,6]=>00110001111=>11110001100
[5,4,1,2,3,12,11,10,7,8,9,6]=>00110001111=>11110001100
[5,4,1,2,7,3,6,10,9,12,11,8]=>00110100111=>11100101100
[5,4,1,2,7,3,6,12,11,9,10,8]=>00110100111=>11100101100
[5,4,1,2,7,3,9,6,8,12,11,10]=>00110101011=>11010101100
[5,4,1,2,7,3,9,6,11,8,10,12]=>00110101010=>01010101100
[5,4,1,2,9,8,3,6,7,12,11,10]=>00110011011=>11011001100
[7,4,1,6,2,3,5,10,9,12,11,8]=>00101100111=>11100110100
[7,4,1,6,2,3,5,12,11,9,10,8]=>00101100111=>11100110100
[7,4,1,6,2,3,9,5,8,12,11,10]=>00101101011=>11010110100
[7,4,1,6,2,3,9,5,11,8,10,12]=>00101101010=>01010110100
[9,4,1,6,2,8,3,5,7,12,11,10]=>00101011011=>11011010100
[9,4,1,6,2,8,3,5,11,7,10,12]=>00101011010=>01011010100
[11,4,1,6,2,8,3,10,5,7,9,12]=>00101010110=>01101010100
[9,4,1,8,7,2,3,5,6,12,11,10]=>00100111011=>11011100100
[7,6,5,1,2,3,4,10,9,12,11,8]=>00011100111=>11100111000
[7,6,5,1,2,3,4,12,11,9,10,8]=>00011100111=>11100111000
[7,6,5,1,2,3,9,4,8,12,11,10]=>00011101011=>11010111000
[9,6,5,1,2,8,3,4,7,12,11,10]=>00011011011=>11011011000
[9,6,5,1,2,8,3,4,11,7,10,12]=>00011011010=>01011011000
[11,6,5,1,2,8,3,10,4,7,9,12]=>00011010110=>01101011000
[9,8,5,1,7,2,3,4,6,12,11,10]=>00010111011=>11011101000
[9,8,5,1,7,2,3,4,11,6,10,12]=>00010111010=>01011101000
[11,8,5,1,7,2,3,10,4,6,9,12]=>00010110110=>01101101000
[9,8,7,6,1,2,3,4,5,12,11,10]=>00001111011=>11011110000
[11,10,7,6,1,2,9,3,4,5,8,12]=>00001101110=>01110110000
[11,10,9,6,1,8,2,3,4,5,7,12]=>00001011110=>01111010000
[11,10,9,8,7,1,2,3,4,5,6,12]=>00000111110=>01111100000
[3,8,5,2,1,4,7,6]=>1001011=>1101001
[3,5,4,8,2,6,7,1]=>0001011=>1101000
[5,4,7,1,8,6,3,2]=>0101111=>1111010
[2,4,1,5,3,6,7,8,9]=>00110000=>00001100
[1,4,8,2,6,5,3,7]=>0001101=>1011000
[8,5,1,3,6,2,4,7]=>0001101=>1011000
[7,5,1,8,3,4,2,6]=>0011011=>1101100
[5,2,8,1,7,4,3,6]=>0011011=>1101100
[1,4,8,2,6,7,3,5]=>0000011=>1100000
[1,2,5,6,8,7,3,4]=>0000011=>1100000
[1,5,6,8,2,7,4,3]=>0010011=>1100100
[2,6,7,3,4,1,8,5]=>0010011=>1100100
[1,6,5,7,8,2,4,3]=>0010101=>1010100
[1,5,6,7,2,8,4,3]=>0010011=>1100100
[3,7,6,1,8,2,4,5]=>0000111=>1110000
[1,3,7,2,6,4,8,5]=>0000111=>1110000
[1,5,8,6,7,3,4,2]=>0010011=>1100100
[1,6,5,8,7,2,4,3]=>0010111=>1110100
[1,5,7,6,2,8,3,4]=>0000111=>1110000
[1,2,5,8,6,7,4,3]=>0010011=>1100100
[1,2,6,5,7,3,8,4]=>0000111=>1110000
[1,7,5,8,6,4,2,3]=>0010111=>1110100
[3,6,5,8,1,2,7,4]=>0000111=>1110000
[5,4,7,8,1,6,3,2]=>0101101=>1011010
[2,5,6,8,1,3,7,4]=>0000011=>1100000
[5,3,6,8,1,2,7,4]=>0001011=>1101000
[4,6,5,8,3,2,7,1]=>0100111=>1110010
[4,5,6,8,2,3,7,1]=>0000011=>1100000
[2,5,8,7,1,6,4,3]=>0010111=>1110100
[4,7,5,8,3,6,2,1]=>1000111=>1110001
[7,3,6,8,5,2,1,4]=>1001011=>1101001
[8,3,6,7,5,2,4,1]=>0011011=>1101100
[8,4,5,7,3,6,2,1]=>1000111=>1110001
[2,4,7,8,5,6,3,1]=>0100101=>1010010
[3,6,8,7,5,2,4,1]=>0011011=>1101100
[6,4,7,8,5,1,3,2]=>0101101=>1011010
[7,8,4,6,5,3,1,2]=>0101101=>1011010
[6,8,4,7,5,1,3,2]=>0101011=>1101010
[4,5,6,7,8,3,9,1,2]=>00000011=>11000000
[8,9,2,3,4,5,1,6,7]=>00010001=>10001000
[5,6,7,4,8,9,1,2,3]=>00000101=>10100000
[7,8,9,2,3,1,4,5,6]=>01000001=>10000010
[6,5,7,8,9,1,2,3,4]=>00001001=>10010000
[7,6,1,2,3,5,4,8]=>0001110=>0111000
[2,8,7,5,1,6,3,4]=>0001111=>1111000
[8,7,6,4,2,1,5,3]=>1011111=>1111101
[3,8,7,5,2,6,4,1]=>0011111=>1111100
[3,8,7,5,1,2,6,4]=>0001111=>1111000
[5,8,3,7,1,4,6,2]=>0000111=>1110000
[3,8,7,4,2,6,5,1]=>0011111=>1111100
[5,8,3,2,4,7,6,1]=>0100111=>1110010
[5,3,8,2,4,6,1,7]=>0001101=>1011000
[4,5,8,3,2,6,1,7]=>0100101=>1010010
[5,8,2,1,4,6,3,7]=>1000101=>1010001
[4,1,5,8,3,6,2,7]=>0010101=>1010100
[4,5,8,3,6,1,2,7]=>0000101=>1010000
[3,2,7,1,8,5,4,6]=>0101011=>1101010
[4,7,8,5,2,3,1,6]=>0101001=>1001010
[6,2,7,8,1,5,3,4]=>0001101=>1011000
[2,7,1,3,8,5,4,6]=>0001011=>1101000
[2,6,7,8,4,1,3,5]=>0010001=>1000100
[2,6,7,8,4,3,1,5]=>0110001=>1000110
[7,1,2,3,4,5,8,6,9]=>00000110=>01100000
[6,1,2,3,4,7,5,8,9]=>00001100=>00110000
[5,1,2,3,6,4,7,8,9]=>00011000=>00011000
[4,1,2,5,3,6,7,8,9]=>00110000=>00001100
[8,1,2,6,5,3,7,4]=>0001111=>1111000
[8,5,4,6,1,2,7,3]=>0001111=>1111000
[7,4,1,8,2,5,3,6]=>0011011=>1101100
[7,2,1,8,3,6,4,5]=>1000111=>1110001
[6,8,7,3,1,2,4,5]=>0100011=>1100010
[7,4,8,3,1,2,6,5]=>0100111=>1110010
[8,4,5,3,1,6,7,2]=>0101011=>1101010
[8,2,3,1,6,7,4,5]=>0100011=>1100010
[8,2,1,7,4,3,5,6]=>1010011=>1100101
[7,2,6,8,4,1,3,5]=>0010011=>1100100
[7,2,5,1,6,8,3,4]=>0001011=>1101000
[6,2,1,7,4,8,3,5]=>1000111=>1110001
[1,7,4,3,2,5,6,8]=>0110010=>0100110
[1,7,4,3,6,2,5,8]=>0010110=>0110100
[3,7,5,8,2,4,6,1]=>0000111=>1110000
[5,2,1,6,3,4,8,7]=>1001101=>1011001
[5,1,3,4,6,2,8,7]=>0001101=>1011000
[3,8,4,5,7,2,6,1]=>0000111=>1110000
[3,8,4,7,5,6,2,1]=>1000111=>1110001
[4,2,8,6,3,7,5,1]=>0011111=>1111100
[4,1,7,6,3,8,5,2]=>0011111=>1111100
[7,4,1,8,5,3,6,2]=>0011111=>1111100
[3,5,6,8,4,7,1,2]=>0000011=>1100000
[5,4,1,8,6,7,2,3]=>0011011=>1101100
[6,2,8,4,5,3,7,1]=>0001111=>1111000
[4,5,2,1,8,7,3,6]=>1001011=>1101001
[4,7,3,8,2,6,5,1]=>0001111=>1111000
[4,7,3,1,8,6,2,5]=>0100111=>1110010
[6,2,1,3,7,4,8,5]=>1000111=>1110001
[6,3,7,1,2,5,8,4]=>0000111=>1110000
[5,1,4,7,8,2,6,3]=>0001101=>1011000
[7,2,5,8,1,3,6,4]=>0000111=>1110000
[8,3,6,7,2,4,5,1]=>0001011=>1101000
[3,8,7,5,2,1,6,4]=>1001111=>1111001
[3,8,5,6,2,7,4,1]=>0010111=>1110100
[3,6,5,8,4,2,7,1]=>0010111=>1110100
[6,8,3,2,5,7,4,1]=>0110011=>1100110
[4,1,5,6,8,7,3,2]=>0110011=>1100110
[8,4,2,3,6,7,5,1]=>0011011=>1101100
[6,1,2,4,5,7,8,3]=>0000101=>1010000
[4,5,1,3,7,6,8,2]=>0001011=>1101000
[3,5,4,8,6,2,7,1]=>0001111=>1111000
[3,6,2,4,5,8,7,1]=>0000111=>1110000
[8,1,2,3,4,5,9,7,6]=>00000111=>11100000
[8,1,2,3,4,9,6,7,5]=>00000111=>11100000
[9,1,2,3,8,5,6,7,4]=>00000111=>11100000
[8,1,3,7,4,5,6,2]=>0000111=>1110000
[9,1,2,3,4,5,6,10,8,7]=>000000111=>111000000
[9,1,2,3,4,5,10,7,8,6]=>000000111=>111000000
[10,1,2,3,4,9,6,7,8,5]=>000000111=>111000000
[10,1,9,3,4,5,6,7,8,2]=>000000111=>111000000
[10,1,2,3,4,5,6,8,9,7]=>000000011=>110000000
[9,1,2,3,4,6,7,8,5]=>00000011=>11000000
[8,1,5,3,6,4,7,2]=>0001111=>1111000
[2,6,4,1,5,8,7,3]=>0010111=>1110100
[7,6,5,2,4,3,8,1]=>0011111=>1111100
[3,6,4,5,2,8,1,7]=>0001101=>1011000
[8,1,5,4,7,3,6,2]=>0001111=>1111000
[7,6,5,4,1,8,2,3]=>0011111=>1111100
[3,6,4,1,5,7,2,8]=>0010110=>0110100
[8,1,5,4,7,6,3,2]=>0101111=>1111010
[2,5,1,4,6,7,3,8]=>0001010=>0101000
[7,6,5,2,8,4,1,3]=>0011111=>1111100
[3,1,6,5,2,8,7,4]=>0101111=>1111010
[1,7,2,4,3,5,8,6]=>0010011=>1100100
[3,8,1,7,4,2,6,5]=>0010111=>1110100
[8,1,7,4,3,5,6,2]=>0010111=>1110100
[6,8,2,4,5,3,7,1]=>0001011=>1101000
[4,8,5,3,6,1,7,2]=>0001111=>1111000
[8,6,3,2,7,4,1,5]=>0110111=>1110110
[2,7,3,1,8,4,5,6]=>0100011=>1100010
[1,2,8,3,5,6,4,7]=>0000101=>1010000
[3,5,7,4,8,1,6,2]=>0000111=>1110000
[2,8,1,3,5,4,6,7]=>0001001=>1001000
[1,3,2,10,6,5,4,9,8,7]=>010110111=>111011010
[1,6,3,2,5,4,10,9,8,7]=>010110111=>111011010
[1,6,3,2,10,5,4,9,8,7]=>010110111=>111011010
[1,10,6,3,2,5,4,9,8,7]=>010110111=>111011010
[1,6,3,2,10,9,5,4,8,7]=>010110111=>111011010
[1,10,6,3,2,9,5,4,8,7]=>010110111=>111011010
[3,1,2,6,5,4,10,9,8,7]=>010110111=>111011010
[3,1,2,10,6,5,4,9,8,7]=>010110111=>111011010
[3,1,6,2,5,4,10,9,8,7]=>010110111=>111011010
[3,1,6,2,10,5,4,9,8,7]=>010110111=>111011010
[3,1,10,6,2,5,4,9,8,7]=>010110111=>111011010
[3,1,6,2,10,9,5,4,8,7]=>010110111=>111011010
[3,1,10,6,2,9,5,4,8,7]=>010110111=>111011010
[6,3,1,2,5,4,10,9,8,7]=>010110111=>111011010
[6,3,1,2,10,5,4,9,8,7]=>010110111=>111011010
[6,3,1,10,2,5,4,9,8,7]=>010110111=>111011010
[10,6,3,1,2,5,4,9,8,7]=>010110111=>111011010
[6,3,1,2,10,9,5,4,8,7]=>010110111=>111011010
[6,3,1,10,2,9,5,4,8,7]=>010110111=>111011010
[10,6,3,1,2,9,5,4,8,7]=>010110111=>111011010
[3,1,6,5,2,4,10,9,8,7]=>010110111=>111011010
[3,1,6,5,2,10,4,9,8,7]=>010110111=>111011010
[3,1,10,6,5,2,4,9,8,7]=>010110111=>111011010
[3,1,6,5,2,10,9,4,8,7]=>010110111=>111011010
[3,1,10,6,5,2,9,4,8,7]=>010110111=>111011010
[6,3,1,5,2,4,10,9,8,7]=>010110111=>111011010
[6,3,1,5,2,10,4,9,8,7]=>010110111=>111011010
[6,3,1,10,5,2,4,9,8,7]=>010110111=>111011010
[10,6,3,1,5,2,4,9,8,7]=>010110111=>111011010
[6,3,1,5,2,10,9,4,8,7]=>010110111=>111011010
[6,3,1,10,5,2,9,4,8,7]=>010110111=>111011010
[10,6,3,1,5,2,9,4,8,7]=>010110111=>111011010
[6,3,1,10,9,5,2,4,8,7]=>010110111=>111011010
[10,6,3,1,9,5,2,4,8,7]=>010110111=>111011010
[3,1,6,5,2,10,9,8,4,7]=>010110111=>111011010
[3,1,10,6,5,2,9,8,4,7]=>010110111=>111011010
[6,3,1,5,2,10,9,8,4,7]=>010110111=>111011010
[6,3,1,10,5,2,9,8,4,7]=>010110111=>111011010
[10,6,3,1,5,2,9,8,4,7]=>010110111=>111011010
[6,3,1,10,9,5,2,8,4,7]=>010110111=>111011010
[1,5,2,8,6,4,3,7]=>0011101=>1011100
[7,4,8,6,3,1,2,5]=>0100111=>1110010
[3,6,8,4,1,2,5,7]=>0010001=>1000100
[4,7,8,5,2,1,3,6]=>1001001=>1001001
[6,1,5,2,8,7,3,4]=>0001111=>1111000
[8,1,3,5,7,4,2,6]=>0010011=>1100100
[3,1,8,5,4,7,2,6]=>0101011=>1101010
[3,1,6,4,8,5,2,7]=>0101101=>1011010
[5,1,3,4,2,6,8,7]=>0011001=>1001100
[3,2,6,4,1,5,7,8]=>0110100=>0010110
[5,4,2,1,8,3,6,7]=>1011001=>1001101
[4,2,5,1,8,7,3,6]=>0011011=>1101100
[6,8,2,7,1,4,3,5]=>0010011=>1100100
[1,8,4,7,3,2,5,6]=>0100011=>1100010
[8,6,3,1,5,7,2,4]=>0100111=>1110010
[5,8,3,1,4,7,6,2]=>0100111=>1110010
[1,2,5,4,7,8,3,6]=>0001001=>1001000
[1,8,3,2,6,4,7,5]=>0100111=>1110010
[4,7,1,2,5,3,6,8]=>0001010=>0101000
[6,8,4,1,3,7,2,5]=>0010011=>1100100
[3,2,6,1,7,8,5,4]=>0101101=>1011010
[7,6,4,1,8,3,5,2]=>0011111=>1111100
[5,4,1,6,7,3,2,8]=>0111010=>0101110
[7,4,1,6,5,8,2,3]=>0010111=>1110100
[8,5,4,1,6,7,3,2]=>0111011=>1101110
[5,2,1,6,4,7,8,3]=>1001101=>1011001
[1,6,2,3,5,7,8,4]=>0000101=>1010000
[1,3,4,8,5,2,6,7]=>0001001=>1001000
[8,2,4,6,1,7,3,5]=>0000111=>1110000
[1,5,7,2,3,6,8,4]=>0000011=>1100000
[7,3,1,4,2,5,8,6]=>0110011=>1100110
[3,2,5,7,8,4,1,6]=>0110001=>1000110
[4,3,5,1,6,2,7,8]=>0011100=>0011100
[8,6,3,5,4,1,2,7]=>0011101=>1011100
[8,3,2,6,1,5,4,7]=>0101101=>1011010
[8,5,1,7,4,6,2,3]=>0001111=>1111000
[4,8,1,7,6,3,5,2]=>0001111=>1111000
[8,5,1,7,4,3,6,2]=>0011111=>1111100
[8,5,7,6,2,1,3,4]=>1000111=>1110001
[5,4,8,3,1,7,2,6]=>0101011=>1101010
[5,1,4,8,3,2,7,6]=>0101011=>1101010
[4,8,1,7,6,5,2,3]=>0001111=>1111000
[4,3,8,7,2,6,1,5]=>0010111=>1110100
[3,8,7,2,6,4,1,5]=>0010111=>1110100
[8,2,5,7,4,3,6,1]=>0010111=>1110100
[3,8,7,4,6,1,2,5]=>0000111=>1110000
[8,7,6,3,5,4,1,2]=>0011111=>1111100
[2,8,4,7,6,1,5,3]=>0001111=>1111000
[2,5,4,8,3,1,7,6]=>0101011=>1101010
[5,4,8,2,1,3,7,6]=>1001011=>1101001
[3,8,7,2,6,1,5,4]=>0001111=>1111000
[1,8,4,7,6,3,5,2]=>0001111=>1111000
[1,8,3,7,6,5,2,4]=>0001111=>1111000
[1,4,3,8,7,2,6,5]=>0010111=>1110100
[7,1,5,4,6,2,3,8]=>0001110=>0111000
[7,4,1,3,6,2,5,8]=>0010110=>0110100
[5,4,3,1,7,6,2,8]=>0111110=>0111110
[4,1,3,7,5,6,2,8]=>0010110=>0110100
[2,6,8,3,1,7,4,5]=>0100011=>1100010
[2,5,4,8,1,7,3,6]=>0001011=>1101000
[7,5,2,4,8,3,6,1]=>0001111=>1111000
[7,8,2,6,3,5,4,1]=>0011101=>1011100
[7,2,6,5,8,3,4,1]=>0010111=>1110100
[5,6,3,1,4,2,7,8]=>0110100=>0010110
[2,6,5,3,4,8,7,1]=>0001111=>1111000
[2,6,1,5,3,4,7,8]=>0001100=>0011000
[3,6,2,7,4,5,1,8]=>0001110=>0111000
[3,4,7,8,5,1,6,2]=>0001101=>1011000
[3,6,2,4,7,8,5,1]=>0001101=>1011000
[5,3,6,4,8,7,2,1]=>1001111=>1111001
[1,5,4,8,6,2,7,3]=>0001111=>1111000
[4,5,2,7,6,3,8,1]=>0001111=>1111000
[5,8,3,1,2,7,6,4]=>0100111=>1110010
[7,6,2,5,3,8,4,1]=>0011111=>1111100
[8,4,6,1,3,7,2,5]=>0000111=>1110000
[4,8,5,1,2,3,6,7]=>0001001=>1001000
[8,6,2,4,5,1,3,7]=>0001101=>1011000
[4,5,1,3,8,6,2,7]=>0001101=>1011000
[7,4,2,3,6,8,5,1]=>0011011=>1101100
[2,1,6,7,4,8,3,5]=>1000011=>1100001
[7,8,1,3,6,4,5,2]=>0001101=>1011000
[7,2,6,8,4,5,3,1]=>0101011=>1101010
[7,3,6,8,5,1,4,2]=>0011011=>1101100
[7,5,8,1,6,2,4,3]=>0010111=>1110100
[5,7,8,1,6,3,2,4]=>0100101=>1010010
[7,2,6,8,5,1,4,3]=>0011011=>1101100
[7,5,2,4,8,3,1,6]=>0101011=>1101010
[7,8,3,1,6,2,5,4]=>0101101=>1011010
[6,7,8,4,3,1,5,2]=>0111001=>1001110
[7,8,3,6,4,1,5,2]=>0011101=>1011100
[7,3,8,1,6,4,5,2]=>0001111=>1111000
[1,7,5,8,2,4,6,3]=>0000111=>1110000
[7,5,2,8,1,4,6,3]=>0001111=>1111000
[3,7,8,2,6,5,1,4]=>0001101=>1011000
[3,7,8,2,1,6,4,5]=>1000101=>1010001
[7,8,1,6,3,5,4,2]=>0011101=>1011100
[6,7,8,2,5,4,3,1]=>0111001=>1001110
[6,7,8,3,1,5,4,2]=>0111001=>1001110
[7,8,1,6,2,5,4,3]=>0011101=>1011100
[5,6,1,4,3,8,2,7]=>0010101=>1010100
[5,1,6,8,3,4,7,2]=>0001011=>1101000
[7,1,6,8,5,4,3,2]=>0111011=>1101110
[5,6,8,1,2,3,7,4]=>0000011=>1100000
[4,8,1,2,7,6,5,3]=>0001111=>1111000
[4,6,1,2,8,5,7,3]=>0000111=>1110000
[6,4,7,3,5,2,1,8]=>1001110=>0111001
[5,7,8,4,2,1,3,6]=>1010001=>1000101
[6,4,8,3,5,2,1,7]=>1001101=>1011001
[3,1,6,2,5,7,8,4]=>0100101=>1010010
[2,1,6,3,5,7,4,8]=>1000110=>0110001
[1,6,4,5,2,7,3,8]=>0001110=>0111000
[1,4,7,3,2,5,6,8]=>0100010=>0100010
[6,2,1,4,5,3,7,8]=>1001100=>0011001
[6,2,1,5,7,3,4,8]=>1000110=>0110001
[1,2,3,4,5,8,9,6,7]=>00000001=>10000000
[1,2,3,4,7,9,5,8,6]=>00000011=>11000000
[1,2,3,6,9,4,7,8,5]=>00000011=>11000000
[1,2,4,6,8,3,7,5]=>0000011=>1100000
[1,2,5,9,3,6,7,8,4]=>00000011=>11000000
[1,3,5,8,2,6,7,4]=>0000011=>1100000
[1,4,9,2,5,6,7,8,3]=>00000011=>11000000
[3,9,1,4,5,6,7,8,2]=>00000011=>11000000
[6,1,3,7,2,8,5,4]=>0001111=>1111000
[6,4,5,8,3,7,1,2]=>0000111=>1110000
[8,1,4,3,6,7,2,5]=>0010011=>1100100
[2,6,8,4,3,1,7,5]=>0110011=>1100110
[8,1,5,2,6,4,3,7]=>0011101=>1011100
[1,6,7,4,2,8,3,5]=>0010011=>1100100
[1,7,8,4,3,6,2,5]=>0010101=>1010100
[1,5,8,7,4,3,2,6]=>0110011=>1100110
[1,4,7,2,3,6,8,5]=>0000011=>1100000
[3,1,2,6,7,8,5,4]=>0101001=>1001010
[3,8,1,6,4,2,7,5]=>0010111=>1110100
[1,6,3,4,7,8,2,5]=>0000101=>1010000
[3,1,5,7,6,2,8,4]=>0100111=>1110010
[6,3,1,4,2,7,8,5]=>0110101=>1010110
[2,4,3,7,6,1,8,5]=>0010111=>1110100
[3,1,7,6,5,2,8,4]=>0101111=>1111010
[1,4,7,6,8,3,2,5]=>0100011=>1100010
[7,2,1,5,6,3,8,4]=>1000111=>1110001
[4,3,1,8,6,2,7,5]=>0110111=>1110110
[3,1,5,2,8,7,6,4]=>0101111=>1111010
[1,2,8,4,3,7,6,5]=>0010111=>1110100
[2,6,1,8,7,4,3,5]=>0010111=>1110100
[7,5,1,8,3,2,6,4]=>0101111=>1111010
[4,7,6,3,1,8,2,5]=>0100111=>1110010
[5,3,1,8,6,2,4,7]=>0101101=>1011010
[5,1,8,6,3,2,4,7]=>0101101=>1011010
[1,5,4,2,8,6,3,7]=>0011101=>1011100
[1,4,2,8,5,3,7,6]=>0011011=>1101100
[8,3,1,6,4,2,5,7]=>0110101=>1010110
[1,7,4,8,3,5,2,6]=>0001011=>1101000
[7,3,2,4,8,5,1,6]=>0101011=>1101010
[5,7,8,1,4,2,6,3]=>0010101=>1010100
[2,6,3,8,1,7,5,4]=>0001111=>1111000
[2,5,1,8,6,3,7,4]=>0001111=>1111000
[2,8,6,4,1,7,3,5]=>0010111=>1110100
[1,8,4,2,7,5,3,6]=>0011011=>1101100
[6,5,1,7,2,8,4,3]=>0011111=>1111100
[2,8,1,7,5,3,6,4]=>0001111=>1111000
[1,2,8,7,6,4,3,5]=>0010111=>1110100
[4,1,7,8,6,3,5,2]=>0011101=>1011100
[1,6,5,7,8,4,2,3]=>0010101=>1010100
[4,1,8,7,6,3,5,2]=>0011111=>1111100
[4,8,2,6,3,5,1,7]=>0001101=>1011000
[4,3,5,7,1,6,2,8]=>0010110=>0110100
[4,1,8,5,3,6,2,7]=>0011101=>1011100
[6,4,2,5,3,1,7,8]=>0111100=>0011110
[3,1,5,8,2,7,4,6]=>0100011=>1100010
[6,4,1,5,3,2,7,8]=>0111100=>0011110
[6,2,1,5,4,3,7,8]=>1011100=>0011101
[3,1,8,5,4,6,2,7]=>0101101=>1011010
[6,1,8,4,5,3,2,7]=>0101101=>1011010
[4,5,2,7,1,6,3,8]=>0001110=>0111000
[4,3,5,7,1,6,8,2]=>0010011=>1100100
[4,1,8,5,3,6,7,2]=>0011011=>1101100
[6,3,8,4,5,1,7,2]=>0001111=>1111000
[3,1,6,8,5,7,4,2]=>0110011=>1100110
[2,6,1,8,5,7,4,3]=>0010111=>1110100
[6,3,8,4,5,2,1,7]=>1001101=>1011001
[6,5,8,7,2,3,4,1]=>0010111=>1110100
[6,3,8,4,5,2,7,1]=>0001111=>1111000
[2,1,6,8,5,3,7,4]=>1001011=>1101001
[3,2,6,8,5,4,7,1]=>0101011=>1101010
[4,1,8,5,2,6,3,7]=>0011101=>1011100
[3,1,6,8,5,2,4,7]=>0101001=>1001010
[6,5,8,7,4,1,2,3]=>0010111=>1110100
[6,5,8,7,4,2,1,3]=>1010111=>1110101
[6,5,8,7,2,4,1,3]=>0010111=>1110100
[6,2,8,4,5,7,1,3]=>0000111=>1110000
[6,1,8,4,5,7,3,2]=>0100111=>1110010
[10,1,11,2,3,4,5,6,7,8,9]=>0000000011=>1100000000
[1,9,2,10,3,4,5,6,7,8]=>000000011=>110000000
[2,8,1,9,3,4,5,6,7]=>00000011=>11000000
[10,11,1,2,3,4,5,6,7,8,9]=>0000000001=>1000000000
[4,2,7,3,5,8,6,1]=>0010111=>1110100
[3,6,2,4,8,5,7,1]=>0000111=>1110000
[2,7,5,4,3,8,6,1]=>0011111=>1111100
[3,5,1,8,4,7,6,2]=>0001111=>1111000
[3,6,1,8,5,4,7,2]=>0001111=>1111000
[2,4,8,3,7,6,5,1]=>0001111=>1111000
[3,6,8,2,5,7,4,1]=>0010011=>1100100
[2,6,8,5,4,3,7,1]=>0011011=>1101100
[3,6,8,2,5,4,7,1]=>0001011=>1101000
[4,6,8,3,2,5,7,1]=>0100011=>1100010
[4,6,2,8,3,5,7,1]=>0000111=>1110000
[3,6,1,8,5,7,4,2]=>0010111=>1110100
[5,2,6,8,4,1,7,3]=>0011011=>1101100
[4,6,3,8,7,2,5,1]=>0001111=>1111000
[3,5,8,2,7,4,6,1]=>0000111=>1110000
[2,6,8,5,7,4,3,1]=>0110011=>1100110
[2,4,8,7,6,3,5,1]=>0001111=>1111000
[7,5,1,6,3,2,8,4]=>0101111=>1111010
[2,7,6,3,4,1,8,5]=>0010111=>1110100
[5,7,6,3,1,2,8,4]=>0100111=>1110010
[4,8,2,1,7,5,6,3]=>1000111=>1110001
[6,3,8,5,7,2,4,1]=>0010111=>1110100
[1,5,4,8,6,2,3,7]=>0001101=>1011000
[8,2,1,7,5,3,6,4]=>1001111=>1111001
[8,2,1,6,7,3,5,4]=>1001011=>1101001
[6,2,8,1,7,5,3,4]=>0001111=>1111000
[3,5,1,8,7,6,2,4]=>0001111=>1111000
[1,4,2,3,6,5,8,7,9]=>00101010=>01010100
[1,3,4,2,6,5,8,7,9]=>00101010=>01010100
[1,4,2,3,6,5,8,7,10,9]=>001010101=>101010100
[2,3,1,4,6,5,8,7,9]=>01001010=>01010010
[4,6,1,2,3,5,8,7,9]=>00001010=>01010000
[3,4,5,1,6,2,8,7,9]=>00011010=>01011000
[3,1,2,4,6,5,8,7,9]=>01001010=>01010010
[1,3,4,2,6,5,8,7,10,9]=>001010101=>101010100
[3,1,4,2,6,5,8,7,10,9,11]=>0110101010=>0101010110
[5,6,2,7,8,1,3,4]=>0000101=>1010000
[4,7,3,5,6,1,2,8]=>0000110=>0110000
[4,7,8,3,5,6,1,2]=>0000101=>1010000
[2,1,3,4,5,6,9,7,8]=>10000001=>10000001
[1,2,3,4,5,6,7,8,10,9,11]=>0000000010=>0100000000
[1,2,3,4,5,7,8,6,9]=>00000010=>01000000
[2,1,3,4,5,6,7,10,8,9]=>100000001=>100000001
[3,2,5,6,8,4,7,1]=>0100011=>1100010
[8,4,5,2,6,3,7,1]=>0001111=>1111000
[2,5,6,4,8,3,7,1]=>0000111=>1110000
[4,2,5,7,3,8,1,6]=>0010011=>1100100
[4,7,3,1,6,8,2,5]=>0100011=>1100010
[4,2,7,6,8,1,3,5]=>0010011=>1100100
[1,7,4,6,8,3,2,5]=>0100011=>1100010
[2,4,3,6,5,8,7,10,9,12,11,1]=>00101010111=>11101010100
[4,7,2,5,6,3,1,8]=>0100110=>0110010
[5,4,1,3,7,8,2,6]=>0011001=>1001100
[6,1,5,8,3,7,2,4]=>0000111=>1110000
[4,1,3,5,7,8,2,6]=>0010001=>1000100
[6,1,5,8,4,3,2,7]=>0110101=>1010110
[7,2,1,6,8,3,5,4]=>1001011=>1101001
[5,6,4,1,8,3,2,7]=>0110101=>1010110
[4,5,2,1,7,8,3,6]=>1001001=>1001001
[2,3,7,8,5,1,6,4]=>0001101=>1011000
[4,1,7,6,2,3,8,5]=>0010111=>1110100
[1,2,6,7,4,3,5,8]=>0010010=>0100100
[10,2,3,4,5,6,7,8,1,9]=>000000101=>101000000
[7,1,9,3,4,5,6,2,8]=>00001101=>10110000
[5,8,6,3,4,1,2,7]=>0010101=>1010100
[3,10,1,4,5,6,7,8,9,2]=>000000011=>110000000
[11,2,3,4,5,6,7,8,9,1,10]=>0000000101=>1010000000
[8,1,10,3,4,5,6,7,2,9]=>000001101=>101100000
[7,2,1,9,4,5,6,3,8]=>10001101=>10110001
[6,9,7,3,4,5,1,2,8]=>00010101=>10101000
[6,2,3,1,8,5,4,7]=>0101101=>1011010
[5,1,2,6,4,8,3,7]=>0001101=>1011000
[8,6,2,3,7,5,1,4]=>0001111=>1111000
[3,8,1,2,9,5,6,7,4]=>00000111=>11100000
[8,7,9,1,2,3,4,5,6]=>00000011=>11000000
[3,11,1,4,5,6,7,8,9,10,2]=>0000000011=>1100000000
[12,2,3,4,5,6,7,8,9,10,1,11]=>00000000101=>10100000000
[9,1,11,3,4,5,6,7,8,2,10]=>0000001101=>1011000000
[8,2,1,10,4,5,6,7,3,9]=>100001101=>101100001
[7,10,8,3,4,5,6,1,2,9]=>000010101=>101010000
[7,2,3,1,9,5,6,4,8]=>01001101=>10110010
[6,1,2,7,4,5,9,3,8]=>00001101=>10110000
[5,9,6,3,4,1,7,2,8]=>00101101=>10110100
[4,5,2,8,6,1,3,7]=>0001101=>1011000
[3,4,8,2,5,6,1,7]=>0000101=>1010000
[3,8,1,4,2,9,6,7,5]=>00100111=>11100100
[9,7,2,3,8,5,6,1,4]=>00001111=>11110000
[3,9,1,2,10,5,6,7,8,4]=>000000111=>111000000
[3,12,1,4,5,6,7,8,9,10,11,2]=>00000000011=>11000000000
[2,8,3,6,7,4,5,1]=>0001011=>1101000
[6,8,2,7,5,3,1,4]=>0101011=>1101010
[6,3,2,5,8,4,1,7]=>0110101=>1010110
[5,6,7,2,8,4,1,3]=>0010011=>1100100
[5,8,3,6,4,1,7,2]=>0010111=>1110100
[4,3,8,5,2,7,1,6]=>0011011=>1101100
[2,8,4,5,1,6,3,7]=>0001101=>1011000
[3,2,5,8,4,7,1,6]=>0100011=>1100010
[2,5,8,1,3,4,7,6]=>0000011=>1100000
[3,5,1,8,7,4,2,6]=>0011011=>1101100
[4,6,1,3,8,2,7,5]=>0000111=>1110000
[8,6,1,2,3,5,7,4]=>0000111=>1110000
[5,1,7,8,3,2,4,6]=>0101001=>1001010
[3,1,7,6,2,8,5,4]=>0101111=>1111010
[5,3,6,7,4,2,8,1]=>0011011=>1101100
[5,4,2,8,6,7,3,1]=>0111011=>1101110
[6,1,4,2,8,7,3,5]=>0010111=>1110100
[3,7,2,6,8,4,5,1]=>0001011=>1101000
[4,6,5,2,7,8,3,1]=>0101101=>1011010
[5,4,6,2,7,8,3,1]=>0101101=>1011010
[5,1,8,6,4,2,7,3]=>0011111=>1111100
[6,2,1,8,5,7,4,3]=>1010111=>1110101
[6,5,7,8,1,3,4,2]=>0010101=>1010100
[2,1,7,6,8,4,5,3]=>1001011=>1101001
[6,4,7,2,8,3,1,5]=>0100111=>1110010
[6,3,2,7,8,4,5,1]=>0101101=>1011010
[4,7,3,1,5,2,8,6]=>0101011=>1101010
[2,1,4,7,5,3,8,6]=>1001011=>1101001
[4,7,6,3,1,5,8,2]=>0100111=>1110010
[2,4,7,3,8,5,1,6]=>0001011=>1101000
[2,7,3,1,8,5,4,6]=>0101011=>1101010
[2,8,3,1,7,4,5,6]=>0100011=>1100010
[7,6,8,9,1,2,3,4,5]=>00000101=>10100000
[5,4,6,7,8,9,1,2,3]=>00010001=>10001000
[1,2,6,8,3,4,7,5]=>0000011=>1100000
[1,5,6,8,3,2,4,7]=>0100001=>1000010
[1,8,2,7,3,5,6,4]=>0000111=>1110000
[1,7,4,8,6,5,3,2]=>0101111=>1111010
[1,6,3,5,7,4,8,2]=>0000111=>1110000
[1,5,4,7,2,8,3,6]=>0001011=>1101000
[3,8,5,2,6,1,7,4]=>0001111=>1111000
[3,7,4,8,5,2,6,1]=>0001111=>1111000
[8,1,2,6,5,3,4,7]=>0001101=>1011000
[3,7,4,2,5,6,1,8]=>0010110=>0110100
[6,8,7,1,3,4,2,5]=>0010011=>1100100
[3,4,2,8,6,7,5,1]=>0011011=>1101100
[3,7,8,6,1,4,2,5]=>0010101=>1010100
[3,6,1,5,2,7,8,4]=>0001101=>1011000
[7,1,6,8,3,4,2,5]=>0010011=>1100100
[8,1,2,6,3,5,7,4]=>0000111=>1110000
[6,2,8,4,7,1,3,5]=>0000111=>1110000
[3,7,8,4,2,5,6,1]=>0010101=>1010100
[3,4,2,8,5,1,6,7]=>0011001=>1001100
[1,4,3,2,5,6,7,8,9]=>01100000=>00000110
[6,8,2,7,5,4,1,3]=>0011011=>1101100
[1,8,4,3,7,6,2,5]=>0010111=>1110100
[4,3,8,7,1,2,6,5]=>0010111=>1110100
[1,8,4,5,7,6,2,3]=>0000111=>1110000
[4,3,8,5,7,1,6,2]=>0010111=>1110100
[6,3,4,8,7,2,1,5]=>1000111=>1110001
[5,3,8,4,7,1,6,2]=>0001111=>1111000
[5,2,8,7,1,4,6,3]=>0001111=>1111000
[3,2,8,7,1,6,4,5]=>0100111=>1110010
[2,7,8,3,1,6,4,5]=>0100101=>1010010
[2,7,8,5,1,4,6,3]=>0001101=>1011000
[3,5,8,7,4,1,6,2]=>0010111=>1110100
[7,4,6,8,3,5,1,2]=>0001011=>1101000
[2,7,8,1,3,6,4,5]=>0000101=>1010000
[2,7,8,1,5,4,6,3]=>0001101=>1011000
[2,7,8,1,4,5,6,3]=>0000101=>1010000
[3,6,7,8,2,4,1,5]=>0010001=>1000100
[4,5,7,8,6,3,1,2]=>0100101=>1010010
[5,4,6,8,7,3,1,2]=>0101011=>1101010
[4,5,8,6,7,1,3,2]=>0100011=>1100010
[5,7,6,8,2,1,3,4]=>1000011=>1100001
[3,7,6,8,2,4,1,5]=>0010011=>1100100
[5,4,7,8,6,3,1,2]=>0101101=>1011010
[4,5,7,8,2,6,1,3]=>0000101=>1010000
[4,5,6,8,7,3,1,2]=>0100011=>1100010
[6,1,5,3,8,4,7,2]=>0001111=>1111000
[1,8,6,2,5,4,7,3]=>0001111=>1111000
[3,8,4,1,7,5,2,6]=>0011011=>1101100
[6,2,7,4,8,3,1,5]=>0100111=>1110010
[2,8,5,1,4,3,7,6]=>0011011=>1101100
[6,8,2,7,5,1,4,3]=>0011011=>1101100
[8,3,4,5,6,1,7,2]=>0000111=>1110000
[5,3,6,4,7,2,1,8]=>1001110=>0111001
[4,2,6,5,7,3,1,8]=>0110110=>0110110
[5,4,6,2,7,3,1,8]=>0101110=>0111010
[3,2,6,5,8,4,1,7]=>0110101=>1010110
[3,2,6,5,8,7,1,4]=>0100111=>1110010
[4,2,6,5,8,7,1,3]=>0010111=>1110100
[5,2,6,4,8,7,1,3]=>0001111=>1111000
[5,4,7,6,8,2,1,3]=>1001011=>1101001
[6,4,7,5,8,3,1,2]=>0100111=>1110010
[4,2,7,5,8,6,1,3]=>0010111=>1110100
[3,2,7,5,8,4,1,6]=>0110011=>1100110
[4,3,7,2,8,5,1,6]=>0011011=>1101100
[4,3,6,2,8,5,1,7]=>0011101=>1011100
[4,3,7,6,8,5,1,2]=>0011011=>1101100
[5,3,7,6,8,2,1,4]=>1001011=>1101001
[5,3,7,2,8,6,1,4]=>0001111=>1111000
[3,2,6,4,8,7,1,5]=>0100111=>1110010
[4,2,7,3,8,6,1,5]=>0010111=>1110100
[5,2,7,6,8,3,1,4]=>0101011=>1101010
[3,2,7,6,8,4,1,5]=>0110011=>1100110
[3,2,7,6,8,5,1,4]=>0101011=>1101010
[6,2,7,5,8,4,1,3]=>0010111=>1110100
[4,8,1,7,3,2,5,6]=>0100011=>1100010
[3,7,4,8,2,1,5,6]=>1000011=>1100001
[3,7,8,2,5,4,6,1]=>0001101=>1011000
[4,7,5,8,3,2,6,1]=>0100111=>1110010
[6,7,1,3,2,5,8,4]=>0100011=>1100010
[8,7,6,4,1,5,3,2]=>0111111=>1111110
[3,8,5,2,6,4,7,1]=>0001111=>1111000
[7,2,5,3,4,8,1,6]=>0001011=>1101000
[4,2,5,3,7,8,6,1]=>0011101=>1011100
[5,3,6,2,4,1,8,7]=>0011101=>1011100
[7,8,6,2,3,5,4,1]=>0011101=>1011100
[5,8,2,6,3,7,4,1]=>0010111=>1110100
[4,8,2,3,7,5,6,1]=>0000111=>1110000
[7,5,6,2,3,8,4,1]=>0010111=>1110100
[2,7,5,6,4,3,8,1]=>0010111=>1110100
[2,8,4,3,7,5,6,1]=>0010111=>1110100
[3,8,5,7,6,4,2,1]=>1010111=>1110101
[7,8,6,3,5,4,2,1]=>1011101=>1011101
[2,7,6,3,8,5,4,1]=>0011111=>1111100
[7,4,2,5,6,3,8,1]=>0010111=>1110100
[6,2,7,5,3,8,4,1]=>0011111=>1111100
[2,4,8,3,7,5,6,1]=>0000111=>1110000
[4,8,3,7,5,6,2,1]=>1000111=>1110001
[6,2,5,8,3,7,4,1]=>0010111=>1110100
[4,7,3,8,2,5,6,1]=>0000111=>1110000
[8,2,5,6,3,7,4,1]=>0010111=>1110100
[4,5,3,7,1,2,6,8]=>0001010=>0101000
[8,5,6,4,1,3,2,7]=>0110101=>1010110
[6,7,2,8,4,3,1,5]=>0110011=>1100110
[6,7,3,2,8,4,1,5]=>0110011=>1100110
[4,7,8,3,1,5,2,6]=>0101001=>1001010
[4,5,8,1,3,2,6,7]=>0100001=>1000010
[4,7,8,1,6,3,2,5]=>0100101=>1010010
[4,7,1,3,8,6,5,2]=>0001111=>1111000
[2,6,7,4,3,8,1,5]=>0010011=>1100100
[3,7,6,4,5,8,1,2]=>0000111=>1110000
[5,7,2,8,3,4,6,1]=>0000111=>1110000
[3,7,2,8,5,6,4,1]=>0010111=>1110100
[3,1,5,8,6,4,7,2]=>0100111=>1110010
[2,3,8,6,4,5,7,1]=>0000111=>1110000
[2,3,8,6,4,7,5,1]=>0001111=>1111000
[3,6,2,8,7,4,5,1]=>0001111=>1111000
[2,5,6,1,8,7,3,4]=>0000111=>1110000
[3,6,2,8,4,7,5,1]=>0001111=>1111000
[2,3,8,5,7,4,6,1]=>0000111=>1110000
[2,3,8,6,7,5,4,1]=>0011011=>1101100
[8,5,6,3,1,4,2,7]=>0110101=>1010110
[8,3,5,1,6,4,2,7]=>0011101=>1011100
[5,7,8,3,4,6,2,1]=>1000101=>1010001
[3,5,1,8,6,4,2,7]=>0011101=>1011100
[7,5,3,8,6,4,2,1]=>1011111=>1111101
[5,1,3,8,6,4,2,7]=>0011101=>1011100
[1,5,8,3,6,4,2,7]=>0010101=>1010100
[7,5,8,3,6,4,2,1]=>1010111=>1110101
[1,5,8,6,3,4,2,7]=>0010101=>1010100
[3,7,5,8,2,6,4,1]=>0010111=>1110100
[5,7,8,1,4,6,2,3]=>0000101=>1010000
[1,3,7,8,4,2,6,5]=>0010101=>1010100
[6,1,2,5,3,4,7,8]=>0001100=>0011000
[5,1,4,6,7,3,2,8]=>0101010=>0101010
[1,4,6,5,7,2,3,8]=>0000110=>0110000
[6,7,3,5,4,1,2,8]=>0011010=>0101100
[8,1,6,7,3,5,4,2]=>0011011=>1101100
[7,2,4,1,6,5,3,8]=>0011110=>0111100
[4,2,5,1,3,7,6,8]=>0011010=>0101100
[1,3,2,6,8,4,7,5]=>0100011=>1100010
[8,2,5,4,1,6,7,3]=>0011011=>1101100
[8,1,7,5,4,2,6,3]=>0011111=>1111100
[1,2,6,4,7,3,5,8]=>0000110=>0110000
[1,6,4,3,7,2,5,8]=>0010110=>0110100
[5,7,8,3,2,6,1,4]=>0100101=>1010010
[2,3,4,5,6,9,8,7,1]=>00000111=>11100000
[2,3,4,5,8,7,9,6,1]=>00001011=>11010000
[2,3,6,5,7,8,9,4,1]=>00101001=>10010100
[2,3,4,5,6,7,8,9,11,10,1]=>0000000011=>1100000000
[2,3,4,5,6,7,10,9,8,1]=>000000111=>111000000
[2,3,4,5,8,9,7,6,1]=>00001101=>10110000
[2,3,4,5,6,9,8,10,7,1]=>000001011=>110100000
[8,4,5,1,3,7,6,2]=>0001111=>1111000
[8,6,4,3,7,1,5,2]=>0011111=>1111100
[7,5,6,8,1,3,2,4]=>0100011=>1100010
[6,8,7,5,4,2,3,1]=>0111011=>1101110
[3,4,5,6,7,1,2,8,9]=>00000100=>00100000
[2,7,3,1,4,8,6,5]=>0100111=>1110010
[3,1,6,5,7,8,4,2]=>0110101=>1010110
[4,7,1,3,2,5,6,8]=>0100010=>0100010
[4,1,6,7,3,2,8,5]=>0110011=>1100110
[1,7,2,5,6,8,4,3]=>0010011=>1100100
[4,7,6,8,3,1,5,2]=>0101011=>1101010
[5,4,8,6,1,7,3,2]=>0101111=>1111010
[3,5,4,7,1,8,6,2]=>0001111=>1111000
[7,1,5,4,2,3,6,8]=>0011010=>0101100
[7,1,3,6,4,5,2,8]=>0001110=>0111000
[6,1,3,8,4,5,2,7]=>0001101=>1011000
[2,1,8,7,3,6,5,4]=>1001111=>1111001
[5,8,6,3,1,2,7,4]=>0100111=>1110010
[5,8,2,7,1,3,6,4]=>0000111=>1110000
[2,6,5,4,1,3,7,8]=>0011100=>0011100
[4,1,5,7,6,3,2,8]=>0110110=>0110110
[6,3,4,2,1,8,7,5]=>1010111=>1110101
[4,5,1,7,6,3,2,8]=>0101110=>0111010
[5,4,2,1,8,7,3,6]=>1011011=>1101101
[6,2,1,5,4,3,8,7]=>1011101=>1011101
[1,4,2,6,7,8,5,3]=>0011001=>1001100
[1,4,2,5,6,8,7,3]=>0010011=>1100100
[2,5,3,6,7,8,4,1]=>0011001=>1001100
[1,8,6,2,4,3,5,7]=>0010101=>1010100
[3,2,4,5,7,8,1,6]=>0100001=>1000010
[2,3,4,7,5,8,6,1]=>0000111=>1110000
[6,5,2,8,7,4,3,1]=>0111111=>1111110
[7,8,5,4,2,1,6,3]=>1011101=>1011101
[7,5,2,8,6,4,3,1]=>0111111=>1111110
[7,8,3,2,6,5,4,1]=>0111101=>1011110
[8,2,6,3,7,5,1,4]=>0001111=>1111000
[8,6,7,2,5,3,1,4]=>0101011=>1101010
[1,6,2,7,8,4,5,3]=>0001101=>1011000
[8,6,2,7,5,4,1,3]=>0011111=>1111100
[1,6,8,2,7,5,3,4]=>0001011=>1101000
[7,6,3,2,8,1,5,4]=>0101111=>1111010
[5,1,7,4,3,8,6,2]=>0011111=>1111100
[8,6,3,7,2,4,1,5]=>0010111=>1110100
[1,7,8,6,4,2,3,5]=>0010101=>1010100
[7,2,8,6,4,1,3,5]=>0010111=>1110100
[1,5,3,7,4,2,6,8]=>0011010=>0101100
[1,7,6,4,3,2,8,5]=>0110111=>1110110
[1,7,6,3,4,2,5,8]=>0010110=>0110100
[1,2,7,4,3,8,6,5]=>0010111=>1110100
[1,5,4,2,3,8,7,6]=>0011011=>1101100
[1,5,3,2,4,6,7,8]=>0101000=>0001010
[1,5,4,2,3,7,8,6]=>0011001=>1001100
[1,2,7,6,3,5,8,4]=>0000111=>1110000
[8,1,3,2,6,5,7,4]=>0100111=>1110010
[3,2,7,5,6,1,8,4]=>0100111=>1110010
[7,5,6,1,3,2,8,4]=>0100111=>1110010
[7,4,5,1,6,3,8,2]=>0001111=>1111000
[7,5,6,1,4,3,8,2]=>0010111=>1110100
[3,2,6,4,8,5,7,1]=>0100111=>1110010
[8,1,4,3,5,2,7,6]=>0011011=>1101100
[7,2,8,1,6,3,5,4]=>0001111=>1111000
[10,5,9,4,8,3,7,2,6,1]=>000011111=>111110000
[1,3,5,2,4,7,6,9,8,10]=>000101010=>010101000
[2,3,5,1,4,7,6,9,8]=>00010101=>10101000
[3,4,1,5,2,7,6,9,8]=>00110101=>10101100
[4,1,2,5,3,7,6,9,8]=>00110101=>10101100
[1,4,2,5,3,7,6,9,8,10]=>001101010=>010101100
[8,3,6,5,4,1,2,7]=>0011101=>1011100
[1,7,5,8,4,6,3,2]=>0100111=>1110010
[6,5,7,1,2,8,3,4]=>0000111=>1110000
[7,1,4,2,3,8,6,5]=>0010111=>1110100
[3,7,5,6,8,1,2,4]=>0000011=>1100000
[8,1,2,5,3,7,6,4]=>0001111=>1111000
[8,6,5,2,4,1,7,3]=>0011111=>1111100
[3,6,5,2,4,1,7,8]=>0011100=>0011100
[6,8,5,2,4,3,1,7]=>0111001=>1001110
[3,4,2,8,6,7,1,5]=>0010011=>1100100
[4,6,7,2,5,1,8,3]=>0001011=>1101000
[3,6,2,5,1,7,8,4]=>0001101=>1011000
[3,4,2,7,8,1,5,6]=>0010001=>1000100
[3,8,5,2,4,7,1,6]=>0001011=>1101000
[10,3,1,5,6,7,8,9,2,4]=>010000011=>110000010
[10,4,1,5,6,7,8,9,2,3]=>001000011=>110000100
[12,3,4,5,6,7,8,9,10,11,1,2]=>00000000011=>11000000000
[7,1,4,2,5,8,6,3]=>0010111=>1110100
[7,8,5,1,2,4,3,6]=>0011001=>1001100
[5,8,1,4,3,6,7,2]=>0010011=>1100100
[7,2,3,8,6,4,1,5]=>0010111=>1110100
[5,2,3,8,7,4,1,6]=>0011011=>1101100
[5,7,6,3,1,2,4,8]=>0100110=>0110010
[4,2,6,8,1,3,5,7,9]=>00100010=>01000100
[4,6,2,8,1,3,5,7,9]=>00001010=>01010000
[4,6,8,2,1,3,5,7,9]=>10000010=>01000001
[4,6,2,7,8,1,3,5]=>0000101=>1010000
[4,6,8,2,9,1,3,5,7]=>00000011=>11000000
[4,6,2,7,9,1,3,5,8]=>00001001=>10010000
[6,2,3,7,1,4,5,8]=>0000110=>0110000
[4,2,5,7,9,1,3,6,8]=>00100001=>10000100
[2,3,5,7,9,1,4,6,8]=>00000001=>10000000
[4,2,6,8,10,1,3,5,7,9]=>001000001=>100000100
[6,4,2,8,1,3,5,7,9]=>00101010=>01010100
[4,6,2,8,10,1,3,5,7,9]=>000010001=>100010000
[8,4,6,2,1,3,5,7,9]=>10001010=>01010001
[4,6,8,2,10,1,3,5,7,9]=>000000101=>101000000
[4,6,8,9,2,1,3,5,7]=>10000001=>10000001
[4,6,8,10,2,1,3,5,7,9]=>100000001=>100000001
[4,6,7,8,2,1,3,5]=>1000001=>1000001
[4,6,2,7,1,3,5,8,9]=>00001100=>00110000
[4,6,8,2,9,1,3,5,7,10]=>000000110=>011000000
[4,8,2,5,9,1,3,6,7]=>00000011=>11000000
[4,6,2,7,9,1,3,5,8,10]=>000010010=>010010000
[6,2,3,7,9,1,4,5,8]=>00001001=>10010000
[4,2,5,7,9,1,3,6,8,10]=>001000010=>010000100
[1,4,5,7,9,2,3,6,8]=>00000001=>10000000
[2,3,5,7,9,1,4,6,8,10]=>000000010=>010000000
[8,6,3,2,1,7,5,4]=>1101111=>1111011
[5,3,4,1,7,8,2,6]=>0011001=>1001100
[8,6,4,9,7,5,3,2,1]=>11011111=>11111011
[7,8,5,9,6,4,3,2,1]=>11101011=>11010111
[8,6,4,2,9,7,5,3,1]=>01111111=>11111110
[7,8,5,3,9,6,4,2,1]=>10111011=>11011101
[7,4,8,5,9,6,3,2,1]=>11001111=>11110011
[6,7,8,4,9,5,3,2,1]=>11010011=>11001011
[7,8,5,3,1,9,6,4,2]=>01111011=>11011110
[7,4,8,5,2,9,6,3,1]=>01011111=>11111010
[6,7,8,4,2,9,5,3,1]=>01110011=>11001110
[6,7,3,8,4,9,5,2,1]=>10010111=>11101001
[5,6,7,8,3,9,4,2,1]=>10100011=>11000101
[6,7,3,8,4,1,9,5,2]=>00110111=>11101100
[5,6,7,8,3,1,9,4,2]=>01100011=>11000110
[6,2,7,3,8,4,9,5,1]=>00011111=>11111000
[5,6,7,2,8,3,9,4,1]=>00100111=>11100100
[4,5,6,7,8,2,9,3,1]=>01000011=>11000010
[5,6,1,7,2,8,3,9,4]=>00001111=>11110000
[4,5,6,7,1,8,2,9,3]=>00000111=>11100000
[9,7,10,8,6,5,4,3,2,1]=>111110111=>111011111
[9,7,5,10,8,6,4,3,2,1]=>111011111=>111110111
[8,9,6,10,7,5,4,3,2,1]=>111101011=>110101111
[9,7,5,3,10,8,6,4,2,1]=>101111111=>111111101
[8,9,6,4,10,7,5,3,2,1]=>110111011=>110111011
[8,5,9,6,10,7,4,3,2,1]=>111001111=>111100111
[7,8,9,5,10,6,4,3,2,1]=>111010011=>110010111
[8,9,6,4,2,10,7,5,3,1]=>011111011=>110111110
[8,5,9,6,3,10,7,4,2,1]=>101011111=>111110101
[7,8,9,5,3,10,6,4,2,1]=>101110011=>110011101
[7,8,4,9,5,10,6,3,2,1]=>110010111=>111010011
[6,7,8,9,4,10,5,3,2,1]=>110100011=>110001011
[8,5,9,6,3,1,10,7,4,2]=>011011111=>111110110
[7,8,9,5,3,1,10,6,4,2]=>011110011=>110011110
[8,5,2,9,6,3,10,7,4,1]=>001111111=>111111100
[6,7,8,9,4,2,10,5,3,1]=>011100011=>110001110
[7,3,8,4,9,5,10,6,2,1]=>100011111=>111110001
[6,7,8,3,9,4,10,5,2,1]=>100100111=>111001001
[5,6,7,8,9,3,10,4,2,1]=>101000011=>110000101
[7,8,4,1,9,5,2,10,6,3]=>001110111=>111011100
[7,3,8,4,9,5,1,10,6,2]=>000111111=>111111000
[6,7,8,3,9,4,1,10,5,2]=>001100111=>111001100
[5,6,7,8,9,3,1,10,4,2]=>011000011=>110000110
[6,7,2,8,3,9,4,10,5,1]=>000101111=>111101000
[5,6,7,8,2,9,3,10,4,1]=>001000111=>111000100
[4,5,6,7,8,9,2,10,3,1]=>010000011=>110000010
[5,6,7,1,8,2,9,3,10,4]=>000001111=>111100000
[4,5,6,7,8,1,9,2,10,3]=>000000111=>111000000
[6,1,3,4,2,5,8,7]=>0010101=>1010100
[5,1,3,6,2,4,8,7]=>0001101=>1011000
[1,5,7,6,8,2,4,3]=>0010011=>1100100
[5,7,1,3,8,4,2,6]=>0010011=>1100100
[2,6,1,4,3,7,8,5]=>0010101=>1010100
[1,6,2,4,3,5,8,7]=>0010101=>1010100
[5,3,7,6,1,8,4,2]=>0011111=>1111100
[1,5,6,3,7,8,4,2]=>0010101=>1010100
[1,5,7,6,3,8,4,2]=>0010111=>1110100
[7,3,5,6,1,8,4,2]=>0010111=>1110100
[7,3,6,1,5,8,4,2]=>0010111=>1110100
[1,6,3,7,8,5,4,2]=>0011101=>1011100
[1,7,8,6,3,5,4,2]=>0011101=>1011100
[3,7,5,6,1,8,4,2]=>0010111=>1110100
[5,6,2,8,4,7,3,1]=>0100111=>1110010
[5,7,6,3,4,8,1,2]=>0000111=>1110000
[3,7,5,4,6,1,2,8]=>0001110=>0111000
[5,3,4,7,6,8,1,2]=>0001011=>1101000
[5,3,7,4,6,1,2,8]=>0001110=>0111000
[7,3,5,4,6,1,2,8]=>0001110=>0111000
[7,8,3,5,4,1,2,6]=>0011001=>1001100
[7,3,5,4,1,2,6,8]=>0011010=>0101100
[5,7,6,3,4,1,2,8]=>0010110=>0110100
[3,5,4,1,2,7,6,8]=>0011010=>0101100
[5,7,6,1,3,2,4,8]=>0100110=>0110010
[5,3,4,1,2,7,6,8]=>0011010=>0101100
[7,8,3,1,2,5,4,6]=>0101001=>1001010
[7,8,5,1,3,2,4,6]=>0101001=>1001010
[7,5,6,1,3,2,4,8]=>0100110=>0110010
[7,5,1,3,8,6,2,4]=>0001111=>1111000
[7,1,3,8,2,5,4,6]=>0001011=>1101000
[3,1,5,4,7,2,6,8]=>0101010=>0101010
[5,7,6,1,3,8,2,4]=>0000111=>1110000
[5,7,6,3,8,1,4,2]=>0010111=>1110100
[5,1,3,7,6,2,4,8]=>0001110=>0111000
[1,6,3,7,2,4,5,8]=>0000110=>0110000
[5,3,2,4,8,1,7,6]=>0101011=>1101010
[6,8,5,3,2,7,1,4]=>0101011=>1101010
[8,3,7,2,6,5,1,4]=>0001111=>1111000
[4,6,2,7,1,3,8,5]=>0000111=>1110000
[3,4,6,5,1,8,7,2]=>0001111=>1111000
[8,7,1,5,3,2,6,4]=>0101111=>1111010
[3,5,1,4,7,2,8,6]=>0001011=>1101000
[5,1,4,8,7,3,2,6]=>0101011=>1101010
[6,1,3,4,2,7,8,5]=>0010101=>1010100
[6,5,2,3,7,8,1,4]=>0001101=>1011000
[1,5,3,8,4,2,7,6]=>0011011=>1101100
[5,4,2,1,8,3,7,6]=>1011011=>1101101
[3,1,7,4,2,6,8,5]=>0110011=>1100110
[7,4,8,2,3,5,1,6]=>0001011=>1101000
[8,4,1,3,2,6,7,5]=>0110011=>1100110
[8,1,7,3,2,5,6,4]=>0100111=>1110010
[8,6,5,2,7,3,1,4]=>0101111=>1111010
[3,1,6,8,4,2,7,5]=>0110011=>1100110
[1,5,2,8,3,6,7,4]=>0001011=>1101000
[2,3,4,5,9,6,7,8,1]=>00000011=>11000000
[2,3,4,9,5,6,7,8,1]=>00000011=>11000000
[2,3,9,4,5,6,7,8,1]=>00000011=>11000000
[2,3,4,5,6,7,10,8,9,1]=>000000011=>110000000
[2,3,4,5,9,7,6,8,1]=>00000111=>11100000
[2,3,4,5,6,10,7,8,9,1]=>000000011=>110000000
[2,3,4,9,6,5,7,8,1]=>00001011=>11010000
[2,3,9,5,4,6,7,8,1]=>00010011=>11001000
[2,3,4,10,5,6,7,8,9,1]=>000000011=>110000000
[2,9,4,3,5,6,7,8,1]=>00100011=>11000100
[2,3,10,4,5,6,7,8,9,1]=>000000011=>110000000
[2,3,4,5,9,7,8,6,1]=>00001011=>11010000
[5,6,2,3,7,4,1,8]=>0010110=>0110100
[6,2,4,7,3,5,1,8]=>0001110=>0111000
[1,4,8,5,3,6,7,2]=>0001011=>1101000
[2,5,6,3,1,8,4,7]=>0100101=>1010010
[4,5,1,2,7,8,6,3]=>0001101=>1011000
[4,8,5,1,2,6,7,3]=>0001011=>1101000
[4,6,7,5,1,2,8,3]=>0001011=>1101000
[7,2,8,1,4,5,3,6]=>0001011=>1101000
[6,1,4,7,3,8,2,5]=>0000111=>1110000
[7,1,6,3,4,8,2,5]=>0000111=>1110000
[2,8,4,6,3,1,5,7]=>0100101=>1010010
[8,2,6,3,5,1,4,7]=>0001101=>1011000
[3,7,4,1,5,8,2,6]=>0010011=>1100100
[3,8,4,1,7,2,5,6]=>0010011=>1100100
[6,7,5,1,3,8,2,4]=>0001011=>1101000
[8,5,1,3,6,7,2,4]=>0001011=>1101000
[7,8,6,2,4,1,3,5]=>0010101=>1010100
[8,2,4,1,3,6,7,5]=>0010011=>1100100
[8,1,3,6,2,5,7,4]=>0000111=>1110000
[1,5,6,3,8,4,7,2]=>0000111=>1110000
[5,6,1,3,7,2,8,4]=>0000111=>1110000
[5,6,1,8,2,3,7,4]=>0000111=>1110000
[5,6,1,2,8,4,7,3]=>0000111=>1110000
[1,7,8,6,3,4,2,5]=>0010101=>1010100
[1,7,3,8,6,4,2,5]=>0010111=>1110100
[5,7,1,8,6,4,2,3]=>0010111=>1110100
[7,8,1,5,6,4,2,3]=>0010101=>1010100
[7,1,8,5,6,4,2,3]=>0010111=>1110100
[7,1,5,8,6,4,2,3]=>0010111=>1110100
[8,1,3,5,6,4,2,7]=>0010101=>1010100
[1,3,8,5,6,4,2,7]=>0010101=>1010100
[1,3,5,8,6,4,2,7]=>0010101=>1010100
[1,5,7,8,6,4,2,3]=>0010101=>1010100
[2,1,4,3,6,5,9,8,10,7]=>101010011=>110010101
[2,1,4,3,7,6,8,5,10,9]=>101001101=>101100101
[2,1,4,3,7,6,9,8,10,5]=>101001011=>110100101
[2,1,4,3,8,7,9,6,10,5]=>101000111=>111000101
[2,1,5,4,6,3,8,7,10,9]=>100110101=>101011001
[2,1,5,4,6,3,9,8,10,7]=>100110011=>110011001
[2,1,5,4,7,6,8,3,10,9]=>100101101=>101101001
[2,1,5,4,7,6,9,8,10,3]=>100101011=>110101001
[2,1,5,4,8,7,9,6,10,3]=>100100111=>111001001
[2,1,6,5,7,4,8,3,10,9]=>100011101=>101110001
[2,1,6,5,7,4,9,8,10,3]=>100011011=>110110001
[2,1,6,5,8,7,9,4,10,3]=>100010111=>111010001
[2,1,7,6,8,5,9,4,10,3]=>100001111=>111100001
[3,2,4,1,6,5,8,7,10,9]=>011010101=>101010110
[3,2,4,1,6,5,9,8,10,7]=>011010011=>110010110
[3,2,4,1,7,6,8,5,10,9]=>011001101=>101100110
[3,2,4,1,7,6,9,8,10,5]=>011001011=>110100110
[3,2,4,1,8,7,9,6,10,5]=>011000111=>111000110
[3,2,5,4,6,1,8,7,10,9]=>010110101=>101011010
[3,2,5,4,6,1,9,8,10,7]=>010110011=>110011010
[3,2,5,4,7,6,8,1,10,9]=>010101101=>101101010
[3,2,5,4,7,6,9,8,10,1]=>010101011=>110101010
[3,2,5,4,8,7,9,6,10,1]=>010100111=>111001010
[3,2,6,5,7,4,8,1,10,9]=>010011101=>101110010
[3,2,6,5,7,4,9,8,10,1]=>010011011=>110110010
[3,2,6,5,8,7,9,4,10,1]=>010010111=>111010010
[3,2,7,6,8,5,9,4,10,1]=>010001111=>111100010
[4,3,5,2,6,1,8,7,10,9]=>001110101=>101011100
[4,3,5,2,6,1,9,8,10,7]=>001110011=>110011100
[4,3,5,2,7,6,8,1,10,9]=>001101101=>101101100
[4,3,5,2,7,6,9,8,10,1]=>001101011=>110101100
[4,3,5,2,8,7,9,6,10,1]=>001100111=>111001100
[4,3,6,5,7,2,8,1,10,9]=>001011101=>101110100
[4,3,6,5,7,2,9,8,10,1]=>001011011=>110110100
[4,3,6,5,8,7,9,2,10,1]=>001010111=>111010100
[4,3,7,6,8,5,9,2,10,1]=>001001111=>111100100
[5,4,6,3,7,2,8,1,10,9]=>000111101=>101111000
[5,4,6,3,7,2,9,8,10,1]=>000111011=>110111000
[5,4,6,3,8,7,9,2,10,1]=>000110111=>111011000
[5,4,7,6,8,3,9,2,10,1]=>000101111=>111101000
[2,1,4,3,6,5,8,7,11,10,12,9]=>10101010011=>11001010101
[2,1,4,3,6,5,9,8,10,7,12,11]=>10101001101=>10110010101
[2,1,4,3,6,5,9,8,11,10,12,7]=>10101001011=>11010010101
[2,1,4,3,6,5,10,9,11,8,12,7]=>10101000111=>11100010101
[2,1,4,3,7,6,8,5,10,9,12,11]=>10100110101=>10101100101
[2,1,4,3,7,6,8,5,11,10,12,9]=>10100110011=>11001100101
[2,1,4,3,7,6,9,8,10,5,12,11]=>10100101101=>10110100101
[2,1,4,3,7,6,9,8,11,10,12,5]=>10100101011=>11010100101
[2,1,4,3,7,6,10,9,11,8,12,5]=>10100100111=>11100100101
[2,1,4,3,8,7,9,6,10,5,12,11]=>10100011101=>10111000101
[2,1,4,3,8,7,9,6,11,10,12,5]=>10100011011=>11011000101
[2,1,4,3,8,7,10,9,11,6,12,5]=>10100010111=>11101000101
[2,1,4,3,9,8,10,7,11,6,12,5]=>10100001111=>11110000101
[2,1,5,4,6,3,8,7,10,9,12,11]=>10011010101=>10101011001
[2,1,5,4,6,3,8,7,11,10,12,9]=>10011010011=>11001011001
[2,1,5,4,6,3,9,8,10,7,12,11]=>10011001101=>10110011001
[2,1,5,4,6,3,9,8,11,10,12,7]=>10011001011=>11010011001
[2,1,5,4,6,3,10,9,11,8,12,7]=>10011000111=>11100011001
[2,1,5,4,7,6,8,3,10,9,12,11]=>10010110101=>10101101001
[2,1,5,4,7,6,8,3,11,10,12,9]=>10010110011=>11001101001
[2,1,5,4,7,6,9,8,10,3,12,11]=>10010101101=>10110101001
[2,1,5,4,7,6,9,8,11,10,12,3]=>10010101011=>11010101001
[2,1,5,4,7,6,10,9,11,8,12,3]=>10010100111=>11100101001
[2,1,5,4,8,7,9,6,10,3,12,11]=>10010011101=>10111001001
[2,1,5,4,8,7,9,6,11,10,12,3]=>10010011011=>11011001001
[2,1,5,4,8,7,10,9,11,6,12,3]=>10010010111=>11101001001
[2,1,5,4,9,8,10,7,11,6,12,3]=>10010001111=>11110001001
[2,1,6,5,7,4,8,3,10,9,12,11]=>10001110101=>10101110001
[2,1,6,5,7,4,8,3,11,10,12,9]=>10001110011=>11001110001
[2,1,6,5,7,4,9,8,10,3,12,11]=>10001101101=>10110110001
[2,1,6,5,7,4,9,8,11,10,12,3]=>10001101011=>11010110001
[2,1,6,5,7,4,10,9,11,8,12,3]=>10001100111=>11100110001
[2,1,6,5,8,7,9,4,10,3,12,11]=>10001011101=>10111010001
[2,1,6,5,8,7,9,4,11,10,12,3]=>10001011011=>11011010001
[2,1,6,5,8,7,10,9,11,4,12,3]=>10001010111=>11101010001
[2,1,6,5,9,8,10,7,11,4,12,3]=>10001001111=>11110010001
[2,1,7,6,8,5,9,4,10,3,12,11]=>10000111101=>10111100001
[2,1,7,6,8,5,9,4,11,10,12,3]=>10000111011=>11011100001
[2,1,7,6,8,5,10,9,11,4,12,3]=>10000110111=>11101100001
[2,1,7,6,9,8,10,5,11,4,12,3]=>10000101111=>11110100001
[2,1,8,7,9,6,10,5,11,4,12,3]=>10000011111=>11111000001
[3,2,4,1,6,5,8,7,10,9,12,11]=>01101010101=>10101010110
[3,2,4,1,6,5,8,7,11,10,12,9]=>01101010011=>11001010110
[3,2,4,1,6,5,9,8,10,7,12,11]=>01101001101=>10110010110
[3,2,4,1,6,5,9,8,11,10,12,7]=>01101001011=>11010010110
[3,2,4,1,6,5,10,9,11,8,12,7]=>01101000111=>11100010110
[3,2,4,1,7,6,8,5,10,9,12,11]=>01100110101=>10101100110
[3,2,4,1,7,6,8,5,11,10,12,9]=>01100110011=>11001100110
[3,2,4,1,7,6,9,8,10,5,12,11]=>01100101101=>10110100110
[3,2,4,1,7,6,9,8,11,10,12,5]=>01100101011=>11010100110
[3,2,4,1,7,6,10,9,11,8,12,5]=>01100100111=>11100100110
[3,2,4,1,8,7,9,6,10,5,12,11]=>01100011101=>10111000110
[3,2,4,1,8,7,9,6,11,10,12,5]=>01100011011=>11011000110
[3,2,4,1,8,7,10,9,11,6,12,5]=>01100010111=>11101000110
[3,2,4,1,9,8,10,7,11,6,12,5]=>01100001111=>11110000110
[3,2,5,4,6,1,8,7,10,9,12,11]=>01011010101=>10101011010
[3,2,5,4,6,1,8,7,11,10,12,9]=>01011010011=>11001011010
[3,2,5,4,6,1,9,8,10,7,12,11]=>01011001101=>10110011010
[3,2,5,4,6,1,9,8,11,10,12,7]=>01011001011=>11010011010
[3,2,5,4,6,1,10,9,11,8,12,7]=>01011000111=>11100011010
[3,2,5,4,7,6,8,1,10,9,12,11]=>01010110101=>10101101010
[3,2,5,4,7,6,8,1,11,10,12,9]=>01010110011=>11001101010
[3,2,5,4,7,6,9,8,10,1,12,11]=>01010101101=>10110101010
[3,2,5,4,7,6,9,8,11,10,12,1]=>01010101011=>11010101010
[3,2,5,4,7,6,10,9,11,8,12,1]=>01010100111=>11100101010
[3,2,5,4,8,7,9,6,10,1,12,11]=>01010011101=>10111001010
[3,2,5,4,8,7,9,6,11,10,12,1]=>01010011011=>11011001010
[3,2,5,4,8,7,10,9,11,6,12,1]=>01010010111=>11101001010
[3,2,5,4,9,8,10,7,11,6,12,1]=>01010001111=>11110001010
[3,2,6,5,7,4,8,1,10,9,12,11]=>01001110101=>10101110010
[3,2,6,5,7,4,8,1,11,10,12,9]=>01001110011=>11001110010
[3,2,6,5,7,4,9,8,10,1,12,11]=>01001101101=>10110110010
[3,2,6,5,7,4,9,8,11,10,12,1]=>01001101011=>11010110010
[3,2,6,5,7,4,10,9,11,8,12,1]=>01001100111=>11100110010
[3,2,6,5,8,7,9,4,10,1,12,11]=>01001011101=>10111010010
[3,2,6,5,8,7,9,4,11,10,12,1]=>01001011011=>11011010010
[3,2,6,5,8,7,10,9,11,4,12,1]=>01001010111=>11101010010
[3,2,6,5,9,8,10,7,11,4,12,1]=>01001001111=>11110010010
[3,2,7,6,8,5,9,4,10,1,12,11]=>01000111101=>10111100010
[3,2,7,6,8,5,9,4,11,10,12,1]=>01000111011=>11011100010
[3,2,7,6,8,5,10,9,11,4,12,1]=>01000110111=>11101100010
[3,2,7,6,9,8,10,5,11,4,12,1]=>01000101111=>11110100010
[3,2,8,7,9,6,10,5,11,4,12,1]=>01000011111=>11111000010
[4,3,5,2,6,1,8,7,10,9,12,11]=>00111010101=>10101011100
[4,3,5,2,6,1,8,7,11,10,12,9]=>00111010011=>11001011100
[4,3,5,2,6,1,9,8,10,7,12,11]=>00111001101=>10110011100
[4,3,5,2,6,1,9,8,11,10,12,7]=>00111001011=>11010011100
[4,3,5,2,6,1,10,9,11,8,12,7]=>00111000111=>11100011100
[4,3,5,2,7,6,8,1,10,9,12,11]=>00110110101=>10101101100
[4,3,5,2,7,6,8,1,11,10,12,9]=>00110110011=>11001101100
[4,3,5,2,7,6,9,8,10,1,12,11]=>00110101101=>10110101100
[4,3,5,2,7,6,9,8,11,10,12,1]=>00110101011=>11010101100
[4,3,5,2,7,6,10,9,11,8,12,1]=>00110100111=>11100101100
[4,3,5,2,8,7,9,6,10,1,12,11]=>00110011101=>10111001100
[4,3,5,2,8,7,9,6,11,10,12,1]=>00110011011=>11011001100
[4,3,5,2,8,7,10,9,11,6,12,1]=>00110010111=>11101001100
[4,3,5,2,9,8,10,7,11,6,12,1]=>00110001111=>11110001100
[4,3,6,5,7,2,8,1,10,9,12,11]=>00101110101=>10101110100
[4,3,6,5,7,2,8,1,11,10,12,9]=>00101110011=>11001110100
[4,3,6,5,7,2,9,8,10,1,12,11]=>00101101101=>10110110100
[4,3,6,5,7,2,9,8,11,10,12,1]=>00101101011=>11010110100
[4,3,6,5,7,2,10,9,11,8,12,1]=>00101100111=>11100110100
[4,3,6,5,8,7,9,2,10,1,12,11]=>00101011101=>10111010100
[4,3,6,5,8,7,9,2,11,10,12,1]=>00101011011=>11011010100
[4,3,6,5,8,7,10,9,11,2,12,1]=>00101010111=>11101010100
[4,3,6,5,9,8,10,7,11,2,12,1]=>00101001111=>11110010100
[4,3,7,6,8,5,9,2,10,1,12,11]=>00100111101=>10111100100
[4,3,7,6,8,5,9,2,11,10,12,1]=>00100111011=>11011100100
[4,3,7,6,8,5,10,9,11,2,12,1]=>00100110111=>11101100100
[4,3,7,6,9,8,10,5,11,2,12,1]=>00100101111=>11110100100
[4,3,8,7,9,6,10,5,11,2,12,1]=>00100011111=>11111000100
[5,4,6,3,7,2,8,1,10,9,12,11]=>00011110101=>10101111000
[5,4,6,3,7,2,8,1,11,10,12,9]=>00011110011=>11001111000
[5,4,6,3,7,2,9,8,10,1,12,11]=>00011101101=>10110111000
[5,4,6,3,7,2,9,8,11,10,12,1]=>00011101011=>11010111000
[5,4,6,3,7,2,10,9,11,8,12,1]=>00011100111=>11100111000
[5,4,6,3,8,7,9,2,10,1,12,11]=>00011011101=>10111011000
[5,4,6,3,8,7,9,2,11,10,12,1]=>00011011011=>11011011000
[5,4,6,3,8,7,10,9,11,2,12,1]=>00011010111=>11101011000
[5,4,6,3,9,8,10,7,11,2,12,1]=>00011001111=>11110011000
[5,4,7,6,8,3,9,2,10,1,12,11]=>00010111101=>10111101000
[5,4,7,6,8,3,9,2,11,10,12,1]=>00010111011=>11011101000
[5,4,7,6,8,3,10,9,11,2,12,1]=>00010110111=>11101101000
[5,4,7,6,9,8,10,3,11,2,12,1]=>00010101111=>11110101000
[5,4,8,7,9,6,10,3,11,2,12,1]=>00010011111=>11111001000
[6,5,7,4,8,3,9,2,10,1,12,11]=>00001111101=>10111110000
[6,5,7,4,8,3,9,2,11,10,12,1]=>00001111011=>11011110000
[6,5,7,4,8,3,10,9,11,2,12,1]=>00001110111=>11101110000
[6,5,7,4,9,8,10,3,11,2,12,1]=>00001101111=>11110110000
[6,5,8,7,9,4,10,3,11,2,12,1]=>00001011111=>11111010000
[7,6,8,5,9,4,10,3,11,2,12,1]=>00000111111=>11111100000
[1,8,2,6,5,3,4,7]=>0001101=>1011000
[8,6,1,5,2,3,4,7]=>0001101=>1011000
[8,5,1,6,2,3,4,7]=>0001101=>1011000
[7,6,1,2,3,8,4,5]=>0000111=>1110000
[2,7,8,4,1,3,5,6]=>0010001=>1000100
[6,8,1,2,3,7,4,5]=>0000011=>1100000
[8,1,3,5,6,7,2,4]=>0000011=>1100000
[8,1,2,5,3,4,7,6]=>0001011=>1101000
[5,2,7,3,4,8,1,6]=>0001011=>1101000
[8,6,4,7,3,5,2,1]=>1001111=>1111001
[4,2,1,6,5,7,8,3]=>1010101=>1010101
[2,7,5,4,1,3,6,8]=>0011010=>0101100
[2,7,4,6,5,1,8,3]=>0001111=>1111000
[6,8,7,5,2,1,4,3]=>1011011=>1101101
[2,8,6,3,5,1,4,7]=>0001101=>1011000
[1,2,8,6,4,5,3,7]=>0001101=>1011000
[1,5,8,7,6,3,4,2]=>0010111=>1110100
[1,4,7,8,5,6,3,2]=>0100101=>1010010
[1,6,4,8,5,7,3,2]=>0100111=>1110010
[1,6,8,5,2,7,3,4]=>0001011=>1101000
[1,6,8,5,4,2,3,7]=>0011001=>1001100
[1,3,4,8,5,2,7,6]=>0001011=>1101000
[2,1,8,3,4,5,6,7,9]=>10000010=>01000001
[3,5,8,7,6,2,4,1]=>0010111=>1110100
[6,5,3,7,4,1,8,2]=>0011111=>1111100
[3,1,5,4,6,8,7,2]=>0101011=>1101010
[3,1,6,4,2,5,8,7]=>0110101=>1010110
[3,6,1,4,5,7,8,2]=>0000101=>1010000
[1,8,4,7,2,3,6,5]=>0000111=>1110000
[5,7,8,2,4,6,1,3]=>0000101=>1010000
[5,4,2,3,6,8,1,7]=>0011001=>1001100
[3,8,1,6,4,2,5,7]=>0010101=>1010100
[7,3,2,1,8,6,4,5]=>1100111=>1110011
[8,7,2,4,1,3,6,5]=>0010111=>1110100
[8,2,6,3,5,7,1,4]=>0000111=>1110000
[1,8,3,7,4,6,5,2]=>0001111=>1111000
[8,2,3,1,7,4,5,6]=>0100011=>1100010
[3,1,7,8,6,2,5,4]=>0101101=>1011010
[4,8,1,2,6,5,7,3]=>0000111=>1110000
[5,6,1,8,3,7,2,4]=>0000111=>1110000
[2,8,1,6,5,3,7,4]=>0001111=>1111000
[2,1,5,7,6,3,8,4]=>1000111=>1110001
[4,1,2,5,7,6,8,3]=>0010011=>1100100
[4,3,5,1,7,8,6,2]=>0011101=>1011100
[1,8,5,2,3,4,7,6]=>0001011=>1101000
[1,9,6,2,3,4,5,8,7]=>00001011=>11010000
[1,5,8,2,3,4,7,6]=>0000011=>1100000
[1,2,7,8,4,5,6,3]=>0000101=>1010000
[1,2,3,4,5,6,9,7,10,8]=>000000011=>110000000
[2,3,4,5,6,9,10,1,7,8]=>000000001=>100000000
[4,3,8,7,6,2,5,1]=>0011111=>1111100
[5,4,8,2,7,6,3,1]=>0101111=>1111010
[2,3,6,1,7,5,8,4]=>0000111=>1110000
[4,6,5,2,1,7,8,3]=>1001101=>1011001
[4,6,1,7,5,8,3,2]=>0100111=>1110010
[4,1,5,7,6,8,3,2]=>0110011=>1100110
[3,5,6,2,1,4,7,8]=>1000100=>0010001
[4,3,6,5,1,7,8,2]=>0011101=>1011100
[4,6,5,3,1,7,8,2]=>0101101=>1011010
[1,2,3,4,5,7,6,8,9,10]=>000001000=>000100000
[1,2,3,5,4,6,7,8,9,10]=>000100000=>000001000
[1,2,3,5,4,7,6,9,8,10]=>000101010=>010101000
[5,8,1,4,2,3,6,7]=>0010001=>1000100
[4,5,8,2,3,1,6,7]=>0100001=>1000010
[3,5,4,8,1,7,2,6]=>0001011=>1101000
[5,3,6,8,1,4,7,2]=>0001011=>1101000
