Identifier
Mp00109:
Permutations
—descent word⟶
Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Mp00104: Binary words —reverse⟶ Binary words
Mp00105: Binary words —complement⟶ Binary words
Images
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[1]=>=>=>
[1,2]=>0=>0=>1
[2,1]=>1=>1=>0
[1,2,3]=>00=>00=>11
[1,3,2]=>01=>10=>01
[2,1,3]=>10=>01=>10
[2,3,1]=>01=>10=>01
[3,1,2]=>10=>01=>10
[3,2,1]=>11=>11=>00
[1,2,3,4]=>000=>000=>111
[1,2,4,3]=>001=>100=>011
[1,3,2,4]=>010=>010=>101
[1,3,4,2]=>001=>100=>011
[1,4,2,3]=>010=>010=>101
[1,4,3,2]=>011=>110=>001
[2,1,3,4]=>100=>001=>110
[2,1,4,3]=>101=>101=>010
[2,3,1,4]=>010=>010=>101
[2,3,4,1]=>001=>100=>011
[2,4,1,3]=>010=>010=>101
[2,4,3,1]=>011=>110=>001
[3,1,2,4]=>100=>001=>110
[3,1,4,2]=>101=>101=>010
[3,2,1,4]=>110=>011=>100
[3,2,4,1]=>101=>101=>010
[3,4,1,2]=>010=>010=>101
[3,4,2,1]=>011=>110=>001
[4,1,2,3]=>100=>001=>110
[4,1,3,2]=>101=>101=>010
[4,2,1,3]=>110=>011=>100
[4,2,3,1]=>101=>101=>010
[4,3,1,2]=>110=>011=>100
[4,3,2,1]=>111=>111=>000
[1,2,3,4,5]=>0000=>0000=>1111
[1,2,3,5,4]=>0001=>1000=>0111
[1,2,4,3,5]=>0010=>0100=>1011
[1,2,4,5,3]=>0001=>1000=>0111
[1,2,5,3,4]=>0010=>0100=>1011
[1,2,5,4,3]=>0011=>1100=>0011
[1,3,2,4,5]=>0100=>0010=>1101
[1,3,2,5,4]=>0101=>1010=>0101
[1,3,4,2,5]=>0010=>0100=>1011
[1,3,4,5,2]=>0001=>1000=>0111
[1,3,5,2,4]=>0010=>0100=>1011
[1,3,5,4,2]=>0011=>1100=>0011
[1,4,2,3,5]=>0100=>0010=>1101
[1,4,2,5,3]=>0101=>1010=>0101
[1,4,3,2,5]=>0110=>0110=>1001
[1,4,3,5,2]=>0101=>1010=>0101
[1,4,5,2,3]=>0010=>0100=>1011
[1,4,5,3,2]=>0011=>1100=>0011
[1,5,2,3,4]=>0100=>0010=>1101
[1,5,2,4,3]=>0101=>1010=>0101
[1,5,3,2,4]=>0110=>0110=>1001
[1,5,3,4,2]=>0101=>1010=>0101
[1,5,4,2,3]=>0110=>0110=>1001
[1,5,4,3,2]=>0111=>1110=>0001
[2,1,3,4,5]=>1000=>0001=>1110
[2,1,3,5,4]=>1001=>1001=>0110
[2,1,4,3,5]=>1010=>0101=>1010
[2,1,4,5,3]=>1001=>1001=>0110
[2,1,5,3,4]=>1010=>0101=>1010
[2,1,5,4,3]=>1011=>1101=>0010
[2,3,1,4,5]=>0100=>0010=>1101
[2,3,1,5,4]=>0101=>1010=>0101
[2,3,4,1,5]=>0010=>0100=>1011
[2,3,4,5,1]=>0001=>1000=>0111
[2,3,5,1,4]=>0010=>0100=>1011
[2,3,5,4,1]=>0011=>1100=>0011
[2,4,1,3,5]=>0100=>0010=>1101
[2,4,1,5,3]=>0101=>1010=>0101
[2,4,3,1,5]=>0110=>0110=>1001
[2,4,3,5,1]=>0101=>1010=>0101
[2,4,5,1,3]=>0010=>0100=>1011
[2,4,5,3,1]=>0011=>1100=>0011
[2,5,1,3,4]=>0100=>0010=>1101
[2,5,1,4,3]=>0101=>1010=>0101
[2,5,3,1,4]=>0110=>0110=>1001
[2,5,3,4,1]=>0101=>1010=>0101
[2,5,4,1,3]=>0110=>0110=>1001
[2,5,4,3,1]=>0111=>1110=>0001
[3,1,2,4,5]=>1000=>0001=>1110
[3,1,2,5,4]=>1001=>1001=>0110
[3,1,4,2,5]=>1010=>0101=>1010
[3,1,4,5,2]=>1001=>1001=>0110
[3,1,5,2,4]=>1010=>0101=>1010
[3,1,5,4,2]=>1011=>1101=>0010
[3,2,1,4,5]=>1100=>0011=>1100
[3,2,1,5,4]=>1101=>1011=>0100
[3,2,4,1,5]=>1010=>0101=>1010
[3,2,4,5,1]=>1001=>1001=>0110
[3,2,5,1,4]=>1010=>0101=>1010
[3,2,5,4,1]=>1011=>1101=>0010
[3,4,1,2,5]=>0100=>0010=>1101
[3,4,1,5,2]=>0101=>1010=>0101
[3,4,2,1,5]=>0110=>0110=>1001
[3,4,2,5,1]=>0101=>1010=>0101
[3,4,5,1,2]=>0010=>0100=>1011
[3,4,5,2,1]=>0011=>1100=>0011
[3,5,1,2,4]=>0100=>0010=>1101
[3,5,1,4,2]=>0101=>1010=>0101
[3,5,2,1,4]=>0110=>0110=>1001
[3,5,2,4,1]=>0101=>1010=>0101
[3,5,4,1,2]=>0110=>0110=>1001
[3,5,4,2,1]=>0111=>1110=>0001
[4,1,2,3,5]=>1000=>0001=>1110
[4,1,2,5,3]=>1001=>1001=>0110
[4,1,3,2,5]=>1010=>0101=>1010
[4,1,3,5,2]=>1001=>1001=>0110
[4,1,5,2,3]=>1010=>0101=>1010
[4,1,5,3,2]=>1011=>1101=>0010
[4,2,1,3,5]=>1100=>0011=>1100
[4,2,1,5,3]=>1101=>1011=>0100
[4,2,3,1,5]=>1010=>0101=>1010
[4,2,3,5,1]=>1001=>1001=>0110
[4,2,5,1,3]=>1010=>0101=>1010
[4,2,5,3,1]=>1011=>1101=>0010
[4,3,1,2,5]=>1100=>0011=>1100
[4,3,1,5,2]=>1101=>1011=>0100
[4,3,2,1,5]=>1110=>0111=>1000
[4,3,2,5,1]=>1101=>1011=>0100
[4,3,5,1,2]=>1010=>0101=>1010
[4,3,5,2,1]=>1011=>1101=>0010
[4,5,1,2,3]=>0100=>0010=>1101
[4,5,1,3,2]=>0101=>1010=>0101
[4,5,2,1,3]=>0110=>0110=>1001
[4,5,2,3,1]=>0101=>1010=>0101
[4,5,3,1,2]=>0110=>0110=>1001
[4,5,3,2,1]=>0111=>1110=>0001
[5,1,2,3,4]=>1000=>0001=>1110
[5,1,2,4,3]=>1001=>1001=>0110
[5,1,3,2,4]=>1010=>0101=>1010
[5,1,3,4,2]=>1001=>1001=>0110
[5,1,4,2,3]=>1010=>0101=>1010
[5,1,4,3,2]=>1011=>1101=>0010
[5,2,1,3,4]=>1100=>0011=>1100
[5,2,1,4,3]=>1101=>1011=>0100
[5,2,3,1,4]=>1010=>0101=>1010
[5,2,3,4,1]=>1001=>1001=>0110
[5,2,4,1,3]=>1010=>0101=>1010
[5,2,4,3,1]=>1011=>1101=>0010
[5,3,1,2,4]=>1100=>0011=>1100
[5,3,1,4,2]=>1101=>1011=>0100
[5,3,2,1,4]=>1110=>0111=>1000
[5,3,2,4,1]=>1101=>1011=>0100
[5,3,4,1,2]=>1010=>0101=>1010
[5,3,4,2,1]=>1011=>1101=>0010
[5,4,1,2,3]=>1100=>0011=>1100
[5,4,1,3,2]=>1101=>1011=>0100
[5,4,2,1,3]=>1110=>0111=>1000
[5,4,2,3,1]=>1101=>1011=>0100
[5,4,3,1,2]=>1110=>0111=>1000
[5,4,3,2,1]=>1111=>1111=>0000
[1,2,3,4,5,6]=>00000=>00000=>11111
[1,2,3,4,6,5]=>00001=>10000=>01111
[1,2,3,5,4,6]=>00010=>01000=>10111
[1,2,3,5,6,4]=>00001=>10000=>01111
[1,2,3,6,4,5]=>00010=>01000=>10111
[1,2,3,6,5,4]=>00011=>11000=>00111
[1,2,4,3,5,6]=>00100=>00100=>11011
[1,2,4,3,6,5]=>00101=>10100=>01011
[1,2,4,5,3,6]=>00010=>01000=>10111
[1,2,4,5,6,3]=>00001=>10000=>01111
[1,2,4,6,3,5]=>00010=>01000=>10111
[1,2,4,6,5,3]=>00011=>11000=>00111
[1,2,5,3,4,6]=>00100=>00100=>11011
[1,2,5,3,6,4]=>00101=>10100=>01011
[1,2,5,4,3,6]=>00110=>01100=>10011
[1,2,5,4,6,3]=>00101=>10100=>01011
[1,2,5,6,3,4]=>00010=>01000=>10111
[1,2,5,6,4,3]=>00011=>11000=>00111
[1,2,6,3,4,5]=>00100=>00100=>11011
[1,2,6,3,5,4]=>00101=>10100=>01011
[1,2,6,4,3,5]=>00110=>01100=>10011
[1,2,6,4,5,3]=>00101=>10100=>01011
[1,2,6,5,3,4]=>00110=>01100=>10011
[1,2,6,5,4,3]=>00111=>11100=>00011
[1,3,2,4,5,6]=>01000=>00010=>11101
[1,3,2,4,6,5]=>01001=>10010=>01101
[1,3,2,5,4,6]=>01010=>01010=>10101
[1,3,2,5,6,4]=>01001=>10010=>01101
[1,3,2,6,4,5]=>01010=>01010=>10101
[1,3,2,6,5,4]=>01011=>11010=>00101
[1,3,4,2,5,6]=>00100=>00100=>11011
[1,3,4,2,6,5]=>00101=>10100=>01011
[1,3,4,5,2,6]=>00010=>01000=>10111
[1,3,4,5,6,2]=>00001=>10000=>01111
[1,3,4,6,2,5]=>00010=>01000=>10111
[1,3,4,6,5,2]=>00011=>11000=>00111
[1,3,5,2,4,6]=>00100=>00100=>11011
[1,3,5,2,6,4]=>00101=>10100=>01011
[1,3,5,4,2,6]=>00110=>01100=>10011
[1,3,5,4,6,2]=>00101=>10100=>01011
[1,3,5,6,2,4]=>00010=>01000=>10111
[1,3,5,6,4,2]=>00011=>11000=>00111
[1,3,6,2,4,5]=>00100=>00100=>11011
[1,3,6,2,5,4]=>00101=>10100=>01011
[1,3,6,4,2,5]=>00110=>01100=>10011
[1,3,6,4,5,2]=>00101=>10100=>01011
[1,3,6,5,2,4]=>00110=>01100=>10011
[1,3,6,5,4,2]=>00111=>11100=>00011
[1,4,2,3,5,6]=>01000=>00010=>11101
[1,4,2,3,6,5]=>01001=>10010=>01101
[1,4,2,5,3,6]=>01010=>01010=>10101
[1,4,2,5,6,3]=>01001=>10010=>01101
[1,4,2,6,3,5]=>01010=>01010=>10101
[1,4,2,6,5,3]=>01011=>11010=>00101
[1,4,3,2,5,6]=>01100=>00110=>11001
[1,4,3,2,6,5]=>01101=>10110=>01001
[1,4,3,5,2,6]=>01010=>01010=>10101
[1,4,3,5,6,2]=>01001=>10010=>01101
[1,4,3,6,2,5]=>01010=>01010=>10101
[1,4,3,6,5,2]=>01011=>11010=>00101
[1,4,5,2,3,6]=>00100=>00100=>11011
[1,4,5,2,6,3]=>00101=>10100=>01011
[1,4,5,3,2,6]=>00110=>01100=>10011
[1,4,5,3,6,2]=>00101=>10100=>01011
[1,4,5,6,2,3]=>00010=>01000=>10111
[1,4,5,6,3,2]=>00011=>11000=>00111
[1,4,6,2,3,5]=>00100=>00100=>11011
[1,4,6,2,5,3]=>00101=>10100=>01011
[1,4,6,3,2,5]=>00110=>01100=>10011
[1,4,6,3,5,2]=>00101=>10100=>01011
[1,4,6,5,2,3]=>00110=>01100=>10011
[1,4,6,5,3,2]=>00111=>11100=>00011
[1,5,2,3,4,6]=>01000=>00010=>11101
[1,5,2,3,6,4]=>01001=>10010=>01101
[1,5,2,4,3,6]=>01010=>01010=>10101
[1,5,2,4,6,3]=>01001=>10010=>01101
[1,5,2,6,3,4]=>01010=>01010=>10101
[1,5,2,6,4,3]=>01011=>11010=>00101
[1,5,3,2,4,6]=>01100=>00110=>11001
[1,5,3,2,6,4]=>01101=>10110=>01001
[1,5,3,4,2,6]=>01010=>01010=>10101
[1,5,3,4,6,2]=>01001=>10010=>01101
[1,5,3,6,2,4]=>01010=>01010=>10101
[1,5,3,6,4,2]=>01011=>11010=>00101
[1,5,4,2,3,6]=>01100=>00110=>11001
[1,5,4,2,6,3]=>01101=>10110=>01001
[1,5,4,3,2,6]=>01110=>01110=>10001
[1,5,4,3,6,2]=>01101=>10110=>01001
[1,5,4,6,2,3]=>01010=>01010=>10101
[1,5,4,6,3,2]=>01011=>11010=>00101
[1,5,6,2,3,4]=>00100=>00100=>11011
[1,5,6,2,4,3]=>00101=>10100=>01011
[1,5,6,3,2,4]=>00110=>01100=>10011
[1,5,6,3,4,2]=>00101=>10100=>01011
[1,5,6,4,2,3]=>00110=>01100=>10011
[1,5,6,4,3,2]=>00111=>11100=>00011
[1,6,2,3,4,5]=>01000=>00010=>11101
[1,6,2,3,5,4]=>01001=>10010=>01101
[1,6,2,4,3,5]=>01010=>01010=>10101
[1,6,2,4,5,3]=>01001=>10010=>01101
[1,6,2,5,3,4]=>01010=>01010=>10101
[1,6,2,5,4,3]=>01011=>11010=>00101
[1,6,3,2,4,5]=>01100=>00110=>11001
[1,6,3,2,5,4]=>01101=>10110=>01001
[1,6,3,4,2,5]=>01010=>01010=>10101
[1,6,3,4,5,2]=>01001=>10010=>01101
[1,6,3,5,2,4]=>01010=>01010=>10101
[1,6,3,5,4,2]=>01011=>11010=>00101
[1,6,4,2,3,5]=>01100=>00110=>11001
[1,6,4,2,5,3]=>01101=>10110=>01001
[1,6,4,3,2,5]=>01110=>01110=>10001
[1,6,4,3,5,2]=>01101=>10110=>01001
[1,6,4,5,2,3]=>01010=>01010=>10101
[1,6,4,5,3,2]=>01011=>11010=>00101
[1,6,5,2,3,4]=>01100=>00110=>11001
[1,6,5,2,4,3]=>01101=>10110=>01001
[1,6,5,3,2,4]=>01110=>01110=>10001
[1,6,5,3,4,2]=>01101=>10110=>01001
[1,6,5,4,2,3]=>01110=>01110=>10001
[1,6,5,4,3,2]=>01111=>11110=>00001
[2,1,3,4,5,6]=>10000=>00001=>11110
[2,1,3,4,6,5]=>10001=>10001=>01110
[2,1,3,5,4,6]=>10010=>01001=>10110
[2,1,3,5,6,4]=>10001=>10001=>01110
[2,1,3,6,4,5]=>10010=>01001=>10110
[2,1,3,6,5,4]=>10011=>11001=>00110
[2,1,4,3,5,6]=>10100=>00101=>11010
[2,1,4,3,6,5]=>10101=>10101=>01010
[2,1,4,5,3,6]=>10010=>01001=>10110
[2,1,4,5,6,3]=>10001=>10001=>01110
[2,1,4,6,3,5]=>10010=>01001=>10110
[2,1,4,6,5,3]=>10011=>11001=>00110
[2,1,5,3,4,6]=>10100=>00101=>11010
[2,1,5,3,6,4]=>10101=>10101=>01010
[2,1,5,4,3,6]=>10110=>01101=>10010
[2,1,5,4,6,3]=>10101=>10101=>01010
[2,1,5,6,3,4]=>10010=>01001=>10110
[2,1,5,6,4,3]=>10011=>11001=>00110
[2,1,6,3,4,5]=>10100=>00101=>11010
[2,1,6,3,5,4]=>10101=>10101=>01010
[2,1,6,4,3,5]=>10110=>01101=>10010
[2,1,6,4,5,3]=>10101=>10101=>01010
[2,1,6,5,3,4]=>10110=>01101=>10010
[2,1,6,5,4,3]=>10111=>11101=>00010
[2,3,1,4,5,6]=>01000=>00010=>11101
[2,3,1,4,6,5]=>01001=>10010=>01101
[2,3,1,5,4,6]=>01010=>01010=>10101
[2,3,1,5,6,4]=>01001=>10010=>01101
[2,3,1,6,4,5]=>01010=>01010=>10101
[2,3,1,6,5,4]=>01011=>11010=>00101
[2,3,4,1,5,6]=>00100=>00100=>11011
[2,3,4,1,6,5]=>00101=>10100=>01011
[2,3,4,5,1,6]=>00010=>01000=>10111
[2,3,4,5,6,1]=>00001=>10000=>01111
[2,3,4,6,1,5]=>00010=>01000=>10111
[2,3,4,6,5,1]=>00011=>11000=>00111
[2,3,5,1,4,6]=>00100=>00100=>11011
[2,3,5,1,6,4]=>00101=>10100=>01011
[2,3,5,4,1,6]=>00110=>01100=>10011
[2,3,5,4,6,1]=>00101=>10100=>01011
[2,3,5,6,1,4]=>00010=>01000=>10111
[2,3,5,6,4,1]=>00011=>11000=>00111
[2,3,6,1,4,5]=>00100=>00100=>11011
[2,3,6,1,5,4]=>00101=>10100=>01011
[2,3,6,4,1,5]=>00110=>01100=>10011
[2,3,6,4,5,1]=>00101=>10100=>01011
[2,3,6,5,1,4]=>00110=>01100=>10011
[2,3,6,5,4,1]=>00111=>11100=>00011
[2,4,1,3,5,6]=>01000=>00010=>11101
[2,4,1,3,6,5]=>01001=>10010=>01101
[2,4,1,5,3,6]=>01010=>01010=>10101
[2,4,1,5,6,3]=>01001=>10010=>01101
[2,4,1,6,3,5]=>01010=>01010=>10101
[2,4,1,6,5,3]=>01011=>11010=>00101
[2,4,3,1,5,6]=>01100=>00110=>11001
[2,4,3,1,6,5]=>01101=>10110=>01001
[2,4,3,5,1,6]=>01010=>01010=>10101
[2,4,3,5,6,1]=>01001=>10010=>01101
[2,4,3,6,1,5]=>01010=>01010=>10101
[2,4,3,6,5,1]=>01011=>11010=>00101
[2,4,5,1,3,6]=>00100=>00100=>11011
[2,4,5,1,6,3]=>00101=>10100=>01011
[2,4,5,3,1,6]=>00110=>01100=>10011
[2,4,5,3,6,1]=>00101=>10100=>01011
[2,4,5,6,1,3]=>00010=>01000=>10111
[2,4,5,6,3,1]=>00011=>11000=>00111
[2,4,6,1,3,5]=>00100=>00100=>11011
[2,4,6,1,5,3]=>00101=>10100=>01011
[2,4,6,3,1,5]=>00110=>01100=>10011
[2,4,6,3,5,1]=>00101=>10100=>01011
[2,4,6,5,1,3]=>00110=>01100=>10011
[2,4,6,5,3,1]=>00111=>11100=>00011
[2,5,1,3,4,6]=>01000=>00010=>11101
[2,5,1,3,6,4]=>01001=>10010=>01101
[2,5,1,4,3,6]=>01010=>01010=>10101
[2,5,1,4,6,3]=>01001=>10010=>01101
[2,5,1,6,3,4]=>01010=>01010=>10101
[2,5,1,6,4,3]=>01011=>11010=>00101
[2,5,3,1,4,6]=>01100=>00110=>11001
[2,5,3,1,6,4]=>01101=>10110=>01001
[2,5,3,4,1,6]=>01010=>01010=>10101
[2,5,3,4,6,1]=>01001=>10010=>01101
[2,5,3,6,1,4]=>01010=>01010=>10101
[2,5,3,6,4,1]=>01011=>11010=>00101
[2,5,4,1,3,6]=>01100=>00110=>11001
[2,5,4,1,6,3]=>01101=>10110=>01001
[2,5,4,3,1,6]=>01110=>01110=>10001
[2,5,4,3,6,1]=>01101=>10110=>01001
[2,5,4,6,1,3]=>01010=>01010=>10101
[2,5,4,6,3,1]=>01011=>11010=>00101
[2,5,6,1,3,4]=>00100=>00100=>11011
[2,5,6,1,4,3]=>00101=>10100=>01011
[2,5,6,3,1,4]=>00110=>01100=>10011
[2,5,6,3,4,1]=>00101=>10100=>01011
[2,5,6,4,1,3]=>00110=>01100=>10011
[2,5,6,4,3,1]=>00111=>11100=>00011
[2,6,1,3,4,5]=>01000=>00010=>11101
[2,6,1,3,5,4]=>01001=>10010=>01101
[2,6,1,4,3,5]=>01010=>01010=>10101
[2,6,1,4,5,3]=>01001=>10010=>01101
[2,6,1,5,3,4]=>01010=>01010=>10101
[2,6,1,5,4,3]=>01011=>11010=>00101
[2,6,3,1,4,5]=>01100=>00110=>11001
[2,6,3,1,5,4]=>01101=>10110=>01001
[2,6,3,4,1,5]=>01010=>01010=>10101
[2,6,3,4,5,1]=>01001=>10010=>01101
[2,6,3,5,1,4]=>01010=>01010=>10101
[2,6,3,5,4,1]=>01011=>11010=>00101
[2,6,4,1,3,5]=>01100=>00110=>11001
[2,6,4,1,5,3]=>01101=>10110=>01001
[2,6,4,3,1,5]=>01110=>01110=>10001
[2,6,4,3,5,1]=>01101=>10110=>01001
[2,6,4,5,1,3]=>01010=>01010=>10101
[2,6,4,5,3,1]=>01011=>11010=>00101
[2,6,5,1,3,4]=>01100=>00110=>11001
[2,6,5,1,4,3]=>01101=>10110=>01001
[2,6,5,3,1,4]=>01110=>01110=>10001
[2,6,5,3,4,1]=>01101=>10110=>01001
[2,6,5,4,1,3]=>01110=>01110=>10001
[2,6,5,4,3,1]=>01111=>11110=>00001
[3,1,2,4,5,6]=>10000=>00001=>11110
[3,1,2,4,6,5]=>10001=>10001=>01110
[3,1,2,5,4,6]=>10010=>01001=>10110
[3,1,2,5,6,4]=>10001=>10001=>01110
[3,1,2,6,4,5]=>10010=>01001=>10110
[3,1,2,6,5,4]=>10011=>11001=>00110
[3,1,4,2,5,6]=>10100=>00101=>11010
[3,1,4,2,6,5]=>10101=>10101=>01010
[3,1,4,5,2,6]=>10010=>01001=>10110
[3,1,4,5,6,2]=>10001=>10001=>01110
[3,1,4,6,2,5]=>10010=>01001=>10110
[3,1,4,6,5,2]=>10011=>11001=>00110
[3,1,5,2,4,6]=>10100=>00101=>11010
[3,1,5,2,6,4]=>10101=>10101=>01010
[3,1,5,4,2,6]=>10110=>01101=>10010
[3,1,5,4,6,2]=>10101=>10101=>01010
[3,1,5,6,2,4]=>10010=>01001=>10110
[3,1,5,6,4,2]=>10011=>11001=>00110
[3,1,6,2,4,5]=>10100=>00101=>11010
[3,1,6,2,5,4]=>10101=>10101=>01010
[3,1,6,4,2,5]=>10110=>01101=>10010
[3,1,6,4,5,2]=>10101=>10101=>01010
[3,1,6,5,2,4]=>10110=>01101=>10010
[3,1,6,5,4,2]=>10111=>11101=>00010
[3,2,1,4,5,6]=>11000=>00011=>11100
[3,2,1,4,6,5]=>11001=>10011=>01100
[3,2,1,5,4,6]=>11010=>01011=>10100
[3,2,1,5,6,4]=>11001=>10011=>01100
[3,2,1,6,4,5]=>11010=>01011=>10100
[3,2,1,6,5,4]=>11011=>11011=>00100
[3,2,4,1,5,6]=>10100=>00101=>11010
[3,2,4,1,6,5]=>10101=>10101=>01010
[3,2,4,5,1,6]=>10010=>01001=>10110
[3,2,4,5,6,1]=>10001=>10001=>01110
[3,2,4,6,1,5]=>10010=>01001=>10110
[3,2,4,6,5,1]=>10011=>11001=>00110
[3,2,5,1,4,6]=>10100=>00101=>11010
[3,2,5,1,6,4]=>10101=>10101=>01010
[3,2,5,4,1,6]=>10110=>01101=>10010
[3,2,5,4,6,1]=>10101=>10101=>01010
[3,2,5,6,1,4]=>10010=>01001=>10110
[3,2,5,6,4,1]=>10011=>11001=>00110
[3,2,6,1,4,5]=>10100=>00101=>11010
[3,2,6,1,5,4]=>10101=>10101=>01010
[3,2,6,4,1,5]=>10110=>01101=>10010
[3,2,6,4,5,1]=>10101=>10101=>01010
[3,2,6,5,1,4]=>10110=>01101=>10010
[3,2,6,5,4,1]=>10111=>11101=>00010
[3,4,1,2,5,6]=>01000=>00010=>11101
[3,4,1,2,6,5]=>01001=>10010=>01101
[3,4,1,5,2,6]=>01010=>01010=>10101
[3,4,1,5,6,2]=>01001=>10010=>01101
[3,4,1,6,2,5]=>01010=>01010=>10101
[3,4,1,6,5,2]=>01011=>11010=>00101
[3,4,2,1,5,6]=>01100=>00110=>11001
[3,4,2,1,6,5]=>01101=>10110=>01001
[3,4,2,5,1,6]=>01010=>01010=>10101
[3,4,2,5,6,1]=>01001=>10010=>01101
[3,4,2,6,1,5]=>01010=>01010=>10101
[3,4,2,6,5,1]=>01011=>11010=>00101
[3,4,5,1,2,6]=>00100=>00100=>11011
[3,4,5,1,6,2]=>00101=>10100=>01011
[3,4,5,2,1,6]=>00110=>01100=>10011
[3,4,5,2,6,1]=>00101=>10100=>01011
[3,4,5,6,1,2]=>00010=>01000=>10111
[3,4,5,6,2,1]=>00011=>11000=>00111
[3,4,6,1,2,5]=>00100=>00100=>11011
[3,4,6,1,5,2]=>00101=>10100=>01011
[3,4,6,2,1,5]=>00110=>01100=>10011
[3,4,6,2,5,1]=>00101=>10100=>01011
[3,4,6,5,1,2]=>00110=>01100=>10011
[3,4,6,5,2,1]=>00111=>11100=>00011
[3,5,1,2,4,6]=>01000=>00010=>11101
[3,5,1,2,6,4]=>01001=>10010=>01101
[3,5,1,4,2,6]=>01010=>01010=>10101
[3,5,1,4,6,2]=>01001=>10010=>01101
[3,5,1,6,2,4]=>01010=>01010=>10101
[3,5,1,6,4,2]=>01011=>11010=>00101
[3,5,2,1,4,6]=>01100=>00110=>11001
[3,5,2,1,6,4]=>01101=>10110=>01001
[3,5,2,4,1,6]=>01010=>01010=>10101
[3,5,2,4,6,1]=>01001=>10010=>01101
[3,5,2,6,1,4]=>01010=>01010=>10101
[3,5,2,6,4,1]=>01011=>11010=>00101
[3,5,4,1,2,6]=>01100=>00110=>11001
[3,5,4,1,6,2]=>01101=>10110=>01001
[3,5,4,2,1,6]=>01110=>01110=>10001
[3,5,4,2,6,1]=>01101=>10110=>01001
[3,5,4,6,1,2]=>01010=>01010=>10101
[3,5,4,6,2,1]=>01011=>11010=>00101
[3,5,6,1,2,4]=>00100=>00100=>11011
[3,5,6,1,4,2]=>00101=>10100=>01011
[3,5,6,2,1,4]=>00110=>01100=>10011
[3,5,6,2,4,1]=>00101=>10100=>01011
[3,5,6,4,1,2]=>00110=>01100=>10011
[3,5,6,4,2,1]=>00111=>11100=>00011
[3,6,1,2,4,5]=>01000=>00010=>11101
[3,6,1,2,5,4]=>01001=>10010=>01101
[3,6,1,4,2,5]=>01010=>01010=>10101
[3,6,1,4,5,2]=>01001=>10010=>01101
[3,6,1,5,2,4]=>01010=>01010=>10101
[3,6,1,5,4,2]=>01011=>11010=>00101
[3,6,2,1,4,5]=>01100=>00110=>11001
[3,6,2,1,5,4]=>01101=>10110=>01001
[3,6,2,4,1,5]=>01010=>01010=>10101
[3,6,2,4,5,1]=>01001=>10010=>01101
[3,6,2,5,1,4]=>01010=>01010=>10101
[3,6,2,5,4,1]=>01011=>11010=>00101
[3,6,4,1,2,5]=>01100=>00110=>11001
[3,6,4,1,5,2]=>01101=>10110=>01001
[3,6,4,2,1,5]=>01110=>01110=>10001
[3,6,4,2,5,1]=>01101=>10110=>01001
[3,6,4,5,1,2]=>01010=>01010=>10101
[3,6,4,5,2,1]=>01011=>11010=>00101
[3,6,5,1,2,4]=>01100=>00110=>11001
[3,6,5,1,4,2]=>01101=>10110=>01001
[3,6,5,2,1,4]=>01110=>01110=>10001
[3,6,5,2,4,1]=>01101=>10110=>01001
[3,6,5,4,1,2]=>01110=>01110=>10001
[3,6,5,4,2,1]=>01111=>11110=>00001
[4,1,2,3,5,6]=>10000=>00001=>11110
[4,1,2,3,6,5]=>10001=>10001=>01110
[4,1,2,5,3,6]=>10010=>01001=>10110
[4,1,2,5,6,3]=>10001=>10001=>01110
[4,1,2,6,3,5]=>10010=>01001=>10110
[4,1,2,6,5,3]=>10011=>11001=>00110
[4,1,3,2,5,6]=>10100=>00101=>11010
[4,1,3,2,6,5]=>10101=>10101=>01010
[4,1,3,5,2,6]=>10010=>01001=>10110
[4,1,3,5,6,2]=>10001=>10001=>01110
[4,1,3,6,2,5]=>10010=>01001=>10110
[4,1,3,6,5,2]=>10011=>11001=>00110
[4,1,5,2,3,6]=>10100=>00101=>11010
[4,1,5,2,6,3]=>10101=>10101=>01010
[4,1,5,3,2,6]=>10110=>01101=>10010
[4,1,5,3,6,2]=>10101=>10101=>01010
[4,1,5,6,2,3]=>10010=>01001=>10110
[4,1,5,6,3,2]=>10011=>11001=>00110
[4,1,6,2,3,5]=>10100=>00101=>11010
[4,1,6,2,5,3]=>10101=>10101=>01010
[4,1,6,3,2,5]=>10110=>01101=>10010
[4,1,6,3,5,2]=>10101=>10101=>01010
[4,1,6,5,2,3]=>10110=>01101=>10010
[4,1,6,5,3,2]=>10111=>11101=>00010
[4,2,1,3,5,6]=>11000=>00011=>11100
[4,2,1,3,6,5]=>11001=>10011=>01100
[4,2,1,5,3,6]=>11010=>01011=>10100
[4,2,1,5,6,3]=>11001=>10011=>01100
[4,2,1,6,3,5]=>11010=>01011=>10100
[4,2,1,6,5,3]=>11011=>11011=>00100
[4,2,3,1,5,6]=>10100=>00101=>11010
[4,2,3,1,6,5]=>10101=>10101=>01010
[4,2,3,5,1,6]=>10010=>01001=>10110
[4,2,3,5,6,1]=>10001=>10001=>01110
[4,2,3,6,1,5]=>10010=>01001=>10110
[4,2,3,6,5,1]=>10011=>11001=>00110
[4,2,5,1,3,6]=>10100=>00101=>11010
[4,2,5,1,6,3]=>10101=>10101=>01010
[4,2,5,3,1,6]=>10110=>01101=>10010
[4,2,5,3,6,1]=>10101=>10101=>01010
[4,2,5,6,1,3]=>10010=>01001=>10110
[4,2,5,6,3,1]=>10011=>11001=>00110
[4,2,6,1,3,5]=>10100=>00101=>11010
[4,2,6,1,5,3]=>10101=>10101=>01010
[4,2,6,3,1,5]=>10110=>01101=>10010
[4,2,6,3,5,1]=>10101=>10101=>01010
[4,2,6,5,1,3]=>10110=>01101=>10010
[4,2,6,5,3,1]=>10111=>11101=>00010
[4,3,1,2,5,6]=>11000=>00011=>11100
[4,3,1,2,6,5]=>11001=>10011=>01100
[4,3,1,5,2,6]=>11010=>01011=>10100
[4,3,1,5,6,2]=>11001=>10011=>01100
[4,3,1,6,2,5]=>11010=>01011=>10100
[4,3,1,6,5,2]=>11011=>11011=>00100
[4,3,2,1,5,6]=>11100=>00111=>11000
[4,3,2,1,6,5]=>11101=>10111=>01000
[4,3,2,5,1,6]=>11010=>01011=>10100
[4,3,2,5,6,1]=>11001=>10011=>01100
[4,3,2,6,1,5]=>11010=>01011=>10100
[4,3,2,6,5,1]=>11011=>11011=>00100
[4,3,5,1,2,6]=>10100=>00101=>11010
[4,3,5,1,6,2]=>10101=>10101=>01010
[4,3,5,2,1,6]=>10110=>01101=>10010
[4,3,5,2,6,1]=>10101=>10101=>01010
[4,3,5,6,1,2]=>10010=>01001=>10110
[4,3,5,6,2,1]=>10011=>11001=>00110
[4,3,6,1,2,5]=>10100=>00101=>11010
[4,3,6,1,5,2]=>10101=>10101=>01010
[4,3,6,2,1,5]=>10110=>01101=>10010
[4,3,6,2,5,1]=>10101=>10101=>01010
[4,3,6,5,1,2]=>10110=>01101=>10010
[4,3,6,5,2,1]=>10111=>11101=>00010
[4,5,1,2,3,6]=>01000=>00010=>11101
[4,5,1,2,6,3]=>01001=>10010=>01101
[4,5,1,3,2,6]=>01010=>01010=>10101
[4,5,1,3,6,2]=>01001=>10010=>01101
[4,5,1,6,2,3]=>01010=>01010=>10101
[4,5,1,6,3,2]=>01011=>11010=>00101
[4,5,2,1,3,6]=>01100=>00110=>11001
[4,5,2,1,6,3]=>01101=>10110=>01001
[4,5,2,3,1,6]=>01010=>01010=>10101
[4,5,2,3,6,1]=>01001=>10010=>01101
[4,5,2,6,1,3]=>01010=>01010=>10101
[4,5,2,6,3,1]=>01011=>11010=>00101
[4,5,3,1,2,6]=>01100=>00110=>11001
[4,5,3,1,6,2]=>01101=>10110=>01001
[4,5,3,2,1,6]=>01110=>01110=>10001
[4,5,3,2,6,1]=>01101=>10110=>01001
[4,5,3,6,1,2]=>01010=>01010=>10101
[4,5,3,6,2,1]=>01011=>11010=>00101
[4,5,6,1,2,3]=>00100=>00100=>11011
[4,5,6,1,3,2]=>00101=>10100=>01011
[4,5,6,2,1,3]=>00110=>01100=>10011
[4,5,6,2,3,1]=>00101=>10100=>01011
[4,5,6,3,1,2]=>00110=>01100=>10011
[4,5,6,3,2,1]=>00111=>11100=>00011
[4,6,1,2,3,5]=>01000=>00010=>11101
[4,6,1,2,5,3]=>01001=>10010=>01101
[4,6,1,3,2,5]=>01010=>01010=>10101
[4,6,1,3,5,2]=>01001=>10010=>01101
[4,6,1,5,2,3]=>01010=>01010=>10101
[4,6,1,5,3,2]=>01011=>11010=>00101
[4,6,2,1,3,5]=>01100=>00110=>11001
[4,6,2,1,5,3]=>01101=>10110=>01001
[4,6,2,3,1,5]=>01010=>01010=>10101
[4,6,2,3,5,1]=>01001=>10010=>01101
[4,6,2,5,1,3]=>01010=>01010=>10101
[4,6,2,5,3,1]=>01011=>11010=>00101
[4,6,3,1,2,5]=>01100=>00110=>11001
[4,6,3,1,5,2]=>01101=>10110=>01001
[4,6,3,2,1,5]=>01110=>01110=>10001
[4,6,3,2,5,1]=>01101=>10110=>01001
[4,6,3,5,1,2]=>01010=>01010=>10101
[4,6,3,5,2,1]=>01011=>11010=>00101
[4,6,5,1,2,3]=>01100=>00110=>11001
[4,6,5,1,3,2]=>01101=>10110=>01001
[4,6,5,2,1,3]=>01110=>01110=>10001
[4,6,5,2,3,1]=>01101=>10110=>01001
[4,6,5,3,1,2]=>01110=>01110=>10001
[4,6,5,3,2,1]=>01111=>11110=>00001
[5,1,2,3,4,6]=>10000=>00001=>11110
[5,1,2,3,6,4]=>10001=>10001=>01110
[5,1,2,4,3,6]=>10010=>01001=>10110
[5,1,2,4,6,3]=>10001=>10001=>01110
[5,1,2,6,3,4]=>10010=>01001=>10110
[5,1,2,6,4,3]=>10011=>11001=>00110
[5,1,3,2,4,6]=>10100=>00101=>11010
[5,1,3,2,6,4]=>10101=>10101=>01010
[5,1,3,4,2,6]=>10010=>01001=>10110
[5,1,3,4,6,2]=>10001=>10001=>01110
[5,1,3,6,2,4]=>10010=>01001=>10110
[5,1,3,6,4,2]=>10011=>11001=>00110
[5,1,4,2,3,6]=>10100=>00101=>11010
[5,1,4,2,6,3]=>10101=>10101=>01010
[5,1,4,3,2,6]=>10110=>01101=>10010
[5,1,4,3,6,2]=>10101=>10101=>01010
[5,1,4,6,2,3]=>10010=>01001=>10110
[5,1,4,6,3,2]=>10011=>11001=>00110
[5,1,6,2,3,4]=>10100=>00101=>11010
[5,1,6,2,4,3]=>10101=>10101=>01010
[5,1,6,3,2,4]=>10110=>01101=>10010
[5,1,6,3,4,2]=>10101=>10101=>01010
[5,1,6,4,2,3]=>10110=>01101=>10010
[5,1,6,4,3,2]=>10111=>11101=>00010
[5,2,1,3,4,6]=>11000=>00011=>11100
[5,2,1,3,6,4]=>11001=>10011=>01100
[5,2,1,4,3,6]=>11010=>01011=>10100
[5,2,1,4,6,3]=>11001=>10011=>01100
[5,2,1,6,3,4]=>11010=>01011=>10100
[5,2,1,6,4,3]=>11011=>11011=>00100
[5,2,3,1,4,6]=>10100=>00101=>11010
[5,2,3,1,6,4]=>10101=>10101=>01010
[5,2,3,4,1,6]=>10010=>01001=>10110
[5,2,3,4,6,1]=>10001=>10001=>01110
[5,2,3,6,1,4]=>10010=>01001=>10110
[5,2,3,6,4,1]=>10011=>11001=>00110
[5,2,4,1,3,6]=>10100=>00101=>11010
[5,2,4,1,6,3]=>10101=>10101=>01010
[5,2,4,3,1,6]=>10110=>01101=>10010
[5,2,4,3,6,1]=>10101=>10101=>01010
[5,2,4,6,1,3]=>10010=>01001=>10110
[5,2,4,6,3,1]=>10011=>11001=>00110
[5,2,6,1,3,4]=>10100=>00101=>11010
[5,2,6,1,4,3]=>10101=>10101=>01010
[5,2,6,3,1,4]=>10110=>01101=>10010
[5,2,6,3,4,1]=>10101=>10101=>01010
[5,2,6,4,1,3]=>10110=>01101=>10010
[5,2,6,4,3,1]=>10111=>11101=>00010
[5,3,1,2,4,6]=>11000=>00011=>11100
[5,3,1,2,6,4]=>11001=>10011=>01100
[5,3,1,4,2,6]=>11010=>01011=>10100
[5,3,1,4,6,2]=>11001=>10011=>01100
[5,3,1,6,2,4]=>11010=>01011=>10100
[5,3,1,6,4,2]=>11011=>11011=>00100
[5,3,2,1,4,6]=>11100=>00111=>11000
[5,3,2,1,6,4]=>11101=>10111=>01000
[5,3,2,4,1,6]=>11010=>01011=>10100
[5,3,2,4,6,1]=>11001=>10011=>01100
[5,3,2,6,1,4]=>11010=>01011=>10100
[5,3,2,6,4,1]=>11011=>11011=>00100
[5,3,4,1,2,6]=>10100=>00101=>11010
[5,3,4,1,6,2]=>10101=>10101=>01010
[5,3,4,2,1,6]=>10110=>01101=>10010
[5,3,4,2,6,1]=>10101=>10101=>01010
[5,3,4,6,1,2]=>10010=>01001=>10110
[5,3,4,6,2,1]=>10011=>11001=>00110
[5,3,6,1,2,4]=>10100=>00101=>11010
[5,3,6,1,4,2]=>10101=>10101=>01010
[5,3,6,2,1,4]=>10110=>01101=>10010
[5,3,6,2,4,1]=>10101=>10101=>01010
[5,3,6,4,1,2]=>10110=>01101=>10010
[5,3,6,4,2,1]=>10111=>11101=>00010
[5,4,1,2,3,6]=>11000=>00011=>11100
[5,4,1,2,6,3]=>11001=>10011=>01100
[5,4,1,3,2,6]=>11010=>01011=>10100
[5,4,1,3,6,2]=>11001=>10011=>01100
[5,4,1,6,2,3]=>11010=>01011=>10100
[5,4,1,6,3,2]=>11011=>11011=>00100
[5,4,2,1,3,6]=>11100=>00111=>11000
[5,4,2,1,6,3]=>11101=>10111=>01000
[5,4,2,3,1,6]=>11010=>01011=>10100
[5,4,2,3,6,1]=>11001=>10011=>01100
[5,4,2,6,1,3]=>11010=>01011=>10100
[5,4,2,6,3,1]=>11011=>11011=>00100
[5,4,3,1,2,6]=>11100=>00111=>11000
[5,4,3,1,6,2]=>11101=>10111=>01000
[5,4,3,2,1,6]=>11110=>01111=>10000
[5,4,3,2,6,1]=>11101=>10111=>01000
[5,4,3,6,1,2]=>11010=>01011=>10100
[5,4,3,6,2,1]=>11011=>11011=>00100
[5,4,6,1,2,3]=>10100=>00101=>11010
[5,4,6,1,3,2]=>10101=>10101=>01010
[5,4,6,2,1,3]=>10110=>01101=>10010
[5,4,6,2,3,1]=>10101=>10101=>01010
[5,4,6,3,1,2]=>10110=>01101=>10010
[5,4,6,3,2,1]=>10111=>11101=>00010
[5,6,1,2,3,4]=>01000=>00010=>11101
[5,6,1,2,4,3]=>01001=>10010=>01101
[5,6,1,3,2,4]=>01010=>01010=>10101
[5,6,1,3,4,2]=>01001=>10010=>01101
[5,6,1,4,2,3]=>01010=>01010=>10101
[5,6,1,4,3,2]=>01011=>11010=>00101
[5,6,2,1,3,4]=>01100=>00110=>11001
[5,6,2,1,4,3]=>01101=>10110=>01001
[5,6,2,3,1,4]=>01010=>01010=>10101
[5,6,2,3,4,1]=>01001=>10010=>01101
[5,6,2,4,1,3]=>01010=>01010=>10101
[5,6,2,4,3,1]=>01011=>11010=>00101
[5,6,3,1,2,4]=>01100=>00110=>11001
[5,6,3,1,4,2]=>01101=>10110=>01001
[5,6,3,2,1,4]=>01110=>01110=>10001
[5,6,3,2,4,1]=>01101=>10110=>01001
[5,6,3,4,1,2]=>01010=>01010=>10101
[5,6,3,4,2,1]=>01011=>11010=>00101
[5,6,4,1,2,3]=>01100=>00110=>11001
[5,6,4,1,3,2]=>01101=>10110=>01001
[5,6,4,2,1,3]=>01110=>01110=>10001
[5,6,4,2,3,1]=>01101=>10110=>01001
[5,6,4,3,1,2]=>01110=>01110=>10001
[5,6,4,3,2,1]=>01111=>11110=>00001
[6,1,2,3,4,5]=>10000=>00001=>11110
[6,1,2,3,5,4]=>10001=>10001=>01110
[6,1,2,4,3,5]=>10010=>01001=>10110
[6,1,2,4,5,3]=>10001=>10001=>01110
[6,1,2,5,3,4]=>10010=>01001=>10110
[6,1,2,5,4,3]=>10011=>11001=>00110
[6,1,3,2,4,5]=>10100=>00101=>11010
[6,1,3,2,5,4]=>10101=>10101=>01010
[6,1,3,4,2,5]=>10010=>01001=>10110
[6,1,3,4,5,2]=>10001=>10001=>01110
[6,1,3,5,2,4]=>10010=>01001=>10110
[6,1,3,5,4,2]=>10011=>11001=>00110
[6,1,4,2,3,5]=>10100=>00101=>11010
[6,1,4,2,5,3]=>10101=>10101=>01010
[6,1,4,3,2,5]=>10110=>01101=>10010
[6,1,4,3,5,2]=>10101=>10101=>01010
[6,1,4,5,2,3]=>10010=>01001=>10110
[6,1,4,5,3,2]=>10011=>11001=>00110
[6,1,5,2,3,4]=>10100=>00101=>11010
[6,1,5,2,4,3]=>10101=>10101=>01010
[6,1,5,3,2,4]=>10110=>01101=>10010
[6,1,5,3,4,2]=>10101=>10101=>01010
[6,1,5,4,2,3]=>10110=>01101=>10010
[6,1,5,4,3,2]=>10111=>11101=>00010
[6,2,1,3,4,5]=>11000=>00011=>11100
[6,2,1,3,5,4]=>11001=>10011=>01100
[6,2,1,4,3,5]=>11010=>01011=>10100
[6,2,1,4,5,3]=>11001=>10011=>01100
[6,2,1,5,3,4]=>11010=>01011=>10100
[6,2,1,5,4,3]=>11011=>11011=>00100
[6,2,3,1,4,5]=>10100=>00101=>11010
[6,2,3,1,5,4]=>10101=>10101=>01010
[6,2,3,4,1,5]=>10010=>01001=>10110
[6,2,3,4,5,1]=>10001=>10001=>01110
[6,2,3,5,1,4]=>10010=>01001=>10110
[6,2,3,5,4,1]=>10011=>11001=>00110
[6,2,4,1,3,5]=>10100=>00101=>11010
[6,2,4,1,5,3]=>10101=>10101=>01010
[6,2,4,3,1,5]=>10110=>01101=>10010
[6,2,4,3,5,1]=>10101=>10101=>01010
[6,2,4,5,1,3]=>10010=>01001=>10110
[6,2,4,5,3,1]=>10011=>11001=>00110
[6,2,5,1,3,4]=>10100=>00101=>11010
[6,2,5,1,4,3]=>10101=>10101=>01010
[6,2,5,3,1,4]=>10110=>01101=>10010
[6,2,5,3,4,1]=>10101=>10101=>01010
[6,2,5,4,1,3]=>10110=>01101=>10010
[6,2,5,4,3,1]=>10111=>11101=>00010
[6,3,1,2,4,5]=>11000=>00011=>11100
[6,3,1,2,5,4]=>11001=>10011=>01100
[6,3,1,4,2,5]=>11010=>01011=>10100
[6,3,1,4,5,2]=>11001=>10011=>01100
[6,3,1,5,2,4]=>11010=>01011=>10100
[6,3,1,5,4,2]=>11011=>11011=>00100
[6,3,2,1,4,5]=>11100=>00111=>11000
[6,3,2,1,5,4]=>11101=>10111=>01000
[6,3,2,4,1,5]=>11010=>01011=>10100
[6,3,2,4,5,1]=>11001=>10011=>01100
[6,3,2,5,1,4]=>11010=>01011=>10100
[6,3,2,5,4,1]=>11011=>11011=>00100
[6,3,4,1,2,5]=>10100=>00101=>11010
[6,3,4,1,5,2]=>10101=>10101=>01010
[6,3,4,2,1,5]=>10110=>01101=>10010
[6,3,4,2,5,1]=>10101=>10101=>01010
[6,3,4,5,1,2]=>10010=>01001=>10110
[6,3,4,5,2,1]=>10011=>11001=>00110
[6,3,5,1,2,4]=>10100=>00101=>11010
[6,3,5,1,4,2]=>10101=>10101=>01010
[6,3,5,2,1,4]=>10110=>01101=>10010
[6,3,5,2,4,1]=>10101=>10101=>01010
[6,3,5,4,1,2]=>10110=>01101=>10010
[6,3,5,4,2,1]=>10111=>11101=>00010
[6,4,1,2,3,5]=>11000=>00011=>11100
[6,4,1,2,5,3]=>11001=>10011=>01100
[6,4,1,3,2,5]=>11010=>01011=>10100
[6,4,1,3,5,2]=>11001=>10011=>01100
[6,4,1,5,2,3]=>11010=>01011=>10100
[6,4,1,5,3,2]=>11011=>11011=>00100
[6,4,2,1,3,5]=>11100=>00111=>11000
[6,4,2,1,5,3]=>11101=>10111=>01000
[6,4,2,3,1,5]=>11010=>01011=>10100
[6,4,2,3,5,1]=>11001=>10011=>01100
[6,4,2,5,1,3]=>11010=>01011=>10100
[6,4,2,5,3,1]=>11011=>11011=>00100
[6,4,3,1,2,5]=>11100=>00111=>11000
[6,4,3,1,5,2]=>11101=>10111=>01000
[6,4,3,2,1,5]=>11110=>01111=>10000
[6,4,3,2,5,1]=>11101=>10111=>01000
[6,4,3,5,1,2]=>11010=>01011=>10100
[6,4,3,5,2,1]=>11011=>11011=>00100
[6,4,5,1,2,3]=>10100=>00101=>11010
[6,4,5,1,3,2]=>10101=>10101=>01010
[6,4,5,2,1,3]=>10110=>01101=>10010
[6,4,5,2,3,1]=>10101=>10101=>01010
[6,4,5,3,1,2]=>10110=>01101=>10010
[6,4,5,3,2,1]=>10111=>11101=>00010
[6,5,1,2,3,4]=>11000=>00011=>11100
[6,5,1,2,4,3]=>11001=>10011=>01100
[6,5,1,3,2,4]=>11010=>01011=>10100
[6,5,1,3,4,2]=>11001=>10011=>01100
[6,5,1,4,2,3]=>11010=>01011=>10100
[6,5,1,4,3,2]=>11011=>11011=>00100
[6,5,2,1,3,4]=>11100=>00111=>11000
[6,5,2,1,4,3]=>11101=>10111=>01000
[6,5,2,3,1,4]=>11010=>01011=>10100
[6,5,2,3,4,1]=>11001=>10011=>01100
[6,5,2,4,1,3]=>11010=>01011=>10100
[6,5,2,4,3,1]=>11011=>11011=>00100
[6,5,3,1,2,4]=>11100=>00111=>11000
[6,5,3,1,4,2]=>11101=>10111=>01000
[6,5,3,2,1,4]=>11110=>01111=>10000
[6,5,3,2,4,1]=>11101=>10111=>01000
[6,5,3,4,1,2]=>11010=>01011=>10100
[6,5,3,4,2,1]=>11011=>11011=>00100
[6,5,4,1,2,3]=>11100=>00111=>11000
[6,5,4,1,3,2]=>11101=>10111=>01000
[6,5,4,2,1,3]=>11110=>01111=>10000
[6,5,4,2,3,1]=>11101=>10111=>01000
[6,5,4,3,1,2]=>11110=>01111=>10000
[6,5,4,3,2,1]=>11111=>11111=>00000
[1,2,3,4,5,6,7]=>000000=>000000=>111111
[1,2,3,4,5,7,6]=>000001=>100000=>011111
[1,2,3,4,6,5,7]=>000010=>010000=>101111
[1,2,3,4,6,7,5]=>000001=>100000=>011111
[1,2,3,4,7,5,6]=>000010=>010000=>101111
[1,2,3,4,7,6,5]=>000011=>110000=>001111
[1,2,3,5,4,6,7]=>000100=>001000=>110111
[1,2,3,5,4,7,6]=>000101=>101000=>010111
[1,2,3,5,6,4,7]=>000010=>010000=>101111
[1,2,3,5,6,7,4]=>000001=>100000=>011111
[1,2,3,5,7,4,6]=>000010=>010000=>101111
[1,2,3,5,7,6,4]=>000011=>110000=>001111
[1,2,3,6,4,5,7]=>000100=>001000=>110111
[1,2,3,6,4,7,5]=>000101=>101000=>010111
[1,2,3,6,5,4,7]=>000110=>011000=>100111
[1,2,3,6,5,7,4]=>000101=>101000=>010111
[1,2,3,6,7,4,5]=>000010=>010000=>101111
[1,2,3,6,7,5,4]=>000011=>110000=>001111
[1,2,3,7,4,5,6]=>000100=>001000=>110111
[1,2,3,7,4,6,5]=>000101=>101000=>010111
[1,2,3,7,5,4,6]=>000110=>011000=>100111
[1,2,3,7,5,6,4]=>000101=>101000=>010111
[1,2,3,7,6,4,5]=>000110=>011000=>100111
[1,2,3,7,6,5,4]=>000111=>111000=>000111
[1,2,4,3,5,6,7]=>001000=>000100=>111011
[1,2,4,3,5,7,6]=>001001=>100100=>011011
[1,2,4,3,6,5,7]=>001010=>010100=>101011
[1,2,4,3,6,7,5]=>001001=>100100=>011011
[1,2,4,3,7,5,6]=>001010=>010100=>101011
[1,2,4,3,7,6,5]=>001011=>110100=>001011
[1,2,4,5,3,6,7]=>000100=>001000=>110111
[1,2,4,5,3,7,6]=>000101=>101000=>010111
[1,2,4,5,6,3,7]=>000010=>010000=>101111
[1,2,4,5,6,7,3]=>000001=>100000=>011111
[1,2,4,5,7,3,6]=>000010=>010000=>101111
[1,2,4,5,7,6,3]=>000011=>110000=>001111
[1,2,4,6,3,5,7]=>000100=>001000=>110111
[1,2,4,6,3,7,5]=>000101=>101000=>010111
[1,2,4,6,5,3,7]=>000110=>011000=>100111
[1,2,4,6,5,7,3]=>000101=>101000=>010111
[1,2,4,6,7,3,5]=>000010=>010000=>101111
[1,2,4,6,7,5,3]=>000011=>110000=>001111
[1,2,4,7,3,5,6]=>000100=>001000=>110111
[1,2,4,7,3,6,5]=>000101=>101000=>010111
[1,2,4,7,5,3,6]=>000110=>011000=>100111
[1,2,4,7,5,6,3]=>000101=>101000=>010111
[1,2,4,7,6,3,5]=>000110=>011000=>100111
[1,2,4,7,6,5,3]=>000111=>111000=>000111
[1,2,5,3,4,6,7]=>001000=>000100=>111011
[1,2,5,3,4,7,6]=>001001=>100100=>011011
[1,2,5,3,6,4,7]=>001010=>010100=>101011
[1,2,5,3,6,7,4]=>001001=>100100=>011011
[1,2,5,3,7,4,6]=>001010=>010100=>101011
[1,2,5,3,7,6,4]=>001011=>110100=>001011
[1,2,5,4,3,6,7]=>001100=>001100=>110011
[1,2,5,4,3,7,6]=>001101=>101100=>010011
[1,2,5,4,6,3,7]=>001010=>010100=>101011
[1,2,5,4,6,7,3]=>001001=>100100=>011011
[1,2,5,4,7,3,6]=>001010=>010100=>101011
[1,2,5,4,7,6,3]=>001011=>110100=>001011
[1,2,5,6,3,4,7]=>000100=>001000=>110111
[1,2,5,6,3,7,4]=>000101=>101000=>010111
[1,2,5,6,4,3,7]=>000110=>011000=>100111
[1,2,5,6,4,7,3]=>000101=>101000=>010111
[1,2,5,6,7,3,4]=>000010=>010000=>101111
[1,2,5,6,7,4,3]=>000011=>110000=>001111
[1,2,5,7,3,4,6]=>000100=>001000=>110111
[1,2,5,7,3,6,4]=>000101=>101000=>010111
[1,2,5,7,4,3,6]=>000110=>011000=>100111
[1,2,5,7,4,6,3]=>000101=>101000=>010111
[1,2,5,7,6,3,4]=>000110=>011000=>100111
[1,2,5,7,6,4,3]=>000111=>111000=>000111
[1,2,6,3,4,5,7]=>001000=>000100=>111011
[1,2,6,3,4,7,5]=>001001=>100100=>011011
[1,2,6,3,5,4,7]=>001010=>010100=>101011
[1,2,6,3,5,7,4]=>001001=>100100=>011011
[1,2,6,3,7,4,5]=>001010=>010100=>101011
[1,2,6,3,7,5,4]=>001011=>110100=>001011
[1,2,6,4,3,5,7]=>001100=>001100=>110011
[1,2,6,4,3,7,5]=>001101=>101100=>010011
[1,2,6,4,5,3,7]=>001010=>010100=>101011
[1,2,6,4,5,7,3]=>001001=>100100=>011011
[1,2,6,4,7,3,5]=>001010=>010100=>101011
[1,2,6,4,7,5,3]=>001011=>110100=>001011
[1,2,6,5,3,4,7]=>001100=>001100=>110011
[1,2,6,5,3,7,4]=>001101=>101100=>010011
[1,2,6,5,4,3,7]=>001110=>011100=>100011
[1,2,6,5,4,7,3]=>001101=>101100=>010011
[1,2,6,5,7,3,4]=>001010=>010100=>101011
[1,2,6,5,7,4,3]=>001011=>110100=>001011
[1,2,6,7,3,4,5]=>000100=>001000=>110111
[1,2,6,7,3,5,4]=>000101=>101000=>010111
[1,2,6,7,4,3,5]=>000110=>011000=>100111
[1,2,6,7,4,5,3]=>000101=>101000=>010111
[1,2,6,7,5,3,4]=>000110=>011000=>100111
[1,2,6,7,5,4,3]=>000111=>111000=>000111
[1,2,7,3,4,5,6]=>001000=>000100=>111011
[1,2,7,3,4,6,5]=>001001=>100100=>011011
[1,2,7,3,5,4,6]=>001010=>010100=>101011
[1,2,7,3,5,6,4]=>001001=>100100=>011011
[1,2,7,3,6,4,5]=>001010=>010100=>101011
[1,2,7,3,6,5,4]=>001011=>110100=>001011
[1,2,7,4,3,5,6]=>001100=>001100=>110011
[1,2,7,4,3,6,5]=>001101=>101100=>010011
[1,2,7,4,5,3,6]=>001010=>010100=>101011
[1,2,7,4,5,6,3]=>001001=>100100=>011011
[1,2,7,4,6,3,5]=>001010=>010100=>101011
[1,2,7,4,6,5,3]=>001011=>110100=>001011
[1,2,7,5,3,4,6]=>001100=>001100=>110011
[1,2,7,5,3,6,4]=>001101=>101100=>010011
[1,2,7,5,4,3,6]=>001110=>011100=>100011
[1,2,7,5,4,6,3]=>001101=>101100=>010011
[1,2,7,5,6,3,4]=>001010=>010100=>101011
[1,2,7,5,6,4,3]=>001011=>110100=>001011
[1,2,7,6,3,4,5]=>001100=>001100=>110011
[1,2,7,6,3,5,4]=>001101=>101100=>010011
[1,2,7,6,4,3,5]=>001110=>011100=>100011
[1,2,7,6,4,5,3]=>001101=>101100=>010011
[1,2,7,6,5,3,4]=>001110=>011100=>100011
[1,2,7,6,5,4,3]=>001111=>111100=>000011
[1,3,2,4,5,6,7]=>010000=>000010=>111101
[1,3,2,4,5,7,6]=>010001=>100010=>011101
[1,3,2,4,6,5,7]=>010010=>010010=>101101
[1,3,2,4,6,7,5]=>010001=>100010=>011101
[1,3,2,4,7,5,6]=>010010=>010010=>101101
[1,3,2,4,7,6,5]=>010011=>110010=>001101
[1,3,2,5,4,6,7]=>010100=>001010=>110101
[1,3,2,5,4,7,6]=>010101=>101010=>010101
[1,3,2,5,6,4,7]=>010010=>010010=>101101
[1,3,2,5,6,7,4]=>010001=>100010=>011101
[1,3,2,5,7,4,6]=>010010=>010010=>101101
[1,3,2,5,7,6,4]=>010011=>110010=>001101
[1,3,2,6,4,5,7]=>010100=>001010=>110101
[1,3,2,6,4,7,5]=>010101=>101010=>010101
[1,3,2,6,5,4,7]=>010110=>011010=>100101
[1,3,2,6,5,7,4]=>010101=>101010=>010101
[1,3,2,6,7,4,5]=>010010=>010010=>101101
[1,3,2,6,7,5,4]=>010011=>110010=>001101
[1,3,2,7,4,5,6]=>010100=>001010=>110101
[1,3,2,7,4,6,5]=>010101=>101010=>010101
[1,3,2,7,5,4,6]=>010110=>011010=>100101
[1,3,2,7,5,6,4]=>010101=>101010=>010101
[1,3,2,7,6,4,5]=>010110=>011010=>100101
[1,3,2,7,6,5,4]=>010111=>111010=>000101
[1,3,4,2,5,6,7]=>001000=>000100=>111011
[1,3,4,2,5,7,6]=>001001=>100100=>011011
[1,3,4,2,6,5,7]=>001010=>010100=>101011
[1,3,4,2,6,7,5]=>001001=>100100=>011011
[1,3,4,2,7,5,6]=>001010=>010100=>101011
[1,3,4,2,7,6,5]=>001011=>110100=>001011
[1,3,4,5,2,6,7]=>000100=>001000=>110111
[1,3,4,5,2,7,6]=>000101=>101000=>010111
[1,3,4,5,6,2,7]=>000010=>010000=>101111
[1,3,4,5,6,7,2]=>000001=>100000=>011111
[1,3,4,5,7,2,6]=>000010=>010000=>101111
[1,3,4,5,7,6,2]=>000011=>110000=>001111
[1,3,4,6,2,5,7]=>000100=>001000=>110111
[1,3,4,6,2,7,5]=>000101=>101000=>010111
[1,3,4,6,5,2,7]=>000110=>011000=>100111
[1,3,4,6,5,7,2]=>000101=>101000=>010111
[1,3,4,6,7,2,5]=>000010=>010000=>101111
[1,3,4,6,7,5,2]=>000011=>110000=>001111
[1,3,4,7,2,5,6]=>000100=>001000=>110111
[1,3,4,7,2,6,5]=>000101=>101000=>010111
[1,3,4,7,5,2,6]=>000110=>011000=>100111
[1,3,4,7,5,6,2]=>000101=>101000=>010111
[1,3,4,7,6,2,5]=>000110=>011000=>100111
[1,3,4,7,6,5,2]=>000111=>111000=>000111
[1,3,5,2,4,6,7]=>001000=>000100=>111011
[1,3,5,2,4,7,6]=>001001=>100100=>011011
[1,3,5,2,6,4,7]=>001010=>010100=>101011
[1,3,5,2,6,7,4]=>001001=>100100=>011011
[1,3,5,2,7,4,6]=>001010=>010100=>101011
[1,3,5,2,7,6,4]=>001011=>110100=>001011
[1,3,5,4,2,6,7]=>001100=>001100=>110011
[1,3,5,4,2,7,6]=>001101=>101100=>010011
[1,3,5,4,6,2,7]=>001010=>010100=>101011
[1,3,5,4,6,7,2]=>001001=>100100=>011011
[1,3,5,4,7,2,6]=>001010=>010100=>101011
[1,3,5,4,7,6,2]=>001011=>110100=>001011
[1,3,5,6,2,4,7]=>000100=>001000=>110111
[1,3,5,6,2,7,4]=>000101=>101000=>010111
[1,3,5,6,4,2,7]=>000110=>011000=>100111
[1,3,5,6,4,7,2]=>000101=>101000=>010111
[1,3,5,6,7,2,4]=>000010=>010000=>101111
[1,3,5,6,7,4,2]=>000011=>110000=>001111
[1,3,5,7,2,4,6]=>000100=>001000=>110111
[1,3,5,7,2,6,4]=>000101=>101000=>010111
[1,3,5,7,4,2,6]=>000110=>011000=>100111
[1,3,5,7,4,6,2]=>000101=>101000=>010111
[1,3,5,7,6,2,4]=>000110=>011000=>100111
[1,3,5,7,6,4,2]=>000111=>111000=>000111
[1,3,6,2,4,5,7]=>001000=>000100=>111011
[1,3,6,2,4,7,5]=>001001=>100100=>011011
[1,3,6,2,5,4,7]=>001010=>010100=>101011
[1,3,6,2,5,7,4]=>001001=>100100=>011011
[1,3,6,2,7,4,5]=>001010=>010100=>101011
[1,3,6,2,7,5,4]=>001011=>110100=>001011
[1,3,6,4,2,5,7]=>001100=>001100=>110011
[1,3,6,4,2,7,5]=>001101=>101100=>010011
[1,3,6,4,5,2,7]=>001010=>010100=>101011
[1,3,6,4,5,7,2]=>001001=>100100=>011011
[1,3,6,4,7,2,5]=>001010=>010100=>101011
[1,3,6,4,7,5,2]=>001011=>110100=>001011
[1,3,6,5,2,4,7]=>001100=>001100=>110011
[1,3,6,5,2,7,4]=>001101=>101100=>010011
[1,3,6,5,4,2,7]=>001110=>011100=>100011
[1,3,6,5,4,7,2]=>001101=>101100=>010011
[1,3,6,5,7,2,4]=>001010=>010100=>101011
[1,3,6,5,7,4,2]=>001011=>110100=>001011
[1,3,6,7,2,4,5]=>000100=>001000=>110111
[1,3,6,7,2,5,4]=>000101=>101000=>010111
[1,3,6,7,4,2,5]=>000110=>011000=>100111
[1,3,6,7,4,5,2]=>000101=>101000=>010111
[1,3,6,7,5,2,4]=>000110=>011000=>100111
[1,3,6,7,5,4,2]=>000111=>111000=>000111
[1,3,7,2,4,5,6]=>001000=>000100=>111011
[1,3,7,2,4,6,5]=>001001=>100100=>011011
[1,3,7,2,5,4,6]=>001010=>010100=>101011
[1,3,7,2,5,6,4]=>001001=>100100=>011011
[1,3,7,2,6,4,5]=>001010=>010100=>101011
[1,3,7,2,6,5,4]=>001011=>110100=>001011
[1,3,7,4,2,5,6]=>001100=>001100=>110011
[1,3,7,4,2,6,5]=>001101=>101100=>010011
[1,3,7,4,5,2,6]=>001010=>010100=>101011
[1,3,7,4,5,6,2]=>001001=>100100=>011011
[1,3,7,4,6,2,5]=>001010=>010100=>101011
[1,3,7,4,6,5,2]=>001011=>110100=>001011
[1,3,7,5,2,4,6]=>001100=>001100=>110011
[1,3,7,5,2,6,4]=>001101=>101100=>010011
[1,3,7,5,4,2,6]=>001110=>011100=>100011
[1,3,7,5,4,6,2]=>001101=>101100=>010011
[1,3,7,5,6,2,4]=>001010=>010100=>101011
[1,3,7,5,6,4,2]=>001011=>110100=>001011
[1,3,7,6,2,4,5]=>001100=>001100=>110011
[1,3,7,6,2,5,4]=>001101=>101100=>010011
[1,3,7,6,4,2,5]=>001110=>011100=>100011
[1,3,7,6,4,5,2]=>001101=>101100=>010011
[1,3,7,6,5,2,4]=>001110=>011100=>100011
[1,3,7,6,5,4,2]=>001111=>111100=>000011
[1,4,2,3,5,6,7]=>010000=>000010=>111101
[1,4,2,3,5,7,6]=>010001=>100010=>011101
[1,4,2,3,6,5,7]=>010010=>010010=>101101
[1,4,2,3,6,7,5]=>010001=>100010=>011101
[1,4,2,3,7,5,6]=>010010=>010010=>101101
[1,4,2,3,7,6,5]=>010011=>110010=>001101
[1,4,2,5,3,6,7]=>010100=>001010=>110101
[1,4,2,5,3,7,6]=>010101=>101010=>010101
[1,4,2,5,6,3,7]=>010010=>010010=>101101
[1,4,2,5,6,7,3]=>010001=>100010=>011101
[1,4,2,5,7,3,6]=>010010=>010010=>101101
[1,4,2,5,7,6,3]=>010011=>110010=>001101
[1,4,2,6,3,5,7]=>010100=>001010=>110101
[1,4,2,6,3,7,5]=>010101=>101010=>010101
[1,4,2,6,5,3,7]=>010110=>011010=>100101
[1,4,2,6,5,7,3]=>010101=>101010=>010101
[1,4,2,6,7,3,5]=>010010=>010010=>101101
[1,4,2,6,7,5,3]=>010011=>110010=>001101
[1,4,2,7,3,5,6]=>010100=>001010=>110101
[1,4,2,7,3,6,5]=>010101=>101010=>010101
[1,4,2,7,5,3,6]=>010110=>011010=>100101
[1,4,2,7,5,6,3]=>010101=>101010=>010101
[1,4,2,7,6,3,5]=>010110=>011010=>100101
[1,4,2,7,6,5,3]=>010111=>111010=>000101
[1,4,3,2,5,6,7]=>011000=>000110=>111001
[1,4,3,2,5,7,6]=>011001=>100110=>011001
[1,4,3,2,6,5,7]=>011010=>010110=>101001
[1,4,3,2,6,7,5]=>011001=>100110=>011001
[1,4,3,2,7,5,6]=>011010=>010110=>101001
[1,4,3,2,7,6,5]=>011011=>110110=>001001
[1,4,3,5,2,6,7]=>010100=>001010=>110101
[1,4,3,5,2,7,6]=>010101=>101010=>010101
[1,4,3,5,6,2,7]=>010010=>010010=>101101
[1,4,3,5,6,7,2]=>010001=>100010=>011101
[1,4,3,5,7,2,6]=>010010=>010010=>101101
[1,4,3,5,7,6,2]=>010011=>110010=>001101
[1,4,3,6,2,5,7]=>010100=>001010=>110101
[1,4,3,6,2,7,5]=>010101=>101010=>010101
[1,4,3,6,5,2,7]=>010110=>011010=>100101
[1,4,3,6,5,7,2]=>010101=>101010=>010101
[1,4,3,6,7,2,5]=>010010=>010010=>101101
[1,4,3,6,7,5,2]=>010011=>110010=>001101
[1,4,3,7,2,5,6]=>010100=>001010=>110101
[1,4,3,7,2,6,5]=>010101=>101010=>010101
[1,4,3,7,5,2,6]=>010110=>011010=>100101
[1,4,3,7,5,6,2]=>010101=>101010=>010101
[1,4,3,7,6,2,5]=>010110=>011010=>100101
[1,4,3,7,6,5,2]=>010111=>111010=>000101
[1,4,5,2,3,6,7]=>001000=>000100=>111011
[1,4,5,2,3,7,6]=>001001=>100100=>011011
[1,4,5,2,6,3,7]=>001010=>010100=>101011
[1,4,5,2,6,7,3]=>001001=>100100=>011011
[1,4,5,2,7,3,6]=>001010=>010100=>101011
[1,4,5,2,7,6,3]=>001011=>110100=>001011
[1,4,5,3,2,6,7]=>001100=>001100=>110011
[1,4,5,3,2,7,6]=>001101=>101100=>010011
[1,4,5,3,6,2,7]=>001010=>010100=>101011
[1,4,5,3,6,7,2]=>001001=>100100=>011011
[1,4,5,3,7,2,6]=>001010=>010100=>101011
[1,4,5,3,7,6,2]=>001011=>110100=>001011
[1,4,5,6,2,3,7]=>000100=>001000=>110111
[1,4,5,6,2,7,3]=>000101=>101000=>010111
[1,4,5,6,3,2,7]=>000110=>011000=>100111
[1,4,5,6,3,7,2]=>000101=>101000=>010111
[1,4,5,6,7,2,3]=>000010=>010000=>101111
[1,4,5,6,7,3,2]=>000011=>110000=>001111
[1,4,5,7,2,3,6]=>000100=>001000=>110111
[1,4,5,7,2,6,3]=>000101=>101000=>010111
[1,4,5,7,3,2,6]=>000110=>011000=>100111
[1,4,5,7,3,6,2]=>000101=>101000=>010111
[1,4,5,7,6,2,3]=>000110=>011000=>100111
[1,4,5,7,6,3,2]=>000111=>111000=>000111
[1,4,6,2,3,5,7]=>001000=>000100=>111011
[1,4,6,2,3,7,5]=>001001=>100100=>011011
[1,4,6,2,5,3,7]=>001010=>010100=>101011
[1,4,6,2,5,7,3]=>001001=>100100=>011011
[1,4,6,2,7,3,5]=>001010=>010100=>101011
[1,4,6,2,7,5,3]=>001011=>110100=>001011
[1,4,6,3,2,5,7]=>001100=>001100=>110011
[1,4,6,3,2,7,5]=>001101=>101100=>010011
[1,4,6,3,5,2,7]=>001010=>010100=>101011
[1,4,6,3,5,7,2]=>001001=>100100=>011011
[1,4,6,3,7,2,5]=>001010=>010100=>101011
[1,4,6,3,7,5,2]=>001011=>110100=>001011
[1,4,6,5,2,3,7]=>001100=>001100=>110011
[1,4,6,5,2,7,3]=>001101=>101100=>010011
[1,4,6,5,3,2,7]=>001110=>011100=>100011
[1,4,6,5,3,7,2]=>001101=>101100=>010011
[1,4,6,5,7,2,3]=>001010=>010100=>101011
[1,4,6,5,7,3,2]=>001011=>110100=>001011
[1,4,6,7,2,3,5]=>000100=>001000=>110111
[1,4,6,7,2,5,3]=>000101=>101000=>010111
[1,4,6,7,3,2,5]=>000110=>011000=>100111
[1,4,6,7,3,5,2]=>000101=>101000=>010111
[1,4,6,7,5,2,3]=>000110=>011000=>100111
[1,4,6,7,5,3,2]=>000111=>111000=>000111
[1,4,7,2,3,5,6]=>001000=>000100=>111011
[1,4,7,2,3,6,5]=>001001=>100100=>011011
[1,4,7,2,5,3,6]=>001010=>010100=>101011
[1,4,7,2,5,6,3]=>001001=>100100=>011011
[1,4,7,2,6,3,5]=>001010=>010100=>101011
[1,4,7,2,6,5,3]=>001011=>110100=>001011
[1,4,7,3,2,5,6]=>001100=>001100=>110011
[1,4,7,3,2,6,5]=>001101=>101100=>010011
[1,4,7,3,5,2,6]=>001010=>010100=>101011
[1,4,7,3,5,6,2]=>001001=>100100=>011011
[1,4,7,3,6,2,5]=>001010=>010100=>101011
[1,4,7,3,6,5,2]=>001011=>110100=>001011
[1,4,7,5,2,3,6]=>001100=>001100=>110011
[1,4,7,5,2,6,3]=>001101=>101100=>010011
[1,4,7,5,3,2,6]=>001110=>011100=>100011
[1,4,7,5,3,6,2]=>001101=>101100=>010011
[1,4,7,5,6,2,3]=>001010=>010100=>101011
[1,4,7,5,6,3,2]=>001011=>110100=>001011
[1,4,7,6,2,3,5]=>001100=>001100=>110011
[1,4,7,6,2,5,3]=>001101=>101100=>010011
[1,4,7,6,3,2,5]=>001110=>011100=>100011
[1,4,7,6,3,5,2]=>001101=>101100=>010011
[1,4,7,6,5,2,3]=>001110=>011100=>100011
[1,4,7,6,5,3,2]=>001111=>111100=>000011
[1,5,2,3,4,6,7]=>010000=>000010=>111101
[1,5,2,3,4,7,6]=>010001=>100010=>011101
[1,5,2,3,6,4,7]=>010010=>010010=>101101
[1,5,2,3,6,7,4]=>010001=>100010=>011101
[1,5,2,3,7,4,6]=>010010=>010010=>101101
[1,5,2,3,7,6,4]=>010011=>110010=>001101
[1,5,2,4,3,6,7]=>010100=>001010=>110101
[1,5,2,4,3,7,6]=>010101=>101010=>010101
[1,5,2,4,6,3,7]=>010010=>010010=>101101
[1,5,2,4,6,7,3]=>010001=>100010=>011101
[1,5,2,4,7,3,6]=>010010=>010010=>101101
[1,5,2,4,7,6,3]=>010011=>110010=>001101
[1,5,2,6,3,4,7]=>010100=>001010=>110101
[1,5,2,6,3,7,4]=>010101=>101010=>010101
[1,5,2,6,4,3,7]=>010110=>011010=>100101
[1,5,2,6,4,7,3]=>010101=>101010=>010101
[1,5,2,6,7,3,4]=>010010=>010010=>101101
[1,5,2,6,7,4,3]=>010011=>110010=>001101
[1,5,2,7,3,4,6]=>010100=>001010=>110101
[1,5,2,7,3,6,4]=>010101=>101010=>010101
[1,5,2,7,4,3,6]=>010110=>011010=>100101
[1,5,2,7,4,6,3]=>010101=>101010=>010101
[1,5,2,7,6,3,4]=>010110=>011010=>100101
[1,5,2,7,6,4,3]=>010111=>111010=>000101
[1,5,3,2,4,6,7]=>011000=>000110=>111001
[1,5,3,2,4,7,6]=>011001=>100110=>011001
[1,5,3,2,6,4,7]=>011010=>010110=>101001
[1,5,3,2,6,7,4]=>011001=>100110=>011001
[1,5,3,2,7,4,6]=>011010=>010110=>101001
[1,5,3,2,7,6,4]=>011011=>110110=>001001
[1,5,3,4,2,6,7]=>010100=>001010=>110101
[1,5,3,4,2,7,6]=>010101=>101010=>010101
[1,5,3,4,6,2,7]=>010010=>010010=>101101
[1,5,3,4,6,7,2]=>010001=>100010=>011101
[1,5,3,4,7,2,6]=>010010=>010010=>101101
[1,5,3,4,7,6,2]=>010011=>110010=>001101
[1,5,3,6,2,4,7]=>010100=>001010=>110101
[1,5,3,6,2,7,4]=>010101=>101010=>010101
[1,5,3,6,4,2,7]=>010110=>011010=>100101
[1,5,3,6,4,7,2]=>010101=>101010=>010101
[1,5,3,6,7,2,4]=>010010=>010010=>101101
[1,5,3,6,7,4,2]=>010011=>110010=>001101
[1,5,3,7,2,4,6]=>010100=>001010=>110101
[1,5,3,7,2,6,4]=>010101=>101010=>010101
[1,5,3,7,4,2,6]=>010110=>011010=>100101
[1,5,3,7,4,6,2]=>010101=>101010=>010101
[1,5,3,7,6,2,4]=>010110=>011010=>100101
[1,5,3,7,6,4,2]=>010111=>111010=>000101
[1,5,4,2,3,6,7]=>011000=>000110=>111001
[1,5,4,2,3,7,6]=>011001=>100110=>011001
[1,5,4,2,6,3,7]=>011010=>010110=>101001
[1,5,4,2,6,7,3]=>011001=>100110=>011001
[1,5,4,2,7,3,6]=>011010=>010110=>101001
[1,5,4,2,7,6,3]=>011011=>110110=>001001
[1,5,4,3,2,6,7]=>011100=>001110=>110001
[1,5,4,3,2,7,6]=>011101=>101110=>010001
[1,5,4,3,6,2,7]=>011010=>010110=>101001
[1,5,4,3,6,7,2]=>011001=>100110=>011001
[1,5,4,3,7,2,6]=>011010=>010110=>101001
[1,5,4,3,7,6,2]=>011011=>110110=>001001
[1,5,4,6,2,3,7]=>010100=>001010=>110101
[1,5,4,6,2,7,3]=>010101=>101010=>010101
[1,5,4,6,3,2,7]=>010110=>011010=>100101
[1,5,4,6,3,7,2]=>010101=>101010=>010101
[1,5,4,6,7,2,3]=>010010=>010010=>101101
[1,5,4,6,7,3,2]=>010011=>110010=>001101
[1,5,4,7,2,3,6]=>010100=>001010=>110101
[1,5,4,7,2,6,3]=>010101=>101010=>010101
[1,5,4,7,3,2,6]=>010110=>011010=>100101
[1,5,4,7,3,6,2]=>010101=>101010=>010101
[1,5,4,7,6,2,3]=>010110=>011010=>100101
[1,5,4,7,6,3,2]=>010111=>111010=>000101
[1,5,6,2,3,4,7]=>001000=>000100=>111011
[1,5,6,2,3,7,4]=>001001=>100100=>011011
[1,5,6,2,4,3,7]=>001010=>010100=>101011
[1,5,6,2,4,7,3]=>001001=>100100=>011011
[1,5,6,2,7,3,4]=>001010=>010100=>101011
[1,5,6,2,7,4,3]=>001011=>110100=>001011
[1,5,6,3,2,4,7]=>001100=>001100=>110011
[1,5,6,3,2,7,4]=>001101=>101100=>010011
[1,5,6,3,4,2,7]=>001010=>010100=>101011
[1,5,6,3,4,7,2]=>001001=>100100=>011011
[1,5,6,3,7,2,4]=>001010=>010100=>101011
[1,5,6,3,7,4,2]=>001011=>110100=>001011
[1,5,6,4,2,3,7]=>001100=>001100=>110011
[1,5,6,4,2,7,3]=>001101=>101100=>010011
[1,5,6,4,3,2,7]=>001110=>011100=>100011
[1,5,6,4,3,7,2]=>001101=>101100=>010011
[1,5,6,4,7,2,3]=>001010=>010100=>101011
[1,5,6,4,7,3,2]=>001011=>110100=>001011
[1,5,6,7,2,3,4]=>000100=>001000=>110111
[1,5,6,7,2,4,3]=>000101=>101000=>010111
[1,5,6,7,3,2,4]=>000110=>011000=>100111
[1,5,6,7,3,4,2]=>000101=>101000=>010111
[1,5,6,7,4,2,3]=>000110=>011000=>100111
[1,5,6,7,4,3,2]=>000111=>111000=>000111
[1,5,7,2,3,4,6]=>001000=>000100=>111011
[1,5,7,2,3,6,4]=>001001=>100100=>011011
[1,5,7,2,4,3,6]=>001010=>010100=>101011
[1,5,7,2,4,6,3]=>001001=>100100=>011011
[1,5,7,2,6,3,4]=>001010=>010100=>101011
[1,5,7,2,6,4,3]=>001011=>110100=>001011
[1,5,7,3,2,4,6]=>001100=>001100=>110011
[1,5,7,3,2,6,4]=>001101=>101100=>010011
[1,5,7,3,4,2,6]=>001010=>010100=>101011
[1,5,7,3,4,6,2]=>001001=>100100=>011011
[1,5,7,3,6,2,4]=>001010=>010100=>101011
[1,5,7,3,6,4,2]=>001011=>110100=>001011
[1,5,7,4,2,3,6]=>001100=>001100=>110011
[1,5,7,4,2,6,3]=>001101=>101100=>010011
[1,5,7,4,3,2,6]=>001110=>011100=>100011
[1,5,7,4,3,6,2]=>001101=>101100=>010011
[1,5,7,4,6,2,3]=>001010=>010100=>101011
[1,5,7,4,6,3,2]=>001011=>110100=>001011
[1,5,7,6,2,3,4]=>001100=>001100=>110011
[1,5,7,6,2,4,3]=>001101=>101100=>010011
[1,5,7,6,3,2,4]=>001110=>011100=>100011
[1,5,7,6,3,4,2]=>001101=>101100=>010011
[1,5,7,6,4,2,3]=>001110=>011100=>100011
[1,5,7,6,4,3,2]=>001111=>111100=>000011
[1,6,2,3,4,5,7]=>010000=>000010=>111101
[1,6,2,3,4,7,5]=>010001=>100010=>011101
[1,6,2,3,5,4,7]=>010010=>010010=>101101
[1,6,2,3,5,7,4]=>010001=>100010=>011101
[1,6,2,3,7,4,5]=>010010=>010010=>101101
[1,6,2,3,7,5,4]=>010011=>110010=>001101
[1,6,2,4,3,5,7]=>010100=>001010=>110101
[1,6,2,4,3,7,5]=>010101=>101010=>010101
[1,6,2,4,5,3,7]=>010010=>010010=>101101
[1,6,2,4,5,7,3]=>010001=>100010=>011101
[1,6,2,4,7,3,5]=>010010=>010010=>101101
[1,6,2,4,7,5,3]=>010011=>110010=>001101
[1,6,2,5,3,4,7]=>010100=>001010=>110101
[1,6,2,5,3,7,4]=>010101=>101010=>010101
[1,6,2,5,4,3,7]=>010110=>011010=>100101
[1,6,2,5,4,7,3]=>010101=>101010=>010101
[1,6,2,5,7,3,4]=>010010=>010010=>101101
[1,6,2,5,7,4,3]=>010011=>110010=>001101
[1,6,2,7,3,4,5]=>010100=>001010=>110101
[1,6,2,7,3,5,4]=>010101=>101010=>010101
[1,6,2,7,4,3,5]=>010110=>011010=>100101
[1,6,2,7,4,5,3]=>010101=>101010=>010101
[1,6,2,7,5,3,4]=>010110=>011010=>100101
[1,6,2,7,5,4,3]=>010111=>111010=>000101
[1,6,3,2,4,5,7]=>011000=>000110=>111001
[1,6,3,2,4,7,5]=>011001=>100110=>011001
[1,6,3,2,5,4,7]=>011010=>010110=>101001
[1,6,3,2,5,7,4]=>011001=>100110=>011001
[1,6,3,2,7,4,5]=>011010=>010110=>101001
[1,6,3,2,7,5,4]=>011011=>110110=>001001
[1,6,3,4,2,5,7]=>010100=>001010=>110101
[1,6,3,4,2,7,5]=>010101=>101010=>010101
[1,6,3,4,5,2,7]=>010010=>010010=>101101
[1,6,3,4,5,7,2]=>010001=>100010=>011101
[1,6,3,4,7,2,5]=>010010=>010010=>101101
[1,6,3,4,7,5,2]=>010011=>110010=>001101
[1,6,3,5,2,4,7]=>010100=>001010=>110101
[1,6,3,5,2,7,4]=>010101=>101010=>010101
[1,6,3,5,4,2,7]=>010110=>011010=>100101
[1,6,3,5,4,7,2]=>010101=>101010=>010101
[1,6,3,5,7,2,4]=>010010=>010010=>101101
[1,6,3,5,7,4,2]=>010011=>110010=>001101
[1,6,3,7,2,4,5]=>010100=>001010=>110101
[1,6,3,7,2,5,4]=>010101=>101010=>010101
[1,6,3,7,4,2,5]=>010110=>011010=>100101
[1,6,3,7,4,5,2]=>010101=>101010=>010101
[1,6,3,7,5,2,4]=>010110=>011010=>100101
[1,6,3,7,5,4,2]=>010111=>111010=>000101
[1,6,4,2,3,5,7]=>011000=>000110=>111001
[1,6,4,2,3,7,5]=>011001=>100110=>011001
[1,6,4,2,5,3,7]=>011010=>010110=>101001
[1,6,4,2,5,7,3]=>011001=>100110=>011001
[1,6,4,2,7,3,5]=>011010=>010110=>101001
[1,6,4,2,7,5,3]=>011011=>110110=>001001
[1,6,4,3,2,5,7]=>011100=>001110=>110001
[1,6,4,3,2,7,5]=>011101=>101110=>010001
[1,6,4,3,5,2,7]=>011010=>010110=>101001
[1,6,4,3,5,7,2]=>011001=>100110=>011001
[1,6,4,3,7,2,5]=>011010=>010110=>101001
[1,6,4,3,7,5,2]=>011011=>110110=>001001
[1,6,4,5,2,3,7]=>010100=>001010=>110101
[1,6,4,5,2,7,3]=>010101=>101010=>010101
[1,6,4,5,3,2,7]=>010110=>011010=>100101
[1,6,4,5,3,7,2]=>010101=>101010=>010101
[1,6,4,5,7,2,3]=>010010=>010010=>101101
[1,6,4,5,7,3,2]=>010011=>110010=>001101
[1,6,4,7,2,3,5]=>010100=>001010=>110101
[1,6,4,7,2,5,3]=>010101=>101010=>010101
[1,6,4,7,3,2,5]=>010110=>011010=>100101
[1,6,4,7,3,5,2]=>010101=>101010=>010101
[1,6,4,7,5,2,3]=>010110=>011010=>100101
[1,6,4,7,5,3,2]=>010111=>111010=>000101
[1,6,5,2,3,4,7]=>011000=>000110=>111001
[1,6,5,2,3,7,4]=>011001=>100110=>011001
[1,6,5,2,4,3,7]=>011010=>010110=>101001
[1,6,5,2,4,7,3]=>011001=>100110=>011001
[1,6,5,2,7,3,4]=>011010=>010110=>101001
[1,6,5,2,7,4,3]=>011011=>110110=>001001
[1,6,5,3,2,4,7]=>011100=>001110=>110001
[1,6,5,3,2,7,4]=>011101=>101110=>010001
[1,6,5,3,4,2,7]=>011010=>010110=>101001
[1,6,5,3,4,7,2]=>011001=>100110=>011001
[1,6,5,3,7,2,4]=>011010=>010110=>101001
[1,6,5,3,7,4,2]=>011011=>110110=>001001
[1,6,5,4,2,3,7]=>011100=>001110=>110001
[1,6,5,4,2,7,3]=>011101=>101110=>010001
[1,6,5,4,3,2,7]=>011110=>011110=>100001
[1,6,5,4,3,7,2]=>011101=>101110=>010001
[1,6,5,4,7,2,3]=>011010=>010110=>101001
[1,6,5,4,7,3,2]=>011011=>110110=>001001
[1,6,5,7,2,3,4]=>010100=>001010=>110101
[1,6,5,7,2,4,3]=>010101=>101010=>010101
[1,6,5,7,3,2,4]=>010110=>011010=>100101
[1,6,5,7,3,4,2]=>010101=>101010=>010101
[1,6,5,7,4,2,3]=>010110=>011010=>100101
[1,6,5,7,4,3,2]=>010111=>111010=>000101
[1,6,7,2,3,4,5]=>001000=>000100=>111011
[1,6,7,2,3,5,4]=>001001=>100100=>011011
[1,6,7,2,4,3,5]=>001010=>010100=>101011
[1,6,7,2,4,5,3]=>001001=>100100=>011011
[1,6,7,2,5,3,4]=>001010=>010100=>101011
[1,6,7,2,5,4,3]=>001011=>110100=>001011
[1,6,7,3,2,4,5]=>001100=>001100=>110011
[1,6,7,3,2,5,4]=>001101=>101100=>010011
[1,6,7,3,4,2,5]=>001010=>010100=>101011
[1,6,7,3,4,5,2]=>001001=>100100=>011011
[1,6,7,3,5,2,4]=>001010=>010100=>101011
[1,6,7,3,5,4,2]=>001011=>110100=>001011
[1,6,7,4,2,3,5]=>001100=>001100=>110011
[1,6,7,4,2,5,3]=>001101=>101100=>010011
[1,6,7,4,3,2,5]=>001110=>011100=>100011
[1,6,7,4,3,5,2]=>001101=>101100=>010011
[1,6,7,4,5,2,3]=>001010=>010100=>101011
[1,6,7,4,5,3,2]=>001011=>110100=>001011
[1,6,7,5,2,3,4]=>001100=>001100=>110011
[1,6,7,5,2,4,3]=>001101=>101100=>010011
[1,6,7,5,3,2,4]=>001110=>011100=>100011
[1,6,7,5,3,4,2]=>001101=>101100=>010011
[1,6,7,5,4,2,3]=>001110=>011100=>100011
[1,6,7,5,4,3,2]=>001111=>111100=>000011
[1,7,2,3,4,5,6]=>010000=>000010=>111101
[1,7,2,3,4,6,5]=>010001=>100010=>011101
[1,7,2,3,5,4,6]=>010010=>010010=>101101
[1,7,2,3,5,6,4]=>010001=>100010=>011101
[1,7,2,3,6,4,5]=>010010=>010010=>101101
[1,7,2,3,6,5,4]=>010011=>110010=>001101
[1,7,2,4,3,5,6]=>010100=>001010=>110101
[1,7,2,4,3,6,5]=>010101=>101010=>010101
[1,7,2,4,5,3,6]=>010010=>010010=>101101
[1,7,2,4,5,6,3]=>010001=>100010=>011101
[1,7,2,4,6,3,5]=>010010=>010010=>101101
[1,7,2,4,6,5,3]=>010011=>110010=>001101
[1,7,2,5,3,4,6]=>010100=>001010=>110101
[1,7,2,5,3,6,4]=>010101=>101010=>010101
[1,7,2,5,4,3,6]=>010110=>011010=>100101
[1,7,2,5,4,6,3]=>010101=>101010=>010101
[1,7,2,5,6,3,4]=>010010=>010010=>101101
[1,7,2,5,6,4,3]=>010011=>110010=>001101
[1,7,2,6,3,4,5]=>010100=>001010=>110101
[1,7,2,6,3,5,4]=>010101=>101010=>010101
[1,7,2,6,4,3,5]=>010110=>011010=>100101
[1,7,2,6,4,5,3]=>010101=>101010=>010101
[1,7,2,6,5,3,4]=>010110=>011010=>100101
[1,7,2,6,5,4,3]=>010111=>111010=>000101
[1,7,3,2,4,5,6]=>011000=>000110=>111001
[1,7,3,2,4,6,5]=>011001=>100110=>011001
[1,7,3,2,5,4,6]=>011010=>010110=>101001
[1,7,3,2,5,6,4]=>011001=>100110=>011001
[1,7,3,2,6,4,5]=>011010=>010110=>101001
[1,7,3,2,6,5,4]=>011011=>110110=>001001
[1,7,3,4,2,5,6]=>010100=>001010=>110101
[1,7,3,4,2,6,5]=>010101=>101010=>010101
[1,7,3,4,5,2,6]=>010010=>010010=>101101
[1,7,3,4,5,6,2]=>010001=>100010=>011101
[1,7,3,4,6,2,5]=>010010=>010010=>101101
[1,7,3,4,6,5,2]=>010011=>110010=>001101
[1,7,3,5,2,4,6]=>010100=>001010=>110101
[1,7,3,5,2,6,4]=>010101=>101010=>010101
[1,7,3,5,4,2,6]=>010110=>011010=>100101
[1,7,3,5,4,6,2]=>010101=>101010=>010101
[1,7,3,5,6,2,4]=>010010=>010010=>101101
[1,7,3,5,6,4,2]=>010011=>110010=>001101
[1,7,3,6,2,4,5]=>010100=>001010=>110101
[1,7,3,6,2,5,4]=>010101=>101010=>010101
[1,7,3,6,4,2,5]=>010110=>011010=>100101
[1,7,3,6,4,5,2]=>010101=>101010=>010101
[1,7,3,6,5,2,4]=>010110=>011010=>100101
[1,7,3,6,5,4,2]=>010111=>111010=>000101
[1,7,4,2,3,5,6]=>011000=>000110=>111001
[1,7,4,2,3,6,5]=>011001=>100110=>011001
[1,7,4,2,5,3,6]=>011010=>010110=>101001
[1,7,4,2,5,6,3]=>011001=>100110=>011001
[1,7,4,2,6,3,5]=>011010=>010110=>101001
[1,7,4,2,6,5,3]=>011011=>110110=>001001
[1,7,4,3,2,5,6]=>011100=>001110=>110001
[1,7,4,3,2,6,5]=>011101=>101110=>010001
[1,7,4,3,5,2,6]=>011010=>010110=>101001
[1,7,4,3,5,6,2]=>011001=>100110=>011001
[1,7,4,3,6,2,5]=>011010=>010110=>101001
[1,7,4,3,6,5,2]=>011011=>110110=>001001
[1,7,4,5,2,3,6]=>010100=>001010=>110101
[1,7,4,5,2,6,3]=>010101=>101010=>010101
[1,7,4,5,3,2,6]=>010110=>011010=>100101
[1,7,4,5,3,6,2]=>010101=>101010=>010101
[1,7,4,5,6,2,3]=>010010=>010010=>101101
[1,7,4,5,6,3,2]=>010011=>110010=>001101
[1,7,4,6,2,3,5]=>010100=>001010=>110101
[1,7,4,6,2,5,3]=>010101=>101010=>010101
[1,7,4,6,3,2,5]=>010110=>011010=>100101
[1,7,4,6,3,5,2]=>010101=>101010=>010101
[1,7,4,6,5,2,3]=>010110=>011010=>100101
[1,7,4,6,5,3,2]=>010111=>111010=>000101
[1,7,5,2,3,4,6]=>011000=>000110=>111001
[1,7,5,2,3,6,4]=>011001=>100110=>011001
[1,7,5,2,4,3,6]=>011010=>010110=>101001
[1,7,5,2,4,6,3]=>011001=>100110=>011001
[1,7,5,2,6,3,4]=>011010=>010110=>101001
[1,7,5,2,6,4,3]=>011011=>110110=>001001
[1,7,5,3,2,4,6]=>011100=>001110=>110001
[1,7,5,3,2,6,4]=>011101=>101110=>010001
[1,7,5,3,4,2,6]=>011010=>010110=>101001
[1,7,5,3,4,6,2]=>011001=>100110=>011001
[1,7,5,3,6,2,4]=>011010=>010110=>101001
[1,7,5,3,6,4,2]=>011011=>110110=>001001
[1,7,5,4,2,3,6]=>011100=>001110=>110001
[1,7,5,4,2,6,3]=>011101=>101110=>010001
[1,7,5,4,3,2,6]=>011110=>011110=>100001
[1,7,5,4,3,6,2]=>011101=>101110=>010001
[1,7,5,4,6,2,3]=>011010=>010110=>101001
[1,7,5,4,6,3,2]=>011011=>110110=>001001
[1,7,5,6,2,3,4]=>010100=>001010=>110101
[1,7,5,6,2,4,3]=>010101=>101010=>010101
[1,7,5,6,3,2,4]=>010110=>011010=>100101
[1,7,5,6,3,4,2]=>010101=>101010=>010101
[1,7,5,6,4,2,3]=>010110=>011010=>100101
[1,7,5,6,4,3,2]=>010111=>111010=>000101
[1,7,6,2,3,4,5]=>011000=>000110=>111001
[1,7,6,2,3,5,4]=>011001=>100110=>011001
[1,7,6,2,4,3,5]=>011010=>010110=>101001
[1,7,6,2,4,5,3]=>011001=>100110=>011001
[1,7,6,2,5,3,4]=>011010=>010110=>101001
[1,7,6,2,5,4,3]=>011011=>110110=>001001
[1,7,6,3,2,4,5]=>011100=>001110=>110001
[1,7,6,3,2,5,4]=>011101=>101110=>010001
[1,7,6,3,4,2,5]=>011010=>010110=>101001
[1,7,6,3,4,5,2]=>011001=>100110=>011001
[1,7,6,3,5,2,4]=>011010=>010110=>101001
[1,7,6,3,5,4,2]=>011011=>110110=>001001
[1,7,6,4,2,3,5]=>011100=>001110=>110001
[1,7,6,4,2,5,3]=>011101=>101110=>010001
[1,7,6,4,3,2,5]=>011110=>011110=>100001
[1,7,6,4,3,5,2]=>011101=>101110=>010001
[1,7,6,4,5,2,3]=>011010=>010110=>101001
[1,7,6,4,5,3,2]=>011011=>110110=>001001
[1,7,6,5,2,3,4]=>011100=>001110=>110001
[1,7,6,5,2,4,3]=>011101=>101110=>010001
[1,7,6,5,3,2,4]=>011110=>011110=>100001
[1,7,6,5,3,4,2]=>011101=>101110=>010001
[1,7,6,5,4,2,3]=>011110=>011110=>100001
[1,7,6,5,4,3,2]=>011111=>111110=>000001
[2,1,3,4,5,6,7]=>100000=>000001=>111110
[2,1,3,4,5,7,6]=>100001=>100001=>011110
[2,1,3,4,6,5,7]=>100010=>010001=>101110
[2,1,3,4,6,7,5]=>100001=>100001=>011110
[2,1,3,4,7,5,6]=>100010=>010001=>101110
[2,1,3,4,7,6,5]=>100011=>110001=>001110
[2,1,3,5,4,6,7]=>100100=>001001=>110110
[2,1,3,5,4,7,6]=>100101=>101001=>010110
[2,1,3,5,6,4,7]=>100010=>010001=>101110
[2,1,3,5,6,7,4]=>100001=>100001=>011110
[2,1,3,5,7,4,6]=>100010=>010001=>101110
[2,1,3,5,7,6,4]=>100011=>110001=>001110
[2,1,3,6,4,5,7]=>100100=>001001=>110110
[2,1,3,6,4,7,5]=>100101=>101001=>010110
[2,1,3,6,5,4,7]=>100110=>011001=>100110
[2,1,3,6,5,7,4]=>100101=>101001=>010110
[2,1,3,6,7,4,5]=>100010=>010001=>101110
[2,1,3,6,7,5,4]=>100011=>110001=>001110
[2,1,3,7,4,5,6]=>100100=>001001=>110110
[2,1,3,7,4,6,5]=>100101=>101001=>010110
[2,1,3,7,5,4,6]=>100110=>011001=>100110
[2,1,3,7,5,6,4]=>100101=>101001=>010110
[2,1,3,7,6,4,5]=>100110=>011001=>100110
[2,1,3,7,6,5,4]=>100111=>111001=>000110
[2,1,4,3,5,6,7]=>101000=>000101=>111010
[2,1,4,3,5,7,6]=>101001=>100101=>011010
[2,1,4,3,6,5,7]=>101010=>010101=>101010
[2,1,4,3,6,7,5]=>101001=>100101=>011010
[2,1,4,3,7,5,6]=>101010=>010101=>101010
[2,1,4,3,7,6,5]=>101011=>110101=>001010
[2,1,4,5,3,6,7]=>100100=>001001=>110110
[2,1,4,5,3,7,6]=>100101=>101001=>010110
[2,1,4,5,6,3,7]=>100010=>010001=>101110
[2,1,4,5,6,7,3]=>100001=>100001=>011110
[2,1,4,5,7,3,6]=>100010=>010001=>101110
[2,1,4,5,7,6,3]=>100011=>110001=>001110
[2,1,4,6,3,5,7]=>100100=>001001=>110110
[2,1,4,6,3,7,5]=>100101=>101001=>010110
[2,1,4,6,5,3,7]=>100110=>011001=>100110
[2,1,4,6,5,7,3]=>100101=>101001=>010110
[2,1,4,6,7,3,5]=>100010=>010001=>101110
[2,1,4,6,7,5,3]=>100011=>110001=>001110
[2,1,4,7,3,5,6]=>100100=>001001=>110110
[2,1,4,7,3,6,5]=>100101=>101001=>010110
[2,1,4,7,5,3,6]=>100110=>011001=>100110
[2,1,4,7,5,6,3]=>100101=>101001=>010110
[2,1,4,7,6,3,5]=>100110=>011001=>100110
[2,1,4,7,6,5,3]=>100111=>111001=>000110
[2,1,5,3,4,6,7]=>101000=>000101=>111010
[2,1,5,3,4,7,6]=>101001=>100101=>011010
[2,1,5,3,6,4,7]=>101010=>010101=>101010
[2,1,5,3,6,7,4]=>101001=>100101=>011010
[2,1,5,3,7,4,6]=>101010=>010101=>101010
[2,1,5,3,7,6,4]=>101011=>110101=>001010
[2,1,5,4,3,6,7]=>101100=>001101=>110010
[2,1,5,4,3,7,6]=>101101=>101101=>010010
[2,1,5,4,6,3,7]=>101010=>010101=>101010
[2,1,5,4,6,7,3]=>101001=>100101=>011010
[2,1,5,4,7,3,6]=>101010=>010101=>101010
[2,1,5,4,7,6,3]=>101011=>110101=>001010
[2,1,5,6,3,4,7]=>100100=>001001=>110110
[2,1,5,6,3,7,4]=>100101=>101001=>010110
[2,1,5,6,4,3,7]=>100110=>011001=>100110
[2,1,5,6,4,7,3]=>100101=>101001=>010110
[2,1,5,6,7,3,4]=>100010=>010001=>101110
[2,1,5,6,7,4,3]=>100011=>110001=>001110
[2,1,5,7,3,4,6]=>100100=>001001=>110110
[2,1,5,7,3,6,4]=>100101=>101001=>010110
[2,1,5,7,4,3,6]=>100110=>011001=>100110
[2,1,5,7,4,6,3]=>100101=>101001=>010110
[2,1,5,7,6,3,4]=>100110=>011001=>100110
[2,1,5,7,6,4,3]=>100111=>111001=>000110
[2,1,6,3,4,5,7]=>101000=>000101=>111010
[2,1,6,3,4,7,5]=>101001=>100101=>011010
[2,1,6,3,5,4,7]=>101010=>010101=>101010
[2,1,6,3,5,7,4]=>101001=>100101=>011010
[2,1,6,3,7,4,5]=>101010=>010101=>101010
[2,1,6,3,7,5,4]=>101011=>110101=>001010
[2,1,6,4,3,5,7]=>101100=>001101=>110010
[2,1,6,4,3,7,5]=>101101=>101101=>010010
[2,1,6,4,5,3,7]=>101010=>010101=>101010
[2,1,6,4,5,7,3]=>101001=>100101=>011010
[2,1,6,4,7,3,5]=>101010=>010101=>101010
[2,1,6,4,7,5,3]=>101011=>110101=>001010
[2,1,6,5,3,4,7]=>101100=>001101=>110010
[2,1,6,5,3,7,4]=>101101=>101101=>010010
[2,1,6,5,4,3,7]=>101110=>011101=>100010
[2,1,6,5,4,7,3]=>101101=>101101=>010010
[2,1,6,5,7,3,4]=>101010=>010101=>101010
[2,1,6,5,7,4,3]=>101011=>110101=>001010
[2,1,6,7,3,4,5]=>100100=>001001=>110110
[2,1,6,7,3,5,4]=>100101=>101001=>010110
[2,1,6,7,4,3,5]=>100110=>011001=>100110
[2,1,6,7,4,5,3]=>100101=>101001=>010110
[2,1,6,7,5,3,4]=>100110=>011001=>100110
[2,1,6,7,5,4,3]=>100111=>111001=>000110
[2,1,7,3,4,5,6]=>101000=>000101=>111010
[2,1,7,3,4,6,5]=>101001=>100101=>011010
[2,1,7,3,5,4,6]=>101010=>010101=>101010
[2,1,7,3,5,6,4]=>101001=>100101=>011010
[2,1,7,3,6,4,5]=>101010=>010101=>101010
[2,1,7,3,6,5,4]=>101011=>110101=>001010
[2,1,7,4,3,5,6]=>101100=>001101=>110010
[2,1,7,4,3,6,5]=>101101=>101101=>010010
[2,1,7,4,5,3,6]=>101010=>010101=>101010
[2,1,7,4,5,6,3]=>101001=>100101=>011010
[2,1,7,4,6,3,5]=>101010=>010101=>101010
[2,1,7,4,6,5,3]=>101011=>110101=>001010
[2,1,7,5,3,4,6]=>101100=>001101=>110010
[2,1,7,5,3,6,4]=>101101=>101101=>010010
[2,1,7,5,4,3,6]=>101110=>011101=>100010
[2,1,7,5,4,6,3]=>101101=>101101=>010010
[2,1,7,5,6,3,4]=>101010=>010101=>101010
[2,1,7,5,6,4,3]=>101011=>110101=>001010
[2,1,7,6,3,4,5]=>101100=>001101=>110010
[2,1,7,6,3,5,4]=>101101=>101101=>010010
[2,1,7,6,4,3,5]=>101110=>011101=>100010
[2,1,7,6,4,5,3]=>101101=>101101=>010010
[2,1,7,6,5,3,4]=>101110=>011101=>100010
[2,1,7,6,5,4,3]=>101111=>111101=>000010
[2,3,1,4,5,6,7]=>010000=>000010=>111101
[2,3,1,4,5,7,6]=>010001=>100010=>011101
[2,3,1,4,6,5,7]=>010010=>010010=>101101
[2,3,1,4,6,7,5]=>010001=>100010=>011101
[2,3,1,4,7,5,6]=>010010=>010010=>101101
[2,3,1,4,7,6,5]=>010011=>110010=>001101
[2,3,1,5,4,6,7]=>010100=>001010=>110101
[2,3,1,5,4,7,6]=>010101=>101010=>010101
[2,3,1,5,6,4,7]=>010010=>010010=>101101
[2,3,1,5,6,7,4]=>010001=>100010=>011101
[2,3,1,5,7,4,6]=>010010=>010010=>101101
[2,3,1,5,7,6,4]=>010011=>110010=>001101
[2,3,1,6,4,5,7]=>010100=>001010=>110101
[2,3,1,6,4,7,5]=>010101=>101010=>010101
[2,3,1,6,5,4,7]=>010110=>011010=>100101
[2,3,1,6,5,7,4]=>010101=>101010=>010101
[2,3,1,6,7,4,5]=>010010=>010010=>101101
[2,3,1,6,7,5,4]=>010011=>110010=>001101
[2,3,1,7,4,5,6]=>010100=>001010=>110101
[2,3,1,7,4,6,5]=>010101=>101010=>010101
[2,3,1,7,5,4,6]=>010110=>011010=>100101
[2,3,1,7,5,6,4]=>010101=>101010=>010101
[2,3,1,7,6,4,5]=>010110=>011010=>100101
[2,3,1,7,6,5,4]=>010111=>111010=>000101
[2,3,4,1,5,6,7]=>001000=>000100=>111011
[2,3,4,1,5,7,6]=>001001=>100100=>011011
[2,3,4,1,6,5,7]=>001010=>010100=>101011
[2,3,4,1,6,7,5]=>001001=>100100=>011011
[2,3,4,1,7,5,6]=>001010=>010100=>101011
[2,3,4,1,7,6,5]=>001011=>110100=>001011
[2,3,4,5,1,6,7]=>000100=>001000=>110111
[2,3,4,5,1,7,6]=>000101=>101000=>010111
[2,3,4,5,6,1,7]=>000010=>010000=>101111
[2,3,4,5,6,7,1]=>000001=>100000=>011111
[2,3,4,5,7,1,6]=>000010=>010000=>101111
[2,3,4,5,7,6,1]=>000011=>110000=>001111
[2,3,4,6,1,5,7]=>000100=>001000=>110111
[2,3,4,6,1,7,5]=>000101=>101000=>010111
[2,3,4,6,5,1,7]=>000110=>011000=>100111
[2,3,4,6,5,7,1]=>000101=>101000=>010111
[2,3,4,6,7,1,5]=>000010=>010000=>101111
[2,3,4,6,7,5,1]=>000011=>110000=>001111
[2,3,4,7,1,5,6]=>000100=>001000=>110111
[2,3,4,7,1,6,5]=>000101=>101000=>010111
[2,3,4,7,5,1,6]=>000110=>011000=>100111
[2,3,4,7,5,6,1]=>000101=>101000=>010111
[2,3,4,7,6,1,5]=>000110=>011000=>100111
[2,3,4,7,6,5,1]=>000111=>111000=>000111
[2,3,5,1,4,6,7]=>001000=>000100=>111011
[2,3,5,1,4,7,6]=>001001=>100100=>011011
[2,3,5,1,6,4,7]=>001010=>010100=>101011
[2,3,5,1,6,7,4]=>001001=>100100=>011011
[2,3,5,1,7,4,6]=>001010=>010100=>101011
[2,3,5,1,7,6,4]=>001011=>110100=>001011
[2,3,5,4,1,6,7]=>001100=>001100=>110011
[2,3,5,4,1,7,6]=>001101=>101100=>010011
[2,3,5,4,6,1,7]=>001010=>010100=>101011
[2,3,5,4,6,7,1]=>001001=>100100=>011011
[2,3,5,4,7,1,6]=>001010=>010100=>101011
[2,3,5,4,7,6,1]=>001011=>110100=>001011
[2,3,5,6,1,4,7]=>000100=>001000=>110111
[2,3,5,6,1,7,4]=>000101=>101000=>010111
[2,3,5,6,4,1,7]=>000110=>011000=>100111
[2,3,5,6,4,7,1]=>000101=>101000=>010111
[2,3,5,6,7,1,4]=>000010=>010000=>101111
[2,3,5,6,7,4,1]=>000011=>110000=>001111
[2,3,5,7,1,4,6]=>000100=>001000=>110111
[2,3,5,7,1,6,4]=>000101=>101000=>010111
[2,3,5,7,4,1,6]=>000110=>011000=>100111
[2,3,5,7,4,6,1]=>000101=>101000=>010111
[2,3,5,7,6,1,4]=>000110=>011000=>100111
[2,3,5,7,6,4,1]=>000111=>111000=>000111
[2,3,6,1,4,5,7]=>001000=>000100=>111011
[2,3,6,1,4,7,5]=>001001=>100100=>011011
[2,3,6,1,5,4,7]=>001010=>010100=>101011
[2,3,6,1,5,7,4]=>001001=>100100=>011011
[2,3,6,1,7,4,5]=>001010=>010100=>101011
[2,3,6,1,7,5,4]=>001011=>110100=>001011
[2,3,6,4,1,5,7]=>001100=>001100=>110011
[2,3,6,4,1,7,5]=>001101=>101100=>010011
[2,3,6,4,5,1,7]=>001010=>010100=>101011
[2,3,6,4,5,7,1]=>001001=>100100=>011011
[2,3,6,4,7,1,5]=>001010=>010100=>101011
[2,3,6,4,7,5,1]=>001011=>110100=>001011
[2,3,6,5,1,4,7]=>001100=>001100=>110011
[2,3,6,5,1,7,4]=>001101=>101100=>010011
[2,3,6,5,4,1,7]=>001110=>011100=>100011
[2,3,6,5,4,7,1]=>001101=>101100=>010011
[2,3,6,5,7,1,4]=>001010=>010100=>101011
[2,3,6,5,7,4,1]=>001011=>110100=>001011
[2,3,6,7,1,4,5]=>000100=>001000=>110111
[2,3,6,7,1,5,4]=>000101=>101000=>010111
[2,3,6,7,4,1,5]=>000110=>011000=>100111
[2,3,6,7,4,5,1]=>000101=>101000=>010111
[2,3,6,7,5,1,4]=>000110=>011000=>100111
[2,3,6,7,5,4,1]=>000111=>111000=>000111
[2,3,7,1,4,5,6]=>001000=>000100=>111011
[2,3,7,1,4,6,5]=>001001=>100100=>011011
[2,3,7,1,5,4,6]=>001010=>010100=>101011
[2,3,7,1,5,6,4]=>001001=>100100=>011011
[2,3,7,1,6,4,5]=>001010=>010100=>101011
[2,3,7,1,6,5,4]=>001011=>110100=>001011
[2,3,7,4,1,5,6]=>001100=>001100=>110011
[2,3,7,4,1,6,5]=>001101=>101100=>010011
[2,3,7,4,5,1,6]=>001010=>010100=>101011
[2,3,7,4,5,6,1]=>001001=>100100=>011011
[2,3,7,4,6,1,5]=>001010=>010100=>101011
[2,3,7,4,6,5,1]=>001011=>110100=>001011
[2,3,7,5,1,4,6]=>001100=>001100=>110011
[2,3,7,5,1,6,4]=>001101=>101100=>010011
[2,3,7,5,4,1,6]=>001110=>011100=>100011
[2,3,7,5,4,6,1]=>001101=>101100=>010011
[2,3,7,5,6,1,4]=>001010=>010100=>101011
[2,3,7,5,6,4,1]=>001011=>110100=>001011
[2,3,7,6,1,4,5]=>001100=>001100=>110011
[2,3,7,6,1,5,4]=>001101=>101100=>010011
[2,3,7,6,4,1,5]=>001110=>011100=>100011
[2,3,7,6,4,5,1]=>001101=>101100=>010011
[2,3,7,6,5,1,4]=>001110=>011100=>100011
[2,3,7,6,5,4,1]=>001111=>111100=>000011
[2,4,1,3,5,6,7]=>010000=>000010=>111101
[2,4,1,3,5,7,6]=>010001=>100010=>011101
[2,4,1,3,6,5,7]=>010010=>010010=>101101
[2,4,1,3,6,7,5]=>010001=>100010=>011101
[2,4,1,3,7,5,6]=>010010=>010010=>101101
[2,4,1,3,7,6,5]=>010011=>110010=>001101
[2,4,1,5,3,6,7]=>010100=>001010=>110101
[2,4,1,5,3,7,6]=>010101=>101010=>010101
[2,4,1,5,6,3,7]=>010010=>010010=>101101
[2,4,1,5,6,7,3]=>010001=>100010=>011101
[2,4,1,5,7,3,6]=>010010=>010010=>101101
[2,4,1,5,7,6,3]=>010011=>110010=>001101
[2,4,1,6,3,5,7]=>010100=>001010=>110101
[2,4,1,6,3,7,5]=>010101=>101010=>010101
[2,4,1,6,5,3,7]=>010110=>011010=>100101
[2,4,1,6,5,7,3]=>010101=>101010=>010101
[2,4,1,6,7,3,5]=>010010=>010010=>101101
[2,4,1,6,7,5,3]=>010011=>110010=>001101
[2,4,1,7,3,5,6]=>010100=>001010=>110101
[2,4,1,7,3,6,5]=>010101=>101010=>010101
[2,4,1,7,5,3,6]=>010110=>011010=>100101
[2,4,1,7,5,6,3]=>010101=>101010=>010101
[2,4,1,7,6,3,5]=>010110=>011010=>100101
[2,4,1,7,6,5,3]=>010111=>111010=>000101
[2,4,3,1,5,6,7]=>011000=>000110=>111001
[2,4,3,1,5,7,6]=>011001=>100110=>011001
[2,4,3,1,6,5,7]=>011010=>010110=>101001
[2,4,3,1,6,7,5]=>011001=>100110=>011001
[2,4,3,1,7,5,6]=>011010=>010110=>101001
[2,4,3,1,7,6,5]=>011011=>110110=>001001
[2,4,3,5,1,6,7]=>010100=>001010=>110101
[2,4,3,5,1,7,6]=>010101=>101010=>010101
[2,4,3,5,6,1,7]=>010010=>010010=>101101
[2,4,3,5,6,7,1]=>010001=>100010=>011101
[2,4,3,5,7,1,6]=>010010=>010010=>101101
[2,4,3,5,7,6,1]=>010011=>110010=>001101
[2,4,3,6,1,5,7]=>010100=>001010=>110101
[2,4,3,6,1,7,5]=>010101=>101010=>010101
[2,4,3,6,5,1,7]=>010110=>011010=>100101
[2,4,3,6,5,7,1]=>010101=>101010=>010101
[2,4,3,6,7,1,5]=>010010=>010010=>101101
[2,4,3,6,7,5,1]=>010011=>110010=>001101
[2,4,3,7,1,5,6]=>010100=>001010=>110101
[2,4,3,7,1,6,5]=>010101=>101010=>010101
[2,4,3,7,5,1,6]=>010110=>011010=>100101
[2,4,3,7,5,6,1]=>010101=>101010=>010101
[2,4,3,7,6,1,5]=>010110=>011010=>100101
[2,4,3,7,6,5,1]=>010111=>111010=>000101
[2,4,5,1,3,6,7]=>001000=>000100=>111011
[2,4,5,1,3,7,6]=>001001=>100100=>011011
[2,4,5,1,6,3,7]=>001010=>010100=>101011
[2,4,5,1,6,7,3]=>001001=>100100=>011011
[2,4,5,1,7,3,6]=>001010=>010100=>101011
[2,4,5,1,7,6,3]=>001011=>110100=>001011
[2,4,5,3,1,6,7]=>001100=>001100=>110011
[2,4,5,3,1,7,6]=>001101=>101100=>010011
[2,4,5,3,6,1,7]=>001010=>010100=>101011
[2,4,5,3,6,7,1]=>001001=>100100=>011011
[2,4,5,3,7,1,6]=>001010=>010100=>101011
[2,4,5,3,7,6,1]=>001011=>110100=>001011
[2,4,5,6,1,3,7]=>000100=>001000=>110111
[2,4,5,6,1,7,3]=>000101=>101000=>010111
[2,4,5,6,3,1,7]=>000110=>011000=>100111
[2,4,5,6,3,7,1]=>000101=>101000=>010111
[2,4,5,6,7,1,3]=>000010=>010000=>101111
[2,4,5,6,7,3,1]=>000011=>110000=>001111
[2,4,5,7,1,3,6]=>000100=>001000=>110111
[2,4,5,7,1,6,3]=>000101=>101000=>010111
[2,4,5,7,3,1,6]=>000110=>011000=>100111
[2,4,5,7,3,6,1]=>000101=>101000=>010111
[2,4,5,7,6,1,3]=>000110=>011000=>100111
[2,4,5,7,6,3,1]=>000111=>111000=>000111
[2,4,6,1,3,5,7]=>001000=>000100=>111011
[2,4,6,1,3,7,5]=>001001=>100100=>011011
[2,4,6,1,5,3,7]=>001010=>010100=>101011
[2,4,6,1,5,7,3]=>001001=>100100=>011011
[2,4,6,1,7,3,5]=>001010=>010100=>101011
[2,4,6,1,7,5,3]=>001011=>110100=>001011
[2,4,6,3,1,5,7]=>001100=>001100=>110011
[2,4,6,3,1,7,5]=>001101=>101100=>010011
[2,4,6,3,5,1,7]=>001010=>010100=>101011
[2,4,6,3,5,7,1]=>001001=>100100=>011011
[2,4,6,3,7,1,5]=>001010=>010100=>101011
[2,4,6,3,7,5,1]=>001011=>110100=>001011
[2,4,6,5,1,3,7]=>001100=>001100=>110011
[2,4,6,5,1,7,3]=>001101=>101100=>010011
[2,4,6,5,3,1,7]=>001110=>011100=>100011
[2,4,6,5,3,7,1]=>001101=>101100=>010011
[2,4,6,5,7,1,3]=>001010=>010100=>101011
[2,4,6,5,7,3,1]=>001011=>110100=>001011
[2,4,6,7,1,3,5]=>000100=>001000=>110111
[2,4,6,7,1,5,3]=>000101=>101000=>010111
[2,4,6,7,3,1,5]=>000110=>011000=>100111
[2,4,6,7,3,5,1]=>000101=>101000=>010111
[2,4,6,7,5,1,3]=>000110=>011000=>100111
[2,4,6,7,5,3,1]=>000111=>111000=>000111
[2,4,7,1,3,5,6]=>001000=>000100=>111011
[2,4,7,1,3,6,5]=>001001=>100100=>011011
[2,4,7,1,5,3,6]=>001010=>010100=>101011
[2,4,7,1,5,6,3]=>001001=>100100=>011011
[2,4,7,1,6,3,5]=>001010=>010100=>101011
[2,4,7,1,6,5,3]=>001011=>110100=>001011
[2,4,7,3,1,5,6]=>001100=>001100=>110011
[2,4,7,3,1,6,5]=>001101=>101100=>010011
[2,4,7,3,5,1,6]=>001010=>010100=>101011
[2,4,7,3,5,6,1]=>001001=>100100=>011011
[2,4,7,3,6,1,5]=>001010=>010100=>101011
[2,4,7,3,6,5,1]=>001011=>110100=>001011
[2,4,7,5,1,3,6]=>001100=>001100=>110011
[2,4,7,5,1,6,3]=>001101=>101100=>010011
[2,4,7,5,3,1,6]=>001110=>011100=>100011
[2,4,7,5,3,6,1]=>001101=>101100=>010011
[2,4,7,5,6,1,3]=>001010=>010100=>101011
[2,4,7,5,6,3,1]=>001011=>110100=>001011
[2,4,7,6,1,3,5]=>001100=>001100=>110011
[2,4,7,6,1,5,3]=>001101=>101100=>010011
[2,4,7,6,3,1,5]=>001110=>011100=>100011
[2,4,7,6,3,5,1]=>001101=>101100=>010011
[2,4,7,6,5,1,3]=>001110=>011100=>100011
[2,4,7,6,5,3,1]=>001111=>111100=>000011
[2,5,1,3,4,6,7]=>010000=>000010=>111101
[2,5,1,3,4,7,6]=>010001=>100010=>011101
[2,5,1,3,6,4,7]=>010010=>010010=>101101
[2,5,1,3,6,7,4]=>010001=>100010=>011101
[2,5,1,3,7,4,6]=>010010=>010010=>101101
[2,5,1,3,7,6,4]=>010011=>110010=>001101
[2,5,1,4,3,6,7]=>010100=>001010=>110101
[2,5,1,4,3,7,6]=>010101=>101010=>010101
[2,5,1,4,6,3,7]=>010010=>010010=>101101
[2,5,1,4,6,7,3]=>010001=>100010=>011101
[2,5,1,4,7,3,6]=>010010=>010010=>101101
[2,5,1,4,7,6,3]=>010011=>110010=>001101
[2,5,1,6,3,4,7]=>010100=>001010=>110101
[2,5,1,6,3,7,4]=>010101=>101010=>010101
[2,5,1,6,4,3,7]=>010110=>011010=>100101
[2,5,1,6,4,7,3]=>010101=>101010=>010101
[2,5,1,6,7,3,4]=>010010=>010010=>101101
[2,5,1,6,7,4,3]=>010011=>110010=>001101
[2,5,1,7,3,4,6]=>010100=>001010=>110101
[2,5,1,7,3,6,4]=>010101=>101010=>010101
[2,5,1,7,4,3,6]=>010110=>011010=>100101
[2,5,1,7,4,6,3]=>010101=>101010=>010101
[2,5,1,7,6,3,4]=>010110=>011010=>100101
[2,5,1,7,6,4,3]=>010111=>111010=>000101
[2,5,3,1,4,6,7]=>011000=>000110=>111001
[2,5,3,1,4,7,6]=>011001=>100110=>011001
[2,5,3,1,6,4,7]=>011010=>010110=>101001
[2,5,3,1,6,7,4]=>011001=>100110=>011001
[2,5,3,1,7,4,6]=>011010=>010110=>101001
[2,5,3,1,7,6,4]=>011011=>110110=>001001
[2,5,3,4,1,6,7]=>010100=>001010=>110101
[2,5,3,4,1,7,6]=>010101=>101010=>010101
[2,5,3,4,6,1,7]=>010010=>010010=>101101
[2,5,3,4,6,7,1]=>010001=>100010=>011101
[2,5,3,4,7,1,6]=>010010=>010010=>101101
[2,5,3,4,7,6,1]=>010011=>110010=>001101
[2,5,3,6,1,4,7]=>010100=>001010=>110101
[2,5,3,6,1,7,4]=>010101=>101010=>010101
[2,5,3,6,4,1,7]=>010110=>011010=>100101
[2,5,3,6,4,7,1]=>010101=>101010=>010101
[2,5,3,6,7,1,4]=>010010=>010010=>101101
[2,5,3,6,7,4,1]=>010011=>110010=>001101
[2,5,3,7,1,4,6]=>010100=>001010=>110101
[2,5,3,7,1,6,4]=>010101=>101010=>010101
[2,5,3,7,4,1,6]=>010110=>011010=>100101
[2,5,3,7,4,6,1]=>010101=>101010=>010101
[2,5,3,7,6,1,4]=>010110=>011010=>100101
[2,5,3,7,6,4,1]=>010111=>111010=>000101
[2,5,4,1,3,6,7]=>011000=>000110=>111001
[2,5,4,1,3,7,6]=>011001=>100110=>011001
[2,5,4,1,6,3,7]=>011010=>010110=>101001
[2,5,4,1,6,7,3]=>011001=>100110=>011001
[2,5,4,1,7,3,6]=>011010=>010110=>101001
[2,5,4,1,7,6,3]=>011011=>110110=>001001
[2,5,4,3,1,6,7]=>011100=>001110=>110001
[2,5,4,3,1,7,6]=>011101=>101110=>010001
[2,5,4,3,6,1,7]=>011010=>010110=>101001
[2,5,4,3,6,7,1]=>011001=>100110=>011001
[2,5,4,3,7,1,6]=>011010=>010110=>101001
[2,5,4,3,7,6,1]=>011011=>110110=>001001
[2,5,4,6,1,3,7]=>010100=>001010=>110101
[2,5,4,6,1,7,3]=>010101=>101010=>010101
[2,5,4,6,3,1,7]=>010110=>011010=>100101
[2,5,4,6,3,7,1]=>010101=>101010=>010101
[2,5,4,6,7,1,3]=>010010=>010010=>101101
[2,5,4,6,7,3,1]=>010011=>110010=>001101
[2,5,4,7,1,3,6]=>010100=>001010=>110101
[2,5,4,7,1,6,3]=>010101=>101010=>010101
[2,5,4,7,3,1,6]=>010110=>011010=>100101
[2,5,4,7,3,6,1]=>010101=>101010=>010101
[2,5,4,7,6,1,3]=>010110=>011010=>100101
[2,5,4,7,6,3,1]=>010111=>111010=>000101
[2,5,6,1,3,4,7]=>001000=>000100=>111011
[2,5,6,1,3,7,4]=>001001=>100100=>011011
[2,5,6,1,4,3,7]=>001010=>010100=>101011
[2,5,6,1,4,7,3]=>001001=>100100=>011011
[2,5,6,1,7,3,4]=>001010=>010100=>101011
[2,5,6,1,7,4,3]=>001011=>110100=>001011
[2,5,6,3,1,4,7]=>001100=>001100=>110011
[2,5,6,3,1,7,4]=>001101=>101100=>010011
[2,5,6,3,4,1,7]=>001010=>010100=>101011
[2,5,6,3,4,7,1]=>001001=>100100=>011011
[2,5,6,3,7,1,4]=>001010=>010100=>101011
[2,5,6,3,7,4,1]=>001011=>110100=>001011
[2,5,6,4,1,3,7]=>001100=>001100=>110011
[2,5,6,4,1,7,3]=>001101=>101100=>010011
[2,5,6,4,3,1,7]=>001110=>011100=>100011
[2,5,6,4,3,7,1]=>001101=>101100=>010011
[2,5,6,4,7,1,3]=>001010=>010100=>101011
[2,5,6,4,7,3,1]=>001011=>110100=>001011
[2,5,6,7,1,3,4]=>000100=>001000=>110111
[2,5,6,7,1,4,3]=>000101=>101000=>010111
[2,5,6,7,3,1,4]=>000110=>011000=>100111
[2,5,6,7,3,4,1]=>000101=>101000=>010111
[2,5,6,7,4,1,3]=>000110=>011000=>100111
[2,5,6,7,4,3,1]=>000111=>111000=>000111
[2,5,7,1,3,4,6]=>001000=>000100=>111011
[2,5,7,1,3,6,4]=>001001=>100100=>011011
[2,5,7,1,4,3,6]=>001010=>010100=>101011
[2,5,7,1,4,6,3]=>001001=>100100=>011011
[2,5,7,1,6,3,4]=>001010=>010100=>101011
[2,5,7,1,6,4,3]=>001011=>110100=>001011
[2,5,7,3,1,4,6]=>001100=>001100=>110011
[2,5,7,3,1,6,4]=>001101=>101100=>010011
[2,5,7,3,4,1,6]=>001010=>010100=>101011
[2,5,7,3,4,6,1]=>001001=>100100=>011011
[2,5,7,3,6,1,4]=>001010=>010100=>101011
[2,5,7,3,6,4,1]=>001011=>110100=>001011
[2,5,7,4,1,3,6]=>001100=>001100=>110011
[2,5,7,4,1,6,3]=>001101=>101100=>010011
[2,5,7,4,3,1,6]=>001110=>011100=>100011
[2,5,7,4,3,6,1]=>001101=>101100=>010011
[2,5,7,4,6,1,3]=>001010=>010100=>101011
[2,5,7,4,6,3,1]=>001011=>110100=>001011
[2,5,7,6,1,3,4]=>001100=>001100=>110011
[2,5,7,6,1,4,3]=>001101=>101100=>010011
[2,5,7,6,3,1,4]=>001110=>011100=>100011
[2,5,7,6,3,4,1]=>001101=>101100=>010011
[2,5,7,6,4,1,3]=>001110=>011100=>100011
[2,5,7,6,4,3,1]=>001111=>111100=>000011
[2,6,1,3,4,5,7]=>010000=>000010=>111101
[2,6,1,3,4,7,5]=>010001=>100010=>011101
[2,6,1,3,5,4,7]=>010010=>010010=>101101
[2,6,1,3,5,7,4]=>010001=>100010=>011101
[2,6,1,3,7,4,5]=>010010=>010010=>101101
[2,6,1,3,7,5,4]=>010011=>110010=>001101
[2,6,1,4,3,5,7]=>010100=>001010=>110101
[2,6,1,4,3,7,5]=>010101=>101010=>010101
[2,6,1,4,5,3,7]=>010010=>010010=>101101
[2,6,1,4,5,7,3]=>010001=>100010=>011101
[2,6,1,4,7,3,5]=>010010=>010010=>101101
[2,6,1,4,7,5,3]=>010011=>110010=>001101
[2,6,1,5,3,4,7]=>010100=>001010=>110101
[2,6,1,5,3,7,4]=>010101=>101010=>010101
[2,6,1,5,4,3,7]=>010110=>011010=>100101
[2,6,1,5,4,7,3]=>010101=>101010=>010101
[2,6,1,5,7,3,4]=>010010=>010010=>101101
[2,6,1,5,7,4,3]=>010011=>110010=>001101
[2,6,1,7,3,4,5]=>010100=>001010=>110101
[2,6,1,7,3,5,4]=>010101=>101010=>010101
[2,6,1,7,4,3,5]=>010110=>011010=>100101
[2,6,1,7,4,5,3]=>010101=>101010=>010101
[2,6,1,7,5,3,4]=>010110=>011010=>100101
[2,6,1,7,5,4,3]=>010111=>111010=>000101
[2,6,3,1,4,5,7]=>011000=>000110=>111001
[2,6,3,1,4,7,5]=>011001=>100110=>011001
[2,6,3,1,5,4,7]=>011010=>010110=>101001
[2,6,3,1,5,7,4]=>011001=>100110=>011001
[2,6,3,1,7,4,5]=>011010=>010110=>101001
[2,6,3,1,7,5,4]=>011011=>110110=>001001
[2,6,3,4,1,5,7]=>010100=>001010=>110101
[2,6,3,4,1,7,5]=>010101=>101010=>010101
[2,6,3,4,5,1,7]=>010010=>010010=>101101
[2,6,3,4,5,7,1]=>010001=>100010=>011101
[2,6,3,4,7,1,5]=>010010=>010010=>101101
[2,6,3,4,7,5,1]=>010011=>110010=>001101
[2,6,3,5,1,4,7]=>010100=>001010=>110101
[2,6,3,5,1,7,4]=>010101=>101010=>010101
[2,6,3,5,4,1,7]=>010110=>011010=>100101
[2,6,3,5,4,7,1]=>010101=>101010=>010101
[2,6,3,5,7,1,4]=>010010=>010010=>101101
[2,6,3,5,7,4,1]=>010011=>110010=>001101
[2,6,3,7,1,4,5]=>010100=>001010=>110101
[2,6,3,7,1,5,4]=>010101=>101010=>010101
[2,6,3,7,4,1,5]=>010110=>011010=>100101
[2,6,3,7,4,5,1]=>010101=>101010=>010101
[2,6,3,7,5,1,4]=>010110=>011010=>100101
[2,6,3,7,5,4,1]=>010111=>111010=>000101
[2,6,4,1,3,5,7]=>011000=>000110=>111001
[2,6,4,1,3,7,5]=>011001=>100110=>011001
[2,6,4,1,5,3,7]=>011010=>010110=>101001
[2,6,4,1,5,7,3]=>011001=>100110=>011001
[2,6,4,1,7,3,5]=>011010=>010110=>101001
[2,6,4,1,7,5,3]=>011011=>110110=>001001
[2,6,4,3,1,5,7]=>011100=>001110=>110001
[2,6,4,3,1,7,5]=>011101=>101110=>010001
[2,6,4,3,5,1,7]=>011010=>010110=>101001
[2,6,4,3,5,7,1]=>011001=>100110=>011001
[2,6,4,3,7,1,5]=>011010=>010110=>101001
[2,6,4,3,7,5,1]=>011011=>110110=>001001
[2,6,4,5,1,3,7]=>010100=>001010=>110101
[2,6,4,5,1,7,3]=>010101=>101010=>010101
[2,6,4,5,3,1,7]=>010110=>011010=>100101
[2,6,4,5,3,7,1]=>010101=>101010=>010101
[2,6,4,5,7,1,3]=>010010=>010010=>101101
[2,6,4,5,7,3,1]=>010011=>110010=>001101
[2,6,4,7,1,3,5]=>010100=>001010=>110101
[2,6,4,7,1,5,3]=>010101=>101010=>010101
[2,6,4,7,3,1,5]=>010110=>011010=>100101
[2,6,4,7,3,5,1]=>010101=>101010=>010101
[2,6,4,7,5,1,3]=>010110=>011010=>100101
[2,6,4,7,5,3,1]=>010111=>111010=>000101
[2,6,5,1,3,4,7]=>011000=>000110=>111001
[2,6,5,1,3,7,4]=>011001=>100110=>011001
[2,6,5,1,4,3,7]=>011010=>010110=>101001
[2,6,5,1,4,7,3]=>011001=>100110=>011001
[2,6,5,1,7,3,4]=>011010=>010110=>101001
[2,6,5,1,7,4,3]=>011011=>110110=>001001
[2,6,5,3,1,4,7]=>011100=>001110=>110001
[2,6,5,3,1,7,4]=>011101=>101110=>010001
[2,6,5,3,4,1,7]=>011010=>010110=>101001
[2,6,5,3,4,7,1]=>011001=>100110=>011001
[2,6,5,3,7,1,4]=>011010=>010110=>101001
[2,6,5,3,7,4,1]=>011011=>110110=>001001
[2,6,5,4,1,3,7]=>011100=>001110=>110001
[2,6,5,4,1,7,3]=>011101=>101110=>010001
[2,6,5,4,3,1,7]=>011110=>011110=>100001
[2,6,5,4,3,7,1]=>011101=>101110=>010001
[2,6,5,4,7,1,3]=>011010=>010110=>101001
[2,6,5,4,7,3,1]=>011011=>110110=>001001
[2,6,5,7,1,3,4]=>010100=>001010=>110101
[2,6,5,7,1,4,3]=>010101=>101010=>010101
[2,6,5,7,3,1,4]=>010110=>011010=>100101
[2,6,5,7,3,4,1]=>010101=>101010=>010101
[2,6,5,7,4,1,3]=>010110=>011010=>100101
[2,6,5,7,4,3,1]=>010111=>111010=>000101
[2,6,7,1,3,4,5]=>001000=>000100=>111011
[2,6,7,1,3,5,4]=>001001=>100100=>011011
[2,6,7,1,4,3,5]=>001010=>010100=>101011
[2,6,7,1,4,5,3]=>001001=>100100=>011011
[2,6,7,1,5,3,4]=>001010=>010100=>101011
[2,6,7,1,5,4,3]=>001011=>110100=>001011
[2,6,7,3,1,4,5]=>001100=>001100=>110011
[2,6,7,3,1,5,4]=>001101=>101100=>010011
[2,6,7,3,4,1,5]=>001010=>010100=>101011
[2,6,7,3,4,5,1]=>001001=>100100=>011011
[2,6,7,3,5,1,4]=>001010=>010100=>101011
[2,6,7,3,5,4,1]=>001011=>110100=>001011
[2,6,7,4,1,3,5]=>001100=>001100=>110011
[2,6,7,4,1,5,3]=>001101=>101100=>010011
[2,6,7,4,3,1,5]=>001110=>011100=>100011
[2,6,7,4,3,5,1]=>001101=>101100=>010011
[2,6,7,4,5,1,3]=>001010=>010100=>101011
[2,6,7,4,5,3,1]=>001011=>110100=>001011
[2,6,7,5,1,3,4]=>001100=>001100=>110011
[2,6,7,5,1,4,3]=>001101=>101100=>010011
[2,6,7,5,3,1,4]=>001110=>011100=>100011
[2,6,7,5,3,4,1]=>001101=>101100=>010011
[2,6,7,5,4,1,3]=>001110=>011100=>100011
[2,6,7,5,4,3,1]=>001111=>111100=>000011
[2,7,1,3,4,5,6]=>010000=>000010=>111101
[2,7,1,3,4,6,5]=>010001=>100010=>011101
[2,7,1,3,5,4,6]=>010010=>010010=>101101
[2,7,1,3,5,6,4]=>010001=>100010=>011101
[2,7,1,3,6,4,5]=>010010=>010010=>101101
[2,7,1,3,6,5,4]=>010011=>110010=>001101
[2,7,1,4,3,5,6]=>010100=>001010=>110101
[2,7,1,4,3,6,5]=>010101=>101010=>010101
[2,7,1,4,5,3,6]=>010010=>010010=>101101
[2,7,1,4,5,6,3]=>010001=>100010=>011101
[2,7,1,4,6,3,5]=>010010=>010010=>101101
[2,7,1,4,6,5,3]=>010011=>110010=>001101
[2,7,1,5,3,4,6]=>010100=>001010=>110101
[2,7,1,5,3,6,4]=>010101=>101010=>010101
[2,7,1,5,4,3,6]=>010110=>011010=>100101
[2,7,1,5,4,6,3]=>010101=>101010=>010101
[2,7,1,5,6,3,4]=>010010=>010010=>101101
[2,7,1,5,6,4,3]=>010011=>110010=>001101
[2,7,1,6,3,4,5]=>010100=>001010=>110101
[2,7,1,6,3,5,4]=>010101=>101010=>010101
[2,7,1,6,4,3,5]=>010110=>011010=>100101
[2,7,1,6,4,5,3]=>010101=>101010=>010101
[2,7,1,6,5,3,4]=>010110=>011010=>100101
[2,7,1,6,5,4,3]=>010111=>111010=>000101
[2,7,3,1,4,5,6]=>011000=>000110=>111001
[2,7,3,1,4,6,5]=>011001=>100110=>011001
[2,7,3,1,5,4,6]=>011010=>010110=>101001
[2,7,3,1,5,6,4]=>011001=>100110=>011001
[2,7,3,1,6,4,5]=>011010=>010110=>101001
[2,7,3,1,6,5,4]=>011011=>110110=>001001
[2,7,3,4,1,5,6]=>010100=>001010=>110101
[2,7,3,4,1,6,5]=>010101=>101010=>010101
[2,7,3,4,5,1,6]=>010010=>010010=>101101
[2,7,3,4,5,6,1]=>010001=>100010=>011101
[2,7,3,4,6,1,5]=>010010=>010010=>101101
[2,7,3,4,6,5,1]=>010011=>110010=>001101
[2,7,3,5,1,4,6]=>010100=>001010=>110101
[2,7,3,5,1,6,4]=>010101=>101010=>010101
[2,7,3,5,4,1,6]=>010110=>011010=>100101
[2,7,3,5,4,6,1]=>010101=>101010=>010101
[2,7,3,5,6,1,4]=>010010=>010010=>101101
[2,7,3,5,6,4,1]=>010011=>110010=>001101
[2,7,3,6,1,4,5]=>010100=>001010=>110101
[2,7,3,6,1,5,4]=>010101=>101010=>010101
[2,7,3,6,4,1,5]=>010110=>011010=>100101
[2,7,3,6,4,5,1]=>010101=>101010=>010101
[2,7,3,6,5,1,4]=>010110=>011010=>100101
[2,7,3,6,5,4,1]=>010111=>111010=>000101
[2,7,4,1,3,5,6]=>011000=>000110=>111001
[2,7,4,1,3,6,5]=>011001=>100110=>011001
[2,7,4,1,5,3,6]=>011010=>010110=>101001
[2,7,4,1,5,6,3]=>011001=>100110=>011001
[2,7,4,1,6,3,5]=>011010=>010110=>101001
[2,7,4,1,6,5,3]=>011011=>110110=>001001
[2,7,4,3,1,5,6]=>011100=>001110=>110001
[2,7,4,3,1,6,5]=>011101=>101110=>010001
[2,7,4,3,5,1,6]=>011010=>010110=>101001
[2,7,4,3,5,6,1]=>011001=>100110=>011001
[2,7,4,3,6,1,5]=>011010=>010110=>101001
[2,7,4,3,6,5,1]=>011011=>110110=>001001
[2,7,4,5,1,3,6]=>010100=>001010=>110101
[2,7,4,5,1,6,3]=>010101=>101010=>010101
[2,7,4,5,3,1,6]=>010110=>011010=>100101
[2,7,4,5,3,6,1]=>010101=>101010=>010101
[2,7,4,5,6,1,3]=>010010=>010010=>101101
[2,7,4,5,6,3,1]=>010011=>110010=>001101
[2,7,4,6,1,3,5]=>010100=>001010=>110101
[2,7,4,6,1,5,3]=>010101=>101010=>010101
[2,7,4,6,3,1,5]=>010110=>011010=>100101
[2,7,4,6,3,5,1]=>010101=>101010=>010101
[2,7,4,6,5,1,3]=>010110=>011010=>100101
[2,7,4,6,5,3,1]=>010111=>111010=>000101
[2,7,5,1,3,4,6]=>011000=>000110=>111001
[2,7,5,1,3,6,4]=>011001=>100110=>011001
[2,7,5,1,4,3,6]=>011010=>010110=>101001
[2,7,5,1,4,6,3]=>011001=>100110=>011001
[2,7,5,1,6,3,4]=>011010=>010110=>101001
[2,7,5,1,6,4,3]=>011011=>110110=>001001
[2,7,5,3,1,4,6]=>011100=>001110=>110001
[2,7,5,3,1,6,4]=>011101=>101110=>010001
[2,7,5,3,4,1,6]=>011010=>010110=>101001
[2,7,5,3,4,6,1]=>011001=>100110=>011001
[2,7,5,3,6,1,4]=>011010=>010110=>101001
[2,7,5,3,6,4,1]=>011011=>110110=>001001
[2,7,5,4,1,3,6]=>011100=>001110=>110001
[2,7,5,4,1,6,3]=>011101=>101110=>010001
[2,7,5,4,3,1,6]=>011110=>011110=>100001
[2,7,5,4,3,6,1]=>011101=>101110=>010001
[2,7,5,4,6,1,3]=>011010=>010110=>101001
[2,7,5,4,6,3,1]=>011011=>110110=>001001
[2,7,5,6,1,3,4]=>010100=>001010=>110101
[2,7,5,6,1,4,3]=>010101=>101010=>010101
[2,7,5,6,3,1,4]=>010110=>011010=>100101
[2,7,5,6,3,4,1]=>010101=>101010=>010101
[2,7,5,6,4,1,3]=>010110=>011010=>100101
[2,7,5,6,4,3,1]=>010111=>111010=>000101
[2,7,6,1,3,4,5]=>011000=>000110=>111001
[2,7,6,1,3,5,4]=>011001=>100110=>011001
[2,7,6,1,4,3,5]=>011010=>010110=>101001
[2,7,6,1,4,5,3]=>011001=>100110=>011001
[2,7,6,1,5,3,4]=>011010=>010110=>101001
[2,7,6,1,5,4,3]=>011011=>110110=>001001
[2,7,6,3,1,4,5]=>011100=>001110=>110001
[2,7,6,3,1,5,4]=>011101=>101110=>010001
[2,7,6,3,4,1,5]=>011010=>010110=>101001
[2,7,6,3,4,5,1]=>011001=>100110=>011001
[2,7,6,3,5,1,4]=>011010=>010110=>101001
[2,7,6,3,5,4,1]=>011011=>110110=>001001
[2,7,6,4,1,3,5]=>011100=>001110=>110001
[2,7,6,4,1,5,3]=>011101=>101110=>010001
[2,7,6,4,3,1,5]=>011110=>011110=>100001
[2,7,6,4,3,5,1]=>011101=>101110=>010001
[2,7,6,4,5,1,3]=>011010=>010110=>101001
[2,7,6,4,5,3,1]=>011011=>110110=>001001
[2,7,6,5,1,3,4]=>011100=>001110=>110001
[2,7,6,5,1,4,3]=>011101=>101110=>010001
[2,7,6,5,3,1,4]=>011110=>011110=>100001
[2,7,6,5,3,4,1]=>011101=>101110=>010001
[2,7,6,5,4,1,3]=>011110=>011110=>100001
[2,7,6,5,4,3,1]=>011111=>111110=>000001
[3,1,2,4,5,6,7]=>100000=>000001=>111110
[3,1,2,4,5,7,6]=>100001=>100001=>011110
[3,1,2,4,6,5,7]=>100010=>010001=>101110
[3,1,2,4,6,7,5]=>100001=>100001=>011110
[3,1,2,4,7,5,6]=>100010=>010001=>101110
[3,1,2,4,7,6,5]=>100011=>110001=>001110
[3,1,2,5,4,6,7]=>100100=>001001=>110110
[3,1,2,5,4,7,6]=>100101=>101001=>010110
[3,1,2,5,6,4,7]=>100010=>010001=>101110
[3,1,2,5,6,7,4]=>100001=>100001=>011110
[3,1,2,5,7,4,6]=>100010=>010001=>101110
[3,1,2,5,7,6,4]=>100011=>110001=>001110
[3,1,2,6,4,5,7]=>100100=>001001=>110110
[3,1,2,6,4,7,5]=>100101=>101001=>010110
[3,1,2,6,5,4,7]=>100110=>011001=>100110
[3,1,2,6,5,7,4]=>100101=>101001=>010110
[3,1,2,6,7,4,5]=>100010=>010001=>101110
[3,1,2,6,7,5,4]=>100011=>110001=>001110
[3,1,2,7,4,5,6]=>100100=>001001=>110110
[3,1,2,7,4,6,5]=>100101=>101001=>010110
[3,1,2,7,5,4,6]=>100110=>011001=>100110
[3,1,2,7,5,6,4]=>100101=>101001=>010110
[3,1,2,7,6,4,5]=>100110=>011001=>100110
[3,1,2,7,6,5,4]=>100111=>111001=>000110
[3,1,4,2,5,6,7]=>101000=>000101=>111010
[3,1,4,2,5,7,6]=>101001=>100101=>011010
[3,1,4,2,6,5,7]=>101010=>010101=>101010
[3,1,4,2,6,7,5]=>101001=>100101=>011010
[3,1,4,2,7,5,6]=>101010=>010101=>101010
[3,1,4,2,7,6,5]=>101011=>110101=>001010
[3,1,4,5,2,6,7]=>100100=>001001=>110110
[3,1,4,5,2,7,6]=>100101=>101001=>010110
[3,1,4,5,6,2,7]=>100010=>010001=>101110
[3,1,4,5,6,7,2]=>100001=>100001=>011110
[3,1,4,5,7,2,6]=>100010=>010001=>101110
[3,1,4,5,7,6,2]=>100011=>110001=>001110
[3,1,4,6,2,5,7]=>100100=>001001=>110110
[3,1,4,6,2,7,5]=>100101=>101001=>010110
[3,1,4,6,5,2,7]=>100110=>011001=>100110
[3,1,4,6,5,7,2]=>100101=>101001=>010110
[3,1,4,6,7,2,5]=>100010=>010001=>101110
[3,1,4,6,7,5,2]=>100011=>110001=>001110
[3,1,4,7,2,5,6]=>100100=>001001=>110110
[3,1,4,7,2,6,5]=>100101=>101001=>010110
[3,1,4,7,5,2,6]=>100110=>011001=>100110
[3,1,4,7,5,6,2]=>100101=>101001=>010110
[3,1,4,7,6,2,5]=>100110=>011001=>100110
[3,1,4,7,6,5,2]=>100111=>111001=>000110
[3,1,5,2,4,6,7]=>101000=>000101=>111010
[3,1,5,2,4,7,6]=>101001=>100101=>011010
[3,1,5,2,6,4,7]=>101010=>010101=>101010
[3,1,5,2,6,7,4]=>101001=>100101=>011010
[3,1,5,2,7,4,6]=>101010=>010101=>101010
[3,1,5,2,7,6,4]=>101011=>110101=>001010
[3,1,5,4,2,6,7]=>101100=>001101=>110010
[3,1,5,4,2,7,6]=>101101=>101101=>010010
[3,1,5,4,6,2,7]=>101010=>010101=>101010
[3,1,5,4,6,7,2]=>101001=>100101=>011010
[3,1,5,4,7,2,6]=>101010=>010101=>101010
[3,1,5,4,7,6,2]=>101011=>110101=>001010
[3,1,5,6,2,4,7]=>100100=>001001=>110110
[3,1,5,6,2,7,4]=>100101=>101001=>010110
[3,1,5,6,4,2,7]=>100110=>011001=>100110
[3,1,5,6,4,7,2]=>100101=>101001=>010110
[3,1,5,6,7,2,4]=>100010=>010001=>101110
[3,1,5,6,7,4,2]=>100011=>110001=>001110
[3,1,5,7,2,4,6]=>100100=>001001=>110110
[3,1,5,7,2,6,4]=>100101=>101001=>010110
[3,1,5,7,4,2,6]=>100110=>011001=>100110
[3,1,5,7,4,6,2]=>100101=>101001=>010110
[3,1,5,7,6,2,4]=>100110=>011001=>100110
[3,1,5,7,6,4,2]=>100111=>111001=>000110
[3,1,6,2,4,5,7]=>101000=>000101=>111010
[3,1,6,2,4,7,5]=>101001=>100101=>011010
[3,1,6,2,5,4,7]=>101010=>010101=>101010
[3,1,6,2,5,7,4]=>101001=>100101=>011010
[3,1,6,2,7,4,5]=>101010=>010101=>101010
[3,1,6,2,7,5,4]=>101011=>110101=>001010
[3,1,6,4,2,5,7]=>101100=>001101=>110010
[3,1,6,4,2,7,5]=>101101=>101101=>010010
[3,1,6,4,5,2,7]=>101010=>010101=>101010
[3,1,6,4,5,7,2]=>101001=>100101=>011010
[3,1,6,4,7,2,5]=>101010=>010101=>101010
[3,1,6,4,7,5,2]=>101011=>110101=>001010
[3,1,6,5,2,4,7]=>101100=>001101=>110010
[3,1,6,5,2,7,4]=>101101=>101101=>010010
[3,1,6,5,4,2,7]=>101110=>011101=>100010
[3,1,6,5,4,7,2]=>101101=>101101=>010010
[3,1,6,5,7,2,4]=>101010=>010101=>101010
[3,1,6,5,7,4,2]=>101011=>110101=>001010
[3,1,6,7,2,4,5]=>100100=>001001=>110110
[3,1,6,7,2,5,4]=>100101=>101001=>010110
[3,1,6,7,4,2,5]=>100110=>011001=>100110
[3,1,6,7,4,5,2]=>100101=>101001=>010110
[3,1,6,7,5,2,4]=>100110=>011001=>100110
[3,1,6,7,5,4,2]=>100111=>111001=>000110
[3,1,7,2,4,5,6]=>101000=>000101=>111010
[3,1,7,2,4,6,5]=>101001=>100101=>011010
[3,1,7,2,5,4,6]=>101010=>010101=>101010
[3,1,7,2,5,6,4]=>101001=>100101=>011010
[3,1,7,2,6,4,5]=>101010=>010101=>101010
[3,1,7,2,6,5,4]=>101011=>110101=>001010
[3,1,7,4,2,5,6]=>101100=>001101=>110010
[3,1,7,4,2,6,5]=>101101=>101101=>010010
[3,1,7,4,5,2,6]=>101010=>010101=>101010
[3,1,7,4,5,6,2]=>101001=>100101=>011010
[3,1,7,4,6,2,5]=>101010=>010101=>101010
[3,1,7,4,6,5,2]=>101011=>110101=>001010
[3,1,7,5,2,4,6]=>101100=>001101=>110010
[3,1,7,5,2,6,4]=>101101=>101101=>010010
[3,1,7,5,4,2,6]=>101110=>011101=>100010
[3,1,7,5,4,6,2]=>101101=>101101=>010010
[3,1,7,5,6,2,4]=>101010=>010101=>101010
[3,1,7,5,6,4,2]=>101011=>110101=>001010
[3,1,7,6,2,4,5]=>101100=>001101=>110010
[3,1,7,6,2,5,4]=>101101=>101101=>010010
[3,1,7,6,4,2,5]=>101110=>011101=>100010
[3,1,7,6,4,5,2]=>101101=>101101=>010010
[3,1,7,6,5,2,4]=>101110=>011101=>100010
[3,1,7,6,5,4,2]=>101111=>111101=>000010
[3,2,1,4,5,6,7]=>110000=>000011=>111100
[3,2,1,4,5,7,6]=>110001=>100011=>011100
[3,2,1,4,6,5,7]=>110010=>010011=>101100
[3,2,1,4,6,7,5]=>110001=>100011=>011100
[3,2,1,4,7,5,6]=>110010=>010011=>101100
[3,2,1,4,7,6,5]=>110011=>110011=>001100
[3,2,1,5,4,6,7]=>110100=>001011=>110100
[3,2,1,5,4,7,6]=>110101=>101011=>010100
[3,2,1,5,6,4,7]=>110010=>010011=>101100
[3,2,1,5,6,7,4]=>110001=>100011=>011100
[3,2,1,5,7,4,6]=>110010=>010011=>101100
[3,2,1,5,7,6,4]=>110011=>110011=>001100
[3,2,1,6,4,5,7]=>110100=>001011=>110100
[3,2,1,6,4,7,5]=>110101=>101011=>010100
[3,2,1,6,5,4,7]=>110110=>011011=>100100
[3,2,1,6,5,7,4]=>110101=>101011=>010100
[3,2,1,6,7,4,5]=>110010=>010011=>101100
[3,2,1,6,7,5,4]=>110011=>110011=>001100
[3,2,1,7,4,5,6]=>110100=>001011=>110100
[3,2,1,7,4,6,5]=>110101=>101011=>010100
[3,2,1,7,5,4,6]=>110110=>011011=>100100
[3,2,1,7,5,6,4]=>110101=>101011=>010100
[3,2,1,7,6,4,5]=>110110=>011011=>100100
[3,2,1,7,6,5,4]=>110111=>111011=>000100
[3,2,4,1,5,6,7]=>101000=>000101=>111010
[3,2,4,1,5,7,6]=>101001=>100101=>011010
[3,2,4,1,6,5,7]=>101010=>010101=>101010
[3,2,4,1,6,7,5]=>101001=>100101=>011010
[3,2,4,1,7,5,6]=>101010=>010101=>101010
[3,2,4,1,7,6,5]=>101011=>110101=>001010
[3,2,4,5,1,6,7]=>100100=>001001=>110110
[3,2,4,5,1,7,6]=>100101=>101001=>010110
[3,2,4,5,6,1,7]=>100010=>010001=>101110
[3,2,4,5,6,7,1]=>100001=>100001=>011110
[3,2,4,5,7,1,6]=>100010=>010001=>101110
[3,2,4,5,7,6,1]=>100011=>110001=>001110
[3,2,4,6,1,5,7]=>100100=>001001=>110110
[3,2,4,6,1,7,5]=>100101=>101001=>010110
[3,2,4,6,5,1,7]=>100110=>011001=>100110
[3,2,4,6,5,7,1]=>100101=>101001=>010110
[3,2,4,6,7,1,5]=>100010=>010001=>101110
[3,2,4,6,7,5,1]=>100011=>110001=>001110
[3,2,4,7,1,5,6]=>100100=>001001=>110110
[3,2,4,7,1,6,5]=>100101=>101001=>010110
[3,2,4,7,5,1,6]=>100110=>011001=>100110
[3,2,4,7,5,6,1]=>100101=>101001=>010110
[3,2,4,7,6,1,5]=>100110=>011001=>100110
[3,2,4,7,6,5,1]=>100111=>111001=>000110
[3,2,5,1,4,6,7]=>101000=>000101=>111010
[3,2,5,1,4,7,6]=>101001=>100101=>011010
[3,2,5,1,6,4,7]=>101010=>010101=>101010
[3,2,5,1,6,7,4]=>101001=>100101=>011010
[3,2,5,1,7,4,6]=>101010=>010101=>101010
[3,2,5,1,7,6,4]=>101011=>110101=>001010
[3,2,5,4,1,6,7]=>101100=>001101=>110010
[3,2,5,4,1,7,6]=>101101=>101101=>010010
[3,2,5,4,6,1,7]=>101010=>010101=>101010
[3,2,5,4,6,7,1]=>101001=>100101=>011010
[3,2,5,4,7,1,6]=>101010=>010101=>101010
[3,2,5,4,7,6,1]=>101011=>110101=>001010
[3,2,5,6,1,4,7]=>100100=>001001=>110110
[3,2,5,6,1,7,4]=>100101=>101001=>010110
[3,2,5,6,4,1,7]=>100110=>011001=>100110
[3,2,5,6,4,7,1]=>100101=>101001=>010110
[3,2,5,6,7,1,4]=>100010=>010001=>101110
[3,2,5,6,7,4,1]=>100011=>110001=>001110
[3,2,5,7,1,4,6]=>100100=>001001=>110110
[3,2,5,7,1,6,4]=>100101=>101001=>010110
[3,2,5,7,4,1,6]=>100110=>011001=>100110
[3,2,5,7,4,6,1]=>100101=>101001=>010110
[3,2,5,7,6,1,4]=>100110=>011001=>100110
[3,2,5,7,6,4,1]=>100111=>111001=>000110
[3,2,6,1,4,5,7]=>101000=>000101=>111010
[3,2,6,1,4,7,5]=>101001=>100101=>011010
[3,2,6,1,5,4,7]=>101010=>010101=>101010
[3,2,6,1,5,7,4]=>101001=>100101=>011010
[3,2,6,1,7,4,5]=>101010=>010101=>101010
[3,2,6,1,7,5,4]=>101011=>110101=>001010
[3,2,6,4,1,5,7]=>101100=>001101=>110010
[3,2,6,4,1,7,5]=>101101=>101101=>010010
[3,2,6,4,5,1,7]=>101010=>010101=>101010
[3,2,6,4,5,7,1]=>101001=>100101=>011010
[3,2,6,4,7,1,5]=>101010=>010101=>101010
[3,2,6,4,7,5,1]=>101011=>110101=>001010
[3,2,6,5,1,4,7]=>101100=>001101=>110010
[3,2,6,5,1,7,4]=>101101=>101101=>010010
[3,2,6,5,4,1,7]=>101110=>011101=>100010
[3,2,6,5,4,7,1]=>101101=>101101=>010010
[3,2,6,5,7,1,4]=>101010=>010101=>101010
[3,2,6,5,7,4,1]=>101011=>110101=>001010
[3,2,6,7,1,4,5]=>100100=>001001=>110110
[3,2,6,7,1,5,4]=>100101=>101001=>010110
[3,2,6,7,4,1,5]=>100110=>011001=>100110
[3,2,6,7,4,5,1]=>100101=>101001=>010110
[3,2,6,7,5,1,4]=>100110=>011001=>100110
[3,2,6,7,5,4,1]=>100111=>111001=>000110
[3,2,7,1,4,5,6]=>101000=>000101=>111010
[3,2,7,1,4,6,5]=>101001=>100101=>011010
[3,2,7,1,5,4,6]=>101010=>010101=>101010
[3,2,7,1,5,6,4]=>101001=>100101=>011010
[3,2,7,1,6,4,5]=>101010=>010101=>101010
[3,2,7,1,6,5,4]=>101011=>110101=>001010
[3,2,7,4,1,5,6]=>101100=>001101=>110010
[3,2,7,4,1,6,5]=>101101=>101101=>010010
[3,2,7,4,5,1,6]=>101010=>010101=>101010
[3,2,7,4,5,6,1]=>101001=>100101=>011010
[3,2,7,4,6,1,5]=>101010=>010101=>101010
[3,2,7,4,6,5,1]=>101011=>110101=>001010
[3,2,7,5,1,4,6]=>101100=>001101=>110010
[3,2,7,5,1,6,4]=>101101=>101101=>010010
[3,2,7,5,4,1,6]=>101110=>011101=>100010
[3,2,7,5,4,6,1]=>101101=>101101=>010010
[3,2,7,5,6,1,4]=>101010=>010101=>101010
[3,2,7,5,6,4,1]=>101011=>110101=>001010
[3,2,7,6,1,4,5]=>101100=>001101=>110010
[3,2,7,6,1,5,4]=>101101=>101101=>010010
[3,2,7,6,4,1,5]=>101110=>011101=>100010
[3,2,7,6,4,5,1]=>101101=>101101=>010010
[3,2,7,6,5,1,4]=>101110=>011101=>100010
[3,2,7,6,5,4,1]=>101111=>111101=>000010
[3,4,1,2,5,6,7]=>010000=>000010=>111101
[3,4,1,2,5,7,6]=>010001=>100010=>011101
[3,4,1,2,6,5,7]=>010010=>010010=>101101
[3,4,1,2,6,7,5]=>010001=>100010=>011101
[3,4,1,2,7,5,6]=>010010=>010010=>101101
[3,4,1,2,7,6,5]=>010011=>110010=>001101
[3,4,1,5,2,6,7]=>010100=>001010=>110101
[3,4,1,5,2,7,6]=>010101=>101010=>010101
[3,4,1,5,6,2,7]=>010010=>010010=>101101
[3,4,1,5,6,7,2]=>010001=>100010=>011101
[3,4,1,5,7,2,6]=>010010=>010010=>101101
[3,4,1,5,7,6,2]=>010011=>110010=>001101
[3,4,1,6,2,5,7]=>010100=>001010=>110101
[3,4,1,6,2,7,5]=>010101=>101010=>010101
[3,4,1,6,5,2,7]=>010110=>011010=>100101
[3,4,1,6,5,7,2]=>010101=>101010=>010101
[3,4,1,6,7,2,5]=>010010=>010010=>101101
[3,4,1,6,7,5,2]=>010011=>110010=>001101
[3,4,1,7,2,5,6]=>010100=>001010=>110101
[3,4,1,7,2,6,5]=>010101=>101010=>010101
[3,4,1,7,5,2,6]=>010110=>011010=>100101
[3,4,1,7,5,6,2]=>010101=>101010=>010101
[3,4,1,7,6,2,5]=>010110=>011010=>100101
[3,4,1,7,6,5,2]=>010111=>111010=>000101
[3,4,2,1,5,6,7]=>011000=>000110=>111001
[3,4,2,1,5,7,6]=>011001=>100110=>011001
[3,4,2,1,6,5,7]=>011010=>010110=>101001
[3,4,2,1,6,7,5]=>011001=>100110=>011001
[3,4,2,1,7,5,6]=>011010=>010110=>101001
[3,4,2,1,7,6,5]=>011011=>110110=>001001
[3,4,2,5,1,6,7]=>010100=>001010=>110101
[3,4,2,5,1,7,6]=>010101=>101010=>010101
[3,4,2,5,6,1,7]=>010010=>010010=>101101
[3,4,2,5,6,7,1]=>010001=>100010=>011101
[3,4,2,5,7,1,6]=>010010=>010010=>101101
[3,4,2,5,7,6,1]=>010011=>110010=>001101
[3,4,2,6,1,5,7]=>010100=>001010=>110101
[3,4,2,6,1,7,5]=>010101=>101010=>010101
[3,4,2,6,5,1,7]=>010110=>011010=>100101
[3,4,2,6,5,7,1]=>010101=>101010=>010101
[3,4,2,6,7,1,5]=>010010=>010010=>101101
[3,4,2,6,7,5,1]=>010011=>110010=>001101
[3,4,2,7,1,5,6]=>010100=>001010=>110101
[3,4,2,7,1,6,5]=>010101=>101010=>010101
[3,4,2,7,5,1,6]=>010110=>011010=>100101
[3,4,2,7,5,6,1]=>010101=>101010=>010101
[3,4,2,7,6,1,5]=>010110=>011010=>100101
[3,4,2,7,6,5,1]=>010111=>111010=>000101
[3,4,5,1,2,6,7]=>001000=>000100=>111011
[3,4,5,1,2,7,6]=>001001=>100100=>011011
[3,4,5,1,6,2,7]=>001010=>010100=>101011
[3,4,5,1,6,7,2]=>001001=>100100=>011011
[3,4,5,1,7,2,6]=>001010=>010100=>101011
[3,4,5,1,7,6,2]=>001011=>110100=>001011
[3,4,5,2,1,6,7]=>001100=>001100=>110011
[3,4,5,2,1,7,6]=>001101=>101100=>010011
[3,4,5,2,6,1,7]=>001010=>010100=>101011
[3,4,5,2,6,7,1]=>001001=>100100=>011011
[3,4,5,2,7,1,6]=>001010=>010100=>101011
[3,4,5,2,7,6,1]=>001011=>110100=>001011
[3,4,5,6,1,2,7]=>000100=>001000=>110111
[3,4,5,6,1,7,2]=>000101=>101000=>010111
[3,4,5,6,2,1,7]=>000110=>011000=>100111
[3,4,5,6,2,7,1]=>000101=>101000=>010111
[3,4,5,6,7,1,2]=>000010=>010000=>101111
[3,4,5,6,7,2,1]=>000011=>110000=>001111
[3,4,5,7,1,2,6]=>000100=>001000=>110111
[3,4,5,7,1,6,2]=>000101=>101000=>010111
[3,4,5,7,2,1,6]=>000110=>011000=>100111
[3,4,5,7,2,6,1]=>000101=>101000=>010111
[3,4,5,7,6,1,2]=>000110=>011000=>100111
[3,4,5,7,6,2,1]=>000111=>111000=>000111
[3,4,6,1,2,5,7]=>001000=>000100=>111011
[3,4,6,1,2,7,5]=>001001=>100100=>011011
[3,4,6,1,5,2,7]=>001010=>010100=>101011
[3,4,6,1,5,7,2]=>001001=>100100=>011011
[3,4,6,1,7,2,5]=>001010=>010100=>101011
[3,4,6,1,7,5,2]=>001011=>110100=>001011
[3,4,6,2,1,5,7]=>001100=>001100=>110011
[3,4,6,2,1,7,5]=>001101=>101100=>010011
[3,4,6,2,5,1,7]=>001010=>010100=>101011
[3,4,6,2,5,7,1]=>001001=>100100=>011011
[3,4,6,2,7,1,5]=>001010=>010100=>101011
[3,4,6,2,7,5,1]=>001011=>110100=>001011
[3,4,6,5,1,2,7]=>001100=>001100=>110011
[3,4,6,5,1,7,2]=>001101=>101100=>010011
[3,4,6,5,2,1,7]=>001110=>011100=>100011
[3,4,6,5,2,7,1]=>001101=>101100=>010011
[3,4,6,5,7,1,2]=>001010=>010100=>101011
[3,4,6,5,7,2,1]=>001011=>110100=>001011
[3,4,6,7,1,2,5]=>000100=>001000=>110111
[3,4,6,7,1,5,2]=>000101=>101000=>010111
[3,4,6,7,2,1,5]=>000110=>011000=>100111
[3,4,6,7,2,5,1]=>000101=>101000=>010111
[3,4,6,7,5,1,2]=>000110=>011000=>100111
[3,4,6,7,5,2,1]=>000111=>111000=>000111
[3,4,7,1,2,5,6]=>001000=>000100=>111011
[3,4,7,1,2,6,5]=>001001=>100100=>011011
[3,4,7,1,5,2,6]=>001010=>010100=>101011
[3,4,7,1,5,6,2]=>001001=>100100=>011011
[3,4,7,1,6,2,5]=>001010=>010100=>101011
[3,4,7,1,6,5,2]=>001011=>110100=>001011
[3,4,7,2,1,5,6]=>001100=>001100=>110011
[3,4,7,2,1,6,5]=>001101=>101100=>010011
[3,4,7,2,5,1,6]=>001010=>010100=>101011
[3,4,7,2,5,6,1]=>001001=>100100=>011011
[3,4,7,2,6,1,5]=>001010=>010100=>101011
[3,4,7,2,6,5,1]=>001011=>110100=>001011
[3,4,7,5,1,2,6]=>001100=>001100=>110011
[3,4,7,5,1,6,2]=>001101=>101100=>010011
[3,4,7,5,2,1,6]=>001110=>011100=>100011
[3,4,7,5,2,6,1]=>001101=>101100=>010011
[3,4,7,5,6,1,2]=>001010=>010100=>101011
[3,4,7,5,6,2,1]=>001011=>110100=>001011
[3,4,7,6,1,2,5]=>001100=>001100=>110011
[3,4,7,6,1,5,2]=>001101=>101100=>010011
[3,4,7,6,2,1,5]=>001110=>011100=>100011
[3,4,7,6,2,5,1]=>001101=>101100=>010011
[3,4,7,6,5,1,2]=>001110=>011100=>100011
[3,4,7,6,5,2,1]=>001111=>111100=>000011
[3,5,1,2,4,6,7]=>010000=>000010=>111101
[3,5,1,2,4,7,6]=>010001=>100010=>011101
[3,5,1,2,6,4,7]=>010010=>010010=>101101
[3,5,1,2,6,7,4]=>010001=>100010=>011101
[3,5,1,2,7,4,6]=>010010=>010010=>101101
[3,5,1,2,7,6,4]=>010011=>110010=>001101
[3,5,1,4,2,6,7]=>010100=>001010=>110101
[3,5,1,4,2,7,6]=>010101=>101010=>010101
[3,5,1,4,6,2,7]=>010010=>010010=>101101
[3,5,1,4,6,7,2]=>010001=>100010=>011101
[3,5,1,4,7,2,6]=>010010=>010010=>101101
[3,5,1,4,7,6,2]=>010011=>110010=>001101
[3,5,1,6,2,4,7]=>010100=>001010=>110101
[3,5,1,6,2,7,4]=>010101=>101010=>010101
[3,5,1,6,4,2,7]=>010110=>011010=>100101
[3,5,1,6,4,7,2]=>010101=>101010=>010101
[3,5,1,6,7,2,4]=>010010=>010010=>101101
[3,5,1,6,7,4,2]=>010011=>110010=>001101
[3,5,1,7,2,4,6]=>010100=>001010=>110101
[3,5,1,7,2,6,4]=>010101=>101010=>010101
[3,5,1,7,4,2,6]=>010110=>011010=>100101
[3,5,1,7,4,6,2]=>010101=>101010=>010101
[3,5,1,7,6,2,4]=>010110=>011010=>100101
[3,5,1,7,6,4,2]=>010111=>111010=>000101
[3,5,2,1,4,6,7]=>011000=>000110=>111001
[3,5,2,1,4,7,6]=>011001=>100110=>011001
[3,5,2,1,6,4,7]=>011010=>010110=>101001
[3,5,2,1,6,7,4]=>011001=>100110=>011001
[3,5,2,1,7,4,6]=>011010=>010110=>101001
[3,5,2,1,7,6,4]=>011011=>110110=>001001
[3,5,2,4,1,6,7]=>010100=>001010=>110101
[3,5,2,4,1,7,6]=>010101=>101010=>010101
[3,5,2,4,6,1,7]=>010010=>010010=>101101
[3,5,2,4,6,7,1]=>010001=>100010=>011101
[3,5,2,4,7,1,6]=>010010=>010010=>101101
[3,5,2,4,7,6,1]=>010011=>110010=>001101
[3,5,2,6,1,4,7]=>010100=>001010=>110101
[3,5,2,6,1,7,4]=>010101=>101010=>010101
[3,5,2,6,4,1,7]=>010110=>011010=>100101
[3,5,2,6,4,7,1]=>010101=>101010=>010101
[3,5,2,6,7,1,4]=>010010=>010010=>101101
[3,5,2,6,7,4,1]=>010011=>110010=>001101
[3,5,2,7,1,4,6]=>010100=>001010=>110101
[3,5,2,7,1,6,4]=>010101=>101010=>010101
[3,5,2,7,4,1,6]=>010110=>011010=>100101
[3,5,2,7,4,6,1]=>010101=>101010=>010101
[3,5,2,7,6,1,4]=>010110=>011010=>100101
[3,5,2,7,6,4,1]=>010111=>111010=>000101
[3,5,4,1,2,6,7]=>011000=>000110=>111001
[3,5,4,1,2,7,6]=>011001=>100110=>011001
[3,5,4,1,6,2,7]=>011010=>010110=>101001
[3,5,4,1,6,7,2]=>011001=>100110=>011001
[3,5,4,1,7,2,6]=>011010=>010110=>101001
[3,5,4,1,7,6,2]=>011011=>110110=>001001
[3,5,4,2,1,6,7]=>011100=>001110=>110001
[3,5,4,2,1,7,6]=>011101=>101110=>010001
[3,5,4,2,6,1,7]=>011010=>010110=>101001
[3,5,4,2,6,7,1]=>011001=>100110=>011001
[3,5,4,2,7,1,6]=>011010=>010110=>101001
[3,5,4,2,7,6,1]=>011011=>110110=>001001
[3,5,4,6,1,2,7]=>010100=>001010=>110101
[3,5,4,6,1,7,2]=>010101=>101010=>010101
[3,5,4,6,2,1,7]=>010110=>011010=>100101
[3,5,4,6,2,7,1]=>010101=>101010=>010101
[3,5,4,6,7,1,2]=>010010=>010010=>101101
[3,5,4,6,7,2,1]=>010011=>110010=>001101
[3,5,4,7,1,2,6]=>010100=>001010=>110101
[3,5,4,7,1,6,2]=>010101=>101010=>010101
[3,5,4,7,2,1,6]=>010110=>011010=>100101
[3,5,4,7,2,6,1]=>010101=>101010=>010101
[3,5,4,7,6,1,2]=>010110=>011010=>100101
[3,5,4,7,6,2,1]=>010111=>111010=>000101
[3,5,6,1,2,4,7]=>001000=>000100=>111011
[3,5,6,1,2,7,4]=>001001=>100100=>011011
[3,5,6,1,4,2,7]=>001010=>010100=>101011
[3,5,6,1,4,7,2]=>001001=>100100=>011011
[3,5,6,1,7,2,4]=>001010=>010100=>101011
[3,5,6,1,7,4,2]=>001011=>110100=>001011
[3,5,6,2,1,4,7]=>001100=>001100=>110011
[3,5,6,2,1,7,4]=>001101=>101100=>010011
[3,5,6,2,4,1,7]=>001010=>010100=>101011
[3,5,6,2,4,7,1]=>001001=>100100=>011011
[3,5,6,2,7,1,4]=>001010=>010100=>101011
[3,5,6,2,7,4,1]=>001011=>110100=>001011
[3,5,6,4,1,2,7]=>001100=>001100=>110011
[3,5,6,4,1,7,2]=>001101=>101100=>010011
[3,5,6,4,2,1,7]=>001110=>011100=>100011
[3,5,6,4,2,7,1]=>001101=>101100=>010011
[3,5,6,4,7,1,2]=>001010=>010100=>101011
[3,5,6,4,7,2,1]=>001011=>110100=>001011
[3,5,6,7,1,2,4]=>000100=>001000=>110111
[3,5,6,7,1,4,2]=>000101=>101000=>010111
[3,5,6,7,2,1,4]=>000110=>011000=>100111
[3,5,6,7,2,4,1]=>000101=>101000=>010111
[3,5,6,7,4,1,2]=>000110=>011000=>100111
[3,5,6,7,4,2,1]=>000111=>111000=>000111
[3,5,7,1,2,4,6]=>001000=>000100=>111011
[3,5,7,1,2,6,4]=>001001=>100100=>011011
[3,5,7,1,4,2,6]=>001010=>010100=>101011
[3,5,7,1,4,6,2]=>001001=>100100=>011011
[3,5,7,1,6,2,4]=>001010=>010100=>101011
[3,5,7,1,6,4,2]=>001011=>110100=>001011
[3,5,7,2,1,4,6]=>001100=>001100=>110011
[3,5,7,2,1,6,4]=>001101=>101100=>010011
[3,5,7,2,4,1,6]=>001010=>010100=>101011
[3,5,7,2,4,6,1]=>001001=>100100=>011011
[3,5,7,2,6,1,4]=>001010=>010100=>101011
[3,5,7,2,6,4,1]=>001011=>110100=>001011
[3,5,7,4,1,2,6]=>001100=>001100=>110011
[3,5,7,4,1,6,2]=>001101=>101100=>010011
[3,5,7,4,2,1,6]=>001110=>011100=>100011
[3,5,7,4,2,6,1]=>001101=>101100=>010011
[3,5,7,4,6,1,2]=>001010=>010100=>101011
[3,5,7,4,6,2,1]=>001011=>110100=>001011
[3,5,7,6,1,2,4]=>001100=>001100=>110011
[3,5,7,6,1,4,2]=>001101=>101100=>010011
[3,5,7,6,2,1,4]=>001110=>011100=>100011
[3,5,7,6,2,4,1]=>001101=>101100=>010011
[3,5,7,6,4,1,2]=>001110=>011100=>100011
[3,5,7,6,4,2,1]=>001111=>111100=>000011
[3,6,1,2,4,5,7]=>010000=>000010=>111101
[3,6,1,2,4,7,5]=>010001=>100010=>011101
[3,6,1,2,5,4,7]=>010010=>010010=>101101
[3,6,1,2,5,7,4]=>010001=>100010=>011101
[3,6,1,2,7,4,5]=>010010=>010010=>101101
[3,6,1,2,7,5,4]=>010011=>110010=>001101
[3,6,1,4,2,5,7]=>010100=>001010=>110101
[3,6,1,4,2,7,5]=>010101=>101010=>010101
[3,6,1,4,5,2,7]=>010010=>010010=>101101
[3,6,1,4,5,7,2]=>010001=>100010=>011101
[3,6,1,4,7,2,5]=>010010=>010010=>101101
[3,6,1,4,7,5,2]=>010011=>110010=>001101
[3,6,1,5,2,4,7]=>010100=>001010=>110101
[3,6,1,5,2,7,4]=>010101=>101010=>010101
[3,6,1,5,4,2,7]=>010110=>011010=>100101
[3,6,1,5,4,7,2]=>010101=>101010=>010101
[3,6,1,5,7,2,4]=>010010=>010010=>101101
[3,6,1,5,7,4,2]=>010011=>110010=>001101
[3,6,1,7,2,4,5]=>010100=>001010=>110101
[3,6,1,7,2,5,4]=>010101=>101010=>010101
[3,6,1,7,4,2,5]=>010110=>011010=>100101
[3,6,1,7,4,5,2]=>010101=>101010=>010101
[3,6,1,7,5,2,4]=>010110=>011010=>100101
[3,6,1,7,5,4,2]=>010111=>111010=>000101
[3,6,2,1,4,5,7]=>011000=>000110=>111001
[3,6,2,1,4,7,5]=>011001=>100110=>011001
[3,6,2,1,5,4,7]=>011010=>010110=>101001
[3,6,2,1,5,7,4]=>011001=>100110=>011001
[3,6,2,1,7,4,5]=>011010=>010110=>101001
[3,6,2,1,7,5,4]=>011011=>110110=>001001
[3,6,2,4,1,5,7]=>010100=>001010=>110101
[3,6,2,4,1,7,5]=>010101=>101010=>010101
[3,6,2,4,5,1,7]=>010010=>010010=>101101
[3,6,2,4,5,7,1]=>010001=>100010=>011101
[3,6,2,4,7,1,5]=>010010=>010010=>101101
[3,6,2,4,7,5,1]=>010011=>110010=>001101
[3,6,2,5,1,4,7]=>010100=>001010=>110101
[3,6,2,5,1,7,4]=>010101=>101010=>010101
[3,6,2,5,4,1,7]=>010110=>011010=>100101
[3,6,2,5,4,7,1]=>010101=>101010=>010101
[3,6,2,5,7,1,4]=>010010=>010010=>101101
[3,6,2,5,7,4,1]=>010011=>110010=>001101
[3,6,2,7,1,4,5]=>010100=>001010=>110101
[3,6,2,7,1,5,4]=>010101=>101010=>010101
[3,6,2,7,4,1,5]=>010110=>011010=>100101
[3,6,2,7,4,5,1]=>010101=>101010=>010101
[3,6,2,7,5,1,4]=>010110=>011010=>100101
[3,6,2,7,5,4,1]=>010111=>111010=>000101
[3,6,4,1,2,5,7]=>011000=>000110=>111001
[3,6,4,1,2,7,5]=>011001=>100110=>011001
[3,6,4,1,5,2,7]=>011010=>010110=>101001
[3,6,4,1,5,7,2]=>011001=>100110=>011001
[3,6,4,1,7,2,5]=>011010=>010110=>101001
[3,6,4,1,7,5,2]=>011011=>110110=>001001
[3,6,4,2,1,5,7]=>011100=>001110=>110001
[3,6,4,2,1,7,5]=>011101=>101110=>010001
[3,6,4,2,5,1,7]=>011010=>010110=>101001
[3,6,4,2,5,7,1]=>011001=>100110=>011001
[3,6,4,2,7,1,5]=>011010=>010110=>101001
[3,6,4,2,7,5,1]=>011011=>110110=>001001
[3,6,4,5,1,2,7]=>010100=>001010=>110101
[3,6,4,5,1,7,2]=>010101=>101010=>010101
[3,6,4,5,2,1,7]=>010110=>011010=>100101
[3,6,4,5,2,7,1]=>010101=>101010=>010101
[3,6,4,5,7,1,2]=>010010=>010010=>101101
[3,6,4,5,7,2,1]=>010011=>110010=>001101
[3,6,4,7,1,2,5]=>010100=>001010=>110101
[3,6,4,7,1,5,2]=>010101=>101010=>010101
[3,6,4,7,2,1,5]=>010110=>011010=>100101
[3,6,4,7,2,5,1]=>010101=>101010=>010101
[3,6,4,7,5,1,2]=>010110=>011010=>100101
[3,6,4,7,5,2,1]=>010111=>111010=>000101
[3,6,5,1,2,4,7]=>011000=>000110=>111001
[3,6,5,1,2,7,4]=>011001=>100110=>011001
[3,6,5,1,4,2,7]=>011010=>010110=>101001
[3,6,5,1,4,7,2]=>011001=>100110=>011001
[3,6,5,1,7,2,4]=>011010=>010110=>101001
[3,6,5,1,7,4,2]=>011011=>110110=>001001
[3,6,5,2,1,4,7]=>011100=>001110=>110001
[3,6,5,2,1,7,4]=>011101=>101110=>010001
[3,6,5,2,4,1,7]=>011010=>010110=>101001
[3,6,5,2,4,7,1]=>011001=>100110=>011001
[3,6,5,2,7,1,4]=>011010=>010110=>101001
[3,6,5,2,7,4,1]=>011011=>110110=>001001
[3,6,5,4,1,2,7]=>011100=>001110=>110001
[3,6,5,4,1,7,2]=>011101=>101110=>010001
[3,6,5,4,2,1,7]=>011110=>011110=>100001
[3,6,5,4,2,7,1]=>011101=>101110=>010001
[3,6,5,4,7,1,2]=>011010=>010110=>101001
[3,6,5,4,7,2,1]=>011011=>110110=>001001
[3,6,5,7,1,2,4]=>010100=>001010=>110101
[3,6,5,7,1,4,2]=>010101=>101010=>010101
[3,6,5,7,2,1,4]=>010110=>011010=>100101
[3,6,5,7,2,4,1]=>010101=>101010=>010101
[3,6,5,7,4,1,2]=>010110=>011010=>100101
[3,6,5,7,4,2,1]=>010111=>111010=>000101
[3,6,7,1,2,4,5]=>001000=>000100=>111011
[3,6,7,1,2,5,4]=>001001=>100100=>011011
[3,6,7,1,4,2,5]=>001010=>010100=>101011
[3,6,7,1,4,5,2]=>001001=>100100=>011011
[3,6,7,1,5,2,4]=>001010=>010100=>101011
[3,6,7,1,5,4,2]=>001011=>110100=>001011
[3,6,7,2,1,4,5]=>001100=>001100=>110011
[3,6,7,2,1,5,4]=>001101=>101100=>010011
[3,6,7,2,4,1,5]=>001010=>010100=>101011
[3,6,7,2,4,5,1]=>001001=>100100=>011011
[3,6,7,2,5,1,4]=>001010=>010100=>101011
[3,6,7,2,5,4,1]=>001011=>110100=>001011
[3,6,7,4,1,2,5]=>001100=>001100=>110011
[3,6,7,4,1,5,2]=>001101=>101100=>010011
[3,6,7,4,2,1,5]=>001110=>011100=>100011
[3,6,7,4,2,5,1]=>001101=>101100=>010011
[3,6,7,4,5,1,2]=>001010=>010100=>101011
[3,6,7,4,5,2,1]=>001011=>110100=>001011
[3,6,7,5,1,2,4]=>001100=>001100=>110011
[3,6,7,5,1,4,2]=>001101=>101100=>010011
[3,6,7,5,2,1,4]=>001110=>011100=>100011
[3,6,7,5,2,4,1]=>001101=>101100=>010011
[3,6,7,5,4,1,2]=>001110=>011100=>100011
[3,6,7,5,4,2,1]=>001111=>111100=>000011
[3,7,1,2,4,5,6]=>010000=>000010=>111101
[3,7,1,2,4,6,5]=>010001=>100010=>011101
[3,7,1,2,5,4,6]=>010010=>010010=>101101
[3,7,1,2,5,6,4]=>010001=>100010=>011101
[3,7,1,2,6,4,5]=>010010=>010010=>101101
[3,7,1,2,6,5,4]=>010011=>110010=>001101
[3,7,1,4,2,5,6]=>010100=>001010=>110101
[3,7,1,4,2,6,5]=>010101=>101010=>010101
[3,7,1,4,5,2,6]=>010010=>010010=>101101
[3,7,1,4,5,6,2]=>010001=>100010=>011101
[3,7,1,4,6,2,5]=>010010=>010010=>101101
[3,7,1,4,6,5,2]=>010011=>110010=>001101
[3,7,1,5,2,4,6]=>010100=>001010=>110101
[3,7,1,5,2,6,4]=>010101=>101010=>010101
[3,7,1,5,4,2,6]=>010110=>011010=>100101
[3,7,1,5,4,6,2]=>010101=>101010=>010101
[3,7,1,5,6,2,4]=>010010=>010010=>101101
[3,7,1,5,6,4,2]=>010011=>110010=>001101
[3,7,1,6,2,4,5]=>010100=>001010=>110101
[3,7,1,6,2,5,4]=>010101=>101010=>010101
[3,7,1,6,4,2,5]=>010110=>011010=>100101
[3,7,1,6,4,5,2]=>010101=>101010=>010101
[3,7,1,6,5,2,4]=>010110=>011010=>100101
[3,7,1,6,5,4,2]=>010111=>111010=>000101
[3,7,2,1,4,5,6]=>011000=>000110=>111001
[3,7,2,1,4,6,5]=>011001=>100110=>011001
[3,7,2,1,5,4,6]=>011010=>010110=>101001
[3,7,2,1,5,6,4]=>011001=>100110=>011001
[3,7,2,1,6,4,5]=>011010=>010110=>101001
[3,7,2,1,6,5,4]=>011011=>110110=>001001
[3,7,2,4,1,5,6]=>010100=>001010=>110101
[3,7,2,4,1,6,5]=>010101=>101010=>010101
[3,7,2,4,5,1,6]=>010010=>010010=>101101
[3,7,2,4,5,6,1]=>010001=>100010=>011101
[3,7,2,4,6,1,5]=>010010=>010010=>101101
[3,7,2,4,6,5,1]=>010011=>110010=>001101
[3,7,2,5,1,4,6]=>010100=>001010=>110101
[3,7,2,5,1,6,4]=>010101=>101010=>010101
[3,7,2,5,4,1,6]=>010110=>011010=>100101
[3,7,2,5,4,6,1]=>010101=>101010=>010101
[3,7,2,5,6,1,4]=>010010=>010010=>101101
[3,7,2,5,6,4,1]=>010011=>110010=>001101
[3,7,2,6,1,4,5]=>010100=>001010=>110101
[3,7,2,6,1,5,4]=>010101=>101010=>010101
[3,7,2,6,4,1,5]=>010110=>011010=>100101
[3,7,2,6,4,5,1]=>010101=>101010=>010101
[3,7,2,6,5,1,4]=>010110=>011010=>100101
[3,7,2,6,5,4,1]=>010111=>111010=>000101
[3,7,4,1,2,5,6]=>011000=>000110=>111001
[3,7,4,1,2,6,5]=>011001=>100110=>011001
[3,7,4,1,5,2,6]=>011010=>010110=>101001
[3,7,4,1,5,6,2]=>011001=>100110=>011001
[3,7,4,1,6,2,5]=>011010=>010110=>101001
[3,7,4,1,6,5,2]=>011011=>110110=>001001
[3,7,4,2,1,5,6]=>011100=>001110=>110001
[3,7,4,2,1,6,5]=>011101=>101110=>010001
[3,7,4,2,5,1,6]=>011010=>010110=>101001
[3,7,4,2,5,6,1]=>011001=>100110=>011001
[3,7,4,2,6,1,5]=>011010=>010110=>101001
[3,7,4,2,6,5,1]=>011011=>110110=>001001
[3,7,4,5,1,2,6]=>010100=>001010=>110101
[3,7,4,5,1,6,2]=>010101=>101010=>010101
[3,7,4,5,2,1,6]=>010110=>011010=>100101
[3,7,4,5,2,6,1]=>010101=>101010=>010101
[3,7,4,5,6,1,2]=>010010=>010010=>101101
[3,7,4,5,6,2,1]=>010011=>110010=>001101
[3,7,4,6,1,2,5]=>010100=>001010=>110101
[3,7,4,6,1,5,2]=>010101=>101010=>010101
[3,7,4,6,2,1,5]=>010110=>011010=>100101
[3,7,4,6,2,5,1]=>010101=>101010=>010101
[3,7,4,6,5,1,2]=>010110=>011010=>100101
[3,7,4,6,5,2,1]=>010111=>111010=>000101
[3,7,5,1,2,4,6]=>011000=>000110=>111001
[3,7,5,1,2,6,4]=>011001=>100110=>011001
[3,7,5,1,4,2,6]=>011010=>010110=>101001
[3,7,5,1,4,6,2]=>011001=>100110=>011001
[3,7,5,1,6,2,4]=>011010=>010110=>101001
[3,7,5,1,6,4,2]=>011011=>110110=>001001
[3,7,5,2,1,4,6]=>011100=>001110=>110001
[3,7,5,2,1,6,4]=>011101=>101110=>010001
[3,7,5,2,4,1,6]=>011010=>010110=>101001
[3,7,5,2,4,6,1]=>011001=>100110=>011001
[3,7,5,2,6,1,4]=>011010=>010110=>101001
[3,7,5,2,6,4,1]=>011011=>110110=>001001
[3,7,5,4,1,2,6]=>011100=>001110=>110001
[3,7,5,4,1,6,2]=>011101=>101110=>010001
[3,7,5,4,2,1,6]=>011110=>011110=>100001
[3,7,5,4,2,6,1]=>011101=>101110=>010001
[3,7,5,4,6,1,2]=>011010=>010110=>101001
[3,7,5,4,6,2,1]=>011011=>110110=>001001
[3,7,5,6,1,2,4]=>010100=>001010=>110101
[3,7,5,6,1,4,2]=>010101=>101010=>010101
[3,7,5,6,2,1,4]=>010110=>011010=>100101
[3,7,5,6,2,4,1]=>010101=>101010=>010101
[3,7,5,6,4,1,2]=>010110=>011010=>100101
[3,7,5,6,4,2,1]=>010111=>111010=>000101
[3,7,6,1,2,4,5]=>011000=>000110=>111001
[3,7,6,1,2,5,4]=>011001=>100110=>011001
[3,7,6,1,4,2,5]=>011010=>010110=>101001
[3,7,6,1,4,5,2]=>011001=>100110=>011001
[3,7,6,1,5,2,4]=>011010=>010110=>101001
[3,7,6,1,5,4,2]=>011011=>110110=>001001
[3,7,6,2,1,4,5]=>011100=>001110=>110001
[3,7,6,2,1,5,4]=>011101=>101110=>010001
[3,7,6,2,4,1,5]=>011010=>010110=>101001
[3,7,6,2,4,5,1]=>011001=>100110=>011001
[3,7,6,2,5,1,4]=>011010=>010110=>101001
[3,7,6,2,5,4,1]=>011011=>110110=>001001
[3,7,6,4,1,2,5]=>011100=>001110=>110001
[3,7,6,4,1,5,2]=>011101=>101110=>010001
[3,7,6,4,2,1,5]=>011110=>011110=>100001
[3,7,6,4,2,5,1]=>011101=>101110=>010001
[3,7,6,4,5,1,2]=>011010=>010110=>101001
[3,7,6,4,5,2,1]=>011011=>110110=>001001
[3,7,6,5,1,2,4]=>011100=>001110=>110001
[3,7,6,5,1,4,2]=>011101=>101110=>010001
[3,7,6,5,2,1,4]=>011110=>011110=>100001
[3,7,6,5,2,4,1]=>011101=>101110=>010001
[3,7,6,5,4,1,2]=>011110=>011110=>100001
[3,7,6,5,4,2,1]=>011111=>111110=>000001
[4,1,2,3,5,6,7]=>100000=>000001=>111110
[4,1,2,3,5,7,6]=>100001=>100001=>011110
[4,1,2,3,6,5,7]=>100010=>010001=>101110
[4,1,2,3,6,7,5]=>100001=>100001=>011110
[4,1,2,3,7,5,6]=>100010=>010001=>101110
[4,1,2,3,7,6,5]=>100011=>110001=>001110
[4,1,2,5,3,6,7]=>100100=>001001=>110110
[4,1,2,5,3,7,6]=>100101=>101001=>010110
[4,1,2,5,6,3,7]=>100010=>010001=>101110
[4,1,2,5,6,7,3]=>100001=>100001=>011110
[4,1,2,5,7,3,6]=>100010=>010001=>101110
[4,1,2,5,7,6,3]=>100011=>110001=>001110
[4,1,2,6,3,5,7]=>100100=>001001=>110110
[4,1,2,6,3,7,5]=>100101=>101001=>010110
[4,1,2,6,5,3,7]=>100110=>011001=>100110
[4,1,2,6,5,7,3]=>100101=>101001=>010110
[4,1,2,6,7,3,5]=>100010=>010001=>101110
[4,1,2,6,7,5,3]=>100011=>110001=>001110
[4,1,2,7,3,5,6]=>100100=>001001=>110110
[4,1,2,7,3,6,5]=>100101=>101001=>010110
[4,1,2,7,5,3,6]=>100110=>011001=>100110
[4,1,2,7,5,6,3]=>100101=>101001=>010110
[4,1,2,7,6,3,5]=>100110=>011001=>100110
[4,1,2,7,6,5,3]=>100111=>111001=>000110
[4,1,3,2,5,6,7]=>101000=>000101=>111010
[4,1,3,2,5,7,6]=>101001=>100101=>011010
[4,1,3,2,6,5,7]=>101010=>010101=>101010
[4,1,3,2,6,7,5]=>101001=>100101=>011010
[4,1,3,2,7,5,6]=>101010=>010101=>101010
[4,1,3,2,7,6,5]=>101011=>110101=>001010
[4,1,3,5,2,6,7]=>100100=>001001=>110110
[4,1,3,5,2,7,6]=>100101=>101001=>010110
[4,1,3,5,6,2,7]=>100010=>010001=>101110
[4,1,3,5,6,7,2]=>100001=>100001=>011110
[4,1,3,5,7,2,6]=>100010=>010001=>101110
[4,1,3,5,7,6,2]=>100011=>110001=>001110
[4,1,3,6,2,5,7]=>100100=>001001=>110110
[4,1,3,6,2,7,5]=>100101=>101001=>010110
[4,1,3,6,5,2,7]=>100110=>011001=>100110
[4,1,3,6,5,7,2]=>100101=>101001=>010110
[4,1,3,6,7,2,5]=>100010=>010001=>101110
[4,1,3,6,7,5,2]=>100011=>110001=>001110
[4,1,3,7,2,5,6]=>100100=>001001=>110110
[4,1,3,7,2,6,5]=>100101=>101001=>010110
[4,1,3,7,5,2,6]=>100110=>011001=>100110
[4,1,3,7,5,6,2]=>100101=>101001=>010110
[4,1,3,7,6,2,5]=>100110=>011001=>100110
[4,1,3,7,6,5,2]=>100111=>111001=>000110
[4,1,5,2,3,6,7]=>101000=>000101=>111010
[4,1,5,2,3,7,6]=>101001=>100101=>011010
[4,1,5,2,6,3,7]=>101010=>010101=>101010
[4,1,5,2,6,7,3]=>101001=>100101=>011010
[4,1,5,2,7,3,6]=>101010=>010101=>101010
[4,1,5,2,7,6,3]=>101011=>110101=>001010
[4,1,5,3,2,6,7]=>101100=>001101=>110010
[4,1,5,3,2,7,6]=>101101=>101101=>010010
[4,1,5,3,6,2,7]=>101010=>010101=>101010
[4,1,5,3,6,7,2]=>101001=>100101=>011010
[4,1,5,3,7,2,6]=>101010=>010101=>101010
[4,1,5,3,7,6,2]=>101011=>110101=>001010
[4,1,5,6,2,3,7]=>100100=>001001=>110110
[4,1,5,6,2,7,3]=>100101=>101001=>010110
[4,1,5,6,3,2,7]=>100110=>011001=>100110
[4,1,5,6,3,7,2]=>100101=>101001=>010110
[4,1,5,6,7,2,3]=>100010=>010001=>101110
[4,1,5,6,7,3,2]=>100011=>110001=>001110
[4,1,5,7,2,3,6]=>100100=>001001=>110110
[4,1,5,7,2,6,3]=>100101=>101001=>010110
[4,1,5,7,3,2,6]=>100110=>011001=>100110
[4,1,5,7,3,6,2]=>100101=>101001=>010110
[4,1,5,7,6,2,3]=>100110=>011001=>100110
[4,1,5,7,6,3,2]=>100111=>111001=>000110
[4,1,6,2,3,5,7]=>101000=>000101=>111010
[4,1,6,2,3,7,5]=>101001=>100101=>011010
[4,1,6,2,5,3,7]=>101010=>010101=>101010
[4,1,6,2,5,7,3]=>101001=>100101=>011010
[4,1,6,2,7,3,5]=>101010=>010101=>101010
[4,1,6,2,7,5,3]=>101011=>110101=>001010
[4,1,6,3,2,5,7]=>101100=>001101=>110010
[4,1,6,3,2,7,5]=>101101=>101101=>010010
[4,1,6,3,5,2,7]=>101010=>010101=>101010
[4,1,6,3,5,7,2]=>101001=>100101=>011010
[4,1,6,3,7,2,5]=>101010=>010101=>101010
[4,1,6,3,7,5,2]=>101011=>110101=>001010
[4,1,6,5,2,3,7]=>101100=>001101=>110010
[4,1,6,5,2,7,3]=>101101=>101101=>010010
[4,1,6,5,3,2,7]=>101110=>011101=>100010
[4,1,6,5,3,7,2]=>101101=>101101=>010010
[4,1,6,5,7,2,3]=>101010=>010101=>101010
[4,1,6,5,7,3,2]=>101011=>110101=>001010
[4,1,6,7,2,3,5]=>100100=>001001=>110110
[4,1,6,7,2,5,3]=>100101=>101001=>010110
[4,1,6,7,3,2,5]=>100110=>011001=>100110
[4,1,6,7,3,5,2]=>100101=>101001=>010110
[4,1,6,7,5,2,3]=>100110=>011001=>100110
[4,1,6,7,5,3,2]=>100111=>111001=>000110
[4,1,7,2,3,5,6]=>101000=>000101=>111010
[4,1,7,2,3,6,5]=>101001=>100101=>011010
[4,1,7,2,5,3,6]=>101010=>010101=>101010
[4,1,7,2,5,6,3]=>101001=>100101=>011010
[4,1,7,2,6,3,5]=>101010=>010101=>101010
[4,1,7,2,6,5,3]=>101011=>110101=>001010
[4,1,7,3,2,5,6]=>101100=>001101=>110010
[4,1,7,3,2,6,5]=>101101=>101101=>010010
[4,1,7,3,5,2,6]=>101010=>010101=>101010
[4,1,7,3,5,6,2]=>101001=>100101=>011010
[4,1,7,3,6,2,5]=>101010=>010101=>101010
[4,1,7,3,6,5,2]=>101011=>110101=>001010
[4,1,7,5,2,3,6]=>101100=>001101=>110010
[4,1,7,5,2,6,3]=>101101=>101101=>010010
[4,1,7,5,3,2,6]=>101110=>011101=>100010
[4,1,7,5,3,6,2]=>101101=>101101=>010010
[4,1,7,5,6,2,3]=>101010=>010101=>101010
[4,1,7,5,6,3,2]=>101011=>110101=>001010
[4,1,7,6,2,3,5]=>101100=>001101=>110010
[4,1,7,6,2,5,3]=>101101=>101101=>010010
[4,1,7,6,3,2,5]=>101110=>011101=>100010
[4,1,7,6,3,5,2]=>101101=>101101=>010010
[4,1,7,6,5,2,3]=>101110=>011101=>100010
[4,1,7,6,5,3,2]=>101111=>111101=>000010
[4,2,1,3,5,6,7]=>110000=>000011=>111100
[4,2,1,3,5,7,6]=>110001=>100011=>011100
[4,2,1,3,6,5,7]=>110010=>010011=>101100
[4,2,1,3,6,7,5]=>110001=>100011=>011100
[4,2,1,3,7,5,6]=>110010=>010011=>101100
[4,2,1,3,7,6,5]=>110011=>110011=>001100
[4,2,1,5,3,6,7]=>110100=>001011=>110100
[4,2,1,5,3,7,6]=>110101=>101011=>010100
[4,2,1,5,6,3,7]=>110010=>010011=>101100
[4,2,1,5,6,7,3]=>110001=>100011=>011100
[4,2,1,5,7,3,6]=>110010=>010011=>101100
[4,2,1,5,7,6,3]=>110011=>110011=>001100
[4,2,1,6,3,5,7]=>110100=>001011=>110100
[4,2,1,6,3,7,5]=>110101=>101011=>010100
[4,2,1,6,5,3,7]=>110110=>011011=>100100
[4,2,1,6,5,7,3]=>110101=>101011=>010100
[4,2,1,6,7,3,5]=>110010=>010011=>101100
[4,2,1,6,7,5,3]=>110011=>110011=>001100
[4,2,1,7,3,5,6]=>110100=>001011=>110100
[4,2,1,7,3,6,5]=>110101=>101011=>010100
[4,2,1,7,5,3,6]=>110110=>011011=>100100
[4,2,1,7,5,6,3]=>110101=>101011=>010100
[4,2,1,7,6,3,5]=>110110=>011011=>100100
[4,2,1,7,6,5,3]=>110111=>111011=>000100
[4,2,3,1,5,6,7]=>101000=>000101=>111010
[4,2,3,1,5,7,6]=>101001=>100101=>011010
[4,2,3,1,6,5,7]=>101010=>010101=>101010
[4,2,3,1,6,7,5]=>101001=>100101=>011010
[4,2,3,1,7,5,6]=>101010=>010101=>101010
[4,2,3,1,7,6,5]=>101011=>110101=>001010
[4,2,3,5,1,6,7]=>100100=>001001=>110110
[4,2,3,5,1,7,6]=>100101=>101001=>010110
[4,2,3,5,6,1,7]=>100010=>010001=>101110
[4,2,3,5,6,7,1]=>100001=>100001=>011110
[4,2,3,5,7,1,6]=>100010=>010001=>101110
[4,2,3,5,7,6,1]=>100011=>110001=>001110
[4,2,3,6,1,5,7]=>100100=>001001=>110110
[4,2,3,6,1,7,5]=>100101=>101001=>010110
[4,2,3,6,5,1,7]=>100110=>011001=>100110
[4,2,3,6,5,7,1]=>100101=>101001=>010110
[4,2,3,6,7,1,5]=>100010=>010001=>101110
[4,2,3,6,7,5,1]=>100011=>110001=>001110
[4,2,3,7,1,5,6]=>100100=>001001=>110110
[4,2,3,7,1,6,5]=>100101=>101001=>010110
[4,2,3,7,5,1,6]=>100110=>011001=>100110
[4,2,3,7,5,6,1]=>100101=>101001=>010110
[4,2,3,7,6,1,5]=>100110=>011001=>100110
[4,2,3,7,6,5,1]=>100111=>111001=>000110
[4,2,5,1,3,6,7]=>101000=>000101=>111010
[4,2,5,1,3,7,6]=>101001=>100101=>011010
[4,2,5,1,6,3,7]=>101010=>010101=>101010
[4,2,5,1,6,7,3]=>101001=>100101=>011010
[4,2,5,1,7,3,6]=>101010=>010101=>101010
[4,2,5,1,7,6,3]=>101011=>110101=>001010
[4,2,5,3,1,6,7]=>101100=>001101=>110010
[4,2,5,3,1,7,6]=>101101=>101101=>010010
[4,2,5,3,6,1,7]=>101010=>010101=>101010
[4,2,5,3,6,7,1]=>101001=>100101=>011010
[4,2,5,3,7,1,6]=>101010=>010101=>101010
[4,2,5,3,7,6,1]=>101011=>110101=>001010
[4,2,5,6,1,3,7]=>100100=>001001=>110110
[4,2,5,6,1,7,3]=>100101=>101001=>010110
[4,2,5,6,3,1,7]=>100110=>011001=>100110
[4,2,5,6,3,7,1]=>100101=>101001=>010110
[4,2,5,6,7,1,3]=>100010=>010001=>101110
[4,2,5,6,7,3,1]=>100011=>110001=>001110
[4,2,5,7,1,3,6]=>100100=>001001=>110110
[4,2,5,7,1,6,3]=>100101=>101001=>010110
[4,2,5,7,3,1,6]=>100110=>011001=>100110
[4,2,5,7,3,6,1]=>100101=>101001=>010110
[4,2,5,7,6,1,3]=>100110=>011001=>100110
[4,2,5,7,6,3,1]=>100111=>111001=>000110
[4,2,6,1,3,5,7]=>101000=>000101=>111010
[4,2,6,1,3,7,5]=>101001=>100101=>011010
[4,2,6,1,5,3,7]=>101010=>010101=>101010
[4,2,6,1,5,7,3]=>101001=>100101=>011010
[4,2,6,1,7,3,5]=>101010=>010101=>101010
[4,2,6,1,7,5,3]=>101011=>110101=>001010
[4,2,6,3,1,5,7]=>101100=>001101=>110010
[4,2,6,3,1,7,5]=>101101=>101101=>010010
[4,2,6,3,5,1,7]=>101010=>010101=>101010
[4,2,6,3,5,7,1]=>101001=>100101=>011010
[4,2,6,3,7,1,5]=>101010=>010101=>101010
[4,2,6,3,7,5,1]=>101011=>110101=>001010
[4,2,6,5,1,3,7]=>101100=>001101=>110010
[4,2,6,5,1,7,3]=>101101=>101101=>010010
[4,2,6,5,3,1,7]=>101110=>011101=>100010
[4,2,6,5,3,7,1]=>101101=>101101=>010010
[4,2,6,5,7,1,3]=>101010=>010101=>101010
[4,2,6,5,7,3,1]=>101011=>110101=>001010
[4,2,6,7,1,3,5]=>100100=>001001=>110110
[4,2,6,7,1,5,3]=>100101=>101001=>010110
[4,2,6,7,3,1,5]=>100110=>011001=>100110
[4,2,6,7,3,5,1]=>100101=>101001=>010110
[4,2,6,7,5,1,3]=>100110=>011001=>100110
[4,2,6,7,5,3,1]=>100111=>111001=>000110
[4,2,7,1,3,5,6]=>101000=>000101=>111010
[4,2,7,1,3,6,5]=>101001=>100101=>011010
[4,2,7,1,5,3,6]=>101010=>010101=>101010
[4,2,7,1,5,6,3]=>101001=>100101=>011010
[4,2,7,1,6,3,5]=>101010=>010101=>101010
[4,2,7,1,6,5,3]=>101011=>110101=>001010
[4,2,7,3,1,5,6]=>101100=>001101=>110010
[4,2,7,3,1,6,5]=>101101=>101101=>010010
[4,2,7,3,5,1,6]=>101010=>010101=>101010
[4,2,7,3,5,6,1]=>101001=>100101=>011010
[4,2,7,3,6,1,5]=>101010=>010101=>101010
[4,2,7,3,6,5,1]=>101011=>110101=>001010
[4,2,7,5,1,3,6]=>101100=>001101=>110010
[4,2,7,5,1,6,3]=>101101=>101101=>010010
[4,2,7,5,3,1,6]=>101110=>011101=>100010
[4,2,7,5,3,6,1]=>101101=>101101=>010010
[4,2,7,5,6,1,3]=>101010=>010101=>101010
[4,2,7,5,6,3,1]=>101011=>110101=>001010
[4,2,7,6,1,3,5]=>101100=>001101=>110010
[4,2,7,6,1,5,3]=>101101=>101101=>010010
[4,2,7,6,3,1,5]=>101110=>011101=>100010
[4,2,7,6,3,5,1]=>101101=>101101=>010010
[4,2,7,6,5,1,3]=>101110=>011101=>100010
[4,2,7,6,5,3,1]=>101111=>111101=>000010
[4,3,1,2,5,6,7]=>110000=>000011=>111100
[4,3,1,2,5,7,6]=>110001=>100011=>011100
[4,3,1,2,6,5,7]=>110010=>010011=>101100
[4,3,1,2,6,7,5]=>110001=>100011=>011100
[4,3,1,2,7,5,6]=>110010=>010011=>101100
[4,3,1,2,7,6,5]=>110011=>110011=>001100
[4,3,1,5,2,6,7]=>110100=>001011=>110100
[4,3,1,5,2,7,6]=>110101=>101011=>010100
[4,3,1,5,6,2,7]=>110010=>010011=>101100
[4,3,1,5,6,7,2]=>110001=>100011=>011100
[4,3,1,5,7,2,6]=>110010=>010011=>101100
[4,3,1,5,7,6,2]=>110011=>110011=>001100
[4,3,1,6,2,5,7]=>110100=>001011=>110100
[4,3,1,6,2,7,5]=>110101=>101011=>010100
[4,3,1,6,5,2,7]=>110110=>011011=>100100
[4,3,1,6,5,7,2]=>110101=>101011=>010100
[4,3,1,6,7,2,5]=>110010=>010011=>101100
[4,3,1,6,7,5,2]=>110011=>110011=>001100
[4,3,1,7,2,5,6]=>110100=>001011=>110100
[4,3,1,7,2,6,5]=>110101=>101011=>010100
[4,3,1,7,5,2,6]=>110110=>011011=>100100
[4,3,1,7,5,6,2]=>110101=>101011=>010100
[4,3,1,7,6,2,5]=>110110=>011011=>100100
[4,3,1,7,6,5,2]=>110111=>111011=>000100
[4,3,2,1,5,6,7]=>111000=>000111=>111000
[4,3,2,1,5,7,6]=>111001=>100111=>011000
[4,3,2,1,6,5,7]=>111010=>010111=>101000
[4,3,2,1,6,7,5]=>111001=>100111=>011000
[4,3,2,1,7,5,6]=>111010=>010111=>101000
[4,3,2,1,7,6,5]=>111011=>110111=>001000
[4,3,2,5,1,6,7]=>110100=>001011=>110100
[4,3,2,5,1,7,6]=>110101=>101011=>010100
[4,3,2,5,6,1,7]=>110010=>010011=>101100
[4,3,2,5,6,7,1]=>110001=>100011=>011100
[4,3,2,5,7,1,6]=>110010=>010011=>101100
[4,3,2,5,7,6,1]=>110011=>110011=>001100
[4,3,2,6,1,5,7]=>110100=>001011=>110100
[4,3,2,6,1,7,5]=>110101=>101011=>010100
[4,3,2,6,5,1,7]=>110110=>011011=>100100
[4,3,2,6,5,7,1]=>110101=>101011=>010100
[4,3,2,6,7,1,5]=>110010=>010011=>101100
[4,3,2,6,7,5,1]=>110011=>110011=>001100
[4,3,2,7,1,5,6]=>110100=>001011=>110100
[4,3,2,7,1,6,5]=>110101=>101011=>010100
[4,3,2,7,5,1,6]=>110110=>011011=>100100
[4,3,2,7,5,6,1]=>110101=>101011=>010100
[4,3,2,7,6,1,5]=>110110=>011011=>100100
[4,3,2,7,6,5,1]=>110111=>111011=>000100
[4,3,5,1,2,6,7]=>101000=>000101=>111010
[4,3,5,1,2,7,6]=>101001=>100101=>011010
[4,3,5,1,6,2,7]=>101010=>010101=>101010
[4,3,5,1,6,7,2]=>101001=>100101=>011010
[4,3,5,1,7,2,6]=>101010=>010101=>101010
[4,3,5,1,7,6,2]=>101011=>110101=>001010
[4,3,5,2,1,6,7]=>101100=>001101=>110010
[4,3,5,2,1,7,6]=>101101=>101101=>010010
[4,3,5,2,6,1,7]=>101010=>010101=>101010
[4,3,5,2,6,7,1]=>101001=>100101=>011010
[4,3,5,2,7,1,6]=>101010=>010101=>101010
[4,3,5,2,7,6,1]=>101011=>110101=>001010
[4,3,5,6,1,2,7]=>100100=>001001=>110110
[4,3,5,6,1,7,2]=>100101=>101001=>010110
[4,3,5,6,2,1,7]=>100110=>011001=>100110
[4,3,5,6,2,7,1]=>100101=>101001=>010110
[4,3,5,6,7,1,2]=>100010=>010001=>101110
[4,3,5,6,7,2,1]=>100011=>110001=>001110
[4,3,5,7,1,2,6]=>100100=>001001=>110110
[4,3,5,7,1,6,2]=>100101=>101001=>010110
[4,3,5,7,2,1,6]=>100110=>011001=>100110
[4,3,5,7,2,6,1]=>100101=>101001=>010110
[4,3,5,7,6,1,2]=>100110=>011001=>100110
[4,3,5,7,6,2,1]=>100111=>111001=>000110
[4,3,6,1,2,5,7]=>101000=>000101=>111010
[4,3,6,1,2,7,5]=>101001=>100101=>011010
[4,3,6,1,5,2,7]=>101010=>010101=>101010
[4,3,6,1,5,7,2]=>101001=>100101=>011010
[4,3,6,1,7,2,5]=>101010=>010101=>101010
[4,3,6,1,7,5,2]=>101011=>110101=>001010
[4,3,6,2,1,5,7]=>101100=>001101=>110010
[4,3,6,2,1,7,5]=>101101=>101101=>010010
[4,3,6,2,5,1,7]=>101010=>010101=>101010
[4,3,6,2,5,7,1]=>101001=>100101=>011010
[4,3,6,2,7,1,5]=>101010=>010101=>101010
[4,3,6,2,7,5,1]=>101011=>110101=>001010
[4,3,6,5,1,2,7]=>101100=>001101=>110010
[4,3,6,5,1,7,2]=>101101=>101101=>010010
[4,3,6,5,2,1,7]=>101110=>011101=>100010
[4,3,6,5,2,7,1]=>101101=>101101=>010010
[4,3,6,5,7,1,2]=>101010=>010101=>101010
[4,3,6,5,7,2,1]=>101011=>110101=>001010
[4,3,6,7,1,2,5]=>100100=>001001=>110110
[4,3,6,7,1,5,2]=>100101=>101001=>010110
[4,3,6,7,2,1,5]=>100110=>011001=>100110
[4,3,6,7,2,5,1]=>100101=>101001=>010110
[4,3,6,7,5,1,2]=>100110=>011001=>100110
[4,3,6,7,5,2,1]=>100111=>111001=>000110
