Identifier
Mp00130:
Permutations
—descent tops⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
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
[8,6,7,4,5,3,2,1]=>1101011=>1101011
[7,6,8,4,5,3,2,1]=>1101011=>1101011
[8,7,5,4,6,3,2,1]=>1101111=>1111011
[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
[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
[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
[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
[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
[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
[7,6,5,4,3,8,2,1]=>1011111=>1111101
[7,5,6,4,3,8,2,1]=>1010111=>1110101
[7,4,5,6,3,8,2,1]=>1000111=>1110001
[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
[7,6,3,4,5,8,2,1]=>1000111=>1110001
[7,5,4,3,6,8,2,1]=>1011011=>1101101
[7,5,3,4,6,8,2,1]=>1001011=>1101001
[6,5,4,3,7,8,2,1]=>1011101=>1011101
[8,7,6,5,4,2,3,1]=>0111111=>1111110
[8,6,7,5,4,2,3,1]=>0111011=>1101110
[7,6,8,5,4,2,3,1]=>0111011=>1101110
[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
[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
[6,5,7,4,8,2,3,1]=>0100111=>1110010
[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
[8,6,5,7,3,2,4,1]=>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
[8,6,7,3,4,2,5,1]=>0011011=>1101100
[7,6,8,3,4,2,5,1]=>0011011=>1101100
[7,6,8,4,2,3,5,1]=>0011011=>1101100
[6,7,8,4,2,3,5,1]=>0011001=>1001100
[8,6,7,3,2,4,5,1]=>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
[8,7,5,3,4,2,6,1]=>0011111=>1111100
[7,8,5,3,4,2,6,1]=>0011101=>1011100
[7,8,4,3,5,2,6,1]=>0011101=>1011100
[8,7,5,3,2,4,6,1]=>0101111=>1111010
[7,8,4,3,2,5,6,1]=>0110101=>1010110
[7,8,3,4,2,5,6,1]=>0010101=>1010100
[7,8,3,2,4,5,6,1]=>0100101=>1010010
[8,6,5,4,3,2,7,1]=>0111111=>1111110
[8,6,4,3,5,2,7,1]=>0011111=>1111100
[8,6,3,4,5,2,7,1]=>0001111=>1111000
[8,4,5,3,6,2,7,1]=>0001111=>1111000
[8,5,6,4,2,3,7,1]=>0010111=>1110100
[8,6,4,2,3,5,7,1]=>0010111=>1110100
[8,5,3,4,2,6,7,1]=>0011011=>1101100
[8,5,4,2,3,6,7,1]=>0011011=>1101100
[7,4,5,6,3,2,8,1]=>0100111=>1110010
[6,4,5,7,3,2,8,1]=>0100111=>1110010
[4,5,6,7,3,2,8,1]=>0100011=>1100010
[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
[5,4,3,6,7,2,8,1]=>0011011=>1101100
[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
[6,7,4,5,2,3,8,1]=>0001011=>1101000
[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
[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
[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
[6,7,3,2,4,5,8,1]=>0100011=>1100010
[6,7,2,3,4,5,8,1]=>0000011=>1100000
[7,5,2,3,4,6,8,1]=>0001011=>1101000
[6,5,4,3,2,7,8,1]=>0111101=>1011110
[5,4,6,3,2,7,8,1]=>0101101=>1011010
[5,4,3,6,2,7,8,1]=>0011101=>1011100
[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
[6,5,2,3,4,7,8,1]=>0001101=>1011000
[5,4,3,2,6,7,8,1]=>0111001=>1001110
[4,3,5,2,6,7,8,1]=>0011001=>1001100
[5,4,2,3,6,7,8,1]=>0011001=>1001100
[4,5,2,3,6,7,8,1]=>0001001=>1001000
[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
[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
[8,7,5,6,4,3,1,2]=>0110111=>1110110
[7,8,5,6,4,3,1,2]=>0110101=>1010110
[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
[5,6,7,8,4,3,1,2]=>0110001=>1000110
[7,8,6,4,5,3,1,2]=>0101101=>1011010
[8,6,7,4,5,3,1,2]=>0101011=>1101010
[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
[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
[5,6,4,7,8,3,1,2]=>0100101=>1010010
[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
[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
[8,5,6,7,3,4,1,2]=>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
[8,7,6,3,4,5,1,2]=>0001111=>1111000
[7,8,6,3,4,5,1,2]=>0001101=>1011000
[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
[7,8,3,4,5,6,1,2]=>0000101=>1010000
[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
[7,6,5,4,3,8,1,2]=>0011111=>1111100
[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
[7,5,6,3,4,8,1,2]=>0000111=>1110000
[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
[6,5,4,3,7,8,1,2]=>0011101=>1011100
[5,4,6,3,7,8,1,2]=>0001101=>1011000
[4,5,6,3,7,8,1,2]=>0000101=>1010000
[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
[7,6,8,5,4,2,1,3]=>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
[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
[7,6,8,4,5,2,1,3]=>1001011=>1101001
[8,7,4,5,6,2,1,3]=>1000111=>1110001
[6,7,5,4,8,2,1,3]=>1001011=>1101001
[7,5,6,4,8,2,1,3]=>1000111=>1110001
[7,6,4,5,8,2,1,3]=>1000111=>1110001
[4,5,6,7,8,2,1,3]=>1000001=>1000001
[8,7,6,5,4,1,2,3]=>0011111=>1111100
[6,7,8,5,4,1,2,3]=>0011001=>1001100
[7,8,5,6,4,1,2,3]=>0010101=>1010100
[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
[8,6,7,4,5,1,2,3]=>0001011=>1101000
[8,7,5,4,6,1,2,3]=>0001111=>1111000
[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
[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
[7,8,5,6,3,1,2,4]=>0100101=>1010010
[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
[7,6,8,5,2,1,3,4]=>1001011=>1101001
[6,7,8,5,2,1,3,4]=>1001001=>1001001
[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
[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
[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
[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
[7,6,8,3,2,1,4,5]=>1100011=>1100011
[6,7,8,3,2,1,4,5]=>1100001=>1000011
[8,7,6,2,3,1,4,5]=>0100111=>1110010
[7,6,8,2,3,1,4,5]=>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
[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
[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
[8,7,5,3,4,2,1,6]=>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
[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
[8,7,5,4,3,1,2,6]=>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
[7,8,5,4,2,1,3,6]=>1011001=>1001101
[7,8,5,4,1,2,3,6]=>0011001=>1001100
[8,7,4,5,1,2,3,6]=>0001011=>1101000
[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
[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
[7,8,4,2,1,3,5,6]=>1010001=>1000101
[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
[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
[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
[8,4,5,6,3,2,1,7]=>1100101=>1010011
[8,6,5,3,4,2,1,7]=>1011101=>1011101
[8,5,6,3,4,2,1,7]=>1010101=>1010101
[8,4,5,3,6,2,1,7]=>1001101=>1011001
[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
[8,6,5,3,2,4,1,7]=>0111101=>1011110
[8,6,5,2,3,4,1,7]=>0011101=>1011100
[8,5,6,2,3,4,1,7]=>0010101=>1010100
[8,6,4,2,3,5,1,7]=>0011101=>1011100
[8,6,3,2,4,5,1,7]=>0101101=>1011010
[8,5,2,3,4,6,1,7]=>0001101=>1011000
[8,6,4,5,3,1,2,7]=>0101101=>1011010
[8,5,6,3,4,1,2,7]=>0010101=>1010100
[8,6,3,4,5,1,2,7]=>0001101=>1011000
[8,4,5,3,6,1,2,7]=>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
[8,5,6,4,1,2,3,7]=>0010101=>1010100
[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
[8,6,3,4,1,2,5,7]=>0010101=>1010100
[8,6,4,2,1,3,5,7]=>1010101=>1010101
[8,6,3,2,1,4,5,7]=>1100101=>1010011
[8,4,5,3,2,1,6,7]=>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
[8,4,2,3,5,1,6,7]=>0011001=>1001100
[8,5,3,4,1,2,6,7]=>0011001=>1001100
[8,5,4,2,1,3,6,7]=>1011001=>1001101
[8,5,3,2,1,4,6,7]=>1101001=>1001011
[8,5,3,1,2,4,6,7]=>0101001=>1001010
[8,4,3,2,1,5,6,7]=>1110001=>1000111
[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
[8,3,2,1,4,5,6,7]=>1100001=>1000011
[8,2,3,1,4,5,6,7]=>0100001=>1000010
[8,3,1,2,4,5,6,7]=>0100001=>1000010
[8,1,2,3,4,5,6,7]=>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
[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
[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
[7,6,3,4,5,2,1,8]=>1001110=>0111001
[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
[5,4,6,3,7,2,1,8]=>1001110=>0111001
[5,4,3,6,7,2,1,8]=>1011010=>0101101
[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
[7,4,5,6,2,3,1,8]=>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
[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
[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
[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
[7,4,5,3,2,6,1,8]=>0101110=>0111010
[7,5,3,4,2,6,1,8]=>0011110=>0111100
[7,4,3,5,2,6,1,8]=>0011110=>0111100
[7,4,5,2,3,6,1,8]=>0001110=>0111000
[7,5,3,2,4,6,1,8]=>0101110=>0111010
[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
[3,4,5,6,2,7,1,8]=>0000110=>0110000
[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
[4,5,2,3,6,7,1,8]=>0001010=>0101000
[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
[7,5,6,3,4,1,2,8]=>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
[3,4,5,6,7,1,2,8]=>0000010=>0100000
[7,4,5,6,2,1,3,8]=>1000110=>0110001
[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
[7,6,5,2,3,1,4,8]=>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
[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
[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
[7,6,2,3,4,1,5,8]=>0010110=>0110100
[6,7,2,3,4,1,5,8]=>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
[6,7,3,1,2,4,5,8]=>0100010=>0100010
[6,7,1,2,3,4,5,8]=>0000010=>0100000
[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
[7,5,3,4,1,2,6,8]=>0011010=>0101100
[7,4,5,1,2,3,6,8]=>0001010=>0101000
[7,5,3,2,1,4,6,8]=>1101010=>0101011
[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
[7,4,3,1,2,5,6,8]=>0110010=>0100110
[7,3,4,1,2,5,6,8]=>0010010=>0100100
[7,3,1,2,4,5,6,8]=>0100010=>0100010
[7,1,2,3,4,5,6,8]=>0000010=>0100000
[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
[5,4,3,6,2,1,7,8]=>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
[5,4,3,2,6,1,7,8]=>0111100=>0011110
[4,5,3,2,6,1,7,8]=>0101100=>0011010
[5,3,2,4,6,1,7,8]=>0101100=>0011010
[6,5,4,3,1,2,7,8]=>0111100=>0011110
[5,6,4,3,1,2,7,8]=>0110100=>0010110
[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
[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
[5,6,3,2,1,4,7,8]=>1100100=>0010011
[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
[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
[5,4,2,1,3,6,7,8]=>1011000=>0001101
[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
[4,5,8,7,6,3,2,1]=>1100111=>1110011
[4,5,7,8,6,3,2,1]=>1100101=>1010011
[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
[3,5,8,7,6,4,2,1]=>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
[3,5,6,7,8,4,2,1]=>1010001=>1000101
[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
[5,4,3,7,8,6,2,1]=>1011101=>1011101
[4,5,3,7,8,6,2,1]=>1001101=>1011001
[4,3,5,7,8,6,2,1]=>1010101=>1010101
[3,4,5,7,8,6,2,1]=>1000101=>1010001
[4,5,6,3,8,7,2,1]=>1000111=>1110001
[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
[5,7,6,4,3,8,2,1]=>1010111=>1110101
[4,7,6,5,3,8,2,1]=>1001111=>1111001
[3,4,7,6,5,8,2,1]=>1000111=>1110001
[4,5,3,7,6,8,2,1]=>1001011=>1101001
[4,3,5,7,6,8,2,1]=>1010011=>1100101
[3,4,6,5,7,8,2,1]=>1000101=>1010001
[2,8,7,6,5,4,3,1]=>0111111=>1111110
[2,7,6,8,5,4,3,1]=>0111011=>1101110
[2,5,6,7,8,4,3,1]=>0110001=>1000110
[2,4,8,7,6,5,3,1]=>0101111=>1111010
[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
[2,4,5,7,8,6,3,1]=>0100101=>1010010
[2,5,6,4,8,7,3,1]=>0100111=>1110010
[2,4,6,5,8,7,3,1]=>0100111=>1110010
[2,7,6,5,4,8,3,1]=>0101111=>1111010
[2,6,7,5,4,8,3,1]=>0101011=>1101010
[2,4,7,6,5,8,3,1]=>0100111=>1110010
[2,6,5,4,7,8,3,1]=>0101101=>1011010
[3,2,8,7,6,5,4,1]=>0111111=>1111110
[3,2,6,8,7,5,4,1]=>0111011=>1101110
[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
[2,3,7,6,5,8,4,1]=>0010111=>1110100
[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
[3,2,4,8,7,6,5,1]=>0101111=>1111010
[2,3,4,8,7,6,5,1]=>0001111=>1111000
[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
[4,3,5,2,8,7,6,1]=>0011111=>1111100
[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
[2,3,5,4,8,7,6,1]=>0001111=>1111000
[4,3,2,5,8,7,6,1]=>0110111=>1110110
[2,4,3,5,8,7,6,1]=>0010111=>1110100
[2,3,4,5,8,7,6,1]=>0000111=>1110000
[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
[2,6,5,4,3,8,7,1]=>0011111=>1111100
[2,4,6,5,3,8,7,1]=>0001111=>1111000
[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
[2,3,4,6,5,8,7,1]=>0000111=>1110000
[5,4,3,2,6,8,7,1]=>0111011=>1101110
[2,5,4,3,6,8,7,1]=>0011011=>1101100
[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
[2,3,4,5,6,8,7,1]=>0000011=>1100000
[4,7,6,5,3,2,8,1]=>0101111=>1111010
[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
[5,4,3,7,6,2,8,1]=>0011111=>1111100
[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
[3,5,4,6,7,2,8,1]=>0001011=>1101000
[2,5,4,7,6,3,8,1]=>0001111=>1111000
[2,4,6,5,7,3,8,1]=>0000111=>1110000
[2,4,5,6,7,3,8,1]=>0000011=>1100000
[3,2,6,7,5,4,8,1]=>0101011=>1101010
[2,3,7,6,5,4,8,1]=>0001111=>1111000
[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
[2,4,3,7,6,5,8,1]=>0010111=>1110100
[3,2,4,7,6,5,8,1]=>0100111=>1110010
[2,3,4,7,6,5,8,1]=>0000111=>1110000
[5,4,3,2,7,6,8,1]=>0111011=>1101110
[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
[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
[2,6,5,4,3,7,8,1]=>0011101=>1011100
[2,5,4,6,3,7,8,1]=>0001101=>1011000
[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
[1,7,6,5,8,4,3,2]=>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
[1,4,5,7,8,6,3,2]=>0100101=>1010010
[1,4,6,5,8,7,3,2]=>0100111=>1110010
[1,5,4,6,8,7,3,2]=>0101011=>1101010
[1,4,7,6,5,8,3,2]=>0100111=>1110010
[1,6,5,4,7,8,3,2]=>0101101=>1011010
[1,5,4,6,7,8,3,2]=>0101001=>1001010
[1,3,8,7,6,5,4,2]=>0011111=>1111100
[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
[1,3,5,7,6,8,4,2]=>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
[1,3,4,8,7,6,5,2]=>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
[1,3,5,4,7,8,6,2]=>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
[1,6,5,4,3,8,7,2]=>0011111=>1111100
[1,5,6,4,3,8,7,2]=>0010111=>1110100
[1,4,6,5,3,8,7,2]=>0001111=>1111000
[1,3,6,5,4,8,7,2]=>0001111=>1111000
[1,4,3,6,5,8,7,2]=>0010111=>1110100
[1,5,4,3,6,8,7,2]=>0011011=>1101100
[1,6,7,5,4,3,8,2]=>0011011=>1101100
[1,3,5,7,6,4,8,2]=>0000111=>1110000
[1,3,4,7,6,5,8,2]=>0000111=>1110000
[1,3,5,4,7,6,8,2]=>0001011=>1101000
[1,4,3,6,5,7,8,2]=>0010101=>1010100
[1,5,4,3,6,7,8,2]=>0011001=>1001100
[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
[2,1,5,7,8,6,4,3]=>1010101=>1010101
[2,1,6,5,8,7,4,3]=>1010111=>1110101
[2,1,7,6,5,8,4,3]=>1010111=>1110101
[2,1,6,7,5,8,4,3]=>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
[2,1,4,6,7,8,5,3]=>1001001=>1001001
[2,1,4,5,8,7,6,3]=>1000111=>1110001
[2,1,4,5,7,8,6,3]=>1000101=>1010001
[2,1,4,6,5,8,7,3]=>1000111=>1110001
[2,1,4,5,6,8,7,3]=>1000011=>1100001
[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
[2,1,4,5,6,7,8,3]=>1000001=>1000001
[1,2,8,7,6,5,4,3]=>0011111=>1111100
[1,2,6,7,8,5,4,3]=>0011001=>1001100
[1,2,6,5,8,7,4,3]=>0010111=>1110100
[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
[1,2,4,6,7,8,5,3]=>0001001=>1001000
[1,2,5,4,8,7,6,3]=>0001111=>1111000
[1,2,5,4,7,8,6,3]=>0001101=>1011000
[1,2,4,5,7,8,6,3]=>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
[1,2,5,7,6,4,8,3]=>0000111=>1110000
[1,2,5,6,7,4,8,3]=>0000011=>1100000
[1,2,4,7,6,5,8,3]=>0000111=>1110000
[1,2,6,5,4,7,8,3]=>0001101=>1011000
[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
[2,3,1,6,8,7,5,4]=>0101011=>1101010
[2,3,1,7,6,8,5,4]=>0101011=>1101010
[2,3,1,6,7,8,5,4]=>0101001=>1001010
[2,3,1,6,5,8,7,4]=>0100111=>1110010
[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
[1,3,2,5,7,8,6,4]=>0100101=>1010010
[1,3,2,6,5,8,7,4]=>0100111=>1110010
[1,3,2,7,6,5,8,4]=>0100111=>1110010
[1,3,2,5,7,6,8,4]=>0100011=>1100010
[1,3,2,6,5,7,8,4]=>0100101=>1010010
[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
[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
[2,4,3,1,6,8,7,5]=>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
[1,4,3,2,7,6,8,5]=>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
[2,1,3,4,7,6,8,5]=>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
[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
[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
[1,3,5,4,2,7,8,6]=>0011001=>1001100
[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
[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
[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
[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
[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
[1,3,2,4,5,7,8,6]=>0100001=>1000010
[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
[5,4,3,6,2,1,8,7]=>1011101=>1011101
[4,5,3,6,2,1,8,7]=>1001101=>1011001
[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
[2,3,6,5,4,1,8,7]=>0011101=>1011100
[2,3,5,6,4,1,8,7]=>0010101=>1010100
[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
[3,4,2,5,6,1,8,7]=>0010101=>1010100
[2,3,4,5,6,1,8,7]=>0000101=>1010000
[1,5,4,6,3,2,8,7]=>0101101=>1011010
[1,3,6,5,4,2,8,7]=>0011101=>1011100
[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
[2,3,1,6,5,4,8,7]=>0101101=>1011010
[2,1,3,6,5,4,8,7]=>1001101=>1011001
[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
[2,1,4,3,6,5,8,7]=>1010101=>1010101
[1,2,4,3,6,5,8,7]=>0010101=>1010100
[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
[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
[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
[4,3,2,1,5,6,8,7]=>1110001=>1000111
[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
[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
[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
[3,4,7,6,5,2,1,8]=>1001110=>0111001
[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
[2,5,6,7,4,3,1,8]=>0110010=>0100110
[2,4,6,7,5,3,1,8]=>0101010=>0101010
[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
[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
[3,2,4,6,7,5,1,8]=>0101010=>0101010
[2,3,4,7,6,5,1,8]=>0001110=>0111000
[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
[3,2,5,4,7,6,1,8]=>0101110=>0111010
[4,3,2,5,7,6,1,8]=>0110110=>0110110
[3,6,5,4,2,7,1,8]=>0011110=>0111100
[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
[3,4,2,6,5,7,1,8]=>0010110=>0110100
[2,4,3,6,5,7,1,8]=>0010110=>0110100
[3,5,4,2,6,7,1,8]=>0011010=>0101100
[2,5,4,3,6,7,1,8]=>0011010=>0101100
[1,5,6,7,4,3,2,8]=>0110010=>0100110
[1,4,6,5,7,3,2,8]=>0100110=>0110010
[1,3,5,7,6,4,2,8]=>0010110=>0110100
[1,3,5,6,7,4,2,8]=>0010010=>0100100
[1,3,5,4,7,6,2,8]=>0001110=>0111000
[1,4,3,5,7,6,2,8]=>0010110=>0110100
[1,5,4,6,3,7,2,8]=>0001110=>0111000
[1,3,6,5,4,7,2,8]=>0001110=>0111000
[1,4,3,6,5,7,2,8]=>0010110=>0110100
[1,5,4,3,6,7,2,8]=>0011010=>0101100
[1,3,4,5,6,7,2,8]=>0000010=>0100000
[2,1,5,6,7,4,3,8]=>1010010=>0100101
[2,1,4,6,7,5,3,8]=>1001010=>0101001
[1,2,5,7,6,4,3,8]=>0010110=>0110100
[1,2,5,6,7,4,3,8]=>0010010=>0100100
[1,2,5,6,4,7,3,8]=>0000110=>0110000
[1,2,5,4,6,7,3,8]=>0001010=>0101000
[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
[1,3,2,5,7,6,4,8]=>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
[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
[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
[3,4,2,5,1,7,6,8]=>0011010=>0101100
[2,4,3,5,1,7,6,8]=>0011010=>0101100
[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
[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
[1,3,2,4,5,7,6,8]=>0100010=>0100010
[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
[4,3,2,6,5,1,7,8]=>0111100=>0011110
[3,5,4,2,6,1,7,8]=>0011100=>0011100
[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
[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
[1,2,4,5,6,3,7,8]=>0000100=>0010000
[3,2,1,5,6,4,7,8]=>1100100=>0010011
[1,3,2,5,6,4,7,8]=>0100100=>0010010
[1,2,3,5,6,4,7,8]=>0000100=>0010000
[4,3,2,1,6,5,7,8]=>1110100=>0010111
[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
[1,3,5,4,2,6,7,8]=>0011000=>0001100
[1,3,4,5,2,6,7,8]=>0001000=>0001000
[1,3,2,5,4,6,7,8]=>0101000=>0001010
[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
[1,2,4,5,8,6,7,3]=>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
[1,2,6,4,5,8,7,3]=>0000111=>1110000
[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
[1,2,7,5,4,6,8,3]=>0001011=>1101000
[1,2,8,5,4,6,7,3]=>0001011=>1101000
[1,2,8,5,4,7,6,3]=>0001111=>1111000
[1,2,8,6,5,4,7,3]=>0001111=>1111000
[1,2,8,7,5,6,4,3]=>0010111=>1110100
[1,3,2,7,5,6,8,4]=>0100011=>1100010
[1,3,2,8,5,7,6,4]=>0100111=>1110010
[1,3,4,5,8,6,7,2]=>0000011=>1100000
[1,3,4,8,5,6,7,2]=>0000011=>1100000
[1,3,6,4,5,2,8,7]=>0001101=>1011000
[1,3,6,4,5,7,2,8]=>0000110=>0110000
[1,3,6,4,5,8,7,2]=>0000111=>1110000
[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
[1,4,3,8,5,6,7,2]=>0010011=>1100100
[1,4,3,8,5,7,6,2]=>0010111=>1110100
[1,4,3,8,6,7,5,2]=>0011011=>1101100
[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
[1,5,3,4,6,7,2,8]=>0001010=>0101000
[1,5,3,4,7,6,2,8]=>0001110=>0111000
[1,5,3,4,8,6,7,2]=>0001011=>1101000
[1,8,3,4,6,7,5,2]=>0001011=>1101000
[1,6,3,5,4,2,7,8]=>0011100=>0011100
[1,6,3,5,4,8,7,2]=>0001111=>1111000
[1,8,3,5,4,7,6,2]=>0001111=>1111000
[1,8,3,5,6,4,7,2]=>0000111=>1110000
[1,8,3,5,7,6,4,2]=>0010111=>1110100
[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
[1,8,4,3,5,6,7,2]=>0010011=>1100100
[1,8,4,3,5,7,6,2]=>0010111=>1110100
[1,7,4,3,6,5,8,2]=>0010111=>1110100
[1,8,4,3,6,7,5,2]=>0011011=>1101100
[1,6,4,5,3,8,7,2]=>0001111=>1111000
[1,8,4,5,6,3,7,2]=>0000111=>1110000
[1,8,4,5,6,7,3,2]=>0100011=>1100010
[1,8,4,6,5,7,3,2]=>0100111=>1110010
[1,8,4,7,6,5,3,2]=>0101111=>1111010
[1,7,5,4,3,6,8,2]=>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
[1,8,6,4,5,7,3,2]=>0100111=>1110010
[1,8,7,4,5,6,3,2]=>0100111=>1110010
[1,8,7,4,6,5,3,2]=>0101111=>1111010
[1,8,6,5,4,7,3,2]=>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
[2,1,4,3,8,6,7,5]=>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
[2,1,8,4,6,5,7,3]=>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
[2,1,8,5,7,6,4,3]=>1010111=>1110101
[2,1,8,7,5,6,4,3]=>1010111=>1110101
[2,3,1,5,8,6,7,4]=>0100011=>1100010
[2,3,1,8,5,6,7,4]=>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
[2,3,6,4,5,1,8,7]=>0001101=>1011000
[2,3,6,4,5,7,8,1]=>0000101=>1010000
[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
[2,3,7,5,4,6,1,8]=>0001110=>0111000
[2,3,7,5,4,6,8,1]=>0001011=>1101000
[2,3,7,5,6,4,1,8]=>0010110=>0110100
[2,3,7,5,6,4,8,1]=>0000111=>1110000
[2,3,8,5,7,6,4,1]=>0010111=>1110100
[2,4,3,1,8,6,7,5]=>0110011=>1100110
[2,4,3,5,8,6,7,1]=>0010011=>1100100
[2,4,3,8,5,6,7,1]=>0010011=>1100100
[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
[2,5,3,4,8,7,6,1]=>0001111=>1111000
[2,6,3,4,5,7,8,1]=>0000101=>1010000
[2,6,3,4,5,8,7,1]=>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
[2,7,3,5,4,6,8,1]=>0001011=>1101000
[2,7,3,5,6,4,8,1]=>0000111=>1110000
[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
[2,5,4,3,8,6,7,1]=>0011011=>1101100
[2,6,4,3,5,7,8,1]=>0010101=>1010100
[2,8,4,3,5,6,7,1]=>0010011=>1100100
[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
[2,7,4,5,6,3,8,1]=>0000111=>1110000
[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
[2,8,5,4,7,6,3,1]=>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
[3,2,4,8,5,6,7,1]=>0100011=>1100010
[3,2,6,4,5,7,1,8]=>0100110=>0110010
[3,2,7,4,6,5,1,8]=>0101110=>0111010
[3,2,7,4,6,5,8,1]=>0100111=>1110010
[3,2,8,5,4,6,7,1]=>0101011=>1101010
[3,2,7,5,6,4,1,8]=>0110110=>0110110
[3,2,8,5,7,6,4,1]=>0110111=>1110110
[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
[4,2,3,1,7,6,8,5]=>0110011=>1100110
[4,2,3,1,8,6,7,5]=>0110011=>1100110
[4,2,3,1,8,7,6,5]=>0110111=>1110110
[4,2,3,5,1,7,8,6]=>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
[4,2,3,6,5,1,7,8]=>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
[4,2,3,8,5,6,7,1]=>0010011=>1100100
[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
[5,2,3,4,1,8,7,6]=>0011011=>1101100
[5,2,3,4,8,7,6,1]=>0001111=>1111000
[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
[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
[7,2,3,6,5,4,1,8]=>0011110=>0111100
[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
[5,2,4,3,7,6,1,8]=>0011110=>0111100
[5,2,4,3,7,6,8,1]=>0011011=>1101100
[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
[8,2,4,3,7,6,5,1]=>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
[8,2,4,7,5,6,3,1]=>0100111=>1110010
[8,2,4,7,6,5,3,1]=>0101111=>1111010
[6,2,5,4,3,1,8,7]=>0111101=>1011110
[7,2,5,4,3,6,1,8]=>0011110=>0111100
[8,2,5,4,3,7,6,1]=>0011111=>1111100
[8,2,5,4,7,6,3,1]=>0101111=>1111010
[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
[8,2,6,5,4,3,7,1]=>0011111=>1111100
[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
[4,3,2,8,6,7,5,1]=>0111011=>1101110
[5,3,2,4,1,6,8,7]=>0111001=>1001110
[5,3,2,4,1,8,7,6]=>0111011=>1101110
[5,3,2,4,6,1,8,7]=>0101101=>1011010
[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
[8,3,2,5,4,7,6,1]=>0101111=>1111010
[8,3,2,5,6,4,7,1]=>0100111=>1110010
[8,3,2,5,7,6,4,1]=>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
[7,3,4,6,5,2,1,8]=>1001110=>0111001
[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
[8,3,5,4,2,6,7,1]=>0011011=>1101100
[7,3,5,4,6,2,1,8]=>1001110=>0111001
[8,3,5,4,7,6,2,1]=>1001111=>1111001
[7,3,6,4,5,2,1,8]=>1001110=>0111001
[8,3,7,4,5,6,2,1]=>1000111=>1110001
[7,3,6,5,4,2,1,8]=>1011110=>0111101
[8,3,7,5,6,4,2,1]=>1010111=>1110101
[5,4,3,2,8,6,7,1]=>0111011=>1101110
[7,4,3,2,6,5,1,8]=>0111110=>0111110
[7,4,3,2,6,5,8,1]=>0110111=>1110110
[8,4,3,2,6,7,5,1]=>0111011=>1101110
[8,4,3,2,7,6,5,1]=>0111111=>1111110
[6,4,3,5,2,1,8,7]=>1011101=>1011101
[8,4,3,5,7,6,2,1]=>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
[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
[8,6,3,5,4,2,7,1]=>0011111=>1111100
[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
[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
[2,4,1,6,3,7,5,8]=>0010110=>0110100
[2,4,6,1,3,7,5,8]=>0000110=>0110000
[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
[2,4,1,6,7,3,8,5]=>0010011=>1100100
[2,4,6,1,7,3,8,5]=>0000111=>1110000
[2,4,6,7,1,3,8,5]=>0000011=>1100000
[2,4,1,6,7,8,3,5]=>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
[2,4,1,7,3,5,8,6]=>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
[2,4,1,7,8,3,5,6]=>0010001=>1000100
[2,4,7,1,8,3,5,6]=>0000011=>1100000
[2,4,1,5,3,7,6,8]=>0011010=>0101100
[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
[2,4,5,7,8,1,3,6]=>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
[2,4,1,5,3,8,6,7]=>0011001=>1001100
[2,1,4,5,8,3,6,7]=>1000001=>1000001
[2,4,1,5,8,3,6,7]=>0010001=>1000100
[2,4,5,8,1,3,6,7]=>0000001=>1000000
[2,4,1,5,6,3,8,7]=>0010101=>1010100
[2,1,4,5,6,8,3,7]=>1000001=>1000001
[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
[2,4,1,5,6,3,7,8]=>0010100=>0010100
[2,4,5,1,6,3,7,8]=>0001100=>0011000
[2,4,5,6,1,3,7,8]=>0000100=>0010000
[2,4,5,6,7,1,3,8]=>0000010=>0100000
[2,4,1,5,6,7,8,3]=>0010001=>1000100
[2,4,5,6,7,1,8,3]=>0000011=>1100000
[2,1,5,3,6,4,8,7]=>1001101=>1011001
[2,1,5,6,3,4,8,7]=>1000101=>1010001
[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
[2,5,1,6,8,3,4,7]=>0001001=>1001000
[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
[2,1,5,3,6,7,8,4]=>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
[2,1,5,6,7,8,3,4]=>1000001=>1000001
[2,5,1,6,7,8,3,4]=>0001001=>1001000
[2,5,6,1,7,8,3,4]=>0000101=>1010000
[2,5,6,7,8,1,3,4]=>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
[2,5,1,3,7,4,6,8]=>0001010=>0101000
[2,1,5,7,3,4,6,8]=>1000010=>0100001
[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
[2,3,5,7,1,8,4,6]=>0000011=>1100000
[2,1,5,3,8,4,6,7]=>1001001=>1001001
[2,1,5,8,3,4,6,7]=>1000001=>1000001
[2,5,1,8,3,4,6,7]=>0001001=>1001000
[2,3,5,1,4,8,6,7]=>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
[2,3,5,6,1,8,4,7]=>0000101=>1010000
[2,3,5,6,8,1,4,7]=>0000001=>1000000
[2,5,1,3,4,6,7,8]=>0001000=>0001000
[2,3,5,6,1,4,7,8]=>0000100=>0010000
[2,3,5,6,1,7,4,8]=>0000110=>0110000
[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
[2,6,7,1,3,4,8,5]=>0000011=>1100000
[2,1,6,3,7,8,4,5]=>1000101=>1010001
[2,1,6,7,3,8,4,5]=>1000011=>1100001
[2,6,1,7,3,8,4,5]=>0000111=>1110000
[2,1,6,7,8,3,4,5]=>1000001=>1000001
[2,6,1,7,8,3,4,5]=>0000101=>1010000
[2,6,7,8,1,3,4,5]=>0000001=>1000000
[2,6,1,7,3,4,5,8]=>0000110=>0110000
[2,6,7,1,3,4,5,8]=>0000010=>0100000
[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
[2,3,6,1,4,7,8,5]=>0000101=>1010000
[2,1,3,6,7,4,8,5]=>1000011=>1100001
[2,3,6,7,1,4,8,5]=>0000011=>1100000
[2,3,1,6,7,8,4,5]=>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
[2,6,1,8,3,4,5,7]=>0000101=>1010000
[2,6,8,1,3,4,5,7]=>0000001=>1000000
[2,1,6,3,4,8,5,7]=>1000101=>1010001
[2,3,1,6,4,8,5,7]=>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
[2,3,6,1,4,5,8,7]=>0000101=>1010000
[2,3,4,1,6,8,5,7]=>0010001=>1000100
[2,3,4,6,1,8,5,7]=>0000101=>1010000
[2,3,6,1,4,5,7,8]=>0000100=>0010000
[2,3,4,6,7,8,1,5]=>0000001=>1000000
[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
[2,1,3,7,4,8,5,6]=>1000011=>1100001
[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
[2,3,1,7,4,5,8,6]=>0100011=>1100010
[2,3,7,1,4,5,8,6]=>0000011=>1100000
[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
[2,3,4,7,8,1,5,6]=>0000001=>1000000
[2,3,4,1,7,5,6,8]=>0010010=>0100100
[2,3,4,7,1,5,6,8]=>0000010=>0100000
[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
[2,3,4,1,5,8,6,7]=>0010001=>1000100
[2,3,4,5,8,1,6,7]=>0000001=>1000000
[3,1,4,2,6,5,8,7]=>0110101=>1010110
[3,4,1,2,6,5,8,7]=>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
[3,1,4,6,8,2,5,7]=>0100001=>1000010
[3,4,1,6,8,2,5,7]=>0010001=>1000100
[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
[3,1,4,2,6,7,8,5]=>0110001=>1000110
[3,4,1,2,6,7,8,5]=>0010001=>1000100
[3,4,6,1,2,7,8,5]=>0000101=>1010000
[3,4,6,1,7,2,8,5]=>0000111=>1110000
[3,1,4,6,7,8,2,5]=>0100001=>1000010
[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
[3,4,7,1,2,5,8,6]=>0000011=>1100000
[3,1,4,2,7,8,5,6]=>0110001=>1000110
[3,4,1,2,7,8,5,6]=>0010001=>1000100
[3,4,7,1,8,2,5,6]=>0000011=>1100000
[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
[3,1,4,2,5,7,8,6]=>0110001=>1000110
[3,4,1,2,5,7,8,6]=>0010001=>1000100
[3,1,4,5,2,7,8,6]=>0101001=>1001010
[3,4,1,5,7,2,8,6]=>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
[3,1,4,2,8,5,6,7]=>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
[3,4,1,5,8,2,6,7]=>0010001=>1000100
[3,4,5,8,1,2,6,7]=>0000001=>1000000
[3,4,1,2,5,6,8,7]=>0010001=>1000100
[3,1,4,5,6,2,8,7]=>0100101=>1010010
[3,4,5,1,6,2,8,7]=>0001101=>1011000
[3,4,5,6,1,2,8,7]=>0000101=>1010000
[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
[3,4,1,5,6,2,7,8]=>0010100=>0010100
[3,4,5,1,6,2,7,8]=>0001100=>0011000
[3,4,1,5,6,7,2,8]=>0010010=>0100100
[3,4,5,6,1,7,2,8]=>0000110=>0110000
[3,1,4,5,6,7,8,2]=>0100001=>1000010
[3,4,5,1,6,7,8,2]=>0001001=>1001000
[3,4,5,6,1,7,8,2]=>0000101=>1010000
[3,1,5,2,6,4,8,7]=>0101101=>1011010
[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
[3,5,1,2,6,8,4,7]=>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
[3,1,5,6,2,4,7,8]=>0100100=>0010010
[3,5,1,6,2,4,7,8]=>0001100=>0011000
[3,5,6,1,2,4,7,8]=>0000100=>0010000
[3,5,1,6,2,7,4,8]=>0001110=>0111000
[3,5,6,1,2,7,4,8]=>0000110=>0110000
[3,5,6,1,7,2,4,8]=>0000110=>0110000
[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
[3,1,5,6,7,8,2,4]=>0100001=>1000010
[3,5,1,6,7,8,2,4]=>0001001=>1001000
[3,5,6,1,7,8,2,4]=>0000101=>1010000
[3,5,6,7,8,1,2,4]=>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
[3,1,5,7,8,2,4,6]=>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
[3,5,1,2,4,7,8,6]=>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
[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
[3,5,1,2,4,6,8,7]=>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
[3,5,1,2,4,6,7,8]=>0001000=>0001000
[1,3,5,2,4,6,7,8]=>0001000=>0001000
[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
[1,3,5,6,2,7,8,4]=>0000101=>1010000
[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
[3,1,6,7,2,8,4,5]=>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
[3,1,6,7,2,4,5,8]=>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
[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
[1,3,6,2,7,4,8,5]=>0000111=>1110000
[1,3,6,7,2,4,8,5]=>0000011=>1100000
[1,3,6,2,7,8,4,5]=>0000101=>1010000
[3,1,6,2,8,4,5,7]=>0100101=>1010010
[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
[3,1,6,2,4,5,8,7]=>0100101=>1010010
[3,1,2,6,4,5,8,7]=>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
[1,3,2,6,4,5,7,8]=>0100100=>0010010
[1,3,6,2,4,5,7,8]=>0000100=>0010000
[3,1,2,4,6,7,5,8]=>0100010=>0100010
[3,1,2,4,6,7,8,5]=>0100001=>1000010
[1,3,4,6,7,2,8,5]=>0000011=>1100000
[3,7,1,2,8,4,5,6]=>0000011=>1100000
[3,1,7,8,2,4,5,6]=>0100001=>1000010
[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
[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
[1,3,4,7,2,5,8,6]=>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
[3,7,1,2,4,5,6,8]=>0000010=>0100000
[1,3,2,7,4,5,6,8]=>0100010=>0100010
[3,1,2,4,7,5,6,8]=>0100010=>0100010
[1,3,4,5,7,2,6,8]=>0000010=>0100000
[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
[3,1,2,8,4,5,6,7]=>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
[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
[4,1,5,6,8,2,3,7]=>0010001=>1000100
[4,5,6,8,1,2,3,7]=>0000001=>1000000
[4,1,5,6,2,3,7,8]=>0010100=>0010100
[4,5,1,6,2,3,7,8]=>0001100=>0011000
[4,5,1,6,2,7,3,8]=>0001110=>0111000
[4,1,5,6,7,2,3,8]=>0010010=>0100100
[4,5,1,6,7,2,3,8]=>0001010=>0101000
[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
[4,1,5,6,7,2,8,3]=>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
[4,5,1,6,7,8,2,3]=>0001001=>1001000
[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
[4,1,5,2,7,8,3,6]=>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
[4,1,5,2,7,3,6,8]=>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
[4,5,1,2,3,7,6,8]=>0001010=>0101000
[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
[4,1,2,5,6,8,3,7]=>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
[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
[4,1,2,5,6,7,3,8]=>0010010=>0100100
[1,4,2,5,6,7,3,8]=>0010010=>0100100
[1,4,5,6,7,2,3,8]=>0000010=>0100000
[4,1,2,5,6,7,8,3]=>0010001=>1000100
[1,4,5,2,6,7,8,3]=>0001001=>1001000
[1,4,5,6,7,2,8,3]=>0000011=>1100000
[4,1,6,2,7,3,8,5]=>0010111=>1110100
[4,1,6,7,2,3,8,5]=>0010011=>1100100
[4,6,7,1,2,3,8,5]=>0000011=>1100000
[4,6,1,2,7,8,3,5]=>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
[4,1,6,2,3,7,5,8]=>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
[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
[1,4,2,6,7,8,3,5]=>0010001=>1000100
[1,4,6,2,7,8,3,5]=>0000101=>1010000
[1,4,6,7,2,8,3,5]=>0000011=>1100000
[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
[4,6,1,2,3,8,5,7]=>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
[4,1,2,6,3,5,8,7]=>0010101=>1010100
[1,4,2,6,3,5,8,7]=>0010101=>1010100
[4,1,2,3,6,5,8,7]=>0010101=>1010100
[1,4,2,3,6,5,8,7]=>0010101=>1010100
[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
[1,4,2,6,3,5,7,8]=>0010100=>0010100
[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
[4,1,2,3,6,7,8,5]=>0010001=>1000100
[1,4,2,3,6,7,8,5]=>0010001=>1000100
[1,2,4,6,7,3,8,5]=>0000011=>1100000
[4,1,7,2,8,3,5,6]=>0010011=>1100100
[4,7,1,2,8,3,5,6]=>0000011=>1100000
[4,7,1,8,2,3,5,6]=>0000011=>1100000
[4,1,7,2,3,8,5,6]=>0010011=>1100100
[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
[4,1,7,2,3,5,8,6]=>0010011=>1100100
[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
[1,2,4,3,7,5,8,6]=>0010011=>1100100
[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
[1,4,2,7,3,5,6,8]=>0010010=>0100100
[4,1,2,3,7,5,6,8]=>0010010=>0100100
[1,4,2,3,7,5,6,8]=>0010010=>0100100
[4,1,2,3,5,7,6,8]=>0010010=>0100100
[1,4,2,3,5,7,6,8]=>0010010=>0100100
[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
[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
[5,1,6,7,2,8,3,4]=>0001011=>1101000
[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
[5,1,6,2,3,7,4,8]=>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
[1,5,6,7,2,3,4,8]=>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
[1,5,6,7,8,2,3,4]=>0000001=>1000000
[5,1,6,2,8,3,4,7]=>0001101=>1011000
[5,6,1,2,8,3,4,7]=>0000101=>1010000
[5,6,8,1,2,3,4,7]=>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
[5,1,2,6,3,4,8,7]=>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
[1,2,5,6,3,4,7,8]=>0000100=>0010000
[5,1,2,3,6,7,4,8]=>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
[1,2,5,6,7,8,3,4]=>0000001=>1000000
[5,1,7,2,8,3,4,6]=>0001011=>1101000
[5,7,1,2,8,3,4,6]=>0000011=>1100000
[5,7,8,1,2,3,4,6]=>0000001=>1000000
[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
[5,1,2,7,3,4,8,6]=>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
[5,7,1,2,3,4,6,8]=>0000010=>0100000
[5,1,2,7,3,4,6,8]=>0001010=>0101000
[1,5,2,7,3,4,6,8]=>0001010=>0101000
[1,2,5,7,3,4,6,8]=>0000010=>0100000
[1,5,2,3,4,7,6,8]=>0001010=>0101000
[1,2,3,5,7,4,6,8]=>0000010=>0100000
[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
[5,1,2,8,3,4,6,7]=>0001001=>1001000
[1,5,2,8,3,4,6,7]=>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
[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
[1,5,2,3,4,6,8,7]=>0001001=>1001000
[1,2,3,5,6,8,4,7]=>0000001=>1000000
[1,5,2,3,4,6,7,8]=>0001000=>0001000
[6,1,7,2,8,3,4,5]=>0000111=>1110000
[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
[1,6,2,7,3,8,4,5]=>0000111=>1110000
[1,6,7,2,3,8,4,5]=>0000011=>1100000
[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
[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
[1,2,6,3,7,8,4,5]=>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
[1,6,2,7,3,4,5,8]=>0000110=>0110000
[1,6,7,2,3,4,5,8]=>0000010=>0100000
[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
[6,1,2,8,3,4,5,7]=>0000101=>1010000
[1,6,2,8,3,4,5,7]=>0000101=>1010000
[1,6,8,2,3,4,5,7]=>0000001=>1000000
[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
[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
[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
[7,1,2,8,3,4,5,6]=>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
[1,2,7,8,3,4,5,6]=>0000001=>1000000
[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
[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
[3,2,5,1,4,6,7,8]=>0101000=>0001010
[5,2,4,1,3,6,7,8]=>0011000=>0001100
[3,2,6,1,4,5,7,8]=>0100100=>0010010
[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
[7,4,6,1,2,3,5,8]=>0000110=>0110000
[3,2,8,1,4,5,6,7]=>0100001=>1000010
[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
[6,5,8,1,2,3,4,7]=>0000101=>1010000
[7,5,8,1,2,3,4,6]=>0000011=>1100000
[8,3,5,1,2,4,6,7]=>0001001=>1001000
[8,3,6,1,2,4,5,7]=>0000101=>1010000
[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
[5,3,4,7,1,2,6,8]=>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
[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
[3,2,7,8,1,4,5,6]=>0100001=>1000010
[4,3,7,8,1,2,5,6]=>0010001=>1000100
[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
[7,3,5,8,1,2,4,6]=>0000011=>1100000
[7,4,5,8,1,2,3,6]=>0000011=>1100000
[8,2,5,6,1,3,4,7]=>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
[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
[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
[5,7,2,6,1,3,4,8]=>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
[5,8,3,6,1,2,4,7]=>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
[6,4,2,5,1,3,7,8]=>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
[6,5,3,7,1,2,4,8]=>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
[7,4,3,6,1,2,5,8]=>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
[6,4,3,8,1,2,5,7]=>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
[7,5,3,8,1,2,4,6]=>0001011=>1101000
[7,6,2,8,1,3,4,5]=>0000111=>1110000
[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
[8,6,2,5,1,3,4,7]=>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
[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
[5,7,3,4,8,1,2,6]=>0000011=>1100000
[3,7,2,6,8,1,4,5]=>0000011=>1100000
[4,7,3,6,8,1,2,5]=>0000011=>1100000
[5,7,4,6,8,1,2,3]=>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
[3,8,2,6,7,1,4,5]=>0000011=>1100000
[4,8,3,6,7,1,2,5]=>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
[7,3,2,6,8,1,4,5]=>0100011=>1100010
[7,5,3,6,8,1,2,4]=>0001011=>1101000
[7,6,3,5,8,1,2,4]=>0000111=>1110000
[8,4,2,5,7,1,3,6]=>0010011=>1100100
[8,5,2,6,7,1,3,4]=>0001011=>1101000
[8,5,3,6,7,1,2,4]=>0001011=>1101000
[8,6,2,5,7,1,3,4]=>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
[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
[6,4,8,2,5,1,3,7]=>0001101=>1011000
[6,4,8,3,5,1,2,7]=>0001101=>1011000
[6,5,8,3,4,1,2,7]=>0010101=>1010100
[4,3,8,2,7,1,5,6]=>0010011=>1100100
[5,4,8,2,7,1,3,6]=>0001011=>1101000
[6,4,8,2,7,1,3,5]=>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
[8,3,6,2,5,1,4,7]=>0001101=>1011000
[8,4,6,2,5,1,3,7]=>0001101=>1011000
[8,3,7,2,5,1,4,6]=>0001011=>1101000
[8,4,7,3,5,1,2,6]=>0001011=>1101000
[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
[5,4,3,2,8,1,6,7]=>0111001=>1001110
[6,5,3,2,8,1,4,7]=>0101101=>1011010
[6,5,4,3,8,1,2,7]=>0011101=>1011100
[7,5,3,2,8,1,4,6]=>0101011=>1101010
[7,6,4,3,8,1,2,5]=>0010111=>1110100
[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
[8,6,5,2,4,1,3,7]=>0011101=>1011100
[8,5,3,2,7,1,4,6]=>0101011=>1101010
[8,6,3,2,7,1,4,5]=>0100111=>1110010
[8,6,5,3,7,1,2,4]=>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
[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
[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
[8,6,3,7,2,5,1,4]=>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
[8,7,4,6,3,5,1,2]=>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
[8,5,4,3,2,7,1,6]=>0111011=>1101110
[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
[8,7,6,5,2,4,1,3]=>0011111=>1111100
[8,1,2,3,7,4,5,6]=>0000011=>1100000
[8,1,2,5,3,4,6,7]=>0001001=>1001000
[6,1,2,5,3,8,4,7]=>0001101=>1011000
[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
[8,1,2,7,6,3,4,5]=>0000111=>1110000
[7,1,2,5,6,3,8,4]=>0000111=>1110000
[4,1,2,5,8,7,3,6]=>0010011=>1100100
[8,1,2,5,6,7,3,4]=>0000011=>1100000
[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
[7,1,5,2,3,4,8,6]=>0001011=>1101000
[6,1,5,2,3,8,4,7]=>0001101=>1011000
[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
[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
[5,1,4,2,8,7,3,6]=>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
[3,1,8,6,2,4,5,7]=>0100101=>1010010
[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
[8,1,4,5,2,3,6,7]=>0001001=>1001000
[7,1,8,6,2,3,4,5]=>0000111=>1110000
[7,1,6,5,2,3,8,4]=>0001111=>1111000
[3,1,4,8,6,2,5,7]=>0100101=>1010010
[3,1,8,5,7,2,4,6]=>0100011=>1100010
[3,1,7,5,6,2,8,4]=>0100111=>1110010
[8,1,4,5,7,2,3,6]=>0000011=>1100000
[8,1,4,7,6,2,3,5]=>0000111=>1110000
[3,1,4,5,8,7,2,6]=>0100011=>1100010
[3,1,8,5,6,7,2,4]=>0100011=>1100010
[8,1,4,5,6,7,2,3]=>0000011=>1100000
[2,8,1,3,7,4,5,6]=>0000011=>1100000
[2,8,1,3,6,7,4,5]=>0000011=>1100000
[2,4,1,8,3,7,5,6]=>0010011=>1100100
[2,6,1,5,3,8,4,7]=>0001101=>1011000
[2,6,1,5,3,7,8,4]=>0001101=>1011000
[2,4,1,8,6,3,5,7]=>0010101=>1010100
[2,8,1,5,7,3,4,6]=>0000011=>1100000
[2,8,1,7,6,3,4,5]=>0000111=>1110000
[2,4,1,5,8,7,3,6]=>0010011=>1100100
[7,3,1,2,4,5,8,6]=>0100011=>1100010
[6,3,1,2,4,8,5,7]=>0100101=>1010010
[6,3,1,2,4,7,8,5]=>0100101=>1010010
[5,3,1,2,8,4,6,7]=>0101001=>1001010
[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
[5,3,1,2,8,7,4,6]=>0101011=>1101010
[5,3,1,2,6,7,8,4]=>0101001=>1001010
[7,6,1,2,3,4,8,5]=>0000111=>1110000
[8,6,1,2,3,7,4,5]=>0000111=>1110000
[5,4,1,2,8,3,6,7]=>0011001=>1001100
[8,4,1,2,7,3,5,6]=>0010011=>1100100
[7,4,1,2,6,3,8,5]=>0010111=>1110100
[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
[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
[4,3,1,6,2,7,8,5]=>0110101=>1010110
[8,3,1,5,2,4,6,7]=>0101001=>1001010
[8,3,1,6,2,4,5,7]=>0100101=>1010010
[7,3,1,6,2,4,8,5]=>0100111=>1110010
[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
[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
[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
[8,4,1,6,2,7,3,5]=>0010111=>1110100
[6,8,1,5,2,7,3,4]=>0001011=>1101000
[6,4,1,5,2,7,8,3]=>0011101=>1011100
[4,3,1,8,7,2,5,6]=>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
[7,8,1,5,6,2,3,4]=>0000101=>1010000
[4,3,1,5,6,8,2,7]=>0110001=>1000110
[8,4,1,5,6,7,2,3]=>0010011=>1100100
[4,3,1,5,6,7,8,2]=>0110001=>1000110
[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
[2,6,4,1,3,8,5,7]=>0010101=>1010100
[2,6,4,1,3,7,8,5]=>0010101=>1010100
[2,7,5,1,3,4,8,6]=>0001011=>1101000
[2,6,8,1,3,7,4,5]=>0000011=>1100000
[2,6,5,1,3,7,8,4]=>0001101=>1011000
[2,8,4,1,7,3,5,6]=>0010011=>1100100
[2,7,4,1,6,3,8,5]=>0010111=>1110100
[2,8,5,1,7,3,4,6]=>0001011=>1101000
[2,7,5,1,6,3,8,4]=>0001111=>1111000
[2,8,4,1,6,7,3,5]=>0010011=>1100100
[2,5,4,1,6,7,8,3]=>0011001=>1001100
[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
[8,3,5,1,2,7,4,6]=>0001011=>1101000
[6,3,8,1,2,7,4,5]=>0000111=>1110000
[7,5,4,1,2,3,8,6]=>0011011=>1101100
[6,7,4,1,2,3,8,5]=>0010011=>1100100
[6,8,5,1,2,3,4,7]=>0001001=>1001000
[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
[8,3,4,1,7,2,5,6]=>0010011=>1100100
[8,3,5,1,6,2,4,7]=>0001101=>1011000
[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
[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
[5,3,4,1,6,7,8,2]=>0011001=>1001100
[2,3,4,8,1,7,5,6]=>0000011=>1100000
[2,3,7,6,1,4,8,5]=>0000111=>1110000
[2,3,6,5,1,8,4,7]=>0001101=>1011000
[2,3,6,5,1,7,8,4]=>0001101=>1011000
[2,8,4,5,1,3,6,7]=>0001001=>1001000
[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
[2,7,6,5,1,3,8,4]=>0001111=>1111000
[2,6,4,5,1,8,3,7]=>0001101=>1011000
[2,8,4,6,1,7,3,5]=>0000111=>1110000
[7,3,8,5,1,2,4,6]=>0001011=>1101000
[8,6,4,5,1,7,2,3]=>0001111=>1111000
[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
[2,3,8,5,7,1,4,6]=>0000011=>1100000
[2,3,7,5,6,1,8,4]=>0000111=>1110000
[2,8,4,7,6,1,3,5]=>0000111=>1110000
[2,8,7,5,6,1,3,4]=>0000111=>1110000
[8,3,4,7,6,1,2,5]=>0000111=>1110000
[8,3,7,5,6,1,2,4]=>0000111=>1110000
[2,3,4,5,8,7,1,6]=>0000011=>1100000
[2,3,4,8,6,7,1,5]=>0000011=>1100000
[2,8,4,5,6,7,1,3]=>0000011=>1100000
[6,5,8,7,3,4,1,2]=>0010111=>1110100
[4,6,7,3,8,5,1,2]=>0001011=>1101000
[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
[3,5,2,7,1,8,6,4]=>0001111=>1111000
[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
[4,6,7,2,8,1,5,3]=>0001011=>1101000
[5,6,7,8,2,1,4,3]=>1010001=>1000101
[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
[4,5,2,3,7,6,1,8]=>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
[8,7,5,4,1,3,2,6]=>0111011=>1101110
[5,8,6,2,4,1,3,7]=>0010101=>1010100
[4,8,2,6,5,1,3,7]=>0001101=>1011000
[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
[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
[1,6,7,8,3,4,5,2]=>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
[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
[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
[7,5,1,3,8,2,6,4]=>0001111=>1111000
[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
[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
[8,7,1,6,5,3,2,4]=>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
[8,1,7,6,5,4,2,3]=>0011111=>1111100
[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
[4,2,5,3,6,1,8,7]=>0011101=>1011100
[4,1,5,3,6,2,8,7]=>0011101=>1011100
[4,3,5,2,7,1,8,6]=>0011011=>1101100
[4,3,5,1,7,2,8,6]=>0011011=>1101100
[4,1,5,3,7,2,8,6]=>0011011=>1101100
[2,1,5,4,7,3,8,6]=>1001011=>1101001
[4,3,6,5,7,1,8,2]=>0010111=>1110100
[5,3,6,4,7,1,8,2]=>0001111=>1111000
[4,1,6,3,7,5,8,2]=>0010111=>1110100
[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
[5,3,6,2,7,4,8,1]=>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
[4,2,6,1,7,3,8,5]=>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
[4,2,6,1,7,5,8,3]=>0010111=>1110100
[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
[5,4,6,2,7,1,8,3]=>0001111=>1111000
[5,1,6,4,7,2,8,3]=>0001111=>1111000
[3,1,6,5,7,2,8,4]=>0100111=>1110010
[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
[8,6,1,3,4,2,5,7]=>0010101=>1010100
[8,3,5,2,1,6,4,7]=>1001101=>1011001
[8,6,3,5,2,4,1,7]=>0011101=>1011100
[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
[8,1,2,4,5,6,3,7]=>0000101=>1010000
[8,2,5,1,3,6,4,7]=>0001101=>1011000
[8,6,1,4,5,3,2,7]=>0101101=>1011010
[8,1,5,6,4,3,2,7]=>0110101=>1010110
[8,5,7,4,3,2,6,1]=>0110111=>1110110
[8,5,7,4,2,1,6,3]=>1010111=>1110101
[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
[3,1,5,8,6,7,4,2]=>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
[1,7,3,5,6,8,2,4]=>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
[5,2,7,1,3,8,4,6]=>0001011=>1101000
[5,3,1,7,8,2,4,6]=>0101001=>1001010
[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
[1,7,3,4,2,5,8,6]=>0010011=>1100100
[4,7,2,1,3,5,8,6]=>1000011=>1100001
[8,7,6,1,3,4,2,5]=>0010111=>1110100
[8,5,7,3,2,1,6,4]=>1100111=>1110011
[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
[8,5,3,7,1,6,2,4]=>0001111=>1111000
[8,5,7,2,1,3,6,4]=>1000111=>1110001
[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
[2,7,6,8,5,4,1,3]=>0011011=>1101100
[1,7,2,5,8,6,4,3]=>0010111=>1110100
[3,7,8,1,6,5,2,4]=>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
[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
[4,2,6,5,3,8,1,7]=>0011101=>1011100
[5,3,1,6,8,2,4,7]=>0101001=>1001010
[5,6,2,8,1,3,4,7]=>0000101=>1010000
[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
[1,4,7,5,8,3,2,6]=>0100011=>1100010
[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
[4,3,7,1,8,6,5,2]=>0011111=>1111100
[4,8,3,7,6,5,2,1]=>1001111=>1111001
[7,5,3,1,8,6,4,2]=>0111111=>1111110
[1,5,8,6,3,7,4,2]=>0010111=>1110100
[6,2,8,7,4,5,1,3]=>0001111=>1111000
[6,1,7,5,3,2,8,4]=>0101111=>1111010
[5,2,6,3,8,7,4,1]=>0011111=>1111100
[6,5,2,1,7,3,8,4]=>1001111=>1111001
[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
[2,4,8,6,3,7,5,1]=>0001111=>1111000
[3,8,6,2,4,7,5,1]=>0001111=>1111000
[3,5,2,7,1,8,4,6]=>0001011=>1101000
[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
[7,8,3,6,2,1,5,4]=>1001101=>1011001
[8,7,3,6,2,5,4,1]=>0011111=>1111100
[4,2,6,8,1,7,5,3]=>0011011=>1101100
[5,4,8,2,7,1,6,3]=>0001111=>1111000
[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
[6,4,8,1,7,2,5,3]=>0001111=>1111000
[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
[6,1,7,2,8,5,4,3]=>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
[4,1,3,2,6,5,8,7]=>0110101=>1010110
[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
[3,5,2,6,4,1,8,7]=>0011101=>1011100
[6,1,2,4,5,3,8,7]=>0001101=>1011000
[5,6,3,2,1,4,8,7]=>1100101=>1010011
[2,1,6,3,5,4,8,7]=>1001101=>1011001
[6,4,3,5,1,2,8,7]=>0011101=>1011100
[5,3,1,4,6,2,8,7]=>0101101=>1011010
[5,7,4,6,2,8,3,1]=>0100111=>1110010
[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
[3,4,8,6,5,7,1,2]=>0000111=>1110000
[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
[8,5,3,7,4,1,6,2]=>0011111=>1111100
[2,1,5,7,4,8,6,3]=>1000111=>1110001
[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
[2,8,1,3,6,5,7,4]=>0000111=>1110000
[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
[8,7,1,6,3,4,2,5]=>0010111=>1110100
[5,3,8,7,4,2,6,1]=>0011111=>1111100
[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
[4,1,3,2,8,5,7,6]=>0110011=>1100110
[2,1,4,3,8,5,7,6]=>1010011=>1100101
[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
[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
[7,1,4,2,5,6,8,3]=>0010011=>1100100
[2,7,4,1,6,5,8,3]=>0010111=>1110100
[4,1,2,5,8,6,7,3]=>0010011=>1100100
[7,3,5,4,6,1,8,2]=>0001111=>1111000
[6,3,4,1,5,7,8,2]=>0010101=>1010100
[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
[6,3,1,5,2,4,8,7]=>0101101=>1011010
[3,1,6,5,4,2,8,7]=>0111101=>1011110
[5,4,3,6,1,2,8,7]=>0011101=>1011100
[5,6,3,2,4,1,8,7]=>0110101=>1010110
[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
[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
[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
[6,8,3,5,2,7,4,1]=>0011011=>1101100
[2,1,8,5,3,7,4,6]=>1001011=>1101001
[6,5,3,2,8,7,1,4]=>0101111=>1111010
[2,4,1,8,7,6,5,3]=>0011111=>1111100
[4,1,2,8,7,5,6,3]=>0010111=>1110100
[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
[7,3,5,4,8,6,1,2]=>0001111=>1111000
[6,4,3,5,8,1,7,2]=>0010111=>1110100
[2,1,7,6,5,8,3,4]=>1000111=>1110001
[5,7,3,6,1,8,2,4]=>0000111=>1110000
[2,7,6,4,5,8,1,3]=>0000111=>1110000
[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
[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
[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
[5,7,3,8,1,4,6,2]=>0000111=>1110000
[2,1,7,8,5,4,6,3]=>1001101=>1011001
[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
[8,4,1,3,7,2,6,5]=>0010111=>1110100
[4,3,8,2,5,1,7,6]=>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
[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
[4,3,8,1,7,2,5,6]=>0010011=>1100100
[6,3,1,4,7,2,5,8]=>0100110=>0110010
[7,8,1,4,6,2,5,3]=>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
[7,8,2,6,4,1,3,5]=>0010101=>1010100
[7,8,1,6,5,4,3,2]=>0111101=>1011110
[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
[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
[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
[2,6,1,4,7,3,5,8]=>0000110=>0110000
[3,6,8,4,7,5,1,2]=>0001011=>1101000
[5,6,7,3,8,4,1,2]=>0010011=>1100100
[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
[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
[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
[4,2,7,1,6,3,8,5]=>0010111=>1110100
[4,3,7,5,6,8,1,2]=>0010011=>1100100
[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
[3,6,7,8,5,1,4,2]=>0011001=>1001100
[3,7,8,5,1,2,4,6]=>0001001=>1001000
[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
[2,8,6,7,5,1,3,4]=>0001011=>1101000