[3,5,1,8,6,4,7,2]=>0001111=>1111000
[4,7,2,8,3,1,6,5]=>0100111=>1110010
[1,2,5,6,8,3,7,4]=>0000011=>1100000
[5,3,8,4,6,2,7,1]=>0001111=>1111000
[7,4,8,1,5,2,6,3]=>0001111=>1111000
[8,3,2,1,6,5,7,4]=>1100111=>1110011
[4,1,5,6,8,7,2,3]=>0010011=>1100100
[1,2,5,6,8,4,7,3]=>0000011=>1100000
[1,5,6,8,4,7,2,3]=>0000011=>1100000
[5,6,8,1,2,4,7,3]=>0000011=>1100000
[6,8,1,4,5,7,2,3]=>0000011=>1100000
[4,3,5,1,8,6,7,2]=>0011011=>1101100
[1,3,5,6,8,4,7,2]=>0000011=>1100000
[5,6,8,2,3,4,7,1]=>0000011=>1100000
[9,8,7,4,5,6,3,2,1]=>11001111=>11110011
[6,5,1,2,4,8,7,3]=>0001111=>1111000
[5,8,7,2,1,3,6,4]=>1000111=>1110001
[5,1,7,2,8,6,3,4]=>0001111=>1111000
[6,1,5,3,4,8,7,2]=>0001111=>1111000
[5,8,6,3,2,1,4,7]=>1100101=>1010011
[8,7,1,6,3,5,4,2]=>0011111=>1111100
[3,2,1,7,8,6,4,5]=>1100101=>1010011
[8,6,7,1,2,5,3,4]=>0001011=>1101000
[1,5,6,4,2,8,7,3]=>0010111=>1110100
[7,5,1,4,8,2,3,6]=>0001011=>1101000
[3,2,8,1,7,5,6,4]=>0100111=>1110010
[8,4,3,1,7,5,6,2]=>0110111=>1110110
[6,1,7,8,4,2,3,5]=>0010101=>1010100
[7,4,3,1,8,5,2,6]=>0111011=>1101110
[7,8,1,6,3,4,5,2]=>0001101=>1011000
[6,8,1,7,3,4,2,5]=>0010011=>1100100
[1,5,6,7,8,9,2,3,4]=>00000001=>10000000
[1,8,9,10,2,3,4,5,6,7]=>000000001=>100000000
[1,7,2,8,9,3,4,5,6]=>00000101=>10100000
[1,6,2,7,8,9,3,4,5]=>00001001=>10010000
[1,5,2,6,7,8,9,3,4]=>00010001=>10001000
[1,5,6,7,8,9,10,2,3,4]=>000000001=>100000000
[3,4,2,1,5,6,7,8,9]=>10100000=>00000101
[4,3,1,2,5,6,7,8,9]=>01100000=>00000110
[2,3,1,4,5,6,7,8,9,10,11]=>0100000000=>0000000010
[3,4,2,1,5,6,7,8,9,10]=>101000000=>000000101
[4,5,2,1,3,6,7,8,9]=>10010000=>00001001
[3,4,2,5,1,6,7,8,9]=>00110000=>00001100
[5,3,1,2,4,6,7,8,9]=>01010000=>00001010
[4,3,5,1,2,6,7,8,9]=>00110000=>00001100
[4,3,1,2,5,6,7,8,9,10]=>011000000=>000000110
[3,1,2,4,5,6,7,8,9,10,11]=>0100000000=>0000000010
[4,6,5,3,8,2,7,1]=>0001111=>1111000
[4,5,6,3,8,1,7,2]=>0000111=>1110000
[7,8,3,5,2,1,6,4]=>1001101=>1011001
[6,3,7,5,2,4,1,8]=>0011110=>0111100
[6,2,4,5,7,3,1,8]=>0100110=>0110010
[7,8,1,5,6,4,3,2]=>0110101=>1010110
[6,3,7,5,1,4,2,8]=>0011110=>0111100
[1,3,8,2,4,6,7,5]=>0000011=>1100000
[6,1,7,3,4,2,5,8]=>0010110=>0110100
[3,1,7,2,5,8,6,4]=>0100111=>1110010
[2,8,7,6,3,5,1,4]=>0001111=>1111000
[2,8,7,1,5,6,4,3]=>0010111=>1110100
[3,5,6,2,8,1,7,4]=>0000111=>1110000
[5,3,1,8,6,2,7,4]=>0101111=>1111010
[3,1,4,6,8,2,7,5]=>0100011=>1100010
[4,1,5,7,3,8,2,6]=>0010011=>1100100
[6,2,5,8,4,7,3,1]=>0100111=>1110010
[7,2,8,5,4,3,6,1]=>0011111=>1111100
[7,1,6,8,2,5,3,4]=>0001011=>1101000
[2,6,5,7,8,4,1,3]=>0010101=>1010100
[3,6,5,7,4,1,8,2]=>0010111=>1110100
[1,6,5,7,4,2,3,8]=>0010110=>0110100
[3,4,7,5,2,1,8,6]=>1001011=>1101001
[3,6,7,5,8,4,1,2]=>0010011=>1100100
[3,4,7,2,5,6,8,1]=>0000011=>1100000
[2,5,3,7,8,6,4,1]=>0011101=>1011100
[7,2,8,4,5,6,3,1]=>0100111=>1110010
[6,2,3,8,5,4,7,1]=>0001111=>1111000
[5,4,3,1,2,6,7,8,9]=>01110000=>00001110
[6,5,4,3,1,2,7,8,9]=>01111000=>00011110
[8,5,4,3,9,1,2,6,7]=>00110011=>11001100
[6,5,4,3,1,2,7,8,9,10]=>011110000=>000011110
[7,6,5,4,3,1,2,8,9,10]=>011111000=>000111110
[9,6,5,4,3,10,1,2,7,8]=>001110011=>110011100
[6,8,7,3,2,4,5,1]=>0101011=>1101010
[3,8,6,1,4,5,7,2]=>0000111=>1110000
[7,5,8,6,4,1,3,2]=>0110111=>1110110
[2,7,6,3,8,5,1,4]=>0001111=>1111000
[2,3,1,8,4,6,5,7]=>0100101=>1010010
[2,3,1,7,6,8,4,5]=>0100011=>1100010
[2,3,1,8,4,6,7,5]=>0100011=>1100010
[6,2,3,4,5,1,9,7,8]=>00011001=>10011000
[2,3,4,5,9,7,1,8,6]=>00000111=>11100000
[2,3,4,9,6,7,1,8,5]=>00000111=>11100000
[2,3,9,5,6,1,7,8,4]=>00001011=>11010000
[2,3,9,5,1,7,4,8,6]=>00010111=>11101000
[2,3,4,5,6,7,10,9,1,8]=>000000011=>110000000
[2,3,4,5,6,10,8,9,1,7]=>000000011=>110000000
[2,3,4,5,6,10,8,1,9,7]=>000000111=>111000000
[2,3,4,5,6,10,8,1,7,9]=>000000101=>101000000
[2,3,4,5,6,10,1,7,8,9]=>000000001=>100000000
[2,3,4,5,10,7,8,9,1,6]=>000000011=>110000000
[2,3,4,5,10,7,8,1,9,6]=>000000111=>111000000
[2,3,4,5,10,7,8,1,6,9]=>000000101=>101000000
[2,3,4,5,10,7,1,9,6,8]=>000001011=>110100000
[2,3,4,5,10,7,1,6,8,9]=>000001001=>100100000
[2,3,4,5,10,1,6,7,8,9]=>000000001=>100000000
[2,3,4,10,6,7,8,1,9,5]=>000000111=>111000000
[2,3,4,10,6,7,8,1,5,9]=>000000101=>101000000
[2,3,4,10,6,7,1,8,9,5]=>000001011=>110100000
[2,3,4,10,6,7,1,9,5,8]=>000001011=>110100000
[2,3,4,10,6,7,1,5,8,9]=>000001001=>100100000
[2,3,4,10,6,1,8,5,9,7]=>000010111=>111010000
[2,3,4,10,6,1,8,5,7,9]=>000010101=>101010000
[2,3,4,10,6,1,5,7,8,9]=>000010001=>100010000
[2,3,4,10,1,5,6,7,8,9]=>000000001=>100000000
[2,3,10,5,6,1,8,9,4,7]=>000010011=>110010000
[2,3,10,5,6,1,8,4,9,7]=>000010111=>111010000
[2,3,10,5,6,1,8,4,7,9]=>000010101=>101010000
[2,3,10,5,6,1,4,7,8,9]=>000010001=>100010000
[2,3,10,5,1,7,4,9,6,8]=>000101011=>110101000
[2,3,10,5,1,7,4,6,8,9]=>000101001=>100101000
[2,3,10,5,1,4,6,7,8,9]=>000100001=>100001000
[2,10,4,1,6,3,8,5,9,7]=>001010111=>111010100
[2,10,4,1,6,3,8,5,7,9]=>001010101=>101010100
[2,10,4,1,6,3,5,7,8,9]=>001010001=>100010100
[2,10,4,1,3,5,6,7,8,9]=>001000001=>100000100
[5,8,7,2,6,4,1,3]=>0010111=>1110100
[6,8,5,1,7,4,3,2]=>0111011=>1101110
[6,8,5,2,7,4,1,3]=>0011011=>1101100
[7,3,8,6,5,2,1,4]=>1001111=>1111001
[7,5,8,1,6,4,3,2]=>0110111=>1110110
[7,5,8,2,6,4,1,3]=>0010111=>1110100
[6,3,2,8,1,7,5,4]=>0101111=>1111010
[2,1,3,4,5,6,8,7,9]=>10000010=>01000001
[2,3,4,5,6,8,7,9,1]=>00000011=>11000000
[2,6,8,7,1,3,5,4]=>0001011=>1101000
[5,3,8,7,6,2,1,4]=>1001111=>1111001
[3,7,6,1,4,5,2,8]=>0001110=>0111000
[4,1,6,2,7,5,3,8]=>0011110=>0111100
[7,6,2,5,3,1,4,8]=>0101110=>0111010
[4,3,1,7,6,2,5,8]=>0110110=>0110110
[4,5,3,1,2,8,6,7]=>0101001=>1001010
[2,4,5,3,1,8,6,7]=>0101001=>1001010
[5,7,6,2,3,1,4,8]=>0100110=>0110010
[4,1,3,7,5,2,6,8]=>0011010=>0101100
[4,1,6,3,2,7,5,8]=>0110110=>0110110
[7,5,4,1,3,2,6,8]=>0111010=>0101110
[2,4,8,5,6,3,1,7]=>0100101=>1010010
[2,5,7,4,1,3,6,8]=>0010010=>0100100
[5,7,4,1,3,2,6,8]=>0110010=>0100110
[2,6,8,4,5,3,1,7]=>0101001=>1001010
[5,2,3,7,4,1,6,8]=>0011010=>0101100
[4,5,1,6,3,2,7,8]=>0101100=>0011010
[5,1,6,3,2,4,7,8]=>0101100=>0011010
[4,2,5,1,6,3,7,8]=>0011100=>0011100
[5,1,6,2,4,3,7,8]=>0011100=>0011100
[5,3,4,8,7,6,2,1]=>1001111=>1111001
[8,3,1,6,7,5,4,2]=>0111011=>1101110
[8,4,6,5,7,2,3,1]=>0100111=>1110010
[1,8,2,6,7,4,5,3]=>0001011=>1101000
[8,5,7,2,4,3,6,1]=>0010111=>1110100
[8,5,3,6,4,7,2,1]=>1001111=>1111001
[8,2,5,3,6,7,4,1]=>0011011=>1101100
[1,2,8,3,4,7,6,5]=>0000111=>1110000
[6,8,5,2,7,1,3,4]=>0001011=>1101000
[7,6,4,5,2,1,8,3]=>1001111=>1111001
[8,2,4,7,6,3,1,5]=>0100111=>1110010
[8,7,5,1,4,6,3,2]=>0101111=>1111010
[7,3,8,5,4,2,1,6]=>1011011=>1101101
[6,3,4,7,2,8,5,1]=>0001111=>1111000
[8,1,7,3,6,4,2,5]=>0010111=>1110100
[7,1,8,5,3,4,2,6]=>0011011=>1101100
[6,8,4,3,1,5,2,7]=>0111001=>1001110
[1,4,5,8,3,2,6,7]=>0100001=>1000010
[1,5,2,4,7,8,6,3]=>0001101=>1011000
[5,2,7,4,3,8,6,1]=>0011111=>1111100
[2,7,3,4,8,5,6,1]=>0000111=>1110000
[2,7,6,8,3,5,4,1]=>0011011=>1101100
[2,7,4,5,3,8,6,1]=>0001111=>1111000
[6,2,3,7,4,5,8,1]=>0000111=>1110000
[1,6,3,2,7,5,8,4]=>0100111=>1110010
[7,3,5,2,6,8,1,4]=>0001011=>1101000
[6,4,2,7,1,5,8,3]=>0010111=>1110100
[2,5,3,6,4,7,8,1]=>0001101=>1011000
[4,2,5,3,6,7,8,1]=>0011001=>1001100
[1,6,5,2,4,7,3,8]=>0001110=>0111000
[1,8,7,2,4,6,3,5]=>0000111=>1110000
[1,8,7,2,5,4,3,6]=>0011011=>1101100
[1,5,4,2,7,3,6,8]=>0011010=>0101100
[1,5,4,2,8,7,3,6]=>0011011=>1101100
[1,6,8,3,5,2,4,7]=>0001001=>1001000
[1,7,6,2,3,5,8,4]=>0000111=>1110000
[1,2,8,3,6,5,4,7]=>0001101=>1011000
[1,3,8,6,5,2,4,7]=>0001101=>1011000
[1,4,7,3,2,8,6,5]=>0100111=>1110010
[1,8,6,5,2,4,7,3]=>0001111=>1111000
[1,6,8,4,3,2,5,7]=>0110001=>1000110
[1,7,5,3,2,6,4,8]=>0101110=>0111010
[1,2,6,5,3,8,4,7]=>0001101=>1011000
[1,7,3,2,8,4,6,5]=>0100111=>1110010
[1,6,5,2,8,4,7,3]=>0001111=>1111000
[1,8,3,7,2,4,6,5]=>0000111=>1110000
[5,4,2,8,7,6,1,3]=>0011111=>1111100
[8,6,3,2,5,7,4,1]=>0110111=>1110110
[7,3,2,1,6,5,8,4]=>1100111=>1110011
[7,3,2,6,1,5,8,4]=>0100111=>1110010
[6,8,5,2,7,1,4,3]=>0011011=>1101100
[6,8,2,5,1,7,4,3]=>0011011=>1101100
[6,8,5,7,2,1,4,3]=>1010011=>1100101
[6,5,8,2,7,4,1,3]=>0010111=>1110100
[6,2,1,7,5,8,4,3]=>1010111=>1110101
[1,6,4,8,5,3,7,2]=>0001111=>1111000
[1,6,5,3,4,7,8,2]=>0001101=>1011000
[4,2,6,7,8,1,3,5]=>0010001=>1000100
[4,6,5,1,3,7,8,2]=>0001101=>1011000
[5,1,7,2,6,4,8,3]=>0001111=>1111000
[4,1,7,6,5,8,2,3]=>0010111=>1110100
[5,2,1,7,6,4,8,3]=>1001111=>1111001
[4,2,3,6,7,8,1,5]=>0010001=>1000100
[4,7,2,1,6,5,8,3]=>1000111=>1110001
[2,7,6,4,1,5,8,3]=>0010111=>1110100
[2,4,3,6,7,8,1,5]=>0010001=>1000100
[6,8,5,2,7,3,1,4]=>0101011=>1101010
[7,5,2,4,1,8,3,6]=>0011011=>1101100
[6,5,1,3,7,8,2,4]=>0001101=>1011000
[7,2,1,4,3,5,8,6]=>1010011=>1100101
[6,1,2,4,3,7,8,5]=>0010101=>1010100
[8,1,5,4,2,3,6,7]=>0011001=>1001100
[7,1,2,4,6,3,8,5]=>0000111=>1110000
[7,1,2,6,5,3,8,4]=>0001111=>1111000
[7,5,6,1,2,4,8,3]=>0000111=>1110000
[7,1,4,5,2,3,6,8]=>0001010=>0101000
[6,1,4,8,7,2,3,5]=>0000111=>1110000
[6,1,8,5,7,2,3,4]=>0000111=>1110000
[1,6,7,5,8,3,4,2]=>0010011=>1100100
[6,1,7,5,8,2,3,4]=>0000111=>1110000
[6,1,4,7,8,2,3,5]=>0000101=>1010000
[8,1,2,3,7,5,4,6]=>0001011=>1101000
[5,8,6,1,2,4,7,3]=>0000111=>1110000
[1,6,8,7,5,3,4,2]=>0011011=>1101100
[6,1,8,7,5,2,3,4]=>0001111=>1111000
[8,3,1,2,4,6,5,7]=>0100101=>1010010
[8,3,1,2,4,5,7,6]=>0100011=>1100010
[6,3,1,2,4,7,5,8]=>0100110=>0110010
[6,7,1,4,2,3,5,8]=>0010010=>0100100
[6,1,7,4,8,2,3,5]=>0000111=>1110000
[6,7,8,5,1,2,4,3]=>0011001=>1001100
[8,6,5,4,3,2,7,9,1]=>01111011=>11011110
[8,9,5,4,3,2,1,6,7]=>11110001=>10001111
[7,6,5,4,3,8,9,1,2]=>00111101=>10111100
[9,6,5,4,3,2,7,1,8]=>01111101=>10111110
[8,7,6,5,4,3,2,9,1,10]=>011111110=>011111110
[9,2,3,4,5,6,1,7,8]=>00001001=>10010000
[3,1,5,6,7,8,9,2,4]=>01000001=>10000010
[2,1,3,5,6,7,8,9,4]=>10000001=>10000001
[4,3,8,5,6,2,7,1]=>0010111=>1110100
[7,4,6,1,5,3,8,2]=>0001111=>1111000
[6,3,8,1,7,2,5,4]=>0001111=>1111000
[6,2,5,4,7,1,8,3]=>0001111=>1111000
[2,6,3,4,8,7,5,1]=>0001111=>1111000
[2,7,4,5,1,8,3,6]=>0001011=>1101000
[8,4,5,7,6,1,2,3]=>0000111=>1110000
[8,4,5,7,1,3,6,2]=>0000111=>1110000
[8,1,3,4,6,7,5,2]=>0001011=>1101000
[8,7,6,2,3,5,4,1]=>0011111=>1111100
[8,3,6,7,5,1,2,4]=>0001011=>1101000
[8,2,1,6,5,7,4,3]=>1010111=>1110101
[2,7,1,8,5,6,4,3]=>0010111=>1110100
[2,7,8,6,1,5,3,4]=>0001101=>1011000
[4,6,8,2,3,5,1,7]=>0001001=>1001000
[6,8,2,1,3,5,4,7]=>1001001=>1001001
[3,5,1,6,4,8,2,7]=>0001101=>1011000
[3,5,8,6,2,1,4,7]=>1000101=>1010001
[2,4,8,5,6,1,3,7]=>0000101=>1010000
[4,8,2,5,6,1,3,7]=>0000101=>1010000
[5,3,8,4,2,7,6,1]=>0011111=>1111100
[2,8,5,3,1,4,7,6]=>0101011=>1101010
[1,7,8,4,6,3,2,5]=>0100101=>1010010
[8,7,2,4,6,3,1,5]=>0100111=>1110010
[8,7,3,2,1,6,4,5]=>1100111=>1110011
[7,8,3,4,6,5,2,1]=>1001101=>1011001
[8,7,3,6,5,2,4,1]=>0011111=>1111100
[3,1,2,8,6,5,7,4]=>0100111=>1110010
[3,8,2,7,5,4,6,1]=>0001111=>1111000
[8,7,1,4,5,3,6,2]=>0001111=>1111000
[2,8,7,4,6,3,5,1]=>0001111=>1111000
[2,8,7,4,6,3,1,5]=>0100111=>1110010
[8,3,4,1,2,5,7,6]=>0010011=>1100100
[8,4,1,3,2,5,7,6]=>0110011=>1100110
[7,3,8,6,2,1,4,5]=>1000111=>1110001
[7,2,8,4,6,5,1,3]=>0001111=>1111000
[5,8,6,4,7,2,3,1]=>0100111=>1110010
[4,7,2,6,5,8,3,1]=>0100111=>1110010
[3,6,8,5,7,4,2,1]=>1010011=>1100101
[6,7,5,2,4,8,3,1]=>0101011=>1101010
[8,1,2,7,5,6,3,4]=>0000111=>1110000
[8,2,7,3,4,6,1,5]=>0000111=>1110000
[6,7,5,4,8,1,3,2]=>0101011=>1101010
[8,3,5,6,4,7,2,1]=>1000111=>1110001
[8,5,6,2,4,3,7,1]=>0010111=>1110100
[6,5,8,1,3,4,2,7]=>0010101=>1010100
[6,8,4,5,1,3,2,7]=>0101001=>1001010
[6,4,8,7,5,3,2,1]=>1101111=>1111011
[6,7,1,4,3,2,8,5]=>0110011=>1100110
[7,2,5,1,4,8,3,6]=>0001011=>1101000
[5,8,1,3,4,2,7,6]=>0010011=>1100100
[1,5,6,3,2,8,7,4]=>0100111=>1110010
[1,3,7,6,8,4,2,5]=>0010011=>1100100
[1,6,7,3,2,8,5,4]=>0101011=>1101010
[3,2,7,6,8,4,5,1]=>0101011=>1101010
[1,3,8,5,2,7,6,4]=>0001111=>1111000
[6,4,1,5,2,8,7,3]=>0011111=>1111100
[7,6,5,3,1,8,2,4]=>0101111=>1111010
[2,5,1,4,7,3,6,8]=>0001010=>0101000
[3,1,6,5,7,2,4,8]=>0100110=>0110010
[2,6,1,5,7,4,8,3]=>0000111=>1110000
[2,5,7,1,6,3,8,4]=>0000111=>1110000
[2,6,1,5,7,4,3,8]=>0010110=>0110100
[3,1,6,5,2,4,7,8]=>0101100=>0011010
[3,6,5,1,4,2,7,8]=>0011100=>0011100
[3,6,5,1,7,2,4,8]=>0001110=>0111000
[3,6,5,2,1,4,7,8]=>1001100=>0011001
[5,4,3,6,1,7,2,8]=>0011110=>0111100
[4,5,2,7,6,1,3,8]=>0001110=>0111000
[4,6,5,3,1,2,7,8]=>0101100=>0011010
[5,4,1,6,3,7,2,8]=>0011110=>0111100
[5,4,2,6,3,7,8,1]=>0011101=>1011100
[3,6,5,7,1,4,2,8]=>0010110=>0110100
[3,6,5,1,4,7,2,8]=>0001110=>0111000
[4,3,6,5,7,1,2,8]=>0010110=>0110100
[4,2,6,5,1,3,7,8]=>0011100=>0011100
[4,1,6,5,3,7,8,2]=>0011101=>1011100
[4,2,5,7,6,1,3,8]=>0010110=>0110100
[3,4,7,6,1,2,5,8]=>0000110=>0110000
[4,2,5,7,6,3,8,1]=>0010111=>1110100
[4,1,6,5,2,7,3,8]=>0011110=>0111100
[3,6,5,7,2,1,4,8]=>1000110=>0110001
[3,5,7,6,2,4,1,8]=>0010110=>0110100
[5,4,2,6,3,7,1,8]=>0011110=>0111100
[4,6,5,2,7,3,1,8]=>0101110=>0111010
[4,6,5,2,1,7,3,8]=>1001110=>0111001
[3,5,8,2,1,4,6,7]=>1000001=>1000001
[3,5,8,2,4,6,7,1]=>0000011=>1100000
[5,3,8,2,1,4,6,7]=>1001001=>1001001
[5,3,1,8,2,4,6,7]=>0101001=>1001010
[5,1,3,8,2,4,6,7]=>0001001=>1001000
[1,5,8,4,2,3,6,7]=>0010001=>1000100
[5,8,2,1,4,3,6,7]=>1010001=>1000101
[5,8,2,4,1,6,7,3]=>0010011=>1100100
[5,8,2,4,6,3,1,7]=>0100101=>1010010
[5,8,2,4,3,6,1,7]=>0010101=>1010100
[5,8,1,4,6,2,3,7]=>0000101=>1010000
[1,5,8,4,6,7,2,3]=>0000011=>1100000
[5,1,8,4,6,7,2,3]=>0001011=>1101000
[5,8,2,4,6,3,7,1]=>0000111=>1110000
[3,8,4,6,7,2,1,5]=>1000011=>1100001
[3,8,4,6,7,2,5,1]=>0001011=>1101000
[8,4,3,6,7,2,5,1]=>0011011=>1101100
[8,4,3,6,7,2,1,5]=>1010011=>1100101
[8,6,2,4,5,3,7,1]=>0001111=>1111000
[1,8,6,4,5,7,2,3]=>0000111=>1110000
[8,6,2,4,5,3,1,7]=>0101101=>1011010
[1,8,6,4,2,3,5,7]=>0010101=>1010100
[3,8,1,6,2,4,5,7]=>0000101=>1010000
[3,8,6,2,1,4,5,7]=>1000101=>1010001
[3,8,6,2,4,1,5,7]=>0010101=>1010100
[3,8,6,2,4,5,7,1]=>0000111=>1110000
[8,3,6,2,4,5,1,7]=>0001101=>1011000
[8,1,3,6,2,4,5,7]=>0000101=>1010000
[8,3,6,7,2,1,4,5]=>1000011=>1100001
[3,8,6,7,2,1,4,5]=>1000011=>1100001
[8,2,6,4,5,1,7,3]=>0001111=>1111000
[1,8,4,6,7,5,2,3]=>0001011=>1101000
[8,4,6,2,3,7,5,1]=>0001111=>1111000
[8,4,7,2,1,3,6,5]=>1000111=>1110001
[2,7,1,6,3,5,8,4]=>0000111=>1110000
[8,4,2,1,5,3,7,6]=>1011011=>1101101
[8,2,1,4,7,3,6,5]=>1000111=>1110001
[1,6,2,5,8,4,7,3]=>0000111=>1110000
[3,2,1,7,4,5,8,6]=>1100011=>1100011
[2,6,8,5,1,7,4,3]=>0011011=>1101100
[2,1,5,8,7,3,6,4]=>1000111=>1110001
[3,2,1,6,7,4,8,5]=>1100011=>1100011
[4,3,1,7,8,5,2,6]=>0111001=>1001110
[5,6,8,2,4,3,7,1]=>0010011=>1100100
[2,8,5,3,6,4,7,1]=>0001111=>1111000
[1,2,8,6,4,7,3,5]=>0000111=>1110000
[5,3,2,7,8,6,4,1]=>0111101=>1011110
[4,2,7,8,3,5,6,1]=>0010101=>1010100
[2,8,3,7,1,4,6,5]=>0000111=>1110000
[2,8,7,1,5,3,6,4]=>0001111=>1111000
[7,3,5,6,4,2,8,1]=>0010111=>1110100
[3,8,4,2,7,6,5,1]=>0011111=>1111100
[4,8,3,2,7,5,6,1]=>0100111=>1110010
[3,2,4,8,7,5,6,1]=>0100111=>1110010
[2,6,8,1,5,3,4,7]=>0001001=>1001000
[3,2,5,6,8,1,4,7]=>0100001=>1000010
[3,8,1,6,4,5,2,7]=>0001101=>1011000
[8,1,3,6,5,4,2,7]=>0011101=>1011100
[7,4,3,6,2,1,8,5]=>1010111=>1110101
[1,2,4,8,6,3,7,5]=>0000111=>1110000
[7,2,1,5,3,4,8,6]=>1001011=>1101001
[5,7,2,3,1,4,8,6]=>0100011=>1100010
[7,1,5,2,4,6,8,3]=>0001011=>1101000
[8,4,2,7,3,5,6,1]=>0010111=>1110100
[1,8,6,4,7,5,3,2]=>0101111=>1111010
[7,4,1,5,8,6,3,2]=>0110111=>1110110
[4,5,8,7,3,1,2,6]=>0100011=>1100010
[1,3,8,7,6,4,2,5]=>0010111=>1110100
[2,8,5,1,7,4,6,3]=>0001111=>1111000
[1,8,6,4,7,5,2,3]=>0001111=>1111000
[2,7,4,6,3,8,5,1]=>0001111=>1111000
[1,2,8,6,4,7,5,3]=>0001111=>1111000
[3,4,5,6,7,9,1,2,8]=>00000001=>10000000
[3,4,5,7,8,9,1,2,6]=>00000001=>10000000
[3,5,6,7,8,9,1,2,4]=>00000001=>10000000
[3,4,5,6,8,9,10,1,2,7]=>000000001=>100000000
[3,5,6,7,8,9,10,1,2,4]=>000000001=>100000000
[3,4,5,6,7,8,9,10,1,2,11]=>0000000010=>0100000000
[3,4,5,6,7,8,1,2,9,10]=>000000100=>001000000
[3,4,5,6,9,1,2,7,8]=>00000001=>10000000
[3,4,5,6,1,2,7,8,9]=>00001000=>00010000
[3,4,5,6,7,9,10,11,1,2,8]=>0000000001=>1000000000
[5,1,6,7,8,9,2,3,4]=>00010001=>10001000
[3,4,6,7,8,9,10,11,1,2,5]=>0000000001=>1000000000
[4,1,8,6,3,7,5,2]=>0011111=>1111100
[8,4,3,1,6,2,5,7]=>0110101=>1010110
[7,5,4,3,8,1,6,2]=>0011111=>1111100
[3,5,4,1,7,8,2,6]=>0011001=>1001100
[6,4,2,1,5,7,3,8]=>1010110=>0110101
[3,1,5,8,7,2,4,6]=>0100011=>1100010
[3,2,5,7,8,4,6,1]=>0100101=>1010010
[5,3,7,4,2,6,8,1]=>0011011=>1101100
[5,3,7,4,2,6,1,8]=>0011110=>0111100
[5,3,8,4,2,1,6,7]=>1011001=>1001101
[5,2,8,4,3,1,6,7]=>0111001=>1001110
[5,1,8,4,3,2,6,7]=>0111001=>1001110
[5,2,7,4,3,6,1,8]=>0011110=>0111100
[5,2,7,4,3,6,8,1]=>0011011=>1101100
[5,3,7,4,1,6,8,2]=>0011011=>1101100
[3,1,5,7,8,4,6,2]=>0100101=>1010010
[3,1,5,7,8,4,2,6]=>0110001=>1000110
[5,2,7,4,1,3,8,6]=>0011011=>1101100
[6,2,3,7,4,8,5,1]=>0001111=>1111000
[6,2,3,7,4,8,1,5]=>0000111=>1110000
[6,2,3,7,4,5,1,8]=>0001110=>0111000
[6,1,3,7,4,5,8,2]=>0000111=>1110000
[1,2,8,6,4,3,5,7]=>0010101=>1010100
[6,1,3,7,4,5,2,8]=>0001110=>0111000
[1,8,6,3,5,4,2,7]=>0011101=>1011100
[2,6,1,8,5,3,4,7]=>0001101=>1011000
[4,5,7,8,1,6,3,2]=>0100101=>1010010
[2,5,7,8,4,6,3,1]=>0100101=>1010010
[1,8,2,7,5,3,4,6]=>0001011=>1101000
[2,5,4,1,8,6,7,3]=>0011011=>1101100
[5,6,8,3,4,2,7,1]=>0010011=>1100100
[4,1,5,3,8,6,7,2]=>0011011=>1101100
[7,3,5,1,4,8,6,2]=>0001111=>1111000
[7,1,3,2,4,5,6,8]=>0100010=>0100010
[3,8,7,1,4,2,5,6]=>0010011=>1100100
[5,1,7,8,2,4,3,6]=>0011001=>1001100
[8,5,4,6,1,7,3,2]=>0101111=>1111010
[5,3,2,1,4,6,8,7]=>1101001=>1001011
[5,3,2,4,8,1,6,7]=>0101001=>1001010
[5,3,2,4,7,1,8,6]=>0101011=>1101010
[8,4,5,3,7,1,2,6]=>0001011=>1101000
[4,8,1,7,3,5,6,2]=>0000111=>1110000
[5,3,2,4,6,8,1,7]=>0101001=>1001010
[1,2,5,6,7,3,8,9,4]=>00000101=>10100000
[1,2,4,3,5,7,8,9,6]=>00100001=>10000100
[2,7,6,3,1,4,8,5]=>0100111=>1110010
[3,7,4,5,6,8,2,1]=>1000011=>1100001
[8,7,1,4,2,5,3,6]=>0011011=>1101100
[4,6,8,3,7,1,5,2]=>0001011=>1101000
[4,7,3,5,8,1,6,2]=>0000111=>1110000
[8,4,3,5,7,1,6,2]=>0010111=>1110100
[1,7,6,4,2,5,3,8]=>0011110=>0111100
[7,6,4,2,8,3,1,5]=>0110111=>1110110
[8,5,2,4,3,7,1,6]=>0011011=>1101100
[8,5,1,4,3,7,6,2]=>0011111=>1111100
[7,5,4,1,3,6,8,2]=>0011011=>1101100
[3,6,7,2,5,1,8,4]=>0001011=>1101000
[2,6,5,7,1,4,8,3]=>0000111=>1110000
[3,5,1,7,8,4,6,2]=>0001101=>1011000
[1,5,2,4,6,8,7,3]=>0001011=>1101000
[8,1,2,4,7,6,5,3]=>0001111=>1111000
[3,4,1,8,6,7,5,2]=>0011011=>1101100
[4,3,8,5,1,7,6,2]=>0011111=>1111100
[6,1,3,2,8,5,7,4]=>0100111=>1110010
[3,1,2,4,5,6,7,9,8]=>01000001=>10000010
[8,5,3,2,4,7,1,6]=>0101011=>1101010
[6,7,4,2,5,8,3,1]=>0110011=>1100110
[8,5,4,2,6,3,1,7]=>0111101=>1011110
[8,5,2,1,6,4,3,7]=>1011101=>1011101
[8,4,6,5,1,3,2,7]=>0101101=>1011010
[1,3,8,4,7,5,2,6]=>0001011=>1101000
[5,3,7,1,4,6,8,2]=>0001011=>1101000
[5,7,2,6,1,4,8,3]=>0000111=>1110000
[3,8,5,7,6,1,2,4]=>0000111=>1110000
[8,4,7,5,2,1,3,6]=>1001011=>1101001
[3,8,6,4,7,2,1,5]=>1000111=>1110001
[5,2,7,4,6,8,3,1]=>0101011=>1101010
[4,8,6,3,7,2,1,5]=>1000111=>1110001
[2,8,3,1,7,6,4,5]=>0100111=>1110010
[2,5,6,4,8,1,7,3]=>0000111=>1110000
[5,7,2,1,6,8,3,4]=>1000011=>1100001
[4,7,8,5,1,6,2,3]=>0001101=>1011000
[4,5,2,1,6,7,8,3]=>1001001=>1001001
[4,5,6,3,1,7,8,2]=>0100101=>1010010
[3,5,6,7,4,1,8,2]=>0010011=>1100100
[3,5,1,4,2,8,7,6]=>0011011=>1101100
[3,5,1,4,2,6,8,7]=>0011001=>1001100
[3,5,1,4,2,6,7,8]=>0011000=>0001100
[1,3,8,4,6,2,5,7]=>0000101=>1010000
[1,8,4,2,3,7,5,6]=>0010011=>1100100
[1,4,8,3,2,7,6,5]=>0100111=>1110010
[1,3,7,6,5,2,4,8]=>0001110=>0111000
[1,2,8,6,7,5,4,3]=>0011011=>1101100
[1,7,5,4,3,2,6,8]=>0111010=>0101110
[8,9,10,1,5,6,7,3,4,2]=>001001001=>100100100
[8,9,10,5,6,7,1,3,4,2]=>001001001=>100100100
[8,9,10,1,5,6,3,4,7,2]=>000011001=>100110000
[8,9,10,5,6,1,3,4,7,2]=>000011001=>100110000
[8,9,10,5,6,3,4,7,1,2]=>000011001=>100110000
[8,9,5,6,10,1,3,4,7,2]=>000001011=>110100000
[8,9,5,6,10,3,4,7,1,2]=>000001011=>110100000
[8,9,10,1,5,6,7,3,2,4]=>010001001=>100100010
[8,9,10,5,6,7,1,3,2,4]=>010001001=>100100010
[8,9,10,1,5,6,3,7,2,4]=>000011001=>100110000
[8,9,10,5,6,1,3,7,2,4]=>000011001=>100110000
[8,9,10,5,6,3,7,1,2,4]=>000011001=>100110000
[8,9,5,6,10,1,3,7,2,4]=>000001011=>110100000
[8,9,5,6,10,3,7,1,2,4]=>000001011=>110100000
[8,9,10,1,5,6,3,2,4,7]=>010010001=>100010010
[8,9,10,5,6,1,3,2,4,7]=>010010001=>100010010
[8,9,10,5,6,3,1,2,4,7]=>010010001=>100010010
[8,9,10,5,6,3,2,4,7,1]=>010011001=>100110010
[8,9,5,6,10,1,3,2,4,7]=>010000011=>110000010
[8,9,5,6,10,3,1,2,4,7]=>010000011=>110000010
[8,9,5,6,10,3,2,4,7,1]=>010001011=>110100010
[8,9,10,1,5,3,6,7,2,4]=>000101001=>100101000
[8,9,10,5,1,3,6,7,2,4]=>000101001=>100101000
[8,9,10,5,3,6,7,1,2,4]=>000101001=>100101000
[8,9,5,10,1,3,6,7,2,4]=>000001011=>110100000
[8,9,5,10,3,6,7,1,2,4]=>000001011=>110100000
[8,9,10,1,5,3,6,2,4,7]=>000110001=>100011000
[8,9,10,5,1,3,6,2,4,7]=>000110001=>100011000
[8,9,10,5,3,6,1,2,4,7]=>000110001=>100011000
[8,9,10,5,3,6,2,4,7,1]=>000111001=>100111000
[8,9,5,10,1,3,6,2,4,7]=>000010011=>110010000
[8,9,5,10,3,6,1,2,4,7]=>000010011=>110010000
[8,9,5,10,3,6,2,4,7,1]=>000011011=>110110000
[8,9,5,3,6,10,1,2,4,7]=>000100011=>110001000
[8,9,5,3,6,10,2,4,7,1]=>000101011=>110101000
[8,5,9,10,1,3,6,7,2,4]=>000001101=>101100000
[8,5,9,10,3,6,7,1,2,4]=>000001101=>101100000
[8,5,9,10,1,3,6,2,4,7]=>000010101=>101010000
[8,5,9,10,3,6,1,2,4,7]=>000010101=>101010000
[8,5,9,10,3,6,2,4,7,1]=>000011101=>101110000
[3,8,5,7,4,6,2,1]=>1000111=>1110001
[4,2,5,7,8,6,3,1]=>0110101=>1010110
[6,7,2,4,5,1,8,3]=>0001011=>1101000
[5,2,7,8,3,6,1,4]=>0001101=>1011000
[2,4,7,8,1,3,6,5]=>0000101=>1010000
[8,5,1,2,3,7,4,6]=>0001011=>1101000
[5,2,8,3,1,4,7,6]=>0101011=>1101010
[8,7,2,5,1,4,3,6]=>0011011=>1101100
[8,4,1,3,2,7,6,5]=>0110111=>1110110
[8,3,5,1,2,4,7,6]=>0001011=>1101000
[8,6,5,1,7,4,2,3]=>0011111=>1111100
[8,7,4,5,1,2,6,3]=>0001111=>1111000
[3,8,6,2,7,1,5,4]=>0001111=>1111000
[3,4,8,2,1,7,6,5]=>1000111=>1110001
[3,8,4,2,1,7,6,5]=>1010111=>1110101
[8,3,1,7,5,6,2,4]=>0100111=>1110010
[8,4,1,7,5,2,6,3]=>0011111=>1111100
[8,4,2,7,5,3,1,6]=>0111011=>1101110
[8,4,3,7,5,1,2,6]=>0011011=>1101100
[8,5,7,6,4,3,1,2]=>0110111=>1110110
[8,4,7,6,5,2,1,3]=>1001111=>1111001
[8,3,1,4,7,6,2,5]=>0100111=>1110010
[8,3,5,7,6,2,4,1]=>0010111=>1110100
[1,4,6,8,2,5,7,3]=>0000011=>1100000
[3,6,2,4,8,1,7,5]=>0000111=>1110000
[7,3,8,2,4,6,1,5]=>0000111=>1110000
[1,5,2,6,8,3,7,4]=>0001011=>1101000
[4,5,3,1,8,2,6,7]=>0101001=>1001010
[7,2,8,4,1,3,5,6]=>0010011=>1100100
[6,1,7,3,2,8,4,5]=>0100111=>1110010
[6,2,1,7,3,8,4,5]=>1000111=>1110001
[5,8,2,1,3,4,6,7]=>1000001=>1000001
[4,2,5,1,8,3,6,7]=>0011001=>1001100
[7,4,2,8,3,1,5,6]=>0110011=>1100110
[7,4,2,8,3,5,1,6]=>0011011=>1101100
[6,7,8,5,2,1,4,3]=>1011001=>1001101
[1,6,2,7,8,4,3,5]=>0010101=>1010100
[10,1,9,5,6,7,8,2,3,4]=>000000111=>111000000
[9,1,10,8,6,7,2,3,4,5]=>000001111=>111100000
[8,1,9,10,7,2,3,4,5,6]=>000001101=>101100000
[10,1,8,9,2,3,4,5,6,7]=>000000011=>110000000
[11,1,10,5,6,7,8,9,2,3,4]=>0000000111=>1110000000
[3,1,10,9,6,7,8,2,4,5]=>010000111=>111000010
[10,1,11,9,6,7,8,2,3,4,5]=>0000001111=>1111000000
[3,1,9,10,8,7,2,4,5,6]=>010001101=>101100010
[9,1,10,11,8,7,2,3,4,5,6]=>0000011101=>1011100000
[3,1,8,9,10,2,4,5,6,7]=>010000001=>100000010
[8,1,9,10,11,2,3,4,5,6,7]=>0000001001=>1001000000
[11,1,10,9,2,3,4,5,6,7,8]=>0000000111=>1110000000
[7,3,4,1,8,6,2,5]=>0010111=>1110100
[4,7,6,3,5,8,2,1]=>1000111=>1110001
[3,7,6,5,2,4,8,1]=>0001111=>1111000
[1,4,7,8,6,2,5,3]=>0001101=>1011000
[1,6,7,8,3,2,5,4]=>0101001=>1001010
[1,3,2,7,8,4,6,5]=>0100101=>1010010
[6,8,2,3,5,7,4,1]=>0010011=>1100100
[5,7,1,4,6,2,8,3]=>0000111=>1110000
[9,8,7,6,5,1,3,4,2]=>00111111=>11111100
[9,8,7,6,1,4,5,3,2]=>01011111=>11111010
[8,7,1,5,4,6,3,2]=>0101111=>1111010
[9,8,7,1,5,6,4,3,2]=>01101111=>11110110
[9,8,1,6,7,5,4,3,2]=>01110111=>11101110
[9,1,7,8,6,5,4,3,2]=>01111011=>11011110
[4,5,7,1,8,6,2,3]=>0000111=>1110000
[4,3,8,6,5,2,7,1]=>0011111=>1111100
[2,3,8,6,5,1,7,4]=>0001111=>1111000
[5,4,7,3,1,2,6,8]=>0101010=>0101010
[7,6,2,1,5,4,3,8]=>1011110=>0111101
[3,1,2,6,5,7,8,4]=>0100101=>1010010
[7,3,2,6,1,4,8,5]=>0100111=>1110010
[3,2,5,6,8,4,1,7]=>0110001=>1000110
[7,2,6,8,5,4,3,1]=>0111011=>1101110
[3,7,5,6,2,4,1,8]=>0010110=>0110100
[1,3,4,5,6,7,2,9,8]=>00000101=>10100000
[3,4,5,6,7,1,9,2,8]=>00000101=>10100000
[3,2,4,1,6,5,8,7,9]=>01101010=>01010110
[4,2,5,1,6,3,8,7,9]=>00111010=>01011100
[4,2,6,1,7,3,8,5,9]=>00101110=>01110100
[4,2,6,1,8,3,9,5,7]=>00101011=>11010100
[4,2,6,1,7,3,5,9,8]=>00101101=>10110100
[4,2,5,1,3,7,6,9,8]=>00110101=>10101100
[3,2,5,4,6,1,8,7,9]=>01011010=>01011010
[4,2,5,1,6,3,8,7,10,9]=>001110101=>101011100
[4,2,5,1,7,6,8,3,9]=>00110110=>01101100
[4,2,6,1,7,3,8,5,10,9]=>001011101=>101110100
[4,2,6,1,7,3,9,8,5]=>00101111=>11110100
[4,2,6,1,8,3,9,5,10,7]=>001010111=>111010100
[4,2,5,1,3,6,8,7]=>0011001=>1001100
[4,2,6,1,7,3,5,8,9]=>00101100=>00110100
[4,2,6,1,8,3,9,5,7,10]=>001010110=>011010100
[4,2,5,1,3,8,9,6,7]=>00110001=>10001100
[4,2,6,1,7,3,5,9,8,10]=>001011010=>010110100
[3,2,1,6,7,4,5,9,8]=>11000101=>10100011
[4,2,5,1,3,7,6,9,8,10]=>001101010=>010101100
[1,4,5,2,3,7,6,9,8]=>00010101=>10101000
[5,3,4,2,7,1,8,6]=>0011011=>1101100
[5,6,8,2,1,3,4,7]=>1000001=>1000001
[6,5,2,1,3,8,4,7]=>1001101=>1011001
[2,4,3,5,6,8,1,7]=>0010001=>1000100
[6,3,2,4,8,5,1,7]=>0101101=>1011010
[6,3,1,2,7,8,4,5]=>0100101=>1010010
[8,4,7,1,2,5,3,6]=>0001011=>1101000
[7,4,6,1,8,5,2,3]=>0001111=>1111000
[8,5,6,7,2,1,4,3]=>1010011=>1100101
[2,5,6,3,8,4,7,1]=>0000111=>1110000
[6,8,4,2,3,1,7,5]=>0110011=>1100110
[1,7,6,2,8,3,5,4]=>0001111=>1111000
[7,1,5,6,3,2,8,4]=>0100111=>1110010
[4,1,3,8,5,2,7,6]=>0011011=>1101100
[1,8,5,4,7,2,3,6]=>0001011=>1101000
[8,2,5,6,4,3,1,7]=>0110101=>1010110
[2,4,3,8,6,5,1,7]=>0011101=>1011100
[3,1,4,5,8,6,2,7]=>0100101=>1010010
[1,8,3,2,5,4,6,7]=>0101001=>1001010
[5,1,7,3,2,8,4,6]=>0101011=>1101010
[5,7,8,1,3,2,4,6]=>0100001=>1000010
[8,2,4,1,6,7,3,5]=>0010011=>1100100
[8,7,3,6,2,4,1,5]=>0010111=>1110100
[1,7,4,8,3,6,2,5]=>0000111=>1110000
[7,8,6,1,3,5,4,2]=>0011101=>1011100
[1,7,5,8,4,3,2,6]=>0110011=>1100110
[6,3,1,2,7,8,5,4]=>0101101=>1011010
[8,2,7,5,3,4,1,6]=>0011011=>1101100
[6,3,1,2,8,7,5,4]=>0101111=>1111010
[8,4,7,2,6,3,1,5]=>0100111=>1110010
[1,2,5,7,8,3,6,4]=>0000101=>1010000
[7,6,3,4,2,1,8,5]=>1010111=>1110101
[8,4,6,2,3,7,1,5]=>0000111=>1110000
[3,4,5,8,1,7,2,6]=>0000011=>1100000
[6,3,4,2,7,8,1,5]=>0010101=>1010100
[5,6,3,7,8,2,1,4]=>1000101=>1010001
[8,6,3,4,7,2,1,5]=>1000111=>1110001
[4,3,8,6,7,5,1,2]=>0011011=>1101100
[4,5,6,2,7,8,3,1]=>0100101=>1010010
[4,5,6,2,7,1,8,3]=>0000111=>1110000
[4,5,6,2,1,7,8,3]=>1000101=>1010001
[4,5,6,2,1,7,3,8]=>1000110=>0110001
[6,8,7,2,3,1,4,5]=>0100011=>1100010
[4,5,1,6,7,3,2,8]=>0101010=>0101010
[2,5,1,8,3,7,4,6]=>0001011=>1101000
[5,7,2,1,3,8,4,6]=>1000011=>1100001
[3,7,5,4,1,6,8,2]=>0011011=>1101100
[7,1,5,4,2,6,3,8]=>0011110=>0111100
[8,5,6,3,7,2,1,4]=>1000111=>1110001
[7,6,5,4,3,1,2,9,8]=>01111101=>10111110
[9,8,7,6,5,4,3,2,1,11,10]=>1111111101=>1011111111
[8,7,6,5,4,3,1,2,10,9]=>011111101=>101111110
[7,6,5,4,2,1,3,9,8]=>10111101=>10111101
[7,6,5,4,1,3,2,9,8]=>01111101=>10111110
[9,8,7,6,5,3,2,4,1]=>01111111=>11111110
[9,8,7,6,5,2,4,3,1]=>01111111=>11111110
[10,9,8,7,6,5,4,2,3,1]=>011111111=>111111110
[2,7,4,5,6,8,1,3]=>0000011=>1100000
[2,3,4,6,8,1,7,5]=>0000011=>1100000
[2,3,4,8,6,7,9,5,1]=>00010011=>11001000
[2,3,8,5,6,7,9,1,4]=>00000011=>11000000
[2,8,4,5,6,7,9,3,1]=>01000011=>11000010
[8,3,4,5,6,7,9,2,1]=>10000011=>11000001
[2,3,4,5,7,9,1,8,6]=>00000011=>11000000
[2,3,4,6,7,1,9,5,8]=>00000101=>10100000
[2,3,4,5,9,7,8,10,6,1]=>000010011=>110010000
[2,3,5,8,1,6,7,4]=>0000011=>1100000
[2,3,5,6,1,7,9,4,8]=>00001001=>10010000
[2,3,4,9,6,7,8,10,1,5]=>000000011=>110000000
[2,4,5,1,6,7,9,8,3]=>00010011=>11001000
[2,3,9,5,6,7,8,10,4,1]=>001000011=>110000100
[2,4,7,5,6,8,1,3]=>0000011=>1100000
[3,4,1,5,6,7,9,2,8]=>00100001=>10000100
[2,9,4,5,6,7,8,10,3,1]=>010000011=>110000010
[3,2,4,5,6,7,9,1,8]=>01000001=>10000010
[9,3,4,5,6,7,8,10,1,2]=>000000011=>110000000
[2,3,4,5,6,8,10,1,9,7]=>000000011=>110000000
[2,3,4,5,6,7,10,9,11,8,1]=>0000001011=>1101000000
[2,3,4,7,6,9,8,5,1]=>00010111=>11101000
[2,3,4,5,7,8,1,10,6,9]=>000000101=>101000000
[2,3,4,5,6,10,8,9,11,7,1]=>0000010011=>1100100000
[2,3,4,6,9,1,7,8,5]=>00000011=>11000000
[2,3,4,6,7,1,8,10,5,9]=>000001001=>100100000
[2,3,4,5,10,7,8,9,11,1,6]=>0000000011=>1100000000
[7,3,4,6,2,8,1,5]=>0000111=>1110000
[2,5,4,6,8,7,9,1,3]=>00010011=>11001000
[2,3,5,7,1,6,9,4,8]=>00000101=>10100000
[2,3,5,6,1,7,8,10,9,4]=>000010011=>110010000
[2,3,4,10,6,7,8,9,11,5,1]=>0001000011=>1100001000
[4,7,6,5,2,8,3,1]=>0101111=>1111010
[4,3,5,8,6,7,9,2,1]=>10100011=>11000101
[2,5,4,8,6,7,3,1]=>0101011=>1101010
[2,4,6,1,5,7,9,3,8]=>00001001=>10010000
[2,4,5,1,6,7,8,10,3,9]=>000100001=>100001000
[7,5,4,1,6,8,2,3]=>0011011=>1101100
[2,4,8,5,6,7,9,1,3]=>00000011=>11000000
[3,5,1,4,6,7,9,8,2]=>00010011=>11001000
[3,4,1,5,6,7,8,10,2,9]=>001000001=>100000100
[2,10,4,5,6,7,8,9,11,1,3]=>0000000011=>1100000000
[4,2,3,5,6,7,9,1,8]=>00100001=>10000100
[3,2,4,5,6,7,8,10,9,1]=>010000011=>110000010
[10,3,4,5,6,7,8,9,11,2,1]=>1000000011=>1100000001
[8,5,2,1,7,6,3,4]=>1001111=>1111001
[2,7,3,6,4,1,8,5]=>0010111=>1110100
[7,2,1,8,5,6,4,3]=>1010111=>1110101
[3,6,5,1,4,8,2,7]=>0001101=>1011000
[6,3,5,4,8,1,2,7]=>0001101=>1011000
[2,5,1,4,6,3,8,7]=>0001101=>1011000
[3,1,5,6,4,2,8,7]=>0110101=>1010110
[8,5,6,4,3,1,7,2]=>0110111=>1110110
[8,3,5,6,7,1,2,4]=>0000011=>1100000
[2,1,4,7,3,6,8,5]=>1000011=>1100001
[5,3,7,6,4,8,2,1]=>1001111=>1111001
[3,7,6,4,2,8,1,5]=>0010111=>1110100
[8,6,1,4,3,7,2,5]=>0010111=>1110100
[8,4,7,5,1,6,3,2]=>0101111=>1111010
[2,1,5,3,7,8,6,4]=>1001101=>1011001
[5,1,4,7,6,8,2,3]=>0001011=>1101000
[8,4,1,3,7,6,5,2]=>0011111=>1111100
[8,3,4,1,6,7,5,2]=>0011011=>1101100
[8,1,4,2,6,5,7,3]=>0010111=>1110100
[8,6,4,3,7,2,1,5]=>1010111=>1110101
[5,8,1,4,3,2,6,7]=>0110001=>1000110
[5,6,4,3,8,2,7,1]=>0010111=>1110100
[1,6,4,3,8,2,7,5]=>0010111=>1110100
[6,7,4,1,3,2,5,8]=>0110010=>0100110
[7,8,1,4,3,2,5,6]=>0110001=>1000110
[7,1,8,4,5,3,6,2]=>0001111=>1111000
[4,3,1,8,6,5,7,2]=>0110111=>1110110
[4,3,2,7,5,1,8,6]=>0111011=>1101110
[5,2,3,7,4,1,8,6]=>0011011=>1101100
[2,1,7,4,3,6,8,5]=>1010011=>1100101
[7,1,2,4,5,6,8,3]=>0000011=>1100000
[2,8,7,1,4,5,6,3]=>0000111=>1110000
[8,7,1,3,4,5,6,2]=>0000111=>1110000
[5,8,3,1,4,6,7,2]=>0100011=>1100010
[1,7,2,5,4,6,8,3]=>0001011=>1101000
[2,5,3,8,1,6,7,4]=>0001011=>1101000
[1,6,4,2,5,7,8,3]=>0010101=>1010100
[6,5,3,4,1,7,8,2]=>0011101=>1011100
[5,6,3,4,1,7,8,2]=>0010101=>1010100
[2,5,3,1,4,7,8,6]=>0101001=>1001010
[6,8,2,3,1,5,7,4]=>0100011=>1100010
[4,3,1,5,2,7,8,6]=>0111001=>1001110
[5,2,3,1,4,7,8,6]=>0101001=>1001010
[7,2,1,3,5,6,8,4]=>1000011=>1100001
[5,2,4,7,8,6,3,1]=>0101101=>1011010
[5,4,8,7,2,3,1,6]=>0101011=>1101010
[8,1,4,5,3,6,2,7]=>0001101=>1011000
[8,3,5,1,4,6,2,7]=>0001101=>1011000
[5,8,2,1,7,4,3,6]=>1010011=>1100101
[6,5,7,2,1,8,4,3]=>1010111=>1110101
[1,5,4,7,3,8,6,2]=>0001111=>1111000
[7,4,1,3,8,5,6,2]=>0010111=>1110100
[3,6,8,4,1,7,2,5]=>0010011=>1100100
[2,1,8,4,7,6,3,5]=>1000111=>1110001
[2,7,5,6,8,4,3,1]=>0110011=>1100110
[3,5,2,4,7,8,6,1]=>0001101=>1011000
[7,5,6,3,8,2,1,4]=>1000111=>1110001
[1,6,2,7,4,5,8,3]=>0000111=>1110000
[7,4,2,6,1,5,8,3]=>0010111=>1110100
[8,4,1,6,2,5,7,3]=>0010111=>1110100
[7,3,4,5,1,6,8,2]=>0001011=>1101000
[1,3,2,5,4,7,6,9,8,11,10]=>0101010101=>1010101010
[1,4,2,6,3,7,5,9,8]=>00101101=>10110100
[1,3,2,6,4,7,5,9,8]=>01001101=>10110010
[2,1,6,3,7,4,8,5,9]=>10001110=>01110001
[8,4,2,7,6,1,5,3]=>0011111=>1111100
[8,4,7,1,2,6,5,3]=>0001111=>1111000
[8,4,7,6,1,2,5,3]=>0001111=>1111000
[8,7,6,2,1,5,3,4]=>1001111=>1111001
[5,7,8,1,6,2,4,3]=>0010101=>1010100
[7,9,6,8,4,5,2,3,1]=>01010011=>11001010
[7,9,5,8,4,6,2,3,1]=>01001011=>11010010
[7,9,5,8,3,6,2,4,1]=>00101011=>11010100
[6,8,4,7,5,2,1,3]=>1001011=>1101001
[7,9,5,8,3,6,4,1,2]=>00101011=>11010100
[7,9,5,8,6,3,4,1,2]=>00101011=>11010100
[7,9,8,5,6,3,4,1,2]=>00101011=>11010100
[6,9,5,8,4,7,2,3,1]=>01000111=>11100010
[7,9,4,8,3,6,2,5,1]=>00011011=>11011000
[7,9,5,8,2,6,1,4,3]=>00101011=>11010100
[6,8,2,7,1,5,4,3]=>0011011=>1101100
[7,9,5,8,3,6,4,2,1]=>10101011=>11010101
[8,10,6,9,4,7,2,5,3,1]=>010101011=>110101010
[6,8,7,4,2,5,1,3]=>0011011=>1101100
[7,9,5,8,6,3,1,4,2]=>01101011=>11010110
[8,10,6,9,4,7,5,2,3,1]=>010101011=>110101010
[7,9,8,5,3,6,4,1,2]=>00111011=>11011100
[8,10,6,9,7,4,5,2,3,1]=>010101011=>110101010
[9,7,5,8,6,3,4,1,2]=>00101111=>11110100
[8,10,9,6,7,4,5,2,3,1]=>010101011=>110101010
[6,8,4,5,7,2,1,3]=>1000011=>1100001
[6,8,4,2,5,1,3,7]=>0011001=>1001100
[6,5,4,3,2,7,1,8,9]=>01111100=>00111110
[5,4,3,2,6,1,7,8,9]=>01111000=>00011110
[4,3,2,5,1,6,7,8,9]=>01110000=>00001110
[3,2,4,1,5,6,7,8,9]=>01100000=>00000110
[2,5,3,7,6,4,8,1]=>0001111=>1111000
[3,1,5,7,6,4,2,8]=>0110110=>0110110
[3,1,6,5,4,7,2,8]=>0101110=>0111010
[2,5,6,8,3,4,7,1]=>0000011=>1100000
[4,1,3,6,5,2,7,8]=>0011100=>0011100
[3,6,2,4,5,7,1,8]=>0000110=>0110000
[3,6,2,5,4,7,1,8]=>0001110=>0111000
[3,5,1,7,6,4,2,8]=>0011110=>0111100
[3,6,1,4,5,7,2,8]=>0000110=>0110000
[4,3,1,6,5,2,7,8]=>0111100=>0011110
[4,1,2,6,5,3,7,8]=>0011100=>0011100
[4,6,1,3,5,2,7,8]=>0001100=>0011000
[3,6,4,2,5,7,1,8]=>0010110=>0110100
[4,2,6,3,5,1,7,8]=>0011100=>0011100
[3,4,7,6,5,1,2,8]=>0001110=>0111000
[4,5,2,7,1,3,6,8]=>0001010=>0101000
[4,6,1,2,5,3,7,8]=>0001100=>0011000
[2,6,5,1,4,8,7,3]=>0001111=>1111000
[5,8,4,7,1,3,6,2]=>0000111=>1110000
[6,4,7,1,3,5,2,8]=>0001110=>0111000
[6,8,1,3,5,7,4,2]=>0010011=>1100100
[5,8,3,2,7,4,6,1]=>0100111=>1110010
[6,8,3,1,5,4,7,2]=>0101011=>1101010
[6,8,1,2,5,3,7,4]=>0001011=>1101000
[5,2,8,3,4,6,7,1]=>0001011=>1101000
[5,2,7,1,6,4,8,3]=>0001111=>1111000
[4,5,2,6,1,3,7,8]=>0001100=>0011000
[4,3,5,8,6,1,7,2]=>0010111=>1110100
[5,1,3,6,7,4,2,8]=>0011010=>0101100
[4,2,8,3,6,7,5,1]=>0011011=>1101100
[3,1,7,8,5,6,2,4]=>0100101=>1010010
[6,2,1,7,5,3,4,8]=>1001110=>0111001
[3,7,1,8,5,2,4,6]=>0001011=>1101000
[4,2,8,6,7,1,3,5]=>0010011=>1100100
[6,1,2,4,7,3,5,8]=>0000110=>0110000
[5,3,1,6,4,7,2,8]=>0101110=>0111010
[1,2,4,5,8,7,3,6]=>0000011=>1100000
[1,3,4,7,5,8,6,2]=>0000111=>1110000
[1,5,2,3,7,8,6,4]=>0001101=>1011000
[4,2,8,1,6,5,7,3]=>0010111=>1110100
[1,3,5,2,7,4,6,9,8]=>00010101=>10101000
[1,2,4,3,6,5,8,7,9]=>00101010=>01010100
[1,3,5,7,2,4,6,9,8]=>00000101=>10100000
[1,3,5,7,2,4,6,9,8,10]=>000001010=>010100000
[1,3,5,7,2,9,4,6,8]=>00000101=>10100000
[5,6,1,4,8,3,2,7]=>0100101=>1010010
[3,6,4,1,7,2,8,5]=>0010111=>1110100
[5,6,2,1,3,7,4,8,9]=>10001100=>00110001
[3,2,5,1,6,4,7,8,9]=>01011000=>00011010
[6,7,2,1,8,3,4,9,5]=>10000111=>11100001
[3,6,4,1,7,2,8,5,9]=>00101110=>01110100
[3,6,7,2,1,4,8,5,9]=>10000110=>01100001
[4,2,6,1,7,5,3,8,9]=>00111100=>00111100
[4,3,2,6,1,7,5,8,9]=>01101100=>00110110
[4,7,2,5,1,8,3,9,6]=>00010111=>11101000
[4,3,7,8,2,1,5,9,6]=>10100011=>11000101
[3,5,2,7,1,8,6,4,9]=>00011110=>01111000
[5,4,3,2,7,1,8,6,9]=>01110110=>01101110
[6,4,2,8,1,9,7,5,3]=>00111111=>11111100
[4,3,6,2,8,1,9,7,5]=>00101111=>11110100
[6,5,4,3,2,8,1,9,7]=>01111011=>11011110
[2,4,1,5,3,6,7,8,9,10]=>001100000=>000001100
[5,6,2,1,3,7,4,8,9,10]=>100011000=>000110001
[3,2,5,1,6,4,7,8,9,10]=>010110000=>000011010
[6,7,2,1,8,3,4,9,5,10]=>100001110=>011100001
[3,6,4,1,7,2,8,5,9,10]=>001011100=>001110100
[3,6,7,2,1,4,8,5,9,10]=>100001100=>001100001
[4,2,6,1,7,5,3,8,9,10]=>001111000=>000111100
[4,3,2,6,1,7,5,8,9,10]=>011011000=>000110110
[3,4,7,1,8,2,9,5,10,6]=>000001111=>111100000
[7,8,9,3,2,1,4,5,10,6]=>110000011=>110000011
[4,7,2,5,1,8,3,9,6,10]=>000101110=>011101000
[4,3,7,8,2,1,5,9,6,10]=>101000110=>011000101
[3,5,2,7,1,8,6,4,9,10]=>000111100=>001111000
[5,4,3,2,7,1,8,6,9,10]=>011101100=>001101110
[5,8,9,2,1,6,3,10,7,4]=>100011011=>110110001
[5,3,8,6,4,1,9,2,10,7]=>001110111=>111011100
[3,5,8,2,6,1,9,4,10,7]=>000010111=>111010000
[5,4,3,8,9,2,1,6,10,7]=>101100011=>110001101
[6,4,2,8,1,9,7,5,3,10]=>001111110=>011111100
[4,3,6,2,8,1,9,7,5,10]=>001011110=>011110100
[6,5,4,3,2,8,1,9,7,10]=>011110110=>011011110
[5,3,7,2,9,1,10,8,6,4]=>000111111=>111111000
[5,4,3,7,2,9,1,10,8,6]=>001101111=>111101100
[7,6,5,4,3,2,9,1,10,8]=>011111011=>110111110
[5,2,6,3,7,8,4,1]=>0011101=>1011100
[2,4,1,3,7,8,6,5]=>0010101=>1010100
[2,6,1,5,7,8,4,3]=>0010101=>1010100
[5,1,6,4,7,8,2,3]=>0001101=>1011000
[8,4,6,3,7,5,1,2]=>0001111=>1111000
[4,7,6,8,2,3,5,1]=>0001011=>1101000
[5,7,4,8,1,2,6,3]=>0000111=>1110000
[3,6,7,5,8,1,4,2]=>0010011=>1100100
[3,7,5,6,8,2,4,1]=>0010011=>1100100
[2,7,1,6,8,4,5,3]=>0001011=>1101000
[1,5,4,7,2,6,3,8]=>0001110=>0111000
[2,4,5,8,3,1,7,6]=>0100011=>1100010
[1,4,7,5,8,3,6,2]=>0000111=>1110000
[2,6,8,7,3,5,1,4]=>0001011=>1101000
[4,7,8,6,2,5,1,3]=>0001101=>1011000
[4,8,7,3,5,6,2,1]=>1000111=>1110001
[1,7,6,3,5,4,2,8]=>0011110=>0111100
[4,3,8,1,6,5,7,2]=>0010111=>1110100
[1,3,6,2,5,8,7,4]=>0000111=>1110000
[5,8,7,1,4,6,3,2]=>0100111=>1110010
[6,2,5,1,3,4,8,7]=>0001101=>1011000
[2,6,5,1,3,4,8,7]=>0001101=>1011000
[4,6,5,1,2,7,3,8]=>0001110=>0111000
[5,6,4,1,2,7,3,8]=>0010110=>0110100
[8,1,5,6,2,4,3,7]=>0010101=>1010100
[6,4,5,1,2,7,3,8]=>0001110=>0111000
[5,4,6,1,3,2,7,8]=>0101100=>0011010
[5,7,1,4,3,2,6,8]=>0110010=>0100110
[2,6,4,1,3,7,5,8]=>0010110=>0110100
[7,8,5,3,2,1,6,4]=>1101101=>1011011
[1,2,6,7,8,4,5,3]=>0001001=>1001000
[6,1,4,8,2,7,5,3]=>0001111=>1111000
[5,2,3,7,1,8,4,6]=>0001011=>1101000
[7,2,3,1,8,4,6,5]=>0100111=>1110010
[5,4,1,7,3,2,8,6]=>0111011=>1101110
[7,3,4,5,1,8,6,2]=>0001111=>1111000
[1,5,6,7,4,8,2,3]=>0000011=>1100000
[6,3,2,5,7,4,8,1]=>0100111=>1110010
[5,7,3,8,1,2,4,6]=>0000011=>1100000
[4,5,2,7,6,3,1,8]=>0101110=>0111010
[4,5,2,1,7,6,3,8]=>1001110=>0111001
[2,6,7,8,3,1,4,5]=>0100001=>1000010
[6,3,2,5,1,7,8,4]=>0101101=>1011010
[4,6,3,7,8,2,1,5]=>1000101=>1010001
[5,6,7,1,8,4,2,3]=>0010011=>1100100
[1,7,8,4,6,5,2,3]=>0001101=>1011000
[1,7,3,2,8,6,5,4]=>0101111=>1111010
[3,7,1,2,8,6,5,4]=>0001111=>1111000
[2,7,8,1,6,5,3,4]=>0001101=>1011000
[2,5,8,1,7,6,3,4]=>0000111=>1110000
[8,1,5,7,3,4,6,2]=>0000111=>1110000
[5,8,2,7,6,3,1,4]=>0100111=>1110010
[2,8,4,7,6,3,1,5]=>0100111=>1110010
[1,8,2,4,7,6,3,5]=>0000111=>1110000
[4,5,8,7,1,6,2,3]=>0000111=>1110000
[1,8,2,4,6,7,5,3]=>0001011=>1101000
[2,5,1,8,4,7,6,3]=>0001111=>1111000
[3,4,2,8,1,7,6,5]=>0010111=>1110100
[2,4,5,8,1,7,6,3]=>0000111=>1110000
[3,1,8,2,6,7,5,4]=>0101011=>1101010
[2,6,8,1,4,3,7,5]=>0010011=>1100100
[4,1,8,2,6,7,3,5]=>0010011=>1100100
[1,6,5,2,8,7,3,4]=>0001111=>1111000
[2,6,1,5,8,7,3,4]=>0000111=>1110000
[8,1,7,3,5,2,4,6]=>0001011=>1101000
[8,1,3,2,7,6,4,5]=>0100111=>1110010
[7,3,4,8,6,2,5,1]=>0001111=>1111000
[7,5,8,1,6,2,3,4]=>0000111=>1110000
[6,8,4,5,3,1,7,2]=>0101011=>1101010
[6,7,5,3,2,8,4,1]=>0111011=>1101110
[7,6,1,3,5,2,4,8]=>0001110=>0111000
[6,2,4,5,3,8,1,7]=>0001101=>1011000
[6,1,5,4,7,2,3,8]=>0001110=>0111000
[6,8,5,4,7,1,3,2]=>0101011=>1101010
[1,6,8,4,2,5,7,3]=>0010011=>1100100
[7,5,8,1,3,4,2,6]=>0010011=>1100100
[1,4,2,8,3,5,7,6]=>0010011=>1100100
[1,3,5,4,8,7,2,6]=>0001011=>1101000
[1,6,2,4,8,3,7,5]=>0000111=>1110000
[1,7,8,5,4,2,6,3]=>0011101=>1011100
[1,5,2,8,6,4,7,3]=>0001111=>1111000
[1,6,5,2,7,4,8,3]=>0001111=>1111000
[5,1,6,7,4,2,8,3]=>0011011=>1101100
[6,8,1,5,2,3,7,4]=>0001011=>1101000
[1,5,4,2,8,6,7,3]=>0011011=>1101100
[1,8,5,4,6,2,7,3]=>0001111=>1111000
[1,7,5,4,6,2,8,3]=>0001111=>1111000
[5,8,4,1,6,2,7,3]=>0010111=>1110100
[6,4,5,1,7,2,8,3]=>0001111=>1111000
[4,8,1,3,7,6,2,5]=>0000111=>1110000
[4,5,3,1,2,8,7,6]=>0101011=>1101010
[6,4,2,3,1,8,7,5]=>0110111=>1110110
[6,5,2,1,3,8,7,4]=>1001111=>1111001
[7,6,1,8,2,5,3,4]=>0001111=>1111000
[8,4,2,3,7,6,1,5]=>0010111=>1110100
[5,7,8,1,2,4,3,6]=>0010001=>1000100
[1,7,6,8,3,5,4,2]=>0011011=>1101100
[5,7,6,4,2,1,3,8]=>1010110=>0110101
[6,5,7,4,1,3,2,8]=>0110110=>0110110
[4,6,1,8,3,5,2,7]=>0001101=>1011000
[7,1,6,8,2,5,4,3]=>0011011=>1101100
[4,7,1,8,3,2,5,6]=>0100011=>1100010
[4,8,3,6,1,5,2,7]=>0001101=>1011000
[1,7,8,6,4,5,3,2]=>0101101=>1011010
[3,2,8,6,4,5,1,7]=>0101101=>1011010
[8,4,3,6,2,5,1,7]=>0011101=>1011100
[1,6,8,7,4,3,5,2]=>0011011=>1101100
[3,1,2,6,8,7,5,4]=>0101011=>1101010
[5,7,4,2,1,8,6,3]=>1010111=>1110101
[8,6,5,7,2,4,3,1]=>0110111=>1110110
[7,4,6,1,8,5,3,2]=>0101111=>1111010
[7,4,6,3,8,1,5,2]=>0001111=>1111000
[7,4,8,1,6,3,2,5]=>0100111=>1110010
[7,4,8,3,6,2,1,5]=>1000111=>1110001
[6,4,8,2,3,5,7,1]=>0000111=>1110000
[6,4,8,2,5,7,1,3]=>0000111=>1110000
[6,2,4,5,8,3,7,1]=>0000111=>1110000
[6,8,2,4,7,3,5,1]=>0001011=>1101000
[8,4,6,2,7,1,3,5]=>0000111=>1110000
[6,8,4,2,7,1,3,5]=>0010011=>1100100
[6,8,2,4,1,7,3,5]=>0010011=>1100100
[7,5,1,6,2,4,8,3]=>0001111=>1111000
[4,2,5,7,1,6,8,3]=>0010011=>1100100
[2,4,8,5,6,7,3,1]=>0100011=>1100010
[4,5,2,3,8,7,1,6]=>0001011=>1101000
[2,5,4,7,6,1,3,8]=>0001110=>0111000
[5,2,3,7,6,1,4,8]=>0001110=>0111000
[4,2,3,7,6,1,5,8]=>0010110=>0110100
[4,2,7,3,5,1,6,8]=>0011010=>0101100
[5,6,2,3,8,4,7,1]=>0000111=>1110000
[5,6,2,3,1,7,8,4]=>0100101=>1010010
[5,7,2,3,4,1,6,8]=>0010010=>0100100
[6,2,7,3,5,1,4,8]=>0001110=>0111000
[7,2,6,3,5,1,4,8]=>0001110=>0111000
[6,5,2,3,1,7,8,4]=>0101101=>1011010
[6,5,2,3,8,4,7,1]=>0001111=>1111000
[7,5,2,1,4,6,8,3]=>1001011=>1101001
[8,5,2,3,1,6,4,7]=>0101101=>1011010
[8,6,2,3,1,5,4,7]=>0101101=>1011010
[8,2,6,3,1,7,4,5]=>0100111=>1110010
[1,6,3,4,2,7,5,8]=>0010110=>0110100
[8,5,2,7,3,4,6,1]=>0001111=>1111000
[1,7,2,4,5,6,8,3]=>0000011=>1100000
[1,8,3,2,5,6,4,7]=>0100101=>1010010
[7,2,8,1,4,6,3,5]=>0000111=>1110000
[2,7,8,1,5,6,3,4]=>0000101=>1010000
[6,8,2,3,1,5,4,7]=>0101001=>1001010
[5,8,2,3,1,6,4,7]=>0100101=>1010010
[5,7,2,1,4,6,8,3]=>1000011=>1100001
[4,2,7,1,5,6,8,3]=>0010011=>1100100
[4,2,3,8,1,7,5,6]=>0010011=>1100100
[4,2,1,5,3,7,6,8]=>1011010=>0101101
[5,1,3,8,4,6,7,2]=>0001011=>1101000
[5,1,3,2,6,7,8,4]=>0101001=>1001010
[5,1,3,4,2,7,6,8]=>0011010=>0101100
[6,1,3,4,2,7,5,8]=>0010110=>0110100
[7,2,1,3,5,8,4,6]=>1000011=>1100001
[6,8,7,2,3,4,5,1]=>0001011=>1101000
[10,9,11,8,7,6,5,4,3,2,1]=>1111111011=>1101111111
[1,9,8,10,7,6,5,4,3,2]=>011111011=>110111110
[2,8,7,9,6,5,4,3,1]=>01111011=>11011110
[3,7,2,8,1,4,5,6]=>0000011=>1100000
[5,2,3,7,4,6,1,8]=>0001110=>0111000
[2,5,3,7,4,6,1,8]=>0001110=>0111000
[2,6,7,3,4,5,1,8]=>0001010=>0101000
[6,2,7,3,4,5,1,8]=>0001110=>0111000
[3,8,4,5,2,1,6,7]=>1001001=>1001001
[2,7,6,3,4,5,1,8]=>0001110=>0111000
[2,8,7,5,1,3,4,6]=>0001011=>1101000
[3,1,2,9,4,5,6,7,8]=>01000001=>10000010
[4,1,2,3,9,5,6,7,8]=>00100001=>10000100
[5,1,2,3,4,9,6,7,8]=>00010001=>10001000
[6,1,2,3,4,5,9,7,8]=>00001001=>10010000
[2,1,10,3,4,5,6,7,8,9]=>100000001=>100000001
[3,1,2,10,4,5,6,7,8,9]=>010000001=>100000010
[3,4,1,2,9,5,6,7,8]=>00100001=>10000100
[4,1,2,3,10,5,6,7,8,9]=>001000001=>100000100
[4,5,1,2,3,9,6,7,8]=>00010001=>10001000
[5,1,2,3,4,10,6,7,8,9]=>000100001=>100001000
[5,6,1,2,3,4,9,7,8]=>00001001=>10010000
[6,1,2,3,4,5,10,7,8,9]=>000010001=>100010000
[6,7,1,2,3,4,5,9,8]=>00000101=>10100000
[7,1,2,3,4,5,6,10,8,9]=>000001001=>100100000
[4,5,7,2,8,3,6,1]=>0000111=>1110000
[9,7,5,3,1,8,6,4,2]=>01111111=>11111110
[9,6,3,8,5,2,7,4,1]=>00111111=>11111100
[8,5,2,9,6,3,7,4,1]=>00111111=>11111100
[9,5,1,6,2,7,3,8,4]=>00011111=>11111000
[9,5,1,8,4,7,3,6,2]=>00011111=>11111000
[8,4,7,3,6,2,9,5,1]=>00011111=>11111000
[7,3,8,4,6,2,9,5,1]=>00011111=>11111000
[9,4,7,2,5,8,3,6,1]=>00001111=>11110000
[9,4,6,1,8,3,5,7,2]=>00001111=>11110000
[8,3,5,7,2,9,4,6,1]=>00001111=>11110000
[7,2,8,3,9,4,5,6,1]=>00001111=>11110000
[8,3,7,2,9,4,5,6,1]=>00001111=>11110000
[5,8,3,7,2,9,4,6,1]=>00001111=>11110000
[4,5,6,9,3,8,2,7,1]=>00000111=>11100000
[4,5,6,8,2,9,3,7,1]=>00000111=>11100000
[9,3,6,5,4,7,1,8,2]=>00011111=>11111000
[8,2,9,3,6,5,4,7,1]=>00011111=>11111000
[6,5,4,8,2,9,3,7,1]=>00011111=>11111000
[5,6,4,8,2,9,3,7,1]=>00001111=>11110000
[9,2,7,4,5,6,3,8,1]=>00001111=>11110000
[7,4,5,6,3,9,2,8,1]=>00001111=>11110000
[5,7,4,6,3,9,2,8,1]=>00001111=>11110000
[10,8,6,4,2,9,7,5,3,1]=>011111111=>111111110
[10,7,4,1,8,5,2,9,6,3]=>001111111=>111111100
[9,6,3,8,5,2,10,7,4,1]=>001111111=>111111100
[9,5,1,7,3,10,6,2,8,4]=>000111111=>111111000
[10,6,2,7,3,8,4,9,5,1]=>000111111=>111111000
[7,3,8,4,10,6,2,9,5,1]=>000111111=>111111000
[8,4,7,3,10,6,2,9,5,1]=>000111111=>111111000
[10,5,8,3,6,1,9,4,7,2]=>000011111=>111110000
[9,4,7,2,10,5,8,3,6,1]=>000011111=>111110000
[10,5,7,2,8,3,9,4,6,1]=>000011111=>111110000
[8,3,10,5,7,2,9,4,6,1]=>000011111=>111110000
[8,3,9,4,7,2,10,5,6,1]=>000011111=>111110000
[9,3,5,7,1,10,4,6,8,2]=>000001111=>111100000
[10,4,6,8,2,9,3,5,7,1]=>000001111=>111100000
[10,4,5,6,7,1,8,2,9,3]=>000001111=>111100000
[8,2,9,3,10,4,5,6,7,1]=>000001111=>111100000
[9,3,8,2,10,4,5,6,7,1]=>000001111=>111100000
[5,6,9,3,7,1,10,4,8,2]=>000001111=>111100000
[5,6,10,4,8,2,9,3,7,1]=>000001111=>111100000
[5,6,9,3,8,2,10,4,7,1]=>000001111=>111100000
[6,5,9,3,8,2,10,4,7,1]=>000011111=>111110000
[9,2,7,6,5,4,10,3,8,1]=>000111111=>111111000
[10,3,7,6,5,4,8,1,9,2]=>000111111=>111111000
[9,2,10,3,7,6,5,4,8,1]=>000111111=>111111000
[7,6,5,4,9,2,10,3,8,1]=>000111111=>111111000
[6,4,7,5,10,3,9,2,8,1]=>000011111=>111110000
[6,4,7,5,9,2,10,3,8,1]=>000011111=>111110000
[7,5,6,4,9,2,10,3,8,1]=>000011111=>111110000
[6,5,7,4,9,2,10,3,8,1]=>000011111=>111110000
[5,6,7,3,8,4,9,1,10,2]=>000001111=>111100000
[5,6,7,3,8,4,10,2,9,1]=>000001111=>111100000
[5,6,8,4,7,3,10,2,9,1]=>000001111=>111100000
[6,5,8,4,7,3,10,2,9,1]=>000011111=>111110000
[5,2,1,3,6,7,8,4]=>1001001=>1001001
[1,6,5,7,2,8,3,4]=>0000111=>1110000
[7,5,2,6,1,8,4,3]=>0011111=>1111100
[6,1,5,2,7,8,4,3]=>0011101=>1011100
[1,6,5,7,2,8,4,3]=>0010111=>1110100
[1,5,4,6,2,8,7,3]=>0001111=>1111000
[1,5,4,6,2,8,3,7]=>0001101=>1011000
[1,5,6,4,8,2,3,7]=>0000101=>1010000
[6,2,1,5,8,4,7,3]=>1000111=>1110001
[7,5,6,8,4,1,3,2]=>0110011=>1100110
[8,3,7,5,1,4,2,6]=>0011011=>1101100
[8,1,5,7,3,6,2,4]=>0000111=>1110000
[8,3,2,6,4,5,1,7]=>0101101=>1011010
[8,5,3,7,4,1,2,6]=>0011011=>1101100
[8,5,6,2,7,1,3,4]=>0000111=>1110000
[8,4,7,2,6,5,1,3]=>0001111=>1111000
[8,5,7,3,2,6,1,4]=>0100111=>1110010
[8,1,2,3,6,4,7,5]=>0000111=>1110000
[7,6,2,3,5,8,1,4]=>0000111=>1110000
[4,5,3,7,8,1,6,2]=>0001101=>1011000
[3,4,2,8,1,6,7,5]=>0010011=>1100100
[8,3,4,1,5,7,6,2]=>0010111=>1110100
[4,3,7,5,1,6,2,8]=>0011110=>0111100
[5,2,6,1,4,3,7,8]=>0011100=>0011100
[3,5,2,8,6,7,4,1]=>0011011=>1101100
[5,3,7,4,2,8,6,1]=>0011111=>1111100
[7,4,8,2,3,5,6,1]=>0000111=>1110000
[5,6,2,8,7,1,4,3]=>0010111=>1110100
[4,6,3,5,2,7,8,1]=>0001101=>1011000
[4,1,6,3,5,7,2,8]=>0010110=>0110100
[3,1,5,7,4,6,8,2]=>0100011=>1100010
[7,2,5,8,6,1,4,3]=>0010111=>1110100
[4,3,6,1,5,7,8,2]=>0010101=>1010100
[3,5,4,1,2,6,7,8]=>0011000=>0001100
[5,3,1,4,6,7,8,2]=>0101001=>1001010
[4,6,7,1,3,5,8,2]=>0000011=>1100000
[5,6,1,3,4,7,2,8]=>0000110=>0110000
[2,5,3,7,8,4,6,1]=>0001101=>1011000
[4,6,2,1,3,7,8,5]=>1000101=>1010001
[3,6,2,4,1,7,5,8]=>0010110=>0110100
[3,2,6,7,4,8,5,1]=>0101011=>1101010
[7,1,3,8,4,5,2,6]=>0001011=>1101000
[7,1,8,3,4,6,2,5]=>0000111=>1110000
[6,3,2,7,5,8,4,1]=>0110111=>1110110
[6,2,7,1,4,5,3,8]=>0001110=>0111000
[4,2,6,1,5,7,3,8]=>0010110=>0110100
[2,5,4,1,3,6,7,8]=>0011000=>0001100
[5,4,1,2,6,7,3,8]=>0011010=>0101100
[6,5,2,7,4,1,3,8]=>0011110=>0111100
[6,5,7,3,1,4,2,8]=>0110110=>0110110
[6,7,4,3,1,5,8,2]=>0110011=>1100110
[4,2,5,6,7,8,9,1,3]=>00100001=>10000100
[3,1,6,7,8,4,5,2]=>0101001=>1001010
[7,4,5,6,2,1,8,3]=>1000111=>1110001
[4,2,5,6,7,8,9,10,1,3]=>001000001=>100000100
[3,4,5,6,7,8,9,10,1,11,2]=>0000000011=>1100000000
[6,4,5,2,7,1,8,3]=>0001111=>1111000
[3,7,5,6,2,1,8,4]=>1000111=>1110001
[1,7,6,3,8,4,5,2]=>0001111=>1111000
[6,4,1,2,7,8,3,5]=>0010101=>1010100
[6,4,1,3,5,2,7,8]=>0011100=>0011100
[5,1,8,3,4,6,2,7]=>0001101=>1011000
[4,5,8,2,3,7,1,6]=>0000011=>1100000
[7,3,4,8,2,5,1,6]=>0001011=>1101000
[4,7,2,5,1,6,8,3]=>0001011=>1101000
[6,5,4,7,2,8,3,1]=>0101111=>1111010
[3,2,4,6,5,8,1,7]=>0100101=>1010010
[3,5,4,8,7,1,6,2]=>0001111=>1111000
[7,5,2,1,6,3,4,8]=>1001110=>0111001
[6,3,1,7,4,2,5,8]=>0110110=>0110110