[4,3,7,1,2,5,6]=>101000=>000101=>111010
[4,3,7,1,2,6,5]=>101001=>100101=>011010
[4,3,7,1,5,2,6]=>101010=>010101=>101010
[4,3,7,1,5,6,2]=>101001=>100101=>011010
[4,3,7,1,6,2,5]=>101010=>010101=>101010
[4,3,7,1,6,5,2]=>101011=>110101=>001010
[4,3,7,2,1,5,6]=>101100=>001101=>110010
[4,3,7,2,1,6,5]=>101101=>101101=>010010
[4,3,7,2,5,1,6]=>101010=>010101=>101010
[4,3,7,2,5,6,1]=>101001=>100101=>011010
[4,3,7,2,6,1,5]=>101010=>010101=>101010
[4,3,7,2,6,5,1]=>101011=>110101=>001010
[4,3,7,5,1,2,6]=>101100=>001101=>110010
[4,3,7,5,1,6,2]=>101101=>101101=>010010
[4,3,7,5,2,1,6]=>101110=>011101=>100010
[4,3,7,5,2,6,1]=>101101=>101101=>010010
[4,3,7,5,6,1,2]=>101010=>010101=>101010
[4,3,7,5,6,2,1]=>101011=>110101=>001010
[4,3,7,6,1,2,5]=>101100=>001101=>110010
[4,3,7,6,1,5,2]=>101101=>101101=>010010
[4,3,7,6,2,1,5]=>101110=>011101=>100010
[4,3,7,6,2,5,1]=>101101=>101101=>010010
[4,3,7,6,5,1,2]=>101110=>011101=>100010
[4,3,7,6,5,2,1]=>101111=>111101=>000010
[4,5,1,2,3,6,7]=>010000=>000010=>111101
[4,5,1,2,3,7,6]=>010001=>100010=>011101
[4,5,1,2,6,3,7]=>010010=>010010=>101101
[4,5,1,2,6,7,3]=>010001=>100010=>011101
[4,5,1,2,7,3,6]=>010010=>010010=>101101
[4,5,1,2,7,6,3]=>010011=>110010=>001101
[4,5,1,3,2,6,7]=>010100=>001010=>110101
[4,5,1,3,2,7,6]=>010101=>101010=>010101
[4,5,1,3,6,2,7]=>010010=>010010=>101101
[4,5,1,3,6,7,2]=>010001=>100010=>011101
[4,5,1,3,7,2,6]=>010010=>010010=>101101
[4,5,1,3,7,6,2]=>010011=>110010=>001101
[4,5,1,6,2,3,7]=>010100=>001010=>110101
[4,5,1,6,2,7,3]=>010101=>101010=>010101
[4,5,1,6,3,2,7]=>010110=>011010=>100101
[4,5,1,6,3,7,2]=>010101=>101010=>010101
[4,5,1,6,7,2,3]=>010010=>010010=>101101
[4,5,1,6,7,3,2]=>010011=>110010=>001101
[4,5,1,7,2,3,6]=>010100=>001010=>110101
[4,5,1,7,2,6,3]=>010101=>101010=>010101
[4,5,1,7,3,2,6]=>010110=>011010=>100101
[4,5,1,7,3,6,2]=>010101=>101010=>010101
[4,5,1,7,6,2,3]=>010110=>011010=>100101
[4,5,1,7,6,3,2]=>010111=>111010=>000101
[4,5,2,1,3,6,7]=>011000=>000110=>111001
[4,5,2,1,3,7,6]=>011001=>100110=>011001
[4,5,2,1,6,3,7]=>011010=>010110=>101001
[4,5,2,1,6,7,3]=>011001=>100110=>011001
[4,5,2,1,7,3,6]=>011010=>010110=>101001
[4,5,2,1,7,6,3]=>011011=>110110=>001001
[4,5,2,3,1,6,7]=>010100=>001010=>110101
[4,5,2,3,1,7,6]=>010101=>101010=>010101
[4,5,2,3,6,1,7]=>010010=>010010=>101101
[4,5,2,3,6,7,1]=>010001=>100010=>011101
[4,5,2,3,7,1,6]=>010010=>010010=>101101
[4,5,2,3,7,6,1]=>010011=>110010=>001101
[4,5,2,6,1,3,7]=>010100=>001010=>110101
[4,5,2,6,1,7,3]=>010101=>101010=>010101
[4,5,2,6,3,1,7]=>010110=>011010=>100101
[4,5,2,6,3,7,1]=>010101=>101010=>010101
[4,5,2,6,7,1,3]=>010010=>010010=>101101
[4,5,2,6,7,3,1]=>010011=>110010=>001101
[4,5,2,7,1,3,6]=>010100=>001010=>110101
[4,5,2,7,1,6,3]=>010101=>101010=>010101
[4,5,2,7,3,1,6]=>010110=>011010=>100101
[4,5,2,7,3,6,1]=>010101=>101010=>010101
[4,5,2,7,6,1,3]=>010110=>011010=>100101
[4,5,2,7,6,3,1]=>010111=>111010=>000101
[4,5,3,1,2,6,7]=>011000=>000110=>111001
[4,5,3,1,2,7,6]=>011001=>100110=>011001
[4,5,3,1,6,2,7]=>011010=>010110=>101001
[4,5,3,1,6,7,2]=>011001=>100110=>011001
[4,5,3,1,7,2,6]=>011010=>010110=>101001
[4,5,3,1,7,6,2]=>011011=>110110=>001001
[4,5,3,2,1,6,7]=>011100=>001110=>110001
[4,5,3,2,1,7,6]=>011101=>101110=>010001
[4,5,3,2,6,1,7]=>011010=>010110=>101001
[4,5,3,2,6,7,1]=>011001=>100110=>011001
[4,5,3,2,7,1,6]=>011010=>010110=>101001
[4,5,3,2,7,6,1]=>011011=>110110=>001001
[4,5,3,6,1,2,7]=>010100=>001010=>110101
[4,5,3,6,1,7,2]=>010101=>101010=>010101
[4,5,3,6,2,1,7]=>010110=>011010=>100101
[4,5,3,6,2,7,1]=>010101=>101010=>010101
[4,5,3,6,7,1,2]=>010010=>010010=>101101
[4,5,3,6,7,2,1]=>010011=>110010=>001101
[4,5,3,7,1,2,6]=>010100=>001010=>110101
[4,5,3,7,1,6,2]=>010101=>101010=>010101
[4,5,3,7,2,1,6]=>010110=>011010=>100101
[4,5,3,7,2,6,1]=>010101=>101010=>010101
[4,5,3,7,6,1,2]=>010110=>011010=>100101
[4,5,3,7,6,2,1]=>010111=>111010=>000101
[4,5,6,1,2,3,7]=>001000=>000100=>111011
[4,5,6,1,2,7,3]=>001001=>100100=>011011
[4,5,6,1,3,2,7]=>001010=>010100=>101011
[4,5,6,1,3,7,2]=>001001=>100100=>011011
[4,5,6,1,7,2,3]=>001010=>010100=>101011
[4,5,6,1,7,3,2]=>001011=>110100=>001011
[4,5,6,2,1,3,7]=>001100=>001100=>110011
[4,5,6,2,1,7,3]=>001101=>101100=>010011
[4,5,6,2,3,1,7]=>001010=>010100=>101011
[4,5,6,2,3,7,1]=>001001=>100100=>011011
[4,5,6,2,7,1,3]=>001010=>010100=>101011
[4,5,6,2,7,3,1]=>001011=>110100=>001011
[4,5,6,3,1,2,7]=>001100=>001100=>110011
[4,5,6,3,1,7,2]=>001101=>101100=>010011
[4,5,6,3,2,1,7]=>001110=>011100=>100011
[4,5,6,3,2,7,1]=>001101=>101100=>010011
[4,5,6,3,7,1,2]=>001010=>010100=>101011
[4,5,6,3,7,2,1]=>001011=>110100=>001011
[4,5,6,7,1,2,3]=>000100=>001000=>110111
[4,5,6,7,1,3,2]=>000101=>101000=>010111
[4,5,6,7,2,1,3]=>000110=>011000=>100111
[4,5,6,7,2,3,1]=>000101=>101000=>010111
[4,5,6,7,3,1,2]=>000110=>011000=>100111
[4,5,6,7,3,2,1]=>000111=>111000=>000111
[4,5,7,1,2,3,6]=>001000=>000100=>111011
[4,5,7,1,2,6,3]=>001001=>100100=>011011
[4,5,7,1,3,2,6]=>001010=>010100=>101011
[4,5,7,1,3,6,2]=>001001=>100100=>011011
[4,5,7,1,6,2,3]=>001010=>010100=>101011
[4,5,7,1,6,3,2]=>001011=>110100=>001011
[4,5,7,2,1,3,6]=>001100=>001100=>110011
[4,5,7,2,1,6,3]=>001101=>101100=>010011
[4,5,7,2,3,1,6]=>001010=>010100=>101011
[4,5,7,2,3,6,1]=>001001=>100100=>011011
[4,5,7,2,6,1,3]=>001010=>010100=>101011
[4,5,7,2,6,3,1]=>001011=>110100=>001011
[4,5,7,3,1,2,6]=>001100=>001100=>110011
[4,5,7,3,1,6,2]=>001101=>101100=>010011
[4,5,7,3,2,1,6]=>001110=>011100=>100011
[4,5,7,3,2,6,1]=>001101=>101100=>010011
[4,5,7,3,6,1,2]=>001010=>010100=>101011
[4,5,7,3,6,2,1]=>001011=>110100=>001011
[4,5,7,6,1,2,3]=>001100=>001100=>110011
[4,5,7,6,1,3,2]=>001101=>101100=>010011
[4,5,7,6,2,1,3]=>001110=>011100=>100011
[4,5,7,6,2,3,1]=>001101=>101100=>010011
[4,5,7,6,3,1,2]=>001110=>011100=>100011
[4,5,7,6,3,2,1]=>001111=>111100=>000011
[4,6,1,2,3,5,7]=>010000=>000010=>111101
[4,6,1,2,3,7,5]=>010001=>100010=>011101
[4,6,1,2,5,3,7]=>010010=>010010=>101101
[4,6,1,2,5,7,3]=>010001=>100010=>011101
[4,6,1,2,7,3,5]=>010010=>010010=>101101
[4,6,1,2,7,5,3]=>010011=>110010=>001101
[4,6,1,3,2,5,7]=>010100=>001010=>110101
[4,6,1,3,2,7,5]=>010101=>101010=>010101
[4,6,1,3,5,2,7]=>010010=>010010=>101101
[4,6,1,3,5,7,2]=>010001=>100010=>011101
[4,6,1,3,7,2,5]=>010010=>010010=>101101
[4,6,1,3,7,5,2]=>010011=>110010=>001101
[4,6,1,5,2,3,7]=>010100=>001010=>110101
[4,6,1,5,2,7,3]=>010101=>101010=>010101
[4,6,1,5,3,2,7]=>010110=>011010=>100101
[4,6,1,5,3,7,2]=>010101=>101010=>010101
[4,6,1,5,7,2,3]=>010010=>010010=>101101
[4,6,1,5,7,3,2]=>010011=>110010=>001101
[4,6,1,7,2,3,5]=>010100=>001010=>110101
[4,6,1,7,2,5,3]=>010101=>101010=>010101
[4,6,1,7,3,2,5]=>010110=>011010=>100101
[4,6,1,7,3,5,2]=>010101=>101010=>010101
[4,6,1,7,5,2,3]=>010110=>011010=>100101
[4,6,1,7,5,3,2]=>010111=>111010=>000101
[4,6,2,1,3,5,7]=>011000=>000110=>111001
[4,6,2,1,3,7,5]=>011001=>100110=>011001
[4,6,2,1,5,3,7]=>011010=>010110=>101001
[4,6,2,1,5,7,3]=>011001=>100110=>011001
[4,6,2,1,7,3,5]=>011010=>010110=>101001
[4,6,2,1,7,5,3]=>011011=>110110=>001001
[4,6,2,3,1,5,7]=>010100=>001010=>110101
[4,6,2,3,1,7,5]=>010101=>101010=>010101
[4,6,2,3,5,1,7]=>010010=>010010=>101101
[4,6,2,3,5,7,1]=>010001=>100010=>011101
[4,6,2,3,7,1,5]=>010010=>010010=>101101
[4,6,2,3,7,5,1]=>010011=>110010=>001101
[4,6,2,5,1,3,7]=>010100=>001010=>110101
[4,6,2,5,1,7,3]=>010101=>101010=>010101
[4,6,2,5,3,1,7]=>010110=>011010=>100101
[4,6,2,5,3,7,1]=>010101=>101010=>010101
[4,6,2,5,7,1,3]=>010010=>010010=>101101
[4,6,2,5,7,3,1]=>010011=>110010=>001101
[4,6,2,7,1,3,5]=>010100=>001010=>110101
[4,6,2,7,1,5,3]=>010101=>101010=>010101
[4,6,2,7,3,1,5]=>010110=>011010=>100101
[4,6,2,7,3,5,1]=>010101=>101010=>010101
[4,6,2,7,5,1,3]=>010110=>011010=>100101
[4,6,2,7,5,3,1]=>010111=>111010=>000101
[4,6,3,1,2,5,7]=>011000=>000110=>111001
[4,6,3,1,2,7,5]=>011001=>100110=>011001
[4,6,3,1,5,2,7]=>011010=>010110=>101001
[4,6,3,1,5,7,2]=>011001=>100110=>011001
[4,6,3,1,7,2,5]=>011010=>010110=>101001
[4,6,3,1,7,5,2]=>011011=>110110=>001001
[4,6,3,2,1,5,7]=>011100=>001110=>110001
[4,6,3,2,1,7,5]=>011101=>101110=>010001
[4,6,3,2,5,1,7]=>011010=>010110=>101001
[4,6,3,2,5,7,1]=>011001=>100110=>011001
[4,6,3,2,7,1,5]=>011010=>010110=>101001
[4,6,3,2,7,5,1]=>011011=>110110=>001001
[4,6,3,5,1,2,7]=>010100=>001010=>110101
[4,6,3,5,1,7,2]=>010101=>101010=>010101
[4,6,3,5,2,1,7]=>010110=>011010=>100101
[4,6,3,5,2,7,1]=>010101=>101010=>010101
[4,6,3,5,7,1,2]=>010010=>010010=>101101
[4,6,3,5,7,2,1]=>010011=>110010=>001101
[4,6,3,7,1,2,5]=>010100=>001010=>110101
[4,6,3,7,1,5,2]=>010101=>101010=>010101
[4,6,3,7,2,1,5]=>010110=>011010=>100101
[4,6,3,7,2,5,1]=>010101=>101010=>010101
[4,6,3,7,5,1,2]=>010110=>011010=>100101
[4,6,3,7,5,2,1]=>010111=>111010=>000101
[4,6,5,1,2,3,7]=>011000=>000110=>111001
[4,6,5,1,2,7,3]=>011001=>100110=>011001
[4,6,5,1,3,2,7]=>011010=>010110=>101001
[4,6,5,1,3,7,2]=>011001=>100110=>011001
[4,6,5,1,7,2,3]=>011010=>010110=>101001
[4,6,5,1,7,3,2]=>011011=>110110=>001001
[4,6,5,2,1,3,7]=>011100=>001110=>110001
[4,6,5,2,1,7,3]=>011101=>101110=>010001
[4,6,5,2,3,1,7]=>011010=>010110=>101001
[4,6,5,2,3,7,1]=>011001=>100110=>011001
[4,6,5,2,7,1,3]=>011010=>010110=>101001
[4,6,5,2,7,3,1]=>011011=>110110=>001001
[4,6,5,3,1,2,7]=>011100=>001110=>110001
[4,6,5,3,1,7,2]=>011101=>101110=>010001
[4,6,5,3,2,1,7]=>011110=>011110=>100001
[4,6,5,3,2,7,1]=>011101=>101110=>010001
[4,6,5,3,7,1,2]=>011010=>010110=>101001
[4,6,5,3,7,2,1]=>011011=>110110=>001001
[4,6,5,7,1,2,3]=>010100=>001010=>110101
[4,6,5,7,1,3,2]=>010101=>101010=>010101
[4,6,5,7,2,1,3]=>010110=>011010=>100101
[4,6,5,7,2,3,1]=>010101=>101010=>010101
[4,6,5,7,3,1,2]=>010110=>011010=>100101
[4,6,5,7,3,2,1]=>010111=>111010=>000101
[4,6,7,1,2,3,5]=>001000=>000100=>111011
[4,6,7,1,2,5,3]=>001001=>100100=>011011
[4,6,7,1,3,2,5]=>001010=>010100=>101011
[4,6,7,1,3,5,2]=>001001=>100100=>011011
[4,6,7,1,5,2,3]=>001010=>010100=>101011
[4,6,7,1,5,3,2]=>001011=>110100=>001011
[4,6,7,2,1,3,5]=>001100=>001100=>110011
[4,6,7,2,1,5,3]=>001101=>101100=>010011
[4,6,7,2,3,1,5]=>001010=>010100=>101011
[4,6,7,2,3,5,1]=>001001=>100100=>011011
[4,6,7,2,5,1,3]=>001010=>010100=>101011
[4,6,7,2,5,3,1]=>001011=>110100=>001011
[4,6,7,3,1,2,5]=>001100=>001100=>110011
[4,6,7,3,1,5,2]=>001101=>101100=>010011
[4,6,7,3,2,1,5]=>001110=>011100=>100011
[4,6,7,3,2,5,1]=>001101=>101100=>010011
[4,6,7,3,5,1,2]=>001010=>010100=>101011
[4,6,7,3,5,2,1]=>001011=>110100=>001011
[4,6,7,5,1,2,3]=>001100=>001100=>110011
[4,6,7,5,1,3,2]=>001101=>101100=>010011
[4,6,7,5,2,1,3]=>001110=>011100=>100011
[4,6,7,5,2,3,1]=>001101=>101100=>010011
[4,6,7,5,3,1,2]=>001110=>011100=>100011
[4,6,7,5,3,2,1]=>001111=>111100=>000011
[4,7,1,2,3,5,6]=>010000=>000010=>111101
[4,7,1,2,3,6,5]=>010001=>100010=>011101
[4,7,1,2,5,3,6]=>010010=>010010=>101101
[4,7,1,2,5,6,3]=>010001=>100010=>011101
[4,7,1,2,6,3,5]=>010010=>010010=>101101
[4,7,1,2,6,5,3]=>010011=>110010=>001101
[4,7,1,3,2,5,6]=>010100=>001010=>110101
[4,7,1,3,2,6,5]=>010101=>101010=>010101
[4,7,1,3,5,2,6]=>010010=>010010=>101101
[4,7,1,3,5,6,2]=>010001=>100010=>011101
[4,7,1,3,6,2,5]=>010010=>010010=>101101
[4,7,1,3,6,5,2]=>010011=>110010=>001101
[4,7,1,5,2,3,6]=>010100=>001010=>110101
[4,7,1,5,2,6,3]=>010101=>101010=>010101
[4,7,1,5,3,2,6]=>010110=>011010=>100101
[4,7,1,5,3,6,2]=>010101=>101010=>010101
[4,7,1,5,6,2,3]=>010010=>010010=>101101
[4,7,1,5,6,3,2]=>010011=>110010=>001101
[4,7,1,6,2,3,5]=>010100=>001010=>110101
[4,7,1,6,2,5,3]=>010101=>101010=>010101
[4,7,1,6,3,2,5]=>010110=>011010=>100101
[4,7,1,6,3,5,2]=>010101=>101010=>010101
[4,7,1,6,5,2,3]=>010110=>011010=>100101
[4,7,1,6,5,3,2]=>010111=>111010=>000101
[4,7,2,1,3,5,6]=>011000=>000110=>111001
[4,7,2,1,3,6,5]=>011001=>100110=>011001
[4,7,2,1,5,3,6]=>011010=>010110=>101001
[4,7,2,1,5,6,3]=>011001=>100110=>011001
[4,7,2,1,6,3,5]=>011010=>010110=>101001
[4,7,2,1,6,5,3]=>011011=>110110=>001001
[4,7,2,3,1,5,6]=>010100=>001010=>110101
[4,7,2,3,1,6,5]=>010101=>101010=>010101
[4,7,2,3,5,1,6]=>010010=>010010=>101101
[4,7,2,3,5,6,1]=>010001=>100010=>011101
[4,7,2,3,6,1,5]=>010010=>010010=>101101
[4,7,2,3,6,5,1]=>010011=>110010=>001101
[4,7,2,5,1,3,6]=>010100=>001010=>110101
[4,7,2,5,1,6,3]=>010101=>101010=>010101
[4,7,2,5,3,1,6]=>010110=>011010=>100101
[4,7,2,5,3,6,1]=>010101=>101010=>010101
[4,7,2,5,6,1,3]=>010010=>010010=>101101
[4,7,2,5,6,3,1]=>010011=>110010=>001101
[4,7,2,6,1,3,5]=>010100=>001010=>110101
[4,7,2,6,1,5,3]=>010101=>101010=>010101
[4,7,2,6,3,1,5]=>010110=>011010=>100101
[4,7,2,6,3,5,1]=>010101=>101010=>010101
[4,7,2,6,5,1,3]=>010110=>011010=>100101
[4,7,2,6,5,3,1]=>010111=>111010=>000101
[4,7,3,1,2,5,6]=>011000=>000110=>111001
[4,7,3,1,2,6,5]=>011001=>100110=>011001
[4,7,3,1,5,2,6]=>011010=>010110=>101001
[4,7,3,1,5,6,2]=>011001=>100110=>011001
[4,7,3,1,6,2,5]=>011010=>010110=>101001
[4,7,3,1,6,5,2]=>011011=>110110=>001001
[4,7,3,2,1,5,6]=>011100=>001110=>110001
[4,7,3,2,1,6,5]=>011101=>101110=>010001
[4,7,3,2,5,1,6]=>011010=>010110=>101001
[4,7,3,2,5,6,1]=>011001=>100110=>011001
[4,7,3,2,6,1,5]=>011010=>010110=>101001
[4,7,3,2,6,5,1]=>011011=>110110=>001001
[4,7,3,5,1,2,6]=>010100=>001010=>110101
[4,7,3,5,1,6,2]=>010101=>101010=>010101
[4,7,3,5,2,1,6]=>010110=>011010=>100101
[4,7,3,5,2,6,1]=>010101=>101010=>010101
[4,7,3,5,6,1,2]=>010010=>010010=>101101
[4,7,3,5,6,2,1]=>010011=>110010=>001101
[4,7,3,6,1,2,5]=>010100=>001010=>110101
[4,7,3,6,1,5,2]=>010101=>101010=>010101
[4,7,3,6,2,1,5]=>010110=>011010=>100101
[4,7,3,6,2,5,1]=>010101=>101010=>010101
[4,7,3,6,5,1,2]=>010110=>011010=>100101
[4,7,3,6,5,2,1]=>010111=>111010=>000101
[4,7,5,1,2,3,6]=>011000=>000110=>111001
[4,7,5,1,2,6,3]=>011001=>100110=>011001
[4,7,5,1,3,2,6]=>011010=>010110=>101001
[4,7,5,1,3,6,2]=>011001=>100110=>011001
[4,7,5,1,6,2,3]=>011010=>010110=>101001
[4,7,5,1,6,3,2]=>011011=>110110=>001001
[4,7,5,2,1,3,6]=>011100=>001110=>110001
[4,7,5,2,1,6,3]=>011101=>101110=>010001
[4,7,5,2,3,1,6]=>011010=>010110=>101001
[4,7,5,2,3,6,1]=>011001=>100110=>011001
[4,7,5,2,6,1,3]=>011010=>010110=>101001
[4,7,5,2,6,3,1]=>011011=>110110=>001001
[4,7,5,3,1,2,6]=>011100=>001110=>110001
[4,7,5,3,1,6,2]=>011101=>101110=>010001
[4,7,5,3,2,1,6]=>011110=>011110=>100001
[4,7,5,3,2,6,1]=>011101=>101110=>010001
[4,7,5,3,6,1,2]=>011010=>010110=>101001
[4,7,5,3,6,2,1]=>011011=>110110=>001001
[4,7,5,6,1,2,3]=>010100=>001010=>110101
[4,7,5,6,1,3,2]=>010101=>101010=>010101
[4,7,5,6,2,1,3]=>010110=>011010=>100101
[4,7,5,6,2,3,1]=>010101=>101010=>010101
[4,7,5,6,3,1,2]=>010110=>011010=>100101
[4,7,5,6,3,2,1]=>010111=>111010=>000101
[4,7,6,1,2,3,5]=>011000=>000110=>111001
[4,7,6,1,2,5,3]=>011001=>100110=>011001
[4,7,6,1,3,2,5]=>011010=>010110=>101001
[4,7,6,1,3,5,2]=>011001=>100110=>011001
[4,7,6,1,5,2,3]=>011010=>010110=>101001
[4,7,6,1,5,3,2]=>011011=>110110=>001001
[4,7,6,2,1,3,5]=>011100=>001110=>110001
[4,7,6,2,1,5,3]=>011101=>101110=>010001
[4,7,6,2,3,1,5]=>011010=>010110=>101001
[4,7,6,2,3,5,1]=>011001=>100110=>011001
[4,7,6,2,5,1,3]=>011010=>010110=>101001
[4,7,6,2,5,3,1]=>011011=>110110=>001001
[4,7,6,3,1,2,5]=>011100=>001110=>110001
[4,7,6,3,1,5,2]=>011101=>101110=>010001
[4,7,6,3,2,1,5]=>011110=>011110=>100001
[4,7,6,3,2,5,1]=>011101=>101110=>010001
[4,7,6,3,5,1,2]=>011010=>010110=>101001
[4,7,6,3,5,2,1]=>011011=>110110=>001001
[4,7,6,5,1,2,3]=>011100=>001110=>110001
[4,7,6,5,1,3,2]=>011101=>101110=>010001
[4,7,6,5,2,1,3]=>011110=>011110=>100001
[4,7,6,5,2,3,1]=>011101=>101110=>010001
[4,7,6,5,3,1,2]=>011110=>011110=>100001
[4,7,6,5,3,2,1]=>011111=>111110=>000001
[5,1,2,3,4,6,7]=>100000=>000001=>111110
[5,1,2,3,4,7,6]=>100001=>100001=>011110
[5,1,2,3,6,4,7]=>100010=>010001=>101110
[5,1,2,3,6,7,4]=>100001=>100001=>011110
[5,1,2,3,7,4,6]=>100010=>010001=>101110
[5,1,2,3,7,6,4]=>100011=>110001=>001110
[5,1,2,4,3,6,7]=>100100=>001001=>110110
[5,1,2,4,3,7,6]=>100101=>101001=>010110
[5,1,2,4,6,3,7]=>100010=>010001=>101110
[5,1,2,4,6,7,3]=>100001=>100001=>011110
[5,1,2,4,7,3,6]=>100010=>010001=>101110
[5,1,2,4,7,6,3]=>100011=>110001=>001110
[5,1,2,6,3,4,7]=>100100=>001001=>110110
[5,1,2,6,3,7,4]=>100101=>101001=>010110
[5,1,2,6,4,3,7]=>100110=>011001=>100110
[5,1,2,6,4,7,3]=>100101=>101001=>010110
[5,1,2,6,7,3,4]=>100010=>010001=>101110
[5,1,2,6,7,4,3]=>100011=>110001=>001110
[5,1,2,7,3,4,6]=>100100=>001001=>110110
[5,1,2,7,3,6,4]=>100101=>101001=>010110
[5,1,2,7,4,3,6]=>100110=>011001=>100110
[5,1,2,7,4,6,3]=>100101=>101001=>010110
[5,1,2,7,6,3,4]=>100110=>011001=>100110
[5,1,2,7,6,4,3]=>100111=>111001=>000110
[5,1,3,2,4,6,7]=>101000=>000101=>111010
[5,1,3,2,4,7,6]=>101001=>100101=>011010
[5,1,3,2,6,4,7]=>101010=>010101=>101010
[5,1,3,2,6,7,4]=>101001=>100101=>011010
[5,1,3,2,7,4,6]=>101010=>010101=>101010
[5,1,3,2,7,6,4]=>101011=>110101=>001010
[5,1,3,4,2,6,7]=>100100=>001001=>110110
[5,1,3,4,2,7,6]=>100101=>101001=>010110
[5,1,3,4,6,2,7]=>100010=>010001=>101110
[5,1,3,4,6,7,2]=>100001=>100001=>011110
[5,1,3,4,7,2,6]=>100010=>010001=>101110
[5,1,3,4,7,6,2]=>100011=>110001=>001110
[5,1,3,6,2,4,7]=>100100=>001001=>110110
[5,1,3,6,2,7,4]=>100101=>101001=>010110
[5,1,3,6,4,2,7]=>100110=>011001=>100110
[5,1,3,6,4,7,2]=>100101=>101001=>010110
[5,1,3,6,7,2,4]=>100010=>010001=>101110
[5,1,3,6,7,4,2]=>100011=>110001=>001110
[5,1,3,7,2,4,6]=>100100=>001001=>110110
[5,1,3,7,2,6,4]=>100101=>101001=>010110
[5,1,3,7,4,2,6]=>100110=>011001=>100110
[5,1,3,7,4,6,2]=>100101=>101001=>010110
[5,1,3,7,6,2,4]=>100110=>011001=>100110
[5,1,3,7,6,4,2]=>100111=>111001=>000110
[5,1,4,2,3,6,7]=>101000=>000101=>111010
[5,1,4,2,3,7,6]=>101001=>100101=>011010
[5,1,4,2,6,3,7]=>101010=>010101=>101010
[5,1,4,2,6,7,3]=>101001=>100101=>011010
[5,1,4,2,7,3,6]=>101010=>010101=>101010
[5,1,4,2,7,6,3]=>101011=>110101=>001010
[5,1,4,3,2,6,7]=>101100=>001101=>110010
[5,1,4,3,2,7,6]=>101101=>101101=>010010
[5,1,4,3,6,2,7]=>101010=>010101=>101010
[5,1,4,3,6,7,2]=>101001=>100101=>011010
[5,1,4,3,7,2,6]=>101010=>010101=>101010
[5,1,4,3,7,6,2]=>101011=>110101=>001010
[5,1,4,6,2,3,7]=>100100=>001001=>110110
[5,1,4,6,2,7,3]=>100101=>101001=>010110
[5,1,4,6,3,2,7]=>100110=>011001=>100110
[5,1,4,6,3,7,2]=>100101=>101001=>010110
[5,1,4,6,7,2,3]=>100010=>010001=>101110
[5,1,4,6,7,3,2]=>100011=>110001=>001110
[5,1,4,7,2,3,6]=>100100=>001001=>110110
[5,1,4,7,2,6,3]=>100101=>101001=>010110
[5,1,4,7,3,2,6]=>100110=>011001=>100110
[5,1,4,7,3,6,2]=>100101=>101001=>010110
[5,1,4,7,6,2,3]=>100110=>011001=>100110
[5,1,4,7,6,3,2]=>100111=>111001=>000110
[5,1,6,2,3,4,7]=>101000=>000101=>111010
[5,1,6,2,3,7,4]=>101001=>100101=>011010
[5,1,6,2,4,3,7]=>101010=>010101=>101010
[5,1,6,2,4,7,3]=>101001=>100101=>011010
[5,1,6,2,7,3,4]=>101010=>010101=>101010
[5,1,6,2,7,4,3]=>101011=>110101=>001010
[5,1,6,3,2,4,7]=>101100=>001101=>110010
[5,1,6,3,2,7,4]=>101101=>101101=>010010
[5,1,6,3,4,2,7]=>101010=>010101=>101010
[5,1,6,3,4,7,2]=>101001=>100101=>011010
[5,1,6,3,7,2,4]=>101010=>010101=>101010
[5,1,6,3,7,4,2]=>101011=>110101=>001010
[5,1,6,4,2,3,7]=>101100=>001101=>110010
[5,1,6,4,2,7,3]=>101101=>101101=>010010
[5,1,6,4,3,2,7]=>101110=>011101=>100010
[5,1,6,4,3,7,2]=>101101=>101101=>010010
[5,1,6,4,7,2,3]=>101010=>010101=>101010
[5,1,6,4,7,3,2]=>101011=>110101=>001010
[5,1,6,7,2,3,4]=>100100=>001001=>110110
[5,1,6,7,2,4,3]=>100101=>101001=>010110
[5,1,6,7,3,2,4]=>100110=>011001=>100110
[5,1,6,7,3,4,2]=>100101=>101001=>010110
[5,1,6,7,4,2,3]=>100110=>011001=>100110
[5,1,6,7,4,3,2]=>100111=>111001=>000110
[5,1,7,2,3,4,6]=>101000=>000101=>111010
[5,1,7,2,3,6,4]=>101001=>100101=>011010
[5,1,7,2,4,3,6]=>101010=>010101=>101010
[5,1,7,2,4,6,3]=>101001=>100101=>011010
[5,1,7,2,6,3,4]=>101010=>010101=>101010
[5,1,7,2,6,4,3]=>101011=>110101=>001010
[5,1,7,3,2,4,6]=>101100=>001101=>110010
[5,1,7,3,2,6,4]=>101101=>101101=>010010
[5,1,7,3,4,2,6]=>101010=>010101=>101010
[5,1,7,3,4,6,2]=>101001=>100101=>011010
[5,1,7,3,6,2,4]=>101010=>010101=>101010
[5,1,7,3,6,4,2]=>101011=>110101=>001010
[5,1,7,4,2,3,6]=>101100=>001101=>110010
[5,1,7,4,2,6,3]=>101101=>101101=>010010
[5,1,7,4,3,2,6]=>101110=>011101=>100010
[5,1,7,4,3,6,2]=>101101=>101101=>010010
[5,1,7,4,6,2,3]=>101010=>010101=>101010
[5,1,7,4,6,3,2]=>101011=>110101=>001010
[5,1,7,6,2,3,4]=>101100=>001101=>110010
[5,1,7,6,2,4,3]=>101101=>101101=>010010
[5,1,7,6,3,2,4]=>101110=>011101=>100010
[5,1,7,6,3,4,2]=>101101=>101101=>010010
[5,1,7,6,4,2,3]=>101110=>011101=>100010
[5,1,7,6,4,3,2]=>101111=>111101=>000010
[5,2,1,3,4,6,7]=>110000=>000011=>111100
[5,2,1,3,4,7,6]=>110001=>100011=>011100
[5,2,1,3,6,4,7]=>110010=>010011=>101100
[5,2,1,3,6,7,4]=>110001=>100011=>011100
[5,2,1,3,7,4,6]=>110010=>010011=>101100
[5,2,1,3,7,6,4]=>110011=>110011=>001100
[5,2,1,4,3,6,7]=>110100=>001011=>110100
[5,2,1,4,3,7,6]=>110101=>101011=>010100
[5,2,1,4,6,3,7]=>110010=>010011=>101100
[5,2,1,4,6,7,3]=>110001=>100011=>011100
[5,2,1,4,7,3,6]=>110010=>010011=>101100
[5,2,1,4,7,6,3]=>110011=>110011=>001100
[5,2,1,6,3,4,7]=>110100=>001011=>110100
[5,2,1,6,3,7,4]=>110101=>101011=>010100
[5,2,1,6,4,3,7]=>110110=>011011=>100100
[5,2,1,6,4,7,3]=>110101=>101011=>010100
[5,2,1,6,7,3,4]=>110010=>010011=>101100
[5,2,1,6,7,4,3]=>110011=>110011=>001100
[5,2,1,7,3,4,6]=>110100=>001011=>110100
[5,2,1,7,3,6,4]=>110101=>101011=>010100
[5,2,1,7,4,3,6]=>110110=>011011=>100100
[5,2,1,7,4,6,3]=>110101=>101011=>010100
[5,2,1,7,6,3,4]=>110110=>011011=>100100
[5,2,1,7,6,4,3]=>110111=>111011=>000100
[5,2,3,1,4,6,7]=>101000=>000101=>111010
[5,2,3,1,4,7,6]=>101001=>100101=>011010
[5,2,3,1,6,4,7]=>101010=>010101=>101010
[5,2,3,1,6,7,4]=>101001=>100101=>011010
[5,2,3,1,7,4,6]=>101010=>010101=>101010
[5,2,3,1,7,6,4]=>101011=>110101=>001010
[5,2,3,4,1,6,7]=>100100=>001001=>110110
[5,2,3,4,1,7,6]=>100101=>101001=>010110
[5,2,3,4,6,1,7]=>100010=>010001=>101110
[5,2,3,4,6,7,1]=>100001=>100001=>011110
[5,2,3,4,7,1,6]=>100010=>010001=>101110
[5,2,3,4,7,6,1]=>100011=>110001=>001110
[5,2,3,6,1,4,7]=>100100=>001001=>110110
[5,2,3,6,1,7,4]=>100101=>101001=>010110
[5,2,3,6,4,1,7]=>100110=>011001=>100110
[5,2,3,6,4,7,1]=>100101=>101001=>010110
[5,2,3,6,7,1,4]=>100010=>010001=>101110
[5,2,3,6,7,4,1]=>100011=>110001=>001110
[5,2,3,7,1,4,6]=>100100=>001001=>110110
[5,2,3,7,1,6,4]=>100101=>101001=>010110
[5,2,3,7,4,1,6]=>100110=>011001=>100110
[5,2,3,7,4,6,1]=>100101=>101001=>010110
[5,2,3,7,6,1,4]=>100110=>011001=>100110
[5,2,3,7,6,4,1]=>100111=>111001=>000110
[5,2,4,1,3,6,7]=>101000=>000101=>111010
[5,2,4,1,3,7,6]=>101001=>100101=>011010
[5,2,4,1,6,3,7]=>101010=>010101=>101010
[5,2,4,1,6,7,3]=>101001=>100101=>011010
[5,2,4,1,7,3,6]=>101010=>010101=>101010
[5,2,4,1,7,6,3]=>101011=>110101=>001010
[5,2,4,3,1,6,7]=>101100=>001101=>110010
[5,2,4,3,1,7,6]=>101101=>101101=>010010
[5,2,4,3,6,1,7]=>101010=>010101=>101010
[5,2,4,3,6,7,1]=>101001=>100101=>011010
[5,2,4,3,7,1,6]=>101010=>010101=>101010
[5,2,4,3,7,6,1]=>101011=>110101=>001010
[5,2,4,6,1,3,7]=>100100=>001001=>110110
[5,2,4,6,1,7,3]=>100101=>101001=>010110
[5,2,4,6,3,1,7]=>100110=>011001=>100110
[5,2,4,6,3,7,1]=>100101=>101001=>010110
[5,2,4,6,7,1,3]=>100010=>010001=>101110
[5,2,4,6,7,3,1]=>100011=>110001=>001110
[5,2,4,7,1,3,6]=>100100=>001001=>110110
[5,2,4,7,1,6,3]=>100101=>101001=>010110
[5,2,4,7,3,1,6]=>100110=>011001=>100110
[5,2,4,7,3,6,1]=>100101=>101001=>010110
[5,2,4,7,6,1,3]=>100110=>011001=>100110
[5,2,4,7,6,3,1]=>100111=>111001=>000110
[5,2,6,1,3,4,7]=>101000=>000101=>111010
[5,2,6,1,3,7,4]=>101001=>100101=>011010
[5,2,6,1,4,3,7]=>101010=>010101=>101010
[5,2,6,1,4,7,3]=>101001=>100101=>011010
[5,2,6,1,7,3,4]=>101010=>010101=>101010
[5,2,6,1,7,4,3]=>101011=>110101=>001010
[5,2,6,3,1,4,7]=>101100=>001101=>110010
[5,2,6,3,1,7,4]=>101101=>101101=>010010
[5,2,6,3,4,1,7]=>101010=>010101=>101010
[5,2,6,3,4,7,1]=>101001=>100101=>011010
[5,2,6,3,7,1,4]=>101010=>010101=>101010
[5,2,6,3,7,4,1]=>101011=>110101=>001010
[5,2,6,4,1,3,7]=>101100=>001101=>110010
[5,2,6,4,1,7,3]=>101101=>101101=>010010
[5,2,6,4,3,1,7]=>101110=>011101=>100010
[5,2,6,4,3,7,1]=>101101=>101101=>010010
[5,2,6,4,7,1,3]=>101010=>010101=>101010
[5,2,6,4,7,3,1]=>101011=>110101=>001010
[5,2,6,7,1,3,4]=>100100=>001001=>110110
[5,2,6,7,1,4,3]=>100101=>101001=>010110
[5,2,6,7,3,1,4]=>100110=>011001=>100110
[5,2,6,7,3,4,1]=>100101=>101001=>010110
[5,2,6,7,4,1,3]=>100110=>011001=>100110
[5,2,6,7,4,3,1]=>100111=>111001=>000110
[5,2,7,1,3,4,6]=>101000=>000101=>111010
[5,2,7,1,3,6,4]=>101001=>100101=>011010
[5,2,7,1,4,3,6]=>101010=>010101=>101010
[5,2,7,1,4,6,3]=>101001=>100101=>011010
[5,2,7,1,6,3,4]=>101010=>010101=>101010
[5,2,7,1,6,4,3]=>101011=>110101=>001010
[5,2,7,3,1,4,6]=>101100=>001101=>110010
[5,2,7,3,1,6,4]=>101101=>101101=>010010
[5,2,7,3,4,1,6]=>101010=>010101=>101010
[5,2,7,3,4,6,1]=>101001=>100101=>011010
[5,2,7,3,6,1,4]=>101010=>010101=>101010
[5,2,7,3,6,4,1]=>101011=>110101=>001010
[5,2,7,4,1,3,6]=>101100=>001101=>110010
[5,2,7,4,1,6,3]=>101101=>101101=>010010
[5,2,7,4,3,1,6]=>101110=>011101=>100010
[5,2,7,4,3,6,1]=>101101=>101101=>010010
[5,2,7,4,6,1,3]=>101010=>010101=>101010
[5,2,7,4,6,3,1]=>101011=>110101=>001010
[5,2,7,6,1,3,4]=>101100=>001101=>110010
[5,2,7,6,1,4,3]=>101101=>101101=>010010
[5,2,7,6,3,1,4]=>101110=>011101=>100010
[5,2,7,6,3,4,1]=>101101=>101101=>010010
[5,2,7,6,4,1,3]=>101110=>011101=>100010
[5,2,7,6,4,3,1]=>101111=>111101=>000010
[5,3,1,2,4,6,7]=>110000=>000011=>111100
[5,3,1,2,4,7,6]=>110001=>100011=>011100
[5,3,1,2,6,4,7]=>110010=>010011=>101100
[5,3,1,2,6,7,4]=>110001=>100011=>011100
[5,3,1,2,7,4,6]=>110010=>010011=>101100
[5,3,1,2,7,6,4]=>110011=>110011=>001100
[5,3,1,4,2,6,7]=>110100=>001011=>110100
[5,3,1,4,2,7,6]=>110101=>101011=>010100
[5,3,1,4,6,2,7]=>110010=>010011=>101100
[5,3,1,4,6,7,2]=>110001=>100011=>011100
[5,3,1,4,7,2,6]=>110010=>010011=>101100
[5,3,1,4,7,6,2]=>110011=>110011=>001100
[5,3,1,6,2,4,7]=>110100=>001011=>110100
[5,3,1,6,2,7,4]=>110101=>101011=>010100
[5,3,1,6,4,2,7]=>110110=>011011=>100100
[5,3,1,6,4,7,2]=>110101=>101011=>010100
[5,3,1,6,7,2,4]=>110010=>010011=>101100
[5,3,1,6,7,4,2]=>110011=>110011=>001100
[5,3,1,7,2,4,6]=>110100=>001011=>110100
[5,3,1,7,2,6,4]=>110101=>101011=>010100
[5,3,1,7,4,2,6]=>110110=>011011=>100100
[5,3,1,7,4,6,2]=>110101=>101011=>010100
[5,3,1,7,6,2,4]=>110110=>011011=>100100
[5,3,1,7,6,4,2]=>110111=>111011=>000100
[5,3,2,1,4,6,7]=>111000=>000111=>111000
[5,3,2,1,4,7,6]=>111001=>100111=>011000
[5,3,2,1,6,4,7]=>111010=>010111=>101000
[5,3,2,1,6,7,4]=>111001=>100111=>011000
[5,3,2,1,7,4,6]=>111010=>010111=>101000
[5,3,2,1,7,6,4]=>111011=>110111=>001000
[5,3,2,4,1,6,7]=>110100=>001011=>110100
[5,3,2,4,1,7,6]=>110101=>101011=>010100
[5,3,2,4,6,1,7]=>110010=>010011=>101100
[5,3,2,4,6,7,1]=>110001=>100011=>011100
[5,3,2,4,7,1,6]=>110010=>010011=>101100
[5,3,2,4,7,6,1]=>110011=>110011=>001100
[5,3,2,6,1,4,7]=>110100=>001011=>110100
[5,3,2,6,1,7,4]=>110101=>101011=>010100
[5,3,2,6,4,1,7]=>110110=>011011=>100100
[5,3,2,6,4,7,1]=>110101=>101011=>010100
[5,3,2,6,7,1,4]=>110010=>010011=>101100
[5,3,2,6,7,4,1]=>110011=>110011=>001100
[5,3,2,7,1,4,6]=>110100=>001011=>110100
[5,3,2,7,1,6,4]=>110101=>101011=>010100
[5,3,2,7,4,1,6]=>110110=>011011=>100100
[5,3,2,7,4,6,1]=>110101=>101011=>010100
[5,3,2,7,6,1,4]=>110110=>011011=>100100
[5,3,2,7,6,4,1]=>110111=>111011=>000100
[5,3,4,1,2,6,7]=>101000=>000101=>111010
[5,3,4,1,2,7,6]=>101001=>100101=>011010
[5,3,4,1,6,2,7]=>101010=>010101=>101010
[5,3,4,1,6,7,2]=>101001=>100101=>011010
[5,3,4,1,7,2,6]=>101010=>010101=>101010
[5,3,4,1,7,6,2]=>101011=>110101=>001010
[5,3,4,2,1,6,7]=>101100=>001101=>110010
[5,3,4,2,1,7,6]=>101101=>101101=>010010
[5,3,4,2,6,1,7]=>101010=>010101=>101010
[5,3,4,2,6,7,1]=>101001=>100101=>011010
[5,3,4,2,7,1,6]=>101010=>010101=>101010
[5,3,4,2,7,6,1]=>101011=>110101=>001010
[5,3,4,6,1,2,7]=>100100=>001001=>110110
[5,3,4,6,1,7,2]=>100101=>101001=>010110
[5,3,4,6,2,1,7]=>100110=>011001=>100110
[5,3,4,6,2,7,1]=>100101=>101001=>010110
[5,3,4,6,7,1,2]=>100010=>010001=>101110
[5,3,4,6,7,2,1]=>100011=>110001=>001110
[5,3,4,7,1,2,6]=>100100=>001001=>110110
[5,3,4,7,1,6,2]=>100101=>101001=>010110
[5,3,4,7,2,1,6]=>100110=>011001=>100110
[5,3,4,7,2,6,1]=>100101=>101001=>010110
[5,3,4,7,6,1,2]=>100110=>011001=>100110
[5,3,4,7,6,2,1]=>100111=>111001=>000110
[5,3,6,1,2,4,7]=>101000=>000101=>111010
[5,3,6,1,2,7,4]=>101001=>100101=>011010
[5,3,6,1,4,2,7]=>101010=>010101=>101010
[5,3,6,1,4,7,2]=>101001=>100101=>011010
[5,3,6,1,7,2,4]=>101010=>010101=>101010
[5,3,6,1,7,4,2]=>101011=>110101=>001010
[5,3,6,2,1,4,7]=>101100=>001101=>110010
[5,3,6,2,1,7,4]=>101101=>101101=>010010
[5,3,6,2,4,1,7]=>101010=>010101=>101010
[5,3,6,2,4,7,1]=>101001=>100101=>011010
[5,3,6,2,7,1,4]=>101010=>010101=>101010
[5,3,6,2,7,4,1]=>101011=>110101=>001010
[5,3,6,4,1,2,7]=>101100=>001101=>110010
[5,3,6,4,1,7,2]=>101101=>101101=>010010
[5,3,6,4,2,1,7]=>101110=>011101=>100010
[5,3,6,4,2,7,1]=>101101=>101101=>010010
[5,3,6,4,7,1,2]=>101010=>010101=>101010
[5,3,6,4,7,2,1]=>101011=>110101=>001010
[5,3,6,7,1,2,4]=>100100=>001001=>110110
[5,3,6,7,1,4,2]=>100101=>101001=>010110
[5,3,6,7,2,1,4]=>100110=>011001=>100110
[5,3,6,7,2,4,1]=>100101=>101001=>010110
[5,3,6,7,4,1,2]=>100110=>011001=>100110
[5,3,6,7,4,2,1]=>100111=>111001=>000110
[5,3,7,1,2,4,6]=>101000=>000101=>111010
[5,3,7,1,2,6,4]=>101001=>100101=>011010
[5,3,7,1,4,2,6]=>101010=>010101=>101010
[5,3,7,1,4,6,2]=>101001=>100101=>011010
[5,3,7,1,6,2,4]=>101010=>010101=>101010
[5,3,7,1,6,4,2]=>101011=>110101=>001010
[5,3,7,2,1,4,6]=>101100=>001101=>110010
[5,3,7,2,1,6,4]=>101101=>101101=>010010
[5,3,7,2,4,1,6]=>101010=>010101=>101010
[5,3,7,2,4,6,1]=>101001=>100101=>011010
[5,3,7,2,6,1,4]=>101010=>010101=>101010
[5,3,7,2,6,4,1]=>101011=>110101=>001010
[5,3,7,4,1,2,6]=>101100=>001101=>110010
[5,3,7,4,1,6,2]=>101101=>101101=>010010
[5,3,7,4,2,1,6]=>101110=>011101=>100010
[5,3,7,4,2,6,1]=>101101=>101101=>010010
[5,3,7,4,6,1,2]=>101010=>010101=>101010
[5,3,7,4,6,2,1]=>101011=>110101=>001010
[5,3,7,6,1,2,4]=>101100=>001101=>110010
[5,3,7,6,1,4,2]=>101101=>101101=>010010
[5,3,7,6,2,1,4]=>101110=>011101=>100010
[5,3,7,6,2,4,1]=>101101=>101101=>010010
[5,3,7,6,4,1,2]=>101110=>011101=>100010
[5,3,7,6,4,2,1]=>101111=>111101=>000010
[5,4,1,2,3,6,7]=>110000=>000011=>111100
[5,4,1,2,3,7,6]=>110001=>100011=>011100
[5,4,1,2,6,3,7]=>110010=>010011=>101100
[5,4,1,2,6,7,3]=>110001=>100011=>011100
[5,4,1,2,7,3,6]=>110010=>010011=>101100
[5,4,1,2,7,6,3]=>110011=>110011=>001100
[5,4,1,3,2,6,7]=>110100=>001011=>110100
[5,4,1,3,2,7,6]=>110101=>101011=>010100
[5,4,1,3,6,2,7]=>110010=>010011=>101100
[5,4,1,3,6,7,2]=>110001=>100011=>011100
[5,4,1,3,7,2,6]=>110010=>010011=>101100
[5,4,1,3,7,6,2]=>110011=>110011=>001100
[5,4,1,6,2,3,7]=>110100=>001011=>110100
[5,4,1,6,2,7,3]=>110101=>101011=>010100
[5,4,1,6,3,2,7]=>110110=>011011=>100100
[5,4,1,6,3,7,2]=>110101=>101011=>010100
[5,4,1,6,7,2,3]=>110010=>010011=>101100
[5,4,1,6,7,3,2]=>110011=>110011=>001100
[5,4,1,7,2,3,6]=>110100=>001011=>110100
[5,4,1,7,2,6,3]=>110101=>101011=>010100
[5,4,1,7,3,2,6]=>110110=>011011=>100100
[5,4,1,7,3,6,2]=>110101=>101011=>010100
[5,4,1,7,6,2,3]=>110110=>011011=>100100
[5,4,1,7,6,3,2]=>110111=>111011=>000100
[5,4,2,1,3,6,7]=>111000=>000111=>111000
[5,4,2,1,3,7,6]=>111001=>100111=>011000
[5,4,2,1,6,3,7]=>111010=>010111=>101000
[5,4,2,1,6,7,3]=>111001=>100111=>011000
[5,4,2,1,7,3,6]=>111010=>010111=>101000
[5,4,2,1,7,6,3]=>111011=>110111=>001000
[5,4,2,3,1,6,7]=>110100=>001011=>110100
[5,4,2,3,1,7,6]=>110101=>101011=>010100
[5,4,2,3,6,1,7]=>110010=>010011=>101100
[5,4,2,3,6,7,1]=>110001=>100011=>011100
[5,4,2,3,7,1,6]=>110010=>010011=>101100
[5,4,2,3,7,6,1]=>110011=>110011=>001100
[5,4,2,6,1,3,7]=>110100=>001011=>110100
[5,4,2,6,1,7,3]=>110101=>101011=>010100
[5,4,2,6,3,1,7]=>110110=>011011=>100100
[5,4,2,6,3,7,1]=>110101=>101011=>010100
[5,4,2,6,7,1,3]=>110010=>010011=>101100
[5,4,2,6,7,3,1]=>110011=>110011=>001100
[5,4,2,7,1,3,6]=>110100=>001011=>110100
[5,4,2,7,1,6,3]=>110101=>101011=>010100
[5,4,2,7,3,1,6]=>110110=>011011=>100100
[5,4,2,7,3,6,1]=>110101=>101011=>010100
[5,4,2,7,6,1,3]=>110110=>011011=>100100
[5,4,2,7,6,3,1]=>110111=>111011=>000100
[5,4,3,1,2,6,7]=>111000=>000111=>111000
[5,4,3,1,2,7,6]=>111001=>100111=>011000
[5,4,3,1,6,2,7]=>111010=>010111=>101000
[5,4,3,1,6,7,2]=>111001=>100111=>011000
[5,4,3,1,7,2,6]=>111010=>010111=>101000
[5,4,3,1,7,6,2]=>111011=>110111=>001000
[5,4,3,2,1,6,7]=>111100=>001111=>110000
[5,4,3,2,1,7,6]=>111101=>101111=>010000
[5,4,3,2,6,1,7]=>111010=>010111=>101000
[5,4,3,2,6,7,1]=>111001=>100111=>011000
[5,4,3,2,7,1,6]=>111010=>010111=>101000
[5,4,3,2,7,6,1]=>111011=>110111=>001000
[5,4,3,6,1,2,7]=>110100=>001011=>110100
[5,4,3,6,1,7,2]=>110101=>101011=>010100
[5,4,3,6,2,1,7]=>110110=>011011=>100100
[5,4,3,6,2,7,1]=>110101=>101011=>010100
[5,4,3,6,7,1,2]=>110010=>010011=>101100
[5,4,3,6,7,2,1]=>110011=>110011=>001100
[5,4,3,7,1,2,6]=>110100=>001011=>110100
[5,4,3,7,1,6,2]=>110101=>101011=>010100
[5,4,3,7,2,1,6]=>110110=>011011=>100100
[5,4,3,7,2,6,1]=>110101=>101011=>010100
[5,4,3,7,6,1,2]=>110110=>011011=>100100
[5,4,3,7,6,2,1]=>110111=>111011=>000100
[5,4,6,1,2,3,7]=>101000=>000101=>111010
[5,4,6,1,2,7,3]=>101001=>100101=>011010
[5,4,6,1,3,2,7]=>101010=>010101=>101010
[5,4,6,1,3,7,2]=>101001=>100101=>011010
[5,4,6,1,7,2,3]=>101010=>010101=>101010
[5,4,6,1,7,3,2]=>101011=>110101=>001010
[5,4,6,2,1,3,7]=>101100=>001101=>110010
[5,4,6,2,1,7,3]=>101101=>101101=>010010
[5,4,6,2,3,1,7]=>101010=>010101=>101010
[5,4,6,2,3,7,1]=>101001=>100101=>011010
[5,4,6,2,7,1,3]=>101010=>010101=>101010
[5,4,6,2,7,3,1]=>101011=>110101=>001010
[5,4,6,3,1,2,7]=>101100=>001101=>110010
[5,4,6,3,1,7,2]=>101101=>101101=>010010
[5,4,6,3,2,1,7]=>101110=>011101=>100010
[5,4,6,3,2,7,1]=>101101=>101101=>010010
[5,4,6,3,7,1,2]=>101010=>010101=>101010
[5,4,6,3,7,2,1]=>101011=>110101=>001010
[5,4,6,7,1,2,3]=>100100=>001001=>110110
[5,4,6,7,1,3,2]=>100101=>101001=>010110
[5,4,6,7,2,1,3]=>100110=>011001=>100110
[5,4,6,7,2,3,1]=>100101=>101001=>010110
[5,4,6,7,3,1,2]=>100110=>011001=>100110
[5,4,6,7,3,2,1]=>100111=>111001=>000110
[5,4,7,1,2,3,6]=>101000=>000101=>111010
[5,4,7,1,2,6,3]=>101001=>100101=>011010
[5,4,7,1,3,2,6]=>101010=>010101=>101010
[5,4,7,1,3,6,2]=>101001=>100101=>011010
[5,4,7,1,6,2,3]=>101010=>010101=>101010
[5,4,7,1,6,3,2]=>101011=>110101=>001010
[5,4,7,2,1,3,6]=>101100=>001101=>110010
[5,4,7,2,1,6,3]=>101101=>101101=>010010
[5,4,7,2,3,1,6]=>101010=>010101=>101010
[5,4,7,2,3,6,1]=>101001=>100101=>011010
[5,4,7,2,6,1,3]=>101010=>010101=>101010
[5,4,7,2,6,3,1]=>101011=>110101=>001010
[5,4,7,3,1,2,6]=>101100=>001101=>110010
[5,4,7,3,1,6,2]=>101101=>101101=>010010
[5,4,7,3,2,1,6]=>101110=>011101=>100010
[5,4,7,3,2,6,1]=>101101=>101101=>010010
[5,4,7,3,6,1,2]=>101010=>010101=>101010
[5,4,7,3,6,2,1]=>101011=>110101=>001010
[5,4,7,6,1,2,3]=>101100=>001101=>110010
[5,4,7,6,1,3,2]=>101101=>101101=>010010
[5,4,7,6,2,1,3]=>101110=>011101=>100010
[5,4,7,6,2,3,1]=>101101=>101101=>010010
[5,4,7,6,3,1,2]=>101110=>011101=>100010
[5,4,7,6,3,2,1]=>101111=>111101=>000010
[5,6,1,2,3,4,7]=>010000=>000010=>111101
[5,6,1,2,3,7,4]=>010001=>100010=>011101
[5,6,1,2,4,3,7]=>010010=>010010=>101101
[5,6,1,2,4,7,3]=>010001=>100010=>011101
[5,6,1,2,7,3,4]=>010010=>010010=>101101
[5,6,1,2,7,4,3]=>010011=>110010=>001101
[5,6,1,3,2,4,7]=>010100=>001010=>110101
[5,6,1,3,2,7,4]=>010101=>101010=>010101
[5,6,1,3,4,2,7]=>010010=>010010=>101101
[5,6,1,3,4,7,2]=>010001=>100010=>011101
[5,6,1,3,7,2,4]=>010010=>010010=>101101
[5,6,1,3,7,4,2]=>010011=>110010=>001101
[5,6,1,4,2,3,7]=>010100=>001010=>110101
[5,6,1,4,2,7,3]=>010101=>101010=>010101
[5,6,1,4,3,2,7]=>010110=>011010=>100101
[5,6,1,4,3,7,2]=>010101=>101010=>010101
[5,6,1,4,7,2,3]=>010010=>010010=>101101
[5,6,1,4,7,3,2]=>010011=>110010=>001101
[5,6,1,7,2,3,4]=>010100=>001010=>110101
[5,6,1,7,2,4,3]=>010101=>101010=>010101
[5,6,1,7,3,2,4]=>010110=>011010=>100101
[5,6,1,7,3,4,2]=>010101=>101010=>010101
[5,6,1,7,4,2,3]=>010110=>011010=>100101
[5,6,1,7,4,3,2]=>010111=>111010=>000101
[5,6,2,1,3,4,7]=>011000=>000110=>111001
[5,6,2,1,3,7,4]=>011001=>100110=>011001
[5,6,2,1,4,3,7]=>011010=>010110=>101001
[5,6,2,1,4,7,3]=>011001=>100110=>011001
[5,6,2,1,7,3,4]=>011010=>010110=>101001
[5,6,2,1,7,4,3]=>011011=>110110=>001001
[5,6,2,3,1,4,7]=>010100=>001010=>110101
[5,6,2,3,1,7,4]=>010101=>101010=>010101
[5,6,2,3,4,1,7]=>010010=>010010=>101101
[5,6,2,3,4,7,1]=>010001=>100010=>011101
[5,6,2,3,7,1,4]=>010010=>010010=>101101
[5,6,2,3,7,4,1]=>010011=>110010=>001101
[5,6,2,4,1,3,7]=>010100=>001010=>110101
[5,6,2,4,1,7,3]=>010101=>101010=>010101
[5,6,2,4,3,1,7]=>010110=>011010=>100101
[5,6,2,4,3,7,1]=>010101=>101010=>010101
[5,6,2,4,7,1,3]=>010010=>010010=>101101
[5,6,2,4,7,3,1]=>010011=>110010=>001101
[5,6,2,7,1,3,4]=>010100=>001010=>110101
[5,6,2,7,1,4,3]=>010101=>101010=>010101
[5,6,2,7,3,1,4]=>010110=>011010=>100101
[5,6,2,7,3,4,1]=>010101=>101010=>010101
[5,6,2,7,4,1,3]=>010110=>011010=>100101
[5,6,2,7,4,3,1]=>010111=>111010=>000101
[5,6,3,1,2,4,7]=>011000=>000110=>111001
[5,6,3,1,2,7,4]=>011001=>100110=>011001
[5,6,3,1,4,2,7]=>011010=>010110=>101001
[5,6,3,1,4,7,2]=>011001=>100110=>011001
[5,6,3,1,7,2,4]=>011010=>010110=>101001
[5,6,3,1,7,4,2]=>011011=>110110=>001001
[5,6,3,2,1,4,7]=>011100=>001110=>110001
[5,6,3,2,1,7,4]=>011101=>101110=>010001
[5,6,3,2,4,1,7]=>011010=>010110=>101001
[5,6,3,2,4,7,1]=>011001=>100110=>011001
[5,6,3,2,7,1,4]=>011010=>010110=>101001
[5,6,3,2,7,4,1]=>011011=>110110=>001001
[5,6,3,4,1,2,7]=>010100=>001010=>110101
[5,6,3,4,1,7,2]=>010101=>101010=>010101
[5,6,3,4,2,1,7]=>010110=>011010=>100101
[5,6,3,4,2,7,1]=>010101=>101010=>010101
[5,6,3,4,7,1,2]=>010010=>010010=>101101
[5,6,3,4,7,2,1]=>010011=>110010=>001101
[5,6,3,7,1,2,4]=>010100=>001010=>110101
[5,6,3,7,1,4,2]=>010101=>101010=>010101
[5,6,3,7,2,1,4]=>010110=>011010=>100101
[5,6,3,7,2,4,1]=>010101=>101010=>010101
[5,6,3,7,4,1,2]=>010110=>011010=>100101
[5,6,3,7,4,2,1]=>010111=>111010=>000101
[5,6,4,1,2,3,7]=>011000=>000110=>111001
[5,6,4,1,2,7,3]=>011001=>100110=>011001
[5,6,4,1,3,2,7]=>011010=>010110=>101001
[5,6,4,1,3,7,2]=>011001=>100110=>011001
[5,6,4,1,7,2,3]=>011010=>010110=>101001
[5,6,4,1,7,3,2]=>011011=>110110=>001001
[5,6,4,2,1,3,7]=>011100=>001110=>110001
[5,6,4,2,1,7,3]=>011101=>101110=>010001
[5,6,4,2,3,1,7]=>011010=>010110=>101001
[5,6,4,2,3,7,1]=>011001=>100110=>011001
[5,6,4,2,7,1,3]=>011010=>010110=>101001
[5,6,4,2,7,3,1]=>011011=>110110=>001001
[5,6,4,3,1,2,7]=>011100=>001110=>110001
[5,6,4,3,1,7,2]=>011101=>101110=>010001
[5,6,4,3,2,1,7]=>011110=>011110=>100001
[5,6,4,3,2,7,1]=>011101=>101110=>010001
[5,6,4,3,7,1,2]=>011010=>010110=>101001
[5,6,4,3,7,2,1]=>011011=>110110=>001001
[5,6,4,7,1,2,3]=>010100=>001010=>110101
[5,6,4,7,1,3,2]=>010101=>101010=>010101
[5,6,4,7,2,1,3]=>010110=>011010=>100101
[5,6,4,7,2,3,1]=>010101=>101010=>010101
[5,6,4,7,3,1,2]=>010110=>011010=>100101
[5,6,4,7,3,2,1]=>010111=>111010=>000101
[5,6,7,1,2,3,4]=>001000=>000100=>111011
[5,6,7,1,2,4,3]=>001001=>100100=>011011
[5,6,7,1,3,2,4]=>001010=>010100=>101011
[5,6,7,1,3,4,2]=>001001=>100100=>011011
[5,6,7,1,4,2,3]=>001010=>010100=>101011
[5,6,7,1,4,3,2]=>001011=>110100=>001011
[5,6,7,2,1,3,4]=>001100=>001100=>110011
[5,6,7,2,1,4,3]=>001101=>101100=>010011
[5,6,7,2,3,1,4]=>001010=>010100=>101011
[5,6,7,2,3,4,1]=>001001=>100100=>011011
[5,6,7,2,4,1,3]=>001010=>010100=>101011
[5,6,7,2,4,3,1]=>001011=>110100=>001011
[5,6,7,3,1,2,4]=>001100=>001100=>110011
[5,6,7,3,1,4,2]=>001101=>101100=>010011
[5,6,7,3,2,1,4]=>001110=>011100=>100011
[5,6,7,3,2,4,1]=>001101=>101100=>010011
[5,6,7,3,4,1,2]=>001010=>010100=>101011
[5,6,7,3,4,2,1]=>001011=>110100=>001011
[5,6,7,4,1,2,3]=>001100=>001100=>110011
[5,6,7,4,1,3,2]=>001101=>101100=>010011
[5,6,7,4,2,1,3]=>001110=>011100=>100011
[5,6,7,4,2,3,1]=>001101=>101100=>010011
[5,6,7,4,3,1,2]=>001110=>011100=>100011
[5,6,7,4,3,2,1]=>001111=>111100=>000011
[5,7,1,2,3,4,6]=>010000=>000010=>111101
[5,7,1,2,3,6,4]=>010001=>100010=>011101
[5,7,1,2,4,3,6]=>010010=>010010=>101101
[5,7,1,2,4,6,3]=>010001=>100010=>011101
[5,7,1,2,6,3,4]=>010010=>010010=>101101
[5,7,1,2,6,4,3]=>010011=>110010=>001101
[5,7,1,3,2,4,6]=>010100=>001010=>110101
[5,7,1,3,2,6,4]=>010101=>101010=>010101
[5,7,1,3,4,2,6]=>010010=>010010=>101101
[5,7,1,3,4,6,2]=>010001=>100010=>011101
[5,7,1,3,6,2,4]=>010010=>010010=>101101
[5,7,1,3,6,4,2]=>010011=>110010=>001101
[5,7,1,4,2,3,6]=>010100=>001010=>110101
[5,7,1,4,2,6,3]=>010101=>101010=>010101
[5,7,1,4,3,2,6]=>010110=>011010=>100101
[5,7,1,4,3,6,2]=>010101=>101010=>010101
[5,7,1,4,6,2,3]=>010010=>010010=>101101
[5,7,1,4,6,3,2]=>010011=>110010=>001101
[5,7,1,6,2,3,4]=>010100=>001010=>110101
[5,7,1,6,2,4,3]=>010101=>101010=>010101
[5,7,1,6,3,2,4]=>010110=>011010=>100101
[5,7,1,6,3,4,2]=>010101=>101010=>010101
[5,7,1,6,4,2,3]=>010110=>011010=>100101
[5,7,1,6,4,3,2]=>010111=>111010=>000101
[5,7,2,1,3,4,6]=>011000=>000110=>111001
[5,7,2,1,3,6,4]=>011001=>100110=>011001
[5,7,2,1,4,3,6]=>011010=>010110=>101001
[5,7,2,1,4,6,3]=>011001=>100110=>011001
[5,7,2,1,6,3,4]=>011010=>010110=>101001
[5,7,2,1,6,4,3]=>011011=>110110=>001001
[5,7,2,3,1,4,6]=>010100=>001010=>110101
[5,7,2,3,1,6,4]=>010101=>101010=>010101
[5,7,2,3,4,1,6]=>010010=>010010=>101101
[5,7,2,3,4,6,1]=>010001=>100010=>011101
[5,7,2,3,6,1,4]=>010010=>010010=>101101
[5,7,2,3,6,4,1]=>010011=>110010=>001101
[5,7,2,4,1,3,6]=>010100=>001010=>110101
[5,7,2,4,1,6,3]=>010101=>101010=>010101
[5,7,2,4,3,1,6]=>010110=>011010=>100101
[5,7,2,4,3,6,1]=>010101=>101010=>010101
[5,7,2,4,6,1,3]=>010010=>010010=>101101
[5,7,2,4,6,3,1]=>010011=>110010=>001101
[5,7,2,6,1,3,4]=>010100=>001010=>110101
[5,7,2,6,1,4,3]=>010101=>101010=>010101
[5,7,2,6,3,1,4]=>010110=>011010=>100101
[5,7,2,6,3,4,1]=>010101=>101010=>010101
[5,7,2,6,4,1,3]=>010110=>011010=>100101
[5,7,2,6,4,3,1]=>010111=>111010=>000101
[5,7,3,1,2,4,6]=>011000=>000110=>111001
[5,7,3,1,2,6,4]=>011001=>100110=>011001
[5,7,3,1,4,2,6]=>011010=>010110=>101001
[5,7,3,1,4,6,2]=>011001=>100110=>011001
[5,7,3,1,6,2,4]=>011010=>010110=>101001
[5,7,3,1,6,4,2]=>011011=>110110=>001001
[5,7,3,2,1,4,6]=>011100=>001110=>110001
[5,7,3,2,1,6,4]=>011101=>101110=>010001
[5,7,3,2,4,1,6]=>011010=>010110=>101001
[5,7,3,2,4,6,1]=>011001=>100110=>011001
[5,7,3,2,6,1,4]=>011010=>010110=>101001
[5,7,3,2,6,4,1]=>011011=>110110=>001001
[5,7,3,4,1,2,6]=>010100=>001010=>110101
[5,7,3,4,1,6,2]=>010101=>101010=>010101
[5,7,3,4,2,1,6]=>010110=>011010=>100101
[5,7,3,4,2,6,1]=>010101=>101010=>010101
[5,7,3,4,6,1,2]=>010010=>010010=>101101
[5,7,3,4,6,2,1]=>010011=>110010=>001101
[5,7,3,6,1,2,4]=>010100=>001010=>110101
[5,7,3,6,1,4,2]=>010101=>101010=>010101
[5,7,3,6,2,1,4]=>010110=>011010=>100101
[5,7,3,6,2,4,1]=>010101=>101010=>010101
[5,7,3,6,4,1,2]=>010110=>011010=>100101
[5,7,3,6,4,2,1]=>010111=>111010=>000101
[5,7,4,1,2,3,6]=>011000=>000110=>111001
[5,7,4,1,2,6,3]=>011001=>100110=>011001
[5,7,4,1,3,2,6]=>011010=>010110=>101001
[5,7,4,1,3,6,2]=>011001=>100110=>011001
[5,7,4,1,6,2,3]=>011010=>010110=>101001
[5,7,4,1,6,3,2]=>011011=>110110=>001001
[5,7,4,2,1,3,6]=>011100=>001110=>110001
[5,7,4,2,1,6,3]=>011101=>101110=>010001
[5,7,4,2,3,1,6]=>011010=>010110=>101001
[5,7,4,2,3,6,1]=>011001=>100110=>011001
[5,7,4,2,6,1,3]=>011010=>010110=>101001
[5,7,4,2,6,3,1]=>011011=>110110=>001001
[5,7,4,3,1,2,6]=>011100=>001110=>110001
[5,7,4,3,1,6,2]=>011101=>101110=>010001
[5,7,4,3,2,1,6]=>011110=>011110=>100001
[5,7,4,3,2,6,1]=>011101=>101110=>010001
[5,7,4,3,6,1,2]=>011010=>010110=>101001
[5,7,4,3,6,2,1]=>011011=>110110=>001001
[5,7,4,6,1,2,3]=>010100=>001010=>110101
[5,7,4,6,1,3,2]=>010101=>101010=>010101
[5,7,4,6,2,1,3]=>010110=>011010=>100101
[5,7,4,6,2,3,1]=>010101=>101010=>010101
[5,7,4,6,3,1,2]=>010110=>011010=>100101
[5,7,4,6,3,2,1]=>010111=>111010=>000101
[5,7,6,1,2,3,4]=>011000=>000110=>111001
[5,7,6,1,2,4,3]=>011001=>100110=>011001
[5,7,6,1,3,2,4]=>011010=>010110=>101001
[5,7,6,1,3,4,2]=>011001=>100110=>011001
[5,7,6,1,4,2,3]=>011010=>010110=>101001
[5,7,6,1,4,3,2]=>011011=>110110=>001001
[5,7,6,2,1,3,4]=>011100=>001110=>110001
[5,7,6,2,1,4,3]=>011101=>101110=>010001
[5,7,6,2,3,1,4]=>011010=>010110=>101001
[5,7,6,2,3,4,1]=>011001=>100110=>011001
[5,7,6,2,4,1,3]=>011010=>010110=>101001
[5,7,6,2,4,3,1]=>011011=>110110=>001001
[5,7,6,3,1,2,4]=>011100=>001110=>110001
[5,7,6,3,1,4,2]=>011101=>101110=>010001
[5,7,6,3,2,1,4]=>011110=>011110=>100001
[5,7,6,3,2,4,1]=>011101=>101110=>010001
[5,7,6,3,4,1,2]=>011010=>010110=>101001
[5,7,6,3,4,2,1]=>011011=>110110=>001001
[5,7,6,4,1,2,3]=>011100=>001110=>110001
[5,7,6,4,1,3,2]=>011101=>101110=>010001
[5,7,6,4,2,1,3]=>011110=>011110=>100001
[5,7,6,4,2,3,1]=>011101=>101110=>010001
[5,7,6,4,3,1,2]=>011110=>011110=>100001
[5,7,6,4,3,2,1]=>011111=>111110=>000001
[6,1,2,3,4,5,7]=>100000=>000001=>111110
[6,1,2,3,4,7,5]=>100001=>100001=>011110
[6,1,2,3,5,4,7]=>100010=>010001=>101110
[6,1,2,3,5,7,4]=>100001=>100001=>011110
[6,1,2,3,7,4,5]=>100010=>010001=>101110
[6,1,2,3,7,5,4]=>100011=>110001=>001110
[6,1,2,4,3,5,7]=>100100=>001001=>110110
[6,1,2,4,3,7,5]=>100101=>101001=>010110
[6,1,2,4,5,3,7]=>100010=>010001=>101110
[6,1,2,4,5,7,3]=>100001=>100001=>011110
[6,1,2,4,7,3,5]=>100010=>010001=>101110
[6,1,2,4,7,5,3]=>100011=>110001=>001110
[6,1,2,5,3,4,7]=>100100=>001001=>110110
[6,1,2,5,3,7,4]=>100101=>101001=>010110
[6,1,2,5,4,3,7]=>100110=>011001=>100110
[6,1,2,5,4,7,3]=>100101=>101001=>010110
[6,1,2,5,7,3,4]=>100010=>010001=>101110
[6,1,2,5,7,4,3]=>100011=>110001=>001110
[6,1,2,7,3,4,5]=>100100=>001001=>110110
[6,1,2,7,3,5,4]=>100101=>101001=>010110
[6,1,2,7,4,3,5]=>100110=>011001=>100110
[6,1,2,7,4,5,3]=>100101=>101001=>010110
[6,1,2,7,5,3,4]=>100110=>011001=>100110
[6,1,2,7,5,4,3]=>100111=>111001=>000110
[6,1,3,2,4,5,7]=>101000=>000101=>111010
[6,1,3,2,4,7,5]=>101001=>100101=>011010
[6,1,3,2,5,4,7]=>101010=>010101=>101010
[6,1,3,2,5,7,4]=>101001=>100101=>011010
[6,1,3,2,7,4,5]=>101010=>010101=>101010
[6,1,3,2,7,5,4]=>101011=>110101=>001010
[6,1,3,4,2,5,7]=>100100=>001001=>110110
[6,1,3,4,2,7,5]=>100101=>101001=>010110
[6,1,3,4,5,2,7]=>100010=>010001=>101110
[6,1,3,4,5,7,2]=>100001=>100001=>011110
[6,1,3,4,7,2,5]=>100010=>010001=>101110
[6,1,3,4,7,5,2]=>100011=>110001=>001110
[6,1,3,5,2,4,7]=>100100=>001001=>110110
[6,1,3,5,2,7,4]=>100101=>101001=>010110
[6,1,3,5,4,2,7]=>100110=>011001=>100110
[6,1,3,5,4,7,2]=>100101=>101001=>010110
[6,1,3,5,7,2,4]=>100010=>010001=>101110
[6,1,3,5,7,4,2]=>100011=>110001=>001110
[6,1,3,7,2,4,5]=>100100=>001001=>110110
[6,1,3,7,2,5,4]=>100101=>101001=>010110
[6,1,3,7,4,2,5]=>100110=>011001=>100110
[6,1,3,7,4,5,2]=>100101=>101001=>010110
[6,1,3,7,5,2,4]=>100110=>011001=>100110
[6,1,3,7,5,4,2]=>100111=>111001=>000110
[6,1,4,2,3,5,7]=>101000=>000101=>111010
[6,1,4,2,3,7,5]=>101001=>100101=>011010
[6,1,4,2,5,3,7]=>101010=>010101=>101010
[6,1,4,2,5,7,3]=>101001=>100101=>011010
[6,1,4,2,7,3,5]=>101010=>010101=>101010
[6,1,4,2,7,5,3]=>101011=>110101=>001010
[6,1,4,3,2,5,7]=>101100=>001101=>110010
[6,1,4,3,2,7,5]=>101101=>101101=>010010
[6,1,4,3,5,2,7]=>101010=>010101=>101010
[6,1,4,3,5,7,2]=>101001=>100101=>011010
[6,1,4,3,7,2,5]=>101010=>010101=>101010
[6,1,4,3,7,5,2]=>101011=>110101=>001010
[6,1,4,5,2,3,7]=>100100=>001001=>110110
[6,1,4,5,2,7,3]=>100101=>101001=>010110
[6,1,4,5,3,2,7]=>100110=>011001=>100110
[6,1,4,5,3,7,2]=>100101=>101001=>010110
[6,1,4,5,7,2,3]=>100010=>010001=>101110
[6,1,4,5,7,3,2]=>100011=>110001=>001110
[6,1,4,7,2,3,5]=>100100=>001001=>110110
[6,1,4,7,2,5,3]=>100101=>101001=>010110
[6,1,4,7,3,2,5]=>100110=>011001=>100110
[6,1,4,7,3,5,2]=>100101=>101001=>010110
[6,1,4,7,5,2,3]=>100110=>011001=>100110
[6,1,4,7,5,3,2]=>100111=>111001=>000110
[6,1,5,2,3,4,7]=>101000=>000101=>111010
[6,1,5,2,3,7,4]=>101001=>100101=>011010
[6,1,5,2,4,3,7]=>101010=>010101=>101010
[6,1,5,2,4,7,3]=>101001=>100101=>011010
[6,1,5,2,7,3,4]=>101010=>010101=>101010
[6,1,5,2,7,4,3]=>101011=>110101=>001010
[6,1,5,3,2,4,7]=>101100=>001101=>110010
[6,1,5,3,2,7,4]=>101101=>101101=>010010
[6,1,5,3,4,2,7]=>101010=>010101=>101010
[6,1,5,3,4,7,2]=>101001=>100101=>011010
[6,1,5,3,7,2,4]=>101010=>010101=>101010
[6,1,5,3,7,4,2]=>101011=>110101=>001010
[6,1,5,4,2,3,7]=>101100=>001101=>110010
[6,1,5,4,2,7,3]=>101101=>101101=>010010
[6,1,5,4,3,2,7]=>101110=>011101=>100010
[6,1,5,4,3,7,2]=>101101=>101101=>010010
[6,1,5,4,7,2,3]=>101010=>010101=>101010
[6,1,5,4,7,3,2]=>101011=>110101=>001010
[6,1,5,7,2,3,4]=>100100=>001001=>110110
[6,1,5,7,2,4,3]=>100101=>101001=>010110
[6,1,5,7,3,2,4]=>100110=>011001=>100110
[6,1,5,7,3,4,2]=>100101=>101001=>010110
[6,1,5,7,4,2,3]=>100110=>011001=>100110
[6,1,5,7,4,3,2]=>100111=>111001=>000110
[6,1,7,2,3,4,5]=>101000=>000101=>111010
[6,1,7,2,3,5,4]=>101001=>100101=>011010
[6,1,7,2,4,3,5]=>101010=>010101=>101010
[6,1,7,2,4,5,3]=>101001=>100101=>011010
[6,1,7,2,5,3,4]=>101010=>010101=>101010
[6,1,7,2,5,4,3]=>101011=>110101=>001010
[6,1,7,3,2,4,5]=>101100=>001101=>110010
[6,1,7,3,2,5,4]=>101101=>101101=>010010
[6,1,7,3,4,2,5]=>101010=>010101=>101010
[6,1,7,3,4,5,2]=>101001=>100101=>011010
[6,1,7,3,5,2,4]=>101010=>010101=>101010
[6,1,7,3,5,4,2]=>101011=>110101=>001010
[6,1,7,4,2,3,5]=>101100=>001101=>110010
[6,1,7,4,2,5,3]=>101101=>101101=>010010
[6,1,7,4,3,2,5]=>101110=>011101=>100010
[6,1,7,4,3,5,2]=>101101=>101101=>010010
[6,1,7,4,5,2,3]=>101010=>010101=>101010
[6,1,7,4,5,3,2]=>101011=>110101=>001010
[6,1,7,5,2,3,4]=>101100=>001101=>110010
[6,1,7,5,2,4,3]=>101101=>101101=>010010
[6,1,7,5,3,2,4]=>101110=>011101=>100010
[6,1,7,5,3,4,2]=>101101=>101101=>010010
[6,1,7,5,4,2,3]=>101110=>011101=>100010
[6,1,7,5,4,3,2]=>101111=>111101=>000010
[6,2,1,3,4,5,7]=>110000=>000011=>111100
[6,2,1,3,4,7,5]=>110001=>100011=>011100
[6,2,1,3,5,4,7]=>110010=>010011=>101100
[6,2,1,3,5,7,4]=>110001=>100011=>011100
[6,2,1,3,7,4,5]=>110010=>010011=>101100
[6,2,1,3,7,5,4]=>110011=>110011=>001100
[6,2,1,4,3,5,7]=>110100=>001011=>110100
[6,2,1,4,3,7,5]=>110101=>101011=>010100
[6,2,1,4,5,3,7]=>110010=>010011=>101100
[6,2,1,4,5,7,3]=>110001=>100011=>011100
[6,2,1,4,7,3,5]=>110010=>010011=>101100
[6,2,1,4,7,5,3]=>110011=>110011=>001100
[6,2,1,5,3,4,7]=>110100=>001011=>110100
[6,2,1,5,3,7,4]=>110101=>101011=>010100
[6,2,1,5,4,3,7]=>110110=>011011=>100100
[6,2,1,5,4,7,3]=>110101=>101011=>010100
[6,2,1,5,7,3,4]=>110010=>010011=>101100
[6,2,1,5,7,4,3]=>110011=>110011=>001100
[6,2,1,7,3,4,5]=>110100=>001011=>110100
[6,2,1,7,3,5,4]=>110101=>101011=>010100
[6,2,1,7,4,3,5]=>110110=>011011=>100100
[6,2,1,7,4,5,3]=>110101=>101011=>010100
[6,2,1,7,5,3,4]=>110110=>011011=>100100
[6,2,1,7,5,4,3]=>110111=>111011=>000100
[6,2,3,1,4,5,7]=>101000=>000101=>111010
[6,2,3,1,4,7,5]=>101001=>100101=>011010
[6,2,3,1,5,4,7]=>101010=>010101=>101010
[6,2,3,1,5,7,4]=>101001=>100101=>011010
[6,2,3,1,7,4,5]=>101010=>010101=>101010
[6,2,3,1,7,5,4]=>101011=>110101=>001010
[6,2,3,4,1,5,7]=>100100=>001001=>110110
[6,2,3,4,1,7,5]=>100101=>101001=>010110
[6,2,3,4,5,1,7]=>100010=>010001=>101110
[6,2,3,4,5,7,1]=>100001=>100001=>011110
[6,2,3,4,7,1,5]=>100010=>010001=>101110
[6,2,3,4,7,5,1]=>100011=>110001=>001110
[6,2,3,5,1,4,7]=>100100=>001001=>110110
[6,2,3,5,1,7,4]=>100101=>101001=>010110
[6,2,3,5,4,1,7]=>100110=>011001=>100110
[6,2,3,5,4,7,1]=>100101=>101001=>010110
[6,2,3,5,7,1,4]=>100010=>010001=>101110
[6,2,3,5,7,4,1]=>100011=>110001=>001110
[6,2,3,7,1,4,5]=>100100=>001001=>110110
[6,2,3,7,1,5,4]=>100101=>101001=>010110
[6,2,3,7,4,1,5]=>100110=>011001=>100110
[6,2,3,7,4,5,1]=>100101=>101001=>010110
[6,2,3,7,5,1,4]=>100110=>011001=>100110
[6,2,3,7,5,4,1]=>100111=>111001=>000110
[6,2,4,1,3,5,7]=>101000=>000101=>111010
[6,2,4,1,3,7,5]=>101001=>100101=>011010
[6,2,4,1,5,3,7]=>101010=>010101=>101010
[6,2,4,1,5,7,3]=>101001=>100101=>011010
[6,2,4,1,7,3,5]=>101010=>010101=>101010
[6,2,4,1,7,5,3]=>101011=>110101=>001010
[6,2,4,3,1,5,7]=>101100=>001101=>110010
[6,2,4,3,1,7,5]=>101101=>101101=>010010
[6,2,4,3,5,1,7]=>101010=>010101=>101010
[6,2,4,3,5,7,1]=>101001=>100101=>011010
[6,2,4,3,7,1,5]=>101010=>010101=>101010
[6,2,4,3,7,5,1]=>101011=>110101=>001010
[6,2,4,5,1,3,7]=>100100=>001001=>110110
[6,2,4,5,1,7,3]=>100101=>101001=>010110
[6,2,4,5,3,1,7]=>100110=>011001=>100110
[6,2,4,5,3,7,1]=>100101=>101001=>010110
[6,2,4,5,7,1,3]=>100010=>010001=>101110
[6,2,4,5,7,3,1]=>100011=>110001=>001110
[6,2,4,7,1,3,5]=>100100=>001001=>110110
[6,2,4,7,1,5,3]=>100101=>101001=>010110
[6,2,4,7,3,1,5]=>100110=>011001=>100110
[6,2,4,7,3,5,1]=>100101=>101001=>010110
[6,2,4,7,5,1,3]=>100110=>011001=>100110
[6,2,4,7,5,3,1]=>100111=>111001=>000110
[6,2,5,1,3,4,7]=>101000=>000101=>111010
[6,2,5,1,3,7,4]=>101001=>100101=>011010
[6,2,5,1,4,3,7]=>101010=>010101=>101010
[6,2,5,1,4,7,3]=>101001=>100101=>011010
[6,2,5,1,7,3,4]=>101010=>010101=>101010
[6,2,5,1,7,4,3]=>101011=>110101=>001010
[6,2,5,3,1,4,7]=>101100=>001101=>110010
[6,2,5,3,1,7,4]=>101101=>101101=>010010
[6,2,5,3,4,1,7]=>101010=>010101=>101010
[6,2,5,3,4,7,1]=>101001=>100101=>011010
[6,2,5,3,7,1,4]=>101010=>010101=>101010
[6,2,5,3,7,4,1]=>101011=>110101=>001010
[6,2,5,4,1,3,7]=>101100=>001101=>110010
[6,2,5,4,1,7,3]=>101101=>101101=>010010
[6,2,5,4,3,1,7]=>101110=>011101=>100010
[6,2,5,4,3,7,1]=>101101=>101101=>010010
[6,2,5,4,7,1,3]=>101010=>010101=>101010
[6,2,5,4,7,3,1]=>101011=>110101=>001010
[6,2,5,7,1,3,4]=>100100=>001001=>110110
[6,2,5,7,1,4,3]=>100101=>101001=>010110
[6,2,5,7,3,1,4]=>100110=>011001=>100110
[6,2,5,7,3,4,1]=>100101=>101001=>010110
[6,2,5,7,4,1,3]=>100110=>011001=>100110
[6,2,5,7,4,3,1]=>100111=>111001=>000110
[6,2,7,1,3,4,5]=>101000=>000101=>111010
[6,2,7,1,3,5,4]=>101001=>100101=>011010
[6,2,7,1,4,3,5]=>101010=>010101=>101010
[6,2,7,1,4,5,3]=>101001=>100101=>011010
[6,2,7,1,5,3,4]=>101010=>010101=>101010
[6,2,7,1,5,4,3]=>101011=>110101=>001010
[6,2,7,3,1,4,5]=>101100=>001101=>110010
[6,2,7,3,1,5,4]=>101101=>101101=>010010
[6,2,7,3,4,1,5]=>101010=>010101=>101010
[6,2,7,3,4,5,1]=>101001=>100101=>011010
[6,2,7,3,5,1,4]=>101010=>010101=>101010
[6,2,7,3,5,4,1]=>101011=>110101=>001010
[6,2,7,4,1,3,5]=>101100=>001101=>110010
[6,2,7,4,1,5,3]=>101101=>101101=>010010
[6,2,7,4,3,1,5]=>101110=>011101=>100010
[6,2,7,4,3,5,1]=>101101=>101101=>010010
[6,2,7,4,5,1,3]=>101010=>010101=>101010
[6,2,7,4,5,3,1]=>101011=>110101=>001010
[6,2,7,5,1,3,4]=>101100=>001101=>110010
[6,2,7,5,1,4,3]=>101101=>101101=>010010
[6,2,7,5,3,1,4]=>101110=>011101=>100010
[6,2,7,5,3,4,1]=>101101=>101101=>010010
[6,2,7,5,4,1,3]=>101110=>011101=>100010
[6,2,7,5,4,3,1]=>101111=>111101=>000010
[6,3,1,2,4,5,7]=>110000=>000011=>111100
[6,3,1,2,4,7,5]=>110001=>100011=>011100
[6,3,1,2,5,4,7]=>110010=>010011=>101100
[6,3,1,2,5,7,4]=>110001=>100011=>011100
[6,3,1,2,7,4,5]=>110010=>010011=>101100
[6,3,1,2,7,5,4]=>110011=>110011=>001100
[6,3,1,4,2,5,7]=>110100=>001011=>110100
[6,3,1,4,2,7,5]=>110101=>101011=>010100
[6,3,1,4,5,2,7]=>110010=>010011=>101100
[6,3,1,4,5,7,2]=>110001=>100011=>011100
[6,3,1,4,7,2,5]=>110010=>010011=>101100
[6,3,1,4,7,5,2]=>110011=>110011=>001100
[6,3,1,5,2,4,7]=>110100=>001011=>110100
[6,3,1,5,2,7,4]=>110101=>101011=>010100
[6,3,1,5,4,2,7]=>110110=>011011=>100100
[6,3,1,5,4,7,2]=>110101=>101011=>010100
[6,3,1,5,7,2,4]=>110010=>010011=>101100
[6,3,1,5,7,4,2]=>110011=>110011=>001100
[6,3,1,7,2,4,5]=>110100=>001011=>110100
[6,3,1,7,2,5,4]=>110101=>101011=>010100
[6,3,1,7,4,2,5]=>110110=>011011=>100100
[6,3,1,7,4,5,2]=>110101=>101011=>010100
[6,3,1,7,5,2,4]=>110110=>011011=>100100
[6,3,1,7,5,4,2]=>110111=>111011=>000100
[6,3,2,1,4,5,7]=>111000=>000111=>111000
[6,3,2,1,4,7,5]=>111001=>100111=>011000
[6,3,2,1,5,4,7]=>111010=>010111=>101000
[6,3,2,1,5,7,4]=>111001=>100111=>011000
[6,3,2,1,7,4,5]=>111010=>010111=>101000
[6,3,2,1,7,5,4]=>111011=>110111=>001000
[6,3,2,4,1,5,7]=>110100=>001011=>110100
[6,3,2,4,1,7,5]=>110101=>101011=>010100
[6,3,2,4,5,1,7]=>110010=>010011=>101100
[6,3,2,4,5,7,1]=>110001=>100011=>011100
[6,3,2,4,7,1,5]=>110010=>010011=>101100
[6,3,2,4,7,5,1]=>110011=>110011=>001100
[6,3,2,5,1,4,7]=>110100=>001011=>110100
[6,3,2,5,1,7,4]=>110101=>101011=>010100
[6,3,2,5,4,1,7]=>110110=>011011=>100100
[6,3,2,5,4,7,1]=>110101=>101011=>010100
[6,3,2,5,7,1,4]=>110010=>010011=>101100
[6,3,2,5,7,4,1]=>110011=>110011=>001100
[6,3,2,7,1,4,5]=>110100=>001011=>110100
[6,3,2,7,1,5,4]=>110101=>101011=>010100
[6,3,2,7,4,1,5]=>110110=>011011=>100100
[6,3,2,7,4,5,1]=>110101=>101011=>010100
[6,3,2,7,5,1,4]=>110110=>011011=>100100
[6,3,2,7,5,4,1]=>110111=>111011=>000100
[6,3,4,1,2,5,7]=>101000=>000101=>111010
[6,3,4,1,2,7,5]=>101001=>100101=>011010
[6,3,4,1,5,2,7]=>101010=>010101=>101010
[6,3,4,1,5,7,2]=>101001=>100101=>011010
[6,3,4,1,7,2,5]=>101010=>010101=>101010
[6,3,4,1,7,5,2]=>101011=>110101=>001010
[6,3,4,2,1,5,7]=>101100=>001101=>110010
[6,3,4,2,1,7,5]=>101101=>101101=>010010
[6,3,4,2,5,1,7]=>101010=>010101=>101010
[6,3,4,2,5,7,1]=>101001=>100101=>011010
[6,3,4,2,7,1,5]=>101010=>010101=>101010
[6,3,4,2,7,5,1]=>101011=>110101=>001010
[6,3,4,5,1,2,7]=>100100=>001001=>110110
[6,3,4,5,1,7,2]=>100101=>101001=>010110
[6,3,4,5,2,1,7]=>100110=>011001=>100110
[6,3,4,5,2,7,1]=>100101=>101001=>010110
[6,3,4,5,7,1,2]=>100010=>010001=>101110
[6,3,4,5,7,2,1]=>100011=>110001=>001110
[6,3,4,7,1,2,5]=>100100=>001001=>110110
[6,3,4,7,1,5,2]=>100101=>101001=>010110
[6,3,4,7,2,1,5]=>100110=>011001=>100110
[6,3,4,7,2,5,1]=>100101=>101001=>010110
[6,3,4,7,5,1,2]=>100110=>011001=>100110
[6,3,4,7,5,2,1]=>100111=>111001=>000110
[6,3,5,1,2,4,7]=>101000=>000101=>111010
[6,3,5,1,2,7,4]=>101001=>100101=>011010
[6,3,5,1,4,2,7]=>101010=>010101=>101010
[6,3,5,1,4,7,2]=>101001=>100101=>011010
[6,3,5,1,7,2,4]=>101010=>010101=>101010
[6,3,5,1,7,4,2]=>101011=>110101=>001010
[6,3,5,2,1,4,7]=>101100=>001101=>110010
[6,3,5,2,1,7,4]=>101101=>101101=>010010
[6,3,5,2,4,1,7]=>101010=>010101=>101010
[6,3,5,2,4,7,1]=>101001=>100101=>011010
[6,3,5,2,7,1,4]=>101010=>010101=>101010
[6,3,5,2,7,4,1]=>101011=>110101=>001010
[6,3,5,4,1,2,7]=>101100=>001101=>110010
[6,3,5,4,1,7,2]=>101101=>101101=>010010
[6,3,5,4,2,1,7]=>101110=>011101=>100010
[6,3,5,4,2,7,1]=>101101=>101101=>010010
[6,3,5,4,7,1,2]=>101010=>010101=>101010
[6,3,5,4,7,2,1]=>101011=>110101=>001010
[6,3,5,7,1,2,4]=>100100=>001001=>110110
[6,3,5,7,1,4,2]=>100101=>101001=>010110
[6,3,5,7,2,1,4]=>100110=>011001=>100110
[6,3,5,7,2,4,1]=>100101=>101001=>010110
[6,3,5,7,4,1,2]=>100110=>011001=>100110
[6,3,5,7,4,2,1]=>100111=>111001=>000110
[6,3,7,1,2,4,5]=>101000=>000101=>111010
[6,3,7,1,2,5,4]=>101001=>100101=>011010
[6,3,7,1,4,2,5]=>101010=>010101=>101010
[6,3,7,1,4,5,2]=>101001=>100101=>011010
[6,3,7,1,5,2,4]=>101010=>010101=>101010
[6,3,7,1,5,4,2]=>101011=>110101=>001010
[6,3,7,2,1,4,5]=>101100=>001101=>110010
[6,3,7,2,1,5,4]=>101101=>101101=>010010
[6,3,7,2,4,1,5]=>101010=>010101=>101010
[6,3,7,2,4,5,1]=>101001=>100101=>011010
[6,3,7,2,5,1,4]=>101010=>010101=>101010
[6,3,7,2,5,4,1]=>101011=>110101=>001010
[6,3,7,4,1,2,5]=>101100=>001101=>110010
[6,3,7,4,1,5,2]=>101101=>101101=>010010
[6,3,7,4,2,1,5]=>101110=>011101=>100010
[6,3,7,4,2,5,1]=>101101=>101101=>010010
[6,3,7,4,5,1,2]=>101010=>010101=>101010
[6,3,7,4,5,2,1]=>101011=>110101=>001010
[6,3,7,5,1,2,4]=>101100=>001101=>110010
[6,3,7,5,1,4,2]=>101101=>101101=>010010
[6,3,7,5,2,1,4]=>101110=>011101=>100010
[6,3,7,5,2,4,1]=>101101=>101101=>010010
[6,3,7,5,4,1,2]=>101110=>011101=>100010
[6,3,7,5,4,2,1]=>101111=>111101=>000010
[6,4,1,2,3,5,7]=>110000=>000011=>111100
[6,4,1,2,3,7,5]=>110001=>100011=>011100
[6,4,1,2,5,3,7]=>110010=>010011=>101100
[6,4,1,2,5,7,3]=>110001=>100011=>011100
[6,4,1,2,7,3,5]=>110010=>010011=>101100
[6,4,1,2,7,5,3]=>110011=>110011=>001100
[6,4,1,3,2,5,7]=>110100=>001011=>110100
[6,4,1,3,2,7,5]=>110101=>101011=>010100
[6,4,1,3,5,2,7]=>110010=>010011=>101100
[6,4,1,3,5,7,2]=>110001=>100011=>011100
[6,4,1,3,7,2,5]=>110010=>010011=>101100
[6,4,1,3,7,5,2]=>110011=>110011=>001100
[6,4,1,5,2,3,7]=>110100=>001011=>110100
[6,4,1,5,2,7,3]=>110101=>101011=>010100
[6,4,1,5,3,2,7]=>110110=>011011=>100100
[6,4,1,5,3,7,2]=>110101=>101011=>010100
[6,4,1,5,7,2,3]=>110010=>010011=>101100
[6,4,1,5,7,3,2]=>110011=>110011=>001100
[6,4,1,7,2,3,5]=>110100=>001011=>110100
[6,4,1,7,2,5,3]=>110101=>101011=>010100
[6,4,1,7,3,2,5]=>110110=>011011=>100100
[6,4,1,7,3,5,2]=>110101=>101011=>010100
[6,4,1,7,5,2,3]=>110110=>011011=>100100
[6,4,1,7,5,3,2]=>110111=>111011=>000100
[6,4,2,1,3,5,7]=>111000=>000111=>111000
[6,4,2,1,3,7,5]=>111001=>100111=>011000
[6,4,2,1,5,3,7]=>111010=>010111=>101000
[6,4,2,1,5,7,3]=>111001=>100111=>011000
[6,4,2,1,7,3,5]=>111010=>010111=>101000
[6,4,2,1,7,5,3]=>111011=>110111=>001000
[6,4,2,3,1,5,7]=>110100=>001011=>110100
[6,4,2,3,1,7,5]=>110101=>101011=>010100
[6,4,2,3,5,1,7]=>110010=>010011=>101100
[6,4,2,3,5,7,1]=>110001=>100011=>011100
[6,4,2,3,7,1,5]=>110010=>010011=>101100
[6,4,2,3,7,5,1]=>110011=>110011=>001100
[6,4,2,5,1,3,7]=>110100=>001011=>110100
[6,4,2,5,1,7,3]=>110101=>101011=>010100
[6,4,2,5,3,1,7]=>110110=>011011=>100100
[6,4,2,5,3,7,1]=>110101=>101011=>010100
[6,4,2,5,7,1,3]=>110010=>010011=>101100
[6,4,2,5,7,3,1]=>110011=>110011=>001100
[6,4,2,7,1,3,5]=>110100=>001011=>110100
[6,4,2,7,1,5,3]=>110101=>101011=>010100
[6,4,2,7,3,1,5]=>110110=>011011=>100100
[6,4,2,7,3,5,1]=>110101=>101011=>010100
[6,4,2,7,5,1,3]=>110110=>011011=>100100
[6,4,2,7,5,3,1]=>110111=>111011=>000100
[6,4,3,1,2,5,7]=>111000=>000111=>111000
[6,4,3,1,2,7,5]=>111001=>100111=>011000
[6,4,3,1,5,2,7]=>111010=>010111=>101000
[6,4,3,1,5,7,2]=>111001=>100111=>011000
[6,4,3,1,7,2,5]=>111010=>010111=>101000
[6,4,3,1,7,5,2]=>111011=>110111=>001000
[6,4,3,2,1,5,7]=>111100=>001111=>110000
[6,4,3,2,1,7,5]=>111101=>101111=>010000
[6,4,3,2,5,1,7]=>111010=>010111=>101000
[6,4,3,2,5,7,1]=>111001=>100111=>011000
[6,4,3,2,7,1,5]=>111010=>010111=>101000
[6,4,3,2,7,5,1]=>111011=>110111=>001000
[6,4,3,5,1,2,7]=>110100=>001011=>110100
[6,4,3,5,1,7,2]=>110101=>101011=>010100
[6,4,3,5,2,1,7]=>110110=>011011=>100100
[6,4,3,5,2,7,1]=>110101=>101011=>010100
[6,4,3,5,7,1,2]=>110010=>010011=>101100
[6,4,3,5,7,2,1]=>110011=>110011=>001100
[6,4,3,7,1,2,5]=>110100=>001011=>110100
[6,4,3,7,1,5,2]=>110101=>101011=>010100
[6,4,3,7,2,1,5]=>110110=>011011=>100100
[6,4,3,7,2,5,1]=>110101=>101011=>010100
[6,4,3,7,5,1,2]=>110110=>011011=>100100
[6,4,3,7,5,2,1]=>110111=>111011=>000100
[6,4,5,1,2,3,7]=>101000=>000101=>111010
[6,4,5,1,2,7,3]=>101001=>100101=>011010
[6,4,5,1,3,2,7]=>101010=>010101=>101010
[6,4,5,1,3,7,2]=>101001=>100101=>011010
[6,4,5,1,7,2,3]=>101010=>010101=>101010
[6,4,5,1,7,3,2]=>101011=>110101=>001010
[6,4,5,2,1,3,7]=>101100=>001101=>110010
[6,4,5,2,1,7,3]=>101101=>101101=>010010
[6,4,5,2,3,1,7]=>101010=>010101=>101010
[6,4,5,2,3,7,1]=>101001=>100101=>011010
[6,4,5,2,7,1,3]=>101010=>010101=>101010
[6,4,5,2,7,3,1]=>101011=>110101=>001010
[6,4,5,3,1,2,7]=>101100=>001101=>110010
[6,4,5,3,1,7,2]=>101101=>101101=>010010
[6,4,5,3,2,1,7]=>101110=>011101=>100010
[6,4,5,3,2,7,1]=>101101=>101101=>010010
[6,4,5,3,7,1,2]=>101010=>010101=>101010
[6,4,5,3,7,2,1]=>101011=>110101=>001010
[6,4,5,7,1,2,3]=>100100=>001001=>110110
[6,4,5,7,1,3,2]=>100101=>101001=>010110
[6,4,5,7,2,1,3]=>100110=>011001=>100110
[6,4,5,7,2,3,1]=>100101=>101001=>010110
[6,4,5,7,3,1,2]=>100110=>011001=>100110
[6,4,5,7,3,2,1]=>100111=>111001=>000110
[6,4,7,1,2,3,5]=>101000=>000101=>111010
[6,4,7,1,2,5,3]=>101001=>100101=>011010
[6,4,7,1,3,2,5]=>101010=>010101=>101010
[6,4,7,1,3,5,2]=>101001=>100101=>011010
[6,4,7,1,5,2,3]=>101010=>010101=>101010
[6,4,7,1,5,3,2]=>101011=>110101=>001010
[6,4,7,2,1,3,5]=>101100=>001101=>110010
[6,4,7,2,1,5,3]=>101101=>101101=>010010
[6,4,7,2,3,1,5]=>101010=>010101=>101010
[6,4,7,2,3,5,1]=>101001=>100101=>011010
[6,4,7,2,5,1,3]=>101010=>010101=>101010
[6,4,7,2,5,3,1]=>101011=>110101=>001010
[6,4,7,3,1,2,5]=>101100=>001101=>110010
[6,4,7,3,1,5,2]=>101101=>101101=>010010
[6,4,7,3,2,1,5]=>101110=>011101=>100010
[6,4,7,3,2,5,1]=>101101=>101101=>010010
[6,4,7,3,5,1,2]=>101010=>010101=>101010
[6,4,7,3,5,2,1]=>101011=>110101=>001010
[6,4,7,5,1,2,3]=>101100=>001101=>110010
[6,4,7,5,1,3,2]=>101101=>101101=>010010
[6,4,7,5,2,1,3]=>101110=>011101=>100010
[6,4,7,5,2,3,1]=>101101=>101101=>010010
[6,4,7,5,3,1,2]=>101110=>011101=>100010
[6,4,7,5,3,2,1]=>101111=>111101=>000010
[6,5,1,2,3,4,7]=>110000=>000011=>111100
[6,5,1,2,3,7,4]=>110001=>100011=>011100
[6,5,1,2,4,3,7]=>110010=>010011=>101100
[6,5,1,2,4,7,3]=>110001=>100011=>011100
[6,5,1,2,7,3,4]=>110010=>010011=>101100
[6,5,1,2,7,4,3]=>110011=>110011=>001100
[6,5,1,3,2,4,7]=>110100=>001011=>110100
[6,5,1,3,2,7,4]=>110101=>101011=>010100
[6,5,1,3,4,2,7]=>110010=>010011=>101100
[6,5,1,3,4,7,2]=>110001=>100011=>011100
[6,5,1,3,7,2,4]=>110010=>010011=>101100
[6,5,1,3,7,4,2]=>110011=>110011=>001100
[6,5,1,4,2,3,7]=>110100=>001011=>110100
[6,5,1,4,2,7,3]=>110101=>101011=>010100
[6,5,1,4,3,2,7]=>110110=>011011=>100100
[6,5,1,4,3,7,2]=>110101=>101011=>010100
[6,5,1,4,7,2,3]=>110010=>010011=>101100
[6,5,1,4,7,3,2]=>110011=>110011=>001100
[6,5,1,7,2,3,4]=>110100=>001011=>110100
[6,5,1,7,2,4,3]=>110101=>101011=>010100
[6,5,1,7,3,2,4]=>110110=>011011=>100100
[6,5,1,7,3,4,2]=>110101=>101011=>010100
[6,5,1,7,4,2,3]=>110110=>011011=>100100
[6,5,1,7,4,3,2]=>110111=>111011=>000100
[6,5,2,1,3,4,7]=>111000=>000111=>111000
[6,5,2,1,3,7,4]=>111001=>100111=>011000
[6,5,2,1,4,3,7]=>111010=>010111=>101000
[6,5,2,1,4,7,3]=>111001=>100111=>011000
[6,5,2,1,7,3,4]=>111010=>010111=>101000
[6,5,2,1,7,4,3]=>111011=>110111=>001000
[6,5,2,3,1,4,7]=>110100=>001011=>110100
[6,5,2,3,1,7,4]=>110101=>101011=>010100
[6,5,2,3,4,1,7]=>110010=>010011=>101100
[6,5,2,3,4,7,1]=>110001=>100011=>011100
[6,5,2,3,7,1,4]=>110010=>010011=>101100
[6,5,2,3,7,4,1]=>110011=>110011=>001100
[6,5,2,4,1,3,7]=>110100=>001011=>110100
[6,5,2,4,1,7,3]=>110101=>101011=>010100
[6,5,2,4,3,1,7]=>110110=>011011=>100100
[6,5,2,4,3,7,1]=>110101=>101011=>010100
[6,5,2,4,7,1,3]=>110010=>010011=>101100
[6,5,2,4,7,3,1]=>110011=>110011=>001100
[6,5,2,7,1,3,4]=>110100=>001011=>110100
[6,5,2,7,1,4,3]=>110101=>101011=>010100
[6,5,2,7,3,1,4]=>110110=>011011=>100100
[6,5,2,7,3,4,1]=>110101=>101011=>010100
[6,5,2,7,4,1,3]=>110110=>011011=>100100
[6,5,2,7,4,3,1]=>110111=>111011=>000100
[6,5,3,1,2,4,7]=>111000=>000111=>111000
[6,5,3,1,2,7,4]=>111001=>100111=>011000
[6,5,3,1,4,2,7]=>111010=>010111=>101000
[6,5,3,1,4,7,2]=>111001=>100111=>011000
[6,5,3,1,7,2,4]=>111010=>010111=>101000
[6,5,3,1,7,4,2]=>111011=>110111=>001000
[6,5,3,2,1,4,7]=>111100=>001111=>110000
[6,5,3,2,1,7,4]=>111101=>101111=>010000
[6,5,3,2,4,1,7]=>111010=>010111=>101000
[6,5,3,2,4,7,1]=>111001=>100111=>011000
[6,5,3,2,7,1,4]=>111010=>010111=>101000
[6,5,3,2,7,4,1]=>111011=>110111=>001000
[6,5,3,4,1,2,7]=>110100=>001011=>110100
[6,5,3,4,1,7,2]=>110101=>101011=>010100
[6,5,3,4,2,1,7]=>110110=>011011=>100100
[6,5,3,4,2,7,1]=>110101=>101011=>010100
[6,5,3,4,7,1,2]=>110010=>010011=>101100
[6,5,3,4,7,2,1]=>110011=>110011=>001100
[6,5,3,7,1,2,4]=>110100=>001011=>110100
[6,5,3,7,1,4,2]=>110101=>101011=>010100
[6,5,3,7,2,1,4]=>110110=>011011=>100100
[6,5,3,7,2,4,1]=>110101=>101011=>010100
[6,5,3,7,4,1,2]=>110110=>011011=>100100
[6,5,3,7,4,2,1]=>110111=>111011=>000100
[6,5,4,1,2,3,7]=>111000=>000111=>111000
[6,5,4,1,2,7,3]=>111001=>100111=>011000
[6,5,4,1,3,2,7]=>111010=>010111=>101000
[6,5,4,1,3,7,2]=>111001=>100111=>011000
[6,5,4,1,7,2,3]=>111010=>010111=>101000
[6,5,4,1,7,3,2]=>111011=>110111=>001000
[6,5,4,2,1,3,7]=>111100=>001111=>110000
[6,5,4,2,1,7,3]=>111101=>101111=>010000
[6,5,4,2,3,1,7]=>111010=>010111=>101000
[6,5,4,2,3,7,1]=>111001=>100111=>011000
[6,5,4,2,7,1,3]=>111010=>010111=>101000
[6,5,4,2,7,3,1]=>111011=>110111=>001000
[6,5,4,3,1,2,7]=>111100=>001111=>110000
[6,5,4,3,1,7,2]=>111101=>101111=>010000
[6,5,4,3,2,1,7]=>111110=>011111=>100000
[6,5,4,3,2,7,1]=>111101=>101111=>010000
[6,5,4,3,7,1,2]=>111010=>010111=>101000
[6,5,4,3,7,2,1]=>111011=>110111=>001000
[6,5,4,7,1,2,3]=>110100=>001011=>110100
[6,5,4,7,1,3,2]=>110101=>101011=>010100
[6,5,4,7,2,1,3]=>110110=>011011=>100100
[6,5,4,7,2,3,1]=>110101=>101011=>010100
[6,5,4,7,3,1,2]=>110110=>011011=>100100
[6,5,4,7,3,2,1]=>110111=>111011=>000100
[6,5,7,1,2,3,4]=>101000=>000101=>111010
[6,5,7,1,2,4,3]=>101001=>100101=>011010
[6,5,7,1,3,2,4]=>101010=>010101=>101010
[6,5,7,1,3,4,2]=>101001=>100101=>011010
[6,5,7,1,4,2,3]=>101010=>010101=>101010
[6,5,7,1,4,3,2]=>101011=>110101=>001010
[6,5,7,2,1,3,4]=>101100=>001101=>110010
[6,5,7,2,1,4,3]=>101101=>101101=>010010
[6,5,7,2,3,1,4]=>101010=>010101=>101010
[6,5,7,2,3,4,1]=>101001=>100101=>011010
[6,5,7,2,4,1,3]=>101010=>010101=>101010
[6,5,7,2,4,3,1]=>101011=>110101=>001010
[6,5,7,3,1,2,4]=>101100=>001101=>110010
[6,5,7,3,1,4,2]=>101101=>101101=>010010
[6,5,7,3,2,1,4]=>101110=>011101=>100010
[6,5,7,3,2,4,1]=>101101=>101101=>010010
[6,5,7,3,4,1,2]=>101010=>010101=>101010
[6,5,7,3,4,2,1]=>101011=>110101=>001010
[6,5,7,4,1,2,3]=>101100=>001101=>110010
[6,5,7,4,1,3,2]=>101101=>101101=>010010
[6,5,7,4,2,1,3]=>101110=>011101=>100010
[6,5,7,4,2,3,1]=>101101=>101101=>010010
[6,5,7,4,3,1,2]=>101110=>011101=>100010
[6,5,7,4,3,2,1]=>101111=>111101=>000010
[6,7,1,2,3,4,5]=>010000=>000010=>111101
[6,7,1,2,3,5,4]=>010001=>100010=>011101
[6,7,1,2,4,3,5]=>010010=>010010=>101101
[6,7,1,2,4,5,3]=>010001=>100010=>011101
[6,7,1,2,5,3,4]=>010010=>010010=>101101
[6,7,1,2,5,4,3]=>010011=>110010=>001101
[6,7,1,3,2,4,5]=>010100=>001010=>110101
[6,7,1,3,2,5,4]=>010101=>101010=>010101
[6,7,1,3,4,2,5]=>010010=>010010=>101101
[6,7,1,3,4,5,2]=>010001=>100010=>011101
[6,7,1,3,5,2,4]=>010010=>010010=>101101
[6,7,1,3,5,4,2]=>010011=>110010=>001101
[6,7,1,4,2,3,5]=>010100=>001010=>110101
[6,7,1,4,2,5,3]=>010101=>101010=>010101
[6,7,1,4,3,2,5]=>010110=>011010=>100101
[6,7,1,4,3,5,2]=>010101=>101010=>010101
[6,7,1,4,5,2,3]=>010010=>010010=>101101
[6,7,1,4,5,3,2]=>010011=>110010=>001101
[6,7,1,5,2,3,4]=>010100=>001010=>110101
[6,7,1,5,2,4,3]=>010101=>101010=>010101
[6,7,1,5,3,2,4]=>010110=>011010=>100101
[6,7,1,5,3,4,2]=>010101=>101010=>010101
[6,7,1,5,4,2,3]=>010110=>011010=>100101
[6,7,1,5,4,3,2]=>010111=>111010=>000101
[6,7,2,1,3,4,5]=>011000=>000110=>111001
[6,7,2,1,3,5,4]=>011001=>100110=>011001
[6,7,2,1,4,3,5]=>011010=>010110=>101001
[6,7,2,1,4,5,3]=>011001=>100110=>011001
[6,7,2,1,5,3,4]=>011010=>010110=>101001
[6,7,2,1,5,4,3]=>011011=>110110=>001001
[6,7,2,3,1,4,5]=>010100=>001010=>110101
[6,7,2,3,1,5,4]=>010101=>101010=>010101
[6,7,2,3,4,1,5]=>010010=>010010=>101101
[6,7,2,3,4,5,1]=>010001=>100010=>011101
[6,7,2,3,5,1,4]=>010010=>010010=>101101
[6,7,2,3,5,4,1]=>010011=>110010=>001101
[6,7,2,4,1,3,5]=>010100=>001010=>110101
[6,7,2,4,1,5,3]=>010101=>101010=>010101
[6,7,2,4,3,1,5]=>010110=>011010=>100101
[6,7,2,4,3,5,1]=>010101=>101010=>010101
[6,7,2,4,5,1,3]=>010010=>010010=>101101
[6,7,2,4,5,3,1]=>010011=>110010=>001101
[6,7,2,5,1,3,4]=>010100=>001010=>110101
[6,7,2,5,1,4,3]=>010101=>101010=>010101
[6,7,2,5,3,1,4]=>010110=>011010=>100101
[6,7,2,5,3,4,1]=>010101=>101010=>010101
[6,7,2,5,4,1,3]=>010110=>011010=>100101
[6,7,2,5,4,3,1]=>010111=>111010=>000101
[6,7,3,1,2,4,5]=>011000=>000110=>111001
[6,7,3,1,2,5,4]=>011001=>100110=>011001
[6,7,3,1,4,2,5]=>011010=>010110=>101001
[6,7,3,1,4,5,2]=>011001=>100110=>011001
[6,7,3,1,5,2,4]=>011010=>010110=>101001
[6,7,3,1,5,4,2]=>011011=>110110=>001001
[6,7,3,2,1,4,5]=>011100=>001110=>110001
[6,7,3,2,1,5,4]=>011101=>101110=>010001
[6,7,3,2,4,1,5]=>011010=>010110=>101001
[6,7,3,2,4,5,1]=>011001=>100110=>011001
[6,7,3,2,5,1,4]=>011010=>010110=>101001
[6,7,3,2,5,4,1]=>011011=>110110=>001001
[6,7,3,4,1,2,5]=>010100=>001010=>110101
[6,7,3,4,1,5,2]=>010101=>101010=>010101
[6,7,3,4,2,1,5]=>010110=>011010=>100101
[6,7,3,4,2,5,1]=>010101=>101010=>010101
[6,7,3,4,5,1,2]=>010010=>010010=>101101
[6,7,3,4,5,2,1]=>010011=>110010=>001101
[6,7,3,5,1,2,4]=>010100=>001010=>110101
[6,7,3,5,1,4,2]=>010101=>101010=>010101
[6,7,3,5,2,1,4]=>010110=>011010=>100101
[6,7,3,5,2,4,1]=>010101=>101010=>010101
[6,7,3,5,4,1,2]=>010110=>011010=>100101
[6,7,3,5,4,2,1]=>010111=>111010=>000101
[6,7,4,1,2,3,5]=>011000=>000110=>111001
[6,7,4,1,2,5,3]=>011001=>100110=>011001
[6,7,4,1,3,2,5]=>011010=>010110=>101001
[6,7,4,1,3,5,2]=>011001=>100110=>011001
[6,7,4,1,5,2,3]=>011010=>010110=>101001
[6,7,4,1,5,3,2]=>011011=>110110=>001001
[6,7,4,2,1,3,5]=>011100=>001110=>110001
[6,7,4,2,1,5,3]=>011101=>101110=>010001
[6,7,4,2,3,1,5]=>011010=>010110=>101001
[6,7,4,2,3,5,1]=>011001=>100110=>011001
[6,7,4,2,5,1,3]=>011010=>010110=>101001
[6,7,4,2,5,3,1]=>011011=>110110=>001001
[6,7,4,3,1,2,5]=>011100=>001110=>110001
[6,7,4,3,1,5,2]=>011101=>101110=>010001
[6,7,4,3,2,1,5]=>011110=>011110=>100001
[6,7,4,3,2,5,1]=>011101=>101110=>010001
[6,7,4,3,5,1,2]=>011010=>010110=>101001
[6,7,4,3,5,2,1]=>011011=>110110=>001001
[6,7,4,5,1,2,3]=>010100=>001010=>110101
[6,7,4,5,1,3,2]=>010101=>101010=>010101
[6,7,4,5,2,1,3]=>010110=>011010=>100101
[6,7,4,5,2,3,1]=>010101=>101010=>010101
[6,7,4,5,3,1,2]=>010110=>011010=>100101
[6,7,4,5,3,2,1]=>010111=>111010=>000101
[6,7,5,1,2,3,4]=>011000=>000110=>111001
[6,7,5,1,2,4,3]=>011001=>100110=>011001
[6,7,5,1,3,2,4]=>011010=>010110=>101001
[6,7,5,1,3,4,2]=>011001=>100110=>011001
[6,7,5,1,4,2,3]=>011010=>010110=>101001
[6,7,5,1,4,3,2]=>011011=>110110=>001001
[6,7,5,2,1,3,4]=>011100=>001110=>110001
[6,7,5,2,1,4,3]=>011101=>101110=>010001
[6,7,5,2,3,1,4]=>011010=>010110=>101001
[6,7,5,2,3,4,1]=>011001=>100110=>011001
[6,7,5,2,4,1,3]=>011010=>010110=>101001
[6,7,5,2,4,3,1]=>011011=>110110=>001001
[6,7,5,3,1,2,4]=>011100=>001110=>110001
[6,7,5,3,1,4,2]=>011101=>101110=>010001
[6,7,5,3,2,1,4]=>011110=>011110=>100001
[6,7,5,3,2,4,1]=>011101=>101110=>010001
[6,7,5,3,4,1,2]=>011010=>010110=>101001
[6,7,5,3,4,2,1]=>011011=>110110=>001001
[6,7,5,4,1,2,3]=>011100=>001110=>110001
[6,7,5,4,1,3,2]=>011101=>101110=>010001
[6,7,5,4,2,1,3]=>011110=>011110=>100001
[6,7,5,4,2,3,1]=>011101=>101110=>010001
[6,7,5,4,3,1,2]=>011110=>011110=>100001
[6,7,5,4,3,2,1]=>011111=>111110=>000001
[7,1,2,3,4,5,6]=>100000=>000001=>111110
[7,1,2,3,4,6,5]=>100001=>100001=>011110
[7,1,2,3,5,4,6]=>100010=>010001=>101110
[7,1,2,3,5,6,4]=>100001=>100001=>011110
[7,1,2,3,6,4,5]=>100010=>010001=>101110
[7,1,2,3,6,5,4]=>100011=>110001=>001110
[7,1,2,4,3,5,6]=>100100=>001001=>110110
[7,1,2,4,3,6,5]=>100101=>101001=>010110
[7,1,2,4,5,3,6]=>100010=>010001=>101110
[7,1,2,4,5,6,3]=>100001=>100001=>011110
[7,1,2,4,6,3,5]=>100010=>010001=>101110
[7,1,2,4,6,5,3]=>100011=>110001=>001110
[7,1,2,5,3,4,6]=>100100=>001001=>110110
[7,1,2,5,3,6,4]=>100101=>101001=>010110
[7,1,2,5,4,3,6]=>100110=>011001=>100110
[7,1,2,5,4,6,3]=>100101=>101001=>010110
[7,1,2,5,6,3,4]=>100010=>010001=>101110
[7,1,2,5,6,4,3]=>100011=>110001=>001110
[7,1,2,6,3,4,5]=>100100=>001001=>110110
[7,1,2,6,3,5,4]=>100101=>101001=>010110
[7,1,2,6,4,3,5]=>100110=>011001=>100110
[7,1,2,6,4,5,3]=>100101=>101001=>010110
[7,1,2,6,5,3,4]=>100110=>011001=>100110
[7,1,2,6,5,4,3]=>100111=>111001=>000110
[7,1,3,2,4,5,6]=>101000=>000101=>111010
[7,1,3,2,4,6,5]=>101001=>100101=>011010
[7,1,3,2,5,4,6]=>101010=>010101=>101010
[7,1,3,2,5,6,4]=>101001=>100101=>011010
[7,1,3,2,6,4,5]=>101010=>010101=>101010
[7,1,3,2,6,5,4]=>101011=>110101=>001010
[7,1,3,4,2,5,6]=>100100=>001001=>110110
[7,1,3,4,2,6,5]=>100101=>101001=>010110
[7,1,3,4,5,2,6]=>100010=>010001=>101110
[7,1,3,4,5,6,2]=>100001=>100001=>011110
[7,1,3,4,6,2,5]=>100010=>010001=>101110
[7,1,3,4,6,5,2]=>100011=>110001=>001110
[7,1,3,5,2,4,6]=>100100=>001001=>110110
[7,1,3,5,2,6,4]=>100101=>101001=>010110
[7,1,3,5,4,2,6]=>100110=>011001=>100110
[7,1,3,5,4,6,2]=>100101=>101001=>010110
[7,1,3,5,6,2,4]=>100010=>010001=>101110
[7,1,3,5,6,4,2]=>100011=>110001=>001110
[7,1,3,6,2,4,5]=>100100=>001001=>110110
[7,1,3,6,2,5,4]=>100101=>101001=>010110
[7,1,3,6,4,2,5]=>100110=>011001=>100110
[7,1,3,6,4,5,2]=>100101=>101001=>010110
[7,1,3,6,5,2,4]=>100110=>011001=>100110
[7,1,3,6,5,4,2]=>100111=>111001=>000110
[7,1,4,2,3,5,6]=>101000=>000101=>111010
[7,1,4,2,3,6,5]=>101001=>100101=>011010
[7,1,4,2,5,3,6]=>101010=>010101=>101010
[7,1,4,2,5,6,3]=>101001=>100101=>011010
[7,1,4,2,6,3,5]=>101010=>010101=>101010
[7,1,4,2,6,5,3]=>101011=>110101=>001010
[7,1,4,3,2,5,6]=>101100=>001101=>110010
[7,1,4,3,2,6,5]=>101101=>101101=>010010
[7,1,4,3,5,2,6]=>101010=>010101=>101010
[7,1,4,3,5,6,2]=>101001=>100101=>011010
[7,1,4,3,6,2,5]=>101010=>010101=>101010
[7,1,4,3,6,5,2]=>101011=>110101=>001010
[7,1,4,5,2,3,6]=>100100=>001001=>110110
[7,1,4,5,2,6,3]=>100101=>101001=>010110
[7,1,4,5,3,2,6]=>100110=>011001=>100110
[7,1,4,5,3,6,2]=>100101=>101001=>010110
[7,1,4,5,6,2,3]=>100010=>010001=>101110
[7,1,4,5,6,3,2]=>100011=>110001=>001110
[7,1,4,6,2,3,5]=>100100=>001001=>110110
[7,1,4,6,2,5,3]=>100101=>101001=>010110
[7,1,4,6,3,2,5]=>100110=>011001=>100110
[7,1,4,6,3,5,2]=>100101=>101001=>010110
[7,1,4,6,5,2,3]=>100110=>011001=>100110
[7,1,4,6,5,3,2]=>100111=>111001=>000110
[7,1,5,2,3,4,6]=>101000=>000101=>111010
[7,1,5,2,3,6,4]=>101001=>100101=>011010
[7,1,5,2,4,3,6]=>101010=>010101=>101010
[7,1,5,2,4,6,3]=>101001=>100101=>011010
[7,1,5,2,6,3,4]=>101010=>010101=>101010
[7,1,5,2,6,4,3]=>101011=>110101=>001010
[7,1,5,3,2,4,6]=>101100=>001101=>110010
[7,1,5,3,2,6,4]=>101101=>101101=>010010
[7,1,5,3,4,2,6]=>101010=>010101=>101010
[7,1,5,3,4,6,2]=>101001=>100101=>011010
[7,1,5,3,6,2,4]=>101010=>010101=>101010
[7,1,5,3,6,4,2]=>101011=>110101=>001010
[7,1,5,4,2,3,6]=>101100=>001101=>110010
[7,1,5,4,2,6,3]=>101101=>101101=>010010
[7,1,5,4,3,2,6]=>101110=>011101=>100010
[7,1,5,4,3,6,2]=>101101=>101101=>010010
[7,1,5,4,6,2,3]=>101010=>010101=>101010
[7,1,5,4,6,3,2]=>101011=>110101=>001010
[7,1,5,6,2,3,4]=>100100=>001001=>110110
[7,1,5,6,2,4,3]=>100101=>101001=>010110
[7,1,5,6,3,2,4]=>100110=>011001=>100110
[7,1,5,6,3,4,2]=>100101=>101001=>010110
[7,1,5,6,4,2,3]=>100110=>011001=>100110
[7,1,5,6,4,3,2]=>100111=>111001=>000110
[7,1,6,2,3,4,5]=>101000=>000101=>111010
[7,1,6,2,3,5,4]=>101001=>100101=>011010
[7,1,6,2,4,3,5]=>101010=>010101=>101010
[7,1,6,2,4,5,3]=>101001=>100101=>011010
[7,1,6,2,5,3,4]=>101010=>010101=>101010
[7,1,6,2,5,4,3]=>101011=>110101=>001010
[7,1,6,3,2,4,5]=>101100=>001101=>110010
[7,1,6,3,2,5,4]=>101101=>101101=>010010
[7,1,6,3,4,2,5]=>101010=>010101=>101010
[7,1,6,3,4,5,2]=>101001=>100101=>011010
[7,1,6,3,5,2,4]=>101010=>010101=>101010
[7,1,6,3,5,4,2]=>101011=>110101=>001010
[7,1,6,4,2,3,5]=>101100=>001101=>110010
[7,1,6,4,2,5,3]=>101101=>101101=>010010
[7,1,6,4,3,2,5]=>101110=>011101=>100010
[7,1,6,4,3,5,2]=>101101=>101101=>010010
[7,1,6,4,5,2,3]=>101010=>010101=>101010
[7,1,6,4,5,3,2]=>101011=>110101=>001010
[7,1,6,5,2,3,4]=>101100=>001101=>110010
[7,1,6,5,2,4,3]=>101101=>101101=>010010
[7,1,6,5,3,2,4]=>101110=>011101=>100010
[7,1,6,5,3,4,2]=>101101=>101101=>010010
[7,1,6,5,4,2,3]=>101110=>011101=>100010
[7,1,6,5,4,3,2]=>101111=>111101=>000010
[7,2,1,3,4,5,6]=>110000=>000011=>111100
[7,2,1,3,4,6,5]=>110001=>100011=>011100
[7,2,1,3,5,4,6]=>110010=>010011=>101100
[7,2,1,3,5,6,4]=>110001=>100011=>011100
[7,2,1,3,6,4,5]=>110010=>010011=>101100
[7,2,1,3,6,5,4]=>110011=>110011=>001100
[7,2,1,4,3,5,6]=>110100=>001011=>110100
[7,2,1,4,3,6,5]=>110101=>101011=>010100
[7,2,1,4,5,3,6]=>110010=>010011=>101100
[7,2,1,4,5,6,3]=>110001=>100011=>011100
[7,2,1,4,6,3,5]=>110010=>010011=>101100
[7,2,1,4,6,5,3]=>110011=>110011=>001100
[7,2,1,5,3,4,6]=>110100=>001011=>110100
[7,2,1,5,3,6,4]=>110101=>101011=>010100
[7,2,1,5,4,3,6]=>110110=>011011=>100100
[7,2,1,5,4,6,3]=>110101=>101011=>010100
[7,2,1,5,6,3,4]=>110010=>010011=>101100
[7,2,1,5,6,4,3]=>110011=>110011=>001100
[7,2,1,6,3,4,5]=>110100=>001011=>110100
[7,2,1,6,3,5,4]=>110101=>101011=>010100
[7,2,1,6,4,3,5]=>110110=>011011=>100100
[7,2,1,6,4,5,3]=>110101=>101011=>010100
[7,2,1,6,5,3,4]=>110110=>011011=>100100
[7,2,1,6,5,4,3]=>110111=>111011=>000100
[7,2,3,1,4,5,6]=>101000=>000101=>111010
[7,2,3,1,4,6,5]=>101001=>100101=>011010
[7,2,3,1,5,4,6]=>101010=>010101=>101010
[7,2,3,1,5,6,4]=>101001=>100101=>011010
[7,2,3,1,6,4,5]=>101010=>010101=>101010
[7,2,3,1,6,5,4]=>101011=>110101=>001010
[7,2,3,4,1,5,6]=>100100=>001001=>110110
[7,2,3,4,1,6,5]=>100101=>101001=>010110
[7,2,3,4,5,1,6]=>100010=>010001=>101110
[7,2,3,4,5,6,1]=>100001=>100001=>011110
[7,2,3,4,6,1,5]=>100010=>010001=>101110
[7,2,3,4,6,5,1]=>100011=>110001=>001110
[7,2,3,5,1,4,6]=>100100=>001001=>110110
[7,2,3,5,1,6,4]=>100101=>101001=>010110
[7,2,3,5,4,1,6]=>100110=>011001=>100110
[7,2,3,5,4,6,1]=>100101=>101001=>010110
[7,2,3,5,6,1,4]=>100010=>010001=>101110
[7,2,3,5,6,4,1]=>100011=>110001=>001110
[7,2,3,6,1,4,5]=>100100=>001001=>110110
[7,2,3,6,1,5,4]=>100101=>101001=>010110
[7,2,3,6,4,1,5]=>100110=>011001=>100110
[7,2,3,6,4,5,1]=>100101=>101001=>010110
[7,2,3,6,5,1,4]=>100110=>011001=>100110
[7,2,3,6,5,4,1]=>100111=>111001=>000110
[7,2,4,1,3,5,6]=>101000=>000101=>111010
[7,2,4,1,3,6,5]=>101001=>100101=>011010
[7,2,4,1,5,3,6]=>101010=>010101=>101010
[7,2,4,1,5,6,3]=>101001=>100101=>011010
[7,2,4,1,6,3,5]=>101010=>010101=>101010
[7,2,4,1,6,5,3]=>101011=>110101=>001010
[7,2,4,3,1,5,6]=>101100=>001101=>110010
[7,2,4,3,1,6,5]=>101101=>101101=>010010
[7,2,4,3,5,1,6]=>101010=>010101=>101010
[7,2,4,3,5,6,1]=>101001=>100101=>011010
[7,2,4,3,6,1,5]=>101010=>010101=>101010
[7,2,4,3,6,5,1]=>101011=>110101=>001010
[7,2,4,5,1,3,6]=>100100=>001001=>110110
[7,2,4,5,1,6,3]=>100101=>101001=>010110
[7,2,4,5,3,1,6]=>100110=>011001=>100110
[7,2,4,5,3,6,1]=>100101=>101001=>010110
[7,2,4,5,6,1,3]=>100010=>010001=>101110
[7,2,4,5,6,3,1]=>100011=>110001=>001110
[7,2,4,6,1,3,5]=>100100=>001001=>110110
[7,2,4,6,1,5,3]=>100101=>101001=>010110
[7,2,4,6,3,1,5]=>100110=>011001=>100110
[7,2,4,6,3,5,1]=>100101=>101001=>010110
[7,2,4,6,5,1,3]=>100110=>011001=>100110
[7,2,4,6,5,3,1]=>100111=>111001=>000110
[7,2,5,1,3,4,6]=>101000=>000101=>111010
[7,2,5,1,3,6,4]=>101001=>100101=>011010
[7,2,5,1,4,3,6]=>101010=>010101=>101010
[7,2,5,1,4,6,3]=>101001=>100101=>011010
[7,2,5,1,6,3,4]=>101010=>010101=>101010
[7,2,5,1,6,4,3]=>101011=>110101=>001010
[7,2,5,3,1,4,6]=>101100=>001101=>110010
[7,2,5,3,1,6,4]=>101101=>101101=>010010
[7,2,5,3,4,1,6]=>101010=>010101=>101010
[7,2,5,3,4,6,1]=>101001=>100101=>011010
[7,2,5,3,6,1,4]=>101010=>010101=>101010
[7,2,5,3,6,4,1]=>101011=>110101=>001010
[7,2,5,4,1,3,6]=>101100=>001101=>110010
[7,2,5,4,1,6,3]=>101101=>101101=>010010
[7,2,5,4,3,1,6]=>101110=>011101=>100010
[7,2,5,4,3,6,1]=>101101=>101101=>010010
[7,2,5,4,6,1,3]=>101010=>010101=>101010
[7,2,5,4,6,3,1]=>101011=>110101=>001010
[7,2,5,6,1,3,4]=>100100=>001001=>110110
[7,2,5,6,1,4,3]=>100101=>101001=>010110
[7,2,5,6,3,1,4]=>100110=>011001=>100110
[7,2,5,6,3,4,1]=>100101=>101001=>010110
[7,2,5,6,4,1,3]=>100110=>011001=>100110
[7,2,5,6,4,3,1]=>100111=>111001=>000110
[7,2,6,1,3,4,5]=>101000=>000101=>111010
[7,2,6,1,3,5,4]=>101001=>100101=>011010
[7,2,6,1,4,3,5]=>101010=>010101=>101010
[7,2,6,1,4,5,3]=>101001=>100101=>011010
[7,2,6,1,5,3,4]=>101010=>010101=>101010
[7,2,6,1,5,4,3]=>101011=>110101=>001010
[7,2,6,3,1,4,5]=>101100=>001101=>110010
[7,2,6,3,1,5,4]=>101101=>101101=>010010
[7,2,6,3,4,1,5]=>101010=>010101=>101010
[7,2,6,3,4,5,1]=>101001=>100101=>011010
[7,2,6,3,5,1,4]=>101010=>010101=>101010
[7,2,6,3,5,4,1]=>101011=>110101=>001010
[7,2,6,4,1,3,5]=>101100=>001101=>110010
[7,2,6,4,1,5,3]=>101101=>101101=>010010
[7,2,6,4,3,1,5]=>101110=>011101=>100010
[7,2,6,4,3,5,1]=>101101=>101101=>010010
[7,2,6,4,5,1,3]=>101010=>010101=>101010
[7,2,6,4,5,3,1]=>101011=>110101=>001010
[7,2,6,5,1,3,4]=>101100=>001101=>110010
[7,2,6,5,1,4,3]=>101101=>101101=>010010
[7,2,6,5,3,1,4]=>101110=>011101=>100010
[7,2,6,5,3,4,1]=>101101=>101101=>010010
[7,2,6,5,4,1,3]=>101110=>011101=>100010
[7,2,6,5,4,3,1]=>101111=>111101=>000010
[7,3,1,2,4,5,6]=>110000=>000011=>111100
[7,3,1,2,4,6,5]=>110001=>100011=>011100
[7,3,1,2,5,4,6]=>110010=>010011=>101100
[7,3,1,2,5,6,4]=>110001=>100011=>011100
[7,3,1,2,6,4,5]=>110010=>010011=>101100
[7,3,1,2,6,5,4]=>110011=>110011=>001100
[7,3,1,4,2,5,6]=>110100=>001011=>110100
[7,3,1,4,2,6,5]=>110101=>101011=>010100
[7,3,1,4,5,2,6]=>110010=>010011=>101100
[7,3,1,4,5,6,2]=>110001=>100011=>011100
[7,3,1,4,6,2,5]=>110010=>010011=>101100
[7,3,1,4,6,5,2]=>110011=>110011=>001100
[7,3,1,5,2,4,6]=>110100=>001011=>110100
[7,3,1,5,2,6,4]=>110101=>101011=>010100
[7,3,1,5,4,2,6]=>110110=>011011=>100100
[7,3,1,5,4,6,2]=>110101=>101011=>010100
[7,3,1,5,6,2,4]=>110010=>010011=>101100
[7,3,1,5,6,4,2]=>110011=>110011=>001100
[7,3,1,6,2,4,5]=>110100=>001011=>110100
[7,3,1,6,2,5,4]=>110101=>101011=>010100
[7,3,1,6,4,2,5]=>110110=>011011=>100100
[7,3,1,6,4,5,2]=>110101=>101011=>010100
[7,3,1,6,5,2,4]=>110110=>011011=>100100
[7,3,1,6,5,4,2]=>110111=>111011=>000100
[7,3,2,1,4,5,6]=>111000=>000111=>111000
[7,3,2,1,4,6,5]=>111001=>100111=>011000
[7,3,2,1,5,4,6]=>111010=>010111=>101000
[7,3,2,1,5,6,4]=>111001=>100111=>011000
[7,3,2,1,6,4,5]=>111010=>010111=>101000
[7,3,2,1,6,5,4]=>111011=>110111=>001000
[7,3,2,4,1,5,6]=>110100=>001011=>110100
[7,3,2,4,1,6,5]=>110101=>101011=>010100
[7,3,2,4,5,1,6]=>110010=>010011=>101100
[7,3,2,4,5,6,1]=>110001=>100011=>011100
[7,3,2,4,6,1,5]=>110010=>010011=>101100
[7,3,2,4,6,5,1]=>110011=>110011=>001100
[7,3,2,5,1,4,6]=>110100=>001011=>110100
[7,3,2,5,1,6,4]=>110101=>101011=>010100
[7,3,2,5,4,1,6]=>110110=>011011=>100100
[7,3,2,5,4,6,1]=>110101=>101011=>010100
[7,3,2,5,6,1,4]=>110010=>010011=>101100
[7,3,2,5,6,4,1]=>110011=>110011=>001100
[7,3,2,6,1,4,5]=>110100=>001011=>110100
[7,3,2,6,1,5,4]=>110101=>101011=>010100
[7,3,2,6,4,1,5]=>110110=>011011=>100100
[7,3,2,6,4,5,1]=>110101=>101011=>010100
[7,3,2,6,5,1,4]=>110110=>011011=>100100
[7,3,2,6,5,4,1]=>110111=>111011=>000100
[7,3,4,1,2,5,6]=>101000=>000101=>111010
[7,3,4,1,2,6,5]=>101001=>100101=>011010
[7,3,4,1,5,2,6]=>101010=>010101=>101010
[7,3,4,1,5,6,2]=>101001=>100101=>011010
[7,3,4,1,6,2,5]=>101010=>010101=>101010
[7,3,4,1,6,5,2]=>101011=>110101=>001010
[7,3,4,2,1,5,6]=>101100=>001101=>110010
[7,3,4,2,1,6,5]=>101101=>101101=>010010
[7,3,4,2,5,1,6]=>101010=>010101=>101010
[7,3,4,2,5,6,1]=>101001=>100101=>011010
[7,3,4,2,6,1,5]=>101010=>010101=>101010
[7,3,4,2,6,5,1]=>101011=>110101=>001010
[7,3,4,5,1,2,6]=>100100=>001001=>110110
[7,3,4,5,1,6,2]=>100101=>101001=>010110
[7,3,4,5,2,1,6]=>100110=>011001=>100110
[7,3,4,5,2,6,1]=>100101=>101001=>010110
[7,3,4,5,6,1,2]=>100010=>010001=>101110
[7,3,4,5,6,2,1]=>100011=>110001=>001110
[7,3,4,6,1,2,5]=>100100=>001001=>110110
[7,3,4,6,1,5,2]=>100101=>101001=>010110
[7,3,4,6,2,1,5]=>100110=>011001=>100110
[7,3,4,6,2,5,1]=>100101=>101001=>010110
[7,3,4,6,5,1,2]=>100110=>011001=>100110
[7,3,4,6,5,2,1]=>100111=>111001=>000110
[7,3,5,1,2,4,6]=>101000=>000101=>111010
[7,3,5,1,2,6,4]=>101001=>100101=>011010
[7,3,5,1,4,2,6]=>101010=>010101=>101010
[7,3,5,1,4,6,2]=>101001=>100101=>011010
[7,3,5,1,6,2,4]=>101010=>010101=>101010
[7,3,5,1,6,4,2]=>101011=>110101=>001010
[7,3,5,2,1,4,6]=>101100=>001101=>110010
[7,3,5,2,1,6,4]=>101101=>101101=>010010
[7,3,5,2,4,1,6]=>101010=>010101=>101010
[7,3,5,2,4,6,1]=>101001=>100101=>011010
[7,3,5,2,6,1,4]=>101010=>010101=>101010
[7,3,5,2,6,4,1]=>101011=>110101=>001010
[7,3,5,4,1,2,6]=>101100=>001101=>110010
[7,3,5,4,1,6,2]=>101101=>101101=>010010
[7,3,5,4,2,1,6]=>101110=>011101=>100010
[7,3,5,4,2,6,1]=>101101=>101101=>010010
[7,3,5,4,6,1,2]=>101010=>010101=>101010
[7,3,5,4,6,2,1]=>101011=>110101=>001010
[7,3,5,6,1,2,4]=>100100=>001001=>110110
[7,3,5,6,1,4,2]=>100101=>101001=>010110
[7,3,5,6,2,1,4]=>100110=>011001=>100110
[7,3,5,6,2,4,1]=>100101=>101001=>010110
[7,3,5,6,4,1,2]=>100110=>011001=>100110
[7,3,5,6,4,2,1]=>100111=>111001=>000110
[7,3,6,1,2,4,5]=>101000=>000101=>111010
[7,3,6,1,2,5,4]=>101001=>100101=>011010
[7,3,6,1,4,2,5]=>101010=>010101=>101010
[7,3,6,1,4,5,2]=>101001=>100101=>011010
[7,3,6,1,5,2,4]=>101010=>010101=>101010
[7,3,6,1,5,4,2]=>101011=>110101=>001010
[7,3,6,2,1,4,5]=>101100=>001101=>110010
[7,3,6,2,1,5,4]=>101101=>101101=>010010
[7,3,6,2,4,1,5]=>101010=>010101=>101010
[7,3,6,2,4,5,1]=>101001=>100101=>011010
[7,3,6,2,5,1,4]=>101010=>010101=>101010
[7,3,6,2,5,4,1]=>101011=>110101=>001010
[7,3,6,4,1,2,5]=>101100=>001101=>110010
[7,3,6,4,1,5,2]=>101101=>101101=>010010
[7,3,6,4,2,1,5]=>101110=>011101=>100010
[7,3,6,4,2,5,1]=>101101=>101101=>010010
[7,3,6,4,5,1,2]=>101010=>010101=>101010
[7,3,6,4,5,2,1]=>101011=>110101=>001010
[7,3,6,5,1,2,4]=>101100=>001101=>110010
[7,3,6,5,1,4,2]=>101101=>101101=>010010
[7,3,6,5,2,1,4]=>101110=>011101=>100010
[7,3,6,5,2,4,1]=>101101=>101101=>010010
[7,3,6,5,4,1,2]=>101110=>011101=>100010
[7,3,6,5,4,2,1]=>101111=>111101=>000010
[7,4,1,2,3,5,6]=>110000=>000011=>111100
[7,4,1,2,3,6,5]=>110001=>100011=>011100
[7,4,1,2,5,3,6]=>110010=>010011=>101100
[7,4,1,2,5,6,3]=>110001=>100011=>011100
[7,4,1,2,6,3,5]=>110010=>010011=>101100
[7,4,1,2,6,5,3]=>110011=>110011=>001100
[7,4,1,3,2,5,6]=>110100=>001011=>110100
[7,4,1,3,2,6,5]=>110101=>101011=>010100
[7,4,1,3,5,2,6]=>110010=>010011=>101100
[7,4,1,3,5,6,2]=>110001=>100011=>011100
[7,4,1,3,6,2,5]=>110010=>010011=>101100
[7,4,1,3,6,5,2]=>110011=>110011=>001100
[7,4,1,5,2,3,6]=>110100=>001011=>110100
[7,4,1,5,2,6,3]=>110101=>101011=>010100
[7,4,1,5,3,2,6]=>110110=>011011=>100100
[7,4,1,5,3,6,2]=>110101=>101011=>010100
[7,4,1,5,6,2,3]=>110010=>010011=>101100
[7,4,1,5,6,3,2]=>110011=>110011=>001100
[7,4,1,6,2,3,5]=>110100=>001011=>110100
[7,4,1,6,2,5,3]=>110101=>101011=>010100
[7,4,1,6,3,2,5]=>110110=>011011=>100100
[7,4,1,6,3,5,2]=>110101=>101011=>010100
[7,4,1,6,5,2,3]=>110110=>011011=>100100
[7,4,1,6,5,3,2]=>110111=>111011=>000100
[7,4,2,1,3,5,6]=>111000=>000111=>111000
[7,4,2,1,3,6,5]=>111001=>100111=>011000
[7,4,2,1,5,3,6]=>111010=>010111=>101000
[7,4,2,1,5,6,3]=>111001=>100111=>011000
[7,4,2,1,6,3,5]=>111010=>010111=>101000
[7,4,2,1,6,5,3]=>111011=>110111=>001000
[7,4,2,3,1,5,6]=>110100=>001011=>110100
[7,4,2,3,1,6,5]=>110101=>101011=>010100
[7,4,2,3,5,1,6]=>110010=>010011=>101100
[7,4,2,3,5,6,1]=>110001=>100011=>011100
[7,4,2,3,6,1,5]=>110010=>010011=>101100
[7,4,2,3,6,5,1]=>110011=>110011=>001100
[7,4,2,5,1,3,6]=>110100=>001011=>110100
[7,4,2,5,1,6,3]=>110101=>101011=>010100
[7,4,2,5,3,1,6]=>110110=>011011=>100100
[7,4,2,5,3,6,1]=>110101=>101011=>010100
[7,4,2,5,6,1,3]=>110010=>010011=>101100
[7,4,2,5,6,3,1]=>110011=>110011=>001100
[7,4,2,6,1,3,5]=>110100=>001011=>110100
[7,4,2,6,1,5,3]=>110101=>101011=>010100
[7,4,2,6,3,1,5]=>110110=>011011=>100100
[7,4,2,6,3,5,1]=>110101=>101011=>010100
[7,4,2,6,5,1,3]=>110110=>011011=>100100
[7,4,2,6,5,3,1]=>110111=>111011=>000100
[7,4,3,1,2,5,6]=>111000=>000111=>111000
[7,4,3,1,2,6,5]=>111001=>100111=>011000
[7,4,3,1,5,2,6]=>111010=>010111=>101000
[7,4,3,1,5,6,2]=>111001=>100111=>011000
[7,4,3,1,6,2,5]=>111010=>010111=>101000
[7,4,3,1,6,5,2]=>111011=>110111=>001000
[7,4,3,2,1,5,6]=>111100=>001111=>110000
[7,4,3,2,1,6,5]=>111101=>101111=>010000
[7,4,3,2,5,1,6]=>111010=>010111=>101000
[7,4,3,2,5,6,1]=>111001=>100111=>011000
[7,4,3,2,6,1,5]=>111010=>010111=>101000
[7,4,3,2,6,5,1]=>111011=>110111=>001000
[7,4,3,5,1,2,6]=>110100=>001011=>110100
[7,4,3,5,1,6,2]=>110101=>101011=>010100
[7,4,3,5,2,1,6]=>110110=>011011=>100100
[7,4,3,5,2,6,1]=>110101=>101011=>010100
[7,4,3,5,6,1,2]=>110010=>010011=>101100
[7,4,3,5,6,2,1]=>110011=>110011=>001100
[7,4,3,6,1,2,5]=>110100=>001011=>110100
[7,4,3,6,1,5,2]=>110101=>101011=>010100
[7,4,3,6,2,1,5]=>110110=>011011=>100100
[7,4,3,6,2,5,1]=>110101=>101011=>010100
[7,4,3,6,5,1,2]=>110110=>011011=>100100
[7,4,3,6,5,2,1]=>110111=>111011=>000100
[7,4,5,1,2,3,6]=>101000=>000101=>111010
[7,4,5,1,2,6,3]=>101001=>100101=>011010
[7,4,5,1,3,2,6]=>101010=>010101=>101010
[7,4,5,1,3,6,2]=>101001=>100101=>011010
[7,4,5,1,6,2,3]=>101010=>010101=>101010
[7,4,5,1,6,3,2]=>101011=>110101=>001010
[7,4,5,2,1,3,6]=>101100=>001101=>110010
[7,4,5,2,1,6,3]=>101101=>101101=>010010
[7,4,5,2,3,1,6]=>101010=>010101=>101010
[7,4,5,2,3,6,1]=>101001=>100101=>011010
[7,4,5,2,6,1,3]=>101010=>010101=>101010
[7,4,5,2,6,3,1]=>101011=>110101=>001010
[7,4,5,3,1,2,6]=>101100=>001101=>110010
[7,4,5,3,1,6,2]=>101101=>101101=>010010
[7,4,5,3,2,1,6]=>101110=>011101=>100010
[7,4,5,3,2,6,1]=>101101=>101101=>010010
[7,4,5,3,6,1,2]=>101010=>010101=>101010
[7,4,5,3,6,2,1]=>101011=>110101=>001010
[7,4,5,6,1,2,3]=>100100=>001001=>110110
[7,4,5,6,1,3,2]=>100101=>101001=>010110
[7,4,5,6,2,1,3]=>100110=>011001=>100110
[7,4,5,6,2,3,1]=>100101=>101001=>010110
[7,4,5,6,3,1,2]=>100110=>011001=>100110
[7,4,5,6,3,2,1]=>100111=>111001=>000110
[7,4,6,1,2,3,5]=>101000=>000101=>111010
[7,4,6,1,2,5,3]=>101001=>100101=>011010
[7,4,6,1,3,2,5]=>101010=>010101=>101010
[7,4,6,1,3,5,2]=>101001=>100101=>011010
[7,4,6,1,5,2,3]=>101010=>010101=>101010
[7,4,6,1,5,3,2]=>101011=>110101=>001010
[7,4,6,2,1,3,5]=>101100=>001101=>110010
[7,4,6,2,1,5,3]=>101101=>101101=>010010
[7,4,6,2,3,1,5]=>101010=>010101=>101010
[7,4,6,2,3,5,1]=>101001=>100101=>011010
[7,4,6,2,5,1,3]=>101010=>010101=>101010
[7,4,6,2,5,3,1]=>101011=>110101=>001010
[7,4,6,3,1,2,5]=>101100=>001101=>110010
[7,4,6,3,1,5,2]=>101101=>101101=>010010
[7,4,6,3,2,1,5]=>101110=>011101=>100010
[7,4,6,3,2,5,1]=>101101=>101101=>010010
[7,4,6,3,5,1,2]=>101010=>010101=>101010
[7,4,6,3,5,2,1]=>101011=>110101=>001010
[7,4,6,5,1,2,3]=>101100=>001101=>110010
[7,4,6,5,1,3,2]=>101101=>101101=>010010
[7,4,6,5,2,1,3]=>101110=>011101=>100010
[7,4,6,5,2,3,1]=>101101=>101101=>010010
[7,4,6,5,3,1,2]=>101110=>011101=>100010
[7,4,6,5,3,2,1]=>101111=>111101=>000010
[7,5,1,2,3,4,6]=>110000=>000011=>111100
[7,5,1,2,3,6,4]=>110001=>100011=>011100
[7,5,1,2,4,3,6]=>110010=>010011=>101100
[7,5,1,2,4,6,3]=>110001=>100011=>011100
[7,5,1,2,6,3,4]=>110010=>010011=>101100
[7,5,1,2,6,4,3]=>110011=>110011=>001100
[7,5,1,3,2,4,6]=>110100=>001011=>110100
[7,5,1,3,2,6,4]=>110101=>101011=>010100
[7,5,1,3,4,2,6]=>110010=>010011=>101100
[7,5,1,3,4,6,2]=>110001=>100011=>011100
[7,5,1,3,6,2,4]=>110010=>010011=>101100
[7,5,1,3,6,4,2]=>110011=>110011=>001100
[7,5,1,4,2,3,6]=>110100=>001011=>110100
[7,5,1,4,2,6,3]=>110101=>101011=>010100
[7,5,1,4,3,2,6]=>110110=>011011=>100100
[7,5,1,4,3,6,2]=>110101=>101011=>010100
[7,5,1,4,6,2,3]=>110010=>010011=>101100
[7,5,1,4,6,3,2]=>110011=>110011=>001100
[7,5,1,6,2,3,4]=>110100=>001011=>110100
[7,5,1,6,2,4,3]=>110101=>101011=>010100
[7,5,1,6,3,2,4]=>110110=>011011=>100100
[7,5,1,6,3,4,2]=>110101=>101011=>010100
[7,5,1,6,4,2,3]=>110110=>011011=>100100
[7,5,1,6,4,3,2]=>110111=>111011=>000100
[7,5,2,1,3,4,6]=>111000=>000111=>111000
[7,5,2,1,3,6,4]=>111001=>100111=>011000
[7,5,2,1,4,3,6]=>111010=>010111=>101000
[7,5,2,1,4,6,3]=>111001=>100111=>011000
[7,5,2,1,6,3,4]=>111010=>010111=>101000
[7,5,2,1,6,4,3]=>111011=>110111=>001000
[7,5,2,3,1,4,6]=>110100=>001011=>110100
[7,5,2,3,1,6,4]=>110101=>101011=>010100
[7,5,2,3,4,1,6]=>110010=>010011=>101100
[7,5,2,3,4,6,1]=>110001=>100011=>011100
[7,5,2,3,6,1,4]=>110010=>010011=>101100
[7,5,2,3,6,4,1]=>110011=>110011=>001100
[7,5,2,4,1,3,6]=>110100=>001011=>110100
[7,5,2,4,1,6,3]=>110101=>101011=>010100
[7,5,2,4,3,1,6]=>110110=>011011=>100100
[7,5,2,4,3,6,1]=>110101=>101011=>010100
[7,5,2,4,6,1,3]=>110010=>010011=>101100
[7,5,2,4,6,3,1]=>110011=>110011=>001100
[7,5,2,6,1,3,4]=>110100=>001011=>110100
[7,5,2,6,1,4,3]=>110101=>101011=>010100
[7,5,2,6,3,1,4]=>110110=>011011=>100100
[7,5,2,6,3,4,1]=>110101=>101011=>010100
[7,5,2,6,4,1,3]=>110110=>011011=>100100
[7,5,2,6,4,3,1]=>110111=>111011=>000100
[7,5,3,1,2,4,6]=>111000=>000111=>111000
[7,5,3,1,2,6,4]=>111001=>100111=>011000
[7,5,3,1,4,2,6]=>111010=>010111=>101000
[7,5,3,1,4,6,2]=>111001=>100111=>011000
[7,5,3,1,6,2,4]=>111010=>010111=>101000
[7,5,3,1,6,4,2]=>111011=>110111=>001000
[7,5,3,2,1,4,6]=>111100=>001111=>110000
[7,5,3,2,1,6,4]=>111101=>101111=>010000
[7,5,3,2,4,1,6]=>111010=>010111=>101000
[7,5,3,2,4,6,1]=>111001=>100111=>011000
[7,5,3,2,6,1,4]=>111010=>010111=>101000
[7,5,3,2,6,4,1]=>111011=>110111=>001000
[7,5,3,4,1,2,6]=>110100=>001011=>110100
[7,5,3,4,1,6,2]=>110101=>101011=>010100
[7,5,3,4,2,1,6]=>110110=>011011=>100100
[7,5,3,4,2,6,1]=>110101=>101011=>010100
[7,5,3,4,6,1,2]=>110010=>010011=>101100
[7,5,3,4,6,2,1]=>110011=>110011=>001100
[7,5,3,6,1,2,4]=>110100=>001011=>110100
[7,5,3,6,1,4,2]=>110101=>101011=>010100
[7,5,3,6,2,1,4]=>110110=>011011=>100100
[7,5,3,6,2,4,1]=>110101=>101011=>010100
[7,5,3,6,4,1,2]=>110110=>011011=>100100
[7,5,3,6,4,2,1]=>110111=>111011=>000100
[7,5,4,1,2,3,6]=>111000=>000111=>111000
[7,5,4,1,2,6,3]=>111001=>100111=>011000
[7,5,4,1,3,2,6]=>111010=>010111=>101000
[7,5,4,1,3,6,2]=>111001=>100111=>011000
[7,5,4,1,6,2,3]=>111010=>010111=>101000
[7,5,4,1,6,3,2]=>111011=>110111=>001000
[7,5,4,2,1,3,6]=>111100=>001111=>110000
[7,5,4,2,1,6,3]=>111101=>101111=>010000
[7,5,4,2,3,1,6]=>111010=>010111=>101000
[7,5,4,2,3,6,1]=>111001=>100111=>011000
[7,5,4,2,6,1,3]=>111010=>010111=>101000
[7,5,4,2,6,3,1]=>111011=>110111=>001000
[7,5,4,3,1,2,6]=>111100=>001111=>110000
[7,5,4,3,1,6,2]=>111101=>101111=>010000
[7,5,4,3,2,1,6]=>111110=>011111=>100000
[7,5,4,3,2,6,1]=>111101=>101111=>010000
[7,5,4,3,6,1,2]=>111010=>010111=>101000
[7,5,4,3,6,2,1]=>111011=>110111=>001000
[7,5,4,6,1,2,3]=>110100=>001011=>110100
[7,5,4,6,1,3,2]=>110101=>101011=>010100
[7,5,4,6,2,1,3]=>110110=>011011=>100100
[7,5,4,6,2,3,1]=>110101=>101011=>010100
[7,5,4,6,3,1,2]=>110110=>011011=>100100
[7,5,4,6,3,2,1]=>110111=>111011=>000100
[7,5,6,1,2,3,4]=>101000=>000101=>111010
[7,5,6,1,2,4,3]=>101001=>100101=>011010
[7,5,6,1,3,2,4]=>101010=>010101=>101010
[7,5,6,1,3,4,2]=>101001=>100101=>011010
[7,5,6,1,4,2,3]=>101010=>010101=>101010
[7,5,6,1,4,3,2]=>101011=>110101=>001010
[7,5,6,2,1,3,4]=>101100=>001101=>110010
[7,5,6,2,1,4,3]=>101101=>101101=>010010
[7,5,6,2,3,1,4]=>101010=>010101=>101010
[7,5,6,2,3,4,1]=>101001=>100101=>011010
[7,5,6,2,4,1,3]=>101010=>010101=>101010
[7,5,6,2,4,3,1]=>101011=>110101=>001010
[7,5,6,3,1,2,4]=>101100=>001101=>110010
[7,5,6,3,1,4,2]=>101101=>101101=>010010
[7,5,6,3,2,1,4]=>101110=>011101=>100010
[7,5,6,3,2,4,1]=>101101=>101101=>010010
[7,5,6,3,4,1,2]=>101010=>010101=>101010
[7,5,6,3,4,2,1]=>101011=>110101=>001010
[7,5,6,4,1,2,3]=>101100=>001101=>110010
[7,5,6,4,1,3,2]=>101101=>101101=>010010
[7,5,6,4,2,1,3]=>101110=>011101=>100010
[7,5,6,4,2,3,1]=>101101=>101101=>010010
[7,5,6,4,3,1,2]=>101110=>011101=>100010
[7,5,6,4,3,2,1]=>101111=>111101=>000010
[7,6,1,2,3,4,5]=>110000=>000011=>111100
[7,6,1,2,3,5,4]=>110001=>100011=>011100
[7,6,1,2,4,3,5]=>110010=>010011=>101100
[7,6,1,2,4,5,3]=>110001=>100011=>011100
[7,6,1,2,5,3,4]=>110010=>010011=>101100
[7,6,1,2,5,4,3]=>110011=>110011=>001100
[7,6,1,3,2,4,5]=>110100=>001011=>110100
[7,6,1,3,2,5,4]=>110101=>101011=>010100
[7,6,1,3,4,2,5]=>110010=>010011=>101100
[7,6,1,3,4,5,2]=>110001=>100011=>011100
[7,6,1,3,5,2,4]=>110010=>010011=>101100
[7,6,1,3,5,4,2]=>110011=>110011=>001100
[7,6,1,4,2,3,5]=>110100=>001011=>110100
[7,6,1,4,2,5,3]=>110101=>101011=>010100
[7,6,1,4,3,2,5]=>110110=>011011=>100100
[7,6,1,4,3,5,2]=>110101=>101011=>010100
[7,6,1,4,5,2,3]=>110010=>010011=>101100
[7,6,1,4,5,3,2]=>110011=>110011=>001100
[7,6,1,5,2,3,4]=>110100=>001011=>110100
[7,6,1,5,2,4,3]=>110101=>101011=>010100
[7,6,1,5,3,2,4]=>110110=>011011=>100100
[7,6,1,5,3,4,2]=>110101=>101011=>010100
[7,6,1,5,4,2,3]=>110110=>011011=>100100
[7,6,1,5,4,3,2]=>110111=>111011=>000100
[7,6,2,1,3,4,5]=>111000=>000111=>111000
[7,6,2,1,3,5,4]=>111001=>100111=>011000
[7,6,2,1,4,3,5]=>111010=>010111=>101000
[7,6,2,1,4,5,3]=>111001=>100111=>011000
[7,6,2,1,5,3,4]=>111010=>010111=>101000
[7,6,2,1,5,4,3]=>111011=>110111=>001000
[7,6,2,3,1,4,5]=>110100=>001011=>110100
[7,6,2,3,1,5,4]=>110101=>101011=>010100
[7,6,2,3,4,1,5]=>110010=>010011=>101100
[7,6,2,3,4,5,1]=>110001=>100011=>011100
[7,6,2,3,5,1,4]=>110010=>010011=>101100
[7,6,2,3,5,4,1]=>110011=>110011=>001100
[7,6,2,4,1,3,5]=>110100=>001011=>110100
[7,6,2,4,1,5,3]=>110101=>101011=>010100
[7,6,2,4,3,1,5]=>110110=>011011=>100100
[7,6,2,4,3,5,1]=>110101=>101011=>010100
[7,6,2,4,5,1,3]=>110010=>010011=>101100
[7,6,2,4,5,3,1]=>110011=>110011=>001100
[7,6,2,5,1,3,4]=>110100=>001011=>110100
[7,6,2,5,1,4,3]=>110101=>101011=>010100
[7,6,2,5,3,1,4]=>110110=>011011=>100100
[7,6,2,5,3,4,1]=>110101=>101011=>010100
[7,6,2,5,4,1,3]=>110110=>011011=>100100
[7,6,2,5,4,3,1]=>110111=>111011=>000100
[7,6,3,1,2,4,5]=>111000=>000111=>111000
[7,6,3,1,2,5,4]=>111001=>100111=>011000
[7,6,3,1,4,2,5]=>111010=>010111=>101000
[7,6,3,1,4,5,2]=>111001=>100111=>011000
[7,6,3,1,5,2,4]=>111010=>010111=>101000
[7,6,3,1,5,4,2]=>111011=>110111=>001000
[7,6,3,2,1,4,5]=>111100=>001111=>110000
[7,6,3,2,1,5,4]=>111101=>101111=>010000
[7,6,3,2,4,1,5]=>111010=>010111=>101000
[7,6,3,2,4,5,1]=>111001=>100111=>011000
[7,6,3,2,5,1,4]=>111010=>010111=>101000
[7,6,3,2,5,4,1]=>111011=>110111=>001000
[7,6,3,4,1,2,5]=>110100=>001011=>110100
[7,6,3,4,1,5,2]=>110101=>101011=>010100
[7,6,3,4,2,1,5]=>110110=>011011=>100100
[7,6,3,4,2,5,1]=>110101=>101011=>010100
[7,6,3,4,5,1,2]=>110010=>010011=>101100
[7,6,3,4,5,2,1]=>110011=>110011=>001100
[7,6,3,5,1,2,4]=>110100=>001011=>110100
[7,6,3,5,1,4,2]=>110101=>101011=>010100
[7,6,3,5,2,1,4]=>110110=>011011=>100100
[7,6,3,5,2,4,1]=>110101=>101011=>010100
[7,6,3,5,4,1,2]=>110110=>011011=>100100
[7,6,3,5,4,2,1]=>110111=>111011=>000100
[7,6,4,1,2,3,5]=>111000=>000111=>111000
[7,6,4,1,2,5,3]=>111001=>100111=>011000
[7,6,4,1,3,2,5]=>111010=>010111=>101000
[7,6,4,1,3,5,2]=>111001=>100111=>011000
[7,6,4,1,5,2,3]=>111010=>010111=>101000
[7,6,4,1,5,3,2]=>111011=>110111=>001000
[7,6,4,2,1,3,5]=>111100=>001111=>110000
[7,6,4,2,1,5,3]=>111101=>101111=>010000
[7,6,4,2,3,1,5]=>111010=>010111=>101000
[7,6,4,2,3,5,1]=>111001=>100111=>011000
[7,6,4,2,5,1,3]=>111010=>010111=>101000
[7,6,4,2,5,3,1]=>111011=>110111=>001000
[7,6,4,3,1,2,5]=>111100=>001111=>110000
[7,6,4,3,1,5,2]=>111101=>101111=>010000
[7,6,4,3,2,1,5]=>111110=>011111=>100000
[7,6,4,3,2,5,1]=>111101=>101111=>010000
[7,6,4,3,5,1,2]=>111010=>010111=>101000
[7,6,4,3,5,2,1]=>111011=>110111=>001000
[7,6,4,5,1,2,3]=>110100=>001011=>110100
[7,6,4,5,1,3,2]=>110101=>101011=>010100
[7,6,4,5,2,1,3]=>110110=>011011=>100100
[7,6,4,5,2,3,1]=>110101=>101011=>010100
[7,6,4,5,3,1,2]=>110110=>011011=>100100
[7,6,4,5,3,2,1]=>110111=>111011=>000100
[7,6,5,1,2,3,4]=>111000=>000111=>111000
[7,6,5,1,2,4,3]=>111001=>100111=>011000
[7,6,5,1,3,2,4]=>111010=>010111=>101000
[7,6,5,1,3,4,2]=>111001=>100111=>011000
[7,6,5,1,4,2,3]=>111010=>010111=>101000
[7,6,5,1,4,3,2]=>111011=>110111=>001000
[7,6,5,2,1,3,4]=>111100=>001111=>110000
[7,6,5,2,1,4,3]=>111101=>101111=>010000
[7,6,5,2,3,1,4]=>111010=>010111=>101000
[7,6,5,2,3,4,1]=>111001=>100111=>011000
[7,6,5,2,4,1,3]=>111010=>010111=>101000
[7,6,5,2,4,3,1]=>111011=>110111=>001000
[7,6,5,3,1,2,4]=>111100=>001111=>110000
[7,6,5,3,1,4,2]=>111101=>101111=>010000
[7,6,5,3,2,1,4]=>111110=>011111=>100000
[7,6,5,3,2,4,1]=>111101=>101111=>010000
[7,6,5,3,4,1,2]=>111010=>010111=>101000
[7,6,5,3,4,2,1]=>111011=>110111=>001000
[7,6,5,4,1,2,3]=>111100=>001111=>110000
[7,6,5,4,1,3,2]=>111101=>101111=>010000
[7,6,5,4,2,1,3]=>111110=>011111=>100000
[7,6,5,4,2,3,1]=>111101=>101111=>010000
[7,6,5,4,3,1,2]=>111110=>011111=>100000
[7,6,5,4,3,2,1]=>111111=>111111=>000000
[8,7,6,5,4,3,2,1]=>1111111=>1111111=>0000000
[7,8,6,5,4,3,2,1]=>0111111=>1111110=>0000001
[8,6,7,5,4,3,2,1]=>1011111=>1111101=>0000010
[7,6,8,5,4,3,2,1]=>1011111=>1111101=>0000010
[6,7,8,5,4,3,2,1]=>0011111=>1111100=>0000011
[8,7,5,6,4,3,2,1]=>1101111=>1111011=>0000100
[7,8,5,6,4,3,2,1]=>0101111=>1111010=>0000101
[8,6,5,7,4,3,2,1]=>1101111=>1111011=>0000100
[8,5,6,7,4,3,2,1]=>1001111=>1111001=>0000110
[7,6,5,8,4,3,2,1]=>1101111=>1111011=>0000100
[6,7,5,8,4,3,2,1]=>0101111=>1111010=>0000101
[7,5,6,8,4,3,2,1]=>1001111=>1111001=>0000110
[6,5,7,8,4,3,2,1]=>1001111=>1111001=>0000110
[5,6,7,8,4,3,2,1]=>0001111=>1111000=>0000111
[8,7,6,4,5,3,2,1]=>1110111=>1110111=>0001000
[8,6,7,4,5,3,2,1]=>1010111=>1110101=>0001010
[7,6,8,4,5,3,2,1]=>1010111=>1110101=>0001010
[8,7,5,4,6,3,2,1]=>1110111=>1110111=>0001000
[8,6,5,4,7,3,2,1]=>1110111=>1110111=>0001000
[8,5,6,4,7,3,2,1]=>1010111=>1110101=>0001010
[8,6,4,5,7,3,2,1]=>1100111=>1110011=>0001100
[7,6,5,4,8,3,2,1]=>1110111=>1110111=>0001000
[6,7,5,4,8,3,2,1]=>0110111=>1110110=>0001001
[7,5,6,4,8,3,2,1]=>1010111=>1110101=>0001010
[6,5,7,4,8,3,2,1]=>1010111=>1110101=>0001010
[5,6,7,4,8,3,2,1]=>0010111=>1110100=>0001011
[7,6,4,5,8,3,2,1]=>1100111=>1110011=>0001100
[6,7,4,5,8,3,2,1]=>0100111=>1110010=>0001101
[7,5,4,6,8,3,2,1]=>1100111=>1110011=>0001100
[7,4,5,6,8,3,2,1]=>1000111=>1110001=>0001110
[6,5,4,7,8,3,2,1]=>1100111=>1110011=>0001100
[5,6,4,7,8,3,2,1]=>0100111=>1110010=>0001101
[6,4,5,7,8,3,2,1]=>1000111=>1110001=>0001110
[5,4,6,7,8,3,2,1]=>1000111=>1110001=>0001110
[4,5,6,7,8,3,2,1]=>0000111=>1110000=>0001111
[8,7,6,5,3,4,2,1]=>1111011=>1101111=>0010000
[7,8,6,5,3,4,2,1]=>0111011=>1101110=>0010001
[7,6,8,5,3,4,2,1]=>1011011=>1101101=>0010010
[8,7,5,6,3,4,2,1]=>1101011=>1101011=>0010100
[7,8,5,6,3,4,2,1]=>0101011=>1101010=>0010101
[8,5,6,7,3,4,2,1]=>1001011=>1101001=>0010110
[7,6,5,8,3,4,2,1]=>1101011=>1101011=>0010100
[6,7,5,8,3,4,2,1]=>0101011=>1101010=>0010101
[5,6,7,8,3,4,2,1]=>0001011=>1101000=>0010111
[8,7,6,4,3,5,2,1]=>1111011=>1101111=>0010000
[7,8,6,4,3,5,2,1]=>0111011=>1101110=>0010001
[7,6,8,4,3,5,2,1]=>1011011=>1101101=>0010010
[6,7,8,4,3,5,2,1]=>0011011=>1101100=>0010011
[8,7,6,3,4,5,2,1]=>1110011=>1100111=>0011000
[7,8,6,3,4,5,2,1]=>0110011=>1100110=>0011001
[8,6,7,3,4,5,2,1]=>1010011=>1100101=>0011010
[7,6,8,3,4,5,2,1]=>1010011=>1100101=>0011010
[6,7,8,3,4,5,2,1]=>0010011=>1100100=>0011011
[8,7,5,4,3,6,2,1]=>1111011=>1101111=>0010000
[7,8,5,4,3,6,2,1]=>0111011=>1101110=>0010001
[7,8,5,3,4,6,2,1]=>0110011=>1100110=>0011001
[8,7,4,3,5,6,2,1]=>1110011=>1100111=>0011000
[8,7,3,4,5,6,2,1]=>1100011=>1100011=>0011100
[7,6,5,4,3,8,2,1]=>1111011=>1101111=>0010000
[7,5,6,4,3,8,2,1]=>1011011=>1101101=>0010010
[7,4,5,6,3,8,2,1]=>1001011=>1101001=>0010110
[6,4,5,7,3,8,2,1]=>1001011=>1101001=>0010110
[5,4,6,7,3,8,2,1]=>1001011=>1101001=>0010110
[4,5,6,7,3,8,2,1]=>0001011=>1101000=>0010111
[7,6,3,4,5,8,2,1]=>1100011=>1100011=>0011100
[7,5,4,3,6,8,2,1]=>1110011=>1100111=>0011000
[7,5,3,4,6,8,2,1]=>1100011=>1100011=>0011100
[6,5,4,3,7,8,2,1]=>1110011=>1100111=>0011000
[8,7,6,5,4,2,3,1]=>1111101=>1011111=>0100000
[8,6,7,5,4,2,3,1]=>1011101=>1011101=>0100010
[7,6,8,5,4,2,3,1]=>1011101=>1011101=>0100010
[8,5,6,7,4,2,3,1]=>1001101=>1011001=>0100110
[7,6,5,8,4,2,3,1]=>1101101=>1011011=>0100100
[6,7,5,8,4,2,3,1]=>0101101=>1011010=>0100101
[7,5,6,8,4,2,3,1]=>1001101=>1011001=>0100110
[5,6,7,8,4,2,3,1]=>0001101=>1011000=>0100111
[8,7,6,4,5,2,3,1]=>1110101=>1010111=>0101000
[8,6,7,4,5,2,3,1]=>1010101=>1010101=>0101010
[7,6,8,4,5,2,3,1]=>1010101=>1010101=>0101010
[8,7,5,4,6,2,3,1]=>1110101=>1010111=>0101000
[8,7,4,5,6,2,3,1]=>1100101=>1010011=>0101100
[8,6,5,4,7,2,3,1]=>1110101=>1010111=>0101000
[8,5,6,4,7,2,3,1]=>1010101=>1010101=>0101010
[8,6,4,5,7,2,3,1]=>1100101=>1010011=>0101100
[7,5,6,4,8,2,3,1]=>1010101=>1010101=>0101010
[6,5,7,4,8,2,3,1]=>1010101=>1010101=>0101010
[4,5,6,7,8,2,3,1]=>0000101=>1010000=>0101111
[8,7,6,5,3,2,4,1]=>1111101=>1011111=>0100000
[7,8,6,5,3,2,4,1]=>0111101=>1011110=>0100001
[8,6,7,5,3,2,4,1]=>1011101=>1011101=>0100010
[7,6,8,5,3,2,4,1]=>1011101=>1011101=>0100010
[6,7,8,5,3,2,4,1]=>0011101=>1011100=>0100011
[8,6,5,7,3,2,4,1]=>1101101=>1011011=>0100100
[8,5,6,7,3,2,4,1]=>1001101=>1011001=>0100110
[7,6,5,8,3,2,4,1]=>1101101=>1011011=>0100100
[6,7,5,8,3,2,4,1]=>0101101=>1011010=>0100101
[5,6,7,8,3,2,4,1]=>0001101=>1011000=>0100111
[8,7,6,5,2,3,4,1]=>1111001=>1001111=>0110000
[8,6,7,5,2,3,4,1]=>1011001=>1001101=>0110010
[7,6,8,5,2,3,4,1]=>1011001=>1001101=>0110010
[6,7,8,5,2,3,4,1]=>0011001=>1001100=>0110011
[8,7,5,6,2,3,4,1]=>1101001=>1001011=>0110100
[7,8,5,6,2,3,4,1]=>0101001=>1001010=>0110101
[8,6,5,7,2,3,4,1]=>1101001=>1001011=>0110100
[8,5,6,7,2,3,4,1]=>1001001=>1001001=>0110110
[7,6,5,8,2,3,4,1]=>1101001=>1001011=>0110100
[6,7,5,8,2,3,4,1]=>0101001=>1001010=>0110101
[6,5,7,8,2,3,4,1]=>1001001=>1001001=>0110110
[5,6,7,8,2,3,4,1]=>0001001=>1001000=>0110111
[8,7,6,4,3,2,5,1]=>1111101=>1011111=>0100000
[7,8,6,4,3,2,5,1]=>0111101=>1011110=>0100001
[8,6,7,4,3,2,5,1]=>1011101=>1011101=>0100010
[7,6,8,4,3,2,5,1]=>1011101=>1011101=>0100010
[6,7,8,4,3,2,5,1]=>0011101=>1011100=>0100011
[8,7,6,3,4,2,5,1]=>1110101=>1010111=>0101000
[8,6,7,3,4,2,5,1]=>1010101=>1010101=>0101010
[7,6,8,3,4,2,5,1]=>1010101=>1010101=>0101010
[7,6,8,4,2,3,5,1]=>1011001=>1001101=>0110010
[6,7,8,4,2,3,5,1]=>0011001=>1001100=>0110011
[8,6,7,3,2,4,5,1]=>1011001=>1001101=>0110010
[6,7,8,3,2,4,5,1]=>0011001=>1001100=>0110011
[8,7,6,2,3,4,5,1]=>1110001=>1000111=>0111000
[7,8,6,2,3,4,5,1]=>0110001=>1000110=>0111001
[8,6,7,2,3,4,5,1]=>1010001=>1000101=>0111010
[7,6,8,2,3,4,5,1]=>1010001=>1000101=>0111010
[6,7,8,2,3,4,5,1]=>0010001=>1000100=>0111011
[8,7,5,3,4,2,6,1]=>1110101=>1010111=>0101000
[7,8,5,3,4,2,6,1]=>0110101=>1010110=>0101001
[8,7,5,3,2,4,6,1]=>1111001=>1001111=>0110000
[7,8,4,3,2,5,6,1]=>0111001=>1001110=>0110001
[7,8,3,4,2,5,6,1]=>0101001=>1001010=>0110101
[7,8,3,2,4,5,6,1]=>0110001=>1000110=>0111001
[8,6,5,4,3,2,7,1]=>1111101=>1011111=>0100000
[8,5,6,3,4,2,7,1]=>1010101=>1010101=>0101010
[8,6,4,3,5,2,7,1]=>1110101=>1010111=>0101000
[8,6,3,4,5,2,7,1]=>1100101=>1010011=>0101100
[8,4,5,3,6,2,7,1]=>1010101=>1010101=>0101010
[8,5,6,4,2,3,7,1]=>1011001=>1001101=>0110010
[8,6,4,2,3,5,7,1]=>1110001=>1000111=>0111000
[8,5,3,4,2,6,7,1]=>1101001=>1001011=>0110100
[8,5,4,2,3,6,7,1]=>1110001=>1000111=>0111000
[7,4,5,6,3,2,8,1]=>1001101=>1011001=>0100110
[6,4,5,7,3,2,8,1]=>1001101=>1011001=>0100110
[4,5,6,7,3,2,8,1]=>0001101=>1011000=>0100111
[7,5,6,3,4,2,8,1]=>1010101=>1010101=>0101010
[6,5,7,3,4,2,8,1]=>1010101=>1010101=>0101010
[7,4,5,3,6,2,8,1]=>1010101=>1010101=>0101010
[6,5,4,3,7,2,8,1]=>1110101=>1010111=>0101000
[6,4,5,3,7,2,8,1]=>1010101=>1010101=>0101010
[5,4,6,3,7,2,8,1]=>1010101=>1010101=>0101010
[4,5,6,3,7,2,8,1]=>0010101=>1010100=>0101011
[6,5,3,4,7,2,8,1]=>1100101=>1010011=>0101100
[5,6,3,4,7,2,8,1]=>0100101=>1010010=>0101101
[5,4,3,6,7,2,8,1]=>1100101=>1010011=>0101100
[6,7,5,4,2,3,8,1]=>0111001=>1001110=>0110001
[7,5,6,4,2,3,8,1]=>1011001=>1001101=>0110010
[6,5,7,4,2,3,8,1]=>1011001=>1001101=>0110010
[5,6,7,4,2,3,8,1]=>0011001=>1001100=>0110011
[6,7,4,5,2,3,8,1]=>0101001=>1001010=>0110101
[7,4,5,6,2,3,8,1]=>1001001=>1001001=>0110110
[6,5,4,7,2,3,8,1]=>1101001=>1001011=>0110100
[5,6,4,7,2,3,8,1]=>0101001=>1001010=>0110101
[6,4,5,7,2,3,8,1]=>1001001=>1001001=>0110110
[5,4,6,7,2,3,8,1]=>1001001=>1001001=>0110110
[4,5,6,7,2,3,8,1]=>0001001=>1001000=>0110111
[6,7,5,3,2,4,8,1]=>0111001=>1001110=>0110001
[6,5,7,3,2,4,8,1]=>1011001=>1001101=>0110010
[7,6,5,2,3,4,8,1]=>1110001=>1000111=>0111000
[5,6,7,2,3,4,8,1]=>0010001=>1000100=>0111011
[6,7,4,3,2,5,8,1]=>0111001=>1001110=>0110001
[7,6,4,2,3,5,8,1]=>1110001=>1000111=>0111000
[6,7,3,2,4,5,8,1]=>0110001=>1000110=>0111001
[6,7,2,3,4,5,8,1]=>0100001=>1000010=>0111101
[7,5,2,3,4,6,8,1]=>1100001=>1000011=>0111100
[6,5,4,3,2,7,8,1]=>1111001=>1001111=>0110000
[5,4,6,3,2,7,8,1]=>1011001=>1001101=>0110010
[5,4,3,6,2,7,8,1]=>1101001=>1001011=>0110100
[3,4,5,6,2,7,8,1]=>0001001=>1001000=>0110111
[6,5,4,2,3,7,8,1]=>1110001=>1000111=>0111000
[5,6,4,2,3,7,8,1]=>0110001=>1000110=>0111001
[6,4,5,2,3,7,8,1]=>1010001=>1000101=>0111010
[5,4,6,2,3,7,8,1]=>1010001=>1000101=>0111010
[6,5,2,3,4,7,8,1]=>1100001=>1000011=>0111100
[5,4,3,2,6,7,8,1]=>1110001=>1000111=>0111000
[4,3,5,2,6,7,8,1]=>1010001=>1000101=>0111010
[5,4,2,3,6,7,8,1]=>1100001=>1000011=>0111100
[4,5,2,3,6,7,8,1]=>0100001=>1000010=>0111101
[5,2,3,4,6,7,8,1]=>1000001=>1000001=>0111110
[4,3,2,5,6,7,8,1]=>1100001=>1000011=>0111100
[3,4,2,5,6,7,8,1]=>0100001=>1000010=>0111101
[3,2,4,5,6,7,8,1]=>1000001=>1000001=>0111110
[2,3,4,5,6,7,8,1]=>0000001=>1000000=>0111111
[8,7,6,5,4,3,1,2]=>1111110=>0111111=>1000000
[7,8,6,5,4,3,1,2]=>0111110=>0111110=>1000001
[8,7,5,6,4,3,1,2]=>1101110=>0111011=>1000100
[7,8,5,6,4,3,1,2]=>0101110=>0111010=>1000101
[7,6,5,8,4,3,1,2]=>1101110=>0111011=>1000100
[6,7,5,8,4,3,1,2]=>0101110=>0111010=>1000101
[7,5,6,8,4,3,1,2]=>1001110=>0111001=>1000110
[5,6,7,8,4,3,1,2]=>0001110=>0111000=>1000111
[7,8,6,4,5,3,1,2]=>0110110=>0110110=>1001001
[8,6,7,4,5,3,1,2]=>1010110=>0110101=>1001010
[8,7,5,4,6,3,1,2]=>1110110=>0110111=>1001000
[8,5,6,4,7,3,1,2]=>1010110=>0110101=>1001010
[6,7,4,5,8,3,1,2]=>0100110=>0110010=>1001101
[5,6,4,7,8,3,1,2]=>0100110=>0110010=>1001101
[4,5,6,7,8,3,1,2]=>0000110=>0110000=>1001111
[8,7,6,5,3,4,1,2]=>1111010=>0101111=>1010000
[7,8,6,5,3,4,1,2]=>0111010=>0101110=>1010001
[6,7,8,5,3,4,1,2]=>0011010=>0101100=>1010011
[8,7,5,6,3,4,1,2]=>1101010=>0101011=>1010100
[7,8,5,6,3,4,1,2]=>0101010=>0101010=>1010101
[8,5,6,7,3,4,1,2]=>1001010=>0101001=>1010110
[7,6,5,8,3,4,1,2]=>1101010=>0101011=>1010100
[6,7,5,8,3,4,1,2]=>0101010=>0101010=>1010101
[7,5,6,8,3,4,1,2]=>1001010=>0101001=>1010110
[6,5,7,8,3,4,1,2]=>1001010=>0101001=>1010110
[5,6,7,8,3,4,1,2]=>0001010=>0101000=>1010111
[7,8,5,4,3,6,1,2]=>0111010=>0101110=>1010001
[8,7,4,5,3,6,1,2]=>1101010=>0101011=>1010100
[7,8,4,5,3,6,1,2]=>0101010=>0101010=>1010101
[7,8,5,3,4,6,1,2]=>0110010=>0100110=>1011001
[8,7,4,3,5,6,1,2]=>1110010=>0100111=>1011000
[7,8,4,3,5,6,1,2]=>0110010=>0100110=>1011001
[7,8,3,4,5,6,1,2]=>0100010=>0100010=>1011101
[8,5,4,3,6,7,1,2]=>1110010=>0100111=>1011000
[8,5,3,4,6,7,1,2]=>1100010=>0100011=>1011100
[8,4,3,5,6,7,1,2]=>1100010=>0100011=>1011100
[7,6,5,4,3,8,1,2]=>1111010=>0101111=>1010000
[5,6,7,4,3,8,1,2]=>0011010=>0101100=>1010011
[6,7,4,5,3,8,1,2]=>0101010=>0101010=>1010101
[5,6,4,7,3,8,1,2]=>0101010=>0101010=>1010101
[5,4,6,7,3,8,1,2]=>1001010=>0101001=>1010110
[4,5,6,7,3,8,1,2]=>0001010=>0101000=>1010111
[7,5,6,3,4,8,1,2]=>1010010=>0100101=>1011010
[7,6,3,4,5,8,1,2]=>1100010=>0100011=>1011100
[7,5,4,3,6,8,1,2]=>1110010=>0100111=>1011000
[7,5,3,4,6,8,1,2]=>1100010=>0100011=>1011100
[6,5,4,3,7,8,1,2]=>1110010=>0100111=>1011000
[5,4,6,3,7,8,1,2]=>1010010=>0100101=>1011010
[4,5,6,3,7,8,1,2]=>0010010=>0100100=>1011011
[5,6,3,4,7,8,1,2]=>0100010=>0100010=>1011101
[6,4,3,5,7,8,1,2]=>1100010=>0100011=>1011100
[6,3,4,5,7,8,1,2]=>1000010=>0100001=>1011110
[5,4,3,6,7,8,1,2]=>1100010=>0100011=>1011100
[4,5,3,6,7,8,1,2]=>0100010=>0100010=>1011101
[5,3,4,6,7,8,1,2]=>1000010=>0100001=>1011110
[4,3,5,6,7,8,1,2]=>1000010=>0100001=>1011110
[3,4,5,6,7,8,1,2]=>0000010=>0100000=>1011111
[8,7,6,5,4,2,1,3]=>1111110=>0111111=>1000000
[7,6,8,5,4,2,1,3]=>1011110=>0111101=>1000010
[6,7,8,5,4,2,1,3]=>0011110=>0111100=>1000011
[8,7,5,6,4,2,1,3]=>1101110=>0111011=>1000100
[7,8,5,6,4,2,1,3]=>0101110=>0111010=>1000101
[7,6,5,8,4,2,1,3]=>1101110=>0111011=>1000100
[6,7,5,8,4,2,1,3]=>0101110=>0111010=>1000101
[7,5,6,8,4,2,1,3]=>1001110=>0111001=>1000110
[6,5,7,8,4,2,1,3]=>1001110=>0111001=>1000110
[5,6,7,8,4,2,1,3]=>0001110=>0111000=>1000111
[7,6,8,4,5,2,1,3]=>1010110=>0110101=>1001010
[8,7,4,5,6,2,1,3]=>1100110=>0110011=>1001100
[6,7,5,4,8,2,1,3]=>0110110=>0110110=>1001001
[7,5,6,4,8,2,1,3]=>1010110=>0110101=>1001010
[7,6,4,5,8,2,1,3]=>1100110=>0110011=>1001100
[4,5,6,7,8,2,1,3]=>0000110=>0110000=>1001111
[8,7,6,5,4,1,2,3]=>1111100=>0011111=>1100000
[6,7,8,5,4,1,2,3]=>0011100=>0011100=>1100011
[7,8,5,6,4,1,2,3]=>0101100=>0011010=>1100101
[8,5,6,7,4,1,2,3]=>1001100=>0011001=>1100110
[7,6,5,8,4,1,2,3]=>1101100=>0011011=>1100100
[6,7,5,8,4,1,2,3]=>0101100=>0011010=>1100101
[7,5,6,8,4,1,2,3]=>1001100=>0011001=>1100110
[6,5,7,8,4,1,2,3]=>1001100=>0011001=>1100110
[5,6,7,8,4,1,2,3]=>0001100=>0011000=>1100111
[8,7,5,4,6,1,2,3]=>1110100=>0010111=>1101000
[8,5,6,4,7,1,2,3]=>1010100=>0010101=>1101010
[8,6,4,5,7,1,2,3]=>1100100=>0010011=>1101100
[7,6,5,4,8,1,2,3]=>1110100=>0010111=>1101000
[6,7,5,4,8,1,2,3]=>0110100=>0010110=>1101001
[7,5,6,4,8,1,2,3]=>1010100=>0010101=>1101010
[6,5,7,4,8,1,2,3]=>1010100=>0010101=>1101010
[5,6,7,4,8,1,2,3]=>0010100=>0010100=>1101011
[7,6,4,5,8,1,2,3]=>1100100=>0010011=>1101100
[6,7,4,5,8,1,2,3]=>0100100=>0010010=>1101101
[7,5,4,6,8,1,2,3]=>1100100=>0010011=>1101100
[7,4,5,6,8,1,2,3]=>1000100=>0010001=>1101110
[6,5,4,7,8,1,2,3]=>1100100=>0010011=>1101100
[5,6,4,7,8,1,2,3]=>0100100=>0010010=>1101101
[6,4,5,7,8,1,2,3]=>1000100=>0010001=>1101110
[5,4,6,7,8,1,2,3]=>1000100=>0010001=>1101110
[4,5,6,7,8,1,2,3]=>0000100=>0010000=>1101111
[8,7,6,5,3,2,1,4]=>1111110=>0111111=>1000000
[7,8,6,5,3,2,1,4]=>0111110=>0111110=>1000001
[8,6,7,5,3,2,1,4]=>1011110=>0111101=>1000010
[7,6,8,5,3,2,1,4]=>1011110=>0111101=>1000010
[6,7,8,5,3,2,1,4]=>0011110=>0111100=>1000011
[8,7,5,6,3,2,1,4]=>1101110=>0111011=>1000100
[7,8,5,6,3,2,1,4]=>0101110=>0111010=>1000101
[8,6,5,7,3,2,1,4]=>1101110=>0111011=>1000100
[8,5,6,7,3,2,1,4]=>1001110=>0111001=>1000110
[7,6,5,8,3,2,1,4]=>1101110=>0111011=>1000100
[6,7,5,8,3,2,1,4]=>0101110=>0111010=>1000101
[7,5,6,8,3,2,1,4]=>1001110=>0111001=>1000110
[6,5,7,8,3,2,1,4]=>1001110=>0111001=>1000110
[5,6,7,8,3,2,1,4]=>0001110=>0111000=>1000111
[8,7,6,5,2,3,1,4]=>1111010=>0101111=>1010000
[7,8,6,5,2,3,1,4]=>0111010=>0101110=>1010001
[8,6,7,5,2,3,1,4]=>1011010=>0101101=>1010010
[7,6,8,5,2,3,1,4]=>1011010=>0101101=>1010010
[6,7,8,5,2,3,1,4]=>0011010=>0101100=>1010011
[8,7,5,6,2,3,1,4]=>1101010=>0101011=>1010100
[7,8,5,6,2,3,1,4]=>0101010=>0101010=>1010101
[8,6,5,7,2,3,1,4]=>1101010=>0101011=>1010100
[8,5,6,7,2,3,1,4]=>1001010=>0101001=>1010110
[7,6,5,8,2,3,1,4]=>1101010=>0101011=>1010100
[6,7,5,8,2,3,1,4]=>0101010=>0101010=>1010101
[7,5,6,8,2,3,1,4]=>1001010=>0101001=>1010110
[6,5,7,8,2,3,1,4]=>1001010=>0101001=>1010110
[5,6,7,8,2,3,1,4]=>0001010=>0101000=>1010111
[8,7,6,5,3,1,2,4]=>1111100=>0011111=>1100000
[7,8,6,5,3,1,2,4]=>0111100=>0011110=>1100001
[7,8,5,6,3,1,2,4]=>0101100=>0011010=>1100101
[7,6,5,8,3,1,2,4]=>1101100=>0011011=>1100100
[6,7,5,8,3,1,2,4]=>0101100=>0011010=>1100101
[7,5,6,8,3,1,2,4]=>1001100=>0011001=>1100110
[6,5,7,8,3,1,2,4]=>1001100=>0011001=>1100110
[5,6,7,8,3,1,2,4]=>0001100=>0011000=>1100111
[8,7,6,5,2,1,3,4]=>1111100=>0011111=>1100000
[7,6,8,5,2,1,3,4]=>1011100=>0011101=>1100010
[6,7,8,5,2,1,3,4]=>0011100=>0011100=>1100011
[7,8,5,6,2,1,3,4]=>0101100=>0011010=>1100101
[8,6,5,7,2,1,3,4]=>1101100=>0011011=>1100100
[8,5,6,7,2,1,3,4]=>1001100=>0011001=>1100110
[7,6,5,8,2,1,3,4]=>1101100=>0011011=>1100100
[6,7,5,8,2,1,3,4]=>0101100=>0011010=>1100101
[7,5,6,8,2,1,3,4]=>1001100=>0011001=>1100110
[6,5,7,8,2,1,3,4]=>1001100=>0011001=>1100110
[5,6,7,8,2,1,3,4]=>0001100=>0011000=>1100111
[8,7,6,5,1,2,3,4]=>1111000=>0001111=>1110000
[7,8,6,5,1,2,3,4]=>0111000=>0001110=>1110001
[8,6,7,5,1,2,3,4]=>1011000=>0001101=>1110010
[7,6,8,5,1,2,3,4]=>1011000=>0001101=>1110010
[6,7,8,5,1,2,3,4]=>0011000=>0001100=>1110011
[8,7,5,6,1,2,3,4]=>1101000=>0001011=>1110100
[7,8,5,6,1,2,3,4]=>0101000=>0001010=>1110101
[8,6,5,7,1,2,3,4]=>1101000=>0001011=>1110100
[8,5,6,7,1,2,3,4]=>1001000=>0001001=>1110110
[7,6,5,8,1,2,3,4]=>1101000=>0001011=>1110100
[6,7,5,8,1,2,3,4]=>0101000=>0001010=>1110101
[7,5,6,8,1,2,3,4]=>1001000=>0001001=>1110110
[6,5,7,8,1,2,3,4]=>1001000=>0001001=>1110110
[5,6,7,8,1,2,3,4]=>0001000=>0001000=>1110111
[8,7,6,4,3,2,1,5]=>1111110=>0111111=>1000000
[7,8,6,4,3,2,1,5]=>0111110=>0111110=>1000001
[8,6,7,4,3,2,1,5]=>1011110=>0111101=>1000010
[7,6,8,4,3,2,1,5]=>1011110=>0111101=>1000010
[6,7,8,4,3,2,1,5]=>0011110=>0111100=>1000011
[8,7,6,3,4,2,1,5]=>1110110=>0110111=>1001000
[7,8,6,3,4,2,1,5]=>0110110=>0110110=>1001001
[6,7,8,3,4,2,1,5]=>0010110=>0110100=>1001011
[8,7,6,4,2,3,1,5]=>1111010=>0101111=>1010000
[7,6,8,4,2,3,1,5]=>1011010=>0101101=>1010010
[6,7,8,4,2,3,1,5]=>0011010=>0101100=>1010011
[8,7,6,3,2,4,1,5]=>1111010=>0101111=>1010000
[8,6,7,3,2,4,1,5]=>1011010=>0101101=>1010010
[6,7,8,3,2,4,1,5]=>0011010=>0101100=>1010011
[8,7,6,2,3,4,1,5]=>1110010=>0100111=>1011000
[6,7,8,2,3,4,1,5]=>0010010=>0100100=>1011011
[8,7,6,4,3,1,2,5]=>1111100=>0011111=>1100000
[6,7,8,4,3,1,2,5]=>0011100=>0011100=>1100011
[8,7,6,3,4,1,2,5]=>1110100=>0010111=>1101000
[6,7,8,3,4,1,2,5]=>0010100=>0010100=>1101011
[8,7,6,4,2,1,3,5]=>1111100=>0011111=>1100000
[7,8,6,4,2,1,3,5]=>0111100=>0011110=>1100001
[8,6,7,4,2,1,3,5]=>1011100=>0011101=>1100010
[6,7,8,4,2,1,3,5]=>0011100=>0011100=>1100011
[8,7,6,4,1,2,3,5]=>1111000=>0001111=>1110000
[7,8,6,4,1,2,3,5]=>0111000=>0001110=>1110001
[7,6,8,4,1,2,3,5]=>1011000=>0001101=>1110010
[6,7,8,4,1,2,3,5]=>0011000=>0001100=>1110011
[8,7,6,3,2,1,4,5]=>1111100=>0011111=>1100000
[7,6,8,3,2,1,4,5]=>1011100=>0011101=>1100010
[6,7,8,3,2,1,4,5]=>0011100=>0011100=>1100011
[8,7,6,2,3,1,4,5]=>1110100=>0010111=>1101000
[7,6,8,2,3,1,4,5]=>1010100=>0010101=>1101010
[6,7,8,2,3,1,4,5]=>0010100=>0010100=>1101011
[8,7,6,3,1,2,4,5]=>1111000=>0001111=>1110000
[7,8,6,3,1,2,4,5]=>0111000=>0001110=>1110001
[6,7,8,3,1,2,4,5]=>0011000=>0001100=>1110011
[8,7,6,2,1,3,4,5]=>1111000=>0001111=>1110000
[7,8,6,2,1,3,4,5]=>0111000=>0001110=>1110001
[6,7,8,2,1,3,4,5]=>0011000=>0001100=>1110011
[8,7,6,1,2,3,4,5]=>1110000=>0000111=>1111000
[7,8,6,1,2,3,4,5]=>0110000=>0000110=>1111001
[8,6,7,1,2,3,4,5]=>1010000=>0000101=>1111010
[7,6,8,1,2,3,4,5]=>1010000=>0000101=>1111010
[6,7,8,1,2,3,4,5]=>0010000=>0000100=>1111011
[8,7,5,4,3,2,1,6]=>1111110=>0111111=>1000000
[7,8,5,4,3,2,1,6]=>0111110=>0111110=>1000001
[8,7,5,3,4,2,1,6]=>1110110=>0110111=>1001000
[8,7,3,4,5,2,1,6]=>1100110=>0110011=>1001100
[7,8,3,4,5,2,1,6]=>0100110=>0110010=>1001101
[8,7,4,5,2,3,1,6]=>1101010=>0101011=>1010100
[7,8,4,5,2,3,1,6]=>0101010=>0101010=>1010101
[8,7,5,3,2,4,1,6]=>1111010=>0101111=>1010000
[8,7,4,3,2,5,1,6]=>1111010=>0101111=>1010000
[7,8,4,3,2,5,1,6]=>0111010=>0101110=>1010001
[8,7,3,4,2,5,1,6]=>1101010=>0101011=>1010100
[7,8,3,4,2,5,1,6]=>0101010=>0101010=>1010101
[8,7,5,4,3,1,2,6]=>1111100=>0011111=>1100000
[7,8,5,4,3,1,2,6]=>0111100=>0011110=>1100001
[8,7,5,3,4,1,2,6]=>1110100=>0010111=>1101000
[7,8,5,3,4,1,2,6]=>0110100=>0010110=>1101001
[7,8,5,4,2,1,3,6]=>0111100=>0011110=>1100001
[7,8,5,4,1,2,3,6]=>0111000=>0001110=>1110001
[8,7,4,5,1,2,3,6]=>1101000=>0001011=>1110100
[8,7,5,3,2,1,4,6]=>1111100=>0011111=>1100000
[7,8,5,3,2,1,4,6]=>0111100=>0011110=>1100001
[8,7,5,2,3,1,4,6]=>1110100=>0010111=>1101000
[8,7,5,3,1,2,4,6]=>1111000=>0001111=>1110000
[7,8,5,3,1,2,4,6]=>0111000=>0001110=>1110001
[8,7,5,2,1,3,4,6]=>1111000=>0001111=>1110000
[7,8,5,2,1,3,4,6]=>0111000=>0001110=>1110001
[8,7,5,1,2,3,4,6]=>1110000=>0000111=>1111000
[7,8,5,1,2,3,4,6]=>0110000=>0000110=>1111001
[8,7,4,3,2,1,5,6]=>1111100=>0011111=>1100000
[7,8,4,3,2,1,5,6]=>0111100=>0011110=>1100001
[8,7,3,4,2,1,5,6]=>1101100=>0011011=>1100100
[7,8,3,4,2,1,5,6]=>0101100=>0011010=>1100101
[7,8,4,2,3,1,5,6]=>0110100=>0010110=>1101001
[8,7,3,2,4,1,5,6]=>1110100=>0010111=>1101000
[7,8,3,2,4,1,5,6]=>0110100=>0010110=>1101001
[7,8,2,3,4,1,5,6]=>0100100=>0010010=>1101101
[7,8,4,3,1,2,5,6]=>0111000=>0001110=>1110001
[8,7,3,4,1,2,5,6]=>1101000=>0001011=>1110100
[7,8,3,4,1,2,5,6]=>0101000=>0001010=>1110101
[7,8,4,2,1,3,5,6]=>0111000=>0001110=>1110001
[7,8,4,1,2,3,5,6]=>0110000=>0000110=>1111001
[8,7,3,2,1,4,5,6]=>1111000=>0001111=>1110000
[7,8,3,2,1,4,5,6]=>0111000=>0001110=>1110001
[7,8,2,3,1,4,5,6]=>0101000=>0001010=>1110101
[7,8,3,1,2,4,5,6]=>0110000=>0000110=>1111001
[7,8,2,1,3,4,5,6]=>0110000=>0000110=>1111001
[7,8,1,2,3,4,5,6]=>0100000=>0000010=>1111101
[8,6,5,4,3,2,1,7]=>1111110=>0111111=>1000000
[8,5,6,4,3,2,1,7]=>1011110=>0111101=>1000010
[8,4,5,6,3,2,1,7]=>1001110=>0111001=>1000110
[8,6,5,3,4,2,1,7]=>1110110=>0110111=>1001000
[8,5,6,3,4,2,1,7]=>1010110=>0110101=>1001010
[8,4,5,3,6,2,1,7]=>1010110=>0110101=>1001010
[8,6,5,4,2,3,1,7]=>1111010=>0101111=>1010000
[8,5,6,4,2,3,1,7]=>1011010=>0101101=>1010010
[8,6,5,3,2,4,1,7]=>1111010=>0101111=>1010000
[8,6,5,2,3,4,1,7]=>1110010=>0100111=>1011000
[8,5,6,2,3,4,1,7]=>1010010=>0100101=>1011010
[8,6,4,2,3,5,1,7]=>1110010=>0100111=>1011000
[8,6,3,2,4,5,1,7]=>1110010=>0100111=>1011000
[8,5,2,3,4,6,1,7]=>1100010=>0100011=>1011100
[8,6,4,5,3,1,2,7]=>1101100=>0011011=>1100100
[8,5,6,3,4,1,2,7]=>1010100=>0010101=>1101010
[8,6,3,4,5,1,2,7]=>1100100=>0010011=>1101100
[8,4,5,3,6,1,2,7]=>1010100=>0010101=>1101010
[8,4,3,5,6,1,2,7]=>1100100=>0010011=>1101100
[8,6,5,4,2,1,3,7]=>1111100=>0011111=>1100000
[8,5,6,4,2,1,3,7]=>1011100=>0011101=>1100010
[8,5,6,4,1,2,3,7]=>1011000=>0001101=>1110010
[8,4,5,6,1,2,3,7]=>1001000=>0001001=>1110110
[8,6,5,3,2,1,4,7]=>1111100=>0011111=>1100000
[8,5,6,3,2,1,4,7]=>1011100=>0011101=>1100010
[8,6,5,2,3,1,4,7]=>1110100=>0010111=>1101000
[8,5,6,2,3,1,4,7]=>1010100=>0010101=>1101010
[8,5,6,3,1,2,4,7]=>1011000=>0001101=>1110010
[8,6,5,2,1,3,4,7]=>1111000=>0001111=>1110000
[8,5,6,2,1,3,4,7]=>1011000=>0001101=>1110010
[8,6,5,1,2,3,4,7]=>1110000=>0000111=>1111000
[8,5,6,1,2,3,4,7]=>1010000=>0000101=>1111010
[8,6,4,3,2,1,5,7]=>1111100=>0011111=>1100000
[8,6,3,4,2,1,5,7]=>1101100=>0011011=>1100100
[8,6,4,2,3,1,5,7]=>1110100=>0010111=>1101000
[8,6,3,2,4,1,5,7]=>1110100=>0010111=>1101000
[8,6,3,4,1,2,5,7]=>1101000=>0001011=>1110100
[8,6,4,2,1,3,5,7]=>1111000=>0001111=>1110000
[8,6,4,1,2,3,5,7]=>1110000=>0000111=>1111000
[8,4,5,3,2,1,6,7]=>1011100=>0011101=>1100010
[8,4,3,5,2,1,6,7]=>1101100=>0011011=>1100100
[8,3,4,5,2,1,6,7]=>1001100=>0011001=>1100110
[8,4,5,2,3,1,6,7]=>1010100=>0010101=>1101010
[8,5,2,3,4,1,6,7]=>1100100=>0010011=>1101100
[8,4,2,3,5,1,6,7]=>1100100=>0010011=>1101100
[8,5,3,4,1,2,6,7]=>1101000=>0001011=>1110100
[8,5,4,2,1,3,6,7]=>1111000=>0001111=>1110000
[8,5,3,2,1,4,6,7]=>1111000=>0001111=>1110000
[8,5,3,1,2,4,6,7]=>1110000=>0000111=>1111000
[8,4,3,2,1,5,6,7]=>1111000=>0001111=>1110000
[8,3,4,1,2,5,6,7]=>1010000=>0000101=>1111010
[8,4,2,1,3,5,6,7]=>1110000=>0000111=>1111000
[8,3,2,1,4,5,6,7]=>1110000=>0000111=>1111000
[8,3,1,2,4,5,6,7]=>1100000=>0000011=>1111100
[8,1,2,3,4,5,6,7]=>1000000=>0000001=>1111110
[7,6,5,4,3,2,1,8]=>1111110=>0111111=>1000000
[6,7,5,4,3,2,1,8]=>0111110=>0111110=>1000001
[7,5,6,4,3,2,1,8]=>1011110=>0111101=>1000010
[6,5,7,4,3,2,1,8]=>1011110=>0111101=>1000010
[5,6,7,4,3,2,1,8]=>0011110=>0111100=>1000011
[7,6,4,5,3,2,1,8]=>1101110=>0111011=>1000100
[7,4,5,6,3,2,1,8]=>1001110=>0111001=>1000110
[6,5,4,7,3,2,1,8]=>1101110=>0111011=>1000100
[5,6,4,7,3,2,1,8]=>0101110=>0111010=>1000101
[4,5,6,7,3,2,1,8]=>0001110=>0111000=>1000111
[7,6,5,3,4,2,1,8]=>1110110=>0110111=>1001000
[6,7,5,3,4,2,1,8]=>0110110=>0110110=>1001001
[7,5,6,3,4,2,1,8]=>1010110=>0110101=>1001010
[6,5,7,3,4,2,1,8]=>1010110=>0110101=>1001010
[5,6,7,3,4,2,1,8]=>0010110=>0110100=>1001011
[7,6,3,4,5,2,1,8]=>1100110=>0110011=>1001100
[7,4,5,3,6,2,1,8]=>1010110=>0110101=>1001010
[7,3,4,5,6,2,1,8]=>1000110=>0110001=>1001110
[6,5,4,3,7,2,1,8]=>1110110=>0110111=>1001000
[5,4,6,3,7,2,1,8]=>1010110=>0110101=>1001010
[5,4,3,6,7,2,1,8]=>1100110=>0110011=>1001100
[7,5,6,4,2,3,1,8]=>1011010=>0101101=>1010010
[5,6,7,4,2,3,1,8]=>0011010=>0101100=>1010011
[7,6,4,5,2,3,1,8]=>1101010=>0101011=>1010100
[6,7,4,5,2,3,1,8]=>0101010=>0101010=>1010101
[7,4,5,6,2,3,1,8]=>1001010=>0101001=>1010110
[6,5,4,7,2,3,1,8]=>1101010=>0101011=>1010100
[5,6,4,7,2,3,1,8]=>0101010=>0101010=>1010101
[5,4,6,7,2,3,1,8]=>1001010=>0101001=>1010110
[4,5,6,7,2,3,1,8]=>0001010=>0101000=>1010111
[5,6,7,3,2,4,1,8]=>0011010=>0101100=>1010011
[7,6,5,2,3,4,1,8]=>1110010=>0100111=>1011000
[6,7,5,2,3,4,1,8]=>0110010=>0100110=>1011001
[7,5,6,2,3,4,1,8]=>1010010=>0100101=>1011010
[6,5,7,2,3,4,1,8]=>1010010=>0100101=>1011010
[5,6,7,2,3,4,1,8]=>0010010=>0100100=>1011011
[6,7,4,3,2,5,1,8]=>0111010=>0101110=>1010001
[6,7,3,4,2,5,1,8]=>0101010=>0101010=>1010101
[7,6,4,2,3,5,1,8]=>1110010=>0100111=>1011000
[7,6,3,2,4,5,1,8]=>1110010=>0100111=>1011000
[6,7,3,2,4,5,1,8]=>0110010=>0100110=>1011001
[7,6,2,3,4,5,1,8]=>1100010=>0100011=>1011100
[6,7,2,3,4,5,1,8]=>0100010=>0100010=>1011101
[7,4,5,3,2,6,1,8]=>1011010=>0101101=>1010010
[7,5,3,4,2,6,1,8]=>1101010=>0101011=>1010100
[7,4,3,5,2,6,1,8]=>1101010=>0101011=>1010100
[7,4,5,2,3,6,1,8]=>1010010=>0100101=>1011010
[7,5,3,2,4,6,1,8]=>1110010=>0100111=>1011000
[7,4,2,3,5,6,1,8]=>1100010=>0100011=>1011100
[5,4,6,3,2,7,1,8]=>1011010=>0101101=>1010010
[5,6,3,4,2,7,1,8]=>0101010=>0101010=>1010101
[6,3,4,5,2,7,1,8]=>1001010=>0101001=>1010110
[5,4,3,6,2,7,1,8]=>1101010=>0101011=>1010100
[4,5,3,6,2,7,1,8]=>0101010=>0101010=>1010101
[3,4,5,6,2,7,1,8]=>0001010=>0101000=>1010111
[6,5,3,2,4,7,1,8]=>1110010=>0100111=>1011000
[6,4,2,3,5,7,1,8]=>1100010=>0100011=>1011100
[6,3,2,4,5,7,1,8]=>1100010=>0100011=>1011100
[6,2,3,4,5,7,1,8]=>1000010=>0100001=>1011110
[5,4,3,2,6,7,1,8]=>1110010=>0100111=>1011000
[4,5,2,3,6,7,1,8]=>0100010=>0100010=>1011101
[7,4,5,6,3,1,2,8]=>1001100=>0011001=>1100110
[5,4,6,7,3,1,2,8]=>1001100=>0011001=>1100110
[4,5,6,7,3,1,2,8]=>0001100=>0011000=>1100111
[7,5,6,3,4,1,2,8]=>1010100=>0010101=>1101010
[7,5,3,4,6,1,2,8]=>1100100=>0010011=>1101100
[6,5,4,3,7,1,2,8]=>1110100=>0010111=>1101000
[3,4,5,6,7,1,2,8]=>0000100=>0010000=>1101111
[7,4,5,6,2,1,3,8]=>1001100=>0011001=>1100110
[4,5,6,7,2,1,3,8]=>0001100=>0011000=>1100111
[7,6,5,4,1,2,3,8]=>1111000=>0001111=>1110000
[7,5,6,4,1,2,3,8]=>1011000=>0001101=>1110010
[7,6,4,5,1,2,3,8]=>1101000=>0001011=>1110100
[7,5,4,6,1,2,3,8]=>1101000=>0001011=>1110100
[7,4,5,6,1,2,3,8]=>1001000=>0001001=>1110110
[4,5,6,7,1,2,3,8]=>0001000=>0001000=>1110111
[7,6,5,2,3,1,4,8]=>1110100=>0010111=>1101000
[6,7,5,2,3,1,4,8]=>0110100=>0010110=>1101001
[7,5,6,2,3,1,4,8]=>1010100=>0010101=>1101010
[6,5,7,2,3,1,4,8]=>1010100=>0010101=>1101010
[5,6,7,2,3,1,4,8]=>0010100=>0010100=>1101011
[7,5,6,3,1,2,4,8]=>1011000=>0001101=>1110010
[7,6,5,2,1,3,4,8]=>1111000=>0001111=>1110000
[7,6,5,1,2,3,4,8]=>1110000=>0000111=>1111000
[6,7,5,1,2,3,4,8]=>0110000=>0000110=>1111001
[7,5,6,1,2,3,4,8]=>1010000=>0000101=>1111010
[6,5,7,1,2,3,4,8]=>1010000=>0000101=>1111010
[5,6,7,1,2,3,4,8]=>0010000=>0000100=>1111011
[7,6,4,3,2,1,5,8]=>1111100=>0011111=>1100000
[6,7,4,3,2,1,5,8]=>0111100=>0011110=>1100001
[7,6,3,2,4,1,5,8]=>1110100=>0010111=>1101000
[7,6,2,3,4,1,5,8]=>1100100=>0010011=>1101100
[6,7,2,3,4,1,5,8]=>0100100=>0010010=>1101101
[7,6,4,2,1,3,5,8]=>1111000=>0001111=>1110000
[7,6,3,2,1,4,5,8]=>1111000=>0001111=>1110000
[6,7,3,2,1,4,5,8]=>0111000=>0001110=>1110001
[7,6,2,3,1,4,5,8]=>1101000=>0001011=>1110100
[6,7,3,1,2,4,5,8]=>0110000=>0000110=>1111001
[6,7,1,2,3,4,5,8]=>0100000=>0000010=>1111101
[7,5,2,3,4,1,6,8]=>1100100=>0010011=>1101100
[7,4,2,3,5,1,6,8]=>1100100=>0010011=>1101100
[7,2,3,4,5,1,6,8]=>1000100=>0010001=>1101110
[7,5,3,4,1,2,6,8]=>1101000=>0001011=>1110100
[7,4,5,1,2,3,6,8]=>1010000=>0000101=>1111010
[7,5,3,2,1,4,6,8]=>1111000=>0001111=>1110000
[7,5,3,1,2,4,6,8]=>1110000=>0000111=>1111000
[7,5,1,2,3,4,6,8]=>1100000=>0000011=>1111100
[7,4,3,2,1,5,6,8]=>1111000=>0001111=>1110000
[7,4,3,1,2,5,6,8]=>1110000=>0000111=>1111000
[7,3,4,1,2,5,6,8]=>1010000=>0000101=>1111010
[7,3,1,2,4,5,6,8]=>1100000=>0000011=>1111100
[7,1,2,3,4,5,6,8]=>1000000=>0000001=>1111110
[5,6,4,3,2,1,7,8]=>0111100=>0011110=>1100001
[5,4,6,3,2,1,7,8]=>1011100=>0011101=>1100010
[4,5,6,3,2,1,7,8]=>0011100=>0011100=>1100011
[6,5,3,4,2,1,7,8]=>1101100=>0011011=>1100100
[5,4,3,6,2,1,7,8]=>1101100=>0011011=>1100100
[3,4,5,6,2,1,7,8]=>0001100=>0011000=>1100111
[5,4,6,2,3,1,7,8]=>1010100=>0010101=>1101010
[5,6,3,2,4,1,7,8]=>0110100=>0010110=>1101001