[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
[7,8,1,2,5,4,6,3]=>0001101=>1011000
[2,6,8,3,1,4,7,5]=>0100011=>1100010
[8,4,1,3,7,6,2,5]=>0010111=>1110100
[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
[1,5,2,4,3,6,7,8]=>0011000=>0001100
[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
[1,8,2,7,3,4,5,6]=>0000011=>1100000
[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
[1,8,2,4,3,7,5,6]=>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
[2,8,4,1,6,5,3,7]=>0011101=>1011100
[2,8,4,1,5,6,7,3]=>0010011=>1100100
[2,8,7,4,1,6,3,5]=>0010111=>1110100
[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
[2,8,5,3,4,1,6,7]=>0011001=>1001100
[2,8,7,6,1,4,5,3]=>0001111=>1111000
[2,8,6,5,7,3,1,4]=>0100111=>1110010
[7,2,8,4,5,6,1,3]=>0000111=>1110000
[6,2,3,8,5,1,7,4]=>0001111=>1111000
[6,3,2,8,5,1,4,7]=>0101101=>1011010
[7,4,8,5,2,1,3,6]=>1001011=>1101001
[6,4,8,5,1,3,7,2]=>0001111=>1111000
[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
[6,5,2,7,4,1,8,3]=>0011111=>1111100
[3,5,2,6,4,8,7,1]=>0001111=>1111000
[6,3,5,8,2,7,4,1]=>0010111=>1110100
[4,3,2,1,8,6,5,7]=>1110101=>1010111
[4,2,1,3,8,7,6,5]=>1010111=>1110101
[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
[6,5,8,4,2,3,7,1]=>0010111=>1110100
[7,5,3,8,2,4,1,6]=>0011011=>1101100
[1,6,5,7,3,4,2,8]=>0010110=>0110100
[5,2,1,8,7,6,3,4]=>1001111=>1111001
[7,1,3,8,4,6,2,5]=>0000111=>1110000
[5,7,8,4,3,6,2,1]=>1010101=>1010101
[4,1,8,3,5,6,7,2]=>0010011=>1100100
[4,1,8,3,6,2,7,5]=>0010111=>1110100
[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
[5,7,1,6,3,8,4,2]=>0010111=>1110100
[3,2,4,1,7,8,5,6]=>0110001=>1000110
[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
[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
[1,8,5,4,3,2,7,6]=>0111011=>1101110
[6,4,7,5,1,3,8,2]=>0001111=>1111000
[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
[2,6,8,4,3,7,1,5]=>0010011=>1100100
[2,7,8,4,3,6,5,1]=>0011101=>1011100
[1,8,7,5,6,3,4,2]=>0010111=>1110100
[2,7,8,5,6,3,4,1]=>0010101=>1010100
[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
[1,8,5,6,7,2,3,4]=>0000011=>1100000
[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
[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
[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
[4,5,3,2,8,1,7,6]=>0101011=>1101010
[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
[3,6,4,8,2,7,1,5]=>0000111=>1110000
[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
[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
[3,6,7,8,5,4,1,2]=>0011001=>1001100
[3,5,7,8,6,1,4,2]=>0010101=>1010100
[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
[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101=>10101010101
[8,1,6,7,3,2,5,4]=>0101011=>1101010
[8,1,6,7,2,3,4,5]=>0000011=>1100000
[8,1,2,4,3,6,5,7]=>0010101=>1010100
[8,1,4,3,2,7,6,5]=>0110111=>1110110
[8,1,5,3,7,2,6,4]=>0001111=>1111000
[8,1,3,5,6,2,7,4]=>0000111=>1110000
[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
[5,4,2,3,1,8,6,7]=>0111001=>1001110
[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
[7,4,1,2,3,8,5,6]=>0010011=>1100100
[6,4,2,1,3,8,5,7]=>1010101=>1010101
[2,6,4,8,3,7,5,1]=>0001111=>1111000
[2,6,5,8,7,3,4,1]=>0010111=>1110100
[6,5,2,1,8,3,4,7]=>1001101=>1011001
[7,5,1,2,8,3,4,6]=>0001011=>1101000
[7,6,1,8,2,3,4,5]=>0000111=>1110000
[7,6,1,8,4,5,2,3]=>0001111=>1111000
[6,7,8,1,4,5,2,3]=>0001001=>1001000
[6,7,8,1,3,2,5,4]=>0101001=>1001010
[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
[5,7,8,3,1,2,6,4]=>0100101=>1010010
[5,7,8,4,1,6,2,3]=>0010101=>1010100
[5,6,4,8,1,7,2,3]=>0000111=>1110000
[4,6,3,8,2,1,7,5]=>1000111=>1110001
[4,2,5,3,7,1,6,8]=>0011010=>0101100
[5,3,6,7,1,2,8,4]=>0001011=>1101000
[3,5,6,7,8,2,1,4]=>1000001=>1000001
[3,4,6,7,2,8,1,5]=>0000011=>1100000
[7,4,6,1,8,3,5,2]=>0001111=>1111000
[7,3,5,1,8,4,6,2]=>0001111=>1111000
[7,3,4,1,8,5,6,2]=>0010111=>1110100
[4,5,7,3,1,8,6,2]=>0100111=>1110010
[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
[3,6,7,5,1,8,4,2]=>0011011=>1101100
[7,5,6,1,8,3,4,2]=>0010111=>1110100
[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
[1,5,3,2,7,6,4,8]=>0101110=>0111010
[2,6,5,1,7,8,4,3]=>0011101=>1011100
[4,5,7,1,6,8,2,3]=>0000011=>1100000
[4,5,7,1,3,8,2,6]=>0000011=>1100000
[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
[2,6,1,5,7,8,3,4]=>0000101=>1010000
[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
[7,4,1,6,8,5,2,3]=>0011011=>1101100
[7,3,1,5,8,6,2,4]=>0100111=>1110010
[6,2,5,1,8,4,7,3]=>0001111=>1111000
[7,1,6,4,8,2,5,3]=>0001111=>1111000
[7,1,5,3,8,2,6,4]=>0001111=>1111000
[6,1,5,2,8,3,7,4]=>0001111=>1111000
[7,3,1,4,8,6,2,5]=>0100111=>1110010
[6,2,1,4,8,7,3,5]=>1000111=>1110001
[5,2,1,3,8,7,4,6]=>1001011=>1101001
[7,4,1,3,8,5,2,6]=>0011011=>1101100
[6,1,4,2,8,3,7,5]=>0010111=>1110100
[7,1,4,3,8,2,6,5]=>0010111=>1110100
[3,6,7,1,4,8,2,5]=>0000011=>1100000
[7,6,1,4,8,3,2,5]=>0100111=>1110010
[5,1,3,2,8,4,7,6]=>0101011=>1101010
[4,2,1,3,8,7,5,6]=>1010011=>1100101
[2,6,1,4,7,8,3,5]=>0000101=>1010000
[7,1,3,5,8,2,4,6]=>0000011=>1100000
[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
[4,6,1,2,5,7,3,8]=>0000110=>0110000
[1,4,8,2,5,7,3,6]=>0000011=>1100000
[7,8,4,2,5,1,3,6]=>0011001=>1001100
[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
[7,8,4,5,3,1,6,2]=>0101101=>1011010
[2,6,4,8,3,7,1,5]=>0000111=>1110000
[1,4,6,8,3,7,5,2]=>0001011=>1101000
[2,5,8,1,4,7,6,3]=>0000111=>1110000
[2,1,8,4,7,3,6,5]=>1000111=>1110001
[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
[6,3,1,2,4,5,8,7]=>0100101=>1010010
[1,4,7,2,5,3,8,6]=>0001011=>1101000
[6,4,7,3,5,8,1,2]=>0000111=>1110000
[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
[2,7,5,6,8,4,1,3]=>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
[3,4,2,8,6,1,7,5]=>0010111=>1110100
[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
[2,6,3,4,5,8,1,7]=>0000101=>1010000
[2,6,4,1,8,3,7,5]=>0010111=>1110100
[3,6,4,5,8,7,1,2]=>0000111=>1110000
[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
[5,6,2,7,3,1,4,8]=>0100110=>0110010
[5,7,6,4,1,8,3,2]=>0110111=>1110110
[6,7,1,5,2,8,3,4]=>0001011=>1101000
[6,1,5,2,8,3,4,7]=>0001101=>1011000
[7,5,2,4,3,1,6,8]=>0111010=>0101110
[6,8,1,3,7,5,4,2]=>0011011=>1101100
[7,4,2,6,5,1,3,8]=>0011110=>0111100
[7,4,6,3,1,5,2,8]=>0101110=>0111010
[7,2,3,5,4,1,6,8]=>0011010=>0101100
[6,8,1,2,3,4,7,5]=>0000011=>1100000
[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
[2,5,7,8,1,4,6,3]=>0000101=>1010000
[3,5,7,4,1,6,2,8]=>0010110=>0110100
[5,2,8,4,6,1,7,3]=>0001111=>1111000
[5,2,1,8,6,3,7,4]=>1001111=>1111001
[4,2,8,5,7,6,3,1]=>0110111=>1110110
[4,1,2,8,5,6,7,3]=>0010011=>1100100
[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
[6,3,1,8,7,2,4,5]=>0100111=>1110010
[5,8,3,7,1,6,4,2]=>0010111=>1110100
[5,8,7,4,1,6,2,3]=>0010111=>1110100
[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
[4,2,6,1,7,3,5,8]=>0010110=>0110100
[4,6,3,1,2,7,5,8]=>0100110=>0110010
[3,5,2,7,8,1,6,4]=>0001101=>1011000
[3,1,4,7,5,6,2,8]=>0100110=>0110010
[3,1,4,5,8,6,7,2]=>0100011=>1100010
[3,4,6,8,5,2,7,1]=>0001011=>1101000
[4,2,5,6,1,8,7,3]=>0010111=>1110100
[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
[7,1,4,2,5,3,8,6]=>0011011=>1101100
[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
[3,2,7,8,1,6,5,4]=>0101101=>1011010
[2,4,1,7,8,6,5,3]=>0011101=>1011100
[2,6,8,3,1,5,7,4]=>0100011=>1100010
[3,6,4,8,5,1,7,2]=>0001111=>1111000
[6,3,7,4,5,1,8,2]=>0001111=>1111000
[6,4,7,5,2,8,1,3]=>0001111=>1111000
[2,6,3,7,5,8,1,4]=>0000111=>1110000
[5,2,1,7,8,3,4,6]=>1001001=>1001001
[5,7,4,6,2,8,1,3]=>0000111=>1110000
[5,7,3,4,6,1,8,2]=>0000111=>1110000
[4,2,8,3,6,7,1,5]=>0010011=>1100100
[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
[3,5,1,8,2,7,4,6]=>0001011=>1101000
[7,5,1,3,6,2,4,8]=>0001110=>0111000
[8,5,4,1,2,6,3,7]=>0011101=>1011100
[5,1,8,4,2,7,3,6]=>0011011=>1101100
[4,1,6,2,8,3,7,5]=>0010111=>1110100
[1,6,2,8,5,3,7,4]=>0001111=>1111000
[6,8,5,3,1,7,4,2]=>0111011=>1101110
[5,6,7,3,1,8,4,2]=>0110011=>1100110
[5,6,2,1,7,8,4,3]=>1010101=>1010101
[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
[6,4,7,2,8,1,5,3]=>0001111=>1111000
[6,7,4,8,3,1,5,2]=>0101011=>1101010
[4,5,7,8,3,1,6,2]=>0100101=>1010010
[4,7,2,5,8,1,6,3]=>0000111=>1110000
[5,7,3,8,2,6,1,4]=>0000111=>1110000
[3,4,7,8,2,6,1,5]=>0000101=>1010000
[8,1,3,4,6,2,5,7]=>0000101=>1010000
[3,8,2,4,6,7,1,5]=>0000011=>1100000
[2,4,5,6,8,1,7,3]=>0000011=>1100000
[4,8,3,5,6,1,7,2]=>0000111=>1110000
[8,4,3,6,5,1,7,2]=>0011111=>1111100
[8,6,5,4,3,1,7,2]=>0111111=>1111110
[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
[3,2,8,6,5,1,7,4]=>0101111=>1111010
[5,1,7,3,6,2,4,8]=>0001110=>0111000
[8,1,6,5,2,3,7,4]=>0001111=>1111000
[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
[5,1,8,3,2,7,4,6]=>0101011=>1101010
[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
[8,7,6,1,5,4,3,2]=>0111111=>1111110
[8,6,7,1,4,5,3,2]=>0101011=>1101010
[7,6,8,1,4,3,5,2]=>0011011=>1101100
[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
[6,5,8,3,2,1,7,4]=>1100111=>1110011
[7,5,8,3,1,4,6,2]=>0100111=>1110010
[8,4,3,7,1,6,5,2]=>0011111=>1111100
[6,4,3,8,2,1,7,5]=>1010111=>1110101
[5,4,3,2,8,1,7,6]=>0111011=>1101110
[4,5,2,3,8,1,7,6]=>0001011=>1101000
[3,2,5,4,8,1,7,6]=>0101011=>1101010
[6,4,3,1,5,2,7,8]=>0111100=>0011110
[7,4,3,1,2,6,5,8]=>0110110=>0110110
[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
[4,6,2,1,5,3,7,8]=>1001100=>0011001
[3,2,6,1,5,4,7,8]=>0101100=>0011010
[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
[7,8,1,2,3,5,6,4]=>0000101=>1010000
[6,8,1,2,4,3,7,5]=>0010011=>1100100
[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
[5,8,7,3,4,1,2,6]=>0010011=>1100100
[6,7,3,8,5,1,2,4]=>0001011=>1101000
[6,7,4,5,1,8,3,2]=>0101011=>1101010
[5,4,7,6,2,3,8,1]=>0001111=>1111000
[5,4,7,6,8,1,2,3]=>0001011=>1101000
[5,3,7,8,6,1,2,4]=>0001101=>1011000
[4,3,8,7,6,1,2,5]=>0010111=>1110100
[4,8,3,7,5,1,2,6]=>0001011=>1101000
[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
[2,5,6,8,1,7,3,4]=>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
[1,4,2,6,8,5,7,3]=>0010011=>1100100
[8,1,3,2,5,4,6,7]=>0101001=>1001010
[2,4,1,6,8,7,5,3]=>0011011=>1101100
[4,3,1,7,6,8,5,2]=>0111011=>1101110
[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
[5,2,7,8,1,6,3,4]=>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
[8,5,6,2,1,4,3,7]=>1010101=>1010101
[5,8,7,1,2,3,4,6]=>0000011=>1100000
[6,7,1,2,8,4,5,3]=>0001011=>1101000
[6,7,1,3,4,8,5,2]=>0001011=>1101000
[5,1,7,3,4,8,6,2]=>0001111=>1111000
[5,1,7,8,2,3,6,4]=>0001101=>1011000
[4,8,1,7,2,3,5,6]=>0000011=>1100000
[3,8,1,2,7,4,5,6]=>0000011=>1100000
[3,1,8,2,7,4,6,5]=>0100111=>1110010
[3,1,2,8,7,5,6,4]=>0100111=>1110010
[4,1,3,7,5,8,6,2]=>0010111=>1110100
[2,1,8,3,4,7,6,5]=>1000111=>1110001
[1,8,2,3,4,5,7,6]=>0000011=>1100000
[1,2,8,3,4,6,7,5]=>0000011=>1100000
[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
[5,8,1,4,7,2,3,6]=>0000011=>1100000
[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
[4,6,1,2,7,8,5,3]=>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
[5,8,1,4,6,7,2,3]=>0000011=>1100000
[6,3,7,4,2,8,5,1]=>0011111=>1111100
[8,7,1,6,2,4,5,3]=>0001111=>1111000
[5,6,1,8,7,3,2,4]=>0100111=>1110010
[3,6,4,5,7,2,8,1]=>0000111=>1110000
[5,4,2,7,3,6,8,1]=>0011011=>1101100
[6,4,1,5,3,8,2,7]=>0011101=>1011100
[8,2,6,3,4,7,5,1]=>0001111=>1111000
[3,6,2,7,4,5,8,1]=>0000111=>1110000
[4,2,5,7,3,6,8,1]=>0010011=>1100100
[1,6,5,3,4,8,2,7]=>0001101=>1011000
[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
[4,8,1,3,7,2,6,5]=>0000111=>1110000
[4,2,8,5,7,3,6,1]=>0010111=>1110100
[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
[7,1,2,8,3,5,4,6]=>0001011=>1101000
[4,2,5,7,1,8,3,6]=>0010011=>1100100
[3,6,2,7,1,8,4,5]=>0000111=>1110000
[6,3,7,2,1,8,4,5]=>1000111=>1110001
[8,2,6,1,7,3,5,4]=>0001111=>1111000
[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
[1,5,3,4,6,8,2,7]=>0001001=>1001000
[4,3,5,1,6,8,2,7]=>0011001=>1001100
[4,7,5,6,8,3,2,1]=>1100011=>1100011
[6,5,4,8,2,7,3,1]=>0101111=>1111010
[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
[5,7,3,8,2,6,4,1]=>0010111=>1110100
[5,4,6,8,2,7,3,1]=>0101011=>1101010
[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
[7,1,8,6,5,3,2,4]=>0101111=>1111010
[1,3,8,7,4,6,2,5]=>0000111=>1110000
[4,7,1,8,6,5,2,3]=>0001111=>1111000
[6,8,7,2,5,4,3,1]=>0111011=>1101110
[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
[6,8,3,5,2,7,1,4]=>0001011=>1101000
[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
[4,6,3,7,2,5,1,8]=>0001110=>0111000
[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
[6,7,3,8,2,5,1,4]=>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
[5,7,3,8,2,4,1,6]=>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
[4,6,5,2,1,3,8,7]=>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
[4,7,8,1,6,3,5,2]=>0001101=>1011000
[7,4,8,1,6,5,3,2]=>0101111=>1111010
[7,4,5,3,1,8,2,6]=>0101011=>1101010
[6,4,8,1,7,5,2,3]=>0001111=>1111000
[6,4,7,1,8,2,5,3]=>0001111=>1111000
[8,5,7,6,4,2,1,3]=>1010111=>1110101
[2,1,6,8,7,4,3,5]=>1010011=>1100101
[2,1,7,8,6,4,5,3]=>1001101=>1011001
[8,4,7,3,6,2,5,1]=>0001111=>1111000
[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
[7,8,4,2,6,5,3,1]=>0111101=>1011110
[4,8,6,2,7,3,1,5]=>0100111=>1110010
[3,6,1,8,7,4,2,5]=>0010111=>1110100
[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
[5,7,4,2,3,8,1,6]=>0010011=>1100100
[2,1,8,6,7,5,3,4]=>1001011=>1101001
[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
[2,1,7,6,8,3,5,4]=>1001011=>1101001
[7,4,6,3,8,1,2,5]=>0000111=>1110000
[7,5,6,8,1,4,2,3]=>0010011=>1100100
[4,1,7,3,6,5,8,2]=>0010111=>1110100
[5,1,8,4,7,6,2,3]=>0001111=>1111000
[8,1,3,7,4,6,5,2]=>0001111=>1111000
[6,1,5,4,3,8,7,2]=>0011111=>1111100
[6,1,4,5,3,7,8,2]=>0001101=>1011000
[5,1,7,8,6,2,4,3]=>0011101=>1011100
[6,1,8,3,4,5,7,2]=>0000111=>1110000
[6,3,2,7,5,1,8,4]=>0101111=>1111010
[8,5,2,1,4,3,7,6]=>1011011=>1101101
[5,6,2,1,4,8,3,7]=>1000101=>1010001
[3,6,1,8,5,2,4,7]=>0001101=>1011000
[3,4,1,2,8,6,5,7]=>0010101=>1010100
[6,3,8,5,2,1,4,7]=>1001101=>1011001
[8,5,2,7,3,1,6,4]=>0101111=>1111010
[2,3,8,5,6,1,7,4]=>0000111=>1110000
[7,4,5,6,3,1,8,2]=>0100111=>1110010
[8,5,6,4,2,1,7,3]=>1010111=>1110101
[7,5,3,6,2,8,1,4]=>0001111=>1111000
[1,7,5,6,3,2,4,8]=>0100110=>0110010
[8,7,5,4,1,6,2,3]=>0011111=>1111100
[2,6,4,1,8,5,7,3]=>0010111=>1110100
[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
[8,6,1,3,7,2,4,5]=>0000111=>1110000
[5,1,8,3,2,4,6,7]=>0101001=>1001010
[5,2,7,8,6,4,1,3]=>0011101=>1011100
[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
[7,8,3,6,5,2,1,4]=>1001101=>1011001
[4,7,2,8,6,1,5,3]=>0001111=>1111000
[4,2,5,7,8,6,1,3]=>0010101=>1010100
[8,2,5,1,7,3,4,6]=>0001011=>1101000
[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
[7,2,5,1,8,3,4,6]=>0001011=>1101000
[7,8,2,1,4,3,5,6]=>1010001=>1000101
[7,6,4,2,3,1,8,5]=>0110111=>1110110
[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
[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
[1,8,7,4,3,2,5,6]=>0110011=>1100110
[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
[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
[1,4,6,2,8,3,7,5]=>0000111=>1110000
[5,2,6,7,8,4,1,3]=>0011001=>1001100
[5,3,6,1,2,8,4,7]=>0001101=>1011000
[1,6,3,2,7,8,4,5]=>0100101=>1010010
[6,7,3,8,5,2,1,4]=>1001011=>1101001
[4,6,2,7,8,1,5,3]=>0001101=>1011000
[1,6,4,7,8,3,5,2]=>0001101=>1011000
[4,5,7,2,1,8,6,3]=>1000111=>1110001
[7,8,3,4,2,1,6,5]=>1010101=>1010101
[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
[7,2,3,1,4,5,8,6]=>0100011=>1100010
[2,4,6,8,10,1,3,5,7,9]=>000000001=>100000000
[2,4,6,8,10,12,1,3,5,7,9,11]=>00000000001=>10000000000
[10,9,8,7,6,1,2,3,4,5]=>000011111=>111110000
[9,10,7,8,5,6,3,4,1,2]=>001010101=>101010100
[5,6,3,4,1,2,8,7]=>0010101=>1010100
[7,8,3,5,4,6,1,2]=>0001101=>1011000
[6,8,3,7,5,1,4,2]=>0011011=>1101100
[2,1,7,8,5,6,3,4]=>1000101=>1010001
[5,7,3,8,1,6,2,4]=>0000111=>1110000
[7,5,8,4,2,6,1,3]=>0010111=>1110100
[8,6,3,7,5,2,4,1]=>0011111=>1111100
[8,5,3,7,2,6,4,1]=>0011111=>1111100
[8,5,7,4,2,6,3,1]=>0110111=>1110110
[7,8,4,6,1,5,2,3]=>0001101=>1011000
[7,8,1,6,4,5,2,3]=>0001101=>1011000
[6,8,1,7,4,5,2,3]=>0001011=>1101000
[1,8,6,7,4,5,2,3]=>0001011=>1101000
[1,8,6,7,3,5,2,4]=>0001011=>1101000
[6,8,1,7,3,5,2,4]=>0001011=>1101000
[7,8,1,6,3,5,2,4]=>0001101=>1011000
[7,8,3,6,1,5,2,4]=>0001101=>1011000
[7,8,3,6,4,5,1,2]=>0001101=>1011000
[7,8,2,6,4,5,1,3]=>0001101=>1011000
[7,8,2,6,3,5,1,4]=>0001101=>1011000
[7,8,1,6,2,5,3,4]=>0001101=>1011000
[1,8,6,7,2,5,3,4]=>0001011=>1101000
[5,8,1,7,2,6,3,4]=>0000111=>1110000
[6,8,2,7,1,5,3,4]=>0001011=>1101000
[6,8,2,7,3,5,1,4]=>0001011=>1101000
[6,8,2,7,4,5,1,3]=>0001011=>1101000
[6,8,3,7,4,5,1,2]=>0001011=>1101000
[3,8,6,7,4,5,1,2]=>0001011=>1101000
[2,8,6,7,4,5,1,3]=>0001011=>1101000
[2,8,6,7,3,5,1,4]=>0001011=>1101000
[2,8,6,7,1,5,3,4]=>0001011=>1101000
[2,8,1,7,5,6,3,4]=>0000111=>1110000
[1,8,2,7,5,6,3,4]=>0000111=>1110000
[2,8,1,7,4,6,3,5]=>0000111=>1110000
[2,8,4,7,1,6,3,5]=>0000111=>1110000
[2,8,4,7,3,6,1,5]=>0000111=>1110000
[2,8,5,7,3,6,1,4]=>0000111=>1110000
[3,8,5,7,4,6,1,2]=>0000111=>1110000
[5,8,3,7,4,6,1,2]=>0000111=>1110000
[5,8,2,7,4,6,1,3]=>0000111=>1110000
[5,8,2,7,3,6,1,4]=>0000111=>1110000
[4,8,2,7,3,6,1,5]=>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
[1,8,4,7,3,6,2,5]=>0000111=>1110000
[4,8,1,7,3,6,2,5]=>0000111=>1110000
[4,8,3,7,1,6,2,5]=>0000111=>1110000
[6,8,3,7,1,5,2,4]=>0001011=>1101000
[5,8,1,7,3,6,2,4]=>0000111=>1110000
[1,8,5,7,3,6,2,4]=>0000111=>1110000
[1,8,5,7,4,6,2,3]=>0000111=>1110000
[5,8,1,7,4,6,2,3]=>0000111=>1110000
[5,8,4,7,1,6,2,3]=>0000111=>1110000
[6,8,4,7,1,5,2,3]=>0001011=>1101000
[6,8,5,7,1,4,2,3]=>0010011=>1100100
[5,8,6,7,3,4,1,2]=>0010011=>1100100
[5,8,6,7,2,4,1,3]=>0010011=>1100100
[5,8,6,7,1,4,2,3]=>0010011=>1100100
[4,8,6,7,1,5,2,3]=>0001011=>1101000
[4,8,5,7,1,6,2,3]=>0000111=>1110000
[1,8,4,7,5,6,2,3]=>0000111=>1110000
[1,8,3,7,5,6,2,4]=>0000111=>1110000
[3,8,5,7,1,6,2,4]=>0000111=>1110000
[3,8,6,7,1,5,2,4]=>0001011=>1101000
[3,8,6,7,2,5,1,4]=>0001011=>1101000
[4,8,6,7,2,5,1,3]=>0001011=>1101000
[4,8,6,7,3,5,1,2]=>0001011=>1101000
[4,8,5,7,3,6,1,2]=>0000111=>1110000
[4,8,5,7,2,6,1,3]=>0000111=>1110000
[3,8,5,7,2,6,1,4]=>0000111=>1110000
[3,8,4,7,2,6,1,5]=>0000111=>1110000
[3,8,4,7,1,6,2,5]=>0000111=>1110000
[3,8,1,7,4,6,2,5]=>0000111=>1110000
[3,8,2,7,5,6,1,4]=>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
[2,8,3,7,1,6,4,5]=>0000111=>1110000
[7,5,2,8,6,4,1,3]=>0011111=>1111100
[7,4,8,6,1,5,2,3]=>0001111=>1111000
[7,1,8,4,5,2,6,3]=>0001111=>1111000
[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
[6,8,1,7,2,3,4,5]=>0000011=>1100000
[1,5,7,8,2,6,3,4]=>0000101=>1010000
[2,6,3,7,8,5,4,1]=>0011101=>1011100
[2,5,3,7,8,1,6,4]=>0001101=>1011000
[2,5,4,1,3,7,8,6]=>0011001=>1001100
[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
[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
[6,4,3,1,2,8,5,7]=>0110101=>1010110
[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
[1,5,7,3,6,8,4,2]=>0010011=>1100100
[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
[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
[4,3,1,5,7,2,6,8]=>0110010=>0100110
[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
[5,3,6,8,4,7,2,1]=>1001011=>1101001
[3,7,2,5,4,8,6,1]=>0001111=>1111000
[4,2,6,5,8,3,7,1]=>0010111=>1110100
[4,1,6,5,8,3,2,7]=>0110101=>1010110
[5,1,6,8,4,3,2,7]=>0111001=>1001110
[6,7,8,1,4,3,2,5]=>0110001=>1000110
[4,7,1,5,8,3,2,6]=>0100011=>1100010
[8,3,1,5,4,7,2,6]=>0101011=>1101010
[8,4,1,5,7,3,2,6]=>0110011=>1100110
[8,4,6,1,7,3,2,5]=>0100111=>1110010
[8,3,6,1,4,7,2,5]=>0000111=>1110000
[8,2,6,1,4,3,7,5]=>0010111=>1110100
[3,7,6,1,4,8,2,5]=>0000111=>1110000
[6,7,8,5,1,3,2,4]=>0101001=>1001010
[6,7,8,2,4,3,5,1]=>0011001=>1001100
[4,7,6,2,8,3,5,1]=>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
[8,4,6,5,7,1,2,3]=>0000111=>1110000
[4,7,6,5,8,1,2,3]=>0000111=>1110000
[8,7,6,5,2,1,4,3]=>1011111=>1111101
[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
[3,8,7,5,4,6,1,2]=>0001111=>1111000
[4,3,6,7,8,5,1,2]=>0011001=>1001100
[3,5,6,4,8,7,1,2]=>0000111=>1110000
[4,6,8,5,3,7,1,2]=>0001011=>1101000
[6,5,2,1,4,7,8,3]=>1001101=>1011001
[4,2,7,5,1,8,6,3]=>0011111=>1111100
[2,1,6,4,8,7,5,3]=>1001111=>1111001
[7,8,1,4,2,6,5,3]=>0011101=>1011100
[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
[1,4,6,2,5,8,3,7]=>0000101=>1010000
[1,6,8,7,4,2,3,5]=>0010011=>1100100
[7,6,1,8,3,2,4,5]=>0100111=>1110010
[7,1,8,6,3,4,2,5]=>0010111=>1110100
[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
[4,2,6,1,8,5,7,3]=>0010111=>1110100
[2,8,1,5,4,6,7,3]=>0001011=>1101000
[1,2,8,3,6,5,7,4]=>0000111=>1110000
[6,1,3,2,7,5,8,4]=>0100111=>1110010
[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
[4,6,3,8,1,2,7,5]=>0000111=>1110000
[4,3,7,1,2,5,8,6]=>0010011=>1100100
[4,1,6,3,8,2,7,5]=>0010111=>1110100
[7,8,1,3,4,2,6,5]=>0010101=>1010100
[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
[3,5,7,8,4,1,2,6]=>0010001=>1000100
[5,4,7,3,6,8,1,2]=>0001011=>1101000
[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
[7,6,3,5,4,8,1,2]=>0001111=>1111000
[4,5,6,3,8,7,1,2]=>0000111=>1110000
[6,3,7,5,8,4,1,2]=>0010111=>1110100
[4,8,2,6,1,5,3,7]=>0001101=>1011000
[4,3,6,2,5,1,8,7]=>0011101=>1011100
[7,8,1,2,5,6,3,4]=>0000101=>1010000
[4,1,6,2,5,7,3,8]=>0010110=>0110100
[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
[3,1,6,4,7,2,5,8]=>0100110=>0110010
[5,8,7,1,2,4,3,6]=>0010011=>1100100
[1,5,7,8,2,4,6,3]=>0000101=>1010000
[6,8,5,1,3,4,2,7]=>0011001=>1001100
[7,6,5,1,4,3,2,8]=>0111110=>0111110
[2,6,4,5,1,3,8,7]=>0001101=>1011000
[3,5,6,4,1,8,2,7]=>0010101=>1010100
[7,8,5,4,1,3,2,6]=>0111001=>1001110
[7,8,2,3,4,1,6,5]=>0010101=>1010100
[4,2,6,3,8,1,7,5]=>0010111=>1110100
[7,2,3,5,4,1,8,6]=>0011011=>1101100
[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
[5,2,7,1,8,4,6,3]=>0001111=>1111000
[6,3,1,2,8,4,5,7]=>0100101=>1010010
[4,2,1,3,6,5,8,7]=>1010101=>1010101
[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
[7,5,1,6,4,3,8,2]=>0011111=>1111100
[5,8,1,6,3,4,7,2]=>0000111=>1110000
[6,8,1,7,5,2,3,4]=>0001011=>1101000
[5,6,1,7,4,8,2,3]=>0000111=>1110000
[7,8,5,1,6,4,2,3]=>0011101=>1011100
[2,6,5,7,3,4,8,1]=>0000111=>1110000
[1,6,4,7,5,8,2,3]=>0000111=>1110000
[1,3,7,4,6,8,2,5]=>0000011=>1100000
[5,2,4,7,3,6,8,1]=>0001011=>1101000
[8,1,6,5,7,2,4,3]=>0010111=>1110100
[7,1,6,5,8,3,2,4]=>0100111=>1110010
[1,2,7,6,8,3,4,5]=>0000011=>1100000
[3,8,6,4,2,7,5,1]=>0011111=>1111100
[7,8,1,6,2,4,5,3]=>0001101=>1011000
[2,8,1,7,4,3,6,5]=>0010111=>1110100
[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
[5,1,2,4,8,3,6,7]=>0001001=>1001000
[4,1,3,2,8,5,6,7]=>0110001=>1000110
[3,2,1,4,8,5,6,7]=>1100001=>1000011
[4,3,6,1,5,8,2,7]=>0010101=>1010100
[2,6,1,4,5,8,3,7]=>0000101=>1010000
[1,6,2,5,8,3,4,7]=>0000101=>1010000
[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
[5,4,3,2,1,8,6,7]=>1111001=>1001111
[2,5,3,4,1,8,6,7]=>0011001=>1001100
[4,3,5,2,1,8,6,7]=>1011001=>1001101
[3,7,6,8,4,5,2,1]=>1001011=>1101001
[1,7,6,8,5,4,2,3]=>0011011=>1101100
[2,4,8,6,7,3,5,1]=>0001011=>1101000
[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
[3,2,8,5,7,4,6,1]=>0100111=>1110010
[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
[5,8,6,7,4,3,2,1]=>1110011=>1100111
[4,8,7,5,6,3,2,1]=>1100111=>1110011
[4,2,1,6,3,5,8,7]=>1010101=>1010101
[6,2,1,4,3,8,5,7]=>1010101=>1010101
[8,2,1,4,3,6,5,7]=>1010101=>1010101
[6,2,4,1,3,8,5,7]=>0010101=>1010100
[2,1,6,4,3,5,8,7]=>1010101=>1010101
[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
[4,6,2,1,3,8,5,7]=>1000101=>1010001
[2,6,1,4,3,8,5,7]=>0010101=>1010100
[2,1,6,4,3,8,5,7]=>1010101=>1010101
[4,8,2,1,3,6,5,7]=>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
[2,6,1,4,8,3,5,7]=>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
[4,2,6,1,8,3,5,7]=>0010101=>1010100
[6,2,4,1,8,3,5,7]=>0010101=>1010100
[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
[8,2,1,6,4,3,5,7]=>1010101=>1010101
[4,2,8,1,6,3,5,7]=>0010101=>1010100
[2,4,1,8,3,6,5,7]=>0010101=>1010100
[2,1,4,8,3,6,5,7]=>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
[2,1,8,6,4,3,5,7]=>1010101=>1010101
[2,8,6,1,4,3,5,7]=>0010101=>1010100
[2,8,6,4,1,3,5,7]=>0010101=>1010100
[4,8,6,2,1,3,5,7]=>1000101=>1010001
[3,2,6,1,5,4,8,7]=>0101101=>1011010
[6,1,5,2,4,3,8,7]=>0011101=>1011100
[6,1,3,2,5,4,8,7]=>0101101=>1011010
[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
[2,1,5,4,8,3,7,6]=>1001011=>1101001
[5,4,7,6,8,1,3,2]=>0101011=>1101010
[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
[7,1,6,5,8,3,4,2]=>0010111=>1110100
[7,4,6,5,8,1,3,2]=>0100111=>1110010
[8,4,6,1,3,2,7,5]=>0100111=>1110010
[8,1,6,3,4,2,7,5]=>0010111=>1110100
[8,3,5,2,6,1,7,4]=>0001111=>1111000
[7,3,5,2,6,4,8,1]=>0001111=>1111000
[8,2,7,1,5,3,6,4]=>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
[2,1,8,3,5,4,7,6]=>1001011=>1101001
[8,1,3,2,5,4,7,6]=>0101011=>1101010
[8,1,5,2,4,3,7,6]=>0011011=>1101100
[8,2,4,1,5,3,7,6]=>0011011=>1101100
[8,2,4,1,7,3,6,5]=>0010111=>1110100
[3,2,8,4,6,1,7,5]=>0100111=>1110010
[3,2,8,1,7,4,6,5]=>0100111=>1110010
[3,2,8,1,5,4,7,6]=>0101011=>1101010
[3,2,4,1,8,5,7,6]=>0110011=>1100110
[4,1,3,2,7,6,8,5]=>0110011=>1100110
[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
[7,2,4,1,8,5,6,3]=>0010111=>1110100
[7,6,8,1,5,2,4,3]=>0011011=>1101100
[7,6,8,1,3,2,5,4]=>0101011=>1101010
[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
[5,4,7,2,6,3,8,1]=>0001111=>1111000
[5,4,8,2,6,1,7,3]=>0001111=>1111000
[6,1,8,4,7,2,5,3]=>0001111=>1111000
[6,5,8,1,3,2,7,4]=>0100111=>1110010
[2,1,6,5,8,3,7,4]=>1000111=>1110001
[6,5,7,4,8,1,3,2]=>0100111=>1110010
[5,4,6,3,8,1,7,2]=>0001111=>1111000
[3,2,1,5,8,4,6,7]=>1100001=>1000011
[2,8,3,1,5,4,6,7]=>0101001=>1001010
[2,4,8,3,5,7,6,1]=>0000111=>1110000
[4,2,5,3,1,8,6,7]=>0111001=>1001110
[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
[5,4,1,3,8,2,6,7]=>0011001=>1001100
[1,5,7,3,8,4,2,6]=>0010011=>1100100
[5,1,4,7,8,3,2,6]=>0101001=>1001010
[8,1,5,3,7,4,6,2]=>0001111=>1111000
[1,4,3,8,7,5,6,2]=>0010111=>1110100
[1,6,8,5,3,7,4,2]=>0011011=>1101100
[6,4,8,1,7,3,5,2]=>0001111=>1111000
[6,4,8,7,1,5,2,3]=>0001111=>1111000
[7,1,6,8,4,3,2,5]=>0110011=>1100110
[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
[4,2,1,7,8,5,3,6]=>1011001=>1001101
[6,2,4,8,3,7,5,1]=>0001111=>1111000
[7,2,6,3,4,1,8,5]=>0010111=>1110100
[2,7,1,8,3,5,4,6]=>0001011=>1101000
[2,1,7,3,5,8,4,6]=>1000011=>1100001
[1,2,7,5,8,3,4,6]=>0000011=>1100000
[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
[2,7,8,4,1,6,5,3]=>0011101=>1011100
[2,8,4,1,6,7,5,3]=>0011011=>1101100
[2,1,8,4,7,5,6,3]=>1000111=>1110001
[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
[7,8,1,6,4,2,5,3]=>0011101=>1011100
[8,7,6,5,1,4,2,3]=>0011111=>1111100
[8,7,6,1,5,3,4,2]=>0011111=>1111100
[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
[8,3,5,7,2,4,1,6]=>0010011=>1100100
[8,5,2,7,4,3,1,6]=>0111011=>1101110
[6,5,3,1,2,4,8,7]=>0101101=>1011010
[4,5,3,6,1,2,8,7]=>0001101=>1011000
[3,5,1,4,6,2,8,7]=>0001101=>1011000
[8,1,4,7,3,6,2,5]=>0000111=>1110000
[8,5,1,4,7,3,2,6]=>0101011=>1101010
[8,5,3,7,1,4,2,6]=>0011011=>1101100
[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
[8,7,1,4,2,6,3,5]=>0010111=>1110100
[8,6,3,1,2,4,7,5]=>0100111=>1110010
[2,1,8,7,5,3,4,6]=>1001011=>1101001
[8,1,7,4,5,2,3,6]=>0001011=>1101000
[2,8,7,5,4,1,3,6]=>0011011=>1101100
[8,7,2,6,4,1,3,5]=>0010111=>1110100
[5,3,7,8,2,4,6,1]=>0001101=>1011000
[5,3,7,6,2,1,8,4]=>1001111=>1111001
[5,7,8,6,4,2,1,3]=>1010101=>1010101
[2,6,7,5,4,8,1,3]=>0001011=>1101000
[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
[4,1,7,2,5,6,8,3]=>0010011=>1100100
[2,4,7,1,6,5,8,3]=>0000111=>1110000
[3,4,6,2,7,8,5,1]=>0001101=>1011000
[4,6,1,2,5,8,7,3]=>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
[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
[6,3,1,4,2,8,5,7]=>0110101=>1010110
[8,4,1,5,2,7,6,3]=>0011111=>1111100
[7,2,5,1,4,3,8,6]=>0011011=>1101100
[3,6,2,7,1,4,8,5]=>0000111=>1110000
[2,7,5,4,1,3,8,6]=>0011011=>1101100
[6,4,3,2,1,8,5,7]=>1110101=>1010111
[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
[5,8,3,2,7,1,6,4]=>0100111=>1110010
[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
[7,2,8,5,6,1,4,3]=>0010111=>1110100
[3,6,5,8,1,4,2,7]=>0010101=>1010100
[4,3,6,8,2,1,5,7]=>1010001=>1000101
[2,5,7,4,8,1,3,6]=>0000011=>1100000
[4,3,6,7,8,1,2,5]=>0010001=>1000100
[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
[8,1,5,2,7,4,6,3]=>0001111=>1111000
[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
[5,3,1,7,2,8,4,6]=>0101011=>1101010
[6,5,2,1,7,8,3,4]=>1001101=>1011001
[5,3,6,4,7,8,1,2]=>0001101=>1011000
[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
[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
[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
[4,6,8,2,7,1,5,3]=>0001011=>1101000
[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
[3,8,7,6,5,1,4,2]=>0011111=>1111100
[2,8,7,6,5,4,1,3]=>0011111=>1111100
[5,4,3,2,1,6,7,8,9,10]=>111100000=>000001111
[6,4,3,2,7,1,5,8,9,10]=>011011000=>000110110
[7,5,3,8,2,6,1,4,9,10]=>000111100=>001111000
[8,6,9,4,7,2,5,1,3,10]=>000101110=>011101000
[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
[7,5,8,3,1,2,6,4]=>0100111=>1110010
[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
[7,5,3,1,6,4,8,2]=>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
[7,5,3,8,4,1,6,2]=>0011111=>1111100
[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
[7,5,3,1,6,2,4,8]=>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
[7,5,3,8,1,6,2,4]=>0001111=>1111000
[7,5,3,8,1,4,2,6]=>0011011=>1101100
[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
[7,5,3,8,6,1,2,4]=>0001111=>1111000
[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
[7,5,3,6,1,8,2,4]=>0001111=>1111000
[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
[7,5,3,1,2,8,6,4]=>0101111=>1111010
[7,5,3,4,1,6,8,2]=>0011011=>1101100
[4,6,8,3,5,7,1,2]=>0000011=>1100000
[6,8,1,2,4,5,7,3]=>0000011=>1100000
[3,6,8,2,5,7,1,4]=>0000011=>1100000
[8,3,5,2,4,1,6,7]=>0011001=>1001100
[3,5,7,2,4,6,1,8]=>0000110=>0110000
[4,2,5,7,3,6,1,8]=>0010110=>0110100
[4,5,2,8,3,1,6,7]=>0101001=>1001010
[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
[3,1,2,6,8,5,7,4]=>0100011=>1100010
[4,3,6,2,7,5,1,8]=>0011110=>0111100
[4,3,1,7,8,2,6,5]=>0110101=>1010110
[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
[4,7,3,6,5,2,1,8]=>1001110=>0111001
[5,3,7,6,4,2,1,8]=>1011110=>0111101
[5,3,1,6,4,2,8,7]=>0111101=>1011110
[1,3,8,5,4,2,7,6]=>0011011=>1101100
[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
[3,1,2,7,6,4,8,5]=>0100111=>1110010
[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
[6,3,7,4,8,5,1,2]=>0001111=>1111000
[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
[6,4,2,7,3,5,1,8]=>0011110=>0111100
[7,3,2,1,8,4,5,6]=>1100011=>1100011
[3,7,2,8,6,1,4,5]=>0000111=>1110000
[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
[8,3,6,5,2,1,4,7]=>1001101=>1011001
[8,2,4,1,6,5,3,7]=>0011101=>1011100
[8,2,4,1,7,6,3,5]=>0010111=>1110100
[8,5,1,2,7,3,6,4]=>0001111=>1111000
[6,1,8,2,3,7,5,4]=>0001111=>1111000
[8,1,2,6,4,3,7,5]=>0010111=>1110100
[2,8,1,7,5,4,3,6]=>0011011=>1101100
[1,2,7,5,4,3,8,6]=>0011011=>1101100
[1,7,2,8,3,6,5,4]=>0001111=>1111000
[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
[4,3,1,2,8,7,6,5]=>0110111=>1110110
[5,1,4,3,2,8,7,6]=>0111011=>1101110
[8,6,4,3,1,5,7,2]=>0110111=>1110110
[8,6,4,1,5,2,7,3]=>0011111=>1111100
[8,6,5,3,2,1,7,4]=>1101111=>1111011
[8,7,2,4,5,3,1,6]=>0101011=>1101010
[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
[8,6,5,1,7,3,2,4]=>0101111=>1111010
[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
[8,5,7,4,6,1,3,2]=>0100111=>1110010
[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
[1,3,5,6,8,4,2,7]=>0010001=>1000100
[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
[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
[5,7,1,2,8,6,3,4]=>0000111=>1110000
[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
[7,1,4,5,2,8,6,3]=>0001111=>1111000
[4,7,3,1,5,8,6,2]=>0100111=>1110010
[8,7,6,4,1,5,2,3]=>0011111=>1111100
[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
[1,8,2,4,6,7,3,5]=>0000011=>1100000
[2,1,5,8,6,4,3,7]=>1010101=>1010101
[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
[1,8,5,7,4,3,2,6]=>0110011=>1100110
[1,6,8,5,4,3,2,7]=>0111001=>1001110
[7,1,5,8,3,4,6,2]=>0000111=>1110000
[7,1,5,8,4,3,2,6]=>0110011=>1100110
[7,1,2,5,8,3,6,4]=>0000111=>1110000
[7,1,6,4,2,3,5,8]=>0010110=>0110100
[2,7,1,4,8,3,5,6]=>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
[3,6,7,1,4,8,5,2]=>0001011=>1101000
[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
[6,5,8,7,2,3,1,4]=>0100111=>1110010
[3,4,7,2,5,8,1,6]=>0000011=>1100000
[4,3,8,1,2,7,5,6]=>0010011=>1100100
[5,6,7,8,1,3,4,2]=>0010001=>1000100
[5,7,8,6,1,2,3,4]=>0000101=>1010000
[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
[2,4,6,1,7,5,8,3]=>0000111=>1110000
[4,7,8,1,2,3,6,5]=>0000101=>1010000
[4,2,1,5,6,3,7,8]=>1010100=>0010101
[5,8,1,6,4,3,2,7]=>0110101=>1010110
[5,8,1,6,3,7,2,4]=>0000111=>1110000
[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
[8,4,5,3,7,2,6,1]=>0001111=>1111000
[4,7,5,2,8,1,6,3]=>0001111=>1111000
[4,6,3,8,5,1,7,2]=>0001111=>1111000
[2,6,4,3,1,5,7,8]=>0110100=>0010110
[3,6,4,8,1,7,2,5]=>0000111=>1110000
[7,3,8,4,1,5,2,6]=>0011011=>1101100
[4,2,8,3,6,1,5,7]=>0010101=>1010100
[6,7,5,8,2,1,4,3]=>1010011=>1100101
[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
[3,6,5,4,2,8,1,7]=>0011101=>1011100
[7,4,5,3,8,2,1,6]=>1001011=>1101001
[1,6,4,7,2,5,3,8]=>0001110=>0111000
[1,4,3,7,2,6,5,8]=>0010110=>0110100
[1,5,7,2,4,8,3,6]=>0000011=>1100000
[1,6,5,7,2,4,3,8]=>0010110=>0110100
[1,7,6,2,8,3,4,5]=>0000111=>1110000
[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
[1,7,6,5,2,8,4,3]=>0011111=>1111100
[1,6,5,2,3,8,4,7]=>0001101=>1011000
[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
[1,4,7,6,2,5,8,3]=>0000111=>1110000
[1,2,6,5,3,7,4,8]=>0001110=>0111000
[1,3,7,5,2,6,8,4]=>0001011=>1101000
[1,7,4,6,2,8,3,5]=>0000111=>1110000
[1,7,3,5,2,8,4,6]=>0001011=>1101000
[1,3,7,4,2,6,8,5]=>0010011=>1100100
[1,4,7,3,2,5,8,6]=>0100011=>1100010
[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
[1,4,3,2,5,8,6,7]=>0110001=>1000110
[1,5,3,2,4,8,6,7]=>0101001=>1001010
[1,6,4,2,3,8,5,7]=>0010101=>1010100
[1,7,6,4,2,8,5,3]=>0011111=>1111100
[1,7,5,3,2,8,6,4]=>0101111=>1111010
[1,6,4,2,3,8,7,5]=>0010111=>1110100
[1,5,3,2,4,8,7,6]=>0101011=>1101010
[6,8,5,4,3,2,1,7]=>1111001=>1001111
[2,8,5,4,3,7,1,6]=>0011011=>1101100
[7,6,1,4,3,8,5,2]=>0011111=>1111100
[7,6,5,1,3,8,4,2]=>0011111=>1111100
[7,3,5,4,8,1,6,2]=>0001111=>1111000
[5,6,8,4,3,1,7,2]=>0110011=>1100110
[6,8,5,4,1,2,7,3]=>0011011=>1101100
[6,8,2,4,3,7,1,5]=>0010011=>1100100
[1,8,3,4,7,2,6,5]=>0000111=>1110000
[7,5,8,4,3,2,1,6]=>1110011=>1100111
[4,8,5,7,3,2,1,6]=>1100011=>1100011
[7,8,1,2,4,3,5,6]=>0010001=>1000100
[7,8,2,1,4,3,6,5]=>1010101=>1010101
[3,4,6,5,7,8,1,2]=>0000101=>1010000
[4,3,6,5,8,7,1,2]=>0010111=>1110100
[4,2,6,1,8,3,7,5]=>0010111=>1110100
[6,7,3,8,4,5,1,2]=>0001011=>1101000
[6,7,4,5,1,8,2,3]=>0001011=>1101000
[4,7,5,6,1,8,2,3]=>0000111=>1110000
[4,5,3,8,6,7,1,2]=>0001011=>1101000
[5,6,3,8,4,7,1,2]=>0000111=>1110000
[5,6,4,7,1,8,2,3]=>0000111=>1110000
[5,6,2,7,3,4,1,8]=>0010110=>0110100
[4,5,1,8,6,7,2,3]=>0001011=>1101000
[7,8,4,5,1,6,2,3]=>0001101=>1011000
[4,5,2,3,1,8,6,7]=>0101001=>1001010
[5,6,2,3,1,8,4,7]=>0100101=>1010010
[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
[7,8,1,5,3,6,2,4]=>0001101=>1011000
[1,8,3,6,5,7,2,4]=>0000111=>1110000
[1,6,4,7,3,8,2,5]=>0000111=>1110000
[1,7,3,6,4,8,2,5]=>0000111=>1110000
[1,7,2,8,4,6,3,5]=>0000111=>1110000
[1,7,5,8,2,6,3,4]=>0000111=>1110000
[6,7,1,5,3,8,2,4]=>0001011=>1101000
[6,7,1,8,2,5,3,4]=>0001011=>1101000
[6,7,1,8,4,5,2,3]=>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
[6,7,3,4,1,8,2,5]=>0010011=>1100100
[3,4,2,7,5,6,1,8]=>0010110=>0110100
[2,7,5,8,1,4,3,6]=>0010011=>1100100
[2,3,1,8,4,7,5,6]=>0100011=>1100010
[2,3,1,8,6,7,4,5]=>0100011=>1100010
[7,8,2,3,1,6,4,5]=>0100101=>1010010
[2,8,1,4,3,7,5,6]=>0010011=>1100100
[2,8,1,7,3,5,4,6]=>0001011=>1101000
[4,5,1,7,3,8,2,6]=>0001011=>1101000
[3,8,1,5,2,7,4,6]=>0001011=>1101000
[3,4,1,8,6,7,2,5]=>0010011=>1100100
[7,8,3,4,1,6,2,5]=>0010101=>1010100
[3,4,2,5,1,8,6,7]=>0011001=>1001100
[3,4,2,8,1,6,5,7]=>0010101=>1010100
[2,5,4,1,6,3,8,7]=>0011101=>1011100
[3,6,5,1,2,4,8,7]=>0001101=>1011000
[5,2,3,6,4,1,8,7]=>0011101=>1011100
[6,1,4,5,3,2,8,7]=>0101101=>1011010
[5,6,7,8,1,4,3,2]=>0110001=>1000110
[4,2,6,8,5,7,3,1]=>0110011=>1100110
[2,1,5,8,7,6,3,4]=>1000111=>1110001
[2,1,4,7,6,3,8,5]=>1000111=>1110001
[6,3,7,1,5,2,8,4]=>0001111=>1111000
[4,2,8,6,7,3,1,5]=>0110011=>1100110
[7,4,3,8,2,1,5,6]=>1010011=>1100101
[2,4,1,5,8,3,7,6]=>0010011=>1100100
[4,7,5,8,1,6,3,2]=>0100111=>1110010
[2,1,5,8,7,3,4,6]=>1000011=>1100001
[8,5,7,3,6,1,4,2]=>0010111=>1110100
[4,2,5,1,6,7,8,3]=>0011001=>1001100
[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
[6,8,7,2,5,3,1,4]=>0101011=>1101010
[8,2,1,6,4,7,5,3]=>1001111=>1111001
[7,8,2,5,6,1,4,3]=>0010101=>1010100
[7,8,4,2,5,1,6,3]=>0011101=>1011100
[6,1,2,3,7,5,8,4]=>0000111=>1110000
[7,6,8,4,2,5,3,1]=>0111011=>1101110
[8,5,7,1,6,3,2,4]=>0100111=>1110010
[4,1,2,3,7,6,8,5]=>0010011=>1100100
[3,2,4,1,8,5,6,7]=>0110001=>1000110
[3,4,8,6,5,2,1,7]=>1001101=>1011001
[4,1,6,3,5,8,7,2]=>0010111=>1110100
[8,6,7,1,5,4,3,2]=>0111011=>1101110
[2,1,6,5,8,4,7,3]=>1000111=>1110001
[4,1,8,5,6,2,3,7]=>0010101=>1010100
[2,6,4,8,7,3,5,1]=>0001111=>1111000
[3,1,8,2,7,5,4,6]=>0101011=>1101010
[8,2,3,1,7,4,6,5]=>0100111=>1110010
[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
[5,8,2,4,3,1,6,7]=>0110001=>1000110
[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
[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
[8,4,2,6,7,5,3,1]=>0111011=>1101110
[7,4,1,6,8,2,5,3]=>0011011=>1101100
[1,8,6,2,5,3,4,7]=>0001101=>1011000
[4,7,1,2,5,3,8,6]=>0001011=>1101000
[8,7,3,6,4,5,2,1]=>1001111=>1111001
[5,7,8,6,2,1,4,3]=>1010101=>1010101
[1,8,6,4,5,2,3,7]=>0001101=>1011000
[1,4,7,2,6,8,3,5]=>0000011=>1100000
[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
[1,8,3,2,5,6,7,4]=>0100011=>1100010
[6,4,1,2,7,5,8,3]=>0010111=>1110100
[4,3,7,8,5,1,6,2]=>0011101=>1011100
[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
[1,2,4,5,8,3,7,6]=>0000011=>1100000
[4,8,1,5,2,3,7,6]=>0001011=>1101000
[2,4,6,3,7,1,8,5]=>0000111=>1110000
[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
[7,6,1,2,8,3,5,4]=>0001111=>1111000
[6,7,8,1,5,2,4,3]=>0011001=>1001100
[5,7,8,4,1,2,6,3]=>0010101=>1010100
[4,7,8,5,6,1,3,2]=>0100101=>1010010
[5,6,4,8,1,2,7,3]=>0000111=>1110000
[6,5,4,1,2,3,8,7]=>0011101=>1011100
[7,5,1,6,2,3,8,4]=>0001111=>1111000
[4,5,6,7,8,1,3,2]=>0100001=>1000010
[8,1,3,6,7,4,5,2]=>0001011=>1101000
[4,2,6,7,3,1,8,5]=>0110011=>1100110
[7,3,1,5,4,8,2,6]=>0101011=>1101010
[4,5,3,2,8,1,6,7]=>0101001=>1001010
[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
[5,6,3,8,1,4,2,7]=>0010101=>1010100
[4,6,3,8,2,1,5,7]=>1000101=>1010001
[4,7,8,3,2,1,5,6]=>1100001=>1000011
[5,7,8,3,1,4,2,6]=>0110001=>1000110
[8,1,7,2,5,4,3,6]=>0011011=>1101100
[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
[7,5,1,3,2,6,8,4]=>0101011=>1101010
[8,1,6,3,2,5,7,4]=>0100111=>1110010
[8,1,5,3,4,2,7,6]=>0011011=>1101100
[5,4,2,3,1,6,8,7]=>0111001=>1001110
[6,3,2,1,5,7,4,8]=>1100110=>0110011
[8,1,4,3,5,6,2,7]=>0010101=>1010100
[3,6,5,8,2,4,1,7]=>0010101=>1010100
[5,3,7,2,4,8,1,6]=>0001011=>1101000
[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
[6,1,4,5,8,3,2,7]=>0100101=>1010010
[6,5,4,3,8,2,1,7]=>1011101=>1011101
[4,6,8,3,7,2,5,1]=>0001011=>1101000
[1,4,3,6,2,7,8,5]=>0010101=>1010100
[4,7,8,5,3,1,2,6]=>0101001=>1001010
[8,5,4,7,6,2,1,3]=>1001111=>1111001
[5,8,7,3,1,4,6,2]=>0100111=>1110010
[8,5,7,4,3,6,1,2]=>0010111=>1110100
[4,7,8,3,6,1,5,2]=>0001101=>1011000
[8,4,6,1,7,3,5,2]=>0001111=>1111000
[1,3,8,6,4,7,5,2]=>0001111=>1111000
[7,6,2,1,4,3,8,5]=>1010111=>1110101
[7,6,8,1,4,3,2,5]=>0110011=>1100110
[1,5,7,3,2,6,8,4]=>0100011=>1100010
[3,2,6,8,5,7,4,1]=>0110011=>1100110
[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
[1,7,4,5,2,8,3,6]=>0001011=>1101000
[3,2,6,8,7,4,5,1]=>0101011=>1101010
[6,3,2,1,7,8,4,5]=>1100101=>1010011
[5,7,3,8,2,1,4,6]=>1000011=>1100001
[3,7,1,8,4,2,5,6]=>0010011=>1100100
[4,2,1,3,7,5,8,6]=>1010011=>1100101
[8,4,2,1,3,7,6,5]=>1010111=>1110101
[8,4,3,7,6,2,1,5]=>1010111=>1110101
[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
[5,8,4,2,7,1,6,3]=>0010111=>1110100
[8,5,3,1,7,2,6,4]=>0101111=>1111010
[8,2,1,6,3,7,5,4]=>1001111=>1111001
[1,4,6,8,2,7,5,3]=>0001011=>1101000
[2,1,7,3,8,6,5,4]=>1001111=>1111001
[8,2,1,7,6,5,4,3]=>1011111=>1111101
[8,6,7,5,1,4,3,2]=>0111011=>1101110
[6,4,7,3,2,1,8,5]=>1100111=>1110011
[4,8,7,3,2,1,6,5]=>1100111=>1110011
[6,5,3,7,2,1,4,8]=>1001110=>0111001
[5,8,3,6,2,1,4,7]=>1000101=>1010001
[6,4,3,7,2,1,8,5]=>1010111=>1110101
[4,8,3,6,2,1,7,5]=>1000111=>1110001
[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
[6,4,2,7,5,1,3,8]=>0011110=>0111100
[5,4,2,6,7,1,3,8]=>0011010=>0101100
[6,2,7,8,5,1,3,4]=>0001101=>1011000
[2,8,7,6,5,1,3,4]=>0001111=>1111000
[6,4,7,3,1,5,8,2]=>0100111=>1110010
[5,4,7,3,1,8,6,2]=>0101111=>1111010
[4,8,7,3,1,5,6,2]=>0100111=>1110010
[6,5,3,7,1,4,8,2]=>0001111=>1111000
[5,8,3,6,1,4,7,2]=>0000111=>1110000
[6,4,3,7,1,5,8,2]=>0010111=>1110100
[4,8,3,6,1,5,7,2]=>0000111=>1110000
[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
[5,8,4,2,1,7,3,6]=>1010011=>1100101
[6,4,7,2,1,5,3,8]=>1001110=>0111001
[5,8,3,2,1,4,7,6]=>1100011=>1100011
[6,3,7,2,1,4,5,8]=>1000110=>0110001
[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
[2,8,7,6,1,4,3,5]=>0010111=>1110100
[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
[4,8,7,1,5,6,3,2]=>0100111=>1110010
[6,5,3,1,8,4,7,2]=>0101111=>1111010
[5,8,3,1,6,4,7,2]=>0100111=>1110010
[6,4,3,1,5,8,7,2]=>0110111=>1110110
[5,8,2,1,6,4,3,7]=>1010101=>1010101
[6,4,2,1,5,8,3,7]=>1010101=>1010101
[3,8,2,1,5,4,6,7]=>1001001=>1001001
[6,2,7,1,5,4,3,8]=>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
[5,4,1,6,7,8,3,2]=>0111001=>1001110
[4,3,1,6,5,7,8,2]=>0110101=>1010110
[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
[5,1,7,6,8,4,3,2]=>0111011=>1101110
[4,1,7,6,5,8,3,2]=>0110111=>1110110
[4,5,8,1,7,2,3,6]=>0000011=>1100000
[4,5,8,1,2,6,3,7]=>0000101=>1010000
[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
[8,2,3,5,6,7,1,4]=>0000011=>1100000
[8,1,2,3,5,4,6,7]=>0001001=>1001000
[8,7,2,1,6,3,4,5]=>1000111=>1110001
[8,7,2,1,3,5,4,6]=>1001011=>1101001
[8,6,4,1,7,5,3,2]=>0111111=>1111110
[2,3,6,7,8,1,5,4]=>0001001=>1001000
[7,4,2,6,8,5,1,3]=>0011011=>1101100
[7,3,2,5,8,6,1,4]=>0100111=>1110010
[7,3,1,8,6,2,4,5]=>0100111=>1110010
[3,1,7,2,5,4,8,6]=>0101011=>1101010
[7,1,8,2,5,3,6,4]=>0001111=>1111000
[7,3,8,4,5,1,6,2]=>0001111=>1111000
[8,3,7,4,6,1,5,2]=>0001111=>1111000
[8,2,7,1,6,4,5,3]=>0001111=>1111000
[8,1,7,5,4,2,3,6]=>0011011=>1101100
[8,1,2,6,5,4,3,7]=>0011101=>1011100
[8,1,7,6,3,2,4,5]=>0100111=>1110010
[8,2,7,5,6,1,4,3]=>0010111=>1110100
[3,6,8,1,7,5,4,2]=>0011011=>1101100
[8,2,6,7,5,4,1,3]=>0011011=>1101100
[8,6,7,2,3,1,5,4]=>0101011=>1101010
[2,7,8,6,3,1,5,4]=>0101101=>1011010
[7,3,1,8,6,5,4,2]=>0111111=>1111110
[8,1,7,6,5,4,3,2]=>0111111=>1111110
[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
[2,1,7,8,3,6,5,4]=>1001101=>1011001
[2,1,4,8,5,7,3,6]=>1000011=>1100001
[7,8,1,5,2,6,3,4]=>0001101=>1011000
[6,4,1,5,2,3,8,7]=>0011101=>1011100
[4,3,7,8,5,2,1,6]=>1011001=>1001101
[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
[5,8,2,1,7,6,4,3]=>1010111=>1110101
[8,3,2,4,1,7,5,6]=>0110011=>1100110
[6,3,4,2,1,7,8,5]=>1010101=>1010101
[7,8,3,1,5,4,6,2]=>0101101=>1011010
[7,2,8,1,4,6,5,3]=>0001111=>1111000
[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
[4,2,1,3,6,7,8,5]=>1010001=>1000101
[2,3,4,1,8,6,5,7]=>0010101=>1010100
[6,3,5,4,1,2,8,7]=>0011101=>1011100
[8,7,3,6,5,1,4,2]=>0011111=>1111100
[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
[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
[8,7,5,4,3,1,6,2]=>0111111=>1111110
[3,4,6,2,8,5,1,7]=>0001101=>1011000
[3,4,6,7,1,8,5,2]=>0001011=>1101000
[3,4,6,8,1,5,2,7]=>0001001=>1001000
[3,4,7,2,8,5,6,1]=>0000111=>1110000
[3,5,2,6,8,4,1,7]=>0011001=>1001100
[3,5,2,7,4,8,6,1]=>0001111=>1111000
[3,5,2,7,8,4,6,1]=>0001101=>1011000
[3,5,6,2,7,8,1,4]=>0000101=>1010000
[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
[3,5,8,2,4,1,6,7]=>0010001=>1000100
[3,6,2,1,7,8,5,4]=>1001101=>1011001
[3,6,2,1,8,5,4,7]=>1001101=>1011001
[3,6,2,7,4,8,5,1]=>0001111=>1111000
[3,6,2,7,8,5,4,1]=>0011101=>1011100
[3,6,8,2,4,5,1,7]=>0001001=>1001000
[3,7,2,1,4,8,6,5]=>1000111=>1110001
[3,7,2,8,4,5,6,1]=>0000111=>1110000
[3,8,2,1,4,5,6,7]=>1000001=>1000001
[4,1,5,7,3,8,6,2]=>0010111=>1110100
[4,1,5,7,8,2,6,3]=>0010101=>1010100
[4,1,5,8,3,2,6,7]=>0110001=>1000110
[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
[4,1,6,8,3,5,2,7]=>0011001=>1001100
[4,1,7,3,8,5,6,2]=>0010111=>1110100
[4,1,8,3,2,5,6,7]=>0110001=>1000110
[4,5,2,7,3,8,6,1]=>0001111=>1111000
[4,5,7,3,2,8,6,1]=>0100111=>1110010
[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
[4,6,2,8,3,5,1,7]=>0001101=>1011000
[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
[5,1,2,8,4,3,6,7]=>0011001=>1001100
[5,1,6,3,7,8,2,4]=>0001101=>1011000
[5,1,6,3,8,4,2,7]=>0011101=>1011100
[5,1,6,7,4,8,2,3]=>0001011=>1101000
[5,6,2,3,8,4,1,7]=>0010101=>1010100
[5,6,2,7,4,8,1,3]=>0000111=>1110000
[5,6,2,7,8,4,1,3]=>0010101=>1010100
[5,6,8,3,4,2,1,7]=>1010001=>1000101
[5,7,8,3,4,2,6,1]=>0010101=>1010100
[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
[6,1,7,8,4,5,3,2]=>0101101=>1011010
[6,7,2,8,4,5,3,1]=>0101011=>1101010
[7,1,2,3,4,8,6,5]=>0000111=>1110000
[7,1,2,3,8,5,6,4]=>0000111=>1110000
[7,1,2,8,4,5,6,3]=>0000111=>1110000
[7,1,8,3,4,5,6,2]=>0000111=>1110000
[2,4,6,1,8,5,7,3]=>0000111=>1110000
[6,4,1,8,2,3,7,5]=>0010111=>1110100
[5,8,1,2,4,3,7,6]=>0010011=>1100100
[5,8,1,6,2,4,3,7]=>0010101=>1010100
[1,3,5,7,2,6,4,8]=>0000110=>0110000
[3,5,8,6,1,2,4,7]=>0000101=>1010000
[3,5,1,8,2,4,7,6]=>0001011=>1101000
[3,1,6,8,2,4,7,5]=>0100011=>1100010
[2,3,5,6,8,1,7,4]=>0000011=>1100000
[5,6,4,8,2,1,7,3]=>1000111=>1110001
[7,1,8,6,3,4,5,2]=>0001111=>1111000
[7,6,5,2,4,8,1,3]=>0001111=>1111000
[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
[7,1,8,6,3,2,4,5]=>0100111=>1110010
[7,8,1,6,4,2,3,5]=>0010101=>1010100
[2,4,8,1,5,6,7,3]=>0000011=>1100000
[8,4,1,2,5,6,3,7]=>0010101=>1010100
[8,3,1,6,5,2,4,7]=>0101101=>1011010
[2,5,3,8,7,6,1,4]=>0001111=>1111000
[5,8,7,4,2,6,1,3]=>0010111=>1110100
[5,1,8,4,7,6,3,2]=>0101111=>1111010
[7,3,2,6,5,1,8,4]=>0101111=>1111010
[8,2,3,6,5,1,7,4]=>0001111=>1111000
[4,8,6,5,7,3,2,1]=>1100111=>1110011
[4,8,5,6,7,3,2,1]=>1100011=>1100011
[3,8,7,4,5,6,2,1]=>1000111=>1110001
[2,8,7,6,3,4,5,1]=>0001111=>1111000
[1,8,7,6,5,2,3,4]=>0001111=>1111000
[7,2,8,6,5,4,1,3]=>0011111=>1111100
[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
[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
[7,6,3,8,5,2,1,4]=>1001111=>1111001
[5,8,7,4,1,6,3,2]=>0110111=>1110110
[4,2,3,1,7,8,5,6]=>0110001=>1000110
[8,6,3,4,7,2,5,1]=>0001111=>1111000
[6,8,3,4,5,1,7,2]=>0001011=>1101000
[5,2,8,4,1,6,7,3]=>0011011=>1101100
[4,1,3,6,8,2,5,7]=>0010001=>1000100
[1,6,3,2,5,8,4,7]=>0100101=>1010010
[8,3,2,1,5,4,7,6]=>1101011=>1101011
[2,5,1,8,4,3,7,6]=>0011011=>1101100
[5,3,6,2,4,8,1,7]=>0001101=>1011000
[1,6,2,4,5,8,3,7]=>0000101=>1010000
[5,3,2,1,6,8,4,7]=>1101001=>1001011
[2,6,5,8,1,3,4,7]=>0000101=>1010000
[4,3,1,6,5,8,2,7]=>0110101=>1010110
[8,3,4,1,5,2,7,6]=>0011011=>1101100
[3,4,6,5,7,1,8,2]=>0000111=>1110000
[8,2,6,4,1,7,3,5]=>0010111=>1110100
[5,4,6,8,1,2,7,3]=>0001011=>1101000
[3,4,7,8,6,2,5,1]=>0001101=>1011000
[7,5,8,2,4,6,1,3]=>0000111=>1110000
[8,2,7,4,6,1,3,5]=>0000111=>1110000
[4,7,3,2,8,1,6,5]=>0100111=>1110010
[3,8,1,7,2,5,6,4]=>0000111=>1110000
[8,3,2,5,7,6,1,4]=>0100111=>1110010
[2,8,6,1,5,7,3,4]=>0000111=>1110000
[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
[5,6,7,3,8,4,2,1]=>1010011=>1100101
[5,7,3,2,4,1,8,6]=>0110011=>1100110
[8,4,1,3,7,2,5,6]=>0010011=>1100100
[2,8,4,7,1,3,5,6]=>0000011=>1100000
[3,5,2,8,6,1,7,4]=>0001111=>1111000
[1,7,6,3,2,5,8,4]=>0100111=>1110010
[3,8,1,5,6,2,7,4]=>0000111=>1110000
[4,3,5,6,7,1,8,2]=>0010011=>1100100
[7,1,5,2,8,6,4,3]=>0011111=>1111100
[6,5,4,8,7,2,1,3]=>1001111=>1111001
[1,8,5,3,6,2,7,4]=>0001111=>1111000
[6,5,8,7,2,1,3,4]=>1000111=>1110001
[3,6,2,1,7,5,8,4]=>1000111=>1110001
[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
[2,1,4,6,8,5,7,3]=>1000011=>1100001
[3,2,5,7,6,1,8,4]=>0100111=>1110010
[4,3,5,6,1,8,7,2]=>0010111=>1110100
[3,1,4,6,5,7,8,2]=>0100101=>1010010
[1,2,3,4,8,6,5,7]=>0000101=>1010000
[1,2,3,8,5,4,6,7]=>0001001=>1001000
[1,2,3,8,5,6,4,7]=>0000101=>1010000
[1,2,3,8,6,5,4,7]=>0001101=>1011000
[1,8,3,4,2,5,6,7]=>0010001=>1000100
[1,2,8,5,4,3,6,7]=>0011001=>1001100
[1,8,4,3,2,5,6,7]=>0110001=>1000110
[8,5,7,6,4,3,2,1]=>1110111=>1110111
[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
[8,4,7,3,6,5,2,1]=>1001111=>1111001
[8,1,7,4,6,5,3,2]=>0101111=>1111010
[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
[8,1,7,2,6,4,5,3]=>0001111=>1111000
[8,3,7,1,6,4,5,2]=>0001111=>1111000
[8,4,7,1,6,3,5,2]=>0001111=>1111000
[8,5,7,1,6,3,4,2]=>0010111=>1110100
[8,6,7,1,5,3,4,2]=>0011011=>1101100
[8,7,6,2,5,3,4,1]=>0011111=>1111100
[8,6,7,2,5,3,4,1]=>0011011=>1101100
[8,5,7,2,6,3,4,1]=>0010111=>1110100
[8,4,7,2,6,3,5,1]=>0001111=>1111000
[8,3,7,2,6,4,5,1]=>0001111=>1111000
[8,2,7,3,6,4,5,1]=>0001111=>1111000
[8,1,7,3,6,4,5,2]=>0001111=>1111000
[8,1,7,4,6,3,5,2]=>0001111=>1111000
[8,2,7,4,6,3,5,1]=>0001111=>1111000
[8,3,7,4,6,2,5,1]=>0001111=>1111000
[8,5,7,3,6,2,4,1]=>0010111=>1110100
[8,6,7,3,5,2,4,1]=>0011011=>1101100
[8,5,7,4,6,2,3,1]=>0100111=>1110010
[8,4,7,5,6,2,3,1]=>0100111=>1110010
[8,3,7,5,6,2,4,1]=>0010111=>1110100
[8,2,7,5,6,3,4,1]=>0010111=>1110100
[8,1,7,5,6,3,4,2]=>0010111=>1110100
[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
[8,7,6,5,4,1,3,2]=>0111111=>1111110
[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
[8,1,7,5,6,2,4,3]=>0010111=>1110100
[8,3,7,5,6,1,4,2]=>0010111=>1110100
[8,4,7,5,6,1,3,2]=>0100111=>1110010
[8,6,7,4,5,1,3,2]=>0101011=>1101010
[8,7,6,4,5,1,3,2]=>0101111=>1111010
[8,6,7,3,5,1,4,2]=>0011011=>1101100
[8,4,7,3,6,1,5,2]=>0001111=>1111000
[8,2,7,4,6,1,5,3]=>0001111=>1111000
[8,1,7,4,6,2,5,3]=>0001111=>1111000
[8,1,7,3,6,2,5,4]=>0001111=>1111000
[8,2,7,3,6,1,5,4]=>0001111=>1111000
[8,3,7,2,6,1,5,4]=>0001111=>1111000
[8,4,7,2,6,1,5,3]=>0001111=>1111000
[8,5,7,2,6,1,4,3]=>0010111=>1110100
[8,6,7,2,5,1,4,3]=>0011011=>1101100
[8,7,6,2,5,1,4,3]=>0011111=>1111100
[8,7,6,1,5,2,4,3]=>0011111=>1111100
[8,6,7,1,5,2,4,3]=>0011011=>1101100
[8,5,7,1,6,2,4,3]=>0010111=>1110100
[8,4,7,1,6,2,5,3]=>0001111=>1111000
[8,3,7,1,6,2,5,4]=>0001111=>1111000
[8,2,7,1,6,3,5,4]=>0001111=>1111000
[4,6,7,3,8,5,2,1]=>1001011=>1101001
[6,7,8,9,10,5,4,3,2,1]=>111100001=>100001111
[5,7,8,9,4,10,6,3,2,1]=>110010011=>110010011
[4,6,8,3,9,5,10,7,2,1]=>100001111=>111100001
[3,5,2,7,4,9,6,10,8,1]=>000101111=>111101000
[1,4,8,2,6,3,5,7]=>0000101=>1010000
[1,6,2,4,8,3,5,7]=>0000101=>1010000
[1,5,2,3,8,4,7,6]=>0001011=>1101000
[1,7,2,3,5,4,8,6]=>0001011=>1101000
[1,8,2,3,5,4,6,7]=>0001001=>1001000
[1,7,8,2,4,5,3,6]=>0001001=>1001000
[1,2,8,3,6,4,5,7]=>0000101=>1010000
[1,5,8,2,3,7,4,6]=>0000011=>1100000
[1,6,8,2,3,5,4,7]=>0001001=>1001000
[5,7,2,6,3,8,1,4]=>0000111=>1110000
[5,7,1,6,8,4,3,2]=>0110011=>1100110
[4,8,1,2,5,7,3,6]=>0000011=>1100000
[1,7,8,4,6,2,5,3]=>0001101=>1011000
[3,7,4,8,5,1,6,2]=>0001111=>1111000
[3,7,5,4,8,2,1,6]=>1001011=>1101001
[4,7,1,3,2,8,6,5]=>0100111=>1110010
[2,7,3,1,5,8,4,6]=>0100011=>1100010
[2,7,5,8,6,4,1,3]=>0010111=>1110100
[3,8,7,1,6,4,5,2]=>0001111=>1111000
[3,4,2,7,8,1,6,5]=>0010101=>1010100
[4,3,2,1,5,8,6,7]=>1110001=>1000111
[4,1,3,7,5,6,8,2]=>0010011=>1100100
[3,4,6,1,5,8,2,7]=>0000101=>1010000
[6,5,8,7,1,4,2,3]=>0010111=>1110100
[4,1,7,3,8,5,2,6]=>0011011=>1101100
[6,1,7,3,5,4,8,2]=>0001111=>1111000
[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
[7,1,3,4,2,8,5,6]=>0010011=>1100100
[7,6,1,4,3,5,8,2]=>0010111=>1110100
[3,5,4,1,6,7,8,2]=>0011001=>1001100
[2,5,3,4,8,6,1,7]=>0001101=>1011000
[2,4,8,3,6,1,7,5]=>0000111=>1110000
[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
[7,3,5,6,1,4,8,2]=>0000111=>1110000
[3,7,6,5,1,4,8,2]=>0001111=>1111000
[2,7,6,5,3,8,1,4]=>0001111=>1111000
[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
[1,2,6,3,4,8,7,5]=>0000111=>1110000
[5,3,6,1,4,7,8,2]=>0001101=>1011000
[6,7,1,3,4,5,8,2]=>0000011=>1100000
[1,7,3,2,4,8,5,6]=>0100011=>1100010
[6,1,4,2,8,3,5,7]=>0010101=>1010100
[5,8,6,7,2,1,4,3]=>1010011=>1100101
[7,4,1,5,8,2,3,6]=>0010011=>1100100
[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
[8,6,1,3,5,4,2,7]=>0011101=>1011100
[2,7,6,3,4,5,8,1]=>0000111=>1110000
[5,3,8,6,1,2,4,7]=>0001101=>1011000
[2,4,8,7,3,5,6,1]=>0000111=>1110000
[2,5,3,6,8,7,4,1]=>0011011=>1101100
[3,8,7,2,6,4,5,1]=>0001111=>1111000
[4,5,8,7,2,6,3,1]=>0100111=>1110010
[8,5,2,7,1,4,3,6]=>0011011=>1101100
[4,5,2,8,3,7,6,1]=>0001111=>1111000
[8,2,3,7,6,4,5,1]=>0001111=>1111000
[3,7,5,8,2,6,1,4]=>0000111=>1110000
[1,6,7,4,8,2,3,5]=>0000011=>1100000
[8,2,1,3,5,6,7,4]=>1000011=>1100001
[4,1,3,8,2,6,7,5]=>0010011=>1100100
[3,6,1,4,7,2,8,5]=>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
[3,2,1,6,4,8,5,7]=>1100101=>1010011
[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
[7,3,2,4,8,6,1,5]=>0100111=>1110010
[7,1,3,2,8,5,4,6]=>0101011=>1101010
[5,1,7,4,2,3,8,6]=>0011011=>1101100
[1,3,4,8,6,5,2,7]=>0001101=>1011000
[4,1,8,6,5,3,2,7]=>0111101=>1011110
[4,8,5,3,6,2,7,1]=>0001111=>1111000
[5,7,4,3,6,2,8,1]=>0010111=>1110100
[6,7,5,1,2,8,3,4]=>0001011=>1101000
[7,5,1,4,2,6,8,3]=>0011011=>1101100
[5,2,6,8,3,4,7,1]=>0001011=>1101000