[8,7,2,1,5,3,6,4]=>1001111=>1111001
[6,8,5,3,7,4,2,1]=>1011011=>1101101
[7,2,8,1,5,6,4,3]=>0010111=>1110100
[8,3,6,4,1,5,7,2]=>0010111=>1110100
[7,5,6,1,4,8,2,3]=>0000111=>1110000
[5,7,2,6,3,8,4,1]=>0010111=>1110100
[8,4,1,2,3,6,7,5]=>0010011=>1100100
[5,6,4,2,1,8,3,7]=>1010101=>1010101
[6,8,1,3,2,7,5,4]=>0101011=>1101010
[5,7,3,6,4,1,2,8]=>0010110=>0110100
[7,2,4,3,8,1,5,6]=>0010011=>1100100
[2,5,4,6,1,3,8,7]=>0001101=>1011000
[2,4,3,5,8,1,6,7]=>0010001=>1000100
[2,6,5,3,8,1,4,7]=>0001101=>1011000
[6,1,2,4,3,5,7,8]=>0010100=>0010100
[1,7,6,8,4,3,2,5]=>0110011=>1100110
[1,7,6,5,3,8,2,4]=>0001111=>1111000
[6,1,2,4,3,5,8,7]=>0010101=>1010100
[4,6,1,3,7,8,5,2]=>0001101=>1011000
[8,4,1,5,2,6,7,3]=>0011011=>1101100
[1,5,6,3,8,7,2,4]=>0000111=>1110000
[5,3,2,6,8,7,1,4]=>0101011=>1101010
[6,3,5,2,7,1,4,8]=>0001110=>0111000
[8,5,2,6,7,1,4,3]=>0011011=>1101100
[5,3,8,7,1,4,2,6]=>0011011=>1101100
[6,4,5,3,1,8,7,2]=>0101111=>1111010
[8,5,1,2,3,6,7,4]=>0001011=>1101000
[2,8,6,1,5,4,7,3]=>0001111=>1111000
[8,3,2,6,1,5,7,4]=>0100111=>1110010
[3,8,6,4,7,1,2,5]=>0000111=>1110000
[1,8,7,5,4,3,2,6]=>0111011=>1101110
[8,6,4,7,1,3,2,5]=>0100111=>1110010
[3,1,4,7,6,2,5,8]=>0100110=>0110010
[5,3,4,1,6,2,7,8]=>0011100=>0011100
[2,7,1,4,6,3,5,8]=>0000110=>0110000
[7,3,1,6,5,2,4,8]=>0101110=>0111010
[7,1,5,2,4,6,3,8]=>0001110=>0111000
[6,1,4,5,2,7,3,8]=>0001110=>0111000
[6,1,5,8,2,7,4,3]=>0010111=>1110100
[7,1,2,3,6,4,5,8]=>0000110=>0110000
[7,1,2,3,9,5,6,10,8,4]=>000001111=>111100000
[6,1,2,9,4,5,3,10,8,7]=>000110111=>111011000
[9,1,2,3,8,5,10,7,6,4]=>000011111=>111110000
[9,1,2,8,4,3,10,7,5,6]=>001001111=>111100100
[8,1,2,7,4,10,6,5,3,9]=>000111101=>101111000
[9,1,8,3,2,5,10,7,4,6]=>010001111=>111100010
[8,1,7,3,2,10,6,4,5,9]=>010011101=>101110010
[7,1,2,3,10,5,6,9,8,4]=>000001111=>111100000
[6,1,2,10,4,5,3,9,8,7]=>000110111=>111011000
[8,1,2,3,10,5,9,6,7,4]=>000001111=>111100000
[8,1,2,10,4,3,9,5,7,6]=>001001111=>111100100
[7,1,2,10,4,9,5,3,6,8]=>000101011=>110101000
[8,1,10,3,2,5,9,4,7,6]=>010001111=>111100010
[7,1,10,3,2,9,4,5,6,8]=>010001011=>110100010
[10,1,2,3,9,5,8,7,6,4]=>000011111=>111110000
[10,1,2,9,4,3,8,7,5,6]=>001001111=>111100100
[10,1,2,9,4,8,3,6,5,7]=>000010111=>111010000
[9,1,2,8,4,7,6,5,3,10]=>000111110=>011111000
[10,1,9,3,2,5,8,7,4,6]=>010001111=>111100010
[10,1,9,3,2,8,5,6,4,7]=>010010111=>111010010
[9,1,8,3,2,7,6,4,5,10]=>010011110=>011110010
[8,1,2,3,10,9,5,7,6,4]=>000011111=>111110000
[8,1,2,10,3,9,4,7,6,5]=>000011111=>111110000
[7,1,2,10,9,4,6,3,5,8]=>000011011=>110110000
[8,1,10,2,4,9,3,7,6,5]=>000011111=>111110000
[7,1,10,2,9,3,6,4,5,8]=>000011011=>110110000
[10,1,2,3,9,8,5,6,7,4]=>000001111=>111100000
[10,1,2,9,3,8,4,6,7,5]=>000001111=>111100000
[10,1,2,9,8,4,3,5,6,7]=>001000111=>111000100
[9,1,2,8,7,4,5,6,3,10]=>000011110=>011110000
[10,1,9,2,4,8,3,6,7,5]=>000001111=>111100000
[10,1,9,2,8,3,4,5,6,7]=>000000111=>111000000
[9,1,8,2,7,3,5,6,4,10]=>000011110=>011110000
[10,1,9,8,3,2,6,4,5,7]=>010010111=>111010010
[9,1,8,7,3,2,4,5,6,10]=>010001110=>011100010
[8,10,1,3,4,9,2,7,6,5]=>000011011=>110110000
[7,10,1,3,9,2,6,4,5,8]=>000010011=>110010000
[10,9,1,3,4,8,2,6,7,5]=>000001111=>111100000
[10,9,1,3,8,2,4,5,6,7]=>000000111=>111000000
[9,8,1,3,7,2,5,6,4,10]=>000011110=>011110000
[10,9,1,8,2,3,6,4,5,7]=>000010111=>111010000
[9,8,1,7,2,3,4,5,6,10]=>000001110=>011100000
[6,3,1,8,5,4,7,2]=>0101111=>1111010
[6,1,3,8,7,4,5,2]=>0001111=>1111000
[2,8,4,6,5,1,7,3]=>0001111=>1111000
[7,4,1,3,6,5,2,8]=>0011110=>0111100
[5,7,2,8,1,3,6,4]=>0000111=>1110000
[5,4,1,2,6,3,8,7]=>0011101=>1011100
[6,5,1,4,7,3,2,8]=>0101110=>0111010
[2,7,8,4,1,3,6,5]=>0010101=>1010100
[2,4,6,5,7,8,1,3]=>0000101=>1010000
[2,4,6,7,5,8,1,3]=>0000011=>1100000
[2,4,6,3,7,8,1,5]=>0000101=>1010000
[2,4,5,6,8,7,1,3]=>0000011=>1100000
[2,4,5,6,8,3,7,1]=>0000011=>1100000
[2,4,5,6,3,8,1,7]=>0000101=>1010000
[2,3,4,6,8,5,1,7]=>0001001=>1001000
[5,2,8,3,4,1,6,7]=>0011001=>1001100
[3,6,4,1,2,7,8,5]=>0010101=>1010100
[4,1,7,3,8,6,2,5]=>0010111=>1110100
[8,4,1,2,5,3,7,6]=>0011011=>1101100
[1,5,2,7,6,8,4,3]=>0011011=>1101100
[4,7,6,8,3,1,2,5]=>0100011=>1100010
[4,8,2,7,6,5,1,3]=>0001111=>1111000
[7,4,2,8,6,5,1,3]=>0011111=>1111100
[8,6,5,2,7,1,4,3]=>0011111=>1111100
[6,5,8,2,7,1,4,3]=>0010111=>1110100
[7,5,8,2,1,6,4,3]=>1010111=>1110101
[3,2,1,6,5,8,4,7]=>1100101=>1010011
[2,6,4,8,5,7,3,1]=>0100111=>1110010
[6,3,1,4,5,8,2,7]=>0100101=>1010010
[3,4,8,5,2,1,7,6]=>1001011=>1101001
[4,8,7,1,3,2,6,5]=>0100111=>1110010
[5,8,7,4,6,1,3,2]=>0100111=>1110010
[3,4,1,8,7,6,2,5]=>0010111=>1110100
[1,3,5,6,8,7,2,4]=>0000011=>1100000
[2,8,7,5,4,1,6,3]=>0011111=>1111100
[8,1,5,7,4,2,6,3]=>0010111=>1110100
[5,8,7,3,4,1,6,2]=>0010111=>1110100
[4,6,1,3,2,8,5,7]=>0100101=>1010010
[2,6,5,8,3,1,4,7]=>0100101=>1010010
[6,7,8,2,4,5,3,1]=>0101001=>1001010
[3,2,8,4,5,7,1,6]=>0100011=>1100010
[6,1,8,2,4,5,3,7]=>0001101=>1011000
[8,3,6,4,2,7,1,5]=>0010111=>1110100
[1,3,8,4,7,6,2,5]=>0000111=>1110000
[8,3,7,5,4,1,2,6]=>0011011=>1101100
[2,6,4,7,8,5,1,3]=>0001101=>1011000
[5,4,3,7,6,1,8,2]=>0011111=>1111100
[8,6,3,7,1,4,2,5]=>0010111=>1110100
[3,1,2,8,7,6,4,5]=>0100111=>1110010
[8,5,4,1,2,3,7,6]=>0011011=>1101100
[8,3,2,1,6,4,7,5]=>1100111=>1110011
[2,3,8,4,1,7,5,6]=>0010011=>1100100
[4,6,1,3,2,7,8,5]=>0100101=>1010010
[6,7,2,5,8,4,1,3]=>0010011=>1100100
[4,1,7,8,2,5,6,3]=>0010101=>1010100
[3,4,6,7,1,5,8,2]=>0000011=>1100000
[3,4,5,7,8,1,6,2]=>0000101=>1010000
[1,8,7,4,3,5,2,6]=>0011011=>1101100
[2,4,5,8,1,3,7,6]=>0000011=>1100000
[2,7,8,6,5,3,1,4]=>0101101=>1011010
[6,3,1,5,8,4,2,7]=>0110101=>1010110
[2,8,3,5,6,1,4,7]=>0000101=>1010000
[1,3,6,4,2,7,5,8]=>0010110=>0110100
[2,3,7,5,8,1,4,6]=>0000011=>1100000
[3,2,8,5,6,1,4,7]=>0100101=>1010010
[7,2,5,8,1,4,6,3]=>0000111=>1110000
[4,7,5,8,1,2,6,3]=>0000111=>1110000
[4,7,5,8,1,2,3,6]=>0000011=>1100000
[3,4,7,5,2,8,1,6]=>0001011=>1101000
[4,3,2,5,7,8,1,6]=>0110001=>1000110
[2,4,7,5,8,3,1,6]=>0100011=>1100010
[2,5,4,7,3,8,1,6]=>0001011=>1101000
[3,7,8,4,2,1,6,5]=>1010101=>1010101
[5,6,7,9,1,2,3,4,8]=>00000001=>10000000
[4,5,6,7,9,1,2,3,8]=>00000001=>10000000
[7,8,10,1,2,3,4,5,6,9]=>000000001=>100000000
[4,5,6,7,8,10,1,2,3,9]=>000000001=>100000000
[8,5,4,7,6,3,1,2]=>0101111=>1111010
[1,5,4,8,7,6,2,3]=>0001111=>1111000
[3,2,4,5,8,1,6,7]=>0100001=>1000010
[3,6,8,4,2,7,1,5]=>0010011=>1100100
[1,4,7,6,3,8,2,5]=>0000111=>1110000
[3,6,5,1,7,2,8,4]=>0001111=>1111000
[7,4,1,6,2,8,5,3]=>0011111=>1111100
[1,3,6,8,2,4,7,5]=>0000011=>1100000
[1,6,7,4,3,8,2,5]=>0010011=>1100100
[7,3,1,6,5,2,8,4]=>0101111=>1111010
[8,5,4,1,6,2,7,3]=>0011111=>1111100
[4,7,2,8,5,1,6,3]=>0001111=>1111000
[7,8,6,2,1,5,4,3]=>1011101=>1011101
[8,6,2,7,3,5,1,4]=>0001111=>1111000
[2,1,3,8,7,5,6,4]=>1000111=>1110001
[8,1,7,3,6,5,2,4]=>0001111=>1111000
[1,6,5,7,4,8,3,9,2]=>00001111=>11110000
[5,4,6,3,8,2,7,1,9]=>00011110=>01111000
[1,6,7,5,8,4,9,3,10,2]=>000001111=>111100000
[6,5,7,4,8,3,9,2,10,1,11]=>0000111110=>0111110000
[1,6,4,7,3,8,5,2]=>0001111=>1111000
[1,7,6,8,5,9,4,10,3,11,2]=>0000011111=>1111100000
[1,2,3,4,5,6,8,10,7,9]=>000000001=>100000000
[3,4,5,6,7,8,2,1,9]=>10000010=>01000001
[3,4,5,6,7,2,1,8,9]=>10000100=>00100001
[4,5,6,7,8,1,2,3,9]=>00000010=>01000000
[4,8,1,6,3,7,2,5]=>0000111=>1110000
[8,5,4,1,6,3,7,2]=>0011111=>1111100
[1,7,6,2,4,8,5,3]=>0001111=>1111000
[5,7,3,2,4,8,6,1]=>0100111=>1110010
[2,6,8,5,4,3,1,7]=>0111001=>1001110
[2,8,4,6,3,5,1,7]=>0001101=>1011000
[2,7,8,3,6,4,5,1]=>0001101=>1011000
[3,8,1,4,6,5,2,7]=>0001101=>1011000
[2,7,5,4,1,8,3,6]=>0011011=>1101100
[4,6,1,8,5,3,2,7]=>0101101=>1011010
[3,8,5,2,1,6,4,7]=>1001101=>1011001
[5,1,4,8,2,6,3,7]=>0001101=>1011000
[4,5,8,1,3,7,6,2]=>0000111=>1110000
[8,6,7,1,4,3,2,5]=>0110011=>1100110
[1,4,7,8,6,3,5,2]=>0001101=>1011000
[8,5,2,6,3,4,7,1]=>0001111=>1111000
[8,3,6,1,2,7,4,5]=>0000111=>1110000
[3,8,6,1,2,5,7,4]=>0000111=>1110000
[3,7,6,2,1,8,5,4]=>1001111=>1111001
[4,3,7,6,1,8,5,2]=>0011111=>1111100
[8,6,3,2,7,1,5,4]=>0101111=>1111010
[6,8,1,5,4,7,2,3]=>0001011=>1101000
[6,7,2,5,4,8,1,3]=>0001011=>1101000
[7,6,2,4,8,5,1,3]=>0001111=>1111000
[4,6,8,7,3,1,2,5]=>0100011=>1100010
[4,7,5,2,6,3,8,1]=>0001111=>1111000
[3,5,6,2,8,1,4,7]=>0000101=>1010000
[8,9,10,4,5,6,2,3,1,7]=>010010001=>100010010
[8,9,4,5,6,10,2,3,1,7]=>010000011=>110000010
[8,9,10,4,5,2,3,6,1,7]=>000110001=>100011000
[8,9,4,5,10,2,3,6,1,7]=>000010011=>110010000
[8,9,4,5,2,3,6,10,1,7]=>000100011=>110001000
[8,4,5,9,10,2,3,6,1,7]=>000010101=>101010000
[8,4,5,9,2,3,6,10,1,7]=>000000111=>111000000
[8,9,10,4,5,6,2,1,3,7]=>100010001=>100010001
[8,9,4,5,6,10,2,1,3,7]=>100000011=>110000001
[8,9,10,4,5,2,6,1,3,7]=>000110001=>100011000
[8,9,4,5,10,2,6,1,3,7]=>000010011=>110010000
[8,9,4,5,2,6,10,1,3,7]=>000100011=>110001000
[8,4,5,9,10,2,6,1,3,7]=>000010101=>101010000
[8,4,5,9,2,6,10,1,3,7]=>000000111=>111000000
[8,9,10,4,5,2,1,3,6,7]=>100100001=>100001001
[8,9,4,5,10,2,1,3,6,7]=>100000011=>110000001
[8,9,4,5,2,10,1,3,6,7]=>000100011=>110001000
[8,9,4,5,2,1,3,6,10,7]=>100100011=>110001001
[8,4,5,9,10,2,1,3,6,7]=>100000101=>101000001
[8,4,5,9,2,10,1,3,6,7]=>000000111=>111000000
[8,4,5,9,2,1,3,6,10,7]=>100000111=>111000001
[8,9,10,4,2,5,6,1,3,7]=>001010001=>100010100
[8,9,4,10,2,5,6,1,3,7]=>000010011=>110010000
[8,9,4,2,5,6,10,1,3,7]=>001000011=>110000100
[8,4,9,10,2,5,6,1,3,7]=>000010101=>101010000
[8,4,9,2,5,6,10,1,3,7]=>000000111=>111000000
[8,9,10,4,2,5,1,3,6,7]=>001100001=>100001100
[8,9,4,10,2,5,1,3,6,7]=>000100011=>110001000
[8,9,4,2,5,10,1,3,6,7]=>001000011=>110000100
[8,9,4,2,5,1,3,6,10,7]=>001100011=>110001100
[8,4,9,10,2,5,1,3,6,7]=>000100101=>101001000
[8,4,9,2,5,1,3,6,10,7]=>000100111=>111001000
[8,4,2,5,9,10,1,3,6,7]=>001000101=>101000100
[8,4,2,5,9,1,3,6,10,7]=>001000111=>111000100
[4,8,9,10,2,5,6,1,3,7]=>000010001=>100010000
[4,8,9,2,5,6,10,1,3,7]=>000000011=>110000000
[4,8,9,10,2,5,1,3,6,7]=>000100001=>100001000
[4,8,9,2,5,10,1,3,6,7]=>000000011=>110000000
[4,8,9,2,5,1,3,6,10,7]=>000100011=>110001000
[4,8,2,5,9,10,1,3,6,7]=>000000101=>101000000
[4,8,2,5,9,1,3,6,10,7]=>000000111=>111000000
[5,1,2,4,3,7,6,8]=>0011010=>0101100
[6,1,8,2,4,3,5,7]=>0010101=>1010100
[1,6,8,2,5,3,4,7]=>0001001=>1001000
[8,7,6,2,4,5,1,3]=>0001111=>1111000
[8,7,6,2,4,5,3,1]=>0101111=>1111010
[5,4,8,7,1,2,6,3]=>0001111=>1111000
[2,5,6,4,3,8,1,7]=>0010101=>1010100
[8,7,3,5,1,4,6,2]=>0001111=>1111000
[8,6,3,5,2,1,4,7]=>1001101=>1011001
[8,7,3,5,2,4,6,1]=>0001111=>1111000
[8,4,2,7,6,5,1,3]=>0011111=>1111100
[4,6,3,8,5,2,7,1]=>0001111=>1111000
[8,7,1,4,5,6,2,3]=>0000111=>1110000
[4,1,3,8,5,6,2,7]=>0010101=>1010100
[5,2,8,3,1,6,7,4]=>0101011=>1101010
[1,7,8,6,3,2,5,4]=>0101101=>1011010
[3,7,2,4,5,6,1,8]=>0000110=>0110000
[3,2,8,1,5,7,4,6]=>0100011=>1100010
[3,4,6,7,2,1,5,8]=>1000010=>0100001
[2,6,7,1,4,3,8,5]=>0010011=>1100100
[4,2,5,3,8,6,7,1]=>0011011=>1101100
[3,2,7,4,8,5,6,1]=>0100111=>1110010
[7,2,5,1,6,3,8,4]=>0001111=>1111000
[6,3,8,5,4,2,7,1]=>0011111=>1111100
[7,4,6,1,3,5,2,8]=>0001110=>0111000
[1,5,3,8,7,4,6,2]=>0001111=>1111000
[5,1,3,8,7,4,6,2]=>0001111=>1111000
[2,5,3,8,7,4,1,6]=>0011011=>1101100
[6,8,3,5,1,2,7,4]=>0001011=>1101000
[5,8,2,7,4,6,3,1]=>0100111=>1110010
[4,5,2,8,3,7,1,6]=>0001011=>1101000
[7,8,5,1,6,4,3,2]=>0111101=>1011110
[8,7,5,1,6,4,3,2]=>0111111=>1111110
[4,5,8,3,1,2,7,6]=>0100011=>1100010
[4,6,8,3,2,1,7,5]=>1100011=>1100011
[4,6,8,3,5,1,2,7]=>0001001=>1001000
[1,4,6,3,7,5,2,8]=>0001110=>0111000
[4,5,2,6,8,7,3,1]=>0101011=>1101010
[1,7,6,3,8,5,2,4]=>0001111=>1111000
[1,3,8,7,4,5,6,2]=>0000111=>1110000
[7,3,1,8,4,5,6,2]=>0100111=>1110010
[3,2,8,7,4,5,6,1]=>0100111=>1110010
[6,2,4,3,7,5,8,1]=>0010111=>1110100
[6,4,2,5,1,7,8,3]=>0011101=>1011100
[3,8,2,1,5,7,6,4]=>1000111=>1110001
[1,3,2,8,7,4,6,5]=>0100111=>1110010
[7,5,2,8,3,1,6,4]=>0101111=>1111010
[5,4,2,7,3,8,6,1]=>0011111=>1111100
[4,6,3,7,8,1,2,5]=>0000101=>1010000
[8,3,5,4,7,1,2,6]=>0001011=>1101000
[6,2,5,4,1,7,8,3]=>0011101=>1011100
[4,1,5,6,3,8,7,2]=>0010111=>1110100
[8,5,1,6,3,2,4,7]=>0101101=>1011010
[6,8,7,4,3,2,5,1]=>0111011=>1101110
[8,1,5,4,6,7,3,2]=>0101011=>1101010
[2,8,5,1,3,7,6,4]=>0001111=>1111000
[2,4,5,8,3,7,6,1]=>0000111=>1110000
[5,6,4,1,8,2,7,3]=>0010111=>1110100
[6,4,5,1,3,8,7,2]=>0001111=>1111000
[6,1,3,5,4,8,2,7]=>0001101=>1011000
[1,3,8,7,2,5,6,4]=>0000111=>1110000
[2,5,4,1,8,3,7,6]=>0011011=>1101100
[5,1,4,8,3,7,6,2]=>0001111=>1111000
[8,4,1,2,7,6,5,3]=>0011111=>1111100
[4,8,3,2,7,6,5,1]=>0101111=>1111010
[1,8,7,3,4,6,5,2]=>0001111=>1111000
[4,3,1,2,6,5,8,7,9]=>01101010=>01010110
[6,5,3,1,2,4,8,7,9]=>01011010=>01011010
[8,7,5,3,1,2,4,6,9]=>01010110=>01101010
[7,5,3,1,2,4,6,9,8]=>01010101=>10101010
[5,3,1,2,4,7,6,9,8]=>01010101=>10101010
[4,1,2,6,5,3,8,7,9]=>00111010=>01011100
[6,5,3,1,2,4,8,7,10,9]=>010110101=>101011010
[6,3,1,2,4,8,7,5,9]=>01001110=>01110010
[8,7,5,3,1,2,4,6,10,9]=>010101101=>101101010
[8,5,3,1,2,4,6,9,7]=>01010011=>11001010
[10,9,7,5,3,1,2,4,6,8]=>010101011=>110101010
[5,3,1,2,4,6,8,7]=>0101001=>1001010
[8,5,7,3,1,2,4,6]=>0100011=>1100010
[7,5,3,1,2,4,6,8,9]=>01010100=>00101010
[3,1,2,8,7,5,4,6]=>0101011=>1101010
[5,3,1,2,4,9,7,6,8]=>01010101=>10101010
[7,5,3,1,2,4,6,9,8,10]=>010101010=>010101010
[3,1,2,7,5,4,6,9,8]=>01010101=>10101010
[5,3,1,2,4,7,6,9,8,10]=>010101010=>010101010
[1,5,3,2,4,7,6,9,8]=>01010101=>10101010
[1,4,3,8,5,7,2,6]=>0010011=>1100100
[6,7,1,5,2,8,4,3]=>0011011=>1101100
[1,5,3,7,6,4,8,2]=>0001111=>1111000
[4,8,1,3,6,2,7,5]=>0000111=>1110000
[2,7,3,4,8,6,5,1]=>0001111=>1111000
[1,8,2,4,7,3,6,5]=>0000111=>1110000
[2,7,1,6,5,8,3,4]=>0000111=>1110000
[6,2,3,8,1,5,7,4]=>0000111=>1110000
[2,5,7,4,8,3,6,1]=>0000111=>1110000
[8,5,6,2,4,7,1,3]=>0000111=>1110000
[4,8,5,6,7,1,3,2]=>0100011=>1100010
[8,1,5,7,3,6,4,2]=>0010111=>1110100
[4,3,7,1,2,8,5,6]=>0010011=>1100100
[2,7,6,4,3,8,5,1]=>0011111=>1111100
[3,8,6,2,7,5,4,1]=>0011111=>1111100
[4,8,1,6,2,5,3,7]=>0001101=>1011000
[1,8,4,2,5,7,3,6]=>0010011=>1100100
[5,8,3,1,2,4,6,7]=>0100001=>1000010
[1,4,8,5,2,3,6,7]=>0001001=>1001000
[1,4,8,5,2,3,7,6]=>0001011=>1101000
[7,1,4,2,6,8,3,5]=>0010011=>1100100
[1,5,8,7,2,4,3,6]=>0010011=>1100100
[1,5,4,2,8,3,7,6]=>0011011=>1101100
[1,2,8,7,3,5,4,6]=>0001011=>1101000
[8,7,1,3,2,5,4,6]=>0101011=>1101010
[6,7,4,2,8,1,3,5]=>0010011=>1100100
[4,1,6,8,7,2,3,5]=>0010011=>1100100
[4,7,5,6,2,8,3,1]=>0100111=>1110010
[8,4,3,6,7,5,2,1]=>1011011=>1101101
[6,7,5,2,8,4,3,1]=>0111011=>1101110
[6,8,4,3,2,7,5,1]=>0111011=>1101110
[2,1,4,3,6,5,9,7,10,8]=>101010011=>110010101
[2,1,4,3,7,5,8,6,10,9]=>101001101=>101100101
[2,1,4,3,7,5,9,6,10,8]=>101001011=>110100101
[2,1,4,3,8,5,9,6,10,7]=>101000111=>111000101
[2,1,5,3,6,4,8,7,10,9]=>100110101=>101011001
[2,1,5,3,6,4,9,7,10,8]=>100110011=>110011001
[2,1,5,3,7,4,8,6,10,9]=>100101101=>101101001
[2,1,5,3,7,4,9,6,10,8]=>100101011=>110101001
[2,1,5,3,8,4,9,6,10,7]=>100100111=>111001001
[2,1,6,3,7,4,8,5,10,9]=>100011101=>101110001
[2,1,6,3,7,4,9,5,10,8]=>100011011=>110110001
[2,1,6,3,8,4,9,5,10,7]=>100010111=>111010001
[2,1,7,3,8,4,9,5,10,6]=>100001111=>111100001
[3,1,4,2,6,5,9,7,10,8]=>011010011=>110010110
[3,1,4,2,7,5,8,6,10,9]=>011001101=>101100110
[3,1,4,2,7,5,9,6,10,8]=>011001011=>110100110
[3,1,4,2,8,5,9,6,10,7]=>011000111=>111000110
[3,1,5,2,6,4,9,7,10,8]=>010110011=>110011010
[3,1,5,2,8,4,9,6,10,7]=>010100111=>111001010
[3,1,6,2,7,4,8,5,10,9]=>010011101=>101110010
[3,1,6,2,7,4,9,5,10,8]=>010011011=>110110010
[3,1,6,2,8,4,9,5,10,7]=>010010111=>111010010
[3,1,7,2,8,4,9,5,10,6]=>010001111=>111100010
[4,1,5,2,6,3,9,7,10,8]=>001110011=>110011100
[4,1,5,2,7,3,8,6,10,9]=>001101101=>101101100
[4,1,5,2,7,3,9,6,10,8]=>001101011=>110101100
[4,1,5,2,8,3,9,6,10,7]=>001100111=>111001100
[4,1,6,2,7,3,8,5,10,9]=>001011101=>101110100
[4,1,6,2,7,3,9,5,10,8]=>001011011=>110110100
[4,1,6,2,8,3,9,5,10,7]=>001010111=>111010100
[4,1,7,2,8,3,9,5,10,6]=>001001111=>111100100
[5,1,6,2,7,3,9,4,10,8]=>000111011=>110111000
[5,1,6,2,8,3,9,4,10,7]=>000110111=>111011000
[5,1,7,2,8,3,9,4,10,6]=>000101111=>111101000
[2,1,4,3,6,5,8,7,11,9,12,10]=>10101010011=>11001010101
[2,1,4,3,6,5,9,7,10,8,12,11]=>10101001101=>10110010101
[2,1,4,3,6,5,9,7,11,8,12,10]=>10101001011=>11010010101
[2,1,4,3,6,5,10,7,11,8,12,9]=>10101000111=>11100010101
[2,1,4,3,7,5,8,6,10,9,12,11]=>10100110101=>10101100101
[2,1,4,3,7,5,8,6,11,9,12,10]=>10100110011=>11001100101
[2,1,4,3,7,5,9,6,10,8,12,11]=>10100101101=>10110100101
[2,1,4,3,7,5,9,6,11,8,12,10]=>10100101011=>11010100101
[2,1,4,3,7,5,10,6,11,8,12,9]=>10100100111=>11100100101
[2,1,4,3,8,5,9,6,10,7,12,11]=>10100011101=>10111000101
[2,1,4,3,8,5,9,6,11,7,12,10]=>10100011011=>11011000101
[2,1,4,3,8,5,10,6,11,7,12,9]=>10100010111=>11101000101
[2,1,4,3,9,5,10,6,11,7,12,8]=>10100001111=>11110000101
[2,1,5,3,6,4,8,7,10,9,12,11]=>10011010101=>10101011001
[2,1,5,3,6,4,8,7,11,9,12,10]=>10011010011=>11001011001
[2,1,5,3,6,4,9,7,10,8,12,11]=>10011001101=>10110011001
[2,1,5,3,6,4,9,7,11,8,12,10]=>10011001011=>11010011001
[2,1,5,3,6,4,10,7,11,8,12,9]=>10011000111=>11100011001
[2,1,5,3,7,4,8,6,10,9,12,11]=>10010110101=>10101101001
[2,1,5,3,7,4,8,6,11,9,12,10]=>10010110011=>11001101001
[2,1,5,3,7,4,9,6,10,8,12,11]=>10010101101=>10110101001
[2,1,5,3,7,4,9,6,11,8,12,10]=>10010101011=>11010101001
[2,1,5,3,7,4,10,6,11,8,12,9]=>10010100111=>11100101001
[2,1,5,3,8,4,9,6,10,7,12,11]=>10010011101=>10111001001
[2,1,5,3,8,4,9,6,11,7,12,10]=>10010011011=>11011001001
[2,1,5,3,8,4,10,6,11,7,12,9]=>10010010111=>11101001001
[2,1,5,3,9,4,10,6,11,7,12,8]=>10010001111=>11110001001
[2,1,6,3,7,4,8,5,10,9,12,11]=>10001110101=>10101110001
[2,1,6,3,7,4,8,5,11,9,12,10]=>10001110011=>11001110001
[2,1,6,3,7,4,9,5,10,8,12,11]=>10001101101=>10110110001
[2,1,6,3,7,4,9,5,11,8,12,10]=>10001101011=>11010110001
[2,1,6,3,7,4,10,5,11,8,12,9]=>10001100111=>11100110001
[2,1,6,3,8,4,9,5,10,7,12,11]=>10001011101=>10111010001
[2,1,6,3,8,4,9,5,11,7,12,10]=>10001011011=>11011010001
[2,1,6,3,8,4,10,5,11,7,12,9]=>10001010111=>11101010001
[2,1,6,3,9,4,10,5,11,7,12,8]=>10001001111=>11110010001
[2,1,7,3,8,4,9,5,10,6,12,11]=>10000111101=>10111100001
[2,1,7,3,8,4,9,5,11,6,12,10]=>10000111011=>11011100001
[2,1,7,3,8,4,10,5,11,6,12,9]=>10000110111=>11101100001
[2,1,7,3,9,4,10,5,11,6,12,8]=>10000101111=>11110100001
[2,1,8,3,9,4,10,5,11,6,12,7]=>10000011111=>11111000001
[3,1,4,2,6,5,8,7,10,9,12,11]=>01101010101=>10101010110
[3,1,4,2,6,5,8,7,11,9,12,10]=>01101010011=>11001010110
[3,1,4,2,6,5,9,7,10,8,12,11]=>01101001101=>10110010110
[3,1,4,2,6,5,9,7,11,8,12,10]=>01101001011=>11010010110
[3,1,4,2,6,5,10,7,11,8,12,9]=>01101000111=>11100010110
[3,1,4,2,7,5,8,6,10,9,12,11]=>01100110101=>10101100110
[3,1,4,2,7,5,8,6,11,9,12,10]=>01100110011=>11001100110
[3,1,4,2,7,5,9,6,10,8,12,11]=>01100101101=>10110100110
[3,1,4,2,7,5,9,6,11,8,12,10]=>01100101011=>11010100110
[3,1,4,2,7,5,10,6,11,8,12,9]=>01100100111=>11100100110
[3,1,4,2,8,5,9,6,10,7,12,11]=>01100011101=>10111000110
[3,1,4,2,8,5,9,6,11,7,12,10]=>01100011011=>11011000110
[3,1,4,2,8,5,10,6,11,7,12,9]=>01100010111=>11101000110
[3,1,4,2,9,5,10,6,11,7,12,8]=>01100001111=>11110000110
[3,1,5,2,6,4,8,7,10,9,12,11]=>01011010101=>10101011010
[3,1,5,2,6,4,8,7,11,9,12,10]=>01011010011=>11001011010
[3,1,5,2,6,4,9,7,10,8,12,11]=>01011001101=>10110011010
[3,1,5,2,6,4,9,7,11,8,12,10]=>01011001011=>11010011010
[3,1,5,2,6,4,10,7,11,8,12,9]=>01011000111=>11100011010
[3,1,5,2,7,4,8,6,10,9,12,11]=>01010110101=>10101101010
[3,1,5,2,7,4,8,6,11,9,12,10]=>01010110011=>11001101010
[3,1,5,2,7,4,9,6,10,8,12,11]=>01010101101=>10110101010
[3,1,5,2,7,4,9,6,11,8,12,10]=>01010101011=>11010101010
[3,1,5,2,7,4,10,6,11,8,12,9]=>01010100111=>11100101010
[3,1,5,2,8,4,9,6,10,7,12,11]=>01010011101=>10111001010
[3,1,5,2,8,4,9,6,11,7,12,10]=>01010011011=>11011001010
[3,1,5,2,8,4,10,6,11,7,12,9]=>01010010111=>11101001010
[3,1,5,2,9,4,10,6,11,7,12,8]=>01010001111=>11110001010
[3,1,6,2,7,4,8,5,10,9,12,11]=>01001110101=>10101110010
[3,1,6,2,7,4,8,5,11,9,12,10]=>01001110011=>11001110010
[3,1,6,2,7,4,9,5,10,8,12,11]=>01001101101=>10110110010
[3,1,6,2,7,4,9,5,11,8,12,10]=>01001101011=>11010110010
[3,1,6,2,7,4,10,5,11,8,12,9]=>01001100111=>11100110010
[3,1,6,2,8,4,9,5,10,7,12,11]=>01001011101=>10111010010
[3,1,6,2,8,4,9,5,11,7,12,10]=>01001011011=>11011010010
[3,1,6,2,8,4,10,5,11,7,12,9]=>01001010111=>11101010010
[3,1,6,2,9,4,10,5,11,7,12,8]=>01001001111=>11110010010
[3,1,7,2,8,4,9,5,10,6,12,11]=>01000111101=>10111100010
[3,1,7,2,8,4,9,5,11,6,12,10]=>01000111011=>11011100010
[3,1,7,2,8,4,10,5,11,6,12,9]=>01000110111=>11101100010
[3,1,7,2,9,4,10,5,11,6,12,8]=>01000101111=>11110100010
[3,1,8,2,9,4,10,5,11,6,12,7]=>01000011111=>11111000010
[4,1,5,2,6,3,8,7,10,9,12,11]=>00111010101=>10101011100
[4,1,5,2,6,3,8,7,11,9,12,10]=>00111010011=>11001011100
[4,1,5,2,6,3,9,7,10,8,12,11]=>00111001101=>10110011100
[4,1,5,2,6,3,9,7,11,8,12,10]=>00111001011=>11010011100
[4,1,5,2,6,3,10,7,11,8,12,9]=>00111000111=>11100011100
[4,1,5,2,7,3,8,6,10,9,12,11]=>00110110101=>10101101100
[4,1,5,2,7,3,8,6,11,9,12,10]=>00110110011=>11001101100
[4,1,5,2,7,3,9,6,10,8,12,11]=>00110101101=>10110101100
[4,1,5,2,7,3,9,6,11,8,12,10]=>00110101011=>11010101100
[4,1,5,2,7,3,10,6,11,8,12,9]=>00110100111=>11100101100
[4,1,5,2,8,3,9,6,10,7,12,11]=>00110011101=>10111001100
[4,1,5,2,8,3,9,6,11,7,12,10]=>00110011011=>11011001100
[4,1,5,2,8,3,10,6,11,7,12,9]=>00110010111=>11101001100
[4,1,5,2,9,3,10,6,11,7,12,8]=>00110001111=>11110001100
[4,1,6,2,7,3,8,5,10,9,12,11]=>00101110101=>10101110100
[4,1,6,2,7,3,8,5,11,9,12,10]=>00101110011=>11001110100
[4,1,6,2,7,3,9,5,10,8,12,11]=>00101101101=>10110110100
[4,1,6,2,7,3,9,5,11,8,12,10]=>00101101011=>11010110100
[4,1,6,2,7,3,10,5,11,8,12,9]=>00101100111=>11100110100
[4,1,6,2,8,3,9,5,10,7,12,11]=>00101011101=>10111010100
[4,1,6,2,8,3,9,5,11,7,12,10]=>00101011011=>11011010100
[4,1,6,2,8,3,10,5,11,7,12,9]=>00101010111=>11101010100
[4,1,6,2,9,3,10,5,11,7,12,8]=>00101001111=>11110010100
[4,1,7,2,8,3,9,5,10,6,12,11]=>00100111101=>10111100100
[4,1,7,2,8,3,9,5,11,6,12,10]=>00100111011=>11011100100
[4,1,7,2,8,3,10,5,11,6,12,9]=>00100110111=>11101100100
[4,1,7,2,9,3,10,5,11,6,12,8]=>00100101111=>11110100100
[4,1,8,2,9,3,10,5,11,6,12,7]=>00100011111=>11111000100
[5,1,6,2,7,3,8,4,10,9,12,11]=>00011110101=>10101111000
[5,1,6,2,7,3,8,4,11,9,12,10]=>00011110011=>11001111000
[5,1,6,2,7,3,9,4,10,8,12,11]=>00011101101=>10110111000
[5,1,6,2,7,3,9,4,11,8,12,10]=>00011101011=>11010111000
[5,1,6,2,7,3,10,4,11,8,12,9]=>00011100111=>11100111000
[5,1,6,2,8,3,9,4,10,7,12,11]=>00011011101=>10111011000
[5,1,6,2,8,3,9,4,11,7,12,10]=>00011011011=>11011011000
[5,1,6,2,8,3,10,4,11,7,12,9]=>00011010111=>11101011000
[5,1,6,2,9,3,10,4,11,7,12,8]=>00011001111=>11110011000
[5,1,7,2,8,3,9,4,10,6,12,11]=>00010111101=>10111101000
[5,1,7,2,8,3,9,4,11,6,12,10]=>00010111011=>11011101000
[5,1,7,2,8,3,10,4,11,6,12,9]=>00010110111=>11101101000
[5,1,7,2,9,3,10,4,11,6,12,8]=>00010101111=>11110101000
[5,1,8,2,9,3,10,4,11,6,12,7]=>00010011111=>11111001000
[6,1,7,2,8,3,9,4,10,5,12,11]=>00001111101=>10111110000
[6,1,7,2,8,3,9,4,11,5,12,10]=>00001111011=>11011110000
[6,1,7,2,8,3,10,4,11,5,12,9]=>00001110111=>11101110000
[6,1,7,2,9,3,10,4,11,5,12,8]=>00001101111=>11110110000
[6,1,8,2,9,3,10,4,11,5,12,7]=>00001011111=>11111010000
[2,9,8,7,6,5,1,4,3]=>00111111=>11111100
[2,10,9,8,7,6,5,1,4,3]=>001111111=>111111100
[6,1,7,3,5,8,2,4]=>0000111=>1110000
[1,3,7,6,4,8,2,5]=>0000111=>1110000
[2,6,4,8,7,3,1,5]=>0100111=>1110010
[2,1,8,7,3,5,4,6]=>1001011=>1101001
[6,1,5,8,7,4,3,2]=>0110111=>1110110
[6,1,8,5,7,4,3,2]=>0110111=>1110110
[8,5,1,4,7,6,3,2]=>0101111=>1111010
[8,1,3,7,2,4,6,5]=>0000111=>1110000
[2,6,7,3,5,8,4,1]=>0010011=>1100100
[2,6,7,3,5,8,1,4]=>0000011=>1100000
[5,3,1,6,4,8,2,7]=>0101101=>1011010
[2,5,6,7,1,4,8,3]=>0000011=>1100000
[4,7,5,3,2,8,1,6]=>0101011=>1101010
[4,7,5,2,8,6,1,3]=>0001111=>1111000
[3,8,6,7,2,5,4,1]=>0011011=>1101100
[5,8,1,2,7,4,3,6]=>0010011=>1100100
[6,3,1,8,2,4,5,7]=>0100101=>1010010
[4,6,3,7,8,1,5,2]=>0001101=>1011000
[6,3,1,8,4,5,2,7]=>0101101=>1011010
[2,1,4,7,5,8,6,3]=>1000111=>1110001
[7,6,2,4,8,3,1,5]=>0100111=>1110010
[6,5,8,1,4,3,7,2]=>0010111=>1110100
[8,1,4,2,7,5,6,3]=>0010111=>1110100
[9,3,4,5,6,7,1,2,10,8]=>000001011=>110100000
[1,7,2,8,3,9,4,10,5,6]=>000001111=>111100000
[1,7,2,8,3,9,10,4,5,6]=>000001101=>101100000
[1,7,2,8,9,3,4,10,5,6]=>000001011=>110100000
[1,7,2,8,9,3,10,4,5,6]=>000001011=>110100000
[1,7,2,8,9,10,3,4,5,6]=>000001001=>100100000
[1,7,8,2,3,9,4,10,5,6]=>000000111=>111000000
[1,7,8,2,3,9,10,4,5,6]=>000000101=>101000000
[1,7,8,2,9,3,4,10,5,6]=>000000111=>111000000
[1,7,8,2,9,3,10,4,5,6]=>000000111=>111000000
[1,7,8,2,9,10,3,4,5,6]=>000000101=>101000000
[1,7,8,9,2,3,4,10,5,6]=>000000011=>110000000
[1,7,8,9,2,3,10,4,5,6]=>000000011=>110000000
[1,7,8,9,2,10,3,4,5,6]=>000000011=>110000000
[7,1,2,8,3,9,4,10,5,6]=>000001111=>111100000
[7,1,2,8,3,9,10,4,5,6]=>000001101=>101100000
[7,1,2,8,9,3,4,10,5,6]=>000001011=>110100000
[7,1,2,8,9,3,10,4,5,6]=>000001011=>110100000
[7,1,2,8,9,10,3,4,5,6]=>000001001=>100100000
[7,1,8,2,3,9,4,10,5,6]=>000001111=>111100000
[7,1,8,2,3,9,10,4,5,6]=>000001101=>101100000
[7,1,8,2,9,3,4,10,5,6]=>000001111=>111100000
[7,1,8,2,9,10,3,4,5,6]=>000001101=>101100000
[7,1,8,9,2,3,4,10,5,6]=>000001011=>110100000
[7,1,8,9,2,3,10,4,5,6]=>000001011=>110100000
[7,1,8,9,2,10,3,4,5,6]=>000001011=>110100000
[7,1,8,9,10,2,3,4,5,6]=>000001001=>100100000
[7,8,1,2,3,9,4,10,5,6]=>000000111=>111000000
[7,8,1,2,3,9,10,4,5,6]=>000000101=>101000000
[7,8,1,2,9,3,4,10,5,6]=>000000111=>111000000
[7,8,1,2,9,3,10,4,5,6]=>000000111=>111000000
[7,8,1,2,9,10,3,4,5,6]=>000000101=>101000000
[7,8,1,9,2,3,4,10,5,6]=>000000111=>111000000
[7,8,1,9,2,3,10,4,5,6]=>000000111=>111000000
[7,8,1,9,2,10,3,4,5,6]=>000000111=>111000000
[7,8,1,9,10,2,3,4,5,6]=>000000101=>101000000
[7,8,9,1,2,3,4,10,5,6]=>000000011=>110000000
[7,8,9,1,2,3,10,4,5,6]=>000000011=>110000000
[7,8,9,1,2,10,3,4,5,6]=>000000011=>110000000
[7,8,9,1,10,2,3,4,5,6]=>000000011=>110000000
[1,8,2,9,3,10,4,11,5,12,6,7]=>00000011111=>11111000000
[1,8,2,9,3,10,4,11,12,5,6,7]=>00000011101=>10111000000
[1,8,2,9,3,10,11,4,5,12,6,7]=>00000011011=>11011000000
[1,8,2,9,3,10,11,4,12,5,6,7]=>00000011011=>11011000000
[1,8,2,9,3,10,11,12,4,5,6,7]=>00000011001=>10011000000
[1,8,2,9,10,3,4,11,5,12,6,7]=>00000010111=>11101000000
[1,8,2,9,10,3,4,11,12,5,6,7]=>00000010101=>10101000000
[1,8,2,9,10,3,11,4,5,12,6,7]=>00000010111=>11101000000
[1,8,2,9,10,3,11,4,12,5,6,7]=>00000010111=>11101000000
[1,8,2,9,10,3,11,12,4,5,6,7]=>00000010101=>10101000000
[1,8,2,9,10,11,3,4,5,12,6,7]=>00000010011=>11001000000
[1,8,2,9,10,11,3,4,12,5,6,7]=>00000010011=>11001000000
[1,8,2,9,10,11,3,12,4,5,6,7]=>00000010011=>11001000000
[1,8,2,9,10,11,12,3,4,5,6,7]=>00000010001=>10001000000
[1,8,9,2,3,10,4,11,5,12,6,7]=>00000001111=>11110000000
[1,8,9,2,3,10,4,11,12,5,6,7]=>00000001101=>10110000000
[1,8,9,2,3,10,11,4,5,12,6,7]=>00000001011=>11010000000
[1,8,9,2,3,10,11,4,12,5,6,7]=>00000001011=>11010000000
[1,8,9,2,3,10,11,12,4,5,6,7]=>00000001001=>10010000000
[1,8,9,2,10,3,4,11,5,12,6,7]=>00000001111=>11110000000
[1,8,9,2,10,3,4,11,12,5,6,7]=>00000001101=>10110000000
[1,8,9,2,10,3,11,4,5,12,6,7]=>00000001111=>11110000000
[1,8,9,2,10,3,11,4,12,5,6,7]=>00000001111=>11110000000
[1,8,9,2,10,3,11,12,4,5,6,7]=>00000001101=>10110000000
[1,8,9,2,10,11,3,4,5,12,6,7]=>00000001011=>11010000000
[1,8,9,2,10,11,3,4,12,5,6,7]=>00000001011=>11010000000
[1,8,9,2,10,11,3,12,4,5,6,7]=>00000001011=>11010000000
[1,8,9,2,10,11,12,3,4,5,6,7]=>00000001001=>10010000000
[1,8,9,10,2,3,4,11,5,12,6,7]=>00000000111=>11100000000
[1,8,9,10,2,3,4,11,12,5,6,7]=>00000000101=>10100000000
[1,8,9,10,2,3,11,4,5,12,6,7]=>00000000111=>11100000000
[1,8,9,10,2,3,11,4,12,5,6,7]=>00000000111=>11100000000
[1,8,9,10,2,3,11,12,4,5,6,7]=>00000000101=>10100000000
[1,8,9,10,2,11,3,4,5,12,6,7]=>00000000111=>11100000000
[1,8,9,10,2,11,3,4,12,5,6,7]=>00000000111=>11100000000
[1,8,9,10,2,11,3,12,4,5,6,7]=>00000000111=>11100000000
[1,8,9,10,2,11,12,3,4,5,6,7]=>00000000101=>10100000000
[1,8,9,10,11,2,3,4,5,12,6,7]=>00000000011=>11000000000
[1,8,9,10,11,2,3,4,12,5,6,7]=>00000000011=>11000000000
[1,8,9,10,11,2,3,12,4,5,6,7]=>00000000011=>11000000000
[1,8,9,10,11,2,12,3,4,5,6,7]=>00000000011=>11000000000
[1,8,9,10,11,12,2,3,4,5,6,7]=>00000000001=>10000000000
[8,1,2,9,3,10,4,11,5,12,6,7]=>00000011111=>11111000000
[8,1,2,9,3,10,4,11,12,5,6,7]=>00000011101=>10111000000
[8,1,2,9,3,10,11,4,5,12,6,7]=>00000011011=>11011000000
[8,1,2,9,3,10,11,4,12,5,6,7]=>00000011011=>11011000000
[8,1,2,9,3,10,11,12,4,5,6,7]=>00000011001=>10011000000
[8,1,2,9,10,3,4,11,5,12,6,7]=>00000010111=>11101000000
[8,1,2,9,10,3,4,11,12,5,6,7]=>00000010101=>10101000000
[8,1,2,9,10,3,11,4,5,12,6,7]=>00000010111=>11101000000
[8,1,2,9,10,3,11,4,12,5,6,7]=>00000010111=>11101000000
[8,1,2,9,10,3,11,12,4,5,6,7]=>00000010101=>10101000000
[8,1,2,9,10,11,3,4,5,12,6,7]=>00000010011=>11001000000
[8,1,2,9,10,11,3,4,12,5,6,7]=>00000010011=>11001000000
[8,1,2,9,10,11,3,12,4,5,6,7]=>00000010011=>11001000000
[8,1,2,9,10,11,12,3,4,5,6,7]=>00000010001=>10001000000
[8,1,9,2,3,10,4,11,5,12,6,7]=>00000011111=>11111000000
[8,1,9,2,3,10,4,11,12,5,6,7]=>00000011101=>10111000000
[8,1,9,2,3,10,11,4,5,12,6,7]=>00000011011=>11011000000
[8,1,9,2,3,10,11,4,12,5,6,7]=>00000011011=>11011000000
[8,1,9,2,3,10,11,12,4,5,6,7]=>00000011001=>10011000000
[8,1,9,2,10,3,4,11,5,12,6,7]=>00000011111=>11111000000
[8,1,9,2,10,3,4,11,12,5,6,7]=>00000011101=>10111000000
[8,1,9,2,10,3,11,4,5,12,6,7]=>00000011111=>11111000000
[8,1,9,2,10,3,11,4,12,5,6,7]=>00000011111=>11111000000
[8,1,9,2,10,3,11,12,4,5,6,7]=>00000011101=>10111000000
[8,1,9,2,10,11,3,4,5,12,6,7]=>00000011011=>11011000000
[8,1,9,2,10,11,3,4,12,5,6,7]=>00000011011=>11011000000
[8,1,9,2,10,11,3,12,4,5,6,7]=>00000011011=>11011000000
[8,1,9,2,10,11,12,3,4,5,6,7]=>00000011001=>10011000000
[8,1,9,10,2,3,4,11,5,12,6,7]=>00000010111=>11101000000
[8,1,9,10,2,3,4,11,12,5,6,7]=>00000010101=>10101000000
[8,1,9,10,2,3,11,4,5,12,6,7]=>00000010111=>11101000000
[8,1,9,10,2,3,11,4,12,5,6,7]=>00000010111=>11101000000
[8,1,9,10,2,3,11,12,4,5,6,7]=>00000010101=>10101000000
[8,1,9,10,2,11,3,4,5,12,6,7]=>00000010111=>11101000000
[8,1,9,10,2,11,3,4,12,5,6,7]=>00000010111=>11101000000
[8,1,9,10,2,11,3,12,4,5,6,7]=>00000010111=>11101000000
[8,1,9,10,2,11,12,3,4,5,6,7]=>00000010101=>10101000000
[8,1,9,10,11,2,3,4,5,12,6,7]=>00000010011=>11001000000
[8,1,9,10,11,2,3,4,12,5,6,7]=>00000010011=>11001000000
[8,1,9,10,11,2,3,12,4,5,6,7]=>00000010011=>11001000000
[8,1,9,10,11,2,12,3,4,5,6,7]=>00000010011=>11001000000
[8,1,9,10,11,12,2,3,4,5,6,7]=>00000010001=>10001000000
[8,9,1,2,3,10,4,11,5,12,6,7]=>00000001111=>11110000000
[8,9,1,2,3,10,4,11,12,5,6,7]=>00000001101=>10110000000
[8,9,1,2,3,10,11,4,5,12,6,7]=>00000001011=>11010000000
[8,9,1,2,3,10,11,4,12,5,6,7]=>00000001011=>11010000000
[8,9,1,2,3,10,11,12,4,5,6,7]=>00000001001=>10010000000
[8,9,1,2,10,3,4,11,5,12,6,7]=>00000001111=>11110000000
[8,9,1,2,10,3,4,11,12,5,6,7]=>00000001101=>10110000000
[8,9,1,2,10,3,11,4,5,12,6,7]=>00000001111=>11110000000
[8,9,1,2,10,3,11,4,12,5,6,7]=>00000001111=>11110000000
[8,9,1,2,10,3,11,12,4,5,6,7]=>00000001101=>10110000000
[8,9,1,2,10,11,3,4,5,12,6,7]=>00000001011=>11010000000
[8,9,1,2,10,11,3,4,12,5,6,7]=>00000001011=>11010000000
[8,9,1,2,10,11,3,12,4,5,6,7]=>00000001011=>11010000000
[8,9,1,2,10,11,12,3,4,5,6,7]=>00000001001=>10010000000
[8,9,1,10,2,3,4,11,5,12,6,7]=>00000001111=>11110000000
[8,9,1,10,2,3,4,11,12,5,6,7]=>00000001101=>10110000000
[8,9,1,10,2,3,11,4,5,12,6,7]=>00000001111=>11110000000
[8,9,1,10,2,3,11,4,12,5,6,7]=>00000001111=>11110000000
[8,9,1,10,2,3,11,12,4,5,6,7]=>00000001101=>10110000000
[8,9,1,10,2,11,3,4,5,12,6,7]=>00000001111=>11110000000
[8,9,1,10,2,11,3,4,12,5,6,7]=>00000001111=>11110000000
[8,9,1,10,2,11,3,12,4,5,6,7]=>00000001111=>11110000000
[8,9,1,10,2,11,12,3,4,5,6,7]=>00000001101=>10110000000
[8,9,1,10,11,2,3,4,5,12,6,7]=>00000001011=>11010000000
[8,9,1,10,11,2,3,4,12,5,6,7]=>00000001011=>11010000000
[8,9,1,10,11,2,3,12,4,5,6,7]=>00000001011=>11010000000
[8,9,1,10,11,2,12,3,4,5,6,7]=>00000001011=>11010000000
[8,9,1,10,11,12,2,3,4,5,6,7]=>00000001001=>10010000000
[8,9,10,1,2,3,4,11,5,12,6,7]=>00000000111=>11100000000
[8,9,10,1,2,3,4,11,12,5,6,7]=>00000000101=>10100000000
[8,9,10,1,2,3,11,4,5,12,6,7]=>00000000111=>11100000000
[8,9,10,1,2,3,11,4,12,5,6,7]=>00000000111=>11100000000
[8,9,10,1,2,3,11,12,4,5,6,7]=>00000000101=>10100000000
[8,9,10,1,2,11,3,4,5,12,6,7]=>00000000111=>11100000000
[8,9,10,1,2,11,3,4,12,5,6,7]=>00000000111=>11100000000
[8,9,10,1,2,11,3,12,4,5,6,7]=>00000000111=>11100000000
[8,9,10,1,2,11,12,3,4,5,6,7]=>00000000101=>10100000000
[8,9,10,1,11,2,3,4,5,12,6,7]=>00000000111=>11100000000
[8,9,10,1,11,2,3,4,12,5,6,7]=>00000000111=>11100000000
[8,9,10,1,11,2,3,12,4,5,6,7]=>00000000111=>11100000000
[8,9,10,1,11,2,12,3,4,5,6,7]=>00000000111=>11100000000
[8,9,10,1,11,12,2,3,4,5,6,7]=>00000000101=>10100000000
[8,9,10,11,1,2,3,4,5,12,6,7]=>00000000011=>11000000000
[8,9,10,11,1,2,3,4,12,5,6,7]=>00000000011=>11000000000
[8,9,10,11,1,2,3,12,4,5,6,7]=>00000000011=>11000000000
[8,9,10,11,1,2,12,3,4,5,6,7]=>00000000011=>11000000000
[8,9,10,11,1,12,2,3,4,5,6,7]=>00000000011=>11000000000
[8,9,10,11,12,1,2,3,4,5,6,7]=>00000000001=>10000000000
[8,6,3,5,2,1,7,4]=>1001111=>1111001
[6,8,3,1,2,5,4,7]=>0101001=>1001010
[5,8,6,4,7,1,2,3]=>0000111=>1110000
[2,5,1,8,7,3,4,6]=>0001011=>1101000
[7,2,4,3,8,6,1,5]=>0010111=>1110100
[1,7,6,5,4,3,2,9,8]=>01111101=>10111110
[6,8,4,3,5,1,7,2]=>0011011=>1101100
[1,4,7,3,6,8,2,5]=>0000011=>1100000
[3,7,1,4,6,8,2,5]=>0000011=>1100000
[2,4,7,3,6,8,1,5]=>0000011=>1100000
[8,5,7,6,1,3,2,4]=>0100111=>1110010
[2,7,5,6,1,8,4,3]=>0010111=>1110100
[1,2,6,7,4,5,8,3]=>0000011=>1100000
[6,5,2,8,7,1,4,3]=>0011111=>1111100
[7,2,3,6,8,1,4,5]=>0000011=>1100000
[2,6,1,3,8,5,4,7]=>0001101=>1011000
[6,4,1,8,3,2,5,7]=>0110101=>1010110
[5,8,1,4,2,7,3,6]=>0010011=>1100100
[2,3,1,6,8,7,4,5]=>0100011=>1100010
[6,4,8,2,1,7,3,5]=>1000111=>1110001
[2,3,1,8,7,5,6,4]=>0100111=>1110010
[1,5,6,7,2,4,3,8]=>0010010=>0100100
[2,8,6,4,1,5,3,7]=>0011101=>1011100
[1,5,7,3,6,2,4,8]=>0000110=>0110000
[6,7,4,5,1,3,8,2]=>0001011=>1101000
[1,6,5,3,8,2,4,7]=>0001101=>1011000
[5,6,1,2,4,8,3,7]=>0000101=>1010000
[8,7,4,5,1,3,2,6]=>0101011=>1101010
[8,5,1,2,7,4,3,6]=>0011011=>1101100
[4,1,8,7,2,5,3,6]=>0011011=>1101100
[2,6,3,8,4,1,7,5]=>0010111=>1110100
[3,2,4,6,1,8,7,5]=>0100111=>1110010
[3,6,7,4,1,2,5,8]=>0010010=>0100100
[1,4,7,5,8,2,3,6]=>0000011=>1100000
[1,6,8,4,7,3,2,5]=>0100011=>1100010
[3,6,7,5,4,8,1,2]=>0001011=>1101000
[4,5,7,2,6,3,8,1]=>0000111=>1110000
[2,1,5,7,4,6,8,3]=>1000011=>1100001
[2,3,5,7,8,1,6,4]=>0000101=>1010000
[1,5,7,4,2,3,6,8]=>0010010=>0100100
[2,4,7,5,3,6,8,1]=>0001011=>1101000
[8,1,7,2,4,6,3,5]=>0000111=>1110000
[1,2,4,7,8,6,3,5]=>0000101=>1010000
[2,4,7,8,3,5,1,6]=>0001001=>1001000
[1,3,6,2,5,8,4,7]=>0000101=>1010000
[1,5,3,6,8,2,4,7]=>0001001=>1001000
[4,8,1,2,6,3,7,5]=>0000111=>1110000
[5,8,1,2,6,3,7,4]=>0000111=>1110000
[1,6,2,3,7,5,8,4]=>0000111=>1110000
[4,1,2,6,5,7,8,3]=>0010101=>1010100
[1,8,4,2,7,3,6,5]=>0010111=>1110100
[1,7,5,2,3,8,6,4]=>0001111=>1111000
[8,1,4,7,3,5,2,6]=>0001011=>1101000
[8,4,3,6,1,7,2,5]=>0010111=>1110100
[2,6,1,8,3,7,4,5]=>0000111=>1110000
[8,4,2,1,3,7,5,6]=>1010011=>1100101
[2,5,1,7,6,8,3,4]=>0001011=>1101000
[5,3,1,8,2,4,7,6]=>0101011=>1101010
[1,2,6,3,7,5,8,4]=>0000111=>1110000
[5,1,8,3,2,4,7,6]=>0101011=>1101010
[3,1,5,4,6,7,8,2]=>0101001=>1001010
[2,8,5,7,3,1,4,6]=>0100011=>1100010
[2,6,8,7,3,1,4,5]=>0100011=>1100010
[7,4,2,1,3,8,5,6]=>1010011=>1100101
[7,2,1,3,8,5,4,6]=>1001011=>1101001
[2,1,7,3,8,6,4,5]=>1000111=>1110001
[1,7,5,3,2,4,8,6]=>0101011=>1101010
[1,4,2,7,6,5,8,3]=>0010111=>1110100
[3,4,1,6,5,7,8,2]=>0010101=>1010100
[2,8,7,3,4,1,5,6]=>0010011=>1100100
[5,7,6,2,3,8,1,4]=>0000111=>1110000
[4,5,7,6,2,8,1,3]=>0000111=>1110000
[3,1,8,7,5,2,6,4]=>0101111=>1111010
[4,5,6,8,7,2,1,3]=>1000011=>1100001
[2,8,3,1,5,4,7,6]=>0101011=>1101010
[3,8,4,1,5,2,7,6]=>0011011=>1101100
[5,1,7,8,3,2,6,4]=>0101101=>1011010
[1,8,6,2,4,3,7,5]=>0010111=>1110100
[4,8,3,1,6,2,7,5]=>0100111=>1110010
[2,8,3,1,6,4,7,5]=>0100111=>1110010
[6,2,7,1,5,8,4,3]=>0010111=>1110100
[1,7,8,9,6,5,4,3,2]=>01111001=>10011110
[1,6,7,8,9,5,4,3,2]=>01110001=>10001110
[1,5,6,7,8,9,4,3,2]=>01100001=>10000110
[1,4,5,6,7,8,9,3,2]=>01000001=>10000010
[1,8,9,10,7,6,5,4,3,2]=>011111001=>100111110
[1,7,6,8,9,5,4,3,2]=>01110101=>10101110
[1,7,8,9,10,6,5,4,3,2]=>011110001=>100011110
[1,6,5,7,8,9,4,3,2]=>01101001=>10010110
[1,6,7,8,9,10,5,4,3,2]=>011100001=>100001110
[1,5,4,6,7,8,9,3,2]=>01010001=>10001010
[1,5,6,7,8,9,10,4,3,2]=>011000001=>100000110
[1,4,5,6,7,8,9,10,3,2]=>010000001=>100000010
[4,8,5,1,3,2,6,7]=>0101001=>1001010
[5,4,3,1,2,7,6,8]=>0111010=>0101110
[4,1,6,5,2,3,7,8]=>0011100=>0011100
[7,1,5,2,3,6,4,8]=>0001110=>0111000
[4,1,6,3,7,2,5,8]=>0010110=>0110100
[4,6,1,2,8,3,7,5]=>0000111=>1110000
[4,1,3,6,7,2,5,8]=>0010010=>0100100
[2,6,5,1,3,4,7,8]=>0001100=>0011000
[2,6,7,4,3,1,5,8]=>0110010=>0100110
[2,6,3,1,7,4,5,8]=>0100110=>0110010
[6,5,3,7,2,4,1,8]=>0011110=>0111100
[2,3,6,7,1,5,4,8]=>0001010=>0101000
[2,7,5,8,1,3,6,4]=>0000111=>1110000
[5,1,6,7,3,2,4,8]=>0101010=>0101010
[5,6,1,4,7,2,3,8]=>0000110=>0110000
[1,2,5,7,8,6,3,4]=>0000101=>1010000
[1,2,6,7,4,5,3,8]=>0001010=>0101000
[1,2,7,8,4,6,3,5]=>0000101=>1010000
[8,6,5,2,1,7,4,3]=>1011111=>1111101
[4,3,8,6,7,1,5,2]=>0011011=>1101100
[8,3,2,4,7,1,6,5]=>0100111=>1110010
[7,3,2,8,6,1,5,4]=>0101111=>1111010
[7,5,8,2,6,1,4,3]=>0010111=>1110100
[5,6,8,2,7,4,1,3]=>0010011=>1100100
[7,4,1,2,6,5,8,3]=>0010111=>1110100
[5,2,7,4,6,1,8,3]=>0001111=>1111000
[7,4,1,2,3,6,8,5]=>0010011=>1100100
[5,4,8,6,3,2,1,7]=>1101101=>1011011
[8,4,6,7,3,1,5,2]=>0101011=>1101010
[4,6,8,5,1,2,7,3]=>0001011=>1101000
[4,1,3,6,8,5,2,7]=>0011001=>1001100
[6,3,5,7,1,2,8,4]=>0000111=>1110000
[1,8,5,3,2,4,6,7]=>0101001=>1001010
[1,6,7,3,4,2,5,8]=>0010010=>0100100
[1,6,8,3,4,2,5,7]=>0010001=>1000100
[1,8,7,5,3,4,2,6]=>0011011=>1101100
[1,7,8,5,3,4,2,6]=>0011001=>1001100
[1,7,6,8,4,2,3,5]=>0010011=>1100100
[1,7,8,6,4,3,2,5]=>0110101=>1010110
[9,8,7,6,5,2,1,3,4]=>10011111=>11111001
[9,8,6,4,7,2,5,1,3]=>00011111=>11111000
[7,2,8,9,10,1,3,4,5,6]=>000001001=>100100000
[9,7,8,6,5,4,3,2,1]=>11111011=>11011111
[5,1,7,8,4,2,3,6]=>0011001=>1001100
[3,8,2,1,6,7,5,4]=>1001011=>1101001
[2,8,3,1,7,5,6,4]=>0100111=>1110010
[8,5,6,2,1,4,7,3]=>1000111=>1110001
[9,10,6,4,2,1,3,5,8,7]=>101010101=>101010101
[10,7,8,4,2,1,3,6,5,9]=>101010101=>101010101
[9,7,10,4,2,1,3,6,8,5]=>101000111=>111000101
[8,9,10,4,2,1,3,7,6,5]=>101011001=>100110101
[10,8,5,6,2,1,4,3,7,9]=>101010101=>101010101
[9,10,5,6,2,1,4,3,8,7]=>101010101=>101010101
[10,7,5,8,2,1,4,6,3,9]=>100011101=>101110001
[9,7,5,10,2,1,4,6,8,3]=>100001111=>111100001
[8,9,5,10,2,1,4,7,6,3]=>100011011=>110110001
[10,6,7,8,2,1,5,4,3,9]=>101100101=>101001101
[9,6,7,10,2,1,5,4,8,3]=>100100111=>111001001
[8,6,9,10,2,1,5,7,4,3]=>101001101=>101100101
[7,8,9,10,2,1,6,5,4,3]=>101110001=>100011101
[10,8,6,3,4,2,1,5,7,9]=>101010101=>101010101
[9,10,6,3,4,2,1,5,8,7]=>101010101=>101010101
[10,7,8,3,4,2,1,6,5,9]=>101010101=>101010101
[9,7,10,3,4,2,1,6,8,5]=>101000111=>111000101
[8,9,10,3,4,2,1,7,6,5]=>101011001=>100110101
[10,8,5,3,6,2,4,1,7,9]=>001110101=>101011100
[9,10,5,3,6,2,4,1,8,7]=>001110101=>101011100
[10,7,5,3,8,2,4,6,1,9]=>000111101=>101111000
[9,7,5,3,10,2,4,6,8,1]=>000101111=>111101000
[8,9,5,3,10,2,4,7,6,1]=>000111011=>110111000
[10,6,7,3,8,2,5,4,1,9]=>001101101=>101101100
[9,6,7,3,10,2,5,4,8,1]=>000101111=>111101000
[8,6,9,3,10,2,5,7,4,1]=>001001111=>111100100
[7,8,9,3,10,2,6,5,4,1]=>001110011=>110011100
[10,8,4,5,6,3,2,1,7,9]=>110010101=>101010011
[9,10,4,5,6,3,2,1,8,7]=>110010101=>101010011
[10,7,4,5,8,3,2,6,1,9]=>010011101=>101110010
[9,7,4,5,10,3,2,6,8,1]=>010001111=>111100010
[8,9,4,5,10,3,2,7,6,1]=>010011011=>110110010
[10,6,4,7,8,3,5,2,1,9]=>100110101=>101011001
[9,6,4,7,10,3,5,2,8,1]=>000110111=>111011000
[8,6,4,9,10,3,5,7,2,1]=>100011101=>101110001
[7,8,4,9,10,3,6,5,2,1]=>100110101=>101011001
[10,5,6,7,8,4,3,2,1,9]=>111000101=>101000111
[9,5,6,7,10,4,3,2,8,1]=>011000111=>111000110
[8,5,6,9,10,4,3,7,2,1]=>101001101=>101100101
[7,5,8,9,10,4,6,3,2,1]=>110011001=>100110011
[12,10,8,6,4,2,1,3,5,7,9,11]=>10101010101=>10101010101
[11,12,8,6,4,2,1,3,5,7,10,9]=>10101010101=>10101010101
[12,9,10,6,4,2,1,3,5,8,7,11]=>10101010101=>10101010101
[11,9,12,6,4,2,1,3,5,8,10,7]=>10101000111=>11100010101
[10,11,12,6,4,2,1,3,5,9,8,7]=>10101011001=>10011010101
[12,10,7,8,4,2,1,3,6,5,9,11]=>10101010101=>10101010101
[11,12,7,8,4,2,1,3,6,5,10,9]=>10101010101=>10101010101
[12,9,7,10,4,2,1,3,6,8,5,11]=>10100011101=>10111000101
[11,9,7,12,4,2,1,3,6,8,10,5]=>10100001111=>11110000101
[10,11,7,12,4,2,1,3,6,9,8,5]=>10100011011=>11011000101
[12,8,9,10,4,2,1,3,7,6,5,11]=>10101100101=>10100110101
[11,8,9,12,4,2,1,3,7,6,10,5]=>10100100111=>11100100101
[10,8,11,12,4,2,1,3,7,9,6,5]=>10101001101=>10110010101
[9,10,11,12,4,2,1,3,8,7,6,5]=>10101110001=>10001110101
[12,10,8,5,6,2,1,4,3,7,9,11]=>10101010101=>10101010101
[11,12,8,5,6,2,1,4,3,7,10,9]=>10101010101=>10101010101
[12,9,10,5,6,2,1,4,3,8,7,11]=>10101010101=>10101010101
[11,9,12,5,6,2,1,4,3,8,10,7]=>10101000111=>11100010101
[10,11,12,5,6,2,1,4,3,9,8,7]=>10101011001=>10011010101
[12,10,7,5,8,2,1,4,6,3,9,11]=>10001110101=>10101110001
[11,12,7,5,8,2,1,4,6,3,10,9]=>10001110101=>10101110001
[12,9,7,5,10,2,1,4,6,8,3,11]=>10000111101=>10111100001
[11,9,7,5,12,2,1,4,6,8,10,3]=>10000101111=>11110100001
[10,11,7,5,12,2,1,4,6,9,8,3]=>10000111011=>11011100001
[12,8,9,5,10,2,1,4,7,6,3,11]=>10001101101=>10110110001
[11,8,9,5,12,2,1,4,7,6,10,3]=>10000101111=>11110100001
[10,8,11,5,12,2,1,4,7,9,6,3]=>10001001111=>11110010001
[9,10,11,5,12,2,1,4,8,7,6,3]=>10001110011=>11001110001
[12,10,6,7,8,2,1,5,4,3,9,11]=>10110010101=>10101001101
[11,12,6,7,8,2,1,5,4,3,10,9]=>10110010101=>10101001101
[12,9,6,7,10,2,1,5,4,8,3,11]=>10010011101=>10111001001
[11,9,6,7,12,2,1,5,4,8,10,3]=>10010001111=>11110001001
[10,11,6,7,12,2,1,5,4,9,8,3]=>10010011011=>11011001001
[12,8,6,9,10,2,1,5,7,4,3,11]=>10100110101=>10101100101
[11,8,6,9,12,2,1,5,7,4,10,3]=>10000110111=>11101100001
[10,8,6,11,12,2,1,5,7,9,4,3]=>10100011101=>10111000101
[9,10,6,11,12,2,1,5,8,7,4,3]=>10100110101=>10101100101
[12,7,8,9,10,2,1,6,5,4,3,11]=>10111000101=>10100011101
[11,7,8,9,12,2,1,6,5,4,10,3]=>10011000111=>11100011001
[10,7,8,11,12,2,1,6,5,9,4,3]=>10101001101=>10110010101
[9,7,10,11,12,2,1,6,8,5,4,3]=>10110011001=>10011001101
[8,9,10,11,12,2,1,7,6,5,4,3]=>10111100001=>10000111101
[12,10,8,6,3,4,2,1,5,7,9,11]=>10101010101=>10101010101
[11,12,8,6,3,4,2,1,5,7,10,9]=>10101010101=>10101010101
[12,9,10,6,3,4,2,1,5,8,7,11]=>10101010101=>10101010101
[11,9,12,6,3,4,2,1,5,8,10,7]=>10101000111=>11100010101
[10,11,12,6,3,4,2,1,5,9,8,7]=>10101011001=>10011010101
[12,10,7,8,3,4,2,1,6,5,9,11]=>10101010101=>10101010101
[11,12,7,8,3,4,2,1,6,5,10,9]=>10101010101=>10101010101
[12,9,7,10,3,4,2,1,6,8,5,11]=>10100011101=>10111000101
[11,9,7,12,3,4,2,1,6,8,10,5]=>10100001111=>11110000101
[10,11,7,12,3,4,2,1,6,9,8,5]=>10100011011=>11011000101
[12,8,9,10,3,4,2,1,7,6,5,11]=>10101100101=>10100110101
[11,8,9,12,3,4,2,1,7,6,10,5]=>10100100111=>11100100101
[10,8,11,12,3,4,2,1,7,9,6,5]=>10101001101=>10110010101
[9,10,11,12,3,4,2,1,8,7,6,5]=>10101110001=>10001110101
[12,10,8,5,3,6,2,4,1,7,9,11]=>00111010101=>10101011100
[11,12,8,5,3,6,2,4,1,7,10,9]=>00111010101=>10101011100
[12,9,10,5,3,6,2,4,1,8,7,11]=>00111010101=>10101011100
[11,9,12,5,3,6,2,4,1,8,10,7]=>00111000111=>11100011100
[10,11,12,5,3,6,2,4,1,9,8,7]=>00111011001=>10011011100
[12,10,7,5,3,8,2,4,6,1,9,11]=>00011110101=>10101111000
[11,12,7,5,3,8,2,4,6,1,10,9]=>00011110101=>10101111000
[12,9,7,5,3,10,2,4,6,8,1,11]=>00010111101=>10111101000
[11,9,7,5,3,12,2,4,6,8,10,1]=>00010101111=>11110101000
[10,11,7,5,3,12,2,4,6,9,8,1]=>00010111011=>11011101000
[12,8,9,5,3,10,2,4,7,6,1,11]=>00011101101=>10110111000
[11,8,9,5,3,12,2,4,7,6,10,1]=>00010101111=>11110101000
[10,8,11,5,3,12,2,4,7,9,6,1]=>00011001111=>11110011000
[9,10,11,5,3,12,2,4,8,7,6,1]=>00011110011=>11001111000
[12,10,6,7,3,8,2,5,4,1,9,11]=>00110110101=>10101101100
[11,12,6,7,3,8,2,5,4,1,10,9]=>00110110101=>10101101100
[12,9,6,7,3,10,2,5,4,8,1,11]=>00010111101=>10111101000
[11,9,6,7,3,12,2,5,4,8,10,1]=>00010101111=>11110101000
[10,11,6,7,3,12,2,5,4,9,8,1]=>00010111011=>11011101000
[12,8,6,9,3,10,2,5,7,4,1,11]=>00100111101=>10111100100
[11,8,6,9,3,12,2,5,7,4,10,1]=>00000111111=>11111100000
[10,8,6,11,3,12,2,5,7,9,4,1]=>00100011111=>11111000100
[9,10,6,11,3,12,2,5,8,7,4,1]=>00100110111=>11101100100
[12,7,8,9,3,10,2,6,5,4,1,11]=>00111001101=>10110011100
[11,7,8,9,3,12,2,6,5,4,10,1]=>00011001111=>11110011000
[10,7,8,11,3,12,2,6,5,9,4,1]=>00101001111=>11110010100
[9,7,10,11,3,12,2,6,8,5,4,1]=>00110011011=>11011001100
[12,10,8,4,5,6,3,2,1,7,9,11]=>11001010101=>10101010011
[11,12,8,4,5,6,3,2,1,7,10,9]=>11001010101=>10101010011
[12,9,10,4,5,6,3,2,1,8,7,11]=>11001010101=>10101010011
[11,9,12,4,5,6,3,2,1,8,10,7]=>11001000111=>11100010011
[10,11,12,4,5,6,3,2,1,9,8,7]=>11001011001=>10011010011
[12,10,7,4,5,8,3,2,6,1,9,11]=>01001110101=>10101110010
[11,12,7,4,5,8,3,2,6,1,10,9]=>01001110101=>10101110010
[12,9,7,4,5,10,3,2,6,8,1,11]=>01000111101=>10111100010
[11,9,7,4,5,12,3,2,6,8,10,1]=>01000101111=>11110100010
[10,11,7,4,5,12,3,2,6,9,8,1]=>01000111011=>11011100010
[12,8,9,4,5,10,3,2,7,6,1,11]=>01001101101=>10110110010
[11,8,9,4,5,12,3,2,7,6,10,1]=>01000101111=>11110100010
[10,8,11,4,5,12,3,2,7,9,6,1]=>01001001111=>11110010010
[9,10,11,4,5,12,3,2,8,7,6,1]=>01001110011=>11001110010
[12,10,6,4,7,8,3,5,2,1,9,11]=>10011010101=>10101011001
[11,12,6,4,7,8,3,5,2,1,10,9]=>10011010101=>10101011001
[12,9,6,4,7,10,3,5,2,8,1,11]=>00011011101=>10111011000
[11,9,6,4,7,12,3,5,2,8,10,1]=>00011001111=>11110011000
[10,11,6,4,7,12,3,5,2,9,8,1]=>00011011011=>11011011000
[12,8,6,4,9,10,3,5,7,2,1,11]=>10001110101=>10101110001
[11,8,6,4,9,12,3,5,7,2,10,1]=>00001110111=>11101110000
[10,8,6,4,11,12,3,5,7,9,2,1]=>10001011101=>10111010001
[9,10,6,4,11,12,3,5,8,7,2,1]=>10001110101=>10101110001
[12,7,8,4,9,10,3,6,5,2,1,11]=>10011010101=>10101011001
[11,7,8,4,9,12,3,6,5,2,10,1]=>00011010111=>11101011000
[10,7,8,4,11,12,3,6,5,9,2,1]=>10001011101=>10111010001
[9,7,10,4,11,12,3,6,8,5,2,1]=>10010011101=>10111001001
[12,10,5,6,7,8,4,3,2,1,9,11]=>11100010101=>10101000111
[11,12,5,6,7,8,4,3,2,1,10,9]=>11100010101=>10101000111
[12,9,5,6,7,10,4,3,2,8,1,11]=>01100011101=>10111000110
[11,9,5,6,7,12,4,3,2,8,10,1]=>01100001111=>11110000110
[10,11,5,6,7,12,4,3,2,9,8,1]=>01100011011=>11011000110
[12,8,5,6,9,10,4,3,7,2,1,11]=>10100110101=>10101100101
[11,8,5,6,9,12,4,3,7,2,10,1]=>00100110111=>11101100100
[10,8,5,6,11,12,4,3,7,9,2,1]=>10100011101=>10111000101
[9,10,5,6,11,12,4,3,8,7,2,1]=>10100110101=>10101100101
[12,7,5,8,9,10,4,6,3,2,1,11]=>11001100101=>10100110011
[11,7,5,8,9,12,4,6,3,2,10,1]=>01001100111=>11100110010
[10,7,5,8,11,12,4,6,3,9,2,1]=>10001101101=>10110110001
[8,9,5,10,11,12,4,7,6,3,2,1]=>11001101001=>10010110011
[12,6,7,8,9,10,5,4,3,2,1,11]=>11110000101=>10100001111
[11,6,7,8,9,12,5,4,3,2,10,1]=>01110000111=>11100001110
[9,6,7,10,11,12,5,4,8,3,2,1]=>11010011001=>10011001011
[8,6,9,10,11,12,5,7,4,3,2,1]=>11100110001=>10001100111
[2,3,4,5,6,7,8,11,10,1,9]=>0000000011=>1100000000
[2,3,4,5,6,7,8,9,12,11,1,10]=>00000000011=>11000000000
[11,3,4,5,6,7,8,10,1,2,9]=>0000000011=>1100000000
[2,10,4,5,6,7,9,1,3,8]=>000000011=>110000000
[10,3,4,5,6,7,1,9,2,8]=>000001011=>110100000
[2,7,4,1,5,8,3,6]=>0010011=>1100100
[2,1,6,4,7,8,3,5]=>1000101=>1010001
[5,7,8,3,4,2,1,6]=>1010001=>1000101
[4,7,5,3,8,2,6,1]=>0001111=>1111000
[2,6,4,7,8,5,3,1]=>0101101=>1011010
[7,8,4,5,6,1,3,2]=>0100101=>1010010
