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Identifier

Mp00109: Permutations —descent word⟶ Binary words

Images

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            [1]=>
[1,2]=>0
[2,1]=>1
[1,2,3]=>00
[1,3,2]=>01
[2,1,3]=>10
[2,3,1]=>01
[3,1,2]=>10
[3,2,1]=>11
[1,2,3,4]=>000
[1,2,4,3]=>001
[1,3,2,4]=>010
[1,3,4,2]=>001
[1,4,2,3]=>010
[1,4,3,2]=>011
[2,1,3,4]=>100
[2,1,4,3]=>101
[2,3,1,4]=>010
[2,3,4,1]=>001
[2,4,1,3]=>010
[2,4,3,1]=>011
[3,1,2,4]=>100
[3,1,4,2]=>101
[3,2,1,4]=>110
[3,2,4,1]=>101
[3,4,1,2]=>010
[3,4,2,1]=>011
[4,1,2,3]=>100
[4,1,3,2]=>101
[4,2,1,3]=>110
[4,2,3,1]=>101
[4,3,1,2]=>110
[4,3,2,1]=>111
[1,2,3,4,5]=>0000
[1,2,3,5,4]=>0001
[1,2,4,3,5]=>0010
[1,2,4,5,3]=>0001
[1,2,5,3,4]=>0010
[1,2,5,4,3]=>0011
[1,3,2,4,5]=>0100
[1,3,2,5,4]=>0101
[1,3,4,2,5]=>0010
[1,3,4,5,2]=>0001
[1,3,5,2,4]=>0010
[1,3,5,4,2]=>0011
[1,4,2,3,5]=>0100
[1,4,2,5,3]=>0101
[1,4,3,2,5]=>0110
[1,4,3,5,2]=>0101
[1,4,5,2,3]=>0010
[1,4,5,3,2]=>0011
[1,5,2,3,4]=>0100
[1,5,2,4,3]=>0101
[1,5,3,2,4]=>0110
[1,5,3,4,2]=>0101
[1,5,4,2,3]=>0110
[1,5,4,3,2]=>0111
[2,1,3,4,5]=>1000
[2,1,3,5,4]=>1001
[2,1,4,3,5]=>1010
[2,1,4,5,3]=>1001
[2,1,5,3,4]=>1010
[2,1,5,4,3]=>1011
[2,3,1,4,5]=>0100
[2,3,1,5,4]=>0101
[2,3,4,1,5]=>0010
[2,3,4,5,1]=>0001
[2,3,5,1,4]=>0010
[2,3,5,4,1]=>0011
[2,4,1,3,5]=>0100
[2,4,1,5,3]=>0101
[2,4,3,1,5]=>0110
[2,4,3,5,1]=>0101
[2,4,5,1,3]=>0010
[2,4,5,3,1]=>0011
[2,5,1,3,4]=>0100
[2,5,1,4,3]=>0101
[2,5,3,1,4]=>0110
[2,5,3,4,1]=>0101
[2,5,4,1,3]=>0110
[2,5,4,3,1]=>0111
[3,1,2,4,5]=>1000
[3,1,2,5,4]=>1001
[3,1,4,2,5]=>1010
[3,1,4,5,2]=>1001
[3,1,5,2,4]=>1010
[3,1,5,4,2]=>1011
[3,2,1,4,5]=>1100
[3,2,1,5,4]=>1101
[3,2,4,1,5]=>1010
[3,2,4,5,1]=>1001
[3,2,5,1,4]=>1010
[3,2,5,4,1]=>1011
[3,4,1,2,5]=>0100
[3,4,1,5,2]=>0101
[3,4,2,1,5]=>0110
[3,4,2,5,1]=>0101
[3,4,5,1,2]=>0010
[3,4,5,2,1]=>0011
[3,5,1,2,4]=>0100
[3,5,1,4,2]=>0101
[3,5,2,1,4]=>0110
[3,5,2,4,1]=>0101
[3,5,4,1,2]=>0110
[3,5,4,2,1]=>0111
[4,1,2,3,5]=>1000
[4,1,2,5,3]=>1001
[4,1,3,2,5]=>1010
[4,1,3,5,2]=>1001
[4,1,5,2,3]=>1010
[4,1,5,3,2]=>1011
[4,2,1,3,5]=>1100
[4,2,1,5,3]=>1101
[4,2,3,1,5]=>1010
[4,2,3,5,1]=>1001
[4,2,5,1,3]=>1010
[4,2,5,3,1]=>1011
[4,3,1,2,5]=>1100
[4,3,1,5,2]=>1101
[4,3,2,1,5]=>1110
[4,3,2,5,1]=>1101
[4,3,5,1,2]=>1010
[4,3,5,2,1]=>1011
[4,5,1,2,3]=>0100
[4,5,1,3,2]=>0101
[4,5,2,1,3]=>0110
[4,5,2,3,1]=>0101
[4,5,3,1,2]=>0110
[4,5,3,2,1]=>0111
[5,1,2,3,4]=>1000
[5,1,2,4,3]=>1001
[5,1,3,2,4]=>1010
[5,1,3,4,2]=>1001
[5,1,4,2,3]=>1010
[5,1,4,3,2]=>1011
[5,2,1,3,4]=>1100
[5,2,1,4,3]=>1101
[5,2,3,1,4]=>1010
[5,2,3,4,1]=>1001
[5,2,4,1,3]=>1010
[5,2,4,3,1]=>1011
[5,3,1,2,4]=>1100
[5,3,1,4,2]=>1101
[5,3,2,1,4]=>1110
[5,3,2,4,1]=>1101
[5,3,4,1,2]=>1010
[5,3,4,2,1]=>1011
[5,4,1,2,3]=>1100
[5,4,1,3,2]=>1101
[5,4,2,1,3]=>1110
[5,4,2,3,1]=>1101
[5,4,3,1,2]=>1110
[5,4,3,2,1]=>1111
[1,2,3,4,5,6]=>00000
[1,2,3,4,6,5]=>00001
[1,2,3,5,4,6]=>00010
[1,2,3,5,6,4]=>00001
[1,2,3,6,4,5]=>00010
[1,2,3,6,5,4]=>00011
[1,2,4,3,5,6]=>00100
[1,2,4,3,6,5]=>00101
[1,2,4,5,3,6]=>00010
[1,2,4,5,6,3]=>00001
[1,2,4,6,3,5]=>00010
[1,2,4,6,5,3]=>00011
[1,2,5,3,4,6]=>00100
[1,2,5,3,6,4]=>00101
[1,2,5,4,3,6]=>00110
[1,2,5,4,6,3]=>00101
[1,2,5,6,3,4]=>00010
[1,2,5,6,4,3]=>00011
[1,2,6,3,4,5]=>00100
[1,2,6,3,5,4]=>00101
[1,2,6,4,3,5]=>00110
[1,2,6,4,5,3]=>00101
[1,2,6,5,3,4]=>00110
[1,2,6,5,4,3]=>00111
[1,3,2,4,5,6]=>01000
[1,3,2,4,6,5]=>01001
[1,3,2,5,4,6]=>01010
[1,3,2,5,6,4]=>01001
[1,3,2,6,4,5]=>01010
[1,3,2,6,5,4]=>01011
[1,3,4,2,5,6]=>00100
[1,3,4,2,6,5]=>00101
[1,3,4,5,2,6]=>00010
[1,3,4,5,6,2]=>00001
[1,3,4,6,2,5]=>00010
[1,3,4,6,5,2]=>00011
[1,3,5,2,4,6]=>00100
[1,3,5,2,6,4]=>00101
[1,3,5,4,2,6]=>00110
[1,3,5,4,6,2]=>00101
[1,3,5,6,2,4]=>00010
[1,3,5,6,4,2]=>00011
[1,3,6,2,4,5]=>00100
[1,3,6,2,5,4]=>00101
[1,3,6,4,2,5]=>00110
[1,3,6,4,5,2]=>00101
[1,3,6,5,2,4]=>00110
[1,3,6,5,4,2]=>00111
[1,4,2,3,5,6]=>01000
[1,4,2,3,6,5]=>01001
[1,4,2,5,3,6]=>01010
[1,4,2,5,6,3]=>01001
[1,4,2,6,3,5]=>01010
[1,4,2,6,5,3]=>01011
[1,4,3,2,5,6]=>01100
[1,4,3,2,6,5]=>01101
[1,4,3,5,2,6]=>01010
[1,4,3,5,6,2]=>01001
[1,4,3,6,2,5]=>01010
[1,4,3,6,5,2]=>01011
[1,4,5,2,3,6]=>00100
[1,4,5,2,6,3]=>00101
[1,4,5,3,2,6]=>00110
[1,4,5,3,6,2]=>00101
[1,4,5,6,2,3]=>00010
[1,4,5,6,3,2]=>00011
[1,4,6,2,3,5]=>00100
[1,4,6,2,5,3]=>00101
[1,4,6,3,2,5]=>00110
[1,4,6,3,5,2]=>00101
[1,4,6,5,2,3]=>00110
[1,4,6,5,3,2]=>00111
[1,5,2,3,4,6]=>01000
[1,5,2,3,6,4]=>01001
[1,5,2,4,3,6]=>01010
[1,5,2,4,6,3]=>01001
[1,5,2,6,3,4]=>01010
[1,5,2,6,4,3]=>01011
[1,5,3,2,4,6]=>01100
[1,5,3,2,6,4]=>01101
[1,5,3,4,2,6]=>01010
[1,5,3,4,6,2]=>01001
[1,5,3,6,2,4]=>01010
[1,5,3,6,4,2]=>01011
[1,5,4,2,3,6]=>01100
[1,5,4,2,6,3]=>01101
[1,5,4,3,2,6]=>01110
[1,5,4,3,6,2]=>01101
[1,5,4,6,2,3]=>01010
[1,5,4,6,3,2]=>01011
[1,5,6,2,3,4]=>00100
[1,5,6,2,4,3]=>00101
[1,5,6,3,2,4]=>00110
[1,5,6,3,4,2]=>00101
[1,5,6,4,2,3]=>00110
[1,5,6,4,3,2]=>00111
[1,6,2,3,4,5]=>01000
[1,6,2,3,5,4]=>01001
[1,6,2,4,3,5]=>01010
[1,6,2,4,5,3]=>01001
[1,6,2,5,3,4]=>01010
[1,6,2,5,4,3]=>01011
[1,6,3,2,4,5]=>01100
[1,6,3,2,5,4]=>01101
[1,6,3,4,2,5]=>01010
[1,6,3,4,5,2]=>01001
[1,6,3,5,2,4]=>01010
[1,6,3,5,4,2]=>01011
[1,6,4,2,3,5]=>01100
[1,6,4,2,5,3]=>01101
[1,6,4,3,2,5]=>01110
[1,6,4,3,5,2]=>01101
[1,6,4,5,2,3]=>01010
[1,6,4,5,3,2]=>01011
[1,6,5,2,3,4]=>01100
[1,6,5,2,4,3]=>01101
[1,6,5,3,2,4]=>01110
[1,6,5,3,4,2]=>01101
[1,6,5,4,2,3]=>01110
[1,6,5,4,3,2]=>01111
[2,1,3,4,5,6]=>10000
[2,1,3,4,6,5]=>10001
[2,1,3,5,4,6]=>10010
[2,1,3,5,6,4]=>10001
[2,1,3,6,4,5]=>10010
[2,1,3,6,5,4]=>10011
[2,1,4,3,5,6]=>10100
[2,1,4,3,6,5]=>10101
[2,1,4,5,3,6]=>10010
[2,1,4,5,6,3]=>10001
[2,1,4,6,3,5]=>10010
[2,1,4,6,5,3]=>10011
[2,1,5,3,4,6]=>10100
[2,1,5,3,6,4]=>10101
[2,1,5,4,3,6]=>10110
[2,1,5,4,6,3]=>10101
[2,1,5,6,3,4]=>10010
[2,1,5,6,4,3]=>10011
[2,1,6,3,4,5]=>10100
[2,1,6,3,5,4]=>10101
[2,1,6,4,3,5]=>10110
[2,1,6,4,5,3]=>10101
[2,1,6,5,3,4]=>10110
[2,1,6,5,4,3]=>10111
[2,3,1,4,5,6]=>01000
[2,3,1,4,6,5]=>01001
[2,3,1,5,4,6]=>01010
[2,3,1,5,6,4]=>01001
[2,3,1,6,4,5]=>01010
[2,3,1,6,5,4]=>01011
[2,3,4,1,5,6]=>00100
[2,3,4,1,6,5]=>00101
[2,3,4,5,1,6]=>00010
[2,3,4,5,6,1]=>00001
[2,3,4,6,1,5]=>00010
[2,3,4,6,5,1]=>00011
[2,3,5,1,4,6]=>00100
[2,3,5,1,6,4]=>00101
[2,3,5,4,1,6]=>00110
[2,3,5,4,6,1]=>00101
[2,3,5,6,1,4]=>00010
[2,3,5,6,4,1]=>00011
[2,3,6,1,4,5]=>00100
[2,3,6,1,5,4]=>00101
[2,3,6,4,1,5]=>00110
[2,3,6,4,5,1]=>00101
[2,3,6,5,1,4]=>00110
[2,3,6,5,4,1]=>00111
[2,4,1,3,5,6]=>01000
[2,4,1,3,6,5]=>01001
[2,4,1,5,3,6]=>01010
[2,4,1,5,6,3]=>01001
[2,4,1,6,3,5]=>01010
[2,4,1,6,5,3]=>01011
[2,4,3,1,5,6]=>01100
[2,4,3,1,6,5]=>01101
[2,4,3,5,1,6]=>01010
[2,4,3,5,6,1]=>01001
[2,4,3,6,1,5]=>01010
[2,4,3,6,5,1]=>01011
[2,4,5,1,3,6]=>00100
[2,4,5,1,6,3]=>00101
[2,4,5,3,1,6]=>00110
[2,4,5,3,6,1]=>00101
[2,4,5,6,1,3]=>00010
[2,4,5,6,3,1]=>00011
[2,4,6,1,3,5]=>00100
[2,4,6,1,5,3]=>00101
[2,4,6,3,1,5]=>00110
[2,4,6,3,5,1]=>00101
[2,4,6,5,1,3]=>00110
[2,4,6,5,3,1]=>00111
[2,5,1,3,4,6]=>01000
[2,5,1,3,6,4]=>01001
[2,5,1,4,3,6]=>01010
[2,5,1,4,6,3]=>01001
[2,5,1,6,3,4]=>01010
[2,5,1,6,4,3]=>01011
[2,5,3,1,4,6]=>01100
[2,5,3,1,6,4]=>01101
[2,5,3,4,1,6]=>01010
[2,5,3,4,6,1]=>01001
[2,5,3,6,1,4]=>01010
[2,5,3,6,4,1]=>01011
[2,5,4,1,3,6]=>01100
[2,5,4,1,6,3]=>01101
[2,5,4,3,1,6]=>01110
[2,5,4,3,6,1]=>01101
[2,5,4,6,1,3]=>01010
[2,5,4,6,3,1]=>01011
[2,5,6,1,3,4]=>00100
[2,5,6,1,4,3]=>00101
[2,5,6,3,1,4]=>00110
[2,5,6,3,4,1]=>00101
[2,5,6,4,1,3]=>00110
[2,5,6,4,3,1]=>00111
[2,6,1,3,4,5]=>01000
[2,6,1,3,5,4]=>01001
[2,6,1,4,3,5]=>01010
[2,6,1,4,5,3]=>01001
[2,6,1,5,3,4]=>01010
[2,6,1,5,4,3]=>01011
[2,6,3,1,4,5]=>01100
[2,6,3,1,5,4]=>01101
[2,6,3,4,1,5]=>01010
[2,6,3,4,5,1]=>01001
[2,6,3,5,1,4]=>01010
[2,6,3,5,4,1]=>01011
[2,6,4,1,3,5]=>01100
[2,6,4,1,5,3]=>01101
[2,6,4,3,1,5]=>01110
[2,6,4,3,5,1]=>01101
[2,6,4,5,1,3]=>01010
[2,6,4,5,3,1]=>01011
[2,6,5,1,3,4]=>01100
[2,6,5,1,4,3]=>01101
[2,6,5,3,1,4]=>01110
[2,6,5,3,4,1]=>01101
[2,6,5,4,1,3]=>01110
[2,6,5,4,3,1]=>01111
[3,1,2,4,5,6]=>10000
[3,1,2,4,6,5]=>10001
[3,1,2,5,4,6]=>10010
[3,1,2,5,6,4]=>10001
[3,1,2,6,4,5]=>10010
[3,1,2,6,5,4]=>10011
[3,1,4,2,5,6]=>10100
[3,1,4,2,6,5]=>10101
[3,1,4,5,2,6]=>10010
[3,1,4,5,6,2]=>10001
[3,1,4,6,2,5]=>10010
[3,1,4,6,5,2]=>10011
[3,1,5,2,4,6]=>10100
[3,1,5,2,6,4]=>10101
[3,1,5,4,2,6]=>10110
[3,1,5,4,6,2]=>10101
[3,1,5,6,2,4]=>10010
[3,1,5,6,4,2]=>10011
[3,1,6,2,4,5]=>10100
[3,1,6,2,5,4]=>10101
[3,1,6,4,2,5]=>10110
[3,1,6,4,5,2]=>10101
[3,1,6,5,2,4]=>10110
[3,1,6,5,4,2]=>10111
[3,2,1,4,5,6]=>11000
[3,2,1,4,6,5]=>11001
[3,2,1,5,4,6]=>11010
[3,2,1,5,6,4]=>11001
[3,2,1,6,4,5]=>11010
[3,2,1,6,5,4]=>11011
[3,2,4,1,5,6]=>10100
[3,2,4,1,6,5]=>10101
[3,2,4,5,1,6]=>10010
[3,2,4,5,6,1]=>10001
[3,2,4,6,1,5]=>10010
[3,2,4,6,5,1]=>10011
[3,2,5,1,4,6]=>10100
[3,2,5,1,6,4]=>10101
[3,2,5,4,1,6]=>10110
[3,2,5,4,6,1]=>10101
[3,2,5,6,1,4]=>10010
[3,2,5,6,4,1]=>10011
[3,2,6,1,4,5]=>10100
[3,2,6,1,5,4]=>10101
[3,2,6,4,1,5]=>10110
[3,2,6,4,5,1]=>10101
[3,2,6,5,1,4]=>10110
[3,2,6,5,4,1]=>10111
[3,4,1,2,5,6]=>01000
[3,4,1,2,6,5]=>01001
[3,4,1,5,2,6]=>01010
[3,4,1,5,6,2]=>01001
[3,4,1,6,2,5]=>01010
[3,4,1,6,5,2]=>01011
[3,4,2,1,5,6]=>01100
[3,4,2,1,6,5]=>01101
[3,4,2,5,1,6]=>01010
[3,4,2,5,6,1]=>01001
[3,4,2,6,1,5]=>01010
[3,4,2,6,5,1]=>01011
[3,4,5,1,2,6]=>00100
[3,4,5,1,6,2]=>00101
[3,4,5,2,1,6]=>00110
[3,4,5,2,6,1]=>00101
[3,4,5,6,1,2]=>00010
[3,4,5,6,2,1]=>00011
[3,4,6,1,2,5]=>00100
[3,4,6,1,5,2]=>00101
[3,4,6,2,1,5]=>00110
[3,4,6,2,5,1]=>00101
[3,4,6,5,1,2]=>00110
[3,4,6,5,2,1]=>00111
[3,5,1,2,4,6]=>01000
[3,5,1,2,6,4]=>01001
[3,5,1,4,2,6]=>01010
[3,5,1,4,6,2]=>01001
[3,5,1,6,2,4]=>01010
[3,5,1,6,4,2]=>01011
[3,5,2,1,4,6]=>01100
[3,5,2,1,6,4]=>01101
[3,5,2,4,1,6]=>01010
[3,5,2,4,6,1]=>01001
[3,5,2,6,1,4]=>01010
[3,5,2,6,4,1]=>01011
[3,5,4,1,2,6]=>01100
[3,5,4,1,6,2]=>01101
[3,5,4,2,1,6]=>01110
[3,5,4,2,6,1]=>01101
[3,5,4,6,1,2]=>01010
[3,5,4,6,2,1]=>01011
[3,5,6,1,2,4]=>00100
[3,5,6,1,4,2]=>00101
[3,5,6,2,1,4]=>00110
[3,5,6,2,4,1]=>00101
[3,5,6,4,1,2]=>00110
[3,5,6,4,2,1]=>00111
[3,6,1,2,4,5]=>01000
[3,6,1,2,5,4]=>01001
[3,6,1,4,2,5]=>01010
[3,6,1,4,5,2]=>01001
[3,6,1,5,2,4]=>01010
[3,6,1,5,4,2]=>01011
[3,6,2,1,4,5]=>01100
[3,6,2,1,5,4]=>01101
[3,6,2,4,1,5]=>01010
[3,6,2,4,5,1]=>01001
[3,6,2,5,1,4]=>01010
[3,6,2,5,4,1]=>01011