[6,5,2,3,4,1,7,8]=>1100100=>0010011=>1101100
[5,6,2,3,4,1,7,8]=>0100100=>0010010=>1101101
[6,4,3,2,5,1,7,8]=>1110100=>0010111=>1101000
[5,4,3,2,6,1,7,8]=>1110100=>0010111=>1101000
[4,5,3,2,6,1,7,8]=>0110100=>0010110=>1101001
[5,3,2,4,6,1,7,8]=>1100100=>0010011=>1101100
[6,5,4,3,1,2,7,8]=>1111000=>0001111=>1110000
[5,6,4,2,1,3,7,8]=>0111000=>0001110=>1110001
[6,4,5,2,1,3,7,8]=>1011000=>0001101=>1110010
[6,4,3,2,1,5,7,8]=>1111000=>0001111=>1110000
[6,3,4,2,1,5,7,8]=>1011000=>0001101=>1110010
[6,4,3,1,2,5,7,8]=>1110000=>0000111=>1111000
[6,4,2,1,3,5,7,8]=>1110000=>0000111=>1111000
[5,4,3,2,1,6,7,8]=>1111000=>0001111=>1110000
[4,5,3,2,1,6,7,8]=>0111000=>0001110=>1110001
[5,3,4,2,1,6,7,8]=>1011000=>0001101=>1110010
[4,3,5,2,1,6,7,8]=>1011000=>0001101=>1110010
[3,4,5,2,1,6,7,8]=>0011000=>0001100=>1110011
[5,4,2,3,1,6,7,8]=>1101000=>0001011=>1110100
[4,5,2,3,1,6,7,8]=>0101000=>0001010=>1110101
[5,3,2,4,1,6,7,8]=>1101000=>0001011=>1110100
[5,2,3,4,1,6,7,8]=>1001000=>0001001=>1110110
[4,3,2,5,1,6,7,8]=>1101000=>0001011=>1110100
[3,4,2,5,1,6,7,8]=>0101000=>0001010=>1110101
[4,2,3,5,1,6,7,8]=>1001000=>0001001=>1110110
[3,2,4,5,1,6,7,8]=>1001000=>0001001=>1110110
[2,3,4,5,1,6,7,8]=>0001000=>0001000=>1110111
[5,4,3,1,2,6,7,8]=>1110000=>0000111=>1111000
[5,3,4,1,2,6,7,8]=>1010000=>0000101=>1111010
[5,4,2,1,3,6,7,8]=>1110000=>0000111=>1111000
[5,4,1,2,3,6,7,8]=>1100000=>0000011=>1111100
[4,5,1,2,3,6,7,8]=>0100000=>0000010=>1111101
[5,3,2,1,4,6,7,8]=>1110000=>0000111=>1111000
[5,2,3,1,4,6,7,8]=>1010000=>0000101=>1111010
[5,3,1,2,4,6,7,8]=>1100000=>0000011=>1111100
[5,2,1,3,4,6,7,8]=>1100000=>0000011=>1111100
[5,1,2,3,4,6,7,8]=>1000000=>0000001=>1111110
[4,3,2,1,5,6,7,8]=>1110000=>0000111=>1111000
[3,4,2,1,5,6,7,8]=>0110000=>0000110=>1111001
[4,2,3,1,5,6,7,8]=>1010000=>0000101=>1111010
[3,2,4,1,5,6,7,8]=>1010000=>0000101=>1111010
[2,3,4,1,5,6,7,8]=>0010000=>0000100=>1111011
[4,3,1,2,5,6,7,8]=>1100000=>0000011=>1111100
[3,4,1,2,5,6,7,8]=>0100000=>0000010=>1111101
[4,2,1,3,5,6,7,8]=>1100000=>0000011=>1111100
[4,1,2,3,5,6,7,8]=>1000000=>0000001=>1111110
[3,2,1,4,5,6,7,8]=>1100000=>0000011=>1111100
[2,3,1,4,5,6,7,8]=>0100000=>0000010=>1111101
[3,1,2,4,5,6,7,8]=>1000000=>0000001=>1111110
[2,1,3,4,5,6,7,8]=>1000000=>0000001=>1111110
[1,2,3,4,5,6,7,8]=>0000000=>0000000=>1111111
[6,8,7,5,4,3,2,1]=>0111111=>1111110=>0000001
[5,8,7,6,4,3,2,1]=>0111111=>1111110=>0000001
[5,7,8,6,4,3,2,1]=>0011111=>1111100=>0000011
[6,5,8,7,4,3,2,1]=>1011111=>1111101=>0000010
[5,6,8,7,4,3,2,1]=>0011111=>1111100=>0000011
[5,7,6,8,4,3,2,1]=>0101111=>1111010=>0000101
[4,8,7,6,5,3,2,1]=>0111111=>1111110=>0000001
[4,7,8,6,5,3,2,1]=>0011111=>1111100=>0000011
[4,6,8,7,5,3,2,1]=>0011111=>1111100=>0000011
[4,7,6,8,5,3,2,1]=>0101111=>1111010=>0000101
[4,6,7,8,5,3,2,1]=>0001111=>1111000=>0000111
[4,5,8,7,6,3,2,1]=>0011111=>1111100=>0000011
[4,5,7,8,6,3,2,1]=>0001111=>1111000=>0000111
[4,6,5,8,7,3,2,1]=>0101111=>1111010=>0000101
[4,5,6,8,7,3,2,1]=>0001111=>1111000=>0000111
[5,7,6,4,8,3,2,1]=>0110111=>1110110=>0001001
[4,7,6,5,8,3,2,1]=>0110111=>1110110=>0001001
[4,6,7,5,8,3,2,1]=>0010111=>1110100=>0001011
[5,4,7,6,8,3,2,1]=>1010111=>1110101=>0001010
[4,5,7,6,8,3,2,1]=>0010111=>1110100=>0001011
[4,6,5,7,8,3,2,1]=>0100111=>1110010=>0001101
[3,8,7,6,5,4,2,1]=>0111111=>1111110=>0000001
[3,5,8,7,6,4,2,1]=>0011111=>1111100=>0000011
[3,5,7,8,6,4,2,1]=>0001111=>1111000=>0000111
[3,5,6,8,7,4,2,1]=>0001111=>1111000=>0000111
[3,7,6,5,8,4,2,1]=>0110111=>1110110=>0001001
[3,6,7,5,8,4,2,1]=>0010111=>1110100=>0001011
[3,5,6,7,8,4,2,1]=>0000111=>1110000=>0001111
[3,4,8,7,6,5,2,1]=>0011111=>1111100=>0000011
[3,4,6,7,8,5,2,1]=>0000111=>1110000=>0001111
[5,4,3,7,8,6,2,1]=>1100111=>1110011=>0001100
[3,4,5,7,8,6,2,1]=>0000111=>1110000=>0001111
[4,5,6,3,8,7,2,1]=>0010111=>1110100=>0001011
[4,3,6,5,8,7,2,1]=>1010111=>1110101=>0001010
[5,4,3,6,8,7,2,1]=>1100111=>1110011=>0001100
[4,5,3,6,8,7,2,1]=>0100111=>1110010=>0001101
[5,7,6,4,3,8,2,1]=>0111011=>1101110=>0010001
[4,7,6,5,3,8,2,1]=>0111011=>1101110=>0010001
[3,4,7,6,5,8,2,1]=>0011011=>1101100=>0010011
[4,5,3,7,6,8,2,1]=>0101011=>1101010=>0010101
[4,3,5,7,6,8,2,1]=>1001011=>1101001=>0010110
[3,4,6,5,7,8,2,1]=>0010011=>1100100=>0011011
[2,8,7,6,5,4,3,1]=>0111111=>1111110=>0000001
[2,7,6,8,5,4,3,1]=>0101111=>1111010=>0000101
[2,5,6,7,8,4,3,1]=>0000111=>1110000=>0001111
[2,4,8,7,6,5,3,1]=>0011111=>1111100=>0000011
[2,4,6,8,7,5,3,1]=>0001111=>1111000=>0000111
[2,4,6,7,8,5,3,1]=>0000111=>1110000=>0001111
[2,5,4,8,7,6,3,1]=>0101111=>1111010=>0000101
[2,4,5,7,8,6,3,1]=>0000111=>1110000=>0001111
[2,5,6,4,8,7,3,1]=>0010111=>1110100=>0001011
[2,4,6,5,8,7,3,1]=>0010111=>1110100=>0001011
[2,7,6,5,4,8,3,1]=>0111011=>1101110=>0010001
[2,6,7,5,4,8,3,1]=>0011011=>1101100=>0010011
[2,4,7,6,5,8,3,1]=>0011011=>1101100=>0010011
[2,6,5,4,7,8,3,1]=>0110011=>1100110=>0011001
[3,2,8,7,6,5,4,1]=>1011111=>1111101=>0000010
[3,2,6,8,7,5,4,1]=>1001111=>1111001=>0000110
[3,2,5,7,6,8,4,1]=>1001011=>1101001=>0010110
[3,2,5,6,7,8,4,1]=>1000011=>1100001=>0011110
[2,3,8,7,6,5,4,1]=>0011111=>1111100=>0000011
[2,3,6,7,8,5,4,1]=>0000111=>1110000=>0001111
[2,3,5,7,8,6,4,1]=>0000111=>1110000=>0001111
[2,3,7,6,5,8,4,1]=>0011011=>1101100=>0010011
[2,3,5,6,7,8,4,1]=>0000011=>1100000=>0011111
[4,3,2,8,7,6,5,1]=>1101111=>1111011=>0000100
[3,4,2,8,7,6,5,1]=>0101111=>1111010=>0000101
[3,4,2,7,8,6,5,1]=>0100111=>1110010=>0001101
[2,4,3,8,7,6,5,1]=>0101111=>1111010=>0000101
[2,4,3,6,8,7,5,1]=>0100111=>1110010=>0001101
[3,2,4,8,7,6,5,1]=>1001111=>1111001=>0000110
[2,3,4,8,7,6,5,1]=>0001111=>1111000=>0000111
[2,3,4,6,7,8,5,1]=>0000011=>1100000=>0011111
[5,4,3,2,8,7,6,1]=>1110111=>1110111=>0001000
[5,4,3,2,7,8,6,1]=>1110011=>1100111=>0011000
[2,5,4,3,8,7,6,1]=>0110111=>1110110=>0001001
[2,5,4,3,7,8,6,1]=>0110011=>1100110=>0011001
[2,4,5,3,8,7,6,1]=>0010111=>1110100=>0001011
[2,3,5,4,8,7,6,1]=>0010111=>1110100=>0001011
[4,3,2,5,8,7,6,1]=>1100111=>1110011=>0001100
[2,4,3,5,8,7,6,1]=>0100111=>1110010=>0001101
[2,3,4,5,8,7,6,1]=>0000111=>1110000=>0001111
[6,5,4,3,2,8,7,1]=>1111011=>1101111=>0010000
[4,6,5,3,2,8,7,1]=>0111011=>1101110=>0010001
[5,4,6,3,2,8,7,1]=>1011011=>1101101=>0010010
[4,5,6,3,2,8,7,1]=>0011011=>1101100=>0010011
[3,6,5,4,2,8,7,1]=>0111011=>1101110=>0010001
[3,5,6,4,2,8,7,1]=>0011011=>1101100=>0010011
[4,3,6,5,2,8,7,1]=>1011011=>1101101=>0010010
[5,4,3,6,2,8,7,1]=>1101011=>1101011=>0010100
[2,6,5,4,3,8,7,1]=>0111011=>1101110=>0010001
[2,4,6,5,3,8,7,1]=>0011011=>1101100=>0010011
[4,3,2,6,5,8,7,1]=>1101011=>1101011=>0010100
[2,4,3,6,5,8,7,1]=>0101011=>1101010=>0010101
[2,3,4,6,5,8,7,1]=>0001011=>1101000=>0010111
[5,4,3,2,6,8,7,1]=>1110011=>1100111=>0011000
[2,5,4,3,6,8,7,1]=>0110011=>1100110=>0011001
[4,3,2,5,6,8,7,1]=>1100011=>1100011=>0011100
[3,4,2,5,6,8,7,1]=>0100011=>1100010=>0011101
[2,4,3,5,6,8,7,1]=>0100011=>1100010=>0011101
[2,3,4,5,6,8,7,1]=>0000011=>1100000=>0011111
[4,7,6,5,3,2,8,1]=>0111101=>1011110=>0100001
[4,6,5,7,3,2,8,1]=>0101101=>1011010=>0100101
[3,5,7,6,4,2,8,1]=>0011101=>1011100=>0100011
[3,5,6,7,4,2,8,1]=>0001101=>1011000=>0100111
[4,3,7,6,5,2,8,1]=>1011101=>1011101=>0100010
[4,3,6,7,5,2,8,1]=>1001101=>1011001=>0100110
[3,4,7,6,5,2,8,1]=>0011101=>1011100=>0100011
[5,4,3,7,6,2,8,1]=>1101101=>1011011=>0100100
[4,6,5,3,7,2,8,1]=>0110101=>1010110=>0101001
[3,6,5,4,7,2,8,1]=>0110101=>1010110=>0101001
[3,5,6,4,7,2,8,1]=>0010101=>1010100=>0101011
[4,3,6,5,7,2,8,1]=>1010101=>1010101=>0101010
[3,5,4,6,7,2,8,1]=>0100101=>1010010=>0101101
[2,5,4,7,6,3,8,1]=>0101101=>1011010=>0100101
[2,4,6,5,7,3,8,1]=>0010101=>1010100=>0101011
[2,4,5,6,7,3,8,1]=>0000101=>1010000=>0101111
[3,2,6,7,5,4,8,1]=>1001101=>1011001=>0100110
[3,2,6,5,7,4,8,1]=>1010101=>1010101=>0101010
[2,3,7,6,5,4,8,1]=>0011101=>1011100=>0100011
[4,3,2,7,6,5,8,1]=>1101101=>1011011=>0100100
[4,3,2,6,7,5,8,1]=>1100101=>1010011=>0101100
[3,4,2,7,6,5,8,1]=>0101101=>1011010=>0100101
[2,4,3,7,6,5,8,1]=>0101101=>1011010=>0100101
[3,2,4,7,6,5,8,1]=>1001101=>1011001=>0100110
[2,3,4,7,6,5,8,1]=>0001101=>1011000=>0100111
[5,4,3,2,7,6,8,1]=>1110101=>1010111=>0101000
[4,3,5,2,7,6,8,1]=>1010101=>1010101=>0101010
[2,5,4,3,7,6,8,1]=>0110101=>1010110=>0101001
[3,2,5,4,7,6,8,1]=>1010101=>1010101=>0101010
[2,3,5,4,7,6,8,1]=>0010101=>1010100=>0101011
[4,3,2,5,7,6,8,1]=>1100101=>1010011=>0101100
[2,4,3,5,7,6,8,1]=>0100101=>1010010=>0101101
[3,2,4,5,7,6,8,1]=>1000101=>1010001=>0101110
[2,3,4,5,7,6,8,1]=>0000101=>1010000=>0101111
[3,6,5,4,2,7,8,1]=>0111001=>1001110=>0110001
[3,5,6,4,2,7,8,1]=>0011001=>1001100=>0110011
[2,6,5,4,3,7,8,1]=>0111001=>1001110=>0110001
[2,5,4,6,3,7,8,1]=>0101001=>1001010=>0110101
[2,3,6,5,4,7,8,1]=>0011001=>1001100=>0110011
[2,3,5,6,4,7,8,1]=>0001001=>1001000=>0110111
[4,3,2,6,5,7,8,1]=>1101001=>1001011=>0110100
[3,4,2,6,5,7,8,1]=>0101001=>1001010=>0110101
[2,4,3,6,5,7,8,1]=>0101001=>1001010=>0110101
[2,3,4,6,5,7,8,1]=>0001001=>1001000=>0110111
[3,5,4,2,6,7,8,1]=>0110001=>1000110=>0111001
[2,5,4,3,6,7,8,1]=>0110001=>1000110=>0111001
[2,4,5,3,6,7,8,1]=>0010001=>1000100=>0111011
[3,2,5,4,6,7,8,1]=>1010001=>1000101=>0111010
[2,3,5,4,6,7,8,1]=>0010001=>1000100=>0111011
[2,4,3,5,6,7,8,1]=>0100001=>1000010=>0111101
[1,8,7,6,5,4,3,2]=>0111111=>1111110=>0000001
[1,7,8,6,5,4,3,2]=>0011111=>1111100=>0000011
[1,6,8,7,5,4,3,2]=>0011111=>1111100=>0000011
[1,7,6,8,5,4,3,2]=>0101111=>1111010=>0000101
[1,6,7,8,5,4,3,2]=>0001111=>1111000=>0000111
[1,7,6,5,8,4,3,2]=>0110111=>1110110=>0001001
[1,6,7,5,8,4,3,2]=>0010111=>1110100=>0001011
[1,5,7,6,8,4,3,2]=>0010111=>1110100=>0001011
[1,6,5,7,8,4,3,2]=>0100111=>1110010=>0001101
[1,5,6,7,8,4,3,2]=>0000111=>1110000=>0001111
[1,4,8,7,6,5,3,2]=>0011111=>1111100=>0000011
[1,4,7,8,6,5,3,2]=>0001111=>1111000=>0000111
[1,4,6,8,7,5,3,2]=>0001111=>1111000=>0000111
[1,4,6,7,8,5,3,2]=>0000111=>1110000=>0001111
[1,4,5,7,8,6,3,2]=>0000111=>1110000=>0001111
[1,4,6,5,8,7,3,2]=>0010111=>1110100=>0001011
[1,4,7,6,5,8,3,2]=>0011011=>1101100=>0010011
[1,6,5,4,7,8,3,2]=>0110011=>1100110=>0011001
[1,3,8,7,6,5,4,2]=>0011111=>1111100=>0000011
[1,3,6,8,7,5,4,2]=>0001111=>1111000=>0000111
[1,3,6,7,8,5,4,2]=>0000111=>1110000=>0001111
[1,3,5,8,7,6,4,2]=>0001111=>1111000=>0000111
[1,3,5,7,8,6,4,2]=>0000111=>1110000=>0001111
[1,3,5,7,6,8,4,2]=>0001011=>1101000=>0010111
[1,3,6,5,7,8,4,2]=>0010011=>1100100=>0011011
[1,3,5,6,7,8,4,2]=>0000011=>1100000=>0011111
[1,4,3,8,7,6,5,2]=>0101111=>1111010=>0000101
[1,4,3,7,8,6,5,2]=>0100111=>1110010=>0001101
[1,4,3,6,8,7,5,2]=>0100111=>1110010=>0001101
[1,4,3,7,6,8,5,2]=>0101011=>1101010=>0010101
[1,3,4,8,7,6,5,2]=>0001111=>1111000=>0000111
[1,3,4,7,6,8,5,2]=>0001011=>1101000=>0010111
[1,3,4,6,7,8,5,2]=>0000011=>1100000=>0011111
[1,5,4,3,8,7,6,2]=>0110111=>1110110=>0001001
[1,3,5,4,7,8,6,2]=>0010011=>1100100=>0011011
[1,4,3,5,8,7,6,2]=>0100111=>1110010=>0001101
[1,4,3,5,7,8,6,2]=>0100011=>1100010=>0011101
[1,3,4,5,8,7,6,2]=>0000111=>1110000=>0001111
[1,6,5,4,3,8,7,2]=>0111011=>1101110=>0010001
[1,5,6,4,3,8,7,2]=>0011011=>1101100=>0010011
[1,4,6,5,3,8,7,2]=>0011011=>1101100=>0010011
[1,3,6,5,4,8,7,2]=>0011011=>1101100=>0010011
[1,4,3,6,5,8,7,2]=>0101011=>1101010=>0010101
[1,5,4,3,6,8,7,2]=>0110011=>1100110=>0011001
[1,6,7,5,4,3,8,2]=>0011101=>1011100=>0100011
[1,3,5,7,6,4,8,2]=>0001101=>1011000=>0100111
[1,3,4,7,6,5,8,2]=>0001101=>1011000=>0100111
[1,3,5,4,7,6,8,2]=>0010101=>1010100=>0101011
[1,4,3,6,5,7,8,2]=>0101001=>1001010=>0110101
[1,5,4,3,6,7,8,2]=>0110001=>1000110=>0111001
[2,1,8,7,6,5,4,3]=>1011111=>1111101=>0000010
[2,1,7,8,6,5,4,3]=>1001111=>1111001=>0000110
[2,1,6,8,7,5,4,3]=>1001111=>1111001=>0000110
[2,1,7,6,8,5,4,3]=>1010111=>1110101=>0001010
[2,1,6,7,8,5,4,3]=>1000111=>1110001=>0001110
[2,1,5,7,8,6,4,3]=>1000111=>1110001=>0001110
[2,1,6,5,8,7,4,3]=>1010111=>1110101=>0001010
[2,1,7,6,5,8,4,3]=>1011011=>1101101=>0010010
[2,1,6,7,5,8,4,3]=>1001011=>1101001=>0010110
[2,1,6,5,7,8,4,3]=>1010011=>1100101=>0011010
[2,1,5,6,7,8,4,3]=>1000011=>1100001=>0011110
[2,1,4,8,7,6,5,3]=>1001111=>1111001=>0000110
[2,1,4,7,8,6,5,3]=>1000111=>1110001=>0001110
[2,1,4,6,8,7,5,3]=>1000111=>1110001=>0001110
[2,1,4,6,7,8,5,3]=>1000011=>1100001=>0011110
[2,1,4,5,8,7,6,3]=>1000111=>1110001=>0001110
[2,1,4,5,7,8,6,3]=>1000011=>1100001=>0011110
[2,1,4,6,5,8,7,3]=>1001011=>1101001=>0010110
[2,1,4,5,6,8,7,3]=>1000011=>1100001=>0011110
[2,1,5,7,6,4,8,3]=>1001101=>1011001=>0100110
[2,1,6,5,7,4,8,3]=>1010101=>1010101=>0101010
[2,1,5,6,7,4,8,3]=>1000101=>1010001=>0101110
[2,1,4,7,6,5,8,3]=>1001101=>1011001=>0100110
[2,1,4,6,7,5,8,3]=>1000101=>1010001=>0101110
[2,1,5,4,7,6,8,3]=>1010101=>1010101=>0101010
[2,1,5,6,4,7,8,3]=>1001001=>1001001=>0110110
[2,1,4,5,6,7,8,3]=>1000001=>1000001=>0111110
[1,2,8,7,6,5,4,3]=>0011111=>1111100=>0000011
[1,2,6,7,8,5,4,3]=>0000111=>1110000=>0001111
[1,2,6,5,8,7,4,3]=>0010111=>1110100=>0001011
[1,2,7,6,5,8,4,3]=>0011011=>1101100=>0010011
[1,2,5,7,6,8,4,3]=>0001011=>1101000=>0010111
[1,2,6,5,7,8,4,3]=>0010011=>1100100=>0011011
[1,2,5,6,7,8,4,3]=>0000011=>1100000=>0011111
[1,2,4,8,7,6,5,3]=>0001111=>1111000=>0000111
[1,2,4,7,8,6,5,3]=>0000111=>1110000=>0001111
[1,2,4,6,8,7,5,3]=>0000111=>1110000=>0001111
[1,2,4,6,7,8,5,3]=>0000011=>1100000=>0011111
[1,2,5,4,8,7,6,3]=>0010111=>1110100=>0001011
[1,2,4,5,7,8,6,3]=>0000011=>1100000=>0011111
[1,2,6,5,4,8,7,3]=>0011011=>1101100=>0010011
[1,2,5,7,6,4,8,3]=>0001101=>1011000=>0100111
[1,2,5,6,7,4,8,3]=>0000101=>1010000=>0101111
[1,2,4,7,6,5,8,3]=>0001101=>1011000=>0100111
[1,2,6,5,4,7,8,3]=>0011001=>1001100=>0110011
[3,2,1,8,7,6,5,4]=>1101111=>1111011=>0000100
[3,2,1,7,8,6,5,4]=>1100111=>1110011=>0001100
[3,2,1,6,8,7,5,4]=>1100111=>1110011=>0001100
[3,2,1,7,6,8,5,4]=>1101011=>1101011=>0010100
[3,2,1,6,7,8,5,4]=>1100011=>1100011=>0011100
[3,2,1,5,8,7,6,4]=>1100111=>1110011=>0001100
[3,2,1,5,7,8,6,4]=>1100011=>1100011=>0011100
[3,2,1,6,5,8,7,4]=>1101011=>1101011=>0010100
[3,2,1,5,6,8,7,4]=>1100011=>1100011=>0011100
[3,2,1,7,6,5,8,4]=>1101101=>1011011=>0100100
[3,2,1,6,7,5,8,4]=>1100101=>1010011=>0101100
[3,2,1,5,7,6,8,4]=>1100101=>1010011=>0101100
[3,2,1,6,5,7,8,4]=>1101001=>1001011=>0110100
[3,2,1,5,6,7,8,4]=>1100001=>1000011=>0111100
[2,3,1,8,7,6,5,4]=>0101111=>1111010=>0000101
[2,3,1,6,8,7,5,4]=>0100111=>1110010=>0001101
[2,3,1,7,6,8,5,4]=>0101011=>1101010=>0010101
[2,3,1,6,7,8,5,4]=>0100011=>1100010=>0011101
[2,3,1,6,5,8,7,4]=>0101011=>1101010=>0010101
[2,3,1,5,6,7,8,4]=>0100001=>1000010=>0111101
[1,3,2,8,7,6,5,4]=>0101111=>1111010=>0000101
[1,3,2,6,8,7,5,4]=>0100111=>1110010=>0001101
[1,3,2,5,7,8,6,4]=>0100011=>1100010=>0011101
[1,3,2,6,5,8,7,4]=>0101011=>1101010=>0010101
[1,3,2,7,6,5,8,4]=>0101101=>1011010=>0100101
[1,3,2,5,7,6,8,4]=>0100101=>1010010=>0101101
[1,3,2,6,5,7,8,4]=>0101001=>1001010=>0110101
[2,1,3,8,7,6,5,4]=>1001111=>1111001=>0000110
[2,1,3,7,8,6,5,4]=>1000111=>1110001=>0001110
[2,1,3,6,8,7,5,4]=>1000111=>1110001=>0001110
[1,2,3,8,7,6,5,4]=>0001111=>1111000=>0000111
[1,2,3,7,8,6,5,4]=>0000111=>1110000=>0001111
[1,2,3,6,8,7,5,4]=>0000111=>1110000=>0001111
[1,2,3,7,6,8,5,4]=>0001011=>1101000=>0010111
[1,2,3,6,7,8,5,4]=>0000011=>1100000=>0011111
[1,2,3,5,8,7,6,4]=>0000111=>1110000=>0001111
[1,2,3,5,7,8,6,4]=>0000011=>1100000=>0011111
[1,2,3,6,5,8,7,4]=>0001011=>1101000=>0010111
[1,2,3,5,6,8,7,4]=>0000011=>1100000=>0011111
[1,2,3,7,6,5,8,4]=>0001101=>1011000=>0100111
[1,2,3,6,7,5,8,4]=>0000101=>1010000=>0101111
[1,2,3,5,7,6,8,4]=>0000101=>1010000=>0101111
[1,2,3,6,5,7,8,4]=>0001001=>1001000=>0110111
[1,2,3,5,6,7,8,4]=>0000001=>1000000=>0111111
[4,3,2,1,8,7,6,5]=>1110111=>1110111=>0001000
[4,3,2,1,7,8,6,5]=>1110011=>1100111=>0011000
[4,3,2,1,6,8,7,5]=>1110011=>1100111=>0011000
[4,3,2,1,7,6,8,5]=>1110101=>1010111=>0101000
[4,3,2,1,6,7,8,5]=>1110001=>1000111=>0111000
[3,4,2,1,8,7,6,5]=>0110111=>1110110=>0001001
[3,4,2,1,7,8,6,5]=>0110011=>1100110=>0011001
[3,4,2,1,6,8,7,5]=>0110011=>1100110=>0011001
[3,4,2,1,7,6,8,5]=>0110101=>1010110=>0101001
[3,4,2,1,6,7,8,5]=>0110001=>1000110=>0111001
[2,4,3,1,8,7,6,5]=>0110111=>1110110=>0001001
[2,4,3,1,6,8,7,5]=>0110011=>1100110=>0011001
[2,4,3,1,7,6,8,5]=>0110101=>1010110=>0101001
[2,4,3,1,6,7,8,5]=>0110001=>1000110=>0111001
[3,2,4,1,8,7,6,5]=>1010111=>1110101=>0001010
[3,2,4,1,7,8,6,5]=>1010011=>1100101=>0011010
[3,2,4,1,6,8,7,5]=>1010011=>1100101=>0011010
[3,2,4,1,7,6,8,5]=>1010101=>1010101=>0101010
[3,2,4,1,6,7,8,5]=>1010001=>1000101=>0111010
[2,3,4,1,8,7,6,5]=>0010111=>1110100=>0001011
[2,3,4,1,7,8,6,5]=>0010011=>1100100=>0011011
[2,3,4,1,6,8,7,5]=>0010011=>1100100=>0011011
[2,3,4,1,7,6,8,5]=>0010101=>1010100=>0101011
[2,3,4,1,6,7,8,5]=>0010001=>1000100=>0111011
[1,4,3,2,8,7,6,5]=>0110111=>1110110=>0001001
[1,4,3,2,7,6,8,5]=>0110101=>1010110=>0101001
[1,4,3,2,6,7,8,5]=>0110001=>1000110=>0111001
[1,3,4,2,8,7,6,5]=>0010111=>1110100=>0001011
[1,3,4,2,7,8,6,5]=>0010011=>1100100=>0011011
[1,3,4,2,6,8,7,5]=>0010011=>1100100=>0011011
[1,3,4,2,7,6,8,5]=>0010101=>1010100=>0101011
[1,3,4,2,6,7,8,5]=>0010001=>1000100=>0111011
[2,1,4,3,8,7,6,5]=>1010111=>1110101=>0001010
[2,1,4,3,7,8,6,5]=>1010011=>1100101=>0011010
[2,1,4,3,6,8,7,5]=>1010011=>1100101=>0011010
[2,1,4,3,7,6,8,5]=>1010101=>1010101=>0101010
[2,1,4,3,6,7,8,5]=>1010001=>1000101=>0111010
[1,2,4,3,8,7,6,5]=>0010111=>1110100=>0001011
[1,2,4,3,7,8,6,5]=>0010011=>1100100=>0011011
[1,2,4,3,6,8,7,5]=>0010011=>1100100=>0011011
[1,2,4,3,7,6,8,5]=>0010101=>1010100=>0101011
[1,2,4,3,6,7,8,5]=>0010001=>1000100=>0111011
[3,2,1,4,8,7,6,5]=>1100111=>1110011=>0001100
[3,2,1,4,7,8,6,5]=>1100011=>1100011=>0011100
[3,2,1,4,6,8,7,5]=>1100011=>1100011=>0011100
[3,2,1,4,7,6,8,5]=>1100101=>1010011=>0101100
[3,2,1,4,6,7,8,5]=>1100001=>1000011=>0111100
[2,3,1,4,8,7,6,5]=>0100111=>1110010=>0001101
[2,3,1,4,7,8,6,5]=>0100011=>1100010=>0011101
[2,3,1,4,7,6,8,5]=>0100101=>1010010=>0101101
[2,3,1,4,6,7,8,5]=>0100001=>1000010=>0111101
[1,3,2,4,8,7,6,5]=>0100111=>1110010=>0001101
[1,3,2,4,6,8,7,5]=>0100011=>1100010=>0011101
[1,3,2,4,7,6,8,5]=>0100101=>1010010=>0101101
[1,3,2,4,6,7,8,5]=>0100001=>1000010=>0111101
[2,1,3,4,8,7,6,5]=>1000111=>1110001=>0001110
[2,1,3,4,7,6,8,5]=>1000101=>1010001=>0101110
[2,1,3,4,6,7,8,5]=>1000001=>1000001=>0111110
[1,2,3,4,8,7,6,5]=>0000111=>1110000=>0001111
[1,2,3,4,7,8,6,5]=>0000011=>1100000=>0011111
[1,2,3,4,6,8,7,5]=>0000011=>1100000=>0011111
[1,2,3,4,7,6,8,5]=>0000101=>1010000=>0101111
[1,2,3,4,6,7,8,5]=>0000001=>1000000=>0111111
[5,4,3,2,1,8,7,6]=>1111011=>1101111=>0010000
[5,4,3,2,1,7,8,6]=>1111001=>1001111=>0110000
[4,5,3,2,1,8,7,6]=>0111011=>1101110=>0010001
[3,5,4,2,1,8,7,6]=>0111011=>1101110=>0010001
[3,5,4,2,1,7,8,6]=>0111001=>1001110=>0110001
[4,3,5,2,1,8,7,6]=>1011011=>1101101=>0010010
[3,4,5,2,1,8,7,6]=>0011011=>1101100=>0010011
[3,4,5,2,1,7,8,6]=>0011001=>1001100=>0110011
[2,5,4,3,1,8,7,6]=>0111011=>1101110=>0010001
[2,5,4,3,1,7,8,6]=>0111001=>1001110=>0110001
[2,4,5,3,1,8,7,6]=>0011011=>1101100=>0010011
[3,2,5,4,1,8,7,6]=>1011011=>1101101=>0010010
[3,2,5,4,1,7,8,6]=>1011001=>1001101=>0110010
[2,3,5,4,1,8,7,6]=>0011011=>1101100=>0010011
[4,3,2,5,1,8,7,6]=>1101011=>1101011=>0010100
[3,4,2,5,1,8,7,6]=>0101011=>1101010=>0010101
[3,4,2,5,1,7,8,6]=>0101001=>1001010=>0110101
[2,4,3,5,1,8,7,6]=>0101011=>1101010=>0010101
[2,4,3,5,1,7,8,6]=>0101001=>1001010=>0110101
[3,2,4,5,1,8,7,6]=>1001011=>1101001=>0010110
[2,3,4,5,1,8,7,6]=>0001011=>1101000=>0010111
[1,3,5,4,2,7,8,6]=>0011001=>1001100=>0110011
[1,4,3,5,2,7,8,6]=>0101001=>1001010=>0110101
[1,3,4,5,2,8,7,6]=>0001011=>1101000=>0010111
[1,3,4,5,2,7,8,6]=>0001001=>1001000=>0110111
[1,2,5,4,3,7,8,6]=>0011001=>1001100=>0110011
[1,2,4,5,3,8,7,6]=>0001011=>1101000=>0010111
[1,2,4,5,3,7,8,6]=>0001001=>1001000=>0110111
[1,3,2,5,4,7,8,6]=>0101001=>1001010=>0110101
[2,1,3,5,4,8,7,6]=>1001011=>1101001=>0010110
[1,2,3,5,4,8,7,6]=>0001011=>1101000=>0010111
[1,2,3,5,4,7,8,6]=>0001001=>1001000=>0110111
[4,3,2,1,5,8,7,6]=>1110011=>1100111=>0011000
[4,3,2,1,5,7,8,6]=>1110001=>1000111=>0111000
[3,2,4,1,5,8,7,6]=>1010011=>1100101=>0011010
[3,2,4,1,5,7,8,6]=>1010001=>1000101=>0111010
[2,3,4,1,5,8,7,6]=>0010011=>1100100=>0011011
[2,3,4,1,5,7,8,6]=>0010001=>1000100=>0111011
[1,4,3,2,5,8,7,6]=>0110011=>1100110=>0011001
[1,4,3,2,5,7,8,6]=>0110001=>1000110=>0111001
[1,3,4,2,5,8,7,6]=>0010011=>1100100=>0011011
[1,3,4,2,5,7,8,6]=>0010001=>1000100=>0111011
[1,2,4,3,5,7,8,6]=>0010001=>1000100=>0111011
[3,2,1,4,5,8,7,6]=>1100011=>1100011=>0011100
[3,2,1,4,5,7,8,6]=>1100001=>1000011=>0111100
[2,3,1,4,5,7,8,6]=>0100001=>1000010=>0111101
[1,3,2,4,5,7,8,6]=>0100001=>1000010=>0111101
[1,2,3,4,5,8,7,6]=>0000011=>1100000=>0011111
[1,2,3,4,5,7,8,6]=>0000001=>1000000=>0111111
[6,5,4,3,2,1,8,7]=>1111101=>1011111=>0100000
[5,6,4,3,2,1,8,7]=>0111101=>1011110=>0100001
[4,6,5,3,2,1,8,7]=>0111101=>1011110=>0100001
[5,4,6,3,2,1,8,7]=>1011101=>1011101=>0100010
[4,5,6,3,2,1,8,7]=>0011101=>1011100=>0100011
[3,6,5,4,2,1,8,7]=>0111101=>1011110=>0100001
[3,5,6,4,2,1,8,7]=>0011101=>1011100=>0100011
[4,3,6,5,2,1,8,7]=>1011101=>1011101=>0100010
[5,4,3,6,2,1,8,7]=>1101101=>1011011=>0100100
[4,5,3,6,2,1,8,7]=>0101101=>1011010=>0100101
[3,4,5,6,2,1,8,7]=>0001101=>1011000=>0100111
[2,6,5,4,3,1,8,7]=>0111101=>1011110=>0100001
[2,5,6,4,3,1,8,7]=>0011101=>1011100=>0100011
[2,4,6,5,3,1,8,7]=>0011101=>1011100=>0100011
[2,3,6,5,4,1,8,7]=>0011101=>1011100=>0100011
[2,3,5,6,4,1,8,7]=>0001101=>1011000=>0100111
[2,4,3,6,5,1,8,7]=>0101101=>1011010=>0100101
[5,4,3,2,6,1,8,7]=>1110101=>1010111=>0101000
[4,5,3,2,6,1,8,7]=>0110101=>1010110=>0101001
[3,5,4,2,6,1,8,7]=>0110101=>1010110=>0101001
[4,3,5,2,6,1,8,7]=>1010101=>1010101=>0101010
[3,4,5,2,6,1,8,7]=>0010101=>1010100=>0101011
[2,5,4,3,6,1,8,7]=>0110101=>1010110=>0101001
[2,4,5,3,6,1,8,7]=>0010101=>1010100=>0101011
[3,2,5,4,6,1,8,7]=>1010101=>1010101=>0101010
[3,4,2,5,6,1,8,7]=>0100101=>1010010=>0101101
[2,3,4,5,6,1,8,7]=>0000101=>1010000=>0101111
[1,5,4,6,3,2,8,7]=>0101101=>1011010=>0100101
[1,3,6,5,4,2,8,7]=>0011101=>1011100=>0100011
[2,1,6,5,4,3,8,7]=>1011101=>1011101=>0100010
[2,1,5,6,4,3,8,7]=>1001101=>1011001=>0100110
[2,1,4,6,5,3,8,7]=>1001101=>1011001=>0100110
[2,1,5,4,6,3,8,7]=>1010101=>1010101=>0101010
[2,1,4,5,6,3,8,7]=>1000101=>1010001=>0101110
[2,3,1,6,5,4,8,7]=>0101101=>1011010=>0100101
[1,2,3,6,5,4,8,7]=>0001101=>1011000=>0100111
[1,2,3,5,6,4,8,7]=>0000101=>1010000=>0101111
[4,3,2,1,6,5,8,7]=>1110101=>1010111=>0101000
[3,4,2,1,6,5,8,7]=>0110101=>1010110=>0101001
[2,4,3,1,6,5,8,7]=>0110101=>1010110=>0101001
[3,2,4,1,6,5,8,7]=>1010101=>1010101=>0101010
[2,3,4,1,6,5,8,7]=>0010101=>1010100=>0101011
[2,1,4,3,6,5,8,7]=>1010101=>1010101=>0101010
[1,2,4,3,6,5,8,7]=>0010101=>1010100=>0101011
[1,3,2,4,6,5,8,7]=>0100101=>1010010=>0101101
[2,1,3,4,6,5,8,7]=>1000101=>1010001=>0101110
[1,2,3,4,6,5,8,7]=>0000101=>1010000=>0101111
[5,4,3,2,1,6,8,7]=>1111001=>1001111=>0110000
[4,5,3,2,1,6,8,7]=>0111001=>1001110=>0110001
[3,5,4,2,1,6,8,7]=>0111001=>1001110=>0110001
[2,5,4,3,1,6,8,7]=>0111001=>1001110=>0110001
[2,4,5,3,1,6,8,7]=>0011001=>1001100=>0110011
[3,2,5,4,1,6,8,7]=>1011001=>1001101=>0110010
[1,3,5,4,2,6,8,7]=>0011001=>1001100=>0110011
[1,3,4,5,2,6,8,7]=>0001001=>1001000=>0110111
[2,1,4,5,3,6,8,7]=>1001001=>1001001=>0110110
[1,2,5,4,3,6,8,7]=>0011001=>1001100=>0110011
[2,1,3,5,4,6,8,7]=>1001001=>1001001=>0110110
[4,3,2,1,5,6,8,7]=>1110001=>1000111=>0111000
[3,2,4,1,5,6,8,7]=>1010001=>1000101=>0111010
[2,3,4,1,5,6,8,7]=>0010001=>1000100=>0111011
[1,4,3,2,5,6,8,7]=>0110001=>1000110=>0111001
[1,3,4,2,5,6,8,7]=>0010001=>1000100=>0111011
[2,1,4,3,5,6,8,7]=>1010001=>1000101=>0111010
[1,2,4,3,5,6,8,7]=>0010001=>1000100=>0111011
[2,1,3,4,5,6,8,7]=>1000001=>1000001=>0111110
[1,2,3,4,5,6,8,7]=>0000001=>1000000=>0111111
[5,7,6,4,3,2,1,8]=>0111110=>0111110=>1000001
[4,7,6,5,3,2,1,8]=>0111110=>0111110=>1000001
[4,6,7,5,3,2,1,8]=>0011110=>0111100=>1000011
[4,5,7,6,3,2,1,8]=>0011110=>0111100=>1000011
[4,6,5,7,3,2,1,8]=>0101110=>0111010=>1000101
[3,5,7,6,4,2,1,8]=>0011110=>0111100=>1000011
[3,5,6,7,4,2,1,8]=>0001110=>0111000=>1000111
[3,4,7,6,5,2,1,8]=>0011110=>0111100=>1000011
[4,5,3,7,6,2,1,8]=>0101110=>0111010=>1000101
[3,5,4,7,6,2,1,8]=>0101110=>0111010=>1000101
[4,3,5,7,6,2,1,8]=>1001110=>0111001=>1000110
[2,5,6,7,4,3,1,8]=>0001110=>0111000=>1000111
[2,4,6,7,5,3,1,8]=>0001110=>0111000=>1000111
[3,2,7,6,5,4,1,8]=>1011110=>0111101=>1000010
[3,2,6,7,5,4,1,8]=>1001110=>0111001=>1000110
[3,2,5,7,6,4,1,8]=>1001110=>0111001=>1000110
[2,3,7,6,5,4,1,8]=>0011110=>0111100=>1000011
[2,3,6,7,5,4,1,8]=>0001110=>0111000=>1000111
[2,3,5,7,6,4,1,8]=>0001110=>0111000=>1000111
[2,3,6,5,7,4,1,8]=>0010110=>0110100=>1001011
[2,3,5,6,7,4,1,8]=>0000110=>0110000=>1001111
[3,2,4,6,7,5,1,8]=>1000110=>0110001=>1001110
[2,3,4,7,6,5,1,8]=>0001110=>0111000=>1000111
[5,4,3,2,7,6,1,8]=>1110110=>0110111=>1001000
[4,5,3,2,7,6,1,8]=>0110110=>0110110=>1001001
[3,5,4,2,7,6,1,8]=>0110110=>0110110=>1001001
[3,2,5,4,7,6,1,8]=>1010110=>0110101=>1001010
[4,3,2,5,7,6,1,8]=>1100110=>0110011=>1001100
[3,6,5,4,2,7,1,8]=>0111010=>0101110=>1010001
[3,4,6,5,2,7,1,8]=>0011010=>0101100=>1010011
[3,5,4,6,2,7,1,8]=>0101010=>0101010=>1010101
[2,5,4,6,3,7,1,8]=>0101010=>0101010=>1010101
[3,2,6,5,4,7,1,8]=>1011010=>0101101=>1010010
[3,4,2,6,5,7,1,8]=>0101010=>0101010=>1010101
[2,4,3,6,5,7,1,8]=>0101010=>0101010=>1010101
[3,5,4,2,6,7,1,8]=>0110010=>0100110=>1011001
[2,5,4,3,6,7,1,8]=>0110010=>0100110=>1011001
[1,5,6,7,4,3,2,8]=>0001110=>0111000=>1000111
[1,4,6,5,7,3,2,8]=>0010110=>0110100=>1001011
[1,3,5,7,6,4,2,8]=>0001110=>0111000=>1000111
[1,3,5,6,7,4,2,8]=>0000110=>0110000=>1001111
[1,3,5,4,7,6,2,8]=>0010110=>0110100=>1001011
[1,4,3,5,7,6,2,8]=>0100110=>0110010=>1001101
[1,5,4,6,3,7,2,8]=>0101010=>0101010=>1010101
[1,3,6,5,4,7,2,8]=>0011010=>0101100=>1010011
[1,4,3,6,5,7,2,8]=>0101010=>0101010=>1010101
[1,5,4,3,6,7,2,8]=>0110010=>0100110=>1011001
[1,3,4,5,6,7,2,8]=>0000010=>0100000=>1011111
[2,1,4,6,7,5,3,8]=>1000110=>0110001=>1001110
[1,2,5,7,6,4,3,8]=>0001110=>0111000=>1000111
[1,2,5,6,7,4,3,8]=>0000110=>0110000=>1001111
[1,2,5,6,4,7,3,8]=>0001010=>0101000=>1010111
[1,2,5,4,6,7,3,8]=>0010010=>0100100=>1011011
[3,2,1,5,7,6,4,8]=>1100110=>0110011=>1001100
[3,2,1,5,6,7,4,8]=>1100010=>0100011=>1011100
[2,3,1,6,7,5,4,8]=>0100110=>0110010=>1001101
[2,3,1,6,5,7,4,8]=>0101010=>0101010=>1010101
[2,3,1,5,6,7,4,8]=>0100010=>0100010=>1011101
[1,3,2,5,7,6,4,8]=>0100110=>0110010=>1001101
[1,3,2,6,5,7,4,8]=>0101010=>0101010=>1010101
[1,3,2,5,6,7,4,8]=>0100010=>0100010=>1011101
[2,1,3,6,7,5,4,8]=>1000110=>0110001=>1001110
[1,2,3,7,6,5,4,8]=>0001110=>0111000=>1000111
[1,2,3,6,7,5,4,8]=>0000110=>0110000=>1001111
[1,2,3,5,7,6,4,8]=>0000110=>0110000=>1001111
[1,2,3,6,5,7,4,8]=>0001010=>0101000=>1010111
[1,2,3,5,6,7,4,8]=>0000010=>0100000=>1011111
[4,3,2,1,7,6,5,8]=>1110110=>0110111=>1001000
[4,3,2,1,6,7,5,8]=>1110010=>0100111=>1011000
[3,2,4,1,7,6,5,8]=>1010110=>0110101=>1001010
[3,2,4,1,6,7,5,8]=>1010010=>0100101=>1011010
[2,3,4,1,7,6,5,8]=>0010110=>0110100=>1001011
[2,3,4,1,6,7,5,8]=>0010010=>0100100=>1011011
[1,4,3,2,7,6,5,8]=>0110110=>0110110=>1001001
[1,4,3,2,6,7,5,8]=>0110010=>0100110=>1011001
[1,3,4,2,6,7,5,8]=>0010010=>0100100=>1011011
[1,2,4,3,6,7,5,8]=>0010010=>0100100=>1011011
[2,3,1,4,6,7,5,8]=>0100010=>0100010=>1011101
[1,3,2,4,7,6,5,8]=>0100110=>0110010=>1001101
[1,2,3,4,7,6,5,8]=>0000110=>0110000=>1001111
[1,2,3,4,6,7,5,8]=>0000010=>0100000=>1011111
[5,4,3,2,1,7,6,8]=>1111010=>0101111=>1010000
[4,5,3,2,1,7,6,8]=>0111010=>0101110=>1010001
[3,5,4,2,1,7,6,8]=>0111010=>0101110=>1010001
[2,5,4,3,1,7,6,8]=>0111010=>0101110=>1010001
[2,4,5,3,1,7,6,8]=>0011010=>0101100=>1010011
[3,2,5,4,1,7,6,8]=>1011010=>0101101=>1010010
[3,4,2,5,1,7,6,8]=>0101010=>0101010=>1010101
[2,4,3,5,1,7,6,8]=>0101010=>0101010=>1010101
[1,3,5,4,2,7,6,8]=>0011010=>0101100=>1010011
[1,4,3,5,2,7,6,8]=>0101010=>0101010=>1010101
[1,3,4,5,2,7,6,8]=>0001010=>0101000=>1010111
[2,3,1,5,4,7,6,8]=>0101010=>0101010=>1010101
[1,3,2,5,4,7,6,8]=>0101010=>0101010=>1010101
[1,2,3,5,4,7,6,8]=>0001010=>0101000=>1010111
[4,3,2,1,5,7,6,8]=>1110010=>0100111=>1011000
[3,2,4,1,5,7,6,8]=>1010010=>0100101=>1011010
[2,3,4,1,5,7,6,8]=>0010010=>0100100=>1011011
[1,4,3,2,5,7,6,8]=>0110010=>0100110=>1011001
[1,3,4,2,5,7,6,8]=>0010010=>0100100=>1011011
[1,3,2,4,5,7,6,8]=>0100010=>0100010=>1011101
[1,2,3,4,5,7,6,8]=>0000010=>0100000=>1011111
[3,6,5,4,2,1,7,8]=>0111100=>0011110=>1100001
[4,3,6,5,2,1,7,8]=>1011100=>0011101=>1100010
[2,4,6,5,3,1,7,8]=>0011100=>0011100=>1100011
[2,4,5,6,3,1,7,8]=>0001100=>0011000=>1100111
[4,3,2,6,5,1,7,8]=>1101100=>0011011=>1100100
[3,5,4,2,6,1,7,8]=>0110100=>0010110=>1101001
[1,5,6,4,3,2,7,8]=>0011100=>0011100=>1100011
[1,4,6,5,3,2,7,8]=>0011100=>0011100=>1100011
[1,5,4,6,3,2,7,8]=>0101100=>0011010=>1100101
[1,4,5,6,3,2,7,8]=>0001100=>0011000=>1100111
[1,3,5,6,4,2,7,8]=>0001100=>0011000=>1100111
[1,4,3,6,5,2,7,8]=>0101100=>0011010=>1100101
[1,5,4,3,6,2,7,8]=>0110100=>0010110=>1101001
[2,1,5,6,4,3,7,8]=>1001100=>0011001=>1100110
[2,1,4,6,5,3,7,8]=>1001100=>0011001=>1100110
[1,2,6,5,4,3,7,8]=>0011100=>0011100=>1100011
[1,2,5,6,4,3,7,8]=>0001100=>0011000=>1100111
[1,2,4,5,6,3,7,8]=>0000100=>0010000=>1101111
[3,2,1,5,6,4,7,8]=>1100100=>0010011=>1101100
[1,3,2,5,6,4,7,8]=>0100100=>0010010=>1101101
[1,2,3,5,6,4,7,8]=>0000100=>0010000=>1101111
[4,3,2,1,6,5,7,8]=>1110100=>0010111=>1101000
[3,2,4,1,6,5,7,8]=>1010100=>0010101=>1101010
[2,3,4,1,6,5,7,8]=>0010100=>0010100=>1101011
[2,1,4,3,6,5,7,8]=>1010100=>0010101=>1101010
[1,2,4,3,6,5,7,8]=>0010100=>0010100=>1101011
[1,3,2,4,6,5,7,8]=>0100100=>0010010=>1101101
[2,1,3,4,6,5,7,8]=>1000100=>0010001=>1101110
[1,2,3,4,6,5,7,8]=>0000100=>0010000=>1101111
[3,5,4,2,1,6,7,8]=>0111000=>0001110=>1110001
[2,5,4,3,1,6,7,8]=>0111000=>0001110=>1110001
[2,4,5,3,1,6,7,8]=>0011000=>0001100=>1110011
[3,2,5,4,1,6,7,8]=>1011000=>0001101=>1110010
[2,3,5,4,1,6,7,8]=>0011000=>0001100=>1110011
[2,4,3,5,1,6,7,8]=>0101000=>0001010=>1110101
[1,3,5,4,2,6,7,8]=>0011000=>0001100=>1110011
[1,3,4,5,2,6,7,8]=>0001000=>0001000=>1110111
[1,3,2,5,4,6,7,8]=>0101000=>0001010=>1110101
[1,2,3,5,4,6,7,8]=>0001000=>0001000=>1110111
[2,4,3,1,5,6,7,8]=>0110000=>0000110=>1111001
[1,4,3,2,5,6,7,8]=>0110000=>0000110=>1111001
[1,3,4,2,5,6,7,8]=>0010000=>0000100=>1111011
[2,1,4,3,5,6,7,8]=>1010000=>0000101=>1111010
[1,2,4,3,5,6,7,8]=>0010000=>0000100=>1111011
[1,3,2,4,5,6,7,8]=>0100000=>0000010=>1111101
[1,2,3,4,8,6,7,5]=>0000101=>1010000=>0101111
[1,2,3,5,8,6,7,4]=>0000101=>1010000=>0101111
[1,2,3,7,5,6,4,8]=>0001010=>0101000=>1010111
[1,2,3,7,5,6,8,4]=>0001001=>1001000=>0110111
[1,2,3,8,5,6,7,4]=>0001001=>1001000=>0110111
[1,2,3,8,5,7,6,4]=>0001011=>1101000=>0010111
[1,2,3,8,6,5,7,4]=>0001101=>1011000=>0100111
[1,2,3,8,6,7,5,4]=>0001011=>1101000=>0010111
[1,2,4,5,8,6,7,3]=>0000101=>1010000=>0101111
[1,2,4,8,5,6,7,3]=>0001001=>1001000=>0110111
[1,2,4,8,6,5,7,3]=>0001101=>1011000=>0100111
[1,2,5,4,8,6,7,3]=>0010101=>1010100=>0101011
[1,2,6,4,5,3,7,8]=>0010100=>0010100=>1101011
[1,2,6,4,5,8,7,3]=>0010011=>1100100=>0011011
[1,2,8,4,5,6,7,3]=>0010001=>1000100=>0111011
[1,2,8,4,6,7,5,3]=>0010011=>1100100=>0011011
[1,2,8,4,7,6,5,3]=>0010111=>1110100=>0001011
[1,2,7,5,4,6,8,3]=>0011001=>1001100=>0110011
[1,2,8,5,4,6,7,3]=>0011001=>1001100=>0110011
[1,2,8,5,4,7,6,3]=>0011011=>1101100=>0010011
[1,2,8,6,5,4,7,3]=>0011101=>1011100=>0100011
[1,2,8,7,5,6,4,3]=>0011011=>1101100=>0010011
[1,3,2,7,5,6,8,4]=>0101001=>1001010=>0110101
[1,3,2,8,5,7,6,4]=>0101011=>1101010=>0010101
[1,3,4,5,8,6,7,2]=>0000101=>1010000=>0101111
[1,3,4,8,5,6,7,2]=>0001001=>1001000=>0110111
[1,3,6,4,5,2,8,7]=>0010101=>1010100=>0101011
[1,3,6,4,5,7,2,8]=>0010010=>0100100=>1011011
[1,3,6,4,5,8,7,2]=>0010011=>1100100=>0011011
[1,3,8,4,5,6,7,2]=>0010001=>1000100=>0111011
[1,3,8,4,6,5,7,2]=>0010101=>1010100=>0101011
[1,3,8,5,4,6,7,2]=>0011001=>1001100=>0110011
[1,3,8,5,4,7,6,2]=>0011011=>1101100=>0010011
[1,3,8,5,6,7,4,2]=>0010011=>1100100=>0011011
[1,3,8,5,7,6,4,2]=>0010111=>1110100=>0001011
[1,3,8,6,5,7,4,2]=>0011011=>1101100=>0010011
[1,3,8,7,5,6,4,2]=>0011011=>1101100=>0010011
[1,4,3,8,5,6,7,2]=>0101001=>1001010=>0110101
[1,4,3,8,5,7,6,2]=>0101011=>1101010=>0010101
[1,4,3,8,6,7,5,2]=>0101011=>1101010=>0010101
[1,5,3,4,2,7,8,6]=>0101001=>1001010=>0110101
[1,5,3,4,6,2,7,8]=>0100100=>0010010=>1101101
[1,5,3,4,6,7,2,8]=>0100010=>0100010=>1011101
[1,5,3,4,7,6,2,8]=>0100110=>0110010=>1001101
[1,5,3,4,8,6,7,2]=>0100101=>1010010=>0101101
[1,8,3,4,6,7,5,2]=>0100011=>1100010=>0011101
[1,6,3,5,4,2,7,8]=>0101100=>0011010=>1100101
[1,6,3,5,4,8,7,2]=>0101011=>1101010=>0010101
[1,8,3,5,4,7,6,2]=>0101011=>1101010=>0010101
[1,8,3,5,6,4,7,2]=>0100101=>1010010=>0101101
[1,8,3,5,7,6,4,2]=>0100111=>1110010=>0001101
[1,8,3,6,5,4,7,2]=>0101101=>1011010=>0100101
[1,8,3,7,5,6,4,2]=>0101011=>1101010=>0010101
[1,8,3,7,6,5,4,2]=>0101111=>1111010=>0000101
[1,6,4,3,5,2,7,8]=>0110100=>0010110=>1101001
[1,8,4,3,5,6,7,2]=>0110001=>1000110=>0111001
[1,8,4,3,5,7,6,2]=>0110011=>1100110=>0011001
[1,7,4,3,6,5,8,2]=>0110101=>1010110=>0101001
[1,8,4,3,6,7,5,2]=>0110011=>1100110=>0011001
[1,6,4,5,3,8,7,2]=>0101011=>1101010=>0010101
[1,8,4,5,6,3,7,2]=>0100101=>1010010=>0101101
[1,8,4,5,6,7,3,2]=>0100011=>1100010=>0011101
[1,8,4,6,5,7,3,2]=>0101011=>1101010=>0010101
[1,8,4,7,6,5,3,2]=>0101111=>1111010=>0000101
[1,7,5,4,3,6,8,2]=>0111001=>1001110=>0110001
[1,8,5,4,3,6,7,2]=>0111001=>1001110=>0110001
[1,8,5,4,3,7,6,2]=>0111011=>1101110=>0010001
[1,8,5,4,6,3,7,2]=>0110101=>1010110=>0101001
[1,8,5,4,6,7,3,2]=>0110011=>1100110=>0011001
[1,8,5,4,7,6,3,2]=>0110111=>1110110=>0001001
[1,8,6,4,5,7,3,2]=>0110011=>1100110=>0011001
[1,8,7,4,5,6,3,2]=>0110011=>1100110=>0011001
[1,8,7,4,6,5,3,2]=>0110111=>1110110=>0001001
[1,8,6,5,4,7,3,2]=>0111011=>1101110=>0010001
[1,8,7,5,4,6,3,2]=>0111011=>1101110=>0010001
[1,8,7,5,6,4,3,2]=>0110111=>1110110=>0001001
[2,1,3,4,8,6,7,5]=>1000101=>1010001=>0101110
[2,1,4,3,8,6,7,5]=>1010101=>1010101=>0101010
[2,1,4,5,8,6,7,3]=>1000101=>1010001=>0101110
[2,1,4,8,5,6,7,3]=>1001001=>1001001=>0110110
[2,1,4,8,5,7,6,3]=>1001011=>1101001=>0010110
[2,1,4,8,6,5,7,3]=>1001101=>1011001=>0100110
[2,1,4,8,6,7,5,3]=>1001011=>1101001=>0010110
[2,1,5,4,8,6,7,3]=>1010101=>1010101=>0101010
[2,1,6,4,5,3,8,7]=>1010101=>1010101=>0101010
[2,1,6,4,5,7,8,3]=>1010001=>1000101=>0111010
[2,1,6,4,5,8,7,3]=>1010011=>1100101=>0011010
[2,1,8,4,5,6,7,3]=>1010001=>1000101=>0111010
[2,1,8,4,5,7,6,3]=>1010011=>1100101=>0011010
[2,1,8,4,6,5,7,3]=>1010101=>1010101=>0101010
[2,1,8,4,6,7,5,3]=>1010011=>1100101=>0011010
[2,1,8,4,7,6,5,3]=>1010111=>1110101=>0001010
[2,1,7,5,4,6,8,3]=>1011001=>1001101=>0110010
[2,1,8,5,4,6,7,3]=>1011001=>1001101=>0110010
[2,1,8,5,4,7,6,3]=>1011011=>1101101=>0010010
[2,1,7,5,6,4,8,3]=>1010101=>1010101=>0101010
[2,1,8,5,6,4,7,3]=>1010101=>1010101=>0101010
[2,1,8,5,7,6,4,3]=>1010111=>1110101=>0001010
[2,1,8,7,5,6,4,3]=>1011011=>1101101=>0010010
[2,3,1,8,5,6,7,4]=>0101001=>1001010=>0110101
[2,3,1,8,6,7,5,4]=>0101011=>1101010=>0010101
[2,3,4,1,8,6,7,5]=>0010101=>1010100=>0101011
[2,3,4,5,8,6,7,1]=>0000101=>1010000=>0101111
[2,3,4,7,5,6,1,8]=>0001010=>0101000=>1010111
[2,3,4,7,5,6,8,1]=>0001001=>1001000=>0110111
[2,3,4,8,5,6,7,1]=>0001001=>1001000=>0110111
[2,3,4,8,5,7,6,1]=>0001011=>1101000=>0010111
[2,3,4,8,6,5,7,1]=>0001101=>1011000=>0100111
[2,3,4,8,6,7,5,1]=>0001011=>1101000=>0010111
[2,3,6,4,5,1,8,7]=>0010101=>1010100=>0101011
[2,3,6,4,5,7,8,1]=>0010001=>1000100=>0111011
[2,3,7,4,5,6,8,1]=>0010001=>1000100=>0111011
[2,3,8,4,5,6,7,1]=>0010001=>1000100=>0111011
[2,3,7,4,6,5,8,1]=>0010101=>1010100=>0101011
[2,3,7,5,4,6,1,8]=>0011010=>0101100=>1010011
[2,3,7,5,4,6,8,1]=>0011001=>1001100=>0110011
[2,3,7,5,6,4,1,8]=>0010110=>0110100=>1001011
[2,3,7,5,6,4,8,1]=>0010101=>1010100=>0101011
[2,3,8,5,7,6,4,1]=>0010111=>1110100=>0001011
[2,4,3,1,8,6,7,5]=>0110101=>1010110=>0101001
[2,4,3,5,8,6,7,1]=>0100101=>1010010=>0101101
[2,4,3,8,5,6,7,1]=>0101001=>1001010=>0110101
[2,4,3,8,6,7,5,1]=>0101011=>1101010=>0010101
[2,5,3,4,1,6,7,8]=>0101000=>0001010=>1110101
[2,5,3,4,1,8,7,6]=>0101011=>1101010=>0010101
[2,5,3,4,6,7,1,8]=>0100010=>0100010=>1011101
[2,5,3,4,8,7,6,1]=>0100111=>1110010=>0001101
[2,6,3,4,5,7,8,1]=>0100001=>1000010=>0111101
[2,6,3,4,5,8,7,1]=>0100011=>1100010=>0011101
[2,6,3,5,4,1,7,8]=>0101100=>0011010=>1100101
[2,6,3,5,4,1,8,7]=>0101101=>1011010=>0100101
[2,6,3,5,4,7,8,1]=>0101001=>1001010=>0110101
[2,7,3,5,4,6,8,1]=>0101001=>1001010=>0110101
[2,7,3,5,6,4,8,1]=>0100101=>1010010=>0101101
[2,8,3,5,7,6,4,1]=>0100111=>1110010=>0001101
[2,7,3,6,5,4,1,8]=>0101110=>0111010=>1000101
[2,8,3,7,5,6,4,1]=>0101011=>1101010=>0010101
[2,5,4,3,8,6,7,1]=>0110101=>1010110=>0101001
[2,6,4,3,5,7,8,1]=>0110001=>1000110=>0111001
[2,8,4,3,7,6,5,1]=>0110111=>1110110=>0001001
[2,6,4,5,3,1,7,8]=>0101100=>0011010=>1100101
[2,6,4,5,3,1,8,7]=>0101101=>1011010=>0100101
[2,6,4,5,3,7,8,1]=>0101001=>1001010=>0110101
[2,6,4,5,3,8,7,1]=>0101011=>1101010=>0010101
[2,7,4,5,6,3,1,8]=>0100110=>0110010=>1001101
[2,7,4,5,6,3,8,1]=>0100101=>1010010=>0101101
[2,7,5,4,3,6,8,1]=>0111001=>1001110=>0110001
[2,8,5,4,3,6,7,1]=>0111001=>1001110=>0110001
[2,8,5,4,3,7,6,1]=>0111011=>1101110=>0010001
[2,7,5,4,6,3,8,1]=>0110101=>1010110=>0101001
[2,8,5,4,7,6,3,1]=>0110111=>1110110=>0001001
[2,8,7,5,4,6,3,1]=>0111011=>1101110=>0010001
[2,8,7,5,6,4,3,1]=>0110111=>1110110=>0001001
[3,2,1,4,8,6,7,5]=>1100101=>1010011=>0101100
[3,2,1,5,8,6,7,4]=>1100101=>1010011=>0101100
[3,2,1,7,5,6,8,4]=>1101001=>1001011=>0110100
[3,2,1,8,5,6,7,4]=>1101001=>1001011=>0110100
[3,2,1,8,5,7,6,4]=>1101011=>1101011=>0010100
[3,2,1,8,6,5,7,4]=>1101101=>1011011=>0100100
[3,2,1,8,6,7,5,4]=>1101011=>1101011=>0010100
[3,2,4,1,8,6,7,5]=>1010101=>1010101=>0101010
[3,2,4,8,5,6,7,1]=>1001001=>1001001=>0110110
[3,2,5,4,8,6,7,1]=>1010101=>1010101=>0101010
[3,2,6,4,5,1,8,7]=>1010101=>1010101=>0101010
[3,2,6,4,5,7,1,8]=>1010010=>0100101=>1011010
[3,2,7,4,6,5,1,8]=>1010110=>0110101=>1001010
[3,2,7,4,6,5,8,1]=>1010101=>1010101=>0101010
[3,2,8,5,4,6,7,1]=>1011001=>1001101=>0110010
[3,2,7,5,6,4,1,8]=>1010110=>0110101=>1001010
[3,2,7,5,6,4,8,1]=>1010101=>1010101=>0101010
[3,2,8,5,6,4,7,1]=>1010101=>1010101=>0101010
[3,2,8,5,7,6,4,1]=>1010111=>1110101=>0001010
[4,2,3,1,6,5,8,7]=>1010101=>1010101=>0101010
[4,2,3,1,6,7,8,5]=>1010001=>1000101=>0111010
[4,2,3,1,6,8,7,5]=>1010011=>1100101=>0011010
[4,2,3,1,7,6,8,5]=>1010101=>1010101=>0101010
[4,2,3,1,8,6,7,5]=>1010101=>1010101=>0101010
[4,2,3,1,8,7,6,5]=>1010111=>1110101=>0001010
[4,2,3,5,1,7,8,6]=>1001001=>1001001=>0110110
[4,2,3,5,1,8,7,6]=>1001011=>1101001=>0010110
[4,2,3,5,6,1,8,7]=>1000101=>1010001=>0101110
[4,2,3,5,6,8,7,1]=>1000011=>1100001=>0011110
[4,2,3,6,5,1,7,8]=>1001100=>0011001=>1100110
[4,2,3,6,5,1,8,7]=>1001101=>1011001=>0100110
[4,2,3,6,5,8,7,1]=>1001011=>1101001=>0010110
[4,2,3,7,5,6,1,8]=>1001010=>0101001=>1010110
[4,2,3,8,5,6,7,1]=>1001001=>1001001=>0110110
[4,2,3,7,6,5,8,1]=>1001101=>1011001=>0100110
[4,2,3,8,6,7,5,1]=>1001011=>1101001=>0010110
[4,2,3,8,7,6,5,1]=>1001111=>1111001=>0000110
[5,2,3,4,1,8,7,6]=>1001011=>1101001=>0010110
[5,2,3,4,8,7,6,1]=>1000111=>1110001=>0001110
[8,2,3,4,7,6,5,1]=>1000111=>1110001=>0001110
[6,2,3,5,4,1,7,8]=>1001100=>0011001=>1100110
[6,2,3,5,4,1,8,7]=>1001101=>1011001=>0100110
[6,2,3,5,4,7,1,8]=>1001010=>0101001=>1010110
[8,2,3,5,4,7,6,1]=>1001011=>1101001=>0010110
[7,2,3,5,6,4,1,8]=>1000110=>0110001=>1001110
[8,2,3,5,6,7,4,1]=>1000011=>1100001=>0011110
[7,2,3,6,5,4,1,8]=>1001110=>0111001=>1000110
[8,2,3,7,5,6,4,1]=>1001011=>1101001=>0010110
[8,2,3,7,6,5,4,1]=>1001111=>1111001=>0000110
[5,2,4,3,1,6,7,8]=>1011000=>0001101=>1110010
[5,2,4,3,1,6,8,7]=>1011001=>1001101=>0110010
[5,2,4,3,1,7,6,8]=>1011010=>0101101=>1010010
[5,2,4,3,1,8,7,6]=>1011011=>1101101=>0010010
[5,2,4,3,6,1,7,8]=>1010100=>0010101=>1101010
[5,2,4,3,6,1,8,7]=>1010101=>1010101=>0101010
[5,2,4,3,7,6,1,8]=>1010110=>0110101=>1001010
[5,2,4,3,7,6,8,1]=>1010101=>1010101=>0101010
[6,2,4,3,5,1,8,7]=>1010101=>1010101=>0101010
[7,2,4,3,6,5,1,8]=>1010110=>0110101=>1001010
[7,2,4,3,6,5,8,1]=>1010101=>1010101=>0101010
[8,2,4,3,6,5,7,1]=>1010101=>1010101=>0101010
[8,2,4,3,7,6,5,1]=>1010111=>1110101=>0001010
[6,2,4,5,3,1,7,8]=>1001100=>0011001=>1100110
[6,2,4,5,3,1,8,7]=>1001101=>1011001=>0100110
[6,2,4,5,3,8,7,1]=>1001011=>1101001=>0010110
[7,2,4,5,3,6,1,8]=>1001010=>0101001=>1010110
[7,2,4,5,3,6,8,1]=>1001001=>1001001=>0110110
[8,2,4,7,5,6,3,1]=>1001011=>1101001=>0010110
[8,2,4,7,6,5,3,1]=>1001111=>1111001=>0000110
[6,2,5,4,3,1,8,7]=>1011101=>1011101=>0100010
[7,2,5,4,3,6,1,8]=>1011010=>0101101=>1010010
[8,2,5,4,3,7,6,1]=>1011011=>1101101=>0010010
[8,2,5,4,7,6,3,1]=>1010111=>1110101=>0001010
[8,2,6,4,5,3,7,1]=>1010101=>1010101=>0101010
[8,2,6,4,5,7,3,1]=>1010011=>1100101=>0011010
[8,2,7,4,5,6,3,1]=>1010011=>1100101=>0011010
[8,2,7,4,6,5,3,1]=>1010111=>1110101=>0001010
[7,2,6,5,4,3,1,8]=>1011110=>0111101=>1000010
[8,2,6,5,4,3,7,1]=>1011101=>1011101=>0100010
[8,2,7,5,4,6,3,1]=>1011011=>1101101=>0010010
[8,2,7,5,6,4,3,1]=>1010111=>1110101=>0001010
[8,2,7,6,5,4,3,1]=>1011111=>1111101=>0000010
[4,3,2,1,8,6,7,5]=>1110101=>1010111=>0101000
[4,3,2,7,5,6,8,1]=>1101001=>1001011=>0110100
[4,3,2,8,5,6,7,1]=>1101001=>1001011=>0110100
[4,3,2,8,6,7,5,1]=>1101011=>1101011=>0010100
[5,3,2,4,1,6,8,7]=>1101001=>1001011=>0110100
[5,3,2,4,1,8,7,6]=>1101011=>1101011=>0010100
[5,3,2,4,6,1,8,7]=>1100101=>1010011=>0101100
[6,3,2,5,4,1,7,8]=>1101100=>0011011=>1100100
[6,3,2,5,4,1,8,7]=>1101101=>1011011=>0100100
[6,3,2,5,4,7,1,8]=>1101010=>0101011=>1010100
[6,3,2,5,4,7,8,1]=>1101001=>1001011=>0110100
[8,3,2,5,4,7,6,1]=>1101011=>1101011=>0010100
[8,3,2,5,6,4,7,1]=>1100101=>1010011=>0101100
[8,3,2,5,7,6,4,1]=>1100111=>1110011=>0001100
[8,3,2,7,5,6,4,1]=>1101011=>1101011=>0010100
[8,3,2,7,6,5,4,1]=>1101111=>1111011=>0000100
[5,3,4,2,1,6,8,7]=>1011001=>1001101=>0110010
[5,3,4,2,1,7,8,6]=>1011001=>1001101=>0110010
[5,3,4,2,1,8,7,6]=>1011011=>1101101=>0010010
[5,3,4,2,6,1,8,7]=>1010101=>1010101=>0101010
[5,3,4,2,7,6,1,8]=>1010110=>0110101=>1001010
[5,3,4,2,7,6,8,1]=>1010101=>1010101=>0101010
[5,3,4,2,8,6,7,1]=>1010101=>1010101=>0101010
[6,3,4,2,5,1,8,7]=>1010101=>1010101=>0101010
[7,3,4,2,6,5,1,8]=>1010110=>0110101=>1001010
[7,3,4,2,6,5,8,1]=>1010101=>1010101=>0101010
[7,3,4,6,5,2,1,8]=>1001110=>0111001=>1000110
[6,3,5,4,2,1,8,7]=>1011101=>1011101=>0100010
[6,3,5,4,2,7,1,8]=>1011010=>0101101=>1010010
[6,3,5,4,2,7,8,1]=>1011001=>1001101=>0110010
[8,3,5,4,2,6,7,1]=>1011001=>1001101=>0110010
[7,3,5,4,6,2,1,8]=>1010110=>0110101=>1001010
[8,3,5,4,7,6,2,1]=>1010111=>1110101=>0001010
[7,3,6,4,5,2,1,8]=>1010110=>0110101=>1001010
[7,3,6,4,5,2,8,1]=>1010101=>1010101=>0101010
[8,3,6,4,5,2,7,1]=>1010101=>1010101=>0101010
[8,3,7,4,5,6,2,1]=>1010011=>1100101=>0011010
[7,3,6,5,4,2,1,8]=>1011110=>0111101=>1000010
[8,3,7,5,6,4,2,1]=>1010111=>1110101=>0001010
[5,4,3,2,8,6,7,1]=>1110101=>1010111=>0101000
[7,4,3,2,6,5,1,8]=>1110110=>0110111=>1001000
[7,4,3,2,6,5,8,1]=>1110101=>1010111=>0101000
[8,4,3,2,6,7,5,1]=>1110011=>1100111=>0011000
[8,4,3,2,7,6,5,1]=>1110111=>1110111=>0001000
[6,4,3,5,2,1,8,7]=>1101101=>1011011=>0100100
[8,4,3,5,7,6,2,1]=>1100111=>1110011=>0001100
[7,4,3,6,5,2,1,8]=>1101110=>0111011=>1000100
[7,4,3,6,5,2,8,1]=>1101101=>1011011=>0100100
[8,4,3,7,5,6,2,1]=>1101011=>1101011=>0010100
[6,5,3,4,2,1,8,7]=>1101101=>1011011=>0100100
[8,5,3,4,2,7,6,1]=>1101011=>1101011=>0010100
[8,5,3,4,7,6,2,1]=>1100111=>1110011=>0001100
[8,7,3,4,6,5,2,1]=>1100111=>1110011=>0001100
[7,6,3,5,4,2,1,8]=>1101110=>0111011=>1000100
[8,6,3,5,4,2,7,1]=>1101101=>1011011=>0100100
[8,7,3,5,4,6,2,1]=>1101011=>1101011=>0010100
[8,7,3,5,6,4,2,1]=>1100111=>1110011=>0001100
[8,7,3,6,5,4,2,1]=>1101111=>1111011=>0000100
[8,5,4,3,2,7,6,1]=>1111011=>1101111=>0010000
[8,5,4,3,7,6,2,1]=>1110111=>1110111=>0001000
[8,7,4,3,6,5,2,1]=>1110111=>1110111=>0001000
[2,4,1,3,6,5,8,7]=>0100101=>1010010=>0101101
[2,1,4,6,3,5,8,7]=>1001001=>1001001=>0110110
[2,4,1,6,3,5,8,7]=>0101001=>1001010=>0110101
[2,4,6,1,3,5,8,7]=>0010001=>1000100=>0111011
[2,1,4,3,6,8,5,7]=>1010010=>0100101=>1011010
[2,4,1,3,6,8,5,7]=>0100010=>0100010=>1011101
[2,1,4,6,3,8,5,7]=>1001010=>0101001=>1010110
[2,4,1,6,3,8,5,7]=>0101010=>0101010=>1010101
[2,4,6,1,3,8,5,7]=>0010010=>0100100=>1011011
[2,1,4,6,8,3,5,7]=>1000100=>0010001=>1101110
[2,4,1,6,8,3,5,7]=>0100100=>0010010=>1101101
[2,4,6,1,8,3,5,7]=>0010100=>0010100=>1101011
[2,4,6,8,1,3,5,7]=>0001000=>0001000=>1110111
[2,4,1,3,6,5,7,8]=>0100100=>0010010=>1101101
[2,4,1,6,3,7,5,8]=>0101010=>0101010=>1010101
[2,4,6,1,3,7,5,8]=>0010010=>0100100=>1011011
[2,4,6,7,1,3,5,8]=>0001000=>0001000=>1110111
[2,4,1,3,6,7,8,5]=>0100001=>1000010=>0111101
[2,1,4,6,3,7,8,5]=>1001001=>1001001=>0110110
[2,4,1,6,3,7,8,5]=>0101001=>1001010=>0110101
[2,4,6,1,3,7,8,5]=>0010001=>1000100=>0111011
[2,4,1,6,7,3,8,5]=>0100101=>1010010=>0101101
[2,4,6,1,7,3,8,5]=>0010101=>1010100=>0101011
[2,4,6,7,1,3,8,5]=>0001001=>1001000=>0110111
[2,4,1,6,7,8,3,5]=>0100010=>0100010=>1011101
[2,4,6,1,7,8,3,5]=>0010010=>0100100=>1011011
[2,4,6,7,1,8,3,5]=>0001010=>0101000=>1010111
[2,4,6,7,8,1,3,5]=>0000100=>0010000=>1101111
[2,1,4,3,7,5,8,6]=>1010101=>1010101=>0101010
[2,4,1,3,7,5,8,6]=>0100101=>1010010=>0101101
[2,4,1,7,3,5,8,6]=>0101001=>1001010=>0110101
[2,4,7,1,3,5,8,6]=>0010001=>1000100=>0111011
[2,1,4,3,7,8,5,6]=>1010010=>0100101=>1011010
[2,4,1,3,7,8,5,6]=>0100010=>0100010=>1011101
[2,4,1,7,3,8,5,6]=>0101010=>0101010=>1010101
[2,4,1,7,8,3,5,6]=>0100100=>0010010=>1101101
[2,4,7,1,8,3,5,6]=>0010100=>0010100=>1101011
[2,4,1,5,3,7,6,8]=>0101010=>0101010=>1010101
[2,4,5,1,7,3,6,8]=>0010100=>0010100=>1101011
[2,4,1,3,5,7,8,6]=>0100001=>1000010=>0111101
[2,4,1,5,3,7,8,6]=>0101001=>1001010=>0110101
[2,4,5,1,3,7,8,6]=>0010001=>1000100=>0111011
[2,1,4,5,7,3,8,6]=>1000101=>1010001=>0101110
[2,4,1,5,7,3,8,6]=>0100101=>1010010=>0101101
[2,4,5,1,7,3,8,6]=>0010101=>1010100=>0101011
[2,4,5,7,1,3,8,6]=>0001001=>1001000=>0110111
[2,4,5,7,8,1,3,6]=>0000100=>0010000=>1101111
[2,1,4,3,8,5,6,7]=>1010100=>0010101=>1101010
[2,4,1,3,8,5,6,7]=>0100100=>0010010=>1101101
[2,1,4,8,3,5,6,7]=>1001000=>0001001=>1110110
[2,4,1,8,3,5,6,7]=>0101000=>0001010=>1110101
[2,4,1,5,3,8,6,7]=>0101010=>0101010=>1010101
[2,1,4,5,8,3,6,7]=>1000100=>0010001=>1101110
[2,4,1,5,8,3,6,7]=>0100100=>0010010=>1101101
[2,4,5,8,1,3,6,7]=>0001000=>0001000=>1110111
[2,4,1,5,6,3,8,7]=>0100101=>1010010=>0101101
[2,1,4,5,6,8,3,7]=>1000010=>0100001=>1011110
[2,4,5,1,6,8,3,7]=>0010010=>0100100=>1011011
[2,4,5,6,1,8,3,7]=>0001010=>0101000=>1010111
[2,4,5,6,8,1,3,7]=>0000100=>0010000=>1101111
[2,4,1,3,5,6,7,8]=>0100000=>0000010=>1111101
[2,4,1,5,6,3,7,8]=>0100100=>0010010=>1101101
[2,4,5,1,6,3,7,8]=>0010100=>0010100=>1101011
[2,4,5,6,1,3,7,8]=>0001000=>0001000=>1110111
[2,4,5,6,7,1,3,8]=>0000100=>0010000=>1101111
[2,4,1,5,6,7,8,3]=>0100001=>1000010=>0111101
[2,4,5,6,7,1,8,3]=>0000101=>1010000=>0101111
[2,1,5,3,6,4,8,7]=>1010101=>1010101=>0101010
[2,1,5,6,3,4,8,7]=>1001001=>1001001=>0110110
[2,1,5,3,6,8,4,7]=>1010010=>0100101=>1011010
[2,5,1,3,6,8,4,7]=>0100010=>0100010=>1011101
[2,5,1,6,8,3,4,7]=>0100100=>0010010=>1101101
[2,1,5,6,3,4,7,8]=>1001000=>0001001=>1110110
[2,5,1,6,3,4,7,8]=>0101000=>0001010=>1110101
[2,1,5,3,6,7,4,8]=>1010010=>0100101=>1011010
[2,1,5,6,3,7,4,8]=>1001010=>0101001=>1010110
[2,5,1,6,3,7,4,8]=>0101010=>0101010=>1010101
[2,5,6,1,3,7,4,8]=>0010010=>0100100=>1011011
[2,1,5,6,7,3,4,8]=>1000100=>0010001=>1101110
[2,5,1,6,7,3,4,8]=>0100100=>0010010=>1101101
[2,1,5,3,6,7,8,4]=>1010001=>1000101=>0111010
[2,5,1,3,6,7,8,4]=>0100001=>1000010=>0111101
[2,1,5,6,3,7,8,4]=>1001001=>1001001=>0110110
[2,5,1,6,3,7,8,4]=>0101001=>1001010=>0110101
[2,5,6,1,3,7,8,4]=>0010001=>1000100=>0111011
[2,1,5,6,7,3,8,4]=>1000101=>1010001=>0101110
[2,5,1,6,7,3,8,4]=>0100101=>1010010=>0101101
[2,1,5,6,7,8,3,4]=>1000010=>0100001=>1011110
[2,5,1,6,7,8,3,4]=>0100010=>0100010=>1011101
[2,5,6,1,7,8,3,4]=>0010010=>0100100=>1011011
[2,5,6,7,8,1,3,4]=>0000100=>0010000=>1101111
[2,1,5,3,7,4,8,6]=>1010101=>1010101=>0101010
[2,5,1,3,7,4,8,6]=>0100101=>1010010=>0101101
[2,1,5,7,3,4,8,6]=>1001001=>1001001=>0110110
[2,5,1,7,3,4,8,6]=>0101001=>1001010=>0110101
[2,5,7,1,3,4,8,6]=>0010001=>1000100=>0111011
[2,1,5,3,7,8,4,6]=>1010010=>0100101=>1011010
[2,5,1,3,7,8,4,6]=>0100010=>0100010=>1011101
[2,1,5,7,3,8,4,6]=>1001010=>0101001=>1010110
[2,1,5,7,8,3,4,6]=>1000100=>0010001=>1101110
[2,5,1,7,8,3,4,6]=>0100100=>0010010=>1101101
[2,5,1,3,7,4,6,8]=>0100100=>0010010=>1101101
[2,1,5,7,3,4,6,8]=>1001000=>0001001=>1110110
[2,3,5,7,1,4,6,8]=>0001000=>0001000=>1110111
[2,3,5,1,7,4,8,6]=>0010101=>1010100=>0101011
[2,3,5,7,1,4,8,6]=>0001001=>1001000=>0110111
[2,3,5,7,1,8,4,6]=>0001010=>0101000=>1010111
[2,1,5,3,8,4,6,7]=>1010100=>0010101=>1101010
[2,1,5,8,3,4,6,7]=>1001000=>0001001=>1110110
[2,5,1,8,3,4,6,7]=>0101000=>0001010=>1110101
[2,3,5,1,4,8,6,7]=>0010010=>0100100=>1011011
[2,3,5,8,1,4,6,7]=>0001000=>0001000=>1110111
[2,1,5,3,4,6,8,7]=>1010001=>1000101=>0111010
[2,3,5,1,6,4,8,7]=>0010101=>1010100=>0101011
[2,3,5,6,1,4,8,7]=>0001001=>1001000=>0110111
[2,3,5,6,1,8,4,7]=>0001010=>0101000=>1010111
[2,3,5,6,8,1,4,7]=>0000100=>0010000=>1101111
[2,3,5,6,1,4,7,8]=>0001000=>0001000=>1110111
[2,3,5,6,1,7,4,8]=>0001010=>0101000=>1010111
[2,3,5,1,6,7,8,4]=>0010001=>1000100=>0111011
[2,3,5,6,1,7,8,4]=>0001001=>1001000=>0110111
[2,3,5,6,7,1,8,4]=>0000101=>1010000=>0101111
[2,3,5,6,7,8,1,4]=>0000010=>0100000=>1011111
[2,1,6,3,7,4,8,5]=>1010101=>1010101=>0101010
[2,6,1,3,7,4,8,5]=>0100101=>1010010=>0101101
[2,6,7,1,3,4,8,5]=>0010001=>1000100=>0111011
[2,1,6,3,7,8,4,5]=>1010010=>0100101=>1011010
[2,1,6,7,3,8,4,5]=>1001010=>0101001=>1010110
[2,6,1,7,3,8,4,5]=>0101010=>0101010=>1010101
[2,1,6,7,8,3,4,5]=>1000100=>0010001=>1101110
[2,6,1,7,8,3,4,5]=>0100100=>0010010=>1101101
[2,6,7,8,1,3,4,5]=>0001000=>0001000=>1110111
[2,6,1,7,3,4,5,8]=>0101000=>0001010=>1110101
[2,6,7,1,3,4,5,8]=>0010000=>0000100=>1111011
[2,3,1,6,4,7,5,8]=>0101010=>0101010=>1010101
[2,3,6,1,4,7,5,8]=>0010010=>0100100=>1011011
[2,3,6,7,1,4,5,8]=>0001000=>0001000=>1110111
[2,1,6,3,4,7,8,5]=>1010001=>1000101=>0111010
[2,3,6,1,4,7,8,5]=>0010001=>1000100=>0111011
[2,1,3,6,7,4,8,5]=>1000101=>1010001=>0101110
[2,3,6,7,1,4,8,5]=>0001001=>1001000=>0110111
[2,3,1,6,7,8,4,5]=>0100010=>0100010=>1011101
[2,3,6,1,7,8,4,5]=>0010010=>0100100=>1011011
[2,3,6,7,1,8,4,5]=>0001010=>0101000=>1010111
[2,3,6,7,8,1,4,5]=>0000100=>0010000=>1101111
[2,6,1,8,3,4,5,7]=>0101000=>0001010=>1110101
[2,6,8,1,3,4,5,7]=>0010000=>0000100=>1111011
[2,1,6,3,4,8,5,7]=>1010010=>0100101=>1011010
[2,3,1,6,4,8,5,7]=>0101010=>0101010=>1010101
[2,3,6,1,4,8,5,7]=>0010010=>0100100=>1011011
[2,3,1,6,8,4,5,7]=>0100100=>0010010=>1101101
[2,3,6,1,8,4,5,7]=>0010100=>0010100=>1101011
[2,3,6,8,1,4,5,7]=>0001000=>0001000=>1110111
[2,1,6,3,4,5,8,7]=>1010001=>1000101=>0111010
[2,6,1,3,4,5,8,7]=>0100001=>1000010=>0111101
[2,3,6,1,4,5,8,7]=>0010001=>1000100=>0111011
[2,3,4,1,6,8,5,7]=>0010010=>0100100=>1011011
[2,3,4,6,1,8,5,7]=>0001010=>0101000=>1010111
[2,3,6,1,4,5,7,8]=>0010000=>0000100=>1111011
[2,3,4,6,7,8,1,5]=>0000010=>0100000=>1011111
[2,7,1,3,8,4,5,6]=>0100100=>0010010=>1101101
[2,1,7,8,3,4,5,6]=>1001000=>0001001=>1110110
[2,7,1,8,3,4,5,6]=>0101000=>0001010=>1110101
[2,7,8,1,3,4,5,6]=>0010000=>0000100=>1111011
[2,1,7,3,4,8,5,6]=>1010010=>0100101=>1011010
[2,1,3,7,4,8,5,6]=>1001010=>0101001=>1010110
[2,3,1,7,4,8,5,6]=>0101010=>0101010=>1010101
[2,3,1,7,8,4,5,6]=>0100100=>0010010=>1101101
[2,3,7,8,1,4,5,6]=>0001000=>0001000=>1110111
[2,1,7,3,4,5,8,6]=>1010001=>1000101=>0111010
[2,3,1,7,4,5,8,6]=>0101001=>1001010=>0110101
[2,3,7,1,4,5,8,6]=>0010001=>1000100=>0111011
[2,3,4,1,7,5,8,6]=>0010101=>1010100=>0101011
[2,3,4,7,1,5,8,6]=>0001001=>1001000=>0110111
[2,1,3,4,7,8,5,6]=>1000010=>0100001=>1011110
[2,3,1,4,7,8,5,6]=>0100010=>0100010=>1011101
[2,3,4,1,7,8,5,6]=>0010010=>0100100=>1011011
[2,3,4,7,8,1,5,6]=>0000100=>0010000=>1101111
[2,3,4,1,7,5,6,8]=>0010100=>0010100=>1101011
[2,3,4,7,1,5,6,8]=>0001000=>0001000=>1110111
[2,1,8,3,4,5,6,7]=>1010000=>0000101=>1111010
[2,8,1,3,4,5,6,7]=>0100000=>0000010=>1111101
[2,3,8,1,4,5,6,7]=>0010000=>0000100=>1111011
[2,1,3,4,8,5,6,7]=>1000100=>0010001=>1101110
[2,3,1,4,8,5,6,7]=>0100100=>0010010=>1101101
[2,3,4,1,8,5,6,7]=>0010100=>0010100=>1101011
[2,3,4,8,1,5,6,7]=>0001000=>0001000=>1110111
[2,3,4,1,5,8,6,7]=>0010010=>0100100=>1011011
[2,3,4,5,8,1,6,7]=>0000100=>0010000=>1101111
[3,1,4,2,6,5,8,7]=>1010101=>1010101=>0101010
[3,4,1,2,6,5,8,7]=>0100101=>1010010=>0101101
[3,1,4,2,6,8,5,7]=>1010010=>0100101=>1011010
[3,4,1,2,6,8,5,7]=>0100010=>0100010=>1011101
[3,1,4,6,2,8,5,7]=>1001010=>0101001=>1010110
[3,1,4,6,8,2,5,7]=>1000100=>0010001=>1101110
[3,4,1,6,8,2,5,7]=>0100100=>0010010=>1101101
[3,1,4,2,6,5,7,8]=>1010100=>0010101=>1101010
[3,4,1,2,6,5,7,8]=>0100100=>0010010=>1101101
[3,1,4,2,6,7,5,8]=>1010010=>0100101=>1011010
[3,4,1,2,6,7,5,8]=>0100010=>0100010=>1011101
[3,4,1,6,2,7,5,8]=>0101010=>0101010=>1010101
[3,4,6,1,2,7,5,8]=>0010010=>0100100=>1011011
[3,1,4,2,6,7,8,5]=>1010001=>1000101=>0111010
[3,4,1,2,6,7,8,5]=>0100001=>1000010=>0111101
[3,4,6,1,2,7,8,5]=>0010001=>1000100=>0111011
[3,4,6,1,7,2,8,5]=>0010101=>1010100=>0101011
[3,1,4,6,7,8,2,5]=>1000010=>0100001=>1011110
[3,4,6,1,7,8,2,5]=>0010010=>0100100=>1011011
[3,4,6,7,1,8,2,5]=>0001010=>0101000=>1010111
[3,4,6,7,8,1,2,5]=>0000100=>0010000=>1101111
[3,1,4,2,7,5,8,6]=>1010101=>1010101=>0101010
[3,4,1,2,7,5,8,6]=>0100101=>1010010=>0101101
[3,4,7,1,2,5,8,6]=>0010001=>1000100=>0111011
[3,1,4,2,7,8,5,6]=>1010010=>0100101=>1011010
[3,4,1,2,7,8,5,6]=>0100010=>0100010=>1011101
[3,4,7,1,8,2,5,6]=>0010100=>0010100=>1101011
[3,1,4,2,7,5,6,8]=>1010100=>0010101=>1101010
[3,4,1,2,7,5,6,8]=>0100100=>0010010=>1101101
[3,4,1,2,5,7,6,8]=>0100010=>0100010=>1011101
[3,1,4,5,2,7,6,8]=>1001010=>0101001=>1010110
[3,4,1,5,2,7,6,8]=>0101010=>0101010=>1010101
[3,4,1,5,7,2,6,8]=>0100100=>0010010=>1101101
[3,1,4,2,5,7,8,6]=>1010001=>1000101=>0111010
[3,4,1,2,5,7,8,6]=>0100001=>1000010=>0111101
[3,1,4,5,2,7,8,6]=>1001001=>1001001=>0110110
[3,4,1,5,7,2,8,6]=>0100101=>1010010=>0101101
[3,4,5,7,1,2,8,6]=>0001001=>1001000=>0110111
[3,1,4,5,7,8,2,6]=>1000010=>0100001=>1011110
[3,4,1,5,7,8,2,6]=>0100010=>0100010=>1011101
[3,4,5,1,7,8,2,6]=>0010010=>0100100=>1011011
[3,1,4,2,8,5,6,7]=>1010100=>0010101=>1101010
[3,4,1,2,8,5,6,7]=>0100100=>0010010=>1101101
[3,1,4,8,2,5,6,7]=>1001000=>0001001=>1110110
[3,4,1,8,2,5,6,7]=>0101000=>0001010=>1110101
[3,4,8,1,2,5,6,7]=>0010000=>0000100=>1111011
[3,1,4,2,5,8,6,7]=>1010010=>0100101=>1011010
[3,4,1,2,5,8,6,7]=>0100010=>0100010=>1011101
[3,4,1,5,2,8,6,7]=>0101010=>0101010=>1010101
[3,4,5,1,2,8,6,7]=>0010010=>0100100=>1011011
[3,4,1,5,8,2,6,7]=>0100100=>0010010=>1101101
[3,4,5,8,1,2,6,7]=>0001000=>0001000=>1110111
[3,4,1,2,5,6,8,7]=>0100001=>1000010=>0111101
[3,1,4,5,6,2,8,7]=>1000101=>1010001=>0101110
[3,4,5,1,6,2,8,7]=>0010101=>1010100=>0101011
[3,4,5,6,1,2,8,7]=>0001001=>1001000=>0110111
[3,4,1,5,6,8,2,7]=>0100010=>0100010=>1011101
[3,4,5,6,1,8,2,7]=>0001010=>0101000=>1010111
[3,4,5,6,8,1,2,7]=>0000100=>0010000=>1101111
[3,1,4,2,5,6,7,8]=>1010000=>0000101=>1111010
[3,4,1,5,6,2,7,8]=>0100100=>0010010=>1101101
[3,4,5,1,6,2,7,8]=>0010100=>0010100=>1101011
[3,4,1,5,6,7,2,8]=>0100010=>0100010=>1011101
[3,4,5,6,1,7,2,8]=>0001010=>0101000=>1010111
[3,1,4,5,6,7,8,2]=>1000001=>1000001=>0111110
[3,4,5,1,6,7,8,2]=>0010001=>1000100=>0111011
[3,4,5,6,1,7,8,2]=>0001001=>1001000=>0110111
[3,1,5,2,6,4,8,7]=>1010101=>1010101=>0101010
[3,1,5,6,2,4,8,7]=>1001001=>1001001=>0110110
[3,5,1,6,2,4,8,7]=>0101001=>1001010=>0110101
[3,5,6,1,2,4,8,7]=>0010001=>1000100=>0111011
[3,5,1,2,6,8,4,7]=>0100010=>0100010=>1011101
[3,1,5,6,2,8,4,7]=>1001010=>0101001=>1010110
[3,5,6,1,2,8,4,7]=>0010010=>0100100=>1011011
[3,1,5,6,8,2,4,7]=>1000100=>0010001=>1101110
[3,5,6,1,8,2,4,7]=>0010100=>0010100=>1101011
[3,1,5,6,2,4,7,8]=>1001000=>0001001=>1110110
[3,5,1,6,2,4,7,8]=>0101000=>0001010=>1110101
[3,5,6,1,2,4,7,8]=>0010000=>0000100=>1111011
[3,5,1,6,2,7,4,8]=>0101010=>0101010=>1010101
[3,5,6,1,2,7,4,8]=>0010010=>0100100=>1011011
[3,5,6,1,7,2,4,8]=>0010100=>0010100=>1101011
[3,1,5,2,6,7,8,4]=>1010001=>1000101=>0111010
[3,5,1,2,6,7,8,4]=>0100001=>1000010=>0111101
[3,1,5,6,2,7,8,4]=>1001001=>1001001=>0110110
[3,5,1,6,2,7,8,4]=>0101001=>1001010=>0110101
[3,5,6,1,2,7,8,4]=>0010001=>1000100=>0111011
[3,1,5,6,7,2,8,4]=>1000101=>1010001=>0101110
[3,5,1,6,7,2,8,4]=>0100101=>1010010=>0101101
[3,5,6,1,7,2,8,4]=>0010101=>1010100=>0101011
[3,1,5,6,7,8,2,4]=>1000010=>0100001=>1011110
[3,5,1,6,7,8,2,4]=>0100010=>0100010=>1011101
[3,5,6,1,7,8,2,4]=>0010010=>0100100=>1011011
[3,5,6,7,8,1,2,4]=>0000100=>0010000=>1101111
[3,1,5,2,7,4,8,6]=>1010101=>1010101=>0101010
[3,5,1,2,7,4,8,6]=>0100101=>1010010=>0101101
[3,1,5,7,2,4,8,6]=>1001001=>1001001=>0110110
[3,5,1,7,2,4,8,6]=>0101001=>1001010=>0110101
[3,5,7,1,2,4,8,6]=>0010001=>1000100=>0111011
[3,1,5,2,7,8,4,6]=>1010010=>0100101=>1011010
[3,5,1,2,7,8,4,6]=>0100010=>0100010=>1011101
[3,1,5,7,2,8,4,6]=>1001010=>0101001=>1010110
[3,5,1,7,2,8,4,6]=>0101010=>0101010=>1010101
[3,1,5,7,8,2,4,6]=>1000100=>0010001=>1101110
[3,5,1,7,8,2,4,6]=>0100100=>0010010=>1101101
[3,5,7,8,1,2,4,6]=>0001000=>0001000=>1110111
[3,1,5,2,7,4,6,8]=>1010100=>0010101=>1101010
[3,5,1,2,7,4,6,8]=>0100100=>0010010=>1101101
[3,1,5,7,2,4,6,8]=>1001000=>0001001=>1110110
[3,5,1,7,2,4,6,8]=>0101000=>0001010=>1110101
[3,5,7,1,2,4,6,8]=>0010000=>0000100=>1111011
[3,1,5,2,4,7,6,8]=>1010010=>0100101=>1011010
[3,5,1,2,4,7,6,8]=>0100010=>0100010=>1011101
[3,1,2,5,4,7,6,8]=>1001010=>0101001=>1010110
[1,3,5,2,4,7,6,8]=>0010010=>0100100=>1011011
[3,1,2,5,7,4,6,8]=>1000100=>0010001=>1101110
[1,3,2,5,7,4,6,8]=>0100100=>0010010=>1101101
[1,3,5,2,7,4,6,8]=>0010100=>0010100=>1101011
[1,3,5,7,2,4,6,8]=>0001000=>0001000=>1110111
[3,5,1,2,4,7,8,6]=>0100001=>1000010=>0111101
[1,3,5,2,4,7,8,6]=>0010001=>1000100=>0111011
[3,1,2,5,7,4,8,6]=>1000101=>1010001=>0101110
[1,3,2,5,7,4,8,6]=>0100101=>1010010=>0101101
[1,3,5,2,7,4,8,6]=>0010101=>1010100=>0101011
[1,3,5,7,2,4,8,6]=>0001001=>1001000=>0110111
[1,3,2,5,7,8,4,6]=>0100010=>0100010=>1011101
[1,3,5,2,7,8,4,6]=>0010010=>0100100=>1011011
[1,3,5,7,2,8,4,6]=>0001010=>0101000=>1010111
[1,3,5,7,8,2,4,6]=>0000100=>0010000=>1101111
[3,1,5,2,8,4,6,7]=>1010100=>0010101=>1101010
[3,5,1,2,8,4,6,7]=>0100100=>0010010=>1101101
[3,1,5,8,2,4,6,7]=>1001000=>0001001=>1110110
[3,5,1,8,2,4,6,7]=>0101000=>0001010=>1110101
[3,1,5,2,4,8,6,7]=>1010010=>0100101=>1011010
[3,5,1,2,4,8,6,7]=>0100010=>0100010=>1011101
[1,3,2,5,4,8,6,7]=>0101010=>0101010=>1010101
[1,3,5,2,4,8,6,7]=>0010010=>0100100=>1011011
[3,1,2,5,8,4,6,7]=>1000100=>0010001=>1101110
[1,3,2,5,8,4,6,7]=>0100100=>0010010=>1101101
[1,3,5,2,8,4,6,7]=>0010100=>0010100=>1101011
[1,3,5,8,2,4,6,7]=>0001000=>0001000=>1110111
[3,5,1,2,4,6,8,7]=>0100001=>1000010=>0111101
[3,1,2,5,4,6,8,7]=>1001001=>1001001=>0110110
[1,3,5,2,4,6,8,7]=>0010001=>1000100=>0111011
[1,3,5,6,2,4,8,7]=>0001001=>1001000=>0110111
[3,1,2,5,6,8,4,7]=>1000010=>0100001=>1011110
[1,3,5,2,6,8,4,7]=>0010010=>0100100=>1011011
[3,5,1,2,4,6,7,8]=>0100000=>0000010=>1111101
[1,3,5,2,4,6,7,8]=>0010000=>0000100=>1111011
[1,3,5,2,6,4,7,8]=>0010100=>0010100=>1101011
[1,3,5,6,2,4,7,8]=>0001000=>0001000=>1110111
[3,1,2,5,6,7,4,8]=>1000010=>0100001=>1011110
[1,3,5,2,6,7,4,8]=>0010010=>0100100=>1011011
[1,3,5,6,2,7,4,8]=>0001010=>0101000=>1010111
[1,3,5,6,7,2,4,8]=>0000100=>0010000=>1101111
[3,1,2,5,6,7,8,4]=>1000001=>1000001=>0111110
[1,3,5,6,2,7,8,4]=>0001001=>1001000=>0110111
[1,3,5,6,7,8,2,4]=>0000010=>0100000=>1011111
[3,1,6,2,7,4,8,5]=>1010101=>1010101=>0101010
[3,6,1,2,7,4,8,5]=>0100101=>1010010=>0101101
[3,6,1,7,2,4,8,5]=>0101001=>1001010=>0110101
[3,6,7,1,2,4,8,5]=>0010001=>1000100=>0111011
[3,1,6,7,2,8,4,5]=>1001010=>0101001=>1010110
[3,6,1,7,2,8,4,5]=>0101010=>0101010=>1010101
[3,6,7,1,2,8,4,5]=>0010010=>0100100=>1011011
[3,6,1,7,8,2,4,5]=>0100100=>0010010=>1101101
[3,6,7,8,1,2,4,5]=>0001000=>0001000=>1110111
[3,1,6,7,2,4,5,8]=>1001000=>0001001=>1110110
[3,6,7,1,2,4,5,8]=>0010000=>0000100=>1111011
[3,1,6,2,4,7,5,8]=>1010010=>0100101=>1011010
[3,6,1,2,4,7,5,8]=>0100010=>0100010=>1011101
[3,1,2,6,4,7,5,8]=>1001010=>0101001=>1010110
[1,3,2,6,4,7,5,8]=>0101010=>0101010=>1010101
[1,3,6,2,4,7,5,8]=>0010010=>0100100=>1011011
[1,3,2,6,7,4,5,8]=>0100100=>0010010=>1101101
[3,1,6,2,4,7,8,5]=>1010001=>1000101=>0111010
[3,6,1,2,4,7,8,5]=>0100001=>1000010=>0111101
[3,1,2,6,4,7,8,5]=>1001001=>1001001=>0110110
[1,3,2,6,4,7,8,5]=>0101001=>1001010=>0110101
[1,3,6,2,4,7,8,5]=>0010001=>1000100=>0111011
[3,1,2,6,7,4,8,5]=>1000101=>1010001=>0101110
[1,3,6,2,7,4,8,5]=>0010101=>1010100=>0101011
[1,3,6,2,7,8,4,5]=>0010010=>0100100=>1011011
[3,1,6,2,8,4,5,7]=>1010100=>0010101=>1101010
[3,1,6,8,2,4,5,7]=>1001000=>0001001=>1110110
[3,6,8,1,2,4,5,7]=>0010000=>0000100=>1111011
[3,1,6,2,4,8,5,7]=>1010010=>0100101=>1011010
[3,6,1,2,4,8,5,7]=>0100010=>0100010=>1011101
[1,3,2,6,4,8,5,7]=>0101010=>0101010=>1010101
[1,3,6,2,4,8,5,7]=>0010010=>0100100=>1011011
[3,1,6,2,4,5,8,7]=>1010001=>1000101=>0111010
[3,1,2,6,4,5,8,7]=>1001001=>1001001=>0110110
[1,3,4,6,2,5,8,7]=>0001001=>1001000=>0110111
[3,1,2,4,6,8,5,7]=>1000010=>0100001=>1011110
[1,3,2,4,6,8,5,7]=>0100010=>0100010=>1011101
[1,3,4,6,8,2,5,7]=>0000100=>0010000=>1101111
[3,1,6,2,4,5,7,8]=>1010000=>0000101=>1111010
[1,3,2,6,4,5,7,8]=>0101000=>0001010=>1110101
[1,3,6,2,4,5,7,8]=>0010000=>0000100=>1111011
[3,1,2,4,6,7,5,8]=>1000010=>0100001=>1011110
[3,1,2,4,6,7,8,5]=>1000001=>1000001=>0111110
[1,3,4,6,7,2,8,5]=>0000101=>1010000=>0101111
[3,7,1,2,8,4,5,6]=>0100100=>0010010=>1101101
[3,1,7,8,2,4,5,6]=>1001000=>0001001=>1110110
[3,1,2,7,4,8,5,6]=>1001010=>0101001=>1010110
[1,3,2,7,4,8,5,6]=>0101010=>0101010=>1010101
[1,3,7,2,4,8,5,6]=>0010010=>0100100=>1011011
[3,1,2,7,8,4,5,6]=>1000100=>0010001=>1101110
[3,7,1,2,4,5,8,6]=>0100001=>1000010=>0111101
[1,3,7,2,4,5,8,6]=>0010001=>1000100=>0111011
[3,1,2,4,7,5,8,6]=>1000101=>1010001=>0101110
[1,3,2,4,7,5,8,6]=>0100101=>1010010=>0101101
[3,1,2,4,7,8,5,6]=>1000010=>0100001=>1011110
[1,3,2,4,7,8,5,6]=>0100010=>0100010=>1011101
[1,3,4,2,7,8,5,6]=>0010010=>0100100=>1011011
[3,7,1,2,4,5,6,8]=>0100000=>0000010=>1111101
[1,3,2,7,4,5,6,8]=>0101000=>0001010=>1110101
[3,1,2,4,7,5,6,8]=>1000100=>0010001=>1101110
[1,3,4,5,7,2,6,8]=>0000100=>0010000=>1101111
[1,3,4,5,7,2,8,6]=>0000101=>1010000=>0101111
[1,3,4,5,7,8,2,6]=>0000010=>0100000=>1011111
[3,1,8,2,4,5,6,7]=>1010000=>0000101=>1111010
[1,3,2,8,4,5,6,7]=>0101000=>0001010=>1110101
[1,3,8,2,4,5,6,7]=>0010000=>0000100=>1111011
[3,1,2,4,8,5,6,7]=>1000100=>0010001=>1101110
[1,3,2,4,8,5,6,7]=>0100100=>0010010=>1101101
[1,3,4,2,8,5,6,7]=>0010100=>0010100=>1101011
[1,3,4,8,2,5,6,7]=>0001000=>0001000=>1110111
[3,1,2,4,5,8,6,7]=>1000010=>0100001=>1011110
[1,3,2,4,5,8,6,7]=>0100010=>0100010=>1011101
[1,3,4,2,5,8,6,7]=>0010010=>0100100=>1011011
[1,3,4,5,2,8,6,7]=>0001010=>0101000=>1010111
[1,3,4,5,8,2,6,7]=>0000100=>0010000=>1101111
[4,1,5,2,6,3,8,7]=>1010101=>1010101=>0101010
[4,1,5,6,2,3,8,7]=>1001001=>1001001=>0110110
[4,5,1,6,2,3,8,7]=>0101001=>1001010=>0110101
[4,5,6,1,2,3,8,7]=>0010001=>1000100=>0111011
[4,1,5,2,6,8,3,7]=>1010010=>0100101=>1011010
[4,5,1,2,6,8,3,7]=>0100010=>0100010=>1011101
[4,1,5,6,2,8,3,7]=>1001010=>0101001=>1010110
[4,5,1,6,2,8,3,7]=>0101010=>0101010=>1010101
[4,1,5,6,8,2,3,7]=>1000100=>0010001=>1101110
[4,5,6,8,1,2,3,7]=>0001000=>0001000=>1110111
[4,1,5,6,2,3,7,8]=>1001000=>0001001=>1110110
[4,5,1,6,2,3,7,8]=>0101000=>0001010=>1110101
[4,5,1,6,2,7,3,8]=>0101010=>0101010=>1010101
[4,1,5,6,7,2,3,8]=>1000100=>0010001=>1101110
[4,5,1,6,7,2,3,8]=>0100100=>0010010=>1101101
[4,1,5,2,6,7,8,3]=>1010001=>1000101=>0111010
[4,5,1,2,6,7,8,3]=>0100001=>1000010=>0111101
[4,5,1,6,2,7,8,3]=>0101001=>1001010=>0110101
[4,1,5,6,7,2,8,3]=>1000101=>1010001=>0101110
[4,5,1,6,7,2,8,3]=>0100101=>1010010=>0101101
[4,5,6,1,7,2,8,3]=>0010101=>1010100=>0101011
[4,5,6,7,1,2,8,3]=>0001001=>1001000=>0110111
[4,1,5,6,7,8,2,3]=>1000010=>0100001=>1011110
[4,5,1,6,7,8,2,3]=>0100010=>0100010=>1011101
[4,5,6,7,1,8,2,3]=>0001010=>0101000=>1010111
[4,1,5,2,7,3,8,6]=>1010101=>1010101=>0101010
[4,5,1,7,2,3,8,6]=>0101001=>1001010=>0110101
[4,1,5,2,7,8,3,6]=>1010010=>0100101=>1011010
[4,5,1,2,7,8,3,6]=>0100010=>0100010=>1011101
[4,1,5,7,2,8,3,6]=>1001010=>0101001=>1010110
[4,5,1,7,2,8,3,6]=>0101010=>0101010=>1010101
[4,5,7,1,2,8,3,6]=>0010010=>0100100=>1011011
[4,5,1,7,8,2,3,6]=>0100100=>0010010=>1101101
[4,1,5,2,7,3,6,8]=>1010100=>0010101=>1101010
[4,5,1,2,7,3,6,8]=>0100100=>0010010=>1101101
[4,1,5,7,2,3,6,8]=>1001000=>0001001=>1110110
[4,5,1,7,2,3,6,8]=>0101000=>0001010=>1110101
[4,5,1,2,3,7,6,8]=>0100010=>0100010=>1011101
[1,4,2,5,3,7,6,8]=>0101010=>0101010=>1010101
[1,4,5,2,3,7,6,8]=>0010010=>0100100=>1011011
[4,1,2,5,7,3,6,8]=>1000100=>0010001=>1101110
[1,4,2,5,7,3,6,8]=>0100100=>0010010=>1101101
[1,4,5,2,7,3,6,8]=>0010100=>0010100=>1101011
[1,4,5,7,2,3,6,8]=>0001000=>0001000=>1110111
[4,1,5,2,3,7,8,6]=>1010001=>1000101=>0111010
[4,1,2,5,3,7,8,6]=>1001001=>1001001=>0110110
[1,4,2,5,3,7,8,6]=>0101001=>1001010=>0110101
[1,4,5,2,3,7,8,6]=>0010001=>1000100=>0111011
[4,1,2,5,7,3,8,6]=>1000101=>1010001=>0101110
[1,4,2,5,7,3,8,6]=>0100101=>1010010=>0101101
[1,4,5,2,7,3,8,6]=>0010101=>1010100=>0101011
[1,4,5,7,2,3,8,6]=>0001001=>1001000=>0110111
[4,1,2,5,7,8,3,6]=>1000010=>0100001=>1011110
[1,4,2,5,7,8,3,6]=>0100010=>0100010=>1011101
[1,4,5,2,7,8,3,6]=>0010010=>0100100=>1011011
[1,4,5,7,8,2,3,6]=>0000100=>0010000=>1101111
[4,1,5,2,8,3,6,7]=>1010100=>0010101=>1101010
[4,5,1,2,8,3,6,7]=>0100100=>0010010=>1101101
[4,1,5,8,2,3,6,7]=>1001000=>0001001=>1110110
[4,5,1,8,2,3,6,7]=>0101000=>0001010=>1110101
[4,5,8,1,2,3,6,7]=>0010000=>0000100=>1111011
[4,1,5,2,3,8,6,7]=>1010010=>0100101=>1011010
[4,5,1,2,3,8,6,7]=>0100010=>0100010=>1011101
[4,1,2,5,3,8,6,7]=>1001010=>0101001=>1010110
[1,4,2,5,3,8,6,7]=>0101010=>0101010=>1010101
[1,4,5,2,3,8,6,7]=>0010010=>0100100=>1011011
[4,1,2,5,8,3,6,7]=>1000100=>0010001=>1101110
[1,4,2,5,8,3,6,7]=>0100100=>0010010=>1101101
[1,4,5,2,8,3,6,7]=>0010100=>0010100=>1101011
[1,4,5,8,2,3,6,7]=>0001000=>0001000=>1110111
[1,4,2,5,3,6,8,7]=>0101001=>1001010=>0110101
[4,1,2,5,6,3,8,7]=>1000101=>1010001=>0101110
[1,4,5,2,6,3,8,7]=>0010101=>1010100=>0101011
[4,1,2,5,6,8,3,7]=>1000010=>0100001=>1011110
[1,4,5,2,6,8,3,7]=>0010010=>0100100=>1011011
[1,4,5,6,2,8,3,7]=>0001010=>0101000=>1010111
[1,4,5,6,8,2,3,7]=>0000100=>0010000=>1101111
[1,4,2,5,3,6,7,8]=>0101000=>0001010=>1110101
[1,4,5,2,3,6,7,8]=>0010000=>0000100=>1111011
[4,1,2,5,6,3,7,8]=>1000100=>0010001=>1101110
[1,4,5,2,6,3,7,8]=>0010100=>0010100=>1101011
[4,1,2,5,6,7,3,8]=>1000010=>0100001=>1011110
[1,4,2,5,6,7,3,8]=>0100010=>0100010=>1011101
[1,4,5,6,7,2,3,8]=>0000100=>0010000=>1101111
[4,1,2,5,6,7,8,3]=>1000001=>1000001=>0111110
[1,4,5,2,6,7,8,3]=>0010001=>1000100=>0111011
[1,4,5,6,7,2,8,3]=>0000101=>1010000=>0101111
[4,1,6,2,7,3,8,5]=>1010101=>1010101=>0101010
[4,1,6,7,2,3,8,5]=>1001001=>1001001=>0110110
[4,6,7,1,2,3,8,5]=>0010001=>1000100=>0111011
[4,6,7,1,2,8,3,5]=>0010010=>0100100=>1011011
[4,6,7,1,8,2,3,5]=>0010100=>0010100=>1101011
[4,6,7,8,1,2,3,5]=>0001000=>0001000=>1110111
[4,1,6,2,7,3,5,8]=>1010100=>0010101=>1101010
[4,6,1,2,7,3,5,8]=>0100100=>0010010=>1101101
[4,1,6,7,2,3,5,8]=>1001000=>0001001=>1110110
[4,6,1,7,2,3,5,8]=>0101000=>0001010=>1110101
[4,1,6,2,3,7,5,8]=>1010010=>0100101=>1011010
[4,6,1,2,3,7,5,8]=>0100010=>0100010=>1011101
[4,1,2,6,3,7,5,8]=>1001010=>0101001=>1010110
[1,4,2,6,3,7,5,8]=>0101010=>0101010=>1010101
[4,1,2,6,7,3,5,8]=>1000100=>0010001=>1101110
[1,4,2,6,7,3,5,8]=>0100100=>0010010=>1101101
[1,4,6,2,7,3,5,8]=>0010100=>0010100=>1101011
[4,1,6,2,3,7,8,5]=>1010001=>1000101=>0111010
[4,1,2,6,3,7,8,5]=>1001001=>1001001=>0110110
[1,4,6,2,3,7,8,5]=>0010001=>1000100=>0111011
[4,1,2,6,7,3,8,5]=>1000101=>1010001=>0101110
[1,4,6,2,7,3,8,5]=>0010101=>1010100=>0101011
[1,4,2,6,7,8,3,5]=>0100010=>0100010=>1011101
[1,4,6,2,7,8,3,5]=>0010010=>0100100=>1011011
[1,4,6,7,2,8,3,5]=>0001010=>0101000=>1010111
[4,1,6,2,8,3,5,7]=>1010100=>0010101=>1101010
[4,6,1,2,8,3,5,7]=>0100100=>0010010=>1101101
[4,1,6,8,2,3,5,7]=>1001000=>0001001=>1110110
[4,6,1,8,2,3,5,7]=>0101000=>0001010=>1110101
[4,6,8,1,2,3,5,7]=>0010000=>0000100=>1111011
[4,6,1,2,3,8,5,7]=>0100010=>0100010=>1011101
[4,1,2,6,3,8,5,7]=>1001010=>0101001=>1010110
[1,4,2,6,3,8,5,7]=>0101010=>0101010=>1010101
[1,4,6,2,3,8,5,7]=>0010010=>0100100=>1011011
[1,4,2,6,8,3,5,7]=>0100100=>0010010=>1101101
[1,4,6,2,8,3,5,7]=>0010100=>0010100=>1101011
[4,1,2,6,3,5,8,7]=>1001001=>1001001=>0110110
[1,4,2,6,3,5,8,7]=>0101001=>1001010=>0110101
[4,1,2,3,6,5,8,7]=>1000101=>1010001=>0101110
[1,4,2,3,6,5,8,7]=>0100101=>1010010=>0101101
[4,1,2,3,6,8,5,7]=>1000010=>0100001=>1011110
[1,2,4,3,6,8,5,7]=>0010010=>0100100=>1011011
[1,2,4,6,8,3,5,7]=>0000100=>0010000=>1101111
[1,4,2,6,3,5,7,8]=>0101000=>0001010=>1110101
[4,1,2,3,6,5,7,8]=>1000100=>0010001=>1101110
[1,4,2,3,6,5,7,8]=>0100100=>0010010=>1101101
[1,2,4,6,3,5,7,8]=>0001000=>0001000=>1110111
[4,1,2,3,6,7,5,8]=>1000010=>0100001=>1011110
[4,1,2,3,6,7,8,5]=>1000001=>1000001=>0111110
[1,4,2,3,6,7,8,5]=>0100001=>1000010=>0111101
[1,2,4,6,7,3,8,5]=>0000101=>1010000=>0101111
[4,1,7,2,8,3,5,6]=>1010100=>0010101=>1101010
[4,7,1,2,8,3,5,6]=>0100100=>0010010=>1101101
[4,7,1,8,2,3,5,6]=>0101000=>0001010=>1110101
[1,4,2,7,3,8,5,6]=>0101010=>0101010=>1010101
[4,1,2,7,8,3,5,6]=>1000100=>0010001=>1101110
[1,4,2,7,8,3,5,6]=>0100100=>0010010=>1101101
[4,1,7,2,3,5,8,6]=>1010001=>1000101=>0111010
[4,1,2,7,3,5,8,6]=>1001001=>1001001=>0110110
[1,4,2,7,3,5,8,6]=>0101001=>1001010=>0110101
[1,4,7,2,3,5,8,6]=>0010001=>1000100=>0111011
[4,1,2,3,7,5,8,6]=>1000101=>1010001=>0101110
[1,2,4,3,7,5,8,6]=>0010101=>1010100=>0101011
[4,1,2,3,7,8,5,6]=>1000010=>0100001=>1011110
[1,4,2,3,7,8,5,6]=>0100010=>0100010=>1011101
[1,2,4,3,7,8,5,6]=>0010010=>0100100=>1011011
[1,2,4,7,8,3,5,6]=>0000100=>0010000=>1101111
[1,4,2,7,3,5,6,8]=>0101000=>0001010=>1110101
[4,1,2,3,7,5,6,8]=>1000100=>0010001=>1101110
[1,4,2,3,7,5,6,8]=>0100100=>0010010=>1101101
[4,1,2,3,5,7,6,8]=>1000010=>0100001=>1011110
[1,4,2,3,5,7,6,8]=>0100010=>0100010=>1011101
[4,1,2,3,5,7,8,6]=>1000001=>1000001=>0111110
[1,4,2,3,5,7,8,6]=>0100001=>1000010=>0111101
[1,2,4,5,7,3,8,6]=>0000101=>1010000=>0101111
[4,8,1,2,3,5,6,7]=>0100000=>0000010=>1111101
[4,1,2,8,3,5,6,7]=>1001000=>0001001=>1110110
[1,4,2,8,3,5,6,7]=>0101000=>0001010=>1110101
[1,4,8,2,3,5,6,7]=>0010000=>0000100=>1111011
[4,1,2,3,8,5,6,7]=>1000100=>0010001=>1101110
[1,4,2,3,8,5,6,7]=>0100100=>0010010=>1101101
[1,2,4,3,8,5,6,7]=>0010100=>0010100=>1101011
[1,2,4,8,3,5,6,7]=>0001000=>0001000=>1110111
[4,1,2,3,5,8,6,7]=>1000010=>0100001=>1011110
[1,4,2,3,5,8,6,7]=>0100010=>0100010=>1011101
[1,2,4,3,5,8,6,7]=>0010010=>0100100=>1011011
[1,2,4,5,3,8,6,7]=>0001010=>0101000=>1010111
[1,2,4,5,8,3,6,7]=>0000100=>0010000=>1101111
[4,1,2,3,5,6,8,7]=>1000001=>1000001=>0111110
[1,4,2,3,5,6,8,7]=>0100001=>1000010=>0111101
[1,2,4,5,6,8,3,7]=>0000010=>0100000=>1011111
[1,4,2,3,5,6,7,8]=>0100000=>0000010=>1111101
[5,1,6,2,7,3,8,4]=>1010101=>1010101=>0101010
[5,6,1,2,7,3,8,4]=>0100101=>1010010=>0101101
[5,1,6,7,2,3,8,4]=>1001001=>1001001=>0110110
[5,6,1,7,2,3,8,4]=>0101001=>1001010=>0110101
[5,6,7,1,2,3,8,4]=>0010001=>1000100=>0111011
[5,1,6,7,2,8,3,4]=>1001010=>0101001=>1010110
[5,6,7,1,2,8,3,4]=>0010010=>0100100=>1011011
[5,1,6,7,8,2,3,4]=>1000100=>0010001=>1101110
[5,6,1,7,8,2,3,4]=>0100100=>0010010=>1101101
[5,6,7,1,8,2,3,4]=>0010100=>0010100=>1101011
[5,1,6,2,7,3,4,8]=>1010100=>0010101=>1101010
[5,1,6,2,3,7,4,8]=>1010010=>0100101=>1011010
[5,1,2,6,3,7,4,8]=>1001010=>0101001=>1010110
[1,5,2,6,3,7,4,8]=>0101010=>0101010=>1010101
[5,1,2,6,7,3,4,8]=>1000100=>0010001=>1101110
[1,5,2,6,7,3,4,8]=>0100100=>0010010=>1101101
[1,5,6,7,2,3,4,8]=>0001000=>0001000=>1110111
[5,1,6,2,3,7,8,4]=>1010001=>1000101=>0111010
[5,6,1,2,3,7,8,4]=>0100001=>1000010=>0111101
[5,1,2,6,3,7,8,4]=>1001001=>1001001=>0110110
[1,5,2,6,3,7,8,4]=>0101001=>1001010=>0110101
[1,5,6,2,3,7,8,4]=>0010001=>1000100=>0111011
[5,1,2,6,7,3,8,4]=>1000101=>1010001=>0101110
[1,5,6,7,2,3,8,4]=>0001001=>1001000=>0110111
[5,1,2,6,7,8,3,4]=>1000010=>0100001=>1011110
[1,5,6,7,8,2,3,4]=>0000100=>0010000=>1101111
[5,1,6,2,8,3,4,7]=>1010100=>0010101=>1101010
[5,6,1,2,8,3,4,7]=>0100100=>0010010=>1101101
[5,6,8,1,2,3,4,7]=>0010000=>0000100=>1111011
[5,1,6,2,3,8,4,7]=>1010010=>0100101=>1011010
[5,6,1,2,3,8,4,7]=>0100010=>0100010=>1011101
[5,1,2,6,3,8,4,7]=>1001010=>0101001=>1010110
[1,5,2,6,3,8,4,7]=>0101010=>0101010=>1010101
[1,5,6,2,3,8,4,7]=>0010010=>0100100=>1011011
[5,1,2,6,8,3,4,7]=>1000100=>0010001=>1101110
[1,5,2,6,8,3,4,7]=>0100100=>0010010=>1101101
[1,5,6,2,8,3,4,7]=>0010100=>0010100=>1101011
[1,5,6,8,2,3,4,7]=>0001000=>0001000=>1110111
[5,1,2,6,3,4,8,7]=>1001001=>1001001=>0110110
[1,5,2,6,3,4,8,7]=>0101001=>1001010=>0110101
[1,5,6,2,3,4,8,7]=>0010001=>1000100=>0111011
[1,2,5,3,6,4,8,7]=>0010101=>1010100=>0101011
[1,2,5,6,3,4,8,7]=>0001001=>1001000=>0110111
[5,1,2,3,6,8,4,7]=>1000010=>0100001=>1011110
[1,5,2,3,6,8,4,7]=>0100010=>0100010=>1011101
[1,2,5,6,3,8,4,7]=>0001010=>0101000=>1010111
[5,1,6,2,3,4,7,8]=>1010000=>0000101=>1111010
[5,1,2,6,3,4,7,8]=>1001000=>0001001=>1110110
[1,5,2,6,3,4,7,8]=>0101000=>0001010=>1110101
[1,2,5,6,3,4,7,8]=>0001000=>0001000=>1110111
[5,1,2,3,6,7,4,8]=>1000010=>0100001=>1011110
[1,2,5,6,3,7,4,8]=>0001010=>0101000=>1010111
[5,1,2,3,6,7,8,4]=>1000001=>1000001=>0111110
[1,5,2,3,6,7,8,4]=>0100001=>1000010=>0111101
[1,2,5,3,6,7,8,4]=>0010001=>1000100=>0111011
[1,2,5,6,3,7,8,4]=>0001001=>1001000=>0110111
[1,2,5,6,7,8,3,4]=>0000010=>0100000=>1011111
[5,1,7,2,8,3,4,6]=>1010100=>0010101=>1101010
[5,7,1,2,8,3,4,6]=>0100100=>0010010=>1101101
[5,7,8,1,2,3,4,6]=>0010000=>0000100=>1111011
[5,1,2,7,3,8,4,6]=>1001010=>0101001=>1010110
[1,5,2,7,3,8,4,6]=>0101010=>0101010=>1010101
[1,5,7,2,3,8,4,6]=>0010010=>0100100=>1011011
[5,1,2,7,8,3,4,6]=>1000100=>0010001=>1101110
[1,5,2,7,8,3,4,6]=>0100100=>0010010=>1101101
[1,5,7,2,8,3,4,6]=>0010100=>0010100=>1101011
[1,5,7,8,2,3,4,6]=>0001000=>0001000=>1110111
[5,1,7,2,3,4,8,6]=>1010001=>1000101=>0111010
[5,1,2,7,3,4,8,6]=>1001001=>1001001=>0110110
[1,5,2,7,3,4,8,6]=>0101001=>1001010=>0110101
[1,5,7,2,3,4,8,6]=>0010001=>1000100=>0111011
[5,1,2,3,7,4,8,6]=>1000101=>1010001=>0101110
[1,5,2,3,7,4,8,6]=>0100101=>1010010=>0101101
[1,2,5,3,7,4,8,6]=>0010101=>1010100=>0101011
[1,2,5,7,3,4,8,6]=>0001001=>1001000=>0110111
[5,1,2,3,7,8,4,6]=>1000010=>0100001=>1011110
[1,5,2,3,7,8,4,6]=>0100010=>0100010=>1011101
[1,2,5,7,3,8,4,6]=>0001010=>0101000=>1010111
[5,7,1,2,3,4,6,8]=>0100000=>0000010=>1111101
[5,1,2,7,3,4,6,8]=>1001000=>0001001=>1110110
[1,5,2,7,3,4,6,8]=>0101000=>0001010=>1110101
[1,2,5,7,3,4,6,8]=>0001000=>0001000=>1110111
[1,5,2,3,4,7,6,8]=>0100010=>0100010=>1011101
[1,2,3,5,7,4,6,8]=>0000100=>0010000=>1101111
[1,5,2,3,4,7,8,6]=>0100001=>1000010=>0111101
[1,2,5,3,4,7,8,6]=>0010001=>1000100=>0111011
[1,2,3,5,7,4,8,6]=>0000101=>1010000=>0101111
[1,2,3,5,7,8,4,6]=>0000010=>0100000=>1011111
[5,1,2,8,3,4,6,7]=>1001000=>0001001=>1110110
[1,5,2,8,3,4,6,7]=>0101000=>0001010=>1110101
[1,5,2,3,8,4,6,7]=>0100100=>0010010=>1101101
[1,2,5,3,8,4,6,7]=>0010100=>0010100=>1101011
[1,2,5,8,3,4,6,7]=>0001000=>0001000=>1110111
[1,5,2,3,4,8,6,7]=>0100010=>0100010=>1011101
[1,2,5,3,4,8,6,7]=>0010010=>0100100=>1011011
[1,2,3,5,4,8,6,7]=>0001010=>0101000=>1010111
[1,2,3,5,8,4,6,7]=>0000100=>0010000=>1101111
[1,5,2,3,4,6,8,7]=>0100001=>1000010=>0111101
[1,2,3,5,6,8,4,7]=>0000010=>0100000=>1011111
[1,5,2,3,4,6,7,8]=>0100000=>0000010=>1111101
[6,1,7,2,8,3,4,5]=>1010100=>0010101=>1101010
[6,1,7,8,2,3,4,5]=>1001000=>0001001=>1110110
[6,7,1,8,2,3,4,5]=>0101000=>0001010=>1110101
[6,1,7,2,3,8,4,5]=>1010010=>0100101=>1011010
[6,7,1,2,3,8,4,5]=>0100010=>0100010=>1011101
[6,1,2,7,3,8,4,5]=>1001010=>0101001=>1010110
[1,6,2,7,3,8,4,5]=>0101010=>0101010=>1010101
[1,6,7,2,3,8,4,5]=>0010010=>0100100=>1011011
[1,6,7,2,8,3,4,5]=>0010100=>0010100=>1101011
[1,6,7,8,2,3,4,5]=>0001000=>0001000=>1110111
[6,1,7,2,3,4,8,5]=>1010001=>1000101=>0111010
[6,7,1,2,3,4,8,5]=>0100001=>1000010=>0111101
[6,1,2,7,3,4,8,5]=>1001001=>1001001=>0110110
[1,6,2,7,3,4,8,5]=>0101001=>1001010=>0110101
[1,6,7,2,3,4,8,5]=>0010001=>1000100=>0111011
[1,6,2,3,7,4,8,5]=>0100101=>1010010=>0101101
[1,2,6,3,7,4,8,5]=>0010101=>1010100=>0101011
[6,1,2,3,7,8,4,5]=>1000010=>0100001=>1011110
[1,2,6,3,7,8,4,5]=>0010010=>0100100=>1011011
[1,2,6,7,3,8,4,5]=>0001010=>0101000=>1010111
[6,1,7,2,3,4,5,8]=>1010000=>0000101=>1111010
[1,6,2,7,3,4,5,8]=>0101000=>0001010=>1110101
[1,6,7,2,3,4,5,8]=>0010000=>0000100=>1111011
[1,6,2,3,4,7,5,8]=>0100010=>0100010=>1011101
[1,2,6,3,4,7,5,8]=>0010010=>0100100=>1011011
[1,2,3,6,4,7,5,8]=>0001010=>0101000=>1010111
[1,2,3,6,7,4,5,8]=>0000100=>0010000=>1101111
[6,1,2,3,4,7,8,5]=>1000001=>1000001=>0111110
[1,6,2,3,4,7,8,5]=>0100001=>1000010=>0111101
[1,2,6,3,4,7,8,5]=>0010001=>1000100=>0111011
[1,2,3,6,4,7,8,5]=>0001001=>1001000=>0110111
[1,2,3,6,7,4,8,5]=>0000101=>1010000=>0101111
[1,2,3,6,7,8,4,5]=>0000010=>0100000=>1011111
[6,1,8,2,3,4,5,7]=>1010000=>0000101=>1111010
[6,1,2,8,3,4,5,7]=>1001000=>0001001=>1110110
[1,6,2,8,3,4,5,7]=>0101000=>0001010=>1110101
[1,6,8,2,3,4,5,7]=>0010000=>0000100=>1111011
[1,6,2,3,8,4,5,7]=>0100100=>0010010=>1101101
[1,2,6,3,8,4,5,7]=>0010100=>0010100=>1101011
[1,2,6,8,3,4,5,7]=>0001000=>0001000=>1110111
[1,6,2,3,4,8,5,7]=>0100010=>0100010=>1011101
[1,2,6,3,4,8,5,7]=>0010010=>0100100=>1011011
[1,2,3,6,4,8,5,7]=>0001010=>0101000=>1010111
[6,1,2,3,4,5,8,7]=>1000001=>1000001=>0111110
[1,6,2,3,4,5,8,7]=>0100001=>1000010=>0111101
[1,2,6,3,4,5,8,7]=>0010001=>1000100=>0111011
[1,2,3,6,4,5,8,7]=>0001001=>1001000=>0110111
[1,2,3,4,6,8,5,7]=>0000010=>0100000=>1011111
[1,6,2,3,4,5,7,8]=>0100000=>0000010=>1111101
[1,2,6,3,4,5,7,8]=>0010000=>0000100=>1111011
[1,2,3,6,4,5,7,8]=>0001000=>0001000=>1110111
[7,1,2,8,3,4,5,6]=>1001000=>0001001=>1110110
[1,7,2,8,3,4,5,6]=>0101000=>0001010=>1110101
[1,7,8,2,3,4,5,6]=>0010000=>0000100=>1111011
[7,1,2,3,8,4,5,6]=>1000100=>0010001=>1101110
[1,2,7,8,3,4,5,6]=>0001000=>0001000=>1110111
[1,2,7,3,4,8,5,6]=>0010010=>0100100=>1011011
[1,2,3,7,4,8,5,6]=>0001010=>0101000=>1010111
[1,2,3,7,8,4,5,6]=>0000100=>0010000=>1101111
[1,2,7,3,4,5,8,6]=>0010001=>1000100=>0111011
[1,2,3,7,4,5,8,6]=>0001001=>1001000=>0110111
[1,2,3,4,7,5,8,6]=>0000101=>1010000=>0101111
[1,2,3,4,7,8,5,6]=>0000010=>0100000=>1011111
[1,7,2,3,4,5,6,8]=>0100000=>0000010=>1111101
[1,2,7,3,4,5,6,8]=>0010000=>0000100=>1111011
[1,2,3,7,4,5,6,8]=>0001000=>0001000=>1110111
[1,2,3,4,7,5,6,8]=>0000100=>0010000=>1101111
[1,8,2,3,4,5,6,7]=>0100000=>0000010=>1111101
[1,2,8,3,4,5,6,7]=>0010000=>0000100=>1111011
[1,2,3,8,4,5,6,7]=>0001000=>0001000=>1110111
[1,2,3,4,8,5,6,7]=>0000100=>0010000=>1101111
[1,2,3,4,5,8,6,7]=>0000010=>0100000=>1011111
[5,3,2,6,1,4,8,7]=>1101001=>1001011=>0110100
[7,3,2,5,4,8,1,6]=>1101010=>0101011=>1010100
[8,4,5,2,3,7,6,1]=>1010011=>1100101=>0011010
[7,4,5,2,3,8,1,6]=>1010010=>0100101=>1011010
[6,4,5,2,3,1,8,7]=>1010101=>1010101=>0101010
[5,4,6,2,1,3,8,7]=>1011001=>1001101=>0110010
[3,6,1,5,4,2,8,7]=>0101101=>1011010=>0100101
[4,6,5,1,3,2,8,7]=>0110101=>1010110=>0101001
[5,6,4,3,1,2,8,7]=>0111001=>1001110=>0110001
[7,5,4,3,2,8,1,6]=>1111010=>0101111=>1010000
[8,6,4,3,7,2,5,1]=>1110101=>1010111=>0101000
[7,6,4,3,8,2,1,5]=>1110110=>0110111=>1001000
[6,7,4,3,8,1,2,5]=>0110100=>0010110=>1101001
[5,7,4,3,1,8,2,6]=>0111010=>0101110=>1010001
[4,7,5,1,3,8,2,6]=>0110010=>0100110=>1011001
[3,7,1,5,4,8,2,6]=>0101010=>0101010=>1010101
[2,1,7,5,4,8,3,6]=>1011010=>0101101=>1010010
[3,8,1,5,4,7,6,2]=>0101011=>1101010=>0010101
[4,8,5,1,3,7,6,2]=>0110011=>1100110=>0011001
[5,8,4,3,1,7,6,2]=>0111011=>1101110=>0010001
[6,8,4,3,7,1,5,2]=>0110101=>1010110=>0101001
[7,8,4,3,6,5,1,2]=>0110110=>0110110=>1001001
[6,8,5,7,3,1,4,2]=>0101101=>1011010=>0100101
[5,8,6,7,1,3,4,2]=>0101001=>1001010=>0110101
[4,8,6,1,7,3,5,2]=>0110101=>1010110=>0101001
[3,8,1,6,7,4,5,2]=>0100101=>1010010=>0101101
[2,1,8,6,7,4,5,3]=>1010101=>1010101=>0101010
[2,1,7,6,8,4,3,5]=>1010110=>0110101=>1001010
[3,7,1,6,8,4,2,5]=>0100110=>0110010=>1001101
[4,7,6,1,8,3,2,5]=>0110110=>0110110=>1001001
[5,7,6,8,1,3,2,4]=>0101010=>0101010=>1010101
[5,4,7,2,1,8,3,6]=>1011010=>0101101=>1010010
[6,4,7,2,8,1,3,5]=>1010100=>0010101=>1101010
[7,4,6,2,8,3,1,5]=>1010110=>0110101=>1001010
[8,4,6,2,7,3,5,1]=>1010101=>1010101=>0101010
[8,3,2,6,7,4,5,1]=>1100101=>1010011=>0101100
[7,3,2,6,8,4,1,5]=>1100110=>0110011=>1001100
[6,3,2,7,8,1,4,5]=>1100100=>0010011=>1101100
[5,3,2,7,1,8,4,6]=>1101010=>0101011=>1010100
[4,3,2,1,7,8,5,6]=>1110010=>0100111=>1011000
[3,4,1,2,8,7,6,5]=>0100111=>1110010=>0001101
[5,3,2,8,1,7,6,4]=>1101011=>1101011=>0010100
[6,3,2,8,7,1,5,4]=>1101101=>1011011=>0100100
[7,3,2,8,6,5,1,4]=>1101110=>0111011=>1000100
[8,4,7,2,6,5,3,1]=>1010111=>1110101=>0001010
[7,4,8,2,6,5,1,3]=>1010110=>0110101=>1001010
[6,4,8,2,7,1,5,3]=>1010101=>1010101=>0101010
[5,4,8,2,1,7,6,3]=>1011011=>1101101=>0010010
[4,5,8,1,2,7,6,3]=>0010011=>1100100=>0011011
[3,5,1,8,2,7,6,4]=>0101011=>1101010=>0010101
[2,1,5,8,3,7,6,4]=>1001011=>1101001=>0010110
[2,1,6,8,7,3,5,4]=>1001101=>1011001=>0100110
[3,6,1,8,7,2,5,4]=>0101101=>1011010=>0100101
[4,6,8,1,7,2,5,3]=>0010101=>1010100=>0101011
[5,6,8,7,1,2,4,3]=>0011001=>1001100=>0110011
[6,5,8,7,2,1,4,3]=>1011101=>1011101=>0100010
[7,5,8,6,2,4,1,3]=>1011010=>0101101=>1010010
[8,5,7,6,2,4,3,1]=>1011011=>1101101=>0010010
[5,7,8,6,1,4,2,3]=>0011010=>0101100=>1010011
[4,7,8,1,6,5,2,3]=>0010110=>0110100=>1001011
[3,7,1,8,6,5,2,4]=>0101110=>0111010=>1000101
[2,1,7,8,6,5,3,4]=>1001110=>0111001=>1000110
[3,8,1,7,6,5,4,2]=>0101111=>1111010=>0000101
[4,8,7,1,6,5,3,2]=>0110111=>1110110=>0001001
[5,8,7,6,1,4,3,2]=>0111011=>1101110=>0010001
[6,8,7,5,4,1,3,2]=>0111101=>1011110=>0100001
[2,1,4,3,6,5,8,7,10,9]=>101010101=>101010101=>010101010
[5,2,4,1,3,6,7,8]=>1010000=>0000101=>1111010
[3,2,6,1,4,5,7,8]=>1010000=>0000101=>1111010
[6,3,5,1,2,4,7,8]=>1010000=>0000101=>1111010
[5,2,7,1,3,4,6,8]=>1010000=>0000101=>1111010
[5,3,7,1,2,4,6,8]=>1010000=>0000101=>1111010
[5,4,7,1,2,3,6,8]=>1010000=>0000101=>1111010
[6,2,7,1,3,4,5,8]=>1010000=>0000101=>1111010
[6,3,7,1,2,4,5,8]=>1010000=>0000101=>1111010
[6,4,7,1,2,3,5,8]=>1010000=>0000101=>1111010
[7,3,5,1,2,4,6,8]=>1010000=>0000101=>1111010
[7,4,6,1,2,3,5,8]=>1010000=>0000101=>1111010
[3,2,8,1,4,5,6,7]=>1010000=>0000101=>1111010
[5,2,8,1,3,4,6,7]=>1010000=>0000101=>1111010
[5,4,8,1,2,3,6,7]=>1010000=>0000101=>1111010
[6,2,8,1,3,4,5,7]=>1010000=>0000101=>1111010
[6,5,8,1,2,3,4,7]=>1010000=>0000101=>1111010
[7,5,8,1,2,3,4,6]=>1010000=>0000101=>1111010
[8,3,5,1,2,4,6,7]=>1010000=>0000101=>1111010
[8,3,6,1,2,4,5,7]=>1010000=>0000101=>1111010
[8,4,7,1,2,3,5,6]=>1010000=>0000101=>1111010
[8,5,7,1,2,3,4,6]=>1010000=>0000101=>1111010
[3,2,5,7,1,4,6,8]=>1001000=>0001001=>1110110
[4,2,5,7,1,3,6,8]=>1001000=>0001001=>1110110
[4,3,5,7,1,2,6,8]=>1001000=>0001001=>1110110
[5,3,4,7,1,2,6,8]=>1001000=>0001001=>1110110
[4,2,6,7,1,3,5,8]=>1001000=>0001001=>1110110
[5,2,6,7,1,3,4,8]=>1001000=>0001001=>1110110
[7,3,5,6,1,2,4,8]=>1001000=>0001001=>1110110
[3,2,5,8,1,4,6,7]=>1001000=>0001001=>1110110
[4,2,5,8,1,3,6,7]=>1001000=>0001001=>1110110
[4,3,5,8,1,2,6,7]=>1001000=>0001001=>1110110
[5,2,4,8,1,3,6,7]=>1001000=>0001001=>1110110
[3,2,6,8,1,4,5,7]=>1001000=>0001001=>1110110
[4,2,6,8,1,3,5,7]=>1001000=>0001001=>1110110
[4,3,6,8,1,2,5,7]=>1001000=>0001001=>1110110
[5,2,6,8,1,3,4,7]=>1001000=>0001001=>1110110
[6,2,4,8,1,3,5,7]=>1001000=>0001001=>1110110
[6,2,5,8,1,3,4,7]=>1001000=>0001001=>1110110
[6,3,5,8,1,2,4,7]=>1001000=>0001001=>1110110
[3,2,7,8,1,4,5,6]=>1001000=>0001001=>1110110
[4,3,7,8,1,2,5,6]=>1001000=>0001001=>1110110
[6,2,7,8,1,3,4,5]=>1001000=>0001001=>1110110
[6,3,7,8,1,2,4,5]=>1001000=>0001001=>1110110
[6,4,7,8,1,2,3,5]=>1001000=>0001001=>1110110
[7,2,4,8,1,3,5,6]=>1001000=>0001001=>1110110
[7,3,5,8,1,2,4,6]=>1001000=>0001001=>1110110
[7,4,5,8,1,2,3,6]=>1001000=>0001001=>1110110
[8,2,5,6,1,3,4,7]=>1001000=>0001001=>1110110
[8,2,4,7,1,3,5,6]=>1001000=>0001001=>1110110
[8,2,5,7,1,3,4,6]=>1001000=>0001001=>1110110
[8,3,5,7,1,2,4,6]=>1001000=>0001001=>1110110
[8,2,6,7,1,3,4,5]=>1001000=>0001001=>1110110
[8,4,6,7,1,2,3,5]=>1001000=>0001001=>1110110
[4,6,2,5,1,3,7,8]=>0101000=>0001010=>1110101
[4,6,3,5,1,2,7,8]=>0101000=>0001010=>1110101
[4,7,3,5,1,2,6,8]=>0101000=>0001010=>1110101
[5,7,2,4,1,3,6,8]=>0101000=>0001010=>1110101
[5,7,3,4,1,2,6,8]=>0101000=>0001010=>1110101
[3,7,2,6,1,4,5,8]=>0101000=>0001010=>1110101
[5,7,2,6,1,3,4,8]=>0101000=>0001010=>1110101
[6,7,2,5,1,3,4,8]=>0101000=>0001010=>1110101
[4,8,2,5,1,3,6,7]=>0101000=>0001010=>1110101
[5,8,3,4,1,2,6,7]=>0101000=>0001010=>1110101
[5,8,3,6,1,2,4,7]=>0101000=>0001010=>1110101
[6,8,2,4,1,3,5,7]=>0101000=>0001010=>1110101
[6,8,3,4,1,2,5,7]=>0101000=>0001010=>1110101
[6,8,3,5,1,2,4,7]=>0101000=>0001010=>1110101
[6,8,4,5,1,2,3,7]=>0101000=>0001010=>1110101
[3,8,2,7,1,4,5,6]=>0101000=>0001010=>1110101
[4,8,2,7,1,3,5,6]=>0101000=>0001010=>1110101
[5,8,2,7,1,3,4,6]=>0101000=>0001010=>1110101
[5,8,3,7,1,2,4,6]=>0101000=>0001010=>1110101
[5,8,4,7,1,2,3,6]=>0101000=>0001010=>1110101
[6,8,2,7,1,3,4,5]=>0101000=>0001010=>1110101
[6,8,3,7,1,2,4,5]=>0101000=>0001010=>1110101
[6,8,5,7,1,2,3,4]=>0101000=>0001010=>1110101
[7,8,2,4,1,3,5,6]=>0101000=>0001010=>1110101
[7,8,2,5,1,3,4,6]=>0101000=>0001010=>1110101
[7,8,3,5,1,2,4,6]=>0101000=>0001010=>1110101
[7,8,4,6,1,2,3,5]=>0101000=>0001010=>1110101
[4,3,2,6,1,5,7,8]=>1101000=>0001011=>1110100
[5,3,2,6,1,4,7,8]=>1101000=>0001011=>1110100
[6,4,2,5,1,3,7,8]=>1101000=>0001011=>1110100
[6,5,2,4,1,3,7,8]=>1101000=>0001011=>1110100
[4,3,2,7,1,5,6,8]=>1101000=>0001011=>1110100
[5,3,2,7,1,4,6,8]=>1101000=>0001011=>1110100
[5,4,3,7,1,2,6,8]=>1101000=>0001011=>1110100
[6,3,2,7,1,4,5,8]=>1101000=>0001011=>1110100
[6,4,2,7,1,3,5,8]=>1101000=>0001011=>1110100
[6,4,3,7,1,2,5,8]=>1101000=>0001011=>1110100
[6,5,3,7,1,2,4,8]=>1101000=>0001011=>1110100
[7,3,2,5,1,4,6,8]=>1101000=>0001011=>1110100
[7,4,2,5,1,3,6,8]=>1101000=>0001011=>1110100
[7,3,2,6,1,4,5,8]=>1101000=>0001011=>1110100
[7,4,3,6,1,2,5,8]=>1101000=>0001011=>1110100
[7,5,2,6,1,3,4,8]=>1101000=>0001011=>1110100
[7,5,3,6,1,2,4,8]=>1101000=>0001011=>1110100
[7,6,3,5,1,2,4,8]=>1101000=>0001011=>1110100
[4,3,2,8,1,5,6,7]=>1101000=>0001011=>1110100
[5,3,2,8,1,4,6,7]=>1101000=>0001011=>1110100
[5,4,3,8,1,2,6,7]=>1101000=>0001011=>1110100
[6,3,2,8,1,4,5,7]=>1101000=>0001011=>1110100
[6,4,3,8,1,2,5,7]=>1101000=>0001011=>1110100
[6,5,2,8,1,3,4,7]=>1101000=>0001011=>1110100
[6,5,3,8,1,2,4,7]=>1101000=>0001011=>1110100
[6,5,4,8,1,2,3,7]=>1101000=>0001011=>1110100
[7,3,2,8,1,4,5,6]=>1101000=>0001011=>1110100
[7,4,2,8,1,3,5,6]=>1101000=>0001011=>1110100
[7,5,3,8,1,2,4,6]=>1101000=>0001011=>1110100
[7,6,2,8,1,3,4,5]=>1101000=>0001011=>1110100
[8,4,2,5,1,3,6,7]=>1101000=>0001011=>1110100
[8,3,2,6,1,4,5,7]=>1101000=>0001011=>1110100
[8,4,2,6,1,3,5,7]=>1101000=>0001011=>1110100
[8,5,3,6,1,2,4,7]=>1101000=>0001011=>1110100
[8,6,2,4,1,3,5,7]=>1101000=>0001011=>1110100
[8,6,2,5,1,3,4,7]=>1101000=>0001011=>1110100
[8,3,2,7,1,4,5,6]=>1101000=>0001011=>1110100
[8,4,2,7,1,3,5,6]=>1101000=>0001011=>1110100
[8,4,3,7,1,2,5,6]=>1101000=>0001011=>1110100
[8,5,2,7,1,3,4,6]=>1101000=>0001011=>1110100
[8,5,3,7,1,2,4,6]=>1101000=>0001011=>1110100
[8,5,4,7,1,2,3,6]=>1101000=>0001011=>1110100
[8,6,3,7,1,2,4,5]=>1101000=>0001011=>1110100
[8,7,2,4,1,3,5,6]=>1101000=>0001011=>1110100
[8,7,2,5,1,3,4,6]=>1101000=>0001011=>1110100
[8,7,3,5,1,2,4,6]=>1101000=>0001011=>1110100
[8,7,2,6,1,3,4,5]=>1101000=>0001011=>1110100
[8,7,3,6,1,2,4,5]=>1101000=>0001011=>1110100
[8,7,4,6,1,2,3,5]=>1101000=>0001011=>1110100
[4,6,3,5,8,1,2,7]=>0100100=>0010010=>1101101
[5,6,2,4,8,1,3,7]=>0100100=>0010010=>1101101
[4,7,2,5,8,1,3,6]=>0100100=>0010010=>1101101
[4,7,3,5,8,1,2,6]=>0100100=>0010010=>1101101
[5,7,3,4,8,1,2,6]=>0100100=>0010010=>1101101
[3,7,2,6,8,1,4,5]=>0100100=>0010010=>1101101
[4,7,3,6,8,1,2,5]=>0100100=>0010010=>1101101
[5,7,4,6,8,1,2,3]=>0100100=>0010010=>1101101
[6,7,3,5,8,1,2,4]=>0100100=>0010010=>1101101
[3,8,2,5,7,1,4,6]=>0100100=>0010010=>1101101
[4,8,2,5,7,1,3,6]=>0100100=>0010010=>1101101
[4,8,3,5,7,1,2,6]=>0100100=>0010010=>1101101
[3,8,2,6,7,1,4,5]=>0100100=>0010010=>1101101
[4,8,3,6,7,1,2,5]=>0100100=>0010010=>1101101
[6,8,2,5,7,1,3,4]=>0100100=>0010010=>1101101
[6,8,3,5,7,1,2,4]=>0100100=>0010010=>1101101
[6,8,4,5,7,1,2,3]=>0100100=>0010010=>1101101
[7,8,2,4,6,1,3,5]=>0100100=>0010010=>1101101
[7,8,2,5,6,1,3,4]=>0100100=>0010010=>1101101
[7,8,3,5,6,1,2,4]=>0100100=>0010010=>1101101
[4,3,2,6,8,1,5,7]=>1100100=>0010011=>1101100
[5,4,2,6,8,1,3,7]=>1100100=>0010011=>1101100
[5,4,3,6,8,1,2,7]=>1100100=>0010011=>1101100
[6,3,2,5,8,1,4,7]=>1100100=>0010011=>1101100
[6,4,3,5,8,1,2,7]=>1100100=>0010011=>1101100
[6,5,2,4,8,1,3,7]=>1100100=>0010011=>1101100
[4,3,2,7,8,1,5,6]=>1100100=>0010011=>1101100
[5,3,2,7,8,1,4,6]=>1100100=>0010011=>1101100
[5,4,2,7,8,1,3,6]=>1100100=>0010011=>1101100
[5,4,3,7,8,1,2,6]=>1100100=>0010011=>1101100
[6,4,2,7,8,1,3,5]=>1100100=>0010011=>1101100
[6,4,3,7,8,1,2,5]=>1100100=>0010011=>1101100
[6,5,2,7,8,1,3,4]=>1100100=>0010011=>1101100
[7,4,2,5,8,1,3,6]=>1100100=>0010011=>1101100
[7,3,2,6,8,1,4,5]=>1100100=>0010011=>1101100
[7,5,3,6,8,1,2,4]=>1100100=>0010011=>1101100
[7,6,3,5,8,1,2,4]=>1100100=>0010011=>1101100
[8,4,2,5,7,1,3,6]=>1100100=>0010011=>1101100
[8,5,2,6,7,1,3,4]=>1100100=>0010011=>1101100
[8,5,3,6,7,1,2,4]=>1100100=>0010011=>1101100
[8,6,3,5,7,1,2,4]=>1100100=>0010011=>1101100
[8,7,2,4,6,1,3,5]=>1100100=>0010011=>1101100
[8,7,3,4,6,1,2,5]=>1100100=>0010011=>1101100
[8,7,2,5,6,1,3,4]=>1100100=>0010011=>1101100
[8,7,3,5,6,1,2,4]=>1100100=>0010011=>1101100
[4,3,7,2,6,1,5,8]=>1010100=>0010101=>1101010
[5,3,7,2,6,1,4,8]=>1010100=>0010101=>1101010
[5,4,7,2,6,1,3,8]=>1010100=>0010101=>1101010
[6,3,7,2,5,1,4,8]=>1010100=>0010101=>1101010
[6,4,7,2,5,1,3,8]=>1010100=>0010101=>1101010
[7,3,6,2,5,1,4,8]=>1010100=>0010101=>1101010
[4,3,8,2,6,1,5,7]=>1010100=>0010101=>1101010
[5,3,8,2,6,1,4,7]=>1010100=>0010101=>1101010
[5,4,8,2,6,1,3,7]=>1010100=>0010101=>1101010
[6,4,8,2,5,1,3,7]=>1010100=>0010101=>1101010
[6,4,8,3,5,1,2,7]=>1010100=>0010101=>1101010
[6,5,8,3,4,1,2,7]=>1010100=>0010101=>1101010
[4,3,8,2,7,1,5,6]=>1010100=>0010101=>1101010
[5,3,8,2,7,1,4,6]=>1010100=>0010101=>1101010
[5,4,8,2,7,1,3,6]=>1010100=>0010101=>1101010
[6,4,8,2,7,1,3,5]=>1010100=>0010101=>1101010
[7,3,8,2,5,1,4,6]=>1010100=>0010101=>1101010
[7,4,8,3,5,1,2,6]=>1010100=>0010101=>1101010
[7,5,8,2,4,1,3,6]=>1010100=>0010101=>1101010
[7,5,8,3,4,1,2,6]=>1010100=>0010101=>1101010
[7,3,8,2,6,1,4,5]=>1010100=>0010101=>1101010
[7,4,8,2,6,1,3,5]=>1010100=>0010101=>1101010
[7,5,8,2,6,1,3,4]=>1010100=>0010101=>1101010
[7,5,8,3,6,1,2,4]=>1010100=>0010101=>1101010
[7,5,8,4,6,1,2,3]=>1010100=>0010101=>1101010
[8,3,6,2,5,1,4,7]=>1010100=>0010101=>1101010
[8,3,7,2,5,1,4,6]=>1010100=>0010101=>1101010
[8,3,7,2,6,1,4,5]=>1010100=>0010101=>1101010
[8,4,7,2,6,1,3,5]=>1010100=>0010101=>1101010
[8,4,7,3,6,1,2,5]=>1010100=>0010101=>1101010
[8,5,7,2,6,1,3,4]=>1010100=>0010101=>1101010
[8,6,7,2,5,1,3,4]=>1010100=>0010101=>1101010
[8,6,7,3,5,1,2,4]=>1010100=>0010101=>1101010
[5,4,3,2,7,1,6,8]=>1110100=>0010111=>1101000
[6,4,3,2,7,1,5,8]=>1110100=>0010111=>1101000
[6,5,3,2,7,1,4,8]=>1110100=>0010111=>1101000
[6,5,4,2,7,1,3,8]=>1110100=>0010111=>1101000
[7,5,3,2,6,1,4,8]=>1110100=>0010111=>1101000
[5,4,3,2,8,1,6,7]=>1110100=>0010111=>1101000
[6,5,3,2,8,1,4,7]=>1110100=>0010111=>1101000
[6,5,4,3,8,1,2,7]=>1110100=>0010111=>1101000
[7,5,3,2,8,1,4,6]=>1110100=>0010111=>1101000
[7,6,4,3,8,1,2,5]=>1110100=>0010111=>1101000
[8,5,3,2,6,1,4,7]=>1110100=>0010111=>1101000
[8,5,4,2,6,1,3,7]=>1110100=>0010111=>1101000
[8,6,5,2,4,1,3,7]=>1110100=>0010111=>1101000
[8,5,3,2,7,1,4,6]=>1110100=>0010111=>1101000
[8,6,3,2,7,1,4,5]=>1110100=>0010111=>1101000
[8,7,3,2,6,1,4,5]=>1110100=>0010111=>1101000
[8,7,4,2,6,1,3,5]=>1110100=>0010111=>1101000
[8,7,4,3,6,1,2,5]=>1110100=>0010111=>1101000
[8,7,5,2,6,1,3,4]=>1110100=>0010111=>1101000
[8,7,6,2,4,1,3,5]=>1110100=>0010111=>1101000
[8,7,6,2,5,1,3,4]=>1110100=>0010111=>1101000
[8,7,6,3,5,1,2,4]=>1110100=>0010111=>1101000
[4,8,3,7,2,6,1,5]=>0101010=>0101010=>1010101
[5,8,3,7,2,6,1,4]=>0101010=>0101010=>1010101
[5,8,4,7,2,6,1,3]=>0101010=>0101010=>1010101
[5,8,4,7,3,6,1,2]=>0101010=>0101010=>1010101
[6,8,3,7,2,5,1,4]=>0101010=>0101010=>1010101
[6,8,4,7,2,5,1,3]=>0101010=>0101010=>1010101
[6,8,4,7,3,5,1,2]=>0101010=>0101010=>1010101
[6,8,5,7,2,4,1,3]=>0101010=>0101010=>1010101
[6,8,5,7,3,4,1,2]=>0101010=>0101010=>1010101
[7,8,3,6,2,5,1,4]=>0101010=>0101010=>1010101
[7,8,4,6,2,5,1,3]=>0101010=>0101010=>1010101
[7,8,4,6,3,5,1,2]=>0101010=>0101010=>1010101
[7,8,5,6,2,4,1,3]=>0101010=>0101010=>1010101
[6,4,3,8,2,7,1,5]=>1101010=>0101011=>1010100
[6,5,3,8,2,7,1,4]=>1101010=>0101011=>1010100
[6,5,4,8,2,7,1,3]=>1101010=>0101011=>1010100
[7,4,3,8,2,6,1,5]=>1101010=>0101011=>1010100
[7,5,3,8,2,6,1,4]=>1101010=>0101011=>1010100
[7,5,4,8,2,6,1,3]=>1101010=>0101011=>1010100
[7,6,3,8,2,5,1,4]=>1101010=>0101011=>1010100
[7,6,4,8,2,5,1,3]=>1101010=>0101011=>1010100
[7,6,5,8,2,4,1,3]=>1101010=>0101011=>1010100
[8,4,3,7,2,6,1,5]=>1101010=>0101011=>1010100
[8,5,3,7,2,6,1,4]=>1101010=>0101011=>1010100
[8,6,3,7,2,5,1,4]=>1101010=>0101011=>1010100
[8,6,4,7,2,5,1,3]=>1101010=>0101011=>1010100
[8,6,5,7,2,4,1,3]=>1101010=>0101011=>1010100
[8,7,3,6,2,5,1,4]=>1101010=>0101011=>1010100
[8,7,4,6,3,5,1,2]=>1101010=>0101011=>1010100
[8,7,5,6,2,4,1,3]=>1101010=>0101011=>1010100
[6,5,4,3,2,8,1,7]=>1111010=>0101111=>1010000
[7,6,4,3,2,8,1,5]=>1111010=>0101111=>1010000
[8,5,4,3,2,7,1,6]=>1111010=>0101111=>1010000
[8,7,4,3,2,6,1,5]=>1111010=>0101111=>1010000
[8,7,5,3,2,6,1,4]=>1111010=>0101111=>1010000
[8,7,5,4,2,6,1,3]=>1111010=>0101111=>1010000
[8,7,6,3,2,5,1,4]=>1111010=>0101111=>1010000
[8,7,6,5,2,4,1,3]=>1111010=>0101111=>1010000
[8,1,2,3,7,4,5,6]=>1000100=>0010001=>1101110
[8,1,2,5,3,4,6,7]=>1001000=>0001001=>1110110
[6,1,2,5,3,8,4,7]=>1001010=>0101001=>1010110
[8,1,2,6,3,7,4,5]=>1001010=>0101001=>1010110
[4,1,2,8,7,3,5,6]=>1001100=>0011001=>1100110
[4,1,2,7,6,3,8,5]=>1001101=>1011001=>0100110
[8,1,2,5,6,3,4,7]=>1000100=>0010001=>1101110
[8,1,2,7,6,3,4,5]=>1001100=>0011001=>1100110
[7,1,2,5,6,3,8,4]=>1000101=>1010001=>0101110
[4,1,2,5,8,7,3,6]=>1000110=>0110001=>1001110
[8,1,2,5,6,7,3,4]=>1000010=>0100001=>1011110
[3,1,7,2,6,4,8,5]=>1010101=>1010101=>0101010
[3,1,5,2,8,7,4,6]=>1010110=>0110101=>1001010
[3,1,8,2,6,7,4,5]=>1010010=>0100101=>1011010
[8,1,4,2,3,5,6,7]=>1010000=>0000101=>1111010
[7,1,4,2,3,5,8,6]=>1010001=>1000101=>0111010
[6,1,4,2,3,8,5,7]=>1010010=>0100101=>1011010
[7,1,5,2,3,4,8,6]=>1010001=>1000101=>0111010
[6,1,5,2,3,8,4,7]=>1010010=>0100101=>1011010
[6,1,8,2,3,7,4,5]=>1010010=>0100101=>1011010
[6,1,5,2,3,7,8,4]=>1010001=>1000101=>0111010
[5,1,4,2,8,3,6,7]=>1010100=>0010101=>1101010
[5,1,4,2,7,3,8,6]=>1010101=>1010101=>0101010
[8,1,4,2,6,3,5,7]=>1010100=>0010101=>1101010
[7,1,4,2,6,3,8,5]=>1010101=>1010101=>0101010
[8,1,5,2,6,3,4,7]=>1010100=>0010101=>1101010
[8,1,5,2,7,3,4,6]=>1010100=>0010101=>1101010
[7,1,8,2,6,3,4,5]=>1010100=>0010101=>1101010
[7,1,5,2,6,3,8,4]=>1010101=>1010101=>0101010
[5,1,4,2,8,7,3,6]=>1010110=>0110101=>1001010
[8,1,4,2,6,7,3,5]=>1010010=>0100101=>1011010
[8,1,5,2,6,7,3,4]=>1010010=>0100101=>1011010
[5,1,4,2,6,7,8,3]=>1010001=>1000101=>0111010
[3,1,8,6,2,4,5,7]=>1011000=>0001101=>1110010
[3,1,6,5,2,8,4,7]=>1011010=>0101101=>1010010
[3,1,8,5,2,7,4,6]=>1011010=>0101101=>1010010
[3,1,8,6,2,7,4,5]=>1011010=>0101101=>1010010
[8,1,4,5,2,3,6,7]=>1001000=>0001001=>1110110
[7,1,8,5,2,3,4,6]=>1011000=>0001101=>1110010
[7,1,8,6,2,3,4,5]=>1011000=>0001101=>1110010
[7,1,6,5,2,3,8,4]=>1011001=>1001101=>0110010
[3,1,4,8,6,2,5,7]=>1001100=>0011001=>1100110
[3,1,8,5,7,2,4,6]=>1010100=>0010101=>1101010
[3,1,7,5,6,2,8,4]=>1010101=>1010101=>0101010
[8,1,4,5,7,2,3,6]=>1000100=>0010001=>1101110
[8,1,4,7,6,2,3,5]=>1001100=>0011001=>1100110
[3,1,4,5,8,7,2,6]=>1000110=>0110001=>1001110
[3,1,8,5,6,7,2,4]=>1010010=>0100101=>1011010
[8,1,4,5,6,7,2,3]=>1000010=>0100001=>1011110
[2,8,1,3,7,4,5,6]=>0100100=>0010010=>1101101
[2,8,1,3,6,7,4,5]=>0100010=>0100010=>1011101
[2,6,1,5,3,8,4,7]=>0101010=>0101010=>1010101
[2,6,1,5,3,7,8,4]=>0101001=>1001010=>0110101
[2,4,1,8,6,3,5,7]=>0101100=>0011010=>1100101
[2,8,1,5,7,3,4,6]=>0100100=>0010010=>1101101
[2,8,1,7,6,3,4,5]=>0101100=>0011010=>1100101
[2,4,1,5,8,7,3,6]=>0100110=>0110010=>1001101
[7,3,1,2,4,5,8,6]=>1100001=>1000011=>0111100
[6,3,1,2,4,8,5,7]=>1100010=>0100011=>1011100
[6,3,1,2,4,7,8,5]=>1100001=>1000011=>0111100
[5,3,1,2,8,4,6,7]=>1100100=>0010011=>1101100
[8,3,1,2,6,4,5,7]=>1100100=>0010011=>1101100
[8,3,1,2,7,4,5,6]=>1100100=>0010011=>1101100
[7,3,1,2,6,4,8,5]=>1100101=>1010011=>0101100
[5,3,1,2,8,7,4,6]=>1100110=>0110011=>1001100
[5,3,1,2,6,7,8,4]=>1100001=>1000011=>0111100
[8,4,1,2,3,7,5,6]=>1100010=>0100011=>1011100
[7,6,1,2,3,4,8,5]=>1100001=>1000011=>0111100
[8,6,1,2,3,7,4,5]=>1100010=>0100011=>1011100
[5,4,1,2,8,3,6,7]=>1100100=>0010011=>1101100
[8,4,1,2,7,3,5,6]=>1100100=>0010011=>1101100
[7,4,1,2,6,3,8,5]=>1100101=>1010011=>0101100
[5,8,1,2,7,3,4,6]=>0100100=>0010010=>1101101
[8,7,1,2,6,3,4,5]=>1100100=>0010011=>1101100
[5,7,1,2,6,3,8,4]=>0100101=>1010010=>0101101
[5,8,1,2,6,7,3,4]=>0100010=>0100010=>1011101
[5,4,1,2,6,7,8,3]=>1100001=>1000011=>0111100
[4,3,1,8,2,5,6,7]=>1101000=>0001011=>1110100
[4,3,1,7,2,5,8,6]=>1101001=>1001011=>0110100
[4,3,1,6,2,8,5,7]=>1101010=>0101011=>1010100
[4,3,1,6,2,7,8,5]=>1101001=>1001011=>0110100
[8,3,1,5,2,4,6,7]=>1101000=>0001011=>1110100
[8,3,1,6,2,4,5,7]=>1101000=>0001011=>1110100
[7,3,1,6,2,4,8,5]=>1101001=>1001011=>0110100
[8,3,1,5,2,7,4,6]=>1101010=>0101011=>1010100
[8,3,1,6,2,7,4,5]=>1101010=>0101011=>1010100
[6,3,1,5,2,7,8,4]=>1101001=>1001011=>0110100
[7,4,1,5,2,3,8,6]=>1101001=>1001011=>0110100
[8,4,1,6,2,3,5,7]=>1101000=>0001011=>1110100
[7,4,1,8,2,3,5,6]=>1101000=>0001011=>1110100
[7,4,1,6,2,3,8,5]=>1101001=>1001011=>0110100
[8,7,1,6,2,3,4,5]=>1101000=>0001011=>1110100
[6,7,1,5,2,3,8,4]=>0101001=>1001010=>0110101
[6,4,1,5,2,8,3,7]=>1101010=>0101011=>1010100
[8,4,1,6,2,7,3,5]=>1101010=>0101011=>1010100
[6,8,1,5,2,7,3,4]=>0101010=>0101010=>1010101
[6,4,1,5,2,7,8,3]=>1101001=>1001011=>0110100
[4,3,1,8,7,2,5,6]=>1101100=>0011011=>1100100
[4,3,1,7,6,2,8,5]=>1101101=>1011011=>0100100
[8,3,1,5,6,2,4,7]=>1100100=>0010011=>1101100
[8,3,1,5,7,2,4,6]=>1100100=>0010011=>1101100
[8,3,1,7,6,2,4,5]=>1101100=>0011011=>1100100
[7,3,1,5,6,2,8,4]=>1100101=>1010011=>0101100
[8,4,1,5,6,2,3,7]=>1100100=>0010011=>1101100
[7,8,1,5,6,2,3,4]=>0100100=>0010010=>1101101
[4,3,1,5,6,8,2,7]=>1100010=>0100011=>1011100
[8,4,1,5,6,7,2,3]=>1100010=>0100011=>1011100
[4,3,1,5,6,7,8,2]=>1100001=>1000011=>0111100
[2,3,7,1,6,4,8,5]=>0010101=>1010100=>0101011
[2,3,5,1,8,7,4,6]=>0010110=>0110100=>1001011
[2,3,8,1,6,7,4,5]=>0010010=>0100100=>1011011
[2,8,4,1,3,5,6,7]=>0110000=>0000110=>1111001
[2,6,4,1,3,8,5,7]=>0110010=>0100110=>1011001
[2,6,4,1,3,7,8,5]=>0110001=>1000110=>0111001
[2,8,4,1,7,3,5,6]=>0110100=>0010110=>1101001
[2,7,4,1,6,3,8,5]=>0110101=>1010110=>0101001
[2,8,5,1,7,3,4,6]=>0110100=>0010110=>1101001
[2,7,5,1,6,3,8,4]=>0110101=>1010110=>0101001
[2,8,4,1,6,7,3,5]=>0110010=>0100110=>1011001
[2,5,4,1,6,7,8,3]=>0110001=>1000110=>0111001
[6,3,4,1,2,7,8,5]=>1010001=>1000101=>0111010
[7,3,5,1,2,4,8,6]=>1010001=>1000101=>0111010
[6,3,7,1,2,4,8,5]=>1010001=>1000101=>0111010
[8,3,5,1,2,7,4,6]=>1010010=>0100101=>1011010
[6,3,8,1,2,7,4,5]=>1010010=>0100101=>1011010
[6,7,4,1,2,3,8,5]=>0110001=>1000110=>0111001
[6,8,5,1,2,3,4,7]=>0110000=>0000110=>1111001
[8,5,4,1,2,7,3,6]=>1110010=>0100111=>1011000
[6,8,4,1,2,7,3,5]=>0110010=>0100110=>1011001
[6,8,5,1,2,7,3,4]=>0110010=>0100110=>1011001
[8,3,4,1,7,2,5,6]=>1010100=>0010101=>1101010
[7,3,4,1,6,2,8,5]=>1010101=>1010101=>0101010
[8,3,5,1,6,2,4,7]=>1010100=>0010101=>1101010
[7,3,8,1,6,2,4,5]=>1010100=>0010101=>1101010
[7,3,5,1,6,2,8,4]=>1010101=>1010101=>0101010
[8,5,4,1,6,2,3,7]=>1110100=>0010111=>1101000
[7,8,4,1,6,2,3,5]=>0110100=>0010110=>1101001
[7,8,5,1,6,2,3,4]=>0110100=>0010110=>1101001
[7,5,4,1,6,2,8,3]=>1110101=>1010111=>0101000
[5,3,4,1,6,7,8,2]=>1010001=>1000101=>0111010
[2,3,4,8,1,7,5,6]=>0001010=>0101000=>1010111
[2,3,7,6,1,4,8,5]=>0011001=>1001100=>0110011
[2,3,6,5,1,8,4,7]=>0011010=>0101100=>1010011
[2,3,6,5,1,7,8,4]=>0011001=>1001100=>0110011
[2,8,4,5,1,3,6,7]=>0101000=>0001010=>1110101
[2,7,4,8,1,3,5,6]=>0101000=>0001010=>1110101
[2,7,4,6,1,3,8,5]=>0101001=>1001010=>0110101
[2,8,6,5,1,3,4,7]=>0111000=>0001110=>1110001
[2,7,8,5,1,3,4,6]=>0011000=>0001100=>1110011
[2,7,6,5,1,3,8,4]=>0111001=>1001110=>0110001
[2,6,4,5,1,8,3,7]=>0101010=>0101010=>1010101
[2,8,4,6,1,7,3,5]=>0101010=>0101010=>1010101
[7,3,8,5,1,2,4,6]=>1011000=>0001101=>1110010
[8,6,4,5,1,7,2,3]=>1101010=>0101011=>1010100
[2,3,4,8,6,1,5,7]=>0001100=>0011000=>1100111
[2,3,4,8,7,1,5,6]=>0001100=>0011000=>1100111
[2,3,4,7,6,1,8,5]=>0001101=>1011000=>0100111
[2,3,8,5,7,1,4,6]=>0010100=>0010100=>1101011
[2,3,7,5,6,1,8,4]=>0010101=>1010100=>0101011
[2,8,4,7,6,1,3,5]=>0101100=>0011010=>1100101
[2,8,7,5,6,1,3,4]=>0110100=>0010110=>1101001
[8,3,4,7,6,1,2,5]=>1001100=>0011001=>1100110
[8,3,7,5,6,1,2,4]=>1010100=>0010101=>1101010
[2,3,4,5,8,7,1,6]=>0000110=>0110000=>1001111
[2,3,4,8,6,7,1,5]=>0001010=>0101000=>1010111
[2,8,4,5,6,7,1,3]=>0100010=>0100010=>1011101
[6,5,8,7,3,4,1,2]=>1011010=>0101101=>1010010
[4,6,7,3,8,5,1,2]=>0010110=>0110100=>1001011
[3,6,7,4,5,8,1,2]=>0010010=>0100100=>1011011
[2,6,7,4,5,1,8,3]=>0010101=>1010100=>0101011
[1,6,7,4,5,2,3,8]=>0010100=>0010100=>1101011
[1,5,4,7,6,2,3,8]=>0101100=>0011010=>1100101
[2,5,4,7,6,1,8,3]=>0101101=>1011010=>0100101
[3,5,4,7,6,8,1,2]=>0101010=>0101010=>1010101
[4,5,3,7,8,6,1,2]=>0100110=>0110010=>1001101
[5,4,3,8,7,6,1,2]=>1101110=>0111011=>1000100
[6,4,8,3,7,5,1,2]=>1010110=>0110101=>1001010
[6,3,8,4,5,7,1,2]=>1010010=>0100101=>1011010
[5,3,4,8,6,7,1,2]=>1001010=>0101001=>1010110
[4,3,5,6,8,7,1,2]=>1000110=>0110001=>1001110
[3,2,5,6,1,8,7,4]=>1001011=>1101001=>0010110
[4,2,5,6,8,1,7,3]=>1000101=>1010001=>0101110
[5,2,4,8,6,1,7,3]=>1001101=>1011001=>0100110
[6,2,8,4,5,1,7,3]=>1010101=>1010101=>0101010
[7,8,2,4,5,1,6,3]=>0100101=>1010010=>0101101
[7,8,1,4,5,2,3,6]=>0100100=>0010010=>1101101
[6,1,8,4,5,2,3,7]=>1010100=>0010101=>1101010
[5,1,4,8,6,2,3,7]=>1001100=>0011001=>1100110
[4,1,3,2,8,6,5,7]=>1010110=>0110101=>1001010
[5,1,3,8,2,6,4,7]=>1001010=>0101001=>1010110
[6,1,8,3,2,5,4,7]=>1011010=>0101101=>1010010
[7,8,1,3,2,5,4,6]=>0101010=>0101010=>1010101
[7,8,2,3,1,5,6,4]=>0101001=>1001010=>0110101
[6,2,8,3,1,5,7,4]=>1011001=>1001101=>0110010
[5,2,3,8,1,6,7,4]=>1001001=>1001001=>0110110
[6,3,8,2,1,7,5,4]=>1011011=>1101101=>0010010
[7,8,3,2,1,6,5,4]=>0111011=>1101110=>0010001
[7,8,4,2,6,1,5,3]=>0110101=>1010110=>0101001
[5,4,2,8,7,1,6,3]=>1101101=>1011011=>0100100
[4,5,2,7,8,1,6,3]=>0100101=>1010010=>0101101
[3,5,2,7,1,8,6,4]=>0101011=>1101010=>0010101
[2,5,3,7,1,6,8,4]=>0101001=>1001010=>0110101
[1,5,3,7,2,6,4,8]=>0101010=>0101010=>1010101
[1,6,7,3,2,5,4,8]=>0011010=>0101100=>1010011
[2,6,7,3,1,5,8,4]=>0011001=>1001100=>0110011
[3,6,7,2,1,8,5,4]=>0011011=>1101100=>0010011
[4,6,7,2,8,1,5,3]=>0010101=>1010100=>0101011
[5,6,7,8,2,1,4,3]=>0001101=>1011000=>0100111
[7,8,5,6,2,1,4,3]=>0101101=>1011010=>0100101
[6,5,8,7,1,2,3,4]=>1011000=>0001101=>1110010
[5,4,1,8,7,2,3,6]=>1101100=>0011011=>1100100
[6,4,8,1,7,2,3,5]=>1010100=>0010101=>1101010
[7,8,3,1,2,6,4,5]=>0110010=>0100110=>1011001
[5,3,1,8,2,7,4,6]=>1101010=>0101011=>1010100
[4,3,1,2,8,7,5,6]=>1100110=>0110011=>1001100
[4,2,1,3,8,5,7,6]=>1100101=>1010011=>0101100
[5,2,1,8,3,4,7,6]=>1101001=>1001011=>0110100
[6,2,8,1,3,4,7,5]=>1010001=>1000101=>0111010
[7,8,2,1,3,4,6,5]=>0110001=>1000110=>0111001
[4,5,2,3,7,6,1,8]=>0100110=>0110010=>1001101
[6,4,3,7,2,5,1,8]=>1101010=>0101011=>1010100
[8,4,3,6,5,1,2,7]=>1101100=>0011011=>1100100
[1,5,6,3,4,8,7,2]=>0010011=>1100100=>0011011
[4,6,2,7,3,5,1,8]=>0101010=>0101010=>1010101
[3,2,6,7,4,5,1,8]=>1001010=>0101001=>1010110
[8,7,5,4,1,3,2,6]=>1111010=>0101111=>1010000
[5,8,6,2,4,1,3,7]=>0110100=>0010110=>1101001
[4,8,2,6,5,1,3,7]=>0101100=>0011010=>1100101
[4,1,2,6,5,8,7,3]=>1001011=>1101001=>0010110
[5,1,6,2,4,8,7,3]=>1010011=>1100101=>0011010
[6,1,5,4,2,8,7,3]=>1011011=>1101101=>0010010
[7,1,5,4,8,2,6,3]=>1010101=>1010101=>0101010
[8,1,5,4,7,6,2,3]=>1010110=>0110101=>1001010
[1,8,6,7,4,5,3,2]=>0101011=>1101010=>0010101
[8,1,6,7,4,5,2,3]=>1001010=>0101001=>1010110
[6,1,7,8,2,4,5,3]=>1001001=>1001001=>0110110
[5,1,7,2,8,4,6,3]=>1010101=>1010101=>0101010
[4,1,2,7,8,5,6,3]=>1000101=>1010001=>0101110
[3,2,1,7,8,5,6,4]=>1100101=>1010011=>0101100
[3,2,8,7,1,5,4,6]=>1011010=>0101101=>1010010
[4,8,2,7,1,5,3,6]=>0101010=>0101010=>1010101
[5,8,7,2,1,4,3,6]=>0111010=>0101110=>1010001
[6,8,7,1,2,4,3,5]=>0110010=>0100110=>1011001
[7,8,6,1,4,2,3,5]=>0110100=>0010110=>1101001
[8,7,6,1,4,3,2,5]=>1110110=>0110111=>1001000
[1,6,7,8,3,4,5,2]=>0001001=>1001000=>0110111
[8,6,7,1,3,4,2,5]=>1010010=>0100101=>1011010
[7,6,8,1,3,2,4,5]=>1010100=>0010101=>1101010
[5,7,8,2,1,3,4,6]=>0011000=>0001100=>1110011
[4,7,2,8,1,3,5,6]=>0101000=>0001010=>1110101
[3,2,6,8,4,1,5,7]=>1001100=>0011001=>1100110
[4,6,2,8,3,1,5,7]=>0101100=>0011010=>1100101
[5,6,8,2,3,1,4,7]=>0010100=>0010100=>1101011
[7,5,8,3,1,2,4,6]=>1011000=>0001101=>1110010
[8,5,7,3,1,4,2,6]=>1011010=>0101101=>1010010
[1,5,7,3,8,4,6,2]=>0010101=>1010100=>0101011
[1,4,3,7,8,5,6,2]=>0100101=>1010010=>0101101
[6,4,3,8,2,1,5,7]=>1101100=>0011011=>1100100
[4,5,2,3,8,1,6,7]=>0100100=>0010010=>1101101
[3,2,5,4,8,1,6,7]=>1010100=>0010101=>1101010
[4,5,2,3,1,8,7,6]=>0101011=>1101010=>0010101
[6,4,3,1,2,8,7,5]=>1110011=>1100111=>0011000
[7,4,3,1,8,2,6,5]=>1110101=>1010111=>0101000
[1,5,8,3,7,6,4,2]=>0010111=>1110100=>0001011
[7,5,1,3,8,2,6,4]=>1100101=>1010011=>0101100
[5,6,1,2,3,8,7,4]=>0100011=>1100010=>0011101
[4,6,2,1,3,8,7,5]=>0110011=>1100110=>0011001
[3,2,6,1,4,8,7,5]=>1010011=>1100101=>0011010
[3,2,7,1,8,4,6,5]=>1010101=>1010101=>0101010
[5,7,1,2,8,3,6,4]=>0100101=>1010010=>0101101
[6,7,1,8,2,3,5,4]=>0101001=>1001010=>0110101
[7,6,1,8,3,2,5,4]=>1101101=>1011011=>0100100
[8,7,1,6,5,3,2,4]=>1101110=>0111011=>1000100
[7,8,1,6,5,2,3,4]=>0101100=>0011010=>1100101
[6,8,1,7,2,5,3,4]=>0101010=>0101010=>1010101
[5,8,1,2,7,6,3,4]=>0100110=>0110010=>1001101
[4,8,2,1,7,6,3,5]=>0110110=>0110110=>1001001
[3,2,8,1,7,6,4,5]=>1010110=>0110101=>1001010
[4,1,2,8,7,6,5,3]=>1001111=>1111001=>0000110
[5,1,8,2,7,6,4,3]=>1010111=>1110101=>0001010
[6,1,8,7,2,5,4,3]=>1011011=>1101101=>0010010
[8,1,7,6,5,4,2,3]=>1011110=>0111101=>1000010
[3,2,5,1,6,4,8,7]=>1010101=>1010101=>0101010
[3,2,5,4,7,1,8,6]=>1010101=>1010101=>0101010
[4,2,5,3,7,6,8,1]=>1010101=>1010101=>0101010
[4,2,5,3,6,1,8,7]=>1010101=>1010101=>0101010
[4,1,5,3,6,2,8,7]=>1010101=>1010101=>0101010
[4,3,5,2,7,1,8,6]=>1010101=>1010101=>0101010
[4,3,5,1,7,2,8,6]=>1010101=>1010101=>0101010
[4,1,5,3,7,2,8,6]=>1010101=>1010101=>0101010
[2,1,5,4,7,3,8,6]=>1010101=>1010101=>0101010
[4,3,6,5,7,1,8,2]=>1010101=>1010101=>0101010
[5,3,6,4,7,1,8,2]=>1010101=>1010101=>0101010
[4,1,6,3,7,5,8,2]=>1010101=>1010101=>0101010
[2,1,6,4,7,5,8,3]=>1010101=>1010101=>0101010
[2,1,6,4,7,3,8,5]=>1010101=>1010101=>0101010
[3,1,6,4,7,2,8,5]=>1010101=>1010101=>0101010
[4,1,6,3,7,2,8,5]=>1010101=>1010101=>0101010
[5,3,6,2,7,4,8,1]=>1010101=>1010101=>0101010
[5,2,6,3,7,4,8,1]=>1010101=>1010101=>0101010
[5,2,6,3,7,1,8,4]=>1010101=>1010101=>0101010
[5,2,6,1,7,3,8,4]=>1010101=>1010101=>0101010
[4,2,6,1,7,3,8,5]=>1010101=>1010101=>0101010
[4,2,6,3,7,1,8,5]=>1010101=>1010101=>0101010
[4,2,6,3,7,5,8,1]=>1010101=>1010101=>0101010
[3,2,6,4,7,5,8,1]=>1010101=>1010101=>0101010
[3,2,6,4,7,1,8,5]=>1010101=>1010101=>0101010
[3,2,6,1,7,4,8,5]=>1010101=>1010101=>0101010
[3,2,5,1,7,4,8,6]=>1010101=>1010101=>0101010
[3,2,4,1,7,5,8,6]=>1010101=>1010101=>0101010
[3,1,4,2,7,6,8,5]=>1010101=>1010101=>0101010
[3,2,5,1,7,6,8,4]=>1010101=>1010101=>0101010
[3,2,6,1,7,5,8,4]=>1010101=>1010101=>0101010
[4,2,6,1,7,5,8,3]=>1010101=>1010101=>0101010
[3,1,5,2,7,6,8,4]=>1010101=>1010101=>0101010
[2,1,5,3,7,6,8,4]=>1010101=>1010101=>0101010
[2,1,6,3,7,5,8,4]=>1010101=>1010101=>0101010
[3,1,6,2,7,5,8,4]=>1010101=>1010101=>0101010
[4,1,6,2,7,5,8,3]=>1010101=>1010101=>0101010
[5,1,6,2,7,4,8,3]=>1010101=>1010101=>0101010
[5,2,6,1,7,4,8,3]=>1010101=>1010101=>0101010
[5,4,6,2,7,1,8,3]=>1010101=>1010101=>0101010
[5,1,6,4,7,2,8,3]=>1010101=>1010101=>0101010
[3,1,6,5,7,2,8,4]=>1010101=>1010101=>0101010
[3,1,6,5,7,4,8,2]=>1010101=>1010101=>0101010
[4,1,6,5,7,3,8,2]=>1010101=>1010101=>0101010
[5,1,6,4,7,3,8,2]=>1010101=>1010101=>0101010
[8,6,1,3,4,2,5,7]=>1100100=>0010011=>1101100
[8,3,5,2,1,6,4,7]=>1011010=>0101101=>1010010
[8,6,3,5,2,4,1,7]=>1101010=>0101011=>1010100
[8,3,7,5,2,4,6,1]=>1011001=>1001101=>0110010
[8,2,4,5,7,3,6,1]=>1000101=>1010001=>0101110
[2,4,5,7,3,1,8,6]=>0001101=>1011000=>0100111
[8,2,4,6,5,3,1,7]=>1001110=>0111001=>1000110
[8,1,2,4,5,6,3,7]=>1000010=>0100001=>1011110
[8,2,5,1,3,6,4,7]=>1010010=>0100101=>1011010
[8,6,1,4,5,3,2,7]=>1100110=>0110011=>1001100
[8,1,5,6,4,3,2,7]=>1001110=>0111001=>1000110
[8,5,7,4,3,2,6,1]=>1011101=>1011101=>0100010
[8,5,7,4,2,1,6,3]=>1011101=>1011101=>0100010
[4,6,3,8,7,1,5,2]=>0101101=>1011010=>0100101
[1,7,4,8,6,3,5,2]=>0101101=>1011010=>0100101
[8,4,7,6,3,5,2,1]=>1011011=>1101101=>0010010
[3,1,5,8,6,7,4,2]=>1001011=>1101001=>0010110
[4,8,1,6,7,3,5,2]=>0100101=>1010010=>0101101
[3,6,4,1,8,7,5,2]=>0110111=>1110110=>0001001
[8,2,6,1,4,7,5,3]=>1010011=>1100101=>0011010
[2,7,6,8,1,4,3,5]=>0101010=>0101010=>1010101
[1,7,3,5,6,8,2,4]=>0100010=>0100010=>1011101
[3,7,6,5,8,2,1,4]=>0110110=>0110110=>1001001
[3,6,8,5,7,2,4,1]=>0010101=>1010100=>0101011
[2,3,5,7,6,8,1,4]=>0001010=>0101000=>1010111
[2,1,6,5,7,8,3,4]=>1010010=>0100101=>1011010
[5,2,7,1,3,8,4,6]=>1010010=>0100101=>1011010
[5,3,1,7,8,2,4,6]=>1100100=>0010011=>1101100
[3,7,2,6,4,8,1,5]=>0101010=>0101010=>1010101
[3,2,6,1,4,7,8,5]=>1010001=>1000101=>0111010
[5,3,7,2,1,8,4,6]=>1011010=>0101101=>1010010
[4,7,3,2,1,5,8,6]=>0111001=>1001110=>0110001
[1,7,3,4,2,5,8,6]=>0101001=>1001010=>0110101
[4,7,2,1,3,5,8,6]=>0110001=>1000110=>0111001
[8,7,6,1,3,4,2,5]=>1110010=>0100111=>1011000
[8,5,7,3,2,1,6,4]=>1011101=>1011101=>0100010
[3,7,8,6,2,1,5,4]=>0011101=>1011100=>0100011
[8,7,6,3,5,2,4,1]=>1110101=>1010111=>0101000
[2,7,4,8,1,6,5,3]=>0101011=>1101010=>0010101
[4,6,8,2,1,7,5,3]=>0011011=>1101100=>0010011
[8,5,3,7,1,6,2,4]=>1101010=>0101011=>1010100
[8,5,7,2,1,3,6,4]=>1011001=>1001101=>0110010
[4,6,1,8,7,2,5,3]=>0101101=>1011010=>0100101
[8,1,2,5,6,7,4,3]=>1000011=>1100001=>0011110
[8,2,6,5,7,4,1,3]=>1010110=>0110101=>1001010
[2,1,7,8,5,6,4,3]=>1001011=>1101001=>0010110
[2,7,6,8,5,4,1,3]=>0101110=>0111010=>1000101
[3,7,8,1,6,5,2,4]=>0010110=>0110100=>1001011
[8,7,6,3,5,1,4,2]=>1110101=>1010111=>0101000
[8,4,7,6,5,1,3,2]=>1011101=>1011101=>0100010
[8,7,1,5,6,4,3,2]=>1100111=>1110011=>0001100
[8,1,6,7,5,4,3,2]=>1001111=>1111001=>0000110
[3,2,5,1,6,8,4,7]=>1010010=>0100101=>1011010
[3,6,2,5,4,8,1,7]=>0101010=>0101010=>1010101
[3,5,2,4,7,1,8,6]=>0100101=>1010010=>0101101
[3,5,8,2,4,7,6,1]=>0010011=>1100100=>0011011
[4,2,6,5,3,8,1,7]=>1011010=>0101101=>1010010
[5,3,1,6,8,2,4,7]=>1100100=>0010011=>1101100
[5,6,2,8,1,3,4,7]=>0101000=>0001010=>1110101
[5,4,3,2,7,1,8,6]=>1110101=>1010111=>0101000
[5,4,3,8,2,7,6,1]=>1101011=>1101011=>0010100
[4,3,7,6,2,1,8,5]=>1011101=>1011101=>0100010
[6,4,3,1,7,2,8,5]=>1110101=>1010111=>0101000
[1,4,7,5,8,3,2,6]=>0010110=>0110100=>1001011
[7,2,5,8,4,1,3,6]=>1001100=>0011001=>1100110
[2,8,5,7,4,6,1,3]=>0101010=>0101010=>1010101
[3,5,8,7,1,4,6,2]=>0011001=>1001100=>0110011
[4,3,7,1,8,6,5,2]=>1010111=>1110101=>0001010
[4,8,3,7,6,5,2,1]=>0101111=>1111010=>0000101
[7,5,3,1,8,6,4,2]=>1110111=>1110111=>0001000
[1,5,8,6,3,7,4,2]=>0011011=>1101100=>0010011
[6,2,8,7,4,5,1,3]=>1011010=>0101101=>1010010
[6,1,7,5,3,2,8,4]=>1011101=>1011101=>0100010
[5,2,6,3,8,7,4,1]=>1010111=>1110101=>0001010
[6,5,2,1,7,3,8,4]=>1110101=>1010111=>0101000
[6,1,7,4,2,8,3,5]=>1011010=>0101101=>1010010
[6,7,2,1,8,3,4,5]=>0110100=>0010110=>1101001
[7,5,8,2,1,3,4,6]=>1011000=>0001101=>1110010
[5,7,3,1,8,2,4,6]=>0110100=>0010110=>1101001
[4,7,1,5,2,8,3,6]=>0101010=>0101010=>1010101
[2,4,8,6,3,7,5,1]=>0011011=>1101100=>0010011
[3,8,6,2,4,7,5,1]=>0110011=>1100110=>0011001
[7,3,6,2,4,1,8,5]=>1010101=>1010101=>0101010
[3,5,2,7,1,8,4,6]=>0101010=>0101010=>1010101
[4,3,7,8,2,1,5,6]=>1001100=>0011001=>1100110
[8,3,7,1,4,6,2,5]=>1010010=>0100101=>1011010
[3,8,2,5,7,1,6,4]=>0100101=>1010010=>0101101
[7,8,3,6,2,1,5,4]=>0101101=>1011010=>0100101
[8,7,3,6,2,5,4,1]=>1101011=>1101011=>0010100
[4,2,6,8,1,7,5,3]=>1001011=>1101001=>0010110
[5,4,8,2,7,1,6,3]=>1010101=>1010101=>0101010
[5,8,3,7,1,6,2,4]=>0101010=>0101010=>1010101
[5,8,7,2,6,1,3,4]=>0110100=>0010110=>1101001
[6,4,8,1,7,2,5,3]=>1010101=>1010101=>0101010
[5,1,6,8,2,7,4,3]=>1001011=>1101001=>0010110
[6,5,2,8,1,7,4,3]=>1101011=>1101011=>0010100
[5,2,7,1,8,6,4,3]=>1010111=>1110101=>0001010
[5,8,2,7,6,4,3,1]=>0101111=>1111010=>0000101
[6,2,8,7,5,4,3,1]=>1011111=>1111101=>0000010
[6,1,7,2,8,5,4,3]=>1010111=>1110101=>0001010
[4,7,1,8,6,2,5,3]=>0101101=>1011010=>0100101
[7,8,3,1,6,5,2,4]=>0110110=>0110110=>1001001
[8,7,4,6,1,5,3,2]=>1101011=>1101011=>0010100
[8,5,7,1,6,4,3,2]=>1010111=>1110101=>0001010
[6,8,1,7,5,4,3,2]=>0101111=>1111010=>0000101
[7,1,8,6,5,4,3,2]=>1011111=>1111101=>0000010
[4,1,3,2,6,5,8,7]=>1010101=>1010101=>0101010
[6,3,5,1,2,4,8,7]=>1010001=>1000101=>0111010
[4,3,5,6,1,2,8,7]=>1001001=>1001001=>0110110
[8,3,7,5,2,1,4,6]=>1011100=>0011101=>1100010
[6,3,7,5,1,8,4,2]=>1011011=>1101101=>0010010
[6,5,2,7,1,8,3,4]=>1101010=>0101011=>1010100
[3,5,2,6,4,1,8,7]=>0101101=>1011010=>0100101
[6,1,2,4,5,3,8,7]=>1000101=>1010001=>0101110
[5,6,3,2,1,4,8,7]=>0111001=>1001110=>0110001
[2,1,6,3,5,4,8,7]=>1010101=>1010101=>0101010
[6,4,3,5,1,2,8,7]=>1101001=>1001011=>0110100
[5,3,1,4,6,2,8,7]=>1100101=>1010011=>0101100
[5,7,4,6,2,8,3,1]=>0101011=>1101010=>0010101
[3,4,7,8,5,2,1,6]=>0001110=>0111000=>1000111
[2,1,8,5,7,3,4,6]=>1010100=>0010101=>1101010
[8,6,3,5,1,7,4,2]=>1101011=>1101011=>0010100
[3,4,8,6,5,7,1,2]=>0011010=>0101100=>1010011
[5,1,4,6,8,2,7,3]=>1000101=>1010001=>0101110
[2,5,4,6,7,1,8,3]=>0100101=>1010010=>0101101
[2,4,6,3,7,5,8,1]=>0010101=>1010100=>0101011
[4,1,6,3,8,5,7,2]=>1010101=>1010101=>0101010
[3,7,4,2,8,6,5,1]=>0110111=>1110110=>0001001
[8,5,3,7,4,1,6,2]=>1101101=>1011011=>0100100
[2,1,5,7,4,8,6,3]=>1001011=>1101001=>0010110
[3,1,8,2,7,6,5,4]=>1010111=>1110101=>0001010
[2,3,8,1,6,7,5,4]=>0010011=>1100100=>0011011
[4,3,7,2,6,8,5,1]=>1010011=>1100101=>0011010
[2,8,1,3,6,5,7,4]=>0100101=>1010010=>0101101
[8,1,2,3,5,6,7,4]=>1000001=>1000001=>0111110
[7,8,2,4,3,6,1,5]=>0101010=>0101010=>1010101
[6,8,3,2,4,1,7,5]=>0110101=>1010110=>0101001
[2,1,8,3,4,6,7,5]=>1010001=>1000101=>0111010
[2,1,7,8,5,4,3,6]=>1001110=>0111001=>1000110
[5,7,3,8,1,4,2,6]=>0101010=>0101010=>1010101
[7,1,8,4,5,3,2,6]=>1010110=>0110101=>1001010
[8,7,1,6,3,4,2,5]=>1101010=>0101011=>1010100
[5,3,8,7,4,2,6,1]=>1011101=>1011101=>0100010
[8,3,6,1,4,2,7,5]=>1010101=>1010101=>0101010
[7,3,5,8,2,4,1,6]=>1001010=>0101001=>1010110
[2,3,4,1,8,5,7,6]=>0010101=>1010100=>0101011
[4,1,3,2,8,5,7,6]=>1010101=>1010101=>0101010
[2,1,4,3,8,5,7,6]=>1010101=>1010101=>0101010
[4,1,3,2,6,7,8,5]=>1010001=>1000101=>0111010
[8,3,5,6,2,7,1,4]=>1001010=>0101001=>1010110
[5,3,6,1,8,7,2,4]=>1010110=>0110101=>1001010
[5,6,2,8,7,4,1,3]=>0101110=>0111010=>1000101
[7,8,5,6,1,4,2,3]=>0101010=>0101010=>1010101
[8,1,6,4,5,7,2,3]=>1010010=>0100101=>1011010
[5,8,3,6,1,7,2,4]=>0101010=>0101010=>1010101
[2,1,8,6,5,7,3,4]=>1011010=>0101101=>1010010
[2,1,7,5,3,6,8,4]=>1011001=>1001101=>0110010
[7,1,4,2,5,6,8,3]=>1010001=>1000101=>0111010
[2,7,4,1,6,5,8,3]=>0110101=>1010110=>0101001
[7,3,5,4,6,1,8,2]=>1010101=>1010101=>0101010
[6,3,4,1,5,7,8,2]=>1010001=>1000101=>0111010
[3,1,4,5,6,8,7,2]=>1000011=>1100001=>0011110
[4,5,2,6,3,1,8,7]=>0101101=>1011010=>0100101
[6,5,2,1,4,3,8,7]=>1110101=>1010111=>0101000
[6,5,2,7,4,8,3,1]=>1101011=>1101011=>0010100
[8,5,2,7,4,1,6,3]=>1101101=>1011011=>0100100
[8,3,7,5,2,1,6,4]=>1011101=>1011101=>0100010
[6,3,7,5,2,8,4,1]=>1011011=>1101101=>0010010
[6,3,1,5,2,4,8,7]=>1101001=>1001011=>0110100
[3,1,6,5,4,2,8,7]=>1011101=>1011101=>0100010
[5,4,3,6,1,2,8,7]=>1101001=>1001011=>0110100
[5,6,3,2,4,1,8,7]=>0110101=>1010110=>0101001
[6,7,2,3,4,8,5,1]=>0100011=>1100010=>0011101
[8,7,2,3,4,1,6,5]=>1100101=>1010011=>0101100
[5,1,7,3,8,4,6,2]=>1010101=>1010101=>0101010
[2,5,7,3,8,6,4,1]=>0010111=>1110100=>0001011
[3,6,7,4,1,8,5,2]=>0011011=>1101100=>0010011
[5,6,3,7,4,8,1,2]=>0101010=>0101010=>1010101
[2,1,6,7,4,8,5,3]=>1001011=>1101001=>0010110
[2,1,8,7,4,3,6,5]=>1011101=>1011101=>0100010
[5,8,3,7,4,2,6,1]=>0101101=>1011010=>0100101
[7,8,1,3,5,2,6,4]=>0100101=>1010010=>0101101
[5,8,7,3,2,6,1,4]=>0111010=>0101110=>1010001
[2,8,6,3,1,5,7,4]=>0111001=>1001110=>0110001
[8,1,6,3,2,5,4,7]=>1011010=>0101101=>1010010
[2,8,4,1,6,3,7,5]=>0110101=>1010110=>0101001
[4,8,1,2,7,6,3,5]=>0100110=>0110010=>1001101
[6,8,3,5,2,7,4,1]=>0101011=>1101010=>0010101
[2,1,8,5,3,7,4,6]=>1011010=>0101101=>1010010
[6,5,3,2,8,7,1,4]=>1110110=>0110111=>1001000
[2,4,1,8,7,6,5,3]=>0101111=>1111010=>0000101
[4,1,2,8,7,5,6,3]=>1001101=>1011001=>0100110
[8,4,2,1,7,5,3,6]=>1110110=>0110111=>1001000
[4,3,1,8,6,7,5,2]=>1101011=>1101011=>0010100
[3,1,4,8,6,5,7,2]=>1001101=>1011001=>0100110
[7,3,5,4,8,6,1,2]=>1010110=>0110101=>1001010
[6,4,3,5,8,1,7,2]=>1100101=>1010011=>0101100
[2,1,7,6,5,8,3,4]=>1011010=>0101101=>1010010
[5,7,3,6,1,8,2,4]=>0101010=>0101010=>1010101
[2,7,6,4,5,8,1,3]=>0110010=>0100110=>1011001
[3,7,5,6,8,4,2,1]=>0100111=>1110010=>0001101
[5,7,1,6,8,2,4,3]=>0100101=>1010010=>0101101
[8,6,2,5,1,7,4,3]=>1101011=>1101011=>0010100
[7,5,2,6,3,8,1,4]=>1101010=>0101011=>1010100
[4,1,2,3,6,8,7,5]=>1000011=>1100001=>0011110
[2,4,3,1,8,5,6,7]=>0110100=>0010110=>1101001
[7,5,2,8,3,4,6,1]=>1101001=>1001011=>0110100
[4,7,2,8,1,5,3,6]=>0101010=>0101010=>1010101
[8,7,2,1,4,5,6,3]=>1110001=>1000111=>0111000
[3,6,8,7,1,5,4,2]=>0011011=>1101100=>0010011
[5,7,8,6,3,4,1,2]=>0011010=>0101100=>1010011
[5,7,3,8,1,4,6,2]=>0101001=>1001010=>0110101
[2,1,7,8,5,4,6,3]=>1001101=>1011001=>0100110
[7,5,8,4,3,6,2,1]=>1011011=>1101101=>0010010
[2,4,8,3,5,6,1,7]=>0010010=>0100100=>1011011
[4,1,8,3,6,5,2,7]=>1010110=>0110101=>1001010
[8,4,1,3,7,2,6,5]=>1100101=>1010011=>0101100
[4,3,8,2,5,1,7,6]=>1010101=>1010101=>0101010
[2,1,4,8,3,5,7,6]=>1001001=>1001001=>0110110
[6,8,2,4,3,5,1,7]=>0101010=>0101010=>1010101
[4,8,2,3,5,1,6,7]=>0100100=>0010010=>1101101
[7,8,5,6,1,4,3,2]=>0101011=>1101010=>0010101
[7,8,4,2,1,5,3,6]=>0111010=>0101110=>1010001
[7,8,2,1,6,5,3,4]=>0110110=>0110110=>1001001
[6,4,1,2,5,7,3,8]=>1100010=>0100011=>1011100
[4,3,8,1,7,2,5,6]=>1010100=>0010101=>1101010
[7,8,1,4,6,2,5,3]=>0100101=>1010010=>0101101
[7,8,3,5,4,2,1,6]=>0101110=>0111010=>1000101
[7,8,4,1,2,3,6,5]=>0110001=>1000110=>0111001
[7,8,3,6,5,4,1,2]=>0101110=>0111010=>1000101
[7,8,2,6,4,1,3,5]=>0101100=>0011010=>1100101
[7,8,1,6,5,4,3,2]=>0101111=>1111010=>0000101
[2,1,8,7,5,4,3,6]=>1011110=>0111101=>1000010
[1,3,8,2,6,4,7,5]=>0010101=>1010100=>0101011
[5,3,7,1,6,4,8,2]=>1010101=>1010101=>0101010
[6,1,2,5,8,7,4,3]=>1000111=>1110001=>0001110
[6,3,1,8,4,2,7,5]=>1101101=>1011011=>0100100
[6,4,2,1,5,3,8,7]=>1110101=>1010111=>0101000
[6,4,3,7,5,8,1,2]=>1101010=>0101011=>1010100
[4,3,8,7,5,6,1,2]=>1011010=>0101101=>1010010
[2,4,7,1,5,3,6,8]=>0010100=>0010100=>1101011
[3,7,2,8,6,4,1,5]=>0101110=>0111010=>1000101
[3,8,1,7,6,4,5,2]=>0101101=>1011010=>0100101
[1,8,5,7,3,6,4,2]=>0101011=>1101010=>0010101
[2,7,5,8,3,6,1,4]=>0101010=>0101010=>1010101
[1,5,6,8,2,4,7,3]=>0001001=>1001000=>0110111
[2,6,1,4,7,3,5,8]=>0100100=>0010010=>1101101
[3,6,8,4,7,5,1,2]=>0010110=>0110100=>1001011
[5,6,7,3,8,4,1,2]=>0010110=>0110100=>1001011
[4,5,6,7,2,8,1,3]=>0001010=>0101000=>1010111
[4,5,7,6,1,8,3,2]=>0011011=>1101100=>0010011
[1,5,8,6,2,7,3,4]=>0011010=>0101100=>1010011
[4,7,5,6,3,1,8,2]=>0101101=>1011010=>0100101
[5,1,6,3,4,2,8,7]=>1010101=>1010101=>0101010
[5,7,1,4,2,3,8,6]=>0101001=>1001010=>0110101
[5,7,6,4,3,8,1,2]=>0111010=>0101110=>1010001
[6,3,4,5,8,7,1,2]=>1000110=>0110001=>1001110
[6,2,4,1,8,3,7,5]=>1010101=>1010101=>0101010
[6,2,3,5,4,8,1,7]=>1001010=>0101001=>1010110
[5,1,4,2,7,6,8,3]=>1010101=>1010101=>0101010
[1,6,2,4,7,8,3,5]=>0100010=>0100010=>1011101
[5,7,2,4,1,6,3,8]=>0101010=>0101010=>1010101
[6,1,4,2,8,5,3,7]=>1010110=>0110101=>1001010
[6,7,5,8,1,4,3,2]=>0101011=>1101010=>0010101
[5,8,7,6,3,4,1,2]=>0111010=>0101110=>1010001
[5,8,7,6,2,3,1,4]=>0111010=>0101110=>1010001
[4,1,7,2,6,5,3,8]=>1010110=>0110101=>1001010
[4,8,2,1,5,6,3,7]=>0110010=>0100110=>1011001
[4,2,7,8,1,6,3,5]=>1001010=>0101001=>1010110
[2,1,8,7,6,5,3,4]=>1011110=>0111101=>1000010
[4,2,7,1,6,3,8,5]=>1010101=>1010101=>0101010
[4,3,7,5,6,8,1,2]=>1010010=>0100101=>1011010
[3,8,6,5,2,4,1,7]=>0111010=>0101110=>1010001
[3,8,5,6,1,4,7,2]=>0101001=>1001010=>0110101
[5,3,7,8,2,1,6,4]=>1001101=>1011001=>0100110
[5,2,8,7,1,6,4,3]=>1011011=>1101101=>0010010
[3,6,7,8,5,1,4,2]=>0001101=>1011000=>0100111
[3,7,8,5,1,2,4,6]=>0011000=>0001100=>1110011
[4,1,8,6,2,3,5,7]=>1011000=>0001101=>1110010
[4,7,8,6,3,5,1,2]=>0011010=>0101100=>1010011
[3,8,7,6,5,4,1,2]=>0111110=>0111110=>1000001
[2,8,6,7,5,1,3,4]=>0101100=>0011010=>1100101
[5,3,7,8,2,1,4,6]=>1001100=>0011001=>1100110
[7,6,1,2,5,8,3,4]=>1100010=>0100011=>1011100
[2,1,7,8,4,3,5,6]=>1001100=>0011001=>1100110
[7,8,1,2,5,4,6,3]=>0100101=>1010010=>0101101
[2,6,8,3,1,4,7,5]=>0011001=>1001100=>0110011
[8,4,1,3,7,6,2,5]=>1100110=>0110011=>1001100
[6,5,2,1,8,7,4,3]=>1110111=>1110111=>0001000
[4,7,2,8,1,3,6,5]=>0101001=>1001010=>0110101
[7,3,8,6,1,2,5,4]=>1011001=>1001101=>0110010
[3,4,7,1,8,2,6,5]=>0010101=>1010100=>0101011
[1,8,2,4,3,5,6,7]=>0101000=>0001010=>1110101
[1,7,2,4,3,5,6,8]=>0101000=>0001010=>1110101
[1,5,2,4,3,6,7,8]=>0101000=>0001010=>1110101
[1,7,2,5,3,4,6,8]=>0101000=>0001010=>1110101
[1,8,2,5,3,4,6,7]=>0101000=>0001010=>1110101
[1,8,2,6,3,4,5,7]=>0101000=>0001010=>1110101
[1,8,2,7,3,4,5,6]=>0101000=>0001010=>1110101
[1,8,2,7,3,5,4,6]=>0101010=>0101010=>1010101
[1,7,2,8,3,5,4,6]=>0101010=>0101010=>1010101
[1,6,2,8,3,5,4,7]=>0101010=>0101010=>1010101
[1,5,2,8,3,6,4,7]=>0101010=>0101010=>1010101
[1,4,2,8,3,6,5,7]=>0101010=>0101010=>1010101
[1,3,2,8,4,6,5,7]=>0101010=>0101010=>1010101
[1,2,3,8,4,6,5,7]=>0001010=>0101000=>1010111
[1,2,3,7,4,6,5,8]=>0001010=>0101000=>1010111
[1,3,2,7,4,6,5,8]=>0101010=>0101010=>1010101
[1,4,2,7,3,6,5,8]=>0101010=>0101010=>1010101
[1,5,2,7,3,6,4,8]=>0101010=>0101010=>1010101
[1,6,2,7,3,5,4,8]=>0101010=>0101010=>1010101
[1,7,2,6,3,5,4,8]=>0101010=>0101010=>1010101
[1,8,2,6,3,5,4,7]=>0101010=>0101010=>1010101
[1,8,2,5,3,6,4,7]=>0101010=>0101010=>1010101
[1,7,2,5,3,6,4,8]=>0101010=>0101010=>1010101
[1,6,2,5,3,7,4,8]=>0101010=>0101010=>1010101
[1,5,2,4,3,7,6,8]=>0101010=>0101010=>1010101
[1,6,2,4,3,7,5,8]=>0101010=>0101010=>1010101
[1,7,2,4,3,6,5,8]=>0101010=>0101010=>1010101
[1,8,2,4,3,6,5,7]=>0101010=>0101010=>1010101
[1,8,2,4,3,7,5,6]=>0101010=>0101010=>1010101
[1,7,2,4,3,8,5,6]=>0101010=>0101010=>1010101
[1,6,2,4,3,8,5,7]=>0101010=>0101010=>1010101
[1,5,2,4,3,8,6,7]=>0101010=>0101010=>1010101
[1,6,2,5,3,8,4,7]=>0101010=>0101010=>1010101
[1,7,2,5,3,8,4,6]=>0101010=>0101010=>1010101
[1,8,2,5,3,7,4,6]=>0101010=>0101010=>1010101
[1,8,2,6,3,7,4,5]=>0101010=>0101010=>1010101
[1,7,2,6,3,8,4,5]=>0101010=>0101010=>1010101
[1,2,3,8,4,7,5,6]=>0001010=>0101000=>1010111
[1,3,2,8,4,7,5,6]=>0101010=>0101010=>1010101
[1,4,2,8,3,7,5,6]=>0101010=>0101010=>1010101
[1,5,2,8,3,7,4,6]=>0101010=>0101010=>1010101
[1,6,2,8,3,7,4,5]=>0101010=>0101010=>1010101
[1,7,2,8,3,6,4,5]=>0101010=>0101010=>1010101
[1,8,2,7,3,6,4,5]=>0101010=>0101010=>1010101
[2,8,4,1,6,5,3,7]=>0110110=>0110110=>1001001
[2,8,4,1,5,6,7,3]=>0110001=>1000110=>0111001
[2,8,7,4,1,6,3,5]=>0111010=>0101110=>1010001
[7,2,8,5,1,6,4,3]=>1011011=>1101101=>0010010
[1,3,7,5,2,6,4,8]=>0011010=>0101100=>1010011
[1,3,7,5,4,2,6,8]=>0011100=>0011100=>1100011
[7,2,8,5,4,1,6,3]=>1011101=>1011101=>0100010
[2,8,5,3,4,1,6,7]=>0110100=>0010110=>1101001
[2,8,7,6,1,4,5,3]=>0111001=>1001110=>0110001
[2,8,6,5,7,3,1,4]=>0110110=>0110110=>1001001
[7,2,8,4,5,6,1,3]=>1010010=>0100101=>1011010
[6,2,3,8,5,1,7,4]=>1001101=>1011001=>0100110
[6,3,2,8,5,1,4,7]=>1101100=>0011011=>1100100
[7,4,8,5,2,1,3,6]=>1011100=>0011101=>1100010
[6,4,8,5,1,3,7,2]=>1011001=>1001101=>0110010
[4,3,7,5,1,2,8,6]=>1011001=>1001101=>0110010
[4,3,7,1,5,6,8,2]=>1010001=>1000101=>0111010
[3,6,1,7,5,2,8,4]=>0101101=>1011010=>0100101
[3,4,1,2,7,6,8,5]=>0100101=>1010010=>0101101
[6,5,2,7,4,1,8,3]=>1101101=>1011011=>0100100
[3,5,2,6,4,8,7,1]=>0101011=>1101010=>0010101
[4,3,2,1,8,6,5,7]=>1110110=>0110111=>1001000
[4,2,1,3,8,7,6,5]=>1100111=>1110011=>0001100
[7,1,6,8,4,3,5,2]=>1001101=>1011001=>0100110
[6,1,2,8,4,5,7,3]=>1001001=>1001001=>0110110
[5,6,8,2,3,1,7,4]=>0010101=>1010100=>0101011
[6,5,8,2,4,3,1,7]=>1010110=>0110101=>1001010
[6,5,8,4,2,3,7,1]=>1011001=>1001101=>0110010
[7,5,3,8,2,4,1,6]=>1101010=>0101011=>1010100
[1,6,5,7,3,4,2,8]=>0101010=>0101010=>1010101
[5,2,1,8,7,6,3,4]=>1101110=>0111011=>1000100
[7,1,3,8,4,6,2,5]=>1001010=>0101001=>1010110
[5,7,8,4,3,6,2,1]=>0011011=>1101100=>0010011
[4,1,8,3,5,6,7,2]=>1010001=>1000101=>0111010
[4,1,8,3,6,2,7,5]=>1010101=>1010101=>0101010
[2,3,4,8,6,1,7,5]=>0001101=>1011000=>0100111
[2,3,4,8,6,5,1,7]=>0001110=>0111000=>1000111
[2,7,3,5,8,6,1,4]=>0100110=>0110010=>1001101
[3,2,4,7,8,6,1,5]=>1000110=>0110001=>1001110
[1,5,4,6,2,7,3,8]=>0101010=>0101010=>1010101
[5,2,4,7,1,8,3,6]=>1001010=>0101001=>1010110
[5,3,6,4,1,8,7,2]=>1011011=>1101101=>0010010
[5,3,6,1,4,8,2,7]=>1010010=>0100101=>1011010
[7,3,5,6,8,4,2,1]=>1000111=>1110001=>0001110
[6,3,5,1,8,2,7,4]=>1010101=>1010101=>0101010
[5,7,1,6,3,8,4,2]=>0101011=>1101010=>0010101
[3,2,4,1,7,8,5,6]=>1010010=>0100101=>1011010
[2,5,4,6,1,7,8,3]=>0101001=>1001010=>0110101
[7,2,1,4,3,6,5,8]=>1101010=>0101011=>1010100
[7,3,4,1,2,6,5,8]=>1010010=>0100101=>1011010
[7,4,3,2,1,6,5,8]=>1111010=>0101111=>1010000
[6,7,3,2,5,4,8,1]=>0110101=>1010110=>0101001
[1,8,3,2,5,4,7,6]=>0110101=>1010110=>0101001
[1,8,4,5,2,3,7,6]=>0101001=>1001010=>0110101
[7,3,5,1,6,2,4,8]=>1010100=>0010101=>1101010
[7,2,1,5,6,3,4,8]=>1100100=>0010011=>1101100
[1,8,5,4,3,2,7,6]=>0111101=>1011110=>0100001
[6,4,7,5,1,3,8,2]=>1011001=>1001101=>0110010
[3,2,1,8,5,4,7,6]=>1101101=>1011011=>0100100
[2,3,8,1,5,4,7,6]=>0010101=>1010100=>0101011
[2,4,8,5,1,3,7,6]=>0011001=>1001100=>0110011
[2,6,8,4,3,7,1,5]=>0011010=>0101100=>1010011
[2,7,8,4,3,6,5,1]=>0011011=>1101100=>0010011
[1,8,7,5,6,3,4,2]=>0110101=>1010110=>0101001
[2,7,8,5,6,3,4,1]=>0010101=>1010100=>0101011
[2,5,8,6,7,1,3,4]=>0010100=>0010100=>1101011
[2,4,8,6,1,7,3,5]=>0011010=>0101100=>1010011
[3,2,1,8,6,7,4,5]=>1101010=>0101011=>1010100
[5,2,1,7,6,8,4,3]=>1101011=>1101011=>0010100
[5,3,7,1,6,8,4,2]=>1010011=>1100101=>0011010
[5,4,7,6,1,8,3,2]=>1011011=>1101101=>0010010
[4,5,7,6,8,1,3,2]=>0010101=>1010100=>0101011
[4,6,7,5,8,3,1,2]=>0010110=>0110100=>1001011
[1,8,5,6,7,2,3,4]=>0100100=>0010010=>1101101
[4,6,5,7,8,2,1,3]=>0100110=>0110010=>1001101
[5,4,6,7,1,8,2,3]=>1001010=>0101001=>1010110
[5,3,6,1,7,8,2,4]=>1010010=>0100101=>1011010
[5,2,1,6,7,8,3,4]=>1100010=>0100011=>1011100
[6,2,1,5,7,3,8,4]=>1100101=>1010011=>0101100
[6,3,5,1,7,2,8,4]=>1010101=>1010101=>0101010
[6,4,5,7,1,2,8,3]=>1001001=>1001001=>0110110
[5,6,4,7,2,8,1,3]=>0101010=>0101010=>1010101
[1,8,4,6,2,7,3,5]=>0101010=>0101010=>1010101
[1,8,3,2,6,7,4,5]=>0110010=>0100110=>1011001
[5,7,3,2,6,8,4,1]=>0110011=>1100110=>0011001
[6,5,3,2,7,1,8,4]=>1110101=>1010111=>0101000
[6,4,3,2,1,7,8,5]=>1111001=>1001111=>0110000
[6,2,1,4,3,7,8,5]=>1101001=>1001011=>0110100
[5,2,1,4,3,8,7,6]=>1101011=>1101011=>0010100
[5,3,4,1,2,8,7,6]=>1010011=>1100101=>0011010
[4,5,3,2,8,1,7,6]=>0110101=>1010110=>0101001
[4,6,3,2,8,7,1,5]=>0110110=>0110110=>1001001
[1,8,3,2,7,6,5,4]=>0110111=>1110110=>0001001
[1,8,4,7,2,6,5,3]=>0101011=>1101010=>0010101
[3,6,4,8,2,7,1,5]=>0101010=>0101010=>1010101
[3,4,5,8,1,2,7,6]=>0001001=>1001000=>0110111
[4,3,5,1,8,2,7,6]=>1010101=>1010101=>0101010
[4,2,1,5,8,3,7,6]=>1100101=>1010011=>0101100
[4,2,1,6,8,7,3,5]=>1100110=>0110011=>1001100
[3,4,6,8,1,7,2,5]=>0001010=>0101000=>1010111
[3,5,6,8,7,1,2,4]=>0001100=>0011000=>1100111
[3,6,5,8,7,2,1,4]=>0101110=>0111010=>1000101
[3,6,7,8,5,4,1,2]=>0001110=>0111000=>1000111
[3,5,7,8,6,1,4,2]=>0001101=>1011000=>0100111
[4,2,1,7,8,6,5,3]=>1100111=>1110011=>0001100
[2,3,8,1,7,6,5,4]=>0010111=>1110100=>0001011
[2,4,8,7,1,6,5,3]=>0011011=>1101100=>0010011
[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101=>10101010101=>01010101010
[8,1,6,7,3,2,5,4]=>1001101=>1011001=>0100110
[8,1,6,7,2,3,4,5]=>1001000=>0001001=>1110110
[8,1,2,4,3,6,5,7]=>1001010=>0101001=>1010110
[8,1,4,3,2,7,6,5]=>1011011=>1101101=>0010010
[8,1,5,3,7,2,6,4]=>1010101=>1010101=>0101010
[8,1,3,5,6,2,7,4]=>1000101=>1010001=>0101110
[6,3,2,1,4,5,8,7]=>1110001=>1000111=>0111000
[4,7,8,5,6,1,2,3]=>0010100=>0010100=>1101011
[3,7,8,5,6,2,1,4]=>0010110=>0110100=>1001011
[3,7,8,4,2,6,1,5]=>0011010=>0101100=>1010011
[3,7,8,2,4,5,1,6]=>0010010=>0100100=>1011011
[3,6,2,8,4,5,1,7]=>0101010=>0101010=>1010101
[2,3,6,7,4,5,8,1]=>0001001=>1001000=>0110111
[3,5,2,4,8,6,1,7]=>0100110=>0110010=>1001101
[3,5,4,2,8,7,1,6]=>0110110=>0110110=>1001001
[4,6,5,8,7,1,2,3]=>0101100=>0011010=>1100101
[6,4,5,1,7,8,2,3]=>1010010=>0100101=>1011010
[5,4,2,3,1,8,6,7]=>1101010=>0101011=>1010100
[6,5,3,1,8,2,7,4]=>1110101=>1010111=>0101000
[6,5,4,1,8,7,2,3]=>1110110=>0110111=>1001000
[7,5,1,4,8,6,2,3]=>1100110=>0110011=>1001100
[7,4,1,3,2,8,6,5]=>1101011=>1101011=>0010100
[7,4,1,2,3,8,5,6]=>1100010=>0100011=>1011100
[6,4,2,1,3,8,5,7]=>1110010=>0100111=>1011000
[2,6,4,8,3,7,5,1]=>0101011=>1101010=>0010101
[2,6,5,8,7,3,4,1]=>0101101=>1011010=>0100101
[6,5,2,1,8,3,4,7]=>1110100=>0010111=>1101000
[7,5,1,2,8,3,4,6]=>1100100=>0010011=>1101100
[7,6,1,8,2,3,4,5]=>1101000=>0001011=>1110100
[7,6,1,8,4,5,2,3]=>1101010=>0101011=>1010100
[6,7,8,1,4,5,2,3]=>0010010=>0100100=>1011011
[6,7,8,1,3,2,5,4]=>0010101=>1010100=>0101011
[2,5,6,7,8,3,4,1]=>0000101=>1010000=>0101111
[2,4,6,7,3,8,5,1]=>0001011=>1101000=>0010111
[4,2,6,7,3,1,5,8]=>1001100=>0011001=>1100110
[4,7,8,2,3,1,5,6]=>0010100=>0010100=>1101011
[4,7,8,3,2,1,6,5]=>0011101=>1011100=>0100011
[5,7,8,3,1,2,6,4]=>0011001=>1001100=>0110011
[5,7,8,4,1,6,2,3]=>0011010=>0101100=>1010011