[2,5,1,8,4,6,7,3]=>0001011=>1101000
[5,2,8,4,6,7,1,3]=>0001011=>1101000
[6,5,8,3,4,2,1,7]=>1010101=>1010101
[1,3,5,8,4,6,7,2]=>0000011=>1100000
[8,2,7,6,3,4,5,1]=>0001111=>1111000
[6,8,7,3,2,1,4,5]=>1100011=>1100011
[3,4,8,2,7,1,5,6]=>0000011=>1100000
[7,2,6,1,4,8,3,5]=>0000111=>1110000
[7,8,1,2,4,6,3,5]=>0000101=>1010000
[7,2,8,3,4,5,1,6]=>0001011=>1101000
[6,1,8,3,4,2,5,7]=>0010101=>1010100
[7,5,1,2,4,3,8,6]=>0011011=>1101100
[7,6,8,1,4,2,3,5]=>0010011=>1100100
[2,4,3,7,8,5,6,1]=>0010101=>1010100
[2,1,7,6,3,4,5,8]=>1000110=>0110001
[6,3,5,2,1,8,4,7]=>1001101=>1011001
[6,1,5,3,8,2,4,7]=>0001101=>1011000
[2,3,6,8,5,1,7,4]=>0001011=>1101000
[3,2,4,8,6,1,7,5]=>0100111=>1110010
[2,1,3,8,4,5,7,6]=>1000011=>1100001
[3,1,2,8,5,4,7,6]=>0101011=>1101010
[2,1,3,7,8,4,6,5]=>1000101=>1010001
[2,1,3,8,4,7,6,5]=>1000111=>1110001
[3,1,2,8,4,5,7,6]=>0100011=>1100010
[1,2,8,7,5,4,6,3]=>0001111=>1111000
[4,6,7,2,3,8,1,5]=>0000011=>1100000
[3,2,6,5,7,8,1,4]=>0100101=>1010010
[3,2,7,5,6,8,1,4]=>0100011=>1100010
[2,1,8,7,4,6,5,3]=>1001111=>1111001
[6,1,5,8,4,7,3,2]=>0100111=>1110010
[1,4,6,8,5,7,2,3]=>0000011=>1100000
[2,8,5,1,6,4,3,7]=>0011101=>1011100
[2,4,7,1,8,3,6,5]=>0000111=>1110000
[6,1,5,4,2,3,8,7]=>0011101=>1011100
[6,4,5,1,2,8,3,7]=>0001101=>1011000
[8,4,1,5,7,6,3,2]=>0110111=>1110110
[8,1,6,3,5,2,4,7]=>0001101=>1011000
[4,6,2,5,3,8,1,7]=>0001101=>1011000
[4,6,5,2,1,8,3,7]=>1001101=>1011001
[5,8,4,3,6,7,2,1]=>1010011=>1100101
[6,8,2,1,5,3,4,7]=>1001001=>1001001
[2,5,3,8,6,7,4,1]=>0011011=>1101100
[3,2,6,5,1,8,4,7]=>0101101=>1011010
[7,4,5,8,1,6,2,3]=>0000111=>1110000
[4,5,8,1,6,7,3,2]=>0100011=>1100010
[5,1,8,4,6,7,3,2]=>0101011=>1101010
[6,5,3,8,1,7,2,4]=>0001111=>1111000
[8,3,7,1,6,2,4,5]=>0000111=>1110000
[8,1,4,6,5,7,2,3]=>0000111=>1110000
[8,1,7,5,6,4,2,3]=>0010111=>1110100
[8,6,1,5,3,7,2,4]=>0001111=>1111000
[7,2,3,6,8,1,5,4]=>0001011=>1101000
[2,6,3,7,8,1,4,5]=>0000101=>1010000
[6,3,8,7,2,1,5,4]=>1001111=>1111001
[7,2,5,6,3,4,8,1]=>0000111=>1110000
[7,2,8,6,3,1,5,4]=>0101111=>1111010
[7,2,4,5,8,6,3,1]=>0100111=>1110010
[6,3,8,4,7,2,5,1]=>0001111=>1111000
[7,2,3,6,8,5,4,1]=>0011011=>1101100
[7,2,8,5,4,1,3,6]=>0011011=>1101100
[7,4,5,2,8,1,6,3]=>0001111=>1111000
[7,5,4,2,8,1,6,3]=>0011111=>1111100
[7,6,3,2,8,4,5,1]=>0101111=>1111010
[7,2,3,6,8,4,5,1]=>0001011=>1101000
[7,2,5,4,8,3,6,1]=>0001111=>1111000
[7,2,8,3,6,1,4,5]=>0000111=>1110000
[7,4,5,2,8,3,6,1]=>0001111=>1111000
[3,1,6,7,4,5,2,8]=>0101010=>0101010
[3,1,5,4,7,6,2,8]=>0101110=>0111010
[7,3,6,8,2,4,5,1]=>0001011=>1101000
[5,1,3,2,4,6,8,7]=>0101001=>1001010
[8,4,2,5,1,7,3,6]=>0011011=>1101100
[6,4,2,5,7,3,8,1]=>0010111=>1110100
[5,7,8,4,2,3,6,1]=>0010101=>1010100
[6,4,5,2,8,3,7,1]=>0001111=>1111000
[6,5,2,4,3,8,7,1]=>0011111=>1111100
[6,5,3,4,1,8,2,7]=>0011101=>1011100
[6,4,5,3,8,1,2,7]=>0001101=>1011000
[5,6,4,8,3,1,2,7]=>0100101=>1010010
[7,2,4,6,3,8,5,1]=>0001111=>1111000
[2,8,3,7,6,1,5,4]=>0001111=>1111000
[5,4,2,6,8,7,3,1]=>0111011=>1101110
[3,7,2,5,8,6,4,1]=>0010111=>1110100
[4,6,5,3,8,1,7,2]=>0001111=>1111000
[2,4,8,7,6,1,5,3]=>0001111=>1111000
[3,2,8,7,4,6,5,1]=>0101111=>1111010
[8,2,6,5,1,4,3,7]=>0011101=>1011100
[4,8,5,2,7,6,3,1]=>0101111=>1111010
[2,8,6,5,7,1,3,4]=>0000111=>1110000
[3,8,4,7,2,1,6,5]=>1000111=>1110001
[4,8,5,1,7,6,3,2]=>0101111=>1111010
[5,8,1,7,6,2,3,4]=>0000111=>1110000
[3,4,6,2,5,7,1,8]=>0000110=>0110000
[1,7,5,2,6,8,3,4]=>0001011=>1101000
[5,1,7,2,4,6,3,8]=>0001110=>0111000
[6,8,2,1,3,4,7,5]=>1000011=>1100001
[5,2,1,7,6,4,3,8]=>1011110=>0111101
[7,4,8,3,6,5,1,2]=>0001111=>1111000
[6,4,8,5,1,7,2,3]=>0001111=>1111000
[5,2,8,1,3,6,7,4]=>0001011=>1101000
[6,3,2,7,4,5,8,1]=>0100111=>1110010
[7,4,3,8,5,6,1,2]=>0010111=>1110100
[6,2,1,8,7,4,5,3]=>1001111=>1111001
[6,2,1,8,7,3,5,4]=>1001111=>1111001
[5,2,1,7,6,3,4,8]=>1001110=>0111001
[4,2,6,8,5,7,1,3]=>0010011=>1100100
[8,6,4,3,2,7,5,1]=>0111111=>1111110
[1,3,4,7,8,2,6,5]=>0000101=>1010000
[1,5,4,3,8,7,2,6]=>0011011=>1101100
[1,2,5,8,4,3,6,7]=>0010001=>1000100
[1,5,8,2,6,4,3,7]=>0010101=>1010100
[10,9,8,6,4,2,1,3,5,7]=>101010111=>111010101
[10,8,7,6,4,2,1,3,5,9]=>101011101=>101110101
[10,7,9,6,4,2,1,3,8,5]=>101010111=>111010101
[10,9,8,7,6,4,2,1,3,5]=>101011111=>111110101
[10,8,6,5,4,2,1,3,7,9]=>101110101=>101011101
[10,9,8,6,5,4,2,1,3,7]=>101110111=>111011101
[10,8,5,7,4,2,1,6,3,9]=>101011101=>101110101
[10,5,9,7,4,2,1,6,8,3]=>101001111=>111100101
[10,9,8,5,7,4,2,1,6,3]=>101011111=>111110101
[10,8,7,6,5,4,2,1,3,9]=>101111101=>101111101
[10,7,9,6,5,4,2,1,8,3]=>101110111=>111011101
[10,6,9,8,5,7,2,1,4,3]=>101001111=>111100101
[10,8,6,4,3,2,1,5,7,9]=>111010101=>101010111
[10,9,8,6,4,3,2,1,5,7]=>111010111=>111010111
[10,8,7,6,4,3,2,1,5,9]=>111011101=>101110111
[10,7,9,6,4,3,2,1,8,5]=>111010111=>111010111
[10,8,6,3,5,2,4,1,7,9]=>001110101=>101011100
[10,9,8,6,3,5,2,4,1,7]=>001110111=>111011100
[10,8,3,7,5,2,4,6,1,9]=>000111101=>101111000
[10,3,9,7,5,2,4,6,8,1]=>000101111=>111101000
[10,9,8,3,7,5,2,4,6,1]=>000111111=>111111000
[10,8,7,6,3,5,2,4,1,9]=>001111101=>101111100
[10,7,9,6,3,5,2,4,8,1]=>000110111=>111011000
[10,9,3,8,6,5,2,7,4,1]=>001111111=>111111100
[10,9,8,7,6,3,5,2,4,1]=>001111111=>111111100
[10,8,6,5,4,3,2,1,7,9]=>111110101=>101011111
[10,8,5,7,4,3,2,6,1,9]=>011011101=>101110110
[10,5,9,7,4,3,2,6,8,1]=>011001111=>111100110
[10,9,8,5,7,4,3,2,6,1]=>011011111=>111110110
[10,8,4,7,6,3,5,2,1,9]=>100111101=>101111001
[10,4,9,7,6,3,5,2,8,1]=>000111111=>111111000
[10,4,9,6,8,3,5,7,2,1]=>100001111=>111100001
[10,9,8,4,7,6,3,5,2,1]=>100111111=>111111001
[10,7,9,6,5,4,3,2,8,1]=>011110111=>111011110
[10,6,9,8,5,4,3,7,2,1]=>101101111=>111101101
[10,5,9,8,7,4,6,3,2,1]=>110011111=>111110011
[12,11,10,8,6,4,2,1,3,5,7,9]=>10101010111=>11101010101
[12,10,9,8,6,4,2,1,3,5,7,11]=>10101011101=>10111010101
[12,9,11,8,6,4,2,1,3,5,10,7]=>10101010111=>11101010101
[12,11,10,9,8,6,4,2,1,3,5,7]=>10101011111=>11111010101
[12,10,8,7,6,4,2,1,3,5,9,11]=>10101110101=>10101110101
[12,11,10,8,7,6,4,2,1,3,5,9]=>10101110111=>11101110101
[12,10,7,9,6,4,2,1,3,8,5,11]=>10101011101=>10111010101
[12,7,11,9,6,4,2,1,3,8,10,5]=>10101001111=>11110010101
[12,11,10,7,9,6,4,2,1,3,8,5]=>10101011111=>11111010101
[12,10,9,8,7,6,4,2,1,3,5,11]=>10101111101=>10111110101
[12,9,11,8,7,6,4,2,1,3,10,5]=>10101110111=>11101110101
[12,8,11,10,7,9,4,2,1,3,6,5]=>10101001111=>11110010101
[12,11,10,9,8,7,6,4,2,1,3,5]=>10101111111=>11111110101
[12,10,8,6,5,4,2,1,3,7,9,11]=>10111010101=>10101011101
[12,11,10,8,6,5,4,2,1,3,7,9]=>10111010111=>11101011101
[12,10,9,8,6,5,4,2,1,3,7,11]=>10111011101=>10111011101
[12,9,11,8,6,5,4,2,1,3,10,7]=>10111010111=>11101011101
[12,11,10,9,8,6,5,4,2,1,3,7]=>10111011111=>11111011101
[12,10,8,5,7,4,2,1,6,3,9,11]=>10101110101=>10101110101
[12,11,10,8,5,7,4,2,1,6,3,9]=>10101110111=>11101110101
[12,10,5,9,7,4,2,1,6,8,3,11]=>10100111101=>10111100101
[12,5,11,9,7,4,2,1,6,8,10,3]=>10100101111=>11110100101
[12,11,10,5,9,7,4,2,1,6,8,3]=>10100111111=>11111100101
[12,10,9,8,5,7,4,2,1,6,3,11]=>10101111101=>10111110101
[12,11,5,10,8,7,4,2,1,9,6,3]=>10101111111=>11111110101
[12,11,10,9,8,5,7,4,2,1,6,3]=>10101111111=>11111110101
[12,10,8,7,6,5,4,2,1,3,9,11]=>10111110101=>10101111101
[12,11,10,8,7,6,5,4,2,1,3,9]=>10111110111=>11101111101
[12,10,7,9,6,5,4,2,1,8,3,11]=>10111011101=>10111011101
[12,7,11,9,6,5,4,2,1,8,10,3]=>10111001111=>11110011101
[12,11,10,7,9,6,5,4,2,1,8,3]=>10111011111=>11111011101
[12,10,6,9,8,5,7,2,1,4,3,11]=>10100111101=>10111100101
[12,6,11,8,10,5,7,2,1,9,4,3]=>10100101111=>11110100101
[12,11,10,6,9,8,5,7,2,1,4,3]=>10100111111=>11111100101
[12,10,9,8,7,6,5,4,2,1,3,11]=>10111111101=>10111111101
[12,9,11,8,7,6,5,4,2,1,10,3]=>10111110111=>11101111101
[12,8,11,10,7,6,5,9,2,1,4,3]=>10101101111=>11110110101
[12,11,10,9,8,7,6,5,4,2,1,3]=>10111111111=>11111111101
[12,10,8,6,4,3,2,1,5,7,9,11]=>11101010101=>10101010111
[12,11,10,8,6,4,3,2,1,5,7,9]=>11101010111=>11101010111
[12,10,9,8,6,4,3,2,1,5,7,11]=>11101011101=>10111010111
[12,9,11,8,6,4,3,2,1,5,10,7]=>11101010111=>11101010111
[12,11,10,9,8,6,4,3,2,1,5,7]=>11101011111=>11111010111
[12,10,8,7,6,4,3,2,1,5,9,11]=>11101110101=>10101110111
[12,11,10,8,7,6,4,3,2,1,5,9]=>11101110111=>11101110111
[12,10,7,9,6,4,3,2,1,8,5,11]=>11101011101=>10111010111
[12,7,11,9,6,4,3,2,1,8,10,5]=>11101001111=>11110010111
[12,11,10,7,9,6,4,3,2,1,8,5]=>11101011111=>11111010111
[12,10,9,8,7,6,4,3,2,1,5,11]=>11101111101=>10111110111
[12,9,11,8,7,6,4,3,2,1,10,5]=>11101110111=>11101110111
[12,8,11,10,7,9,4,3,2,1,6,5]=>11101001111=>11110010111
[12,11,10,9,8,7,6,4,3,2,1,5]=>11101111111=>11111110111
[12,10,8,6,3,5,2,4,1,7,9,11]=>00111010101=>10101011100
[12,11,10,8,6,3,5,2,4,1,7,9]=>00111010111=>11101011100
[12,10,9,8,6,3,5,2,4,1,7,11]=>00111011101=>10111011100
[12,9,11,8,6,3,5,2,4,1,10,7]=>00111010111=>11101011100
[12,11,10,9,8,6,3,5,2,4,1,7]=>00111011111=>11111011100
[12,10,8,3,7,5,2,4,6,1,9,11]=>00011110101=>10101111000
[12,11,10,8,3,7,5,2,4,6,1,9]=>00011110111=>11101111000
[12,10,3,9,7,5,2,4,6,8,1,11]=>00010111101=>10111101000
[12,3,11,9,7,5,2,4,6,8,10,1]=>00010101111=>11110101000
[12,11,10,3,9,7,5,2,4,6,8,1]=>00010111111=>11111101000
[12,10,9,8,3,7,5,2,4,6,1,11]=>00011111101=>10111111000
[12,9,11,8,3,7,5,2,4,6,10,1]=>00010110111=>11101101000
[12,11,3,10,8,7,5,2,4,9,6,1]=>00011111111=>11111111000
[12,11,10,9,8,3,7,5,2,4,6,1]=>00011111111=>11111111000
[12,11,10,8,7,6,3,5,2,4,1,9]=>00111110111=>11101111100
[12,10,7,9,6,3,5,2,4,8,1,11]=>00011011101=>10111011000
[12,7,11,9,6,3,5,2,4,8,10,1]=>00011001111=>11110011000
[12,11,10,7,9,6,3,5,2,4,8,1]=>00011011111=>11111011000
[12,10,9,3,8,6,5,2,7,4,1,11]=>00111111101=>10111111100
[12,9,11,3,8,6,5,2,7,4,10,1]=>00011110111=>11101111000
[12,11,10,9,3,8,6,5,2,7,4,1]=>00111111111=>11111111100
[12,10,9,8,7,6,3,5,2,4,1,11]=>00111111101=>10111111100
[12,9,11,8,7,6,3,5,2,4,10,1]=>00011110111=>11101111000
[12,8,11,10,7,6,3,5,2,9,4,1]=>00111101111=>11110111100
[12,11,10,3,9,7,6,8,2,5,4,1]=>00110111111=>11111101100
[12,11,10,9,8,7,6,3,5,2,4,1]=>00111111111=>11111111100
[12,10,8,6,5,4,3,2,1,7,9,11]=>11111010101=>10101011111
[12,11,10,8,6,5,4,3,2,1,7,9]=>11111010111=>11101011111
[12,10,9,8,6,5,4,3,2,1,7,11]=>11111011101=>10111011111
[12,9,11,8,6,5,4,3,2,1,10,7]=>11111010111=>11101011111
[12,11,10,9,8,6,5,4,3,2,1,7]=>11111011111=>11111011111
[12,10,8,5,7,4,3,2,6,1,9,11]=>01101110101=>10101110110
[12,11,10,8,5,7,4,3,2,6,1,9]=>01101110111=>11101110110
[12,10,5,9,7,4,3,2,6,8,1,11]=>01100111101=>10111100110
[12,11,10,5,9,7,4,3,2,6,8,1]=>01100111111=>11111100110
[12,10,9,8,5,7,4,3,2,6,1,11]=>01101111101=>10111110110
[12,9,11,8,5,7,4,3,2,6,10,1]=>01100110111=>11101100110
[12,11,5,10,8,7,4,3,2,9,6,1]=>01101111111=>11111110110
[12,11,10,9,8,5,7,4,3,2,6,1]=>01101111111=>11111110110
[12,10,8,4,7,6,3,5,2,1,9,11]=>10011110101=>10101111001
[12,11,10,8,4,7,6,3,5,2,1,9]=>10011110111=>11101111001
[12,10,4,9,7,6,3,5,2,8,1,11]=>00011111101=>10111111000
[12,4,11,9,7,6,3,5,2,8,10,1]=>00011101111=>11110111000
[12,11,10,4,9,7,6,3,5,2,8,1]=>00011111111=>11111111000
[12,10,4,9,6,8,3,5,7,2,1,11]=>10000111101=>10111100001
[12,4,11,9,6,8,3,5,7,2,10,1]=>00000111111=>11111100000
[12,4,11,6,10,8,3,5,7,9,2,1]=>10000011111=>11111000001
[12,10,9,8,4,7,6,3,5,2,1,11]=>10011111101=>10111111001
[12,9,11,8,4,7,6,3,5,2,10,1]=>00011110111=>11101111000
[12,11,4,10,7,9,6,3,8,5,2,1]=>10011011111=>11111011001
[12,11,10,9,8,4,7,6,3,5,2,1]=>10011111111=>11111111001
[12,10,8,7,6,5,4,3,2,1,9,11]=>11111110101=>10101111111
[12,11,10,8,7,6,5,4,3,2,1,9]=>11111110111=>11101111111
[12,10,7,9,6,5,4,3,2,8,1,11]=>01111011101=>10111011110
[12,7,11,9,6,5,4,3,2,8,10,1]=>01111001111=>11110011110
[12,11,10,7,9,6,5,4,3,2,8,1]=>01111011111=>11111011110
[12,10,6,9,8,5,4,3,7,2,1,11]=>10110111101=>10111101101
[12,6,11,9,8,5,4,3,7,2,10,1]=>00110111111=>11111101100
[12,11,10,6,9,8,5,4,3,7,2,1]=>10110111111=>11111101101
[12,10,5,9,8,7,4,6,3,2,1,11]=>11001111101=>10111110011
[12,5,11,9,8,7,4,6,3,2,10,1]=>01001111111=>11111110010
[12,11,10,5,9,8,7,4,6,3,2,1]=>11001111111=>11111110011
[12,9,11,8,7,6,5,4,3,2,10,1]=>01111110111=>11101111110
[12,8,11,10,7,6,5,4,3,9,2,1]=>10111101111=>11110111101
[12,7,11,10,9,6,5,4,8,3,2,1]=>11011011111=>11111011011
[12,6,11,10,9,8,5,7,4,3,2,1]=>11100111111=>11111100111
[3,5,6,2,4,7,8,1]=>0000101=>1010000
[3,5,6,7,2,4,8,1]=>0000011=>1100000
[3,5,7,6,8,2,4,1]=>0010011=>1100100
[3,5,7,2,6,8,4,1]=>0010011=>1100100
[3,5,2,7,6,8,4,1]=>0011011=>1101100
[3,5,7,4,2,6,8,1]=>0010011=>1100100
[3,5,4,7,2,6,8,1]=>0001011=>1101000
[3,4,5,7,2,6,8,1]=>0000011=>1100000
[3,4,5,7,2,8,6,1]=>0000111=>1110000
[3,5,4,7,8,2,6,1]=>0001101=>1011000
[3,5,4,7,2,8,6,1]=>0001111=>1111000
[3,2,5,7,4,8,6,1]=>0100111=>1110010
[3,5,7,4,2,8,6,1]=>0010111=>1110100
[3,5,7,8,4,2,6,1]=>0010101=>1010100
[2,3,5,7,8,4,6,1]=>0000101=>1010000
[3,5,2,7,8,6,4,1]=>0011101=>1011100
[3,5,7,8,2,6,4,1]=>0010101=>1010100
[3,5,7,8,6,2,4,1]=>0010101=>1010100
[3,2,5,6,7,8,9,1,4]=>01000001=>10000010
[4,2,5,6,7,3,8,1]=>0010011=>1100100
[4,2,5,6,7,8,9,3,1]=>01100001=>10000110
[3,2,4,5,6,7,8,9,10,11,1]=>0100000001=>1000000010
[8,6,1,4,3,5,2,7]=>0011101=>1011100
[6,1,8,4,3,5,2,7]=>0011101=>1011100
[5,1,6,4,8,2,3,7]=>0001101=>1011000
[8,1,4,2,5,3,6,7]=>0011001=>1001100
[2,8,4,1,5,3,6,7]=>0011001=>1001100
[8,4,1,3,5,2,6,7]=>0011001=>1001100
[4,1,8,3,5,2,6,7]=>0011001=>1001100
[8,3,1,2,5,4,6,7]=>0101001=>1001010
[3,1,8,2,5,4,6,7]=>0101001=>1001010
[4,2,5,1,8,7,6,3]=>0011111=>1111100
[5,2,4,8,1,7,6,3]=>0001111=>1111000
[7,3,2,4,6,8,1,5]=>0100011=>1100010
[1,4,8,6,7,2,5,3]=>0001011=>1101000
[1,4,5,7,3,8,2,6]=>0000011=>1100000
[1,2,5,6,7,4,8,9,3]=>00000101=>10100000
[4,6,8,1,2,5,3,7]=>0001001=>1001000
[3,5,6,8,2,1,4,7]=>1000001=>1000001
[8,2,5,4,1,3,7,6]=>0011011=>1101100
[2,4,5,8,6,3,1,7]=>0100101=>1010010
[5,4,8,2,3,1,7,6]=>0101011=>1101010
[4,7,5,8,2,3,1,6]=>0100011=>1100010
[4,6,7,5,1,8,3,2]=>0101011=>1101010
[1,7,3,6,5,8,2,4]=>0000111=>1110000
[8,3,4,2,6,7,1,5]=>0010011=>1100100
[7,5,3,8,6,2,1,4]=>1001111=>1111001
[7,3,1,8,2,6,5,4]=>0101111=>1111010
[4,6,7,5,2,8,3,1]=>0101011=>1101010
[5,8,7,2,4,3,1,6]=>0110011=>1100110
[5,1,2,8,6,7,3,4]=>0001011=>1101000
[2,5,7,8,6,1,4,3]=>0010101=>1010100
[7,2,6,8,4,5,1,3]=>0001011=>1101000
[5,1,7,6,8,2,3,4]=>0001011=>1101000
[1,7,6,2,4,3,8,5]=>0010111=>1110100
[7,1,6,2,4,5,3,8]=>0001110=>0111000
[5,7,1,6,2,3,4,8]=>0000110=>0110000
[6,2,5,8,3,4,1,7]=>0010101=>1010100
[5,6,8,7,1,3,2,4]=>0100011=>1100010
[1,5,3,4,8,2,6,7]=>0001001=>1001000
[2,1,3,6,5,8,4,7]=>1000101=>1010001
[2,8,6,5,7,4,3,1]=>0110111=>1110110
[2,8,6,5,7,4,1,3]=>0010111=>1110100
[6,5,2,7,4,3,1,8]=>0111110=>0111110
[6,5,2,8,4,3,7,1]=>0011111=>1111100
[7,5,8,3,4,2,1,6]=>1010011=>1100101
[7,6,8,5,2,4,1,3]=>0011011=>1101100
[5,3,7,2,4,1,8,6]=>0011011=>1101100
[5,1,2,8,6,3,7,4]=>0001111=>1111000
[6,1,5,7,2,4,3,8]=>0010110=>0110100
[4,1,8,2,6,5,7,3]=>0010111=>1110100
[6,1,4,7,8,5,3,2]=>0101101=>1011010
[6,1,5,7,8,4,2,3]=>0010101=>1010100
[4,6,1,5,7,2,8,3]=>0000111=>1110000
[2,5,8,4,6,3,7,1]=>0000111=>1110000
[4,3,7,1,2,6,8,5]=>0010011=>1100100
[8,1,6,5,2,7,4,3]=>0011111=>1111100
[6,8,1,5,2,7,4,3]=>0011011=>1101100
[5,6,2,7,4,8,3,1]=>0100111=>1110010
[1,7,3,2,4,8,6,5]=>0100111=>1110010
[4,3,1,8,2,6,7,5]=>0110011=>1100110
[4,8,1,3,2,5,7,6]=>0100011=>1100010
[1,7,5,3,8,6,2,4]=>0001111=>1111000
[2,5,3,8,1,4,7,6]=>0001011=>1101000
[4,2,5,8,1,3,7,6]=>0010011=>1100100
[8,1,2,4,3,5,7,6]=>0010011=>1100100
[2,4,3,8,1,5,7,6]=>0010011=>1100100
[3,1,7,4,8,6,5,2]=>0101111=>1111010
[6,4,5,3,2,8,7,1]=>0101111=>1111010
[2,7,3,8,5,1,6,4]=>0001111=>1111000
[8,7,3,2,5,6,4,1]=>0110111=>1110110
[3,1,8,2,6,5,4,7]=>0101101=>1011010
[7,6,2,8,1,4,5,3]=>0001111=>1111000
[2,3,8,4,1,5,7,6]=>0010011=>1100100
[8,4,2,3,1,5,7,6]=>0110011=>1100110
[8,2,3,4,1,5,7,6]=>0010011=>1100100
[7,1,6,2,4,8,3,5]=>0000111=>1110000
[2,7,8,1,4,3,6,5]=>0010101=>1010100
[6,5,8,1,3,2,4,7]=>0100101=>1010010
[2,1,8,5,3,4,6,7]=>1001001=>1001001
[8,4,1,3,2,5,6,7]=>0110001=>1000110
[8,6,1,2,3,5,4,7]=>0001101=>1011000
[7,8,1,5,2,4,6,3]=>0001101=>1011000
[2,8,6,3,1,5,4,7]=>0101101=>1011010
[5,7,2,8,4,1,6,3]=>0010111=>1110100
[2,5,6,3,8,1,4,7]=>0000101=>1010000
[1,3,4,5,6,7,2,8,9]=>00000100=>00100000
[7,4,5,6,8,1,3,2]=>0100011=>1100010
[7,6,8,1,4,5,3,2]=>0101011=>1101010
[7,5,1,8,4,6,3,2]=>0101111=>1111010
[1,7,8,5,6,4,3,2]=>0110101=>1010110
[2,8,1,7,4,5,3,6]=>0001011=>1101000
[7,3,6,2,5,4,8,1]=>0001111=>1111000
[1,6,2,3,5,8,4,7]=>0000101=>1010000
[1,8,5,6,4,3,7,2]=>0010111=>1110100
[2,6,8,4,5,1,7,3]=>0001011=>1101000
[4,6,5,7,8,1,3,2]=>0100101=>1010010
[2,5,8,6,4,7,1,3]=>0000111=>1110000
[5,3,2,1,7,8,4,6]=>1101001=>1001011
[8,4,1,3,6,7,2,5]=>0010011=>1100100
[1,6,5,3,8,4,7,2]=>0001111=>1111000
[7,6,2,3,5,1,4,8]=>0001110=>0111000
[6,2,5,3,4,8,1,7]=>0001101=>1011000
[6,2,5,3,4,8,7,1]=>0001111=>1111000
[2,6,5,3,4,8,1,7]=>0001101=>1011000
[5,3,4,8,1,7,2,6]=>0001011=>1101000
[5,1,3,4,8,7,2,6]=>0001011=>1101000
[1,5,3,4,8,7,2,6]=>0001011=>1101000
[5,1,3,8,4,7,6,2]=>0001111=>1111000
[5,3,8,1,4,7,6,2]=>0001111=>1111000
[4,3,5,8,1,7,6,2]=>0010111=>1110100
[3,6,5,4,8,1,2,7]=>0001101=>1011000
[3,6,5,4,8,2,7,1]=>0001111=>1111000
[3,5,2,4,8,7,6,1]=>0001111=>1111000
[2,5,3,6,8,4,1,7]=>0011001=>1001100
[4,6,2,5,1,7,8,3]=>0001101=>1011000
[2,3,6,5,8,4,1,7]=>0010101=>1010100
[2,3,1,7,4,8,6,5]=>0100111=>1110010
[2,3,8,7,6,4,1,5]=>0010111=>1110100
[2,6,3,7,4,1,5,8]=>0010110=>0110100
[7,5,2,3,1,6,4,8]=>0101110=>0111010
[1,8,3,6,4,2,7,5]=>0010111=>1110100
[2,1,7,4,8,5,3,6]=>1001011=>1101001
[8,1,7,3,2,5,4,6]=>0101011=>1101010
[7,8,5,2,6,4,3,1]=>0111101=>1011110
[4,2,8,1,3,6,7,5]=>0010011=>1100100
[8,1,2,5,7,4,6,3]=>0000111=>1110000
[7,4,6,3,1,2,5,8]=>0100110=>0110010
[6,4,1,3,7,2,5,8]=>0010110=>0110100
[3,7,5,1,4,6,2,8]=>0001110=>0111000
[6,8,7,4,1,5,2,3]=>0011011=>1101100
[8,6,4,7,5,1,3,2]=>0101111=>1111010
[6,1,2,4,7,8,3,5]=>0000101=>1010000
[2,4,6,5,7,1,8,3]=>0000111=>1110000
[3,2,8,9,10,1,4,5,6,7]=>010000001=>100000010
[4,2,6,7,8,5,3,1]=>0111001=>1001110
[6,2,4,7,8,5,3,1]=>0101101=>1011010
[3,5,2,1,7,8,6,4]=>1001101=>1011001
[4,2,7,8,6,5,1,3]=>0011101=>1011100
[1,2,7,8,6,4,5,3]=>0001101=>1011000
[4,8,1,2,6,5,3,7]=>0001101=>1011000
[7,1,6,3,2,4,8,5]=>0100111=>1110010
[6,4,8,1,2,3,7,5]=>0000111=>1110000
[7,4,1,3,6,8,5,2]=>0011011=>1101100
[7,1,8,3,2,6,5,4]=>0101111=>1111010
[7,2,5,1,6,4,3,8]=>0011110=>0111100
[5,2,7,1,4,6,3,8]=>0001110=>0111000
[6,3,8,5,7,1,4,2]=>0010111=>1110100
[2,4,3,8,5,7,1,6]=>0010011=>1100100
[2,8,3,1,4,6,5,7]=>0100101=>1010010
[4,5,7,6,1,3,8,2]=>0000111=>1110000
[3,7,1,6,5,8,2,4]=>0000111=>1110000
[7,4,3,6,8,2,1,5]=>1010011=>1100101
[3,8,5,4,7,6,1,2]=>0001111=>1111000
[1,4,6,8,7,3,5,2]=>0001011=>1101000
[4,6,5,1,3,8,7,2]=>0001111=>1111000
[5,4,6,2,1,8,7,3]=>1001111=>1111001
[3,2,8,5,1,4,6,7]=>0101001=>1001010
[3,5,4,1,2,8,6,7]=>0011001=>1001100
[5,3,8,1,4,2,6,7]=>0011001=>1001100
[5,3,8,1,4,2,7,6]=>0011011=>1101100
[1,4,7,5,8,6,2,3]=>0000111=>1110000
[8,5,7,6,3,4,1,2]=>0010111=>1110100
[7,5,2,6,1,4,8,3]=>0001111=>1111000
[2,4,5,1,8,3,7,6]=>0001011=>1101000
[7,2,8,5,3,4,1,6]=>0011011=>1101100
[6,4,5,3,1,7,8,2]=>0101101=>1011010
[7,3,5,6,4,1,8,2]=>0010111=>1110100
[1,4,7,6,8,5,2,3]=>0001011=>1101000
[2,3,4,7,8,9,1,5,6]=>00000001=>10000000
[2,3,6,7,8,9,1,4,5]=>00000001=>10000000
[2,5,6,7,8,9,1,3,4]=>00000001=>10000000
[2,3,4,5,1,9,6,7,8]=>00010001=>10001000
[2,3,4,1,8,9,5,6,7]=>00100001=>10000100
[2,3,4,5,8,9,10,1,6,7]=>000000001=>100000000
[2,3,1,7,8,9,4,5,6]=>01000001=>10000010
[2,3,4,7,8,9,10,1,5,6]=>000000001=>100000000
[2,1,6,7,8,9,3,4,5]=>10000001=>10000001
[2,3,6,7,8,9,10,1,4,5]=>000000001=>100000000
[2,5,6,7,8,9,10,1,3,4]=>000000001=>100000000
[2,5,6,3,4,1,8,7]=>0010101=>1010100
[4,6,2,1,5,8,3,7]=>1000101=>1010001
[4,6,7,2,3,8,5,1]=>0001011=>1101000
[2,3,5,8,7,4,1,6]=>0010011=>1100100
[2,3,5,8,7,4,6,1]=>0000111=>1110000
[4,5,3,7,8,1,2,6]=>0001001=>1001000
[2,3,5,8,1,6,4,7]=>0000101=>1010000
[1,7,4,5,8,3,6,2]=>0000111=>1110000
[8,6,1,5,4,2,7,3]=>0011111=>1111100
[2,8,5,6,3,1,4,7]=>0100101=>1010010
[4,8,2,6,1,5,7,3]=>0000111=>1110000
[2,3,7,8,1,5,4,6]=>0001001=>1001000
[5,2,6,7,8,3,1,4]=>0101001=>1001010
[5,6,2,7,8,3,1,4]=>0100101=>1010010
[2,3,7,5,8,4,6,1]=>0000111=>1110000
[3,7,8,5,1,4,6,2]=>0001101=>1011000
[2,5,6,7,1,8,4,3]=>0010011=>1100100
[8,5,3,6,4,2,1,7]=>1011101=>1011101
[2,3,7,8,5,4,6,1]=>0001101=>1011000
[6,4,7,8,1,2,5,3]=>0001101=>1011000
[7,5,8,1,2,3,6,4]=>0000111=>1110000
[1,2,8,7,4,6,5,3]=>0001111=>1111000
[5,1,4,8,7,3,6,2]=>0001111=>1111000
[4,3,1,8,7,5,6,2]=>0110111=>1110110
[4,3,2,7,6,1,5,8]=>0110110=>0110110
[7,2,6,5,3,1,4,8]=>0101110=>0111010
[1,3,7,6,2,4,8,5]=>0000111=>1110000
[1,3,8,2,7,4,6,5]=>0000111=>1110000
[8,2,7,1,6,4,3,5]=>0010111=>1110100
[4,3,2,8,1,7,5,6]=>0110011=>1100110
[7,5,4,1,6,3,8,2]=>0011111=>1111100
[1,6,5,3,2,4,8,7]=>0101101=>1011010
[1,7,3,5,2,4,8,6]=>0001011=>1101000
[4,3,7,2,5,1,6,8]=>0011010=>0101100
[5,1,4,3,2,6,8,7]=>0111001=>1001110
[7,2,1,3,5,4,6,8]=>1001010=>0101001
[8,3,7,5,4,2,6,1]=>0011111=>1111100
[1,6,8,7,5,2,3,4]=>0001011=>1101000
[4,3,6,1,8,5,2,7]=>0011101=>1011100
[1,3,6,2,5,4,8,7]=>0001101=>1011000
[1,4,8,7,3,6,2,5]=>0000111=>1110000
[1,2,7,3,8,4,9,5,10,6]=>000001111=>111100000
[3,6,5,1,4,7,8,2]=>0001101=>1011000
[5,4,1,8,7,3,6,2]=>0011111=>1111100
[6,2,4,7,5,3,1,8]=>0101110=>0111010
[6,2,5,1,8,7,3,4]=>0001111=>1111000
[3,2,6,1,5,8,7,4]=>0100111=>1110010
[1,6,3,8,4,7,2,5]=>0000111=>1110000
[8,1,5,2,4,7,3,6]=>0001011=>1101000
[7,5,8,1,4,2,3,6]=>0010011=>1100100
[4,1,2,3,6,5,8,7,9]=>00101010=>01010100
[4,1,2,3,6,5,8,7,10,9]=>001010101=>101010100
[4,1,6,2,3,5,8,7,9]=>00101010=>01010100
[1,3,4,8,5,6,2,7]=>0000101=>1010000
[3,2,7,1,8,6,5,4]=>0101111=>1111010
[1,3,8,5,6,7,2,4]=>0000011=>1100000
[6,2,4,1,5,7,8,3]=>0010101=>1010100
[5,8,4,1,3,6,7,2]=>0010011=>1100100
[6,7,2,3,8,1,4,5]=>0000011=>1100000
[3,2,7,4,8,1,5,6]=>0100011=>1100010
[5,2,8,1,7,4,6,3]=>0001111=>1111000
[2,5,4,7,3,1,8,6]=>0101011=>1101010
[4,6,3,1,2,5,7,8]=>0100100=>0010010
[7,4,6,8,3,1,2,5]=>0100011=>1100010
[8,5,4,7,3,1,2,6]=>0101011=>1101010
[7,3,2,1,5,4,8,6]=>1101011=>1101011
[2,5,6,4,8,1,3,7]=>0000101=>1010000
[5,4,1,6,2,3,7,8]=>0011100=>0011100
[1,3,6,5,2,4,7,8]=>0001100=>0011000
[6,4,5,1,2,8,7,3]=>0001111=>1111000
[5,4,1,2,7,6,3,8]=>0011110=>0111100
[5,8,7,3,1,2,4,6]=>0100011=>1100010
[2,7,8,1,4,5,3,6]=>0001001=>1001000
[4,1,2,8,7,3,6,5]=>0010111=>1110100
[6,1,2,4,3,8,7,5]=>0010111=>1110100
[3,7,8,1,2,4,6,5]=>0000101=>1010000
[7,3,4,1,2,6,8,5]=>0010011=>1100100
[8,4,3,1,2,6,5,7]=>0110101=>1010110
[3,8,2,7,4,5,1,6]=>0001011=>1101000
[8,6,2,3,5,4,1,7]=>0011101=>1011100
[8,2,6,1,3,5,4,7]=>0001101=>1011000
[8,4,3,7,2,5,6,1]=>0010111=>1110100
[8,3,1,7,4,5,2,6]=>0101011=>1101010
[8,2,4,5,1,7,3,6]=>0001011=>1101000
[6,8,2,4,5,1,7,3]=>0001011=>1101000
[4,3,8,1,7,5,6,2]=>0010111=>1110100
[8,4,3,7,1,5,6,2]=>0010111=>1110100
[8,3,4,7,2,6,5,1]=>0001111=>1111000
[8,1,3,7,6,4,5,2]=>0001111=>1111000
[8,3,7,1,4,5,6,2]=>0000111=>1110000
[8,7,3,6,1,2,5,4]=>0001111=>1111000
[8,3,7,6,2,4,5,1]=>0001111=>1111000
[8,7,2,3,6,1,5,4]=>0001111=>1111000
[8,2,7,1,3,4,6,5]=>0000111=>1110000
[5,1,8,4,2,3,7,6]=>0011011=>1101100
[8,2,4,7,3,1,6,5]=>0100111=>1110010
[8,2,7,6,3,1,4,5]=>0100111=>1110010
[6,8,1,4,7,3,2,5]=>0100011=>1100010
[8,5,7,2,6,3,1,4]=>0100111=>1110010
[5,8,2,7,3,1,6,4]=>0100111=>1110010
[8,1,2,6,7,5,4,3]=>0011011=>1101100
[8,4,1,7,5,6,2,3]=>0010111=>1110100
[8,2,4,7,6,5,1,3]=>0001111=>1111000
[8,2,7,6,4,5,1,3]=>0001111=>1111000
[8,4,7,2,3,6,5,1]=>0001111=>1111000
[8,2,4,7,3,6,5,1]=>0001111=>1111000
[8,1,7,6,4,5,2,3]=>0001111=>1111000
[8,1,2,7,6,4,5,3]=>0001111=>1111000
[8,1,4,7,3,6,5,2]=>0001111=>1111000
[2,3,1,9,8,7,6,5,4]=>01011111=>11111010
[3,4,2,1,9,8,7,6,5]=>10101111=>11110101
[4,5,3,2,1,9,8,7,6]=>11010111=>11101011
[5,6,4,3,2,1,9,8,7]=>11101011=>11010111
[6,7,5,4,3,2,1,9,8]=>11110101=>10101111
[2,8,1,5,3,7,6,4]=>0001111=>1111000
[1,8,2,4,7,5,6,3]=>0000111=>1110000
[2,3,8,4,7,1,6,5]=>0000111=>1110000
[1,8,2,3,5,6,4,7]=>0000101=>1010000
[1,4,7,6,2,3,5,8]=>0000110=>0110000
[1,7,6,2,3,8,4,5]=>0000111=>1110000
[1,8,2,3,7,6,4,5]=>0000111=>1110000
[1,7,3,8,6,2,5,4]=>0001111=>1111000
[5,8,2,3,7,4,1,6]=>0010011=>1100100
[4,2,8,3,7,6,1,5]=>0010111=>1110100
[1,3,5,6,4,8,2,7]=>0000101=>1010000
[3,1,7,8,5,2,4,6]=>0101001=>1001010
[7,1,2,3,4,5,9,6,10,8]=>000001011=>110100000
[4,6,1,8,2,7,5,3]=>0001111=>1111000
[6,3,5,2,8,4,7,1]=>0001111=>1111000
[1,6,3,5,2,8,4,7]=>0001101=>1011000
[5,4,8,6,3,7,2,1]=>1001111=>1111001
[6,4,5,8,1,3,7,2]=>0000111=>1110000
[6,3,5,1,8,4,7,2]=>0001111=>1111000
[2,6,3,1,5,8,4,7]=>0100101=>1010010
[2,5,4,8,6,3,1,7]=>0101101=>1011010
[2,5,4,8,6,3,7,1]=>0001111=>1111000
[1,2,5,4,8,6,3,7]=>0001101=>1011000
[6,4,5,8,2,1,7,3]=>1000111=>1110001
[5,3,4,1,2,6,8,7]=>0011001=>1001100
[1,4,3,5,2,8,6,7]=>0011001=>1001100
[1,3,5,4,8,2,6,7]=>0001001=>1001000
[3,5,4,8,2,6,1,7]=>0001101=>1011000
[3,6,4,5,1,2,8,7]=>0001101=>1011000
[4,3,5,1,8,6,2,7]=>0011101=>1011100
[3,5,4,8,1,6,2,7]=>0001101=>1011000
[3,4,8,5,6,1,2,7]=>0000101=>1010000
[3,4,8,5,6,2,1,7]=>1000101=>1010001
[3,5,4,8,1,6,7,2]=>0001011=>1101000
[2,4,3,1,5,8,6,7]=>0110001=>1000110
[1,7,6,2,5,4,8,3]=>0001111=>1111000
[5,6,1,7,4,3,8,2]=>0010111=>1110100
[3,7,2,1,5,6,8,4]=>1000011=>1100001
[3,1,5,6,4,2,7,8]=>0110100=>0010110
[8,3,4,1,6,5,7,2]=>0010111=>1110100
[8,1,6,4,3,5,2,7]=>0011101=>1011100
[1,3,7,8,2,6,4,5]=>0000101=>1010000
[2,1,6,5,3,8,7,4]=>1001111=>1111001
[3,7,5,6,4,2,1,8]=>1010110=>0110101
[6,1,4,3,7,5,8,2]=>0010111=>1110100
[4,6,8,5,3,7,2,1]=>1001011=>1101001
[4,6,8,5,1,3,7,2]=>0001011=>1101000
[8,3,5,4,6,1,2,7]=>0001101=>1011000
[3,4,5,6,1,7,2,9,8]=>00001101=>10110000
[1,7,4,5,2,6,8,3]=>0001011=>1101000
[1,4,5,9,6,7,2,8,3]=>00000111=>11100000
[3,4,5,6,7,1,8,2,10,9]=>000001101=>101100000
[2,4,5,9,6,1,7,3,8]=>00001101=>10110000
[3,4,5,7,6,1,9,2,8]=>00001101=>10110000
[1,4,2,6,5,3,8,7]=>0011101=>1011100
[3,1,5,8,4,6,2,7]=>0100101=>1010010
[3,5,6,9,7,1,8,2,4]=>00000111=>11100000
[1,4,8,5,6,2,7,9,3]=>00001011=>11010000
[1,4,5,6,10,7,8,2,9,3]=>000000111=>111000000
[3,4,5,6,7,8,1,9,2,11,10]=>0000001101=>1011000000
[2,4,5,6,10,7,1,8,3,9]=>000001101=>101100000
[3,4,5,6,8,7,1,10,2,9]=>000001101=>101100000
[2,5,9,6,7,3,1,4,8]=>01000101=>10100010
[4,1,5,2,7,6,3,9,8]=>00111101=>10111100
[3,4,1,6,9,5,7,2,8]=>00100101=>10100100
[8,2,6,3,4,1,5,7]=>0010101=>1010100
[4,6,5,8,2,1,3,7]=>1000101=>1010001
[1,4,8,3,5,6,2,7]=>0000101=>1010000
[1,8,7,4,2,3,6,5]=>0010111=>1110100
[6,7,9,8,1,3,4,2,5]=>00100011=>11000100
[9,1,5,2,8,6,3,7,4]=>00011111=>11111000
[3,5,6,7,10,8,1,9,2,4]=>000000111=>111000000
[1,7,4,5,2,6,8,9,3]=>00010101=>10101000
[1,4,5,9,6,7,2,8,10,3]=>000001011=>110100000
[1,4,5,6,7,11,8,9,2,10,3]=>0000000111=>1110000000
[4,3,1,8,5,7,2,6]=>0110011=>1100110
[7,3,2,4,8,1,6,5]=>0100111=>1110010
[3,7,2,4,5,8,1,6]=>0000011=>1100000
[3,2,7,4,6,1,8,5]=>0100111=>1110010
[8,3,2,4,6,1,7,5]=>0100111=>1110010
[8,3,2,4,5,7,1,6]=>0100011=>1100010
[7,4,6,2,1,3,8,5]=>1000111=>1110001
[3,6,7,2,4,1,8,5]=>0010011=>1100100
[8,4,7,2,3,5,6,1]=>0000111=>1110000
[3,8,6,7,1,5,4,2]=>0011011=>1101100
[4,3,2,8,6,1,5,7]=>0110101=>1010110
[4,1,6,3,2,5,7,8]=>0110100=>0010110
[5,7,1,8,4,3,6,2]=>0010111=>1110100
[5,4,8,7,6,2,3,1]=>0101111=>1111010
[8,4,6,3,1,5,2,7]=>0101101=>1011010
[3,6,1,5,2,4,7,8]=>0001100=>0011000
[3,7,6,2,5,4,1,8]=>0011110=>0111100
[2,7,1,5,3,4,6,8]=>0001010=>0101000
[8,4,5,1,2,7,6,3]=>0001111=>1111000
[5,2,3,8,7,1,6,4]=>0001111=>1111000
[7,5,2,4,1,3,8,6]=>0011011=>1101100
[7,2,6,8,5,1,3,4]=>0001011=>1101000
[8,6,5,4,1,3,7,2]=>0011111=>1111100
[8,2,3,4,1,6,7,5]=>0010011=>1100100
[9,2,3,4,5,6,1,8,7]=>00001011=>11010000
[9,2,3,4,5,1,7,8,6]=>00010011=>11001000
[9,2,3,4,1,6,7,8,5]=>00100011=>11000100
[9,2,3,1,5,6,7,8,4]=>01000011=>11000010
[9,2,1,4,5,6,7,8,3]=>10000011=>11000001
[10,2,3,4,5,6,7,1,9,8]=>000001011=>110100000
[5,2,3,4,1,9,6,8,7]=>00110011=>11001100
[10,2,3,4,5,6,1,8,9,7]=>000010011=>110010000
[4,2,3,1,9,5,7,8,6]=>01100011=>11000110
[10,2,3,4,5,1,7,8,9,6]=>000100011=>110001000
[3,2,1,9,4,6,7,8,5]=>11000011=>11000011
[10,2,3,4,1,6,7,8,9,5]=>001000011=>110000100
[2,1,9,3,5,6,7,8,4]=>10000011=>11000001
[10,2,3,1,5,6,7,8,9,4]=>010000011=>110000010
[10,2,1,4,5,6,7,8,9,3]=>100000011=>110000001
[7,4,3,8,1,6,5,2]=>0011111=>1111100
[6,5,1,4,3,8,7,2]=>0011111=>1111100
[4,7,6,2,5,8,1,3]=>0000111=>1110000
[6,3,2,4,5,8,1,7]=>0100101=>1010010
[2,6,4,5,8,3,1,7]=>0100101=>1010010
[3,7,4,8,6,2,5,1]=>0001111=>1111000
[7,3,5,2,8,1,4,6]=>0001011=>1101000
[1,5,8,7,4,2,3,6]=>0010011=>1100100
[1,7,2,4,5,8,6,3]=>0000111=>1110000
[1,4,6,8,7,2,5,3]=>0001011=>1101000
[1,6,2,7,5,3,4,8]=>0001110=>0111000
[1,3,7,2,6,4,5,8]=>0000110=>0110000
[1,7,3,2,8,5,6,4]=>0100111=>1110010
[1,6,5,2,4,8,3,7]=>0001101=>1011000
[1,7,3,8,4,2,5,6]=>0010011=>1100100
[1,6,2,4,7,5,8,3]=>0000111=>1110000
[1,6,2,7,4,3,8,5]=>0010111=>1110100
[1,5,8,2,3,6,4,7]=>0000101=>1010000
[6,8,9,1,2,3,4,5,7]=>00000001=>10000000
[5,8,9,1,2,3,4,6,7]=>00000001=>10000000
[2,5,3,6,7,1,4,8]=>0001010=>0101000
[6,4,1,5,7,2,3,8]=>0010110=>0110100
[6,4,1,5,7,3,8,2]=>0010111=>1110100
[1,2,7,3,8,5,6,4]=>0000111=>1110000
[7,4,1,6,3,8,2,5]=>0010111=>1110100
[1,5,7,4,3,8,6,2]=>0010111=>1110100
[2,7,3,1,4,5,8,6]=>0100011=>1100010
[2,3,4,5,1,7,6,9,8]=>00010101=>10101000
[2,3,4,1,6,5,8,7,9]=>00101010=>01010100
[2,3,4,5,6,7,1,9,8,10]=>000001010=>010100000
[2,3,4,5,1,8,6,9,7]=>00010011=>11001000
[2,3,4,1,7,5,8,6,9]=>00100110=>01100100
[2,3,4,5,1,7,6,9,8,10]=>000101010=>010101000
[6,5,8,3,2,7,1,4]=>0100111=>1110010
[8,4,3,1,7,6,5,2]=>0111111=>1111110
[1,2,6,7,5,3,4,8]=>0001010=>0101000
[1,2,6,8,7,4,5,3]=>0001011=>1101000
[3,4,5,6,7,9,1,8,2]=>00000011=>11000000
[3,4,5,6,8,2,7,1]=>0000011=>1100000
[3,4,5,6,7,8,10,1,9,2]=>000000011=>110000000
[3,4,5,6,7,9,2,8,1]=>00000011=>11000000
[3,4,5,6,7,1,9,8,2]=>00000111=>11100000
[7,2,1,4,5,6,3,8]=>1000110=>0110001
[1,5,6,7,3,4,2,8]=>0010010=>0100100
[4,6,8,5,2,1,7,3]=>1001011=>1101001
[1,6,7,8,2,4,5,3]=>0001001=>1001000
[4,7,8,2,1,3,5,6]=>1000001=>1000001
[5,7,8,3,2,4,6,1]=>0100101=>1010010
[5,7,8,2,3,1,6,4]=>0100101=>1010010
[5,3,4,2,1,9,8,7,6]=>10110111=>11101101
[6,5,3,4,2,1,9,8,7]=>10111011=>11011101
[7,6,4,5,3,2,1,9,8]=>11011101=>10111011
[4,5,2,7,8,6,1,3]=>0001101=>1011000
[1,3,5,8,7,2,6,4]=>0000111=>1110000
[6,4,1,8,5,7,3,2]=>0110111=>1110110
[4,1,3,8,7,5,2,6]=>0011011=>1101100
[8,5,1,6,7,2,4,3]=>0011011=>1101100
[3,6,7,2,1,5,8,4]=>1000011=>1100001
[2,5,6,1,3,8,7,4]=>0000111=>1110000
[7,2,5,6,1,3,8,4]=>0000111=>1110000
[6,4,1,2,5,8,3,7]=>0010101=>1010100
[4,6,3,5,7,1,8,2]=>0000111=>1110000
[4,7,3,5,2,6,8,1]=>0001011=>1101000
[2,3,5,4,7,1,8,6]=>0001011=>1101000
[6,8,4,1,5,7,3,2]=>0110011=>1100110
[8,1,6,2,3,7,5,4]=>0001111=>1111000
[7,8,9,6,1,2,3,4,10,5]=>000010011=>110010000
[2,8,9,10,7,1,3,4,5,6]=>000001001=>100100000
[8,9,10,7,6,1,2,3,4,11,5]=>0000110011=>1100110000
[8,9,7,5,6,1,2,3,10,4]=>000011011=>110110000
[2,9,10,8,6,7,1,3,4,5]=>000001101=>101100000
[2,9,10,11,8,7,1,3,4,5,6]=>0000011001=>1001100000
[8,9,10,11,7,1,2,3,4,5,12,6]=>00000100011=>11000100000
[7,8,9,10,1,2,3,4,5,11,6]=>0000000011=>1100000000
[7,8,9,5,1,2,3,4,10,6]=>000100011=>110001000
[7,8,9,1,6,2,3,4,10,5]=>000010011=>110010000
[2,8,9,10,6,1,3,4,5,7]=>000010001=>100010000
[2,8,9,10,1,7,3,4,5,6]=>000001001=>100100000
[2,8,9,10,11,1,3,4,5,6,7]=>0000000001=>1000000000
[2,9,10,11,12,8,1,3,4,5,6,7]=>00000010001=>10001000000
[2,8,3,6,4,1,7,5]=>0010111=>1110100
[6,5,3,4,8,2,1,7]=>1001101=>1011001
[5,4,8,7,3,6,2,1]=>1001111=>1111001
[3,4,5,1,2,6,7,8,9]=>00010000=>00001000
[5,2,7,6,8,3,4,1]=>0011011=>1101100
[7,3,4,2,8,5,6,1]=>0010111=>1110100
[4,2,3,5,6,7,8,9,10,1]=>001000001=>100000100
[2,3,4,5,6,7,8,11,1,9,10]=>0000000001=>1000000000
[2,3,4,5,6,7,11,1,8,9,10]=>0000000001=>1000000000
[2,3,4,5,6,11,1,7,8,9,10]=>0000000001=>1000000000
[2,3,4,5,11,1,6,7,8,9,10]=>0000000001=>1000000000
[2,3,4,11,1,5,6,7,8,9,10]=>0000000001=>1000000000
[2,3,11,1,4,5,6,7,8,9,10]=>0000000001=>1000000000
[1,7,8,4,3,6,5,2]=>0011101=>1011100
[1,7,8,3,6,5,4,2]=>0011101=>1011100
[6,4,5,8,7,2,1,3]=>1000111=>1110001
[5,8,1,7,2,4,3,6]=>0010011=>1100100
[2,5,7,3,8,1,4,6]=>0000011=>1100000
[8,3,5,2,1,6,7,4]=>1001011=>1101001
[2,6,4,7,1,8,5,3]=>0001111=>1111000
[1,6,5,7,3,8,2,4]=>0000111=>1110000
[1,8,5,3,7,6,2,4]=>0001111=>1111000
[6,4,2,3,8,7,5,1]=>0011111=>1111100
[6,5,1,3,8,4,2,7]=>0011101=>1011100
[6,1,4,2,7,8,3,5]=>0010101=>1010100
[6,5,1,3,7,8,4,2]=>0011101=>1011100
[5,1,3,2,7,8,6,4]=>0101101=>1011010
[5,6,8,2,4,7,1,3]=>0000011=>1100000
[6,7,4,2,3,8,5,1]=>0011011=>1101100
[5,8,7,3,2,4,6,1]=>0100111=>1110010
[5,1,3,2,6,8,4,7]=>0101001=>1001010
[5,7,1,4,6,8,2,3]=>0000011=>1100000
[2,4,1,7,5,6,3,8]=>0010110=>0110100
[1,4,3,7,6,2,8,5]=>0010111=>1110100
[1,6,2,5,7,3,8,4]=>0000111=>1110000
[1,4,3,8,2,5,7,6]=>0010011=>1100100
[1,5,7,3,6,4,2,8]=>0010110=>0110100
[1,6,7,2,4,8,3,5]=>0000011=>1100000
[3,7,2,8,4,1,5,6]=>0010011=>1100100
[2,4,1,5,3,6,8,7,9]=>00110010=>01001100
[2,4,1,7,3,8,5,6,9]=>00100110=>01100100
[5,3,4,1,7,8,6,2]=>0011101=>1011100
[4,7,6,5,8,2,3,1]=>0100111=>1110010
[2,3,8,4,5,7,1,6]=>0000011=>1100000
[4,1,8,3,2,6,5,7]=>0110101=>1010110
[1,2,6,8,4,3,5,7]=>0010001=>1000100
[7,2,6,3,1,8,4,5]=>0100111=>1110010
[5,8,4,1,3,7,2,6]=>0010011=>1100100
[3,4,2,1,6,8,5,7]=>1010001=>1000101
[8,1,3,5,6,4,7,2]=>0000111=>1110000
[3,4,7,1,5,6,2,8]=>0000110=>0110000
[4,8,2,6,5,3,7,1]=>0001111=>1111000
[4,8,7,2,5,6,1,3]=>0000111=>1110000
[5,8,6,4,7,3,2,1]=>1100111=>1110011
[8,5,2,3,1,6,7,4]=>0101011=>1101010
[2,8,6,3,5,1,7,4]=>0001111=>1111000
[8,3,2,6,4,1,7,5]=>0110111=>1110110
[8,4,1,5,3,6,7,2]=>0011011=>1101100
[8,3,5,1,4,6,7,2]=>0001011=>1101000
[8,5,1,3,4,6,7,2]=>0001011=>1101000
[3,8,6,2,5,4,7,1]=>0001111=>1111000
[3,8,4,6,5,2,7,1]=>0001111=>1111000
[8,1,7,4,2,5,3,6]=>0011011=>1101100
[8,3,2,5,1,4,7,6]=>0101011=>1101010
[8,4,5,1,2,6,7,3]=>0001011=>1101000
[8,1,5,3,2,6,7,4]=>0101011=>1101010
[8,1,5,2,4,6,7,3]=>0001011=>1101000
[5,2,6,4,1,3,8,7]=>0011101=>1011100
[7,1,3,5,2,8,6,4]=>0001111=>1111000
[8,6,4,7,1,3,5,2]=>0001111=>1111000
[6,8,4,3,2,1,7,5]=>1110011=>1100111
[2,1,8,5,4,3,7,6]=>1011011=>1101101
[6,2,8,5,4,1,3,7]=>0011101=>1011100
[6,4,8,5,3,2,7,1]=>0101111=>1111010
[9,10,6,7,4,5,2,3,1,8]=>010101001=>100101010
[8,5,4,6,2,7,1,3]=>0001111=>1111000
[6,8,5,4,7,2,3,1]=>0101011=>1101010
[2,5,7,3,4,8,1,6]=>0000011=>1100000
[5,2,4,7,8,1,3,6]=>0001001=>1001000
[8,5,9,3,6,1,2,4,7]=>00001011=>11010000
[9,7,1,5,8,3,6,2,4]=>00001111=>11110000
[9,7,5,4,1,3,8,2,6]=>00110111=>11101100
[8,9,4,5,10,1,2,3,6,7]=>000000011=>110000000
[8,4,3,9,10,1,2,5,6,7]=>001000101=>101000100
[9,6,10,1,3,7,8,2,4,5]=>000000111=>111000000
[9,10,6,7,4,5,1,2,3,8]=>000101001=>100101000
[9,6,4,10,3,7,1,2,5,8]=>000011011=>110110000
[10,1,8,9,6,7,4,5,2,3]=>000101011=>110101000
[10,8,6,1,4,9,3,7,2,5]=>000011111=>111110000
[10,8,6,5,4,1,3,9,2,7]=>001110111=>111011100
[10,8,7,6,5,4,3,1,2,9]=>011111101=>101111110
[4,8,5,6,1,2,7,3]=>0000111=>1110000
[2,5,6,8,7,1,4,3]=>0010011=>1100100
[1,7,8,5,4,6,2,3]=>0001101=>1011000
[4,6,8,1,5,2,7,3]=>0001011=>1101000
[5,3,8,1,2,6,7,4]=>0001011=>1101000
[8,2,3,6,4,1,7,5]=>0010111=>1110100
[2,3,7,5,8,6,1,4]=>0000111=>1110000
[3,8,5,1,2,4,7,6]=>0001011=>1101000
[1,3,6,4,8,2,7,5]=>0000111=>1110000
[1,2,3,4,6,5,7,8,9,10]=>000010000=>000010000
[1,2,3,4,5,6,8,7,9,10]=>000000100=>001000000
[1,7,6,2,8,5,3,4]=>0001111=>1111000
[1,5,8,6,4,7,2,3]=>0000111=>1110000
[5,6,2,8,1,7,3,4]=>0000111=>1110000
[6,8,4,5,1,3,7,2]=>0001011=>1101000
[5,2,3,8,1,4,6,7]=>0001001=>1001000
[1,6,8,3,2,4,5,7]=>0100001=>1000010
[9,6,5,4,3,2,1,7,8]=>11111001=>10011111
[10,7,6,5,4,3,2,1,8,9]=>111111001=>100111111
[9,8,5,4,3,2,1,6,7]=>11110011=>11001111
[8,6,5,2,4,3,7,1]=>0011111=>1111100
[6,2,5,3,7,4,8,1]=>0001111=>1111000
[8,5,4,2,6,3,7,1]=>0011111=>1111100
[8,5,3,2,6,4,7,1]=>0101111=>1111010
[7,4,6,5,8,2,3,1]=>0100111=>1110010
[7,3,6,5,8,2,4,1]=>0010111=>1110100
[7,3,6,4,8,2,5,1]=>0001111=>1111000
[7,3,5,4,8,2,6,1]=>0001111=>1111000
[7,3,6,8,4,5,1,2]=>0001011=>1101000
[1,6,5,7,4,2,8,3]=>0010111=>1110100
[1,2,7,4,8,5,6,3]=>0000111=>1110000
[2,6,7,4,8,5,1,3]=>0001011=>1101000
[2,5,8,6,4,3,7,1]=>0010111=>1110100
[6,4,2,5,7,1,8,3]=>0010111=>1110100
[2,7,5,4,6,8,1,3]=>0001011=>1101000
[9,1,2,3,4,5,8,7,6]=>00000111=>11100000
[9,1,2,3,4,8,6,7,5]=>00000111=>11100000
[8,1,4,7,3,5,6,2]=>0000111=>1110000
[9,1,2,8,4,5,6,7,3]=>00000111=>11100000
[8,3,7,2,4,5,6,1]=>0000111=>1110000
[9,1,8,3,4,5,6,7,2]=>00000111=>11100000
[10,1,2,3,4,5,6,9,8,7]=>000000111=>111000000
[9,1,2,3,4,7,8,6,5]=>00001011=>11010000
[10,1,2,3,4,5,9,7,8,6]=>000000111=>111000000
[9,1,2,3,6,8,5,7,4]=>00000111=>11100000
[9,1,2,5,8,4,6,7,3]=>00000111=>11100000
[10,1,2,3,9,5,6,7,8,4]=>000000111=>111000000
[8,1,4,5,7,3,6,2]=>0000111=>1110000
[9,1,4,8,3,5,6,7,2]=>00000111=>11100000
[10,1,2,9,4,5,6,7,8,3]=>000000111=>111000000
[9,3,8,2,4,5,6,7,1]=>00000111=>11100000
[5,6,3,4,2,8,7,1]=>0010111=>1110100
[2,5,7,4,6,8,1,3]=>0000011=>1100000
[2,5,6,4,1,3,8,7]=>0010101=>1010100
[4,6,1,3,5,7,2,8]=>0000110=>0110000
[3,2,7,5,8,1,6,4]=>0100111=>1110010
[4,3,6,8,5,2,1,7]=>1011001=>1001101
[4,5,3,2,1,8,6,7]=>1101001=>1001011
[3,6,5,8,1,7,4,2]=>0010111=>1110100
[4,1,6,8,5,2,3,7]=>0011001=>1001100
[4,5,2,8,6,7,1,3]=>0001011=>1101000
[4,5,2,8,6,7,3,1]=>0101011=>1101010
[3,5,8,6,2,4,7,1]=>0000111=>1110000
[2,5,1,6,4,8,3,7]=>0001101=>1011000
[3,2,4,5,8,6,1,7]=>0100101=>1010010
[4,5,2,1,3,8,6,7]=>1001001=>1001001
[4,2,3,6,8,5,1,7]=>0011001=>1001100
[4,5,1,3,2,8,6,7]=>0101001=>1001010
[3,4,5,8,6,1,7,2]=>0000111=>1110000
[3,4,5,8,6,1,2,7]=>0000101=>1010000
[6,4,1,3,7,8,2,5]=>0010101=>1010100
[6,3,1,2,5,4,8,7]=>0101101=>1011010
[7,3,1,2,5,4,8,6]=>0101011=>1101010
[8,2,6,4,1,3,7,5]=>0010111=>1110100
[1,5,8,2,4,3,7,6]=>0010011=>1100100
[4,3,7,8,2,6,5,1]=>0011101=>1011100
[3,8,5,1,2,6,7,4]=>0001011=>1101000
[2,4,7,8,3,6,5,1]=>0001101=>1011000
[5,4,7,8,3,6,1,2]=>0001101=>1011000
[6,8,1,3,2,5,7,4]=>0100011=>1100010
[1,4,8,5,7,2,3,6]=>0000011=>1100000
[1,8,7,3,2,4,5,6]=>0100011=>1100010
[8,6,2,7,3,4,1,5]=>0010111=>1110100
[8,6,2,7,3,4,5,1]=>0001111=>1111000
[5,6,3,2,8,7,1,4]=>0100111=>1110010
[5,1,6,7,8,3,2,4]=>0101001=>1001010
[1,5,6,3,7,2,4,8]=>0000110=>0110000
[1,5,6,7,4,2,3,8]=>0010010=>0100100
[5,1,6,7,3,4,2,8]=>0011010=>0101100
[8,6,1,7,3,4,5,2]=>0001111=>1111000
[6,8,5,1,7,4,2,3]=>0011011=>1101100
[8,4,2,3,5,7,6,1]=>0010111=>1110100
[4,8,5,2,3,1,6,7]=>0101001=>1001010
[5,4,8,3,1,2,6,7]=>0101001=>1001010
[8,4,7,3,2,5,6,1]=>0100111=>1110010
[6,8,5,1,7,3,4,2]=>0011011=>1101100
[6,2,7,3,8,1,4,5]=>0000111=>1110000
[8,4,2,6,7,1,5,3]=>0011011=>1101100
[1,7,8,3,6,5,2,4]=>0001101=>1011000
[4,6,7,5,1,8,2,3]=>0001011=>1101000
[3,5,2,6,8,7,4,1]=>0011011=>1101100
[7,3,6,8,4,1,2,5]=>0010011=>1100100
[6,4,2,3,7,5,8,1]=>0010111=>1110100
[6,3,7,5,1,2,8,4]=>0001111=>1111000
[7,2,5,4,8,6,3,1]=>0101111=>1111010
[6,2,3,8,7,4,5,1]=>0001111=>1111000
[7,1,2,8,4,6,5,3]=>0001111=>1111000
[3,5,8,1,2,7,6,4]=>0000111=>1110000
[1,4,3,6,8,5,2,7]=>0011001=>1001100
[7,6,2,8,5,3,4,1]=>0011111=>1111100
[6,8,3,5,4,7,2,1]=>1001011=>1101001
[8,2,7,6,4,1,3,5]=>0010111=>1110100
[8,3,7,5,1,6,2,4]=>0001111=>1111000
[8,5,7,1,4,2,6,3]=>0010111=>1110100
[4,7,1,5,6,3,2,8]=>0100110=>0110010
[4,5,7,1,6,3,8,2]=>0000111=>1110000
[3,9,2,1,4,5,6,7,8]=>10000001=>10000001
[4,6,5,7,2,3,8,1]=>0000111=>1110000
[3,6,7,2,5,8,4,1]=>0010011=>1100100
[5,3,6,7,4,8,1,2]=>0001011=>1101000
[4,2,7,8,3,6,5,1]=>0011101=>1011100
[4,2,7,8,5,6,1,3]=>0010101=>1010100
[5,4,3,7,8,1,6,2]=>0011101=>1011100
[3,5,7,8,4,2,1,6]=>1010001=>1000101
[4,6,7,3,2,8,1,5]=>0100011=>1100010
[4,6,5,3,7,8,1,2]=>0001101=>1011000
[5,6,2,4,7,8,3,1]=>0100101=>1010010
[5,6,3,2,8,4,7,1]=>0100111=>1110010
[5,6,2,8,3,4,7,1]=>0000111=>1110000
[3,7,4,8,1,6,5,2]=>0001111=>1111000
[5,2,4,8,6,7,3,1]=>0101011=>1101010
[5,2,6,4,8,7,3,1]=>0101111=>1111010
[2,4,7,8,6,5,1,3]=>0001101=>1011000
[3,4,5,6,8,9,1,7,2]=>00000101=>10100000
[3,4,6,7,8,9,1,5,2]=>00010001=>10001000
[3,5,6,7,8,9,1,4,2]=>00100001=>10000100
[4,5,6,7,8,9,1,3,2]=>01000001=>10000010
[3,4,5,6,7,9,10,1,8,2]=>000000101=>101000000
[3,4,5,7,8,9,10,1,6,2]=>000010001=>100010000
[5,2,6,7,8,1,4,3]=>0011001=>1001100
[3,4,6,7,8,9,10,1,5,2]=>000100001=>100001000
[4,5,6,7,8,9,10,1,3,2]=>010000001=>100000010
[3,1,4,5,6,7,8,9,11,2,10]=>0100000001=>1000000010
[4,8,2,7,5,3,1,6]=>0101011=>1101010
[1,2,4,6,5,8,3,7]=>0000101=>1010000
[5,4,2,3,1,7,8,6]=>0111001=>1001110
[3,5,8,1,7,4,2,6]=>0010011=>1100100
[5,8,6,1,7,2,3,4]=>0000111=>1110000
[5,1,4,3,8,2,6,7]=>0011001=>1001100
[8,4,7,5,6,2,1,3]=>1000111=>1110001
[3,8,6,7,5,2,4,1]=>0011011=>1101100
[8,2,5,4,7,3,6,1]=>0001111=>1111000
[4,2,8,7,3,6,5,1]=>0011111=>1111100
[3,7,8,6,1,4,5,2]=>0001101=>1011000
[4,6,7,8,2,1,5,3]=>1001001=>1001001
[4,7,6,3,8,1,5,2]=>0001111=>1111000
[3,8,1,4,6,2,5,7]=>0000101=>1010000
[2,4,5,3,8,7,1,6]=>0001011=>1101000
[4,7,5,6,2,8,1,3]=>0000111=>1110000
[8,7,5,1,6,3,2,4]=>0101111=>1111010
[7,8,6,2,3,5,1,4]=>0001101=>1011000
[2,8,4,6,7,3,5,1]=>0001011=>1101000
[4,1,6,7,8,2,5,3]=>0011001=>1001100
[8,6,3,4,1,2,7,5]=>0010111=>1110100
[2,5,8,4,6,1,3,7]=>0000101=>1010000
[4,7,8,6,5,1,3,2]=>0101101=>1011010
[8,4,6,7,3,5,2,1]=>1001011=>1101001
[6,8,4,7,3,5,2,1]=>1001011=>1101001
[7,4,5,8,3,6,2,1]=>1000111=>1110001
[8,4,7,3,5,6,2,1]=>1000111=>1110001
[3,6,4,2,8,1,7,5]=>0010111=>1110100
[3,4,8,6,2,1,7,5]=>1000111=>1110001
[8,4,6,2,1,7,3,5]=>1000111=>1110001
[3,8,6,2,1,7,4,5]=>1000111=>1110001
[3,1,8,2,4,6,5,7]=>0100101=>1010010
[8,1,7,6,2,5,4,3]=>0011111=>1111100
[8,5,4,3,7,6,1,2]=>0011111=>1111100
[4,8,1,3,6,7,5,2]=>0001011=>1101000
[3,5,8,6,1,7,4,2]=>0010111=>1110100
[8,1,4,7,5,2,6,3]=>0001111=>1111000
[1,4,8,6,7,3,5,2]=>0001011=>1101000
[4,1,6,7,8,5,3,2]=>0111001=>1001110
[3,7,8,6,4,1,5,2]=>0011101=>1011100
[5,4,2,3,6,7,8,9,1]=>00110001=>10001100
[6,5,4,2,3,7,8,9,1]=>00111001=>10011100
[7,6,5,4,2,3,8,9,1]=>00111101=>10111100
[4,6,1,5,7,2,3,8]=>0000110=>0110000
[4,8,5,3,2,7,1,6]=>0101011=>1101010
[5,4,8,1,3,7,2,6]=>0001011=>1101000
[8,4,5,3,1,7,2,6]=>0101011=>1101010
[7,4,5,3,1,8,6,2]=>0101111=>1111010
[5,6,8,7,2,4,3,1]=>0110011=>1100110
[5,7,8,6,4,2,3,1]=>0110101=>1010110
[6,8,7,5,1,3,2,4]=>0101011=>1101010
[3,8,2,6,7,5,1,4]=>0001011=>1101000
[4,7,6,3,8,2,5,1]=>0001111=>1111000
[6,7,4,1,8,2,5,3]=>0011011=>1101100
[5,7,6,8,3,2,4,1]=>0110011=>1100110
[7,6,4,2,8,1,5,3]=>0011111=>1111100
[6,3,4,8,7,1,2,5]=>0000111=>1110000
[2,7,4,8,1,6,3,5]=>0000111=>1110000
[5,3,1,6,7,8,2,4]=>0101001=>1001010
[3,4,7,8,6,1,2,5]=>0000101=>1010000
[2,1,4,7,8,6,3,5]=>1000101=>1010001
[2,4,5,8,1,6,3,7]=>0000101=>1010000
[3,4,6,8,2,5,7,1]=>0000011=>1100000
[1,8,5,6,4,2,3,7]=>0010101=>1010100
[1,8,7,6,2,4,5,3]=>0001111=>1111000
[6,4,8,5,7,3,1,2]=>0100111=>1110010
[1,6,4,7,2,5,8,3]=>0000111=>1110000
[2,7,5,1,8,6,3,4]=>0001111=>1111000
[4,7,1,6,5,3,8,2]=>0001111=>1111000
[1,7,5,6,4,8,2,3]=>0000111=>1110000
[2,4,8,5,7,3,1,6]=>0100011=>1100010
[8,3,1,4,6,2,7,5]=>0100111=>1110010
[7,2,6,4,5,8,1,3]=>0000111=>1110000
[7,2,5,4,6,8,1,3]=>0001011=>1101000
[4,6,7,8,9,1,2,3,5]=>00000001=>10000000
[5,7,8,9,1,2,3,4,6]=>00000001=>10000000
[6,4,5,7,3,8,2,9,1,10]=>000011110=>011110000
[2,7,1,5,3,8,6,4]=>0001111=>1111000
[3,5,7,2,8,4,1,6]=>0010011=>1100100
[2,4,3,8,5,1,7,6]=>0011011=>1101100
[7,3,2,1,4,8,6,5]=>1100111=>1110011
[2,8,3,4,1,7,6,5]=>0010111=>1110100
[4,7,6,8,2,5,3,1]=>0101011=>1101010
[2,6,7,1,4,5,8,3]=>0000011=>1100000
[8,7,2,6,1,5,3,4]=>0001111=>1111000
[7,1,3,8,2,6,4,5]=>0000111=>1110000
[2,7,3,4,1,5,8,6]=>0010011=>1100100
[2,5,8,1,6,7,3,4]=>0000011=>1100000
[6,2,8,3,4,5,1,7]=>0001101=>1011000
[7,3,4,6,8,2,1,5]=>1000011=>1100001
[5,1,3,7,2,8,4,6]=>0001011=>1101000
[5,2,4,6,1,7,8,3]=>0001101=>1011000
[3,8,4,6,1,5,7,2]=>0000111=>1110000
[8,7,3,2,5,1,6,4]=>0101111=>1111010
[3,6,4,1,2,5,8,7]=>0010101=>1010100
[5,2,7,1,4,3,6,8]=>0011010=>0101100
[6,3,1,4,2,5,8,7]=>0110101=>1010110
[5,2,3,1,4,6,8,7]=>0101001=>1001010
[4,2,7,1,3,5,8,6]=>0010011=>1100100
[3,5,1,7,6,2,8,4]=>0001111=>1111000
[8,3,6,2,7,5,4,1]=>0011111=>1111100
[8,4,2,6,5,3,7,1]=>0011111=>1111100
[5,4,2,7,1,8,6,3]=>0011111=>1111100
[4,1,7,6,5,3,2,8]=>0111110=>0111110
[2,3,6,7,1,8,5,4]=>0001011=>1101000
[3,6,1,2,7,8,5,4]=>0001101=>1011000
[4,5,1,8,7,6,3,2]=>0101111=>1111010
[8,4,5,2,7,6,3,1]=>0101111=>1111010
[4,1,3,6,7,5,2,8]=>0011010=>0101100
[3,1,4,5,7,6,2,8]=>0100110=>0110010
[4,5,1,3,6,8,7,2]=>0001011=>1101000
[3,8,5,1,2,4,6,7]=>0001001=>1001000
[8,5,1,2,4,3,6,7]=>0011001=>1001100
[5,8,4,1,2,3,6,7]=>0010001=>1000100
[3,5,8,1,4,2,7,6]=>0010011=>1100100
[2,8,5,7,1,4,3,6]=>0010011=>1100100
[4,8,7,5,1,2,3,6]=>0001011=>1101000
[8,1,2,4,6,3,7,5]=>0000111=>1110000
[7,6,1,4,2,3,8,5]=>0010111=>1110100
[6,1,2,7,8,4,3,5]=>0010101=>1010100
[7,8,1,2,5,3,4,6]=>0001001=>1001000
[1,8,4,7,5,2,3,6]=>0001011=>1101000
[8,4,7,2,1,6,3,5]=>1000111=>1110001
[4,5,8,2,1,6,7,3]=>1000011=>1100001
[7,4,2,5,3,6,1,8]=>0011110=>0111100
[3,1,6,7,5,2,4,8]=>0101010=>0101010
[8,4,2,5,3,6,7,1]=>0011011=>1101100
[4,8,1,5,3,6,7,2]=>0001011=>1101000
[4,1,7,5,2,6,3,8]=>0011110=>0111100
[5,1,4,6,3,7,8,2]=>0001101=>1011000
[7,1,5,3,6,8,2,4]=>0001011=>1101000
[8,1,5,3,6,7,2,4]=>0001011=>1101000
[3,6,5,2,4,7,8,1]=>0001101=>1011000
[1,7,5,4,6,8,2,3]=>0001011=>1101000
[4,7,8,2,5,6,1,3]=>0000101=>1010000
[2,8,5,4,6,7,1,3]=>0001011=>1101000
[7,5,1,3,2,6,4,8,9]=>01011100=>00111010
[9,6,1,3,4,2,7,8,5]=>00101011=>11010100
[8,3,6,1,4,2,7,5,9]=>00101110=>01110100
[9,8,1,7,2,3,4,5,6]=>00000111=>11100000
[9,3,4,7,1,5,2,8,6]=>00010111=>11101000
[7,5,1,3,2,6,4,8,9,10]=>010111000=>000111010
[9,6,1,3,4,2,7,8,5,10]=>001010110=>011010100
[8,3,6,1,4,2,7,5,9,10]=>001011100=>001110100
[10,1,8,3,2,5,7,4,9,6]=>010001111=>111100010
[10,3,7,1,4,5,2,8,9,6]=>000101011=>110101000
[9,3,4,7,1,5,2,8,6,10]=>000101110=>011101000
[7,10,1,3,8,2,6,5,9,4]=>000010111=>111010000
[10,9,5,1,8,2,4,3,6,7]=>001100111=>111001100
[10,3,4,5,8,1,6,2,9,7]=>000010111=>111010000
[4,5,2,6,1,8,3,7]=>0001101=>1011000
[5,1,8,6,7,3,4,2]=>0011011=>1101100
[6,8,3,2,4,1,5,7]=>0110001=>1000110
[6,5,2,4,1,7,8,3]=>0011101=>1011100
[5,4,8,2,1,3,6,7]=>1001001=>1001001
[1,4,8,3,2,6,5,7]=>0100101=>1010010
[1,3,8,4,2,7,5,6]=>0010011=>1100100
[7,2,8,3,1,4,5,6]=>0100011=>1100010
[8,1,3,2,7,5,4,6]=>0101011=>1101010
[9,8,7,5,6,4,3,2,10,1]=>011011111=>111110110
[8,7,5,4,6,3,2,9,1]=>01011111=>11111010
[8,7,4,6,5,3,2,9,1]=>01011111=>11111010
[2,3,4,7,8,9,6,5,1]=>00011001=>10011000
[2,3,6,7,8,9,5,4,1]=>00110001=>10001100
[2,5,6,7,8,9,4,3,1]=>01100001=>10000110
[2,3,4,5,6,1,9,8,7]=>00001011=>11010000
[2,3,4,5,1,9,8,7,6]=>00010111=>11101000
[2,3,4,5,6,9,10,8,7,1]=>000001101=>101100000
[2,3,4,1,8,9,7,6,5]=>00101101=>10110100
[2,3,4,5,8,9,10,7,6,1]=>000011001=>100110000
[2,3,1,7,8,9,6,5,4]=>01011001=>10011010
[2,3,4,7,8,9,10,6,5,1]=>000110001=>100011000
[2,1,6,7,8,9,5,4,3]=>10110001=>10001101
[2,3,6,7,8,9,10,5,4,1]=>001100001=>100001100
[2,5,6,7,8,9,10,4,3,1]=>011000001=>100000110
[9,10,2,4,6,8,1,3,5,7]=>000000101=>101000000
[7,8,2,4,6,10,1,3,5,9]=>000000101=>101000000
[9,7,10,2,4,6,8,1,3,5]=>000000111=>111000000
[8,9,10,7,2,4,6,1,3,5]=>000011001=>100110000
[5,6,2,4,8,10,1,3,7,9]=>000010001=>100010000
[5,6,9,10,2,4,8,1,3,7]=>000000101=>101000000
[7,5,8,2,4,6,10,1,3,9]=>000001101=>101100000
[7,9,5,10,2,4,6,8,1,3]=>000000111=>111000000
[5,8,9,10,7,2,4,6,1,3]=>000011001=>100110000
[6,7,8,5,2,4,10,1,3,9]=>000100101=>101001000
[9,6,7,5,10,2,4,8,1,3]=>000001111=>111100000
[8,9,6,10,5,7,2,4,1,3]=>001001011=>110100100
[7,8,9,10,6,5,2,4,1,3]=>001110001=>100011100
[3,4,2,6,8,10,1,5,7,9]=>001000001=>100000100
[3,4,9,10,2,6,8,1,5,7]=>000000101=>101000000
[3,4,7,8,2,6,10,1,5,9]=>000000101=>101000000
[9,3,4,7,10,2,6,8,1,5]=>000000111=>111000000
[8,9,10,3,4,7,2,6,1,5]=>000011001=>100110000
[5,3,6,2,4,8,10,1,7,9]=>000110001=>100011000
[5,3,6,9,10,2,4,8,1,7]=>000100101=>101001000
[5,7,3,8,2,4,6,10,1,9]=>000001101=>101100000