[3,6,4,1,2,5]=>01100
[3,6,4,1,5,2]=>01101
[3,6,4,2,1,5]=>01110
[3,6,4,2,5,1]=>01101
[3,6,4,5,1,2]=>01010
[3,6,4,5,2,1]=>01011
[3,6,5,1,2,4]=>01100
[3,6,5,1,4,2]=>01101
[3,6,5,2,1,4]=>01110
[3,6,5,2,4,1]=>01101
[3,6,5,4,1,2]=>01110
[3,6,5,4,2,1]=>01111
[4,1,2,3,5,6]=>10000
[4,1,2,3,6,5]=>10001
[4,1,2,5,3,6]=>10010
[4,1,2,5,6,3]=>10001
[4,1,2,6,3,5]=>10010
[4,1,2,6,5,3]=>10011
[4,1,3,2,5,6]=>10100
[4,1,3,2,6,5]=>10101
[4,1,3,5,2,6]=>10010
[4,1,3,5,6,2]=>10001
[4,1,3,6,2,5]=>10010
[4,1,3,6,5,2]=>10011
[4,1,5,2,3,6]=>10100
[4,1,5,2,6,3]=>10101
[4,1,5,3,2,6]=>10110
[4,1,5,3,6,2]=>10101
[4,1,5,6,2,3]=>10010
[4,1,5,6,3,2]=>10011
[4,1,6,2,3,5]=>10100
[4,1,6,2,5,3]=>10101
[4,1,6,3,2,5]=>10110
[4,1,6,3,5,2]=>10101
[4,1,6,5,2,3]=>10110
[4,1,6,5,3,2]=>10111
[4,2,1,3,5,6]=>11000
[4,2,1,3,6,5]=>11001
[4,2,1,5,3,6]=>11010
[4,2,1,5,6,3]=>11001
[4,2,1,6,3,5]=>11010
[4,2,1,6,5,3]=>11011
[4,2,3,1,5,6]=>10100
[4,2,3,1,6,5]=>10101
[4,2,3,5,1,6]=>10010
[4,2,3,5,6,1]=>10001
[4,2,3,6,1,5]=>10010
[4,2,3,6,5,1]=>10011
[4,2,5,1,3,6]=>10100
[4,2,5,1,6,3]=>10101
[4,2,5,3,1,6]=>10110
[4,2,5,3,6,1]=>10101
[4,2,5,6,1,3]=>10010
[4,2,5,6,3,1]=>10011
[4,2,6,1,3,5]=>10100
[4,2,6,1,5,3]=>10101
[4,2,6,3,1,5]=>10110
[4,2,6,3,5,1]=>10101
[4,2,6,5,1,3]=>10110
[4,2,6,5,3,1]=>10111
[4,3,1,2,5,6]=>11000
[4,3,1,2,6,5]=>11001
[4,3,1,5,2,6]=>11010
[4,3,1,5,6,2]=>11001
[4,3,1,6,2,5]=>11010
[4,3,1,6,5,2]=>11011
[4,3,2,1,5,6]=>11100
[4,3,2,1,6,5]=>11101
[4,3,2,5,1,6]=>11010
[4,3,2,5,6,1]=>11001
[4,3,2,6,1,5]=>11010
[4,3,2,6,5,1]=>11011
[4,3,5,1,2,6]=>10100
[4,3,5,1,6,2]=>10101
[4,3,5,2,1,6]=>10110
[4,3,5,2,6,1]=>10101
[4,3,5,6,1,2]=>10010
[4,3,5,6,2,1]=>10011
[4,3,6,1,2,5]=>10100
[4,3,6,1,5,2]=>10101
[4,3,6,2,1,5]=>10110
[4,3,6,2,5,1]=>10101
[4,3,6,5,1,2]=>10110
[4,3,6,5,2,1]=>10111
[4,5,1,2,3,6]=>01000
[4,5,1,2,6,3]=>01001
[4,5,1,3,2,6]=>01010
[4,5,1,3,6,2]=>01001
[4,5,1,6,2,3]=>01010
[4,5,1,6,3,2]=>01011
[4,5,2,1,3,6]=>01100
[4,5,2,1,6,3]=>01101
[4,5,2,3,1,6]=>01010
[4,5,2,3,6,1]=>01001
[4,5,2,6,1,3]=>01010
[4,5,2,6,3,1]=>01011
[4,5,3,1,2,6]=>01100
[4,5,3,1,6,2]=>01101
[4,5,3,2,1,6]=>01110
[4,5,3,2,6,1]=>01101
[4,5,3,6,1,2]=>01010
[4,5,3,6,2,1]=>01011
[4,5,6,1,2,3]=>00100
[4,5,6,1,3,2]=>00101
[4,5,6,2,1,3]=>00110
[4,5,6,2,3,1]=>00101
[4,5,6,3,1,2]=>00110
[4,5,6,3,2,1]=>00111
[4,6,1,2,3,5]=>01000
[4,6,1,2,5,3]=>01001
[4,6,1,3,2,5]=>01010
[4,6,1,3,5,2]=>01001
[4,6,1,5,2,3]=>01010
[4,6,1,5,3,2]=>01011
[4,6,2,1,3,5]=>01100
[4,6,2,1,5,3]=>01101
[4,6,2,3,1,5]=>01010
[4,6,2,3,5,1]=>01001
[4,6,2,5,1,3]=>01010
[4,6,2,5,3,1]=>01011
[4,6,3,1,2,5]=>01100
[4,6,3,1,5,2]=>01101
[4,6,3,2,1,5]=>01110
[4,6,3,2,5,1]=>01101
[4,6,3,5,1,2]=>01010
[4,6,3,5,2,1]=>01011
[4,6,5,1,2,3]=>01100
[4,6,5,1,3,2]=>01101
[4,6,5,2,1,3]=>01110
[4,6,5,2,3,1]=>01101
[4,6,5,3,1,2]=>01110
[4,6,5,3,2,1]=>01111
[5,1,2,3,4,6]=>10000
[5,1,2,3,6,4]=>10001
[5,1,2,4,3,6]=>10010
[5,1,2,4,6,3]=>10001
[5,1,2,6,3,4]=>10010
[5,1,2,6,4,3]=>10011
[5,1,3,2,4,6]=>10100
[5,1,3,2,6,4]=>10101
[5,1,3,4,2,6]=>10010
[5,1,3,4,6,2]=>10001
[5,1,3,6,2,4]=>10010
[5,1,3,6,4,2]=>10011
[5,1,4,2,3,6]=>10100
[5,1,4,2,6,3]=>10101
[5,1,4,3,2,6]=>10110
[5,1,4,3,6,2]=>10101
[5,1,4,6,2,3]=>10010
[5,1,4,6,3,2]=>10011
[5,1,6,2,3,4]=>10100
[5,1,6,2,4,3]=>10101
[5,1,6,3,2,4]=>10110
[5,1,6,3,4,2]=>10101
[5,1,6,4,2,3]=>10110
[5,1,6,4,3,2]=>10111
[5,2,1,3,4,6]=>11000
[5,2,1,3,6,4]=>11001
[5,2,1,4,3,6]=>11010
[5,2,1,4,6,3]=>11001
[5,2,1,6,3,4]=>11010
[5,2,1,6,4,3]=>11011
[5,2,3,1,4,6]=>10100
[5,2,3,1,6,4]=>10101
[5,2,3,4,1,6]=>10010
[5,2,3,4,6,1]=>10001
[5,2,3,6,1,4]=>10010
[5,2,3,6,4,1]=>10011
[5,2,4,1,3,6]=>10100
[5,2,4,1,6,3]=>10101
[5,2,4,3,1,6]=>10110
[5,2,4,3,6,1]=>10101
[5,2,4,6,1,3]=>10010
[5,2,4,6,3,1]=>10011
[5,2,6,1,3,4]=>10100
[5,2,6,1,4,3]=>10101
[5,2,6,3,1,4]=>10110
[5,2,6,3,4,1]=>10101
[5,2,6,4,1,3]=>10110
[5,2,6,4,3,1]=>10111
[5,3,1,2,4,6]=>11000
[5,3,1,2,6,4]=>11001
[5,3,1,4,2,6]=>11010
[5,3,1,4,6,2]=>11001
[5,3,1,6,2,4]=>11010
[5,3,1,6,4,2]=>11011
[5,3,2,1,4,6]=>11100
[5,3,2,1,6,4]=>11101
[5,3,2,4,1,6]=>11010
[5,3,2,4,6,1]=>11001
[5,3,2,6,1,4]=>11010
[5,3,2,6,4,1]=>11011
[5,3,4,1,2,6]=>10100
[5,3,4,1,6,2]=>10101
[5,3,4,2,1,6]=>10110
[5,3,4,2,6,1]=>10101
[5,3,4,6,1,2]=>10010
[5,3,4,6,2,1]=>10011
[5,3,6,1,2,4]=>10100
[5,3,6,1,4,2]=>10101
[5,3,6,2,1,4]=>10110
[5,3,6,2,4,1]=>10101
[5,3,6,4,1,2]=>10110
[5,3,6,4,2,1]=>10111
[5,4,1,2,3,6]=>11000
[5,4,1,2,6,3]=>11001
[5,4,1,3,2,6]=>11010
[5,4,1,3,6,2]=>11001
[5,4,1,6,2,3]=>11010
[5,4,1,6,3,2]=>11011
[5,4,2,1,3,6]=>11100
[5,4,2,1,6,3]=>11101
[5,4,2,3,1,6]=>11010
[5,4,2,3,6,1]=>11001
[5,4,2,6,1,3]=>11010
[5,4,2,6,3,1]=>11011
[5,4,3,1,2,6]=>11100
[5,4,3,1,6,2]=>11101
[5,4,3,2,1,6]=>11110
[5,4,3,2,6,1]=>11101
[5,4,3,6,1,2]=>11010
[5,4,3,6,2,1]=>11011
[5,4,6,1,2,3]=>10100
[5,4,6,1,3,2]=>10101
[5,4,6,2,1,3]=>10110
[5,4,6,2,3,1]=>10101
[5,4,6,3,1,2]=>10110
[5,4,6,3,2,1]=>10111
[5,6,1,2,3,4]=>01000
[5,6,1,2,4,3]=>01001
[5,6,1,3,2,4]=>01010
[5,6,1,3,4,2]=>01001
[5,6,1,4,2,3]=>01010
[5,6,1,4,3,2]=>01011
[5,6,2,1,3,4]=>01100
[5,6,2,1,4,3]=>01101
[5,6,2,3,1,4]=>01010
[5,6,2,3,4,1]=>01001
[5,6,2,4,1,3]=>01010
[5,6,2,4,3,1]=>01011
[5,6,3,1,2,4]=>01100
[5,6,3,1,4,2]=>01101
[5,6,3,2,1,4]=>01110
[5,6,3,2,4,1]=>01101
[5,6,3,4,1,2]=>01010
[5,6,3,4,2,1]=>01011
[5,6,4,1,2,3]=>01100
[5,6,4,1,3,2]=>01101
[5,6,4,2,1,3]=>01110
[5,6,4,2,3,1]=>01101
[5,6,4,3,1,2]=>01110
[5,6,4,3,2,1]=>01111
[6,1,2,3,4,5]=>10000
[6,1,2,3,5,4]=>10001
[6,1,2,4,3,5]=>10010
[6,1,2,4,5,3]=>10001
[6,1,2,5,3,4]=>10010
[6,1,2,5,4,3]=>10011
[6,1,3,2,4,5]=>10100
[6,1,3,2,5,4]=>10101
[6,1,3,4,2,5]=>10010
[6,1,3,4,5,2]=>10001
[6,1,3,5,2,4]=>10010
[6,1,3,5,4,2]=>10011
[6,1,4,2,3,5]=>10100
[6,1,4,2,5,3]=>10101
[6,1,4,3,2,5]=>10110
[6,1,4,3,5,2]=>10101
[6,1,4,5,2,3]=>10010
[6,1,4,5,3,2]=>10011
[6,1,5,2,3,4]=>10100
[6,1,5,2,4,3]=>10101
[6,1,5,3,2,4]=>10110
[6,1,5,3,4,2]=>10101
[6,1,5,4,2,3]=>10110
[6,1,5,4,3,2]=>10111
[6,2,1,3,4,5]=>11000
[6,2,1,3,5,4]=>11001
[6,2,1,4,3,5]=>11010
[6,2,1,4,5,3]=>11001
[6,2,1,5,3,4]=>11010
[6,2,1,5,4,3]=>11011
[6,2,3,1,4,5]=>10100
[6,2,3,1,5,4]=>10101
[6,2,3,4,1,5]=>10010
[6,2,3,4,5,1]=>10001
[6,2,3,5,1,4]=>10010
[6,2,3,5,4,1]=>10011
[6,2,4,1,3,5]=>10100
[6,2,4,1,5,3]=>10101
[6,2,4,3,1,5]=>10110
[6,2,4,3,5,1]=>10101
[6,2,4,5,1,3]=>10010
[6,2,4,5,3,1]=>10011
[6,2,5,1,3,4]=>10100
[6,2,5,1,4,3]=>10101
[6,2,5,3,1,4]=>10110
[6,2,5,3,4,1]=>10101
[6,2,5,4,1,3]=>10110
[6,2,5,4,3,1]=>10111
[6,3,1,2,4,5]=>11000
[6,3,1,2,5,4]=>11001
[6,3,1,4,2,5]=>11010
[6,3,1,4,5,2]=>11001
[6,3,1,5,2,4]=>11010
[6,3,1,5,4,2]=>11011
[6,3,2,1,4,5]=>11100
[6,3,2,1,5,4]=>11101
[6,3,2,4,1,5]=>11010
[6,3,2,4,5,1]=>11001
[6,3,2,5,1,4]=>11010
[6,3,2,5,4,1]=>11011
[6,3,4,1,2,5]=>10100
[6,3,4,1,5,2]=>10101
[6,3,4,2,1,5]=>10110
[6,3,4,2,5,1]=>10101
[6,3,4,5,1,2]=>10010
[6,3,4,5,2,1]=>10011
[6,3,5,1,2,4]=>10100
[6,3,5,1,4,2]=>10101
[6,3,5,2,1,4]=>10110
[6,3,5,2,4,1]=>10101
[6,3,5,4,1,2]=>10110
[6,3,5,4,2,1]=>10111
[6,4,1,2,3,5]=>11000
[6,4,1,2,5,3]=>11001
[6,4,1,3,2,5]=>11010
[6,4,1,3,5,2]=>11001
[6,4,1,5,2,3]=>11010
[6,4,1,5,3,2]=>11011
[6,4,2,1,3,5]=>11100
[6,4,2,1,5,3]=>11101
[6,4,2,3,1,5]=>11010
[6,4,2,3,5,1]=>11001
[6,4,2,5,1,3]=>11010
[6,4,2,5,3,1]=>11011
[6,4,3,1,2,5]=>11100
[6,4,3,1,5,2]=>11101
[6,4,3,2,1,5]=>11110
[6,4,3,2,5,1]=>11101
[6,4,3,5,1,2]=>11010
[6,4,3,5,2,1]=>11011
[6,4,5,1,2,3]=>10100
[6,4,5,1,3,2]=>10101
[6,4,5,2,1,3]=>10110
[6,4,5,2,3,1]=>10101
[6,4,5,3,1,2]=>10110
[6,4,5,3,2,1]=>10111
[6,5,1,2,3,4]=>11000
[6,5,1,2,4,3]=>11001
[6,5,1,3,2,4]=>11010
[6,5,1,3,4,2]=>11001
[6,5,1,4,2,3]=>11010
[6,5,1,4,3,2]=>11011
[6,5,2,1,3,4]=>11100
[6,5,2,1,4,3]=>11101
[6,5,2,3,1,4]=>11010
[6,5,2,3,4,1]=>11001
[6,5,2,4,1,3]=>11010
[6,5,2,4,3,1]=>11011
[6,5,3,1,2,4]=>11100
[6,5,3,1,4,2]=>11101
[6,5,3,2,1,4]=>11110
[6,5,3,2,4,1]=>11101
[6,5,3,4,1,2]=>11010
[6,5,3,4,2,1]=>11011
[6,5,4,1,2,3]=>11100
[6,5,4,1,3,2]=>11101
[6,5,4,2,1,3]=>11110
[6,5,4,2,3,1]=>11101
[6,5,4,3,1,2]=>11110
[6,5,4,3,2,1]=>11111
[1,2,3,4,5,6,7]=>000000
[1,2,3,4,5,7,6]=>000001
[1,2,3,4,6,5,7]=>000010
[1,2,3,4,6,7,5]=>000001
[1,2,3,4,7,5,6]=>000010
[1,2,3,4,7,6,5]=>000011
[1,2,3,5,4,6,7]=>000100
[1,2,3,5,4,7,6]=>000101
[1,2,3,5,6,4,7]=>000010
[1,2,3,5,6,7,4]=>000001
[1,2,3,5,7,4,6]=>000010
[1,2,3,5,7,6,4]=>000011
[1,2,3,6,4,5,7]=>000100
[1,2,3,6,4,7,5]=>000101
[1,2,3,6,5,4,7]=>000110
[1,2,3,6,5,7,4]=>000101
[1,2,3,6,7,4,5]=>000010
[1,2,3,6,7,5,4]=>000011
[1,2,3,7,4,5,6]=>000100
[1,2,3,7,4,6,5]=>000101
[1,2,3,7,5,4,6]=>000110
[1,2,3,7,5,6,4]=>000101
[1,2,3,7,6,4,5]=>000110
[1,2,3,7,6,5,4]=>000111
[1,2,4,3,5,6,7]=>001000
[1,2,4,3,5,7,6]=>001001
[1,2,4,3,6,5,7]=>001010
[1,2,4,3,6,7,5]=>001001
[1,2,4,3,7,5,6]=>001010
[1,2,4,3,7,6,5]=>001011
[1,2,4,5,3,6,7]=>000100
[1,2,4,5,3,7,6]=>000101
[1,2,4,5,6,3,7]=>000010
[1,2,4,5,6,7,3]=>000001
[1,2,4,5,7,3,6]=>000010
[1,2,4,5,7,6,3]=>000011
[1,2,4,6,3,5,7]=>000100
[1,2,4,6,3,7,5]=>000101
[1,2,4,6,5,3,7]=>000110
[1,2,4,6,5,7,3]=>000101
[1,2,4,6,7,3,5]=>000010
[1,2,4,6,7,5,3]=>000011
[1,2,4,7,3,5,6]=>000100
[1,2,4,7,3,6,5]=>000101
[1,2,4,7,5,3,6]=>000110
[1,2,4,7,5,6,3]=>000101
[1,2,4,7,6,3,5]=>000110
[1,2,4,7,6,5,3]=>000111
[1,2,5,3,4,6,7]=>001000
[1,2,5,3,4,7,6]=>001001
[1,2,5,3,6,4,7]=>001010
[1,2,5,3,6,7,4]=>001001
[1,2,5,3,7,4,6]=>001010
[1,2,5,3,7,6,4]=>001011
[1,2,5,4,3,6,7]=>001100
[1,2,5,4,3,7,6]=>001101
[1,2,5,4,6,3,7]=>001010
[1,2,5,4,6,7,3]=>001001
[1,2,5,4,7,3,6]=>001010
[1,2,5,4,7,6,3]=>001011
[1,2,5,6,3,4,7]=>000100
[1,2,5,6,3,7,4]=>000101
[1,2,5,6,4,3,7]=>000110
[1,2,5,6,4,7,3]=>000101
[1,2,5,6,7,3,4]=>000010
[1,2,5,6,7,4,3]=>000011
[1,2,5,7,3,4,6]=>000100
[1,2,5,7,3,6,4]=>000101
[1,2,5,7,4,3,6]=>000110
[1,2,5,7,4,6,3]=>000101
[1,2,5,7,6,3,4]=>000110
[1,2,5,7,6,4,3]=>000111
[1,2,6,3,4,5,7]=>001000
[1,2,6,3,4,7,5]=>001001
[1,2,6,3,5,4,7]=>001010
[1,2,6,3,5,7,4]=>001001
[1,2,6,3,7,4,5]=>001010
[1,2,6,3,7,5,4]=>001011
[1,2,6,4,3,5,7]=>001100
[1,2,6,4,3,7,5]=>001101
[1,2,6,4,5,3,7]=>001010
[1,2,6,4,5,7,3]=>001001
[1,2,6,4,7,3,5]=>001010
[1,2,6,4,7,5,3]=>001011
[1,2,6,5,3,4,7]=>001100
[1,2,6,5,3,7,4]=>001101
[1,2,6,5,4,3,7]=>001110
[1,2,6,5,4,7,3]=>001101
[1,2,6,5,7,3,4]=>001010
[1,2,6,5,7,4,3]=>001011
[1,2,6,7,3,4,5]=>000100
[1,2,6,7,3,5,4]=>000101
[1,2,6,7,4,3,5]=>000110
[1,2,6,7,4,5,3]=>000101
[1,2,6,7,5,3,4]=>000110
[1,2,6,7,5,4,3]=>000111