[7,6,2,4,5,8,3,1]=>0100111=>1110010
[2,6,3,8,4,7,5,1]=>0001111=>1111000
[6,2,7,5,8,3,1,4]=>0100111=>1110010
[2,1,5,6,8,3,7,4]=>1000011=>1100001
[1,2,7,4,8,3,6,5]=>0000111=>1110000
[1,6,8,3,2,7,4,5]=>0100011=>1100010
[1,6,7,5,2,8,3,4]=>0001011=>1101000
[7,5,1,2,8,4,6,3]=>0001111=>1111000
[5,8,2,7,4,3,6,1]=>0010111=>1110100
[5,7,3,8,2,4,6,1]=>0000111=>1110000
[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
[3,6,2,4,7,1,8,5]=>0000111=>1110000
[4,2,8,5,1,6,7,3]=>0011011=>1101100
[2,1,6,4,8,5,3,7]=>1001101=>1011001
[1,2,8,3,7,5,4,6]=>0001011=>1101000
[1,6,3,8,7,4,2,5]=>0010111=>1110100
[4,3,8,1,2,6,7,5]=>0010011=>1100100
[6,4,5,8,1,2,7,3]=>0000111=>1110000
[7,4,6,5,2,1,8,3]=>1001111=>1111001
[5,1,8,6,7,4,3,2]=>0111011=>1101110
[3,8,5,7,1,4,2,6]=>0010011=>1100100
[4,7,2,5,1,3,8,6]=>0001011=>1101000
[5,1,7,4,8,6,3,2]=>0101111=>1111010
[3,6,5,2,1,8,7,4]=>1001111=>1111001
[5,2,8,4,7,3,1,6]=>0101011=>1101010
[5,2,7,4,1,3,6,8]=>0011010=>0101100
[5,2,6,4,1,8,7,3]=>0011111=>1111100
[6,3,2,1,4,8,7,5]=>1100111=>1110011
[3,1,4,6,2,8,7,5]=>0100111=>1110010
[6,3,5,1,7,4,2,8]=>0011110=>0111100
[5,4,7,6,3,8,1,2]=>0001111=>1111000
[4,6,3,7,5,8,1,2]=>0000111=>1110000
[5,7,4,3,8,1,2,6]=>0010011=>1100100
[1,5,7,4,8,6,3,2]=>0100111=>1110010
[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
[8,2,4,3,6,1,5,7]=>0010101=>1010100
[1,7,8,5,4,3,6,2]=>0011101=>1011100
[7,3,8,1,4,2,6,5]=>0010111=>1110100
[1,8,4,5,3,2,6,7]=>0101001=>1001010
[3,8,7,4,2,6,1,5]=>0010111=>1110100
[3,7,8,1,2,6,5,4]=>0001101=>1011000
[3,5,6,2,7,1,4,8]=>0000110=>0110000
[3,7,1,6,8,2,4,5]=>0000011=>1100000
[8,1,7,6,2,4,3,5]=>0010111=>1110100
[1,6,4,5,7,2,3,8]=>0000110=>0110000
[8,3,6,1,7,2,4,5]=>0000111=>1110000
[1,7,5,3,6,8,4,2]=>0011011=>1101100
[7,3,5,2,1,8,4,6]=>1001011=>1101001
[7,4,1,6,5,8,3,2]=>0110111=>1110110
[6,4,2,8,7,5,1,3]=>0011111=>1111100
[4,2,1,5,8,7,3,6]=>1010011=>1100101
[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
[6,4,5,7,2,8,1,3]=>0000111=>1110000
[5,3,6,4,2,8,1,7]=>0011101=>1011100
[4,1,5,3,8,2,7,6]=>0011011=>1101100
[2,6,3,5,4,8,1,7]=>0001101=>1011000
[3,7,4,5,6,8,1,2]=>0000011=>1100000
[2,5,7,3,6,8,1,4]=>0000011=>1100000
[7,6,4,5,2,8,1,3]=>0001111=>1111000
[5,4,3,1,8,2,7,6]=>0111011=>1101110
[8,2,6,4,7,3,1,5]=>0100111=>1110010
[1,2,8,3,5,4,6,7]=>0001001=>1001000
[1,7,8,4,3,5,6,2]=>0010101=>1010100
[3,1,6,8,4,5,7,2]=>0100011=>1100010
[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
[3,7,2,1,8,4,5,6]=>1000011=>1100001
[2,1,5,8,3,6,7,4]=>1000011=>1100001
[4,2,7,1,8,3,6,5]=>0010111=>1110100
[4,3,1,6,8,2,7,5]=>0110011=>1100110
[5,3,4,6,8,2,7,1]=>0001011=>1101000
[3,5,1,6,8,2,7,4]=>0001011=>1101000
[5,1,8,7,4,2,3,6]=>0011011=>1101100
[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
[3,8,7,4,5,6,1,2]=>0000111=>1110000
[2,7,6,3,5,4,1,8]=>0011110=>0111100
[3,8,7,4,6,2,5,1]=>0001111=>1111000
[5,8,3,7,6,2,4,1]=>0010111=>1110100
[8,7,2,5,4,3,1,6]=>0111011=>1101110
[6,8,3,2,5,4,7,1]=>0101011=>1101010
[5,8,7,4,3,6,2,1]=>1010111=>1110101
[5,8,6,4,3,7,1,2]=>0010111=>1110100
[6,5,8,4,3,1,7,2]=>0110111=>1110110
[2,6,4,7,1,5,3,8]=>0001110=>0111000
[2,5,6,8,4,3,7,1]=>0010011=>1100100
[5,3,8,1,7,6,4,2]=>0011111=>1111100
[5,4,8,7,1,6,3,2]=>0101111=>1111010
[4,8,6,7,5,3,1,2]=>0101011=>1101010
[4,8,6,5,7,2,1,3]=>1000111=>1110001
[4,8,5,6,7,1,2,3]=>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
[6,2,1,5,8,3,7,4]=>1000111=>1110001
[6,5,4,8,2,1,7,3]=>1001111=>1111001
[5,8,4,7,2,6,3,1]=>0100111=>1110010
[5,8,3,2,7,6,4,1]=>0110111=>1110110
[5,8,3,2,6,7,1,4]=>0100011=>1100010
[6,5,3,2,8,1,7,4]=>0101111=>1111010
[6,4,3,2,1,8,7,5]=>1110111=>1110111
[6,3,4,1,2,8,7,5]=>0010111=>1110100
[6,2,1,4,3,8,7,5]=>1010111=>1110101
[5,2,1,4,3,6,7,8]=>1011000=>0001101
[4,6,3,2,5,1,7,8]=>0101100=>0011010
[3,5,7,4,2,6,1,8]=>0010110=>0110100
[4,3,6,1,5,2,7,8]=>0011100=>0011100
[4,2,1,6,5,3,7,8]=>1011100=>0011101
[4,2,1,5,7,6,3,8]=>1010110=>0110101
[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
[3,4,6,5,8,1,7,2]=>0000111=>1110000
[4,3,5,1,6,8,7,2]=>0011011=>1101100
[2,1,5,3,8,4,7,6]=>1001011=>1101001
[3,1,8,2,5,4,7,6]=>0101011=>1101010
[8,1,3,2,6,4,7,5]=>0100111=>1110010
[3,1,8,2,6,4,7,5]=>0100111=>1110010
[2,1,8,3,6,4,7,5]=>1000111=>1110001
[2,1,6,3,8,4,7,5]=>1000111=>1110001
[2,1,7,3,5,4,8,6]=>1001011=>1101001
[2,1,7,3,6,4,8,5]=>1000111=>1110001
[2,1,7,3,8,4,6,5]=>1000111=>1110001
[8,1,4,2,7,3,6,5]=>0010111=>1110100
[4,1,7,2,8,3,6,5]=>0010111=>1110100
[3,1,7,2,8,4,6,5]=>0100111=>1110010
[3,1,6,2,5,4,8,7]=>0101101=>1011010
[7,1,3,2,5,4,8,6]=>0101011=>1101010
[7,1,3,2,6,4,8,5]=>0100111=>1110010
[7,1,8,2,4,3,6,5]=>0010111=>1110100
[7,1,5,2,8,3,6,4]=>0001111=>1111000
[6,1,4,2,5,3,8,7]=>0011101=>1011100
[4,1,6,2,5,3,8,7]=>0011101=>1011100
[4,1,7,2,5,3,8,6]=>0011011=>1101100
[4,1,7,2,6,3,8,5]=>0010111=>1110100
[5,1,7,2,6,3,8,4]=>0001111=>1111000
[5,1,7,2,8,3,6,4]=>0001111=>1111000
[8,1,5,2,7,3,6,4]=>0001111=>1111000
[8,1,5,2,6,3,7,4]=>0001111=>1111000
[5,1,8,2,6,3,7,4]=>0001111=>1111000
[5,1,6,2,8,3,7,4]=>0001111=>1111000
[3,1,6,2,8,4,7,5]=>0100111=>1110010
[4,1,8,2,6,3,7,5]=>0010111=>1110100
[8,1,4,2,6,3,7,5]=>0010111=>1110100
[8,1,4,2,5,3,7,6]=>0011011=>1101100
[4,1,8,2,5,3,7,6]=>0011011=>1101100
[4,1,5,2,8,3,7,6]=>0011011=>1101100
[3,1,5,2,8,4,7,6]=>0101011=>1101010
[3,1,4,2,8,5,7,6]=>0110011=>1100110
[4,1,3,2,7,5,8,6]=>0110011=>1100110
[5,1,4,2,8,3,7,6]=>0011011=>1101100
[6,1,3,2,8,4,7,5]=>0100111=>1110010
[6,1,3,2,7,4,8,5]=>0100111=>1110010
[5,1,3,2,7,4,8,6]=>0101011=>1101010
[5,1,3,2,6,4,8,7]=>0101101=>1011010
[5,1,4,2,6,3,8,7]=>0011101=>1011100
[6,1,4,2,7,3,8,5]=>0010111=>1110100
[6,1,5,2,7,3,8,4]=>0001111=>1111000
[6,1,7,2,8,3,5,4]=>0001111=>1111000
[5,1,6,2,4,3,8,7]=>0011101=>1011100
[7,8,3,1,2,5,6,4]=>0100101=>1010010
[7,8,1,3,2,4,6,5]=>0100101=>1010010
[2,5,3,6,1,8,7,4]=>0001111=>1111000
[6,2,8,1,3,5,4,7]=>0001101=>1011000
[6,2,8,3,1,7,4,5]=>0100111=>1110010
[3,2,5,7,1,8,4,6]=>0100011=>1100010
[3,5,2,8,1,7,4,6]=>0001011=>1101000
[4,3,1,2,7,8,6,5]=>0110101=>1010110
[5,3,4,7,8,6,1,2]=>0001101=>1011000
[4,1,3,2,6,8,7,5]=>0110011=>1100110
[5,1,3,7,2,6,8,4]=>0001011=>1101000
[5,2,4,7,8,1,6,3]=>0001101=>1011000
[2,5,4,6,8,1,7,3]=>0001011=>1101000
[4,2,5,7,6,1,8,3]=>0010111=>1110100
[6,1,8,3,2,4,7,5]=>0100111=>1110010
[4,3,5,7,6,8,1,2]=>0010011=>1100100
[4,2,1,3,7,6,8,5]=>1010011=>1100101
[2,4,3,1,8,5,7,6]=>0110011=>1100110
[5,2,1,8,3,6,4,7]=>1001101=>1011001
[3,2,4,1,8,6,5,7]=>0110101=>1010110
[3,4,2,1,8,7,5,6]=>1010011=>1100101
[7,6,4,3,2,1,8,5]=>1110111=>1110111
[7,6,5,8,2,1,4,3]=>1010111=>1110101
[7,6,8,3,2,1,5,4]=>1101011=>1101011
[7,8,4,3,2,1,6,5]=>1110101=>1010111
[8,5,4,3,2,1,7,6]=>1111011=>1101111
[7,6,3,8,2,1,5,4]=>1001111=>1111001
[7,6,5,8,4,1,3,2]=>0110111=>1110110
[7,4,8,3,2,1,6,5]=>1100111=>1110011
[7,6,8,5,2,1,4,3]=>1011011=>1101101
[4,8,6,1,7,5,2,3]=>0001111=>1111000
[4,8,7,2,6,5,1,3]=>0001111=>1111000
[4,7,8,2,6,1,5,3]=>0001101=>1011000
[4,6,8,2,7,1,3,5]=>0000011=>1100000
[8,6,4,2,7,5,3,1]=>0111111=>1111110
[8,4,7,3,6,5,1,2]=>0001111=>1111000
[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
[6,8,4,3,7,2,1,5]=>1010011=>1100101
[6,7,4,2,8,3,1,5]=>0110011=>1100110
[11,12,9,10,7,8,5,6,3,4,1,2]=>00101010101=>10101010100
[2,8,7,6,5,1,4,3]=>0011111=>1111100
[7,3,2,5,4,1,6,8]=>0111010=>0101110
[7,3,5,4,2,1,6,8]=>1011010=>0101101
[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
[7,1,4,2,6,3,5,8]=>0010110=>0110100
[7,3,4,1,5,6,2,8]=>0010110=>0110100
[7,3,2,5,1,6,4,8]=>0101110=>0111010
[7,4,1,3,5,2,6,8]=>0011010=>0101100
[7,3,1,2,4,6,5,8]=>0100110=>0110010
[3,6,2,1,4,8,5,7]=>1000101=>1010001
[2,3,6,1,4,8,7,5]=>0000111=>1110000
[3,6,7,4,1,5,8,2]=>0010011=>1100100
[3,1,2,8,6,5,4,7]=>0101101=>1011010
[5,4,8,6,1,2,3,7]=>0001101=>1011000
[5,6,8,2,4,1,3,7]=>0010001=>1000100
[5,6,8,7,4,3,1,2]=>0110011=>1100110
[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
[1,8,4,5,2,6,7,3]=>0001011=>1101000
[3,1,4,6,5,8,7,2]=>0100111=>1110010
[3,7,5,4,6,8,2,1]=>1001011=>1101001
[5,3,2,1,7,6,8,4]=>1101011=>1101011
[5,6,1,4,7,2,8,3]=>0000111=>1110000
[4,3,1,7,5,6,8,2]=>0110011=>1100110
[1,8,4,3,6,2,7,5]=>0010111=>1110100
[5,6,7,3,2,8,1,4]=>0100011=>1100010
[5,3,2,1,4,8,6,7]=>1101001=>1001011
[3,4,7,8,1,2,6,5]=>0000101=>1010000
[3,6,7,8,1,4,5,2]=>0001001=>1001000
[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
[1,8,4,2,3,5,7,6]=>0010011=>1100100
[6,3,4,8,2,5,7,1]=>0000111=>1110000
[7,5,4,8,3,6,2,1]=>1001111=>1111001
[7,3,2,5,8,4,6,1]=>0100111=>1110010
[5,7,8,3,1,4,6,2]=>0100101=>1010010
[7,4,8,3,2,5,1,6]=>0101011=>1101010
[7,3,8,2,4,5,6,1]=>0000111=>1110000
[4,2,7,1,5,3,8,6]=>0011011=>1101100
[2,7,1,3,5,4,8,6]=>0001011=>1101000
[1,2,7,3,4,8,6,5]=>0000111=>1110000
[4,7,2,1,5,8,6,3]=>1000111=>1110001
[2,3,4,8,1,6,5,7]=>0000101=>1010000
[3,1,4,8,2,6,7,5]=>0100011=>1100010
[4,8,3,6,5,1,7,2]=>0001111=>1111000
[6,4,7,3,5,1,8,2]=>0001111=>1111000
[3,1,6,4,7,8,2,5]=>0100101=>1010010
[7,3,1,6,8,2,4,5]=>0100011=>1100010
[7,3,5,1,6,8,2,4]=>0001011=>1101000
[4,7,3,5,6,1,8,2]=>0000111=>1110000
[1,8,2,3,5,7,4,6]=>0000011=>1100000
[2,7,3,6,1,4,5,8]=>0000110=>0110000
[1,2,5,8,3,7,4,6]=>0000011=>1100000
[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
[2,1,8,6,7,3,5,4]=>1001011=>1101001
[1,2,8,6,3,4,7,5]=>0000111=>1110000
[7,3,2,5,6,1,4,8]=>0100110=>0110010
[8,4,1,2,7,5,3,6]=>0011011=>1101100
[1,5,2,8,6,3,7,4]=>0001111=>1111000
[5,8,6,3,1,7,4,2]=>0110111=>1110110
[7,8,1,4,2,5,3,6]=>0011001=>1001100
[5,6,2,7,1,3,4,8]=>0000110=>0110000
[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
[2,7,1,8,5,6,3,4]=>0000111=>1110000
[2,1,7,8,6,3,4,5]=>1000101=>1010001
[7,8,6,2,1,3,5,4]=>1001101=>1011001
[4,1,2,6,5,3,8,7]=>0011101=>1011100
[2,6,5,3,1,4,8,7]=>0101101=>1011010
[6,1,3,4,2,8,7,5]=>0010111=>1110100
[8,2,6,4,7,3,5,1]=>0001111=>1111000
[2,5,1,8,7,4,6,3]=>0001111=>1111000
[6,2,3,8,4,7,5,1]=>0001111=>1111000
[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
[2,1,6,3,4,8,7,5]=>1000111=>1110001
[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
[8,1,4,2,5,6,7,3]=>0010011=>1100100
[3,4,2,1,8,6,7,5]=>1010011=>1100101
[2,7,6,8,1,5,3,4]=>0001011=>1101000
[8,1,3,2,5,6,7,4]=>0100011=>1100010
[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
[7,1,5,8,2,6,3,4]=>0000111=>1110000
[3,6,8,2,4,1,5,7]=>0010001=>1000100
[6,2,8,1,7,5,4,3]=>0011111=>1111100
[2,8,5,3,6,7,1,4]=>0001011=>1101000
[7,8,5,6,4,1,3,2]=>0110101=>1010110
[3,8,1,4,5,6,2,7]=>0000101=>1010000
[5,8,7,3,6,1,4,2]=>0010111=>1110100
[5,8,3,7,6,1,4,2]=>0010111=>1110100
[7,5,8,4,6,1,3,2]=>0100111=>1110010
[6,5,8,4,7,1,3,2]=>0100111=>1110010
[2,4,8,1,3,7,6,5]=>0000111=>1110000
[2,5,1,3,8,4,7,6]=>0001011=>1101000
[2,8,1,5,4,7,3,6]=>0001011=>1101000
[3,1,8,2,5,7,4,6]=>0100011=>1100010
[8,3,2,6,1,4,7,5]=>0100111=>1110010
[2,6,1,3,8,7,5,4]=>0001111=>1111000
[2,5,7,1,3,8,6,4]=>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
[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
[7,4,5,8,6,2,1,3]=>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
[5,1,7,6,4,2,8,3]=>0011111=>1111100
[5,1,8,7,6,4,3,2]=>0111111=>1111110
[8,5,2,1,6,3,7,4]=>1001111=>1111001
[5,1,6,2,8,7,4,3]=>0011111=>1111100
[4,5,6,1,8,7,2,3]=>0000111=>1110000
[3,5,6,8,7,1,4,2]=>0010011=>1100100
[3,6,1,7,4,8,2,5]=>0000111=>1110000
[8,4,2,6,3,1,5,7]=>0110101=>1010110
[4,1,5,8,7,2,3,6]=>0010011=>1100100
[3,4,8,7,1,2,6,5]=>0000111=>1110000
[3,4,6,8,5,7,1,2]=>0000011=>1100000
[4,6,8,3,5,7,2,1]=>1000011=>1100001
[4,7,3,5,8,2,6,1]=>0000111=>1110000
[6,3,7,2,4,8,1,5]=>0000111=>1110000
[5,6,8,3,7,2,1,4]=>1000011=>1100001
[5,6,8,4,2,7,3,1]=>0110011=>1100110
[6,5,2,7,1,3,8,4]=>0001111=>1111000
[6,5,4,1,7,2,8,3]=>0011111=>1111100
[6,4,7,3,1,8,2,5]=>0100111=>1110010
[6,8,5,7,4,3,2,1]=>1110011=>1100111
[7,5,8,4,6,3,2,1]=>1100111=>1110011
[5,6,3,7,4,2,1,8]=>1010110=>0110101
[6,1,3,8,5,2,4,7]=>0001101=>1011000
[7,4,2,6,3,5,1,8]=>0011110=>0111100
[3,4,7,5,6,2,1,8]=>1000110=>0110001
[8,1,3,4,5,2,6,7]=>0001001=>1001000
[1,6,8,4,2,5,3,7]=>0011001=>1001100
[3,6,8,4,1,7,5,2]=>0011011=>1101100
[8,7,2,3,6,1,4,5]=>0000111=>1110000
[6,7,4,8,5,1,2,3]=>0001011=>1101000
[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
[8,1,2,3,6,5,7,4]=>0000111=>1110000
[6,1,8,4,3,7,2,5]=>0010111=>1110100
[1,5,2,4,8,7,3,6]=>0001011=>1101000
[3,2,6,4,1,8,7,5]=>0110111=>1110110
[7,6,4,3,1,8,2,5]=>0110111=>1110110
[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
[8,2,7,6,5,1,3,4]=>0001111=>1111000
[4,8,6,7,1,5,3,2]=>0101011=>1101010
[1,8,6,7,2,3,4,5]=>0000011=>1100000
[7,6,3,2,1,8,5,4]=>1101111=>1111011
[3,5,4,2,7,1,8,6]=>0011011=>1101100
[8,6,3,1,4,5,7,2]=>0100111=>1110010
[3,2,6,1,5,7,4,8]=>0100110=>0110010
[5,2,1,4,7,6,3,8]=>1001110=>0111001
[4,2,1,3,5,8,7,6]=>1010011=>1100101
[7,4,1,5,3,6,8,2]=>0011011=>1101100
[3,1,5,2,7,4,9,6,8,10]=>010101010=>010101010
[6,8,5,3,7,1,2,4]=>0001011=>1101000
[6,8,2,4,5,1,3,7]=>0001001=>1001000
[6,8,3,4,1,5,2,7]=>0011001=>1001100
[5,8,4,1,7,2,6,3]=>0010111=>1110100
[6,8,3,1,4,5,7,2]=>0100011=>1100010
[5,3,8,4,2,6,7,1]=>0011011=>1101100
[4,1,8,3,5,7,2,6]=>0010011=>1100100
[2,4,6,3,5,8,1,7]=>0000101=>1010000
[4,5,7,2,3,6,8,1]=>0000011=>1100000
[2,6,3,4,7,5,8,1]=>0000111=>1110000
[4,5,2,7,1,6,8,3]=>0001011=>1101000
[2,3,1,7,6,4,8,5]=>0100111=>1110010
[3,4,1,6,5,8,2,7]=>0010101=>1010100
[7,3,1,4,8,5,6,2]=>0100111=>1110010
[7,5,1,2,8,6,3,4]=>0001111=>1111000
[6,4,2,8,7,1,5,3]=>0011111=>1111100
[3,1,8,2,7,6,4,5]=>0100111=>1110010
[6,2,8,4,1,7,5,3]=>0011111=>1111100
[3,6,4,7,2,5,1,8]=>0001110=>0111000
[7,3,2,8,6,1,4,5]=>0100111=>1110010
[4,3,8,7,1,2,5,6]=>0010011=>1100100
[1,2,5,8,4,7,3,6]=>0000011=>1100000
[1,3,6,8,5,2,7,4]=>0001011=>1101000
[2,5,7,4,1,8,6,3]=>0010111=>1110100
[2,4,6,1,8,3,7,5]=>0000111=>1110000
[1,4,2,5,8,7,3,6]=>0010011=>1100100
[3,5,1,7,2,8,6,4]=>0001111=>1111000
[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
[4,8,7,3,6,5,1,2]=>0001111=>1111000
[6,3,8,7,5,4,1,2]=>0011111=>1111100
[4,3,8,7,6,5,1,2]=>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
[4,1,8,7,6,5,3,2]=>0111111=>1111110
[3,1,8,7,6,5,4,2]=>0111111=>1111110
[7,8,2,6,1,5,4,3]=>0011101=>1011100
[4,2,8,1,7,6,5,3]=>0011111=>1111100
[3,2,8,1,7,6,5,4]=>0101111=>1111010
[2,8,7,1,6,5,4,3]=>0011111=>1111100
[3,8,2,1,7,6,5,4]=>1001111=>1111001
[4,8,2,7,6,1,5,3]=>0001111=>1111000
[3,8,2,7,1,6,5,4]=>0001111=>1111000
[3,8,7,2,1,6,5,4]=>1001111=>1111001
[4,8,7,2,6,1,5,3]=>0001111=>1111000
[5,8,7,6,2,1,4,3]=>1010111=>1110101
[6,5,8,7,1,4,3,2]=>0110111=>1110110
[3,8,7,1,6,5,4,2]=>0011111=>1111100
[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
[5,3,1,8,7,6,4,2]=>0111111=>1111110
[4,3,1,8,7,6,5,2]=>0111111=>1111110
[4,2,1,8,7,6,5,3]=>1011111=>1111101
[7,8,2,1,6,5,4,3]=>1011101=>1011101
[6,5,3,1,8,7,4,2]=>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
[6,1,4,2,3,5,8,7]=>0010101=>1010100
[8,6,1,4,2,3,5,7]=>0010101=>1010100
[6,8,1,4,2,3,5,7]=>0010001=>1000100
[4,6,2,3,8,1,5,7]=>0000101=>1010000
[6,2,3,8,4,1,5,7]=>0010101=>1010100
[6,4,2,3,8,1,5,7]=>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
[2,4,8,3,6,1,5,7]=>0000101=>1010000
[2,4,6,3,8,1,5,7]=>0000101=>1010000
[8,3,6,2,4,1,5,7]=>0010101=>1010100
[8,3,6,2,1,4,5,7]=>1000101=>1010001
[2,1,8,3,6,4,5,7]=>1000101=>1010001
[6,3,8,2,1,4,5,7]=>1000101=>1010001
[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
[3,4,6,8,7,5,1,2]=>0001011=>1101000
[5,4,6,3,8,7,1,2]=>0001111=>1111000
[6,4,8,5,3,7,1,2]=>0001111=>1111000
[1,8,5,2,6,3,7,4]=>0001111=>1111000
[1,4,6,2,8,5,7,3]=>0000111=>1110000
[7,8,1,4,2,5,6,3]=>0010101=>1010100
[3,6,5,2,4,1,8,7]=>0011101=>1011100
[4,8,5,3,1,6,2,7]=>0101101=>1011010
[5,2,8,6,4,1,3,7]=>0011101=>1011100
[5,1,6,2,8,7,3,4]=>0001111=>1111000
[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
[7,8,1,2,4,6,5,3]=>0001101=>1011000
[1,2,6,4,8,7,5,3]=>0001111=>1111000
[1,8,2,5,4,7,6,3]=>0001111=>1111000
[1,2,7,3,5,8,6,4]=>0000111=>1110000
[4,6,2,1,7,5,3,8]=>1001110=>0111001
[4,6,2,3,7,8,1,5]=>0000101=>1010000
[4,2,1,3,5,7,8,6]=>1010001=>1000101
[7,3,2,4,5,1,8,6]=>0101011=>1101010
[7,8,3,2,4,1,6,5]=>0110101=>1010110
[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
[7,5,2,8,3,4,1,6]=>0011011=>1101100
[4,3,6,8,1,2,7,5]=>0010011=>1100100
[6,4,3,5,2,8,1,7]=>0011101=>1011100
[6,5,8,4,2,3,1,7]=>0110101=>1010110
[4,1,3,6,5,8,7,2]=>0010111=>1110100
[2,4,1,3,8,5,7,6]=>0010011=>1100100
[2,4,1,3,5,8,7,6]=>0010011=>1100100
[4,6,1,3,5,8,7,2]=>0000111=>1110000
[1,4,6,3,5,8,7,2]=>0000111=>1110000
[4,2,1,3,6,5,7,8]=>1010100=>0010101
[4,2,1,6,3,5,7,8]=>1010100=>0010101
[4,2,1,8,3,5,7,6]=>1010011=>1100101
[6,2,1,8,3,5,7,4]=>1000111=>1110001
[6,4,1,3,8,5,7,2]=>0010111=>1110100
[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
[8,2,1,3,6,5,7,4]=>1000111=>1110001
[8,2,1,4,3,5,7,6]=>1010011=>1100101
[8,1,4,6,3,5,7,2]=>0000111=>1110000
[6,1,4,8,3,5,7,2]=>0000111=>1110000
[6,4,8,1,3,5,7,2]=>0000111=>1110000
[2,4,8,1,3,5,7,6]=>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
[1,4,6,8,3,5,7,2]=>0000011=>1100000
[1,4,6,3,8,5,7,2]=>0000111=>1110000
[4,6,1,3,8,5,7,2]=>0000111=>1110000
[2,6,1,3,8,5,7,4]=>0000111=>1110000
[2,6,1,8,3,5,7,4]=>0000111=>1110000
[2,1,6,3,8,5,7,4]=>1000111=>1110001
[2,1,3,6,8,5,7,4]=>1000011=>1100001
[4,1,3,6,8,5,7,2]=>0010011=>1100100
[1,4,3,6,8,5,7,2]=>0010011=>1100100
[2,1,8,3,6,5,7,4]=>1000111=>1110001
[2,1,8,6,3,5,7,4]=>1000111=>1110001
[2,1,8,4,3,5,7,6]=>1010011=>1100101
[4,1,8,3,6,5,7,2]=>0010111=>1110100
[2,8,4,1,3,5,7,6]=>0010011=>1100100
[6,8,1,4,3,5,7,2]=>0010011=>1100100
[1,8,6,4,3,5,7,2]=>0010111=>1110100
[8,6,1,4,3,5,7,2]=>0010111=>1110100
[8,6,4,1,3,5,7,2]=>0010111=>1110100
[8,4,2,1,3,5,7,6]=>1010011=>1100101
[8,5,7,4,3,2,1,6]=>1110011=>1100111
[8,7,6,5,1,4,3,2]=>0111111=>1111110
[8,7,4,3,6,2,1,5]=>1010111=>1110101
[8,7,3,6,5,2,1,4]=>1001111=>1111001
[6,5,8,4,3,2,1,7]=>1110101=>1010111
[8,4,7,6,3,2,1,5]=>1100111=>1110011
[5,8,7,4,3,2,1,6]=>1110011=>1100111
[4,5,2,7,3,1,8,6]=>0101011=>1101010
[4,8,2,6,3,5,7,1]=>0000111=>1110000
[8,6,1,2,7,4,3,5]=>0010111=>1110100
[4,3,7,8,6,5,1,2]=>0011101=>1011100
[4,6,2,1,7,8,5,3]=>1001101=>1011001
[2,3,8,7,4,1,6,5]=>0010111=>1110100
[7,8,2,1,5,6,4,3]=>1010101=>1010101
[1,6,2,5,8,4,3,7]=>0010101=>1010100
[1,5,8,6,2,3,7,4]=>0000111=>1110000
[5,2,7,1,8,6,3,4]=>0001111=>1111000
[1,2,8,3,7,6,5,4]=>0001111=>1111000
[6,5,2,8,1,7,3,4]=>0001111=>1111000
[2,8,3,5,1,7,4,6]=>0001011=>1101000
[2,8,5,6,1,7,3,4]=>0000111=>1110000
[5,4,2,8,6,1,7,3]=>0011111=>1111100
[8,5,4,3,7,2,6,1]=>0011111=>1111100
[8,3,7,4,2,6,5,1]=>0011111=>1111100
[3,8,7,4,1,6,5,2]=>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
[2,8,6,4,1,7,5,3]=>0011111=>1111100
[8,4,7,6,2,5,3,1]=>0101111=>1111010
[4,8,7,6,1,5,3,2]=>0101111=>1111010
[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
[5,4,2,3,8,1,6,7]=>0011001=>1001100
[3,7,8,4,1,2,6,5]=>0010101=>1010100
[8,7,4,6,3,5,2,1]=>1001111=>1111001
[7,3,4,8,2,1,5,6]=>1000011=>1100001
[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
[2,4,3,8,1,6,5,7]=>0010101=>1010100
[2,3,8,4,1,6,7,5]=>0010011=>1100100
[8,3,4,7,2,5,6,1]=>0000111=>1110000
[3,4,8,7,1,5,6,2]=>0000111=>1110000
[2,5,3,8,1,6,4,7]=>0001101=>1011000
[3,7,4,8,1,5,2,6]=>0001011=>1101000
[8,4,6,7,2,3,5,1]=>0001011=>1101000
[2,6,8,5,1,3,7,4]=>0001011=>1101000
[2,6,8,4,1,3,7,5]=>0010011=>1100100
[3,7,5,8,1,4,2,6]=>0010011=>1100100
[2,6,5,8,1,4,3,7]=>0010101=>1010100
[2,5,8,3,1,4,7,6]=>0100011=>1100010
[4,7,6,8,1,3,2,5]=>0100011=>1100010
[5,6,8,7,1,3,4,2]=>0010011=>1100100
[8,7,4,1,6,2,5,3]=>0011111=>1111100
[6,3,7,4,5,8,2,1]=>1000111=>1110001
[3,5,7,4,6,8,2,1]=>1000011=>1100001
[6,8,4,1,7,2,5,3]=>0011011=>1101100
[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
[5,4,2,7,8,3,6,1]=>0011101=>1011100
[8,1,6,2,4,3,5,7]=>0010101=>1010100
[8,7,1,2,4,3,5,6]=>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
[8,7,1,4,5,3,2,6]=>0101011=>1101010
[1,7,6,2,4,3,5,8]=>0010110=>0110100
[8,7,4,2,6,5,1,3]=>0011111=>1111100
[8,7,3,2,4,6,5,1]=>0101111=>1111010
[1,7,2,5,4,3,6,8]=>0011010=>0101100
[6,8,4,3,7,5,2,1]=>1011011=>1101101
[6,4,7,3,8,5,2,1]=>1001111=>1111001
[6,3,7,2,4,8,5,1]=>0001111=>1111000
[8,1,2,5,4,3,6,7]=>0011001=>1001100
[2,7,1,5,6,3,4,8]=>0000110=>0110000
[4,7,3,2,5,6,1,8]=>0100110=>0110010
[3,6,4,1,2,8,7,5]=>0010111=>1110100
[3,6,5,1,8,2,7,4]=>0001111=>1111000
[4,6,5,1,8,7,2,3]=>0001111=>1111000
[5,7,1,4,8,6,2,3]=>0000111=>1110000
[5,7,1,3,8,2,6,4]=>0000111=>1110000
[6,3,7,2,8,4,5,1]=>0001111=>1111000
[6,7,1,8,3,2,5,4]=>0101011=>1101010
[8,7,6,1,4,5,2,3]=>0001111=>1111000
[8,7,6,1,3,2,5,4]=>0101111=>1111010
[8,7,3,5,1,2,6,4]=>0001111=>1111000
[8,7,4,5,1,6,2,3]=>0001111=>1111000
[8,5,6,4,1,7,2,3]=>0010111=>1110100
[8,4,6,2,3,1,7,5]=>0100111=>1110010
[8,3,5,4,2,1,7,6]=>1011011=>1101101
[4,7,3,5,2,1,6,8]=>1001010=>0101001
[6,7,8,4,1,5,3,2]=>0111001=>1001110
[7,1,6,8,4,5,3,2]=>0101011=>1101010
[7,5,1,6,4,2,3,8]=>0011110=>0111100
[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
[4,8,5,1,6,7,3,2]=>0101011=>1101010
[8,4,1,5,6,7,3,2]=>0110011=>1100110
[8,1,4,5,6,7,3,2]=>0100011=>1100010
[8,2,5,6,1,4,7,3]=>0000111=>1110000
[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
[8,5,6,1,2,4,3,7]=>0010101=>1010100
[2,8,3,1,5,6,7,4]=>0100011=>1100010
[8,2,4,3,6,7,1,5]=>0010011=>1100100
[8,3,2,7,1,5,6,4]=>0100111=>1110010
[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
[7,3,1,5,6,2,4,8]=>0100110=>0110010
[2,7,3,6,5,8,1,4]=>0000111=>1110000
[7,2,8,1,6,4,5,3]=>0001111=>1111000
[7,8,2,6,4,1,5,3]=>0011101=>1011100
[8,7,2,4,1,6,5,3]=>0011111=>1111100
[1,2,8,6,3,7,5,4]=>0001111=>1111000
[1,8,7,2,3,6,5,4]=>0001111=>1111000
[1,7,8,2,6,4,3,5]=>0010101=>1010100
[2,1,7,3,6,8,4,5]=>1000011=>1100001
[7,2,1,5,8,3,4,6]=>1000011=>1100001
[7,1,5,8,3,2,4,6]=>0100011=>1100010
[7,8,1,5,2,4,3,6]=>0011001=>1001100
[8,7,1,2,5,4,3,6]=>0011011=>1101100
[1,6,2,8,4,3,7,5]=>0010111=>1110100
[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
[2,1,8,3,5,7,4,6]=>1000011=>1100001
[1,2,3,4,8,5,7,6]=>0000011=>1100000
[8,3,5,2,4,1,7,6]=>0011011=>1101100
[8,6,2,5,3,1,7,4]=>0101111=>1111010
[3,7,2,5,6,4,1,8]=>0010110=>0110100
[7,6,2,5,4,3,1,8]=>0111110=>0111110
[4,7,5,2,6,3,1,8]=>0101110=>0111010
[5,6,7,2,4,3,1,8]=>0110010=>0100110
[1,8,3,4,2,7,5,6]=>0010011=>1100100
[2,8,3,4,1,6,7,5]=>0010011=>1100100
[7,8,2,4,3,1,6,5]=>0110101=>1010110
[6,1,3,5,7,2,4,8]=>0000110=>0110000
[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
[6,2,5,8,1,4,7,3]=>0000111=>1110000
[3,2,8,5,1,6,7,4]=>0101011=>1101010
[2,3,8,1,5,6,7,4]=>0000011=>1100000
[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
[4,8,7,5,1,6,3,2]=>0101111=>1111010
[5,8,6,7,1,4,3,2]=>0110011=>1100110
[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
[3,4,8,5,6,1,7,2]=>0000111=>1110000
[8,3,7,4,1,6,5,2]=>0011111=>1111100
[3,5,6,8,4,1,7,2]=>0010011=>1100100
[5,6,4,7,8,1,3,2]=>0100101=>1010010
[6,2,3,1,5,4,7,8]=>0101100=>0011010
[8,5,1,3,2,4,7,6]=>0101011=>1101010
[7,5,1,3,2,6,4,8]=>0101110=>0111010
[3,6,4,1,5,2,7,8]=>0011100=>0011100
[4,5,6,1,3,2,7,8]=>0100100=>0010010
[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
[7,8,1,2,5,3,6,4]=>0001101=>1011000
[6,8,1,4,2,3,7,5]=>0010011=>1100100
[4,5,8,1,2,3,7,6]=>0000011=>1100000
[1,8,2,7,5,4,6,3]=>0001111=>1111000
[1,8,6,3,7,2,4,5]=>0000111=>1110000
[1,8,5,3,4,7,2,6]=>0001011=>1101000
[1,8,5,4,7,2,6,3]=>0001111=>1111000
[1,8,2,5,4,6,7,3]=>0001011=>1101000
[7,4,3,8,2,5,6,1]=>0010111=>1110100
[7,2,8,4,3,5,6,1]=>0010111=>1110100
[7,2,8,1,3,6,4,5]=>0000111=>1110000
[1,4,7,5,2,6,8,3]=>0001011=>1101000
[4,6,5,3,7,1,8,2]=>0001111=>1111000
[5,6,2,7,3,1,8,4]=>0100111=>1110010
[1,6,3,7,5,8,2,4]=>0000111=>1110000
[5,2,4,8,1,3,7,6]=>0001011=>1101000
[6,2,5,4,8,3,7,1]=>0001111=>1111000
[3,5,2,4,7,1,6,8]=>0001010=>0101000
[6,4,5,3,8,2,1,7]=>1001101=>1011001
[6,5,3,4,8,7,1,2]=>0001111=>1111000
[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
[5,4,8,1,2,7,3,6]=>0001011=>1101000
[6,2,4,8,5,1,3,7]=>0001101=>1011000
[7,6,3,8,5,1,2,4]=>0001111=>1111000
[6,3,8,1,7,2,4,5]=>0000111=>1110000
[7,2,8,6,1,3,4,5]=>0000111=>1110000
[7,2,8,6,1,5,3,4]=>0001111=>1111000
[3,2,4,7,8,1,5,6]=>0100001=>1000010
[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
[1,5,3,6,8,2,7,4]=>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
[4,2,3,6,8,1,5,7]=>0010001=>1000100
[2,6,1,5,4,8,3,7]=>0001101=>1011000
[3,2,1,8,7,5,6,4]=>1100111=>1110011
[3,1,6,2,5,8,4,7]=>0100101=>1010010
[6,5,1,3,4,8,2,7]=>0001101=>1011000
[6,2,4,5,8,1,3,7]=>0000101=>1010000
[2,6,1,5,8,3,4,7]=>0000101=>1010000
[2,3,4,8,1,7,6,5]=>0000111=>1110000
[6,3,1,7,8,4,5,2]=>0101101=>1011010
[6,2,7,8,4,5,1,3]=>0001101=>1011000
[3,1,4,8,7,6,2,5]=>0100111=>1110010
[2,3,6,5,8,7,1,4]=>0000111=>1110000
[8,4,1,2,7,6,3,5]=>0010111=>1110100
[3,4,8,2,7,5,1,6]=>0001011=>1101000
[6,3,2,8,5,7,4,1]=>0110111=>1110110
[3,2,6,8,5,1,7,4]=>0101011=>1101010
[5,2,4,1,7,8,6,3]=>0011101=>1011100
[3,8,4,7,2,5,6,1]=>0000111=>1110000
[1,8,7,2,4,5,6,3]=>0000111=>1110000
[5,3,4,7,1,8,6,2]=>0001111=>1111000
[5,3,7,1,6,2,8,4]=>0001111=>1111000
[4,7,6,5,8,2,1,3]=>1000111=>1110001
[7,5,1,2,6,8,4,3]=>0011011=>1101100
[1,2,5,3,8,7,6,4]=>0001111=>1111000
[2,8,1,5,6,3,7,4]=>0000111=>1110000
[4,8,2,3,6,7,1,5]=>0000011=>1100000
[8,2,4,6,7,1,3,5]=>0000011=>1100000
[3,7,5,1,8,4,6,2]=>0001111=>1111000
[6,5,3,1,8,4,2,7]=>0111101=>1011110
[5,7,4,3,8,6,2,1]=>1010111=>1110101
[4,2,3,8,5,6,1,7]=>0010101=>1010100
[3,6,4,2,8,5,7,1]=>0010111=>1110100
[4,7,3,2,5,1,8,6]=>0101011=>1101010
[2,4,8,7,1,3,5,6]=>0000011=>1100000
[2,4,3,5,1,8,6,7]=>0011001=>1001100
[8,6,1,2,4,3,5,7]=>0010101=>1010100
[8,6,2,5,4,1,3,7]=>0011101=>1011100
[8,3,5,7,6,2,1,4]=>1000111=>1110001
[6,7,5,3,8,2,4,1]=>0011011=>1101100
[8,2,6,3,4,5,1,7]=>0001101=>1011000
[8,1,5,4,3,6,2,7]=>0011101=>1011100
[8,6,4,2,1,5,3,7]=>1011101=>1011101
[8,3,2,4,6,1,5,7]=>0100101=>1010010
[8,2,3,4,7,6,1,5]=>0000111=>1110000
[5,7,1,8,3,4,6,2]=>0000111=>1110000
[1,5,6,7,3,4,8,2]=>0000011=>1100000
[8,1,3,7,6,4,2,5]=>0010111=>1110100
[4,8,1,2,7,3,6,5]=>0000111=>1110000
[2,5,7,8,4,1,3,6]=>0010001=>1000100
[6,3,5,8,7,2,4,1]=>0010111=>1110100
[5,2,8,7,1,3,4,6]=>0001011=>1101000
[5,2,7,4,8,1,6,3]=>0001111=>1111000
[8,3,7,4,2,5,6,1]=>0010111=>1110100
[8,1,7,4,5,2,6,3]=>0001111=>1111000
[1,7,8,3,5,4,6,2]=>0001101=>1011000
[4,6,3,5,8,1,7,2]=>0000111=>1110000
[8,2,4,1,5,6,7,3]=>0010011=>1100100
[3,5,1,7,6,8,2,4]=>0001011=>1101000
[2,1,7,6,4,5,8,3]=>1000111=>1110001
[1,7,6,5,2,4,8,3]=>0001111=>1111000
[5,1,7,6,2,8,4,3]=>0011111=>1111100
[4,6,2,5,3,8,7,1]=>0001111=>1111000
[8,6,4,2,3,1,7,5]=>0110111=>1110110
[8,6,4,2,1,3,7,5]=>1010111=>1110101
[2,5,7,3,8,4,6,1]=>0000111=>1110000
[4,2,7,1,8,5,3,6]=>0011011=>1101100
[8,3,6,7,1,5,4,2]=>0011011=>1101100
[1,3,7,5,8,6,4,2]=>0010111=>1110100
[2,7,4,5,8,3,6,1]=>0000111=>1110000
[3,5,7,1,4,8,6,2]=>0000111=>1110000
[3,4,1,2,8,5,7,6]=>0010011=>1100100
[8,7,3,1,2,6,4,5]=>0100111=>1110010
[6,2,3,1,4,8,7,5]=>0100111=>1110010
[8,4,3,2,5,7,1,6]=>0110011=>1100110
[5,3,6,8,2,1,4,7]=>1001001=>1001001
[3,2,6,8,5,4,1,7]=>0111001=>1001110
[7,3,8,2,5,4,1,6]=>0011011=>1101100
[7,4,2,5,8,3,1,6]=>0110011=>1100110
[3,1,2,8,5,6,4,7]=>0100101=>1010010
[5,2,1,6,8,3,4,7]=>1001001=>1001001
[3,1,8,6,5,4,2,7]=>0111101=>1011110
[5,6,8,1,4,3,2,7]=>0110001=>1000110
[6,4,8,3,7,2,5,1]=>0001111=>1111000
[4,7,3,6,2,1,8,5]=>1000111=>1110001
[7,8,4,1,5,3,2,6]=>0111001=>1001110
[7,3,8,5,1,4,2,6]=>0011011=>1101100
[1,5,4,8,3,7,6,2]=>0001111=>1111000
[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
[3,1,2,7,5,6,8,4]=>0100011=>1100010
[3,6,1,2,7,5,8,4]=>0000111=>1110000
[3,6,2,5,8,7,4,1]=>0010111=>1110100
[8,5,2,3,6,7,4,1]=>0011011=>1101100
[2,7,3,1,5,6,8,4]=>0100011=>1100010
[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
[4,7,2,6,3,8,1,5]=>0000111=>1110000
[4,8,2,6,3,7,5,1]=>0001111=>1111000
[3,7,2,4,6,1,8,5]=>0000111=>1110000
[5,3,7,2,8,1,4,6]=>0001011=>1101000
[7,1,8,3,4,2,5,6]=>0010011=>1100100
[7,2,4,1,8,3,5,6]=>0010011=>1100100
[4,8,7,6,3,2,1,5]=>1100111=>1110011
[7,3,8,2,6,5,1,4]=>0001111=>1111000
[7,8,2,4,6,1,5,3]=>0001101=>1011000
[3,5,1,8,7,2,6,4]=>0001111=>1111000
[5,2,8,1,7,6,3,4]=>0001111=>1111000
[6,2,1,3,8,7,5,4]=>1001111=>1111001
[5,6,1,2,8,7,4,3]=>0010111=>1110100
[6,7,8,1,2,5,4,3]=>0011001=>1001100
[5,8,7,1,6,4,3,2]=>0110111=>1110110
[6,8,7,5,1,4,3,2]=>0111011=>1101110
[8,6,4,3,2,1,7,5]=>1110111=>1110111
[6,5,4,3,8,2,7,1]=>0011111=>1111100
[7,5,4,3,2,8,6,1]=>0111111=>1111110
[8,5,4,3,7,2,1,6]=>1011011=>1101101
[8,4,3,2,1,7,6,5]=>1110111=>1110111
[3,7,5,8,1,4,6,2]=>0000111=>1110000
[4,7,5,8,3,2,1,6]=>1100011=>1100011
[5,7,2,3,6,1,8,4]=>0000111=>1110000
[7,3,1,4,8,2,5,6]=>0100011=>1100010
[7,4,1,2,5,8,3,6]=>0010011=>1100100
[4,7,1,6,5,8,3,2]=>0100111=>1110010
[2,7,5,4,3,8,1,6]=>0011011=>1101100
[8,6,4,2,3,7,5,1]=>0011111=>1111100
[7,6,4,2,3,8,1,5]=>0010111=>1110100
[6,4,7,1,3,8,5,2]=>0001111=>1111000
[3,1,2,4,8,7,6,5]=>0100111=>1110010
[6,5,8,7,3,1,2,4]=>0100111=>1110010
[5,6,7,8,1,4,2,3]=>0010001=>1000100
[2,6,7,4,5,3,1,8]=>0101010=>0101010
[1,3,7,4,2,8,5,6]=>0010011=>1100100
[4,6,1,3,7,2,5,8]=>0000110=>0110000
[6,5,7,8,3,1,4,2]=>0110101=>1010110
[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
[6,1,4,2,7,8,5,3]=>0011101=>1011100
[7,3,8,4,1,2,6,5]=>0010111=>1110100
[6,8,3,2,7,1,5,4]=>0101011=>1101010
[5,1,4,3,6,2,7,8]=>0011100=>0011100
[4,8,5,6,3,2,1,7]=>1100101=>1010011
[2,8,5,6,3,7,1,4]=>0000111=>1110000
[6,7,3,1,4,2,8,5]=>0110011=>1100110
[3,2,6,7,4,8,1,5]=>0100011=>1100010
[3,7,1,2,4,6,5,8]=>0000110=>0110000
[4,1,8,2,6,3,5,7]=>0010101=>1010100
[7,5,6,8,2,1,4,3]=>1010011=>1100101
[5,8,6,7,1,2,3,4]=>0000011=>1100000
[4,8,1,5,7,2,3,6]=>0000011=>1100000
[3,5,1,4,7,6,8,2]=>0001011=>1101000
[5,3,2,7,1,6,8,4]=>0101011=>1101010
[8,4,3,7,5,1,6,2]=>0011111=>1111100
[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
[4,8,3,6,5,2,1,7]=>1001101=>1011001
[1,8,6,5,4,2,3,7]=>0011101=>1011100
[8,1,7,4,2,5,6,3]=>0010111=>1110100
[1,8,7,2,5,3,4,6]=>0001011=>1101000
[4,8,1,5,2,6,3,7]=>0001101=>1011000
[3,6,8,5,1,2,4,7]=>0001001=>1001000
[1,5,2,7,8,4,6,3]=>0001101=>1011000
[6,7,2,8,5,3,1,4]=>0101011=>1101010
[6,7,2,8,3,1,5,4]=>0101011=>1101010
[7,1,2,8,3,5,6,4]=>0000111=>1110000
[6,7,5,2,8,1,4,3]=>0011011=>1101100
[7,1,4,5,8,6,2,3]=>0000111=>1110000
[3,1,4,6,7,8,5,2]=>0101001=>1001010
[5,7,6,4,2,8,1,3]=>0010111=>1110100
[7,4,6,1,8,2,3,5]=>0000111=>1110000
[3,4,5,1,6,8,7,2]=>0001011=>1101000
[5,1,6,8,4,2,7,3]=>0011011=>1101100
[7,4,8,2,3,6,5,1]=>0001111=>1111000
[7,5,8,6,3,4,2,1]=>1010111=>1110101
[5,7,8,3,1,6,4,2]=>0110101=>1010110
[7,5,8,3,2,4,1,6]=>0110011=>1100110
[6,4,1,8,2,5,7,3]=>0010111=>1110100
[5,8,2,6,3,1,4,7]=>0100101=>1010010
[3,6,5,1,8,4,7,2]=>0001111=>1111000
[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
[7,5,1,6,2,8,4,3]=>0011111=>1111100
[6,2,7,3,8,4,1,5]=>0010111=>1110100
[3,7,2,4,8,5,1,6]=>0001011=>1101000
[1,5,2,6,3,8,7,4]=>0001111=>1111000
[1,3,6,2,4,8,7,5]=>0000111=>1110000
[7,3,5,2,4,1,6,8]=>0011010=>0101100
[8,3,6,2,5,4,1,7]=>0011101=>1011100
[3,5,8,2,4,6,1,7]=>0000101=>1010000
[6,4,7,8,2,3,1,5]=>0100101=>1010010
[7,4,8,5,3,2,1,6]=>1101011=>1101011
[1,5,3,2,8,4,7,6]=>0101011=>1101010
[2,8,7,3,5,1,4,6]=>0001011=>1101000
[3,8,4,7,5,1,2,6]=>0001011=>1101000
[6,1,2,7,3,8,5,4]=>0001111=>1111000
[2,1,7,3,4,8,6,5]=>1000111=>1110001
[8,3,1,6,7,2,5,4]=>0101011=>1101010
[4,8,3,7,1,5,2,6]=>0001011=>1101000
[1,3,5,8,2,4,7,6]=>0000011=>1100000
[5,7,4,8,2,1,3,6]=>1000011=>1100001
[4,6,8,2,5,1,3,7]=>0001001=>1001000
[5,3,7,2,1,4,6,8]=>1001010=>0101001
[6,4,2,8,3,1,5,7]=>0110101=>1010110
[5,7,2,3,8,1,4,6]=>0000011=>1100000
[6,4,7,5,8,1,2,3]=>0000111=>1110000
[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
[7,4,8,1,6,3,5,2]=>0001111=>1111000
[3,6,1,8,2,4,7,5]=>0000111=>1110000
[6,4,1,8,3,2,7,5]=>0110111=>1110110
[1,4,8,7,2,6,5,3]=>0001111=>1111000
[5,4,1,8,7,3,2,6]=>0111011=>1101110
[5,8,4,1,7,6,2,3]=>0010111=>1110100
[8,6,1,7,5,4,3,2]=>0111111=>1111110
[3,1,8,7,6,5,2,4]=>0101111=>1111010
[8,1,2,4,5,3,6,7]=>0001001=>1001000
[1,8,7,6,4,5,3,2]=>0101111=>1111010
[2,6,8,1,3,7,5,4]=>0001011=>1101000
[2,4,8,1,5,7,6,3]=>0000111=>1110000
[3,2,8,6,1,7,5,4]=>0101111=>1111010
[6,2,8,3,1,7,5,4]=>0101111=>1111010
[7,4,3,8,5,2,1,6]=>1011011=>1101101
[6,5,2,8,4,3,1,7]=>0111101=>1011110
[4,3,8,7,5,1,6,2]=>0011111=>1111100
[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
[3,2,5,8,6,1,4,7]=>0100101=>1010010
[8,4,3,7,5,2,6,1]=>0011111=>1111100
[4,3,7,8,5,1,2,6]=>0011001=>1001100
[4,2,6,8,5,1,3,7]=>0011001=>1001100
[3,5,2,8,4,6,1,7]=>0001101=>1011000
[5,2,6,8,4,1,3,7]=>0011001=>1001100
[5,3,7,8,4,1,2,6]=>0011001=>1001100
[5,6,2,8,3,4,1,7]=>0010101=>1010100
[5,3,8,7,4,1,6,2]=>0011111=>1111100
[6,4,2,8,5,3,1,7]=>0111101=>1011110
[8,7,5,3,6,2,4,1]=>0011111=>1111100
[8,7,4,3,6,2,5,1]=>0011111=>1111100
[8,6,5,3,7,2,4,1]=>0011111=>1111100
[7,6,4,3,8,2,5,1]=>0011111=>1111100
[6,4,5,3,8,2,7,1]=>0001111=>1111000
[7,4,5,3,8,2,6,1]=>0001111=>1111000
[7,5,6,3,8,2,4,1]=>0010111=>1110100
[8,5,6,3,7,2,4,1]=>0010111=>1110100
[8,4,6,3,7,2,5,1]=>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
[7,5,8,3,4,2,6,1]=>0010111=>1110100
[7,6,8,3,5,2,4,1]=>0011011=>1101100
[7,5,8,4,6,2,3,1]=>0100111=>1110010
[7,5,8,3,6,2,4,1]=>0010111=>1110100
[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
[5,4,7,3,6,2,8,1]=>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
[6,5,7,3,8,2,4,1]=>0010111=>1110100
[5,4,6,3,8,2,7,1]=>0001111=>1111000
[6,5,3,7,8,2,1,4]=>1001101=>1011001
[6,5,4,2,8,7,1,3]=>0011111=>1111100
[6,4,3,7,5,2,1,8]=>1011110=>0111101
[6,3,7,8,5,2,1,4]=>1001101=>1011001
[6,3,7,2,5,4,1,8]=>0011110=>0111100
[6,3,2,7,5,4,1,8]=>0111110=>0111110
[4,8,2,6,3,7,1,5]=>0000111=>1110000
[5,8,4,1,2,7,3,6]=>0010011=>1100100
[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
[5,8,1,7,4,2,3,6]=>0010011=>1100100
[4,8,6,7,2,3,1,5]=>0100011=>1100010
[4,8,7,3,6,2,1,5]=>1000111=>1110001
[4,3,8,2,7,1,6,5]=>0010111=>1110100
[4,1,8,7,3,2,5,6]=>0110011=>1100110
[4,7,8,1,2,5,3,6]=>0001001=>1001000
[4,7,5,1,2,8,3,6]=>0001011=>1101000
[2,3,6,7,4,1,8,5]=>0010011=>1100100
[2,6,3,4,7,8,1,5]=>0000101=>1010000
[3,1,7,8,4,2,5,6]=>0110001=>1000110
[4,3,1,2,8,5,7,6]=>0110011=>1100110
[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
[3,7,8,2,6,4,1,5]=>0010101=>1010100
[4,2,3,8,1,6,7,5]=>0010011=>1100100
[3,7,2,8,4,6,1,5]=>0000111=>1110000
[4,2,8,3,6,1,7,5]=>0010111=>1110100
[4,2,8,6,3,1,7,5]=>0110111=>1110110
[2,6,8,4,7,3,1,5]=>0100011=>1100010
[2,4,6,8,3,1,7,5]=>0100011=>1100010
[3,7,2,4,8,6,1,5]=>0000111=>1110000
[1,3,6,4,7,2,5,8]=>0000110=>0110000
[2,4,6,3,8,1,7,5]=>0000111=>1110000
[2,6,4,3,8,7,1,5]=>0010111=>1110100
[2,4,3,6,1,8,7,5]=>0010111=>1110100
[3,1,7,4,8,2,5,6]=>0100011=>1100010
[2,6,7,3,8,4,1,5]=>0010011=>1100100
[2,6,3,7,4,8,1,5]=>0000111=>1110000
[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
[1,3,5,2,7,6,8,4]=>0001011=>1101000
[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
[1,3,5,7,8,6,2,4]=>0000101=>1010000
[2,3,6,1,7,8,5,4]=>0001101=>1011000
[2,3,7,1,4,8,6,5]=>0000111=>1110000
[2,6,1,3,7,8,5,4]=>0001101=>1011000
[2,3,6,8,4,5,1,7]=>0001001=>1001000
[2,5,7,3,4,8,6,1]=>0000111=>1110000
[2,6,7,3,4,8,5,1]=>0001011=>1101000
[6,5,2,4,3,7,1,8]=>0011110=>0111100
[2,5,4,6,7,1,3,8]=>0001010=>0101000
[1,7,6,3,5,4,8,2]=>0001111=>1111000
[2,4,6,3,7,5,1,8]=>0001110=>0111000
[4,7,2,3,5,6,1,8]=>0000110=>0110000
[5,3,2,7,4,6,1,8]=>0101110=>0111010
[1,6,8,5,7,3,4,2]=>0010011=>1100100
[4,1,2,5,8,3,7,6]=>0010011=>1100100
[4,6,1,2,5,8,3,7]=>0000101=>1010000
[4,1,7,2,6,5,8,3]=>0010111=>1110100
[5,6,7,2,1,4,8,3]=>1000011=>1100001
[6,4,5,7,1,3,8,2]=>0000111=>1110000
[6,8,5,2,4,1,7,3]=>0011011=>1101100
[5,7,6,8,1,4,2,3]=>0010011=>1100100
[4,1,6,2,8,5,7,3]=>0010111=>1110100
[7,1,4,2,3,6,8,5]=>0010011=>1100100
[6,4,2,1,3,8,7,5]=>1010111=>1110101
[1,5,8,3,4,6,7,2]=>0000011=>1100000
[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
[4,3,2,8,1,6,5,7]=>0110101=>1010110
[3,8,6,4,2,1,5,7]=>1010101=>1010101
[3,8,2,1,5,6,4,7]=>1000101=>1010001
[8,5,2,4,3,1,6,7]=>0111001=>1001110
[8,3,2,5,4,1,6,7]=>0111001=>1001110
[6,1,2,7,5,3,8,4]=>0001111=>1111000
[2,6,1,4,7,3,8,5]=>0000111=>1110000
[7,3,2,8,6,4,1,5]=>0110111=>1110110
[2,7,8,4,6,3,1,5]=>0100101=>1010010
[7,8,2,5,3,6,1,4]=>0001101=>1011000
[6,3,7,5,1,8,2,4]=>0001111=>1111000
[8,1,6,3,5,7,2,4]=>0000111=>1110000
[8,3,2,6,4,7,1,5]=>0100111=>1110010
[5,8,4,6,1,7,2,3]=>0000111=>1110000
[8,4,2,5,6,7,1,3]=>0010011=>1100100
[2,3,8,7,6,5,1,4]=>0001111=>1111000
[1,5,8,7,2,6,4,3]=>0010111=>1110100
[2,5,8,7,3,6,1,4]=>0000111=>1110000
[4,1,8,7,2,6,5,3]=>0011111=>1111100
[1,2,8,7,3,6,5,4]=>0001111=>1111000
[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
[2,6,8,3,7,5,1,4]=>0001011=>1101000
[1,6,8,4,7,2,5,3]=>0001011=>1101000
[1,6,8,3,7,2,5,4]=>0001011=>1101000
[2,5,8,1,7,6,4,3]=>0010111=>1110100
[2,5,8,3,7,6,1,4]=>0000111=>1110000
[3,2,8,4,7,6,1,5]=>0100111=>1110010
[1,5,8,4,7,2,6,3]=>0000111=>1110000
[1,5,8,3,7,2,6,4]=>0000111=>1110000
[3,1,8,4,7,2,6,5]=>0100111=>1110010
[5,6,8,1,2,7,4,3]=>0010011=>1100100
[1,6,8,4,2,7,5,3]=>0011011=>1101100
[1,6,8,2,3,7,5,4]=>0001011=>1101000
[1,5,8,4,2,7,6,3]=>0010111=>1110100
[5,6,8,4,3,2,1,7]=>1110001=>1000111
[7,1,4,8,6,2,5,3]=>0001111=>1111000
[7,3,1,8,6,2,5,4]=>0101111=>1111010
[7,3,4,8,6,2,1,5]=>1000111=>1110001
[7,1,5,8,2,6,4,3]=>0010111=>1110100
[7,1,4,8,2,6,5,3]=>0001111=>1111000
[7,4,5,8,1,2,6,3]=>0000111=>1110000
[3,6,2,8,7,5,1,4]=>0001111=>1111000
[1,6,4,8,7,2,5,3]=>0001111=>1111000
[3,2,4,8,7,6,1,5]=>0100111=>1110010
[1,4,5,8,7,2,6,3]=>0000111=>1110000
[3,1,4,8,7,2,6,5]=>0100111=>1110010
[1,6,5,8,2,7,4,3]=>0010111=>1110100
[2,6,5,8,3,7,1,4]=>0000111=>1110000
[1,6,4,8,2,7,5,3]=>0001111=>1111000
[2,6,1,8,3,7,5,4]=>0001111=>1111000
[2,4,5,8,3,7,1,6]=>0000011=>1100000
[1,4,5,8,3,2,7,6]=>0100011=>1100010
[4,6,5,8,3,2,1,7]=>1100101=>1010011
[7,6,2,3,8,5,1,4]=>0001111=>1111000
[7,6,1,4,8,2,5,3]=>0001111=>1111000
[7,6,3,4,8,2,1,5]=>1000111=>1110001
[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
[2,6,5,3,8,7,1,4]=>0001111=>1111000
[2,6,1,4,8,7,5,3]=>0001111=>1111000
[1,3,5,4,8,2,7,6]=>0001011=>1101000
[7,6,5,1,2,8,4,3]=>0011111=>1111100
[7,1,5,2,3,8,6,4]=>0001111=>1111000
[7,1,2,4,3,8,6,5]=>0010111=>1110100
[7,2,5,4,3,8,1,6]=>0011011=>1101100
[1,6,2,4,3,8,7,5]=>0010111=>1110100
[2,6,5,4,3,8,1,7]=>0011101=>1011100
[7,6,5,1,3,2,8,4]=>0101111=>1111010
[8,2,7,6,5,4,1,3]=>0011111=>1111100
[7,2,8,6,5,4,3,1]=>0111111=>1111110
[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
[4,8,5,7,6,3,2,1]=>1100111=>1110011
[3,2,4,6,8,1,5,7]=>0100001=>1000010
[3,5,7,2,4,8,1,6]=>0000011=>1100000
[3,5,7,2,4,6,8,1]=>0000011=>1100000
[4,5,1,3,6,8,2,7]=>0001001=>1001000
[4,3,5,7,2,6,8,1]=>0010011=>1100100
[4,3,5,1,7,8,2,6]=>0011001=>1001100
[4,6,3,5,1,7,8,2]=>0001101=>1011000
[4,6,3,5,7,2,8,1]=>0000111=>1110000
[5,1,6,7,3,4,8,2]=>0001011=>1101000
[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
[1,4,6,7,3,8,2,5]=>0000011=>1100000
[3,5,2,6,7,4,8,1]=>0001011=>1101000
[6,3,1,7,8,2,4,5]=>0100101=>1010010
[5,7,2,8,1,3,4,6]=>0000011=>1100000
[6,3,7,2,8,1,4,5]=>0000111=>1110000
[6,3,7,2,5,8,1,4]=>0000111=>1110000
[6,2,4,5,7,3,8,1]=>0000111=>1110000
[2,4,6,7,1,5,8,3]=>0000011=>1100000
[2,4,7,1,5,6,8,3]=>0000011=>1100000
[3,7,1,5,6,8,2,4]=>0000011=>1100000
[4,6,7,1,2,5,8,3]=>0000011=>1100000
[1,5,6,7,2,4,8,3]=>0000011=>1100000
[5,6,2,4,1,7,8,3]=>0010101=>1010100
[1,5,4,6,2,7,8,3]=>0001101=>1011000
[5,6,4,7,1,3,8,2]=>0000111=>1110000
[8,4,5,2,6,1,3,7]=>0001101=>1011000
[6,4,3,7,2,5,8,1]=>0010111=>1110100
[6,4,3,7,2,8,1,5]=>0010111=>1110100
[7,4,5,3,1,6,8,2]=>0101011=>1101010
[6,4,3,7,5,1,8,2]=>0011111=>1111100
[5,6,3,7,4,1,8,2]=>0010111=>1110100
[6,7,4,2,1,5,8,3]=>1010011=>1100101
[6,7,4,2,1,8,3,5]=>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
[5,6,7,2,8,1,3,4]=>0000011=>1100000
[6,7,3,8,1,2,4,5]=>0000011=>1100000
[6,7,3,2,8,1,4,5]=>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
[7,5,3,2,6,1,8,4]=>0101111=>1111010
[6,5,3,2,7,8,1,4]=>0101101=>1011010
[6,4,7,2,5,1,8,3]=>0001111=>1111000
[6,4,7,5,1,2,8,3]=>0001111=>1111000
[5,6,4,2,7,3,8,1]=>0010111=>1110100
[6,5,3,7,1,8,2,4]=>0001111=>1111000
[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
[5,3,7,8,1,6,4,2]=>0011101=>1011100
[5,3,7,8,6,1,4,2]=>0011101=>1011100
[7,3,5,8,6,1,4,2]=>0010111=>1110100
[7,3,8,5,6,1,4,2]=>0010111=>1110100
[7,8,3,5,6,1,4,2]=>0010101=>1010100
[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
[5,1,7,8,6,3,4,2]=>0011101=>1011100
[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
[7,3,8,5,1,6,4,2]=>0011111=>1111100
[7,3,5,8,1,6,4,2]=>0010111=>1110100
[7,3,5,1,8,6,4,2]=>0011111=>1111100
[5,3,7,1,8,6,4,2]=>0011111=>1111100
[3,5,7,1,8,6,4,2]=>0010111=>1110100
[1,5,7,3,8,6,4,2]=>0010111=>1110100
[1,7,5,3,8,6,4,2]=>0011111=>1111100
[3,7,5,1,8,6,4,2]=>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
[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
[7,8,1,3,5,6,4,2]=>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
[5,1,3,7,8,6,4,2]=>0011101=>1011100
[3,1,5,7,8,6,4,2]=>0110101=>1010110
[4,3,1,2,6,5,8,7]=>0110101=>1010110
[6,1,4,3,5,2,8,7]=>0011101=>1011100
[4,6,3,5,1,2,8,7]=>0001101=>1011000
[6,2,4,5,1,3,8,7]=>0001101=>1011000
[2,3,6,1,5,4,8,7]=>0001101=>1011000
[2,1,6,5,3,4,8,7]=>1001101=>1011001
[3,5,6,2,4,1,8,7]=>0010101=>1010100
[8,7,6,1,3,2,4,5]=>0100111=>1110010
[2,5,3,4,8,1,7,6]=>0001011=>1101000
[5,1,8,2,3,4,7,6]=>0001011=>1101000
[5,4,7,6,2,8,1,3]=>0001111=>1111000
[2,1,6,8,5,7,3,4]=>1000011=>1100001
[2,1,8,4,6,7,3,5]=>1000011=>1100001
[3,1,8,6,2,7,5,4]=>0101111=>1111010
[3,8,1,5,6,7,2,4]=>0000011=>1100000
[8,2,3,5,7,1,6,4]=>0000111=>1110000
[5,8,4,3,7,1,6,2]=>0010111=>1110100
[2,8,3,6,7,5,1,4]=>0001011=>1101000
[8,1,2,7,3,5,6,4]=>0000111=>1110000
[6,8,4,2,1,3,7,5]=>1010011=>1100101
[4,3,8,2,7,6,1,5]=>0010111=>1110100
[2,1,4,5,8,3,7,6]=>1000011=>1100001
[8,4,7,1,5,2,3,6]=>0001011=>1101000
[7,3,5,8,4,2,1,6]=>1010011=>1100101
[2,4,8,3,5,6,7,1]=>0000011=>1100000
[6,4,7,5,2,3,8,1]=>0001111=>1111000
[6,4,8,1,7,3,2,5]=>0100111=>1110010
[4,2,3,1,8,7,5,6]=>0110011=>1100110
[2,1,4,3,8,7,5,6]=>1010011=>1100101
[4,3,1,2,8,6,7,5]=>0110011=>1100110
[5,1,6,7,8,4,3,2]=>0111001=>1001110
[8,7,2,6,4,1,5,3]=>0011111=>1111100
[2,1,5,7,8,4,6,3]=>1000101=>1010001
[6,4,1,5,7,2,8,3]=>0010111=>1110100
[7,4,8,1,2,5,6,3]=>0000111=>1110000
[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
[7,1,4,8,3,5,6,2]=>0000111=>1110000
[3,4,8,2,5,7,6,1]=>0000111=>1110000
[3,7,1,4,5,6,8,2]=>0000011=>1100000
[4,7,5,6,8,3,1,2]=>0100011=>1100010
[6,5,3,8,4,7,1,2]=>0001111=>1111000
[8,6,4,7,5,3,1,2]=>0101111=>1111010
[1,6,3,7,5,8,4,2]=>0010111=>1110100
[1,3,7,4,5,8,6,2]=>0000111=>1110000
[7,3,8,5,4,6,1,2]=>0001111=>1111000
[3,4,8,5,6,7,1,2]=>0000011=>1100000
[4,7,3,8,5,6,1,2]=>0000111=>1110000
[6,8,4,7,5,3,1,2]=>0101011=>1101010
[1,7,6,5,3,8,4,2]=>0011111=>1111100
[2,7,6,3,1,4,5,8]=>0100110=>0110010
[2,7,6,4,5,1,3,8]=>0001110=>0111000
[5,7,2,6,4,1,3,8]=>0010110=>0110100
[7,6,1,5,3,8,4,2]=>0011111=>1111100
[1,8,2,7,3,6,5,4]=>0001111=>1111000
[2,1,3,8,4,7,5,6]=>1000011=>1100001
[3,1,2,8,4,6,7,5]=>0100011=>1100010
[4,1,7,2,8,5,6,3]=>0010111=>1110100
[5,1,2,4,8,3,7,6]=>0001011=>1101000
[2,8,4,1,5,6,3,7]=>0010101=>1010100
[1,7,2,8,5,3,6,4]=>0001111=>1111000
[1,2,3,8,4,5,7,6]=>0000011=>1100000
[2,4,8,3,1,5,6,7]=>0100001=>1000010
[3,4,2,7,1,5,6,8]=>0010010=>0100100
[3,2,5,6,1,4,7,8]=>0100100=>0010010
[4,7,3,8,2,1,5,6]=>1000011=>1100001
[7,4,8,3,2,1,5,6]=>1100011=>1100011
[1,3,7,2,8,4,6,5]=>0000111=>1110000
[2,6,4,5,7,1,3,8]=>0000110=>0110000
[5,4,6,2,7,1,3,8]=>0001110=>0111000
[7,6,8,5,1,4,3,2]=>0111011=>1101110
[6,5,1,2,8,3,7,4]=>0001111=>1111000
[6,8,4,1,3,7,5,2]=>0011011=>1101100
[6,3,7,1,8,4,5,2]=>0001111=>1111000
[5,8,3,1,7,4,6,2]=>0100111=>1110010
[4,7,1,2,8,3,6,5]=>0000111=>1110000
[3,4,1,8,5,6,7,2]=>0010011=>1100100
[1,2,8,7,6,3,5,4]=>0001111=>1111000
[2,3,1,8,7,4,5,6]=>0100011=>1100010
[2,6,1,4,8,7,3,5]=>0000111=>1110000
[5,8,2,1,7,6,3,4]=>1000111=>1110001
[8,7,1,6,5,4,3,2]=>0111111=>1111110
[3,1,8,7,6,4,5,2]=>0101111=>1111010
[1,2,3,4,8,7,5,6]=>0000011=>1100000
[1,2,3,8,6,4,5,7]=>0000101=>1010000
[1,2,8,5,3,4,6,7]=>0001001=>1001000
[1,8,4,2,3,5,6,7]=>0010001=>1000100
[2,4,7,5,6,8,3,1]=>0100011=>1100010
[2,5,3,8,7,4,6,1]=>0001111=>1111000
[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
[2,7,6,4,5,8,3,1]=>0100111=>1110010
[4,8,1,7,6,3,2,5]=>0100111=>1110010
[7,3,6,4,2,8,5,1]=>0011111=>1111100
[4,7,8,1,3,6,2,5]=>0000101=>1010000
[5,8,7,1,4,3,2,6]=>0110011=>1100110
[5,6,1,2,4,3,8,7]=>0010101=>1010100
[3,6,8,1,2,7,5,4]=>0001011=>1101000
[8,4,6,2,1,3,7,5]=>1000111=>1110001
[4,8,1,5,3,7,2,6]=>0001011=>1101000
[5,4,8,7,3,1,2,6]=>0101011=>1101010
[6,4,3,8,1,5,2,7]=>0011101=>1011100
[6,8,3,7,2,5,4,1]=>0011011=>1101100
[5,3,6,8,7,2,4,1]=>0011011=>1101100
[5,7,4,2,8,3,6,1]=>0010111=>1110100
[6,4,7,2,1,8,3,5]=>1000111=>1110001
[6,5,3,1,4,7,2,8]=>0101110=>0111010
[5,7,8,2,6,4,1,3]=>0010101=>1010100
[2,6,8,4,5,7,1,3]=>0000011=>1100000
[3,6,8,5,7,1,4,2]=>0010011=>1100100
[1,7,4,8,6,2,3,5]=>0000111=>1110000
[2,7,4,8,5,6,1,3]=>0000111=>1110000
[6,3,7,2,8,5,1,4]=>0001111=>1111000
[3,6,2,5,7,8,1,4]=>0000101=>1010000
[5,3,6,7,1,8,4,2]=>0011011=>1101100
[8,1,3,6,7,2,4,5]=>0000011=>1100000
[8,1,4,2,7,5,3,6]=>0011011=>1101100
[6,1,3,8,2,7,4,5]=>0000111=>1110000
[4,1,5,3,2,8,6,7]=>0111001=>1001110
[2,7,1,4,3,8,5,6]=>0010011=>1100100
[1,7,5,2,8,6,3,4]=>0001111=>1111000
[7,4,2,5,1,8,6,3]=>0011111=>1111100
[5,6,3,2,1,8,7,4]=>1100111=>1110011
[4,5,3,2,7,1,8,6]=>0101011=>1101010
[5,3,6,2,8,1,7,4]=>0001111=>1111000
[6,4,2,8,5,1,7,3]=>0011111=>1111100
[1,8,4,7,2,5,3,6]=>0001011=>1101000
[1,5,8,4,2,6,3,7]=>0010101=>1010100
[3,5,7,4,1,6,8,2]=>0010011=>1100100
[4,5,8,3,1,7,6,2]=>0100111=>1110010
[3,4,7,8,2,1,6,5]=>1000101=>1010001
[4,6,3,5,2,1,8,7]=>1001101=>1011001
[3,5,7,1,2,6,4,8]=>0000110=>0110000
[3,6,2,1,4,7,5,8]=>1000110=>0110001
[7,4,1,2,8,6,3,5]=>0010111=>1110100
[5,2,6,1,3,4,8,7]=>0001101=>1011000
[3,8,2,6,5,4,1,7]=>0011101=>1011100
[3,8,7,2,5,4,1,6]=>0011011=>1101100
[7,5,1,6,8,4,3,2]=>0111011=>1101110
[7,4,2,1,5,6,3,8]=>1010110=>0110101
[7,3,8,1,5,4,6,2]=>0001111=>1111000
[7,2,8,6,5,1,3,4]=>0001111=>1111000
[6,2,7,8,5,4,1,3]=>0011101=>1011100
[5,3,2,6,7,4,1,8]=>0111010=>0101110
[4,8,2,6,5,7,1,3]=>0000111=>1110000
[4,3,7,2,5,6,1,8]=>0010110=>0110100
[3,8,7,6,2,4,1,5]=>0010111=>1110100
[6,7,1,4,3,2,5,8]=>0110010=>0100110
[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
[2,7,1,3,6,5,4,8]=>0001110=>0111000
[5,7,1,4,6,3,2,8]=>0100110=>0110010
[6,3,7,1,5,4,2,8]=>0011110=>0111100
[4,7,1,6,3,5,2,8]=>0001110=>0111000
[8,7,3,6,1,5,4,2]=>0011111=>1111100
[5,7,8,3,2,1,4,6]=>1100001=>1000011
[5,4,2,1,7,8,3,6]=>1011001=>1001101
[4,7,8,3,5,2,1,6]=>1001001=>1001001
[8,3,7,6,4,2,1,5]=>1010111=>1110101
[8,3,2,1,4,7,6,5]=>1100111=>1110011
[6,4,1,7,3,8,5,2]=>0011111=>1111100
[1,7,5,3,8,2,6,4]=>0001111=>1111000
[5,1,7,4,2,8,6,3]=>0011111=>1111100
[8,6,3,2,7,5,1,4]=>0101111=>1111010
[2,7,5,1,3,8,6,4]=>0001111=>1111000
[8,7,4,2,6,1,5,3]=>0011111=>1111100
[5,2,6,1,8,7,4,3]=>0011111=>1111100
[1,7,6,4,3,8,2,5]=>0010111=>1110100
[1,3,8,2,4,7,6,5]=>0000111=>1110000
[3,7,5,1,8,6,2,4]=>0001111=>1111000
[5,1,4,3,2,7,8,6]=>0111001=>1001110
[3,7,6,2,4,1,8,5]=>0010111=>1110100
[5,3,1,7,8,4,2,6]=>0111001=>1001110
[4,1,7,8,5,3,2,6]=>0111001=>1001110
[2,7,6,4,1,3,8,5]=>0010111=>1110100
[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
[8,4,7,3,1,6,5,2]=>0101111=>1111010
[4,1,6,8,5,7,3,2]=>0110011=>1100110
[1,8,6,7,3,4,2,5]=>0010011=>1100100
[6,7,1,8,3,4,2,5]=>0010011=>1100100
[7,8,1,6,3,4,2,5]=>0010101=>1010100
[7,8,2,5,1,6,3,4]=>0001101=>1011000
[1,8,5,6,2,7,3,4]=>0000111=>1110000
[5,7,1,6,2,8,3,4]=>0000111=>1110000
[5,6,2,7,1,8,3,4]=>0000111=>1110000
[6,7,2,5,1,8,3,4]=>0001011=>1101000
[6,7,2,4,3,8,1,5]=>0010011=>1100100
[2,5,1,8,6,7,3,4]=>0001011=>1101000
[2,6,5,8,1,7,3,4]=>0000111=>1110000
[1,8,2,7,4,5,3,6]=>0001011=>1101000
[2,4,3,8,5,6,1,7]=>0010101=>1010100
[2,3,1,8,5,6,4,7]=>0100101=>1010010
[4,6,2,7,1,5,3,8]=>0001110=>0111000
[4,7,1,6,2,5,3,8]=>0001110=>0111000
[4,6,3,5,1,7,2,8]=>0001110=>0111000
[5,6,3,7,1,4,2,8]=>0010110=>0110100
[1,8,5,6,3,4,2,7]=>0010101=>1010100
[4,7,1,8,5,6,2,3]=>0000111=>1110000
[3,4,2,6,5,8,1,7]=>0010101=>1010100
[3,5,4,6,2,8,1,7]=>0001101=>1011000
[3,7,1,6,2,8,4,5]=>0000111=>1110000
[3,5,2,7,4,8,1,6]=>0001011=>1101000
[4,7,2,3,1,8,5,6]=>0100011=>1100010
[2,4,3,8,1,7,5,6]=>0010011=>1100100
[6,1,2,7,4,5,8,3]=>0000111=>1110000
[2,5,8,3,4,1,6,7]=>0010001=>1000100
[5,6,2,7,4,3,8,1]=>0010111=>1110100
[5,1,7,3,4,2,8,6]=>0011011=>1101100
[4,6,7,3,2,5,8,1]=>0100011=>1100010
[3,7,2,1,4,5,8,6]=>1000011=>1100001
[2,7,1,3,4,8,6,5]=>0000111=>1110000
[2,6,7,3,8,5,4,1]=>0011011=>1101100
[2,6,1,8,4,5,3,7]=>0001101=>1011000
[4,2,1,6,5,3,8,7]=>1011101=>1011101
[6,2,4,3,1,5,8,7]=>0110101=>1010110
[4,6,2,1,5,3,8,7]=>1001101=>1011001
[8,4,2,1,6,5,3,7]=>1011101=>1011101
[2,6,4,5,1,8,7,3]=>0001111=>1111000
[6,8,7,2,1,4,3,5]=>1010011=>1100101
[6,8,2,1,7,4,3,5]=>1010011=>1100101
[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
[2,8,4,6,7,3,1,5]=>0100011=>1100010
[2,8,6,7,4,3,1,5]=>0110011=>1100110
[6,8,7,2,4,3,1,5]=>0110011=>1100110
[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
[4,2,6,3,8,7,5,1]=>0011111=>1111100
[8,2,4,3,6,5,1,7]=>0011101=>1011100
[4,2,1,6,8,7,5,3]=>1011011=>1101101
[4,2,1,6,5,8,7,3]=>1010111=>1110101
[4,2,1,3,6,8,7,5]=>1010011=>1100101
[2,4,3,1,8,6,5,7]=>0110101=>1010110
[6,2,1,8,7,4,3,5]=>1010111=>1110101
[6,2,1,8,4,3,7,5]=>1010111=>1110101
[4,6,8,7,5,2,1,3]=>1001011=>1101001
[4,6,5,8,7,2,1,3]=>1000111=>1110001
[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
[6,4,8,2,1,5,7,3]=>1000111=>1110001
[2,6,8,4,7,1,5,3]=>0001011=>1101000
[4,6,5,8,2,1,7,3]=>1000111=>1110001
[4,8,6,7,2,1,3,5]=>1000011=>1100001
[6,2,3,5,1,4,8,7]=>0001101=>1011000
[7,4,5,2,3,8,6,1]=>0001111=>1111000
[7,3,2,5,4,8,6,1]=>0101111=>1111010
[3,5,1,6,4,2,8,7]=>0011101=>1011100
[3,6,2,4,5,1,8,7]=>0001101=>1011000
[7,2,3,4,5,8,6,1]=>0000111=>1110000
[8,2,3,4,5,7,1,6]=>0000011=>1100000
[6,7,3,4,8,5,2,1]=>1001011=>1101001
[5,7,1,3,8,6,2,4]=>0000111=>1110000
[4,7,3,2,8,6,1,5]=>0100111=>1110010
[3,8,2,6,7,4,5,1]=>0001011=>1101000
[4,8,1,5,6,7,3,2]=>0100011=>1100010
[6,8,2,5,1,7,3,4]=>0001011=>1101000
[7,8,3,4,6,2,1,5]=>1000101=>1010001
[4,8,2,5,1,6,7,3]=>0001011=>1101000
[3,8,2,5,4,7,6,1]=>0001111=>1111000
[3,7,6,1,8,5,2,4]=>0001111=>1111000
[4,7,2,3,8,5,1,6]=>0001011=>1101000
[4,6,7,1,8,5,3,2]=>0101011=>1101010
[3,6,1,7,8,5,4,2]=>0011101=>1011100
[2,1,5,7,3,8,6,4]=>1000111=>1110001
[6,4,7,2,8,5,3,1]=>0101111=>1111010
[7,6,1,4,8,5,2,3]=>0001111=>1111000
[4,1,2,3,7,8,6,5]=>0010101=>1010100
[3,4,2,1,8,5,6,7]=>1010001=>1000101
[8,2,3,5,7,1,4,6]=>0000011=>1100000
[8,1,3,6,4,7,2,5]=>0000111=>1110000
[5,4,8,3,6,7,1,2]=>0001011=>1101000
[4,5,8,3,6,7,2,1]=>1000011=>1100001
[2,1,5,8,4,6,7,3]=>1000011=>1100001
[4,6,8,3,5,2,7,1]=>0001011=>1101000
[5,7,8,3,2,4,1,6]=>0110001=>1000110
[3,8,2,4,5,6,7,1]=>0000011=>1100000
[6,8,2,3,1,4,5,7]=>0100001=>1000010
[4,3,1,6,5,8,7,2]=>0110111=>1110110
[8,2,7,4,1,3,6,5]=>0010111=>1110100
[3,7,8,2,1,4,6,5]=>1000101=>1010001
[3,7,5,2,8,4,1,6]=>0011011=>1101100
[3,1,5,2,4,8,7,6]=>0101011=>1101010
[3,6,4,5,1,8,7,2]=>0001111=>1111000
[4,3,6,1,2,8,7,5]=>0010111=>1110100
[6,1,3,5,4,8,7,2]=>0001111=>1111000
[1,7,3,8,4,6,2,5]=>0000111=>1110000
[1,6,7,4,8,5,3,2]=>0101011=>1101010
[8,1,2,5,4,6,3,7]=>0001101=>1011000
[6,8,3,1,4,7,5,2]=>0101011=>1101010
[8,4,2,5,7,1,6,3]=>0010111=>1110100
[1,8,5,3,7,4,6,2]=>0001111=>1111000
[5,3,2,8,7,1,4,6]=>0101011=>1101010
[1,2,8,7,5,6,3,4]=>0000111=>1110000
[4,2,1,7,5,3,6,8]=>1011010=>0101101
[1,4,8,6,5,7,2,3]=>0000111=>1110000
[3,5,4,8,6,1,2,7]=>0001101=>1011000
[4,3,5,8,1,7,2,6]=>0010011=>1100100
[1,4,5,8,6,7,3,2]=>0100011=>1100010
[1,7,6,5,8,3,4,2]=>0010111=>1110100
[7,3,6,1,8,2,4,5]=>0000111=>1110000
[7,6,4,5,8,1,3,2]=>0100111=>1110010
[1,6,5,4,8,2,3,7]=>0001101=>1011000
[5,2,6,3,8,1,4,7]=>0001101=>1011000
[4,3,1,6,8,7,5,2]=>0111011=>1101110
[4,3,1,8,5,6,7,2]=>0110011=>1100110
[6,2,8,4,3,1,7,5]=>0110111=>1110110
[7,1,6,2,3,4,5,8]=>0000110=>0110000
[3,8,6,1,2,5,4,7]=>0001101=>1011000
[1,8,5,4,3,6,2,7]=>0011101=>1011100
[5,3,8,4,1,2,7,6]=>0011011=>1101100
[1,8,3,6,5,2,7,4]=>0001111=>1111000
[4,7,1,8,2,6,5,3]=>0001111=>1111000
[1,8,2,4,7,6,5,3]=>0001111=>1111000
[1,4,8,3,5,7,6,2]=>0000111=>1110000
[8,2,1,4,6,5,7,3]=>1000111=>1110001
[6,1,5,2,4,7,8,3]=>0001101=>1011000
[4,1,8,5,2,7,6,3]=>0011111=>1111100
[4,3,8,5,1,2,6,7]=>0011001=>1001100
[6,3,5,1,4,2,8,7]=>0011101=>1011100
[4,1,8,2,3,7,5,6]=>0010011=>1100100
[5,3,8,7,2,1,4,6]=>1001011=>1101001
[7,6,5,4,1,3,2,8]=>0111110=>0111110
[1,8,7,6,2,5,4,3]=>0011111=>1111100
[1,2,3,4,5,10,9,8,7,6]=>000001111=>111100000
[4,6,3,1,5,2,7,8]=>0101100=>0011010
[6,2,7,4,5,1,3,8]=>0001110=>0111000
[5,2,7,4,1,6,3,8]=>0011110=>0111100
[5,7,3,4,1,6,2,8]=>0010110=>0110100
[4,2,8,1,5,6,7,3]=>0010011=>1100100
[1,7,8,4,5,6,2,3]=>0000101=>1010000
[1,6,8,4,5,2,7,3]=>0001011=>1101000
[1,5,8,4,2,6,7,3]=>0010011=>1100100
[1,5,3,8,2,6,7,4]=>0001011=>1101000
[1,6,3,8,5,2,7,4]=>0001111=>1111000
[1,7,3,8,5,6,2,4]=>0000111=>1110000
[6,2,3,7,5,1,4,8]=>0001110=>0111000
[4,2,6,1,5,3,7,8]=>0011100=>0011100
[5,2,6,4,1,3,7,8]=>0011100=>0011100
[1,2,7,8,5,6,3,4]=>0000101=>1010000
[1,2,6,8,5,3,7,4]=>0001011=>1101000
[1,2,6,4,8,3,7,5]=>0000111=>1110000
[8,7,3,2,1,6,5,4]=>1101111=>1111011
[8,7,4,1,6,2,3,5]=>0010111=>1110100
[10,9,8,5,1,7,2,3,4,6]=>000101111=>111101000
[10,9,4,1,6,2,8,3,5,7]=>001010111=>111010100
[10,3,1,5,2,7,4,9,6,8]=>010101011=>110101010
[1,8,3,2,6,4,5,7]=>0100101=>1010010
[7,3,8,1,5,2,4,6]=>0001011=>1101000
[3,1,7,2,6,4,5,8]=>0100110=>0110010
[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
[3,1,7,5,4,2,8,6]=>0111011=>1101110
[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
[6,4,2,8,1,5,7,3]=>0010111=>1110100
[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
[2,6,8,3,4,7,1,5]=>0000011=>1100000
[2,5,6,8,3,4,1,7]=>0010001=>1000100
[2,7,8,3,6,1,4,5]=>0000101=>1010000
[2,1,3,7,8,5,6,4]=>1000101=>1010001
[5,1,2,4,8,7,3,6]=>0001011=>1101000
[2,3,6,1,8,5,7,4]=>0000111=>1110000
[5,2,6,1,7,8,4,3]=>0011101=>1011100
[3,6,5,4,1,8,7,2]=>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
[2,6,4,1,5,3,8,7]=>0011101=>1011100
[1,5,8,2,4,7,3,6]=>0000011=>1100000