[5,7,9,3,10,2,4,6,8,1]=>000000111=>111000000
[8,5,9,10,3,7,2,4,6,1]=>000011101=>101110000
[3,6,7,8,5,2,4,10,1,9]=>000100101=>101001000
[9,3,6,7,5,10,2,4,8,1]=>000001111=>111100000
[6,8,3,9,10,5,7,2,4,1]=>001001101=>101100100
[7,8,9,10,3,6,5,2,4,1]=>001110001=>100011100
[4,5,6,3,2,8,10,1,7,9]=>010010001=>100010010
[4,5,6,3,9,10,2,8,1,7]=>000010101=>101010000
[7,4,5,3,8,2,6,10,1,9]=>000101101=>101101000
[7,4,5,9,3,10,2,6,8,1]=>000001111=>111100000
[4,8,5,9,10,3,7,2,6,1]=>000011101=>101110000
[6,7,4,8,3,5,2,10,1,9]=>000101101=>101101000
[6,7,9,4,3,5,10,2,8,1]=>001000111=>111000100
[8,6,9,4,10,3,5,7,2,1]=>100001111=>111100001
[7,4,8,9,10,6,3,5,2,1]=>100111001=>100111001
[5,6,7,8,4,3,2,10,1,9]=>011000101=>101000110
[9,5,6,7,4,3,10,2,8,1]=>001001111=>111100100
[8,9,5,6,4,10,3,7,2,1]=>100011011=>110110001
[7,8,9,5,10,4,6,3,2,1]=>110010011=>110010011
[11,12,2,4,6,8,10,1,3,5,7,9]=>00000000101=>10100000000
[9,10,2,4,6,8,12,1,3,5,7,11]=>00000000101=>10100000000
[11,9,12,2,4,6,8,10,1,3,5,7]=>00000000111=>11100000000
[10,11,12,9,2,4,6,8,1,3,5,7]=>00000011001=>10011000000
[7,8,2,4,6,10,12,1,3,5,9,11]=>00000010001=>10001000000
[7,8,11,12,2,4,6,10,1,3,5,9]=>00000000101=>10100000000
[9,7,10,2,4,6,8,12,1,3,5,11]=>00000001101=>10110000000
[9,11,7,12,2,4,6,8,10,1,3,5]=>00000000111=>11100000000
[7,10,11,12,9,2,4,6,8,1,3,5]=>00000011001=>10011000000
[8,9,10,7,2,4,6,12,1,3,5,11]=>00000100101=>10100100000
[11,8,9,7,12,2,4,6,10,1,3,5]=>00000001111=>11110000000
[9,10,11,12,8,7,2,4,6,1,3,5]=>00001110001=>10001110000
[5,6,2,4,8,10,12,1,3,7,9,11]=>00001000001=>10000010000
[5,6,11,12,2,4,8,10,1,3,7,9]=>00000000101=>10100000000
[5,6,9,10,2,4,8,12,1,3,7,11]=>00000000101=>10100000000
[11,5,6,9,12,2,4,8,10,1,3,7]=>00000000111=>11100000000
[10,11,12,5,6,9,2,4,8,1,3,7]=>00000011001=>10011000000
[7,5,8,2,4,6,10,12,1,3,9,11]=>00000110001=>10001100000
[7,5,8,11,12,2,4,6,10,1,3,9]=>00000100101=>10100100000
[7,9,5,10,2,4,6,8,12,1,3,11]=>00000001101=>10110000000
[7,9,11,5,12,2,4,6,8,10,1,3]=>00000000111=>11100000000
[10,7,11,12,5,9,2,4,6,8,1,3]=>00000011101=>10111000000
[5,8,9,10,7,2,4,6,12,1,3,11]=>00000100101=>10100100000
[11,5,8,9,7,12,2,4,6,10,1,3]=>00000001111=>11110000000
[9,10,11,12,5,8,7,2,4,6,1,3]=>00001110001=>10001110000
[6,7,8,5,2,4,10,12,1,3,9,11]=>00010010001=>10001001000
[6,7,8,5,11,12,2,4,10,1,3,9]=>00000010101=>10101000000
[9,6,7,5,10,2,4,8,12,1,3,11]=>00000101101=>10110100000
[9,6,7,11,5,12,2,4,8,10,1,3]=>00000001111=>11110000000
[6,10,7,11,12,5,9,2,4,8,1,3]=>00000011101=>10111000000
[8,9,6,10,5,7,2,4,12,1,3,11]=>00000101101=>10110100000
[8,9,11,6,5,7,12,2,4,10,1,3]=>00001000111=>11100010000
[10,8,11,6,12,5,7,9,2,4,1,3]=>00100001111=>11110000100
[11,7,8,9,6,5,12,2,4,10,1,3]=>00001001111=>11110010000
[10,11,7,8,6,12,5,9,2,4,1,3]=>00100011011=>11011000100
[3,4,2,6,8,10,12,1,5,7,9,11]=>00100000001=>10000000100
[3,4,11,12,2,6,8,10,1,5,7,9]=>00000000101=>10100000000
[3,4,9,10,2,6,8,12,1,5,7,11]=>00000000101=>10100000000
[11,3,4,9,12,2,6,8,10,1,5,7]=>00000000111=>11100000000
[10,11,12,3,4,9,2,6,8,1,5,7]=>00000011001=>10011000000
[3,4,7,8,2,6,10,12,1,5,9,11]=>00000010001=>10001000000
[3,4,7,8,11,12,2,6,10,1,5,9]=>00000000101=>10100000000
[9,3,4,7,10,2,6,8,12,1,5,11]=>00000001101=>10110000000
[9,11,3,4,7,12,2,6,8,10,1,5]=>00000000111=>11100000000
[3,10,11,12,4,7,9,2,6,8,1,5]=>00000011001=>10011000000
[8,9,10,3,4,7,2,6,12,1,5,11]=>00000100101=>10100100000
[11,8,9,3,4,7,12,2,6,10,1,5]=>00000001111=>11110000000
[9,10,11,12,8,3,4,7,2,6,1,5]=>00001110001=>10001110000
[5,3,6,2,4,8,10,12,1,7,9,11]=>00011000001=>10000011000
[5,3,6,11,12,2,4,8,10,1,7,9]=>00010000101=>10100001000
[5,3,6,9,10,2,4,8,12,1,7,11]=>00010000101=>10100001000
[5,11,3,6,9,12,2,4,8,10,1,7]=>00000000111=>11100000000
[5,10,11,12,3,6,9,2,4,8,1,7]=>00000011001=>10011000000
[5,7,3,8,2,4,6,10,12,1,9,11]=>00000110001=>10001100000
[5,7,3,8,11,12,2,4,6,10,1,9]=>00000100101=>10100100000
[5,7,9,3,10,2,4,6,8,12,1,11]=>00000001101=>10110000000
[5,7,9,11,3,12,2,4,6,8,10,1]=>00000000111=>11100000000
[10,5,7,11,12,3,9,2,4,6,8,1]=>00000011101=>10111000000
[8,5,9,10,3,7,2,4,6,12,1,11]=>00000110101=>10101100000
[8,11,5,9,3,7,12,2,4,6,10,1]=>00000001111=>11110000000
[5,9,10,11,12,8,3,7,2,4,6,1]=>00001110001=>10001110000
[3,6,7,8,5,2,4,10,12,1,9,11]=>00010010001=>10001001000
[3,6,7,8,5,11,12,2,4,10,1,9]=>00000010101=>10101000000
[9,3,6,7,5,10,2,4,8,12,1,11]=>00000101101=>10110100000
[9,3,6,7,11,5,12,2,4,8,10,1]=>00000001111=>11110000000
[6,10,3,7,11,12,5,9,2,4,8,1]=>00000011101=>10111000000
[6,8,3,9,10,5,7,2,4,12,1,11]=>00000110101=>10101100000
[6,8,9,3,11,5,7,12,2,4,10,1]=>00000001111=>11110000000
[10,6,8,3,11,12,5,7,9,2,4,1]=>00100011101=>10111000100
[11,7,8,9,3,6,5,12,2,4,10,1]=>00001001111=>11110010000
[10,11,7,8,3,6,12,5,9,2,4,1]=>00100011011=>11011000100
[4,5,6,3,2,8,10,12,1,7,9,11]=>01001000001=>10000010010
[4,5,6,3,11,12,2,8,10,1,7,9]=>00001000101=>10100010000
[4,5,6,3,9,10,2,8,12,1,7,11]=>00001000101=>10100010000
[4,5,6,11,3,9,12,2,8,10,1,7]=>00000000111=>11100000000
[4,5,6,10,11,12,3,9,2,8,1,7]=>00000011001=>10011000000
[7,4,5,3,8,11,12,2,6,10,1,9]=>00010100101=>10100101000
[7,4,5,9,3,10,2,6,8,12,1,11]=>00000101101=>10110100000
[7,4,5,9,11,3,12,2,6,8,10,1]=>00000100111=>11100100000
[7,10,4,5,11,12,3,9,2,6,8,1]=>00000011101=>10111000000
[4,8,5,9,10,3,7,2,6,12,1,11]=>00000110101=>10101100000
[4,8,11,5,9,3,7,12,2,6,10,1]=>00000001111=>11110000000
[4,5,9,10,11,12,8,3,7,2,6,1]=>00001110001=>10001110000
[6,7,4,8,3,5,11,12,2,10,1,9]=>00000110101=>10101100000
[6,7,9,4,11,3,5,12,2,8,10,1]=>00000001111=>11110000000
[10,6,7,4,11,12,3,5,9,2,8,1]=>00000111101=>10111100000
[8,6,9,4,10,3,5,7,2,12,1,11]=>00000111101=>10111100000
[8,6,9,11,4,3,5,7,12,2,10,1]=>00100010111=>11101000100
[7,11,4,8,9,6,3,5,12,2,10,1]=>00001001111=>11110010000
[9,7,10,4,11,12,6,8,3,5,2,1]=>10010011101=>10111001001
[5,6,7,8,4,3,11,12,2,10,1,9]=>00100010101=>10101000100
[9,5,6,7,4,3,10,2,8,12,1,11]=>00100101101=>10110100100
[9,5,6,7,4,11,3,12,2,8,10,1]=>00000101111=>11110100000
[5,10,6,7,4,11,12,3,9,2,8,1]=>00000111101=>10111100000
[8,9,5,6,4,10,3,7,2,12,1,11]=>00001101101=>10110110000
[8,9,5,6,11,4,3,7,12,2,10,1]=>00100001111=>11110000100
[10,8,5,6,11,4,12,3,7,9,2,1]=>10000011111=>11111000001
[9,5,10,6,11,12,4,8,3,7,2,1]=>10000111101=>10111100001
[7,8,9,11,5,4,6,3,12,2,10,1]=>00011000111=>11100011000
[10,7,8,11,5,4,6,12,3,9,2,1]=>10010001111=>11110001001
[9,10,7,11,5,12,4,6,8,3,2,1]=>11000010111=>11101000011
[8,9,5,10,11,12,7,4,6,3,2,1]=>11001101001=>10010110011
[11,6,7,8,9,5,4,3,12,2,10,1]=>00110001111=>11110001100
[10,11,6,7,8,5,4,12,3,9,2,1]=>10010011011=>11011001001
[8,9,10,11,6,12,5,7,4,3,2,1]=>11100100011=>11000100111
[7,6,1,8,2,5,4,3]=>0011111=>1111100
[8,4,1,6,7,3,5,2]=>0011011=>1101100
[5,8,4,2,1,6,3,7]=>1010101=>1010101
[7,6,4,1,2,5,3,8]=>0011110=>0111100
[5,4,2,8,1,6,3,7]=>0011101=>1011100
[8,7,2,6,4,5,3,1]=>0101111=>1111010
[7,2,8,4,3,6,1,5]=>0010111=>1110100
[1,7,5,4,8,6,2,3]=>0001111=>1111000
[4,8,6,3,5,2,1,7]=>1001101=>1011001
[5,8,6,3,2,7,1,4]=>0100111=>1110010
[5,7,6,3,2,4,8,1]=>0100111=>1110010
[5,7,3,2,8,6,4,1]=>0110111=>1110110
[4,5,1,6,8,2,7,3]=>0001011=>1101000
[1,2,4,5,6,8,10,9,3,7]=>000000011=>110000000
[1,2,3,5,7,8,10,6,9,4]=>000000011=>110000000
[1,2,4,5,7,8,10,3,9,6]=>000000011=>110000000
[1,2,4,6,7,5,10,8,3,9]=>000001101=>101100000
[1,3,4,2,7,8,10,5,9,6]=>001000011=>110000100
[1,3,4,6,7,2,10,8,5,9]=>000001101=>101100000
[1,2,3,5,6,9,8,10,7,4]=>000001011=>110100000
[1,2,4,5,6,9,8,10,3,7]=>000000011=>110000000
[1,2,3,5,7,9,6,10,8,4]=>000000111=>111000000
[1,2,4,5,7,9,3,10,8,6]=>000000111=>111000000
[1,2,4,6,5,9,7,10,3,8]=>000010011=>110010000
[1,3,4,2,7,9,5,10,8,6]=>001000111=>111000100
[1,3,4,6,2,9,7,10,5,8]=>000010011=>110010000
[1,2,3,5,8,7,9,6,10,4]=>000000111=>111000000
[1,2,4,5,8,7,9,3,10,6]=>000000111=>111000000
[1,2,4,6,8,5,9,3,10,7]=>000000111=>111000000
[1,2,4,7,6,8,5,9,3,10]=>000001110=>011100000
[1,3,4,2,8,7,9,5,10,6]=>001000111=>111000100
[1,3,4,6,8,2,9,5,10,7]=>000000111=>111000000
[1,3,4,7,6,8,2,9,5,10]=>000001110=>011100000
[1,2,3,6,5,9,7,10,8,4]=>000010111=>111010000
[1,2,4,6,3,9,7,10,8,5]=>000010111=>111010000
[1,2,5,4,6,9,7,10,3,8]=>000100011=>110001000
[1,3,2,6,4,9,7,10,8,5]=>010010111=>111010010
[1,3,5,2,6,9,7,10,4,8]=>000100011=>110001000
[1,2,3,6,8,5,9,7,10,4]=>000000111=>111000000
[1,2,4,6,8,3,9,7,10,5]=>000000111=>111000000
[1,2,5,4,8,6,9,3,10,7]=>000100111=>111001000
[1,2,5,7,4,8,6,9,3,10]=>000001110=>011100000
[1,3,2,6,8,4,9,7,10,5]=>010000111=>111000010
[1,3,5,2,8,6,9,4,10,7]=>000100111=>111001000
[1,3,5,7,2,8,6,9,4,10]=>000001110=>011100000
[1,4,3,5,8,2,9,6,10,7]=>001000111=>111000100
[1,4,3,7,5,8,2,9,6,10]=>001001110=>011100100
[2,1,3,6,4,9,7,10,8,5]=>100010111=>111010001
[2,1,5,3,6,9,7,10,4,8]=>100100011=>110001001
[2,1,3,6,8,4,9,7,10,5]=>100000111=>111000001
[2,1,5,3,8,6,9,4,10,7]=>100100111=>111001001
[2,1,5,7,3,8,6,9,4,10]=>100001110=>011100001
[2,4,1,5,8,3,9,6,10,7]=>001000111=>111000100
[2,4,1,7,5,8,3,9,6,10]=>001001110=>011100100
[1,6,3,7,2,4,8,5]=>0000111=>1110000
[8,9,7,6,5,4,3,1,2]=>01111101=>10111110
[8,6,7,5,4,3,2,1,9]=>11110110=>01101111
[8,7,9,6,5,4,3,1,2]=>01111011=>11011110
[9,7,8,6,5,4,3,1,2]=>01111011=>11011110
[4,3,7,1,6,2,5,8]=>0010110=>0110100
[4,3,1,6,7,2,5,8]=>0110010=>0100110
[6,3,1,5,7,2,4,8]=>0100110=>0110010
[8,7,5,4,3,6,9,2,1]=>10110111=>11101101
[8,7,6,9,5,3,4,2,1]=>10110111=>11101101
[8,7,9,6,5,4,2,3,1]=>01111011=>11011110
[5,2,1,4,8,6,7,3]=>1001011=>1101001
[4,5,2,1,3,7,6,8]=>1001010=>0101001
[8,2,7,4,1,6,5,3]=>0011111=>1111100
[3,2,8,4,1,6,5,7]=>0110101=>1010110
[3,7,6,4,1,5,8,2]=>0010111=>1110100
[7,1,6,5,4,2,8,3]=>0011111=>1111100
[7,1,8,4,2,3,6,5]=>0010111=>1110100
[2,7,6,4,5,1,8,3]=>0001111=>1111000
[4,6,8,1,7,3,5,2]=>0001011=>1101000
[3,6,8,1,5,7,4,2]=>0010011=>1100100
[2,8,3,1,6,7,4,5]=>0100011=>1100010
[4,5,6,8,2,1,7,3]=>1000011=>1100001
[4,5,6,8,1,3,7,2]=>0000011=>1100000
[4,5,8,3,2,1,7,6]=>1100011=>1100011
[4,5,1,3,2,6,7,8]=>0101000=>0001010
[4,7,3,2,1,6,5,8]=>1100110=>0110011
[4,7,8,3,5,1,6,2]=>0001101=>1011000
[4,7,1,3,5,6,2,8]=>0000110=>0110000
[4,8,3,2,1,6,7,5]=>1100011=>1100011
[5,2,8,1,4,6,7,3]=>0001011=>1101000
[5,6,3,7,8,1,4,2]=>0010101=>1010100
[5,7,1,4,3,6,2,8]=>0010110=>0110100
[6,2,3,7,1,5,4,8]=>0001110=>0111000
[6,2,8,1,5,4,7,3]=>0001111=>1111000
[6,1,3,4,5,2,7,8]=>0001100=>0011000
[7,1,3,4,5,6,2,8]=>0000110=>0110000
[7,2,5,1,3,6,4,8]=>0001110=>0111000
[6,5,2,7,8,4,3,1]=>0111101=>1011110
[7,5,3,6,4,2,1,8]=>1011110=>0111101
[2,3,6,5,8,4,7,1]=>0000111=>1110000
[1,3,6,7,5,2,4,8]=>0001010=>0101000
[1,5,2,6,8,7,3,4]=>0001011=>1101000
[3,2,1,5,6,7,8,9,4]=>11000001=>10000011
[3,2,6,1,4,7,8,9,5]=>01001001=>10010010
[4,3,2,1,6,7,8,9,5]=>11100001=>10000111
[3,2,7,8,1,4,5,9,6]=>01000011=>11000010
[4,7,2,5,1,3,8,9,6]=>00010101=>10101000
[4,3,2,7,1,5,8,9,6]=>01100101=>10100110
[5,4,3,2,1,7,8,9,6]=>11110001=>10001111
[4,3,2,8,9,1,5,6,7]=>01100001=>10000110
[8,5,6,3,4,1,2,9,7]=>00101011=>11010100
[5,3,8,2,6,1,4,9,7]=>00011011=>11011000
[5,4,3,2,8,1,6,9,7]=>01110011=>11001110
[6,5,4,3,2,1,8,9,7]=>11111001=>10011111
[6,9,4,7,2,5,1,3,8]=>00010101=>10101000
[6,4,3,9,2,7,1,5,8]=>00101101=>10110100
[6,5,4,3,2,9,1,7,8]=>01111001=>10011110
[5,6,1,2,3,7,8,9,10,4]=>000010001=>100010000
[2,5,1,3,6,7,8,9,10,4]=>000100001=>100001000
[3,2,1,5,6,7,8,9,10,4]=>110000001=>100000011
[6,7,8,1,2,3,4,9,10,5]=>000000101=>101000000
[2,6,7,1,3,4,8,9,10,5]=>000001001=>100100000
[6,3,4,1,2,7,8,9,10,5]=>001010001=>100010100
[3,2,6,1,4,7,8,9,10,5]=>010010001=>100010010
[4,3,2,1,6,7,8,9,10,5]=>111000001=>100000111
[2,7,8,9,1,3,4,5,10,6]=>000000011=>110000000
[7,3,4,8,1,2,5,9,10,6]=>000001101=>101100000
[3,2,7,8,1,4,5,9,10,6]=>010000101=>101000010
[4,7,2,5,1,3,8,9,10,6]=>000101001=>100101000
[4,3,2,7,1,5,8,9,10,6]=>011001001=>100100110
[5,4,3,2,1,7,8,9,10,6]=>111100001=>100001111
[8,3,4,9,10,1,2,5,6,7]=>000000101=>101000000
[8,9,4,5,6,1,2,3,10,7]=>000010011=>110010000
[4,3,2,8,9,1,5,6,10,7]=>011000011=>110000110
[8,5,6,3,4,1,2,9,10,7]=>001010101=>101010100
[5,3,8,2,6,1,4,9,10,7]=>000110101=>101011000
[5,4,3,2,8,1,6,9,10,7]=>011100101=>101001110
[6,5,4,3,2,1,8,9,10,7]=>111110001=>100011111
[5,9,10,2,6,7,1,3,4,8]=>000001001=>100100000
[9,5,6,3,4,10,1,2,7,8]=>000010011=>110010000
[5,3,9,2,6,10,1,4,7,8]=>000100011=>110001000
[5,4,3,2,9,10,1,6,7,8]=>011100001=>100001110
[6,9,4,7,2,5,1,3,10,8]=>000101011=>110101000
[6,4,3,9,2,7,1,5,10,8]=>001011011=>110110100
[6,5,4,3,2,9,1,7,10,8]=>011110011=>110011110
[7,6,5,4,3,2,1,9,10,8]=>111111001=>100111111
[10,7,8,5,6,3,4,1,2,9]=>001010101=>101010100
[7,5,10,3,8,2,6,1,4,9]=>000011101=>101110000
[7,5,4,3,10,2,8,1,6,9]=>001101101=>101101100
[7,6,5,4,3,2,10,1,8,9]=>011111001=>100111110
[5,3,4,7,2,1,6,8]=>1001010=>0101001
[7,6,9,5,4,3,2,1,8]=>11110101=>10101111
[4,8,5,7,1,2,3,6]=>0000011=>1100000
[4,2,3,7,6,1,8,5]=>0010111=>1110100
[4,2,6,3,1,5,7,8]=>0110100=>0010110
[2,1,8,7,4,3,6,5,10,9]=>101011101=>101110101
[6,5,2,1,4,3,12,11,8,7,10,9]=>10111010111=>11101011101
[4,6,3,2,5,8,7,1]=>0100111=>1110010
[5,8,4,3,2,6,1,7]=>0110101=>1010110
[1,5,7,4,8,6,2,3]=>0000111=>1110000
[6,1,5,7,3,8,2,4]=>0000111=>1110000
[1,2,7,8,6,4,3,5]=>0010101=>1010100
[3,5,1,7,8,6,2,4]=>0001101=>1011000
[5,2,4,1,7,6,8,3]=>0011011=>1101100
[2,1,4,3,6,5,7,9,10,8]=>101010001=>100010101
[2,1,4,3,5,7,8,6,10,9]=>101000101=>101000101
[2,1,4,3,5,7,6,9,10,8]=>101001001=>100100101
[2,1,4,3,5,6,8,9,10,7]=>101000001=>100000101
[2,1,3,5,6,4,8,7,10,9]=>100010101=>101010001
[2,1,3,5,6,4,7,9,10,8]=>100010001=>100010001
[2,1,3,5,4,7,8,6,10,9]=>100100101=>101001001
[2,1,3,5,4,7,6,9,10,8]=>100101001=>100101001
[2,1,3,5,4,6,8,9,10,7]=>100100001=>100001001
[2,1,3,4,6,7,8,5,10,9]=>100000101=>101000001
[2,1,3,4,6,7,5,9,10,8]=>100001001=>100100001
[2,1,3,4,6,5,8,9,10,7]=>100010001=>100010001
[2,1,3,4,5,7,8,9,10,6]=>100000001=>100000001
[1,3,4,2,6,5,7,9,10,8]=>001010001=>100010100
[1,3,4,2,5,7,8,6,10,9]=>001000101=>101000100
[1,3,4,2,5,7,6,9,10,8]=>001001001=>100100100
[1,3,4,2,5,6,8,9,10,7]=>001000001=>100000100
[1,3,2,5,6,4,8,7,10,9]=>010010101=>101010010
[1,3,2,5,6,4,7,9,10,8]=>010010001=>100010010
[1,3,2,5,4,7,8,6,10,9]=>010100101=>101001010
[1,3,2,5,4,7,6,9,10,8]=>010101001=>100101010
[1,3,2,5,4,6,8,9,10,7]=>010100001=>100001010
[1,3,2,4,6,7,8,5,10,9]=>010000101=>101000010
[1,3,2,4,6,7,5,9,10,8]=>010001001=>100100010
[1,3,2,4,6,5,8,9,10,7]=>010010001=>100010010
[1,3,2,4,5,7,8,9,10,6]=>010000001=>100000010
[1,2,4,5,6,3,8,7,10,9]=>000010101=>101010000
[1,2,4,5,6,3,7,9,10,8]=>000010001=>100010000
[1,2,4,5,3,7,8,6,10,9]=>000100101=>101001000
[1,2,4,5,3,7,6,9,10,8]=>000101001=>100101000
[1,2,4,5,3,6,8,9,10,7]=>000100001=>100001000
[1,2,4,3,6,7,8,5,10,9]=>001000101=>101000100
[1,2,4,3,6,7,5,9,10,8]=>001001001=>100100100
[1,2,4,3,6,5,8,9,10,7]=>001010001=>100010100
[1,2,4,3,5,7,8,9,10,6]=>001000001=>100000100
[1,2,3,5,6,7,8,4,10,9]=>000000101=>101000000
[1,2,3,5,6,7,4,9,10,8]=>000001001=>100100000
[1,2,3,5,6,4,8,9,10,7]=>000010001=>100010000
[1,2,3,5,4,7,8,9,10,6]=>000100001=>100001000
[2,1,4,3,6,5,8,7,9,11,12,10]=>10101010001=>10001010101
[2,1,4,3,6,5,7,9,10,8,12,11]=>10101000101=>10100010101
[2,1,4,3,6,5,7,9,8,11,12,10]=>10101001001=>10010010101
[2,1,4,3,6,5,7,8,10,11,12,9]=>10101000001=>10000010101
[2,1,4,3,5,7,8,6,10,9,12,11]=>10100010101=>10101000101
[2,1,4,3,5,7,8,6,9,11,12,10]=>10100010001=>10001000101
[2,1,4,3,5,7,6,9,10,8,12,11]=>10100100101=>10100100101
[2,1,4,3,5,7,6,9,8,11,12,10]=>10100101001=>10010100101
[2,1,4,3,5,7,6,8,10,11,12,9]=>10100100001=>10000100101
[2,1,4,3,5,6,8,9,10,7,12,11]=>10100000101=>10100000101
[2,1,4,3,5,6,8,9,7,11,12,10]=>10100001001=>10010000101
[2,1,4,3,5,6,8,7,10,11,12,9]=>10100010001=>10001000101
[2,1,4,3,5,6,7,9,10,11,12,8]=>10100000001=>10000000101
[2,1,3,5,6,4,8,7,10,9,12,11]=>10001010101=>10101010001
[2,1,3,5,6,4,8,7,9,11,12,10]=>10001010001=>10001010001
[2,1,3,5,6,4,7,9,10,8,12,11]=>10001000101=>10100010001
[2,1,3,5,6,4,7,9,8,11,12,10]=>10001001001=>10010010001
[2,1,3,5,6,4,7,8,10,11,12,9]=>10001000001=>10000010001
[2,1,3,5,4,7,8,6,10,9,12,11]=>10010010101=>10101001001
[2,1,3,5,4,7,8,6,9,11,12,10]=>10010010001=>10001001001
[2,1,3,5,4,7,6,9,10,8,12,11]=>10010100101=>10100101001
[2,1,3,5,4,7,6,9,8,11,12,10]=>10010101001=>10010101001
[2,1,3,5,4,7,6,8,10,11,12,9]=>10010100001=>10000101001
[2,1,3,5,4,6,8,9,10,7,12,11]=>10010000101=>10100001001
[2,1,3,5,4,6,8,9,7,11,12,10]=>10010001001=>10010001001
[2,1,3,5,4,6,8,7,10,11,12,9]=>10010010001=>10001001001
[2,1,3,5,4,6,7,9,10,11,12,8]=>10010000001=>10000001001
[2,1,3,4,6,7,8,5,10,9,12,11]=>10000010101=>10101000001
[2,1,3,4,6,7,8,5,9,11,12,10]=>10000010001=>10001000001
[2,1,3,4,6,7,5,8,10,11,12,9]=>10000100001=>10000100001
[2,1,3,4,6,5,8,9,10,7,12,11]=>10001000101=>10100010001
[2,1,3,4,6,5,8,9,7,11,12,10]=>10001001001=>10010010001
[2,1,3,4,6,5,8,7,10,11,12,9]=>10001010001=>10001010001
[2,1,3,4,6,5,7,9,10,11,12,8]=>10001000001=>10000010001
[2,1,3,4,5,7,8,9,10,6,12,11]=>10000000101=>10100000001
[2,1,3,4,5,7,8,9,6,11,12,10]=>10000001001=>10010000001
[2,1,3,4,5,7,8,6,10,11,12,9]=>10000010001=>10001000001
[2,1,3,4,5,7,6,9,10,11,12,8]=>10000100001=>10000100001
[2,1,3,4,5,6,8,9,10,11,12,7]=>10000000001=>10000000001
[1,3,4,2,6,5,8,7,10,9,12,11]=>00101010101=>10101010100
[1,3,4,2,6,5,8,7,9,11,12,10]=>00101010001=>10001010100
[1,3,4,2,6,5,7,9,10,8,12,11]=>00101000101=>10100010100
[1,3,4,2,6,5,7,9,8,11,12,10]=>00101001001=>10010010100
[1,3,4,2,6,5,7,8,10,11,12,9]=>00101000001=>10000010100
[1,3,4,2,5,7,8,6,10,9,12,11]=>00100010101=>10101000100
[1,3,4,2,5,7,8,6,9,11,12,10]=>00100010001=>10001000100
[1,3,4,2,5,7,6,9,10,8,12,11]=>00100100101=>10100100100
[1,3,4,2,5,7,6,9,8,11,12,10]=>00100101001=>10010100100
[1,3,4,2,5,7,6,8,10,11,12,9]=>00100100001=>10000100100
[1,3,4,2,5,6,8,9,7,11,12,10]=>00100001001=>10010000100
[1,3,4,2,5,6,8,7,10,11,12,9]=>00100010001=>10001000100
[1,3,4,2,5,6,7,9,10,11,12,8]=>00100000001=>10000000100
[1,3,2,5,6,4,8,7,10,9,12,11]=>01001010101=>10101010010
[1,3,2,5,6,4,8,7,9,11,12,10]=>01001010001=>10001010010
[1,3,2,5,6,4,7,9,10,8,12,11]=>01001000101=>10100010010
[1,3,2,5,6,4,7,9,8,11,12,10]=>01001001001=>10010010010
[1,3,2,5,6,4,7,8,10,11,12,9]=>01001000001=>10000010010
[1,3,2,5,4,7,8,6,10,9,12,11]=>01010010101=>10101001010
[1,3,2,5,4,7,8,6,9,11,12,10]=>01010010001=>10001001010
[1,3,2,5,4,7,6,9,10,8,12,11]=>01010100101=>10100101010
[1,3,2,5,4,7,6,9,8,11,12,10]=>01010101001=>10010101010
[1,3,2,5,4,7,6,8,10,11,12,9]=>01010100001=>10000101010
[1,3,2,5,4,6,8,9,7,11,12,10]=>01010001001=>10010001010
[1,3,2,5,4,6,8,7,10,11,12,9]=>01010010001=>10001001010
[1,3,2,5,4,6,7,9,10,11,12,8]=>01010000001=>10000001010
[1,3,2,4,6,7,8,5,9,11,12,10]=>01000010001=>10001000010
[1,3,2,4,6,7,5,9,10,8,12,11]=>01000100101=>10100100010
[1,3,2,4,6,7,5,9,8,11,12,10]=>01000101001=>10010100010
[1,3,2,4,6,7,5,8,10,11,12,9]=>01000100001=>10000100010
[1,3,2,4,6,5,8,9,10,7,12,11]=>01001000101=>10100010010
[1,3,2,4,6,5,8,9,7,11,12,10]=>01001001001=>10010010010
[1,3,2,4,6,5,8,7,10,11,12,9]=>01001010001=>10001010010
[1,3,2,4,6,5,7,9,10,11,12,8]=>01001000001=>10000010010
[1,3,2,4,5,7,8,9,10,6,12,11]=>01000000101=>10100000010
[1,3,2,4,5,7,8,9,6,11,12,10]=>01000001001=>10010000010
[1,3,2,4,5,7,8,6,10,11,12,9]=>01000010001=>10001000010
[1,3,2,4,5,7,6,9,10,11,12,8]=>01000100001=>10000100010
[1,3,2,4,5,6,8,9,10,11,12,7]=>01000000001=>10000000010
[1,2,4,5,6,3,8,7,10,9,12,11]=>00001010101=>10101010000
[1,2,4,5,6,3,8,7,9,11,12,10]=>00001010001=>10001010000
[1,2,4,5,6,3,7,9,10,8,12,11]=>00001000101=>10100010000
[1,2,4,5,6,3,7,9,8,11,12,10]=>00001001001=>10010010000
[1,2,4,5,6,3,7,8,10,11,12,9]=>00001000001=>10000010000
[1,2,4,5,3,7,8,6,10,9,12,11]=>00010010101=>10101001000
[1,2,4,5,3,7,8,6,9,11,12,10]=>00010010001=>10001001000
[1,2,4,5,3,7,6,9,10,8,12,11]=>00010100101=>10100101000
[1,2,4,5,3,7,6,9,8,11,12,10]=>00010101001=>10010101000
[1,2,4,5,3,7,6,8,10,11,12,9]=>00010100001=>10000101000
[1,2,4,5,3,6,8,9,10,7,12,11]=>00010000101=>10100001000
[1,2,4,5,3,6,8,9,7,11,12,10]=>00010001001=>10010001000
[1,2,4,5,3,6,8,7,10,11,12,9]=>00010010001=>10001001000
[1,2,4,3,6,7,8,5,10,9,12,11]=>00100010101=>10101000100
[1,2,4,3,6,7,8,5,9,11,12,10]=>00100010001=>10001000100
[1,2,4,3,6,7,5,9,10,8,12,11]=>00100100101=>10100100100
[1,2,4,3,6,7,5,9,8,11,12,10]=>00100101001=>10010100100
[1,2,4,3,6,7,5,8,10,11,12,9]=>00100100001=>10000100100
[1,2,4,3,6,5,8,9,10,7,12,11]=>00101000101=>10100010100
[1,2,4,3,6,5,8,9,7,11,12,10]=>00101001001=>10010010100
[1,2,4,3,6,5,8,7,10,11,12,9]=>00101010001=>10001010100
[1,2,4,3,6,5,7,9,10,11,12,8]=>00101000001=>10000010100
[1,2,4,3,5,7,8,9,6,11,12,10]=>00100001001=>10010000100
[1,2,4,3,5,7,8,6,10,11,12,9]=>00100010001=>10001000100
[1,2,4,3,5,7,6,9,10,11,12,8]=>00100100001=>10000100100
[1,2,4,3,5,6,8,9,10,11,12,7]=>00100000001=>10000000100
[1,2,3,5,6,7,8,4,10,9,12,11]=>00000010101=>10101000000
[1,2,3,5,6,7,8,4,9,11,12,10]=>00000010001=>10001000000
[1,2,3,5,6,7,4,9,10,8,12,11]=>00000100101=>10100100000
[1,2,3,5,6,7,4,9,8,11,12,10]=>00000101001=>10010100000
[1,2,3,5,6,7,4,8,10,11,12,9]=>00000100001=>10000100000
[1,2,3,5,6,4,8,9,10,7,12,11]=>00001000101=>10100010000
[1,2,3,5,6,4,8,9,7,11,12,10]=>00001001001=>10010010000
[1,2,3,5,6,4,8,7,10,11,12,9]=>00001010001=>10001010000
[1,2,3,5,6,4,7,9,10,11,12,8]=>00001000001=>10000010000
[1,2,3,5,4,7,8,9,10,6,12,11]=>00010000101=>10100001000
[1,2,3,5,4,7,8,9,6,11,12,10]=>00010001001=>10010001000
[1,2,3,5,4,7,8,6,10,11,12,9]=>00010010001=>10001001000
[1,2,3,5,4,7,6,9,10,11,12,8]=>00010100001=>10000101000
[1,2,3,4,6,7,8,9,10,5,12,11]=>00000000101=>10100000000
[1,2,3,4,6,7,8,9,5,11,12,10]=>00000001001=>10010000000
[1,2,3,4,6,7,8,5,10,11,12,9]=>00000010001=>10001000000
[1,2,3,4,6,7,5,9,10,11,12,8]=>00000100001=>10000100000
[1,2,3,4,6,5,8,9,10,11,12,7]=>00001000001=>10000010000
[1,2,3,4,5,7,8,9,10,11,12,6]=>00000000001=>10000000000
[2,3,4,9,6,7,8,5,1]=>00010011=>11001000
[2,3,9,5,6,7,8,4,1]=>00100011=>11000100
[2,9,4,5,6,7,8,3,1]=>01000011=>11000010
[9,3,4,5,6,7,8,2,1]=>10000011=>11000001
[2,3,4,5,6,10,8,9,7,1]=>000001011=>110100000
[2,3,4,1,9,7,8,6,5]=>00101011=>11010100
[2,3,4,5,10,7,8,9,6,1]=>000010011=>110010000
[2,3,1,9,6,7,8,5,4]=>01010011=>11001010
[2,3,4,10,6,7,8,9,5,1]=>000100011=>110001000
[2,1,9,5,6,7,8,4,3]=>10100011=>11000101
[2,3,10,5,6,7,8,9,4,1]=>001000011=>110000100
[1,9,4,5,6,7,8,3,2]=>01000011=>11000010
[2,10,4,5,6,7,8,9,3,1]=>010000011=>110000010
[10,3,4,5,6,7,8,9,2,1]=>100000011=>110000001
[5,6,4,7,3,9,1,8,2]=>00001111=>11110000
[5,6,4,9,1,8,2,7,3]=>00001111=>11110000
[5,9,1,8,2,7,3,6,4]=>00001111=>11110000
[9,1,8,2,7,3,6,4,5]=>00001111=>11110000
[5,4,3,8,1,7,2,6]=>0011011=>1101100
[5,4,9,1,8,2,7,3,6]=>00010111=>11101000
[5,4,6,3,9,1,8,2,7]=>00011011=>11011000
[5,4,6,3,7,2,9,1,8]=>00011101=>10111000
[6,5,7,4,8,3,10,1,9,2]=>000011111=>111110000
[5,6,4,8,2,9,1,7,3]=>00001111=>11110000
[6,5,7,4,10,1,9,2,8,3]=>000011111=>111110000
[5,7,3,9,1,8,2,6,4]=>00001111=>11110000
[6,5,10,1,9,2,8,3,7,4]=>000011111=>111110000
[6,4,9,1,8,2,7,3,5]=>00001111=>11110000
[4,5,9,1,8,2,7,3,6]=>00000111=>11100000
[5,10,1,9,2,8,3,7,4,6]=>000001111=>111100000
[6,4,5,3,9,1,8,2,7]=>00011011=>11011000
[5,6,4,10,1,9,2,8,3,7]=>000010111=>111010000
[5,4,7,3,6,2,9,1,8]=>00011101=>10111000
[5,6,4,7,3,10,1,9,2,8]=>000011011=>110110000
[5,6,4,7,3,8,2,10,1,9]=>000011101=>101110000
[7,3,1,5,6,8,4,2]=>0110011=>1100110
[2,10,1,3,4,5,6,9,7,8]=>000000011=>110000000
[2,9,1,3,4,5,6,7,10,8]=>000000011=>110000000
[12,1,2,3,4,5,6,7,8,11,9,10]=>00000000011=>11000000000
[2,11,1,3,4,5,6,7,10,8,9]=>0000000011=>1100000000
[10,3,1,2,4,5,6,9,7,8]=>010000011=>110000010
[3,1,10,2,4,5,6,9,7,8]=>010000011=>110000010
[9,3,1,2,4,5,6,7,10,8]=>010000011=>110000010
[3,1,9,2,4,5,6,7,10,8]=>010000011=>110000010
[2,10,1,3,4,5,6,7,8,11,9]=>0000000011=>1100000000
[7,2,3,1,6,8,4,5]=>0100011=>1100010
[4,1,8,2,5,6,3,7]=>0010101=>1010100
[5,7,8,1,6,2,3,4]=>0000101=>1010000
[1,6,4,2,7,3,8,5]=>0010111=>1110100
[1,4,2,5,8,6,3,7]=>0010101=>1010100
[5,4,3,2,1,8,9,7,6]=>11110101=>10101111
[4,3,2,1,8,9,7,6,5]=>11101101=>10110111
[3,2,1,8,9,7,6,5,4]=>11011101=>10111011
[2,1,8,9,7,6,5,4,3]=>10111101=>10111101
[4,8,2,1,5,7,3,6]=>1000011=>1100001
[5,2,7,1,6,3,4,8]=>0001110=>0111000
[4,8,2,5,1,6,3,7]=>0001101=>1011000
[5,8,1,2,4,6,3,7]=>0000101=>1010000
[5,1,7,3,6,4,2,8]=>0011110=>0111100
[3,2,7,5,6,1,4,8]=>0100110=>0110010
[3,2,7,1,6,4,5,8]=>0100110=>0110010
[6,3,1,7,5,4,2,8]=>0111110=>0111110
[9,8,3,4,5,6,7,1,2]=>00000111=>11100000
[9,8,2,3,4,5,6,1,7]=>00001011=>11010000
[6,2,8,7,3,4,5,1]=>0001111=>1111000
[9,4,5,6,7,8,2,1,3]=>10000011=>11000001
[9,3,4,5,6,7,2,1,8]=>10000101=>10100001
[11,2,1,3,4,5,6,7,8,9,10]=>1000000001=>1000000001
[12,11,1,2,3,4,5,6,7,8,9,10]=>00000000011=>11000000000
[11,10,2,3,4,5,6,7,8,9,1]=>0000000111=>1110000000
[10,9,3,4,5,6,7,8,1,2]=>000000111=>111000000
[10,9,2,3,4,5,6,7,1,8]=>000001011=>110100000
[7,2,9,8,3,4,5,6,1]=>00001111=>11110000
[9,8,2,3,4,5,1,6,7]=>00010011=>11001000
[7,3,4,8,5,6,2,1]=>1000111=>1110001
[9,5,6,7,8,2,1,3,4]=>10000011=>11000001
[7,3,6,8,4,5,2,1]=>1001011=>1101001
[8,3,9,4,5,6,7,2,1]=>10000111=>11100001
[10,4,5,6,7,8,9,2,1,3]=>100000011=>110000001
[9,3,4,5,6,2,1,7,8]=>10001001=>10010001
[10,3,4,5,6,7,8,2,1,9]=>100000101=>101000001
[11,3,4,5,6,7,8,9,10,2,1]=>1000000011=>1100000001
[12,2,1,3,4,5,6,7,8,9,10,11]=>10000000001=>10000000001
[5,6,2,8,3,1,7,4]=>0100111=>1110010
[1,4,7,5,6,2,8,3]=>0000111=>1110000
[1,7,4,8,3,5,6,2]=>0000111=>1110000
[5,3,1,4,8,6,2,7]=>0101101=>1011010
[5,2,4,8,3,1,6,7]=>0101001=>1001010
[7,4,5,1,8,6,2,3]=>0001111=>1111000
[8,1,5,7,6,3,2,4]=>0100111=>1110010
[1,8,6,7,5,3,2,4]=>0101011=>1101010
[7,4,8,3,1,6,5,2]=>0101111=>1111010
[8,1,5,3,7,6,2,4]=>0001111=>1111000
[6,4,8,7,3,5,1,2]=>0001111=>1111000
[6,1,4,2,3,5,7,8]=>0010100=>0010100
[6,5,1,8,3,7,4,2]=>0011111=>1111100
[7,1,4,3,8,6,5,2]=>0011111=>1111100
[8,5,4,1,7,3,2,6]=>0111011=>1101110
[4,5,3,8,1,7,6,2]=>0001111=>1111000
[4,7,6,3,2,8,5,1]=>0101111=>1111010
[5,7,6,3,8,2,4,1]=>0010111=>1110100
[6,8,4,7,1,2,5,3]=>0001011=>1101000
[1,3,7,6,8,4,5,2]=>0001011=>1101000
[6,1,5,7,2,8,3,4]=>0000111=>1110000
[1,8,7,2,5,6,3,4]=>0000111=>1110000
[1,8,2,6,7,4,3,5]=>0010011=>1100100
[2,5,4,8,7,6,1,3]=>0001111=>1111000
[1,8,7,6,3,5,4,2]=>0011111=>1111100
[1,8,5,7,6,4,3,2]=>0110111=>1110110
[1,6,2,7,3,8,4,9,5]=>00001111=>11110000
[1,8,5,2,9,6,3,10,7,4]=>000111111=>111111000
[7,2,4,1,8,5,3,6]=>0011011=>1101100
[7,3,2,1,4,6,8,5]=>1100011=>1100011
[4,7,2,6,1,8,3,5]=>0000111=>1110000
[8,7,3,5,2,1,6,4]=>1001111=>1111001
[7,5,3,2,1,6,8,4]=>1101011=>1101011
[6,8,1,3,4,2,5,7]=>0010001=>1000100
[2,5,7,1,3,6,4,8]=>0000110=>0110000
[1,4,7,2,5,3,6,8]=>0001010=>0101000
[4,5,3,1,2,6,8,7]=>0101001=>1001010
[4,5,1,3,8,2,6,7]=>0001001=>1001000
[4,1,5,3,2,7,6,8]=>0111010=>0101110
[7,3,5,1,4,2,6,8]=>0011010=>0101100
[6,2,1,7,4,3,8,5]=>1010111=>1110101
[2,4,3,6,7,1,5,8]=>0010010=>0100100
[7,3,5,2,1,6,4,8]=>1001110=>0111001
[4,6,5,2,1,3,7,8]=>1001100=>0011001
[2,5,6,1,4,3,7,8]=>0010100=>0010100
[6,1,5,3,7,2,4,8]=>0001110=>0111000
[3,6,5,4,1,7,2,8]=>0011110=>0111100
[10,9,3,8,7,6,5,4,2,1]=>101111111=>111111101
[8,7,6,4,5,3,2,1,10,9]=>110111101=>101111011
[10,9,8,6,5,4,7,3,2,1]=>110111111=>111111011
[9,11,1,2,3,4,5,6,7,8,10]=>0000000001=>1000000000
[6,7,1,9,2,3,4,5,8]=>00000101=>10100000
[6,1,8,9,2,3,4,5,7]=>00001001=>10010000
[8,1,9,10,2,3,4,5,6,7]=>000000101=>101000000
[6,8,7,5,4,2,1,3]=>1011011=>1101101
[1,6,8,7,3,2,4,5]=>0100011=>1100010
[8,7,5,4,6,1,3,2]=>0101111=>1111010
[1,7,8,2,4,6,3,5]=>0000101=>1010000
[7,5,4,8,1,3,6,2]=>0001111=>1111000
[5,6,1,8,4,3,7,2]=>0010111=>1110100
[1,8,2,6,7,5,4,3]=>0011011=>1101100
[2,7,5,1,6,8,3,4]=>0001011=>1101000
[8,5,4,2,7,3,6,1]=>0011111=>1111100
[3,8,6,1,2,4,5,7]=>0000101=>1010000
[1,8,5,3,2,7,4,6]=>0101011=>1101010
[1,8,4,7,2,3,5,6]=>0000011=>1100000
[3,2,8,1,7,5,4,6]=>0101011=>1101010
[3,4,5,6,2,1,7,8,9]=>10001000=>00010001
[3,4,5,2,1,6,7,8,9]=>10010000=>00001001
[7,1,5,6,2,3,4,8]=>0000110=>0110000
[6,5,1,7,2,3,4,8]=>0001110=>0111000
[1,6,8,2,7,3,4,5]=>0000011=>1100000
[1,6,8,7,3,4,2,5]=>0010011=>1100100
[4,1,3,6,7,8,5,2]=>0011001=>1001100
[7,4,1,5,6,8,3,2]=>0110011=>1100110
[4,1,2,6,7,8,5,3]=>0011001=>1001100
[5,10,4,9,3,8,2,1,7,6]=>100001111=>111100001
[5,10,4,9,3,2,8,7,1,6]=>010001111=>111100010
[5,10,4,9,3,2,8,1,7,6]=>010001111=>111100010
[5,10,4,9,3,2,1,8,7,6]=>110001111=>111100011
[5,10,4,3,9,8,2,7,1,6]=>001001111=>111100100
[5,10,4,3,9,8,2,1,7,6]=>101001111=>111100101
[5,10,4,3,9,2,8,7,1,6]=>001001111=>111100100
[5,10,4,3,9,2,8,1,7,6]=>001001111=>111100100
[5,10,4,3,9,2,1,8,7,6]=>101001111=>111100101
[5,10,4,3,2,9,8,7,1,6]=>011001111=>111100110
[5,10,4,3,2,9,8,1,7,6]=>011001111=>111100110
[5,10,4,3,2,9,1,8,7,6]=>011001111=>111100110
[5,10,4,3,2,1,9,8,7,6]=>111001111=>111100111
[5,4,10,9,3,8,2,7,1,6]=>000101111=>111101000
[5,4,10,9,3,8,2,1,7,6]=>100101111=>111101001
[5,4,10,9,3,2,8,7,1,6]=>010101111=>111101010
[5,4,10,9,3,2,8,1,7,6]=>010101111=>111101010
[5,4,10,9,3,2,1,8,7,6]=>110101111=>111101011
[5,4,10,3,9,8,2,7,1,6]=>000101111=>111101000
[5,4,10,3,9,8,2,1,7,6]=>100101111=>111101001
[5,4,10,3,9,2,8,7,1,6]=>000101111=>111101000
[5,4,10,3,9,2,8,1,7,6]=>000101111=>111101000
[5,4,10,3,9,2,1,8,7,6]=>100101111=>111101001
[5,4,10,3,2,9,8,7,1,6]=>010101111=>111101010
[5,4,10,3,2,9,8,1,7,6]=>010101111=>111101010
[5,4,10,3,2,9,1,8,7,6]=>010101111=>111101010
[5,4,10,3,2,1,9,8,7,6]=>110101111=>111101011
[5,4,3,10,9,8,2,7,1,6]=>001101111=>111101100
[5,4,3,10,9,8,2,1,7,6]=>101101111=>111101101
[5,4,3,10,9,2,8,7,1,6]=>001101111=>111101100
[5,4,3,10,9,2,8,1,7,6]=>001101111=>111101100
[5,4,3,10,9,2,1,8,7,6]=>101101111=>111101101
[5,4,3,10,2,9,8,7,1,6]=>001101111=>111101100
[5,4,3,10,2,9,8,1,7,6]=>001101111=>111101100
[5,4,3,10,2,9,1,8,7,6]=>001101111=>111101100
[5,4,3,10,2,1,9,8,7,6]=>101101111=>111101101
[5,4,3,2,10,9,8,7,1,6]=>011101111=>111101110
[5,4,3,2,10,9,8,1,7,6]=>011101111=>111101110
[5,4,3,2,10,9,1,8,7,6]=>011101111=>111101110
[5,4,3,2,10,1,9,8,7,6]=>011101111=>111101110
[6,12,5,11,4,10,3,9,2,1,8,7]=>10000011111=>11111000001
[6,12,5,11,4,10,3,2,9,8,1,7]=>01000011111=>11111000010
[6,12,5,11,4,10,3,2,9,1,8,7]=>01000011111=>11111000010
[6,12,5,11,4,3,10,9,2,8,1,7]=>00100011111=>11111000100
[6,12,5,11,4,3,10,2,9,8,1,7]=>00100011111=>11111000100
[6,12,5,11,4,3,10,2,9,1,8,7]=>00100011111=>11111000100
[6,12,5,11,4,3,2,1,10,9,8,7]=>11100011111=>11111000111
[6,12,5,4,11,10,3,9,2,8,1,7]=>00010011111=>11111001000
[6,12,5,4,11,3,10,9,2,8,1,7]=>00010011111=>11111001000
[6,12,5,4,11,3,10,2,9,8,1,7]=>00010011111=>11111001000
[6,12,5,4,11,3,10,2,9,1,8,7]=>00010011111=>11111001000
[6,12,5,4,3,11,10,9,2,8,1,7]=>00110011111=>11111001100
[6,12,5,4,3,11,10,2,9,8,1,7]=>00110011111=>11111001100
[6,12,5,4,3,11,10,2,9,1,8,7]=>00110011111=>11111001100
[6,12,5,4,3,11,2,10,9,8,1,7]=>00110011111=>11111001100
[6,12,5,4,3,11,2,10,9,1,8,7]=>00110011111=>11111001100
[6,12,5,4,3,11,2,10,1,9,8,7]=>00110011111=>11111001100
[6,12,5,4,3,2,1,11,10,9,8,7]=>11110011111=>11111001111
[6,5,12,11,4,10,3,9,2,8,1,7]=>00001011111=>11111010000
[6,5,12,11,4,10,3,9,2,1,8,7]=>10001011111=>11111010001
[6,5,12,11,4,3,10,9,2,8,1,7]=>00101011111=>11111010100
[6,5,12,11,4,3,10,9,2,1,8,7]=>10101011111=>11111010101
[6,5,12,11,4,3,10,2,9,8,1,7]=>00101011111=>11111010100
[6,5,12,11,4,3,10,2,9,1,8,7]=>00101011111=>11111010100
[6,5,12,11,4,3,10,2,1,9,8,7]=>10101011111=>11111010101
[6,5,12,11,4,3,2,10,9,8,1,7]=>01101011111=>11111010110
[6,5,12,11,4,3,2,10,9,1,8,7]=>01101011111=>11111010110
[6,5,12,11,4,3,2,10,1,9,8,7]=>01101011111=>11111010110
[6,5,12,11,4,3,2,1,10,9,8,7]=>11101011111=>11111010111
[6,5,12,4,11,10,3,9,2,8,1,7]=>00001011111=>11111010000
[6,5,12,4,11,10,3,9,2,1,8,7]=>10001011111=>11111010001
[6,5,12,4,11,3,10,9,2,8,1,7]=>00001011111=>11111010000
[6,5,12,4,11,3,10,9,2,1,8,7]=>10001011111=>11111010001
[6,5,12,4,11,3,10,2,9,8,1,7]=>00001011111=>11111010000
[6,5,12,4,11,3,10,2,9,1,8,7]=>00001011111=>11111010000
[6,5,12,4,11,3,10,2,1,9,8,7]=>10001011111=>11111010001
[6,5,12,4,3,11,10,9,2,8,1,7]=>00101011111=>11111010100
[6,5,12,4,3,11,10,9,2,1,8,7]=>10101011111=>11111010101
[6,5,12,4,3,11,10,2,9,8,1,7]=>00101011111=>11111010100
[6,5,12,4,3,11,10,2,9,1,8,7]=>00101011111=>11111010100
[6,5,12,4,3,11,10,2,1,9,8,7]=>10101011111=>11111010101
[6,5,12,4,3,11,2,10,9,8,1,7]=>00101011111=>11111010100
[6,5,12,4,3,11,2,10,9,1,8,7]=>00101011111=>11111010100
[6,5,12,4,3,11,2,10,1,9,8,7]=>00101011111=>11111010100
[6,5,12,4,3,11,2,1,10,9,8,7]=>10101011111=>11111010101
[6,5,12,4,3,2,11,10,9,8,1,7]=>01101011111=>11111010110
[6,5,12,4,3,2,11,10,9,1,8,7]=>01101011111=>11111010110
[6,5,12,4,3,2,11,10,1,9,8,7]=>01101011111=>11111010110
[6,5,12,4,3,2,11,1,10,9,8,7]=>01101011111=>11111010110
[6,5,12,4,3,2,1,11,10,9,8,7]=>11101011111=>11111010111
[6,5,4,12,11,10,3,9,2,8,1,7]=>00011011111=>11111011000
[6,5,4,12,11,10,3,9,2,1,8,7]=>10011011111=>11111011001
[6,5,4,12,11,10,3,2,9,8,1,7]=>01011011111=>11111011010
[6,5,4,12,11,10,3,2,9,1,8,7]=>01011011111=>11111011010
[6,5,4,12,11,10,3,2,1,9,8,7]=>11011011111=>11111011011
[6,5,4,12,11,3,10,9,2,8,1,7]=>00011011111=>11111011000
[6,5,4,12,11,3,10,9,2,1,8,7]=>10011011111=>11111011001
[6,5,4,12,11,3,10,2,9,8,1,7]=>00011011111=>11111011000
[6,5,4,12,11,3,10,2,9,1,8,7]=>00011011111=>11111011000
[6,5,4,12,11,3,10,2,1,9,8,7]=>10011011111=>11111011001
[6,5,4,12,11,3,2,10,9,8,1,7]=>01011011111=>11111011010
[6,5,4,12,11,3,2,10,9,1,8,7]=>01011011111=>11111011010
[6,5,4,12,11,3,2,10,1,9,8,7]=>01011011111=>11111011010
[6,5,4,12,11,3,2,1,10,9,8,7]=>11011011111=>11111011011
[6,5,4,12,3,11,10,9,2,8,1,7]=>00011011111=>11111011000
[6,5,4,12,3,11,10,9,2,1,8,7]=>10011011111=>11111011001
[6,5,4,12,3,11,10,2,9,8,1,7]=>00011011111=>11111011000
[6,5,4,12,3,11,10,2,9,1,8,7]=>00011011111=>11111011000
[6,5,4,12,3,11,10,2,1,9,8,7]=>10011011111=>11111011001
[6,5,4,12,3,11,2,10,9,8,1,7]=>00011011111=>11111011000
[6,5,4,12,3,11,2,10,9,1,8,7]=>00011011111=>11111011000
[6,5,4,12,3,11,2,10,1,9,8,7]=>00011011111=>11111011000
[6,5,4,12,3,11,2,1,10,9,8,7]=>10011011111=>11111011001
[6,5,4,12,3,2,11,10,9,8,1,7]=>01011011111=>11111011010
[6,5,4,12,3,2,11,10,9,1,8,7]=>01011011111=>11111011010
[6,5,4,12,3,2,11,10,1,9,8,7]=>01011011111=>11111011010
[6,5,4,12,3,2,11,1,10,9,8,7]=>01011011111=>11111011010
[6,5,4,12,3,2,1,11,10,9,8,7]=>11011011111=>11111011011
[6,5,4,3,12,11,10,9,2,8,1,7]=>00111011111=>11111011100
[6,5,4,3,12,11,10,9,2,1,8,7]=>10111011111=>11111011101
[6,5,4,3,12,11,10,2,9,8,1,7]=>00111011111=>11111011100
[6,5,4,3,12,11,10,2,9,1,8,7]=>00111011111=>11111011100
[6,5,4,3,12,11,10,2,1,9,8,7]=>10111011111=>11111011101
[6,5,4,3,12,11,2,10,9,8,1,7]=>00111011111=>11111011100
[6,5,4,3,12,11,2,10,9,1,8,7]=>00111011111=>11111011100
[6,5,4,3,12,11,2,10,1,9,8,7]=>00111011111=>11111011100
[6,5,4,3,12,11,2,1,10,9,8,7]=>10111011111=>11111011101
[6,5,4,3,12,2,11,10,9,8,1,7]=>00111011111=>11111011100
[6,5,4,3,12,2,11,10,9,1,8,7]=>00111011111=>11111011100
[6,5,4,3,12,2,11,10,1,9,8,7]=>00111011111=>11111011100
[6,5,4,3,12,2,11,1,10,9,8,7]=>00111011111=>11111011100
[6,5,4,3,12,2,1,11,10,9,8,7]=>10111011111=>11111011101
[6,5,4,3,2,12,11,10,9,8,1,7]=>01111011111=>11111011110
[6,5,4,3,2,12,11,10,9,1,8,7]=>01111011111=>11111011110
[6,5,4,3,2,12,11,10,1,9,8,7]=>01111011111=>11111011110
[6,5,4,3,2,12,11,1,10,9,8,7]=>01111011111=>11111011110
[6,5,4,3,2,12,1,11,10,9,8,7]=>01111011111=>11111011110
[3,4,5,8,9,1,2,6,7]=>00000001=>10000000
[3,4,7,8,9,1,2,5,6]=>00000001=>10000000
[3,6,7,8,9,1,2,4,5]=>00000001=>10000000
[3,4,5,6,1,7,2,8,9]=>00001100=>00110000
[3,4,5,1,6,2,7,8,9]=>00011000=>00011000
[3,4,5,6,7,10,1,2,8,9]=>000000001=>100000000
[3,4,1,5,9,2,6,7,8]=>00100001=>10000100
[3,4,5,6,9,10,1,2,7,8]=>000000001=>100000000
[3,4,5,8,9,10,1,2,6,7]=>000000001=>100000000
[1,3,7,8,9,2,4,5,6]=>00000001=>10000000
[3,4,7,8,9,10,1,2,5,6]=>000000001=>100000000
[2,6,7,8,9,1,3,4,5]=>00000001=>10000000
[3,6,7,8,9,10,1,2,4,5]=>000000001=>100000000
[3,7,8,2,1,4,5,6]=>1000001=>1000001
[6,3,7,1,8,2,4,5]=>0000111=>1110000
[3,7,8,1,5,2,6,4]=>0001101=>1011000
[2,1,4,3,6,5,10,7,9,8]=>101010011=>110010101
[2,1,4,3,8,5,7,6,10,9]=>101001101=>101100101
[2,1,4,3,10,9,7,5,6,8]=>101001011=>110100101
[2,1,4,3,10,5,6,8,9,7]=>101000011=>110000101
[2,1,6,3,5,4,8,7,10,9]=>100110101=>101011001
[2,1,6,3,5,4,10,7,9,8]=>100110011=>110011001
[2,1,8,7,5,3,4,6,10,9]=>100101101=>101101001
[2,1,10,7,5,9,4,3,6,8]=>101001011=>110100101
[2,1,10,8,5,3,6,4,9,7]=>100110111=>111011001
[2,1,8,3,4,6,7,5,10,9]=>100001101=>101100001
[2,1,10,9,4,6,7,3,5,8]=>100001011=>110100001
[2,1,10,3,9,6,4,8,5,7]=>100010111=>111010001
[2,1,10,3,4,5,7,8,9,6]=>100000011=>110000001
[4,1,3,2,6,5,8,7,10,9]=>011010101=>101010110
[4,1,3,2,6,5,10,7,9,8]=>011010011=>110010110
[4,1,3,2,8,5,7,6,10,9]=>011001101=>101100110
[4,1,3,2,10,9,7,5,6,8]=>011001011=>110100110
[4,1,3,2,10,5,6,8,9,7]=>011000011=>110000110
[6,5,3,1,2,4,10,7,9,8]=>010110011=>110011010
[8,5,3,7,2,1,4,6,10,9]=>100101101=>101101001
[10,5,3,7,2,9,4,1,6,8]=>001101011=>110101100
[10,5,3,8,2,1,6,4,9,7]=>100110111=>111011001
[8,6,3,1,4,2,7,5,10,9]=>011011101=>101110110
[10,6,3,9,4,2,7,1,5,8]=>001011011=>110110100
[10,6,3,1,9,2,4,8,5,7]=>010010111=>111010010
[10,7,3,1,4,5,2,8,9,6]=>010101011=>110101010
[6,1,2,4,5,3,8,7,10,9]=>000110101=>101011000
[6,1,2,4,5,3,10,7,9,8]=>000110011=>110011000
[8,7,2,4,5,1,3,6,10,9]=>000101101=>101101000
[10,7,2,4,5,9,3,1,6,8]=>010001011=>110100010
[10,8,2,4,5,1,6,3,9,7]=>000110111=>111011000
[8,1,7,4,2,6,3,5,10,9]=>001011101=>101110100
[10,9,7,4,2,6,3,1,5,8]=>011011011=>110110110
[10,1,8,4,9,6,2,3,5,7]=>000010111=>111010000
[10,1,8,4,2,5,7,3,9,6]=>001001111=>111100100
[8,1,2,3,5,6,7,4,10,9]=>000001101=>101100000
[10,9,2,3,5,6,7,1,4,8]=>000001011=>110100000
[10,1,9,3,5,6,2,8,4,7]=>000010111=>111010000
[10,1,2,9,5,3,7,8,4,6]=>000100111=>111001000
[2,1,4,3,6,5,8,7,12,9,11,10]=>10101010011=>11001010101
[2,1,4,3,6,5,10,7,9,8,12,11]=>10101001101=>10110010101
[2,1,4,3,6,5,12,11,9,7,8,10]=>10101001011=>11010010101
[2,1,4,3,8,5,7,6,10,9,12,11]=>10100110101=>10101100101
[2,1,4,3,8,5,7,6,12,9,11,10]=>10100110011=>11001100101
[2,1,4,3,10,9,7,5,6,8,12,11]=>10100101101=>10110100101
[2,1,4,3,12,9,7,11,6,5,8,10]=>10101001011=>11010010101
[2,1,4,3,12,5,11,8,6,10,7,9]=>10100010111=>11101000101
[2,1,6,3,5,4,8,7,10,9,12,11]=>10011010101=>10101011001
[2,1,6,3,5,4,8,7,12,9,11,10]=>10011010011=>11001011001
[2,1,6,3,5,4,10,7,9,8,12,11]=>10011001101=>10110011001
[2,1,6,3,5,4,12,11,9,7,8,10]=>10011001011=>11010011001
[2,1,8,7,5,3,4,6,10,9,12,11]=>10010110101=>10101101001
[2,1,8,7,5,3,4,6,12,9,11,10]=>10010110011=>11001101001
[2,1,10,7,5,9,4,3,6,8,12,11]=>10100101101=>10110100101
[2,1,12,7,5,9,4,11,6,3,8,10]=>10001101011=>11010110001
[2,1,12,8,5,11,6,4,9,3,7,10]=>10001011011=>11011010001
[2,1,12,8,5,3,11,4,6,10,7,9]=>10010010111=>11101001001
[2,1,12,9,5,3,6,7,4,10,11,8]=>10010101011=>11010101001
[2,1,10,9,4,6,7,3,5,8,12,11]=>10000101101=>10110100001
[2,1,12,10,4,6,7,3,8,5,11,9]=>10000110111=>11101100001
[2,1,10,3,9,6,4,8,5,7,12,11]=>10001011101=>10111010001
[2,1,12,3,10,6,11,8,4,5,7,9]=>10000010111=>11101000001
[2,1,12,3,10,6,4,7,9,5,11,8]=>10001001111=>11110010001
[2,1,10,3,4,5,7,8,9,6,12,11]=>10000001101=>10110000001
[2,1,12,11,4,5,7,8,9,3,6,10]=>10000001011=>11010000001
[2,1,12,3,11,5,7,8,4,10,6,9]=>10000010111=>11101000001
[4,1,3,2,6,5,8,7,10,9,12,11]=>01101010101=>10101010110
[4,1,3,2,6,5,8,7,12,9,11,10]=>01101010011=>11001010110
[4,1,3,2,6,5,10,7,9,8,12,11]=>01101001101=>10110010110
[4,1,3,2,6,5,12,11,9,7,8,10]=>01101001011=>11010010110
[4,1,3,2,8,5,7,6,10,9,12,11]=>01100110101=>10101100110
[4,1,3,2,8,5,7,6,12,9,11,10]=>01100110011=>11001100110
[4,1,3,2,10,9,7,5,6,8,12,11]=>01100101101=>10110100110
[4,1,3,2,12,9,7,11,6,5,8,10]=>01101001011=>11010010110
[4,1,3,2,12,10,7,5,8,6,11,9]=>01100110111=>11101100110
[4,1,3,2,12,5,11,8,6,10,7,9]=>01100010111=>11101000110
[6,5,3,1,2,4,8,7,10,9,12,11]=>01011010101=>10101011010
[6,5,3,1,2,4,8,7,12,9,11,10]=>01011010011=>11001011010
[6,5,3,1,2,4,10,7,9,8,12,11]=>01011001101=>10110011010
[6,5,3,1,2,4,12,11,9,7,8,10]=>01011001011=>11010011010
[8,5,3,7,2,1,4,6,10,9,12,11]=>10010110101=>10101101001
[8,5,3,7,2,1,4,6,12,9,11,10]=>10010110011=>11001101001
[10,5,3,7,2,9,4,1,6,8,12,11]=>00110101101=>10110101100
[12,5,3,7,2,9,4,11,6,1,8,10]=>00011101011=>11010111000
[12,5,3,7,2,10,4,1,8,6,11,9]=>00110110111=>11101101100
[12,5,3,8,2,11,6,4,9,1,7,10]=>00011011011=>11011011000
[12,5,3,8,2,1,11,4,6,10,7,9]=>10010010111=>11101001001
[12,5,3,9,2,1,6,7,4,10,11,8]=>10010101011=>11010101001
[8,6,3,1,4,2,7,5,10,9,12,11]=>01101110101=>10101110110
[10,6,3,9,4,2,7,1,5,8,12,11]=>00101101101=>10110110100
[12,6,3,9,4,2,7,11,5,1,8,10]=>00111001011=>11010011100
[12,6,3,10,4,2,7,1,8,5,11,9]=>00101110111=>11101110100
[10,6,3,1,9,2,4,8,5,7,12,11]=>01001011101=>10111010010
[12,6,3,11,9,2,4,8,5,1,7,10]=>00011011011=>11011011000
[12,6,3,1,10,2,11,8,4,5,7,9]=>01001010111=>11101010010
[12,6,3,1,10,2,4,7,9,5,11,8]=>01001001111=>11110010010
[10,7,3,1,4,5,2,8,9,6,12,11]=>01010101101=>10110101010
[12,7,3,11,4,5,2,8,9,1,6,10]=>00010101011=>11010101000
[12,7,3,1,11,5,2,8,4,10,6,9]=>01010110111=>11101101010
[6,1,2,4,5,3,8,7,10,9,12,11]=>00011010101=>10101011000
[6,1,2,4,5,3,8,7,12,9,11,10]=>00011010011=>11001011000
[6,1,2,4,5,3,10,7,9,8,12,11]=>00011001101=>10110011000
[6,1,2,4,5,3,12,11,9,7,8,10]=>00011001011=>11010011000
[8,7,2,4,5,1,3,6,10,9,12,11]=>00010110101=>10101101000
[8,7,2,4,5,1,3,6,12,9,11,10]=>00010110011=>11001101000
[12,7,2,4,5,9,3,11,6,1,8,10]=>00001101011=>11010110000
[12,7,2,4,5,10,3,1,8,6,11,9]=>01000110111=>11101100010
[10,8,2,4,5,1,6,3,9,7,12,11]=>00011011101=>10111011000
[12,8,2,4,5,11,6,3,9,1,7,10]=>00001011011=>11011010000
[12,8,2,4,5,1,11,3,6,10,7,9]=>00010010111=>11101001000
[12,9,2,4,5,1,6,7,3,10,11,8]=>00010101011=>11010101000
[8,1,7,4,2,6,3,5,10,9,12,11]=>00101110101=>10101110100
[8,1,7,4,2,6,3,5,12,9,11,10]=>00101110011=>11001110100
[10,9,7,4,2,6,3,1,5,8,12,11]=>01101101101=>10110110110
[12,9,7,4,2,6,3,11,5,1,8,10]=>00111101011=>11010111100
[12,10,7,4,2,6,3,1,8,5,11,9]=>01101110111=>11101110110
[10,1,8,4,9,6,2,3,5,7,12,11]=>00001011101=>10111010000
[12,11,8,4,9,6,2,3,5,1,7,10]=>00011011011=>11011011000
[12,1,8,4,10,6,11,3,2,5,7,9]=>01000010111=>11101000010
[12,1,9,4,10,6,2,7,3,5,11,8]=>00001101111=>11110110000
[10,1,8,4,2,5,7,3,9,6,12,11]=>00100111101=>10111100100
[12,11,8,4,2,5,7,3,9,1,6,10]=>00100111011=>11011100100
[12,1,8,4,11,5,7,3,2,10,6,9]=>01000110111=>11101100010
[12,1,9,4,2,5,6,8,3,10,11,7]=>00100011011=>11011000100
[8,1,2,3,5,6,7,4,10,9,12,11]=>00000110101=>10101100000
[8,1,2,3,5,6,7,4,12,9,11,10]=>00000110011=>11001100000
[10,9,2,3,5,6,7,1,4,8,12,11]=>00000101101=>10110100000
[12,9,2,3,5,6,7,11,4,1,8,10]=>00100001011=>11010000100
[12,10,2,3,5,6,7,1,8,4,11,9]=>00000110111=>11101100000
[10,1,9,3,5,6,2,8,4,7,12,11]=>00001011101=>10111010000
[12,11,9,3,5,6,2,8,4,1,7,10]=>00101011011=>11011010100
[12,1,10,3,5,6,11,8,2,4,7,9]=>00000010111=>11101000000
[12,1,10,3,5,6,2,7,9,4,11,8]=>00001001111=>11110010000
[10,1,2,9,5,3,7,8,4,6,12,11]=>00010011101=>10111001000
[12,11,2,9,5,3,7,8,4,1,6,10]=>00110011011=>11011001100
[12,1,11,10,5,3,7,8,2,4,6,9]=>00010010111=>11101001000
[12,1,2,10,5,11,7,3,9,4,6,8]=>00000101111=>11110100000
[12,1,2,10,5,3,6,8,9,4,11,7]=>00010001111=>11110001000
[10,1,2,3,4,6,7,8,9,5,12,11]=>00000001101=>10110000000
[12,11,2,3,4,6,7,8,9,1,5,10]=>00000001011=>11010000000
[12,1,11,3,4,6,7,8,2,10,5,9]=>00000010111=>11101000000
[12,1,2,11,4,6,7,3,9,10,5,8]=>00000100111=>11100100000
[12,1,2,3,11,6,4,8,9,10,5,7]=>00001000111=>11100010000
[1,5,4,7,8,3,6,2]=>0001101=>1011000
[5,1,4,7,8,3,6,2]=>0001101=>1011000
[4,8,1,5,6,2,3,7]=>0000101=>1010000
[5,6,4,1,7,3,8,2]=>0010111=>1110100
[4,3,7,8,2,5,1,6]=>0011001=>1001100
[3,7,8,5,4,2,1,6]=>1011001=>1001101
[1,7,4,5,6,8,3,2]=>0100011=>1100010
[7,2,4,5,6,8,3,1]=>0100011=>1100010
[2,7,4,5,6,8,3,1]=>0100011=>1100010
[2,4,7,8,3,1,6,5]=>0100101=>1010010
[5,4,3,6,8,1,7,2]=>0011011=>1101100
[3,7,4,5,8,1,6,2]=>0000111=>1110000
[1,4,3,5,6,8,2,7]=>0010001=>1000100
[1,4,6,5,8,2,7,3]=>0000111=>1110000
[4,6,1,7,3,2,8,5]=>0100111=>1110010
[1,7,3,6,4,2,8,5]=>0010111=>1110100
[4,7,3,5,1,2,8,6]=>0001011=>1101000
[1,6,4,2,3,5,8,7]=>0010101=>1010100
[4,8,3,5,2,1,6,7]=>1001001=>1001001
[10,9,7,6,5,4,3,8,2,1]=>101111111=>111111101
[1,6,8,4,7,5,3,2]=>0101011=>1101010
[8,7,3,1,5,2,6,4]=>0101111=>1111010
[4,7,1,6,8,2,3,5]=>0000011=>1100000
[4,6,5,8,2,3,7,1]=>0000111=>1110000
[7,1,8,2,4,5,3,6]=>0001011=>1101000
[5,7,8,2,3,4,1,6]=>0010001=>1000100
[5,2,3,8,7,1,4,6]=>0001011=>1101000
[11,10,9,8,6,7,5,4,3,2,1]=>1111011111=>1111101111
[8,7,1,3,2,6,4,5]=>0100111=>1110010
[2,7,6,4,8,3,1,5]=>0100111=>1110010
[2,6,3,7,5,8,4,1]=>0010111=>1110100
[7,5,1,2,3,8,4,6]=>0001011=>1101000
[4,3,5,2,6,1,7,8,9]=>00111000=>00011100
[4,5,3,6,2,7,1,8,9]=>00011100=>00111000
[3,2,4,1,5,6,7,8,9,10]=>011000000=>000000110
[3,4,2,5,1,6,7,8,9,10]=>001100000=>000001100
[4,3,5,2,6,1,7,8,9,10]=>001110000=>000011100
[4,5,3,6,2,7,1,8,9,10]=>000111000=>000111000
[5,4,6,3,7,2,8,1,9,10]=>000111100=>001111000
[8,6,2,1,3,7,4,5]=>1000111=>1110001
[4,2,3,6,8,5,7,1]=>0010011=>1100100
[4,7,3,2,6,5,1,8]=>0101110=>0111010
[4,3,7,8,2,1,6,5]=>1010101=>1010101
[4,8,7,2,1,5,6,3]=>1000111=>1110001
[7,3,8,2,5,1,6,4]=>0001111=>1111000
[4,5,3,8,6,1,2,7]=>0001101=>1011000
[6,3,5,8,4,1,2,7]=>0010101=>1010100
[7,3,8,4,5,1,2,6]=>0001011=>1101000
[4,8,7,5,1,2,6,3]=>0001111=>1111000
[7,8,4,6,1,3,5,2]=>0001101=>1011000
[4,8,7,5,1,3,6,2]=>0001111=>1111000
[4,5,3,6,8,1,2,7]=>0001001=>1001000
[7,8,6,2,1,4,3,5]=>1010101=>1010101
[7,8,6,3,1,2,5,4]=>0101101=>1011010
[3,7,6,4,1,5,2,8]=>0011110=>0111100
[5,2,8,4,7,1,3,6]=>0001011=>1101000
[7,3,1,2,8,6,5,4]=>0101111=>1111010
[8,7,1,3,2,4,5,6]=>0100011=>1100010
[4,1,3,6,5,7,2,8]=>0010110=>0110100
[4,1,3,5,7,2,8,6]=>0010011=>1100100
[5,1,8,2,4,6,3,7]=>0001101=>1011000
[6,8,2,1,4,5,3,7]=>1001001=>1001001
[4,2,7,3,6,8,5,1]=>0011011=>1101100
[3,1,5,8,6,7,2,4]=>0100011=>1100010
[6,8,2,1,4,5,7,3]=>1000011=>1100001
[2,1,4,3,6,5,10,7,8,9]=>101010001=>100010101
[2,1,4,3,8,5,6,7,10,9]=>101000101=>101000101
[2,1,4,3,10,9,6,5,8,7]=>101010111=>111010101
[2,1,4,3,10,5,6,7,8,9]=>101000001=>100000101
[2,1,6,3,4,5,8,7,10,9]=>100010101=>101010001
[2,1,6,3,4,5,10,7,8,9]=>100010001=>100010001
[2,1,10,7,4,9,6,3,8,5]=>100011111=>111110001
[2,1,10,9,4,3,6,7,8,5]=>101000111=>111000101
[2,1,8,3,4,5,6,7,10,9]=>100000101=>101000001
[2,1,10,9,4,5,6,3,8,7]=>100010111=>111010001
[2,1,10,3,8,5,4,7,6,9]=>100101101=>101101001
[4,1,2,3,6,5,10,7,8,9]=>001010001=>100010100
[4,1,2,3,8,5,6,7,10,9]=>001000101=>101000100
[4,1,2,3,10,9,6,5,8,7]=>001010111=>111010100
[6,5,2,1,4,3,8,7,10,9]=>101110101=>101011101
[6,5,2,1,4,3,10,7,8,9]=>101110001=>100011101
[8,5,2,7,4,1,6,3,10,9]=>001111101=>101111100
[10,5,2,7,4,9,6,1,8,3]=>000111111=>111111000
[10,5,2,9,4,1,6,7,8,3]=>001100111=>111001100
[8,7,2,1,4,5,6,3,10,9]=>100011101=>101110001
[10,7,2,9,4,5,6,1,8,3]=>000011111=>111110000
[10,9,2,1,8,5,4,7,6,3]=>100111111=>111111001
[10,9,2,1,4,5,6,7,8,3]=>100000111=>111000001
[6,1,2,3,4,5,8,7,10,9]=>000010101=>101010000
[8,7,2,3,4,1,6,5,10,9]=>001011101=>101110100
[10,7,2,3,4,9,6,1,8,5]=>000011111=>111110000
[10,9,2,3,4,1,6,7,8,5]=>001000111=>111000100
[8,1,6,3,2,5,4,7,10,9]=>010110101=>101011010
[10,9,6,3,2,5,4,1,8,7]=>011110111=>111011110
[10,1,6,3,8,5,2,7,4,9]=>000111101=>101111000
[10,1,8,3,2,5,6,7,4,9]=>010001101=>101100010
[10,9,2,3,4,5,6,1,8,7]=>000010111=>111010000
[10,1,8,3,4,5,2,7,6,9]=>000101101=>101101000
[10,1,2,7,4,3,6,5,8,9]=>001011001=>100110100
[2,1,4,3,6,5,8,7,12,9,10,11]=>10101010001=>10001010101
[2,1,4,3,6,5,10,7,8,9,12,11]=>10101000101=>10100010101
[2,1,4,3,6,5,12,11,8,7,10,9]=>10101010111=>11101010101