[1,2,7,3,4,5,6]=>001000
[1,2,7,3,4,6,5]=>001001
[1,2,7,3,5,4,6]=>001010
[1,2,7,3,5,6,4]=>001001
[1,2,7,3,6,4,5]=>001010
[1,2,7,3,6,5,4]=>001011
[1,2,7,4,3,5,6]=>001100
[1,2,7,4,3,6,5]=>001101
[1,2,7,4,5,3,6]=>001010
[1,2,7,4,5,6,3]=>001001
[1,2,7,4,6,3,5]=>001010
[1,2,7,4,6,5,3]=>001011
[1,2,7,5,3,4,6]=>001100
[1,2,7,5,3,6,4]=>001101
[1,2,7,5,4,3,6]=>001110
[1,2,7,5,4,6,3]=>001101
[1,2,7,5,6,3,4]=>001010
[1,2,7,5,6,4,3]=>001011
[1,2,7,6,3,4,5]=>001100
[1,2,7,6,3,5,4]=>001101
[1,2,7,6,4,3,5]=>001110
[1,2,7,6,4,5,3]=>001101
[1,2,7,6,5,3,4]=>001110
[1,2,7,6,5,4,3]=>001111
[1,3,2,4,5,6,7]=>010000
[1,3,2,4,5,7,6]=>010001
[1,3,2,4,6,5,7]=>010010
[1,3,2,4,6,7,5]=>010001
[1,3,2,4,7,5,6]=>010010
[1,3,2,4,7,6,5]=>010011
[1,3,2,5,4,6,7]=>010100
[1,3,2,5,4,7,6]=>010101
[1,3,2,5,6,4,7]=>010010
[1,3,2,5,6,7,4]=>010001
[1,3,2,5,7,4,6]=>010010
[1,3,2,5,7,6,4]=>010011
[1,3,2,6,4,5,7]=>010100
[1,3,2,6,4,7,5]=>010101
[1,3,2,6,5,4,7]=>010110
[1,3,2,6,5,7,4]=>010101
[1,3,2,6,7,4,5]=>010010
[1,3,2,6,7,5,4]=>010011
[1,3,2,7,4,5,6]=>010100
[1,3,2,7,4,6,5]=>010101
[1,3,2,7,5,4,6]=>010110
[1,3,2,7,5,6,4]=>010101
[1,3,2,7,6,4,5]=>010110
[1,3,2,7,6,5,4]=>010111
[1,3,4,2,5,6,7]=>001000
[1,3,4,2,5,7,6]=>001001
[1,3,4,2,6,5,7]=>001010
[1,3,4,2,6,7,5]=>001001
[1,3,4,2,7,5,6]=>001010
[1,3,4,2,7,6,5]=>001011
[1,3,4,5,2,6,7]=>000100
[1,3,4,5,2,7,6]=>000101
[1,3,4,5,6,2,7]=>000010
[1,3,4,5,6,7,2]=>000001
[1,3,4,5,7,2,6]=>000010
[1,3,4,5,7,6,2]=>000011
[1,3,4,6,2,5,7]=>000100
[1,3,4,6,2,7,5]=>000101
[1,3,4,6,5,2,7]=>000110
[1,3,4,6,5,7,2]=>000101
[1,3,4,6,7,2,5]=>000010
[1,3,4,6,7,5,2]=>000011
[1,3,4,7,2,5,6]=>000100
[1,3,4,7,2,6,5]=>000101
[1,3,4,7,5,2,6]=>000110
[1,3,4,7,5,6,2]=>000101
[1,3,4,7,6,2,5]=>000110
[1,3,4,7,6,5,2]=>000111
[1,3,5,2,4,6,7]=>001000
[1,3,5,2,4,7,6]=>001001
[1,3,5,2,6,4,7]=>001010
[1,3,5,2,6,7,4]=>001001
[1,3,5,2,7,4,6]=>001010
[1,3,5,2,7,6,4]=>001011
[1,3,5,4,2,6,7]=>001100
[1,3,5,4,2,7,6]=>001101
[1,3,5,4,6,2,7]=>001010
[1,3,5,4,6,7,2]=>001001
[1,3,5,4,7,2,6]=>001010
[1,3,5,4,7,6,2]=>001011
[1,3,5,6,2,4,7]=>000100
[1,3,5,6,2,7,4]=>000101
[1,3,5,6,4,2,7]=>000110
[1,3,5,6,4,7,2]=>000101
[1,3,5,6,7,2,4]=>000010
[1,3,5,6,7,4,2]=>000011
[1,3,5,7,2,4,6]=>000100
[1,3,5,7,2,6,4]=>000101
[1,3,5,7,4,2,6]=>000110
[1,3,5,7,4,6,2]=>000101
[1,3,5,7,6,2,4]=>000110
[1,3,5,7,6,4,2]=>000111
[1,3,6,2,4,5,7]=>001000
[1,3,6,2,4,7,5]=>001001
[1,3,6,2,5,4,7]=>001010
[1,3,6,2,5,7,4]=>001001
[1,3,6,2,7,4,5]=>001010
[1,3,6,2,7,5,4]=>001011
[1,3,6,4,2,5,7]=>001100
[1,3,6,4,2,7,5]=>001101
[1,3,6,4,5,2,7]=>001010
[1,3,6,4,5,7,2]=>001001
[1,3,6,4,7,2,5]=>001010
[1,3,6,4,7,5,2]=>001011
[1,3,6,5,2,4,7]=>001100
[1,3,6,5,2,7,4]=>001101
[1,3,6,5,4,2,7]=>001110
[1,3,6,5,4,7,2]=>001101
[1,3,6,5,7,2,4]=>001010
[1,3,6,5,7,4,2]=>001011
[1,3,6,7,2,4,5]=>000100
[1,3,6,7,2,5,4]=>000101
[1,3,6,7,4,2,5]=>000110
[1,3,6,7,4,5,2]=>000101
[1,3,6,7,5,2,4]=>000110
[1,3,6,7,5,4,2]=>000111
[1,3,7,2,4,5,6]=>001000
[1,3,7,2,4,6,5]=>001001
[1,3,7,2,5,4,6]=>001010
[1,3,7,2,5,6,4]=>001001
[1,3,7,2,6,4,5]=>001010
[1,3,7,2,6,5,4]=>001011
[1,3,7,4,2,5,6]=>001100
[1,3,7,4,2,6,5]=>001101
[1,3,7,4,5,2,6]=>001010
[1,3,7,4,5,6,2]=>001001
[1,3,7,4,6,2,5]=>001010
[1,3,7,4,6,5,2]=>001011
[1,3,7,5,2,4,6]=>001100
[1,3,7,5,2,6,4]=>001101
[1,3,7,5,4,2,6]=>001110
[1,3,7,5,4,6,2]=>001101
[1,3,7,5,6,2,4]=>001010
[1,3,7,5,6,4,2]=>001011
[1,3,7,6,2,4,5]=>001100
[1,3,7,6,2,5,4]=>001101
[1,3,7,6,4,2,5]=>001110
[1,3,7,6,4,5,2]=>001101
[1,3,7,6,5,2,4]=>001110
[1,3,7,6,5,4,2]=>001111
[1,4,2,3,5,6,7]=>010000
[1,4,2,3,5,7,6]=>010001
[1,4,2,3,6,5,7]=>010010
[1,4,2,3,6,7,5]=>010001
[1,4,2,3,7,5,6]=>010010
[1,4,2,3,7,6,5]=>010011
[1,4,2,5,3,6,7]=>010100
[1,4,2,5,3,7,6]=>010101
[1,4,2,5,6,3,7]=>010010
[1,4,2,5,6,7,3]=>010001
[1,4,2,5,7,3,6]=>010010
[1,4,2,5,7,6,3]=>010011
[1,4,2,6,3,5,7]=>010100
[1,4,2,6,3,7,5]=>010101
[1,4,2,6,5,3,7]=>010110
[1,4,2,6,5,7,3]=>010101
[1,4,2,6,7,3,5]=>010010
[1,4,2,6,7,5,3]=>010011
[1,4,2,7,3,5,6]=>010100
[1,4,2,7,3,6,5]=>010101
[1,4,2,7,5,3,6]=>010110
[1,4,2,7,5,6,3]=>010101
[1,4,2,7,6,3,5]=>010110
[1,4,2,7,6,5,3]=>010111
[1,4,3,2,5,6,7]=>011000
[1,4,3,2,5,7,6]=>011001
[1,4,3,2,6,5,7]=>011010
[1,4,3,2,6,7,5]=>011001
[1,4,3,2,7,5,6]=>011010
[1,4,3,2,7,6,5]=>011011
[1,4,3,5,2,6,7]=>010100
[1,4,3,5,2,7,6]=>010101
[1,4,3,5,6,2,7]=>010010
[1,4,3,5,6,7,2]=>010001
[1,4,3,5,7,2,6]=>010010
[1,4,3,5,7,6,2]=>010011
[1,4,3,6,2,5,7]=>010100
[1,4,3,6,2,7,5]=>010101
[1,4,3,6,5,2,7]=>010110
[1,4,3,6,5,7,2]=>010101
[1,4,3,6,7,2,5]=>010010
[1,4,3,6,7,5,2]=>010011
[1,4,3,7,2,5,6]=>010100
[1,4,3,7,2,6,5]=>010101
[1,4,3,7,5,2,6]=>010110
[1,4,3,7,5,6,2]=>010101
[1,4,3,7,6,2,5]=>010110
[1,4,3,7,6,5,2]=>010111
[1,4,5,2,3,6,7]=>001000
[1,4,5,2,3,7,6]=>001001
[1,4,5,2,6,3,7]=>001010
[1,4,5,2,6,7,3]=>001001
[1,4,5,2,7,3,6]=>001010
[1,4,5,2,7,6,3]=>001011
[1,4,5,3,2,6,7]=>001100
[1,4,5,3,2,7,6]=>001101
[1,4,5,3,6,2,7]=>001010
[1,4,5,3,6,7,2]=>001001
[1,4,5,3,7,2,6]=>001010
[1,4,5,3,7,6,2]=>001011
[1,4,5,6,2,3,7]=>000100
[1,4,5,6,2,7,3]=>000101
[1,4,5,6,3,2,7]=>000110
[1,4,5,6,3,7,2]=>000101
[1,4,5,6,7,2,3]=>000010
[1,4,5,6,7,3,2]=>000011
[1,4,5,7,2,3,6]=>000100
[1,4,5,7,2,6,3]=>000101
[1,4,5,7,3,2,6]=>000110
[1,4,5,7,3,6,2]=>000101
[1,4,5,7,6,2,3]=>000110
[1,4,5,7,6,3,2]=>000111
[1,4,6,2,3,5,7]=>001000
[1,4,6,2,3,7,5]=>001001
[1,4,6,2,5,3,7]=>001010
[1,4,6,2,5,7,3]=>001001
[1,4,6,2,7,3,5]=>001010
[1,4,6,2,7,5,3]=>001011
[1,4,6,3,2,5,7]=>001100
[1,4,6,3,2,7,5]=>001101
[1,4,6,3,5,2,7]=>001010
[1,4,6,3,5,7,2]=>001001
[1,4,6,3,7,2,5]=>001010
[1,4,6,3,7,5,2]=>001011
[1,4,6,5,2,3,7]=>001100
[1,4,6,5,2,7,3]=>001101
[1,4,6,5,3,2,7]=>001110
[1,4,6,5,3,7,2]=>001101
[1,4,6,5,7,2,3]=>001010
[1,4,6,5,7,3,2]=>001011
[1,4,6,7,2,3,5]=>000100
[1,4,6,7,2,5,3]=>000101
[1,4,6,7,3,2,5]=>000110
[1,4,6,7,3,5,2]=>000101
[1,4,6,7,5,2,3]=>000110
[1,4,6,7,5,3,2]=>000111
[1,4,7,2,3,5,6]=>001000
[1,4,7,2,3,6,5]=>001001
[1,4,7,2,5,3,6]=>001010
[1,4,7,2,5,6,3]=>001001
[1,4,7,2,6,3,5]=>001010
[1,4,7,2,6,5,3]=>001011
[1,4,7,3,2,5,6]=>001100
[1,4,7,3,2,6,5]=>001101
[1,4,7,3,5,2,6]=>001010
[1,4,7,3,5,6,2]=>001001
[1,4,7,3,6,2,5]=>001010
[1,4,7,3,6,5,2]=>001011
[1,4,7,5,2,3,6]=>001100
[1,4,7,5,2,6,3]=>001101
[1,4,7,5,3,2,6]=>001110
[1,4,7,5,3,6,2]=>001101
[1,4,7,5,6,2,3]=>001010
[1,4,7,5,6,3,2]=>001011
[1,4,7,6,2,3,5]=>001100
[1,4,7,6,2,5,3]=>001101
[1,4,7,6,3,2,5]=>001110
[1,4,7,6,3,5,2]=>001101
[1,4,7,6,5,2,3]=>001110
[1,4,7,6,5,3,2]=>001111
[1,5,2,3,4,6,7]=>010000
[1,5,2,3,4,7,6]=>010001
[1,5,2,3,6,4,7]=>010010
[1,5,2,3,6,7,4]=>010001
[1,5,2,3,7,4,6]=>010010
[1,5,2,3,7,6,4]=>010011
[1,5,2,4,3,6,7]=>010100
[1,5,2,4,3,7,6]=>010101
[1,5,2,4,6,3,7]=>010010
[1,5,2,4,6,7,3]=>010001
[1,5,2,4,7,3,6]=>010010
[1,5,2,4,7,6,3]=>010011
[1,5,2,6,3,4,7]=>010100
[1,5,2,6,3,7,4]=>010101
[1,5,2,6,4,3,7]=>010110
[1,5,2,6,4,7,3]=>010101
[1,5,2,6,7,3,4]=>010010
[1,5,2,6,7,4,3]=>010011
[1,5,2,7,3,4,6]=>010100
[1,5,2,7,3,6,4]=>010101
[1,5,2,7,4,3,6]=>010110
[1,5,2,7,4,6,3]=>010101
[1,5,2,7,6,3,4]=>010110
[1,5,2,7,6,4,3]=>010111
[1,5,3,2,4,6,7]=>011000
[1,5,3,2,4,7,6]=>011001
[1,5,3,2,6,4,7]=>011010
[1,5,3,2,6,7,4]=>011001
[1,5,3,2,7,4,6]=>011010
[1,5,3,2,7,6,4]=>011011
[1,5,3,4,2,6,7]=>010100
[1,5,3,4,2,7,6]=>010101
[1,5,3,4,6,2,7]=>010010
[1,5,3,4,6,7,2]=>010001
[1,5,3,4,7,2,6]=>010010
[1,5,3,4,7,6,2]=>010011
[1,5,3,6,2,4,7]=>010100
[1,5,3,6,2,7,4]=>010101
[1,5,3,6,4,2,7]=>010110
[1,5,3,6,4,7,2]=>010101
[1,5,3,6,7,2,4]=>010010
[1,5,3,6,7,4,2]=>010011
[1,5,3,7,2,4,6]=>010100
[1,5,3,7,2,6,4]=>010101
[1,5,3,7,4,2,6]=>010110
[1,5,3,7,4,6,2]=>010101
[1,5,3,7,6,2,4]=>010110
[1,5,3,7,6,4,2]=>010111
[1,5,4,2,3,6,7]=>011000
[1,5,4,2,3,7,6]=>011001
[1,5,4,2,6,3,7]=>011010
[1,5,4,2,6,7,3]=>011001
[1,5,4,2,7,3,6]=>011010
[1,5,4,2,7,6,3]=>011011
[1,5,4,3,2,6,7]=>011100
[1,5,4,3,2,7,6]=>011101
[1,5,4,3,6,2,7]=>011010
[1,5,4,3,6,7,2]=>011001
[1,5,4,3,7,2,6]=>011010
[1,5,4,3,7,6,2]=>011011
[1,5,4,6,2,3,7]=>010100
[1,5,4,6,2,7,3]=>010101
[1,5,4,6,3,2,7]=>010110
[1,5,4,6,3,7,2]=>010101
[1,5,4,6,7,2,3]=>010010
[1,5,4,6,7,3,2]=>010011
[1,5,4,7,2,3,6]=>010100
[1,5,4,7,2,6,3]=>010101
[1,5,4,7,3,2,6]=>010110
[1,5,4,7,3,6,2]=>010101
[1,5,4,7,6,2,3]=>010110
[1,5,4,7,6,3,2]=>010111
[1,5,6,2,3,4,7]=>001000
[1,5,6,2,3,7,4]=>001001
[1,5,6,2,4,3,7]=>001010
[1,5,6,2,4,7,3]=>001001
[1,5,6,2,7,3,4]=>001010
[1,5,6,2,7,4,3]=>001011
[1,5,6,3,2,4,7]=>001100
[1,5,6,3,2,7,4]=>001101
[1,5,6,3,4,2,7]=>001010
[1,5,6,3,4,7,2]=>001001
[1,5,6,3,7,2,4]=>001010
[1,5,6,3,7,4,2]=>001011
[1,5,6,4,2,3,7]=>001100
[1,5,6,4,2,7,3]=>001101
[1,5,6,4,3,2,7]=>001110
[1,5,6,4,3,7,2]=>001101
[1,5,6,4,7,2,3]=>001010
[1,5,6,4,7,3,2]=>001011
[1,5,6,7,2,3,4]=>000100
[1,5,6,7,2,4,3]=>000101
[1,5,6,7,3,2,4]=>000110
[1,5,6,7,3,4,2]=>000101
[1,5,6,7,4,2,3]=>000110
[1,5,6,7,4,3,2]=>000111
[1,5,7,2,3,4,6]=>001000
[1,5,7,2,3,6,4]=>001001
[1,5,7,2,4,3,6]=>001010
[1,5,7,2,4,6,3]=>001001
[1,5,7,2,6,3,4]=>001010
[1,5,7,2,6,4,3]=>001011
[1,5,7,3,2,4,6]=>001100
[1,5,7,3,2,6,4]=>001101
[1,5,7,3,4,2,6]=>001010
[1,5,7,3,4,6,2]=>001001
[1,5,7,3,6,2,4]=>001010
[1,5,7,3,6,4,2]=>001011
[1,5,7,4,2,3,6]=>001100
[1,5,7,4,2,6,3]=>001101
[1,5,7,4,3,2,6]=>001110
[1,5,7,4,3,6,2]=>001101
[1,5,7,4,6,2,3]=>001010
[1,5,7,4,6,3,2]=>001011
[1,5,7,6,2,3,4]=>001100
[1,5,7,6,2,4,3]=>001101
[1,5,7,6,3,2,4]=>001110
[1,5,7,6,3,4,2]=>001101
[1,5,7,6,4,2,3]=>001110
[1,5,7,6,4,3,2]=>001111
[1,6,2,3,4,5,7]=>010000
[1,6,2,3,4,7,5]=>010001
[1,6,2,3,5,4,7]=>010010
[1,6,2,3,5,7,4]=>010001
[1,6,2,3,7,4,5]=>010010
[1,6,2,3,7,5,4]=>010011
[1,6,2,4,3,5,7]=>010100
[1,6,2,4,3,7,5]=>010101
[1,6,2,4,5,3,7]=>010010
[1,6,2,4,5,7,3]=>010001
[1,6,2,4,7,3,5]=>010010
[1,6,2,4,7,5,3]=>010011
[1,6,2,5,3,4,7]=>010100
[1,6,2,5,3,7,4]=>010101
[1,6,2,5,4,3,7]=>010110
[1,6,2,5,4,7,3]=>010101
[1,6,2,5,7,3,4]=>010010
[1,6,2,5,7,4,3]=>010011
[1,6,2,7,3,4,5]=>010100
[1,6,2,7,3,5,4]=>010101
[1,6,2,7,4,3,5]=>010110
[1,6,2,7,4,5,3]=>010101
[1,6,2,7,5,3,4]=>010110
[1,6,2,7,5,4,3]=>010111
[1,6,3,2,4,5,7]=>011000
[1,6,3,2,4,7,5]=>011001
[1,6,3,2,5,4,7]=>011010
[1,6,3,2,5,7,4]=>011001
[1,6,3,2,7,4,5]=>011010
[1,6,3,2,7,5,4]=>011011
[1,6,3,4,2,5,7]=>010100
[1,6,3,4,2,7,5]=>010101
[1,6,3,4,5,2,7]=>010010
[1,6,3,4,5,7,2]=>010001
[1,6,3,4,7,2,5]=>010010
[1,6,3,4,7,5,2]=>010011
[1,6,3,5,2,4,7]=>010100
[1,6,3,5,2,7,4]=>010101