[5,6,4,8,1,7,2,3]=>0101010=>0101010=>1010101
[4,6,3,8,2,1,7,5]=>0101101=>1011010=>0100101
[4,2,5,3,7,1,6,8]=>1010100=>0010101=>1101010
[5,3,6,7,1,2,8,4]=>1001001=>1001001=>0110110
[3,5,6,7,8,2,1,4]=>0000110=>0110000=>1001111
[3,4,6,7,2,8,1,5]=>0001010=>0101000=>1010111
[7,4,6,1,8,3,5,2]=>1010101=>1010101=>0101010
[7,3,5,1,8,4,6,2]=>1010101=>1010101=>0101010
[7,3,4,1,8,5,6,2]=>1010101=>1010101=>0101010
[4,5,7,3,1,8,6,2]=>0011011=>1101100=>0010011
[4,5,6,2,1,8,7,3]=>0011011=>1101100=>0010011
[1,6,5,2,7,4,3,8]=>0110110=>0110110=>1001001
[7,4,3,1,8,6,5,2]=>1110111=>1110111=>0001000
[3,6,7,5,1,8,4,2]=>0011011=>1101100=>0010011
[7,5,6,1,8,3,4,2]=>1010101=>1010101=>0101010
[7,6,5,1,8,4,3,2]=>1110111=>1110111=>0001000
[7,6,4,1,8,5,3,2]=>1110111=>1110111=>0001000
[6,4,2,1,8,7,5,3]=>1110111=>1110111=>0001000
[1,5,3,2,7,6,4,8]=>0110110=>0110110=>1001001
[2,6,5,1,7,8,4,3]=>0110011=>1100110=>0011001
[4,5,7,1,6,8,2,3]=>0010010=>0100100=>1011011
[4,5,7,1,3,8,2,6]=>0010010=>0100100=>1011011
[6,4,1,2,8,5,3,7]=>1100110=>0110011=>1001100
[5,3,1,2,8,6,4,7]=>1100110=>0110011=>1001100
[4,3,1,2,8,6,5,7]=>1100110=>0110011=>1001100
[6,1,2,5,8,3,4,7]=>1000100=>0010001=>1101110
[7,1,3,4,8,2,5,6]=>1000100=>0010001=>1101110
[2,6,1,5,7,8,3,4]=>0100010=>0100010=>1011101
[7,6,1,5,8,3,2,4]=>1100110=>0110011=>1001100
[3,6,7,1,5,8,2,4]=>0010010=>0100100=>1011011
[7,1,6,5,8,2,4,3]=>1010101=>1010101=>0101010
[7,5,1,6,8,4,2,3]=>1100110=>0110011=>1001100
[7,4,1,6,8,5,2,3]=>1100110=>0110011=>1001100
[5,2,3,1,8,6,7,4]=>1010101=>1010101=>0101010
[7,3,1,5,8,6,2,4]=>1100110=>0110011=>1001100
[6,2,4,1,8,5,7,3]=>1010101=>1010101=>0101010
[6,2,5,1,8,4,7,3]=>1010101=>1010101=>0101010
[7,1,6,4,8,2,5,3]=>1010101=>1010101=>0101010
[7,1,5,3,8,2,6,4]=>1010101=>1010101=>0101010
[6,1,5,2,8,3,7,4]=>1010101=>1010101=>0101010
[7,3,1,4,8,6,2,5]=>1100110=>0110011=>1001100
[6,2,1,4,8,7,3,5]=>1100110=>0110011=>1001100
[5,2,1,3,8,7,4,6]=>1100110=>0110011=>1001100
[7,4,1,3,8,5,2,6]=>1100110=>0110011=>1001100
[6,1,4,2,8,3,7,5]=>1010101=>1010101=>0101010
[7,1,4,3,8,2,6,5]=>1010101=>1010101=>0101010
[3,6,7,1,4,8,2,5]=>0010010=>0100100=>1011011
[7,6,1,4,8,3,2,5]=>1100110=>0110011=>1001100
[5,1,3,2,8,4,7,6]=>1010101=>1010101=>0101010
[4,2,1,3,8,7,5,6]=>1100110=>0110011=>1001100
[2,6,1,4,7,8,3,5]=>0100010=>0100010=>1011101
[7,1,3,5,8,2,4,6]=>1000100=>0010001=>1101110
[7,8,5,6,1,3,4,2]=>0101001=>1001010=>0110101
[7,8,1,3,6,2,5,4]=>0100101=>1010010=>0101101
[1,3,8,4,7,2,5,6]=>0010100=>0010100=>1101011
[4,6,1,2,5,7,3,8]=>0100010=>0100010=>1011101
[1,4,8,2,5,7,3,6]=>0010010=>0100100=>1011011
[7,8,4,2,5,1,3,6]=>0110100=>0010110=>1101001
[7,8,1,5,4,6,3,2]=>0101011=>1101010=>0010101
[7,8,2,1,6,3,4,5]=>0110100=>0010110=>1101001
[7,8,3,5,6,4,1,2]=>0100110=>0110010=>1001101
[7,8,4,5,3,1,6,2]=>0101101=>1011010=>0100101
[2,6,4,8,3,7,1,5]=>0101010=>0101010=>1010101
[1,4,6,8,3,7,5,2]=>0001011=>1101000=>0010111
[2,4,8,5,3,1,6,7]=>0011100=>0011100=>1100011
[2,5,8,1,4,7,6,3]=>0010011=>1100100=>0011011
[2,1,8,4,7,3,6,5]=>1010101=>1010101=>0101010
[3,5,8,4,7,6,1,2]=>0010110=>0110100=>1001011
[1,6,2,4,7,3,8,5]=>0100101=>1010010=>0101101
[4,6,2,5,3,1,8,7]=>0101101=>1011010=>0100101
[4,7,5,1,3,6,8,2]=>0110001=>1000110=>0111001
[7,5,3,6,2,4,1,8]=>1101010=>0101011=>1010100
[5,7,3,6,1,4,8,2]=>0101001=>1001010=>0110101
[5,3,6,7,2,1,8,4]=>1001101=>1011001=>0100110
[6,3,1,2,4,5,8,7]=>1100001=>1000011=>0111100
[1,4,7,2,5,3,8,6]=>0010101=>1010100=>0101011
[6,4,7,3,5,8,1,2]=>1010010=>0100101=>1011010
[3,5,6,7,8,1,4,2]=>0000101=>1010000=>0101111
[3,6,5,7,8,2,1,4]=>0100110=>0110010=>1001101
[5,2,7,6,1,4,3,8]=>1011010=>0101101=>1010010
[2,7,5,6,8,4,1,3]=>0100110=>0110010=>1001101
[2,1,6,8,4,5,3,7]=>1001010=>0101001=>1010110
[2,7,1,8,5,3,4,6]=>0101100=>0011010=>1100101
[3,7,6,8,5,4,1,2]=>0101110=>0111010=>1000101
[4,3,8,5,6,7,1,2]=>1010010=>0100101=>1011010
[4,2,8,1,6,3,7,5]=>1010101=>1010101=>0101010
[3,1,8,5,4,6,7,2]=>1011001=>1001101=>0110010
[3,4,2,8,6,1,7,5]=>0101101=>1011010=>0100101
[1,7,3,8,5,2,6,4]=>0101101=>1011010=>0100101
[4,1,8,3,6,2,5,7]=>1010100=>0010101=>1101010
[5,7,8,6,3,2,1,4]=>0011110=>0111100=>1000011
[5,7,8,6,1,3,4,2]=>0011001=>1001100=>0110011
[7,6,5,8,1,3,4,2]=>1101001=>1001011=>0110100
[1,6,4,3,8,2,5,7]=>0110100=>0010110=>1101001
[2,6,3,4,5,8,1,7]=>0100010=>0100010=>1011101
[2,6,4,1,8,3,7,5]=>0110101=>1010110=>0101001
[3,6,4,5,8,7,1,2]=>0100110=>0110010=>1001101
[7,1,6,5,3,8,4,2]=>1011011=>1101101=>0010010
[7,2,5,6,3,8,1,4]=>1001010=>0101001=>1010110
[5,6,2,7,3,1,4,8]=>0101100=>0011010=>1100101
[5,7,6,4,1,8,3,2]=>0111011=>1101110=>0010001
[6,7,1,5,2,8,3,4]=>0101010=>0101010=>1010101
[6,1,5,2,8,3,4,7]=>1010100=>0010101=>1101010
[7,5,2,4,3,1,6,8]=>1101100=>0011011=>1100100
[6,8,1,3,7,5,4,2]=>0100111=>1110010=>0001101
[7,4,2,6,5,1,3,8]=>1101100=>0011011=>1100100
[7,4,6,3,1,5,2,8]=>1011010=>0101101=>1010010
[7,2,3,5,4,1,6,8]=>1001100=>0011001=>1100110
[6,8,1,2,3,4,7,5]=>0100001=>1000010=>0111101
[2,5,1,7,8,3,6,4]=>0100101=>1010010=>0101101
[2,5,3,6,8,4,7,1]=>0100101=>1010010=>0101101
[2,1,4,7,8,5,6,3]=>1000101=>1010001=>0101110
[2,5,7,8,1,4,6,3]=>0001001=>1001000=>0110111
[3,5,7,4,1,6,2,8]=>0011010=>0101100=>1010011
[5,2,8,4,6,1,7,3]=>1010101=>1010101=>0101010
[4,2,8,5,7,6,3,1]=>1010111=>1110101=>0001010
[4,1,2,8,5,6,7,3]=>1001001=>1001001=>0110110
[1,4,2,7,5,8,6,3]=>0101011=>1101010=>0010101
[4,1,8,6,7,5,3,2]=>1010111=>1110101=>0001010
[5,3,8,7,6,2,4,1]=>1011101=>1011101=>0100010
[5,8,4,7,6,2,1,3]=>0101110=>0111010=>1000101
[5,8,7,4,3,6,1,2]=>0111010=>0101110=>1010001
[6,4,8,3,1,7,2,5]=>1011010=>0101101=>1010010
[6,4,2,8,7,1,3,5]=>1101100=>0011011=>1100100
[6,3,8,7,2,5,1,4]=>1011010=>0101101=>1010010
[6,3,1,8,7,2,4,5]=>1101100=>0011011=>1100100
[5,8,3,7,1,6,4,2]=>0101011=>1101010=>0010101
[5,1,8,4,6,2,7,3]=>1010101=>1010101=>0101010
[5,8,7,4,1,6,2,3]=>0111010=>0101110=>1010001
[6,8,5,2,4,3,7,1]=>0110101=>1010110=>0101001
[6,8,5,3,1,2,7,4]=>0111001=>1001110=>0110001
[4,5,1,2,7,6,3,8]=>0100110=>0110010=>1001101
[4,5,1,2,6,8,7,3]=>0100011=>1100010=>0011101
[3,5,6,1,8,4,7,2]=>0010101=>1010100=>0101011
[3,5,7,1,2,8,6,4]=>0010011=>1100100=>0011011
[4,2,6,1,7,3,5,8]=>1010100=>0010101=>1101010
[4,6,3,1,2,7,5,8]=>0110010=>0100110=>1011001
[3,5,2,7,8,1,6,4]=>0100101=>1010010=>0101101
[3,1,4,7,5,6,2,8]=>1001010=>0101001=>1010110
[4,2,5,6,1,8,7,3]=>1001011=>1101001=>0010110
[2,1,7,5,8,6,4,3]=>1010111=>1110101=>0001010
[1,2,7,5,3,8,6,4]=>0011011=>1101100=>0010011
[4,1,2,7,3,8,6,5]=>1001011=>1101001=>0010110
[7,1,4,2,5,3,8,6]=>1010101=>1010101=>0101010
[6,1,3,7,5,2,4,8]=>1001100=>0011001=>1100110
[3,1,2,6,8,5,4,7]=>1000110=>0110001=>1001110
[3,7,1,2,5,4,8,6]=>0100101=>1010010=>0101101
[1,3,7,2,4,8,6,5]=>0010011=>1100100=>0011011
[3,2,7,8,1,6,5,4]=>1001011=>1101001=>0010110
[2,4,1,7,8,6,5,3]=>0100111=>1110010=>0001101
[2,6,8,3,1,5,7,4]=>0011001=>1001100=>0110011
[3,6,4,8,5,1,7,2]=>0101101=>1011010=>0100101
[6,3,7,4,5,1,8,2]=>1010101=>1010101=>0101010
[6,4,7,5,2,8,1,3]=>1011010=>0101101=>1010010
[2,6,3,7,5,8,1,4]=>0101010=>0101010=>1010101
[5,2,1,7,8,3,4,6]=>1100100=>0010011=>1101100
[5,7,4,6,2,8,1,3]=>0101010=>0101010=>1010101
[5,7,3,4,6,1,8,2]=>0100101=>1010010=>0101101
[4,2,8,3,6,7,1,5]=>1010010=>0100101=>1011010
[4,8,3,1,7,2,5,6]=>0110100=>0010110=>1101001
[5,2,8,4,7,1,6,3]=>1010101=>1010101=>0101010
[5,8,4,7,3,1,6,2]=>0101101=>1011010=>0100101
[4,6,8,3,1,7,5,2]=>0011011=>1101100=>0010011
[6,3,8,2,7,1,5,4]=>1010101=>1010101=>0101010
[6,3,1,8,2,4,7,5]=>1101001=>1001011=>0110100
[3,5,1,8,2,7,4,6]=>0101010=>0101010=>1010101
[7,5,1,3,6,2,4,8]=>1100100=>0010011=>1101100
[8,5,4,1,2,6,3,7]=>1110010=>0100111=>1011000
[5,1,8,4,2,7,3,6]=>1011010=>0101101=>1010010
[4,1,6,2,8,3,7,5]=>1010101=>1010101=>0101010
[1,6,2,8,5,3,7,4]=>0101101=>1011010=>0100101
[6,8,5,3,1,7,4,2]=>0111011=>1101110=>0010001
[5,6,7,3,1,8,4,2]=>0011011=>1101100=>0010011
[5,6,2,1,7,8,4,3]=>0110011=>1100110=>0011001
[8,4,5,1,2,6,3,7]=>1010010=>0100101=>1011010
[1,6,3,7,2,8,4,5]=>0101010=>0101010=>1010101
[6,3,2,7,8,5,1,4]=>1100110=>0110011=>1001100
[6,4,7,2,8,1,5,3]=>1010101=>1010101=>0101010
[6,7,4,8,3,1,5,2]=>0101101=>1011010=>0100101
[4,5,7,8,3,1,6,2]=>0001101=>1011000=>0100111
[4,7,2,5,8,1,6,3]=>0100101=>1010010=>0101101
[5,7,3,8,2,6,1,4]=>0101010=>0101010=>1010101
[3,4,7,8,2,6,1,5]=>0001010=>0101000=>1010111
[8,1,3,4,6,2,5,7]=>1000100=>0010001=>1101110
[3,8,2,4,6,7,1,5]=>0100010=>0100010=>1011101
[2,4,5,6,8,1,7,3]=>0000101=>1010000=>0101111
[4,8,3,5,6,1,7,2]=>0100101=>1010010=>0101101
[8,4,3,6,5,1,7,2]=>1101101=>1011011=>0100100
[8,6,5,4,3,1,7,2]=>1111101=>1011111=>0100000
[1,8,6,5,2,7,3,4]=>0111010=>0101110=>1010001
[8,7,5,4,1,6,3,2]=>1111011=>1101111=>0010000
[7,8,5,4,1,3,6,2]=>0111001=>1001110=>0110001
[6,8,5,4,2,1,7,3]=>0111101=>1011110=>0100001
[5,8,6,2,4,1,7,3]=>0110101=>1010110=>0101001
[3,2,8,6,5,1,7,4]=>1011101=>1011101=>0100010
[5,1,7,3,6,2,4,8]=>1010100=>0010101=>1101010
[8,1,6,5,2,3,7,4]=>1011001=>1001101=>0110010
[1,2,8,3,7,4,5,6]=>0010100=>0010100=>1101011
[8,1,7,2,6,3,5,4]=>1010101=>1010101=>0101010
[7,1,8,2,6,4,3,5]=>1010110=>0110101=>1001010
[5,1,8,3,2,7,4,6]=>1011010=>0101101=>1010010
[3,2,1,8,4,7,5,6]=>1101010=>0101011=>1010100
[3,2,8,7,1,6,5,4]=>1011011=>1101101=>0010010
[4,8,2,7,1,6,5,3]=>0101011=>1101010=>0010101
[5,8,7,2,1,6,4,3]=>0111011=>1101110=>0010001
[8,7,6,1,5,4,3,2]=>1110111=>1110111=>0001000
[8,6,7,1,4,5,3,2]=>1010011=>1100101=>0011010
[7,6,8,1,4,3,5,2]=>1010101=>1010101=>0101010
[6,7,8,1,3,4,5,2]=>0010001=>1000100=>0111011
[5,7,8,2,1,4,6,3]=>0011001=>1001100=>0110011
[4,7,2,8,1,5,6,3]=>0101001=>1001010=>0110101
[3,2,7,8,1,5,6,4]=>1001001=>1001001=>0110110
[3,2,6,8,4,1,7,5]=>1001101=>1011001=>0100110
[4,6,2,8,3,1,7,5]=>0101101=>1011010=>0100101
[6,5,8,3,2,1,7,4]=>1011101=>1011101=>0100010
[7,5,8,3,1,4,6,2]=>1011001=>1001101=>0110010
[8,4,3,7,1,6,5,2]=>1101011=>1101011=>0010100
[6,4,3,8,2,1,7,5]=>1101101=>1011011=>0100100
[5,4,3,2,8,1,7,6]=>1110101=>1010111=>0101000
[4,5,2,3,8,1,7,6]=>0100101=>1010010=>0101101
[3,2,5,4,8,1,7,6]=>1010101=>1010101=>0101010
[6,4,3,1,5,2,7,8]=>1110100=>0010111=>1101000
[7,4,3,1,2,6,5,8]=>1110010=>0100111=>1011000
[1,5,4,2,3,6,7,8]=>0110000=>0000110=>1111001
[8,5,1,4,2,3,7,6]=>1101001=>1001011=>0110100
[7,5,1,4,2,6,3,8]=>1101010=>0101011=>1010100
[4,6,2,1,5,3,7,8]=>0110100=>0010110=>1101001
[3,2,6,1,5,4,7,8]=>1010100=>0010101=>1101010
[5,7,1,3,2,6,4,8]=>0101010=>0101010=>1010101
[6,7,1,2,4,5,3,8]=>0100010=>0100010=>1011101
[7,6,1,2,5,4,3,8]=>1100110=>0110011=>1001100
[7,8,1,2,3,5,6,4]=>0100001=>1000010=>0111101
[6,8,1,2,4,3,7,5]=>0100101=>1010010=>0101101
[4,8,2,1,3,5,7,6]=>0110001=>1000110=>0111001
[3,2,8,1,4,5,7,6]=>1010001=>1000101=>0111010
[4,1,3,2,5,6,7,8]=>1010000=>0000101=>1111010
[5,1,2,4,3,6,7,8]=>1001000=>0001001=>1110110
[5,8,7,3,4,1,2,6]=>0110100=>0010110=>1101001
[6,7,3,8,5,1,2,4]=>0101100=>0011010=>1100101
[6,7,4,5,1,8,3,2]=>0101011=>1101010=>0010101
[5,4,7,6,2,3,8,1]=>1011001=>1001101=>0110010
[5,4,7,6,8,1,2,3]=>1010100=>0010101=>1101010
[5,3,7,8,6,1,2,4]=>1001100=>0011001=>1100110
[4,3,8,7,6,1,2,5]=>1011100=>0011101=>1100010
[4,8,3,7,5,1,2,6]=>0101100=>0011010=>1100101
[4,5,6,7,1,8,3,2]=>0001011=>1101000=>0010111
[3,5,6,2,7,4,8,1]=>0010101=>1010100=>0101011
[3,5,6,1,7,8,4,2]=>0010011=>1100100=>0011011
[2,5,6,8,1,7,3,4]=>0001010=>0101000=>1010111
[8,2,4,5,1,6,3,7]=>1001010=>0101001=>1010110
[1,4,8,6,2,3,7,5]=>0011001=>1001100=>0110011
[1,5,6,8,2,3,7,4]=>0001001=>1001000=>0110111
[1,5,6,2,8,4,7,3]=>0010101=>1010100=>0101011
[1,4,2,6,8,5,7,3]=>0100101=>1010010=>0101101
[8,1,3,2,5,4,6,7]=>1010100=>0010101=>1101010
[2,4,1,6,8,7,5,3]=>0100111=>1110010=>0001101
[4,3,1,7,6,8,5,2]=>1101011=>1101011=>0010100
[3,8,2,1,7,5,4,6]=>0110110=>0110110=>1001001
[8,3,2,1,6,5,4,7]=>1110110=>0110111=>1001000
[8,4,2,6,1,5,3,7]=>1101010=>0101011=>1010100
[4,2,8,7,1,6,3,5]=>1011010=>0101101=>1010010
[5,2,7,8,1,6,3,4]=>1001010=>0101001=>1010110
[5,3,7,2,6,4,8,1]=>1010101=>1010101=>0101010
[6,7,3,1,5,8,4,2]=>0110011=>1100110=>0011001
[6,7,2,1,8,5,4,3]=>0110111=>1110110=>0001001
[6,7,2,8,1,5,3,4]=>0101010=>0101010=>1010101
[6,7,8,2,1,4,3,5]=>0011010=>0101100=>1010011
[8,5,6,2,1,4,3,7]=>1011010=>0101101=>1010010
[5,8,7,1,2,3,4,6]=>0110000=>0000110=>1111001
[6,7,1,2,8,4,5,3]=>0100101=>1010010=>0101101
[6,7,1,3,4,8,5,2]=>0100011=>1100010=>0011101
[5,1,7,3,4,8,6,2]=>1010011=>1100101=>0011010
[5,1,7,8,2,3,6,4]=>1001001=>1001001=>0110110
[4,8,1,7,2,3,5,6]=>0101000=>0001010=>1110101
[3,8,1,2,7,4,5,6]=>0100100=>0010010=>1101101
[3,1,8,2,7,4,6,5]=>1010101=>1010101=>0101010
[3,1,2,8,7,5,6,4]=>1001101=>1011001=>0100110
[4,1,3,7,5,8,6,2]=>1001011=>1101001=>0010110
[2,1,8,3,4,7,6,5]=>1010011=>1100101=>0011010
[1,8,2,3,4,5,7,6]=>0100001=>1000010=>0111101
[1,2,8,3,4,6,7,5]=>0010001=>1000100=>0111011
[6,3,8,5,2,7,4,1]=>1011011=>1101101=>0010010
[6,5,2,8,4,7,3,1]=>1101011=>1101011=>0010100
[6,3,4,5,8,7,2,1]=>1000111=>1110001=>0001110
[5,8,1,4,7,2,3,6]=>0100100=>0010010=>1101101
[3,6,4,8,5,7,1,2]=>0101010=>0101010=>1010101
[5,1,4,8,6,3,7,2]=>1001101=>1011001=>0100110
[3,4,7,1,8,6,5,2]=>0010111=>1110100=>0001011
[6,3,8,4,2,7,1,5]=>1011010=>0101101=>1010010
[3,6,8,7,1,4,2,5]=>0011010=>0101100=>1010011
[5,3,7,1,6,8,2,4]=>1010010=>0100101=>1011010
[4,6,1,2,7,8,5,3]=>0100011=>1100010=>0011101
[3,6,4,2,8,7,5,1]=>0110111=>1110110=>0001001
[6,3,7,5,2,8,1,4]=>1011010=>0101101=>1010010
[6,5,2,7,4,8,1,3]=>1101010=>0101011=>1010100
[5,8,1,4,6,7,2,3]=>0100010=>0100010=>1011101
[6,3,7,4,2,8,5,1]=>1011011=>1101101=>0010010
[8,7,1,6,2,4,5,3]=>1101001=>1001011=>0110100
[5,6,1,8,7,3,2,4]=>0101110=>0111010=>1000101
[3,6,4,5,7,2,8,1]=>0100101=>1010010=>0101101
[5,4,2,7,3,6,8,1]=>1101001=>1001011=>0110100
[6,4,1,5,3,8,2,7]=>1101010=>0101011=>1010100
[8,2,6,3,4,7,5,1]=>1010011=>1100101=>0011010
[4,2,5,7,3,6,8,1]=>1001001=>1001001=>0110110
[1,6,5,3,4,8,2,7]=>0110010=>0100110=>1011001
[6,8,3,1,7,2,5,4]=>0110101=>1010110=>0101001
[1,8,6,3,7,5,2,4]=>0110110=>0110110=>1001001
[8,7,5,2,6,4,3,1]=>1110111=>1110111=>0001000
[8,7,1,6,2,5,4,3]=>1101011=>1101011=>0010100
[2,8,1,7,3,5,6,4]=>0101001=>1001010=>0110101
[4,8,1,3,7,2,6,5]=>0100101=>1010010=>0101101
[4,2,8,5,7,3,6,1]=>1010101=>1010101=>0101010
[6,7,3,1,8,4,2,5]=>0110110=>0110110=>1001001
[1,7,3,8,4,5,2,6]=>0101010=>0101010=>1010101
[1,7,2,8,5,3,4,6]=>0101100=>0011010=>1100101
[7,6,1,8,4,3,2,5]=>1101110=>0111011=>1000100
[7,1,2,8,3,5,4,6]=>1001010=>0101001=>1010110
[6,3,7,2,1,8,4,5]=>1011010=>0101101=>1010010
[8,2,6,1,7,3,5,4]=>1010101=>1010101=>0101010
[4,2,1,5,8,3,6,7]=>1100100=>0010011=>1101100
[5,4,3,1,6,8,2,7]=>1110010=>0100111=>1011000
[1,5,3,4,6,8,2,7]=>0100010=>0100010=>1011101
[4,3,5,1,6,8,2,7]=>1010010=>0100101=>1011010
[4,7,5,6,8,3,2,1]=>0100111=>1110010=>0001101
[6,5,1,8,7,4,2,3]=>1101110=>0111011=>1000100
[8,6,4,7,5,3,2,1]=>1101111=>1111011=>0000100
[5,7,3,8,2,6,4,1]=>0101011=>1101010=>0010101
[2,3,8,7,4,5,6,1]=>0011001=>1001100=>0110011
[7,2,8,6,4,3,5,1]=>1011101=>1011101=>0100010
[2,1,8,7,5,6,3,4]=>1011010=>0101101=>1010010
[7,1,8,6,5,3,2,4]=>1011110=>0111101=>1000010
[4,7,1,8,6,5,2,3]=>0101110=>0111010=>1000101
[6,8,7,2,5,4,3,1]=>0110111=>1110110=>0001001
[6,7,4,8,3,5,1,2]=>0101010=>0101010=>1010101
[6,7,4,5,2,8,1,3]=>0101010=>0101010=>1010101
[5,7,4,6,2,3,1,8]=>0101010=>0101010=>1010101
[5,7,4,6,3,8,1,2]=>0101010=>0101010=>1010101
[5,7,4,8,3,6,1,2]=>0101010=>0101010=>1010101
[6,8,4,5,3,7,1,2]=>0101010=>0101010=>1010101
[5,8,4,6,3,7,1,2]=>0101010=>0101010=>1010101
[5,6,4,8,3,7,1,2]=>0101010=>0101010=>1010101
[5,6,3,7,2,4,1,8]=>0101010=>0101010=>1010101
[5,6,3,7,2,8,1,4]=>0101010=>0101010=>1010101
[5,6,3,8,2,7,1,4]=>0101010=>0101010=>1010101
[5,6,4,8,2,7,1,3]=>0101010=>0101010=>1010101
[5,8,4,6,2,7,1,3]=>0101010=>0101010=>1010101
[6,8,4,5,2,7,1,3]=>0101010=>0101010=>1010101
[7,8,4,5,2,6,1,3]=>0101010=>0101010=>1010101
[6,8,4,5,2,3,1,7]=>0101010=>0101010=>1010101
[5,8,4,6,2,3,1,7]=>0101010=>0101010=>1010101
[5,6,4,8,2,3,1,7]=>0101010=>0101010=>1010101
[5,6,3,8,2,4,1,7]=>0101010=>0101010=>1010101
[5,6,3,4,2,8,1,7]=>0101010=>0101010=>1010101
[4,6,3,5,2,7,1,8]=>0101010=>0101010=>1010101
[4,6,3,5,2,8,1,7]=>0101010=>0101010=>1010101
[4,6,3,8,2,5,1,7]=>0101010=>0101010=>1010101
[4,8,3,6,2,5,1,7]=>0101010=>0101010=>1010101
[5,8,3,6,2,4,1,7]=>0101010=>0101010=>1010101
[6,8,3,5,2,4,1,7]=>0101010=>0101010=>1010101
[7,8,3,5,2,4,1,6]=>0101010=>0101010=>1010101
[7,8,3,5,2,6,1,4]=>0101010=>0101010=>1010101
[6,8,3,5,2,7,1,4]=>0101010=>0101010=>1010101
[5,8,3,6,2,7,1,4]=>0101010=>0101010=>1010101
[4,8,3,6,2,7,1,5]=>0101010=>0101010=>1010101
[4,6,3,8,2,7,1,5]=>0101010=>0101010=>1010101
[4,6,3,7,2,8,1,5]=>0101010=>0101010=>1010101
[4,6,3,7,2,5,1,8]=>0101010=>0101010=>1010101
[4,7,3,6,2,5,1,8]=>0101010=>0101010=>1010101
[4,7,3,6,2,8,1,5]=>0101010=>0101010=>1010101
[4,7,3,8,2,6,1,5]=>0101010=>0101010=>1010101
[5,7,4,8,2,6,1,3]=>0101010=>0101010=>1010101
[5,7,3,6,2,8,1,4]=>0101010=>0101010=>1010101
[5,7,3,6,2,4,1,8]=>0101010=>0101010=>1010101
[6,7,3,5,2,4,1,8]=>0101010=>0101010=>1010101
[6,7,3,5,2,8,1,4]=>0101010=>0101010=>1010101
[6,7,3,8,2,5,1,4]=>0101010=>0101010=>1010101
[6,7,4,8,2,5,1,3]=>0101010=>0101010=>1010101
[6,7,5,8,2,4,1,3]=>0101010=>0101010=>1010101
[6,8,5,7,2,3,1,4]=>0101010=>0101010=>1010101
[6,7,4,8,2,3,1,5]=>0101010=>0101010=>1010101
[6,7,3,8,2,4,1,5]=>0101010=>0101010=>1010101
[6,7,3,4,2,8,1,5]=>0101010=>0101010=>1010101
[5,7,3,4,2,6,1,8]=>0101010=>0101010=>1010101
[5,7,3,4,2,8,1,6]=>0101010=>0101010=>1010101
[5,7,3,8,2,4,1,6]=>0101010=>0101010=>1010101
[5,7,4,8,2,3,1,6]=>0101010=>0101010=>1010101
[5,8,4,7,2,3,1,6]=>0101010=>0101010=>1010101
[6,8,4,7,2,3,1,5]=>0101010=>0101010=>1010101
[7,8,4,6,2,3,1,5]=>0101010=>0101010=>1010101
[7,8,3,6,2,4,1,5]=>0101010=>0101010=>1010101
[6,8,3,7,2,4,1,5]=>0101010=>0101010=>1010101
[5,8,3,7,2,4,1,6]=>0101010=>0101010=>1010101
[4,8,3,7,2,5,1,6]=>0101010=>0101010=>1010101
[4,7,3,8,2,5,1,6]=>0101010=>0101010=>1010101
[4,7,3,5,2,8,1,6]=>0101010=>0101010=>1010101
[4,7,3,5,2,6,1,8]=>0101010=>0101010=>1010101
[4,5,3,7,2,6,1,8]=>0101010=>0101010=>1010101
[4,5,3,7,2,8,1,6]=>0101010=>0101010=>1010101
[4,5,3,8,2,7,1,6]=>0101010=>0101010=>1010101
[4,8,3,5,2,7,1,6]=>0101010=>0101010=>1010101
[5,8,3,4,2,7,1,6]=>0101010=>0101010=>1010101
[6,8,3,4,2,7,1,5]=>0101010=>0101010=>1010101
[7,8,3,4,2,6,1,5]=>0101010=>0101010=>1010101
[6,8,3,4,2,5,1,7]=>0101010=>0101010=>1010101
[5,8,3,4,2,6,1,7]=>0101010=>0101010=>1010101
[4,8,3,5,2,6,1,7]=>0101010=>0101010=>1010101
[4,5,3,8,2,6,1,7]=>0101010=>0101010=>1010101
[4,5,3,6,2,8,1,7]=>0101010=>0101010=>1010101
[4,7,5,2,1,8,3,6]=>0111010=>0101110=>1010001
[4,6,5,2,1,3,8,7]=>0111001=>1001110=>0110001
[5,6,4,2,3,1,8,7]=>0110101=>1010110=>0101001
[6,4,5,3,1,2,8,7]=>1011001=>1001101=>0110010
[5,4,6,1,3,2,8,7]=>1010101=>1010101=>0101010
[4,6,8,1,7,3,2,5]=>0010110=>0110100=>1001011
[4,7,8,1,6,3,5,2]=>0010101=>1010100=>0101011
[7,4,8,1,6,5,3,2]=>1010111=>1110101=>0001010
[7,4,5,3,1,8,2,6]=>1011010=>0101101=>1010010
[6,4,8,1,7,5,2,3]=>1010110=>0110101=>1001010
[6,4,7,1,8,2,5,3]=>1010101=>1010101=>0101010
[8,5,7,6,4,2,1,3]=>1011110=>0111101=>1000010
[2,1,6,8,7,4,3,5]=>1001110=>0111001=>1000110
[2,1,7,8,6,4,5,3]=>1001101=>1011001=>0100110
[8,4,7,3,6,2,5,1]=>1010101=>1010101=>0101010
[7,6,8,5,2,4,3,1]=>1011011=>1101101=>0010010
[5,7,8,6,2,3,1,4]=>0011010=>0101100=>1010011
[5,8,7,6,3,2,1,4]=>0111110=>0111110=>1000001
[6,8,7,5,3,2,4,1]=>0111101=>1011110=>0100001
[7,8,4,2,6,5,3,1]=>0110111=>1110110=>0001001
[4,8,6,2,7,3,1,5]=>0110110=>0110110=>1001001
[3,6,1,8,7,4,2,5]=>0101110=>0111010=>1000101
[4,7,6,2,8,1,3,5]=>0110100=>0010110=>1101001
[6,7,4,2,8,1,5,3]=>0110101=>1010110=>0101001
[6,8,4,2,7,5,1,3]=>0110110=>0110110=>1001001
[5,7,4,2,3,8,1,6]=>0110010=>0100110=>1011001
[2,1,8,6,7,5,3,4]=>1010110=>0110101=>1001010
[8,6,4,3,7,5,1,2]=>1110110=>0110111=>1001000
[5,8,6,7,3,1,2,4]=>0101100=>0011010=>1100101
[6,7,5,8,1,3,4,2]=>0101001=>1001010=>0110101
[7,6,5,8,1,4,3,2]=>1101011=>1101011=>0010100
[8,6,5,7,4,1,3,2]=>1101101=>1011011=>0100100
[7,6,4,3,8,1,5,2]=>1110101=>1010111=>0101000
[2,1,7,6,8,3,5,4]=>1010101=>1010101=>0101010
[7,5,6,8,1,4,2,3]=>1001010=>0101001=>1010110
[4,1,7,3,6,5,8,2]=>1010101=>1010101=>0101010
[5,1,8,4,7,6,2,3]=>1010110=>0110101=>1001010
[8,1,3,7,4,6,5,2]=>1001011=>1101001=>0010110
[6,1,5,4,3,8,7,2]=>1011011=>1101101=>0010010
[6,1,4,5,3,7,8,2]=>1001001=>1001001=>0110110
[5,1,7,8,6,2,4,3]=>1001101=>1011001=>0100110
[6,1,8,3,4,5,7,2]=>1010001=>1000101=>0111010
[8,5,2,1,4,3,7,6]=>1110101=>1010111=>0101000
[5,6,2,1,4,8,3,7]=>0110010=>0100110=>1011001
[3,6,1,8,5,2,4,7]=>0101100=>0011010=>1100101
[3,4,1,2,8,6,5,7]=>0100110=>0110010=>1001101
[6,3,8,5,2,1,4,7]=>1011100=>0011101=>1100010
[8,5,2,7,3,1,6,4]=>1101101=>1011011=>0100100
[2,3,8,5,6,1,7,4]=>0010101=>1010100=>0101011
[7,4,5,6,3,1,8,2]=>1001101=>1011001=>0100110
[8,5,6,4,2,1,7,3]=>1011101=>1011101=>0100010
[7,5,3,6,2,8,1,4]=>1101010=>0101011=>1010100
[1,7,5,6,3,2,4,8]=>0101100=>0011010=>1100101
[8,7,5,4,1,6,2,3]=>1111010=>0101111=>1010000
[2,6,4,1,8,5,7,3]=>0110101=>1010110=>0101001
[6,1,2,3,8,5,7,4]=>1000101=>1010001=>0101110
[7,1,2,3,6,5,8,4]=>1000101=>1010001=>0101110
[7,2,1,3,8,6,4,5]=>1100110=>0110011=>1001100
[1,5,7,3,2,4,6,8]=>0011000=>0001100=>1110011
[5,2,7,3,1,8,4,6]=>1011010=>0101101=>1010010
[5,8,2,4,1,3,7,6]=>0101001=>1001010=>0110101
[8,7,2,6,3,4,1,5]=>1101010=>0101011=>1010100
[4,8,1,6,3,2,7,5]=>0101101=>1011010=>0100101
[3,1,8,6,4,2,7,5]=>1011101=>1011101=>0100010
[8,1,6,7,4,3,2,5]=>1001110=>0111001=>1000110
[3,5,8,7,2,4,1,6]=>0011010=>0101100=>1010011
[4,2,1,3,7,8,5,6]=>1100010=>0100011=>1011100
[8,6,1,3,7,2,4,5]=>1100100=>0010011=>1101100
[5,1,8,3,2,4,6,7]=>1011000=>0001101=>1110010
[5,2,7,8,6,4,1,3]=>1001110=>0111001=>1000110
[1,4,2,7,8,6,3,5]=>0100110=>0110010=>1001101
[1,6,2,4,8,5,3,7]=>0100110=>0110010=>1001101
[1,6,2,4,7,5,3,8]=>0100110=>0110010=>1001101
[1,7,3,8,5,2,4,6]=>0101100=>0011010=>1100101
[1,7,3,2,8,6,4,5]=>0110110=>0110110=>1001001
[7,8,3,6,5,2,1,4]=>0101110=>0111010=>1000101
[4,7,2,8,6,1,5,3]=>0101101=>1011010=>0100101
[4,2,5,7,8,6,1,3]=>1000110=>0110001=>1001110
[8,2,5,1,7,3,4,6]=>1010100=>0010101=>1101010
[1,3,6,4,8,5,7,2]=>0010101=>1010100=>0101011
[1,3,6,4,7,5,8,2]=>0010101=>1010100=>0101011
[6,2,4,7,5,8,1,3]=>1001010=>0101001=>1010110
[6,2,7,3,5,1,8,4]=>1010101=>1010101=>0101010
[6,2,1,3,7,8,4,5]=>1100010=>0100011=>1011100
[7,2,5,1,8,3,4,6]=>1010100=>0010101=>1101010
[7,8,2,1,4,3,5,6]=>0110100=>0010110=>1101001
[7,6,4,2,3,1,8,5]=>1110101=>1010111=>0101000
[7,5,4,2,6,8,1,3]=>1110010=>0100111=>1011000
[1,7,5,3,4,6,8,2]=>0110001=>1000110=>0111001
[8,2,5,4,6,7,1,3]=>1010010=>0100101=>1011010
[8,2,6,4,3,1,7,5]=>1011101=>1011101=>0100010
[8,2,7,4,1,3,5,6]=>1011000=>0001101=>1110010
[1,2,8,4,3,5,6,7]=>0011000=>0001100=>1110011
[1,8,7,4,3,2,5,6]=>0111100=>0011110=>1100001
[5,8,4,7,2,1,6,3]=>0101101=>1011010=>0100101
[1,8,7,5,4,3,6,2]=>0111101=>1011110=>0100001
[1,6,8,4,3,7,5,2]=>0011011=>1101100=>0010011
[6,8,7,3,2,5,1,4]=>0111010=>0101110=>1010001
[5,3,8,1,2,7,4,6]=>1010010=>0100101=>1011010
[5,1,8,3,2,6,4,7]=>1011010=>0101101=>1010010
[5,7,3,1,2,6,4,8]=>0110010=>0100110=>1011001
[1,4,6,2,8,3,7,5]=>0010101=>1010100=>0101011
[5,2,6,7,8,4,1,3]=>1000110=>0110001=>1001110
[5,3,6,1,2,8,4,7]=>1010010=>0100101=>1011010
[1,6,3,2,7,8,4,5]=>0110010=>0100110=>1011001
[6,7,3,8,5,2,1,4]=>0101110=>0111010=>1000101
[4,6,2,7,8,1,5,3]=>0100101=>1010010=>0101101
[1,6,4,7,8,3,5,2]=>0100101=>1010010=>0101101
[4,5,7,2,1,8,6,3]=>0011011=>1101100=>0010011
[7,8,3,4,2,1,6,5]=>0101101=>1011010=>0100101
[6,3,4,1,2,5,8,7]=>1010001=>1000101=>0111010
[6,3,1,4,2,7,5,8]=>1101010=>0101011=>1010100
[1,8,3,2,4,5,6,7]=>0110000=>0000110=>1111001
[8,6,3,2,4,1,7,5]=>1110101=>1010111=>0101000
[8,5,3,2,6,7,1,4]=>1110010=>0100111=>1011000
[4,5,2,6,8,1,7,3]=>0100101=>1010010=>0101101
[4,2,5,6,7,8,1,3]=>1000010=>0100001=>1011110
[7,2,3,1,4,5,8,6]=>1010001=>1000101=>0111010
[2,4,6,8,10,1,3,5,7,9]=>000010000=>000010000=>111101111
[10,9,8,7,6,1,2,3,4,5]=>111110000=>000011111=>111100000
[9,10,7,8,5,6,3,4,1,2]=>010101010=>010101010=>101010101
[5,6,3,4,1,2,8,7]=>0101001=>1001010=>0110101
[7,8,3,5,4,6,1,2]=>0101010=>0101010=>1010101
[6,8,3,7,5,1,4,2]=>0101101=>1011010=>0100101
[2,1,7,8,5,6,3,4]=>1001010=>0101001=>1010110
[5,7,3,8,1,6,2,4]=>0101010=>0101010=>1010101
[7,5,8,4,2,6,1,3]=>1011010=>0101101=>1010010
[8,6,3,7,5,2,4,1]=>1101101=>1011011=>0100100
[8,5,3,7,2,6,4,1]=>1101011=>1101011=>0010100
[8,5,7,4,2,6,3,1]=>1011011=>1101101=>0010010
[7,8,4,6,1,5,2,3]=>0101010=>0101010=>1010101
[7,8,1,6,4,5,2,3]=>0101010=>0101010=>1010101
[6,8,1,7,4,5,2,3]=>0101010=>0101010=>1010101
[1,8,6,7,4,5,2,3]=>0101010=>0101010=>1010101
[1,8,6,7,3,5,2,4]=>0101010=>0101010=>1010101
[6,8,1,7,3,5,2,4]=>0101010=>0101010=>1010101
[7,8,1,6,3,5,2,4]=>0101010=>0101010=>1010101
[7,8,3,6,1,5,2,4]=>0101010=>0101010=>1010101
[7,8,3,6,4,5,1,2]=>0101010=>0101010=>1010101
[7,8,2,6,4,5,1,3]=>0101010=>0101010=>1010101
[7,8,2,6,3,5,1,4]=>0101010=>0101010=>1010101
[7,8,2,6,1,5,3,4]=>0101010=>0101010=>1010101
[7,8,1,6,2,5,3,4]=>0101010=>0101010=>1010101
[1,8,6,7,2,5,3,4]=>0101010=>0101010=>1010101
[1,8,5,7,2,6,3,4]=>0101010=>0101010=>1010101
[5,8,1,7,2,6,3,4]=>0101010=>0101010=>1010101
[5,8,2,7,1,6,3,4]=>0101010=>0101010=>1010101
[6,8,2,7,1,5,3,4]=>0101010=>0101010=>1010101
[6,8,2,7,3,5,1,4]=>0101010=>0101010=>1010101
[6,8,2,7,4,5,1,3]=>0101010=>0101010=>1010101
[6,8,3,7,4,5,1,2]=>0101010=>0101010=>1010101
[3,8,6,7,4,5,1,2]=>0101010=>0101010=>1010101
[2,8,6,7,4,5,1,3]=>0101010=>0101010=>1010101
[2,8,6,7,3,5,1,4]=>0101010=>0101010=>1010101
[2,8,6,7,1,5,3,4]=>0101010=>0101010=>1010101
[2,8,5,7,1,6,3,4]=>0101010=>0101010=>1010101
[2,8,1,7,5,6,3,4]=>0101010=>0101010=>1010101
[1,8,2,7,5,6,3,4]=>0101010=>0101010=>1010101
[1,8,2,7,4,6,3,5]=>0101010=>0101010=>1010101
[2,8,1,7,4,6,3,5]=>0101010=>0101010=>1010101
[2,8,4,7,1,6,3,5]=>0101010=>0101010=>1010101
[2,8,4,7,3,6,1,5]=>0101010=>0101010=>1010101
[2,8,5,7,3,6,1,4]=>0101010=>0101010=>1010101
[3,8,5,7,4,6,1,2]=>0101010=>0101010=>1010101
[5,8,3,7,4,6,1,2]=>0101010=>0101010=>1010101
[5,8,2,7,4,6,1,3]=>0101010=>0101010=>1010101
[5,8,2,7,3,6,1,4]=>0101010=>0101010=>1010101
[4,8,2,7,3,6,1,5]=>0101010=>0101010=>1010101
[4,8,2,7,1,6,3,5]=>0101010=>0101010=>1010101
[4,8,1,7,2,6,3,5]=>0101010=>0101010=>1010101
[1,8,4,7,2,6,3,5]=>0101010=>0101010=>1010101
[1,8,4,7,3,6,2,5]=>0101010=>0101010=>1010101
[4,8,1,7,3,6,2,5]=>0101010=>0101010=>1010101
[4,8,3,7,1,6,2,5]=>0101010=>0101010=>1010101
[6,8,3,7,1,5,2,4]=>0101010=>0101010=>1010101
[5,8,1,7,3,6,2,4]=>0101010=>0101010=>1010101
[1,8,5,7,3,6,2,4]=>0101010=>0101010=>1010101
[1,8,5,7,4,6,2,3]=>0101010=>0101010=>1010101
[5,8,1,7,4,6,2,3]=>0101010=>0101010=>1010101
[5,8,4,7,1,6,2,3]=>0101010=>0101010=>1010101
[6,8,4,7,1,5,2,3]=>0101010=>0101010=>1010101
[6,8,5,7,1,4,2,3]=>0101010=>0101010=>1010101
[5,8,6,7,3,4,1,2]=>0101010=>0101010=>1010101
[5,8,6,7,2,4,1,3]=>0101010=>0101010=>1010101
[5,8,6,7,1,4,2,3]=>0101010=>0101010=>1010101
[4,8,6,7,1,5,2,3]=>0101010=>0101010=>1010101
[4,8,5,7,1,6,2,3]=>0101010=>0101010=>1010101
[4,8,1,7,5,6,2,3]=>0101010=>0101010=>1010101
[1,8,4,7,5,6,2,3]=>0101010=>0101010=>1010101
[1,8,3,7,5,6,2,4]=>0101010=>0101010=>1010101
[3,8,1,7,5,6,2,4]=>0101010=>0101010=>1010101
[3,8,5,7,1,6,2,4]=>0101010=>0101010=>1010101
[3,8,6,7,1,5,2,4]=>0101010=>0101010=>1010101
[3,8,6,7,2,5,1,4]=>0101010=>0101010=>1010101
[4,8,6,7,2,5,1,3]=>0101010=>0101010=>1010101
[4,8,6,7,3,5,1,2]=>0101010=>0101010=>1010101
[4,8,5,7,3,6,1,2]=>0101010=>0101010=>1010101
[4,8,5,7,2,6,1,3]=>0101010=>0101010=>1010101
[3,8,5,7,2,6,1,4]=>0101010=>0101010=>1010101
[3,8,4,7,2,6,1,5]=>0101010=>0101010=>1010101
[3,8,4,7,1,6,2,5]=>0101010=>0101010=>1010101
[3,8,1,7,4,6,2,5]=>0101010=>0101010=>1010101
[1,8,3,7,4,6,2,5]=>0101010=>0101010=>1010101
[1,8,3,7,2,6,4,5]=>0101010=>0101010=>1010101
[3,8,1,7,2,6,4,5]=>0101010=>0101010=>1010101
[3,8,2,7,1,6,4,5]=>0101010=>0101010=>1010101
[3,8,2,7,4,6,1,5]=>0101010=>0101010=>1010101
[3,8,2,7,5,6,1,4]=>0101010=>0101010=>1010101
[4,8,2,7,5,6,1,3]=>0101010=>0101010=>1010101
[4,8,3,7,5,6,1,2]=>0101010=>0101010=>1010101
[3,8,4,7,5,6,1,2]=>0101010=>0101010=>1010101
[2,8,4,7,5,6,1,3]=>0101010=>0101010=>1010101
[2,8,3,7,5,6,1,4]=>0101010=>0101010=>1010101
[2,8,3,7,4,6,1,5]=>0101010=>0101010=>1010101
[2,8,3,7,1,6,4,5]=>0101010=>0101010=>1010101
[2,8,1,7,3,6,4,5]=>0101010=>0101010=>1010101
[7,5,2,8,6,4,1,3]=>1101110=>0111011=>1000100
[7,4,8,6,1,5,2,3]=>1011010=>0101101=>1010010
[7,1,8,4,5,2,6,3]=>1010101=>1010101=>0101010
[1,6,7,4,2,8,5,3]=>0011011=>1101100=>0010011
[1,6,7,3,8,5,2,4]=>0010110=>0110100=>1001011
[7,1,8,3,5,6,2,4]=>1010010=>0100101=>1011010
[7,3,8,6,2,5,1,4]=>1011010=>0101101=>1010010
[7,4,2,8,6,1,3,5]=>1101100=>0011011=>1100100
[6,8,1,7,2,3,4,5]=>0101000=>0001010=>1110101
[2,6,3,7,8,5,4,1]=>0100111=>1110010=>0001101
[2,5,3,7,8,1,6,4]=>0100101=>1010010=>0101101
[2,5,4,1,3,7,8,6]=>0110001=>1000110=>0111001
[3,1,5,4,7,8,2,6]=>1010010=>0100101=>1011010
[5,2,4,8,6,1,3,7]=>1001100=>0011001=>1100110
[4,8,1,3,6,7,2,5]=>0100010=>0100010=>1011101
[5,3,8,2,4,7,1,6]=>1010010=>0100101=>1011010
[5,4,3,8,1,2,7,6]=>1101001=>1001011=>0110100
[6,4,3,1,2,8,5,7]=>1110010=>0100111=>1011000
[6,4,2,8,1,3,7,5]=>1101001=>1001011=>0110100
[6,3,8,2,5,1,7,4]=>1010101=>1010101=>0101010
[6,3,8,1,4,7,2,5]=>1010010=>0100101=>1011010
[1,5,7,3,6,8,4,2]=>0010011=>1100100=>0011011
[1,5,7,4,2,6,8,3]=>0011001=>1001100=>0110011
[5,8,1,4,2,6,3,7]=>0101010=>0101010=>1010101
[6,5,1,2,8,7,3,4]=>1100110=>0110011=>1001100
[6,5,3,1,4,2,8,7]=>1110101=>1010111=>0101000
[5,3,1,6,4,2,7,8]=>1101100=>0011011=>1100100
[5,2,6,4,1,7,3,8]=>1011010=>0101101=>1010010
[4,6,1,7,5,2,8,3]=>0101101=>1011010=>0100101
[3,5,7,1,8,6,2,4]=>0010110=>0110100=>1001011
[3,6,2,7,5,1,8,4]=>0101101=>1011010=>0100101
[3,4,7,2,8,6,1,5]=>0010110=>0110100=>1001011
[3,4,5,8,2,7,1,6]=>0001010=>0101000=>1010111
[3,4,6,2,8,1,5,7]=>0010100=>0010100=>1101011
[3,5,2,6,8,1,7,4]=>0100101=>1010010=>0101101
[5,3,6,8,4,7,2,1]=>1001011=>1101001=>0010110
[3,7,2,5,4,8,6,1]=>0101011=>1101010=>0010101
[4,2,6,5,8,3,7,1]=>1010101=>1010101=>0101010
[4,1,6,5,8,3,2,7]=>1010110=>0110101=>1001010
[5,1,6,8,4,3,2,7]=>1001110=>0111001=>1000110
[6,7,8,1,4,3,2,5]=>0010110=>0110100=>1001011
[4,7,1,5,8,3,2,6]=>0100110=>0110010=>1001101
[8,3,1,5,4,7,2,6]=>1101010=>0101011=>1010100
[8,4,1,5,7,3,2,6]=>1100110=>0110011=>1001100
[8,4,6,1,7,3,2,5]=>1010110=>0110101=>1001010
[8,3,6,1,4,7,2,5]=>1010010=>0100101=>1011010
[8,2,6,1,4,3,7,5]=>1010101=>1010101=>0101010
[3,7,6,1,4,8,2,5]=>0110010=>0100110=>1011001
[6,7,8,5,1,3,2,4]=>0011010=>0101100=>1010011
[6,7,8,2,4,3,5,1]=>0010101=>1010100=>0101011
[4,7,6,2,8,3,5,1]=>0110101=>1010110=>0101001
[3,7,6,2,4,8,5,1]=>0110011=>1100110=>0011001
[5,7,3,8,4,6,2,1]=>0101011=>1101010=>0010101
[8,7,3,1,4,6,2,5]=>1110010=>0100111=>1011000
[8,7,6,3,2,5,4,1]=>1111011=>1101111=>0010000
[8,7,3,5,1,6,2,4]=>1101010=>0101011=>1010100
[8,7,2,5,1,3,6,4]=>1101001=>1001011=>0110100
[8,4,6,5,7,1,2,3]=>1010100=>0010101=>1101010
[4,7,6,5,8,1,2,3]=>0110100=>0010110=>1101001
[8,7,6,5,2,1,4,3]=>1111101=>1011111=>0100000
[3,6,4,8,7,5,1,2]=>0101110=>0111010=>1000101
[5,6,4,3,8,7,1,2]=>0110110=>0110110=>1001001
[1,6,2,4,7,8,5,3]=>0100011=>1100010=>0011101
[3,6,2,4,8,1,5,7]=>0100100=>0010010=>1101101
[3,4,7,2,8,1,6,5]=>0010101=>1010100=>0101011
[1,4,7,2,5,8,6,3]=>0010011=>1100100=>0011011
[3,8,7,5,4,6,1,2]=>0111010=>0101110=>1010001
[4,3,6,7,8,5,1,2]=>1000110=>0110001=>1001110
[3,5,6,4,8,7,1,2]=>0010110=>0110100=>1001011
[4,6,8,5,3,7,1,2]=>0011010=>0101100=>1010011
[4,2,7,5,1,8,6,3]=>1011011=>1101101=>0010010
[2,1,6,4,8,7,5,3]=>1010111=>1110101=>0001010
[7,8,1,4,2,6,5,3]=>0101011=>1101010=>0010101
[6,5,1,3,4,2,8,7]=>1100101=>1010011=>0101100
[4,8,5,3,1,7,2,6]=>0111010=>0101110=>1010001
[7,4,5,3,2,8,1,6]=>1011010=>0101101=>1010010
[5,8,3,6,1,4,2,7]=>0101010=>0101010=>1010101
[1,4,6,2,5,8,3,7]=>0010010=>0100100=>1011011
[1,6,8,7,4,2,3,5]=>0011100=>0011100=>1100011
[7,6,1,8,3,2,4,5]=>1101100=>0011011=>1100100
[7,1,8,6,3,4,2,5]=>1011010=>0101101=>1010010
[1,8,7,6,4,3,2,5]=>0111110=>0111110=>1000001
[2,1,7,5,6,3,8,4]=>1010101=>1010101=>0101010
[3,1,6,7,5,8,2,4]=>1001010=>0101001=>1010110
[7,8,1,6,5,3,2,4]=>0101110=>0111010=>1000101
[7,8,2,1,4,5,6,3]=>0110001=>1000110=>0111001
[4,2,6,1,8,5,7,3]=>1010101=>1010101=>0101010
[2,8,1,5,4,6,7,3]=>0101001=>1001010=>0110101
[1,2,8,3,6,5,7,4]=>0010101=>1010100=>0101011
[6,1,3,2,7,5,8,4]=>1010101=>1010101=>0101010
[2,6,4,1,7,5,8,3]=>0110101=>1010110=>0101001
[7,6,5,8,1,4,2,3]=>1101010=>0101011=>1010100
[5,8,6,7,3,2,1,4]=>0101110=>0111010=>1000101
[1,6,4,3,7,2,8,5]=>0110101=>1010110=>0101001
[4,6,3,8,1,2,7,5]=>0101001=>1001010=>0110101
[4,1,6,3,8,2,7,5]=>1010101=>1010101=>0101010
[7,8,1,3,4,2,6,5]=>0100101=>1010010=>0101101
[2,8,5,7,4,3,1,6]=>0101110=>0111010=>1000101
[7,2,5,8,3,4,1,6]=>1001010=>0101001=>1010110
[5,3,8,7,1,2,6,4]=>1011001=>1001101=>0110010
[6,5,3,8,2,1,7,4]=>1101101=>1011011=>0100100
[3,5,7,8,4,1,2,6]=>0001100=>0011000=>1100111
[5,4,7,3,6,8,1,2]=>1010010=>0100101=>1011010
[3,4,7,2,5,1,6,8]=>0010100=>0010100=>1101011
[1,4,7,2,5,8,3,6]=>0010010=>0100100=>1011011
[3,6,2,4,7,1,5,8]=>0100100=>0010010=>1101101
[7,6,3,5,4,8,1,2]=>1101010=>0101011=>1010100
[4,5,6,3,8,7,1,2]=>0010110=>0110100=>1001011
[6,3,7,5,8,4,1,2]=>1010110=>0110101=>1001010
[4,8,2,6,1,5,3,7]=>0101010=>0101010=>1010101
[4,3,6,2,5,1,8,7]=>1010101=>1010101=>0101010
[7,8,1,2,5,6,3,4]=>0100010=>0100010=>1011101
[4,1,6,2,5,7,3,8]=>1010010=>0100101=>1011010
[2,1,8,6,4,7,3,5]=>1011010=>0101101=>1010010
[7,1,3,6,8,4,2,5]=>1000110=>0110001=>1001110
[1,8,3,6,7,4,5,2]=>0100101=>1010010=>0101101
[7,1,5,8,3,6,2,4]=>1001010=>0101001=>1010110
[3,1,6,4,7,2,5,8]=>1010100=>0010101=>1101010
[5,8,7,1,2,4,3,6]=>0110010=>0100110=>1011001
[1,5,7,8,2,4,6,3]=>0001001=>1001000=>0110111
[6,8,5,1,3,4,2,7]=>0110010=>0100110=>1011001
[7,6,5,1,4,3,2,8]=>1110110=>0110111=>1001000
[2,6,4,5,1,3,8,7]=>0101001=>1001010=>0110101
[3,5,6,4,1,8,2,7]=>0011010=>0101100=>1010011
[7,8,5,4,1,3,2,6]=>0111010=>0101110=>1010001
[7,8,2,3,4,1,6,5]=>0100101=>1010010=>0101101
[4,2,6,3,8,1,7,5]=>1010101=>1010101=>0101010
[7,2,3,5,4,1,8,6]=>1001101=>1011001=>0100110
[6,2,4,3,1,5,7,8]=>1011000=>0001101=>1110010
[4,2,8,3,1,7,5,6]=>1011010=>0101101=>1010010
[1,3,7,4,8,2,5,6]=>0010100=>0010100=>1101011
[5,3,7,4,1,6,2,8]=>1011010=>0101101=>1010010
[2,4,7,3,6,1,8,5]=>0010101=>1010100=>0101011
[5,8,7,6,3,1,2,4]=>0111100=>0011110=>1100001
[7,5,6,8,1,4,3,2]=>1001011=>1101001=>0010110
[2,4,7,1,6,5,3,8]=>0010110=>0110100=>1001011
[5,2,7,1,8,4,6,3]=>1010101=>1010101=>0101010
[6,3,1,2,8,4,5,7]=>1100100=>0010011=>1101100
[4,2,1,3,6,5,8,7]=>1100101=>1010011=>0101100
[4,2,6,1,8,5,3,7]=>1010110=>0110101=>1001010
[7,8,2,1,4,5,3,6]=>0110010=>0100110=>1011001
[7,8,4,1,5,3,6,2]=>0110101=>1010110=>0101001
[7,5,1,6,4,3,8,2]=>1101101=>1011011=>0100100
[5,8,1,6,3,4,7,2]=>0101001=>1001010=>0110101
[6,8,1,7,5,2,3,4]=>0101100=>0011010=>1100101
[5,6,1,7,4,8,2,3]=>0101010=>0101010=>1010101
[7,8,5,1,6,4,2,3]=>0110110=>0110110=>1001001
[2,6,5,7,3,4,8,1]=>0101001=>1001010=>0110101
[1,6,4,7,5,8,2,3]=>0101010=>0101010=>1010101
[1,3,7,4,6,8,2,5]=>0010010=>0100100=>1011011
[5,2,4,7,3,6,8,1]=>1001001=>1001001=>0110110
[8,1,6,5,7,2,4,3]=>1010101=>1010101=>0101010
[7,1,6,5,8,3,2,4]=>1010110=>0110101=>1001010
[1,2,7,6,8,3,4,5]=>0010100=>0010100=>1101011
[3,8,6,4,2,7,5,1]=>0111011=>1101110=>0010001
[7,8,1,6,2,4,5,3]=>0101001=>1001010=>0110101
[2,8,1,7,4,3,6,5]=>0101101=>1011010=>0100101
[3,7,4,1,8,5,2,6]=>0110110=>0110110=>1001001
[6,7,1,4,8,3,2,5]=>0100110=>0110010=>1001101
[2,7,1,8,4,5,3,6]=>0101010=>0101010=>1010101
[6,1,2,8,4,3,5,7]=>1001100=>0011001=>1100110
[5,1,2,4,8,3,6,7]=>1000100=>0010001=>1101110
[4,1,3,2,8,5,6,7]=>1010100=>0010101=>1101010
[3,2,1,4,8,5,6,7]=>1100100=>0010011=>1101100
[4,3,6,1,5,8,2,7]=>1010010=>0100101=>1011010
[2,6,1,4,5,8,3,7]=>0100010=>0100010=>1011101
[1,6,2,5,8,3,4,7]=>0100100=>0010010=>1101101
[7,4,2,1,8,5,3,6]=>1110110=>0110111=>1001000
[1,5,4,2,8,3,6,7]=>0110100=>0010110=>1101001
[6,4,3,1,5,8,2,7]=>1110010=>0100111=>1011000
[5,4,3,2,1,8,6,7]=>1111010=>0101111=>1010000
[2,5,3,4,1,8,6,7]=>0101010=>0101010=>1010101
[4,3,5,2,1,8,6,7]=>1011010=>0101101=>1010010
[3,7,6,8,4,5,2,1]=>0101011=>1101010=>0010101
[1,7,6,8,5,4,2,3]=>0101110=>0111010=>1000101
[2,4,8,6,7,3,5,1]=>0010101=>1010100=>0101011
[3,4,8,5,6,7,2,1]=>0010011=>1100100=>0011011
[6,3,5,8,4,7,2,1]=>1001011=>1101001=>0010110
[5,4,3,8,6,7,2,1]=>1101011=>1101011=>0010100
[3,2,8,5,7,4,6,1]=>1010101=>1010101=>0101010
[2,1,8,7,4,6,3,5]=>1011010=>0101101=>1010010
[3,1,8,5,7,6,2,4]=>1010110=>0110101=>1001010
[6,1,5,8,7,4,2,3]=>1001110=>0111001=>1000110
[5,8,6,7,4,3,2,1]=>0101111=>1111010=>0000101
[4,8,7,5,6,3,2,1]=>0110111=>1110110=>0001001
[4,2,1,6,3,5,8,7]=>1101001=>1001011=>0110100
[6,2,1,4,3,8,5,7]=>1101010=>0101011=>1010100
[8,2,1,4,3,6,5,7]=>1101010=>0101011=>1010100
[6,2,4,1,3,8,5,7]=>1010010=>0100101=>1011010
[2,1,6,4,3,5,8,7]=>1011001=>1001101=>0110010
[6,4,2,1,3,5,8,7]=>1110001=>1000111=>0111000
[8,4,2,1,3,6,5,7]=>1110010=>0100111=>1011000
[8,4,2,1,6,3,5,7]=>1110100=>0010111=>1101000
[6,4,2,1,8,3,5,7]=>1110100=>0010111=>1101000
[4,6,2,1,3,8,5,7]=>0110010=>0100110=>1011001
[2,6,1,4,3,8,5,7]=>0101010=>0101010=>1010101
[2,1,6,4,3,8,5,7]=>1011010=>0101101=>1010010
[4,8,2,1,3,6,5,7]=>0110010=>0100110=>1011001
[6,8,2,1,4,3,5,7]=>0110100=>0010110=>1101001
[8,6,2,1,4,3,5,7]=>1110100=>0010111=>1101000
[2,8,1,4,6,3,5,7]=>0100100=>0010010=>1101101
[2,6,1,4,8,3,5,7]=>0100100=>0010010=>1101101
[2,6,4,1,8,3,5,7]=>0110100=>0010110=>1101001
[2,6,4,8,1,3,5,7]=>0101000=>0001010=>1110101
[4,2,6,1,8,3,5,7]=>1010100=>0010101=>1101010
[6,2,4,1,8,3,5,7]=>1010100=>0010101=>1101010
[4,2,1,6,8,3,5,7]=>1100100=>0010011=>1101100
[4,2,1,6,3,8,5,7]=>1101010=>0101011=>1010100
[4,2,1,3,6,8,5,7]=>1100010=>0100011=>1011100
[2,1,4,3,8,6,5,7]=>1010110=>0110101=>1001010
[2,4,1,3,8,6,5,7]=>0100110=>0110010=>1001101
[4,2,1,3,8,6,5,7]=>1100110=>0110011=>1001100
[4,2,1,8,3,6,5,7]=>1101010=>0101011=>1010100
[4,2,1,8,6,3,5,7]=>1101100=>0011011=>1100100
[8,2,1,6,4,3,5,7]=>1101100=>0011011=>1100100
[4,2,8,1,6,3,5,7]=>1010100=>0010101=>1101010
[2,4,1,8,3,6,5,7]=>0101010=>0101010=>1010101
[2,1,4,8,3,6,5,7]=>1001010=>0101001=>1010110
[2,4,8,1,6,3,5,7]=>0010100=>0010100=>1101011
[2,4,8,6,1,3,5,7]=>0011000=>0001100=>1110011
[4,2,8,6,1,3,5,7]=>1011000=>0001101=>1110010
[2,1,8,6,4,3,5,7]=>1011100=>0011101=>1100010
[2,8,6,1,4,3,5,7]=>0110100=>0010110=>1101001
[2,8,6,4,1,3,5,7]=>0111000=>0001110=>1110001
[4,8,6,2,1,3,5,7]=>0111000=>0001110=>1110001
[3,2,6,1,5,4,8,7]=>1010101=>1010101=>0101010
[6,1,5,2,4,3,8,7]=>1010101=>1010101=>0101010
[6,1,3,2,5,4,8,7]=>1010101=>1010101=>0101010
[4,3,6,1,5,2,8,7]=>1010101=>1010101=>0101010
[4,3,5,2,8,1,7,6]=>1010101=>1010101=>0101010
[4,3,7,2,6,5,8,1]=>1010101=>1010101=>0101010
[4,3,8,2,6,1,7,5]=>1010101=>1010101=>0101010
[4,3,8,1,5,2,7,6]=>1010101=>1010101=>0101010
[5,4,7,6,8,1,3,2]=>1010101=>1010101=>0101010
[4,3,7,1,8,5,6,2]=>1010101=>1010101=>0101010
[4,3,6,5,8,1,7,2]=>1010101=>1010101=>0101010
[6,3,5,4,7,2,8,1]=>1010101=>1010101=>0101010
[6,3,5,4,8,1,7,2]=>1010101=>1010101=>0101010
[7,1,6,3,8,4,5,2]=>1010101=>1010101=>0101010
[7,1,6,5,8,3,4,2]=>1010101=>1010101=>0101010
[7,4,6,5,8,1,3,2]=>1010101=>1010101=>0101010
[8,4,6,1,3,2,7,5]=>1010101=>1010101=>0101010
[8,1,6,3,4,2,7,5]=>1010101=>1010101=>0101010
[8,3,5,2,6,1,7,4]=>1010101=>1010101=>0101010
[7,3,5,2,6,4,8,1]=>1010101=>1010101=>0101010
[8,2,7,1,5,3,6,4]=>1010101=>1010101=>0101010
[8,1,7,2,4,3,6,5]=>1010101=>1010101=>0101010
[8,1,3,2,7,4,6,5]=>1010101=>1010101=>0101010
[2,1,8,3,7,4,6,5]=>1010101=>1010101=>0101010
[2,1,8,3,5,4,7,6]=>1010101=>1010101=>0101010
[8,1,3,2,5,4,7,6]=>1010101=>1010101=>0101010
[8,1,5,2,4,3,7,6]=>1010101=>1010101=>0101010
[8,2,4,1,5,3,7,6]=>1010101=>1010101=>0101010
[8,2,4,1,7,3,6,5]=>1010101=>1010101=>0101010
[3,2,8,4,6,1,7,5]=>1010101=>1010101=>0101010
[3,2,8,1,7,4,6,5]=>1010101=>1010101=>0101010
[3,2,8,1,5,4,7,6]=>1010101=>1010101=>0101010
[3,2,4,1,8,5,7,6]=>1010101=>1010101=>0101010
[4,1,3,2,7,6,8,5]=>1010101=>1010101=>0101010
[3,2,7,6,8,1,5,4]=>1010101=>1010101=>0101010
[3,2,7,1,8,5,6,4]=>1010101=>1010101=>0101010
[3,2,6,5,8,1,7,4]=>1010101=>1010101=>0101010
[7,2,4,1,8,5,6,3]=>1010101=>1010101=>0101010
[7,6,8,1,5,2,4,3]=>1010101=>1010101=>0101010
[7,6,8,1,3,2,5,4]=>1010101=>1010101=>0101010
[7,1,8,5,6,2,4,3]=>1010101=>1010101=>0101010
[7,1,8,2,6,4,5,3]=>1010101=>1010101=>0101010
[7,2,8,1,5,4,6,3]=>1010101=>1010101=>0101010
[5,4,7,2,6,3,8,1]=>1010101=>1010101=>0101010
[5,4,8,2,6,1,7,3]=>1010101=>1010101=>0101010
[6,1,8,4,7,2,5,3]=>1010101=>1010101=>0101010
[6,5,8,1,3,2,7,4]=>1010101=>1010101=>0101010
[6,5,7,4,8,1,3,2]=>1010101=>1010101=>0101010
[5,4,6,3,8,1,7,2]=>1010101=>1010101=>0101010
[3,2,1,5,8,4,6,7]=>1100100=>0010011=>1101100
[2,4,8,3,5,7,6,1]=>0010011=>1100100=>0011011
[4,2,5,3,1,8,6,7]=>1011010=>0101101=>1010010
[1,8,4,2,5,3,6,7]=>0110100=>0010110=>1101001
[8,1,5,3,2,4,6,7]=>1011000=>0001101=>1110010
[3,8,1,5,2,4,6,7]=>0101000=>0001010=>1110101
[5,4,1,3,8,2,6,7]=>1100100=>0010011=>1101100
[1,5,7,3,8,4,2,6]=>0010110=>0110100=>1001011
[5,1,4,7,8,3,2,6]=>1000110=>0110001=>1001110
[8,1,5,3,7,4,6,2]=>1010101=>1010101=>0101010
[1,4,3,8,7,5,6,2]=>0101101=>1011010=>0100101
[1,6,8,5,3,7,4,2]=>0011011=>1101100=>0010011
[6,4,8,1,7,3,5,2]=>1010101=>1010101=>0101010
[6,4,8,7,1,5,2,3]=>1011010=>0101101=>1010010
[7,1,6,8,4,3,2,5]=>1001110=>0111001=>1000110
[1,6,7,2,8,4,3,5]=>0010110=>0110100=>1001011
[6,7,1,4,2,8,3,5]=>0101010=>0101010=>1010101
[6,3,7,1,4,8,2,5]=>1010010=>0100101=>1011010
[3,7,8,1,5,2,4,6]=>0010100=>0010100=>1101011
[7,1,2,8,5,3,4,6]=>1001100=>0011001=>1100110
[1,7,2,8,4,5,3,6]=>0101010=>0101010=>1010101
[4,2,1,7,8,5,3,6]=>1100110=>0110011=>1001100
[6,2,4,8,3,7,5,1]=>1001011=>1101001=>0010110
[7,2,6,3,4,1,8,5]=>1010101=>1010101=>0101010
[2,7,1,8,3,5,4,6]=>0101010=>0101010=>1010101
[2,1,7,3,5,8,4,6]=>1010010=>0100101=>1011010
[1,2,7,5,8,3,4,6]=>0010100=>0010100=>1101011
[8,7,1,3,6,2,4,5]=>1100100=>0010011=>1101100
[8,2,1,7,3,5,6,4]=>1101001=>1001011=>0110100
[2,7,8,4,1,6,5,3]=>0011011=>1101100=>0010011
[2,8,4,1,6,7,5,3]=>0110011=>1100110=>0011001
[2,1,8,4,7,5,6,3]=>1010101=>1010101=>0101010
[8,3,7,1,5,6,2,4]=>1010010=>0100101=>1011010
[8,6,1,2,7,5,3,4]=>1100110=>0110011=>1001100
[8,1,6,2,7,4,5,3]=>1010101=>1010101=>0101010
[1,8,5,2,6,7,4,3]=>0110011=>1100110=>0011001
[5,2,1,8,6,7,4,3]=>1101011=>1101011=>0010100
[8,7,6,5,1,4,2,3]=>1111010=>0101111=>1010000
[8,7,6,1,5,3,4,2]=>1110101=>1010111=>0101000
[8,1,7,5,6,4,3,2]=>1010111=>1110101=>0001010
[1,8,6,7,5,4,3,2]=>0101111=>1111010=>0000101
[6,3,5,2,1,4,8,7]=>1011001=>1001101=>0110010
[8,3,5,7,2,4,1,6]=>1001010=>0101001=>1010110
[8,5,2,7,4,3,1,6]=>1101110=>0111011=>1000100
[6,5,3,1,2,4,8,7]=>1110001=>1000111=>0111000
[4,5,3,6,1,2,8,7]=>0101001=>1001010=>0110101
[3,5,1,4,6,2,8,7]=>0100101=>1010010=>0101101
[8,1,4,7,3,6,2,5]=>1001010=>0101001=>1010110
[8,5,1,4,7,3,2,6]=>1100110=>0110011=>1001100
[8,5,3,7,1,4,2,6]=>1101010=>0101011=>1010100
[6,3,4,7,5,8,1,2]=>1001010=>0101001=>1010110
[5,1,4,6,8,3,7,2]=>1000101=>1010001=>0101110
[4,7,1,3,5,8,6,2]=>0100011=>1100010=>0011101
[4,8,3,7,1,2,6,5]=>0101001=>1001010=>0110101
[8,7,1,4,2,6,3,5]=>1101010=>0101011=>1010100
[8,6,3,1,2,4,7,5]=>1110001=>1000111=>0111000
[2,1,8,7,5,3,4,6]=>1011100=>0011101=>1100010
[8,1,7,4,5,2,3,6]=>1010100=>0010101=>1101010
[2,8,7,5,4,1,3,6]=>0111100=>0011110=>1100001
[8,7,2,6,4,1,3,5]=>1101100=>0011011=>1100100
[5,3,7,8,2,4,6,1]=>1001001=>1001001=>0110110
[5,3,7,6,2,1,8,4]=>1011101=>1011101=>0100010
[5,7,8,6,4,2,1,3]=>0011110=>0111100=>1000011
[2,6,7,5,4,8,1,3]=>0011010=>0101100=>1010011
[6,7,3,5,1,8,2,4]=>0101010=>0101010=>1010101
[2,1,6,7,5,8,3,4]=>1001010=>0101001=>1010110
[2,1,5,7,3,6,8,4]=>1001001=>1001001=>0110110
[4,1,7,2,5,6,8,3]=>1010001=>1000101=>0111010
[2,4,7,1,6,5,8,3]=>0010101=>1010100=>0101011
[3,4,6,2,7,8,5,1]=>0010011=>1100100=>0011011
[4,6,1,2,5,8,7,3]=>0100011=>1100010=>0011101
[5,6,3,1,8,7,2,4]=>0110110=>0110110=>1001001
[3,5,6,4,7,1,8,2]=>0010101=>1010100=>0101011
[3,4,6,1,5,7,8,2]=>0010001=>1000100=>0111011
[3,4,1,5,7,6,8,2]=>0100101=>1010010=>0101101
[4,2,1,7,3,5,8,6]=>1101001=>1001011=>0110100
[7,3,1,5,4,2,8,6]=>1101101=>1011011=>0100100
[6,3,1,4,2,8,5,7]=>1101010=>0101011=>1010100
[8,4,1,5,2,7,6,3]=>1101011=>1101011=>0010100
[7,2,5,1,4,3,8,6]=>1010101=>1010101=>0101010
[3,6,2,7,1,4,8,5]=>0101001=>1001010=>0110101
[2,7,5,4,1,3,8,6]=>0111001=>1001110=>0110001
[6,4,3,2,1,8,5,7]=>1111010=>0101111=>1010000
[1,7,6,2,4,8,3,5]=>0110010=>0100110=>1011001
[2,7,3,6,4,8,1,5]=>0101010=>0101010=>1010101
[6,2,7,5,3,8,1,4]=>1011010=>0101101=>1010010
[7,1,8,5,3,6,4,2]=>1011011=>1101101=>0010010
[5,8,3,2,7,1,6,4]=>0110101=>1010110=>0101001
[8,7,2,6,1,5,4,3]=>1101011=>1101011=>0010100
[1,8,5,7,4,3,6,2]=>0101101=>1011010=>0100101
[1,8,5,7,2,4,6,3]=>0101001=>1001010=>0110101
[3,8,6,1,7,2,5,4]=>0110101=>1010110=>0101001
[7,2,8,5,6,1,4,3]=>1010101=>1010101=>0101010
[3,6,5,8,1,4,2,7]=>0101010=>0101010=>1010101
[4,3,6,8,2,1,5,7]=>1001100=>0011001=>1100110
[4,3,6,7,8,1,2,5]=>1000100=>0010001=>1101110
[5,4,6,7,2,8,1,3]=>1001010=>0101001=>1010110
[3,5,7,1,4,8,2,6]=>0010010=>0100100=>1011011
[8,1,5,2,7,4,6,3]=>1010101=>1010101=>0101010
[8,4,1,5,7,3,6,2]=>1100101=>1010011=>0101100
[6,4,2,5,8,3,1,7]=>1100110=>0110011=>1001100
[5,4,1,6,8,2,3,7]=>1100100=>0010011=>1101100
[5,3,1,7,2,8,4,6]=>1101010=>0101011=>1010100
[5,3,6,4,7,8,1,2]=>1010010=>0100101=>1011010
[6,3,7,4,8,5,2,1]=>1010111=>1110101=>0001010
[4,7,2,5,8,6,3,1]=>0100111=>1110010=>0001101
[6,3,1,8,4,7,5,2]=>1101011=>1101011=>0010100
[5,4,8,1,7,6,2,3]=>1010110=>0110101=>1001010
[5,2,8,1,7,3,6,4]=>1010101=>1010101=>0101010
[5,7,3,8,1,6,4,2]=>0101011=>1101010=>0010101
[6,4,7,8,1,5,3,2]=>1001011=>1101001=>0010110
[4,6,8,2,7,1,5,3]=>0010101=>1010100=>0101011
[2,5,8,7,1,3,6,4]=>0011001=>1001100=>0110011
[8,3,7,6,1,5,4,2]=>1011011=>1101101=>0010010
[8,2,7,6,5,1,4,3]=>1011101=>1011101=>0100010
[4,3,8,7,6,2,1,5]=>1011110=>0111101=>1000010
[2,4,8,7,6,1,3,5]=>0011100=>0011100=>1100011
[3,5,8,7,2,6,1,4]=>0011010=>0101100=>1010011
[4,7,3,8,6,5,1,2]=>0101110=>0111010=>1000101
[7,5,8,6,4,3,2,1]=>1011111=>1111101=>0000010
[5,8,7,3,6,4,2,1]=>0110111=>1110110=>0001001
[3,8,7,6,5,1,4,2]=>0111101=>1011110=>0100001
[2,8,7,6,5,4,1,3]=>0111110=>0111110=>1000001
[5,4,3,2,1,6,7,8,9,10]=>111100000=>000001111=>111110000
[6,4,3,2,7,1,5,8,9,10]=>111010000=>000010111=>111101000
[7,5,3,8,2,6,1,4,9,10]=>110101000=>000101011=>111010100
[8,6,9,4,7,2,5,1,3,10]=>101010100=>001010101=>110101010
[7,8,5,6,3,1,4,2]=>0101101=>1011010=>0100101
[7,8,5,3,6,1,2,4]=>0110100=>0010110=>1101001
[7,5,6,3,1,4,2,8]=>1011010=>0101101=>1010010
[7,5,8,3,1,4,2,6]=>1011010=>0101101=>1010010
[7,8,5,3,1,4,2,6]=>0111010=>0101110=>1010001
[7,8,5,3,1,6,2,4]=>0111010=>0101110=>1010001
[7,8,5,3,1,6,4,2]=>0111011=>1101110=>0010001
[7,8,5,3,6,1,4,2]=>0110101=>1010110=>0101001
[7,8,5,3,6,4,1,2]=>0110110=>0110110=>1001001
[7,8,5,3,4,1,6,2]=>0110101=>1010110=>0101001
[7,8,5,3,1,4,6,2]=>0111001=>1001110=>0110001
[7,5,8,3,1,2,6,4]=>1011001=>1001101=>0110010
[7,5,8,3,4,1,6,2]=>1010101=>1010101=>0101010
[7,5,8,3,4,6,1,2]=>1010010=>0100101=>1011010
[7,5,6,3,4,1,8,2]=>1010101=>1010101=>0101010
[7,5,6,3,1,4,8,2]=>1011001=>1001101=>0110010
[7,5,3,1,6,4,8,2]=>1110101=>1010111=>0101000
[7,5,3,6,1,4,8,2]=>1101001=>1001011=>0110100
[7,5,3,6,4,1,8,2]=>1101101=>1011011=>0100100
[7,5,3,6,4,8,1,2]=>1101010=>0101011=>1010100
[7,5,3,8,4,6,1,2]=>1101010=>0101011=>1010100
[7,5,3,8,4,1,6,2]=>1101101=>1011011=>0100100
[7,5,3,8,1,4,6,2]=>1101001=>1001011=>0110100
[7,5,3,1,8,4,6,2]=>1110101=>1010111=>0101000
[7,5,3,1,8,2,6,4]=>1110101=>1010111=>0101000
[7,5,3,1,6,2,4,8]=>1110100=>0010111=>1101000
[7,5,3,1,6,4,2,8]=>1110110=>0110111=>1001000
[7,5,3,1,8,4,2,6]=>1110110=>0110111=>1001000
[7,5,3,1,8,6,2,4]=>1110110=>0110111=>1001000
[7,5,3,8,1,6,4,2]=>1101011=>1101011=>0010100
[7,5,3,8,6,1,4,2]=>1101101=>1011011=>0100100
[7,5,3,8,6,4,1,2]=>1101110=>0111011=>1000100
[7,5,8,3,6,4,1,2]=>1010110=>0110101=>1001010
[7,5,8,3,6,1,4,2]=>1010101=>1010101=>0101010
[7,5,8,3,1,6,4,2]=>1011011=>1101101=>0010010
[7,5,8,3,1,6,2,4]=>1011010=>0101101=>1010010
[7,5,3,8,1,6,2,4]=>1101010=>0101011=>1010100
[7,5,3,8,1,4,2,6]=>1101010=>0101011=>1010100
[7,5,3,6,1,4,2,8]=>1101010=>0101011=>1010100
[7,5,3,6,4,1,2,8]=>1101100=>0011011=>1100100
[7,5,3,8,4,1,2,6]=>1101100=>0011011=>1100100
[7,5,3,8,6,1,2,4]=>1101100=>0011011=>1100100
[7,5,8,6,3,1,2,4]=>1011100=>0011101=>1100010
[7,5,8,6,3,1,4,2]=>1011101=>1011101=>0100010
[7,5,8,6,3,4,1,2]=>1011010=>0101101=>1010010
[7,5,6,8,3,1,4,2]=>1001101=>1011001=>0100110
[7,5,6,3,8,1,2,4]=>1010100=>0010101=>1101010
[7,5,3,6,1,8,2,4]=>1101010=>0101011=>1010100
[7,5,6,3,1,8,2,4]=>1011010=>0101101=>1010010
[7,5,6,3,1,8,4,2]=>1011011=>1101101=>0010010
[7,5,6,3,8,1,4,2]=>1010101=>1010101=>0101010
[7,5,6,3,8,4,1,2]=>1010110=>0110101=>1001010
[7,5,3,6,8,4,1,2]=>1100110=>0110011=>1001100
[7,5,3,6,8,1,4,2]=>1100101=>1010011=>0101100
[7,5,3,6,1,8,4,2]=>1101011=>1101011=>0010100
[7,5,3,1,6,8,4,2]=>1110011=>1100111=>0011000
[7,5,3,1,6,8,2,4]=>1110010=>0100111=>1011000
[7,5,3,1,2,8,6,4]=>1110011=>1100111=>0011000
[7,5,3,4,1,6,8,2]=>1101001=>1001011=>0110100
[4,6,8,3,5,7,1,2]=>0010010=>0100100=>1011011
[6,8,1,2,4,5,7,3]=>0100001=>1000010=>0111101
[3,6,8,2,5,7,1,4]=>0010010=>0100100=>1011011
[8,3,5,2,4,1,6,7]=>1010100=>0010101=>1101010
[3,5,7,2,4,6,1,8]=>0010010=>0100100=>1011011
[4,2,5,7,3,6,1,8]=>1001010=>0101001=>1010110
[4,5,2,8,3,1,6,7]=>0101100=>0011010=>1100101
[2,1,6,8,4,7,3,5]=>1001010=>0101001=>1010110
[1,2,5,8,3,6,7,4]=>0001001=>1001000=>0110111
[5,3,6,8,4,7,1,2]=>1001010=>0101001=>1010110
[3,1,2,6,8,5,7,4]=>1000101=>1010001=>0101110
[4,3,6,2,7,5,1,8]=>1010110=>0110101=>1001010
[4,3,1,7,8,2,6,5]=>1100101=>1010011=>0101100
[5,4,7,3,8,6,1,2]=>1010110=>0110101=>1001010
[5,8,4,7,6,3,1,2]=>0101110=>0111010=>1000101
[8,3,5,1,2,7,6,4]=>1010011=>1100101=>0011010
[4,7,3,6,5,2,1,8]=>0101110=>0111010=>1000101
[5,3,7,6,4,2,1,8]=>1011110=>0111101=>1000010
[5,3,1,6,4,2,8,7]=>1101101=>1011011=>0100100
[1,3,8,5,4,2,7,6]=>0011101=>1011100=>0100011
[1,8,3,6,2,7,5,4]=>0101011=>1101010=>0010101
[1,6,8,7,4,2,5,3]=>0011101=>1011100=>0100011
[6,4,8,7,5,3,1,2]=>1011110=>0111101=>1000010
[3,1,2,7,6,4,8,5]=>1001101=>1011001=>0100110
[5,2,6,3,7,4,1,8]=>1010110=>0110101=>1001010
[2,8,5,3,1,6,4,7]=>0111010=>0101110=>1010001
[2,1,7,3,8,5,4,6]=>1010110=>0110101=>1001010
[1,6,2,3,7,8,5,4]=>0100011=>1100010=>0011101
[1,6,7,2,8,4,5,3]=>0010101=>1010100=>0101011
[6,3,7,4,8,5,1,2]=>1010110=>0110101=>1001010
[5,7,1,8,2,4,6,3]=>0101001=>1001010=>0110101
[5,1,2,7,8,3,6,4]=>1000101=>1010001=>0101110
[4,2,1,7,3,8,5,6]=>1101010=>0101011=>1010100
[6,2,8,4,3,1,5,7]=>1011100=>0011101=>1100010
[6,4,2,7,3,5,1,8]=>1101010=>0101011=>1010100
[7,3,2,1,8,4,5,6]=>1110100=>0010111=>1101000
[3,7,2,8,6,1,4,5]=>0101100=>0011010=>1100101
[7,8,3,2,5,6,1,4]=>0110010=>0100110=>1011001
[7,1,8,2,4,5,6,3]=>1010001=>1000101=>0111010
[8,7,6,1,2,4,5,3]=>1110001=>1000111=>0111000
[8,3,6,5,2,1,4,7]=>1011100=>0011101=>1100010
[8,2,4,1,6,5,3,7]=>1010110=>0110101=>1001010
[8,2,4,1,7,6,3,5]=>1010110=>0110101=>1001010
[8,5,1,2,7,3,6,4]=>1100101=>1010011=>0101100
[6,1,8,2,3,7,5,4]=>1010011=>1100101=>0011010
[2,8,1,7,5,4,3,6]=>0101110=>0111010=>1000101
[1,7,2,8,3,6,5,4]=>0101011=>1101010=>0010101
[7,3,8,6,5,4,1,2]=>1011110=>0111101=>1000010
[1,8,7,6,5,2,4,3]=>0111101=>1011110=>0100001
[8,1,7,3,2,6,5,4]=>1011011=>1101101=>0010010
[4,3,1,2,8,7,6,5]=>1100111=>1110011=>0001100
[5,1,4,3,2,8,7,6]=>1011011=>1101101=>0010010
[8,6,4,3,1,5,7,2]=>1111001=>1001111=>0110000
[8,6,4,1,5,2,7,3]=>1110101=>1010111=>0101000
[8,6,5,3,2,1,7,4]=>1111101=>1011111=>0100000
[8,7,2,4,5,3,1,6]=>1100110=>0110011=>1001100
[8,5,1,2,6,7,3,4]=>1100010=>0100011=>1011100
[8,5,1,6,4,2,7,3]=>1101101=>1011011=>0100100
[8,5,1,3,6,4,7,2]=>1100101=>1010011=>0101100
[8,6,5,1,7,3,2,4]=>1110110=>0110111=>1001000
[7,4,8,3,1,6,2,5]=>1011010=>0101101=>1010010
[7,1,5,8,3,2,6,4]=>1001101=>1011001=>0100110
[5,7,4,1,8,2,6,3]=>0110101=>1010110=>0101001
[5,7,4,3,1,8,6,2]=>0111011=>1101110=>0010001
[8,5,7,4,6,1,3,2]=>1010101=>1010101=>0101010
[1,8,7,2,5,4,6,3]=>0110101=>1010110=>0101001
[4,3,1,8,7,5,2,6]=>1101110=>0111011=>1000100
[1,3,5,6,8,4,2,7]=>0000110=>0110000=>1001111
[3,1,4,6,8,7,2,5]=>1000110=>0110001=>1001110
[1,6,3,8,7,2,5,4]=>0101101=>1011010=>0100101
[1,6,2,4,8,7,5,3]=>0100111=>1110010=>0001101
[8,4,1,6,7,5,3,2]=>1100111=>1110011=>0001100
[7,3,6,8,5,1,2,4]=>1001100=>0011001=>1100110
[1,3,7,2,6,8,4,5]=>0010010=>0100100=>1011011
[3,6,5,2,8,1,4,7]=>0110100=>0010110=>1101001
[6,1,2,7,8,5,3,4]=>1000110=>0110001=>1001110
[6,1,2,7,4,8,5,3]=>1001011=>1101001=>0010110
[3,1,6,4,7,8,5,2]=>1010011=>1100101=>0011010
[5,7,1,3,8,4,6,2]=>0100101=>1010010=>0101101
[5,7,1,8,4,2,6,3]=>0101101=>1011010=>0100101
[5,7,1,2,8,6,3,4]=>0100110=>0110010=>1001101
[4,2,6,3,8,1,5,7]=>1010100=>0010101=>1101010
[4,2,6,7,3,5,1,8]=>1001010=>0101001=>1010110
[3,6,2,4,7,5,1,8]=>0100110=>0110010=>1001101
[3,6,2,4,1,8,5,7]=>0101010=>0101010=>1010101
[7,1,4,5,2,8,6,3]=>1001011=>1101001=>0010110
[4,7,3,1,5,8,6,2]=>0110011=>1100110=>0011001
[8,7,6,4,1,5,2,3]=>1111010=>0101111=>1010000
[3,8,2,7,1,5,4,6]=>0101010=>0101010=>1010101
[3,6,8,2,1,5,4,7]=>0011010=>0101100=>1010011
[2,4,8,1,6,5,3,7]=>0010110=>0110100=>1001011
[4,2,8,1,5,7,3,6]=>1010010=>0100101=>1011010
[8,5,7,6,1,4,2,3]=>1011010=>0101101=>1010010
[1,8,2,4,6,7,3,5]=>0100010=>0100010=>1011101
[2,1,5,8,6,4,3,7]=>1001110=>0111001=>1000110
[1,2,5,7,8,4,3,6]=>0000110=>0110000=>1001111
[1,2,7,4,8,6,3,5]=>0010110=>0110100=>1001011
[1,2,7,8,3,6,5,4]=>0001011=>1101000=>0010111
[1,8,5,7,4,3,2,6]=>0101110=>0111010=>1000101
[1,6,8,5,4,3,2,7]=>0011110=>0111100=>1000011
[7,1,5,8,3,4,6,2]=>1001001=>1001001=>0110110
[7,1,5,8,4,3,2,6]=>1001110=>0111001=>1000110
[7,1,2,5,8,3,6,4]=>1000101=>1010001=>0101110
[7,1,6,4,2,3,5,8]=>1011000=>0001101=>1110010
[2,7,1,4,8,3,5,6]=>0100100=>0010010=>1101101
[7,1,4,6,5,8,3,2]=>1001011=>1101001=>0010110
[7,1,2,3,8,5,4,6]=>1000110=>0110001=>1001110
[7,1,5,4,3,8,2,6]=>1011010=>0101101=>1010010
[7,1,3,4,2,6,8,5]=>1001001=>1001001=>0110110
[3,6,7,1,4,8,5,2]=>0010011=>1100100=>0011011
[3,5,1,4,8,6,2,7]=>0100110=>0110010=>1001101
[3,6,2,4,7,8,1,5]=>0100010=>0100010=>1011101
[5,6,2,4,8,7,1,3]=>0100110=>0110010=>1001101
[6,5,8,7,2,3,1,4]=>1011010=>0101101=>1010010
[3,4,7,2,5,8,1,6]=>0010010=>0100100=>1011011
[4,3,8,1,2,7,5,6]=>1010010=>0100101=>1011010
[5,6,7,8,1,3,4,2]=>0001001=>1001000=>0110111
[5,7,8,6,1,2,3,4]=>0011000=>0001100=>1110011
[2,8,3,1,5,6,4,7]=>0110010=>0100110=>1011001
[3,8,7,1,5,4,2,6]=>0110110=>0110110=>1001001
[4,3,1,7,6,8,2,5]=>1101010=>0101011=>1010100
[3,4,1,7,5,6,8,2]=>0101001=>1001010=>0110101
[3,4,1,5,7,6,2,8]=>0100110=>0110010=>1001101
[2,4,6,1,7,5,8,3]=>0010101=>1010100=>0101011
[4,7,8,1,2,3,6,5]=>0010001=>1000100=>0111011
[4,2,1,5,6,3,7,8]=>1100100=>0010011=>1101100
[5,8,1,6,4,3,2,7]=>0101110=>0111010=>1000101
[5,8,1,6,3,7,2,4]=>0101010=>0101010=>1010101
[7,6,5,1,3,8,2,4]=>1110010=>0100111=>1011000
[7,6,5,1,3,4,8,2]=>1110001=>1000111=>0111000
[7,2,6,4,1,3,8,5]=>1011001=>1001101=>0110010
[8,4,5,3,7,2,6,1]=>1010101=>1010101=>0101010
[4,7,5,2,8,1,6,3]=>0110101=>1010110=>0101001
[4,6,3,8,5,1,7,2]=>0101101=>1011010=>0100101
[2,6,4,3,1,5,7,8]=>0111000=>0001110=>1110001
[3,6,4,8,1,7,2,5]=>0101010=>0101010=>1010101
[7,3,8,4,1,5,2,6]=>1011010=>0101101=>1010010
[4,2,8,3,6,1,5,7]=>1010100=>0010101=>1101010
[6,7,5,8,2,1,4,3]=>0101101=>1011010=>0100101
[6,8,5,7,2,1,3,4]=>0101100=>0011010=>1100101
[4,8,5,2,7,1,3,6]=>0110100=>0010110=>1101001
[6,3,5,2,1,7,4,8]=>1011010=>0101101=>1010010
[3,6,5,4,2,8,1,7]=>0111010=>0101110=>1010001
[7,4,5,3,8,2,1,6]=>1010110=>0110101=>1001010
[1,6,4,7,2,5,3,8]=>0101010=>0101010=>1010101
[1,4,3,7,2,6,5,8]=>0101010=>0101010=>1010101
[1,5,7,2,4,8,3,6]=>0010010=>0100100=>1011011
[1,6,5,7,2,4,3,8]=>0101010=>0101010=>1010101
[1,7,6,2,8,3,4,5]=>0110100=>0010110=>1101001
[1,4,2,3,5,8,7,6]=>0100011=>1100010=>0011101
[1,5,2,3,4,8,7,6]=>0100011=>1100010=>0011101
[1,6,5,2,3,8,7,4]=>0110011=>1100110=>0011001
[1,7,6,5,2,8,4,3]=>0111011=>1101110=>0010001
[1,6,5,2,3,8,4,7]=>0110010=>0100110=>1011001
[1,6,7,5,2,3,8,4]=>0011001=>1001100=>0110011
[1,7,5,2,8,4,3,6]=>0110110=>0110110=>1001001
[1,7,5,6,2,8,3,4]=>0101010=>0101010=>1010101
[1,5,7,6,2,4,8,3]=>0011001=>1001100=>0110011
[1,4,7,6,2,5,8,3]=>0011001=>1001100=>0110011
[1,2,6,5,3,7,4,8]=>0011010=>0101100=>1010011
[1,3,7,5,2,6,8,4]=>0011001=>1001100=>0110011
[1,7,4,6,2,8,3,5]=>0101010=>0101010=>1010101
[1,7,3,5,2,8,4,6]=>0101010=>0101010=>1010101
[1,3,7,4,2,6,8,5]=>0011001=>1001100=>0110011
[1,4,7,3,2,5,8,6]=>0011001=>1001100=>0110011
[1,5,7,3,2,4,8,6]=>0011001=>1001100=>0110011
[1,7,3,4,2,8,5,6]=>0101010=>0101010=>1010101
[1,7,4,2,8,5,3,6]=>0110110=>0110110=>1001001
[1,6,7,4,2,3,8,5]=>0011001=>1001100=>0110011
[1,4,3,2,5,8,6,7]=>0110010=>0100110=>1011001
[1,5,3,2,4,8,6,7]=>0110010=>0100110=>1011001
[1,6,4,2,3,8,5,7]=>0110010=>0100110=>1011001
[1,7,6,4,2,8,5,3]=>0111011=>1101110=>0010001
[1,7,5,3,2,8,6,4]=>0111011=>1101110=>0010001
[1,6,4,2,3,8,7,5]=>0110011=>1100110=>0011001
[1,5,3,2,4,8,7,6]=>0110011=>1100110=>0011001
[6,8,5,4,3,2,1,7]=>0111110=>0111110=>1000001
[2,8,5,4,3,7,1,6]=>0111010=>0101110=>1010001
[7,6,1,4,3,8,5,2]=>1101011=>1101011=>0010100
[7,6,5,1,3,8,4,2]=>1110011=>1100111=>0011000
[7,3,5,4,8,1,6,2]=>1010101=>1010101=>0101010
[5,6,8,4,3,1,7,2]=>0011101=>1011100=>0100011
[6,8,5,4,1,2,7,3]=>0111001=>1001110=>0110001
[6,8,2,4,3,7,1,5]=>0101010=>0101010=>1010101
[1,8,3,4,7,2,6,5]=>0100101=>1010010=>0101101
[7,5,8,4,3,2,1,6]=>1011110=>0111101=>1000010
[4,8,5,7,3,2,1,6]=>0101110=>0111010=>1000101
[7,8,1,2,4,3,5,6]=>0100100=>0010010=>1101101
[7,8,2,1,4,3,6,5]=>0110101=>1010110=>0101001
[3,4,6,5,7,8,1,2]=>0010010=>0100100=>1011011
[4,3,6,5,8,7,1,2]=>1010110=>0110101=>1001010
[4,2,6,1,8,3,7,5]=>1010101=>1010101=>0101010
[6,7,3,8,4,5,1,2]=>0101010=>0101010=>1010101
[6,7,4,5,1,8,2,3]=>0101010=>0101010=>1010101
[4,5,3,8,6,7,1,2]=>0101010=>0101010=>1010101
[5,6,3,8,4,7,1,2]=>0101010=>0101010=>1010101
[5,6,4,7,1,8,2,3]=>0101010=>0101010=>1010101
[5,6,2,7,3,4,1,8]=>0101010=>0101010=>1010101
[4,5,1,8,6,7,2,3]=>0101010=>0101010=>1010101
[7,8,4,5,1,6,2,3]=>0101010=>0101010=>1010101
[4,5,2,3,1,8,6,7]=>0101010=>0101010=>1010101
[5,6,2,3,1,8,4,7]=>0101010=>0101010=>1010101
[5,6,3,4,1,8,2,7]=>0101010=>0101010=>1010101
[3,6,4,5,2,7,1,8]=>0101010=>0101010=>1010101
[3,6,4,5,1,8,2,7]=>0101010=>0101010=>1010101
[2,6,4,8,1,5,3,7]=>0101010=>0101010=>1010101
[2,8,3,6,1,5,4,7]=>0101010=>0101010=>1010101
[2,8,3,4,1,6,5,7]=>0101010=>0101010=>1010101
[7,8,1,5,3,6,2,4]=>0101010=>0101010=>1010101
[1,8,3,6,5,7,2,4]=>0101010=>0101010=>1010101
[1,6,4,7,3,8,2,5]=>0101010=>0101010=>1010101
[1,7,3,6,4,8,2,5]=>0101010=>0101010=>1010101
[1,7,2,8,4,6,3,5]=>0101010=>0101010=>1010101
[1,7,5,8,2,6,3,4]=>0101010=>0101010=>1010101
[6,7,1,5,3,8,2,4]=>0101010=>0101010=>1010101
[6,7,1,8,2,5,3,4]=>0101010=>0101010=>1010101
[6,7,1,8,4,5,2,3]=>0101010=>0101010=>1010101
[6,7,5,8,1,4,2,3]=>0101010=>0101010=>1010101
[5,8,6,7,2,3,1,4]=>0101010=>0101010=>1010101
[6,7,2,3,1,8,4,5]=>0101010=>0101010=>1010101
[6,7,2,8,1,4,3,5]=>0101010=>0101010=>1010101
[6,7,3,4,1,8,2,5]=>0101010=>0101010=>1010101
[3,4,2,7,5,6,1,8]=>0101010=>0101010=>1010101
[2,7,5,8,1,4,3,6]=>0101010=>0101010=>1010101
[2,3,1,8,4,7,5,6]=>0101010=>0101010=>1010101
[2,3,1,8,6,7,4,5]=>0101010=>0101010=>1010101
[7,8,2,3,1,6,4,5]=>0101010=>0101010=>1010101
[2,8,1,4,3,7,5,6]=>0101010=>0101010=>1010101
[2,8,1,7,3,5,4,6]=>0101010=>0101010=>1010101
[4,5,1,7,3,8,2,6]=>0101010=>0101010=>1010101
[3,8,1,5,2,7,4,6]=>0101010=>0101010=>1010101
[3,4,1,8,6,7,2,5]=>0101010=>0101010=>1010101
[7,8,3,4,1,6,2,5]=>0101010=>0101010=>1010101
[3,4,2,5,1,8,6,7]=>0101010=>0101010=>1010101
[3,4,2,8,1,6,5,7]=>0101010=>0101010=>1010101
[2,5,4,1,6,3,8,7]=>0110101=>1010110=>0101001
[3,6,5,1,2,4,8,7]=>0110001=>1000110=>0111001
[5,2,3,6,4,1,8,7]=>1001101=>1011001=>0100110
[6,1,4,5,3,2,8,7]=>1001101=>1011001=>0100110
[5,6,7,8,1,4,3,2]=>0001011=>1101000=>0010111
[4,2,6,8,5,7,3,1]=>1001011=>1101001=>0010110
[2,1,5,8,7,6,3,4]=>1001110=>0111001=>1000110
[2,1,4,7,6,3,8,5]=>1001101=>1011001=>0100110
[6,3,7,1,5,2,8,4]=>1010101=>1010101=>0101010
[4,2,8,6,7,3,1,5]=>1010110=>0110101=>1001010
[7,4,3,8,2,1,5,6]=>1101100=>0011011=>1100100
[2,4,1,5,8,3,7,6]=>0100101=>1010010=>0101101
[4,7,5,8,1,6,3,2]=>0101011=>1101010=>0010101
[2,1,5,8,7,3,4,6]=>1001100=>0011001=>1100110
[8,5,7,3,6,1,4,2]=>1010101=>1010101=>0101010
[4,2,5,1,6,7,8,3]=>1010001=>1000101=>0111010
[7,2,3,4,8,5,6,1]=>1000101=>1010001=>0101110
[6,1,8,5,2,7,4,3]=>1011011=>1101101=>0010010
[2,1,7,4,5,8,6,3]=>1010011=>1100101=>0011010
[2,1,8,3,6,7,5,4]=>1010011=>1100101=>0011010
[6,8,7,2,5,3,1,4]=>0110110=>0110110=>1001001
[8,2,1,6,4,7,5,3]=>1101011=>1101011=>0010100
[7,8,4,2,5,1,6,3]=>0110101=>1010110=>0101001
[6,1,2,3,7,5,8,4]=>1000101=>1010001=>0101110
[7,6,8,4,2,5,3,1]=>1011011=>1101101=>0010010
[8,5,7,1,6,3,2,4]=>1010110=>0110101=>1001010
[4,1,2,3,7,6,8,5]=>1000101=>1010001=>0101110
[3,2,4,1,8,5,6,7]=>1010100=>0010101=>1101010
[3,4,8,6,5,2,1,7]=>0011110=>0111100=>1000011
[4,1,6,3,5,8,7,2]=>1010011=>1100101=>0011010
[8,6,7,1,5,4,3,2]=>1010111=>1110101=>0001010
[2,1,6,5,8,4,7,3]=>1010101=>1010101=>0101010
[4,1,8,5,6,2,3,7]=>1010100=>0010101=>1101010
[2,6,4,8,7,3,5,1]=>0101101=>1011010=>0100101
[3,1,8,2,7,5,4,6]=>1010110=>0110101=>1001010
[8,2,3,1,7,4,6,5]=>1010101=>1010101=>0101010
[7,4,8,6,3,2,5,1]=>1011101=>1011101=>0100010
[5,8,4,7,2,1,3,6]=>0101100=>0011010=>1100101
[2,1,8,4,3,7,5,6]=>1011010=>0101101=>1010010
[6,3,8,2,4,5,7,1]=>1010001=>1000101=>0111010
[5,8,2,4,3,1,6,7]=>0101100=>0011010=>1100101
[7,3,5,8,1,4,2,6]=>1001010=>0101001=>1010110
[3,8,7,6,1,4,2,5]=>0111010=>0101110=>1010001
[5,1,8,3,6,7,2,4]=>1010010=>0100101=>1011010
[3,6,1,4,7,8,5,2]=>0100011=>1100010=>0011101
[1,6,8,4,7,5,2,3]=>0010110=>0110100=>1001011
[6,8,1,3,5,7,2,4]=>0100010=>0100010=>1011101
[7,6,1,4,3,8,2,5]=>1101010=>0101011=>1010100
[8,4,2,6,7,5,3,1]=>1100111=>1110011=>0001100
[7,4,1,6,8,2,5,3]=>1100101=>1010011=>0101100
[1,8,6,2,5,3,4,7]=>0110100=>0010110=>1101001
[4,7,1,2,5,3,8,6]=>0100101=>1010010=>0101101
[8,7,3,6,4,5,2,1]=>1101011=>1101011=>0010100
[5,7,8,6,2,1,4,3]=>0011101=>1011100=>0100011
[1,8,6,4,5,2,3,7]=>0110100=>0010110=>1101001
[1,4,7,2,6,8,3,5]=>0010010=>0100100=>1011011
[2,5,4,3,6,8,1,7]=>0110010=>0100110=>1011001
[3,8,5,4,6,2,1,7]=>0110110=>0110110=>1001001
[4,8,2,1,3,7,5,6]=>0110010=>0100110=>1011001
[1,8,3,2,5,6,7,4]=>0110001=>1000110=>0111001
[6,4,1,2,7,5,8,3]=>1100101=>1010011=>0101100
[4,3,7,8,5,1,6,2]=>1001101=>1011001=>0100110
[1,2,7,3,6,5,8,4]=>0010101=>1010100=>0101011
[2,8,7,6,3,4,1,5]=>0111010=>0101110=>1010001
[5,8,2,6,3,4,1,7]=>0101010=>0101010=>1010101
[4,1,7,5,8,6,2,3]=>1010110=>0110101=>1001010
[1,2,4,5,8,3,7,6]=>0000101=>1010000=>0101111
[4,8,1,5,2,3,7,6]=>0101001=>1001010=>0110101
[2,4,6,3,7,1,8,5]=>0010101=>1010100=>0101011
[6,5,8,7,1,3,4,2]=>1011001=>1001101=>0110010
[3,6,7,2,4,8,1,5]=>0010010=>0100100=>1011011
[1,5,2,7,4,3,8,6]=>0101101=>1011010=>0100101
[7,6,1,2,8,3,5,4]=>1100101=>1010011=>0101100
[6,7,8,1,5,2,4,3]=>0010101=>1010100=>0101011
[5,7,8,4,1,2,6,3]=>0011001=>1001100=>0110011
[4,7,8,5,6,1,3,2]=>0010101=>1010100=>0101011
[5,6,4,8,1,2,7,3]=>0101001=>1001010=>0110101
[6,5,4,1,2,3,8,7]=>1110001=>1000111=>0111000
[7,5,1,6,2,3,8,4]=>1101001=>1001011=>0110100
[4,5,6,7,8,1,3,2]=>0000101=>1010000=>0101111
[8,1,3,6,7,4,5,2]=>1000101=>1010001=>0101110
[4,2,6,7,3,1,8,5]=>1001101=>1011001=>0100110
[7,3,1,5,4,8,2,6]=>1101010=>0101011=>1010100
[4,5,3,2,8,1,6,7]=>0110100=>0010110=>1101001
[7,4,1,5,3,2,6,8]=>1101100=>0011011=>1100100
[8,1,5,4,3,2,6,7]=>1011100=>0011101=>1100010
[8,1,6,4,2,5,3,7]=>1011010=>0101101=>1010010
[6,5,3,1,2,7,4,8]=>1110010=>0100111=>1011000
[5,6,3,8,1,4,2,7]=>0101010=>0101010=>1010101
[4,6,3,8,2,1,5,7]=>0101100=>0011010=>1100101
[4,7,8,3,2,1,5,6]=>0011100=>0011100=>1100011
[5,7,8,3,1,4,2,6]=>0011010=>0101100=>1010011
[8,1,7,2,5,4,3,6]=>1010110=>0110101=>1001010
[8,1,7,2,4,5,6,3]=>1010001=>1000101=>0111010
[7,6,1,2,4,5,8,3]=>1100001=>1000011=>0111100
[4,7,8,2,3,1,6,5]=>0010101=>1010100=>0101011
[7,5,1,3,2,6,8,4]=>1101001=>1001011=>0110100
[8,1,6,3,2,5,7,4]=>1011001=>1001101=>0110010
[8,1,5,3,4,2,7,6]=>1010101=>1010101=>0101010
[5,4,2,3,1,6,8,7]=>1101001=>1001011=>0110100
[6,3,2,1,5,7,4,8]=>1110010=>0100111=>1011000
[8,1,4,3,5,6,2,7]=>1010010=>0100101=>1011010
[3,6,5,8,2,4,1,7]=>0101010=>0101010=>1010101
[6,2,4,5,8,3,1,7]=>1000110=>0110001=>1001110
[4,8,1,2,5,6,3,7]=>0100010=>0100010=>1011101
[8,1,3,5,2,6,4,7]=>1001010=>0101001=>1010110
[5,2,1,6,3,8,4,7]=>1101010=>0101011=>1010100
[6,1,4,5,8,3,2,7]=>1000110=>0110001=>1001110
[6,5,4,3,8,2,1,7]=>1110110=>0110111=>1001000
[4,6,8,3,7,2,5,1]=>0010101=>1010100=>0101011
[1,4,3,6,2,7,8,5]=>0101001=>1001010=>0110101
[4,7,8,5,3,1,2,6]=>0011100=>0011100=>1100011
[8,5,7,4,3,6,1,2]=>1011010=>0101101=>1010010
[4,7,8,3,6,1,5,2]=>0010101=>1010100=>0101011
[8,4,6,1,7,3,5,2]=>1010101=>1010101=>0101010
[1,3,8,6,4,7,5,2]=>0011011=>1101100=>0010011
[7,6,2,1,4,3,8,5]=>1110101=>1010111=>0101000
[7,6,8,1,4,3,2,5]=>1010110=>0110101=>1001010
[1,5,7,3,2,6,8,4]=>0011001=>1001100=>0110011
[3,2,6,8,5,7,4,1]=>1001011=>1101001=>0010110
[7,5,2,3,1,6,8,4]=>1101001=>1001011=>0110100
[1,6,4,7,2,3,8,5]=>0101001=>1001010=>0110101
[3,1,7,5,2,8,4,6]=>1011010=>0101101=>1010010
[1,7,4,5,2,8,3,6]=>0101010=>0101010=>1010101
[3,2,6,8,7,4,5,1]=>1001101=>1011001=>0100110
[6,3,2,1,7,8,4,5]=>1110010=>0100111=>1011000
[5,7,3,8,2,1,4,6]=>0101100=>0011010=>1100101
[3,7,1,8,4,2,5,6]=>0101100=>0011010=>1100101
[4,2,1,3,7,5,8,6]=>1100101=>1010011=>0101100
[8,4,3,7,6,2,1,5]=>1101110=>0111011=>1000100
[3,6,2,8,7,1,5,4]=>0101101=>1011010=>0100101
[7,3,2,8,1,6,5,4]=>1101011=>1101011=>0010100
[3,8,7,2,6,5,4,1]=>0110111=>1110110=>0001001
[4,2,7,8,6,1,5,3]=>1001101=>1011001=>0100110
[5,8,4,2,7,1,6,3]=>0110101=>1010110=>0101001
[8,5,3,1,7,2,6,4]=>1110101=>1010111=>0101000
[8,2,1,6,3,7,5,4]=>1101011=>1101011=>0010100
[1,4,6,8,2,7,5,3]=>0001011=>1101000=>0010111
[2,1,7,3,8,6,5,4]=>1010111=>1110101=>0001010
[8,2,1,7,6,5,4,3]=>1101111=>1111011=>0000100
[8,6,7,5,1,4,3,2]=>1011011=>1101101=>0010010
[6,4,7,3,2,1,8,5]=>1011101=>1011101=>0100010
[4,8,7,3,2,1,6,5]=>0111101=>1011110=>0100001
[6,5,3,7,2,1,4,8]=>1101100=>0011011=>1100100
[5,8,3,6,2,1,4,7]=>0101100=>0011010=>1100101
[6,4,3,7,2,1,8,5]=>1101101=>1011011=>0100100
[4,8,3,6,2,1,7,5]=>0101101=>1011010=>0100101
[6,3,7,8,2,1,4,5]=>1001100=>0011001=>1100110
[5,3,7,6,2,1,4,8]=>1011100=>0011101=>1100010
[3,8,7,6,2,1,4,5]=>0111100=>0011110=>1100001
[5,8,4,2,6,1,3,7]=>0110100=>0010110=>1101001
[4,8,7,2,5,1,3,6]=>0110100=>0010110=>1101001
[5,8,3,2,6,1,4,7]=>0110100=>0010110=>1101001
[4,8,3,2,5,1,7,6]=>0110101=>1010110=>0101001
[4,3,7,2,5,1,8,6]=>1010101=>1010101=>0101010
[6,4,2,7,5,1,3,8]=>1101100=>0011011=>1100100
[5,4,2,6,7,1,3,8]=>1100100=>0010011=>1101100
[6,2,7,8,5,1,3,4]=>1001100=>0011001=>1100110
[2,8,7,6,5,1,3,4]=>0111100=>0011110=>1100001
[6,4,7,3,1,5,8,2]=>1011001=>1001101=>0110010
[4,8,7,3,1,5,6,2]=>0111001=>1001110=>0110001
[6,5,3,7,1,4,8,2]=>1101001=>1001011=>0110100
[5,8,3,6,1,4,7,2]=>0101001=>1001010=>0110101
[6,4,3,7,1,5,8,2]=>1101001=>1001011=>0110100
[4,8,3,6,1,5,7,2]=>0101001=>1001010=>0110101
[5,3,7,6,1,4,8,2]=>1011001=>1001101=>0110010
[4,3,7,6,1,5,8,2]=>1011001=>1001101=>0110010
[3,8,7,6,1,4,5,2]=>0111001=>1001110=>0110001
[5,8,4,2,1,7,3,6]=>0111010=>0101110=>1010001
[6,4,7,2,1,5,3,8]=>1011010=>0101101=>1010010
[5,8,3,2,1,4,7,6]=>0111001=>1001110=>0110001
[6,3,7,2,1,4,5,8]=>1011000=>0001101=>1110010
[6,5,2,7,1,4,3,8]=>1101010=>0101011=>1010100
[5,8,2,6,1,4,3,7]=>0101010=>0101010=>1010101
[6,4,2,7,1,5,3,8]=>1101010=>0101011=>1010100
[2,8,7,6,1,4,3,5]=>0111010=>0101110=>1010001
[6,5,4,1,8,7,3,2]=>1110111=>1110111=>0001000
[6,4,7,1,5,8,3,2]=>1010011=>1100101=>0011010
[4,8,7,1,5,6,3,2]=>0110011=>1100110=>0011001
[6,5,3,1,8,4,7,2]=>1110101=>1010111=>0101000
[5,8,3,1,6,4,7,2]=>0110101=>1010110=>0101001
[6,4,3,1,5,8,7,2]=>1110011=>1100111=>0011000
[5,8,2,1,6,4,3,7]=>0110110=>0110110=>1001001
[6,4,2,1,5,8,3,7]=>1110010=>0100111=>1011000
[3,8,2,1,5,4,6,7]=>0110100=>0010110=>1101001
[6,2,7,1,5,4,3,8]=>1010110=>0110101=>1001010
[3,2,7,1,5,4,6,8]=>1010100=>0010101=>1101010
[2,8,7,1,5,4,3,6]=>0110110=>0110110=>1001001
[6,5,1,7,8,4,3,2]=>1100111=>1110011=>0001100
[5,4,1,6,7,8,3,2]=>1100011=>1100011=>0011100
[4,3,1,6,5,7,8,2]=>1101001=>1001011=>0110100
[4,2,1,6,5,7,3,8]=>1101010=>0101011=>1010100
[2,8,1,6,5,4,3,7]=>0101110=>0111010=>1000101
[6,1,7,8,5,4,3,2]=>1001111=>1111001=>0000110
[5,1,7,6,8,4,3,2]=>1010111=>1110101=>0001010
[4,1,7,6,5,8,3,2]=>1011011=>1101101=>0010010
[4,5,8,1,7,2,3,6]=>0010100=>0010100=>1101011
[4,5,8,1,2,6,3,7]=>0010010=>0100100=>1011011
[8,1,3,5,7,2,4,6]=>1000100=>0010001=>1101110
[3,6,8,1,7,2,4,5]=>0010100=>0010100=>1101011
[3,4,5,6,8,1,7,2]=>0000101=>1010000=>0101111
[8,2,3,5,6,7,1,4]=>1000010=>0100001=>1011110
[8,1,2,3,5,4,6,7]=>1000100=>0010001=>1101110
[4,5,8,1,7,6,3,2]=>0010111=>1110100=>0001011
[8,7,2,1,6,3,4,5]=>1110100=>0010111=>1101000
[8,7,2,1,3,5,4,6]=>1110010=>0100111=>1011000
[8,6,4,1,7,5,3,2]=>1110111=>1110111=>0001000
[2,3,6,7,8,1,5,4]=>0000101=>1010000=>0101111
[7,4,2,6,8,5,1,3]=>1100110=>0110011=>1001100
[7,3,2,5,8,6,1,4]=>1100110=>0110011=>1001100
[7,3,1,8,6,2,4,5]=>1101100=>0011011=>1100100
[3,1,7,2,5,4,8,6]=>1010101=>1010101=>0101010
[7,1,4,2,8,3,6,5]=>1010101=>1010101=>0101010
[7,1,8,2,5,3,6,4]=>1010101=>1010101=>0101010
[7,3,8,4,5,1,6,2]=>1010101=>1010101=>0101010
[8,3,7,4,6,1,5,2]=>1010101=>1010101=>0101010
[8,2,7,1,6,4,5,3]=>1010101=>1010101=>0101010
[8,1,7,5,4,2,3,6]=>1011100=>0011101=>1100010
[8,1,2,6,5,4,3,7]=>1001110=>0111001=>1000110
[8,1,7,6,3,2,4,5]=>1011100=>0011101=>1100010
[8,2,7,5,6,1,4,3]=>1010101=>1010101=>0101010
[3,6,8,1,7,5,4,2]=>0010111=>1110100=>0001011
[8,2,6,7,5,4,1,3]=>1001110=>0111001=>1000110
[8,6,7,2,3,1,5,4]=>1010101=>1010101=>0101010
[2,7,8,6,3,1,5,4]=>0011101=>1011100=>0100011
[7,3,1,8,6,5,4,2]=>1101111=>1111011=>0000100
[8,1,7,6,5,4,3,2]=>1011111=>1111101=>0000010
[2,1,8,6,3,7,4,5]=>1011010=>0101101=>1010010
[8,6,1,5,2,7,4,3]=>1101011=>1101011=>0010100
[8,5,1,7,4,2,6,3]=>1101101=>1011011=>0100100
[2,1,7,8,3,6,5,4]=>1001011=>1101001=>0010110
[2,1,4,8,5,7,3,6]=>1001010=>0101001=>1010110
[7,8,1,5,2,6,3,4]=>0101010=>0101010=>1010101
[6,4,1,5,2,3,8,7]=>1101001=>1001011=>0110100
[4,3,7,8,5,2,1,6]=>1001110=>0111001=>1000110
[5,3,7,4,6,8,1,2]=>1010010=>0100101=>1011010
[5,8,3,7,6,2,1,4]=>0101110=>0111010=>1000101
[4,2,6,3,8,5,1,7]=>1010110=>0110101=>1001010
[5,8,2,1,7,6,4,3]=>0110111=>1110110=>0001001
[8,3,2,4,1,7,5,6]=>1101010=>0101011=>1010100
[6,3,4,2,1,7,8,5]=>1011001=>1001101=>0110010
[7,2,8,1,4,6,5,3]=>1010011=>1100101=>0011010
[6,8,1,4,5,3,2,7]=>0100110=>0110010=>1001101
[8,2,6,1,4,7,3,5]=>1010010=>0100101=>1011010
[4,2,1,3,6,7,8,5]=>1100001=>1000011=>0111100
[2,3,4,1,8,6,5,7]=>0010110=>0110100=>1001011
[6,3,5,4,1,2,8,7]=>1011001=>1001101=>0110010
[8,7,3,6,5,1,4,2]=>1101101=>1011011=>0100100
[3,4,7,2,8,1,5,6]=>0010100=>0010100=>1101011
[3,8,4,7,1,6,5,2]=>0101011=>1101010=>0010101
[3,2,4,6,1,5,8,7]=>1001001=>1001001=>0110110
[6,8,5,4,3,7,2,1]=>0111011=>1101110=>0010001
[5,8,4,3,2,1,7,6]=>0111101=>1011110=>0100001
[6,5,4,3,1,8,7,2]=>1111011=>1101111=>0010000
[8,7,5,4,3,1,6,2]=>1111101=>1011111=>0100000
[3,4,6,2,8,5,1,7]=>0010110=>0110100=>1001011
[3,4,6,7,1,8,5,2]=>0001011=>1101000=>0010111
[3,4,6,8,1,5,2,7]=>0001010=>0101000=>1010111
[3,4,7,2,8,5,6,1]=>0010101=>1010100=>0101011
[3,4,8,2,1,5,6,7]=>0011000=>0001100=>1110011
[3,5,2,6,8,4,1,7]=>0100110=>0110010=>1001101
[3,5,2,7,4,8,6,1]=>0101011=>1101010=>0010101
[3,5,6,2,7,8,1,4]=>0010010=>0100100=>1011011
[3,5,6,2,8,4,1,7]=>0010110=>0110100=>1001011
[3,5,6,8,4,1,2,7]=>0001100=>0011000=>1100111
[3,5,7,2,4,8,6,1]=>0010011=>1100100=>0011011
[3,5,7,2,8,4,6,1]=>0010101=>1010100=>0101011
[3,5,7,8,4,1,6,2]=>0001101=>1011000=>0100111
[3,5,8,2,4,1,6,7]=>0010100=>0010100=>1101011
[3,6,2,1,7,8,5,4]=>0110011=>1100110=>0011001
[3,6,2,1,8,5,4,7]=>0110110=>0110110=>1001001
[3,6,2,7,4,8,5,1]=>0101011=>1101010=>0010101
[3,6,2,7,8,5,4,1]=>0100111=>1110010=>0001101
[3,6,8,2,4,5,1,7]=>0010010=>0100100=>1011011
[3,7,2,1,4,8,6,5]=>0110011=>1100110=>0011001
[3,7,2,8,4,5,6,1]=>0101001=>1001010=>0110101
[3,8,2,1,4,5,6,7]=>0110000=>0000110=>1111001
[4,1,5,6,7,8,3,2]=>1000011=>1100001=>0011110
[4,1,5,7,3,8,6,2]=>1001011=>1101001=>0010110
[4,1,5,7,8,2,6,3]=>1000101=>1010001=>0101110
[4,1,5,8,3,2,6,7]=>1001100=>0011001=>1100110
[4,1,6,3,7,8,5,2]=>1010011=>1100101=>0011010
[4,1,6,3,8,5,2,7]=>1010110=>0110101=>1001010
[4,1,6,7,3,8,5,2]=>1001011=>1101001=>0010110
[4,1,6,8,3,5,2,7]=>1001010=>0101001=>1010110
[4,1,7,3,8,5,6,2]=>1010101=>1010101=>0101010
[4,1,8,3,2,5,6,7]=>1011000=>0001101=>1110010
[4,5,2,7,3,8,6,1]=>0101011=>1101010=>0010101
[4,5,7,3,2,8,6,1]=>0011011=>1101100=>0010011
[4,5,8,3,2,1,6,7]=>0011100=>0011100=>1100011
[4,6,2,3,8,5,1,7]=>0100110=>0110010=>1001101
[4,6,2,8,3,5,1,7]=>0101010=>0101010=>1010101
[4,6,7,3,2,8,5,1]=>0011011=>1101100=>0010011
[4,7,2,8,3,5,6,1]=>0101001=>1001010=>0110101
[4,7,8,3,2,5,6,1]=>0011001=>1001100=>0110011
[4,8,2,3,1,5,6,7]=>0101000=>0001010=>1110101
[5,1,2,6,8,4,3,7]=>1000110=>0110001=>1001110
[5,1,2,8,4,3,6,7]=>1001100=>0011001=>1100110
[5,1,6,3,7,8,2,4]=>1010010=>0100101=>1011010
[5,1,6,3,8,4,2,7]=>1010110=>0110101=>1001010
[5,1,6,7,4,8,2,3]=>1001010=>0101001=>1010110
[5,6,2,3,8,4,1,7]=>0100110=>0110010=>1001101
[5,6,2,7,4,8,1,3]=>0101010=>0101010=>1010101
[5,6,2,7,8,4,1,3]=>0100110=>0110010=>1001101
[5,6,8,3,4,2,1,7]=>0010110=>0110100=>1001011
[5,7,8,3,4,2,6,1]=>0010101=>1010100=>0101011
[6,1,2,3,7,8,5,4]=>1000011=>1100001=>0011110
[6,1,2,3,8,5,4,7]=>1000110=>0110001=>1001110
[6,1,2,7,8,5,4,3]=>1000111=>1110001=>0001110
[6,1,7,8,4,5,3,2]=>1001011=>1101001=>0010110
[6,7,2,8,4,5,3,1]=>0101011=>1101010=>0010101
[7,1,2,3,4,8,6,5]=>1000011=>1100001=>0011110
[7,1,2,3,8,5,6,4]=>1000101=>1010001=>0101110
[7,1,2,8,4,5,6,3]=>1001001=>1001001=>0110110
[7,1,8,3,4,5,6,2]=>1010001=>1000101=>0111010
[2,4,6,1,8,5,7,3]=>0010101=>1010100=>0101011
[6,4,1,8,2,3,7,5]=>1101001=>1001011=>0110100
[5,8,1,2,4,3,7,6]=>0100101=>1010010=>0101101
[5,8,1,6,2,4,3,7]=>0101010=>0101010=>1010101
[1,3,5,7,2,6,4,8]=>0001010=>0101000=>1010111
[3,5,8,6,1,2,4,7]=>0011000=>0001100=>1110011
[3,5,1,8,2,4,7,6]=>0101001=>1001010=>0110101
[3,1,6,8,2,4,7,5]=>1001001=>1001001=>0110110
[2,3,5,6,8,1,7,4]=>0000101=>1010000=>0101111
[5,6,4,8,2,1,7,3]=>0101101=>1011010=>0100101
[7,1,8,6,3,4,5,2]=>1011001=>1001101=>0110010
[7,6,5,2,4,8,1,3]=>1110010=>0100111=>1011000
[6,7,4,5,2,1,8,3]=>0101101=>1011010=>0100101
[5,1,7,8,6,4,3,2]=>1001111=>1111001=>0000110
[2,5,7,8,6,3,1,4]=>0001110=>0111000=>1000111
[7,1,8,6,3,2,4,5]=>1011100=>0011101=>1100010
[7,8,1,6,4,2,3,5]=>0101100=>0011010=>1100101
[2,4,8,1,5,6,7,3]=>0010001=>1000100=>0111011
[8,4,1,2,5,6,3,7]=>1100010=>0100011=>1011100
[8,3,1,6,5,2,4,7]=>1101100=>0011011=>1100100
[2,5,3,8,7,6,1,4]=>0101110=>0111010=>1000101
[5,8,7,4,2,6,1,3]=>0111010=>0101110=>1010001
[5,1,8,4,7,6,3,2]=>1010111=>1110101=>0001010
[7,3,2,6,5,1,8,4]=>1101101=>1011011=>0100100
[8,2,3,6,5,1,7,4]=>1001101=>1011001=>0100110
[4,8,6,5,7,3,2,1]=>0110111=>1110110=>0001001
[4,8,5,6,7,3,2,1]=>0100111=>1110010=>0001101
[3,8,7,4,5,6,2,1]=>0110011=>1100110=>0011001
[2,8,7,6,3,4,5,1]=>0111001=>1001110=>0110001
[1,8,7,6,5,2,3,4]=>0111100=>0011110=>1100001
[7,2,8,6,5,4,1,3]=>1011110=>0111101=>1000010
[6,3,2,8,5,1,7,4]=>1101101=>1011011=>0100100
[8,4,7,2,5,6,3,1]=>1010011=>1100101=>0011010
[6,8,5,4,3,1,7,2]=>0111101=>1011110=>0100001
[5,8,6,4,1,3,7,2]=>0111001=>1001110=>0110001
[3,6,1,8,5,2,7,4]=>0101101=>1011010=>0100101
[3,4,1,2,8,6,7,5]=>0100101=>1010010=>0101101
[6,8,3,5,4,1,7,2]=>0101101=>1011010=>0100101
[7,6,3,8,5,2,1,4]=>1101110=>0111011=>1000100
[5,8,7,4,1,6,3,2]=>0111011=>1101110=>0010001
[4,2,3,1,7,8,5,6]=>1010010=>0100101=>1011010
[8,6,3,4,7,2,5,1]=>1100101=>1010011=>0101100
[5,2,8,4,1,6,7,3]=>1011001=>1001101=>0110010
[4,1,3,6,8,2,5,7]=>1000100=>0010001=>1101110
[1,6,3,2,5,8,4,7]=>0110010=>0100110=>1011001
[8,3,2,1,5,4,7,6]=>1110101=>1010111=>0101000
[5,3,6,2,4,8,1,7]=>1010010=>0100101=>1011010
[1,6,2,4,5,8,3,7]=>0100010=>0100010=>1011101
[5,3,2,1,6,8,4,7]=>1110010=>0100111=>1011000
[2,6,5,8,1,3,4,7]=>0101000=>0001010=>1110101
[4,3,1,6,5,8,2,7]=>1101010=>0101011=>1010100
[3,4,6,5,7,1,8,2]=>0010101=>1010100=>0101011
[8,2,6,4,1,7,3,5]=>1011010=>0101101=>1010010
[5,4,6,8,1,2,7,3]=>1001001=>1001001=>0110110
[3,4,7,8,6,2,5,1]=>0001101=>1011000=>0100111
[7,5,8,2,4,6,1,3]=>1010010=>0100101=>1011010
[8,2,7,4,6,1,3,5]=>1010100=>0010101=>1101010
[4,7,3,2,8,1,6,5]=>0110101=>1010110=>0101001
[3,8,1,7,2,5,6,4]=>0101001=>1001010=>0110101
[8,3,2,5,7,6,1,4]=>1100110=>0110011=>1001100
[2,8,6,1,5,7,3,4]=>0110010=>0100110=>1011001
[1,2,8,3,5,6,7,4]=>0010001=>1000100=>0111011
[4,2,3,7,1,8,6,5]=>1001011=>1101001=>0010110
[3,2,6,4,8,1,7,5]=>1010101=>1010101=>0101010
[8,2,1,6,7,3,4,5]=>1100100=>0010011=>1101100
[2,7,8,5,4,1,3,6]=>0011100=>0011100=>1100011
[1,7,5,3,8,4,2,6]=>0110110=>0110110=>1001001
[4,7,5,3,1,2,8,6]=>0111001=>1001110=>0110001
[5,6,7,3,8,4,2,1]=>0010111=>1110100=>0001011
[5,7,3,2,4,1,8,6]=>0110101=>1010110=>0101001
[8,4,1,3,7,2,5,6]=>1100100=>0010011=>1101100
[2,8,4,7,1,3,5,6]=>0101000=>0001010=>1110101
[3,5,2,8,6,1,7,4]=>0101101=>1011010=>0100101
[1,7,6,3,2,5,8,4]=>0111001=>1001110=>0110001
[3,8,1,5,6,2,7,4]=>0100101=>1010010=>0101101
[4,3,5,6,7,1,8,2]=>1000101=>1010001=>0101110
[7,1,5,2,8,6,4,3]=>1010111=>1110101=>0001010
[6,5,4,8,7,2,1,3]=>1101110=>0111011=>1000100
[1,8,5,3,6,2,7,4]=>0110101=>1010110=>0101001
[6,5,8,7,2,1,3,4]=>1011100=>0011101=>1100010
[3,6,2,1,7,5,8,4]=>0110101=>1010110=>0101001
[4,7,2,6,5,8,1,3]=>0101010=>0101010=>1010101
[6,8,1,4,2,7,3,5]=>0101010=>0101010=>1010101
[6,3,4,7,1,8,2,5]=>1001010=>0101001=>1010110
[3,4,7,8,2,5,6,1]=>0001001=>1001000=>0110111
[1,8,2,4,5,6,7,3]=>0100001=>1000010=>0111101
[2,1,4,6,8,5,7,3]=>1000101=>1010001=>0101110
[3,2,5,7,6,1,8,4]=>1001101=>1011001=>0100110
[3,1,4,6,5,7,8,2]=>1001001=>1001001=>0110110
[1,2,3,4,8,6,5,7]=>0000110=>0110000=>1001111
[1,2,3,8,5,4,6,7]=>0001100=>0011000=>1100111
[1,2,3,8,5,6,4,7]=>0001010=>0101000=>1010111
[1,2,3,8,6,5,4,7]=>0001110=>0111000=>1000111
[1,8,3,4,2,5,6,7]=>0101000=>0001010=>1110101
[1,2,8,5,4,3,6,7]=>0011100=>0011100=>1100011
[1,8,4,3,2,5,6,7]=>0111000=>0001110=>1110001
[8,5,7,6,4,3,2,1]=>1011111=>1111101=>0000010
[8,4,7,6,5,3,2,1]=>1011111=>1111101=>0000010
[8,4,7,5,6,3,2,1]=>1010111=>1110101=>0001010
[8,5,7,4,6,3,2,1]=>1010111=>1110101=>0001010
[8,7,6,3,5,4,2,1]=>1110111=>1110111=>0001000
[8,6,7,3,5,4,2,1]=>1010111=>1110101=>0001010
[8,5,7,3,6,4,2,1]=>1010111=>1110101=>0001010
[8,4,7,3,6,5,2,1]=>1010111=>1110101=>0001010
[8,1,7,4,6,5,3,2]=>1010111=>1110101=>0001010
[8,3,7,2,6,5,4,1]=>1010111=>1110101=>0001010
[8,5,7,2,6,4,3,1]=>1010111=>1110101=>0001010
[8,6,7,2,5,4,3,1]=>1010111=>1110101=>0001010
[8,7,6,2,5,4,3,1]=>1110111=>1110111=>0001000
[8,4,7,1,6,5,3,2]=>1010111=>1110101=>0001010
[8,3,7,1,6,5,4,2]=>1010111=>1110101=>0001010
[8,2,7,1,6,5,4,3]=>1010111=>1110101=>0001010
[8,1,7,2,6,5,4,3]=>1010111=>1110101=>0001010
[8,1,7,2,6,4,5,3]=>1010101=>1010101=>0101010
[8,3,7,1,6,4,5,2]=>1010101=>1010101=>0101010
[8,4,7,1,6,3,5,2]=>1010101=>1010101=>0101010
[8,5,7,1,6,3,4,2]=>1010101=>1010101=>0101010
[8,6,7,1,5,3,4,2]=>1010101=>1010101=>0101010
[8,7,6,2,5,3,4,1]=>1110101=>1010111=>0101000
[8,6,7,2,5,3,4,1]=>1010101=>1010101=>0101010
[8,5,7,2,6,3,4,1]=>1010101=>1010101=>0101010
[8,4,7,2,6,3,5,1]=>1010101=>1010101=>0101010
[8,3,7,2,6,4,5,1]=>1010101=>1010101=>0101010
[8,2,7,3,6,4,5,1]=>1010101=>1010101=>0101010
[8,1,7,3,6,4,5,2]=>1010101=>1010101=>0101010
[8,1,7,4,6,3,5,2]=>1010101=>1010101=>0101010
[8,2,7,4,6,3,5,1]=>1010101=>1010101=>0101010
[8,3,7,4,6,2,5,1]=>1010101=>1010101=>0101010
[8,5,7,3,6,2,4,1]=>1010101=>1010101=>0101010
[8,6,7,3,5,2,4,1]=>1010101=>1010101=>0101010
[8,5,7,4,6,2,3,1]=>1010101=>1010101=>0101010
[8,4,7,5,6,2,3,1]=>1010101=>1010101=>0101010
[8,3,7,5,6,2,4,1]=>1010101=>1010101=>0101010
[8,2,7,5,6,3,4,1]=>1010101=>1010101=>0101010
[8,1,7,5,6,3,4,2]=>1010101=>1010101=>0101010
[8,3,7,6,5,2,4,1]=>1011101=>1011101=>0100010
[8,4,7,6,5,2,3,1]=>1011101=>1011101=>0100010
[8,5,7,6,4,2,3,1]=>1011101=>1011101=>0100010
[8,7,6,5,4,1,3,2]=>1111101=>1011111=>0100000
[8,6,7,5,4,1,3,2]=>1011101=>1011101=>0100010
[8,5,7,6,4,1,3,2]=>1011101=>1011101=>0100010
[8,3,7,6,5,1,4,2]=>1011101=>1011101=>0100010
[8,1,7,5,6,2,4,3]=>1010101=>1010101=>0101010
[8,3,7,5,6,1,4,2]=>1010101=>1010101=>0101010
[8,4,7,5,6,1,3,2]=>1010101=>1010101=>0101010
[8,6,7,4,5,1,3,2]=>1010101=>1010101=>0101010
[8,7,6,4,5,1,3,2]=>1110101=>1010111=>0101000
[8,6,7,3,5,1,4,2]=>1010101=>1010101=>0101010
[8,4,7,3,6,1,5,2]=>1010101=>1010101=>0101010
[8,2,7,4,6,1,5,3]=>1010101=>1010101=>0101010
[8,1,7,4,6,2,5,3]=>1010101=>1010101=>0101010
[8,1,7,3,6,2,5,4]=>1010101=>1010101=>0101010
[8,2,7,3,6,1,5,4]=>1010101=>1010101=>0101010
[8,3,7,2,6,1,5,4]=>1010101=>1010101=>0101010
[8,4,7,2,6,1,5,3]=>1010101=>1010101=>0101010
[8,5,7,2,6,1,4,3]=>1010101=>1010101=>0101010
[8,6,7,2,5,1,4,3]=>1010101=>1010101=>0101010
[8,7,6,2,5,1,4,3]=>1110101=>1010111=>0101000
[8,7,6,1,5,2,4,3]=>1110101=>1010111=>0101000
[8,6,7,1,5,2,4,3]=>1010101=>1010101=>0101010
[8,5,7,1,6,2,4,3]=>1010101=>1010101=>0101010
[8,4,7,1,6,2,5,3]=>1010101=>1010101=>0101010
[8,3,7,1,6,2,5,4]=>1010101=>1010101=>0101010
[8,2,7,1,6,3,5,4]=>1010101=>1010101=>0101010
[4,6,7,3,8,5,2,1]=>0010111=>1110100=>0001011
[6,7,8,9,10,5,4,3,2,1]=>000011111=>111110000=>000001111
[5,7,8,9,4,10,6,3,2,1]=>000101111=>111101000=>000010111
[4,6,8,3,9,5,10,7,2,1]=>001010111=>111010100=>000101011
[3,5,2,7,4,9,6,10,8,1]=>010101011=>110101010=>001010101
[1,4,8,2,6,3,5,7]=>0010100=>0010100=>1101011
[1,6,2,4,8,3,5,7]=>0100100=>0010010=>1101101
[1,5,2,3,8,4,7,6]=>0100101=>1010010=>0101101
[1,7,2,3,5,4,8,6]=>0100101=>1010010=>0101101
[1,8,2,3,5,4,6,7]=>0100100=>0010010=>1101101
[1,7,8,2,4,5,3,6]=>0010010=>0100100=>1011011
[1,2,8,3,6,4,5,7]=>0010100=>0010100=>1101011
[1,5,8,2,3,7,4,6]=>0010010=>0100100=>1011011
[1,6,8,2,3,5,4,7]=>0010010=>0100100=>1011011
[5,7,2,6,3,8,1,4]=>0101010=>0101010=>1010101
[5,7,1,6,8,4,3,2]=>0100111=>1110010=>0001101
[4,8,1,2,5,7,3,6]=>0100010=>0100010=>1011101
[1,7,8,4,6,2,5,3]=>0010101=>1010100=>0101011
[3,7,4,8,5,1,6,2]=>0101101=>1011010=>0100101
[3,7,5,4,8,2,1,6]=>0110110=>0110110=>1001001
[4,7,1,3,2,8,6,5]=>0101011=>1101010=>0010101
[2,7,3,1,5,8,4,6]=>0110010=>0100110=>1011001
[2,7,5,8,6,4,1,3]=>0101110=>0111010=>1000101
[3,4,2,7,8,1,6,5]=>0100101=>1010010=>0101101
[4,3,2,1,5,8,6,7]=>1110010=>0100111=>1011000
[4,1,3,7,5,6,8,2]=>1001001=>1001001=>0110110
[3,4,6,1,5,8,2,7]=>0010010=>0100100=>1011011
[6,5,8,7,1,4,2,3]=>1011010=>0101101=>1010010
[4,1,7,3,8,5,2,6]=>1010110=>0110101=>1001010
[6,1,7,3,5,4,8,2]=>1010101=>1010101=>0101010
[5,6,8,7,2,4,1,3]=>0011010=>0101100=>1010011
[6,8,5,7,1,2,4,3]=>0101001=>1001010=>0110101
[7,1,3,4,2,8,5,6]=>1001010=>0101001=>1010110
[7,6,1,4,3,5,8,2]=>1101001=>1001011=>0110100
[3,5,4,1,6,7,8,2]=>0110001=>1000110=>0111001
[2,5,3,4,8,6,1,7]=>0100110=>0110010=>1001101
[2,4,8,3,6,1,7,5]=>0010101=>1010100=>0101011
[8,2,4,3,7,5,6,1]=>1010101=>1010101=>0101010
[6,8,2,1,5,7,3,4]=>0110010=>0100110=>1011001
[7,2,8,4,1,6,3,5]=>1011010=>0101101=>1010010
[1,2,4,8,6,5,3,7]=>0001110=>0111000=>1000111
[7,1,5,6,8,4,3,2]=>1000111=>1110001=>0001110
[7,3,5,6,1,4,8,2]=>1001001=>1001001=>0110110
[3,7,6,5,1,4,8,2]=>0111001=>1001110=>0110001
[2,7,6,5,3,8,1,4]=>0111010=>0101110=>1010001
[2,7,8,1,4,6,3,5]=>0010010=>0100100=>1011011
[4,8,2,5,7,1,6,3]=>0100101=>1010010=>0101101
[4,1,6,8,5,3,7,2]=>1001101=>1011001=>0100110
[5,2,6,4,8,3,1,7]=>1010110=>0110101=>1001010
[1,2,6,3,4,8,7,5]=>0010011=>1100100=>0011011
[5,3,6,1,4,7,8,2]=>1010001=>1000101=>0111010
[6,7,1,3,4,5,8,2]=>0100001=>1000010=>0111101
[1,7,3,2,4,8,5,6]=>0110010=>0100110=>1011001
[6,1,4,2,8,3,5,7]=>1010100=>0010101=>1101010
[5,8,6,7,2,1,4,3]=>0101101=>1011010=>0100101
[7,4,1,5,8,2,3,6]=>1100100=>0010011=>1101100
[6,3,4,2,8,7,5,1]=>1010111=>1110101=>0001010
[4,3,8,7,5,2,6,1]=>1011101=>1011101=>0100010
[6,8,7,4,2,3,5,1]=>0111001=>1001110=>0110001
[8,6,1,3,5,4,2,7]=>1100110=>0110011=>1001100
[2,7,6,3,4,5,8,1]=>0110001=>1000110=>0111001
[5,3,8,6,1,2,4,7]=>1011000=>0001101=>1110010
[2,4,8,7,3,5,6,1]=>0011001=>1001100=>0110011
[2,5,3,6,8,7,4,1]=>0100111=>1110010=>0001101
[3,8,7,2,6,4,5,1]=>0110101=>1010110=>0101001
[4,5,8,7,2,6,3,1]=>0011011=>1101100=>0010011
[8,5,2,7,1,4,3,6]=>1101010=>0101011=>1010100
[5,1,7,2,4,3,8,6]=>1010101=>1010101=>0101010
[4,5,2,8,3,7,6,1]=>0101011=>1101010=>0010101
[8,2,3,7,6,4,5,1]=>1001101=>1011001=>0100110
[3,7,5,8,2,6,1,4]=>0101010=>0101010=>1010101
[1,6,7,4,8,2,3,5]=>0010100=>0010100=>1101011
[8,2,1,3,5,6,7,4]=>1100001=>1000011=>0111100
[4,1,3,8,2,6,7,5]=>1001001=>1001001=>0110110
[3,6,1,4,7,2,8,5]=>0100101=>1010010=>0101101
[6,2,7,4,5,8,1,3]=>1010010=>0100101=>1011010
[2,1,8,4,5,7,3,6]=>1010010=>0100101=>1011010
[1,8,5,7,3,2,4,6]=>0101100=>0011010=>1100101
[3,2,1,6,4,8,5,7]=>1101010=>0101011=>1010100
[2,1,8,5,4,3,6,7]=>1011100=>0011101=>1100010
[2,7,4,1,5,3,8,6]=>0110101=>1010110=>0101001
[7,4,8,6,2,3,1,5]=>1011010=>0101101=>1010010
[7,3,2,4,8,6,1,5]=>1100110=>0110011=>1001100
[7,1,3,2,8,5,4,6]=>1010110=>0110101=>1001010
[5,1,7,4,2,3,8,6]=>1011001=>1001101=>0110010
[1,3,4,8,6,5,2,7]=>0001110=>0111000=>1000111
[4,1,8,6,5,3,2,7]=>1011110=>0111101=>1000010
[4,8,5,3,6,2,7,1]=>0110101=>1010110=>0101001
[5,7,4,3,6,2,8,1]=>0110101=>1010110=>0101001
[6,7,5,1,2,8,3,4]=>0110010=>0100110=>1011001
[7,5,1,4,2,6,8,3]=>1101001=>1001011=>0110100
[5,2,6,8,3,4,7,1]=>1001001=>1001001=>0110110
[7,6,2,4,5,8,3,1]=>1100011=>1100011=>0011100
[2,6,3,8,4,7,5,1]=>0101011=>1101010=>0010101
[6,2,7,5,8,3,1,4]=>1010110=>0110101=>1001010
[2,1,5,6,8,3,7,4]=>1000101=>1010001=>0101110
[1,2,7,4,8,3,6,5]=>0010101=>1010100=>0101011
[1,6,8,3,2,7,4,5]=>0011010=>0101100=>1010011
[1,6,7,5,2,8,3,4]=>0011010=>0101100=>1010011
[7,5,1,2,8,4,6,3]=>1100101=>1010011=>0101100
[5,4,8,3,6,2,7,1]=>1010101=>1010101=>0101010
[5,8,2,7,4,3,6,1]=>0101101=>1011010=>0100101
[5,7,3,8,2,4,6,1]=>0101001=>1001010=>0110101
[6,4,5,8,2,7,3,1]=>1001011=>1101001=>0010110
[5,7,3,6,4,8,2,1]=>0101011=>1101010=>0010101
[1,5,6,4,8,2,7,3]=>0010101=>1010100=>0101011
[3,6,2,4,7,1,8,5]=>0100101=>1010010=>0101101
[4,2,8,5,1,6,7,3]=>1011001=>1001101=>0110010
[2,1,6,4,8,5,3,7]=>1010110=>0110101=>1001010
[1,2,8,3,7,5,4,6]=>0010110=>0110100=>1001011
[1,6,3,8,7,4,2,5]=>0101110=>0111010=>1000101
[4,3,8,1,2,6,7,5]=>1010001=>1000101=>0111010
[6,4,5,8,1,2,7,3]=>1001001=>1001001=>0110110
[7,4,6,5,2,1,8,3]=>1011101=>1011101=>0100010
[5,1,8,6,7,4,3,2]=>1010111=>1110101=>0001010
[3,8,5,7,1,4,2,6]=>0101010=>0101010=>1010101
[4,7,2,5,1,3,8,6]=>0101001=>1001010=>0110101
[5,1,7,4,8,6,3,2]=>1010111=>1110101=>0001010
[3,6,5,2,1,8,7,4]=>0111011=>1101110=>0010001
[5,2,8,4,7,3,1,6]=>1010110=>0110101=>1001010
[5,2,7,4,1,3,6,8]=>1011000=>0001101=>1110010
[5,2,6,4,1,8,7,3]=>1011011=>1101101=>0010010
[6,3,2,1,4,8,7,5]=>1110011=>1100111=>0011000
[3,1,4,6,2,8,7,5]=>1001011=>1101001=>0010110
[6,3,5,1,7,4,2,8]=>1010110=>0110101=>1001010
[4,6,3,7,5,8,1,2]=>0101010=>0101010=>1010101
[5,7,4,3,8,1,2,6]=>0110100=>0010110=>1101001
[1,5,7,4,8,6,3,2]=>0010111=>1110100=>0001011
[1,8,2,7,6,5,4,3]=>0101111=>1111010=>0000101
[3,8,1,6,7,5,4,2]=>0100111=>1110010=>0001101
[3,7,2,6,8,5,1,4]=>0100110=>0110010=>1001101
[8,2,4,3,6,1,5,7]=>1010100=>0010101=>1101010
[1,7,8,5,4,3,6,2]=>0011101=>1011100=>0100011
[7,3,8,1,4,2,6,5]=>1010101=>1010101=>0101010
[1,8,4,5,3,2,6,7]=>0101100=>0011010=>1100101
[3,8,7,4,2,6,1,5]=>0111010=>0101110=>1010001
[3,7,8,1,2,6,5,4]=>0010011=>1100100=>0011011
[3,5,6,2,7,1,4,8]=>0010100=>0010100=>1101011
[3,7,1,6,8,2,4,5]=>0100100=>0010010=>1101101
[8,1,7,6,2,4,3,5]=>1011010=>0101101=>1010010
[1,6,4,5,7,2,3,8]=>0100100=>0010010=>1101101
[8,3,6,1,7,2,4,5]=>1010100=>0010101=>1101010
[1,7,5,3,6,8,4,2]=>0110011=>1100110=>0011001
[7,3,5,2,1,8,4,6]=>1011010=>0101101=>1010010
[7,4,1,6,5,8,3,2]=>1101011=>1101011=>0010100
[6,4,2,8,7,5,1,3]=>1101110=>0111011=>1000100
[4,2,1,5,8,7,3,6]=>1100110=>0110011=>1001100
[1,5,3,6,8,7,4,2]=>0100111=>1110010=>0001101
[3,5,4,6,1,8,2,7]=>0101010=>0101010=>1010101
[3,1,5,7,6,8,2,4]=>1001010=>0101001=>1010110
[6,4,5,7,2,8,1,3]=>1001010=>0101001=>1010110
[5,3,6,4,2,8,1,7]=>1011010=>0101101=>1010010
[4,1,5,3,8,2,7,6]=>1010101=>1010101=>0101010
[2,6,3,5,4,8,1,7]=>0101010=>0101010=>1010101
[3,7,4,5,6,8,1,2]=>0100010=>0100010=>1011101
[2,5,7,3,6,8,1,4]=>0010010=>0100100=>1011011
[7,6,4,5,2,8,1,3]=>1101010=>0101011=>1010100
[5,4,3,1,8,2,7,6]=>1110101=>1010111=>0101000
[8,2,6,4,7,3,1,5]=>1010110=>0110101=>1001010
[8,6,1,7,4,5,2,3]=>1101010=>0101011=>1010100
[1,2,8,3,5,4,6,7]=>0010100=>0010100=>1101011
[1,7,8,4,3,5,6,2]=>0011001=>1001100=>0110011
[3,1,6,8,4,5,7,2]=>1001001=>1001001=>0110110
[1,4,5,8,3,6,7,2]=>0001001=>1001000=>0110111
[2,5,7,1,8,3,6,4]=>0010101=>1010100=>0101011
[6,2,7,1,8,4,5,3]=>1010101=>1010101=>0101010
[4,7,1,3,8,5,6,2]=>0100101=>1010010=>0101101
[3,7,2,1,8,4,5,6]=>0110100=>0010110=>1101001
[2,1,5,8,3,6,7,4]=>1001001=>1001001=>0110110
[4,2,7,1,8,3,6,5]=>1010101=>1010101=>0101010
[4,3,1,6,8,2,7,5]=>1100101=>1010011=>0101100
[5,3,4,6,8,2,7,1]=>1000101=>1010001=>0101110
[3,5,1,6,8,2,7,4]=>0100101=>1010010=>0101101
[5,1,8,7,4,2,3,6]=>1011100=>0011101=>1100010
[5,8,3,2,6,4,1,7]=>0110110=>0110110=>1001001
[6,8,2,4,7,5,1,3]=>0100110=>0110010=>1001101
[7,3,8,2,6,4,1,5]=>1010110=>0110101=>1001010
[3,8,7,4,5,6,1,2]=>0110010=>0100110=>1011001
[2,7,6,3,5,4,1,8]=>0110110=>0110110=>1001001
[3,8,7,4,6,2,5,1]=>0110101=>1010110=>0101001
[5,8,3,7,6,2,4,1]=>0101101=>1011010=>0100101
[8,7,2,5,4,3,1,6]=>1101110=>0111011=>1000100
[6,8,3,2,5,4,7,1]=>0110101=>1010110=>0101001
[5,8,7,4,3,6,2,1]=>0111011=>1101110=>0010001
[5,8,6,4,3,7,1,2]=>0111010=>0101110=>1010001
[6,5,8,4,3,1,7,2]=>1011101=>1011101=>0100010
[2,6,4,7,1,5,3,8]=>0101010=>0101010=>1010101
[2,5,6,8,4,3,7,1]=>0001101=>1011000=>0100111
[5,3,8,1,7,6,4,2]=>1010111=>1110101=>0001010
[5,4,8,7,1,6,3,2]=>1011011=>1101101=>0010010
[4,8,6,7,5,3,1,2]=>0101110=>0111010=>1000101
[4,8,6,5,7,2,1,3]=>0110110=>0110110=>1001001
[4,8,5,6,7,1,2,3]=>0100100=>0010010=>1101101
[5,4,8,6,1,7,2,3]=>1011010=>0101101=>1010010
[5,3,8,1,6,7,2,4]=>1010010=>0100101=>1011010
[5,2,1,8,6,7,3,4]=>1101010=>0101011=>1010100
[6,2,1,5,8,3,7,4]=>1100101=>1010011=>0101100
[6,5,4,8,2,1,7,3]=>1101101=>1011011=>0100100
[5,8,4,7,2,6,3,1]=>0101011=>1101010=>0010101
[5,8,3,2,7,6,4,1]=>0110111=>1110110=>0001001
[5,8,3,2,6,7,1,4]=>0110010=>0100110=>1011001
[6,5,3,2,8,1,7,4]=>1110101=>1010111=>0101000
[6,4,3,2,1,8,7,5]=>1111011=>1101111=>0010000
[6,3,4,1,2,8,7,5]=>1010011=>1100101=>0011010
[6,2,1,4,3,8,7,5]=>1101011=>1101011=>0010100
[5,2,1,4,3,6,7,8]=>1101000=>0001011=>1110100
[4,6,3,2,5,1,7,8]=>0110100=>0010110=>1101001
[3,5,7,4,2,6,1,8]=>0011010=>0101100=>1010011
[4,3,6,1,5,2,7,8]=>1010100=>0010101=>1101010
[4,2,1,6,5,3,7,8]=>1101100=>0011011=>1100100
[4,2,1,5,7,6,3,8]=>1100110=>0110011=>1001100
[3,5,4,7,1,6,2,8]=>0101010=>0101010=>1010101
[3,4,7,5,6,1,2,8]=>0010100=>0010100=>1101011
[3,4,5,8,6,7,1,2]=>0001010=>0101000=>1010111
[3,4,6,5,8,1,7,2]=>0010101=>1010100=>0101011
[4,3,5,1,6,8,7,2]=>1010011=>1100101=>0011010
[2,1,5,3,8,4,7,6]=>1010101=>1010101=>0101010
[3,1,8,2,5,4,7,6]=>1010101=>1010101=>0101010
[8,1,3,2,6,4,7,5]=>1010101=>1010101=>0101010
[3,1,8,2,6,4,7,5]=>1010101=>1010101=>0101010
[2,1,8,3,6,4,7,5]=>1010101=>1010101=>0101010
[2,1,6,3,8,4,7,5]=>1010101=>1010101=>0101010
[2,1,7,3,5,4,8,6]=>1010101=>1010101=>0101010
[2,1,7,3,6,4,8,5]=>1010101=>1010101=>0101010
[2,1,7,3,8,4,6,5]=>1010101=>1010101=>0101010
[8,1,4,2,7,3,6,5]=>1010101=>1010101=>0101010
[4,1,8,2,7,3,6,5]=>1010101=>1010101=>0101010
[4,1,7,2,8,3,6,5]=>1010101=>1010101=>0101010
[3,1,7,2,8,4,6,5]=>1010101=>1010101=>0101010
[3,1,6,2,5,4,8,7]=>1010101=>1010101=>0101010
[7,1,3,2,5,4,8,6]=>1010101=>1010101=>0101010
[7,1,3,2,6,4,8,5]=>1010101=>1010101=>0101010
[7,1,3,2,8,4,6,5]=>1010101=>1010101=>0101010
[7,1,8,2,4,3,6,5]=>1010101=>1010101=>0101010
[8,1,7,2,5,3,6,4]=>1010101=>1010101=>0101010
[7,1,5,2,8,3,6,4]=>1010101=>1010101=>0101010
[6,1,4,2,5,3,8,7]=>1010101=>1010101=>0101010
[4,1,6,2,5,3,8,7]=>1010101=>1010101=>0101010
[4,1,7,2,5,3,8,6]=>1010101=>1010101=>0101010
[4,1,7,2,6,3,8,5]=>1010101=>1010101=>0101010
[5,1,7,2,6,3,8,4]=>1010101=>1010101=>0101010
[5,1,7,2,8,3,6,4]=>1010101=>1010101=>0101010
[5,1,8,2,7,3,6,4]=>1010101=>1010101=>0101010
[8,1,5,2,7,3,6,4]=>1010101=>1010101=>0101010
[8,1,5,2,6,3,7,4]=>1010101=>1010101=>0101010
[5,1,8,2,6,3,7,4]=>1010101=>1010101=>0101010
[5,1,6,2,8,3,7,4]=>1010101=>1010101=>0101010
[3,1,6,2,8,4,7,5]=>1010101=>1010101=>0101010
[4,1,8,2,6,3,7,5]=>1010101=>1010101=>0101010
[8,1,4,2,6,3,7,5]=>1010101=>1010101=>0101010
[8,1,4,2,5,3,7,6]=>1010101=>1010101=>0101010
[4,1,8,2,5,3,7,6]=>1010101=>1010101=>0101010
[4,1,5,2,8,3,7,6]=>1010101=>1010101=>0101010
[3,1,5,2,8,4,7,6]=>1010101=>1010101=>0101010
[3,1,4,2,8,5,7,6]=>1010101=>1010101=>0101010
[4,1,3,2,7,5,8,6]=>1010101=>1010101=>0101010
[5,1,4,2,8,3,7,6]=>1010101=>1010101=>0101010
[5,1,8,2,4,3,7,6]=>1010101=>1010101=>0101010
[8,1,6,2,4,3,7,5]=>1010101=>1010101=>0101010
[6,1,8,2,4,3,7,5]=>1010101=>1010101=>0101010
[6,1,3,2,8,4,7,5]=>1010101=>1010101=>0101010
[6,1,3,2,7,4,8,5]=>1010101=>1010101=>0101010
[5,1,3,2,7,4,8,6]=>1010101=>1010101=>0101010
[5,1,3,2,6,4,8,7]=>1010101=>1010101=>0101010
[5,1,4,2,6,3,8,7]=>1010101=>1010101=>0101010
[6,1,4,2,7,3,8,5]=>1010101=>1010101=>0101010
[6,1,5,2,7,3,8,4]=>1010101=>1010101=>0101010
[6,1,8,2,5,3,7,4]=>1010101=>1010101=>0101010
[8,1,6,2,5,3,7,4]=>1010101=>1010101=>0101010
[8,1,6,2,7,3,5,4]=>1010101=>1010101=>0101010
[6,1,8,2,7,3,5,4]=>1010101=>1010101=>0101010
[6,1,7,2,8,3,5,4]=>1010101=>1010101=>0101010
[6,1,7,2,5,3,8,4]=>1010101=>1010101=>0101010
[6,1,7,2,4,3,8,5]=>1010101=>1010101=>0101010
[5,1,6,2,4,3,8,7]=>1010101=>1010101=>0101010
[7,1,5,2,4,3,8,6]=>1010101=>1010101=>0101010
[7,1,6,2,4,3,8,5]=>1010101=>1010101=>0101010
[7,1,6,2,5,3,8,4]=>1010101=>1010101=>0101010
[7,1,6,2,8,3,5,4]=>1010101=>1010101=>0101010
[7,1,8,2,6,3,5,4]=>1010101=>1010101=>0101010
[7,8,3,1,2,5,6,4]=>0110001=>1000110=>0111001
[7,8,1,3,2,4,6,5]=>0101001=>1001010=>0110101
[6,2,8,1,3,5,4,7]=>1010010=>0100101=>1011010
[6,2,8,3,1,7,4,5]=>1011010=>0101101=>1010010
[3,2,5,7,1,8,4,6]=>1001010=>0101001=>1010110
[3,5,2,8,1,7,4,6]=>0101010=>0101010=>1010101
[4,3,1,2,7,8,6,5]=>1100011=>1100011=>0011100
[5,3,4,7,8,6,1,2]=>1000110=>0110001=>1001110
[4,1,3,2,6,8,7,5]=>1010011=>1100101=>0011010
[5,1,3,7,2,6,8,4]=>1001001=>1001001=>0110110
[5,2,4,7,8,1,6,3]=>1000101=>1010001=>0101110
[2,5,4,6,8,1,7,3]=>0100101=>1010010=>0101101
[4,3,5,7,6,8,1,2]=>1001010=>0101001=>1010110
[4,2,1,3,7,6,8,5]=>1100101=>1010011=>0101100
[2,4,3,1,8,5,7,6]=>0110101=>1010110=>0101001
[3,2,4,1,8,6,5,7]=>1010110=>0110101=>1001010
[3,4,2,1,8,7,5,6]=>0110110=>0110110=>1001001
[7,6,4,3,2,1,8,5]=>1111101=>1011111=>0100000
[7,6,5,8,2,1,4,3]=>1101101=>1011011=>0100100
[7,6,8,3,2,1,5,4]=>1011101=>1011101=>0100010
[7,8,4,3,2,1,6,5]=>0111101=>1011110=>0100001
[8,5,4,3,2,1,7,6]=>1111101=>1011111=>0100000
[7,6,3,8,2,1,5,4]=>1101101=>1011011=>0100100
[7,6,5,8,4,1,3,2]=>1101101=>1011011=>0100100
[7,4,8,3,2,1,6,5]=>1011101=>1011101=>0100010
[7,6,8,5,2,1,4,3]=>1011101=>1011101=>0100010
[4,8,6,1,7,5,2,3]=>0110110=>0110110=>1001001
[4,8,7,2,6,5,1,3]=>0110110=>0110110=>1001001
[4,7,8,2,6,1,5,3]=>0010101=>1010100=>0101011
[4,6,8,2,7,1,3,5]=>0010100=>0010100=>1101011
[8,6,4,2,7,5,3,1]=>1110111=>1110111=>0001000
[8,4,7,3,6,5,1,2]=>1010110=>0110101=>1001010
[6,4,7,1,8,3,2,5]=>1010110=>0110101=>1001010
[7,4,8,3,6,1,5,2]=>1010101=>1010101=>0101010
[7,8,4,3,6,2,5,1]=>0110101=>1010110=>0101001
[6,8,4,3,7,2,1,5]=>0110110=>0110110=>1001001
[6,7,4,2,8,3,1,5]=>0110110=>0110110=>1001001
[11,12,9,10,7,8,5,6,3,4,1,2]=>01010101010=>01010101010=>10101010101
[2,8,7,6,5,1,4,3]=>0111101=>1011110=>0100001
[7,3,2,5,4,1,6,8]=>1101100=>0011011=>1100100
[7,3,5,4,2,1,6,8]=>1011100=>0011101=>1100010
[2,7,6,3,1,5,8,4]=>0111001=>1001110=>0110001
[1,8,4,3,6,5,2,7]=>0110110=>0110110=>1001001
[1,8,4,6,5,3,2,7]=>0101110=>0111010=>1000101
[7,1,4,2,6,3,5,8]=>1010100=>0010101=>1101010
[7,3,4,1,5,6,2,8]=>1010010=>0100101=>1011010
[7,3,2,5,1,6,4,8]=>1101010=>0101011=>1010100
[7,4,1,3,5,2,6,8]=>1100100=>0010011=>1101100
[7,3,1,2,4,6,5,8]=>1100010=>0100011=>1011100
[3,6,2,1,4,8,5,7]=>0110010=>0100110=>1011001
[2,3,6,1,4,8,7,5]=>0010011=>1100100=>0011011
[3,6,7,4,1,5,8,2]=>0011001=>1001100=>0110011
[3,1,2,8,6,5,4,7]=>1001110=>0111001=>1000110
[5,4,8,6,1,2,3,7]=>1011000=>0001101=>1110010
[5,6,8,2,4,1,3,7]=>0010100=>0010100=>1101011
[5,6,8,7,4,3,1,2]=>0011110=>0111100=>1000011
[6,4,8,5,3,1,7,2]=>1011101=>1011101=>0100010
[5,7,8,6,1,3,2,4]=>0011010=>0101100=>1010011
[2,4,8,1,6,3,7,5]=>0010101=>1010100=>0101011
[1,8,4,5,2,6,7,3]=>0101001=>1001010=>0110101
[3,1,4,6,5,8,7,2]=>1001011=>1101001=>0010110
[3,7,5,4,6,8,2,1]=>0110011=>1100110=>0011001
[5,3,2,1,7,6,8,4]=>1110101=>1010111=>0101000
[5,6,1,4,7,2,8,3]=>0100101=>1010010=>0101101
[4,3,1,7,5,6,8,2]=>1101001=>1001011=>0110100
[1,8,4,3,6,2,7,5]=>0110101=>1010110=>0101001
[5,6,7,3,2,8,1,4]=>0011010=>0101100=>1010011
[5,3,2,1,4,8,6,7]=>1110010=>0100111=>1011000
[3,4,7,8,1,2,6,5]=>0001001=>1001000=>0110111
[3,6,7,8,1,4,5,2]=>0001001=>1001000=>0110111
[2,3,6,8,5,1,4,7]=>0001100=>0011000=>1100111
[3,1,6,4,8,2,5,7]=>1010100=>0010101=>1101010
[7,3,2,6,8,5,1,4]=>1100110=>0110011=>1001100
[7,3,5,8,4,6,1,2]=>1001010=>0101001=>1010110
[7,5,2,8,4,1,6,3]=>1101101=>1011011=>0100100
[1,8,4,2,3,5,7,6]=>0110001=>1000110=>0111001
[6,3,4,8,2,5,7,1]=>1001001=>1001001=>0110110
[7,5,4,8,3,6,2,1]=>1101011=>1101011=>0010100
[7,3,2,5,8,4,6,1]=>1100101=>1010011=>0101100
[5,7,8,3,1,4,6,2]=>0011001=>1001100=>0110011
[7,4,8,3,2,5,1,6]=>1011010=>0101101=>1010010
[7,3,8,2,4,5,6,1]=>1010001=>1000101=>0111010
[4,2,7,1,5,3,8,6]=>1010101=>1010101=>0101010
[2,7,1,3,5,4,8,6]=>0100101=>1010010=>0101101
[1,2,7,3,4,8,6,5]=>0010011=>1100100=>0011011
[4,7,2,1,5,8,6,3]=>0110011=>1100110=>0011001
[2,3,4,8,1,6,5,7]=>0001010=>0101000=>1010111
[3,1,4,8,2,6,7,5]=>1001001=>1001001=>0110110
[4,8,3,6,5,1,7,2]=>0101101=>1011010=>0100101
[6,4,7,3,5,1,8,2]=>1010101=>1010101=>0101010
[3,1,6,4,7,8,2,5]=>1010010=>0100101=>1011010
[7,3,1,6,8,2,4,5]=>1100100=>0010011=>1101100
[7,3,5,1,6,8,2,4]=>1010010=>0100101=>1011010
[4,7,3,5,6,1,8,2]=>0100101=>1010010=>0101101
[4,6,8,2,1,5,7,3]=>0011001=>1001100=>0110011
[1,8,2,3,5,7,4,6]=>0100010=>0100010=>1011101
[2,7,3,6,1,4,5,8]=>0101000=>0001010=>1110101
[1,2,5,8,3,7,4,6]=>0001010=>0101000=>1010111
[8,2,4,1,7,5,6,3]=>1010101=>1010101=>0101010
[3,8,4,7,5,1,6,2]=>0101101=>1011010=>0100101
[8,4,3,6,1,7,5,2]=>1101011=>1101011=>0010100
[2,1,8,6,7,3,5,4]=>1010101=>1010101=>0101010
[1,2,8,6,3,4,7,5]=>0011001=>1001100=>0110011
[7,3,2,5,6,1,4,8]=>1100100=>0010011=>1101100
[8,4,1,2,7,5,3,6]=>1100110=>0110011=>1001100
[1,5,2,8,6,3,7,4]=>0101101=>1011010=>0100101
[5,8,6,3,1,7,4,2]=>0111011=>1101110=>0010001
[7,8,1,4,2,5,3,6]=>0101010=>0101010=>1010101
[1,6,2,7,4,8,3,5]=>0101010=>0101010=>1010101
[6,2,1,7,8,5,3,4]=>1100110=>0110011=>1001100
[6,7,3,8,4,1,5,2]=>0101101=>1011010=>0100101
[2,7,1,8,5,6,3,4]=>0101010=>0101010=>1010101
[2,1,7,8,6,3,4,5]=>1001100=>0011001=>1100110
[7,8,6,2,1,3,5,4]=>0111001=>1001110=>0110001
[5,2,6,3,4,1,8,7]=>1010101=>1010101=>0101010
[4,1,2,6,5,3,8,7]=>1001101=>1011001=>0100110
[2,6,5,3,1,4,8,7]=>0111001=>1001110=>0110001
[6,1,3,4,2,8,7,5]=>1001011=>1101001=>0010110
[8,2,6,4,7,3,5,1]=>1010101=>1010101=>0101010
[3,8,5,1,7,2,4,6]=>0110100=>0010110=>1101001
[2,1,7,4,8,5,6,3]=>1010101=>1010101=>0101010
[2,5,1,8,7,4,6,3]=>0101101=>1011010=>0100101
[7,1,3,8,6,4,5,2]=>1001101=>1011001=>0100110
[2,3,5,8,6,7,4,1]=>0001011=>1101000=>0010111
[7,4,2,1,8,6,5,3]=>1110111=>1110111=>0001000
[2,1,6,3,4,8,7,5]=>1010011=>1100101=>0011010
[4,6,7,2,5,8,3,1]=>0010011=>1100100=>0011011
[7,6,2,5,3,8,1,4]=>1101010=>0101011=>1010100
[6,2,1,3,4,8,7,5]=>1100011=>1100011=>0011100
[8,1,4,2,5,6,7,3]=>1010001=>1000101=>0111010
[3,4,2,1,8,6,7,5]=>0110101=>1010110=>0101001
[2,7,6,8,1,5,3,4]=>0101010=>0101010=>1010101
[8,1,3,2,5,6,7,4]=>1010001=>1000101=>0111010
[3,2,8,7,4,5,1,6]=>1011010=>0101101=>1010010
[6,3,8,5,7,4,2,1]=>1010111=>1110101=>0001010
[7,4,6,8,5,1,2,3]=>1001100=>0011001=>1100110
[2,1,4,8,7,5,3,6]=>1001110=>0111001=>1000110
[7,1,5,8,2,6,3,4]=>1001010=>0101001=>1010110
[3,6,8,2,4,1,5,7]=>0010100=>0010100=>1101011
[6,2,8,1,7,5,4,3]=>1010111=>1110101=>0001010
[2,8,5,3,6,7,1,4]=>0110010=>0100110=>1011001
[3,8,1,4,5,6,2,7]=>0100010=>0100010=>1011101
[5,8,7,3,6,1,4,2]=>0110101=>1010110=>0101001
[5,8,3,7,6,1,4,2]=>0101101=>1011010=>0100101
[7,5,8,4,6,1,3,2]=>1010101=>1010101=>0101010
[6,5,8,4,7,1,3,2]=>1010101=>1010101=>0101010
[2,4,8,1,3,7,6,5]=>0010011=>1100100=>0011011
[2,5,1,3,8,4,7,6]=>0100101=>1010010=>0101101
[2,8,1,5,4,7,3,6]=>0101010=>0101010=>1010101
[3,1,8,2,5,7,4,6]=>1010010=>0100101=>1011010
[8,3,2,6,1,4,7,5]=>1101001=>1001011=>0110100
[2,6,1,3,8,7,5,4]=>0100111=>1110010=>0001101
[2,5,7,1,3,8,6,4]=>0010011=>1100100=>0011011
[2,8,1,7,6,5,4,3]=>0101111=>1111010=>0000101
[8,3,2,7,1,6,5,4]=>1101011=>1101011=>0010100
[7,4,2,8,1,6,5,3]=>1101011=>1101011=>0010100
[8,7,5,3,2,1,6,4]=>1111101=>1011111=>0100000
[7,5,2,6,3,1,4,8]=>1101100=>0011011=>1100100
[7,4,6,2,1,8,3,5]=>1011010=>0101101=>1010010
[7,4,5,8,6,2,1,3]=>1001110=>0111001=>1000110
[6,8,4,5,2,1,7,3]=>0101101=>1011010=>0100101
[4,6,8,5,1,7,3,2]=>0011011=>1101100=>0010011
[4,7,5,1,3,8,6,2]=>0110011=>1100110=>0011001
[5,1,7,6,4,2,8,3]=>1011101=>1011101=>0100010
[5,1,8,7,6,4,3,2]=>1011111=>1111101=>0000010
[8,5,2,1,6,3,7,4]=>1110101=>1010111=>0101000
[5,1,6,2,8,7,4,3]=>1010111=>1110101=>0001010
[4,5,6,1,8,7,2,3]=>0010110=>0110100=>1001011
[3,5,6,8,7,1,4,2]=>0001101=>1011000=>0100111
[3,6,1,7,4,8,2,5]=>0101010=>0101010=>1010101
[8,4,2,6,3,1,5,7]=>1101100=>0011011=>1100100
[4,1,8,5,7,3,6,2]=>1010101=>1010101=>0101010
[4,1,5,8,7,2,3,6]=>1001100=>0011001=>1100110
[3,4,8,7,1,2,6,5]=>0011001=>1001100=>0110011
[3,4,6,8,5,7,1,2]=>0001010=>0101000=>1010111
[4,6,8,3,5,7,2,1]=>0010011=>1100100=>0011011
[4,7,3,5,8,2,6,1]=>0100101=>1010010=>0101101
[5,4,8,2,7,3,6,1]=>1010101=>1010101=>0101010
[6,3,7,2,4,8,1,5]=>1010010=>0100101=>1011010
[5,6,8,3,7,2,1,4]=>0010110=>0110100=>1001011
[6,5,2,7,1,3,8,4]=>1101001=>1001011=>0110100
[6,5,4,1,7,2,8,3]=>1110101=>1010111=>0101000
[6,4,7,3,1,8,2,5]=>1011010=>0101101=>1010010
[6,8,5,7,4,3,2,1]=>0101111=>1111010=>0000101
[7,5,8,4,6,3,2,1]=>1010111=>1110101=>0001010
[5,6,3,7,4,2,1,8]=>0101110=>0111010=>1000101
[6,1,3,8,5,2,4,7]=>1001100=>0011001=>1100110
[7,4,2,6,3,5,1,8]=>1101010=>0101011=>1010100
[3,4,7,5,6,2,1,8]=>0010110=>0110100=>1001011
[8,1,3,4,5,2,6,7]=>1000100=>0010001=>1101110
[1,6,8,4,2,5,3,7]=>0011010=>0101100=>1010011
[3,6,8,4,1,7,5,2]=>0011011=>1101100=>0010011
[8,7,2,3,6,1,4,5]=>1100100=>0010011=>1101100
[6,7,4,8,5,1,2,3]=>0101100=>0011010=>1100101
[3,2,8,1,5,4,6,7]=>1010100=>0010101=>1101010
[6,1,4,8,5,3,7,2]=>1001101=>1011001=>0100110
[1,4,8,5,2,6,7,3]=>0011001=>1001100=>0110011
[8,1,2,3,6,5,7,4]=>1000101=>1010001=>0101110
[6,1,8,4,3,7,2,5]=>1011010=>0101101=>1010010
[3,2,6,4,1,8,7,5]=>1011011=>1101101=>0010010
[7,6,4,3,1,8,2,5]=>1111010=>0101111=>1010000
[8,4,6,5,1,7,2,3]=>1011010=>0101101=>1010010
[7,5,4,6,1,2,8,3]=>1101001=>1001011=>0110100
[3,2,5,6,1,7,8,4]=>1001001=>1001001=>0110110
[3,2,8,7,6,1,4,5]=>1011100=>0011101=>1100010
[6,8,4,7,2,1,3,5]=>0101100=>0011010=>1100101
[3,8,7,5,6,1,2,4]=>0110100=>0010110=>1101001
[8,2,7,6,5,1,3,4]=>1011100=>0011101=>1100010
[4,8,6,7,1,5,3,2]=>0101011=>1101010=>0010101
[1,8,6,7,2,3,4,5]=>0101000=>0001010=>1110101
[7,6,3,2,1,8,5,4]=>1111011=>1101111=>0010000
[3,5,4,2,7,1,8,6]=>0110101=>1010110=>0101001
[8,6,3,1,4,5,7,2]=>1110001=>1000111=>0111000
[3,2,6,1,5,7,4,8]=>1010010=>0100101=>1011010
[5,2,1,4,7,6,3,8]=>1100110=>0110011=>1001100
[4,2,1,3,5,8,7,6]=>1100011=>1100011=>0011100
[7,4,1,5,3,6,8,2]=>1101001=>1001011=>0110100
[3,1,5,2,7,4,9,6,8,10]=>101010100=>001010101=>110101010
[6,8,2,4,5,1,3,7]=>0100100=>0010010=>1101101
[6,8,3,4,1,5,2,7]=>0101010=>0101010=>1010101
[5,8,4,1,7,2,6,3]=>0110101=>1010110=>0101001
[6,8,3,1,4,5,7,2]=>0110001=>1000110=>0111001
[5,3,8,4,2,6,7,1]=>1011001=>1001101=>0110010
[4,1,8,3,5,7,2,6]=>1010010=>0100101=>1011010
[2,4,6,3,5,8,1,7]=>0010010=>0100100=>1011011
[4,5,7,2,3,6,8,1]=>0010001=>1000100=>0111011
[2,6,3,4,7,5,8,1]=>0100101=>1010010=>0101101
[4,5,2,7,1,6,8,3]=>0101001=>1001010=>0110101
[2,3,1,7,6,4,8,5]=>0101101=>1011010=>0100101
[3,4,1,6,5,8,2,7]=>0101010=>0101010=>1010101
[7,3,1,4,8,5,6,2]=>1100101=>1010011=>0101100
[6,4,2,8,7,1,5,3]=>1101101=>1011011=>0100100
[3,1,8,2,7,6,4,5]=>1010110=>0110101=>1001010
[6,2,8,4,1,7,5,3]=>1011011=>1101101=>0010010
[3,6,4,7,2,5,1,8]=>0101010=>0101010=>1010101
[7,3,2,8,6,1,4,5]=>1101100=>0011011=>1100100
[4,3,8,7,1,2,5,6]=>1011000=>0001101=>1110010
[1,2,5,8,4,7,3,6]=>0001010=>0101000=>1010111
[1,3,6,8,5,2,7,4]=>0001101=>1011000=>0100111
[2,5,7,4,1,8,6,3]=>0011011=>1101100=>0010011
[2,4,6,1,8,3,7,5]=>0010101=>1010100=>0101011
[3,5,1,7,2,8,6,4]=>0101011=>1101010=>0010101
[4,6,3,1,7,8,5,2]=>0110011=>1100110=>0011001
[5,3,1,6,7,8,4,2]=>1100011=>1100011=>0011100
[4,1,6,2,7,8,5,3]=>1010011=>1100101=>0011010
[2,1,3,4,8,7,5,6]=>1000110=>0110001=>1001110
[4,8,7,3,6,5,1,2]=>0110110=>0110110=>1001001
[6,3,8,7,5,4,1,2]=>1011110=>0111101=>1000010
[4,3,8,7,6,5,1,2]=>1011110=>0111101=>1000010
[2,8,7,6,1,5,4,3]=>0111011=>1101110=>0010001
[5,2,8,7,6,1,4,3]=>1011101=>1011101=>0100010
[6,2,8,7,5,1,4,3]=>1011101=>1011101=>0100010
[7,8,2,6,5,1,4,3]=>0101101=>1011010=>0100101
[6,1,8,7,5,4,3,2]=>1011111=>1111101=>0000010
[4,1,8,7,6,5,3,2]=>1011111=>1111101=>0000010
[3,1,8,7,6,5,4,2]=>1011111=>1111101=>0000010
[7,8,2,6,1,5,4,3]=>0101011=>1101010=>0010101
[4,2,8,1,7,6,5,3]=>1010111=>1110101=>0001010
[3,2,8,1,7,6,5,4]=>1010111=>1110101=>0001010
[2,8,7,1,6,5,4,3]=>0110111=>1110110=>0001001
[3,8,2,1,7,6,5,4]=>0110111=>1110110=>0001001
[4,8,2,7,6,1,5,3]=>0101101=>1011010=>0100101
[3,8,2,7,1,6,5,4]=>0101011=>1101010=>0010101
[3,8,7,2,1,6,5,4]=>0111011=>1101110=>0010001
[4,8,7,2,6,1,5,3]=>0110101=>1010110=>0101001
[5,8,7,6,2,1,4,3]=>0111101=>1011110=>0100001
[6,5,8,7,1,4,3,2]=>1011011=>1101101=>0010010
[3,8,7,1,6,5,4,2]=>0110111=>1110110=>0001001
[4,8,1,7,6,5,3,2]=>0101111=>1111010=>0000101
[5,4,1,8,7,6,3,2]=>1101111=>1111011=>0000100
[6,4,8,1,7,5,3,2]=>1010111=>1110101=>0001010
[7,8,4,1,6,5,3,2]=>0110111=>1110110=>0001001
[7,8,3,1,6,5,4,2]=>0110111=>1110110=>0001001
[5,3,1,8,7,6,4,2]=>1101111=>1111011=>0000100
[4,3,1,8,7,6,5,2]=>1101111=>1111011=>0000100
[4,2,1,8,7,6,5,3]=>1101111=>1111011=>0000100
[6,5,3,1,8,7,4,2]=>1110111=>1110111=>0001000
[7,5,2,1,8,6,4,3]=>1110111=>1110111=>0001000
[5,4,2,1,8,7,6,3]=>1110111=>1110111=>0001000
[7,3,2,1,8,6,5,4]=>1110111=>1110111=>0001000
[6,1,4,2,3,5,8,7]=>1010001=>1000101=>0111010
[8,6,1,4,2,3,5,7]=>1101000=>0001011=>1110100
[6,8,1,4,2,3,5,7]=>0101000=>0001010=>1110101
[4,6,2,3,8,1,5,7]=>0100100=>0010010=>1101101
[8,2,3,6,4,1,5,7]=>1001100=>0011001=>1100110
[6,2,3,8,4,1,5,7]=>1001100=>0011001=>1100110
[8,4,2,3,6,1,5,7]=>1100100=>0010011=>1101100
[6,4,2,3,8,1,5,7]=>1100100=>0010011=>1101100
[2,8,4,3,6,1,5,7]=>0110100=>0010110=>1101001
[2,6,3,8,4,1,5,7]=>0101100=>0011010=>1100101
[6,3,8,4,2,1,5,7]=>1011100=>0011101=>1100010
[2,4,8,3,6,1,5,7]=>0010100=>0010100=>1101011
[2,4,6,3,8,1,5,7]=>0010100=>0010100=>1101011
[8,3,6,2,4,1,5,7]=>1010100=>0010101=>1101010
[8,3,6,2,1,4,5,7]=>1011000=>0001101=>1110010
[2,1,8,3,6,4,5,7]=>1010100=>0010101=>1101010
[6,3,8,2,1,4,5,7]=>1011000=>0001101=>1110010
[6,2,4,3,8,1,5,7]=>1010100=>0010101=>1101010
[3,6,4,7,8,5,1,2]=>0100110=>0110010=>1001101
[1,6,4,2,7,5,8,3]=>0110101=>1010110=>0101001
[3,4,6,8,7,5,1,2]=>0001110=>0111000=>1000111
[5,4,6,3,8,7,1,2]=>1010110=>0110101=>1001010
[6,4,8,5,3,7,1,2]=>1011010=>0101101=>1010010
[1,8,5,2,6,3,7,4]=>0110101=>1010110=>0101001
[1,4,6,2,8,5,7,3]=>0010101=>1010100=>0101011
[7,8,1,4,2,5,6,3]=>0101001=>1001010=>0110101
[3,6,5,2,4,1,8,7]=>0110101=>1010110=>0101001
[4,8,5,3,1,6,2,7]=>0111010=>0101110=>1010001
[5,1,6,2,8,7,3,4]=>1010110=>0110101=>1001010
[6,1,8,7,4,2,3,5]=>1011100=>0011101=>1100010
[1,2,8,5,7,3,6,4]=>0010101=>1010100=>0101011
[1,3,6,8,7,5,2,4]=>0001110=>0111000=>1000111
[7,8,1,2,4,6,5,3]=>0100011=>1100010=>0011101
[1,2,6,4,8,7,5,3]=>0010111=>1110100=>0001011
[1,8,2,5,4,7,6,3]=>0101011=>1101010=>0010101
[1,2,7,3,5,8,6,4]=>0010011=>1100100=>0011011
[4,6,2,1,7,5,3,8]=>0110110=>0110110=>1001001
[4,6,2,3,7,8,1,5]=>0100010=>0100010=>1011101
[4,2,1,3,5,7,8,6]=>1100001=>1000011=>0111100
[7,3,2,4,5,1,8,6]=>1100101=>1010011=>0101100
[7,8,3,2,4,1,6,5]=>0110101=>1010110=>0101001
[7,8,4,2,6,3,1,5]=>0110110=>0110110=>1001001
[4,2,6,3,8,7,1,5]=>1010110=>0110101=>1001010
[5,8,2,7,4,3,1,6]=>0101110=>0111010=>1000101
[7,5,2,8,3,4,1,6]=>1101010=>0101011=>1010100
[4,3,6,8,1,2,7,5]=>1001001=>1001001=>0110110
[6,4,3,5,2,8,1,7]=>1101010=>0101011=>1010100
[6,5,8,4,2,3,1,7]=>1011010=>0101101=>1010010
[4,1,3,6,5,8,7,2]=>1001011=>1101001=>0010110
[2,4,1,3,8,5,7,6]=>0100101=>1010010=>0101101
[2,4,1,3,5,8,7,6]=>0100011=>1100010=>0011101
[4,6,1,3,5,8,7,2]=>0100011=>1100010=>0011101
[1,4,6,3,5,8,7,2]=>0010011=>1100100=>0011011
[4,2,1,3,6,5,7,8]=>1100100=>0010011=>1101100
[4,2,1,6,3,5,7,8]=>1101000=>0001011=>1110100
[4,2,1,8,3,5,7,6]=>1101001=>1001011=>0110100
[6,2,1,8,3,5,7,4]=>1101001=>1001011=>0110100
[6,4,1,3,8,5,7,2]=>1100101=>1010011=>0101100
[6,1,4,3,8,5,7,2]=>1010101=>1010101=>0101010
[1,6,4,3,8,5,7,2]=>0110101=>1010110=>0101001
[8,1,4,3,6,5,7,2]=>1010101=>1010101=>0101010
[8,2,1,3,6,5,7,4]=>1100101=>1010011=>0101100
[8,2,1,4,3,5,7,6]=>1101001=>1001011=>0110100
[8,1,4,6,3,5,7,2]=>1001001=>1001001=>0110110
[6,1,4,8,3,5,7,2]=>1001001=>1001001=>0110110
[6,4,8,1,3,5,7,2]=>1010001=>1000101=>0111010
[2,4,8,1,3,5,7,6]=>0010001=>1000100=>0111011
[4,6,8,1,3,5,7,2]=>0010001=>1000100=>0111011
[4,6,1,8,3,5,7,2]=>0101001=>1001010=>0110101
[4,1,6,8,3,5,7,2]=>1001001=>1001001=>0110110
[1,4,6,8,3,5,7,2]=>0001001=>1001000=>0110111
[1,4,6,3,8,5,7,2]=>0010101=>1010100=>0101011
[4,6,1,3,8,5,7,2]=>0100101=>1010010=>0101101
[2,6,1,3,8,5,7,4]=>0100101=>1010010=>0101101
[2,1,6,3,8,5,7,4]=>1010101=>1010101=>0101010
[2,1,3,6,8,5,7,4]=>1000101=>1010001=>0101110
[4,1,3,6,8,5,7,2]=>1000101=>1010001=>0101110
[1,4,3,6,8,5,7,2]=>0100101=>1010010=>0101101
[2,1,8,3,6,5,7,4]=>1010101=>1010101=>0101010
[2,1,8,4,3,5,7,6]=>1011001=>1001101=>0110010
[4,1,8,3,6,5,7,2]=>1010101=>1010101=>0101010
[2,8,4,1,3,5,7,6]=>0110001=>1000110=>0111001
[6,8,1,4,3,5,7,2]=>0101001=>1001010=>0110101
[1,8,6,4,3,5,7,2]=>0111001=>1001110=>0110001
[8,6,1,4,3,5,7,2]=>1101001=>1001011=>0110100
[8,6,4,1,3,5,7,2]=>1110001=>1000111=>0111000
[8,4,2,1,3,5,7,6]=>1110001=>1000111=>0111000
[8,5,7,4,3,2,1,6]=>1011110=>0111101=>1000010
[8,7,6,5,1,4,3,2]=>1111011=>1101111=>0010000
[8,7,4,3,6,2,1,5]=>1110110=>0110111=>1001000
[8,7,3,6,5,2,1,4]=>1101110=>0111011=>1000100
[6,5,8,4,3,2,1,7]=>1011110=>0111101=>1000010
[8,4,7,6,3,2,1,5]=>1011110=>0111101=>1000010
[5,8,7,4,3,2,1,6]=>0111110=>0111110=>1000001
[4,5,2,7,3,1,8,6]=>0101101=>1011010=>0100101
[4,8,2,6,3,5,7,1]=>0101001=>1001010=>0110101
[8,6,1,2,7,4,3,5]=>1100110=>0110011=>1001100
[4,6,2,1,7,8,5,3]=>0110011=>1100110=>0011001
[2,3,8,7,4,1,6,5]=>0011101=>1011100=>0100011
[1,6,2,5,8,4,3,7]=>0100110=>0110010=>1001101
[1,5,8,6,2,3,7,4]=>0011001=>1001100=>0110011
[5,2,7,1,8,6,3,4]=>1010110=>0110101=>1001010
[1,2,8,3,7,6,5,4]=>0010111=>1110100=>0001011
[6,5,2,8,1,7,3,4]=>1101010=>0101011=>1010100
[2,8,3,5,1,7,4,6]=>0101010=>0101010=>1010101
[2,8,5,6,1,7,3,4]=>0101010=>0101010=>1010101
[5,4,2,8,6,1,7,3]=>1101101=>1011011=>0100100
[8,5,4,3,7,2,6,1]=>1110101=>1010111=>0101000
[8,3,7,4,2,6,5,1]=>1011011=>1101101=>0010010
[3,8,7,4,1,6,5,2]=>0111011=>1101110=>0010001
[6,3,2,8,4,1,7,5]=>1101101=>1011011=>0100100
[2,8,3,4,1,7,5,6]=>0101010=>0101010=>1010101
[5,4,2,8,3,1,7,6]=>1101101=>1011011=>0100100
[2,8,6,4,1,7,5,3]=>0111011=>1101110=>0010001
[8,4,7,6,2,5,3,1]=>1011011=>1101101=>0010010
[4,8,7,6,1,5,3,2]=>0111011=>1101110=>0010001
[7,3,8,5,2,1,6,4]=>1011101=>1011101=>0100010
[7,3,8,4,2,1,6,5]=>1011101=>1011101=>0100010
[7,5,4,3,8,2,1,6]=>1110110=>0110111=>1001000
[5,4,2,3,8,1,6,7]=>1100100=>0010011=>1101100
[3,7,8,4,1,2,6,5]=>0011001=>1001100=>0110011
[8,7,4,6,3,5,2,1]=>1101011=>1101011=>0010100
[7,3,4,8,2,1,5,6]=>1001100=>0011001=>1100110
[7,5,8,6,2,1,4,3]=>1011101=>1011101=>0100010
[6,5,8,7,3,1,4,2]=>1011101=>1011101=>0100010
[2,4,8,3,1,5,7,6]=>0011001=>1001100=>0110011
[6,3,2,4,8,1,5,7]=>1100100=>0010011=>1101100
[2,4,3,8,1,6,5,7]=>0101010=>0101010=>1010101
[2,3,8,4,1,6,7,5]=>0011001=>1001100=>0110011
[8,3,4,7,2,5,6,1]=>1001001=>1001001=>0110110
[3,4,8,7,1,5,6,2]=>0011001=>1001100=>0110011
[2,5,3,8,1,6,4,7]=>0101010=>0101010=>1010101
[3,7,4,8,1,5,2,6]=>0101010=>0101010=>1010101
[8,4,6,7,2,3,5,1]=>1001001=>1001001=>0110110
[2,6,8,5,1,3,7,4]=>0011001=>1001100=>0110011
[2,6,8,4,1,3,7,5]=>0011001=>1001100=>0110011
[3,7,5,8,1,4,2,6]=>0101010=>0101010=>1010101
[2,6,5,8,1,4,3,7]=>0101010=>0101010=>1010101
[2,5,8,3,1,4,7,6]=>0011001=>1001100=>0110011
[4,7,6,8,1,3,2,5]=>0101010=>0101010=>1010101
[5,6,8,7,1,3,4,2]=>0011001=>1001100=>0110011
[8,7,4,1,6,2,5,3]=>1110101=>1010111=>0101000
[6,3,7,4,5,8,2,1]=>1010011=>1100101=>0011010
[3,5,7,4,6,8,2,1]=>0010011=>1100100=>0011011
[6,8,4,1,7,2,5,3]=>0110101=>1010110=>0101001
[3,8,5,4,6,7,2,1]=>0110011=>1100110=>0011001
[6,8,3,4,5,7,2,1]=>0100011=>1100010=>0011101
[2,5,7,4,6,3,8,1]=>0010101=>1010100=>0101011
[5,4,2,7,8,3,6,1]=>1100101=>1010011=>0101100
[8,1,6,2,4,3,5,7]=>1010100=>0010101=>1101010
[8,7,1,2,4,3,5,6]=>1100100=>0010011=>1101100
[6,8,3,1,4,7,2,5]=>0110010=>0100110=>1011001
[6,4,7,2,8,5,1,3]=>1010110=>0110101=>1001010
[5,8,1,4,7,3,2,6]=>0100110=>0110010=>1001101
[8,7,1,4,5,3,2,6]=>1100110=>0110011=>1001100
[1,7,6,2,4,3,5,8]=>0110100=>0010110=>1101001
[8,7,4,2,6,5,1,3]=>1110110=>0110111=>1001000
[8,7,3,2,4,6,5,1]=>1110011=>1100111=>0011000
[1,7,2,5,4,3,6,8]=>0101100=>0011010=>1100101
[6,8,4,3,7,5,2,1]=>0110111=>1110110=>0001001
[6,4,7,3,8,5,2,1]=>1010111=>1110101=>0001010
[6,3,7,2,4,8,5,1]=>1010011=>1100101=>0011010
[8,1,2,5,4,3,6,7]=>1001100=>0011001=>1100110
[2,6,3,1,4,5,8,7]=>0110001=>1000110=>0111001
[4,7,3,2,5,6,1,8]=>0110010=>0100110=>1011001
[3,6,4,1,2,8,7,5]=>0110011=>1100110=>0011001
[3,6,5,1,8,2,7,4]=>0110101=>1010110=>0101001
[4,6,5,1,8,7,2,3]=>0110110=>0110110=>1001001
[5,7,1,4,8,6,2,3]=>0100110=>0110010=>1001101
[5,7,1,3,8,2,6,4]=>0100101=>1010010=>0101101
[6,3,7,2,8,4,5,1]=>1010101=>1010101=>0101010
[6,7,1,8,3,2,5,4]=>0101101=>1011010=>0100101
[8,7,6,1,4,5,2,3]=>1110010=>0100111=>1011000
[8,7,6,1,3,2,5,4]=>1110101=>1010111=>0101000
[8,7,3,5,1,2,6,4]=>1101001=>1001011=>0110100
[8,7,4,5,1,6,2,3]=>1101010=>0101011=>1010100
[8,5,6,4,1,7,2,3]=>1011010=>0101101=>1010010
[8,4,6,2,3,1,7,5]=>1010101=>1010101=>0101010
[8,3,5,4,2,1,7,6]=>1011101=>1011101=>0100010
[7,1,6,8,4,5,3,2]=>1001011=>1101001=>0010110
[7,5,1,6,4,2,3,8]=>1101100=>0011011=>1100100
[8,1,5,7,4,6,3,2]=>1001011=>1101001=>0010110
[1,8,4,6,7,5,3,2]=>0100111=>1110010=>0001101
[6,1,8,4,7,5,3,2]=>1010111=>1110101=>0001010
[8,4,1,5,6,7,3,2]=>1100011=>1100011=>0011100
[8,2,5,6,1,4,7,3]=>1001001=>1001001=>0110110
[4,8,5,2,1,6,7,3]=>0111001=>1001110=>0110001
[1,8,4,6,2,5,3,7]=>0101010=>0101010=>1010101
[8,5,6,1,2,4,3,7]=>1010010=>0100101=>1011010
[2,8,3,1,5,6,7,4]=>0110001=>1000110=>0111001
[8,2,4,3,6,7,1,5]=>1010010=>0100101=>1011010
[8,3,2,7,1,5,6,4]=>1101001=>1001011=>0110100
[3,2,8,5,7,1,6,4]=>1010101=>1010101=>0101010
[3,6,2,8,5,1,7,4]=>0101101=>1011010=>0100101
[6,2,1,8,4,7,5,3]=>1101011=>1101011=>0010100
[2,8,7,1,4,6,5,3]=>0110011=>1100110=>0011001
[8,2,7,1,5,4,6,3]=>1010101=>1010101=>0101010
[7,3,1,5,6,2,4,8]=>1100100=>0010011=>1101100
[2,7,3,6,5,8,1,4]=>0101010=>0101010=>1010101
[7,2,8,1,6,4,5,3]=>1010101=>1010101=>0101010
[7,8,2,6,4,1,5,3]=>0101101=>1011010=>0100101
[8,7,2,4,1,6,5,3]=>1101011=>1101011=>0010100
[1,2,8,6,3,7,5,4]=>0011011=>1101100=>0010011
[1,8,7,2,3,6,5,4]=>0110011=>1100110=>0011001
[1,7,8,2,6,4,3,5]=>0010110=>0110100=>1001011
[7,2,1,5,8,3,4,6]=>1100100=>0010011=>1101100
[7,1,5,8,3,2,4,6]=>1001100=>0011001=>1100110
[7,8,1,5,2,4,3,6]=>0101010=>0101010=>1010101
[8,7,1,2,5,4,3,6]=>1100110=>0110011=>1001100
[1,6,2,8,4,3,7,5]=>0101101=>1011010=>0100101
[1,8,3,7,2,5,4,6]=>0101010=>0101010=>1010101
[8,1,4,7,3,2,5,6]=>1001100=>0011001=>1100110
[4,7,8,1,3,2,5,6]=>0010100=>0010100=>1101011
[2,1,8,3,5,7,4,6]=>1010010=>0100101=>1011010
[1,2,3,4,8,5,7,6]=>0000101=>1010000=>0101111
[8,3,5,2,4,1,7,6]=>1010101=>1010101=>0101010
[8,6,2,5,3,1,7,4]=>1101101=>1011011=>0100100
[3,7,2,5,6,4,1,8]=>0100110=>0110010=>1001101
[7,6,2,5,4,3,1,8]=>1101110=>0111011=>1000100
[4,7,5,2,6,3,1,8]=>0110110=>0110110=>1001001
[5,6,7,2,4,3,1,8]=>0010110=>0110100=>1001011
[1,8,3,4,2,7,5,6]=>0101010=>0101010=>1010101
[2,8,3,4,1,6,7,5]=>0101001=>1001010=>0110101
[7,8,2,4,3,1,6,5]=>0101101=>1011010=>0100101
[6,1,3,5,7,2,4,8]=>1000100=>0010001=>1101110
[8,1,3,6,2,4,7,5]=>1001001=>1001001=>0110110
[2,1,8,3,7,5,4,6]=>1010110=>0110101=>1001010
[7,1,8,2,5,6,3,4]=>1010010=>0100101=>1011010
[6,1,5,8,2,7,3,4]=>1001010=>0101001=>1010110
[6,2,5,8,1,4,7,3]=>1001001=>1001001=>0110110
[2,3,8,1,5,6,7,4]=>0010001=>1000100=>0111011
[1,3,8,2,5,7,4,6]=>0010010=>0100100=>1011011
[2,8,7,1,6,4,5,3]=>0110101=>1010110=>0101001
[3,8,7,1,5,6,4,2]=>0110011=>1100110=>0011001
[4,8,7,5,1,6,3,2]=>0111011=>1101110=>0010001
[5,8,6,7,1,4,3,2]=>0101011=>1101010=>0010101
[6,7,8,5,1,4,3,2]=>0011011=>1101100=>0010011
[5,6,3,8,4,1,7,2]=>0101101=>1011010=>0100101
[7,3,8,5,4,1,6,2]=>1011101=>1011101=>0100010
[3,4,8,5,6,1,7,2]=>0010101=>1010100=>0101011
[8,3,7,4,1,6,5,2]=>1011011=>1101101=>0010010
[3,5,6,8,4,1,7,2]=>0001101=>1011000=>0100111
[5,6,4,7,8,1,3,2]=>0100101=>1010010=>0101101
[6,2,3,1,5,4,7,8]=>1010100=>0010101=>1101010
[8,5,1,3,2,4,7,6]=>1101001=>1001011=>0110100
[7,5,1,3,2,6,4,8]=>1101010=>0101011=>1010100
[3,6,4,1,5,2,7,8]=>0110100=>0010110=>1101001
[4,5,6,1,3,2,7,8]=>0010100=>0010100=>1101011
[6,7,1,4,2,5,3,8]=>0101010=>0101010=>1010101
[2,7,1,3,5,6,4,8]=>0100010=>0100010=>1011101
[8,6,1,2,4,3,7,5]=>1100101=>1010011=>0101100
[7,8,1,2,5,3,6,4]=>0100101=>1010010=>0101101
[6,8,1,4,2,3,7,5]=>0101001=>1001010=>0110101
[4,5,8,1,2,3,7,6]=>0010001=>1000100=>0111011
[1,8,2,7,5,4,6,3]=>0101101=>1011010=>0100101
[1,8,6,3,7,2,4,5]=>0110100=>0010110=>1101001
[1,8,5,3,4,7,2,6]=>0110010=>0100110=>1011001
[1,8,2,5,4,6,7,3]=>0101001=>1001010=>0110101
[7,4,3,8,2,5,6,1]=>1101001=>1001011=>0110100
[7,2,8,4,3,5,6,1]=>1011001=>1001101=>0110010
[7,2,8,1,3,6,4,5]=>1010010=>0100101=>1011010
[1,4,7,5,2,6,8,3]=>0011001=>1001100=>0110011
[4,6,5,3,7,1,8,2]=>0110101=>1010110=>0101001
[5,6,2,7,3,1,8,4]=>0101101=>1011010=>0100101
[1,6,3,7,5,8,2,4]=>0101010=>0101010=>1010101
[5,2,4,8,1,3,7,6]=>1001001=>1001001=>0110110
[6,2,5,4,8,3,7,1]=>1010101=>1010101=>0101010
[3,5,2,4,7,1,6,8]=>0100100=>0010010=>1101101
[6,4,5,3,8,2,1,7]=>1010110=>0110101=>1001010
[6,5,3,4,8,7,1,2]=>1100110=>0110011=>1001100
[7,6,3,8,5,4,1,2]=>1101110=>0111011=>1000100
[5,4,8,1,2,7,3,6]=>1010010=>0100101=>1011010
[6,2,4,8,5,1,3,7]=>1001100=>0011001=>1100110
[7,6,3,8,5,1,2,4]=>1101100=>0011011=>1100100
[6,3,8,1,7,2,4,5]=>1010100=>0010101=>1101010
[7,2,8,6,1,3,4,5]=>1011000=>0001101=>1110010
[7,2,8,6,1,5,3,4]=>1011010=>0101101=>1010010
[3,2,4,7,8,1,5,6]=>1000100=>0010001=>1101110
[1,5,7,4,2,8,6,3]=>0011011=>1101100=>0010011
[1,3,7,2,8,6,4,5]=>0010110=>0110100=>1001011
[1,5,3,6,8,2,7,4]=>0100101=>1010010=>0101101
[4,3,6,5,7,8,1,2]=>1010010=>0100101=>1011010
[4,2,3,5,6,8,1,7]=>1000010=>0100001=>1011110
[4,2,6,7,3,8,5,1]=>1001011=>1101001=>0010110
[3,2,5,6,8,1,7,4]=>1000101=>1010001=>0101110
[4,2,3,6,8,1,5,7]=>1000100=>0010001=>1101110
[2,6,1,5,4,8,3,7]=>0101010=>0101010=>1010101
[3,2,1,8,7,5,6,4]=>1101101=>1011011=>0100100
[3,1,6,2,5,8,4,7]=>1010010=>0100101=>1011010
[6,5,1,3,4,8,2,7]=>1100010=>0100011=>1011100
[6,2,4,5,8,1,3,7]=>1000100=>0010001=>1101110
[2,6,1,5,8,3,4,7]=>0100100=>0010010=>1101101
[2,3,4,8,1,7,6,5]=>0001011=>1101000=>0010111
[6,3,1,7,8,4,5,2]=>1100101=>1010011=>0101100
[6,2,7,8,4,5,1,3]=>1001010=>0101001=>1010110
[3,1,4,8,7,6,2,5]=>1001110=>0111001=>1000110
[2,3,6,5,8,7,1,4]=>0010110=>0110100=>1001011
[8,4,1,2,7,6,3,5]=>1100110=>0110011=>1001100
[3,4,8,2,7,5,1,6]=>0010110=>0110100=>1001011
[6,3,2,8,5,7,4,1]=>1101011=>1101011=>0010100
[3,2,6,8,5,1,7,4]=>1001101=>1011001=>0100110
[5,2,4,1,7,8,6,3]=>1010011=>1100101=>0011010
[3,8,4,7,2,5,6,1]=>0101001=>1001010=>0110101
[1,8,7,2,4,5,6,3]=>0110001=>1000110=>0111001
[5,3,4,7,1,8,6,2]=>1001011=>1101001=>0010110
[5,3,7,1,6,2,8,4]=>1010101=>1010101=>0101010
[4,7,6,5,8,2,1,3]=>0110110=>0110110=>1001001
[7,5,1,2,6,8,4,3]=>1100011=>1100011=>0011100
[1,2,5,3,8,7,6,4]=>0010111=>1110100=>0001011
[2,8,1,5,6,3,7,4]=>0100101=>1010010=>0101101
[4,8,2,3,6,7,1,5]=>0100010=>0100010=>1011101
[8,2,4,6,7,1,3,5]=>1000100=>0010001=>1101110
[3,7,5,1,8,4,6,2]=>0110101=>1010110=>0101001
[6,5,3,1,8,4,2,7]=>1110110=>0110111=>1001000
[5,7,4,3,8,6,2,1]=>0110111=>1110110=>0001001
[4,2,3,8,5,6,1,7]=>1001010=>0101001=>1010110
[3,6,4,2,8,5,7,1]=>0110101=>1010110=>0101001
[4,7,3,2,5,1,8,6]=>0110101=>1010110=>0101001
[2,4,8,7,1,3,5,6]=>0011000=>0001100=>1110011
[2,4,3,5,1,8,6,7]=>0101010=>0101010=>1010101
[8,6,1,2,4,3,5,7]=>1100100=>0010011=>1101100
[8,6,2,5,4,1,3,7]=>1101100=>0011011=>1100100
[8,3,5,7,6,2,1,4]=>1001110=>0111001=>1000110
[6,7,5,3,8,2,4,1]=>0110101=>1010110=>0101001
[8,2,6,3,4,5,1,7]=>1010010=>0100101=>1011010
[8,1,5,4,3,6,2,7]=>1011010=>0101101=>1010010
[8,6,4,2,1,5,3,7]=>1111010=>0101111=>1010000
[8,3,2,4,6,1,5,7]=>1100100=>0010011=>1101100
[8,2,3,4,7,6,1,5]=>1000110=>0110001=>1001110
[5,7,1,8,3,4,6,2]=>0101001=>1001010=>0110101
[1,5,6,7,3,4,8,2]=>0001001=>1001000=>0110111
[4,8,1,2,7,3,6,5]=>0100101=>1010010=>0101101
[2,5,7,8,4,1,3,6]=>0001100=>0011000=>1100111
[6,3,5,8,7,2,4,1]=>1001101=>1011001=>0100110
[5,2,8,7,1,3,4,6]=>1011000=>0001101=>1110010
[5,2,7,4,8,1,6,3]=>1010101=>1010101=>0101010
[8,3,7,4,2,5,6,1]=>1011001=>1001101=>0110010
[8,1,7,4,5,2,6,3]=>1010101=>1010101=>0101010
[1,7,8,3,5,4,6,2]=>0010101=>1010100=>0101011
[4,6,3,5,8,1,7,2]=>0100101=>1010010=>0101101
[8,2,4,1,5,6,7,3]=>1010001=>1000101=>0111010
[3,5,1,7,6,8,2,4]=>0101010=>0101010=>1010101
[2,1,7,6,4,5,8,3]=>1011001=>1001101=>0110010
[1,7,6,5,2,4,8,3]=>0111001=>1001110=>0110001
[5,1,7,6,2,8,4,3]=>1011011=>1101101=>0010010
[4,6,2,5,3,8,7,1]=>0101011=>1101010=>0010101
[8,6,4,2,3,1,7,5]=>1110101=>1010111=>0101000
[8,6,4,2,1,3,7,5]=>1111001=>1001111=>0110000
[4,2,8,3,1,5,6,7]=>1011000=>0001101=>1110010
[2,5,7,3,8,4,6,1]=>0010101=>1010100=>0101011
[4,2,7,1,8,5,3,6]=>1010110=>0110101=>1001010
[1,3,7,5,8,6,4,2]=>0010111=>1110100=>0001011
[2,7,4,5,8,3,6,1]=>0100101=>1010010=>0101101
[3,5,7,1,4,8,6,2]=>0010011=>1100100=>0011011
[3,4,1,2,8,5,7,6]=>0100101=>1010010=>0101101
[6,2,3,1,4,8,7,5]=>1010011=>1100101=>0011010
[8,4,3,2,5,7,1,6]=>1110010=>0100111=>1011000
[5,3,6,8,2,1,4,7]=>1001100=>0011001=>1100110
[3,2,6,8,5,4,1,7]=>1001110=>0111001=>1000110
[7,3,8,2,5,4,1,6]=>1010110=>0110101=>1001010
[7,4,2,5,8,3,1,6]=>1100110=>0110011=>1001100
[3,1,2,8,5,6,4,7]=>1001010=>0101001=>1010110
[5,2,1,6,8,3,4,7]=>1100100=>0010011=>1101100
[3,1,8,6,5,4,2,7]=>1011110=>0111101=>1000010
[5,6,8,1,4,3,2,7]=>0010110=>0110100=>1001011
[6,4,8,3,7,2,5,1]=>1010101=>1010101=>0101010
[4,7,3,6,2,1,8,5]=>0101101=>1011010=>0100101
[7,8,4,1,5,3,2,6]=>0110110=>0110110=>1001001
[7,3,8,5,1,4,2,6]=>1011010=>0101101=>1010010
[1,5,4,8,3,7,6,2]=>0101011=>1101010=>0010101
[4,7,8,3,1,6,5,2]=>0011011=>1101100=>0010011
[8,7,5,3,6,4,2,1]=>1110111=>1110111=>0001000
[4,6,1,3,8,7,5,2]=>0100111=>1110010=>0001101
[3,1,2,7,5,6,8,4]=>1001001=>1001001=>0110110
[3,6,1,2,7,5,8,4]=>0100101=>1010010=>0101101
[3,6,2,5,8,7,4,1]=>0100111=>1110010=>0001101
[8,5,2,3,6,7,4,1]=>1100011=>1100011=>0011100
[6,7,1,3,2,8,4,5]=>0101010=>0101010=>1010101
[6,2,7,1,3,4,8,5]=>1010001=>1000101=>0111010
[5,2,1,7,3,8,4,6]=>1101010=>0101011=>1010100
[4,7,2,6,3,8,1,5]=>0101010=>0101010=>1010101
[4,8,2,6,3,7,5,1]=>0101011=>1101010=>0010101
[3,7,2,4,6,1,8,5]=>0100101=>1010010=>0101101
[5,3,7,2,8,1,4,6]=>1010100=>0010101=>1101010
[7,1,8,3,4,2,5,6]=>1010100=>0010101=>1101010
[7,2,4,1,8,3,5,6]=>1010100=>0010101=>1101010
[4,8,7,6,3,2,1,5]=>0111110=>0111110=>1000001
[7,3,8,2,6,5,1,4]=>1010110=>0110101=>1001010
[7,8,2,4,6,1,5,3]=>0100101=>1010010=>0101101
[3,5,1,8,7,2,6,4]=>0101101=>1011010=>0100101
[5,2,8,1,7,6,3,4]=>1010110=>0110101=>1001010
[6,2,1,3,8,7,5,4]=>1100111=>1110011=>0001100
[6,7,8,1,2,5,4,3]=>0010011=>1100100=>0011011
[5,8,7,1,6,4,3,2]=>0110111=>1110110=>0001001
[6,8,7,5,1,4,3,2]=>0111011=>1101110=>0010001
[8,6,4,3,2,1,7,5]=>1111101=>1011111=>0100000
[6,5,4,3,8,2,7,1]=>1110101=>1010111=>0101000
[7,5,4,3,2,8,6,1]=>1111011=>1101111=>0010000
[8,5,4,3,7,2,1,6]=>1110110=>0110111=>1001000
[8,4,3,2,1,7,6,5]=>1111011=>1101111=>0010000
[3,7,5,8,1,4,6,2]=>0101001=>1001010=>0110101
[4,7,5,8,3,2,1,6]=>0101110=>0111010=>1000101
[5,7,2,3,6,1,8,4]=>0100101=>1010010=>0101101
[7,3,1,4,8,2,5,6]=>1100100=>0010011=>1101100
[7,4,1,2,5,8,3,6]=>1100010=>0100011=>1011100
[4,7,1,6,5,8,3,2]=>0101011=>1101010=>0010101
[2,7,5,4,3,8,1,6]=>0111010=>0101110=>1010001
[8,6,4,2,3,7,5,1]=>1110011=>1100111=>0011000
[7,6,4,2,3,8,1,5]=>1110010=>0100111=>1011000
[6,4,7,1,3,8,5,2]=>1010011=>1100101=>0011010
[3,1,2,4,8,7,6,5]=>1000111=>1110001=>0001110
[6,5,8,7,3,1,2,4]=>1011100=>0011101=>1100010
[5,6,7,8,1,4,2,3]=>0001010=>0101000=>1010111
[2,6,7,4,5,3,1,8]=>0010110=>0110100=>1001011
[1,3,7,4,2,8,5,6]=>0011010=>0101100=>1010011
[4,6,1,3,7,2,5,8]=>0100100=>0010010=>1101101
[6,5,7,8,3,1,4,2]=>1001101=>1011001=>0100110
[7,5,8,6,2,1,3,4]=>1011100=>0011101=>1100010
[2,8,1,3,6,5,4,7]=>0100110=>0110010=>1001101
[2,8,7,3,5,4,1,6]=>0110110=>0110110=>1001001
[3,4,2,6,8,7,1,5]=>0100110=>0110010=>1001101
[6,1,4,2,7,8,5,3]=>1010011=>1100101=>0011010
[7,3,8,4,1,2,6,5]=>1011001=>1001101=>0110010
[6,8,3,2,7,1,5,4]=>0110101=>1010110=>0101001
[5,1,4,3,6,2,7,8]=>1010100=>0010101=>1101010
[4,8,5,6,3,2,1,7]=>0101110=>0111010=>1000101
[2,8,5,6,3,7,1,4]=>0101010=>0101010=>1010101
[6,7,3,1,4,2,8,5]=>0110101=>1010110=>0101001
[3,2,6,7,4,8,1,5]=>1001010=>0101001=>1010110
[3,7,1,2,4,6,5,8]=>0100010=>0100010=>1011101
[4,1,8,2,6,3,5,7]=>1010100=>0010101=>1101010
[7,5,6,8,2,1,4,3]=>1001101=>1011001=>0100110
[5,8,6,7,1,2,3,4]=>0101000=>0001010=>1110101
[4,8,1,5,7,2,3,6]=>0100100=>0010010=>1101101
[3,5,1,4,7,6,8,2]=>0100101=>1010010=>0101101
[5,3,2,7,1,6,8,4]=>1101001=>1001011=>0110100
[8,4,3,7,5,1,6,2]=>1101101=>1011011=>0100100
[5,1,7,2,4,6,8,3]=>1010001=>1000101=>0111010
[4,5,7,1,2,6,8,3]=>0010001=>1000100=>0111011
[5,4,1,7,3,6,8,2]=>1101001=>1001011=>0110100
[3,6,4,7,5,2,8,1]=>0101101=>1011010=>0100101
[3,4,7,6,2,5,8,1]=>0011001=>1001100=>0110011
[4,8,3,6,5,2,1,7]=>0101110=>0111010=>1000101
[1,8,6,5,4,2,3,7]=>0111100=>0011110=>1100001
[8,1,7,4,2,5,6,3]=>1011001=>1001101=>0110010
[1,8,7,2,5,3,4,6]=>0110100=>0010110=>1101001
[4,8,1,5,2,6,3,7]=>0101010=>0101010=>1010101
[3,6,8,5,1,2,4,7]=>0011000=>0001100=>1110011
[1,5,2,7,8,4,6,3]=>0100101=>1010010=>0101101
[6,7,2,8,5,3,1,4]=>0101110=>0111010=>1000101
[6,7,2,8,3,1,5,4]=>0101101=>1011010=>0100101
[7,1,2,8,3,5,6,4]=>1001001=>1001001=>0110110
[6,7,5,2,8,1,4,3]=>0110101=>1010110=>0101001
[7,1,4,5,8,6,2,3]=>1000110=>0110001=>1001110
[3,1,4,6,7,8,5,2]=>1000011=>1100001=>0011110
[5,7,6,4,2,8,1,3]=>0111010=>0101110=>1010001
[7,4,6,1,8,2,3,5]=>1010100=>0010101=>1101010
[3,4,5,1,6,8,7,2]=>0010011=>1100100=>0011011
[5,1,6,8,4,2,7,3]=>1001101=>1011001=>0100110
[7,4,8,2,3,6,5,1]=>1010011=>1100101=>0011010
[7,5,8,6,3,4,2,1]=>1011011=>1101101=>0010010
[5,7,8,3,1,6,4,2]=>0011011=>1101100=>0010011
[7,5,8,3,2,4,1,6]=>1011010=>0101101=>1010010
[6,4,1,8,2,5,7,3]=>1101001=>1001011=>0110100
[5,8,2,6,3,1,4,7]=>0101100=>0011010=>1100101
[3,6,5,1,8,4,7,2]=>0110101=>1010110=>0101001
[8,2,7,5,4,1,3,6]=>1011100=>0011101=>1100010
[6,8,5,2,3,4,1,7]=>0110010=>0100110=>1011001
[2,6,8,7,1,5,3,4]=>0011010=>0101100=>1010011
[7,5,1,6,2,8,4,3]=>1101011=>1101011=>0010100
[6,2,7,3,8,4,1,5]=>1010110=>0110101=>1001010
[3,7,2,4,8,5,1,6]=>0100110=>0110010=>1001101
[1,5,2,6,3,8,7,4]=>0101011=>1101010=>0010101
[1,3,6,2,4,8,7,5]=>0010011=>1100100=>0011011
[7,3,5,2,4,1,6,8]=>1010100=>0010101=>1101010
[8,3,6,2,5,4,1,7]=>1010110=>0110101=>1001010
[3,5,8,2,4,6,1,7]=>0010010=>0100100=>1011011
[6,4,7,8,2,3,1,5]=>1001010=>0101001=>1010110
[7,4,8,5,3,2,1,6]=>1011110=>0111101=>1000010
[1,5,3,2,8,4,7,6]=>0110101=>1010110=>0101001
[2,8,7,3,5,1,4,6]=>0110100=>0010110=>1101001
[3,8,4,7,5,1,2,6]=>0101100=>0011010=>1100101
[6,1,2,7,3,8,5,4]=>1001011=>1101001=>0010110
[2,1,7,3,4,8,6,5]=>1010011=>1100101=>0011010
[8,3,1,6,7,2,5,4]=>1100101=>1010011=>0101100
[4,8,3,7,1,5,2,6]=>0101010=>0101010=>1010101
[1,3,5,8,2,4,7,6]=>0001001=>1001000=>0110111
[5,3,7,2,1,4,6,8]=>1011000=>0001101=>1110010
[6,4,2,8,3,1,5,7]=>1101100=>0011011=>1100100
[5,7,2,3,8,1,4,6]=>0100100=>0010010=>1101101
[6,4,7,5,8,1,2,3]=>1010100=>0010101=>1101010
[8,6,4,2,1,7,5,3]=>1111011=>1101111=>0010000
[7,4,2,1,5,8,6,3]=>1110011=>1100111=>0011000
[7,6,4,1,8,5,2,3]=>1110110=>0110111=>1001000
[1,6,4,8,7,5,3,2]=>0101111=>1111010=>0000101
[6,3,1,2,8,4,7,5]=>1100101=>1010011=>0101100
[3,6,1,8,2,4,7,5]=>0101001=>1001010=>0110101
[6,4,1,8,3,2,7,5]=>1101101=>1011011=>0100100
[1,4,8,7,2,6,5,3]=>0011011=>1101100=>0010011
[5,4,1,8,7,3,2,6]=>1101110=>0111011=>1000100
[5,8,4,1,7,6,2,3]=>0110110=>0110110=>1001001
[8,6,1,7,5,4,3,2]=>1101111=>1111011=>0000100
[3,1,8,7,6,5,2,4]=>1011110=>0111101=>1000010
[8,1,2,4,5,3,6,7]=>1000100=>0010001=>1101110
[1,8,7,6,4,5,3,2]=>0111011=>1101110=>0010001
[2,6,8,1,3,7,5,4]=>0010011=>1100100=>0011011
[2,4,8,1,5,7,6,3]=>0010011=>1100100=>0011011
[3,2,8,6,1,7,5,4]=>1011011=>1101101=>0010010
[6,2,8,3,1,7,5,4]=>1011011=>1101101=>0010010
[7,4,3,8,5,2,1,6]=>1101110=>0111011=>1000100
[6,5,2,8,4,3,1,7]=>1101110=>0111011=>1000100
[4,3,8,7,5,1,6,2]=>1011101=>1011101=>0100010
[4,2,3,8,5,1,6,7]=>1001100=>0011001=>1100110
[4,2,8,5,1,7,6,3]=>1011011=>1101101=>0010010
[3,4,2,8,5,6,1,7]=>0101010=>0101010=>1010101
[3,2,4,8,6,1,5,7]=>1001100=>0011001=>1100110
[3,2,5,8,6,1,4,7]=>1001100=>0011001=>1100110
[8,4,3,7,5,2,6,1]=>1101101=>1011011=>0100100
[4,3,7,8,5,1,2,6]=>1001100=>0011001=>1100110
[4,2,6,8,5,1,3,7]=>1001100=>0011001=>1100110