[2,1,4,3,6,5,12,7,8,9,10,11]=>10101000001=>10000010101
[2,1,4,3,8,5,6,7,10,9,12,11]=>10100010101=>10101000101
[2,1,4,3,8,5,6,7,12,9,10,11]=>10100010001=>10001000101
[2,1,4,3,10,9,6,5,8,7,12,11]=>10101011101=>10111010101
[2,1,4,3,12,11,6,5,8,9,10,7]=>10101000111=>11100010101
[2,1,4,3,10,5,6,7,8,9,12,11]=>10100000101=>10100000101
[2,1,4,3,12,11,6,7,8,5,10,9]=>10100010111=>11101000101
[2,1,4,3,12,5,10,7,6,9,8,11]=>10100101101=>10110100101
[2,1,4,3,12,5,6,7,8,9,10,11]=>10100000001=>10000000101
[2,1,6,3,4,5,8,7,10,9,12,11]=>10001010101=>10101010001
[2,1,6,3,4,5,8,7,12,9,10,11]=>10001010001=>10001010001
[2,1,6,3,4,5,10,7,8,9,12,11]=>10001000101=>10100010001
[2,1,6,3,4,5,12,11,8,7,10,9]=>10001010111=>11101010001
[2,1,6,3,4,5,12,7,8,9,10,11]=>10001000001=>10000010001
[2,1,8,7,4,3,6,5,10,9,12,11]=>10101110101=>10101110101
[2,1,8,7,4,3,6,5,12,9,10,11]=>10101110001=>10001110101
[2,1,10,7,4,9,6,3,8,5,12,11]=>10001111101=>10111110001
[2,1,12,7,4,11,6,3,8,9,10,5]=>10001100111=>11100110001
[2,1,10,9,4,3,6,7,8,5,12,11]=>10100011101=>10111000101
[2,1,12,9,4,11,6,7,8,3,10,5]=>10000011111=>11111000001
[2,1,12,11,4,3,10,7,6,9,8,5]=>10100111111=>11111100101
[2,1,8,3,4,5,6,7,10,9,12,11]=>10000010101=>10101000001
[2,1,8,3,4,5,6,7,12,9,10,11]=>10000010001=>10001000001
[2,1,10,9,4,5,6,3,8,7,12,11]=>10001011101=>10111010001
[2,1,12,9,4,5,6,11,8,3,10,7]=>10000011111=>11111000001
[2,1,12,11,4,5,6,3,8,9,10,7]=>10001000111=>11100010001
[2,1,10,3,8,5,4,7,6,9,12,11]=>10010110101=>10101101001
[2,1,12,11,8,5,4,7,6,3,10,9]=>10011110111=>11101111001
[2,1,12,3,8,5,10,7,4,9,6,11]=>10000111101=>10111100001
[2,1,10,3,4,5,6,7,8,9,12,11]=>10000000101=>10100000001
[2,1,12,11,4,5,6,7,8,3,10,9]=>10000010111=>11101000001
[2,1,12,3,10,5,6,7,4,9,8,11]=>10000101101=>10110100001
[2,1,12,3,4,5,6,7,8,9,10,11]=>10000000001=>10000000001
[4,1,2,3,6,5,8,7,10,9,12,11]=>00101010101=>10101010100
[4,1,2,3,6,5,8,7,12,9,10,11]=>00101010001=>10001010100
[4,1,2,3,6,5,10,7,8,9,12,11]=>00101000101=>10100010100
[4,1,2,3,6,5,12,11,8,7,10,9]=>00101010111=>11101010100
[4,1,2,3,6,5,12,7,8,9,10,11]=>00101000001=>10000010100
[4,1,2,3,8,5,6,7,10,9,12,11]=>00100010101=>10101000100
[4,1,2,3,8,5,6,7,12,9,10,11]=>00100010001=>10001000100
[4,1,2,3,10,9,6,5,8,7,12,11]=>00101011101=>10111010100
[4,1,2,3,12,9,6,11,8,5,10,7]=>00100011111=>11111000100
[4,1,2,3,12,11,6,5,8,9,10,7]=>00101000111=>11100010100
[4,1,2,3,12,11,6,7,8,5,10,9]=>00100010111=>11101000100
[4,1,2,3,12,5,10,7,6,9,8,11]=>00100101101=>10110100100
[4,1,2,3,12,5,6,7,8,9,10,11]=>00100000001=>10000000100
[6,5,2,1,4,3,8,7,10,9,12,11]=>10111010101=>10101011101
[6,5,2,1,4,3,8,7,12,9,10,11]=>10111010001=>10001011101
[6,5,2,1,4,3,10,7,8,9,12,11]=>10111000101=>10100011101
[6,5,2,1,4,3,12,7,8,9,10,11]=>10111000001=>10000011101
[8,5,2,7,4,1,6,3,12,9,10,11]=>00111110001=>10001111100
[10,5,2,7,4,9,6,1,8,3,12,11]=>00011111101=>10111111000
[12,5,2,7,4,9,6,11,8,1,10,3]=>00010111111=>11111101000
[12,5,2,7,4,11,6,1,8,9,10,3]=>00011100111=>11100111000
[10,5,2,9,4,1,6,7,8,3,12,11]=>00110011101=>10111001100
[12,5,2,9,4,11,6,7,8,1,10,3]=>00010011111=>11111001000
[12,5,2,11,4,1,10,7,6,9,8,3]=>00110111111=>11111101100
[8,7,2,1,4,5,6,3,10,9,12,11]=>10001110101=>10101110001
[8,7,2,1,4,5,6,3,12,9,10,11]=>10001110001=>10001110001
[10,7,2,9,4,5,6,1,8,3,12,11]=>00001111101=>10111110000
[12,7,2,9,4,5,6,11,8,1,10,3]=>00000111111=>11111100000
[12,7,2,11,4,5,6,1,8,9,10,3]=>00001100111=>11100110000
[10,9,2,1,8,5,4,7,6,3,12,11]=>10011111101=>10111111001
[12,9,2,11,8,5,4,7,6,1,10,3]=>00011111111=>11111111000
[12,11,2,1,8,5,10,7,4,9,6,3]=>10001111111=>11111110001
[10,9,2,1,4,5,6,7,8,3,12,11]=>10000011101=>10111000001
[12,9,2,11,4,5,6,7,8,1,10,3]=>00000011111=>11111000000
[12,11,2,1,4,9,6,5,8,7,10,3]=>10001011111=>11111010001
[12,11,2,1,4,5,6,7,8,9,10,3]=>10000000111=>11100000001
[6,1,2,3,4,5,8,7,10,9,12,11]=>00001010101=>10101010000
[6,1,2,3,4,5,8,7,12,9,10,11]=>00001010001=>10001010000
[6,1,2,3,4,5,10,7,8,9,12,11]=>00001000101=>10100010000
[6,1,2,3,4,5,12,11,8,7,10,9]=>00001010111=>11101010000
[6,1,2,3,4,5,12,7,8,9,10,11]=>00001000001=>10000010000
[8,7,2,3,4,1,6,5,10,9,12,11]=>00101110101=>10101110100
[8,7,2,3,4,1,6,5,12,9,10,11]=>00101110001=>10001110100
[10,7,2,3,4,9,6,1,8,5,12,11]=>00001111101=>10111110000
[12,7,2,3,4,9,6,11,8,1,10,5]=>00000111111=>11111100000
[12,7,2,3,4,11,6,1,8,9,10,5]=>00001100111=>11100110000
[10,9,2,3,4,1,6,7,8,5,12,11]=>00100011101=>10111000100
[12,9,2,3,4,11,6,7,8,1,10,5]=>00000011111=>11111000000
[12,11,2,3,4,1,10,7,6,9,8,5]=>00100111111=>11111100100
[12,11,2,3,4,1,6,7,8,9,10,5]=>00100000111=>11100000100
[8,1,6,3,2,5,4,7,10,9,12,11]=>01011010101=>10101011010
[10,9,6,3,2,5,4,1,8,7,12,11]=>01111011101=>10111011110
[12,9,6,3,2,5,4,11,8,1,10,7]=>01011011111=>11111011010
[10,1,6,3,8,5,2,7,4,9,12,11]=>00011110101=>10101111000
[12,11,6,3,8,5,2,7,4,1,10,9]=>00111110111=>11101111100
[12,1,6,3,8,5,10,7,2,9,4,11]=>00001111101=>10111110000
[12,1,6,3,10,5,2,7,8,9,4,11]=>00011001101=>10110011000
[12,11,8,3,2,5,6,7,4,1,10,9]=>01100110111=>11101100110
[12,1,8,3,10,5,6,7,2,9,4,11]=>00000111101=>10111100000
[8,1,2,3,4,5,6,7,10,9,12,11]=>00000010101=>10101000000
[8,1,2,3,4,5,6,7,12,9,10,11]=>00000010001=>10001000000
[10,9,2,3,4,5,6,1,8,7,12,11]=>00001011101=>10111010000
[12,9,2,3,4,5,6,11,8,1,10,7]=>00000011111=>11111000000
[12,11,2,3,4,5,6,1,8,9,10,7]=>00001000111=>11100010000
[10,1,8,3,4,5,2,7,6,9,12,11]=>00010110101=>10101101000
[12,11,8,3,4,5,2,7,6,1,10,9]=>00011110111=>11101111000
[12,1,8,3,4,5,10,7,2,9,6,11]=>00000111101=>10111100000
[12,11,2,7,4,3,6,5,8,1,10,9]=>00101110111=>11101110100
[12,1,10,7,4,3,6,5,2,9,8,11]=>00111101101=>10110111100
[10,1,2,3,4,5,6,7,8,9,12,11]=>00000000101=>10100000000
[12,11,2,3,4,5,6,7,8,1,10,9]=>00000010111=>11101000000
[12,1,10,3,4,5,6,7,2,9,8,11]=>00000101101=>10110100000
[12,1,2,3,4,5,6,7,8,9,10,11]=>00000000001=>10000000000
[1,5,4,8,7,3,2,6]=>0101011=>1101010
[4,3,1,2,6,5,7,8]=>0110100=>0010110
[7,1,4,5,8,3,6,2]=>0000111=>1110000
[7,5,8,1,2,4,6,3]=>0000111=>1110000
[6,1,5,2,8,7,4,3]=>0011111=>1111100
[8,4,6,3,1,2,7,5]=>0100111=>1110010
[3,8,6,4,1,5,7,2]=>0010111=>1110100
[8,7,1,4,5,2,3,6]=>0001011=>1101000
[3,8,6,4,5,1,7,2]=>0001111=>1111000
[3,7,6,4,5,1,2,8]=>0001110=>0111000
[7,4,6,3,1,2,8,5]=>0100111=>1110010
[4,6,2,5,7,8,1,3]=>0000101=>1010000
[4,6,3,5,7,1,2,8]=>0000110=>0110000
[4,7,3,5,8,6,1,2]=>0000111=>1110000
[4,8,3,5,7,1,6,2]=>0000111=>1110000
[4,8,3,5,6,1,2,7]=>0000101=>1010000
[4,7,2,5,6,8,1,3]=>0000011=>1100000
[4,8,2,5,6,7,1,3]=>0000011=>1100000
[1,4,7,2,6,5,8,3]=>0000111=>1110000
[1,5,7,2,6,4,8,3]=>0000111=>1110000
[7,2,4,6,1,8,3,5]=>0000111=>1110000
[1,2,7,8,3,5,4,6]=>0001001=>1001000
[1,7,6,2,8,5,4,3]=>0011111=>1111100
[1,2,7,8,3,4,6,5]=>0000101=>1010000
[1,7,6,8,3,4,2,5]=>0010011=>1100100
[3,4,1,7,8,6,5,2]=>0011101=>1011100
[2,4,8,6,5,7,1,3]=>0000111=>1110000
[5,1,3,4,8,2,7,6]=>0001011=>1101000
[8,7,3,6,1,4,2,5]=>0010111=>1110100
[6,5,1,8,3,4,7,2]=>0001111=>1111000
[8,2,1,5,6,4,7,3]=>1000111=>1110001
[7,5,6,1,3,4,8,2]=>0000111=>1110000
[5,7,2,4,6,1,8,3]=>0000111=>1110000
[2,1,5,6,3,8,7,4]=>1000111=>1110001
[3,2,7,5,8,6,4,1]=>0110111=>1110110
[2,4,5,3,8,1,7,6]=>0001011=>1101000
[7,2,5,4,3,8,6,1]=>0011111=>1111100
[8,5,3,1,2,6,7,4]=>0101011=>1101010
[7,2,5,1,3,6,8,4]=>0001011=>1101000
[8,4,7,3,1,2,6,5]=>0100111=>1110010
[1,8,7,3,5,2,6,4]=>0001111=>1111000
[2,4,8,3,6,5,7,1]=>0000111=>1110000
[3,1,8,2,6,5,7,4]=>0100111=>1110010
[4,6,7,8,5,2,1,3]=>1001001=>1001001
[4,7,2,1,8,6,5,3]=>1001111=>1111001
[5,6,2,8,4,1,7,3]=>0010111=>1110100
[5,7,2,4,8,6,1,3]=>0000111=>1110000
[6,7,2,4,8,5,1,3]=>0001011=>1101000
[6,7,3,2,8,5,1,4]=>0101011=>1101010
[7,2,3,1,8,6,5,4]=>0101111=>1111010
[7,2,8,3,5,6,1,4]=>0000111=>1110000
[7,2,3,8,4,6,1,5]=>0000111=>1110000
[1,7,3,4,8,5,2,6]=>0001011=>1101000
[1,7,3,8,5,4,2,6]=>0011011=>1101100
[7,2,8,4,5,3,1,6]=>0101011=>1101010
[2,8,6,4,3,1,7,5]=>0110111=>1110110
[1,7,3,4,8,2,5,6]=>0000011=>1100000
[1,5,8,3,4,6,2,7]=>0000101=>1010000
[1,3,8,4,2,5,7,6]=>0010011=>1100100
[1,4,7,6,2,3,8,5]=>0000111=>1110000
[1,8,4,6,7,2,3,5]=>0000011=>1100000
[1,4,2,3,7,8,6,5]=>0010101=>1010100
[5,7,1,6,4,8,3,2]=>0100111=>1110010
[1,2,9,7,5,3,10,8,6,4]=>000111111=>111111000
[7,4,5,8,1,3,6,2]=>0000111=>1110000
[1,4,3,6,2,5,8,7]=>0010101=>1010100
[1,4,6,3,2,5,8,7]=>0100101=>1010010
[1,3,6,5,8,2,4,7]=>0000101=>1010000
[1,4,6,3,2,8,5,7]=>0100101=>1010010
[6,8,4,1,5,7,2,3]=>0010011=>1100100
[5,2,6,7,4,1,8,3]=>0011011=>1101100
[8,5,6,4,1,7,3,2]=>0110111=>1110110
[7,8,3,1,6,4,5,2]=>0101101=>1011010
[5,8,2,6,3,1,7,4]=>0100111=>1110010
[4,5,8,1,6,3,7,2]=>0000111=>1110000
[8,1,4,6,2,5,7,3]=>0000111=>1110000
[4,5,8,1,6,2,7,3]=>0000111=>1110000
[5,2,6,8,1,4,3,7]=>0011001=>1001100
[6,7,3,8,2,1,4,5]=>1000011=>1100001
[2,4,1,5,6,7,8,10,3,9]=>001000001=>100000100
[2,7,3,5,4,1,8,6]=>0011011=>1101100
[2,6,3,7,4,1,8,5]=>0010111=>1110100
[2,1,4,8,5,3,7,6]=>1001011=>1101001
[2,7,3,8,4,1,6,5]=>0010111=>1110100
[2,6,3,1,5,4,8,7]=>0101101=>1011010
[1,5,8,3,4,7,2,6]=>0000011=>1100000
[5,3,8,1,4,6,2,7]=>0001101=>1011000
[4,5,8,1,3,6,2,7]=>0000101=>1010000
[7,4,6,5,2,8,3,1]=>0101111=>1111010
[4,1,3,8,5,7,6,2]=>0010111=>1110100
[4,1,3,7,2,8,6,5]=>0010111=>1110100
[4,6,3,1,7,2,8,5]=>0100111=>1110010
[7,2,6,3,1,8,5,4]=>0101111=>1111010
[4,8,7,2,5,3,1,6]=>0101011=>1101010
[1,6,3,2,8,7,4,5]=>0100111=>1110010
[2,8,1,7,5,4,6,3]=>0001111=>1111000
[6,8,3,1,5,7,2,4]=>0100011=>1100010
[8,7,3,1,2,5,6,4]=>0100111=>1110010
[7,4,5,1,2,6,8,3]=>0001011=>1101000
[1,3,5,7,2,8,4,9,6]=>00000111=>11100000
[1,3,5,6,2,7,4,9,8]=>00001101=>10110000
[1,3,4,5,2,7,6,9,8]=>00010101=>10101000
[3,5,7,1,2,4,6,9,8]=>00000101=>10100000
[1,3,5,7,2,9,4,6,8,10]=>000001010=>010100000
[3,5,7,8,1,9,2,4,6]=>00000011=>11000000
[1,3,5,7,2,9,4,10,6,8]=>000001011=>110100000
[3,5,6,7,1,8,2,9,4]=>00000111=>11100000
[1,3,5,7,2,8,4,9,6,10]=>000001110=>011100000
[1,3,5,6,2,7,4,9,8,10]=>000011010=>010110000
[1,3,4,5,2,7,6,9,8,10]=>000101010=>010101000
[5,4,3,6,1,7,8,2]=>0011101=>1011100
[3,2,7,8,5,6,1,4]=>0100101=>1010010
[4,8,3,2,1,7,5,6]=>1100011=>1100011
[5,1,2,6,4,7,8,3]=>0001101=>1011000
[7,1,2,3,4,9,6,8,5]=>00000111=>11100000
[7,1,2,3,4,8,6,9,5]=>00000111=>11100000
[8,1,2,3,9,5,6,7,4]=>00000111=>11100000
[7,1,2,3,9,5,6,8,4]=>00000111=>11100000
[7,1,2,3,8,5,6,9,4]=>00000111=>11100000
[6,1,2,3,8,5,9,7,4]=>00001111=>11110000
[6,1,2,3,7,5,8,9,4]=>00001101=>10110000
[6,1,2,8,4,5,9,7,3]=>00001111=>11110000
[6,1,2,7,4,5,8,9,3]=>00001101=>10110000
[5,1,2,7,4,9,6,8,3]=>00010111=>11101000
[5,1,2,7,4,8,6,9,3]=>00010111=>11101000
[5,1,2,6,4,7,8,9,3]=>00011001=>10011000
[4,1,6,3,8,5,9,7,2]=>00101111=>11110100
[4,1,6,3,7,5,8,9,2]=>00101101=>10110100
[4,1,5,3,6,7,8,9,2]=>00110001=>10001100
[10,1,2,3,4,5,7,8,9,6]=>000000011=>110000000
[8,1,2,3,4,5,10,7,9,6]=>000000111=>111000000
[8,1,2,3,4,5,9,7,10,6]=>000000111=>111000000
[9,1,2,3,4,10,6,7,8,5]=>000000111=>111000000
[8,1,2,3,4,10,6,7,9,5]=>000000111=>111000000
[8,1,2,3,4,9,6,7,10,5]=>000000111=>111000000
[7,1,2,3,4,9,6,10,8,5]=>000001111=>111100000
[7,1,2,3,4,8,6,9,10,5]=>000001101=>101100000
[8,1,2,3,10,5,6,7,9,4]=>000000111=>111000000
[8,1,2,3,9,5,6,7,10,4]=>000000111=>111000000
[7,1,2,3,10,5,6,8,9,4]=>000001011=>110100000
[7,1,2,3,8,5,6,9,10,4]=>000001101=>101100000
[6,1,2,3,8,5,10,7,9,4]=>000010111=>111010000
[6,1,2,3,8,5,9,7,10,4]=>000010111=>111010000
[6,1,2,3,7,5,8,9,10,4]=>000011001=>100110000
[6,1,2,9,4,5,10,7,8,3]=>000010111=>111010000
[6,1,2,8,4,5,10,7,9,3]=>000010111=>111010000
[6,1,2,8,4,5,9,7,10,3]=>000010111=>111010000
[6,1,2,7,4,5,8,9,10,3]=>000011001=>100110000
[5,1,2,7,4,9,6,10,8,3]=>000101111=>111101000
[5,1,2,7,4,8,6,9,10,3]=>000101101=>101101000
[5,1,2,6,4,7,8,9,10,3]=>000110001=>100011000
[4,1,6,3,8,5,9,7,10,2]=>001010111=>111010100
[4,1,6,3,7,5,8,9,10,2]=>001011001=>100110100
[4,1,5,3,6,7,8,9,10,2]=>001100001=>100001100
[1,9,8,7,6,4,3,2,5]=>01101111=>11110110
[1,9,8,7,5,4,3,2,6]=>01110111=>11101110
[1,9,8,6,5,4,3,2,7]=>01111011=>11011110
[1,9,7,6,5,4,3,2,8]=>01111101=>10111110
[1,9,8,7,6,5,2,3,4]=>00011111=>11111000
[1,10,9,8,7,6,5,3,2,4]=>010111111=>111111010
[1,9,8,7,6,3,4,2,5]=>00101111=>11110100
[1,10,9,8,7,6,4,3,2,5]=>011011111=>111110110
[1,9,8,7,4,5,3,2,6]=>01010111=>11101010
[1,10,9,8,7,5,4,3,2,6]=>011101111=>111101110
[1,9,8,5,6,4,3,2,7]=>01101011=>11010110
[1,10,9,8,6,5,4,3,2,7]=>011110111=>111011110
[1,8,4,5,6,3,2,7]=>0100101=>1010010
[1,9,6,7,5,4,3,2,8]=>01110101=>10101110
[1,10,9,7,6,5,4,3,2,8]=>011111011=>110111110
[1,7,8,6,5,4,3,2,9]=>01111010=>01011110
[1,10,8,7,6,5,4,3,2,9]=>011111101=>101111110
[8,5,1,7,4,6,3,2]=>0101111=>1111010
[3,4,8,1,6,7,2,5]=>0000011=>1100000
[3,6,7,8,4,1,5,2]=>0011001=>1001100
[2,3,7,8,4,6,1,5]=>0000101=>1010000
[1,3,7,8,4,6,2,5]=>0000101=>1010000
[3,1,7,8,4,6,2,5]=>0100101=>1010010
[4,3,8,1,6,7,2,5]=>0010011=>1100100
[4,8,7,3,6,1,2,5]=>0000111=>1110000
[5,8,4,3,7,1,2,6]=>0010011=>1100100
[4,1,8,3,7,5,2,6]=>0011011=>1101100
[2,4,8,3,6,7,1,5]=>0000011=>1100000
[1,6,5,8,7,3,2,4]=>0100111=>1110010
[5,6,4,8,7,2,1,3]=>1000111=>1110001
[7,2,6,8,3,5,1,4]=>0001011=>1101000
[7,2,8,6,5,3,1,4]=>0101111=>1111010
[4,8,3,7,6,1,2,5]=>0000111=>1110000
[2,8,4,7,1,3,6,5]=>0000111=>1110000
[8,9,2,3,4,5,6,1,7]=>00001001=>10010000
[7,8,9,2,3,4,5,1,6]=>00010001=>10001000
[6,7,8,9,2,3,4,1,5]=>00100001=>10000100
[5,6,7,8,9,2,3,1,4]=>01000001=>10000010
[9,10,2,3,4,5,6,7,1,8]=>000001001=>100100000
[8,9,10,2,3,4,5,6,1,7]=>000010001=>100010000
[7,8,9,2,3,4,1,5,6]=>00100001=>10000100
[7,8,9,10,2,3,4,5,1,6]=>000100001=>100001000
[6,7,8,9,2,3,1,4,5]=>01000001=>10000010
[5,6,7,8,9,10,2,3,1,4]=>010000001=>100000010
[4,5,6,7,8,1,9,2,3]=>00000011=>11000000
[4,5,6,7,8,9,10,2,1,3]=>100000001=>100000001
[6,8,3,4,5,2,1,7]=>1001001=>1001001
[3,7,1,4,5,6,2,8]=>0000110=>0110000
[7,9,3,4,5,6,2,1,8]=>10001001=>10010001
[3,9,2,1,5,6,7,8,4]=>10000011=>11000001
[3,6,1,4,5,2,7,8]=>0001100=>0011000
[3,8,1,4,5,6,7,2,9]=>00000110=>01100000
[8,10,3,4,5,6,7,2,1,9]=>100001001=>100100001
[6,9,3,4,5,2,7,1,8]=>00010101=>10101000
[3,8,2,4,5,1,7,6]=>0001011=>1101000
[3,9,2,4,1,6,7,8,5]=>00100011=>11000100
[3,7,2,1,5,6,4,8]=>1000110=>0110001
[3,6,8,1,5,4,7,2]=>0001011=>1101000
[3,8,9,1,5,6,7,4,2]=>00100101=>10100100
[3,10,2,1,5,6,7,8,9,4]=>100000011=>110000001
[3,7,1,4,5,6,2,8,9]=>00001100=>00110000
[3,9,1,4,5,6,7,8,2,10]=>000000110=>011000000
[1,7,4,6,3,5,2,8]=>0001110=>0111000
[1,3,6,5,7,2,4,8]=>0000110=>0110000
[1,7,2,5,6,4,3,8]=>0010110=>0110100
[1,6,8,5,4,3,7,2]=>0011011=>1101100
[2,5,7,8,4,3,1,6]=>0110001=>1000110
[6,8,5,3,2,4,1,7]=>0111001=>1001110
[1,6,8,5,3,2,7,4]=>0101011=>1101010
[4,6,1,8,7,5,3,2]=>0101111=>1111010
[1,3,7,6,8,5,2,4]=>0001011=>1101000
[4,1,7,8,6,5,2,3]=>0011101=>1011100
[5,4,3,7,6,1,2,8]=>0011110=>0111100
[4,7,6,1,2,3,8,5]=>0000111=>1110000
[4,5,2,6,7,8,1,3]=>0001001=>1001000
[2,8,7,6,5,4,3,1,9]=>01111110=>01111110
[2,1,4,9,8,7,6,5,3]=>10011111=>11111001
[3,7,6,5,4,2,1,9,8]=>10111101=>10111101
[3,2,1,6,9,8,7,5,4]=>11010111=>11101011
[4,6,5,3,2,1,9,8,7]=>11011011=>11011011
[1,7,6,2,3,8,5,4]=>0001111=>1111000
[4,5,1,3,7,6,2,8]=>0001110=>0111000
[7,2,3,8,6,4,5,1]=>0001111=>1111000
[1,5,4,3,8,6,2,7]=>0011101=>1011100
[1,3,7,5,8,4,6,2]=>0000111=>1110000
[7,8,1,5,3,4,6,2]=>0001101=>1011000
[7,3,5,4,1,6,2,8]=>0011110=>0111100
[3,5,7,1,6,4,2,8]=>0010110=>0110100
[3,7,5,6,1,4,2,8]=>0010110=>0110100
[1,7,5,6,3,4,8,2]=>0000111=>1110000
[5,3,1,2,7,8,4,6]=>0101001=>1001010
[5,1,3,7,8,2,6,4]=>0001101=>1011000
[5,8,1,2,7,6,4,3]=>0010111=>1110100
[1,6,7,4,5,3,2,8]=>0101010=>0101010
[1,4,2,6,7,5,3,8]=>0011010=>0101100
[1,8,2,4,6,5,3,7]=>0001101=>1011000
[7,2,1,6,4,3,8,5]=>1010111=>1110101
[1,4,8,7,2,3,6,5]=>0000111=>1110000
[4,1,3,6,5,8,2,7]=>0010101=>1010100
[4,3,7,1,5,8,2,6]=>0010011=>1100100
[1,8,6,5,2,7,4,3]=>0011111=>1111100
[1,8,6,2,7,4,3,5]=>0010111=>1110100
[7,2,6,4,1,8,5,3]=>0011111=>1111100
[6,4,1,8,3,7,5,2]=>0011111=>1111100
[4,5,8,7,3,6,2,1]=>1000111=>1110001
[3,5,4,1,7,8,6,2]=>0011101=>1011100
[2,9,8,7,6,1,5,4,3]=>00111111=>11111100
[6,8,7,2,1,5,4,3]=>1011011=>1101101
[4,9,8,7,6,5,2,1,3]=>10011111=>11111001
[5,9,8,7,6,2,1,4,3]=>10101111=>11110101
[2,10,9,8,7,6,1,5,4,3]=>001111111=>111111100
[6,9,8,7,2,1,5,4,3]=>10110111=>11101101
[7,9,8,2,1,6,5,4,3]=>10111011=>11011101
[2,10,9,8,1,7,6,5,4,3]=>001111111=>111111100
[8,9,2,1,7,6,5,4,3]=>10111101=>10111101
[2,10,9,1,8,7,6,5,4,3]=>001111111=>111111100
[8,1,6,3,7,5,4,2]=>0011111=>1111100
[8,5,1,3,7,6,4,2]=>0011111=>1111100
[8,3,6,5,4,2,1,7]=>1011101=>1011101
[6,1,3,5,7,2,8,4]=>0000111=>1110000
[2,8,1,5,6,4,3,7]=>0010101=>1010100
[1,6,7,5,8,4,2,3]=>0010011=>1100100
[7,4,1,6,5,2,8,3]=>0011111=>1111100
[7,4,2,8,6,5,3,1]=>0111111=>1111110
[6,8,4,7,3,2,5,1]=>0101011=>1101010
[5,8,7,3,2,1,6,4]=>1100111=>1110011
[5,8,7,2,6,4,3,1]=>0110111=>1110110
[6,8,7,3,5,1,4,2]=>0011011=>1101100
[7,2,5,6,8,3,4,1]=>0010011=>1100100
[1,6,5,7,8,3,2,4]=>0100101=>1010010
[8,6,7,2,3,5,4,1]=>0011011=>1101100
[5,4,8,6,7,3,1,2]=>0101011=>1101010
[4,2,7,3,1,6,8,5]=>0110011=>1100110
[7,3,6,4,2,1,8,5]=>1010111=>1110101
[4,8,5,2,7,3,1,6]=>0101011=>1101010
[6,4,3,1,8,5,2,7]=>0111101=>1011110
[7,4,3,1,5,8,6,2]=>0110111=>1110110
[7,4,8,6,5,3,1,2]=>0101111=>1111010
[4,8,5,2,6,7,3,1]=>0101011=>1101010
[7,3,2,1,8,5,6,4]=>1100111=>1110011
[7,8,1,9,2,3,4,5,6]=>00000011=>11000000
[6,7,8,1,9,2,3,4,5]=>00000011=>11000000
[5,6,7,8,1,9,2,3,4]=>00000011=>11000000
[9,1,2,3,4,5,7,6,8]=>00000101=>10100000
[2,1,3,4,5,9,6,7,8]=>10000001=>10000001
[1,5,7,2,4,3,8,6]=>0010011=>1100100
[1,2,7,5,8,4,3,6]=>0010011=>1100100
[5,1,3,8,2,7,4,6]=>0001011=>1101000
[5,7,1,3,2,8,4,6]=>0100011=>1100010
[7,1,6,3,2,8,4,5]=>0100111=>1110010
[8,1,7,2,3,6,5,4]=>0001111=>1111000
[7,1,2,6,4,3,8,5]=>0010111=>1110100
[1,4,7,8,3,2,5,6]=>0100001=>1000010
[8,7,1,3,2,4,6,5]=>0100111=>1110010
[8,1,6,3,2,4,7,5]=>0100111=>1110010
[1,8,2,7,6,3,5,4]=>0001111=>1111000
[8,1,6,3,2,7,4,5]=>0100111=>1110010
[8,2,1,7,6,3,4,5]=>1000111=>1110001
[6,8,4,3,5,1,2,7]=>0011001=>1001100
[8,7,3,5,4,1,2,6]=>0011011=>1101100
[6,3,8,5,7,2,1,4]=>1000111=>1110001
[8,7,3,6,4,1,2,5]=>0010111=>1110100
[5,2,7,4,6,1,3,8]=>0001110=>0111000
[8,7,2,3,5,1,4,6]=>0001011=>1101000
[7,6,3,4,1,8,2,5]=>0010111=>1110100
[6,3,5,2,8,1,4,7]=>0001101=>1011000
[6,4,5,3,1,7,2,8]=>0101110=>0111010
[8,7,2,4,3,1,5,6]=>0110011=>1100110
[7,6,2,3,1,4,8,5]=>0100111=>1110010
[4,7,6,2,3,1,5,8]=>0100110=>0110010
[4,7,6,1,3,2,8,5]=>0100111=>1110010
[7,2,6,5,4,3,1,9,8]=>01111101=>10111110
[3,2,1,9,5,8,7,6,4]=>11001111=>11110011
[6,3,5,4,2,1,9,8,7]=>10111011=>11011101
[4,3,2,1,9,7,8,6,5]=>11101011=>11010111
[2,8,1,3,5,6,4,7]=>0000101=>1010000
[2,6,3,4,7,8,5,1]=>0001101=>1011000
[7,6,3,1,8,5,2,4]=>0101111=>1111010
[7,2,1,3,6,8,5,4]=>1001011=>1101001
[7,6,3,8,1,5,2,4]=>0001111=>1111000
[1,6,4,7,8,5,3,2]=>0101101=>1011010
[7,2,5,8,6,1,3,4]=>0000111=>1110000
[4,1,3,6,2,5,8,7]=>0010101=>1010100
[7,1,4,6,3,2,5,8]=>0100110=>0110010
[7,4,5,8,6,2,3,1]=>0100111=>1110010
[6,7,2,3,8,4,1,5]=>0010011=>1100100
[2,7,8,1,5,4,3,6]=>0011001=>1001100
[1,5,2,6,8,7,4,3]=>0011011=>1101100
[1,2,3,4,5,6,8,9,7,10]=>000000010=>010000000
[1,8,3,7,5,2,6,4]=>0001111=>1111000
[8,1,3,6,5,2,7,4]=>0001111=>1111000
[7,1,3,8,5,2,6,4]=>0001111=>1111000
[4,7,1,5,2,6,8,3]=>0001011=>1101000
[7,4,1,5,2,6,8,3]=>0011011=>1101100
[3,1,6,7,5,2,8,4]=>0101011=>1101010
[8,6,2,4,5,1,7,3]=>0001111=>1111000
[8,6,7,5,2,1,4,3]=>1011011=>1101101
[7,1,4,5,2,6,8,3]=>0001011=>1101000
[4,1,6,2,3,8,7,5]=>0010111=>1110100
[4,1,7,6,5,2,8,3]=>0011111=>1111100
[8,4,1,5,6,2,7,3]=>0010111=>1110100
[8,4,5,3,6,1,7,2]=>0001111=>1111000
[2,8,4,7,3,5,6,1]=>0000111=>1110000
[1,5,4,8,3,2,6,7]=>0101001=>1001010
[1,5,7,6,3,8,2,4]=>0000111=>1110000
[2,6,3,1,7,8,4,5]=>0100101=>1010010
[2,1,7,8,3,5,4,6]=>1001001=>1001001
[1,5,8,6,7,4,2,3]=>0010011=>1100100
[8,7,1,3,5,2,6,4]=>0001111=>1111000
[3,7,8,2,5,4,1,6]=>0011001=>1001100
[4,7,6,5,8,1,3,2]=>0100111=>1110010
[4,7,8,6,2,1,5,3]=>1001101=>1011001
[4,8,6,3,2,1,7,5]=>1100111=>1110011
[5,1,4,7,6,8,3,2]=>0101011=>1101010
[5,6,4,7,1,8,3,2]=>0100111=>1110010
[5,3,7,4,6,1,8,2]=>0001111=>1111000
[4,1,5,7,8,6,3,2]=>0110101=>1010110
[3,6,7,1,5,4,8,2]=>0001011=>1101000
[3,6,4,7,5,8,2,1]=>1000111=>1110001
[9,1,2,3,4,8,6,5,7]=>00001011=>11010000
[9,1,2,3,8,5,6,4,7]=>00001011=>11010000
[8,1,2,9,4,5,6,3,7]=>00001011=>11010000
[9,1,8,3,4,5,6,2,7]=>00001011=>11010000
[7,1,2,3,4,9,5,8,6]=>00000111=>11100000
[10,1,2,3,4,5,9,7,6,8]=>000001011=>110100000
[6,1,2,3,8,4,5,9,7]=>00001011=>11010000
[10,1,2,3,4,9,6,7,5,8]=>000001011=>110100000
[5,1,2,8,3,4,6,9,7]=>00010011=>11001000
[9,1,2,3,10,5,6,7,4,8]=>000001011=>110100000
[4,1,9,2,3,5,6,8,7]=>00100011=>11000100
[10,1,2,9,4,5,6,7,3,8]=>000001011=>110100000
[3,8,1,2,4,5,6,9,7]=>00000011=>11000000
[10,1,9,3,4,5,6,7,2,8]=>000001011=>110100000
[8,2,1,3,4,5,6,9,7]=>10000011=>11000001
[8,1,2,3,4,5,10,6,9,7]=>000000111=>111000000
[11,1,2,3,4,5,6,10,8,7,9]=>0000001011=>1101000000
[9,1,2,3,8,5,4,7,6]=>00010111=>11101000
[7,1,2,3,4,9,5,6,10,8]=>000001011=>110100000
[11,1,2,3,4,5,10,7,8,6,9]=>0000001011=>1101000000
[6,1,2,3,9,4,7,8,5]=>00001011=>11010000
[6,1,2,3,9,4,5,7,10,8]=>000010011=>110010000
[10,1,2,3,4,11,6,7,8,5,9]=>0000001011=>1101000000
[5,1,2,8,3,6,4,9,7]=>00011011=>11011000
[5,1,2,10,3,4,6,7,9,8]=>000100011=>110001000
[11,1,2,3,10,5,6,7,8,4,9]=>0000001011=>1101000000
[9,8,2,1,4,5,6,7,3]=>10000111=>11100001
[8,1,7,3,2,4,5,6]=>0100011=>1100010
[4,1,8,2,5,3,6,9,7]=>00110011=>11001100
[4,1,9,2,3,5,6,7,10,8]=>001000011=>110000100
[11,1,2,10,4,5,6,7,8,3,9]=>0000001011=>1101000000
[3,9,1,4,2,5,6,8,7]=>00100011=>11000100
[3,9,1,2,4,5,6,7,10,8]=>000000011=>110000000
[10,1,11,3,4,5,6,7,8,2,9]=>0000001011=>1101000000
[8,2,3,1,4,5,6,9,7]=>01000011=>11000010
[10,2,1,3,4,5,6,7,9,8]=>100000011=>110000001
[11,10,2,3,4,5,6,7,8,1,9]=>0000001011=>1101000000
[6,4,7,1,5,2,8,3]=>0001111=>1111000
[4,8,1,3,5,2,7,6]=>0001011=>1101000
[1,6,5,2,8,7,4,3]=>0011111=>1111100
[2,3,4,5,7,8,1,9,6]=>00000011=>11000000
[1,3,4,5,2,6,7,8,9]=>00010000=>00001000
[1,2,3,4,5,7,8,6,9,10]=>000000100=>001000000
[2,3,4,5,7,9,1,6,8]=>00000001=>10000000
[1,2,3,4,5,7,8,9,6,10]=>000000010=>010000000
[2,3,4,5,1,6,7,9,8]=>00010001=>10001000
[4,5,6,1,7,8,9,2,3]=>00001001=>10010000
[2,1,4,5,3,6,7,8,9]=>10010000=>00001001
[2,4,5,6,1,7,8,9,10,3]=>000010001=>100010000
[1,3,2,5,4,6,7,8,9]=>01010000=>00001010
[2,3,5,6,1,7,8,9,10,4]=>000010001=>100010000
[4,1,7,2,5,8,3,6]=>0010011=>1100100
[3,2,5,8,6,1,7,4]=>0100111=>1110010
[4,5,1,7,2,8,6,3]=>0001111=>1111000
[2,8,5,3,6,7,4,1]=>0011011=>1101100
[2,3,4,5,9,8,6,7,1]=>00000111=>11100000
[2,3,4,9,7,5,8,6,1]=>00001111=>11110000
[2,3,9,6,4,7,8,5,1]=>00011011=>11011000
[8,3,5,2,6,7,4,1]=>0011011=>1101100
[2,8,6,3,4,7,5,1]=>0001111=>1111000
[2,9,5,3,6,7,8,4,1]=>00110011=>11001100
[9,4,2,5,6,7,8,3,1]=>01100011=>11000110
[4,7,1,8,5,3,6,2]=>0001111=>1111000
[6,4,7,2,5,3,1,8]=>0101110=>0111010
[7,1,4,3,6,8,2,5]=>0010011=>1100100
[6,3,1,5,4,8,7,2]=>0101111=>1111010
[4,1,6,2,8,3,5,7,9]=>00101010=>01010100
[4,1,6,2,8,3,9,5,7]=>00101011=>11010100
[4,1,6,2,7,3,8,5,9]=>00101110=>01110100
[7,1,3,8,5,4,2,6]=>0011011=>1101100
[4,8,7,3,5,1,6,2]=>0001111=>1111000
[5,3,8,7,1,6,2,4]=>0001111=>1111000
[3,4,1,6,2,8,7,5]=>0010111=>1110100
[5,2,6,7,4,3,1,8]=>0111010=>0101110
[8,5,1,6,4,3,2,7]=>0111101=>1011110
[8,6,3,5,2,7,1,4]=>0001111=>1111000
[8,4,6,2,1,5,7,3]=>1000111=>1110001
[8,5,2,1,6,4,7,3]=>1001111=>1111001
[1,7,2,8,5,4,6,3]=>0001111=>1111000
[6,7,1,4,8,5,3,2]=>0101011=>1101010
[7,3,2,8,5,1,4,6]=>0101011=>1101010
[4,1,7,3,2,8,5,6]=>0110011=>1100110
[8,3,5,2,4,7,1,6]=>0001011=>1101000
[4,3,7,8,6,1,5,2]=>0011101=>1011100
[1,2,6,3,7,8,5,4]=>0001101=>1011000
[6,1,3,7,8,5,4,2]=>0011101=>1011100
[8,7,9,1,4,5,6,2,3]=>00001011=>11010000
[7,6,9,1,4,5,2,8,3]=>00010111=>11101000
[9,8,10,1,4,5,6,7,2,3]=>000001011=>110100000
[11,10,2,1,4,5,6,7,8,9,3]=>1000000111=>1110000001
[2,6,4,7,5,3,1,8]=>0101110=>0111010
[5,6,3,7,2,8,4,1]=>0010111=>1110100
[4,5,1,8,6,2,7,3]=>0001111=>1111000
[5,6,1,8,7,2,3,4]=>0000111=>1110000
[4,5,1,6,8,7,3,2]=>0101011=>1101010
[3,9,2,4,5,6,7,8,1]=>00000011=>11000000
[3,8,6,1,5,2,4,7]=>0001101=>1011000
[3,2,8,1,5,6,4,7]=>0100101=>1010010
[5,8,7,3,2,1,4,6]=>1100011=>1100011
[3,4,7,6,8,2,1,5]=>1000011=>1100001
[2,8,1,3,7,5,6,4]=>0000111=>1110000
[1,8,7,2,5,6,4,3]=>0010111=>1110100
[3,4,7,1,5,8,2,6]=>0000011=>1100000
[4,2,7,1,5,8,3,6]=>0010011=>1100100
[1,3,5,2,4,6,7,8,9]=>00010000=>00001000
[4,1,2,3,5,6,8,7,9]=>00100010=>01000100
[1,2,4,7,3,5,6,8,9]=>00000100=>00100000
[5,1,2,3,4,7,6,8,9]=>00010100=>00101000
[2,4,6,3,5,1,7,8]=>0001100=>0011000
[4,1,6,2,5,8,3,7]=>0010101=>1010100
[1,8,2,5,7,3,4,6]=>0000011=>1100000
[1,4,6,3,8,5,2,7]=>0001101=>1011000
[4,5,6,3,1,7,2,8]=>0100110=>0110010
[3,4,6,2,5,1,7,8]=>0001100=>0011000
[1,4,7,5,2,3,6,8]=>0001010=>0101000
[1,4,6,5,8,2,3,7]=>0000101=>1010000
[1,4,8,3,7,6,2,5]=>0000111=>1110000
[1,4,5,3,7,2,6,8]=>0001010=>0101000
[2,5,7,6,8,3,4,1]=>0010011=>1100100
[3,1,6,7,2,8,5,4]=>0101011=>1101010
[1,5,3,6,8,4,7,2]=>0001011=>1101000
[6,5,1,3,8,4,7,2]=>0001111=>1111000
[1,7,4,8,5,3,2,6]=>0101011=>1101010
[7,3,1,6,8,4,5,2]=>0101011=>1101010
[8,5,1,4,6,7,3,2]=>0101011=>1101010
[3,4,7,5,6,8,2,1]=>1000011=>1100001
[3,4,7,8,5,2,6,1]=>0001101=>1011000
[7,4,2,3,6,5,1,8]=>0011110=>0111100
[7,2,4,3,1,5,6,8]=>0110010=>0100110
[6,3,1,4,8,5,7,2]=>0100111=>1110010
[6,3,5,4,8,7,1,2]=>0001111=>1111000
[2,6,4,3,1,7,5,8]=>0110110=>0110110
[4,8,1,7,5,6,3,2]=>0100111=>1110010
[1,5,7,2,8,4,6,3]=>0000111=>1110000
[5,8,7,2,3,6,4,1]=>0010111=>1110100
[4,6,5,1,2,3,7,8]=>0001100=>0011000
[1,8,7,5,2,6,3,4]=>0001111=>1111000
[1,7,6,3,4,5,8,2]=>0000111=>1110000
[1,8,7,4,5,6,2,3]=>0000111=>1110000
[1,8,7,3,6,4,2,5]=>0010111=>1110100
[1,4,7,5,8,2,6,3]=>0000111=>1110000
[1,4,7,2,3,6,5,8]=>0000110=>0110000
[1,7,2,5,6,3,4,8]=>0000110=>0110000
[1,2,6,5,8,3,4,7]=>0000101=>1010000
[1,5,8,2,6,3,4,7]=>0000101=>1010000
[6,8,3,2,7,5,1,4]=>0101011=>1101010
[7,3,6,8,1,2,5,4]=>0001011=>1101000
[4,1,5,7,2,6,3,8]=>0010110=>0110100
[5,7,2,1,3,6,4,8]=>1000110=>0110001
[10,11,8,1,2,3,4,5,6,7,9]=>0000001001=>1001000000
[7,1,10,9,2,3,4,5,6,8]=>000001011=>110100000
[6,7,9,1,2,3,4,5,10,8]=>000000011=>110000000
[2,8,1,9,10,3,4,5,6,7]=>000000101=>101000000
[8,7,1,10,2,3,4,5,6,9]=>000001101=>101100000
[3,5,6,7,2,4,1,8]=>0010010=>0100100
[6,4,7,5,2,3,1,8]=>0101110=>0111010
[1,5,6,4,8,3,2,7]=>0100101=>1010010
[2,1,5,6,4,8,3,7]=>1000101=>1010001
[5,1,4,7,8,6,2,3]=>0001101=>1011000
[1,6,7,2,8,5,4,3]=>0011011=>1101100
[5,3,2,1,7,8,6,4]=>1101101=>1011011
[7,4,3,8,6,1,5,2]=>0011111=>1111100
[4,3,7,1,5,8,6,2]=>0010111=>1110100
[8,2,4,5,3,1,7,6]=>0101011=>1101010
[1,4,3,2,7,5,8,6]=>0110011=>1100110
[1,5,2,8,6,3,10,9,7,4]=>000111111=>111111000
[4,1,5,2,8,6,3,10,9,7]=>001110111=>111011100
[1,7,5,2,8,6,3,10,9,4]=>000111111=>111111000
[4,1,7,5,2,8,3,10,9,6]=>001101111=>111101100
[6,4,1,7,5,2,8,3,10,9]=>001111101=>101111100
[3,4,1,7,2,8,5,10,9,6]=>001001111=>111100100
[3,6,4,1,7,2,8,5,10,9]=>001011101=>101110100
[1,5,2,9,8,6,3,10,7,4]=>000111111=>111111000
[4,1,5,2,9,8,6,3,10,7]=>001110111=>111011100
[1,7,5,2,9,6,3,10,8,4]=>000111111=>111111000
[4,1,7,5,2,9,3,10,8,6]=>001101111=>111101100
[4,1,9,6,5,2,7,3,10,8]=>001111011=>110111100
[3,4,1,7,2,9,5,10,8,6]=>001001111=>111100100
[3,6,1,9,4,2,7,5,10,8]=>001011011=>110110100
[1,8,7,5,2,9,6,3,10,4]=>000111111=>111111000
[4,1,8,7,5,2,9,3,10,6]=>001101111=>111101100
[6,4,1,8,5,2,9,3,10,7]=>001110111=>111011100
[7,6,4,1,8,5,2,9,3,10]=>001111110=>011111100
[3,4,1,8,7,2,9,5,10,6]=>001001111=>111100100
[3,6,4,1,8,2,9,5,10,7]=>001010111=>111010100
[3,7,6,4,1,8,2,9,5,10]=>001011110=>011110100
[1,9,6,5,2,7,3,10,8,4]=>000111111=>111111000
[6,1,9,4,2,7,3,10,8,5]=>001011111=>111110100
[5,4,1,9,6,2,7,3,10,8]=>001111011=>110111100
[9,3,1,6,2,7,4,10,8,5]=>010011111=>111110010
[9,5,3,1,6,2,7,4,10,8]=>010111011=>110111010
[6,1,8,5,2,9,7,3,10,4]=>000111111=>111111000
[6,4,1,8,2,9,7,3,10,5]=>001011111=>111110100
[8,5,4,1,6,2,9,3,10,7]=>001110111=>111011100
[5,7,4,1,8,6,2,9,3,10]=>001011110=>011110100
[3,6,1,8,2,9,7,4,10,5]=>000011111=>111110000
[5,8,3,1,6,2,9,4,10,7]=>010010111=>111010010
[5,3,7,1,8,6,2,9,4,10]=>000111110=>011111000
[4,3,8,1,9,5,2,6,10,7]=>001100111=>111001100
[7,4,3,5,1,8,2,9,6,10]=>001101110=>011101100
[9,6,2,1,3,7,4,10,8,5]=>100011111=>111110001
[5,9,2,1,6,3,7,4,10,8]=>100011011=>110110001
[6,8,2,1,3,9,7,4,10,5]=>100001111=>111100001
[8,2,5,1,6,3,9,4,10,7]=>000110111=>111011000
[2,5,7,1,8,6,3,9,4,10]=>000011110=>011110000
[2,4,8,1,9,5,3,6,10,7]=>000100111=>111001000
[4,8,7,2,6,1,3,5]=>0000111=>1110000
[4,5,8,2,1,7,3,6]=>1000011=>1100001
[6,8,4,1,7,3,2,5]=>0110011=>1100110
[5,6,4,3,2,1,7,8,9]=>11101000=>00010111
[5,6,4,3,2,1,7,8,9,10]=>111010000=>000010111
[4,5,3,2,1,6,7,8,9]=>11010000=>00001011
[6,7,5,4,3,2,1,8,9,10,11]=>1111010000=>0000101111
[6,7,5,4,3,2,1,8,9,10]=>111101000=>000101111
[6,7,4,3,2,1,5,8,9]=>11100100=>00100111
[5,6,4,3,2,7,1,8,9]=>01101100=>00110110
[7,5,4,3,1,2,6,8,9]=>01110100=>00101110
[6,5,4,3,7,1,2,8,9]=>00111100=>00111100
[7,6,5,4,3,1,2,8,9,10,11]=>0111110000=>0000111110
[6,7,9,8,5,4,3,2,1]=>11110011=>11001111
[7,6,8,9,5,4,3,2,1]=>11110101=>10101111
[9,11,10,8,7,6,5,4,3,2,1]=>1111111011=>1101111111
[7,8,10,9,6,5,4,3,2,1]=>111110011=>110011111
[6,7,5,9,8,4,3,2,1]=>11100111=>11100111
[5,7,9,8,6,4,3,2,1]=>11101011=>11010111
[7,6,8,5,9,4,3,2,1]=>11100111=>11100111
[6,5,8,9,7,4,3,2,1]=>11101101=>10110111
[8,7,9,10,6,5,4,3,2,1]=>111110101=>101011111
[6,3,1,8,2,7,5,4]=>0101111=>1111010
[6,4,1,3,2,5,7,8]=>0110100=>0010110
[4,1,7,8,3,2,5,6]=>0110001=>1000110
[5,4,7,1,3,6,2,8]=>0001110=>0111000
[7,6,2,8,4,5,3,1]=>0101111=>1111010
[5,8,2,1,3,6,4,7]=>1000101=>1010001
[7,6,4,3,5,2,1,9,8]=>10111101=>10111101
[7,6,3,5,4,2,1,9,8]=>10111101=>10111101
[8,5,1,7,3,4,6,2]=>0001111=>1111000
[5,7,6,3,4,1,8,2]=>0010111=>1110100
[7,8,9,10,1,5,6,3,4,2]=>001010001=>100010100
[1,8,3,5,2,6,4,7]=>0001101=>1011000
[3,4,6,1,8,5,7,2]=>0000111=>1110000
[2,3,8,7,4,5,1,6]=>0001011=>1101000
[1,8,3,5,7,4,2,6]=>0010011=>1100100
[2,5,8,4,6,7,1,3]=>0000011=>1100000
[9,8,6,1,2,3,4,5,7]=>00001011=>11010000
[9,8,7,5,1,2,3,4,6]=>00010111=>11101000
[9,8,7,6,4,1,2,3,5]=>00101111=>11110100
[9,8,7,6,5,3,1,2,4]=>01011111=>11111010
[7,1,2,6,4,3,5,8]=>0010110=>0110100
[7,1,2,6,5,3,4,8]=>0001110=>0111000
[4,7,8,6,2,3,5,1]=>0001101=>1011000
[7,1,2,4,8,6,5,3]=>0001111=>1111000
[2,7,5,6,4,8,1,3]=>0000111=>1110000
[2,8,3,6,5,7,1,4]=>0000111=>1110000
[9,8,4,7,6,5,3,2,1]=>11011111=>11111011
[9,8,3,7,6,5,4,2,1]=>10111111=>11111101
[9,3,8,7,6,5,4,2,1]=>10111111=>11111101
[9,2,8,7,6,5,4,3,1]=>01111111=>11111110
[10,9,8,5,7,6,4,3,2,1]=>111011111=>111110111
[9,8,4,6,5,7,3,2,1]=>11001111=>11110011
[10,9,8,4,7,6,5,3,2,1]=>110111111=>111111011
[9,8,3,6,5,4,7,2,1]=>10011111=>11111001
[10,9,4,8,7,6,5,3,2,1]=>110111111=>111111011
[9,3,7,6,5,4,8,2,1]=>10011111=>11111001
[9,2,7,6,5,4,3,8,1]=>00111111=>11111100
[10,3,9,8,7,6,5,4,2,1]=>101111111=>111111101
[10,2,9,8,7,6,5,4,3,1]=>011111111=>111111110
[7,4,3,1,6,5,2,8]=>0111110=>0111110
[3,5,1,2,6,8,7,4]=>0001011=>1101000
[3,1,2,4,8,7,5,6]=>0100011=>1100010
[5,4,1,2,3,7,8,6]=>0011001=>1001100
[1,6,7,2,5,8,3,4]=>0000011=>1100000
[7,8,5,6,2,4,3,1]=>0110101=>1010110
[5,3,8,6,2,4,1,7]=>0011101=>1011100
[2,7,4,6,3,8,1,5]=>0000111=>1110000
[5,4,7,8,6,2,1,3]=>1001101=>1011001
[2,7,4,8,3,1,5,6]=>0100011=>1100010
[8,2,1,3,7,4,6,5]=>1000111=>1110001
[6,5,8,2,3,4,7,1]=>0000111=>1110000
[7,8,2,3,6,4,5,1]=>0001101=>1011000
[8,2,4,1,3,7,5,6]=>0010011=>1100100
[4,2,6,7,5,1,8,3]=>0011011=>1101100
[4,7,2,5,3,8,1,6]=>0001011=>1101000
[3,5,7,4,2,8,1,6]=>0010011=>1100100
[2,4,7,6,3,8,1,5]=>0000111=>1110000
[4,6,8,5,1,2,3,7]=>0001001=>1001000
[4,6,5,7,1,2,3,8]=>0000110=>0110000
[4,6,5,7,1,3,8,2]=>0000111=>1110000
[3,4,7,6,1,8,2,5]=>0000111=>1110000
[8,5,2,1,6,3,4,7]=>1001101=>1011001
[7,1,8,5,3,2,4,6]=>0101011=>1101010
[9,10,2,1,6,4,3,5,7,8]=>101010001=>100010101
[7,10,2,1,8,4,3,5,6,9]=>101000101=>101000101
[2,9,1,10,7,4,3,5,6,8]=>001001011=>110100100
[2,8,1,9,4,3,10,5,6,7]=>001000111=>111000100
[10,8,5,2,1,6,3,4,7,9]=>100110101=>101011001
[9,5,2,1,10,6,3,4,7,8]=>100110011=>110011001
[10,7,2,1,8,5,3,4,6,9]=>100101101=>101101001
[9,2,1,10,7,5,3,4,6,8]=>100101011=>110101001
[2,8,1,9,3,10,5,4,6,7]=>000100111=>111001000
[10,6,2,1,7,3,8,4,5,9]=>100011101=>101110001
[9,2,1,10,6,3,7,4,5,8]=>100011011=>110110001
[8,2,1,9,3,10,6,4,5,7]=>100010111=>111010001
[7,2,1,8,3,9,4,10,5,6]=>100001111=>111100001
[10,8,6,3,1,4,2,5,7,9]=>011010101=>101010110
[3,9,1,10,6,4,2,5,7,8]=>001010011=>110010100
[10,7,3,1,8,4,2,5,6,9]=>011001101=>101100110
[9,3,1,10,7,4,2,5,6,8]=>011001011=>110100110
[8,3,1,9,4,2,10,5,6,7]=>011000111=>111000110
[10,8,5,1,6,3,2,4,7,9]=>010110101=>101011010
[9,5,1,10,6,3,2,4,7,8]=>010110011=>110011010
[10,7,1,8,5,3,2,4,6,9]=>010101101=>101101010
[9,1,10,7,5,3,2,4,6,8]=>010101011=>110101010
[8,3,1,9,2,10,5,4,6,7]=>010100111=>111001010
[10,6,1,7,3,2,8,4,5,9]=>010011101=>101110010
[9,1,10,6,3,2,7,4,5,8]=>010011011=>110110010
[8,1,9,3,2,10,6,4,5,7]=>010010111=>111010010
[7,1,8,3,2,9,4,10,5,6]=>010001111=>111100010
[10,8,4,1,5,2,6,3,7,9]=>001110101=>101011100
[9,4,1,10,5,2,6,3,7,8]=>001110011=>110011100
[10,7,1,8,4,2,5,3,6,9]=>001101101=>101101100
[9,1,10,7,4,2,5,3,6,8]=>001101011=>110101100
[8,1,9,4,2,10,5,3,6,7]=>001100111=>111001100
[10,6,1,7,2,8,4,3,5,9]=>001011101=>101110100
[9,1,10,6,2,7,4,3,5,8]=>001011011=>110110100
[8,1,9,2,10,6,4,3,5,7]=>001010111=>111010100
[7,1,8,2,9,4,3,10,5,6]=>001001111=>111100100
[10,5,1,6,2,7,3,8,4,9]=>000111101=>101111000
[9,1,10,5,2,6,3,7,4,8]=>000111011=>110111000
[8,1,9,2,10,5,3,6,4,7]=>000110111=>111011000
[7,1,8,2,9,3,10,5,4,6]=>000101111=>111101000
[11,12,8,2,1,6,4,3,5,7,9,10]=>10101010001=>10001010101
[12,2,9,1,10,6,4,3,5,7,8,11]=>00101001101=>10110010100
[11,12,2,1,9,6,4,3,5,7,8,10]=>10101001001=>10010010101
[10,2,4,1,11,3,12,6,5,7,8,9]=>00101000111=>11100010100
[7,12,10,2,1,8,4,3,5,6,9,11]=>10100010101=>10101000101
[2,11,7,1,12,8,4,3,5,6,9,10]=>00100110011=>11001100100
[9,12,2,1,10,7,4,3,5,6,8,11]=>10100100101=>10100100101
[2,11,1,12,9,7,4,3,5,6,8,10]=>00100101011=>11010100100
[2,11,1,12,8,4,3,9,5,6,7,10]=>00100011011=>11011000100
[2,10,1,11,4,3,12,8,5,6,7,9]=>00100010111=>11101000100
[2,9,1,10,4,3,11,5,12,6,7,8]=>00100001111=>11110000100
[12,10,8,5,2,1,6,3,4,7,9,11]=>10011010101=>10101011001
[12,9,5,2,1,10,6,3,4,7,8,11]=>10011001101=>10110011001
[11,5,2,1,12,9,6,3,4,7,8,10]=>10011001011=>11010011001
[12,10,7,2,1,8,5,3,4,6,9,11]=>10010110101=>10101101001
[11,7,2,1,12,8,5,3,4,6,9,10]=>10010110011=>11001101001
[12,9,2,1,10,7,5,3,4,6,8,11]=>10010101101=>10110101001
[11,2,1,12,9,7,5,3,4,6,8,10]=>10010101011=>11010101001
[11,8,2,1,12,3,9,5,4,6,7,10]=>10010011011=>11011001001
[2,10,1,11,3,12,8,5,4,6,7,9]=>00010010111=>11101001000
[2,9,1,10,3,11,5,4,12,6,7,8]=>00010001111=>11110001000
[12,10,6,2,1,7,3,8,4,5,9,11]=>10001110101=>10101110001
[11,6,2,1,12,7,3,8,4,5,9,10]=>10001110011=>11001110001
[12,9,2,1,10,6,3,7,4,5,8,11]=>10001101101=>10110110001
[11,2,1,12,9,6,3,7,4,5,8,10]=>10001101011=>11010110001
[10,2,1,11,6,3,12,7,4,5,8,9]=>10001100111=>11100110001
[12,8,2,1,9,3,10,6,4,5,7,11]=>10001011101=>10111010001
[11,2,1,12,8,3,9,6,4,5,7,10]=>10001011011=>11011010001
[10,2,1,11,3,12,8,6,4,5,7,9]=>10001010111=>11101010001
[2,9,1,10,3,11,4,12,6,5,7,8]=>00001001111=>11110010000
[12,7,2,1,8,3,9,4,10,5,6,11]=>10000111101=>10111100001
[11,2,1,12,7,3,8,4,9,5,6,10]=>10000111011=>11011100001
[10,2,1,11,3,12,7,4,8,5,6,9]=>10000110111=>11101100001
[9,2,1,10,3,11,4,12,7,5,6,8]=>10000101111=>11110100001
[8,2,1,9,3,10,4,11,5,12,6,7]=>10000011111=>11111000001
[12,10,8,6,3,1,4,2,5,7,9,11]=>01101010101=>10101010110
[3,11,1,12,9,6,4,2,5,7,8,10]=>00101001011=>11010010100
[3,10,4,1,11,2,12,6,5,7,8,9]=>00101000111=>11100010100
[12,10,7,3,1,8,4,2,5,6,9,11]=>01100110101=>10101100110
[11,7,3,1,12,8,4,2,5,6,9,10]=>01100110011=>11001100110
[12,9,3,1,10,7,4,2,5,6,8,11]=>01100101101=>10110100110
[11,3,1,12,9,7,4,2,5,6,8,10]=>01100101011=>11010100110
[3,10,1,11,4,2,12,7,5,6,8,9]=>00100100111=>11100100100
[12,8,3,1,9,4,2,10,5,6,7,11]=>01100011101=>10111000110
[11,3,1,12,8,4,2,9,5,6,7,10]=>01100011011=>11011000110
[10,3,1,11,4,2,12,8,5,6,7,9]=>01100010111=>11101000110
[9,3,1,10,4,2,11,5,12,6,7,8]=>01100001111=>11110000110
[12,10,8,5,1,6,3,2,4,7,9,11]=>01011010101=>10101011010
[12,9,5,1,10,6,3,2,4,7,8,11]=>01011001101=>10110011010
[11,5,1,12,9,6,3,2,4,7,8,10]=>01011001011=>11010011010
[3,10,1,11,5,2,12,6,4,7,8,9]=>00011000111=>11100011000
[12,10,7,1,8,5,3,2,4,6,9,11]=>01010110101=>10101101010
[11,7,1,12,8,5,3,2,4,6,9,10]=>01010110011=>11001101010
[12,9,1,10,7,5,3,2,4,6,8,11]=>01010101101=>10110101010
[11,1,12,9,7,5,3,2,4,6,8,10]=>01010101011=>11010101010
[3,10,1,11,2,12,7,5,4,6,8,9]=>00010100111=>11100101000
[11,8,1,12,3,2,9,5,4,6,7,10]=>01010011011=>11011001010
[10,3,1,11,2,12,8,5,4,6,7,9]=>01010010111=>11101001010
[9,3,1,10,2,11,5,4,12,6,7,8]=>01010001111=>11110001010
[12,10,6,1,7,3,2,8,4,5,9,11]=>01001110101=>10101110010
[11,6,1,12,7,3,2,8,4,5,9,10]=>01001110011=>11001110010
[12,9,1,10,6,3,2,7,4,5,8,11]=>01001101101=>10110110010
[11,1,12,9,6,3,2,7,4,5,8,10]=>01001101011=>11010110010
[10,1,11,6,3,2,12,7,4,5,8,9]=>01001100111=>11100110010
[12,8,1,9,3,2,10,6,4,5,7,11]=>01001011101=>10111010010
[11,1,12,8,3,2,9,6,4,5,7,10]=>01001011011=>11011010010
[10,1,11,3,2,12,8,6,4,5,7,9]=>01001010111=>11101010010
[9,3,1,10,2,11,4,12,6,5,7,8]=>01001001111=>11110010010
[12,7,1,8,3,2,9,4,10,5,6,11]=>01000111101=>10111100010
[11,1,12,7,3,2,8,4,9,5,6,10]=>01000111011=>11011100010
[10,1,11,3,2,12,7,4,8,5,6,9]=>01000110111=>11101100010
[9,1,10,3,2,11,4,12,7,5,6,8]=>01000101111=>11110100010
[8,1,9,3,2,10,4,11,5,12,6,7]=>01000011111=>11111000010
[12,10,8,4,1,5,2,6,3,7,9,11]=>00111010101=>10101011100
[4,11,1,12,8,5,2,6,3,7,9,10]=>00011010011=>11001011000
[12,9,4,1,10,5,2,6,3,7,8,11]=>00111001101=>10110011100
[11,4,1,12,9,5,2,6,3,7,8,10]=>00111001011=>11010011100
[10,4,1,11,5,2,12,6,3,7,8,9]=>00111000111=>11100011100
[12,10,7,1,8,4,2,5,3,6,9,11]=>00110110101=>10101101100
[11,7,1,12,8,4,2,5,3,6,9,10]=>00110110011=>11001101100
[12,9,1,10,7,4,2,5,3,6,8,11]=>00110101101=>10110101100
[11,1,12,9,7,4,2,5,3,6,8,10]=>00110101011=>11010101100
[10,4,1,11,2,12,7,5,3,6,8,9]=>00110100111=>11100101100
[12,8,1,9,4,2,10,5,3,6,7,11]=>00110011101=>10111001100
[11,1,12,8,4,2,9,5,3,6,7,10]=>00110011011=>11011001100
[10,1,11,4,2,12,8,5,3,6,7,9]=>00110010111=>11101001100
[9,1,10,4,2,11,5,3,12,6,7,8]=>00110001111=>11110001100
[12,10,6,1,7,2,8,4,3,5,9,11]=>00101110101=>10101110100
[11,6,1,12,7,2,8,4,3,5,9,10]=>00101110011=>11001110100
[12,9,1,10,6,2,7,4,3,5,8,11]=>00101101101=>10110110100
[11,1,12,9,6,2,7,4,3,5,8,10]=>00101101011=>11010110100
[10,1,11,6,2,12,7,4,3,5,8,9]=>00101100111=>11100110100
[12,8,1,9,2,10,6,4,3,5,7,11]=>00101011101=>10111010100
[11,1,12,8,2,9,6,4,3,5,7,10]=>00101011011=>11011010100
[10,1,11,2,12,8,6,4,3,5,7,9]=>00101010111=>11101010100
[9,1,10,4,2,11,3,12,6,5,7,8]=>00101001111=>11110010100
[12,7,1,8,2,9,4,3,10,5,6,11]=>00100111101=>10111100100
[11,1,12,7,2,8,4,3,9,5,6,10]=>00100111011=>11011100100
[10,1,11,2,12,7,4,3,8,5,6,9]=>00100110111=>11101100100
[9,1,10,2,11,4,3,12,7,5,6,8]=>00100101111=>11110100100
[8,1,9,2,10,4,3,11,5,12,6,7]=>00100011111=>11111000100
[12,10,5,1,6,2,7,3,8,4,9,11]=>00011110101=>10101111000
[11,5,1,12,6,2,7,3,8,4,9,10]=>00011110011=>11001111000
[12,9,1,10,5,2,6,3,7,4,8,11]=>00011101101=>10110111000
[11,1,12,9,5,2,6,3,7,4,8,10]=>00011101011=>11010111000
[10,1,11,5,2,12,6,3,7,4,8,9]=>00011100111=>11100111000
[12,8,1,9,2,10,5,3,6,4,7,11]=>00011011101=>10111011000
[11,1,12,8,2,9,5,3,6,4,7,10]=>00011011011=>11011011000
[10,1,11,2,12,8,5,3,6,4,7,9]=>00011010111=>11101011000
[9,1,10,2,11,5,3,12,6,4,7,8]=>00011001111=>11110011000
[12,7,1,8,2,9,3,10,5,4,6,11]=>00010111101=>10111101000
[11,1,12,7,2,8,3,9,5,4,6,10]=>00010111011=>11011101000
[10,1,11,2,12,7,3,8,5,4,6,9]=>00010110111=>11101101000
[9,1,10,2,11,3,12,7,5,4,6,8]=>00010101111=>11110101000
[8,1,9,2,10,3,11,5,4,12,6,7]=>00010011111=>11111001000
[12,6,1,7,2,8,3,9,4,10,5,11]=>00001111101=>10111110000
[11,1,12,6,2,7,3,8,4,9,5,10]=>00001111011=>11011110000
[10,1,11,2,12,6,3,7,4,8,5,9]=>00001110111=>11101110000
[9,1,10,2,11,3,12,6,4,7,5,8]=>00001101111=>11110110000
[8,1,9,2,10,3,11,4,12,6,5,7]=>00001011111=>11111010000
[8,6,1,3,2,7,5,4]=>0101111=>1111010
[8,1,7,5,2,4,6,3]=>0001111=>1111000
[8,2,7,5,4,1,6,3]=>0011111=>1111100
[8,6,1,2,7,3,5,4]=>0001111=>1111000
[4,2,8,5,7,1,6,3]=>0010111=>1110100
[6,8,7,4,5,3,2,1]=>1101011=>1101011
[5,2,6,7,4,8,3,1]=>0101011=>1101010
[6,5,8,1,7,3,2,4]=>0100111=>1110010
[6,4,8,1,5,2,3,7]=>0001101=>1011000
[7,2,4,1,6,3,5,8]=>0010110=>0110100
[4,2,1,3,6,5,8,7,9]=>10101010=>01010101
[4,2,1,3,6,5,8,7,10,9]=>101010101=>101010101
[6,2,1,4,3,5,8,7,9]=>10101010=>01010101
[2,6,1,5,3,4,8,7]=>0001101=>1011000
[3,8,7,5,4,2,6,1]=>0011111=>1111100
[5,7,8,2,3,6,4,1]=>0010101=>1010100
[2,8,7,3,1,4,5,6]=>0100011=>1100010
[5,6,1,2,4,7,8,3]=>0000101=>1010000
[10,2,3,1,4,5,6,7,8,9]=>010000001=>100000010
[9,2,3,4,1,5,6,7,8]=>00100001=>10000100
[9,8,4,5,7,6,3,2,1]=>11001111=>11110011
[9,8,5,4,6,7,3,2,1]=>11010111=>11101011
[10,9,8,6,5,7,4,3,2,1]=>111011111=>111110111
[11,10,9,8,5,7,6,4,3,2,1]=>1110111111=>1111110111
[10,9,8,4,5,7,6,3,2,1]=>110011111=>111110011
[9,8,4,5,3,7,6,2,1]=>10011111=>11111001
[9,8,3,5,7,6,4,2,1]=>10101111=>11110101
[9,8,5,4,6,3,7,2,1]=>10011111=>11111001
[9,8,4,3,6,7,5,2,1]=>10110111=>11101101
[10,9,8,5,4,6,7,3,2,1]=>110101111=>111101011
[11,10,9,8,6,5,7,4,3,2,1]=>1110111111=>1111110111
[3,8,6,7,5,4,2,1]=>1011011=>1101101
[7,8,5,1,4,6,2,3]=>0001101=>1011000
[8,2,7,5,4,6,1,3]=>0001111=>1111000
[8,4,7,6,3,1,2,5]=>0100111=>1110010
[4,6,7,1,3,2,8,5]=>0100011=>1100010
[6,4,7,5,3,2,8,1]=>0101111=>1111010
[8,4,6,3,1,5,7,2]=>0100111=>1110010
[7,3,1,4,5,6,8,2]=>0100011=>1100010
[6,7,3,4,2,1,8,5]=>1010011=>1100101
[6,4,8,3,1,5,7,2]=>0100111=>1110010
[7,4,2,3,5,1,8,6]=>0011011=>1101100
[3,1,6,5,2,4,8,7]=>0101101=>1011010
[2,5,3,8,6,4,1,7]=>0011101=>1011100
[5,8,4,1,3,2,7,6]=>0110011=>1100110
[5,3,4,7,6,1,8,2]=>0001111=>1111000
[4,5,2,1,6,3,8,7]=>1001101=>1011001
[4,5,2,1,6,7,3,8]=>1001010=>0101001
[5,3,8,6,2,4,7,1]=>0001111=>1111000
[2,5,1,6,4,3,8,7]=>0011101=>1011100
[3,6,2,8,5,7,1,4]=>0000111=>1110000
[4,6,8,1,5,7,2,3]=>0000011=>1100000
[4,1,2,5,7,6,3,8]=>0010110=>0110100
[4,6,5,8,1,7,3,2]=>0100111=>1110010
[2,1,3,6,4,8,7,5]=>1000111=>1110001
[4,8,1,2,7,5,6,3]=>0000111=>1110000
[1,6,4,3,8,7,5,2]=>0011111=>1111100
[4,5,1,6,8,7,2,3]=>0001011=>1101000
[3,4,7,2,5,8,6,1]=>0000111=>1110000
[2,5,1,8,6,4,7,3]=>0001111=>1111000
[2,5,8,7,3,1,4,6]=>0100011=>1100010
[9,8,7,4,3,2,1,5,6]=>11100111=>11100111
[9,8,7,6,3,2,1,4,5]=>11001111=>11110011
[3,8,7,2,6,1,4,5]=>0000111=>1110000
[8,4,5,1,6,7,2,3]=>0001011=>1101000
[8,4,7,3,1,5,2,6]=>0101011=>1101010
[2,5,1,8,3,6,4,7]=>0001101=>1011000
[5,8,4,7,3,2,1,6]=>1100011=>1100011
[5,6,8,4,2,7,1,3]=>0010011=>1100100
[4,3,8,6,1,2,5,7]=>0010101=>1010100
[4,8,6,5,7,1,3,2]=>0100111=>1110010
[7,2,3,5,6,8,4,1]=>0010011=>1100100
[5,8,1,3,4,7,2,6]=>0000011=>1100000
[8,3,4,2,7,6,1,5]=>0010111=>1110100
[8,7,5,6,4,1,3,2]=>0110111=>1110110
[8,7,4,2,3,6,5,1]=>0011111=>1111100
[8,4,2,3,7,6,5,1]=>0011111=>1111100
[7,2,4,5,3,1,6,8]=>0101010=>0101010
[7,6,3,1,4,5,8,2]=>0100111=>1110010
[3,7,4,6,2,1,8,5]=>1000111=>1110001
[5,4,1,7,8,6,2,3]=>0011101=>1011100
[5,3,4,7,8,1,6,2]=>0001101=>1011000
[4,3,7,6,5,1,8,2]=>0011111=>1111100
[5,1,4,8,2,3,7,6]=>0001011=>1101000
[3,2,8,5,4,1,6,7]=>0111001=>1001110
[7,8,9,1,3,4,5,6,2]=>00001001=>10010000
[6,1,2,9,3,4,5,7,8]=>00001001=>10010000
[4,1,2,3,5,9,6,7,8]=>00100001=>10000100
[3,1,2,4,5,6,9,7,8]=>01000001=>10000010
[1,2,8,3,4,6,5,7]=>0000101=>1010000
[8,1,2,7,3,5,4,6]=>0001011=>1101000
[5,7,1,2,6,3,4,8]=>0000110=>0110000
[1,2,7,5,6,3,4,8]=>0000110=>0110000
[5,1,4,7,2,3,6,8]=>0001010=>0101000
[4,8,1,2,3,6,5,7]=>0000101=>1010000
[1,3,4,2,5,6,7,8,9]=>00100000=>00000100
[1,2,4,5,6,3,7,8,9]=>00001000=>00010000
[1,2,3,5,6,7,8,4,9]=>00000010=>01000000
[2,1,5,3,6,7,4,8,9]=>10010100=>00101001
[1,3,5,6,4,2,7,8,9]=>00101000=>00010100
[3,5,2,1,6,4,7,8,9]=>10011000=>00011001
[2,1,3,6,4,7,8,9,5]=>10001001=>10010001
[1,3,4,6,7,2,8,5,9]=>00000110=>01100000
[3,2,6,1,4,7,8,5,9]=>01001010=>01010010
[2,4,6,1,7,5,3,8,9]=>00011100=>00111000
[4,6,3,2,1,7,5,8,9]=>11001100=>00110011
[2,4,1,7,5,8,3,9,6]=>00100111=>11100100
[4,3,7,2,1,5,8,9,6]=>10100101=>10100101
[1,3,5,7,8,6,4,2,9]=>00101010=>01010100
[3,5,7,2,1,8,6,4,9]=>10001110=>01110001
[5,7,4,3,2,1,8,6,9]=>11100110=>01100111
[2,4,6,8,1,9,7,5,3]=>00010111=>11101000
[4,6,8,3,2,1,9,7,5]=>11000111=>11100011
[6,8,5,4,3,2,1,9,7]=>11110011=>11001111
[1,3,4,2,5,6,7,8,9,10]=>001000000=>000000100
[1,2,4,5,6,3,7,8,9,10]=>000010000=>000010000
[1,2,3,5,6,7,8,4,9,10]=>000000100=>001000000
[2,1,5,3,6,7,4,8,9,10]=>100101000=>000101001
[1,3,5,6,4,2,7,8,9,10]=>001010000=>000010100
[3,5,2,1,6,4,7,8,9,10]=>100110000=>000011001
[2,1,3,6,4,7,8,9,5,10]=>100010010=>010010001
[1,3,4,6,7,2,8,5,9,10]=>000001100=>001100000
[3,2,6,1,4,7,8,5,9,10]=>010010100=>001010010
[2,4,6,1,7,5,3,8,9,10]=>000111000=>000111000
[4,6,3,2,1,7,5,8,9,10]=>110011000=>000110011
[1,3,4,2,7,8,5,9,10,6]=>001000101=>101000100
[3,2,1,7,4,5,8,9,10,6]=>110001001=>100100011
[1,2,4,5,7,8,9,6,3,10]=>000010010=>010010000
[4,3,7,2,1,5,8,9,6,10]=>101001010=>010100101
[1,3,5,7,8,6,4,2,9,10]=>001010100=>001010100
[3,5,7,2,1,8,6,4,9,10]=>100011100=>001110001
[5,7,4,3,2,1,8,6,9,10]=>111001100=>001100111
[2,1,5,3,8,6,9,10,7,4]=>100101101=>101101001
[1,3,5,6,8,9,4,2,10,7]=>001000011=>110000100
[3,5,2,8,1,6,9,4,10,7]=>000100111=>111001000
[5,4,8,3,2,1,6,9,10,7]=>110100101=>101001011
[2,4,6,8,1,9,7,5,3,10]=>000101110=>011101000
[4,6,8,3,2,1,9,7,5,10]=>110001110=>011100011
[6,8,5,4,3,2,1,9,7,10]=>111100110=>011001111
[3,5,7,9,2,1,10,8,6,4]=>100010111=>111010001
[5,7,9,4,3,2,1,10,8,6]=>111000111=>111000111
[7,9,6,5,4,3,2,1,10,8]=>111110011=>110011111
[6,2,3,8,7,1,4,5]=>0000111=>1110000
[8,2,3,6,4,7,5,1]=>0001111=>1111000
[7,2,3,6,4,8,1,5]=>0000111=>1110000
[4,5,6,3,7,2,8,1,9]=>00001110=>01110000
[1,5,6,7,4,8,3,9,2]=>00000111=>11100000
[4,5,1,3,2,6,8,7]=>0101001=>1001010
[6,4,7,5,1,3,2,8]=>0101110=>0111010
[5,3,1,6,2,7,8,4]=>0101101=>1011010
[6,7,2,4,1,8,3,5]=>0010011=>1100100
[5,1,6,3,2,7,8,4]=>0101101=>1011010
[5,2,1,6,4,7,3,8]=>1001110=>0111001
[5,4,1,6,2,7,8,3]=>0011101=>1011100
[6,7,2,5,4,1,3,8]=>0011010=>0101100
[7,1,3,5,4,2,8,6]=>0011011=>1101100
[7,6,8,2,4,5,3,1]=>0101011=>1101010
[4,2,8,6,5,1,3,7]=>0011101=>1011100
[3,8,5,4,7,1,2,6]=>0001011=>1101000
[1,4,8,3,6,2,7,5]=>0000111=>1110000
[6,3,2,4,8,7,1,5]=>0100111=>1110010
[8,3,2,7,4,1,5,6]=>0110011=>1100110
[7,3,2,6,5,8,1,4]=>0100111=>1110010
[3,6,2,5,7,4,8,1]=>0000111=>1110000
[2,7,1,5,8,6,4,3]=>0010111=>1110100
[7,2,4,1,6,8,5,3]=>0011011=>1101100
[6,4,7,2,3,8,5,1]=>0001111=>1111000
[6,1,8,5,7,4,2,3]=>0010111=>1110100
[7,1,4,3,6,5,8,2]=>0010111=>1110100
[7,1,5,6,3,4,8,2]=>0000111=>1110000
[6,1,8,5,4,7,3,2]=>0101111=>1111010
[7,6,1,5,4,2,8,3]=>0011111=>1111100
[5,1,6,8,7,2,4,3]=>0011011=>1101100
[4,6,7,5,3,1,8,2]=>0101011=>1101010
[5,3,2,6,8,7,4,1]=>0111011=>1101110
[5,4,6,2,8,7,3,1]=>0101111=>1111010
[4,5,8,6,7,2,3,1]=>0100011=>1100010
[4,5,7,6,1,2,8,3]=>0000111=>1110000
[4,6,5,7,2,1,8,3]=>1000111=>1110001
[2,3,7,5,6,1,10,9,4,8]=>000011011=>110110000
[2,3,4,10,6,9,8,5,1,7]=>000100111=>111001000
[2,3,6,5,9,10,8,4,1,7]=>001010101=>101010100
[2,3,9,5,8,7,4,1,10,6]=>001001111=>111100100
[2,5,4,9,6,10,8,3,1,7]=>010100111=>111001010
[2,5,4,8,9,7,3,1,10,6]=>010101011=>110101010
[2,3,4,10,6,7,1,9,8,5]=>000001111=>111100000
[2,3,7,5,6,1,10,9,8,4]=>000011111=>111110000
[2,3,4,10,6,8,9,1,7,5]=>000001011=>110100000
[2,3,6,5,8,10,9,1,7,4]=>000011011=>110110000