[1,6,3,5,4,2,7]=>010110
[1,6,3,5,4,7,2]=>010101
[1,6,3,5,7,2,4]=>010010
[1,6,3,5,7,4,2]=>010011
[1,6,3,7,2,4,5]=>010100
[1,6,3,7,2,5,4]=>010101
[1,6,3,7,4,2,5]=>010110
[1,6,3,7,4,5,2]=>010101
[1,6,3,7,5,2,4]=>010110
[1,6,3,7,5,4,2]=>010111
[1,6,4,2,3,5,7]=>011000
[1,6,4,2,3,7,5]=>011001
[1,6,4,2,5,3,7]=>011010
[1,6,4,2,5,7,3]=>011001
[1,6,4,2,7,3,5]=>011010
[1,6,4,2,7,5,3]=>011011
[1,6,4,3,2,5,7]=>011100
[1,6,4,3,2,7,5]=>011101
[1,6,4,3,5,2,7]=>011010
[1,6,4,3,5,7,2]=>011001
[1,6,4,3,7,2,5]=>011010
[1,6,4,3,7,5,2]=>011011
[1,6,4,5,2,3,7]=>010100
[1,6,4,5,2,7,3]=>010101
[1,6,4,5,3,2,7]=>010110
[1,6,4,5,3,7,2]=>010101
[1,6,4,5,7,2,3]=>010010
[1,6,4,5,7,3,2]=>010011
[1,6,4,7,2,3,5]=>010100
[1,6,4,7,2,5,3]=>010101
[1,6,4,7,3,2,5]=>010110
[1,6,4,7,3,5,2]=>010101
[1,6,4,7,5,2,3]=>010110
[1,6,4,7,5,3,2]=>010111
[1,6,5,2,3,4,7]=>011000
[1,6,5,2,3,7,4]=>011001
[1,6,5,2,4,3,7]=>011010
[1,6,5,2,4,7,3]=>011001
[1,6,5,2,7,3,4]=>011010
[1,6,5,2,7,4,3]=>011011
[1,6,5,3,2,4,7]=>011100
[1,6,5,3,2,7,4]=>011101
[1,6,5,3,4,2,7]=>011010
[1,6,5,3,4,7,2]=>011001
[1,6,5,3,7,2,4]=>011010
[1,6,5,3,7,4,2]=>011011
[1,6,5,4,2,3,7]=>011100
[1,6,5,4,2,7,3]=>011101
[1,6,5,4,3,2,7]=>011110
[1,6,5,4,3,7,2]=>011101
[1,6,5,4,7,2,3]=>011010
[1,6,5,4,7,3,2]=>011011
[1,6,5,7,2,3,4]=>010100
[1,6,5,7,2,4,3]=>010101
[1,6,5,7,3,2,4]=>010110
[1,6,5,7,3,4,2]=>010101
[1,6,5,7,4,2,3]=>010110
[1,6,5,7,4,3,2]=>010111
[1,6,7,2,3,4,5]=>001000
[1,6,7,2,3,5,4]=>001001
[1,6,7,2,4,3,5]=>001010
[1,6,7,2,4,5,3]=>001001
[1,6,7,2,5,3,4]=>001010
[1,6,7,2,5,4,3]=>001011
[1,6,7,3,2,4,5]=>001100
[1,6,7,3,2,5,4]=>001101
[1,6,7,3,4,2,5]=>001010
[1,6,7,3,4,5,2]=>001001
[1,6,7,3,5,2,4]=>001010
[1,6,7,3,5,4,2]=>001011
[1,6,7,4,2,3,5]=>001100
[1,6,7,4,2,5,3]=>001101
[1,6,7,4,3,2,5]=>001110
[1,6,7,4,3,5,2]=>001101
[1,6,7,4,5,2,3]=>001010
[1,6,7,4,5,3,2]=>001011
[1,6,7,5,2,3,4]=>001100
[1,6,7,5,2,4,3]=>001101
[1,6,7,5,3,2,4]=>001110
[1,6,7,5,3,4,2]=>001101
[1,6,7,5,4,2,3]=>001110
[1,6,7,5,4,3,2]=>001111
[1,7,2,3,4,5,6]=>010000
[1,7,2,3,4,6,5]=>010001
[1,7,2,3,5,4,6]=>010010
[1,7,2,3,5,6,4]=>010001
[1,7,2,3,6,4,5]=>010010
[1,7,2,3,6,5,4]=>010011
[1,7,2,4,3,5,6]=>010100
[1,7,2,4,3,6,5]=>010101
[1,7,2,4,5,3,6]=>010010
[1,7,2,4,5,6,3]=>010001
[1,7,2,4,6,3,5]=>010010
[1,7,2,4,6,5,3]=>010011
[1,7,2,5,3,4,6]=>010100
[1,7,2,5,3,6,4]=>010101
[1,7,2,5,4,3,6]=>010110
[1,7,2,5,4,6,3]=>010101
[1,7,2,5,6,3,4]=>010010
[1,7,2,5,6,4,3]=>010011
[1,7,2,6,3,4,5]=>010100
[1,7,2,6,3,5,4]=>010101
[1,7,2,6,4,3,5]=>010110
[1,7,2,6,4,5,3]=>010101
[1,7,2,6,5,3,4]=>010110
[1,7,2,6,5,4,3]=>010111
[1,7,3,2,4,5,6]=>011000
[1,7,3,2,4,6,5]=>011001
[1,7,3,2,5,4,6]=>011010
[1,7,3,2,5,6,4]=>011001
[1,7,3,2,6,4,5]=>011010
[1,7,3,2,6,5,4]=>011011
[1,7,3,4,2,5,6]=>010100
[1,7,3,4,2,6,5]=>010101
[1,7,3,4,5,2,6]=>010010
[1,7,3,4,5,6,2]=>010001
[1,7,3,4,6,2,5]=>010010
[1,7,3,4,6,5,2]=>010011
[1,7,3,5,2,4,6]=>010100
[1,7,3,5,2,6,4]=>010101
[1,7,3,5,4,2,6]=>010110
[1,7,3,5,4,6,2]=>010101
[1,7,3,5,6,2,4]=>010010
[1,7,3,5,6,4,2]=>010011
[1,7,3,6,2,4,5]=>010100
[1,7,3,6,2,5,4]=>010101
[1,7,3,6,4,2,5]=>010110
[1,7,3,6,4,5,2]=>010101
[1,7,3,6,5,2,4]=>010110
[1,7,3,6,5,4,2]=>010111
[1,7,4,2,3,5,6]=>011000
[1,7,4,2,3,6,5]=>011001
[1,7,4,2,5,3,6]=>011010
[1,7,4,2,5,6,3]=>011001
[1,7,4,2,6,3,5]=>011010
[1,7,4,2,6,5,3]=>011011
[1,7,4,3,2,5,6]=>011100
[1,7,4,3,2,6,5]=>011101
[1,7,4,3,5,2,6]=>011010
[1,7,4,3,5,6,2]=>011001
[1,7,4,3,6,2,5]=>011010
[1,7,4,3,6,5,2]=>011011
[1,7,4,5,2,3,6]=>010100
[1,7,4,5,2,6,3]=>010101
[1,7,4,5,3,2,6]=>010110
[1,7,4,5,3,6,2]=>010101
[1,7,4,5,6,2,3]=>010010
[1,7,4,5,6,3,2]=>010011
[1,7,4,6,2,3,5]=>010100
[1,7,4,6,2,5,3]=>010101
[1,7,4,6,3,2,5]=>010110
[1,7,4,6,3,5,2]=>010101
[1,7,4,6,5,2,3]=>010110
[1,7,4,6,5,3,2]=>010111
[1,7,5,2,3,4,6]=>011000
[1,7,5,2,3,6,4]=>011001
[1,7,5,2,4,3,6]=>011010
[1,7,5,2,4,6,3]=>011001
[1,7,5,2,6,3,4]=>011010
[1,7,5,2,6,4,3]=>011011
[1,7,5,3,2,4,6]=>011100
[1,7,5,3,2,6,4]=>011101
[1,7,5,3,4,2,6]=>011010
[1,7,5,3,4,6,2]=>011001
[1,7,5,3,6,2,4]=>011010
[1,7,5,3,6,4,2]=>011011
[1,7,5,4,2,3,6]=>011100
[1,7,5,4,2,6,3]=>011101
[1,7,5,4,3,2,6]=>011110
[1,7,5,4,3,6,2]=>011101
[1,7,5,4,6,2,3]=>011010
[1,7,5,4,6,3,2]=>011011
[1,7,5,6,2,3,4]=>010100
[1,7,5,6,2,4,3]=>010101
[1,7,5,6,3,2,4]=>010110
[1,7,5,6,3,4,2]=>010101
[1,7,5,6,4,2,3]=>010110
[1,7,5,6,4,3,2]=>010111
[1,7,6,2,3,4,5]=>011000
[1,7,6,2,3,5,4]=>011001
[1,7,6,2,4,3,5]=>011010
[1,7,6,2,4,5,3]=>011001
[1,7,6,2,5,3,4]=>011010
[1,7,6,2,5,4,3]=>011011
[1,7,6,3,2,4,5]=>011100
[1,7,6,3,2,5,4]=>011101
[1,7,6,3,4,2,5]=>011010
[1,7,6,3,4,5,2]=>011001
[1,7,6,3,5,2,4]=>011010
[1,7,6,3,5,4,2]=>011011
[1,7,6,4,2,3,5]=>011100
[1,7,6,4,2,5,3]=>011101
[1,7,6,4,3,2,5]=>011110
[1,7,6,4,3,5,2]=>011101
[1,7,6,4,5,2,3]=>011010
[1,7,6,4,5,3,2]=>011011
[1,7,6,5,2,3,4]=>011100
[1,7,6,5,2,4,3]=>011101
[1,7,6,5,3,2,4]=>011110
[1,7,6,5,3,4,2]=>011101
[1,7,6,5,4,2,3]=>011110
[1,7,6,5,4,3,2]=>011111
[2,1,3,4,5,6,7]=>100000
[2,1,3,4,5,7,6]=>100001
[2,1,3,4,6,5,7]=>100010
[2,1,3,4,6,7,5]=>100001
[2,1,3,4,7,5,6]=>100010
[2,1,3,4,7,6,5]=>100011
[2,1,3,5,4,6,7]=>100100
[2,1,3,5,4,7,6]=>100101
[2,1,3,5,6,4,7]=>100010
[2,1,3,5,6,7,4]=>100001
[2,1,3,5,7,4,6]=>100010
[2,1,3,5,7,6,4]=>100011
[2,1,3,6,4,5,7]=>100100
[2,1,3,6,4,7,5]=>100101
[2,1,3,6,5,4,7]=>100110
[2,1,3,6,5,7,4]=>100101
[2,1,3,6,7,4,5]=>100010
[2,1,3,6,7,5,4]=>100011
[2,1,3,7,4,5,6]=>100100
[2,1,3,7,4,6,5]=>100101
[2,1,3,7,5,4,6]=>100110
[2,1,3,7,5,6,4]=>100101
[2,1,3,7,6,4,5]=>100110
[2,1,3,7,6,5,4]=>100111
[2,1,4,3,5,6,7]=>101000
[2,1,4,3,5,7,6]=>101001
[2,1,4,3,6,5,7]=>101010
[2,1,4,3,6,7,5]=>101001
[2,1,4,3,7,5,6]=>101010
[2,1,4,3,7,6,5]=>101011
[2,1,4,5,3,6,7]=>100100
[2,1,4,5,3,7,6]=>100101
[2,1,4,5,6,3,7]=>100010
[2,1,4,5,6,7,3]=>100001
[2,1,4,5,7,3,6]=>100010
[2,1,4,5,7,6,3]=>100011
[2,1,4,6,3,5,7]=>100100
[2,1,4,6,3,7,5]=>100101
[2,1,4,6,5,3,7]=>100110
[2,1,4,6,5,7,3]=>100101
[2,1,4,6,7,3,5]=>100010
[2,1,4,6,7,5,3]=>100011
[2,1,4,7,3,5,6]=>100100
[2,1,4,7,3,6,5]=>100101
[2,1,4,7,5,3,6]=>100110
[2,1,4,7,5,6,3]=>100101
[2,1,4,7,6,3,5]=>100110
[2,1,4,7,6,5,3]=>100111
[2,1,5,3,4,6,7]=>101000
[2,1,5,3,4,7,6]=>101001
[2,1,5,3,6,4,7]=>101010
[2,1,5,3,6,7,4]=>101001
[2,1,5,3,7,4,6]=>101010
[2,1,5,3,7,6,4]=>101011
[2,1,5,4,3,6,7]=>101100
[2,1,5,4,3,7,6]=>101101
[2,1,5,4,6,3,7]=>101010
[2,1,5,4,6,7,3]=>101001
[2,1,5,4,7,3,6]=>101010
[2,1,5,4,7,6,3]=>101011
[2,1,5,6,3,4,7]=>100100
[2,1,5,6,3,7,4]=>100101
[2,1,5,6,4,3,7]=>100110
[2,1,5,6,4,7,3]=>100101
[2,1,5,6,7,3,4]=>100010
[2,1,5,6,7,4,3]=>100011
[2,1,5,7,3,4,6]=>100100
[2,1,5,7,3,6,4]=>100101
[2,1,5,7,4,3,6]=>100110
[2,1,5,7,4,6,3]=>100101
[2,1,5,7,6,3,4]=>100110
[2,1,5,7,6,4,3]=>100111
[2,1,6,3,4,5,7]=>101000
[2,1,6,3,4,7,5]=>101001
[2,1,6,3,5,4,7]=>101010
[2,1,6,3,5,7,4]=>101001
[2,1,6,3,7,4,5]=>101010
[2,1,6,3,7,5,4]=>101011
[2,1,6,4,3,5,7]=>101100
[2,1,6,4,3,7,5]=>101101
[2,1,6,4,5,3,7]=>101010
[2,1,6,4,5,7,3]=>101001
[2,1,6,4,7,3,5]=>101010
[2,1,6,4,7,5,3]=>101011
[2,1,6,5,3,4,7]=>101100
[2,1,6,5,3,7,4]=>101101
[2,1,6,5,4,3,7]=>101110
[2,1,6,5,4,7,3]=>101101
[2,1,6,5,7,3,4]=>101010
[2,1,6,5,7,4,3]=>101011
[2,1,6,7,3,4,5]=>100100
[2,1,6,7,3,5,4]=>100101
[2,1,6,7,4,3,5]=>100110
[2,1,6,7,4,5,3]=>100101
[2,1,6,7,5,3,4]=>100110
[2,1,6,7,5,4,3]=>100111
[2,1,7,3,4,5,6]=>101000
[2,1,7,3,4,6,5]=>101001
[2,1,7,3,5,4,6]=>101010
[2,1,7,3,5,6,4]=>101001
[2,1,7,3,6,4,5]=>101010
[2,1,7,3,6,5,4]=>101011
[2,1,7,4,3,5,6]=>101100
[2,1,7,4,3,6,5]=>101101
[2,1,7,4,5,3,6]=>101010
[2,1,7,4,5,6,3]=>101001
[2,1,7,4,6,3,5]=>101010
[2,1,7,4,6,5,3]=>101011
[2,1,7,5,3,4,6]=>101100
[2,1,7,5,3,6,4]=>101101
[2,1,7,5,4,3,6]=>101110
[2,1,7,5,4,6,3]=>101101
[2,1,7,5,6,3,4]=>101010
[2,1,7,5,6,4,3]=>101011
[2,1,7,6,3,4,5]=>101100
[2,1,7,6,3,5,4]=>101101
[2,1,7,6,4,3,5]=>101110
[2,1,7,6,4,5,3]=>101101
[2,1,7,6,5,3,4]=>101110
[2,1,7,6,5,4,3]=>101111
[2,3,1,4,5,6,7]=>010000
[2,3,1,4,5,7,6]=>010001
[2,3,1,4,6,5,7]=>010010
[2,3,1,4,6,7,5]=>010001
[2,3,1,4,7,5,6]=>010010
[2,3,1,4,7,6,5]=>010011
[2,3,1,5,4,6,7]=>010100
[2,3,1,5,4,7,6]=>010101
[2,3,1,5,6,4,7]=>010010
[2,3,1,5,6,7,4]=>010001
[2,3,1,5,7,4,6]=>010010
[2,3,1,5,7,6,4]=>010011
[2,3,1,6,4,5,7]=>010100
[2,3,1,6,4,7,5]=>010101
[2,3,1,6,5,4,7]=>010110
[2,3,1,6,5,7,4]=>010101
[2,3,1,6,7,4,5]=>010010
[2,3,1,6,7,5,4]=>010011
[2,3,1,7,4,5,6]=>010100
[2,3,1,7,4,6,5]=>010101
[2,3,1,7,5,4,6]=>010110
[2,3,1,7,5,6,4]=>010101
[2,3,1,7,6,4,5]=>010110
[2,3,1,7,6,5,4]=>010111
[2,3,4,1,5,6,7]=>001000
[2,3,4,1,5,7,6]=>001001
[2,3,4,1,6,5,7]=>001010
[2,3,4,1,6,7,5]=>001001
[2,3,4,1,7,5,6]=>001010
[2,3,4,1,7,6,5]=>001011
[2,3,4,5,1,6,7]=>000100
[2,3,4,5,1,7,6]=>000101
[2,3,4,5,6,1,7]=>000010
[2,3,4,5,6,7,1]=>000001
[2,3,4,5,7,1,6]=>000010
[2,3,4,5,7,6,1]=>000011
[2,3,4,6,1,5,7]=>000100
[2,3,4,6,1,7,5]=>000101
[2,3,4,6,5,1,7]=>000110
[2,3,4,6,5,7,1]=>000101
[2,3,4,6,7,1,5]=>000010
[2,3,4,6,7,5,1]=>000011
[2,3,4,7,1,5,6]=>000100
[2,3,4,7,1,6,5]=>000101
[2,3,4,7,5,1,6]=>000110
[2,3,4,7,5,6,1]=>000101
[2,3,4,7,6,1,5]=>000110
[2,3,4,7,6,5,1]=>000111
[2,3,5,1,4,6,7]=>001000
[2,3,5,1,4,7,6]=>001001
[2,3,5,1,6,4,7]=>001010
[2,3,5,1,6,7,4]=>001001
[2,3,5,1,7,4,6]=>001010
[2,3,5,1,7,6,4]=>001011
[2,3,5,4,1,6,7]=>001100
[2,3,5,4,1,7,6]=>001101
[2,3,5,4,6,1,7]=>001010
[2,3,5,4,6,7,1]=>001001
[2,3,5,4,7,1,6]=>001010
[2,3,5,4,7,6,1]=>001011
[2,3,5,6,1,4,7]=>000100
[2,3,5,6,1,7,4]=>000101
[2,3,5,6,4,1,7]=>000110
[2,3,5,6,4,7,1]=>000101
[2,3,5,6,7,1,4]=>000010
[2,3,5,6,7,4,1]=>000011
[2,3,5,7,1,4,6]=>000100
[2,3,5,7,1,6,4]=>000101
[2,3,5,7,4,1,6]=>000110
[2,3,5,7,4,6,1]=>000101
[2,3,5,7,6,1,4]=>000110
[2,3,5,7,6,4,1]=>000111
[2,3,6,1,4,5,7]=>001000
[2,3,6,1,4,7,5]=>001001
[2,3,6,1,5,4,7]=>001010
[2,3,6,1,5,7,4]=>001001
[2,3,6,1,7,4,5]=>001010
[2,3,6,1,7,5,4]=>001011
[2,3,6,4,1,5,7]=>001100
[2,3,6,4,1,7,5]=>001101
[2,3,6,4,5,1,7]=>001010
[2,3,6,4,5,7,1]=>001001
[2,3,6,4,7,1,5]=>001010
[2,3,6,4,7,5,1]=>001011
[2,3,6,5,1,4,7]=>001100
[2,3,6,5,1,7,4]=>001101
[2,3,6,5,4,1,7]=>001110
[2,3,6,5,4,7,1]=>001101
[2,3,6,5,7,1,4]=>001010
[2,3,6,5,7,4,1]=>001011
[2,3,6,7,1,4,5]=>000100
[2,3,6,7,1,5,4]=>000101
[2,3,6,7,4,1,5]=>000110
[2,3,6,7,4,5,1]=>000101
[2,3,6,7,5,1,4]=>000110
[2,3,6,7,5,4,1]=>000111
[2,3,7,1,4,5,6]=>001000
[2,3,7,1,4,6,5]=>001001
[2,3,7,1,5,4,6]=>001010