[3,5,2,8,4,6,1,7]=>0101010=>0101010=>1010101
[5,2,6,8,4,1,3,7]=>1001100=>0011001=>1100110
[5,3,7,8,4,1,2,6]=>1001100=>0011001=>1100110
[5,6,2,8,3,4,1,7]=>0101010=>0101010=>1010101
[5,3,8,7,4,1,6,2]=>1011101=>1011101=>0100010
[6,4,2,8,5,3,1,7]=>1101110=>0111011=>1000100
[8,7,5,3,6,2,4,1]=>1110101=>1010111=>0101000
[8,7,4,3,6,2,5,1]=>1110101=>1010111=>0101000
[8,6,5,3,7,2,4,1]=>1110101=>1010111=>0101000
[7,6,4,3,8,2,5,1]=>1110101=>1010111=>0101000
[6,4,5,3,8,2,7,1]=>1010101=>1010101=>0101010
[7,4,5,3,8,2,6,1]=>1010101=>1010101=>0101010
[7,5,6,3,8,2,4,1]=>1010101=>1010101=>0101010
[8,5,6,3,7,2,4,1]=>1010101=>1010101=>0101010
[8,4,6,3,7,2,5,1]=>1010101=>1010101=>0101010
[8,4,7,3,5,2,6,1]=>1010101=>1010101=>0101010
[8,5,7,3,4,2,6,1]=>1010101=>1010101=>0101010
[7,5,8,4,3,2,6,1]=>1011101=>1011101=>0100010
[6,5,8,3,4,2,7,1]=>1010101=>1010101=>0101010
[7,5,8,3,4,2,6,1]=>1010101=>1010101=>0101010
[7,6,8,3,5,2,4,1]=>1010101=>1010101=>0101010
[7,5,8,4,6,2,3,1]=>1010101=>1010101=>0101010
[7,5,8,3,6,2,4,1]=>1010101=>1010101=>0101010
[7,4,8,3,6,2,5,1]=>1010101=>1010101=>0101010
[7,4,8,3,5,2,6,1]=>1010101=>1010101=>0101010
[6,4,8,3,5,2,7,1]=>1010101=>1010101=>0101010
[5,4,7,3,6,2,8,1]=>1010101=>1010101=>0101010
[5,4,8,3,7,2,6,1]=>1010101=>1010101=>0101010
[6,5,8,3,7,2,4,1]=>1010101=>1010101=>0101010
[6,5,8,4,7,2,3,1]=>1010101=>1010101=>0101010
[6,5,8,4,7,3,2,1]=>1010111=>1110101=>0001010
[6,5,7,3,8,2,4,1]=>1010101=>1010101=>0101010
[5,4,6,3,8,2,7,1]=>1010101=>1010101=>0101010
[6,5,3,7,8,2,1,4]=>1100110=>0110011=>1001100
[6,5,4,2,8,7,1,3]=>1110110=>0110111=>1001000
[6,4,3,7,5,2,1,8]=>1101110=>0111011=>1000100
[6,3,7,8,5,2,1,4]=>1001110=>0111001=>1000110
[6,3,7,2,5,4,1,8]=>1010110=>0110101=>1001010
[6,3,2,7,5,4,1,8]=>1101110=>0111011=>1000100
[4,8,2,6,3,7,1,5]=>0101010=>0101010=>1010101
[5,8,4,1,2,7,3,6]=>0110010=>0100110=>1011001
[5,4,8,1,2,3,7,6]=>1010001=>1000101=>0111010
[1,4,7,6,3,2,5,8]=>0011100=>0011100=>1100011
[4,8,3,2,7,6,1,5]=>0110110=>0110110=>1001001
[5,8,1,7,4,2,3,6]=>0101100=>0011010=>1100101
[4,8,6,7,2,3,1,5]=>0101010=>0101010=>1010101
[4,8,7,3,6,2,1,5]=>0110110=>0110110=>1001001
[4,3,8,2,7,1,6,5]=>1010101=>1010101=>0101010
[4,1,8,7,3,2,5,6]=>1011100=>0011101=>1100010
[4,7,8,1,2,5,3,6]=>0010010=>0100100=>1011011
[4,7,5,1,2,8,3,6]=>0110010=>0100110=>1011001
[2,3,6,7,4,1,8,5]=>0001101=>1011000=>0100111
[2,6,3,4,7,8,1,5]=>0100010=>0100010=>1011101
[3,1,7,8,4,2,5,6]=>1001100=>0011001=>1100110
[4,3,1,2,8,5,7,6]=>1100101=>1010011=>0101100
[3,7,6,8,4,2,1,5]=>0101110=>0111010=>1000101
[4,7,1,8,5,2,3,6]=>0101100=>0011010=>1100101
[2,6,8,7,4,3,1,5]=>0011110=>0111100=>1000011
[3,7,8,6,2,4,1,5]=>0011010=>0101100=>1010011
[3,7,8,2,6,4,1,5]=>0010110=>0110100=>1001011
[4,2,3,8,1,6,7,5]=>1001001=>1001001=>0110110
[3,7,2,8,4,6,1,5]=>0101010=>0101010=>1010101
[4,2,8,3,6,1,7,5]=>1010101=>1010101=>0101010
[4,2,8,6,3,1,7,5]=>1011101=>1011101=>0100010
[2,6,8,4,7,3,1,5]=>0010110=>0110100=>1001011
[2,4,6,8,3,1,7,5]=>0001101=>1011000=>0100111
[3,7,2,4,8,6,1,5]=>0100110=>0110010=>1001101
[1,3,6,4,7,2,5,8]=>0010100=>0010100=>1101011
[2,4,6,3,8,1,7,5]=>0010101=>1010100=>0101011
[2,6,4,3,8,7,1,5]=>0110110=>0110110=>1001001
[2,4,3,6,1,8,7,5]=>0101011=>1101010=>0010101
[3,1,7,4,8,2,5,6]=>1010100=>0010101=>1101010
[2,6,3,7,4,8,1,5]=>0101010=>0101010=>1010101
[1,3,5,7,6,8,2,4]=>0001010=>0101000=>1010111
[1,3,5,7,6,2,8,4]=>0001101=>1011000=>0100111
[1,3,5,7,2,6,8,4]=>0001001=>1001000=>0110111
[1,3,5,2,7,6,8,4]=>0010101=>1010100=>0101011
[1,3,5,2,7,6,4,8]=>0010110=>0110100=>1001011
[1,3,5,7,6,2,4,8]=>0001100=>0011000=>1100111
[1,3,5,7,4,6,8,2]=>0001001=>1001000=>0110111
[1,3,5,7,4,6,2,8]=>0001010=>0101000=>1010111
[1,3,5,7,4,2,6,8]=>0001100=>0011000=>1100111
[1,3,5,4,7,2,6,8]=>0010100=>0010100=>1101011
[1,3,5,4,7,8,2,6]=>0010010=>0100100=>1011011
[1,3,5,4,7,2,8,6]=>0010101=>1010100=>0101011
[1,3,5,7,4,2,8,6]=>0001101=>1011000=>0100111
[1,3,5,7,4,8,2,6]=>0001010=>0101000=>1010111
[1,3,5,7,4,8,6,2]=>0001011=>1101000=>0010111
[1,3,5,7,8,4,6,2]=>0000101=>1010000=>0101111
[1,3,5,7,8,4,2,6]=>0000110=>0110000=>1001111
[1,3,5,2,7,8,6,4]=>0010011=>1100100=>0011011
[1,3,5,7,2,8,6,4]=>0001011=>1101000=>0010111
[1,3,5,7,8,2,6,4]=>0000101=>1010000=>0101111
[1,3,5,7,8,6,2,4]=>0000110=>0110000=>1001111
[2,3,6,1,7,8,5,4]=>0010011=>1100100=>0011011
[2,3,7,1,4,8,6,5]=>0010011=>1100100=>0011011
[2,6,1,3,7,8,5,4]=>0100011=>1100010=>0011101
[2,3,6,8,4,5,1,7]=>0001010=>0101000=>1010111
[2,5,7,3,4,8,6,1]=>0010011=>1100100=>0011011
[2,6,7,3,4,8,5,1]=>0010011=>1100100=>0011011
[6,5,2,4,3,7,1,8]=>1101010=>0101011=>1010100
[2,5,4,6,7,1,3,8]=>0100100=>0010010=>1101101
[1,7,6,3,5,4,8,2]=>0110101=>1010110=>0101001
[2,4,6,3,7,5,1,8]=>0010110=>0110100=>1001011
[4,7,2,3,5,6,1,8]=>0100010=>0100010=>1011101
[5,3,2,7,4,6,1,8]=>1101010=>0101011=>1010100
[1,6,8,5,7,3,4,2]=>0010101=>1010100=>0101011
[4,1,2,5,8,3,7,6]=>1000101=>1010001=>0101110
[4,6,1,2,5,8,3,7]=>0100010=>0100010=>1011101
[4,1,7,2,6,5,8,3]=>1010101=>1010101=>0101010
[5,6,7,2,1,4,8,3]=>0011001=>1001100=>0110011
[6,4,5,7,1,3,8,2]=>1001001=>1001001=>0110110
[6,8,5,2,4,1,7,3]=>0110101=>1010110=>0101001
[5,7,6,8,1,4,2,3]=>0101010=>0101010=>1010101
[4,1,6,2,8,5,7,3]=>1010101=>1010101=>0101010
[7,1,4,2,3,6,8,5]=>1010001=>1000101=>0111010
[6,4,2,1,3,8,7,5]=>1110011=>1100111=>0011000
[1,5,8,3,4,6,7,2]=>0010001=>1000100=>0111011
[8,1,2,3,4,6,7,5]=>1000001=>1000001=>0111110
[2,8,1,3,5,4,7,6]=>0100101=>1010010=>0101101
[8,7,1,4,3,5,2,6]=>1101010=>0101011=>1010100
[8,3,2,1,4,5,7,6]=>1110001=>1000111=>0111000
[4,3,2,8,1,6,5,7]=>1101010=>0101011=>1010100
[3,8,6,4,2,1,5,7]=>0111100=>0011110=>1100001
[3,8,2,1,5,6,4,7]=>0110010=>0100110=>1011001
[8,5,2,4,3,1,6,7]=>1101100=>0011011=>1100100
[8,3,2,5,4,1,6,7]=>1101100=>0011011=>1100100
[6,1,2,7,5,3,8,4]=>1001101=>1011001=>0100110
[2,6,1,4,7,3,8,5]=>0100101=>1010010=>0101101
[7,3,2,8,6,4,1,5]=>1101110=>0111011=>1000100
[7,8,2,5,3,6,1,4]=>0101010=>0101010=>1010101
[6,3,7,5,1,8,2,4]=>1011010=>0101101=>1010010
[8,1,6,3,5,7,2,4]=>1010010=>0100101=>1011010
[8,3,2,6,4,7,1,5]=>1101010=>0101011=>1010100
[5,8,4,6,1,7,2,3]=>0101010=>0101010=>1010101
[8,4,2,5,6,7,1,3]=>1100010=>0100011=>1011100
[2,3,8,7,6,5,1,4]=>0011110=>0111100=>1000011
[1,5,8,7,2,6,4,3]=>0011011=>1101100=>0010011
[2,5,8,7,3,6,1,4]=>0011010=>0101100=>1010011
[4,1,8,7,2,6,5,3]=>1011011=>1101101=>0010010
[1,2,8,7,3,6,5,4]=>0011011=>1101100=>0010011
[4,5,8,7,1,2,6,3]=>0011001=>1001100=>0110011
[1,5,8,7,3,2,6,4]=>0011101=>1011100=>0100011
[4,5,8,7,3,2,1,6]=>0011110=>0111100=>1000011
[2,6,8,1,7,5,4,3]=>0010111=>1110100=>0001011
[2,6,8,3,7,5,1,4]=>0010110=>0110100=>1001011
[1,6,8,4,7,2,5,3]=>0010101=>1010100=>0101011
[1,6,8,3,7,2,5,4]=>0010101=>1010100=>0101011
[2,5,8,1,7,6,4,3]=>0010111=>1110100=>0001011
[2,5,8,3,7,6,1,4]=>0010110=>0110100=>1001011
[3,2,8,4,7,6,1,5]=>1010110=>0110101=>1001010
[1,5,8,4,7,2,6,3]=>0010101=>1010100=>0101011
[1,5,8,3,7,2,6,4]=>0010101=>1010100=>0101011
[3,1,8,4,7,2,6,5]=>1010101=>1010101=>0101010
[5,6,8,1,2,7,4,3]=>0010011=>1100100=>0011011
[1,6,8,2,3,7,5,4]=>0010011=>1100100=>0011011
[1,5,8,4,2,7,6,3]=>0011011=>1101100=>0010011
[5,6,8,4,3,2,1,7]=>0011110=>0111100=>1000011
[7,1,4,8,6,2,5,3]=>1001101=>1011001=>0100110
[7,3,4,8,6,2,1,5]=>1001110=>0111001=>1000110
[7,1,5,8,2,6,4,3]=>1001011=>1101001=>0010110
[7,1,4,8,2,6,5,3]=>1001011=>1101001=>0010110
[7,4,5,8,1,2,6,3]=>1001001=>1001001=>0110110
[3,6,2,8,7,5,1,4]=>0101110=>0111010=>1000101
[1,6,4,8,7,2,5,3]=>0101101=>1011010=>0100101
[3,2,4,8,7,6,1,5]=>1001110=>0111001=>1000110
[1,4,5,8,7,2,6,3]=>0001101=>1011000=>0100111
[3,1,4,8,7,2,6,5]=>1001101=>1011001=>0100110
[1,6,5,8,2,7,4,3]=>0101011=>1101010=>0010101
[2,6,5,8,3,7,1,4]=>0101010=>0101010=>1010101
[1,6,4,8,2,7,5,3]=>0101011=>1101010=>0010101
[2,6,1,8,3,7,5,4]=>0101011=>1101010=>0010101
[1,4,5,8,3,2,7,6]=>0001101=>1011000=>0100111
[4,6,5,8,3,2,1,7]=>0101110=>0111010=>1000101
[7,6,2,3,8,5,1,4]=>1100110=>0110011=>1001100
[7,6,1,4,8,2,5,3]=>1100101=>1010011=>0101100
[7,6,3,4,8,2,1,5]=>1100110=>0110011=>1001100
[7,2,5,3,8,6,1,4]=>1010110=>0110101=>1001010
[7,2,1,4,8,6,5,3]=>1100111=>1110011=>0001100
[7,2,1,3,8,6,5,4]=>1100111=>1110011=>0001100
[2,6,5,3,8,7,1,4]=>0110110=>0110110=>1001001
[2,6,1,4,8,7,5,3]=>0100111=>1110010=>0001101
[1,3,5,4,8,2,7,6]=>0010101=>1010100=>0101011
[7,6,5,1,2,8,4,3]=>1110011=>1100111=>0011000
[7,1,5,2,3,8,6,4]=>1010011=>1100101=>0011010
[7,1,2,4,3,8,6,5]=>1001011=>1101001=>0010110
[7,2,5,4,3,8,1,6]=>1011010=>0101101=>1010010
[1,6,2,4,3,8,7,5]=>0101011=>1101010=>0010101
[2,6,5,4,3,8,1,7]=>0111010=>0101110=>1010001
[7,6,5,1,3,2,8,4]=>1110101=>1010111=>0101000
[8,2,7,6,5,4,1,3]=>1011110=>0111101=>1000010
[7,2,8,6,5,4,3,1]=>1011111=>1111101=>0000010
[3,2,8,7,6,5,1,4]=>1011110=>0111101=>1000010
[4,8,7,6,5,3,1,2]=>0111110=>0111110=>1000001
[7,8,6,1,5,4,3,2]=>0110111=>1110110=>0001001
[4,8,5,7,6,3,2,1]=>0101111=>1111010=>0000101
[3,2,4,6,8,1,5,7]=>1000100=>0010001=>1101110
[3,5,7,2,4,8,1,6]=>0010010=>0100100=>1011011
[3,5,7,2,4,6,8,1]=>0010001=>1000100=>0111011
[4,5,1,3,6,8,2,7]=>0100010=>0100010=>1011101
[4,3,5,7,2,6,8,1]=>1001001=>1001001=>0110110
[4,3,5,1,7,8,2,6]=>1010010=>0100101=>1011010
[4,6,3,5,1,7,8,2]=>0101001=>1001010=>0110101
[4,6,3,5,7,2,8,1]=>0100101=>1010010=>0101101
[5,1,6,7,3,4,8,2]=>1001001=>1001001=>0110110
[1,6,7,3,4,5,8,2]=>0010001=>1000100=>0111011
[2,6,7,4,5,8,1,3]=>0010010=>0100100=>1011011
[2,6,7,4,8,1,3,5]=>0010100=>0010100=>1101011
[1,4,6,7,3,8,2,5]=>0001010=>0101000=>1010111
[3,5,2,6,7,4,8,1]=>0100101=>1010010=>0101101
[6,3,1,7,8,2,4,5]=>1100100=>0010011=>1101100
[5,7,2,8,1,3,4,6]=>0101000=>0001010=>1110101
[6,3,7,2,8,1,4,5]=>1010100=>0010101=>1101010
[6,3,7,2,5,8,1,4]=>1010010=>0100101=>1011010
[6,2,4,5,7,3,8,1]=>1000101=>1010001=>0101110
[2,4,6,7,1,5,8,3]=>0001001=>1001000=>0110111
[2,4,7,1,5,6,8,3]=>0010001=>1000100=>0111011
[3,7,1,5,6,8,2,4]=>0100010=>0100010=>1011101
[4,6,7,1,2,5,8,3]=>0010001=>1000100=>0111011
[1,5,6,7,2,4,8,3]=>0001001=>1001000=>0110111
[5,6,2,4,1,7,8,3]=>0101001=>1001010=>0110101
[1,5,4,6,2,7,8,3]=>0101001=>1001010=>0110101
[5,6,4,7,1,3,8,2]=>0101001=>1001010=>0110101
[8,4,5,2,6,1,3,7]=>1010100=>0010101=>1101010
[6,4,3,7,2,5,8,1]=>1101001=>1001011=>0110100
[6,4,3,7,2,8,1,5]=>1101010=>0101011=>1010100
[7,4,5,3,1,6,8,2]=>1011001=>1001101=>0110010
[6,4,3,7,5,1,8,2]=>1101101=>1011011=>0100100
[5,6,3,7,4,1,8,2]=>0101101=>1011010=>0100101
[6,7,4,2,1,5,8,3]=>0111001=>1001110=>0110001
[6,7,4,2,1,8,3,5]=>0111010=>0101110=>1010001
[5,6,7,3,1,8,2,4]=>0011010=>0101100=>1010011
[5,6,3,7,8,1,2,4]=>0100100=>0010010=>1101101
[5,6,3,7,2,4,8,1]=>0101001=>1001010=>0110101
[5,6,7,2,3,8,1,4]=>0010010=>0100100=>1011011
[5,6,7,2,8,1,3,4]=>0010100=>0010100=>1101011
[6,7,3,8,1,2,4,5]=>0101000=>0001010=>1110101
[6,7,3,2,8,1,4,5]=>0110100=>0010110=>1101001
[7,6,4,2,1,3,8,5]=>1111001=>1001111=>0110000
[7,6,3,4,1,2,8,5]=>1101001=>1001011=>0110100
[7,6,3,2,4,1,8,5]=>1110101=>1010111=>0101000
[7,5,3,2,6,1,8,4]=>1110101=>1010111=>0101000
[6,5,3,2,7,8,1,4]=>1110010=>0100111=>1011000
[6,4,7,2,5,1,8,3]=>1010101=>1010101=>0101010
[6,4,7,5,1,2,8,3]=>1011001=>1001101=>0110010
[5,6,4,2,7,3,8,1]=>0110101=>1010110=>0101001
[6,5,3,7,1,8,2,4]=>1101010=>0101011=>1010100
[6,5,7,2,1,4,8,3]=>1011001=>1001101=>0110010
[5,4,6,7,3,1,8,2]=>1001101=>1011001=>0100110
[5,7,8,3,6,4,1,2]=>0010110=>0110100=>1001011
[3,7,8,5,6,4,1,2]=>0010110=>0110100=>1001011
[3,7,8,5,6,1,4,2]=>0010101=>1010100=>0101011
[1,7,8,5,6,3,4,2]=>0010101=>1010100=>0101011
[1,7,5,8,6,3,4,2]=>0101101=>1011010=>0100101
[3,7,5,8,6,1,4,2]=>0101101=>1011010=>0100101
[3,7,5,8,6,4,1,2]=>0101110=>0111010=>1000101
[5,7,3,8,6,4,1,2]=>0101110=>0111010=>1000101
[7,3,8,5,6,4,1,2]=>1010110=>0110101=>1001010
[7,3,5,8,6,4,1,2]=>1001110=>0111001=>1000110
[3,5,7,8,6,4,1,2]=>0001110=>0111000=>1000111
[1,5,7,8,6,3,4,2]=>0001101=>1011000=>0100111
[1,5,7,8,3,6,4,2]=>0001011=>1101000=>0010111
[5,3,7,8,1,6,4,2]=>1001011=>1101001=>0010110
[5,3,7,8,6,1,4,2]=>1001101=>1011001=>0100110
[7,3,5,8,6,1,4,2]=>1001101=>1011001=>0100110
[7,3,8,5,6,1,4,2]=>1010101=>1010101=>0101010
[7,8,3,5,6,1,4,2]=>0100101=>1010010=>0101101
[7,8,1,5,6,3,4,2]=>0100101=>1010010=>0101101
[7,1,8,5,6,3,4,2]=>1010101=>1010101=>0101010
[7,1,5,8,6,3,4,2]=>1001101=>1011001=>0100110
[5,1,7,8,6,3,4,2]=>1001101=>1011001=>0100110
[5,1,7,8,3,6,4,2]=>1001011=>1101001=>0010110
[3,1,7,8,5,6,4,2]=>1001011=>1101001=>0010110
[1,3,7,8,5,6,4,2]=>0001011=>1101000=>0010111
[3,1,7,5,8,6,4,2]=>1010111=>1110101=>0001010
[5,1,7,3,8,6,4,2]=>1010111=>1110101=>0001010
[7,1,5,3,8,6,4,2]=>1010111=>1110101=>0001010
[7,1,5,8,3,6,4,2]=>1001011=>1101001=>0010110
[7,8,1,5,3,6,4,2]=>0101011=>1101010=>0010101
[7,8,3,5,1,6,4,2]=>0101011=>1101010=>0010101
[7,3,8,5,1,6,4,2]=>1011011=>1101101=>0010010
[7,3,5,8,1,6,4,2]=>1001011=>1101001=>0010110
[7,3,5,1,8,6,4,2]=>1010111=>1110101=>0001010
[5,3,7,1,8,6,4,2]=>1010111=>1110101=>0001010
[3,5,7,1,8,6,4,2]=>0010111=>1110100=>0001011
[1,5,7,3,8,6,4,2]=>0010111=>1110100=>0001011
[1,7,5,3,8,6,4,2]=>0110111=>1110110=>0001001
[3,7,5,1,8,6,4,2]=>0110111=>1110110=>0001001
[5,7,3,1,8,6,4,2]=>0110111=>1110110=>0001001
[5,7,3,8,6,1,4,2]=>0101101=>1011010=>0100101
[3,7,5,8,1,6,4,2]=>0101011=>1101010=>0010101
[1,7,5,8,3,6,4,2]=>0101011=>1101010=>0010101
[1,7,8,5,3,6,4,2]=>0011011=>1101100=>0010011
[3,7,8,5,1,6,4,2]=>0011011=>1101100=>0010011
[5,7,8,3,6,1,4,2]=>0010101=>1010100=>0101011
[5,7,8,6,3,1,4,2]=>0011101=>1011100=>0100011
[7,5,8,6,1,3,4,2]=>1011001=>1001101=>0110010
[5,7,8,1,6,3,4,2]=>0010101=>1010100=>0101011
[5,7,8,1,3,6,4,2]=>0010011=>1100100=>0011011
[1,7,8,3,5,6,4,2]=>0010011=>1100100=>0011011
[1,7,3,8,5,6,4,2]=>0101011=>1101010=>0010101
[3,7,1,8,5,6,4,2]=>0101011=>1101010=>0010101
[5,7,1,8,3,6,4,2]=>0101011=>1101010=>0010101
[5,7,1,8,6,3,4,2]=>0101101=>1011010=>0100101
[7,5,1,8,6,3,4,2]=>1101101=>1011011=>0100100
[7,5,8,1,6,3,4,2]=>1010101=>1010101=>0101010
[7,8,5,1,6,3,4,2]=>0110101=>1010110=>0101001
[7,8,5,1,3,6,4,2]=>0110011=>1100110=>0011001
[7,5,8,1,3,6,4,2]=>1010011=>1100101=>0011010
[7,5,1,8,3,6,4,2]=>1101011=>1101011=>0010100
[7,5,1,3,8,6,4,2]=>1100111=>1110011=>0001100
[5,7,1,3,8,6,4,2]=>0100111=>1110010=>0001101
[3,7,1,5,8,6,4,2]=>0100111=>1110010=>0001101
[1,7,3,5,8,6,4,2]=>0100111=>1110010=>0001101
[1,5,3,7,8,6,4,2]=>0100111=>1110010=>0001101
[3,5,1,7,8,6,4,2]=>0100111=>1110010=>0001101
[5,3,1,7,8,6,4,2]=>1100111=>1110011=>0001100
[7,3,1,5,8,6,4,2]=>1100111=>1110011=>0001100
[7,3,1,8,5,6,4,2]=>1101011=>1101011=>0010100
[7,8,1,3,5,6,4,2]=>0100011=>1100010=>0011101
[7,1,8,3,5,6,4,2]=>1010011=>1100101=>0011010
[7,1,3,8,5,6,4,2]=>1001011=>1101001=>0010110
[7,1,3,5,8,6,4,2]=>1000111=>1110001=>0001110
[5,1,3,7,8,6,4,2]=>1000111=>1110001=>0001110
[3,1,5,7,8,6,4,2]=>1000111=>1110001=>0001110
[4,3,1,2,6,5,8,7]=>1100101=>1010011=>0101100
[6,1,4,3,5,2,8,7]=>1010101=>1010101=>0101010
[4,6,3,5,1,2,8,7]=>0101001=>1001010=>0110101
[6,2,4,5,1,3,8,7]=>1001001=>1001001=>0110110
[2,3,6,1,5,4,8,7]=>0010101=>1010100=>0101011
[2,1,6,5,3,4,8,7]=>1011001=>1001101=>0110010
[3,5,6,2,4,1,8,7]=>0010101=>1010100=>0101011
[8,7,6,1,3,2,4,5]=>1110100=>0010111=>1101000
[2,5,3,4,8,1,7,6]=>0100101=>1010010=>0101101
[5,1,8,2,3,4,7,6]=>1010001=>1000101=>0111010
[5,4,7,6,2,8,1,3]=>1011010=>0101101=>1010010
[2,1,6,8,5,7,3,4]=>1001010=>0101001=>1010110
[2,1,8,4,6,7,3,5]=>1010010=>0100101=>1011010
[3,1,8,6,2,7,5,4]=>1011011=>1101101=>0010010
[3,8,1,5,6,7,2,4]=>0100010=>0100010=>1011101
[8,2,3,5,7,1,6,4]=>1000101=>1010001=>0101110
[5,8,4,3,7,1,6,2]=>0110101=>1010110=>0101001
[2,8,3,6,7,5,1,4]=>0100110=>0110010=>1001101
[8,1,2,7,3,5,6,4]=>1001001=>1001001=>0110110
[6,8,4,2,1,3,7,5]=>0111001=>1001110=>0110001
[4,3,8,2,7,6,1,5]=>1010110=>0110101=>1001010
[2,1,4,5,8,3,7,6]=>1000101=>1010001=>0101110
[8,4,7,1,5,2,3,6]=>1010100=>0010101=>1101010
[7,3,5,8,4,2,1,6]=>1001110=>0111001=>1000110
[2,4,8,3,5,6,7,1]=>0010001=>1000100=>0111011
[6,4,7,5,2,3,8,1]=>1011001=>1001101=>0110010
[6,4,8,1,7,3,2,5]=>1010110=>0110101=>1001010
[2,1,4,3,8,7,5,6]=>1010110=>0110101=>1001010
[4,3,1,2,8,6,7,5]=>1100101=>1010011=>0101100
[5,1,6,7,8,4,3,2]=>1000111=>1110001=>0001110
[8,7,2,6,4,1,5,3]=>1101101=>1011011=>0100100
[2,1,5,7,8,4,6,3]=>1000101=>1010001=>0101110
[6,4,1,5,7,2,8,3]=>1100101=>1010011=>0101100
[7,4,8,1,2,5,6,3]=>1010001=>1000101=>0111010
[6,1,7,4,3,2,8,5]=>1011101=>1011101=>0100010
[6,8,3,4,2,1,7,5]=>0101101=>1011010=>0100101
[4,2,6,1,5,7,8,3]=>1010001=>1000101=>0111010
[7,1,4,8,3,5,6,2]=>1001001=>1001001=>0110110
[3,4,8,2,5,7,6,1]=>0010011=>1100100=>0011011
[3,7,1,4,5,6,8,2]=>0100001=>1000010=>0111101
[6,5,3,8,4,7,1,2]=>1101010=>0101011=>1010100
[8,6,4,7,5,3,1,2]=>1101110=>0111011=>1000100
[1,6,3,7,5,8,4,2]=>0101011=>1101010=>0010101
[1,3,7,4,5,8,6,2]=>0010011=>1100100=>0011011
[7,3,8,5,4,6,1,2]=>1011010=>0101101=>1010010
[3,4,8,5,6,7,1,2]=>0010010=>0100100=>1011011
[4,7,3,8,5,6,1,2]=>0101010=>0101010=>1010101
[6,8,4,7,5,3,1,2]=>0101110=>0111010=>1000101
[1,7,6,5,3,8,4,2]=>0111011=>1101110=>0010001
[2,7,6,3,1,4,5,8]=>0111000=>0001110=>1110001
[2,7,6,4,5,1,3,8]=>0110100=>0010110=>1101001
[5,7,2,6,4,1,3,8]=>0101100=>0011010=>1100101
[7,6,1,5,3,8,4,2]=>1101011=>1101011=>0010100
[1,8,2,7,3,6,5,4]=>0101011=>1101010=>0010101
[2,1,3,8,4,7,5,6]=>1001010=>0101001=>1010110
[3,1,2,8,4,6,7,5]=>1001001=>1001001=>0110110
[4,1,7,2,8,5,6,3]=>1010101=>1010101=>0101010
[5,1,2,4,8,3,7,6]=>1000101=>1010001=>0101110
[2,8,4,1,5,6,3,7]=>0110010=>0100110=>1011001
[1,7,2,8,5,3,6,4]=>0101101=>1011010=>0100101
[1,2,3,8,4,5,7,6]=>0001001=>1001000=>0110111
[2,4,8,3,1,5,6,7]=>0011000=>0001100=>1110011
[3,2,5,6,1,4,7,8]=>1001000=>0001001=>1110110
[4,7,3,8,2,1,5,6]=>0101100=>0011010=>1100101
[7,4,8,3,2,1,5,6]=>1011100=>0011101=>1100010
[7,6,8,5,1,4,3,2]=>1011011=>1101101=>0010010
[6,5,1,2,8,3,7,4]=>1100101=>1010011=>0101100
[6,8,4,1,3,7,5,2]=>0110011=>1100110=>0011001
[6,3,7,1,8,4,5,2]=>1010101=>1010101=>0101010
[5,8,3,1,7,4,6,2]=>0110101=>1010110=>0101001
[4,7,1,2,8,3,6,5]=>0100101=>1010010=>0101101
[3,4,1,8,5,6,7,2]=>0101001=>1001010=>0110101
[1,2,8,7,6,3,5,4]=>0011101=>1011100=>0100011
[2,3,1,8,7,4,5,6]=>0101100=>0011010=>1100101
[2,6,1,4,8,7,3,5]=>0100110=>0110010=>1001101
[5,8,2,1,7,6,3,4]=>0110110=>0110110=>1001001
[8,7,1,6,5,4,3,2]=>1101111=>1111011=>0000100
[3,1,8,7,6,4,5,2]=>1011101=>1011101=>0100010
[1,2,3,4,8,7,5,6]=>0000110=>0110000=>1001111
[1,2,3,8,6,4,5,7]=>0001100=>0011000=>1100111
[1,2,8,5,3,4,6,7]=>0011000=>0001100=>1110011
[1,8,4,2,3,5,6,7]=>0110000=>0000110=>1111001
[2,4,7,5,6,8,3,1]=>0010011=>1100100=>0011011
[2,5,3,8,7,4,6,1]=>0101101=>1011010=>0100101
[3,1,8,5,7,4,2,6]=>1010110=>0110101=>1001010
[8,3,5,7,4,2,6,1]=>1001101=>1011001=>0100110
[8,3,6,2,4,5,7,1]=>1010001=>1000101=>0111010
[2,7,6,4,5,8,3,1]=>0110011=>1100110=>0011001
[4,8,1,7,6,3,2,5]=>0101110=>0111010=>1000101
[3,7,1,8,6,2,5,4]=>0101101=>1011010=>0100101
[7,3,6,4,2,8,5,1]=>1011011=>1101101=>0010010
[5,8,7,1,4,3,2,6]=>0110110=>0110110=>1001001
[5,6,1,2,4,3,8,7]=>0100101=>1010010=>0101101
[3,6,8,1,2,7,5,4]=>0010011=>1100100=>0011011
[8,4,6,2,1,3,7,5]=>1011001=>1001101=>0110010
[4,8,1,5,3,7,2,6]=>0101010=>0101010=>1010101
[5,4,8,7,3,1,2,6]=>1011100=>0011101=>1100010
[6,4,3,8,1,5,2,7]=>1101010=>0101011=>1010100
[6,8,3,7,2,5,4,1]=>0101011=>1101010=>0010101
[5,3,6,8,7,2,4,1]=>1001101=>1011001=>0100110
[5,7,4,2,8,3,6,1]=>0110101=>1010110=>0101001
[6,4,7,2,1,8,3,5]=>1011010=>0101101=>1010010
[5,7,8,2,6,4,1,3]=>0010110=>0110100=>1001011
[2,6,8,4,5,7,1,3]=>0010010=>0100100=>1011011
[1,7,4,8,6,2,3,5]=>0101100=>0011010=>1100101
[2,7,4,8,5,6,1,3]=>0101010=>0101010=>1010101
[6,3,7,2,8,5,1,4]=>1010110=>0110101=>1001010
[3,6,2,5,7,8,1,4]=>0100010=>0100010=>1011101
[5,3,6,7,1,8,4,2]=>1001011=>1101001=>0010110
[8,1,3,6,7,2,4,5]=>1000100=>0010001=>1101110
[8,1,4,2,7,5,3,6]=>1010110=>0110101=>1001010
[6,1,3,8,2,7,4,5]=>1001010=>0101001=>1010110
[4,1,5,3,2,8,6,7]=>1011010=>0101101=>1010010
[2,7,1,4,3,8,5,6]=>0101010=>0101010=>1010101
[1,7,5,2,8,6,3,4]=>0110110=>0110110=>1001001
[7,4,2,5,1,8,6,3]=>1101011=>1101011=>0010100
[5,6,3,2,1,8,7,4]=>0111011=>1101110=>0010001
[4,5,3,2,7,1,8,6]=>0110101=>1010110=>0101001
[5,3,6,2,8,1,7,4]=>1010101=>1010101=>0101010
[6,4,2,8,5,1,7,3]=>1101101=>1011011=>0100100
[1,8,4,7,2,5,3,6]=>0101010=>0101010=>1010101
[1,5,8,4,2,6,3,7]=>0011010=>0101100=>1010011
[3,5,7,4,1,6,8,2]=>0011001=>1001100=>0110011
[4,5,8,3,1,7,6,2]=>0011011=>1101100=>0010011
[3,4,7,8,2,1,6,5]=>0001101=>1011000=>0100111
[4,6,3,5,2,1,8,7]=>0101101=>1011010=>0100101
[3,5,7,1,2,6,4,8]=>0010010=>0100100=>1011011
[7,4,1,2,8,6,3,5]=>1100110=>0110011=>1001100
[5,2,6,1,3,4,8,7]=>1010001=>1000101=>0111010
[3,8,2,6,5,4,1,7]=>0101110=>0111010=>1000101
[3,8,7,2,5,4,1,6]=>0110110=>0110110=>1001001
[7,5,1,6,8,4,3,2]=>1100111=>1110011=>0001100
[7,4,2,1,5,6,3,8]=>1110010=>0100111=>1011000
[7,3,8,1,5,4,6,2]=>1010101=>1010101=>0101010
[7,2,8,6,5,1,3,4]=>1011100=>0011101=>1100010
[6,2,7,8,5,4,1,3]=>1001110=>0111001=>1000110
[5,3,2,6,7,4,1,8]=>1100110=>0110011=>1001100
[4,8,2,6,5,7,1,3]=>0101010=>0101010=>1010101
[4,3,7,2,5,6,1,8]=>1010010=>0100101=>1011010
[3,8,7,6,2,4,1,5]=>0111010=>0101110=>1010001
[6,7,1,4,3,2,5,8]=>0101100=>0011010=>1100101
[3,5,6,2,4,7,1,8]=>0010010=>0100100=>1011011
[3,5,8,7,2,4,6,1]=>0011001=>1001100=>0110011
[1,7,8,2,5,4,3,6]=>0010110=>0110100=>1001011
[2,7,1,3,6,5,4,8]=>0100110=>0110010=>1001101
[5,7,1,4,6,3,2,8]=>0100110=>0110010=>1001101
[6,3,7,1,5,4,2,8]=>1010110=>0110101=>1001010
[4,7,1,6,3,5,2,8]=>0101010=>0101010=>1010101
[8,7,3,6,1,5,4,2]=>1101011=>1101011=>0010100
[5,7,8,3,2,1,4,6]=>0011100=>0011100=>1100011
[5,4,2,1,7,8,3,6]=>1110010=>0100111=>1011000
[4,7,8,3,5,2,1,6]=>0010110=>0110100=>1001011
[8,3,7,6,4,2,1,5]=>1011110=>0111101=>1000010
[8,3,2,1,4,7,6,5]=>1110011=>1100111=>0011000
[6,4,1,7,3,8,5,2]=>1101011=>1101011=>0010100
[1,7,5,3,8,2,6,4]=>0110101=>1010110=>0101001
[5,1,7,4,2,8,6,3]=>1011011=>1101101=>0010010
[8,6,3,2,7,5,1,4]=>1110110=>0110111=>1001000
[2,7,5,1,3,8,6,4]=>0110011=>1100110=>0011001
[8,7,4,2,6,1,5,3]=>1110101=>1010111=>0101000
[5,2,6,1,8,7,4,3]=>1010111=>1110101=>0001010
[1,7,6,4,3,8,2,5]=>0111010=>0101110=>1010001
[1,3,8,2,4,7,6,5]=>0010011=>1100100=>0011011
[3,7,5,1,8,6,2,4]=>0110110=>0110110=>1001001
[5,1,4,3,2,7,8,6]=>1011001=>1001101=>0110010
[3,7,6,2,4,1,8,5]=>0110101=>1010110=>0101001
[5,3,1,7,8,4,2,6]=>1100110=>0110011=>1001100
[4,1,7,8,5,3,2,6]=>1001110=>0111001=>1000110
[2,7,6,4,1,3,8,5]=>0111001=>1001110=>0110001
[8,4,2,7,6,3,1,5]=>1101110=>0111011=>1000100
[6,3,1,7,5,2,8,4]=>1101101=>1011011=>0100100
[6,2,7,5,3,1,8,4]=>1011101=>1011101=>0100010
[1,5,8,2,7,4,6,3]=>0010101=>1010100=>0101011
[8,4,7,3,1,6,5,2]=>1011011=>1101101=>0010010
[4,1,6,8,5,7,3,2]=>1001011=>1101001=>0010110
[1,8,6,7,3,4,2,5]=>0101010=>0101010=>1010101
[6,7,1,8,3,4,2,5]=>0101010=>0101010=>1010101
[7,8,1,6,3,4,2,5]=>0101010=>0101010=>1010101
[7,8,2,5,1,6,3,4]=>0101010=>0101010=>1010101
[1,8,5,6,2,7,3,4]=>0101010=>0101010=>1010101
[5,7,1,6,2,8,3,4]=>0101010=>0101010=>1010101
[5,6,2,7,1,8,3,4]=>0101010=>0101010=>1010101
[6,7,2,5,1,8,3,4]=>0101010=>0101010=>1010101
[6,7,2,4,3,8,1,5]=>0101010=>0101010=>1010101
[2,5,1,8,6,7,3,4]=>0101010=>0101010=>1010101
[2,6,5,8,1,7,3,4]=>0101010=>0101010=>1010101
[1,8,2,7,4,5,3,6]=>0101010=>0101010=>1010101
[2,4,3,8,5,6,1,7]=>0101010=>0101010=>1010101
[2,3,1,8,5,6,4,7]=>0101010=>0101010=>1010101
[4,6,2,7,1,5,3,8]=>0101010=>0101010=>1010101
[4,7,1,6,2,5,3,8]=>0101010=>0101010=>1010101
[4,6,3,5,1,7,2,8]=>0101010=>0101010=>1010101
[5,6,3,7,1,4,2,8]=>0101010=>0101010=>1010101
[1,8,5,6,3,4,2,7]=>0101010=>0101010=>1010101
[4,7,1,8,5,6,2,3]=>0101010=>0101010=>1010101
[3,4,2,6,5,8,1,7]=>0101010=>0101010=>1010101
[3,5,4,6,2,8,1,7]=>0101010=>0101010=>1010101
[3,7,1,6,2,8,4,5]=>0101010=>0101010=>1010101
[3,5,2,7,4,8,1,6]=>0101010=>0101010=>1010101
[4,7,2,3,1,8,5,6]=>0101010=>0101010=>1010101
[2,4,3,8,1,7,5,6]=>0101010=>0101010=>1010101
[6,1,2,7,4,5,8,3]=>1001001=>1001001=>0110110
[2,5,8,3,4,1,6,7]=>0010100=>0010100=>1101011
[5,6,2,7,4,3,8,1]=>0101101=>1011010=>0100101
[5,1,7,3,4,2,8,6]=>1010101=>1010101=>0101010
[4,6,7,3,2,5,8,1]=>0011001=>1001100=>0110011
[3,7,2,1,4,5,8,6]=>0110001=>1000110=>0111001
[2,7,1,3,4,8,6,5]=>0100011=>1100010=>0011101
[2,6,7,3,8,5,4,1]=>0010111=>1110100=>0001011
[2,6,1,8,4,5,3,7]=>0101010=>0101010=>1010101
[4,2,1,6,5,3,8,7]=>1101101=>1011011=>0100100
[6,2,4,3,1,5,8,7]=>1011001=>1001101=>0110010
[4,6,2,1,5,3,8,7]=>0110101=>1010110=>0101001
[8,4,2,1,6,5,3,7]=>1110110=>0110111=>1001000
[2,6,4,5,1,8,7,3]=>0101011=>1101010=>0010101
[6,8,7,2,1,4,3,5]=>0111010=>0101110=>1010001
[6,8,2,1,7,4,3,5]=>0110110=>0110110=>1001001
[6,8,2,1,4,3,7,5]=>0110101=>1010110=>0101001
[8,6,2,4,3,1,5,7]=>1101100=>0011011=>1100100
[6,8,2,4,3,1,7,5]=>0101101=>1011010=>0100101
[2,8,4,6,7,3,1,5]=>0100110=>0110010=>1001101
[2,8,6,7,4,3,1,5]=>0101110=>0111010=>1000101
[6,8,7,2,4,3,1,5]=>0110110=>0110110=>1001001
[4,6,5,2,8,3,7,1]=>0110101=>1010110=>0101001
[2,6,4,5,8,3,7,1]=>0100101=>1010010=>0101101
[6,4,2,8,3,5,7,1]=>1101001=>1001011=>0110100
[8,4,2,6,3,5,1,7]=>1101010=>0101011=>1010100
[4,2,6,3,8,7,5,1]=>1010111=>1110101=>0001010
[8,2,4,3,6,5,1,7]=>1010110=>0110101=>1001010
[4,2,1,6,8,7,5,3]=>1100111=>1110011=>0001100
[4,2,1,6,5,8,7,3]=>1101011=>1101011=>0010100
[4,2,1,3,6,8,7,5]=>1100011=>1100011=>0011100
[2,4,3,1,8,6,5,7]=>0110110=>0110110=>1001001
[6,2,1,8,7,4,3,5]=>1101110=>0111011=>1000100
[4,6,8,7,5,2,1,3]=>0011110=>0111100=>1000011
[4,6,5,8,7,2,1,3]=>0101110=>0111010=>1000101
[2,6,8,7,4,5,1,3]=>0011010=>0101100=>1010011
[2,4,8,6,7,5,1,3]=>0010110=>0110100=>1001011
[4,2,8,6,5,7,1,3]=>1011010=>0101101=>1010010
[6,4,8,2,1,5,7,3]=>1011001=>1001101=>0110010
[2,6,8,4,7,1,5,3]=>0010101=>1010100=>0101011
[4,6,5,8,2,1,7,3]=>0101101=>1011010=>0100101
[4,8,6,7,2,1,3,5]=>0101100=>0011010=>1100101
[6,2,3,5,1,4,8,7]=>1001001=>1001001=>0110110
[7,4,5,2,3,8,6,1]=>1010011=>1100101=>0011010
[7,3,2,5,4,8,6,1]=>1101011=>1101011=>0010100
[3,5,1,6,4,2,8,7]=>0101101=>1011010=>0100101
[3,6,2,4,5,1,8,7]=>0100101=>1010010=>0101101
[7,2,3,4,5,8,6,1]=>1000011=>1100001=>0011110
[8,2,3,4,5,7,1,6]=>1000010=>0100001=>1011110
[6,7,3,4,8,5,2,1]=>0100111=>1110010=>0001101
[5,7,1,3,8,6,2,4]=>0100110=>0110010=>1001101
[4,7,3,2,8,6,1,5]=>0110110=>0110110=>1001001
[3,8,2,6,7,4,5,1]=>0100101=>1010010=>0101101
[4,8,1,5,6,7,3,2]=>0100011=>1100010=>0011101
[6,8,2,5,1,7,3,4]=>0101010=>0101010=>1010101
[7,8,3,4,6,2,1,5]=>0100110=>0110010=>1001101
[4,8,2,5,1,6,7,3]=>0101001=>1001010=>0110101
[3,8,2,5,4,7,6,1]=>0101011=>1101010=>0010101
[3,7,6,1,8,5,2,4]=>0110110=>0110110=>1001001
[4,7,2,3,8,5,1,6]=>0100110=>0110010=>1001101
[4,6,7,1,8,5,3,2]=>0010111=>1110100=>0001011
[3,6,1,7,8,5,4,2]=>0100111=>1110010=>0001101
[2,1,5,7,3,8,6,4]=>1001011=>1101001=>0010110
[6,4,7,2,8,5,3,1]=>1010111=>1110101=>0001010
[7,6,1,4,8,5,2,3]=>1100110=>0110011=>1001100
[4,1,2,3,7,8,6,5]=>1000011=>1100001=>0011110
[3,4,2,1,8,5,6,7]=>0110100=>0010110=>1101001
[8,2,3,5,7,1,4,6]=>1000100=>0010001=>1101110
[8,1,3,6,4,7,2,5]=>1001010=>0101001=>1010110
[5,4,8,3,6,7,1,2]=>1010010=>0100101=>1011010
[4,5,8,3,6,7,2,1]=>0010011=>1100100=>0011011
[2,1,5,8,4,6,7,3]=>1001001=>1001001=>0110110
[4,6,8,3,5,2,7,1]=>0010101=>1010100=>0101011
[3,8,2,4,5,6,7,1]=>0100001=>1000010=>0111101
[6,8,2,3,1,4,5,7]=>0101000=>0001010=>1110101
[4,3,1,6,5,8,7,2]=>1101011=>1101011=>0010100
[8,2,7,4,1,3,6,5]=>1011001=>1001101=>0110010
[3,7,8,2,1,4,6,5]=>0011001=>1001100=>0110011
[3,7,5,2,8,4,1,6]=>0110110=>0110110=>1001001
[3,1,5,2,4,8,7,6]=>1010011=>1100101=>0011010
[3,6,4,5,1,8,7,2]=>0101011=>1101010=>0010101
[4,3,6,1,2,8,7,5]=>1010011=>1100101=>0011010
[6,1,3,5,4,8,7,2]=>1001011=>1101001=>0010110
[1,7,3,8,4,6,2,5]=>0101010=>0101010=>1010101
[1,6,7,4,8,5,3,2]=>0010111=>1110100=>0001011
[8,1,2,5,4,6,3,7]=>1001010=>0101001=>1010110
[6,8,3,1,4,7,5,2]=>0110011=>1100110=>0011001
[8,4,2,5,7,1,6,3]=>1100101=>1010011=>0101100
[1,8,5,3,7,4,6,2]=>0110101=>1010110=>0101001
[5,3,2,8,7,1,4,6]=>1101100=>0011011=>1100100
[1,2,8,7,5,6,3,4]=>0011010=>0101100=>1010011
[1,4,8,6,5,7,2,3]=>0011010=>0101100=>1010011
[3,5,4,8,6,1,2,7]=>0101100=>0011010=>1100101
[4,3,5,8,1,7,2,6]=>1001010=>0101001=>1010110
[1,4,5,8,6,7,3,2]=>0001011=>1101000=>0010111
[1,7,6,5,8,3,4,2]=>0110101=>1010110=>0101001
[7,3,6,1,8,2,4,5]=>1010100=>0010101=>1101010
[7,6,4,5,8,1,3,2]=>1100101=>1010011=>0101100
[1,6,5,4,8,2,3,7]=>0110100=>0010110=>1101001
[5,2,6,3,8,1,4,7]=>1010100=>0010101=>1101010
[4,3,1,6,8,7,5,2]=>1100111=>1110011=>0001100
[4,3,1,8,5,6,7,2]=>1101001=>1001011=>0110100
[6,2,8,4,3,1,7,5]=>1011101=>1011101=>0100010
[7,1,6,2,3,4,5,8]=>1010000=>0000101=>1111010
[3,8,6,1,2,5,4,7]=>0110010=>0100110=>1011001
[1,8,5,4,3,6,2,7]=>0111010=>0101110=>1010001
[5,3,8,4,1,2,7,6]=>1011001=>1001101=>0110010
[1,8,3,6,5,2,7,4]=>0101101=>1011010=>0100101
[4,7,1,8,2,6,5,3]=>0101011=>1101010=>0010101
[1,8,2,4,7,6,5,3]=>0100111=>1110010=>0001101
[1,4,8,3,5,7,6,2]=>0010011=>1100100=>0011011
[8,2,1,4,6,5,7,3]=>1100101=>1010011=>0101100
[6,1,5,2,4,7,8,3]=>1010001=>1000101=>0111010
[4,1,8,5,2,7,6,3]=>1011011=>1101101=>0010010
[4,3,8,5,1,2,6,7]=>1011000=>0001101=>1110010
[6,3,5,1,4,2,8,7]=>1010101=>1010101=>0101010
[4,1,8,2,3,7,5,6]=>1010010=>0100101=>1011010
[5,3,8,7,2,1,4,6]=>1011100=>0011101=>1100010
[7,6,5,4,1,3,2,8]=>1111010=>0101111=>1010000
[1,8,7,6,2,5,4,3]=>0111011=>1101110=>0010001
[1,2,3,4,5,10,9,8,7,6]=>000001111=>111100000=>000011111
[4,6,3,1,5,2,7,8]=>0110100=>0010110=>1101001
[6,2,7,4,5,1,3,8]=>1010100=>0010101=>1101010
[5,2,7,4,1,6,3,8]=>1011010=>0101101=>1010010
[5,7,3,4,1,6,2,8]=>0101010=>0101010=>1010101
[4,2,8,1,5,6,7,3]=>1010001=>1000101=>0111010
[1,7,8,4,5,6,2,3]=>0010010=>0100100=>1011011
[1,6,8,4,5,2,7,3]=>0010101=>1010100=>0101011
[1,5,8,4,2,6,7,3]=>0011001=>1001100=>0110011
[1,5,3,8,2,6,7,4]=>0101001=>1001010=>0110101
[1,6,3,8,5,2,7,4]=>0101101=>1011010=>0100101
[1,7,3,8,5,6,2,4]=>0101010=>0101010=>1010101
[6,2,3,7,5,1,4,8]=>1001100=>0011001=>1100110
[4,2,6,1,5,3,7,8]=>1010100=>0010101=>1101010
[5,2,6,4,1,3,7,8]=>1011000=>0001101=>1110010
[1,2,7,8,5,6,3,4]=>0001010=>0101000=>1010111
[1,2,6,4,8,3,7,5]=>0010101=>1010100=>0101011
[8,7,3,2,1,6,5,4]=>1111011=>1101111=>0010000
[8,7,4,1,6,2,3,5]=>1110100=>0010111=>1101000
[8,5,1,7,2,3,4,6]=>1101000=>0001011=>1110100
[10,9,8,5,1,7,2,3,4,6]=>111101000=>000101111=>111010000
[10,9,4,1,6,2,8,3,5,7]=>111010100=>001010111=>110101000
[10,3,1,5,2,7,4,9,6,8]=>110101010=>010101011=>101010100
[1,8,3,2,6,4,5,7]=>0110100=>0010110=>1101001
[7,3,8,1,5,2,4,6]=>1010100=>0010101=>1101010
[3,1,7,2,6,4,5,8]=>1010100=>0010101=>1101010
[1,8,4,2,3,6,7,5]=>0110001=>1000110=>0111001
[2,5,8,3,4,6,7,1]=>0010001=>1000100=>0111011
[4,1,7,2,3,6,8,5]=>1010001=>1000101=>0111010
[3,1,7,5,4,2,8,6]=>1011101=>1011101=>0100010
[4,6,2,1,5,7,8,3]=>0110001=>1000110=>0111001
[4,5,2,3,1,7,8,6]=>0101001=>1001010=>0110101
[3,2,6,7,4,1,8,5]=>1001101=>1011001=>0100110
[5,6,2,7,1,4,8,3]=>0101001=>1001010=>0110101
[6,4,2,8,1,5,7,3]=>1101001=>1001011=>0110100
[7,3,6,8,5,2,4,1]=>1001101=>1011001=>0100110
[2,7,8,3,6,5,1,4]=>0010110=>0110100=>1001011
[2,7,8,5,4,6,3,1]=>0011011=>1101100=>0010011
[2,6,8,3,4,7,1,5]=>0010010=>0100100=>1011011
[2,5,6,8,3,4,1,7]=>0001010=>0101000=>1010111
[2,7,8,3,6,1,4,5]=>0010100=>0010100=>1101011
[2,1,3,7,8,5,6,4]=>1000101=>1010001=>0101110
[5,1,2,4,8,7,3,6]=>1000110=>0110001=>1001110
[2,3,6,1,8,5,7,4]=>0010101=>1010100=>0101011
[5,2,6,1,7,8,4,3]=>1010011=>1100101=>0011010
[3,6,5,4,1,8,7,2]=>0111011=>1101110=>0010001
[5,4,2,3,7,8,6,1]=>1100011=>1100011=>0011100
[4,1,8,2,5,7,3,6]=>1010010=>0100101=>1011010
[3,1,8,4,7,2,5,6]=>1010100=>0010101=>1101010
[2,6,4,1,5,3,8,7]=>0110101=>1010110=>0101001
[1,5,8,2,4,7,3,6]=>0010010=>0100100=>1011011
[6,2,1,4,7,8,3,5]=>1100010=>0100011=>1011100
[3,8,1,4,2,6,5,7]=>0101010=>0101010=>1010101
[8,3,4,2,1,6,5,7]=>1011010=>0101101=>1010010
[5,3,2,8,1,6,4,7]=>1101010=>0101011=>1010100
[2,4,5,8,3,6,1,7]=>0001010=>0101000=>1010111
[3,5,8,1,2,6,4,7]=>0010010=>0100100=>1011011
[8,6,1,3,5,2,4,7]=>1100100=>0010011=>1101100
[5,7,4,3,6,1,8,2]=>0110101=>1010110=>0101001
[2,6,4,3,7,8,5,1]=>0110011=>1100110=>0011001
[7,4,1,8,3,2,5,6]=>1101100=>0011011=>1100100
[2,4,6,5,1,7,8,3]=>0011001=>1001100=>0110011
[5,6,1,7,4,2,8,3]=>0101101=>1011010=>0100101
[1,3,8,6,2,7,4,5]=>0011010=>0101100=>1010011
[6,4,7,8,2,1,3,5]=>1001100=>0011001=>1100110
[6,7,3,8,4,1,2,5]=>0101100=>0011010=>1100101
[2,7,8,3,4,6,1,5]=>0010010=>0100100=>1011011
[3,7,8,1,5,4,2,6]=>0010110=>0110100=>1001011
[7,5,8,4,1,3,2,6]=>1011010=>0101101=>1010010
[4,7,5,8,3,1,2,6]=>0101100=>0011010=>1100101
[5,7,3,1,6,8,4,2]=>0110011=>1100110=>0011001
[4,6,7,2,8,3,1,5]=>0010110=>0110100=>1001011
[4,8,1,2,3,5,7,6]=>0100001=>1000010=>0111101
[4,5,6,7,3,1,8,2]=>0001101=>1011000=>0100111
[8,5,3,2,7,6,1,4]=>1110110=>0110111=>1001000
[7,5,4,6,2,8,1,3]=>1101010=>0101011=>1010100
[2,5,1,3,6,8,7,4]=>0100011=>1100010=>0011101
[7,5,2,8,4,1,3,6]=>1101100=>0011011=>1100100
[7,3,8,5,2,1,4,6]=>1011100=>0011101=>1100010
[5,8,3,6,4,7,1,2]=>0101010=>0101010=>1010101
[3,7,8,4,1,5,6,2]=>0011001=>1001100=>0110011
[3,5,8,6,7,4,2,1]=>0010111=>1110100=>0001011
[3,7,6,8,1,2,5,4]=>0101001=>1001010=>0110101
[4,1,6,3,2,5,8,7]=>1011001=>1001101=>0110010
[8,6,1,7,2,5,4,3]=>1101011=>1101011=>0010100
[8,7,6,1,2,3,5,4]=>1110001=>1000111=>0111000
[5,4,1,6,2,3,8,7]=>1101001=>1001011=>0110100
[2,6,5,3,4,1,8,7]=>0110101=>1010110=>0101001
[5,8,7,6,1,2,3,4]=>0111000=>0001110=>1110001
[8,2,7,1,5,4,3,6]=>1010110=>0110101=>1001010
[2,1,6,3,8,5,4,7]=>1010110=>0110101=>1001010
[2,6,3,1,8,5,4,7]=>0110110=>0110110=>1001001
[4,6,2,8,5,1,3,7]=>0101100=>0011010=>1100101
[6,5,2,7,4,3,8,1]=>1101101=>1011011=>0100100
[4,6,5,2,7,3,8,1]=>0110101=>1010110=>0101001
[3,1,6,2,4,8,7,5]=>1010011=>1100101=>0011010
[8,7,5,1,2,6,4,3]=>1110011=>1100111=>0011000
[2,1,7,6,3,8,4,5]=>1011010=>0101101=>1010010
[8,2,3,4,6,7,1,5]=>1000010=>0100001=>1011110
[2,8,5,7,4,1,3,6]=>0101100=>0011010=>1100101
[7,8,5,3,6,4,2,1]=>0110111=>1110110=>0001001
[2,1,4,8,7,5,6,3]=>1001101=>1011001=>0100110
[7,4,6,8,5,1,3,2]=>1001101=>1011001=>0100110
[6,4,8,3,5,7,1,2]=>1010010=>0100101=>1011010
[8,5,7,4,6,2,1,3]=>1010110=>0110101=>1001010
[4,1,8,5,6,3,2,7]=>1010110=>0110101=>1001010
[5,8,3,2,4,6,1,7]=>0110010=>0100110=>1011001
[2,8,4,1,5,3,7,6]=>0110101=>1010110=>0101001
[4,8,7,6,5,2,3,1]=>0111101=>1011110=>0100001
[2,1,8,6,4,3,7,5]=>1011101=>1011101=>0100010
[3,6,7,1,8,5,2,4]=>0010110=>0110100=>1001011
[4,2,3,6,8,7,5,1]=>1000111=>1110001=>0001110
[6,5,7,3,1,8,4,2]=>1011011=>1101101=>0010010
[8,4,2,5,6,1,7,3]=>1100101=>1010011=>0101100
[6,1,5,7,2,4,8,3]=>1001001=>1001001=>0110110
[8,4,7,6,2,1,5,3]=>1011101=>1011101=>0100010
[3,5,7,6,4,1,8,2]=>0011101=>1011100=>0100011
[2,4,7,5,6,3,8,1]=>0010101=>1010100=>0101011
[5,4,1,7,6,2,8,3]=>1101101=>1011011=>0100100
[3,5,6,7,1,4,8,2]=>0001001=>1001000=>0110111
[4,7,5,2,1,3,8,6]=>0111001=>1001110=>0110001
[5,7,2,3,6,4,8,1]=>0100101=>1010010=>0101101
[7,1,2,3,5,8,4,6]=>1000010=>0100001=>1011110
[8,6,2,3,7,1,4,5]=>1100100=>0010011=>1101100
[6,1,8,2,7,3,4,5]=>1010100=>0010101=>1101010
[7,8,6,1,3,2,5,4]=>0110101=>1010110=>0101001
[8,1,5,7,2,3,6,4]=>1001001=>1001001=>0110110
[1,4,5,2,8,6,7,3]=>0010101=>1010100=>0101011
[2,3,1,7,8,6,4,5]=>0100110=>0110010=>1001101
[2,1,4,6,8,3,7,5]=>1000101=>1010001=>0101110
[3,5,7,6,2,8,1,4]=>0011010=>0101100=>1010011
[5,4,1,6,3,8,7,2]=>1101011=>1101011=>0010100
[4,5,6,1,2,8,7,3]=>0010011=>1100100=>0011011
[3,5,6,2,4,8,7,1]=>0010011=>1100100=>0011011
[5,4,1,2,8,7,6,3]=>1100111=>1110011=>0001100
[5,6,3,7,8,4,2,1]=>0100111=>1110010=>0001101
[4,3,2,6,8,1,7,5]=>1100101=>1010011=>0101100
[7,1,5,6,3,8,2,4]=>1001010=>0101001=>1010110
[1,5,4,2,7,8,3,6]=>0110010=>0100110=>1011001
[6,1,2,8,7,4,3,5]=>1001110=>0111001=>1000110
[5,1,6,8,4,7,2,3]=>1001010=>0101001=>1010110
[5,1,3,8,4,2,7,6]=>1001101=>1011001=>0100110
[3,1,6,8,7,4,2,5]=>1001110=>0111001=>1000110
[3,6,5,8,4,7,1,2]=>0101010=>0101010=>1010101
[6,5,8,4,3,1,2,7]=>1011100=>0011101=>1100010
[8,5,1,3,7,4,6,2]=>1100101=>1010011=>0101100
[3,2,8,1,4,7,6,5]=>1010011=>1100101=>0011010
[6,4,3,8,2,5,7,1]=>1101001=>1001011=>0110100
[3,2,5,8,4,1,7,6]=>1001101=>1011001=>0100110
[6,8,2,3,4,7,5,1]=>0100011=>1100010=>0011101
[2,1,7,8,3,4,6,5]=>1001001=>1001001=>0110110
[7,5,1,8,4,2,6,3]=>1101101=>1011011=>0100100
[5,6,1,8,2,7,4,3]=>0101011=>1101010=>0010101
[3,6,8,5,2,7,4,1]=>0011011=>1101100=>0010011
[2,1,6,5,4,8,3,7]=>1011010=>0101101=>1010010
[2,1,7,3,5,8,6,4]=>1010011=>1100101=>0011010
[7,8,1,2,4,5,6,3]=>0100001=>1000010=>0111101
[3,6,8,1,5,7,2,4]=>0010010=>0100100=>1011011
[3,5,7,8,4,6,1,2]=>0001010=>0101000=>1010111
[7,5,2,8,4,6,3,1]=>1101011=>1101011=>0010100
[7,8,2,4,3,1,5,6]=>0101100=>0011010=>1100101
[8,4,3,1,7,5,2,6]=>1110110=>0110111=>1001000
[7,6,2,8,5,1,4,3]=>1101101=>1011011=>0100100
[4,3,8,7,1,6,5,2]=>1011011=>1101101=>0010010
[4,7,1,8,5,2,6,3]=>0101101=>1011010=>0100101
[3,7,5,8,1,6,2,4]=>0101010=>0101010=>1010101
[3,7,6,4,5,1,8,2]=>0110101=>1010110=>0101001
[4,7,5,6,3,8,2,1]=>0101011=>1101010=>0010101
[4,2,7,5,8,3,6,1]=>1010101=>1010101=>0101010
[5,8,2,7,3,4,6,1]=>0101001=>1001010=>0110101
[5,7,2,1,8,3,6,4]=>0110101=>1010110=>0101001
[7,8,1,2,3,4,6,5]=>0100001=>1000010=>0111101
[5,6,2,4,3,1,8,7]=>0101101=>1011010=>0100101
[4,6,2,1,7,8,3,5]=>0110010=>0100110=>1011001
[6,3,2,1,4,8,5,7]=>1110010=>0100111=>1011000
[7,1,8,3,5,4,6,2]=>1010101=>1010101=>0101010
[7,1,2,4,8,5,6,3]=>1000101=>1010001=>0101110
[8,7,6,5,1,3,2,4]=>1111010=>0101111=>1010000
[8,7,6,2,4,3,1,5]=>1110110=>0110111=>1001000
[7,6,8,1,5,4,3,2]=>1010111=>1110101=>0001010
[7,6,1,8,5,4,3,2]=>1101111=>1111011=>0000100
[6,5,8,1,7,4,3,2]=>1010111=>1110101=>0001010
[4,3,8,7,6,1,5,2]=>1011101=>1011101=>0100010
[6,5,8,7,4,1,3,2]=>1011101=>1011101=>0100010
[5,4,8,7,6,3,1,2]=>1011110=>0111101=>1000010
[1,4,8,6,3,2,5,7]=>0011100=>0011100=>1100011
[7,4,1,6,3,8,5,2]=>1101011=>1101011=>0010100
[7,6,3,1,5,8,4,2]=>1110011=>1100111=>0011000
[1,6,3,8,5,2,4,7]=>0101100=>0011010=>1100101
[4,6,3,7,5,2,1,8]=>0101110=>0111010=>1000101
[3,7,2,6,5,4,1,8]=>0101110=>0111010=>1000101
[1,7,4,6,2,8,5,3]=>0101011=>1101010=>0010101
[6,2,5,1,7,4,8,3]=>1010101=>1010101=>0101010
[3,5,7,4,8,6,1,2]=>0010110=>0110100=>1001011
[5,2,7,4,1,6,8,3]=>1011001=>1001101=>0110010
[4,5,8,2,1,7,6,3]=>0011011=>1101100=>0010011
[1,6,4,8,5,2,7,3]=>0101101=>1011010=>0100101
[7,4,1,5,3,8,2,6]=>1101010=>0101011=>1010100
[3,4,1,2,7,8,6,5]=>0100011=>1100010=>0011101
[4,1,3,2,8,6,7,5]=>1010101=>1010101=>0101010
[3,1,2,4,7,6,8,5]=>1000101=>1010001=>0101110
[8,1,3,5,4,7,2,6]=>1001010=>0101001=>1010110
[7,1,4,3,5,2,8,6]=>1010101=>1010101=>0101010
[3,2,8,1,6,5,4,7]=>1010110=>0110101=>1001010
[6,8,4,1,2,5,3,7]=>0110010=>0100110=>1011001
[8,2,1,5,6,4,3,7]=>1100110=>0110011=>1001100
[4,7,1,8,2,5,3,6]=>0101010=>0101010=>1010101
[6,7,8,1,4,5,3,2]=>0010011=>1100100=>0011011
[3,2,5,4,7,8,1,6]=>1010010=>0100101=>1011010
[8,4,7,6,2,3,1,5]=>1011010=>0101101=>1010010
[6,1,2,8,7,3,5,4]=>1001101=>1011001=>0100110
[1,2,7,5,6,8,3,4]=>0010010=>0100100=>1011011
[5,7,2,3,8,1,6,4]=>0100101=>1010010=>0101101
[3,5,2,6,1,8,7,4]=>0101011=>1101010=>0010101
[3,2,5,6,7,8,1,4]=>1000010=>0100001=>1011110
[5,4,2,6,8,7,1,3]=>1100110=>0110011=>1001100
[6,4,1,2,8,7,3,5]=>1100110=>0110011=>1001100
[4,3,8,5,2,1,6,7]=>1011100=>0011101=>1100010
[3,6,4,5,2,1,8,7]=>0101101=>1011010=>0100101
[7,5,4,2,3,8,1,6]=>1110010=>0100111=>1011000
[5,6,3,1,8,2,7,4]=>0110101=>1010110=>0101001
[6,5,4,3,1,2,8,7]=>1111001=>1001111=>0110000
[4,5,2,1,6,8,3,7]=>0110010=>0100110=>1011001
[5,6,2,8,1,7,4,3]=>0101011=>1101010=>0010101
[2,1,4,5,8,6,3,7]=>1000110=>0110001=>1001110
[6,7,1,3,4,8,2,5]=>0100010=>0100010=>1011101
[6,7,8,2,3,5,4,1]=>0010011=>1100100=>0011011
[5,8,6,2,3,7,4,1]=>0110011=>1100110=>0011001
[1,8,3,4,7,6,2,5]=>0100110=>0110010=>1001101
[5,8,6,1,7,2,4,3]=>0110101=>1010110=>0101001
[3,1,2,8,6,4,5,7]=>1001100=>0011001=>1100110
[1,3,2,8,5,4,6,7]=>0101100=>0011010=>1100101
[3,2,1,8,6,5,4,7]=>1101110=>0111011=>1000100
[5,2,7,1,8,4,3,6]=>1010110=>0110101=>1001010
[6,7,2,1,8,4,3,5]=>0110110=>0110110=>1001001
[6,7,3,1,5,8,2,4]=>0110010=>0100110=>1011001
[2,4,1,6,8,5,3,7]=>0100110=>0110010=>1001101
[2,5,6,1,8,4,3,7]=>0010110=>0110100=>1001011
[5,4,7,6,1,8,2,3]=>1011010=>0101101=>1010010
[3,5,6,8,4,7,2,1]=>0001011=>1101000=>0010111
[2,5,6,8,7,3,4,1]=>0001101=>1011000=>0100111
[2,4,8,5,7,3,6,1]=>0010101=>1010100=>0101011
[5,3,7,8,4,6,2,1]=>1001011=>1101001=>0010110
[6,7,3,8,4,5,2,1]=>0101011=>1101010=>0010101
[4,2,8,6,7,3,5,1]=>1010101=>1010101=>0101010
[3,2,8,7,5,4,6,1]=>1011101=>1011101=>0100010
[2,1,8,7,6,4,3,5]=>1011110=>0111101=>1000010
[6,3,8,7,5,1,2,4]=>1011100=>0011101=>1100010
[2,8,7,4,1,3,5,6]=>0111000=>0001110=>1110001
[2,5,3,7,6,8,1,4]=>0101010=>0101010=>1010101
[2,8,7,1,4,5,3,6]=>0110010=>0100110=>1011001
[4,2,1,8,7,3,5,6]=>1101100=>0011011=>1100100
[8,7,4,6,2,3,1,5]=>1101010=>0101011=>1010100
[5,1,6,3,2,8,7,4]=>1011011=>1101101=>0010010
[8,7,2,3,5,4,1,6]=>1100110=>0110011=>1001100
[3,4,2,8,6,1,5,7]=>0101100=>0011010=>1100101
[8,1,4,2,3,6,7,5]=>1010001=>1000101=>0111010
[6,8,3,5,4,7,1,2]=>0101010=>0101010=>1010101
[1,8,2,5,7,6,3,4]=>0100110=>0110010=>1001101
[4,1,6,8,2,3,7,5]=>1001001=>1001001=>0110110
[1,4,6,3,7,2,8,5]=>0010101=>1010100=>0101011
[6,2,1,8,4,5,3,7]=>1101010=>0101011=>1010100
[4,7,3,8,5,2,1,6]=>0101110=>0111010=>1000101
[3,1,7,4,8,5,2,6]=>1010110=>0110101=>1001010
[7,4,1,6,3,2,8,5]=>1101101=>1011011=>0100100
[3,8,6,2,7,4,1,5]=>0110110=>0110110=>1001001
[7,3,1,4,5,2,8,6]=>1100101=>1010011=>0101100
[8,1,2,4,6,7,5,3]=>1000011=>1100001=>0011110
[8,1,3,6,7,5,4,2]=>1000111=>1110001=>0001110
[6,4,2,8,5,1,3,7]=>1101100=>0011011=>1100100
[8,6,2,4,1,3,7,5]=>1101001=>1001011=>0110100
[4,7,5,1,8,6,3,2]=>0110111=>1110110=>0001001
[6,7,5,1,4,2,8,3]=>0110101=>1010110=>0101001
[6,2,4,1,7,5,8,3]=>1010101=>1010101=>0101010
[3,6,5,8,4,1,7,2]=>0101101=>1011010=>0100101
[7,3,8,2,5,6,4,1]=>1010011=>1100101=>0011010
[5,7,3,1,6,4,8,2]=>0110101=>1010110=>0101001
[6,1,3,7,4,8,5,2]=>1001011=>1101001=>0010110
[3,2,1,7,4,8,5,6]=>1101010=>0101011=>1010100
[4,1,5,2,7,6,3,8]=>1010110=>0110101=>1001010
[6,2,7,1,4,8,5,3]=>1010011=>1100101=>0011010
[7,5,4,1,3,8,6,2]=>1110011=>1100111=>0011000
[4,3,2,1,8,5,7,6]=>1110101=>1010111=>0101000
[4,2,1,7,3,6,5,8]=>1101010=>0101011=>1010100
[7,4,3,2,8,1,6,5]=>1110101=>1010111=>0101000
[2,7,5,3,8,1,4,6]=>0110100=>0010110=>1101001
[1,8,5,3,6,4,2,7]=>0110110=>0110110=>1001001
[8,1,6,2,7,4,3,5]=>1010110=>0110101=>1001010
[7,3,1,6,5,4,2,8]=>1101110=>0111011=>1000100
[8,5,7,4,3,6,2,1]=>1011011=>1101101=>0010010
[2,8,5,6,1,4,3,7]=>0101010=>0101010=>1010101
[3,7,5,8,2,1,4,6]=>0101100=>0011010=>1100101
[5,4,8,3,2,1,7,6]=>1011101=>1011101=>0100010
[2,4,7,1,3,6,5,8]=>0010010=>0100100=>1011011
[5,7,4,8,1,3,6,2]=>0101001=>1001010=>0110101
[5,1,7,8,2,4,6,3]=>1001001=>1001001=>0110110
[3,6,7,8,1,2,5,4]=>0001001=>1001000=>0110111
[4,6,7,2,8,1,3,5]=>0010100=>0010100=>1101011
[6,3,7,1,8,2,5,4]=>1010101=>1010101=>0101010
[5,7,1,4,8,2,6,3]=>0100101=>1010010=>0101101
[2,7,4,1,8,3,6,5]=>0110101=>1010110=>0101001
[6,1,2,7,8,3,5,4]=>1000101=>1010001=>0101110
[3,6,4,7,8,1,2,5]=>0100100=>0010010=>1101101
[3,7,4,8,5,2,1,6]=>0101110=>0111010=>1000101
[7,2,5,8,6,3,1,4]=>1001110=>0111001=>1000110
[4,8,1,7,6,2,3,5]=>0101100=>0011010=>1100101
[4,8,2,1,7,5,3,6]=>0110110=>0110110=>1001001
[5,8,7,1,3,6,4,2]=>0110011=>1100110=>0011001
[2,8,7,1,6,3,5,4]=>0110101=>1010110=>0101001
[2,7,6,5,1,4,3,8]=>0111010=>0101110=>1010001
[3,8,7,6,2,1,5,4]=>0111101=>1011110=>0100001
[5,8,7,2,6,1,4,3]=>0110101=>1010110=>0101001
[7,3,8,6,5,1,2,4]=>1011100=>0011101=>1100010
[5,8,6,4,3,2,1,7]=>0111110=>0111110=>1000001
[8,7,6,2,5,3,1,4]=>1110110=>0110111=>1001000
[8,1,2,3,4,7,6,5]=>1000011=>1100001=>0011110
[3,8,2,7,6,5,4,1]=>0101111=>1111010=>0000101
[4,2,8,7,6,5,3,1]=>1011111=>1111101=>0000010
[8,3,1,7,6,5,4,2]=>1101111=>1111011=>0000100
[5,2,8,7,6,4,3,1]=>1011111=>1111101=>0000010
[8,3,2,1,7,6,5,4]=>1110111=>1110111=>0001000
[8,4,1,7,6,5,3,2]=>1101111=>1111011=>0000100
[6,4,1,3,2,8,5,7]=>1101010=>0101011=>1010100
[2,5,8,6,3,1,4,7]=>0011100=>0011100=>1100011
[3,2,7,4,5,8,1,6]=>1010010=>0100101=>1011010
[8,1,6,2,4,5,3,7]=>1010010=>0100101=>1011010
[5,8,1,6,2,3,4,7]=>0101000=>0001010=>1110101
[5,4,6,1,3,8,2,7]=>1010010=>0100101=>1011010
[2,4,1,7,5,8,3,6]=>0101010=>0101010=>1010101
[2,4,7,6,8,3,5,1]=>0010101=>1010100=>0101011
[4,8,6,5,7,1,2,3]=>0110100=>0010110=>1101001
[8,5,7,4,3,1,6,2]=>1011101=>1011101=>0100010
[8,1,7,4,2,3,6,5]=>1011001=>1001101=>0110010
[8,2,3,1,5,7,6,4]=>1010011=>1100101=>0011010
[1,4,8,2,3,6,7,5]=>0010001=>1000100=>0111011
[3,1,2,7,8,6,4,5]=>1000110=>0110001=>1001110
[7,5,1,8,2,4,3,6]=>1101010=>0101011=>1010100
[3,5,8,1,2,4,7,6]=>0010001=>1000100=>0111011
[8,4,1,5,2,3,7,6]=>1101001=>1001011=>0110100
[3,8,4,1,2,7,6,5]=>0110011=>1100110=>0011001
[2,7,5,8,3,4,1,6]=>0101010=>0101010=>1010101
[1,4,7,3,2,8,5,6]=>0011010=>0101100=>1010011
[6,4,1,3,2,7,8,5]=>1101001=>1001011=>0110100
[2,3,7,6,8,1,5,4]=>0010101=>1010100=>0101011
[2,6,3,5,1,8,7,4]=>0101011=>1101010=>0010101
[2,7,1,6,8,3,5,4]=>0100101=>1010010=>0101101
[6,7,5,4,2,1,8,3]=>0111101=>1011110=>0100001
[4,2,1,5,8,7,6,3]=>1100111=>1110011=>0001100
[8,5,3,2,6,1,7,4]=>1110101=>1010111=>0101000
[6,2,1,5,3,8,7,4]=>1101011=>1101011=>0010100
[7,8,4,1,2,5,3,6]=>0110010=>0100110=>1011001
[7,8,1,2,6,5,3,4]=>0100110=>0110010=>1001101
[6,1,4,2,7,5,3,8]=>1010110=>0110101=>1001010
[1,2,8,7,5,4,3,6]=>0011110=>0111100=>1000011
[1,2,8,3,6,4,7,5]=>0010101=>1010100=>0101011
[5,1,7,3,6,4,8,2]=>1010101=>1010101=>0101010
[6,2,3,7,4,1,5,8]=>1001100=>0011001=>1100110
[6,2,4,1,7,3,5,8]=>1010100=>0010101=>1101010
[3,4,8,7,5,6,1,2]=>0011010=>0101100=>1010011
[2,7,3,8,6,4,1,5]=>0101110=>0111010=>1000101
[1,8,3,7,6,4,5,2]=>0101101=>1011010=>0100101
[2,6,8,5,3,1,7,4]=>0011101=>1011100=>0100011
[5,6,2,1,7,3,8,4]=>0110101=>1010110=>0101001
[5,3,6,2,4,1,7,8]=>1010100=>0010101=>1101010
[5,7,4,2,1,3,6,8]=>0111000=>0001110=>1110001
[6,4,2,1,5,3,7,8]=>1110100=>0010111=>1101000
[5,3,1,4,6,2,7,8]=>1100100=>0010011=>1101100
[5,1,2,4,7,6,8,3]=>1000101=>1010001=>0101110
[1,6,4,2,8,7,3,5]=>0110110=>0110110=>1001001
[4,8,1,2,6,7,3,5]=>0100010=>0100010=>1011101
[3,1,2,4,6,8,7,5]=>1000011=>1100001=>0011110
[4,2,8,1,5,3,7,6]=>1010101=>1010101=>0101010
[4,3,8,5,7,6,1,2]=>1010110=>0110101=>1001010
[4,8,6,3,7,5,1,2]=>0110110=>0110110=>1001001
[3,8,6,5,2,7,1,4]=>0111010=>0101110=>1010001
[3,8,5,6,1,7,4,2]=>0101011=>1101010=>0010101
[3,7,8,5,2,1,6,4]=>0011101=>1011100=>0100011
[4,2,7,8,1,3,6,5]=>1001001=>1001001=>0110110
[2,1,8,7,6,3,5,4]=>1011101=>1011101=>0100010
[5,4,1,6,3,2,8,7]=>1101101=>1011011=>0100100
[6,8,1,5,4,7,3,2]=>0101011=>1101010=>0010101
[4,6,2,5,1,3,8,7]=>0101001=>1001010=>0110101
[2,6,4,3,1,5,8,7]=>0111001=>1001110=>0110001
[5,1,7,2,8,6,4,3]=>1010111=>1110101=>0001010
[6,8,2,7,4,3,1,5]=>0101110=>0111010=>1000101
[6,8,2,5,4,7,1,3]=>0101010=>0101010=>1010101
[2,1,7,6,3,8,5,4]=>1011011=>1101101=>0010010
[7,6,2,8,4,3,1,5]=>1101110=>0111011=>1000100
[2,6,5,1,8,4,3,7]=>0110110=>0110110=>1001001
[4,2,1,6,3,8,7,5]=>1101011=>1101011=>0010100
[5,8,3,2,7,6,1,4]=>0110110=>0110110=>1001001
[2,4,8,3,1,7,5,6]=>0011010=>0101100=>1010011
[4,8,3,2,1,7,6,5]=>0111011=>1101110=>0010001
[3,5,8,2,7,1,4,6]=>0010100=>0010100=>1101011
[4,5,8,2,6,1,3,7]=>0010100=>0010100=>1101011
[2,6,8,3,7,1,4,5]=>0010100=>0010100=>1101011
[6,8,3,7,2,1,5,4]=>0101101=>1011010=>0100101
[5,8,3,1,6,2,7,4]=>0110101=>1010110=>0101001
[5,1,7,3,6,2,8,4]=>1010101=>1010101=>0101010
[4,5,8,1,6,3,2,7]=>0010110=>0110100=>1001011
[6,8,4,7,1,5,3,2]=>0101011=>1101010=>0010101
[4,3,2,1,6,8,5,7]=>1110010=>0100111=>1011000
[2,4,1,3,8,7,6,5]=>0100111=>1110010=>0001101
[4,8,6,5,1,7,3,2]=>0111011=>1101110=>0010001
[6,5,3,1,7,2,8,4]=>1110101=>1010111=>0101000
[2,1,5,4,8,7,3,6]=>1010110=>0110101=>1001010
[3,8,5,4,2,1,7,6]=>0111101=>1011110=>0100001
[2,3,8,5,4,1,6,7]=>0011100=>0011100=>1100011
[2,1,4,8,6,5,3,7]=>1001110=>0111001=>1000110
[4,3,2,8,7,6,1,5]=>1101110=>0111011=>1000100
[3,2,8,7,5,4,1,6]=>1011110=>0111101=>1000010
[2,8,6,5,4,3,1,7]=>0111110=>0111110=>1000001
[5,4,2,6,3,1,8,7]=>1101101=>1011011=>0100100
[7,5,2,6,3,8,4,1]=>1101011=>1101011=>0010100
[7,3,6,5,2,8,4,1]=>1011011=>1101101=>0010010
[5,6,3,1,2,4,8,7]=>0110001=>1000110=>0111001
[7,1,5,3,8,4,6,2]=>1010101=>1010101=>0101010
[2,7,5,3,8,6,4,1]=>0110111=>1110110=>0001001
[3,7,6,4,2,8,5,1]=>0111011=>1101110=>0010001
[5,7,3,6,2,8,4,1]=>0101011=>1101010=>0010101
[2,1,8,7,4,3,5,6]=>1011100=>0011101=>1100010
[2,8,6,3,1,4,7,5]=>0111001=>1001110=>0110001
[3,5,7,4,8,6,2,1]=>0010111=>1110100=>0001011
[4,5,3,6,8,2,7,1]=>0100101=>1010010=>0101101
[5,6,3,7,4,8,2,1]=>0101011=>1101010=>0010101
[2,6,7,4,5,8,3,1]=>0010011=>1100100=>0011011
[6,3,7,5,8,4,2,1]=>1010111=>1110101=>0001010
[8,5,2,6,1,7,3,4]=>1101010=>0101011=>1010100
[5,4,2,6,8,3,7,1]=>1100101=>1010011=>0101100
[7,6,8,5,1,4,2,3]=>1011010=>0101101=>1010010
[7,1,8,5,4,2,3,6]=>1011100=>0011101=>1100010
[5,7,3,8,4,1,2,6]=>0101100=>0011010=>1100101
[2,1,7,8,5,3,4,6]=>1001100=>0011001=>1100110
[2,4,8,1,5,6,3,7]=>0010010=>0100100=>1011011
[4,1,8,2,6,5,3,7]=>1010110=>0110101=>1001010
[4,7,3,8,1,2,6,5]=>0101001=>1001010=>0110101
[4,8,1,2,5,3,6,7]=>0100100=>0010010=>1101101
[3,8,1,2,4,6,5,7]=>0100010=>0100010=>1011101
[4,8,7,6,3,5,2,1]=>0111011=>1101110=>0010001
[3,8,7,6,5,2,4,1]=>0111101=>1011110=>0100001
[4,8,7,3,6,5,2,1]=>0110111=>1110110=>0001001
[4,8,7,6,3,2,5,1]=>0111101=>1011110=>0100001
[3,8,7,6,5,2,1,4]=>0111110=>0111110=>1000001
[7,5,8,3,6,2,1,4]=>1010110=>0110101=>1001010
[7,5,8,3,2,6,1,4]=>1011010=>0101101=>1010010
[7,5,8,3,2,1,6,4]=>1011101=>1011101=>0100010
[2,3,7,8,4,1,6,5]=>0001101=>1011000=>0100111
[2,1,7,5,8,4,6,3]=>1010101=>1010101=>0101010
[2,5,6,8,1,7,4,3]=>0001011=>1101000=>0010111
[4,2,8,6,1,7,3,5]=>1011010=>0101101=>1010010
[8,6,4,1,3,2,5,7]=>1110100=>0010111=>1101000
[8,1,3,2,6,5,4,7]=>1010110=>0110101=>1001010
[8,5,3,6,2,4,1,7]=>1101010=>0101011=>1010100
[8,4,1,2,6,5,3,7]=>1100110=>0110011=>1001100
[8,3,5,6,2,1,4,7]=>1001100=>0011001=>1100110
[8,4,2,1,5,6,3,7]=>1110010=>0100111=>1011000
[5,4,7,6,8,2,3,1]=>1010101=>1010101=>0101010
[4,1,8,2,3,7,6,5]=>1010011=>1100101=>0011010
[3,7,4,5,8,2,1,6]=>0100110=>0110010=>1001101
[6,3,8,5,7,4,1,2]=>1010110=>0110101=>1001010
[7,4,1,8,3,5,6,2]=>1101001=>1001011=>0110100
[5,3,8,7,4,6,1,2]=>1011010=>0101101=>1010010
[7,5,8,2,1,4,6,3]=>1011001=>1001101=>0110010
[8,7,4,2,1,3,6,5]=>1111001=>1001111=>0110000
[7,4,8,3,2,6,1,5]=>1011010=>0101101=>1010010
[6,8,2,3,1,7,5,4]=>0101011=>1101010=>0010101
[7,4,3,2,6,8,5,1]=>1110011=>1100111=>0011000
[5,1,2,3,6,8,7,4]=>1000011=>1100001=>0011110
[2,4,7,3,8,1,6,5]=>0010101=>1010100=>0101011
[6,3,8,2,7,4,1,5]=>1010110=>0110101=>1001010
[8,2,1,3,6,4,7,5]=>1100101=>1010011=>0101100
[5,7,8,2,1,4,3,6]=>0011010=>0101100=>1010011
[3,5,1,7,8,4,2,6]=>0100110=>0110010=>1001101
[1,7,8,4,5,3,2,6]=>0010110=>0110100=>1001011
[3,2,4,8,6,7,1,5]=>1001010=>0101001=>1010110
[8,3,1,6,7,4,2,5]=>1100110=>0110011=>1001100
[3,2,5,7,4,8,1,6]=>1001010=>0101001=>1010110
[8,4,7,1,3,2,5,6]=>1010100=>0010101=>1101010
[8,4,7,2,1,3,5,6]=>1011000=>0001101=>1110010
[6,4,2,1,3,7,8,5]=>1110001=>1000111=>0111000
[7,1,6,3,5,8,2,4]=>1010010=>0100101=>1011010
[3,8,5,1,6,7,2,4]=>0110010=>0100110=>1011001
[5,3,6,7,8,4,2,1]=>1000111=>1110001=>0001110
[1,5,2,7,8,6,4,3]=>0100111=>1110010=>0001101
[1,4,2,8,6,5,7,3]=>0101101=>1011010=>0100101
[4,1,7,5,2,6,8,3]=>1011001=>1001101=>0110010
[7,6,2,4,5,1,8,3]=>1100101=>1010011=>0101100
[8,1,4,5,2,6,7,3]=>1001001=>1001001=>0110110
[8,4,6,5,2,1,7,3]=>1011101=>1011101=>0100010
[3,5,7,2,1,6,8,4]=>0011001=>1001100=>0110011
[4,2,1,5,6,7,8,3]=>1100001=>1000011=>0111100
[3,7,5,4,6,8,1,2]=>0110010=>0100110=>1011001
[8,3,4,1,5,6,7,2]=>1010001=>1000101=>0111010
[3,5,2,4,7,6,1,8]=>0100110=>0110010=>1001101
[7,3,5,2,4,6,1,8]=>1010010=>0100101=>1011010
[5,3,7,2,4,6,1,8]=>1010010=>0100101=>1011010
[3,5,2,7,4,6,1,8]=>0101010=>0101010=>1010101
[3,2,5,7,4,6,1,8]=>1001010=>0101001=>1010110
[3,7,5,2,4,6,1,8]=>0110010=>0100110=>1011001
[5,7,3,2,4,6,1,8]=>0110010=>0100110=>1011001
[1,5,3,2,4,7,6,8]=>0110010=>0100110=>1011001
[1,5,3,2,7,4,6,8]=>0110100=>0010110=>1101001
[3,7,2,5,4,1,6,8]=>0101100=>0011010=>1100101
[3,2,7,5,4,1,6,8]=>1011100=>0011101=>1100010
[5,1,3,2,4,7,6,8]=>1010010=>0100101=>1011010
[5,1,3,2,7,4,6,8]=>1010100=>0010101=>1101010
[7,1,3,2,5,4,6,8]=>1010100=>0010101=>1101010
[1,7,3,2,5,4,6,8]=>0110100=>0010110=>1101001
[1,7,3,5,2,4,6,8]=>0101000=>0001010=>1110101
[7,1,3,5,2,4,6,8]=>1001000=>0001001=>1110110
[5,1,3,7,2,4,6,8]=>1001000=>0001001=>1110110
[3,7,5,1,2,4,6,8]=>0110000=>0000110=>1111001
[5,7,3,1,2,4,6,8]=>0110000=>0000110=>1111001
[1,5,3,7,2,4,6,8]=>0101000=>0001010=>1110101
[3,5,7,2,1,4,6,8]=>0011000=>0001100=>1110011
[3,5,2,7,1,4,6,8]=>0101000=>0001010=>1110101
[3,2,5,7,4,1,6,8]=>1001100=>0011001=>1100110
[3,5,2,7,4,1,6,8]=>0101100=>0011010=>1100101
[3,5,7,2,4,1,6,8]=>0010100=>0010100=>1101011
[5,3,7,2,4,1,6,8]=>1010100=>0010101=>1101010
[7,3,5,2,1,4,6,8]=>1011000=>0001101=>1110010
[5,3,2,4,7,1,6,8]=>1100100=>0010011=>1101100
[3,2,5,4,7,1,6,8]=>1010100=>0010101=>1101010
[1,3,2,7,5,4,6,8]=>0101100=>0011010=>1100101
[1,3,7,2,5,4,6,8]=>0010100=>0010100=>1101011
[7,3,1,2,5,4,6,8]=>1100100=>0010011=>1101100
[5,3,1,2,7,4,6,8]=>1100100=>0010011=>1101100
[5,3,1,2,4,7,6,8]=>1100010=>0100011=>1011100
[3,5,2,1,4,7,6,8]=>0110010=>0100110=>1011001
[3,2,5,1,7,4,6,8]=>1010100=>0010101=>1101010
[3,5,2,1,7,4,6,8]=>0110100=>0010110=>1101001
[5,3,1,7,2,4,6,8]=>1101000=>0001011=>1110100
[7,3,1,5,2,4,6,8]=>1101000=>0001011=>1110100
[1,3,7,5,2,4,6,8]=>0011000=>0001100=>1110011
[7,5,1,3,2,4,6,8]=>1101000=>0001011=>1110100
[5,7,1,3,2,4,6,8]=>0101000=>0001010=>1110101
[3,7,1,5,2,4,6,8]=>0101000=>0001010=>1110101
[3,7,1,2,5,4,6,8]=>0100100=>0010010=>1101101
[3,1,2,7,5,4,6,8]=>1001100=>0011001=>1100110
[3,1,7,2,5,4,6,8]=>1010100=>0010101=>1101010
[3,1,7,5,2,4,6,8]=>1011000=>0001101=>1110010
[5,1,7,3,2,4,6,8]=>1011000=>0001101=>1110010
[7,1,5,3,2,4,6,8]=>1011000=>0001101=>1110010
[1,7,5,3,2,4,6,8]=>0111000=>0001110=>1110001
[5,8,7,1,2,6,4,3]=>0110011=>1100110=>0011001
[6,8,2,1,7,5,4,3]=>0110111=>1110110=>0001001
[1,8,7,6,3,2,5,4]=>0111101=>1011110=>0100001
[5,8,7,4,1,2,6,3]=>0111001=>1001110=>0110001
[2,8,7,4,3,6,1,5]=>0111010=>0101110=>1010001
[1,8,5,4,2,7,6,3]=>0111011=>1101110=>0010001
[7,6,4,2,8,5,3,1]=>1110111=>1110111=>0001000
[7,6,4,8,5,1,2,3]=>1101100=>0011011=>1100100
[1,6,7,5,3,8,4,2]=>0011011=>1101100=>0010011
[7,6,3,5,2,4,8,1]=>1101001=>1001011=>0110100
[7,6,4,2,5,1,8,3]=>1110101=>1010111=>0101000
[7,6,2,8,3,1,4,5]=>1101100=>0011011=>1100100
[1,6,7,5,8,2,3,4]=>0010100=>0010100=>1101011
[2,6,5,7,8,3,4,1]=>0100101=>1010010=>0101101
[3,2,5,1,7,8,4,6]=>1010010=>0100101=>1011010
[5,2,3,4,8,6,1,7]=>1000110=>0110001=>1001110
[5,3,4,8,2,7,6,1]=>1001011=>1101001=>0010110
[5,3,8,2,4,1,7,6]=>1010101=>1010101=>0101010
[5,2,8,4,1,7,3,6]=>1011010=>0101101=>1010010
[6,4,2,5,1,8,7,3]=>1101011=>1101011=>0010100
[6,4,3,5,8,2,1,7]=>1100110=>0110011=>1001100
[6,3,5,4,8,2,7,1]=>1010101=>1010101=>0101010
[6,3,5,8,7,1,2,4]=>1001100=>0011001=>1100110
[1,5,7,3,4,8,6,2]=>0010011=>1100100=>0011011
[5,8,4,1,3,7,6,2]=>0110011=>1100110=>0011001
[6,4,3,8,5,7,2,1]=>1101011=>1101011=>0010100
[5,4,2,6,3,1,7,8]=>1101100=>0011011=>1100100
[4,6,5,3,7,1,2,8]=>0110100=>0010110=>1101001
[3,5,6,1,4,8,7,2]=>0010011=>1100100=>0011011
[3,5,7,6,1,4,8,2]=>0011001=>1001100=>0110011
[3,6,5,7,4,8,1,2]=>0101010=>0101010=>1010101
[4,2,6,5,1,7,3,8]=>1011010=>0101101=>1010010
[4,3,5,7,2,1,6,8]=>1001100=>0011001=>1100110
[3,5,4,7,2,6,1,8]=>0101010=>0101010=>1010101
[3,4,7,6,8,1,2,5]=>0010100=>0010100=>1101011
[1,8,4,3,7,5,6,2]=>0110101=>1010110=>0101001
[5,2,8,6,4,7,3,1]=>1011011=>1101101=>0010010
[1,8,6,3,7,4,2,5]=>0110110=>0110110=>1001001
[1,8,6,5,7,2,3,4]=>0110100=>0010110=>1101001
[4,2,8,3,5,7,1,6]=>1010010=>0100101=>1011010
[4,3,8,6,5,7,1,2]=>1011010=>0101101=>1010010
[1,3,7,2,6,5,8,4]=>0010101=>1010100=>0101011
[1,5,7,2,4,6,8,3]=>0010001=>1000100=>0111011
[1,3,6,4,2,5,8,7]=>0011001=>1001100=>0110011
[5,6,3,4,7,1,8,2]=>0100101=>1010010=>0101101
[3,5,2,7,4,1,8,6]=>0101101=>1011010=>0100101
[5,2,3,8,4,1,7,6]=>1001101=>1011001=>0100110
[7,5,3,4,8,2,1,6]=>1100110=>0110011=>1001100
[7,6,3,8,4,2,1,5]=>1101110=>0111011=>1000100
[7,2,8,5,1,6,3,4]=>1011010=>0101101=>1010010
[7,4,3,8,5,2,6,1]=>1101101=>1011011=>0100100
[7,2,8,5,1,3,4,6]=>1011000=>0001101=>1110010
[7,6,8,1,2,5,3,4]=>1010010=>0100101=>1011010
[1,5,3,7,6,8,4,2]=>0101011=>1101010=>0010101
[1,2,6,4,5,8,3,7]=>0010010=>0100100=>1011011
[1,2,7,4,8,5,3,6]=>0010110=>0110100=>1001011
[1,6,3,7,8,2,4,5]=>0100100=>0010010=>1101101
[3,2,6,7,8,1,4,5]=>1000100=>0010001=>1101110
[1,4,7,3,5,2,6,8]=>0010100=>0010100=>1101011
[3,8,4,7,6,1,5,2]=>0101101=>1011010=>0100101
[5,7,4,2,6,3,1,8]=>0110110=>0110110=>1001001
[2,4,5,8,1,6,7,3]=>0001001=>1001000=>0110111
[6,1,3,7,4,2,5,8]=>1001100=>0011001=>1100110
[2,1,8,3,6,7,4,5]=>1010010=>0100101=>1011010
[5,1,8,6,2,7,3,4]=>1011010=>0101101=>1010010
[5,7,1,4,2,6,3,8]=>0101010=>0101010=>1010101
[3,2,6,8,1,5,7,4]=>1001001=>1001001=>0110110
[8,2,6,1,5,4,7,3]=>1010101=>1010101=>0101010
[7,8,5,4,1,6,3,2]=>0111011=>1101110=>0010001
[3,6,2,7,8,1,5,4]=>0100101=>1010010=>0101101
[2,7,3,8,1,5,6,4]=>0101001=>1001010=>0110101
[2,6,8,4,1,5,7,3]=>0011001=>1001100=>0110011
[5,7,8,4,1,6,3,2]=>0011011=>1101100=>0010011
[3,4,8,1,2,5,7,6]=>0010001=>1000100=>0111011
[6,3,1,7,5,2,4,8]=>1101100=>0011011=>1100100
[6,3,1,8,2,7,4,5]=>1101010=>0101011=>1010100
[7,8,1,2,4,3,6,5]=>0100101=>1010010=>0101101
[5,2,8,1,3,4,7,6]=>1010001=>1000101=>0111010
[3,2,1,6,4,7,8,5]=>1101001=>1001011=>0110100
[4,1,3,6,5,7,8,2]=>1001001=>1001001=>0110110
[5,1,3,4,2,7,8,6]=>1001001=>1001001=>0110110
[6,1,3,4,2,8,5,7]=>1001010=>0101001=>1010110
[8,1,4,3,5,7,6,2]=>1010011=>1100101=>0011010
[5,2,4,1,3,7,8,6]=>1010001=>1000101=>0111010
[3,2,6,1,5,7,8,4]=>1010001=>1000101=>0111010
[1,4,6,3,5,7,8,2]=>0010001=>1000100=>0111011
[3,5,1,6,4,7,8,2]=>0101001=>1001010=>0110101
[3,6,4,2,1,7,8,5]=>0111001=>1001110=>0110001
[3,8,6,1,4,7,5,2]=>0110011=>1100110=>0011001
[1,8,3,2,6,7,5,4]=>0110011=>1100110=>0011001
[8,7,1,3,6,5,4,2]=>1100111=>1110011=>0001100
[1,8,5,7,4,2,6,3]=>0101101=>1011010=>0100101
[4,7,5,3,8,2,1,6]=>0110110=>0110110=>1001001
[2,7,6,5,8,3,1,4]=>0110110=>0110110=>1001001
[1,4,7,6,8,2,3,5]=>0010100=>0010100=>1101011
[3,5,7,4,8,1,2,6]=>0010100=>0010100=>1101011
[4,6,1,7,5,8,2,3]=>0101010=>0101010=>1010101
[2,3,6,7,5,8,1,4]=>0001010=>0101000=>1010111
[1,3,7,5,6,8,2,4]=>0010010=>0100100=>1011011
[3,2,7,1,6,8,4,5]=>1010010=>0100101=>1011010
[8,1,5,4,7,2,6,3]=>1010101=>1010101=>0101010
[8,2,5,3,7,1,6,4]=>1010101=>1010101=>0101010
[2,1,4,7,5,8,3,6]=>1001010=>0101001=>1010110
[1,2,6,7,4,8,3,5]=>0001010=>0101000=>1010111
[3,6,4,7,8,5,2,1]=>0100111=>1110010=>0001101
[3,2,5,8,6,7,4,1]=>1001011=>1101001=>0010110
[6,3,5,8,7,4,1,2]=>1001110=>0111001=>1000110
[8,3,5,7,6,4,2,1]=>1001111=>1111001=>0000110
[4,1,8,3,7,5,6,2]=>1010101=>1010101=>0101010
[4,7,2,8,5,6,3,1]=>0101011=>1101010=>0010101
[1,4,8,7,3,5,6,2]=>0011001=>1001100=>0110011
[3,2,8,7,1,5,6,4]=>1011001=>1001101=>0110010
[1,5,8,7,4,6,2,3]=>0011010=>0101100=>1010011
[4,7,6,8,5,3,1,2]=>0101110=>0111010=>1000101
[4,8,6,7,5,3,2,1]=>0101111=>1111010=>0000101
[3,8,7,5,6,4,2,1]=>0110111=>1110110=>0001001
[8,1,5,6,3,2,4,7]=>1001100=>0011001=>1100110
[1,7,8,3,5,2,4,6]=>0010100=>0010100=>1101011
[8,2,5,3,1,6,4,7]=>1011010=>0101101=>1010010
[8,3,2,1,5,6,4,7]=>1110010=>0100111=>1011000
[8,6,5,1,3,4,2,7]=>1110010=>0100111=>1011000
[1,7,8,5,4,3,2,6]=>0011110=>0111100=>1000011
[2,6,8,7,4,3,5,1]=>0011101=>1011100=>0100011
[2,7,6,8,4,3,1,5]=>0101110=>0111010=>1000101
[1,2,6,7,8,4,3,5]=>0000110=>0110000=>1001111
[8,5,7,1,3,4,6,2]=>1010001=>1000101=>0111010
[3,5,8,6,7,4,1,2]=>0010110=>0110100=>1001011
[3,1,6,5,8,7,4,2]=>1010111=>1110101=>0001010
[3,7,6,4,8,1,2,5]=>0110100=>0010110=>1101001
[2,3,6,5,7,1,8,4]=>0010101=>1010100=>0101011
[2,3,6,4,1,7,8,5]=>0011001=>1001100=>0110011
[4,7,2,1,5,3,8,6]=>0110101=>1010110=>0101001
[3,1,7,4,5,2,8,6]=>1010101=>1010101=>0101010
[3,7,5,4,2,1,8,6]=>0111101=>1011110=>0100001
[1,3,6,7,4,2,8,5]=>0001101=>1011000=>0100111
[4,3,7,2,6,8,1,5]=>1010010=>0100101=>1011010
[5,4,2,1,3,7,8,6]=>1110001=>1000111=>0111000
[8,7,1,5,6,3,2,4]=>1100110=>0110011=>1001100
[8,7,2,5,4,6,1,3]=>1101010=>0101011=>1010100
[8,7,1,2,4,5,6,3]=>1100001=>1000011=>0111100
[8,7,2,5,3,1,6,4]=>1101101=>1011011=>0100100
[8,7,3,2,1,5,6,4]=>1111001=>1001111=>0110000
[8,7,6,5,1,3,4,2]=>1111001=>1001111=>0110000
[8,7,6,1,4,5,3,2]=>1110011=>1100111=>0011000
[8,7,5,6,1,4,3,2]=>1101011=>1101011=>0010100
[6,8,7,1,5,4,3,2]=>0110111=>1110110=>0001001
[8,5,7,6,1,4,3,2]=>1011011=>1101101=>0010010
[6,7,8,1,5,4,3,2]=>0010111=>1110100=>0001011
[8,7,4,6,5,1,3,2]=>1101101=>1011011=>0100100
[8,5,6,7,1,4,3,2]=>1001011=>1101001=>0010110
[8,7,6,3,5,4,1,2]=>1110110=>0110111=>1001000
[8,7,4,5,6,1,3,2]=>1100101=>1010011=>0101100
[8,7,6,5,2,4,3,1]=>1111011=>1101111=>0010000
[4,2,8,7,6,5,1,3]=>1011110=>0111101=>1000010
[7,5,8,1,6,4,3,2]=>1010111=>1110101=>0001010
[1,5,8,7,6,2,4,3]=>0011101=>1011100=>0100011
[7,5,8,4,1,6,3,2]=>1011011=>1101101=>0010010
[6,8,5,1,7,4,3,2]=>0110111=>1110110=>0001001
[1,6,8,7,2,5,4,3]=>0011011=>1101100=>0010011
[7,3,8,4,6,1,5,2]=>1010101=>1010101=>0101010
[4,8,5,7,1,6,3,2]=>0101011=>1101010=>0010101
[4,3,7,6,5,1,8,2]=>1011101=>1011101=>0100010
[5,4,3,6,7,1,8,2]=>1100101=>1010011=>0101100
[5,4,7,3,6,1,8,2]=>1010101=>1010101=>0101010
[4,8,7,6,3,1,5,2]=>0111101=>1011110=>0100001
[2,4,6,3,1,7,8,5]=>0011001=>1001100=>0110011
[6,8,5,7,3,2,1,4]=>0101110=>0111010=>1000101
[6,8,5,3,7,2,1,4]=>0110110=>0110110=>1001001
[6,8,5,7,4,2,1,3]=>0101110=>0111010=>1000101
[2,1,8,7,6,3,4,5]=>1011100=>0011101=>1100010
[5,8,7,6,2,4,1,3]=>0111010=>0101110=>1010001
[6,8,2,7,5,1,4,3]=>0101101=>1011010=>0100101
[5,8,7,2,6,4,1,3]=>0110110=>0110110=>1001001
[6,8,7,5,2,4,1,3]=>0111010=>0101110=>1010001
[5,8,7,6,4,2,3,1]=>0111101=>1011110=>0100001
[2,3,6,1,7,5,8,4]=>0010101=>1010100=>0101011
[2,3,6,1,8,5,4,7]=>0010110=>0110100=>1001011
[2,4,1,6,7,5,8,3]=>0100101=>1010010=>0101101
[2,4,1,7,3,8,6,5]=>0101011=>1101010=>0010101
[2,4,5,3,7,1,8,6]=>0010101=>1010100=>0101011
[2,4,5,7,3,8,6,1]=>0001011=>1101000=>0010111
[2,4,6,3,1,8,5,7]=>0011010=>0101100=>1010011
[2,4,6,3,8,5,1,7]=>0010110=>0110100=>1001011
[2,4,6,8,3,5,1,7]=>0001010=>0101000=>1010111
[2,4,7,3,1,5,8,6]=>0011001=>1001100=>0110011
[2,4,7,3,1,8,6,5]=>0011011=>1101100=>0010011
[2,4,7,8,3,5,6,1]=>0001001=>1001000=>0110111
[2,5,1,6,4,8,3,7]=>0101010=>0101010=>1010101
[2,5,1,6,7,4,8,3]=>0100101=>1010010=>0101101
[2,5,1,7,4,3,8,6]=>0101101=>1011010=>0100101
[2,5,6,3,4,8,1,7]=>0010010=>0100100=>1011011
[2,5,6,3,7,4,8,1]=>0010101=>1010100=>0101011
[2,5,6,3,8,4,1,7]=>0010110=>0110100=>1001011
[2,5,6,7,8,4,1,3]=>0000110=>0110000=>1001111
[2,5,6,8,4,3,1,7]=>0001110=>0111000=>1000111
[2,6,1,7,4,8,5,3]=>0101011=>1101010=>0010101
[1,4,2,6,3,8,5,10,7,9]=>010101010=>010101010=>101010101
[6,8,4,3,2,1,7,5]=>0111101=>1011110=>0100001
[7,6,5,2,8,4,1,3]=>1110110=>0110111=>1001000
[7,6,3,8,2,4,1,5]=>1101010=>0101011=>1010100
[5,1,2,3,4,8,7,6]=>1000011=>1100001=>0011110
[4,1,2,3,7,6,5,8]=>1000110=>0110001=>1001110
[7,6,5,8,2,4,3,1]=>1101011=>1101011=>0010100
[6,8,7,4,5,2,3,1]=>0110101=>1010110=>0101001
[6,8,4,7,5,2,3,1]=>0101101=>1011010=>0100101
[6,8,4,7,2,5,3,1]=>0101011=>1101010=>0010101
[6,4,8,7,5,2,3,1]=>1011101=>1011101=>0100010
[6,8,4,2,7,5,3,1]=>0110111=>1110110=>0001001
[6,8,4,7,2,1,5,3]=>0101101=>1011010=>0100101
[6,8,4,7,3,5,2,1]=>0101011=>1101010=>0010101
[6,4,8,2,7,5,3,1]=>1010111=>1110101=>0001010
[6,8,4,2,7,1,5,3]=>0110101=>1010110=>0101001
[6,4,2,8,7,5,3,1]=>1101111=>1111011=>0000100
[6,8,4,7,3,2,5,1]=>0101101=>1011010=>0100101
[6,8,4,2,1,7,5,3]=>0111011=>1101110=>0010001
[6,8,4,7,3,2,1,5]=>0101110=>0111010=>1000101
[6,8,5,7,1,4,3,2]=>0101011=>1101010=>0010101
[1,8,7,3,6,2,5,4]=>0110101=>1010110=>0101001
[5,8,7,2,3,6,1,4]=>0110010=>0100110=>1011001
[6,8,2,7,5,4,1,3]=>0101110=>0111010=>1000101
[6,8,3,7,5,2,1,4]=>0101110=>0111010=>1000101
[6,8,1,7,3,5,4,2]=>0101011=>1101010=>0010101
[6,8,4,7,3,1,5,2]=>0101101=>1011010=>0100101
[6,8,1,7,3,2,5,4]=>0101101=>1011010=>0100101
[3,8,2,7,6,5,1,4]=>0101110=>0111010=>1000101
[1,8,4,7,6,2,5,3]=>0101101=>1011010=>0100101
[3,8,1,7,6,2,5,4]=>0101101=>1011010=>0100101
[1,8,4,7,3,6,5,2]=>0101011=>1101010=>0010101
[4,8,5,7,1,2,6,3]=>0101001=>1001010=>0110101
[1,8,4,7,3,2,6,5]=>0101101=>1011010=>0100101
[6,8,5,2,7,4,1,3]=>0110110=>0110110=>1001001
[6,8,3,4,7,1,5,2]=>0100101=>1010010=>0101101
[6,8,1,3,7,2,5,4]=>0100101=>1010010=>0101101
[2,8,1,3,7,6,5,4]=>0100111=>1110010=>0001101
[2,8,3,4,7,6,1,5]=>0100110=>0110010=>1001101
[6,8,5,4,2,7,1,3]=>0111010=>0101110=>1010001
[6,8,1,4,3,7,5,2]=>0101011=>1101010=>0010101
[6,8,1,4,2,7,5,3]=>0101011=>1101010=>0010101
[6,5,4,3,8,7,1,2]=>1110110=>0110111=>1001000
[3,1,7,2,8,5,6,4]=>1010101=>1010101=>0101010
[3,1,6,7,4,8,5,2]=>1001011=>1101001=>0010110
[3,1,5,7,8,4,6,2]=>1000101=>1010001=>0101110
[8,6,5,7,1,4,3,2]=>1101011=>1101011=>0010100
[8,6,4,2,7,5,1,3]=>1110110=>0110111=>1001000
[6,4,8,2,7,5,1,3]=>1010110=>0110101=>1001010
[8,4,7,6,2,5,1,3]=>1011010=>0101101=>1010010
[3,4,5,6,8,7,1,2]=>0000110=>0110000=>1001111
[3,4,5,7,8,6,1,2]=>0000110=>0110000=>1001111
[3,4,5,8,7,6,1,2]=>0001110=>0111000=>1000111
[3,4,6,7,8,5,1,2]=>0000110=>0110000=>1001111
[6,4,7,3,5,2,1,8]=>1010110=>0110101=>1001010
[5,4,7,3,6,2,1,8]=>1010110=>0110101=>1001010
[4,8,7,3,5,2,1,6]=>0110110=>0110110=>1001001
[7,5,3,6,8,2,1,4]=>1100110=>0110011=>1001100
[5,8,3,6,7,2,1,4]=>0100110=>0110010=>1001101
[5,8,7,3,2,4,1,6]=>0111010=>0101110=>1010001
[6,4,7,3,2,5,1,8]=>1011010=>0101101=>1010010
[6,5,3,7,2,4,1,8]=>1101010=>0101011=>1010100
[7,3,8,6,2,4,1,5]=>1011010=>0101101=>1010010
[6,3,7,8,2,4,1,5]=>1001010=>0101001=>1010110
[5,3,7,6,2,4,1,8]=>1011010=>0101101=>1010010
[7,5,8,2,6,4,1,3]=>1010110=>0110101=>1001010
[7,4,8,2,5,6,1,3]=>1010010=>0100101=>1011010
[5,4,7,2,6,8,1,3]=>1010010=>0100101=>1011010
[4,8,7,2,5,6,1,3]=>0110010=>0100110=>1011001
[5,4,3,2,6,8,1,7]=>1110010=>0100111=>1011000
[4,8,3,2,5,6,1,7]=>0110010=>0100110=>1011001
[5,3,7,2,6,4,1,8]=>1010110=>0110101=>1001010
[7,5,2,6,8,4,1,3]=>1100110=>0110011=>1001100
[6,4,2,7,5,8,1,3]=>1101010=>0101011=>1010100
[7,5,8,4,1,2,6,3]=>1011001=>1001101=>0110010
[7,1,8,2,3,6,5,4]=>1010011=>1100101=>0011010
[7,3,8,4,6,2,1,5]=>1010110=>0110101=>1001010
[7,1,8,4,2,6,5,3]=>1011011=>1101101=>0010010
[7,1,8,3,6,2,5,4]=>1010101=>1010101=>0101010
[7,2,3,4,5,1,8,6]=>1000101=>1010001=>0101110
[2,8,3,4,5,1,6,7]=>0100100=>0010010=>1101101
[2,7,3,4,1,5,6,8]=>0101000=>0001010=>1110101
[5,3,6,1,2,7,4,8]=>1010010=>0100101=>1011010
[10,8,6,4,2,1,3,5,7,9]=>111110000=>000011111=>111100000
[2,8,5,3,4,6,7,1]=>0110001=>1000110=>0111001
[6,5,4,3,7,8,9,10,1,2]=>111000010=>010000111=>101111000
[3,8,1,4,5,6,7,2]=>0100001=>1000010=>0111101
[4,5,3,1,2,8,7,6]=>0110011=>1100110=>0011001
[5,7,3,4,1,6,8,2]=>0101001=>1001010=>0110101
[4,5,3,1,2,6,8,7]=>0110001=>1000110=>0111001
[3,4,1,2,5,8,7,6]=>0100011=>1100010=>0011101
[6,5,3,2,1,8,7,4]=>1111011=>1101111=>0010000
[4,5,2,1,8,7,6,3]=>0110111=>1110110=>0001001
[3,4,1,8,7,6,5,2]=>0101111=>1111010=>0000101
[8,1,2,4,5,6,7,3]=>1000001=>1000001=>0111110
[7,1,2,3,4,6,8,5]=>1000001=>1000001=>0111110
[6,1,2,3,5,8,7,4]=>1000011=>1100001=>0011110
[5,1,2,4,8,6,7,3]=>1000101=>1010001=>0101110
[4,1,3,8,5,6,7,2]=>1001001=>1001001=>0110110
[7,1,2,3,5,8,6,4]=>1000011=>1100001=>0011110
[6,1,2,3,5,7,8,4]=>1000001=>1000001=>0111110
[10,1,2,3,4,6,7,8,9,5]=>100000001=>100000001=>011111110
[5,1,3,8,4,6,7,2]=>1001001=>1001001=>0110110
[4,1,3,5,8,6,7,2]=>1000101=>1010001=>0101110
[8,6,3,5,2,7,4,1]=>1101011=>1101011=>0010100
[7,5,2,8,6,3,4,1]=>1101101=>1011011=>0100100
[5,2,8,6,7,3,4,1]=>1010101=>1010101=>0101010
[7,5,2,3,8,6,4,1]=>1100111=>1110011=>0001100
[5,2,3,8,6,7,4,1]=>1001011=>1101001=>0010110
[8,4,1,7,3,5,6,2]=>1101001=>1001011=>0110100
[7,4,1,2,6,8,5,3]=>1100011=>1100011=>0011100
[5,3,8,4,1,2,6,7]=>1011000=>0001101=>1110010
[6,3,5,8,4,1,2,7]=>1001100=>0011001=>1100110
[7,3,5,6,8,4,1,2]=>1000110=>0110001=>1001110
[7,4,5,1,2,8,6,3]=>1010011=>1100101=>0011010
[6,3,8,4,5,1,2,7]=>1010100=>0010101=>1101010
[8,5,1,7,4,6,2,3]=>1101010=>0101011=>1010100
[7,4,5,1,8,6,2,3]=>1010110=>0110101=>1001010
[8,4,5,1,7,3,6,2]=>1010101=>1010101=>0101010
[4,2,7,5,8,6,3,1]=>1010111=>1110101=>0001010
[4,2,8,5,6,3,1,7]=>1010110=>0110101=>1001010
[8,6,3,1,5,7,4,2]=>1110011=>1100111=>0011000
[7,4,2,8,5,6,3,1]=>1101011=>1101011=>0010100
[4,2,8,5,6,7,3,1]=>1010011=>1100101=>0011010
[7,4,8,5,6,1,2,3]=>1010100=>0010101=>1101010
[7,5,8,6,1,2,3,4]=>1011000=>0001101=>1110010
[7,3,4,8,5,6,1,2]=>1001010=>0101001=>1010110
[7,3,4,5,8,6,1,2]=>1000110=>0110001=>1001110
[6,4,8,5,2,3,1,7]=>1011010=>0101101=>1010010
[8,6,3,1,7,5,2,4]=>1110110=>0110111=>1001000
[7,2,8,3,4,5,6,1]=>1010001=>1000101=>0111010
[7,4,5,2,8,6,3,1]=>1010111=>1110101=>0001010
[8,5,2,7,4,6,3,1]=>1101011=>1101011=>0010100
[5,2,4,8,6,7,3,1]=>1001011=>1101001=>0010110
[7,5,8,6,2,3,1,4]=>1011010=>0101101=>1010010
[7,4,8,5,6,2,3,1]=>1010101=>1010101=>0101010
[7,3,1,8,4,5,6,2]=>1101001=>1001011=>0110100
[7,2,4,5,6,8,3,1]=>1000011=>1100001=>0011110
[3,4,5,7,6,8,1,2]=>0001010=>0101000=>1010111
[4,8,2,5,1,3,7,6]=>0101001=>1001010=>0110101
[2,1,8,7,3,4,6,5]=>1011001=>1001101=>0110010
[2,7,4,5,6,8,1,3]=>0100010=>0100010=>1011101
[4,1,2,8,7,5,3,6]=>1001110=>0111001=>1000110
[4,1,2,6,8,3,7,5]=>1000101=>1010001=>0101110
[3,1,7,6,8,2,4,5]=>1010100=>0010101=>1101010
[8,2,6,3,1,5,4,7]=>1011010=>0101101=>1010010
[2,1,7,8,9,10,6,5,4,3]=>100001111=>111100001=>000011110
[7,3,5,1,8,2,4,6]=>1010100=>0010101=>1101010
[7,8,3,1,5,2,4,6]=>0110100=>0010110=>1101001
[12,10,8,6,4,2,1,3,5,7,9,11]=>11111100000=>00000111111=>11111000000
[9,8,7,6,1,2,3,4,5,10]=>111100000=>000001111=>111110000
[1,5,6,7,8,3,4,2]=>0000101=>1010000=>0101111
[1,4,6,7,8,3,5,2]=>0000101=>1010000=>0101111
[1,5,6,3,7,8,4,2]=>0010011=>1100100=>0011011
[6,1,2,3,4,8,7,5]=>1000011=>1100001=>0011110
[5,1,2,3,8,7,6,4]=>1000111=>1110001=>0001110
[5,1,2,3,8,6,7,4]=>1000101=>1010001=>0101110
[2,8,5,3,1,4,6,7]=>0111000=>0001110=>1110001
[2,4,3,5,7,8,1,6]=>0100010=>0100010=>1011101
[2,6,3,7,8,1,4,5]=>0100100=>0010010=>1101101
[3,4,6,1,7,8,5,2]=>0010011=>1100100=>0011011
[3,4,6,1,8,5,7,2]=>0010101=>1010100=>0101011
[3,4,8,1,5,6,7,2]=>0010001=>1000100=>0111011
[3,5,1,7,4,8,6,2]=>0101011=>1101010=>0010101
[3,5,6,4,8,1,7,2]=>0010101=>1010100=>0101011
[3,5,8,4,1,6,7,2]=>0011001=>1001100=>0110011
[3,6,1,8,5,4,7,2]=>0101101=>1011010=>0100101
[3,6,7,4,8,5,1,2]=>0010110=>0110100=>1001011
[3,6,8,4,5,1,7,2]=>0010101=>1010100=>0101011
[4,1,5,6,8,3,7,2]=>1000101=>1010001=>0101110
[4,1,5,7,8,6,3,2]=>1000111=>1110001=>0001110
[4,1,7,3,5,8,6,2]=>1010011=>1100101=>0011010
[4,1,7,8,5,6,3,2]=>1001011=>1101001=>0010110
[4,5,7,3,8,6,1,2]=>0010110=>0110100=>1001011
[4,5,7,8,1,6,3,2]=>0001011=>1101000=>0010111
[4,5,8,3,1,6,7,2]=>0011001=>1001100=>0110011
[4,6,3,1,8,5,7,2]=>0110101=>1010110=>0101001
[4,6,7,3,5,8,1,2]=>0010010=>0100100=>1011011
[4,6,7,8,5,1,3,2]=>0001101=>1011000=>0100111
[4,6,8,3,5,1,7,2]=>0010101=>1010100=>0101011
[4,7,3,1,8,6,5,2]=>0110111=>1110110=>0001001
[4,7,8,3,5,6,1,2]=>0010010=>0100100=>1011011
[5,1,6,7,4,8,3,2]=>1001011=>1101001=>0010110
[5,1,6,7,8,3,4,2]=>1000101=>1010001=>0101110
[5,6,3,4,8,1,7,2]=>0100101=>1010010=>0101101
[5,6,7,8,4,1,3,2]=>0001101=>1011000=>0100111
[5,7,3,4,1,8,6,2]=>0101011=>1101010=>0010101
[5,7,3,4,8,6,1,2]=>0100110=>0110010=>1001101
[5,7,3,8,4,6,1,2]=>0101010=>0101010=>1010101
[5,7,8,4,3,6,1,2]=>0011010=>0101100=>1010011
[6,1,3,7,8,5,4,2]=>1000111=>1110001=>0001110
[6,1,7,4,5,8,3,2]=>1010011=>1100101=>0011010
[6,1,8,4,5,3,7,2]=>1010101=>1010101=>0101010
[6,7,3,8,5,4,1,2]=>0101110=>0111010=>1000101
[7,1,3,4,8,6,5,2]=>1000111=>1110001=>0001110
[8,4,1,3,2,5,6,7]=>1101000=>0001011=>1110100
[8,5,1,2,4,3,6,7]=>1100100=>0010011=>1101100
[8,6,1,2,3,5,4,7]=>1100010=>0100011=>1011100
[8,7,1,2,3,4,6,5]=>1100001=>1000011=>0111100
[8,5,1,4,2,3,6,7]=>1101000=>0001011=>1110100
[8,6,1,2,5,3,4,7]=>1100100=>0010011=>1101100
[8,7,1,2,3,6,4,5]=>1100010=>0100011=>1011100
[8,6,1,2,5,4,3,7]=>1100110=>0110011=>1001100
[2,5,8,6,1,7,3,4]=>0011010=>0101100=>1010011
[4,5,6,8,7,2,1,3]=>0001110=>0111000=>1000111
[5,6,8,7,2,3,1,4]=>0011010=>0101100=>1010011
[4,5,7,6,2,8,1,3]=>0011010=>0101100=>1010011
[4,8,2,5,6,1,3,7]=>0100100=>0010010=>1101101
[5,2,3,6,7,8,1,4]=>1000010=>0100001=>1011110
[4,2,8,7,5,3,1,6]=>1011110=>0111101=>1000010
[4,2,8,6,7,5,3,1]=>1010111=>1110101=>0001010
[1,3,2,4,8,5,7,6]=>0100101=>1010010=>0101101
[1,6,3,2,5,7,8,4]=>0110001=>1000110=>0111001
[2,5,6,1,8,7,3,4]=>0010110=>0110100=>1001011
[7,6,2,1,4,8,3,5]=>1110010=>0100111=>1011000
[2,6,5,1,8,7,3,4]=>0110110=>0110110=>1001001
[2,7,3,1,8,4,5,6]=>0110100=>0010110=>1101001
[1,4,2,7,3,8,6,5]=>0101011=>1101010=>0010101
[1,2,7,3,8,6,5,4]=>0010111=>1110100=>0001011
[3,1,8,4,6,2,7,5]=>1010101=>1010101=>0101010
[3,4,5,1,8,2,7,6]=>0010101=>1010100=>0101011
[3,8,1,6,5,2,7,4]=>0101101=>1011010=>0100101
[1,5,2,3,8,7,4,6]=>0100110=>0110010=>1001101
[2,8,7,6,3,1,4,5]=>0111100=>0011110=>1100001
[8,7,2,5,3,1,4,6]=>1101100=>0011011=>1100100
[7,6,2,3,4,8,1,5]=>1100010=>0100011=>1011100
[8,7,6,2,1,4,3,5]=>1111010=>0101111=>1010000
[8,2,7,4,1,5,3,6]=>1011010=>0101101=>1010010
[1,7,3,2,4,5,8,6]=>0110001=>1000110=>0111001
[1,3,8,6,2,4,7,5]=>0011001=>1001100=>0110011
[1,2,3,8,4,7,6,5]=>0001011=>1101000=>0010111
[1,6,2,3,7,5,8,4]=>0100101=>1010010=>0101101
[4,5,1,2,8,3,7,6]=>0100101=>1010010=>0101101
[1,4,8,2,6,3,7,5]=>0010101=>1010100=>0101011
[8,4,1,7,3,2,5,6]=>1101100=>0011011=>1100100
[1,8,7,3,2,4,6,5]=>0111001=>1001110=>0110001
[8,3,1,5,6,2,7,4]=>1100101=>1010011=>0101100
[3,4,1,6,5,7,2,8]=>0101010=>0101010=>1010101
[3,5,1,6,2,8,7,4]=>0101011=>1101010=>0010101
[5,4,3,6,1,7,2,8]=>1101010=>0101011=>1010100
[4,8,7,2,1,6,5,3]=>0111011=>1101110=>0010001
[6,2,1,8,7,5,4,3]=>1101111=>1111011=>0000100
[7,5,8,6,3,2,4,1]=>1011101=>1011101=>0100010
[5,8,7,6,3,2,4,1]=>0111101=>1011110=>0100001
[5,4,7,2,8,1,6,3]=>1010101=>1010101=>0101010
[8,1,5,4,6,3,7,2]=>1010101=>1010101=>0101010
[2,1,5,8,3,7,4,6]=>1001010=>0101001=>1010110
[2,1,7,4,8,3,6,5]=>1010101=>1010101=>0101010
[1,2,3,5,8,7,4,6]=>0000110=>0110000=>1001111
[6,1,2,7,8,4,3,5]=>1000110=>0110001=>1001110
[5,1,4,8,2,7,3,6]=>1001010=>0101001=>1010110
[3,4,1,2,8,7,5,6]=>0100110=>0110010=>1001101
[1,2,5,7,8,6,3,4]=>0000110=>0110000=>1001111
[2,1,3,4,8,5,7,6]=>1000101=>1010001=>0101110
[6,2,5,1,7,3,8,4]=>1010101=>1010101=>0101010
[1,5,4,8,6,2,7,3]=>0101101=>1011010=>0100101
[2,5,1,8,6,3,7,4]=>0101101=>1011010=>0100101
[2,1,3,7,4,8,6,5]=>1001011=>1101001=>0010110
[4,2,5,8,1,7,3,6]=>1001010=>0101001=>1010110
[2,6,8,5,1,7,3,4]=>0011010=>0101100=>1010011
[1,3,2,7,8,5,4,6]=>0100110=>0110010=>1001101
[7,1,2,3,6,8,4,5]=>1000010=>0100001=>1011110
[5,1,2,3,8,4,7,6]=>1000101=>1010001=>0101110
[3,4,5,1,8,7,2,6]=>0010110=>0110100=>1001011
[4,1,2,3,8,7,5,6]=>1000110=>0110001=>1001110
[2,3,1,8,5,4,7,6]=>0101101=>1011010=>0100101
[2,3,8,4,1,5,7,6]=>0011001=>1001100=>0110011
[5,3,1,8,7,2,4,6]=>1101100=>0011011=>1100100
[3,6,1,8,7,2,4,5]=>0101100=>0011010=>1100101
[1,3,8,4,2,7,6,5]=>0011011=>1101100=>0010011
[1,2,3,8,5,7,4,6]=>0001010=>0101000=>1010111
[6,1,7,2,5,8,3,4]=>1010010=>0100101=>1011010
[4,5,1,8,7,2,3,6]=>0101100=>0011010=>1100101
[1,4,2,8,5,3,7,6]=>0101101=>1011010=>0100101
[3,1,5,2,8,6,7,4]=>1010101=>1010101=>0101010
[7,8,6,5,2,1,4,3]=>0111101=>1011110=>0100001
[8,6,7,5,2,1,4,3]=>1011101=>1011101=>0100010
[6,7,8,2,1,5,4,3]=>0011011=>1101100=>0010011
[8,7,5,6,2,1,4,3]=>1101101=>1011011=>0100100
[3,2,8,5,6,7,1,4]=>1010010=>0100101=>1011010
[4,2,5,1,8,7,3,6]=>1010110=>0110101=>1001010
[5,2,7,8,6,3,1,4]=>1001110=>0111001=>1000110
[4,2,6,1,5,8,3,7]=>1010010=>0100101=>1011010
[7,2,4,5,8,3,6,1]=>1000101=>1010001=>0101110
[2,4,7,8,6,1,5,3]=>0001101=>1011000=>0100111
[4,2,7,1,5,6,8,3]=>1010001=>1000101=>0111010
[3,2,5,8,1,6,7,4]=>1001001=>1001001=>0110110
[8,1,4,3,2,5,6,7]=>1011000=>0001101=>1110010
[1,7,3,2,4,5,6,8]=>0110000=>0000110=>1111001
[1,6,3,2,4,5,7,8]=>0110000=>0000110=>1111001
[1,3,8,4,2,5,6,7]=>0011000=>0001100=>1110011
[6,2,5,1,8,3,4,7]=>1010100=>0010101=>1101010
[5,1,8,2,4,3,6,7]=>1010100=>0010101=>1101010
[8,2,3,1,5,6,7,4]=>1010001=>1000101=>0111010
[1,7,2,4,5,8,6,3]=>0100011=>1100010=>0011101
[1,5,7,8,4,6,2,3]=>0001010=>0101000=>1010111
[6,5,8,3,4,2,1,7]=>1010110=>0110101=>1001010
[6,5,8,2,3,4,1,7]=>1010010=>0100101=>1011010
[3,2,5,4,7,6,9,8,1,10]=>101010110=>011010101=>100101010
[1,4,3,6,5,8,7,10,9,2]=>010101011=>110101010=>001010101
[3,2,5,4,7,6,9,8,11,10,1,12]=>10101010110=>01101010101=>10010101010
[1,4,3,6,5,8,7,10,9,12,11,2]=>01010101011=>11010101010=>00101010101
[4,2,1,3,5,8,6,7]=>1100010=>0100011=>1011100
[1,3,8,2,6,4,5,7]=>0010100=>0010100=>1101011
[6,1,2,7,4,3,8,5]=>1001101=>1011001=>0100110
[5,4,1,2,3,8,6,7]=>1100010=>0100011=>1011100
[7,6,8,5,2,4,1,3]=>1011010=>0101101=>1010010
[6,7,8,5,2,4,1,3]=>0011010=>0101100=>1010011
[3,4,5,8,2,1,7,6]=>0001101=>1011000=>0100111
[3,4,6,2,7,1,5,8]=>0010100=>0010100=>1101011
[3,4,6,2,8,1,7,5]=>0010101=>1010100=>0101011
[3,4,6,8,1,5,7,2]=>0001001=>1001000=>0110111
[3,4,6,1,5,2,7,8]=>0010100=>0010100=>1101011
[3,4,7,2,1,6,5,8]=>0011010=>0101100=>1010011
[3,4,7,1,5,6,2,8]=>0010010=>0100100=>1011011
[3,5,2,6,1,4,7,8]=>0101000=>0001010=>1110101
[3,5,2,7,1,6,4,8]=>0101010=>0101010=>1010101
[3,5,6,4,8,2,1,7]=>0010110=>0110100=>1001011
[3,5,6,4,1,2,7,8]=>0011000=>0001100=>1110011
[3,5,6,8,4,2,1,7]=>0001110=>0111000=>1000111
[3,5,6,8,1,2,7,4]=>0001001=>1001000=>0110111
[3,5,6,1,4,2,7,8]=>0010100=>0010100=>1101011
[3,5,7,4,2,8,1,6]=>0011010=>0101100=>1010011
[3,5,7,4,2,1,6,8]=>0011100=>0011100=>1100011
[3,5,7,4,8,1,6,2]=>0010101=>1010100=>0101011
[3,5,7,8,1,6,2,4]=>0001010=>0101000=>1010111
[3,5,7,1,4,6,2,8]=>0010010=>0100100=>1011011
[3,5,8,4,2,6,1,7]=>0011010=>0101100=>1010011
[3,5,8,1,4,6,7,2]=>0010001=>1000100=>0111011
[3,6,2,4,8,1,7,5]=>0100101=>1010010=>0101101
[3,6,2,7,8,5,1,4]=>0100110=>0110010=>1001101
[3,6,2,7,8,1,4,5]=>0100100=>0010010=>1101101
[3,6,2,1,5,4,7,8]=>0110100=>0010110=>1101001
[3,6,7,8,5,1,2,4]=>0001100=>0011000=>1100111
[3,6,7,8,1,5,2,4]=>0001010=>0101000=>1010111
[3,7,2,4,5,8,1,6]=>0100010=>0100010=>1011101
[3,7,2,4,8,1,6,5]=>0100101=>1010010=>0101101
[3,7,2,4,1,6,5,8]=>0101010=>0101010=>1010101
[3,7,2,8,5,6,1,4]=>0101010=>0101010=>1010101
[3,7,8,4,5,1,6,2]=>0010101=>1010100=>0101011
[3,7,8,4,1,6,5,2]=>0011011=>1101100=>0010011
[3,8,2,4,1,6,7,5]=>0101001=>1001010=>0110101
[3,8,2,1,5,6,7,4]=>0110001=>1000110=>0111001
[8,1,5,4,3,6,7,2]=>1011001=>1001101=>0110010
[8,1,4,5,3,6,7,2]=>1001001=>1001001=>0110110
[4,1,6,3,5,7,8,2]=>1010001=>1000101=>0111010
[4,1,7,3,5,6,8,2]=>1010001=>1000101=>0111010
[4,1,3,6,7,8,5,2]=>1000011=>1100001=>0011110
[4,6,2,3,5,1,7,8]=>0100100=>0010010=>1101101
[3,5,2,4,1,6,7,8]=>0101000=>0001010=>1110101
[5,8,2,3,4,6,1,7]=>0100010=>0100010=>1011101
[4,7,2,3,5,1,6,8]=>0100100=>0010010=>1101101
[5,7,2,3,4,6,8,1]=>0100001=>1000010=>0111101
[4,6,2,3,5,7,1,8]=>0100010=>0100010=>1011101
[2,3,7,8,1,6,5,4]=>0001011=>1101000=>0010111
[2,7,6,1,4,8,3,5]=>0110010=>0100110=>1011001
[2,6,8,1,4,5,7,3]=>0010001=>1000100=>0111011
[2,6,5,8,1,3,7,4]=>0101001=>1001010=>0110101
[6,4,7,5,8,2,3,1]=>1010101=>1010101=>0101010
[6,7,4,1,8,2,3,5]=>0110100=>0010110=>1101001
[6,7,8,1,4,2,5,3]=>0010101=>1010100=>0101011
[5,2,6,1,4,8,3,7]=>1010010=>0100101=>1011010
[7,2,3,5,8,1,4,6]=>1000100=>0010001=>1101110
[2,4,7,5,8,1,3,6]=>0010100=>0010100=>1101011
[2,3,6,5,1,8,7,4]=>0011011=>1101100=>0010011
[2,3,4,8,1,5,7,6]=>0001001=>1001000=>0110111
[2,3,4,7,8,1,6,5]=>0000101=>1010000=>0101111
[2,7,8,5,1,4,6,3]=>0011001=>1001100=>0110011
[2,3,7,5,8,1,4,6]=>0010100=>0010100=>1101011
[2,3,6,8,5,1,7,4]=>0001101=>1011000=>0100111
[7,6,4,5,1,8,2,3]=>1101010=>0101011=>1010100
[7,4,6,8,1,5,2,3]=>1001010=>0101001=>1010110
[2,7,4,6,5,8,3,1]=>0101011=>1101010=>0010101
[2,6,7,8,5,3,1,4]=>0001110=>0111000=>1000111
[2,5,6,1,4,8,3,7]=>0010010=>0100100=>1011011
[2,6,4,8,5,7,3,1]=>0101011=>1101010=>0010101
[2,5,8,1,4,6,7,3]=>0010001=>1000100=>0111011
[7,2,3,4,8,1,6,5]=>1000101=>1010001=>0101110
[3,2,5,7,8,1,6,4]=>1000101=>1010001=>0101110
[6,4,1,7,8,2,3,5]=>1100100=>0010011=>1101100
[5,7,1,6,2,8,4,3]=>0101011=>1101010=>0010101
[5,6,1,8,2,3,7,4]=>0101001=>1001010=>0110101
[7,3,5,1,6,8,4,2]=>1010011=>1100101=>0011010
[6,3,4,5,8,2,1,7]=>1000110=>0110001=>1001110
[5,7,6,1,2,8,3,4]=>0110010=>0100110=>1011001
[5,6,8,1,2,4,7,3]=>0010001=>1000100=>0111011
[6,2,3,4,5,8,1,7]=>1000010=>0100001=>1011110
[4,7,1,3,8,2,6,5]=>0100101=>1010010=>0101101
[5,4,1,6,7,8,2,3]=>1100010=>0100011=>1011100
[7,4,1,5,8,2,6,3]=>1100101=>1010011=>0101100
[5,7,1,8,6,2,3,4]=>0101100=>0011010=>1100101
[7,3,5,1,8,2,6,4]=>1010101=>1010101=>0101010
[4,8,1,3,5,6,7,2]=>0100001=>1000010=>0111101
[8,1,2,3,7,5,6,4]=>1000101=>1010001=>0101110
[2,1,8,3,7,5,6,4]=>1010101=>1010101=>0101010
[5,6,7,3,8,2,1,4]=>0010110=>0110100=>1001011
[5,6,8,3,1,2,7,4]=>0011001=>1001100=>0110011
[5,7,3,2,8,6,1,4]=>0110110=>0110110=>1001001
[5,7,8,3,1,6,2,4]=>0011010=>0101100=>1010011
[5,8,3,2,1,6,7,4]=>0111001=>1001110=>0110001
[6,2,7,3,8,5,1,4]=>1010110=>0110101=>1001010
[6,2,3,7,8,5,1,4]=>1000110=>0110001=>1001110
[6,7,3,2,8,5,1,4]=>0110110=>0110110=>1001001
[6,7,8,3,5,1,2,4]=>0010100=>0010100=>1101011
[1,5,6,7,8,3,2,4]=>0000110=>0110000=>1001111
[1,5,8,3,2,6,7,4]=>0011001=>1001100=>0110011
[1,6,8,3,5,2,7,4]=>0010101=>1010100=>0101011
[1,7,3,2,8,6,5,4]=>0110111=>1110110=>0001001
[1,7,8,3,5,6,2,4]=>0010010=>0100100=>1011011
[1,6,7,8,4,2,3,5]=>0001100=>0011000=>1100111
[1,2,6,8,4,3,7,5]=>0001101=>1011000=>0100111
[1,8,3,4,2,6,7,5]=>0101001=>1001010=>0110101
[1,2,8,4,3,6,7,5]=>0011001=>1001100=>0110011
[6,2,7,8,4,1,3,5]=>1001100=>0011001=>1100110
[6,2,3,7,8,1,4,5]=>1000100=>0010001=>1101110
[4,5,7,1,8,6,2,3]=>0010110=>0110100=>1001011
[4,5,7,8,2,6,1,3]=>0001010=>0101000=>1010111
[4,6,2,8,5,1,7,3]=>0101101=>1011010=>0100101
[4,6,7,1,8,5,2,3]=>0010110=>0110100=>1001011
[4,7,2,8,5,6,1,3]=>0101010=>0101010=>1010101
[4,8,2,1,5,6,7,3]=>0110001=>1000110=>0111001
[1,2,8,4,5,3,7,6]=>0010101=>1010100=>0101011
[1,2,3,8,5,4,7,6]=>0001101=>1011000=>0100111
[1,7,3,8,5,4,2,6]=>0101110=>0111010=>1000101
[5,2,7,4,8,6,1,3]=>1010110=>0110101=>1001010
[5,2,7,8,4,6,1,3]=>1001010=>0101001=>1010110
[7,2,3,8,5,4,1,6]=>1001110=>0111001=>1000110
[5,6,2,7,8,1,4,3]=>0100101=>1010010=>0101101
[5,8,2,4,1,6,7,3]=>0101001=>1001010=>0110101
[6,2,1,7,8,5,4,3]=>1100111=>1110011=>0001100
[6,7,2,4,8,5,1,3]=>0100110=>0110010=>1001101
[6,7,2,8,5,4,1,3]=>0101110=>0111010=>1000101
[6,8,2,4,5,1,7,3]=>0100101=>1010010=>0101101
[3,2,5,6,8,1,4,7]=>1000100=>0010001=>1101110
[8,1,2,3,7,5,4,6]=>1000110=>0110001=>1001110
[4,1,8,2,7,5,3,6]=>1010110=>0110101=>1001010
[7,1,8,3,4,5,2,6]=>1010010=>0100101=>1011010
[7,1,6,3,8,2,4,5]=>1010100=>0010101=>1101010
[6,1,5,8,2,3,4,7]=>1001000=>0001001=>1110110
[8,1,6,7,4,2,3,5]=>1001100=>0011001=>1100110
[6,1,5,8,2,3,7,4]=>1001001=>1001001=>0110110
[4,1,7,2,5,8,3,6]=>1010010=>0100101=>1011010
[8,1,6,3,4,7,2,5]=>1010010=>0100101=>1011010
[7,1,6,8,2,5,3,4]=>1001010=>0101001=>1010110
[4,1,8,2,5,6,3,7]=>1010010=>0100101=>1011010
[4,1,8,2,5,6,7,3]=>1010001=>1000101=>0111010
[3,8,1,2,7,5,4,6]=>0100110=>0110010=>1001101
[3,8,1,7,4,5,2,6]=>0101010=>0101010=>1010101
[5,4,7,1,2,8,3,6]=>1010010=>0100101=>1011010
[8,4,7,1,3,2,6,5]=>1010101=>1010101=>0101010
[8,5,7,3,1,2,6,4]=>1011001=>1001101=>0110010
[3,8,1,2,4,5,7,6]=>0100001=>1000010=>0111101
[7,6,2,1,8,4,3,5]=>1110110=>0110111=>1001000
[8,5,2,3,6,1,4,7]=>1100100=>0010011=>1101100
[8,5,7,1,4,3,2,6]=>1010110=>0110101=>1001010
[3,6,1,4,2,8,5,7]=>0101010=>0101010=>1010101
[7,6,8,1,4,5,2,3]=>1010010=>0100101=>1011010
[3,7,1,4,2,8,6,5]=>0101011=>1101010=>0010101
[5,4,3,8,2,1,7,6]=>1101101=>1011011=>0100100
[5,8,7,3,2,1,6,4]=>0111101=>1011110=>0100001
[2,3,7,1,6,8,5,4]=>0010011=>1100100=>0011011
[2,6,1,5,7,4,8,3]=>0100101=>1010010=>0101101
[2,3,6,1,8,4,7,5]=>0010101=>1010100=>0101011
[3,5,1,4,6,7,8,2]=>0100001=>1000010=>0111101
[4,5,6,2,1,7,8,3]=>0011001=>1001100=>0110011
[5,2,4,7,6,3,8,1]=>1001101=>1011001=>0100110
[8,7,6,1,4,3,5,2]=>1110101=>1010111=>0101000
[8,7,6,1,3,4,5,2]=>1110001=>1000111=>0111000
[8,7,1,4,5,6,3,2]=>1100011=>1100011=>0011100
[8,1,5,6,7,4,3,2]=>1000111=>1110001=>0001110
[5,8,3,4,1,6,2,7]=>0101010=>0101010=>1010101
[4,2,6,1,7,8,5,3]=>1010011=>1100101=>0011010
[1,5,2,6,7,8,4,3]=>0100011=>1100010=>0011101
[4,5,2,7,8,6,1,3]=>0100110=>0110010=>1001101
[1,5,6,7,4,8,2,3]=>0001010=>0101000=>1010111
[4,2,6,8,5,1,7,3]=>1001101=>1011001=>0100110
[4,2,7,8,5,6,1,3]=>1001010=>0101001=>1010110
[3,5,2,7,4,6,8,1]=>0101001=>1001010=>0110101
[5,6,2,7,3,8,4,1]=>0101011=>1101010=>0010101
[3,5,2,8,4,6,7,1]=>0101001=>1001010=>0110101
[3,7,2,8,4,1,5,6]=>0101100=>0011010=>1100101
[3,5,2,4,7,8,6,1]=>0100011=>1100010=>0011101
[3,7,1,5,8,2,4,6]=>0100100=>0010010=>1101101
[5,1,3,8,2,4,6,7]=>1001000=>0001001=>1110110
[4,2,1,3,8,5,6,7]=>1100100=>0010011=>1101100
[1,8,7,6,3,4,5,2]=>0111001=>1001110=>0110001
[8,5,7,6,3,1,4,2]=>1011101=>1011101=>0100010
[8,5,7,6,3,2,1,4]=>1011110=>0111101=>1000010
[8,7,5,3,1,6,4,2]=>1111011=>1101111=>0010000
[4,2,8,3,1,6,7,5]=>1011001=>1001101=>0110010
[7,8,1,4,5,6,3,2]=>0100011=>1100010=>0011101
[4,2,8,3,5,1,7,6]=>1010101=>1010101=>0101010
[4,2,7,8,1,6,5,3]=>1001011=>1101001=>0010110
[6,8,1,4,5,3,7,2]=>0100101=>1010010=>0101101
[5,1,3,4,2,6,7,8]=>1001000=>0001001=>1110110
[4,2,7,3,1,6,5,8]=>1011010=>0101101=>1010010
[2,3,4,5,8,1,7,6]=>0000101=>1010000=>0101111
[4,1,5,3,6,7,8,2]=>1010001=>1000101=>0111010
[2,3,4,8,1,6,7,5]=>0001001=>1001000=>0110111
[5,1,4,6,3,7,8,2]=>1001001=>1001001=>0110110
[5,1,6,3,4,7,8,2]=>1010001=>1000101=>0111010
[2,1,7,5,3,8,6,4]=>1011011=>1101101=>0010010
[2,1,8,7,5,3,6,4]=>1011101=>1011101=>0100010
[7,5,3,2,1,8,6,4]=>1111011=>1101111=>0010000
[5,2,3,4,1,8,6,7]=>1001010=>0101001=>1010110
[3,8,1,2,5,4,7,6]=>0100101=>1010010=>0101101
[7,4,6,8,5,3,2,1]=>1001111=>1111001=>0000110
[7,5,8,6,3,2,1,4]=>1011110=>0111101=>1000010
[7,4,8,5,6,3,2,1]=>1010111=>1110101=>0001010
[7,5,8,6,4,2,1,3]=>1011110=>0111101=>1000010
[6,4,2,1,8,5,3,7]=>1110110=>0110111=>1001000
[5,3,8,7,4,2,1,6]=>1011110=>0111101=>1000010
[7,4,2,1,6,8,5,3]=>1110011=>1100111=>0011000
[5,3,8,4,2,1,6,7]=>1011100=>0011101=>1100010
[8,6,3,5,7,4,2,1]=>1100111=>1110011=>0001100
[6,3,5,8,4,2,1,7]=>1001110=>0111001=>1000110
[6,4,8,7,5,2,1,3]=>1011110=>0111101=>1000010
[7,5,2,1,3,8,6,4]=>1110011=>1100111=>0011000
[6,3,8,7,4,5,2,1]=>1011011=>1101101=>0010010
[7,4,5,2,1,8,6,3]=>1011011=>1101101=>0010010
[8,5,2,1,7,4,6,3]=>1110101=>1010111=>0101000
[6,3,8,4,5,2,1,7]=>1010110=>0110101=>1001010
[7,3,6,8,4,5,2,1]=>1001011=>1101001=>0010110
[7,3,4,5,8,6,2,1]=>1000111=>1110001=>0001110
[7,3,8,4,5,6,2,1]=>1010011=>1100101=>0011010
[1,8,7,2,6,5,4,3]=>0110111=>1110110=>0001001
[1,8,7,6,2,3,4,5]=>0111000=>0001110=>1110001
[1,8,2,5,7,6,4,3]=>0100111=>1110010=>0001101
[1,8,2,5,6,7,4,3]=>0100011=>1100010=>0011101
[1,2,8,3,4,5,7,6]=>0010001=>1000100=>0111011
[7,6,1,2,3,8,4,5]=>1100010=>0100011=>1011100
[1,6,2,3,4,8,7,5]=>0100011=>1100010=>0011101
[6,4,1,2,8,3,5,7]=>1100100=>0010011=>1101100
[4,8,1,2,3,7,5,6]=>0100010=>0100010=>1011101
[6,4,1,7,2,3,8,5]=>1101001=>1001011=>0110100
[7,1,6,2,3,8,4,5]=>1010010=>0100101=>1011010
[6,5,1,2,3,8,4,7]=>1100010=>0100011=>1011100
[1,8,5,2,3,7,4,6]=>0110010=>0100110=>1011001
[6,5,1,2,7,3,8,4]=>1100101=>1010011=>0101100
[7,6,4,1,8,2,3,5]=>1110100=>0010111=>1101000
[1,5,2,3,6,8,7,4]=>0100011=>1100010=>0011101
[7,3,1,2,8,4,5,6]=>1100100=>0010011=>1101100
[7,6,3,1,8,2,4,5]=>1110100=>0010111=>1101000
[5,3,6,1,2,4,8,7]=>1010001=>1000101=>0111010
[5,8,3,1,7,2,4,6]=>0110100=>0010110=>1101001
[7,5,4,1,8,2,3,6]=>1110100=>0010111=>1101000
[7,6,1,4,8,2,3,5]=>1100100=>0010011=>1101100
[1,2,8,5,3,7,4,6]=>0011010=>0101100=>1010011
[1,2,7,3,8,6,4,5]=>0010110=>0110100=>1001011
[7,5,1,6,8,2,3,4]=>1100100=>0010011=>1101100
[4,1,2,8,6,3,7,5]=>1001101=>1011001=>0100110
[6,3,4,1,7,2,8,5]=>1010101=>1010101=>0101010
[6,5,3,1,8,2,4,7]=>1110100=>0010111=>1101000
[3,8,1,6,7,2,4,5]=>0100100=>0010010=>1101101
[6,5,3,7,1,2,8,4]=>1101001=>1001011=>0110100
[7,1,4,2,8,5,3,6]=>1010110=>0110101=>1001010
[1,2,6,8,3,5,4,7]=>0001010=>0101000=>1010111
[1,2,3,7,8,6,4,5]=>0000110=>0110000=>1001111
[1,6,8,5,2,7,3,4]=>0011010=>0101100=>1010011
[7,6,3,4,1,8,2,5]=>1101010=>0101011=>1010100
[1,4,8,2,3,7,6,5]=>0010011=>1100100=>0011011
[1,2,8,3,5,7,6,4]=>0010011=>1100100=>0011011
[4,5,1,7,6,8,2,3]=>0101010=>0101010=>1010101
[3,4,8,1,2,6,7,5]=>0010001=>1000100=>0111011
[3,1,8,2,5,6,7,4]=>1010001=>1000101=>0111010
[1,4,2,5,6,8,7,3]=>0100011=>1100010=>0011101
[4,5,6,3,7,1,8,2]=>0010101=>1010100=>0101011
[4,2,5,6,7,8,3,1]=>1000011=>1100001=>0011110
[8,2,7,3,1,5,6,4]=>1011001=>1001101=>0110010
[7,2,1,8,4,5,6,3]=>1101001=>1001011=>0110100
[4,2,7,1,3,8,6,5]=>1010011=>1100101=>0011010
[8,2,6,3,4,7,1,5]=>1010010=>0100101=>1011010
[7,2,3,4,1,8,6,5]=>1001011=>1101001=>0010110
[6,1,8,2,7,5,3,4]=>1010110=>0110101=>1001010
[4,2,8,1,5,6,3,7]=>1010010=>0100101=>1011010
[8,2,7,3,1,4,5,6]=>1011000=>0001101=>1110010
[5,2,1,3,6,7,8,4]=>1100001=>1000011=>0111100
[6,4,8,7,3,2,1,5]=>1011110=>0111101=>1000010
[6,5,3,8,7,2,1,4]=>1101110=>0111011=>1000100
[5,4,8,7,3,2,1,6]=>1011110=>0111101=>1000010
[6,4,3,8,7,2,1,5]=>1101110=>0111011=>1000100
[6,3,8,7,5,2,1,4]=>1011110=>0111101=>1000010
[5,6,8,1,4,2,7,3]=>0010101=>1010100=>0101011
[5,6,3,1,4,2,7,8]=>0110100=>0010110=>1101001
[5,7,3,8,4,1,6,2]=>0101101=>1011010=>0100101
[5,7,3,1,4,6,2,8]=>0110010=>0100110=>1011001
[5,7,3,4,8,1,6,2]=>0100101=>1010010=>0101101
[5,2,6,1,4,3,7,8]=>1010100=>0010101=>1101010
[5,8,3,1,4,6,7,2]=>0110001=>1000110=>0111001
[6,2,7,4,1,5,3,8]=>1011010=>0101101=>1010010
[6,7,3,8,1,5,2,4]=>0101010=>0101010=>1010101
[6,7,3,4,1,5,2,8]=>0101010=>0101010=>1010101
[6,7,8,1,5,4,2,3]=>0010110=>0110100=>1001011
[4,5,6,7,1,3,2,8]=>0001010=>0101000=>1010111
[6,7,1,4,5,3,2,8]=>0100110=>0110010=>1001101
[4,5,7,8,2,1,6,3]=>0001101=>1011000=>0100111
[7,2,3,8,1,6,5,4]=>1001011=>1101001=>0010110
[7,2,3,8,5,1,6,4]=>1001101=>1011001=>0100110
[7,2,3,1,5,6,4,8]=>1010010=>0100101=>1011010
[7,2,8,4,1,6,5,3]=>1011011=>1101101=>0010010
[7,2,8,4,5,1,6,3]=>1010101=>1010101=>0101010
[4,6,3,8,1,5,7,2]=>0101001=>1001010=>0110101
[7,8,3,4,1,6,5,2]=>0101011=>1101010=>0010101
[4,6,7,3,8,1,2,5]=>0010100=>0010100=>1101011
[4,6,7,8,1,5,3,2]=>0001011=>1101000=>0010111
[4,6,7,1,5,2,3,8]=>0010100=>0010100=>1101011
[4,6,8,3,1,5,7,2]=>0011001=>1001100=>0110011
[4,6,1,3,5,2,7,8]=>0100100=>0010010=>1101101
[4,7,3,8,5,1,6,2]=>0101101=>1011010=>0100101
[4,7,3,8,1,6,5,2]=>0101011=>1101010=>0010101
[1,7,2,3,4,6,8,5]=>0100001=>1000010=>0111101
[8,1,2,3,5,6,4,7]=>1000010=>0100001=>1011110
[4,1,8,2,7,3,5,6]=>1010100=>0010101=>1101010
[1,8,4,2,7,3,5,6]=>0110100=>0010110=>1101001
[7,4,1,2,6,8,3,5]=>1100010=>0100011=>1011100
[8,7,1,2,4,5,3,6]=>1100010=>0100011=>1011100
[4,1,8,2,3,5,7,6]=>1010001=>1000101=>0111010
[6,1,2,8,3,4,7,5]=>1001001=>1001001=>0110110
[5,4,1,2,7,8,3,6]=>1100010=>0100011=>1011100
[1,5,2,8,3,4,7,6]=>0101001=>1001010=>0110101
[7,1,2,5,3,6,8,4]=>1001001=>1001001=>0110110
[1,8,2,5,6,3,7,4]=>0100101=>1010010=>0101101
[1,5,2,4,6,7,8,3]=>0100001=>1000010=>0111101
[6,8,1,3,4,2,5,7]=>0100100=>0010010=>1101101
[3,1,8,2,5,4,6,7]=>1010100=>0010101=>1101010
[3,1,7,5,8,2,4,6]=>1010100=>0010101=>1101010
[1,7,3,2,8,4,5,6]=>0110100=>0010110=>1101001
[6,3,5,1,8,2,4,7]=>1010100=>0010101=>1101010
[1,6,4,2,3,5,8,7]=>0110001=>1000110=>0111001
[1,7,4,2,3,5,8,6]=>0110001=>1000110=>0111001
[1,7,4,2,3,6,8,5]=>0110001=>1000110=>0111001
[1,2,7,3,8,4,6,5]=>0010101=>1010100=>0101011
[7,1,3,4,5,8,2,6]=>1000010=>0100001=>1011110
[7,6,1,3,4,8,2,5]=>1100010=>0100011=>1011100
[1,8,7,6,3,2,4,5]=>0111100=>0011110=>1100001
[1,8,2,7,5,3,6,4]=>0101101=>1011010=>0100101
[1,7,4,5,2,6,8,3]=>0101001=>1001010=>0110101
[1,4,8,5,6,2,7,3]=>0010101=>1010100=>0101011
[3,2,1,8,7,6,4,5]=>1101110=>0111011=>1000100
[3,2,1,8,7,5,4,6]=>1101110=>0111011=>1000100
[3,2,1,8,7,4,6,5]=>1101101=>1011011=>0100100
[3,2,1,8,7,4,5,6]=>1101100=>0011011=>1100100
[3,2,1,8,4,7,6,5]=>1101011=>1101011=>0010100
[3,2,8,7,6,1,5,4]=>1011101=>1011101=>0100010
[5,3,8,7,6,2,1,4]=>1011110=>0111101=>1000010
[6,5,8,7,3,2,1,4]=>1011110=>0111101=>1000010
[7,4,8,5,6,3,1,2]=>1010110=>0110101=>1001010
[4,5,3,8,6,2,7,1]=>0101101=>1011010=>0100101
[4,6,2,8,5,3,7,1]=>0101101=>1011010=>0100101
[5,3,8,4,6,2,7,1]=>1010101=>1010101=>0101010
[4,6,2,7,1,8,5,3]=>0101011=>1101010=>0010101
[4,7,1,6,2,8,5,3]=>0101011=>1101010=>0010101
[6,2,5,3,8,4,7,1]=>1010101=>1010101=>0101010
[4,6,5,3,8,2,7,1]=>0110101=>1010110=>0101001
[6,3,7,4,5,2,8,1]=>1010101=>1010101=>0101010
[5,7,8,4,3,2,1,6]=>0011110=>0111100=>1000011
[4,6,8,7,3,2,1,5]=>0011110=>0111100=>1000011
[2,4,8,7,6,5,1,3]=>0011110=>0111100=>1000011
[4,7,6,8,3,2,1,5]=>0101110=>0111010=>1000101
[3,6,8,5,7,2,1,4]=>0010110=>0110100=>1001011
[4,6,7,8,3,2,1,5]=>0001110=>0111000=>1000111
[3,5,6,8,7,2,1,4]=>0001110=>0111000=>1000111
[1,4,8,7,6,3,5,2]=>0011101=>1011100=>0100011
[2,4,5,8,7,6,1,3]=>0001110=>0111000=>1000111
[2,5,4,7,3,8,1,6]=>0101010=>0101010=>1010101
[2,6,4,7,8,3,1,5]=>0100110=>0110010=>1001101
[2,4,7,1,8,3,6,5]=>0010101=>1010100=>0101011
[2,4,6,1,5,8,3,7]=>0010010=>0100100=>1011011
[3,4,1,7,6,8,5,2]=>0101011=>1101010=>0010101
[3,6,1,7,8,4,2,5]=>0100110=>0110010=>1001101
[3,5,1,7,2,6,8,4]=>0101001=>1001010=>0110101
[4,3,6,2,8,1,7,5]=>1010101=>1010101=>0101010
[5,3,4,7,2,8,1,6]=>1001010=>0101001=>1010110
[4,5,7,2,1,8,3,6]=>0011010=>0101100=>1010011
[4,5,7,2,1,6,8,3]=>0011001=>1001100=>0110011
[4,6,5,2,8,7,3,1]=>0110111=>1110110=>0001001
[4,5,8,2,1,6,7,3]=>0011001=>1001100=>0110011
[3,4,1,5,6,8,7,2]=>0100011=>1100010=>0011101
[3,6,1,7,2,5,8,4]=>0101001=>1001010=>0110101
[7,3,4,5,8,2,1,6]=>1000110=>0110001=>1001110
[6,3,7,8,2,5,1,4]=>1001010=>0101001=>1010110
[6,7,4,8,2,5,3,1]=>0101011=>1101010=>0010101
[3,5,1,4,7,2,8,6]=>0100101=>1010010=>0101101
[4,3,7,5,6,2,8,1]=>1010101=>1010101=>0101010
[7,3,4,8,6,2,5,1]=>1001101=>1011001=>0100110
[4,7,8,5,6,2,1,3]=>0010110=>0110100=>1001011
[3,5,1,4,8,7,2,6]=>0100110=>0110010=>1001101
[4,5,6,3,8,2,1,7]=>0010110=>0110100=>1001011
[4,2,6,3,7,8,1,5]=>1010010=>0100101=>1011010
[4,2,7,3,5,8,1,6]=>1010010=>0100101=>1011010
[4,5,3,7,8,1,6,2]=>0100101=>1010010=>0101101
[4,2,6,8,5,3,1,7]=>1001110=>0111001=>1000110
[5,1,2,7,8,6,4,3]=>1000111=>1110001=>0001110
[4,1,2,7,8,6,3,5]=>1000110=>0110001=>1001110
[4,1,8,7,2,6,3,5]=>1011010=>0101101=>1010010
[4,1,5,8,7,3,2,6]=>1001110=>0111001=>1000110
[5,1,8,2,7,6,3,4]=>1010110=>0110101=>1001010
[7,1,6,2,8,3,4,5]=>1010100=>0010101=>1101010
[4,7,8,3,2,5,1,6]=>0011010=>0101100=>1010011
[4,5,2,8,7,3,1,6]=>0101110=>0111010=>1000101
[4,5,7,6,8,3,1,2]=>0010110=>0110100=>1001011
[8,2,1,7,4,6,3,5]=>1101010=>0101011=>1010100
[5,2,1,6,8,4,7,3]=>1100101=>1010011=>0101100
[4,5,2,8,7,1,6,3]=>0101101=>1011010=>0100101
[5,2,7,6,8,3,4,1]=>1010101=>1010101=>0101010
[4,2,5,7,3,1,8,6]=>1001101=>1011001=>0100110
[4,2,8,7,1,3,6,5]=>1011001=>1001101=>0110010
[8,2,1,7,3,5,4,6]=>1101010=>0101011=>1010100
[5,2,6,3,8,7,1,4]=>1010110=>0110101=>1001010
[5,2,8,6,4,1,7,3]=>1011101=>1011101=>0100010
[5,2,3,8,7,1,4,6]=>1001100=>0011001=>1100110
[5,1,8,3,7,4,2,6]=>1010110=>0110101=>1001010
[8,1,2,7,5,4,3,6]=>1001110=>0111001=>1000110
[6,1,2,8,3,7,4,5]=>1001010=>0101001=>1010110
[5,6,7,3,8,1,2,4]=>0010100=>0010100=>1101011
[4,1,7,6,8,3,2,5]=>1010110=>0110101=>1001010
[8,1,7,3,5,4,2,6]=>1010110=>0110101=>1001010
[7,1,6,3,4,2,8,5]=>1010101=>1010101=>0101010
[7,1,6,8,5,2,3,4]=>1001100=>0011001=>1100110
[8,1,7,3,5,2,6,4]=>1010101=>1010101=>0101010
[6,2,3,8,7,5,1,4]=>1001110=>0111001=>1000110
[3,8,5,7,2,4,1,6]=>0101010=>0101010=>1010101
[3,6,5,8,2,1,7,4]=>0101101=>1011010=>0100101
[4,7,1,8,3,5,2,6]=>0101010=>0101010=>1010101
[7,6,2,3,4,1,8,5]=>1100101=>1010011=>0101100
[4,8,6,7,1,2,3,5]=>0101000=>0001010=>1110101
[8,5,7,3,1,6,2,4]=>1011010=>0101101=>1010010
[3,4,7,2,1,5,8,6]=>0011001=>1001100=>0110011
[3,8,6,1,4,7,2,5]=>0110010=>0100110=>1011001
[3,7,6,8,2,5,1,4]=>0101010=>0101010=>1010101
[8,6,2,3,1,5,7,4]=>1101001=>1001011=>0110100
[3,8,7,1,2,5,6,4]=>0110001=>1000110=>0111001
[3,4,8,2,5,6,7,1]=>0010001=>1000100=>0111011
[4,2,1,3,7,6,5,8]=>1100110=>0110011=>1001100
[6,3,4,8,7,5,1,2]=>1001110=>0111001=>1000110
[8,3,5,7,6,1,4,2]=>1001101=>1011001=>0100110
[2,1,8,5,6,7,3,4]=>1010010=>0100101=>1011010
[6,8,4,5,7,2,3,1]=>0100101=>1010010=>0101101
[8,3,2,5,6,7,1,4]=>1100010=>0100011=>1011100
[7,3,2,6,8,5,4,1]=>1100111=>1110011=>0001100
[4,8,5,3,2,7,6,1]=>0111011=>1101110=>0010001
[7,3,5,6,8,1,4,2]=>1000101=>1010001=>0101110
[7,4,8,3,6,5,2,1]=>1010111=>1110101=>0001010
[7,5,6,3,8,4,2,1]=>1010111=>1110101=>0001010
[7,4,5,2,8,3,6,1]=>1010101=>1010101=>0101010
[4,8,6,7,3,5,2,1]=>0101011=>1101010=>0010101
[4,3,1,2,6,7,8,5]=>1100001=>1000011=>0111100
[7,4,6,5,8,3,2,1]=>1010111=>1110101=>0001010
[4,8,5,2,6,7,3,1]=>0110011=>1100110=>0011001
[2,5,8,6,7,3,1,4]=>0010110=>0110100=>1001011
[1,4,6,5,2,7,3,8]=>0011010=>0101100=>1010011
[3,7,4,8,6,2,5,1]=>0101101=>1011010=>0100101
[2,3,4,1,8,7,5,6]=>0010110=>0110100=>1001011
[4,2,6,5,1,8,7,3]=>1011011=>1101101=>0010010
[6,5,4,1,3,2,8,7]=>1110101=>1010111=>0101000
[6,5,4,2,1,3,8,7]=>1111001=>1001111=>0110000
[8,7,4,3,6,1,5,2]=>1110101=>1010111=>0101000
[7,8,4,2,1,5,6,3]=>0111001=>1001110=>0110001
[8,6,7,2,4,5,1,3]=>1010010=>0100101=>1011010
[7,8,2,3,6,1,5,4]=>0100101=>1010010=>0101101
[6,8,2,7,3,5,4,1]=>0101011=>1101010=>0010101
[2,1,7,8,4,5,6,3]=>1001001=>1001001=>0110110
[7,5,8,3,2,4,6,1]=>1011001=>1001101=>0110010
[8,6,7,3,4,1,5,2]=>1010101=>1010101=>0101010
[8,6,2,7,1,3,5,4]=>1101001=>1001011=>0110100
[8,3,2,7,6,4,1,5]=>1101110=>0111011=>1000100
[8,5,4,1,3,7,6,2]=>1110011=>1100111=>0011000
[5,8,2,3,4,7,6,1]=>0100011=>1100010=>0011101
[6,8,2,7,3,4,1,5]=>0101010=>0101010=>1010101
[5,6,1,4,7,2,3,8]=>0100100=>0010010=>1101101
[4,5,1,6,3,2,8,7]=>0101101=>1011010=>0100101
[3,6,7,4,1,2,5,8]=>0011000=>0001100=>1110011
[2,5,1,4,3,7,6,8]=>0101010=>0101010=>1010101
[1,4,5,3,7,2,8,6]=>0010101=>1010100=>0101011
[5,1,4,3,7,2,8,6]=>1010101=>1010101=>0101010
[1,6,7,4,3,2,8,5]=>0011101=>1011100=>0100011
[2,6,7,3,1,4,5,8]=>0011000=>0001100=>1110011
[5,1,4,6,7,2,3,8]=>1000100=>0010001=>1101110
[2,6,4,3,1,8,5,7]=>0111010=>0101110=>1010001
[1,6,5,2,3,4,8,7]=>0110001=>1000110=>0111001
[7,8,2,1,5,4,3,6]=>0110110=>0110110=>1001001
[7,8,1,2,3,6,4,5]=>0100010=>0100010=>1011101
[1,4,7,8,5,2,3,6]=>0001100=>0011000=>1100111
[1,3,2,6,5,8,4,7]=>0101010=>0101010=>1010101
[2,1,5,7,8,4,3,6]=>1000110=>0110001=>1001110
[3,1,7,2,6,5,8,4]=>1010101=>1010101=>0101010
[1,3,2,7,5,4,8,6]=>0101101=>1011010=>0100101
[1,4,5,8,6,2,3,7]=>0001100=>0011000=>1100111
[1,6,7,2,3,5,8,4]=>0010001=>1000100=>0111011
[2,4,1,8,6,5,3,7]=>0101110=>0111010=>1000101
[7,1,4,5,8,3,6,2]=>1000101=>1010001=>0101110
[3,7,8,5,4,6,1,2]=>0011010=>0101100=>1010011
[5,1,7,2,6,4,8,3]=>1010101=>1010101=>0101010
[2,3,4,6,8,5,7,1]=>0000101=>1010000=>0101111
[3,6,2,4,7,5,8,1]=>0100101=>1010010=>0101101
[3,7,2,8,4,6,5,1]=>0101011=>1101010=>0010101
[4,7,5,2,3,6,8,1]=>0110001=>1000110=>0111001
[4,3,5,8,7,2,6,1]=>1001101=>1011001=>0100110
[2,3,4,8,7,5,6,1]=>0001101=>1011000=>0100111
[5,1,6,3,7,8,4,2]=>1010011=>1100101=>0011010
[4,2,6,7,5,1,8,3]=>1001101=>1011001=>0100110
[5,7,6,3,4,8,1,2]=>0110010=>0100110=>1011001
[6,4,7,5,8,3,2,1]=>1010111=>1110101=>0001010
[3,6,7,5,8,1,4,2]=>0010101=>1010100=>0101011
[1,8,5,6,7,3,4,2]=>0100101=>1010010=>0101101
[3,2,7,4,6,1,8,5]=>1010101=>1010101=>0101010
[3,8,4,5,6,7,2,1]=>0100011=>1100010=>0011101
[8,2,4,1,6,7,5,3]=>1010011=>1100101=>0011010
[3,4,8,7,6,1,5,2]=>0011101=>1011100=>0100011
[4,3,8,7,6,2,5,1]=>1011101=>1011101=>0100010
[3,7,8,5,6,4,2,1]=>0010111=>1110100=>0001011
[3,4,7,5,8,6,1,2]=>0010110=>0110100=>1001011
[5,4,6,2,3,1,8,7]=>1010101=>1010101=>0101010
[6,3,1,5,4,2,8,7]=>1101101=>1011011=>0100100
[6,4,5,3,2,1,8,7]=>1011101=>1011101=>0100010
[7,8,3,4,6,5,1,2]=>0100110=>0110010=>1001101
[2,1,7,6,8,4,5,3]=>1010101=>1010101=>0101010
[2,5,4,8,6,3,7,1]=>0101101=>1011010=>0100101
[3,5,4,7,6,1,8,2]=>0101101=>1011010=>0100101
[2,6,5,3,7,4,8,1]=>0110101=>1010110=>0101001
[2,1,8,5,3,7,6,4]=>1011011=>1101101=>0010010
[6,5,4,2,7,8,3,1]=>1110011=>1100111=>0011000
[2,6,8,5,7,4,3,1]=>0010111=>1110100=>0001011
[2,1,8,6,7,5,4,3]=>1010111=>1110101=>0001010
[2,5,3,1,6,4,7,8]=>0110100=>0010110=>1101001
[7,5,4,2,3,1,8,6]=>1110101=>1010111=>0101000
[6,3,2,4,5,8,1,7]=>1100010=>0100011=>1011100
[3,5,4,2,8,6,1,7]=>0110110=>0110110=>1001001
[5,6,8,7,3,2,1,4]=>0011110=>0111100=>1000011
[6,4,5,3,2,8,1,7]=>1011010=>0101101=>1010010
[4,2,5,7,3,1,6,8]=>1001100=>0011001=>1100110
[7,4,1,3,2,6,8,5]=>1101001=>1001011=>0110100
[6,1,4,3,2,7,8,5]=>1011001=>1001101=>0110010
[1,6,4,2,3,7,8,5]=>0110001=>1000110=>0111001
[1,4,5,3,8,2,6,7]=>0010100=>0010100=>1101011
[2,5,4,3,8,1,6,7]=>0110100=>0010110=>1101001
[6,2,5,1,3,7,4,8]=>1010010=>0100101=>1011010
[7,6,5,8,1,2,4,3]=>1101001=>1001011=>0110100
[5,7,4,1,3,6,2,8]=>0110010=>0100110=>1011001
[4,3,8,1,6,7,2,5]=>1010010=>0100101=>1011010
[4,3,8,1,6,5,7,2]=>1010101=>1010101=>0101010
[4,3,8,2,5,6,7,1]=>1010001=>1000101=>0111010
[5,4,8,2,3,6,7,1]=>1010001=>1000101=>0111010
[3,2,8,1,6,7,4,5]=>1010010=>0100101=>1011010
[5,2,8,1,6,7,3,4]=>1010010=>0100101=>1011010
[7,2,6,3,8,1,5,4]=>1010101=>1010101=>0101010
[6,3,4,5,8,2,7,1]=>1000101=>1010001=>0101110
[7,3,8,1,4,5,6,2]=>1010001=>1000101=>0111010
[7,3,4,5,8,1,6,2]=>1000101=>1010001=>0101110
[7,4,8,1,5,6,2,3]=>1010010=>0100101=>1011010
[7,2,8,1,6,5,4,3]=>1010111=>1110101=>0001010
[8,1,3,4,6,5,2,7]=>1000110=>0110001=>1001110
[8,6,5,7,2,1,4,3]=>1101101=>1011011=>0100100
[1,8,6,3,7,4,5,2]=>0110101=>1010110=>0101001
[3,8,5,1,7,6,4,2]=>0110111=>1110110=>0001001
[2,8,1,3,5,6,7,4]=>0100001=>1000010=>0111101
[2,4,8,7,5,6,3,1]=>0011011=>1101100=>0010011
[3,8,7,5,2,6,4,1]=>0111011=>1101110=>0010001
[1,8,7,3,4,6,5,2]=>0110011=>1100110=>0011001
[2,8,1,4,5,7,6,3]=>0100011=>1100010=>0011101
[1,2,7,6,8,4,5,3]=>0010101=>1010100=>0101011
[1,2,5,3,7,6,8,4]=>0010101=>1010100=>0101011
[3,7,8,1,5,6,2,4]=>0010010=>0100100=>1011011
[1,2,4,8,3,6,5,7]=>0001010=>0101000=>1010111
[4,1,3,7,6,8,5,2]=>1001011=>1101001=>0010110
[6,5,7,8,1,4,3,2]=>1001011=>1101001=>0010110
[3,1,8,6,7,5,4,2]=>1010111=>1110101=>0001010
[2,8,3,1,7,5,4,6]=>0110110=>0110110=>1001001
[2,8,3,7,1,4,5,6]=>0101000=>0001010=>1110101
[4,8,2,7,5,1,3,6]=>0101100=>0011010=>1100101
[4,1,2,6,7,5,3,8]=>1000110=>0110001=>1001110
[1,2,5,3,8,6,4,7]=>0010110=>0110100=>1001011
[5,8,7,6,2,1,3,4]=>0111100=>0011110=>1100001
[6,4,8,3,7,5,2,1]=>1010111=>1110101=>0001010
[3,6,8,2,5,7,4,1]=>0010011=>1100100=>0011011
[4,8,7,5,2,6,3,1]=>0111011=>1101110=>0010001
[3,2,8,5,6,1,7,4]=>1010101=>1010101=>0101010
[3,4,8,1,5,7,6,2]=>0010011=>1100100=>0011011
[4,5,6,2,7,3,8,1]=>0010101=>1010100=>0101011
[4,7,5,6,2,3,8,1]=>0101001=>1001010=>0110101
[3,5,7,6,2,4,8,1]=>0011001=>1001100=>0110011
[1,6,8,7,4,5,3,2]=>0011011=>1101100=>0010011
[8,3,5,7,6,2,4,1]=>1001101=>1011001=>0100110
[6,4,5,2,8,7,3,1]=>1010111=>1110101=>0001010
[6,4,2,7,8,5,3,1]=>1100111=>1110011=>0001100
[2,4,5,8,6,7,1,3]=>0001010=>0101000=>1010111
[1,3,5,6,8,7,2,4]=>0000110=>0110000=>1001111
[5,7,4,1,6,2,8,3]=>0110101=>1010110=>0101001
[3,5,6,7,8,2,4,1]=>0000101=>1010000=>0101111
[5,2,4,1,6,7,8,3]=>1010001=>1000101=>0111010
[8,5,6,7,2,4,3,1]=>1001011=>1101001=>0010110
[7,8,4,5,1,6,3,2]=>0101011=>1101010=>0010101
[3,5,8,6,4,7,2,1]=>0011011=>1101100=>0010011
[4,5,6,8,3,7,2,1]=>0001011=>1101000=>0010111
[8,4,5,7,6,2,3,1]=>1001101=>1011001=>0100110
[4,8,6,7,5,2,3,1]=>0101101=>1011010=>0100101
[8,7,4,3,6,5,1,2]=>1110110=>0110111=>1001000
[8,1,4,3,6,5,2,7]=>1010110=>0110101=>1001010
[6,1,2,5,4,3,8,7]=>1001101=>1011001=>0100110
[2,8,6,3,4,7,1,5]=>0110010=>0100110=>1011001
[8,1,2,3,5,7,4,6]=>1000010=>0100001=>1011110
[8,1,2,3,6,5,4,7]=>1000110=>0110001=>1001110
[8,1,2,3,7,6,5,4]=>1000111=>1110001=>0001110
[2,8,1,6,7,5,3,4]=>0100110=>0110010=>1001101
[8,1,2,3,5,4,7,6]=>1000101=>1010001=>0101110
[4,8,5,2,7,1,6,3]=>0110101=>1010110=>0101001
[3,7,8,6,4,2,1,5]=>0011110=>0111100=>1000011
[3,7,8,4,6,2,1,5]=>0010110=>0110100=>1001011
[8,3,1,5,7,6,2,4]=>1100110=>0110011=>1001100
[4,5,2,8,6,7,1,3]=>0101010=>0101010=>1010101
[8,4,5,1,3,2,6,7]=>1010100=>0010101=>1101010
[8,1,2,3,6,7,5,4]=>1000011=>1100001=>0011110
[8,1,6,7,2,5,4,3]=>1001011=>1101001=>0010110
[5,4,1,3,2,8,7,6]=>1101011=>1101011=>0010100
[5,4,2,1,3,8,7,6]=>1110011=>1100111=>0011000
[3,2,7,4,1,6,5,8]=>1011010=>0101101=>1010010
[5,7,3,2,1,6,4,8]=>0111010=>0101110=>1010001
[7,6,5,1,3,4,2,8]=>1110010=>0100111=>1011000
[7,6,5,2,1,4,3,8]=>1111010=>0101111=>1010000
[8,6,2,4,3,5,1,7]=>1101010=>0101011=>1010100
[7,6,5,1,4,2,3,8]=>1110100=>0010111=>1101000
[1,7,6,3,2,4,5,8]=>0111000=>0001110=>1110001
[8,7,3,2,1,6,4,5]=>1111010=>0101111=>1010000
[1,5,7,2,4,3,6,8]=>0010100=>0010100=>1101011
[5,2,8,1,4,3,7,6]=>1010101=>1010101=>0101010
[7,1,6,8,2,4,5,3]=>1001001=>1001001=>0110110
[8,4,6,2,3,7,1,5]=>1010010=>0100101=>1011010
[8,6,1,3,7,5,2,4]=>1100110=>0110011=>1001100
[5,8,1,3,4,7,2,6]=>0100010=>0100010=>1011101
[5,8,6,2,3,1,4,7]=>0110100=>0010110=>1101001
[5,8,7,3,2,4,6,1]=>0111001=>1001110=>0110001
[7,6,2,8,3,5,4,1]=>1101011=>1101011=>0010100
[8,7,5,2,6,3,1,4]=>1110110=>0110111=>1001000
[8,4,7,3,1,5,2,6]=>1011010=>0101101=>1010010
[8,2,6,3,1,4,7,5]=>1011001=>1001101=>0110010
[8,3,2,7,6,1,4,5]=>1101100=>0011011=>1100100
[3,8,2,7,6,4,1,5]=>0101110=>0111010=>1000101
[3,6,7,5,8,2,1,4]=>0010110=>0110100=>1001011
[6,3,5,2,8,7,4,1]=>1010111=>1110101=>0001010
[5,8,4,3,2,7,6,1]=>0111011=>1101110=>0010001
[2,4,6,8,7,3,5,1]=>0001101=>1011000=>0100111
[6,3,5,7,8,2,4,1]=>1000101=>1010001=>0101110
[4,6,8,7,5,2,3,1]=>0011101=>1011100=>0100011
[3,5,6,8,7,2,4,1]=>0001101=>1011000=>0100111
[1,6,8,4,7,5,3,2]=>0010111=>1110100=>0001011
[3,8,6,5,1,7,2,4]=>0111010=>0101110=>1010001
[8,4,6,7,5,2,3,1]=>1001101=>1011001=>0100110
[8,4,5,7,2,6,3,1]=>1001011=>1101001=>0010110
[6,7,4,3,8,5,2,1]=>0110111=>1110110=>0001001
[2,6,8,5,4,7,3,1]=>0011011=>1101100=>0010011
[2,7,4,6,8,5,3,1]=>0100111=>1110010=>0001101
[6,4,7,8,3,5,2,1]=>1001011=>1101001=>0010110
[5,2,4,1,6,3,8,7]=>1010101=>1010101=>0101010
[6,3,5,2,7,4,8,1]=>1010101=>1010101=>0101010
[7,3,4,2,6,1,8,5]=>1010101=>1010101=>0101010
[2,3,7,4,6,1,8,5]=>0010101=>1010100=>0101011
[2,1,7,4,6,3,8,5]=>1010101=>1010101=>0101010
[7,5,4,2,6,3,8,1]=>1110101=>1010111=>0101000
[5,4,7,2,6,1,8,3]=>1010101=>1010101=>0101010
[5,2,7,4,6,1,8,3]=>1010101=>1010101=>0101010
[5,2,4,1,7,6,8,3]=>1010101=>1010101=>0101010
[4,2,7,5,6,1,8,3]=>1010101=>1010101=>0101010
[4,2,7,5,6,3,8,1]=>1010101=>1010101=>0101010
[6,2,4,3,7,5,8,1]=>1010101=>1010101=>0101010
[2,6,4,3,7,5,8,1]=>0110101=>1010110=>0101001
[2,7,5,4,8,6,3,1]=>0110111=>1110110=>0001001
[4,3,7,5,8,6,1,2]=>1010110=>0110101=>1001010
[6,7,4,8,3,5,2,1]=>0101011=>1101010=>0010101
[2,1,5,8,7,4,6,3]=>1001101=>1011001=>0100110
[5,8,3,4,6,7,2,1]=>0100011=>1100010=>0011101
[6,4,3,8,7,2,5,1]=>1101101=>1011011=>0100100
[3,6,8,5,4,7,1,2]=>0011010=>0101100=>1010011
[7,5,3,6,8,4,2,1]=>1100111=>1110011=>0001100
[8,4,3,5,7,2,6,1]=>1100101=>1010011=>0101100
[4,7,8,6,3,5,2,1]=>0011011=>1101100=>0010011
[6,7,5,8,2,4,3,1]=>0101011=>1101010=>0010101
[2,5,4,1,7,8,6,3]=>0110011=>1100110=>0011001
[4,3,1,5,6,8,7,2]=>1100011=>1100011=>0011100
[1,6,3,2,5,8,7,4]=>0110011=>1100110=>0011001
[8,1,5,3,2,6,7,4]=>1011001=>1001101=>0110010
[1,6,8,3,2,4,7,5]=>0011001=>1001100=>0110011
[1,8,7,6,4,2,3,5]=>0111100=>0011110=>1100001
[8,1,7,3,5,4,6,2]=>1010101=>1010101=>0101010
[7,1,3,8,4,6,5,2]=>1001011=>1101001=>0010110
[3,2,8,1,5,6,7,4]=>1010001=>1000101=>0111010
[8,6,1,2,4,5,7,3]=>1100001=>1000011=>0111100
[1,8,6,7,3,4,5,2]=>0101001=>1001010=>0110101
[1,7,3,8,2,4,6,5]=>0101001=>1001010=>0110101
[8,4,3,1,5,6,7,2]=>1110001=>1000111=>0111000
[1,8,7,6,3,4,2,5]=>0111010=>0101110=>1010001
[1,8,5,3,7,6,2,4]=>0110110=>0110110=>1001001
[3,5,2,6,1,4,8,7]=>0101001=>1001010=>0110101
[4,5,7,2,3,8,6,1]=>0010011=>1100100=>0011011
[4,5,7,2,3,8,1,6]=>0010010=>0100100=>1011011
[4,5,6,2,3,1,8,7]=>0010101=>1010100=>0101011
[4,5,6,2,1,3,8,7]=>0011001=>1001100=>0110011
[4,5,6,1,3,2,8,7]=>0010101=>1010100=>0101011
[4,5,6,3,1,2,8,7]=>0011001=>1001100=>0110011
[4,5,7,3,2,8,1,6]=>0011010=>0101100=>1010011
[4,6,7,3,8,2,5,1]=>0010101=>1010100=>0101011
[4,6,7,3,8,2,1,5]=>0010110=>0110100=>1001011
[4,5,7,3,1,8,2,6]=>0011010=>0101100=>1010011
[3,5,1,7,4,8,2,6]=>0101010=>0101010=>1010101
[2,1,5,7,4,8,3,6]=>1001010=>0101001=>1010110
[4,5,7,1,3,8,6,2]=>0010011=>1100100=>0011011
[4,6,7,3,8,1,5,2]=>0010101=>1010100=>0101011
[5,6,7,8,3,1,4,2]=>0001101=>1011000=>0100111
[4,6,7,1,8,3,5,2]=>0010101=>1010100=>0101011
[3,6,1,7,8,4,5,2]=>0100101=>1010010=>0101101
[2,1,6,7,8,4,5,3]=>1000101=>1010001=>0101110
[2,1,6,7,8,4,3,5]=>1000110=>0110001=>1001110
[4,6,7,1,8,3,2,5]=>0010110=>0110100=>1001011
[5,6,7,8,1,3,2,4]=>0001010=>0101000=>1010111
[4,6,7,2,8,3,5,1]=>0010101=>1010100=>0101011
[3,6,2,7,8,4,5,1]=>0100101=>1010010=>0101101
[3,6,2,7,8,4,1,5]=>0100110=>0110010=>1001101
[3,4,2,1,7,8,5,6]=>0110010=>0100110=>1011001
[4,6,7,2,8,5,3,1]=>0010111=>1110100=>0001011
[4,6,7,2,8,5,1,3]=>0010110=>0110100=>1001011
[4,5,7,1,2,8,6,3]=>0010011=>1100100=>0011011
[2,1,6,7,8,3,5,4]=>1000101=>1010001=>0101110
[3,6,1,7,8,2,5,4]=>0100101=>1010010=>0101101
[4,6,7,1,8,2,5,3]=>0010101=>1010100=>0101011
[5,6,7,8,1,2,4,3]=>0001001=>1001000=>0110111
[5,6,7,8,2,4,1,3]=>0001010=>0101000=>1010111
[5,6,7,8,2,4,3,1]=>0001011=>1101000=>0010111
[3,6,1,7,8,5,2,4]=>0100110=>0110010=>1001101
[2,1,6,7,8,5,3,4]=>1000110=>0110001=>1001110
[3,4,2,1,6,5,8,7,10,9]=>011010101=>101010110=>010101001
[3,5,2,6,4,1,8,7,10,9]=>010110101=>101011010=>010100101
[3,5,2,7,4,8,6,1,10,9]=>010101101=>101101010=>010010101
[2,1,5,6,4,3,8,7,10,9]=>100110101=>101011001=>010100110
[4,5,6,3,2,1,8,7,10,9]=>001110101=>101011100=>010100011
[4,5,7,3,2,8,6,1,10,9]=>001101101=>101101100=>010010011
[4,5,7,3,2,9,6,10,8,1]=>001101011=>110101100=>001010011
[2,1,5,7,4,8,6,3,10,9]=>100101101=>101101001=>010010110
[4,6,7,3,8,5,2,1,10,9]=>001011101=>101110100=>010001011
[4,6,7,3,9,5,2,10,8,1]=>001011011=>110110100=>001001011
[2,1,5,7,4,9,6,10,8,3]=>100101011=>110101001=>001010110
[2,1,4,3,7,8,6,5,10,9]=>101001101=>101100101=>010011010
[3,4,2,1,7,8,6,5,10,9]=>011001101=>101100110=>010011001
[3,6,2,7,8,5,4,1,10,9]=>010011101=>101110010=>010001101
[3,6,2,7,9,5,4,10,8,1]=>010011011=>110110010=>001001101
[2,1,6,7,8,5,4,3,10,9]=>100011101=>101110001=>010001110
[5,6,7,8,4,3,2,1,10,9]=>000111101=>101111000=>010000111
[5,6,7,9,4,3,2,10,8,1]=>000111011=>110111000=>001000111
[2,1,6,7,9,5,4,10,8,3]=>100011011=>110110001=>001001110
[5,6,8,9,4,3,10,7,2,1]=>000110111=>111011000=>000100111
[2,1,4,3,7,9,6,10,8,5]=>101001011=>110100101=>001011010
[3,4,2,1,7,9,6,10,8,5]=>011001011=>110100110=>001011001
[3,6,2,8,9,5,10,7,4,1]=>010010111=>111010010=>000101101
[2,1,6,8,9,5,10,7,4,3]=>100010111=>111010001=>000101110
[2,1,4,3,6,5,9,10,8,7]=>101010011=>110010101=>001101010
[3,4,2,1,6,5,9,10,8,7]=>011010011=>110010110=>001101001
[3,5,2,6,4,1,9,10,8,7]=>010110011=>110011010=>001100101
[3,5,2,8,4,9,10,7,6,1]=>010100111=>111001010=>000110101
[2,1,5,6,4,3,9,10,8,7]=>100110011=>110011001=>001100110
[4,5,6,3,2,1,9,10,8,7]=>001110011=>110011100=>001100011
[4,5,8,3,2,9,10,7,6,1]=>001100111=>111001100=>000110011
[2,1,5,8,4,9,10,7,6,3]=>100100111=>111001001=>000110110
[4,7,8,3,9,10,6,5,2,1]=>001001111=>111100100=>000011011
[2,1,4,3,8,9,10,7,6,5]=>101000111=>111000101=>000111010
[3,4,2,1,8,9,10,7,6,5]=>011000111=>111000110=>000111001
[3,7,2,8,9,10,6,5,4,1]=>010001111=>111100010=>000011101
[5,3,1,6,2,4,8,7]=>1101001=>1001011=>0110100
[7,3,1,5,2,8,4,6]=>1101010=>0101011=>1010100
[8,4,5,1,2,7,3,6]=>1010010=>0100101=>1011010
[7,4,5,1,2,8,3,6]=>1010010=>0100101=>1011010
[6,4,5,1,2,3,8,7]=>1010001=>1000101=>0111010
[5,4,6,1,2,3,8,7]=>1010001=>1000101=>0111010
[3,6,1,5,2,4,8,7]=>0101001=>1001010=>0110101
[4,6,5,1,2,3,8,7]=>0110001=>1000110=>0111001
[5,6,4,1,2,3,8,7]=>0110001=>1000110=>0111001
[7,5,4,1,2,8,3,6]=>1110010=>0100111=>1011000
[8,6,4,1,7,2,3,5]=>1110100=>0010111=>1101000
[5,7,4,1,2,8,3,6]=>0110010=>0100110=>1011001
[3,7,1,5,2,8,4,6]=>0101010=>0101010=>1010101
[2,1,7,5,3,8,4,6]=>1011010=>0101101=>1010010
[4,8,5,1,2,7,3,6]=>0110010=>0100110=>1011001
[6,8,4,1,7,2,3,5]=>0110100=>0010110=>1101001
[4,8,6,1,7,2,3,5]=>0110100=>0010110=>1101001
[2,1,8,6,7,3,4,5]=>1010100=>0010101=>1101010
[2,1,7,6,8,3,4,5]=>1010100=>0010101=>1101010
[4,7,6,1,8,2,3,5]=>0110100=>0010110=>1101001
[5,7,6,8,1,2,3,4]=>0101000=>0001010=>1110101
[6,4,7,1,8,2,3,5]=>1010100=>0010101=>1101010
[8,4,6,1,7,2,3,5]=>1010100=>0010101=>1101010
[8,3,1,6,7,2,4,5]=>1100100=>0010011=>1101100
[4,3,1,2,7,8,5,6]=>1100010=>0100011=>1011100
[8,4,7,1,6,2,3,5]=>1010100=>0010101=>1101010
[7,4,8,1,6,2,3,5]=>1010100=>0010101=>1101010
[4,5,8,1,2,7,3,6]=>0010010=>0100100=>1011011
[2,1,6,8,7,3,4,5]=>1001100=>0011001=>1100110
[4,6,8,1,7,2,3,5]=>0010100=>0010100=>1101011
[5,6,8,7,1,2,3,4]=>0011000=>0001100=>1110011
[8,5,7,6,1,2,3,4]=>1011000=>0001101=>1110010
[4,7,8,1,6,2,3,5]=>0010100=>0010100=>1101011
[3,7,1,8,6,2,4,5]=>0101100=>0011010=>1100101
[3,8,1,7,6,2,4,5]=>0101100=>0011010=>1100101
[4,8,7,1,6,2,3,5]=>0110100=>0010110=>1101001
[6,8,7,5,1,2,3,4]=>0111000=>0001110=>1110001
[6,4,7,3,8,5,1,2]=>1010110=>0110101=>1001010
[5,4,2,7,6,1,3,8]=>1101100=>0011011=>1100100
[5,4,2,7,6,1,8,3]=>1101101=>1011011=>0100100
[5,4,3,7,6,8,1,2]=>1101010=>0101011=>1010100
[5,4,3,7,8,6,1,2]=>1100110=>0110011=>1001100
[5,4,3,8,6,7,1,2]=>1101010=>0101011=>1010100
[5,4,3,6,8,7,1,2]=>1100110=>0110011=>1001100
[5,4,2,6,7,1,8,3]=>1100101=>1010011=>0101100
[5,3,2,6,1,7,4,8]=>1101010=>0101011=>1010100
[5,3,2,6,1,7,8,4]=>1101001=>1001011=>0110100
[5,3,2,6,1,8,7,4]=>1101011=>1101011=>0010100
[5,4,2,6,8,1,7,3]=>1100101=>1010011=>0101100
[6,4,8,2,5,1,7,3]=>1010101=>1010101=>0101010
[5,4,2,8,6,1,3,7]=>1101100=>0011011=>1100100
[5,3,2,6,1,8,4,7]=>1101010=>0101011=>1010100
[6,3,8,2,1,5,4,7]=>1011010=>0101101=>1010010
[7,8,3,2,1,5,4,6]=>0111010=>0101110=>1010001
[7,8,3,2,1,5,6,4]=>0111001=>1001110=>0110001
[6,3,8,2,1,5,7,4]=>1011001=>1001101=>0110010
[5,3,2,8,1,6,7,4]=>1101001=>1001011=>0110100
[5,4,2,7,8,1,6,3]=>1100101=>1010011=>0101100
[5,3,2,7,1,8,6,4]=>1101011=>1101011=>0010100
[5,3,2,7,1,6,4,8]=>1101010=>0101011=>1010100
[6,3,7,2,1,5,4,8]=>1011010=>0101101=>1010010
[6,3,7,2,1,5,8,4]=>1011001=>1001101=>0110010
[6,3,7,2,1,8,5,4]=>1011011=>1101101=>0010010
[6,5,7,8,2,1,4,3]=>1001101=>1011001=>0100110
[6,3,7,2,1,4,8,5]=>1011001=>1001101=>0110010
[5,3,2,7,1,4,8,6]=>1101001=>1001011=>0110100
[5,4,2,8,7,1,3,6]=>1101100=>0011011=>1100100
[7,8,4,2,6,1,3,5]=>0110100=>0010110=>1101001
[7,8,3,2,1,6,4,5]=>0111010=>0101110=>1010001
[6,3,8,2,1,7,4,5]=>1011010=>0101101=>1010010
[5,3,2,8,1,7,4,6]=>1101010=>0101011=>1010100
[4,3,2,1,8,7,5,6]=>1110110=>0110111=>1001000
[4,3,2,1,7,5,8,6]=>1110101=>1010111=>0101000
[4,3,2,1,7,5,6,8]=>1110100=>0010111=>1101000
[5,3,2,8,1,4,7,6]=>1101001=>1001011=>0110100
[6,3,8,2,1,4,7,5]=>1011001=>1001101=>0110010
[7,8,3,2,1,4,6,5]=>0111001=>1001110=>0110001
[4,3,2,1,8,5,6,7]=>1110100=>0010111=>1101000
[7,8,5,6,1,2,4,3]=>0101001=>1001010=>0110101
[7,8,4,1,6,2,5,3]=>0110101=>1010110=>0101001
[1,6,8,3,2,7,5,4]=>0011011=>1101100=>0010011
[6,1,8,3,2,7,5,4]=>1011011=>1101101=>0010010
[7,8,1,3,2,6,5,4]=>0101011=>1101010=>0010101
[7,8,3,1,2,6,5,4]=>0110011=>1100110=>0011001
[7,8,2,3,1,6,5,4]=>0101011=>1101010=>0010101
[7,8,2,1,3,6,5,4]=>0110011=>1100110=>0011001
[7,8,1,2,3,6,5,4]=>0100011=>1100010=>0011101
[1,5,2,8,3,7,6,4]=>0101011=>1101010=>0010101
[5,1,2,8,3,7,6,4]=>1001011=>1101001=>0010110
[5,2,1,8,3,7,6,4]=>1101011=>1101011=>0010100
[6,2,8,1,3,7,5,4]=>1010011=>1100101=>0011010
[6,2,8,4,7,1,5,3]=>1010101=>1010101=>0101010
[6,3,8,4,7,5,1,2]=>1010110=>0110101=>1001010
[2,6,8,3,1,7,5,4]=>0011011=>1101100=>0010011
[2,5,1,8,3,7,6,4]=>0101011=>1101010=>0010101
[1,2,5,8,3,7,6,4]=>0001011=>1101000=>0010111
[2,5,3,8,1,7,6,4]=>0101011=>1101010=>0010101
[2,5,4,8,7,1,6,3]=>0101101=>1011010=>0100101
[3,5,4,8,7,6,1,2]=>0101110=>0111010=>1000101
[5,3,4,8,7,6,1,2]=>1001110=>0111001=>1000110
[5,2,4,8,7,1,6,3]=>1001101=>1011001=>0100110
[5,2,3,8,1,7,6,4]=>1001011=>1101001=>0010110
[4,1,2,3,8,7,6,5]=>1000111=>1110001=>0001110
[1,4,2,3,8,7,6,5]=>0100111=>1110010=>0001101
[4,1,3,2,8,7,6,5]=>1010111=>1110101=>0001010
[6,3,8,1,2,7,5,4]=>1010011=>1100101=>0011010
[5,3,1,8,2,7,6,4]=>1101011=>1101011=>0010100
[5,1,3,8,2,7,6,4]=>1001011=>1101001=>0010110
[1,5,3,8,2,7,6,4]=>0101011=>1101010=>0010101
[1,5,4,8,7,2,6,3]=>0101101=>1011010=>0100101
[5,1,4,8,7,2,6,3]=>1001101=>1011001=>0100110
[5,4,1,8,7,2,6,3]=>1101101=>1011011=>0100100
[6,5,8,7,1,2,4,3]=>1011001=>1001101=>0110010
[5,6,8,7,3,4,1,2]=>0011010=>0101100=>1010011
[5,6,8,7,2,1,4,3]=>0011101=>1011100=>0100011
[4,5,1,8,7,2,6,3]=>0101101=>1011010=>0100101
[4,1,5,8,7,2,6,3]=>1001101=>1011001=>0100110
[1,3,5,8,2,7,6,4]=>0001011=>1101000=>0010111
[3,1,5,8,2,7,6,4]=>1001011=>1101001=>0010110
[3,6,8,2,1,7,5,4]=>0011011=>1101100=>0010011
[4,6,8,3,7,5,1,2]=>0010110=>0110100=>1001011
[4,5,3,8,7,6,1,2]=>0101110=>0111010=>1000101
[3,5,2,8,1,7,6,4]=>0101011=>1101010=>0010101
[3,1,4,2,8,7,6,5]=>1010111=>1110101=>0001010
[3,2,5,8,1,7,6,4]=>1001011=>1101001=>0010110
[4,2,5,8,7,1,6,3]=>1001101=>1011001=>0100110
[4,3,5,8,7,6,1,2]=>1001110=>0111001=>1000110
[2,4,5,8,7,1,6,3]=>0001101=>1011000=>0100111
[2,3,5,8,1,7,6,4]=>0001011=>1101000=>0010111
[6,2,5,1,4,3,8,7]=>1010101=>1010101=>0101010
[5,2,6,1,4,3,8,7]=>1010101=>1010101=>0101010
[5,2,7,1,4,3,8,6]=>1010101=>1010101=>0101010
[6,2,8,1,4,3,7,5]=>1010101=>1010101=>0101010
[6,2,7,1,4,3,8,5]=>1010101=>1010101=>0101010
[7,2,6,1,4,3,8,5]=>1010101=>1010101=>0101010
[8,2,5,1,4,3,7,6]=>1010101=>1010101=>0101010
[8,1,4,3,7,2,6,5]=>1010101=>1010101=>0101010
[8,2,6,1,5,3,7,4]=>1010101=>1010101=>0101010
[7,2,6,1,5,3,8,4]=>1010101=>1010101=>0101010
[6,2,7,1,5,3,8,4]=>1010101=>1010101=>0101010
[6,2,8,1,5,3,7,4]=>1010101=>1010101=>0101010
[7,4,8,1,3,2,6,5]=>1010101=>1010101=>0101010
[8,3,7,1,4,2,6,5]=>1010101=>1010101=>0101010
[8,3,7,1,5,2,6,4]=>1010101=>1010101=>0101010
[7,3,8,1,5,2,6,4]=>1010101=>1010101=>0101010
[6,2,7,3,8,1,5,4]=>1010101=>1010101=>0101010
[6,2,8,3,7,1,5,4]=>1010101=>1010101=>0101010
[5,1,8,3,7,2,6,4]=>1010101=>1010101=>0101010
[4,1,8,3,7,2,6,5]=>1010101=>1010101=>0101010
[3,1,7,4,8,2,6,5]=>1010101=>1010101=>0101010
[4,1,7,3,8,2,6,5]=>1010101=>1010101=>0101010
[5,1,7,3,8,2,6,4]=>1010101=>1010101=>0101010
[7,3,8,2,6,1,5,4]=>1010101=>1010101=>0101010
[8,2,6,3,7,1,5,4]=>1010101=>1010101=>0101010
[3,4,2,6,8,1,5,7]=>0100100=>0010010=>1101101
[5,3,6,2,8,1,4,7]=>1010100=>0010101=>1101010
[7,4,2,5,8,3,6,1]=>1100101=>1010011=>0101100
[4,5,2,6,3,8,1,7]=>0101010=>0101010=>1010101
[3,5,6,1,4,8,2,7]=>0010010=>0100100=>1011011
[4,1,5,6,3,8,2,7]=>1001010=>0101001=>1010110
[4,5,1,6,3,8,2,7]=>0101010=>0101010=>1010101
[4,5,6,3,2,8,1,7]=>0011010=>0101100=>1010011
[6,7,4,8,3,2,5,1]=>0101101=>1011010=>0100101
[6,7,4,8,3,2,1,5]=>0101110=>0111010=>1000101
[6,7,4,1,8,3,2,5]=>0110110=>0110110=>1001001
[5,3,7,8,1,4,2,6]=>1001010=>0101001=>1010110
[7,3,5,8,1,4,6,2]=>1001001=>1001001=>0110110
[4,5,1,7,8,3,6,2]=>0100101=>1010010=>0101101
[7,4,1,5,8,3,6,2]=>1100101=>1010011=>0101100
[6,7,4,3,8,1,5,2]=>0110101=>1010110=>0101001
[5,6,1,7,3,8,4,2]=>0101011=>1101010=>0010101
[5,1,6,7,3,8,4,2]=>1001011=>1101001=>0010110
[6,4,7,1,8,3,5,2]=>1010101=>1010101=>0101010
[6,7,8,3,1,4,5,2]=>0011001=>1001100=>0110011
[6,7,2,8,4,5,1,3]=>0101010=>0101010=>1010101
[6,7,2,8,4,1,3,5]=>0101100=>0011010=>1100101
[6,1,7,4,8,3,2,5]=>1010110=>0110101=>1001010
[5,1,6,7,3,2,8,4]=>1001101=>1011001=>0100110
[5,6,1,7,3,2,8,4]=>0101101=>1011010=>0100101
[5,6,7,3,2,1,8,4]=>0011101=>1011100=>0100011
[5,6,7,3,2,8,4,1]=>0011011=>1101100=>0010011
[7,4,2,5,1,8,3,6]=>1101010=>0101011=>1010100
[6,7,4,2,8,3,5,1]=>0110101=>1010110=>0101001
[3,6,7,2,8,4,5,1]=>0010101=>1010100=>0101011
[3,6,7,2,8,4,1,5]=>0010110=>0110100=>1001011
[3,6,7,2,1,8,4,5]=>0011010=>0101100=>1010011
[3,4,7,8,2,1,5,6]=>0001100=>0011000=>1100111
[3,7,8,1,4,6,2,5]=>0010010=>0100100=>1011011
[3,6,7,2,8,5,1,4]=>0010110=>0110100=>1001011
[3,6,7,8,5,2,1,4]=>0001110=>0111000=>1000111
[3,6,7,8,5,2,4,1]=>0001101=>1011000=>0100111
[6,4,7,8,2,5,3,1]=>1001011=>1101001=>0010110
[6,4,7,8,2,1,5,3]=>1001101=>1011001=>0100110
[5,3,7,8,1,6,2,4]=>1001010=>0101001=>1010110
[6,7,2,8,5,1,3,4]=>0101100=>0011010=>1100101
[6,4,1,7,8,2,5,3]=>1100101=>1010011=>0101100
[5,1,6,2,7,8,4,3]=>1010011=>1100101=>0011010
[5,6,2,7,1,8,4,3]=>0101011=>1101010=>0010101
[5,6,2,7,8,4,3,1]=>0100111=>1110010=>0001101
[5,6,7,2,8,4,3,1]=>0010111=>1110100=>0001011
[5,6,7,2,1,8,4,3]=>0011011=>1101100=>0010011
[5,6,1,7,2,8,4,3]=>0101011=>1101010=>0010101
[5,1,6,7,2,8,4,3]=>1001011=>1101001=>0010110
[6,7,8,3,5,1,4,2]=>0010101=>1010100=>0101011
[5,6,1,7,8,4,3,2]=>0100111=>1110010=>0001101
[5,6,7,1,8,4,3,2]=>0010111=>1110100=>0001011
[8,3,2,5,1,6,4,7]=>1101010=>0101011=>1010100
[5,3,2,7,4,1,8,6]=>1101101=>1011011=>0100100
[7,5,3,8,2,4,6,1]=>1101001=>1001011=>0110100
[8,2,4,5,6,3,1,7]=>1000110=>0110001=>1001110
[8,2,4,5,6,1,3,7]=>1000100=>0010001=>1101110
[8,5,3,6,4,1,2,7]=>1101100=>0011011=>1100100
[8,4,1,5,6,3,2,7]=>1100110=>0110011=>1001100
[8,1,4,5,6,3,2,7]=>1000110=>0110001=>1001110
[4,5,3,7,2,1,8,6]=>0101101=>1011010=>0100101
[7,4,5,8,3,2,6,1]=>1001101=>1011001=>0100110
[4,3,6,7,2,8,5,1]=>1001011=>1101001=>0010110
[4,3,6,7,2,8,1,5]=>1001010=>0101001=>1010110
[1,4,3,6,7,2,8,5]=>0100101=>1010010=>0101101
[4,5,3,7,1,8,2,6]=>0101010=>0101010=>1010101
[5,3,4,7,1,2,8,6]=>1001001=>1001001=>0110110
[7,4,5,8,3,6,1,2]=>1001010=>0101001=>1010110
[4,3,6,7,8,1,5,2]=>1000101=>1010001=>0101110
[3,5,6,7,8,4,1,2]=>0000110=>0110000=>1001111
[3,1,5,6,7,8,4,2]=>1000011=>1100001=>0011110
[4,6,1,7,8,3,5,2]=>0100101=>1010010=>0101101
[6,2,4,1,7,8,5,3]=>1010011=>1100101=>0011010
[2,6,7,1,4,8,3,5]=>0010010=>0100100=>1011011
[1,5,3,6,7,8,2,4]=>0100010=>0100010=>1011101
[4,5,2,7,8,1,3,6]=>0100100=>0010010=>1101101
[4,2,6,7,8,3,1,5]=>1000110=>0110001=>1001110
[4,2,6,7,8,3,5,1]=>1000101=>1010001=>0101110
[3,6,2,7,4,8,1,5]=>0101010=>0101010=>1010101
[3,7,4,2,1,5,8,6]=>0111001=>1001110=>0110001
[7,8,4,2,1,3,6,5]=>0111001=>1001110=>0110001
[6,3,2,7,1,8,5,4]=>1101011=>1101011=>0010100
[3,6,2,7,1,8,5,4]=>0101011=>1101010=>0010101
[6,7,3,8,2,5,4,1]=>0101011=>1101010=>0010101
[6,4,7,8,5,2,3,1]=>1001101=>1011001=>0100110
[2,6,4,7,8,1,5,3]=>0100101=>1010010=>0101101
[7,4,1,5,8,6,2,3]=>1100110=>0110011=>1001100
[7,5,8,2,1,6,3,4]=>1011010=>0101101=>1010010
[6,2,7,1,3,8,5,4]=>1010011=>1100101=>0011010
[6,3,1,7,8,2,5,4]=>1100101=>1010011=>0101100
[4,6,1,7,8,5,2,3]=>0100110=>0110010=>1001101
[5,1,2,6,7,8,4,3]=>1000011=>1100001=>0011110
[5,2,6,7,8,4,3,1]=>1000111=>1110001=>0001110
[1,6,4,7,8,5,2,3]=>0100110=>0110010=>1001101
[2,6,7,1,3,8,5,4]=>0010011=>1100100=>0011011
[6,7,3,8,5,1,4,2]=>0101101=>1011010=>0100101
[6,4,7,8,5,3,1,2]=>1001110=>0111001=>1000110
[3,1,2,6,5,8,7,4]=>1001011=>1101001=>0010110
[4,5,1,2,3,8,7,6]=>0100011=>1100010=>0011101
[4,6,1,2,3,8,7,5]=>0100011=>1100010=>0011101
[1,6,5,3,4,8,7,2]=>0110011=>1100110=>0011001
[6,1,5,2,4,8,7,3]=>1010011=>1100101=>0011010
[6,5,1,2,3,8,7,4]=>1100011=>1100011=>0011100
[6,4,1,2,3,8,7,5]=>1100011=>1100011=>0011100
[5,4,1,2,3,8,7,6]=>1100011=>1100011=>0011100
[5,4,1,2,7,3,6,8]=>1100100=>0010011=>1101100
[6,4,1,7,2,3,5,8]=>1101000=>0001011=>1110100
[6,4,1,8,2,3,5,7]=>1101000=>0001011=>1110100
[7,4,1,2,8,3,6,5]=>1100101=>1010011=>0101100
[7,5,1,2,8,3,6,4]=>1100101=>1010011=>0101100
[7,1,5,2,8,4,6,3]=>1010101=>1010101=>0101010
[1,7,5,3,8,4,6,2]=>0110101=>1010110=>0101001
[8,4,1,2,7,3,6,5]=>1100101=>1010011=>0101100
[8,4,1,7,2,3,5,6]=>1101000=>0001011=>1110100
[7,4,1,6,2,3,5,8]=>1101000=>0001011=>1110100
[8,6,1,7,2,3,5,4]=>1101001=>1001011=>0110100
[8,1,6,7,2,4,5,3]=>1001001=>1001001=>0110110
[1,7,6,8,3,4,5,2]=>0101001=>1001010=>0110101
[7,6,1,8,2,3,5,4]=>1101001=>1001011=>0110100
[3,1,2,7,8,5,6,4]=>1000101=>1010001=>0101110
[3,1,8,7,2,4,5,6]=>1011000=>0001101=>1110010
[3,1,7,6,2,4,5,8]=>1011000=>0001101=>1110010
[4,7,1,6,2,3,5,8]=>0101000=>0001010=>1110101
[4,8,1,6,2,3,5,7]=>0101000=>0001010=>1110101
[5,8,1,2,7,3,6,4]=>0100101=>1010010=>0101101
[5,1,8,2,7,4,6,3]=>1010101=>1010101=>0101010
[1,5,8,3,7,4,6,2]=>0010101=>1010100=>0101011
[1,6,8,7,3,4,5,2]=>0011001=>1001100=>0110011
[6,1,8,7,2,4,5,3]=>1011001=>1001101=>0110010
[6,8,1,7,2,3,5,4]=>0101001=>1001010=>0110101
[6,8,7,1,2,3,4,5]=>0110000=>0000110=>1111001
[5,8,6,1,2,3,4,7]=>0110000=>0000110=>1111001
[5,7,6,1,2,3,4,8]=>0110000=>0000110=>1111001
[7,8,1,6,2,3,5,4]=>0101001=>1001010=>0110101
[7,1,8,6,2,4,5,3]=>1011001=>1001101=>0110010
[1,7,8,6,3,4,5,2]=>0011001=>1001100=>0110011
[8,1,7,6,2,4,5,3]=>1011001=>1001101=>0110010
[8,7,1,6,2,3,5,4]=>1101001=>1001011=>0110100
[8,5,3,7,2,1,4,6]=>1101100=>0011011=>1100100
[6,8,1,4,5,7,3,2]=>0100011=>1100010=>0011101
[8,7,2,4,5,1,3,6]=>1100100=>0010011=>1101100
[2,6,1,4,5,3,8,7]=>0100101=>1010010=>0101101
[6,3,1,4,5,2,8,7]=>1100101=>1010011=>0101100
[3,1,6,4,5,2,8,7]=>1010101=>1010101=>0101010
[8,3,7,4,5,1,2,6]=>1010100=>0010101=>1101010
[5,8,7,4,2,6,3,1]=>0111011=>1101110=>0010001
[8,1,7,4,2,6,3,5]=>1011010=>0101101=>1010010
[3,7,8,4,5,1,2,6]=>0010100=>0010100=>1101011
[5,6,3,8,1,7,2,4]=>0101010=>0101010=>1010101
[7,6,1,4,5,8,3,2]=>1100011=>1100011=>0011100
[3,7,6,4,5,8,2,1]=>0110011=>1100110=>0011001
[8,5,7,4,1,6,3,2]=>1011011=>1101101=>0010010
[2,5,8,4,7,6,1,3]=>0010110=>0110100=>1001011
[3,8,4,2,5,6,7,1]=>0110001=>1000110=>0111001
[8,4,1,3,5,6,7,2]=>1100001=>1000011=>0111100
[7,5,8,4,3,6,1,2]=>1011010=>0101101=>1010010
[6,5,3,8,4,1,7,2]=>1101101=>1011011=>0100100
[2,1,4,8,3,6,7,5]=>1001001=>1001001=>0110110
[7,3,8,4,2,6,1,5]=>1011010=>0101101=>1010010
[8,3,1,2,5,6,7,4]=>1100001=>1000011=>0111100
[4,8,2,3,5,6,7,1]=>0100001=>1000010=>0111101
[2,7,8,4,5,3,1,6]=>0010110=>0110100=>1001011
[8,7,1,4,3,6,2,5]=>1101010=>0101011=>1010100
[5,6,3,8,4,2,7,1]=>0101101=>1011010=>0100101
[8,6,3,1,4,2,7,5]=>1110101=>1010111=>0101000
[8,6,3,5,1,2,7,4]=>1101001=>1001011=>0110100
[5,8,3,2,6,1,7,4]=>0110101=>1010110=>0101001
[3,5,8,4,7,6,2,1]=>0010111=>1110100=>0001011
[5,8,2,4,7,6,1,3]=>0100110=>0110010=>1001101
[7,1,6,4,5,8,2,3]=>1010010=>0100101=>1011010
[2,1,8,5,3,6,7,4]=>1011001=>1001101=>0110010
[6,8,3,5,2,1,7,4]=>0101101=>1011010=>0100101
[7,8,5,4,2,6,1,3]=>0111010=>0101110=>1010001
[4,8,1,2,5,6,7,3]=>0100001=>1000010=>0111101
[3,4,2,8,5,6,7,1]=>0101001=>1001010=>0110101
[2,4,1,8,5,6,7,3]=>0101001=>1001010=>0110101
[8,4,2,1,5,6,7,3]=>1110001=>1000111=>0111000
[7,5,2,4,8,6,1,3]=>1100110=>0110011=>1001100
[2,1,5,3,8,6,7,4]=>1010101=>1010101=>0101010
[3,1,4,8,5,6,7,2]=>1001001=>1001001=>0110110
[6,5,3,7,2,8,4,1]=>1101011=>1101011=>0010100
[6,7,2,4,5,8,3,1]=>0100011=>1100010=>0011101
[2,5,7,4,8,6,3,1]=>0010111=>1110100=>0001011
[5,6,3,7,1,8,4,2]=>0101011=>1101010=>0010101
[3,8,7,4,5,2,1,6]=>0110110=>0110110=>1001001
[3,7,5,4,8,6,2,1]=>0110111=>1110110=>0001001
[4,6,3,5,8,2,7,1]=>0100101=>1010010=>0101101
[3,7,8,4,1,6,2,5]=>0011010=>0101100=>1010011
[5,4,2,3,7,6,1,8]=>1100110=>0110011=>1001100
[3,2,7,6,4,5,1,8]=>1011010=>0101101=>1010010
[4,7,2,6,3,5,1,8]=>0101010=>0101010=>1010101
[5,7,6,2,3,4,1,8]=>0110010=>0100110=>1011001
[1,7,5,2,8,3,4,6]=>0110100=>0010110=>1101001
[6,8,5,2,3,1,4,7]=>0110100=>0010110=>1101001
[4,8,2,6,3,1,5,7]=>0101100=>0011010=>1100101
[3,2,8,6,4,1,5,7]=>1011100=>0011101=>1100010
[7,1,5,2,8,3,4,6]=>1010100=>0010101=>1101010
[1,8,5,2,7,3,4,6]=>0110100=>0010110=>1101001
[7,1,6,8,2,3,4,5]=>1001000=>0001001=>1110110
[3,2,1,7,8,4,5,6]=>1100100=>0010011=>1101100
[3,2,8,7,1,4,5,6]=>1011000=>0001101=>1110010
[5,8,7,2,1,3,4,6]=>0111000=>0001110=>1110001
[1,7,6,8,2,3,4,5]=>0101000=>0001010=>1110101
[6,5,8,2,3,1,4,7]=>1010100=>0010101=>1101010
[8,5,7,2,1,3,4,6]=>1011000=>0001101=>1110010
[3,2,5,4,1,8,6,7]=>1011010=>0101101=>1010010
[7,4,2,1,8,3,5,6]=>1110100=>0010111=>1101000
[8,4,2,1,7,3,5,6]=>1110100=>0010111=>1101000
[1,4,2,8,7,3,5,6]=>0101100=>0011010=>1100101
[1,5,8,2,7,3,4,6]=>0010100=>0010100=>1101011
[8,5,1,2,7,3,4,6]=>1100100=>0010011=>1101100
[3,2,6,1,4,8,5,7]=>1010010=>0100101=>1011010
[3,2,7,1,8,4,5,6]=>1010100=>0010101=>1101010
[4,7,2,1,8,3,5,6]=>0110100=>0010110=>1101001
[8,6,1,7,2,3,4,5]=>1101000=>0001011=>1110100
[1,6,8,7,2,3,4,5]=>0011000=>0001100=>1110011
[1,7,8,6,2,3,4,5]=>0011000=>0001100=>1110011
[7,8,1,6,2,3,4,5]=>0101000=>0001010=>1110101
[4,8,2,1,7,3,5,6]=>0110100=>0010110=>1101001
[3,2,8,1,7,4,5,6]=>1010100=>0010101=>1101010
[5,1,8,2,7,3,4,6]=>1010100=>0010101=>1101010
[6,1,8,7,2,3,4,5]=>1011000=>0001101=>1110010
[8,1,7,6,2,3,4,5]=>1011000=>0001101=>1110010
[2,8,4,1,6,5,7,3]=>0110101=>1010110=>0101001
[2,8,5,6,7,4,3,1]=>0100111=>1110010=>0001101
[7,5,8,6,1,4,2,3]=>1011010=>0101101=>1010010
[3,5,7,6,1,4,2,8]=>0011010=>0101100=>1010011
[7,5,8,2,4,1,6,3]=>1010101=>1010101=>0101010
[2,8,5,3,4,7,6,1]=>0110011=>1100110=>0011001
[2,8,5,3,4,1,7,6]=>0110101=>1010110=>0101001
[2,8,5,3,6,1,7,4]=>0110101=>1010110=>0101001
[2,8,5,6,7,4,1,3]=>0100110=>0110010=>1001101
[2,8,5,3,4,7,1,6]=>0110010=>0100110=>1011001
[2,8,5,3,4,6,1,7]=>0110010=>0100110=>1011001
[6,5,2,7,3,1,4,8]=>1101100=>0011011=>1100100
[6,5,2,8,3,1,7,4]=>1101101=>1011011=>0100100
[6,5,2,8,3,1,4,7]=>1101100=>0011011=>1100100
[7,5,8,2,4,6,3,1]=>1010011=>1100101=>0011010
[7,5,8,6,1,4,3,2]=>1011011=>1101101=>0010010
[6,5,8,2,1,3,7,4]=>1011001=>1001101=>0110010
[3,5,6,2,1,8,7,4]=>0011011=>1101100=>0010011
[3,5,7,2,4,1,8,6]=>0010101=>1010100=>0101011
[6,5,2,7,3,1,8,4]=>1101101=>1011011=>0100100
[4,5,2,6,3,1,7,8]=>0101100=>0011010=>1100101
[6,5,2,7,3,4,8,1]=>1101001=>1001011=>0110100
[5,1,6,7,4,3,8,2]=>1001101=>1011001=>0100110
[5,1,2,6,4,8,7,3]=>1001011=>1101001=>0010110
[5,1,2,8,6,4,7,3]=>1001101=>1011001=>0100110
[5,1,6,8,7,3,4,2]=>1001101=>1011001=>0100110
[6,5,2,8,3,7,4,1]=>1101011=>1101011=>0010100
[4,1,2,3,8,6,5,7]=>1000110=>0110001=>1001110
[4,1,2,3,8,6,7,5]=>1000101=>1010001=>0101110
[4,1,2,3,8,5,7,6]=>1000101=>1010001=>0101110
[6,5,8,2,4,3,7,1]=>1010101=>1010101=>0101010
[6,5,2,8,3,7,1,4]=>1101010=>0101011=>1010100
[6,5,2,7,3,4,1,8]=>1101010=>0101011=>1010100
[5,1,6,7,4,3,2,8]=>1001110=>0111001=>1000110
[5,1,6,8,7,3,2,4]=>1001110=>0111001=>1000110
[5,7,8,6,3,4,2,1]=>0011011=>1101100=>0010011
[3,1,4,8,6,2,7,5]=>1001101=>1011001=>0100110
[3,1,4,8,6,5,2,7]=>1001110=>0111001=>1000110
[4,1,6,7,8,3,2,5]=>1000110=>0110001=>1001110
[4,1,6,5,7,3,2,8]=>1010110=>0110101=>1001010