[6,2,1,4,7,8,3,5]=>1000101=>1010001
[3,8,1,4,2,6,5,7]=>0010101=>1010100
[8,3,4,2,1,6,5,7]=>1010101=>1010101
[5,3,2,8,1,6,4,7]=>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
[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
[2,4,6,5,1,7,8,3]=>0001101=>1011000
[5,6,1,7,4,2,8,3]=>0010111=>1110100
[1,3,8,6,2,7,4,5]=>0000111=>1110000
[4,3,7,5,6,1,8,2]=>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
[3,7,8,1,5,4,2,6]=>0011001=>1001100
[7,5,8,4,1,3,2,6]=>0110011=>1100110
[4,7,5,8,3,1,2,6]=>0100011=>1100010
[5,7,3,1,6,8,4,2]=>0110011=>1100110
[4,6,7,2,8,3,1,5]=>0100011=>1100010
[4,8,1,2,3,5,7,6]=>0000011=>1100000
[4,5,6,7,3,1,8,2]=>0100011=>1100010
[8,5,3,2,7,6,1,4]=>0101111=>1111010
[7,5,4,6,2,8,1,3]=>0001111=>1111000
[2,5,1,3,6,8,7,4]=>0001011=>1101000
[7,5,2,8,4,1,3,6]=>0011011=>1101100
[7,3,8,5,2,1,4,6]=>1001011=>1101001
[5,8,3,6,4,7,1,2]=>0000111=>1110000
[3,5,8,6,7,4,2,1]=>1010011=>1100101
[3,7,6,8,1,2,5,4]=>0001011=>1101000
[4,1,6,3,2,5,8,7]=>0110101=>1010110
[8,6,1,7,2,5,4,3]=>0011111=>1111100
[8,7,6,1,2,3,5,4]=>0001111=>1111000
[5,4,1,6,2,3,8,7]=>0011101=>1011100
[2,6,5,3,4,1,8,7]=>0011101=>1011100
[5,8,7,6,1,2,3,4]=>0000111=>1110000
[8,2,7,1,5,4,3,6]=>0011011=>1101100
[2,1,6,3,8,5,4,7]=>1001101=>1011001
[2,6,3,1,8,5,4,7]=>0101101=>1011010
[4,6,2,8,5,1,3,7]=>0001101=>1011000
[6,5,2,7,4,3,8,1]=>0011111=>1111100
[4,6,5,2,7,3,8,1]=>0001111=>1111000
[3,1,6,2,4,8,7,5]=>0100111=>1110010
[8,7,5,1,2,6,4,3]=>0011111=>1111100
[2,1,7,6,3,8,4,5]=>1000111=>1110001
[8,2,3,4,6,7,1,5]=>0000011=>1100000
[2,8,5,7,4,1,3,6]=>0010011=>1100100
[7,8,5,3,6,4,2,1]=>1011101=>1011101
[2,1,4,8,7,5,6,3]=>1000111=>1110001
[7,4,6,8,5,1,3,2]=>0101011=>1101010
[6,4,8,3,5,7,1,2]=>0000111=>1110000
[8,5,7,4,6,2,1,3]=>1000111=>1110001
[4,1,8,5,6,3,2,7]=>0110101=>1010110
[5,8,3,2,4,6,1,7]=>0100101=>1010010
[2,8,4,1,5,3,7,6]=>0011011=>1101100
[4,8,7,6,5,2,3,1]=>0101111=>1111010
[2,1,8,6,4,3,7,5]=>1010111=>1110101
[3,6,7,1,8,5,2,4]=>0001011=>1101000
[4,2,3,6,8,7,5,1]=>0011011=>1101100
[6,5,7,3,1,8,4,2]=>0110111=>1110110
[8,4,2,5,6,1,7,3]=>0010111=>1110100
[6,1,5,7,2,4,8,3]=>0000111=>1110000
[7,4,5,1,2,3,8,6]=>0001011=>1101000
[8,4,7,6,2,1,5,3]=>1001111=>1111001
[3,5,7,6,4,1,8,2]=>0010111=>1110100
[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
[4,7,5,2,1,3,8,6]=>1001011=>1101001
[5,7,2,3,6,4,8,1]=>0000111=>1110000
[7,1,2,3,5,8,4,6]=>0000011=>1100000
[6,1,8,2,7,3,4,5]=>0000111=>1110000
[7,8,6,1,3,2,5,4]=>0101101=>1011010
[1,8,5,7,2,3,4,6]=>0000011=>1100000
[8,1,5,7,2,3,6,4]=>0000111=>1110000
[1,4,5,2,8,6,7,3]=>0001011=>1101000
[2,3,1,7,8,6,4,5]=>0100101=>1010010
[2,1,4,6,8,3,7,5]=>1000011=>1100001
[3,5,7,6,2,8,1,4]=>0000111=>1110000
[5,4,1,6,3,8,7,2]=>0011111=>1111100
[4,5,6,1,2,8,7,3]=>0000111=>1110000
[3,5,6,2,4,8,7,1]=>0000111=>1110000
[5,4,1,2,8,7,6,3]=>0011111=>1111100
[5,6,3,7,8,4,2,1]=>1010101=>1010101
[4,3,2,6,8,1,7,5]=>0110011=>1100110
[7,1,5,6,3,8,2,4]=>0000111=>1110000
[1,5,4,2,7,8,3,6]=>0011001=>1001100
[6,1,2,8,7,4,3,5]=>0010111=>1110100
[5,1,6,8,4,7,2,3]=>0001011=>1101000
[5,1,3,8,4,2,7,6]=>0011011=>1101100
[3,1,6,8,7,4,2,5]=>0110011=>1100110
[3,6,5,8,4,7,1,2]=>0000111=>1110000
[6,5,8,4,3,1,2,7]=>0110101=>1010110
[8,5,1,3,7,4,6,2]=>0001111=>1111000
[3,2,8,1,4,7,6,5]=>0100111=>1110010
[6,4,3,8,2,5,7,1]=>0010111=>1110100
[3,2,5,8,4,1,7,6]=>0110011=>1100110
[6,8,2,3,4,7,5,1]=>0001011=>1101000
[2,1,7,8,3,4,6,5]=>1000101=>1010001
[7,5,1,8,4,2,6,3]=>0011111=>1111100
[5,6,1,8,2,7,4,3]=>0010111=>1110100
[3,6,8,5,2,7,4,1]=>0011011=>1101100
[2,1,6,5,4,8,3,7]=>1001101=>1011001
[2,1,7,3,5,8,6,4]=>1000111=>1110001
[7,8,1,2,4,5,6,3]=>0000101=>1010000
[3,8,7,4,1,2,5,6]=>0010011=>1100100
[3,6,8,1,5,7,2,4]=>0000011=>1100000
[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
[8,4,3,1,7,5,2,6]=>0111011=>1101110
[7,6,2,8,5,1,4,3]=>0011111=>1111100
[4,3,8,7,1,6,5,2]=>0011111=>1111100
[4,7,1,8,5,2,6,3]=>0001111=>1111000
[3,7,5,8,1,6,2,4]=>0000111=>1110000
[3,7,6,4,5,1,8,2]=>0001111=>1111000
[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
[5,7,2,1,8,3,6,4]=>1000111=>1110001
[7,8,1,2,3,4,6,5]=>0000101=>1010000
[6,8,5,2,1,7,3,4]=>1001011=>1101001
[5,6,2,4,3,1,8,7]=>0110101=>1010110
[4,6,2,1,7,8,3,5]=>1000101=>1010001
[6,3,2,1,4,8,5,7]=>1100101=>1010011
[7,1,8,3,5,4,6,2]=>0001111=>1111000
[7,1,2,4,8,5,6,3]=>0000111=>1110000
[8,7,6,5,1,3,2,4]=>0101111=>1111010
[8,7,6,2,4,3,1,5]=>0110111=>1110110
[7,6,8,1,5,4,3,2]=>0111011=>1101110
[7,6,1,8,5,4,3,2]=>0111111=>1111110
[6,5,8,1,7,4,3,2]=>0110111=>1110110
[4,3,8,7,6,1,5,2]=>0011111=>1111100
[6,5,8,7,4,1,3,2]=>0110111=>1110110
[5,4,8,7,6,3,1,2]=>0101111=>1111010
[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
[1,6,3,8,5,2,4,7]=>0001101=>1011000
[4,6,3,7,5,2,1,8]=>1001110=>0111001
[3,7,2,6,5,4,1,8]=>0011110=>0111100
[3,2,1,6,8,4,5,7]=>1100001=>1000011
[1,7,4,6,2,8,5,3]=>0001111=>1111000
[6,2,5,1,7,4,8,3]=>0001111=>1111000
[3,5,7,4,8,6,1,2]=>0000111=>1110000
[5,2,7,4,1,6,8,3]=>0011011=>1101100
[4,5,8,2,1,7,6,3]=>1000111=>1110001
[1,6,4,8,5,2,7,3]=>0001111=>1111000
[7,4,1,5,3,8,2,6]=>0011011=>1101100
[3,4,1,2,7,8,6,5]=>0010101=>1010100
[4,1,3,2,8,6,7,5]=>0110011=>1100110
[3,1,2,4,7,6,8,5]=>0100011=>1100010
[8,1,3,5,4,7,2,6]=>0001011=>1101000
[7,1,4,3,5,2,8,6]=>0011011=>1101100
[3,2,8,1,6,5,4,7]=>0101101=>1011010
[6,8,4,1,2,5,3,7]=>0011001=>1001100
[8,2,1,5,6,4,3,7]=>1010101=>1010101
[4,7,1,8,2,5,3,6]=>0001011=>1101000
[6,7,8,1,4,5,3,2]=>0101001=>1001010
[3,2,5,4,7,8,1,6]=>0101001=>1001010
[8,4,7,6,2,3,1,5]=>0100111=>1110010
[6,1,2,8,7,3,5,4]=>0001111=>1111000
[1,2,7,5,6,8,3,4]=>0000011=>1100000
[5,7,2,3,8,1,6,4]=>0000111=>1110000
[3,5,2,6,1,8,7,4]=>0001111=>1111000
[3,2,5,6,7,8,1,4]=>0100001=>1000010
[5,4,2,6,8,7,1,3]=>0011011=>1101100
[6,4,1,2,8,7,3,5]=>0010111=>1110100
[4,3,8,5,2,1,6,7]=>1011001=>1001101
[3,6,4,5,2,1,8,7]=>1001101=>1011001
[7,5,4,2,3,8,1,6]=>0011011=>1101100
[5,6,3,1,8,2,7,4]=>0100111=>1110010
[6,5,4,3,1,2,8,7]=>0111101=>1011110
[4,5,2,1,6,8,3,7]=>1001001=>1001001
[5,6,2,8,1,7,4,3]=>0010111=>1110100
[1,5,6,3,4,8,2,7]=>0000101=>1010000
[2,1,4,5,8,6,3,7]=>1000101=>1010001
[6,7,1,3,4,8,2,5]=>0000011=>1100000
[6,7,8,2,3,5,4,1]=>0011001=>1001100
[5,8,6,2,3,7,4,1]=>0010111=>1110100
[1,8,3,4,7,6,2,5]=>0000111=>1110000
[5,8,6,1,7,2,4,3]=>0010111=>1110100
[3,1,2,8,6,4,5,7]=>0100101=>1010010
[1,3,2,8,5,4,6,7]=>0101001=>1001010
[3,2,1,8,6,5,4,7]=>1101101=>1011011
[5,2,7,1,8,4,3,6]=>0011011=>1101100
[6,7,2,1,8,4,3,5]=>1010011=>1100101
[6,7,3,1,5,8,2,4]=>0100011=>1100010
[2,4,1,6,8,5,3,7]=>0011001=>1001100
[2,5,6,1,8,4,3,7]=>0010101=>1010100
[5,4,7,6,1,8,2,3]=>0001111=>1111000
[3,5,6,8,4,7,2,1]=>1000011=>1100001
[2,5,6,8,7,3,4,1]=>0010011=>1100100
[2,4,8,5,7,3,6,1]=>0000111=>1110000
[5,3,7,8,4,6,2,1]=>1001101=>1011001
[6,7,3,8,4,5,2,1]=>1001011=>1101001
[4,2,8,6,7,3,5,1]=>0011011=>1101100
[3,2,8,7,5,4,6,1]=>0101111=>1111010
[2,1,8,7,6,4,3,5]=>1010111=>1110101
[6,3,8,7,5,1,2,4]=>0001111=>1111000
[2,8,7,4,1,3,5,6]=>0010011=>1100100
[2,5,3,7,6,8,1,4]=>0001011=>1101000
[2,8,7,1,4,5,3,6]=>0001011=>1101000
[4,2,1,8,7,3,5,6]=>1010011=>1100101
[8,7,4,6,2,3,1,5]=>0100111=>1110010
[5,1,6,3,2,8,7,4]=>0101111=>1111010
[8,7,2,3,5,4,1,6]=>0011011=>1101100
[3,4,2,8,6,1,5,7]=>0010101=>1010100
[8,1,4,2,3,6,7,5]=>0010011=>1100100
[6,8,3,5,4,7,1,2]=>0001011=>1101000
[1,8,2,5,7,6,3,4]=>0000111=>1110000
[4,1,6,8,2,3,7,5]=>0010011=>1100100
[1,4,6,3,7,2,8,5]=>0000111=>1110000
[6,2,1,8,4,5,3,7]=>1001101=>1011001
[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
[8,1,2,4,6,7,5,3]=>0001011=>1101000
[8,1,3,6,7,5,4,2]=>0011011=>1101100
[6,4,2,8,5,1,3,7]=>0011101=>1011100
[8,6,2,4,1,3,7,5]=>0010111=>1110100
[4,7,5,1,8,6,3,2]=>0101111=>1111010
[6,7,5,1,4,2,8,3]=>0011011=>1101100
[6,2,4,1,7,5,8,3]=>0010111=>1110100
[5,2,1,8,3,6,7,4]=>1001011=>1101001
[3,6,5,8,4,1,7,2]=>0010111=>1110100
[7,3,8,2,5,6,4,1]=>0010111=>1110100
[5,7,3,1,6,4,8,2]=>0100111=>1110010
[6,1,3,7,4,8,5,2]=>0001111=>1111000
[3,2,1,7,4,8,5,6]=>1100011=>1100011
[3,1,5,4,2,8,6,7]=>0111001=>1001110
[4,1,5,2,7,6,3,8]=>0011110=>0111100
[6,2,7,1,4,8,5,3]=>0001111=>1111000
[7,5,4,1,3,8,6,2]=>0011111=>1111100
[4,3,2,1,8,5,7,6]=>1110011=>1100111
[4,2,1,7,3,6,5,8]=>1010110=>0110101
[7,4,3,2,8,1,6,5]=>0110111=>1110110
[2,7,5,3,8,1,4,6]=>0001011=>1101000
[1,8,5,3,6,4,2,7]=>0011101=>1011100
[8,1,6,2,7,4,3,5]=>0010111=>1110100
[7,3,1,6,5,4,2,8]=>0111110=>0111110
[8,5,7,4,3,6,2,1]=>1010111=>1110101
[2,8,5,6,1,4,3,7]=>0010101=>1010100
[3,7,5,8,2,1,4,6]=>1000011=>1100001
[6,5,8,4,1,3,7,2]=>0010111=>1110100
[5,4,8,3,2,1,7,6]=>1101011=>1101011
[2,4,7,1,3,6,5,8]=>0000110=>0110000
[5,7,4,8,1,3,6,2]=>0000111=>1110000
[5,1,7,8,2,4,6,3]=>0001101=>1011000
[3,6,7,8,1,2,5,4]=>0001001=>1001000
[4,6,7,2,8,1,3,5]=>0000011=>1100000
[6,3,7,1,8,2,5,4]=>0001111=>1111000
[5,7,1,4,8,2,6,3]=>0000111=>1110000
[2,7,4,1,8,3,6,5]=>0010111=>1110100
[6,1,2,7,8,3,5,4]=>0001101=>1011000
[3,6,4,7,8,1,2,5]=>0000101=>1010000
[3,7,4,8,5,2,1,6]=>1001011=>1101001
[7,2,5,8,6,3,1,4]=>0100111=>1110010
[4,8,1,7,6,2,3,5]=>0000111=>1110000
[4,8,2,1,7,5,3,6]=>1001011=>1101001
[7,3,8,1,6,4,2,5]=>0010111=>1110100
[5,8,7,1,3,6,4,2]=>0010111=>1110100
[2,8,7,1,6,3,5,4]=>0001111=>1111000
[2,7,6,5,1,4,3,8]=>0011110=>0111100
[3,8,7,6,2,1,5,4]=>1001111=>1111001
[5,8,7,2,6,1,4,3]=>0010111=>1110100
[7,3,8,6,5,1,2,4]=>0001111=>1111000
[5,8,6,4,3,2,1,7]=>1110101=>1010111
[8,7,6,2,5,3,1,4]=>0101111=>1111010
[8,1,2,3,4,7,6,5]=>0000111=>1110000
[3,8,2,7,6,5,4,1]=>0011111=>1111100
[4,2,8,7,6,5,3,1]=>0111111=>1111110
[8,3,1,7,6,5,4,2]=>0111111=>1111110
[5,2,8,7,6,4,3,1]=>0111111=>1111110
[8,3,2,1,7,6,5,4]=>1101111=>1111011
[8,4,1,7,6,5,3,2]=>0111111=>1111110
[6,4,1,3,2,8,5,7]=>0110101=>1010110
[2,5,8,6,3,1,4,7]=>0100101=>1010010
[4,5,6,2,3,8,1,7]=>0000101=>1010000
[3,2,7,4,5,8,1,6]=>0100011=>1100010
[8,1,6,2,4,5,3,7]=>0001101=>1011000
[5,8,1,6,2,3,4,7]=>0000101=>1010000
[5,4,6,1,3,8,2,7]=>0001101=>1011000
[2,4,1,7,5,8,3,6]=>0010011=>1100100
[2,4,7,6,8,3,5,1]=>0001011=>1101000
[4,8,6,5,7,1,2,3]=>0000111=>1110000
[8,5,7,4,3,1,6,2]=>0110111=>1110110
[8,1,7,4,2,3,6,5]=>0010111=>1110100
[8,2,3,1,5,7,6,4]=>0100111=>1110010
[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
[8,4,1,5,2,3,7,6]=>0011011=>1101100
[3,8,4,1,2,7,6,5]=>0010111=>1110100
[2,7,5,8,3,4,1,6]=>0010011=>1100100
[1,4,7,3,2,8,5,6]=>0100011=>1100010
[6,4,1,3,2,7,8,5]=>0110101=>1010110
[2,3,7,6,8,1,5,4]=>0001011=>1101000
[2,6,3,5,1,8,7,4]=>0001111=>1111000
[2,7,1,6,8,3,5,4]=>0001011=>1101000
[6,7,5,4,2,1,8,3]=>1011011=>1101101
[4,2,1,5,8,7,6,3]=>1010111=>1110101
[8,5,3,2,6,1,7,4]=>0101111=>1111010
[6,2,1,5,3,8,7,4]=>1001111=>1111001
[7,8,4,1,2,5,3,6]=>0011001=>1001100
[7,8,1,2,6,5,3,4]=>0001101=>1011000
[6,1,4,2,7,5,3,8]=>0011110=>0111100
[7,8,2,1,6,3,5,4]=>1001101=>1011001
[1,2,8,7,5,4,3,6]=>0011011=>1101100
[1,2,8,3,6,4,7,5]=>0000111=>1110000
[5,1,7,3,6,4,8,2]=>0001111=>1111000
[6,2,3,7,4,1,5,8]=>0010110=>0110100
[6,2,4,1,7,3,5,8]=>0010110=>0110100
[3,4,8,7,5,6,1,2]=>0000111=>1110000
[2,7,3,8,6,4,1,5]=>0010111=>1110100
[1,8,3,7,6,4,5,2]=>0001111=>1111000
[2,6,8,5,3,1,7,4]=>0101011=>1101010
[5,6,2,1,7,3,8,4]=>1000111=>1110001
[5,3,6,2,4,1,7,8]=>0011100=>0011100
[5,7,4,2,1,3,6,8]=>1010010=>0100101
[6,4,2,1,5,3,7,8]=>1011100=>0011101
[5,3,1,4,6,2,7,8]=>0101100=>0011010
[5,1,2,4,7,6,8,3]=>0001011=>1101000
[1,6,4,2,8,7,3,5]=>0010111=>1110100
[4,8,1,2,6,7,3,5]=>0000011=>1100000
[3,1,2,4,6,8,7,5]=>0100011=>1100010
[4,2,8,1,5,3,7,6]=>0011011=>1101100
[4,3,8,5,7,6,1,2]=>0010111=>1110100
[4,8,6,3,7,5,1,2]=>0001111=>1111000
[3,8,6,5,2,7,1,4]=>0001111=>1111000
[3,8,5,6,1,7,4,2]=>0010111=>1110100
[3,7,8,5,2,1,6,4]=>1001101=>1011001
[4,2,7,8,1,3,6,5]=>0010101=>1010100
[2,1,8,7,6,3,5,4]=>1001111=>1111001
[5,4,1,6,3,2,8,7]=>0111101=>1011110
[6,8,1,5,4,7,3,2]=>0101011=>1101010
[2,6,4,3,1,5,8,7]=>0110101=>1010110
[5,1,7,2,8,6,4,3]=>0011111=>1111100
[6,8,2,7,4,3,1,5]=>0110011=>1100110
[6,8,2,5,4,7,1,3]=>0001011=>1101000
[2,1,7,6,3,8,5,4]=>1001111=>1111001
[7,6,2,8,4,3,1,5]=>0110111=>1110110
[2,6,5,1,8,4,3,7]=>0011101=>1011100
[4,2,1,6,3,8,7,5]=>1010111=>1110101
[5,8,3,2,7,6,1,4]=>0100111=>1110010
[2,4,8,3,1,7,5,6]=>0100011=>1100010
[4,8,3,2,1,7,6,5]=>1100111=>1110011
[2,6,8,3,7,1,4,5]=>0000011=>1100000
[6,8,3,7,2,1,5,4]=>1001011=>1101001
[5,8,3,1,6,2,7,4]=>0100111=>1110010
[4,5,8,1,6,3,2,7]=>0100101=>1010010
[6,8,4,7,1,5,3,2]=>0101011=>1101010
[4,3,2,1,6,8,5,7]=>1110001=>1000111
[2,4,1,3,8,7,6,5]=>0010111=>1110100
[4,8,6,5,1,7,3,2]=>0101111=>1111010
[6,5,3,1,7,2,8,4]=>0101111=>1111010
[2,1,5,4,8,7,3,6]=>1001011=>1101001
[3,8,5,4,2,1,7,6]=>1011011=>1101101
[2,3,8,5,4,1,6,7]=>0011001=>1001100
[2,1,4,8,6,5,3,7]=>1001101=>1011001
[4,3,2,8,7,6,1,5]=>0110111=>1110110
[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
[7,5,2,6,3,8,4,1]=>0011111=>1111100
[7,3,6,5,2,8,4,1]=>0011111=>1111100
[5,6,3,1,2,4,8,7]=>0100101=>1010010
[7,1,5,3,8,4,6,2]=>0001111=>1111000
[2,7,5,3,8,6,4,1]=>0011111=>1111100
[3,7,6,4,2,8,5,1]=>0011111=>1111100
[5,7,3,6,2,8,4,1]=>0010111=>1110100
[2,1,8,7,4,3,5,6]=>1010011=>1100101
[2,8,6,3,1,4,7,5]=>0100111=>1110010
[3,8,4,1,5,7,2,6]=>0010011=>1100100
[5,6,3,1,8,7,4,2]=>0110111=>1110110
[3,5,7,4,8,6,2,1]=>1000111=>1110001
[4,5,3,6,8,2,7,1]=>0001011=>1101000
[5,6,3,7,4,8,2,1]=>1000111=>1110001
[2,6,7,4,5,8,3,1]=>0100011=>1100010
[6,3,7,5,8,4,2,1]=>1010111=>1110101
[8,5,2,6,1,7,3,4]=>0001111=>1111000
[5,4,2,6,8,3,7,1]=>0011011=>1101100
[7,6,8,5,1,4,2,3]=>0011011=>1101100
[7,1,8,5,4,2,3,6]=>0011011=>1101100
[5,7,3,8,4,1,2,6]=>0010011=>1100100
[2,1,7,8,5,3,4,6]=>1001001=>1001001
[2,4,8,1,5,6,3,7]=>0000101=>1010000
[4,1,8,2,6,5,3,7]=>0011101=>1011100
[4,7,3,8,1,2,6,5]=>0000111=>1110000
[4,8,1,2,5,3,6,7]=>0001001=>1001000
[3,8,1,2,4,6,5,7]=>0000101=>1010000
[4,8,7,6,3,5,2,1]=>1001111=>1111001
[3,8,7,6,5,2,4,1]=>0011111=>1111100
[4,8,7,3,6,5,2,1]=>1001111=>1111001
[4,8,7,6,3,2,5,1]=>0101111=>1111010
[3,8,7,6,5,2,1,4]=>1001111=>1111001
[7,5,8,3,6,2,1,4]=>1000111=>1110001
[7,5,8,3,2,6,1,4]=>0100111=>1110010
[7,5,8,3,2,1,6,4]=>1100111=>1110011
[2,3,7,8,4,1,6,5]=>0010101=>1010100
[2,1,7,5,8,4,6,3]=>1000111=>1110001
[2,5,6,8,1,7,4,3]=>0010011=>1100100
[4,2,8,6,1,7,3,5]=>0010111=>1110100
[8,6,4,1,3,2,5,7]=>0110101=>1010110
[8,1,3,2,6,5,4,7]=>0101101=>1011010
[8,5,3,6,2,4,1,7]=>0011101=>1011100
[8,4,1,2,6,5,3,7]=>0011101=>1011100
[8,3,5,6,2,1,4,7]=>1000101=>1010001
[8,4,2,1,5,6,3,7]=>1010101=>1010101
[5,4,7,6,8,2,3,1]=>0101011=>1101010
[4,1,8,2,3,7,6,5]=>0010111=>1110100
[3,7,4,5,8,2,1,6]=>1000011=>1100001
[6,3,8,5,7,4,1,2]=>0010111=>1110100
[7,4,1,8,3,5,6,2]=>0010111=>1110100
[5,3,8,7,4,6,1,2]=>0001111=>1111000
[7,5,8,2,1,4,6,3]=>1000111=>1110001
[8,7,4,2,1,3,6,5]=>1010111=>1110101
[7,4,8,3,2,6,1,5]=>0100111=>1110010
[6,8,2,3,1,7,5,4]=>0101011=>1101010
[7,4,3,2,6,8,5,1]=>0111011=>1101110
[5,1,2,3,6,8,7,4]=>0001011=>1101000
[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
[5,7,8,2,1,4,3,6]=>1010001=>1000101
[3,5,1,7,8,4,2,6]=>0011001=>1001100
[1,7,8,4,5,3,2,6]=>0101001=>1001010
[3,2,4,8,6,7,1,5]=>0100011=>1100010
[8,3,1,6,7,4,2,5]=>0110011=>1100110
[3,2,5,7,4,8,1,6]=>0100011=>1100010
[8,4,7,1,3,2,5,6]=>0100011=>1100010
[8,4,7,2,1,3,5,6]=>1000011=>1100001
[6,4,2,1,3,7,8,5]=>1010101=>1010101
[7,1,6,3,5,8,2,4]=>0000111=>1110000
[3,8,5,1,6,7,2,4]=>0001011=>1101000
[5,3,6,7,8,4,2,1]=>1011001=>1001101
[1,5,2,7,8,6,4,3]=>0011101=>1011100
[1,4,2,8,6,5,7,3]=>0010111=>1110100
[4,1,7,5,2,6,8,3]=>0011011=>1101100
[7,6,2,4,5,1,8,3]=>0001111=>1111000
[8,1,4,5,2,6,7,3]=>0001011=>1101000
[8,4,6,5,2,1,7,3]=>1001111=>1111001
[3,5,7,2,1,6,8,4]=>1000011=>1100001
[3,7,5,4,6,8,1,2]=>0001011=>1101000
[8,3,4,1,5,6,7,2]=>0010011=>1100100
[3,5,2,4,7,6,1,8]=>0001110=>0111000
[7,3,5,2,4,6,1,8]=>0001110=>0111000
[5,3,7,2,4,6,1,8]=>0001110=>0111000
[3,5,2,7,4,6,1,8]=>0001110=>0111000
[3,2,5,7,4,6,1,8]=>0100110=>0110010
[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
[3,7,5,2,4,1,6,8]=>0011010=>0101100
[3,7,2,5,4,1,6,8]=>0011010=>0101100
[3,2,7,5,4,1,6,8]=>0111010=>0101110
[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
[1,7,3,5,2,4,6,8]=>0001010=>0101000
[7,1,3,5,2,4,6,8]=>0001010=>0101000
[5,1,3,7,2,4,6,8]=>0001010=>0101000
[3,2,1,5,7,4,6,8]=>1100010=>0100011
[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
[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
[3,5,7,2,4,1,6,8]=>0010010=>0100100
[5,3,7,2,4,1,6,8]=>0011010=>0101100
[7,3,5,2,1,4,6,8]=>1001010=>0101001
[5,3,2,4,7,1,6,8]=>0101010=>0101010
[3,2,5,4,7,1,6,8]=>0101010=>0101010
[3,5,2,4,1,7,6,8]=>0011010=>0101100
[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
[3,5,2,1,4,7,6,8]=>1001010=>0101001
[3,2,5,1,7,4,6,8]=>0101010=>0101010
[3,5,2,1,7,4,6,8]=>1001010=>0101001
[5,3,1,7,2,4,6,8]=>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
[3,1,2,7,5,4,6,8]=>0101010=>0101010
[3,1,7,2,5,4,6,8]=>0101010=>0101010
[3,1,7,5,2,4,6,8]=>0101010=>0101010
[5,1,7,3,2,4,6,8]=>0101010=>0101010
[7,1,5,3,2,4,6,8]=>0101010=>0101010
[1,7,5,3,2,4,6,8]=>0101010=>0101010
[5,8,7,1,2,6,4,3]=>0010111=>1110100
[6,8,2,1,7,5,4,3]=>1011011=>1101101
[1,8,7,6,3,2,5,4]=>0101111=>1111010
[5,8,7,4,1,2,6,3]=>0010111=>1110100
[2,8,7,4,3,6,1,5]=>0010111=>1110100
[1,8,5,4,2,7,6,3]=>0011111=>1111100
[7,6,4,2,8,5,3,1]=>0111111=>1111110
[7,6,4,8,5,1,2,3]=>0001111=>1111000
[7,6,4,5,1,3,8,2]=>0001111=>1111000
[1,6,7,5,3,8,4,2]=>0011011=>1101100
[7,6,3,5,2,4,8,1]=>0001111=>1111000
[7,6,4,2,5,1,8,3]=>0011111=>1111100
[7,6,2,8,3,1,4,5]=>0100111=>1110010
[1,6,7,5,8,2,3,4]=>0000011=>1100000
[2,6,3,7,5,1,8,4]=>0001111=>1111000
[2,6,5,7,8,3,4,1]=>0010101=>1010100
[3,2,5,1,7,8,4,6]=>0101001=>1001010
[5,2,3,4,8,6,1,7]=>0001101=>1011000
[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
[6,3,5,4,8,2,7,1]=>0001111=>1111000
[6,3,5,8,7,1,2,4]=>0000111=>1110000
[1,5,7,3,4,8,6,2]=>0000111=>1110000
[5,8,4,1,3,7,6,2]=>0010111=>1110100
[6,4,5,3,8,1,7,2]=>0001111=>1111000
[6,4,3,8,5,7,2,1]=>1010111=>1110101
[5,4,2,6,3,1,7,8]=>0111100=>0011110
[4,6,5,3,7,1,2,8]=>0001110=>0111000
[3,5,6,1,4,8,7,2]=>0000111=>1110000
[3,5,7,6,1,4,8,2]=>0000111=>1110000
[3,6,5,7,4,8,1,2]=>0000111=>1110000
[4,2,6,5,1,7,3,8]=>0011110=>0111100
[4,3,5,7,2,1,6,8]=>1010010=>0100101
[3,5,4,7,2,6,1,8]=>0001110=>0111000
[3,4,7,6,8,1,2,5]=>0000011=>1100000
[1,8,4,3,7,5,6,2]=>0010111=>1110100
[5,2,8,6,4,7,3,1]=>0101111=>1111010
[1,8,6,3,7,4,2,5]=>0010111=>1110100
[1,8,6,5,7,2,3,4]=>0000111=>1110000
[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
[1,5,7,2,4,6,8,3]=>0000011=>1100000
[1,3,6,4,2,5,8,7]=>0010101=>1010100
[5,6,3,4,7,1,8,2]=>0000111=>1110000
[3,5,2,7,4,1,8,6]=>0011011=>1101100
[5,2,3,8,4,1,7,6]=>0011011=>1101100
[7,5,3,4,8,2,1,6]=>1001011=>1101001
[7,6,3,8,4,2,1,5]=>1010111=>1110101
[7,2,8,5,1,6,3,4]=>0001111=>1111000
[7,4,3,8,5,2,6,1]=>0011111=>1111100
[7,2,8,5,1,3,4,6]=>0001011=>1101000
[7,6,8,1,2,5,3,4]=>0001011=>1101000
[1,5,3,7,6,8,4,2]=>0011011=>1101100
[1,2,6,4,5,8,3,7]=>0000101=>1010000
[1,2,7,4,8,5,3,6]=>0001011=>1101000
[1,6,3,7,8,2,4,5]=>0000101=>1010000
[3,2,6,7,8,1,4,5]=>0100001=>1000010
[1,4,7,3,5,2,6,8]=>0001010=>0101000
[3,8,4,7,6,1,5,2]=>0001111=>1111000
[5,7,4,2,6,3,1,8]=>0110110=>0110110
[2,4,5,8,1,6,7,3]=>0000011=>1100000
[6,1,3,7,4,2,5,8]=>0010110=>0110100
[2,1,8,3,6,7,4,5]=>1000011=>1100001
[5,1,8,6,2,7,3,4]=>0001111=>1111000
[5,7,1,4,2,6,3,8]=>0010110=>0110100
[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
[7,8,5,4,1,6,3,2]=>0111101=>1011110
[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
[3,6,2,7,8,1,5,4]=>0001101=>1011000
[2,7,3,8,1,5,6,4]=>0000111=>1110000
[2,6,8,4,1,5,7,3]=>0010011=>1100100
[5,7,8,4,1,6,3,2]=>0110101=>1010110
[8,4,6,5,3,1,7,2]=>0101111=>1111010
[5,6,4,8,3,1,7,2]=>0100111=>1110010
[3,4,8,1,2,5,7,6]=>0000011=>1100000
[6,3,1,7,5,2,4,8]=>0101110=>0111010
[6,3,1,8,2,7,4,5]=>0100111=>1110010
[7,8,1,2,4,3,6,5]=>0010101=>1010100
[5,2,8,1,3,4,7,6]=>0001011=>1101000
[3,2,1,6,4,7,8,5]=>1100101=>1010011
[4,1,3,6,5,7,8,2]=>0010101=>1010100
[5,1,3,4,2,7,8,6]=>0011001=>1001100
[6,1,3,4,2,8,5,7]=>0010101=>1010100
[8,1,4,3,5,7,6,2]=>0010111=>1110100
[5,2,4,1,3,7,8,6]=>0011001=>1001100
[3,2,6,1,5,7,8,4]=>0100101=>1010010
[1,4,6,3,5,7,8,2]=>0000101=>1010000
[3,5,1,6,4,7,8,2]=>0001101=>1011000
[3,6,4,2,1,7,8,5]=>1010101=>1010101
[3,8,6,1,4,7,5,2]=>0001111=>1111000
[1,8,3,2,6,7,5,4]=>0101011=>1101010
[8,7,1,3,6,5,4,2]=>0011111=>1111100
[1,8,5,7,4,2,6,3]=>0010111=>1110100
[4,7,5,3,8,2,1,6]=>1001011=>1101001
[2,7,6,5,8,3,1,4]=>0100111=>1110010
[1,4,7,6,8,2,3,5]=>0000011=>1100000
[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
[3,2,7,1,6,8,4,5]=>0100011=>1100010
[8,1,5,4,7,2,6,3]=>0001111=>1111000
[8,2,5,3,7,1,6,4]=>0001111=>1111000
[2,1,4,7,5,8,3,6]=>1000011=>1100001
[1,2,6,7,4,8,3,5]=>0000011=>1100000
[3,6,4,7,8,5,2,1]=>1001101=>1011001
[3,2,5,8,6,7,4,1]=>0110011=>1100110
[6,3,5,8,7,4,1,2]=>0010111=>1110100
[8,3,5,7,6,4,2,1]=>1010111=>1110101
[4,1,8,3,7,5,6,2]=>0010111=>1110100
[4,7,2,8,5,6,3,1]=>0100111=>1110010
[1,4,8,7,3,5,6,2]=>0000111=>1110000
[3,2,8,7,1,5,6,4]=>0100111=>1110010
[1,5,8,7,4,6,2,3]=>0000111=>1110000
[4,7,6,8,5,3,1,2]=>0101011=>1101010
[4,8,6,7,5,3,2,1]=>1101011=>1101011
[3,8,7,5,6,4,2,1]=>1010111=>1110101
[8,1,5,6,3,2,4,7]=>0100101=>1010010
[1,7,8,3,5,2,4,6]=>0001001=>1001000
[8,2,5,3,1,6,4,7]=>0101101=>1011010
[8,3,2,1,5,6,4,7]=>1100101=>1010011
[8,6,5,1,3,4,2,7]=>0011101=>1011100
[1,7,8,5,4,3,2,6]=>0111001=>1001110
[2,6,8,7,4,3,5,1]=>0011011=>1101100
[2,7,6,8,4,3,1,5]=>0110011=>1100110
[1,2,6,7,8,4,3,5]=>0010001=>1000100
[8,5,7,1,3,4,6,2]=>0000111=>1110000
[3,5,8,6,7,4,1,2]=>0010011=>1100100
[3,1,6,5,8,7,4,2]=>0110111=>1110110
[3,7,6,4,8,1,2,5]=>0000111=>1110000
[2,3,6,5,7,1,8,4]=>0000111=>1110000
[2,3,6,4,1,7,8,5]=>0010101=>1010100
[4,7,2,1,5,3,8,6]=>1001011=>1101001
[3,1,7,4,5,2,8,6]=>0101011=>1101010
[3,7,5,4,2,1,8,6]=>1011011=>1101101
[1,3,6,7,4,2,8,5]=>0010011=>1100100
[4,3,7,2,6,8,1,5]=>0010011=>1100100
[5,4,2,1,3,7,8,6]=>1011001=>1001101
[8,7,1,5,6,3,2,4]=>0100111=>1110010
[1,7,8,2,6,4,5,3]=>0001101=>1011000
[8,7,2,5,4,6,1,3]=>0001111=>1111000
[8,7,1,2,4,5,6,3]=>0000111=>1110000
[8,7,2,5,3,1,6,4]=>0101111=>1111010
[8,7,3,2,1,5,6,4]=>1100111=>1110011
[8,7,6,5,1,3,4,2]=>0011111=>1111100
[8,7,6,1,4,5,3,2]=>0101111=>1111010
[8,7,5,6,1,4,3,2]=>0110111=>1110110
[6,8,7,1,5,4,3,2]=>0111011=>1101110
[8,5,7,6,1,4,3,2]=>0110111=>1110110
[6,7,8,1,5,4,3,2]=>0111001=>1001110
[8,7,4,6,5,1,3,2]=>0101111=>1111010
[8,5,6,7,1,4,3,2]=>0110011=>1100110
[8,7,6,3,5,4,1,2]=>0011111=>1111100
[8,7,4,5,6,1,3,2]=>0100111=>1110010
[8,7,6,5,2,4,3,1]=>0111111=>1111110
[4,2,8,7,6,5,1,3]=>0011111=>1111100
[7,5,8,1,6,4,3,2]=>0110111=>1110110
[1,5,8,7,6,2,4,3]=>0010111=>1110100
[7,5,8,4,1,6,3,2]=>0110111=>1110110
[6,8,5,1,7,4,3,2]=>0111011=>1101110
[1,6,8,7,2,5,4,3]=>0011011=>1101100
[7,3,8,4,6,1,5,2]=>0001111=>1111000
[4,8,5,7,1,6,3,2]=>0100111=>1110010
[4,3,7,6,5,1,8,2]=>0011111=>1111100
[5,4,3,6,7,1,8,2]=>0011011=>1101100
[5,4,7,3,6,1,8,2]=>0001111=>1111000
[4,8,7,6,3,1,5,2]=>0101111=>1111010
[2,4,6,3,1,7,8,5]=>0100101=>1010010
[6,8,5,7,3,2,1,4]=>1100011=>1100011
[6,8,5,3,7,2,1,4]=>1001011=>1101001
[6,8,5,7,4,2,1,3]=>1010011=>1100101
[2,1,8,7,6,3,4,5]=>1000111=>1110001
[5,8,7,6,2,4,1,3]=>0010111=>1110100
[6,8,2,7,5,1,4,3]=>0011011=>1101100
[5,8,7,2,6,4,1,3]=>0010111=>1110100
[6,8,7,5,2,4,1,3]=>0011011=>1101100
[5,8,7,6,4,2,3,1]=>0110111=>1110110
[2,3,6,1,7,5,8,4]=>0000111=>1110000
[2,3,6,1,8,5,4,7]=>0001101=>1011000
[2,4,1,6,7,5,8,3]=>0010011=>1100100
[2,4,1,7,3,8,6,5]=>0010111=>1110100
[2,4,1,7,8,5,6,3]=>0010101=>1010100
[2,4,5,3,7,1,8,6]=>0001011=>1101000
[2,4,5,7,3,8,6,1]=>0000111=>1110000
[2,4,6,3,1,8,5,7]=>0100101=>1010010
[2,4,6,3,8,5,1,7]=>0001101=>1011000
[2,4,6,8,3,5,1,7]=>0001001=>1001000
[2,4,7,3,1,5,8,6]=>0100011=>1100010
[2,4,7,3,1,8,6,5]=>0100111=>1110010
[2,4,7,8,3,5,6,1]=>0000101=>1010000
[2,5,1,6,4,8,3,7]=>0001101=>1011000
[2,5,1,6,7,4,8,3]=>0001011=>1101000
[2,5,1,7,4,3,8,6]=>0011011=>1101100
[2,5,1,7,8,4,6,3]=>0001101=>1011000
[2,5,6,3,4,8,1,7]=>0000101=>1010000
[2,5,6,3,7,4,8,1]=>0000111=>1110000
[2,5,6,3,8,4,1,7]=>0010101=>1010100
[2,5,6,7,8,4,1,3]=>0010001=>1000100
[2,5,6,8,4,3,1,7]=>0110001=>1000110
[2,6,1,7,4,8,5,3]=>0001111=>1111000
[1,4,2,6,3,8,5,10,7,9]=>001010101=>101010100
[6,8,4,3,2,1,7,5]=>1110011=>1100111
[7,6,4,8,2,1,3,5]=>1000111=>1110001
[7,6,5,2,8,4,1,3]=>0011111=>1111100
[7,6,3,8,2,4,1,5]=>0010111=>1110100
[5,1,2,3,4,8,7,6]=>0001011=>1101000
[4,1,2,3,7,6,5,8]=>0010110=>0110100
[7,6,5,8,2,4,3,1]=>0110111=>1110110
[6,8,7,4,5,2,3,1]=>0101011=>1101010
[6,8,4,7,5,2,3,1]=>0101011=>1101010
[6,8,4,7,2,5,3,1]=>0101011=>1101010
[6,4,8,7,5,2,3,1]=>0101111=>1111010
[6,8,4,2,7,5,3,1]=>0111011=>1101110
[6,8,4,7,2,1,5,3]=>1001011=>1101001
[6,8,4,7,3,5,2,1]=>1001011=>1101001
[6,4,8,2,7,5,3,1]=>0101111=>1111010
[6,8,4,2,7,1,5,3]=>0011011=>1101100
[6,4,2,8,7,5,3,1]=>0111111=>1111110
[6,8,4,7,3,2,5,1]=>0101011=>1101010
[6,8,4,2,1,7,5,3]=>1011011=>1101101
[6,8,4,7,3,2,1,5]=>1100011=>1100011
[6,8,5,7,1,4,3,2]=>0110011=>1100110
[1,8,7,3,6,2,5,4]=>0001111=>1111000
[5,8,7,2,3,6,1,4]=>0000111=>1110000
[6,8,2,7,5,4,1,3]=>0011011=>1101100
[6,8,3,7,5,2,1,4]=>1001011=>1101001
[6,8,1,7,3,5,4,2]=>0011011=>1101100
[6,8,4,7,3,1,5,2]=>0101011=>1101010
[6,8,1,7,3,2,5,4]=>0101011=>1101010
[3,8,5,7,6,1,4,2]=>0010111=>1110100
[3,8,2,7,6,5,1,4]=>0001111=>1111000
[1,8,4,7,6,2,5,3]=>0001111=>1111000
[3,8,1,7,6,2,5,4]=>0001111=>1111000
[1,8,4,7,3,6,5,2]=>0001111=>1111000
[4,8,5,7,1,2,6,3]=>0000111=>1110000
[1,8,4,7,3,2,6,5]=>0100111=>1110010
[6,8,5,2,7,4,1,3]=>0011011=>1101100
[6,8,3,4,7,1,5,2]=>0001011=>1101000
[6,8,1,3,7,2,5,4]=>0001011=>1101000
[2,8,1,3,7,6,5,4]=>0001111=>1111000
[2,8,3,4,7,6,1,5]=>0000111=>1110000
[6,8,5,4,2,7,1,3]=>0011011=>1101100
[6,8,1,4,3,7,5,2]=>0011011=>1101100
[6,8,1,4,2,7,5,3]=>0011011=>1101100
[6,5,4,3,8,7,1,2]=>0011111=>1111100
[3,1,7,2,8,5,6,4]=>0100111=>1110010
[3,1,6,7,4,8,5,2]=>0101011=>1101010
[3,1,5,7,8,4,6,2]=>0100101=>1010010
[8,6,5,7,1,4,3,2]=>0110111=>1110110
[8,6,4,2,7,5,1,3]=>0011111=>1111100
[6,4,8,2,7,5,1,3]=>0001111=>1111000
[8,4,7,6,2,5,1,3]=>0001111=>1111000
[3,4,5,6,8,7,1,2]=>0000011=>1100000
[3,4,5,7,8,6,1,2]=>0000101=>1010000
[3,4,5,8,7,6,1,2]=>0000111=>1110000
[3,4,6,7,8,5,1,2]=>0001001=>1001000
[6,4,7,3,5,2,1,8]=>1001110=>0111001
[5,4,7,3,6,2,1,8]=>1001110=>0111001
[4,8,7,3,5,2,1,6]=>1001011=>1101001
[7,5,3,6,8,2,1,4]=>1001011=>1101001
[5,8,3,6,7,2,1,4]=>1000011=>1100001
[6,4,7,8,2,5,1,3]=>0001101=>1011000
[5,8,7,3,2,4,1,6]=>0110011=>1100110
[6,4,7,3,2,5,1,8]=>0101110=>0111010
[6,5,3,7,2,4,1,8]=>0011110=>0111100
[7,3,8,6,2,4,1,5]=>0010111=>1110100
[6,3,7,8,2,4,1,5]=>0010101=>1010100
[5,3,7,6,2,4,1,8]=>0011110=>0111100
[7,5,8,2,6,4,1,3]=>0010111=>1110100
[7,4,8,2,5,6,1,3]=>0000111=>1110000
[5,4,7,2,6,8,1,3]=>0001011=>1101000
[4,8,7,2,5,6,1,3]=>0000111=>1110000
[5,4,3,2,6,8,1,7]=>0111001=>1001110
[4,8,3,2,5,6,1,7]=>0100101=>1010010
[5,3,7,2,6,4,1,8]=>0011110=>0111100
[7,5,2,6,8,4,1,3]=>0011011=>1101100
[6,4,2,7,5,8,1,3]=>0010111=>1110100
[7,5,8,4,1,2,6,3]=>0010111=>1110100
[7,1,8,2,3,6,5,4]=>0001111=>1111000
[7,3,8,4,6,2,1,5]=>1000111=>1110001
[7,1,8,4,2,6,5,3]=>0011111=>1111100
[7,1,8,3,6,2,5,4]=>0001111=>1111000
[7,2,3,4,5,1,8,6]=>0001011=>1101000
[2,8,3,4,5,1,6,7]=>0001001=>1001000
[2,7,3,4,1,5,6,8]=>0010010=>0100100
[5,3,6,1,2,7,4,8]=>0001110=>0111000
[10,8,6,4,2,1,3,5,7,9]=>101010101=>101010101
[2,8,5,3,4,6,7,1]=>0001011=>1101000
[6,5,4,3,7,8,9,10,1,2]=>001110001=>100011100
[3,8,1,4,5,6,7,2]=>0000011=>1100000
[4,5,3,1,2,8,7,6]=>0101011=>1101010
[5,7,3,4,1,6,8,2]=>0010011=>1100100
[4,5,3,1,2,6,8,7]=>0101001=>1001010
[3,4,1,2,5,8,7,6]=>0010011=>1100100
[6,5,3,2,1,8,7,4]=>1101111=>1111011
[4,5,2,1,8,7,6,3]=>1001111=>1111001
[3,4,1,8,7,6,5,2]=>0011111=>1111100
[8,1,2,4,5,6,7,3]=>0000011=>1100000
[7,1,2,3,4,6,8,5]=>0000011=>1100000
[6,1,2,3,5,8,7,4]=>0000111=>1110000
[5,1,2,4,8,6,7,3]=>0001011=>1101000
[4,1,3,8,5,6,7,2]=>0010011=>1100100
[7,1,2,3,5,8,6,4]=>0000111=>1110000
[6,1,2,3,5,7,8,4]=>0000101=>1010000
[10,1,2,3,4,6,7,8,9,5]=>000000011=>110000000
[5,1,3,8,4,6,7,2]=>0001011=>1101000
[4,1,3,5,8,6,7,2]=>0010011=>1100100
[8,6,3,5,2,7,4,1]=>0011111=>1111100
[7,5,2,8,6,3,4,1]=>0011111=>1111100
[5,2,8,6,7,3,4,1]=>0011011=>1101100
[7,5,2,3,8,6,4,1]=>0011111=>1111100
[5,2,3,8,6,7,4,1]=>0011011=>1101100
[8,4,1,7,3,5,6,2]=>0010111=>1110100
[7,4,1,2,6,8,5,3]=>0011011=>1101100
[5,3,8,4,1,2,6,7]=>0011001=>1001100
[6,3,5,8,4,1,2,7]=>0010101=>1010100
[7,3,5,6,8,4,1,2]=>0010011=>1100100
[7,4,5,1,2,8,6,3]=>0001111=>1111000
[6,3,8,4,5,1,2,7]=>0001101=>1011000
[8,5,1,7,4,6,2,3]=>0001111=>1111000
[7,4,5,1,8,6,2,3]=>0001111=>1111000
[8,4,5,1,7,3,6,2]=>0001111=>1111000
[4,2,7,5,8,6,3,1]=>0110111=>1110110
[4,2,8,5,6,3,1,7]=>0110101=>1010110
[8,6,3,1,5,7,4,2]=>0110111=>1110110
[7,4,2,8,5,6,3,1]=>0110111=>1110110
[4,2,8,5,6,7,3,1]=>0110011=>1100110
[7,4,8,5,6,1,2,3]=>0000111=>1110000
[7,5,8,6,1,2,3,4]=>0000111=>1110000
[7,3,4,8,5,6,1,2]=>0000111=>1110000
[7,3,4,5,8,6,1,2]=>0000111=>1110000
[6,4,8,5,2,3,1,7]=>0101101=>1011010
[8,6,3,1,7,5,2,4]=>0101111=>1111010
[7,2,8,3,4,5,6,1]=>0000111=>1110000
[7,4,5,2,8,6,3,1]=>0101111=>1111010
[8,5,2,7,4,6,3,1]=>0101111=>1111010
[5,2,4,8,6,7,3,1]=>0101011=>1101010
[7,5,8,6,2,3,1,4]=>0100111=>1110010
[7,4,8,5,6,2,3,1]=>0100111=>1110010
[7,3,1,8,4,5,6,2]=>0100111=>1110010
[7,2,4,5,6,8,3,1]=>0100011=>1100010
[3,4,5,7,6,8,1,2]=>0000011=>1100000
[4,8,2,5,1,3,7,6]=>0001011=>1101000
[2,1,8,7,3,4,6,5]=>1000111=>1110001
[2,7,4,5,6,8,1,3]=>0000011=>1100000
[4,1,2,8,7,5,3,6]=>0011011=>1101100
[4,1,2,6,8,3,7,5]=>0010011=>1100100
[3,1,7,6,8,2,4,5]=>0100011=>1100010
[8,2,6,3,1,5,4,7]=>0101101=>1011010
[2,1,7,8,9,10,6,5,4,3]=>101110001=>100011101
[7,3,5,1,8,2,4,6]=>0001011=>1101000
[7,8,3,1,5,2,4,6]=>0101001=>1001010
[12,10,8,6,4,2,1,3,5,7,9,11]=>10101010101=>10101010101
[9,8,7,6,1,2,3,4,5,10]=>000011110=>011110000
[1,5,6,7,8,3,4,2]=>0010001=>1000100
[1,4,6,7,8,3,5,2]=>0001001=>1001000
[1,5,6,3,7,8,4,2]=>0010101=>1010100
[6,1,2,3,4,8,7,5]=>0000111=>1110000
[5,1,2,3,8,7,6,4]=>0001111=>1111000
[5,1,2,3,8,6,7,4]=>0001011=>1101000
[2,8,5,3,1,4,6,7]=>0101001=>1001010
[2,4,3,5,7,8,1,6]=>0010001=>1000100
[2,6,3,7,8,1,4,5]=>0000101=>1010000
[3,4,6,1,7,8,5,2]=>0001101=>1011000
[3,4,6,1,8,5,7,2]=>0000111=>1110000
[3,4,8,1,5,6,7,2]=>0000011=>1100000
[3,5,1,7,4,8,6,2]=>0001111=>1111000
[3,5,6,4,8,1,7,2]=>0000111=>1110000
[3,5,8,4,1,6,7,2]=>0010011=>1100100
[3,6,1,8,5,4,7,2]=>0001111=>1111000
[3,6,7,4,8,5,1,2]=>0001011=>1101000
[3,6,8,4,5,1,7,2]=>0001011=>1101000
[4,1,5,6,8,3,7,2]=>0010011=>1100100
[4,1,5,7,8,6,3,2]=>0110101=>1010110
[4,1,7,3,5,8,6,2]=>0010111=>1110100
[4,1,7,8,5,6,3,2]=>0110101=>1010110
[4,5,7,8,1,6,3,2]=>0100101=>1010010
[4,5,8,3,1,6,7,2]=>0100011=>1100010
[4,6,3,1,8,5,7,2]=>0100111=>1110010
[4,6,7,3,5,8,1,2]=>0000011=>1100000
[4,6,7,8,5,1,3,2]=>0101001=>1001010
[4,6,8,3,5,1,7,2]=>0001011=>1101000
[4,7,3,1,8,6,5,2]=>0101111=>1111010
[4,7,8,3,5,6,1,2]=>0000101=>1010000
[5,1,6,7,4,8,3,2]=>0101011=>1101010
[5,1,6,7,8,3,4,2]=>0011001=>1001100
[5,6,3,4,8,1,7,2]=>0000111=>1110000
[5,6,7,8,4,1,3,2]=>0110001=>1000110
[5,7,3,4,1,8,6,2]=>0010111=>1110100
[5,7,3,4,8,6,1,2]=>0000111=>1110000
[5,7,3,8,4,6,1,2]=>0000111=>1110000
[5,7,8,4,3,6,1,2]=>0010101=>1010100
[6,1,3,7,8,5,4,2]=>0011101=>1011100
[6,1,7,4,5,8,3,2]=>0100111=>1110010
[6,1,8,4,5,3,7,2]=>0001111=>1111000
[6,7,3,8,5,4,1,2]=>0011011=>1101100
[7,1,3,4,8,6,5,2]=>0001111=>1111000
[8,4,1,3,2,5,6,7]=>0110001=>1000110
[8,5,1,2,4,3,6,7]=>0011001=>1001100
[8,6,1,2,3,5,4,7]=>0001101=>1011000
[8,7,1,2,3,4,6,5]=>0000111=>1110000
[8,5,1,4,2,3,6,7]=>0011001=>1001100
[8,6,1,2,5,3,4,7]=>0001101=>1011000
[8,7,1,2,3,6,4,5]=>0000111=>1110000
[8,6,1,2,5,4,3,7]=>0011101=>1011100
[2,5,8,6,1,7,3,4]=>0000111=>1110000
[4,5,6,8,7,2,1,3]=>1000011=>1100001
[5,6,8,7,2,3,1,4]=>0100011=>1100010
[4,1,5,2,8,7,6,3]=>0011111=>1111100
[4,8,2,5,6,1,3,7]=>0000101=>1010000
[5,2,3,6,7,8,1,4]=>0001001=>1001000
[4,2,8,7,5,3,1,6]=>0111011=>1101110
[4,2,8,6,7,5,3,1]=>0111011=>1101110
[1,3,2,4,8,5,7,6]=>0100011=>1100010
[1,6,3,2,5,7,8,4]=>0100101=>1010010
[2,5,6,1,8,7,3,4]=>0000111=>1110000
[7,6,2,1,4,8,3,5]=>1000111=>1110001
[2,6,5,1,8,7,3,4]=>0001111=>1111000
[1,4,2,7,3,8,6,5]=>0010111=>1110100
[1,2,7,3,8,6,5,4]=>0001111=>1111000
[3,1,8,4,6,2,7,5]=>0100111=>1110010
[3,4,5,1,8,2,7,6]=>0001011=>1101000
[3,8,1,6,5,2,7,4]=>0001111=>1111000
[1,5,2,3,8,7,4,6]=>0001011=>1101000
[2,8,7,6,3,1,4,5]=>0100111=>1110010
[8,7,2,5,3,1,4,6]=>0101011=>1101010
[7,6,2,3,4,8,1,5]=>0000111=>1110000
[8,7,6,2,1,4,3,5]=>1010111=>1110101
[8,2,7,4,1,5,3,6]=>0011011=>1101100
[1,7,3,2,4,5,8,6]=>0100011=>1100010
[1,3,8,6,2,4,7,5]=>0000111=>1110000
[8,7,3,1,4,2,6,5]=>0110111=>1110110
[1,2,5,3,4,8,7,6]=>0001011=>1101000
[1,2,3,8,4,7,6,5]=>0000111=>1110000
[1,6,2,3,7,5,8,4]=>0000111=>1110000
[4,5,1,2,8,3,7,6]=>0001011=>1101000
[1,4,8,2,6,3,7,5]=>0000111=>1110000
[8,4,1,7,3,2,5,6]=>0110011=>1100110
[1,8,7,3,2,4,6,5]=>0100111=>1110010
[8,3,1,5,6,2,7,4]=>0100111=>1110010
[3,4,1,6,5,7,2,8]=>0010110=>0110100
[3,5,1,6,2,8,7,4]=>0001111=>1111000
[5,4,3,6,1,7,2,8]=>0011110=>0111100
[4,8,7,2,1,6,5,3]=>1001111=>1111001
[6,2,1,8,7,5,4,3]=>1011111=>1111101
[7,5,8,6,3,2,4,1]=>0110111=>1110110
[5,8,7,6,3,2,4,1]=>0110111=>1110110
[5,4,7,2,8,1,6,3]=>0001111=>1111000
[8,1,5,4,6,3,7,2]=>0001111=>1111000
[2,1,5,8,3,7,4,6]=>1000011=>1100001
[2,1,7,4,8,3,6,5]=>1000111=>1110001
[1,2,3,5,8,7,4,6]=>0000011=>1100000
[6,1,2,7,8,4,3,5]=>0010101=>1010100
[5,1,4,8,2,7,3,6]=>0001011=>1101000
[3,4,1,2,8,7,5,6]=>0010011=>1100100
[1,2,5,7,8,6,3,4]=>0000101=>1010000
[2,1,3,4,8,5,7,6]=>1000011=>1100001
[6,2,5,1,7,3,8,4]=>0001111=>1111000
[2,4,8,1,3,7,5,6]=>0000011=>1100000
[1,5,4,8,6,2,7,3]=>0001111=>1111000
[2,5,1,8,6,3,7,4]=>0001111=>1111000
[2,1,3,7,4,8,6,5]=>1000111=>1110001
[4,2,5,8,1,7,3,6]=>0010011=>1100100
[2,6,8,5,1,7,3,4]=>0001011=>1101000
[1,3,2,7,8,5,4,6]=>0101001=>1001010
[7,1,2,3,6,8,4,5]=>0000011=>1100000
[5,1,2,3,8,4,7,6]=>0001011=>1101000
[3,4,5,1,8,7,2,6]=>0001011=>1101000
[4,1,2,3,8,7,5,6]=>0010011=>1100100
[7,4,1,6,8,2,3,5]=>0010011=>1100100
[2,3,1,8,5,4,7,6]=>0101011=>1101010
[2,3,8,4,1,5,7,6]=>0010011=>1100100
[5,3,1,8,7,2,4,6]=>0101011=>1101010
[3,6,1,8,7,2,4,5]=>0000111=>1110000
[1,3,8,4,2,7,6,5]=>0010111=>1110100
[1,2,3,8,5,7,4,6]=>0000011=>1100000
[6,1,7,2,5,8,3,4]=>0000111=>1110000
[4,5,1,8,7,2,3,6]=>0001011=>1101000
[1,4,2,8,5,3,7,6]=>0011011=>1101100
[4,3,8,1,6,2,7,5]=>0010111=>1110100
[7,8,6,5,2,1,4,3]=>1011101=>1011101
[8,6,7,5,2,1,4,3]=>1011011=>1101101
[6,7,8,2,1,5,4,3]=>1011001=>1001101
[8,7,5,6,2,1,4,3]=>1010111=>1110101
[3,2,8,5,6,7,1,4]=>0100011=>1100010
[4,2,5,1,8,7,3,6]=>0011011=>1101100
[5,2,7,8,6,3,1,4]=>0101101=>1011010
[4,2,6,1,5,8,3,7]=>0010101=>1010100
[7,2,4,5,8,3,6,1]=>0000111=>1110000
[2,4,7,8,6,1,5,3]=>0001101=>1011000
[4,2,7,1,5,6,8,3]=>0010011=>1100100
[3,2,5,8,1,6,7,4]=>0100011=>1100010
[8,1,4,3,2,5,6,7]=>0110001=>1000110
[1,7,3,2,4,5,6,8]=>0100010=>0100010
[1,6,3,2,4,5,7,8]=>0100100=>0010010
[1,3,8,4,2,5,6,7]=>0010001=>1000100
[6,2,5,1,8,3,4,7]=>0001101=>1011000
[5,1,8,2,4,3,6,7]=>0011001=>1001100
[8,2,3,1,5,6,7,4]=>0100011=>1100010
[1,7,2,4,5,8,6,3]=>0000111=>1110000
[1,5,7,8,4,6,2,3]=>0000101=>1010000
[6,5,8,3,4,2,1,7]=>1010101=>1010101
[6,5,8,2,3,4,1,7]=>0010101=>1010100
[3,2,5,4,7,6,9,8,1,10]=>010101110=>011101010
[1,4,3,6,5,8,7,10,9,2]=>001010111=>111010100
[1,4,3,6,5,8,7,10,9,12,11,2]=>00101010111=>11101010100
[4,2,1,3,5,8,6,7]=>1010001=>1000101
[1,3,8,2,6,4,5,7]=>0000101=>1010000
[6,1,2,7,4,3,8,5]=>0010111=>1110100
[7,6,1,3,8,2,4,5]=>0000111=>1110000
[5,4,1,2,3,8,6,7]=>0011001=>1001100
[7,6,8,5,2,4,1,3]=>0011011=>1101100
[6,7,8,5,2,4,1,3]=>0011001=>1001100
[3,4,5,8,2,1,7,6]=>1000011=>1100001
[3,4,6,2,7,1,5,8]=>0000110=>0110000
[3,4,6,2,8,1,7,5]=>0000111=>1110000
[3,4,6,8,1,5,7,2]=>0000011=>1100000
[3,4,6,1,5,2,7,8]=>0001100=>0011000
[3,4,7,2,1,6,5,8]=>1000110=>0110001
[3,4,7,1,5,6,2,8]=>0000110=>0110000
[3,5,2,6,1,4,7,8]=>0001100=>0011000
[3,5,2,7,1,6,4,8]=>0001110=>0111000
[3,5,2,1,4,6,7,8]=>1001000=>0001001
[3,5,6,4,8,2,1,7]=>1000101=>1010001
[3,5,6,4,1,2,7,8]=>0010100=>0010100
[3,5,6,8,4,2,1,7]=>1010001=>1000101
[3,5,6,8,1,2,7,4]=>0000011=>1100000
[3,5,6,1,4,2,7,8]=>0010100=>0010100
[3,5,7,4,2,8,1,6]=>0010011=>1100100
[3,5,7,4,2,1,6,8]=>1010010=>0100101
[3,5,7,4,8,1,6,2]=>0000111=>1110000
[3,5,7,8,1,6,2,4]=>0000101=>1010000
[3,5,7,1,4,6,2,8]=>0000110=>0110000
[3,5,8,4,2,6,1,7]=>0010101=>1010100
[3,5,8,1,4,6,7,2]=>0000011=>1100000
[3,6,2,4,8,1,7,5]=>0000111=>1110000
[3,6,2,7,8,5,1,4]=>0001101=>1011000
[3,6,2,7,8,1,4,5]=>0000101=>1010000
[3,6,2,1,5,4,7,8]=>1001100=>0011001
[3,6,7,8,5,1,2,4]=>0001001=>1001000
[3,6,7,8,1,5,2,4]=>0001001=>1001000
[3,7,2,4,5,8,1,6]=>0000011=>1100000
[3,7,2,4,8,1,6,5]=>0000111=>1110000
[3,7,2,4,1,6,5,8]=>0010110=>0110100
[3,7,2,8,5,6,1,4]=>0000111=>1110000
[3,7,2,1,5,6,4,8]=>1000110=>0110001
[3,7,8,4,5,1,6,2]=>0001101=>1011000
[3,7,8,4,1,6,5,2]=>0011101=>1011100
[3,8,2,4,1,6,7,5]=>0010011=>1100100
[3,8,2,1,5,6,7,4]=>1000011=>1100001
[8,1,5,4,3,6,7,2]=>0011011=>1101100
[8,1,4,5,3,6,7,2]=>0001011=>1101000
[4,1,6,3,5,7,8,2]=>0010101=>1010100
[4,1,7,3,5,6,8,2]=>0010011=>1100100
[6,1,7,3,8,4,5,2]=>0001111=>1111000
[4,1,3,6,7,8,5,2]=>0011001=>1001100
[4,6,2,3,5,1,7,8]=>0001100=>0011000
[3,5,2,4,1,6,7,8]=>0011000=>0001100
[5,8,2,3,4,6,1,7]=>0000101=>1010000
[4,7,2,3,5,1,6,8]=>0001010=>0101000
[5,7,2,3,4,6,8,1]=>0000011=>1100000
[4,6,2,3,5,7,1,8]=>0000110=>0110000
[2,3,7,8,1,6,5,4]=>0001101=>1011000
[2,7,6,1,4,8,3,5]=>0000111=>1110000
[2,6,8,1,4,5,7,3]=>0000011=>1100000
[2,6,5,8,1,3,7,4]=>0000111=>1110000
[6,4,7,5,8,2,3,1]=>0100111=>1110010
[6,7,4,1,8,2,3,5]=>0010011=>1100100
[6,7,8,1,4,2,5,3]=>0011001=>1001100
[5,2,6,1,4,8,3,7]=>0001101=>1011000
[7,2,3,5,8,1,4,6]=>0000011=>1100000
[2,4,7,5,8,1,3,6]=>0000011=>1100000
[2,3,6,5,1,8,7,4]=>0001111=>1111000
[2,3,4,8,1,5,7,6]=>0000011=>1100000
[2,3,4,7,8,1,6,5]=>0000101=>1010000
[2,7,8,5,1,4,6,3]=>0001101=>1011000
[2,3,7,5,8,1,4,6]=>0000011=>1100000
[2,3,6,8,5,1,7,4]=>0001011=>1101000
[7,6,4,5,1,8,2,3]=>0001111=>1111000
[7,4,6,8,1,5,2,3]=>0001011=>1101000
[2,7,4,6,5,8,3,1]=>0100111=>1110010
[2,6,7,8,5,3,1,4]=>0101001=>1001010
[2,5,6,1,4,8,3,7]=>0000101=>1010000
[2,6,4,8,5,7,3,1]=>0100111=>1110010
[2,5,8,1,4,6,7,3]=>0000011=>1100000
[7,2,3,4,8,1,6,5]=>0000111=>1110000
[3,2,5,7,8,1,6,4]=>0100101=>1010010
[6,4,1,7,8,2,3,5]=>0010101=>1010100
[5,7,1,6,2,8,4,3]=>0010111=>1110100
[5,6,1,8,2,3,7,4]=>0000111=>1110000
[7,3,5,1,6,8,4,2]=>0011011=>1101100
[6,3,4,5,8,2,1,7]=>1000101=>1010001
[5,7,6,1,2,8,3,4]=>0000111=>1110000
[5,7,4,8,2,6,3,1]=>0100111=>1110010
[5,6,8,1,2,4,7,3]=>0000011=>1100000
[6,2,3,4,5,8,1,7]=>0000101=>1010000
[4,7,1,3,8,2,6,5]=>0000111=>1110000
[5,4,1,6,7,8,2,3]=>0011001=>1001100
[7,4,1,5,8,2,6,3]=>0010111=>1110100
[5,7,1,8,6,2,3,4]=>0000111=>1110000
[7,3,5,1,8,2,6,4]=>0001111=>1111000
[4,8,1,3,5,6,7,2]=>0000011=>1100000
[8,1,2,3,7,5,6,4]=>0000111=>1110000
[2,1,8,3,7,5,6,4]=>1000111=>1110001
[5,6,7,3,8,2,1,4]=>1000011=>1100001
[5,6,8,3,1,2,7,4]=>0100011=>1100010
[5,7,3,2,8,6,1,4]=>0100111=>1110010
[5,7,8,3,1,6,2,4]=>0100101=>1010010
[5,8,3,2,1,6,7,4]=>1100011=>1100011
[6,2,7,3,8,5,1,4]=>0001111=>1111000
[6,2,3,7,8,5,1,4]=>0001101=>1011000
[6,7,3,2,8,5,1,4]=>0101011=>1101010
[6,7,8,3,5,1,2,4]=>0001001=>1001000
[1,5,6,7,8,3,2,4]=>0100001=>1000010
[6,8,3,2,5,1,7,4]=>0101011=>1101010
[1,5,8,3,2,6,7,4]=>0100011=>1100010
[1,6,7,8,5,2,3,4]=>0001001=>1001000
[1,6,8,3,5,2,7,4]=>0001011=>1101000
[1,7,3,2,8,6,5,4]=>0101111=>1111010
[1,7,8,3,5,6,2,4]=>0000101=>1010000
[1,6,7,8,4,2,3,5]=>0010001=>1000100
[1,2,6,8,4,3,7,5]=>0010011=>1100100
[1,8,3,4,2,6,7,5]=>0010011=>1100100
[1,2,8,4,3,6,7,5]=>0010011=>1100100
[6,2,7,8,4,1,3,5]=>0010101=>1010100
[6,2,3,7,8,1,4,5]=>0000101=>1010000
[4,5,7,1,8,6,2,3]=>0000111=>1110000
[4,5,7,8,2,6,1,3]=>0000101=>1010000
[4,6,2,8,5,1,7,3]=>0001111=>1111000
[4,6,7,1,8,5,2,3]=>0001011=>1101000
[4,7,2,8,5,6,1,3]=>0000111=>1110000
[4,8,2,1,5,6,7,3]=>1000011=>1100001
[1,2,8,4,5,3,7,6]=>0001011=>1101000
[1,2,3,7,8,5,4,6]=>0001001=>1001000
[1,2,3,8,5,4,7,6]=>0001011=>1101000
[1,7,3,8,5,4,2,6]=>0011011=>1101100
[5,2,7,4,8,6,1,3]=>0001111=>1111000
[5,2,7,8,4,6,1,3]=>0001101=>1011000
[7,2,3,8,5,4,1,6]=>0011011=>1101100
[5,6,2,7,8,1,4,3]=>0010101=>1010100
[5,8,2,4,1,6,7,3]=>0010011=>1100100
[6,2,1,7,8,5,4,3]=>1011101=>1011101
[6,7,2,4,8,5,1,3]=>0001011=>1101000
[6,7,2,8,5,4,1,3]=>0011011=>1101100
[6,8,2,4,5,1,7,3]=>0001011=>1101000
[3,2,5,6,8,1,4,7]=>0100001=>1000010
[7,1,3,2,8,4,5,6]=>0100011=>1100010
[8,1,2,3,7,5,4,6]=>0001011=>1101000
[4,1,8,2,7,5,3,6]=>0011011=>1101100
[7,1,8,3,4,5,2,6]=>0001011=>1101000
[7,1,6,3,8,2,4,5]=>0000111=>1110000
[6,1,5,8,2,3,4,7]=>0000101=>1010000
[8,1,6,7,4,2,3,5]=>0010011=>1100100
[6,1,5,8,2,3,7,4]=>0000111=>1110000
[4,1,7,2,5,8,3,6]=>0010011=>1100100
[8,1,6,3,4,7,2,5]=>0000111=>1110000
[7,1,6,8,2,5,3,4]=>0001011=>1101000
[4,1,8,2,5,6,3,7]=>0010101=>1010100
[8,1,7,3,2,5,6,4]=>0100111=>1110010
[4,1,8,2,5,6,7,3]=>0010011=>1100100
[3,8,1,2,7,5,4,6]=>0001011=>1101000
[5,4,7,1,2,8,3,6]=>0001011=>1101000
[8,4,7,1,3,2,6,5]=>0100111=>1110010
[8,5,7,3,1,2,6,4]=>0100111=>1110010
[3,8,1,2,4,5,7,6]=>0000011=>1100000
[7,6,2,1,8,4,3,5]=>1010111=>1110101
[8,5,2,3,6,1,4,7]=>0001101=>1011000
[8,5,7,1,4,3,2,6]=>0110011=>1100110
[3,6,1,4,2,8,5,7]=>0010101=>1010100
[7,6,8,1,4,5,2,3]=>0001011=>1101000
[3,7,1,4,2,8,6,5]=>0010111=>1110100
[5,4,3,8,2,1,7,6]=>1011011=>1101101
[5,8,7,3,2,1,6,4]=>1100111=>1110011
[2,3,7,1,6,8,5,4]=>0001011=>1101000
[2,6,1,5,7,4,8,3]=>0000111=>1110000
[2,3,6,1,8,4,7,5]=>0000111=>1110000
[3,5,1,4,6,7,8,2]=>0001001=>1001000
[4,5,6,2,1,7,8,3]=>1000101=>1010001
[5,2,4,7,6,3,8,1]=>0001111=>1111000
[8,7,6,1,4,3,5,2]=>0011111=>1111100
[8,7,6,1,3,4,5,2]=>0001111=>1111000
[8,7,1,4,5,6,3,2]=>0100111=>1110010
[8,1,5,6,7,4,3,2]=>0110011=>1100110
[5,8,3,4,1,6,2,7]=>0010101=>1010100
[4,2,6,1,7,8,5,3]=>0011101=>1011100
[1,5,2,6,7,8,4,3]=>0011001=>1001100
[4,5,2,7,8,6,1,3]=>0001101=>1011000
[1,5,6,7,4,8,2,3]=>0000011=>1100000
[4,2,6,8,5,1,7,3]=>0011011=>1101100
[4,2,7,8,5,6,1,3]=>0010101=>1010100
[3,5,2,7,4,6,8,1]=>0001011=>1101000
[5,6,2,7,3,8,4,1]=>0010111=>1110100
[3,5,2,8,4,6,7,1]=>0001011=>1101000
[3,7,2,8,4,1,5,6]=>0010011=>1100100
[3,5,2,4,7,8,6,1]=>0001101=>1011000
[3,7,1,5,8,2,4,6]=>0000011=>1100000
[5,1,3,8,2,4,6,7]=>0001001=>1001000
[4,2,1,3,8,5,6,7]=>1010001=>1000101
[1,8,7,6,3,4,5,2]=>0001111=>1111000
[8,5,7,6,3,1,4,2]=>0110111=>1110110
[8,5,7,6,3,2,1,4]=>1100111=>1110011
[8,7,5,3,1,6,4,2]=>0111111=>1111110
[4,2,8,3,1,6,7,5]=>0110011=>1100110
[7,8,1,4,5,6,3,2]=>0100101=>1010010
[4,2,8,3,5,1,7,6]=>0011011=>1101100
[4,2,7,8,1,6,5,3]=>0011101=>1011100
[6,8,1,4,5,3,7,2]=>0001011=>1101000
[5,1,3,4,2,6,7,8]=>0011000=>0001100
[4,2,7,3,1,6,5,8]=>0110110=>0110110
[2,3,4,5,8,1,7,6]=>0000011=>1100000
[4,1,5,3,6,7,8,2]=>0011001=>1001100
[2,3,4,8,1,6,7,5]=>0000011=>1100000
[5,1,4,6,3,7,8,2]=>0001101=>1011000
[5,1,6,3,4,7,8,2]=>0001101=>1011000
[2,1,7,5,3,8,6,4]=>1001111=>1111001
[2,1,8,7,5,3,6,4]=>1001111=>1111001
[7,5,3,2,1,8,6,4]=>1101111=>1111011
[5,2,3,4,1,8,6,7]=>0011001=>1001100
[3,2,1,6,4,5,7,8]=>1100100=>0010011
[3,8,1,2,5,4,7,6]=>0001011=>1101000
[7,4,6,8,5,3,2,1]=>1101011=>1101011
[7,5,8,6,3,2,1,4]=>1100111=>1110011
[7,4,8,5,6,3,2,1]=>1100111=>1110011
[7,5,8,6,4,2,1,3]=>1010111=>1110101
[6,4,2,1,8,5,3,7]=>1011101=>1011101
[5,3,8,7,4,2,1,6]=>1011011=>1101101
[7,4,2,1,6,8,5,3]=>1011011=>1101101
[5,3,8,4,2,1,6,7]=>1011001=>1001101
[8,6,3,5,7,4,2,1]=>1010111=>1110101
[7,4,2,1,8,5,6,3]=>1010111=>1110101
[6,3,5,8,4,2,1,7]=>1010101=>1010101
[6,4,8,7,5,2,1,3]=>1001111=>1111001
[7,5,2,1,3,8,6,4]=>1001111=>1111001
[7,5,2,1,8,6,3,4]=>1001111=>1111001
[6,3,8,7,4,5,2,1]=>1001111=>1111001
[7,4,5,2,1,8,6,3]=>1001111=>1111001
[8,5,2,1,7,4,6,3]=>1001111=>1111001
[6,3,8,4,5,2,1,7]=>1001101=>1011001
[7,3,6,8,4,5,2,1]=>1001011=>1101001
[7,4,8,5,6,2,1,3]=>1000111=>1110001
[7,3,4,5,8,6,2,1]=>1000111=>1110001
[7,3,8,4,5,6,2,1]=>1000111=>1110001
[1,8,7,2,6,5,4,3]=>0011111=>1111100
[1,8,7,6,2,3,4,5]=>0000111=>1110000
[1,8,2,5,7,6,4,3]=>0010111=>1110100
[1,8,2,5,6,7,4,3]=>0010011=>1100100
[1,2,8,3,4,5,7,6]=>0000011=>1100000
[7,6,1,2,3,8,4,5]=>0000111=>1110000
[1,6,2,3,4,8,7,5]=>0000111=>1110000
[7,4,1,2,8,3,5,6]=>0010011=>1100100
[6,4,1,2,8,3,5,7]=>0010101=>1010100
[4,8,1,2,3,7,5,6]=>0000011=>1100000
[6,4,1,7,2,3,8,5]=>0010111=>1110100
[6,5,1,2,3,8,4,7]=>0001101=>1011000
[1,8,5,2,3,7,4,6]=>0001011=>1101000
[6,5,1,2,7,3,8,4]=>0001111=>1111000
[7,6,4,1,8,2,3,5]=>0010111=>1110100
[1,5,2,3,6,8,7,4]=>0001011=>1101000
[7,3,1,2,8,4,5,6]=>0100011=>1100010
[7,6,3,1,8,2,4,5]=>0100111=>1110010
[5,3,6,1,2,4,8,7]=>0001101=>1011000
[5,8,3,1,7,2,4,6]=>0100011=>1100010
[7,5,4,1,8,2,3,6]=>0011011=>1101100
[7,6,1,4,8,2,3,5]=>0000111=>1110000
[1,2,8,5,3,7,4,6]=>0001011=>1101000
[1,2,7,3,8,6,4,5]=>0000111=>1110000
[7,5,1,6,8,2,3,4]=>0001011=>1101000
[4,1,2,8,6,3,7,5]=>0010111=>1110100
[5,4,1,6,2,7,8,3]=>0011101=>1011100
[6,3,4,1,7,2,8,5]=>0010111=>1110100
[6,5,3,1,8,2,4,7]=>0101101=>1011010
[3,8,1,6,7,2,4,5]=>0000011=>1100000
[6,5,3,7,1,2,8,4]=>0001111=>1111000
[7,1,4,2,8,5,3,6]=>0011011=>1101100
[7,1,4,2,6,8,3,5]=>0010011=>1100100
[1,2,6,8,3,5,4,7]=>0001001=>1001000
[1,2,3,7,8,6,4,5]=>0000101=>1010000
[1,6,8,5,2,7,3,4]=>0001011=>1101000
[7,6,3,4,1,8,2,5]=>0010111=>1110100
[1,4,8,2,3,7,6,5]=>0000111=>1110000
[1,2,8,3,5,7,6,4]=>0000111=>1110000
[4,5,1,7,6,8,2,3]=>0001011=>1101000
[3,4,8,1,2,6,7,5]=>0000011=>1100000
[3,1,8,2,5,6,7,4]=>0100011=>1100010
[1,4,2,5,6,8,7,3]=>0010011=>1100100
[4,5,6,3,7,1,8,2]=>0000111=>1110000
[8,2,7,3,1,5,6,4]=>0100111=>1110010
[7,2,1,8,4,5,6,3]=>1000111=>1110001
[4,2,7,1,3,8,6,5]=>0010111=>1110100
[8,2,6,3,4,7,1,5]=>0000111=>1110000
[7,2,3,4,1,8,6,5]=>0010111=>1110100
[6,1,8,2,7,5,3,4]=>0001111=>1111000
[4,2,8,1,5,6,3,7]=>0010101=>1010100
[8,2,7,3,1,4,5,6]=>0100011=>1100010
[5,3,1,6,2,7,8,4]=>0101101=>1011010
[5,2,1,3,6,7,8,4]=>1001001=>1001001
[6,4,8,7,3,2,1,5]=>1100111=>1110011
[6,5,3,8,7,2,1,4]=>1001111=>1111001
[5,4,8,7,3,2,1,6]=>1101011=>1101011
[6,4,3,8,7,2,1,5]=>1010111=>1110101
[6,3,8,7,5,2,1,4]=>1001111=>1111001
[5,6,8,1,4,2,7,3]=>0010011=>1100100
[5,6,3,1,4,2,7,8]=>0110100=>0010110
[5,7,3,8,4,1,6,2]=>0010111=>1110100
[5,7,3,1,4,6,2,8]=>0100110=>0110010
[5,7,3,4,8,1,6,2]=>0000111=>1110000
[5,2,6,1,4,3,7,8]=>0011100=>0011100
[5,8,3,1,4,6,7,2]=>0100011=>1100010
[6,2,7,4,1,5,3,8]=>0011110=>0111100
[6,7,3,8,1,5,2,4]=>0001011=>1101000
[6,7,3,4,1,5,2,8]=>0011010=>0101100
[6,7,8,1,5,4,2,3]=>0011001=>1001100
[4,5,6,7,1,3,2,8]=>0100010=>0100010
[6,7,1,4,5,3,2,8]=>0101010=>0101010
[4,5,7,8,2,1,6,3]=>1000101=>1010001
[7,2,3,8,1,6,5,4]=>0001111=>1111000
[7,2,3,8,5,1,6,4]=>0001111=>1111000
[7,2,3,1,5,6,4,8]=>0100110=>0110010
[7,2,8,4,1,6,5,3]=>0011111=>1111100
[7,2,8,4,5,1,6,3]=>0001111=>1111000
[4,6,3,8,1,5,7,2]=>0000111=>1110000
[7,8,3,4,1,6,5,2]=>0011101=>1011100
[4,6,7,3,8,1,2,5]=>0000011=>1100000
[4,6,7,8,1,5,3,2]=>0101001=>1001010
[4,6,7,1,5,2,3,8]=>0001010=>0101000
[4,6,8,3,1,5,7,2]=>0100011=>1100010
[4,6,1,3,5,2,7,8]=>0001100=>0011000
[4,7,3,8,5,1,6,2]=>0001111=>1111000
[4,7,3,8,1,6,5,2]=>0001111=>1111000
[1,7,2,3,4,6,8,5]=>0000011=>1100000
[8,1,2,3,5,6,4,7]=>0000101=>1010000
[4,1,8,2,7,3,5,6]=>0010011=>1100100
[1,8,4,2,7,3,5,6]=>0010011=>1100100
[7,4,1,2,6,8,3,5]=>0010011=>1100100
[8,7,1,2,4,5,3,6]=>0001011=>1101000
[4,1,8,2,3,5,7,6]=>0010011=>1100100
[6,1,2,8,3,4,7,5]=>0000111=>1110000
[5,4,1,2,7,8,3,6]=>0011001=>1001100
[1,5,2,8,3,4,7,6]=>0001011=>1101000
[7,1,2,5,3,6,8,4]=>0001011=>1101000
[1,8,2,5,6,3,7,4]=>0000111=>1110000
[1,5,2,4,6,7,8,3]=>0001001=>1001000
[6,8,1,3,4,2,5,7]=>0010001=>1000100
[3,1,8,2,5,4,6,7]=>0101001=>1001010
[3,1,7,5,8,2,4,6]=>0100011=>1100010
[1,7,3,2,8,4,5,6]=>0100011=>1100010
[6,3,5,1,8,2,4,7]=>0001101=>1011000
[1,6,4,2,3,5,8,7]=>0010101=>1010100
[1,7,4,2,3,5,8,6]=>0010011=>1100100
[1,7,4,2,3,6,8,5]=>0010011=>1100100
[1,2,7,3,8,4,6,5]=>0000111=>1110000
[7,1,3,4,5,8,2,6]=>0000011=>1100000
[7,6,1,3,4,8,2,5]=>0000111=>1110000
[1,8,7,6,3,2,4,5]=>0100111=>1110010
[1,8,2,7,5,3,6,4]=>0001111=>1111000
[1,7,4,5,2,6,8,3]=>0001011=>1101000
[1,4,8,5,6,2,7,3]=>0000111=>1110000
[3,2,1,8,7,6,4,5]=>1100111=>1110011
[3,2,1,8,7,5,4,6]=>1101011=>1101011
[3,2,1,8,7,4,6,5]=>1100111=>1110011
[3,2,1,8,7,4,5,6]=>1100011=>1100011
[3,2,1,8,4,7,6,5]=>1100111=>1110011
[3,2,8,7,6,1,5,4]=>0101111=>1111010
[5,3,8,7,6,2,1,4]=>1001111=>1111001
[6,5,8,7,3,2,1,4]=>1100111=>1110011
[7,4,8,5,6,3,1,2]=>0100111=>1110010
[4,5,3,8,6,2,7,1]=>0001111=>1111000
[4,6,2,8,5,3,7,1]=>0001111=>1111000
[5,3,8,4,6,2,7,1]=>0001111=>1111000
[4,6,2,7,1,8,5,3]=>0001111=>1111000
[4,7,1,6,2,8,5,3]=>0001111=>1111000
[6,2,5,3,8,4,7,1]=>0001111=>1111000
[4,6,5,3,8,2,7,1]=>0001111=>1111000
[5,7,8,4,3,2,1,6]=>1110001=>1000111
[4,6,8,7,3,2,1,5]=>1100011=>1100011
[2,4,8,7,6,5,1,3]=>0001111=>1111000
[4,7,6,8,3,2,1,5]=>1100011=>1100011
[3,6,8,5,7,2,1,4]=>1000011=>1100001
[4,6,7,8,3,2,1,5]=>1100001=>1000011
[3,5,6,8,7,2,1,4]=>1000011=>1100001
[1,4,8,7,6,3,5,2]=>0001111=>1111000
[2,4,5,8,7,6,1,3]=>0000111=>1110000
[2,5,4,7,3,8,1,6]=>0001011=>1101000
[2,6,4,7,8,3,1,5]=>0100101=>1010010
[2,4,7,1,8,3,6,5]=>0000111=>1110000
[2,4,6,1,5,8,3,7]=>0000101=>1010000
[2,5,4,8,6,7,3,1]=>0101011=>1101010
[3,4,1,7,6,8,5,2]=>0011011=>1101100
[3,6,1,7,8,4,2,5]=>0010101=>1010100
[3,5,1,7,2,6,8,4]=>0001011=>1101000
[4,3,6,2,8,1,7,5]=>0010111=>1110100
[5,3,4,7,2,8,1,6]=>0001011=>1101000
[4,5,7,2,1,8,3,6]=>1000011=>1100001
[4,6,5,2,8,7,3,1]=>0101111=>1111010
[5,6,4,8,2,7,3,1]=>0100111=>1110010
[4,5,8,2,1,6,7,3]=>1000011=>1100001
[3,4,1,5,6,8,7,2]=>0010011=>1100100
[3,6,1,7,2,5,8,4]=>0000111=>1110000
[7,3,4,5,8,2,1,6]=>1000011=>1100001
[6,3,7,8,2,5,1,4]=>0001101=>1011000
[6,7,4,8,2,5,3,1]=>0101011=>1101010
[3,5,1,4,7,2,8,6]=>0001011=>1101000
[4,3,7,5,6,2,8,1]=>0010111=>1110100
[7,3,4,8,6,2,5,1]=>0001111=>1111000
[4,7,8,5,6,2,1,3]=>1000101=>1010001
[3,5,1,4,8,7,2,6]=>0001011=>1101000
[4,5,6,3,8,2,1,7]=>1000101=>1010001
[4,2,6,3,7,8,1,5]=>0010101=>1010100
[4,2,7,3,5,8,1,6]=>0010011=>1100100
[4,5,3,7,8,1,6,2]=>0001101=>1011000
[4,2,6,8,5,3,1,7]=>0111001=>1001110
[5,1,2,7,8,6,4,3]=>0011101=>1011100
[4,1,2,7,8,6,3,5]=>0010101=>1010100
[4,1,8,7,2,6,3,5]=>0010111=>1110100
[4,1,5,8,7,3,2,6]=>0110011=>1100110
[5,1,8,2,7,6,3,4]=>0001111=>1111000
[7,1,6,2,8,3,4,5]=>0000111=>1110000
[4,7,8,3,2,5,1,6]=>0101001=>1001010
[4,5,2,8,7,3,1,6]=>0101011=>1101010
[4,5,7,6,8,3,1,2]=>0100011=>1100010
[8,2,1,7,4,6,3,5]=>1000111=>1110001
[5,2,1,6,8,4,7,3]=>1001011=>1101001
[4,5,2,8,7,1,6,3]=>0001111=>1111000
[4,2,5,7,3,1,8,6]=>0110011=>1100110
[4,2,8,7,1,3,6,5]=>0010111=>1110100
[8,2,1,7,3,5,4,6]=>1001011=>1101001
[5,2,6,3,8,7,1,4]=>0001111=>1111000
[5,2,8,6,4,1,7,3]=>0011111=>1111100
[5,2,3,8,7,1,4,6]=>0001011=>1101000
[5,1,8,3,7,4,2,6]=>0011011=>1101100
[8,1,2,7,5,4,3,6]=>0011011=>1101100
[6,1,2,8,3,7,4,5]=>0000111=>1110000
[5,6,7,3,8,1,2,4]=>0000011=>1100000
[4,1,7,6,8,3,2,5]=>0110011=>1100110
[8,1,7,3,5,4,2,6]=>0011011=>1101100
[7,1,6,3,4,2,8,5]=>0010111=>1110100
[7,1,6,8,5,2,3,4]=>0001011=>1101000
[8,1,7,3,5,2,6,4]=>0001111=>1111000
[6,2,3,8,7,5,1,4]=>0001111=>1111000
[3,8,5,7,2,4,1,6]=>0010011=>1100100
[3,6,5,8,2,1,7,4]=>1000111=>1110001
[4,7,1,8,3,5,2,6]=>0001011=>1101000
[7,6,2,3,4,1,8,5]=>0010111=>1110100
[4,8,6,7,1,2,3,5]=>0000011=>1100000
[8,5,7,3,1,6,2,4]=>0100111=>1110010
[3,4,7,2,1,5,8,6]=>1000011=>1100001
[3,8,6,1,4,7,2,5]=>0000111=>1110000
[3,7,6,8,2,5,1,4]=>0001011=>1101000
[8,6,2,3,1,5,7,4]=>0100111=>1110010
[3,8,7,1,2,5,6,4]=>0000111=>1110000
[3,4,8,2,5,6,7,1]=>0000011=>1100000
[4,2,1,3,7,6,5,8]=>1010110=>0110101
[6,3,4,8,7,5,1,2]=>0001111=>1111000
[8,3,5,7,6,1,4,2]=>0010111=>1110100
[2,1,8,5,6,7,3,4]=>1000011=>1100001
[6,8,4,5,7,2,3,1]=>0100011=>1100010
[8,3,2,5,6,7,1,4]=>0100011=>1100010
[7,3,2,6,8,5,4,1]=>0111011=>1101110
[4,8,5,3,2,7,6,1]=>0101111=>1111010
[7,3,5,6,8,1,4,2]=>0010011=>1100100
[7,4,8,3,6,5,2,1]=>1001111=>1111001
[7,5,6,3,8,4,2,1]=>1010111=>1110101
[7,4,5,2,8,3,6,1]=>0001111=>1111000
[4,8,6,7,3,5,2,1]=>1001011=>1101001
[4,3,1,2,6,7,8,5]=>0110001=>1000110
[7,4,6,5,8,3,2,1]=>1100111=>1110011
[4,8,5,2,6,7,3,1]=>0101011=>1101010
[2,5,8,6,7,3,1,4]=>0100011=>1100010
[1,4,6,5,2,7,3,8]=>0001110=>0111000
[3,7,4,8,6,2,5,1]=>0001111=>1111000
[2,3,4,1,8,7,5,6]=>0010011=>1100100
[4,2,6,5,1,8,7,3]=>0011111=>1111100
[6,5,4,1,3,2,8,7]=>0111101=>1011110
[6,5,4,2,1,3,8,7]=>1011101=>1011101
[8,7,4,3,6,1,5,2]=>0011111=>1111100
[7,8,4,2,1,5,6,3]=>1010101=>1010101
[8,6,7,2,4,5,1,3]=>0001011=>1101000
[7,8,2,3,6,1,5,4]=>0001101=>1011000
[6,8,2,7,3,5,4,1]=>0011011=>1101100
[2,1,7,8,4,5,6,3]=>1000101=>1010001
[7,5,8,3,2,4,6,1]=>0100111=>1110010
[8,6,7,3,4,1,5,2]=>0011011=>1101100
[8,6,2,7,1,3,5,4]=>0001111=>1111000
[8,3,2,7,6,4,1,5]=>0110111=>1110110
[8,5,4,1,3,7,6,2]=>0011111=>1111100
[5,8,2,3,4,7,6,1]=>0000111=>1110000
[6,8,2,7,3,4,1,5]=>0010011=>1100100
[5,6,1,4,7,2,3,8]=>0000110=>0110000
[4,5,1,6,3,2,8,7]=>0101101=>1011010
[3,6,7,4,1,2,5,8]=>0010010=>0100100
[2,5,1,4,3,7,6,8]=>0011010=>0101100
[1,4,5,3,7,2,8,6]=>0001011=>1101000
[5,1,4,3,7,2,8,6]=>0011011=>1101100
[1,6,7,4,3,2,8,5]=>0110011=>1100110
[2,6,7,3,1,4,5,8]=>0100010=>0100010
[5,1,4,6,7,2,3,8]=>0001010=>0101000
[2,6,4,3,1,8,5,7]=>0110101=>1010110
[1,6,5,2,3,4,8,7]=>0001101=>1011000
[7,8,2,1,5,4,3,6]=>1011001=>1001101
[7,8,1,2,3,6,4,5]=>0000101=>1010000
[1,4,7,8,5,2,3,6]=>0001001=>1001000
[1,3,2,6,5,8,4,7]=>0100101=>1010010
[2,1,5,7,8,4,3,6]=>1010001=>1000101
[3,1,7,2,6,5,8,4]=>0100111=>1110010
[1,3,2,7,5,4,8,6]=>0101011=>1101010
[1,4,5,8,6,2,3,7]=>0000101=>1010000
[1,6,7,2,3,5,8,4]=>0000011=>1100000
[2,4,1,8,6,5,3,7]=>0011101=>1011100
[2,5,4,7,8,6,1,3]=>0001101=>1011000
[7,1,4,5,8,3,6,2]=>0000111=>1110000
[3,7,8,5,4,6,1,2]=>0001101=>1011000
[5,1,7,2,6,4,8,3]=>0001111=>1111000
[3,1,7,8,6,4,5,2]=>0101101=>1011010
[2,3,4,6,8,5,7,1]=>0000011=>1100000
[3,6,2,4,7,5,8,1]=>0000111=>1110000
[3,7,2,8,4,6,5,1]=>0001111=>1111000
[4,7,5,2,3,6,8,1]=>0001011=>1101000
[4,3,5,8,7,2,6,1]=>0010111=>1110100
[2,3,4,8,7,5,6,1]=>0000111=>1110000
[5,1,6,3,7,8,4,2]=>0011101=>1011100
[4,2,6,7,5,1,8,3]=>0011011=>1101100
[5,7,6,3,4,8,1,2]=>0000111=>1110000
[6,4,7,5,8,3,2,1]=>1100111=>1110011