[2,3,8,5,7,9,1,10,6,4]=>000010111=>111010000
[2,5,4,8,6,10,9,1,7,3]=>000101111=>111101000
[2,5,4,7,8,9,1,10,6,3]=>000110011=>110011000
[2,3,4,10,6,9,8,7,5,1]=>000101111=>111101000
[2,3,6,5,9,10,8,7,4,1]=>001011101=>101110100
[2,3,7,5,9,8,10,6,4,1]=>001011011=>110110100
[2,3,9,5,8,7,6,4,1,10]=>001011110=>011110100
[2,5,4,9,6,10,8,7,3,1]=>010101111=>111101010
[2,5,4,9,7,8,10,6,3,1]=>010110011=>110011010
[2,5,4,8,9,7,6,3,1,10]=>010111010=>010111010
[2,3,4,10,7,9,8,1,6,5]=>000010111=>111010000
[2,3,5,7,10,9,8,1,6,4]=>000010111=>111010000
[2,3,8,6,9,7,1,10,5,4]=>000101111=>111101000
[2,4,7,5,10,9,8,1,6,3]=>000011111=>111110000
[2,4,6,8,9,7,1,10,5,3]=>000101011=>110101000
[2,3,4,10,7,8,9,6,5,1]=>000110011=>110011000
[2,3,5,7,10,8,9,6,4,1]=>001010011=>110010100
[2,3,7,6,8,9,10,5,4,1]=>001101001=>100101100
[2,3,9,6,7,8,5,4,1,10]=>001100110=>011001100
[2,4,7,5,10,8,9,6,3,1]=>010011011=>110110010
[2,4,6,7,8,9,10,5,3,1]=>010100001=>100001010
[2,4,6,9,7,8,5,3,1,10]=>010100110=>011001010
[2,6,5,8,9,7,10,4,3,1]=>011010011=>110010110
[2,6,5,7,8,9,4,3,1,10]=>011010010=>010010110
[3,7,4,5,10,9,8,1,6,2]=>000011111=>111110000
[3,6,4,8,9,7,1,10,5,2]=>000111011=>110111000
[3,7,4,5,10,8,9,6,2,1]=>100011011=>110110001
[3,6,4,7,8,9,10,5,2,1]=>100110001=>100011001
[3,6,4,9,7,8,5,2,1,10]=>100110110=>011011001
[3,5,6,8,9,7,10,4,2,1]=>101000011=>110000101
[3,5,6,7,8,9,4,2,1,10]=>101000010=>010000101
[7,4,8,6,3,5,1,2]=>0001111=>1111000
[2,3,4,7,8,6,1,5]=>0000101=>1010000
[6,3,7,1,4,2,8,5]=>0010111=>1110100
[4,3,2,7,6,5,1,9,8,10]=>011111010=>010111110
[4,3,2,1,7,6,9,8,5,10]=>111001110=>011100111
[4,3,2,7,6,1,9,8,5,10]=>011011110=>011110110
[4,3,2,7,6,9,8,5,1,10]=>011101110=>011101110
[4,3,7,6,2,1,9,8,5,10]=>101011110=>011110101
[4,3,7,6,2,9,8,5,1,10]=>001111110=>011111100
[4,3,2,1,7,6,5,9,10,8]=>111011001=>100110111
[4,3,2,7,6,5,1,9,10,8]=>011111001=>100111110
[4,3,2,1,7,6,9,5,10,8]=>111001011=>110100111
[4,3,2,7,6,1,9,5,10,8]=>011011011=>110110110
[4,3,2,7,6,9,5,1,10,8]=>011101011=>110101110
[4,3,7,6,2,1,9,5,10,8]=>101011011=>110110101
[4,3,7,6,2,9,5,1,10,8]=>001111011=>110111100
[4,3,2,1,7,6,9,10,8,5]=>111001101=>101100111
[4,3,2,7,6,1,9,10,8,5]=>011011101=>101110110
[4,3,2,7,6,9,1,10,8,5]=>011001111=>111100110
[4,3,2,7,6,9,10,8,5,1]=>011101101=>101101110
[4,3,7,6,2,1,9,10,8,5]=>101011101=>101110101
[4,3,7,6,2,9,1,10,8,5]=>001011111=>111110100
[4,3,7,6,2,9,10,8,5,1]=>001111101=>101111100
[4,3,2,1,7,9,6,5,10,8]=>111010011=>110010111
[4,3,2,7,1,9,6,5,10,8]=>011011011=>110110110
[4,3,2,7,9,6,5,1,10,8]=>011110011=>110011110
[4,3,7,2,1,9,6,5,10,8]=>101011011=>110110101
[4,3,7,2,9,6,5,1,10,8]=>001111011=>110111100
[4,3,2,1,7,9,6,10,8,5]=>111000111=>111000111
[4,3,2,7,1,9,6,10,8,5]=>011001111=>111100110
[4,3,2,7,9,6,1,10,8,5]=>011010111=>111010110
[4,3,2,7,9,6,10,8,5,1]=>011100111=>111001110
[4,3,7,2,1,9,6,10,8,5]=>101001111=>111100101
[4,3,7,2,9,6,1,10,8,5]=>001011111=>111110100
[4,3,7,2,9,6,10,8,5,1]=>001101111=>111101100
[4,3,7,9,6,2,1,10,8,5]=>101010111=>111010101
[4,3,7,9,6,2,10,8,5,1]=>001110111=>111011100
[4,7,3,2,1,9,6,5,10,8]=>110011011=>110110011
[4,7,3,2,9,6,5,1,10,8]=>010111011=>110111010
[4,7,3,2,1,9,6,10,8,5]=>110001111=>111100011
[4,7,3,2,9,6,1,10,8,5]=>010011111=>111110010
[4,7,3,2,9,6,10,8,5,1]=>010101111=>111101010
[4,7,3,9,6,2,1,10,8,5]=>100011111=>111110001
[4,6,3,5,1,8,2,7]=>0001101=>1011000
[8,5,7,6,2,3,4,1]=>0010111=>1110100
[3,5,6,7,8,9,2,4,1]=>00100001=>10000100
[3,4,6,7,8,2,5,1]=>0001001=>1001000
[2,4,6,7,8,9,1,3,5]=>00000001=>10000000
[2,5,6,7,3,8,1,4]=>0000011=>1100000
[2,5,6,7,8,9,3,1,4]=>01000001=>10000010
[5,8,4,6,2,1,7,3]=>1000111=>1110001
[2,4,7,5,8,6,3,1]=>0100111=>1110010
[1,6,8,3,4,2,7,5]=>0010011=>1100100
[4,1,7,6,2,8,3,5]=>0010111=>1110100
[4,1,8,2,7,5,3,6]=>0011011=>1101100
[4,1,7,2,8,5,3,6]=>0011011=>1101100
[2,5,6,3,7,4,8,1]=>0000111=>1110000
[2,6,5,3,8,4,7,1]=>0001111=>1111000
[2,6,5,3,7,4,8,1]=>0001111=>1111000
[7,1,6,3,5,4,8,2]=>0001111=>1111000
[5,7,3,2,8,4,1,6]=>0110011=>1100110
[2,8,6,1,7,5,3,4]=>0001111=>1111000
[8,1,5,2,7,4,3,6]=>0011011=>1101100
[7,1,4,2,8,5,3,6]=>0011011=>1101100
[2,6,8,1,7,5,3,4]=>0001011=>1101000
[1,4,6,5,3,8,2,7]=>0001101=>1011000
[2,4,5,8,7,1,3,6]=>0000011=>1100000
[3,1,6,8,7,5,4,2]=>0111011=>1101110
[3,1,8,7,5,6,4,2]=>0110111=>1110110
[5,1,8,7,6,3,4,2]=>0011111=>1111100
[8,2,7,5,3,6,4,1]=>0011111=>1111100
[8,7,2,3,1,5,6,4]=>0100111=>1110010
[2,8,5,7,6,1,3,4]=>0000111=>1110000
[1,8,7,2,6,4,5,3]=>0001111=>1111000
[8,7,2,1,6,4,5,3]=>1001111=>1111001
[1,8,4,7,6,2,5,3]=>0001111=>1111000
[8,7,1,6,4,3,5,2]=>0011111=>1111100
[8,4,1,7,3,6,5,2]=>0011111=>1111100
[5,4,6,3,8,1,7,2,9]=>00011110=>01111000
[1,6,5,7,4,9,2,8,3]=>00001111=>11110000
[5,6,4,7,3,9,1,8,2,10]=>000011110=>011110000
[5,4,8,1,7,2,6,3,9]=>00011110=>01111000
[5,4,8,1,6,3,7,2,9]=>00011110=>01111000
[1,6,5,9,2,8,3,7,4]=>00001111=>11110000
[1,6,5,9,2,7,4,8,3]=>00001111=>11110000
[1,6,7,5,8,4,10,2,9,3]=>000001111=>111100000
[8,3,6,2,1,5,4,7]=>1001101=>1011001
[4,5,6,7,8,9,1,10,2,3]=>000000011=>110000000
[2,5,6,7,8,1,9,3,4]=>00000011=>11000000
[4,5,6,7,1,2,8,3,9]=>00000110=>01100000
[1,3,6,7,8,9,2,4,5]=>00000001=>10000000
[3,5,6,7,8,1,2,9,4]=>00000011=>11000000
[3,2,5,4,7,6,8,10,9,1]=>010101011=>110101010
[3,2,5,4,6,9,7,8,10,1]=>010100011=>110001010
[3,2,5,4,6,8,7,10,9,1]=>010100111=>111001010
[3,2,5,4,6,7,10,8,9,1]=>010100011=>110001010
[3,2,4,7,5,6,9,8,10,1]=>010001011=>110100010
[3,2,4,7,5,6,8,10,9,1]=>010001011=>110100010
[3,2,4,6,5,9,7,8,10,1]=>010010011=>110010010
[3,2,4,6,5,8,7,10,9,1]=>010010111=>111010010
[3,2,4,6,5,7,10,8,9,1]=>010010011=>110010010
[3,2,4,5,9,6,7,8,10,1]=>010000011=>110000010
[3,2,4,5,8,6,7,10,9,1]=>010000111=>111000010
[3,2,4,5,7,6,10,8,9,1]=>010001011=>110100010
[3,2,4,5,6,10,7,8,9,1]=>010000011=>110000010
[2,5,3,4,7,6,9,8,10,1]=>000101011=>110101000
[2,5,3,4,7,6,8,10,9,1]=>000101011=>110101000
[2,5,3,4,6,9,7,8,10,1]=>000100011=>110001000
[2,5,3,4,6,8,7,10,9,1]=>000100111=>111001000
[2,5,3,4,6,7,10,8,9,1]=>000100011=>110001000
[2,4,3,7,5,6,9,8,10,1]=>001001011=>110100100
[2,4,3,7,5,6,8,10,9,1]=>001001011=>110100100
[2,4,3,6,5,9,7,8,10,1]=>001010011=>110010100
[2,4,3,6,5,7,10,8,9,1]=>001010011=>110010100
[2,4,3,5,9,6,7,8,10,1]=>001000011=>110000100
[2,4,3,5,8,6,7,10,9,1]=>001000111=>111000100
[2,4,3,5,7,6,10,8,9,1]=>001001011=>110100100
[2,4,3,5,6,10,7,8,9,1]=>001000011=>110000100
[2,3,7,4,5,6,9,8,10,1]=>000001011=>110100000
[2,3,7,4,5,6,8,10,9,1]=>000001011=>110100000
[2,3,6,4,5,9,7,8,10,1]=>000010011=>110010000
[2,3,6,4,5,8,7,10,9,1]=>000010111=>111010000
[2,3,6,4,5,7,10,8,9,1]=>000010011=>110010000
[2,3,5,4,9,6,7,8,10,1]=>000100011=>110001000
[2,3,5,4,8,6,7,10,9,1]=>000100111=>111001000
[2,3,5,4,7,6,10,8,9,1]=>000101011=>110101000
[2,3,5,4,6,10,7,8,9,1]=>000100011=>110001000
[2,3,4,9,5,6,7,8,10,1]=>000000011=>110000000
[2,3,4,8,5,6,7,10,9,1]=>000000111=>111000000
[2,3,4,7,5,6,10,8,9,1]=>000001011=>110100000
[2,3,4,6,5,10,7,8,9,1]=>000010011=>110010000
[3,2,5,4,7,6,9,8,10,12,11,1]=>01010101011=>11010101010
[3,2,5,4,7,6,8,11,9,10,12,1]=>01010100011=>11000101010
[3,2,5,4,7,6,8,10,9,12,11,1]=>01010100111=>11100101010
[3,2,5,4,7,6,8,9,12,10,11,1]=>01010100011=>11000101010
[3,2,5,4,6,8,7,10,9,12,11,1]=>01010010111=>11101001010
[3,2,5,4,6,7,10,8,9,12,11,1]=>01010000111=>11100001010
[3,2,4,7,5,6,8,11,9,10,12,1]=>01000100011=>11000100010
[3,2,4,7,5,6,8,9,12,10,11,1]=>01000100011=>11000100010
[3,2,4,6,5,8,7,10,9,12,11,1]=>01001010111=>11101010010
[3,2,4,5,9,6,7,8,11,10,12,1]=>01000001011=>11010000010
[3,2,4,5,9,6,7,8,10,12,11,1]=>01000001011=>11010000010
[3,2,4,5,8,6,7,10,9,12,11,1]=>01000010111=>11101000010
[3,2,4,5,7,6,11,8,9,10,12,1]=>01000100011=>11000100010
[3,2,4,5,7,6,8,12,9,10,11,1]=>01000100011=>11000100010
[3,2,4,5,6,11,7,8,9,10,12,1]=>01000000011=>11000000010
[3,2,4,5,6,9,7,8,12,10,11,1]=>01000001011=>11010000010
[3,2,4,5,6,7,12,8,9,10,11,1]=>01000000011=>11000000010
[2,5,3,4,7,6,9,8,11,10,12,1]=>00010101011=>11010101000
[2,5,3,4,7,6,9,8,10,12,11,1]=>00010101011=>11010101000
[2,5,3,4,7,6,8,10,9,12,11,1]=>00010100111=>11100101000
[2,5,3,4,6,9,7,8,11,10,12,1]=>00010001011=>11010001000
[2,5,3,4,6,9,7,8,10,12,11,1]=>00010001011=>11010001000
[2,5,3,4,6,8,7,10,9,12,11,1]=>00010010111=>11101001000
[2,5,3,4,6,7,11,8,9,10,12,1]=>00010000011=>11000001000
[2,5,3,4,6,7,9,8,12,10,11,1]=>00010001011=>11010001000
[2,5,3,4,6,7,8,12,9,10,11,1]=>00010000011=>11000001000
[2,4,3,7,5,6,9,8,11,10,12,1]=>00100101011=>11010100100
[2,4,3,7,5,6,9,8,10,12,11,1]=>00100101011=>11010100100
[2,4,3,7,5,6,8,10,9,12,11,1]=>00100100111=>11100100100
[2,4,3,6,5,9,7,8,11,10,12,1]=>00101001011=>11010010100
[2,4,3,6,5,9,7,8,10,12,11,1]=>00101001011=>11010010100
[2,4,3,6,5,8,7,11,9,10,12,1]=>00101010011=>11001010100
[2,4,3,6,5,8,7,9,12,10,11,1]=>00101010011=>11001010100
[2,4,3,6,5,7,11,8,9,10,12,1]=>00101000011=>11000010100
[2,4,3,6,5,7,10,8,9,12,11,1]=>00101000111=>11100010100
[2,4,3,6,5,7,9,8,12,10,11,1]=>00101001011=>11010010100
[2,4,3,6,5,7,8,12,9,10,11,1]=>00101000011=>11000010100
[2,4,3,5,9,6,7,8,11,10,12,1]=>00100001011=>11010000100
[2,4,3,5,9,6,7,8,10,12,11,1]=>00100001011=>11010000100
[2,4,3,5,8,6,7,10,9,12,11,1]=>00100010111=>11101000100
[2,4,3,5,7,6,10,8,9,12,11,1]=>00100100111=>11100100100
[2,4,3,5,7,6,9,8,12,10,11,1]=>00100101011=>11010100100
[2,4,3,5,6,10,7,8,9,12,11,1]=>00100000111=>11100000100
[2,4,3,5,6,9,7,8,12,10,11,1]=>00100001011=>11010000100
[2,3,7,4,5,6,9,8,11,10,12,1]=>00000101011=>11010100000
[2,3,7,4,5,6,9,8,10,12,11,1]=>00000101011=>11010100000
[2,3,7,4,5,6,8,11,9,10,12,1]=>00000100011=>11000100000
[2,3,7,4,5,6,8,10,9,12,11,1]=>00000100111=>11100100000
[2,3,7,4,5,6,8,9,12,10,11,1]=>00000100011=>11000100000
[2,3,6,4,5,8,7,10,9,12,11,1]=>00001010111=>11101010000
[2,3,6,4,5,7,10,8,9,12,11,1]=>00001000111=>11100010000
[2,3,5,4,9,6,7,8,11,10,12,1]=>00010001011=>11010001000
[2,3,5,4,9,6,7,8,10,12,11,1]=>00010001011=>11010001000
[2,3,5,4,8,6,7,10,9,12,11,1]=>00010010111=>11101001000
[2,3,5,4,7,6,10,8,9,12,11,1]=>00010100111=>11100101000
[2,3,5,4,7,6,9,8,12,10,11,1]=>00010101011=>11010101000
[2,3,5,4,6,11,7,8,9,10,12,1]=>00010000011=>11000001000
[2,3,5,4,6,9,7,8,12,10,11,1]=>00010001011=>11010001000
[2,3,5,4,6,7,12,8,9,10,11,1]=>00010000011=>11000001000
[2,3,4,9,5,6,7,8,11,10,12,1]=>00000001011=>11010000000
[2,3,4,9,5,6,7,8,10,12,11,1]=>00000001011=>11010000000
[2,3,4,8,5,6,7,11,9,10,12,1]=>00000010011=>11001000000
[2,3,4,8,5,6,7,10,9,12,11,1]=>00000010111=>11101000000
[2,3,4,8,5,6,7,9,12,10,11,1]=>00000010011=>11001000000
[2,3,4,7,5,6,11,8,9,10,12,1]=>00000100011=>11000100000
[2,3,4,7,5,6,10,8,9,12,11,1]=>00000100111=>11100100000
[2,3,4,7,5,6,9,8,12,10,11,1]=>00000101011=>11010100000
[2,3,4,7,5,6,8,12,9,10,11,1]=>00000100011=>11000100000
[2,3,4,6,5,10,7,8,9,12,11,1]=>00001000111=>11100010000
[2,3,4,5,11,6,7,8,9,10,12,1]=>00000000011=>11000000000
[2,3,4,5,10,6,7,8,9,12,11,1]=>00000000111=>11100000000
[2,3,4,5,9,6,7,8,12,10,11,1]=>00000001011=>11010000000
[2,3,4,5,8,6,7,12,9,10,11,1]=>00000010011=>11001000000
[2,3,4,5,7,6,12,8,9,10,11,1]=>00000100011=>11000100000
[1,7,3,6,8,2,5,4]=>0001011=>1101000
[4,5,1,8,7,3,6,2]=>0001111=>1111000
[3,8,5,2,6,7,4,1]=>0011011=>1101100
[4,3,8,5,2,6,1,7]=>0011101=>1011100
[3,6,4,7,5,2,1,8]=>1001110=>0111001
[5,7,4,1,2,6,8,3]=>0010011=>1100100
[2,8,6,7,5,3,1,4]=>0101011=>1101010
[7,4,5,2,6,3,1,8]=>0101110=>0111010
[8,6,3,4,5,1,7,2]=>0001111=>1111000
[8,6,3,5,4,1,7,2]=>0011111=>1111100
[8,7,4,5,1,3,6,2]=>0001111=>1111000
[8,6,2,5,3,1,4,7]=>0101101=>1011010
[8,4,7,3,1,2,5,6]=>0100011=>1100010
[8,7,3,5,1,6,4,2]=>0011111=>1111100
[4,8,3,2,6,1,7,5]=>0100111=>1110010
[4,3,7,6,1,5,2,8]=>0011110=>0111100
[7,5,4,3,6,1,8,2]=>0011111=>1111100
[4,6,8,5,3,1,2,7]=>0101001=>1001010
[5,6,8,4,3,7,2,1]=>1010011=>1100101
[7,5,8,4,2,1,6,3]=>1010111=>1110101
[1,4,8,7,6,2,5,3]=>0001111=>1111000
[7,2,4,1,5,3,8,6]=>0011011=>1101100
[8,5,3,4,1,7,2,6]=>0011011=>1101100
[2,8,5,4,3,6,1,7]=>0011101=>1011100
[8,6,5,3,1,2,7,4]=>0101111=>1111010
[7,4,6,5,3,2,8,1]=>0101111=>1111010
[5,6,7,2,3,8,4,1]=>0010011=>1100100
[8,4,2,6,5,7,3,1]=>0110111=>1110110
[1,7,4,2,8,5,6,3]=>0010111=>1110100
[3,2,1,7,4,6,8,5]=>1100011=>1100011
[6,2,5,7,1,4,3,8]=>0010110=>0110100
[4,8,5,3,1,2,6,7]=>0101001=>1001010
[8,5,2,4,6,1,3,7]=>0001101=>1011000
[1,5,3,4,7,2,6,8]=>0001010=>0101000
[8,4,6,1,5,7,3,2]=>0100111=>1110010
[6,4,7,2,1,3,8,5]=>1000111=>1110001
[6,7,3,1,2,4,8,5]=>0100011=>1100010
[3,1,8,7,6,2,5,4]=>0101111=>1111010
[1,3,8,6,7,2,5,4]=>0001011=>1101000
[5,2,3,6,1,8,4,7]=>0001101=>1011000
[3,2,6,4,7,1,5,8]=>0100110=>0110010
[3,6,2,5,7,8,4,1]=>0010101=>1010100
[2,7,4,6,8,3,5,1]=>0001011=>1101000
[3,7,6,8,1,5,4,2]=>0011011=>1101100
[1,5,7,6,8,4,2,3]=>0010011=>1100100
[2,7,4,6,8,5,3,1]=>0101011=>1101010
[3,7,6,8,5,1,4,2]=>0011011=>1101100
[7,1,3,8,6,2,4,5]=>0000111=>1110000
[2,7,1,8,6,5,3,4]=>0001111=>1111000
[2,3,4,5,7,6,8,9,1]=>00000101=>10100000
[2,3,4,5,7,8,6,9,1]=>00000011=>11000000
[2,3,4,5,8,7,6,9,1]=>00000111=>11100000
[2,3,4,5,7,9,8,6,1]=>00001011=>11010000
[4,5,6,3,7,8,9,2,1]=>10001001=>10010001
[3,4,5,6,2,7,8,9,10,1]=>000010001=>100010000
[2,4,5,6,3,7,8,9,10,1]=>000010001=>100010000
[2,3,5,6,4,7,8,9,10,1]=>000010001=>100010000
[8,1,5,2,6,4,7,3]=>0001111=>1111000
[4,6,7,5,1,2,3,8]=>0001010=>0101000
[5,3,4,7,6,2,1,8]=>1001110=>0111001
[7,4,5,3,8,1,6,2]=>0001111=>1111000
[7,3,6,1,4,2,8,5]=>0010111=>1110100
[8,7,2,6,4,5,1,3]=>0001111=>1111000
[1,2,3,4,7,9,5,6,8]=>00000001=>10000000
[1,2,3,4,6,7,9,5,8]=>00000001=>10000000
[1,2,3,4,8,5,6,9,7]=>00000011=>11000000
[1,2,3,4,7,8,5,9,6]=>00000011=>11000000
[2,6,4,8,3,5,1,7]=>0001101=>1011000
[1,4,8,5,3,2,7,6]=>0101011=>1101010
[3,5,8,4,6,7,1,2]=>0000011=>1100000
[1,2,4,8,5,7,3,6]=>0000011=>1100000
[7,3,4,1,8,2,5,6]=>0010011=>1100100
[5,6,3,1,8,2,4,7]=>0100101=>1010010
[7,3,6,5,1,8,4,2]=>0011111=>1111100
[5,7,2,1,4,8,6,3]=>1000111=>1110001
[7,6,3,5,2,1,8,4]=>1001111=>1111001
[7,1,4,6,8,5,3,2]=>0101011=>1101010
[7,2,5,1,6,4,8,3]=>0001111=>1111000
[2,7,1,5,6,4,8,3]=>0000111=>1110000
[1,5,7,8,4,6,3,2]=>0100101=>1010010
[1,4,8,5,7,6,3,2]=>0100111=>1110010
[2,8,1,5,6,4,7,3]=>0000111=>1110000
[3,7,2,8,1,5,6,4]=>0000111=>1110000
[7,3,2,5,1,6,8,4]=>0101011=>1101010
[8,7,2,1,3,6,5,4]=>1001111=>1111001
[7,3,2,8,1,4,6,5]=>0100111=>1110010
[3,6,2,1,8,4,7,5]=>1000111=>1110001
[4,6,5,3,1,8,7,2]=>0101111=>1111010
[4,5,2,6,7,3,8,1]=>0001011=>1101000
[9,3,10,1,2,4,5,6,7,8]=>000000011=>110000000
[10,3,1,9,2,4,5,6,7,8]=>010000011=>110000010
[3,1,4,10,2,5,6,7,8,9]=>010000001=>100000010
[8,6,7,4,3,1,5,2]=>0111011=>1101110
[4,7,1,8,5,3,2,6]=>0101011=>1101010
[8,6,7,1,4,3,5,2]=>0011011=>1101100
[8,6,7,2,1,3,5,4]=>1001011=>1101001
[8,5,6,1,7,4,2,3]=>0010111=>1110100
[6,4,1,2,5,7,8,3]=>0010101=>1010100
[6,1,5,4,2,7,3,8]=>0011110=>0111100
[6,4,2,3,1,7,5,8]=>0110110=>0110110
[3,4,6,1,8,2,7,5]=>0000111=>1110000
[5,3,1,4,7,6,2,8]=>0101110=>0111010
[6,4,5,2,7,1,3,8]=>0001110=>0111000
[7,4,3,5,1,6,2,8]=>0011110=>0111100
[7,5,3,6,2,1,4,8]=>1001110=>0111001
[6,4,3,7,1,8,2,5]=>0010111=>1110100
[3,1,2,7,6,4,5,8]=>0100110=>0110010
[5,1,2,7,6,3,4,8]=>0001110=>0111000
[5,6,1,7,2,4,3,8]=>0010110=>0110100
[3,5,6,8,1,2,7,4]=>0000011=>1100000
[2,6,5,7,1,3,4,8]=>0000110=>0110000
[2,3,7,1,5,6,4,8]=>0000110=>0110000
[2,6,5,3,4,1,7,8]=>0011100=>0011100
[2,6,1,3,5,4,7,8]=>0001100=>0011000
[4,6,1,5,2,8,7,3]=>0001111=>1111000
[6,1,5,4,2,7,8,3]=>0011101=>1011100
[4,6,1,5,2,7,8,3]=>0001101=>1011000
[2,8,6,5,1,3,7,4]=>0001111=>1111000
[5,1,8,6,2,7,4,3]=>0011111=>1111100
[3,6,8,2,7,5,1,4]=>0001011=>1101000
[5,6,4,1,7,2,8,3]=>0010111=>1110100
[3,8,6,1,5,7,4,2]=>0010111=>1110100
[8,1,6,3,4,2,5,7]=>0010101=>1010100
[7,4,2,3,1,6,8,5]=>0110011=>1100110
[6,4,2,3,7,8,1,5]=>0010101=>1010100
[4,3,6,2,5,8,1,7]=>0010101=>1010100
[9,8,10,7,6,5,4,3,1,2]=>011111011=>110111110
[8,7,9,6,5,4,2,1,3]=>10111011=>11011101
[8,9,7,6,5,4,2,1,3]=>10111101=>10111101
[8,9,7,6,5,4,2,3,1]=>01111101=>10111110
[8,9,1,2,3,4,5,6,10,11,7]=>0000000101=>1010000000
[10,7,1,2,3,4,8,9,5,6]=>000001011=>110100000
[1,6,4,5,7,3,2,8]=>0100110=>0110010
[1,6,4,5,7,2,8,3]=>0000111=>1110000
[1,7,5,6,4,8,3,2]=>0100111=>1110010
[1,5,6,7,3,2,4,8]=>0100010=>0100010
[8,2,4,3,1,7,5,6]=>0110011=>1100110
[8,2,1,4,3,7,5,6]=>1010011=>1100101
[7,6,8,2,1,5,3,4]=>1001011=>1101001
[8,6,2,5,1,3,7,4]=>0001111=>1111000
[7,1,6,8,3,2,4,5]=>0100011=>1100010
[5,7,2,6,4,1,8,3]=>0010111=>1110100
[4,5,6,1,3,8,2,7]=>0000101=>1010000
[6,3,5,7,4,2,8,1]=>0010111=>1110100
[7,6,4,8,5,3,1,2]=>0101111=>1111010
[8,2,1,6,4,7,3,5]=>1000111=>1110001
[1,3,8,6,5,2,7,4]=>0001111=>1111000
[2,7,3,8,5,6,4,1]=>0010111=>1110100
[1,2,8,5,7,4,6,3]=>0000111=>1110000
[1,6,8,5,4,7,2,3]=>0001011=>1101000
[5,7,1,8,3,2,6,4]=>0100111=>1110010
[2,1,3,8,6,4,7,5]=>1000111=>1110001
[8,2,5,4,3,7,1,6]=>0011011=>1101100
[5,8,4,3,7,6,2,1]=>1010111=>1110101
[8,1,5,3,4,7,2,6]=>0001011=>1101000
[6,1,8,7,4,5,3,2]=>0101111=>1111010
[1,5,8,6,4,3,7,2]=>0010111=>1110100
[5,8,6,4,2,1,7,3]=>1010111=>1110101
[2,6,1,8,4,7,5,3]=>0001111=>1111000
[5,3,8,6,1,2,7,4]=>0001111=>1111000
[5,8,1,4,6,2,7,3]=>0000111=>1110000
[3,7,6,2,1,4,8,5]=>1000111=>1110001
[4,6,2,3,7,1,8,5]=>0000111=>1110000
[6,8,7,5,1,3,4,2]=>0011011=>1101100
[6,4,3,2,7,8,5,1]=>0111101=>1011110
[2,7,6,1,5,3,8,4]=>0001111=>1111000
[7,8,6,4,2,5,3,1]=>0111101=>1011110
[6,4,5,8,7,1,3,2]=>0100111=>1110010
[6,4,1,7,8,3,2,5]=>0110101=>1010110
[2,3,4,5,8,6,7,9,1]=>00000011=>11000000
[2,3,4,5,9,6,8,7,1]=>00000111=>11100000
[9,3,4,5,2,6,7,8,1]=>00010011=>11001000
[6,2,3,4,5,7,8,9,10,1]=>000010001=>100010000
[2,6,3,4,5,7,8,9,10,1]=>000010001=>100010000
[2,3,6,4,5,7,8,9,10,1]=>000010001=>100010000
[6,4,3,8,7,2,5,1]=>0011111=>1111100
[5,4,7,2,1,3,8,6]=>1001011=>1101001
[7,8,2,3,4,5,1,6,9]=>00010010=>01001000
[1,8,9,3,4,5,6,2,7]=>00001001=>10010000
[2,6,4,5,7,1,8,3]=>0000111=>1110000
[3,7,4,6,1,5,8,2]=>0000111=>1110000
[3,4,6,5,2,8,1,7]=>0001101=>1011000
[4,6,7,5,8,2,1,3]=>1000011=>1100001
[2,5,7,6,4,1,8,3]=>0010111=>1110100
[5,1,4,6,2,7,8,3]=>0001101=>1011000
[1,2,5,3,7,8,6,4]=>0001101=>1011000
[4,8,3,5,1,2,7,6]=>0001011=>1101000
[6,1,3,7,2,8,4,5]=>0000111=>1110000
[3,8,5,4,1,7,2,6]=>0011011=>1101100
[3,1,5,8,2,6,7,4]=>0100011=>1100010
[2,8,5,3,1,7,4,6]=>0101011=>1101010
[6,5,2,3,7,1,8,4]=>0001111=>1111000
[7,2,1,6,4,8,3,5]=>1000111=>1110001
[2,1,3,7,5,8,4,6]=>1000011=>1100001
[6,2,4,5,7,1,8,3]=>0000111=>1110000
[2,3,8,7,1,4,6,5]=>0000111=>1110000
[4,2,7,5,6,8,1,3]=>0010011=>1100100
[2,1,3,4,5,8,6,7,9]=>10000010=>01000001
[6,8,2,5,4,7,3,1]=>0101011=>1101010
[9,2,3,4,5,1,6,7,8]=>00010001=>10001000
[7,2,3,4,5,6,9,1,8]=>00000101=>10100000
[10,2,3,4,5,6,7,1,8,9]=>000001001=>100100000
[6,2,3,4,5,9,1,7,8]=>00001001=>10010000
[10,2,3,4,5,6,1,7,8,9]=>000010001=>100010000
[5,2,3,4,9,1,6,7,8]=>00010001=>10001000
[10,2,3,4,5,1,6,7,8,9]=>000100001=>100001000
[4,2,3,9,1,5,6,7,8]=>00100001=>10000100
[10,2,3,4,1,5,6,7,8,9]=>001000001=>100000100
[3,2,9,1,4,5,6,7,8]=>01000001=>10000010
[2,7,6,3,8,4,5,1]=>0001111=>1111000
[4,6,8,2,3,1,7,5]=>0100011=>1100010
[4,7,2,3,5,1,8,6]=>0001011=>1101000
[6,4,2,1,3,7,5,8]=>1010110=>0110101
[2,8,1,3,4,5,6,10,7,9]=>000000101=>101000000
[10,7,1,2,3,4,5,9,6,8]=>000001011=>110100000
[5,3,2,7,6,1,8,4]=>0101111=>1111010
[5,6,4,2,8,7,1,3]=>0010111=>1110100
[5,7,4,2,6,1,8,3]=>0010111=>1110100
[5,4,7,1,6,2,8,3]=>0001111=>1111000
[4,5,8,7,6,2,1,3]=>1000111=>1110001
[6,4,7,1,2,3,8,5]=>0000111=>1110000
[4,5,6,8,2,9,3,10,7,1]=>000001111=>111100000
[10,4,5,6,9,3,8,2,7,1]=>000001111=>111100000
[4,5,10,6,9,3,8,2,7,1]=>000001111=>111100000
[4,5,8,2,6,10,9,3,7,1]=>000001111=>111100000
[10,6,9,5,4,3,8,2,7,1]=>001101111=>111101100
[8,2,6,10,9,5,4,3,7,1]=>001101111=>111101100
[8,2,10,4,5,6,7,1,9,3]=>000001111=>111100000
[4,5,6,8,2,10,7,1,9,3]=>000001111=>111100000
[10,4,5,6,8,2,7,1,9,3]=>000001111=>111100000
[4,5,10,6,8,2,7,1,9,3]=>000001111=>111100000
[4,5,10,8,2,6,7,1,9,3]=>000001111=>111100000
[10,6,8,2,7,1,9,5,4,3]=>001101111=>111101100
[10,8,2,6,7,1,9,5,4,3]=>001101111=>111101100
[8,2,7,1,9,3,10,4,5,6]=>000001111=>111100000
[4,5,8,2,7,1,9,3,10,6]=>000001111=>111100000
[4,5,9,3,10,7,1,8,2,6]=>000001111=>111100000
[4,5,7,1,9,3,8,2,6,10]=>000001110=>011100000
[8,2,7,1,9,5,4,3,10,6]=>001101111=>111101100
[9,5,4,3,10,7,1,8,2,6]=>001101111=>111101100
[7,1,9,5,4,3,8,2,6,10]=>001101110=>011101100
[8,2,6,10,4,5,7,1,9,3]=>000001111=>111100000
[4,8,2,6,10,5,7,1,9,3]=>000001111=>111100000
[4,10,8,2,5,6,7,1,9,3]=>000001111=>111100000
[8,2,6,10,5,7,1,9,4,3]=>001001111=>111100100
[10,8,2,5,6,7,1,9,4,3]=>001001111=>111100100
[9,3,10,4,5,7,1,8,2,6]=>000001111=>111100000
[4,9,3,10,5,7,1,8,2,6]=>000001111=>111100000
[4,9,3,10,7,1,8,2,5,6]=>000001111=>111100000
[4,7,1,9,3,8,2,5,6,10]=>000001110=>011100000
[9,4,3,10,5,7,1,8,2,6]=>001001111=>111100100
[9,4,3,10,7,1,8,2,5,6]=>001001111=>111100100
[7,1,9,4,3,8,2,5,6,10]=>001001110=>011100100
[5,10,7,1,8,2,4,3,9,6]=>001001111=>111100100
[5,7,1,8,2,4,3,9,6,10]=>001001110=>011100100
[10,5,7,1,9,4,2,6,8,3]=>001001111=>111100100
[9,4,2,5,6,7,1,10,8,3]=>001001111=>111100100
[10,5,7,1,8,3,9,4,2,6]=>001001111=>111100100
[10,7,1,8,3,9,4,2,5,6]=>001001111=>111100100
[7,1,8,3,9,4,2,5,6,10]=>001001110=>011100100
[4,2,5,10,7,1,8,3,9,6]=>001001111=>111100100
[4,2,5,7,1,8,3,9,6,10]=>001001110=>011100100
[6,1,7,3,8,4,5,2]=>0001111=>1111000
[8,2,3,1,6,4,7,5]=>0100111=>1110010
[1,8,7,2,3,4,6,5]=>0000111=>1110000
[1,8,3,7,6,2,5,4]=>0001111=>1111000
[1,3,8,2,5,6,4,7]=>0000101=>1010000
[1,3,2,7,4,6,8,5]=>0100011=>1100010
[1,3,8,4,6,2,7,5]=>0000111=>1110000
[8,2,3,6,7,4,5,1]=>0001011=>1101000
[5,6,4,2,1,7,3,8]=>1010110=>0110101
[2,5,7,6,3,8,4,1]=>0010111=>1110100
[6,4,7,1,2,5,3,8]=>0001110=>0111000
[4,5,6,7,8,9,1,2,10,3]=>000000011=>110000000
[4,5,6,7,8,1,3,9,2]=>00000011=>11000000
[1,2,7,5,8,6,3,4]=>0000111=>1110000
[2,1,9,8,7,6,5,3,4]=>10011111=>11111001
[2,1,9,8,7,6,4,3,5]=>10101111=>11110101
[2,1,9,8,7,6,3,5,4]=>10011111=>11111001
[2,1,10,9,8,7,6,5,3,4]=>100111111=>111111001
[7,4,5,1,6,8,2,3]=>0001011=>1101000
[1,7,8,4,2,6,3,5]=>0010101=>1010100
[6,3,2,5,7,4,1,8]=>0110110=>0110110
[6,2,1,5,3,7,8,4]=>1001101=>1011001
[6,2,5,1,3,8,7,4]=>0001111=>1111000
[6,2,8,5,1,3,7,4]=>0001111=>1111000
[10,9,7,3,6,1,2,4,8,5]=>000011111=>111110000
[9,7,3,6,1,2,4,10,8,5]=>000011111=>111110000
[7,3,10,9,6,1,2,4,8,5]=>000011111=>111110000
[7,3,9,6,1,2,4,10,8,5]=>000011111=>111110000
[9,6,1,2,4,10,7,3,8,5]=>000011111=>111110000
[8,4,10,9,7,3,6,1,2,5]=>000011111=>111110000
[10,8,4,9,7,3,6,1,2,5]=>000011111=>111110000
[7,3,8,4,10,9,6,1,2,5]=>000011111=>111110000
[7,3,10,8,4,9,6,1,2,5]=>000011111=>111110000
[10,7,3,8,4,9,6,1,2,5]=>000011111=>111110000
[6,1,2,7,3,8,4,10,9,5]=>000011111=>111110000
[6,1,2,7,3,10,8,4,9,5]=>000011111=>111110000
[6,1,2,10,7,3,8,4,9,5]=>000011111=>111110000
[10,6,1,2,7,3,8,4,9,5]=>000011111=>111110000
[6,1,3,10,9,7,2,4,8,5]=>000011111=>111110000
[6,1,3,9,7,2,4,10,8,5]=>000011111=>111110000
[10,9,6,1,3,7,2,4,8,5]=>000011111=>111110000
[9,6,1,3,7,2,4,10,8,5]=>000011111=>111110000
[10,7,2,4,9,6,1,3,8,5]=>000011111=>111110000
[6,1,3,8,4,10,9,7,2,5]=>000011111=>111110000
[6,1,3,10,8,4,9,7,2,5]=>000011111=>111110000
[8,4,10,9,6,1,3,7,2,5]=>000011111=>111110000
[10,8,4,9,6,1,3,7,2,5]=>000011111=>111110000
[9,6,1,3,8,4,10,7,2,5]=>000011111=>111110000
[7,2,6,1,3,8,4,10,9,5]=>000011111=>111110000
[7,2,6,1,3,10,8,4,9,5]=>000011111=>111110000
[10,7,2,6,1,3,8,4,9,5]=>000011111=>111110000
[7,2,10,6,1,3,8,4,9,5]=>000011111=>111110000
[8,3,6,1,4,10,9,7,2,5]=>000011111=>111110000
[10,8,3,6,1,4,9,7,2,5]=>000011111=>111110000
[10,9,6,1,4,8,3,7,2,5]=>000011111=>111110000
[9,6,1,4,10,8,3,7,2,5]=>000011111=>111110000
[8,3,9,6,1,4,10,7,2,5]=>000011111=>111110000
[8,3,7,2,6,1,4,10,9,5]=>000011111=>111110000
[10,8,3,7,2,6,1,4,9,5]=>000011111=>111110000
[8,3,10,7,2,6,1,4,9,5]=>000011111=>111110000
[7,2,8,3,10,6,1,4,9,5]=>000011111=>111110000
[9,4,10,8,3,7,2,6,1,5]=>000011111=>111110000
[8,3,9,4,10,7,2,6,1,5]=>000011111=>111110000
[7,2,8,3,9,4,10,6,1,5]=>000011111=>111110000
[12,11,9,5,10,7,1,2,4,8,3,6]=>00000111111=>11111100000
[11,9,5,12,10,7,1,2,4,8,3,6]=>00000111111=>11111100000
[10,7,1,2,4,9,5,12,11,8,3,6]=>00000111111=>11111100000
[12,10,7,1,2,4,9,5,11,8,3,6]=>00000111111=>11111100000
[10,7,1,2,4,12,9,5,11,8,3,6]=>00000111111=>11111100000
[8,3,7,1,2,4,12,11,9,5,10,6]=>00000111111=>11111100000
[8,3,7,1,2,4,11,9,5,12,10,6]=>00000111111=>11111100000
[12,11,8,3,7,1,2,4,9,5,10,6]=>00000111111=>11111100000
[11,8,3,7,1,2,4,9,5,12,10,6]=>00000111111=>11111100000
[12,9,5,11,8,3,7,1,2,4,10,6]=>00000111111=>11111100000
[8,3,12,11,7,1,2,4,9,5,10,6]=>00000111111=>11111100000
[8,3,11,7,1,2,4,9,5,12,10,6]=>00000111111=>11111100000
[8,3,12,9,5,11,7,1,2,4,10,6]=>00000111111=>11111100000
[12,8,3,9,5,11,7,1,2,4,10,6]=>00000111111=>11111100000
[10,7,1,2,5,12,11,9,4,8,3,6]=>00000111111=>11111100000
[12,10,7,1,2,5,11,9,4,8,3,6]=>00000111111=>11111100000
[9,4,10,7,1,2,5,12,11,8,3,6]=>00000111111=>11111100000
[9,4,12,10,7,1,2,5,11,8,3,6]=>00000111111=>11111100000
[12,9,4,10,7,1,2,5,11,8,3,6]=>00000111111=>11111100000
[12,11,9,4,8,3,7,1,2,5,10,6]=>00000111111=>11111100000
[11,9,4,8,3,7,1,2,5,12,10,6]=>00000111111=>11111100000
[9,4,12,11,8,3,7,1,2,5,10,6]=>00000111111=>11111100000
[9,4,11,8,3,7,1,2,5,12,10,6]=>00000111111=>11111100000
[11,8,3,7,1,2,5,12,9,4,10,6]=>00000111111=>11111100000
[8,3,9,4,12,11,7,1,2,5,10,6]=>00000111111=>11111100000
[8,3,9,4,11,7,1,2,5,12,10,6]=>00000111111=>11111100000
[8,3,11,7,1,2,5,12,9,4,10,6]=>00000111111=>11111100000
[11,7,1,2,5,12,8,3,9,4,10,6]=>00000111111=>11111100000
[10,5,12,11,9,4,8,3,7,1,2,6]=>00000111111=>11111100000
[12,10,5,11,9,4,8,3,7,1,2,6]=>00000111111=>11111100000
[9,4,10,5,12,11,8,3,7,1,2,6]=>00000111111=>11111100000
[9,4,12,10,5,11,8,3,7,1,2,6]=>00000111111=>11111100000
[12,9,4,10,5,11,8,3,7,1,2,6]=>00000111111=>11111100000
[8,3,9,4,10,5,12,11,7,1,2,6]=>00000111111=>11111100000
[8,3,9,4,12,10,5,11,7,1,2,6]=>00000111111=>11111100000
[8,3,12,9,4,10,5,11,7,1,2,6]=>00000111111=>11111100000
[12,8,3,9,4,10,5,11,7,1,2,6]=>00000111111=>11111100000
[7,1,2,8,3,9,4,10,5,12,11,6]=>00000111111=>11111100000
[7,1,2,8,3,9,4,12,10,5,11,6]=>00000111111=>11111100000
[7,1,2,8,3,12,9,4,10,5,11,6]=>00000111111=>11111100000
[7,1,2,12,8,3,9,4,10,5,11,6]=>00000111111=>11111100000
[12,7,1,2,8,3,9,4,10,5,11,6]=>00000111111=>11111100000
[8,2,4,12,11,9,5,10,7,1,3,6]=>00000111111=>11111100000
[8,2,4,11,9,5,12,10,7,1,3,6]=>00000111111=>11111100000
[12,11,8,2,4,9,5,10,7,1,3,6]=>00000111111=>11111100000
[11,8,2,4,9,5,12,10,7,1,3,6]=>00000111111=>11111100000
[12,9,5,11,8,2,4,10,7,1,3,6]=>00000111111=>11111100000
[7,1,3,8,2,4,12,11,9,5,10,6]=>00000111111=>11111100000
[7,1,3,8,2,4,11,9,5,12,10,6]=>00000111111=>11111100000
[7,1,3,12,11,8,2,4,9,5,10,6]=>00000111111=>11111100000
[7,1,3,11,8,2,4,9,5,12,10,6]=>00000111111=>11111100000
[7,1,3,12,9,5,11,8,2,4,10,6]=>00000111111=>11111100000
[12,11,7,1,3,8,2,4,9,5,10,6]=>00000111111=>11111100000
[11,7,1,3,8,2,4,9,5,12,10,6]=>00000111111=>11111100000
[12,9,5,11,7,1,3,8,2,4,10,6]=>00000111111=>11111100000
[11,7,1,3,9,5,12,8,2,4,10,6]=>00000111111=>11111100000
[12,11,9,4,8,2,5,10,7,1,3,6]=>00000111111=>11111100000
[11,9,4,8,2,5,12,10,7,1,3,6]=>00000111111=>11111100000
[9,4,12,11,8,2,5,10,7,1,3,6]=>00000111111=>11111100000
[9,4,11,8,2,5,12,10,7,1,3,6]=>00000111111=>11111100000
[11,8,2,5,12,9,4,10,7,1,3,6]=>00000111111=>11111100000
[7,1,3,12,11,9,4,8,2,5,10,6]=>00000111111=>11111100000
[7,1,3,11,9,4,8,2,5,12,10,6]=>00000111111=>11111100000
[7,1,3,9,4,12,11,8,2,5,10,6]=>00000111111=>11111100000
[7,1,3,9,4,11,8,2,5,12,10,6]=>00000111111=>11111100000
[7,1,3,11,8,2,5,12,9,4,10,6]=>00000111111=>11111100000
[9,4,12,11,7,1,3,8,2,5,10,6]=>00000111111=>11111100000
[9,4,11,7,1,3,8,2,5,12,10,6]=>00000111111=>11111100000
[11,7,1,3,8,2,5,12,9,4,10,6]=>00000111111=>11111100000
[12,8,2,5,11,7,1,3,9,4,10,6]=>00000111111=>11111100000
[7,1,3,10,5,12,11,9,4,8,2,6]=>00000111111=>11111100000
[7,1,3,12,10,5,11,9,4,8,2,6]=>00000111111=>11111100000
[7,1,3,9,4,10,5,12,11,8,2,6]=>00000111111=>11111100000
[7,1,3,9,4,12,10,5,11,8,2,6]=>00000111111=>11111100000
[7,1,3,12,9,4,10,5,11,8,2,6]=>00000111111=>11111100000
[9,4,10,5,12,11,7,1,3,8,2,6]=>00000111111=>11111100000
[9,4,12,10,5,11,7,1,3,8,2,6]=>00000111111=>11111100000
[12,9,4,10,5,11,7,1,3,8,2,6]=>00000111111=>11111100000
[11,7,1,3,9,4,10,5,12,8,2,6]=>00000111111=>11111100000
[8,2,7,1,3,9,4,10,5,12,11,6]=>00000111111=>11111100000
[8,2,7,1,3,9,4,12,10,5,11,6]=>00000111111=>11111100000
[8,2,7,1,3,12,9,4,10,5,11,6]=>00000111111=>11111100000
[12,8,2,7,1,3,9,4,10,5,11,6]=>00000111111=>11111100000
[8,2,12,7,1,3,9,4,10,5,11,6]=>00000111111=>11111100000
[10,7,1,4,8,2,5,12,11,9,3,6]=>00000111111=>11111100000
[12,10,7,1,4,8,2,5,11,9,3,6]=>00000111111=>11111100000
[12,11,8,2,5,10,7,1,4,9,3,6]=>00000111111=>11111100000
[11,8,2,5,12,10,7,1,4,9,3,6]=>00000111111=>11111100000
[10,7,1,4,11,8,2,5,12,9,3,6]=>00000111111=>11111100000
[12,11,9,3,7,1,4,8,2,5,10,6]=>00000111111=>11111100000
[11,9,3,7,1,4,8,2,5,12,10,6]=>00000111111=>11111100000
[9,3,7,1,4,12,11,8,2,5,10,6]=>00000111111=>11111100000
[9,3,7,1,4,11,8,2,5,12,10,6]=>00000111111=>11111100000
[11,8,2,5,12,9,3,7,1,4,10,6]=>00000111111=>11111100000
[12,11,7,1,4,9,3,8,2,5,10,6]=>00000111111=>11111100000
[11,7,1,4,9,3,8,2,5,12,10,6]=>00000111111=>11111100000
[12,9,3,8,2,5,11,7,1,4,10,6]=>00000111111=>11111100000
[9,3,12,8,2,5,11,7,1,4,10,6]=>00000111111=>11111100000
[10,5,12,11,9,3,7,1,4,8,2,6]=>00000111111=>11111100000
[12,10,5,11,9,3,7,1,4,8,2,6]=>00000111111=>11111100000
[9,3,7,1,4,10,5,12,11,8,2,6]=>00000111111=>11111100000
[9,3,7,1,4,12,10,5,11,8,2,6]=>00000111111=>11111100000
[12,9,3,7,1,4,10,5,11,8,2,6]=>00000111111=>11111100000
[10,5,12,11,7,1,4,9,3,8,2,6]=>00000111111=>11111100000
[12,10,5,11,7,1,4,9,3,8,2,6]=>00000111111=>11111100000
[11,7,1,4,10,5,12,9,3,8,2,6]=>00000111111=>11111100000
[9,3,11,7,1,4,10,5,12,8,2,6]=>00000111111=>11111100000
[9,3,8,2,7,1,4,10,5,12,11,6]=>00000111111=>11111100000
[9,3,8,2,7,1,4,12,10,5,11,6]=>00000111111=>11111100000
[12,9,3,8,2,7,1,4,10,5,11,6]=>00000111111=>11111100000
[9,3,12,8,2,7,1,4,10,5,11,6]=>00000111111=>11111100000
[8,2,9,3,12,7,1,4,10,5,11,6]=>00000111111=>11111100000
[12,11,9,3,7,1,5,10,4,8,2,6]=>00000111111=>11111100000
[11,9,3,7,1,5,12,10,4,8,2,6]=>00000111111=>11111100000
[10,4,9,3,7,1,5,12,11,8,2,6]=>00000111111=>11111100000
[12,10,4,9,3,7,1,5,11,8,2,6]=>00000111111=>11111100000
[10,4,12,9,3,7,1,5,11,8,2,6]=>00000111111=>11111100000
[12,11,7,1,5,10,4,9,3,8,2,6]=>00000111111=>11111100000
[11,7,1,5,12,10,4,9,3,8,2,6]=>00000111111=>11111100000
[10,4,11,7,1,5,12,9,3,8,2,6]=>00000111111=>11111100000
[9,3,10,4,11,7,1,5,12,8,2,6]=>00000111111=>11111100000
[10,4,9,3,8,2,7,1,5,12,11,6]=>00000111111=>11111100000
[12,10,4,9,3,8,2,7,1,5,11,6]=>00000111111=>11111100000
[10,4,12,9,3,8,2,7,1,5,11,6]=>00000111111=>11111100000
[9,3,10,4,12,8,2,7,1,5,11,6]=>00000111111=>11111100000
[8,2,9,3,10,4,12,7,1,5,11,6]=>00000111111=>11111100000
[12,11,5,10,4,9,3,8,2,7,1,6]=>00000111111=>11111100000
[11,5,12,10,4,9,3,8,2,7,1,6]=>00000111111=>11111100000
[10,4,11,5,12,9,3,8,2,7,1,6]=>00000111111=>11111100000
[9,3,10,4,11,5,12,8,2,7,1,6]=>00000111111=>11111100000
[8,2,9,3,10,4,11,5,12,7,1,6]=>00000111111=>11111100000
[4,1,7,8,3,6,5,2]=>0011101=>1011100
[6,4,2,1,7,3,5,8]=>1010110=>0110101
[5,8,4,2,1,3,6,7]=>1010001=>1000101
[4,5,3,6,7,8,9,1,2]=>00010001=>10001000
[5,3,4,6,7,8,9,1,2]=>00010001=>10001000
[1,7,5,8,4,3,6,2]=>0010111=>1110100
[5,8,1,6,4,7,2,3]=>0000111=>1110000
[2,4,7,5,1,8,6,3]=>0001111=>1111000
[2,3,7,1,8,5,6,4]=>0000111=>1110000
[6,5,1,2,7,4,8,3]=>0001111=>1111000
[3,6,5,7,8,2,4,1]=>0010101=>1010100
[3,6,5,1,8,7,4,2]=>0011111=>1111100
[7,8,1,2,5,4,3,6]=>0011001=>1001100
[2,8,4,3,5,1,7,6]=>0011011=>1101100
[5,2,4,7,6,8,1,3]=>0001011=>1101000
[3,1,5,7,4,8,6,2]=>0100111=>1110010
[4,1,7,6,8,2,5,3]=>0011011=>1101100
[7,2,6,4,1,5,3,8]=>0011110=>0111100
[1,2,6,5,8,3,7,4]=>0000111=>1110000
[7,3,5,6,1,4,2,8]=>0010110=>0110100
[5,8,3,1,6,7,4,2]=>0110011=>1100110
[4,5,8,1,7,3,6,2]=>0000111=>1110000
[4,7,1,6,8,5,2,3]=>0001011=>1101000
[5,8,7,1,6,4,2,3]=>0010111=>1110100
[1,7,3,8,2,5,4,6]=>0001011=>1101000
[8,4,1,3,6,7,5,2]=>0011011=>1101100
[5,3,1,8,6,7,4,2]=>0111011=>1101110
[6,2,7,1,4,3,5,8]=>0010110=>0110100
[9,5,4,3,2,1,6,7,8]=>11110001=>10001111
[10,3,4,1,2,5,6,7,8,9]=>001000001=>100000100
[8,3,2,6,5,1,7,4]=>0101111=>1111010
[7,3,2,6,5,1,4,8]=>0101110=>0111010
[2,6,8,4,7,1,3,5]=>0000011=>1100000
[7,8,6,3,2,5,4,1]=>0111101=>1011110
[5,2,8,6,3,1,4,7]=>0101101=>1011010
[1,6,4,8,2,3,5,7]=>0000101=>1010000
[2,8,5,6,4,1,7,3]=>0010111=>1110100
[1,4,7,3,5,8,6,2]=>0000111=>1110000
[3,7,8,2,5,1,6,4]=>0001101=>1011000
[8,6,1,4,3,2,7,5]=>0110111=>1110110
[7,3,8,2,4,1,5,6]=>0010011=>1100100
[6,3,7,8,1,2,5,4]=>0001101=>1011000
[7,6,1,5,2,3,8,4]=>0001111=>1111000
[5,1,8,6,7,2,3,4]=>0001011=>1101000
[5,7,1,6,8,2,3,4]=>0000011=>1100000
[6,8,4,2,1,7,3,5]=>1010011=>1100101
[6,3,2,8,1,7,4,5]=>0100111=>1110010
[6,4,1,3,7,8,5,2]=>0011101=>1011100
[6,8,5,4,3,7,1,2]=>0011011=>1101100
[5,7,4,8,3,1,2,6]=>0100011=>1100010
[6,1,2,4,8,3,7,5]=>0000111=>1110000
[2,5,6,8,1,4,7,3]=>0000011=>1100000
[7,4,1,6,5,2,3,8]=>0011110=>0111100
[4,1,6,5,2,3,8,7]=>0011101=>1011100
[4,5,1,7,8,6,2,3]=>0001101=>1011000
[8,5,7,3,4,6,2,1]=>1000111=>1110001
[6,8,7,4,3,5,2,1]=>1011011=>1101101
[6,8,7,5,3,4,2,1]=>1011011=>1101101
[5,8,6,2,4,7,3,1]=>0100111=>1110010
[4,8,6,2,5,7,3,1]=>0100111=>1110010
[1,6,4,7,5,3,2,8]=>0101110=>0111010
[1,6,5,3,2,7,4,8]=>0101110=>0111010
[1,6,8,7,4,5,3,2]=>0101011=>1101010
[1,4,7,5,3,2,6,8]=>0101010=>0101010
[1,7,5,4,3,2,8,6]=>0111011=>1101110
[1,4,7,5,3,2,8,6]=>0101011=>1101010
[1,7,4,6,8,5,3,2]=>0101011=>1101010
[6,8,7,2,3,5,4,1]=>0011011=>1101100
[5,7,6,1,8,2,4,3]=>0010111=>1110100
[4,8,6,5,7,2,3,1]=>0100111=>1110010
[2,7,8,5,1,4,3,6]=>0011001=>1001100
[8,5,6,2,4,7,3,1]=>0100111=>1110010
[3,5,8,4,2,6,1,7]=>0010101=>1010100
[8,1,3,6,4,5,2,7]=>0001101=>1011000
[1,2,3,7,4,8,5,9,6]=>00000111=>11100000
[1,2,3,4,7,5,9,8,6]=>00000111=>11100000
[1,2,6,3,7,4,9,8,5]=>00001111=>11110000
[1,2,3,8,6,4,9,7,5]=>00001111=>11110000
[1,2,3,6,4,9,8,7,5]=>00001111=>11110000
[5,1,6,2,7,3,9,8,4]=>00011111=>11111000
[1,5,2,8,6,3,9,7,4]=>00011111=>11111000
[1,5,2,6,3,9,8,7,4]=>00011111=>11111000
[1,2,7,5,3,9,8,6,4]=>00011111=>11111000
[1,2,5,3,9,8,7,6,4]=>00011111=>11111000
[4,1,7,5,2,9,8,6,3]=>00111111=>11111100
[4,1,5,2,9,8,7,6,3]=>00111111=>11111100
[1,6,4,2,9,8,7,5,3]=>00111111=>11111100
[1,4,2,9,8,7,6,5,3]=>00111111=>11111100
[7,5,3,1,9,8,6,4,2]=>01111111=>11111110
[5,3,1,9,8,7,6,4,2]=>01111111=>11111110
[1,2,3,4,8,5,9,6,10,7]=>000000111=>111000000
[1,2,3,4,5,8,6,10,9,7]=>000000111=>111000000
[1,2,3,7,4,8,5,10,9,6]=>000001111=>111100000
[1,2,3,4,9,7,5,10,8,6]=>000001111=>111100000
[1,2,3,4,7,5,10,9,8,6]=>000001111=>111100000
[1,6,2,7,3,8,4,10,9,5]=>000011111=>111110000
[1,2,6,3,9,7,4,10,8,5]=>000011111=>111110000
[1,2,6,3,7,4,10,9,8,5]=>000011111=>111110000
[1,2,3,8,6,4,10,9,7,5]=>000011111=>111110000
[1,2,3,6,4,10,9,8,7,5]=>000011111=>111110000
[5,1,6,2,9,7,3,10,8,4]=>000111111=>111111000
[5,1,6,2,7,3,10,9,8,4]=>000111111=>111111000
[1,5,2,6,3,10,9,8,7,4]=>000111111=>111111000
[1,2,7,5,3,10,9,8,6,4]=>000111111=>111111000
[1,2,5,3,10,9,8,7,6,4]=>000111111=>111111000
[7,4,1,8,5,2,10,9,6,3]=>001111111=>111111100
[4,1,9,7,5,2,10,8,6,3]=>001111111=>111111100
[4,1,7,5,2,10,9,8,6,3]=>001111111=>111111100
[4,1,5,2,10,9,8,7,6,3]=>001111111=>111111100
[1,8,6,4,2,10,9,7,5,3]=>001111111=>111111100
[1,6,4,2,10,9,8,7,5,3]=>001111111=>111111100
[1,4,2,10,9,8,7,6,5,3]=>001111111=>111111100
[7,5,3,1,10,9,8,6,4,2]=>011111111=>111111110
[5,3,1,10,9,8,7,6,4,2]=>011111111=>111111110
[4,3,1,6,2,5,8,7]=>0110101=>1010110
[7,5,2,1,8,4,3,6]=>1011011=>1101101
[5,3,1,4,7,8,2,6]=>0101001=>1001010
[7,1,2,4,8,3,5,6]=>0000011=>1100000
[8,6,1,3,5,7,4,2]=>0010111=>1110100
[7,1,5,8,2,3,4,6]=>0000011=>1100000
[3,6,8,5,1,4,2,7]=>0011001=>1001100
[5,2,4,1,6,8,3,7]=>0011001=>1001100
[2,5,3,4,6,8,1,7]=>0001001=>1001000
[4,7,1,2,5,6,3,8]=>0000110=>0110000
[6,7,3,1,8,2,4,5]=>0100011=>1100010
[7,3,1,4,6,2,8,5]=>0100111=>1110010
[7,4,1,2,5,6,3,8]=>0010110=>0110100
[5,4,1,3,6,8,7,2]=>0011011=>1101100
[5,7,4,8,1,6,3,2]=>0100111=>1110010
[4,3,1,2,5,7,6,8]=>0110010=>0100110
[2,3,4,5,8,7,6,1,9]=>00001110=>01110000
[1,3,4,5,6,9,8,7,2]=>00000111=>11100000
[1,2,3,4,5,8,9,7,6]=>00000101=>10100000
[1,2,3,4,8,9,6,7,5]=>00000101=>10100000
[1,2,3,8,9,5,6,7,4]=>00000101=>10100000
[1,2,4,7,8,5,6,3]=>0000101=>1010000
[1,2,8,9,4,5,6,7,3]=>00000101=>10100000
[8,3,6,5,7,4,2,1]=>1010111=>1110101
[8,2,6,5,7,4,3,1]=>0110111=>1110110
[8,4,7,1,5,2,6,3]=>0001111=>1111000
[8,2,6,3,7,5,4,1]=>0011111=>1111100
[8,2,5,3,7,6,4,1]=>0011111=>1111100
[8,5,7,1,4,3,6,2]=>0010111=>1110100
[5,3,1,8,4,2,6,7]=>0111001=>1001110
[4,5,3,6,8,7,1,2]=>0001011=>1101000
[2,1,6,5,8,7,3,4]=>1000111=>1110001
[6,1,5,4,7,3,8,2]=>0001111=>1111000
[9,4,2,3,5,6,7,8,1]=>00100011=>11000100
[3,1,8,4,2,7,6,5]=>0110111=>1110110
[2,8,7,4,1,3,6,5]=>0010111=>1110100
[8,2,3,1,7,6,4,5]=>0100111=>1110010
[8,7,2,3,1,6,4,5]=>0100111=>1110010
[7,2,5,8,3,1,4,6]=>0100011=>1100010
[6,8,2,3,1,7,4,5]=>0100011=>1100010
[8,2,5,7,3,1,4,6]=>0100011=>1100010
[8,2,7,3,1,4,5,6]=>0100011=>1100010
[5,3,2,8,7,1,6,4]=>0101111=>1111010
[8,6,7,4,1,3,5,2]=>0011011=>1101100
[4,1,3,6,5,2,8,7]=>0011101=>1011100
[4,6,3,2,5,1,8,7]=>0101101=>1011010
[4,8,3,2,6,5,7,1]=>0100111=>1110010
[4,8,3,6,5,2,7,1]=>0001111=>1111000
[8,1,6,2,5,4,7,3]=>0001111=>1111000
[2,4,3,8,6,1,7,5]=>0010111=>1110100
[2,6,3,8,5,4,7,1]=>0001111=>1111000
[6,1,3,2,5,8,7,4]=>0100111=>1110010
[6,8,4,2,5,3,7,1]=>0011011=>1101100
[6,8,4,3,5,2,7,1]=>0011011=>1101100
[8,1,4,6,5,3,7,2]=>0001111=>1111000
[1,4,2,5,6,7,9,8,3]=>00100011=>11000100
[2,3,4,5,6,7,8,9,1,11,10]=>0000000101=>1010000000
[2,1,4,5,6,9,7,3,8]=>10000101=>10100001
[3,5,4,6,1,2,8,7]=>0001101=>1011000
[3,1,5,2,9,6,7,8,4]=>01010011=>11001010
[4,5,1,6,8,7,9,2,3]=>00010011=>11001000
[1,4,2,5,6,7,8,10,9,3]=>001000011=>110000100
[3,4,1,5,6,7,8,9,10,11,2]=>0010000001=>1000000100
[1,3,4,5,6,7,8,9,11,2,10]=>0000000001=>1000000000
[2,1,4,5,6,7,10,8,3,9]=>100000101=>101000001
[2,3,1,5,9,6,7,4,8]=>01000101=>10100010
[1,2,4,5,7,9,6,3,8]=>00001001=>10010000
[3,4,6,5,7,1,2,9,8]=>00001101=>10110000
[3,1,9,4,2,6,7,8,5]=>01100011=>11000110
[7,3,5,6,1,8,2,4]=>0000111=>1110000
[1,2,5,3,9,6,8,7,4]=>00010111=>11101000
[3,1,5,2,6,10,7,8,9,4]=>010100011=>110001010
[4,5,1,7,6,8,2,9,3]=>00010111=>11101000
[4,5,1,6,7,9,8,10,2,3]=>000100011=>110001000
[3,4,1,5,6,7,8,9,10,11,12,2]=>00100000001=>10000000100
[5,7,6,3,4,2,8,1]=>0010111=>1110100
[4,6,7,2,3,5,8,1]=>0000011=>1100000
[6,5,4,8,7,2,3,1]=>0101111=>1111010
[7,2,8,3,9,4,10,5,1,6]=>000101111=>111101000
[7,2,8,3,9,4,10,1,5,6]=>000001111=>111100000
[7,2,8,3,9,10,4,5,1,6]=>000101101=>101101000
[7,2,8,3,9,10,4,1,5,6]=>001001101=>101100100
[7,2,8,3,9,10,1,4,5,6]=>000001101=>101100000
[7,2,8,9,3,4,10,5,1,6]=>000101011=>110101000
[7,2,8,9,3,4,10,1,5,6]=>000001011=>110100000
[7,2,8,9,3,10,4,5,1,6]=>000101011=>110101000
[7,2,8,9,3,10,4,1,5,6]=>001001011=>110100100
[7,2,8,9,3,10,1,4,5,6]=>000001011=>110100000
[7,2,8,9,10,3,4,5,1,6]=>000101001=>100101000
[7,2,8,9,10,3,4,1,5,6]=>001001001=>100100100
[7,2,8,9,10,3,1,4,5,6]=>010001001=>100100010
[7,8,2,3,9,4,10,5,1,6]=>000100111=>111001000
[7,8,2,3,9,4,10,1,5,6]=>000000111=>111000000
[7,8,2,3,9,10,4,5,1,6]=>000100101=>101001000
[7,8,2,3,9,10,4,1,5,6]=>001000101=>101000100
[7,8,2,3,9,10,1,4,5,6]=>000000101=>101000000
[7,8,2,9,3,4,10,5,1,6]=>000100111=>111001000
[7,8,2,9,3,4,10,1,5,6]=>000000111=>111000000
[7,8,2,9,3,10,4,5,1,6]=>000100111=>111001000
[7,8,2,9,3,10,4,1,5,6]=>001000111=>111000100
[7,8,2,9,3,10,1,4,5,6]=>000000111=>111000000
[7,8,2,9,10,3,4,5,1,6]=>000100101=>101001000
[7,8,2,9,10,3,4,1,5,6]=>001000101=>101000100
[7,8,2,9,10,3,1,4,5,6]=>010000101=>101000010
[7,8,2,9,10,1,3,4,5,6]=>000000101=>101000000
[7,8,9,2,3,4,10,5,1,6]=>000100011=>110001000
[7,8,9,2,3,4,10,1,5,6]=>000000011=>110000000
[7,8,9,2,3,10,4,5,1,6]=>000100011=>110001000
[7,8,9,2,3,10,4,1,5,6]=>001000011=>110000100
[7,8,9,2,3,10,1,4,5,6]=>000000011=>110000000
[7,8,9,2,10,3,4,5,1,6]=>000100011=>110001000
[7,8,9,2,10,3,4,1,5,6]=>001000011=>110000100
[7,8,9,2,10,3,1,4,5,6]=>010000011=>110000010
[7,8,9,2,10,1,3,4,5,6]=>000000011=>110000000
[7,8,9,10,2,3,4,1,5,6]=>001000001=>100000100
[7,8,9,10,2,3,1,4,5,6]=>010000001=>100000010
[7,8,9,10,2,1,3,4,5,6]=>100000001=>100000001
[8,2,9,3,10,4,11,5,12,6,1,7]=>00001011111=>11111010000
[8,2,9,3,10,4,11,5,12,1,6,7]=>00000011111=>11111000000
[8,2,9,3,10,4,11,12,5,6,1,7]=>00001011101=>10111010000
[8,2,9,3,10,4,11,12,5,1,6,7]=>00010011101=>10111001000
[8,2,9,3,10,4,11,12,1,5,6,7]=>00000011101=>10111000000
[8,2,9,3,10,11,4,5,12,6,1,7]=>00001011011=>11011010000
[8,2,9,3,10,11,4,5,12,1,6,7]=>00000011011=>11011000000
[8,2,9,3,10,11,4,12,5,6,1,7]=>00001011011=>11011010000
[8,2,9,3,10,11,4,12,5,1,6,7]=>00010011011=>11011001000
[8,2,9,3,10,11,4,12,1,5,6,7]=>00000011011=>11011000000
[8,2,9,3,10,11,12,1,4,5,6,7]=>00000011001=>10011000000
[8,2,9,10,3,4,11,5,12,6,1,7]=>00001010111=>11101010000
[8,2,9,10,3,4,11,5,12,1,6,7]=>00000010111=>11101000000
[8,2,9,10,3,4,11,12,5,6,1,7]=>00001010101=>10101010000
[8,2,9,10,3,4,11,12,5,1,6,7]=>00010010101=>10101001000
[8,2,9,10,3,4,11,12,1,5,6,7]=>00000010101=>10101000000
[8,2,9,10,3,11,4,5,12,6,1,7]=>00001010111=>11101010000
[8,2,9,10,3,11,4,5,12,1,6,7]=>00000010111=>11101000000
[8,2,9,10,3,11,4,12,5,6,1,7]=>00001010111=>11101010000
[8,2,9,10,3,11,4,12,5,1,6,7]=>00010010111=>11101001000
[8,2,9,10,3,11,4,12,1,5,6,7]=>00000010111=>11101000000
[8,2,9,10,3,11,12,4,5,6,1,7]=>00001010101=>10101010000
[8,2,9,10,3,11,12,4,5,1,6,7]=>00010010101=>10101001000
[8,2,9,10,3,11,12,4,1,5,6,7]=>00100010101=>10101000100
[8,2,9,10,3,11,12,1,4,5,6,7]=>00000010101=>10101000000
[8,2,9,10,11,3,4,5,12,1,6,7]=>00000010011=>11001000000
[8,2,9,10,11,3,4,12,1,5,6,7]=>00000010011=>11001000000
[8,2,9,10,11,3,12,1,4,5,6,7]=>00000010011=>11001000000
[8,2,9,10,11,12,3,4,5,6,1,7]=>00001010001=>10001010000
[8,2,9,10,11,12,3,4,5,1,6,7]=>00010010001=>10001001000
[8,2,9,10,11,12,3,4,1,5,6,7]=>00100010001=>10001000100
[8,2,9,10,11,12,3,1,4,5,6,7]=>01000010001=>10001000010
[8,2,9,10,11,12,1,3,4,5,6,7]=>00000010001=>10001000000
[8,9,2,3,10,4,11,5,12,6,1,7]=>00001001111=>11110010000
[8,9,2,3,10,4,11,5,12,1,6,7]=>00000001111=>11110000000
[8,9,2,3,10,4,11,12,1,5,6,7]=>00000001101=>10110000000
[8,9,2,3,10,11,4,5,12,1,6,7]=>00000001011=>11010000000
[8,9,2,3,10,11,4,12,5,1,6,7]=>00010001011=>11010001000
[8,9,2,3,10,11,4,12,1,5,6,7]=>00000001011=>11010000000
[8,9,2,3,10,11,12,4,5,6,1,7]=>00001001001=>10010010000
[8,9,2,3,10,11,12,4,5,1,6,7]=>00010001001=>10010001000
[8,9,2,3,10,11,12,4,1,5,6,7]=>00100001001=>10010000100
[8,9,2,3,10,11,12,1,4,5,6,7]=>00000001001=>10010000000
[8,9,2,10,3,4,11,5,12,6,1,7]=>00001001111=>11110010000
[8,9,2,10,3,4,11,5,12,1,6,7]=>00000001111=>11110000000
[8,9,2,10,3,4,11,12,1,5,6,7]=>00000001101=>10110000000
[8,9,2,10,3,11,4,5,12,6,1,7]=>00001001111=>11110010000
[8,9,2,10,3,11,4,5,12,1,6,7]=>00000001111=>11110000000
[8,9,2,10,3,11,4,12,5,6,1,7]=>00001001111=>11110010000
[8,9,2,10,3,11,4,12,5,1,6,7]=>00010001111=>11110001000
[8,9,2,10,3,11,4,12,1,5,6,7]=>00000001111=>11110000000
[8,9,2,10,3,11,12,1,4,5,6,7]=>00000001101=>10110000000
[8,9,2,10,11,3,4,5,12,1,6,7]=>00000001011=>11010000000
[8,9,2,10,11,3,4,12,5,1,6,7]=>00010001011=>11010001000
[8,9,2,10,11,3,4,12,1,5,6,7]=>00000001011=>11010000000
[8,9,2,10,11,3,12,4,5,1,6,7]=>00010001011=>11010001000
[8,9,2,10,11,3,12,4,1,5,6,7]=>00100001011=>11010000100
[8,9,2,10,11,3,12,1,4,5,6,7]=>00000001011=>11010000000
[8,9,2,10,11,12,3,4,5,6,1,7]=>00001001001=>10010010000
[8,9,2,10,11,12,3,4,5,1,6,7]=>00010001001=>10010001000
[8,9,2,10,11,12,3,4,1,5,6,7]=>00100001001=>10010000100
[8,9,2,10,11,12,3,1,4,5,6,7]=>01000001001=>10010000010
[8,9,2,10,11,12,1,3,4,5,6,7]=>00000001001=>10010000000
[8,9,10,2,3,4,11,5,12,6,1,7]=>00001000111=>11100010000
[8,9,10,2,3,4,11,5,12,1,6,7]=>00000000111=>11100000000
[8,9,10,2,3,4,11,12,5,6,1,7]=>00001000101=>10100010000
[8,9,10,2,3,4,11,12,5,1,6,7]=>00010000101=>10100001000
[8,9,10,2,3,4,11,12,1,5,6,7]=>00000000101=>10100000000
[8,9,10,2,3,11,4,5,12,6,1,7]=>00001000111=>11100010000
[8,9,10,2,3,11,4,5,12,1,6,7]=>00000000111=>11100000000
[8,9,10,2,3,11,4,12,5,6,1,7]=>00001000111=>11100010000
[8,9,10,2,3,11,4,12,1,5,6,7]=>00000000111=>11100000000
[8,9,10,2,3,11,12,4,5,6,1,7]=>00001000101=>10100010000
[8,9,10,2,3,11,12,4,5,1,6,7]=>00010000101=>10100001000
[8,9,10,2,3,11,12,1,4,5,6,7]=>00000000101=>10100000000
[8,9,10,2,11,3,4,5,12,6,1,7]=>00001000111=>11100010000
[8,9,10,2,11,3,4,5,12,1,6,7]=>00000000111=>11100000000
[8,9,10,2,11,3,4,12,5,6,1,7]=>00001000111=>11100010000
[8,9,10,2,11,3,4,12,1,5,6,7]=>00000000111=>11100000000
[8,9,10,2,11,3,12,4,5,6,1,7]=>00001000111=>11100010000
[8,9,10,2,11,3,12,4,1,5,6,7]=>00100000111=>11100000100
[8,9,10,2,11,3,12,1,4,5,6,7]=>00000000111=>11100000000
[8,9,10,2,11,12,3,4,5,6,1,7]=>00001000101=>10100010000
[8,9,10,2,11,12,3,4,5,1,6,7]=>00010000101=>10100001000
[8,9,10,2,11,12,3,1,4,5,6,7]=>01000000101=>10100000010
[8,9,10,2,11,12,1,3,4,5,6,7]=>00000000101=>10100000000
[8,9,10,11,2,3,4,5,12,1,6,7]=>00000000011=>11000000000
[8,9,10,11,2,3,4,12,5,1,6,7]=>00010000011=>11000001000
[8,9,10,11,2,3,4,12,1,5,6,7]=>00000000011=>11000000000
[8,9,10,11,2,3,12,4,5,1,6,7]=>00010000011=>11000001000
[8,9,10,11,2,3,12,1,4,5,6,7]=>00000000011=>11000000000
[8,9,10,11,2,12,3,4,5,1,6,7]=>00010000011=>11000001000
[8,9,10,11,2,12,3,1,4,5,6,7]=>01000000011=>11000000010
[8,9,10,11,2,12,1,3,4,5,6,7]=>00000000011=>11000000000
[8,9,10,11,12,2,3,4,5,6,1,7]=>00001000001=>10000010000
[8,9,10,11,12,2,3,4,1,5,6,7]=>00100000001=>10000000100
[8,9,10,11,12,2,3,1,4,5,6,7]=>01000000001=>10000000010
[8,9,10,11,12,2,1,3,4,5,6,7]=>10000000001=>10000000001
[4,8,7,6,5,3,2,1,9]=>11011110=>01111011
[5,9,8,7,6,4,3,2,1,10]=>111011110=>011110111
[5,8,7,4,6,3,2,1,9]=>11001110=>01110011
[8,4,7,6,5,3,2,1,9]=>11011110=>01111011
[5,7,4,3,6,2,1,8]=>1010110=>0110101
[6,9,8,5,7,4,1,3,2]=>01100111=>11100110
[9,8,7,5,1,6,4,3,2]=>01111111=>11111110
[10,9,8,6,1,7,5,4,3,2]=>011111111=>111111110
[1,2,8,3,4,5,6,9,7]=>00000011=>11000000
[1,9,5,2,3,8,4,6,7]=>00010011=>11001000
[1,2,9,3,4,5,6,7,10,8]=>000000011=>110000000
[1,8,2,9,4,3,5,6,7]=>00100011=>11000100
[1,3,2,4,9,8,5,6,7]=>01000011=>11000010
[2,1,3,4,5,9,8,6,7]=>10000011=>11000001
[1,2,3,4,5,9,6,7,10,8]=>000000011=>110000000
[9,1,7,2,3,4,5,8,6]=>00000111=>11100000
[1,10,6,2,3,4,9,5,7,8]=>000010011=>110010000
[1,2,10,3,4,5,6,7,8,11,9]=>0000000011=>1100000000
[1,8,5,2,3,4,6,9,7]=>00010011=>11001000
[9,8,1,2,3,5,6,4,7]=>00001011=>11010000
[1,5,2,9,3,10,4,6,7,8]=>000100011=>110001000
[1,4,2,3,9,5,6,8,7]=>00100011=>11000100
[1,8,5,6,2,3,7,4]=>0000111=>1110000
[4,9,8,1,2,5,3,6,7]=>00010011=>11001000
[1,2,4,3,10,9,5,6,7,8]=>001000011=>110000100
[1,3,2,4,5,9,6,8,7]=>01000011=>11000010
[1,8,3,9,4,2,5,6,7]=>00100011=>11000100
[1,3,2,4,5,10,9,6,7,8]=>010000011=>110000010
[1,2,3,4,5,10,6,7,8,11,9]=>0000000011=>1100000000
[2,3,1,4,9,8,5,6,7]=>01000011=>11000010
[2,1,3,4,5,9,6,10,7,8]=>100000011=>110000001
[7,2,4,6,8,1,5,3]=>0001011=>1101000
[6,2,5,4,7,8,1,3]=>0001101=>1011000
[3,8,2,6,1,7,4,5]=>0000111=>1110000
[8,5,6,1,3,2,7,4]=>0100111=>1110010
[5,3,7,8,2,6,1,4]=>0001101=>1011000
[4,5,8,3,6,1,7,2]=>0000111=>1110000
[4,5,8,7,2,3,1,6]=>0100011=>1100010
[8,2,6,4,3,7,5,1]=>0011111=>1111100
[6,3,1,8,7,4,5,2]=>0101111=>1111010
[8,6,3,2,7,4,5,1]=>0101111=>1111010
[1,3,6,8,7,4,5,2]=>0001011=>1101000
[5,7,1,3,6,2,4,8]=>0000110=>0110000
[4,7,5,2,3,6,8,1]=>0001011=>1101000
[3,6,4,1,2,5,7,8]=>0010100=>0010100