[4,5,2,6,3,7,1,8]=>0101010=>0101010=>1010101
[4,5,2,7,3,8,1,6]=>0101010=>0101010=>1010101
[3,5,6,2,4,8,1,7]=>0010010=>0100100=>1011011
[3,7,5,6,8,4,1,2]=>0100110=>0110010=>1001101
[3,6,5,2,8,1,7,4]=>0110101=>1010110=>0101001
[6,1,2,5,8,4,7,3]=>1000101=>1010001=>0101110
[4,1,2,3,5,8,7,6]=>1000011=>1100001=>0011110
[4,1,6,7,8,3,5,2]=>1000101=>1010001=>0101110
[4,1,2,6,8,5,7,3]=>1000101=>1010001=>0101110
[4,1,2,5,6,8,7,3]=>1000011=>1100001=>0011110
[4,5,2,6,3,7,8,1]=>0101001=>1001010=>0110101
[6,4,2,7,1,3,8,5]=>1101001=>1001011=>0110100
[7,4,2,5,1,3,8,6]=>1101001=>1001011=>0110100
[8,5,3,6,1,7,2,4]=>1101010=>0101011=>1010100
[7,3,6,2,4,8,1,5]=>1010010=>0100101=>1011010
[6,3,7,4,1,2,8,5]=>1011001=>1001101=>0110010
[3,7,5,1,2,4,8,6]=>0110001=>1000110=>0111001
[7,4,8,5,2,6,1,3]=>1011010=>0101101=>1010010
[5,8,2,6,3,7,1,4]=>0101010=>0101010=>1010101
[3,8,6,2,4,7,1,5]=>0110010=>0100110=>1011001
[3,8,5,7,1,2,4,6]=>0101000=>0001010=>1110101
[2,8,5,7,1,3,4,6]=>0101000=>0001010=>1110101
[4,8,6,2,7,1,3,5]=>0110100=>0010110=>1101001
[3,6,5,8,1,2,4,7]=>0101000=>0001010=>1110101
[5,4,7,3,8,1,2,6]=>1010100=>0010101=>1101010
[8,4,1,6,7,2,3,5]=>1100100=>0010011=>1101100
[6,5,1,2,7,8,3,4]=>1100010=>0100011=>1011100
[4,7,1,5,8,6,2,3]=>0100110=>0110010=>1001101
[7,6,1,8,5,2,3,4]=>1101100=>0011011=>1100100
[5,7,2,8,1,6,3,4]=>0101010=>0101010=>1010101
[6,3,7,8,5,1,2,4]=>1001100=>0011001=>1100110
[3,6,8,2,7,1,4,5]=>0010100=>0010100=>1101011
[5,3,8,7,1,2,4,6]=>1011000=>0001101=>1110010
[8,3,7,6,1,2,4,5]=>1011000=>0001101=>1110010
[8,4,7,6,1,2,3,5]=>1011000=>0001101=>1110010
[5,4,8,7,1,2,3,6]=>1011000=>0001101=>1110010
[3,5,8,7,1,2,4,6]=>0011000=>0001100=>1110011
[2,5,8,7,1,3,4,6]=>0011000=>0001100=>1110011
[6,8,4,7,5,1,2,3]=>0101100=>0011010=>1100101
[5,8,7,1,6,2,3,4]=>0110100=>0010110=>1101001
[2,8,7,6,1,3,4,5]=>0111000=>0001110=>1110001
[3,8,7,6,1,2,4,5]=>0111000=>0001110=>1110001
[4,8,7,6,1,2,3,5]=>0111000=>0001110=>1110001
[5,6,3,1,4,2,8,7]=>0110101=>1010110=>0101001
[7,5,3,8,2,1,6,4]=>1101101=>1011011=>0100100
[3,8,7,4,5,1,6,2]=>0110101=>1010110=>0101001
[6,7,1,4,5,8,2,3]=>0100010=>0100010=>1011101
[2,1,7,8,5,3,6,4]=>1001101=>1011001=>0100110
[5,7,3,8,1,2,6,4]=>0101001=>1001010=>0110101
[7,5,1,4,8,6,3,2]=>1100111=>1110011=>0001100
[6,4,3,8,1,5,7,2]=>1101001=>1001011=>0110100
[8,6,3,1,2,5,7,4]=>1110001=>1000111=>0111000
[8,7,1,4,2,6,5,3]=>1101011=>1101011=>0010100
[7,3,8,4,1,6,5,2]=>1011011=>1101101=>0010010
[5,3,2,7,4,6,8,1]=>1101001=>1001011=>0110100
[7,5,3,6,2,4,8,1]=>1101001=>1001011=>0110100
[6,3,2,5,1,8,4,7]=>1101010=>0101011=>1010100
[8,5,3,6,2,7,1,4]=>1101010=>0101011=>1010100
[7,2,6,3,4,5,8,1]=>1010001=>1000101=>0111010
[6,2,7,3,4,5,8,1]=>1010001=>1000101=>0111010
[6,7,3,5,2,4,8,1]=>0101001=>1001010=>0110101
[3,7,6,2,4,5,8,1]=>0110001=>1000110=>0111001
[6,5,3,1,2,8,4,7]=>1110010=>0100111=>1011000
[8,6,5,2,3,7,1,4]=>1110010=>0100111=>1011000
[8,5,2,1,7,3,4,6]=>1110100=>0010111=>1101000
[7,5,2,1,8,3,4,6]=>1110100=>0010111=>1101000
[1,6,3,2,8,4,5,7]=>0110100=>0010110=>1101001
[4,2,6,5,1,8,3,7]=>1011010=>0101101=>1010010
[5,4,8,6,2,7,1,3]=>1011010=>0101101=>1010010
[7,8,5,2,3,6,1,4]=>0110010=>0100110=>1011001
[6,8,2,1,7,3,4,5]=>0110100=>0010110=>1101001
[2,8,1,7,3,4,5,6]=>0101000=>0001010=>1110101
[3,8,6,1,7,2,4,5]=>0110100=>0010110=>1101001
[4,2,8,3,7,1,5,6]=>1010100=>0010101=>1101010
[8,1,2,7,3,4,5,6]=>1001000=>0001001=>1110110
[6,3,7,1,2,8,4,5]=>1010010=>0100101=>1011010
[7,2,6,1,8,3,4,5]=>1010100=>0010101=>1101010
[7,3,1,5,8,2,4,6]=>1100100=>0010011=>1101100
[5,4,1,3,6,8,2,7]=>1100010=>0100011=>1011100
[8,5,3,7,6,1,2,4]=>1101100=>0011011=>1100100
[6,1,8,3,7,2,4,5]=>1010100=>0010101=>1101010
[7,6,8,2,3,5,1,4]=>1010010=>0100101=>1011010
[3,7,8,2,4,6,1,5]=>0010010=>0100100=>1011011
[5,4,7,8,2,6,1,3]=>1001010=>0101001=>1010110
[4,2,5,8,7,1,3,6]=>1001100=>0011001=>1100110
[2,3,8,7,1,4,5,6]=>0011000=>0001100=>1110011
[2,1,8,7,3,4,5,6]=>1011000=>0001101=>1110010
[8,2,7,6,1,3,4,5]=>1011000=>0001101=>1110010
[1,2,8,7,3,4,5,6]=>0011000=>0001100=>1110011
[1,3,8,7,2,4,5,6]=>0011000=>0001100=>1110011
[1,7,8,3,6,2,4,5]=>0010100=>0010100=>1101011
[5,4,8,7,6,1,2,3]=>1011100=>0011101=>1100010
[6,8,3,7,5,1,2,4]=>0101100=>0011010=>1100101
[7,8,6,2,5,1,3,4]=>0110100=>0010110=>1101001
[8,1,6,7,3,2,4,5]=>1001100=>0011001=>1100110
[8,1,5,3,7,2,4,6]=>1010100=>0010101=>1101010
[8,1,5,3,6,2,4,7]=>1010100=>0010101=>1101010
[7,4,8,3,2,6,5,1]=>1011011=>1101101=>0010010
[7,4,1,3,2,6,5,8]=>1101010=>0101011=>1010100
[8,1,4,3,2,6,5,7]=>1011010=>0101101=>1010010
[8,1,4,3,2,7,5,6]=>1011010=>0101101=>1010010
[8,1,5,4,6,7,2,3]=>1010010=>0100101=>1011010
[8,1,5,3,6,2,7,4]=>1010101=>1010101=>0101010
[8,1,4,3,2,6,7,5]=>1011001=>1001101=>0110010
[8,1,4,3,2,5,7,6]=>1011001=>1001101=>0110010
[7,4,1,3,2,5,6,8]=>1101000=>0001011=>1110100
[7,4,8,3,2,5,6,1]=>1011001=>1001101=>0110010
[6,4,3,1,2,5,8,7]=>1110001=>1000111=>0111000
[7,4,1,3,2,5,8,6]=>1101001=>1001011=>0110100
[7,5,1,3,6,2,8,4]=>1100101=>1010011=>0101100
[7,5,1,4,6,8,2,3]=>1100010=>0100011=>1011100
[6,4,3,8,2,5,1,7]=>1101010=>0101011=>1010100
[5,4,3,2,8,6,1,7]=>1110110=>0110111=>1001000
[5,4,3,2,8,7,1,6]=>1110110=>0110111=>1001000
[6,5,4,8,7,1,2,3]=>1101100=>0011011=>1100100
[6,5,4,1,7,8,2,3]=>1110010=>0100111=>1011000
[6,4,3,1,2,7,8,5]=>1110001=>1000111=>0111000
[7,4,1,3,2,8,5,6]=>1101010=>0101011=>1010100
[6,4,3,1,2,7,5,8]=>1110010=>0100111=>1011000
[6,4,3,8,2,7,5,1]=>1101011=>1101011=>0010100
[6,5,3,8,7,2,4,1]=>1101101=>1011011=>0100100
[6,5,3,1,7,2,4,8]=>1110100=>0010111=>1101000
[7,5,1,3,8,2,4,6]=>1100100=>0010011=>1101100
[6,5,3,7,8,2,4,1]=>1100101=>1010011=>0101100
[6,4,3,7,2,8,5,1]=>1101011=>1101011=>0010100
[6,4,3,7,2,1,5,8]=>1101100=>0011011=>1100100
[7,5,8,4,1,6,2,3]=>1011010=>0101101=>1010010
[6,5,4,8,1,7,2,3]=>1101010=>0101011=>1010100
[6,5,3,8,1,2,7,4]=>1101001=>1001011=>0110100
[6,5,4,7,1,8,2,3]=>1101010=>0101011=>1010100
[5,4,3,2,7,8,1,6]=>1110010=>0100111=>1011000
[4,6,3,8,5,1,2,7]=>0101100=>0011010=>1100101
[5,6,8,3,4,1,2,7]=>0010100=>0010100=>1101011
[5,6,8,3,4,1,7,2]=>0010101=>1010100=>0101011
[4,6,2,7,5,3,1,8]=>0101110=>0111010=>1000101
[5,6,8,4,3,1,2,7]=>0011100=>0011100=>1100011
[5,7,8,4,1,3,6,2]=>0011001=>1001100=>0110011
[5,6,8,4,2,1,7,3]=>0011101=>1011100=>0100011
[5,6,8,2,4,1,7,3]=>0010101=>1010100=>0101011
[3,2,6,8,5,1,4,7]=>1001100=>0011001=>1100110
[5,6,8,4,2,1,3,7]=>0011100=>0011100=>1100011
[5,7,8,4,1,3,2,6]=>0011010=>0101100=>1010011
[5,7,8,4,1,2,3,6]=>0011000=>0001100=>1110011
[6,7,8,1,5,2,3,4]=>0010100=>0010100=>1101011
[6,7,8,1,5,3,2,4]=>0010110=>0110100=>1001011
[6,7,8,1,3,5,2,4]=>0010010=>0100100=>1011011
[5,7,8,2,1,6,3,4]=>0011010=>0101100=>1010011
[4,7,2,8,1,6,3,5]=>0101010=>0101010=>1010101
[3,2,7,8,1,6,4,5]=>1001010=>0101001=>1010110
[4,7,2,8,1,6,5,3]=>0101011=>1101010=>0010101
[5,7,8,2,1,6,4,3]=>0011011=>1101100=>0010011
[6,7,8,1,3,5,4,2]=>0010011=>1100100=>0011011
[6,7,8,1,5,3,4,2]=>0010101=>1010100=>0101011
[6,7,8,1,4,3,5,2]=>0010101=>1010100=>0101011
[5,6,8,3,2,1,7,4]=>0011101=>1011100=>0100011
[4,7,3,8,1,6,2,5]=>0101010=>0101010=>1010101
[4,7,3,8,1,5,6,2]=>0101001=>1001010=>0110101
[4,7,3,8,1,5,2,6]=>0101010=>0101010=>1010101
[4,7,3,8,1,2,5,6]=>0101000=>0001010=>1110101
[5,7,8,3,1,2,4,6]=>0011000=>0001100=>1110011
[5,6,8,3,2,1,4,7]=>0011100=>0011100=>1100011
[3,2,7,8,1,5,4,6]=>1001010=>0101001=>1010110
[6,7,8,1,3,4,2,5]=>0010010=>0100100=>1011011
[6,7,8,1,4,2,3,5]=>0010100=>0010100=>1101011
[6,7,8,1,2,5,3,4]=>0010010=>0100100=>1011011
[6,7,8,1,2,4,5,3]=>0010001=>1000100=>0111011
[5,7,8,2,1,3,6,4]=>0011001=>1001100=>0110011
[3,2,7,8,1,4,6,5]=>1001001=>1001001=>0110110
[6,7,8,1,3,2,4,5]=>0010100=>0010100=>1101011
[6,7,8,1,2,4,3,5]=>0010010=>0100100=>1011011
[6,7,8,1,2,3,5,4]=>0010001=>1000100=>0111011
[8,3,5,1,7,4,6,2]=>1010101=>1010101=>0101010
[8,3,4,1,7,5,6,2]=>1010101=>1010101=>0101010
[4,8,3,1,7,5,6,2]=>0110101=>1010110=>0101001
[4,6,2,1,7,5,8,3]=>0110101=>1010110=>0101001
[1,4,6,2,7,5,8,3]=>0010101=>1010100=>0101011
[1,7,5,2,6,8,4,3]=>0110011=>1100110=>0011001
[7,5,2,1,6,8,4,3]=>1110011=>1100111=>0011000
[6,8,4,3,1,7,5,2]=>0111011=>1101110=>0010001
[4,7,5,6,1,8,3,2]=>0101011=>1101010=>0010101
[6,7,5,1,8,4,3,2]=>0110111=>1110110=>0001001
[6,8,4,1,7,5,3,2]=>0110111=>1110110=>0001001
[6,7,5,3,1,8,4,2]=>0111011=>1101110=>0010001
[8,4,2,1,6,7,5,3]=>1110011=>1100111=>0011000
[1,8,4,2,6,7,5,3]=>0110011=>1100110=>0011001
[1,5,3,2,7,6,8,4]=>0110101=>1010110=>0101001
[2,5,3,1,7,6,8,4]=>0110101=>1010110=>0101001
[2,7,5,1,6,8,4,3]=>0110011=>1100110=>0011001
[4,7,1,6,5,8,2,3]=>0101010=>0101010=>1010101
[4,6,1,2,7,5,8,3]=>0100101=>1010010=>0101101
[8,4,1,2,6,7,5,3]=>1100011=>1100011=>0011100
[5,3,1,2,7,6,8,4]=>1100101=>1010011=>0101100
[4,3,1,2,7,6,8,5]=>1100101=>1010011=>0101100
[3,5,1,2,7,6,8,4]=>0100101=>1010010=>0101101
[6,7,1,5,8,2,3,4]=>0100100=>0010010=>1101101
[2,7,6,1,5,8,3,4]=>0110010=>0100110=>1011001
[2,3,5,1,7,6,8,4]=>0010101=>1010100=>0101011
[8,4,1,6,7,5,2,3]=>1100110=>0110011=>1001100
[5,2,3,1,7,6,8,4]=>1010101=>1010101=>0101010
[3,5,2,1,7,6,8,4]=>0110101=>1010110=>0101001
[1,7,6,2,5,8,3,4]=>0110010=>0100110=>1011001
[7,6,2,1,5,8,3,4]=>1110010=>0100111=>1011000
[8,2,6,4,7,1,5,3]=>1010101=>1010101=>0101010
[6,1,5,2,7,4,8,3]=>1010101=>1010101=>0101010
[7,6,2,5,8,3,1,4]=>1100110=>0110011=>1001100
[1,8,3,5,7,6,2,4]=>0100110=>0110010=>1001101
[1,5,2,3,7,6,8,4]=>0100101=>1010010=>0101101
[5,2,1,3,7,6,8,4]=>1100101=>1010011=>0101100
[8,4,2,6,7,5,1,3]=>1100110=>0110011=>1001100
[6,1,4,2,7,5,8,3]=>1010101=>1010101=>0101010
[8,2,6,5,7,1,4,3]=>1010101=>1010101=>0101010
[5,1,3,2,7,6,8,4]=>1010101=>1010101=>0101010
[1,4,2,3,7,6,8,5]=>0100101=>1010010=>0101101
[2,4,1,3,7,6,8,5]=>0100101=>1010010=>0101101
[2,5,1,3,7,6,8,4]=>0100101=>1010010=>0101101
[2,8,3,5,7,6,1,4]=>0100110=>0110010=>1001101
[6,8,2,3,5,7,1,4]=>0100010=>0100010=>1011101
[6,7,1,3,5,8,2,4]=>0100010=>0100010=>1011101
[8,3,5,7,6,1,2,4]=>1001100=>0011001=>1100110
[5,1,2,3,7,6,8,4]=>1000101=>1010001=>0101110
[4,7,1,2,8,6,5,3]=>0100111=>1110010=>0001101
[4,6,8,1,2,7,5,3]=>0010011=>1100100=>0011011
[6,8,7,1,5,3,2,4]=>0110110=>0110110=>1001001
[6,8,7,3,5,1,2,4]=>0110100=>0010110=>1101001
[7,8,1,3,6,5,2,4]=>0100110=>0110010=>1001101
[1,7,3,4,8,6,5,2]=>0100111=>1110010=>0001101
[4,2,7,1,8,6,5,3]=>1010111=>1110101=>0001010
[7,8,2,3,6,5,1,4]=>0100110=>0110010=>1001101
[8,5,7,1,6,2,3,4]=>1010100=>0010101=>1101010
[8,5,7,1,2,6,3,4]=>1010010=>0100101=>1011010
[6,8,2,7,1,3,5,4]=>0101001=>1001010=>0110101
[6,2,4,8,7,1,5,3]=>1001101=>1011001=>0100110
[1,6,8,3,7,4,5,2]=>0010101=>1010100=>0101011
[1,6,8,3,4,7,5,2]=>0010011=>1100100=>0011011
[6,2,4,8,1,7,5,3]=>1001011=>1101001=>0010110
[6,8,7,2,3,5,1,4]=>0110010=>0100110=>1011001
[6,8,2,1,7,3,5,4]=>0110101=>1010110=>0101001
[8,5,7,2,1,6,3,4]=>1011010=>0101101=>1010010
[8,5,7,1,2,3,6,4]=>1010001=>1000101=>0111010
[8,5,7,2,3,1,6,4]=>1010101=>1010101=>0101010
[1,8,7,5,3,4,6,2]=>0111001=>1001110=>0110001
[1,8,7,3,5,4,6,2]=>0110101=>1010110=>0101001
[8,2,5,4,7,1,6,3]=>1010101=>1010101=>0101010
[8,7,6,1,2,4,3,5]=>1110010=>0100111=>1011000
[8,7,6,1,4,2,3,5]=>1110100=>0010111=>1101000
[8,7,6,4,1,3,2,5]=>1111010=>0101111=>1010000
[8,5,7,1,3,2,6,4]=>1010101=>1010101=>0101010
[5,8,4,7,1,2,6,3]=>0101001=>1001010=>0110101
[8,1,2,6,5,7,4,3]=>1001011=>1101001=>0010110
[8,2,5,6,7,4,1,3]=>1000110=>0110001=>1001110
[4,8,5,1,7,2,6,3]=>0110101=>1010110=>0101001
[8,5,3,7,1,2,6,4]=>1101001=>1001011=>0110100
[4,6,2,8,1,7,5,3]=>0101011=>1101010=>0010101
[1,6,4,8,3,7,5,2]=>0101011=>1101010=>0010101
[1,8,7,4,5,3,6,2]=>0110101=>1010110=>0101001
[4,8,5,7,2,1,6,3]=>0101101=>1011010=>0100101
[8,5,3,7,2,1,6,4]=>1101101=>1011011=>0100100
[8,7,6,3,1,4,2,5]=>1111010=>0101111=>1010000
[8,5,3,2,7,1,6,4]=>1110101=>1010111=>0101000
[1,8,7,4,3,5,6,2]=>0111001=>1001110=>0110001
[1,8,7,3,4,5,6,2]=>0110001=>1000110=>0111001
[8,2,4,5,7,1,6,3]=>1000101=>1010001=>0101110
[8,5,2,3,7,1,6,4]=>1100101=>1010011=>0101100
[8,3,1,5,2,7,6,4]=>1101011=>1101011=>0010100
[8,5,4,2,1,7,3,6]=>1111010=>0101111=>1010000
[8,5,4,2,1,7,6,3]=>1111011=>1101111=>0010000
[6,5,4,2,3,1,8,7]=>1110101=>1010111=>0101000
[6,3,2,5,1,4,8,7]=>1101001=>1001011=>0110100
[8,5,4,1,2,7,6,3]=>1110011=>1100111=>0011000
[8,7,4,1,6,3,2,5]=>1110110=>0110111=>1001000
[8,7,4,1,6,3,5,2]=>1110101=>1010111=>0101000
[8,7,4,1,6,5,3,2]=>1110111=>1110111=>0001000
[8,5,4,3,1,7,6,2]=>1111011=>1101111=>0010000
[8,3,2,5,1,7,6,4]=>1101011=>1101011=>0010100
[8,3,2,5,1,7,4,6]=>1101010=>0101011=>1010100
[8,5,4,3,1,7,2,6]=>1111010=>0101111=>1010000
[8,5,4,1,3,7,2,6]=>1110010=>0100111=>1011000
[8,7,4,1,6,5,2,3]=>1110110=>0110111=>1001000
[2,1,8,7,6,4,5,3]=>1011101=>1011101=>0100010
[8,3,2,7,6,4,5,1]=>1101101=>1011011=>0100100
[8,5,4,2,3,7,6,1]=>1110011=>1100111=>0011000
[8,7,4,2,6,5,3,1]=>1110111=>1110111=>0001000
[8,7,4,2,6,3,5,1]=>1110101=>1010111=>0101000
[8,7,4,2,6,3,1,5]=>1110110=>0110111=>1001000
[8,3,1,7,6,4,2,5]=>1101110=>0111011=>1000100
[8,3,1,7,6,4,5,2]=>1101101=>1011011=>0100100
[8,3,1,5,4,7,6,2]=>1101011=>1101011=>0010100
[8,3,1,7,6,5,2,4]=>1101110=>0111011=>1000100
[8,3,1,7,6,2,5,4]=>1101101=>1011011=>0100100
[8,5,4,2,3,7,1,6]=>1110010=>0100111=>1011000
[8,3,2,5,4,7,1,6]=>1101010=>0101011=>1010100
[2,1,8,5,4,7,3,6]=>1011010=>0101101=>1010010
[8,3,2,7,6,5,1,4]=>1101110=>0111011=>1000100
[8,7,6,5,3,1,4,2]=>1111101=>1011111=>0100000
[8,3,2,7,6,1,5,4]=>1101101=>1011011=>0100100
[8,7,6,5,1,2,4,3]=>1111001=>1001111=>0110000
[5,2,3,1,6,4,8,7]=>1010101=>1010101=>0101010
[7,4,5,2,3,1,8,6]=>1010101=>1010101=>0101010
[7,3,5,2,4,1,8,6]=>1010101=>1010101=>0101010
[6,3,5,2,4,1,8,7]=>1010101=>1010101=>0101010
[4,1,6,3,5,2,8,7]=>1010101=>1010101=>0101010
[6,3,4,1,5,2,8,7]=>1010101=>1010101=>0101010
[5,2,7,3,4,1,8,6]=>1010101=>1010101=>0101010
[6,2,8,5,7,3,4,1]=>1010101=>1010101=>0101010
[6,2,7,3,4,1,8,5]=>1010101=>1010101=>0101010
[7,3,4,1,5,2,8,6]=>1010101=>1010101=>0101010
[4,1,7,3,5,2,8,6]=>1010101=>1010101=>0101010
[2,1,7,4,5,3,8,6]=>1010101=>1010101=>0101010
[3,1,8,6,7,4,5,2]=>1010101=>1010101=>0101010
[4,1,8,6,7,3,5,2]=>1010101=>1010101=>0101010
[8,5,7,3,4,1,6,2]=>1010101=>1010101=>0101010
[8,5,6,2,7,3,4,1]=>1010101=>1010101=>0101010
[8,4,7,3,5,1,6,2]=>1010101=>1010101=>0101010
[5,1,8,4,7,3,6,2]=>1010101=>1010101=>0101010
[3,1,8,5,7,4,6,2]=>1010101=>1010101=>0101010
[2,1,8,5,7,4,6,3]=>1010101=>1010101=>0101010
[3,1,7,4,6,2,8,5]=>1010101=>1010101=>0101010
[4,1,7,3,6,2,8,5]=>1010101=>1010101=>0101010
[6,2,8,4,7,3,5,1]=>1010101=>1010101=>0101010
[7,3,6,2,5,1,8,4]=>1010101=>1010101=>0101010
[5,2,4,1,7,3,8,6]=>1010101=>1010101=>0101010
[6,2,4,1,7,3,8,5]=>1010101=>1010101=>0101010
[7,4,6,2,3,1,8,5]=>1010101=>1010101=>0101010
[6,2,3,1,7,4,8,5]=>1010101=>1010101=>0101010
[5,2,3,1,7,4,8,6]=>1010101=>1010101=>0101010
[4,2,3,1,7,5,8,6]=>1010101=>1010101=>0101010
[3,1,4,2,8,6,7,5]=>1010101=>1010101=>0101010
[6,2,3,1,8,5,7,4]=>1010101=>1010101=>0101010
[8,5,6,2,3,1,7,4]=>1010101=>1010101=>0101010
[7,3,8,5,6,2,4,1]=>1010101=>1010101=>0101010
[8,5,6,2,4,1,7,3]=>1010101=>1010101=>0101010
[5,2,4,1,8,6,7,3]=>1010101=>1010101=>0101010
[4,1,5,2,8,6,7,3]=>1010101=>1010101=>0101010
[3,1,6,2,8,5,7,4]=>1010101=>1010101=>0101010
[5,1,6,2,8,4,7,3]=>1010101=>1010101=>0101010
[8,4,6,2,5,1,7,3]=>1010101=>1010101=>0101010
[7,3,8,4,6,2,5,1]=>1010101=>1010101=>0101010
[6,2,7,3,8,4,5,1]=>1010101=>1010101=>0101010
[8,4,5,1,6,2,7,3]=>1010101=>1010101=>0101010
[4,1,8,5,6,2,7,3]=>1010101=>1010101=>0101010
[3,1,8,5,6,2,7,4]=>1010101=>1010101=>0101010
[2,1,8,5,6,3,7,4]=>1010101=>1010101=>0101010
[3,1,7,4,8,5,6,2]=>1010101=>1010101=>0101010
[7,3,6,2,8,4,5,1]=>1010101=>1010101=>0101010
[6,8,7,3,4,1,2,5]=>0110100=>0010110=>1101001
[5,4,8,7,2,6,3,1]=>1011011=>1101101=>0010010
[5,3,8,7,6,1,2,4]=>1011100=>0011101=>1100010
[8,3,4,6,5,1,2,7]=>1001100=>0011001=>1100110
[3,4,8,7,6,1,2,5]=>0011100=>0011100=>1100011
[3,5,8,7,6,1,2,4]=>0011100=>0011100=>1100011
[4,5,8,7,6,1,2,3]=>0011100=>0011100=>1100011
[4,5,8,7,1,6,3,2]=>0011011=>1101100=>0010011
[3,5,8,2,7,6,4,1]=>0010111=>1110100=>0001011
[3,5,8,1,7,6,4,2]=>0010111=>1110100=>0001011
[2,5,8,7,1,6,3,4]=>0011010=>0101100=>1010011
[2,4,8,7,1,6,3,5]=>0011010=>0101100=>1010011
[2,8,4,7,1,5,3,6]=>0101010=>0101010=>1010101
[8,2,4,6,1,5,3,7]=>1001010=>0101001=>1010110
[8,1,4,6,2,5,3,7]=>1001010=>0101001=>1010110
[1,4,8,7,2,6,3,5]=>0011010=>0101100=>1010011
[1,5,8,7,2,6,3,4]=>0011010=>0101100=>1010011
[1,5,8,2,7,6,4,3]=>0010111=>1110100=>0001011
[2,5,8,3,7,6,4,1]=>0010111=>1110100=>0001011
[1,4,2,8,7,6,5,3]=>0101111=>1111010=>0000101
[1,3,8,2,7,6,4,5]=>0010110=>0110100=>1001011
[1,8,3,2,7,5,4,6]=>0110110=>0110110=>1001001
[8,2,3,1,6,5,4,7]=>1010110=>0110101=>1001010
[2,3,8,1,7,6,4,5]=>0010110=>0110100=>1001011
[5,2,8,7,1,6,3,4]=>1011010=>0101101=>1010010
[5,2,8,1,7,6,4,3]=>1010111=>1110101=>0001010
[5,3,8,2,7,6,4,1]=>1010111=>1110101=>0001010
[6,8,3,2,7,5,4,1]=>0110111=>1110110=>0001001
[6,8,3,1,7,5,4,2]=>0110111=>1110110=>0001001
[6,8,1,2,7,5,4,3]=>0100111=>1110010=>0001101
[6,8,2,3,7,5,4,1]=>0100111=>1110010=>0001101
[5,2,8,3,7,6,4,1]=>1010111=>1110101=>0001010
[5,1,8,3,7,6,4,2]=>1010111=>1110101=>0001010
[5,1,8,7,2,6,3,4]=>1011010=>0101101=>1010010
[4,8,1,7,2,5,3,6]=>0101010=>0101010=>1010101
[8,4,1,6,2,5,3,7]=>1101010=>0101011=>1010100
[8,3,1,2,6,5,4,7]=>1100110=>0110011=>1001100
[3,1,2,8,7,6,5,4]=>1001111=>1111001=>0000110
[4,1,3,8,7,6,5,2]=>1001111=>1111001=>0000110
[3,1,4,8,7,6,5,2]=>1001111=>1111001=>0000110
[2,1,8,3,7,6,4,5]=>1010110=>0110101=>1001010
[2,8,1,3,7,5,4,6]=>0100110=>0110010=>1001101
[8,2,1,3,6,5,4,7]=>1100110=>0110011=>1001100
[1,8,2,3,7,5,4,6]=>0100110=>0110010=>1001101
[1,2,8,3,7,6,4,5]=>0010110=>0110100=>1001011
[1,4,3,6,8,2,5,7]=>0100100=>0010010=>1101101
[1,4,5,2,8,3,7,6]=>0010101=>1010100=>0101011
[1,4,2,6,5,8,3,7]=>0101010=>0101010=>1010101
[1,5,4,2,6,8,3,7]=>0110010=>0100110=>1011001
[3,1,6,5,8,2,4,7]=>1010100=>0010101=>1101010
[1,6,4,2,5,8,3,7]=>0110010=>0100110=>1011001
[1,5,2,6,4,8,3,7]=>0101010=>0101010=>1010101
[1,2,6,5,4,8,3,7]=>0011010=>0101100=>1010011
[1,2,5,4,7,3,8,6]=>0010101=>1010100=>0101011
[4,1,2,6,3,8,7,5]=>1001011=>1101001=>0010110
[7,1,5,4,2,8,3,6]=>1011010=>0101101=>1010010
[1,4,7,5,2,8,3,6]=>0011010=>0101100=>1010011
[7,1,3,5,2,8,4,6]=>1001010=>0101001=>1010110
[1,4,5,2,8,7,3,6]=>0010110=>0110100=>1001011
[1,6,4,2,8,3,7,5]=>0110101=>1010110=>0101001
[1,4,2,8,3,7,6,5]=>0101011=>1101010=>0010101
[1,2,8,6,5,3,7,4]=>0011101=>1011100=>0100011
[6,2,1,8,7,3,4,5]=>1101100=>0011011=>1100100
[7,6,2,1,8,3,4,5]=>1110100=>0010111=>1101000
[7,3,1,6,2,8,4,5]=>1101010=>0101011=>1010100
[1,7,6,4,2,8,3,5]=>0111010=>0101110=>1010001
[1,7,5,2,6,3,8,4]=>0110101=>1010110=>0101001
[1,6,2,7,5,3,8,4]=>0101101=>1011010=>0100101
[1,2,7,6,5,3,8,4]=>0011101=>1011100=>0100011
[1,2,6,5,3,8,7,4]=>0011011=>1101100=>0010011
[1,5,2,7,6,3,8,4]=>0101101=>1011010=>0100101
[1,6,5,2,7,3,8,4]=>0110101=>1010110=>0101001
[1,5,7,4,2,8,3,6]=>0011010=>0101100=>1010011
[3,1,8,6,2,4,7,5]=>1011001=>1001101=>0110010
[4,3,7,1,8,2,5,6]=>1010100=>0010101=>1101010
[8,3,1,6,2,4,7,5]=>1101001=>1001011=>0110100
[7,1,8,3,2,4,6,5]=>1011001=>1001101=>0110010
[1,4,2,8,7,3,6,5]=>0101101=>1011010=>0100101
[1,7,4,2,8,3,6,5]=>0110101=>1010110=>0101001
[8,1,5,4,2,7,3,6]=>1011010=>0101101=>1010010
[1,4,8,5,2,7,3,6]=>0011010=>0101100=>1010011
[8,5,3,1,7,2,4,6]=>1110100=>0010111=>1101000
[8,6,2,1,7,3,4,5]=>1110100=>0010111=>1101000
[1,8,6,4,2,7,3,5]=>0111010=>0101110=>1010001
[1,5,2,7,3,8,6,4]=>0101011=>1101010=>0010101
[1,2,8,5,3,7,6,4]=>0011011=>1101100=>0010011
[1,2,6,3,8,7,5,4]=>0010111=>1110100=>0001011
[1,2,7,6,3,8,5,4]=>0011011=>1101100=>0010011
[1,6,2,7,3,8,5,4]=>0101011=>1101010=>0010101
[1,7,4,2,8,6,3,5]=>0110110=>0110110=>1001001
[7,1,8,3,2,6,4,5]=>1011010=>0101101=>1010010
[7,2,1,8,6,3,4,5]=>1101100=>0011011=>1100100
[1,8,7,3,2,6,4,5]=>0111010=>0101110=>1010001
[1,4,2,8,7,6,3,5]=>0101110=>0111010=>1000101
[1,2,8,7,5,3,6,4]=>0011101=>1011100=>0100011
[5,1,8,7,6,2,4,3]=>1011101=>1011101=>0100010
[8,1,7,6,3,4,5,2]=>1011001=>1001101=>0110010
[5,7,8,6,2,4,1,3]=>0011010=>0101100=>1010011
[5,7,1,6,2,4,3,8]=>0101010=>0101010=>1010101
[6,4,1,5,2,7,3,8]=>1101010=>0101011=>1010100
[8,1,4,5,3,7,6,2]=>1001011=>1101001=>0010110
[6,1,4,5,3,8,7,2]=>1001011=>1101001=>0010110
[7,1,4,5,3,8,6,2]=>1001011=>1101001=>0010110
[7,1,4,5,3,6,8,2]=>1001001=>1001001=>0110110
[7,4,1,5,2,6,3,8]=>1101010=>0101011=>1010100
[6,3,5,7,2,1,4,8]=>1001100=>0011001=>1100110
[6,3,5,8,2,1,7,4]=>1001101=>1011001=>0100110
[6,3,5,7,2,1,8,4]=>1001101=>1011001=>0100110
[8,4,5,7,3,6,1,2]=>1001010=>0101001=>1010110
[6,4,5,8,3,7,2,1]=>1001011=>1101001=>0010110
[5,4,8,6,3,1,7,2]=>1011101=>1011101=>0100010
[5,4,1,8,2,3,7,6]=>1101001=>1001011=>0110100
[8,4,1,5,2,6,3,7]=>1101010=>0101011=>1010100
[6,3,5,8,2,1,4,7]=>1001100=>0011001=>1100110
[2,3,8,5,1,4,7,6]=>0011001=>1001100=>0110011
[2,3,8,6,1,5,7,4]=>0011001=>1001100=>0110011
[2,8,6,7,1,3,5,4]=>0101001=>1001010=>0110101
[8,3,5,7,2,1,6,4]=>1001101=>1011001=>0100110
[8,4,5,6,3,1,7,2]=>1001101=>1011001=>0100110
[7,3,5,6,2,8,1,4]=>1001010=>0101001=>1010110
[7,3,5,8,2,1,6,4]=>1001101=>1011001=>0100110
[7,3,5,6,2,1,4,8]=>1001100=>0011001=>1100110
[2,7,6,5,1,3,4,8]=>0111000=>0001110=>1110001
[2,7,6,8,1,3,5,4]=>0101001=>1001010=>0110101
[8,7,5,6,1,4,2,3]=>1101010=>0101011=>1010100
[2,7,1,3,6,5,8,4]=>0100101=>1010010=>0101101
[2,7,6,1,8,3,4,5]=>0110100=>0010110=>1101001
[2,7,6,1,4,3,5,8]=>0110100=>0010110=>1101001
[7,3,5,1,2,8,4,6]=>1010010=>0100101=>1011010
[2,3,8,6,4,1,7,5]=>0011101=>1011100=>0100011
[2,8,6,1,7,3,4,5]=>0110100=>0010110=>1101001
[2,3,8,1,6,4,7,5]=>0010101=>1010100=>0101011
[2,3,8,1,4,5,7,6]=>0010001=>1000100=>0111011
[5,2,6,1,4,8,7,3]=>1010011=>1100101=>0011010
[5,7,2,3,8,6,1,4]=>0100110=>0110010=>1001101
[5,6,2,3,1,8,7,4]=>0101011=>1101010=>0010101
[5,6,2,1,3,8,7,4]=>0110011=>1100110=>0011001
[5,1,6,4,2,8,7,3]=>1011011=>1101101=>0010010
[5,6,1,3,2,8,7,4]=>0101011=>1101010=>0010101
[5,6,3,1,2,8,7,4]=>0110011=>1100110=>0011001
[5,7,3,2,8,1,6,4]=>0110101=>1010110=>0101001
[6,7,3,8,2,1,5,4]=>0101101=>1011010=>0100101
[6,7,3,8,1,2,5,4]=>0101001=>1001010=>0110101
[5,7,3,1,8,2,6,4]=>0110101=>1010110=>0101001
[5,1,7,4,8,2,6,3]=>1010101=>1010101=>0101010
[1,5,7,4,8,3,6,2]=>0010101=>1010100=>0101011
[5,1,7,4,8,6,2,3]=>1010110=>0110101=>1001010
[5,7,3,1,8,6,2,4]=>0110110=>0110110=>1001001
[6,7,8,3,1,4,2,5]=>0011010=>0101100=>1010011
[6,7,1,8,3,5,2,4]=>0101010=>0101010=>1010101
[6,1,7,8,4,5,2,3]=>1001010=>0101001=>1010110
[1,6,7,8,4,5,3,2]=>0001011=>1101000=>0010111
[1,6,7,8,4,3,5,2]=>0001101=>1011000=>0100111
[6,1,7,8,4,2,5,3]=>1001101=>1011001=>0100110
[6,7,2,8,1,3,5,4]=>0101001=>1001010=>0110101
[6,7,2,8,3,5,1,4]=>0101010=>0101010=>1010101
[6,2,7,8,4,1,5,3]=>1001101=>1011001=>0100110
[6,2,7,8,1,4,5,3]=>1001001=>1001001=>0110110
[4,2,1,7,8,5,6,3]=>1100101=>1010011=>0101100
[4,1,2,7,8,6,5,3]=>1000111=>1110001=>0001110
[6,2,7,8,1,5,4,3]=>1001011=>1101001=>0010110
[6,2,7,8,5,1,4,3]=>1001101=>1011001=>0100110
[5,7,2,1,8,6,3,4]=>0110110=>0110110=>1001001
[1,6,7,8,3,5,4,2]=>0001011=>1101000=>0010111
[6,1,7,8,2,5,4,3]=>1001011=>1101001=>0010110
[6,7,8,2,4,1,3,5]=>0010100=>0010100=>1101011
[6,7,8,2,4,3,1,5]=>0010110=>0110100=>1001011
[6,7,1,8,5,2,3,4]=>0101100=>0011010=>1100101
[6,1,7,8,5,2,4,3]=>1001101=>1011001=>0100110
[1,6,7,8,5,3,4,2]=>0001101=>1011000=>0100111
[6,1,7,8,5,4,2,3]=>1001110=>0111001=>1000110
[6,7,1,8,5,3,2,4]=>0101110=>0111010=>1000101
[6,7,8,4,1,3,2,5]=>0011010=>0101100=>1010011
[3,7,4,8,5,6,1,2]=>0101010=>0101010=>1010101
[3,7,1,8,5,6,2,4]=>0101010=>0101010=>1010101
[2,7,3,8,5,6,1,4]=>0101010=>0101010=>1010101
[1,7,4,8,5,6,2,3]=>0101010=>0101010=>1010101
[2,7,3,8,4,6,1,5]=>0101010=>0101010=>1010101
[3,7,1,8,4,6,2,5]=>0101010=>0101010=>1010101
[1,5,2,8,6,7,3,4]=>0101010=>0101010=>1010101
[2,6,1,8,5,7,3,4]=>0101010=>0101010=>1010101
[1,6,2,8,5,7,3,4]=>0101010=>0101010=>1010101
[1,6,2,8,4,7,3,5]=>0101010=>0101010=>1010101
[2,6,1,8,4,7,3,5]=>0101010=>0101010=>1010101
[3,7,2,6,1,8,4,5]=>0101010=>0101010=>1010101
[4,8,1,6,2,7,3,5]=>0101010=>0101010=>1010101
[5,8,1,6,2,7,3,4]=>0101010=>0101010=>1010101
[5,8,2,6,1,7,3,4]=>0101010=>0101010=>1010101
[4,8,2,6,1,7,3,5]=>0101010=>0101010=>1010101
[1,7,3,6,2,8,4,5]=>0101010=>0101010=>1010101
[2,7,3,6,1,8,4,5]=>0101010=>0101010=>1010101
[8,6,1,4,3,2,5,7]=>1101100=>0011011=>1100100
[3,7,5,1,8,2,4,6]=>0110100=>0010110=>1101001
[4,1,5,2,8,7,3,6]=>1010110=>0110101=>1001010
[8,1,2,4,6,5,3,7]=>1000110=>0110001=>1001110
[8,2,6,5,1,3,4,7]=>1011000=>0001101=>1110010
[8,3,1,6,2,5,4,7]=>1101010=>0101011=>1010100
[8,1,2,6,4,5,3,7]=>1001010=>0101001=>1010110
[8,1,2,5,6,4,3,7]=>1000110=>0110001=>1001110
[1,7,5,4,2,8,3,6]=>0111010=>0101110=>1010001
[1,4,6,8,2,7,3,5]=>0001010=>0101000=>1010111
[1,4,7,6,2,8,3,5]=>0011010=>0101100=>1010011
[5,1,4,7,2,8,3,6]=>1001010=>0101001=>1010110
[3,7,5,1,2,8,4,6]=>0110010=>0100110=>1011001
[4,1,5,8,2,7,3,6]=>1001010=>0101001=>1010110
[1,4,6,2,8,7,3,5]=>0010110=>0110100=>1001011
[1,4,2,8,6,7,3,5]=>0101010=>0101010=>1010101
[3,1,2,6,4,8,7,5]=>1001011=>1101001=>0010110
[2,1,7,6,3,4,8,5]=>1011001=>1001101=>0110010
[3,1,2,7,4,6,8,5]=>1001001=>1001001=>0110110
[1,2,3,6,8,5,7,4]=>0000101=>1010000=>0101111
[5,1,4,2,7,8,3,6]=>1010010=>0100101=>1011010
[1,4,2,7,6,8,3,5]=>0101010=>0101010=>1010101
[1,4,2,6,8,7,3,5]=>0100110=>0110010=>1001101
[5,3,7,1,8,2,4,6]=>1010100=>0010101=>1101010
[1,7,4,3,2,5,8,6]=>0111001=>1001110=>0110001
[4,8,7,2,1,3,5,6]=>0111000=>0001110=>1110001
[1,8,7,3,4,2,5,6]=>0110100=>0010110=>1101001
[3,1,7,8,2,6,4,5]=>1001010=>0101001=>1010110
[1,4,2,7,8,3,6,5]=>0100101=>1010010=>0101101
[2,1,8,6,3,4,7,5]=>1011001=>1001101=>0110010
[1,4,2,6,8,3,7,5]=>0100101=>1010010=>0101101
[1,2,3,7,8,5,6,4]=>0000101=>1010000=>0101111
[1,2,3,7,5,8,6,4]=>0001011=>1101000=>0010111
[3,1,7,2,8,6,4,5]=>1010110=>0110101=>1001010
[1,2,3,8,7,5,6,4]=>0001101=>1011000=>0100111
[5,7,8,4,2,6,1,3]=>0011010=>0101100=>1010011
[6,7,8,4,2,5,1,3]=>0011010=>0101100=>1010011
[8,6,3,7,2,1,5,4]=>1101101=>1011011=>0100100
[6,7,8,3,2,1,5,4]=>0011101=>1011100=>0100011
[5,7,8,3,2,1,6,4]=>0011101=>1011100=>0100011
[2,7,8,4,3,5,6,1]=>0011001=>1001100=>0110011
[3,7,8,4,2,5,1,6]=>0011010=>0101100=>1010011
[7,6,3,8,2,1,4,5]=>1101100=>0011011=>1100100
[8,6,3,7,2,1,4,5]=>1101100=>0011011=>1100100
[5,6,3,8,2,1,4,7]=>0101100=>0011010=>1100101
[3,6,4,8,2,5,1,7]=>0101010=>0101010=>1010101
[2,6,4,8,3,5,7,1]=>0101001=>1001010=>0110101
[2,6,4,7,3,5,8,1]=>0101001=>1001010=>0110101
[4,6,3,7,2,1,5,8]=>0101100=>0011010=>1100101
[5,6,3,7,2,1,4,8]=>0101100=>0011010=>1100101
[8,4,3,2,1,6,5,7]=>1111010=>0101111=>1010000
[6,4,3,2,1,7,5,8]=>1111010=>0101111=>1010000
[4,5,3,2,7,1,6,8]=>0110100=>0010110=>1101001
[7,4,3,2,1,8,5,6]=>1111010=>0101111=>1010000
[8,4,3,2,1,7,5,6]=>1111010=>0101111=>1010000
[7,4,3,2,1,8,6,5]=>1111011=>1101111=>0010000
[5,6,3,8,2,1,7,4]=>0101101=>1011010=>0100101
[7,5,3,2,8,1,6,4]=>1110101=>1010111=>0101000
[8,5,4,2,7,6,1,3]=>1110110=>0110111=>1001000
[7,5,4,2,8,6,1,3]=>1110110=>0110111=>1001000
[6,5,4,2,7,8,1,3]=>1110010=>0100111=>1011000
[8,5,4,2,6,7,1,3]=>1110010=>0100111=>1011000
[5,6,3,7,2,1,8,4]=>0101101=>1011010=>0100101
[4,6,3,7,2,1,8,5]=>0101101=>1011010=>0100101
[3,6,4,7,2,8,1,5]=>0101010=>0101010=>1010101
[2,6,4,7,3,8,5,1]=>0101011=>1101010=>0010101
[3,5,4,2,7,8,1,6]=>0110010=>0100110=>1011001
[7,4,3,2,1,6,8,5]=>1111001=>1001111=>0110000
[8,4,3,2,1,6,7,5]=>1111001=>1001111=>0110000
[8,4,3,2,1,5,7,6]=>1111001=>1001111=>0110000
[7,4,3,2,1,5,8,6]=>1111001=>1001111=>0110000
[6,4,3,2,1,5,8,7]=>1111001=>1001111=>0110000
[3,5,4,2,6,8,1,7]=>0110010=>0100110=>1011001
[3,2,6,4,8,5,1,7]=>1010110=>0110101=>1001010
[4,2,5,8,3,1,6,7]=>1001100=>0011001=>1100110
[4,3,2,7,5,1,6,8]=>1101100=>0011011=>1100100
[4,3,6,2,5,1,7,8]=>1010100=>0010101=>1101010
[4,5,1,7,3,2,6,8]=>0101100=>0011010=>1100101
[5,2,1,4,3,7,8,6]=>1101001=>1001011=>0110100
[5,3,6,4,1,2,7,8]=>1011000=>0001101=>1110010
[4,3,6,1,7,2,5,8]=>1010100=>0010101=>1101010
[6,2,4,1,3,7,8,5]=>1010001=>1000101=>0111010
[3,6,4,1,2,7,5,8]=>0110010=>0100110=>1011001
[4,6,3,1,7,2,5,8]=>0110100=>0010110=>1101001
[4,5,2,7,3,1,6,8]=>0101100=>0011010=>1100101
[4,6,2,1,7,3,5,8]=>0110100=>0010110=>1101001
[3,2,6,1,4,7,5,8]=>1010010=>0100101=>1011010
[7,3,1,4,6,8,2,5]=>1100010=>0100011=>1011100
[7,4,1,5,6,2,3,8]=>1100100=>0010011=>1101100
[7,3,1,5,2,6,4,8]=>1101010=>0101011=>1010100
[6,3,5,1,2,7,4,8]=>1010010=>0100101=>1011010
[3,6,5,1,2,7,4,8]=>0110010=>0100110=>1011001
[2,4,1,5,3,8,7,6]=>0101011=>1101010=>0010101
[3,4,5,1,2,8,7,6]=>0010011=>1100100=>0011011
[1,8,4,5,3,2,7,6]=>0101101=>1011010=>0100101
[2,4,8,5,3,1,7,6]=>0011101=>1011100=>0100011
[3,4,5,2,8,1,7,6]=>0010101=>1010100=>0101011
[3,4,6,2,1,7,8,5]=>0011001=>1001100=>0110011
[3,4,6,2,1,7,5,8]=>0011010=>0101100=>1010011
[3,5,6,2,7,1,8,4]=>0010101=>1010100=>0101011
[3,4,6,2,8,7,1,5]=>0010110=>0110100=>1001011
[3,4,6,8,2,7,1,5]=>0001010=>0101000=>1010111
[2,4,8,6,3,7,1,5]=>0011010=>0101100=>1010011
[1,8,4,6,3,7,2,5]=>0101010=>0101010=>1010101
[1,8,4,6,3,7,5,2]=>0101011=>1101010=>0010101
[3,4,6,8,2,7,5,1]=>0001011=>1101000=>0010111
[3,4,6,2,8,7,5,1]=>0010111=>1110100=>0001011
[3,5,6,2,7,8,4,1]=>0010011=>1100100=>0011011
[3,5,6,2,7,4,1,8]=>0010110=>0110100=>1001011
[4,5,6,7,2,8,3,1]=>0001011=>1101000=>0010111
[2,5,8,6,7,3,4,1]=>0010101=>1010100=>0101011
[1,8,5,6,7,3,2,4]=>0100110=>0110010=>1001101
[4,5,6,7,2,1,8,3]=>0001101=>1011000=>0100111
[3,4,6,1,8,7,2,5]=>0010110=>0110100=>1001011
[2,4,1,6,8,7,3,5]=>0100110=>0110010=>1001101
[2,5,1,6,7,8,4,3]=>0100011=>1100010=>0011101
[2,5,1,6,7,4,3,8]=>0100110=>0110010=>1001101
[3,5,6,1,7,4,2,8]=>0010110=>0110100=>1001011
[3,5,6,1,7,4,8,2]=>0010101=>1010100=>0101011
[3,4,6,1,8,7,5,2]=>0010111=>1110100=>0001011
[3,4,6,8,1,7,5,2]=>0001011=>1101000=>0010111
[2,4,8,6,1,7,5,3]=>0011011=>1101100=>0010011
[1,8,4,6,2,7,5,3]=>0101011=>1101010=>0010101
[1,8,5,6,7,2,4,3]=>0100101=>1010010=>0101101
[2,5,8,6,7,1,4,3]=>0010101=>1010100=>0101011
[4,5,6,7,1,3,8,2]=>0001001=>1001000=>0110111
[3,5,6,8,7,4,1,2]=>0001110=>0111000=>1000111
[2,5,8,6,7,4,1,3]=>0010110=>0110100=>1001011
[1,8,5,6,7,4,2,3]=>0100110=>0110010=>1001101
[1,8,5,6,7,4,3,2]=>0100111=>1110010=>0001101
[2,5,8,6,7,4,3,1]=>0010111=>1110100=>0001011
[8,2,4,3,7,1,6,5]=>1010101=>1010101=>0101010
[5,8,2,4,3,7,1,6]=>0101010=>0101010=>1010101
[4,2,5,6,1,8,3,7]=>1001010=>0101001=>1010110
[4,2,5,6,1,7,3,8]=>1001010=>0101001=>1010110
[6,1,5,7,3,2,4,8]=>1001100=>0011001=>1100110
[6,1,5,8,3,2,4,7]=>1001100=>0011001=>1100110
[3,8,2,4,7,1,5,6]=>0100100=>0010010=>1101101
[3,6,8,2,4,7,1,5]=>0010010=>0100100=>1011011
[7,3,2,4,6,1,5,8]=>1100100=>0010011=>1101100
[3,2,5,1,8,4,6,7]=>1010100=>0010101=>1101010
[7,8,3,2,4,6,1,5]=>0110010=>0100110=>1011001
[6,1,5,7,8,3,2,4]=>1000110=>0110001=>1001110
[4,2,5,6,1,7,8,3]=>1001001=>1001001=>0110110
[5,7,6,1,8,3,4,2]=>0110101=>1010110=>0101001
[5,8,6,1,7,3,4,2]=>0110101=>1010110=>0101001
[6,1,5,8,7,3,2,4]=>1001110=>0111001=>1000110
[8,7,3,2,4,6,1,5]=>1110010=>0100111=>1011000
[3,2,5,1,8,7,4,6]=>1010110=>0110101=>1001010
[3,2,5,1,6,4,7,8]=>1010100=>0010101=>1101010
[3,2,4,1,8,7,5,6]=>1010110=>0110101=>1001010
[3,2,5,1,6,8,7,4]=>1010011=>1100101=>0011010
[3,8,6,5,1,7,4,2]=>0111011=>1101110=>0010001
[3,7,6,5,1,8,4,2]=>0111011=>1101110=>0010001
[6,5,1,7,8,4,2,3]=>1100110=>0110011=>1001100
[3,2,5,1,6,7,8,4]=>1010001=>1000101=>0111010
[3,2,4,1,7,5,6,8]=>1010100=>0010101=>1101010
[3,2,4,1,6,8,5,7]=>1010010=>0100101=>1011010
[8,3,2,4,7,6,1,5]=>1100110=>0110011=>1001100
[3,2,5,1,8,4,7,6]=>1010101=>1010101=>0101010
[3,2,5,1,6,7,4,8]=>1010010=>0100101=>1011010
[6,5,1,7,4,2,3,8]=>1101100=>0011011=>1100100
[6,5,1,8,4,2,3,7]=>1101100=>0011011=>1100100
[8,4,2,3,7,5,1,6]=>1100110=>0110011=>1001100
[5,2,6,1,8,3,7,4]=>1010101=>1010101=>0101010
[5,2,6,1,8,4,7,3]=>1010101=>1010101=>0101010
[7,4,2,3,8,5,1,6]=>1100110=>0110011=>1001100
[8,5,1,6,4,2,3,7]=>1101100=>0011011=>1100100
[3,2,5,1,7,6,4,8]=>1010110=>0110101=>1001010
[3,2,5,1,8,6,4,7]=>1010110=>0110101=>1001010
[8,6,1,5,7,3,2,4]=>1100110=>0110011=>1001100
[8,5,6,1,7,3,4,2]=>1010101=>1010101=>0101010
[3,6,8,5,1,7,4,2]=>0011011=>1101100=>0010011
[8,5,1,6,7,4,2,3]=>1100110=>0110011=>1001100
[3,2,5,1,8,6,7,4]=>1010101=>1010101=>0101010
[3,2,4,1,5,8,6,7]=>1010010=>0100101=>1011010
[3,2,5,1,7,8,6,4]=>1010011=>1100101=>0011010
[8,7,5,1,6,4,2,3]=>1110110=>0110111=>1001000
[3,2,5,1,8,7,6,4]=>1010111=>1110101=>0001010
[4,6,3,7,1,8,5,2]=>0101011=>1101010=>0010101
[4,6,3,7,5,1,8,2]=>0101101=>1011010=>0100101
[4,2,6,1,7,5,3,8]=>1010110=>0110101=>1001010
[2,5,7,4,1,6,3,8]=>0011010=>0101100=>1010011
[2,5,7,4,1,6,8,3]=>0011001=>1001100=>0110011
[5,4,7,8,3,1,6,2]=>1001101=>1011001=>0100110
[4,3,7,5,1,8,6,2]=>1011011=>1101101=>0010010
[6,4,3,8,5,1,7,2]=>1101101=>1011011=>0100100
[5,8,4,3,6,1,7,2]=>0110101=>1010110=>0101001
[5,4,8,3,6,1,7,2]=>1010101=>1010101=>0101010
[2,5,4,6,1,7,3,8]=>0101010=>0101010=>1010101
[4,6,2,1,8,5,7,3]=>0110101=>1010110=>0101001
[2,4,1,7,5,8,6,3]=>0101011=>1101010=>0010101
[2,4,1,7,5,3,8,6]=>0101101=>1011010=>0100101
[2,6,4,1,8,5,3,7]=>0110110=>0110110=>1001001
[5,4,8,2,1,6,3,7]=>1011010=>0101101=>1010010
[2,5,8,4,1,6,3,7]=>0011010=>0101100=>1010011
[3,2,5,6,1,8,4,7]=>1001010=>0101001=>1010110
[4,8,3,2,6,1,5,7]=>0110100=>0010110=>1101001
[3,5,2,8,1,6,4,7]=>0101010=>0101010=>1010101
[3,2,1,6,8,5,4,7]=>1100110=>0110011=>1001100
[3,2,7,1,5,4,8,6]=>1010101=>1010101=>0101010
[3,2,7,1,5,8,6,4]=>1010011=>1100101=>0011010
[3,8,2,5,1,6,7,4]=>0101001=>1001010=>0110101
[4,8,3,2,6,7,1,5]=>0110010=>0100110=>1011001
[4,3,8,2,6,7,1,5]=>1010010=>0100101=>1011010
[4,3,2,6,7,8,1,5]=>1100010=>0100011=>1011100
[4,3,2,6,7,1,5,8]=>1100100=>0010011=>1101100
[4,3,7,8,2,6,1,5]=>1001010=>0101001=>1010110
[2,5,7,4,8,1,6,3]=>0010101=>1010100=>0101011
[3,2,5,7,1,6,8,4]=>1001001=>1001001=>0110110
[3,2,5,7,1,6,4,8]=>1001010=>0101001=>1010110
[6,3,2,7,1,5,4,8]=>1101010=>0101011=>1010100
[6,3,2,7,1,5,8,4]=>1101001=>1001011=>0110100
[6,3,2,7,8,1,5,4]=>1100101=>1010011=>0101100
[6,5,2,1,7,8,4,3]=>1110011=>1100111=>0011000
[6,2,1,8,5,3,7,4]=>1101101=>1011011=>0100100
[6,3,2,7,1,4,8,5]=>1101001=>1001011=>0110100
[6,3,2,1,4,7,8,5]=>1110001=>1000111=>0111000
[6,3,2,1,4,7,5,8]=>1110010=>0100111=>1011000
[3,5,2,1,7,8,4,6]=>0110010=>0100110=>1011001
[4,6,2,1,8,3,7,5]=>0110101=>1010110=>0101001
[3,2,7,1,4,8,6,5]=>1010011=>1100101=>0011010
[3,5,8,2,1,7,4,6]=>0011010=>0101100=>1010011
[4,8,3,7,2,1,5,6]=>0101100=>0011010=>1100101
[4,3,7,2,8,1,5,6]=>1010100=>0010101=>1101010
[4,3,7,2,1,5,6,8]=>1011000=>0001101=>1110010
[4,8,3,2,7,1,5,6]=>0110100=>0010110=>1101001
[6,3,2,8,1,4,7,5]=>1101001=>1001011=>0110100
[3,2,1,4,7,5,8,6]=>1100101=>1010011=>0101100
[5,3,2,1,8,4,6,7]=>1110100=>0010111=>1101000
[4,8,3,2,1,5,6,7]=>0111000=>0001110=>1110001
[4,3,8,2,1,5,6,7]=>1011000=>0001101=>1110010
[6,2,3,1,5,4,8,7]=>1010101=>1010101=>0101010
[8,4,5,2,3,1,7,6]=>1010101=>1010101=>0101010
[8,2,5,3,4,1,7,6]=>1010101=>1010101=>0101010
[6,2,5,3,4,1,8,7]=>1010101=>1010101=>0101010
[6,4,5,1,3,2,8,7]=>1010101=>1010101=>0101010
[6,1,5,3,4,2,8,7]=>1010101=>1010101=>0101010
[8,3,7,2,4,1,6,5]=>1010101=>1010101=>0101010
[8,3,5,1,4,2,7,6]=>1010101=>1010101=>0101010
[8,4,5,1,3,2,7,6]=>1010101=>1010101=>0101010
[2,1,8,4,5,3,7,6]=>1010101=>1010101=>0101010
[8,1,7,3,4,2,6,5]=>1010101=>1010101=>0101010
[8,2,7,1,4,3,6,5]=>1010101=>1010101=>0101010
[8,2,7,3,4,1,6,5]=>1010101=>1010101=>0101010
[8,4,7,2,3,1,6,5]=>1010101=>1010101=>0101010
[8,2,3,1,5,4,7,6]=>1010101=>1010101=>0101010
[4,2,3,1,8,5,7,6]=>1010101=>1010101=>0101010
[8,2,3,1,7,5,6,4]=>1010101=>1010101=>0101010
[8,6,7,1,3,2,5,4]=>1010101=>1010101=>0101010
[8,1,3,2,7,5,6,4]=>1010101=>1010101=>0101010
[2,1,8,5,7,3,6,4]=>1010101=>1010101=>0101010
[4,5,8,6,3,2,7,1]=>0011101=>1011100=>0100011
[1,5,8,7,3,6,2,4]=>0011010=>0101100=>1010011
[1,7,2,8,4,6,5,3]=>0101011=>1101010=>0010101
[6,7,2,8,4,1,5,3]=>0101101=>1011010=>0100101
[3,6,2,8,4,5,7,1]=>0101001=>1001010=>0110101
[2,6,1,8,4,5,7,3]=>0101001=>1001010=>0110101
[2,8,4,6,1,5,7,3]=>0101001=>1001010=>0110101
[6,3,1,8,4,5,7,2]=>1101001=>1001011=>0110100
[2,3,6,8,4,5,7,1]=>0001001=>1001000=>0110111
[6,3,7,8,4,1,5,2]=>1001101=>1011001=>0100110
[1,3,7,8,4,6,5,2]=>0001011=>1101000=>0010111
[3,6,7,8,4,2,5,1]=>0001101=>1011000=>0100111
[7,6,1,8,4,2,5,3]=>1101101=>1011011=>0100100
[2,8,3,7,1,6,5,4]=>0101011=>1101010=>0010101
[5,2,8,7,3,6,1,4]=>1011010=>0101101=>1010010
[7,2,1,8,4,6,5,3]=>1101011=>1101011=>0010100
[3,2,7,8,4,6,5,1]=>1001011=>1101001=>0010110
[5,2,7,8,1,4,6,3]=>1001001=>1001001=>0110110
[1,2,7,8,5,4,6,3]=>0001101=>1011000=>0100111
[7,2,5,8,3,4,6,1]=>1001001=>1001001=>0110110
[6,2,8,5,4,3,1,7]=>1011110=>0111101=>1000010
[2,8,3,5,4,1,6,7]=>0101100=>0011010=>1100101
[2,8,4,5,3,1,6,7]=>0101100=>0011010=>1100101
[7,3,5,8,2,4,6,1]=>1001001=>1001001=>0110110
[4,3,1,2,8,5,6,7]=>1100100=>0010011=>1101100
[2,7,6,8,4,3,5,1]=>0101101=>1011010=>0100101
[1,7,5,8,3,4,6,2]=>0101001=>1001010=>0110101
[4,6,8,5,1,3,2,7]=>0011010=>0101100=>1010011
[2,4,8,3,6,5,1,7]=>0010110=>0110100=>1001011
[4,1,8,3,5,6,2,7]=>1010010=>0100101=>1011010
[5,6,8,4,1,3,2,7]=>0011010=>0101100=>1010011
[4,6,8,1,5,3,2,7]=>0010110=>0110100=>1001011
[1,6,8,4,5,3,2,7]=>0010110=>0110100=>1001011
[1,7,3,8,5,4,6,2]=>0101101=>1011010=>0100101
[3,7,1,8,5,4,6,2]=>0101101=>1011010=>0100101
[2,7,3,8,4,6,5,1]=>0101011=>1101010=>0010101
[2,8,7,4,1,6,5,3]=>0111011=>1101110=>0010001
[2,8,5,4,3,1,6,7]=>0111100=>0011110=>1100001
[1,4,3,2,8,5,6,7]=>0110100=>0010110=>1101001
[7,3,2,8,5,4,6,1]=>1101101=>1011011=>0100100
[6,4,8,2,5,3,1,7]=>1010110=>0110101=>1001010
[2,8,4,3,5,1,6,7]=>0110100=>0010110=>1101001
[6,2,8,4,5,3,1,7]=>1010110=>0110101=>1001010
[7,2,3,8,5,4,6,1]=>1001101=>1011001=>0100110
[4,2,3,1,8,5,6,7]=>1010100=>0010101=>1101010
[5,1,3,2,4,8,6,7]=>1010010=>0100101=>1011010
[2,8,1,5,3,4,7,6]=>0101001=>1001010=>0110101
[1,4,2,8,5,3,6,7]=>0101100=>0011010=>1100101
[3,5,1,4,8,2,6,7]=>0100100=>0010010=>1101101
[1,5,2,8,4,3,6,7]=>0101100=>0011010=>1100101
[1,2,5,4,3,8,6,7]=>0011010=>0101100=>1010011
[1,2,4,8,5,3,7,6]=>0001101=>1011000=>0100111
[1,5,2,7,8,4,3,6]=>0100110=>0110010=>1001101
[5,1,2,7,4,8,3,6]=>1001010=>0101001=>1010110
[8,3,5,1,4,7,2,6]=>1010010=>0100101=>1011010
[1,2,8,5,7,4,3,6]=>0010110=>0110100=>1001011
[1,2,4,8,7,5,3,6]=>0001110=>0111000=>1000111
[2,8,1,4,3,7,6,5]=>0101011=>1101010=>0010101
[7,6,1,4,2,8,3,5]=>1101010=>0101011=>1010100
[7,1,6,2,8,4,3,5]=>1010110=>0110101=>1001010
[1,4,2,7,8,5,3,6]=>0100110=>0110010=>1001101
[6,1,2,8,4,3,7,5]=>1001101=>1011001=>0100110
[6,4,1,2,8,3,7,5]=>1100101=>1010011=>0101100
[7,6,1,3,2,4,8,5]=>1101001=>1001011=>0110100
[6,7,1,3,2,4,8,5]=>0101001=>1001010=>0110101
[1,2,7,3,5,8,4,6]=>0010010=>0100100=>1011011
[5,8,1,3,7,2,4,6]=>0100100=>0010010=>1101101
[1,2,5,8,7,3,4,6]=>0001100=>0011000=>1100111
[8,6,1,3,2,4,7,5]=>1101001=>1001011=>0110100
[4,2,8,1,7,3,6,5]=>1010101=>1010101=>0101010
[7,1,2,8,4,3,6,5]=>1001101=>1011001=>0100110
[1,2,8,4,7,5,3,6]=>0010110=>0110100=>1001011
[1,2,8,7,4,5,3,6]=>0011010=>0101100=>1010011
[2,8,1,7,5,3,4,6]=>0101100=>0011010=>1100101
[8,3,7,1,5,2,4,6]=>1010100=>0010101=>1101010
[8,6,1,4,2,7,3,5]=>1101010=>0101011=>1010100
[7,1,2,8,6,4,3,5]=>1001110=>0111001=>1000110
[3,7,4,8,1,6,2,5]=>0101010=>0101010=>1010101
[3,4,8,7,1,6,2,5]=>0011010=>0101100=>1010011
[4,2,8,1,7,6,3,5]=>1010110=>0110101=>1001010
[2,8,1,7,6,4,3,5]=>0101110=>0111010=>1000101
[7,8,3,4,1,5,2,6]=>0101010=>0101010=>1010101
[6,8,3,4,1,7,2,5]=>0101010=>0101010=>1010101
[5,7,3,4,1,8,2,6]=>0101010=>0101010=>1010101
[5,8,3,4,1,7,2,6]=>0101010=>0101010=>1010101
[4,7,3,5,1,6,2,8]=>0101010=>0101010=>1010101
[4,8,3,5,1,6,2,7]=>0101010=>0101010=>1010101
[4,8,3,5,1,7,2,6]=>0101010=>0101010=>1010101
[4,7,3,5,1,8,2,6]=>0101010=>0101010=>1010101
[5,6,2,3,1,7,4,8]=>0101010=>0101010=>1010101
[5,6,2,4,1,8,3,7]=>0101010=>0101010=>1010101
[5,6,2,4,1,7,3,8]=>0101010=>0101010=>1010101
[4,6,2,5,1,7,3,8]=>0101010=>0101010=>1010101
[4,6,2,5,1,8,3,7]=>0101010=>0101010=>1010101
[4,5,1,8,3,7,2,6]=>0101010=>0101010=>1010101
[4,6,2,7,3,8,1,5]=>0101010=>0101010=>1010101
[5,6,2,7,3,8,1,4]=>0101010=>0101010=>1010101
[5,6,2,8,4,7,1,3]=>0101010=>0101010=>1010101
[5,6,2,8,3,7,1,4]=>0101010=>0101010=>1010101
[4,6,2,8,3,7,1,5]=>0101010=>0101010=>1010101
[4,5,1,7,3,6,2,8]=>0101010=>0101010=>1010101
[4,5,1,8,3,6,2,7]=>0101010=>0101010=>1010101
[6,5,3,2,1,4,8,7]=>1111001=>1001111=>0110000
[8,7,3,5,2,4,1,6]=>1101010=>0101011=>1010100
[6,8,2,4,5,7,3,1]=>0100011=>1100010=>0011101
[3,6,1,4,5,2,8,7]=>0100101=>1010010=>0101101
[8,3,7,4,5,2,1,6]=>1010110=>0110101=>1001010
[6,3,8,4,5,7,2,1]=>1010011=>1100101=>0011010
[8,1,7,4,3,6,2,5]=>1011010=>0101101=>1010010
[8,7,3,5,1,4,2,6]=>1101010=>0101011=>1010100
[2,1,6,8,5,7,4,3]=>1001011=>1101001=>0010110
[6,8,3,5,1,7,4,2]=>0101011=>1101010=>0010101
[2,5,8,4,7,6,3,1]=>0010111=>1110100=>0001011
[4,3,8,1,5,6,7,2]=>1010001=>1000101=>0111010
[4,8,3,6,1,2,7,5]=>0101001=>1001010=>0110101
[3,8,7,4,1,6,2,5]=>0111010=>0101110=>1010001
[3,8,1,2,5,6,7,4]=>0100001=>1000010=>0111101
[2,8,7,4,5,1,3,6]=>0110100=>0010110=>1101001
[8,7,2,4,1,6,3,5]=>1101010=>0101011=>1010100
[5,8,3,6,2,4,7,1]=>0101001=>1001010=>0110101
[8,6,3,2,1,4,7,5]=>1111001=>1001111=>0110000
[8,7,3,5,2,1,4,6]=>1101100=>0011011=>1100100
[5,8,3,6,2,1,7,4]=>0101101=>1011010=>0100101
[6,1,8,4,5,7,2,3]=>1010010=>0100101=>1011010
[6,8,3,5,1,7,2,4]=>0101010=>0101010=>1010101
[5,8,3,6,1,2,7,4]=>0101001=>1001010=>0110101
[5,8,1,4,7,6,2,3]=>0100110=>0110010=>1001101
[4,5,3,8,6,1,7,2]=>0101101=>1011010=>0100101
[4,5,7,6,2,3,8,1]=>0011001=>1001100=>0110011
[3,5,7,2,6,4,8,1]=>0010101=>1010100=>0101011
[2,5,7,3,6,4,8,1]=>0010101=>1010100=>0101011
[8,4,3,7,6,1,5,2]=>1101101=>1011011=>0100100
[6,7,2,3,5,4,8,1]=>0100101=>1010010=>0101101
[5,2,7,3,6,4,8,1]=>1010101=>1010101=>0101010
[8,3,4,7,6,1,5,2]=>1001101=>1011001=>0100110
[8,2,4,7,1,6,5,3]=>1001011=>1101001=>0010110
[3,1,4,7,6,8,5,2]=>1001011=>1101001=>0010110
[5,1,7,3,6,8,4,2]=>1010011=>1100101=>0011010
[6,7,1,3,5,8,4,2]=>0100011=>1100010=>0011101
[4,8,3,7,6,1,5,2]=>0101101=>1011010=>0100101
[2,8,4,7,1,6,5,3]=>0101011=>1101010=>0010101
[8,1,4,7,2,6,5,3]=>1001011=>1101001=>0010110
[8,1,3,2,7,6,5,4]=>1010111=>1110101=>0001010
[2,8,3,1,7,6,5,4]=>0110111=>1110110=>0001001
[6,7,1,2,8,5,4,3]=>0100111=>1110010=>0001101
[8,2,3,1,7,6,5,4]=>1010111=>1110101=>0001010
[1,4,2,7,8,6,5,3]=>0100111=>1110010=>0001101
[8,4,2,7,1,6,5,3]=>1101011=>1101011=>0010100
[8,5,7,2,1,6,4,3]=>1011011=>1101101=>0010010
[1,5,7,2,8,6,4,3]=>0010111=>1110100=>0001011
[2,5,7,1,8,6,4,3]=>0010111=>1110100=>0001011
[3,5,7,1,6,8,4,2]=>0010011=>1100100=>0011011
[6,7,4,5,8,1,3,2]=>0100101=>1010010=>0101101
[2,5,7,8,1,6,4,3]=>0001011=>1101000=>0010111
[1,5,7,8,2,6,4,3]=>0001011=>1101000=>0010111
[8,5,7,1,2,6,4,3]=>1010011=>1100101=>0011010
[8,4,1,7,2,6,5,3]=>1101011=>1101011=>0010100
[6,7,2,8,1,5,4,3]=>0101011=>1101010=>0010101
[5,2,7,8,1,6,4,3]=>1001011=>1101001=>0010110
[4,2,8,7,1,6,5,3]=>1011011=>1101101=>0010010
[1,3,8,2,7,6,5,4]=>0010111=>1110100=>0001011
[8,3,1,2,7,6,5,4]=>1100111=>1110011=>0001100
[8,2,1,3,7,6,5,4]=>1100111=>1110011=>0001100
[2,1,8,3,7,6,5,4]=>1010111=>1110101=>0001010
[5,1,7,8,2,6,4,3]=>1001011=>1101001=>0010110
[6,7,1,8,2,5,4,3]=>0101011=>1101010=>0010101
[4,8,1,7,2,6,5,3]=>0101011=>1101010=>0010101
[3,8,1,2,7,6,5,4]=>0100111=>1110010=>0001101
[1,8,2,3,7,6,5,4]=>0100111=>1110010=>0001101
[3,7,1,5,8,2,6,4]=>0100101=>1010010=>0101101
[2,7,1,5,8,3,6,4]=>0100101=>1010010=>0101101
[2,6,5,1,8,3,7,4]=>0110101=>1010110=>0101001
[5,6,4,1,8,7,2,3]=>0110110=>0110110=>1001001
[8,1,4,5,7,6,2,3]=>1000110=>0110001=>1001110
[6,4,5,1,8,7,2,3]=>1010110=>0110101=>1001010
[5,4,6,1,8,7,2,3]=>1010110=>0110101=>1001010
[3,5,6,1,8,2,7,4]=>0010101=>1010100=>0101011
[2,5,6,1,8,3,7,4]=>0010101=>1010100=>0101011
[2,4,6,1,3,8,7,5]=>0010011=>1100100=>0011011
[3,4,6,1,2,8,7,5]=>0010011=>1100100=>0011011
[5,3,6,1,8,2,7,4]=>1010101=>1010101=>0101010
[7,3,1,5,8,2,6,4]=>1100101=>1010011=>0101100
[8,1,3,5,7,2,6,4]=>1000101=>1010001=>0101110
[8,1,2,5,7,3,6,4]=>1000101=>1010001=>0101110
[7,2,1,5,8,3,6,4]=>1100101=>1010011=>0101100
[6,2,5,1,8,3,7,4]=>1010101=>1010101=>0101010
[4,2,6,1,3,8,7,5]=>1010011=>1100101=>0011010
[4,2,5,3,1,8,7,6]=>1011011=>1101101=>0010010
[6,2,4,1,3,8,7,5]=>1010011=>1100101=>0011010
[7,2,1,4,3,8,6,5]=>1101011=>1101011=>0010100
[8,1,2,4,3,7,6,5]=>1001011=>1101001=>0010110
[8,1,3,4,2,7,6,5]=>1001011=>1101001=>0010110
[7,3,1,4,2,8,6,5]=>1101011=>1101011=>0010100
[4,6,3,1,2,8,7,5]=>0110011=>1100110=>0011001
[2,6,4,1,3,8,7,5]=>0110011=>1100110=>0011001
[2,7,1,4,3,8,6,5]=>0101011=>1101010=>0010101
[8,1,6,7,2,3,5,4]=>1001001=>1001001=>0110110
[4,7,1,2,3,8,6,5]=>0100011=>1100010=>0011101
[3,7,1,2,4,8,6,5]=>0100011=>1100010=>0011101
[2,6,3,1,4,8,7,5]=>0110011=>1100110=>0011001
[3,6,2,1,4,8,7,5]=>0110011=>1100110=>0011001
[5,6,2,1,8,3,7,4]=>0110101=>1010110=>0101001
[6,5,2,1,8,3,7,4]=>1110101=>1010111=>0101000
[8,1,4,2,3,7,6,5]=>1010011=>1100101=>0011010
[7,4,1,2,3,8,6,5]=>1100011=>1100011=>0011100
[5,4,2,3,1,8,7,6]=>1101011=>1101011=>0010100
[3,5,2,4,1,8,7,6]=>0101011=>1101010=>0010101
[7,3,1,2,4,8,6,5]=>1100011=>1100011=>0011100
[8,1,3,2,4,7,6,5]=>1010011=>1100101=>0011010
[7,2,1,3,4,8,6,5]=>1100011=>1100011=>0011100
[2,4,3,6,1,5,8,7]=>0101001=>1001010=>0110101
[2,4,3,6,5,8,1,7]=>0101010=>0101010=>1010101
[2,4,6,3,5,8,7,1]=>0010011=>1100100=>0011011
[2,4,6,3,5,1,8,7]=>0010101=>1010100=>0101011
[2,4,6,3,1,5,8,7]=>0011001=>1001100=>0110011
[2,4,1,6,5,3,8,7]=>0101101=>1011010=>0100101
[2,4,6,1,5,3,8,7]=>0010101=>1010100=>0101011
[4,2,6,5,3,1,8,7]=>1011101=>1011101=>0100010
[4,2,6,5,1,3,8,7]=>1011001=>1001101=>0110010
[4,2,6,5,8,1,7,3]=>1010101=>1010101=>0101010
[4,2,6,5,8,1,3,7]=>1010100=>0010101=>1101010
[4,2,6,5,8,3,1,7]=>1010110=>0110101=>1001010
[2,4,1,6,5,8,3,7]=>0101010=>0101010=>1010101
[2,1,4,6,5,8,3,7]=>1001010=>0101001=>1010110
[2,4,1,6,5,8,7,3]=>0101011=>1101010=>0010101
[2,4,6,1,5,8,7,3]=>0010011=>1100100=>0011011
[4,2,6,5,3,8,7,1]=>1011011=>1101101=>0010010
[2,6,4,3,8,7,5,1]=>0110111=>1110110=>0001001
[4,2,6,8,5,3,7,1]=>1001101=>1011001=>0100110
[2,4,6,8,1,5,7,3]=>0001001=>1001000=>0110111
[2,4,1,6,8,5,7,3]=>0100101=>1010010=>0101101
[2,1,4,6,8,5,3,7]=>1000110=>0110001=>1001110
[2,4,6,1,8,5,3,7]=>0010110=>0110100=>1001011
[2,4,6,8,1,5,3,7]=>0001010=>0101000=>1010111
[2,4,6,8,3,5,7,1]=>0001001=>1001000=>0110111
[2,4,6,8,3,1,5,7]=>0001100=>0011000=>1100111
[2,4,6,3,8,5,7,1]=>0010101=>1010100=>0101011
[2,4,3,6,8,5,7,1]=>0100101=>1010010=>0101101
[2,4,3,6,8,5,1,7]=>0100110=>0110010=>1001101
[2,4,3,6,8,1,5,7]=>0100100=>0010010=>1101101
[2,4,3,6,1,8,5,7]=>0101010=>0101010=>1010101
[2,4,3,1,6,8,5,7]=>0110010=>0100110=>1011001
[2,4,1,3,6,8,7,5]=>0100011=>1100010=>0011101
[2,4,3,6,8,1,7,5]=>0100101=>1010010=>0101101
[4,6,5,2,8,7,1,3]=>0110110=>0110110=>1001001
[4,6,2,5,8,7,1,3]=>0100110=>0110010=>1001101
[4,6,2,5,8,7,3,1]=>0100111=>1110010=>0001101
[2,4,6,3,1,8,7,5]=>0011011=>1101100=>0010011
[2,4,1,6,3,8,7,5]=>0101011=>1101010=>0010101
[2,1,4,6,3,8,7,5]=>1001011=>1101001=>0010110
[2,4,1,6,8,3,7,5]=>0100101=>1010010=>0101101
[2,4,6,8,1,3,7,5]=>0001001=>1001000=>0110111
[4,6,2,8,5,7,3,1]=>0101011=>1101010=>0010101
[4,6,2,8,5,7,1,3]=>0101010=>0101010=>1010101
[6,2,4,8,7,1,3,5]=>1001100=>0011001=>1100110
[2,6,4,8,1,7,5,3]=>0101011=>1101010=>0010101
[2,6,4,1,8,7,5,3]=>0110111=>1110110=>0001001
[2,1,6,4,8,7,3,5]=>1010110=>0110101=>1001010
[2,6,4,1,8,7,3,5]=>0110110=>0110110=>1001001
[2,6,4,8,1,7,3,5]=>0101010=>0101010=>1010101
[6,2,4,8,7,3,5,1]=>1001101=>1011001=>0100110
[6,2,4,8,7,3,1,5]=>1001110=>0111001=>1000110
[1,3,7,4,5,8,2,6]=>0010010=>0100100=>1011011
[1,7,6,3,4,8,2,5]=>0110010=>0100110=>1011001
[8,1,6,3,7,2,4,5]=>1010100=>0010101=>1101010
[1,2,7,4,8,3,5,6]=>0010100=>0010100=>1101011
[6,1,7,3,4,8,2,5]=>1010010=>0100101=>1011010
[2,1,7,4,5,8,3,6]=>1010010=>0100101=>1011010
[5,1,4,7,3,8,2,6]=>1001010=>0101001=>1010110
[4,3,1,7,5,8,2,6]=>1101010=>0101011=>1010100
[2,8,6,3,7,1,4,5]=>0110100=>0010110=>1101001
[6,8,1,3,7,2,4,5]=>0100100=>0010010=>1101101
[5,8,2,1,7,3,4,6]=>0110100=>0010110=>1101001
[5,7,2,1,8,3,4,6]=>0110100=>0010110=>1101001
[6,7,1,3,8,2,4,5]=>0100100=>0010010=>1101101
[8,5,1,3,7,2,4,6]=>1100100=>0010011=>1101100
[1,5,3,2,8,4,6,7]=>0110100=>0010110=>1101001
[2,6,4,8,7,1,3,5]=>0101100=>0011010=>1100101
[1,6,4,8,7,2,3,5]=>0101100=>0011010=>1100101
[4,3,2,8,7,1,5,6]=>1101100=>0011011=>1100100
[5,2,4,8,7,1,3,6]=>1001100=>0011001=>1100110
[6,2,8,3,7,1,4,5]=>1010100=>0010101=>1101010
[5,1,4,8,7,2,3,6]=>1001100=>0011001=>1100110
[3,7,2,1,5,4,8,6]=>0110101=>1010110=>0101001
[3,8,2,1,5,4,7,6]=>0110101=>1010110=>0101001
[8,3,2,1,5,4,6,7]=>1110100=>0010111=>1101000
[8,3,2,1,6,4,5,7]=>1110100=>0010111=>1101000
[8,4,2,5,1,6,3,7]=>1101010=>0101011=>1010100
[8,3,2,1,4,6,5,7]=>1110010=>0100111=>1011000
[3,8,2,1,4,5,7,6]=>0110001=>1000110=>0111001
[3,2,7,1,4,6,8,5]=>1010001=>1000101=>0111010
[3,2,8,1,4,6,7,5]=>1010001=>1000101=>0111010
[3,8,2,1,4,7,5,6]=>0110010=>0100110=>1011001
[3,8,2,1,5,7,4,6]=>0110010=>0100110=>1011001
[4,8,2,5,1,7,3,6]=>0101010=>0101010=>1010101
[4,7,2,5,1,8,3,6]=>0101010=>0101010=>1010101
[3,7,2,1,5,8,4,6]=>0110010=>0100110=>1011001
[3,7,2,1,4,8,5,6]=>0110010=>0100110=>1011001
[3,2,1,7,5,8,6,4]=>1101011=>1101011=>0010100
[4,2,7,6,1,8,3,5]=>1011010=>0101101=>1010010
[4,3,7,6,8,1,2,5]=>1010100=>0010101=>1101010
[4,3,8,6,7,1,2,5]=>1010100=>0010101=>1101010
[3,8,2,1,7,4,5,6]=>0110100=>0010110=>1101001
[3,2,8,1,6,4,7,5]=>1010101=>1010101=>0101010
[3,2,7,1,6,4,8,5]=>1010101=>1010101=>0101010
[4,2,7,6,1,3,8,5]=>1011001=>1001101=>0110010
[4,2,8,6,1,3,7,5]=>1011001=>1001101=>0110010
[5,7,8,3,4,1,2,6]=>0010100=>0010100=>1101011
[4,2,6,8,1,3,7,5]=>1001001=>1001001=>0110110
[4,2,6,7,1,3,8,5]=>1001001=>1001001=>0110110
[3,2,6,1,8,4,7,5]=>1010101=>1010101=>0101010
[3,7,2,1,8,5,4,6]=>0110110=>0110110=>1001001
[4,7,3,8,5,1,2,6]=>0101100=>0011010=>1100101
[4,3,7,8,6,1,2,5]=>1001100=>0011001=>1100110
[3,2,7,1,8,6,4,5]=>1010110=>0110101=>1001010
[3,2,1,6,8,5,7,4]=>1100101=>1010011=>0101100
[3,2,6,1,8,7,4,5]=>1010110=>0110101=>1001010
[4,2,6,8,1,7,3,5]=>1001010=>0101001=>1010110
[4,3,6,8,7,1,2,5]=>1001100=>0011001=>1100110
[4,2,6,7,1,8,3,5]=>1001010=>0101001=>1010110
[3,2,6,1,7,8,4,5]=>1010010=>0100101=>1011010
[5,3,6,4,8,7,1,2]=>1010110=>0110101=>1001010
[1,4,6,2,7,8,5,3]=>0010011=>1100100=>0011011
[3,1,8,5,4,2,6,7]=>1011100=>0011101=>1100010
[1,2,7,5,4,8,6,3]=>0011011=>1101100=>0010011
[6,3,7,5,4,8,1,2]=>1011010=>0101101=>1010010
[1,6,2,5,4,8,7,3]=>0101011=>1101010=>0010101
[1,8,2,5,7,3,6,4]=>0100101=>1010010=>0101101
[6,2,1,5,4,8,7,3]=>1101011=>1101011=>0010100
[4,1,6,2,8,7,5,3]=>1010111=>1110101=>0001010
[7,8,3,1,4,2,6,5]=>0110101=>1010110=>0101001
[4,3,6,1,8,2,7,5]=>1010101=>1010101=>0101010
[7,5,1,6,4,3,2,8]=>1101110=>0111011=>1000100
[6,1,5,7,4,3,2,8]=>1001110=>0111001=>1000110
[1,5,8,6,4,3,2,7]=>0011110=>0111100=>1000011
[7,8,5,1,6,3,2,4]=>0110110=>0110110=>1001001
[2,6,1,5,7,3,8,4]=>0100101=>1010010=>0101101
[1,6,8,7,4,3,2,5]=>0011110=>0111100=>1000011
[6,8,1,7,4,3,2,5]=>0101110=>0111010=>1000101
[5,6,1,7,4,3,2,8]=>0101110=>0111010=>1000101
[5,1,7,6,4,3,2,8]=>1011110=>0111101=>1000010
[6,1,7,8,4,3,2,5]=>1001110=>0111001=>1000110
[7,1,8,6,4,3,2,5]=>1011110=>0111101=>1000010
[7,2,1,5,4,6,8,3]=>1101001=>1001011=>0110100
[1,2,8,5,6,3,7,4]=>0010101=>1010100=>0101011
[6,1,2,5,7,3,8,4]=>1000101=>1010001=>0101110
[4,3,6,1,5,7,2,8]=>1010010=>0100101=>1011010
[1,3,6,8,5,7,2,4]=>0001010=>0101000=>1010111
[1,3,6,4,8,7,2,5]=>0010110=>0110100=>1001011
[4,1,6,7,3,8,2,5]=>1001010=>0101001=>1010110
[5,4,6,1,3,7,2,8]=>1010010=>0100101=>1011010
[6,4,1,5,2,3,7,8]=>1101000=>0001011=>1110100
[4,1,7,5,2,3,8,6]=>1011001=>1001101=>0110010
[2,8,3,5,4,1,7,6]=>0101101=>1011010=>0100101
[7,8,1,4,6,3,2,5]=>0100110=>0110010=>1001101
[5,1,8,7,4,3,2,6]=>1011110=>0111101=>1000010
[6,5,1,8,4,3,2,7]=>1101110=>0111011=>1000100
[6,5,7,1,4,3,2,8]=>1010110=>0110101=>1001010
[7,5,8,1,4,3,2,6]=>1010110=>0110101=>1001010
[1,5,7,8,4,3,2,6]=>0001110=>0111000=>1000111
[2,4,7,5,1,3,8,6]=>0011001=>1001100=>0110011
[7,8,4,6,1,3,2,5]=>0101010=>0101010=>1010101
[1,6,5,8,4,3,2,7]=>0101110=>0111010=>1000101
[6,8,5,1,4,3,2,7]=>0110110=>0110110=>1001001
[3,6,2,5,4,1,7,8]=>0101100=>0011010=>1100101
[4,3,6,2,8,1,5,7]=>1010100=>0010101=>1101010
[6,1,2,5,4,7,8,3]=>1001001=>1001001=>0110110
[6,2,4,5,1,3,7,8]=>1001000=>0001001=>1110110
[4,2,8,5,1,3,7,6]=>1011001=>1001101=>0110010
[4,3,6,8,1,7,2,5]=>1001010=>0101001=>1010110
[5,3,6,4,1,7,2,8]=>1011010=>0101101=>1010010
[1,6,7,4,8,3,5,2]=>0010101=>1010100=>0101011
[1,4,6,3,7,5,8,2]=>0010101=>1010100=>0101011
[4,6,7,2,5,8,1,3]=>0010010=>0100100=>1011011
[2,4,6,1,7,5,3,8]=>0010110=>0110100=>1001011
[2,7,5,4,1,6,3,8]=>0111010=>0101110=>1010001
[1,7,5,4,3,8,6,2]=>0111011=>1101110=>0010001
[1,5,8,4,3,6,7,2]=>0011001=>1001100=>0110011
[5,4,6,2,7,8,1,3]=>1010010=>0100101=>1011010
[2,5,4,1,6,7,3,8]=>0110010=>0100110=>1011001
[5,6,3,2,7,1,4,8]=>0110100=>0010110=>1101001
[5,6,3,2,7,1,8,4]=>0110101=>1010110=>0101001
[8,5,6,3,2,7,1,4]=>1011010=>0101101=>1010010
[5,4,6,2,8,1,7,3]=>1010101=>1010101=>0101010
[2,4,1,7,8,5,3,6]=>0100110=>0110010=>1001101
[5,6,3,2,1,8,4,7]=>0111010=>0101110=>1010001
[3,5,2,1,6,4,7,8]=>0110100=>0010110=>1101001
[6,8,4,3,2,1,5,7]=>0111100=>0011110=>1100001
[5,3,8,2,1,6,4,7]=>1011010=>0101101=>1010010
[7,3,2,8,5,1,6,4]=>1101101=>1011011=>0100100
[8,4,6,3,2,1,7,5]=>1011101=>1011101=>0100010
[5,4,7,2,1,8,6,3]=>1011011=>1101101=>0010010
[5,7,3,2,1,6,8,4]=>0111001=>1001110=>0110001
[6,3,7,2,5,1,8,4]=>1010101=>1010101=>0101010
[6,7,8,3,5,2,1,4]=>0010110=>0110100=>1001011
[6,2,5,7,8,4,1,3]=>1000110=>0110001=>1001110
[2,1,5,7,8,6,3,4]=>1000110=>0110001=>1001110
[3,6,7,2,8,1,4,5]=>0010100=>0010100=>1101011
[3,2,6,1,7,4,5,8]=>1010100=>0010101=>1101010
[2,5,8,4,1,3,7,6]=>0011001=>1001100=>0110011
[2,4,1,7,8,3,6,5]=>0100101=>1010010=>0101101
[3,6,8,2,1,7,4,5]=>0011010=>0101100=>1010011
[5,3,8,2,1,4,7,6]=>1011001=>1001101=>0110010
[4,8,7,3,2,1,5,6]=>0111100=>0011110=>1100001
[4,7,3,2,1,5,6,8]=>0111000=>0001110=>1110001
[8,4,7,3,2,1,5,6]=>1011100=>0011101=>1100010
[8,3,5,2,1,4,7,6]=>1011001=>1001101=>0110010
[3,5,2,1,4,6,8,7]=>0110001=>1000110=>0111001
[2,7,6,5,1,8,3,4]=>0111010=>0101110=>1010001
[2,7,6,5,1,8,4,3]=>0111011=>1101110=>0010001
[2,3,6,5,1,4,8,7]=>0011001=>1001100=>0110011
[2,3,6,4,1,5,8,7]=>0011001=>1001100=>0110011
[2,7,6,1,4,8,5,3]=>0110011=>1100110=>0011001
[7,3,5,1,8,4,2,6]=>1010110=>0110101=>1001010
[2,7,6,1,5,8,4,3]=>0110011=>1100110=>0011001
[2,7,6,4,1,8,5,3]=>0111011=>1101110=>0010001
[2,7,6,4,1,8,3,5]=>0111010=>0101110=>1010001
[7,3,5,1,8,6,2,4]=>1010110=>0110101=>1001010
[2,3,4,8,7,6,1,5]=>0001110=>0111000=>1000111
[2,3,4,8,5,7,1,6]=>0001010=>0101000=>1010111
[7,3,5,4,8,1,2,6]=>1010100=>0010101=>1101010
[6,4,3,5,8,7,2,1]=>1100111=>1110011=>0001100
[2,1,4,5,8,7,3,6]=>1000110=>0110001=>1001110
[6,4,3,5,8,7,1,2]=>1100110=>0110011=>1001100
[2,3,4,8,7,5,1,6]=>0001110=>0111000=>1000111
[2,7,6,5,4,8,1,3]=>0111010=>0101110=>1010001
[7,3,5,6,8,1,2,4]=>1000100=>0010001=>1101110
[6,4,1,5,8,7,2,3]=>1100110=>0110011=>1001100
[6,4,1,5,8,7,3,2]=>1100111=>1110011=>0001100
[6,4,1,5,8,3,7,2]=>1100101=>1010011=>0101100
[5,7,1,6,3,8,2,4]=>0101010=>0101010=>1010101
[6,4,1,5,8,3,2,7]=>1100110=>0110011=>1001100
[6,3,5,7,8,2,1,4]=>1000110=>0110001=>1001110
[5,7,3,6,1,8,4,2]=>0101011=>1101010=>0010101
[7,3,5,4,8,6,2,1]=>1010111=>1110101=>0001010
[2,3,4,8,5,6,1,7]=>0001010=>0101000=>1010111
[2,3,4,8,7,1,6,5]=>0001101=>1011000=>0100111
[2,3,4,8,5,1,7,6]=>0001101=>1011000=>0100111
[7,4,3,5,8,2,1,6]=>1100110=>0110011=>1001100
[7,4,3,5,8,2,6,1]=>1100101=>1010011=>0101100
[6,3,5,4,8,2,1,7]=>1010110=>0110101=>1001010
[2,3,4,8,5,1,6,7]=>0001100=>0011000=>1100111
[6,1,4,2,8,5,7,3]=>1010101=>1010101=>0101010
[4,8,6,5,3,2,7,1]=>0111101=>1011110=>0100001
[8,6,5,1,2,4,7,3]=>1110001=>1000111=>0111000
[1,7,5,8,2,6,4,3]=>0101011=>1101010=>0010101
[1,3,8,5,7,6,2,4]=>0010110=>0110100=>1001011
[6,3,8,5,7,1,2,4]=>1010100=>0010101=>1101010
[6,8,5,2,1,4,7,3]=>0111001=>1001110=>0110001
[3,8,2,5,6,1,7,4]=>0100101=>1010010=>0101101
[8,1,2,5,6,3,7,4]=>1000101=>1010001=>0101110
[8,6,1,5,7,2,3,4]=>1100100=>0010011=>1101100
[3,8,6,5,7,1,2,4]=>0110100=>0010110=>1101001
[5,1,7,6,8,4,2,3]=>1010110=>0110101=>1001010
[5,1,3,7,8,6,2,4]=>1000110=>0110001=>1001110
[7,2,5,8,1,6,4,3]=>1001011=>1101001=>0010110
[3,2,8,5,7,6,1,4]=>1010110=>0110101=>1001010
[8,2,1,5,7,6,3,4]=>1100110=>0110011=>1001100
[5,2,8,6,1,7,3,4]=>1011010=>0101101=>1010010
[1,2,8,6,5,7,3,4]=>0011010=>0101100=>1010011
[8,2,5,6,3,7,1,4]=>1001010=>0101001=>1010110
[7,2,6,5,4,1,8,3]=>1011101=>1011101=>0100010
[6,1,3,5,4,7,8,2]=>1001001=>1001001=>0110110
[6,1,5,3,4,7,8,2]=>1010001=>1000101=>0111010
[7,5,6,2,4,1,8,3]=>1010101=>1010101=>0101010
[8,5,2,6,3,7,1,4]=>1101010=>0101011=>1010100
[8,1,6,5,7,3,2,4]=>1010110=>0110101=>1001010
[3,5,8,6,2,7,1,4]=>0011010=>0101100=>1010011
[1,8,5,6,3,7,2,4]=>0101010=>0101010=>1010101
[1,7,6,5,4,2,8,3]=>0111101=>1011110=>0100001
[5,7,6,1,4,2,8,3]=>0110101=>1010110=>0101001
[7,1,4,2,6,5,8,3]=>1010101=>1010101=>0101010
[2,7,4,1,5,6,8,3]=>0110001=>1000110=>0111001
[5,7,6,4,1,2,8,3]=>0111001=>1001110=>0110001
[4,7,6,1,5,2,8,3]=>0110101=>1010110=>0101001
[1,7,6,4,5,2,8,3]=>0110101=>1010110=>0101001
[3,8,1,6,5,7,2,4]=>0101010=>0101010=>1010101
[8,1,3,5,7,6,2,4]=>1000110=>0110001=>1001110
[7,8,5,4,1,6,2,3]=>0111010=>0101110=>1010001
[6,1,5,4,3,7,8,2]=>1011001=>1001101=>0110010
[7,5,6,4,2,1,8,3]=>1011101=>1011101=>0100010
[8,3,2,6,5,7,1,4]=>1101010=>0101011=>1010100
[7,4,6,2,5,1,8,3]=>1010101=>1010101=>0101010
[6,1,4,3,5,7,8,2]=>1010001=>1000101=>0111010
[6,1,3,4,5,7,8,2]=>1000001=>1000001=>0111110
[7,2,6,4,5,1,8,3]=>1010101=>1010101=>0101010
[8,2,3,6,5,7,1,4]=>1001010=>0101001=>1010110
[2,1,4,3,6,5,8,7,11,12,10,9]=>10101010011=>11001010101=>00110101010
[2,1,4,3,6,5,9,10,8,7,12,11]=>10101001101=>10110010101=>01001101010
[2,1,4,3,6,5,9,11,8,12,10,7]=>10101001011=>11010010101=>00101101010
[2,1,4,3,6,5,10,11,12,9,8,7]=>10101000111=>11100010101=>00011101010
[2,1,4,3,7,8,6,5,10,9,12,11]=>10100110101=>10101100101=>01010011010
[2,1,4,3,7,8,6,5,11,12,10,9]=>10100110011=>11001100101=>00110011010
[2,1,4,3,7,9,6,10,8,5,12,11]=>10100101101=>10110100101=>01001011010
[2,1,4,3,7,9,6,11,8,12,10,5]=>10100101011=>11010100101=>00101011010
[2,1,4,3,7,10,6,11,12,9,8,5]=>10100100111=>11100100101=>00011011010
[2,1,4,3,8,9,10,7,6,5,12,11]=>10100011101=>10111000101=>01000111010
[2,1,4,3,8,9,11,7,6,12,10,5]=>10100011011=>11011000101=>00100111010
[2,1,4,3,8,10,11,7,12,9,6,5]=>10100010111=>11101000101=>00010111010
[2,1,4,3,9,10,11,12,8,7,6,5]=>10100001111=>11110000101=>00001111010
[2,1,5,6,4,3,8,7,10,9,12,11]=>10011010101=>10101011001=>01010100110
[2,1,5,6,4,3,8,7,11,12,10,9]=>10011010011=>11001011001=>00110100110
[2,1,5,6,4,3,9,10,8,7,12,11]=>10011001101=>10110011001=>01001100110
[2,1,5,6,4,3,9,11,8,12,10,7]=>10011001011=>11010011001=>00101100110
[2,1,5,6,4,3,10,11,12,9,8,7]=>10011000111=>11100011001=>00011100110
[2,1,5,7,4,8,6,3,10,9,12,11]=>10010110101=>10101101001=>01010010110
[2,1,5,7,4,8,6,3,11,12,10,9]=>10010110011=>11001101001=>00110010110
[2,1,5,7,4,9,6,10,8,3,12,11]=>10010101101=>10110101001=>01001010110
[2,1,5,7,4,9,6,11,8,12,10,3]=>10010101011=>11010101001=>00101010110
[2,1,5,7,4,10,6,11,12,9,8,3]=>10010100111=>11100101001=>00011010110
[2,1,5,8,4,9,10,7,6,3,12,11]=>10010011101=>10111001001=>01000110110
[2,1,5,8,4,9,11,7,6,12,10,3]=>10010011011=>11011001001=>00100110110
[2,1,5,8,4,10,11,7,12,9,6,3]=>10010010111=>11101001001=>00010110110
[2,1,5,9,4,10,11,12,8,7,6,3]=>10010001111=>11110001001=>00001110110
[2,1,6,7,8,5,4,3,10,9,12,11]=>10001110101=>10101110001=>01010001110
[2,1,6,7,8,5,4,3,11,12,10,9]=>10001110011=>11001110001=>00110001110
[2,1,6,7,9,5,4,10,8,3,12,11]=>10001101101=>10110110001=>01001001110
[2,1,6,7,9,5,4,11,8,12,10,3]=>10001101011=>11010110001=>00101001110
[2,1,6,7,10,5,4,11,12,9,8,3]=>10001100111=>11100110001=>00011001110
[2,1,6,8,9,5,10,7,4,3,12,11]=>10001011101=>10111010001=>01000101110
[2,1,6,8,9,5,11,7,4,12,10,3]=>10001011011=>11011010001=>00100101110
[2,1,6,8,10,5,11,7,12,9,4,3]=>10001010111=>11101010001=>00010101110
[2,1,6,9,10,5,11,12,8,7,4,3]=>10001001111=>11110010001=>00001101110
[2,1,7,8,9,10,6,5,4,3,12,11]=>10000111101=>10111100001=>01000011110
[2,1,7,8,9,11,6,5,4,12,10,3]=>10000111011=>11011100001=>00100011110
[2,1,7,8,10,11,6,5,12,9,4,3]=>10000110111=>11101100001=>00010011110
[2,1,7,9,10,11,6,12,8,5,4,3]=>10000101111=>11110100001=>00001011110
[2,1,8,9,10,11,12,7,6,5,4,3]=>10000011111=>11111000001=>00000111110
[3,4,2,1,6,5,8,7,10,9,12,11]=>01101010101=>10101010110=>01010101001
[3,4,2,1,6,5,8,7,11,12,10,9]=>01101010011=>11001010110=>00110101001
[3,4,2,1,6,5,9,10,8,7,12,11]=>01101001101=>10110010110=>01001101001
[3,4,2,1,6,5,9,11,8,12,10,7]=>01101001011=>11010010110=>00101101001
[3,4,2,1,6,5,10,11,12,9,8,7]=>01101000111=>11100010110=>00011101001
[3,4,2,1,7,8,6,5,10,9,12,11]=>01100110101=>10101100110=>01010011001
[3,4,2,1,7,8,6,5,11,12,10,9]=>01100110011=>11001100110=>00110011001
[3,4,2,1,7,9,6,10,8,5,12,11]=>01100101101=>10110100110=>01001011001
[3,4,2,1,7,9,6,11,8,12,10,5]=>01100101011=>11010100110=>00101011001
[3,4,2,1,7,10,6,11,12,9,8,5]=>01100100111=>11100100110=>00011011001
[3,4,2,1,8,9,10,7,6,5,12,11]=>01100011101=>10111000110=>01000111001
[3,4,2,1,8,9,11,7,6,12,10,5]=>01100011011=>11011000110=>00100111001
[3,4,2,1,8,10,11,7,12,9,6,5]=>01100010111=>11101000110=>00010111001
[3,4,2,1,9,10,11,12,8,7,6,5]=>01100001111=>11110000110=>00001111001
[3,5,2,6,4,1,8,7,10,9,12,11]=>01011010101=>10101011010=>01010100101
[3,5,2,6,4,1,8,7,11,12,10,9]=>01011010011=>11001011010=>00110100101
[3,5,2,6,4,1,9,10,8,7,12,11]=>01011001101=>10110011010=>01001100101
[3,5,2,6,4,1,9,11,8,12,10,7]=>01011001011=>11010011010=>00101100101
[3,5,2,6,4,1,10,11,12,9,8,7]=>01011000111=>11100011010=>00011100101
[3,5,2,7,4,8,6,1,10,9,12,11]=>01010110101=>10101101010=>01010010101
[3,5,2,7,4,8,6,1,11,12,10,9]=>01010110011=>11001101010=>00110010101
[3,5,2,7,4,9,6,10,8,1,12,11]=>01010101101=>10110101010=>01001010101
[3,5,2,7,4,9,6,11,8,12,10,1]=>01010101011=>11010101010=>00101010101
[3,5,2,7,4,10,6,11,12,9,8,1]=>01010100111=>11100101010=>00011010101
[3,5,2,8,4,9,10,7,6,1,12,11]=>01010011101=>10111001010=>01000110101
[3,5,2,8,4,9,11,7,6,12,10,1]=>01010011011=>11011001010=>00100110101
[3,5,2,8,4,10,11,7,12,9,6,1]=>01010010111=>11101001010=>00010110101
[3,5,2,9,4,10,11,12,8,7,6,1]=>01010001111=>11110001010=>00001110101
[3,6,2,7,8,5,4,1,10,9,12,11]=>01001110101=>10101110010=>01010001101
[3,6,2,7,8,5,4,1,11,12,10,9]=>01001110011=>11001110010=>00110001101
[3,6,2,7,9,5,4,10,8,1,12,11]=>01001101101=>10110110010=>01001001101
[3,6,2,7,9,5,4,11,8,12,10,1]=>01001101011=>11010110010=>00101001101
[3,6,2,7,10,5,4,11,12,9,8,1]=>01001100111=>11100110010=>00011001101
[3,6,2,8,9,5,10,7,4,1,12,11]=>01001011101=>10111010010=>01000101101
[3,6,2,8,9,5,11,7,4,12,10,1]=>01001011011=>11011010010=>00100101101
[3,6,2,8,10,5,11,7,12,9,4,1]=>01001010111=>11101010010=>00010101101
[3,6,2,9,10,5,11,12,8,7,4,1]=>01001001111=>11110010010=>00001101101
[3,7,2,8,9,10,6,5,4,1,12,11]=>01000111101=>10111100010=>01000011101
[3,7,2,8,9,11,6,5,4,12,10,1]=>01000111011=>11011100010=>00100011101
[3,7,2,8,10,11,6,5,12,9,4,1]=>01000110111=>11101100010=>00010011101
[3,7,2,9,10,11,6,12,8,5,4,1]=>01000101111=>11110100010=>00001011101
[3,8,2,9,10,11,12,7,6,5,4,1]=>01000011111=>11111000010=>00000111101
[4,5,6,3,2,1,8,7,10,9,12,11]=>00111010101=>10101011100=>01010100011
[4,5,6,3,2,1,8,7,11,12,10,9]=>00111010011=>11001011100=>00110100011
[4,5,6,3,2,1,9,10,8,7,12,11]=>00111001101=>10110011100=>01001100011
[4,5,6,3,2,1,9,11,8,12,10,7]=>00111001011=>11010011100=>00101100011
[4,5,6,3,2,1,10,11,12,9,8,7]=>00111000111=>11100011100=>00011100011
[4,5,7,3,2,8,6,1,10,9,12,11]=>00110110101=>10101101100=>01010010011
[4,5,7,3,2,8,6,1,11,12,10,9]=>00110110011=>11001101100=>00110010011
[4,5,7,3,2,9,6,10,8,1,12,11]=>00110101101=>10110101100=>01001010011
[4,5,7,3,2,9,6,11,8,12,10,1]=>00110101011=>11010101100=>00101010011
[4,5,7,3,2,10,6,11,12,9,8,1]=>00110100111=>11100101100=>00011010011
[4,5,8,3,2,9,10,7,6,1,12,11]=>00110011101=>10111001100=>01000110011
[4,5,8,3,2,9,11,7,6,12,10,1]=>00110011011=>11011001100=>00100110011
[4,5,8,3,2,10,11,7,12,9,6,1]=>00110010111=>11101001100=>00010110011
[4,5,9,3,2,10,11,12,8,7,6,1]=>00110001111=>11110001100=>00001110011
[4,6,7,3,8,5,2,1,10,9,12,11]=>00101110101=>10101110100=>01010001011
[4,6,7,3,8,5,2,1,11,12,10,9]=>00101110011=>11001110100=>00110001011
[4,6,7,3,9,5,2,10,8,1,12,11]=>00101101101=>10110110100=>01001001011
[4,6,7,3,9,5,2,11,8,12,10,1]=>00101101011=>11010110100=>00101001011
[4,6,7,3,10,5,2,11,12,9,8,1]=>00101100111=>11100110100=>00011001011
[4,6,8,3,9,5,10,7,2,1,12,11]=>00101011101=>10111010100=>01000101011
[4,6,8,3,9,5,11,7,2,12,10,1]=>00101011011=>11011010100=>00100101011
[4,6,8,3,10,5,11,7,12,9,2,1]=>00101010111=>11101010100=>00010101011
[4,6,9,3,10,5,11,12,8,7,2,1]=>00101001111=>11110010100=>00001101011
[4,7,8,3,9,10,6,5,2,1,12,11]=>00100111101=>10111100100=>01000011011
[4,7,8,3,9,11,6,5,2,12,10,1]=>00100111011=>11011100100=>00100011011
[4,7,8,3,10,11,6,5,12,9,2,1]=>00100110111=>11101100100=>00010011011
[4,7,9,3,10,11,6,12,8,5,2,1]=>00100101111=>11110100100=>00001011011
[4,8,9,3,10,11,12,7,6,5,2,1]=>00100011111=>11111000100=>00000111011
[5,6,7,8,4,3,2,1,10,9,12,11]=>00011110101=>10101111000=>01010000111
[5,6,7,8,4,3,2,1,11,12,10,9]=>00011110011=>11001111000=>00110000111
[5,6,7,9,4,3,2,10,8,1,12,11]=>00011101101=>10110111000=>01001000111
[5,6,7,9,4,3,2,11,8,12,10,1]=>00011101011=>11010111000=>00101000111
[5,6,7,10,4,3,2,11,12,9,8,1]=>00011100111=>11100111000=>00011000111
[5,6,8,9,4,3,10,7,2,1,12,11]=>00011011101=>10111011000=>01000100111
[5,6,8,9,4,3,11,7,2,12,10,1]=>00011011011=>11011011000=>00100100111
[5,6,8,10,4,3,11,7,12,9,2,1]=>00011010111=>11101011000=>00010100111
[5,6,9,10,4,3,11,12,8,7,2,1]=>00011001111=>11110011000=>00001100111
[5,7,8,9,4,10,6,3,2,1,12,11]=>00010111101=>10111101000=>01000010111
[5,7,8,9,4,11,6,3,2,12,10,1]=>00010111011=>11011101000=>00100010111
[5,7,8,10,4,11,6,3,12,9,2,1]=>00010110111=>11101101000=>00010010111
[5,7,9,10,4,11,6,12,8,3,2,1]=>00010101111=>11110101000=>00001010111
[5,8,9,10,4,11,12,7,6,3,2,1]=>00010011111=>11111001000=>00000110111
[6,7,8,9,10,5,4,3,2,1,12,11]=>00001111101=>10111110000=>01000001111
[6,7,8,9,11,5,4,3,2,12,10,1]=>00001111011=>11011110000=>00100001111
[6,7,8,10,11,5,4,3,12,9,2,1]=>00001110111=>11101110000=>00010001111
[6,7,9,10,11,5,4,12,8,3,2,1]=>00001101111=>11110110000=>00001001111
[6,8,9,10,11,5,12,7,4,3,2,1]=>00001011111=>11111010000=>00000101111
[7,8,9,10,11,12,6,5,4,3,2,1]=>00000111111=>11111100000=>00000011111
[3,8,2,7,6,1,5,4]=>0101101=>1011010=>0100101
[4,8,7,2,6,5,3,1]=>0110111=>1110110=>0001001
[4,8,7,3,1,6,5,2]=>0111011=>1101110=>0010001
[4,8,7,3,2,6,1,5]=>0111010=>0101110=>1010001
[4,8,7,3,2,6,5,1]=>0111011=>1101110=>0010001
[4,8,7,3,6,2,5,1]=>0110101=>1010110=>0101001
[4,8,7,3,6,1,5,2]=>0110101=>1010110=>0101001
[5,8,7,6,3,4,2,1]=>0111011=>1101110=>0010001
[5,8,7,6,3,1,4,2]=>0111101=>1011110=>0100001
[5,8,7,6,2,4,3,1]=>0111011=>1101110=>0010001
[5,8,7,6,4,2,1,3]=>0111110=>0111110=>1000001
[5,8,7,6,4,1,3,2]=>0111101=>1011110=>0100001
[5,8,7,6,4,3,1,2]=>0111110=>0111110=>1000001
[7,3,4,2,1,6,5,8]=>1011010=>0101101=>1010010
[7,3,5,2,6,1,4,8]=>1010100=>0010101=>1101010
[7,3,5,2,6,4,1,8]=>1010110=>0110101=>1001010
[7,2,1,5,6,4,3,8]=>1100110=>0110011=>1001100
[7,3,5,1,6,4,2,8]=>1010110=>0110101=>1001010
[7,4,5,6,1,3,2,8]=>1001010=>0101001=>1010110
[1,4,5,7,3,2,8,6]=>0001101=>1011000=>0100111
[6,4,5,7,3,1,8,2]=>1001101=>1011001=>0100110
[6,3,5,1,7,4,8,2]=>1010101=>1010101=>0101010
[6,2,1,5,7,4,8,3]=>1100101=>1010011=>0101100
[3,2,1,5,7,4,8,6]=>1100101=>1010011=>0101100
[2,4,6,7,3,8,1,5]=>0001010=>0101000=>1010111
[1,4,6,7,3,8,5,2]=>0001011=>1101000=>0010111
[2,5,6,7,8,3,1,4]=>0000110=>0110000=>1001111
[3,2,1,6,7,8,4,5]=>1100010=>0100011=>1011100
[5,2,1,6,7,8,4,3]=>1100011=>1100011=>0011100
[5,3,6,1,7,8,4,2]=>1010011=>1100101=>0011010
[5,4,6,7,1,8,3,2]=>1001011=>1101001=>0010110
[6,4,5,7,2,1,8,3]=>1001101=>1011001=>0100110
[5,4,6,7,2,8,3,1]=>1001011=>1101001=>0010110
[5,3,6,2,7,8,4,1]=>1010011=>1100101=>0011010
[5,3,6,2,7,8,1,4]=>1010010=>0100101=>1011010
[6,3,5,2,7,1,8,4]=>1010101=>1010101=>0101010
[5,3,4,1,2,7,8,6]=>1010001=>1000101=>0111010
[4,3,6,2,7,8,1,5]=>1010010=>0100101=>1011010
[4,3,6,2,7,8,5,1]=>1010011=>1100101=>0011010
[1,3,6,2,7,8,5,4]=>0010011=>1100100=>0011011
[1,4,6,7,2,8,5,3]=>0001011=>1101000=>0010111
[3,4,6,7,2,8,5,1]=>0001011=>1101000=>0010111
[3,4,5,7,2,1,8,6]=>0001101=>1011000=>0100111
[4,2,1,5,7,3,8,6]=>1100101=>1010011=>0101100
[4,2,1,6,7,8,3,5]=>1100010=>0100011=>1011100
[4,3,6,1,7,8,2,5]=>1010010=>0100101=>1011010
[1,5,6,7,8,2,4,3]=>0000101=>1010000=>0101111
[1,5,6,7,8,4,2,3]=>0000110=>0110000=>1001111
[4,3,6,1,7,8,5,2]=>1010011=>1100101=>0011010
[4,2,1,6,7,8,5,3]=>1100011=>1100011=>0011100
[2,4,6,7,1,8,5,3]=>0001011=>1101000=>0010111
[2,5,6,7,8,1,4,3]=>0000101=>1010000=>0101111
[1,4,3,6,2,5,7,8]=>0101000=>0001010=>1110101
[1,4,3,7,2,5,6,8]=>0101000=>0001010=>1110101
[1,4,3,7,6,8,2,5]=>0101010=>0101010=>1010101
[1,4,3,7,5,8,2,6]=>0101010=>0101010=>1010101
[1,5,3,7,4,8,2,6]=>0101010=>0101010=>1010101
[1,5,4,8,2,6,3,7]=>0101010=>0101010=>1010101
[1,5,4,8,3,7,2,6]=>0101010=>0101010=>1010101
[1,2,3,6,5,8,4,7]=>0001010=>0101000=>1010111
[6,8,2,4,5,7,1,3]=>0100010=>0100010=>1011101
[3,7,8,4,5,2,6,1]=>0010101=>1010100=>0101011
[7,8,1,4,5,3,6,2]=>0100101=>1010010=>0101101
[5,8,1,4,7,6,3,2]=>0100111=>1110010=>0001101
[7,5,1,8,6,2,4,3]=>1101101=>1011011=>0100100
[7,4,1,8,2,6,3,5]=>1101010=>0101011=>1010100
[7,1,8,4,2,6,3,5]=>1011010=>0101101=>1010010
[7,3,1,8,4,2,6,5]=>1101101=>1011011=>0100100
[7,2,8,3,6,5,1,4]=>1010110=>0110101=>1001010
[7,2,8,3,6,1,5,4]=>1010101=>1010101=>0101010
[6,1,2,8,3,5,4,7]=>1001010=>0101001=>1010110
[5,2,3,8,1,4,7,6]=>1001001=>1001001=>0110110
[6,2,4,1,8,7,3,5]=>1010110=>0110101=>1001010
[3,1,6,4,2,8,5,7]=>1011010=>0101101=>1010010
[2,6,3,8,7,1,5,4]=>0101101=>1011010=>0100101
[2,6,3,8,5,1,4,7]=>0101100=>0011010=>1100101
[2,5,1,8,3,4,7,6]=>0101001=>1001010=>0110101
[1,2,5,3,8,4,7,6]=>0010101=>1010100=>0101011
[1,2,4,8,3,7,6,5]=>0001011=>1101000=>0010111
[2,4,8,3,7,1,6,5]=>0010101=>1010100=>0101011
[2,4,8,3,7,6,1,5]=>0010110=>0110100=>1001011
[2,5,3,8,1,7,4,6]=>0101010=>0101010=>1010101
[2,5,4,1,3,8,7,6]=>0110011=>1100110=>0011001
[3,1,5,4,8,2,7,6]=>1010101=>1010101=>0101010
[5,3,1,4,8,2,7,6]=>1100101=>1010011=>0101100
[5,2,3,8,4,7,1,6]=>1001010=>0101001=>1010110
[4,8,2,3,7,6,1,5]=>0100110=>0110010=>1001101
[4,8,2,3,7,1,6,5]=>0100101=>1010010=>0101101
[4,8,1,2,3,7,6,5]=>0100011=>1100010=>0011101
[1,4,8,3,7,2,6,5]=>0010101=>1010100=>0101011
[6,3,8,1,5,2,4,7]=>1010100=>0010101=>1101010
[5,3,8,1,2,4,7,6]=>1010001=>1000101=>0111010
[5,1,3,8,2,4,7,6]=>1001001=>1001001=>0110110
[1,5,3,8,2,4,7,6]=>0101001=>1001010=>0110101
[1,5,4,8,2,7,6,3]=>0101011=>1101010=>0010101
[5,1,4,8,2,7,6,3]=>1001011=>1101001=>0010110
[5,4,8,1,2,7,6,3]=>1010011=>1100101=>0011010
[6,5,1,2,8,7,4,3]=>1100111=>1110011=>0001100
[4,1,5,8,2,7,6,3]=>1001011=>1101001=>0010110
[4,1,2,5,8,7,6,3]=>1000111=>1110001=>0001110
[1,4,2,5,8,7,6,3]=>0100111=>1110010=>0001101
[1,3,5,2,8,7,4,6]=>0010110=>0110100=>1001011
[3,5,1,2,8,7,4,6]=>0100110=>0110010=>1001101
[4,2,6,1,8,7,3,5]=>1010110=>0110101=>1001010
[4,3,1,5,8,2,7,6]=>1100101=>1010011=>0101100
[3,5,2,8,7,1,4,6]=>0101100=>0011010=>1100101
[3,4,8,7,2,6,1,5]=>0011010=>0101100=>1010011
[3,4,8,1,7,2,6,5]=>0010101=>1010100=>0101011
[1,3,4,8,7,2,6,5]=>0001101=>1011000=>0100111
[1,3,4,8,2,7,6,5]=>0001011=>1101000=>0010111
[3,4,8,1,2,7,6,5]=>0010011=>1100100=>0011011
[3,4,8,2,7,1,6,5]=>0010101=>1010100=>0101011
[3,4,8,2,7,6,1,5]=>0010110=>0110100=>1001011
[4,2,5,8,1,7,6,3]=>1001011=>1101001=>0010110
[4,3,1,2,5,8,7,6]=>1100011=>1100011=>0011100
[3,1,4,2,5,8,7,6]=>1010011=>1100101=>0011010
[2,3,5,1,8,7,6,4]=>0010111=>1110100=>0001011
[7,8,2,1,5,3,6,4]=>0110101=>1010110=>0101001
[6,4,1,2,7,3,5,8]=>1100100=>0010011=>1101100
[2,3,7,5,4,1,8,6]=>0011101=>1011100=>0100011
[6,3,1,5,4,2,7,8]=>1101100=>0011011=>1100100
[7,8,1,5,4,2,6,3]=>0101101=>1011010=>0100101
[7,8,3,5,4,1,6,2]=>0101101=>1011010=>0100101
[7,8,2,5,4,1,3,6]=>0101100=>0011010=>1100101
[7,8,2,5,4,6,1,3]=>0101010=>0101010=>1010101
[6,2,1,5,4,7,3,8]=>1101010=>0101011=>1010100
[5,3,6,2,4,7,1,8]=>1010010=>0100101=>1011010
[6,4,2,1,7,3,8,5]=>1110101=>1010111=>0101000
[2,7,6,5,3,1,4,8]=>0111100=>0011110=>1100001
[3,7,6,4,8,5,1,2]=>0110110=>0110110=>1001001
[5,7,6,3,8,4,1,2]=>0110110=>0110110=>1001001
[5,1,6,2,4,8,3,7]=>1010010=>0100101=>1011010
[4,7,6,5,2,1,3,8]=>0111100=>0011110=>1100001
[4,7,6,5,2,8,1,3]=>0111010=>0101110=>1010001
[4,7,6,5,1,8,3,2]=>0111011=>1101110=>0010001
[1,7,6,5,2,8,3,4]=>0111010=>0101110=>1010001
[1,7,6,5,3,2,8,4]=>0111101=>1011110=>0100001
[4,7,6,5,1,2,8,3]=>0111001=>1001110=>0110001
[4,7,6,5,3,1,8,2]=>0111101=>1011110=>0100001
[5,2,6,3,4,1,7,8]=>1010100=>0010101=>1101010
[5,1,6,2,4,7,8,3]=>1010001=>1000101=>0111010
[1,7,2,4,8,3,6,5]=>0100101=>1010010=>0101101
[4,7,2,1,5,3,6,8]=>0110100=>0010110=>1101001
[4,7,1,6,2,3,8,5]=>0101001=>1001010=>0110101
[1,7,2,6,8,3,5,4]=>0100101=>1010010=>0101101
[1,2,6,7,4,8,5,3]=>0001011=>1101000=>0010111
[3,1,6,7,4,2,8,5]=>1001101=>1011001=>0100110
[3,2,8,5,4,6,1,7]=>1011010=>0101101=>1010010
[4,7,6,3,5,8,1,2]=>0110010=>0100110=>1011001
[3,7,6,5,2,4,1,8]=>0111010=>0101110=>1010001
[3,7,6,5,2,1,8,4]=>0111101=>1011110=>0100001
[1,7,6,5,8,2,4,3]=>0110101=>1010110=>0101001
[3,7,6,5,8,1,4,2]=>0110101=>1010110=>0101001
[3,7,6,5,1,2,4,8]=>0111000=>0001110=>1110001
[3,1,6,8,4,2,5,7]=>1001100=>0011001=>1100110
[4,7,6,8,3,5,1,2]=>0101010=>0101010=>1010101
[2,7,6,5,8,1,3,4]=>0110100=>0010110=>1101001
[2,7,6,5,8,4,1,3]=>0110110=>0110110=>1001001
[3,7,5,8,2,4,1,6]=>0101010=>0101010=>1010101
[5,1,7,8,4,3,2,6]=>1001110=>0111001=>1000110
[5,1,2,6,4,3,8,7]=>1001101=>1011001=>0100110
[5,1,2,4,6,3,8,7]=>1000101=>1010001=>0101110
[4,1,5,7,8,3,2,6]=>1000110=>0110001=>1001110
[4,7,1,8,3,6,2,5]=>0101010=>0101010=>1010101
[4,1,7,8,5,2,3,6]=>1001100=>0011001=>1100110
[5,1,7,4,8,2,3,6]=>1010100=>0010101=>1101010
[5,1,8,4,7,2,3,6]=>1010100=>0010101=>1101010
[4,1,8,7,5,2,3,6]=>1011100=>0011101=>1100010
[4,7,1,6,3,2,8,5]=>0101101=>1011010=>0100101
[7,1,2,3,8,6,5,4]=>1000111=>1110001=>0001110
[6,8,1,4,3,7,2,5]=>0101010=>0101010=>1010101
[8,7,3,2,4,1,6,5]=>1110101=>1010111=>0101000
[6,7,1,4,3,8,2,5]=>0101010=>0101010=>1010101
[8,1,2,3,5,7,6,4]=>1000011=>1100001=>0011110
[7,1,2,3,6,8,5,4]=>1000011=>1100001=>0011110
[7,1,8,5,4,3,2,6]=>1011110=>0111101=>1000010
[7,8,2,6,3,4,1,5]=>0101010=>0101010=>1010101
[6,7,2,8,3,4,1,5]=>0101010=>0101010=>1010101
[3,8,7,1,4,2,6,5]=>0110101=>1010110=>0101001
[3,7,8,1,4,2,6,5]=>0010101=>1010100=>0101011
[3,6,8,1,4,2,7,5]=>0010101=>1010100=>0101011
[3,5,7,8,2,4,1,6]=>0001010=>0101000=>1010111
[3,6,7,1,4,2,8,5]=>0010101=>1010100=>0101011
[8,6,2,7,3,1,4,5]=>1101100=>0011011=>1100100
[8,1,7,5,4,3,2,6]=>1011110=>0111101=>1000010
[8,1,7,4,5,3,2,6]=>1010110=>0110101=>1001010
[5,8,3,7,1,4,2,6]=>0101010=>0101010=>1010101
[2,1,7,3,4,6,8,5]=>1010001=>1000101=>0111010
[6,7,3,2,4,1,8,5]=>0110101=>1010110=>0101001
[8,7,2,4,3,6,1,5]=>1101010=>0101011=>1010100
[7,1,2,3,5,6,8,4]=>1000001=>1000001=>0111110
[6,1,2,3,8,7,4,5]=>1000110=>0110001=>1001110
[5,1,2,3,7,8,6,4]=>1000011=>1100001=>0011110
[8,6,2,4,3,1,7,5]=>1101101=>1011011=>0100100
[7,6,3,2,4,8,1,5]=>1110010=>0100111=>1011000
[8,6,3,2,4,7,1,5]=>1110010=>0100111=>1011000
[7,6,2,4,3,1,8,5]=>1101101=>1011011=>0100100
[7,8,1,2,6,3,5,4]=>0100101=>1010010=>0101101
[1,4,8,2,7,3,5,6]=>0010100=>0010100=>1101011
[1,2,8,5,4,7,3,6]=>0011010=>0101100=>1010011
[2,3,6,8,4,7,1,5]=>0001010=>0101000=>1010111
[1,3,6,8,4,7,5,2]=>0001011=>1101000=>0010111
[2,4,8,1,7,3,6,5]=>0010101=>1010100=>0101011
[3,4,8,5,7,6,1,2]=>0010110=>0110100=>1001011
[1,2,6,8,4,5,7,3]=>0001001=>1001000=>0110111
[7,5,1,2,4,3,6,8]=>1100100=>0010011=>1101100
[7,4,6,1,5,2,3,8]=>1010100=>0010101=>1101010
[6,8,1,4,7,2,3,5]=>0100100=>0010010=>1101101
[1,6,4,2,8,3,5,7]=>0110100=>0010110=>1101001
[1,6,3,8,5,4,2,7]=>0101110=>0111010=>1000101
[7,1,3,6,5,4,2,8]=>1001110=>0111001=>1000110
[7,2,1,4,6,3,5,8]=>1100100=>0010011=>1101100
[7,2,3,6,5,1,4,8]=>1001100=>0011001=>1100110
[7,1,2,3,6,5,4,8]=>1000110=>0110001=>1001110
[6,8,1,2,7,3,5,4]=>0100101=>1010010=>0101101
[1,6,2,3,8,5,4,7]=>0100110=>0110010=>1001101
[1,5,8,2,7,6,3,4]=>0010110=>0110100=>1001011
[5,8,2,7,6,3,4,1]=>0101101=>1011010=>0100101
[6,2,8,1,7,3,5,4]=>1010101=>1010101=>0101010
[3,6,4,1,2,8,5,7]=>0110010=>0100110=>1011001
[2,5,1,8,7,6,3,4]=>0101110=>0111010=>1000101
[1,2,5,3,8,7,4,6]=>0010110=>0110100=>1001011
[2,5,3,8,7,1,6,4]=>0101101=>1011010=>0100101
[2,5,8,4,1,7,6,3]=>0011011=>1101100=>0010011
[3,5,8,7,1,4,2,6]=>0011010=>0101100=>1010011
[5,3,8,4,1,7,6,2]=>1011011=>1101101=>0010010
[4,2,8,7,6,3,5,1]=>1011101=>1011101=>0100010
[6,3,1,8,7,2,5,4]=>1101101=>1011011=>0100100
[5,1,3,8,7,6,2,4]=>1001110=>0111001=>1000110
[1,5,3,8,7,6,2,4]=>0101110=>0111010=>1000101
[5,1,8,4,7,2,6,3]=>1010101=>1010101=>0101010
[5,8,7,4,6,1,2,3]=>0110100=>0010110=>1101001
[6,8,5,1,2,4,7,3]=>0110001=>1000110=>0111001
[4,5,8,1,7,2,6,3]=>0010101=>1010100=>0101011
[1,3,2,5,8,7,4,6]=>0100110=>0110010=>1001101
[3,5,1,8,7,4,6,2]=>0101101=>1011010=>0100101
[4,3,6,1,2,8,5,7]=>1010010=>0100101=>1011010
[4,5,8,3,1,7,2,6]=>0011010=>0101100=>1010011
[4,5,2,8,7,1,3,6]=>0101100=>0011010=>1100101
[3,2,5,8,7,1,6,4]=>1001101=>1011001=>0100110
[3,4,8,7,6,2,1,5]=>0011110=>0111100=>1000011
[3,4,8,7,6,5,1,2]=>0011110=>0111100=>1000011
[1,3,4,8,7,6,2,5]=>0001110=>0111000=>1000111
[3,4,8,7,6,2,5,1]=>0011101=>1011100=>0100011
[3,2,5,8,7,4,6,1]=>1001101=>1011001=>0100110
[2,1,3,5,8,7,4,6]=>1000110=>0110001=>1001110
[1,2,7,5,8,6,4,3]=>0010111=>1110100=>0001011
[6,8,1,3,7,5,2,4]=>0100110=>0110010=>1001101
[1,3,7,8,2,6,5,4]=>0001011=>1101000=>0010111
[2,7,8,1,3,6,5,4]=>0010011=>1100100=>0011011
[8,1,2,6,7,3,5,4]=>1000101=>1010001=>0101110
[8,1,2,6,7,5,3,4]=>1000110=>0110001=>1001110
[8,2,5,7,1,3,6,4]=>1001001=>1001001=>0110110
[2,8,1,6,7,3,5,4]=>0100101=>1010010=>0101101
[2,6,8,3,7,1,5,4]=>0010101=>1010100=>0101011
[2,8,6,4,7,1,5,3]=>0110101=>1010110=>0101001
[6,8,3,4,1,7,5,2]=>0101011=>1101010=>0010101
[6,8,3,7,4,1,5,2]=>0101101=>1011010=>0100101
[8,2,5,7,1,6,3,4]=>1001010=>0101001=>1010110
[8,4,7,2,3,6,1,5]=>1010010=>0100101=>1011010
[8,5,7,4,2,6,1,3]=>1011010=>0101101=>1010010
[8,3,5,7,4,1,6,2]=>1001101=>1011001=>0100110
[8,5,2,4,7,1,6,3]=>1100101=>1010011=>0101100
[8,2,4,7,3,6,1,5]=>1001010=>0101001=>1010110
[8,2,7,1,4,6,3,5]=>1010010=>0100101=>1011010
[8,7,1,2,4,6,3,5]=>1100010=>0100011=>1011100
[8,7,1,4,6,2,3,5]=>1100100=>0010011=>1101100
[8,4,7,1,3,6,2,5]=>1010010=>0100101=>1011010
[8,3,5,7,1,2,6,4]=>1001001=>1001001=>0110110
[5,8,7,1,3,6,2,4]=>0110010=>0100110=>1011001
[8,5,4,7,1,6,2,3]=>1101010=>0101011=>1010100
[8,5,4,7,1,2,6,3]=>1101001=>1001011=>0110100
[8,5,1,4,7,2,6,3]=>1100101=>1010011=>0101100
[8,5,6,3,1,7,4,2]=>1011011=>1101101=>0010010
[1,8,4,5,7,2,6,3]=>0100101=>1010010=>0101101
[5,8,7,3,6,1,2,4]=>0110100=>0010110=>1101001
[8,3,5,7,1,6,2,4]=>1001010=>0101001=>1010110
[1,6,8,3,7,5,2,4]=>0010110=>0110100=>1001011
[6,3,8,2,7,5,1,4]=>1010110=>0110101=>1001010
[8,6,4,7,3,1,5,2]=>1101101=>1011011=>0100100
[8,4,5,7,3,1,6,2]=>1001101=>1011001=>0100110
[8,3,4,7,2,6,1,5]=>1001010=>0101001=>1010110
[8,7,1,3,4,6,2,5]=>1100010=>0100011=>1011100
[8,3,7,2,4,6,1,5]=>1010010=>0100101=>1011010
[2,8,4,5,7,1,6,3]=>0100101=>1010010=>0101101
[8,7,3,4,5,1,6,2]=>1100101=>1010011=>0101100
[8,7,4,5,2,6,1,3]=>1101010=>0101011=>1010100
[8,7,2,3,4,6,1,5]=>1100010=>0100011=>1011100
[8,6,5,1,3,2,7,4]=>1110101=>1010111=>0101000
[8,6,3,1,7,2,4,5]=>1110100=>0010111=>1101000
[8,7,3,1,5,2,4,6]=>1110100=>0010111=>1101000
[8,6,1,2,4,7,3,5]=>1100010=>0100011=>1011100
[8,6,1,5,3,4,7,2]=>1101001=>1001011=>0110100
[8,6,1,5,2,4,7,3]=>1101001=>1001011=>0110100
[8,6,1,2,5,7,3,4]=>1100010=>0100011=>1011100
[5,1,4,2,3,8,6,7]=>1010010=>0100101=>1011010
[5,1,4,2,7,3,6,8]=>1010100=>0010101=>1101010
[5,7,8,1,2,4,6,3]=>0010001=>1000100=>0111011
[5,7,8,1,3,4,6,2]=>0010001=>1000100=>0111011
[5,8,1,7,3,4,6,2]=>0101001=>1001010=>0110101
[8,1,5,7,2,4,6,3]=>1001001=>1001001=>0110110
[1,4,2,3,8,7,5,6]=>0100110=>0110010=>1001101
[1,4,2,7,6,3,5,8]=>0101100=>0011010=>1100101
[6,1,2,8,7,5,3,4]=>1001110=>0111001=>1000110
[6,1,2,4,8,7,5,3]=>1000111=>1110001=>0001110
[3,1,8,4,6,7,5,2]=>1010011=>1100101=>0011010
[3,1,7,6,4,8,5,2]=>1011011=>1101101=>0010010
[7,1,2,4,6,8,5,3]=>1000011=>1100001=>0011110
[7,1,2,6,8,5,3,4]=>1000110=>0110001=>1001110
[7,1,5,3,2,8,6,4]=>1011011=>1101101=>0010010
[8,1,7,5,3,2,6,4]=>1011101=>1011101=>0100010
[8,3,7,1,2,6,4,5]=>1010010=>0100101=>1011010
[3,1,2,8,4,7,5,6]=>1001010=>0101001=>1010110
[1,4,2,3,8,6,5,7]=>0100110=>0110010=>1001101
[1,4,2,3,8,5,7,6]=>0100101=>1010010=>0101101
[5,8,1,7,2,4,6,3]=>0101001=>1001010=>0110101
[5,8,1,3,4,7,6,2]=>0100011=>1100010=>0011101
[3,1,8,6,4,7,5,2]=>1011011=>1101101=>0010010
[8,1,2,6,7,4,5,3]=>1000101=>1010001=>0101110
[1,2,3,5,8,4,7,6]=>0000101=>1010000=>0101111
[1,2,3,5,8,6,4,7]=>0000110=>0110000=>1001111
[7,1,2,8,3,6,5,4]=>1001011=>1101001=>0010110
[7,1,2,8,6,4,5,3]=>1001101=>1011001=>0100110
[3,1,7,8,4,6,5,2]=>1001011=>1101001=>0010110
[8,1,2,7,4,6,5,3]=>1001011=>1101001=>0010110
[8,1,2,7,3,6,5,4]=>1001011=>1101001=>0010110
[1,2,3,6,8,5,4,7]=>0000110=>0110000=>1001111
[3,6,2,5,4,1,8,7]=>0101101=>1011010=>0100101
[3,5,2,8,4,7,6,1]=>0101011=>1101010=>0010101
[5,4,7,3,2,8,6,1]=>1011011=>1101101=>0010010
[5,4,8,3,2,7,6,1]=>1011011=>1101101=>0010010
[5,3,2,6,4,1,8,7]=>1101101=>1011011=>0100100
[4,5,8,3,2,7,6,1]=>0011011=>1101100=>0010011
[4,7,6,3,8,5,2,1]=>0110111=>1110110=>0001001
[4,8,6,3,7,5,2,1]=>0110111=>1110110=>0001001
[5,3,2,8,4,7,6,1]=>1101011=>1101011=>0010100
[2,1,5,8,4,7,6,3]=>1001011=>1101001=>0010110
[5,3,2,7,4,8,6,1]=>1101011=>1101011=>0010100
[5,7,4,3,2,8,6,1]=>0111011=>1101110=>0010001
[4,7,5,3,2,8,6,1]=>0111011=>1101110=>0010001
[4,7,8,3,6,5,2,1]=>0010111=>1110100=>0001011
[4,6,8,3,7,5,2,1]=>0010111=>1110100=>0001011
[7,6,4,3,8,5,2,1]=>1110111=>1110111=>0001000
[8,3,2,6,7,5,4,1]=>1100111=>1110011=>0001100
[8,6,4,3,7,5,2,1]=>1110111=>1110111=>0001000
[8,4,5,3,2,7,6,1]=>1011011=>1101101=>0010010
[8,4,6,3,7,5,2,1]=>1010111=>1110101=>0001010
[7,4,6,3,8,5,2,1]=>1010111=>1110101=>0001010
[3,7,2,6,8,5,4,1]=>0100111=>1110010=>0001101
[3,8,2,6,7,5,4,1]=>0100111=>1110010=>0001101
[3,7,2,8,6,5,4,1]=>0101111=>1111010=>0000101
[3,6,2,8,7,5,4,1]=>0101111=>1111010=>0000101
[7,4,5,3,2,8,6,1]=>1011011=>1101101=>0010010
[2,1,7,5,4,8,6,3]=>1011011=>1101101=>0010010
[7,3,2,8,6,5,4,1]=>1101111=>1111011=>0000100
[7,8,4,3,6,5,2,1]=>0110111=>1110110=>0001001
[6,3,2,8,7,5,4,1]=>1101111=>1111011=>0000100
[6,3,2,7,8,5,4,1]=>1100111=>1110011=>0001100
[1,6,4,8,2,5,3,7]=>0101010=>0101010=>1010101
[1,6,5,8,2,4,3,7]=>0101010=>0101010=>1010101
[1,6,8,2,4,3,7,5]=>0010101=>1010100=>0101011
[1,6,2,4,3,7,8,5]=>0101001=>1001010=>0110101
[1,5,6,2,4,7,3,8]=>0010010=>0100100=>1011011
[1,5,6,2,4,7,8,3]=>0010001=>1000100=>0111011
[1,6,7,2,4,3,8,5]=>0010101=>1010100=>0101011
[1,5,8,2,4,6,7,3]=>0010001=>1000100=>0111011
[1,5,7,8,3,2,4,6]=>0001100=>0011000=>1100111
[1,5,8,3,2,4,6,7]=>0011000=>0001100=>1110011
[1,5,6,2,4,8,3,7]=>0010010=>0100100=>1011011
[1,7,3,4,2,8,6,5]=>0101011=>1101010=>0010101
[1,5,6,2,4,8,7,3]=>0010011=>1100100=>0011011
[1,5,8,7,3,2,4,6]=>0011100=>0011100=>1100011
[1,7,4,2,8,6,5,3]=>0110111=>1110110=>0001001
[1,5,8,3,2,4,7,6]=>0011001=>1001100=>0110011
[1,6,5,2,3,7,4,8]=>0110010=>0100110=>1011001
[1,6,5,2,3,7,8,4]=>0110001=>1000110=>0111001
[1,6,8,4,2,3,7,5]=>0011001=>1001100=>0110011
[1,6,8,5,2,3,7,4]=>0011001=>1001100=>0110011
[1,6,4,2,3,7,5,8]=>0110010=>0100110=>1011001
[1,5,8,6,2,4,7,3]=>0011001=>1001100=>0110011
[1,7,5,2,8,6,4,3]=>0110111=>1110110=>0001001
[3,7,5,6,1,4,8,2]=>0101001=>1001010=>0110101
[8,6,1,4,2,7,5,3]=>1101011=>1101011=>0010100
[1,6,7,4,3,5,8,2]=>0011001=>1001100=>0110011
[6,7,1,4,3,5,8,2]=>0101001=>1001010=>0110101
[4,7,1,6,3,5,8,2]=>0101001=>1001010=>0110101
[3,1,4,7,6,5,8,2]=>1001101=>1011001=>0100110
[6,1,7,4,3,5,8,2]=>1011001=>1001101=>0110010
[7,1,6,4,3,5,8,2]=>1011001=>1001101=>0110010
[1,7,6,4,3,5,8,2]=>0111001=>1001110=>0110001
[8,1,6,4,2,7,5,3]=>1011011=>1101101=>0010010
[4,7,1,3,8,2,5,6]=>0100100=>0010010=>1101101
[7,4,1,3,8,2,5,6]=>1100100=>0010011=>1101100
[1,3,6,4,2,8,5,7]=>0011010=>0101100=>1010011
[4,7,3,1,2,8,5,6]=>0110010=>0100110=>1011001
[4,7,8,1,2,6,5,3]=>0010011=>1100100=>0011011
[1,8,6,4,2,7,5,3]=>0111011=>1101110=>0010001
[4,8,1,3,7,2,5,6]=>0100100=>0010010=>1101101
[8,7,1,3,6,2,5,4]=>1100101=>1010011=>0101100
[1,8,4,3,7,2,5,6]=>0110100=>0010110=>1101001
[3,7,4,6,8,2,1,5]=>0100110=>0110010=>1001101
[2,4,3,7,8,6,1,5]=>0100110=>0110010=>1001101
[1,4,7,3,8,2,5,6]=>0010100=>0010100=>1101011
[5,7,6,8,3,2,1,4]=>0101110=>0111010=>1000101
[6,1,4,3,8,2,5,7]=>1010100=>0010101=>1101010
[4,1,7,3,8,2,5,6]=>1010100=>0010101=>1101010
[8,1,4,3,7,2,5,6]=>1010100=>0010101=>1101010
[4,2,3,7,8,6,1,5]=>1000110=>0110001=>1001110
[2,7,5,6,3,8,1,4]=>0101010=>0101010=>1010101
[5,7,2,6,8,4,1,3]=>0100110=>0110010=>1001101
[7,2,5,6,8,4,1,3]=>1000110=>0110001=>1001110
[5,2,3,8,7,6,1,4]=>1001110=>0111001=>1000110
[8,2,3,7,5,6,1,4]=>1001010=>0101001=>1010110
[6,1,8,3,7,2,5,4]=>1010101=>1010101=>0101010
[1,7,8,4,2,6,5,3]=>0011011=>1101100=>0010011
[4,7,1,8,2,5,6,3]=>0101001=>1001010=>0110101
[1,4,8,3,6,2,5,7]=>0010100=>0010100=>1101011
[3,7,5,8,6,2,1,4]=>0101110=>0111010=>1000101
[3,7,8,6,5,2,1,4]=>0011110=>0111100=>1000011
[6,8,7,5,3,2,1,4]=>0111110=>0111110=>1000001
[5,7,6,8,3,4,1,2]=>0101010=>0101010=>1010101
[3,7,6,8,4,5,1,2]=>0101010=>0101010=>1010101
[1,5,4,7,6,8,2,3]=>0101010=>0101010=>1010101
[1,7,4,6,5,8,2,3]=>0101010=>0101010=>1010101
[3,7,4,6,5,8,1,2]=>0101010=>0101010=>1010101
[3,5,4,8,6,7,1,2]=>0101010=>0101010=>1010101
[3,8,4,6,5,7,1,2]=>0101010=>0101010=>1010101
[3,6,4,7,5,8,1,2]=>0101010=>0101010=>1010101
[1,6,2,7,5,8,3,4]=>0101010=>0101010=>1010101
[1,6,4,8,5,7,2,3]=>0101010=>0101010=>1010101
[1,8,4,6,5,7,2,3]=>0101010=>0101010=>1010101
[1,5,4,8,6,7,2,3]=>0101010=>0101010=>1010101
[7,8,1,5,4,6,2,3]=>0101010=>0101010=>1010101
[1,8,2,6,5,7,3,4]=>0101010=>0101010=>1010101
[1,7,2,8,5,6,3,4]=>0101010=>0101010=>1010101
[1,7,2,6,5,8,3,4]=>0101010=>0101010=>1010101
[1,5,2,7,6,8,3,4]=>0101010=>0101010=>1010101
[1,7,6,8,2,5,3,4]=>0101010=>0101010=>1010101
[1,7,6,8,4,5,2,3]=>0101010=>0101010=>1010101
[7,8,5,6,1,3,2,4]=>0101010=>0101010=>1010101
[5,8,6,7,1,3,2,4]=>0101010=>0101010=>1010101
[1,3,2,7,6,8,4,5]=>0101010=>0101010=>1010101
[1,7,6,8,2,4,3,5]=>0101010=>0101010=>1010101
[1,3,2,8,6,7,4,5]=>0101010=>0101010=>1010101
[7,8,1,3,2,6,4,5]=>0101010=>0101010=>1010101
[7,8,1,6,2,4,3,5]=>0101010=>0101010=>1010101
[1,8,6,7,2,4,3,5]=>0101010=>0101010=>1010101
[7,8,1,4,2,6,3,5]=>0101010=>0101010=>1010101
[6,4,8,5,2,7,1,3]=>1011010=>0101101=>1010010
[8,4,7,5,2,6,1,3]=>1011010=>0101101=>1010010
[5,4,6,8,2,1,7,3]=>1001101=>1011001=>0100110
[4,8,7,5,6,1,3,2]=>0110101=>1010110=>0101001
[2,7,5,1,8,4,3,6]=>0110110=>0110110=>1001001
[2,8,6,7,4,3,5,1]=>0101101=>1011010=>0100101
[3,8,7,1,4,6,5,2]=>0110011=>1100110=>0011001
[5,7,1,2,4,3,8,6]=>0100101=>1010010=>0101101
[4,3,7,6,8,2,5,1]=>1010101=>1010101=>0101010
[5,3,6,8,1,7,2,4]=>1001010=>0101001=>1010110
[3,2,6,8,5,7,1,4]=>1001010=>0101001=>1010110
[7,4,8,6,5,2,1,3]=>1011110=>0111101=>1000010
[7,1,8,2,5,4,3,6]=>1010110=>0110101=>1001010
[2,5,3,7,4,1,8,6]=>0101101=>1011010=>0100101
[3,6,4,7,5,1,8,2]=>0101101=>1011010=>0100101
[8,4,7,1,2,5,6,3]=>1010001=>1000101=>0111010
[4,2,8,7,3,5,6,1]=>1011001=>1001101=>0110010
[6,4,1,5,8,2,7,3]=>1100101=>1010011=>0101100
[8,3,5,6,7,4,1,2]=>1000110=>0110001=>1001110
[7,4,3,2,8,5,6,1]=>1110101=>1010111=>0101000
[4,2,7,1,8,5,6,3]=>1010101=>1010101=>0101010
[4,7,8,3,1,5,6,2]=>0011001=>1001100=>0110011
[3,7,1,4,8,5,6,2]=>0100101=>1010010=>0101101
[2,6,3,5,8,7,1,4]=>0100110=>0110010=>1001101
[7,6,2,1,5,8,4,3]=>1110011=>1100111=>0011000
[4,5,2,7,6,1,8,3]=>0101101=>1011010=>0100101
[3,6,8,7,5,2,1,4]=>0011110=>0111100=>1000011
[7,4,8,6,5,2,3,1]=>1011101=>1011101=>0100010
[8,1,6,4,7,3,2,5]=>1010110=>0110101=>1001010
[7,6,4,1,2,3,8,5]=>1110001=>1000111=>0111000
[2,6,4,8,5,3,7,1]=>0101101=>1011010=>0100101
[4,8,7,5,6,1,2,3]=>0110100=>0010110=>1101001
[6,1,4,8,7,3,5,2]=>1001101=>1011001=>0100110
[4,7,8,1,3,5,6,2]=>0010001=>1000100=>0111011
[8,7,3,4,1,5,6,2]=>1101001=>1001011=>0110100
[4,8,2,7,3,5,6,1]=>0101001=>1001010=>0110101
[3,1,8,7,2,5,6,4]=>1011001=>1001101=>0110010
[8,2,3,7,1,5,6,4]=>1001001=>1001001=>0110110
[6,4,8,7,1,3,2,5]=>1011010=>0101101=>1010010
[7,8,2,4,3,5,6,1]=>0101001=>1001010=>0110101
[2,8,3,7,1,5,6,4]=>0101001=>1001010=>0110101
[5,3,8,6,2,1,4,7]=>1011100=>0011101=>1100010
[4,6,5,2,8,3,1,7]=>0110110=>0110110=>1001001
[4,3,7,5,1,8,2,6]=>1011010=>0101101=>1010010
[6,8,5,2,7,4,3,1]=>0110111=>1110110=>0001001
[3,6,8,1,4,5,2,7]=>0010010=>0100100=>1011011
[6,8,1,2,4,5,3,7]=>0100010=>0100010=>1011101
[4,1,6,5,8,2,3,7]=>1010100=>0010101=>1101010
[4,3,8,6,2,5,1,7]=>1011010=>0101101=>1010010
[8,3,6,1,4,5,2,7]=>1010010=>0100101=>1011010
[6,3,8,7,4,2,5,1]=>1011101=>1011101=>0100010
[5,8,4,3,7,6,1,2]=>0110110=>0110110=>1001001
[8,7,4,3,1,6,2,5]=>1111010=>0101111=>1010000
[1,7,4,3,8,6,2,5]=>0110110=>0110110=>1001001
[7,1,5,3,4,8,2,6]=>1010010=>0100101=>1011010
[2,8,6,1,7,4,5,3]=>0110101=>1010110=>0101001
[4,7,6,8,2,1,5,3]=>0101101=>1011010=>0100101
[6,1,8,7,4,3,5,2]=>1011101=>1011101=>0100010
[8,5,4,3,1,6,7,2]=>1111001=>1001111=>0110000
[1,5,8,6,3,4,7,2]=>0011001=>1001100=>0110011
[2,5,8,6,3,4,7,1]=>0011001=>1001100=>0110011
[4,6,5,2,8,1,7,3]=>0110101=>1010110=>0101001
[1,8,5,2,3,6,7,4]=>0110001=>1000110=>0111001
[4,8,3,2,5,6,7,1]=>0110001=>1000110=>0111001
[2,1,8,3,5,6,7,4]=>1010001=>1000101=>0111010
[4,2,7,1,8,6,3,5]=>1010110=>0110101=>1001010
[3,8,4,1,2,6,7,5]=>0110001=>1000110=>0111001
[5,8,3,6,7,4,1,2]=>0100110=>0110010=>1001101
[2,3,1,6,8,4,7,5]=>0100101=>1010010=>0101101
[2,4,3,7,1,8,5,6]=>0101010=>0101010=>1010101
[2,4,1,8,6,3,7,5]=>0101101=>1011010=>0100101
[8,4,1,3,6,2,7,5]=>1100101=>1010011=>0101100
[6,8,5,1,7,2,3,4]=>0110100=>0010110=>1101001
[7,3,6,5,8,2,1,4]=>1010110=>0110101=>1001010
[7,6,3,5,8,2,1,4]=>1100110=>0110011=>1001100
[4,5,8,7,3,6,1,2]=>0011010=>0101100=>1010011
[8,6,5,4,1,2,7,3]=>1111001=>1001111=>0110000
[6,1,5,3,8,7,2,4]=>1010110=>0110101=>1001010
[2,8,6,3,7,1,5,4]=>0110101=>1010110=>0101001
[7,6,1,5,8,2,3,4]=>1100100=>0010011=>1101100
[3,6,8,5,1,2,7,4]=>0011001=>1001100=>0110011
[6,5,2,4,8,1,7,3]=>1100101=>1010011=>0101100
[5,1,4,8,2,6,7,3]=>1001001=>1001001=>0110110
[3,4,8,5,2,6,7,1]=>0011001=>1001100=>0110011
[4,2,1,8,5,6,7,3]=>1101001=>1001011=>0110100
[1,5,4,8,2,6,7,3]=>0101001=>1001010=>0110101
[7,2,1,5,8,6,3,4]=>1100110=>0110011=>1001100
[2,8,4,5,1,6,7,3]=>0101001=>1001010=>0110101
[5,4,8,3,7,6,1,2]=>1010110=>0110101=>1001010
[3,1,5,8,6,2,7,4]=>1001101=>1011001=>0100110
[6,3,4,8,5,1,7,2]=>1001101=>1011001=>0100110
[5,3,4,8,1,6,7,2]=>1001001=>1001001=>0110110
[6,5,4,8,7,1,3,2]=>1101101=>1011011=>0100100
[6,5,4,8,1,2,7,3]=>1101001=>1001011=>0110100
[7,5,1,6,8,2,4,3]=>1100101=>1010011=>0101100
[6,5,4,1,8,2,7,3]=>1110101=>1010111=>0101000
[6,5,4,7,1,2,8,3]=>1101001=>1001011=>0110100
[6,5,4,7,8,1,3,2]=>1100101=>1010011=>0101100
[6,5,3,7,1,4,2,8]=>1101010=>0101011=>1010100
[7,5,1,4,8,3,2,6]=>1100110=>0110011=>1001100
[8,1,6,4,7,3,5,2]=>1010101=>1010101=>0101010
[7,5,1,4,8,3,6,2]=>1100101=>1010011=>0101100
[7,4,1,5,3,8,6,2]=>1101011=>1101011=>0010100
[8,1,5,4,3,7,6,2]=>1011011=>1101101=>0010010
[8,1,5,4,3,7,2,6]=>1011010=>0101101=>1010010
[6,5,3,8,1,4,2,7]=>1101010=>0101011=>1010100
[8,1,7,2,5,4,6,3]=>1010101=>1010101=>0101010
[7,6,1,2,5,4,8,3]=>1100101=>1010011=>0101100
[6,5,3,8,1,4,7,2]=>1101001=>1001011=>0110100
[6,5,3,1,2,7,8,4]=>1110001=>1000111=>0111000
[8,1,6,4,2,5,7,3]=>1011001=>1001101=>0110010
[8,1,5,4,3,2,7,6]=>1011101=>1011101=>0100010
[7,4,1,5,3,2,8,6]=>1101101=>1011011=>0100100
[6,4,3,1,5,2,8,7]=>1110101=>1010111=>0101000
[6,4,3,1,5,7,2,8]=>1110010=>0100111=>1011000
[7,4,1,5,3,6,2,8]=>1101010=>0101011=>1010100
[6,4,3,1,5,7,8,2]=>1110001=>1000111=>0111000
[8,6,7,1,4,2,5,3]=>1010101=>1010101=>0101010
[8,6,3,7,5,1,2,4]=>1101100=>0011011=>1100100
[7,6,1,8,3,5,2,4]=>1101010=>0101011=>1010100
[7,6,2,8,3,5,1,4]=>1101010=>0101011=>1010100
[8,7,1,5,2,6,3,4]=>1101010=>0101011=>1010100
[8,7,1,5,2,3,6,4]=>1101001=>1001011=>0110100
[8,5,2,3,1,7,6,4]=>1101011=>1101011=>0010100
[8,6,2,3,7,1,5,4]=>1100101=>1010011=>0101100
[8,6,2,7,3,1,5,4]=>1101101=>1011011=>0100100
[8,7,2,5,1,6,3,4]=>1101010=>0101011=>1010100
[8,5,7,2,1,4,3,6]=>1011010=>0101101=>1010010
[5,8,7,3,1,4,2,6]=>0111010=>0101110=>1010001
[8,5,7,2,1,4,6,3]=>1011001=>1001101=>0110010
[8,6,1,3,7,2,5,4]=>1100101=>1010011=>0101100
[8,4,7,5,1,6,2,3]=>1011010=>0101101=>1010010
[8,4,7,5,1,2,3,6]=>1011000=>0001101=>1110010
[8,3,2,6,5,1,4,7]=>1101100=>0011011=>1100100
[4,8,7,3,1,5,2,6]=>0111010=>0101110=>1010001
[8,4,7,2,1,5,3,6]=>1011010=>0101101=>1010010
[8,7,3,1,2,4,6,5]=>1110001=>1000111=>0111000
[8,4,7,2,1,5,6,3]=>1011001=>1001101=>0110010
[1,2,7,3,5,4,8,6]=>0010101=>1010100=>0101011
[1,5,7,2,3,6,4,8]=>0010010=>0100100=>1011011
[1,3,8,2,4,5,7,6]=>0010001=>1000100=>0111011
[1,2,3,8,4,6,7,5]=>0001001=>1001000=>0110111
[1,7,8,2,3,6,4,5]=>0010010=>0100100=>1011011
[1,6,7,8,2,3,5,4]=>0001001=>1001000=>0110111
[1,7,8,2,5,3,6,4]=>0010101=>1010100=>0101011
[1,8,2,3,6,4,5,7]=>0100100=>0010010=>1101101
[1,2,7,8,3,6,4,5]=>0001010=>0101000=>1010111
[1,5,2,7,8,3,6,4]=>0100101=>1010010=>0101101
[1,3,2,8,4,6,7,5]=>0101001=>1001010=>0110101
[1,8,2,3,4,6,7,5]=>0100001=>1000010=>0111101
[1,7,8,2,4,3,6,5]=>0010101=>1010100=>0101011
[7,6,3,1,5,2,4,8]=>1110100=>0010111=>1101000
[6,7,3,1,5,2,8,4]=>0110101=>1010110=>0101001
[6,8,3,1,5,2,7,4]=>0110101=>1010110=>0101001
[6,8,4,5,1,2,7,3]=>0101001=>1001010=>0110101
[6,7,4,5,1,2,8,3]=>0101001=>1001010=>0110101
[7,2,1,6,5,3,4,8]=>1101100=>0011011=>1100100
[7,3,6,1,5,2,4,8]=>1010100=>0010101=>1101010
[7,4,6,5,1,2,3,8]=>1011000=>0001101=>1110010
[6,7,5,4,1,2,8,3]=>0111001=>1001110=>0110001
[5,8,6,4,1,7,2,3]=>0111010=>0101110=>1010001
[5,7,6,4,1,8,2,3]=>0111010=>0101110=>1010001
[5,6,7,4,1,8,2,3]=>0011010=>0101100=>1010011
[6,5,7,4,1,2,8,3]=>1011001=>1001101=>0110010
[6,2,1,7,5,3,8,4]=>1101101=>1011011=>0100100
[6,3,8,1,5,2,7,4]=>1010101=>1010101=>0101010
[6,4,8,5,1,2,7,3]=>1011001=>1001101=>0110010
[6,5,8,4,1,2,7,3]=>1011001=>1001101=>0110010
[5,6,8,4,1,7,2,3]=>0011010=>0101100=>1010011
[4,6,8,5,7,1,2,3]=>0010100=>0010100=>1101011
[4,5,8,6,7,1,2,3]=>0010100=>0010100=>1101011
[5,2,1,7,6,8,3,4]=>1101010=>0101011=>1010100
[4,5,7,6,8,1,2,3]=>0010100=>0010100=>1101011
[4,6,7,5,8,1,2,3]=>0010100=>0010100=>1101011
[4,7,5,6,8,1,2,3]=>0100100=>0010010=>1101101
[4,6,5,7,8,1,2,3]=>0100100=>0010010=>1101101
[5,7,4,6,1,8,2,3]=>0101010=>0101010=>1010101
[5,8,3,1,6,7,2,4]=>0110010=>0100110=>1011001
[5,7,3,1,6,8,2,4]=>0110010=>0100110=>1011001
[5,6,3,1,7,8,2,4]=>0110010=>0100110=>1011001
[5,8,3,1,7,6,2,4]=>0110110=>0110110=>1001001
[5,7,4,8,1,6,2,3]=>0101010=>0101010=>1010101
[5,2,1,6,8,7,3,4]=>1100110=>0110011=>1001100
[5,4,6,8,1,7,2,3]=>1001010=>0101001=>1010110
[4,5,6,8,7,1,2,3]=>0001100=>0011000=>1100111
[4,7,5,8,6,1,2,3]=>0101100=>0011010=>1100101
[4,8,5,7,6,1,2,3]=>0101100=>0011010=>1100101
[4,8,6,7,5,1,2,3]=>0101100=>0011010=>1100101
[4,7,6,8,5,1,2,3]=>0101100=>0011010=>1100101
[4,6,7,8,5,1,2,3]=>0001100=>0011000=>1100111
[4,5,7,8,6,1,2,3]=>0001100=>0011000=>1100111
[5,4,7,8,1,6,2,3]=>1001010=>0101001=>1010110
[5,3,7,1,8,6,2,4]=>1010110=>0110101=>1001010
[5,2,1,7,8,6,3,4]=>1100110=>0110011=>1001100
[5,3,8,1,7,6,2,4]=>1010110=>0110101=>1001010
[5,4,8,7,1,6,2,3]=>1011010=>0101101=>1010010
[4,6,8,7,5,1,2,3]=>0011100=>0011100=>1100011
[4,7,8,6,5,1,2,3]=>0011100=>0011100=>1100011
[4,8,7,6,5,1,2,3]=>0111100=>0011110=>1100001
[2,5,4,7,3,6,1,8]=>0101010=>0101010=>1010101
[4,2,7,3,6,5,1,8]=>1010110=>0110101=>1001010
[4,2,6,3,1,5,8,7]=>1011001=>1001101=>0110010
[2,5,3,1,6,4,8,7]=>0110101=>1010110=>0101001
[2,5,3,7,6,4,1,8]=>0101110=>0111010=>1000101
[2,6,5,3,7,4,1,8]=>0110110=>0110110=>1001001
[4,2,7,6,3,5,1,8]=>1011010=>0101101=>1010010
[2,7,5,3,6,4,1,8]=>0110110=>0110110=>1001001
[2,6,3,7,5,4,1,8]=>0101110=>0111010=>1000101
[1,7,5,2,3,8,4,6]=>0110010=>0100110=>1011001
[2,1,3,7,5,4,8,6]=>1001101=>1011001=>0100110
[2,3,1,8,6,5,4,7]=>0101110=>0111010=>1000101
[2,5,3,1,8,6,4,7]=>0110110=>0110110=>1001001
[4,2,8,3,1,6,5,7]=>1011010=>0101101=>1010010
[8,3,2,6,4,1,5,7]=>1101100=>0011011=>1100100
[3,6,8,2,1,4,5,7]=>0011000=>0001100=>1110011
[1,2,6,3,8,7,4,5]=>0010110=>0110100=>1001011
[1,2,7,6,3,4,8,5]=>0011001=>1001100=>0110011
[2,1,3,8,7,5,4,6]=>1001110=>0111001=>1000110
[1,2,3,8,6,4,7,5]=>0001101=>1011000=>0100111
[1,2,3,7,4,8,6,5]=>0001011=>1101000=>0010111
[1,2,7,6,3,8,4,5]=>0011010=>0101100=>1010011
[1,2,3,6,4,8,7,5]=>0001011=>1101000=>0010111
[1,2,3,7,6,4,8,5]=>0001101=>1011000=>0100111
[2,1,3,8,5,4,7,6]=>1001101=>1011001=>0100110
[7,1,8,4,2,3,5,6]=>1011000=>0001101=>1110010
[4,2,6,3,1,8,5,7]=>1011010=>0101101=>1010010
[5,4,2,8,3,1,6,7]=>1101100=>0011011=>1100100
[2,5,4,8,3,1,6,7]=>0101100=>0011010=>1100101
[1,8,7,4,2,3,5,6]=>0111000=>0001110=>1110001
[1,5,2,8,7,3,4,6]=>0101100=>0011010=>1100101
[1,2,7,3,6,4,8,5]=>0010101=>1010100=>0101011
[1,2,8,6,3,7,4,5]=>0011010=>0101100=>1010011
[1,2,6,3,8,4,7,5]=>0010101=>1010100=>0101011
[4,2,1,8,3,7,5,6]=>1101010=>0101011=>1010100
[8,3,2,1,7,4,5,6]=>1110100=>0010111=>1101000
[1,2,3,8,7,4,6,5]=>0001101=>1011000=>0100111
[1,2,3,8,7,6,4,5]=>0001110=>0111000=>1000111
[2,6,5,7,1,4,3,8]=>0101010=>0101010=>1010101
[2,6,5,7,1,3,8,4]=>0101001=>1001010=>0110101
[3,8,5,7,1,2,6,4]=>0101001=>1001010=>0110101
[3,8,5,7,2,6,4,1]=>0101011=>1101010=>0010101
[3,4,8,6,2,5,7,1]=>0011001=>1001100=>0110011
[3,4,8,6,1,2,5,7]=>0011000=>0001100=>1110011
[2,5,7,1,4,8,6,3]=>0010011=>1100100=>0011011
[2,8,1,7,5,6,4,3]=>0101011=>1101010=>0010101
[2,3,8,1,6,5,7,4]=>0010101=>1010100=>0101011
[3,5,7,6,1,2,4,8]=>0011000=>0001100=>1110011
[4,8,6,7,2,3,5,1]=>0101001=>1001010=>0110101
[4,8,6,7,1,3,5,2]=>0101001=>1001010=>0110101
[3,4,8,6,1,5,7,2]=>0011001=>1001100=>0110011
[3,8,5,7,1,6,4,2]=>0101011=>1101010=>0010101
[3,8,5,7,2,1,6,4]=>0101101=>1011010=>0100101
[3,4,8,6,2,1,5,7]=>0011100=>0011100=>1100011
[3,5,7,6,2,1,4,8]=>0011100=>0011100=>1100011
[5,8,6,7,3,4,2,1]=>0101011=>1101010=>0010101
[5,8,6,7,2,1,3,4]=>0101100=>0011010=>1100101
[4,8,6,7,2,1,5,3]=>0101101=>1011010=>0100101
[4,3,1,7,5,2,8,6]=>1101101=>1011011=>0100100
[4,3,2,8,5,1,7,6]=>1101101=>1011011=>0100100
[4,3,8,5,1,6,7,2]=>1011001=>1001101=>0110010
[5,8,6,7,2,3,4,1]=>0101001=>1001010=>0110101
[5,8,6,7,2,4,3,1]=>0101011=>1101010=>0010101
[5,8,6,7,1,2,4,3]=>0101001=>1001010=>0110101
[3,2,5,7,6,1,4,8]=>1001100=>0011001=>1100110
[4,8,6,7,1,3,2,5]=>0101010=>0101010=>1010101
[4,8,6,7,1,2,5,3]=>0101001=>1001010=>0110101
[4,8,6,7,2,5,3,1]=>0101011=>1101010=>0010101
[4,3,8,5,2,6,7,1]=>1011001=>1001101=>0110010
[4,2,6,7,5,1,3,8]=>1001100=>0011001=>1100110
[3,8,4,7,1,5,2,6]=>0101010=>0101010=>1010101
[3,5,1,7,4,6,2,8]=>0101010=>0101010=>1010101
[3,8,4,7,2,5,1,6]=>0101010=>0101010=>1010101
[4,1,3,8,5,2,6,7]=>1001100=>0011001=>1100110
[4,2,6,7,5,3,8,1]=>1001101=>1011001=>0100110
[4,8,6,7,3,2,5,1]=>0101101=>1011010=>0100101
[4,8,6,7,3,1,2,5]=>0101100=>0011010=>1100101
[3,1,5,7,6,2,4,8]=>1001100=>0011001=>1100110
[3,4,1,7,5,6,2,8]=>0101010=>0101010=>1010101
[4,1,7,5,2,8,6,3]=>1011011=>1101101=>0010010
[4,1,6,7,5,2,3,8]=>1001100=>0011001=>1100110
[5,8,6,7,3,2,4,1]=>0101101=>1011010=>0100101
[5,8,6,7,4,2,3,1]=>0101101=>1011010=>0100101
[5,8,6,7,4,1,2,3]=>0101100=>0011010=>1100101
[5,8,6,7,4,1,3,2]=>0101101=>1011010=>0100101
[5,8,6,7,3,1,4,2]=>0101101=>1011010=>0100101
[4,8,6,7,3,1,5,2]=>0101101=>1011010=>0100101
[4,1,6,7,5,3,8,2]=>1001101=>1011001=>0100110
[4,1,7,5,3,2,8,6]=>1011101=>1011101=>0100010
[4,2,8,5,3,1,7,6]=>1011101=>1011101=>0100010
[4,2,1,6,7,5,3,8]=>1100110=>0110011=>1001100
[4,8,6,7,3,2,1,5]=>0101110=>0111010=>1000101
[5,8,6,7,4,2,1,3]=>0101110=>0111010=>1000101
[5,8,6,7,4,3,1,2]=>0101110=>0111010=>1000101
[6,1,5,2,8,4,7,3]=>1010101=>1010101=>0101010
[4,6,1,8,5,7,2,3]=>0101010=>0101010=>1010101
[4,7,1,2,8,5,6,3]=>0100101=>1010010=>0101101
[1,4,7,2,8,5,6,3]=>0010101=>1010100=>0101011
[1,7,3,5,8,6,2,4]=>0100110=>0110010=>1001101
[7,3,5,8,6,1,2,4]=>1001100=>0011001=>1100110
[6,8,1,5,7,2,3,4]=>0100100=>0010010=>1101101
[7,1,2,5,8,6,3,4]=>1000110=>0110001=>1001110
[1,7,2,5,8,6,3,4]=>0100110=>0110010=>1001101
[1,7,6,8,2,3,5,4]=>0101001=>1001010=>0110101
[7,6,8,1,2,3,5,4]=>1010001=>1000101=>0111010
[2,7,1,5,8,6,3,4]=>0100110=>0110010=>1001101
[2,4,7,1,8,5,6,3]=>0010101=>1010100=>0101011
[4,7,5,8,3,1,6,2]=>0101101=>1011010=>0100101
[4,7,2,1,8,5,6,3]=>0110101=>1010110=>0101001
[7,3,5,8,6,2,1,4]=>1001110=>0111001=>1000110
[7,6,8,2,1,3,5,4]=>1011001=>1001101=>0110010
[1,2,7,6,8,3,5,4]=>0010101=>1010100=>0101011
[3,7,6,8,2,1,5,4]=>0101101=>1011010=>0100101
[6,7,4,1,8,5,3,2]=>0110111=>1110110=>0001001
[6,7,4,3,1,8,5,2]=>0111011=>1101110=>0010001
[2,7,4,1,6,8,5,3]=>0110011=>1100110=>0011001
[3,1,7,6,8,2,5,4]=>1010101=>1010101=>0101010
[1,3,7,6,8,2,5,4]=>0010101=>1010100=>0101011
[1,7,4,2,6,8,5,3]=>0110011=>1100110=>0011001
[7,1,4,2,8,5,6,3]=>1010101=>1010101=>0101010
[7,1,8,2,5,4,6,3]=>1010101=>1010101=>0101010
[7,1,6,8,5,4,2,3]=>1001110=>0111001=>1000110
[7,1,2,6,8,5,4,3]=>1000111=>1110001=>0001110
[1,7,2,6,8,5,4,3]=>0100111=>1110010=>0001101
[1,7,6,8,3,2,5,4]=>0101101=>1011010=>0100101
[7,6,8,3,1,2,5,4]=>1011001=>1001101=>0110010
[7,1,5,8,6,3,2,4]=>1001110=>0111001=>1000110
[3,6,7,1,8,5,4,2]=>0010111=>1110100=>0001011
[7,2,6,8,5,4,1,3]=>1001110=>0111001=>1000110
[7,6,8,2,3,1,5,4]=>1010101=>1010101=>0101010
[2,7,6,8,3,1,5,4]=>0101101=>1011010=>0100101
[2,7,1,6,8,5,4,3]=>0100111=>1110010=>0001101
[6,7,3,1,8,5,4,2]=>0110111=>1110110=>0001001
[6,7,1,8,5,4,3,2]=>0101111=>1111010=>0000101
[7,2,1,6,8,5,4,3]=>1100111=>1110011=>0001100
[7,8,4,2,1,6,5,3]=>0111011=>1101110=>0010001
[6,2,3,4,8,7,1,5]=>1000110=>0110001=>1001110
[6,2,3,4,7,8,1,5]=>1000010=>0100001=>1011110
[7,8,3,6,4,2,1,5]=>0101110=>0111010=>1000101
[7,8,3,5,6,2,1,4]=>0100110=>0110010=>1001101
[5,2,6,3,8,1,7,4]=>1010101=>1010101=>0101010
[6,3,2,5,8,7,1,4]=>1100110=>0110011=>1001100
[6,3,2,8,4,7,1,5]=>1101010=>0101011=>1010100
[6,4,3,8,7,5,1,2]=>1101110=>0111011=>1000100
[6,4,3,7,8,5,1,2]=>1100110=>0110011=>1001100
[6,3,2,7,4,8,1,5]=>1101010=>0101011=>1010100
[6,3,2,5,7,8,1,4]=>1100010=>0100011=>1011100
[5,8,2,3,6,1,7,4]=>0100101=>1010010=>0101101
[4,5,6,8,3,2,1,7]=>0001110=>0111000=>1000111
[4,6,8,5,3,2,1,7]=>0011110=>0111100=>1000011
[5,6,1,4,2,3,7,8]=>0101000=>0001010=>1110101
[5,6,8,4,3,7,1,2]=>0011010=>0101100=>1010011
[5,6,1,4,2,3,8,7]=>0101001=>1001010=>0110101
[5,2,8,3,4,1,7,6]=>1010101=>1010101=>0101010
[4,5,8,6,3,2,1,7]=>0011110=>0111100=>1000011
[4,7,5,6,3,2,1,8]=>0101110=>0111010=>1000101
[5,1,4,3,6,2,8,7]=>1010101=>1010101=>0101010
[5,1,4,3,8,2,7,6]=>1010101=>1010101=>0101010
[5,6,2,4,1,8,7,3]=>0101011=>1101010=>0010101
[5,7,2,4,1,8,6,3]=>0101011=>1101010=>0010101
[6,1,4,2,8,7,5,3]=>1010111=>1110101=>0001010
[5,8,2,4,1,7,6,3]=>0101011=>1101010=>0010101
[5,4,1,3,7,2,6,8]=>1100100=>0010011=>1101100
[5,8,1,4,2,3,7,6]=>0101001=>1001010=>0110101
[5,1,6,3,4,2,7,8]=>1010100=>0010101=>1101010
[4,8,6,5,3,2,1,7]=>0111110=>0111110=>1000001
[5,4,7,8,3,2,1,6]=>1001110=>0111001=>1000110
[4,7,8,5,3,2,1,6]=>0011110=>0111100=>1000011
[5,7,1,3,4,2,6,8]=>0100100=>0010010=>1101101
[5,1,8,4,2,3,6,7]=>1011000=>0001101=>1110010
[5,1,7,4,2,3,6,8]=>1011000=>0001101=>1110010
[5,8,1,3,4,2,6,7]=>0100100=>0010010=>1101101
[4,8,7,5,3,2,1,6]=>0111110=>0111110=>1000001
[4,7,8,6,3,2,1,5]=>0011110=>0111100=>1000011
[4,8,2,3,6,7,5,1]=>0100011=>1100010=>0011101
[4,8,3,1,6,7,5,2]=>0110011=>1100110=>0011001
[4,3,8,1,6,2,5,7]=>1010100=>0010101=>1101010
[1,4,8,7,3,5,2,6]=>0011010=>0101100=>1010011
[4,3,8,7,2,5,1,6]=>1011010=>0101101=>1010010
[5,8,1,4,7,2,6,3]=>0100101=>1010010=>0101101
[6,8,1,2,4,3,5,7]=>0100100=>0010010=>1101101
[5,8,7,1,3,4,2,6]=>0110010=>0100110=>1011001
[4,8,7,6,3,1,2,5]=>0111100=>0011110=>1100001
[5,8,4,7,3,1,2,6]=>0101100=>0011010=>1100101
[4,3,8,2,7,5,6,1]=>1010101=>1010101=>0101010
[1,4,8,3,7,5,6,2]=>0010101=>1010100=>0101011
[1,4,3,8,2,6,5,7]=>0101010=>0101010=>1010101
[4,1,3,8,2,6,5,7]=>1001010=>0101001=>1010110
[4,1,8,7,3,5,2,6]=>1011010=>0101101=>1010010
[3,4,8,1,6,2,5,7]=>0010100=>0010100=>1101011
[3,4,8,7,2,5,1,6]=>0011010=>0101100=>1010011
[3,4,8,2,7,5,6,1]=>0010101=>1010100=>0101011
[1,2,4,3,8,6,5,7]=>0010110=>0110100=>1001011
[3,4,2,1,8,6,5,7]=>0110110=>0110110=>1001001
[3,4,1,8,2,6,5,7]=>0101010=>0101010=>1010101
[3,6,7,8,4,1,2,5]=>0001100=>0011000=>1100111
[4,1,2,8,3,6,5,7]=>1001010=>0101001=>1010110
[1,4,3,2,8,6,5,7]=>0110110=>0110110=>1001001
[4,2,3,1,8,6,5,7]=>1010110=>0110101=>1001010
[3,7,8,2,6,4,5,1]=>0010101=>1010100=>0101011
[4,2,3,8,1,6,5,7]=>1001010=>0101001=>1010110
[4,3,1,8,2,6,5,7]=>1101010=>0101011=>1010100
[1,4,7,8,5,3,2,6]=>0001110=>0111000=>1000111
[4,2,8,6,3,1,5,7]=>1011100=>0011101=>1100010
[2,4,8,6,3,1,5,7]=>0011100=>0011100=>1100011
[7,3,6,8,4,2,1,5]=>1001110=>0111001=>1000110
[1,7,3,8,4,6,5,2]=>0101011=>1101010=>0010101
[1,3,4,8,2,6,5,7]=>0001010=>0101000=>1010111
[3,2,4,8,1,6,5,7]=>1001010=>0101001=>1010110
[7,3,8,2,6,4,5,1]=>1010101=>1010101=>0101010
[6,2,8,7,4,3,5,1]=>1011101=>1011101=>0100010
[7,4,1,8,5,2,6,3]=>1101101=>1011011=>0100100
[7,3,2,8,4,6,5,1]=>1101011=>1101011=>0010100
[1,3,4,2,8,6,5,7]=>0010110=>0110100=>1001011
[1,3,2,4,8,6,5,7]=>0100110=>0110010=>1001101
[3,2,1,4,8,6,5,7]=>1100110=>0110011=>1001100
[3,1,2,4,8,6,5,7]=>1000110=>0110001=>1001110
[3,1,4,2,8,6,5,7]=>1010110=>0110101=>1001010
[3,1,4,8,2,6,5,7]=>1001010=>0101001=>1010110
[7,3,4,8,5,1,6,2]=>1001101=>1011001=>0100110
[3,7,4,8,5,1,2,6]=>0101100=>0011010=>1100101
[6,7,2,8,3,5,4,1]=>0101011=>1101010=>0010101
[2,3,1,4,8,6,5,7]=>0100110=>0110010=>1001101
[2,1,3,4,8,6,5,7]=>1000110=>0110001=>1001110
[3,5,7,8,6,1,2,4]=>0001100=>0011000=>1100111
[3,1,5,6,8,2,7,4]=>1000101=>1010001=>0101110
[5,1,6,3,8,4,7,2]=>1010101=>1010101=>0101010
[2,5,1,6,8,3,7,4]=>0100101=>1010010=>0101101
[5,1,2,6,8,3,7,4]=>1000101=>1010001=>0101110
[1,5,2,7,8,6,3,4]=>0100110=>0110010=>1001101
[6,1,7,5,2,8,3,4]=>1011010=>0101101=>1010010
[2,6,7,5,1,8,3,4]=>0011010=>0101100=>1010011
[5,7,2,8,6,1,3,4]=>0101100=>0011010=>1100101
[3,5,7,8,6,2,1,4]=>0001110=>0111000=>1000111
[3,2,5,7,8,6,1,4]=>1000110=>0110001=>1001110
[6,2,7,5,1,8,3,4]=>1011010=>0101101=>1010010
[1,2,6,7,5,8,3,4]=>0001010=>0101000=>1010111
[6,2,7,5,4,1,8,3]=>1011101=>1011101=>0100010
[6,7,5,2,4,1,8,3]=>0110101=>1010110=>0101001
[6,7,2,5,3,8,1,4]=>0101010=>0101010=>1010101
[5,1,7,8,6,3,2,4]=>1001110=>0111001=>1000110
[1,6,7,5,3,8,2,4]=>0011010=>0101100=>1010011
[1,6,7,5,4,2,8,3]=>0011101=>1011100=>0100011
[5,7,8,6,4,1,2,3]=>0011100=>0011100=>1100011
[6,7,4,1,5,2,8,3]=>0110101=>1010110=>0101001
[1,6,7,4,5,2,8,3]=>0010101=>1010100=>0101011
[6,3,1,7,5,8,2,4]=>1101010=>0101011=>1010100
[2,5,3,7,8,6,1,4]=>0100110=>0110010=>1001101
[6,3,2,7,5,8,1,4]=>1101010=>0101011=>1010100
[6,7,4,2,5,1,8,3]=>0110101=>1010110=>0101001
[6,2,7,4,5,1,8,3]=>1010101=>1010101=>0101010
[6,2,3,7,5,8,1,4]=>1001010=>0101001=>1010110
[7,5,1,6,3,8,2,4]=>1101010=>0101011=>1010100
[7,5,1,6,3,8,4,2]=>1101011=>1101011=>0010100
[2,7,6,1,3,8,4,5]=>0110010=>0100110=>1011001
[2,7,6,1,3,8,5,4]=>0110011=>1100110=>0011001
[2,6,7,1,5,8,3,4]=>0010010=>0100100=>1011011
[2,6,7,4,1,8,3,5]=>0011010=>0101100=>1010011
[2,1,6,7,3,8,5,4]=>1001011=>1101001=>0010110
[2,6,7,4,1,8,5,3]=>0011011=>1101100=>0010011
[2,6,7,1,5,8,4,3]=>0010011=>1100100=>0011011
[3,6,5,1,8,4,2,7]=>0110110=>0110110=>1001001
[3,7,5,4,8,1,6,2]=>0110101=>1010110=>0101001
[3,7,5,4,8,1,2,6]=>0110100=>0010110=>1101001
[4,6,1,5,8,7,3,2]=>0100111=>1110010=>0001101
[4,6,1,5,8,7,2,3]=>0100110=>0110010=>1001101
[4,6,1,5,8,2,7,3]=>0100101=>1010010=>0101101
[7,5,1,6,2,8,3,4]=>1101010=>0101011=>1010100
[4,6,1,5,8,2,3,7]=>0100100=>0010010=>1101101
[4,7,1,5,8,3,6,2]=>0100101=>1010010=>0101101
[8,3,4,6,2,1,5,7]=>1001100=>0011001=>1100110
[3,5,6,2,1,8,4,7]=>0011010=>0101100=>1010011
[7,5,3,2,8,4,1,6]=>1110110=>0110111=>1001000
[7,5,3,2,8,4,6,1]=>1110101=>1010111=>0101000
[4,2,5,6,8,3,1,7]=>1000110=>0110001=>1001110
[5,3,6,8,1,4,2,7]=>1001010=>0101001=>1010110
[4,5,6,8,1,3,2,7]=>0001010=>0101000=>1010111
[1,4,5,6,8,3,2,7]=>0000110=>0110000=>1001111
[4,5,3,7,2,8,6,1]=>0101011=>1101010=>0010101
[6,4,7,3,2,8,5,1]=>1011011=>1101101=>0010010
[6,1,4,7,3,2,8,5]=>1001101=>1011001=>0100110
[5,1,7,3,8,4,2,6]=>1010110=>0110101=>1001010
[5,3,7,1,4,8,6,2]=>1010011=>1100101=>0011010
[6,4,3,1,7,8,5,2]=>1110011=>1100111=>0011000
[5,6,1,3,7,8,4,2]=>0100011=>1100010=>0011101
[5,6,1,7,8,3,4,2]=>0100101=>1010010=>0101101
[1,6,3,7,4,8,5,2]=>0101011=>1101010=>0010101
[6,7,2,4,1,8,5,3]=>0101011=>1101010=>0010101
[6,7,2,1,4,3,8,5]=>0110101=>1010110=>0101001
[6,4,7,3,1,2,8,5]=>1011001=>1001101=>0110010
[5,6,3,1,2,7,8,4]=>0110001=>1000110=>0111001
[5,6,1,3,2,7,8,4]=>0101001=>1001010=>0110101
[5,6,3,2,1,7,8,4]=>0111001=>1001110=>0110001
[5,6,3,2,7,8,4,1]=>0110011=>1100110=>0011001
[2,5,6,3,7,8,4,1]=>0010011=>1100100=>0011011
[2,5,6,3,1,7,8,4]=>0011001=>1001100=>0110011
[2,6,4,7,3,1,8,5]=>0101101=>1011010=>0100101
[6,3,7,2,8,4,1,5]=>1010110=>0110101=>1001010
[6,3,2,7,1,8,4,5]=>1101010=>0101011=>1010100
[7,5,3,2,1,8,4,6]=>1111010=>0101111=>1010000
[7,3,8,4,2,1,5,6]=>1011100=>0011101=>1100010
[4,7,2,1,3,8,6,5]=>0110011=>1100110=>0011001
[1,3,7,8,6,4,2,5]=>0001110=>0111000=>1000111
[5,7,3,8,2,1,6,4]=>0101101=>1011010=>0100101
[4,6,2,7,8,5,3,1]=>0100111=>1110010=>0001101
[2,5,1,7,3,8,6,4]=>0101011=>1101010=>0010101
[6,7,2,1,3,8,5,4]=>0110011=>1100110=>0011001
[5,1,6,7,8,2,4,3]=>1000101=>1010001=>0101110
[6,3,7,1,8,5,2,4]=>1010110=>0110101=>1001010
[6,2,1,7,3,8,5,4]=>1101011=>1101011=>0010100
[6,2,7,1,8,5,4,3]=>1010111=>1110101=>0001010
[6,3,1,7,8,5,4,2]=>1100111=>1110011=>0001100
[5,3,2,1,8,4,7,6]=>1110101=>1010111=>0101000
[4,5,2,1,3,8,7,6]=>0110011=>1100110=>0011001
[3,2,6,4,5,8,1,7]=>1010010=>0100101=>1011010
[2,4,6,5,8,1,3,7]=>0010100=>0010100=>1101011
[1,3,4,6,5,8,2,7]=>0001010=>0101000=>1010111
[1,6,3,4,5,8,2,7]=>0100010=>0100010=>1011101
[3,4,1,8,5,2,7,6]=>0101101=>1011010=>0100101
[2,8,4,1,7,6,3,5]=>0110110=>0110110=>1001001
[1,5,3,2,8,7,4,6]=>0110110=>0110110=>1001001
[8,2,1,7,5,3,4,6]=>1101100=>0011011=>1100100
[1,7,6,4,5,8,3,2]=>0110011=>1100110=>0011001
[5,8,7,4,6,2,1,3]=>0110110=>0110110=>1001001
[3,4,2,5,8,6,7,1]=>0100101=>1010010=>0101101
[4,1,3,5,6,8,7,2]=>1000011=>1100001=>0011110
[2,4,8,6,7,1,3,5]=>0010100=>0010100=>1101011
[3,7,4,8,2,1,6,5]=>0101101=>1011010=>0100101
[2,3,5,8,6,7,1,4]=>0001010=>0101000=>1010111
[3,2,5,6,8,7,1,4]=>1000110=>0110001=>1001110
[7,2,4,8,5,3,1,6]=>1001110=>0111001=>1000110
[4,8,3,1,2,7,6,5]=>0110011=>1100110=>0011001
[8,4,2,3,7,1,5,6]=>1100100=>0010011=>1101100
[3,5,2,7,6,1,8,4]=>0101101=>1011010=>0100101
[5,8,7,3,4,6,2,1]=>0110011=>1100110=>0011001
[5,8,2,7,4,1,6,3]=>0101101=>1011010=>0100101
[5,1,4,2,8,7,6,3]=>1010111=>1110101=>0001010
[5,2,6,8,7,1,3,4]=>1001100=>0011001=>1100110
[6,3,2,1,8,5,7,4]=>1110101=>1010111=>0101000
[2,7,5,4,1,8,6,3]=>0111011=>1101110=>0010001
[4,2,5,6,8,7,1,3]=>1000110=>0110001=>1001110
[1,8,4,2,5,6,7,3]=>0110001=>1000110=>0111001
[3,8,4,1,5,6,7,2]=>0110001=>1000110=>0111001
[4,2,8,5,6,7,1,3]=>1010010=>0100101=>1011010
[5,2,4,7,1,8,6,3]=>1001011=>1101001=>0010110
[8,1,3,6,5,2,4,7]=>1001100=>0011001=>1100110
[8,3,2,4,6,5,1,7]=>1100110=>0110011=>1001100
[8,3,6,4,1,5,2,7]=>1011010=>0101101=>1010010
[1,3,4,8,5,7,2,6]=>0001010=>0101000=>1010111
[5,8,4,7,6,2,3,1]=>0101101=>1011010=>0100101
[1,3,4,7,5,8,2,6]=>0001010=>0101000=>1010111
[1,3,5,2,4,8,7,6]=>0010011=>1100100=>0011011
[2,6,5,1,3,8,7,4]=>0110011=>1100110=>0011001
[2,8,5,1,4,7,6,3]=>0110011=>1100110=>0011001
[4,3,1,5,8,6,7,2]=>1100101=>1010011=>0101100
[5,4,2,1,6,8,7,3]=>1110011=>1100111=>0011000
[6,8,4,3,2,7,1,5]=>0111010=>0101110=>1010001
[5,1,3,2,8,6,7,4]=>1010101=>1010101=>0101010
[5,3,1,2,8,6,7,4]=>1100101=>1010011=>0101100
[5,2,3,1,6,8,7,4]=>1010011=>1100101=>0011010
[5,3,2,1,8,6,7,4]=>1110101=>1010111=>0101000
[5,2,1,3,6,8,7,4]=>1100011=>1100011=>0011100
[2,7,4,5,8,3,1,6]=>0100110=>0110010=>1001101
[1,8,4,3,7,2,6,5]=>0110101=>1010110=>0101001
[3,4,8,7,2,1,6,5]=>0011101=>1011100=>0100011
[5,4,7,8,3,6,2,1]=>1001011=>1101001=>0010110
[6,3,8,7,4,1,2,5]=>1011100=>0011101=>1100010
[8,4,7,2,3,1,5,6]=>1010100=>0010101=>1101010
[8,6,4,1,3,2,7,5]=>1110101=>1010111=>0101000
[3,5,7,2,6,1,8,4]=>0010101=>1010100=>0101011
[6,1,3,8,5,7,2,4]=>1001010=>0101001=>1010110
[2,8,1,5,4,7,6,3]=>0101011=>1101010=>0010101
[1,7,2,4,6,5,8,3]=>0100101=>1010010=>0101101
[5,8,2,6,1,3,7,4]=>0101001=>1001010=>0110101
[6,3,5,8,7,2,1,4]=>1001110=>0111001=>1000110
[2,5,7,8,4,1,6,3]=>0001101=>1011000=>0100111
[4,1,5,2,6,8,7,3]=>1010011=>1100101=>0011010
[4,1,8,5,2,6,7,3]=>1011001=>1001101=>0110010
[2,7,1,8,5,4,6,3]=>0101101=>1011010=>0100101
[5,8,6,2,1,3,7,4]=>0111001=>1001110=>0110001
[3,4,5,1,8,6,7,2]=>0010101=>1010100=>0101011
[1,3,2,7,5,8,6,4]=>0101011=>1101010=>0010101
[1,4,2,5,8,3,7,6]=>0100101=>1010010=>0101101
[4,1,2,6,8,5,3,7]=>1000110=>0110001=>1001110
[1,5,2,4,8,7,6,3]=>0100111=>1110010=>0001101
[1,2,7,4,8,6,5,3]=>0010111=>1110100=>0001011
[1,3,2,8,5,7,4,6]=>0101010=>0101010=>1010101
[1,2,6,4,8,7,3,5]=>0010110=>0110100=>1001011
[1,3,8,2,6,7,4,5]=>0010010=>0100100=>1011011
[1,6,7,8,2,5,3,4]=>0001010=>0101000=>1010111
[1,5,7,8,2,3,6,4]=>0001001=>1001000=>0110111
[1,2,8,4,7,3,6,5]=>0010101=>1010100=>0101011
[1,5,2,4,8,3,7,6]=>0100101=>1010010=>0101101
[1,8,3,5,2,7,4,6]=>0101010=>0101010=>1010101
[1,4,8,6,7,2,3,5]=>0010100=>0010100=>1101011
[1,5,7,8,6,2,3,4]=>0001100=>0011000=>1100111
[1,3,7,6,2,8,4,5]=>0011010=>0101100=>1010011
[1,2,5,8,7,6,3,4]=>0001110=>0111000=>1000111
[1,2,6,8,7,5,3,4]=>0001110=>0111000=>1000111
[1,2,7,8,6,5,3,4]=>0001110=>0111000=>1000111
[5,2,6,7,3,4,8,1]=>1001001=>1001001=>0110110
[5,6,2,1,7,8,3,4]=>0110010=>0100110=>1011001
[5,6,2,1,4,8,7,3]=>0110011=>1100110=>0011001
[2,6,1,4,5,8,7,3]=>0100011=>1100010=>0011101
[5,4,2,7,6,3,8,1]=>1101101=>1011011=>0100100
[2,3,7,6,4,5,8,1]=>0011001=>1001100=>0110011
[2,6,1,7,5,8,3,4]=>0101010=>0101010=>1010101
[5,1,2,7,8,4,3,6]=>1000110=>0110001=>1001110
[2,6,1,7,4,8,3,5]=>0101010=>0101010=>1010101
[3,6,4,1,7,8,2,5]=>0110010=>0100110=>1011001
[5,4,6,1,7,8,2,3]=>1010010=>0100101=>1011010
[5,4,6,1,3,8,7,2]=>1010011=>1100101=>0011010
[3,6,4,1,5,8,7,2]=>0110011=>1100110=>0011001
[2,6,1,5,4,8,7,3]=>0101011=>1101010=>0010101
[2,6,1,4,7,8,5,3]=>0100011=>1100010=>0011101
[5,1,2,4,8,7,6,3]=>1000111=>1110001=>0001110
[2,1,5,3,8,6,4,7]=>1010110=>0110101=>1001010
[5,1,2,4,8,6,3,7]=>1000110=>0110001=>1001110
[5,6,3,1,4,8,2,7]=>0110010=>0100110=>1011001
[2,5,4,3,1,8,6,7]=>0111010=>0101110=>1010001
[5,4,6,3,1,8,7,2]=>1011011=>1101101=>0010010
[2,1,3,7,8,6,4,5]=>1000110=>0110001=>1001110
[5,1,4,2,8,6,7,3]=>1010101=>1010101=>0101010
[1,2,3,8,6,7,4,5]=>0001010=>0101000=>1010111
[1,2,3,8,7,5,4,6]=>0001110=>0111000=>1000111
[1,2,3,8,7,4,5,6]=>0001100=>0011000=>1100111
[2,1,3,6,8,7,4,5]=>1000110=>0110001=>1001110
[3,1,6,2,8,7,5,4]=>1010111=>1110101=>0001010
[6,8,1,3,2,5,4,7]=>0101010=>0101010=>1010101
[6,8,1,4,2,5,3,7]=>0101010=>0101010=>1010101
[7,8,3,6,1,4,2,5]=>0101010=>0101010=>1010101
[7,8,2,5,1,4,3,6]=>0101010=>0101010=>1010101
[7,8,1,4,3,6,2,5]=>0101010=>0101010=>1010101
[5,8,1,4,3,7,2,6]=>0101010=>0101010=>1010101
[6,8,2,5,1,4,3,7]=>0101010=>0101010=>1010101
[6,8,2,5,3,7,1,4]=>0101010=>0101010=>1010101
[2,5,4,7,6,8,1,3]=>0101010=>0101010=>1010101
[2,6,1,4,3,7,5,8]=>0101010=>0101010=>1010101
[2,6,1,5,3,7,4,8]=>0101010=>0101010=>1010101
[2,6,4,7,5,8,1,3]=>0101010=>0101010=>1010101
[5,8,2,6,4,7,1,3]=>0101010=>0101010=>1010101
[6,8,3,7,1,4,2,5]=>0101010=>0101010=>1010101
[5,8,1,3,2,6,4,7]=>0101010=>0101010=>1010101
[5,8,4,7,1,3,2,6]=>0101010=>0101010=>1010101
[6,8,4,7,1,3,2,5]=>0101010=>0101010=>1010101
[6,8,5,7,1,3,2,4]=>0101010=>0101010=>1010101
[5,7,6,8,2,4,1,3]=>0101010=>0101010=>1010101
[4,7,5,8,1,3,2,6]=>0101010=>0101010=>1010101
[4,7,1,3,2,6,5,8]=>0101010=>0101010=>1010101
[3,7,1,4,2,6,5,8]=>0101010=>0101010=>1010101
[3,7,6,8,1,4,2,5]=>0101010=>0101010=>1010101
[4,7,6,8,2,5,1,3]=>0101010=>0101010=>1010101
[4,7,5,8,3,6,1,2]=>0101010=>0101010=>1010101
[4,7,5,8,2,6,1,3]=>0101010=>0101010=>1010101
[3,7,4,8,2,6,1,5]=>0101010=>0101010=>1010101
[3,7,1,5,2,6,4,8]=>0101010=>0101010=>1010101
[3,7,2,6,1,5,4,8]=>0101010=>0101010=>1010101
[3,7,2,6,5,8,1,4]=>0101010=>0101010=>1010101
[4,7,3,6,5,8,1,2]=>0101010=>0101010=>1010101
[2,6,5,8,4,7,1,3]=>0101010=>0101010=>1010101
[2,6,3,7,1,5,4,8]=>0101010=>0101010=>1010101
[7,6,4,8,5,2,3,1]=>1101101=>1011011=>0100100
[6,7,4,3,5,1,8,2]=>0110101=>1010110=>0101001
[6,7,3,5,4,8,2,1]=>0101011=>1101010=>0010101
[6,8,3,7,5,2,4,1]=>0101101=>1011010=>0100101
[7,6,3,5,8,2,4,1]=>1100101=>1010011=>0101100
[7,6,2,8,4,1,5,3]=>1101101=>1011011=>0100100
[7,6,3,4,8,2,5,1]=>1100101=>1010011=>0101100
[6,8,3,7,4,5,2,1]=>0101011=>1101010=>0010101
[6,7,3,5,8,4,2,1]=>0100111=>1110010=>0001101
[5,7,8,3,6,2,1,4]=>0010110=>0110100=>1001011
[6,3,4,8,7,2,5,1]=>1001101=>1011001=>0100110
[6,3,8,4,7,2,1,5]=>1010110=>0110101=>1001010
[6,3,4,7,5,8,2,1]=>1001011=>1101001=>0010110
[6,3,5,7,8,4,2,1]=>1000111=>1110001=>0001110
[5,7,3,6,8,2,1,4]=>0100110=>0110010=>1001101
[5,6,7,3,4,1,8,2]=>0010101=>1010100=>0101011
[4,6,7,8,3,5,2,1]=>0001011=>1101000=>0010111
[4,7,3,5,6,8,2,1]=>0100011=>1100010=>0011101
[5,3,4,7,8,2,1,6]=>1000110=>0110001=>1001110
[5,3,8,2,4,1,6,7]=>1010100=>0010101=>1101010
[5,3,4,8,2,6,1,7]=>1001010=>0101001=>1010110
[4,8,3,6,2,5,7,1]=>0101001=>1001010=>0110101
[4,8,3,5,7,2,6,1]=>0100101=>1010010=>0101101
[4,8,3,5,6,7,2,1]=>0100011=>1100010=>0011101
[4,7,8,3,5,6,2,1]=>0010011=>1100100=>0011011
[4,7,8,3,6,2,5,1]=>0010101=>1010100=>0101011
[4,8,3,6,7,2,5,1]=>0100101=>1010010=>0101101
[4,8,3,7,2,5,6,1]=>0101001=>1001010=>0110101
[5,8,3,7,2,6,4,1]=>0101011=>1101010=>0010101
[5,7,3,4,8,2,1,6]=>0100110=>0110010=>1001101
[5,8,4,2,3,1,6,7]=>0110100=>0010110=>1101001
[5,8,4,2,3,1,7,6]=>0110101=>1010110=>0101001
[6,4,8,5,3,7,2,1]=>1011011=>1101101=>0010010
[6,4,2,7,3,1,8,5]=>1101101=>1011011=>0100100
[6,4,3,7,8,5,2,1]=>1100111=>1110011=>0001100
[6,4,5,3,7,1,8,2]=>1010101=>1010101=>0101010
[5,7,4,2,3,1,6,8]=>0110100=>0010110=>1101001
[5,6,3,7,1,8,2,4]=>0101010=>0101010=>1010101
[5,6,3,4,8,2,1,7]=>0100110=>0110010=>1001101
[6,3,5,7,4,8,2,1]=>1001011=>1101001=>0010110
[6,3,5,4,7,8,2,1]=>1010011=>1100101=>0011010
[6,4,3,5,7,1,8,2]=>1100101=>1010011=>0101100
[6,4,2,5,1,7,3,8]=>1101010=>0101011=>1010100
[5,3,4,7,2,6,1,8]=>1001010=>0101001=>1010110
[4,7,3,6,2,5,8,1]=>0101001=>1001010=>0110101
[4,7,3,6,8,2,5,1]=>0100101=>1010010=>0101101
[4,6,7,3,5,8,2,1]=>0010011=>1100100=>0011011
[4,5,7,8,3,6,2,1]=>0001011=>1101000=>0010111
[4,5,8,3,7,2,6,1]=>0010101=>1010100=>0101011
[5,3,4,6,8,2,1,7]=>1000110=>0110001=>1001110
[5,3,6,7,1,8,2,4]=>1001010=>0101001=>1010110
[5,3,4,6,7,1,8,2]=>1000101=>1010001=>0101110
[4,6,3,5,7,8,2,1]=>0100011=>1100010=>0011101
[4,5,7,3,6,8,2,1]=>0010011=>1100100=>0011011
[7,1,5,8,4,2,3,6]=>1001100=>0011001=>1100110
[8,1,5,7,4,2,3,6]=>1001100=>0011001=>1100110
[7,1,4,5,8,2,3,6]=>1000100=>0010001=>1101110
[7,4,1,6,2,8,3,5]=>1101010=>0101011=>1010100
[8,4,1,7,2,6,3,5]=>1101010=>0101011=>1010100
[8,1,4,7,5,2,3,6]=>1001100=>0011001=>1100110
[8,1,5,4,7,2,3,6]=>1010100=>0010101=>1101010
[2,1,7,5,8,3,4,6]=>1010100=>0010101=>1101010
[7,1,5,4,8,2,3,6]=>1010100=>0010101=>1101010
[7,1,4,8,5,2,3,6]=>1001100=>0011001=>1100110
[7,8,3,1,2,4,6,5]=>0110001=>1000110=>0111001
[8,7,1,6,4,2,3,5]=>1101100=>0011011=>1100100
[8,6,1,7,4,2,3,5]=>1101100=>0011011=>1100100
[7,6,1,8,4,2,3,5]=>1101100=>0011011=>1100100
[7,3,8,1,2,4,6,5]=>1010001=>1000101=>0111010
[8,3,7,1,2,4,6,5]=>1010001=>1000101=>0111010
[8,3,6,1,2,4,7,5]=>1010001=>1000101=>0111010
[8,3,7,5,1,2,4,6]=>1011000=>0001101=>1110010
[7,3,6,1,2,4,8,5]=>1010001=>1000101=>0111010
[6,7,1,8,4,2,3,5]=>0101100=>0011010=>1100101
[6,8,1,7,4,2,3,5]=>0101100=>0011010=>1100101
[7,1,8,4,5,2,3,6]=>1010100=>0010101=>1101010
[7,6,3,1,2,4,8,5]=>1110001=>1000111=>0111000
[6,1,2,3,8,7,5,4]=>1000111=>1110001=>0001110
[6,8,3,1,2,7,4,5]=>0110010=>0100110=>1011001
[6,7,3,1,2,8,4,5]=>0110010=>0100110=>1011001
[6,7,1,4,2,3,8,5]=>0101001=>1001010=>0110101
[4,3,6,8,5,7,1,2]=>1001010=>0101001=>1010110
[6,1,2,5,4,8,3,7]=>1001010=>0101001=>1010110
[3,2,8,5,4,1,7,6]=>1011101=>1011101=>0100010
[7,8,2,1,4,6,3,5]=>0110010=>0100110=>1011001
[2,4,8,5,1,3,6,7]=>0011000=>0001100=>1110011
[3,5,6,1,8,4,2,7]=>0010110=>0110100=>1001011
[1,3,6,8,7,4,2,5]=>0001110=>0111000=>1000111
[1,2,8,5,7,3,4,6]=>0010100=>0010100=>1101011
[3,1,5,6,4,8,7,2]=>1001011=>1101001=>0010110
[1,3,6,2,5,7,8,4]=>0010001=>1000100=>0111011
[3,6,1,4,2,7,8,5]=>0101001=>1001010=>0110101
[1,3,6,5,2,7,8,4]=>0011001=>1001100=>0110011
[1,2,6,4,3,8,5,7]=>0011010=>0101100=>1010011
[1,2,6,3,5,8,7,4]=>0010011=>1100100=>0011011
[2,3,5,1,8,4,7,6]=>0010101=>1010100=>0101011
[1,2,7,4,6,8,3,5]=>0010010=>0100100=>1011011
[2,3,7,5,1,8,4,6]=>0011010=>0101100=>1010011
[4,7,2,5,3,8,6,1]=>0101011=>1101010=>0010101
[3,1,7,5,4,8,6,2]=>1011011=>1101101=>0010010
[1,2,7,6,4,8,5,3]=>0011011=>1101100=>0010011
[1,2,7,3,6,8,5,4]=>0010011=>1100100=>0011011
[3,1,5,4,8,7,6,2]=>1010111=>1110101=>0001010
[1,2,6,8,5,4,7,3]=>0001101=>1011000=>0100111
[3,5,7,4,8,2,1,6]=>0010110=>0110100=>1001011
[2,4,7,6,8,3,1,5]=>0010110=>0110100=>1001011
[1,4,6,8,3,5,2,7]=>0001010=>0101000=>1010111
[1,3,6,8,5,2,4,7]=>0001100=>0011000=>1100111
[1,2,6,8,5,4,3,7]=>0001110=>0111000=>1000111
[1,2,5,8,4,3,7,6]=>0001101=>1011000=>0100111
[1,3,6,8,2,5,4,7]=>0001010=>0101000=>1010111
[1,4,6,8,3,2,5,7]=>0001100=>0011000=>1100111
[2,3,6,5,8,1,7,4]=>0010101=>1010100=>0101011
[3,5,4,6,8,2,1,7]=>0100110=>0110010=>1001101
[3,5,4,6,8,1,2,7]=>0100100=>0010010=>1101101
[1,2,4,7,5,8,3,6]=>0001010=>0101000=>1010111
[3,6,4,7,1,8,5,2]=>0101011=>1101010=>0010101
[1,2,6,7,3,8,5,4]=>0001011=>1101000=>0010111
[1,2,5,7,3,8,6,4]=>0001011=>1101000=>0010111
[3,1,5,7,6,8,4,2]=>1001011=>1101001=>0010110
[3,5,4,6,8,2,7,1]=>0100101=>1010010=>0101101
[4,2,6,1,8,7,5,3]=>1010111=>1110101=>0001010
[1,2,7,4,6,8,5,3]=>0010011=>1100100=>0011011
[1,2,7,5,6,8,4,3]=>0010011=>1100100=>0011011
[3,1,6,7,5,8,4,2]=>1001011=>1101001=>0010110
[4,6,2,7,5,8,3,1]=>0101011=>1101010=>0010101
[3,5,7,4,8,2,6,1]=>0010101=>1010100=>0101011
[1,3,6,8,2,5,7,4]=>0001001=>1001000=>0110111
[1,3,5,8,2,7,4,6]=>0001010=>0101000=>1010111
[1,2,5,8,4,7,6,3]=>0001011=>1101000=>0010111
[1,2,4,8,7,3,6,5]=>0001101=>1011000=>0100111
[1,2,5,8,7,4,3,6]=>0001110=>0111000=>1000111
[1,3,5,8,7,2,4,6]=>0001100=>0011000=>1100111
[2,3,7,6,8,5,1,4]=>0010110=>0110100=>1001011
[5,7,1,2,8,6,4,3]=>0100111=>1110010=>0001101
[3,1,7,6,8,5,4,2]=>1010111=>1110101=>0001010
[1,2,6,8,5,7,4,3]=>0001011=>1101000=>0010111
[1,2,5,8,7,4,6,3]=>0001101=>1011000=>0100111
[1,2,4,8,7,6,3,5]=>0001110=>0111000=>1000111
[3,2,7,4,6,8,1,5]=>1010010=>0100101=>1011010
[5,3,6,2,7,1,4,8]=>1010100=>0010101=>1101010
[2,6,3,4,7,1,5,8]=>0100100=>0010010=>1101101
[2,7,3,4,5,8,1,6]=>0100010=>0100010=>1011101
[4,7,6,2,3,8,1,5]=>0110010=>0100110=>1011001
[7,3,5,2,4,8,1,6]=>1010010=>0100101=>1011010
[7,6,2,4,5,8,1,3]=>1100010=>0100011=>1011100
[6,5,2,3,4,8,1,7]=>1100010=>0100011=>1011100
[5,3,1,2,8,4,7,6]=>1100101=>1010011=>0101100
[6,5,2,3,7,1,4,8]=>1100100=>0010011=>1101100
[5,2,1,7,3,4,6,8]=>1101000=>0001011=>1110100
[5,2,1,8,3,4,6,7]=>1101000=>0001011=>1110100
[6,3,2,8,4,5,7,1]=>1101001=>1001011=>0110100
[7,3,1,2,8,4,6,5]=>1100101=>1010011=>0101100
[6,2,3,1,8,4,7,5]=>1010101=>1010101=>0101010
[8,3,5,2,7,1,4,6]=>1010100=>0010101=>1101010
[8,6,2,4,7,1,5,3]=>1100101=>1010011=>0101100
[8,2,1,7,3,4,5,6]=>1101000=>0001011=>1110100
[8,6,3,7,2,4,5,1]=>1101001=>1001011=>0110100
[8,2,7,3,4,5,6,1]=>1010001=>1000101=>0111010
[8,1,6,2,3,4,5,7]=>1010000=>0000101=>1111010
[8,1,7,3,4,5,6,2]=>1010001=>1000101=>0111010
[8,6,1,7,2,4,5,3]=>1101001=>1001011=>0110100
[1,7,5,8,2,3,6,4]=>0101001=>1001010=>0110101
[7,2,1,8,3,4,5,6]=>1101000=>0001011=>1110100
[1,7,8,3,4,5,6,2]=>0010001=>1000100=>0111011
[1,6,2,8,4,5,7,3]=>0101001=>1001010=>0110101
[4,1,3,6,8,2,7,5]=>1000101=>1010001=>0101110
[4,6,3,8,7,1,2,5]=>0101100=>0011010=>1100101
[6,4,5,8,7,1,2,3]=>1001100=>0011001=>1100110
[5,3,4,8,7,1,2,6]=>1001100=>0011001=>1100110
[3,2,8,7,1,4,6,5]=>1011001=>1001101=>0110010
[3,1,8,7,2,4,6,5]=>1011001=>1001101=>0110010
[5,3,7,6,1,2,4,8]=>1011000=>0001101=>1110010
[1,8,3,7,2,4,5,6]=>0101000=>0001010=>1110101
[3,8,1,7,2,4,5,6]=>0101000=>0001010=>1110101
[6,8,2,3,5,1,4,7]=>0100100=>0010010=>1101101
[4,7,8,2,6,1,3,5]=>0010100=>0010100=>1101011
[6,2,8,7,1,4,5,3]=>1011001=>1001101=>0110010
[3,8,7,1,4,5,6,2]=>0110001=>1000110=>0111001
[2,8,6,1,3,4,5,7]=>0110000=>0000110=>1111001
[2,7,6,1,3,4,5,8]=>0110000=>0000110=>1111001
[1,7,6,2,3,4,5,8]=>0110000=>0000110=>1111001
[1,8,6,2,3,4,5,7]=>0110000=>0000110=>1111001
[2,8,7,3,4,5,6,1]=>0110001=>1000110=>0111001
[3,8,7,2,4,5,6,1]=>0110001=>1000110=>0111001
[7,8,3,6,2,4,5,1]=>0101001=>1001010=>0110101
[1,5,8,7,2,3,6,4]=>0011001=>1001100=>0110011
[7,8,10,9,5,6,3,4,1,2]=>001101010=>010101100=>101010011
[9,10,5,6,8,7,3,4,1,2]=>010011010=>010110010=>101001101
[5,8,10,6,9,7,3,4,1,2]=>001011010=>010110100=>101001011
[5,6,7,10,9,8,3,4,1,2]=>000111010=>010111000=>101000111
[9,10,7,8,3,4,6,5,1,2]=>010100110=>011001010=>100110101
[7,8,10,9,3,4,6,5,1,2]=>001100110=>011001100=>100110011
[9,10,3,6,8,4,7,5,1,2]=>010010110=>011010010=>100101101
[3,8,10,6,9,4,7,5,1,2]=>001010110=>011010100=>100101011
[3,6,7,10,9,4,8,5,1,2]=>000110110=>011011000=>100100111
[9,10,3,4,5,8,7,6,1,2]=>010001110=>011100010=>100011101
[3,8,10,4,5,9,7,6,1,2]=>001001110=>011100100=>100011011
[3,4,7,10,5,9,8,6,1,2]=>000101110=>011101000=>100010111
[3,4,5,6,10,9,8,7,1,2]=>000011110=>011110000=>100001111
[9,10,7,8,5,6,1,2,4,3]=>010101001=>100101010=>011010101
[7,8,10,9,5,6,1,2,4,3]=>001101001=>100101100=>011010011
[9,10,5,6,8,7,1,2,4,3]=>010011001=>100110010=>011001101
[5,8,10,6,9,7,1,2,4,3]=>001011001=>100110100=>011001011
[5,6,7,10,9,8,1,2,4,3]=>000111001=>100111000=>011000111
[9,10,7,8,1,4,6,2,5,3]=>010100101=>101001010=>010110101
[7,8,10,9,1,4,6,2,5,3]=>001100101=>101001100=>010110011
[9,10,1,6,8,4,7,2,5,3]=>010010101=>101010010=>010101101
[1,8,10,6,9,4,7,2,5,3]=>001010101=>101010100=>010101011
[1,6,7,10,9,4,8,2,5,3]=>000110101=>101011000=>010100111
[9,10,1,4,5,8,7,2,6,3]=>010001101=>101100010=>010011101
[1,8,10,4,5,9,7,2,6,3]=>001001101=>101100100=>010011011
[1,4,7,10,5,9,8,2,6,3]=>000101101=>101101000=>010010111
[1,4,5,6,10,9,8,2,7,3]=>000011101=>101110000=>010001111
[9,10,7,8,1,2,3,6,5,4]=>010100011=>110001010=>001110101
[7,8,10,9,1,2,3,6,5,4]=>001100011=>110001100=>001110011
[9,10,1,6,8,2,3,7,5,4]=>010010011=>110010010=>001101101
[1,8,10,6,9,2,3,7,5,4]=>001010011=>110010100=>001101011
[1,6,7,10,9,2,3,8,5,4]=>000110011=>110011000=>001100111
[9,10,1,2,5,8,3,7,6,4]=>010001011=>110100010=>001011101
[1,8,10,2,5,9,3,7,6,4]=>001001011=>110100100=>001011011
[1,2,7,10,5,9,3,8,6,4]=>000101011=>110101000=>001010111
[1,2,5,6,10,9,3,8,7,4]=>000011011=>110110000=>001001111
[9,10,1,2,3,4,8,7,6,5]=>010000111=>111000010=>000111101
[1,8,10,2,3,4,9,7,6,5]=>001000111=>111000100=>000111011
[1,2,7,10,3,4,9,8,6,5]=>000100111=>111001000=>000110111
[1,2,3,6,10,4,9,8,7,5]=>000010111=>111010000=>000101111
[3,4,5,6,7,12,11,10,9,8,1,2]=>00000111110=>01111100000=>10000011111
[9,10,12,11,1,6,8,4,7,2,5,3]=>00110010101=>10101001100=>01010110011
[1,10,12,8,11,6,9,4,7,2,5,3]=>00101010101=>10101010100=>01010101011
[1,10,12,8,11,6,9,2,3,7,5,4]=>00101010011=>11001010100=>00110101011
[1,10,12,8,11,2,5,9,3,7,6,4]=>00101001011=>11010010100=>00101101011
[1,10,12,2,7,11,5,9,3,8,6,4]=>00100101011=>11010100100=>00101011011
[1,2,9,12,7,11,5,10,3,8,6,4]=>00010101011=>11010101000=>00101010111
[1,2,7,8,12,11,3,4,10,9,6,5]=>00001100111=>11100110000=>00011001111
[1,2,3,6,7,12,11,4,10,9,8,5]=>00000110111=>11101100000=>00010011111
[1,7,3,6,5,2,8,4]=>0101101=>1011010=>0100101
[8,6,2,5,4,1,7,3]=>1101101=>1011011=>0100100
[3,2,6,4,7,5,1,8]=>1010110=>0110101=>1001010
[6,2,3,7,5,4,1,8]=>1001110=>0111001=>1000110
[1,3,4,7,6,2,8,5]=>0001101=>1011000=>0100111
[2,8,3,6,1,7,5,4]=>0101011=>1101010=>0010101
[8,7,2,5,1,6,4,3]=>1101011=>1101011=>0010100
[3,8,2,6,5,1,7,4]=>0101101=>1011010=>0100101
[7,8,2,5,4,1,6,3]=>0101101=>1011010=>0100101
[4,8,5,2,6,1,7,3]=>0110101=>1010110=>0101001
[4,5,1,3,7,2,8,6]=>0100101=>1010010=>0101101
[6,1,3,7,5,2,8,4]=>1001101=>1011001=>0100110
[7,1,3,6,2,8,5,4]=>1001011=>1101001=>0010110
[8,1,3,6,2,7,5,4]=>1001011=>1101001=>0010110
[1,2,4,7,3,8,6,5]=>0001011=>1101000=>0010111
[7,1,8,2,6,5,4,3]=>1010111=>1110101=>0001010
[4,1,7,8,2,6,5,3]=>1001011=>1101001=>0010110
[3,4,8,6,5,1,7,2]=>0011101=>1011100=>0100011
[8,3,7,5,1,6,4,2]=>1011011=>1101101=>0010010
[1,4,8,6,2,7,5,3]=>0011011=>1101100=>0010011
[8,4,6,7,1,5,3,2]=>1001011=>1101001=>0010110
[3,4,6,5,1,2,8,7]=>0011001=>1001100=>0110011
[7,3,5,1,2,8,6,4]=>1010011=>1100101=>0011010
[1,4,6,2,3,8,7,5]=>0010011=>1100100=>0011011
[1,3,2,7,4,8,6,5]=>0101011=>1101010=>0010101
[7,2,1,6,3,8,5,4]=>1101011=>1101011=>0010100
[4,5,2,1,7,3,8,6]=>0110101=>1010110=>0101001
[5,6,7,1,2,8,4,3]=>0010011=>1100100=>0011011
[4,7,5,1,2,8,6,3]=>0110011=>1100110=>0011001
[3,7,1,6,2,8,5,4]=>0101011=>1101010=>0010101
[7,6,1,2,8,5,4,3]=>1100111=>1110011=>0001100
[2,7,1,3,8,6,5,4]=>0100111=>1110010=>0001101
[8,6,1,2,7,5,4,3]=>1100111=>1110011=>0001100
[1,7,2,3,8,6,5,4]=>0100111=>1110010=>0001101
[8,7,1,2,6,5,4,3]=>1100111=>1110011=>0001100
[7,8,1,2,6,5,4,3]=>0100111=>1110010=>0001101
[3,8,1,6,2,7,5,4]=>0101011=>1101010=>0010101
[4,8,5,1,2,7,6,3]=>0110011=>1100110=>0011001
[2,1,4,3,6,5,10,9,7,8]=>101010110=>011010101=>100101010
[2,1,4,3,8,7,5,6,10,9]=>101011001=>100110101=>011001010
[2,1,4,3,10,7,5,9,6,8]=>101011010=>010110101=>101001010
[2,1,4,3,10,9,8,5,6,7]=>101011100=>001110101=>110001010
[2,1,6,5,3,4,8,7,10,9]=>101100101=>101001101=>010110010
[2,1,6,5,3,4,10,9,7,8]=>101100110=>011001101=>100110010
[2,1,8,5,3,7,4,6,10,9]=>101101001=>100101101=>011010010
[2,1,10,5,3,7,4,9,6,8]=>101101010=>010101101=>101010010
[2,1,10,5,3,9,8,4,6,7]=>101101100=>001101101=>110010010
[2,1,8,7,6,3,4,5,10,9]=>101110001=>100011101=>011100010