[3,6,7,5,8,1,4,2]=>0010011=>1100100
[1,8,5,6,7,3,4,2]=>0010011=>1100100
[3,2,7,4,6,1,8,5]=>0100111=>1110010
[3,8,4,5,6,7,2,1]=>1000011=>1100001
[8,2,4,1,6,7,5,3]=>0011011=>1101100
[3,4,8,7,6,1,5,2]=>0001111=>1111000
[4,3,8,7,6,2,5,1]=>0011111=>1111100
[3,7,8,5,6,4,2,1]=>1010101=>1010101
[4,3,7,5,8,6,2,1]=>1010111=>1110101
[3,4,7,5,8,6,1,2]=>0000111=>1110000
[6,3,1,5,4,2,8,7]=>0111101=>1011110
[6,4,5,3,2,1,8,7]=>1101101=>1011011
[2,7,5,6,8,3,4,1]=>0010011=>1100100
[7,8,3,4,6,5,1,2]=>0001101=>1011000
[2,1,7,6,8,4,5,3]=>1001011=>1101001
[2,5,4,8,6,3,7,1]=>0001111=>1111000
[3,5,4,7,6,1,8,2]=>0001111=>1111000
[2,6,5,3,7,4,8,1]=>0001111=>1111000
[2,1,8,5,3,7,6,4]=>1001111=>1111001
[6,5,4,2,7,8,3,1]=>0111101=>1011110
[2,6,8,5,7,4,3,1]=>0110011=>1100110
[2,1,8,6,7,5,4,3]=>1011011=>1101101
[2,5,3,1,6,4,7,8]=>0101100=>0011010
[7,5,4,2,3,1,8,6]=>0111011=>1101110
[6,3,2,4,5,8,1,7]=>0100101=>1010010
[3,5,4,2,8,6,1,7]=>0011101=>1011100
[5,6,8,7,3,2,1,4]=>1100011=>1100011
[6,4,5,3,2,8,1,7]=>0101101=>1011010
[4,2,5,7,3,1,6,8]=>0110010=>0100110
[7,4,1,3,2,6,8,5]=>0110011=>1100110
[6,1,4,3,2,7,8,5]=>0110101=>1010110
[1,6,4,2,3,7,8,5]=>0010101=>1010100
[1,4,5,3,8,2,6,7]=>0001001=>1001000
[2,5,4,3,8,1,6,7]=>0011001=>1001100
[6,2,5,1,3,7,4,8]=>0001110=>0111000
[7,6,5,8,1,2,4,3]=>0010111=>1110100
[5,7,4,1,3,6,2,8]=>0010110=>0110100
[4,3,8,1,6,7,2,5]=>0010011=>1100100
[4,3,8,1,6,5,7,2]=>0010111=>1110100
[4,3,8,2,5,6,7,1]=>0010011=>1100100
[5,4,8,2,3,6,7,1]=>0001011=>1101000
[3,2,8,1,6,7,4,5]=>0100011=>1100010
[5,2,8,1,6,7,3,4]=>0001011=>1101000
[7,2,6,3,8,1,5,4]=>0001111=>1111000
[7,2,8,1,6,3,5,4]=>0001111=>1111000
[6,3,4,5,8,2,7,1]=>0000111=>1110000
[7,4,8,2,3,5,6,1]=>0000111=>1110000
[7,3,8,1,4,5,6,2]=>0000111=>1110000
[7,3,4,5,8,1,6,2]=>0000111=>1110000
[7,4,8,1,5,6,2,3]=>0000111=>1110000
[7,2,8,1,6,5,4,3]=>0011111=>1111100
[8,1,3,4,6,5,2,7]=>0001101=>1011000
[8,6,5,7,2,1,4,3]=>1010111=>1110101
[2,4,7,8,5,6,3,1]=>0100101=>1010010
[1,8,6,3,7,4,5,2]=>0001111=>1111000
[3,8,5,1,7,6,4,2]=>0011111=>1111100
[2,8,1,3,5,6,7,4]=>0000011=>1100000
[2,4,8,7,5,6,3,1]=>0100111=>1110010
[3,8,7,5,2,6,4,1]=>0011111=>1111100
[1,8,7,3,4,6,5,2]=>0001111=>1111000
[2,8,1,4,5,7,6,3]=>0000111=>1110000
[1,2,7,6,8,4,5,3]=>0001011=>1101000
[1,2,6,7,8,3,5,4]=>0001001=>1001000
[1,2,6,8,7,3,4,5]=>0000011=>1100000
[1,2,5,3,7,6,8,4]=>0001011=>1101000
[3,7,8,1,5,6,2,4]=>0000101=>1010000
[1,2,4,8,3,6,5,7]=>0000101=>1010000
[4,1,3,7,6,8,5,2]=>0011011=>1101100
[6,5,7,8,1,4,3,2]=>0110101=>1010110
[3,1,8,6,7,5,4,2]=>0111011=>1101110
[2,8,3,1,7,5,4,6]=>0101011=>1101010
[2,8,3,7,1,4,5,6]=>0000011=>1100000
[4,8,2,7,5,1,3,6]=>0001011=>1101000
[4,1,2,6,7,5,3,8]=>0011010=>0101100
[1,2,5,3,8,6,4,7]=>0001101=>1011000
[5,8,7,6,2,1,3,4]=>1000111=>1110001
[6,4,8,3,7,5,2,1]=>1001111=>1111001
[3,6,8,2,5,7,4,1]=>0010011=>1100100
[5,4,2,6,1,8,7,3]=>0011111=>1111100
[4,8,7,5,2,6,3,1]=>0101111=>1111010
[3,2,8,5,6,1,7,4]=>0100111=>1110010
[3,4,8,1,5,7,6,2]=>0000111=>1110000
[4,5,6,2,7,3,8,1]=>0000111=>1110000
[3,5,8,7,4,6,2,1]=>1000111=>1110001
[4,7,5,6,2,3,8,1]=>0000111=>1110000
[3,5,7,6,2,4,8,1]=>0000111=>1110000
[1,6,8,7,4,5,3,2]=>0101011=>1101010
[8,3,5,7,6,2,4,1]=>0010111=>1110100
[6,4,5,2,8,7,3,1]=>0101111=>1111010
[6,4,2,7,8,5,3,1]=>0111101=>1011110
[2,4,5,8,6,7,1,3]=>0000011=>1100000
[1,3,5,6,8,7,2,4]=>0000011=>1100000
[5,7,4,1,6,2,8,3]=>0010111=>1110100
[3,5,6,7,8,2,4,1]=>0010001=>1000100
[5,2,4,1,6,7,8,3]=>0011001=>1001100
[8,5,6,7,2,4,3,1]=>0110011=>1100110
[7,8,4,5,1,6,3,2]=>0101101=>1011010
[3,5,8,6,4,7,2,1]=>1000111=>1110001
[4,5,6,8,3,7,2,1]=>1000011=>1100001
[8,4,5,7,6,2,3,1]=>0100111=>1110010
[4,8,6,7,5,2,3,1]=>0101011=>1101010
[8,7,4,3,6,5,1,2]=>0011111=>1111100
[8,1,4,3,6,5,2,7]=>0011101=>1011100
[6,1,2,5,4,3,8,7]=>0011101=>1011100
[2,8,6,3,4,7,1,5]=>0000111=>1110000
[8,1,2,3,5,7,4,6]=>0000011=>1100000
[8,1,2,3,6,5,4,7]=>0001101=>1011000
[8,1,2,3,7,6,5,4]=>0001111=>1111000
[2,8,1,6,7,5,3,4]=>0001011=>1101000
[8,1,2,3,5,4,7,6]=>0001011=>1101000
[4,8,5,2,7,1,6,3]=>0001111=>1111000
[3,7,8,6,4,2,1,5]=>1010101=>1010101
[3,7,8,4,6,2,1,5]=>1000101=>1010001
[8,3,1,5,7,6,2,4]=>0100111=>1110010
[4,5,2,8,6,7,1,3]=>0001011=>1101000
[8,4,5,1,3,2,6,7]=>0101001=>1001010
[8,1,2,3,6,7,5,4]=>0001011=>1101000
[8,1,6,7,2,5,4,3]=>0011011=>1101100
[5,4,1,3,2,8,7,6]=>0111011=>1101110
[5,4,2,1,3,8,7,6]=>1011011=>1101101
[3,2,7,4,1,6,5,8]=>0110110=>0110110
[5,7,3,2,1,6,4,8]=>1100110=>0110011
[7,6,5,1,3,4,2,8]=>0011110=>0111100
[7,6,5,2,1,4,3,8]=>1011110=>0111101
[8,6,2,4,3,5,1,7]=>0011101=>1011100
[7,6,5,1,4,2,3,8]=>0011110=>0111100
[1,7,6,3,2,4,5,8]=>0100110=>0110010
[8,7,3,2,1,6,4,5]=>1100111=>1110011
[1,5,7,2,4,3,6,8]=>0010010=>0100100
[5,2,8,1,4,3,7,6]=>0011011=>1101100
[7,1,6,8,2,4,5,3]=>0001011=>1101000
[8,4,6,2,3,7,1,5]=>0000111=>1110000
[8,6,1,3,7,5,2,4]=>0001111=>1111000
[5,8,1,3,4,7,2,6]=>0000011=>1100000
[5,8,6,2,3,1,4,7]=>0100101=>1010010
[5,8,7,3,2,4,6,1]=>0100111=>1110010
[7,6,2,8,3,5,4,1]=>0011111=>1111100
[8,7,5,2,6,3,1,4]=>0101111=>1111010
[8,4,7,3,1,5,2,6]=>0101011=>1101010
[8,2,6,3,1,4,7,5]=>0100111=>1110010
[8,3,2,7,6,1,4,5]=>0100111=>1110010
[3,8,2,7,6,4,1,5]=>0010111=>1110100
[3,6,7,5,8,2,1,4]=>1000011=>1100001
[6,3,5,2,8,7,4,1]=>0011111=>1111100
[5,8,4,3,2,7,6,1]=>0110111=>1110110
[2,4,6,8,7,3,5,1]=>0001011=>1101000
[6,3,5,7,8,2,4,1]=>0010101=>1010100
[4,6,8,7,5,2,3,1]=>0101011=>1101010
[3,5,6,8,7,2,4,1]=>0010011=>1100100
[1,6,8,4,7,5,3,2]=>0101011=>1101010
[3,8,6,5,1,7,2,4]=>0001111=>1111000
[8,4,6,7,5,2,3,1]=>0101011=>1101010
[6,5,8,3,7,4,2,1]=>1010111=>1110101
[8,4,5,7,2,6,3,1]=>0100111=>1110010
[6,7,4,3,8,5,2,1]=>1011011=>1101101
[2,6,8,5,4,7,3,1]=>0101011=>1101010
[2,7,4,6,8,5,3,1]=>0101011=>1101010
[6,4,7,8,3,5,2,1]=>1001101=>1011001
[6,3,5,2,7,4,8,1]=>0001111=>1111000
[7,3,4,2,6,1,8,5]=>0010111=>1110100
[2,3,7,4,6,1,8,5]=>0000111=>1110000
[7,5,4,2,6,3,8,1]=>0011111=>1111100
[5,4,7,2,6,1,8,3]=>0001111=>1111000
[5,2,7,4,6,1,8,3]=>0001111=>1111000
[5,2,4,1,7,6,8,3]=>0011011=>1101100
[4,2,7,5,6,1,8,3]=>0010111=>1110100
[4,2,7,5,6,3,8,1]=>0010111=>1110100
[6,2,4,3,7,5,8,1]=>0010111=>1110100
[2,6,4,3,7,5,8,1]=>0010111=>1110100
[2,7,5,4,8,6,3,1]=>0101111=>1111010
[4,3,7,5,8,6,1,2]=>0010111=>1110100
[6,7,4,8,3,5,2,1]=>1001011=>1101001
[2,1,5,8,7,4,6,3]=>1000111=>1110001
[5,8,3,4,6,7,2,1]=>1000011=>1100001
[6,4,3,8,7,2,5,1]=>0011111=>1111100
[3,6,8,5,4,7,1,2]=>0001011=>1101000
[7,5,3,6,8,4,2,1]=>1011011=>1101101
[8,4,3,5,7,2,6,1]=>0010111=>1110100
[4,7,8,6,3,5,2,1]=>1001101=>1011001
[6,7,5,8,2,4,3,1]=>0110011=>1100110
[2,5,4,1,7,8,6,3]=>0011101=>1011100
[4,3,1,5,6,8,7,2]=>0110011=>1100110
[1,6,3,2,5,8,7,4]=>0100111=>1110010
[8,1,5,3,2,6,7,4]=>0101011=>1101010
[1,6,8,3,2,4,7,5]=>0100011=>1100010
[1,8,7,6,4,2,3,5]=>0010111=>1110100
[8,1,7,3,5,4,6,2]=>0001111=>1111000
[7,1,3,8,4,6,5,2]=>0001111=>1111000
[3,2,8,1,5,6,7,4]=>0100011=>1100010
[8,6,1,2,4,5,7,3]=>0000111=>1110000
[1,8,6,7,3,4,5,2]=>0001011=>1101000
[1,7,3,8,2,4,6,5]=>0000111=>1110000
[8,4,3,1,5,6,7,2]=>0110011=>1100110
[1,7,3,8,2,6,5,4]=>0001111=>1111000
[1,8,7,6,3,4,2,5]=>0010111=>1110100
[7,1,3,8,4,5,2,6]=>0001011=>1101000
[1,8,5,3,7,6,2,4]=>0001111=>1111000
[3,5,2,6,1,4,8,7]=>0001101=>1011000
[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
[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
[4,6,7,3,8,2,5,1]=>0001011=>1101000
[4,6,7,3,8,2,1,5]=>1000011=>1100001
[4,5,7,3,1,8,2,6]=>0100011=>1100010
[3,5,1,7,4,8,2,6]=>0001011=>1101000
[2,1,5,7,4,8,3,6]=>1000011=>1100001
[4,5,7,1,3,8,6,2]=>0000111=>1110000
[4,6,7,3,8,1,5,2]=>0001011=>1101000
[5,6,7,8,3,1,4,2]=>0110001=>1000110
[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
[4,6,7,1,8,3,2,5]=>0100011=>1100010
[5,6,7,8,1,3,2,4]=>0100001=>1000010
[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
[3,4,2,1,7,8,5,6]=>1010001=>1000101
[4,6,7,2,8,5,3,1]=>0101011=>1101010
[4,6,7,2,8,5,1,3]=>0001011=>1101000
[4,5,7,1,2,8,6,3]=>0000111=>1110000
[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
[5,6,7,8,2,4,1,3]=>0010001=>1000100
[5,6,7,8,2,4,3,1]=>0110001=>1000110
[3,6,1,7,8,5,2,4]=>0001101=>1011000
[2,1,6,7,8,5,3,4]=>1001001=>1001001
[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
[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
[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
[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
[5,3,1,6,2,4,8,7]=>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
[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
[7,5,4,1,2,8,3,6]=>0011011=>1101100
[8,6,4,1,7,2,3,5]=>0010111=>1110100
[5,7,4,1,2,8,3,6]=>0010011=>1100100
[3,7,1,5,2,8,4,6]=>0001011=>1101000
[2,1,7,5,3,8,4,6]=>1001011=>1101001
[4,8,5,1,2,7,3,6]=>0001011=>1101000
[6,8,4,1,7,2,3,5]=>0010011=>1100100
[4,8,6,1,7,2,3,5]=>0000111=>1110000
[2,1,8,6,7,3,4,5]=>1000011=>1100001
[2,1,7,6,8,3,4,5]=>1000011=>1100001
[4,7,6,1,8,2,3,5]=>0000111=>1110000
[5,7,6,8,1,2,3,4]=>0000011=>1100000
[6,4,7,1,8,2,3,5]=>0000111=>1110000
[8,4,6,1,7,2,3,5]=>0000111=>1110000
[8,3,1,6,7,2,4,5]=>0100011=>1100010
[4,3,1,2,7,8,5,6]=>0110001=>1000110
[8,4,7,1,6,2,3,5]=>0000111=>1110000
[7,4,8,1,6,2,3,5]=>0000111=>1110000
[4,5,8,1,2,7,3,6]=>0000011=>1100000
[2,1,6,8,7,3,4,5]=>1000011=>1100001
[4,6,8,1,7,2,3,5]=>0000011=>1100000
[5,6,8,7,1,2,3,4]=>0000011=>1100000
[8,5,7,6,1,2,3,4]=>0000111=>1110000
[4,7,8,1,6,2,3,5]=>0000101=>1010000
[3,7,1,8,6,2,4,5]=>0000111=>1110000
[3,8,1,7,6,2,4,5]=>0000111=>1110000
[4,8,7,1,6,2,3,5]=>0000111=>1110000
[6,8,7,5,1,2,3,4]=>0001011=>1101000
[6,4,7,3,8,5,1,2]=>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
[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
[5,3,2,6,1,7,4,8]=>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
[6,4,8,2,5,1,7,3]=>0001111=>1111000
[5,4,2,8,6,1,3,7]=>0011101=>1011100
[5,3,2,6,1,8,4,7]=>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
[5,3,2,7,1,6,4,8]=>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
[6,5,7,8,2,1,4,3]=>1010101=>1010101
[6,3,7,2,1,4,8,5]=>1000111=>1110001
[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
[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
[4,3,2,1,8,5,6,7]=>1110001=>1000111
[7,8,5,6,1,2,4,3]=>0010101=>1010100
[7,8,4,1,6,2,5,3]=>0011101=>1011100
[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
[7,8,2,3,1,6,5,4]=>0101101=>1011010
[7,8,2,1,3,6,5,4]=>1001101=>1011001
[7,8,1,2,3,6,5,4]=>0001101=>1011000
[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
[6,2,8,4,7,1,5,3]=>0001111=>1111000
[6,3,8,4,7,5,1,2]=>0001111=>1111000
[2,6,8,3,1,7,5,4]=>0101011=>1101010
[2,5,1,8,3,7,6,4]=>0001111=>1111000
[1,2,5,8,3,7,6,4]=>0000111=>1110000
[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
[4,1,2,3,8,7,6,5]=>0010111=>1110100
[1,4,2,3,8,7,6,5]=>0010111=>1110100
[4,1,3,2,8,7,6,5]=>0110111=>1110110
[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
[6,5,8,7,1,2,4,3]=>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
[1,3,5,8,2,7,6,4]=>0000111=>1110000
[3,1,5,8,2,7,6,4]=>0100111=>1110010
[3,6,8,2,1,7,5,4]=>1001011=>1101001
[4,6,8,3,7,5,1,2]=>0001011=>1101000
[4,5,3,8,7,6,1,2]=>0001111=>1111000
[3,5,2,8,1,7,6,4]=>0001111=>1111000
[3,1,4,2,8,7,6,5]=>0110111=>1110110
[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
[2,4,5,8,7,1,6,3]=>0000111=>1110000
[2,3,5,8,1,7,6,4]=>0000111=>1110000
[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
[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
[8,2,5,1,4,3,7,6]=>0011011=>1101100
[8,1,4,3,7,2,6,5]=>0010111=>1110100
[8,2,6,1,5,3,7,4]=>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
[7,4,8,1,3,2,6,5]=>0100111=>1110010
[8,3,7,1,4,2,6,5]=>0010111=>1110100
[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
[5,1,8,3,7,2,6,4]=>0001111=>1111000
[4,1,8,3,7,2,6,5]=>0010111=>1110100
[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
[3,4,2,6,8,1,5,7]=>0010001=>1000100
[5,3,6,2,8,1,4,7]=>0001101=>1011000
[7,4,2,5,8,3,6,1]=>0010111=>1110100
[4,5,2,6,3,8,1,7]=>0001101=>1011000
[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
[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
[5,3,7,8,1,4,2,6]=>0011001=>1001100
[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
[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
[7,4,2,5,1,8,3,6]=>0011011=>1101100
[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
[3,4,7,8,2,1,5,6]=>1000001=>1000001
[3,7,8,1,4,6,2,5]=>0000101=>1010000
[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
[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
[5,6,2,7,1,8,4,3]=>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
[6,7,8,3,5,1,4,2]=>0011001=>1001100
[5,6,1,7,8,4,3,2]=>0110101=>1010110
[5,6,7,1,8,4,3,2]=>0110011=>1100110
[8,3,2,5,1,6,4,7]=>0101101=>1011010
[5,3,2,7,4,1,8,6]=>0111011=>1101110
[7,5,3,8,2,4,6,1]=>0001111=>1111000
[8,2,4,5,6,3,1,7]=>0100101=>1010010
[8,2,4,5,6,1,3,7]=>0000101=>1010000
[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
[5,3,4,7,1,2,8,6]=>0001011=>1101000
[7,4,5,8,3,6,1,2]=>0000111=>1110000
[4,3,6,7,8,1,5,2]=>0011001=>1001100
[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
[6,2,4,1,7,8,5,3]=>0011101=>1011100
[2,6,7,1,4,8,3,5]=>0000011=>1100000
[1,5,3,6,7,8,2,4]=>0001001=>1001000
[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
[3,6,2,7,4,8,1,5]=>0000111=>1110000
[3,7,4,2,1,5,8,6]=>1010011=>1100101
[7,8,4,2,1,3,6,5]=>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
[7,4,1,5,8,6,2,3]=>0010111=>1110100
[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
[5,2,6,7,8,4,3,1]=>0111001=>1001110
[1,6,4,7,8,5,2,3]=>0001101=>1011000
[2,6,7,1,3,8,5,4]=>0001011=>1101000
[6,7,3,8,5,1,4,2]=>0011011=>1101100
[6,4,7,8,5,3,1,2]=>0101101=>1011010
[3,1,2,6,5,8,7,4]=>0100111=>1110010
[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
[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
[1,7,6,8,3,4,5,2]=>0001011=>1101000
[7,6,1,8,2,3,5,4]=>0001111=>1111000
[3,1,2,7,8,5,6,4]=>0100101=>1010010
[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
[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
[5,8,6,1,2,3,4,7]=>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
[8,1,7,6,2,4,5,3]=>0001111=>1111000
[8,7,1,6,2,3,5,4]=>0001111=>1111000
[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
[2,6,1,4,5,3,8,7]=>0001101=>1011000
[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
[8,1,7,4,2,6,3,5]=>0010111=>1110100
[3,7,8,4,5,1,2,6]=>0001001=>1001000
[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
[2,5,8,4,7,6,1,3]=>0000111=>1110000
[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
[2,1,4,8,3,6,7,5]=>1000011=>1100001
[7,3,8,4,2,6,1,5]=>0010111=>1110100
[8,3,1,2,5,6,7,4]=>0100011=>1100010
[4,8,2,3,5,6,7,1]=>0000011=>1100000
[2,7,8,4,5,3,1,6]=>0101001=>1001010
[8,7,1,4,3,6,2,5]=>0010111=>1110100
[5,6,3,8,4,2,7,1]=>0010111=>1110100
[8,6,3,1,4,2,7,5]=>0110111=>1110110
[8,6,3,5,1,2,7,4]=>0001111=>1111000
[5,8,3,2,6,1,7,4]=>0100111=>1110010
[3,5,8,4,7,6,2,1]=>1000111=>1110001
[5,8,2,4,7,6,1,3]=>0000111=>1110000
[7,1,6,4,5,8,2,3]=>0000111=>1110000
[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
[4,8,1,2,5,6,7,3]=>0000011=>1100000
[3,4,2,8,5,6,7,1]=>0010011=>1100100
[2,4,1,8,5,6,7,3]=>0010011=>1100100
[8,4,2,1,5,6,7,3]=>1010011=>1100101
[7,5,2,4,8,6,1,3]=>0001111=>1111000
[2,1,5,3,8,6,7,4]=>1001011=>1101001
[3,1,4,8,5,6,7,2]=>0100011=>1100010
[6,5,3,7,2,8,4,1]=>0011111=>1111100
[6,7,2,4,5,8,3,1]=>0100011=>1100010
[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
[4,6,3,5,8,2,7,1]=>0000111=>1110000
[3,7,8,4,1,6,2,5]=>0010101=>1010100
[5,4,2,3,7,6,1,8]=>0011110=>0111100
[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
[1,7,5,2,8,3,4,6]=>0001011=>1101000
[6,8,5,2,3,1,4,7]=>0101001=>1001010
[4,8,2,6,3,1,5,7]=>0100101=>1010010
[3,2,8,6,4,1,5,7]=>0110101=>1010110
[7,1,5,2,8,3,4,6]=>0001011=>1101000
[1,8,5,2,7,3,4,6]=>0001011=>1101000
[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
[3,2,5,4,1,8,6,7]=>0111001=>1001110
[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
[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
[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
[4,8,2,1,7,3,5,6]=>1000011=>1100001
[3,2,8,1,7,4,5,6]=>0100011=>1100010
[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
[2,8,4,1,6,5,7,3]=>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
[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
[2,8,5,3,6,1,7,4]=>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
[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
[3,5,7,2,4,1,8,6]=>0010011=>1100100
[6,5,2,7,3,1,8,4]=>0101111=>1111010
[4,5,2,6,3,1,7,8]=>0101100=>0011010
[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
[4,1,2,3,8,6,5,7]=>0010101=>1010100
[4,1,2,3,8,6,7,5]=>0010011=>1100100
[4,1,2,3,8,5,7,6]=>0010011=>1100100
[6,5,8,2,4,3,7,1]=>0010111=>1110100
[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
[5,7,8,6,3,4,2,1]=>1010101=>1010101
[3,1,4,8,6,2,7,5]=>0100111=>1110010
[3,1,4,8,6,5,2,7]=>0101101=>1011010
[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
[3,5,6,2,4,8,1,7]=>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
[4,1,2,3,5,8,7,6]=>0010011=>1100100
[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
[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
[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
[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
[8,6,4,2,3,7,1,5]=>0010111=>1110100
[4,7,6,3,8,1,2,5]=>0000111=>1110000
[5,7,2,6,1,8,3,4]=>0000111=>1110000
[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
[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
[3,6,5,8,1,2,4,7]=>0000101=>1010000
[5,4,7,3,8,1,2,6]=>0001011=>1101000
[8,4,6,3,7,1,2,5]=>0000111=>1110000
[8,4,1,6,7,2,3,5]=>0010011=>1100100
[5,4,1,7,8,2,3,6]=>0011001=>1001100
[6,5,1,2,7,8,3,4]=>0001101=>1011000
[4,7,1,5,8,6,2,3]=>0000111=>1110000
[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
[6,3,7,8,5,1,2,4]=>0001101=>1011000
[3,6,8,2,7,1,4,5]=>0000011=>1100000
[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
[4,7,1,8,6,2,3,5]=>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
[7,5,1,4,8,6,3,2]=>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
[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
[7,2,6,3,4,5,8,1]=>0000111=>1110000
[6,2,7,3,4,5,8,1]=>0000111=>1110000
[6,7,3,5,2,4,8,1]=>0001011=>1101000
[3,7,6,2,4,5,8,1]=>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
[4,2,6,5,1,8,3,7]=>0011101=>1011100
[5,4,8,6,2,7,1,3]=>0001111=>1111000
[7,8,5,2,3,6,1,4]=>0001101=>1011000
[6,8,2,1,7,3,4,5]=>1000011=>1100001
[2,8,1,7,3,4,5,6]=>0000011=>1100000
[3,8,6,1,7,2,4,5]=>0000111=>1110000
[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
[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
[5,4,1,3,6,8,2,7]=>0011001=>1001100
[8,5,3,7,6,1,2,4]=>0001111=>1111000
[6,1,8,3,7,2,4,5]=>0000111=>1110000
[7,6,8,2,3,5,1,4]=>0001011=>1101000
[3,7,8,2,4,6,1,5]=>0000101=>1010000
[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
[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
[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
[8,1,6,7,3,2,4,5]=>0100011=>1100010
[8,1,5,3,7,2,4,6]=>0001011=>1101000
[8,1,5,3,6,2,4,7]=>0001101=>1011000
[7,4,8,3,2,6,5,1]=>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
[8,1,5,4,6,7,2,3]=>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
[7,4,1,3,2,5,6,8]=>0110010=>0100110
[7,4,8,3,2,5,6,1]=>0100111=>1110010
[6,4,3,1,2,5,8,7]=>0110101=>1010110
[7,4,1,3,2,5,8,6]=>0110011=>1100110
[7,5,1,3,6,2,8,4]=>0001111=>1111000
[7,5,1,4,6,8,2,3]=>0001011=>1101000
[6,4,3,8,2,5,1,7]=>0011101=>1011100
[5,4,3,2,8,6,1,7]=>0111101=>1011110
[5,4,3,2,8,7,1,6]=>0111011=>1101110
[6,5,4,8,7,1,2,3]=>0001111=>1111000
[6,5,4,1,7,8,2,3]=>0011101=>1011100
[6,4,3,1,2,7,8,5]=>0110101=>1010110
[7,4,1,3,2,8,5,6]=>0110011=>1100110
[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
[7,5,1,3,8,2,4,6]=>0001011=>1101000
[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
[7,5,8,4,1,6,2,3]=>0010111=>1110100
[6,5,4,8,1,7,2,3]=>0001111=>1111000
[6,5,3,8,1,2,7,4]=>0001111=>1111000
[6,5,4,7,1,8,2,3]=>0001111=>1111000
[5,4,3,2,7,8,1,6]=>0111001=>1001110
[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
[5,6,8,4,3,1,2,7]=>0110001=>1000110
[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
[3,2,6,8,5,1,4,7]=>0101001=>1001010
[5,6,8,4,2,1,3,7]=>1010001=>1000101
[5,7,8,4,1,3,2,6]=>0110001=>1000110
[5,7,8,4,1,2,3,6]=>0010001=>1000100
[6,7,8,1,5,2,3,4]=>0001001=>1001000
[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
[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
[6,7,8,1,4,3,5,2]=>0011001=>1001100
[5,6,8,3,2,1,7,4]=>1100011=>1100011
[4,7,3,8,1,6,2,5]=>0000111=>1110000
[4,7,3,8,1,5,6,2]=>0000111=>1110000
[4,7,3,8,1,5,2,6]=>0001011=>1101000
[4,7,3,8,1,2,5,6]=>0000011=>1100000
[5,7,8,3,1,2,4,6]=>0100001=>1000010
[5,6,8,3,2,1,4,7]=>1100001=>1000011
[3,2,7,8,1,5,4,6]=>0101001=>1001010
[6,7,8,1,3,4,2,5]=>0010001=>1000100
[6,7,8,1,4,2,3,5]=>0010001=>1000100
[6,7,8,1,2,5,3,4]=>0001001=>1001000
[6,7,8,1,2,4,5,3]=>0001001=>1001000
[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
[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
[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
[2,5,3,1,7,6,8,4]=>0101011=>1101010
[2,7,5,1,6,8,4,3]=>0011011=>1101100
[4,7,1,6,5,8,2,3]=>0000111=>1110000
[4,6,1,2,7,5,8,3]=>0000111=>1110000
[8,4,1,2,6,7,5,3]=>0011011=>1101100
[5,3,1,2,7,6,8,4]=>0101011=>1101010
[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
[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
[1,7,6,2,5,8,3,4]=>0000111=>1110000
[7,6,2,1,5,8,3,4]=>1000111=>1110001
[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
[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
[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
[5,1,3,2,7,6,8,4]=>0101011=>1101010
[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
[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
[7,8,1,3,6,5,2,4]=>0001101=>1011000
[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
[6,2,4,8,7,1,5,3]=>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
[8,5,7,2,3,1,6,4]=>0100111=>1110010
[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
[8,7,6,1,2,4,3,5]=>0010111=>1110100
[8,7,6,1,4,2,3,5]=>0010111=>1110100
[8,7,6,4,1,3,2,5]=>0110111=>1110110
[8,5,7,1,3,2,6,4]=>0100111=>1110010
[5,8,4,7,1,2,6,3]=>0000111=>1110000
[8,1,2,6,5,7,4,3]=>0010111=>1110100
[8,2,5,6,7,4,1,3]=>0010011=>1100100
[4,8,5,1,7,2,6,3]=>0001111=>1111000
[8,5,3,7,1,2,6,4]=>0001111=>1111000
[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
[8,5,3,2,7,1,6,4]=>0101111=>1111010
[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
[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
[6,5,4,2,3,1,8,7]=>0111101=>1011110
[6,3,2,5,1,4,8,7]=>0101101=>1011010
[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
[8,5,4,3,1,7,6,2]=>0111111=>1111110
[8,3,2,5,1,7,6,4]=>0101111=>1111010
[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
[2,1,8,7,6,4,5,3]=>1001111=>1111001
[8,3,2,7,6,4,5,1]=>0101111=>1111010
[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
[8,3,1,5,4,7,6,2]=>0101111=>1111010
[8,3,1,7,6,5,2,4]=>0101111=>1111010
[8,3,1,7,6,2,5,4]=>0101111=>1111010
[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
[8,7,6,5,3,1,4,2]=>0111111=>1111110
[8,3,2,7,6,1,5,4]=>0101111=>1111010
[8,7,6,5,1,2,4,3]=>0011111=>1111100
[7,4,5,2,3,1,8,6]=>0101011=>1101010
[6,3,5,2,4,1,8,7]=>0011101=>1011100
[4,1,6,3,5,2,8,7]=>0011101=>1011100
[5,2,7,3,4,1,8,6]=>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
[3,1,8,6,7,4,5,2]=>0101011=>1101010
[4,1,8,6,7,3,5,2]=>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
[2,1,8,5,7,4,6,3]=>1000111=>1110001
[4,1,7,3,6,2,8,5]=>0010111=>1110100
[6,2,8,4,7,3,5,1]=>0001111=>1111000
[7,3,6,2,5,1,8,4]=>0001111=>1111000
[6,2,4,1,7,3,8,5]=>0010111=>1110100
[8,5,6,2,3,1,7,4]=>0100111=>1110010
[7,3,8,5,6,2,4,1]=>0010111=>1110100
[8,5,6,2,4,1,7,3]=>0010111=>1110100
[3,1,6,2,8,5,7,4]=>0100111=>1110010
[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
[4,1,8,5,6,2,7,3]=>0010111=>1110100
[3,1,8,5,6,2,7,4]=>0100111=>1110010
[7,3,6,2,8,4,5,1]=>0001111=>1111000
[6,8,7,3,4,1,2,5]=>0010011=>1100100
[5,4,8,7,2,6,3,1]=>0101111=>1111010
[5,3,8,7,6,1,2,4]=>0001111=>1111000
[8,3,4,6,5,1,2,7]=>0001101=>1011000
[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
[3,5,8,2,7,6,4,1]=>0010111=>1110100
[3,5,8,1,7,6,4,2]=>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
[1,4,8,7,2,6,3,5]=>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
[8,2,3,1,6,5,4,7]=>0101101=>1011010
[2,3,8,1,7,6,4,5]=>0000111=>1110000
[5,2,8,7,1,6,3,4]=>0001111=>1111000
[5,2,8,1,7,6,4,3]=>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
[6,8,1,2,7,5,4,3]=>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
[4,8,1,7,2,5,3,6]=>0001011=>1101000
[8,4,1,6,2,5,3,7]=>0011101=>1011100
[8,3,1,2,6,5,4,7]=>0101101=>1011010
[3,1,2,8,7,6,5,4]=>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
[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
[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
[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
[1,2,8,6,5,3,7,4]=>0001111=>1111000
[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
[1,5,2,7,6,3,8,4]=>0001111=>1111000
[1,6,5,2,7,3,8,4]=>0001111=>1111000
[1,5,7,4,2,8,3,6]=>0010011=>1100100
[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
[1,4,2,8,7,3,6,5]=>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
[1,5,2,7,3,8,6,4]=>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
[1,7,4,2,8,6,3,5]=>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
[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
[7,1,4,5,3,8,6,2]=>0001111=>1111000
[7,1,4,5,3,6,8,2]=>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
[5,4,8,6,3,1,7,2]=>0101111=>1111010
[5,4,1,8,2,3,7,6]=>0011011=>1101100
[8,4,1,5,2,6,3,7]=>0011101=>1011100
[6,3,5,8,2,1,4,7]=>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
[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
[8,7,5,6,1,4,2,3]=>0010111=>1110100
[2,7,1,3,6,5,8,4]=>0000111=>1110000
[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
[2,3,8,6,4,1,7,5]=>0010111=>1110100
[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
[5,2,6,1,4,8,7,3]=>0001111=>1111000
[5,7,2,3,8,6,1,4]=>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
[5,7,3,2,8,1,6,4]=>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
[5,1,7,4,8,2,6,3]=>0001111=>1111000
[1,5,7,4,8,3,6,2]=>0000111=>1110000
[5,1,7,4,8,6,2,3]=>0001111=>1111000
[5,7,3,1,8,6,2,4]=>0100111=>1110010
[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
[6,7,2,8,1,3,5,4]=>0001011=>1101000
[6,7,2,8,3,5,1,4]=>0001011=>1101000
[6,2,7,8,4,1,5,3]=>0011101=>1011100
[6,2,7,8,1,4,5,3]=>0001101=>1011000
[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
[5,7,2,1,8,6,3,4]=>1000111=>1110001
[1,6,7,8,3,5,4,2]=>0011001=>1001100
[6,1,7,8,2,5,4,3]=>0011101=>1011100
[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
[3,7,4,8,5,6,1,2]=>0000111=>1110000
[3,7,1,8,5,6,2,4]=>0000111=>1110000
[2,7,3,8,5,6,1,4]=>0000111=>1110000
[1,7,4,8,5,6,2,3]=>0000111=>1110000
[2,7,3,8,4,6,1,5]=>0000111=>1110000
[3,7,1,8,4,6,2,5]=>0000111=>1110000
[1,5,2,8,6,7,3,4]=>0001011=>1101000
[2,6,1,8,5,7,3,4]=>0000111=>1110000
[1,6,2,8,5,7,3,4]=>0000111=>1110000
[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
[4,8,1,6,2,7,3,5]=>0000111=>1110000
[5,8,1,6,2,7,3,4]=>0000111=>1110000
[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
[8,6,1,4,3,2,5,7]=>0110101=>1010110
[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
[8,2,6,5,1,3,4,7]=>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
[1,7,5,4,2,8,3,6]=>0011011=>1101100
[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
[3,7,5,1,2,8,4,6]=>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
[1,2,3,6,8,5,7,4]=>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
[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
[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
[3,1,7,2,8,6,4,5]=>0100111=>1110010
[1,2,3,8,7,5,6,4]=>0000111=>1110000
[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
[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
[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
[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
[7,4,3,2,1,8,5,6]=>1110011=>1100111
[8,4,3,2,1,7,5,6]=>1110011=>1100111
[7,4,3,2,1,8,6,5]=>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
[6,5,4,2,7,8,1,3]=>0011101=>1011100
[8,5,4,2,6,7,1,3]=>0011011=>1101100
[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
[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
[3,2,6,4,8,5,1,7]=>0101101=>1011010
[3,2,5,8,4,6,1,7]=>0100101=>1010010
[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
[4,1,5,3,8,2,6,7]=>0011001=>1001100
[4,3,2,7,5,1,6,8]=>0111010=>0101110
[4,3,6,2,5,1,7,8]=>0011100=>0011100
[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
[4,3,1,7,5,2,6,8]=>0111010=>0101110
[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
[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
[3,6,7,2,4,5,1,8]=>0001010=>0101000
[7,2,1,4,6,3,8,5]=>1000111=>1110001
[7,3,1,4,6,8,2,5]=>0100011=>1100010
[3,6,2,1,5,7,4,8]=>1000110=>0110001
[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
[4,6,5,1,7,2,3,8]=>0001110=>0111000
[3,6,5,1,2,7,4,8]=>0001110=>0111000
[2,4,1,5,3,8,7,6]=>0011011=>1101100
[3,4,5,1,2,8,7,6]=>0001011=>1101000
[1,8,4,5,3,2,7,6]=>0101011=>1101010
[2,4,8,5,3,1,7,6]=>0101011=>1101010
[3,4,5,2,8,1,7,6]=>0001011=>1101000
[3,4,6,2,1,7,8,5]=>1000101=>1010001
[3,4,6,2,1,7,5,8]=>1000110=>0110001
[3,5,6,2,7,1,8,4]=>0000111=>1110000
[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
[2,5,8,6,7,3,4,1]=>0010011=>1100100
[1,8,5,6,7,3,2,4]=>0100011=>1100010
[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
[2,5,1,6,7,8,4,3]=>0011001=>1001100
[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
[4,5,6,7,1,3,8,2]=>0000011=>1100000
[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
[8,2,4,3,7,1,6,5]=>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
[7,3,2,4,6,1,5,8]=>0100110=>0110010
[3,2,5,1,8,4,6,7]=>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
[3,2,4,1,7,5,6,8]=>0110010=>0100110
[3,2,4,1,6,8,5,7]=>0110001=>1000110
[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
[5,2,6,1,8,3,7,4]=>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
[3,2,5,1,7,6,4,8]=>0101110=>0111010
[3,2,5,1,8,6,4,7]=>0101101=>1011010
[8,6,1,5,7,3,2,4]=>0100111=>1110010
[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
[3,2,4,1,5,8,6,7]=>0110001=>1000110
[3,2,5,1,7,8,6,4]=>0101101=>1011010
[8,7,5,1,6,4,2,3]=>0011111=>1111100
[3,2,5,1,8,7,6,4]=>0101111=>1111010
[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
[5,4,7,8,3,1,6,2]=>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
[2,5,4,6,1,7,3,8]=>0001110=>0111000
[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
[4,3,7,8,2,6,1,5]=>0010101=>1010100
[2,5,7,4,8,1,6,3]=>0000111=>1110000
[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
[6,5,2,1,7,8,4,3]=>1011101=>1011101
[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
[3,5,2,1,7,8,4,6]=>1001001=>1001001
[4,6,2,1,8,3,7,5]=>1000111=>1110001
[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
[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
[6,2,3,1,5,4,8,7]=>0101101=>1011010
[8,4,5,2,3,1,7,6]=>0101011=>1101010
[8,2,5,3,4,1,7,6]=>0011011=>1101100
[6,2,5,3,4,1,8,7]=>0011101=>1011100
[6,4,5,1,3,2,8,7]=>0101101=>1011010
[6,1,5,3,4,2,8,7]=>0011101=>1011100
[8,3,7,2,4,1,6,5]=>0010111=>1110100
[8,3,5,1,4,2,7,6]=>0011011=>1101100
[8,4,5,1,3,2,7,6]=>0101011=>1101010
[2,1,8,4,5,3,7,6]=>1001011=>1101001
[8,1,7,3,4,2,6,5]=>0010111=>1110100
[8,2,7,1,4,3,6,5]=>0010111=>1110100
[8,2,7,3,4,1,6,5]=>0010111=>1110100
[8,4,7,2,3,1,6,5]=>0100111=>1110010
[8,2,3,1,5,4,7,6]=>0101011=>1101010
[4,2,3,1,8,5,7,6]=>0110011=>1100110
[8,2,3,1,7,5,6,4]=>0100111=>1110010
[8,6,7,1,3,2,5,4]=>0101011=>1101010
[8,1,3,2,7,5,6,4]=>0100111=>1110010
[2,1,8,5,7,3,6,4]=>1000111=>1110001
[4,5,8,6,3,2,7,1]=>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
[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
[3,6,7,8,4,2,5,1]=>0011001=>1001100
[7,6,1,8,4,2,5,3]=>0011111=>1111100
[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
[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
[7,3,5,8,2,4,6,1]=>0000111=>1110000
[4,3,1,2,8,5,6,7]=>0110001=>1000110
[2,7,6,8,4,3,5,1]=>0011011=>1101100
[1,7,5,8,3,4,6,2]=>0000111=>1110000
[4,6,8,5,1,3,2,7]=>0101001=>1001010
[2,4,8,3,6,5,1,7]=>0001101=>1011000
[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
[2,8,7,4,1,6,5,3]=>0011111=>1111100
[2,8,5,4,3,1,6,7]=>0111001=>1001110
[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
[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
[5,1,3,2,4,8,6,7]=>0101001=>1001010
[2,8,1,5,3,4,7,6]=>0001011=>1101000
[1,4,2,8,5,3,6,7]=>0011001=>1001100
[3,5,1,4,8,2,6,7]=>0001001=>1001000
[1,5,2,8,4,3,6,7]=>0011001=>1001100
[1,2,5,4,3,8,6,7]=>0011001=>1001100
[1,2,4,8,5,3,7,6]=>0001011=>1101000
[1,5,2,7,8,4,3,6]=>0011001=>1001100
[5,1,2,7,4,8,3,6]=>0001011=>1101000
[8,3,5,1,4,7,2,6]=>0001011=>1101000
[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
[7,6,1,4,2,8,3,5]=>0010111=>1110100
[7,1,6,2,8,4,3,5]=>0010111=>1110100
[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
[5,8,1,3,7,2,4,6]=>0000011=>1100000
[1,2,5,8,7,3,4,6]=>0000011=>1100000
[8,6,1,3,2,4,7,5]=>0100111=>1110010
[4,2,8,1,7,3,6,5]=>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
[8,6,1,4,2,7,3,5]=>0010111=>1110100
[7,1,2,8,6,4,3,5]=>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
[6,8,3,4,1,7,2,5]=>0010011=>1100100
[5,7,3,4,1,8,2,6]=>0010011=>1100100
[5,8,3,4,1,7,2,6]=>0010011=>1100100
[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
[4,6,2,7,3,8,1,5]=>0000111=>1110000
[5,6,2,7,3,8,1,4]=>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
[6,5,3,2,1,4,8,7]=>1101101=>1011011
[8,7,3,5,2,4,1,6]=>0011011=>1101100
[6,8,2,4,5,7,3,1]=>0100011=>1100010
[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
[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
[2,5,8,4,7,6,3,1]=>0100111=>1110010
[4,3,8,1,5,6,7,2]=>0010011=>1100100
[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
[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
[6,1,8,4,5,7,2,3]=>0000111=>1110000
[6,8,3,5,1,7,2,4]=>0001011=>1101000
[5,8,3,6,1,2,7,4]=>0000111=>1110000
[5,8,1,4,7,6,2,3]=>0000111=>1110000
[4,5,3,8,6,1,7,2]=>0001111=>1111000
[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
[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
[5,1,7,3,6,8,4,2]=>0011011=>1101100
[6,7,1,3,5,8,4,2]=>0010011=>1100100
[4,8,3,7,6,1,5,2]=>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
[6,7,1,2,8,5,4,3]=>0011011=>1101100
[8,2,3,1,7,6,5,4]=>0101111=>1111010
[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
[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
[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
[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
[2,1,8,3,7,6,5,4]=>1001111=>1111001
[5,1,7,8,2,6,4,3]=>0011101=>1011100
[6,7,1,8,2,5,4,3]=>0011011=>1101100
[4,8,1,7,2,6,5,3]=>0001111=>1111000
[3,8,1,2,7,6,5,4]=>0001111=>1111000
[1,8,2,3,7,6,5,4]=>0001111=>1111000
[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
[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
[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
[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
[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
[4,6,3,1,2,8,7,5]=>0100111=>1110010
[2,6,4,1,3,8,7,5]=>0010111=>1110100
[2,7,1,4,3,8,6,5]=>0010111=>1110100
[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
[2,6,3,1,4,8,7,5]=>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
[8,1,4,2,3,7,6,5]=>0010111=>1110100
[7,4,1,2,3,8,6,5]=>0010111=>1110100
[5,4,2,3,1,8,7,6]=>0111011=>1101110
[3,5,2,4,1,8,7,6]=>0011011=>1101100
[7,3,1,2,4,8,6,5]=>0100111=>1110010
[8,1,3,2,4,7,6,5]=>0100111=>1110010
[7,2,1,3,4,8,6,5]=>1000111=>1110001
[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
[2,4,6,3,5,1,8,7]=>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
[4,2,6,5,8,1,7,3]=>0010111=>1110100
[4,2,6,5,8,1,3,7]=>0010101=>1010100
[4,2,6,5,8,3,1,7]=>0110101=>1010110
[2,4,1,6,5,8,3,7]=>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
[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
[2,4,1,6,8,5,7,3]=>0010011=>1100100
[2,1,4,6,8,5,3,7]=>1001001=>1001001
[2,4,6,1,8,5,3,7]=>0001101=>1011000
[2,4,6,8,1,5,3,7]=>0001001=>1001000
[2,4,6,8,3,5,7,1]=>0000011=>1100000
[2,4,6,8,3,1,5,7]=>0100001=>1000010
[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
[2,4,3,6,8,1,7,5]=>0010011=>1100100
[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
[2,4,6,3,1,8,7,5]=>0100111=>1110010
[2,4,1,6,3,8,7,5]=>0010111=>1110100
[2,1,4,6,3,8,7,5]=>1000111=>1110001
[2,4,1,6,8,3,7,5]=>0010011=>1100100
[2,4,6,8,1,3,7,5]=>0000011=>1100000
[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
[2,6,4,8,1,7,5,3]=>0001111=>1111000
[2,6,4,1,8,7,5,3]=>0011111=>1111100
[2,1,6,4,8,7,3,5]=>1000111=>1110001
[2,6,4,1,8,7,3,5]=>0010111=>1110100
[2,6,4,8,1,7,3,5]=>0000111=>1110000
[6,2,4,8,7,3,5,1]=>0001111=>1111000
[6,2,4,8,7,3,1,5]=>0100111=>1110010
[1,3,7,4,5,8,2,6]=>0000011=>1100000
[1,7,6,3,4,8,2,5]=>0000111=>1110000
[8,1,6,3,7,2,4,5]=>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
[8,5,1,3,7,2,4,6]=>0001011=>1101000
[1,5,3,2,8,4,6,7]=>0101001=>1001010
[2,6,4,8,7,1,3,5]=>0000111=>1110000
[1,6,4,8,7,2,3,5]=>0000111=>1110000
[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
[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
[8,3,2,1,4,6,5,7]=>1100101=>1010011
[3,8,2,1,4,5,7,6]=>1000011=>1100001
[3,2,7,1,4,6,8,5]=>0100011=>1100010
[3,2,8,1,4,6,7,5]=>0100011=>1100010
[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
[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
[3,8,2,1,7,4,5,6]=>1000011=>1100001
[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
[5,7,8,3,4,1,2,6]=>0010001=>1000100
[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
[3,7,2,1,8,5,4,6]=>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
[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
[1,6,2,5,4,8,7,3]=>0001111=>1111000
[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
[7,8,3,1,4,2,6,5]=>0110101=>1010110
[4,3,6,1,8,2,7,5]=>0010111=>1110100
[7,5,1,6,4,3,2,8]=>0111110=>0111110
[6,1,5,7,4,3,2,8]=>0110110=>0110110
[1,5,8,6,4,3,2,7]=>0110101=>1010110
[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
[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
[4,3,6,1,5,7,2,8]=>0010110=>0110100
[1,3,6,8,5,7,2,4]=>0000011=>1100000
[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
[2,8,3,5,4,1,7,6]=>0011011=>1101100
[7,8,1,4,6,3,2,5]=>0100101=>1010010
[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
[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
[1,6,5,8,4,3,2,7]=>0110101=>1010110
[6,8,5,1,4,3,2,7]=>0111001=>1001110
[3,6,2,5,4,1,7,8]=>0011100=>0011100
[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
[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
[1,7,5,4,3,8,6,2]=>0011111=>1111100
[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
[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
[7,3,2,8,5,1,6,4]=>0101111=>1111010
[8,4,6,3,2,1,7,5]=>1100111=>1110011
[5,4,7,2,1,8,6,3]=>1001111=>1111001
[5,7,3,2,1,6,8,4]=>1100011=>1100011
[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
[3,2,6,1,7,4,5,8]=>0100110=>0110010
[2,5,8,4,1,3,7,6]=>0010011=>1100100
[2,4,1,7,8,3,6,5]=>0010101=>1010100
[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
[3,5,2,1,4,6,8,7]=>1001001=>1001001
[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
[2,7,6,1,4,8,5,3]=>0001111=>1111000
[7,3,5,1,8,4,2,6]=>0011011=>1101100
[2,7,6,1,5,8,4,3]=>0010111=>1110100
[2,7,6,4,1,8,5,3]=>0011111=>1111100
[2,7,6,4,1,8,3,5]=>0010111=>1110100
[7,3,5,1,8,6,2,4]=>0001111=>1111000
[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
[2,3,4,8,7,5,1,6]=>0001011=>1101000
[2,7,6,5,4,8,1,3]=>0001111=>1111000
[7,3,5,6,8,1,2,4]=>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
[6,3,5,7,8,2,1,4]=>1000101=>1010001
[5,7,3,6,1,8,4,2]=>0010111=>1110100
[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
[2,3,4,8,5,1,7,6]=>0001011=>1101000
[7,4,3,5,8,2,1,6]=>1010011=>1100101
[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
[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
[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
[6,8,5,2,1,4,7,3]=>1001011=>1101001
[3,8,2,5,6,1,7,4]=>0000111=>1110000
[8,1,2,5,6,3,7,4]=>0000111=>1110000
[8,6,1,5,7,2,3,4]=>0000111=>1110000
[3,8,6,5,7,1,2,4]=>0000111=>1110000
[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
[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
[8,1,6,5,7,3,2,4]=>0100111=>1110010
[3,5,8,6,2,7,1,4]=>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
[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
[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
[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
[3,8,2,7,6,1,5,4]=>0001111=>1111000
[4,8,7,2,6,5,3,1]=>0101111=>1111010
[4,8,7,3,1,6,5,2]=>0101111=>1111010
[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
[4,8,7,3,6,1,5,2]=>0001111=>1111000
[5,8,7,6,3,4,2,1]=>1010111=>1110101
[5,8,7,6,3,1,4,2]=>0110111=>1110110
[5,8,7,6,2,4,3,1]=>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
[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
[6,4,5,7,3,1,8,2]=>0100111=>1110010
[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
[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
[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
[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
[4,3,6,1,7,8,5,2]=>0011101=>1011100
[4,2,1,6,7,8,5,3]=>1011001=>1001101
[2,4,6,7,1,8,5,3]=>0001011=>1101000
[2,5,6,7,8,1,4,3]=>0010001=>1000100
[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
[1,5,3,7,4,8,2,6]=>0001011=>1101000
[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
[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
[7,3,1,8,4,2,6,5]=>0110111=>1110110
[7,2,8,3,6,5,1,4]=>0001111=>1111000
[7,2,8,3,6,1,5,4]=>0001111=>1111000
[6,1,2,8,3,5,4,7]=>0001101=>1011000
[5,2,3,8,1,4,7,6]=>0001011=>1101000
[6,2,4,1,8,7,3,5]=>0010111=>1110100
[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
[1,2,5,3,8,4,7,6]=>0001011=>1101000
[1,2,4,8,3,7,6,5]=>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
[1,4,8,3,7,2,6,5]=>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
[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
[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
[3,4,8,1,7,2,6,5]=>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
[5,3,6,2,4,7,1,8]=>0001110=>0111000
[6,4,2,1,7,3,8,5]=>1010111=>1110101
[2,7,6,5,3,1,4,8]=>0101110=>0111010
[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
[5,2,6,3,4,1,7,8]=>0011100=>0011100
[5,1,6,2,4,7,8,3]=>0001101=>1011000
[1,7,2,4,8,3,6,5]=>0000111=>1110000
[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
[3,7,6,5,2,4,1,8]=>0011110=>0111100
[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
[2,7,6,5,8,1,3,4]=>0000111=>1110000
[2,7,6,5,8,4,1,3]=>0010111=>1110100
[3,7,5,8,2,4,1,6]=>0010011=>1100100
[5,1,7,8,4,3,2,6]=>0111001=>1001110
[5,1,2,6,4,3,8,7]=>0011101=>1011100
[5,1,2,4,6,3,8,7]=>0001101=>1011000
[4,1,5,7,8,3,2,6]=>0110001=>1000110
[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
[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
[7,1,2,3,8,6,5,4]=>0001111=>1111000
[6,8,1,4,3,7,2,5]=>0010011=>1100100
[8,7,3,2,4,1,6,5]=>0110111=>1110110
[6,7,1,4,3,8,2,5]=>0010011=>1100100
[8,1,2,3,5,7,6,4]=>0000111=>1110000
[7,1,2,3,6,8,5,4]=>0001011=>1101000
[7,1,8,5,4,3,2,6]=>0111011=>1101110
[7,8,2,6,3,4,1,5]=>0010101=>1010100
[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
[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
[8,6,2,4,3,1,7,5]=>0110111=>1110110
[7,6,3,2,4,8,1,5]=>0100111=>1110010
[8,6,3,2,4,7,1,5]=>0100111=>1110010
[7,6,2,4,3,1,8,5]=>0110111=>1110110
[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
[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
[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
[7,1,3,6,5,4,2,8]=>0011110=>0111100
[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
[5,8,2,7,6,3,4,1]=>0010111=>1110100
[6,2,8,1,7,3,5,4]=>0001111=>1111000
[3,6,4,1,2,8,5,7]=>0010101=>1010100
[2,5,1,8,7,6,3,4]=>0001111=>1111000
[1,2,5,3,8,7,4,6]=>0001011=>1101000
[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
[6,3,1,8,7,2,5,4]=>0101111=>1111010
[5,1,3,8,7,6,2,4]=>0001111=>1111000
[1,5,3,8,7,6,2,4]=>0001111=>1111000
[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
[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
[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
[3,4,8,7,6,5,1,2]=>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
[2,1,3,5,8,7,4,6]=>1000011=>1100001
[1,2,7,5,8,6,4,3]=>0010111=>1110100
[6,8,1,3,7,5,2,4]=>0001011=>1101000
[1,3,7,8,2,6,5,4]=>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
[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
[8,2,4,7,3,6,1,5]=>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
[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
[8,5,6,3,1,7,4,2]=>0110111=>1110110
[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
[8,6,4,7,3,1,5,2]=>0101111=>1111010
[8,4,5,7,3,1,6,2]=>0100111=>1110010
[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
[8,7,2,3,4,6,1,5]=>0000111=>1110000
[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
[8,6,1,2,4,7,3,5]=>0000111=>1110000
[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
[5,1,4,2,3,8,6,7]=>0011001=>1001100
[5,1,4,2,7,3,6,8]=>0011010=>0101100
[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
[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
[7,1,5,3,2,8,6,4]=>0101111=>1111010
[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
[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
[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
[8,1,2,7,4,6,5,3]=>0001111=>1111000
[8,1,2,7,3,6,5,4]=>0001111=>1111000
[1,2,3,6,8,5,4,7]=>0001001=>1001000
[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
[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
[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
[8,3,2,6,7,5,4,1]=>0111011=>1101110
[8,6,4,3,7,5,2,1]=>1011111=>1111101
[8,4,5,3,2,7,6,1]=>0101111=>1111010
[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
[3,7,2,8,6,5,4,1]=>0011111=>1111100
[3,6,2,8,7,5,4,1]=>0011111=>1111100
[7,4,5,3,2,8,6,1]=>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
[6,3,2,8,7,5,4,1]=>0111111=>1111110
[6,3,2,7,8,5,4,1]=>0111101=>1011110
[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
[1,6,7,2,4,3,8,5]=>0010011=>1100100
[1,5,8,2,4,6,7,3]=>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
[1,7,3,4,2,8,6,5]=>0010111=>1110100
[1,5,6,2,4,8,7,3]=>0000111=>1110000
[1,5,8,7,3,2,4,6]=>0100011=>1100010
[1,7,4,2,8,6,5,3]=>0011111=>1111100
[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
[1,6,8,5,2,3,7,4]=>0001011=>1101000
[1,6,4,2,3,7,5,8]=>0010110=>0110100
[1,5,8,6,2,4,7,3]=>0000111=>1110000
[1,7,5,2,8,6,4,3]=>0011111=>1111100
[3,7,5,6,1,4,8,2]=>0000111=>1110000
[8,6,1,4,2,7,5,3]=>0011111=>1111100
[1,6,7,4,3,5,8,2]=>0010011=>1100100
[6,7,1,4,3,5,8,2]=>0010011=>1100100
[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
[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
[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
[1,8,4,3,7,2,5,6]=>0010011=>1100100
[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
[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
[4,2,3,7,8,6,1,5]=>0010101=>1010100
[2,7,5,6,3,8,1,4]=>0000111=>1110000
[5,7,2,6,8,4,1,3]=>0010011=>1100100
[7,2,5,6,8,4,1,3]=>0010011=>1100100
[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
[1,4,8,3,6,2,5,7]=>0000101=>1010000
[3,7,5,8,6,2,1,4]=>1000111=>1110001
[3,7,8,6,5,2,1,4]=>1001101=>1011001
[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
[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
[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
[1,3,2,8,6,7,4,5]=>0100011=>1100010
[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
[6,4,8,5,2,7,1,3]=>0001111=>1111000
[8,4,7,5,2,6,1,3]=>0001111=>1111000
[5,4,6,8,2,1,7,3]=>1001011=>1101001
[4,8,7,5,6,1,3,2]=>0100111=>1110010
[2,7,5,1,8,4,3,6]=>0011011=>1101100
[2,8,6,7,4,3,5,1]=>0011011=>1101100
[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
[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
[8,4,7,1,2,5,6,3]=>0000111=>1110000
[4,2,8,7,3,5,6,1]=>0010111=>1110100
[6,4,1,5,8,2,7,3]=>0010111=>1110100
[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
[4,7,8,3,1,5,6,2]=>0100101=>1010010
[3,7,1,4,8,5,6,2]=>0000111=>1110000
[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
[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
[4,8,7,5,6,1,2,3]=>0000111=>1110000
[6,1,4,8,7,3,5,2]=>0001111=>1111000
[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
[8,2,3,7,1,5,6,4]=>0000111=>1110000
[6,4,8,7,1,3,2,5]=>0100111=>1110010
[7,8,2,4,3,5,6,1]=>0010101=>1010100
[2,8,3,7,1,5,6,4]=>0000111=>1110000
[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
[3,6,8,1,4,5,2,7]=>0001001=>1001000
[6,8,1,2,4,5,3,7]=>0001001=>1001000
[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
[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
[4,7,6,8,2,1,5,3]=>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
[4,6,5,2,8,1,7,3]=>0001111=>1111000
[1,8,5,2,3,6,7,4]=>0001011=>1101000
[4,8,3,2,5,6,7,1]=>0100011=>1100010
[2,1,8,3,5,6,7,4]=>1000011=>1100001
[4,2,7,1,8,6,3,5]=>0010111=>1110100
[3,8,4,1,2,6,7,5]=>0010011=>1100100
[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
[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
[8,6,5,4,1,2,7,3]=>0011111=>1111100
[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
[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
[6,5,4,8,7,1,3,2]=>0101111=>1111010
[6,5,4,8,1,2,7,3]=>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
[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
[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
[6,5,3,8,1,4,2,7]=>0011101=>1011100
[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
[8,1,6,4,2,5,7,3]=>0010111=>1110100
[8,1,5,4,3,2,7,6]=>0111011=>1101110
[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
[6,4,3,1,5,7,8,2]=>0110101=>1010110
[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
[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
[8,5,7,2,1,4,6,3]=>1000111=>1110001
[8,5,2,7,1,3,6,4]=>0001111=>1111000
[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
[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
[8,3,2,6,5,1,4,7]=>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
[8,7,3,1,6,2,4,5]=>0100111=>1110010
[8,7,3,1,2,4,6,5]=>0100111=>1110010
[8,3,2,1,7,4,6,5]=>1100111=>1110011
[8,4,7,2,1,5,6,3]=>1000111=>1110001
[8,7,2,1,3,6,4,5]=>1000111=>1110001
[8,7,2,1,3,4,6,5]=>1000111=>1110001
[1,2,7,3,5,4,8,6]=>0001011=>1101000
[1,5,7,2,3,6,4,8]=>0000110=>0110000
[1,3,8,2,4,5,7,6]=>0000011=>1100000
[1,2,3,8,4,6,7,5]=>0000011=>1100000
[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
[1,8,2,3,6,4,5,7]=>0000101=>1010000
[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
[6,2,1,7,5,3,8,4]=>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
[5,2,1,7,6,8,3,4]=>1001011=>1101001
[4,5,7,6,8,1,2,3]=>0000011=>1100000
[4,6,7,5,8,1,2,3]=>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
[5,8,3,1,6,7,2,4]=>0100011=>1100010
[5,7,3,1,6,8,2,4]=>0100011=>1100010
[5,6,3,1,7,8,2,4]=>0100101=>1010010
[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
[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
[1,2,6,3,8,7,4,5]=>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
[2,1,3,8,5,4,7,6]=>1001011=>1101001
[7,1,8,4,2,3,5,6]=>0010011=>1100100
[4,2,6,3,1,8,5,7]=>0110101=>1010110
[5,4,2,8,3,1,6,7]=>0111001=>1001110
[2,5,4,8,3,1,6,7]=>0101001=>1001010
[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
[1,2,6,3,8,4,7,5]=>0000111=>1110000
[4,2,1,8,3,7,5,6]=>1010011=>1100101
[8,3,2,1,7,4,5,6]=>1100011=>1100011
[1,2,3,8,7,4,6,5]=>0000111=>1110000
[1,2,3,8,7,6,4,5]=>0000111=>1110000
[2,6,5,7,1,4,3,8]=>0010110=>0110100
[2,6,5,7,1,3,8,4]=>0000111=>1110000
[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
[2,8,1,7,5,6,4,3]=>0010111=>1110100
[2,3,8,1,6,5,7,4]=>0000111=>1110000
[3,5,7,6,1,2,4,8]=>0000110=>0110000
[4,8,6,7,2,3,5,1]=>0001011=>1101000
[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
[3,8,5,7,2,1,6,4]=>1000111=>1110001
[3,4,8,6,2,1,5,7]=>1000101=>1010001
[3,5,7,6,2,1,4,8]=>1000110=>0110001
[5,8,6,7,3,4,2,1]=>1010011=>1100101
[5,8,6,7,2,1,3,4]=>1000011=>1100001
[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
[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
[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
[4,2,6,7,5,1,3,8]=>0011010=>0101100
[3,8,4,7,1,5,2,6]=>0001011=>1101000
[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
[4,2,6,7,5,3,8,1]=>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
[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
[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
[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
[7,3,5,8,6,2,1,4]=>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
[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
[3,1,7,6,8,2,5,4]=>0101011=>1101010
[1,3,7,6,8,2,5,4]=>0001011=>1101000
[1,7,4,2,6,8,5,3]=>0011011=>1101100
[7,1,4,2,8,5,6,3]=>0010111=>1110100
[7,1,8,2,5,4,6,3]=>0001111=>1111000
[7,1,6,8,5,4,2,3]=>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
[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
[7,8,4,2,1,6,5,3]=>1011101=>1011101
[6,2,3,4,8,7,1,5]=>0000111=>1110000
[6,2,3,4,7,8,1,5]=>0000101=>1010000
[7,8,3,6,4,2,1,5]=>1010101=>1010101
[7,8,3,5,6,2,1,4]=>1000101=>1010001
[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
[6,3,2,7,4,8,1,5]=>0100111=>1110010
[6,3,2,5,7,8,1,4]=>0100101=>1010010
[5,8,2,3,6,1,7,4]=>0000111=>1110000