[2,3,7,1,5,6,4]=>001001
[2,3,7,1,6,4,5]=>001010
[2,3,7,1,6,5,4]=>001011
[2,3,7,4,1,5,6]=>001100
[2,3,7,4,1,6,5]=>001101
[2,3,7,4,5,1,6]=>001010
[2,3,7,4,5,6,1]=>001001
[2,3,7,4,6,1,5]=>001010
[2,3,7,4,6,5,1]=>001011
[2,3,7,5,1,4,6]=>001100
[2,3,7,5,1,6,4]=>001101
[2,3,7,5,4,1,6]=>001110
[2,3,7,5,4,6,1]=>001101
[2,3,7,5,6,1,4]=>001010
[2,3,7,5,6,4,1]=>001011
[2,3,7,6,1,4,5]=>001100
[2,3,7,6,1,5,4]=>001101
[2,3,7,6,4,1,5]=>001110
[2,3,7,6,4,5,1]=>001101
[2,3,7,6,5,1,4]=>001110
[2,3,7,6,5,4,1]=>001111
[2,4,1,3,5,6,7]=>010000
[2,4,1,3,5,7,6]=>010001
[2,4,1,3,6,5,7]=>010010
[2,4,1,3,6,7,5]=>010001
[2,4,1,3,7,5,6]=>010010
[2,4,1,3,7,6,5]=>010011
[2,4,1,5,3,6,7]=>010100
[2,4,1,5,3,7,6]=>010101
[2,4,1,5,6,3,7]=>010010
[2,4,1,5,6,7,3]=>010001
[2,4,1,5,7,3,6]=>010010
[2,4,1,5,7,6,3]=>010011
[2,4,1,6,3,5,7]=>010100
[2,4,1,6,3,7,5]=>010101
[2,4,1,6,5,3,7]=>010110
[2,4,1,6,5,7,3]=>010101
[2,4,1,6,7,3,5]=>010010
[2,4,1,6,7,5,3]=>010011
[2,4,1,7,3,5,6]=>010100
[2,4,1,7,3,6,5]=>010101
[2,4,1,7,5,3,6]=>010110
[2,4,1,7,5,6,3]=>010101
[2,4,1,7,6,3,5]=>010110
[2,4,1,7,6,5,3]=>010111
[2,4,3,1,5,6,7]=>011000
[2,4,3,1,5,7,6]=>011001
[2,4,3,1,6,5,7]=>011010
[2,4,3,1,6,7,5]=>011001
[2,4,3,1,7,5,6]=>011010
[2,4,3,1,7,6,5]=>011011
[2,4,3,5,1,6,7]=>010100
[2,4,3,5,1,7,6]=>010101
[2,4,3,5,6,1,7]=>010010
[2,4,3,5,6,7,1]=>010001
[2,4,3,5,7,1,6]=>010010
[2,4,3,5,7,6,1]=>010011
[2,4,3,6,1,5,7]=>010100
[2,4,3,6,1,7,5]=>010101
[2,4,3,6,5,1,7]=>010110
[2,4,3,6,5,7,1]=>010101
[2,4,3,6,7,1,5]=>010010
[2,4,3,6,7,5,1]=>010011
[2,4,3,7,1,5,6]=>010100
[2,4,3,7,1,6,5]=>010101
[2,4,3,7,5,1,6]=>010110
[2,4,3,7,5,6,1]=>010101
[2,4,3,7,6,1,5]=>010110
[2,4,3,7,6,5,1]=>010111
[2,4,5,1,3,6,7]=>001000
[2,4,5,1,3,7,6]=>001001
[2,4,5,1,6,3,7]=>001010
[2,4,5,1,6,7,3]=>001001
[2,4,5,1,7,3,6]=>001010
[2,4,5,1,7,6,3]=>001011
[2,4,5,3,1,6,7]=>001100
[2,4,5,3,1,7,6]=>001101
[2,4,5,3,6,1,7]=>001010
[2,4,5,3,6,7,1]=>001001
[2,4,5,3,7,1,6]=>001010
[2,4,5,3,7,6,1]=>001011
[2,4,5,6,1,3,7]=>000100
[2,4,5,6,1,7,3]=>000101
[2,4,5,6,3,1,7]=>000110
[2,4,5,6,3,7,1]=>000101
[2,4,5,6,7,1,3]=>000010
[2,4,5,6,7,3,1]=>000011
[2,4,5,7,1,3,6]=>000100
[2,4,5,7,1,6,3]=>000101
[2,4,5,7,3,1,6]=>000110
[2,4,5,7,3,6,1]=>000101
[2,4,5,7,6,1,3]=>000110
[2,4,5,7,6,3,1]=>000111
[2,4,6,1,3,5,7]=>001000
[2,4,6,1,3,7,5]=>001001
[2,4,6,1,5,3,7]=>001010
[2,4,6,1,5,7,3]=>001001
[2,4,6,1,7,3,5]=>001010
[2,4,6,1,7,5,3]=>001011
[2,4,6,3,1,5,7]=>001100
[2,4,6,3,1,7,5]=>001101
[2,4,6,3,5,1,7]=>001010
[2,4,6,3,5,7,1]=>001001
[2,4,6,3,7,1,5]=>001010
[2,4,6,3,7,5,1]=>001011
[2,4,6,5,1,3,7]=>001100
[2,4,6,5,1,7,3]=>001101
[2,4,6,5,3,1,7]=>001110
[2,4,6,5,3,7,1]=>001101
[2,4,6,5,7,1,3]=>001010
[2,4,6,5,7,3,1]=>001011
[2,4,6,7,1,3,5]=>000100
[2,4,6,7,1,5,3]=>000101
[2,4,6,7,3,1,5]=>000110
[2,4,6,7,3,5,1]=>000101
[2,4,6,7,5,1,3]=>000110
[2,4,6,7,5,3,1]=>000111
[2,4,7,1,3,5,6]=>001000
[2,4,7,1,3,6,5]=>001001
[2,4,7,1,5,3,6]=>001010
[2,4,7,1,5,6,3]=>001001
[2,4,7,1,6,3,5]=>001010
[2,4,7,1,6,5,3]=>001011
[2,4,7,3,1,5,6]=>001100
[2,4,7,3,1,6,5]=>001101
[2,4,7,3,5,1,6]=>001010
[2,4,7,3,5,6,1]=>001001
[2,4,7,3,6,1,5]=>001010
[2,4,7,3,6,5,1]=>001011
[2,4,7,5,1,3,6]=>001100
[2,4,7,5,1,6,3]=>001101
[2,4,7,5,3,1,6]=>001110
[2,4,7,5,3,6,1]=>001101
[2,4,7,5,6,1,3]=>001010
[2,4,7,5,6,3,1]=>001011
[2,4,7,6,1,3,5]=>001100
[2,4,7,6,1,5,3]=>001101
[2,4,7,6,3,1,5]=>001110
[2,4,7,6,3,5,1]=>001101
[2,4,7,6,5,1,3]=>001110
[2,4,7,6,5,3,1]=>001111
[2,5,1,3,4,6,7]=>010000
[2,5,1,3,4,7,6]=>010001
[2,5,1,3,6,4,7]=>010010
[2,5,1,3,6,7,4]=>010001
[2,5,1,3,7,4,6]=>010010
[2,5,1,3,7,6,4]=>010011
[2,5,1,4,3,6,7]=>010100
[2,5,1,4,3,7,6]=>010101
[2,5,1,4,6,3,7]=>010010
[2,5,1,4,6,7,3]=>010001
[2,5,1,4,7,3,6]=>010010
[2,5,1,4,7,6,3]=>010011
[2,5,1,6,3,4,7]=>010100
[2,5,1,6,3,7,4]=>010101
[2,5,1,6,4,3,7]=>010110
[2,5,1,6,4,7,3]=>010101
[2,5,1,6,7,3,4]=>010010
[2,5,1,6,7,4,3]=>010011
[2,5,1,7,3,4,6]=>010100
[2,5,1,7,3,6,4]=>010101
[2,5,1,7,4,3,6]=>010110
[2,5,1,7,4,6,3]=>010101
[2,5,1,7,6,3,4]=>010110
[2,5,1,7,6,4,3]=>010111
[2,5,3,1,4,6,7]=>011000
[2,5,3,1,4,7,6]=>011001
[2,5,3,1,6,4,7]=>011010
[2,5,3,1,6,7,4]=>011001
[2,5,3,1,7,4,6]=>011010
[2,5,3,1,7,6,4]=>011011
[2,5,3,4,1,6,7]=>010100
[2,5,3,4,1,7,6]=>010101
[2,5,3,4,6,1,7]=>010010
[2,5,3,4,6,7,1]=>010001
[2,5,3,4,7,1,6]=>010010
[2,5,3,4,7,6,1]=>010011
[2,5,3,6,1,4,7]=>010100
[2,5,3,6,1,7,4]=>010101
[2,5,3,6,4,1,7]=>010110
[2,5,3,6,4,7,1]=>010101
[2,5,3,6,7,1,4]=>010010
[2,5,3,6,7,4,1]=>010011
[2,5,3,7,1,4,6]=>010100
[2,5,3,7,1,6,4]=>010101
[2,5,3,7,4,1,6]=>010110
[2,5,3,7,4,6,1]=>010101
[2,5,3,7,6,1,4]=>010110
[2,5,3,7,6,4,1]=>010111
[2,5,4,1,3,6,7]=>011000
[2,5,4,1,3,7,6]=>011001
[2,5,4,1,6,3,7]=>011010
[2,5,4,1,6,7,3]=>011001
[2,5,4,1,7,3,6]=>011010
[2,5,4,1,7,6,3]=>011011
[2,5,4,3,1,6,7]=>011100
[2,5,4,3,1,7,6]=>011101
[2,5,4,3,6,1,7]=>011010
[2,5,4,3,6,7,1]=>011001
[2,5,4,3,7,1,6]=>011010
[2,5,4,3,7,6,1]=>011011
[2,5,4,6,1,3,7]=>010100
[2,5,4,6,1,7,3]=>010101
[2,5,4,6,3,1,7]=>010110
[2,5,4,6,3,7,1]=>010101
[2,5,4,6,7,1,3]=>010010
[2,5,4,6,7,3,1]=>010011
[2,5,4,7,1,3,6]=>010100
[2,5,4,7,1,6,3]=>010101
[2,5,4,7,3,1,6]=>010110
[2,5,4,7,3,6,1]=>010101
[2,5,4,7,6,1,3]=>010110
[2,5,4,7,6,3,1]=>010111
[2,5,6,1,3,4,7]=>001000
[2,5,6,1,3,7,4]=>001001
[2,5,6,1,4,3,7]=>001010
[2,5,6,1,4,7,3]=>001001
[2,5,6,1,7,3,4]=>001010
[2,5,6,1,7,4,3]=>001011
[2,5,6,3,1,4,7]=>001100
[2,5,6,3,1,7,4]=>001101
[2,5,6,3,4,1,7]=>001010
[2,5,6,3,4,7,1]=>001001
[2,5,6,3,7,1,4]=>001010
[2,5,6,3,7,4,1]=>001011
[2,5,6,4,1,3,7]=>001100
[2,5,6,4,1,7,3]=>001101
[2,5,6,4,3,1,7]=>001110
[2,5,6,4,3,7,1]=>001101
[2,5,6,4,7,1,3]=>001010
[2,5,6,4,7,3,1]=>001011
[2,5,6,7,1,3,4]=>000100
[2,5,6,7,1,4,3]=>000101
[2,5,6,7,3,1,4]=>000110
[2,5,6,7,3,4,1]=>000101
[2,5,6,7,4,1,3]=>000110
[2,5,6,7,4,3,1]=>000111
[2,5,7,1,3,4,6]=>001000
[2,5,7,1,3,6,4]=>001001
[2,5,7,1,4,3,6]=>001010
[2,5,7,1,4,6,3]=>001001
[2,5,7,1,6,3,4]=>001010
[2,5,7,1,6,4,3]=>001011
[2,5,7,3,1,4,6]=>001100
[2,5,7,3,1,6,4]=>001101
[2,5,7,3,4,1,6]=>001010
[2,5,7,3,4,6,1]=>001001
[2,5,7,3,6,1,4]=>001010
[2,5,7,3,6,4,1]=>001011
[2,5,7,4,1,3,6]=>001100
[2,5,7,4,1,6,3]=>001101
[2,5,7,4,3,1,6]=>001110
[2,5,7,4,3,6,1]=>001101
[2,5,7,4,6,1,3]=>001010
[2,5,7,4,6,3,1]=>001011
[2,5,7,6,1,3,4]=>001100
[2,5,7,6,1,4,3]=>001101
[2,5,7,6,3,1,4]=>001110
[2,5,7,6,3,4,1]=>001101
[2,5,7,6,4,1,3]=>001110
[2,5,7,6,4,3,1]=>001111
[2,6,1,3,4,5,7]=>010000
[2,6,1,3,4,7,5]=>010001
[2,6,1,3,5,4,7]=>010010
[2,6,1,3,5,7,4]=>010001
[2,6,1,3,7,4,5]=>010010
[2,6,1,3,7,5,4]=>010011
[2,6,1,4,3,5,7]=>010100
[2,6,1,4,3,7,5]=>010101
[2,6,1,4,5,3,7]=>010010
[2,6,1,4,5,7,3]=>010001
[2,6,1,4,7,3,5]=>010010
[2,6,1,4,7,5,3]=>010011
[2,6,1,5,3,4,7]=>010100
[2,6,1,5,3,7,4]=>010101
[2,6,1,5,4,3,7]=>010110
[2,6,1,5,4,7,3]=>010101
[2,6,1,5,7,3,4]=>010010
[2,6,1,5,7,4,3]=>010011
[2,6,1,7,3,4,5]=>010100
[2,6,1,7,3,5,4]=>010101
[2,6,1,7,4,3,5]=>010110
[2,6,1,7,4,5,3]=>010101
[2,6,1,7,5,3,4]=>010110
[2,6,1,7,5,4,3]=>010111
[2,6,3,1,4,5,7]=>011000
[2,6,3,1,4,7,5]=>011001
[2,6,3,1,5,4,7]=>011010
[2,6,3,1,5,7,4]=>011001
[2,6,3,1,7,4,5]=>011010
[2,6,3,1,7,5,4]=>011011
[2,6,3,4,1,5,7]=>010100
[2,6,3,4,1,7,5]=>010101
[2,6,3,4,5,1,7]=>010010
[2,6,3,4,5,7,1]=>010001
[2,6,3,4,7,1,5]=>010010
[2,6,3,4,7,5,1]=>010011
[2,6,3,5,1,4,7]=>010100
[2,6,3,5,1,7,4]=>010101
[2,6,3,5,4,1,7]=>010110
[2,6,3,5,4,7,1]=>010101
[2,6,3,5,7,1,4]=>010010
[2,6,3,5,7,4,1]=>010011
[2,6,3,7,1,4,5]=>010100
[2,6,3,7,1,5,4]=>010101
[2,6,3,7,4,1,5]=>010110
[2,6,3,7,4,5,1]=>010101
[2,6,3,7,5,1,4]=>010110
[2,6,3,7,5,4,1]=>010111
[2,6,4,1,3,5,7]=>011000
[2,6,4,1,3,7,5]=>011001
[2,6,4,1,5,3,7]=>011010
[2,6,4,1,5,7,3]=>011001
[2,6,4,1,7,3,5]=>011010
[2,6,4,1,7,5,3]=>011011
[2,6,4,3,1,5,7]=>011100
[2,6,4,3,1,7,5]=>011101
[2,6,4,3,5,1,7]=>011010
[2,6,4,3,5,7,1]=>011001
[2,6,4,3,7,1,5]=>011010
[2,6,4,3,7,5,1]=>011011
[2,6,4,5,1,3,7]=>010100
[2,6,4,5,1,7,3]=>010101
[2,6,4,5,3,1,7]=>010110
[2,6,4,5,3,7,1]=>010101
[2,6,4,5,7,1,3]=>010010
[2,6,4,5,7,3,1]=>010011
[2,6,4,7,1,3,5]=>010100
[2,6,4,7,1,5,3]=>010101
[2,6,4,7,3,1,5]=>010110
[2,6,4,7,3,5,1]=>010101
[2,6,4,7,5,1,3]=>010110
[2,6,4,7,5,3,1]=>010111
[2,6,5,1,3,4,7]=>011000
[2,6,5,1,3,7,4]=>011001
[2,6,5,1,4,3,7]=>011010
[2,6,5,1,4,7,3]=>011001
[2,6,5,1,7,3,4]=>011010
[2,6,5,1,7,4,3]=>011011
[2,6,5,3,1,4,7]=>011100
[2,6,5,3,1,7,4]=>011101
[2,6,5,3,4,1,7]=>011010
[2,6,5,3,4,7,1]=>011001
[2,6,5,3,7,1,4]=>011010
[2,6,5,3,7,4,1]=>011011
[2,6,5,4,1,3,7]=>011100
[2,6,5,4,1,7,3]=>011101
[2,6,5,4,3,1,7]=>011110
[2,6,5,4,3,7,1]=>011101
[2,6,5,4,7,1,3]=>011010
[2,6,5,4,7,3,1]=>011011
[2,6,5,7,1,3,4]=>010100
[2,6,5,7,1,4,3]=>010101
[2,6,5,7,3,1,4]=>010110
[2,6,5,7,3,4,1]=>010101
[2,6,5,7,4,1,3]=>010110
[2,6,5,7,4,3,1]=>010111
[2,6,7,1,3,4,5]=>001000
[2,6,7,1,3,5,4]=>001001
[2,6,7,1,4,3,5]=>001010
[2,6,7,1,4,5,3]=>001001
[2,6,7,1,5,3,4]=>001010
[2,6,7,1,5,4,3]=>001011
[2,6,7,3,1,4,5]=>001100
[2,6,7,3,1,5,4]=>001101
[2,6,7,3,4,1,5]=>001010
[2,6,7,3,4,5,1]=>001001
[2,6,7,3,5,1,4]=>001010
[2,6,7,3,5,4,1]=>001011
[2,6,7,4,1,3,5]=>001100
[2,6,7,4,1,5,3]=>001101
[2,6,7,4,3,1,5]=>001110
[2,6,7,4,3,5,1]=>001101
[2,6,7,4,5,1,3]=>001010
[2,6,7,4,5,3,1]=>001011
[2,6,7,5,1,3,4]=>001100
[2,6,7,5,1,4,3]=>001101
[2,6,7,5,3,1,4]=>001110
[2,6,7,5,3,4,1]=>001101
[2,6,7,5,4,1,3]=>001110
[2,6,7,5,4,3,1]=>001111
[2,7,1,3,4,5,6]=>010000
[2,7,1,3,4,6,5]=>010001
[2,7,1,3,5,4,6]=>010010
[2,7,1,3,5,6,4]=>010001
[2,7,1,3,6,4,5]=>010010
[2,7,1,3,6,5,4]=>010011
[2,7,1,4,3,5,6]=>010100
[2,7,1,4,3,6,5]=>010101
[2,7,1,4,5,3,6]=>010010
[2,7,1,4,5,6,3]=>010001
[2,7,1,4,6,3,5]=>010010
[2,7,1,4,6,5,3]=>010011
[2,7,1,5,3,4,6]=>010100
[2,7,1,5,3,6,4]=>010101
[2,7,1,5,4,3,6]=>010110
[2,7,1,5,4,6,3]=>010101
[2,7,1,5,6,3,4]=>010010
[2,7,1,5,6,4,3]=>010011
[2,7,1,6,3,4,5]=>010100
[2,7,1,6,3,5,4]=>010101
[2,7,1,6,4,3,5]=>010110
[2,7,1,6,4,5,3]=>010101
[2,7,1,6,5,3,4]=>010110
[2,7,1,6,5,4,3]=>010111
[2,7,3,1,4,5,6]=>011000
[2,7,3,1,4,6,5]=>011001
[2,7,3,1,5,4,6]=>011010
[2,7,3,1,5,6,4]=>011001
[2,7,3,1,6,4,5]=>011010
[2,7,3,1,6,5,4]=>011011
[2,7,3,4,1,5,6]=>010100
[2,7,3,4,1,6,5]=>010101
[2,7,3,4,5,1,6]=>010010
[2,7,3,4,5,6,1]=>010001
[2,7,3,4,6,1,5]=>010010
[2,7,3,4,6,5,1]=>010011
[2,7,3,5,1,4,6]=>010100
[2,7,3,5,1,6,4]=>010101
[2,7,3,5,4,1,6]=>010110
[2,7,3,5,4,6,1]=>010101
[2,7,3,5,6,1,4]=>010010