[2,1,10,7,6,3,4,9,5,8]=>101110010=>010011101=>101100010
[2,1,10,9,6,3,8,4,5,7]=>101110100=>001011101=>110100010
[2,1,10,9,8,7,3,4,5,6]=>101111000=>000111101=>111000010
[4,3,1,2,6,5,8,7,10,9]=>110010101=>101010011=>010101100
[4,3,1,2,6,5,10,9,7,8]=>110010110=>011010011=>100101100
[4,3,1,2,8,7,5,6,10,9]=>110011001=>100110011=>011001100
[4,3,1,2,10,7,5,9,6,8]=>110011010=>010110011=>101001100
[4,3,1,2,10,9,8,5,6,7]=>110011100=>001110011=>110001100
[6,3,1,5,2,4,8,7,10,9]=>110100101=>101001011=>010110100
[6,3,1,5,2,4,10,9,7,8]=>110100110=>011001011=>100110100
[8,3,1,5,2,7,4,6,10,9]=>110101001=>100101011=>011010100
[10,3,1,5,2,9,8,4,6,7]=>110101100=>001101011=>110010100
[8,3,1,7,6,2,4,5,10,9]=>110110001=>100011011=>011100100
[10,3,1,7,6,2,4,9,5,8]=>110110010=>010011011=>101100100
[10,3,1,9,6,2,8,4,5,7]=>110110100=>001011011=>110100100
[10,3,1,9,8,7,2,4,5,6]=>110111000=>000111011=>111000100
[6,5,4,1,2,3,8,7,10,9]=>111000101=>101000111=>010111000
[6,5,4,1,2,3,10,9,7,8]=>111000110=>011000111=>100111000
[8,5,4,1,2,7,3,6,10,9]=>111001001=>100100111=>011011000
[10,5,4,1,2,7,3,9,6,8]=>111001010=>010100111=>101011000
[10,5,4,1,2,9,8,3,6,7]=>111001100=>001100111=>110011000
[8,7,4,1,6,2,3,5,10,9]=>111010001=>100010111=>011101000
[10,7,4,1,6,2,3,9,5,8]=>111010010=>010010111=>101101000
[10,9,4,1,8,7,2,3,5,6]=>111011000=>000110111=>111001000
[8,7,6,5,1,2,3,4,10,9]=>111100001=>100001111=>011110000
[10,7,6,5,1,2,3,9,4,8]=>111100010=>010001111=>101110000
[10,9,6,5,1,2,8,3,4,7]=>111100100=>001001111=>110110000
[2,1,4,3,6,5,8,7,12,11,9,10]=>10101010110=>01101010101=>10010101010
[2,1,4,3,6,5,10,9,7,8,12,11]=>10101011001=>10011010101=>01100101010
[2,1,4,3,6,5,12,11,10,7,8,9]=>10101011100=>00111010101=>11000101010
[2,1,4,3,8,7,5,6,10,9,12,11]=>10101100101=>10100110101=>01011001010
[2,1,4,3,10,7,5,9,6,8,12,11]=>10101101001=>10010110101=>01101001010
[2,1,4,3,10,9,8,5,6,7,12,11]=>10101110001=>10001110101=>01110001010
[2,1,4,3,12,9,8,5,6,11,7,10]=>10101110010=>01001110101=>10110001010
[2,1,4,3,12,11,8,5,10,6,7,9]=>10101110100=>00101110101=>11010001010
[2,1,4,3,12,11,10,9,5,6,7,8]=>10101111000=>00011110101=>11100001010
[2,1,6,5,3,4,8,7,10,9,12,11]=>10110010101=>10101001101=>01010110010
[2,1,8,5,3,7,4,6,10,9,12,11]=>10110100101=>10100101101=>01011010010
[2,1,12,5,3,11,8,4,10,6,7,9]=>10110110100=>00101101101=>11010010010
[2,1,8,7,6,3,4,5,10,9,12,11]=>10111000101=>10100011101=>01011100010
[2,1,8,7,6,3,4,5,12,11,9,10]=>10111000110=>01100011101=>10011100010
[2,1,10,7,6,3,4,9,5,8,12,11]=>10111001001=>10010011101=>01101100010
[2,1,12,11,6,3,10,9,4,5,7,8]=>10111011000=>00011011101=>11100100010
[2,1,10,9,8,7,3,4,5,6,12,11]=>10111100001=>10000111101=>01111000010
[2,1,12,9,8,7,3,4,5,11,6,10]=>10111100010=>01000111101=>10111000010
[2,1,12,11,10,7,3,9,4,5,6,8]=>10111101000=>00010111101=>11101000010
[4,3,1,2,6,5,8,7,10,9,12,11]=>11001010101=>10101010011=>01010101100
[4,3,1,2,6,5,10,9,7,8,12,11]=>11001011001=>10011010011=>01100101100
[4,3,1,2,8,7,5,6,10,9,12,11]=>11001100101=>10100110011=>01011001100
[4,3,1,2,8,7,5,6,12,11,9,10]=>11001100110=>01100110011=>10011001100
[4,3,1,2,12,7,5,11,10,6,8,9]=>11001101100=>00110110011=>11001001100
[4,3,1,2,12,9,8,5,6,11,7,10]=>11001110010=>01001110011=>10110001100
[6,3,1,5,2,4,8,7,10,9,12,11]=>11010010101=>10101001011=>01010110100
[12,3,1,5,2,7,4,9,6,11,8,10]=>11010101010=>01010101011=>10101010100
[12,3,1,5,2,11,8,4,10,6,7,9]=>11010110100=>00101101011=>11010010100
[10,3,1,7,6,2,4,9,5,8,12,11]=>11011001001=>10010011011=>01101100100
[10,3,1,9,6,2,8,4,5,7,12,11]=>11011010001=>10001011011=>01110100100
[12,3,1,9,6,2,8,4,5,11,7,10]=>11011010010=>01001011011=>10110100100
[12,3,1,11,6,2,10,9,4,5,7,8]=>11011011000=>00011011011=>11100100100
[6,5,4,1,2,3,8,7,10,9,12,11]=>11100010101=>10101000111=>01010111000
[6,5,4,1,2,3,10,9,7,8,12,11]=>11100011001=>10011000111=>01100111000
[6,5,4,1,2,3,12,11,10,7,8,9]=>11100011100=>00111000111=>11000111000
[8,5,4,1,2,7,3,6,10,9,12,11]=>11100100101=>10100100111=>01011011000
[12,5,4,1,2,9,8,3,6,11,7,10]=>11100110010=>01001100111=>10110011000
[12,5,4,1,2,11,10,9,3,6,7,8]=>11100111000=>00011100111=>11100011000
[12,11,4,1,6,2,10,9,3,5,7,8]=>11101011000=>00011010111=>11100101000
[10,9,4,1,8,7,2,3,5,6,12,11]=>11101100001=>10000110111=>01111001000
[12,9,4,1,8,7,2,3,5,11,6,10]=>11101100010=>01000110111=>10111001000
[12,11,4,1,10,7,2,9,3,5,6,8]=>11101101000=>00010110111=>11101001000
[8,7,6,5,1,2,3,4,10,9,12,11]=>11110000101=>10100001111=>01011110000
[8,7,6,5,1,2,3,4,12,11,9,10]=>11110000110=>01100001111=>10011110000
[10,7,6,5,1,2,3,9,4,8,12,11]=>11110001001=>10010001111=>01101110000
[10,9,6,5,1,2,8,3,4,7,12,11]=>11110010001=>10001001111=>01110110000
[12,9,6,5,1,2,8,3,4,11,7,10]=>11110010010=>01001001111=>10110110000
[12,11,6,5,1,2,8,3,10,4,7,9]=>11110010100=>00101001111=>11010110000
[12,11,6,5,1,2,10,9,3,4,7,8]=>11110011000=>00011001111=>11100110000
[10,9,8,5,1,7,2,3,4,6,12,11]=>11110100001=>10000101111=>01111010000
[12,9,8,5,1,7,2,3,4,11,6,10]=>11110100010=>01000101111=>10111010000
[12,11,8,5,1,7,2,3,10,4,6,9]=>11110100100=>00100101111=>11011010000
[12,11,10,5,1,7,2,9,3,4,6,8]=>11110101000=>00010101111=>11101010000
[12,11,10,5,1,9,8,2,3,4,6,7]=>11110110000=>00001101111=>11110010000
[10,9,8,7,6,1,2,3,4,5,12,11]=>11111000001=>10000011111=>01111100000
[12,11,10,9,8,7,1,2,3,4,5,6]=>11111100000=>00000111111=>11111000000
[1,8,2,7,4,3,5,6]=>0101100=>0011010=>1100101
[1,8,6,4,7,2,3,5]=>0110100=>0010110=>1101001
[1,8,4,2,6,3,5,7]=>0110100=>0010110=>1101001
[7,4,8,1,5,2,3,6]=>1010100=>0010101=>1101010
[4,1,7,2,6,3,5,8]=>1010100=>0010101=>1101010
[5,1,7,4,3,6,2,8]=>1011010=>0101101=>1010010
[1,8,5,4,3,7,2,6]=>0111010=>0101110=>1010001
[1,8,4,2,5,3,7,6]=>0110101=>1010110=>0101001
[1,8,5,4,2,6,7,3]=>0111001=>1001110=>0110001
[7,4,8,2,1,3,5,6]=>1011000=>0001101=>1110010
[4,1,7,3,2,5,6,8]=>1011000=>0001101=>1110010
[7,5,4,8,2,3,6,1]=>1101001=>1001011=>0110100
[7,3,8,1,5,6,2,4]=>1010010=>0100101=>1011010
[3,1,7,2,6,8,4,5]=>1010010=>0100101=>1011010
[5,1,7,4,2,6,8,3]=>1011001=>1001101=>0110010
[4,3,1,6,2,5,7,8]=>1101000=>0001011=>1110100
[6,5,4,3,7,1,8,2]=>1110101=>1010111=>0101000
[6,3,2,8,5,7,1,4]=>1101010=>0101011=>1010100
[5,4,8,2,1,7,3,6]=>1011010=>0101101=>1010010
[7,2,8,6,3,1,4,5]=>1011100=>0011101=>1100010
[2,1,7,8,3,6,4,5]=>1001010=>0101001=>1010110
[4,2,1,6,7,3,5,8]=>1100100=>0010011=>1101100
[4,3,1,5,2,7,6,8]=>1101010=>0101011=>1010100
[5,4,2,7,3,8,1,6]=>1101010=>0101011=>1010100
[3,1,6,2,8,7,4,5]=>1010110=>0110101=>1001010
[6,3,1,7,8,5,2,4]=>1100110=>0110011=>1001100
[6,5,4,1,7,8,3,2]=>1110011=>1100111=>0011000
[5,4,3,1,6,7,2,8]=>1110010=>0100111=>1011000
[5,4,2,6,3,8,7,1]=>1101011=>1101011=>0010100
[4,3,1,5,2,6,8,7]=>1101001=>1001011=>0110100
[5,4,2,1,6,7,8,3]=>1110001=>1000111=>0111000
[5,4,3,1,6,7,8,2]=>1110001=>1000111=>0111000
[7,8,2,4,5,1,3,6]=>0100100=>0010010=>1101101
[4,6,7,2,5,1,3,8]=>0010100=>0010100=>1101011
[7,8,1,3,2,4,5,6]=>0101000=>0001010=>1110101
[7,8,4,1,5,2,3,6]=>0110100=>0010110=>1101001
[3,6,7,2,1,4,5,8]=>0011000=>0001100=>1110011
[5,2,3,6,1,4,7,8]=>1001000=>0001001=>1110110
[2,5,3,6,1,4,7,8]=>0101000=>0001010=>1110101
[6,4,7,1,5,2,3,8]=>1010100=>0010101=>1101010
[6,2,7,3,1,4,5,8]=>1011000=>0001101=>1110010
[3,5,4,6,7,8,1,2]=>0100010=>0100010=>1011101
[1,5,4,6,7,2,3,8]=>0100100=>0010010=>1101101
[1,6,7,3,2,4,5,8]=>0011000=>0001100=>1110011
[1,5,3,6,2,4,7,8]=>0101000=>0001010=>1110101
[5,1,3,6,2,4,7,8]=>1001000=>0001001=>1110110
[5,2,4,6,7,1,3,8]=>1000100=>0010001=>1101110
[2,6,7,4,5,1,3,8]=>0010100=>0010100=>1101011
[4,2,5,6,7,1,3,8]=>1000100=>0010001=>1101110
[4,5,2,6,7,1,3,8]=>0100100=>0010010=>1101101
[5,3,1,6,2,4,7,8]=>1101000=>0001011=>1110100
[6,1,7,3,2,4,5,8]=>1011000=>0001101=>1110010
[6,1,7,4,5,2,3,8]=>1010100=>0010101=>1101010
[6,3,7,4,5,8,1,2]=>1010010=>0100101=>1011010
[5,4,1,6,7,2,3,8]=>1100100=>0010011=>1101100
[5,2,1,6,3,4,7,8]=>1101000=>0001011=>1110100
[1,3,6,7,5,2,8,4]=>0001101=>1011000=>0100111
[7,3,4,1,6,2,5,8]=>1010100=>0010101=>1101010
[7,3,4,1,6,5,2,8]=>1010110=>0110101=>1001010
[7,3,4,1,5,2,6,8]=>1010100=>0010101=>1101010
[1,3,6,7,2,5,8,4]=>0001001=>1001000=>0110111
[4,3,1,7,2,6,8,5]=>1101001=>1001011=>0110100
[5,6,1,4,7,3,8,2]=>0100101=>1010010=>0101101
[5,3,2,1,7,4,8,6]=>1110101=>1010111=>0101000
[1,3,4,5,8,7,2,6]=>0000110=>0110000=>1001111
[6,3,4,5,8,1,7,2]=>1000101=>1010001=>0101110
[2,4,5,1,6,8,7,3]=>0010011=>1100100=>0011011
[3,1,2,5,6,8,7,4]=>1000011=>1100001=>0011110
[4,3,2,5,6,8,1,7]=>1100010=>0100011=>1011100
[3,1,4,6,5,8,2,7]=>1001010=>0101001=>1010110
[2,3,4,5,8,6,1,7]=>0000110=>0110000=>1001111
[4,3,1,7,6,5,8,2]=>1101101=>1011011=>0100100
[1,4,5,2,6,8,7,3]=>0010011=>1100100=>0011011
[3,7,5,2,6,8,1,4]=>0110010=>0100110=>1011001
[3,7,5,2,6,8,4,1]=>0110011=>1100110=>0011001
[5,6,1,2,7,4,8,3]=>0100101=>1010010=>0101101
[6,3,5,2,4,7,8,1]=>1010001=>1000101=>0111010
[5,3,2,1,4,7,8,6]=>1110001=>1000111=>0111000
[5,3,1,4,2,7,8,6]=>1101001=>1001011=>0110100
[5,3,1,2,4,7,8,6]=>1100001=>1000011=>0111100
[7,1,5,2,6,8,4,3]=>1010011=>1100101=>0011010
[7,1,5,2,6,8,3,4]=>1010010=>0100101=>1011010
[1,7,4,6,5,8,3,2]=>0101011=>1101010=>0010101
[2,7,4,6,1,8,3,5]=>0101010=>0101010=>1010101
[2,7,4,6,1,8,5,3]=>0101011=>1101010=>0010101
[2,3,6,7,1,5,8,4]=>0001001=>1001000=>0110111
[2,3,6,7,5,1,8,4]=>0001101=>1011000=>0100111
[4,3,2,6,7,1,8,5]=>1100101=>1010011=>0101100
[7,3,2,5,6,8,1,4]=>1100010=>0100011=>1011100
[7,1,5,4,6,8,2,3]=>1010010=>0100101=>1011010
[2,7,4,6,5,8,1,3]=>0101010=>0101010=>1010101
[7,3,4,5,8,1,2,6]=>1000100=>0010001=>1101110
[1,3,4,5,8,6,2,7]=>0000110=>0110000=>1001111
[1,3,4,5,8,2,7,6]=>0000101=>1010000=>0101111
[7,1,5,4,6,8,3,2]=>1010011=>1100101=>0011010
[7,3,2,5,6,8,4,1]=>1100011=>1100011=>0011100
[5,7,4,6,1,8,3,2]=>0101011=>1101010=>0010101
[6,3,4,5,8,1,2,7]=>1000100=>0010001=>1101110
[7,3,4,5,8,2,6,1]=>1000101=>1010001=>0101110
[4,2,1,8,3,6,7,5]=>1101001=>1001011=>0110100
[6,2,1,7,3,5,8,4]=>1101001=>1001011=>0110100
[2,7,3,1,4,8,5,6]=>0110010=>0100110=>1011001
[3,2,1,5,7,8,4,6]=>1100010=>0100011=>1011100
[4,3,6,8,5,1,7,2]=>1001101=>1011001=>0100110
[2,1,6,8,3,7,4,5]=>1001010=>0101001=>1010110
[3,2,1,5,6,8,4,7]=>1100010=>0100011=>1011100
[2,4,7,1,8,5,3,6]=>0010110=>0110100=>1001011
[2,4,8,5,1,6,3,7]=>0011010=>0101100=>1010011
[6,2,1,7,3,4,8,5]=>1101001=>1001011=>0110100
[6,2,1,7,8,3,5,4]=>1100101=>1010011=>0101100
[3,2,1,6,7,4,5,8]=>1100100=>0010011=>1101100
[2,4,8,5,1,6,7,3]=>0011001=>1001100=>0110011
[3,2,1,8,4,5,6,7]=>1101000=>0001011=>1110100
[1,6,8,3,7,2,4,5]=>0010100=>0010100=>1101011
[3,8,1,5,7,2,4,6]=>0100100=>0010010=>1101101
[1,2,6,8,4,7,3,5]=>0001010=>0101000=>1010111
[6,1,5,8,2,4,7,3]=>1001001=>1001001=>0110110
[1,2,4,8,3,6,7,5]=>0001001=>1001000=>0110111
[4,1,2,7,8,3,6,5]=>1000101=>1010001=>0101110
[5,3,8,4,7,6,1,2]=>1010110=>0110101=>1001010
[8,7,1,2,5,4,6,3]=>1100101=>1010011=>0101100
[5,8,1,2,3,7,6,4]=>0100011=>1100010=>0011101
[1,2,8,4,3,5,7,6]=>0011001=>1001100=>0110011
[1,2,5,3,7,6,4,8]=>0010110=>0110100=>1001011
[6,1,2,8,7,4,5,3]=>1001101=>1011001=>0100110
[7,1,6,2,8,4,5,3]=>1010101=>1010101=>0101010
[1,2,6,3,8,5,4,7]=>0010110=>0110100=>1001011
[1,2,8,5,3,6,4,7]=>0011010=>0101100=>1010011
[1,2,7,3,8,5,4,6]=>0010110=>0110100=>1001011
[1,6,2,8,4,3,5,7]=>0101100=>0011010=>1100101
[1,6,4,2,7,3,5,8]=>0110100=>0010110=>1101001
[1,8,6,3,2,4,5,7]=>0111000=>0001110=>1110001
[3,1,7,8,6,2,4,5]=>1001100=>0011001=>1100110
[1,8,7,3,5,6,2,4]=>0110010=>0100110=>1011001
[1,3,2,8,7,4,5,6]=>0101100=>0011010=>1100101
[1,2,8,4,3,7,5,6]=>0011010=>0101100=>1010011
[8,5,1,7,2,4,6,3]=>1101001=>1001011=>0110100
[3,8,6,4,7,5,1,2]=>0110110=>0110110=>1001001
[6,1,8,2,7,4,5,3]=>1010101=>1010101=>0101010
[1,2,7,5,3,6,4,8]=>0011010=>0101100=>1010011
[1,2,6,3,7,5,4,8]=>0010110=>0110100=>1001011
[1,2,3,7,5,4,8,6]=>0001101=>1011000=>0100111
[3,7,4,8,6,5,1,2]=>0101110=>0111010=>1000101
[1,8,2,7,6,4,5,3]=>0101101=>1011010=>0100101
[7,4,6,3,8,5,1,2]=>1010110=>0110101=>1001010
[8,4,6,2,7,5,3,1]=>1010111=>1110101=>0001010
[6,5,7,8,4,1,3,2]=>1001101=>1011001=>0100110
[7,5,6,8,2,4,1,3]=>1001010=>0101001=>1010110
[7,4,6,2,8,5,1,3]=>1010110=>0110101=>1001010
[4,3,2,6,8,5,1,7]=>1100110=>0110011=>1001100
[3,5,6,8,2,4,1,7]=>0001010=>0101000=>1010111
[2,6,7,8,1,4,5,3]=>0001001=>1001000=>0110111
[3,6,7,8,1,4,2,5]=>0001010=>0101000=>1010111
[3,5,7,8,2,1,4,6]=>0001100=>0011000=>1100111
[2,6,7,8,1,4,3,5]=>0001010=>0101000=>1010111
[2,5,7,8,3,1,4,6]=>0001100=>0011000=>1100111
[2,4,7,3,8,1,5,6]=>0010100=>0010100=>1101011
[6,4,7,3,8,1,5,2]=>1010101=>1010101=>0101010
[6,4,7,3,8,1,2,5]=>1010100=>0010101=>1101010
[7,4,6,3,8,2,1,5]=>1010110=>0110101=>1001010
[6,3,2,5,4,8,1,7]=>1101010=>0101011=>1010100
[6,4,5,2,3,8,1,7]=>1010010=>0100101=>1011010
[5,4,6,3,8,2,1,7]=>1010110=>0110101=>1001010
[5,4,7,3,8,1,6,2]=>1010101=>1010101=>0101010
[2,5,7,8,3,1,6,4]=>0001101=>1011000=>0100111
[4,5,7,8,3,1,2,6]=>0001100=>0011000=>1100111
[4,5,6,8,2,3,1,7]=>0001010=>0101000=>1010111
[5,4,6,2,8,3,1,7]=>1010110=>0110101=>1001010
[5,3,2,6,8,4,1,7]=>1100110=>0110011=>1001100
[5,4,7,2,8,1,3,6]=>1010100=>0010101=>1101010
[4,5,7,8,2,1,3,6]=>0001100=>0011000=>1100111
[4,6,7,8,1,3,2,5]=>0001010=>0101000=>1010111
[4,6,7,8,1,3,5,2]=>0001001=>1001000=>0110111
[2,6,7,8,1,3,5,4]=>0001001=>1001000=>0110111
[2,6,7,8,1,5,3,4]=>0001010=>0101000=>1010111
[4,6,7,8,1,5,2,3]=>0001010=>0101000=>1010111
[4,6,7,8,1,2,5,3]=>0001001=>1001000=>0110111
[5,3,2,7,8,1,6,4]=>1100101=>1010011=>0101100
[4,3,2,7,8,1,6,5]=>1100101=>1010011=>0101100
[3,5,7,8,2,1,6,4]=>0001101=>1011000=>0100111
[3,6,7,8,1,5,4,2]=>0001011=>1101000=>0010111
[2,6,7,8,1,5,4,3]=>0001011=>1101000=>0010111
[4,5,8,3,6,7,1,2]=>0010010=>0100100=>1011011
[4,5,8,3,7,6,1,2]=>0010110=>0110100=>1001011
[4,2,8,3,7,1,6,5]=>1010101=>1010101=>0101010
[7,2,3,4,8,1,5,6]=>1000100=>0010001=>1101110
[7,6,3,4,8,5,1,2]=>1100110=>0110011=>1001100
[7,6,3,5,8,4,1,2]=>1100110=>0110011=>1001100
[7,6,3,8,4,5,1,2]=>1101010=>0101011=>1010100
[7,2,3,8,5,1,4,6]=>1001100=>0011001=>1100110
[2,6,4,8,1,5,7,3]=>0101001=>1001010=>0110101
[7,2,3,8,4,1,5,6]=>1001100=>0011001=>1100110
[7,8,2,3,6,1,4,5]=>0100100=>0010010=>1101101
[4,2,6,3,7,1,5,8]=>1010100=>0010101=>1101010
[7,2,3,5,8,1,6,4]=>1000101=>1010001=>0101110
[7,2,3,8,4,1,6,5]=>1001101=>1011001=>0100110
[2,6,4,8,1,3,7,5]=>0101001=>1001010=>0110101
[3,6,4,8,1,7,5,2]=>0101011=>1101010=>0010101
[7,6,5,1,2,3,8,4]=>1110001=>1000111=>0111000
[7,6,5,1,4,2,8,3]=>1110101=>1010111=>0101000
[7,8,5,4,1,2,6,3]=>0111001=>1001110=>0110001
[3,5,6,4,1,2,8,7]=>0011001=>1001100=>0110011
[7,6,5,1,2,4,3,8]=>1110010=>0100111=>1011000
[7,6,5,1,2,4,8,3]=>1110001=>1000111=>0111000
[7,6,5,1,3,2,4,8]=>1110100=>0010111=>1101000
[2,6,4,3,1,8,7,5]=>0111011=>1101110=>0010001
[3,5,8,4,1,2,7,6]=>0011001=>1001100=>0110011
[3,5,8,4,1,2,6,7]=>0011000=>0001100=>1110011
[3,5,8,4,1,6,2,7]=>0011010=>0101100=>1010011
[2,5,8,4,1,7,3,6]=>0011010=>0101100=>1010011
[3,6,4,2,1,7,5,8]=>0111010=>0101110=>1010001
[3,5,6,4,1,8,7,2]=>0011011=>1101100=>0010011
[2,6,4,5,1,3,7,8]=>0101000=>0001010=>1110101
[7,6,5,1,4,3,8,2]=>1110101=>1010111=>0101000
[7,6,5,1,2,8,3,4]=>1110010=>0100111=>1011000
[7,6,5,1,8,2,4,3]=>1110101=>1010111=>0101000
[7,6,5,1,8,2,3,4]=>1110100=>0010111=>1101000
[7,6,5,1,8,3,2,4]=>1110110=>0110111=>1001000
[7,6,5,1,4,8,2,3]=>1110010=>0100111=>1011000
[3,6,4,5,1,7,2,8]=>0101010=>0101010=>1010101
[2,5,6,4,1,7,8,3]=>0011001=>1001100=>0110011
[2,5,6,4,1,7,3,8]=>0011010=>0101100=>1010011
[3,6,4,5,1,7,8,2]=>0101001=>1001010=>0110101
[7,6,5,1,4,8,3,2]=>1110011=>1100111=>0011000
[7,6,5,1,8,3,4,2]=>1110101=>1010111=>0101000
[7,6,5,1,8,4,2,3]=>1110110=>0110111=>1001000
[6,7,4,2,5,3,1,8]=>0110110=>0110110=>1001001
[7,6,4,8,3,1,5,2]=>1101101=>1011011=>0100100
[7,4,8,5,6,1,3,2]=>1010101=>1010101=>0101010
[7,4,2,5,6,3,1,8]=>1100110=>0110011=>1001100
[4,2,7,5,6,3,1,8]=>1010110=>0110101=>1001010
[4,7,3,5,6,2,1,8]=>0100110=>0110010=>1001101
[1,6,8,5,2,7,4,3]=>0011011=>1101100=>0010011
[6,2,8,5,1,7,4,3]=>1011011=>1101101=>0010010
[6,7,4,8,2,1,5,3]=>0101101=>1011010=>0100101
[3,2,7,8,6,1,5,4]=>1001101=>1011001=>0100110
[6,8,4,1,2,3,7,5]=>0110001=>1000110=>0111001
[1,8,2,5,6,4,3,7]=>0100110=>0110010=>1001101
[6,1,8,5,3,7,4,2]=>1011011=>1101101=>0010010
[3,8,1,5,2,7,6,4]=>0101011=>1101010=>0010101
[8,2,1,5,3,7,6,4]=>1101011=>1101011=>0010100
[8,1,6,5,3,7,2,4]=>1011010=>0101101=>1010010
[7,1,4,6,3,2,8,5]=>1001101=>1011001=>0100110
[3,2,6,4,1,7,8,5]=>1011001=>1001101=>0110010
[7,6,4,3,1,2,8,5]=>1111001=>1001111=>0110000
[8,6,3,5,1,7,2,4]=>1101010=>0101011=>1010100
[4,5,3,1,6,7,8,2]=>0110001=>1000110=>0111001
[3,5,2,1,6,7,8,4]=>0110001=>1000110=>0111001
[5,2,3,1,6,7,8,4]=>1010001=>1000101=>0111010
[1,5,3,2,6,7,8,4]=>0110001=>1000110=>0111001
[8,2,7,5,6,1,3,4]=>1010100=>0010101=>1101010
[1,7,4,6,2,3,8,5]=>0101001=>1001010=>0110101
[7,6,4,2,1,5,8,3]=>1111001=>1001111=>0110000
[5,7,4,6,1,3,8,2]=>0101001=>1001010=>0110101
[8,6,4,7,3,1,2,5]=>1101100=>0011011=>1100100
[5,2,4,3,7,1,8,6]=>1010101=>1010101=>0101010
[8,6,4,1,3,5,2,7]=>1110010=>0100111=>1011000
[6,7,4,1,5,3,8,2]=>0110101=>1010110=>0101001
[7,5,4,1,2,6,8,3]=>1110001=>1000111=>0111000
[1,8,2,5,3,7,6,4]=>0101011=>1101010=>0010101
[3,8,1,5,6,4,2,7]=>0100110=>0110010=>1001101
[7,6,4,1,5,2,8,3]=>1110101=>1010111=>0101000
[8,6,1,5,4,7,2,3]=>1101010=>0101011=>1010100
[5,2,1,4,6,7,8,3]=>1100001=>1000011=>0111100
[5,4,1,3,6,7,8,2]=>1100001=>1000011=>0111100
[8,4,1,5,3,7,2,6]=>1101010=>0101011=>1010100
[7,5,4,1,3,2,8,6]=>1110101=>1010111=>0101000
[3,2,5,1,4,7,8,6]=>1010001=>1000101=>0111010
[5,1,3,4,6,7,8,2]=>1000001=>1000001=>0111110
[3,8,1,7,5,6,4,2]=>0101011=>1101010=>0010101
[8,2,5,7,3,6,4,1]=>1001011=>1101001=>0010110
[1,8,6,7,5,3,4,2]=>0101101=>1011010=>0100101
[8,2,6,7,5,3,4,1]=>1001101=>1011001=>0100110
[5,4,8,6,2,3,7,1]=>1011001=>1001101=>0110010
[2,7,6,1,3,5,4,8]=>0110010=>0100110=>1011001
[2,8,6,1,3,5,4,7]=>0110010=>0100110=>1011001
[5,7,4,1,8,6,3,2]=>0110111=>1110110=>0001001
[5,6,4,2,8,3,7,1]=>0110101=>1010110=>0101001
[5,6,4,2,7,3,1,8]=>0110110=>0110110=>1001001
[5,8,1,4,6,3,7,2]=>0100101=>1010010=>0101101
[3,6,7,4,5,8,2,1]=>0010011=>1100100=>0011011
[5,4,6,1,7,8,3,2]=>1010011=>1100101=>0011010
[5,6,4,1,8,7,3,2]=>0110111=>1110110=>0001001
[3,5,8,4,6,7,2,1]=>0010011=>1100100=>0011011
[3,6,8,4,5,7,2,1]=>0010011=>1100100=>0011011
[3,7,8,4,5,6,2,1]=>0010011=>1100100=>0011011
[3,7,1,5,4,6,2,8]=>0101010=>0101010=>1010101
[3,8,1,5,4,6,7,2]=>0101001=>1001010=>0110101
[3,7,1,5,4,6,8,2]=>0101001=>1001010=>0110101
[6,7,1,4,5,3,8,2]=>0100101=>1010010=>0101101
[5,7,1,4,6,3,8,2]=>0100101=>1010010=>0101101
[5,4,7,2,8,3,1,6]=>1010110=>0110101=>1001010
[5,4,7,2,8,3,6,1]=>1010101=>1010101=>0101010
[5,6,4,2,8,3,1,7]=>0110110=>0110110=>1001001
[5,8,1,4,6,3,2,7]=>0100110=>0110010=>1001101
[3,8,1,5,4,6,2,7]=>0101010=>0101010=>1010101
[3,6,1,5,4,2,7,8]=>0101100=>0011010=>1100101
[3,6,1,5,4,8,2,7]=>0101010=>0101010=>1010101
[6,8,3,1,4,2,5,7]=>0110100=>0010110=>1101001
[7,3,8,1,4,2,5,6]=>1010100=>0010101=>1101010
[3,6,1,5,4,7,8,2]=>0101001=>1001010=>0110101
[3,4,1,2,7,6,5,8]=>0100110=>0110010=>1001101
[3,4,1,2,6,8,7,5]=>0100011=>1100010=>0011101
[7,8,1,4,5,3,2,6]=>0100110=>0110010=>1001101
[3,8,1,5,4,7,2,6]=>0101010=>0101010=>1010101
[3,6,1,5,4,8,7,2]=>0101011=>1101010=>0010101
[3,6,1,5,4,7,2,8]=>0101010=>0101010=>1010101
[6,7,3,1,4,2,5,8]=>0110100=>0010110=>1101001
[6,8,3,1,4,2,7,5]=>0110101=>1010110=>0101001
[7,8,3,1,4,6,2,5]=>0110010=>0100110=>1011001
[7,8,4,2,6,5,1,3]=>0110110=>0110110=>1001001
[6,5,8,7,3,4,2,1]=>1011011=>1101101=>0010010
[7,8,3,1,4,6,5,2]=>0110011=>1100110=>0011001
[6,7,3,1,4,5,2,8]=>0110010=>0100110=>1011001
[3,7,1,5,4,2,6,8]=>0101100=>0011010=>1100101
[3,8,1,5,4,2,7,6]=>0101101=>1011010=>0100101
[5,8,1,4,7,3,6,2]=>0100101=>1010010=>0101101
[6,3,7,1,4,8,5,2]=>1010011=>1100101=>0011010
[3,7,1,5,4,8,6,2]=>0101011=>1101010=>0010101
[3,7,1,5,4,2,8,6]=>0101101=>1011010=>0100101
[6,7,3,1,4,5,8,2]=>0110001=>1000110=>0111001
[7,3,8,1,4,5,2,6]=>1010010=>0100101=>1011010
[6,8,3,1,4,5,2,7]=>0110010=>0100110=>1011001
[3,8,1,5,4,2,6,7]=>0101100=>0011010=>1100101
[2,3,5,4,1,8,6,7]=>0011010=>0101100=>1010011
[2,3,6,4,8,1,5,7]=>0010100=>0010100=>1101011
[1,8,4,6,3,5,2,7]=>0101010=>0101010=>1010101
[5,4,8,6,2,1,3,7]=>1011100=>0011101=>1100010
[2,3,6,8,1,5,4,7]=>0001010=>0101000=>1010111
[2,5,6,1,4,7,8,3]=>0010001=>1000100=>0111011
[2,5,6,1,4,7,3,8]=>0010010=>0100100=>1011011
[2,7,6,1,8,5,4,3]=>0110111=>1110110=>0001001
[2,7,6,8,1,4,5,3]=>0101001=>1001010=>0110101
[5,7,8,6,2,3,4,1]=>0011001=>1001100=>0110011
[2,7,6,1,8,5,3,4]=>0110110=>0110110=>1001001
[6,3,5,1,7,2,4,8]=>1010100=>0010101=>1101010
[2,3,4,7,6,1,5,8]=>0001100=>0011000=>1100111
[7,3,5,8,4,1,2,6]=>1001100=>0011001=>1100110
[1,8,4,5,2,7,3,6]=>0101010=>0101010=>1010101
[1,8,4,5,2,7,6,3]=>0101011=>1101010=>0010101
[7,3,5,8,4,1,6,2]=>1001101=>1011001=>0100110
[2,7,6,4,8,5,1,3]=>0110110=>0110110=>1001001
[7,3,5,4,6,8,1,2]=>1010010=>0100101=>1011010
[6,3,5,4,7,1,8,2]=>1010101=>1010101=>0101010
[6,3,5,4,7,1,2,8]=>1010100=>0010101=>1101010
[3,7,1,6,8,5,2,4]=>0100110=>0110010=>1001101
[2,3,1,8,6,4,7,5]=>0101101=>1011010=>0100101
[1,8,4,3,6,2,5,7]=>0110100=>0010110=>1101001
[2,3,1,8,6,4,5,7]=>0101100=>0011010=>1100101
[3,7,1,6,8,5,4,2]=>0100111=>1110010=>0001101
[6,3,5,4,7,2,1,8]=>1010110=>0110101=>1001010
[7,3,5,4,6,8,2,1]=>1010011=>1100101=>0011010
[2,7,6,4,8,5,3,1]=>0110111=>1110110=>0001001
[1,8,4,5,2,6,3,7]=>0101010=>0101010=>1010101
[6,4,8,5,3,1,2,7]=>1011100=>0011101=>1100010
[7,3,5,8,4,6,2,1]=>1001011=>1101001=>0010110
[2,3,4,6,5,8,1,7]=>0001010=>0101000=>1010111
[2,3,4,7,5,1,8,6]=>0001101=>1011000=>0100111
[2,3,4,7,5,1,6,8]=>0001100=>0011000=>1100111
[2,3,4,7,1,6,5,8]=>0001010=>0101000=>1010111
[2,3,4,7,1,6,8,5]=>0001001=>1001000=>0110111
[2,3,4,6,1,8,7,5]=>0001011=>1101000=>0010111
[6,3,5,8,4,2,7,1]=>1001101=>1011001=>0100110
[1,8,4,5,2,3,6,7]=>0101000=>0001010=>1110101
[7,4,8,5,3,2,6,1]=>1011101=>1011101=>0100010
[3,4,8,7,5,2,6,1]=>0011101=>1011100=>0100011
[3,2,8,6,1,5,4,7]=>1011010=>0101101=>1010010
[8,7,3,6,4,2,5,1]=>1101101=>1011011=>0100100
[3,8,7,2,5,4,6,1]=>0110101=>1010110=>0101001
[8,7,2,4,5,6,3,1]=>1100011=>1100011=>0011100
[5,3,6,2,4,8,7,1]=>1010011=>1100101=>0011010
[3,5,2,8,6,1,4,7]=>0101100=>0011010=>1100101
[3,7,2,5,1,4,8,6]=>0101001=>1001010=>0110101
[5,1,8,6,2,3,4,7]=>1011000=>0001101=>1110010
[2,5,4,1,8,6,3,7]=>0110110=>0110110=>1001001
[3,7,6,1,8,2,5,4]=>0110101=>1010110=>0101001
[8,2,3,6,1,4,7,5]=>1001001=>1001001=>0110110
[1,8,2,6,3,4,7,5]=>0101001=>1001010=>0110101
[7,1,3,6,4,8,2,5]=>1001010=>0101001=>1010110
[8,2,1,3,5,7,4,6]=>1100010=>0100011=>1011100
[7,5,4,1,3,8,2,6]=>1110010=>0100111=>1011000
[7,3,8,5,4,1,2,6]=>1011100=>0011101=>1100010
[7,2,3,6,1,4,8,5]=>1001001=>1001001=>0110110
[1,3,7,2,5,8,4,6]=>0010010=>0100100=>1011011
[1,7,2,3,5,8,4,6]=>0100010=>0100010=>1011101
[7,4,8,1,3,6,2,5]=>1010010=>0100101=>1011010
[8,6,1,4,7,3,2,5]=>1100110=>0110011=>1001100
[2,6,3,7,1,4,8,5]=>0101001=>1001010=>0110101
[2,6,3,8,1,4,7,5]=>0101001=>1001010=>0110101
[7,5,4,8,1,3,2,6]=>1101010=>0101011=>1010100
[8,5,4,7,1,3,2,6]=>1101010=>0101011=>1010100
[2,3,1,8,5,4,6,7]=>0101100=>0011010=>1100101
[8,5,1,7,6,3,4,2]=>1101101=>1011011=>0100100
[3,4,7,6,1,8,5,2]=>0011011=>1101100=>0010011
[3,5,2,6,7,1,8,4]=>0100101=>1010010=>0101101
[3,2,8,4,7,5,1,6]=>1010110=>0110101=>1001010
[8,4,7,5,1,3,2,6]=>1011010=>0101101=>1010010
[6,8,3,1,7,2,4,5]=>0110100=>0010110=>1101001
[3,7,2,5,6,1,8,4]=>0100101=>1010010=>0101101
[6,8,4,2,5,1,7,3]=>0110101=>1010110=>0101001
[2,7,5,3,8,4,1,6]=>0110110=>0110110=>1001001
[8,3,1,4,7,2,6,5]=>1100101=>1010011=>0101100
[8,3,2,1,5,7,4,6]=>1110010=>0100111=>1011000
[2,8,3,6,4,7,1,5]=>0101010=>0101010=>1010101
[7,3,6,4,8,1,2,5]=>1010100=>0010101=>1101010
[8,3,6,4,7,1,2,5]=>1010100=>0010101=>1101010
[1,2,8,3,5,7,4,6]=>0010010=>0100100=>1011011
[1,8,3,2,5,7,4,6]=>0110010=>0100110=>1011001
[6,5,1,7,4,2,8,3]=>1101101=>1011011=>0100100
[7,3,6,4,8,2,1,5]=>1010110=>0110101=>1001010
[4,6,1,7,3,5,2,8]=>0101010=>0101010=>1010101
[5,6,1,7,3,4,2,8]=>0101010=>0101010=>1010101
[6,1,7,3,4,2,8,5]=>1010101=>1010101=>0101010
[7,3,8,1,6,5,2,4]=>1010110=>0110101=>1001010
[8,3,7,1,6,5,2,4]=>1010110=>0110101=>1001010
[2,8,1,7,6,5,3,4]=>0101110=>0111010=>1000101
[4,2,8,6,5,1,7,3]=>1011101=>1011101=>0100010
[8,6,4,7,1,5,2,3]=>1101010=>0101011=>1010100
[7,6,4,8,1,5,2,3]=>1101010=>0101011=>1010100
[5,1,6,4,2,3,8,7]=>1011001=>1001101=>0110010
[4,2,3,8,7,5,1,6]=>1001110=>0111001=>1000110
[3,8,7,1,6,5,2,4]=>0110110=>0110110=>1001001
[2,4,3,8,1,6,7,5]=>0101001=>1001010=>0110101
[2,4,3,7,1,6,8,5]=>0101001=>1001010=>0110101
[4,2,3,7,8,5,1,6]=>1000110=>0110001=>1001110
[5,1,6,4,2,3,7,8]=>1011000=>0001101=>1110010
[6,4,7,8,1,5,2,3]=>1001010=>0101001=>1010110
[8,7,4,6,1,5,2,3]=>1101010=>0101011=>1010100
[6,5,7,8,1,4,2,3]=>1001010=>0101001=>1010110
[4,7,8,6,1,5,2,3]=>0011010=>0101100=>1010011
[3,2,4,8,7,1,5,6]=>1001100=>0011001=>1100110
[4,8,7,6,1,5,2,3]=>0111010=>0101110=>1010001
[5,8,7,6,1,4,2,3]=>0111010=>0101110=>1010001
[8,6,5,7,1,4,2,3]=>1101010=>0101011=>1010100
[5,1,6,7,4,2,3,8]=>1001100=>0011001=>1100110
[6,7,4,8,1,5,2,3]=>0101010=>0101010=>1010101
[8,4,7,6,1,5,2,3]=>1011010=>0101101=>1010010
[8,3,2,4,7,1,5,6]=>1100100=>0010011=>1101100
[7,3,2,4,8,1,5,6]=>1100100=>0010011=>1101100
[2,5,3,7,1,6,4,8]=>0101010=>0101010=>1010101
[8,4,6,7,1,5,2,3]=>1001010=>0101001=>1010110
[5,1,6,8,4,2,3,7]=>1001100=>0011001=>1100110
[4,2,3,7,5,1,6,8]=>1001100=>0011001=>1100110
[2,4,3,7,1,6,5,8]=>0101010=>0101010=>1010101
[2,4,7,1,5,8,6,3]=>0010011=>1100100=>0011011
[3,2,4,7,6,1,5,8]=>1001100=>0011001=>1100110
[4,7,6,8,1,5,2,3]=>0101010=>0101010=>1010101
[8,5,6,7,1,4,2,3]=>1001010=>0101001=>1010110
[8,6,7,5,1,4,2,3]=>1011010=>0101101=>1010010
[6,8,7,5,1,4,2,3]=>0111010=>0101110=>1010001
[5,6,8,7,1,4,2,3]=>0011010=>0101100=>1010011
[4,6,8,7,1,5,2,3]=>0011010=>0101100=>1010011
[3,2,4,6,1,5,7,8]=>1001000=>0001001=>1110110
[6,7,8,5,1,4,2,3]=>0011010=>0101100=>1010011
[7,8,6,5,1,4,2,3]=>0111010=>0101110=>1010001
[2,1,8,5,4,6,3,7]=>1011010=>0101101=>1010010
[4,1,8,5,2,3,6,7]=>1011000=>0001101=>1110010
[5,4,1,3,6,7,2,8]=>1100010=>0100011=>1011100
[8,4,1,2,6,3,7,5]=>1100101=>1010011=>0101100
[8,2,7,1,5,3,4,6]=>1010100=>0010101=>1101010
[3,2,7,1,5,8,4,6]=>1010010=>0100101=>1011010
[7,3,8,1,5,4,2,6]=>1010110=>0110101=>1001010
[7,1,5,3,8,4,2,6]=>1010110=>0110101=>1001010
[3,6,8,1,5,4,2,7]=>0010110=>0110100=>1001011
[6,8,3,1,5,4,2,7]=>0110110=>0110110=>1001001
[7,6,3,1,5,4,2,8]=>1110110=>0110111=>1001000
[3,6,2,1,5,8,4,7]=>0110010=>0100110=>1011001
[8,6,2,1,5,3,4,7]=>1110100=>0010111=>1101000
[2,3,8,1,5,7,4,6]=>0010010=>0100100=>1011011
[7,1,3,2,8,6,4,5]=>1010110=>0110101=>1001010
[4,7,1,2,6,3,8,5]=>0100101=>1010010=>0101101
[2,7,8,1,5,3,4,6]=>0010100=>0010100=>1101011
[6,7,2,1,5,3,4,8]=>0110100=>0010110=>1101001
[4,7,2,1,8,5,3,6]=>0110110=>0110110=>1001001
[8,7,2,1,4,5,3,6]=>1110010=>0100111=>1011000
[5,7,8,6,1,4,3,2]=>0011011=>1101100=>0010011
[2,7,4,1,6,5,3,8]=>0110110=>0110110=>1001001
[7,1,6,4,5,8,3,2]=>1010011=>1100101=>0011010
[2,6,4,1,7,5,3,8]=>0110110=>0110110=>1001001
[5,6,8,7,1,4,3,2]=>0011011=>1101100=>0010011
[4,2,8,1,6,5,3,7]=>1010110=>0110101=>1001010
[6,2,4,1,8,5,3,7]=>1010110=>0110101=>1001010
[8,3,1,4,5,6,7,2]=>1100001=>1000011=>0111100
[5,3,1,4,8,6,7,2]=>1100101=>1010011=>0101100
[7,5,1,6,3,4,8,2]=>1101001=>1001011=>0110100
[7,1,5,8,4,3,6,2]=>1001101=>1011001=>0100110
[5,8,1,6,4,3,7,2]=>0101101=>1011010=>0100101
[5,3,1,8,4,6,7,2]=>1101001=>1001011=>0110100
[8,3,1,5,4,6,7,2]=>1101001=>1001011=>0110100
[8,2,6,1,4,5,3,7]=>1010010=>0100101=>1011010
[6,2,8,1,4,5,3,7]=>1010010=>0100101=>1011010
[7,2,6,1,5,3,4,8]=>1010100=>0010101=>1101010
[2,8,6,1,5,3,4,7]=>0110100=>0010110=>1101001
[4,2,1,5,6,3,8,7]=>1100101=>1010011=>0101100
[7,1,2,5,8,3,4,6]=>1000100=>0010001=>1101110
[7,1,4,5,6,8,3,2]=>1000011=>1100001=>0011110
[2,6,7,1,4,5,3,8]=>0010010=>0100100=>1011011
[3,5,1,7,4,6,8,2]=>0101001=>1001010=>0110101
[7,1,5,6,4,8,3,2]=>1001011=>1101001=>0010110
[7,1,6,5,4,8,3,2]=>1011011=>1101101=>0010010
[2,7,6,1,4,5,3,8]=>0110010=>0100110=>1011001
[5,7,6,8,1,4,3,2]=>0101011=>1101010=>0010101
[7,8,6,5,1,4,3,2]=>0111011=>1101110=>0010001
[5,3,1,2,4,8,7,6]=>1100011=>1100011=>0011100
[5,3,6,2,1,8,7,4]=>1011011=>1101101=>0010010
[5,3,7,2,8,4,1,6]=>1010110=>0110101=>1001010
[7,2,4,5,8,3,1,6]=>1000110=>0110001=>1001110
[7,2,4,5,1,3,6,8]=>1001000=>0001001=>1110110
[6,2,4,5,1,8,7,3]=>1001011=>1101001=>0010110
[3,1,4,5,2,8,7,6]=>1001011=>1101001=>0010110
[1,6,4,5,2,8,7,3]=>0101011=>1101010=>0010101
[3,7,4,5,1,2,6,8]=>0101000=>0001010=>1110101
[1,7,4,2,6,3,5,8]=>0110100=>0010110=>1101001
[8,7,4,5,2,1,6,3]=>1101101=>1011011=>0100100
[6,3,7,1,8,4,2,5]=>1010110=>0110101=>1001010
[5,7,4,1,6,3,2,8]=>0110110=>0110110=>1001001
[1,7,4,8,6,3,2,5]=>0101110=>0111010=>1000101
[5,7,4,8,6,3,1,2]=>0101110=>0111010=>1000101
[4,8,3,5,6,7,1,2]=>0100010=>0100010=>1011101
[1,8,3,5,6,7,2,4]=>0100010=>0100010=>1011101
[4,8,1,5,6,7,2,3]=>0100010=>0100010=>1011101
[4,1,3,5,6,7,2,8]=>1000010=>0100001=>1011110
[5,8,4,3,6,1,2,7]=>0110100=>0010110=>1101001
[5,3,8,4,1,7,2,6]=>1011010=>0101101=>1010010
[1,5,8,4,6,7,3,2]=>0010011=>1100100=>0011011
[1,4,8,3,6,7,5,2]=>0010011=>1100100=>0011011
[4,3,8,2,1,7,5,6]=>1011010=>0101101=>1010010
[3,8,4,2,6,1,5,7]=>0110100=>0010110=>1101001
[3,8,1,5,6,7,4,2]=>0100011=>1100010=>0011101
[3,8,2,5,6,7,1,4]=>0100010=>0100010=>1011101
[8,2,1,5,6,7,4,3]=>1100011=>1100011=>0011100
[8,1,3,5,6,7,4,2]=>1000011=>1100001=>0011110
[7,1,4,3,6,2,5,8]=>1010100=>0010101=>1101010
[7,8,4,3,6,2,1,5]=>0110110=>0110110=>1001001
[4,3,1,8,5,7,6,2]=>1101011=>1101011=>0010100
[6,3,5,8,2,7,1,4]=>1001010=>0101001=>1010110
[7,5,4,8,6,2,1,3]=>1101110=>0111011=>1000100
[7,1,4,8,6,2,3,5]=>1001100=>0011001=>1100110
[7,5,4,1,6,2,3,8]=>1110100=>0010111=>1101000
[1,6,4,5,8,2,3,7]=>0100100=>0010010=>1101101
[1,8,5,3,6,7,4,2]=>0110011=>1100110=>0011001
[8,3,5,2,1,7,4,6]=>1011010=>0101101=>1010010
[4,1,8,5,6,7,3,2]=>1010011=>1100101=>0011010
[1,2,8,5,6,7,3,4]=>0010010=>0100100=>1011011
[4,2,1,5,6,7,3,8]=>1100010=>0100011=>1011100
[1,5,3,8,6,7,4,2]=>0101011=>1101010=>0010101
[1,4,8,5,6,7,2,3]=>0010010=>0100100=>1011011
[6,2,4,3,8,7,5,1]=>1010111=>1110101=>0001010
[7,3,5,4,1,8,6,2]=>1011011=>1101101=>0010010
[5,2,7,1,3,4,8,6]=>1010001=>1000101=>0111010
[2,6,5,7,3,1,4,8]=>0101100=>0011010=>1100101
[2,6,5,7,3,1,8,4]=>0101101=>1011010=>0100101
[6,3,1,4,7,8,5,2]=>1100011=>1100011=>0011100
[6,8,2,1,3,4,5,7]=>0110000=>0000110=>1111001
[3,7,1,8,4,5,2,6]=>0101010=>0101010=>1010101
[6,3,2,4,7,5,8,1]=>1100101=>1010011=>0101100
[6,3,2,4,7,5,1,8]=>1100110=>0110011=>1001100
[4,2,1,6,3,7,5,8]=>1101010=>0101011=>1010100
[4,2,1,6,3,7,8,5]=>1101001=>1001011=>0110100
[7,4,3,5,8,6,1,2]=>1100110=>0110011=>1001100
[2,7,6,8,3,1,4,5]=>0101100=>0011010=>1100101
[7,4,3,5,8,6,2,1]=>1100111=>1110011=>0001100
[4,2,1,7,3,8,6,5]=>1101011=>1101011=>0010100
[4,2,1,3,7,8,6,5]=>1100011=>1100011=>0011100
[5,8,1,7,4,3,6,2]=>0101101=>1011010=>0100101
[5,8,1,7,4,3,2,6]=>0101110=>0111010=>1000101
[3,7,8,6,2,1,4,5]=>0011100=>0011100=>1100011
[4,2,1,8,3,5,6,7]=>1101000=>0001011=>1110100
[4,2,1,3,6,7,5,8]=>1100010=>0100011=>1011100
[4,2,1,3,7,5,6,8]=>1100100=>0010011=>1101100
[7,3,2,4,8,6,5,1]=>1100111=>1110011=>0001100
[4,2,1,7,3,5,6,8]=>1101000=>0001011=>1110100
[3,6,7,5,2,1,4,8]=>0011100=>0011100=>1100011
[3,6,7,5,2,1,8,4]=>0011101=>1011100=>0100011
[7,3,4,2,6,8,5,1]=>1010011=>1100101=>0011010
[4,8,6,2,7,3,5,1]=>0110101=>1010110=>0101001
[7,3,4,2,6,8,1,5]=>1010010=>0100101=>1011010
[3,6,7,5,2,4,8,1]=>0011001=>1001100=>0110011
[3,6,7,5,2,4,1,8]=>0011010=>0101100=>1010011
[4,2,1,7,3,6,8,5]=>1101001=>1001011=>0110100
[3,7,6,8,4,2,5,1]=>0101101=>1011010=>0100101
[5,8,1,7,4,2,6,3]=>0101101=>1011010=>0100101
[3,7,8,6,2,4,5,1]=>0011001=>1001100=>0110011
[4,2,1,3,8,6,7,5]=>1100101=>1010011=>0101100
[4,2,1,3,5,7,6,8]=>1100010=>0100011=>1011100
[4,8,1,7,3,6,5,2]=>0101011=>1101010=>0010101
[4,2,1,8,3,7,6,5]=>1101011=>1101011=>0010100
[4,2,1,3,5,6,8,7]=>1100001=>1000011=>0111100
[7,8,2,4,1,3,6,5]=>0101001=>1001010=>0110101
[2,6,1,5,4,7,8,3]=>0101001=>1001010=>0110101
[4,6,3,5,8,7,1,2]=>0100110=>0110010=>1001101
[2,3,6,8,4,1,5,7]=>0001100=>0011000=>1100111
[2,7,5,1,8,3,4,6]=>0110100=>0010110=>1101001
[4,7,5,2,1,3,6,8]=>0111000=>0001110=>1110001
[3,5,6,2,4,1,7,8]=>0010100=>0010100=>1101011
[3,1,8,5,2,7,6,4]=>1011011=>1101101=>0010010
[8,3,7,6,1,4,5,2]=>1011001=>1001101=>0110010
[3,1,7,8,2,5,6,4]=>1001001=>1001001=>0110110
[4,8,1,5,2,7,3,6]=>0101010=>0101010=>1010101
[4,1,2,5,3,8,7,6]=>1001011=>1101001=>0010110
[4,3,6,8,7,5,1,2]=>1001110=>0111001=>1000110
[6,4,8,1,2,5,3,7]=>1010010=>0100101=>1011010
[6,7,3,1,4,8,5,2]=>0110011=>1100110=>0011001
[6,5,1,2,3,4,8,7]=>1100001=>1000011=>0111100
[1,2,6,7,5,3,8,4]=>0001101=>1011000=>0100111
[1,7,5,3,2,8,4,6]=>0111010=>0101110=>1010001
[1,6,5,7,2,3,8,4]=>0101001=>1001010=>0110101
[1,3,8,2,6,5,7,4]=>0010101=>1010100=>0101011
[1,2,5,7,6,3,4,8]=>0001100=>0011000=>1100111
[1,3,4,8,2,5,7,6]=>0001001=>1001000=>0110111
[1,5,7,6,2,3,4,8]=>0011000=>0001100=>1110011
[1,5,3,8,2,6,4,7]=>0101010=>0101010=>1010101
[1,4,8,3,2,5,7,6]=>0011001=>1001100=>0110011
[1,2,4,8,3,5,7,6]=>0001001=>1001000=>0110111
[1,3,8,4,2,6,7,5]=>0011001=>1001100=>0110011
[1,4,8,2,3,5,7,6]=>0010001=>1000100=>0111011
[4,2,6,7,5,8,3,1]=>1001011=>1101001=>0010110
[6,7,5,2,1,8,4,3]=>0111011=>1101110=>0010001
[3,4,8,7,5,2,1,6]=>0011110=>0111100=>1000011
[1,7,5,2,8,4,6,3]=>0110101=>1010110=>0101001
[5,6,8,3,1,7,2,4]=>0011010=>0101100=>1010011
[6,1,4,8,3,2,7,5]=>1001101=>1011001=>0100110
[3,4,7,1,8,6,2,5]=>0010110=>0110100=>1001011
[3,4,6,8,2,1,5,7]=>0001100=>0011000=>1100111
[3,8,2,5,6,1,4,7]=>0100100=>0010010=>1101101
[3,5,2,8,6,4,1,7]=>0101110=>0111010=>1000101
[4,2,5,7,3,8,6,1]=>1001011=>1101001=>0010110
[7,4,2,5,3,8,1,6]=>1101010=>0101011=>1010100
[1,5,6,8,3,4,2,7]=>0001010=>0101000=>1010111
[4,5,1,6,8,3,2,7]=>0100110=>0110010=>1001101
[4,5,7,3,8,2,6,1]=>0010101=>1010100=>0101011
[6,4,3,7,8,2,5,1]=>1100101=>1010011=>0101100
[6,4,3,1,7,8,2,5]=>1110010=>0100111=>1011000
[4,5,3,1,7,8,2,6]=>0110010=>0100110=>1011001
[7,1,3,5,4,8,2,6]=>1001010=>0101001=>1010110
[7,5,2,8,1,4,3,6]=>1101010=>0101011=>1010100
[1,4,5,7,3,8,6,2]=>0001011=>1101000=>0010111
[4,6,3,7,8,5,2,1]=>0100111=>1110010=>0001101
[1,5,3,6,7,8,4,2]=>0100011=>1100010=>0011101
[4,6,1,7,3,8,5,2]=>0101011=>1101010=>0010101
[6,7,2,4,8,1,5,3]=>0100101=>1010010=>0101101
[5,2,3,6,7,8,4,1]=>1000011=>1100001=>0011110
[6,4,2,7,1,8,3,5]=>1101010=>0101011=>1010100
[4,2,6,3,7,8,5,1]=>1010011=>1100101=>0011010
[6,7,3,8,2,4,5,1]=>0101001=>1001010=>0110101
[3,6,2,7,4,1,8,5]=>0101101=>1011010=>0100101
[6,7,3,2,1,4,8,5]=>0111001=>1001110=>0110001
[7,2,4,8,6,1,3,5]=>1001100=>0011001=>1100110
[3,5,7,2,1,8,6,4]=>0011011=>1101100=>0010011
[6,7,8,3,2,5,1,4]=>0011010=>0101100=>1010011
[6,3,7,8,2,5,4,1]=>1001011=>1101001=>0010110
[2,6,7,4,8,5,3,1]=>0010111=>1110100=>0001011
[6,2,4,7,1,8,5,3]=>1001011=>1101001=>0010110
[1,7,4,8,5,2,6,3]=>0101101=>1011010=>0100101
[1,3,7,8,5,2,6,4]=>0001101=>1011000=>0100111
[2,5,7,8,1,6,3,4]=>0001010=>0101000=>1010111
[1,6,4,7,8,2,5,3]=>0100101=>1010010=>0101101
[2,5,6,1,7,8,4,3]=>0010011=>1100100=>0011011
[5,6,1,2,7,8,4,3]=>0100011=>1100010=>0011101
[6,7,2,1,8,5,3,4]=>0110110=>0110110=>1001001
[6,4,5,2,3,8,7,1]=>1010011=>1100101=>0011010
[4,6,5,2,3,1,8,7]=>0110101=>1010110=>0101001
[6,4,2,5,3,1,8,7]=>1101101=>1011011=>0100100
[6,4,2,5,3,8,7,1]=>1101011=>1101011=>0010100
[8,6,4,7,5,2,3,1]=>1101101=>1011011=>0100100
[8,6,2,7,4,5,3,1]=>1101011=>1101011=>0010100
[6,4,2,5,8,7,3,1]=>1100111=>1110011=>0001100
[4,6,5,2,3,8,7,1]=>0110011=>1100110=>0011001
[6,8,2,7,4,5,3,1]=>0101011=>1101010=>0010101
[8,6,4,7,2,5,3,1]=>1101011=>1101011=>0010100
[8,6,2,4,7,5,3,1]=>1100111=>1110011=>0001100
[6,8,2,4,7,5,3,1]=>0100111=>1110010=>0001101
[4,8,2,6,7,5,3,1]=>0100111=>1110010=>0001101
[2,8,4,6,7,5,3,1]=>0100111=>1110010=>0001101
[2,8,6,7,4,5,3,1]=>0101011=>1101010=>0010101
[6,8,7,2,4,5,3,1]=>0110011=>1100110=>0011001
[2,6,4,5,8,7,3,1]=>0100111=>1110010=>0001101
[2,6,4,8,7,5,3,1]=>0101111=>1111010=>0000101
[4,6,2,8,7,5,3,1]=>0101111=>1111010=>0000101
[8,2,4,6,7,5,3,1]=>1000111=>1110001=>0001110
[6,2,4,8,7,5,3,1]=>1001111=>1111001=>0000110
[4,2,6,8,7,5,3,1]=>1001111=>1111001=>0000110
[4,2,6,5,8,7,3,1]=>1010111=>1110101=>0001010
[6,2,4,5,8,7,3,1]=>1000111=>1110001=>0001110
[8,2,6,7,4,5,3,1]=>1001011=>1101001=>0010110
[8,6,7,2,4,5,3,1]=>1010011=>1100101=>0011010
[6,4,5,8,7,2,3,1]=>1001101=>1011001=>0100110
[8,6,7,4,2,5,3,1]=>1011011=>1101101=>0010010
[8,4,6,7,2,5,3,1]=>1001011=>1101001=>0010110
[6,4,8,7,2,5,3,1]=>1011011=>1101101=>0010010
[6,2,8,7,4,5,3,1]=>1011011=>1101101=>0010010
[4,6,5,8,7,2,3,1]=>0101101=>1011010=>0100101
[2,1,6,8,7,4,5,3]=>1001101=>1011001=>0100110
[2,6,8,7,4,5,3,1]=>0011011=>1101100=>0010011
[2,4,8,6,7,5,3,1]=>0010111=>1110100=>0001011
[6,2,8,4,7,5,3,1]=>1010111=>1110101=>0001010
[8,2,6,4,7,5,3,1]=>1010111=>1110101=>0001010
[4,6,8,2,7,5,3,1]=>0010111=>1110100=>0001011
[2,6,8,4,7,5,3,1]=>0010111=>1110100=>0001011
[4,6,8,7,2,5,3,1]=>0011011=>1101100=>0010011
[4,6,5,8,2,7,3,1]=>0101011=>1101010=>0010101
[2,1,6,8,4,7,5,3]=>1001011=>1101001=>0010110
[2,1,8,6,4,7,5,3]=>1011011=>1101101=>0010010
[6,8,7,4,2,5,3,1]=>0111011=>1101110=>0010001
[2,8,6,4,7,5,3,1]=>0110111=>1110110=>0001001
[4,8,6,2,7,5,3,1]=>0110111=>1110110=>0001001
[3,7,8,5,6,1,2,4]=>0010100=>0010100=>1101011
[3,6,1,8,4,7,2,5]=>0101010=>0101010=>1010101
[3,1,6,8,4,7,2,5]=>1001010=>0101001=>1010110
[4,1,6,8,3,2,7,5]=>1001101=>1011001=>0100110
[4,6,1,8,3,2,7,5]=>0101101=>1011010=>0100101
[4,7,8,1,3,2,6,5]=>0010101=>1010100=>0101011
[4,7,8,3,1,2,6,5]=>0011001=>1001100=>0110011
[2,7,8,3,4,6,5,1]=>0010011=>1100100=>0011011
[4,7,8,2,1,3,6,5]=>0011001=>1001100=>0110011
[4,6,1,8,2,3,7,5]=>0101001=>1001010=>0110101
[4,5,2,1,8,3,7,6]=>0110101=>1010110=>0101001
[4,6,2,8,1,3,7,5]=>0101001=>1001010=>0110101
[3,6,2,8,4,7,1,5]=>0101010=>0101010=>1010101
[2,3,6,8,4,7,5,1]=>0001011=>1101000=>0010111
[3,2,6,8,4,7,1,5]=>1001010=>0101001=>1010110
[4,2,6,8,3,1,7,5]=>1001101=>1011001=>0100110
[4,2,5,1,8,3,7,6]=>1010101=>1010101=>0101010
[5,1,2,4,3,8,7,6]=>1001011=>1101001=>0010110
[5,2,4,1,3,8,7,6]=>1010011=>1100101=>0011010
[4,2,5,3,8,1,7,6]=>1010101=>1010101=>0101010
[3,2,5,4,8,7,1,6]=>1010110=>0110101=>1001010
[3,5,2,4,8,7,1,6]=>0100110=>0110010=>1001101
[5,1,4,2,3,8,7,6]=>1010011=>1100101=>0011010
[5,4,3,1,2,8,7,6]=>1110011=>1100111=>0011000
[4,5,3,1,8,2,7,6]=>0110101=>1010110=>0101001
[4,5,1,3,8,2,7,6]=>0100101=>1010010=>0101101
[3,1,5,4,8,7,2,6]=>1010110=>0110101=>1001010
[3,5,4,1,8,7,2,6]=>0110110=>0110110=>1001001
[3,6,5,8,7,1,2,4]=>0101100=>0011010=>1100101
[3,4,1,5,8,7,2,6]=>0100110=>0110010=>1001101
[4,1,3,5,8,2,7,6]=>1000101=>1010001=>0101110
[4,3,6,8,2,1,7,5]=>1001101=>1011001=>0100110
[2,4,6,8,3,7,5,1]=>0001011=>1101000=>0010111
[3,4,5,2,8,7,1,6]=>0010110=>0110100=>1001011
[5,3,1,4,2,8,7,6]=>1101011=>1101011=>0010100
[5,1,3,4,2,8,7,6]=>1001011=>1101001=>0010110
[5,1,3,2,4,8,7,6]=>1010011=>1100101=>0011010
[5,3,2,1,4,8,7,6]=>1110011=>1100111=>0011000
[4,3,2,5,8,1,7,6]=>1100101=>1010011=>0101100
[3,4,2,5,8,7,1,6]=>0100110=>0110010=>1001101
[3,2,4,5,8,7,1,6]=>1000110=>0110001=>1001110
[4,2,3,5,8,1,7,6]=>1000101=>1010001=>0101110
[5,2,3,1,4,8,7,6]=>1010011=>1100101=>0011010
[5,2,1,3,4,8,7,6]=>1100011=>1100011=>0011100
[1,7,2,3,5,6,8,4]=>0100001=>1000010=>0111101
[3,7,4,2,1,5,6,8]=>0111000=>0001110=>1110001
[3,4,6,2,8,5,7,1]=>0010101=>1010100=>0101011
[4,2,1,7,5,8,3,6]=>1101010=>0101011=>1010100
[4,7,2,6,5,1,3,8]=>0101100=>0011010=>1100101
[3,7,4,1,2,5,8,6]=>0110001=>1000110=>0111001
[4,7,1,6,5,2,8,3]=>0101101=>1011010=>0100101
[4,7,3,6,5,1,8,2]=>0101101=>1011010=>0100101
[4,3,7,1,6,8,5,2]=>1010011=>1100101=>0011010
[4,2,1,7,5,6,8,3]=>1101001=>1001011=>0110100
[4,2,6,8,7,3,1,5]=>1001110=>0111001=>1000110
[3,4,6,1,8,5,2,7]=>0010110=>0110100=>1001011
[4,1,6,7,5,8,2,3]=>1001010=>0101001=>1010110
[4,3,6,7,5,1,2,8]=>1001100=>0011001=>1100110
[4,3,7,1,6,8,2,5]=>1010010=>0100101=>1011010
[4,3,7,5,6,8,2,1]=>1010011=>1100101=>0011010
[4,1,7,3,6,5,2,8]=>1010110=>0110101=>1001010
[2,8,7,4,5,3,1,6]=>0110110=>0110110=>1001001
[2,8,7,4,3,5,1,6]=>0111010=>0101110=>1010001
[4,1,7,3,6,2,5,8]=>1010100=>0010101=>1101010
[5,8,7,6,1,2,4,3]=>0111001=>1001110=>0110001
[4,1,7,2,6,8,5,3]=>1010011=>1100101=>0011010
[4,2,7,3,6,1,8,5]=>1010101=>1010101=>0101010
[4,2,7,3,6,5,8,1]=>1010101=>1010101=>0101010
[3,8,5,6,2,4,1,7]=>0101010=>0101010=>1010101
[2,8,6,5,3,7,1,4]=>0111010=>0101110=>1010001
[3,8,6,5,1,4,7,2]=>0111001=>1001110=>0110001
[3,8,2,1,4,6,7,5]=>0110001=>1000110=>0111001
[3,8,2,5,4,6,7,1]=>0101001=>1001010=>0110101
[4,2,6,7,5,3,1,8]=>1001110=>0111001=>1000110
[3,2,6,1,4,5,8,7]=>1010001=>1000101=>0111010
[2,8,7,3,4,5,1,6]=>0110010=>0100110=>1011001
[5,8,7,6,1,3,4,2]=>0111001=>1001110=>0110001
[5,8,7,6,2,3,4,1]=>0111001=>1001110=>0110001
[4,1,7,5,6,2,3,8]=>1010100=>0010101=>1101010
[3,8,1,5,2,6,4,7]=>0101010=>0101010=>1010101
[2,8,7,5,3,4,1,6]=>0111010=>0101110=>1010001
[2,8,7,5,4,3,1,6]=>0111110=>0111110=>1000001
[4,1,7,5,6,3,2,8]=>1010110=>0110101=>1001010
[5,8,7,6,1,3,2,4]=>0111010=>0101110=>1010001
[5,8,7,6,4,1,2,3]=>0111100=>0011110=>1100001
[8,1,7,2,4,5,3,6]=>1010010=>0100101=>1011010
[8,1,3,6,2,5,4,7]=>1001010=>0101001=>1010110
[7,2,1,6,3,5,4,8]=>1101010=>0101011=>1010100
[2,7,1,6,3,5,4,8]=>0101010=>0101010=>1010101
[2,7,1,5,4,3,6,8]=>0101100=>0011010=>1100101
[7,2,1,5,4,3,6,8]=>1101100=>0011011=>1100100
[8,1,3,5,4,2,6,7]=>1001100=>0011001=>1100110
[8,1,5,3,4,2,6,7]=>1010100=>0010101=>1101010
[8,1,5,6,2,3,7,4]=>1001001=>1001001=>0110110
[8,1,4,5,3,2,6,7]=>1001100=>0011001=>1100110
[8,1,4,3,5,2,6,7]=>1010100=>0010101=>1101010
[7,2,1,4,5,3,6,8]=>1100100=>0010011=>1101100
[2,7,1,4,5,3,6,8]=>0100100=>0010010=>1101101
[2,6,3,1,5,4,7,8]=>0110100=>0010110=>1101001
[6,3,2,1,5,4,7,8]=>1110100=>0010111=>1101000
[7,3,1,4,5,2,6,8]=>1100100=>0010011=>1101100
[7,3,1,5,4,2,6,8]=>1101100=>0011011=>1100100
[7,3,1,6,2,5,4,8]=>1101010=>0101011=>1010100
[3,7,1,6,2,5,4,8]=>0101010=>0101010=>1010101
[3,7,1,4,5,2,6,8]=>0100100=>0010010=>1101101
[2,3,6,1,5,4,7,8]=>0010100=>0010100=>1101011
[6,3,4,1,5,2,7,8]=>1010100=>0010101=>1101010
[6,2,4,1,5,3,7,8]=>1010100=>0010101=>1101010
[2,6,4,1,5,3,7,8]=>0110100=>0010110=>1101001
[2,6,5,1,3,7,4,8]=>0110010=>0100110=>1011001
[6,5,2,1,3,7,4,8]=>1110010=>0100111=>1011000
[7,6,1,2,4,5,3,8]=>1100010=>0100011=>1011100
[6,7,1,2,8,3,5,4]=>0100101=>1010010=>0101101
[6,7,1,2,5,4,3,8]=>0100110=>0110010=>1001101
[5,6,2,1,3,7,4,8]=>0110010=>0100110=>1011001
[5,2,6,1,3,7,4,8]=>1010010=>0100101=>1011010
[2,4,6,1,5,3,7,8]=>0010100=>0010100=>1101011
[4,7,1,3,5,2,6,8]=>0100100=>0010010=>1101101
[4,7,1,5,3,2,6,8]=>0101100=>0011010=>1100101
[5,7,1,6,2,3,8,4]=>0101001=>1001010=>0110101
[5,6,3,1,2,7,4,8]=>0110010=>0100110=>1011001
[4,2,5,3,1,6,7,8]=>1011000=>0001101=>1110010
[8,5,6,2,7,1,4,3]=>1010101=>1010101=>0101010
[6,5,1,2,7,8,4,3]=>1100011=>1100011=>0011100
[4,7,6,1,5,3,8,2]=>0110101=>1010110=>0101001
[5,7,6,4,1,3,8,2]=>0111001=>1001110=>0110001
[7,6,2,4,5,3,8,1]=>1100101=>1010011=>0101100
[6,1,7,5,3,8,4,2]=>1011011=>1101101=>0010010
[8,6,7,5,3,1,4,2]=>1011101=>1011101=>0100010
[8,5,2,7,1,6,4,3]=>1101011=>1101011=>0010100
[5,6,2,4,7,8,1,3]=>0100010=>0100010=>1011101
[3,4,8,6,7,1,5,2]=>0010101=>1010100=>0101011
[4,8,5,6,7,2,3,1]=>0100101=>1010010=>0101101
[5,8,6,4,1,2,7,3]=>0111001=>1001110=>0110001
[5,8,7,3,2,6,4,1]=>0111011=>1101110=>0010001
[5,8,1,7,2,6,4,3]=>0101011=>1101010=>0010101
[8,1,5,7,2,6,4,3]=>1001011=>1101001=>0010110
[8,1,7,2,5,6,3,4]=>1010010=>0100101=>1011010
[6,8,7,2,5,1,3,4]=>0110100=>0010110=>1101001
[5,8,7,2,1,6,3,4]=>0111010=>0101110=>1010001
[4,8,1,5,2,6,7,3]=>0101001=>1001010=>0110101
[3,7,8,5,1,6,2,4]=>0011010=>0101100=>1010011
[6,5,2,7,8,1,4,3]=>1100101=>1010011=>0101100
[7,1,2,8,5,6,3,4]=>1001010=>0101001=>1010110
[8,7,2,1,5,6,3,4]=>1110010=>0100111=>1011000
[8,6,7,1,5,2,3,4]=>1010100=>0010101=>1101010
[6,1,7,8,5,2,3,4]=>1001100=>0011001=>1100110
[7,5,6,2,1,8,4,3]=>1011011=>1101101=>0010010
[8,7,5,2,1,6,4,3]=>1111011=>1101111=>0010000
[7,1,3,5,8,6,2,4]=>1000110=>0110001=>1001110
[5,1,3,4,6,8,7,2]=>1000011=>1100001=>0011110
[8,4,3,1,2,6,7,5]=>1110001=>1000111=>0111000
[8,5,1,6,3,4,7,2]=>1101001=>1001011=>0110100
[5,1,8,6,3,4,7,2]=>1011001=>1001101=>0110010
[4,6,8,1,5,3,7,2]=>0010101=>1010100=>0101011
[6,4,5,8,3,2,7,1]=>1001101=>1011001=>0100110
[3,6,4,8,7,1,5,2]=>0101101=>1011010=>0100101
[6,5,8,1,3,4,7,2]=>1010001=>1000101=>0111010
[6,1,8,3,5,2,7,4]=>1010101=>1010101=>0101010
[7,6,8,3,5,2,1,4]=>1010110=>0110101=>1001010
[8,6,1,3,5,2,7,4]=>1100101=>1010011=>0101100
[8,7,1,3,5,6,2,4]=>1100010=>0100011=>1011100
[5,8,2,4,3,6,7,1]=>0101001=>1001010=>0110101
[5,8,2,3,1,6,7,4]=>0101001=>1001010=>0110101
[6,8,2,3,5,1,7,4]=>0100101=>1010010=>0101101
[7,8,2,3,5,6,1,4]=>0100010=>0100010=>1011101
[8,6,5,1,4,3,7,2]=>1110101=>1010111=>0101000
[2,4,8,6,1,3,7,5]=>0011001=>1001100=>0110011
[6,7,1,8,4,3,5,2]=>0101101=>1011010=>0100101
[2,7,8,6,1,4,3,5]=>0011010=>0101100=>1010011
[2,7,3,8,1,6,4,5]=>0101010=>0101010=>1010101
[7,5,1,8,2,4,6,3]=>1101001=>1001011=>0110100
[2,7,8,4,1,6,3,5]=>0011010=>0101100=>1010011
[2,6,5,4,1,3,8,7]=>0111001=>1001110=>0110001
[4,1,7,6,3,8,2,5]=>1011010=>0101101=>1010010
[4,8,2,5,7,6,3,1]=>0100111=>1110010=>0001101
[3,4,6,5,1,8,2,7]=>0011010=>0101100=>1010011
[4,6,1,5,2,3,8,7]=>0101001=>1001010=>0110101
[2,6,7,5,1,8,4,3]=>0011011=>1101100=>0010011
[7,6,5,2,8,3,4,1]=>1110101=>1010111=>0101000
[2,4,7,6,5,8,1,3]=>0011010=>0101100=>1010011
[2,1,4,8,7,6,3,5]=>1001110=>0111001=>1000110
[8,1,3,5,7,4,6,2]=>1000101=>1010001=>0101110
[3,2,8,7,5,1,6,4]=>1011101=>1011101=>0100010
[4,8,5,1,6,7,2,3]=>0110010=>0100110=>1011001
[7,8,6,1,3,5,2,4]=>0110010=>0100110=>1011001
[2,5,1,8,6,7,4,3]=>0101011=>1101010=>0010101
[3,5,1,8,6,7,4,2]=>0101011=>1101010=>0010101
[8,3,5,4,6,7,1,2]=>1010010=>0100101=>1011010
[5,1,3,8,6,7,4,2]=>1001011=>1101001=>0010110
[5,6,3,2,8,1,4,7]=>0110100=>0010110=>1101001
[8,1,6,3,5,2,7,4]=>1010101=>1010101=>0101010
[4,7,6,8,3,2,5,1]=>0101101=>1011010=>0100101
[2,7,5,8,1,3,4,6]=>0101000=>0001010=>1110101
[8,1,3,7,5,2,6,4]=>1001101=>1011001=>0100110
[3,4,8,7,5,1,6,2]=>0011101=>1011100=>0100011
[6,3,8,1,4,2,5,7]=>1010100=>0010101=>1101010
[3,6,8,2,4,1,7,5]=>0010101=>1010100=>0101011
[4,5,8,2,6,7,3,1]=>0010011=>1100100=>0011011
[2,5,8,4,6,7,3,1]=>0010011=>1100100=>0011011
[8,4,3,2,6,7,1,5]=>1110010=>0100111=>1011000
[4,2,8,1,6,7,3,5]=>1010010=>0100101=>1011010
[2,4,8,1,6,7,3,5]=>0010010=>0100100=>1011011
[5,1,8,2,6,7,3,4]=>1010010=>0100101=>1011010
[3,4,8,7,2,1,5,6]=>0011100=>0011100=>1100011
[5,8,4,1,6,7,2,3]=>0110010=>0100110=>1011001
[3,8,1,4,6,7,2,5]=>0100010=>0100010=>1011101
[1,6,4,5,2,3,7,8]=>0101000=>0001010=>1110101
[1,7,4,5,2,3,6,8]=>0101000=>0001010=>1110101
[1,6,3,5,2,4,7,8]=>0101000=>0001010=>1110101
[1,6,3,4,2,5,7,8]=>0101000=>0001010=>1110101
[1,7,3,4,2,5,6,8]=>0101000=>0001010=>1110101
[1,8,5,7,3,4,2,6]=>0101010=>0101010=>1010101
[1,7,3,4,2,6,5,8]=>0101010=>0101010=>1010101
[1,5,2,8,4,7,3,6]=>0101010=>0101010=>1010101
[1,4,2,8,5,7,3,6]=>0101010=>0101010=>1010101
[1,7,3,5,2,6,4,8]=>0101010=>0101010=>1010101
[1,8,4,7,3,5,2,6]=>0101010=>0101010=>1010101
[1,7,3,6,2,5,4,8]=>0101010=>0101010=>1010101
[1,7,3,6,2,4,5,8]=>0101000=>0001010=>1110101
[1,7,4,6,2,3,5,8]=>0101000=>0001010=>1110101
[1,8,5,6,2,3,4,7]=>0101000=>0001010=>1110101
[1,8,5,6,2,4,3,7]=>0101010=>0101010=>1010101
[1,3,2,8,5,6,4,7]=>0101010=>0101010=>1010101
[1,4,2,8,5,6,3,7]=>0101010=>0101010=>1010101
[1,5,2,8,4,6,3,7]=>0101010=>0101010=>1010101
[1,6,2,8,4,5,3,7]=>0101010=>0101010=>1010101
[8,6,4,7,2,1,3,5]=>1101100=>0011011=>1100100
[3,8,6,2,4,5,1,7]=>0110010=>0100110=>1011001
[1,7,6,4,8,2,3,5]=>0110100=>0010110=>1101001
[5,8,7,4,1,2,3,6]=>0111000=>0001110=>1110001
[6,8,3,7,2,1,4,5]=>0101100=>0011010=>1100101
[6,1,3,7,4,8,2,5]=>1001010=>0101001=>1010110
[7,1,6,4,8,2,3,5]=>1010100=>0010101=>1101010
[3,8,7,5,1,2,4,6]=>0111000=>0001110=>1110001
[3,7,6,1,2,4,5,8]=>0110000=>0000110=>1111001
[4,7,6,1,2,3,5,8]=>0110000=>0000110=>1111001
[8,5,7,4,1,2,3,6]=>1011000=>0001101=>1110010
[8,6,2,3,1,7,4,5]=>1101010=>0101011=>1010100
[1,7,2,8,6,3,4,5]=>0101100=>0011010=>1100101
[7,5,8,1,3,6,2,4]=>1010010=>0100101=>1011010
[5,4,1,8,2,3,6,7]=>1101000=>0001011=>1110100
[1,4,8,7,2,3,5,6]=>0011000=>0001100=>1110011
[1,5,8,7,2,3,4,6]=>0011000=>0001100=>1110011
[5,7,1,3,8,2,4,6]=>0100100=>0010010=>1101101
[7,1,5,8,6,2,3,4]=>1001100=>0011001=>1100110
[5,1,8,7,2,3,4,6]=>1011000=>0001101=>1110010
[7,1,5,8,3,4,2,6]=>1001010=>0101001=>1010110
[7,1,4,3,2,5,6,8]=>1011000=>0001101=>1110010
[6,4,2,3,8,5,7,1]=>1100101=>1010011=>0101100
[6,4,2,7,5,8,3,1]=>1101011=>1101011=>0010100
[7,1,4,6,5,2,3,8]=>1001100=>0011001=>1100110
[7,1,4,6,5,8,2,3]=>1001010=>0101001=>1010110
[7,1,4,6,3,8,2,5]=>1001010=>0101001=>1010110
[7,1,4,3,2,5,8,6]=>1011001=>1001101=>0110010
[7,1,4,6,5,2,8,3]=>1001101=>1011001=>0100110
[7,1,4,6,5,3,8,2]=>1001101=>1011001=>0100110
[7,1,4,6,5,3,2,8]=>1001110=>0111001=>1000110
[6,4,2,7,5,3,8,1]=>1101101=>1011011=>0100100
[3,4,7,2,6,8,5,1]=>0010011=>1100100=>0011011
[3,4,7,1,6,8,2,5]=>0010010=>0100100=>1011011
[3,4,7,1,6,8,5,2]=>0010011=>1100100=>0011011
[2,4,1,7,5,3,6,8]=>0101100=>0011010=>1100101
[3,4,1,7,8,6,2,5]=>0100110=>0110010=>1001101
[6,4,2,3,8,5,1,7]=>1100110=>0110011=>1001100
[6,4,2,7,5,3,1,8]=>1101110=>0111011=>1000100
[3,4,7,2,6,8,1,5]=>0010010=>0100100=>1011011
[5,4,7,3,6,8,2,1]=>1010011=>1100101=>0011010
[3,4,7,2,6,5,1,8]=>0010110=>0110100=>1001011
[4,8,7,3,5,1,2,6]=>0110100=>0010110=>1101001
[4,8,7,1,3,5,2,6]=>0110010=>0100110=>1011001
[4,8,3,1,2,6,5,7]=>0110010=>0100110=>1011001
[3,4,7,1,6,2,5,8]=>0010100=>0010100=>1101011
[3,4,7,1,6,2,8,5]=>0010101=>1010100=>0101011
[3,4,7,2,6,5,8,1]=>0010101=>1010100=>0101011
[4,8,3,1,2,6,7,5]=>0110001=>1000110=>0111001
[5,8,1,6,3,4,2,7]=>0101010=>0101010=>1010101
[6,8,5,1,3,7,2,4]=>0110010=>0100110=>1011001
[6,8,5,1,3,4,7,2]=>0110001=>1000110=>0111001
[5,8,3,4,2,6,7,1]=>0101001=>1001010=>0110101
[6,4,3,7,5,1,2,8]=>1101100=>0011011=>1100100
[3,8,7,4,1,5,2,6]=>0111010=>0101110=>1010001
[2,4,7,3,6,1,5,8]=>0010100=>0010100=>1101011
[5,8,3,2,1,6,4,7]=>0111010=>0101110=>1010001
[5,8,7,4,3,1,2,6]=>0111100=>0011110=>1100001
[5,3,6,2,4,7,8,1]=>1010001=>1000101=>0111010
[5,3,6,1,4,8,7,2]=>1010011=>1100101=>0011010
[5,3,7,2,4,6,8,1]=>1010001=>1000101=>0111010
[4,2,1,5,8,6,3,7]=>1100110=>0110011=>1001100
[4,2,1,5,8,6,7,3]=>1100101=>1010011=>0101100
[4,3,1,5,7,8,6,2]=>1100011=>1100011=>0011100
[4,3,1,7,5,8,6,2]=>1101011=>1101011=>0010100
[6,7,3,1,4,8,2,5]=>0110010=>0100110=>1011001
[5,3,7,1,4,8,2,6]=>1010010=>0100101=>1011010
[4,3,1,5,7,8,2,6]=>1100010=>0100011=>1011100
[3,2,1,8,5,4,6,7]=>1101100=>0011011=>1100100
[3,2,1,8,5,7,4,6]=>1101010=>0101011=>1010100
[6,7,2,1,8,4,5,3]=>0110101=>1010110=>0101001
[3,2,1,8,5,6,4,7]=>1101010=>0101011=>1010100
[4,3,1,6,7,8,5,2]=>1100011=>1100011=>0011100
[4,2,1,6,8,5,7,3]=>1100101=>1010011=>0101100
[4,2,1,6,8,5,3,7]=>1100110=>0110011=>1001100
[5,2,6,1,8,4,3,7]=>1010110=>0110101=>1001010
[5,2,6,1,8,7,3,4]=>1010110=>0110101=>1001010
[5,2,6,1,8,3,4,7]=>1010100=>0010101=>1101010
[4,2,1,6,8,3,7,5]=>1100101=>1010011=>0101100
[4,3,1,6,7,8,2,5]=>1100010=>0100011=>1011100
[4,2,1,7,8,6,3,5]=>1100110=>0110011=>1001100
[3,2,1,8,6,4,7,5]=>1101101=>1011011=>0100100
[3,2,1,8,6,4,5,7]=>1101100=>0011011=>1100100
[3,2,1,8,4,6,5,7]=>1101010=>0101011=>1010100
[3,2,1,8,4,6,7,5]=>1101001=>1001011=>0110100
[4,2,1,7,8,3,6,5]=>1100101=>1010011=>0101100
[5,2,7,1,8,3,6,4]=>1010101=>1010101=>0101010
[6,7,2,1,8,3,5,4]=>0110101=>1010110=>0101001
[5,2,7,1,8,3,4,6]=>1010100=>0010101=>1101010
[4,2,1,7,8,3,5,6]=>1100100=>0010011=>1101100
[3,2,1,8,4,5,7,6]=>1101001=>1001011=>0110100
[7,4,8,6,2,5,3,1]=>1011011=>1101101=>0010010
[7,3,8,6,2,4,5,1]=>1011001=>1001101=>0110010
[7,4,3,1,8,2,5,6]=>1110100=>0010111=>1101000
[7,4,2,8,5,6,1,3]=>1101010=>0101011=>1010100
[7,3,8,5,2,4,6,1]=>1011001=>1001101=>0110010
[6,3,8,2,4,5,1,7]=>1010010=>0100101=>1011010
[6,3,8,2,5,7,4,1]=>1010011=>1100101=>0011010
[5,6,7,3,8,2,4,1]=>0010101=>1010100=>0101011
[5,3,8,2,4,6,7,1]=>1010001=>1000101=>0111010
[6,3,8,2,4,7,5,1]=>1010011=>1100101=>0011010
[5,7,4,2,6,8,1,3]=>0110010=>0100110=>1011001
[6,5,3,1,4,2,7,8]=>1110100=>0010111=>1101000
[5,7,4,2,6,1,3,8]=>0110100=>0010110=>1101001
[5,6,4,2,3,8,1,7]=>0110010=>0100110=>1011001
[5,6,3,7,8,2,4,1]=>0100101=>1010010=>0101101
[5,6,3,8,2,4,7,1]=>0101001=>1001010=>0110101
[6,3,7,2,4,5,1,8]=>1010010=>0100101=>1011010
[6,3,7,2,5,8,4,1]=>1010011=>1100101=>0011010
[5,3,6,8,2,4,7,1]=>1001001=>1001001=>0110110
[5,4,6,2,3,8,1,7]=>1010010=>0100101=>1011010
[5,3,6,7,8,2,4,1]=>1000101=>1010001=>0101110
[3,6,4,2,1,5,8,7]=>0111001=>1001110=>0110001
[3,5,8,6,4,2,1,7]=>0011110=>0111100=>1000011
[5,8,6,3,4,2,1,7]=>0110110=>0110110=>1001001
[5,6,3,4,2,1,8,7]=>0101101=>1011010=>0100101
[6,3,4,2,1,5,8,7]=>1011001=>1001101=>0110010
[5,6,4,2,1,3,8,7]=>0111001=>1001110=>0110001
[2,7,8,5,4,1,6,3]=>0011101=>1011100=>0100011
[2,8,5,4,1,6,3,7]=>0111010=>0101110=>1010001
[2,6,3,8,5,4,1,7]=>0101110=>0111010=>1000101
[2,8,6,3,5,4,1,7]=>0110110=>0110110=>1001001
[5,8,6,4,2,1,3,7]=>0111100=>0011110=>1100001
[4,2,1,5,7,8,6,3]=>1100011=>1100011=>0011100
[2,7,8,6,3,5,4,1]=>0011011=>1101100=>0010011
[4,3,8,5,7,6,2,1]=>1010111=>1110101=>0001010
[2,1,8,5,6,4,3,7]=>1010110=>0110101=>1001010
[4,2,1,8,5,6,3,7]=>1101010=>0101011=>1010100
[6,3,4,2,1,8,5,7]=>1011010=>0101101=>1010010
[3,8,5,6,4,2,1,7]=>0101110=>0111010=>1000101
[3,6,4,2,1,8,5,7]=>0111010=>0101110=>1010001
[8,5,3,7,6,2,4,1]=>1101101=>1011011=>0100100
[7,6,2,4,1,8,5,3]=>1101011=>1101011=>0010100
[8,5,4,1,7,6,2,3]=>1110110=>0110111=>1001000
[7,6,2,3,8,5,4,1]=>1100111=>1110011=>0001100
[2,1,7,8,6,4,3,5]=>1001110=>0111001=>1000110
[2,1,6,4,3,7,8,5]=>1011001=>1001101=>0110010
[6,3,7,8,4,2,1,5]=>1001110=>0111001=>1000110
[7,8,4,2,1,6,3,5]=>0111010=>0101110=>1010001
[5,7,6,2,3,8,4,1]=>0110011=>1100110=>0011001
[2,6,1,8,4,3,7,5]=>0101101=>1011010=>0100101
[2,6,1,7,5,8,4,3]=>0101011=>1101010=>0010101
[8,4,2,3,7,5,6,1]=>1100101=>1010011=>0101100
[8,5,7,6,2,1,4,3]=>1011101=>1011101=>0100010
[4,8,5,7,6,2,1,3]=>0101110=>0111010=>1000101
[4,7,6,2,1,3,8,5]=>0111001=>1001110=>0110001
[7,5,6,1,8,4,2,3]=>1010110=>0110101=>1001010
[2,7,5,8,4,3,6,1]=>0101101=>1011010=>0100101
[2,8,4,3,6,1,7,5]=>0110101=>1010110=>0101001
[8,4,2,6,3,1,7,5]=>1101101=>1011011=>0100100
[1,5,3,7,4,2,8,6]=>0101101=>1011010=>0100101
[1,6,7,3,4,2,8,5]=>0010101=>1010100=>0101011
[8,6,5,2,3,1,7,4]=>1110101=>1010111=>0101000
[1,7,6,3,4,2,8,5]=>0110101=>1010110=>0101001
[1,8,6,3,2,5,7,4]=>0111001=>1001110=>0110001
[8,7,5,2,1,4,6,3]=>1111001=>1001111=>0110000
[7,8,5,2,1,4,6,3]=>0111001=>1001110=>0110001
[6,8,5,2,3,1,7,4]=>0110101=>1010110=>0101001
[5,8,6,2,3,1,7,4]=>0110101=>1010110=>0101001
[4,8,2,6,3,1,7,5]=>0101101=>1011010=>0100101
[3,2,8,6,4,1,7,5]=>1011101=>1011101=>0100010
[3,2,1,7,5,4,8,6]=>1101101=>1011011=>0100100
[4,1,3,7,5,2,8,6]=>1001101=>1011001=>0100110
[7,1,6,3,2,5,8,4]=>1011001=>1001101=>0110010
[1,2,7,4,3,6,8,5]=>0011001=>1001100=>0110011
[6,1,8,2,4,5,7,3]=>1010001=>1000101=>0111010
[5,1,8,3,2,6,7,4]=>1011001=>1001101=>0110010
[4,8,2,7,1,5,6,3]=>0101001=>1001010=>0110101
[5,8,7,2,1,4,6,3]=>0111001=>1001110=>0110001
[6,8,7,1,3,4,5,2]=>0110001=>1000110=>0111001
[7,8,6,1,3,4,5,2]=>0110001=>1000110=>0111001
[1,7,8,2,4,5,6,3]=>0010001=>1000100=>0111011
[8,6,7,1,3,4,5,2]=>1010001=>1000101=>0111010
[7,6,8,1,3,4,5,2]=>1010001=>1000101=>0111010
[6,5,8,2,3,1,7,4]=>1010101=>1010101=>0101010
[1,6,8,3,2,5,7,4]=>0011001=>1001100=>0110011
[8,4,2,7,1,5,6,3]=>1101001=>1001011=>0110100
[7,4,2,8,1,5,6,3]=>1101001=>1001011=>0110100
[6,4,2,8,3,1,7,5]=>1101101=>1011011=>0100100
[5,4,2,3,8,1,7,6]=>1100101=>1010011=>0101100
[4,5,2,3,1,6,8,7]=>0101001=>1001010=>0110101
[7,4,2,1,3,6,8,5]=>1110001=>1000111=>0111000
[8,4,2,1,3,6,7,5]=>1110001=>1000111=>0111000
[1,5,3,2,4,7,8,6]=>0110001=>1000110=>0111001
[8,5,1,3,2,6,7,4]=>1101001=>1001011=>0110100
[5,6,1,3,4,2,8,7]=>0100101=>1010010=>0101101
[4,7,2,1,3,6,8,5]=>0110001=>1000110=>0111001
[5,7,1,3,2,6,8,4]=>0101001=>1001010=>0110101
[6,7,1,2,4,5,8,3]=>0100001=>1000010=>0111101
[1,8,2,3,5,6,7,4]=>0100001=>1000010=>0111101
[5,8,1,3,2,6,7,4]=>0101001=>1001010=>0110101
[4,8,2,1,3,6,7,5]=>0110001=>1000110=>0111001
[4,1,3,2,5,7,8,6]=>1010001=>1000101=>0111010
[5,1,2,4,3,7,8,6]=>1001001=>1001001=>0110110
[8,7,5,2,6,3,4,1]=>1110101=>1010111=>0101000
[8,6,5,2,7,3,4,1]=>1110101=>1010111=>0101000
[1,2,6,4,7,5,8,3]=>0010101=>1010100=>0101011
[3,1,7,5,4,2,6,8]=>1011100=>0011101=>1100010
[6,3,8,5,4,7,1,2]=>1011010=>0101101=>1010010
[1,6,2,5,4,7,8,3]=>0101001=>1001010=>0110101
[1,2,6,4,8,5,7,3]=>0010101=>1010100=>0101011
[7,8,3,1,4,2,5,6]=>0110100=>0010110=>1101001
[4,8,1,5,2,3,6,7]=>0101000=>0001010=>1110101
[7,4,1,5,2,3,6,8]=>1101000=>0001011=>1110100
[5,6,1,8,4,3,2,7]=>0101110=>0111010=>1000101
[5,1,8,6,4,3,2,7]=>1011110=>0111101=>1000010
[5,1,6,3,8,7,2,4]=>1010110=>0110101=>1001010
[6,1,2,5,8,3,7,4]=>1000101=>1010001=>0101110
[6,1,8,7,4,3,2,5]=>1011110=>0111101=>1000010
[7,1,2,5,4,8,6,3]=>1001011=>1101001=>0010110
[1,2,7,5,8,3,6,4]=>0010101=>1010100=>0101011
[4,1,6,3,7,5,2,8]=>1010110=>0110101=>1001010
[1,3,6,7,8,5,2,4]=>0000110=>0110000=>1001111
[1,2,6,4,7,8,5,3]=>0010011=>1100100=>0011011
[4,1,6,3,7,8,2,5]=>1010010=>0100101=>1011010
[3,1,6,4,8,2,7,5]=>1010101=>1010101=>0101010
[7,8,4,1,6,3,2,5]=>0110110=>0110110=>1001001
[4,1,6,3,8,7,2,5]=>1010110=>0110101=>1001010
[7,5,1,8,4,3,2,6]=>1101110=>0111011=>1000100
[6,5,1,7,4,3,2,8]=>1101110=>0111011=>1000100
[4,1,8,5,2,3,7,6]=>1011001=>1001101=>0110010
[4,1,6,8,3,7,2,5]=>1001010=>0101001=>1010110
[6,5,8,1,4,3,2,7]=>1010110=>0110101=>1001010
[1,6,3,2,7,4,8,5]=>0110101=>1010110=>0101001
[1,3,7,2,5,4,8,6]=>0010101=>1010100=>0101011
[1,3,7,5,2,4,8,6]=>0011001=>1001100=>0110011
[2,5,3,7,4,8,1,6]=>0101010=>0101010=>1010101
[3,2,6,7,8,1,5,4]=>1000101=>1010001=>0101110
[3,5,2,7,8,4,1,6]=>0100110=>0110010=>1001101
[3,5,2,6,8,4,7,1]=>0100101=>1010010=>0101101
[2,5,7,4,3,8,6,1]=>0011011=>1101100=>0010011
[1,5,7,2,4,8,6,3]=>0010011=>1100100=>0011011
[4,6,3,7,2,8,5,1]=>0101011=>1101010=>0010101
[1,4,7,3,8,6,2,5]=>0010110=>0110100=>1001011
[5,1,6,8,2,4,3,7]=>1001010=>0101001=>1010110
[5,3,7,8,2,4,1,6]=>1001010=>0101001=>1010110
[8,5,3,7,2,4,1,6]=>1101010=>0101011=>1010100
[8,2,4,7,3,1,5,6]=>1001100=>0011001=>1100110
[2,4,7,8,3,1,5,6]=>0001100=>0011000=>1100111
[6,3,1,5,8,2,4,7]=>1100100=>0010011=>1101100
[6,5,3,4,2,8,1,7]=>1101010=>0101011=>1010100
[5,2,4,3,8,1,6,7]=>1010100=>0010101=>1101010
[3,2,4,8,1,5,6,7]=>1001000=>0001001=>1110110
[8,1,5,7,3,2,4,6]=>1001100=>0011001=>1100110
[8,4,6,7,2,3,1,5]=>1001010=>0101001=>1010110
[4,6,7,8,2,3,1,5]=>0001010=>0101000=>1010111
[7,4,6,8,2,3,1,5]=>1001010=>0101001=>1010110
[7,2,4,8,3,1,5,6]=>1001100=>0011001=>1100110
[5,3,8,7,2,4,1,6]=>1011010=>0101101=>1010010
[2,4,8,7,3,1,5,6]=>0011100=>0011100=>1100011
[4,6,8,7,2,3,1,5]=>0011010=>0101100=>1010011
[6,4,8,7,2,3,1,5]=>1011010=>0101101=>1010010
[3,1,7,4,2,8,6,5]=>1011011=>1101101=>0010010
[3,2,8,4,1,7,6,5]=>1011011=>1101101=>0010010
[7,6,4,8,2,3,1,5]=>1101010=>0101011=>1010100
[5,7,6,8,2,3,1,4]=>0101010=>0101010=>1010101
[4,7,6,8,2,3,1,5]=>0101010=>0101010=>1010101
[8,6,4,7,2,3,1,5]=>1101010=>0101011=>1010100
[8,2,3,7,4,1,6,5]=>1001101=>1011001=>0100110
[3,7,4,8,2,5,1,6]=>0101010=>0101010=>1010101
[2,3,7,4,1,6,8,5]=>0011001=>1001100=>0110011
[8,1,6,4,2,3,7,5]=>1011001=>1001101=>0110010
[4,7,8,6,2,3,1,5]=>0011010=>0101100=>1010011
[6,3,1,7,4,2,8,5]=>1101101=>1011011=>0100100
[8,5,7,6,2,3,1,4]=>1011010=>0101101=>1010010
[7,1,6,4,2,3,8,5]=>1011001=>1001101=>0110010
[3,1,7,6,4,2,8,5]=>1011101=>1011101=>0100010
[4,8,7,6,2,3,1,5]=>0111010=>0101110=>1010001
[6,8,7,5,2,3,1,4]=>0111010=>0101110=>1010001
[4,3,6,1,5,8,7,2]=>1010011=>1100101=>0011010
[4,3,6,5,1,8,7,2]=>1011011=>1101101=>0010010
[4,6,3,5,1,8,7,2]=>0101011=>1101010=>0010101
[4,6,3,1,5,8,7,2]=>0110011=>1100110=>0011001
[4,1,6,5,3,8,7,2]=>1011011=>1101101=>0010010
[4,6,1,5,3,8,7,2]=>0101011=>1101010=>0010101
[2,6,5,3,1,8,7,4]=>0111011=>1101110=>0010001
[2,6,5,8,3,1,7,4]=>0101101=>1011010=>0100101
[2,6,5,3,8,1,7,4]=>0110101=>1010110=>0101001
[4,6,1,5,8,3,7,2]=>0100101=>1010010=>0101101
[4,1,6,5,8,3,7,2]=>1010101=>1010101=>0101010
[1,4,6,5,8,3,7,2]=>0010101=>1010100=>0101011
[4,1,6,5,8,7,3,2]=>1010111=>1110101=>0001010
[6,4,3,8,7,1,5,2]=>1101101=>1011011=>0100100
[6,4,8,3,7,1,5,2]=>1010101=>1010101=>0101010
[2,6,8,5,3,7,1,4]=>0011010=>0101100=>1010011
[4,6,8,1,5,7,3,2]=>0010011=>1100100=>0011011
[4,6,1,8,5,7,3,2]=>0101011=>1101010=>0010101
[1,4,6,8,5,7,3,2]=>0001011=>1101000=>0010111
[1,4,6,8,5,3,7,2]=>0001101=>1011000=>0100111
[4,6,1,8,5,3,7,2]=>0101101=>1011010=>0100101
[4,6,3,8,5,7,1,2]=>0101010=>0101010=>1010101
[4,3,6,8,1,5,7,2]=>1001001=>1001001=>0110110
[4,3,6,1,8,5,7,2]=>1010101=>1010101=>0101010
[4,3,1,6,8,5,7,2]=>1100101=>1010011=>0101100
[4,1,3,6,8,7,5,2]=>1000111=>1110001=>0001110
[4,3,6,1,8,7,5,2]=>1010111=>1110101=>0001010
[4,3,6,8,1,7,5,2]=>1001011=>1101001=>0010110
[6,5,2,8,7,3,1,4]=>1101110=>0111011=>1000100
[6,5,2,8,7,1,3,4]=>1101100=>0011011=>1100100
[6,2,5,8,7,1,3,4]=>1001100=>0011001=>1100110
[6,2,5,8,7,3,1,4]=>1001110=>0111001=>1000110
[4,6,3,8,1,7,5,2]=>0101011=>1101010=>0010101
[4,6,3,1,8,7,5,2]=>0110111=>1110110=>0001001
[4,1,6,3,8,7,5,2]=>1010111=>1110101=>0001010
[1,4,6,3,8,7,5,2]=>0010111=>1110100=>0001011
[4,1,6,8,3,7,5,2]=>1001011=>1101001=>0010110
[4,6,1,8,3,7,5,2]=>0101011=>1101010=>0010101
[4,6,8,1,3,7,5,2]=>0010011=>1100100=>0011011
[6,2,8,5,7,3,1,4]=>1010110=>0110101=>1001010
[6,2,8,5,7,1,3,4]=>1010100=>0010101=>1101010
[2,4,8,7,1,5,3,6]=>0011010=>0101100=>1010011
[6,4,1,8,7,5,3,2]=>1101111=>1111011=>0000100
[6,1,4,8,7,5,3,2]=>1001111=>1111001=>0000110
[1,6,4,8,7,3,5,2]=>0101101=>1011010=>0100101
[6,4,1,8,7,3,5,2]=>1101101=>1011011=>0100100
[4,2,8,7,5,1,3,6]=>1011100=>0011101=>1100010
[2,4,8,7,3,5,1,6]=>0011010=>0101100=>1010011
[1,5,3,2,6,4,7,8]=>0110100=>0010110=>1101001
[1,5,3,2,6,7,4,8]=>0110010=>0100110=>1011001
[1,7,3,2,8,5,4,6]=>0110110=>0110110=>1001001
[1,7,3,2,5,8,4,6]=>0110010=>0100110=>1011001
[6,4,2,5,3,7,1,8]=>1101010=>0101011=>1010100
[5,4,7,6,2,3,1,8]=>1011010=>0101101=>1010010
[3,6,4,8,2,1,5,7]=>0101100=>0011010=>1100101
[1,6,2,8,5,3,4,7]=>0101100=>0011010=>1100101
[4,6,2,3,7,5,1,8]=>0100110=>0110010=>1001101
[4,7,2,3,6,5,1,8]=>0100110=>0110010=>1001101
[5,3,2,6,4,7,1,8]=>1101010=>0101011=>1010100
[3,5,2,1,6,8,4,7]=>0110010=>0100110=>1011001
[1,5,2,6,8,4,3,7]=>0100110=>0110010=>1001101
[1,5,7,2,8,4,3,6]=>0010110=>0110100=>1001011
[3,5,2,1,8,6,4,7]=>0110110=>0110110=>1001001
[3,6,8,4,2,1,5,7]=>0011100=>0011100=>1100011
[4,3,2,6,1,8,5,7]=>1101010=>0101011=>1010100
[1,5,8,2,7,4,3,6]=>0010110=>0110100=>1001011
[1,7,2,3,4,8,6,5]=>0100011=>1100010=>0011101
[6,8,2,3,4,1,7,5]=>0100101=>1010010=>0101101
[2,3,1,8,4,5,7,6]=>0101001=>1001010=>0110101
[7,3,2,1,4,5,8,6]=>1110001=>1000111=>0111000
[7,8,1,4,3,5,2,6]=>0101010=>0101010=>1010101
[1,8,2,3,4,7,6,5]=>0100011=>1100010=>0011101
[3,8,2,1,6,5,4,7]=>0110110=>0110110=>1001001
[1,7,8,3,5,4,2,6]=>0010110=>0110100=>1001011
[7,4,1,8,3,5,2,6]=>1101010=>0101011=>1010100
[8,4,1,7,3,5,2,6]=>1101010=>0101011=>1010100
[3,8,4,6,2,1,5,7]=>0101100=>0011010=>1100101
[8,4,2,5,3,1,6,7]=>1101100=>0011011=>1100100
[4,3,2,5,1,8,6,7]=>1101010=>0101011=>1010100
[3,5,2,4,1,8,6,7]=>0101010=>0101010=>1010101
[2,4,7,8,1,5,3,6]=>0001010=>0101000=>1010111
[1,8,7,3,5,4,2,6]=>0110110=>0110110=>1001001
[5,1,8,2,7,4,3,6]=>1010110=>0110101=>1001010
[5,1,7,2,8,4,3,6]=>1010110=>0110101=>1001010
[6,1,2,8,5,3,4,7]=>1001100=>0011001=>1100110
[6,3,2,1,8,4,5,7]=>1110100=>0010111=>1101000
[7,3,2,8,4,5,1,6]=>1101010=>0101011=>1010100
[2,7,8,4,3,5,1,6]=>0011010=>0101100=>1010011
[7,1,8,3,5,4,2,6]=>1010110=>0110101=>1001010
[7,8,2,3,4,6,1,5]=>0100010=>0100010=>1011101
[6,8,1,3,4,7,2,5]=>0100010=>0100010=>1011101
[8,6,2,3,4,1,7,5]=>1100101=>1010011=>0101100
[8,3,2,7,4,5,1,6]=>1101010=>0101011=>1010100
[6,7,2,3,4,1,8,5]=>0100101=>1010010=>0101101
[8,6,2,3,4,7,1,5]=>1100010=>0100011=>1011100
[4,8,7,3,5,6,1,2]=>0110010=>0100110=>1011001
[4,8,7,5,3,6,1,2]=>0111010=>0101110=>1010001
[5,8,7,3,4,6,1,2]=>0110010=>0100110=>1011001
[5,8,4,2,1,6,7,3]=>0111001=>1001110=>0110001
[5,8,4,1,2,6,7,3]=>0110001=>1000110=>0111001
[5,3,7,2,6,1,8,4]=>1010101=>1010101=>0101010
[5,2,8,1,6,3,7,4]=>1010101=>1010101=>0101010
[5,8,2,1,4,7,6,3]=>0110011=>1100110=>0011001
[4,8,2,5,1,7,6,3]=>0101011=>1101010=>0010101
[7,8,4,1,2,6,5,3]=>0110011=>1100110=>0011001
[4,8,1,5,2,7,6,3]=>0101011=>1101010=>0010101
[5,8,1,2,4,7,6,3]=>0100011=>1100010=>0011101
[5,2,8,3,6,7,1,4]=>1010010=>0100101=>1011010
[2,8,7,6,4,1,3,5]=>0111100=>0011110=>1100001
[7,8,2,6,5,1,3,4]=>0101100=>0011010=>1100101
[1,8,7,6,2,4,3,5]=>0111010=>0101110=>1010001
[2,8,1,4,5,6,7,3]=>0100001=>1000010=>0111101
[2,1,7,3,6,5,8,4]=>1010101=>1010101=>0101010
[3,2,7,1,6,5,8,4]=>1010101=>1010101=>0101010
[6,1,2,8,5,7,3,4]=>1001010=>0101001=>1010110
[6,2,1,8,5,7,3,4]=>1101010=>0101011=>1010100
[6,3,1,8,5,7,2,4]=>1101010=>0101011=>1010100
[6,4,2,1,7,5,8,3]=>1110101=>1010111=>0101000
[6,1,3,8,5,2,7,4]=>1001101=>1011001=>0100110
[1,3,7,2,6,8,5,4]=>0010011=>1100100=>0011011
[7,8,2,6,5,3,1,4]=>0101110=>0111010=>1000101
[3,2,6,7,5,8,1,4]=>1001010=>0101001=>1010110
[1,2,7,5,6,3,8,4]=>0010101=>1010100=>0101011
[2,8,7,6,4,3,1,5]=>0111110=>0111110=>1000001
[3,8,7,6,1,2,5,4]=>0111001=>1001110=>0110001
[4,8,7,6,2,1,3,5]=>0111100=>0011110=>1100001
[4,8,7,6,1,3,2,5]=>0111010=>0101110=>1010001
[3,8,7,6,4,1,2,5]=>0111100=>0011110=>1100001
[7,8,3,6,5,1,2,4]=>0101100=>0011010=>1100101
[2,3,7,5,6,8,1,4]=>0010010=>0100100=>1011011
[3,8,7,6,4,2,1,5]=>0111110=>0111110=>1000001
[3,4,2,6,7,8,1,5]=>0100010=>0100010=>1011101
[3,1,4,2,6,8,7,5]=>1010011=>1100101=>0011010
[8,3,4,2,6,1,7,5]=>1010101=>1010101=>0101010
[2,6,7,3,5,4,1,8]=>0010110=>0110100=>1001011
[2,7,8,3,5,4,1,6]=>0010110=>0110100=>1001011
[2,6,8,3,5,4,1,7]=>0010110=>0110100=>1001011
[4,7,1,2,8,5,3,6]=>0100110=>0110010=>1001101
[4,8,1,2,7,5,3,6]=>0100110=>0110010=>1001101
[2,1,6,3,7,5,4,8]=>1010110=>0110101=>1001010
[2,7,1,3,6,8,4,5]=>0100010=>0100010=>1011101
[7,4,1,2,8,5,3,6]=>1100110=>0110011=>1001100
[8,7,4,2,1,5,3,6]=>1111010=>0101111=>1010000
[7,4,1,2,6,5,3,8]=>1100110=>0110011=>1001100
[7,4,3,1,5,6,8,2]=>1110001=>1000111=>0111000
[6,7,4,1,5,8,3,2]=>0110011=>1100110=>0011001
[4,7,5,1,6,8,3,2]=>0110011=>1100110=>0011001
[4,5,3,1,7,6,8,2]=>0110101=>1010110=>0101001
[4,6,1,2,7,5,3,8]=>0100110=>0110010=>1001101
[4,6,1,2,8,5,3,7]=>0100110=>0110010=>1001101
[4,5,3,1,8,6,7,2]=>0110101=>1010110=>0101001
[4,8,5,6,3,1,7,2]=>0101101=>1011010=>0100101
[5,1,3,4,8,6,7,2]=>1000101=>1010001=>0101110
[5,4,3,8,1,6,7,2]=>1101001=>1001011=>0110100
[8,5,3,4,1,6,7,2]=>1101001=>1001011=>0110100
[6,4,8,2,1,5,3,7]=>1011010=>0101101=>1010010
[6,7,3,2,5,1,4,8]=>0110100=>0010110=>1101001
[6,8,3,2,5,1,4,7]=>0110100=>0010110=>1101001
[5,7,1,4,6,8,3,2]=>0100011=>1100010=>0011101
[5,1,3,4,7,6,8,2]=>1000101=>1010001=>0101110
[5,4,3,7,1,6,8,2]=>1101001=>1001011=>0110100
[6,7,5,4,1,8,3,2]=>0111011=>1101110=>0010001
[7,6,4,2,1,5,3,8]=>1111010=>0101111=>1010000
[8,5,6,1,3,2,4,7]=>1010100=>0010101=>1101010
[8,6,1,5,3,2,4,7]=>1101100=>0011011=>1100100
[7,8,1,5,3,2,4,6]=>0101100=>0011010=>1100101
[8,1,7,5,3,2,4,6]=>1011100=>0011101=>1100010
[8,6,1,4,5,2,3,7]=>1100100=>0010011=>1101100
[8,6,3,1,5,2,4,7]=>1110100=>0010111=>1101000
[8,4,6,1,5,2,3,7]=>1010100=>0010101=>1101010
[8,6,2,1,5,4,3,7]=>1110110=>0110111=>1001000
[8,5,2,6,1,4,3,7]=>1101010=>0101011=>1010100
[8,5,2,1,7,4,3,6]=>1110110=>0110111=>1001000
[8,2,7,5,1,3,4,6]=>1011000=>0001101=>1110010
[8,4,1,7,5,2,3,6]=>1101100=>0011011=>1100100
[8,2,6,1,7,4,3,5]=>1010110=>0110101=>1001010
[8,1,7,4,3,2,6,5]=>1011101=>1011101=>0100010
[8,1,5,7,3,2,6,4]=>1001101=>1011001=>0100110
[5,7,8,1,3,2,6,4]=>0010101=>1010100=>0101011
[8,2,6,1,5,7,3,4]=>1010010=>0100101=>1011010
[5,8,1,6,7,2,3,4]=>0100100=>0010010=>1101101
[5,7,6,1,8,2,3,4]=>0110100=>0010110=>1101001
[8,1,5,6,7,2,3,4]=>1000100=>0010001=>1101110
[6,5,7,1,8,2,3,4]=>1010100=>0010101=>1101010
[8,1,6,4,7,2,3,5]=>1010100=>0010101=>1101010
[7,5,8,1,3,2,4,6]=>1010100=>0010101=>1101010
[7,8,4,1,3,2,5,6]=>0110100=>0010110=>1101001
[8,3,7,4,1,2,5,6]=>1011000=>0001101=>1110010
[8,5,1,7,3,2,4,6]=>1101100=>0011011=>1100100
[6,8,1,7,3,2,4,5]=>0101100=>0011010=>1100101
[7,1,8,4,3,6,2,5]=>1011010=>0101101=>1010010
[7,3,1,8,6,4,2,5]=>1101110=>0111011=>1000100
[8,3,1,7,4,6,2,5]=>1101010=>0101011=>1010100
[8,4,5,1,7,2,3,6]=>1010100=>0010101=>1101010
[5,6,8,1,7,2,3,4]=>0010100=>0010100=>1101011
[6,5,8,1,2,7,3,4]=>1010010=>0100101=>1011010
[7,3,1,8,5,6,2,4]=>1101010=>0101011=>1010100
[6,2,7,8,3,1,5,4]=>1001101=>1011001=>0100110
[5,8,1,7,3,2,6,4]=>0101101=>1011010=>0100101
[8,4,1,7,3,2,6,5]=>1101101=>1011011=>0100100
[8,3,4,7,1,2,6,5]=>1001001=>1001001=>0110110
[7,4,8,2,1,3,6,5]=>1011001=>1001101=>0110010
[7,4,3,8,1,2,6,5]=>1101001=>1001011=>0110100
[8,2,3,6,7,1,5,4]=>1000101=>1010001=>0101110
[2,6,8,7,1,5,4,3]=>0011011=>1101100=>0010011
[7,8,5,2,3,6,4,1]=>0110011=>1100110=>0011001
[8,7,5,2,3,1,6,4]=>1110101=>1010111=>0101000
[6,8,5,2,3,4,7,1]=>0110001=>1000110=>0111001
[5,7,3,4,6,8,1,2]=>0100010=>0100010=>1011101
[5,7,3,4,6,1,2,8]=>0100100=>0010010=>1101101
[7,3,5,6,1,2,8,4]=>1001001=>1001001=>0110110
[5,7,3,1,4,6,8,2]=>0110001=>1000110=>0111001
[5,7,3,1,4,8,6,2]=>0110011=>1100110=>0011001
[5,7,3,1,4,8,2,6]=>0110010=>0100110=>1011001
[5,3,7,4,1,2,8,6]=>1011001=>1001101=>0110010
[5,3,7,4,1,2,6,8]=>1011000=>0001101=>1110010
[5,3,7,1,4,2,6,8]=>1010100=>0010101=>1101010
[5,3,7,1,4,2,8,6]=>1010101=>1010101=>0101010
[3,7,5,1,2,8,6,4]=>0110011=>1100110=>0011001
[7,8,3,5,1,2,6,4]=>0101001=>1001010=>0110101
[7,3,8,5,1,2,6,4]=>1011001=>1001101=>0110010
[7,3,5,8,1,2,6,4]=>1001001=>1001001=>0110110
[3,7,5,1,2,6,4,8]=>0110010=>0100110=>1011001
[3,7,5,1,2,6,8,4]=>0110001=>1000110=>0111001
[3,5,7,2,8,6,1,4]=>0010110=>0110100=>1001011
[2,5,7,4,8,6,1,3]=>0010110=>0110100=>1001011
[2,6,4,8,7,5,1,3]=>0101110=>0111010=>1000101
[3,6,2,5,8,7,1,4]=>0100110=>0110010=>1001101
[5,2,8,4,7,6,1,3]=>1010110=>0110101=>1001010
[6,2,4,8,7,5,1,3]=>1001110=>0111001=>1000110
[2,5,1,4,7,3,8,6]=>0100101=>1010010=>0101101
[3,1,5,6,2,8,7,4]=>1001011=>1101001=>0010110
[7,1,4,2,8,6,5,3]=>1010111=>1110101=>0001010
[4,1,5,3,2,8,7,6]=>1011011=>1101101=>0010010
[7,2,3,5,1,8,6,4]=>1001011=>1101001=>0010110
[1,6,4,2,8,7,5,3]=>0110111=>1110110=>0001001
[4,6,2,7,5,1,8,3]=>0101101=>1011010=>0100101
[1,5,3,6,2,8,7,4]=>0101011=>1101010=>0010101
[3,6,2,5,1,4,8,7]=>0101001=>1001010=>0110101
[5,2,8,4,1,3,7,6]=>1011001=>1001101=>0110010
[2,4,8,7,1,3,6,5]=>0011001=>1001100=>0110011
[6,3,1,7,2,8,5,4]=>1101011=>1101011=>0010100
[7,5,1,2,8,6,4,3]=>1100111=>1110011=>0001100
[1,5,2,3,8,7,6,4]=>0100111=>1110010=>0001101
[4,5,1,2,8,7,6,3]=>0100111=>1110010=>0001101
[3,5,8,7,2,6,4,1]=>0011011=>1101100=>0010011
[5,8,2,7,1,6,4,3]=>0101011=>1101010=>0010101
[2,1,6,4,5,8,3,7]=>1010010=>0100101=>1011010
[8,6,3,7,5,2,1,4]=>1101110=>0111011=>1000100
[4,6,3,8,5,2,1,7]=>0101110=>0111010=>1000101
[4,6,3,7,5,2,8,1]=>0101101=>1011010=>0100101
[3,5,7,8,2,6,1,4]=>0001010=>0101000=>1010111
[4,2,3,6,1,5,8,7]=>1001001=>1001001=>0110110
[3,8,6,4,5,1,2,7]=>0110100=>0010110=>1101001
[4,8,3,7,5,2,1,6]=>0101110=>0111010=>1000101
[8,7,3,6,5,1,2,4]=>1101100=>0011011=>1100100
[5,2,8,3,7,6,1,4]=>1010110=>0110101=>1001010
[8,2,7,3,1,6,4,5]=>1011010=>0101101=>1010010
[8,6,7,4,1,5,3,2]=>1011011=>1101101=>0010010
[4,8,6,7,5,1,3,2]=>0101101=>1011010=>0100101
[7,1,8,4,6,5,2,3]=>1010110=>0110101=>1001010
[8,7,1,5,4,6,2,3]=>1101010=>0101011=>1010100
[8,5,7,1,4,6,3,2]=>1010011=>1100101=>0011010
[6,4,8,5,1,7,3,2]=>1011011=>1101101=>0010010
[8,4,7,1,5,6,3,2]=>1010011=>1100101=>0011010
[8,7,5,1,4,6,2,3]=>1110010=>0100111=>1011000
[8,7,2,5,1,4,6,3]=>1101001=>1001011=>0110100
[4,8,7,2,5,1,6,3]=>0110101=>1010110=>0101001
[8,7,1,4,2,5,6,3]=>1101001=>1001011=>0110100
[8,7,5,1,2,4,6,3]=>1110001=>1000111=>0111000
[7,1,8,5,6,2,3,4]=>1010100=>0010101=>1101010
[3,5,8,7,1,2,6,4]=>0011001=>1001100=>0110011
[2,3,8,5,7,1,6,4]=>0010101=>1010100=>0101011
[3,8,7,1,5,6,2,4]=>0110010=>0100110=>1011001
[3,5,8,7,1,6,2,4]=>0011010=>0101100=>1010011
[2,3,8,6,7,5,1,4]=>0010110=>0110100=>1001011
[3,2,8,6,7,5,1,4]=>1010110=>0110101=>1001010
[4,1,8,6,2,7,5,3]=>1011011=>1101101=>0010010
[8,7,4,1,2,6,5,3]=>1110011=>1100111=>0011000
[1,3,8,6,7,5,2,4]=>0010110=>0110100=>1001011
[5,7,1,8,2,6,3,4]=>0101010=>0101010=>1010101
[2,8,7,1,5,6,3,4]=>0110010=>0100110=>1011001
[8,7,1,5,2,4,6,3]=>1101001=>1001011=>0110100
[7,1,8,2,4,6,5,3]=>1010011=>1100101=>0011010
[1,6,2,8,4,7,5,3]=>0101011=>1101010=>0010101
[1,3,8,5,7,2,6,4]=>0010101=>1010100=>0101011
[1,8,3,7,2,5,6,4]=>0101001=>1001010=>0110101
[2,8,7,1,3,5,6,4]=>0110001=>1000110=>0111001
[5,7,1,8,2,3,6,4]=>0101001=>1001010=>0110101
[7,1,8,2,3,5,6,4]=>1010001=>1000101=>0111010
[8,6,3,7,4,1,5,2]=>1101101=>1011011=>0100100
[4,2,8,6,7,5,1,3]=>1010110=>0110101=>1001010
[8,4,2,7,5,6,1,3]=>1101010=>0101011=>1010100
[4,8,3,6,1,7,5,2]=>0101011=>1101010=>0010101
[8,3,4,7,5,1,6,2]=>1001101=>1011001=>0100110
[8,3,7,4,5,1,6,2]=>1010101=>1010101=>0101010
[8,7,4,2,5,6,1,3]=>1110010=>0100111=>1011000
[8,7,5,1,6,2,3,4]=>1110100=>0010111=>1101000
[8,7,2,4,1,5,6,3]=>1101001=>1001011=>0110100
[4,8,6,1,7,2,5,3]=>0110101=>1010110=>0101001
[4,2,8,6,7,1,5,3]=>1010101=>1010101=>0101010
[8,7,4,1,2,5,6,3]=>1110001=>1000111=>0111000
[8,2,7,1,6,3,4,5]=>1010100=>0010101=>1101010
[8,2,7,1,3,6,4,5]=>1010010=>0100101=>1011010
[2,8,3,6,7,1,5,4]=>0100101=>1010010=>0101101
[8,7,2,1,3,5,6,4]=>1110001=>1000111=>0111000
[1,8,7,2,3,6,4,5]=>0110010=>0100110=>1011001
[1,8,7,2,6,3,4,5]=>0110100=>0010110=>1101001
[8,2,7,3,6,1,4,5]=>1010100=>0010101=>1101010
[1,8,7,3,6,2,4,5]=>0110100=>0010110=>1101001
[1,8,2,7,6,3,4,5]=>0101100=>0011010=>1100101
[8,2,7,4,1,5,6,3]=>1011001=>1001101=>0110010
[8,2,1,7,5,6,3,4]=>1101010=>0101011=>1010100
[8,7,3,1,5,6,2,4]=>1110010=>0100111=>1011000
[2,8,7,3,5,6,1,4]=>0110010=>0100110=>1011001
[8,3,1,6,7,5,2,4]=>1100110=>0110011=>1001100
[8,5,2,1,6,7,4,3]=>1110011=>1100111=>0011000
[1,5,2,8,6,7,4,3]=>0101011=>1101010=>0010101
[1,2,8,6,7,5,3,4]=>0010110=>0110100=>1001011
[1,8,3,6,7,5,2,4]=>0100110=>0110010=>1001101
[8,2,3,6,7,5,1,4]=>1000110=>0110001=>1001110
[8,3,7,2,5,6,1,4]=>1010010=>0100101=>1011010
[8,1,3,7,5,6,2,4]=>1001010=>0101001=>1010110
[8,4,1,2,7,5,6,3]=>1100101=>1010011=>0101100
[8,1,4,2,6,7,5,3]=>1010011=>1100101=>0011010
[1,2,8,6,7,3,5,4]=>0010101=>1010100=>0101011
[8,1,2,7,3,6,4,5]=>1001010=>0101001=>1010110
[8,1,7,3,6,2,4,5]=>1010100=>0010101=>1101010
[8,1,7,2,6,3,4,5]=>1010100=>0010101=>1101010
[8,1,7,2,3,6,4,5]=>1010010=>0100101=>1011010
[8,1,3,7,2,5,6,4]=>1001001=>1001001=>0110110
[1,8,3,6,7,2,5,4]=>0100101=>1010010=>0101101
[1,7,8,2,3,6,5,4]=>0010011=>1100100=>0011011
[8,3,7,1,2,5,6,4]=>1010001=>1000101=>0111010
[7,4,2,6,1,5,3,8]=>1101010=>0101011=>1010100
[7,4,2,5,6,1,3,8]=>1100100=>0010011=>1101100
[7,3,5,6,4,2,1,8]=>1001110=>0111001=>1000110
[7,4,3,1,5,6,2,8]=>1110010=>0100111=>1011000
[7,4,5,2,6,1,3,8]=>1010100=>0010101=>1101010
[5,3,7,2,8,6,4,1]=>1010111=>1110101=>0001010
[5,3,8,2,6,7,4,1]=>1010011=>1100101=>0011010
[6,3,8,2,5,4,7,1]=>1010101=>1010101=>0101010
[6,4,3,1,8,2,7,5]=>1110101=>1010111=>0101000
[5,3,7,8,2,6,4,1]=>1001011=>1101001=>0010110
[4,7,8,5,6,3,2,1]=>0010111=>1110100=>0001011
[5,3,7,6,8,2,4,1]=>1010101=>1010101=>0101010
[5,7,8,4,6,2,1,3]=>0010110=>0110100=>1001011
[5,8,4,3,6,7,1,2]=>0110010=>0100110=>1011001
[5,8,6,4,7,2,1,3]=>0110110=>0110110=>1001001
[5,3,8,6,2,7,4,1]=>1011011=>1101101=>0010010
[4,7,5,8,6,3,2,1]=>0101111=>1111010=>0000101
[6,3,8,7,2,4,1,5]=>1011010=>0101101=>1010010
[5,3,8,7,2,6,4,1]=>1011011=>1101101=>0010010
[5,3,8,6,7,2,4,1]=>1010101=>1010101=>0101010
[5,3,7,8,6,2,4,1]=>1001101=>1011001=>0100110
[5,7,6,4,8,2,1,3]=>0110110=>0110110=>1001001
[5,8,4,6,7,2,1,3]=>0100110=>0110010=>1001101
[6,4,2,8,1,7,3,5]=>1101010=>0101011=>1010100
[6,5,2,4,3,7,8,1]=>1101001=>1001011=>0110100
[5,4,6,2,8,7,1,3]=>1010110=>0110101=>1001010
[5,6,3,8,7,2,4,1]=>0101101=>1011010=>0100101
[6,7,4,3,1,8,2,5]=>0111010=>0101110=>1010001
[5,7,4,3,6,8,1,2]=>0110010=>0100110=>1011001
[5,7,3,8,6,2,4,1]=>0101101=>1011010=>0100101
[4,5,8,6,7,3,2,1]=>0010111=>1110100=>0001011
[4,6,8,5,7,3,2,1]=>0010111=>1110100=>0001011
[5,6,8,3,7,2,4,1]=>0010101=>1010100=>0101011
[5,4,6,8,2,7,1,3]=>1001010=>0101001=>1010110
[7,8,4,5,1,3,2,6]=>0101010=>0101010=>1010101
[6,7,1,3,2,5,4,8]=>0101010=>0101010=>1010101
[6,7,1,4,3,5,2,8]=>0101010=>0101010=>1010101
[7,8,2,3,1,5,4,6]=>0101010=>0101010=>1010101
[7,8,2,4,3,5,1,6]=>0101010=>0101010=>1010101
[7,8,2,4,1,5,3,6]=>0101010=>0101010=>1010101
[1,4,2,6,5,7,3,8]=>0101010=>0101010=>1010101
[5,6,1,4,2,7,3,8]=>0101010=>0101010=>1010101
[6,7,2,4,1,5,3,8]=>0101010=>0101010=>1010101
[6,7,2,4,3,5,1,8]=>0101010=>0101010=>1010101
[6,7,2,3,1,5,4,8]=>0101010=>0101010=>1010101
[6,7,3,5,4,8,1,2]=>0101010=>0101010=>1010101
[2,4,1,6,5,7,3,8]=>0101010=>0101010=>1010101
[1,5,2,6,4,7,3,8]=>0101010=>0101010=>1010101
[2,5,1,6,4,7,3,8]=>0101010=>0101010=>1010101
[5,6,2,4,3,7,1,8]=>0101010=>0101010=>1010101
[4,5,2,6,1,7,3,8]=>0101010=>0101010=>1010101
[4,5,1,6,3,7,2,8]=>0101010=>0101010=>1010101
[4,5,3,6,1,7,2,8]=>0101010=>0101010=>1010101
[5,6,3,4,1,7,2,8]=>0101010=>0101010=>1010101
[5,6,1,4,3,7,2,8]=>0101010=>0101010=>1010101
[5,6,1,3,2,7,4,8]=>0101010=>0101010=>1010101
[5,6,4,7,1,3,2,8]=>0101010=>0101010=>1010101
[6,7,4,5,1,3,2,8]=>0101010=>0101010=>1010101
[6,7,5,8,1,3,2,4]=>0101010=>0101010=>1010101
[4,5,1,3,2,7,6,8]=>0101010=>0101010=>1010101
[4,6,5,7,1,3,2,8]=>0101010=>0101010=>1010101
[4,6,1,3,2,7,5,8]=>0101010=>0101010=>1010101
[1,4,3,6,2,7,5,8]=>0101010=>0101010=>1010101
[4,5,2,3,1,7,6,8]=>0101010=>0101010=>1010101
[4,5,3,7,6,8,1,2]=>0101010=>0101010=>1010101
[4,6,5,7,3,8,1,2]=>0101010=>0101010=>1010101
[4,6,5,7,2,3,1,8]=>0101010=>0101010=>1010101
[3,5,4,6,1,7,2,8]=>0101010=>0101010=>1010101
[3,5,1,6,4,7,2,8]=>0101010=>0101010=>1010101
[1,5,3,6,4,7,2,8]=>0101010=>0101010=>1010101
[1,5,3,6,2,7,4,8]=>0101010=>0101010=>1010101
[3,5,2,6,1,7,4,8]=>0101010=>0101010=>1010101
[3,5,2,6,4,7,1,8]=>0101010=>0101010=>1010101
[3,4,2,6,1,7,5,8]=>0101010=>0101010=>1010101
[4,6,2,3,1,7,5,8]=>0101010=>0101010=>1010101
[2,4,3,6,1,7,5,8]=>0101010=>0101010=>1010101
[2,5,3,6,4,7,1,8]=>0101010=>0101010=>1010101
[2,5,3,6,1,7,4,8]=>0101010=>0101010=>1010101
[3,6,2,7,5,4,8,1]=>0101101=>1011010=>0100101
[5,2,6,7,4,3,8,1]=>1001101=>1011001=>0100110
[3,5,2,7,6,4,8,1]=>0101101=>1011010=>0100101
[1,3,7,2,8,5,6,4]=>0010101=>1010100=>0101011
[2,1,5,6,8,4,3,7]=>1000110=>0110001=>1001110
[1,3,7,2,8,5,4,6]=>0010110=>0110100=>1001011
[1,5,4,3,6,8,2,7]=>0110010=>0100110=>1011001
[1,6,4,5,7,8,3,2]=>0100011=>1100010=>0011101
[2,1,5,6,8,4,7,3]=>1000101=>1010001=>0101110
[2,1,5,6,8,7,3,4]=>1000110=>0110001=>1001110
[3,6,5,2,7,8,4,1]=>0110011=>1100110=>0011001
[6,2,4,7,5,8,3,1]=>1001011=>1101001=>0010110
[1,5,7,8,4,2,6,3]=>0001101=>1011000=>0100111
[3,7,4,1,8,6,2,5]=>0110110=>0110110=>1001001
[3,4,6,8,5,7,2,1]=>0001011=>1101000=>0010111
[4,5,6,2,8,7,3,1]=>0010111=>1110100=>0001011
[4,5,6,1,8,7,3,2]=>0010111=>1110100=>0001011
[4,5,6,3,1,8,7,2]=>0011011=>1101100=>0010011
[4,3,6,2,1,7,5,8]=>1011010=>0101101=>1010010
[4,6,3,2,1,7,5,8]=>0111010=>0101110=>1010001
[4,6,3,1,7,5,2,8]=>0110110=>0110110=>1001001
[4,5,3,7,6,1,8,2]=>0101101=>1011010=>0100101
[4,5,1,7,3,8,6,2]=>0101011=>1101010=>0010101
[2,5,7,1,4,3,8,6]=>0010101=>1010100=>0101011
[4,3,5,7,6,1,8,2]=>1001101=>1011001=>0100110
[4,3,6,1,7,5,2,8]=>1010110=>0110101=>1001010
[4,3,2,6,1,7,5,8]=>1101010=>0101011=>1010100
[5,3,2,1,6,4,7,8]=>1110100=>0010111=>1101000
[5,3,1,6,2,7,4,8]=>1101010=>0101011=>1010100
[5,1,6,3,2,7,4,8]=>1011010=>0101101=>1010010
[2,6,1,4,7,5,3,8]=>0100110=>0110010=>1001101
[3,6,1,7,4,2,5,8]=>0101100=>0011010=>1100101
[4,6,1,7,5,3,2,8]=>0101110=>0111010=>1000101
[5,1,6,3,7,4,2,8]=>1010110=>0110101=>1001010
[5,3,6,4,2,1,7,8]=>1011100=>0011101=>1100010
[5,3,2,6,4,1,7,8]=>1101100=>0011011=>1100100
[5,2,1,6,3,7,4,8]=>1101010=>0101011=>1010100
[5,2,6,3,1,7,4,8]=>1011010=>0101101=>1010010
[4,2,6,3,1,7,8,5]=>1011001=>1001101=>0110010
[3,6,2,1,7,4,5,8]=>0110100=>0010110=>1101001
[3,6,2,7,4,1,5,8]=>0101100=>0011010=>1100101
[3,5,7,2,8,6,4,1]=>0010111=>1110100=>0001011
[2,6,1,3,7,5,4,8]=>0100110=>0110010=>1001101
[3,6,1,7,5,2,4,8]=>0101100=>0011010=>1100101
[5,1,6,2,7,4,3,8]=>1010110=>0110101=>1001010
[5,2,6,4,3,1,7,8]=>1011100=>0011101=>1100010
[5,2,1,6,4,3,7,8]=>1101100=>0011011=>1100100
[5,4,2,1,6,3,7,8]=>1110100=>0010111=>1101000
[5,4,1,6,2,7,3,8]=>1101010=>0101011=>1010100
[5,1,6,4,2,7,3,8]=>1011010=>0101101=>1010010
[3,6,1,7,5,4,8,2]=>0101101=>1011010=>0100101
[2,6,1,5,4,3,7,8]=>0101100=>0011010=>1100101
[3,1,6,2,5,4,7,8]=>1010100=>0010101=>1101010
[4,1,6,3,2,7,8,5]=>1011001=>1001101=>0110010
[5,1,6,4,3,2,7,8]=>1011100=>0011101=>1100010
[5,4,1,6,3,2,7,8]=>1101100=>0011011=>1100100
[5,4,3,1,6,2,7,8]=>1110100=>0010111=>1101000
[1,2,8,7,4,6,3,5]=>0011010=>0101100=>1010011
[4,5,1,8,7,6,2,3]=>0101110=>0111010=>1000101
[4,1,5,8,7,6,2,3]=>1001110=>0111001=>1000110
[7,5,8,4,2,6,3,1]=>1011011=>1101101=>0010010
[6,8,4,5,2,7,3,1]=>0101011=>1101010=>0010101
[6,8,2,5,3,7,4,1]=>0101011=>1101010=>0010101
[6,3,8,4,2,7,5,1]=>1011011=>1101101=>0010010
[7,2,5,3,8,6,4,1]=>1010111=>1110101=>0001010
[3,4,7,5,8,6,2,1]=>0010111=>1110100=>0001011
[3,6,7,4,8,5,2,1]=>0010111=>1110100=>0001011
[6,7,4,2,8,5,3,1]=>0110111=>1110110=>0001001
[4,7,5,2,8,6,3,1]=>0110111=>1110110=>0001001
[5,6,2,8,3,7,4,1]=>0101011=>1101010=>0010101
[1,5,8,2,7,3,6,4]=>0010101=>1010100=>0101011
[5,8,4,7,2,3,6,1]=>0101001=>1001010=>0110101
[6,7,4,8,1,5,3,2]=>0101011=>1101010=>0010101
[6,8,5,3,7,2,4,1]=>0110101=>1010110=>0101001
[7,5,3,8,2,6,4,1]=>1101011=>1101011=>0010100
[3,7,4,5,8,6,2,1]=>0100111=>1110010=>0001101
[7,4,2,5,8,6,3,1]=>1100111=>1110011=>0001100
[6,8,4,2,5,7,3,1]=>0110011=>1100110=>0011001
[7,5,8,3,4,6,2,1]=>1010011=>1100101=>0011010
[7,4,5,8,1,6,3,2]=>1001011=>1101001=>0010110
[6,3,4,7,8,5,2,1]=>1000111=>1110001=>0001110
[3,6,8,4,5,7,1,2]=>0010010=>0100100=>1011011
[1,6,8,4,7,2,3,5]=>0010100=>0010100=>1101011
[1,4,5,7,8,2,6,3]=>0000101=>1010000=>0101111
[1,4,5,8,7,2,3,6]=>0001100=>0011000=>1100111
[1,2,5,8,3,6,4,7]=>0001010=>0101000=>1010111
[7,8,1,4,6,2,3,5]=>0100100=>0010010=>1101101
[1,6,7,4,8,2,5,3]=>0010101=>1010100=>0101011
[1,4,5,6,8,2,7,3]=>0000101=>1010000=>0101111
[1,4,5,8,6,2,7,3]=>0001101=>1011000=>0100111
[1,2,5,8,3,4,7,6]=>0001001=>1001000=>0110111
[7,8,1,2,3,5,4,6]=>0100010=>0100010=>1011101
[1,6,7,2,3,5,4,8]=>0010010=>0100100=>1011011
[1,4,5,7,6,2,3,8]=>0001100=>0011000=>1100111
[1,2,5,7,3,6,4,8]=>0001010=>0101000=>1010111
[1,2,5,7,3,6,8,4]=>0001001=>1001000=>0110111
[1,6,8,2,3,5,7,4]=>0010001=>1000100=>0111011
[1,6,8,4,5,2,3,7]=>0010100=>0010100=>1101011
[1,6,8,2,3,4,7,5]=>0010001=>1000100=>0111011
[1,6,8,2,3,7,4,5]=>0010010=>0100100=>1011011
[1,4,5,7,6,2,8,3]=>0001101=>1011000=>0100111
[7,8,1,4,5,2,6,3]=>0100101=>1010010=>0101101
[1,6,7,2,3,8,5,4]=>0010011=>1100100=>0011011
[1,2,5,6,3,8,7,4]=>0001011=>1101000=>0010111
[2,7,4,8,3,5,1,6]=>0101010=>0101010=>1010101
[2,7,4,8,3,5,6,1]=>0101001=>1001010=>0110101
[7,2,8,4,3,5,1,6]=>1011010=>0101101=>1010010
[8,4,2,1,5,3,6,7]=>1110100=>0010111=>1101000
[8,4,1,5,3,2,6,7]=>1101100=>0011011=>1100100
[6,7,3,8,4,2,5,1]=>0101101=>1011010=>0100101
[6,7,3,8,4,2,1,5]=>0101110=>0111010=>1000101
[7,1,8,4,3,5,2,6]=>1011010=>0101101=>1010010
[1,7,8,4,3,5,2,6]=>0011010=>0101100=>1010011
[7,1,4,8,3,5,2,6]=>1001010=>0101001=>1010110
[7,1,8,4,3,5,6,2]=>1011001=>1001101=>0110010
[6,7,3,1,8,4,5,2]=>0110101=>1010110=>0101001
[6,7,1,4,8,3,5,2]=>0100101=>1010010=>0101101
[6,7,4,1,3,8,2,5]=>0110010=>0100110=>1011001
[1,6,7,8,4,3,2,5]=>0001110=>0111000=>1000111
[7,2,1,8,4,5,3,6]=>1101010=>0101011=>1010100
[6,2,7,1,8,4,3,5]=>1010110=>0110101=>1001010
[6,2,7,8,4,3,1,5]=>1001110=>0111001=>1000110
[6,2,7,8,4,3,5,1]=>1001101=>1011001=>0100110
[2,6,7,4,8,3,5,1]=>0010101=>1010100=>0101011
[2,6,7,4,8,3,1,5]=>0010110=>0110100=>1001011
[7,8,1,3,6,2,4,5]=>0100100=>0010010=>1101101
[1,2,7,8,6,3,4,5]=>0001100=>0011000=>1100111
[2,6,7,1,8,5,3,4]=>0010110=>0110100=>1001011
[2,6,7,8,5,3,4,1]=>0001101=>1011000=>0100111
[6,2,7,8,4,5,3,1]=>1001011=>1101001=>0010110
[1,7,2,8,4,5,6,3]=>0101001=>1001010=>0110101
[6,3,7,8,1,5,2,4]=>1001010=>0101001=>1010110
[6,7,1,2,8,5,3,4]=>0100110=>0110010=>1001101
[1,6,7,8,4,2,5,3]=>0001101=>1011000=>0100111
[3,1,2,7,6,5,8,4]=>1001101=>1011001=>0100110
[6,1,2,4,7,3,8,5]=>1000101=>1010001=>0101110
[1,7,5,3,6,4,8,2]=>0110101=>1010110=>0101001
[5,1,2,6,7,4,8,3]=>1000101=>1010001=>0101110
[4,1,5,7,3,2,6,8]=>1001100=>0011001=>1100110
[4,6,1,7,3,2,5,8]=>0101100=>0011010=>1100101
[4,6,1,8,3,2,5,7]=>0101100=>0011010=>1100101
[4,1,7,8,6,2,3,5]=>1001100=>0011001=>1100110
[1,6,5,7,8,3,4,2]=>0100101=>1010010=>0101101
[1,6,5,8,7,3,4,2]=>0101101=>1011010=>0100101
[4,1,8,7,6,2,3,5]=>1011100=>0011101=>1100010
[4,8,1,7,3,5,2,6]=>0101010=>0101010=>1010101
[4,8,1,6,3,2,5,7]=>0101100=>0011010=>1100101
[4,7,1,6,3,2,5,8]=>0101100=>0011010=>1100101
[6,1,2,3,7,5,4,8]=>1000110=>0110001=>1001110
[6,8,1,5,3,7,2,4]=>0101010=>0101010=>1010101
[8,7,5,2,4,1,6,3]=>1110101=>1010111=>0101000
[1,5,8,3,4,7,6,2]=>0010011=>1100100=>0011011
[7,8,5,2,4,1,6,3]=>0110101=>1010110=>0101001
[7,1,2,3,5,6,4,8]=>1000010=>0100001=>1011110
[7,1,8,4,6,3,2,5]=>1010110=>0110101=>1001010
[6,8,2,4,3,1,5,7]=>0101100=>0011010=>1100101
[6,7,2,4,3,1,5,8]=>0101100=>0011010=>1100101
[3,7,1,8,6,4,2,5]=>0101110=>0111010=>1000101
[1,6,4,3,7,5,8,2]=>0110101=>1010110=>0101001
[3,1,2,6,7,5,8,4]=>1000101=>1010001=>0101110
[3,8,1,7,6,4,2,5]=>0101110=>0111010=>1000101
[7,6,2,4,3,1,5,8]=>1101100=>0011011=>1100100
[8,7,2,4,3,5,1,6]=>1101010=>0101011=>1010100
[8,1,7,4,6,3,2,5]=>1010110=>0110101=>1001010
[8,1,7,6,5,3,2,4]=>1011110=>0111101=>1000010
[1,5,7,3,4,6,8,2]=>0010001=>1000100=>0111011
[8,7,2,5,3,6,1,4]=>1101010=>0101011=>1010100
[7,1,2,3,5,4,8,6]=>1000101=>1010001=>0101110
[6,1,2,3,5,8,4,7]=>1000010=>0100001=>1011110
[6,1,2,3,5,7,4,8]=>1000010=>0100001=>1011110
[5,1,2,3,7,6,4,8]=>1000110=>0110001=>1001110
[5,1,2,3,8,6,4,7]=>1000110=>0110001=>1001110
[1,5,6,3,4,7,8,2]=>0010001=>1000100=>0111011
[8,6,5,2,4,7,1,3]=>1110010=>0100111=>1011000
[7,6,2,5,3,1,8,4]=>1101101=>1011011=>0100100
[6,7,3,5,1,4,8,2]=>0101001=>1001010=>0110101
[5,3,6,7,4,8,2,1]=>1001011=>1101001=>0010110
[5,3,2,8,6,7,4,1]=>1101011=>1101011=>0010100
[5,4,8,2,6,7,3,1]=>1010011=>1100101=>0011010
[5,4,8,6,2,7,3,1]=>1011011=>1101101=>0010010
[5,6,3,8,4,7,2,1]=>0101011=>1101010=>0010101
[6,7,3,8,5,2,4,1]=>0101101=>1011010=>0100101
[3,5,7,8,4,6,2,1]=>0001011=>1101000=>0010111
[5,7,8,2,4,6,3,1]=>0010011=>1100100=>0011011
[2,5,8,4,3,7,6,1]=>0011011=>1101100=>0010011
[3,7,4,8,6,2,1,5]=>0101110=>0111010=>1000101
[3,6,4,8,7,2,5,1]=>0101101=>1011010=>0100101
[3,5,4,8,2,7,6,1]=>0101011=>1101010=>0010101
[4,5,7,3,8,6,2,1]=>0010111=>1110100=>0001011
[6,3,1,8,7,5,4,2]=>1101111=>1111011=>0000100
[5,4,8,1,7,6,3,2]=>1010111=>1110101=>0001010
[5,8,4,1,7,6,3,2]=>0110111=>1110110=>0001001
[7,5,4,1,8,6,3,2]=>1110111=>1110111=>0001000
[8,5,4,1,7,6,3,2]=>1110111=>1110111=>0001000
[1,8,2,5,6,3,4,7]=>0100100=>0010010=>1101101
[7,2,8,4,5,1,3,6]=>1010100=>0010101=>1101010
[1,3,7,5,6,2,4,8]=>0010100=>0010100=>1101011
[1,6,7,4,3,5,2,8]=>0011010=>0101100=>1010011
[1,8,2,5,3,6,7,4]=>0101001=>1001010=>0110101
[2,6,8,4,3,5,7,1]=>0011001=>1001100=>0110011
[7,2,8,4,1,5,6,3]=>1011001=>1001101=>0110010
[7,5,8,1,2,6,3,4]=>1010010=>0100101=>1011010
[1,5,2,6,4,7,8,3]=>0101001=>1001010=>0110101
[1,5,4,6,2,3,7,8]=>0101000=>0001010=>1110101
[6,2,5,7,1,4,8,3]=>1001001=>1001001=>0110110
[6,5,4,3,8,1,7,2]=>1110101=>1010111=>0101000
[2,6,5,8,3,4,1,7]=>0101010=>0101010=>1010101
[2,6,5,7,3,4,1,8]=>0101010=>0101010=>1010101
[6,2,5,7,4,1,3,8]=>1001100=>0011001=>1100110
[6,2,5,8,4,1,3,7]=>1001100=>0011001=>1100110
[2,7,8,4,6,1,3,5]=>0010100=>0010100=>1101011
[6,1,2,8,5,4,7,3]=>1001101=>1011001=>0100110
[6,2,5,7,8,1,3,4]=>1000100=>0010001=>1101110
[1,5,4,2,6,7,3,8]=>0110010=>0100110=>1011001
[2,6,5,7,3,8,1,4]=>0101010=>0101010=>1010101
[1,6,2,7,5,8,4,3]=>0101011=>1101010=>0010101
[1,3,2,7,8,5,6,4]=>0100101=>1010010=>0101101
[1,6,2,4,8,7,3,5]=>0100110=>0110010=>1001101
[6,5,2,1,8,7,3,4]=>1110110=>0110111=>1001000
[2,6,5,3,7,8,4,1]=>0110011=>1100110=>0011001
[6,5,2,3,8,7,1,4]=>1100110=>0110011=>1001100
[5,1,4,2,3,7,8,6]=>1010001=>1000101=>0111010
[1,5,4,2,6,3,8,7]=>0110101=>1010110=>0101001
[5,1,6,3,8,2,7,4]=>1010101=>1010101=>0101010
[6,5,8,7,4,3,1,2]=>1011110=>0111101=>1000010
[6,4,2,7,8,5,1,3]=>1100110=>0110011=>1001100
[6,1,4,8,7,5,2,3]=>1001110=>0111001=>1000110
[1,6,4,8,7,5,2,3]=>0101110=>0111010=>1000101
[1,8,6,2,4,7,3,5]=>0110010=>0100110=>1011001
[8,1,6,2,4,7,3,5]=>1010010=>0100101=>1011010
[6,4,1,7,8,5,2,3]=>1100110=>0110011=>1001100
[7,6,1,2,4,8,3,5]=>1100010=>0100011=>1011100
[1,8,6,3,4,7,2,5]=>0110010=>0100110=>1011001
[1,7,2,5,4,8,3,6]=>0101010=>0101010=>1010101
[7,1,2,5,4,8,3,6]=>1001010=>0101001=>1010110
[2,7,1,5,4,8,3,6]=>0101010=>0101010=>1010101
[2,8,6,1,4,7,3,5]=>0110010=>0100110=>1011001
[7,2,1,5,4,8,3,6]=>1101010=>0101011=>1010100
[1,2,7,5,4,8,3,6]=>0011010=>0101100=>1010011
[3,2,7,5,4,8,1,6]=>1011010=>0101101=>1010010
[2,5,8,4,7,3,1,6]=>0010110=>0110100=>1001011
[2,3,7,5,4,8,1,6]=>0011010=>0101100=>1010011
[6,8,3,2,4,7,1,5]=>0110010=>0100110=>1011001
[3,7,2,5,4,8,1,6]=>0101010=>0101010=>1010101
[3,1,7,5,4,8,2,6]=>1011010=>0101101=>1010010
[1,3,7,5,4,8,2,6]=>0011010=>0101100=>1010011
[1,5,8,4,7,3,2,6]=>0010110=>0110100=>1001011
[5,1,8,4,7,3,2,6]=>1010110=>0110101=>1001010
[5,8,2,4,7,3,1,6]=>0100110=>0110010=>1001101
[6,8,4,3,7,5,1,2]=>0110110=>0110110=>1001001
[8,5,2,4,7,3,1,6]=>1100110=>0110011=>1001100
[8,1,5,4,7,3,2,6]=>1010110=>0110101=>1001010
[1,8,5,4,7,3,2,6]=>0110110=>0110110=>1001001
[1,7,3,5,4,8,2,6]=>0101010=>0101010=>1010101
[8,6,3,1,4,7,2,5]=>1110010=>0100111=>1011000
[8,6,4,1,7,2,5,3]=>1110101=>1010111=>0101000
[5,3,7,4,6,8,2,1]=>1010011=>1100101=>0011010
[4,1,3,2,7,8,5,6]=>1010010=>0100101=>1011010
[1,4,3,2,7,8,5,6]=>0110010=>0100110=>1011001
[2,4,3,1,7,8,5,6]=>0110010=>0100110=>1011001
[2,7,3,5,4,8,1,6]=>0101010=>0101010=>1010101
[2,8,5,4,7,3,1,6]=>0110110=>0110110=>1001001
[5,7,3,4,6,8,2,1]=>0100011=>1100010=>0011101
[8,2,5,4,7,3,1,6]=>1010110=>0110101=>1001010
[7,2,3,5,4,8,1,6]=>1001010=>0101001=>1010110
[3,2,1,4,7,8,5,6]=>1100010=>0100011=>1011100
[8,1,7,6,4,3,5,2]=>1011101=>1011101=>0100010
[8,6,4,5,2,7,1,3]=>1101010=>0101011=>1010100
[7,1,8,6,4,3,5,2]=>1011101=>1011101=>0100010
[7,4,2,5,1,6,3,8]=>1101010=>0101011=>1010100
[7,3,6,5,2,1,4,8]=>1011100=>0011101=>1100010
[8,3,6,5,2,1,7,4]=>1011101=>1011101=>0100010
[7,3,6,5,2,1,8,4]=>1011101=>1011101=>0100010
[5,4,2,8,1,3,7,6]=>1101001=>1001011=>0110100
[5,8,2,6,4,1,3,7]=>0101100=>0011010=>1100101
[6,4,2,5,1,8,3,7]=>1101010=>0101011=>1010100
[6,3,5,2,1,4,7,8]=>1011000=>0001101=>1110010
[2,3,5,8,1,4,7,6]=>0001001=>1001000=>0110111
[2,3,6,8,1,5,7,4]=>0001001=>1001000=>0110111
[6,3,8,5,2,7,1,4]=>1011010=>0101101=>1010010
[6,3,7,5,2,1,4,8]=>1011100=>0011101=>1100010
[2,5,7,6,3,1,4,8]=>0011100=>0011100=>1100011
[2,8,7,6,3,1,5,4]=>0111101=>1011110=>0100001
[2,5,8,7,6,3,1,4]=>0011110=>0111100=>1000011
[2,4,8,1,6,5,7,3]=>0010101=>1010100=>0101011
[2,8,7,3,6,1,4,5]=>0110100=>0010110=>1101001
[8,4,2,5,1,3,7,6]=>1101001=>1001011=>0110100
[2,3,6,8,1,4,7,5]=>0001001=>1001000=>0110111
[2,7,8,6,3,1,4,5]=>0011100=>0011100=>1100011
[2,8,6,3,1,4,5,7]=>0111000=>0001110=>1110001
[8,3,5,2,1,4,6,7]=>1011000=>0001101=>1110010
[2,5,8,1,7,3,6,4]=>0010101=>1010100=>0101011
[2,7,1,5,8,3,4,6]=>0100100=>0010010=>1101101
[3,7,5,8,1,2,6,4]=>0101001=>1001010=>0110101
[7,3,6,1,2,8,4,5]=>1010010=>0100101=>1011010
[7,4,8,1,6,5,2,3]=>1010110=>0110101=>1001010
[6,8,4,5,1,7,2,3]=>0101010=>0101010=>1010101
[5,1,8,7,6,2,3,4]=>1011100=>0011101=>1100010
[4,6,1,8,7,5,2,3]=>0101110=>0111010=>1000101
[3,4,8,7,1,2,5,6]=>0011000=>0001100=>1110011
[6,4,8,7,1,2,5,3]=>1011001=>1001101=>0110010
[6,5,1,8,2,7,3,4]=>1101010=>0101011=>1010100
[6,5,1,7,2,8,3,4]=>1101010=>0101011=>1010100
[6,5,1,7,2,3,8,4]=>1101001=>1001011=>0110100
[5,6,8,7,4,1,2,3]=>0011100=>0011100=>1100011
[6,8,3,1,5,2,4,7]=>0110100=>0010110=>1101001
[4,2,7,1,6,3,5,8]=>1010100=>0010101=>1101010
[5,1,7,4,2,6,3,8]=>1011010=>0101101=>1010010
[5,8,2,1,4,7,3,6]=>0110010=>0100110=>1011001
[6,8,4,3,1,5,7,2]=>0111001=>1001110=>0110001
[6,8,4,2,1,5,7,3]=>0111001=>1001110=>0110001
[6,8,3,2,1,4,5,7]=>0111000=>0001110=>1110001
[4,2,1,6,5,8,3,7]=>1101010=>0101011=>1010100
[6,3,2,1,7,4,5,8]=>1110100=>0010111=>1101000
[6,4,2,1,7,5,3,8]=>1110110=>0110111=>1001000
[5,3,2,7,6,1,4,8]=>1101100=>0011011=>1100100
[5,3,2,8,6,1,4,7]=>1101100=>0011011=>1100100
[6,3,2,8,7,1,4,5]=>1101100=>0011011=>1100100
[4,2,8,1,7,3,5,6]=>1010100=>0010101=>1101010
[4,3,8,7,2,1,5,6]=>1011100=>0011101=>1100010
[2,1,5,8,4,7,3,6]=>1001010=>0101001=>1010110
[4,3,2,5,8,1,6,7]=>1100100=>0010011=>1101100
[4,3,2,5,7,1,6,8]=>1100100=>0010011=>1101100
[4,3,1,6,2,7,5,8]=>1101010=>0101011=>1010100
[5,4,1,7,2,8,6,3]=>1101011=>1101011=>0010100
[3,2,1,4,8,7,5,6]=>1100110=>0110011=>1001100
[3,2,1,4,6,8,5,7]=>1100010=>0100011=>1011100
[8,6,1,4,5,7,2,3]=>1100010=>0100011=>1011100
[3,8,6,4,5,7,1,2]=>0110010=>0100110=>1011001
[5,2,8,3,7,4,6,1]=>1010101=>1010101=>0101010
[6,2,8,5,4,7,3,1]=>1011011=>1101101=>0010010
[5,2,8,4,3,6,7,1]=>1011001=>1001101=>0110010
[5,4,2,7,3,6,1,8]=>1101010=>0101011=>1010100
[5,4,2,8,3,6,1,7]=>1101010=>0101011=>1010100
[6,5,3,8,4,7,2,1]=>1101011=>1101011=>0010100
[5,2,8,4,3,7,1,6]=>1011010=>0101101=>1010010
[6,2,8,3,7,4,1,5]=>1010110=>0110101=>1001010
[5,4,2,7,3,1,8,6]=>1101101=>1011011=>0100100
[6,4,3,7,1,2,8,5]=>1101001=>1001011=>0110100
[6,4,3,8,1,2,7,5]=>1101001=>1001011=>0110100
[7,2,8,4,3,1,5,6]=>1011100=>0011101=>1100010
[7,5,3,8,4,2,6,1]=>1101101=>1011011=>0100100
[6,4,2,7,3,1,5,8]=>1101100=>0011011=>1100100
[7,6,4,8,2,3,5,1]=>1101001=>1001011=>0110100
[5,3,1,7,8,4,6,2]=>1100101=>1010011=>0101100
[5,3,2,7,8,4,6,1]=>1100101=>1010011=>0101100
[6,5,1,7,8,2,3,4]=>1100100=>0010011=>1101100
[6,3,1,7,8,4,2,5]=>1100110=>0110011=>1001100
[5,4,1,7,3,8,2,6]=>1101010=>0101011=>1010100
[6,3,2,7,8,4,1,5]=>1100110=>0110011=>1001100
[6,1,5,4,3,2,8,7]=>1011101=>1011101=>0100010
[8,7,6,1,3,5,2,4]=>1110010=>0100111=>1011000
[8,1,6,5,7,3,4,2]=>1010101=>1010101=>0101010
[8,4,1,5,7,6,2,3]=>1100110=>0110011=>1001100
[7,8,6,2,5,3,1,4]=>0110110=>0110110=>1001001
[6,1,3,5,2,8,4,7]=>1001010=>0101001=>1010110
[8,1,3,7,4,2,5,6]=>1001100=>0011001=>1100110
[4,3,8,7,5,2,1,6]=>1011110=>0111101=>1000010
[6,7,1,8,5,3,4,2]=>0101101=>1011010=>0100101
[2,7,6,4,8,3,5,1]=>0110101=>1010110=>0101001
[6,5,2,7,1,4,8,3]=>1101001=>1001011=>0110100
[7,4,6,1,3,2,8,5]=>1010101=>1010101=>0101010
[7,5,2,1,3,8,4,6]=>1110010=>0100111=>1011000
[8,4,7,6,3,1,5,2]=>1011101=>1011101=>0100010
[7,4,1,5,6,3,8,2]=>1100101=>1010011=>0101100
[3,4,7,5,6,1,8,2]=>0010101=>1010100=>0101011
[2,7,6,1,3,4,8,5]=>0110001=>1000110=>0111001
[5,7,2,1,6,3,8,4]=>0110101=>1010110=>0101001
[4,7,2,5,6,3,8,1]=>0100101=>1010010=>0101101
[8,6,2,5,7,1,4,3]=>1100101=>1010011=>0101100
[2,7,4,5,3,8,1,6]=>0101010=>0101010=>1010101
[6,8,7,1,3,2,5,4]=>0110101=>1010110=>0101001
[2,8,6,5,7,1,4,3]=>0110101=>1010110=>0101001
[5,8,4,3,2,6,7,1]=>0111001=>1001110=>0110001
[1,8,5,6,2,4,7,3]=>0101001=>1001010=>0110101
[8,1,5,6,2,4,7,3]=>1001001=>1001001=>0110110
[6,4,8,1,3,2,7,5]=>1010101=>1010101=>0101010
[5,4,1,2,8,6,7,3]=>1100101=>1010011=>0101100
[8,4,5,2,1,6,7,3]=>1011001=>1001101=>0110010
[3,1,2,6,8,4,7,5]=>1000101=>1010001=>0101110
[5,1,3,2,7,8,4,6]=>1010010=>0100101=>1011010
[4,6,7,8,3,1,5,2]=>0001101=>1011000=>0100111
[5,2,8,6,3,4,7,1]=>1011001=>1001101=>0110010
[5,6,8,4,3,2,7,1]=>0011101=>1011100=>0100011
[5,3,8,1,7,2,4,6]=>1010100=>0010101=>1101010
[3,6,7,8,4,2,1,5]=>0001110=>0111000=>1000111
[6,5,1,8,4,3,7,2]=>1101101=>1011011=>0100100
[6,3,8,4,2,1,7,5]=>1011101=>1011101=>0100010
[2,5,8,3,1,6,7,4]=>0011001=>1001100=>0110011
[3,5,8,1,2,6,7,4]=>0010001=>1000100=>0111011
[3,2,7,8,4,6,1,5]=>1001010=>0101001=>1010110
[5,1,8,3,4,6,7,2]=>1010001=>1000101=>0111010
[4,8,7,2,1,6,3,5]=>0111010=>0101110=>1010001
[2,8,1,6,3,4,7,5]=>0101001=>1001010=>0110101
[3,6,1,2,5,8,4,7]=>0100010=>0100010=>1011101
[1,4,5,8,2,3,7,6]=>0001001=>1001000=>0110111
[1,5,2,4,6,8,3,7]=>0100010=>0100010=>1011101
[3,6,1,5,8,2,4,7]=>0100100=>0010010=>1101101
[2,6,5,1,4,8,3,7]=>0110010=>0100110=>1011001
[2,5,1,8,4,7,3,6]=>0101010=>0101010=>1010101
[2,7,1,4,3,6,8,5]=>0101001=>1001010=>0110101
[1,3,7,5,8,2,4,6]=>0010100=>0010100=>1101011
[8,2,1,5,7,3,4,6]=>1100100=>0010011=>1101100
[2,5,4,8,1,3,7,6]=>0101001=>1001010=>0110101
[2,4,1,3,8,6,7,5]=>0100101=>1010010=>0101101
[8,4,3,7,1,2,6,5]=>1101001=>1001011=>0110100
[1,7,3,5,8,2,6,4]=>0100101=>1010010=>0101101
[1,8,4,2,6,7,3,5]=>0110010=>0100110=>1011001
[3,1,6,8,7,2,4,5]=>1001100=>0011001=>1100110
[7,2,1,6,8,3,4,5]=>1100100=>0010011=>1101100
[4,1,7,2,6,8,3,5]=>1010010=>0100101=>1011010
[5,1,7,2,3,6,8,4]=>1010001=>1000101=>0111010
[7,2,1,6,3,5,8,4]=>1101001=>1001011=>0110100
[2,6,1,7,3,5,8,4]=>0101001=>1001010=>0110101
[8,1,3,2,4,6,7,5]=>1010001=>1000101=>0111010
[7,3,1,2,4,6,8,5]=>1100001=>1000011=>0111100
[1,8,3,4,7,2,5,6]=>0100100=>0010010=>1101101
[3,5,8,1,2,7,4,6]=>0010010=>0100100=>1011011
[3,6,8,1,2,4,7,5]=>0010001=>1000100=>0111011
[4,1,3,8,7,2,6,5]=>1001101=>1011001=>0100110
[1,3,7,4,8,2,6,5]=>0010101=>1010100=>0101011
[1,4,6,8,2,3,7,5]=>0001001=>1001000=>0110111
[3,5,8,1,7,2,4,6]=>0010100=>0010100=>1101011
[2,6,8,1,7,3,4,5]=>0010100=>0010100=>1101011
[1,8,3,2,7,5,6,4]=>0110101=>1010110=>0101001
[2,6,7,3,8,1,5,4]=>0010101=>1010100=>0101011
[8,4,1,7,3,6,2,5]=>1101010=>0101011=>1010100
[3,7,2,8,6,1,5,4]=>0101101=>1011010=>0100101
[6,2,3,8,7,1,5,4]=>1001101=>1011001=>0100110
[5,1,7,8,4,2,6,3]=>1001101=>1011001=>0100110
[5,1,8,7,4,2,6,3]=>1011101=>1011101=>0100010
[4,7,2,8,3,6,5,1]=>0101011=>1101010=>0010101
[4,1,7,8,5,3,6,2]=>1001101=>1011001=>0100110
[5,1,7,4,8,3,6,2]=>1010101=>1010101=>0101010
[4,1,8,7,5,3,6,2]=>1011101=>1011101=>0100010
[4,8,2,7,3,6,5,1]=>0101011=>1101010=>0010101
[4,7,2,6,3,5,8,1]=>0101001=>1001010=>0110101
[6,8,2,4,3,7,5,1]=>0101011=>1101010=>0010101
[6,7,2,4,3,8,5,1]=>0101011=>1101010=>0010101
[3,8,7,2,4,1,5,6]=>0110100=>0010110=>1101001
[3,7,8,2,4,1,5,6]=>0010100=>0010100=>1101011
[3,6,8,2,4,5,7,1]=>0010001=>1000100=>0111011
[3,6,7,2,4,5,8,1]=>0010001=>1000100=>0111011
[1,7,5,3,8,2,4,6]=>0110100=>0010110=>1101001
[1,7,2,4,5,8,3,6]=>0100010=>0100010=>1011101
[1,7,4,5,8,3,2,6]=>0100110=>0110010=>1001101
[2,6,4,7,8,3,5,1]=>0100101=>1010010=>0101101
[1,2,6,4,7,8,3,5]=>0010010=>0100100=>1011011
[2,7,4,5,8,1,3,6]=>0100100=>0010010=>1101101
[2,7,5,3,1,8,4,6]=>0111010=>0101110=>1010001
[6,1,4,7,8,3,5,2]=>1000101=>1010001=>0101110
[3,6,4,7,8,1,5,2]=>0100101=>1010010=>0101101
[4,3,6,7,1,8,5,2]=>1001011=>1101001=>0010110
[4,3,6,7,1,8,2,5]=>1001010=>0101001=>1010110
[3,7,4,5,2,1,8,6]=>0101101=>1011010=>0100101
[1,3,6,4,7,2,8,5]=>0010101=>1010100=>0101011
[3,6,4,7,2,8,5,1]=>0101011=>1101010=>0010101
[6,1,7,3,8,2,5,4]=>1010101=>1010101=>0101010
[1,6,7,3,8,2,5,4]=>0010101=>1010100=>0101011
[6,1,4,7,8,5,2,3]=>1000110=>0110001=>1001110
[6,3,2,1,7,8,5,4]=>1110011=>1100111=>0011000
[6,2,7,3,1,8,5,4]=>1011011=>1101101=>0010010
[6,2,4,7,8,1,5,3]=>1000101=>1010001=>0101110
[2,6,7,3,1,8,5,4]=>0011011=>1101100=>0010011
[8,6,5,1,3,2,4,7]=>1110100=>0010111=>1101000
[6,4,7,8,3,2,5,1]=>1001101=>1011001=>0100110
[3,8,4,7,1,2,5,6]=>0101000=>0001010=>1110101
[4,8,6,1,5,3,2,7]=>0110110=>0110110=>1001001
[5,8,6,4,1,3,2,7]=>0111010=>0101110=>1010001
[8,3,6,4,5,2,1,7]=>1010110=>0110101=>1001010
[6,8,5,7,4,2,3,1]=>0101101=>1011010=>0100101
[2,3,8,7,1,6,4,5]=>0011010=>0101100=>1010011
[4,3,7,8,1,6,2,5]=>1001010=>0101001=>1010110
[3,5,8,7,4,1,2,6]=>0011100=>0011100=>1100011
[7,3,8,4,1,2,5,6]=>1011000=>0001101=>1110010
[4,8,1,2,7,3,5,6]=>0100100=>0010010=>1101101
[6,8,1,2,7,4,5,3]=>0100101=>1010010=>0101101
[5,6,8,4,1,3,7,2]=>0011001=>1001100=>0110011
[8,5,4,7,1,6,3,2]=>1101011=>1101011=>0010100
[2,5,8,7,3,6,4,1]=>0011011=>1101100=>0010011
[2,4,8,7,5,6,1,3]=>0011010=>0101100=>1010011
[3,7,4,8,5,6,2,1]=>0101011=>1101010=>0010101
[6,4,8,7,5,1,2,3]=>1011100=>0011101=>1100010
[3,8,5,2,4,6,7,1]=>0110001=>1000110=>0111001
[5,7,1,8,4,6,2,3]=>0101010=>0101010=>1010101
[6,3,8,7,2,1,4,5]=>1011100=>0011101=>1100010
[2,3,7,8,5,6,1,4]=>0001010=>0101000=>1010111
[3,7,6,8,5,1,2,4]=>0101100=>0011010=>1100101
[2,6,7,8,5,1,3,4]=>0001100=>0011000=>1100111
[2,4,7,8,1,6,3,5]=>0001010=>0101000=>1010111
[5,4,7,8,2,6,3,1]=>1001011=>1101001=>0010110
[2,8,3,4,1,5,7,6]=>0101001=>1001010=>0110101
[6,8,3,4,1,2,7,5]=>0101001=>1001010=>0110101
[6,8,7,1,5,2,3,4]=>0110100=>0010110=>1101001
[2,5,3,1,8,6,7,4]=>0110101=>1010110=>0101001
[4,5,3,2,8,6,7,1]=>0110101=>1010110=>0101001
[3,5,8,6,1,4,7,2]=>0011001=>1001100=>0110011
[2,8,5,6,1,4,7,3]=>0101001=>1001010=>0110101
[4,8,6,1,5,2,7,3]=>0110101=>1010110=>0101001
[5,8,2,3,7,6,1,4]=>0100110=>0110010=>1001101
[4,6,8,5,3,2,7,1]=>0011101=>1011100=>0100011
[2,6,4,8,5,1,7,3]=>0101101=>1011010=>0100101
[7,6,4,8,5,2,1,3]=>1101110=>0111011=>1000100
[3,4,8,6,5,2,7,1]=>0011101=>1011100=>0100011
[3,4,8,7,5,6,2,1]=>0011011=>1101100=>0010011
[7,5,3,2,8,6,1,4]=>1110110=>0110111=>1001000
[2,5,1,3,8,6,7,4]=>0100101=>1010010=>0101101
[4,5,1,2,8,6,7,3]=>0100101=>1010010=>0101101
[5,4,8,1,3,6,7,2]=>1010001=>1000101=>0111010
[8,3,5,4,1,6,7,2]=>1011001=>1001101=>0110010
[5,1,6,4,3,2,8,7]=>1011101=>1011101=>0100010
[8,3,7,1,4,6,5,2]=>1010011=>1100101=>0011010
[2,8,3,6,4,7,5,1]=>0101011=>1101010=>0010101
[6,2,1,7,5,8,3,4]=>1101010=>0101011=>1010100
[6,7,2,1,5,8,4,3]=>0110011=>1100110=>0011001
[1,6,4,8,3,2,5,7]=>0101100=>0011010=>1100101
[1,8,3,5,6,2,4,7]=>0100100=>0010010=>1101101
[1,4,8,5,6,2,3,7]=>0010100=>0010100=>1101011
[6,1,4,8,2,3,5,7]=>1001000=>0001001=>1110110
[8,7,2,5,6,1,4,3]=>1100101=>1010011=>0101100
[1,8,2,5,4,7,3,6]=>0101010=>0101010=>1010101
[5,7,4,1,2,3,8,6]=>0110001=>1000110=>0111001
[1,7,4,2,5,3,8,6]=>0110101=>1010110=>0101001
[6,7,4,2,1,3,8,5]=>0111001=>1001110=>0110001
[6,4,3,8,5,7,1,2]=>1101010=>0101011=>1010100
[6,8,4,2,3,1,5,7]=>0110100=>0010110=>1101001
[8,6,4,1,3,7,2,5]=>1110010=>0100111=>1011000
[5,3,6,1,8,2,4,7]=>1010100=>0010101=>1101010
[3,1,8,5,4,7,6,2]=>1011011=>1101101=>0010010
[4,1,5,8,3,7,6,2]=>1001011=>1101001=>0010110
[4,1,5,3,8,7,6,2]=>1010111=>1110101=>0001010
[4,5,1,8,2,7,6,3]=>0101011=>1101010=>0010101
[4,8,5,3,1,7,6,2]=>0111011=>1101110=>0010001
[4,5,2,8,1,7,6,3]=>0101011=>1101010=>0010101
[4,6,2,8,7,1,5,3]=>0101101=>1011010=>0100101
[4,8,6,3,7,1,5,2]=>0110101=>1010110=>0101001
[4,6,8,2,7,5,1,3]=>0010110=>0110100=>1001011
[4,6,2,8,7,5,1,3]=>0101110=>0111010=>1000101
[5,6,2,7,4,1,8,3]=>0101101=>1011010=>0100101
[5,6,7,2,3,1,8,4]=>0010101=>1010100=>0101011
[5,6,7,2,8,3,1,4]=>0010110=>0110100=>1001011
[5,6,7,2,1,8,3,4]=>0011010=>0101100=>1010011
[5,6,7,2,1,3,8,4]=>0011001=>1001100=>0110011
[5,6,1,7,8,2,4,3]=>0100101=>1010010=>0101101
[5,6,1,7,2,4,8,3]=>0101001=>1001010=>0110101
[4,1,6,8,7,3,5,2]=>1001101=>1011001=>0100110
[4,1,6,8,7,5,3,2]=>1001111=>1111001=>0000110
[5,6,1,7,8,4,2,3]=>0100110=>0110010=>1001101
[4,6,8,1,7,5,2,3]=>0010110=>0110100=>1001011
[4,8,6,1,7,5,3,2]=>0110111=>1110110=>0001001
[5,6,7,1,8,3,2,4]=>0010110=>0110100=>1001011
[5,6,7,1,3,8,2,4]=>0010010=>0100100=>1011011
[5,6,7,1,3,2,8,4]=>0010101=>1010100=>0101011
[5,6,7,3,1,2,8,4]=>0011001=>1001100=>0110011
[5,6,8,7,4,2,1,3]=>0011110=>0111100=>1000011
[7,8,1,3,5,6,2,4]=>0100010=>0100010=>1011101
[7,8,3,1,5,6,2,4]=>0110010=>0100110=>1011001
[7,1,3,8,5,6,2,4]=>1001010=>0101001=>1010110
[5,1,7,8,3,4,6,2]=>1001001=>1001001=>0110110
[1,5,7,8,3,4,6,2]=>0001001=>1001000=>0110111
[3,7,1,5,8,6,2,4]=>0100110=>0110010=>1001101
[1,3,7,8,2,5,6,4]=>0001001=>1001000=>0110111
[3,1,7,8,5,2,6,4]=>1001101=>1011001=>0100110
[1,3,7,5,8,2,6,4]=>0010101=>1010100=>0101011
[3,1,7,5,8,2,6,4]=>1010101=>1010101=>0101010
[3,5,7,1,8,4,6,2]=>0010101=>1010100=>0101011
[3,5,7,8,1,4,6,2]=>0001001=>1001000=>0110111
[5,3,7,8,4,6,1,2]=>1001010=>0101001=>1010110
[5,3,7,8,4,1,6,2]=>1001101=>1011001=>0100110
[5,3,7,8,1,4,6,2]=>1001001=>1001001=>0110110
[5,3,7,1,8,4,6,2]=>1010101=>1010101=>0101010
[1,5,3,7,8,4,2,6]=>0100110=>0110010=>1001101
[5,1,3,7,8,4,2,6]=>1000110=>0110001=>1001110
[3,6,2,1,4,5,8,7]=>0110001=>1000110=>0111001
[6,4,2,5,1,3,8,7]=>1101001=>1001011=>0110100
[8,6,1,7,3,2,4,5]=>1101100=>0011011=>1100100
[2,5,8,1,7,3,4,6]=>0010100=>0010100=>1101011
[6,8,2,7,3,1,4,5]=>0101100=>0011010=>1100101
[6,8,2,3,7,1,4,5]=>0100100=>0010010=>1101101
[8,6,2,7,4,5,1,3]=>1101010=>0101011=>1010100
[5,2,8,1,7,3,4,6]=>1010100=>0010101=>1101010
[4,2,3,8,1,5,6,7]=>1001000=>0001001=>1110110
[5,2,8,3,7,1,4,6]=>1010100=>0010101=>1101010
[5,2,8,4,6,1,3,7]=>1010100=>0010101=>1101010
[2,1,5,8,4,3,6,7]=>1001100=>0011001=>1100110
[5,8,3,2,7,1,4,6]=>0110100=>0010110=>1101001
[4,1,3,8,2,5,6,7]=>1001000=>0001001=>1110110
[5,1,8,3,7,2,4,6]=>1010100=>0010101=>1101010
[5,1,8,4,6,2,3,7]=>1010100=>0010101=>1101010
[5,8,4,1,6,2,3,7]=>0110100=>0010110=>1101001
[4,5,8,1,6,2,3,7]=>0010100=>0010100=>1101011
[5,4,8,1,6,2,3,7]=>1010100=>0010101=>1101010
[4,8,5,1,6,2,3,7]=>0110100=>0010110=>1101001
[2,1,5,4,8,3,6,7]=>1010100=>0010101=>1101010
[2,4,3,8,1,5,6,7]=>0101000=>0001010=>1110101
[3,1,8,4,2,5,6,7]=>1011000=>0001101=>1110010
[3,8,4,2,1,5,6,7]=>0111000=>0001110=>1110001
[2,3,8,4,1,5,6,7]=>0011000=>0001100=>1110011
[3,4,2,8,1,5,6,7]=>0101000=>0001010=>1110101
[3,8,5,2,7,1,4,6]=>0110100=>0010110=>1101001
[4,8,5,2,6,1,3,7]=>0110100=>0010110=>1101001
[2,1,4,8,5,3,6,7]=>1001100=>0011001=>1100110
[3,2,8,4,1,5,6,7]=>1011000=>0001101=>1110010
[2,8,4,3,1,5,6,7]=>0111000=>0001110=>1110001
[4,1,7,5,6,2,8,3]=>1010101=>1010101=>0101010
[5,7,4,3,8,1,6,2]=>0110101=>1010110=>0101001
[5,7,4,3,8,2,6,1]=>0110101=>1010110=>0101001
[3,8,4,2,6,7,5,1]=>0110011=>1100110=>0011001
[3,8,4,1,6,7,5,2]=>0110011=>1100110=>0011001
[6,1,7,5,2,8,4,3]=>1011011=>1101101=>0010010
[5,6,4,3,2,8,1,7]=>0111010=>0101110=>1010001
[2,6,7,5,3,8,4,1]=>0011011=>1101100=>0010011
[2,1,6,7,5,3,8,4]=>1001101=>1011001=>0100110
[3,8,4,2,1,6,7,5]=>0111001=>1001110=>0110001
[5,7,4,3,8,2,1,6]=>0110110=>0110110=>1001001
[6,7,4,8,1,2,5,3]=>0101001=>1001010=>0110101
[6,7,5,8,1,2,4,3]=>0101001=>1001010=>0110101
[6,7,4,8,3,1,2,5]=>0101100=>0011010=>1100101
[6,1,3,4,8,2,5,7]=>1000100=>0010001=>1101110
[6,2,3,4,8,1,5,7]=>1000100=>0010001=>1101110
[3,4,8,2,1,5,7,6]=>0011001=>1001100=>0110011
[6,7,5,8,3,1,4,2]=>0101101=>1011010=>0100101
[2,5,7,6,1,4,8,3]=>0011001=>1001100=>0110011
[6,7,4,8,2,3,5,1]=>0101001=>1001010=>0110101
[6,7,4,8,1,3,5,2]=>0101001=>1001010=>0110101
[2,6,7,5,1,3,8,4]=>0011001=>1001100=>0110011
[6,3,1,4,8,2,5,7]=>1100100=>0010011=>1101100
[6,7,4,8,1,3,2,5]=>0101010=>0101010=>1010101
[6,7,5,8,4,1,3,2]=>0101101=>1011010=>0100101
[6,7,4,8,2,1,3,5]=>0101100=>0011010=>1100101
[6,7,4,8,1,2,3,5]=>0101000=>0001010=>1110101
[7,8,3,2,6,1,4,5]=>0110100=>0010110=>1101001
[3,4,8,2,6,1,7,5]=>0010101=>1010100=>0101011
[7,8,4,1,5,6,3,2]=>0110011=>1100110=>0011001
[7,8,1,2,6,3,4,5]=>0100100=>0010010=>1101101
[7,8,5,1,4,6,3,2]=>0110011=>1100110=>0011001
[5,3,8,4,1,6,7,2]=>1011001=>1001101=>0110010
[6,2,4,8,1,5,3,7]=>1001010=>0101001=>1010110
[3,4,8,5,1,6,7,2]=>0011001=>1001100=>0110011
[5,3,8,1,4,6,7,2]=>1010001=>1000101=>0111010
[4,2,6,8,1,5,3,7]=>1001010=>0101001=>1010110
[7,4,2,8,1,5,3,6]=>1101010=>0101011=>1010100
[6,1,7,5,8,4,3,2]=>1010111=>1110101=>0001010
[1,2,7,8,5,3,4,6]=>0001100=>0011000=>1100111
[6,3,7,8,5,4,1,2]=>1001110=>0111001=>1000110
[6,1,5,7,8,4,3,2]=>1000111=>1110001=>0001110
[1,7,5,6,8,4,3,2]=>0100111=>1110010=>0001101
[3,1,8,4,5,6,7,2]=>1010001=>1000101=>0111010
[4,2,1,8,6,5,3,7]=>1101110=>0111011=>1000100
[3,2,7,8,5,1,4,6]=>1001100=>0011001=>1100110
[2,3,7,8,5,1,4,6]=>0001100=>0011000=>1100111
[2,7,3,8,5,1,4,6]=>0101100=>0011010=>1100101
[3,6,2,8,5,1,4,7]=>0101100=>0011010=>1100101
[1,4,2,8,7,5,3,6]=>0101110=>0111010=>1000101
[7,3,6,8,5,4,1,2]=>1001110=>0111001=>1000110
[7,2,1,8,5,3,4,6]=>1101100=>0011011=>1100100
[1,2,6,8,4,5,3,7]=>0001010=>0101000=>1010111
[7,1,6,5,8,4,3,2]=>1010111=>1110101=>0001010
[6,5,7,1,8,4,3,2]=>1010111=>1110101=>0001010
[5,7,6,1,8,4,3,2]=>0110111=>1110110=>0001001
[6,7,1,5,8,4,3,2]=>0100111=>1110010=>0001101
[7,1,2,8,4,5,3,6]=>1001010=>0101001=>1010110
[7,6,1,5,8,4,3,2]=>1100111=>1110011=>0001100
[7,5,6,1,8,4,3,2]=>1010111=>1110101=>0001010
[9,10,7,8,5,6,2,1,3,4]=>010101100=>001101010=>110010101
[9,10,7,8,4,3,5,6,1,2]=>010110010=>010011010=>101100101
[9,10,7,8,4,2,5,1,3,6]=>010110100=>001011010=>110100101
[9,10,7,8,3,2,1,4,5,6]=>010111000=>000111010=>111000101
[9,10,6,5,7,8,3,4,1,2]=>011001010=>010100110=>101011001
[9,10,6,5,7,8,2,1,3,4]=>011001100=>001100110=>110011001
[9,10,6,4,7,3,5,8,1,2]=>011010010=>010010110=>101101001
[9,10,6,4,7,2,5,1,3,8]=>011010100=>001010110=>110101001
[9,10,6,3,7,2,1,4,5,8]=>011011000=>000110110=>111001001
[9,10,5,4,3,6,7,8,1,2]=>011100010=>010001110=>101110001
[9,10,5,4,2,6,7,1,3,8]=>011100100=>001001110=>110110001
[9,10,5,3,2,6,1,4,7,8]=>011101000=>000101110=>111010001
[9,10,4,3,2,1,5,6,7,8]=>011110000=>000011110=>111100001
[8,7,9,10,5,6,3,4,1,2]=>100101010=>010101001=>101010110
[8,7,9,10,5,6,2,1,3,4]=>100101100=>001101001=>110010110
[8,7,9,10,4,3,5,6,1,2]=>100110010=>010011001=>101100110
[8,7,9,10,4,2,5,1,3,6]=>100110100=>001011001=>110100110
[8,7,9,10,3,2,1,4,5,6]=>100111000=>000111001=>111000110
[8,6,9,5,7,10,3,4,1,2]=>101001010=>010100101=>101011010
[8,6,9,5,7,10,2,1,3,4]=>101001100=>001100101=>110011010
[8,6,9,4,7,3,5,10,1,2]=>101010010=>010010101=>101101010
[8,6,9,3,7,2,1,4,5,10]=>101011000=>000110101=>111001010
[8,5,9,4,3,6,7,10,1,2]=>101100010=>010001101=>101110010
[8,5,9,4,2,6,7,1,3,10]=>101100100=>001001101=>110110010
[8,5,9,3,2,6,1,4,7,10]=>101101000=>000101101=>111010010
[8,4,9,3,2,1,5,6,7,10]=>101110000=>000011101=>111100010
[7,6,5,8,9,10,3,4,1,2]=>110001010=>010100011=>101011100
[7,6,5,8,9,10,2,1,3,4]=>110001100=>001100011=>110011100
[7,6,4,8,9,3,5,10,1,2]=>110010010=>010010011=>101101100
[7,6,4,8,9,2,5,1,3,10]=>110010100=>001010011=>110101100
[7,6,3,8,9,2,1,4,5,10]=>110011000=>000110011=>111001100
[7,5,4,8,3,6,9,10,1,2]=>110100010=>010001011=>101110100
[7,5,4,8,2,6,9,1,3,10]=>110100100=>001001011=>110110100
[7,4,3,8,2,1,5,6,9,10]=>110110000=>000011011=>111100100
[6,5,4,2,7,8,9,1,3,10]=>111000100=>001000111=>110111000
[6,5,3,2,7,8,1,4,9,10]=>111001000=>000100111=>111011000
[11,12,7,5,3,8,2,6,1,4,9,10]=>01110101000=>00010101110=>11101010001
[10,9,11,12,6,4,7,2,5,1,3,8]=>10011010100=>00101011001=>11010100110
[10,8,11,6,9,4,7,2,5,1,3,12]=>10101010100=>00101010101=>11010101010
[9,7,5,10,3,8,2,6,1,4,11,12]=>11010101000=>00010101011=>11101010100
[8,6,5,3,9,2,7,10,1,4,11,12]=>11101001000=>00010010111=>11101101000
[7,1,6,5,3,2,4,8]=>1011100=>0011101=>1100010
[1,8,7,5,3,2,4,6]=>0111100=>0011110=>1100001
[1,8,7,4,2,5,3,6]=>0111010=>0101110=>1010001
[8,7,4,2,5,3,6,1]=>1110101=>1010111=>0101000
[7,1,6,4,2,5,3,8]=>1011010=>0101101=>1010010
[2,6,5,4,7,1,3,8]=>0110100=>0010110=>1101001
[7,1,5,3,6,4,2,8]=>1010110=>0110101=>1001010
[5,3,7,1,6,4,2,8]=>1010110=>0110101=>1001010
[5,3,6,4,2,7,1,8]=>1011010=>0101101=>1010010
[1,5,3,8,7,4,2,6]=>0101110=>0111010=>1000101
[7,4,2,8,6,3,5,1]=>1101101=>1011011=>0100100
[5,3,6,1,8,7,4,2]=>1010111=>1110101=>0001010
[6,1,5,3,8,7,4,2]=>1010111=>1110101=>0001010
[2,8,7,5,4,6,1,3]=>0111010=>0101110=>1010001
[2,3,1,8,7,5,4,6]=>0101110=>0111010=>1000101
[7,4,2,1,8,6,3,5]=>1110110=>0110111=>1001000
[1,8,6,3,5,7,4,2]=>0110011=>1100110=>0011001
[6,3,8,5,2,1,7,4]=>1011101=>1011101=>0100010
[8,6,3,7,4,2,1,5]=>1101110=>0111011=>1000100
[2,8,6,4,7,5,1,3]=>0110110=>0110110=>1001001
[5,1,8,6,3,7,4,2]=>1011011=>1101101=>0010010
[6,3,7,4,1,8,5,2]=>1011011=>1101101=>0010010
[8,5,2,6,3,7,4,1]=>1101011=>1101011=>0010100
[6,1,8,7,4,2,5,3]=>1011101=>1011101=>0100010
[8,6,3,7,4,2,5,1]=>1101101=>1011011=>0100100
[1,8,6,3,2,4,7,5]=>0111001=>1001110=>0110001
[8,6,3,2,4,7,5,1]=>1110011=>1100111=>0011000
[7,5,1,8,6,3,2,4]=>1101110=>0111011=>1000100
[6,1,8,7,5,3,2,4]=>1011110=>0111101=>1000010
[2,4,5,1,3,8,7,6]=>0010011=>1100100=>0011011
[1,7,5,8,6,3,2,4]=>0101110=>0111010=>1000101
[1,7,4,2,5,8,6,3]=>0110011=>1100110=>0011001
[8,6,3,1,7,4,2,5]=>1110110=>0110111=>1001000
[8,7,4,2,5,3,1,6]=>1110110=>0110111=>1001000
[5,3,1,8,7,4,2,6]=>1101110=>0111011=>1000100
[4,1,8,7,5,3,2,6]=>1011110=>0111101=>1000010
[2,8,6,4,1,3,7,5]=>0111001=>1001110=>0110001
[4,1,8,6,3,2,7,5]=>1011101=>1011101=>0100010
[7,4,2,8,6,3,1,5]=>1101110=>0111011=>1000100
[6,3,1,8,5,2,7,4]=>1101101=>1011011=>0100100
[8,5,2,6,3,1,7,4]=>1101101=>1011011=>0100100
[7,4,8,5,2,6,3,1]=>1011011=>1101101=>0010010
[1,8,5,2,7,4,6,3]=>0110101=>1010110=>0101001
[7,4,6,3,1,8,5,2]=>1011011=>1101101=>0010010
[6,3,1,7,4,8,5,2]=>1101011=>1101011=>0010100
[4,1,7,5,8,6,3,2]=>1010111=>1110101=>0001010
[2,3,1,7,5,8,6,4]=>0101011=>1101010=>0010101
[7,4,8,5,2,1,6,3]=>1011101=>1011101=>0100010
[1,7,4,6,3,8,5,2]=>0101011=>1101010=>0010101
[3,6,5,2,1,4,8,7]=>0111001=>1001110=>0110001
[3,5,6,2,1,4,8,7]=>0011001=>1001100=>0110011
[3,5,7,8,1,4,2,6]=>0001010=>0101000=>1010111
[4,1,8,5,7,3,2,6]=>1010110=>0110101=>1001010
[4,1,7,5,8,3,2,6]=>1010110=>0110101=>1001010
[2,1,5,8,7,4,3,6]=>1001110=>0111001=>1000110
[5,1,7,4,8,3,2,6]=>1010110=>0110101=>1001010
[4,7,2,8,3,6,1,5]=>0101010=>0101010=>1010101
[4,6,2,7,3,1,8,5]=>0101101=>1011010=>0100101
[3,7,8,2,4,1,6,5]=>0010101=>1010100=>0101011
[3,8,7,2,4,1,6,5]=>0110101=>1010110=>0101001
[3,8,6,2,4,1,7,5]=>0110101=>1010110=>0101001
[6,2,8,4,1,7,3,5]=>1011010=>0101101=>1010010
[7,3,4,8,1,6,2,5]=>1001010=>0101001=>1010110
[6,3,4,8,1,7,2,5]=>1001010=>0101001=>1010110
[5,3,4,8,1,2,7,6]=>1001001=>1001001=>0110110
[4,3,5,8,1,2,7,6]=>1001001=>1001001=>0110110
[1,8,5,4,2,3,7,6]=>0111001=>1001110=>0110001
[3,5,4,8,1,2,7,6]=>0101001=>1001010=>0110101
[4,5,3,8,1,2,7,6]=>0101001=>1001010=>0110101
[6,4,3,8,1,7,2,5]=>1101010=>0101011=>1010100
[7,4,3,8,1,6,2,5]=>1101010=>0101011=>1010100
[6,5,3,8,7,1,2,4]=>1101100=>0011011=>1100100
[5,6,3,8,7,1,2,4]=>0101100=>0011010=>1100101
[4,6,3,8,1,7,2,5]=>0101010=>0101010=>1010101
[2,6,8,4,1,7,3,5]=>0011010=>0101100=>1010011
[1,8,7,4,2,6,3,5]=>0111010=>0101110=>1010001
[5,7,3,8,6,1,2,4]=>0101100=>0011010=>1100101
[3,7,5,8,6,1,2,4]=>0101100=>0011010=>1100101
[2,7,8,5,6,1,3,4]=>0010100=>0010100=>1101011
[1,8,7,5,6,2,3,4]=>0110100=>0010110=>1101001
[2,6,8,5,7,1,3,4]=>0010100=>0010100=>1101011
[5,3,6,8,7,1,2,4]=>1001100=>0011001=>1100110
[7,2,8,5,6,1,3,4]=>1010100=>0010101=>1101010
[5,2,8,6,7,1,3,4]=>1010100=>0010101=>1101010
[1,8,3,2,7,6,4,5]=>0110110=>0110110=>1001001
[5,2,8,7,6,1,3,4]=>1011100=>0011101=>1100010
[6,2,8,7,5,1,3,4]=>1011100=>0011101=>1100010
[3,4,7,8,1,6,2,5]=>0001010=>0101000=>1010111
[1,8,5,7,6,2,3,4]=>0101100=>0011010=>1100101
[2,5,8,7,6,1,3,4]=>0011100=>0011100=>1100011
[7,4,6,5,8,1,2,3]=>1010100=>0010101=>1101010
[2,6,8,7,5,1,3,4]=>0011100=>0011100=>1100011
[1,8,6,7,5,2,3,4]=>0101100=>0011010=>1100101
[2,7,8,6,5,1,3,4]=>0011100=>0011100=>1100011
[5,7,6,4,8,1,2,3]=>0110100=>0010110=>1101001
[6,1,3,2,4,8,7,5]=>1010011=>1100101=>0011010
[8,7,4,2,3,6,1,5]=>1110010=>0100111=>1011000
[8,7,1,5,4,2,3,6]=>1101100=>0011011=>1100100
[3,7,1,5,2,8,6,4]=>0101011=>1101010=>0010101
[8,7,2,5,4,1,3,6]=>1101100=>0011011=>1100100
[5,2,8,7,1,4,3,6]=>1011010=>0101101=>1010010
[7,1,8,6,2,4,3,5]=>1011010=>0101101=>1010010
[8,1,6,2,7,5,3,4]=>1010110=>0110101=>1001010
[7,1,6,2,8,5,3,4]=>1010110=>0110101=>1001010
[7,2,4,3,5,1,8,6]=>1010101=>1010101=>0101010
[5,1,7,2,3,8,6,4]=>1010011=>1100101=>0011010
[8,2,3,5,1,7,6,4]=>1001011=>1101001=>0010110
[7,6,3,1,4,8,2,5]=>1110010=>0100111=>1011000
[7,2,8,1,6,5,3,4]=>1010110=>0110101=>1001010
[7,2,6,4,3,8,1,5]=>1011010=>0101101=>1010010
[5,1,7,4,3,8,2,6]=>1011010=>0101101=>1010010
[5,3,1,7,4,8,2,6]=>1101010=>0101011=>1010100
[7,4,8,2,1,5,3,6]=>1011010=>0101101=>1010010
[8,2,4,1,6,3,7,5]=>1010101=>1010101=>0101010
[8,2,7,5,1,6,4,3]=>1011011=>1101101=>0010010
[6,1,7,3,2,8,5,4]=>1011011=>1101101=>0010010
[4,7,2,1,6,3,8,5]=>0110101=>1010110=>0101001
[6,2,1,5,3,8,4,7]=>1101010=>0101011=>1010100
[5,3,1,6,2,8,4,7]=>1101010=>0101011=>1010100
[6,1,5,2,8,4,3,7]=>1010110=>0110101=>1001010
[7,4,3,8,1,5,2,6]=>1101010=>0101011=>1010100
[7,4,8,1,5,3,2,6]=>1010110=>0110101=>1001010
[6,1,5,3,2,8,4,7]=>1011010=>0101101=>1010010
[6,3,2,8,4,1,5,7]=>1101100=>0011011=>1100100
[7,3,4,2,8,5,1,6]=>1010110=>0110101=>1001010
[8,5,1,3,7,4,2,6]=>1100110=>0110011=>1001100
[3,8,6,1,5,2,7,4]=>0110101=>1010110=>0101001
[4,8,5,6,1,7,3,2]=>0101011=>1101010=>0010101
[6,7,1,3,8,5,2,4]=>0100110=>0110010=>1001101
[3,6,7,1,5,2,8,4]=>0010101=>1010100=>0101011
[7,1,3,8,4,2,6,5]=>1001101=>1011001=>0100110
[5,6,2,7,1,3,8,4]=>0101001=>1001010=>0110101
[5,6,2,8,1,3,7,4]=>0101001=>1001010=>0110101
[6,1,8,3,7,5,2,4]=>1010110=>0110101=>1001010
[7,4,2,1,5,8,3,6]=>1110010=>0100111=>1011000
[7,4,1,5,8,3,2,6]=>1100110=>0110011=>1001100
[7,3,2,6,4,8,1,5]=>1101010=>0101011=>1010100
[6,4,2,7,3,8,1,5]=>1101010=>0101011=>1010100
[7,4,8,3,1,5,2,6]=>1011010=>0101101=>1010010
[5,2,1,7,4,8,3,6]=>1101010=>0101011=>1010100
[6,1,8,4,5,2,7,3]=>1010101=>1010101=>0101010
[7,1,6,4,5,2,8,3]=>1010101=>1010101=>0101010
[3,5,2,7,1,6,8,4]=>0101001=>1001010=>0110101
[4,5,7,3,1,6,8,2]=>0011001=>1001100=>0110011
[4,5,7,2,8,6,1,3]=>0010110=>0110100=>1001011
[4,5,7,2,8,1,3,6]=>0010100=>0010100=>1101011
[4,6,7,2,1,5,8,3]=>0011001=>1001100=>0110011
[4,6,7,1,3,8,5,2]=>0010011=>1100100=>0011011
[3,6,1,5,7,8,4,2]=>0100011=>1100010=>0011101
[4,6,7,1,5,8,3,2]=>0010011=>1100100=>0011011
[6,1,4,2,5,3,7,8]=>1010100=>0010101=>1101010
[1,3,7,5,4,2,8,6]=>0011101=>1011100=>0100011
[6,1,3,5,4,2,7,8]=>1001100=>0011001=>1100110
[6,1,2,5,4,7,3,8]=>1001010=>0101001=>1010110
[5,2,6,3,4,7,1,8]=>1010010=>0100101=>1011010
[2,4,7,1,5,3,8,6]=>0010101=>1010100=>0101011
[2,3,6,7,4,8,1,5]=>0001010=>0101000=>1010111
[1,3,6,7,4,8,5,2]=>0001011=>1101000=>0010111
[2,7,6,5,3,1,8,4]=>0111101=>1011110=>0100001
[5,2,6,1,4,7,8,3]=>1010001=>1000101=>0111010
[4,7,6,5,2,1,8,3]=>0111101=>1011110=>0100001
[6,3,1,5,4,7,8,2]=>1101001=>1001011=>0110100
[5,3,6,1,4,2,7,8]=>1010100=>0010101=>1101010
[1,7,4,2,6,3,8,5]=>0110101=>1010110=>0101001
[5,7,4,1,2,3,6,8]=>0110000=>0000110=>1111001
[6,4,1,2,5,3,7,8]=>1100100=>0010011=>1101100
[4,7,6,3,8,5,1,2]=>0110110=>0110110=>1001001
[3,7,6,5,2,8,1,4]=>0111010=>0101110=>1010001
[3,7,6,5,1,2,8,4]=>0111001=>1001110=>0110001
[4,7,2,6,1,3,8,5]=>0101001=>1001010=>0110101
[2,7,6,5,8,1,4,3]=>0110101=>1010110=>0101001
[4,2,6,8,3,1,5,7]=>1001100=>0011001=>1100110
[3,7,6,2,4,5,1,8]=>0110010=>0100110=>1011001
[2,3,6,5,8,1,4,7]=>0010100=>0010100=>1101011
[2,3,5,8,6,1,4,7]=>0001100=>0011000=>1100111
[4,2,3,8,6,1,5,7]=>1001100=>0011001=>1100110
[1,2,3,7,4,6,8,5]=>0001001=>1001000=>0110111
[3,2,7,1,4,5,8,6]=>1010001=>1000101=>0111010
[2,1,5,3,8,7,4,6]=>1010110=>0110101=>1001010
[5,8,3,2,4,1,6,7]=>0110100=>0010110=>1101001
[4,2,7,1,8,3,5,6]=>1010100=>0010101=>1101010
[1,2,7,5,3,8,4,6]=>0011010=>0101100=>1010011
[3,2,7,1,4,8,5,6]=>1010010=>0100101=>1011010
[1,2,3,7,6,8,4,5]=>0001010=>0101000=>1010111
[1,2,3,6,8,7,4,5]=>0000110=>0110000=>1001111
[1,2,3,7,8,4,6,5]=>0000101=>1010000=>0101111
[1,2,3,6,8,4,7,5]=>0000101=>1010000=>0101111
[6,2,8,3,7,5,1,4]=>1010110=>0110101=>1001010
[4,2,8,3,7,5,6,1]=>1010101=>1010101=>0101010
[7,3,4,8,6,5,1,2]=>1001110=>0111001=>1000110
[5,3,4,8,7,2,6,1]=>1001101=>1011001=>0100110
[4,6,3,8,5,7,2,1]=>0101011=>1101010=>0010101
[7,5,3,8,6,2,4,1]=>1101101=>1011011=>0100100
[2,6,8,3,7,4,5,1]=>0010101=>1010100=>0101011
[2,5,8,3,7,4,6,1]=>0010101=>1010100=>0101011
[7,4,3,8,6,2,5,1]=>1101101=>1011011=>0100100
[3,5,4,8,7,2,6,1]=>0101101=>1011010=>0100101
[4,5,3,8,6,7,2,1]=>0101011=>1101010=>0010101
[3,6,7,8,4,5,2,1]=>0001011=>1101000=>0010111
[1,8,5,6,4,7,3,2]=>0101011=>1101010=>0010101
[2,5,8,6,4,7,3,1]=>0011011=>1101100=>0010011
[6,3,7,8,4,5,2,1]=>1001011=>1101001=>0010110
[4,3,7,8,5,6,2,1]=>1001011=>1101001=>0010110
[4,2,8,6,5,7,3,1]=>1011011=>1101101=>0010010
[3,2,8,6,7,4,5,1]=>1010101=>1010101=>0101010
[2,3,8,7,5,4,6,1]=>0011101=>1011100=>0100011
[1,8,2,7,4,5,6,3]=>0101001=>1001010=>0110101
[7,2,8,6,3,4,5,1]=>1011001=>1001101=>0110010
[6,2,8,4,5,7,3,1]=>1010011=>1100101=>0011010
[5,2,8,4,6,7,3,1]=>1010011=>1100101=>0011010
[4,3,6,8,5,7,2,1]=>1001011=>1101001=>0010110
[3,4,6,8,7,2,5,1]=>0001101=>1011000=>0100111
[7,3,5,8,6,2,4,1]=>1001101=>1011001=>0100110
[1,8,3,5,7,4,6,2]=>0100101=>1010010=>0101101
[2,7,8,4,5,6,3,1]=>0010011=>1100100=>0011011
[3,7,5,8,4,6,2,1]=>0101011=>1101010=>0010101
[5,7,4,6,8,3,2,1]=>0100111=>1110010=>0001101
[3,6,5,8,4,7,2,1]=>0101011=>1101010=>0010101
[2,6,8,4,5,7,3,1]=>0010011=>1100100=>0011011
[4,2,7,1,3,8,5,6]=>1010010=>0100101=>1011010
[4,2,5,1,3,8,6,7]=>1010010=>0100101=>1011010
[5,3,6,1,7,2,4,8]=>1010100=>0010101=>1101010
[3,7,1,2,5,8,6,4]=>0100011=>1100010=>0011101
[3,7,4,1,2,8,5,6]=>0110010=>0100110=>1011001
[7,5,1,3,4,8,6,2]=>1100011=>1100011=>0011100
[7,5,1,2,4,8,6,3]=>1100011=>1100011=>0011100
[6,4,2,3,7,1,5,8]=>1100100=>0010011=>1101100
[7,6,3,8,1,2,5,4]=>1101001=>1001011=>0110100
[7,4,2,3,8,1,6,5]=>1100101=>1010011=>0101100
[4,7,5,2,8,1,3,6]=>0110100=>0010110=>1101001
[8,2,6,3,7,1,4,5]=>1010100=>0010101=>1101010
[8,6,1,2,7,4,5,3]=>1100101=>1010011=>0101100
[8,4,7,1,2,3,6,5]=>1010001=>1000101=>0111010
[8,5,7,1,2,4,6,3]=>1010001=>1000101=>0111010
[3,8,5,6,1,2,4,7]=>0101000=>0001010=>1110101
[3,7,5,8,1,2,4,6]=>0101000=>0001010=>1110101
[7,6,4,8,1,3,5,2]=>1101001=>1001011=>0110100
[6,5,8,1,2,4,7,3]=>1010001=>1000101=>0111010
[3,6,8,1,2,5,7,4]=>0010001=>1000100=>0111011
[4,6,3,8,1,2,5,7]=>0101000=>0001010=>1110101
[4,6,3,7,1,2,5,8]=>0101000=>0001010=>1110101
[4,1,7,8,2,3,6,5]=>1001001=>1001001=>0110110
[5,1,2,8,6,3,4,7]=>1001100=>0011001=>1100110
[5,3,8,1,6,2,4,7]=>1010100=>0010101=>1101010
[6,1,8,5,2,3,4,7]=>1011000=>0001101=>1110010
[6,1,7,5,2,3,4,8]=>1011000=>0001101=>1110010
[6,8,1,3,7,4,5,2]=>0100101=>1010010=>0101101
[7,2,8,1,6,3,4,5]=>1010100=>0010101=>1101010
[4,7,8,2,5,1,3,6]=>0010100=>0010100=>1101011
[6,8,2,7,1,4,5,3]=>0101001=>1001010=>0110101
[4,8,7,1,3,5,6,2]=>0110001=>1000110=>0111001
[3,8,7,1,2,4,6,5]=>0110001=>1000110=>0111001
[4,8,7,1,2,3,6,5]=>0110001=>1000110=>0111001
[5,8,7,1,2,4,6,3]=>0110001=>1000110=>0111001
[5,8,7,1,3,4,6,2]=>0110001=>1000110=>0111001
[7,1,8,6,2,3,5,4]=>1011001=>1001101=>0110010
[5,8,6,4,1,2,3,7]=>0111000=>0001110=>1110001
[5,1,3,4,6,7,2,8]=>1000010=>0100001=>1011110
[1,3,4,8,7,5,2,6]=>0001110=>0111000=>1000111
[8,2,4,1,7,3,5,6]=>1010100=>0010101=>1101010
[8,6,1,4,2,3,7,5]=>1101001=>1001011=>0110100
[3,6,1,4,2,8,7,5]=>0101011=>1101010=>0010101
[1,6,8,4,3,7,2,5]=>0011010=>0101100=>1010011
[3,1,4,7,8,5,2,6]=>1000110=>0110001=>1001110
[6,1,7,4,3,8,2,5]=>1011010=>0101101=>1010010
[1,8,7,4,3,6,2,5]=>0111010=>0101110=>1010001
[7,4,1,3,8,2,6,5]=>1100101=>1010011=>0101100
[4,8,2,3,1,5,7,6]=>0101001=>1001010=>0110101
[4,8,6,2,1,3,7,5]=>0111001=>1001110=>0110001
[2,7,4,1,8,3,5,6]=>0110100=>0010110=>1101001
[1,7,8,4,2,3,6,5]=>0011001=>1001100=>0110011
[8,7,1,3,4,2,6,5]=>1100101=>1010011=>0101100
[1,7,4,3,6,2,8,5]=>0110101=>1010110=>0101001
[3,8,6,4,5,2,1,7]=>0110110=>0110110=>1001001
[3,8,4,6,5,2,1,7]=>0101110=>0111010=>1000101
[2,4,3,7,5,8,1,6]=>0101010=>0101010=>1010101
[1,4,7,3,6,2,8,5]=>0010101=>1010100=>0101011
[6,4,1,3,7,2,8,5]=>1100101=>1010011=>0101100
[8,1,4,3,6,2,7,5]=>1010101=>1010101=>0101010
[4,2,3,8,5,7,1,6]=>1001010=>0101001=>1010110
[2,8,5,7,3,4,1,6]=>0101010=>0101010=>1010101
[5,8,2,6,4,3,1,7]=>0101110=>0111010=>1000101
[7,2,5,8,4,3,1,6]=>1001110=>0111001=>1000110
[4,2,3,5,8,7,1,6]=>1000110=>0110001=>1001110
[8,2,3,5,4,7,1,6]=>1001010=>0101001=>1010110
[6,1,8,3,4,2,7,5]=>1010101=>1010101=>0101010
[1,8,6,4,2,3,7,5]=>0111001=>1001110=>0110001
[3,8,4,5,6,2,1,7]=>0100110=>0110010=>1001101
[3,8,6,5,4,2,1,7]=>0111110=>0111110=>1000001
[6,3,1,4,2,8,7,5]=>1101011=>1101011=>0010100
[7,3,8,1,2,6,4,5]=>1010010=>0100101=>1011010
[7,1,4,5,3,2,6,8]=>1001100=>0011001=>1100110
[1,8,4,2,6,5,3,7]=>0110110=>0110110=>1001001
[5,1,4,8,6,3,2,7]=>1001110=>0111001=>1000110
[5,3,1,8,4,7,2,6]=>1101010=>0101011=>1010100
[4,3,8,1,5,7,2,6]=>1010010=>0100101=>1011010
[6,3,1,2,5,7,4,8]=>1100010=>0100011=>1011100
[7,1,4,2,6,5,3,8]=>1010110=>0110101=>1001010
[3,8,4,1,6,5,2,7]=>0110110=>0110110=>1001001
[7,5,3,6,4,8,2,1]=>1101011=>1101011=>0010100
[7,3,6,4,5,8,2,1]=>1010011=>1100101=>0011010
[8,7,2,4,5,1,6,3]=>1100101=>1010011=>0101100
[7,1,5,4,8,6,3,2]=>1010111=>1110101=>0001010
[5,8,3,7,4,1,6,2]=>0101101=>1011010=>0100101
[8,1,7,4,2,6,5,3]=>1011011=>1101101=>0010010
[5,6,3,1,8,4,7,2]=>0110101=>1010110=>0101001
[5,7,1,4,8,6,3,2]=>0100111=>1110010=>0001101
[5,3,7,4,8,6,2,1]=>1010111=>1110101=>0001010
[8,5,3,6,1,4,7,2]=>1101001=>1001011=>0110100
[5,4,3,6,8,2,7,1]=>1100101=>1010011=>0101100
[6,5,3,7,4,8,2,1]=>1101011=>1101011=>0010100
[2,7,8,4,5,1,6,3]=>0010101=>1010100=>0101011
[5,6,3,8,1,4,7,2]=>0101001=>1001010=>0110101
[8,4,1,2,5,6,7,3]=>1100001=>1000011=>0111100
[6,8,3,1,2,5,7,4]=>0110001=>1000110=>0111001
[8,7,1,4,5,2,6,3]=>1100101=>1010011=>0101100
[8,7,3,1,5,4,2,6]=>1110110=>0110111=>1001000
[3,5,4,7,6,1,2,8]=>0101100=>0011010=>1100101
[3,5,7,4,6,1,8,2]=>0010101=>1010100=>0101011
[3,5,7,4,6,1,2,8]=>0010100=>0010100=>1101011
[3,5,7,4,6,2,1,8]=>0010110=>0110100=>1001011
[3,5,2,7,6,4,1,8]=>0101110=>0111010=>1000101
[3,5,7,2,6,4,1,8]=>0010110=>0110100=>1001011
[5,3,7,6,1,2,8,4]=>1011001=>1001101=>0110010
[5,3,7,6,1,4,2,8]=>1011010=>0101101=>1010010
[5,3,7,6,4,1,2,8]=>1011100=>0011101=>1100010
[3,5,7,2,6,1,4,8]=>0010100=>0010100=>1101011
[3,5,2,7,6,1,4,8]=>0101100=>0011010=>1100101
[5,3,7,6,4,1,8,2]=>1011101=>1011101=>0100010
[3,7,5,4,1,8,2,6]=>0111010=>0101110=>1010001
[3,7,5,4,1,8,6,2]=>0111011=>1101110=>0010001
[3,7,5,1,4,8,6,2]=>0110011=>1100110=>0011001
[3,7,5,1,4,8,2,6]=>0110010=>0100110=>1011001
[3,5,7,1,2,6,8,4]=>0010001=>1000100=>0111011
[3,5,7,2,1,6,4,8]=>0011010=>0101100=>1010011
[5,3,7,1,6,2,4,8]=>1010100=>0010101=>1101010
[3,5,7,1,4,6,8,2]=>0010001=>1000100=>0111011
[3,5,7,1,4,2,6,8]=>0010100=>0010100=>1101011
[3,5,7,4,1,2,6,8]=>0011000=>0001100=>1110011
[3,5,4,7,1,6,8,2]=>0101001=>1001010=>0110101
[3,5,4,7,1,2,6,8]=>0101000=>0001010=>1110101
[3,5,4,7,2,1,6,8]=>0101100=>0011010=>1100101
[3,5,4,2,7,1,6,8]=>0110100=>0010110=>1101001
[3,5,4,7,2,1,8,6]=>0101101=>1011010=>0100101
[3,5,4,7,1,2,8,6]=>0101001=>1001010=>0110101
[5,7,6,3,1,8,4,2]=>0111011=>1101110=>0010001
[5,7,6,3,1,8,2,4]=>0111010=>0101110=>1010001
[3,5,7,4,1,2,8,6]=>0011001=>1001100=>0110011
[3,5,7,4,2,1,8,6]=>0011101=>1011100=>0100011
[3,2,5,7,4,1,8,6]=>1001101=>1011001=>0100110
[3,2,5,7,1,4,8,6]=>1001001=>1001001=>0110110
[3,5,2,7,1,4,8,6]=>0101001=>1001010=>0110101
[3,5,7,2,1,4,8,6]=>0011001=>1001100=>0110011
[3,5,7,1,4,2,8,6]=>0010101=>1010100=>0101011
[3,7,5,2,1,8,6,4]=>0111011=>1101110=>0010001
[3,7,2,5,1,8,6,4]=>0101011=>1101010=>0010101
[3,2,7,5,1,8,6,4]=>1011011=>1101101=>0010010
[3,2,7,5,1,8,4,6]=>1011010=>0101101=>1010010
[3,7,2,5,1,8,4,6]=>0101010=>0101010=>1010101
[3,7,5,2,1,8,4,6]=>0111010=>0101110=>1010001
[5,8,3,4,1,7,6,2]=>0101011=>1101010=>0010101
[5,8,7,2,4,1,6,3]=>0110101=>1010110=>0101001
[3,8,6,4,1,7,5,2]=>0111011=>1101110=>0010001
[4,3,5,6,8,1,7,2]=>1000101=>1010001=>0101110
[3,7,6,4,1,8,5,2]=>0111011=>1101110=>0010001
[3,7,4,1,8,6,5,2]=>0110111=>1110110=>0001001
[3,8,4,1,7,6,5,2]=>0110111=>1110110=>0001001
[3,2,7,6,1,5,4,8]=>1011010=>0101101=>1010010
[5,7,8,2,4,1,6,3]=>0010101=>1010100=>0101011
[4,2,5,8,1,6,7,3]=>1001001=>1001001=>0110110
[5,8,2,4,1,6,3,7]=>0101010=>0101010=>1010101
[8,4,2,6,5,1,3,7]=>1101100=>0011011=>1100100
[3,2,6,8,1,5,4,7]=>1001010=>0101001=>1010110
[8,3,2,5,6,1,4,7]=>1100100=>0010011=>1101100
[3,2,8,6,7,1,5,4]=>1010101=>1010101=>0101010
[3,2,6,8,7,1,5,4]=>1001101=>1011001=>0100110
[3,2,6,7,1,5,4,8]=>1001010=>0101001=>1010110
[8,7,3,2,5,6,1,4]=>1110010=>0100111=>1011000
[7,2,8,1,5,3,6,4]=>1010101=>1010101=>0101010
[8,4,2,7,5,1,3,6]=>1101100=>0011011=>1100100
[7,4,2,8,5,1,3,6]=>1101100=>0011011=>1100100
[7,2,4,1,8,3,6,5]=>1010101=>1010101=>0101010
[7,5,3,4,2,8,1,6]=>1101010=>0101011=>1010100
[8,5,3,6,2,4,7,1]=>1101001=>1001011=>0110100
[8,5,6,3,7,4,2,1]=>1010111=>1110101=>0001010
[8,5,6,2,7,4,3,1]=>1010111=>1110101=>0001010
[8,7,6,3,4,1,5,2]=>1110101=>1010111=>0101000
[1,7,2,3,6,8,5,4]=>0100011=>1100010=>0011101
[3,5,6,4,8,2,7,1]=>0010101=>1010100=>0101011
[3,5,1,4,8,2,7,6]=>0100101=>1010010=>0101101
[1,7,5,4,8,2,6,3]=>0110101=>1010110=>0101001
[3,7,5,1,6,4,8,2]=>0110101=>1010110=>0101001
[2,7,5,4,8,1,3,6]=>0110100=>0010110=>1101001
[2,7,5,4,8,6,1,3]=>0110110=>0110110=>1001001
[1,7,5,4,8,6,3,2]=>0110111=>1110110=>0001001
[2,5,1,4,8,7,3,6]=>0100110=>0110010=>1001101
[3,6,4,2,8,7,1,5]=>0110110=>0110110=>1001001
[3,5,2,4,8,1,6,7]=>0100100=>0010010=>1101101
[4,5,6,1,7,3,8,2]=>0010101=>1010100=>0101011
[3,5,6,4,8,1,2,7]=>0010100=>0010100=>1101011
[1,5,6,4,8,7,2,3]=>0010110=>0110100=>1001011
[3,6,4,1,8,7,2,5]=>0110110=>0110110=>1001001
[3,6,4,5,8,7,2,1]=>0100111=>1110010=>0001101
[1,6,4,3,8,5,2,7]=>0110110=>0110110=>1001001
[7,6,1,4,5,3,8,2]=>1100101=>1010011=>0101100
[7,6,1,3,5,4,8,2]=>1100101=>1010011=>0101100
[7,1,3,2,5,8,4,6]=>1010010=>0100101=>1011010
[1,6,4,2,8,5,3,7]=>0110110=>0110110=>1001001
[7,6,5,8,3,1,4,2]=>1101101=>1011011=>0100100
[2,6,4,3,8,1,7,5]=>0110101=>1010110=>0101001
[2,6,4,3,8,5,7,1]=>0110101=>1010110=>0101001
[7,2,3,1,5,8,6,4]=>1010011=>1100101=>0011010
[7,1,5,6,3,8,4,2]=>1001011=>1101001=>0010110
[7,3,6,5,1,4,8,2]=>1011001=>1001101=>0110010
[7,2,6,5,3,8,1,4]=>1011010=>0101101=>1010010
[7,2,3,1,4,8,6,5]=>1010011=>1100101=>0011010
[7,2,3,5,4,8,6,1]=>1001011=>1101001=>0010110
[2,6,4,5,8,1,7,3]=>0100101=>1010010=>0101101
[1,5,6,4,8,3,7,2]=>0010101=>1010100=>0101011
[2,5,6,4,8,3,1,7]=>0010110=>0110100=>1001011
[3,5,6,1,4,7,8,2]=>0010001=>1000100=>0111011
[7,6,1,3,4,5,8,2]=>1100001=>1000011=>0111100
[7,1,3,2,4,8,5,6]=>1010010=>0100101=>1011010
[7,6,1,5,3,4,8,2]=>1101001=>1001011=>0110100
[7,6,1,5,4,3,8,2]=>1101101=>1011011=>0100100
[1,6,4,5,8,3,2,7]=>0100110=>0110010=>1001101
[7,6,5,8,1,3,2,4]=>1101010=>0101011=>1010100
[3,4,6,8,7,2,1,5]=>0001110=>0111000=>1000111
[3,5,6,8,2,1,7,4]=>0001101=>1011000=>0100111
[4,2,1,5,3,7,8,6]=>1101001=>1001011=>0110100
[4,2,5,6,3,1,8,7]=>1001101=>1011001=>0100110
[3,5,6,8,1,7,2,4]=>0001010=>0101000=>1010111
[4,1,5,6,3,2,8,7]=>1001101=>1011001=>0100110