[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
[4,7,5,6,3,2,1,8]=>1100110=>0110011
[5,1,4,3,6,2,8,7]=>0011101=>1011100
[5,1,4,3,8,2,7,6]=>0011011=>1101100
[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
[5,8,2,4,1,7,6,3]=>0010111=>1110100
[5,4,1,3,7,2,6,8]=>0011010=>0101100
[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
[5,4,7,8,3,2,1,6]=>1101001=>1001011
[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
[4,8,2,3,6,7,5,1]=>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
[5,8,1,4,7,2,6,3]=>0000111=>1110000
[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
[4,1,3,8,2,6,5,7]=>0010101=>1010100
[4,1,8,7,3,5,2,6]=>0011011=>1101100
[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
[1,2,4,3,8,6,5,7]=>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
[4,1,2,8,3,6,5,7]=>0010101=>1010100
[1,4,3,2,8,6,5,7]=>0110101=>1010110
[4,2,3,1,8,6,5,7]=>0110101=>1010110
[3,7,8,2,6,4,5,1]=>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
[4,2,8,6,3,1,5,7]=>0110101=>1010110
[2,4,8,6,3,1,5,7]=>0100101=>1010010
[7,3,6,8,4,2,1,5]=>1010011=>1100101
[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
[7,3,8,2,6,4,5,1]=>0001111=>1111000
[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
[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
[3,5,7,8,6,1,2,4]=>0000101=>1010000
[3,1,5,6,8,2,7,4]=>0100011=>1100010
[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
[1,5,2,7,8,6,3,4]=>0001101=>1011000
[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
[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
[5,1,7,8,6,3,2,4]=>0101101=>1011010
[1,6,7,5,3,8,2,4]=>0001011=>1101000
[1,6,7,5,4,2,8,3]=>0011011=>1101100
[5,7,8,6,4,1,2,3]=>0010101=>1010100
[6,7,4,1,5,2,8,3]=>0011011=>1101100
[1,6,7,4,5,2,8,3]=>0001011=>1101000
[6,3,1,7,5,8,2,4]=>0100111=>1110010
[2,5,3,7,8,6,1,4]=>0001101=>1011000
[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
[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
[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
[3,6,5,1,8,4,2,7]=>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
[4,6,1,5,8,2,3,7]=>0000101=>1010000
[4,7,1,5,8,3,6,2]=>0000111=>1110000
[8,3,4,6,2,1,5,7]=>1000101=>1010001
[3,5,6,2,1,8,4,7]=>1000101=>1010001
[7,5,3,2,8,4,1,6]=>0111011=>1101110
[7,5,3,2,8,4,6,1]=>0101111=>1111010
[4,2,5,6,8,3,1,7]=>0110001=>1000110
[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
[4,5,3,7,2,8,6,1]=>0001111=>1111000
[6,4,7,3,2,8,5,1]=>0101111=>1111010
[6,1,4,7,3,2,8,5]=>0100111=>1110010
[5,1,7,3,8,4,2,6]=>0011011=>1101100
[5,3,7,1,4,8,6,2]=>0001111=>1111000
[6,4,3,1,7,8,5,2]=>0111101=>1011110
[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
[5,6,3,2,7,8,4,1]=>0110101=>1010110
[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
[6,3,7,2,8,4,1,5]=>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
[5,7,3,8,2,1,6,4]=>1000111=>1110001
[4,6,2,7,8,5,3,1]=>0101101=>1011010
[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
[5,3,2,1,8,4,7,6]=>1101011=>1101011
[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
[1,3,4,6,5,8,2,7]=>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
[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
[5,8,7,4,6,2,1,3]=>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
[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
[7,2,4,8,5,3,1,6]=>0101011=>1101010
[4,8,3,1,2,7,6,5]=>0100111=>1110010
[8,4,2,3,7,1,5,6]=>0010011=>1100100
[3,5,2,7,6,1,8,4]=>0001111=>1111000
[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
[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
[8,1,3,6,5,2,4,7]=>0001101=>1011000
[8,3,2,4,6,5,1,7]=>0101101=>1011010
[8,3,6,4,1,5,2,7]=>0011101=>1011100
[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
[2,8,5,1,4,7,6,3]=>0001111=>1111000
[4,3,1,5,8,6,7,2]=>0110011=>1100110
[5,4,2,1,6,8,7,3]=>1011011=>1101101
[6,8,4,3,2,7,1,5]=>0110011=>1100110
[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
[2,7,4,5,8,3,1,6]=>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
[6,3,8,7,4,1,2,5]=>0010111=>1110100
[8,4,7,2,3,1,5,6]=>0100011=>1100010
[8,6,4,1,3,2,7,5]=>0110111=>1110110
[3,5,7,2,6,1,8,4]=>0000111=>1110000
[6,1,3,8,5,7,2,4]=>0000111=>1110000
[2,8,1,5,4,7,6,3]=>0001111=>1111000
[1,7,2,4,6,5,8,3]=>0000111=>1110000
[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
[4,1,5,2,6,8,7,3]=>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
[3,4,5,1,8,6,7,2]=>0001011=>1101000
[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
[1,2,7,4,8,6,5,3]=>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
[1,2,6,4,8,7,3,5]=>0000111=>1110000
[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
[1,4,7,2,8,3,6,5]=>0000111=>1110000
[1,6,7,3,4,8,5,2]=>0001011=>1101000
[1,5,3,7,4,8,6,2]=>0001111=>1111000
[1,3,6,4,2,8,7,5]=>0010111=>1110100
[1,3,7,4,2,8,6,5]=>0010111=>1110100
[1,2,8,4,7,3,6,5]=>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
[1,4,8,6,7,2,3,5]=>0000011=>1100000
[1,5,6,8,7,2,3,4]=>0000011=>1100000
[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
[1,5,7,8,6,2,3,4]=>0000101=>1010000
[1,3,7,6,2,8,4,5]=>0000111=>1110000
[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
[5,6,2,1,7,8,3,4]=>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
[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
[5,4,6,1,7,8,2,3]=>0001101=>1011000
[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
[5,1,2,4,8,7,6,3]=>0001111=>1111000
[2,1,5,3,8,6,4,7]=>1001101=>1011001
[5,1,2,4,8,6,3,7]=>0001101=>1011000
[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
[2,1,3,7,8,6,4,5]=>1000101=>1010001
[5,1,4,2,8,6,7,3]=>0011011=>1101100
[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
[2,1,3,6,8,7,4,5]=>1000011=>1100001
[3,1,6,2,8,7,5,4]=>0101111=>1111010
[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
[7,8,2,5,1,4,3,6]=>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
[2,5,4,7,6,8,1,3]=>0001011=>1101000
[2,6,1,4,3,7,5,8]=>0010110=>0110100
[2,6,1,5,3,7,4,8]=>0001110=>0111000
[2,6,4,7,5,8,1,3]=>0000111=>1110000
[5,8,2,6,4,7,1,3]=>0000111=>1110000
[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
[4,7,5,8,1,3,2,6]=>0100011=>1100010
[4,7,1,3,2,6,5,8]=>0100110=>0110010
[3,7,1,4,2,6,5,8]=>0010110=>0110100
[3,7,6,8,1,4,2,5]=>0010011=>1100100
[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
[3,7,4,8,2,6,1,5]=>0000111=>1110000
[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
[2,6,5,8,4,7,1,3]=>0000111=>1110000
[2,6,3,7,1,5,4,8]=>0001110=>0111000
[7,6,4,8,5,2,3,1]=>0101111=>1111010
[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
[7,6,3,5,8,2,4,1]=>0010111=>1110100
[7,6,2,8,4,1,5,3]=>0011111=>1111100
[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
[6,3,4,8,7,2,5,1]=>0001111=>1111000
[6,3,8,4,7,2,1,5]=>1000111=>1110001
[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
[5,6,7,3,4,1,8,2]=>0010011=>1100100
[4,6,7,8,3,5,2,1]=>1001001=>1001001
[4,7,3,5,6,8,2,1]=>1000011=>1100001
[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
[5,8,3,7,2,6,4,1]=>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
[6,4,8,5,3,7,2,1]=>1001111=>1111001
[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
[5,6,3,4,8,2,1,7]=>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
[5,3,4,7,2,6,1,8]=>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
[4,5,8,3,7,2,6,1]=>0000111=>1110000
[5,3,4,6,8,2,1,7]=>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
[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
[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
[7,1,8,4,5,2,3,6]=>0001011=>1101000
[7,6,3,1,2,4,8,5]=>0100111=>1110010
[6,1,2,3,8,7,5,4]=>0001111=>1111000
[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
[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
[3,1,5,6,4,8,7,2]=>0100111=>1110010
[1,3,6,2,5,7,8,4]=>0000101=>1010000
[3,6,1,4,2,7,8,5]=>0010101=>1010100
[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
[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
[3,1,5,4,8,7,6,2]=>0101111=>1111010
[1,2,6,8,5,4,7,3]=>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
[1,3,6,8,2,5,4,7]=>0001001=>1001000
[1,4,6,8,3,2,5,7]=>0100001=>1000010
[2,3,6,5,8,1,7,4]=>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
[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
[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
[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
[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
[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
[6,2,3,1,8,4,7,5]=>0100111=>1110010
[8,3,5,2,7,1,4,6]=>0001011=>1101000
[8,6,2,4,7,1,5,3]=>0001111=>1111000
[8,2,1,7,3,4,5,6]=>1000011=>1100001
[8,6,3,7,2,4,5,1]=>0001111=>1111000
[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
[1,7,5,8,2,3,6,4]=>0000111=>1110000
[7,2,1,8,3,4,5,6]=>1000011=>1100001
[1,7,8,3,4,5,6,2]=>0000101=>1010000
[1,6,2,8,4,5,7,3]=>0000111=>1110000
[4,1,3,6,8,2,7,5]=>0010011=>1100100
[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
[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
[9,10,12,11,7,8,5,6,3,4,1,2]=>00101010011=>11001010100
[7,10,12,8,11,9,5,6,3,4,1,2]=>00101001011=>11010010100
[5,10,12,8,11,6,9,7,3,4,1,2]=>00100101011=>11010100100
[3,10,12,8,11,6,9,4,7,5,1,2]=>00010101011=>11010101000
[3,8,9,12,11,4,5,10,7,6,1,2]=>00001100111=>11100110000
[3,4,9,12,5,6,11,10,8,7,1,2]=>00000110111=>11101100000
[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
[7,10,12,8,11,9,5,6,1,2,4,3]=>00101001011=>11010010100
[5,10,12,8,11,6,9,7,1,2,4,3]=>00100101011=>11010100100
[1,10,12,8,11,6,9,4,7,2,5,3]=>00010101011=>11010101000
[1,8,9,12,11,4,5,10,7,2,6,3]=>00001100111=>11100110000
[1,4,9,12,5,6,11,10,8,2,7,3]=>00000110111=>11101100000
[1,10,12,8,11,6,9,2,3,7,5,4]=>00010101011=>11010101000
[1,8,9,12,11,2,5,10,3,7,6,4]=>00001100111=>11100110000
[1,2,9,12,5,6,11,10,3,8,7,4]=>00000110111=>11101100000
[1,8,9,12,11,2,3,4,10,7,6,5]=>00001100111=>11100110000
[1,2,9,12,3,6,11,4,10,8,7,5]=>00000110111=>11101100000
[1,2,9,12,3,4,5,11,10,8,7,6]=>00000110111=>11101100000
[1,7,3,6,5,2,8,4]=>0001111=>1111000
[8,6,2,5,4,1,7,3]=>0011111=>1111100
[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
[4,1,7,8,2,6,5,3]=>0011101=>1011100
[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
[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
[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
[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
[10,3,1,5,2,9,8,4,6,7]=>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
[10,9,4,1,8,7,2,3,5,6]=>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
[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
[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
[1,8,5,4,3,7,2,6]=>0011011=>1101100
[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
[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
[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
[7,2,8,6,3,1,4,5]=>0100111=>1110010
[2,1,7,8,3,6,4,5]=>1000101=>1010001
[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
[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
[6,5,4,1,7,8,3,2]=>0111101=>1011110
[5,4,3,1,6,7,2,8]=>0111010=>0101110
[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
[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
[6,4,7,1,5,2,3,8]=>0001110=>0111000
[6,2,7,3,1,4,5,8]=>0100110=>0110010
[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
[2,6,7,4,5,1,3,8]=>0001010=>0101000
[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
[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
[7,3,4,1,5,2,6,8]=>0011010=>0101100
[1,3,6,7,2,5,8,4]=>0000011=>1100000
[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
[3,1,4,6,5,8,2,7]=>0100101=>1010010
[2,3,4,5,8,6,1,7]=>0000101=>1010000
[4,3,1,7,6,5,8,2]=>0110111=>1110110
[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
[7,3,4,5,8,1,2,6]=>0000011=>1100000
[1,3,4,5,8,6,2,7]=>0000101=>1010000
[1,3,4,5,8,2,7,6]=>0000011=>1100000
[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
[7,3,4,5,8,2,6,1]=>0000111=>1110000
[6,2,1,7,3,5,4,8]=>1001110=>0111001
[2,1,8,6,3,5,4,7]=>1001101=>1011001
[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
[6,2,1,7,3,5,8,4]=>1000111=>1110001
[2,7,3,1,4,8,5,6]=>0100011=>1100010
[3,2,1,5,7,8,4,6]=>1100001=>1000011
[2,4,7,5,1,6,8,3]=>0001011=>1101000
[4,3,6,8,5,1,7,2]=>0011011=>1101100
[2,1,6,8,3,7,4,5]=>1000011=>1100001
[3,2,1,5,6,8,4,7]=>1100001=>1000011
[2,1,7,3,6,4,5,8]=>1000110=>0110001
[2,1,6,3,5,8,4,7]=>1000101=>1010001
[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
[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
[3,2,1,6,7,4,5,8]=>1100010=>0100011
[3,2,1,7,4,5,6,8]=>1100010=>0100011
[2,1,8,3,7,4,5,6]=>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
[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
[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
[3,1,7,8,6,2,4,5]=>0100101=>1010010
[1,8,7,3,5,6,2,4]=>0000111=>1110000
[1,3,2,8,7,4,5,6]=>0100011=>1100010
[1,2,8,4,3,7,5,6]=>0010011=>1100100
[8,5,1,7,2,4,6,3]=>0001111=>1111000
[3,8,6,4,7,5,1,2]=>0001111=>1111000
[6,1,8,2,7,4,5,3]=>0001111=>1111000
[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
[7,4,6,3,8,5,1,2]=>0001111=>1111000
[8,4,6,2,7,5,3,1]=>0101111=>1111010
[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
[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
[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
[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
[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
[3,6,7,8,1,5,4,2]=>0011001=>1001100
[2,6,7,8,1,5,4,3]=>0011001=>1001100
[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
[7,2,3,4,8,1,5,6]=>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
[2,6,4,8,1,5,7,3]=>0000111=>1110000
[7,2,3,8,4,1,5,6]=>0010011=>1100100
[7,8,2,3,6,1,4,5]=>0000101=>1010000
[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
[7,8,5,4,1,2,6,3]=>0011101=>1011100
[3,5,6,4,1,2,8,7]=>0010101=>1010100
[7,6,5,1,2,4,3,8]=>0011110=>0111100
[7,6,5,1,2,4,8,3]=>0001111=>1111000
[7,6,5,1,3,2,4,8]=>0101110=>0111010
[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
[2,5,8,4,1,7,3,6]=>0010011=>1100100
[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
[7,6,5,1,2,8,3,4]=>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
[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
[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
[4,7,3,5,6,2,1,8]=>1000110=>0110001
[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
[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
[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
[8,2,7,5,6,1,3,4]=>0000111=>1110000
[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
[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
[1,8,2,5,3,7,6,4]=>0001111=>1111000
[3,8,1,5,6,4,2,7]=>0010101=>1010100
[7,6,4,1,5,2,8,3]=>0011111=>1111100
[8,6,1,5,4,7,2,3]=>0001111=>1111000
[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
[5,1,3,4,6,7,8,2]=>0001001=>1001000
[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
[5,4,8,6,2,3,7,1]=>0001111=>1111000
[2,7,6,1,3,5,4,8]=>0001110=>0111000
[2,8,6,1,3,5,4,7]=>0001101=>1011000
[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
[5,8,1,4,6,3,7,2]=>0000111=>1110000
[3,6,7,4,5,8,2,1]=>1000011=>1100001
[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
[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
[5,4,7,2,8,3,1,6]=>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
[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
[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
[6,3,7,1,4,8,5,2]=>0001111=>1111000
[3,7,1,5,4,8,6,2]=>0001111=>1111000
[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
[6,8,3,1,4,5,2,7]=>0101001=>1001010
[3,8,1,5,4,2,6,7]=>0011001=>1001100
[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
[2,7,6,1,8,5,4,3]=>0011111=>1111100
[2,7,6,8,1,4,5,3]=>0001011=>1101000
[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
[3,7,1,6,8,5,2,4]=>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
[1,8,4,5,2,3,6,7]=>0001001=>1001000
[7,4,8,5,3,2,6,1]=>0101111=>1111010
[3,4,8,7,5,2,6,1]=>0001111=>1111000
[3,2,8,6,1,5,4,7]=>0101101=>1011010
[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
[8,2,3,6,1,4,7,5]=>0000111=>1110000
[1,8,2,6,3,4,7,5]=>0000111=>1110000
[7,1,3,6,4,8,2,5]=>0000111=>1110000
[8,2,1,3,5,7,4,6]=>1000011=>1100001
[7,5,4,1,3,8,2,6]=>0011011=>1101100
[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
[8,6,1,4,7,3,2,5]=>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
[8,5,1,7,6,3,4,2]=>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
[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
[2,8,1,7,6,5,3,4]=>0001111=>1111000
[4,2,8,6,5,1,7,3]=>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
[3,2,4,8,7,1,5,6]=>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
[5,1,6,8,4,2,3,7]=>0011001=>1001100
[4,2,3,7,5,1,6,8]=>0011010=>0101100
[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
[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
[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
[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
[7,3,8,1,5,4,2,6]=>0011011=>1101100
[7,1,5,3,8,4,2,6]=>0011011=>1101100
[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
[2,3,8,1,5,7,4,6]=>0000011=>1100000
[7,1,3,2,8,6,4,5]=>0100111=>1110010
[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
[5,7,8,6,1,4,3,2]=>0110101=>1010110
[2,7,4,1,6,5,3,8]=>0011110=>0111100
[7,1,6,4,5,8,3,2]=>0100111=>1110010
[2,6,4,1,7,5,3,8]=>0011110=>0111100
[5,6,8,7,1,4,3,2]=>0110011=>1100110
[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
[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
[5,3,1,2,4,8,7,6]=>0101011=>1101010
[5,3,6,2,1,8,7,4]=>1001111=>1111001
[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
[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
[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
[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
[1,6,4,5,8,2,3,7]=>0000101=>1010000
[1,8,5,3,6,7,4,2]=>0011011=>1101100
[8,3,5,2,1,7,4,6]=>1001011=>1101001
[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
[1,4,8,5,6,7,2,3]=>0000011=>1100000
[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
[7,3,2,4,8,6,5,1]=>0101111=>1111010
[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
[4,2,1,7,3,6,8,5]=>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
[4,2,1,3,5,7,6,8]=>1010010=>0100101
[4,8,1,7,3,6,5,2]=>0001111=>1111000
[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
[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
[3,1,8,5,2,7,6,4]=>0101111=>1111010
[8,3,7,6,1,4,5,2]=>0001111=>1111000
[3,1,7,8,2,5,6,4]=>0100101=>1010010
[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
[6,4,8,1,2,5,3,7]=>0001101=>1011000
[6,7,3,1,4,8,5,2]=>0101011=>1101010
[6,5,1,2,3,4,8,7]=>0001101=>1011000
[6,7,4,1,2,5,3,8]=>0011010=>0101100
[1,2,6,7,5,3,8,4]=>0001011=>1101000
[1,7,5,3,2,8,4,6]=>0101011=>1101010
[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
[1,2,4,8,3,5,7,6]=>0000011=>1100000
[1,3,8,4,2,6,7,5]=>0010011=>1100100
[1,4,8,2,3,5,7,6]=>0000011=>1100000
[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
[1,5,6,8,3,4,2,7]=>0010001=>1000100
[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
[1,4,5,7,3,8,6,2]=>0000111=>1110000
[4,6,3,7,8,5,2,1]=>1001101=>1011001
[1,5,3,6,7,8,4,2]=>0011001=>1001100
[4,6,1,7,3,8,5,2]=>0001111=>1111000
[6,7,2,4,8,1,5,3]=>0001011=>1101000
[5,2,3,6,7,8,4,1]=>0011001=>1001100
[6,4,2,7,1,8,3,5]=>0010111=>1110100
[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
[7,2,4,8,6,1,3,5]=>0000111=>1110000
[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
[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
[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
[6,4,5,2,3,8,7,1]=>0001111=>1111000
[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
[4,6,5,2,3,8,7,1]=>0001111=>1111000
[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
[6,4,5,8,7,2,3,1]=>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
[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
[6,2,8,4,7,5,3,1]=>0101111=>1111010
[8,2,6,4,7,5,3,1]=>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
[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
[4,5,2,1,8,3,7,6]=>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
[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
[5,1,4,2,3,8,7,6]=>0011011=>1101100
[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
[3,5,4,1,8,7,2,6]=>0011011=>1101100
[3,6,5,8,7,1,2,4]=>0000111=>1110000
[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
[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
[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
[4,1,7,3,6,2,5,8]=>0010110=>0110100
[5,8,7,6,1,2,4,3]=>0010111=>1110100
[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
[3,8,5,6,2,4,1,7]=>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
[4,2,6,7,5,3,1,8]=>0111010=>0101110
[3,2,6,1,4,5,8,7]=>0100101=>1010010
[2,8,7,3,4,5,1,6]=>0001011=>1101000
[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
[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
[2,3,6,1,5,4,7,8]=>0001100=>0011000
[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
[6,5,2,1,3,7,4,8]=>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
[5,7,1,6,2,3,8,4]=>0000111=>1110000
[5,6,3,1,2,7,4,8]=>0100110=>0110010
[4,2,5,3,1,6,7,8]=>0111000=>0001110
[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
[5,6,2,4,7,8,1,3]=>0000101=>1010000
[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
[5,8,7,3,2,6,4,1]=>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
[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
[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
[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
[4,6,1,5,2,3,8,7]=>0001101=>1011000
[2,6,7,5,1,8,4,3]=>0011011=>1101100
[7,6,5,2,8,3,4,1]=>0011111=>1111100
[2,4,7,6,5,8,1,3]=>0000111=>1110000
[2,1,4,8,7,6,3,5]=>1000111=>1110001
[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
[7,8,6,1,3,5,2,4]=>0001101=>1011000
[2,5,1,8,6,7,4,3]=>0011011=>1101100
[3,5,1,8,6,7,4,2]=>0011011=>1101100
[8,3,5,4,6,7,1,2]=>0001011=>1101000
[5,1,3,8,6,7,4,2]=>0011011=>1101100
[5,6,3,2,8,1,4,7]=>0100101=>1010010
[8,1,6,3,5,2,7,4]=>0001111=>1111000
[4,7,6,8,3,2,5,1]=>0101011=>1101010
[2,7,5,8,1,3,4,6]=>0000011=>1100000
[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
[3,6,8,2,4,1,7,5]=>0010011=>1100100
[4,5,8,2,6,7,3,1]=>0100011=>1100010
[2,5,8,4,6,7,3,1]=>0100011=>1100010
[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
[5,8,4,1,6,7,2,3]=>0010011=>1100100
[3,8,1,4,6,7,2,5]=>0000011=>1100000
[1,6,4,5,2,3,7,8]=>0001100=>0011000
[1,7,4,5,2,3,6,8]=>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
[1,8,5,7,3,4,2,6]=>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
[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
[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
[7,6,2,3,8,1,4,5]=>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
[7,5,8,1,3,6,2,4]=>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
[4,1,8,7,2,3,5,6]=>0010011=>1100100
[5,1,8,7,2,3,4,6]=>0001011=>1101000
[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
[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
[6,4,2,7,5,3,1,8]=>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
[4,8,7,3,5,1,2,6]=>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
[6,4,3,7,5,1,2,8]=>0011110=>0111100
[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
[5,3,6,2,4,7,8,1]=>0001101=>1011000
[5,3,6,1,4,8,7,2]=>0001111=>1111000
[5,3,7,2,4,6,8,1]=>0001011=>1101000
[4,2,1,5,8,6,3,7]=>1010101=>1010101
[4,2,1,5,8,6,7,3]=>1010011=>1100101
[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
[6,7,2,1,8,4,5,3]=>1001011=>1101001
[3,2,1,8,5,6,4,7]=>1100101=>1010011
[4,3,1,6,7,8,5,2]=>0111001=>1001110
[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
[5,2,6,1,8,7,3,4]=>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
[4,2,1,7,8,6,3,5]=>1010101=>1010101
[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
[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
[7,4,8,6,2,5,3,1]=>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
[6,3,8,2,4,5,1,7]=>0001101=>1011000
[6,3,8,2,5,7,4,1]=>0010111=>1110100
[5,6,7,3,8,2,4,1]=>0010011=>1100100
[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
[6,5,3,1,4,2,7,8]=>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
[2,7,8,5,4,1,6,3]=>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
[2,1,8,5,6,4,3,7]=>1010101=>1010101
[4,2,1,8,5,6,3,7]=>1010101=>1010101
[6,3,4,2,1,8,5,7]=>1010101=>1010101
[3,8,5,6,4,2,1,7]=>1010101=>1010101
[3,6,4,2,1,8,5,7]=>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
[6,3,7,8,4,2,1,5]=>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
[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
[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
[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
[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
[4,7,2,1,3,6,8,5]=>1000011=>1100001
[5,7,1,3,2,6,8,4]=>0100011=>1100010
[6,7,1,2,4,5,8,3]=>0000011=>1100000
[1,8,2,3,5,6,7,4]=>0000011=>1100000
[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
[8,7,5,2,6,3,4,1]=>0011111=>1111100
[8,6,5,2,7,3,4,1]=>0011111=>1111100
[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
[1,2,6,4,8,5,7,3]=>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
[6,5,8,1,4,3,2,7]=>0110101=>1010110
[1,6,3,2,7,4,8,5]=>0100111=>1110010
[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
[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
[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
[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
[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
[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
[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
[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
[6,3,1,7,4,2,8,5]=>0110111=>1110110
[8,5,7,6,2,3,1,4]=>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
[2,6,5,8,3,1,7,4]=>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
[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
[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
[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
[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
[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
[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
[5,3,2,6,4,7,1,8]=>0101110=>0111010
[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
[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
[1,8,2,3,4,7,6,5]=>0000111=>1110000
[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
[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
[6,8,1,3,4,7,2,5]=>0000011=>1100000
[8,6,2,3,4,1,7,5]=>0010111=>1110100
[8,3,2,7,4,5,1,6]=>0101011=>1101010
[6,7,2,3,4,1,8,5]=>0010011=>1100100
[8,6,2,3,4,7,1,5]=>0000111=>1110000
[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
[2,8,7,6,4,1,3,5]=>0010111=>1110100
[7,8,2,6,5,1,3,4]=>0001101=>1011000
[1,8,7,6,2,4,3,5]=>0010111=>1110100
[2,8,1,4,5,6,7,3]=>0000011=>1100000
[2,1,7,3,6,5,8,4]=>1000111=>1110001
[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
[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
[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
[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
[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
[4,6,1,2,8,5,3,7]=>0001101=>1011000
[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
[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
[8,5,6,1,3,2,4,7]=>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
[8,2,7,5,1,3,4,6]=>0001011=>1101000
[8,4,1,7,5,2,3,6]=>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
[8,1,5,6,7,2,3,4]=>0000011=>1100000
[6,5,7,1,8,2,3,4]=>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
[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
[5,7,3,4,6,8,1,2]=>0000011=>1100000
[5,7,3,4,6,1,2,8]=>0000110=>0110000
[7,3,5,6,1,2,8,4]=>0000111=>1110000
[5,7,3,1,4,6,8,2]=>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
[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
[2,6,4,8,7,5,1,3]=>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
[2,3,5,7,6,1,8,4]=>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
[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
[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
[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
[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
[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
[4,2,3,6,1,5,8,7]=>0010101=>1010100
[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
[5,2,8,3,7,6,1,4]=>0001111=>1111000
[8,2,7,3,1,6,4,5]=>0100111=>1110010
[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
[8,4,7,1,5,6,3,2]=>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
[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
[3,5,8,7,1,2,6,4]=>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
[4,2,8,6,7,1,5,3]=>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
[7,4,2,6,1,5,3,8]=>0011110=>0111100
[7,4,2,5,6,1,3,8]=>0010110=>0110100
[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
[6,4,3,1,8,2,7,5]=>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
[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
[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
[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
[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
[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
[4,5,6,2,8,7,3,1]=>0100111=>1110010
[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
[2,6,1,3,7,5,4,8]=>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
[5,4,1,6,2,7,3,8]=>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
[4,1,6,3,2,7,8,5]=>0110101=>1010110
[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
[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
[5,2,7,8,3,6,4,1]=>0011101=>1011100
[4,6,7,8,2,5,3,1]=>0101001=>1001010
[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
[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
[3,7,4,5,8,6,2,1]=>1000111=>1110001
[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
[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
[1,4,5,8,7,2,3,6]=>0000011=>1100000
[1,2,5,8,3,6,4,7]=>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
[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
[1,6,8,2,3,4,7,5]=>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
[1,6,7,2,3,8,5,4]=>0001011=>1101000
[1,2,5,6,3,8,7,4]=>0000111=>1110000
[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
[8,4,1,5,3,2,6,7]=>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
[7,1,8,4,3,5,6,2]=>0010111=>1110100
[6,7,3,1,8,4,5,2]=>0101011=>1101010
[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
[2,6,7,8,5,3,4,1]=>0011001=>1001100
[6,2,7,8,4,5,3,1]=>0101101=>1011010
[1,7,2,8,4,5,6,3]=>0000111=>1110000
[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
[4,1,7,8,6,2,3,5]=>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
[1,5,8,3,4,7,6,2]=>0000111=>1110000
[7,8,5,2,4,1,6,3]=>0011101=>1011100
[7,1,2,3,5,6,4,8]=>0000110=>0110000
[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
[3,7,1,8,6,4,2,5]=>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
[6,7,3,5,1,4,8,2]=>0001011=>1101000
[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
[5,3,6,7,4,8,2,1]=>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
[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
[5,7,8,2,4,6,3,1]=>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
[4,5,7,3,8,6,2,1]=>1000111=>1110001
[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
[1,8,2,5,3,6,7,4]=>0001011=>1101000
[2,6,8,4,3,5,7,1]=>0010011=>1100100
[7,2,8,4,1,5,6,3]=>0010111=>1110100
[7,5,8,1,2,6,3,4]=>0000111=>1110000
[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
[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
[6,1,2,8,5,4,7,3]=>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
[6,5,2,3,8,7,1,4]=>0001111=>1111000
[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
[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
[6,4,1,7,8,5,2,3]=>0011101=>1011100
[7,6,1,2,4,8,3,5]=>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
[2,8,6,1,4,7,3,5]=>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
[8,5,2,4,7,3,1,6]=>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
[8,6,4,1,7,2,5,3]=>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
[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
[2,3,5,8,1,4,7,6]=>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
[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
[2,8,6,3,1,4,5,7]=>0100101=>1010010
[8,3,5,2,1,4,6,7]=>1001001=>1001001
[2,5,8,1,7,3,6,4]=>0000111=>1110000
[2,8,1,5,7,3,6,4]=>0000111=>1110000
[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
[6,8,4,5,1,7,2,3]=>0001011=>1101000
[5,1,8,7,6,2,3,4]=>0001111=>1111000
[4,6,1,8,7,5,2,3]=>0001111=>1111000
[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
[6,5,1,8,2,7,3,4]=>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
[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
[5,8,2,1,4,7,3,6]=>1000011=>1100001
[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
[5,4,7,2,1,6,8,3]=>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
[6,3,2,1,7,4,5,8]=>1100110=>0110011
[6,4,2,1,7,5,3,8]=>1011110=>0111101
[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
[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
[7,2,8,4,3,1,5,6]=>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
[5,3,1,7,8,4,6,2]=>0101101=>1011010
[5,3,2,7,8,4,6,1]=>0101101=>1011010
[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
[2,7,6,1,3,4,8,5]=>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
[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
[4,6,7,8,3,1,5,2]=>0101001=>1001010
[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
[3,2,7,8,4,6,1,5]=>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
[3,6,1,2,5,8,4,7]=>0000101=>1010000
[1,4,5,8,2,3,7,6]=>0000011=>1100000
[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
[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
[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
[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
[1,8,3,2,7,5,6,4]=>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
[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
[1,7,5,3,8,2,4,6]=>0001011=>1101000
[1,7,2,4,5,8,3,6]=>0000011=>1100000
[1,7,4,5,8,3,2,6]=>0100011=>1100010
[2,6,4,7,8,3,5,1]=>0001101=>1011000
[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
[3,7,4,5,2,1,8,6]=>1001011=>1101001
[1,3,6,4,7,2,8,5]=>0000111=>1110000
[3,6,4,7,2,8,5,1]=>0001111=>1111000
[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
[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
[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
[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
[6,7,2,1,5,8,4,3]=>1010011=>1100101
[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
[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
[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
[8,6,4,1,3,7,2,5]=>0010111=>1110100
[6,4,3,1,8,2,5,7]=>0110101=>1010110
[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
[4,6,2,8,7,1,5,3]=>0001111=>1111000
[4,8,6,3,7,1,5,2]=>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
[4,1,6,8,7,3,5,2]=>0011011=>1101100
[4,1,6,8,7,5,3,2]=>0111011=>1101110
[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
[5,6,8,7,4,2,1,3]=>1010011=>1100101
[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
[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
[2,1,5,8,4,3,6,7]=>1010001=>1000101
[5,8,3,2,7,1,4,6]=>0100011=>1100010
[5,1,8,3,7,2,4,6]=>0001011=>1101000
[5,1,8,4,6,2,3,7]=>0001101=>1011000
[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
[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
[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
[6,7,5,8,3,1,4,2]=>0110011=>1100110
[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
[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
[7,8,1,2,6,3,4,5]=>0000101=>1010000
[7,8,5,1,4,6,3,2]=>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
[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
[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
[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
[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
[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
[6,5,4,2,7,8,9,1,3,10]=>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
[11,12,9,10,6,5,7,8,3,4,1,2]=>00101010101=>10101010100
[11,12,9,10,6,5,7,8,2,1,3,4]=>10001010101=>10101010001
[11,12,9,10,5,4,3,6,7,8,1,2]=>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
[11,12,5,4,3,2,1,6,7,8,9,10]=>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
[10,9,11,12,6,5,7,8,3,4,1,2]=>00101010101=>10101010100
[10,9,11,12,6,5,7,8,2,1,3,4]=>10001010101=>10101010001
[10,9,11,12,5,4,3,6,7,8,1,2]=>00110010101=>10101001100
[10,9,11,12,5,3,2,6,1,4,7,8]=>01011000101=>10100011010
[10,8,11,6,9,3,7,2,1,4,5,12]=>10000101110=>01110100001
[10,8,11,4,9,3,2,1,5,6,7,12]=>11000001110=>01110000011
[10,7,11,6,3,8,9,2,1,4,5,12]=>10001001110=>01110010001
[9,7,6,10,3,8,11,2,1,4,5,12]=>10000101110=>01110100001
[9,7,5,10,4,8,2,6,11,1,3,12]=>00000111110=>01111100000
[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
[7,4,2,1,8,6,3,5]=>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
[2,4,5,1,3,8,7,6]=>0001011=>1101000
[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
[7,4,6,3,1,8,5,2]=>0101111=>1111010
[6,3,1,7,4,8,5,2]=>0101111=>1111010
[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
[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
[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
[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
[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
[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
[6,1,3,2,4,8,7,5]=>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
[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
[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
[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
[8,5,1,3,7,4,2,6]=>0011011=>1101100
[3,8,6,1,5,2,7,4]=>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
[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
[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
[6,1,4,2,5,3,7,8]=>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
[5,2,6,3,4,7,1,8]=>0001110=>0111000
[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
[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
[2,7,6,5,8,1,4,3]=>0010111=>1110100
[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
[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
[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
[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
[4,6,3,8,5,7,2,1]=>1000111=>1110001
[7,5,3,8,6,2,4,1]=>0011111=>1111100
[2,6,8,3,7,4,5,1]=>0001011=>1101000
[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
[1,8,5,6,4,7,3,2]=>0100111=>1110010
[2,5,8,6,4,7,3,1]=>0100111=>1110010
[6,3,7,8,4,5,2,1]=>1001101=>1011001
[4,3,7,8,5,6,2,1]=>1010101=>1010101
[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
[4,3,6,8,5,7,2,1]=>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
[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
[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
[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
[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
[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
[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
[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
[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
[2,7,8,4,5,1,6,3]=>0001101=>1011000
[5,6,3,8,1,4,7,2]=>0000111=>1110000
[8,4,1,2,5,6,7,3]=>0010011=>1100100
[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
[3,5,4,7,6,1,2,8]=>0001110=>0111000
[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
[3,5,2,7,6,4,1,8]=>0011110=>0111100
[3,5,7,2,6,4,1,8]=>0010110=>0110100
[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
[3,5,7,2,1,6,4,8]=>1000110=>0110001
[5,3,7,1,6,2,4,8]=>0001110=>0111000
[3,5,7,1,4,6,8,2]=>0000011=>1100000
[3,5,7,1,4,2,6,8]=>0010010=>0100100
[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
[3,5,4,7,2,1,8,6]=>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
[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
[5,7,8,2,4,1,6,3]=>0010101=>1010100
[4,2,5,8,1,6,7,3]=>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
[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
[4,5,6,1,7,3,8,2]=>0000111=>1110000
[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
[7,6,1,4,5,3,8,2]=>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
[7,6,5,8,3,1,4,2]=>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
[5,3,1,4,2,6,7,8]=>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
[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
[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
[6,4,8,5,2,3,7,1]=>0001111=>1111000
[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
[2,1,6,8,4,5,7,3]=>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
[5,1,8,3,6,4,7,2]=>0001111=>1111000
[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
[6,2,8,4,3,7,5,1]=>0011111=>1111100
[3,6,5,8,7,1,4,2]=>0010111=>1110100
[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
[6,3,4,8,2,7,5,1]=>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
[6,3,1,8,7,5,2,4]=>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
[8,4,2,5,7,6,3,1]=>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
[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
[7,5,2,1,3,6,4,8]=>1001110=>0111001
[8,7,5,2,1,3,6,4]=>1001111=>1111001
[1,3,7,6,5,8,2,4]=>0000111=>1110000
[8,6,4,7,5,2,1,3]=>1001111=>1111001
[6,4,7,5,2,1,3,8]=>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
[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
[6,3,5,2,7,4,1,8]=>0011110=>0111100
[4,6,7,2,5,3,1,8]=>0101010=>0101010
[3,6,7,4,8,1,5,2]=>0001011=>1101000
[3,4,6,8,7,1,5,2]=>0001011=>1101000
[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
[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
[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
[3,6,4,2,7,8,1,5]=>0010101=>1010100
[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
[7,6,1,3,8,4,2,5]=>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
[7,2,3,8,5,6,4,1]=>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
[4,3,7,1,6,2,8,5]=>0010111=>1110100
[5,4,8,2,6,3,7,1]=>0001111=>1111000
[4,1,7,5,2,3,6,8]=>0011010=>0101100
[4,1,7,8,6,3,2,5]=>0110101=>1010110
[1,2,6,8,3,7,4,5]=>0000011=>1100000
[6,8,3,2,1,4,7,5]=>1100011=>1100011
[6,8,2,4,1,3,7,5]=>0010011=>1100100
[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
[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
[5,8,2,4,3,7,6,1]=>0010111=>1110100
[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
[2,4,6,7,8,1,5,3]=>0001001=>1001000
[2,4,6,8,1,7,5,3]=>0001011=>1101000
[7,4,3,8,6,2,1,5]=>1010111=>1110101
[4,3,6,2,1,8,5,7]=>1010101=>1010101
[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
[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
[1,2,6,5,8,7,3,4]=>0000111=>1110000
[5,6,3,4,8,7,2,1]=>1000111=>1110001
[6,5,3,4,8,7,2,1]=>1001111=>1111001
[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
[6,1,8,2,3,5,7,4]=>0000111=>1110000
[6,1,7,2,3,5,8,4]=>0000111=>1110000
[4,3,8,7,5,6,2,1]=>1010111=>1110101
[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
[8,6,1,2,3,4,7,5]=>0000111=>1110000
[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
[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
[8,2,1,5,7,6,4,3]=>1010111=>1110101
[6,1,8,2,7,5,4,3]=>0011111=>1111100
[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
[6,2,8,1,5,7,3,4]=>0000111=>1110000
[7,2,5,4,1,8,6,3]=>0011111=>1111100
[7,3,2,8,5,6,1,4]=>0100111=>1110010
[4,7,6,5,1,3,8,2]=>0001111=>1111000
[5,4,6,8,7,2,1,3]=>1001011=>1101001
[1,7,6,3,2,8,4,5]=>0100111=>1110010
[5,4,2,1,7,3,6,8]=>1011010=>0101101
[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
[3,7,6,2,8,4,5,1]=>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
[4,1,2,7,8,5,3,6]=>0011001=>1001100
[4,7,3,1,2,6,8,5]=>0100011=>1100010
[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
[5,2,1,4,7,8,3,6]=>1001001=>1001001
[5,6,2,7,3,4,8,1]=>0000111=>1110000
[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
[7,4,6,2,8,3,5,1]=>0001111=>1111000
[3,4,6,5,1,2,7,8]=>0001100=>0011000
[4,3,8,2,5,7,1,6]=>0010011=>1100100
[4,1,6,2,5,3,7,8]=>0011100=>0011100
[4,2,6,1,5,3,8,7]=>0011101=>1011100
[6,7,2,3,1,5,8,4]=>0100011=>1100010
[2,1,5,7,8,3,6,4]=>1000101=>1010001
[4,7,5,8,6,3,1,2]=>0100111=>1110010
[7,3,2,5,8,1,6,4]=>0100111=>1110010
[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
[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
[5,6,2,7,4,3,1,8]=>0110110=>0110110
[3,7,8,2,6,1,4,5]=>0000101=>1010000
[3,7,8,5,2,1,4,6]=>1001001=>1001001
[4,8,6,5,1,2,7,3]=>0001111=>1111000
[4,8,6,5,1,2,3,7]=>0001101=>1011000
[3,8,7,6,5,1,2,4]=>0001111=>1111000
[5,8,2,6,1,4,7,3]=>0000111=>1110000
[3,8,7,5,6,1,4,2]=>0010111=>1110100
[7,4,6,5,1,3,8,2]=>0001111=>1111000
[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
[3,5,8,1,7,6,2,4]=>0000111=>1110000
[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
[1,3,8,2,5,7,6,4]=>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
[2,1,8,3,5,7,6,4]=>1000111=>1110001
[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
[5,6,8,1,4,2,3,7]=>0010001=>1000100
[5,7,4,8,1,2,3,6]=>0000011=>1100000
[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
[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
[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
[3,7,1,2,8,4,6,5]=>0000111=>1110000
[1,5,8,7,6,2,3,4]=>0000111=>1110000
[7,8,6,1,5,2,3,4]=>0001101=>1011000
[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
[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
[1,3,8,7,6,2,4,5]=>0000111=>1110000
[1,4,6,8,7,2,3,5]=>0000011=>1100000
[7,6,4,8,5,1,3,2]=>0101111=>1111010
[7,2,6,5,8,1,3,4]=>0000111=>1110000
[3,6,7,5,2,8,4,1]=>0011011=>1101100
[4,6,5,7,2,8,1,3]=>0000111=>1110000
[5,3,6,7,8,1,4,2]=>0011001=>1001100
[6,3,2,8,5,4,1,7]=>0111101=>1011110
[3,8,4,1,5,2,6,7]=>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
[3,1,7,2,5,6,4,8]=>0100110=>0110010
[3,7,5,4,2,1,6,8]=>1011010=>0101101
[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
[5,6,3,8,7,4,1,2]=>0010111=>1110100
[5,2,6,8,7,4,1,3]=>0011011=>1101100
[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
[4,2,7,3,8,5,1,6]=>0011011=>1101100
[5,3,1,2,4,8,6,7]=>0101001=>1001010
[1,3,2,6,4,8,7,5]=>0100111=>1110010
[1,6,2,5,3,8,7,4]=>0001111=>1111000
[1,8,2,6,3,7,5,4]=>0001111=>1111000
[1,8,3,6,4,7,5,2]=>0001111=>1111000
[1,7,2,6,3,8,5,4]=>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
[2,6,3,8,1,5,4,7]=>0001101=>1011000
[8,3,1,4,2,6,5,7]=>0110101=>1010110
[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
[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
[3,7,5,4,6,2,8,1]=>0001111=>1111000
[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
[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
[7,8,4,1,6,3,5,2]=>0011101=>1011100
[8,7,5,6,1,3,4,2]=>0010111=>1110100
[1,4,5,8,6,3,2,7]=>0100101=>1010010
[8,4,5,7,2,6,1,3]=>0000111=>1110000
[8,1,7,5,3,6,2,4]=>0001111=>1111000
[5,2,6,3,1,7,8,4]=>0101101=>1011010
[5,7,6,1,2,3,8,4]=>0000111=>1110000
[5,3,2,1,8,6,4,7]=>1101101=>1011011
[4,3,6,2,1,8,7,5]=>1010111=>1110101
[5,3,6,4,8,2,1,7]=>1001101=>1011001
[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
[3,8,5,6,2,7,1,4]=>0000111=>1110000
[2,4,5,8,7,3,1,6]=>0100011=>1100010
[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
[4,5,1,8,6,7,3,2]=>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
[3,8,6,5,2,7,4,1]=>0011111=>1111100
[3,8,7,5,2,1,4,6]=>1001011=>1101001
[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
[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
[2,6,7,4,3,8,5,1]=>0011011=>1101100
[1,2,6,7,4,3,8,5]=>0010011=>1100100
[1,7,5,8,2,4,3,6]=>0010011=>1100100
[2,7,1,8,4,6,3,5]=>0000111=>1110000
[2,7,5,8,1,6,3,4]=>0000111=>1110000
[1,6,7,3,8,5,4,2]=>0011011=>1101100
[6,7,1,8,4,5,3,2]=>0101011=>1101010
[8,6,1,5,4,3,2,7]=>0111101=>1011110
[2,4,3,8,5,1,6,7]=>0011001=>1001100
[1,5,6,7,3,8,2,4]=>0000011=>1100000
[1,6,5,4,8,3,2,7]=>0101101=>1011010
[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
[4,8,1,7,5,3,2,6]=>0101011=>1101010
[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
[6,4,1,7,5,3,2,8]=>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
[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
[1,8,6,3,4,2,5,7]=>0010101=>1010100
[3,1,6,4,5,8,7,2]=>0100111=>1110010
[3,1,6,4,5,7,2,8]=>0100110=>0110010
[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
[8,2,7,6,1,4,5,3]=>0001111=>1111000
[5,2,3,7,1,6,8,4]=>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
[4,1,6,5,7,8,2,3]=>0010101=>1010100
[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
[5,1,4,6,7,8,2,3]=>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
[8,1,7,6,4,2,5,3]=>0011111=>1111100
[1,3,6,4,7,8,2,5]=>0000101=>1010000
[5,1,3,4,7,8,2,6]=>0001001=>1001000
[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
[3,2,6,4,1,8,5,7]=>0110101=>1010110
[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
[4,2,5,1,7,8,3,6]=>0011001=>1001100
[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
[3,7,2,8,1,5,4,6]=>0001011=>1101000
[7,3,8,1,6,5,4,2]=>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
[6,4,7,1,5,3,2,8]=>0101110=>0111010
[3,4,6,2,1,8,5,7]=>1000101=>1010001
[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
[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
[6,8,3,2,1,7,4,5]=>1100011=>1100011
[3,7,6,2,4,8,1,5]=>0000111=>1110000
[4,3,7,2,8,6,1,5]=>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
[6,2,5,4,1,8,7,3]=>0011111=>1111100
[4,6,3,2,1,8,7,5]=>1100111=>1110011
[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
[6,4,3,8,5,2,1,7]=>1011101=>1011101
[8,2,5,4,7,6,1,3]=>0001111=>1111000
[7,2,5,4,8,6,1,3]=>0001111=>1111000
[6,2,8,7,5,4,1,3]=>0011111=>1111100
[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
[6,3,2,1,8,7,4,5]=>1100111=>1110011
[6,2,3,1,8,7,4,5]=>0100111=>1110010
[3,4,8,1,7,5,6,2]=>0000111=>1110000
[7,2,1,5,8,4,6,3]=>1000111=>1110001
[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
[6,7,1,4,3,8,5,2]=>0011011=>1101100
[7,1,6,4,8,3,5,2]=>0001111=>1111000
[8,5,3,6,1,7,4,2]=>0011111=>1111100
[8,5,6,1,2,7,4,3]=>0010111=>1110100
[3,6,1,5,7,8,2,4]=>0000101=>1010000
[2,1,5,8,6,3,7,4]=>1000111=>1110001
[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
[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
[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
[6,3,2,4,7,1,8,5]=>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
[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
[1,2,5,3,6,8,7,4]=>0001011=>1101000
[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
[1,3,7,8,5,6,2,4]=>0000101=>1010000
[7,5,4,8,6,1,2,3]=>0001111=>1111000
[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
[8,1,3,7,5,6,4,2]=>0010111=>1110100
[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
[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
[8,4,7,6,5,1,2,3]=>0001111=>1111000
[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
[8,2,5,7,1,4,6,3]=>0000111=>1110000
[3,5,8,1,7,4,6,2]=>0000111=>1110000
[8,4,7,1,3,6,5,2]=>0001111=>1111000
[5,1,7,8,3,4,2,6]=>0011001=>1001100
[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
[6,8,1,2,5,7,4,3]=>0010011=>1100100
[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
[6,4,7,1,3,2,8,5]=>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
[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
[3,5,6,8,1,4,2,7]=>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
[6,5,3,7,2,4,8,1]=>0001111=>1111000
[5,6,2,8,4,3,7,1]=>0010111=>1110100
[4,6,2,7,8,3,5,1]=>0001101=>1011000
[3,1,2,4,8,5,7,6]=>0100011=>1100010
[5,1,2,4,6,7,8,3]=>0001001=>1001000
[4,6,3,5,2,8,7,1]=>0001111=>1111000
[5,3,2,6,8,4,7,1]=>0101011=>1101010
[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
[5,4,2,8,6,3,7,1]=>0011111=>1111100
[5,7,4,2,6,3,8,1]=>0010111=>1110100
[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
[6,3,7,8,2,4,5,1]=>0001101=>1011000
[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
[5,7,3,2,6,4,8,1]=>0100111=>1110010
[5,3,2,8,6,4,7,1]=>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
[6,3,7,5,2,4,8,1]=>0001111=>1111000
[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
[6,3,8,5,4,7,2,1]=>1001111=>1111001
[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
[1,6,7,2,5,3,4,8]=>0001010=>0101000
[1,8,6,2,7,3,4,5]=>0000111=>1110000
[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
[1,7,3,2,6,8,4,5]=>0100011=>1100010
[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
[1,6,2,8,5,4,3,7]=>0011101=>1011100
[1,7,2,3,8,6,4,5]=>0000111=>1110000
[1,5,3,8,2,7,4,6]=>0001011=>1101000
[1,7,2,5,3,4,8,6]=>0001011=>1101000
[1,4,8,2,5,6,3,7]=>0000101=>1010000
[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
[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
[8,3,5,1,7,6,2,4]=>0001111=>1111000
[3,5,6,1,8,7,2,4]=>0000111=>1110000
[2,4,6,8,7,3,1,5]=>0100011=>1100010
[7,2,4,8,6,3,1,5]=>0100111=>1110010
[2,3,6,4,1,8,7,5]=>0010111=>1110100
[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
[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
[6,3,1,2,4,8,7,5]=>0100111=>1110010
[2,6,4,5,8,1,3,7]=>0000101=>1010000
[6,4,1,3,5,8,2,7]=>0010101=>1010100
[3,1,6,4,8,7,5,2]=>0101111=>1111010
[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
[3,7,8,4,2,6,5,1]=>0011101=>1011100
[7,1,3,8,4,5,6,2]=>0000111=>1110000
[7,8,1,4,3,5,6,2]=>0010101=>1010100