[2,7,3,5,6,4,1]=>010011
[2,7,3,6,1,4,5]=>010100
[2,7,3,6,1,5,4]=>010101
[2,7,3,6,4,1,5]=>010110
[2,7,3,6,4,5,1]=>010101
[2,7,3,6,5,1,4]=>010110
[2,7,3,6,5,4,1]=>010111
[2,7,4,1,3,5,6]=>011000
[2,7,4,1,3,6,5]=>011001
[2,7,4,1,5,3,6]=>011010
[2,7,4,1,5,6,3]=>011001
[2,7,4,1,6,3,5]=>011010
[2,7,4,1,6,5,3]=>011011
[2,7,4,3,1,5,6]=>011100
[2,7,4,3,1,6,5]=>011101
[2,7,4,3,5,1,6]=>011010
[2,7,4,3,5,6,1]=>011001
[2,7,4,3,6,1,5]=>011010
[2,7,4,3,6,5,1]=>011011
[2,7,4,5,1,3,6]=>010100
[2,7,4,5,1,6,3]=>010101
[2,7,4,5,3,1,6]=>010110
[2,7,4,5,3,6,1]=>010101
[2,7,4,5,6,1,3]=>010010
[2,7,4,5,6,3,1]=>010011
[2,7,4,6,1,3,5]=>010100
[2,7,4,6,1,5,3]=>010101
[2,7,4,6,3,1,5]=>010110
[2,7,4,6,3,5,1]=>010101
[2,7,4,6,5,1,3]=>010110
[2,7,4,6,5,3,1]=>010111
[2,7,5,1,3,4,6]=>011000
[2,7,5,1,3,6,4]=>011001
[2,7,5,1,4,3,6]=>011010
[2,7,5,1,4,6,3]=>011001
[2,7,5,1,6,3,4]=>011010
[2,7,5,1,6,4,3]=>011011
[2,7,5,3,1,4,6]=>011100
[2,7,5,3,1,6,4]=>011101
[2,7,5,3,4,1,6]=>011010
[2,7,5,3,4,6,1]=>011001
[2,7,5,3,6,1,4]=>011010
[2,7,5,3,6,4,1]=>011011
[2,7,5,4,1,3,6]=>011100
[2,7,5,4,1,6,3]=>011101
[2,7,5,4,3,1,6]=>011110
[2,7,5,4,3,6,1]=>011101
[2,7,5,4,6,1,3]=>011010
[2,7,5,4,6,3,1]=>011011
[2,7,5,6,1,3,4]=>010100
[2,7,5,6,1,4,3]=>010101
[2,7,5,6,3,1,4]=>010110
[2,7,5,6,3,4,1]=>010101
[2,7,5,6,4,1,3]=>010110
[2,7,5,6,4,3,1]=>010111
[2,7,6,1,3,4,5]=>011000
[2,7,6,1,3,5,4]=>011001
[2,7,6,1,4,3,5]=>011010
[2,7,6,1,4,5,3]=>011001
[2,7,6,1,5,3,4]=>011010
[2,7,6,1,5,4,3]=>011011
[2,7,6,3,1,4,5]=>011100
[2,7,6,3,1,5,4]=>011101
[2,7,6,3,4,1,5]=>011010
[2,7,6,3,4,5,1]=>011001
[2,7,6,3,5,1,4]=>011010
[2,7,6,3,5,4,1]=>011011
[2,7,6,4,1,3,5]=>011100
[2,7,6,4,1,5,3]=>011101
[2,7,6,4,3,1,5]=>011110
[2,7,6,4,3,5,1]=>011101
[2,7,6,4,5,1,3]=>011010
[2,7,6,4,5,3,1]=>011011
[2,7,6,5,1,3,4]=>011100
[2,7,6,5,1,4,3]=>011101
[2,7,6,5,3,1,4]=>011110
[2,7,6,5,3,4,1]=>011101
[2,7,6,5,4,1,3]=>011110
[2,7,6,5,4,3,1]=>011111
[3,1,2,4,5,6,7]=>100000
[3,1,2,4,5,7,6]=>100001
[3,1,2,4,6,5,7]=>100010
[3,1,2,4,6,7,5]=>100001
[3,1,2,4,7,5,6]=>100010
[3,1,2,4,7,6,5]=>100011
[3,1,2,5,4,6,7]=>100100
[3,1,2,5,4,7,6]=>100101
[3,1,2,5,6,4,7]=>100010
[3,1,2,5,6,7,4]=>100001
[3,1,2,5,7,4,6]=>100010
[3,1,2,5,7,6,4]=>100011
[3,1,2,6,4,5,7]=>100100
[3,1,2,6,4,7,5]=>100101
[3,1,2,6,5,4,7]=>100110
[3,1,2,6,5,7,4]=>100101
[3,1,2,6,7,4,5]=>100010
[3,1,2,6,7,5,4]=>100011
[3,1,2,7,4,5,6]=>100100
[3,1,2,7,4,6,5]=>100101
[3,1,2,7,5,4,6]=>100110
[3,1,2,7,5,6,4]=>100101
[3,1,2,7,6,4,5]=>100110
[3,1,2,7,6,5,4]=>100111
[3,1,4,2,5,6,7]=>101000
[3,1,4,2,5,7,6]=>101001
[3,1,4,2,6,5,7]=>101010
[3,1,4,2,6,7,5]=>101001
[3,1,4,2,7,5,6]=>101010
[3,1,4,2,7,6,5]=>101011
[3,1,4,5,2,6,7]=>100100
[3,1,4,5,2,7,6]=>100101
[3,1,4,5,6,2,7]=>100010
[3,1,4,5,6,7,2]=>100001
[3,1,4,5,7,2,6]=>100010
[3,1,4,5,7,6,2]=>100011
[3,1,4,6,2,5,7]=>100100
[3,1,4,6,2,7,5]=>100101
[3,1,4,6,5,2,7]=>100110
[3,1,4,6,5,7,2]=>100101
[3,1,4,6,7,2,5]=>100010
[3,1,4,6,7,5,2]=>100011
[3,1,4,7,2,5,6]=>100100
[3,1,4,7,2,6,5]=>100101
[3,1,4,7,5,2,6]=>100110
[3,1,4,7,5,6,2]=>100101
[3,1,4,7,6,2,5]=>100110
[3,1,4,7,6,5,2]=>100111
[3,1,5,2,4,6,7]=>101000
[3,1,5,2,4,7,6]=>101001
[3,1,5,2,6,4,7]=>101010
[3,1,5,2,6,7,4]=>101001
[3,1,5,2,7,4,6]=>101010
[3,1,5,2,7,6,4]=>101011
[3,1,5,4,2,6,7]=>101100
[3,1,5,4,2,7,6]=>101101
[3,1,5,4,6,2,7]=>101010
[3,1,5,4,6,7,2]=>101001
[3,1,5,4,7,2,6]=>101010
[3,1,5,4,7,6,2]=>101011
[3,1,5,6,2,4,7]=>100100
[3,1,5,6,2,7,4]=>100101
[3,1,5,6,4,2,7]=>100110
[3,1,5,6,4,7,2]=>100101
[3,1,5,6,7,2,4]=>100010
[3,1,5,6,7,4,2]=>100011
[3,1,5,7,2,4,6]=>100100
[3,1,5,7,2,6,4]=>100101
[3,1,5,7,4,2,6]=>100110
[3,1,5,7,4,6,2]=>100101
[3,1,5,7,6,2,4]=>100110
[3,1,5,7,6,4,2]=>100111
[3,1,6,2,4,5,7]=>101000
[3,1,6,2,4,7,5]=>101001
[3,1,6,2,5,4,7]=>101010
[3,1,6,2,5,7,4]=>101001
[3,1,6,2,7,4,5]=>101010
[3,1,6,2,7,5,4]=>101011
[3,1,6,4,2,5,7]=>101100
[3,1,6,4,2,7,5]=>101101
[3,1,6,4,5,2,7]=>101010
[3,1,6,4,5,7,2]=>101001
[3,1,6,4,7,2,5]=>101010
[3,1,6,4,7,5,2]=>101011
[3,1,6,5,2,4,7]=>101100
[3,1,6,5,2,7,4]=>101101
[3,1,6,5,4,2,7]=>101110
[3,1,6,5,4,7,2]=>101101
[3,1,6,5,7,2,4]=>101010
[3,1,6,5,7,4,2]=>101011
[3,1,6,7,2,4,5]=>100100
[3,1,6,7,2,5,4]=>100101
[3,1,6,7,4,2,5]=>100110
[3,1,6,7,4,5,2]=>100101
[3,1,6,7,5,2,4]=>100110
[3,1,6,7,5,4,2]=>100111
[3,1,7,2,4,5,6]=>101000
[3,1,7,2,4,6,5]=>101001
[3,1,7,2,5,4,6]=>101010
[3,1,7,2,5,6,4]=>101001
[3,1,7,2,6,4,5]=>101010
[3,1,7,2,6,5,4]=>101011
[3,1,7,4,2,5,6]=>101100
[3,1,7,4,2,6,5]=>101101
[3,1,7,4,5,2,6]=>101010
[3,1,7,4,5,6,2]=>101001
[3,1,7,4,6,2,5]=>101010
[3,1,7,4,6,5,2]=>101011
[3,1,7,5,2,4,6]=>101100
[3,1,7,5,2,6,4]=>101101
[3,1,7,5,4,2,6]=>101110
[3,1,7,5,4,6,2]=>101101
[3,1,7,5,6,2,4]=>101010
[3,1,7,5,6,4,2]=>101011
[3,1,7,6,2,4,5]=>101100
[3,1,7,6,2,5,4]=>101101
[3,1,7,6,4,2,5]=>101110
[3,1,7,6,4,5,2]=>101101
[3,1,7,6,5,2,4]=>101110
[3,1,7,6,5,4,2]=>101111
[3,2,1,4,5,6,7]=>110000
[3,2,1,4,5,7,6]=>110001
[3,2,1,4,6,5,7]=>110010
[3,2,1,4,6,7,5]=>110001
[3,2,1,4,7,5,6]=>110010
[3,2,1,4,7,6,5]=>110011
[3,2,1,5,4,6,7]=>110100
[3,2,1,5,4,7,6]=>110101
[3,2,1,5,6,4,7]=>110010
[3,2,1,5,6,7,4]=>110001
[3,2,1,5,7,4,6]=>110010
[3,2,1,5,7,6,4]=>110011
[3,2,1,6,4,5,7]=>110100
[3,2,1,6,4,7,5]=>110101
[3,2,1,6,5,4,7]=>110110
[3,2,1,6,5,7,4]=>110101
[3,2,1,6,7,4,5]=>110010
[3,2,1,6,7,5,4]=>110011
[3,2,1,7,4,5,6]=>110100
[3,2,1,7,4,6,5]=>110101
[3,2,1,7,5,4,6]=>110110
[3,2,1,7,5,6,4]=>110101
[3,2,1,7,6,4,5]=>110110
[3,2,1,7,6,5,4]=>110111
[3,2,4,1,5,6,7]=>101000
[3,2,4,1,5,7,6]=>101001
[3,2,4,1,6,5,7]=>101010
[3,2,4,1,6,7,5]=>101001
[3,2,4,1,7,5,6]=>101010
[3,2,4,1,7,6,5]=>101011
[3,2,4,5,1,6,7]=>100100
[3,2,4,5,1,7,6]=>100101
[3,2,4,5,6,1,7]=>100010
[3,2,4,5,6,7,1]=>100001
[3,2,4,5,7,1,6]=>100010
[3,2,4,5,7,6,1]=>100011
[3,2,4,6,1,5,7]=>100100
[3,2,4,6,1,7,5]=>100101
[3,2,4,6,5,1,7]=>100110
[3,2,4,6,5,7,1]=>100101
[3,2,4,6,7,1,5]=>100010
[3,2,4,6,7,5,1]=>100011
[3,2,4,7,1,5,6]=>100100
[3,2,4,7,1,6,5]=>100101
[3,2,4,7,5,1,6]=>100110
[3,2,4,7,5,6,1]=>100101
[3,2,4,7,6,1,5]=>100110
[3,2,4,7,6,5,1]=>100111
[3,2,5,1,4,6,7]=>101000
[3,2,5,1,4,7,6]=>101001
[3,2,5,1,6,4,7]=>101010
[3,2,5,1,6,7,4]=>101001
[3,2,5,1,7,4,6]=>101010
[3,2,5,1,7,6,4]=>101011
[3,2,5,4,1,6,7]=>101100
[3,2,5,4,1,7,6]=>101101
[3,2,5,4,6,1,7]=>101010
[3,2,5,4,6,7,1]=>101001
[3,2,5,4,7,1,6]=>101010
[3,2,5,4,7,6,1]=>101011
[3,2,5,6,1,4,7]=>100100
[3,2,5,6,1,7,4]=>100101
[3,2,5,6,4,1,7]=>100110
[3,2,5,6,4,7,1]=>100101
[3,2,5,6,7,1,4]=>100010
[3,2,5,6,7,4,1]=>100011
[3,2,5,7,1,4,6]=>100100
[3,2,5,7,1,6,4]=>100101
[3,2,5,7,4,1,6]=>100110
[3,2,5,7,4,6,1]=>100101
[3,2,5,7,6,1,4]=>100110
[3,2,5,7,6,4,1]=>100111
[3,2,6,1,4,5,7]=>101000
[3,2,6,1,4,7,5]=>101001
[3,2,6,1,5,4,7]=>101010
[3,2,6,1,5,7,4]=>101001
[3,2,6,1,7,4,5]=>101010
[3,2,6,1,7,5,4]=>101011
[3,2,6,4,1,5,7]=>101100
[3,2,6,4,1,7,5]=>101101
[3,2,6,4,5,1,7]=>101010
[3,2,6,4,5,7,1]=>101001
[3,2,6,4,7,1,5]=>101010
[3,2,6,4,7,5,1]=>101011
[3,2,6,5,1,4,7]=>101100
[3,2,6,5,1,7,4]=>101101
[3,2,6,5,4,1,7]=>101110
[3,2,6,5,4,7,1]=>101101
[3,2,6,5,7,1,4]=>101010
[3,2,6,5,7,4,1]=>101011
[3,2,6,7,1,4,5]=>100100
[3,2,6,7,1,5,4]=>100101
[3,2,6,7,4,1,5]=>100110
[3,2,6,7,4,5,1]=>100101
[3,2,6,7,5,1,4]=>100110
[3,2,6,7,5,4,1]=>100111
[3,2,7,1,4,5,6]=>101000
[3,2,7,1,4,6,5]=>101001
[3,2,7,1,5,4,6]=>101010
[3,2,7,1,5,6,4]=>101001
[3,2,7,1,6,4,5]=>101010
[3,2,7,1,6,5,4]=>101011
[3,2,7,4,1,5,6]=>101100
[3,2,7,4,1,6,5]=>101101
[3,2,7,4,5,1,6]=>101010
[3,2,7,4,5,6,1]=>101001
[3,2,7,4,6,1,5]=>101010
[3,2,7,4,6,5,1]=>101011
[3,2,7,5,1,4,6]=>101100
[3,2,7,5,1,6,4]=>101101
[3,2,7,5,4,1,6]=>101110
[3,2,7,5,4,6,1]=>101101
[3,2,7,5,6,1,4]=>101010
[3,2,7,5,6,4,1]=>101011
[3,2,7,6,1,4,5]=>101100
[3,2,7,6,1,5,4]=>101101
[3,2,7,6,4,1,5]=>101110
[3,2,7,6,4,5,1]=>101101
[3,2,7,6,5,1,4]=>101110
[3,2,7,6,5,4,1]=>101111
[3,4,1,2,5,6,7]=>010000
[3,4,1,2,5,7,6]=>010001
[3,4,1,2,6,5,7]=>010010
[3,4,1,2,6,7,5]=>010001
[3,4,1,2,7,5,6]=>010010
[3,4,1,2,7,6,5]=>010011
[3,4,1,5,2,6,7]=>010100
[3,4,1,5,2,7,6]=>010101
[3,4,1,5,6,2,7]=>010010
[3,4,1,5,6,7,2]=>010001
[3,4,1,5,7,2,6]=>010010
[3,4,1,5,7,6,2]=>010011
[3,4,1,6,2,5,7]=>010100
[3,4,1,6,2,7,5]=>010101
[3,4,1,6,5,2,7]=>010110
[3,4,1,6,5,7,2]=>010101
[3,4,1,6,7,2,5]=>010010
[3,4,1,6,7,5,2]=>010011
[3,4,1,7,2,5,6]=>010100
[3,4,1,7,2,6,5]=>010101
[3,4,1,7,5,2,6]=>010110
[3,4,1,7,5,6,2]=>010101
[3,4,1,7,6,2,5]=>010110
[3,4,1,7,6,5,2]=>010111
[3,4,2,1,5,6,7]=>011000
[3,4,2,1,5,7,6]=>011001
[3,4,2,1,6,5,7]=>011010
[3,4,2,1,6,7,5]=>011001
[3,4,2,1,7,5,6]=>011010
[3,4,2,1,7,6,5]=>011011
[3,4,2,5,1,6,7]=>010100
[3,4,2,5,1,7,6]=>010101
[3,4,2,5,6,1,7]=>010010
[3,4,2,5,6,7,1]=>010001
[3,4,2,5,7,1,6]=>010010
[3,4,2,5,7,6,1]=>010011
[3,4,2,6,1,5,7]=>010100
[3,4,2,6,1,7,5]=>010101
[3,4,2,6,5,1,7]=>010110
[3,4,2,6,5,7,1]=>010101
[3,4,2,6,7,1,5]=>010010
[3,4,2,6,7,5,1]=>010011
[3,4,2,7,1,5,6]=>010100
[3,4,2,7,1,6,5]=>010101
[3,4,2,7,5,1,6]=>010110
[3,4,2,7,5,6,1]=>010101
[3,4,2,7,6,1,5]=>010110
[3,4,2,7,6,5,1]=>010111
[3,4,5,1,2,6,7]=>001000
[3,4,5,1,2,7,6]=>001001
[3,4,5,1,6,2,7]=>001010
[3,4,5,1,6,7,2]=>001001
[3,4,5,1,7,2,6]=>001010
[3,4,5,1,7,6,2]=>001011
[3,4,5,2,1,6,7]=>001100
[3,4,5,2,1,7,6]=>001101
[3,4,5,2,6,1,7]=>001010
[3,4,5,2,6,7,1]=>001001
[3,4,5,2,7,1,6]=>001010
[3,4,5,2,7,6,1]=>001011
[3,4,5,6,1,2,7]=>000100
[3,4,5,6,1,7,2]=>000101
[3,4,5,6,2,1,7]=>000110
[3,4,5,6,2,7,1]=>000101
[3,4,5,6,7,1,2]=>000010
[3,4,5,6,7,2,1]=>000011
[3,4,5,7,1,2,6]=>000100
[3,4,5,7,1,6,2]=>000101
[3,4,5,7,2,1,6]=>000110
[3,4,5,7,2,6,1]=>000101
[3,4,5,7,6,1,2]=>000110
[3,4,5,7,6,2,1]=>000111
[3,4,6,1,2,5,7]=>001000
[3,4,6,1,2,7,5]=>001001
[3,4,6,1,5,2,7]=>001010
[3,4,6,1,5,7,2]=>001001
[3,4,6,1,7,2,5]=>001010
[3,4,6,1,7,5,2]=>001011
[3,4,6,2,1,5,7]=>001100
[3,4,6,2,1,7,5]=>001101
[3,4,6,2,5,1,7]=>001010
[3,4,6,2,5,7,1]=>001001
[3,4,6,2,7,1,5]=>001010
[3,4,6,2,7,5,1]=>001011
[3,4,6,5,1,2,7]=>001100
[3,4,6,5,1,7,2]=>001101
[3,4,6,5,2,1,7]=>001110
[3,4,6,5,2,7,1]=>001101
[3,4,6,5,7,1,2]=>001010
[3,4,6,5,7,2,1]=>001011
[3,4,6,7,1,2,5]=>000100
[3,4,6,7,1,5,2]=>000101
[3,4,6,7,2,1,5]=>000110
[3,4,6,7,2,5,1]=>000101
[3,4,6,7,5,1,2]=>000110
[3,4,6,7,5,2,1]=>000111
[3,4,7,1,2,5,6]=>001000
[3,4,7,1,2,6,5]=>001001
[3,4,7,1,5,2,6]=>001010
[3,4,7,1,5,6,2]=>001001
[3,4,7,1,6,2,5]=>001010
[3,4,7,1,6,5,2]=>001011