[4,5,3,1,7,2,8,6]=>0110101=>1010110=>0101001
[4,1,3,5,2,7,8,6]=>1001001=>1001001=>0110110
[2,5,4,7,3,8,6,1]=>0101011=>1101010=>0010101
[3,5,7,1,8,4,2,6]=>0010110=>0110100=>1001011
[4,1,5,3,2,7,8,6]=>1011001=>1001101=>0110010
[4,5,3,7,1,2,8,6]=>0101001=>1001010=>0110101
[4,3,6,1,2,7,5,8]=>1010010=>0100101=>1011010
[5,1,3,2,4,6,7,8]=>1010000=>0000101=>1111010
[3,6,1,7,4,5,2,8]=>0101010=>0101010=>1010101
[5,3,1,4,2,6,7,8]=>1101000=>0001011=>1110100
[4,5,2,3,7,1,8,6]=>0100101=>1010010=>0101101
[4,2,6,1,3,7,5,8]=>1010010=>0100101=>1011010
[4,6,2,1,3,7,5,8]=>0110010=>0100110=>1011001
[3,6,2,1,7,4,8,5]=>0110101=>1010110=>0101001
[3,1,4,7,6,5,2,8]=>1001110=>0111001=>1000110
[3,6,2,7,1,5,8,4]=>0101001=>1001010=>0110101
[4,6,2,7,1,3,5,8]=>0101000=>0001010=>1110101
[3,5,7,1,8,2,6,4]=>0010101=>1010100=>0101011
[5,1,4,2,3,6,7,8]=>1010000=>0000101=>1111010
[2,6,5,3,4,7,8,1]=>0110001=>1000110=>0111001
[3,6,1,7,5,4,2,8]=>0101110=>0111010=>1000101
[5,1,4,3,2,6,7,8]=>1011000=>0001101=>1110010
[5,4,1,3,2,6,7,8]=>1101000=>0001011=>1110100
[6,4,2,5,3,8,1,7]=>1101010=>0101011=>1010100
[4,6,2,3,5,1,8,7]=>0100101=>1010010=>0101101
[6,2,4,5,1,8,3,7]=>1001010=>0101001=>1010110
[8,2,6,7,1,4,5,3]=>1001001=>1001001=>0110110
[8,2,6,7,4,1,5,3]=>1001101=>1011001=>0100110
[4,6,2,3,5,8,1,7]=>0100010=>0100010=>1011101
[2,6,4,1,5,8,3,7]=>0110010=>0100110=>1011001
[2,8,1,6,7,4,5,3]=>0100101=>1010010=>0101101
[2,8,6,1,4,7,5,3]=>0110011=>1100110=>0011001
[2,8,1,6,4,7,5,3]=>0101011=>1101010=>0010101
[2,6,1,4,8,5,3,7]=>0100110=>0110010=>1001101
[6,4,5,2,8,3,1,7]=>1010110=>0110101=>1001010
[4,2,3,6,1,8,5,7]=>1001010=>0101001=>1010110
[4,2,3,1,6,8,5,7]=>1010010=>0100101=>1011010
[4,2,3,8,6,1,7,5]=>1001101=>1011001=>0100110
[6,4,5,8,2,3,7,1]=>1001001=>1001001=>0110110
[6,4,8,5,2,3,7,1]=>1011001=>1001101=>0110010
[2,4,8,1,3,6,7,5]=>0010001=>1000100=>0111011
[2,4,1,8,3,6,7,5]=>0101001=>1001010=>0110101
[2,1,4,8,6,3,7,5]=>1001101=>1011001=>0100110
[6,4,8,2,5,3,7,1]=>1010101=>1010101=>0101010
[8,6,2,4,7,5,1,3]=>1100110=>0110011=>1001100
[4,6,8,2,3,5,7,1]=>0010001=>1000100=>0111011
[2,1,6,8,4,5,7,3]=>1001001=>1001001=>0110110
[2,8,1,4,6,7,3,5]=>0100010=>0100010=>1011101
[4,8,6,2,3,7,5,1]=>0110011=>1100110=>0011001
[8,4,2,6,7,3,1,5]=>1100110=>0110011=>1001100
[5,1,8,3,6,4,7,2]=>1010101=>1010101=>0101010
[5,1,3,8,7,6,4,2]=>1001111=>1111001=>0000110
[3,8,5,6,1,7,2,4]=>0101010=>0101010=>1010101
[6,7,4,8,5,1,3,2]=>0101101=>1011010=>0100101
[3,6,5,8,7,1,4,2]=>0101101=>1011010=>0100101
[6,5,3,8,2,7,4,1]=>1101011=>1101011=>0010100
[6,4,8,1,3,7,5,2]=>1010011=>1100101=>0011010
[7,6,3,1,4,2,5,8]=>1110100=>0010111=>1101000
[1,5,4,3,7,8,2,6]=>0110010=>0100110=>1011001
[7,8,4,2,5,3,1,6]=>0110110=>0110110=>1001001
[4,2,7,8,5,3,1,6]=>1001110=>0111001=>1000110
[4,2,5,3,1,7,8,6]=>1011001=>1001101=>0110010
[4,2,8,7,6,3,1,5]=>1011110=>0111101=>1000010
[4,2,7,6,3,1,5,8]=>1011100=>0011101=>1100010
[6,3,1,8,7,5,2,4]=>1101110=>0111011=>1000100
[4,2,7,6,3,1,8,5]=>1011101=>1011101=>0100010
[7,6,3,1,8,4,2,5]=>1110110=>0110111=>1001000
[7,6,4,2,1,8,3,5]=>1111010=>0101111=>1010000
[1,8,2,7,6,4,3,5]=>0101110=>0111010=>1000101
[8,4,2,5,7,6,3,1]=>1100111=>1110011=>0001100
[7,5,2,4,8,6,3,1]=>1100111=>1110011=>0001100
[8,7,5,2,4,6,3,1]=>1110011=>1100111=>0011000
[7,5,2,4,6,3,1,8]=>1100110=>0110011=>1001100
[5,2,8,6,3,7,4,1]=>1011011=>1101101=>0010010
[8,4,7,5,2,6,3,1]=>1011011=>1101101=>0010010
[8,3,6,4,7,5,2,1]=>1010111=>1110101=>0001010
[7,5,2,1,8,3,6,4]=>1110101=>1010111=>0101000
[7,5,2,6,3,1,8,4]=>1101101=>1011011=>0100100
[5,2,7,4,1,8,6,3]=>1011011=>1101101=>0010010
[5,2,8,7,4,1,6,3]=>1011101=>1011101=>0100010
[8,7,4,1,5,2,6,3]=>1110101=>1010111=>0101000
[7,4,1,5,2,8,6,3]=>1101011=>1101011=>0010100
[7,6,3,1,4,2,8,5]=>1110101=>1010111=>0101000
[7,5,2,8,6,3,1,4]=>1101110=>0111011=>1000100
[7,5,2,1,3,6,4,8]=>1110010=>0100111=>1011000
[8,7,5,2,1,3,6,4]=>1111001=>1001111=>0110000
[1,3,7,6,5,8,2,4]=>0011010=>0101100=>1010011
[8,6,4,7,5,2,1,3]=>1101110=>0111011=>1000100
[6,4,7,5,2,1,3,8]=>1011100=>0011101=>1100010
[6,3,1,4,7,5,2,8]=>1100110=>0110011=>1001100
[6,3,1,4,8,7,5,2]=>1100111=>1110011=>0001100
[8,6,3,1,4,7,5,2]=>1110011=>1100111=>0011000
[1,8,2,6,4,7,5,3]=>0101011=>1101010=>0010101
[7,5,2,1,6,4,8,3]=>1110101=>1010111=>0101000
[6,3,8,7,4,1,5,2]=>1011101=>1011101=>0100010
[6,3,7,4,1,5,2,8]=>1011010=>0101101=>1010010
[7,4,1,6,3,5,2,8]=>1101010=>0101011=>1010100
[7,4,1,8,6,3,5,2]=>1101101=>1011011=>0100100
[8,4,6,3,1,7,5,2]=>1011011=>1101101=>0010010
[6,4,7,5,2,1,8,3]=>1011101=>1011101=>0100010
[1,6,4,7,5,3,8,2]=>0101101=>1011010=>0100101
[6,3,5,2,7,4,1,8]=>1010110=>0110101=>1001010
[4,6,7,2,5,3,1,8]=>0010110=>0110100=>1001011
[2,4,7,8,1,6,5,3]=>0001011=>1101000=>0010111
[4,2,6,8,7,1,5,3]=>1001101=>1011001=>0100110
[5,1,8,4,2,7,6,3]=>1011011=>1101101=>0010010
[4,6,7,1,2,8,5,3]=>0010011=>1100100=>0011011
[5,7,4,1,2,8,6,3]=>0110011=>1100110=>0011001
[6,3,7,1,2,8,5,4]=>1010011=>1100101=>0011010
[1,8,2,3,6,5,4,7]=>0100110=>0110010=>1001101
[3,5,8,4,7,2,6,1]=>0010101=>1010100=>0101011
[1,8,5,4,6,2,3,7]=>0110100=>0010110=>1101001
[3,8,5,4,6,1,2,7]=>0110100=>0010110=>1101001
[3,8,5,1,6,4,2,7]=>0110110=>0110110=>1001001
[2,8,5,4,6,1,3,7]=>0110100=>0010110=>1101001
[2,8,5,4,6,3,1,7]=>0110110=>0110110=>1001001
[1,8,5,4,6,3,2,7]=>0110110=>0110110=>1001001
[2,5,8,4,7,3,6,1]=>0010101=>1010100=>0101011
[3,6,4,2,7,8,5,1]=>0110011=>1100110=>0011001
[3,6,4,2,7,8,1,5]=>0110010=>0100110=>1011001
[3,5,4,1,6,2,7,8]=>0110100=>0010110=>1101001
[4,5,8,1,7,6,2,3]=>0010110=>0110100=>1001011
[3,5,8,4,7,1,6,2]=>0010101=>1010100=>0101011
[1,5,8,4,7,3,6,2]=>0010101=>1010100=>0101011
[3,6,4,1,7,8,5,2]=>0110011=>1100110=>0011001
[3,6,4,8,7,5,2,1]=>0101111=>1111010=>0000101
[1,6,4,3,7,8,5,2]=>0110011=>1100110=>0011001
[7,6,1,3,8,4,2,5]=>1100110=>0110011=>1001100
[1,6,4,2,7,8,3,5]=>0110010=>0100110=>1011001
[2,6,4,3,7,1,8,5]=>0110101=>1010110=>0101001
[2,6,4,1,7,8,3,5]=>0110010=>0100110=>1011001
[7,2,3,4,8,6,5,1]=>1000111=>1110001=>0001110
[7,2,3,1,8,6,4,5]=>1010110=>0110101=>1001010
[7,2,3,4,1,6,8,5]=>1001001=>1001001=>0110110
[1,2,4,3,8,5,7,6]=>0010101=>1010100=>0101011
[7,3,8,6,1,4,2,5]=>1011010=>0101101=>1010010
[7,2,8,6,3,4,1,5]=>1011010=>0101101=>1010010
[7,2,3,1,5,6,8,4]=>1010001=>1000101=>0111010
[7,2,3,8,5,6,4,1]=>1001011=>1101001=>0010110
[2,6,4,8,7,1,5,3]=>0101101=>1011010=>0100101
[1,5,8,4,7,6,2,3]=>0010110=>0110100=>1001011
[3,5,8,1,6,7,2,4]=>0010010=>0100100=>1011011
[7,6,1,3,5,8,2,4]=>1100010=>0100011=>1011100
[7,1,3,2,5,6,8,4]=>1010001=>1000101=>0111010
[7,1,3,8,2,6,5,4]=>1001011=>1101001=>0010110
[7,6,1,8,5,4,2,3]=>1101110=>0111011=>1000100
[3,2,6,5,8,4,7,1]=>1010101=>1010101=>0101010
[4,3,7,1,6,5,8,2]=>1010101=>1010101=>0101010
[5,2,6,4,8,3,7,1]=>1010101=>1010101=>0101010
[4,3,7,5,8,2,6,1]=>1010101=>1010101=>0101010
[5,3,7,4,8,2,6,1]=>1010101=>1010101=>0101010
[5,3,7,4,8,1,6,2]=>1010101=>1010101=>0101010
[5,4,8,2,6,3,7,1]=>1010101=>1010101=>0101010
[4,1,7,5,2,3,6,8]=>1011000=>0001101=>1110010
[4,1,7,8,6,3,2,5]=>1001110=>0111001=>1000110
[6,8,3,2,1,4,7,5]=>0111001=>1001110=>0110001
[6,8,2,4,1,3,7,5]=>0101001=>1001010=>0110101
[6,1,2,7,5,8,4,3]=>1001011=>1101001=>0010110
[4,2,7,3,8,5,6,1]=>1010101=>1010101=>0101010
[4,5,2,6,8,3,7,1]=>0100101=>1010010=>0101101
[4,8,3,2,5,7,6,1]=>0110011=>1100110=>0011001
[8,4,7,6,2,3,5,1]=>1011001=>1001101=>0110010
[6,8,4,1,5,3,7,2]=>0110101=>1010110=>0101001
[8,3,4,7,6,2,5,1]=>1001101=>1011001=>0100110
[1,8,3,5,2,6,7,4]=>0101001=>1001010=>0110101
[5,8,2,4,3,7,6,1]=>0101011=>1101010=>0010101
[6,5,3,8,4,2,7,1]=>1101101=>1011011=>0100100
[7,4,5,1,6,2,8,3]=>1010101=>1010101=>0101010
[4,7,3,5,6,2,8,1]=>0100101=>1010010=>0101101
[6,7,8,4,1,3,5,2]=>0011001=>1001100=>0110011
[3,1,6,8,4,7,5,2]=>1001011=>1101001=>0010110
[8,3,6,1,5,7,4,2]=>1010011=>1100101=>0011010
[3,2,7,5,8,6,1,4]=>1010110=>0110101=>1001010
[2,4,6,7,8,1,5,3]=>0000101=>1010000=>0101111
[2,4,6,8,1,7,5,3]=>0001011=>1101000=>0010111
[7,4,3,8,6,2,1,5]=>1101110=>0111011=>1000100
[4,3,6,2,1,8,5,7]=>1011010=>0101101=>1010010
[4,6,2,3,7,5,8,1]=>0100101=>1010010=>0101101
[5,8,4,2,3,6,7,1]=>0110001=>1000110=>0111001
[8,4,5,3,2,1,7,6]=>1011101=>1011101=>0100010
[6,8,4,2,3,7,5,1]=>0110011=>1100110=>0011001
[6,4,8,3,2,7,1,5]=>1011010=>0101101=>1010010
[5,8,3,7,2,1,6,4]=>0101101=>1011010=>0100101
[2,5,6,4,7,1,8,3]=>0010101=>1010100=>0101011
[2,5,4,8,1,6,7,3]=>0101001=>1001010=>0110101
[1,2,6,5,8,7,3,4]=>0010110=>0110100=>1001011
[5,6,3,4,8,7,2,1]=>0100111=>1110010=>0001101
[6,5,3,4,8,7,2,1]=>1100111=>1110011=>0001100
[7,5,3,8,4,6,2,1]=>1101011=>1101011=>0010100
[8,5,3,7,4,6,2,1]=>1101011=>1101011=>0010100
[5,8,1,2,3,4,7,6]=>0100001=>1000010=>0111101
[7,1,2,8,3,6,4,5]=>1001010=>0101001=>1010110
[6,1,8,2,3,5,7,4]=>1010001=>1000101=>0111010
[6,1,7,2,3,5,8,4]=>1010001=>1000101=>0111010
[4,3,8,7,5,6,2,1]=>1011011=>1101101=>0010010
[7,1,6,2,3,5,8,4]=>1010001=>1000101=>0111010
[8,1,6,2,3,5,7,4]=>1010001=>1000101=>0111010
[8,1,7,2,3,5,6,4]=>1010001=>1000101=>0111010
[5,8,3,7,4,6,2,1]=>0101011=>1101010=>0010101
[6,8,7,3,4,5,2,1]=>0110011=>1100110=>0011001
[8,6,1,2,3,4,7,5]=>1100001=>1000011=>0111100
[8,6,2,3,5,1,4,7]=>1100100=>0010011=>1101100
[8,2,4,5,7,3,1,6]=>1000110=>0110001=>1001110
[2,6,3,8,7,5,4,1]=>0101111=>1111010=>0000101
[8,2,3,7,5,4,1,6]=>1001110=>0111001=>1000110
[8,2,6,3,5,4,1,7]=>1010110=>0110101=>1001010
[8,6,1,5,2,4,3,7]=>1101010=>0101011=>1010100
[8,6,2,4,1,5,3,7]=>1101010=>0101011=>1010100
[8,4,1,6,5,3,2,7]=>1101110=>0111011=>1000100
[8,3,6,1,5,4,2,7]=>1010110=>0110101=>1001010
[8,3,2,6,5,4,1,7]=>1101110=>0111011=>1000100
[8,3,2,5,7,4,1,6]=>1100110=>0110011=>1001100
[8,3,1,7,5,4,2,6]=>1101110=>0111011=>1000100
[6,1,3,8,7,5,4,2]=>1001111=>1111001=>0000110
[3,6,1,8,7,5,4,2]=>0101111=>1111010=>0000101
[3,8,1,5,7,6,4,2]=>0100111=>1110010=>0001101
[3,5,2,8,7,6,4,1]=>0101111=>1111010=>0000101
[3,4,8,2,7,6,5,1]=>0010111=>1110100=>0001011
[3,4,8,7,1,6,5,2]=>0011011=>1101100=>0010011
[8,1,3,5,7,6,4,2]=>1000111=>1110001=>0001110
[4,1,8,5,7,6,3,2]=>1010111=>1110101=>0001010
[8,2,7,1,4,5,6,3]=>1010001=>1000101=>0111010
[8,1,7,3,4,6,2,5]=>1010010=>0100101=>1011010
[8,3,1,7,2,6,5,4]=>1101011=>1101011=>0010100
[3,8,2,4,7,6,5,1]=>0100111=>1110010=>0001101
[2,8,3,7,4,6,5,1]=>0101011=>1101010=>0010101
[8,2,3,7,1,6,5,4]=>1001011=>1101001=>0010110
[8,2,7,1,3,6,5,4]=>1010011=>1100101=>0011010
[8,1,7,2,6,4,3,5]=>1010110=>0110101=>1001010
[8,1,7,5,2,4,3,6]=>1011010=>0101101=>1010010
[8,2,3,7,4,6,1,5]=>1001010=>0101001=>1010110
[2,4,8,5,7,6,3,1]=>0010111=>1110100=>0001011
[8,2,4,3,7,6,1,5]=>1010110=>0110101=>1001010
[8,2,7,3,5,1,4,6]=>1010100=>0010101=>1101010
[8,2,7,4,3,1,5,6]=>1011100=>0011101=>1100010
[8,2,1,5,7,6,4,3]=>1100111=>1110011=>0001100
[6,1,8,2,7,5,4,3]=>1010111=>1110101=>0001010
[8,1,5,2,7,6,4,3]=>1010111=>1110101=>0001010
[8,1,7,2,4,6,5,3]=>1010011=>1100101=>0011010
[8,2,4,1,7,6,5,3]=>1010111=>1110101=>0001010
[4,2,8,3,7,6,5,1]=>1010111=>1110101=>0001010
[4,8,2,1,7,6,5,3]=>0110111=>1110110=>0001001
[5,1,8,7,2,6,4,3]=>1011011=>1101101=>0010010
[5,8,1,3,7,6,2,4]=>0100110=>0110010=>1001101
[8,2,5,4,1,7,6,3]=>1011011=>1101101=>0010010
[5,1,4,8,7,6,3,2]=>1001111=>1111001=>0000110
[8,1,4,3,7,6,5,2]=>1010111=>1110101=>0001010
[4,8,1,3,7,6,5,2]=>0100111=>1110010=>0001101
[4,3,8,1,7,6,5,2]=>1010111=>1110101=>0001010
[6,2,8,1,5,7,3,4]=>1010010=>0100101=>1011010
[7,2,5,4,1,8,6,3]=>1011011=>1101101=>0010010
[7,3,2,8,5,6,1,4]=>1101010=>0101011=>1010100
[5,4,6,8,7,2,1,3]=>1001110=>0111001=>1000110
[1,7,6,3,2,8,4,5]=>0111010=>0101110=>1010001
[6,5,8,3,4,1,7,2]=>1010101=>1010101=>0101010
[4,1,2,8,5,3,6,7]=>1001100=>0011001=>1100110
[3,5,8,2,6,1,7,4]=>0010101=>1010100=>0101011
[3,7,6,2,8,4,5,1]=>0110101=>1010110=>0101001
[4,3,6,8,5,1,2,7]=>1001100=>0011001=>1100110
[2,7,1,5,8,4,3,6]=>0100110=>0110010=>1001101
[2,7,6,1,8,4,3,5]=>0110110=>0110110=>1001001
[7,1,2,6,3,5,4,8]=>1001010=>0101001=>1010110
[7,2,6,3,4,5,1,8]=>1010010=>0100101=>1011010
[4,1,2,7,8,5,3,6]=>1000110=>0110001=>1001110
[4,7,3,1,2,6,8,5]=>0110001=>1000110=>0111001
[3,8,5,6,4,2,7,1]=>0101101=>1011010=>0100101
[3,2,6,4,7,8,5,1]=>1010011=>1100101=>0011010
[4,2,7,5,8,3,1,6]=>1010110=>0110101=>1001010
[5,2,1,4,7,8,3,6]=>1100010=>0100011=>1011100
[5,6,2,7,3,4,8,1]=>0101001=>1001010=>0110101
[1,5,8,6,4,2,3,7]=>0011100=>0011100=>1100011
[2,5,8,6,4,1,7,3]=>0011101=>1011100=>0100011
[4,7,2,3,1,6,8,5]=>0101001=>1001010=>0110101
[7,4,6,2,8,3,5,1]=>1010101=>1010101=>0101010
[3,4,6,5,1,2,7,8]=>0011000=>0001100=>1110011
[4,3,8,2,5,7,1,6]=>1010010=>0100101=>1011010
[4,1,6,2,5,3,7,8]=>1010100=>0010101=>1101010
[4,2,6,1,5,3,8,7]=>1010101=>1010101=>0101010
[6,7,2,3,1,5,8,4]=>0101001=>1001010=>0110101
[2,1,5,7,8,3,6,4]=>1000101=>1010001=>0101110
[4,7,5,8,6,3,1,2]=>0101110=>0111010=>1000101
[2,4,8,3,7,1,5,6]=>0010100=>0010100=>1101011
[5,2,8,4,1,6,3,7]=>1011010=>0101101=>1010010
[7,6,5,2,1,8,4,3]=>1111011=>1101111=>0010000
[2,7,5,1,8,3,6,4]=>0110101=>1010110=>0101001
[5,1,8,7,4,3,6,2]=>1011101=>1011101=>0100010
[3,8,7,2,4,6,1,5]=>0110010=>0100110=>1011001
[5,7,1,3,2,4,8,6]=>0101001=>1001010=>0110101
[4,2,7,6,3,5,8,1]=>1011001=>1001101=>0110010
[8,4,7,6,3,5,1,2]=>1011010=>0101101=>1010010
[8,1,7,4,2,3,5,6]=>1011000=>0001101=>1110010
[6,5,1,3,8,7,4,2]=>1100111=>1110011=>0001100
[6,1,8,5,3,7,2,4]=>1011010=>0101101=>1010010
[5,1,6,8,3,7,4,2]=>1001011=>1101001=>0010110
[8,6,5,1,7,4,3,2]=>1110111=>1110111=>0001000
[7,6,4,1,3,5,8,2]=>1110001=>1000111=>0111000
[8,2,3,7,1,4,5,6]=>1001000=>0001001=>1110110
[5,6,2,7,4,3,1,8]=>0101110=>0111010=>1000101
[3,7,8,2,6,1,4,5]=>0010100=>0010100=>1101011
[3,7,8,5,2,1,4,6]=>0011100=>0011100=>1100011
[4,8,6,5,1,2,7,3]=>0111001=>1001110=>0110001
[4,8,6,5,1,2,3,7]=>0111000=>0001110=>1110001
[3,8,7,6,5,1,2,4]=>0111100=>0011110=>1100001
[5,8,2,6,1,4,7,3]=>0101001=>1001010=>0110101
[3,8,7,5,6,1,4,2]=>0110101=>1010110=>0101001
[4,6,3,8,7,5,1,2]=>0101110=>0111010=>1000101
[2,8,4,1,5,7,6,3]=>0110011=>1100110=>0011001
[1,8,4,2,5,7,6,3]=>0110011=>1100110=>0011001
[2,8,5,4,1,7,6,3]=>0111011=>1101110=>0010001
[2,5,8,3,7,1,6,4]=>0010101=>1010100=>0101011
[1,8,5,2,4,7,6,3]=>0110011=>1100110=>0011001
[1,4,6,2,8,7,5,3]=>0010111=>1110100=>0001011
[7,8,2,4,1,6,5,3]=>0101011=>1101010=>0010101
[2,4,6,1,8,7,5,3]=>0010111=>1110100=>0001011
[2,8,4,5,1,7,6,3]=>0101011=>1101010=>0010101
[3,5,8,1,7,6,2,4]=>0010110=>0110100=>1001011
[3,5,8,2,7,6,1,4]=>0010110=>0110100=>1001011
[2,1,6,8,7,5,3,4]=>1001110=>0111001=>1000110
[1,8,2,4,5,7,6,3]=>0100011=>1100010=>0011101
[1,3,8,2,5,7,6,4]=>0010011=>1100100=>0011011
[2,3,8,1,5,7,6,4]=>0010011=>1100100=>0011011
[2,6,1,8,7,5,3,4]=>0101110=>0111010=>1000101
[1,6,2,8,7,5,3,4]=>0101110=>0111010=>1000101
[1,6,3,8,7,5,2,4]=>0101110=>0111010=>1000101
[2,6,3,8,7,5,1,4]=>0101110=>0111010=>1000101
[3,2,8,1,5,7,6,4]=>1010011=>1100101=>0011010
[3,1,8,2,5,7,6,4]=>1010011=>1100101=>0011010
[2,1,8,3,5,7,6,4]=>1010011=>1100101=>0011010
[7,8,2,1,4,6,5,3]=>0110011=>1100110=>0011001
[2,3,6,8,7,5,1,4]=>0001110=>0111000=>1000111
[3,1,6,8,7,2,5,4]=>1001101=>1011001=>0100110
[3,8,4,5,1,6,2,7]=>0101010=>0101010=>1010101
[6,1,4,5,7,2,3,8]=>1000100=>0010001=>1101110
[8,1,4,7,6,3,2,5]=>1001110=>0111001=>1000110
[8,3,1,6,4,7,2,5]=>1101010=>0101011=>1010100
[5,3,8,6,2,7,1,4]=>1011010=>0101101=>1010010
[8,3,6,1,5,7,2,4]=>1010010=>0100101=>1011010
[8,4,6,3,1,2,5,7]=>1011000=>0001101=>1110010
[6,8,1,4,5,2,3,7]=>0100100=>0010010=>1101101
[1,5,8,4,6,2,3,7]=>0010100=>0010100=>1101011
[5,6,8,1,4,2,3,7]=>0010100=>0010100=>1101011
[5,7,4,8,1,2,3,6]=>0101000=>0001010=>1110101
[4,7,8,1,2,6,3,5]=>0010010=>0100100=>1011011
[8,7,1,5,6,2,3,4]=>1100100=>0010011=>1101100
[1,6,5,8,7,2,3,4]=>0101100=>0011010=>1100101
[3,7,1,6,2,4,8,5]=>0101001=>1001010=>0110101
[5,1,2,7,6,8,3,4]=>1001010=>0101001=>1010110
[1,7,6,5,8,2,3,4]=>0110100=>0010110=>1101001
[1,6,8,5,7,2,3,4]=>0010100=>0010100=>1101011
[7,5,1,2,6,8,3,4]=>1100010=>0100011=>1011100
[6,1,5,2,7,8,3,4]=>1010010=>0100101=>1011010
[5,1,2,6,8,7,3,4]=>1000110=>0110001=>1001110
[1,8,6,2,5,7,3,4]=>0110010=>0100110=>1011001
[5,7,8,1,2,6,3,4]=>0010010=>0100100=>1011011
[8,1,5,7,6,2,3,4]=>1001100=>0011001=>1100110
[3,7,1,2,8,4,6,5]=>0100101=>1010010=>0101101
[1,5,8,7,6,2,3,4]=>0011100=>0011100=>1100011
[7,8,6,1,5,2,3,4]=>0110100=>0010110=>1101001
[4,5,7,2,3,1,8,6]=>0010101=>1010100=>0101011
[3,7,8,1,4,6,5,2]=>0010011=>1100100=>0011011
[2,5,8,7,4,1,3,6]=>0011100=>0011100=>1100011
[2,6,4,7,5,3,8,1]=>0101101=>1011010=>0100101
[6,2,4,7,1,3,8,5]=>1001001=>1001001=>0110110
[7,3,5,1,4,2,8,6]=>1010101=>1010101=>0101010
[5,4,7,1,3,2,8,6]=>1010101=>1010101=>0101010
[6,1,4,7,5,3,8,2]=>1001101=>1011001=>0100110
[8,7,4,3,1,5,6,2]=>1111001=>1001111=>0110000
[8,7,1,4,3,5,6,2]=>1101001=>1001011=>0110100
[6,1,8,4,7,3,2,5]=>1010110=>0110101=>1001010
[4,7,3,6,1,2,8,5]=>0101001=>1001010=>0110101
[5,2,1,7,4,3,8,6]=>1101101=>1011011=>0100100
[4,7,6,2,3,1,8,5]=>0110101=>1010110=>0101001
[7,6,8,2,5,3,4,1]=>1010101=>1010101=>0101010
[2,3,6,1,8,7,5,4]=>0010111=>1110100=>0001011
[2,6,8,7,5,3,1,4]=>0011110=>0111100=>1000011
[6,4,1,7,5,2,8,3]=>1101101=>1011011=>0100100
[5,7,8,2,3,6,1,4]=>0010010=>0100100=>1011011
[4,8,7,1,2,5,6,3]=>0110001=>1000110=>0111001
[2,8,7,4,1,5,6,3]=>0111001=>1001110=>0110001
[8,6,2,1,5,7,4,3]=>1110011=>1100111=>0011000
[3,8,6,7,5,2,1,4]=>0101110=>0111010=>1000101
[6,1,3,7,5,8,2,4]=>1001010=>0101001=>1010110
[4,7,3,1,8,5,6,2]=>0110101=>1010110=>0101001
[1,3,8,5,2,7,4,6]=>0011010=>0101100=>1010011
[1,3,8,6,7,2,4,5]=>0010100=>0010100=>1101011
[2,8,3,7,6,1,4,5]=>0101100=>0011010=>1100101
[1,3,8,7,6,2,4,5]=>0011100=>0011100=>1100011
[1,4,6,8,7,2,3,5]=>0001100=>0011000=>1100111
[7,6,4,8,5,1,3,2]=>1101101=>1011011=>0100100
[7,2,6,5,8,1,3,4]=>1010100=>0010101=>1101010
[3,6,7,5,2,8,4,1]=>0011011=>1101100=>0010011
[4,6,5,7,2,8,1,3]=>0101010=>0101010=>1010101
[5,3,6,7,8,1,4,2]=>1000101=>1010001=>0101110
[6,3,2,8,5,4,1,7]=>1101110=>0111011=>1000100
[3,8,4,1,5,2,6,7]=>0110100=>0010110=>1101001
[2,5,7,4,3,1,6,8]=>0011100=>0011100=>1100011
[5,3,4,2,7,1,6,8]=>1010100=>0010101=>1101010
[3,7,5,4,1,2,6,8]=>0111000=>0001110=>1110001
[4,2,5,1,3,8,7,6]=>1010011=>1100101=>0011010
[4,3,5,1,2,7,6,8]=>1010010=>0100101=>1011010
[5,3,4,1,7,2,6,8]=>1010100=>0010101=>1101010
[4,1,6,3,5,2,7,8]=>1010100=>0010101=>1101010
[3,1,7,2,5,6,4,8]=>1010010=>0100101=>1011010
[3,7,5,4,2,1,6,8]=>0111100=>0011110=>1100001
[7,3,2,1,6,4,5,8]=>1110100=>0010111=>1101000
[2,8,6,1,7,4,3,5]=>0110110=>0110110=>1001001
[2,5,4,6,1,3,7,8]=>0101000=>0001010=>1110101
[2,5,6,4,1,3,7,8]=>0011000=>0001100=>1110011
[8,5,2,6,1,3,7,4]=>1101001=>1001011=>0110100
[7,1,5,6,3,2,4,8]=>1001100=>0011001=>1100110
[7,1,2,5,4,6,3,8]=>1001010=>0101001=>1010110
[2,4,1,6,5,3,7,8]=>0101100=>0011010=>1100101
[4,1,2,7,5,6,3,8]=>1001010=>0101001=>1010110
[7,1,2,6,5,4,3,8]=>1001110=>0111001=>1000110
[8,2,1,5,6,3,7,4]=>1100101=>1010011=>0101100
[6,1,4,5,3,2,7,8]=>1001100=>0011001=>1100110
[3,1,6,5,4,2,7,8]=>1011100=>0011101=>1100010
[3,1,4,6,5,2,7,8]=>1001100=>0011001=>1100110
[5,6,3,8,7,4,1,2]=>0101110=>0111010=>1000101
[5,2,6,8,7,4,1,3]=>1001110=>0111001=>1000110
[5,2,3,1,4,8,6,7]=>1010010=>0100101=>1011010
[5,4,1,3,2,8,6,7]=>1101010=>0101011=>1010100
[5,1,3,4,2,8,6,7]=>1001010=>0101001=>1010110
[4,2,7,3,8,5,1,6]=>1010110=>0110101=>1001010
[4,3,7,2,8,5,6,1]=>1010101=>1010101=>0101010
[5,3,1,2,4,8,6,7]=>1100010=>0100011=>1011100
[1,3,2,6,4,8,7,5]=>0101011=>1101010=>0010101
[1,6,2,5,3,8,7,4]=>0101011=>1101010=>0010101
[1,8,2,6,3,7,5,4]=>0101011=>1101010=>0010101
[1,8,3,6,4,7,5,2]=>0101011=>1101010=>0010101
[1,7,2,6,3,8,5,4]=>0101011=>1101010=>0010101
[1,5,2,7,4,8,6,3]=>0101011=>1101010=>0010101
[1,4,2,8,5,7,6,3]=>0101011=>1101010=>0010101
[4,8,1,3,2,6,5,7]=>0101010=>0101010=>1010101
[1,5,3,8,4,7,6,2]=>0101011=>1101010=>0010101
[2,6,3,8,1,5,4,7]=>0101010=>0101010=>1010101
[8,3,1,4,2,6,5,7]=>1101010=>0101011=>1010100
[6,8,7,3,5,2,4,1]=>0110101=>1010110=>0101001
[8,3,5,1,2,6,4,7]=>1010010=>0100101=>1011010
[8,6,3,1,5,4,2,7]=>1110110=>0110111=>1001000
[8,6,4,1,5,3,2,7]=>1110110=>0110111=>1001000
[8,6,5,4,1,3,2,7]=>1111010=>0101111=>1010000
[5,3,8,7,4,6,2,1]=>1011011=>1101101=>0010010
[2,3,8,7,4,6,1,5]=>0011010=>0101100=>1010011
[8,3,5,7,4,1,2,6]=>1001100=>0011001=>1100110
[4,8,5,3,1,2,7,6]=>0111001=>1001110=>0110001
[6,8,7,3,1,5,4,2]=>0111011=>1101110=>0010001
[6,8,5,4,1,3,7,2]=>0111001=>1001110=>0110001
[2,5,8,7,4,6,3,1]=>0011011=>1101100=>0010011
[4,8,7,6,5,1,3,2]=>0111101=>1011110=>0100001
[3,8,7,5,1,6,2,4]=>0111010=>0101110=>1010001
[2,3,8,7,5,6,1,4]=>0011010=>0101100=>1010011
[2,8,7,1,3,6,4,5]=>0110010=>0100110=>1011001
[8,5,4,7,2,1,3,6]=>1101100=>0011011=>1100100
[6,8,7,3,5,2,1,4]=>0110110=>0110110=>1001001
[3,5,8,6,4,2,7,1]=>0011101=>1011100=>0100011
[6,8,4,1,5,2,7,3]=>0110101=>1010110=>0101001
[6,8,2,1,7,5,3,4]=>0110110=>0110110=>1001001
[5,8,4,6,1,2,7,3]=>0101001=>1001010=>0110101
[2,4,8,6,5,1,7,3]=>0011101=>1011100=>0100011
[4,8,7,6,5,2,1,3]=>0111110=>0111110=>1000001
[4,8,7,5,1,6,2,3]=>0111010=>0101110=>1010001
[4,5,2,1,8,6,7,3]=>0110101=>1010110=>0101001
[2,8,3,5,6,7,1,4]=>0100010=>0100010=>1011101
[5,6,2,4,7,1,8,3]=>0100101=>1010010=>0101101
[2,7,5,4,6,1,8,3]=>0110101=>1010110=>0101001
[3,7,5,4,6,2,8,1]=>0110101=>1010110=>0101001
[2,6,7,4,1,3,8,5]=>0011001=>1001100=>0110011
[6,5,7,4,1,3,8,2]=>1011001=>1001101=>0110010
[2,4,6,3,5,7,8,1]=>0010001=>1000100=>0111011
[3,6,4,2,5,7,8,1]=>0110001=>1000110=>0111001
[2,3,6,1,5,7,8,4]=>0010001=>1000100=>0111011
[4,3,6,2,5,7,8,1]=>1010001=>1000101=>0111010
[4,6,1,2,5,7,8,3]=>0100001=>1000010=>0111101
[2,6,4,1,5,7,8,3]=>0110001=>1000110=>0111001
[2,4,1,6,5,7,8,3]=>0101001=>1001010=>0110101
[7,8,4,1,6,3,5,2]=>0110101=>1010110=>0101001
[8,7,5,6,1,3,4,2]=>1101001=>1001011=>0110100
[1,4,5,8,6,3,2,7]=>0001110=>0111000=>1000111
[8,4,5,7,2,6,1,3]=>1001010=>0101001=>1010110
[8,1,7,5,3,6,2,4]=>1011010=>0101101=>1010010
[5,2,8,3,6,1,4,7]=>1010100=>0010101=>1101010
[5,2,6,3,1,7,8,4]=>1011001=>1001101=>0110010
[5,7,6,1,2,3,8,4]=>0110001=>1000110=>0111001
[5,3,2,1,8,6,4,7]=>1110110=>0110111=>1001000
[4,3,6,2,1,8,7,5]=>1011011=>1101101=>0010010
[5,3,6,4,8,2,1,7]=>1010110=>0110101=>1001010
[3,7,4,5,1,6,2,8]=>0101010=>0101010=>1010101
[3,6,4,5,8,2,1,7]=>0100110=>0110010=>1001101
[6,1,4,5,2,8,7,3]=>1001011=>1101001=>0010110
[7,2,4,5,1,6,3,8]=>1001010=>0101001=>1010110
[7,5,4,1,6,3,2,8]=>1110110=>0110111=>1001000
[1,5,4,8,6,3,2,7]=>0101110=>0111010=>1000101
[7,5,4,8,6,3,1,2]=>1101110=>0111011=>1000100
[1,8,7,5,3,6,4,2]=>0111011=>1101110=>0010001
[8,3,7,4,1,6,2,5]=>1011010=>0101101=>1010010
[8,5,4,1,6,3,2,7]=>1110110=>0110111=>1001000
[1,7,4,2,6,5,3,8]=>0110110=>0110110=>1001001
[8,2,1,5,6,7,3,4]=>1100010=>0100011=>1011100
[6,3,1,8,4,7,2,5]=>1101010=>0101011=>1010100
[7,1,4,8,6,3,2,5]=>1001110=>0111001=>1000110
[4,1,8,5,6,7,2,3]=>1010010=>0100101=>1011010
[5,7,4,8,6,2,1,3]=>0101110=>0111010=>1000101
[5,3,6,8,2,7,1,4]=>1001010=>0101001=>1010110
[6,3,7,4,8,2,1,5]=>1010110=>0110101=>1001010
[5,3,6,1,4,7,2,8]=>1010010=>0100101=>1011010
[4,3,6,8,2,7,1,5]=>1001010=>0101001=>1010110
[5,3,7,4,8,2,1,6]=>1010110=>0110101=>1001010
[5,3,8,4,1,6,2,7]=>1011010=>0101101=>1010010
[5,3,8,1,4,7,2,6]=>1010010=>0100101=>1011010
[5,8,4,1,6,3,2,7]=>0110110=>0110110=>1001001
[7,3,8,4,1,6,2,5]=>1011010=>0101101=>1010010
[1,5,8,3,6,7,4,2]=>0010011=>1100100=>0011011
[1,8,2,5,6,7,3,4]=>0100010=>0100010=>1011101
[7,8,4,1,6,5,2,3]=>0110110=>0110110=>1001001
[6,3,8,1,5,7,2,4]=>1010010=>0100101=>1011010
[8,3,1,2,5,7,4,6]=>1100010=>0100011=>1011100
[8,1,4,2,6,5,3,7]=>1010110=>0110101=>1001010
[3,8,5,6,2,7,1,4]=>0101010=>0101010=>1010101
[2,4,5,8,7,3,1,6]=>0001110=>0111000=>1000111
[4,3,1,5,6,2,8,7]=>1100101=>1010011=>0101100
[4,1,5,8,6,7,2,3]=>1001010=>0101001=>1010110
[4,3,7,6,1,2,8,5]=>1011001=>1001101=>0110010
[4,7,5,6,1,2,8,3]=>0101001=>1001010=>0110101
[4,5,1,8,6,7,3,2]=>0101011=>1101010=>0010101
[3,4,5,8,6,7,2,1]=>0001011=>1101000=>0010111
[2,1,5,8,6,7,4,3]=>1001011=>1101001=>0010110
[3,4,5,8,7,1,2,6]=>0001100=>0011000=>1100111
[4,7,1,5,6,2,8,3]=>0100101=>1010010=>0101101
[2,6,4,7,1,3,8,5]=>0101001=>1001010=>0110101
[5,3,8,6,4,7,2,1]=>1011011=>1101101=>0010010
[6,4,1,5,7,8,3,2]=>1100011=>1100011=>0011100
[3,6,4,7,2,1,8,5]=>0101101=>1011010=>0100101
[3,8,4,6,1,7,2,5]=>0101010=>0101010=>1010101
[3,8,5,6,4,7,2,1]=>0101011=>1101010=>0010101
[3,8,6,5,2,7,4,1]=>0111011=>1101110=>0010001
[3,8,7,5,2,1,4,6]=>0111100=>0011110=>1100001
[6,4,1,7,3,2,8,5]=>1101101=>1011011=>0100100
[5,1,4,6,7,2,8,3]=>1000101=>1010001=>0101110
[6,5,4,7,1,3,8,2]=>1101001=>1001011=>0110100
[2,1,6,5,3,7,8,4]=>1011001=>1001101=>0110010
[6,1,4,7,2,3,8,5]=>1001001=>1001001=>0110110
[1,6,2,5,4,8,3,7]=>0101010=>0101010=>1010101
[4,1,2,7,5,8,3,6]=>1001010=>0101001=>1010110
[6,1,3,5,8,2,4,7]=>1000100=>0010001=>1101110
[5,6,4,3,1,8,2,7]=>0111010=>0101110=>1010001
[6,2,3,5,8,1,4,7]=>1000100=>0010001=>1101110
[6,7,2,3,8,4,5,1]=>0100101=>1010010=>0101101
[6,7,2,1,3,8,4,5]=>0110010=>0100110=>1011001
[5,7,4,1,8,3,2,6]=>0110110=>0110110=>1001001
[4,1,7,5,8,3,6,2]=>1010101=>1010101=>0101010
[6,7,1,3,8,4,5,2]=>0100101=>1010010=>0101101
[1,6,7,4,3,8,5,2]=>0011011=>1101100=>0010011
[6,1,7,4,2,8,5,3]=>1011011=>1101101=>0010010
[2,1,6,7,4,3,8,5]=>1001101=>1011001=>0100110
[6,7,3,2,1,8,4,5]=>0111010=>0101110=>1010001
[2,5,7,3,1,4,8,6]=>0011001=>1001100=>0110011
[6,7,3,2,8,4,5,1]=>0110101=>1010110=>0101001
[2,6,7,4,3,8,5,1]=>0011011=>1101100=>0010011
[1,2,6,7,4,3,8,5]=>0001101=>1011000=>0100111
[1,7,5,8,2,4,3,6]=>0101010=>0101010=>1010101
[2,7,1,8,4,6,3,5]=>0101010=>0101010=>1010101
[2,7,5,8,1,6,3,4]=>0101010=>0101010=>1010101
[1,6,7,3,8,5,4,2]=>0010111=>1110100=>0001011
[6,7,1,8,4,5,3,2]=>0101011=>1101010=>0010101
[8,6,1,5,4,3,2,7]=>1101110=>0111011=>1000100
[2,4,3,8,5,1,6,7]=>0101100=>0011010=>1100101
[1,5,6,7,3,8,2,4]=>0001010=>0101000=>1010111
[1,6,5,4,8,3,2,7]=>0110110=>0110110=>1001001
[3,8,7,2,4,6,5,1]=>0110011=>1100110=>0011001
[1,3,7,6,4,8,5,2]=>0011011=>1101100=>0010011
[3,1,8,7,6,4,2,5]=>1011110=>0111101=>1000010
[3,1,8,7,5,4,2,6]=>1011110=>0111101=>1000010
[3,1,7,6,5,4,2,8]=>1011110=>0111101=>1000010
[4,7,1,6,5,3,2,8]=>0101110=>0111010=>1000101
[4,8,1,6,5,3,2,7]=>0101110=>0111010=>1000101
[4,8,1,7,5,3,2,6]=>0101110=>0111010=>1000101
[8,4,1,7,6,3,2,5]=>1101110=>0111011=>1000100
[5,4,1,8,6,3,2,7]=>1101110=>0111011=>1000100
[5,4,1,7,6,3,2,8]=>1101110=>0111011=>1000100
[6,4,1,7,5,3,2,8]=>1101110=>0111011=>1000100
[6,4,1,8,5,3,2,7]=>1101110=>0111011=>1000100
[8,4,1,7,5,3,2,6]=>1101110=>0111011=>1000100
[7,4,1,6,5,3,2,8]=>1101110=>0111011=>1000100
[7,5,6,1,4,3,2,8]=>1010110=>0110101=>1001010
[8,5,6,1,4,3,2,7]=>1010110=>0110101=>1001010
[5,7,6,1,4,3,2,8]=>0110110=>0110110=>1001001
[5,8,6,1,4,3,2,7]=>0110110=>0110110=>1001001
[6,7,5,1,4,3,2,8]=>0110110=>0110110=>1001001
[8,7,5,1,4,3,2,6]=>1110110=>0110111=>1001000
[8,6,5,1,4,3,2,7]=>1110110=>0110111=>1001000
[1,8,6,3,4,2,5,7]=>0110100=>0010110=>1101001
[3,1,6,4,5,7,2,8]=>1010010=>0100101=>1011010
[7,6,3,8,4,5,2,1]=>1101011=>1101011=>0010100
[8,2,7,6,1,4,3,5]=>1011010=>0101101=>1010010
[5,2,7,8,1,4,3,6]=>1001010=>0101001=>1010110
[8,2,7,6,1,4,5,3]=>1011001=>1001101=>0110010
[5,2,3,7,1,6,8,4]=>1001001=>1001001=>0110110
[1,7,5,2,6,4,8,3]=>0110101=>1010110=>0101001
[7,1,3,6,8,2,4,5]=>1000100=>0010001=>1101110
[1,2,5,7,8,4,6,3]=>0000101=>1010000=>0101111
[3,1,2,7,5,4,8,6]=>1001101=>1011001=>0100110
[6,7,4,1,3,2,8,5]=>0110101=>1010110=>0101001
[1,7,2,8,4,3,5,6]=>0101100=>0011010=>1100101
[4,1,6,5,7,8,2,3]=>1010010=>0100101=>1011010
[1,6,3,5,7,8,2,4]=>0100010=>0100010=>1011101
[8,6,1,7,5,2,4,3]=>1101101=>1011011=>0100100
[7,6,4,1,8,3,2,5]=>1110110=>0110111=>1001000
[8,4,1,6,5,2,7,3]=>1101101=>1011011=>0100100
[1,5,3,4,7,8,2,6]=>0100010=>0100010=>1011101
[4,2,1,5,7,8,3,6]=>1100010=>0100011=>1011100
[5,1,4,6,7,8,2,3]=>1000010=>0100001=>1011110
[4,1,5,3,7,8,2,6]=>1010010=>0100101=>1011010
[8,1,4,6,5,2,7,3]=>1001101=>1011001=>0100110
[7,1,5,4,6,3,2,8]=>1010110=>0110101=>1001010
[8,2,1,6,7,5,4,3]=>1100111=>1110011=>0001100
[1,2,4,7,6,3,8,5]=>0001101=>1011000=>0100111
[6,7,4,1,8,5,2,3]=>0110110=>0110110=>1001001
[8,6,4,1,5,7,3,2]=>1110011=>1100111=>0011000
[5,2,4,3,7,1,6,8]=>1010100=>0010101=>1101010
[6,1,5,4,8,3,2,7]=>1010110=>0110101=>1001010
[1,2,8,7,4,3,6,5]=>0011101=>1011100=>0100011
[3,2,1,7,5,8,4,6]=>1101010=>0101011=>1010100
[8,1,7,6,4,2,5,3]=>1011101=>1011101=>0100010
[1,3,6,4,7,8,2,5]=>0010010=>0100100=>1011011
[5,1,3,4,7,8,2,6]=>1000010=>0100001=>1011110
[4,5,1,3,7,8,2,6]=>0100010=>0100010=>1011101
[5,2,3,1,7,8,4,6]=>1010010=>0100101=>1011010
[1,6,4,3,7,8,2,5]=>0110010=>0100110=>1011001
[7,6,4,3,1,5,2,8]=>1111010=>0101111=>1010000
[3,2,6,4,1,8,5,7]=>1011010=>0101101=>1010010
[7,5,4,6,1,3,2,8]=>1101010=>0101011=>1010100
[8,4,6,5,1,2,7,3]=>1011001=>1001101=>0110010
[1,5,6,3,7,8,2,4]=>0010010=>0100100=>1011011
[4,2,5,1,7,8,3,6]=>1010010=>0100101=>1011010
[3,5,8,6,1,4,2,7]=>0011010=>0101100=>1010011
[1,8,4,2,7,6,3,5]=>0110110=>0110110=>1001001
[7,3,8,1,6,5,4,2]=>1010111=>1110101=>0001010
[2,4,1,8,7,3,6,5]=>0101101=>1011010=>0100101
[7,3,8,6,1,5,4,2]=>1011011=>1101101=>0010010
[3,5,1,7,8,2,6,4]=>0100101=>1010010=>0101101
[5,4,7,8,2,1,6,3]=>1001101=>1011001=>0100110
[5,3,6,1,8,4,2,7]=>1010110=>0110101=>1001010
[3,4,6,2,1,8,5,7]=>0011010=>0101100=>1010011
[5,6,4,8,3,2,1,7]=>0101110=>0111010=>1000101
[5,7,4,8,2,1,6,3]=>0101101=>1011010=>0100101
[4,7,5,8,2,1,6,3]=>0101101=>1011010=>0100101
[4,7,3,2,8,1,5,6]=>0110100=>0010110=>1101001
[7,1,2,6,3,8,5,4]=>1001011=>1101001=>0010110
[8,1,2,6,3,7,5,4]=>1001011=>1101001=>0010110
[8,1,2,7,6,3,5,4]=>1001101=>1011001=>0100110
[4,8,7,3,1,6,2,5]=>0111010=>0101110=>1010001
[4,7,8,3,1,6,2,5]=>0011010=>0101100=>1010011
[7,4,3,1,6,2,8,5]=>1110101=>1010111=>0101000
[7,4,3,1,8,6,2,5]=>1110110=>0110111=>1001000
[6,8,3,2,1,7,4,5]=>0111010=>0101110=>1010001
[3,7,6,2,4,8,1,5]=>0110010=>0100110=>1011001
[4,3,7,2,8,6,1,5]=>1010110=>0110101=>1001010
[5,1,2,6,3,8,7,4]=>1001011=>1101001=>0010110
[5,1,2,7,3,8,6,4]=>1001011=>1101001=>0010110
[6,1,2,7,3,5,8,4]=>1001001=>1001001=>0110110
[6,2,5,4,1,8,7,3]=>1011011=>1101101=>0010010
[4,6,3,2,1,8,7,5]=>0111011=>1101110=>0010001
[8,4,3,2,7,6,1,5]=>1110110=>0110111=>1001000
[1,5,8,4,7,6,3,2]=>0010111=>1110100=>0001011
[3,2,7,4,8,6,1,5]=>1010110=>0110101=>1001010
[7,4,3,2,8,6,1,5]=>1110110=>0110111=>1001000
[6,4,3,8,5,2,1,7]=>1101110=>0111011=>1000100
[8,2,5,4,7,6,1,3]=>1010110=>0110101=>1001010
[7,2,5,4,8,6,1,3]=>1010110=>0110101=>1001010
[6,2,8,7,5,4,1,3]=>1011110=>0111101=>1000010
[4,5,3,2,8,6,1,7]=>0110110=>0110110=>1001001
[3,2,5,4,8,6,1,7]=>1010110=>0110101=>1001010
[3,2,8,6,5,4,1,7]=>1011110=>0111101=>1000010
[8,4,3,6,5,2,1,7]=>1101110=>0111011=>1000100
[8,4,3,7,5,2,1,6]=>1101110=>0111011=>1000100
[3,2,7,8,5,4,1,6]=>1001110=>0111001=>1000110
[6,8,7,4,3,2,1,5]=>0111110=>0111110=>1000001
[6,3,2,1,8,7,4,5]=>1110110=>0110111=>1001000
[6,2,3,1,8,7,4,5]=>1010110=>0110101=>1001010
[7,2,1,5,8,4,6,3]=>1100101=>1010011=>0101100
[7,3,1,5,2,8,6,4]=>1101011=>1101011=>0010100
[7,1,6,4,2,8,5,3]=>1011011=>1101101=>0010010
[3,7,4,1,5,8,6,2]=>0110011=>1100110=>0011001
[6,7,1,4,3,8,5,2]=>0101011=>1101010=>0010101
[7,1,6,4,8,3,5,2]=>1010101=>1010101=>0101010
[8,5,3,6,1,7,4,2]=>1101011=>1101011=>0010100
[8,5,6,1,2,7,4,3]=>1010011=>1100101=>0011010
[3,6,4,1,5,2,8,7]=>0110101=>1010110=>0101001
[4,6,7,2,1,8,3,5]=>0011010=>0101100=>1010011
[3,7,1,8,2,5,4,6]=>0101010=>0101010=>1010101
[4,5,8,6,1,3,7,2]=>0011001=>1001100=>0110011
[4,5,8,6,2,7,3,1]=>0011011=>1101100=>0010011
[4,6,7,1,5,3,8,2]=>0010101=>1010100=>0101011
[4,6,7,2,1,8,5,3]=>0011011=>1101100=>0010011
[4,1,3,5,6,7,8,2]=>1000001=>1000001=>0111110
[4,6,8,3,2,7,1,5]=>0011010=>0101100=>1010011
[4,6,8,2,3,7,1,5]=>0010010=>0100100=>1011011
[4,5,8,3,7,1,2,6]=>0010100=>0010100=>1101011
[4,5,8,3,7,2,1,6]=>0010110=>0110100=>1001011
[3,7,8,4,6,2,5,1]=>0010101=>1010100=>0101011
[3,6,1,5,7,8,2,4]=>0100010=>0100010=>1011101
[3,8,2,5,4,7,1,6]=>0101010=>0101010=>1010101
[3,8,6,2,5,1,7,4]=>0110101=>1010110=>0101001
[4,5,8,6,2,1,7,3]=>0011101=>1011100=>0100011
[4,5,8,6,1,2,7,3]=>0011001=>1001100=>0110011
[2,1,5,8,6,3,7,4]=>1001101=>1011001=>0100110
[4,6,8,5,2,7,1,3]=>0011010=>0101100=>1010011
[3,7,8,5,2,6,1,4]=>0011010=>0101100=>1010011
[3,7,8,5,4,1,6,2]=>0011101=>1011100=>0100011
[4,6,8,5,3,1,7,2]=>0011101=>1011100=>0100011
[7,8,2,3,5,4,1,6]=>0100110=>0110010=>1001101
[4,6,5,1,7,3,8,2]=>0110101=>1010110=>0101001
[5,7,3,1,2,4,8,6]=>0110001=>1000110=>0111001
[6,3,2,5,1,7,4,8]=>1101010=>0101011=>1010100
[6,1,2,4,8,5,3,7]=>1000110=>0110001=>1001110
[6,3,1,7,2,5,8,4]=>1101001=>1001011=>0110100
[3,7,2,8,5,1,4,6]=>0101100=>0011010=>1100101
[3,6,5,2,4,7,1,8]=>0110010=>0100110=>1011001
[1,5,7,8,3,4,2,6]=>0001010=>0101000=>1010111
[6,8,4,3,1,7,2,5]=>0111010=>0101110=>1010001
[8,4,1,3,7,5,6,2]=>1100101=>1010011=>0101100
[4,8,1,3,7,5,6,2]=>0100101=>1010010=>0101101
[1,8,5,7,4,2,3,6]=>0101100=>0011010=>1100101
[2,1,6,8,5,3,4,7]=>1001100=>0011001=>1100110
[4,5,1,3,8,6,7,2]=>0100101=>1010010=>0101101
[1,2,6,8,5,3,4,7]=>0001100=>0011000=>1100111
[5,6,8,7,3,1,2,4]=>0011100=>0011100=>1100011
[1,5,6,8,4,2,3,7]=>0001100=>0011000=>1100111
[5,7,8,3,6,1,2,4]=>0010100=>0010100=>1101011
[1,5,8,6,2,4,3,7]=>0011010=>0101100=>1010011
[1,5,3,7,2,6,8,4]=>0101001=>1001010=>0110101
[1,5,2,4,8,6,7,3]=>0100101=>1010010=>0101101
[1,5,4,2,6,8,7,3]=>0110011=>1100110=>0011001
[5,7,6,8,3,1,2,4]=>0101100=>0011010=>1100101
[1,2,5,3,6,8,7,4]=>0010011=>1100100=>0011011
[7,1,5,6,2,3,8,4]=>1001001=>1001001=>0110110
[8,2,1,4,6,7,3,5]=>1100010=>0100011=>1011100
[7,2,6,1,3,4,8,5]=>1010001=>1000101=>0111010
[4,1,3,7,2,5,8,6]=>1001001=>1001001=>0110110
[6,2,7,5,1,3,8,4]=>1011001=>1001101=>0110010
[1,7,5,6,2,3,8,4]=>0101001=>1001010=>0110101
[3,7,6,1,2,4,8,5]=>0110001=>1000110=>0111001
[8,6,1,3,5,7,2,4]=>1100010=>0100011=>1011100
[1,7,4,3,8,2,5,6]=>0110100=>0010110=>1101001
[6,1,5,3,4,8,2,7]=>1010010=>0100101=>1011010
[3,6,7,5,2,8,1,4]=>0011010=>0101100=>1010011
[7,8,4,1,5,6,2,3]=>0110010=>0100110=>1011001
[5,8,1,3,6,7,2,4]=>0100010=>0100010=>1011101
[2,8,4,3,7,1,5,6]=>0110100=>0010110=>1101001
[3,8,4,6,7,1,2,5]=>0100100=>0010010=>1101101
[6,3,8,4,7,1,2,5]=>1010100=>0010101=>1101010
[1,2,5,4,8,3,6,7]=>0010100=>0010100=>1101011
[7,1,3,8,2,4,5,6]=>1001000=>0001001=>1110110
[8,1,3,7,2,4,5,6]=>1001000=>0001001=>1110110
[3,5,4,7,8,1,2,6]=>0100100=>0010010=>1101101
[8,3,1,4,7,2,5,6]=>1100100=>0010011=>1101100
[1,6,4,7,8,2,3,5]=>0100100=>0010010=>1101101
[1,3,7,8,5,6,2,4]=>0001010=>0101000=>1010111
[7,5,4,8,6,1,2,3]=>1101100=>0011011=>1100100
[8,2,6,7,5,1,3,4]=>1001100=>0011001=>1100110
[8,1,7,4,6,2,3,5]=>1010100=>0010101=>1101010
[2,5,8,4,7,1,3,6]=>0010100=>0010100=>1101011
[4,5,8,7,1,2,3,6]=>0011000=>0001100=>1110011
[4,1,8,5,7,2,3,6]=>1010100=>0010101=>1101010
[1,8,7,4,6,2,3,5]=>0110100=>0010110=>1101001
[2,6,5,4,1,8,3,7]=>0111010=>0101110=>1010001
[6,2,5,1,4,8,3,7]=>1010010=>0100101=>1011010
[6,5,4,1,3,8,2,7]=>1110010=>0100111=>1011000
[6,3,5,4,2,8,1,7]=>1011010=>0101101=>1010010
[1,3,8,7,4,2,6,5]=>0011101=>1011100=>0100011
[8,7,4,3,1,5,2,6]=>1111010=>0101111=>1010000
[8,2,5,1,4,6,7,3]=>1010001=>1000101=>0111010
[3,8,4,5,1,6,7,2]=>0101001=>1001010=>0110101
[8,5,4,1,3,6,7,2]=>1110001=>1000111=>0111000
[8,3,1,7,5,6,4,2]=>1101011=>1101011=>0010100
[8,4,7,6,5,3,1,2]=>1011110=>0111101=>1000010
[8,1,3,7,5,6,4,2]=>1001011=>1101001=>0010110
[8,1,4,5,7,6,3,2]=>1000111=>1110001=>0001110
[2,4,1,8,5,7,6,3]=>0101011=>1101010=>0010101
[8,2,1,4,7,6,3,5]=>1100110=>0110011=>1001100
[8,3,1,7,4,2,6,5]=>1101101=>1011011=>0100100
[8,2,7,3,1,6,5,4]=>1011011=>1101101=>0010010
[1,8,4,2,3,7,6,5]=>0110011=>1100110=>0011001
[3,1,2,8,7,4,6,5]=>1001101=>1011001=>0100110
[8,5,1,2,4,3,7,6]=>1100101=>1010011=>0101100
[2,8,3,7,4,1,6,5]=>0101101=>1011010=>0100101
[2,3,1,8,7,6,4,5]=>0101110=>0111010=>1000101
[4,2,8,7,3,1,5,6]=>1011100=>0011101=>1100010
[1,3,4,8,7,2,5,6]=>0001100=>0011000=>1100111
[8,1,3,4,6,7,2,5]=>1000010=>0100001=>1011110
[3,4,8,2,6,7,1,5]=>0010010=>0100100=>1011011
[3,6,8,2,5,1,7,4]=>0010101=>1010100=>0101011
[3,8,2,5,7,4,6,1]=>0100101=>1010010=>0101101
[8,4,2,1,7,5,6,3]=>1110101=>1010111=>0101000
[8,2,7,5,6,4,1,3]=>1010110=>0110101=>1001010
[6,2,8,5,4,1,7,3]=>1011101=>1011101=>0100010
[6,8,5,4,1,7,2,3]=>0111010=>0101110=>1010001
[2,8,1,5,7,6,3,4]=>0100110=>0110010=>1001101
[3,1,8,2,7,5,6,4]=>1010101=>1010101=>0101010
[8,5,7,1,6,4,2,3]=>1010110=>0110101=>1001010
[8,4,7,6,5,1,2,3]=>1011100=>0011101=>1100010
[2,8,4,7,3,6,5,1]=>0101011=>1101010=>0010101
[8,4,7,2,1,6,5,3]=>1011011=>1101101=>0010010
[1,8,4,7,6,5,2,3]=>0101110=>0111010=>1000101
[8,2,5,7,1,4,6,3]=>1001001=>1001001=>0110110
[3,5,8,1,7,4,6,2]=>0010101=>1010100=>0101011
[8,4,7,1,3,6,5,2]=>1010011=>1100101=>0011010
[5,1,7,8,3,4,2,6]=>1001010=>0101001=>1010110
[5,3,6,1,4,2,8,7]=>1010101=>1010101=>0101010
[5,7,2,1,4,3,8,6]=>0110101=>1010110=>0101001
[7,1,8,3,5,2,4,6]=>1010100=>0010101=>1101010
[7,2,4,8,1,5,6,3]=>1001001=>1001001=>0110110
[7,1,8,4,2,5,6,3]=>1011001=>1001101=>0110010
[6,4,2,5,8,1,7,3]=>1100101=>1010011=>0101100
[2,1,7,5,8,3,6,4]=>1010101=>1010101=>0101010
[7,3,8,5,6,2,1,4]=>1010110=>0110101=>1001010
[2,7,4,8,1,5,6,3]=>0101001=>1001010=>0110101
[7,4,8,3,1,5,6,2]=>1011001=>1001101=>0110010
[6,1,5,8,3,7,4,2]=>1001011=>1101001=>0010110
[2,6,3,5,8,7,4,1]=>0100111=>1110010=>0001101
[6,8,1,2,5,7,4,3]=>0100011=>1100010=>0011101
[8,6,5,3,7,2,1,4]=>1110110=>0110111=>1001000
[4,8,5,3,7,2,1,6]=>0110110=>0110110=>1001001
[7,4,8,6,5,3,2,1]=>1011111=>1111101=>0000010
[6,4,7,1,3,2,8,5]=>1010101=>1010101=>0101010
[7,8,4,1,3,5,6,2]=>0110001=>1000110=>0111001
[7,8,3,4,1,5,6,2]=>0101001=>1001010=>0110101
[7,3,1,8,2,5,6,4]=>1101001=>1001011=>0110100
[7,2,3,8,1,5,6,4]=>1001001=>1001001=>0110110
[2,7,4,8,6,3,1,5]=>0101110=>0111010=>1000101
[6,4,8,2,3,1,7,5]=>1010101=>1010101=>0101010
[7,2,1,8,3,5,6,4]=>1101001=>1001011=>0110100
[5,1,6,3,8,2,4,7]=>1010100=>0010101=>1101010
[3,5,6,8,1,4,2,7]=>0001010=>0101000=>1010111
[4,3,5,8,2,1,6,7]=>1001100=>0011001=>1100110
[6,4,7,2,3,1,5,8]=>1010100=>0010101=>1101010
[6,8,1,5,4,2,7,3]=>0101101=>1011010=>0100101
[7,8,6,3,1,4,2,5]=>0111010=>0101110=>1010001
[7,8,6,3,5,1,2,4]=>0110100=>0010110=>1101001
[7,2,8,5,4,6,3,1]=>1011011=>1101101=>0010010
[6,1,8,4,7,2,3,5]=>1010100=>0010101=>1101010
[6,5,3,7,2,4,8,1]=>1101001=>1001011=>0110100
[5,6,2,8,4,3,7,1]=>0101101=>1011010=>0100101
[4,6,2,7,8,3,5,1]=>0100101=>1010010=>0101101
[3,1,2,4,8,5,7,6]=>1000101=>1010001=>0101110
[5,1,2,4,6,7,8,3]=>1000001=>1000001=>0111110
[4,6,3,5,2,8,7,1]=>0101011=>1101010=>0010101
[5,3,2,6,8,4,7,1]=>1100101=>1010011=>0101100
[5,6,3,4,8,2,7,1]=>0100101=>1010010=>0101101
[5,2,6,4,1,7,8,3]=>1011001=>1001101=>0110010
[5,8,4,6,3,2,7,1]=>0101101=>1011010=>0100101
[5,4,3,8,6,2,7,1]=>1101101=>1011011=>0100100
[5,7,8,2,4,3,6,1]=>0010101=>1010100=>0101011
[5,6,2,4,8,3,7,1]=>0100101=>1010010=>0101101
[5,4,2,8,6,3,7,1]=>1101101=>1011011=>0100100
[5,7,4,2,6,3,8,1]=>0110101=>1010110=>0101001
[6,4,7,8,2,3,5,1]=>1001001=>1001001=>0110110
[3,7,5,2,4,8,1,6]=>0110010=>0100110=>1011001
[4,7,5,2,3,8,6,1]=>0110011=>1100110=>0011001
[6,4,7,3,2,5,8,1]=>1011001=>1001101=>0110010
[6,3,7,8,2,4,5,1]=>1001001=>1001001=>0110110
[5,7,3,2,8,4,6,1]=>0110101=>1010110=>0101001
[5,3,7,2,8,4,6,1]=>1010101=>1010101=>0101010
[4,3,7,2,5,8,6,1]=>1010011=>1100101=>0011010
[4,7,3,2,5,8,6,1]=>0110011=>1100110=>0011001
[4,7,3,2,6,8,5,1]=>0110011=>1100110=>0011001
[7,5,3,2,6,4,8,1]=>1110101=>1010111=>0101000
[5,7,3,2,6,4,8,1]=>0110101=>1010110=>0101001
[5,3,2,8,6,4,7,1]=>1101101=>1011011=>0100100
[8,5,2,6,7,3,4,1]=>1100101=>1010011=>0101100
[8,4,2,6,3,7,5,1]=>1101011=>1101011=>0010100
[7,4,6,2,3,8,5,1]=>1010011=>1100101=>0011010
[7,5,6,2,8,3,4,1]=>1010101=>1010101=>0101010
[6,3,7,5,2,4,8,1]=>1011001=>1001101=>0110010
[5,7,6,2,8,3,4,1]=>0110101=>1010110=>0101001
[4,7,6,2,3,8,5,1]=>0110011=>1100110=>0011001
[7,6,3,2,5,8,1,4]=>1110010=>0100111=>1011000
[7,6,4,2,5,8,3,1]=>1110011=>1100111=>0011000
[6,3,8,5,4,7,2,1]=>1011011=>1101101=>0010010
[4,8,3,7,1,6,5,2]=>0101011=>1101010=>0010101
[8,7,2,6,5,1,4,3]=>1101101=>1011011=>0100100
[5,8,3,2,1,7,6,4]=>0111011=>1101110=>0010001
[5,4,3,8,1,7,6,2]=>1101011=>1101011=>0010100
[6,5,3,8,7,1,4,2]=>1101101=>1011011=>0100100
[4,3,8,2,7,6,5,1]=>1010111=>1110101=>0001010
[4,8,2,7,6,5,3,1]=>0101111=>1111010=>0000101
[7,8,2,6,5,4,1,3]=>0101110=>0111010=>1000101
[3,8,7,6,2,5,1,4]=>0111010=>0101110=>1010001
[4,8,3,7,2,1,6,5]=>0101101=>1011010=>0100101
[8,6,3,1,7,5,4,2]=>1110111=>1110111=>0001000
[8,6,3,7,1,5,4,2]=>1101011=>1101011=>0010100
[4,8,3,7,6,2,5,1]=>0101101=>1011010=>0100101
[5,8,2,7,6,4,1,3]=>0101110=>0111010=>1000101
[8,4,2,1,7,6,5,3]=>1110111=>1110111=>0001000
[1,6,4,2,5,3,7,8]=>0110100=>0010110=>1101001
[1,6,7,2,5,3,4,8]=>0010100=>0010100=>1101011
[1,8,6,2,7,3,4,5]=>0110100=>0010110=>1101001
[1,5,2,6,4,3,7,8]=>0101100=>0011010=>1100101
[1,5,2,4,6,3,7,8]=>0100100=>0010010=>1101101
[1,8,6,2,3,7,4,5]=>0110010=>0100110=>1011001
[1,5,2,8,6,3,4,7]=>0101100=>0011010=>1100101
[1,7,3,2,6,8,4,5]=>0110010=>0100110=>1011001
[1,3,6,8,2,7,4,5]=>0001010=>0101000=>1010111
[1,4,3,8,2,5,6,7]=>0101000=>0001010=>1110101
[1,7,2,3,8,5,4,6]=>0100110=>0110010=>1001101
[1,6,2,8,5,4,3,7]=>0101110=>0111010=>1000101
[1,7,2,3,8,6,4,5]=>0100110=>0110010=>1001101
[1,5,3,8,2,7,4,6]=>0101010=>0101010=>1010101
[1,7,2,5,3,4,8,6]=>0101001=>1001010=>0110101
[1,4,8,2,5,6,3,7]=>0010010=>0100100=>1011011
[1,2,7,3,6,8,4,5]=>0010010=>0100100=>1011011
[1,7,2,3,6,8,4,5]=>0100010=>0100010=>1011101
[1,4,8,3,2,5,6,7]=>0011000=>0001100=>1110011
[1,7,2,5,8,3,4,6]=>0100100=>0010010=>1101101
[1,5,6,3,4,2,7,8]=>0010100=>0010100=>1101011
[1,5,6,3,4,7,2,8]=>0010010=>0100100=>1011011
[1,5,3,6,4,2,7,8]=>0101100=>0011010=>1100101
[1,7,5,6,8,3,4,2]=>0100101=>1010010=>0101101
[1,7,5,6,3,8,4,2]=>0101011=>1101010=>0010101
[1,3,7,5,2,8,6,4]=>0011011=>1101100=>0010011
[1,3,7,2,5,8,6,4]=>0010011=>1100100=>0011011
[1,5,3,7,4,6,2,8]=>0101010=>0101010=>1010101
[1,5,3,7,6,4,2,8]=>0101110=>0111010=>1000101
[1,5,3,6,7,4,2,8]=>0100110=>0110010=>1001101
[1,5,6,3,7,4,2,8]=>0010110=>0110100=>1001011
[1,5,7,6,3,4,8,2]=>0011001=>1001100=>0110011
[1,5,7,3,6,4,8,2]=>0010101=>1010100=>0101011
[1,3,7,2,5,6,8,4]=>0010001=>1000100=>0111011
[1,3,7,5,6,2,8,4]=>0010101=>1010100=>0101011
[2,5,7,4,1,3,8,6]=>0011001=>1001100=>0110011
[6,7,3,1,8,5,2,4]=>0110110=>0110110=>1001001
[8,3,5,1,7,6,2,4]=>1010110=>0110101=>1001010
[3,5,6,1,8,7,2,4]=>0010110=>0110100=>1001011
[2,4,6,8,7,3,1,5]=>0001110=>0111000=>1000111
[2,3,6,4,1,8,7,5]=>0011011=>1101100=>0010011
[4,7,5,2,1,8,6,3]=>0111011=>1101110=>0010001
[8,5,3,6,2,1,7,4]=>1101101=>1011011=>0100100
[4,5,7,3,1,2,8,6]=>0011001=>1001100=>0110011
[4,5,1,8,3,2,7,6]=>0101101=>1011010=>0100101
[3,6,1,2,4,8,7,5]=>0100011=>1100010=>0011101
[2,5,3,8,4,1,7,6]=>0101101=>1011010=>0100101
[8,6,2,3,1,7,5,4]=>1101011=>1101011=>0010100
[6,3,1,2,4,8,7,5]=>1100011=>1100011=>0011100
[2,6,4,5,8,1,3,7]=>0100100=>0010010=>1101101
[4,2,6,1,3,7,8,5]=>1010001=>1000101=>0111010
[8,5,4,2,7,6,3,1]=>1110111=>1110111=>0001000
[2,8,4,6,7,1,3,5]=>0100100=>0010010=>1101101
[5,8,2,1,4,6,7,3]=>0110001=>1000110=>0111001
[3,7,8,4,2,6,5,1]=>0011011=>1101100=>0010011
[7,1,3,8,4,5,6,2]=>1001001=>1001001=>0110110
[7,8,1,4,3,5,6,2]=>0101001=>1001010=>0110101
[3,6,7,1,8,2,5,4]=>0010101=>1010100=>0101011
[3,1,5,7,2,8,6,4]=>1001011=>1101001=>0010110
[4,1,8,3,2,7,6,5]=>1011011=>1101101=>0010010
[3,8,2,4,7,1,6,5]=>0100101=>1010010=>0101101
[3,2,4,8,7,1,6,5]=>1001101=>1011001=>0100110
[3,2,5,7,1,8,6,4]=>1001011=>1101001=>0010110
[4,2,8,3,1,7,6,5]=>1011011=>1101101=>0010010
[4,8,2,1,3,7,6,5]=>0110011=>1100110=>0011001
[4,2,8,1,3,7,6,5]=>1010011=>1100101=>0011010
[2,4,6,5,1,3,8,7]=>0011001=>1001100=>0110011
[2,3,4,6,8,7,1,5]=>0000110=>0110000=>1001111
[2,1,4,6,8,7,3,5]=>1000110=>0110001=>1001110
[4,5,7,1,6,8,3,2]=>0010011=>1100100=>0011011
[6,7,2,8,3,1,4,5]=>0101100=>0011010=>1100101
[7,8,5,2,4,1,3,6]=>0110100=>0010110=>1101001
[7,6,2,3,1,8,4,5]=>1101010=>0101011=>1010100
[4,1,3,7,8,5,2,6]=>1000110=>0110001=>1001110
[4,3,1,8,5,2,7,6]=>1101101=>1011011=>0100100
[3,1,8,5,4,2,7,6]=>1011101=>1011101=>0100010
[5,1,3,2,4,7,8,6]=>1010001=>1000101=>0111010
[2,4,8,5,6,1,7,3]=>0010101=>1010100=>0101011
[2,8,7,4,5,1,6,3]=>0110101=>1010110=>0101001
[1,3,8,5,2,6,7,4]=>0011001=>1001100=>0110011
[8,6,2,4,1,5,7,3]=>1101001=>1001011=>0110100
[1,6,4,3,2,7,8,5]=>0111001=>1001110=>0110001
[8,5,3,2,1,6,7,4]=>1111001=>1001111=>0110000
[1,7,5,2,3,6,8,4]=>0110001=>1000110=>0111001
[8,1,2,5,3,6,7,4]=>1001001=>1001001=>0110110
[8,2,6,4,3,5,1,7]=>1011010=>0101101=>1010010
[8,3,1,4,6,5,2,7]=>1100110=>0110011=>1001100
[5,8,3,1,2,6,4,7]=>0110010=>0100110=>1011001
[4,8,1,7,5,2,3,6]=>0101100=>0011010=>1100101
[4,8,1,7,5,2,6,3]=>0101101=>1011010=>0100101
[8,5,1,4,2,6,3,7]=>1101010=>0101011=>1010100
[8,4,1,3,5,6,2,7]=>1100010=>0100011=>1011100
[8,5,3,2,1,6,4,7]=>1111010=>0101111=>1010000
[8,1,5,4,2,6,3,7]=>1011010=>0101101=>1010010
[8,5,2,4,1,6,3,7]=>1101010=>0101011=>1010100
[4,8,7,1,5,2,6,3]=>0110101=>1010110=>0101001
[4,8,7,1,5,2,3,6]=>0110100=>0010110=>1101001
[7,6,8,4,1,3,2,5]=>1011010=>0101101=>1010010
[7,6,8,4,1,3,5,2]=>1011001=>1001101=>0110010
[8,4,2,7,5,1,6,3]=>1101101=>1011011=>0100100
[3,8,7,5,4,1,2,6]=>0111100=>0011110=>1100001
[7,6,8,4,1,5,2,3]=>1011010=>0101101=>1010010
[8,7,6,1,5,2,3,4]=>1110100=>0010111=>1101000
[7,1,4,8,6,3,5,2]=>1001101=>1011001=>0100110
[8,1,6,5,3,4,7,2]=>1011001=>1001101=>0110010
[8,6,2,5,3,4,7,1]=>1101001=>1001011=>0110100
[8,6,5,1,3,4,7,2]=>1110001=>1000111=>0111000
[8,7,5,1,3,6,2,4]=>1110010=>0100111=>1011000
[8,7,1,5,3,6,2,4]=>1101010=>0101011=>1010100
[8,6,1,3,5,4,7,2]=>1100101=>1010011=>0101100
[8,1,6,3,5,4,7,2]=>1010101=>1010101=>0101010
[7,1,4,8,3,6,5,2]=>1001011=>1101001=>0010110
[8,3,2,7,4,6,5,1]=>1101011=>1101011=>0010100
[7,8,5,2,4,3,6,1]=>0110101=>1010110=>0101001
[7,3,8,2,5,4,6,1]=>1010101=>1010101=>0101010
[8,4,2,5,3,7,6,1]=>1101011=>1101011=>0010100
[4,8,1,5,3,7,6,2]=>0101011=>1101010=>0010101
[7,4,8,2,6,3,5,1]=>1010101=>1010101=>0101010
[7,4,8,2,6,3,1,5]=>1010110=>0110101=>1001010
[8,7,3,1,6,4,2,5]=>1110110=>0110111=>1001000
[8,7,3,1,6,4,5,2]=>1110101=>1010111=>0101000
[8,7,3,1,4,6,5,2]=>1110011=>1100111=>0011000
[8,4,3,2,7,5,6,1]=>1110101=>1010111=>0101000
[6,4,1,7,8,5,3,2]=>1100111=>1110011=>0001100
[7,6,3,4,1,8,5,2]=>1101011=>1101011=>0010100
[8,7,3,1,6,2,5,4]=>1110101=>1010111=>0101000
[7,8,6,4,2,5,1,3]=>0111010=>0101110=>1010001
[7,8,2,4,6,5,1,3]=>0100110=>0110010=>1001101
[8,1,7,3,5,6,2,4]=>1010010=>0100101=>1011010
[8,7,1,6,5,2,3,4]=>1101100=>0011011=>1100100
[8,7,5,2,4,6,1,3]=>1110010=>0100111=>1011000
[8,1,7,5,4,6,2,3]=>1011010=>0101101=>1010010
[8,7,3,2,6,1,5,4]=>1110101=>1010111=>0101000
[8,1,7,6,5,2,3,4]=>1011100=>0011101=>1100010
[8,7,2,6,5,1,3,4]=>1101100=>0011011=>1100100
[1,4,8,6,7,5,3,2]=>0010111=>1110100=>0001011
[8,6,2,5,7,4,3,1]=>1100111=>1110011=>0001100
[7,1,3,6,8,5,4,2]=>1000111=>1110001=>0001110
[8,1,7,6,4,5,3,2]=>1011011=>1101101=>0010010
[7,1,8,6,4,5,3,2]=>1011011=>1101101=>0010010
[6,5,7,2,8,3,4,1]=>1010101=>1010101=>0101010
[6,7,2,5,8,1,4,3]=>0100101=>1010010=>0101101
[6,3,7,5,8,2,4,1]=>1010101=>1010101=>0101010
[6,5,7,3,8,1,4,2]=>1010101=>1010101=>0101010
[6,3,7,4,8,2,5,1]=>1010101=>1010101=>0101010
[6,3,7,4,8,1,5,2]=>1010101=>1010101=>0101010
[8,7,6,4,2,5,3,1]=>1111011=>1101111=>0010000
[8,7,4,6,2,3,5,1]=>1101001=>1001011=>0110100
[6,8,4,5,7,3,2,1]=>0100111=>1110010=>0001101
[6,7,5,1,4,3,8,2]=>0110101=>1010110=>0101001
[2,7,6,8,3,5,1,4]=>0101010=>0101010=>1010101
[7,2,1,5,3,8,6,4]=>1101011=>1101011=>0010100
[5,8,2,7,6,1,3,4]=>0101100=>0011010=>1100101
[4,2,3,1,5,8,6,7]=>1010010=>0100101=>1011010
[1,5,7,3,6,8,2,4]=>0010010=>0100100=>1011011
[8,4,6,2,5,7,1,3]=>1010010=>0100101=>1011010
[1,3,4,7,6,8,2,5]=>0001010=>0101000=>1010111
[8,1,3,6,7,4,2,5]=>1000110=>0110001=>1001110
[1,2,4,7,8,5,3,6]=>0000110=>0110000=>1001111
[2,1,4,7,8,5,3,6]=>1000110=>0110001=>1001110
[3,1,4,7,6,8,2,5]=>1001010=>0101001=>1010110
[4,1,3,7,6,8,2,5]=>1001010=>0101001=>1010110
[5,1,7,3,6,8,2,4]=>1010010=>0100101=>1011010
[6,7,8,2,4,5,1,3]=>0010010=>0100100=>1011011
[5,8,6,2,4,7,1,3]=>0110010=>0100110=>1011001
[3,8,2,6,5,7,1,4]=>0101010=>0101010=>1010101
[2,8,3,6,7,4,1,5]=>0100110=>0110010=>1001101
[1,8,3,6,7,4,2,5]=>0100110=>0110010=>1001101
[8,7,2,5,6,3,1,4]=>1100110=>0110011=>1001100
[8,7,1,6,4,3,2,5]=>1101110=>0111011=>1000100
[1,8,2,7,5,4,3,6]=>0101110=>0111010=>1000101
[3,8,1,7,5,4,2,6]=>0101110=>0111010=>1000101
[4,8,1,6,7,3,2,5]=>0100110=>0110010=>1001101
[5,8,6,1,7,3,2,4]=>0110110=>0110110=>1001001
[6,7,1,2,8,4,3,5]=>0100110=>0110010=>1001101
[2,1,3,8,6,5,4,7]=>1001110=>0111001=>1000110
[8,2,1,7,5,4,3,6]=>1101110=>0111011=>1000100
[1,3,2,8,6,5,4,7]=>0101110=>0111010=>1000101
[3,4,1,7,6,8,2,5]=>0101010=>0101010=>1010101
[2,5,7,1,8,4,3,6]=>0010110=>0110100=>1001011
[3,5,7,1,6,8,2,4]=>0010010=>0100100=>1011011
[4,5,7,6,1,8,2,3]=>0011010=>0101100=>1010011
[5,4,7,6,8,3,1,2]=>1010110=>0110101=>1001010
[1,5,7,8,6,3,2,4]=>0001110=>0111000=>1000111
[8,4,6,7,5,2,1,3]=>1001110=>0111001=>1000110
[8,3,7,5,6,2,1,4]=>1010110=>0110101=>1001010
[1,4,8,6,7,3,2,5]=>0010110=>0110100=>1001011
[2,4,8,6,7,3,1,5]=>0010110=>0110100=>1001011
[2,3,8,7,5,4,1,6]=>0011110=>0111100=>1000011
[1,3,8,7,5,4,2,6]=>0011110=>0111100=>1000011
[8,2,7,6,4,3,1,5]=>1011110=>0111101=>1000010
[8,1,7,6,4,3,2,5]=>1011110=>0111101=>1000010
[4,1,8,6,7,3,2,5]=>1010110=>0110101=>1001010
[4,8,7,5,6,2,1,3]=>0110110=>0110110=>1001001
[8,1,7,2,5,6,4,3]=>1010011=>1100101=>0011010
[8,1,3,5,2,7,6,4]=>1001011=>1101001=>0010110
[8,1,7,4,3,6,5,2]=>1011011=>1101101=>0010010
[2,7,1,5,4,8,6,3]=>0101011=>1101010=>0010101
[8,6,2,4,3,7,5,1]=>1101011=>1101011=>0010100
[8,1,4,5,6,3,7,2]=>1000101=>1010001=>0101110
[8,1,4,5,6,2,7,3]=>1000101=>1010001=>0101110
[8,1,4,7,6,2,5,3]=>1001101=>1011001=>0100110
[2,5,1,7,8,6,4,3]=>0100111=>1110010=>0001101
[3,5,6,2,8,7,4,1]=>0010111=>1110100=>0001011
[3,5,6,1,8,7,4,2]=>0010111=>1110100=>0001011
[2,4,5,1,7,6,3,8]=>0010110=>0110100=>1001011
[7,3,1,5,6,4,2,8]=>1100110=>0110011=>1001100
[8,6,2,4,7,3,1,5]=>1100110=>0110011=>1001100
[8,4,7,3,5,2,1,6]=>1010110=>0110101=>1001010
[8,4,5,3,7,6,2,1]=>1010111=>1110101=>0001010
[3,4,5,6,2,8,1,7]=>0001010=>0101000=>1010111
[3,7,4,2,8,5,1,6]=>0110110=>0110110=>1001001
[7,3,4,1,6,8,2,5]=>1010010=>0100101=>1011010
[2,6,3,1,4,7,5,8]=>0110010=>0100110=>1011001
[7,2,1,6,3,4,8,5]=>1101001=>1001011=>0110100
[7,3,4,1,6,5,8,2]=>1010101=>1010101=>0101010
[3,7,4,2,5,8,6,1]=>0110011=>1100110=>0011001
[2,3,5,1,4,8,7,6]=>0010011=>1100100=>0011011
[2,7,1,3,6,8,5,4]=>0100011=>1100010=>0011101
[2,7,1,3,8,4,6,5]=>0100101=>1010010=>0101101
[3,8,7,1,6,2,5,4]=>0110101=>1010110=>0101001
[3,8,7,1,4,5,2,6]=>0110010=>0100110=>1011001
[3,7,4,2,1,8,6,5]=>0111011=>1101110=>0010001
[4,8,5,7,2,6,3,1]=>0101011=>1101010=>0010101
[8,4,5,7,3,2,6,1]=>1001101=>1011001=>0100110
[8,3,7,2,4,1,5,6]=>1010100=>0010101=>1101010
[8,6,7,2,1,4,3,5]=>1011010=>0101101=>1010010
[8,3,7,5,1,2,6,4]=>1011001=>1001101=>0110010
[7,3,4,6,2,1,5,8]=>1001100=>0011001=>1100110
[3,7,4,6,1,5,2,8]=>0101010=>0101010=>1010101
[3,4,7,6,1,2,8,5]=>0011001=>1001100=>0110011
[4,5,8,7,6,1,3,2]=>0011101=>1011100=>0100011
[8,6,3,7,5,1,4,2]=>1101101=>1011011=>0100100
[8,7,3,5,6,1,4,2]=>1100101=>1010011=>0101100
[7,6,3,8,1,4,5,2]=>1101001=>1001011=>0110100
[8,5,2,7,6,1,3,4]=>1101100=>0011011=>1100100
[7,6,4,8,1,2,5,3]=>1101001=>1001011=>0110100
[8,7,3,1,4,5,2,6]=>1110010=>0100111=>1011000
[8,4,2,5,1,6,7,3]=>1101001=>1001011=>0110100
[8,5,3,1,6,4,7,2]=>1110101=>1010111=>0101000
[8,7,3,1,4,5,6,2]=>1110001=>1000111=>0111000
[8,7,4,1,5,6,2,3]=>1110010=>0100111=>1011000
[8,6,4,1,7,5,2,3]=>1110110=>0110111=>1001000
[8,6,3,1,7,4,5,2]=>1110101=>1010111=>0101000
[8,5,3,1,6,7,4,2]=>1110011=>1100111=>0011000
[8,5,3,7,1,6,4,2]=>1101011=>1101011=>0010100
[7,6,3,8,1,4,2,5]=>1101010=>0101011=>1010100
[7,4,8,2,6,1,5,3]=>1010101=>1010101=>0101010
[8,5,3,1,6,4,2,7]=>1110110=>0110111=>1001000
[8,7,4,1,5,2,3,6]=>1110100=>0010111=>1101000
[8,7,5,1,2,6,3,4]=>1110010=>0100111=>1011000
[8,6,4,1,2,7,5,3]=>1110011=>1100111=>0011000
[8,7,3,1,4,2,5,6]=>1110100=>0010111=>1101000
[8,7,4,1,2,5,3,6]=>1110010=>0100111=>1011000
[8,7,5,1,2,3,6,4]=>1110001=>1000111=>0111000
[1,6,7,3,2,8,4,5]=>0011010=>0101100=>1010011
[1,8,6,3,2,7,4,5]=>0111010=>0101110=>1010001
[1,5,3,7,2,8,4,6]=>0101010=>0101010=>1010101
[1,4,6,2,8,5,3,7]=>0010110=>0110100=>1001011
[1,5,6,2,8,4,3,7]=>0010110=>0110100=>1001011
[3,5,2,6,4,7,8,1]=>0101001=>1001010=>0110101
[1,2,5,3,8,6,7,4]=>0010101=>1010100=>0101011
[2,4,6,3,1,7,5,8]=>0011010=>0101100=>1010011
[3,4,8,6,5,7,2,1]=>0011011=>1101100=>0010011
[2,3,8,6,7,1,5,4]=>0010101=>1010100=>0101011
[1,2,5,7,4,6,8,3]=>0001001=>1001000=>0110111
[2,3,6,8,1,7,4,5]=>0001010=>0101000=>1010111
[2,4,8,5,6,7,1,3]=>0010010=>0100100=>1011011
[1,4,8,5,6,7,3,2]=>0010011=>1100100=>0011011
[6,1,3,5,4,2,8,7]=>1001101=>1011001=>0100110
[3,6,4,2,5,1,8,7]=>0110101=>1010110=>0101001
[2,1,5,8,6,4,7,3]=>1001101=>1011001=>0100110
[1,8,3,5,6,2,7,4]=>0100101=>1010010=>0101101
[8,3,2,5,6,1,7,4]=>1100101=>1010011=>0101100
[4,2,5,1,6,8,7,3]=>1010011=>1100101=>0011010
[5,4,2,7,8,6,1,3]=>1100110=>0110011=>1001100
[6,7,1,8,3,2,4,5]=>0101100=>0011010=>1100101
[6,7,2,8,1,3,4,5]=>0101000=>0001010=>1110101
[1,7,8,5,2,6,3,4]=>0011010=>0101100=>1010011
[5,8,7,2,6,3,4,1]=>0110101=>1010110=>0101001
[7,6,2,4,8,1,5,3]=>1100101=>1010011=>0101100
[4,8,3,1,7,6,5,2]=>0110111=>1110110=>0001001
[5,3,8,7,1,6,4,2]=>1011011=>1101101=>0010010
[5,8,7,3,1,6,4,2]=>0111011=>1101110=>0010001
[5,3,8,2,1,7,6,4]=>1011011=>1101101=>0010010
[3,8,7,2,6,5,1,4]=>0110110=>0110110=>1001001
[7,4,1,8,6,5,3,2]=>1101111=>1111011=>0000100
[5,4,2,8,1,7,6,3]=>1101011=>1101011=>0010100
[5,8,4,7,1,6,3,2]=>0101011=>1101010=>0010101
[8,5,6,1,4,7,2,3]=>1010010=>0100101=>1011010
[6,7,4,1,2,5,8,3]=>0110001=>1000110=>0111001
[3,6,7,5,8,1,2,4]=>0010100=>0010100=>1101011
[6,5,8,7,4,2,3,1]=>1011101=>1011101=>0100010
[5,7,6,2,8,3,1,4]=>0110110=>0110110=>1001001
[2,5,6,3,1,4,8,7]=>0011001=>1001100=>0110011
[3,8,7,2,1,5,4,6]=>0111010=>0101110=>1010001
[4,8,5,6,7,3,1,2]=>0100110=>0110010=>1001101
[3,7,6,2,8,5,1,4]=>0110110=>0110110=>1001001
[6,1,7,3,8,5,2,4]=>1010110=>0110101=>1001010
[4,8,5,6,7,2,1,3]=>0100110=>0110010=>1001101
[5,8,6,2,7,4,1,3]=>0110110=>0110110=>1001001
[4,6,5,8,7,3,1,2]=>0101110=>0111010=>1000101
[8,3,1,7,2,6,4,5]=>1101010=>0101011=>1010100
[8,4,5,1,7,6,2,3]=>1010110=>0110101=>1001010
[8,5,6,1,7,2,4,3]=>1010101=>1010101=>0101010
[7,5,6,1,3,8,4,2]=>1010011=>1100101=>0011010
[5,7,6,1,3,8,4,2]=>0110011=>1100110=>0011001
[6,7,1,4,2,8,5,3]=>0101011=>1101010=>0010101
[2,1,6,4,8,3,7,5]=>1010101=>1010101=>0101010
[5,8,7,4,6,2,3,1]=>0110101=>1010110=>0101001
[6,8,7,1,5,3,4,2]=>0110101=>1010110=>0101001
[2,7,8,4,6,5,1,3]=>0010110=>0110100=>1001011
[3,7,8,5,4,6,2,1]=>0011011=>1101100=>0010011
[2,8,7,5,3,6,4,1]=>0111011=>1101110=>0010001
[1,8,7,3,6,4,5,2]=>0110101=>1010110=>0101001
[2,8,7,4,6,1,5,3]=>0110101=>1010110=>0101001
[4,8,7,2,5,6,3,1]=>0110011=>1100110=>0011001
[4,7,8,5,3,6,2,1]=>0011011=>1101100=>0010011
[6,4,8,1,5,7,3,2]=>1010011=>1100101=>0011010
[4,5,8,6,3,7,2,1]=>0011011=>1101100=>0010011
[2,6,7,8,4,5,1,3]=>0001010=>0101000=>1010111
[6,1,2,8,4,7,5,3]=>1001011=>1101001=>0010110
[4,7,1,8,5,6,3,2]=>0101011=>1101010=>0010101
[5,7,1,8,2,6,4,3]=>0101011=>1101010=>0010101
[7,2,1,8,6,4,5,3]=>1101101=>1011011=>0100100
[5,3,8,4,7,6,2,1]=>1010111=>1110101=>0001010
[2,5,8,1,7,4,6,3]=>0010101=>1010100=>0101011
[4,5,8,3,7,6,2,1]=>0010111=>1110100=>0001011
[1,7,2,8,6,4,5,3]=>0101101=>1011010=>0100101
[2,4,7,8,5,6,1,3]=>0001010=>0101000=>1010111
[2,4,8,5,7,6,1,3]=>0010110=>0110100=>1001011
[2,6,3,8,5,1,7,4]=>0101101=>1011010=>0100101
[4,1,5,8,6,7,3,2]=>1001011=>1101001=>0010110
[3,4,6,8,2,1,7,5]=>0001101=>1011000=>0100111
[5,3,4,7,6,1,2,8]=>1001100=>0011001=>1100110
[1,2,7,8,4,3,6,5]=>0001101=>1011000=>0100111
[2,8,5,4,1,3,7,6]=>0111001=>1001110=>0110001
[4,2,8,7,1,3,5,6]=>1011000=>0001101=>1110010
[5,4,6,3,1,7,2,8]=>1011010=>0101101=>1010010
[4,3,6,5,1,8,2,7]=>1011010=>0101101=>1010010
[1,5,6,8,7,3,2,4]=>0001110=>0111000=>1000111
[1,4,8,3,6,5,2,7]=>0010110=>0110100=>1001011
[1,2,8,6,4,3,7,5]=>0011101=>1011100=>0100011
[6,5,1,8,7,3,2,4]=>1101110=>0111011=>1000100
[8,3,2,6,1,7,4,5]=>1101010=>0101011=>1010100
[6,5,1,8,7,4,3,2]=>1101111=>1111011=>0000100
[7,5,1,8,6,4,3,2]=>1101111=>1111011=>0000100
[8,5,1,7,6,4,3,2]=>1101111=>1111011=>0000100
[8,5,3,7,6,1,4,2]=>1101101=>1011011=>0100100
[3,8,7,6,1,5,4,2]=>0111011=>1101110=>0010001
[8,5,2,6,1,4,7,3]=>1101001=>1001011=>0110100
[2,7,5,8,1,4,6,3]=>0101001=>1001010=>0110101
[8,5,6,1,7,3,2,4]=>1010110=>0110101=>1001010
[3,2,6,7,1,8,5,4]=>1001011=>1101001=>0010110
[3,4,6,7,8,2,1,5]=>0000110=>0110000=>1001111
[6,7,1,3,8,5,4,2]=>0100111=>1110010=>0001101
[6,7,1,8,5,2,4,3]=>0101101=>1011010=>0100101
[1,6,2,7,8,5,3,4]=>0100110=>0110010=>1001101
[1,2,6,7,8,5,3,4]=>0000110=>0110000=>1001111
[1,6,7,4,8,3,2,5]=>0010110=>0110100=>1001011
[1,4,6,7,8,3,2,5]=>0000110=>0110000=>1001111
[8,6,1,2,7,3,4,5]=>1100100=>0010011=>1101100
[3,6,8,2,7,1,5,4]=>0010101=>1010100=>0101011
[2,8,6,1,4,5,7,3]=>0110001=>1000110=>0111001
[6,8,7,2,5,4,1,3]=>0110110=>0110110=>1001001
[3,7,2,1,8,4,6,5]=>0110101=>1010110=>0101001
[3,7,2,4,1,8,6,5]=>0101011=>1101010=>0010101
[3,2,6,4,8,7,5,1]=>1010111=>1110101=>0001010
[4,7,2,8,6,5,1,3]=>0101110=>0111010=>1000101
[4,7,1,8,6,5,3,2]=>0101111=>1111010=>0000101
[2,7,4,8,3,6,1,5]=>0101010=>0101010=>1010101
[4,7,3,8,6,1,5,2]=>0101101=>1011010=>0100101
[4,7,3,8,6,2,1,5]=>0101110=>0111010=>1000101
[4,3,6,8,7,2,5,1]=>1001101=>1011001=>0100110
[4,3,8,2,5,7,6,1]=>1010011=>1100101=>0011010
[4,3,8,1,5,7,6,2]=>1010011=>1100101=>0011010
[4,1,2,6,8,7,5,3]=>1000111=>1110001=>0001110
[2,4,3,6,8,7,1,5]=>0100110=>0110010=>1001101
[3,1,6,4,8,7,2,5]=>1010110=>0110101=>1001010
[4,1,6,8,7,5,2,3]=>1001110=>0111001=>1000110
[3,8,1,4,5,7,2,6]=>0100010=>0100010=>1011101
[3,8,1,4,2,5,7,6]=>0101001=>1001010=>0110101
[4,1,8,3,5,2,7,6]=>1010101=>1010101=>0101010
[4,2,3,6,8,7,1,5]=>1000110=>0110001=>1001110
[4,2,8,3,5,7,6,1]=>1010011=>1100101=>0011010
[3,8,2,4,5,7,6,1]=>0100011=>1100010=>0011101
[3,8,2,4,1,5,7,6]=>0101001=>1001010=>0110101
[3,8,2,5,1,4,7,6]=>0101001=>1001010=>0110101
[4,2,8,5,7,1,3,6]=>1010100=>0010101=>1101010
[3,8,1,5,2,4,7,6]=>0101001=>1001010=>0110101
[7,5,6,4,1,3,2,8]=>1011010=>0101101=>1010010
[7,8,6,4,1,3,2,5]=>0111010=>0101110=>1010001
[7,1,4,2,5,6,3,8]=>1010010=>0100101=>1011010
[7,3,2,1,4,6,5,8]=>1110010=>0100111=>1011000
[7,6,1,4,3,2,5,8]=>1101100=>0011011=>1100100
[7,4,1,3,5,6,2,8]=>1100010=>0100011=>1011100
[7,3,1,2,5,6,4,8]=>1100010=>0100011=>1011100
[2,7,1,3,5,6,8,4]=>0100001=>1000010=>0111101
[3,6,2,1,5,8,7,4]=>0110011=>1100110=>0011001
[2,3,6,1,5,8,7,4]=>0010011=>1100100=>0011011
[3,1,7,2,5,6,8,4]=>1010001=>1000101=>0111010
[3,4,7,1,5,6,8,2]=>0010001=>1000100=>0111011
[3,6,7,4,1,2,8,5]=>0011001=>1001100=>0110011
[4,3,2,7,1,6,8,5]=>1101001=>1001011=>0110100
[7,3,2,8,1,6,4,5]=>1101010=>0101011=>1010100
[7,4,8,1,5,6,3,2]=>1010011=>1100101=>0011010
[2,6,8,1,5,3,7,4]=>0010101=>1010100=>0101011
[6,8,2,1,5,3,7,4]=>0110101=>1010110=>0101001
[4,8,2,5,3,6,7,1]=>0101001=>1001010=>0110101
[4,5,8,2,3,6,7,1]=>0010001=>1000100=>0111011
[2,4,8,5,3,6,7,1]=>0011001=>1001100=>0110011
[4,1,8,6,5,3,7,2]=>1011101=>1011101=>0100010
[5,7,8,4,6,3,2,1]=>0010111=>1110100=>0001011
[5,3,2,6,4,8,7,1]=>1101011=>1101011=>0010100
[2,4,5,3,8,6,7,1]=>0010101=>1010100=>0101011
[4,3,5,2,8,6,7,1]=>1010101=>1010101=>0101010
[4,5,2,3,8,6,7,1]=>0100101=>1010010=>0101101
[4,8,5,3,2,6,7,1]=>0111001=>1001110=>0110001
[3,8,4,5,2,6,7,1]=>0101001=>1001010=>0110101
[3,5,4,2,8,6,7,1]=>0110101=>1010110=>0101001
[4,1,2,7,5,6,8,3]=>1001001=>1001001=>0110110
[4,8,1,6,5,2,7,3]=>0101101=>1011010=>0100101
[5,6,7,4,2,8,3,1]=>0011011=>1101100=>0010011
[2,5,7,4,6,8,3,1]=>0010011=>1100100=>0011011
[7,3,5,4,2,8,6,1]=>1011011=>1101101=>0010010
[7,5,2,4,3,8,6,1]=>1101011=>1101011=>0010100
[6,8,1,2,5,4,7,3]=>0100101=>1010010=>0101101
[6,4,1,8,5,2,7,3]=>1101101=>1011011=>0100100
[2,6,1,8,5,4,7,3]=>0101101=>1011010=>0100101
[7,1,2,8,5,6,4,3]=>1001011=>1101001=>0010110
[4,3,2,6,8,5,7,1]=>1100101=>1010011=>0101100
[3,7,6,4,8,5,2,1]=>0110111=>1110110=>0001001
[3,1,6,8,5,4,7,2]=>1001101=>1011001=>0100110
[2,3,5,8,4,6,7,1]=>0001001=>1001000=>0110111
[3,4,5,8,2,6,7,1]=>0001001=>1001000=>0110111
[5,4,2,8,3,6,7,1]=>1101001=>1001011=>0110100
[5,3,4,8,2,6,7,1]=>1001001=>1001001=>0110110
[2,5,4,8,3,6,7,1]=>0101001=>1001010=>0110101
[6,3,2,5,8,4,7,1]=>1100101=>1010011=>0101100
[6,1,8,3,5,4,7,2]=>1010101=>1010101=>0101010
[5,4,8,3,2,6,7,1]=>1011001=>1001101=>0110010
[5,8,2,3,4,6,7,1]=>0100001=>1000010=>0111101
[3,4,5,2,7,1,6,8]=>0010100=>0010100=>1101011
[7,5,6,1,2,3,8,4]=>1010001=>1000101=>0111010
[1,5,7,6,3,2,8,4]=>0011101=>1011100=>0100011
[8,4,6,7,3,2,5,1]=>1001101=>1011001=>0100110
[8,4,6,2,3,1,5,7]=>1010100=>0010101=>1101010
[7,5,2,1,4,3,8,6]=>1110101=>1010111=>0101000
[3,1,7,8,5,4,2,6]=>1001110=>0111001=>1000110
[3,4,5,2,1,8,6,7]=>0011010=>0101100=>1010011
[7,6,4,8,3,1,2,5]=>1101100=>0011011=>1100100
[6,2,8,5,1,3,4,7]=>1011000=>0001101=>1110010
[3,2,7,8,6,1,4,5]=>1001100=>0011001=>1100110
[6,8,2,5,1,3,7,4]=>0101001=>1001010=>0110101
[6,7,4,2,1,5,3,8]=>0111010=>0101110=>1010001
[5,6,8,1,3,7,2,4]=>0010010=>0100100=>1011011
[1,6,8,5,3,2,4,7]=>0011100=>0011100=>1100011
[7,2,8,4,6,1,3,5]=>1010100=>0010101=>1101010
[4,1,6,8,7,3,2,5]=>1001110=>0111001=>1000110
[5,1,4,6,7,3,8,2]=>1000101=>1010001=>0101110
[7,1,3,4,6,2,8,5]=>1000101=>1010001=>0101110
[5,8,7,4,2,1,3,6]=>0111100=>0011110=>1100001
[3,1,5,2,7,8,6,4]=>1010011=>1100101=>0011010
[1,8,7,3,2,5,4,6]=>0111010=>0101110=>1010001
[1,2,5,4,8,7,3,6]=>0010110=>0110100=>1001011
[1,2,4,8,6,3,5,7]=>0001100=>0011000=>1100111
[8,5,3,2,1,4,7,6]=>1111001=>1001111=>0110000
[1,2,7,6,8,4,3,5]=>0010110=>0110100=>1001011
[1,7,3,4,2,6,8,5]=>0101001=>1001010=>0110101
[1,6,3,5,8,4,2,7]=>0100110=>0110010=>1001101
[1,5,6,3,2,8,4,7]=>0011010=>0101100=>1010011
[1,2,5,8,4,6,3,7]=>0001010=>0101000=>1010111
[1,2,7,8,4,5,3,6]=>0001010=>0101000=>1010111
[1,5,3,2,7,8,4,6]=>0110010=>0100110=>1011001
[4,1,8,6,2,3,7,5]=>1011001=>1001101=>0110010
[1,7,6,4,3,8,5,2]=>0111011=>1101110=>0010001
[1,8,5,7,6,3,2,4]=>0101110=>0111010=>1000101
[1,6,3,5,7,8,4,2]=>0100011=>1100010=>0011101
[1,5,6,3,2,7,8,4]=>0011001=>1001100=>0110011
[1,8,4,7,5,3,2,6]=>0101110=>0111010=>1000101
[7,6,2,5,3,4,1,8]=>1101010=>0101011=>1010100
[7,6,2,4,5,3,1,8]=>1100110=>0110011=>1001100
[7,6,2,4,3,5,1,8]=>1101010=>0101011=>1010100
[7,6,2,3,5,4,1,8]=>1100110=>0110011=>1001100
[8,4,2,7,1,6,3,5]=>1101010=>0101011=>1010100
[8,7,6,1,5,3,2,4]=>1110110=>0110111=>1001000
[8,7,6,1,3,5,4,2]=>1110011=>1100111=>0011000
[8,7,6,1,5,4,2,3]=>1110110=>0110111=>1001000
[4,5,3,8,2,1,6,7]=>0101100=>0011010=>1100101
[8,3,5,4,2,1,6,7]=>1011100=>0011101=>1100010
[7,8,4,3,1,5,2,6]=>0111010=>0101110=>1010001
[7,5,8,2,1,4,3,6]=>1011010=>0101101=>1010010
[8,6,3,7,1,5,2,4]=>1101010=>0101011=>1010100
[8,7,6,1,2,5,3,4]=>1110010=>0100111=>1011000
[8,7,6,1,2,5,4,3]=>1110011=>1100111=>0011000
[8,7,6,1,4,2,5,3]=>1110101=>1010111=>0101000
[2,4,7,3,5,6,1,8]=>0010010=>0100100=>1011011
[5,7,6,4,2,3,1,8]=>0111010=>0101110=>1010001
[3,1,4,8,5,6,2,7]=>1001010=>0101001=>1010110
[5,8,2,4,6,1,3,7]=>0100100=>0010010=>1101101
[2,4,1,8,5,6,3,7]=>0101010=>0101010=>1010101
[6,1,4,8,5,2,7,3]=>1001101=>1011001=>0100110
[4,1,2,8,5,3,7,6]=>1001101=>1011001=>0100110
[2,4,6,8,5,1,7,3]=>0001101=>1011000=>0100111
[3,1,6,8,5,2,7,4]=>1001101=>1011001=>0100110
[2,3,8,1,5,6,4,7]=>0010010=>0100100=>1011011
[5,1,8,2,4,6,7,3]=>1010001=>1000101=>0111010
[4,1,8,2,3,6,7,5]=>1010001=>1000101=>0111010
[5,8,2,7,3,4,1,6]=>0101010=>0101010=>1010101
[3,8,7,5,2,6,1,4]=>0111010=>0101110=>1010001
[5,3,8,1,6,7,4,2]=>1010011=>1100101=>0011010
[5,8,2,1,3,7,6,4]=>0110011=>1100110=>0011001
[4,8,2,1,3,5,6,7]=>0110000=>0000110=>1111001
[5,1,8,3,6,7,4,2]=>1010011=>1100101=>0011010
[8,4,1,6,5,2,3,7]=>1101100=>0011011=>1100100
[6,8,7,3,2,4,1,5]=>0111010=>0101110=>1010001
[1,3,7,5,6,8,4,2]=>0010011=>1100100=>0011011
[3,2,4,7,5,8,1,6]=>1001010=>0101001=>1010110
[1,2,7,4,6,3,8,5]=>0010101=>1010100=>0101011
[2,8,7,6,4,5,1,3]=>0111010=>0101110=>1010001
[3,5,2,4,7,6,8,1]=>0100101=>1010010=>0101101
[3,5,2,4,6,7,8,1]=>0100001=>1000010=>0111101
[5,3,2,6,4,7,8,1]=>1101001=>1001011=>0110100
[5,3,2,6,7,4,8,1]=>1100101=>1010011=>0101100
[5,3,2,7,6,4,8,1]=>1101101=>1011011=>0100100
[7,3,5,2,8,4,6,1]=>1010101=>1010101=>0101010
[3,2,5,7,4,6,8,1]=>1001001=>1001001=>0110110
[2,3,5,7,4,6,8,1]=>0001001=>1001000=>0110111
[3,2,7,5,4,8,6,1]=>1011011=>1101101=>0010010
[3,7,5,2,4,8,6,1]=>0110011=>1100110=>0011001
[7,5,3,2,8,6,4,1]=>1110111=>1110111=>0001000
[2,3,7,5,4,8,6,1]=>0011011=>1101100=>0010011
[2,4,8,7,5,1,3,6]=>0011100=>0011100=>1100011
[3,5,7,6,1,8,4,2]=>0011011=>1101100=>0010011
[3,5,7,6,2,8,4,1]=>0011011=>1101100=>0010011
[2,4,6,3,8,7,5,1]=>0010111=>1110100=>0001011
[1,5,3,2,8,7,6,4]=>0110111=>1110110=>0001001
[6,3,1,8,7,4,2,5]=>1101110=>0111011=>1000100
[5,3,6,2,8,7,4,1]=>1010111=>1110101=>0001010
[5,8,3,1,7,6,4,2]=>0110111=>1110110=>0001001
[6,3,5,2,1,8,7,4]=>1011011=>1101101=>0010010
[3,8,1,4,7,6,5,2]=>0100111=>1110010=>0001101
[6,2,3,8,7,5,4,1]=>1001111=>1111001=>0000110
[4,1,3,5,8,7,6,2]=>1000111=>1110001=>0001110
[4,2,5,3,7,6,1,8]=>1010110=>0110101=>1001010
[6,2,4,3,7,5,1,8]=>1010110=>0110101=>1001010
[1,3,6,4,7,5,2,8]=>0010110=>0110100=>1001011
[8,2,5,3,6,4,1,7]=>1010110=>0110101=>1001010
[7,2,5,3,6,4,1,8]=>1010110=>0110101=>1001010
[6,2,5,3,7,4,1,8]=>1010110=>0110101=>1001010
[4,2,6,3,7,5,1,8]=>1010110=>0110101=>1001010
[5,2,7,3,6,4,1,8]=>1010110=>0110101=>1001010
[7,3,6,2,5,4,1,8]=>1010110=>0110101=>1001010
[6,3,8,2,5,4,1,7]=>1010110=>0110101=>1001010
[7,3,1,4,6,5,2,8]=>1100110=>0110011=>1001100
[8,3,7,2,5,4,1,6]=>1010110=>0110101=>1001010
[5,2,8,3,6,4,1,7]=>1010110=>0110101=>1001010
[4,2,8,3,6,5,1,7]=>1010110=>0110101=>1001010
[3,2,8,4,6,5,1,7]=>1010110=>0110101=>1001010
[1,4,7,3,6,5,2,8]=>0010110=>0110100=>1001011
[8,2,5,4,1,6,3,7]=>1011010=>0101101=>1010010
[1,3,6,5,2,7,4,8]=>0011010=>0101100=>1010011
[8,2,6,4,1,5,3,7]=>1011010=>0101101=>1010010
[1,4,8,3,7,5,2,6]=>0010110=>0110100=>1001011
[6,2,1,4,8,5,3,7]=>1100110=>0110011=>1001100
[5,2,1,4,8,6,3,7]=>1100110=>0110011=>1001100
[3,2,1,5,8,6,4,7]=>1100110=>0110011=>1001100
[4,2,8,3,7,5,1,6]=>1010110=>0110101=>1001010
[5,2,8,3,7,4,1,6]=>1010110=>0110101=>1001010
[8,3,7,2,6,4,1,5]=>1010110=>0110101=>1001010
[7,3,1,4,8,5,2,6]=>1100110=>0110011=>1001100
[1,3,7,4,8,5,2,6]=>0010110=>0110100=>1001011
[8,2,6,3,7,4,1,5]=>1010110=>0110101=>1001010
[7,2,6,3,8,4,1,5]=>1010110=>0110101=>1001010
[5,2,7,3,8,4,1,6]=>1010110=>0110101=>1001010
[3,2,7,4,8,5,1,6]=>1010110=>0110101=>1001010
[5,2,6,3,8,4,1,7]=>1010110=>0110101=>1001010
[6,2,5,3,8,4,1,7]=>1010110=>0110101=>1001010
[7,2,5,3,8,4,1,6]=>1010110=>0110101=>1001010
[8,2,5,3,7,4,1,6]=>1010110=>0110101=>1001010
[1,3,6,4,8,5,2,7]=>0010110=>0110100=>1001011
[1,3,5,4,8,6,2,7]=>0010110=>0110100=>1001011
[8,2,4,3,7,5,1,6]=>1010110=>0110101=>1001010
[7,2,4,3,8,5,1,6]=>1010110=>0110101=>1001010
[6,2,4,3,8,5,1,7]=>1010110=>0110101=>1001010
[5,2,4,3,8,6,1,7]=>1010110=>0110101=>1001010
[4,2,5,3,8,6,1,7]=>1010110=>0110101=>1001010
[4,2,5,3,1,7,6,8]=>1011010=>0101101=>1010010
[6,2,4,3,1,7,5,8]=>1011010=>0101101=>1010010
[7,2,4,3,1,6,5,8]=>1011010=>0101101=>1010010
[8,5,1,3,6,4,2,7]=>1100110=>0110011=>1001100
[8,4,1,3,6,5,2,7]=>1100110=>0110011=>1001100
[1,5,2,4,7,6,3,8]=>0100110=>0110010=>1001101
[7,2,5,3,1,6,4,8]=>1011010=>0101101=>1010010
[6,2,5,3,1,7,4,8]=>1011010=>0101101=>1010010
[4,2,6,3,1,7,5,8]=>1011010=>0101101=>1010010
[3,2,6,4,1,7,5,8]=>1011010=>0101101=>1010010
[5,2,7,3,1,6,4,8]=>1011010=>0101101=>1010010
[6,2,7,3,1,5,4,8]=>1011010=>0101101=>1010010
[7,2,6,3,1,5,4,8]=>1011010=>0101101=>1010010
[1,5,2,4,8,6,3,7]=>0100110=>0110010=>1001101
[8,4,1,3,7,5,2,6]=>1100110=>0110011=>1001100
[6,2,1,5,3,7,4,8]=>1101010=>0101011=>1010100
[3,2,1,6,4,7,5,8]=>1101010=>0101011=>1010100
[3,2,8,5,1,6,4,7]=>1011010=>0101101=>1010010
[4,2,8,5,1,6,3,7]=>1011010=>0101101=>1010010
[6,2,8,4,1,5,3,7]=>1011010=>0101101=>1010010
[1,4,8,5,2,6,3,7]=>0011010=>0101100=>1010011
[8,3,7,4,1,5,2,6]=>1011010=>0101101=>1010010
[7,1,3,2,5,6,4,8]=>1010010=>0100101=>1011010
[1,5,2,8,7,4,3,6]=>0101110=>0111010=>1000101
[5,7,2,8,1,4,3,6]=>0101010=>0101010=>1010101
[7,1,5,3,2,6,8,4]=>1011001=>1001101=>0110010
[1,7,3,4,5,2,8,6]=>0100101=>1010010=>0101101
[8,6,7,3,5,2,1,4]=>1010110=>0110101=>1001010
[3,2,1,7,8,5,4,6]=>1100110=>0110011=>1001100
[7,3,4,2,1,5,8,6]=>1011001=>1001101=>0110010
[1,7,6,3,2,4,8,5]=>0111001=>1001110=>0110001
[1,8,5,3,2,4,7,6]=>0111001=>1001110=>0110001
[1,2,8,4,6,3,5,7]=>0010100=>0010100=>1101011
[2,6,1,5,4,7,3,8]=>0101010=>0101010=>1010101
[1,2,8,5,4,6,3,7]=>0011010=>0101100=>1010011
[1,3,8,5,4,2,6,7]=>0011100=>0011100=>1100011
[1,3,6,8,4,5,7,2]=>0001001=>1001000=>0110111
[1,2,8,4,6,3,7,5]=>0010101=>1010100=>0101011
[4,6,3,5,7,8,1,2]=>0100010=>0100010=>1011101
[2,7,6,5,1,4,8,3]=>0111001=>1001110=>0110001
[2,7,4,8,1,3,6,5]=>0101001=>1001010=>0110101
[2,3,6,8,4,1,7,5]=>0001101=>1011000=>0100111
[1,2,6,8,4,7,5,3]=>0001011=>1101000=>0010111
[1,7,2,8,6,3,5,4]=>0101101=>1011010=>0100101
[2,3,8,5,4,7,1,6]=>0011010=>0101100=>1010011
[2,7,4,1,6,3,5,8]=>0110100=>0010110=>1101001
[1,2,8,4,7,3,5,6]=>0010100=>0010100=>1101011
[2,6,1,4,8,3,7,5]=>0100101=>1010010=>0101101
[3,7,6,5,2,1,4,8]=>0111100=>0011110=>1100001
[2,5,6,1,4,8,7,3]=>0010011=>1100100=>0011011
[7,1,5,2,6,4,3,8]=>1010110=>0110101=>1001010
[1,8,5,6,2,7,4,3]=>0101011=>1101010=>0010101
[4,2,7,6,1,8,5,3]=>1011011=>1101101=>0010010
[7,3,2,1,6,4,8,5]=>1110101=>1010111=>0101000
[6,7,2,4,3,5,8,1]=>0101001=>1001010=>0110101
[4,5,3,7,2,1,6,8]=>0101100=>0011010=>1100101
[4,3,8,2,1,5,7,6]=>1011001=>1001101=>0110010
[4,3,2,8,1,6,7,5]=>1101001=>1001011=>0110100
[4,5,8,3,2,7,1,6]=>0011010=>0101100=>1010011
[5,4,7,8,2,3,6,1]=>1001001=>1001001=>0110110
[4,3,8,2,1,6,7,5]=>1011001=>1001101=>0110010
[4,6,7,2,5,3,8,1]=>0010101=>1010100=>0101011
[6,4,7,8,3,1,5,2]=>1001101=>1011001=>0100110
[8,4,7,3,1,5,6,2]=>1011001=>1001101=>0110010
[5,6,7,1,8,3,4,2]=>0010101=>1010100=>0101011
[7,1,8,6,2,5,4,3]=>1011011=>1101101=>0010010
[8,5,1,7,6,4,2,3]=>1101110=>0111011=>1000100
[1,5,8,2,6,4,7,3]=>0010101=>1010100=>0101011
[1,5,7,4,6,8,3,2]=>0010011=>1100100=>0011011
[8,1,2,6,4,5,7,3]=>1001001=>1001001=>0110110
[3,1,8,6,5,2,7,4]=>1011101=>1011101=>0100010
[2,3,7,6,5,8,1,4]=>0011010=>0101100=>1010011
[2,3,7,6,5,1,8,4]=>0011101=>1011100=>0100011
[7,3,5,2,1,6,8,4]=>1011001=>1001101=>0110010
[3,7,2,6,8,1,5,4]=>0100101=>1010010=>0101101
[2,7,6,8,5,1,4,3]=>0101101=>1011010=>0100101
[1,5,4,7,8,6,2,3]=>0100110=>0110010=>1001101
[7,3,1,6,8,2,5,4]=>1100101=>1010011=>0101100
[7,1,6,8,5,2,4,3]=>1001101=>1011001=>0100110
[2,7,6,4,8,1,5,3]=>0110101=>1010110=>0101001
[3,6,2,1,4,7,8,5]=>0110001=>1000110=>0111001
[6,3,8,7,5,4,2,1]=>1011111=>1111101=>0000010
[6,8,2,7,5,4,3,1]=>0101111=>1111010=>0000101
[5,8,1,7,6,4,3,2]=>0101111=>1111010=>0000101
[4,2,6,3,8,5,7,1]=>1010101=>1010101=>0101010
[8,2,6,5,7,3,4,1]=>1010101=>1010101=>0101010
[5,1,8,3,7,4,6,2]=>1010101=>1010101=>0101010
[8,3,7,1,5,4,6,2]=>1010101=>1010101=>0101010
[8,4,7,1,5,3,6,2]=>1010101=>1010101=>0101010
[8,2,7,4,5,1,6,3]=>1010101=>1010101=>0101010
[5,8,7,1,4,2,3,6]=>0110100=>0010110=>1101001
[1,7,5,2,4,8,6,3]=>0110011=>1100110=>0011001
[2,6,3,7,1,4,5,8]=>0101000=>0001010=>1110101
[7,2,8,5,3,1,6,4]=>1011101=>1011101=>0100010
[7,2,4,1,3,8,5,6]=>1010010=>0100101=>1011010
[4,7,6,1,5,8,3,2]=>0110011=>1100110=>0011001
[4,7,3,8,6,2,5,1]=>0101101=>1011010=>0100101
[5,4,7,3,8,2,1,6]=>1010110=>0110101=>1001010
[4,3,5,7,2,6,1,8]=>1001010=>0101001=>1010110
[1,7,2,8,5,4,3,6]=>0101110=>0111010=>1000101
[5,4,8,3,6,2,1,7]=>1010110=>0110101=>1001010
[6,8,3,5,7,2,4,1]=>0100101=>1010010=>0101101
[3,8,6,2,7,5,1,4]=>0110110=>0110110=>1001001
[4,7,3,2,5,1,6,8]=>0110100=>0010110=>1101001
[4,2,5,3,8,7,1,6]=>1010110=>0110101=>1001010
[7,2,5,3,8,4,6,1]=>1010101=>1010101=>0101010
[6,7,3,2,5,4,1,8]=>0110110=>0110110=>1001001
[8,7,3,2,5,4,6,1]=>1110101=>1010111=>0101000
[4,5,6,2,7,3,1,8]=>0010110=>0110100=>1001011
[7,3,4,8,2,1,6,5]=>1001101=>1011001=>0100110
[3,8,1,7,5,2,4,6]=>0101100=>0011010=>1100101
[4,5,8,2,7,3,1,6]=>0010110=>0110100=>1001011
[6,5,8,2,7,3,1,4]=>1010110=>0110101=>1001010
[6,4,8,2,7,3,1,5]=>1010110=>0110101=>1001010
[4,3,8,2,7,5,1,6]=>1010110=>0110101=>1001010
[4,5,7,8,3,2,1,6]=>0001110=>0111000=>1000111
[8,1,5,4,6,2,7,3]=>1010101=>1010101=>0101010
[5,3,7,2,1,8,6,4]=>1011011=>1101101=>0010010
[5,4,8,3,2,7,1,6]=>1011010=>0101101=>1010010
[5,4,3,7,8,2,6,1]=>1100101=>1010011=>0101100
[5,4,3,8,2,6,7,1]=>1101001=>1001011=>0110100
[5,4,3,7,8,2,1,6]=>1100110=>0110011=>1001100
[2,3,8,7,5,1,6,4]=>0011101=>1011100=>0100011
[4,1,3,5,6,2,8,7]=>1000101=>1010001=>0101110
[6,4,8,7,3,5,2,1]=>1011011=>1101101=>0010010
[8,3,4,5,1,6,7,2]=>1001001=>1001001=>0110110
[7,8,1,5,6,3,2,4]=>0100110=>0110010=>1001101
[1,7,8,3,2,5,4,6]=>0011010=>0101100=>1010011
[7,8,1,3,5,4,2,6]=>0100110=>0110010=>1001101
[7,8,1,3,2,5,6,4]=>0101001=>1001010=>0110101
[7,8,1,3,5,4,6,2]=>0100101=>1010010=>0101101
[7,8,1,3,5,2,4,6]=>0100100=>0010010=>1101101
[1,3,7,8,5,2,4,6]=>0001100=>0011000=>1100111
[1,7,8,3,5,2,6,4]=>0010101=>1010100=>0101011
[1,7,8,3,2,5,6,4]=>0011001=>1001100=>0110011
[3,5,7,6,4,8,1,2]=>0011010=>0101100=>1010011
[1,3,7,8,5,4,6,2]=>0001101=>1011000=>0100111
[1,3,7,8,5,4,2,6]=>0001110=>0111000=>1000111
[1,3,7,8,2,5,4,6]=>0001010=>0101000=>1010111
[1,7,8,5,6,3,2,4]=>0010110=>0110100=>1001011
[5,7,6,8,1,3,4,2]=>0101001=>1001010=>0110101
[1,5,7,6,8,3,2,4]=>0010110=>0110100=>1001011
[3,5,4,7,8,6,1,2]=>0100110=>0110010=>1001101
[3,5,7,6,8,4,1,2]=>0010110=>0110100=>1001011
[1,5,7,6,8,3,4,2]=>0010101=>1010100=>0101011
[3,5,7,4,6,8,1,2]=>0010010=>0100100=>1011011
[7,2,8,6,5,1,4,3]=>1011101=>1011101=>0100010
[3,2,5,4,7,6,1,10,8,9]=>101011010=>010110101=>101001010
[3,2,5,4,9,8,6,7,1,10]=>101011010=>010110101=>101001010
[3,2,5,4,1,8,6,10,7,9]=>101101010=>010101101=>101010010
[3,2,5,4,1,10,9,6,7,8]=>101101100=>001101101=>110010010
[3,2,7,6,4,5,9,8,1,10]=>101100110=>011001101=>100110010
[3,2,7,6,4,5,1,10,8,9]=>101101010=>010101101=>101010010
[3,2,9,6,4,8,5,7,1,10]=>101101010=>010101101=>101010010
[3,2,1,6,4,8,5,10,7,9]=>110101010=>010101011=>101010100
[3,2,1,6,4,10,9,5,7,8]=>110101100=>001101011=>110010100
[3,2,9,8,7,4,5,6,1,10]=>101110010=>010011101=>101100010
[3,2,1,8,7,4,5,10,6,9]=>110110010=>010011011=>101100100
[3,2,1,10,7,4,9,5,6,8]=>110110100=>001011011=>110100100
[3,2,1,10,9,8,4,5,6,7]=>110111000=>000111011=>111000100
[5,4,2,3,7,6,9,8,1,10]=>110010110=>011010011=>100101100
[5,4,2,3,7,6,1,10,8,9]=>110011010=>010110011=>101001100
[5,4,2,3,9,8,6,7,1,10]=>110011010=>010110011=>101001100
[5,4,2,3,1,8,6,10,7,9]=>110101010=>010101011=>101010100
[5,4,2,3,1,10,9,6,7,8]=>110101100=>001101011=>110010100
[7,4,2,6,3,5,9,8,1,10]=>110100110=>011001011=>100110100
[7,4,2,6,3,5,1,10,8,9]=>110101010=>010101011=>101010100
[9,4,2,6,3,8,5,7,1,10]=>110101010=>010101011=>101010100
[1,4,2,6,3,10,9,5,7,8]=>010101100=>001101010=>110010101
[9,4,2,8,7,3,5,6,1,10]=>110110010=>010011011=>101100100
[1,4,2,8,7,3,5,10,6,9]=>010110010=>010011010=>101100101
[1,4,2,10,7,3,9,5,6,8]=>010110100=>001011010=>110100101
[1,4,2,10,9,8,3,5,6,7]=>010111000=>000111010=>111000101
[7,6,5,2,3,4,9,8,1,10]=>111000110=>011000111=>100111000
[7,6,5,2,3,4,1,10,8,9]=>111001010=>010100111=>101011000
[9,6,5,2,3,8,4,7,1,10]=>111001010=>010100111=>101011000
[1,6,5,2,3,8,4,10,7,9]=>011001010=>010100110=>101011001
[1,6,5,2,3,10,9,4,7,8]=>011001100=>001100110=>110011001
[9,8,5,2,7,3,4,6,1,10]=>111010010=>010010111=>101101000
[1,8,5,2,7,3,4,10,6,9]=>011010010=>010010110=>101101001
[1,10,5,2,7,3,9,4,6,8]=>011010100=>001010110=>110101001
[1,10,5,2,9,8,3,4,6,7]=>011011000=>000110110=>111001001
[9,8,7,6,2,3,4,5,1,10]=>111100010=>010001111=>101110000
[1,8,7,6,2,3,4,10,5,9]=>011100010=>010001110=>101110001
[1,10,7,6,2,3,9,4,5,8]=>011100100=>001001110=>110110001
[1,10,9,6,2,8,3,4,5,7]=>011101000=>000101110=>111010001
[1,10,9,8,7,2,3,4,5,6]=>011110000=>000011110=>111100001
[3,2,5,4,11,10,9,6,7,8,1,12]=>10101110010=>01001110101=>10110001010
[3,2,5,4,1,12,9,6,11,7,8,10]=>10110110100=>00101101101=>11010010010
[3,2,1,6,4,8,5,10,7,12,9,11]=>11010101010=>01010101011=>10101010100
[3,2,1,6,4,12,9,5,11,7,8,10]=>11010110100=>00101101011=>11010010100
[3,2,9,8,7,4,5,6,11,10,1,12]=>10111000110=>01100011101=>10011100010
[3,2,1,10,7,4,9,5,6,12,8,11]=>11011010010=>01001011011=>10110100100
[3,2,1,12,7,4,11,10,5,6,8,9]=>11011011000=>00011011011=>11100100100
[3,2,11,10,9,8,4,5,6,7,1,12]=>10111100010=>01000111101=>10111000010
[5,4,2,3,7,6,1,12,11,8,9,10]=>11001101100=>00110110011=>11001001100
[5,4,2,3,9,8,6,7,11,10,1,12]=>11001100110=>01100110011=>10011001100
[5,4,2,3,1,8,6,10,7,12,9,11]=>11010101010=>01010101011=>10101010100
[5,4,2,3,11,10,9,6,7,8,1,12]=>11001110010=>01001110011=>10110001100
[5,4,2,3,1,12,9,6,11,7,8,10]=>11010110100=>00101101011=>11010010100
[7,4,2,6,3,5,1,10,8,12,9,11]=>11010101010=>01010101011=>10101010100
[9,4,2,6,3,8,5,7,1,12,10,11]=>11010101010=>01010101011=>10101010100
[11,4,2,6,3,8,5,10,7,9,1,12]=>11010101010=>01010101011=>10101010100
[1,4,2,6,3,8,5,10,7,12,9,11]=>01010101010=>01010101010=>10101010101
[11,4,2,10,7,3,9,5,6,8,1,12]=>11011010010=>01001011011=>10110100100
[11,6,5,2,3,10,9,4,7,8,1,12]=>11100110010=>01001100111=>10110011000
[11,10,5,2,9,8,3,4,6,7,1,12]=>11101100010=>01000110111=>10111001000
[9,8,7,6,2,3,4,5,11,10,1,12]=>11110000110=>01100001111=>10011110000
[11,10,7,6,2,3,9,4,5,8,1,12]=>11110010010=>01001001111=>10110110000
[11,10,9,6,2,8,3,4,5,7,1,12]=>11110100010=>01000101111=>10111010000
[1,12,11,6,2,8,3,10,4,5,7,9]=>01110101000=>00010101110=>11101010001
[4,2,7,5,3,1,8,6]=>1011101=>1011101=>0100010
[7,3,2,5,4,1,8,6]=>1101101=>1011011=>0100100
[3,6,4,1,8,2,7,5]=>0110101=>1010110=>0101001
[4,6,3,8,7,2,1,5]=>0101110=>0111010=>1000101
[4,3,5,1,8,7,2,6]=>1010110=>0110101=>1001010
[8,4,3,2,7,5,1,6]=>1110110=>0110111=>1001000
[7,5,2,8,4,3,1,6]=>1101110=>0111011=>1000100
[1,7,2,4,5,3,6,8]=>0100100=>0010010=>1101101
[1,7,4,5,3,2,6,8]=>0101100=>0011010=>1100101
[1,6,4,7,3,5,2,8]=>0101010=>0101010=>1010101
[8,3,5,6,1,4,7,2]=>1001001=>1001001=>0110110
[1,6,4,7,5,2,3,8]=>0101100=>0011010=>1100101
[1,5,2,6,7,4,3,8]=>0100110=>0110010=>1001101
[8,5,6,1,4,3,7,2]=>1010101=>1010101=>0101010
[5,4,7,8,3,1,2,6]=>1001100=>0011001=>1100110
[2,5,4,7,8,3,1,6]=>0100110=>0110010=>1001101
[6,4,5,8,2,3,1,7]=>1001010=>0101001=>1010110
[8,6,1,3,2,5,7,4]=>1101001=>1001011=>0110100
[7,5,8,1,4,6,3,2]=>1010011=>1100101=>0011010
[4,2,6,7,8,1,5,3]=>1000101=>1010001=>0101110
[3,4,6,7,8,1,5,2]=>0000101=>1010000=>0101111
[4,3,2,7,5,8,1,6]=>1101010=>0101011=>1010100
[4,8,5,3,2,6,1,7]=>0111010=>0101110=>1010001
[2,8,4,5,3,6,1,7]=>0101010=>0101010=>1010101
[8,1,5,3,2,4,7,6]=>1011001=>1001101=>0110010
[8,1,2,4,5,3,7,6]=>1000101=>1010001=>0101110
[8,1,4,5,3,2,7,6]=>1001101=>1011001=>0100110
[7,8,4,1,3,6,5,2]=>0110011=>1100110=>0011001
[8,6,1,3,2,7,4,5]=>1101010=>0101011=>1010100
[7,3,8,2,4,1,6,5]=>1010101=>1010101=>0101010
[6,2,3,7,8,1,5,4]=>1000101=>1010001=>0101110
[6,3,7,8,1,5,4,2]=>1001011=>1101001=>0010110
[2,6,3,7,8,1,5,4]=>0100101=>1010010=>0101101
[7,5,8,1,6,4,2,3]=>1010110=>0110101=>1001010
[7,4,3,2,5,8,1,6]=>1110010=>0100111=>1011000
[7,2,4,3,5,8,1,6]=>1010010=>0100101=>1011010
[1,3,6,4,2,5,7,8]=>0011000=>0001100=>1110011
[1,7,6,4,2,3,5,8]=>0111000=>0001110=>1110001
[1,2,3,7,6,4,5,8]=>0001100=>0011000=>1100111
[1,3,2,5,8,6,4,7]=>0100110=>0110010=>1001101
[4,8,2,7,1,3,6,5]=>0101001=>1001010=>0110101
[1,7,4,6,8,3,5,2]=>0100101=>1010010=>0101101
[4,1,5,2,3,8,7,6]=>1010011=>1100101=>0011010
[6,3,5,8,2,4,7,1]=>1001001=>1001001=>0110110
[2,8,7,1,4,6,3,5]=>0110010=>0100110=>1011001
[3,1,2,8,5,7,4,6]=>1001010=>0101001=>1010110
[6,4,1,5,3,2,8,7]=>1101101=>1011011=>0100100
[6,3,8,1,2,5,4,7]=>1010010=>0100101=>1011010
[2,1,8,6,3,7,5,4]=>1011011=>1101101=>0010010
[1,6,5,3,2,4,7,8]=>0111000=>0001110=>1110001
[1,7,2,4,6,5,3,8]=>0100110=>0110010=>1001101
[1,4,7,2,6,5,3,8]=>0010110=>0110100=>1001011
[1,3,7,2,4,6,5,8]=>0010010=>0100100=>1011011
[1,7,2,6,4,3,5,8]=>0101100=>0011010=>1100101
[1,2,6,8,7,4,3,5]=>0001110=>0111000=>1000111
[1,2,7,4,3,5,8,6]=>0011001=>1001100=>0110011
[1,8,6,3,5,2,7,4]=>0110101=>1010110=>0101001
[1,6,2,8,7,4,3,5]=>0101110=>0111010=>1000101
[1,3,8,7,5,4,6,2]=>0011101=>1011100=>0100011
[1,2,8,6,3,5,7,4]=>0011001=>1001100=>0110011
[1,8,5,2,3,6,4,7]=>0110010=>0100110=>1011001
[1,7,4,8,5,2,3,6]=>0101100=>0011010=>1100101
[1,4,7,5,8,6,3,2]=>0010111=>1110100=>0001011
[1,4,7,5,2,8,6,3]=>0011011=>1101100=>0010011
[1,6,3,7,4,2,8,5]=>0101101=>1011010=>0100101
[1,8,5,2,7,4,3,6]=>0110110=>0110110=>1001001
[1,4,8,6,3,2,7,5]=>0011101=>1011100=>0100011
[1,4,8,7,5,3,2,6]=>0011110=>0111100=>1000011
[1,2,5,8,6,3,7,4]=>0001101=>1011000=>0100111
[1,2,4,7,5,8,6,3]=>0001011=>1101000=>0010111
[1,3,5,8,7,6,2,4]=>0001110=>0111000=>1000111
[1,5,2,4,3,6,8,7]=>0101001=>1001010=>0110101
[1,6,8,7,5,3,2,4]=>0011110=>0111100=>1000011
[1,2,5,7,4,3,8,6]=>0001101=>1011000=>0100111
[1,5,3,2,6,8,7,4]=>0110011=>1100110=>0011001
[1,4,2,6,8,7,5,3]=>0100111=>1110010=>0001101
[1,5,8,6,3,2,7,4]=>0011101=>1011100=>0100011
[1,8,5,2,6,3,4,7]=>0110100=>0010110=>1101001
[1,7,4,6,3,2,8,5]=>0101101=>1011010=>0100101
[1,6,3,2,8,5,4,7]=>0110110=>0110110=>1001001
[1,4,2,8,6,3,5,7]=>0101100=>0011010=>1100101
[1,3,8,6,4,2,5,7]=>0011100=>0011100=>1100011
[1,5,7,4,2,3,8,6]=>0011001=>1001100=>0110011
[8,2,7,3,1,5,4,6]=>1011010=>0101101=>1010010
[8,4,7,2,5,3,1,6]=>1010110=>0110101=>1001010
[8,3,4,5,2,1,7,6]=>1001101=>1011001=>0100110
[8,6,1,4,7,3,5,2]=>1100101=>1010011=>0101100
[5,3,6,7,2,8,4,1]=>1001011=>1101001=>0010110
[5,3,6,7,2,4,8,1]=>1001001=>1001001=>0110110
[1,3,8,2,5,6,7,4]=>0010001=>1000100=>0111011
[5,4,2,3,6,1,8,7]=>1100101=>1010011=>0101100
[5,1,7,4,3,6,8,2]=>1011001=>1001101=>0110010
[7,1,3,6,5,2,8,4]=>1001101=>1011001=>0100110
[6,1,8,5,2,7,3,4]=>1011010=>0101101=>1010010
[8,7,2,6,3,1,4,5]=>1101100=>0011011=>1100100
[5,4,1,3,7,2,8,6]=>1100101=>1010011=>0101100
[8,3,4,7,6,2,1,5]=>1001110=>0111001=>1000110
[3,1,8,7,5,2,4,6]=>1011100=>0011101=>1100010
[6,5,8,7,2,4,3,1]=>1011011=>1101101=>0010010
[4,3,6,5,8,2,1,7]=>1010110=>0110101=>1001010
[3,2,6,8,7,1,4,5]=>1001100=>0011001=>1100110
[4,7,3,1,8,5,2,6]=>0110110=>0110110=>1001001
[3,7,8,2,5,6,1,4]=>0010010=>0100100=>1011011
[3,1,2,5,7,8,6,4]=>1000011=>1100001=>0011110
[7,5,1,4,2,3,6,8]=>1101000=>0001011=>1110100
[7,8,6,1,2,4,5,3]=>0110001=>1000110=>0111001
[1,5,3,4,7,8,6,2]=>0100011=>1100010=>0011101
[5,1,2,4,7,8,6,3]=>1000011=>1100001=>0011110
[5,1,7,8,6,2,3,4]=>1001100=>0011001=>1100110
[8,5,1,6,7,2,3,4]=>1100100=>0010011=>1101100
[8,5,1,2,4,6,7,3]=>1100001=>1000011=>0111100
[1,8,5,3,4,6,7,2]=>0110001=>1000110=>0111001
[7,5,1,2,4,6,8,3]=>1100001=>1000011=>0111100
[6,1,5,2,7,3,4,8]=>1010100=>0010101=>1101010
[7,1,2,6,4,5,8,3]=>1001001=>1001001=>0110110
[1,7,3,6,4,5,8,2]=>0101001=>1001010=>0110101
[1,8,3,6,4,5,7,2]=>0101001=>1001010=>0110101
[8,1,6,2,7,3,4,5]=>1010100=>0010101=>1101010
[7,1,5,2,6,3,4,8]=>1010100=>0010101=>1101010
[7,1,6,2,5,3,4,8]=>1010100=>0010101=>1101010
[8,1,6,2,5,3,4,7]=>1010100=>0010101=>1101010
[8,1,7,2,5,3,4,6]=>1010100=>0010101=>1101010
[8,1,2,7,4,5,6,3]=>1001001=>1001001=>0110110
[1,8,3,7,4,5,6,2]=>0101001=>1001010=>0110101
[8,1,6,7,5,2,3,4]=>1001100=>0011001=>1100110
[8,1,6,4,2,3,5,7]=>1011000=>0001101=>1110010
[7,3,1,2,6,4,5,8]=>1100100=>0010011=>1101100
[8,3,1,2,4,6,7,5]=>1100001=>1000011=>0111100
[3,1,2,8,5,6,7,4]=>1001001=>1001001=>0110110
[6,3,1,2,7,4,5,8]=>1100100=>0010011=>1101100
[6,1,7,4,2,3,5,8]=>1011000=>0001101=>1110010
[6,1,8,4,2,3,5,7]=>1011000=>0001101=>1110010
[1,7,3,4,6,8,5,2]=>0100011=>1100010=>0011101
[1,7,3,8,4,5,6,2]=>0101001=>1001010=>0110101
[7,1,8,2,5,3,4,6]=>1010100=>0010101=>1101010
[6,1,8,2,5,3,4,7]=>1010100=>0010101=>1101010
[6,1,7,2,5,3,4,8]=>1010100=>0010101=>1101010
[5,1,7,2,6,3,4,8]=>1010100=>0010101=>1101010
[5,1,8,2,6,3,4,7]=>1010100=>0010101=>1101010
[1,6,3,8,4,5,7,2]=>0101001=>1001010=>0110101
[1,6,3,7,4,5,8,2]=>0101001=>1001010=>0110101
[2,7,4,3,8,5,1,6]=>0110110=>0110110=>1001001
[2,4,7,3,5,1,6,8]=>0010100=>0010100=>1101011
[2,5,8,4,6,3,1,7]=>0010110=>0110100=>1001011
[2,4,8,6,3,5,1,7]=>0011010=>0101100=>1010011
[2,3,7,5,4,1,6,8]=>0011100=>0011100=>1100011
[3,4,6,2,1,5,8,7]=>0011001=>1001100=>0110011
[2,6,8,3,5,1,4,7]=>0010100=>0010100=>1101011
[2,3,6,1,5,8,4,7]=>0010010=>0100100=>1011011
[2,3,7,1,6,5,8,4]=>0010101=>1010100=>0101011
[2,4,7,1,3,6,8,5]=>0010001=>1000100=>0111011
[5,4,7,8,1,3,2,6]=>1001010=>0101001=>1010110
[2,5,7,1,4,6,3,8]=>0010010=>0100100=>1011011
[2,4,7,1,6,3,5,8]=>0010100=>0010100=>1101011
[2,3,7,1,6,5,4,8]=>0010110=>0110100=>1001011
[2,5,7,1,4,3,6,8]=>0010100=>0010100=>1101011
[2,5,7,3,1,4,6,8]=>0011000=>0001100=>1110011
[3,4,7,2,1,6,8,5]=>0011001=>1001100=>0110011
[5,7,3,2,8,1,4,6]=>0110100=>0010110=>1101001
[3,6,8,5,4,1,7,2]=>0011101=>1011100=>0100011
[5,4,7,8,1,3,6,2]=>1001001=>1001001=>0110110
[2,5,7,1,4,6,8,3]=>0010001=>1000100=>0111011
[2,4,7,1,6,3,8,5]=>0010101=>1010100=>0101011
[2,4,7,1,6,8,3,5]=>0010010=>0100100=>1011011
[2,4,8,3,1,7,6,5]=>0011011=>1101100=>0010011
[8,6,5,1,2,4,3,7]=>1110010=>0100111=>1011000
[7,6,1,4,2,3,5,8]=>1101000=>0001011=>1110100
[7,5,4,8,3,2,6,1]=>1101101=>1011011=>0100100
[8,7,5,1,4,2,3,6]=>1110100=>0010111=>1101000
[8,4,1,2,5,3,6,7]=>1100100=>0010011=>1101100
[4,3,8,1,5,2,6,7]=>1010100=>0010101=>1101010
[8,6,1,4,2,5,3,7]=>1101010=>0101011=>1010100
[2,8,3,7,4,5,6,1]=>0101001=>1001010=>0110101
[8,7,5,2,4,3,6,1]=>1110101=>1010111=>0101000
[6,8,3,2,4,5,1,7]=>0110010=>0100110=>1011001
[3,8,5,2,4,6,1,7]=>0110010=>0100110=>1011001
[8,2,4,5,3,1,6,7]=>1001100=>0011001=>1100110
[4,8,2,5,3,1,6,7]=>0101100=>0011010=>1100101
[4,3,7,5,2,1,6,8]=>1011100=>0011101=>1100010
[1,6,7,4,3,2,5,8]=>0011100=>0011100=>1100011
[1,4,5,7,3,2,6,8]=>0001100=>0011000=>1100111
[3,5,1,4,7,2,6,8]=>0100100=>0010010=>1101101
[2,5,4,7,8,1,3,6]=>0100100=>0010010=>1101101
[2,5,1,4,7,8,3,6]=>0100010=>0100010=>1011101
[4,3,7,1,5,2,6,8]=>1010100=>0010101=>1101010
[3,5,1,6,4,2,7,8]=>0101100=>0011010=>1100101
[6,4,3,1,7,2,5,8]=>1110100=>0010111=>1101000
[6,2,7,4,3,1,5,8]=>1011100=>0011101=>1100010
[2,6,4,1,7,3,5,8]=>0110100=>0010110=>1101001
[6,3,2,7,4,5,1,8]=>1101010=>0101011=>1010100
[7,2,4,1,3,6,8,5]=>1010001=>1000101=>0111010
[6,3,2,5,7,1,4,8]=>1100100=>0010011=>1101100
[3,2,6,5,7,1,4,8]=>1010100=>0010101=>1101010
[1,7,3,2,5,6,4,8]=>0110010=>0100110=>1011001
[2,1,7,3,5,6,8,4]=>1010001=>1000101=>0111010
[2,1,6,3,5,7,8,4]=>1010001=>1000101=>0111010
[1,6,3,2,5,7,4,8]=>0110010=>0100110=>1011001
[5,6,2,1,4,3,7,8]=>0110100=>0010110=>1101001
[2,5,1,6,4,3,7,8]=>0101100=>0011010=>1100101
[2,5,4,1,6,3,7,8]=>0110100=>0010110=>1101001
[4,6,1,5,2,7,3,8]=>0101010=>0101010=>1010101
[1,6,5,3,7,2,4,8]=>0110100=>0010110=>1101001
[2,6,1,8,5,4,3,7]=>0101110=>0111010=>1000101
[5,8,6,2,3,4,1,7]=>0110010=>0100110=>1011001
[4,5,8,6,2,1,3,7]=>0011100=>0011100=>1100011
[6,3,7,4,2,5,8,1]=>1011001=>1001101=>0110010
[7,5,6,2,4,3,8,1]=>1010101=>1010101=>0101010
[6,2,5,7,4,3,8,1]=>1001101=>1011001=>0100110
[4,6,2,5,7,3,8,1]=>0100101=>1010010=>0101101
[4,2,8,5,3,6,1,7]=>1011010=>0101101=>1010010
[8,1,7,4,5,6,2,3]=>1010010=>0100101=>1011010
[8,4,6,2,5,3,7,1]=>1010101=>1010101=>0101010
[5,6,3,2,8,1,7,4]=>0110101=>1010110=>0101001
[8,2,6,3,1,5,7,4]=>1011001=>1001101=>0110010
[8,2,5,6,7,4,3,1]=>1000111=>1110001=>0001110
[8,2,5,3,4,7,6,1]=>1010011=>1100101=>0011010
[7,5,3,2,4,1,8,6]=>1110101=>1010111=>0101000
[6,5,3,2,4,8,1,7]=>1110010=>0100111=>1011000
[3,1,8,4,6,5,7,2]=>1010101=>1010101=>0101010
[3,4,7,5,8,2,6,1]=>0010101=>1010100=>0101011
[8,7,1,4,6,5,2,3]=>1100110=>0110011=>1001100
[8,3,7,6,4,5,1,2]=>1011010=>0101101=>1010010
[5,3,8,6,4,1,7,2]=>1011101=>1011101=>0100010
[6,4,7,1,8,5,2,3]=>1010110=>0110101=>1001010
[5,7,4,2,3,8,6,1]=>0110011=>1100110=>0011001
[3,8,2,5,1,7,4,6]=>0101010=>0101010=>1010101
[5,8,4,2,3,7,1,6]=>0110010=>0100110=>1011001
[4,8,5,2,1,7,3,6]=>0111010=>0101110=>1010001
[8,5,7,6,1,2,4,3]=>1011001=>1001101=>0110010
[7,8,6,5,2,4,3,1]=>0111011=>1101110=>0010001
[7,8,4,2,6,3,5,1]=>0110101=>1010110=>0101001
[5,7,6,8,4,1,3,2]=>0101101=>1011010=>0100101
[7,3,1,6,8,5,4,2]=>1100111=>1110011=>0001100
[5,3,1,7,4,8,6,2]=>1101011=>1101011=>0010100
[7,3,1,8,6,4,5,2]=>1101101=>1011011=>0100100
[8,6,4,1,7,3,2,5]=>1110110=>0110111=>1001000
[4,6,8,3,7,1,2,5]=>0010100=>0010100=>1101011
[3,5,2,8,4,7,1,6]=>0101010=>0101010=>1010101
[3,7,2,8,6,4,5,1]=>0101101=>1011010=>0100101
[8,6,5,7,1,3,2,4]=>1101010=>0101011=>1010100
[6,4,8,3,7,2,1,5]=>1010110=>0110101=>1001010
[3,6,2,8,7,4,1,5]=>0101110=>0111010=>1000101
[6,8,4,2,7,3,1,5]=>0110110=>0110110=>1001001
[3,4,7,8,5,1,2,6]=>0001100=>0011000=>1100111
[5,7,2,4,3,6,8,1]=>0101001=>1001010=>0110101
[4,7,3,2,5,6,8,1]=>0110001=>1000110=>0111001
[3,2,7,6,4,5,8,1]=>1011001=>1001101=>0110010
[1,7,3,6,8,4,2,5]=>0100110=>0110010=>1001101
[8,3,1,2,6,4,7,5]=>1100101=>1010011=>0101100
[1,7,8,2,4,3,5,6]=>0010100=>0010100=>1101011
[3,6,4,7,1,2,8,5]=>0101001=>1001010=>0110101
[2,4,7,8,5,1,3,6]=>0001100=>0011000=>1100111
[5,7,4,8,1,3,2,6]=>0101010=>0101010=>1010101
[4,3,7,8,1,5,2,6]=>1001010=>0101001=>1010110
[8,5,4,2,6,1,7,3]=>1110101=>1010111=>0101000
[3,2,6,8,7,4,1,5]=>1001110=>0111001=>1000110
[2,3,7,5,1,8,6,4]=>0011011=>1101100=>0010011
[6,3,1,2,8,7,4,5]=>1100110=>0110011=>1001100
[5,2,1,3,8,7,6,4]=>1100111=>1110011=>0001100
[7,2,1,5,3,8,4,6]=>1101010=>0101011=>1010100
[1,5,8,2,4,3,6,7]=>0010100=>0010100=>1101011
[4,3,6,8,1,5,2,7]=>1001010=>0101001=>1010110
[2,4,6,8,5,1,3,7]=>0001100=>0011000=>1100111
[1,6,8,2,4,3,5,7]=>0010100=>0010100=>1101011
[5,4,6,8,3,1,7,2]=>1001101=>1011001=>0100110
[8,6,1,7,2,4,3,5]=>1101010=>0101011=>1010100
[7,3,1,2,8,6,4,5]=>1100110=>0110011=>1001100
[2,3,7,6,1,8,5,4]=>0011011=>1101100=>0010011
[3,2,7,8,6,4,1,5]=>1001110=>0111001=>1000110
[6,2,8,3,1,4,7,5]=>1011001=>1001101=>0110010
[3,1,2,8,7,4,5,6]=>1001100=>0011001=>1100110
[2,1,3,8,7,4,6,5]=>1001101=>1011001=>0100110
[2,1,3,8,7,4,5,6]=>1001100=>0011001=>1100110
[8,5,1,7,2,4,3,6]=>1101010=>0101011=>1010100
[8,3,1,6,2,7,5,4]=>1101011=>1101011=>0010100
[1,3,2,8,7,6,4,5]=>0101110=>0111010=>1000101
[2,1,3,8,7,6,4,5]=>1001110=>0111001=>1000110
[5,7,2,8,4,1,3,6]=>0101100=>0011010=>1100101
[3,5,8,2,4,1,7,6]=>0010101=>1010100=>0101011
[2,4,8,3,1,6,7,5]=>0011001=>1001100=>0110011
[1,3,6,8,5,4,2,7]=>0001110=>0111000=>1000111
[1,4,2,5,7,6,3,8]=>0100110=>0110010=>1001101
[1,4,2,6,8,5,3,7]=>0100110=>0110010=>1001101
[1,5,3,2,6,8,4,7]=>0110010=>0100110=>1011001
[1,5,4,2,3,6,8,7]=>0110001=>1000110=>0111001
[1,6,8,3,5,4,2,7]=>0010110=>0110100=>1001011
[1,5,3,2,4,6,8,7]=>0110001=>1000110=>0111001
[1,5,8,7,6,3,2,4]=>0011110=>0111100=>1000011
[1,5,7,6,3,2,4,8]=>0011100=>0011100=>1100011
[1,6,3,2,4,7,5,8]=>0110010=>0100110=>1011001
[1,6,3,2,4,8,7,5]=>0110011=>1100110=>0011001
[1,2,7,6,4,3,5,8]=>0011100=>0011100=>1100011
[1,8,7,5,2,4,6,3]=>0111001=>1001110=>0110001
[1,7,5,2,4,6,3,8]=>0110010=>0100110=>1011001
[1,7,4,2,5,3,6,8]=>0110100=>0010110=>1101001
[1,8,4,7,5,2,6,3]=>0101101=>1011010=>0100101
[1,7,5,2,3,6,4,8]=>0110010=>0100110=>1011001
[1,7,5,2,6,3,4,8]=>0110100=>0010110=>1101001
[1,6,3,7,4,2,5,8]=>0101100=>0011010=>1100101
[1,6,3,2,7,5,4,8]=>0110110=>0110110=>1001001
[1,4,8,7,5,2,6,3]=>0011101=>1011100=>0100011
[1,4,7,5,2,6,3,8]=>0011010=>0101100=>1010011
[1,3,6,4,8,7,5,2]=>0010111=>1110100=>0001011
[1,3,7,6,4,2,5,8]=>0011100=>0011100=>1100011
[1,3,8,7,5,2,4,6]=>0011100=>0011100=>1100011
[1,4,6,3,2,7,5,8]=>0011010=>0101100=>1010011
[1,4,6,3,2,8,7,5]=>0011011=>1101100=>0010011
[1,5,7,6,4,2,3,8]=>0011100=>0011100=>1100011
[1,2,6,4,7,5,3,8]=>0010110=>0110100=>1001011
[1,6,3,2,8,4,7,5]=>0110101=>1010110=>0101001
[1,5,2,7,4,3,6,8]=>0101100=>0011010=>1100101
[1,6,3,5,2,7,4,8]=>0101010=>0101010=>1010101
[1,6,3,5,2,8,7,4]=>0101011=>1101010=>0010101
[1,8,3,7,5,2,4,6]=>0101100=>0011010=>1100101
[1,8,4,6,3,2,7,5]=>0101101=>1011010=>0100101
[6,4,7,1,5,3,8,2]=>1010101=>1010101=>0101010
[5,3,8,2,6,4,7,1]=>1010101=>1010101=>0101010
[4,3,8,2,6,5,7,1]=>1010101=>1010101=>0101010
[2,6,1,8,3,4,7,5]=>0101001=>1001010=>0110101
[6,5,7,1,4,3,8,2]=>1010101=>1010101=>0101010
[4,8,3,5,7,6,1,2]=>0100110=>0110010=>1001101
[5,7,6,1,2,4,8,3]=>0110001=>1000110=>0111001
[4,8,3,5,7,6,2,1]=>0100111=>1110010=>0001101
[5,7,6,2,4,8,3,1]=>0110011=>1100110=>0011001
[6,7,5,2,3,8,4,1]=>0110011=>1100110=>0011001
[6,7,5,3,8,4,2,1]=>0110111=>1110110=>0001001
[7,3,1,4,2,6,5,8]=>1101010=>0101011=>1010100
[7,4,1,6,2,5,3,8]=>1101010=>0101011=>1010100
[5,4,1,8,2,6,3,7]=>1101010=>0101011=>1010100
[4,7,1,5,2,6,3,8]=>0101010=>0101010=>1010101
[6,5,1,4,2,7,3,8]=>1101010=>0101011=>1010100
[5,4,1,6,2,8,3,7]=>1101010=>0101011=>1010100
[8,4,2,3,1,6,5,7]=>1101010=>0101011=>1010100
[4,8,6,2,3,1,7,5]=>0110101=>1010110=>0101001
[2,8,6,4,5,1,7,3]=>0110101=>1010110=>0101001
[8,2,4,6,7,1,5,3]=>1000101=>1010001=>0101110
[2,8,3,1,4,5,7,6]=>0110001=>1000110=>0111001
[8,7,4,5,1,6,3,2]=>1101011=>1101011=>0010100
[7,2,8,1,4,5,6,3]=>1010001=>1000101=>0111010
[2,1,4,3,6,5,8,10,9,7]=>101010011=>110010101=>001101010
[2,1,4,3,6,8,7,5,10,9]=>101001101=>101100101=>010011010
[2,1,4,3,8,10,7,9,5,6]=>101001010=>010100101=>101011010
[2,1,4,3,6,7,10,8,9,5]=>101000101=>101000101=>010111010
[2,1,4,6,5,3,8,7,10,9]=>100110101=>101011001=>010100110
[2,1,4,6,5,3,8,10,9,7]=>100110011=>110011001=>001100110
[2,1,6,8,5,7,3,4,10,9]=>100101001=>100101001=>011010110
[2,1,8,7,5,10,4,9,3,6]=>101101010=>010101101=>101010010
[2,1,6,7,5,10,8,4,9,3]=>100101101=>101101001=>010010110
[2,1,4,5,8,6,7,3,10,9]=>100010101=>101010001=>010101110
[2,1,8,5,10,6,7,9,3,4]=>101010010=>010010101=>101101010
[2,1,4,7,10,6,9,8,3,5]=>100010110=>011010001=>100101110
[2,1,4,5,6,10,7,8,9,3]=>100001001=>100100001=>011011110
[2,4,3,1,6,5,8,7,10,9]=>011010101=>101010110=>010101001
[2,4,3,1,6,5,8,10,9,7]=>011010011=>110010110=>001101001
[2,4,3,1,6,8,7,5,10,9]=>011001101=>101100110=>010011001
[2,4,3,1,8,10,7,9,5,6]=>011001010=>010100110=>101011001
[2,4,3,1,6,7,10,8,9,5]=>011000101=>101000110=>010111001
[4,6,3,5,1,2,8,7,10,9]=>010100101=>101001010=>010110101
[4,6,3,5,1,2,8,10,9,7]=>010100011=>110001010=>001110101
[6,5,3,8,2,7,1,4,10,9]=>110101001=>100101011=>011010100
[8,5,3,7,2,10,4,9,1,6]=>110101010=>010101011=>101010100
[6,5,3,7,2,10,8,4,9,1]=>110101101=>101101011=>010010100
[4,5,3,8,6,2,7,1,10,9]=>010110101=>101011010=>010100101
[8,6,3,5,10,2,7,9,1,4]=>110010010=>010010011=>101101100
[4,7,3,6,10,1,9,8,2,5]=>010010110=>011010010=>100101101
[4,5,3,6,10,7,1,8,9,2]=>010011001=>100110010=>011001101
[2,3,6,4,5,1,8,7,10,9]=>001010101=>101010100=>010101011
[2,3,6,4,5,1,8,10,9,7]=>001010011=>110010100=>001101011
[6,3,8,4,5,7,1,2,10,9]=>101001001=>100100101=>011011010
[8,3,7,4,5,10,2,9,1,6]=>101001010=>010100101=>101011010
[6,3,7,4,5,10,8,2,9,1]=>101001101=>101100101=>010011010
[2,5,8,4,7,6,1,3,10,9]=>001011001=>100110100=>011001011
[8,5,10,4,7,6,2,9,1,3]=>101011010=>010110101=>101001010
[2,7,10,4,8,6,9,5,1,3]=>001010110=>011010100=>100101011
[2,5,6,4,10,8,7,3,9,1]=>001011101=>101110100=>010001011
[2,3,4,8,5,6,7,1,10,9]=>000100101=>101001000=>010110111
[8,3,4,10,5,6,7,9,1,2]=>100100010=>010001001=>101110110
[2,7,4,10,5,6,9,8,1,3]=>010100110=>011001010=>100110101
[2,3,6,10,5,9,7,8,1,4]=>000101010=>010101000=>101010111
[2,3,4,5,10,6,7,8,9,1]=>000010001=>100010000=>011101111
[2,1,4,3,6,5,8,7,10,12,11,9]=>10101010011=>11001010101=>00110101010
[2,1,4,3,6,5,8,10,9,7,12,11]=>10101001101=>10110010101=>01001101010
[2,1,4,3,6,8,7,5,10,9,12,11]=>10100110101=>10101100101=>01010011010
[2,1,4,3,6,8,7,5,10,12,11,9]=>10100110011=>11001100101=>00110011010
[2,1,4,3,8,9,7,12,10,6,11,5]=>10100101101=>10110100101=>01001011010
[2,1,4,6,5,3,8,7,10,9,12,11]=>10011010101=>10101011001=>01010100110
[2,1,4,6,5,3,8,7,10,12,11,9]=>10011010011=>11001011001=>00110100110
[2,1,4,6,5,3,8,10,9,7,12,11]=>10011001101=>10110011001=>01001100110
[2,1,6,7,5,10,8,4,9,3,12,11]=>10010110101=>10101101001=>01010010110
[2,1,4,5,8,6,7,3,10,9,12,11]=>10001010101=>10101010001=>01010101110
[2,1,8,5,9,6,7,12,10,4,11,3]=>10101001101=>10110010101=>01001101010
[2,1,4,7,8,6,12,10,9,5,11,3]=>10001011101=>10111010001=>01000101110
[2,4,3,1,6,5,8,7,10,9,12,11]=>01101010101=>10101010110=>01010101001
[2,4,3,1,6,5,8,7,10,12,11,9]=>01101010011=>11001010110=>00110101001
[2,4,3,1,6,5,8,10,9,7,12,11]=>01101001101=>10110010110=>01001101001
[2,4,3,1,6,8,7,5,10,9,12,11]=>01100110101=>10101100110=>01010011001
[2,4,3,1,6,8,7,5,10,12,11,9]=>01100110011=>11001100110=>00110011001
[2,4,3,1,8,9,7,12,10,6,11,5]=>01100101101=>10110100110=>01001011001
[10,5,3,7,2,9,4,12,6,11,1,8]=>11010101010=>01010101011=>10101010100
[4,5,3,8,6,2,7,1,10,9,12,11]=>01011010101=>10101011010=>01010100101
[4,5,3,8,6,2,7,1,10,12,11,9]=>01011010011=>11001011010=>00110100101
[8,6,3,5,9,2,7,12,10,4,11,1]=>11001001101=>10110010011=>01001101100
[4,7,3,6,8,1,12,10,9,5,11,2]=>01001011101=>10111010010=>01000101101
[4,5,3,8,7,12,2,11,9,10,1,6]=>01010101010=>01010101010=>10101010101
[2,3,6,4,5,1,8,7,10,9,12,11]=>00101010101=>10101010100=>01010101011
[2,3,6,4,5,1,8,7,10,12,11,9]=>00101010011=>11001010100=>00110101011
[8,3,7,4,5,9,2,12,10,6,11,1]=>10100101101=>10110100101=>01001011010
[6,3,7,4,5,10,8,2,9,1,12,11]=>10100110101=>10101100101=>01010011010
[8,5,10,4,7,6,2,9,1,3,12,11]=>10101101001=>10010110101=>01101001010
[2,7,8,4,12,6,9,10,1,3,11,5]=>00101001001=>10010010100=>01101101011
[2,5,6,4,10,8,7,3,9,1,12,11]=>00101110101=>10101110100=>01010001011
[10,5,6,4,12,8,7,3,9,11,1,2]=>10101110010=>01001110101=>10110001010
[2,5,8,4,12,9,7,11,6,10,3,1]=>00101101011=>11010110100=>00101001011
[2,7,4,8,5,6,12,10,9,3,11,1]=>01010011101=>10111001010=>01000110101
[10,3,4,5,12,6,7,8,9,11,1,2]=>10001000010=>01000010001=>10111101110
[8,2,3,7,4,5,6,1]=>1001001=>1001001=>0110110
[8,6,2,5,4,7,3,1]=>1101011=>1101011=>0010100
[8,5,7,2,3,6,4,1]=>1010011=>1100101=>0011010
[7,5,2,1,6,8,3,4]=>1110010=>0100111=>1011000
[7,6,1,5,4,8,2,3]=>1101010=>0101011=>1010100
[7,6,3,2,1,8,4,5]=>1111010=>0101111=>1010000
[2,8,7,3,4,6,1,5]=>0110010=>0100110=>1011001
[6,5,1,3,7,2,8,4]=>1100101=>1010011=>0101100
[1,8,7,3,4,5,2,6]=>0110010=>0100110=>1011001
[8,2,7,3,4,5,1,6]=>1010010=>0100101=>1011010
[1,7,8,3,4,5,2,6]=>0010010=>0100100=>1011011
[8,1,7,3,4,5,2,6]=>1010010=>0100101=>1011010
[6,8,7,3,4,2,1,5]=>0110110=>0110110=>1001001
[1,8,5,3,4,6,2,7]=>0110010=>0100110=>1011001
[7,1,6,5,4,3,8,2]=>1011101=>1011101=>0100010
[7,1,3,6,4,5,8,2]=>1001001=>1001001=>0110110
[7,1,5,3,6,4,8,2]=>1010101=>1010101=>0101010
[6,1,5,3,7,8,2,4]=>1010010=>0100101=>1011010
[5,7,1,3,2,8,6,4]=>0101011=>1101010=>0010101
[5,8,7,1,2,6,3,4]=>0110010=>0100110=>1011001
[6,8,2,3,4,7,1,5]=>0100010=>0100010=>1011101
[6,7,2,3,4,8,1,5]=>0100010=>0100010=>1011101
[5,1,7,3,8,6,2,4]=>1010110=>0110101=>1001010
[6,1,3,2,4,7,8,5]=>1010001=>1000101=>0111010
[6,2,1,3,4,7,8,5]=>1100001=>1000011=>0111100
[3,2,5,8,7,4,1,6]=>1001110=>0111001=>1000110
[4,2,5,8,7,3,1,6]=>1001110=>0111001=>1000110
[8,3,4,1,6,5,2,7]=>1010110=>0110101=>1001010
[3,4,8,5,7,2,1,6]=>0010110=>0110100=>1001011
[3,6,4,8,5,7,2,1]=>0101011=>1101010=>0010101
[5,8,4,7,3,6,2,1]=>0101011=>1101010=>0010101
[4,2,8,7,3,1,6,5]=>1011101=>1011101=>0100010
[6,5,8,2,1,7,4,3]=>1011011=>1101101=>0010010
[6,1,4,3,8,7,2,5]=>1010110=>0110101=>1001010
[5,1,3,2,6,8,7,4]=>1010011=>1100101=>0011010
[6,1,3,8,7,2,4,5]=>1001100=>0011001=>1100110
[1,2,8,4,5,7,3,6]=>0010010=>0100100=>1011011
[4,2,1,8,7,6,3,5]=>1101110=>0111011=>1000100
[3,2,5,8,7,1,4,6]=>1001100=>0011001=>1100110
[5,6,3,8,7,2,1,4]=>0101110=>0111010=>1000101
[2,5,8,4,7,1,6,3]=>0010101=>1010100=>0101011
[1,6,2,4,8,5,7,3]=>0100101=>1010010=>0101101
[3,1,6,5,8,7,2,4]=>1010110=>0110101=>1001010
[4,8,5,3,6,7,1,2]=>0110010=>0100110=>1011001
[1,8,5,3,4,7,6,2]=>0110011=>1100110=>0011001
[1,4,6,2,5,3,7,8]=>0010100=>0010100=>1101011
[4,3,6,5,1,2,7,8]=>1011000=>0001101=>1110010
[1,3,8,7,6,5,2,4]=>0011110=>0111100=>1000011
[1,8,7,2,6,3,5,4]=>0110101=>1010110=>0101001
[8,7,1,2,4,3,6,5]=>1100101=>1010011=>0101100
[2,8,7,1,6,3,4,5]=>0110100=>0010110=>1101001
[6,2,1,8,7,5,3,4]=>1101110=>0111011=>1000100
[3,2,1,4,5,8,6,7]=>1100010=>0100011=>1011100
[1,3,7,5,4,8,6,2]=>0011011=>1101100=>0010011
[5,2,1,4,3,6,8,7]=>1101001=>1001011=>0110100
[1,5,6,3,8,4,2,7]=>0010110=>0110100=>1001011
[2,6,5,3,8,4,1,7]=>0110110=>0110110=>1001001
[5,7,3,8,4,2,6,1]=>0101101=>1011010=>0100101
[2,3,6,5,4,8,1,7]=>0011010=>0101100=>1010011
[2,7,5,1,8,4,6,3]=>0110101=>1010110=>0101001
[1,7,6,4,8,2,5,3]=>0110101=>1010110=>0101001
[6,3,8,7,2,4,5,1]=>1011001=>1001101=>0110010
[2,4,3,8,7,1,6,5]=>0101101=>1011010=>0100101
[2,8,7,6,1,5,3,4]=>0111010=>0101110=>1010001
[5,4,7,6,3,1,2,8]=>1011100=>0011101=>1100010
[3,6,4,8,1,5,2,7]=>0101010=>0101010=>1010101
[3,6,8,4,1,5,2,7]=>0011010=>0101100=>1010011
[7,8,1,4,2,3,5,6]=>0101000=>0001010=>1110101
[8,7,1,4,2,3,5,6]=>1101000=>0001011=>1110100
[3,8,6,4,1,5,2,7]=>0111010=>0101110=>1010001
[3,8,4,6,1,5,2,7]=>0101010=>0101010=>1010101
[8,3,7,2,1,6,5,4]=>1011011=>1101101=>0010010
[8,4,7,3,6,2,1,5]=>1010110=>0110101=>1001010
[3,8,7,5,6,4,1,2]=>0110110=>0110110=>1001001
[3,8,7,5,6,2,1,4]=>0110110=>0110110=>1001001
[3,8,7,5,6,2,4,1]=>0110101=>1010110=>0101001
[2,8,7,5,6,4,1,3]=>0110110=>0110110=>1001001
[3,6,2,4,8,7,1,5]=>0100110=>0110010=>1001101
[1,5,6,3,8,2,7,4]=>0010101=>1010100=>0101011
[2,6,3,8,4,7,1,5]=>0101010=>0101010=>1010101
[2,6,3,5,7,8,1,4]=>0100010=>0100010=>1011101
[1,5,6,3,7,2,8,4]=>0010101=>1010100=>0101011
[1,7,5,3,6,2,8,4]=>0110101=>1010110=>0101001
[1,5,7,3,4,2,8,6]=>0010101=>1010100=>0101011
[1,5,8,3,4,2,7,6]=>0010101=>1010100=>0101011
[1,4,5,3,8,2,7,6]=>0010101=>1010100=>0101011
[6,5,1,4,2,7,8,3]=>1101001=>1001011=>0110100
[6,5,1,4,2,8,7,3]=>1101011=>1101011=>0010100
[1,7,5,4,2,8,6,3]=>0111011=>1101110=>0010001
[5,1,6,8,3,7,2,4]=>1001010=>0101001=>1010110
[1,4,3,6,5,10,9,7,8,2]=>010101101=>101101010=>010010101
[1,4,3,8,7,5,6,10,9,2]=>010110011=>110011010=>001100101
[1,4,3,10,7,5,9,6,8,2]=>010110101=>101011010=>010100101
[1,4,3,10,9,8,5,6,7,2]=>010111001=>100111010=>011000101
[1,6,5,3,4,8,7,10,9,2]=>011001011=>110100110=>001011001
[1,6,5,3,4,10,9,7,8,2]=>011001101=>101100110=>010011001
[1,8,5,3,7,4,6,10,9,2]=>011010011=>110010110=>001101001
[1,10,5,3,7,4,9,6,8,2]=>011010101=>101010110=>010101001
[1,10,5,3,9,8,4,6,7,2]=>011011001=>100110110=>011001001
[1,8,7,6,3,4,5,10,9,2]=>011100011=>110001110=>001110001
[1,10,7,6,3,4,9,5,8,2]=>011100101=>101001110=>010110001
[1,10,9,6,3,8,4,5,7,2]=>011101001=>100101110=>011010001
[1,10,9,8,7,3,4,5,6,2]=>011110001=>100011110=>011100001
[3,1,2,6,5,8,7,10,9,4]=>100101011=>110101001=>001010110
[3,1,2,6,5,10,9,7,8,4]=>100101101=>101101001=>010010110
[3,1,2,8,7,5,6,10,9,4]=>100110011=>110011001=>001100110
[3,1,2,10,7,5,9,6,8,4]=>100110101=>101011001=>010100110
[3,1,2,10,9,8,5,6,7,4]=>100111001=>100111001=>011000110
[3,1,5,2,4,8,7,10,9,6]=>101001011=>110100101=>001011010
[3,1,5,2,4,10,9,7,8,6]=>101001101=>101100101=>010011010
[3,1,5,2,7,4,6,10,9,8]=>101010011=>110010101=>001101010
[3,1,5,2,9,8,4,6,7,10]=>101011000=>000110101=>111001010
[3,1,7,6,2,4,5,10,9,8]=>101100011=>110001101=>001110010
[3,1,7,6,2,4,9,5,8,10]=>101100100=>001001101=>110110010
[3,1,9,6,2,8,4,5,7,10]=>101101000=>000101101=>111010010
[3,1,9,8,7,2,4,5,6,10]=>101110000=>000011101=>111100010
[5,4,1,2,3,8,7,10,9,6]=>110001011=>110100011=>001011100
[5,4,1,2,3,10,9,7,8,6]=>110001101=>101100011=>010011100
[5,4,1,2,7,3,6,10,9,8]=>110010011=>110010011=>001101100
[5,4,1,2,7,3,9,6,8,10]=>110010100=>001010011=>110101100
[5,4,1,2,9,8,3,6,7,10]=>110011000=>000110011=>111001100
[7,4,1,6,2,3,5,10,9,8]=>110100011=>110001011=>001110100
[7,4,1,6,2,3,9,5,8,10]=>110100100=>001001011=>110110100
[9,4,1,6,2,8,3,5,7,10]=>110101000=>000101011=>111010100
[9,4,1,8,7,2,3,5,6,10]=>110110000=>000011011=>111100100
[7,6,5,1,2,3,4,10,9,8]=>111000011=>110000111=>001111000
[7,6,5,1,2,3,9,4,8,10]=>111000100=>001000111=>110111000
[9,6,5,1,2,8,3,4,7,10]=>111001000=>000100111=>111011000
[9,8,5,1,7,2,3,4,6,10]=>111010000=>000010111=>111101000
[1,4,3,6,5,8,7,12,11,9,10,2]=>01010101101=>10110101010=>01001010101
[1,4,3,6,5,10,9,7,8,12,11,2]=>01010110011=>11001101010=>00110010101
[1,4,3,6,5,12,9,7,11,8,10,2]=>01010110101=>10101101010=>01010010101
[1,4,3,8,7,5,6,10,9,12,11,2]=>01011001011=>11010011010=>00101100101
[1,4,3,8,7,5,6,12,11,9,10,2]=>01011001101=>10110011010=>01001100101
[1,4,3,10,7,5,9,6,8,12,11,2]=>01011010011=>11001011010=>00110100101
[1,4,3,12,7,5,9,6,11,8,10,2]=>01011010101=>10101011010=>01010100101
[1,4,3,12,11,10,9,5,6,7,8,2]=>01011110001=>10001111010=>01110000101
[1,6,5,3,4,8,7,10,9,12,11,2]=>01100101011=>11010100110=>00101011001
[1,6,5,3,4,8,7,12,11,9,10,2]=>01100101101=>10110100110=>01001011001
[1,6,5,3,4,10,9,7,8,12,11,2]=>01100110011=>11001100110=>00110011001
[1,6,5,3,4,12,9,7,11,8,10,2]=>01100110101=>10101100110=>01010011001
[1,8,5,3,7,4,6,10,9,12,11,2]=>01101001011=>11010010110=>00101101001
[1,8,5,3,7,4,6,12,11,9,10,2]=>01101001101=>10110010110=>01001101001
[1,10,5,3,7,4,9,6,8,12,11,2]=>01101010011=>11001010110=>00110101001
[1,12,5,3,7,4,9,6,11,8,10,2]=>01101010101=>10101010110=>01010101001
[3,1,2,6,5,8,7,10,9,12,11,4]=>10010101011=>11010101001=>00101010110
[3,1,2,6,5,8,7,12,11,9,10,4]=>10010101101=>10110101001=>01001010110
[3,1,2,6,5,10,9,7,8,12,11,4]=>10010110011=>11001101001=>00110010110
[3,1,2,6,5,12,9,7,11,8,10,4]=>10010110101=>10101101001=>01010010110
[3,1,2,8,7,5,6,10,9,12,11,4]=>10011001011=>11010011001=>00101100110
[3,1,2,8,7,5,6,12,11,9,10,4]=>10011001101=>10110011001=>01001100110
[3,1,2,10,7,5,9,6,8,12,11,4]=>10011010011=>11001011001=>00110100110
[3,1,2,12,7,5,9,6,11,8,10,4]=>10011010101=>10101011001=>01010100110
[3,1,2,12,11,8,5,10,6,7,9,4]=>10011101001=>10010111001=>01101000110
[3,1,5,2,4,8,7,10,9,12,11,6]=>10100101011=>11010100101=>00101011010
[3,1,5,2,4,8,7,12,11,9,10,6]=>10100101101=>10110100101=>01001011010
[3,1,5,2,4,10,9,7,8,12,11,6]=>10100110011=>11001100101=>00110011010
[3,1,5,2,4,12,9,7,11,8,10,6]=>10100110101=>10101100101=>01010011010
[3,1,5,2,7,4,6,10,9,12,11,8]=>10101001011=>11010010101=>00101101010
[3,1,5,2,7,4,6,12,11,9,10,8]=>10101001101=>10110010101=>01001101010
[3,1,5,2,7,4,9,6,8,12,11,10]=>10101010011=>11001010101=>00110101010
[3,1,5,2,7,4,9,6,11,8,10,12]=>10101010100=>00101010101=>11010101010
[3,1,7,6,2,4,5,10,9,12,11,8]=>10110001011=>11010001101=>00101110010
[3,1,7,6,2,4,9,5,8,12,11,10]=>10110010011=>11001001101=>00110110010
[5,4,1,2,7,3,6,12,11,9,10,8]=>11001001101=>10110010011=>01001101100
[7,4,1,6,2,3,9,5,8,12,11,10]=>11010010011=>11001001011=>00110110100
[11,4,1,6,2,8,3,10,5,7,9,12]=>11010101000=>00010101011=>11101010100
[9,6,5,1,2,8,3,4,7,12,11,10]=>11100100011=>11000100111=>00111011000
[11,8,5,1,7,2,3,10,4,6,9,12]=>11101001000=>00010010111=>11101101000
[3,8,5,2,1,4,7,6]=>0111001=>1001110=>0110001
[3,5,4,8,2,6,7,1]=>0101001=>1001010=>0110101
[1,4,8,2,6,5,3,7]=>0010110=>0110100=>1001011
[7,5,1,8,3,4,2,6]=>1101010=>0101011=>1010100
[1,4,8,2,6,7,3,5]=>0010010=>0100100=>1011011
[1,2,5,6,8,7,3,4]=>0000110=>0110000=>1001111
[1,5,6,8,2,7,4,3]=>0001011=>1101000=>0010111
[2,6,7,3,4,1,8,5]=>0010101=>1010100=>0101011
[1,6,5,7,8,2,4,3]=>0100101=>1010010=>0101101
[1,5,6,7,2,8,4,3]=>0001011=>1101000=>0010111
[1,3,7,2,6,4,8,5]=>0010101=>1010100=>0101011
[1,5,8,6,7,3,4,2]=>0010101=>1010100=>0101011
[1,6,5,8,7,2,4,3]=>0101101=>1011010=>0100101
[1,5,7,6,2,8,3,4]=>0011010=>0101100=>1010011
[1,2,5,8,6,7,4,3]=>0001011=>1101000=>0010111
[1,2,6,5,7,3,8,4]=>0010101=>1010100=>0101011
[1,7,5,8,6,4,2,3]=>0101110=>0111010=>1000101
[7,6,1,2,3,5,4,8]=>1100010=>0100011=>1011100
[8,5,2,6,4,3,1,7]=>1101110=>0111011=>1000100
[5,8,3,7,1,4,6,2]=>0101001=>1001010=>0110101
[3,8,7,4,2,6,5,1]=>0111011=>1101110=>0010001
[5,8,3,2,4,7,6,1]=>0110011=>1100110=>0011001
[6,1,3,4,2,5,7,8]=>1001000=>0001001=>1110110
[5,3,8,2,4,6,1,7]=>1010010=>0100101=>1011010
[4,1,5,6,3,2,7,8]=>1001100=>0011001=>1100110
[4,5,8,3,2,6,1,7]=>0011010=>0101100=>1010011
[5,8,2,1,4,6,3,7]=>0110010=>0100110=>1011001
[4,1,5,8,3,6,2,7]=>1001010=>0101001=>1010110
[4,5,8,3,6,1,2,7]=>0010100=>0010100=>1101011
[1,6,3,4,7,8,5,2]=>0100011=>1100010=>0011101
[8,1,3,4,2,6,5,7]=>1001010=>0101001=>1010110
[4,7,8,5,2,3,1,6]=>0011010=>0101100=>1010011
[4,1,5,8,6,2,3,7]=>1001100=>0011001=>1100110
[5,8,2,1,6,3,4,7]=>0110100=>0010110=>1101001
[2,7,1,3,8,5,4,6]=>0100110=>0110010=>1001101
[2,6,7,8,4,1,3,5]=>0001100=>0011000=>1100111
[2,6,7,8,4,3,1,5]=>0001110=>0111000=>1000111
[1,6,4,3,2,5,7,8]=>0111000=>0001110=>1110001
[1,7,4,3,2,5,6,8]=>0111000=>0001110=>1110001
[1,8,4,3,2,7,6,5]=>0111011=>1101110=>0010001
[1,7,4,3,6,2,5,8]=>0110100=>0010110=>1101001
[1,7,8,5,4,2,3,6]=>0011100=>0011100=>1100011
[8,1,5,3,6,4,7,2]=>1010101=>1010101=>0101010
[2,6,4,8,3,1,5,7]=>0101100=>0011010=>1100101
[3,6,4,5,2,8,1,7]=>0101010=>0101010=>1010101
[8,1,5,4,7,3,6,2]=>1010101=>1010101=>0101010
[3,6,4,1,5,7,2,8]=>0110010=>0100110=>1011001
[8,1,5,4,7,6,3,2]=>1010111=>1110101=>0001010
[2,5,1,4,6,7,3,8]=>0100010=>0100010=>1011101
[3,6,4,1,5,7,8,2]=>0110001=>1000110=>0111001
[8,6,3,5,4,1,2,7]=>1101100=>0011011=>1100100
[8,2,6,5,4,1,3,7]=>1011100=>0011101=>1100010
[8,2,6,5,4,3,1,7]=>1011110=>0111101=>1000010
[8,3,2,6,1,5,4,7]=>1101010=>0101011=>1010100
[8,1,6,5,4,3,2,7]=>1011110=>0111101=>1000010
[4,8,1,7,6,3,5,2]=>0101101=>1011010=>0100101
[8,5,1,7,4,3,6,2]=>1101101=>1011011=>0100100
[8,5,7,6,2,1,3,4]=>1011100=>0011101=>1100010
[5,4,8,3,1,7,2,6]=>1011010=>0101101=>1010010
[5,1,4,8,3,2,7,6]=>1001101=>1011001=>0100110
[4,8,1,7,6,5,2,3]=>0101110=>0111010=>1000101
[4,3,8,7,2,6,1,5]=>1011010=>0101101=>1010010
[3,8,7,2,6,4,1,5]=>0110110=>0110110=>1001001
[8,2,7,6,4,1,5,3]=>1011101=>1011101=>0100010
[4,3,8,7,2,6,5,1]=>1011011=>1101101=>0010010
[8,2,5,7,4,3,6,1]=>1001101=>1011001=>0100110
[3,8,7,4,6,1,2,5]=>0110100=>0010110=>1101001
[8,3,7,5,4,1,6,2]=>1011101=>1011101=>0100010
[2,8,4,7,6,1,5,3]=>0101101=>1011010=>0100101
[2,5,4,8,3,1,7,6]=>0101101=>1011010=>0100101
[5,4,8,2,1,3,7,6]=>1011001=>1001101=>0110010
[3,8,7,2,6,1,5,4]=>0110101=>1010110=>0101001
[1,8,4,7,6,3,5,2]=>0101101=>1011010=>0100101
[1,8,3,7,6,5,2,4]=>0101110=>0111010=>1000101
[1,4,3,8,7,2,6,5]=>0101101=>1011010=>0100101
[8,1,2,7,6,5,4,3]=>1001111=>1111001=>0000110
[7,8,3,1,6,2,5,4]=>0110101=>1010110=>0101001
[6,1,5,2,4,8,3,7]=>1010010=>0100101=>1011010
[1,5,6,3,8,2,4,7]=>0010100=>0010100=>1101011
[7,5,2,8,1,4,6,3]=>1101001=>1001011=>0110100
[7,2,8,1,6,4,3,5]=>1010110=>0110101=>1001010
[1,6,4,5,2,7,3,8]=>0101010=>0101010=>1010101
[1,4,7,3,2,5,6,8]=>0011000=>0001100=>1110011
[1,6,7,4,2,8,3,5]=>0011010=>0101100=>1010011
[1,5,8,7,4,3,2,6]=>0011110=>0111100=>1000011
[1,4,7,2,3,6,8,5]=>0010001=>1000100=>0111011
[3,1,2,6,7,8,5,4]=>1000011=>1100001=>0011110
[1,6,3,4,7,8,2,5]=>0100010=>0100010=>1011101
[3,1,5,7,6,2,8,4]=>1001101=>1011001=>0100110
[6,3,1,4,2,7,8,5]=>1101001=>1001011=>0110100
[2,4,3,7,6,1,8,5]=>0101101=>1011010=>0100101
[3,1,6,5,2,8,7,4]=>1011011=>1101101=>0010010
[3,1,7,6,5,2,8,4]=>1011101=>1011101=>0100010
[1,4,7,6,8,3,2,5]=>0010110=>0110100=>1001011
[7,2,1,5,6,3,8,4]=>1100101=>1010011=>0101100
[4,3,1,8,6,2,7,5]=>1101101=>1011011=>0100100
[3,1,5,2,8,7,6,4]=>1010111=>1110101=>0001010
[1,2,8,4,3,7,6,5]=>0011011=>1101100=>0010011
[1,8,5,4,2,7,3,6]=>0111010=>0101110=>1010001
[3,1,8,5,4,7,2,6]=>1011010=>0101101=>1010010
[2,6,1,8,7,4,3,5]=>0101110=>0111010=>1000101
[7,5,1,8,3,2,6,4]=>1101101=>1011011=>0100100
[4,7,6,3,1,8,2,5]=>0111010=>0101110=>1010001
[5,3,1,8,6,2,4,7]=>1101100=>0011011=>1100100
[5,1,8,6,3,2,4,7]=>1011100=>0011101=>1100010
[1,5,4,2,8,6,3,7]=>0110110=>0110110=>1001001
[8,3,1,6,4,2,5,7]=>1101100=>0011011=>1100100
[3,6,7,1,8,4,2,5]=>0010110=>0110100=>1001011
[1,7,4,8,3,5,2,6]=>0101010=>0101010=>1010101
[7,3,2,4,8,5,1,6]=>1100110=>0110011=>1001100
[6,3,4,7,1,8,5,2]=>1001011=>1101001=>0010110
[5,7,8,1,4,2,6,3]=>0010101=>1010100=>0101011
[5,7,1,2,3,8,6,4]=>0100011=>1100010=>0011101
[7,2,8,1,4,3,6,5]=>1010101=>1010101=>0101010
[2,6,3,8,1,7,5,4]=>0101011=>1101010=>0010101
[1,8,3,6,4,7,2,5]=>0101010=>0101010=>1010101
[2,8,6,4,1,7,3,5]=>0111010=>0101110=>1010001
[1,8,4,2,7,5,3,6]=>0110110=>0110110=>1001001
[6,5,1,7,2,8,4,3]=>1101011=>1101011=>0010100
[2,8,1,7,5,3,6,4]=>0101101=>1011010=>0100101
[1,2,8,7,6,4,3,5]=>0011110=>0111100=>1000011
[4,1,7,8,6,3,5,2]=>1001101=>1011001=>0100110
[1,6,5,7,8,4,2,3]=>0100110=>0110010=>1001101
[1,6,5,8,7,4,2,3]=>0101110=>0111010=>1000101
[4,1,8,7,6,3,5,2]=>1011101=>1011101=>0100010
[4,8,2,6,3,5,1,7]=>0101010=>0101010=>1010101
[6,7,2,5,3,8,4,1]=>0101011=>1101010=>0010101
[4,3,5,7,1,6,2,8]=>1001010=>0101001=>1010110
[4,2,8,5,3,6,7,1]=>1011001=>1001101=>0110010
[4,1,8,5,3,6,2,7]=>1011010=>0101101=>1010010
[6,4,2,5,3,1,7,8]=>1101100=>0011011=>1100100
[3,1,5,8,2,7,4,6]=>1001010=>0101001=>1010110
[6,4,1,5,3,2,7,8]=>1101100=>0011011=>1100100
[6,2,1,5,4,3,7,8]=>1101100=>0011011=>1100100
[3,1,8,5,4,6,2,7]=>1011010=>0101101=>1010010
[6,2,8,4,5,3,7,1]=>1010101=>1010101=>0101010
[6,1,8,4,5,3,2,7]=>1010110=>0110101=>1001010
[4,5,2,7,1,6,3,8]=>0101010=>0101010=>1010101
[4,3,5,7,1,6,8,2]=>1001001=>1001001=>0110110
[4,1,8,5,3,6,7,2]=>1011001=>1001101=>0110010
[6,3,8,4,5,1,7,2]=>1010101=>1010101=>0101010
[3,1,6,8,5,7,4,2]=>1001011=>1101001=>0010110
[2,6,1,8,5,7,4,3]=>0101011=>1101010=>0010101
[6,5,8,7,1,3,2,4]=>1011010=>0101101=>1010010
[6,5,8,7,2,3,4,1]=>1011001=>1001101=>0110010
[6,5,8,7,3,2,4,1]=>1011101=>1011101=>0100010
[6,3,8,4,5,2,7,1]=>1010101=>1010101=>0101010
[3,1,6,8,5,7,2,4]=>1001010=>0101001=>1010110
[2,1,6,8,5,3,7,4]=>1001101=>1011001=>0100110
[3,1,6,8,5,4,2,7]=>1001110=>0111001=>1000110
[3,2,6,8,5,4,7,1]=>1001101=>1011001=>0100110
[4,1,8,5,2,6,3,7]=>1011010=>0101101=>1010010
[3,1,6,8,5,2,4,7]=>1001100=>0011001=>1100110
[6,2,8,4,5,1,3,7]=>1010100=>0010101=>1101010
[6,5,8,7,4,1,2,3]=>1011100=>0011101=>1100010
[6,5,8,7,4,2,1,3]=>1011110=>0111101=>1000010
[6,5,8,7,2,4,1,3]=>1011010=>0101101=>1010010
[6,2,8,4,5,7,1,3]=>1010010=>0100101=>1011010
[6,1,8,4,5,7,3,2]=>1010011=>1100101=>0011010
[4,2,7,3,5,8,6,1]=>1010011=>1100101=>0011010
[3,6,2,4,8,5,7,1]=>0100101=>1010010=>0101101
[2,7,5,4,3,8,6,1]=>0111011=>1101110=>0010001
[3,5,1,8,4,7,6,2]=>0101011=>1101010=>0010101
[2,4,8,3,7,6,5,1]=>0010111=>1110100=>0001011
[3,6,8,5,2,4,7,1]=>0011001=>1001100=>0110011
[2,6,8,5,4,3,7,1]=>0011101=>1011100=>0100011
[3,6,8,2,5,4,7,1]=>0010101=>1010100=>0101011
[4,6,8,3,2,5,7,1]=>0011001=>1001100=>0110011
[4,6,2,8,3,5,7,1]=>0101001=>1001010=>0110101
[3,6,1,8,5,7,4,2]=>0101011=>1101010=>0010101
[4,6,3,8,7,2,5,1]=>0101101=>1011010=>0100101
[3,5,8,2,7,4,6,1]=>0010101=>1010100=>0101011
[2,4,8,7,3,6,5,1]=>0011011=>1101100=>0010011
[2,5,8,7,4,3,6,1]=>0011101=>1011100=>0100011
[2,4,8,7,6,3,5,1]=>0011101=>1011100=>0100011
[4,7,2,5,6,3,1,8]=>0100110=>0110010=>1001101
[6,1,2,8,7,3,4,5]=>1001100=>0011001=>1100110
[4,1,3,5,7,8,2,6]=>1000010=>0100001=>1011110
[6,1,5,8,4,3,2,7]=>1001110=>0111001=>1000110
[2,3,7,8,5,1,6,4]=>0001101=>1011000=>0100111
[8,1,3,2,5,6,4,7]=>1010010=>0100101=>1011010
[3,2,5,8,4,7,1,6]=>1001010=>0101001=>1010110
[8,6,4,1,5,2,3,7]=>1110100=>0010111=>1101000
[2,5,8,1,3,4,7,6]=>0010001=>1000100=>0111011
[3,5,1,8,7,4,2,6]=>0101110=>0111010=>1000101
[4,6,1,3,8,2,7,5]=>0100101=>1010010=>0101101
[6,2,1,8,5,7,4,3]=>1101011=>1101011=>0010100
[5,4,7,1,3,8,6,2]=>1010011=>1100101=>0011010
[6,5,7,8,1,3,4,2]=>1001001=>1001001=>0110110
[4,8,1,2,7,6,5,3]=>0100111=>1110010=>0001101
[3,7,4,8,5,2,6,1]=>0101101=>1011010=>0100101
[8,1,2,6,5,3,4,7]=>1001100=>0011001=>1100110
[3,4,2,8,6,7,5,1]=>0101011=>1101010=>0010101
[3,7,8,6,1,4,2,5]=>0011010=>0101100=>1010011
[3,6,1,5,2,7,8,4]=>0101001=>1001010=>0110101
[6,2,8,4,7,1,3,5]=>1010100=>0010101=>1101010
[1,8,4,3,7,6,2,5]=>0110110=>0110110=>1001001
[4,3,8,7,1,2,6,5]=>1011001=>1001101=>0110010
[1,8,3,6,7,2,4,5]=>0100100=>0010010=>1101101
[1,8,4,5,7,6,2,3]=>0100110=>0110010=>1001101
[4,3,8,5,7,1,6,2]=>1010101=>1010101=>0101010
[6,3,4,8,7,2,1,5]=>1001110=>0111001=>1000110
[5,3,8,4,7,1,6,2]=>1010101=>1010101=>0101010
[5,2,8,7,1,4,6,3]=>1011001=>1001101=>0110010
[3,2,8,7,1,6,4,5]=>1011010=>0101101=>1010010
[2,7,8,3,1,6,4,5]=>0011010=>0101100=>1010011
[3,5,8,7,4,1,6,2]=>0011101=>1011100=>0100011
[7,4,6,8,3,5,1,2]=>1001010=>0101001=>1010110
[7,2,8,4,1,3,6,5]=>1011001=>1001101=>0110010
[2,7,8,1,3,6,4,5]=>0010010=>0100100=>1011011
[2,7,8,1,5,4,6,3]=>0010101=>1010100=>0101011
[2,7,8,1,4,5,6,3]=>0010001=>1000100=>0111011
[3,6,7,8,2,4,1,5]=>0001010=>0101000=>1010111
[4,5,7,8,6,3,1,2]=>0001110=>0111000=>1000111
[5,4,6,8,7,3,1,2]=>1001110=>0111001=>1000110
[4,5,8,6,7,1,3,2]=>0010101=>1010100=>0101011
[5,7,6,8,2,1,3,4]=>0101100=>0011010=>1100101
[3,7,6,8,2,4,1,5]=>0101010=>0101010=>1010101
[5,4,7,8,6,3,1,2]=>1001110=>0111001=>1000110
[3,6,7,8,2,1,4,5]=>0001100=>0011000=>1100111
[4,5,6,8,7,3,1,2]=>0001110=>0111000=>1000111
[4,2,5,3,7,8,6,1]=>1010011=>1100101=>0011010
[5,3,6,2,4,1,8,7]=>1010101=>1010101=>0101010
[7,8,6,2,3,5,4,1]=>0110011=>1100110=>0011001
[5,8,2,6,3,7,4,1]=>0101011=>1101010=>0010101
[4,8,2,3,7,5,6,1]=>0100101=>1010010=>0101101
[7,5,6,2,3,8,4,1]=>1010011=>1100101=>0011010
[2,7,5,6,4,3,8,1]=>0101101=>1011010=>0100101
[2,8,4,3,7,5,6,1]=>0110101=>1010110=>0101001
[2,7,5,6,3,8,4,1]=>0101011=>1101010=>0010101
[7,6,3,8,5,4,2,1]=>1101111=>1111011=>0000100
[3,8,5,7,6,4,2,1]=>0101111=>1111010=>0000101
[7,8,6,3,5,4,2,1]=>0110111=>1110110=>0001001
[2,7,6,3,8,5,4,1]=>0110111=>1110110=>0001001
[4,2,8,5,3,7,6,1]=>1011011=>1101101=>0010010
[7,4,2,5,6,3,8,1]=>1100101=>1010011=>0101100
[6,2,7,5,3,8,4,1]=>1011011=>1101101=>0010010
[2,4,8,3,7,5,6,1]=>0010101=>1010100=>0101011
[4,8,3,7,5,6,2,1]=>0101011=>1101010=>0010101
[6,2,5,8,3,7,4,1]=>1001011=>1101001=>0010110
[7,6,2,5,3,8,4,1]=>1101011=>1101011=>0010100
[4,7,3,8,2,5,6,1]=>0101001=>1001010=>0110101
[8,2,5,6,3,7,4,1]=>1001011=>1101001=>0010110
[4,5,3,7,1,2,6,8]=>0101000=>0001010=>1110101
[6,7,2,8,4,3,1,5]=>0101110=>0111010=>1000101
[6,7,3,2,8,4,1,5]=>0110110=>0110110=>1001001
[4,5,8,1,3,2,6,7]=>0010100=>0010100=>1101011
[4,5,8,1,3,7,2,6]=>0010010=>0100100=>1011011
[2,6,7,4,3,8,1,5]=>0011010=>0101100=>1010011
[3,7,6,4,5,8,1,2]=>0110010=>0100110=>1011001
[5,7,2,8,3,4,6,1]=>0101001=>1001010=>0110101
[3,1,5,8,6,4,7,2]=>1001101=>1011001=>0100110
[3,6,2,8,7,4,5,1]=>0101101=>1011010=>0100101
[3,6,2,8,4,7,5,1]=>0101011=>1101010=>0010101
[8,3,5,1,6,4,2,7]=>1010110=>0110101=>1001010
[5,7,8,3,4,6,2,1]=>0010011=>1100100=>0011011
[3,1,5,8,6,2,4,7]=>1001100=>0011001=>1100110
[1,5,8,6,3,4,2,7]=>0011010=>0101100=>1010011
[3,7,8,5,2,6,4,1]=>0011011=>1101100=>0010011
[5,3,7,8,4,2,6,1]=>1001101=>1011001=>0100110
[5,1,6,4,3,8,7,2]=>1011011=>1101101=>0010010
[4,7,1,3,2,5,6,8]=>0101000=>0001010=>1110101
[4,7,6,8,3,1,5,2]=>0101101=>1011010=>0100101
[5,4,8,6,1,7,3,2]=>1011011=>1101101=>0010010
[3,5,4,7,1,8,6,2]=>0101011=>1101010=>0010101
[1,8,5,4,2,3,6,7]=>0111000=>0001110=>1110001
[7,1,5,4,2,3,6,8]=>1011000=>0001101=>1110010
[7,1,3,6,4,5,2,8]=>1001010=>0101001=>1010110
[6,1,3,8,4,5,2,7]=>1001010=>0101001=>1010110
[5,8,6,3,1,2,7,4]=>0111001=>1001110=>0110001
[5,8,2,7,1,3,6,4]=>0101001=>1001010=>0110101
[2,6,5,4,1,3,7,8]=>0111000=>0001110=>1110001
[4,1,5,7,6,3,2,8]=>1001110=>0111001=>1000110
[7,6,3,2,8,5,1,4]=>1110110=>0110111=>1001000
[5,3,8,2,7,1,6,4]=>1010101=>1010101=>0101010
[6,3,4,2,1,8,7,5]=>1011011=>1101101=>0010010
[4,5,1,7,6,3,2,8]=>0101110=>0111010=>1000101
[1,5,3,7,4,2,6,8]=>0101100=>0011010=>1100101
[1,2,7,4,3,8,6,5]=>0011011=>1101100=>0010011
[1,5,4,2,3,8,7,6]=>0110011=>1100110=>0011001
[1,5,4,2,3,8,6,7]=>0110010=>0100110=>1011001
[1,5,3,2,4,6,7,8]=>0110000=>0000110=>1111001
[1,5,4,2,3,7,8,6]=>0110001=>1000110=>0111001
[3,6,5,2,4,1,7,8]=>0110100=>0010110=>1101001
[4,6,7,2,5,1,8,3]=>0010101=>1010100=>0101011
[3,6,2,5,1,7,8,4]=>0101001=>1001010=>0110101
[3,4,2,7,8,6,1,5]=>0100110=>0110010=>1001101
[3,4,2,7,8,1,5,6]=>0100100=>0010010=>1101101
[3,8,5,2,4,7,1,6]=>0110010=>0100110=>1011001
[6,4,3,2,8,1,7,5]=>1110101=>1010111=>0101000
[6,2,4,3,8,1,7,5]=>1010101=>1010101=>0101010
[8,7,3,6,2,1,5,4]=>1101101=>1011011=>0100100
[3,7,5,4,6,1,2,8]=>0110100=>0010110=>1101001
[5,3,4,7,6,8,1,2]=>1001010=>0101001=>1010110
[5,3,7,4,6,1,2,8]=>1010100=>0010101=>1101010
[7,3,5,4,6,1,2,8]=>1010100=>0010101=>1101010
[7,8,3,5,4,1,2,6]=>0101100=>0011010=>1100101
[7,3,5,4,1,2,6,8]=>1011000=>0001101=>1110010
[5,7,6,3,1,2,4,8]=>0111000=>0001110=>1110001
[5,7,6,3,4,1,2,8]=>0110100=>0010110=>1101001
[7,5,6,8,1,3,2,4]=>1001010=>0101001=>1010110
[3,5,4,1,2,7,6,8]=>0110010=>0100110=>1011001
[5,7,6,1,3,2,4,8]=>0110100=>0010110=>1101001
[3,5,4,1,7,2,6,8]=>0110100=>0010110=>1101001
[5,3,4,1,2,7,6,8]=>1010010=>0100101=>1011010
[7,8,3,1,2,5,4,6]=>0110010=>0100110=>1011001
[7,8,5,1,3,2,4,6]=>0110100=>0010110=>1101001
[7,5,6,1,3,2,4,8]=>1010100=>0010101=>1101010
[7,1,3,8,2,5,4,6]=>1001010=>0101001=>1010110
[5,1,3,7,6,2,4,8]=>1001100=>0011001=>1100110
[6,7,1,8,3,4,5,2]=>0101001=>1001010=>0110101
[3,7,1,6,8,4,5,2]=>0100101=>1010010=>0101101
[8,7,1,5,3,2,6,4]=>1101101=>1011011=>0100100
[3,7,1,6,5,2,8,4]=>0101101=>1011010=>0100101
[8,6,7,2,5,3,1,4]=>1010110=>0110101=>1001010
[1,8,2,6,5,3,4,7]=>0101100=>0011010=>1100101
[8,6,1,5,2,3,4,7]=>1101000=>0001011=>1110100
[8,5,1,6,2,3,4,7]=>1101000=>0001011=>1110100
[8,1,4,2,3,5,7,6]=>1010001=>1000101=>0111010
[1,7,8,2,5,3,4,6]=>0010100=>0010100=>1101011
[2,7,8,4,1,3,5,6]=>0011000=>0001100=>1110011
[6,8,1,2,3,7,4,5]=>0100010=>0100010=>1011101
[1,2,8,6,4,5,3,7]=>0011010=>0101100=>1010011
[1,5,8,7,6,3,4,2]=>0011101=>1011100=>0100011
[1,2,7,8,4,3,5,6]=>0001100=>0011000=>1100111
[1,5,7,8,4,2,3,6]=>0001100=>0011000=>1100111
[1,6,8,5,4,2,3,7]=>0011100=>0011100=>1100011
[1,2,3,7,5,4,6,8]=>0001100=>0011000=>1100111
[4,6,5,2,1,7,8,3]=>0111001=>1001110=>0110001
[4,6,1,7,5,8,3,2]=>0101011=>1101010=>0010101
[3,5,6,2,1,4,7,8]=>0011000=>0001100=>1110011
[4,3,6,5,1,7,8,2]=>1011001=>1001101=>0110010
[4,6,5,3,1,7,8,2]=>0111001=>1001110=>0110001
[5,1,3,4,8,2,6,7]=>1000100=>0010001=>1101110
[5,8,1,4,2,3,6,7]=>0101000=>0001010=>1110101
[4,3,1,8,5,2,6,7]=>1101100=>0011011=>1100100
[4,5,8,2,3,1,6,7]=>0010100=>0010100=>1101011
[3,5,4,8,1,7,2,6]=>0101010=>0101010=>1010101
[5,3,6,8,1,4,7,2]=>1001001=>1001001=>0110110
[5,1,6,8,3,4,7,2]=>1001001=>1001001=>0110110
[3,5,1,8,6,4,7,2]=>0101101=>1011010=>0100101
[6,4,8,1,5,7,2,3]=>1010010=>0100101=>1011010
[4,7,2,8,3,1,6,5]=>0101101=>1011010=>0100101
[1,2,5,6,8,3,7,4]=>0000101=>1010000=>0101111
[5,1,6,8,7,2,3,4]=>1001100=>0011001=>1100110
[1,5,6,8,3,7,2,4]=>0001010=>0101000=>1010111
[5,6,8,1,2,3,7,4]=>0010001=>1000100=>0111011
[2,8,1,3,5,7,4,6]=>0100010=>0100010=>1011101
[7,4,8,1,5,2,6,3]=>1010101=>1010101=>0101010
[8,3,2,1,6,5,7,4]=>1110101=>1010111=>0101000
[4,1,5,6,8,7,2,3]=>1000110=>0110001=>1001110
[1,2,5,6,8,4,7,3]=>0000101=>1010000=>0101111
[1,5,6,8,4,7,2,3]=>0001010=>0101000=>1010111
[6,8,1,4,5,7,2,3]=>0100010=>0100010=>1011101
[4,3,5,1,8,6,7,2]=>1010101=>1010101=>0101010
[1,3,5,6,8,4,7,2]=>0000101=>1010000=>0101111
[5,6,8,1,3,4,7,2]=>0010001=>1000100=>0111011
[5,6,8,2,3,4,7,1]=>0010001=>1000100=>0111011
[5,7,8,3,2,6,1,4]=>0011010=>0101100=>1010011
[7,5,8,6,4,1,3,2]=>1011101=>1011101=>0100010
[5,1,8,6,4,2,7,3]=>1011101=>1011101=>0100010
[2,7,6,3,8,5,1,4]=>0110110=>0110110=>1001001
[2,3,1,8,4,6,5,7]=>0101010=>0101010=>1010101
[2,3,1,7,6,8,4,5]=>0101010=>0101010=>1010101
[2,3,1,8,4,6,7,5]=>0101001=>1001010=>0110101
[2,7,4,1,3,6,8,5]=>0110001=>1000110=>0111001
[6,3,2,8,1,7,5,4]=>1101011=>1101011=>0010100
[2,6,8,7,1,3,5,4]=>0011001=>1001100=>0110011
[3,7,6,1,4,5,2,8]=>0110010=>0100110=>1011001
[4,1,6,2,7,5,3,8]=>1010110=>0110101=>1001010
[7,6,2,5,3,1,4,8]=>1101100=>0011011=>1100100
[4,3,1,7,6,2,5,8]=>1101100=>0011011=>1100100
[4,5,3,1,2,8,6,7]=>0110010=>0100110=>1011001
[2,4,5,3,1,8,6,7]=>0011010=>0101100=>1010011
[5,7,6,2,3,1,4,8]=>0110100=>0010110=>1101001
[4,1,3,7,5,2,6,8]=>1001100=>0011001=>1100110
[4,1,6,3,2,7,5,8]=>1011010=>0101101=>1010010
[2,7,5,4,1,3,6,8]=>0111000=>0001110=>1110001
[7,5,4,1,3,2,6,8]=>1110100=>0010111=>1101000
[2,4,8,5,6,3,1,7]=>0010110=>0110100=>1001011
[2,5,7,4,1,3,6,8]=>0011000=>0001100=>1110011
[5,7,4,1,3,2,6,8]=>0110100=>0010110=>1101001
[6,2,4,5,7,3,1,8]=>1000110=>0110001=>1001110
[2,6,8,4,5,3,1,7]=>0010110=>0110100=>1001011
[2,5,3,8,4,1,6,7]=>0101100=>0011010=>1100101
[5,2,3,7,4,1,6,8]=>1001100=>0011001=>1100110
[4,5,1,6,3,2,7,8]=>0101100=>0011010=>1100101
[5,1,6,3,2,4,7,8]=>1011000=>0001101=>1110010
[4,2,5,1,6,3,7,8]=>1010100=>0010101=>1101010
[5,1,6,2,4,3,7,8]=>1010100=>0010101=>1101010
[4,3,5,1,6,2,7,8]=>1010100=>0010101=>1101010
[6,2,1,7,5,8,4,3]=>1101011=>1101011=>0010100
[1,5,7,8,6,4,2,3]=>0001110=>0111000=>1000111
[1,6,4,8,5,3,7,2]=>0101101=>1011010=>0100101
[1,6,5,3,4,7,8,2]=>0110001=>1000110=>0111001
[4,2,6,7,8,1,3,5]=>1000100=>0010001=>1101110
[4,5,1,7,6,3,8,2]=>0101101=>1011010=>0100101
[4,6,5,1,3,7,8,2]=>0110001=>1000110=>0111001
[5,2,1,7,6,4,8,3]=>1101101=>1011011=>0100100
[6,8,5,2,7,3,1,4]=>0110110=>0110110=>1001001
[6,1,2,4,3,7,8,5]=>1001001=>1001001=>0110110
[8,1,5,4,2,3,6,7]=>1011000=>0001101=>1110010
[7,1,2,4,6,3,8,5]=>1000101=>1010001=>0101110
[7,1,2,6,5,3,8,4]=>1001101=>1011001=>0100110
[7,5,6,1,2,4,8,3]=>1010001=>1000101=>0111010
[7,1,4,5,2,3,6,8]=>1001000=>0001001=>1110110
[6,1,4,8,7,2,3,5]=>1001100=>0011001=>1100110
[6,1,8,5,7,2,3,4]=>1010100=>0010101=>1101010
[1,6,7,5,8,3,4,2]=>0010101=>1010100=>0101011
[6,1,7,5,8,2,3,4]=>1010100=>0010101=>1101010
[6,1,4,7,8,2,3,5]=>1000100=>0010001=>1101110
[5,8,6,1,2,4,7,3]=>0110001=>1000110=>0111001
[1,6,8,7,5,3,4,2]=>0011101=>1011100=>0100011
[6,8,7,5,1,2,4,3]=>0111001=>1001110=>0110001
[6,1,8,7,5,2,3,4]=>1011100=>0011101=>1100010
[8,3,1,2,4,6,5,7]=>1100010=>0100011=>1011100
[8,3,1,2,4,5,7,6]=>1100001=>1000011=>0111100
[6,3,1,2,4,7,5,8]=>1100010=>0100011=>1011100
[6,7,1,4,2,3,5,8]=>0101000=>0001010=>1110101
[6,1,7,4,8,2,3,5]=>1010100=>0010101=>1101010
[6,7,8,5,1,2,4,3]=>0011001=>1001100=>0110011
[4,6,8,2,3,5,1,7]=>0010010=>0100100=>1011011
[6,8,2,1,3,5,4,7]=>0110010=>0100110=>1011001
[3,5,1,6,4,8,2,7]=>0101010=>0101010=>1010101
[3,5,8,6,2,1,4,7]=>0011100=>0011100=>1100011
[2,4,8,5,6,1,3,7]=>0010100=>0010100=>1101011
[5,3,8,4,2,7,6,1]=>1011011=>1101101=>0010010
[2,8,5,3,1,4,7,6]=>0111001=>1001110=>0110001
[3,7,8,5,1,4,2,6]=>0011010=>0101100=>1010011
[1,7,8,4,6,3,2,5]=>0010110=>0110100=>1001011
[8,7,2,4,6,3,1,5]=>1100110=>0110011=>1001100
[7,8,3,4,6,5,2,1]=>0100111=>1110010=>0001101
[8,7,3,6,5,2,4,1]=>1101101=>1011011=>0100100
[3,1,2,8,6,5,7,4]=>1001101=>1011001=>0100110
[3,8,2,7,5,4,6,1]=>0101101=>1011010=>0100101
[8,7,1,4,5,3,6,2]=>1100101=>1010011=>0101100
[2,8,7,4,6,3,5,1]=>0110101=>1010110=>0101001
[2,8,7,4,6,3,1,5]=>0110110=>0110110=>1001001
[8,3,4,1,2,5,7,6]=>1010001=>1000101=>0111010
[8,4,1,3,2,5,7,6]=>1101001=>1001011=>0110100
[7,4,8,2,3,5,1,6]=>1010010=>0100101=>1011010
[7,3,8,6,2,1,4,5]=>1011100=>0011101=>1100010
[7,2,8,4,6,5,1,3]=>1010110=>0110101=>1001010
[5,8,6,4,7,2,3,1]=>0110101=>1010110=>0101001
[4,7,2,6,5,8,3,1]=>0101011=>1101010=>0010101
[3,6,8,5,7,4,2,1]=>0010111=>1110100=>0001011
[6,7,5,2,4,8,3,1]=>0110011=>1100110=>0011001
[8,7,2,4,6,1,5,3]=>1100101=>1010011=>0101100
[8,1,2,7,5,6,3,4]=>1001010=>0101001=>1010110
[8,2,7,3,4,6,1,5]=>1010010=>0100101=>1011010
[6,7,5,4,8,1,3,2]=>0110101=>1010110=>0101001
[2,5,1,4,7,3,6,8]=>0100100=>0010010=>1101101
[3,1,6,5,7,2,4,8]=>1010100=>0010101=>1101010
[2,5,7,1,6,3,4,8]=>0010100=>0010100=>1101011
[2,5,7,1,6,3,8,4]=>0010101=>1010100=>0101011
[2,6,1,5,7,4,3,8]=>0100110=>0110010=>1001101
[3,1,6,5,2,4,7,8]=>1011000=>0001101=>1110010
[3,6,5,1,4,2,7,8]=>0110100=>0010110=>1101001
[3,5,6,2,8,1,7,4]=>0010101=>1010100=>0101011
[3,6,5,1,7,2,4,8]=>0110100=>0010110=>1101001
[3,6,5,2,1,4,7,8]=>0111000=>0001110=>1110001
[4,5,2,7,6,1,3,8]=>0101100=>0011010=>1100101
[4,6,5,3,1,2,7,8]=>0111000=>0001110=>1110001
[5,4,1,6,3,7,2,8]=>1101010=>0101011=>1010100
[5,4,2,6,3,7,8,1]=>1101001=>1001011=>0110100
[3,6,5,7,1,4,2,8]=>0101010=>0101010=>1010101
[3,6,5,1,4,7,2,8]=>0110010=>0100110=>1011001
[4,3,6,5,7,1,2,8]=>1010100=>0010101=>1101010
[4,2,6,5,1,3,7,8]=>1011000=>0001101=>1110010
[4,1,6,5,3,7,8,2]=>1011001=>1001101=>0110010
[4,1,5,7,6,3,8,2]=>1001101=>1011001=>0100110
[4,2,5,7,6,1,3,8]=>1001100=>0011001=>1100110
[3,4,7,6,1,2,5,8]=>0011000=>0001100=>1110011
[3,4,7,6,8,2,5,1]=>0010101=>1010100=>0101011
[4,2,5,7,6,3,8,1]=>1001101=>1011001=>0100110
[4,1,6,5,2,7,3,8]=>1011010=>0101101=>1010010
[4,2,6,5,7,3,1,8]=>1010110=>0110101=>1001010
[3,6,5,7,2,1,4,8]=>0101100=>0011010=>1100101
[3,5,7,6,2,4,1,8]=>0011010=>0101100=>1010011
[5,4,2,6,3,7,1,8]=>1101010=>0101011=>1010100
[4,6,5,2,7,3,1,8]=>0110110=>0110110=>1001001
[4,5,2,7,6,3,8,1]=>0101101=>1011010=>0100101
[4,6,5,2,1,7,3,8]=>0111010=>0101110=>1010001
[3,5,8,2,1,4,6,7]=>0011000=>0001100=>1110011
[3,5,8,2,4,6,7,1]=>0010001=>1000100=>0111011
[5,3,8,2,1,4,6,7]=>1011000=>0001101=>1110010
[5,3,1,8,2,4,6,7]=>1101000=>0001011=>1110100
[1,5,3,8,2,4,6,7]=>0101000=>0001010=>1110101
[1,5,8,4,2,3,6,7]=>0011000=>0001100=>1110011
[5,8,2,1,4,3,6,7]=>0110100=>0010110=>1101001
[5,8,2,4,6,3,1,7]=>0100110=>0110010=>1001101
[5,8,2,4,3,6,1,7]=>0101010=>0101010=>1010101
[5,8,1,4,6,2,3,7]=>0100100=>0010010=>1101101
[1,5,8,4,6,7,2,3]=>0010010=>0100100=>1011011
[5,1,8,4,6,7,2,3]=>1010010=>0100101=>1011010
[5,8,2,4,6,3,7,1]=>0100101=>1010010=>0101101
[3,8,4,6,7,2,1,5]=>0100110=>0110010=>1001101
[3,8,4,6,7,2,5,1]=>0100101=>1010010=>0101101
[8,4,3,6,7,2,5,1]=>1100101=>1010011=>0101100
[8,4,3,6,7,2,1,5]=>1100110=>0110011=>1001100
[8,6,2,4,5,3,7,1]=>1100101=>1010011=>0101100
[8,6,4,1,5,7,2,3]=>1110010=>0100111=>1011000
[1,8,6,4,5,7,2,3]=>0110010=>0100110=>1011001
[8,1,6,4,5,2,3,7]=>1010100=>0010101=>1101010
[8,6,2,4,5,3,1,7]=>1100110=>0110011=>1001100
[1,8,6,4,2,3,5,7]=>0111000=>0001110=>1110001
[3,8,1,6,2,4,5,7]=>0101000=>0001010=>1110101
[1,3,8,6,2,4,5,7]=>0011000=>0001100=>1110011
[3,8,6,2,1,4,5,7]=>0111000=>0001110=>1110001
[3,8,6,2,4,1,5,7]=>0110100=>0010110=>1101001
[3,8,6,2,4,5,7,1]=>0110001=>1000110=>0111001
[8,3,6,2,4,5,1,7]=>1010010=>0100101=>1011010
[1,8,3,6,2,4,5,7]=>0101000=>0001010=>1110101
[8,1,3,6,2,4,5,7]=>1001000=>0001001=>1110110
[8,3,6,7,2,1,4,5]=>1001100=>0011001=>1100110
[2,5,8,4,6,1,7,3]=>0010101=>1010100=>0101011
[3,8,6,7,2,1,4,5]=>0101100=>0011010=>1100101
[3,1,8,6,7,2,4,5]=>1010100=>0010101=>1101010
[8,2,6,4,5,1,7,3]=>1010101=>1010101=>0101010
[8,4,6,1,7,2,5,3]=>1010101=>1010101=>0101010
[1,8,4,6,7,5,2,3]=>0100110=>0110010=>1001101
[8,1,4,6,7,5,2,3]=>1000110=>0110001=>1001110
[8,4,6,1,3,7,2,5]=>1010010=>0100101=>1011010
[8,1,4,6,3,7,2,5]=>1001010=