[3,6,7,1,8,2,5,4]=>0001011=>1101000
[3,1,5,7,2,8,6,4]=>0100111=>1110010
[4,1,8,3,2,7,6,5]=>0110111=>1110110
[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
[2,4,6,5,1,3,8,7]=>0001101=>1011000
[2,3,4,6,8,7,1,5]=>0000011=>1100000
[2,1,4,6,8,7,3,5]=>1000011=>1100001
[6,7,2,8,3,1,4,5]=>0100011=>1100010
[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
[4,1,3,7,8,5,2,6]=>0011001=>1001100
[4,3,1,8,5,2,7,6]=>0111011=>1101110
[3,1,8,5,4,2,7,6]=>0111011=>1101110
[5,1,3,2,4,7,8,6]=>0101001=>1001010
[2,3,7,8,5,4,1,6]=>0011001=>1001100
[2,4,8,5,6,1,7,3]=>0000111=>1110000
[2,8,7,4,5,1,6,3]=>0001111=>1111000
[1,3,8,5,2,6,7,4]=>0001011=>1101000
[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
[8,1,2,5,3,6,7,4]=>0001011=>1101000
[8,2,6,4,3,5,1,7]=>0011101=>1011100
[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
[8,4,2,7,5,1,6,3]=>0011111=>1111100
[3,8,7,5,4,1,2,6]=>0011011=>1101100
[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
[8,1,6,3,5,4,7,2]=>0001111=>1111000
[7,1,4,8,3,6,5,2]=>0001111=>1111000
[8,3,2,7,4,6,5,1]=>0101111=>1111010
[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
[8,7,1,6,5,2,3,4]=>0001111=>1111000
[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
[8,1,7,6,5,2,3,4]=>0001111=>1111000
[8,7,2,6,5,1,3,4]=>0001111=>1111000
[1,4,8,6,7,5,3,2]=>0101011=>1101010
[8,6,2,5,7,4,3,1]=>0110111=>1110110
[7,1,3,6,8,5,4,2]=>0011011=>1101100
[8,1,7,6,4,5,3,2]=>0101111=>1111010
[7,1,8,6,4,5,3,2]=>0101111=>1111010
[6,7,2,5,8,1,4,3]=>0010011=>1100100
[6,3,7,5,8,2,4,1]=>0010111=>1110100
[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
[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
[4,2,3,1,5,8,6,7]=>0110001=>1000110
[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
[2,1,4,7,8,5,3,6]=>1001001=>1001001
[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
[1,8,3,6,7,4,2,5]=>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
[4,8,1,6,7,3,2,5]=>0100011=>1100010
[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
[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
[8,1,7,2,5,6,4,3]=>0010111=>1110100
[8,1,3,5,2,7,6,4]=>0001111=>1111000
[8,1,7,4,3,6,5,2]=>0011111=>1111100
[2,7,1,5,4,8,6,3]=>0001111=>1111000
[8,6,2,4,3,7,5,1]=>0011111=>1111100
[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
[3,5,6,1,8,7,4,2]=>0010111=>1110100
[2,4,5,1,7,6,3,8]=>0001110=>0111000
[7,3,1,5,6,4,2,8]=>0110110=>0110110
[8,6,2,4,7,3,1,5]=>0100111=>1110010
[8,4,7,3,5,2,1,6]=>1001011=>1101001
[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
[7,6,4,8,1,2,5,3]=>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
[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
[8,7,3,1,4,2,5,6]=>0110011=>1100110
[8,7,4,1,2,5,3,6]=>0011011=>1101100
[8,7,5,1,2,3,6,4]=>0001111=>1111000
[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
[3,5,2,6,4,7,8,1]=>0001101=>1011000
[1,2,5,3,8,6,7,4]=>0001011=>1101000
[2,4,6,3,1,7,5,8]=>0100110=>0110010
[3,4,8,6,5,7,2,1]=>1000111=>1110001
[2,3,8,6,7,1,5,4]=>0001011=>1101000
[1,2,5,7,4,6,8,3]=>0000011=>1100000
[1,2,4,7,6,8,3,5]=>0000011=>1100000
[2,3,6,8,1,7,4,5]=>0000011=>1100000
[2,4,8,5,6,7,1,3]=>0000011=>1100000
[1,4,8,5,6,7,3,2]=>0100011=>1100010
[6,1,3,5,4,2,8,7]=>0011101=>1011100
[2,1,5,8,6,4,7,3]=>1000111=>1110001
[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
[6,7,1,8,3,2,4,5]=>0100011=>1100010
[6,7,2,8,1,3,4,5]=>0000011=>1100000
[1,7,8,5,2,6,3,4]=>0001101=>1011000
[5,8,7,2,6,3,4,1]=>0010111=>1110100
[7,6,2,4,8,1,5,3]=>0001111=>1111000
[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
[5,8,4,7,1,6,3,2]=>0100111=>1110010
[8,5,6,1,4,7,2,3]=>0000111=>1110000
[6,7,4,1,2,5,8,3]=>0010011=>1100100
[3,6,7,5,8,1,2,4]=>0000011=>1100000
[6,5,8,7,4,2,3,1]=>0110111=>1110110
[5,7,6,2,8,3,1,4]=>0100111=>1110010
[2,5,6,3,1,4,8,7]=>0100101=>1010010
[3,8,7,2,1,5,4,6]=>1001011=>1101001
[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
[4,8,5,6,7,2,1,3]=>1000011=>1100001
[5,8,6,2,7,4,1,3]=>0010111=>1110100
[4,6,5,8,7,3,1,2]=>0100111=>1110010
[8,3,1,7,2,6,4,5]=>0100111=>1110010
[8,4,5,1,7,6,2,3]=>0001111=>1111000
[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
[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
[2,8,7,5,3,6,4,1]=>0011111=>1111100
[1,8,7,3,6,4,5,2]=>0001111=>1111000
[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
[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
[2,4,7,8,5,6,1,3]=>0000101=>1010000
[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
[3,4,6,8,2,1,7,5]=>1000011=>1100001
[5,3,4,7,6,1,2,8]=>0001110=>0111000
[2,8,7,1,4,3,6,5]=>0010111=>1110100
[1,2,7,8,4,3,6,5]=>0010101=>1010100
[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
[1,2,8,6,4,3,7,5]=>0010111=>1110100
[6,5,1,8,7,3,2,4]=>0101111=>1111010
[8,3,2,6,1,7,4,5]=>0100111=>1110010
[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
[8,5,2,6,1,4,7,3]=>0001111=>1111000
[2,7,5,8,1,4,6,3]=>0000111=>1110000
[8,5,6,1,7,3,2,4]=>0100111=>1110010
[3,2,6,7,1,8,5,4]=>0101011=>1101010
[3,4,6,7,8,2,1,5]=>1000001=>1000001
[6,7,1,3,8,5,4,2]=>0011011=>1101100
[6,7,1,8,5,2,4,3]=>0011011=>1101100
[1,6,2,7,8,5,3,4]=>0001101=>1011000
[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
[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
[3,7,2,1,8,4,6,5]=>1000111=>1110001
[3,7,2,4,1,8,6,5]=>0010111=>1110100
[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
[4,7,3,8,6,2,1,5]=>1000111=>1110001
[4,3,6,8,7,2,5,1]=>0011011=>1101100
[4,3,8,2,5,7,6,1]=>0010111=>1110100
[4,3,8,1,5,7,6,2]=>0010111=>1110100
[4,1,2,6,8,7,5,3]=>0011011=>1101100
[2,4,3,6,8,7,1,5]=>0010011=>1100100
[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
[4,2,3,6,8,7,1,5]=>0010011=>1100100
[4,2,8,3,5,7,6,1]=>0010111=>1110100
[3,8,2,4,5,7,6,1]=>0000111=>1110000
[3,8,2,4,1,5,7,6]=>0010011=>1100100
[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
[7,3,1,2,5,6,4,8]=>0100110=>0110010
[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
[3,1,7,2,5,6,8,4]=>0100011=>1100010
[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
[4,1,8,6,5,3,7,2]=>0011111=>1111100
[5,7,8,4,6,3,2,1]=>1100101=>1010011
[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
[4,5,2,3,8,6,7,1]=>0001011=>1101000
[4,8,5,3,2,6,7,1]=>0101011=>1101010
[3,8,4,5,2,6,7,1]=>0001011=>1101000
[3,5,4,2,8,6,7,1]=>0011011=>1101100
[4,1,2,7,5,6,8,3]=>0010011=>1100100
[4,8,1,6,5,2,7,3]=>0001111=>1111000
[5,6,7,4,2,8,3,1]=>0110011=>1100110
[2,5,7,4,6,8,3,1]=>0100011=>1100010
[7,3,5,4,2,8,6,1]=>0011111=>1111100
[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
[3,4,5,8,2,6,7,1]=>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
[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
[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
[5,7,4,1,6,8,2,3]=>0010011=>1100100
[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
[7,2,8,4,6,1,3,5]=>0000111=>1110000
[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
[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
[8,5,3,2,1,4,7,6]=>1101011=>1101011
[1,2,7,6,8,4,3,5]=>0010011=>1100100
[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
[1,2,7,8,4,5,3,6]=>0001001=>1001000
[1,5,3,2,7,8,4,6]=>0101001=>1001010
[4,1,8,6,2,3,7,5]=>0010111=>1110100
[1,7,6,4,3,8,5,2]=>0011111=>1111100
[1,8,5,7,6,3,2,4]=>0100111=>1110010
[1,6,3,5,7,8,4,2]=>0010101=>1010100
[1,5,6,3,2,7,8,4]=>0100101=>1010010
[1,8,4,7,5,3,2,6]=>0101011=>1101010
[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
[8,7,6,1,3,5,4,2]=>0011111=>1111100
[8,7,6,1,5,4,2,3]=>0011111=>1111100
[4,5,3,8,2,1,6,7]=>1001001=>1001001
[8,3,5,4,2,1,6,7]=>1011001=>1001101
[7,8,4,3,1,5,2,6]=>0111001=>1001110
[7,5,8,2,1,4,3,6]=>1010011=>1100101
[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
[2,4,7,3,5,6,1,8]=>0000110=>0110000
[5,7,6,4,2,3,1,8]=>0110110=>0110110
[3,1,4,8,5,6,2,7]=>0100101=>1010010
[5,8,2,4,6,1,3,7]=>0000101=>1010000
[2,4,1,8,5,6,3,7]=>0010101=>1010100
[6,1,4,8,5,2,7,3]=>0001111=>1111000
[4,1,2,8,5,3,7,6]=>0011011=>1101100
[2,4,6,8,5,1,7,3]=>0001011=>1101000
[3,1,6,8,5,2,7,4]=>0101011=>1101010
[2,3,8,1,5,6,4,7]=>0000101=>1010000
[5,1,8,2,4,6,7,3]=>0001011=>1101000
[4,1,8,2,3,6,7,5]=>0010011=>1100100
[5,8,2,7,3,4,1,6]=>0010011=>1100100
[3,8,7,5,2,6,1,4]=>0001111=>1111000
[5,3,8,1,6,7,4,2]=>0011011=>1101100
[5,8,2,1,3,7,6,4]=>1000111=>1110001
[4,8,2,1,3,5,6,7]=>1000001=>1000001
[5,1,8,3,6,7,4,2]=>0011011=>1101100
[8,4,1,6,5,2,3,7]=>0011101=>1011100
[6,8,7,3,2,4,1,5]=>0110011=>1100110
[1,3,7,5,6,8,4,2]=>0010011=>1100100
[3,2,4,7,5,8,1,6]=>0100011=>1100010
[1,2,7,4,6,3,8,5]=>0000111=>1110000
[2,8,7,6,4,5,1,3]=>0001111=>1111000
[3,5,2,4,7,6,8,1]=>0001011=>1101000
[3,5,2,4,6,7,8,1]=>0001001=>1001000
[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
[3,2,5,7,4,6,8,1]=>0100011=>1100010
[2,3,5,7,4,6,8,1]=>0000011=>1100000
[3,2,7,5,4,8,6,1]=>0101111=>1111010
[3,7,5,2,4,8,6,1]=>0001111=>1111000
[7,5,3,2,8,6,4,1]=>0111111=>1111110
[2,3,7,5,4,8,6,1]=>0001111=>1111000
[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
[2,4,6,3,8,7,5,1]=>0001111=>1111000
[1,5,3,2,8,7,6,4]=>0101111=>1111010
[6,3,1,8,7,4,2,5]=>0110111=>1110110
[5,3,6,2,8,7,4,1]=>0011111=>1111100
[5,8,3,1,7,6,4,2]=>0110111=>1110110
[6,3,5,2,1,8,7,4]=>1001111=>1111001
[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
[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
[4,2,8,3,6,5,1,7]=>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
[1,3,6,5,2,7,4,8]=>0001110=>0111000
[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
[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
[4,2,8,5,1,6,3,7]=>0011101=>1011100
[6,2,8,4,1,5,3,7]=>0011101=>1011100
[1,4,8,5,2,6,3,7]=>0001101=>1011000
[8,3,7,4,1,5,2,6]=>0011011=>1101100
[7,1,3,2,5,6,4,8]=>0100110=>0110010
[1,5,2,8,7,4,3,6]=>0011011=>1101100
[5,7,2,8,1,4,3,6]=>0010011=>1100100
[2,7,1,5,6,4,3,8]=>0010110=>0110100
[7,1,5,3,2,6,8,4]=>0101011=>1101010
[1,7,3,4,5,2,8,6]=>0001011=>1101000
[8,6,7,3,5,2,1,4]=>1001011=>1101001
[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
[1,8,5,3,2,4,7,6]=>0101011=>1101010
[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
[1,3,8,5,4,2,6,7]=>0011001=>1001100
[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
[2,7,4,1,6,3,5,8]=>0010110=>0110100
[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
[7,1,5,2,6,4,3,8]=>0011110=>0111100
[1,8,5,6,2,7,4,3]=>0010111=>1110100
[4,2,7,6,1,8,5,3]=>0011111=>1111100
[7,3,2,1,6,4,8,5]=>1100111=>1110011
[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
[5,4,7,8,2,3,6,1]=>0001101=>1011000
[4,3,8,2,1,6,7,5]=>1010011=>1100101
[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
[5,6,7,1,8,3,4,2]=>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
[8,1,2,6,4,5,7,3]=>0000111=>1110000
[3,1,8,6,5,2,7,4]=>0101111=>1111010
[2,3,7,6,5,8,1,4]=>0000111=>1110000
[2,3,7,6,5,1,8,4]=>0001111=>1111000
[7,3,5,2,1,6,8,4]=>1001011=>1101001
[3,7,2,6,8,1,5,4]=>0001011=>1101000
[2,7,6,8,5,1,4,3]=>0011011=>1101100
[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
[2,7,6,4,8,1,5,3]=>0001111=>1111000
[3,6,2,1,4,7,8,5]=>1000101=>1010001
[6,3,8,7,5,4,2,1]=>1011111=>1111101
[6,8,2,7,5,4,3,1]=>0111011=>1101110
[5,8,1,7,6,4,3,2]=>0110111=>1110110
[4,2,6,3,8,5,7,1]=>0010111=>1110100
[8,2,6,5,7,3,4,1]=>0010111=>1110100
[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
[8,2,7,4,5,1,6,3]=>0001111=>1111000
[5,8,7,1,4,2,3,6]=>0010011=>1100100
[1,7,5,2,4,8,6,3]=>0001111=>1111000
[2,6,3,7,1,4,5,8]=>0000110=>0110000
[7,2,8,5,3,1,6,4]=>0101111=>1111010
[4,7,6,1,5,8,3,2]=>0100111=>1110010
[4,7,3,8,6,2,5,1]=>0001111=>1111000
[5,4,7,3,8,2,1,6]=>1001011=>1101001
[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
[6,8,3,5,7,2,4,1]=>0010011=>1100100
[3,8,6,2,7,5,1,4]=>0001111=>1111000
[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
[6,7,3,2,5,4,1,8]=>0111010=>0101110
[8,7,3,2,5,4,6,1]=>0101111=>1111010
[4,5,6,2,7,3,1,8]=>0100110=>0110010
[7,3,4,8,2,1,6,5]=>1000111=>1110001
[7,4,8,6,5,1,2,3]=>0001111=>1111000
[3,8,1,7,5,2,4,6]=>0001011=>1101000
[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
[8,1,5,4,6,2,7,3]=>0001111=>1111000
[5,3,7,2,1,8,6,4]=>1001111=>1111001
[5,4,8,3,2,7,1,6]=>0101011=>1101010
[5,4,3,7,2,1,6,8]=>1011010=>0101101
[5,4,3,7,8,2,6,1]=>0011101=>1011100
[5,4,3,8,2,6,7,1]=>0011011=>1101100
[5,4,3,7,8,2,1,6]=>1011001=>1001101
[6,1,3,5,8,7,4,2]=>0010111=>1110100
[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
[5,2,4,6,1,3,8,7]=>0001101=>1011000
[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
[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
[3,2,4,5,1,8,6,7]=>0101001=>1001010
[4,2,5,6,8,7,3,1]=>0110011=>1100110
[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
[7,8,1,3,5,4,2,6]=>0011001=>1001100
[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
[3,5,7,6,4,8,1,2]=>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
[1,7,8,5,6,3,2,4]=>0100101=>1010010
[5,7,6,8,1,3,4,2]=>0010011=>1100100
[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
[7,2,8,6,5,1,4,3]=>0011111=>1111100
[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
[1,4,2,6,3,10,9,5,7,8]=>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
[3,2,5,4,1,12,11,10,6,7,8,9]=>01110000111=>11100001110
[3,2,7,6,4,5,9,8,1,12,10,11]=>01001111001=>10011110010
[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
[3,2,9,8,7,4,5,6,1,12,10,11]=>01001111001=>10011110010
[3,2,1,12,11,8,4,10,5,6,7,9]=>11000010111=>11101000011
[5,4,2,3,7,6,1,10,8,12,9,11]=>00111100101=>10100111100
[5,4,2,3,1,12,11,10,6,7,8,9]=>01110000111=>11100001110
[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
[1,4,2,6,3,12,9,5,11,7,8,10]=>00101001011=>11010010100
[1,4,2,12,7,3,9,5,11,6,8,10]=>00100101011=>11010100100
[7,6,5,2,3,4,9,8,1,12,10,11]=>00011111001=>10011111000
[7,6,5,2,3,4,1,10,8,12,9,11]=>00111100101=>10100111100
[9,6,5,2,3,8,4,7,1,12,10,11]=>00011111001=>10011111000
[9,8,5,2,7,3,4,6,1,12,10,11]=>00011111001=>10011111000
[1,12,5,2,7,3,9,4,11,6,8,10]=>00010101011=>11010101000
[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
[11,10,7,6,2,3,9,4,5,8,1,12]=>00001111110=>01111110000
[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
[11,10,9,8,7,2,3,4,5,6,1,12]=>00001111110=>01111110000
[1,12,11,8,7,2,3,10,4,5,6,9]=>00000110111=>11101100000
[4,2,7,5,3,1,8,6]=>0111011=>1101110
[7,3,2,5,4,1,8,6]=>0111011=>1101110
[3,6,4,1,8,2,7,5]=>0010111=>1110100
[4,6,3,8,7,2,1,5]=>1000111=>1110001
[4,3,5,1,8,7,2,6]=>0011011=>1101100
[8,4,3,2,7,5,1,6]=>0111011=>1101110
[7,5,2,8,4,3,1,6]=>0111011=>1101110
[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
[8,3,5,6,1,4,7,2]=>0000111=>1110000
[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
[5,4,7,8,3,1,2,6]=>0101001=>1001010
[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
[4,3,2,7,5,8,1,6]=>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
[8,1,2,4,5,3,7,6]=>0001011=>1101000
[8,1,4,5,3,2,7,6]=>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
[7,4,3,2,5,8,1,6]=>0110011=>1100110
[7,2,4,3,5,8,1,6]=>0010011=>1100100
[1,3,6,4,2,5,7,8]=>0010100=>0010100
[1,7,6,4,2,3,5,8]=>0010110=>0110100
[1,2,3,7,6,4,5,8]=>0000110=>0110000
[1,3,2,5,8,6,4,7]=>0100101=>1010010
[4,8,2,7,1,3,6,5]=>0000111=>1110000
[7,1,8,4,6,3,5,2]=>0001111=>1111000
[1,7,4,6,8,3,5,2]=>0001011=>1101000
[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
[3,1,2,8,5,7,4,6]=>0100011=>1100010
[6,4,1,5,3,2,8,7]=>0111101=>1011110
[6,3,8,1,2,5,4,7]=>0001101=>1011000
[2,1,8,6,3,7,5,4]=>1001111=>1111001
[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
[1,3,7,2,4,6,5,8]=>0000110=>0110000
[1,7,2,6,4,3,5,8]=>0010110=>0110100
[1,2,6,8,7,4,3,5]=>0010011=>1100100
[1,2,7,4,3,5,8,6]=>0010011=>1100100
[1,8,6,3,5,2,7,4]=>0001111=>1111000
[1,6,2,8,7,4,3,5]=>0010111=>1110100
[1,3,8,7,5,4,6,2]=>0001111=>1111000
[1,2,8,6,3,5,7,4]=>0000111=>1110000
[1,8,5,2,3,6,4,7]=>0001101=>1011000
[1,7,4,8,5,2,3,6]=>0001011=>1101000
[1,4,7,5,8,6,3,2]=>0100111=>1110010
[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
[1,4,8,6,3,2,7,5]=>0100111=>1110010
[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
[1,3,5,8,7,6,2,4]=>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
[1,4,2,8,6,3,5,7]=>0010101=>1010100
[1,3,8,6,4,2,5,7]=>0010101=>1010100
[1,5,7,4,2,3,8,6]=>0010011=>1100100
[8,2,7,3,1,5,4,6]=>0101011=>1101010
[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
[1,3,8,2,5,6,7,4]=>0000011=>1100000
[5,4,2,3,6,1,8,7]=>0011101=>1011100
[5,1,7,4,3,6,8,2]=>0011011=>1101100
[7,1,3,6,5,2,8,4]=>0001111=>1111000
[6,1,8,5,2,7,3,4]=>0001111=>1111000
[8,7,2,6,3,1,4,5]=>0100111=>1110010
[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
[3,2,6,8,7,1,4,5]=>0100011=>1100010
[4,7,3,1,8,5,2,6]=>0101011=>1101010
[3,1,2,5,7,8,6,4]=>0100101=>1010010
[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
[8,5,1,2,4,6,7,3]=>0001011=>1101000
[1,8,5,3,4,6,7,2]=>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
[7,1,5,2,6,3,4,8]=>0001110=>0111000
[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
[8,1,6,4,2,3,5,7]=>0010101=>1010100
[7,3,1,2,6,4,5,8]=>0100110=>0110010
[8,3,1,2,4,6,7,5]=>0100011=>1100010
[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
[6,1,8,4,2,3,5,7]=>0010101=>1010100
[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
[6,1,8,2,5,3,4,7]=>0001101=>1011000
[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
[1,6,3,8,4,5,7,2]=>0000111=>1110000
[1,6,3,7,4,5,8,2]=>0000111=>1110000
[2,7,4,3,8,5,1,6]=>0011011=>1101100
[2,4,7,3,5,1,6,8]=>0001010=>0101000
[2,5,8,4,6,3,1,7]=>0100101=>1010010
[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
[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
[5,7,3,2,8,1,4,6]=>0100011=>1100010
[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
[8,6,5,1,2,4,3,7]=>0011101=>1011100
[7,6,1,4,2,3,5,8]=>0010110=>0110100
[7,5,4,8,3,2,6,1]=>0101111=>1111010
[8,7,5,1,4,2,3,6]=>0011011=>1101100
[8,4,1,2,5,3,6,7]=>0011001=>1001100
[4,3,8,1,5,2,6,7]=>0011001=>1001100
[8,6,1,4,2,5,3,7]=>0011101=>1011100
[2,8,3,7,4,5,6,1]=>0000111=>1110000
[8,7,5,2,4,3,6,1]=>0011111=>1111100
[6,8,3,2,4,5,1,7]=>0101001=>1001010
[3,8,5,2,4,6,1,7]=>0001101=>1011000
[8,2,4,5,3,1,6,7]=>0101001=>1001010
[4,8,2,5,3,1,6,7]=>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
[2,5,4,7,8,1,3,6]=>0001001=>1001000
[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
[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
[2,6,1,8,5,4,3,7]=>0011101=>1011100
[5,8,6,2,3,4,1,7]=>0010101=>1010100
[4,5,8,6,2,1,3,7]=>1000101=>1010001
[6,3,7,4,2,5,8,1]=>0010111=>1110100
[7,5,6,2,4,3,8,1]=>0010111=>1110100
[6,2,5,7,4,3,8,1]=>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
[8,4,6,2,5,3,7,1]=>0001111=>1111000
[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
[6,5,3,2,4,8,1,7]=>0101101=>1011010
[3,1,8,4,6,5,7,2]=>0100111=>1110010
[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
[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
[7,8,6,5,2,4,3,1]=>0111101=>1011110
[7,8,4,2,6,3,5,1]=>0011101=>1011100
[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
[3,7,2,8,6,4,5,1]=>0001111=>1111000
[8,6,5,7,1,3,2,4]=>0100111=>1110010
[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
[3,4,7,8,5,1,2,6]=>0001001=>1001000
[5,7,2,4,3,6,8,1]=>0010011=>1100100
[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
[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
[2,4,7,8,5,1,3,6]=>0001001=>1001000
[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
[2,4,6,8,5,1,3,7]=>0001001=>1001000
[1,6,8,2,4,3,5,7]=>0010001=>1000100
[5,4,6,8,3,1,7,2]=>0101011=>1101010
[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
[8,5,1,7,2,4,3,6]=>0011011=>1101100
[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
[5,7,2,8,4,1,3,6]=>0010011=>1100100
[3,5,8,2,4,1,7,6]=>0010011=>1100100
[2,4,8,3,1,6,7,5]=>0100011=>1100010
[1,3,6,8,5,4,2,7]=>0011001=>1001100
[1,4,2,5,7,6,3,8]=>0010110=>0110100
[1,4,2,6,8,5,3,7]=>0011001=>1001100
[1,5,3,2,6,8,4,7]=>0101001=>1001010
[1,5,4,2,3,6,8,7]=>0011001=>1001100
[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
[1,4,8,7,5,2,6,3]=>0001111=>1111000
[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
[1,3,8,7,5,2,4,6]=>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
[1,2,6,4,7,5,3,8]=>0001110=>0111000
[1,6,3,2,8,4,7,5]=>0100111=>1110010
[1,5,2,7,4,3,6,8]=>0011010=>0101100
[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
[1,8,4,6,3,2,7,5]=>0100111=>1110010
[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
[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
[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
[4,7,1,5,2,6,3,8]=>0001110=>0111000
[6,5,1,4,2,7,3,8]=>0011110=>0111100
[5,4,1,6,2,8,3,7]=>0011101=>1011100
[8,4,2,3,1,6,5,7]=>0110101=>1010110
[4,8,6,2,3,1,7,5]=>0100111=>1110010
[2,8,6,4,5,1,7,3]=>0001111=>1111000
[8,2,4,6,7,1,5,3]=>0001011=>1101000
[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
[8,7,4,5,1,6,3,2]=>0101111=>1111010
[7,2,8,1,4,5,6,3]=>0000111=>1110000
[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
[2,4,3,1,6,5,8,7,10,9]=>011010101=>101010110
[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
[2,1,8,5,9,6,7,12,10,4,11,3]=>10000011111=>11111000001
[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
[2,4,3,1,6,5,8,7,10,9,12,11]=>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
[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
[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
[8,6,3,5,9,2,7,12,10,4,11,1]=>00001011111=>11111010000
[10,6,3,7,12,2,9,8,4,11,1,5]=>00001011111=>11111010000
[4,7,3,6,8,1,12,10,9,5,11,2]=>00000111111=>11111100000
[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
[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
[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
[2,5,6,4,10,8,7,3,9,1,12,11]=>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
[2,3,4,8,5,6,7,1,10,12,11,9]=>00000110011=>11001100000
[10,7,4,12,5,6,9,8,2,11,1,3]=>00000111111=>11111100000
[2,7,4,8,5,6,12,10,9,3,11,1]=>00000111111=>11111100000
[2,3,4,5,10,6,7,8,9,1,12,11]=>00000001101=>10110000000
[2,3,4,5,6,12,7,8,9,10,11,1]=>00000000011=>11000000000
[8,2,3,7,4,5,6,1]=>0000111=>1110000
[8,6,2,5,4,7,3,1]=>0101111=>1111010
[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
[1,8,7,3,4,5,2,6]=>0001011=>1101000
[8,2,7,3,4,5,1,6]=>0001011=>1101000
[1,7,8,3,4,5,2,6]=>0001001=>1001000
[8,1,7,3,4,5,2,6]=>0001011=>1101000
[6,8,7,3,4,2,1,5]=>1010011=>1100101
[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
[5,7,1,3,2,8,6,4]=>0100111=>1110010
[5,8,7,1,2,6,3,4]=>0000111=>1110000
[6,8,2,3,4,7,1,5]=>0000011=>1100000
[6,7,2,3,4,8,1,5]=>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
[3,2,5,8,7,4,1,6]=>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
[1,4,6,2,5,3,7,8]=>0001100=>0011000
[4,3,6,5,1,2,7,8]=>0011100=>0011100
[1,3,8,7,6,5,2,4]=>0001111=>1111000
[1,8,7,2,6,3,5,4]=>0001111=>1111000
[8,7,1,2,4,3,6,5]=>0010111=>1110100
[2,8,7,1,6,3,4,5]=>0000111=>1110000
[6,2,1,8,7,5,3,4]=>1001111=>1111001
[3,2,1,4,5,8,6,7]=>1100001=>1000011
[1,3,7,5,4,8,6,2]=>0001111=>1111000
[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
[2,3,6,5,4,8,1,7]=>0001101=>1011000
[2,7,5,1,8,4,6,3]=>0001111=>1111000
[1,7,6,4,8,2,5,3]=>0001111=>1111000
[6,3,8,7,2,4,5,1]=>0001111=>1111000
[2,4,3,8,7,1,6,5]=>0010111=>1110100
[2,8,7,6,1,5,3,4]=>0001111=>1111000
[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
[7,8,1,4,2,3,5,6]=>0010001=>1000100
[8,7,1,4,2,3,5,6]=>0010011=>1100100
[3,8,6,4,1,5,2,7]=>0011101=>1011100
[3,8,4,6,1,5,2,7]=>0001101=>1011000
[8,3,7,2,1,6,5,4]=>1001111=>1111001
[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
[3,6,2,4,8,7,1,5]=>0000111=>1110000
[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
[1,4,5,3,8,2,7,6]=>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
[1,4,3,6,5,10,9,7,8,2]=>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
[3,1,9,6,2,8,4,5,7,12,11,10]=>01001011011=>11011010010
[3,1,9,8,7,2,4,5,6,12,11,10]=>01000111011=>11011100010
[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
[5,4,1,2,9,8,3,6,7,12,11,10]=>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
[9,4,1,6,2,8,3,5,7,12,11,10]=>00101011011=>11011010100
[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
[9,8,5,1,7,2,3,4,6,12,11,10]=>00010111011=>11011101000
[9,8,7,6,1,2,3,4,5,12,11,10]=>00001111011=>11011110000
[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
[1,4,8,2,6,5,3,7]=>0001101=>1011000
[7,5,1,8,3,4,2,6]=>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
[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
[7,6,1,2,3,5,4,8]=>0001110=>0111000
[8,5,2,6,4,3,1,7]=>0111101=>1011110
[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
[6,1,3,4,2,5,7,8]=>0010100=>0010100
[5,3,8,2,4,6,1,7]=>0001101=>1011000
[4,1,5,6,3,2,7,8]=>0110100=>0010110
[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
[1,6,3,4,7,8,5,2]=>0001101=>1011000
[8,1,3,4,2,6,5,7]=>0010101=>1010100
[4,7,8,5,2,3,1,6]=>0101001=>1001010
[4,1,5,8,6,2,3,7]=>0010101=>1010100
[5,8,2,1,6,3,4,7]=>1000101=>1010001
[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
[1,6,4,3,2,5,7,8]=>0110100=>0010110
[1,7,4,3,2,5,6,8]=>0110010=>0100110
[1,8,4,3,2,7,6,5]=>0110111=>1110110
[1,7,4,3,6,2,5,8]=>0010110=>0110100
[1,7,8,5,4,2,3,6]=>0011001=>1001100
[8,1,5,3,6,4,7,2]=>0001111=>1111000
[3,6,4,5,2,8,1,7]=>0001101=>1011000
[8,1,5,4,7,3,6,2]=>0001111=>1111000
[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
[8,6,3,5,4,1,2,7]=>0011101=>1011100
[8,2,6,5,4,1,3,7]=>0011101=>1011100
[8,2,6,5,4,3,1,7]=>0111101=>1011110
[8,3,2,6,1,5,4,7]=>0101101=>1011010
[8,1,6,5,4,3,2,7]=>0111101=>1011110
[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
[8,2,7,6,4,1,5,3]=>0011111=>1111100
[4,3,8,7,2,6,5,1]=>0011111=>1111100
[8,2,5,7,4,3,6,1]=>0010111=>1110100
[3,8,7,4,6,1,2,5]=>0000111=>1110000
[8,3,7,5,4,1,6,2]=>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
[8,1,2,7,6,5,4,3]=>0011111=>1111100
[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
[6,7,8,3,5,4,2,1]=>1011001=>1001101
[6,7,8,4,2,1,5,3]=>1011001=>1001101
[7,2,6,8,4,3,1,5]=>0110011=>1100110
[7,5,2,4,8,3,1,6]=>0101011=>1101010
[5,6,2,4,3,8,1,7]=>0010101=>1010100
[7,8,3,1,6,2,5,4]=>0101101=>1011010
[6,7,8,4,3,1,5,2]=>0111001=>1001110
[7,8,2,6,3,5,4,1]=>0011101=>1011100
[7,8,3,6,4,1,5,2]=>0011101=>1011100
[6,1,5,2,4,8,3,7]=>0001101=>1011000
[1,5,6,3,8,2,4,7]=>0000101=>1010000
[7,3,8,1,6,4,5,2]=>0001111=>1111000
[7,2,6,8,4,3,5,1]=>0011011=>1101100
[7,5,2,4,8,3,6,1]=>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
[7,2,8,1,6,4,3,5]=>0010111=>1110100
[7,8,1,6,3,5,4,2]=>0011101=>1011100
[6,7,8,3,2,5,4,1]=>0111001=>1001110
[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
[1,6,4,5,2,7,3,8]=>0001110=>0111000
[1,4,7,3,2,5,6,8]=>0100010=>0100010
[6,2,1,5,7,3,4,8]=>1000110=>0110001
[1,6,7,4,2,8,3,5]=>0010011=>1100100
[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
[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
[3,1,6,5,2,8,7,4]=>0101111=>1111010
[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
[1,8,5,4,2,7,3,6]=>0011011=>1101100
[3,1,8,5,4,7,2,6]=>0101011=>1101010
[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
[8,3,1,6,4,2,5,7]=>0110101=>1010110
[3,6,7,1,8,4,2,5]=>0010011=>1100100
[1,7,4,8,3,5,2,6]=>0001011=>1101000
[7,3,2,4,8,5,1,6]=>0101011=>1101010
[6,3,4,7,1,8,5,2]=>0001111=>1111000
[5,7,8,1,4,2,6,3]=>0010101=>1010100
[5,7,1,2,3,8,6,4]=>0000111=>1110000
[7,2,8,1,4,3,6,5]=>0010111=>1110100
[2,6,3,8,1,7,5,4]=>0001111=>1111000
[1,8,3,6,4,7,2,5]=>0000111=>1110000
[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
[1,6,5,8,7,4,2,3]=>0010111=>1110100
[4,1,8,7,6,3,5,2]=>0011111=>1111100
[4,8,2,6,3,5,1,7]=>0001101=>1011000
[6,7,2,5,3,8,4,1]=>0011011=>1101100
[4,3,5,7,1,6,2,8]=>0010110=>0110100
[4,2,8,5,3,6,7,1]=>0011011=>1101100
[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
[6,2,8,4,5,3,7,1]=>0001111=>1111000
[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
[6,5,8,7,1,3,2,4]=>0100111=>1110010
[6,5,8,7,2,3,4,1]=>0010111=>1110100
[6,5,8,7,3,2,4,1]=>0110111=>1110110
[6,3,8,4,5,2,7,1]=>0001111=>1111000
[3,1,6,8,5,7,2,4]=>0100011=>1100010
[2,1,6,8,5,3,7,4]=>1001011=>1101001
[3,1,6,8,5,4,2,7]=>0111001=>1001110
[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
[6,2,8,4,5,1,3,7]=>0001101=>1011000
[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
[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
[2,4,8,3,7,6,5,1]=>0001111=>1111000
[3,6,8,5,2,4,7,1]=>0001011=>1101000
[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
[4,6,3,8,7,2,5,1]=>0001111=>1111000
[3,5,8,2,7,4,6,1]=>0000111=>1110000
[2,4,8,7,3,6,5,1]=>0001111=>1111000
[2,5,8,7,4,3,6,1]=>0010111=>1110100
[2,4,8,7,6,3,5,1]=>0001111=>1111000
[4,7,2,5,6,3,1,8]=>0100110=>0110010
[6,1,2,8,7,3,4,5]=>0000111=>1110000
[4,1,3,5,7,8,2,6]=>0010001=>1000100
[6,1,5,8,4,3,2,7]=>0110101=>1010110
[3,2,6,1,5,8,4,7]=>0100101=>1010010
[4,5,2,1,7,8,3,6]=>1001001=>1001001
[2,3,7,8,5,1,6,4]=>0001101=>1011000
[8,1,3,2,5,6,4,7]=>0100101=>1010010
[3,2,5,8,4,7,1,6]=>0100011=>1100010
[8,6,4,1,5,2,3,7]=>0011101=>1011100
[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
[8,1,5,2,3,7,6,4]=>0001111=>1111000
[6,2,1,8,5,7,4,3]=>1010111=>1110101
[5,4,7,1,3,8,6,2]=>0001111=>1111000
[6,5,7,8,1,3,4,2]=>0010101=>1010100
[6,4,7,2,8,3,1,5]=>0100111=>1110010
[4,8,1,2,7,6,5,3]=>0001111=>1111000
[3,7,4,8,5,2,6,1]=>0001111=>1111000
[8,1,2,6,5,3,4,7]=>0001101=>1011000
[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
[6,2,8,4,7,1,3,5]=>0000111=>1110000
[1,8,4,3,7,6,2,5]=>0010111=>1110100
[4,3,8,7,1,2,6,5]=>0010111=>1110100
[1,8,3,6,7,2,4,5]=>0000011=>1100000
[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
[3,5,8,7,4,1,6,2]=>0010111=>1110100
[7,4,6,8,3,5,1,2]=>0001011=>1101000
[7,2,8,4,1,3,6,5]=>0010111=>1110100
[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
[3,6,7,8,2,1,4,5]=>1000001=>1000001
[4,5,6,8,7,3,1,2]=>0100011=>1100010
[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
[2,7,5,6,3,8,4,1]=>0010111=>1110100
[7,6,3,8,5,4,2,1]=>1011111=>1111101
[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
[4,2,8,5,3,7,6,1]=>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
[7,6,2,5,3,8,4,1]=>0011111=>1111100
[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
[6,7,2,8,4,3,1,5]=>0110011=>1100110
[6,7,3,2,8,4,1,5]=>0110011=>1100110
[4,5,8,1,3,2,6,7]=>0100001=>1000010
[4,5,8,1,3,7,2,6]=>0000011=>1100000
[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
[3,1,5,8,6,4,7,2]=>0100111=>1110010
[3,6,2,8,7,4,5,1]=>0001111=>1111000
[3,6,2,8,4,7,5,1]=>0001111=>1111000
[2,3,8,6,7,5,4,1]=>0011011=>1101100
[8,3,5,1,6,4,2,7]=>0011101=>1011100
[5,7,8,3,4,6,2,1]=>1000101=>1010001
[3,1,5,8,6,2,4,7]=>0100101=>1010010
[1,5,8,6,3,4,2,7]=>0010101=>1010100
[5,3,7,8,4,2,6,1]=>0011101=>1011100
[5,1,6,4,3,8,7,2]=>0011111=>1111100
[4,7,1,3,2,5,6,8]=>0100010=>0100010
[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
[1,8,5,4,2,3,6,7]=>0011001=>1001100
[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
[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
[7,6,3,2,8,5,1,4]=>0101111=>1111010
[5,3,8,2,7,1,6,4]=>0001111=>1111000
[6,3,4,2,1,8,7,5]=>1010111=>1110101
[4,5,1,7,6,3,2,8]=>0101110=>0111010
[1,5,3,7,4,2,6,8]=>0011010=>0101100
[1,2,7,4,3,8,6,5]=>0010111=>1110100
[1,5,4,2,3,8,7,6]=>0011011=>1101100
[1,5,4,2,3,8,6,7]=>0011001=>1001100
[1,5,3,2,4,6,7,8]=>0101000=>0001010
[1,5,4,2,3,7,8,6]=>0011001=>1001100
[3,6,5,2,4,1,7,8]=>0011100=>0011100
[4,6,7,2,5,1,8,3]=>0001011=>1101000
[3,6,2,5,1,7,8,4]=>0001101=>1011000
[3,4,2,7,8,6,1,5]=>0010101=>1010100
[3,4,2,7,8,1,5,6]=>0010001=>1000100
[3,8,5,2,4,7,1,6]=>0001011=>1101000
[6,4,3,2,8,1,7,5]=>0110111=>1110110
[6,2,4,3,8,1,7,5]=>0010111=>1110100
[8,7,3,6,2,1,5,4]=>1001111=>1111001
[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
[5,7,6,3,1,2,4,8]=>0100110=>0110010
[5,7,6,3,4,1,2,8]=>0010110=>0110100
[7,5,6,8,1,3,2,4]=>0100011=>1100010
[3,5,4,1,2,7,6,8]=>0011010=>0101100
[5,7,6,1,3,2,4,8]=>0100110=>0110010
[3,5,4,1,7,2,6,8]=>0011010=>0101100
[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
[7,1,3,8,2,5,4,6]=>0001011=>1101000
[5,1,3,7,6,2,4,8]=>0001110=>0111000
[6,7,1,8,3,4,5,2]=>0001011=>1101000
[3,7,1,6,8,4,5,2]=>0001011=>1101000
[8,7,1,5,3,2,6,4]=>0101111=>1111010
[3,7,1,6,5,2,8,4]=>0001111=>1111000
[8,6,7,2,5,3,1,4]=>0101011=>1101010
[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
[8,1,4,2,3,5,7,6]=>0010011=>1100100
[1,7,8,2,5,3,4,6]=>0001001=>1001000
[2,7,8,4,1,3,5,6]=>0010001=>1000100
[6,8,1,2,3,7,4,5]=>0000011=>1100000
[1,2,8,6,4,5,3,7]=>0001101=>1011000
[1,5,8,7,6,3,4,2]=>0010111=>1110100
[1,2,7,8,4,3,5,6]=>0010001=>1000100
[1,5,7,8,4,2,3,6]=>0010001=>1000100
[1,6,8,5,4,2,3,7]=>0011001=>1001100
[1,2,3,7,5,4,6,8]=>0001010=>0101000
[1,3,4,8,5,2,7,6]=>0001011=>1101000
[4,6,5,2,1,7,8,3]=>1001101=>1011001
[4,6,1,7,5,8,3,2]=>0100111=>1110010
[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
[5,1,3,4,8,2,6,7]=>0001001=>1001000
[5,8,1,4,2,3,6,7]=>0010001=>1000100
[4,3,1,8,5,2,6,7]=>0111001=>1001110
[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
[5,1,6,8,3,4,7,2]=>0001011=>1101000
[3,5,1,8,6,4,7,2]=>0001111=>1111000
[6,4,8,1,5,7,2,3]=>0000111=>1110000
[4,7,2,8,3,1,6,5]=>0100111=>1110010
[1,2,5,6,8,3,7,4]=>0000011=>1100000
[5,1,6,8,7,2,3,4]=>0001011=>1101000
[1,5,6,8,3,7,2,4]=>0000011=>1100000
[5,6,8,1,2,3,7,4]=>0000011=>1100000
[2,8,1,3,5,7,4,6]=>0000011=>1100000
[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
[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
[5,6,8,1,3,4,7,2]=>0000011=>1100000
[5,6,8,2,3,4,7,1]=>0000011=>1100000
[5,7,8,3,2,6,1,4]=>0100101=>1010010
[7,5,8,6,4,1,3,2]=>0110111=>1110110
[5,1,8,6,4,2,7,3]=>0011111=>1111100
[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
[2,7,4,1,3,6,8,5]=>0010011=>1100100
[6,3,2,8,1,7,5,4]=>0101111=>1111010
[2,6,8,7,1,3,5,4]=>0001011=>1101000
[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
[2,7,5,4,1,3,6,8]=>0011010=>0101100
[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
[6,2,4,5,7,3,1,8]=>0100110=>0110010
[2,6,8,4,5,3,1,7]=>0101001=>1001010
[2,5,3,8,4,1,6,7]=>0011001=>1001100
[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
[4,3,5,1,6,2,7,8]=>0011100=>0011100
[6,2,1,7,5,8,4,3]=>1010111=>1110101
[1,5,7,8,6,4,2,3]=>0010101=>1010100
[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
[4,5,1,7,6,3,8,2]=>0001111=>1111000
[4,6,5,1,3,7,8,2]=>0001101=>1011000
[5,2,1,7,6,4,8,3]=>1001111=>1111001
[6,8,5,2,7,3,1,4]=>0101011=>1101010
[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
[5,8,6,1,2,4,7,3]=>0000111=>1110000
[1,6,8,7,5,3,4,2]=>0011011=>1101100
[6,8,7,5,1,2,4,3]=>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
[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
[5,3,8,4,2,7,6,1]=>0011111=>1111100
[2,8,5,3,1,4,7,6]=>0101011=>1101010
[3,7,8,5,1,4,2,6]=>0011001=>1001100
[1,7,8,4,6,3,2,5]=>0100101=>1010010
[8,7,2,4,6,3,1,5]=>0100111=>1110010
[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
[7,4,8,2,3,5,1,6]=>0001011=>1101000
[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
[8,7,2,4,6,1,5,3]=>0001111=>1111000
[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
[2,5,1,4,7,3,6,8]=>0001010=>0101000
[3,1,6,5,7,2,4,8]=>0100110=>0110010
[2,5,7,1,6,3,4,8]=>0000110=>0110000
[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
[3,5,6,2,8,1,7,4]=>0000111=>1110000
[3,6,5,1,7,2,4,8]=>0001110=>0111000
[3,6,5,2,1,4,7,8]=>1001100=>0011001
[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
[4,1,5,7,6,3,8,2]=>0010111=>1110100
[4,2,5,7,6,1,3,8]=>0010110=>0110100
[3,4,7,6,1,2,5,8]=>0000110=>0110000
[3,4,7,6,8,2,5,1]=>0001011=>1101000
[4,2,5,7,6,3,8,1]=>0010111=>1110100
[4,1,6,5,2,7,3,8]=>0011110=>0111100
[4,2,6,5,7,3,1,8]=>0110110=>0110110
[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
[4,5,2,7,6,3,8,1]=>0001111=>1111000
[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
[1,5,3,8,2,4,6,7]=>0001001=>1001000
[1,5,8,4,2,3,6,7]=>0010001=>1000100
[5,8,2,1,4,3,6,7]=>1010001=>1000101
[5,8,2,4,6,3,1,7]=>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
[8,6,4,1,5,7,2,3]=>0010111=>1110100
[1,8,6,4,5,7,2,3]=>0000111=>1110000
[8,1,6,4,5,2,3,7]=>0001101=>1011000
[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
[1,3,8,6,2,4,5,7]=>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
[1,8,3,6,2,4,5,7]=>0000101=>1010000
[8,1,3,6,2,4,5,7]=>0000101=>1010000
[8,3,6,7,2,1,4,5]=>1000011=>1100001
[2,5,8,4,6,1,7,3]=>0000111=>1110000
[3,8,6,7,2,1,4,5]=>1000011=>1100001
[3,1,8,6,7,2,4,5]=>0100011=>1100010
[8,2,6,4,5,1,7,3]=>0001111=>1111000
[8,4,6,1,7,2,5,3]=>0001111=>1111000
[1,8,4,6,7,5,2,3]=>0001011=>1101000
[8,1,4,6,7,5,2,3]=>0001011=>1101000
[8,4,6,1,3,7,2,5]=>0000111=>1110000
[8,1,4,6,3,7,2,5]=>0000111=>1110000
[8,4,1,6,3,7,2,5]=>0010111=>1110100
[8,2,4,6,1,7,5,3]=>0001111=>1111000
[8,4,6,2,3,7,5,1]=>0001111=>1111000
[8,4,7,3,1,6,2,5]=>0100111=>1110010
[8,4,7,2,1,3,6,5]=>1000111=>1110001
[8,4,2,1,5,3,7,6]=>1011011=>1101101
[8,2,1,4,7,3,6,5]=>1000111=>1110001
[3,2,1,7,4,5,8,6]=>1100011=>1100011
[2,8,4,1,7,5,3,6]=>0011011=>1101100
[2,6,8,5,1,7,4,3]=>0011011=>1101100
[4,7,3,1,8,6,2,5]=>0100111=>1110010
[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
[5,8,2,6,4,3,7,1]=>0010111=>1110100
[2,8,5,3,6,4,7,1]=>0001111=>1111000
[1,2,8,6,4,7,3,5]=>0000111=>1110000
[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
[3,8,4,2,7,6,5,1]=>0011111=>1111100
[3,8,4,2,5,1,7,6]=>0011011=>1101100
[4,8,3,2,7,5,6,1]=>0100111=>1110010
[3,2,4,8,7,5,6,1]=>0100111=>1110010
[3,5,2,6,4,8,1,7]=>0001101=>1011000
[2,6,8,1,5,3,4,7]=>0001001=>1001000
[8,1,5,2,4,6,3,7]=>0001101=>1011000
[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
[8,6,3,2,7,4,1,5]=>0110111=>1110110
[4,5,8,7,3,1,2,6]=>0100011=>1100010
[1,3,8,7,6,4,2,5]=>0010111=>1110100
[8,6,4,7,5,1,2,3]=>0001111=>1111000
[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
[8,6,2,1,5,7,3,4]=>1000111=>1110001
[1,6,5,4,3,8,2,7]=>0011101=>1011100
[6,4,2,1,5,7,3,8]=>1010110=>0110101
[3,1,5,8,7,2,4,6]=>0100011=>1100010
[3,2,5,7,8,4,1,6]=>0110001=>1000110
[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
[5,2,8,4,3,1,6,7]=>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
[3,1,5,7,8,4,2,6]=>0110001=>1000110
[1,2,8,6,4,5,7,3]=>0000111=>1110000
[6,2,3,7,4,1,8,5]=>0010111=>1110100
[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
[6,1,3,7,4,2,8,5]=>0010111=>1110100
[6,2,3,7,4,5,1,8]=>0001110=>0111000
[6,2,3,7,4,5,8,1]=>0000111=>1110000
[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
[2,5,4,1,8,6,7,3]=>0011011=>1101100
[1,8,5,3,2,6,7,4]=>0101011=>1101010
[5,6,8,3,4,2,7,1]=>0010011=>1100100
[6,3,8,2,4,1,7,5]=>0010111=>1110100
[5,1,7,8,2,4,3,6]=>0011001=>1001100
[5,3,2,4,8,1,7,6]=>0101011=>1101010
[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
[7,6,4,2,8,3,1,5]=>0110111=>1110110
[1,2,6,4,7,3,5,8]=>0000110=>0110000
[8,5,2,4,3,7,1,6]=>0011011=>1101100
[7,5,4,1,3,6,8,2]=>0011011=>1101100
[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
[8,2,3,4,7,1,5,6]=>0000011=>1100000
[2,7,8,5,6,1,4,3]=>0010101=>1010100
[2,4,7,8,1,3,6,5]=>0000101=>1010000
[5,2,8,3,1,4,7,6]=>0101011=>1101010
[8,7,2,5,1,4,3,6]=>0011011=>1101100
[8,3,5,1,2,4,7,6]=>0001011=>1101000
[8,6,5,1,7,4,2,3]=>0011111=>1111100
[8,3,6,5,4,1,2,7]=>0011101=>1011100
[8,7,4,5,1,2,6,3]=>0001111=>1111000
[3,4,8,2,1,7,6,5]=>1000111=>1110001
[8,3,5,2,7,4,6,1]=>0001111=>1111000
[8,3,1,7,5,6,2,4]=>0100111=>1110010
[8,4,1,7,5,2,6,3]=>0011111=>1111100
[8,3,4,2,7,5,6,1]=>0010111=>1110100
[8,3,2,7,5,6,1,4]=>0100111=>1110010
[8,4,2,7,5,3,1,6]=>0111011=>1101110
[8,2,6,5,7,1,3,4]=>0000111=>1110000
[8,4,3,7,5,1,2,6]=>0011011=>1101100
[8,5,7,6,4,3,1,2]=>0110111=>1110110
[8,5,7,6,4,1,2,3]=>0010111=>1110100
[8,2,4,7,1,5,6,3]=>0000111=>1110000
[8,4,7,6,5,2,1,3]=>1001111=>1111001
[8,3,1,4,7,6,2,5]=>0100111=>1110010
[1,5,2,6,8,3,7,4]=>0001011=>1101000
[7,2,8,4,1,3,5,6]=>0010011=>1100100
[6,7,8,5,2,1,4,3]=>1011001=>1001101
[1,6,2,7,8,4,3,5]=>0010101=>1010100
[4,3,8,6,5,2,7,1]=>0011111=>1111100
[2,3,8,6,5,1,7,4]=>0001111=>1111000
[7,3,2,6,1,4,8,5]=>0100111=>1110010
[3,2,5,6,8,4,1,7]=>0110001=>1000110
[2,6,8,1,5,4,3,7]=>0011001=>1001100
[8,4,7,1,2,5,3,6]=>0001011=>1101000
[8,5,6,7,2,1,4,3]=>1010011=>1100101
[8,5,6,7,3,1,4,2]=>0110011=>1100110
[1,8,3,2,5,4,6,7]=>0101001=>1001010
[5,1,7,3,2,8,4,6]=>0101011=>1101010
[8,2,5,3,1,7,4,6]=>0101011=>1101010
[1,4,8,5,3,2,6,7]=>0101001=>1001010
[5,8,3,1,4,2,6,7]=>0110001=>1000110
[1,5,4,8,2,3,6,7]=>0001001=>1001000
[1,5,4,8,2,3,7,6]=>0001011=>1101000
[5,7,8,1,3,2,4,6]=>0100001=>1000010
[8,2,7,5,1,4,6,3]=>0001111=>1111000
[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
[7,1,8,5,3,4,2,6]=>0011011=>1101100
[1,2,7,8,3,5,6,4]=>0000101=>1010000
[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
[8,2,4,7,6,3,1,5]=>0100111=>1110010
[1,2,5,7,8,3,6,4]=>0000101=>1010000
[7,6,3,4,2,1,8,5]=>1010111=>1110101
[8,2,4,6,3,7,1,5]=>0000111=>1110000
[3,4,5,8,1,7,2,6]=>0000011=>1100000
[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
[4,5,6,2,1,7,3,8]=>1000110=>0110001
[4,5,6,1,7,8,3,2]=>0100101=>1010010
[4,5,1,6,7,8,3,2]=>0101001=>1001010
[4,5,1,6,7,3,8,2]=>0001011=>1101000
[4,5,1,6,7,3,2,8]=>0101010=>0101010
[4,5,6,1,7,3,2,8]=>0100110=>0110010
[8,6,4,3,7,2,1,5]=>1010111=>1110101
[5,8,1,4,3,2,7,6]=>0110011=>1100110
[1,6,4,3,8,2,7,5]=>0010111=>1110100
[7,8,1,4,3,2,5,6]=>0110001=>1000110
[1,7,8,4,5,3,6,2]=>0001101=>1011000
[2,7,6,3,4,1,8,5]=>0010111=>1110100
[8,1,7,4,3,5,6,2]=>0010111=>1110100
[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
[7,8,1,3,4,5,6,2]=>0000101=>1010000
[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
[8,5,3,1,4,6,7,2]=>0101011=>1101010
[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
[2,6,1,4,3,7,8,5]=>0010101=>1010100
[6,8,2,3,1,5,7,4]=>0100011=>1100010
[6,1,3,4,2,7,8,5]=>0010101=>1010100
[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
[8,4,2,7,6,1,5,3]=>0011111=>1111100
[5,3,7,6,1,8,4,2]=>0011111=>1111100
[8,6,4,1,2,5,3,7]=>0011101=>1011100
[8,6,1,4,2,5,7,3]=>0010111=>1110100
[8,6,4,1,2,5,7,3]=>0010111=>1110100
[8,6,1,4,7,2,5,3]=>0001111=>1111000
[4,8,6,2,3,1,5,7]=>0100101=>1010010
[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
[3,6,4,2,5,7,1,8]=>0010110=>0110100
[4,2,6,3,5,1,7,8]=>0011100=>0011100
[3,4,6,8,7,1,2,5]=>0000011=>1100000
[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
[2,5,4,8,3,7,6,1]=>0001111=>1111000
[1,3,6,2,5,8,7,4]=>0000111=>1110000
[1,3,5,8,6,4,7,2]=>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
[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
[5,4,1,6,7,2,8,3]=>0011011=>1101100
[4,1,6,5,2,7,8,3]=>0011101=>1011100
[5,4,6,2,7,8,3,1]=>0101101=>1011010
[3,5,2,6,7,8,4,1]=>0011001=>1001100
[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
[5,6,7,2,8,4,1,3]=>0010011=>1100100
[1,7,8,4,6,5,2,3]=>0001101=>1011000
[6,4,1,8,7,2,5,3]=>0011111=>1111100
[3,7,2,8,6,5,1,4]=>0001111=>1111000
[2,7,8,1,6,5,3,4]=>0001101=>1011000
[2,5,8,1,7,6,3,4]=>0000111=>1110000
[2,8,4,7,6,3,1,5]=>0100111=>1110010
[4,5,8,7,1,6,2,3]=>0000111=>1110000
[6,4,8,7,2,1,5,3]=>1001111=>1111001
[3,2,8,7,6,4,1,5]=>0110111=>1110110
[2,5,1,8,4,7,6,3]=>0001111=>1111000
[2,4,5,8,1,7,6,3]=>0000111=>1110000
[2,6,8,1,4,3,7,5]=>0010011=>1100100
[4,1,8,2,6,7,3,5]=>0010011=>1100100
[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
[7,5,8,1,6,2,3,4]=>0000111=>1110000
[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
[1,2,5,4,7,8,3,6]=>0001001=>1001000
[3,6,2,4,7,8,5,1]=>0001101=>1011000
[1,8,5,4,6,7,2,3]=>0001011=>1101000
[1,3,5,4,8,7,2,6]=>0001011=>1101000
[1,6,2,4,8,3,7,5]=>0000111=>1110000
[7,1,4,2,3,8,6,5]=>0010111=>1110100
[1,7,3,2,4,6,5,8]=>0100110=>0110010
[8,1,3,2,6,5,7,4]=>0100111=>1110010
[1,5,7,3,2,6,4,8]=>0100110=>0110010
[5,1,3,7,2,6,4,8]=>0001110=>0111000
[1,7,8,5,4,2,6,3]=>0011101=>1011100
[8,1,7,5,4,2,6,3]=>0011111=>1111100
[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
[1,5,4,2,8,6,7,3]=>0011011=>1101100
[1,6,3,5,2,7,8,4]=>0001101=>1011000
[5,8,4,1,6,2,7,3]=>0010111=>1110100
[3,1,2,6,8,7,5,4]=>0101011=>1101010
[6,4,8,2,3,5,7,1]=>0000111=>1110000
[6,4,8,2,5,7,1,3]=>0000111=>1110000
[6,8,2,4,7,3,5,1]=>0001011=>1101000
[8,6,2,4,5,1,3,7]=>0001101=>1011000
[6,8,4,2,7,1,3,5]=>0010011=>1100100
[6,8,2,4,1,7,3,5]=>0010011=>1100100
[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
[8,5,2,1,4,6,7,3]=>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
[8,6,1,3,4,5,7,2]=>0000111=>1110000
[6,8,1,3,4,5,7,2]=>0000011=>1100000
[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
[4,2,3,8,1,7,5,6]=>0010011=>1100100
[5,2,3,8,1,7,4,6]=>0001011=>1101000
[2,5,4,8,1,7,3,6]=>0001011=>1101000
[2,5,4,1,3,8,6,7]=>0011001=>1001100
[4,2,1,5,3,7,6,8]=>1011010=>0101101
[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
[6,1,2,4,5,7,8,3]=>0000101=>1010000
[6,8,7,2,3,4,5,1]=>0001011=>1101000
[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
[6,2,8,3,5,1,4,7]=>0001101=>1011000
[3,8,4,5,2,1,6,7]=>1001001=>1001001
[8,2,6,3,5,1,4,7]=>0001101=>1011000
[2,7,6,3,4,5,1,8]=>0001110=>0111000
[2,8,6,3,5,1,4,7]=>0001101=>1011000
[2,8,7,5,1,3,4,6]=>0001011=>1101000
[1,5,7,3,6,2,8,4]=>0000111=>1110000
[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
[8,3,7,5,1,4,2,6]=>0011011=>1101100
[8,3,7,1,6,4,2,5]=>0010111=>1110100
[4,2,6,5,3,1,7,8]=>0111100=>0011110
[4,3,7,5,1,6,2,8]=>0011110=>0111100
[3,5,2,8,6,7,4,1]=>0011011=>1101100
[5,3,7,4,2,8,6,1]=>0011111=>1111100
[5,6,2,8,7,1,4,3]=>0010111=>1110100
[4,3,7,5,2,6,1,8]=>0011110=>0111100
[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
[7,8,4,5,1,3,6,2]=>0001101=>1011000
[4,3,6,1,5,7,8,2]=>0010101=>1010100
[6,4,7,1,3,5,2,8]=>0001110=>0111000
[3,5,4,1,2,6,7,8]=>0011000=>0001100
[5,3,1,4,6,7,8,2]=>0101001=>1001010
[6,2,1,4,7,5,8,3]=>1000111=>1110001
[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
[4,5,7,2,3,6,1,8]=>0000110=>0110000
[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
[7,3,4,8,5,2,1,6]=>1001011=>1101001
[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
[2,7,5,8,6,3,4,1]=>0010111=>1110100
[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
[5,4,2,3,6,8,1,7]=>0011001=>1001100
[6,4,1,2,7,8,3,5]=>0010101=>1010100
[5,1,8,3,4,6,2,7]=>0001101=>1011000
[4,5,8,2,3,7,1,6]=>0000011=>1100000
[5,1,4,7,2,6,8,3]=>0001011=>1101000
[2,6,5,3,8,1,4,7]=>0001101=>1011000
[5,2,6,8,3,7,1,4]=>0001011=>1101000
[1,7,6,5,3,8,2,4]=>0001111=>1111000
[1,7,2,4,3,5,8,6]=>0010011=>1100100
[4,6,1,3,7,8,5,2]=>0001101=>1011000
[8,4,1,5,2,6,7,3]=>0011011=>1101100
[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
[2,3,8,4,1,7,6,5]=>0010111=>1110100
[6,5,1,4,7,3,2,8]=>0101110=>0111010
[2,7,8,4,1,3,6,5]=>0010101=>1010100
[3,6,5,1,4,8,2,7]=>0001101=>1011000
[3,6,4,1,2,7,8,5]=>0010101=>1010100
[4,1,7,3,8,6,2,5]=>0010111=>1110100
[4,8,2,7,6,5,1,3]=>0001111=>1111000
[5,4,2,8,7,6,1,3]=>0011111=>1111100
[7,4,2,8,6,5,1,3]=>0011111=>1111100
[6,5,8,2,7,4,1,3]=>0010111=>1110100
[8,6,5,2,7,1,4,3]=>0011111=>1111100
[7,8,5,2,1,6,4,3]=>1011101=>1011101
[6,8,5,2,7,1,4,3]=>0011011=>1101100
[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
[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
[3,5,1,4,2,8,7,6]=>0011011=>1101100
[5,8,7,4,6,1,3,2]=>0100111=>1110010
[5,1,8,7,4,6,3,2]=>0101111=>1111010
[3,4,1,8,7,6,2,5]=>0010111=>1110100
[3,5,2,8,6,4,7,1]=>0001111=>1111000
[2,8,7,5,4,1,6,3]=>0011111=>1111100
[4,2,5,8,6,7,1,3]=>0010011=>1100100
[8,1,5,7,4,2,6,3]=>0010111=>1110100
[8,4,5,3,1,6,7,2]=>0101011=>1101010
[5,8,7,3,4,1,6,2]=>0010111=>1110100
[2,4,5,8,1,3,7,6]=>0000011=>1100000
[7,1,4,3,8,5,6,2]=>0010111=>1110100
[6,3,2,5,8,4,1,7]=>0110101=>1010110
[8,7,1,4,6,3,2,5]=>0100111=>1110010
[8,4,1,3,7,6,5,2]=>0011111=>1111100
[2,7,8,6,5,3,1,4]=>0101101=>1011010
[5,1,6,4,7,8,2,3]=>0001101=>1011000
[2,8,3,5,6,1,4,7]=>0000101=>1010000
[1,3,6,4,2,7,5,8]=>0010110=>0110100
[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
[5,4,7,8,2,1,3,6]=>1001001=>1001001
[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
[5,4,8,6,2,3,1,7]=>0101101=>1011010
[2,4,7,5,8,3,1,6]=>0100011=>1100010
[7,2,5,8,1,6,3,4]=>0000111=>1110000
[3,7,8,4,2,1,6,5]=>1010101=>1010101
[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
[2,4,6,8,3,7,1,5]=>0000011=>1100000
[1,4,7,6,3,8,2,5]=>0000111=>1110000
[3,6,5,1,7,2,8,4]=>0001111=>1111000
[6,4,1,7,2,8,5,3]=>0011111=>1111100
[7,4,1,6,2,8,5,3]=>0011111=>1111100
[2,8,3,7,5,1,6,4]=>0001111=>1111000
[1,3,6,8,2,4,7,5]=>0000011=>1100000
[8,5,4,1,6,2,7,3]=>0011111=>1111100
[4,7,2,8,5,1,6,3]=>0001111=>1111000
[8,6,2,7,3,5,1,4]=>0001111=>1111000
[5,7,3,2,4,8,6,1]=>0100111=>1110010
[2,8,4,6,3,5,1,7]=>0001101=>1011000
[2,7,8,3,6,4,5,1]=>0001101=>1011000
[4,5,2,6,7,1,8,3]=>0001011=>1101000
[4,7,5,2,6,3,8,1]=>0001111=>1111000
[3,5,6,2,8,1,4,7]=>0000101=>1010000
[5,7,2,1,8,4,3,6]=>1010011=>1100101
[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
[8,7,3,5,1,4,6,2]=>0001111=>1111000
[8,6,3,5,2,1,4,7]=>1001101=>1011001
[8,7,3,2,6,5,1,4]=>0101111=>1111010
[8,4,2,7,6,5,1,3]=>0011111=>1111100
[5,2,8,7,6,4,1,3]=>0011111=>1111100
[8,7,1,4,5,6,2,3]=>0000111=>1110000
[4,1,3,8,5,6,2,7]=>0010101=>1010100
[3,2,4,8,5,7,1,6]=>0100011=>1100010
[6,3,8,5,4,2,7,1]=>0011111=>1111100
[7,4,6,1,3,5,2,8]=>0001110=>0111000
[6,2,3,8,5,4,7,1]=>0001111=>1111000
[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
[5,2,1,8,7,4,6,3]=>1001111=>1111001
[6,8,3,5,1,2,7,4]=>0001011=>1101000
[5,8,2,7,4,6,3,1]=>0100111=>1110010
[6,8,7,3,1,2,4,5]=>0100011=>1100010
[4,5,2,8,3,7,1,6]=>0001011=>1101000
[4,5,8,1,3,7,6,2]=>0000111=>1110000
[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
[7,1,6,8,5,4,3,2]=>0111011=>1101110
[5,8,1,3,4,2,7,6]=>0010011=>1100100
[1,4,6,3,7,5,2,8]=>0001110=>0111000
[4,5,2,6,8,7,3,1]=>0101011=>1101010
[3,2,8,7,4,5,6,1]=>0100111=>1110010
[6,4,2,5,1,7,8,3]=>0011101=>1011100
[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
[6,7,1,3,2,5,8,4]=>0100011=>1100010
[8,3,5,4,7,1,2,6]=>0001011=>1101000
[6,3,5,4,8,1,2,7]=>0001101=>1011000
[6,2,5,4,1,7,8,3]=>0011101=>1011100
[4,1,5,6,3,8,7,2]=>0010111=>1110100
[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
[6,1,3,5,4,8,2,7]=>0001101=>1011000
[1,3,8,7,2,5,6,4]=>0000111=>1110000
[2,5,4,1,8,3,7,6]=>0011011=>1101100
[6,1,5,4,3,8,2,7]=>0011101=>1011100
[1,4,8,3,2,7,6,5]=>0100111=>1110010
[5,1,4,8,3,7,6,2]=>0001111=>1111000
[3,5,8,2,1,4,7,6]=>1000011=>1100001
[8,4,1,2,7,6,5,3]=>0011111=>1111100
[4,8,3,2,7,6,5,1]=>0101111=>1111010
[2,4,8,1,7,6,5,3]=>0001111=>1111000
[8,7,3,2,1,4,6,5]=>1100111=>1110011
[1,4,8,5,2,3,6,7]=>0001001=>1001000
[1,4,8,5,2,3,7,6]=>0001011=>1101000
[6,1,4,2,8,7,3,5]=>0010111=>1110100
[1,5,8,7,2,4,3,6]=>0010011=>1100100
[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
[4,7,5,6,2,8,3,1]=>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
[6,1,5,8,7,4,3,2]=>0110111=>1110110
[8,5,1,4,7,6,3,2]=>0101111=>1111010
[8,2,1,7,5,3,6,4]=>1001111=>1111001
[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
[6,4,8,3,5,2,1,7]=>1001101=>1011001
[1,4,2,7,5,8,3,6]=>0010011=>1100100
[4,7,5,2,8,6,1,3]=>0001111=>1111000
[1,6,5,7,3,8,4,2]=>0010111=>1110100
[5,8,1,2,7,4,3,6]=>0010011=>1100100
[4,6,3,7,8,1,5,2]=>0001101=>1011000
[2,1,4,7,5,8,6,3]=>1000111=>1110001
[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
[6,8,1,7,5,4,2,3]=>0011011=>1101100
[4,8,2,7,5,3,6,1]=>0001111=>1111000
[7,2,4,3,8,6,1,5]=>0010111=>1110100
[5,8,4,3,1,6,7,2]=>0110011=>1100110
[6,8,7,4,5,1,3,2]=>0101011=>1101010
[1,4,7,3,6,8,2,5]=>0000011=>1100000
[2,4,7,3,6,8,1,5]=>0000011=>1100000
[2,7,3,1,8,5,4,6]=>0101011=>1101010
[2,3,1,6,8,7,4,5]=>0100011=>1100010
[6,4,8,2,1,7,3,5]=>1000111=>1110001
[2,3,1,7,8,5,6,4]=>0100101=>1010010
[2,3,1,8,7,5,6,4]=>0100111=>1110010
[8,7,4,5,1,3,2,6]=>0101011=>1101010
[8,5,1,2,7,4,3,6]=>0011011=>1101100
[1,3,7,6,8,4,2,5]=>0010011=>1100100
[4,5,7,8,6,2,1,3]=>1000101=>1010001
[2,1,5,7,4,6,8,3]=>1000011=>1100001
[2,3,5,7,8,1,6,4]=>0000101=>1010000
[1,6,4,2,3,5,7,8]=>0010100=>0010100
[1,5,7,4,2,3,6,8]=>0010010=>0100100
[8,1,7,2,4,6,3,5]=>0000111=>1110000
[1,5,7,2,3,6,8,4]=>0000011=>1100000
[2,4,7,8,6,1,3,5]=>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
[2,8,5,1,4,3,7,6]=>0011011=>1101100
[6,1,5,8,3,2,7,4]=>0100111=>1110010
[1,8,6,2,4,3,7,5]=>0010111=>1110100
[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
[2,3,6,7,1,5,4,8]=>0001010=>0101000
[3,7,5,6,2,1,4,8]=>1000110=>0110001
[2,7,5,8,1,3,6,4]=>0000111=>1110000
[5,1,6,7,3,2,4,8]=>0101010=>0101010
[5,1,3,6,7,4,2,8]=>0011010=>0101100
[2,5,6,3,8,4,7,1]=>0000111=>1110000
[7,4,1,2,3,6,8,5]=>0010011=>1100100
[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
[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
[2,7,4,1,5,8,3,6]=>0010011=>1100100
[6,1,7,3,4,2,5,8]=>0010110=>0110100
[2,6,4,7,8,5,3,1]=>0101101=>1011010
[5,2,8,4,6,7,1,3]=>0001011=>1101000
[1,3,5,8,4,6,7,2]=>0000011=>1100000
[8,2,7,6,3,4,5,1]=>0001111=>1111000
[1,8,3,7,4,2,5,6]=>0010011=>1100100
[8,5,7,2,4,3,6,1]=>0010111=>1110100
[7,8,6,2,4,1,3,5]=>0010101=>1010100
[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
[6,8,4,3,1,5,2,7]=>0111001=>1001110
[5,8,2,1,7,4,3,6]=>1010011=>1100101
[1,7,2,6,3,4,8,5]=>0000111=>1110000
[7,5,1,2,4,3,8,6]=>0011011=>1101100
[7,6,8,1,4,2,3,5]=>0010011=>1100100
[6,3,5,2,1,8,4,7]=>1001101=>1011001
[3,2,4,8,6,1,7,5]=>0100111=>1110010
[2,1,3,8,4,5,7,6]=>1000011=>1100001
[1,4,7,5,2,3,8,6]=>0001011=>1101000
[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
[1,3,6,8,2,7,5,4]=>0001011=>1101000
[3,2,7,5,6,8,1,4]=>0100011=>1100010
[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
[6,4,5,1,8,3,2,7]=>0101101=>1011010
[3,6,8,2,5,1,4,7]=>0001001=>1001000
[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
[4,8,3,1,6,7,2,5]=>0100011=>1100010
[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
[5,4,3,7,2,8,6,1]=>0011111=>1111100
[4,6,5,3,8,1,7,2]=>0001111=>1111000
[2,4,8,7,6,1,5,3]=>0001111=>1111000
[4,8,5,2,7,6,3,1]=>0101111=>1111010
[2,8,6,5,7,1,3,4]=>0000111=>1110000
[4,1,8,6,2,5,7,3]=>0010111=>1110100
[3,8,4,7,2,1,6,5]=>1000111=>1110001
[1,8,7,4,5,2,3,6]=>0001011=>1101000
[5,8,1,7,6,2,3,4]=>0000111=>1110000
[6,8,2,1,3,4,7,5]=>1000011=>1100001
[4,8,1,3,7,6,2,5]=>0000111=>1110000