[3,4,7,2,1,5,6]=>001100
[3,4,7,2,1,6,5]=>001101
[3,4,7,2,5,1,6]=>001010
[3,4,7,2,5,6,1]=>001001
[3,4,7,2,6,1,5]=>001010
[3,4,7,2,6,5,1]=>001011
[3,4,7,5,1,2,6]=>001100
[3,4,7,5,1,6,2]=>001101
[3,4,7,5,2,1,6]=>001110
[3,4,7,5,2,6,1]=>001101
[3,4,7,5,6,1,2]=>001010
[3,4,7,5,6,2,1]=>001011
[3,4,7,6,1,2,5]=>001100
[3,4,7,6,1,5,2]=>001101
[3,4,7,6,2,1,5]=>001110
[3,4,7,6,2,5,1]=>001101
[3,4,7,6,5,1,2]=>001110
[3,4,7,6,5,2,1]=>001111
[3,5,1,2,4,6,7]=>010000
[3,5,1,2,4,7,6]=>010001
[3,5,1,2,6,4,7]=>010010
[3,5,1,2,6,7,4]=>010001
[3,5,1,2,7,4,6]=>010010
[3,5,1,2,7,6,4]=>010011
[3,5,1,4,2,6,7]=>010100
[3,5,1,4,2,7,6]=>010101
[3,5,1,4,6,2,7]=>010010
[3,5,1,4,6,7,2]=>010001
[3,5,1,4,7,2,6]=>010010
[3,5,1,4,7,6,2]=>010011
[3,5,1,6,2,4,7]=>010100
[3,5,1,6,2,7,4]=>010101
[3,5,1,6,4,2,7]=>010110
[3,5,1,6,4,7,2]=>010101
[3,5,1,6,7,2,4]=>010010
[3,5,1,6,7,4,2]=>010011
[3,5,1,7,2,4,6]=>010100
[3,5,1,7,2,6,4]=>010101
[3,5,1,7,4,2,6]=>010110
[3,5,1,7,4,6,2]=>010101
[3,5,1,7,6,2,4]=>010110
[3,5,1,7,6,4,2]=>010111
[3,5,2,1,4,6,7]=>011000
[3,5,2,1,4,7,6]=>011001
[3,5,2,1,6,4,7]=>011010
[3,5,2,1,6,7,4]=>011001
[3,5,2,1,7,4,6]=>011010
[3,5,2,1,7,6,4]=>011011
[3,5,2,4,1,6,7]=>010100
[3,5,2,4,1,7,6]=>010101
[3,5,2,4,6,1,7]=>010010
[3,5,2,4,6,7,1]=>010001
[3,5,2,4,7,1,6]=>010010
[3,5,2,4,7,6,1]=>010011
[3,5,2,6,1,4,7]=>010100
[3,5,2,6,1,7,4]=>010101
[3,5,2,6,4,1,7]=>010110
[3,5,2,6,4,7,1]=>010101
[3,5,2,6,7,1,4]=>010010
[3,5,2,6,7,4,1]=>010011
[3,5,2,7,1,4,6]=>010100
[3,5,2,7,1,6,4]=>010101
[3,5,2,7,4,1,6]=>010110
[3,5,2,7,4,6,1]=>010101
[3,5,2,7,6,1,4]=>010110
[3,5,2,7,6,4,1]=>010111
[3,5,4,1,2,6,7]=>011000
[3,5,4,1,2,7,6]=>011001
[3,5,4,1,6,2,7]=>011010
[3,5,4,1,6,7,2]=>011001
[3,5,4,1,7,2,6]=>011010
[3,5,4,1,7,6,2]=>011011
[3,5,4,2,1,6,7]=>011100
[3,5,4,2,1,7,6]=>011101
[3,5,4,2,6,1,7]=>011010
[3,5,4,2,6,7,1]=>011001
[3,5,4,2,7,1,6]=>011010
[3,5,4,2,7,6,1]=>011011
[3,5,4,6,1,2,7]=>010100
[3,5,4,6,1,7,2]=>010101
[3,5,4,6,2,1,7]=>010110
[3,5,4,6,2,7,1]=>010101
[3,5,4,6,7,1,2]=>010010
[3,5,4,6,7,2,1]=>010011
[3,5,4,7,1,2,6]=>010100
[3,5,4,7,1,6,2]=>010101
[3,5,4,7,2,1,6]=>010110
[3,5,4,7,2,6,1]=>010101
[3,5,4,7,6,1,2]=>010110
[3,5,4,7,6,2,1]=>010111
[3,5,6,1,2,4,7]=>001000
[3,5,6,1,2,7,4]=>001001
[3,5,6,1,4,2,7]=>001010
[3,5,6,1,4,7,2]=>001001
[3,5,6,1,7,2,4]=>001010
[3,5,6,1,7,4,2]=>001011
[3,5,6,2,1,4,7]=>001100
[3,5,6,2,1,7,4]=>001101
[3,5,6,2,4,1,7]=>001010
[3,5,6,2,4,7,1]=>001001
[3,5,6,2,7,1,4]=>001010
[3,5,6,2,7,4,1]=>001011
[3,5,6,4,1,2,7]=>001100
[3,5,6,4,1,7,2]=>001101
[3,5,6,4,2,1,7]=>001110
[3,5,6,4,2,7,1]=>001101
[3,5,6,4,7,1,2]=>001010
[3,5,6,4,7,2,1]=>001011
[3,5,6,7,1,2,4]=>000100
[3,5,6,7,1,4,2]=>000101
[3,5,6,7,2,1,4]=>000110
[3,5,6,7,2,4,1]=>000101
[3,5,6,7,4,1,2]=>000110
[3,5,6,7,4,2,1]=>000111
[3,5,7,1,2,4,6]=>001000
[3,5,7,1,2,6,4]=>001001
[3,5,7,1,4,2,6]=>001010
[3,5,7,1,4,6,2]=>001001
[3,5,7,1,6,2,4]=>001010
[3,5,7,1,6,4,2]=>001011
[3,5,7,2,1,4,6]=>001100
[3,5,7,2,1,6,4]=>001101
[3,5,7,2,4,1,6]=>001010
[3,5,7,2,4,6,1]=>001001
[3,5,7,2,6,1,4]=>001010
[3,5,7,2,6,4,1]=>001011
[3,5,7,4,1,2,6]=>001100
[3,5,7,4,1,6,2]=>001101
[3,5,7,4,2,1,6]=>001110
[3,5,7,4,2,6,1]=>001101
[3,5,7,4,6,1,2]=>001010
[3,5,7,4,6,2,1]=>001011
[3,5,7,6,1,2,4]=>001100
[3,5,7,6,1,4,2]=>001101
[3,5,7,6,2,1,4]=>001110
[3,5,7,6,2,4,1]=>001101
[3,5,7,6,4,1,2]=>001110
[3,5,7,6,4,2,1]=>001111
[3,6,1,2,4,5,7]=>010000
[3,6,1,2,4,7,5]=>010001
[3,6,1,2,5,4,7]=>010010
[3,6,1,2,5,7,4]=>010001
[3,6,1,2,7,4,5]=>010010
[3,6,1,2,7,5,4]=>010011
[3,6,1,4,2,5,7]=>010100
[3,6,1,4,2,7,5]=>010101
[3,6,1,4,5,2,7]=>010010
[3,6,1,4,5,7,2]=>010001
[3,6,1,4,7,2,5]=>010010
[3,6,1,4,7,5,2]=>010011
[3,6,1,5,2,4,7]=>010100
[3,6,1,5,2,7,4]=>010101
[3,6,1,5,4,2,7]=>010110
[3,6,1,5,4,7,2]=>010101
[3,6,1,5,7,2,4]=>010010
[3,6,1,5,7,4,2]=>010011
[3,6,1,7,2,4,5]=>010100
[3,6,1,7,2,5,4]=>010101
[3,6,1,7,4,2,5]=>010110
[3,6,1,7,4,5,2]=>010101
[3,6,1,7,5,2,4]=>010110
[3,6,1,7,5,4,2]=>010111
[3,6,2,1,4,5,7]=>011000
[3,6,2,1,4,7,5]=>011001
[3,6,2,1,5,4,7]=>011010
[3,6,2,1,5,7,4]=>011001
[3,6,2,1,7,4,5]=>011010
[3,6,2,1,7,5,4]=>011011
[3,6,2,4,1,5,7]=>010100
[3,6,2,4,1,7,5]=>010101
[3,6,2,4,5,1,7]=>010010
[3,6,2,4,5,7,1]=>010001
[3,6,2,4,7,1,5]=>010010
[3,6,2,4,7,5,1]=>010011
[3,6,2,5,1,4,7]=>010100
[3,6,2,5,1,7,4]=>010101
[3,6,2,5,4,1,7]=>010110
[3,6,2,5,4,7,1]=>010101
[3,6,2,5,7,1,4]=>010010
[3,6,2,5,7,4,1]=>010011
[3,6,2,7,1,4,5]=>010100
[3,6,2,7,1,5,4]=>010101
[3,6,2,7,4,1,5]=>010110
[3,6,2,7,4,5,1]=>010101
[3,6,2,7,5,1,4]=>010110
[3,6,2,7,5,4,1]=>010111
[3,6,4,1,2,5,7]=>011000
[3,6,4,1,2,7,5]=>011001
[3,6,4,1,5,2,7]=>011010
[3,6,4,1,5,7,2]=>011001
[3,6,4,1,7,2,5]=>011010
[3,6,4,1,7,5,2]=>011011
[3,6,4,2,1,5,7]=>011100
[3,6,4,2,1,7,5]=>011101
[3,6,4,2,5,1,7]=>011010
[3,6,4,2,5,7,1]=>011001
[3,6,4,2,7,1,5]=>011010
[3,6,4,2,7,5,1]=>011011
[3,6,4,5,1,2,7]=>010100
[3,6,4,5,1,7,2]=>010101
[3,6,4,5,2,1,7]=>010110
[3,6,4,5,2,7,1]=>010101
[3,6,4,5,7,1,2]=>010010
[3,6,4,5,7,2,1]=>010011
[3,6,4,7,1,2,5]=>010100
[3,6,4,7,1,5,2]=>010101
[3,6,4,7,2,1,5]=>010110
[3,6,4,7,2,5,1]=>010101
[3,6,4,7,5,1,2]=>010110
[3,6,4,7,5,2,1]=>010111
[3,6,5,1,2,4,7]=>011000
[3,6,5,1,2,7,4]=>011001
[3,6,5,1,4,2,7]=>011010
[3,6,5,1,4,7,2]=>011001
[3,6,5,1,7,2,4]=>011010
[3,6,5,1,7,4,2]=>011011
[3,6,5,2,1,4,7]=>011100
[3,6,5,2,1,7,4]=>011101
[3,6,5,2,4,1,7]=>011010
[3,6,5,2,4,7,1]=>011001
[3,6,5,2,7,1,4]=>011010
[3,6,5,2,7,4,1]=>011011
[3,6,5,4,1,2,7]=>011100
[3,6,5,4,1,7,2]=>011101
[3,6,5,4,2,1,7]=>011110
[3,6,5,4,2,7,1]=>011101
[3,6,5,4,7,1,2]=>011010
[3,6,5,4,7,2,1]=>011011
[3,6,5,7,1,2,4]=>010100
[3,6,5,7,1,4,2]=>010101
[3,6,5,7,2,1,4]=>010110
[3,6,5,7,2,4,1]=>010101
[3,6,5,7,4,1,2]=>010110
[3,6,5,7,4,2,1]=>010111
[3,6,7,1,2,4,5]=>001000
[3,6,7,1,2,5,4]=>001001
[3,6,7,1,4,2,5]=>001010
[3,6,7,1,4,5,2]=>001001
[3,6,7,1,5,2,4]=>001010
[3,6,7,1,5,4,2]=>001011
[3,6,7,2,1,4,5]=>001100
[3,6,7,2,1,5,4]=>001101
[3,6,7,2,4,1,5]=>001010
[3,6,7,2,4,5,1]=>001001
[3,6,7,2,5,1,4]=>001010
[3,6,7,2,5,4,1]=>001011
[3,6,7,4,1,2,5]=>001100
[3,6,7,4,1,5,2]=>001101
[3,6,7,4,2,1,5]=>001110
[3,6,7,4,2,5,1]=>001101
[3,6,7,4,5,1,2]=>001010
[3,6,7,4,5,2,1]=>001011
[3,6,7,5,1,2,4]=>001100
[3,6,7,5,1,4,2]=>001101
[3,6,7,5,2,1,4]=>001110
[3,6,7,5,2,4,1]=>001101
[3,6,7,5,4,1,2]=>001110
[3,6,7,5,4,2,1]=>001111
[3,7,1,2,4,5,6]=>010000
[3,7,1,2,4,6,5]=>010001
[3,7,1,2,5,4,6]=>010010
[3,7,1,2,5,6,4]=>010001
[3,7,1,2,6,4,5]=>010010
[3,7,1,2,6,5,4]=>010011
[3,7,1,4,2,5,6]=>010100
[3,7,1,4,2,6,5]=>010101
[3,7,1,4,5,2,6]=>010010
[3,7,1,4,5,6,2]=>010001
[3,7,1,4,6,2,5]=>010010
[3,7,1,4,6,5,2]=>010011
[3,7,1,5,2,4,6]=>010100
[3,7,1,5,2,6,4]=>010101
[3,7,1,5,4,2,6]=>010110
[3,7,1,5,4,6,2]=>010101
[3,7,1,5,6,2,4]=>010010
[3,7,1,5,6,4,2]=>010011
[3,7,1,6,2,4,5]=>010100
[3,7,1,6,2,5,4]=>010101
[3,7,1,6,4,2,5]=>010110
[3,7,1,6,4,5,2]=>010101
[3,7,1,6,5,2,4]=>010110
[3,7,1,6,5,4,2]=>010111
[3,7,2,1,4,5,6]=>011000
[3,7,2,1,4,6,5]=>011001
[3,7,2,1,5,4,6]=>011010
[3,7,2,1,5,6,4]=>011001
[3,7,2,1,6,4,5]=>011010
[3,7,2,1,6,5,4]=>011011
[3,7,2,4,1,5,6]=>010100
[3,7,2,4,1,6,5]=>010101
[3,7,2,4,5,1,6]=>010010
[3,7,2,4,5,6,1]=>010001
[3,7,2,4,6,1,5]=>010010
[3,7,2,4,6,5,1]=>010011
[3,7,2,5,1,4,6]=>010100
[3,7,2,5,1,6,4]=>010101
[3,7,2,5,4,1,6]=>010110
[3,7,2,5,4,6,1]=>010101
[3,7,2,5,6,1,4]=>010010
[3,7,2,5,6,4,1]=>010011
[3,7,2,6,1,4,5]=>010100
[3,7,2,6,1,5,4]=>010101
[3,7,2,6,4,1,5]=>010110
[3,7,2,6,4,5,1]=>010101
[3,7,2,6,5,1,4]=>010110
[3,7,2,6,5,4,1]=>010111
[3,7,4,1,2,5,6]=>011000
[3,7,4,1,2,6,5]=>011001
[3,7,4,1,5,2,6]=>011010
[3,7,4,1,5,6,2]=>011001
[3,7,4,1,6,2,5]=>011010
[3,7,4,1,6,5,2]=>011011
[3,7,4,2,1,5,6]=>011100
[3,7,4,2,1,6,5]=>011101
[3,7,4,2,5,1,6]=>011010
[3,7,4,2,5,6,1]=>011001
[3,7,4,2,6,1,5]=>011010
[3,7,4,2,6,5,1]=>011011
[3,7,4,5,1,2,6]=>010100
[3,7,4,5,1,6,2]=>010101
[3,7,4,5,2,1,6]=>010110
[3,7,4,5,2,6,1]=>010101
[3,7,4,5,6,1,2]=>010010
[3,7,4,5,6,2,1]=>010011
[3,7,4,6,1,2,5]=>010100
[3,7,4,6,1,5,2]=>010101
[3,7,4,6,2,1,5]=>010110
[3,7,4,6,2,5,1]=>010101
[3,7,4,6,5,1,2]=>010110
[3,7,4,6,5,2,1]=>010111
[3,7,5,1,2,4,6]=>011000
[3,7,5,1,2,6,4]=>011001
[3,7,5,1,4,2,6]=>011010
[3,7,5,1,4,6,2]=>011001
[3,7,5,1,6,2,4]=>011010
[3,7,5,1,6,4,2]=>011011
[3,7,5,2,1,4,6]=>011100
[3,7,5,2,1,6,4]=>011101
[3,7,5,2,4,1,6]=>011010
[3,7,5,2,4,6,1]=>011001
[3,7,5,2,6,1,4]=>011010
[3,7,5,2,6,4,1]=>011011
[3,7,5,4,1,2,6]=>011100
[3,7,5,4,1,6,2]=>011101
[3,7,5,4,2,1,6]=>011110
[3,7,5,4,2,6,1]=>011101
[3,7,5,4,6,1,2]=>011010
[3,7,5,4,6,2,1]=>011011
[3,7,5,6,1,2,4]=>010100
[3,7,5,6,1,4,2]=>010101
[3,7,5,6,2,1,4]=>010110
[3,7,5,6,2,4,1]=>010101
[3,7,5,6,4,1,2]=>010110
[3,7,5,6,4,2,1]=>010111
[3,7,6,1,2,4,5]=>011000
[3,7,6,1,2,5,4]=>011001
[3,7,6,1,4,2,5]=>011010
[3,7,6,1,4,5,2]=>011001
[3,7,6,1,5,2,4]=>011010
[3,7,6,1,5,4,2]=>011011
[3,7,6,2,1,4,5]=>011100
[3,7,6,2,1,5,4]=>011101
[3,7,6,2,4,1,5]=>011010
[3,7,6,2,4,5,1]=>011001
[3,7,6,2,5,1,4]=>011010
[3,7,6,2,5,4,1]=>011011
[3,7,6,4,1,2,5]=>011100
[3,7,6,4,1,5,2]=>011101
[3,7,6,4,2,1,5]=>011110
[3,7,6,4,2,5,1]=>011101
[3,7,6,4,5,1,2]=>011010
[3,7,6,4,5,2,1]=>011011
[3,7,6,5,1,2,4]=>011100
[3,7,6,5,1,4,2]=>011101
[3,7,6,5,2,1,4]=>011110
[3,7,6,5,2,4,1]=>011101
[3,7,6,5,4,1,2]=>011110
[3,7,6,5,4,2,1]=>011111
[4,1,2,3,5,6,7]=>100000
[4,1,2,3,5,7,6]=>100001
[4,1,2,3,6,5,7]=>100010
[4,1,2,3,6,7,5]=>100001
[4,1,2,3,7,5,6]=>100010
[4,1,2,3,7,6,5]=>100011
[4,1,2,5,3,6,7]=>100100
[4,1,2,5,3,7,6]=>100101
[4,1,2,5,6,3,7]=>100010
[4,1,2,5,6,7,3]=>100001
[4,1,2,5,7,3,6]=>100010
[4,1,2,5,7,6,3]=>100011
[4,1,2,6,3,5,7]=>100100
[4,1,2,6,3,7,5]=>100101
[4,1,2,6,5,3,7]=>100110
[4,1,2,6,5,7,3]=>100101
[4,1,2,6,7,3,5]=>100010
[4,1,2,6,7,5,3]=>100011
[4,1,2,7,3,5,6]=>100100
[4,1,2,7,3,6,5]=>100101
[4,1,2,7,5,3,6]=>100110
[4,1,2,7,5,6,3]=>100101
[4,1,2,7,6,3,5]=>100110
[4,1,2,7,6,5,3]=>100111
[4,1,3,2,5,6,7]=>101000
[4,1,3,2,5,7,6]=>101001
[4,1,3,2,6,5,7]=>101010
[4,1,3,2,6,7,5]=>101001
[4,1,3,2,7,5,6]=>101010
[4,1,3,2,7,6,5]=>101011
[4,1,3,5,2,6,7]=>100100
[4,1,3,5,2,7,6]=>100101
[4,1,3,5,6,2,7]=>100010
[4,1,3,5,6,7,2]=>100001
[4,1,3,5,7,2,6]=>100010
[4,1,3,5,7,6,2]=>100011
[4,1,3,6,2,5,7]=>100100
[4,1,3,6,2,7,5]=>100101
[4,1,3,6,5,2,7]=>100110
[4,1,3,6,5,7,2]=>100101
[4,1,3,6,7,2,5]=>100010
[4,1,3,6,7,5,2]=>100011
[4,1,3,7,2,5,6]=>100100
[4,1,3,7,2,6,5]=>100101