[4,7,1,3,2,5,8,6]=>0100011=>1100010
[4,7,1,3,2,6,8,5]=>0100011=>1100010
[5,7,1,3,6,2,8,4]=>0000111=>1110000
[6,8,2,5,7,3,1,4]=>0100011=>1100010
[4,8,5,2,3,6,1,7]=>0001101=>1011000
[5,8,6,3,4,7,2,1]=>1000111=>1110001
[3,7,5,4,2,8,1,6]=>0011011=>1101100
[4,6,5,1,7,8,2,3]=>0001101=>1011000
[4,7,1,3,2,8,5,6]=>0100011=>1100010
[3,6,5,1,8,2,4,7]=>0001101=>1011000
[5,8,7,3,4,2,6,1]=>0010111=>1110100
[8,7,6,5,4,1,9,3,2]=>01111111=>11111110
[8,7,6,5,2,9,1,3,4]=>00011111=>11111000
[8,7,6,3,9,2,1,4,5]=>10001111=>11110001
[8,7,4,9,3,2,1,6,5]=>11001111=>11110011
[8,5,9,4,3,2,1,6,7]=>11100011=>11000111
[6,9,5,4,3,2,1,7,8]=>11110001=>10001111
[9,8,7,6,5,4,1,10,3,2]=>011111111=>111111110
[10,9,8,7,6,5,4,2,1,3,11]=>1011111110=>0111111101
[8,7,6,5,2,1,4,3,9]=>10111110=>01111101
[9,8,7,6,5,2,10,1,3,4]=>000111111=>111111000
[10,9,8,7,6,5,3,2,1,4,11]=>1101111110=>0111111011
[8,7,6,3,2,5,1,4,9]=>01011110=>01111010
[8,7,6,5,1,9,4,3,2]=>01111111=>11111110
[9,8,7,6,3,10,2,1,4,5]=>100011111=>111110001
[10,9,8,7,6,4,3,2,1,11,5]=>1110111111=>1111110111
[8,7,4,3,6,2,1,9,5]=>10101111=>11110101
[8,7,6,2,9,5,1,3,4]=>00011111=>11111000
[9,8,7,4,10,3,2,1,6,5]=>110011111=>111110011
[10,9,8,7,5,4,3,2,1,6,11]=>1111011110=>0111101111
[8,5,4,7,3,2,1,6,9]=>11010110=>01101011
[8,7,3,9,6,2,1,4,5]=>10001111=>11110001
[9,8,5,10,4,3,2,1,6,7]=>111000111=>111000111
[10,9,8,6,5,4,3,2,1,7,11]=>1111101110=>0111011111
[6,5,8,4,3,2,1,7,9]=>11101010=>01010111
[8,4,9,7,3,2,1,6,5]=>11001111=>11110011
[9,6,10,5,4,3,2,1,7,8]=>111100011=>110001111
[10,9,7,6,5,4,3,2,1,11,8]=>1111110111=>1110111111
[5,9,8,4,3,2,1,6,7]=>11100011=>11000111
[7,10,6,5,4,3,2,1,9,8]=>111110011=>110011111
[10,8,7,6,5,4,3,2,1,9,11]=>1111111010=>0101111111
[8,5,2,3,7,4,6,1]=>0001111=>1111000
[6,3,1,5,4,8,2,7]=>0101101=>1011010
[4,7,6,3,5,2,8,1]=>0001111=>1111000
[1,7,5,3,4,8,6,2]=>0001111=>1111000
[5,8,2,3,4,7,6,1]=>0000111=>1110000
[8,7,3,2,6,4,5,1]=>0101111=>1111010
[8,3,1,4,7,5,2,6]=>0101011=>1101010
[5,3,1,6,4,8,7,2]=>0101111=>1111010
[3,4,8,5,7,2,6,1]=>0000111=>1110000
[8,5,1,2,7,6,4,3]=>0011111=>1111100
[10,7,8,1,2,3,4,5,6,9]=>000000101=>101000000
[6,7,10,1,2,3,4,5,8,9]=>000000001=>100000000
[8,2,6,3,1,5,4,7]=>0101101=>1011010
[3,7,8,5,6,2,4,1]=>0010101=>1010100
[1,10,2,3,4,7,5,6,8,9]=>000001001=>100100000
[7,4,3,6,2,5,8,1]=>0010111=>1110100
[4,3,8,7,1,6,2,5]=>0010111=>1110100
[1,5,3,8,4,7,2,6]=>0001011=>1101000
[8,2,3,1,6,5,7,4]=>0100111=>1110010
[8,4,2,7,1,3,6,5]=>0010111=>1110100
[8,4,2,3,1,6,7,5]=>0110011=>1100110
[4,7,2,3,6,5,8,1]=>0000111=>1110000
[3,8,2,6,4,7,1,5]=>0000111=>1110000
[1,7,5,8,6,2,4,3]=>0010111=>1110100
[6,5,1,7,4,8,3,2]=>0101111=>1111010
[10,9,8,6,7,5,4,3,2,1]=>111101111=>111101111
[7,6,3,5,1,4,8,2]=>0001111=>1111000
[6,5,4,1,7,2,3,8]=>0011110=>0111100
[8,3,6,1,7,4,5,2]=>0001111=>1111000
[7,1,2,6,4,8,3,5]=>0000111=>1110000
[3,5,1,8,6,2,4,7]=>0001101=>1011000
[8,7,5,6,4,3,2,1,9]=>11101110=>01110111
[8,6,5,7,4,3,2,1,9]=>11101110=>01110111
[9,8,7,6,4,3,2,5,1]=>01111111=>11111110
[9,8,7,6,4,3,5,2,1]=>10111111=>11111101
[8,5,6,7,4,3,2,1,9]=>11100110=>01100111
[10,9,7,6,8,5,4,3,2,1]=>111101111=>111101111
[6,7,5,8,4,3,2,1,9]=>11100110=>01100111
[10,8,7,6,9,5,4,3,2,1]=>111101111=>111101111
[8,9,7,6,4,3,2,1,5]=>11101101=>10110111
[7,6,5,3,2,1,4,8,9]=>11011100=>00111011
[9,8,7,6,4,3,5,1,2]=>00111111=>11111100
[9,8,7,6,4,3,2,5,1,10]=>011111110=>011111110
[9,8,7,6,4,5,2,3,1]=>01011111=>11111010
[9,8,7,6,4,3,5,2,1,10]=>101111110=>011111101
[9,8,7,6,5,3,4,2,1]=>10111111=>11111101
[1,8,7,5,4,6,2,3]=>0001111=>1111000
[8,1,6,7,4,5,3,2]=>0101011=>1101010
[8,1,6,4,7,5,3,2]=>0101111=>1111010
[6,4,8,1,5,3,7,2]=>0001111=>1111000
[1,6,4,3,5,8,2,7]=>0010101=>1010100
[5,1,4,3,7,8,6,2]=>0011101=>1011100
[5,7,1,8,6,3,2,4]=>0100111=>1110010
[5,7,6,3,4,2,1,8]=>1010110=>0110101
[4,1,3,7,6,5,2,8]=>0011110=>0111100
[8,7,6,5,4,2,3,1,9]=>01111110=>01111110
[4,3,6,1,2,7,8,5]=>0010101=>1010100
[1,10,9,8,6,5,7,4,3,2]=>011011111=>111110110
[2,9,8,6,5,7,4,3,1]=>01101111=>11110110
[3,1,4,5,6,7,9,2,10,8]=>010000011=>110000010
[5,8,3,6,7,2,4,1]=>0010011=>1100100
[8,1,6,2,5,7,4,3]=>0010111=>1110100
[2,7,1,5,3,6,8,4]=>0001011=>1101000
[6,8,7,3,4,2,5,1]=>0011011=>1101100
[1,8,6,2,4,7,5,3]=>0001111=>1111000
[5,7,3,6,4,2,1,8]=>1010110=>0110101
[5,7,3,6,4,1,8,2]=>0010111=>1110100
[3,7,5,6,4,1,8,2]=>0010111=>1110100
[7,1,8,2,3,4,5,9,6]=>00000111=>11100000
[6,8,1,2,3,4,5,9,7]=>00000011=>11000000
[9,6,7,4,5,2,3,1,8]=>01010101=>10101010
[8,9,6,7,4,5,2,1,3]=>10010101=>10101001
[10,8,9,6,7,4,5,2,1,3]=>100101011=>110101001
[9,8,6,5,4,3,7,2,1]=>10111111=>11111101
[2,8,5,7,3,4,6,1]=>0000111=>1110000
[2,3,6,4,5,1,7,8,9]=>00011000=>00011000
[2,3,4,8,5,6,7,1,9]=>00000110=>01100000
[3,5,4,7,2,6,1,8,9]=>00011100=>00111000
[2,6,4,1,5,3,7,8,9]=>00111000=>00011100
[4,5,2,6,3,1,7,8,9]=>01011000=>00011010
[3,6,4,5,9,2,7,8,1]=>00001011=>11010000
[2,5,4,7,8,6,3,1,9]=>01011010=>01011010
[4,6,2,5,8,3,7,1,9]=>00001110=>01110000
[3,5,7,6,1,4,2,8,9]=>00101100=>00110100
[5,6,2,3,7,4,1,8,9]=>00101100=>00110100
[5,7,2,3,6,9,4,8,1]=>00000111=>11100000
[2,8,4,1,6,3,7,5,9]=>00101110=>01110100
[4,6,7,8,3,1,5,2,9]=>01010010=>01001010
[6,7,2,3,4,8,5,1,9]=>00010110=>01101000
[3,5,9,7,1,8,2,6,4]=>00001111=>11110000
[5,7,8,3,9,4,1,6,2]=>00101011=>11010100
[7,8,2,3,4,5,9,6,1]=>00001011=>11010000
[2,4,3,1,5,6,7,8,9,10]=>011000000=>000000110
[2,3,6,4,5,1,7,8,9,10]=>000110000=>000011000
[3,4,5,2,1,6,7,8,9,10]=>100100000=>000001001
[2,3,4,8,5,6,7,1,9,10]=>000001100=>001100000
[3,5,4,7,2,6,1,8,9,10]=>000111000=>000111000
[2,6,4,1,5,3,7,8,9,10]=>001110000=>000011100
[4,5,2,6,3,1,7,8,9,10]=>010110000=>000011010
[3,6,4,5,9,2,7,8,1,10]=>000010110=>011010000
[2,5,4,7,8,6,3,1,9,10]=>010110100=>001011010
[4,6,2,5,8,3,7,1,9,10]=>000011100=>001110000
[3,5,7,6,1,4,2,8,9,10]=>001011000=>000110100
[5,6,2,3,7,4,1,8,9,10]=>001011000=>000110100
[2,5,4,8,6,10,7,3,9,1]=>000101111=>111101000
[4,7,2,5,6,10,3,8,9,1]=>000001011=>110100000
[2,3,9,5,6,1,7,8,4,10]=>000010110=>011010000
[5,7,2,3,6,9,4,8,1,10]=>000001110=>011100000
[2,8,4,1,6,3,7,5,9,10]=>001011100=>001110100
[4,6,7,8,3,1,5,2,9,10]=>010100100=>001001010
[6,7,2,3,4,8,5,1,9,10]=>000101100=>001101000
[3,6,4,10,8,7,1,5,9,2]=>000011111=>111110000
[2,7,4,9,6,3,10,8,5,1]=>000111111=>111111000
[4,6,8,7,3,9,10,5,2,1]=>100101101=>101101001
[6,8,2,3,4,7,10,5,9,1]=>000000111=>111000000
[3,5,9,7,1,8,2,6,4,10]=>000011110=>011110000
[5,7,8,3,9,4,1,6,2,10]=>001010110=>011010100
[7,8,2,3,4,5,9,6,1,10]=>000010110=>011010000
[4,6,8,10,9,1,5,2,7,3]=>000101011=>110101000
[6,8,9,3,4,10,5,1,7,2]=>000101011=>110101000
[8,9,2,3,4,5,6,10,7,1]=>000001011=>110100000
[2,1,3,8,5,4,6,7]=>1001001=>1001001
[5,3,6,8,2,4,1,7]=>0011001=>1001100
[1,7,8,6,3,2,4,5]=>0100101=>1010010
[7,1,2,5,3,8,4,6]=>0001011=>1101000
[3,7,4,2,5,1,8,6]=>0011011=>1101100
[1,8,3,4,5,7,2,6]=>0000011=>1100000
[2,6,7,5,3,8,1,4]=>0001011=>1101000
[4,5,2,6,8,7,1,3]=>0001011=>1101000
[4,5,2,6,8,3,1,7]=>0101001=>1001010
[4,5,7,6,2,1,3,8]=>1000110=>0110001
[7,8,2,6,5,4,3,1]=>0111101=>1011110
[5,3,7,8,4,2,1,6]=>1011001=>1001101
[7,3,6,8,1,5,4,2]=>0011011=>1101100
[9,7,8,5,6,2,4,1,3]=>00101011=>11010100
[9,7,8,4,6,2,5,1,3]=>00011011=>11011000
[9,6,8,4,7,2,5,1,3]=>00010111=>11101000
[8,9,6,4,7,2,5,1,3]=>00011101=>10111000
[8,9,6,7,4,2,5,1,3]=>00110101=>10101100
[9,7,8,3,6,2,5,1,4]=>00011011=>11011000
[9,5,8,4,7,2,6,1,3]=>00001111=>11110000
[7,6,9,4,8,2,5,1,3]=>00010111=>11101000
[8,6,9,7,4,2,5,1,3]=>00110111=>11101100
[10,8,9,6,4,7,2,5,1,3]=>000111011=>110111000
[8,9,6,4,7,5,2,1,3]=>10011101=>10111001
[10,8,9,6,7,4,2,5,1,3]=>001101011=>110101100
[8,9,6,7,4,2,5,3,1]=>01110101=>10101110
[7,5,8,2,4,3,6,1]=>0010111=>1110100
[6,5,8,2,3,4,1,7]=>0010101=>1010100
[8,1,5,3,4,6,2,7]=>0001101=>1011000
[5,8,7,2,4,3,6,1]=>0010111=>1110100
[1,7,2,4,8,5,6,3]=>0000111=>1110000
[5,8,2,3,7,4,6,1]=>0000111=>1110000
[7,8,2,3,5,4,6,1]=>0001101=>1011000
[8,4,1,3,2,6,5,7]=>0110101=>1010110
[8,7,2,3,5,4,6,1]=>0001111=>1111000
[1,7,6,8,4,5,3,2]=>0101011=>1101010
[2,7,3,1,8,5,6,4]=>0100111=>1110010
[3,8,5,2,1,6,7,4]=>1001011=>1101001
[10,1,2,9,6,3,4,5,7,8]=>000010011=>110010000
[4,1,2,10,3,5,9,6,7,8]=>001000011=>110000100
[2,8,6,1,5,7,4,3]=>0010111=>1110100
[8,3,5,1,7,6,4,2]=>0011111=>1111100
[8,3,5,4,7,1,6,2]=>0001111=>1111000
[6,4,1,5,7,8,2,3]=>0010101=>1010100
[4,8,7,1,2,5,3,6]=>0001011=>1101000
[8,7,2,6,1,4,3,5]=>0010111=>1110100
[6,1,7,3,8,2,4,5]=>0000111=>1110000
[7,1,8,6,4,2,3,5]=>0010111=>1110100
[4,1,3,5,8,2,6,7]=>0010001=>1000100
[1,8,5,7,4,6,3,2]=>0100111=>1110010
[1,4,7,6,8,3,5,2]=>0001011=>1101000
[1,7,2,8,6,5,3,4]=>0001111=>1111000
[5,7,1,6,4,2,3,8]=>0010110=>0110100
[4,8,2,7,5,1,6,3]=>0001111=>1111000
[2,8,4,6,7,1,5,3]=>0001011=>1101000
[3,8,5,1,4,2,6,7]=>0011001=>1001100
[1,7,6,2,5,3,8,4]=>0001111=>1111000
[1,7,5,2,4,3,8,6]=>0011011=>1101100
[2,8,5,1,4,3,6,7]=>0011001=>1001100
[9,7,6,5,4,3,2,8,1]=>01111111=>11111110
[3,1,4,6,2,5,8,7,9]=>01001010=>01010010
[1,3,2,5,7,4,6,9,8]=>01000101=>10100010
[7,6,3,5,4,8,2,1]=>1001111=>1111001
[1,9,8,5,6,7,4,3,2]=>01100111=>11100110
[1,10,9,8,5,6,7,4,3,2]=>011001111=>111100110
[1,9,8,5,4,6,7,3,2]=>01010111=>11101010
[1,10,9,5,6,7,8,4,3,2]=>011000111=>111000110
[1,9,5,4,6,7,8,3,2]=>01010011=>11001010
[1,10,4,5,6,7,8,9,3,2]=>010000011=>110000010
[3,1,2,5,7,6,8,4]=>0100011=>1100010
[5,1,7,3,2,6,8,4]=>0101011=>1101010
[4,7,2,3,5,1,6,8]=>0001010=>0101000
[4,8,2,3,7,5,1,6]=>0001011=>1101000
[8,7,2,4,3,5,6,1]=>0010111=>1110100
[8,6,2,4,3,5,1,7]=>0011101=>1011100
[8,1,2,4,7,3,5,6]=>0000011=>1100000
[7,6,2,8,4,5,1,3]=>0001111=>1111000
[6,8,1,5,7,3,2,4]=>0100011=>1100010
[4,1,7,5,6,8,2,3]=>0010011=>1100100
[3,7,6,2,1,4,5,8]=>1000110=>0110001
[1,6,8,7,2,5,4,3]=>0011011=>1101100
[1,4,8,7,6,3,5,2]=>0001111=>1111000
[1,2,3,4,7,5,6,9,8]=>00000101=>10100000
[3,1,8,4,5,2,7,6]=>0101011=>1101010
[2,3,7,6,1,8,4,5]=>0000111=>1110000
[4,8,5,2,1,3,7,6]=>1001011=>1101001
[5,8,4,2,1,3,7,6]=>1010011=>1100101
[9,8,7,6,5,3,1,4,2]=>01111111=>11111110
[9,8,7,6,4,1,5,3,2]=>01111111=>11111110
[9,8,6,1,7,5,4,3,2]=>01111111=>11111110
[9,7,1,8,6,5,4,3,2]=>01111111=>11111110
[4,6,7,5,2,3,1,8]=>0101010=>0101010
[6,2,5,3,1,8,7,4]=>0101111=>1111010
[6,2,5,3,8,7,1,4]=>0001111=>1111000
[6,4,5,3,8,7,1,2]=>0001111=>1111000
[1,6,4,5,8,7,3,2]=>0100111=>1110010
[8,4,7,5,2,3,1,6]=>0101011=>1101010
[8,2,7,4,5,3,1,6]=>0101011=>1101010
[8,2,4,7,5,3,1,6]=>0101011=>1101010
[8,2,6,7,5,3,1,4]=>0101011=>1101010
[8,4,6,7,5,3,1,2]=>0101011=>1101010
[6,4,5,8,7,3,1,2]=>0100111=>1110010
[6,2,8,7,5,3,1,4]=>0101111=>1111010
[4,6,5,3,8,7,1,2]=>0001111=>1111000
[6,7,2,4,5,3,1,8]=>0101010=>0101010
[6,8,7,4,5,3,1,2]=>0101011=>1101010
[2,8,4,7,5,3,1,6]=>0101011=>1101010
[5,8,7,4,6,3,1,2]=>0100111=>1110010
[6,5,8,4,7,2,1,3]=>1000111=>1110001
[4,8,6,2,5,7,1,3]=>0000111=>1110000
[8,1,6,2,5,7,3,4]=>0000111=>1110000
[6,8,1,2,4,7,3,5]=>0000011=>1100000
[8,1,5,3,2,7,4,6]=>0101011=>1101010
[8,3,7,6,2,5,4,1]=>0011111=>1111100
[1,2,7,4,5,6,8,9,3]=>00000101=>10100000
[5,3,1,2,6,7,8,9,10,4]=>010100001=>100001010
[7,3,4,5,1,2,8,9,10,6]=>000101001=>100101000
[8,3,4,5,6,1,2,9,10,7]=>000010101=>101010000
[1,2,3,4,7,8,5,6,9]=>00000010=>01000000
[1,2,3,4,6,5,8,7,9]=>00001010=>01010000
[1,2,3,4,8,9,5,6,7]=>00000001=>10000000
[4,6,1,3,5,8,2,7]=>0000101=>1010000
[4,5,1,3,8,7,2,6]=>0001011=>1101000
[6,2,7,1,8,3,4,5]=>0000111=>1110000
[6,4,5,8,1,7,2,3]=>0000111=>1110000
[6,2,8,5,1,4,7,3]=>0001111=>1111000
[2,4,7,6,1,8,3,5]=>0000111=>1110000
[2,1,7,8,9,3,4,5,6]=>10000001=>10000001
[2,6,7,8,9,10,1,3,4,5]=>000000001=>100000000
[9,7,5,3,8,6,4,2,1]=>10111111=>11111101
[10,8,9,7,6,5,4,3,2,1]=>111111011=>110111111
[7,4,5,8,6,3,2,1]=>1100111=>1110011
[8,6,9,7,4,3,2,1,5]=>11100111=>11100111
[8,6,3,2,1,4,9,7,5]=>11001111=>11110011
[8,6,4,9,7,5,2,1,3]=>10011111=>11111001
[10,8,6,4,9,7,5,3,2,1]=>110111111=>111111011
[9,7,5,3,8,6,4,1,2]=>00111111=>11111100
[10,8,6,4,2,1,9,7,5,3]=>101111111=>111111101
[11,9,10,8,7,6,5,4,3,2,1]=>1111111011=>1101111111
[9,6,7,8,5,4,3,2,1]=>11110011=>11001111
[10,8,9,6,5,4,3,2,1,7]=>111110011=>110011111
[10,8,11,9,7,6,5,4,3,2,1]=>1111110111=>1110111111
[8,5,6,9,7,4,3,2,1]=>11100111=>11100111
[9,7,10,8,5,4,3,2,1,6]=>111100111=>111001111
[10,8,6,5,4,3,2,1,11,9,7]=>1111101111=>1111011111
[8,6,3,2,1,9,7,4,5]=>11001111=>11110011
[9,7,8,4,3,2,1,5,6]=>11100011=>11000111
[9,7,4,3,2,1,5,10,8,6]=>111001111=>111100111
[10,8,6,11,9,7,5,4,3,2,1]=>1111011111=>1111101111
[8,6,3,4,9,7,5,2,1]=>10011111=>11111001
[8,6,9,7,3,2,1,4,5]=>11000111=>11100011
[9,7,5,10,8,6,3,2,1,4]=>110011111=>111110011
[11,9,7,5,10,8,6,4,3,2,1]=>1110111111=>1111110111
[9,7,5,2,3,8,6,4,1]=>00111111=>11111100
[8,6,2,1,3,4,9,7,5]=>10001111=>11110001
[10,8,6,4,9,7,5,2,1,3]=>100111111=>111111001
[11,9,7,5,3,2,1,10,8,6,4]=>1101111111=>1111111011
[8,6,4,9,7,5,1,2,3]=>00011111=>11111000
[10,8,6,4,1,2,9,7,5,3]=>001111111=>111111100
[11,9,7,5,3,10,8,6,4,2,1]=>1011111111=>1111111101
[10,8,6,4,2,11,9,7,5,3,1]=>0111111111=>1111111110
[2,5,1,6,3,7,4,8,9]=>00011100=>00111000
[2,6,1,7,3,8,4,9,5]=>00001111=>11110000
[3,4,6,1,7,2,8,5,9]=>00001110=>01110000
[3,2,6,1,7,4,8,5,9]=>01001110=>01110010
[4,2,5,6,1,7,3,8,9]=>00101100=>00110100
[3,4,2,6,1,7,5,8,9]=>00101100=>00110100
[4,2,5,7,1,8,3,9,6]=>00100111=>11100100
[3,4,2,7,1,8,5,9,6]=>00100111=>11100100
[5,3,6,4,7,1,8,2,9]=>00011110=>01111000
[3,5,2,6,7,1,8,4,9]=>00010110=>01101000
[4,3,5,2,7,1,8,6,9]=>00110110=>01101100
[4,6,2,7,5,8,1,9,3]=>00001111=>11110000
[4,3,6,2,7,8,1,9,5]=>00101011=>11010100
[4,5,3,6,2,8,1,9,7]=>00011011=>11011000
[2,5,1,6,3,7,4,8,9,10]=>000111000=>000111000
[3,4,5,1,6,2,7,8,9,10]=>000110000=>000011000
[2,6,1,7,3,8,4,9,5,10]=>000011110=>011110000
[3,4,6,1,7,2,8,5,9,10]=>000011100=>001110000
[3,2,6,1,7,4,8,5,9,10]=>010011100=>001110010
[4,2,5,6,1,7,3,8,9,10]=>001011000=>000110100
[3,4,2,6,1,7,5,8,9,10]=>001011000=>000110100
[3,2,7,1,8,4,9,5,10,6]=>010001111=>111100010
[4,5,6,7,1,8,2,9,3,10]=>000001110=>011100000
[3,4,2,7,1,8,5,9,6,10]=>001001110=>011100100
[5,3,6,4,7,1,8,2,9,10]=>000111100=>001111000
[3,5,2,6,7,1,8,4,9,10]=>000101100=>001101000
[4,3,5,2,7,1,8,6,9,10]=>001101100=>001101100
[5,2,6,7,8,1,9,3,10,4]=>000100111=>111001000
[5,3,6,4,8,1,9,2,10,7]=>000110111=>111011000
[3,5,2,6,8,1,9,4,10,7]=>000100111=>111001000
[4,3,5,2,8,1,9,6,10,7]=>001100111=>111001100
[4,6,2,7,5,8,1,9,3,10]=>000011110=>011110000
[4,3,6,2,7,8,1,9,5,10]=>001010110=>011010100
[4,5,3,6,2,8,1,9,7,10]=>000110110=>011011000
[5,3,7,2,8,6,9,1,10,4]=>000101111=>111101000
[4,5,3,7,2,8,9,1,10,6]=>000101011=>110101000
[5,4,6,3,7,2,9,1,10,8]=>000111011=>110111000
[7,6,5,9,4,3,2,1,8]=>11101101=>10110111
[7,6,5,4,3,9,2,1,8]=>10111101=>10111101
[7,9,8,5,4,3,2,1,6]=>11110011=>11001111
[8,7,10,6,5,4,3,2,1,9]=>111110101=>101011111
[7,6,9,8,4,3,2,1,5]=>11100111=>11100111
[8,7,6,10,5,4,3,2,1,9]=>111101101=>101101111
[7,6,5,9,8,3,2,1,4]=>11001111=>11110011
[7,6,5,4,9,8,2,1,3]=>10011111=>11111001
[8,7,6,5,4,10,3,2,1,9]=>110111101=>101111011
[7,6,5,4,3,9,8,1,2]=>00111111=>11111100
[8,7,6,5,4,3,10,2,1,9]=>101111101=>101111101
[1,6,2,3,8,5,7,4]=>0000111=>1110000
[3,4,2,6,8,5,7,1]=>0010011=>1100100
[9,8,7,6,5,2,3,4,1]=>00111111=>11111100
[6,1,7,8,9,2,3,4,5]=>00001001=>10010000
[5,6,7,8,9,11,1,2,3,4,10]=>0000000001=>1000000000
[4,5,6,7,1,9,2,3,8]=>00000101=>10100000
[3,5,6,7,9,1,2,4,8]=>00000001=>10000000
[5,1,6,7,8,2,9,3,4]=>00010011=>11001000
[4,1,6,7,8,9,2,3,5]=>00100001=>10000100
[5,1,6,7,8,9,10,2,3,4]=>000100001=>100001000
[6,1,7,8,9,10,11,2,3,4,5]=>0000100001=>1000010000
[7,4,1,3,6,8,2,5]=>0010011=>1100100
[6,8,1,2,7,3,4,5]=>0000011=>1100000
[1,6,2,8,7,3,4,5]=>0000111=>1110000
[1,6,8,5,7,4,3,2]=>0110011=>1100110
[3,8,1,2,4,7,6,5]=>0000111=>1110000
[1,4,5,7,3,6,8,2]=>0000011=>1100000
[2,3,8,1,4,6,5,7]=>0000101=>1010000
[3,6,2,4,7,5,8,1]=>0000111=>1110000
[3,1,8,4,6,2,5,7]=>0100101=>1010010
[4,2,7,3,5,8,1,6]=>0010011=>1100100
[3,1,8,4,5,6,2,7]=>0100101=>1010010
[4,2,7,8,6,3,1,5]=>0110101=>1010110
[7,1,4,2,8,6,3,5]=>0010111=>1110100
[2,3,7,4,8,1,6,5]=>0000111=>1110000
[1,6,3,5,8,7,4,2]=>0010111=>1110100
[8,4,6,3,5,1,7,2]=>0001111=>1111000
[7,3,2,6,8,4,5,1]=>0101011=>1101010
[2,4,5,7,1,6,8,3]=>0000011=>1100000
[8,4,2,6,7,3,5,1]=>0011011=>1101100
[4,1,5,7,8,6,2,3]=>0010101=>1010100
[6,1,4,8,2,3,7,5]=>0000111=>1110000
[7,6,2,3,5,8,4,1]=>0010111=>1110100
[2,8,5,7,6,3,4,1]=>0010111=>1110100
[2,5,7,8,6,4,1,3]=>0010101=>1010100
[7,4,1,6,2,5,8,3]=>0010111=>1110100
[8,7,4,6,2,5,3,1]=>0101111=>1111010
[1,7,5,4,6,2,3,8]=>0001110=>0111000
[6,2,7,5,3,1,4,8]=>0101110=>0111010
[6,1,7,4,8,5,2,3]=>0001111=>1111000
[8,2,4,6,3,1,7,5]=>0100111=>1110010
[2,3,1,5,6,8,9,4,7]=>01000001=>10000010
[5,6,2,4,8,7,3,1]=>0100111=>1110010
[8,5,6,2,3,7,4,1]=>0010111=>1110100
[7,8,1,4,5,6,2,3]=>0000101=>1010000
[5,6,7,8,9,1,3,4,2]=>00100001=>10000100
[6,7,8,9,1,3,4,5,2]=>00010001=>10001000
[6,7,8,9,1,4,5,2,3]=>00010001=>10001000
[6,7,8,9,1,4,5,3,2]=>01010001=>10001010
[6,7,8,9,1,5,4,3,2]=>01110001=>10001110
[7,8,9,1,4,5,6,2,3]=>00001001=>10010000
[7,8,9,1,4,5,6,3,2]=>01001001=>10010010
[7,8,9,1,5,6,3,4,2]=>00101001=>10010100
[7,8,9,1,5,6,4,3,2]=>01101001=>10010110
[7,8,9,1,6,5,4,3,2]=>01111001=>10011110
[8,9,1,5,6,7,3,4,2]=>00100101=>10100100
[8,9,1,5,6,7,4,3,2]=>01100101=>10100110
[8,9,1,6,7,4,5,2,3]=>00010101=>10101000
[8,9,1,6,7,4,5,3,2]=>01010101=>10101010
[8,9,1,6,7,5,4,3,2]=>01110101=>10101110
[9,1,7,8,5,6,3,4,2]=>00101011=>11010100
[9,1,7,8,5,6,4,3,2]=>01101011=>11010110
[5,6,7,8,9,10,1,3,4,2]=>001000001=>100000100
[5,6,7,8,9,10,1,4,3,2]=>011000001=>100000110
[7,8,9,10,1,4,5,6,2,3]=>000010001=>100010000
[7,8,9,10,1,4,5,6,3,2]=>010010001=>100010010
[7,8,9,10,1,5,6,4,3,2]=>011010001=>100010110
[7,8,9,10,1,6,5,4,3,2]=>011110001=>100011110
[8,9,10,1,4,5,6,7,2,3]=>000001001=>100100000
[8,9,10,1,4,5,6,7,3,2]=>010001001=>100100010
[8,9,10,1,5,6,7,2,3,4]=>000001001=>100100000
[8,9,10,1,5,6,7,4,3,2]=>011001001=>100100110
[8,9,10,1,6,7,4,5,2,3]=>000101001=>100101000
[8,9,10,1,6,7,4,5,3,2]=>010101001=>100101010
[8,9,10,1,6,7,5,4,3,2]=>011101001=>100101110
[8,9,10,1,7,6,5,4,3,2]=>011111001=>100111110
[9,10,1,6,7,8,3,4,5,2]=>000100101=>101001000
[9,10,1,6,7,8,4,5,2,3]=>000100101=>101001000
[9,10,1,6,7,8,4,5,3,2]=>010100101=>101001010
[9,10,1,6,7,8,5,4,3,2]=>011100101=>101001110
[9,10,1,7,8,5,6,3,4,2]=>001010101=>101010100
[9,10,1,7,8,5,6,4,3,2]=>011010101=>101010110
[9,10,1,7,8,6,5,4,3,2]=>011110101=>101011110
[10,1,8,9,6,7,4,5,3,2]=>010101011=>110101010
[10,1,8,9,6,7,5,4,3,2]=>011101011=>110101110
[10,1,8,9,7,6,5,4,3,2]=>011111011=>110111110
[8,3,1,2,5,4,7,6]=>0101011=>1101010
[8,1,5,3,7,4,2,6]=>0011011=>1101100
[1,2,6,7,8,3,5,4]=>0001001=>1001000
[1,2,4,8,6,7,3,5]=>0000011=>1100000
[8,1,2,6,5,7,3,4]=>0000111=>1110000
[7,1,2,6,5,8,3,4]=>0000111=>1110000
[7,4,8,3,5,6,2,1]=>1000111=>1110001
[2,6,1,4,7,5,8,3]=>0000111=>1110000
[3,1,5,7,2,6,8,4]=>0100011=>1100010
[3,1,7,5,2,6,8,4]=>0101011=>1101010
[3,2,7,5,1,6,8,4]=>0101011=>1101010
[5,2,7,3,1,6,8,4]=>0101011=>1101010
[6,7,2,1,3,4,8,5]=>1000011=>1100001
[4,6,3,1,2,7,8,5]=>0100101=>1010010
[2,3,4,5,7,9,6,8,1]=>00000011=>11000000
[2,3,4,6,9,5,7,8,1]=>00000011=>11000000
[2,3,5,6,8,4,7,1]=>0000011=>1100000
[2,3,5,9,4,6,7,8,1]=>00000011=>11000000
[2,4,5,8,3,6,7,1]=>0000011=>1100000
[2,4,9,3,5,6,7,8,1]=>00000011=>11000000
[5,9,8,7,6,4,3,1,2]=>01101111=>11110110
[5,4,8,7,6,3,2,1,9]=>11011110=>01111011
[4,5,8,7,6,3,1,2]=>0100111=>1110010
[6,5,9,8,7,4,3,1,2]=>01101111=>11110110
[8,7,4,6,5,3,1,2]=>0101111=>1111010
[9,5,8,7,6,4,3,1,2]=>01101111=>11110110
[6,10,9,8,7,5,4,3,1,2]=>011101111=>111101110
[8,1,4,3,6,2,5,7]=>0010101=>1010100
[1,6,3,7,8,4,2,5]=>0010101=>1010100
[5,3,8,4,6,7,2,1]=>1001011=>1101001
[4,3,5,8,6,7,2,1]=>1010011=>1100101
[3,2,7,8,5,6,4,1]=>0110101=>1010110
[4,7,3,8,5,6,2,1]=>1000111=>1110001
[7,1,4,8,5,6,3,2]=>0100111=>1110010
[4,3,8,7,2,5,6,1]=>0010111=>1110100
[1,7,3,8,6,4,5,2]=>0001111=>1111000
[7,4,2,8,5,6,3,1]=>0110111=>1110110
[3,4,8,2,6,7,5,1]=>0001011=>1101000
[1,6,3,8,7,4,5,2]=>0001111=>1111000
[1,4,5,8,7,6,2,3]=>0000111=>1110000
[5,2,1,3,8,4,6,7]=>1001001=>1001001
[1,4,3,5,8,2,6,7]=>0010001=>1000100
[2,1,3,8,6,4,5,7]=>1000101=>1010001
[1,3,6,4,5,8,2,7]=>0000101=>1010000
[6,1,4,3,5,8,2,7]=>0010101=>1010100
[6,5,1,3,8,2,4,7]=>0001101=>1011000
[1,4,3,8,6,2,5,7]=>0010101=>1010100
[4,1,3,8,6,2,5,7]=>0010101=>1010100
[7,1,5,4,6,3,8,2]=>0001111=>1111000
[8,9,7,6,5,4,3,2,10,1]=>011111011=>110111110
[7,6,8,5,4,3,2,9,1]=>01110111=>11101110
[6,8,7,5,4,3,2,9,1]=>01110111=>11101110
[6,4,7,8,3,5,1,2]=>0001101=>1011000
[3,5,6,7,1,8,4,2]=>0010011=>1100100
[3,5,2,4,8,6,7,1]=>0001011=>1101000
[3,7,6,1,4,8,5,2]=>0001111=>1111000
[8,4,7,1,5,6,2,3]=>0000111=>1110000
[2,7,8,3,6,1,5,4]=>0001101=>1011000
[1,7,8,3,6,2,5,4]=>0001101=>1011000
[7,4,3,5,8,1,6,2]=>0010111=>1110100
[7,3,6,4,1,8,5,2]=>0011111=>1111100
[7,8,4,3,6,1,5,2]=>0011101=>1011100
[7,1,6,4,3,8,5,2]=>0011111=>1111100
[8,7,3,4,1,5,2,6]=>0011011=>1101100
[7,2,6,4,3,8,5,1]=>0011111=>1111100
[1,7,5,4,3,8,2,6]=>0011011=>1101100
[2,3,4,5,6,1,8,9,7]=>00001001=>10010000
[2,3,4,5,1,7,8,9,6]=>00010001=>10001000
[2,6,3,1,4,7,8,5]=>0100101=>1010010
[2,9,3,4,5,6,1,7,8]=>00001001=>10010000
[2,3,4,5,6,7,1,9,10,8]=>000001001=>100100000
[2,7,3,4,1,8,5,6]=>0010011=>1100100
[2,8,3,4,5,1,6,9,7]=>00010011=>11001000
[2,7,3,4,1,5,8,9,6]=>00100101=>10100100
[2,3,4,5,1,7,8,9,10,6]=>000100001=>100001000
[2,6,3,1,4,7,8,9,5]=>01001001=>10010010
[2,3,1,5,6,7,8,9,10,4]=>010000001=>100000010
[8,6,4,5,1,3,7,2]=>0001111=>1111000
[7,4,8,5,3,6,1,2]=>0001111=>1111000
[8,4,6,5,1,3,7,2]=>0001111=>1111000
[4,5,3,8,7,1,2,6]=>0001011=>1101000
[8,5,4,7,6,1,2,3]=>0001111=>1111000
[7,5,8,2,4,3,1,6]=>0110011=>1100110
[2,3,7,8,1,4,6,5]=>0000101=>1010000
[8,2,3,5,4,1,7,6]=>0011011=>1101100
[7,1,3,8,2,4,6,5]=>0000111=>1110000
[7,2,3,6,4,1,8,5]=>0010111=>1110100
[6,5,2,4,1,8,3,7]=>0011101=>1011100
[5,7,2,4,1,3,8,6]=>0010011=>1100100
[6,2,5,4,1,8,3,7]=>0011101=>1011100
[4,2,5,3,7,6,9,8,1]=>00110111=>11101100
[4,2,6,3,7,5,9,8,1]=>00101111=>11110100
[4,2,6,3,8,5,9,7,1]=>00101111=>11110100
[4,2,6,3,8,5,1,7,9]=>00111010=>01011100
[4,2,6,3,5,8,1,7]=>0010101=>1010100
[4,2,6,3,8,5,7,1,9]=>00101110=>01110100
[4,2,6,3,5,8,7,1,9]=>00101110=>01110100
[4,2,3,6,5,8,7,1,9]=>00101110=>01110100
[4,2,5,3,7,6,9,8,1,10]=>001101110=>011101100
[5,2,6,3,7,4,9,8,1]=>00011111=>11111000
[4,2,6,3,7,5,9,8,1,10]=>001011110=>011110100
[4,2,7,3,8,5,9,6,1]=>00101111=>11110100
[4,2,6,3,8,5,9,7,1,10]=>001011110=>011110100
[4,2,6,3,9,5,1,7,8]=>00111001=>10011100
[4,2,6,3,8,5,10,7,1,9]=>001011101=>101110100
[4,2,6,3,8,5,7,9,1]=>00101011=>11010100
[4,2,6,3,8,5,10,7,9,1]=>001010111=>111010100
[4,2,6,3,5,8,1,7,9]=>00101010=>01010100
[4,2,6,3,8,5,7,10,9,1]=>001010111=>111010100
[4,2,3,6,8,5,7,1,9]=>00100110=>01100100
[4,2,6,3,5,8,7,10,9,1]=>001010111=>111010100
[2,4,6,3,5,8,7,1,9]=>00001110=>01110000
[4,2,3,6,5,8,7,10,9,1]=>001010111=>111010100
[7,4,2,6,8,5,3,1]=>0111011=>1101110
[8,5,2,4,6,3,1,7]=>0101101=>1011010
[7,4,1,2,8,5,6,3]=>0010111=>1110100
[6,4,1,8,5,2,3,7]=>0011101=>1011100
[8,4,1,6,3,5,2,7]=>0011101=>1011100
[7,3,4,1,6,8,5,2]=>0011011=>1101100
[8,6,2,3,5,7,4,1]=>0010111=>1110100
[8,6,2,5,7,3,4,1]=>0010111=>1110100
[6,3,4,8,5,1,2,7]=>0001101=>1011000
[8,5,1,2,7,4,6,3]=>0001111=>1111000
[7,2,6,8,3,4,5,1]=>0001011=>1101000
[1,6,7,5,4,8,2,3]=>0001011=>1101000
[1,8,5,4,2,6,3,7]=>0011101=>1011100
[3,4,5,6,9,2,1,8,7]=>10000011=>11000001
[3,4,5,8,2,9,1,7,6]=>00000111=>11100000
[3,4,7,2,8,9,1,5,6]=>00000101=>10100000
[3,6,2,7,8,9,1,5,4]=>00011001=>10011000
[5,2,6,7,8,9,1,4,3]=>00110001=>10001100
[3,4,5,6,7,8,9,11,1,10,2]=>0000000011=>1100000000
[3,4,5,6,9,1,7,8,2]=>00000011=>11000000
[3,4,5,6,7,10,2,1,9,8]=>100000011=>110000001
[3,4,5,6,7,8,10,11,1,9,2]=>0000000101=>1010000000
[3,4,5,8,9,6,1,7,2]=>00001101=>10110000
[3,4,5,6,9,2,10,1,8,7]=>000000111=>111000000
[3,4,7,8,5,9,1,2,6]=>00000011=>11000000
[3,4,5,9,2,6,1,8,7]=>00001011=>11010000
[3,4,5,8,2,9,10,1,6,7]=>000000101=>101000000
[3,4,5,6,8,9,10,11,1,7,2]=>0000010001=>1000100000
[3,6,7,4,8,9,1,5,2]=>00010101=>10101000
[3,4,8,2,5,9,1,7,6]=>00000111=>11100000
[3,4,7,2,8,9,10,1,6,5]=>000011001=>100110000
[3,4,5,7,8,9,10,11,1,6,2]=>0000100001=>1000010000
[5,6,3,7,8,9,1,4,2]=>00101001=>10010100
[3,7,2,4,8,9,1,5,6]=>00000101=>10100000
[3,6,2,7,8,9,10,1,5,4]=>000110001=>100011000
[6,2,3,7,8,9,1,5,4]=>00011001=>10011000
[5,2,6,7,8,9,10,1,3,4]=>000100001=>100001000
[3,5,6,7,8,9,10,11,1,4,2]=>0010000001=>1000000100
[4,5,6,7,8,9,10,11,1,3,2]=>0100000001=>1000000010
[8,9,7,6,5,4,1,3,2]=>01111101=>10111110
[8,7,9,6,5,4,1,3,2]=>01111011=>11011110
[9,7,8,6,5,4,1,3,2]=>01111011=>11011110
[9,10,8,7,6,5,4,1,3,2]=>011111101=>101111110
[10,8,7,6,5,4,3,2,9,1]=>011111111=>111111110
[5,7,3,6,2,1,4,8]=>1000110=>0110001
[1,3,2,4,5,6,9,7,8]=>01000001=>10000010
[2,3,1,4,5,6,9,7,8]=>01000001=>10000010
[5,8,6,1,2,4,3,7]=>0010101=>1010100
[4,1,5,7,3,6,8,2]=>0010011=>1100100
[1,4,5,7,6,8,2,3]=>0000011=>1100000
[5,7,2,1,6,8,4,3]=>1010011=>1100101
[2,6,3,1,7,8,5,4]=>0101101=>1011010
[6,2,5,7,4,1,8,3]=>0010111=>1110100
[3,6,1,8,7,4,5,2]=>0001111=>1111000
[4,3,9,5,6,7,8,2,1]=>10100011=>11000101
[10,2,3,4,5,6,7,8,9,11,1]=>0000000011=>1100000000
[2,9,4,5,6,7,8,1,10,3]=>000000111=>111000000
[3,2,8,5,6,7,1,9,4]=>01000111=>11100010
[7,8,4,5,6,1,3,9,2]=>00001011=>11010000
[3,4,1,9,6,7,8,2,5]=>00100011=>11000100
[4,8,9,5,6,7,2,1,3]=>10000101=>10100001
[4,3,10,5,6,7,8,9,2,1]=>101000011=>110000101
[11,2,3,4,5,6,7,8,9,10,12,1]=>00000000011=>11000000000
[2,10,4,5,6,7,8,9,1,11,3]=>0000000111=>1110000000
[3,2,9,5,6,7,8,1,10,4]=>010000111=>111000010
[8,9,4,5,6,7,1,3,10,2]=>000001011=>110100000
[4,2,3,8,6,7,1,9,5]=>00100111=>11100100
[6,8,4,5,1,3,7,9,2]=>00010011=>11001000
[4,7,1,3,5,6,8,2]=>0000011=>1100000
[4,3,5,7,8,2,6,1]=>0010101=>1010100
[3,5,1,4,9,7,8,2,6]=>00010011=>11001000
[8,3,4,9,6,7,2,5,1]=>00010111=>11101000
[3,4,1,10,6,7,8,9,2,5]=>001000011=>110000100
[4,7,9,5,6,2,1,8,3]=>10001011=>11010001
[4,9,10,5,6,7,8,2,1,3]=>100000101=>101000001
[5,3,2,7,6,4,1,8]=>0111110=>0111110
[5,3,7,4,6,2,1,8]=>1001110=>0111001
[5,7,3,2,1,8,6,4]=>1100111=>1110011
[5,7,6,3,2,1,8,4]=>1100111=>1110011
[3,2,7,5,4,1,8,6]=>0111011=>1101110
[1,7,3,5,4,2,6,8]=>0011010=>0101100
[5,3,7,4,1,8,6,2]=>0011111=>1111100
[7,3,5,4,1,6,8,2]=>0011011=>1101100
[7,5,1,6,8,3,2,4]=>0101011=>1101010
[5,3,1,7,6,8,2,4]=>0101011=>1101010
[7,1,5,3,2,4,8,6]=>0101011=>1101010
[8,1,2,5,3,4,6,7,9]=>00010010=>01001000
[7,1,5,2,4,3,6,8]=>0011010=>0101100
[1,9,2,3,6,4,5,7,8]=>00001001=>10010000
[9,1,2,3,6,4,5,7,8,10]=>000010010=>010010000
[8,1,2,6,4,3,5,7,9]=>00101010=>01010100
[8,1,2,6,3,5,4,7,9]=>00011010=>01011000
[1,9,2,3,7,5,4,6,8]=>00010101=>10101000
[1,9,2,3,7,4,6,5,8]=>00001101=>10110000
[6,8,7,3,2,1,5,4]=>1101011=>1101011
[3,6,8,7,2,4,1,5]=>0010011=>1100100
[5,7,3,6,2,1,8,4]=>1000111=>1110001
[3,6,5,2,4,8,1,7]=>0001101=>1011000
[5,6,7,8,9,3,2,1,4]=>11000001=>10000011
[6,7,8,9,3,4,1,2,5]=>00100001=>10000100
[6,7,8,9,3,4,2,1,5]=>10100001=>10000101
[7,8,9,3,4,5,1,2,6]=>00010001=>10001000
[7,8,9,3,4,5,2,1,6]=>10010001=>10001001
[7,8,9,4,5,2,3,1,6]=>01010001=>10001010
[7,8,9,4,5,3,2,1,6]=>11010001=>10001011
[8,9,4,5,6,2,3,1,7]=>01001001=>10010010
[8,9,4,5,6,3,2,1,7]=>11001001=>10010011
[8,9,5,6,3,4,1,2,7]=>00101001=>10010100
[8,9,5,6,3,4,2,1,7]=>10101001=>10010101
[8,9,5,6,4,3,2,1,7]=>11101001=>10010111
[9,6,7,4,5,3,2,1,8]=>11010101=>10101011
[5,6,7,8,9,10,3,2,1,4]=>110000001=>100000011
[7,8,9,10,3,4,5,1,2,6]=>000100001=>100001000
[7,8,9,10,3,4,5,2,1,6]=>100100001=>100001001
[7,8,9,10,4,5,2,3,1,6]=>010100001=>100001010
[7,8,9,10,4,5,3,2,1,6]=>110100001=>100001011
[7,8,9,10,5,4,3,2,1,6]=>111100001=>100001111
[8,9,10,3,4,5,6,1,2,7]=>000010001=>100010000
[8,9,10,3,4,5,6,2,1,7]=>100010001=>100010001
[8,9,10,4,5,6,1,2,3,7]=>000010001=>100010000
[8,9,10,4,5,6,3,2,1,7]=>110010001=>100010011
[8,9,10,5,6,3,4,1,2,7]=>001010001=>100010100
[8,9,10,5,6,3,4,2,1,7]=>101010001=>100010101
[8,9,10,5,6,4,3,2,1,7]=>111010001=>100010111
[8,9,10,6,5,4,3,2,1,7]=>111110001=>100011111
[9,10,5,6,7,2,3,4,1,8]=>001001001=>100100100
[9,10,5,6,7,3,4,1,2,8]=>001001001=>100100100
[9,10,5,6,7,3,4,2,1,8]=>101001001=>100100101
[9,10,5,6,7,4,3,2,1,8]=>111001001=>100100111
[9,10,6,7,4,5,3,2,1,8]=>110101001=>100101011
[9,10,6,7,5,4,3,2,1,8]=>111101001=>100101111
[9,10,7,6,5,4,3,2,1,8]=>111111001=>100111111
[10,7,8,5,6,3,4,2,1,9]=>101010101=>101010101
[10,7,8,5,6,4,3,2,1,9]=>111010101=>101010111
[10,7,8,6,5,4,3,2,1,9]=>111110101=>101011111
[1,8,3,6,2,4,7,5]=>0000111=>1110000
[1,8,7,5,6,4,2,3]=>0010111=>1110100
[6,8,2,1,5,4,3,7]=>1011001=>1001101
[10,9,1,2,3,7,8,4,5,6]=>000000111=>111000000
[10,9,1,2,8,7,3,4,5,6]=>000001111=>111100000
[9,8,1,10,7,2,3,4,5,6]=>000001111=>111100000
[8,6,1,2,3,4,5,9,10,7]=>000010101=>101010000
[5,7,1,2,3,4,8,9,10,6]=>000001001=>100100000
[8,11,1,2,3,4,5,9,10,6,7]=>0000000011=>1100000000
[10,4,1,2,3,7,8,9,5,6]=>001000011=>110000100
[10,11,1,2,3,4,8,9,5,6,7]=>0000000101=>1010000000
[10,3,1,2,9,7,8,4,5,6]=>010000111=>111000010
[10,11,1,2,3,9,8,4,5,6,7]=>0000001101=>1011000000
[2,9,1,10,8,7,3,4,5,6]=>000001111=>111100000
[10,9,1,2,11,8,3,4,5,6,7]=>0000001111=>1111000000
[9,8,1,10,11,2,3,4,5,6,7]=>0000001101=>1011000000
[11,8,9,10,1,2,3,4,5,6,7]=>0000000011=>1100000000
[6,3,2,1,5,8,4,7]=>1100101=>1010011
[4,3,5,6,2,8,1,7]=>0010101=>1010100
[6,3,5,2,7,8,4,1]=>0011101=>1011100
[4,5,3,1,6,8,2,7]=>0101001=>1001010
[3,4,6,7,5,1,8,2]=>0001011=>1101000
[7,4,1,2,5,6,8,3]=>0010011=>1100100
[4,8,2,6,7,1,5,3]=>0001011=>1101000
[6,5,8,3,7,1,4,2]=>0010111=>1110100
[4,2,6,1,3,5,8,7,9]=>00101010=>01010100
[4,2,6,1,8,3,5,7,9]=>00101010=>01010100
[4,2,6,1,3,5,8,7,10,9]=>001010101=>101010100
[4,2,8,1,3,6,5,7,9]=>00101010=>01010100
[4,2,6,1,8,3,5,7,10,9]=>001010101=>101010100
[4,2,6,1,9,3,5,8,7]=>00101011=>11010100
[4,2,6,1,8,3,10,5,7,9]=>001010101=>101010100
[9,7,1,8,2,3,4,5,6]=>00000111=>11100000
[9,6,1,7,2,8,3,4,5]=>00001111=>11110000
[8,6,1,9,7,2,3,4,5]=>00001111=>11110000
[9,8,6,1,7,2,3,4,5]=>00001111=>11110000
[8,5,1,9,6,2,7,3,4]=>00011111=>11111000
[9,8,5,1,6,2,7,3,4]=>00011111=>11111000
[9,7,5,1,8,6,2,3,4]=>00011111=>11111000
[9,8,7,5,1,6,2,3,4]=>00011111=>11111000
[9,7,4,1,8,5,2,6,3]=>00111111=>11111100
[9,8,7,4,1,5,2,6,3]=>00111111=>11111100
[8,6,4,1,9,7,5,2,3]=>00111111=>11111100
[9,8,6,4,1,7,5,2,3]=>00111111=>11111100
[9,8,7,6,4,1,5,2,3]=>00111111=>11111100
[9,8,7,5,3,1,6,4,2]=>01111111=>11111110
[10,7,1,8,2,9,3,4,5,6]=>000001111=>111100000
[9,7,1,10,8,2,3,4,5,6]=>000001111=>111100000
[10,9,7,1,8,2,3,4,5,6]=>000001111=>111100000
[10,6,1,7,2,8,3,9,4,5]=>000011111=>111110000
[9,6,1,10,7,2,8,3,4,5]=>000011111=>111110000
[10,9,6,1,7,2,8,3,4,5]=>000011111=>111110000
[10,8,6,1,9,7,2,3,4,5]=>000011111=>111110000
[10,9,8,6,1,7,2,3,4,5]=>000011111=>111110000
[9,5,1,10,6,2,7,3,8,4]=>000111111=>111111000
[10,9,5,1,6,2,7,3,8,4]=>000111111=>111111000
[8,5,1,9,6,2,10,7,3,4]=>000111111=>111111000
[10,8,5,1,9,6,2,7,3,4]=>000111111=>111111000
[10,9,8,5,1,6,2,7,3,4]=>000111111=>111111000
[9,7,5,1,10,8,6,2,3,4]=>000111111=>111111000
[10,9,7,5,1,8,6,2,3,4]=>000111111=>111111000
[10,9,8,7,5,1,6,2,3,4]=>000111111=>111111000
[9,7,4,1,10,8,5,2,6,3]=>001111111=>111111100
[10,9,7,4,1,8,5,2,6,3]=>001111111=>111111100
[10,9,8,7,4,1,5,2,6,3]=>001111111=>111111100
[10,8,6,4,1,9,7,5,2,3]=>001111111=>111111100
[10,9,8,6,4,1,7,5,2,3]=>001111111=>111111100
[10,9,8,7,6,4,1,5,2,3]=>001111111=>111111100
[10,9,7,5,3,1,8,6,4,2]=>011111111=>111111110
[10,9,8,7,5,3,1,6,4,2]=>011111111=>111111110
[10,9,8,7,6,5,3,1,4,2]=>011111111=>111111110
[9,1,2,8,4,3,5,6,7]=>00100011=>11000100
[8,1,9,3,2,4,6,5,7]=>01001011=>11010010
[9,8,2,1,3,5,6,4,7]=>10001011=>11010001
[8,1,9,2,4,5,6,3,7]=>00001011=>11010000
[2,3,4,10,6,7,8,9,1,5]=>000000011=>110000000
[2,3,10,5,6,7,8,9,1,4]=>000000011=>110000000
[2,3,4,5,6,10,1,9,7,8]=>000000011=>110000000
[2,3,4,5,6,7,11,9,10,1,8]=>0000000011=>1100000000
[2,3,4,5,10,1,8,9,6,7]=>000000011=>110000000
[2,3,4,5,6,11,8,9,10,1,7]=>0000000011=>1100000000
[2,3,4,5,11,7,8,9,10,1,6]=>0000000011=>1100000000
[2,3,10,1,6,7,8,9,4,5]=>000000011=>110000000
[2,3,4,11,6,7,8,9,10,1,5]=>0000000011=>1100000000
[2,3,11,5,6,7,8,9,10,1,4]=>0000000011=>1100000000
[1,5,2,4,7,6,8,3]=>0001011=>1101000
[1,4,3,6,5,8,7,9,2]=>00101011=>11010100
[1,4,2,6,5,8,7,9,3]=>00101011=>11010100
[1,5,2,6,4,8,7,9,3]=>00011011=>11011000
[1,5,2,7,4,8,6,9,3]=>00010111=>11101000
[1,5,2,7,4,9,6,8,3]=>00010111=>11101000
[1,5,2,7,4,6,9,8,3]=>00010111=>11101000
[1,5,2,4,7,6,9,8,3]=>00010111=>11101000
[1,2,5,4,7,6,9,8,3]=>00010111=>11101000
[1,4,2,6,5,8,7,10,9,3]=>001010111=>111010100
[1,5,2,6,3,8,7,9,4]=>00011011=>11011000
[1,5,2,6,4,8,7,10,9,3]=>000110111=>111011000
[1,6,2,7,4,8,5,9,3]=>00001111=>11110000
[1,5,2,7,4,8,6,10,9,3]=>000101111=>111101000
[1,5,2,8,4,9,6,7,3]=>00010111=>11101000
[1,5,2,7,4,9,6,10,8,3]=>000101111=>111101000
[1,5,2,7,4,6,8,9,3]=>00010101=>10101000
[1,5,2,7,4,9,6,8,10,3]=>000101011=>110101000
[1,5,2,4,7,9,6,8,3]=>00010011=>11001000
[1,5,2,7,4,6,9,8,10,3]=>000101011=>110101000
[1,2,5,7,4,6,9,8,3]=>00000111=>11100000
[1,5,2,4,7,6,9,8,10,3]=>000101011=>110101000
[1,2,5,4,7,6,9,8,10,3]=>000101011=>110101000
[2,5,4,7,1,8,3,6]=>0001011=>1101000
[1,5,4,7,3,8,2,6]=>0001011=>1101000
[1,2,6,7,3,5,4,8]=>0001010=>0101000
[9,10,7,8,5,3,6,4,1,2]=>001110101=>101011100
[9,10,7,8,5,3,1,6,4,2]=>011110101=>101011110
[9,10,7,5,8,6,3,4,1,2]=>001011101=>101110100
[9,10,7,5,8,6,3,1,4,2]=>011011101=>101110110
[9,10,7,5,8,3,6,4,1,2]=>001011101=>101110100
[9,10,7,5,8,3,1,6,4,2]=>011011101=>101110110
[9,10,7,5,3,8,6,4,1,2]=>001111101=>101111100
[9,10,7,5,3,8,6,1,4,2]=>001111101=>101111100
[9,10,7,5,3,8,1,6,4,2]=>001111101=>101111100
[9,10,7,5,3,1,8,6,4,2]=>011111101=>101111110
[9,7,10,8,5,6,3,1,4,2]=>011010111=>111010110
[9,7,10,8,5,3,6,4,1,2]=>001110111=>111011100
[9,7,10,8,5,3,6,1,4,2]=>001110111=>111011100
[9,7,10,8,5,3,1,6,4,2]=>011110111=>111011110
[9,7,10,5,8,6,3,1,4,2]=>011010111=>111010110
[9,7,10,5,8,3,1,6,4,2]=>011010111=>111010110
[9,7,10,5,3,8,6,4,1,2]=>001110111=>111011100
[9,7,10,5,3,8,6,1,4,2]=>001110111=>111011100
[9,7,10,5,3,8,1,6,4,2]=>001110111=>111011100
[9,7,10,5,3,1,8,6,4,2]=>011110111=>111011110
[9,7,5,10,8,6,3,4,1,2]=>001011111=>111110100
[9,7,5,10,8,6,3,1,4,2]=>011011111=>111110110
[9,7,5,10,8,3,6,4,1,2]=>001011111=>111110100
[9,7,5,10,8,3,6,1,4,2]=>001011111=>111110100
[9,7,5,10,8,3,1,6,4,2]=>011011111=>111110110
[9,7,5,10,3,8,6,4,1,2]=>001011111=>111110100
[9,7,5,10,3,8,6,1,4,2]=>001011111=>111110100
[9,7,5,10,3,8,1,6,4,2]=>001011111=>111110100
[9,7,5,10,3,1,8,6,4,2]=>011011111=>111110110
[9,7,5,3,10,8,6,4,1,2]=>001111111=>111111100
[9,7,5,3,10,8,6,1,4,2]=>001111111=>111111100
[9,7,5,3,10,8,1,6,4,2]=>001111111=>111111100
[9,7,5,3,10,1,8,6,4,2]=>001111111=>111111100
[11,12,9,10,7,8,5,6,3,1,4,2]=>01101010101=>10101010110
[11,12,9,10,7,8,5,3,6,4,1,2]=>00111010101=>10101011100
[11,12,9,10,7,8,5,3,6,1,4,2]=>00111010101=>10101011100
[11,12,9,10,7,8,5,3,1,6,4,2]=>01111010101=>10101011110
[11,12,9,10,7,5,8,6,3,4,1,2]=>00101110101=>10101110100
[11,12,9,10,7,5,8,6,3,1,4,2]=>01101110101=>10101110110
[11,12,9,10,7,5,8,3,6,4,1,2]=>00101110101=>10101110100
[11,12,9,10,7,5,8,3,6,1,4,2]=>00101110101=>10101110100
[11,12,9,10,7,5,8,3,1,6,4,2]=>01101110101=>10101110110
[11,12,9,10,7,5,3,1,8,6,4,2]=>01111110101=>10101111110
[11,12,9,7,10,8,5,6,3,4,1,2]=>00101011101=>10111010100
[11,12,9,7,10,8,5,6,3,1,4,2]=>01101011101=>10111010110
[11,12,9,7,10,8,5,3,6,4,1,2]=>00111011101=>10111011100
[11,12,9,7,10,8,5,3,6,1,4,2]=>00111011101=>10111011100
[11,12,9,7,10,8,5,3,1,6,4,2]=>01111011101=>10111011110
[11,12,9,7,10,5,8,6,3,4,1,2]=>00101011101=>10111010100
[11,12,9,7,10,5,8,6,3,1,4,2]=>01101011101=>10111010110
[11,12,9,7,10,5,8,3,6,4,1,2]=>00101011101=>10111010100
[11,12,9,7,10,5,8,3,6,1,4,2]=>00101011101=>10111010100
[11,12,9,7,10,5,8,3,1,6,4,2]=>01101011101=>10111010110
[11,12,9,7,10,5,3,8,6,4,1,2]=>00111011101=>10111011100
[11,12,9,7,10,5,3,8,6,1,4,2]=>00111011101=>10111011100
[11,12,9,7,10,5,3,8,1,6,4,2]=>00111011101=>10111011100
[11,12,9,7,10,5,3,1,8,6,4,2]=>01111011101=>10111011110
[11,12,9,7,5,10,8,6,3,4,1,2]=>00101111101=>10111110100
[11,12,9,7,5,10,8,6,3,1,4,2]=>01101111101=>10111110110
[11,12,9,7,5,10,8,3,6,4,1,2]=>00101111101=>10111110100
[11,12,9,7,5,10,8,3,6,1,4,2]=>00101111101=>10111110100
[11,12,9,7,5,10,8,3,1,6,4,2]=>01101111101=>10111110110
[11,12,9,7,5,10,3,8,6,4,1,2]=>00101111101=>10111110100
[11,12,9,7,5,10,3,8,6,1,4,2]=>00101111101=>10111110100
[11,12,9,7,5,10,3,8,1,6,4,2]=>00101111101=>10111110100
[11,12,9,7,5,10,3,1,8,6,4,2]=>01101111101=>10111110110
[11,12,9,7,5,3,10,8,6,4,1,2]=>00111111101=>10111111100
[11,12,9,7,5,3,10,8,6,1,4,2]=>00111111101=>10111111100
[11,12,9,7,5,3,10,8,1,6,4,2]=>00111111101=>10111111100
[11,12,9,7,5,3,10,1,8,6,4,2]=>00111111101=>10111111100
[11,12,9,7,5,3,1,10,8,6,4,2]=>01111111101=>10111111110
[11,9,12,10,7,8,5,6,3,4,1,2]=>00101010111=>11101010100
[11,9,12,10,7,8,5,6,3,1,4,2]=>01101010111=>11101010110
[11,9,12,10,7,8,5,3,6,4,1,2]=>00111010111=>11101011100
[11,9,12,10,7,8,5,3,6,1,4,2]=>00111010111=>11101011100
[11,9,12,10,7,8,5,3,1,6,4,2]=>01111010111=>11101011110
[11,9,12,10,7,5,8,6,3,4,1,2]=>00101110111=>11101110100
[11,9,12,10,7,5,8,6,3,1,4,2]=>01101110111=>11101110110
[11,9,12,10,7,5,8,3,6,4,1,2]=>00101110111=>11101110100
[11,9,12,10,7,5,8,3,6,1,4,2]=>00101110111=>11101110100
[11,9,12,10,7,5,8,3,1,6,4,2]=>01101110111=>11101110110
[11,9,12,10,7,5,3,8,6,4,1,2]=>00111110111=>11101111100
[11,9,12,10,7,5,3,8,6,1,4,2]=>00111110111=>11101111100
[11,9,12,10,7,5,3,8,1,6,4,2]=>00111110111=>11101111100
[11,9,12,10,7,5,3,1,8,6,4,2]=>01111110111=>11101111110
[11,9,12,7,10,8,5,6,3,4,1,2]=>00101010111=>11101010100
[11,9,12,7,10,8,5,6,3,1,4,2]=>01101010111=>11101010110
[11,9,12,7,10,8,5,3,6,4,1,2]=>00111010111=>11101011100
[11,9,12,7,10,8,5,3,6,1,4,2]=>00111010111=>11101011100
[11,9,12,7,10,8,5,3,1,6,4,2]=>01111010111=>11101011110
[11,9,12,7,10,5,8,6,3,4,1,2]=>00101010111=>11101010100
[11,9,12,7,10,5,8,6,3,1,4,2]=>01101010111=>11101010110
[11,9,12,7,10,5,8,3,6,4,1,2]=>00101010111=>11101010100
[11,9,12,7,10,5,8,3,6,1,4,2]=>00101010111=>11101010100
[11,9,12,7,10,5,8,3,1,6,4,2]=>01101010111=>11101010110
[11,9,12,7,10,5,3,8,6,4,1,2]=>00111010111=>11101011100
[11,9,12,7,10,5,3,8,6,1,4,2]=>00111010111=>11101011100
[11,9,12,7,10,5,3,8,1,6,4,2]=>00111010111=>11101011100
[11,9,12,7,10,5,3,1,8,6,4,2]=>01111010111=>11101011110
[11,9,12,7,5,10,8,6,3,4,1,2]=>00101110111=>11101110100
[11,9,12,7,5,10,8,6,3,1,4,2]=>01101110111=>11101110110
[11,9,12,7,5,10,8,3,6,4,1,2]=>00101110111=>11101110100
[11,9,12,7,5,10,8,3,6,1,4,2]=>00101110111=>11101110100
[11,9,12,7,5,10,8,3,1,6,4,2]=>01101110111=>11101110110
[11,9,12,7,5,10,3,8,6,4,1,2]=>00101110111=>11101110100
[11,9,12,7,5,10,3,8,6,1,4,2]=>00101110111=>11101110100
[11,9,12,7,5,10,3,8,1,6,4,2]=>00101110111=>11101110100
[11,9,12,7,5,10,3,1,8,6,4,2]=>01101110111=>11101110110
[11,9,12,7,5,3,10,8,6,4,1,2]=>00111110111=>11101111100
[11,9,12,7,5,3,10,8,6,1,4,2]=>00111110111=>11101111100
[11,9,12,7,5,3,10,8,1,6,4,2]=>00111110111=>11101111100
[11,9,12,7,5,3,10,1,8,6,4,2]=>00111110111=>11101111100
[11,9,12,7,5,3,1,10,8,6,4,2]=>01111110111=>11101111110
[11,9,7,12,10,8,5,6,3,4,1,2]=>00101011111=>11111010100
[11,9,7,12,10,8,5,6,3,1,4,2]=>01101011111=>11111010110
[11,9,7,12,10,8,5,3,6,4,1,2]=>00111011111=>11111011100
[11,9,7,12,10,8,5,3,6,1,4,2]=>00111011111=>11111011100
[11,9,7,12,10,8,5,3,1,6,4,2]=>01111011111=>11111011110
[11,9,7,12,10,5,8,6,3,4,1,2]=>00101011111=>11111010100
[11,9,7,12,10,5,8,6,3,1,4,2]=>01101011111=>11111010110
[11,9,7,12,10,5,8,3,6,4,1,2]=>00101011111=>11111010100
[11,9,7,12,10,5,8,3,6,1,4,2]=>00101011111=>11111010100
[11,9,7,12,10,5,8,3,1,6,4,2]=>01101011111=>11111010110
[11,9,7,12,10,5,3,8,6,4,1,2]=>00111011111=>11111011100
[11,9,7,12,10,5,3,8,6,1,4,2]=>00111011111=>11111011100
[11,9,7,12,10,5,3,8,1,6,4,2]=>00111011111=>11111011100
[11,9,7,12,10,5,3,1,8,6,4,2]=>01111011111=>11111011110
[11,9,7,12,5,10,8,6,3,4,1,2]=>00101011111=>11111010100
[11,9,7,12,5,10,8,6,3,1,4,2]=>01101011111=>11111010110
[11,9,7,12,5,10,8,3,6,4,1,2]=>00101011111=>11111010100
[11,9,7,12,5,10,8,3,6,1,4,2]=>00101011111=>11111010100
[11,9,7,12,5,10,8,3,1,6,4,2]=>01101011111=>11111010110
[11,9,7,12,5,10,3,8,6,4,1,2]=>00101011111=>11111010100
[11,9,7,12,5,10,3,8,6,1,4,2]=>00101011111=>11111010100
[11,9,7,12,5,10,3,8,1,6,4,2]=>00101011111=>11111010100
[11,9,7,12,5,10,3,1,8,6,4,2]=>01101011111=>11111010110
[11,9,7,12,5,3,10,8,6,4,1,2]=>00111011111=>11111011100
[11,9,7,12,5,3,10,8,6,1,4,2]=>00111011111=>11111011100
[11,9,7,12,5,3,10,8,1,6,4,2]=>00111011111=>11111011100
[11,9,7,12,5,3,10,1,8,6,4,2]=>00111011111=>11111011100
[11,9,7,12,5,3,1,10,8,6,4,2]=>01111011111=>11111011110
[11,9,7,5,12,10,8,6,3,4,1,2]=>00101111111=>11111110100
[11,9,7,5,12,10,8,6,3,1,4,2]=>01101111111=>11111110110
[11,9,7,5,12,10,8,3,6,4,1,2]=>00101111111=>11111110100
[11,9,7,5,12,10,8,3,6,1,4,2]=>00101111111=>11111110100
[11,9,7,5,12,10,8,3,1,6,4,2]=>01101111111=>11111110110
[11,9,7,5,12,10,3,8,6,4,1,2]=>00101111111=>11111110100
[11,9,7,5,12,10,3,8,6,1,4,2]=>00101111111=>11111110100
[11,9,7,5,12,10,3,8,1,6,4,2]=>00101111111=>11111110100
[11,9,7,5,12,10,3,1,8,6,4,2]=>01101111111=>11111110110
[11,9,7,5,12,3,10,8,6,4,1,2]=>00101111111=>11111110100
[11,9,7,5,12,3,10,8,6,1,4,2]=>00101111111=>11111110100
[11,9,7,5,12,3,10,8,1,6,4,2]=>00101111111=>11111110100
[11,9,7,5,12,3,10,1,8,6,4,2]=>00101111111=>11111110100
[11,9,7,5,12,3,1,10,8,6,4,2]=>01101111111=>11111110110
[11,9,7,5,3,12,10,8,6,4,1,2]=>00111111111=>11111111100
[11,9,7,5,3,12,10,8,6,1,4,2]=>00111111111=>11111111100
[11,9,7,5,3,12,10,8,1,6,4,2]=>00111111111=>11111111100
[11,9,7,5,3,12,10,1,8,6,4,2]=>00111111111=>11111111100
[11,9,7,5,3,12,1,10,8,6,4,2]=>00111111111=>11111111100
[8,1,2,4,6,3,5,7]=>0000101=>1010000
[4,5,6,7,9,8,3,2,1]=>11000011=>11000011
[5,4,6,7,8,9,3,2,1]=>11010001=>10001011
[5,6,7,8,10,9,4,3,2,1]=>111000011=>110000111
[6,5,7,8,9,4,3,2,1]=>11101001=>10010111
[6,5,7,8,9,10,4,3,2,1]=>111010001=>100010111
[5,6,7,8,9,11,10,4,3,2,1]=>1110000011=>1100000111
[4,5,6,7,8,10,9,3,2,1]=>110000011=>110000011
[4,5,6,7,3,9,8,2,1]=>10000111=>11100001
[3,5,6,7,9,8,4,2,1]=>10100011=>11000101
[5,4,6,7,8,3,9,2,1]=>10010011=>11001001
[4,3,6,7,8,9,5,2,1]=>10110001=>10001101
[5,4,6,7,8,9,10,3,2,1]=>110100001=>100001011
[6,5,7,8,9,10,11,4,3,2,1]=>1110100001=>1000010111
[3,4,5,6,8,9,7,1,2]=>00000101=>10100000
[3,4,5,7,8,9,6,1,2]=>00001001=>10010000
[3,5,6,7,8,9,4,1,2]=>00100001=>10000100
[4,5,6,7,8,9,3,1,2]=>01000001=>10000010
[3,4,5,6,7,9,10,8,1,2]=>000000101=>101000000
[3,4,5,8,1,9,7,6,2]=>00001111=>11110000
[3,4,5,6,8,9,10,7,1,2]=>000001001=>100100000
[3,4,7,1,8,9,6,5,2]=>00011101=>10111000
[3,6,1,7,8,9,4,5,2]=>00011001=>10011000
[3,4,6,7,8,9,10,5,1,2]=>000100001=>100001000
[5,1,6,7,8,9,4,3,2]=>01110001=>10001110
[3,5,6,7,8,9,10,4,1,2]=>001000001=>100000100
[1,5,6,7,8,9,3,2,4]=>01000001=>10000010
[3,4,5,6,7,10,1,8,9,2]=>000000011=>110000000
[3,4,5,6,7,8,10,11,9,1,2]=>0000000101=>1010000000
[3,4,5,8,9,6,7,1,2]=>00000101=>10100000
[3,4,5,6,9,1,10,8,7,2]=>000001111=>111100000
[3,4,5,6,7,9,10,11,8,1,2]=>0000001001=>1001000000
[3,4,7,8,5,9,6,1,2]=>00001011=>11010000
[3,4,5,9,1,6,7,8,2]=>00000011=>11000000
[3,4,5,8,1,9,10,7,6,2]=>000011101=>101110000
[3,4,8,1,5,9,7,6,2]=>00001111=>11110000
[3,4,7,1,8,9,10,5,6,2]=>000011001=>100110000
[3,4,5,7,8,9,10,11,6,1,2]=>0000100001=>1000010000
[5,6,3,7,8,9,4,1,2]=>00101001=>10010100
[3,7,8,4,5,6,1,2]=>0000101=>1010000
[3,7,1,4,8,9,6,5,2]=>00011101=>10111000
[3,6,1,7,8,9,10,5,4,2]=>001110001=>100011100
[3,4,6,7,8,9,10,11,5,1,2]=>0001000001=>1000001000
[5,2,6,7,8,9,3,1,4]=>01010001=>10001010
[6,1,3,7,8,9,4,5,2]=>00011001=>10011000
[5,1,6,7,8,9,10,4,3,2]=>011100001=>100001110
[1,2,6,7,8,9,4,3,5]=>00100001=>10000100
[4,5,6,7,8,9,10,11,3,1,2]=>0100000001=>1000000010
[4,5,6,7,8,9,10,11,2,1,3]=>1000000001=>1000000001
[1,3,8,6,7,4,5,2]=>0001011=>1101000
[2,6,5,3,7,1,8,4]=>0001111=>1111000
[5,7,1,3,6,4,8,2]=>0000111=>1110000
[8,2,5,4,1,7,3,6]=>0011011=>1101100
[8,1,7,6,4,2,3,5]=>0010111=>1110100
[1,8,6,3,7,4,5,2]=>0001111=>1111000
[5,7,3,4,2,8,6,1]=>0010111=>1110100
[5,8,3,4,2,7,6,1]=>0010111=>1110100
[7,6,4,2,3,8,5,1]=>0011111=>1111100
[3,5,6,8,2,4,7,1]=>0000011=>1100000
[4,8,7,3,2,5,6,1]=>0100111=>1110010
[3,7,4,2,6,8,5,1]=>0011011=>1101100
[6,4,8,7,3,2,5,1]=>0101111=>1111010
[5,6,2,8,7,4,3,1]=>0110111=>1110110
[6,2,8,3,7,4,5,1]=>0001111=>1111000
[3,7,5,6,4,2,8,1]=>0010111=>1110100
[5,2,3,8,6,1,4,7]=>0001101=>1011000
[1,4,3,8,5,6,2,7]=>0010101=>1010100
[7,8,2,6,4,3,5,1]=>0011101=>1011100
[4,5,8,7,2,3,6,1]=>0000111=>1110000
[7,8,6,1,4,2,5,3]=>0011101=>1011100
[6,10,5,1,2,3,4,7,8,9]=>000100001=>100001000
[10,5,4,1,2,3,6,7,8,9]=>001100001=>100001100
[8,3,6,5,2,7,1,4]=>0001111=>1111000
[5,1,3,6,4,2,7,8]=>0011100=>0011100
[6,1,2,4,7,5,3,8]=>0001110=>0111000
[8,3,1,4,6,7,2,5]=>0100011=>1100010
[7,8,5,1,2,6,3,4]=>0001101=>1011000
[6,4,5,1,8,7,3,2]=>0101111=>1111010
[8,6,2,1,7,3,5,4]=>1001111=>1111001
[9,3,4,5,6,8,7,2,1]=>10000111=>11100001
[9,4,3,5,6,7,8,2,1]=>10100011=>11000101
[10,9,3,4,5,6,8,7,2,1]=>100001111=>111100001
[9,8,3,4,5,7,6,2,1]=>10001111=>11110001
[9,8,4,3,5,6,7,2,1]=>10100111=>11100101
[10,9,4,3,5,6,7,8,2,1]=>101000111=>111000101
[11,10,3,4,5,6,7,9,8,2,1]=>1000001111=>1111000001
[10,3,4,5,6,7,9,8,2,1]=>100000111=>111000001
[9,3,4,5,6,2,8,7,1]=>00001111=>11110000
[9,2,4,5,6,8,7,3,1]=>01000111=>11100010
[9,4,3,5,6,7,2,8,1]=>00100111=>11100100
[9,3,2,5,6,7,8,4,1]=>01100011=>11000110
[10,4,3,5,6,7,8,9,2,1]=>101000011=>110000101
[11,10,4,3,5,6,7,8,9,2,1]=>1010000111=>1110000101
[7,8,6,1,4,3,5,2]=>0011101=>1011100
[4,6,3,5,7,2,8,1,9]=>00001110=>01110000
[5,6,3,4,7,2,8,1,9]=>00001110=>01110000
[4,3,6,2,5,7,1,8]=>0010110=>0110100
[1,5,7,4,6,8,3,9,2]=>00000111=>11100000
[1,6,5,7,3,4,8,2]=>0000111=>1110000
[1,6,7,4,5,8,3,9,2]=>00000111=>11100000
[1,7,5,6,8,4,9,3,10,2]=>000001111=>111100000
[1,2,3,4,8,5,9,6,7]=>00000011=>11000000
[1,2,3,4,5,8,6,9,7,10]=>000000110=>011000000
[1,2,3,7,4,5,8,6,9]=>00000110=>01100000
[1,2,3,4,8,6,5,7,9]=>00001010=>01010000
[1,2,3,4,9,7,5,6,8]=>00000101=>10100000
[1,2,3,4,5,9,6,10,7,8]=>000000011=>110000000
[8,2,6,5,1,7,4,3]=>0011111=>1111100
[7,6,4,1,2,5,8,3]=>0010111=>1110100
[2,6,5,4,8,7,1,3]=>0001111=>1111000
[5,6,7,1,3,2,4,8]=>0100010=>0100010
[7,1,8,4,3,2,6,5]=>0110111=>1110110
[2,1,4,9,3,5,6,7,8]=>10000001=>10000001
[3,7,1,2,4,5,6,9,8]=>00000101=>10100000
[3,1,2,6,9,4,5,7,8]=>01000001=>10000010
[4,6,1,2,3,5,9,7,8]=>00001001=>10010000
[1,8,5,2,7,6,4,3]=>0011111=>1111100
[1,7,6,8,2,5,4,3]=>0011011=>1101100
[1,7,8,6,2,5,4,3]=>0011101=>1011100
[4,6,5,7,1,8,2,3]=>0000111=>1110000
[7,5,3,6,8,4,2,1]=>1011011=>1101101
[7,2,5,6,4,8,3,1]=>0100111=>1110010
[7,4,6,2,8,5,3,1]=>0101111=>1111010
[9,7,6,5,4,3,8,2,1]=>10111111=>11111101
[9,8,6,5,4,7,3,2,1]=>11011111=>11111011
[5,4,3,2,1,9,7,8,6]=>11110011=>11001111
[10,8,7,6,5,4,3,9,2,1]=>101111111=>111111101
[10,9,7,6,5,4,8,3,2,1]=>110111111=>111111011
[1,6,3,4,2,5,8,7]=>0010101=>1010100
[1,5,7,6,2,3,8,4]=>0000111=>1110000
[1,4,3,7,6,2,5,8]=>0010110=>0110100
[1,3,7,4,6,8,5,2]=>0001011=>1101000
[3,7,4,6,8,1,5,2]=>0001011=>1101000
[2,6,7,5,3,4,1,8]=>0011010=>0101100
[2,4,1,7,5,6,8,3]=>0010011=>1100100
[7,2,4,8,3,5,1,6]=>0001011=>1101000
[5,6,1,4,3,8,7,2]=>0010111=>1110100
[5,8,6,4,3,1,7,2]=>0110111=>1110110
[4,1,3,7,8,6,5,2]=>0011101=>1011100
Map
descent tops
Description
The descent tops of a permutation as a binary word.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Since 1 is never a descent top, it is omitted and the first letter of the word corresponds to the element 2.
Map
reverse
Description
Return the reversal of a binary word.
searching the database
Sorry, this map was not found in the database.