[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
[5,2,7,1,3,8,6,4]=>0001111=>1111000
[6,3,7,2,5,4,8,1]=>0001111=>1111000
[5,2,1,7,6,3,8,4]=>1001111=>1111001
[6,3,2,7,4,5,8,1]=>0100111=>1110010
[7,4,3,8,5,6,1,2]=>0010111=>1110100
[7,3,2,8,4,6,1,5]=>0100111=>1110010
[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
[7,4,3,8,5,6,2,1]=>1010111=>1110101
[4,2,8,3,6,7,5,1]=>0011011=>1101100
[4,2,6,8,5,7,1,3]=>0010011=>1100100
[4,2,1,6,5,7,8,3]=>1010101=>1010101
[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
[2,8,6,4,1,5,3,7]=>0011101=>1011100
[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
[3,4,8,1,5,2,6,7]=>0001001=>1001000
[4,1,8,3,5,2,6,7]=>0011001=>1001100
[8,3,1,2,5,4,6,7]=>0101001=>1001010
[2,8,1,3,5,4,6,7]=>0001001=>1001000
[1,7,6,2,4,3,8,5]=>0010111=>1110100
[1,4,5,8,3,2,6,7]=>0100001=>1000010
[5,6,8,7,1,3,2,4]=>0100011=>1100010
[2,8,6,5,7,4,3,1]=>0110111=>1110110
[6,3,7,5,1,4,2,8]=>0011110=>0111100
[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
[6,3,7,5,1,4,8,2]=>0001111=>1111000
[5,3,7,2,4,1,8,6]=>0011011=>1101100
[5,1,2,8,6,3,7,4]=>0001111=>1111000
[6,5,2,8,4,7,1,3]=>0001111=>1111000
[6,5,8,3,1,2,7,4]=>0100111=>1110010
[6,1,5,7,2,4,3,8]=>0010110=>0110100
[7,1,6,8,2,5,4,3]=>0011011=>1101100
[4,1,8,2,6,5,7,3]=>0010111=>1110100
[6,1,4,7,8,5,3,2]=>0101101=>1011010
[5,1,4,6,7,3,2,8]=>0101010=>0101010
[6,1,5,7,8,4,2,3]=>0010101=>1010100
[1,8,4,5,6,7,2,3]=>0000011=>1100000
[4,2,8,6,7,1,3,5]=>0010011=>1100100
[6,4,2,7,1,5,8,3]=>0010111=>1110100
[5,6,2,7,4,8,3,1]=>0100111=>1110010
[5,3,6,7,4,2,8,1]=>0011011=>1101100
[2,6,3,7,5,4,8,1]=>0001111=>1111000
[1,7,3,2,4,8,6,5]=>0100111=>1110010
[6,4,1,3,8,7,5,2]=>0011111=>1111100
[4,3,1,8,2,6,7,5]=>0110011=>1100110
[4,8,1,3,2,5,7,6]=>0100011=>1100010
[7,2,6,5,8,3,4,1]=>0010111=>1110100
[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
[7,5,2,3,8,4,6,1]=>0001111=>1111000
[2,7,5,1,4,8,3,6]=>0001011=>1101000
[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
[1,5,8,2,6,4,3,7]=>0010101=>1010100
[3,1,8,2,6,5,4,7]=>0101101=>1011010
[7,6,2,8,1,4,5,3]=>0001111=>1111000
[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
[4,5,2,6,1,3,8,7]=>0001101=>1011000
[2,7,8,1,4,3,6,5]=>0010101=>1010100
[6,5,8,1,3,2,4,7]=>0100101=>1010010
[5,7,2,1,8,4,6,3]=>1000111=>1110001
[2,1,8,5,3,4,6,7]=>1001001=>1001001
[7,8,1,5,2,4,6,3]=>0001101=>1011000
[7,4,1,8,2,5,6,3]=>0010111=>1110100
[2,1,6,7,4,8,3,5]=>1000011=>1100001
[2,8,6,3,1,5,4,7]=>0101101=>1011010
[5,8,6,3,2,1,4,7]=>1100101=>1010011
[5,7,2,8,4,1,6,3]=>0010111=>1110100
[2,5,6,3,8,1,4,7]=>0000101=>1010000
[7,3,5,6,1,8,4,2]=>0010111=>1110100
[7,4,5,6,8,1,3,2]=>0100011=>1100010
[7,5,1,8,4,6,3,2]=>0101111=>1111010
[2,8,1,7,4,5,3,6]=>0001011=>1101000
[7,3,6,2,5,4,8,1]=>0001111=>1111000
[6,1,5,3,8,4,7,2]=>0001111=>1111000
[1,6,5,3,8,4,7,2]=>0001111=>1111000
[7,6,2,3,5,4,8,1]=>0001111=>1111000
[7,6,2,3,5,1,4,8]=>0001110=>0111000
[6,1,5,2,3,4,8,7]=>0001101=>1011000
[6,2,5,3,4,8,1,7]=>0001101=>1011000
[6,2,5,3,4,8,7,1]=>0001111=>1111000
[2,6,5,3,4,8,7,1]=>0001111=>1111000
[2,6,5,3,4,8,1,7]=>0001101=>1011000
[2,5,1,4,8,3,7,6]=>0001011=>1101000
[1,2,5,4,8,3,7,6]=>0001011=>1101000
[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
[4,3,5,8,2,1,7,6]=>1010011=>1100101
[3,5,2,4,8,7,6,1]=>0001111=>1111000
[2,3,6,5,8,4,1,7]=>0010101=>1010100
[5,2,3,8,7,4,1,6]=>0011011=>1101100
[2,3,1,7,4,8,6,5]=>0100111=>1110010
[2,3,8,7,6,4,1,5]=>0010111=>1110100
[7,5,2,3,1,6,4,8]=>0101110=>0111010
[4,2,8,5,1,3,6,7]=>0011001=>1001100
[7,4,1,3,6,2,5,8]=>0010110=>0110100
[7,4,6,3,1,2,5,8]=>0100110=>0110010
[7,2,5,8,1,3,6,4]=>0000111=>1110000
[1,2,6,5,3,4,7,8]=>0001100=>0011000
[1,4,6,5,7,2,3,8]=>0000110=>0110000
[2,4,6,5,7,1,8,3]=>0000111=>1110000
[3,5,2,1,7,8,6,4]=>1001101=>1011001
[1,2,7,8,6,4,5,3]=>0001101=>1011000
[7,1,6,3,2,4,8,5]=>0100111=>1110010
[8,5,1,2,3,6,7,4]=>0001011=>1101000
[6,4,8,1,2,3,7,5]=>0000111=>1110000
[4,3,5,1,7,8,6,2]=>0011101=>1011100
[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
[1,7,4,5,8,3,6,2]=>0000111=>1110000
[7,3,6,8,5,2,1,4]=>1001011=>1101001
[7,1,5,2,4,8,3,6]=>0001011=>1101000
[8,1,5,2,4,7,3,6]=>0001011=>1101000
[7,5,8,1,4,2,3,6]=>0010011=>1100100
[1,7,5,8,4,2,3,6]=>0010011=>1100100
[1,3,4,8,5,6,2,7]=>0000101=>1010000
[4,8,3,6,1,7,2,5]=>0000111=>1110000
[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
[1,5,6,4,2,3,7,8]=>0010100=>0010100
[1,3,6,5,2,4,7,8]=>0001100=>0011000
[1,5,6,3,2,4,7,8]=>0100100=>0010010
[5,7,8,1,2,4,3,6]=>0010001=>1000100
[6,5,1,2,4,3,8,7]=>0011101=>1011100
[2,5,1,4,6,3,8,7]=>0001101=>1011000
[5,8,7,3,1,2,4,6]=>0100011=>1100010
[2,7,8,1,4,5,3,6]=>0001001=>1001000
[4,3,7,1,2,6,8,5]=>0010011=>1100100
[4,1,2,8,7,3,6,5]=>0010111=>1110100
[8,7,5,1,2,4,3,6]=>0011011=>1101100
[6,1,2,4,3,8,7,5]=>0010111=>1110100
[3,7,8,1,2,4,6,5]=>0000101=>1010000
[7,8,5,1,2,4,3,6]=>0011001=>1001100
[8,3,4,1,2,6,7,5]=>0010011=>1100100
[2,1,4,7,3,6,8,5]=>1000011=>1100001
[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
[8,5,3,4,2,7,1,6]=>0011011=>1101100
[8,4,3,7,2,5,6,1]=>0010111=>1110100
[5,3,4,1,8,2,7,6]=>0011011=>1101100
[8,3,1,7,4,5,2,6]=>0101011=>1101010
[8,2,4,5,1,7,3,6]=>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
[8,1,4,3,7,5,6,2]=>0010111=>1110100
[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
[8,7,1,2,6,5,3,4]=>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
[6,2,8,5,1,7,3,4]=>0001111=>1111000
[8,4,1,7,5,6,2,3]=>0010111=>1110100
[8,1,2,4,7,6,5,3]=>0001111=>1111000
[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
[8,1,4,2,7,5,6,3]=>0010111=>1110100
[8,1,5,7,3,6,4,2]=>0010111=>1110100
[8,1,4,7,3,6,5,2]=>0001111=>1111000
[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
[1,2,4,6,8,3,7,5]=>0000011=>1100000
[1,3,5,6,4,8,2,7]=>0000101=>1010000
[3,1,7,8,5,2,4,6]=>0101001=>1001010
[6,3,5,7,1,4,2,8]=>0010110=>0110100
[6,3,5,2,8,4,7,1]=>0001111=>1111000
[1,6,3,5,2,8,4,7]=>0001101=>1011000
[1,5,4,8,6,3,7,2]=>0001111=>1111000
[5,4,8,6,3,7,2,1]=>1001111=>1111001
[5,4,8,6,3,7,1,2]=>0001111=>1111000
[6,4,5,8,3,1,7,2]=>0100111=>1110010
[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
[1,2,5,4,8,6,3,7]=>0001101=>1011000
[2,4,8,5,6,7,3,1]=>0100011=>1100010
[4,8,5,6,7,1,3,2]=>0100011=>1100010
[6,4,5,8,2,1,7,3]=>1000111=>1110001
[5,3,8,2,6,7,1,4]=>0001011=>1101000
[6,3,5,2,8,1,7,4]=>0001111=>1111000
[5,3,4,1,2,6,8,7]=>0011001=>1001100
[4,3,5,2,8,6,1,7]=>0011101=>1011100
[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
[3,4,8,5,6,2,7,1]=>0000111=>1110000
[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
[3,7,2,1,5,6,8,4]=>1000011=>1100001
[8,1,6,4,3,5,2,7]=>0011101=>1011100
[1,3,7,8,2,6,4,5]=>0000101=>1010000
[4,6,8,5,1,3,7,2]=>0001011=>1101000
[4,6,8,3,7,1,5,2]=>0001011=>1101000
[4,3,1,8,5,7,2,6]=>0110011=>1100110
[4,8,3,6,1,5,2,7]=>0001101=>1011000
[8,3,2,4,7,1,6,5]=>0100111=>1110010
[7,3,2,4,8,1,6,5]=>0100111=>1110010
[8,3,2,4,6,1,7,5]=>0100111=>1110010
[8,3,2,4,5,7,1,6]=>0100011=>1100010
[8,3,6,2,4,1,7,5]=>0010111=>1110100
[7,4,6,2,1,3,8,5]=>1000111=>1110001
[3,2,4,5,7,8,1,6]=>0100001=>1000010
[3,6,7,2,4,1,8,5]=>0010011=>1100100
[5,3,2,8,7,6,4,1]=>0111111=>1111110
[4,3,6,1,8,5,2,7]=>0011101=>1011100
[4,3,7,5,8,2,1,6]=>1010011=>1100101
[7,3,5,2,8,1,4,6]=>0001011=>1101000
[2,6,8,4,5,1,7,3]=>0001011=>1101000
[1,5,8,7,4,2,3,6]=>0010011=>1100100
[1,5,2,7,6,4,8,3]=>0001111=>1111000
[1,4,6,8,7,2,5,3]=>0001011=>1101000
[1,3,6,8,7,2,5,4]=>0001011=>1101000
[1,4,3,6,8,7,2,5]=>0010011=>1100100
[1,6,2,7,5,3,4,8]=>0001110=>0111000
[1,7,2,5,4,3,8,6]=>0011011=>1101100
[1,6,3,7,2,4,5,8]=>0000110=>0110000
[1,3,2,6,8,5,4,7]=>0101001=>1001010
[1,6,3,2,7,4,5,8]=>0100110=>0110010
[1,5,8,6,2,7,4,3]=>0010111=>1110100
[1,3,7,2,6,4,5,8]=>0000110=>0110000
[1,3,7,5,8,6,2,4]=>0000111=>1110000
[1,7,3,2,8,5,6,4]=>0100111=>1110010
[1,6,5,2,4,8,3,7]=>0001101=>1011000
[1,4,7,6,2,3,5,8]=>0000110=>0110000
[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
[2,6,7,3,4,8,1,5]=>0000011=>1100000
[4,1,3,8,7,5,2,6]=>0011011=>1101100
[3,6,7,2,1,5,8,4]=>1000011=>1100001
[2,5,6,1,3,8,7,4]=>0000111=>1110000
[2,1,3,8,6,7,4,5]=>1000011=>1100001
[3,8,5,2,1,6,4,7]=>1001101=>1011001
[5,4,7,8,1,6,3,2]=>0101101=>1011010
[7,3,4,2,8,5,6,1]=>0010111=>1110100
[7,2,8,3,6,4,5,1]=>0001111=>1111000
[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
[1,8,4,2,3,7,5,6]=>0010011=>1100100
[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
[6,4,2,3,7,8,5,1]=>0011101=>1011100
[5,6,8,2,4,7,1,3]=>0000011=>1100000
[6,7,4,2,3,8,5,1]=>0011011=>1101100
[5,1,3,2,6,8,4,7]=>0101001=>1001010
[5,7,1,4,6,8,2,3]=>0000011=>1100000
[5,7,8,3,2,4,6,1]=>0100101=>1010010
[1,5,7,3,6,4,2,8]=>0010110=>0110100
[1,6,3,5,7,4,8,2]=>0000111=>1110000
[1,7,2,4,8,3,5,6]=>0000011=>1100000
[1,6,7,2,4,8,3,5]=>0000011=>1100000
[1,6,7,8,2,4,3,5]=>0010001=>1000100
[3,1,6,7,8,4,2,5]=>0110001=>1000110
[3,1,6,7,8,4,5,2]=>0101001=>1001010
[1,6,7,8,2,4,5,3]=>0001001=>1001000
[4,2,7,6,8,5,1,3]=>0011011=>1101100
[5,3,4,1,7,8,6,2]=>0011101=>1011100
[3,7,5,6,1,8,4,2]=>0010111=>1110100
[1,2,6,8,4,3,5,7]=>0010001=>1000100
[2,4,7,5,8,3,6,1]=>0000111=>1110000
[6,8,7,4,2,5,1,3]=>0011011=>1101100
[7,6,3,1,2,8,5,4]=>0101111=>1111010
[3,1,8,6,4,7,2,5]=>0100111=>1110010
[6,2,7,8,3,4,5,1]=>0001101=>1011000
[8,1,3,5,6,4,7,2]=>0000111=>1110000
[2,3,7,5,8,4,6,1]=>0000111=>1110000
[2,5,7,4,6,1,3,8]=>0000110=>0110000
[4,8,2,6,5,3,7,1]=>0001111=>1111000
[5,8,6,4,7,3,2,1]=>1100111=>1110011
[8,5,2,3,1,6,7,4]=>0101011=>1101010
[8,5,4,2,1,6,7,3]=>1011011=>1101101
[8,3,5,2,1,6,7,4]=>1001011=>1101001
[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
[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
[3,8,6,2,5,4,7,1]=>0001111=>1111000
[3,8,4,6,5,2,7,1]=>0001111=>1111000
[2,8,6,4,7,3,1,5]=>0100111=>1110010
[8,3,5,4,2,7,1,6]=>0011011=>1101100
[8,1,7,4,2,5,3,6]=>0011011=>1101100
[8,3,2,5,1,4,7,6]=>0101011=>1101010
[8,4,1,3,2,6,7,5]=>0110011=>1100110
[8,4,5,1,2,6,7,3]=>0001011=>1101000
[8,1,5,2,4,6,7,3]=>0001011=>1101000
[8,3,1,5,2,6,7,4]=>0101011=>1101010
[2,8,1,6,5,3,7,4]=>0001111=>1111000
[8,3,2,1,6,4,7,5]=>1100111=>1110011
[5,2,6,4,1,3,8,7]=>0011101=>1011100
[2,1,8,5,4,3,7,6]=>1011011=>1101101
[6,2,8,5,4,1,3,7]=>0011101=>1011100
[7,2,8,5,4,1,3,6]=>0011011=>1101100
[3,7,5,8,4,1,2,6]=>0010011=>1100100
[5,2,4,7,8,1,3,6]=>0001001=>1001000
[1,7,6,2,8,5,3,4]=>0001111=>1111000
[5,6,2,8,1,7,3,4]=>0000111=>1110000
[3,1,2,4,8,6,7,5]=>0100011=>1100010
[1,8,7,2,3,4,5,6]=>0000011=>1100000
[8,6,3,2,5,4,7,1]=>0101111=>1111010
[8,6,4,2,5,3,7,1]=>0011111=>1111100
[8,6,5,2,4,3,7,1]=>0011111=>1111100
[8,5,6,2,4,3,7,1]=>0010111=>1110100
[6,2,5,3,7,4,8,1]=>0001111=>1111000
[8,4,5,2,6,3,7,1]=>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
[3,7,5,2,8,1,4,6]=>0001011=>1101000
[1,2,7,4,8,5,6,3]=>0000111=>1110000
[2,6,7,1,8,4,5,3]=>0001011=>1101000
[5,6,3,4,2,8,7,1]=>0010111=>1110100
[3,2,7,5,8,1,6,4]=>0100111=>1110010
[3,6,5,8,2,7,4,1]=>0010111=>1110100
[2,7,1,8,5,6,4,3]=>0010111=>1110100
[4,3,6,8,5,2,1,7]=>1011001=>1001101
[4,3,6,8,5,2,7,1]=>0011011=>1101100
[4,5,3,2,1,8,6,7]=>1101001=>1001011
[3,6,5,8,1,7,4,2]=>0010111=>1110100
[3,6,5,8,1,2,7,4]=>0000111=>1110000
[4,1,6,8,5,2,3,7]=>0011001=>1001100
[4,5,2,8,6,7,3,1]=>0101011=>1101010
[3,5,8,6,2,4,7,1]=>0000111=>1110000
[3,2,4,5,8,6,1,7]=>0100101=>1010010
[3,4,5,8,6,2,1,7]=>1000101=>1010001
[3,4,5,8,6,2,7,1]=>0000111=>1110000
[4,5,2,1,3,8,6,7]=>1001001=>1001001
[4,2,3,6,8,5,1,7]=>0011001=>1001100
[4,1,3,6,8,5,2,7]=>0011001=>1001100
[3,1,4,5,8,6,2,7]=>0100101=>1010010
[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
[8,2,5,4,1,3,7,6]=>0011011=>1101100
[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
[7,3,8,4,1,5,6,2]=>0010111=>1110100
[8,6,7,1,4,3,2,5]=>0110011=>1100110
[3,8,5,1,2,6,7,4]=>0001011=>1101000
[3,7,8,2,5,4,6,1]=>0001101=>1011000
[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
[2,4,8,3,5,7,1,6]=>0000011=>1100000
[1,4,8,5,7,2,3,6]=>0000011=>1100000
[1,8,7,3,2,4,5,6]=>0100011=>1100010
[2,8,4,3,5,7,1,6]=>0010011=>1100100
[5,6,2,7,8,3,1,4]=>0100101=>1010010
[8,6,2,7,3,4,1,5]=>0010111=>1110100
[8,6,2,7,3,4,5,1]=>0001111=>1111000
[5,6,2,7,8,3,4,1]=>0010101=>1010100
[5,6,3,2,8,7,1,4]=>0100111=>1110010
[6,8,5,3,1,7,2,4]=>0101011=>1101010
[8,6,1,7,3,4,2,5]=>0010111=>1110100
[5,1,6,7,8,3,2,4]=>0101001=>1001010
[1,5,6,3,7,2,4,8]=>0000110=>0110000
[6,2,4,8,3,7,1,5]=>0000111=>1110000
[1,6,8,7,5,2,3,4]=>0001011=>1101000
[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
[6,1,8,7,4,5,2,3]=>0001111=>1111000
[2,6,8,4,7,5,1,3]=>0001011=>1101000
[6,8,5,1,7,4,2,3]=>0011011=>1101100
[4,6,5,7,2,3,8,1]=>0000111=>1110000
[5,3,7,4,6,2,8,1]=>0001111=>1111000
[3,6,7,2,5,8,4,1]=>0010011=>1100100
[3,5,7,6,8,2,1,4]=>1000011=>1100001
[5,3,6,7,4,8,1,2]=>0001011=>1101000
[3,5,7,6,8,1,4,2]=>0010011=>1100100
[4,2,7,8,3,6,5,1]=>0011101=>1011100
[5,4,3,7,8,1,6,2]=>0011101=>1011100
[5,3,6,7,8,2,1,4]=>1001001=>1001001
[3,5,7,8,4,2,1,6]=>1010001=>1000101
[4,6,7,8,2,1,3,5]=>1000001=>1000001
[4,6,7,3,2,8,1,5]=>0100011=>1100010
[4,6,5,3,7,8,1,2]=>0001101=>1011000
[4,6,5,2,7,8,3,1]=>0101101=>1011010
[3,7,5,2,8,6,1,4]=>0001111=>1111000
[5,6,2,4,7,8,3,1]=>0100101=>1010010
[5,4,6,2,8,3,7,1]=>0001111=>1111000
[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
[5,2,6,4,8,7,3,1]=>0101111=>1111010
[2,4,7,8,6,5,1,3]=>0001101=>1011000
[2,5,7,8,6,1,4,3]=>0010101=>1010100
[1,3,6,4,8,2,7,5]=>0000111=>1110000
[2,4,5,3,8,7,1,6]=>0001011=>1101000
[8,6,3,7,2,4,1,5]=>0010111=>1110100
[8,4,6,7,3,5,2,1]=>1001011=>1101001
[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
[8,4,6,3,7,5,1,2]=>0001111=>1111000
[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
[6,8,4,1,7,5,2,3]=>0011011=>1101100
[7,5,4,2,1,8,6,3]=>1011111=>1111101
[5,7,6,8,3,2,4,1]=>0110011=>1100110
[7,6,4,2,8,1,5,3]=>0011111=>1111100
[7,4,6,3,8,1,5,2]=>0001111=>1111000
[3,4,6,8,2,5,7,1]=>0000011=>1100000
[1,8,5,6,4,2,3,7]=>0010101=>1010100
[1,8,4,5,6,2,3,7]=>0000101=>1010000
[6,4,8,5,7,3,1,2]=>0100111=>1110010
[1,7,6,2,3,5,8,4]=>0000111=>1110000
[7,2,5,4,6,8,1,3]=>0001011=>1101000
[7,2,4,5,6,8,1,3]=>0000011=>1100000
[8,1,6,5,2,7,4,3]=>0011111=>1111100
[2,7,1,5,3,8,6,4]=>0001111=>1111000
[3,5,7,2,8,4,1,6]=>0010011=>1100100
[7,3,2,1,4,8,6,5]=>1100111=>1110011
[8,3,7,2,6,5,1,4]=>0001111=>1111000
[7,8,6,1,4,5,2,3]=>0001101=>1011000
[7,5,8,2,6,1,4,3]=>0010111=>1110100
[8,5,1,3,2,4,6,7]=>0101001=>1001010
[3,8,5,1,2,4,6,7]=>0001001=>1001000
[5,1,3,2,4,6,8,7]=>0101001=>1001010
[5,3,8,1,4,2,6,7]=>0011001=>1001100
[5,8,4,1,2,3,6,7]=>0010001=>1000100
[5,1,7,8,4,2,3,6]=>0011001=>1001100
[1,5,7,8,2,4,3,6]=>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
[8,6,4,1,2,3,7,5]=>0010111=>1110100
[8,1,2,4,6,3,7,5]=>0000111=>1110000
[6,3,8,4,1,7,2,5]=>0010111=>1110100
[7,6,1,4,2,3,8,5]=>0010111=>1110100
[1,7,5,2,3,4,8,6]=>0001011=>1101000
[7,8,1,2,5,3,4,6]=>0001001=>1001000
[1,8,7,5,2,3,4,6]=>0001011=>1101000
[7,1,4,8,2,3,6,5]=>0000111=>1110000
[1,8,4,7,5,2,3,6]=>0001011=>1101000
[7,3,4,1,8,6,2,5]=>0010111=>1110100
[8,4,7,2,1,6,3,5]=>1000111=>1110001
[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
[2,7,5,4,6,8,1,3]=>0001011=>1101000
[1,7,5,4,6,8,2,3]=>0001011=>1101000
[2,7,5,3,6,8,1,4]=>0001011=>1101000
[4,7,8,2,5,6,1,3]=>0000101=>1010000
[2,8,5,4,6,7,1,3]=>0001011=>1101000
[4,7,5,3,8,1,2,6]=>0001011=>1101000
[4,2,7,6,8,1,3,5]=>0010011=>1100100
[3,1,7,8,5,6,2,4]=>0100101=>1010010
[1,3,8,5,6,7,2,4]=>0000011=>1100000
[3,4,7,8,6,1,2,5]=>0000101=>1010000
[6,8,3,2,4,1,5,7]=>0110001=>1000110
[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
[10,11,12,9,2,4,6,8,1,3,5,7]=>00000011001=>10011000000
[9,7,10,2,4,6,8,12,1,3,5,11]=>00000001101=>10110000000
[7,10,11,12,9,2,4,6,8,1,3,5]=>00000011001=>10011000000
[5,6,2,4,8,10,12,1,3,7,9,11]=>00001000001=>10000010000
[10,11,12,5,6,9,2,4,8,1,3,7]=>00000011001=>10011000000
[7,9,5,10,2,4,6,8,12,1,3,11]=>00000001101=>10110000000
[6,7,8,5,2,4,10,12,1,3,9,11]=>00010010001=>10001001000
[10,11,12,3,4,9,2,6,8,1,5,7]=>00000011001=>10011000000
[9,3,4,7,10,2,6,8,12,1,5,11]=>00000001101=>10110000000
[3,10,11,12,4,7,9,2,6,8,1,5]=>00000011001=>10011000000
[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
[5,10,11,12,3,6,9,2,4,8,1,7]=>00000011001=>10011000000
[5,7,9,3,10,2,4,6,8,12,1,11]=>00000001101=>10110000000
[3,6,7,8,5,2,4,10,12,1,9,11]=>00010010001=>10001001000
[4,5,6,3,2,8,10,12,1,7,9,11]=>01001000001=>10000010010
[4,5,6,10,11,12,3,9,2,8,1,7]=>00000011001=>10011000000
[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
[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
[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
[7,6,1,8,2,5,3,4]=>0001111=>1111000
[5,8,4,2,1,6,3,7]=>1010101=>1010101
[7,6,4,1,2,5,3,8]=>0011110=>0111100
[8,7,2,6,4,5,3,1]=>0101111=>1111010
[5,2,3,7,1,8,4,6]=>0001011=>1101000
[4,8,6,5,1,3,7,2]=>0001111=>1111000
[1,7,5,4,8,6,2,3]=>0001111=>1111000
[4,5,1,6,8,2,7,3]=>0001011=>1101000
[1,6,3,7,2,4,8,5]=>0000111=>1110000
[8,7,2,4,1,5,3,6]=>0011011=>1101100
[5,2,4,1,8,3,6,7]=>0011001=>1001100
[4,3,1,6,7,2,5,8]=>0110010=>0100110
[6,3,1,5,7,2,4,8]=>0100110=>0110010
[6,1,8,2,4,5,3,7]=>0001101=>1011000
[4,5,2,1,3,7,6,8]=>1001010=>0101001
[8,2,7,4,1,6,5,3]=>0011111=>1111100
[3,7,6,4,1,5,8,2]=>0010111=>1110100
[2,7,6,4,5,1,8,3]=>0001111=>1111000
[4,6,8,1,7,3,5,2]=>0001011=>1101000
[2,8,4,6,3,1,5,7]=>0100101=>1010010
[2,8,3,1,6,7,4,5]=>0100011=>1100010
[1,3,7,6,5,2,4,8]=>0001110=>0111000
[1,3,6,7,5,2,4,8]=>0001010=>0101000
[1,5,2,6,8,7,3,4]=>0001011=>1101000
[4,8,5,7,1,2,3,6]=>0000011=>1100000
[7,8,6,1,4,3,2,5]=>0110101=>1010110
[7,4,8,3,6,2,1,5]=>1000111=>1110001
[1,5,7,4,8,6,2,3]=>0000111=>1110000
[4,8,7,5,2,3,1,6]=>0101011=>1101010
[1,2,7,8,6,4,3,5]=>0010101=>1010100
[3,5,1,7,8,6,2,4]=>0001101=>1011000
[1,8,6,7,4,2,3,5]=>0010011=>1100100
[7,1,3,2,6,5,8,4]=>0100111=>1110010
[2,4,6,5,8,3,1,7]=>0100101=>1010010
[2,4,6,5,8,1,7,3]=>0000111=>1110000
[2,4,6,3,8,7,1,5]=>0000111=>1110000
[1,5,4,7,3,8,6,2]=>0001111=>1111000
[2,5,6,4,1,3,8,7]=>0010101=>1010100
[7,2,3,1,6,8,4,5]=>0100011=>1100010
[5,7,8,1,6,2,3,4]=>0000101=>1010000
[1,4,8,3,2,7,5,6]=>0100011=>1100010
[1,6,3,8,2,7,4,5]=>0000111=>1110000
[1,6,4,2,7,3,8,5]=>0010111=>1110100
[1,4,2,5,8,6,3,7]=>0010101=>1010100
[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
[3,1,7,5,6,2,4,8]=>0100110=>0110010
[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
[5,8,3,2,4,1,7,6]=>0110011=>1100110
[6,1,4,3,7,5,8,2]=>0010111=>1110100
[2,7,5,6,8,3,1,4]=>0100011=>1100010
[1,7,8,6,3,4,2,5]=>0010101=>1010100
[6,4,1,8,2,7,5,3]=>0011111=>1111100
[1,5,6,8,4,2,7,3]=>0010011=>1100100
[7,3,2,1,4,6,8,5]=>1100011=>1100011
[7,8,5,3,2,1,6,4]=>1101101=>1011011
[4,7,2,6,1,8,3,5]=>0000111=>1110000
[8,7,3,5,2,1,6,4]=>1001111=>1111001
[3,8,6,2,1,7,4,5]=>1000111=>1110001
[2,5,7,1,3,6,4,8]=>0000110=>0110000
[1,4,7,2,5,3,6,8]=>0001010=>0101000
[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
[7,5,2,4,1,3,8,6]=>0011011=>1101100
[6,2,1,7,4,3,8,5]=>1010111=>1110101
[2,4,3,6,7,1,5,8]=>0010010=>0100100
[3,1,7,4,2,6,8,5]=>0110011=>1100110
[7,3,5,2,1,6,4,8]=>1001110=>0111001
[4,6,5,2,1,3,7,8]=>1001100=>0011001
[1,4,7,2,5,6,3,8]=>0000110=>0110000
[7,2,5,6,1,3,8,4]=>0000111=>1110000
[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
[1,7,4,5,6,8,2,3]=>0000011=>1100000
[6,8,5,7,2,1,4,3]=>1010011=>1100101
[1,6,8,7,3,4,2,5]=>0010011=>1100100
[1,4,2,6,7,8,5,3]=>0011001=>1001100
[5,6,4,2,1,8,3,7]=>1010101=>1010101
[4,1,2,6,7,8,5,3]=>0011001=>1001100
[5,6,2,7,8,1,3,4]=>0000101=>1010000
[3,7,8,2,1,4,5,6]=>1000001=>1000001
[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
[6,5,3,1,2,4,8,7,10,9]=>010110101=>101011010
[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
[2,1,12,10,4,6,7,3,8,5,11,9]=>10000110111=>11101100001
[2,1,10,3,9,6,4,8,5,7,12,11]=>10001011101=>10111010001
[2,1,12,3,10,6,4,7,9,5,11,8]=>10001001111=>11110010001
[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
[4,1,3,2,12,5,11,8,6,10,7,9]=>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
[12,5,3,8,2,11,6,4,9,1,7,10]=>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
[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
[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
[12,7,2,4,5,10,3,1,8,6,11,9]=>01000110111=>11101100010
[10,8,2,4,5,1,6,3,9,7,12,11]=>00011011101=>10111011000
[12,9,2,4,5,1,6,7,3,10,11,8]=>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
[12,11,8,4,9,6,2,3,5,1,7,10]=>00011011011=>11011011000
[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
[8,1,2,3,5,6,7,4,12,9,11,10]=>00000110011=>11001100000
[12,10,2,3,5,6,7,1,8,4,11,9]=>00000110111=>11101100000
[12,11,9,3,5,6,2,8,4,1,7,10]=>00101011011=>11011010100
[12,11,2,9,5,3,7,8,4,1,6,10]=>00110011011=>11011001100
[10,1,2,3,4,6,7,8,9,5,12,11]=>00000001101=>10110000000
[12,1,2,3,4,5,7,8,9,10,11,6]=>00000000011=>11000000000
[1,5,4,7,8,3,6,2]=>0001101=>1011000
[5,1,4,7,8,3,6,2]=>0001101=>1011000
[5,6,4,1,7,3,8,2]=>0010111=>1110100
[8,3,7,5,4,2,6,1]=>0011111=>1111100
[4,3,7,8,2,5,1,6]=>0011001=>1001100
[2,7,1,6,5,8,3,4]=>0000111=>1110000
[3,7,8,5,4,2,1,6]=>1011001=>1001101
[1,7,4,5,6,8,3,2]=>0100011=>1100010
[2,7,4,5,6,8,3,1]=>0100011=>1100010
[2,8,3,5,6,4,1,7]=>0010101=>1010100
[2,4,7,8,3,1,6,5]=>0100101=>1010010
[5,4,3,6,8,1,7,2]=>0011011=>1101100
[3,7,4,5,8,1,2,6]=>0000011=>1100000
[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
[2,4,3,5,8,1,6,7]=>0010001=>1000100
[4,6,1,7,3,2,8,5]=>0100111=>1110010
[1,7,3,6,4,2,8,5]=>0010111=>1110100
[1,3,7,6,2,4,8,5]=>0000111=>1110000
[4,7,3,5,1,2,8,6]=>0001011=>1101000
[2,5,1,8,3,7,4,6]=>0001011=>1101000
[5,1,2,4,3,6,8,7]=>0011001=>1001100
[4,8,3,5,2,1,6,7]=>1001001=>1001001
[8,7,3,1,5,2,6,4]=>0101111=>1111010
[3,8,4,1,7,5,2,6]=>0011011=>1101100
[7,8,5,3,6,2,1,4]=>1001101=>1011001
[6,7,1,5,2,8,4,3]=>0011011=>1101100
[2,7,6,4,8,3,1,5]=>0100111=>1110010
[2,6,3,7,5,8,4,1]=>0010111=>1110100
[4,7,3,2,6,5,1,8]=>0101110=>0111010
[4,7,5,2,3,6,1,8]=>0001110=>0111000
[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
[4,5,3,8,2,1,7,6]=>1001011=>1101001
[4,5,3,8,6,1,2,7]=>0001101=>1011000
[7,3,8,4,5,1,2,6]=>0001011=>1101000
[4,8,7,5,1,3,2,6]=>0101011=>1101010
[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
[4,7,5,8,2,1,3,6]=>1000011=>1100001
[4,8,5,7,1,3,2,6]=>0100011=>1100010
[7,8,6,3,1,2,5,4]=>0101101=>1011010
[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
[2,1,4,7,5,3,8,6]=>1001011=>1101001
[6,8,1,3,5,7,4,2]=>0010011=>1100100
[5,8,3,2,7,4,6,1]=>0100111=>1110010
[4,1,3,7,5,6,2,8]=>0010110=>0110100
[5,1,7,2,4,6,3,8]=>0001110=>0111000
[4,2,7,3,6,8,5,1]=>0011011=>1101100
[5,8,4,7,1,3,6,2]=>0000111=>1110000
[3,1,5,8,6,7,2,4]=>0100011=>1100010
[6,8,2,1,4,5,7,3]=>1000011=>1100001
[5,3,1,2,4,6,8,7]=>0101001=>1001010
[3,6,7,5,8,4,1,2]=>0010011=>1100100
[6,1,5,2,8,7,4,3]=>0011111=>1111100
[3,2,6,1,5,8,7,4]=>0100111=>1110010
[4,5,2,1,6,7,8,3]=>1001001=>1001001
[8,4,6,3,1,2,7,5]=>0100111=>1110010
[3,7,6,4,1,5,2,8]=>0011110=>0111100
[3,8,6,4,1,5,7,2]=>0010111=>1110100
[8,7,1,4,5,2,3,6]=>0001011=>1101000
[8,7,1,4,2,5,3,6]=>0011011=>1101100
[4,8,7,3,1,2,6,5]=>0100111=>1110010
[3,8,6,4,5,1,7,2]=>0001111=>1111000
[3,7,6,4,5,1,2,8]=>0001110=>0111000
[8,4,6,2,1,7,3,5]=>1000111=>1110001
[7,4,6,3,1,2,8,5]=>0100111=>1110010
[4,6,3,5,7,1,8,2]=>0000111=>1110000
[4,6,2,5,7,8,1,3]=>0000101=>1010000
[4,7,3,5,8,1,6,2]=>0000111=>1110000
[4,6,3,5,7,1,2,8]=>0000110=>0110000
[4,7,3,5,8,6,1,2]=>0000111=>1110000
[4,7,3,5,6,1,2,8]=>0000110=>0110000
[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
[1,2,7,8,3,5,4,6]=>0001001=>1001000
[1,6,7,8,3,2,5,4]=>0101001=>1001010
[1,7,6,2,8,5,4,3]=>0011111=>1111100
[1,6,7,8,3,2,4,5]=>0100001=>1000010
[1,2,7,8,3,4,6,5]=>0000101=>1010000
[1,7,6,8,3,4,2,5]=>0010011=>1100100
[8,4,7,3,1,2,6,5]=>0100111=>1110010
[4,2,8,1,6,5,7,3]=>0010111=>1110100
[3,1,8,2,6,5,7,4]=>0100111=>1110010
[2,8,4,3,1,6,5,7]=>0110101=>1010110
[2,4,3,8,6,5,1,7]=>0011101=>1011100
[2,8,6,4,3,1,7,5]=>0110111=>1110110
[7,4,5,8,1,3,6,2]=>0000111=>1110000
[1,4,6,3,2,5,8,7]=>0100101=>1010010
[4,2,5,7,1,6,8,3]=>0010011=>1100100
[4,5,3,7,1,6,8,2]=>0001011=>1101000
[6,8,4,1,5,7,3,2]=>0110011=>1100110
[6,8,4,1,5,7,2,3]=>0010011=>1100100
[5,2,6,7,4,1,8,3]=>0011011=>1101100
[5,6,7,4,3,1,8,2]=>0110011=>1100110
[8,5,6,4,1,7,3,2]=>0110111=>1110110
[5,8,2,6,1,7,4,3]=>0010111=>1110100
[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
[4,8,1,3,6,2,7,5]=>0000111=>1110000
[4,5,8,1,6,2,7,3]=>0000111=>1110000
[5,2,6,8,1,4,3,7]=>0011001=>1001100
[6,2,7,3,8,1,4,5]=>0000111=>1110000
[6,7,3,8,2,1,4,5]=>1000011=>1100001
[6,2,7,8,3,1,4,5]=>0100101=>1010010
[8,7,3,1,2,5,6,4]=>0100111=>1110010
[2,8,3,6,4,1,7,5]=>0010111=>1110100
[6,1,3,7,2,8,5,4]=>0001111=>1111000
[5,4,3,6,1,7,8,2]=>0011101=>1011100
[4,8,3,2,1,7,5,6]=>1100011=>1100011
[1,2,4,6,5,8,3,7]=>0000101=>1010000
[2,4,8,6,3,1,7,5]=>0100111=>1110010
[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
[4,8,7,3,6,1,2,5]=>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
[2,4,8,6,5,7,1,3]=>0000111=>1110000
[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
[4,1,7,8,6,5,2,3]=>0011101=>1011100
[2,1,8,7,3,5,4,6]=>1001011=>1101001
[1,7,6,2,3,8,5,4]=>0001111=>1111000
[1,8,5,3,2,7,4,6]=>0101011=>1101010
[4,5,1,3,7,6,2,8]=>0001110=>0111000
[7,2,3,8,6,4,5,1]=>0001111=>1111000
[3,5,8,1,7,4,2,6]=>0010011=>1100100
[5,8,1,2,7,6,4,3]=>0010111=>1110100
[8,7,1,3,2,6,4,5]=>0100111=>1110010
[1,3,8,5,2,4,6,7]=>0001001=>1001000
[7,8,6,1,3,2,4,5]=>0100101=>1010010
[8,1,6,3,7,5,4,2]=>0011111=>1111100
[8,5,1,3,7,6,4,2]=>0011111=>1111100
[1,6,4,7,3,8,5,2]=>0001111=>1111000
[2,8,1,5,6,4,3,7]=>0010101=>1010100
[1,2,6,8,3,4,7,5]=>0000011=>1100000
[1,6,7,5,8,4,2,3]=>0010011=>1100100
[7,4,1,6,5,2,8,3]=>0011111=>1111100
[5,3,8,2,7,6,1,4]=>0001111=>1111000
[7,4,2,8,6,5,3,1]=>0111111=>1111110
[5,8,2,7,6,1,4,3]=>0010111=>1110100
[7,4,8,3,1,6,5,2]=>0101111=>1111010
[5,8,7,2,6,4,3,1]=>0110111=>1110110
[6,8,7,5,2,1,4,3]=>1011011=>1101101
[6,8,7,3,5,1,4,2]=>0011011=>1101100
[1,8,6,4,7,3,2,5]=>0100111=>1110010
[7,2,5,4,1,3,8,6]=>0011011=>1101100
[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
[7,2,6,8,5,1,3,4]=>0001011=>1101000
[7,3,6,4,2,1,8,5]=>1010111=>1110101
[4,8,5,2,7,3,1,6]=>0101011=>1101010
[5,8,6,3,2,1,7,4]=>1100111=>1110011
[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
[7,8,5,2,6,4,3,1]=>0111101=>1011110
[7,3,2,1,8,5,6,4]=>1100111=>1110011
[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
[1,7,2,5,8,4,3,6]=>0010011=>1100100
[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
[1,8,6,2,7,4,3,5]=>0010111=>1110100
[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
[8,5,3,6,4,2,1,7]=>1011101=>1011101
[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
[6,4,5,3,1,7,8,2]=>0101101=>1011010
[6,4,5,3,1,8,7,2]=>0101111=>1111010
[8,7,3,2,5,1,6,4]=>0101111=>1111010
[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
[1,8,2,3,5,6,4,7]=>0000101=>1010000
[2,8,1,3,5,6,4,7]=>0000101=>1010000
[2,5,7,4,8,3,6,1]=>0000111=>1110000
[2,6,3,4,7,8,5,1]=>0001101=>1011000
[2,3,5,4,7,1,8,6]=>0001011=>1101000
[7,4,1,3,6,8,5,2]=>0011011=>1101100
[7,2,1,3,6,8,4,5]=>1000011=>1100001
[7,4,2,3,6,8,5,1]=>0011011=>1101100
[7,2,3,6,8,5,4,1]=>0011011=>1101100
[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
[7,2,5,1,6,4,3,8]=>0011110=>0111100
[1,2,4,6,8,5,7,3]=>0000011=>1100000
[8,5,2,3,7,4,1,6]=>0011011=>1101100
[2,6,3,7,4,1,8,5]=>0010111=>1110100
[6,1,3,2,8,5,7,4]=>0100111=>1110010
[3,8,5,1,2,4,7,6]=>0001011=>1101000
[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
[4,6,2,5,3,1,7,8]=>0101100=>0011010
[7,1,4,5,2,6,8,3]=>0001011=>1101000
[5,7,6,8,2,1,4,3]=>1010011=>1100101
[3,5,4,7,8,2,6,1]=>0001101=>1011000
[5,1,4,7,6,8,3,2]=>0101011=>1101010
[5,2,4,7,6,8,3,1]=>0101011=>1101010
[5,6,4,7,1,8,3,2]=>0100111=>1110010
[3,6,7,5,1,4,8,2]=>0001011=>1101000
[6,3,7,1,2,5,8,4]=>0000111=>1110000
[5,1,4,7,8,2,6,3]=>0001101=>1011000
[6,3,7,5,1,2,8,4]=>0001111=>1111000
[5,3,7,4,6,1,8,2]=>0001111=>1111000
[5,4,1,7,6,8,3,2]=>0111011=>1101110
[4,2,5,3,6,7,8,1]=>0011001=>1001100
[4,5,1,3,6,7,8,2]=>0001001=>1001000
[3,6,7,1,5,4,8,2]=>0001011=>1101000
[3,6,4,7,5,8,2,1]=>1000111=>1110001
[6,4,7,1,5,2,8,3]=>0001111=>1111000
[3,5,6,2,1,7,8,4]=>1000101=>1010001
[2,5,6,7,1,8,4,3]=>0010011=>1100100
[8,1,4,3,5,2,7,6]=>0011011=>1101100
[4,8,1,3,5,2,7,6]=>0001011=>1101000
[4,5,1,6,2,8,7,3]=>0001111=>1111000
[3,2,5,8,6,1,7,4]=>0100111=>1110010
[4,5,1,7,2,8,6,3]=>0001111=>1111000
[7,1,4,3,6,8,2,5]=>0010011=>1100100
[5,6,3,2,7,4,1,8]=>0110110=>0110110
[5,2,6,7,4,3,1,8]=>0111010=>0101110
[8,5,1,6,4,3,2,7]=>0111101=>1011110
[8,5,1,6,4,3,7,2]=>0011111=>1111100
[8,5,2,1,6,4,3,7]=>1011101=>1011101
[8,6,3,5,2,7,1,4]=>0001111=>1111000
[8,4,6,2,1,5,7,3]=>1000111=>1110001
[5,6,2,1,8,4,7,3]=>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
[7,4,8,2,1,5,6,3]=>1000111=>1110001
[7,3,2,8,5,1,4,6]=>0101011=>1101010
[6,7,1,4,3,2,8,5]=>0110011=>1100110
[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
[6,2,8,4,3,7,1,5]=>0010111=>1110100
[1,2,6,3,7,8,5,4]=>0001101=>1011000
[6,1,3,2,7,8,5,4]=>0101101=>1011010
[6,7,1,3,2,8,5,4]=>0101011=>1101010
[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
[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
[3,8,2,5,4,1,6,7]=>0011001=>1001100
[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
[6,2,1,5,8,3,4,7]=>1000101=>1010001
[1,5,7,3,6,2,4,8]=>0000110=>0110000
[1,4,7,5,2,3,6,8]=>0001010=>0101000
[1,4,6,5,8,2,3,7]=>0000101=>1010000
[1,5,8,6,2,3,4,7]=>0000101=>1010000
[1,4,8,3,7,6,2,5]=>0000111=>1110000
[1,4,5,3,7,2,6,8]=>0001010=>0101000
[1,4,8,7,3,6,2,5]=>0000111=>1110000
[8,3,5,1,6,4,7,2]=>0001111=>1111000
[5,8,4,3,6,2,7,1]=>0010111=>1110100
[4,6,5,8,3,2,7,1]=>0100111=>1110010
[3,4,7,5,6,8,2,1]=>1000011=>1100001
[3,4,7,8,5,2,6,1]=>0001101=>1011000
[2,3,8,4,7,1,6,5]=>0000111=>1110000
[1,8,7,5,2,6,3,4]=>0001111=>1111000
[1,8,7,5,4,3,2,6]=>0111011=>1101110
[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
[1,8,7,2,4,6,3,5]=>0000111=>1110000
[1,4,7,8,6,2,5,3]=>0001101=>1011000
[1,7,6,4,2,5,3,8]=>0011110=>0111100
[1,4,7,5,8,2,3,6]=>0000011=>1100000
[1,4,7,5,8,2,6,3]=>0000111=>1110000
[1,6,8,3,4,2,5,7]=>0010001=>1000100
[1,4,7,2,3,6,5,8]=>0000110=>0110000
[1,3,2,6,8,4,7,5]=>0100011=>1100010
[1,7,2,5,6,3,4,8]=>0000110=>0110000
[1,5,8,3,6,4,7,2]=>0000111=>1110000
[1,2,6,5,8,3,4,7]=>0000101=>1010000
[1,6,8,2,7,3,4,5]=>0000011=>1100000
[1,4,5,8,2,6,3,7]=>0000101=>1010000
[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
[5,2,6,4,8,7,1,3]=>0001111=>1111000
[2,1,5,6,4,8,3,7]=>1000101=>1010001
[5,1,4,7,8,6,2,3]=>0001101=>1011000
[2,5,7,1,8,6,3,4]=>0000111=>1110000
[1,6,7,2,8,5,4,3]=>0011011=>1101100
[4,6,1,7,8,5,3,2]=>0101101=>1011010
[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
[8,5,3,2,4,1,7,6]=>0111011=>1101110
[1,4,3,2,7,5,8,6]=>0110011=>1100110
[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
[7,6,2,8,4,5,3,1]=>0101111=>1111010
[7,8,2,6,4,5,3,1]=>0101101=>1011010
[2,8,3,1,7,5,6,4]=>0100111=>1110010
[1,8,3,5,2,6,4,7]=>0001101=>1011000
[2,5,8,4,6,1,3,7]=>0000101=>1010000
[1,8,4,5,6,2,7,3]=>0000111=>1110000
[2,3,8,7,4,5,1,6]=>0001011=>1101000
[2,4,8,5,7,3,1,6]=>0100011=>1100010
[1,8,3,5,7,4,2,6]=>0010011=>1100100
[2,5,8,4,6,7,1,3]=>0000011=>1100000
[3,5,6,8,4,7,1,2]=>0000011=>1100000
[3,5,6,8,4,2,7,1]=>0010011=>1100100
[2,5,8,4,6,3,7,1]=>0000111=>1110000
[1,8,4,5,6,3,2,7]=>0100101=>1010010
[7,2,5,3,4,6,1,8]=>0001110=>0111000
[7,1,2,6,4,3,5,8]=>0010110=>0110100
[7,1,2,6,3,4,5,8]=>0000110=>0110000
[7,1,2,6,4,5,3,8]=>0001110=>0111000
[7,1,2,6,5,3,4,8]=>0001110=>0111000
[5,3,1,4,7,2,8,6]=>0101011=>1101010
[7,1,3,8,2,6,4,5]=>0000111=>1110000
[1,8,3,7,2,4,6,5]=>0000111=>1110000
[2,7,5,6,4,8,1,3]=>0000111=>1110000
[2,8,3,6,5,7,1,4]=>0000111=>1110000
[7,4,3,1,6,5,2,8]=>0111110=>0111110
[3,5,1,2,6,8,7,4]=>0001011=>1101000
[1,5,2,4,3,8,7,6]=>0011011=>1101100
[3,1,2,4,8,7,5,6]=>0100011=>1100010
[5,2,1,6,3,8,7,4]=>1001111=>1111001
[3,4,6,7,2,1,5,8]=>1000010=>0100001
[2,5,7,4,6,8,1,3]=>0000011=>1100000
[4,6,2,7,5,8,1,3]=>0000111=>1110000
[4,7,2,5,3,8,1,6]=>0001011=>1101000
[2,4,7,6,3,8,1,5]=>0000111=>1110000
[5,8,3,6,4,1,7,2]=>0010111=>1110100
[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
[8,5,6,7,4,1,3,2]=>0110011=>1100110
[1,6,5,7,3,8,2,4]=>0000111=>1110000
[7,2,4,8,6,1,5,3]=>0001111=>1111000
[7,1,4,8,6,5,2,3]=>0001111=>1111000
[8,6,2,1,3,7,5,4]=>1001111=>1111001
[8,1,4,6,7,2,5,3]=>0001011=>1101000
[8,1,4,6,2,7,5,3]=>0001111=>1111000
[8,6,1,3,2,7,5,4]=>0101111=>1111010
[8,1,7,5,2,4,6,3]=>0001111=>1111000
[8,6,2,7,5,3,1,4]=>0101111=>1111010
[8,2,7,5,4,1,6,3]=>0011111=>1111100
[8,2,1,6,7,4,5,3]=>1001011=>1101001
[8,7,2,1,5,3,6,4]=>1001111=>1111001
[8,6,1,2,7,3,5,4]=>0001111=>1111000
[8,1,6,2,4,7,5,3]=>0001111=>1111000
[5,2,6,7,4,8,3,1]=>0101011=>1101010
[6,2,3,8,7,4,5,1]=>0001111=>1111000
[4,3,7,1,2,8,5,6]=>0010011=>1100100
[8,5,7,1,4,2,6,3]=>0010111=>1110100
[2,6,7,1,4,3,8,5]=>0010011=>1100100
[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
[5,2,3,8,7,1,6,4]=>0001111=>1111000
[3,2,8,1,7,5,4,6]=>0101011=>1101010
[4,8,5,1,3,7,2,6]=>0001011=>1101000
[4,6,5,8,1,7,3,2]=>0100111=>1110010
[2,1,3,6,4,8,7,5]=>1000111=>1110001
[4,8,2,1,6,7,5,3]=>1001011=>1101001
[4,8,1,2,7,5,6,3]=>0000111=>1110000
[5,2,8,1,7,4,6,3]=>0001111=>1111000
[5,7,4,8,1,2,6,3]=>0000111=>1110000
[8,1,6,7,3,4,2,5]=>0010011=>1100100
[4,5,1,6,8,7,2,3]=>0001011=>1101000
[3,4,7,2,5,8,6,1]=>0000111=>1110000
[3,4,7,1,5,8,2,6]=>0000011=>1100000
[6,2,7,4,5,3,1,8]=>0101110=>0111010
[6,8,7,5,4,1,2,3]=>0011011=>1101100
[4,3,8,6,1,2,5,7]=>0010101=>1010100
[4,8,6,5,7,1,3,2]=>0100111=>1110010
[4,8,1,5,3,6,7,2]=>0001011=>1101000
[8,4,6,7,5,1,3,2]=>0101011=>1101010
[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
[8,6,4,7,5,1,3,2]=>0101111=>1111010
[5,3,6,4,1,2,8,7]=>0011101=>1011100
[5,4,1,7,8,6,2,3]=>0011101=>1011100
[6,1,4,7,5,8,2,3]=>0000111=>1110000
[2,1,7,5,8,6,3,4]=>1000111=>1110001
[5,3,4,7,8,1,6,2]=>0001101=>1011000
[5,1,4,8,2,3,7,6]=>0001011=>1101000
[5,8,6,3,1,2,4,7]=>0100101=>1010010
[4,5,2,3,8,6,1,7]=>0001101=>1011000
[4,5,1,3,2,6,8,7]=>0101001=>1001010
[4,7,1,8,5,3,6,2]=>0001111=>1111000
[6,4,7,5,1,3,2,8]=>0101110=>0111010
[6,7,2,4,1,8,3,5]=>0010011=>1100100
[5,1,6,3,2,7,8,4]=>0101101=>1011010
[2,3,7,8,5,4,6,1]=>0001101=>1011000
[7,4,5,1,2,6,8,3]=>0001011=>1101000
[6,7,8,2,1,5,3,4]=>1001001=>1001001
[5,2,1,6,4,7,3,8]=>1001110=>0111001
[6,7,2,5,4,1,3,8]=>0011010=>0101100
[7,4,8,6,3,5,1,2]=>0001111=>1111000
[8,4,1,6,2,7,5,3]=>0011111=>1111100
[4,2,7,1,5,8,3,6]=>0010011=>1100100
[4,6,3,5,1,8,2,7]=>0001101=>1011000
[8,5,7,6,2,3,4,1]=>0010111=>1110100
[8,4,2,3,6,7,5,1]=>0011011=>1101100
[2,4,7,5,8,6,3,1]=>0100111=>1110010
[4,1,7,6,2,8,3,5]=>0010111=>1110100
[2,7,5,3,1,4,8,6]=>0101011=>1101010
[4,1,7,2,8,5,3,6]=>0011011=>1101100
[2,6,5,3,8,4,7,1]=>0001111=>1111000
[7,1,4,3,6,5,8,2]=>0010111=>1110100
[7,1,6,3,5,4,8,2]=>0001111=>1111000
[5,7,3,2,8,4,1,6]=>0110011=>1100110
[2,8,7,1,6,5,3,4]=>0001111=>1111000
[2,8,6,1,7,5,3,4]=>0001111=>1111000
[8,1,5,2,7,4,3,6]=>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
[1,3,8,4,7,2,6,5]=>0000111=>1110000
[1,8,2,4,7,3,6,5]=>0000111=>1110000
[8,2,7,5,3,6,4,1]=>0011111=>1111100
[8,4,1,3,6,7,2,5]=>0010011=>1100100
[8,7,2,3,1,5,6,4]=>0100111=>1110010
[1,2,8,6,7,5,4,3]=>0011011=>1101100
[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
[8,7,2,4,3,6,5,1]=>0011111=>1111100
[4,2,8,7,3,6,5,1]=>0011111=>1111100
[8,7,1,6,4,3,5,2]=>0011111=>1111100
[8,4,1,7,3,6,5,2]=>0011111=>1111100
[4,5,1,8,7,3,6,2]=>0001111=>1111000
[4,3,8,5,2,6,1,7]=>0011101=>1011100
[4,3,8,5,2,7,1,6]=>0011011=>1101100
[5,6,8,2,3,4,1,7]=>0010001=>1000100
[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
[8,4,5,3,6,1,7,2]=>0001111=>1111000
[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
[8,4,5,2,6,1,7,3]=>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
[8,6,2,3,5,1,7,4]=>0001111=>1111000
[4,8,3,2,6,1,7,5]=>0100111=>1110010
[5,2,6,3,7,8,4,1]=>0011101=>1011100
[3,6,2,5,7,8,4,1]=>0010101=>1010100
[2,7,4,6,8,3,5,1]=>0001011=>1101000
[2,7,3,6,8,5,4,1]=>0011011=>1101100
[3,7,6,8,1,5,4,2]=>0011011=>1101100
[4,7,6,8,2,3,5,1]=>0001011=>1101000
[3,7,5,6,8,2,4,1]=>0010011=>1100100
[3,7,2,6,8,4,5,1]=>0001011=>1101000
[1,5,7,6,8,4,2,3]=>0010011=>1100100
[2,7,5,6,8,4,3,1]=>0110011=>1100110
[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
[8,1,5,2,6,4,7,3]=>0001111=>1111000
[5,3,4,7,6,2,1,8]=>1001110=>0111001
[8,7,2,6,4,5,1,3]=>0001111=>1111000
[3,1,2,8,7,5,4,6]=>0101011=>1101010
[3,1,2,8,7,6,4,5]=>0100111=>1110010
[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
[8,2,1,5,6,4,7,3]=>1000111=>1110001
[2,8,5,1,6,4,3,7]=>0011101=>1011100
[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
[2,7,8,1,5,4,3,6]=>0011001=>1001100
[3,6,2,1,8,4,7,5]=>1000111=>1110001
[4,5,2,6,7,3,8,1]=>0001011=>1101000
[3,5,1,6,7,4,8,2]=>0001011=>1101000
[6,5,8,1,4,3,7,2]=>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
[4,6,1,3,5,7,2,8]=>0000110=>0110000
[2,4,5,7,3,6,1,8]=>0000110=>0110000
[3,4,6,1,8,2,7,5]=>0000111=>1110000
[2,4,1,7,5,6,3,8]=>0010110=>0110100
[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
[2,6,5,7,1,3,4,8]=>0000110=>0110000
[2,3,7,1,5,6,4,8]=>0000110=>0110000
[5,6,1,3,2,4,7,8]=>0100100=>0010010
[2,6,5,3,4,1,7,8]=>0011100=>0011100
[2,6,1,3,5,4,7,8]=>0001100=>0011000
[3,6,7,1,4,2,5,8]=>0010010=>0100100
[3,6,5,2,7,1,4,8]=>0001110=>0111000
[7,1,5,4,2,6,3,8]=>0011110=>0111100
[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
[4,5,1,7,6,2,8,3]=>0001111=>1111000
[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
[7,8,5,3,2,6,1,4]=>0101101=>1011010
[6,8,3,2,7,5,1,4]=>0101011=>1101010
[5,6,4,1,7,2,8,3]=>0010111=>1110100
[3,8,6,1,5,7,4,2]=>0010111=>1110100
[1,6,7,2,4,3,5,8]=>0010010=>0100100
[8,1,3,2,4,6,5,7]=>0100101=>1010010
[6,4,2,3,7,8,1,5]=>0010101=>1010100
[5,4,3,1,7,2,8,6]=>0111011=>1101110
[5,3,1,6,4,7,2,8]=>0101110=>0111010
[6,5,2,4,1,7,8,3]=>0011101=>1011100
[4,3,6,2,5,8,1,7]=>0010101=>1010100
[1,6,2,7,8,4,5,3]=>0001101=>1011000
[1,6,7,8,3,4,2,5]=>0010001=>1000100
[7,2,1,8,3,6,4,5]=>1000111=>1110001
[5,4,2,3,1,7,8,6]=>0111001=>1001110
[2,1,3,8,6,4,7,5]=>1000111=>1110001
[4,6,1,3,2,8,5,7]=>0100101=>1010010
[4,6,5,3,8,2,1,7]=>1001101=>1011001
[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
[2,5,8,6,4,3,7,1]=>0010111=>1110100
[8,5,4,1,2,3,7,6]=>0011011=>1101100
[8,5,2,4,1,3,7,6]=>0011011=>1101100
[4,5,8,7,3,6,2,1]=>1000111=>1110001
[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
[6,3,2,8,4,5,1,7]=>0101101=>1011010
[5,4,7,2,1,3,8,6]=>1001011=>1101001
[8,4,6,5,2,7,3,1]=>0101111=>1111010
[6,4,7,5,8,3,1,2]=>0100111=>1110010
[4,6,7,5,1,8,3,2]=>0101011=>1101010
[2,6,4,5,7,1,8,3]=>0000111=>1110000
[4,1,7,6,5,2,8,3]=>0011111=>1111100
[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
[6,4,7,1,2,3,8,5]=>0000111=>1110000
[8,2,3,1,6,4,7,5]=>0100111=>1110010
[3,1,8,5,7,2,6,4]=>0100111=>1110010
[5,6,4,2,1,7,3,8]=>1010110=>0110101
[6,5,7,1,2,8,3,4]=>0000111=>1110000
[6,4,7,1,2,5,3,8]=>0001110=>0111000
[5,7,6,3,1,2,8,4]=>0100111=>1110010
[1,2,4,8,5,7,3,6]=>0000011=>1100000
[1,2,7,5,8,6,3,4]=>0000111=>1110000
[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
[6,4,7,5,3,8,1,2]=>0001111=>1111000
[6,2,1,5,3,7,8,4]=>1001101=>1011001
[7,5,6,1,4,3,8,2]=>0010111=>1110100
[4,1,7,8,3,6,5,2]=>0011101=>1011100
[6,3,2,4,8,5,1,7]=>0101101=>1011010
[6,4,2,1,7,3,5,8]=>1010110=>0110101
[5,7,4,2,1,6,3,8]=>1010110=>0110101
[5,8,4,2,1,3,6,7]=>1010001=>1000101
[2,7,3,8,5,6,4,1]=>0010111=>1110100
[8,3,2,6,5,1,7,4]=>0101111=>1111010
[1,8,5,6,4,3,7,2]=>0010111=>1110100
[1,7,5,8,4,6,3,2]=>0100111=>1110010
[8,3,5,6,1,7,2,4]=>0000111=>1110000
[1,5,3,7,8,4,6,2]=>0001101=>1011000
[1,4,7,3,5,8,6,2]=>0000111=>1110000
[1,6,3,7,8,5,4,2]=>0011101=>1011100
[8,5,6,1,7,4,2,3]=>0010111=>1110100
[8,6,1,4,3,7,2,5]=>0010111=>1110100
[3,7,8,2,5,1,6,4]=>0001101=>1011000
[8,1,3,5,6,4,2,7]=>0010101=>1010100
[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
[7,5,8,1,2,3,6,4]=>0000111=>1110000
[8,6,1,5,3,7,2,4]=>0001111=>1111000
[8,1,7,5,6,4,2,3]=>0010111=>1110100
[8,1,4,7,6,5,2,3]=>0001111=>1111000
[6,1,4,8,2,7,5,3]=>0001111=>1111000
[4,6,8,5,1,2,7,3]=>0001011=>1101000
[2,8,4,6,1,3,7,5]=>0000111=>1110000
[5,2,7,8,4,1,3,6]=>0011001=>1001100
[4,6,8,5,3,1,2,7]=>0101001=>1001010
[8,6,4,2,7,3,5,1]=>0011111=>1111100
[6,8,7,5,2,1,3,4]=>1001011=>1101001
[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
[5,1,7,6,8,2,3,4]=>0001011=>1101000
[6,1,5,7,2,8,3,4]=>0000111=>1110000
[6,8,4,2,1,7,3,5]=>1010011=>1100101
[5,8,6,1,7,2,3,4]=>0000111=>1110000
[6,3,2,8,1,7,4,5]=>0100111=>1110010
[1,4,7,8,3,5,2,6]=>0001001=>1001000
[2,5,6,8,1,4,7,3]=>0000011=>1100000
[8,4,5,1,6,7,2,3]=>0001011=>1101000
[7,3,6,1,4,2,8,5]=>0010111=>1110100
[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
[8,3,1,4,6,2,7,5]=>0100111=>1110010
[2,5,3,4,6,8,1,7]=>0001001=>1001000
[8,3,6,1,5,2,4,7]=>0001101=>1011000
[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
[4,5,1,3,6,8,7,2]=>0001011=>1101000
[8,4,1,2,5,7,3,6]=>0010011=>1100100
[8,4,1,3,6,7,5,2]=>0011011=>1101100
[5,4,1,6,3,7,8,2]=>0011101=>1011100
[6,7,3,1,5,2,4,8]=>0101010=>0101010
[5,4,1,3,6,8,7,2]=>0011011=>1101100
[6,4,1,2,5,8,3,7]=>0010101=>1010100
[5,7,4,8,1,6,3,2]=>0100111=>1110010
[7,5,3,6,4,2,1,8]=>1011110=>0111101
[4,3,1,2,6,5,7,8]=>0110100=>0010110
[4,3,1,2,5,7,6,8]=>0110010=>0100110
[4,7,3,1,5,2,8,6]=>0101011=>1101010
[8,3,6,5,7,4,2,1]=>1010111=>1110101
[8,2,6,5,7,4,3,1]=>0110111=>1110110
[8,1,4,2,6,5,7,3]=>0010111=>1110100
[8,4,7,1,5,2,6,3]=>0001111=>1111000
[8,2,6,3,7,4,5,1]=>0001111=>1111000
[8,2,6,3,7,5,4,1]=>0011111=>1111100
[8,2,5,3,7,6,4,1]=>0011111=>1111100
[8,6,7,1,4,3,5,2]=>0011011=>1101100
[8,5,7,1,4,3,6,2]=>0010111=>1110100
[4,5,3,6,8,7,1,2]=>0001011=>1101000
[6,5,1,2,7,4,8,3]=>0001111=>1111000
[6,8,5,1,7,3,4,2]=>0011011=>1101100
[5,3,8,1,4,2,7,6]=>0011011=>1101100
[6,5,3,4,1,8,2,7]=>0011101=>1011100
[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
[5,2,4,1,6,8,3,7]=>0011001=>1001100
[8,7,2,3,1,6,4,5]=>0100111=>1110010
[6,2,3,1,7,8,4,5]=>0100101=>1010010
[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
[2,5,8,7,3,1,4,6]=>0100011=>1100010
[2,8,7,3,1,4,5,6]=>0100011=>1100010
[8,2,3,1,6,7,4,5]=>0100011=>1100010
[2,8,4,1,3,6,7,5]=>0010011=>1100100
[2,7,3,1,4,5,8,6]=>0100011=>1100010
[7,2,8,3,1,4,5,6]=>0100011=>1100010
[2,7,8,3,1,4,5,6]=>0100001=>1000010
[5,3,2,8,7,1,6,4]=>0101111=>1111010
[6,8,7,2,1,5,4,3]=>1011011=>1101101
[8,2,5,4,1,6,7,3]=>0011011=>1101100
[7,2,4,6,8,1,5,3]=>0001011=>1101000
[6,2,5,4,7,8,1,3]=>0001101=>1011000
[6,3,5,2,7,1,4,8]=>0001110=>0111000
[8,5,6,3,7,2,1,4]=>1000111=>1110001
[3,8,2,6,1,7,4,5]=>0000111=>1110000
[5,7,1,3,6,2,4,8]=>0000110=>0110000
[3,6,4,1,2,5,7,8]=>0010100=>0010100
[3,6,4,1,2,5,8,7]=>0010101=>1010100
[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
[3,8,5,4,2,1,6,7]=>1011001=>1001101
[4,8,5,3,6,1,7,2]=>0001111=>1111000
[6,3,1,5,4,8,2,7]=>0101101=>1011010
[8,4,2,6,5,7,3,1]=>0110111=>1110110
[4,7,6,3,5,2,8,1]=>0001111=>1111000
[1,7,5,3,4,8,6,2]=>0001111=>1111000
[4,8,6,2,5,7,3,1]=>0100111=>1110010
[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
[4,1,7,8,3,2,5,6]=>0110001=>1000110
[8,5,1,2,7,6,4,3]=>0011111=>1111100
[4,6,5,3,1,8,7,2]=>0101111=>1111010
[8,1,6,7,4,5,3,2]=>0101011=>1101010
[6,4,8,1,5,3,7,2]=>0001111=>1111000
[6,4,7,2,5,3,1,8]=>0101110=>0111010
[4,3,6,1,2,7,8,5]=>0010101=>1010100
[2,7,4,6,3,8,1,5]=>0000111=>1110000
[7,3,5,6,4,1,8,2]=>0010111=>1110100
[5,7,6,3,4,2,1,8]=>1010110=>0110101
[3,7,5,6,4,2,1,8]=>1010110=>0110101
[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
[5,7,6,3,4,1,8,2]=>0010111=>1110100
[3,2,7,5,6,1,8,4]=>0100111=>1110010
[5,3,4,7,6,1,8,2]=>0001111=>1111000
[5,3,4,2,7,1,8,6]=>0011011=>1101100
[3,5,4,1,7,8,6,2]=>0011101=>1011100
[2,4,6,5,1,8,7,3]=>0001111=>1111000
[2,4,6,5,1,8,3,7]=>0001101=>1011000
[2,4,6,1,8,7,3,5]=>0000111=>1110000
[2,4,6,5,8,3,7,1]=>0000111=>1110000
[2,4,6,8,5,3,1,7]=>0101001=>1001010
[2,4,6,8,5,3,7,1]=>0001011=>1101000
[2,4,6,8,5,7,3,1]=>0100011=>1100010
[2,4,6,5,3,8,1,7]=>0001101=>1011000
[2,4,6,5,8,7,1,3]=>0000111=>1110000
[2,4,6,8,7,5,1,3]=>0001011=>1101000
[2,4,6,8,5,7,1,3]=>0000011=>1100000
[2,4,6,8,7,1,5,3]=>0001011=>1101000
[2,4,6,8,7,1,3,5]=>0000011=>1100000
[2,4,6,8,1,7,3,5]=>0000011=>1100000
[2,7,6,4,3,8,5,1]=>0011111=>1111100
[2,6,7,5,3,8,1,4]=>0001011=>1101000
[3,6,7,5,8,2,4,1]=>0010011=>1100100
[4,5,2,6,8,7,1,3]=>0001011=>1101000
[4,5,2,6,8,3,1,7]=>0101001=>1001010
[4,5,3,6,8,2,1,7]=>1001001=>1001001
[3,1,2,7,5,8,4,6]=>0100011=>1100010
[4,8,1,6,2,5,3,7]=>0001101=>1011000
[1,5,8,3,4,6,2,7]=>0000101=>1010000
[7,5,8,2,4,3,6,1]=>0010111=>1110100
[8,1,5,3,4,6,2,7]=>0001101=>1011000
[8,1,2,4,7,5,6,3]=>0000111=>1110000
[2,7,3,8,4,5,6,1]=>0000111=>1110000
[1,7,8,6,4,5,3,2]=>0101101=>1011010
[5,8,7,2,4,3,6,1]=>0010111=>1110100
[1,8,2,4,7,5,6,3]=>0000111=>1110000
[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
[2,8,3,1,4,6,5,7]=>0100101=>1010010
[8,7,2,3,5,4,6,1]=>0001111=>1111000
[1,7,6,8,4,5,3,2]=>0101011=>1101010
[8,5,2,3,7,4,6,1]=>0001111=>1111000
[7,4,1,3,8,5,6,2]=>0010111=>1110100
[2,7,3,1,8,5,6,4]=>0100111=>1110010
[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
[8,4,1,5,6,2,7,3]=>0010111=>1110100
[1,8,5,3,2,4,6,7]=>0101001=>1001010
[4,8,5,1,2,3,6,7]=>0001001=>1001000
[3,5,1,4,2,6,8,7]=>0011001=>1001100
[4,8,7,1,2,5,3,6]=>0001011=>1101000
[8,7,2,6,1,4,3,5]=>0010111=>1110100
[1,7,6,8,4,2,3,5]=>0010011=>1100100
[1,7,4,8,2,5,3,6]=>0001011=>1101000
[6,1,7,3,8,2,4,5]=>0000111=>1110000
[1,5,8,2,3,4,7,6]=>0000011=>1100000
[8,4,2,7,1,3,6,5]=>0010111=>1110100
[7,1,8,6,4,2,3,5]=>0010111=>1110100
[1,7,8,6,4,2,3,5]=>0010101=>1010100
[3,1,2,5,7,6,8,4]=>0100011=>1100010
[7,1,3,2,4,6,8,5]=>0100011=>1100010
[7,4,2,3,1,6,8,5]=>0110011=>1100110
[5,1,7,3,2,6,8,4]=>0101011=>1101010
[4,8,2,3,7,5,1,6]=>0001011=>1101000
[6,8,5,3,4,2,1,7]=>1011001=>1001101
[8,7,2,4,3,5,6,1]=>0010111=>1110100
[8,1,3,6,4,5,2,7]=>0001101=>1011000
[8,1,3,7,4,5,6,2]=>0000111=>1110000
[8,1,3,2,7,5,4,6]=>0101011=>1101010
[8,1,2,4,7,3,5,6]=>0000011=>1100000
[7,1,2,4,8,3,5,6]=>0000011=>1100000
[7,6,2,8,4,5,1,3]=>0001111=>1111000
[8,7,5,3,2,6,4,1]=>0111111=>1111110
[4,8,3,2,5,1,6,7]=>0101001=>1001010
[4,3,8,5,1,2,7,6]=>0011011=>1101100
[3,1,8,4,5,2,7,6]=>0101011=>1101010
[8,3,6,2,1,5,4,7]=>1001101=>1011001
[8,2,1,6,5,3,4,7]=>1001101=>1011001
[2,3,7,6,1,8,4,5]=>0000111=>1110000
[4,7,8,2,1,3,5,6]=>1000001=>1000001
[4,8,5,2,1,3,7,6]=>1001011=>1101001
[2,3,7,4,1,8,6,5]=>0010111=>1110100
[5,8,4,2,1,3,7,6]=>1010011=>1100101
[4,5,2,3,8,7,1,6]=>0001011=>1101000
[4,6,7,5,2,3,1,8]=>0101010=>0101010
[6,5,2,3,1,8,7,4]=>0101111=>1111010
[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
[6,2,4,7,5,3,1,8]=>0101110=>0111010
[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
[2,4,8,7,5,3,1,6]=>0101011=>1101010
[4,6,8,7,5,3,1,2]=>0101011=>1101010
[4,6,5,3,8,7,1,2]=>0001111=>1111000
[2,6,5,8,7,3,1,4]=>0100111=>1110010
[6,7,2,4,5,3,1,8]=>0101010=>0101010
[4,5,8,7,2,3,1,6]=>0100011=>1100010
[4,8,7,2,5,3,1,6]=>0101011=>1101010
[6,8,7,4,5,3,1,2]=>0101011=>1101010
[2,8,4,7,5,3,1,6]=>0101011=>1101010
[4,8,2,7,5,3,1,6]=>0101011=>1101010
[6,8,2,7,5,3,1,4]=>0101011=>1101010
[7,4,3,8,1,6,5,2]=>0011111=>1111100
[3,7,4,6,2,1,8,5]=>1000111=>1110001
[2,6,5,7,8,3,1,4]=>0100101=>1010010
[3,4,8,6,2,1,7,5]=>1000111=>1110001
[1,6,2,3,8,5,7,4]=>0000111=>1110000
[1,2,7,3,8,5,6,4]=>0000111=>1110000
[2,3,6,5,8,4,7,1]=>0000111=>1110000
[3,4,2,6,8,5,7,1]=>0010011=>1100100
[2,4,7,3,8,5,1,6]=>0001011=>1101000
[1,2,8,3,5,4,7,6]=>0001011=>1101000
[1,3,6,7,4,5,8,2]=>0000011=>1100000
[7,4,1,3,6,8,2,5]=>0010011=>1100100
[5,1,7,3,4,6,8,2]=>0001011=>1101000
[6,1,7,3,5,8,2,4]=>0000111=>1110000
[6,8,1,2,7,3,4,5]=>0000011=>1100000
[5,6,2,1,8,3,4,7]=>1000101=>1010001
[6,4,1,3,7,8,2,5]=>0010101=>1010100
[1,6,2,8,7,3,4,5]=>0000111=>1110000
[5,2,8,4,7,1,3,6]=>0001011=>1101000
[3,8,7,2,6,1,4,5]=>0000111=>1110000
[2,5,1,8,3,6,4,7]=>0001101=>1011000
[2,3,8,1,4,6,5,7]=>0000101=>1010000
[1,3,8,2,5,4,7,6]=>0001011=>1101000
[3,1,8,4,6,2,5,7]=>0100101=>1010010
[6,3,2,4,8,7,1,5]=>0100111=>1110010
[1,4,8,6,2,3,5,7]=>0000101=>1010000
[3,1,8,4,5,6,2,7]=>0100101=>1010010
[4,5,8,3,6,1,7,2]=>0000111=>1110000
[3,5,4,8,6,1,7,2]=>0001111=>1111000
[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
[1,6,2,7,4,5,3,8]=>0001110=>0111000
[1,7,5,4,6,2,3,8]=>0001110=>0111000
[5,2,8,6,3,1,4,7]=>0101101=>1011010
[5,2,8,6,3,1,7,4]=>0101111=>1111010
[7,1,5,6,3,2,8,4]=>0100111=>1110010
[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
[8,3,1,2,5,4,7,6]=>0101011=>1101010
[6,5,1,2,8,4,7,3]=>0001111=>1111000
[8,1,5,3,7,4,2,6]=>0011011=>1101100
[1,3,4,8,6,2,7,5]=>0000111=>1110000
[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
[7,1,6,8,3,2,4,5]=>0100011=>1100010
[7,4,8,3,5,6,2,1]=>1000111=>1110001
[2,6,1,4,7,5,8,3]=>0000111=>1110000
[5,1,4,3,7,8,6,2]=>0011101=>1011100
[6,4,1,3,7,8,5,2]=>0011101=>1011100
[3,1,5,7,2,6,8,4]=>0100011=>1100010
[7,2,4,8,5,1,6,3]=>0001111=>1111000
[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
[6,7,3,1,2,4,8,5]=>0100011=>1100010
[3,8,5,2,1,6,7,4]=>1001011=>1101001
[6,8,2,3,5,7,4,1]=>0010011=>1100100
[5,3,8,4,6,7,2,1]=>1001011=>1101001
[6,2,8,1,7,4,5,3]=>0001111=>1111000
[4,2,6,7,8,5,3,1]=>0111001=>1001110
[4,3,5,8,6,7,2,1]=>1010011=>1100101
[6,2,4,7,8,5,3,1]=>0101101=>1011010
[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
[3,4,8,2,6,7,5,1]=>0001011=>1101000
[1,2,6,8,7,4,5,3]=>0001011=>1101000
[1,6,3,8,7,4,5,2]=>0001111=>1111000
[1,4,5,8,7,6,2,3]=>0000111=>1110000
[6,4,7,8,3,5,1,2]=>0001101=>1011000
[6,4,7,8,1,2,5,3]=>0001101=>1011000
[3,5,6,7,1,8,4,2]=>0010011=>1100100
[1,7,4,5,2,8,6,3]=>0001111=>1111000
[1,7,3,8,2,5,4,6]=>0001011=>1101000
[2,7,8,3,6,1,5,4]=>0001101=>1011000
[1,7,8,3,6,2,5,4]=>0001101=>1011000
[1,4,7,5,8,3,6,2]=>0000111=>1110000
[3,4,7,5,8,2,1,6]=>1000011=>1100001
[7,2,6,4,1,8,5,3]=>0011111=>1111100
[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
[8,6,4,5,1,3,7,2]=>0001111=>1111000
[7,5,8,4,1,3,6,2]=>0010111=>1110100
[4,7,5,3,6,8,1,2]=>0001011=>1101000
[4,8,5,3,7,1,2,6]=>0001011=>1101000
[2,8,1,6,5,7,3,4]=>0000111=>1110000
[4,7,5,3,8,1,6,2]=>0001111=>1111000
[7,4,8,5,3,6,1,2]=>0001111=>1111000
[7,4,5,3,8,1,6,2]=>0001111=>1111000
[8,4,6,5,1,3,7,2]=>0001111=>1111000
[6,3,5,8,1,7,4,2]=>0010111=>1110100
[7,3,6,1,5,8,4,2]=>0010111=>1110100
[4,5,3,8,7,1,2,6]=>0001011=>1101000
[8,5,4,7,6,1,2,3]=>0001111=>1111000
[3,7,6,1,5,8,4,2]=>0010111=>1110100
[8,2,3,6,4,1,7,5]=>0010111=>1110100
[2,7,3,6,4,1,8,5]=>0010111=>1110100
[2,3,7,8,1,4,6,5]=>0000101=>1010000
[2,7,3,5,4,1,8,6]=>0011011=>1101100
[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
[8,1,2,5,3,7,6,4]=>0001111=>1111000
[1,6,4,3,7,5,2,8]=>0011110=>0111100
[1,6,7,5,4,8,2,3]=>0001011=>1101000
[1,8,5,4,2,6,3,7]=>0011101=>1011100
[4,2,8,1,5,7,6,3]=>0010111=>1110100
[6,7,3,5,4,1,2,8]=>0011010=>0101100
[5,7,3,6,2,1,4,8]=>1000110=>0110001
[5,6,8,4,2,7,1,3]=>0010011=>1100100
[6,8,7,3,2,1,5,4]=>1101011=>1101011
[3,6,8,7,2,4,1,5]=>0010011=>1100100
[3,7,6,4,2,8,1,5]=>0010111=>1110100
[2,8,6,4,7,3,5,1]=>0001111=>1111000
[3,8,6,4,2,7,1,5]=>0010111=>1110100
[5,7,3,6,2,1,8,4]=>1000111=>1110001
[2,4,8,6,5,7,3,1]=>0100111=>1110010
[3,6,5,2,4,8,1,7]=>0001101=>1011000
[4,6,3,2,5,1,8,7]=>0101101=>1011010
[8,3,6,5,4,2,1,7]=>1011101=>1011101
[5,4,8,7,6,2,3,1]=>0101111=>1111010
[6,8,4,7,5,1,3,2]=>0101011=>1101010
[6,5,8,3,7,1,4,2]=>0010111=>1110100
[7,4,6,1,5,3,8,2]=>0001111=>1111000
[6,1,5,4,7,3,8,2]=>0001111=>1111000
[7,1,5,4,6,3,8,2]=>0001111=>1111000
[2,5,4,7,1,8,3,6]=>0001011=>1101000
[1,5,4,7,3,8,2,6]=>0001011=>1101000
[1,5,6,8,3,2,4,7]=>0100001=>1000010
[1,2,6,7,3,5,4,8]=>0001010=>0101000
[1,5,6,7,2,4,3,8]=>0010010=>0100100
[1,7,2,5,6,8,3,4]=>0000011=>1100000
[4,1,7,5,6,8,2,3]=>0010011=>1100100
[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
[7,3,8,4,2,6,5,1]=>0011111=>1111100
[3,5,6,8,2,4,7,1]=>0000011=>1100000
[8,4,7,3,2,5,6,1]=>0100111=>1110010
[4,8,7,3,2,5,6,1]=>0100111=>1110010
[8,5,7,3,2,4,6,1]=>0100111=>1110010
[3,7,4,2,6,8,5,1]=>0011011=>1101100
[7,2,8,4,5,6,3,1]=>0100111=>1110010
[6,2,8,3,7,4,5,1]=>0001111=>1111000
[4,3,7,8,6,2,5,1]=>0011101=>1011100
[1,5,8,3,2,7,4,6]=>0100011=>1100010
[8,1,4,3,6,7,2,5]=>0010011=>1100100
[8,3,1,4,6,7,2,5]=>0100011=>1100010
[7,8,5,1,2,6,3,4]=>0001101=>1011000
[8,3,6,7,5,1,2,4]=>0001011=>1101000
[7,6,4,2,5,3,1,8]=>0111110=>0111110
[1,8,6,5,2,7,4,3]=>0011111=>1111100
[8,2,6,5,1,7,4,3]=>0011111=>1111100
[6,1,4,7,2,5,8,3]=>0000111=>1110000
[6,8,2,5,1,7,4,3]=>0011011=>1101100
[1,6,4,7,2,5,8,3]=>0000111=>1110000
[7,6,4,1,2,5,8,3]=>0010111=>1110100
[6,8,1,5,2,7,4,3]=>0011011=>1101100
[8,6,5,2,1,7,4,3]=>1011111=>1111101
[1,6,5,2,8,7,4,3]=>0011111=>1111100
[1,8,5,2,7,6,4,3]=>0011111=>1111100
[1,8,6,7,2,5,4,3]=>0011011=>1101100
[1,7,6,8,2,5,4,3]=>0011011=>1101100
[1,7,8,6,2,5,4,3]=>0011101=>1011100
[8,1,7,6,2,5,4,3]=>0011111=>1111100
[5,2,4,7,3,8,6,1]=>0001111=>1111000
[1,5,6,3,2,8,7,4]=>0100111=>1110010
[4,6,5,7,1,8,2,3]=>0000111=>1110000
[6,7,5,3,8,2,1,4]=>1001011=>1101001
[7,2,5,6,4,8,3,1]=>0100111=>1110010
[7,4,6,2,8,5,3,1]=>0101111=>1111010
[7,2,6,3,8,5,4,1]=>0011111=>1111100
[1,2,6,5,3,8,4,7]=>0001101=>1011000
[6,5,3,4,8,2,1,7]=>1001101=>1011001
[1,7,8,6,3,5,4,2]=>0011101=>1011100
[1,4,2,3,7,8,6,5]=>0010101=>1010100
[1,8,4,2,3,6,5,7]=>0010101=>1010100
[1,3,8,5,6,4,2,7]=>0010101=>1010100
[1,6,3,7,8,4,2,5]=>0010101=>1010100
[1,6,3,8,4,2,5,7]=>0010101=>1010100
[1,7,8,4,2,3,5,6]=>0010001=>1000100
[1,7,8,5,6,4,2,3]=>0010101=>1010100
[1,6,3,4,2,5,8,7]=>0010101=>1010100
[1,3,5,8,6,4,2,7]=>0010101=>1010100
[1,7,6,2,3,8,4,5]=>0000111=>1110000
[1,5,7,6,2,3,8,4]=>0000111=>1110000
[1,3,7,6,2,4,5,8]=>0000110=>0110000
[1,4,3,7,6,2,5,8]=>0010110=>0110100
[1,5,8,4,3,7,6,2]=>0010111=>1110100
[1,7,5,8,4,3,6,2]=>0010111=>1110100
[4,1,5,7,3,8,2,6]=>0010011=>1100100
[1,3,7,4,6,8,5,2]=>0001011=>1101000
[1,5,2,6,8,7,4,3]=>0011011=>1101100
[1,3,7,6,4,8,2,5]=>0000111=>1110000
[6,5,1,4,3,8,7,2]=>0011111=>1111100
[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
[8,5,6,4,3,1,7,2]=>0110111=>1110110
[8,4,3,1,7,6,5,2]=>0111111=>1111110
[3,2,7,1,8,6,5,4]=>0101111=>1111010
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.