[4,1,3,7,5,2,6]=>100110
[4,1,3,7,5,6,2]=>100101
[4,1,3,7,6,2,5]=>100110
[4,1,3,7,6,5,2]=>100111
[4,1,5,2,3,6,7]=>101000
[4,1,5,2,3,7,6]=>101001
[4,1,5,2,6,3,7]=>101010
[4,1,5,2,6,7,3]=>101001
[4,1,5,2,7,3,6]=>101010
[4,1,5,2,7,6,3]=>101011
[4,1,5,3,2,6,7]=>101100
[4,1,5,3,2,7,6]=>101101
[4,1,5,3,6,2,7]=>101010
[4,1,5,3,6,7,2]=>101001
[4,1,5,3,7,2,6]=>101010
[4,1,5,3,7,6,2]=>101011
[4,1,5,6,2,3,7]=>100100
[4,1,5,6,2,7,3]=>100101
[4,1,5,6,3,2,7]=>100110
[4,1,5,6,3,7,2]=>100101
[4,1,5,6,7,2,3]=>100010
[4,1,5,6,7,3,2]=>100011
[4,1,5,7,2,3,6]=>100100
[4,1,5,7,2,6,3]=>100101
[4,1,5,7,3,2,6]=>100110
[4,1,5,7,3,6,2]=>100101
[4,1,5,7,6,2,3]=>100110
[4,1,5,7,6,3,2]=>100111
[4,1,6,2,3,5,7]=>101000
[4,1,6,2,3,7,5]=>101001
[4,1,6,2,5,3,7]=>101010
[4,1,6,2,5,7,3]=>101001
[4,1,6,2,7,3,5]=>101010
[4,1,6,2,7,5,3]=>101011
[4,1,6,3,2,5,7]=>101100
[4,1,6,3,2,7,5]=>101101
[4,1,6,3,5,2,7]=>101010
[4,1,6,3,5,7,2]=>101001
[4,1,6,3,7,2,5]=>101010
[4,1,6,3,7,5,2]=>101011
[4,1,6,5,2,3,7]=>101100
[4,1,6,5,2,7,3]=>101101
[4,1,6,5,3,2,7]=>101110
[4,1,6,5,3,7,2]=>101101
[4,1,6,5,7,2,3]=>101010
[4,1,6,5,7,3,2]=>101011
[4,1,6,7,2,3,5]=>100100
[4,1,6,7,2,5,3]=>100101
[4,1,6,7,3,2,5]=>100110
[4,1,6,7,3,5,2]=>100101
[4,1,6,7,5,2,3]=>100110
[4,1,6,7,5,3,2]=>100111
[4,1,7,2,3,5,6]=>101000
[4,1,7,2,3,6,5]=>101001
[4,1,7,2,5,3,6]=>101010
[4,1,7,2,5,6,3]=>101001
[4,1,7,2,6,3,5]=>101010
[4,1,7,2,6,5,3]=>101011
[4,1,7,3,2,5,6]=>101100
[4,1,7,3,2,6,5]=>101101
[4,1,7,3,5,2,6]=>101010
[4,1,7,3,5,6,2]=>101001
[4,1,7,3,6,2,5]=>101010
[4,1,7,3,6,5,2]=>101011
[4,1,7,5,2,3,6]=>101100
[4,1,7,5,2,6,3]=>101101
[4,1,7,5,3,2,6]=>101110
[4,1,7,5,3,6,2]=>101101
[4,1,7,5,6,2,3]=>101010
[4,1,7,5,6,3,2]=>101011
[4,1,7,6,2,3,5]=>101100
[4,1,7,6,2,5,3]=>101101
[4,1,7,6,3,2,5]=>101110
[4,1,7,6,3,5,2]=>101101
[4,1,7,6,5,2,3]=>101110
[4,1,7,6,5,3,2]=>101111
[4,2,1,3,5,6,7]=>110000
[4,2,1,3,5,7,6]=>110001
[4,2,1,3,6,5,7]=>110010
[4,2,1,3,6,7,5]=>110001
[4,2,1,3,7,5,6]=>110010
[4,2,1,3,7,6,5]=>110011
[4,2,1,5,3,6,7]=>110100
[4,2,1,5,3,7,6]=>110101
[4,2,1,5,6,3,7]=>110010
[4,2,1,5,6,7,3]=>110001
[4,2,1,5,7,3,6]=>110010
[4,2,1,5,7,6,3]=>110011
[4,2,1,6,3,5,7]=>110100
[4,2,1,6,3,7,5]=>110101
[4,2,1,6,5,3,7]=>110110
[4,2,1,6,5,7,3]=>110101
[4,2,1,6,7,3,5]=>110010
[4,2,1,6,7,5,3]=>110011
[4,2,1,7,3,5,6]=>110100
[4,2,1,7,3,6,5]=>110101
[4,2,1,7,5,3,6]=>110110
[4,2,1,7,5,6,3]=>110101
[4,2,1,7,6,3,5]=>110110
[4,2,1,7,6,5,3]=>110111
[4,2,3,1,5,6,7]=>101000
[4,2,3,1,5,7,6]=>101001
[4,2,3,1,6,5,7]=>101010
[4,2,3,1,6,7,5]=>101001
[4,2,3,1,7,5,6]=>101010
[4,2,3,1,7,6,5]=>101011
[4,2,3,5,1,6,7]=>100100
[4,2,3,5,1,7,6]=>100101
[4,2,3,5,6,1,7]=>100010
[4,2,3,5,6,7,1]=>100001
[4,2,3,5,7,1,6]=>100010
[4,2,3,5,7,6,1]=>100011
[4,2,3,6,1,5,7]=>100100
[4,2,3,6,1,7,5]=>100101
[4,2,3,6,5,1,7]=>100110
[4,2,3,6,5,7,1]=>100101
[4,2,3,6,7,1,5]=>100010
[4,2,3,6,7,5,1]=>100011
[4,2,3,7,1,5,6]=>100100
[4,2,3,7,1,6,5]=>100101
[4,2,3,7,5,1,6]=>100110
[4,2,3,7,5,6,1]=>100101
[4,2,3,7,6,1,5]=>100110
[4,2,3,7,6,5,1]=>100111
[4,2,5,1,3,6,7]=>101000
[4,2,5,1,3,7,6]=>101001
[4,2,5,1,6,3,7]=>101010
[4,2,5,1,6,7,3]=>101001
[4,2,5,1,7,3,6]=>101010
[4,2,5,1,7,6,3]=>101011
[4,2,5,3,1,6,7]=>101100
[4,2,5,3,1,7,6]=>101101
[4,2,5,3,6,1,7]=>101010
[4,2,5,3,6,7,1]=>101001
[4,2,5,3,7,1,6]=>101010
[4,2,5,3,7,6,1]=>101011
[4,2,5,6,1,3,7]=>100100
[4,2,5,6,1,7,3]=>100101
[4,2,5,6,3,1,7]=>100110
[4,2,5,6,3,7,1]=>100101
[4,2,5,6,7,1,3]=>100010
[4,2,5,6,7,3,1]=>100011
[4,2,5,7,1,3,6]=>100100
[4,2,5,7,1,6,3]=>100101
[4,2,5,7,3,1,6]=>100110
[4,2,5,7,3,6,1]=>100101
[4,2,5,7,6,1,3]=>100110
[4,2,5,7,6,3,1]=>100111
[4,2,6,1,3,5,7]=>101000
[4,2,6,1,3,7,5]=>101001
[4,2,6,1,5,3,7]=>101010
[4,2,6,1,5,7,3]=>101001
[4,2,6,1,7,3,5]=>101010
[4,2,6,1,7,5,3]=>101011
[4,2,6,3,1,5,7]=>101100
[4,2,6,3,1,7,5]=>101101
[4,2,6,3,5,1,7]=>101010
[4,2,6,3,5,7,1]=>101001
[4,2,6,3,7,1,5]=>101010
[4,2,6,3,7,5,1]=>101011
[4,2,6,5,1,3,7]=>101100
[4,2,6,5,1,7,3]=>101101
[4,2,6,5,3,1,7]=>101110
[4,2,6,5,3,7,1]=>101101
[4,2,6,5,7,1,3]=>101010
[4,2,6,5,7,3,1]=>101011
[4,2,6,7,1,3,5]=>100100
[4,2,6,7,1,5,3]=>100101
[4,2,6,7,3,1,5]=>100110
[4,2,6,7,3,5,1]=>100101
[4,2,6,7,5,1,3]=>100110
[4,2,6,7,5,3,1]=>100111
[4,2,7,1,3,5,6]=>101000
[4,2,7,1,3,6,5]=>101001
[4,2,7,1,5,3,6]=>101010
[4,2,7,1,5,6,3]=>101001
[4,2,7,1,6,3,5]=>101010
[4,2,7,1,6,5,3]=>101011
[4,2,7,3,1,5,6]=>101100
[4,2,7,3,1,6,5]=>101101
[4,2,7,3,5,1,6]=>101010
[4,2,7,3,5,6,1]=>101001
[4,2,7,3,6,1,5]=>101010
[4,2,7,3,6,5,1]=>101011
[4,2,7,5,1,3,6]=>101100
[4,2,7,5,1,6,3]=>101101
[4,2,7,5,3,1,6]=>101110
[4,2,7,5,3,6,1]=>101101
[4,2,7,5,6,1,3]=>101010
[4,2,7,5,6,3,1]=>101011
[4,2,7,6,1,3,5]=>101100
[4,2,7,6,1,5,3]=>101101
[4,2,7,6,3,1,5]=>101110
[4,2,7,6,3,5,1]=>101101
[4,2,7,6,5,1,3]=>101110
[4,2,7,6,5,3,1]=>101111
[4,3,1,2,5,6,7]=>110000
[4,3,1,2,5,7,6]=>110001
[4,3,1,2,6,5,7]=>110010
[4,3,1,2,6,7,5]=>110001
[4,3,1,2,7,5,6]=>110010
[4,3,1,2,7,6,5]=>110011
[4,3,1,5,2,6,7]=>110100
[4,3,1,5,2,7,6]=>110101
[4,3,1,5,6,2,7]=>110010
[4,3,1,5,6,7,2]=>110001
[4,3,1,5,7,2,6]=>110010
[4,3,1,5,7,6,2]=>110011
[4,3,1,6,2,5,7]=>110100
[4,3,1,6,2,7,5]=>110101
[4,3,1,6,5,2,7]=>110110
[4,3,1,6,5,7,2]=>110101
[4,3,1,6,7,2,5]=>110010
[4,3,1,6,7,5,2]=>110011
[4,3,1,7,2,5,6]=>110100
[4,3,1,7,2,6,5]=>110101
[4,3,1,7,5,2,6]=>110110
[4,3,1,7,5,6,2]=>110101
[4,3,1,7,6,2,5]=>110110
[4,3,1,7,6,5,2]=>110111
[4,3,2,1,5,6,7]=>111000
[4,3,2,1,5,7,6]=>111001
[4,3,2,1,6,5,7]=>111010
[4,3,2,1,6,7,5]=>111001
[4,3,2,1,7,5,6]=>111010
[4,3,2,1,7,6,5]=>111011
[4,3,2,5,1,6,7]=>110100
[4,3,2,5,1,7,6]=>110101
[4,3,2,5,6,1,7]=>110010
[4,3,2,5,6,7,1]=>110001
[4,3,2,5,7,1,6]=>110010
[4,3,2,5,7,6,1]=>110011
[4,3,2,6,1,5,7]=>110100
[4,3,2,6,1,7,5]=>110101
[4,3,2,6,5,1,7]=>110110
[4,3,2,6,5,7,1]=>110101
[4,3,2,6,7,1,5]=>110010
[4,3,2,6,7,5,1]=>110011
[4,3,2,7,1,5,6]=>110100
[4,3,2,7,1,6,5]=>110101
[4,3,2,7,5,1,6]=>110110
[4,3,2,7,5,6,1]=>110101
[4,3,2,7,6,1,5]=>110110
[4,3,2,7,6,5,1]=>110111
[4,3,5,1,2,6,7]=>101000
[4,3,5,1,2,7,6]=>101001
[4,3,5,1,6,2,7]=>101010
[4,3,5,1,6,7,2]=>101001
[4,3,5,1,7,2,6]=>101010
[4,3,5,1,7,6,2]=>101011
[4,3,5,2,1,6,7]=>101100
[4,3,5,2,1,7,6]=>101101
[4,3,5,2,6,1,7]=>101010
[4,3,5,2,6,7,1]=>101001
[4,3,5,2,7,1,6]=>101010
[4,3,5,2,7,6,1]=>101011
[4,3,5,6,1,2,7]=>100100
[4,3,5,6,1,7,2]=>100101
[4,3,5,6,2,1,7]=>100110
[4,3,5,6,2,7,1]=>100101
[4,3,5,6,7,1,2]=>100010
[4,3,5,6,7,2,1]=>100011
[4,3,5,7,1,2,6]=>100100
[4,3,5,7,1,6,2]=>100101
[4,3,5,7,2,1,6]=>100110
[4,3,5,7,2,6,1]=>100101
[4,3,5,7,6,1,2]=>100110
[4,3,5,7,6,2,1]=>100111
[4,3,6,1,2,5,7]=>101000
[4,3,6,1,2,7,5]=>101001
[4,3,6,1,5,2,7]=>101010
[4,3,6,1,5,7,2]=>101001
[4,3,6,1,7,2,5]=>101010
[4,3,6,1,7,5,2]=>101011
[4,3,6,2,1,5,7]=>101100
[4,3,6,2,1,7,5]=>101101
[4,3,6,2,5,1,7]=>101010
[4,3,6,2,5,7,1]=>101001
[4,3,6,2,7,1,5]=>101010
[4,3,6,2,7,5,1]=>101011
[4,3,6,5,1,2,7]=>101100
[4,3,6,5,1,7,2]=>101101
[4,3,6,5,2,1,7]=>101110
[4,3,6,5,2,7,1]=>101101
[4,3,6,5,7,1,2]=>101010
[4,3,6,5,7,2,1]=>101011
[4,3,6,7,1,2,5]=>100100
[4,3,6,7,1,5,2]=>100101
[4,3,6,7,2,1,5]=>100110
[4,3,6,7,2,5,1]=>100101
[4,3,6,7,5,1,2]=>100110
[4,3,6,7,5,2,1]=>100111
[4,3,7,1,2,5,6]=>101000
[4,3,7,1,2,6,5]=>101001
[4,3,7,1,5,2,6]=>101010
[4,3,7,1,5,6,2]=>101001
[4,3,7,1,6,2,5]=>101010
[4,3,7,1,6,5,2]=>101011
[4,3,7,2,1,5,6]=>101100
[4,3,7,2,1,6,5]=>101101
[4,3,7,2,5,1,6]=>101010
[4,3,7,2,5,6,1]=>101001
[4,3,7,2,6,1,5]=>101010
[4,3,7,2,6,5,1]=>101011
[4,3,7,5,1,2,6]=>101100
[4,3,7,5,1,6,2]=>101101
[4,3,7,5,2,1,6]=>101110
[4,3,7,5,2,6,1]=>101101
[4,3,7,5,6,1,2]=>101010
[4,3,7,5,6,2,1]=>101011
[4,3,7,6,1,2,5]=>101100
[4,3,7,6,1,5,2]=>101101
[4,3,7,6,2,1,5]=>101110
[4,3,7,6,2,5,1]=>101101
[4,3,7,6,5,1,2]=>101110
[4,3,7,6,5,2,1]=>101111
[4,5,1,2,3,6,7]=>010000
[4,5,1,2,3,7,6]=>010001
[4,5,1,2,6,3,7]=>010010
[4,5,1,2,6,7,3]=>010001
[4,5,1,2,7,3,6]=>010010
[4,5,1,2,7,6,3]=>010011
[4,5,1,3,2,6,7]=>010100
[4,5,1,3,2,7,6]=>010101
[4,5,1,3,6,2,7]=>010010
[4,5,1,3,6,7,2]=>010001
[4,5,1,3,7,2,6]=>010010
[4,5,1,3,7,6,2]=>010011
[4,5,1,6,2,3,7]=>010100
[4,5,1,6,2,7,3]=>010101
[4,5,1,6,3,2,7]=>010110
[4,5,1,6,3,7,2]=>010101
[4,5,1,6,7,2,3]=>010010
[4,5,1,6,7,3,2]=>010011
[4,5,1,7,2,3,6]=>010100
[4,5,1,7,2,6,3]=>010101
[4,5,1,7,3,2,6]=>010110
[4,5,1,7,3,6,2]=>010101
[4,5,1,7,6,2,3]=>010110
[4,5,1,7,6,3,2]=>010111
[4,5,2,1,3,6,7]=>011000
[4,5,2,1,3,7,6]=>011001
[4,5,2,1,6,3,7]=>011010
[4,5,2,1,6,7,3]=>011001
[4,5,2,1,7,3,6]=>011010
[4,5,2,1,7,6,3]=>011011
[4,5,2,3,1,6,7]=>010100
[4,5,2,3,1,7,6]=>010101
[4,5,2,3,6,1,7]=>010010
[4,5,2,3,6,7,1]=>010001
[4,5,2,3,7,1,6]=>010010
[4,5,2,3,7,6,1]=>010011
[4,5,2,6,1,3,7]=>010100
[4,5,2,6,1,7,3]=>010101
[4,5,2,6,3,1,7]=>010110
[4,5,2,6,3,7,1]=>010101
[4,5,2,6,7,1,3]=>010010
[4,5,2,6,7,3,1]=>010011
[4,5,2,7,1,3,6]=>010100
[4,5,2,7,1,6,3]=>010101
[4,5,2,7,3,1,6]=>010110
[4,5,2,7,3,6,1]=>010101
[4,5,2,7,6,1,3]=>010110
[4,5,2,7,6,3,1]=>010111
[4,5,3,1,2,6,7]=>011000
[4,5,3,1,2,7,6]=>011001
[4,5,3,1,6,2,7]=>011010
[4,5,3,1,6,7,2]=>011001
[4,5,3,1,7,2,6]=>011010
[4,5,3,1,7,6,2]=>011011
[4,5,3,2,1,6,7]=>011100
[4,5,3,2,1,7,6]=>011101
[4,5,3,2,6,1,7]=>011010
[4,5,3,2,6,7,1]=>011001
[4,5,3,2,7,1,6]=>011010
[4,5,3,2,7,6,1]=>011011
[4,5,3,6,1,2,7]=>010100
[4,5,3,6,1,7,2]=>010101
[4,5,3,6,2,1,7]=>010110
[4,5,3,6,2,7,1]=>010101
[4,5,3,6,7,1,2]=>010010
[4,5,3,6,7,2,1]=>010011
[4,5,3,7,1,2,6]=>010100
[4,5,3,7,1,6,2]=>010101
[4,5,3,7,2,1,6]=>010110
[4,5,3,7,2,6,1]=>010101
[4,5,3,7,6,1,2]=>010110
[4,5,3,7,6,2,1]=>010111
[4,5,6,1,2,3,7]=>001000
[4,5,6,1,2,7,3]=>001001
[4,5,6,1,3,2,7]=>001010
[4,5,6,1,3,7,2]=>001001
[4,5,6,1,7,2,3]=>001010
[4,5,6,1,7,3,2]=>001011
[4,5,6,2,1,3,7]=>001100
[4,5,6,2,1,7,3]=>001101
[4,5,6,2,3,1,7]=>001010
[4,5,6,2,3,7,1]=>001001
[4,5,6,2,7,1,3]=>001010
[4,5,6,2,7,3,1]=>001011
[4,5,6,3,1,2,7]=>001100
[4,5,6,3,1,7,2]=>001101
[4,5,6,3,2,1,7]=>001110
[4,5,6,3,2,7,1]=>001101
[4,5,6,3,7,1,2]=>001010
[4,5,6,3,7,2,1]=>001011
[4,5,6,7,1,2,3]=>000100
[4,5,6,7,1,3,2]=>000101
[4,5,6,7,2,1,3]=>000110
[4,5,6,7,2,3,1]=>000101
[4,5,6,7,3,1,2]=>000110
[4,5,6,7,3,2,1]=>000111
[4,5,7,1,2,3,6]=>001000
[4,5,7,1,2,6,3]=>001001
[4,5,7,1,3,2,6]=>001010
[4,5,7,1,3,6,2]=>001001
[4,5,7,1,6,2,3]=>001010
[4,5,7,1,6,3,2]=>001011
[4,5,7,2,1,3,6]=>001100
[4,5,7,2,1,6,3]=>001101
[4,5,7,2,3,1,6]=>001010
[4,5,7,2,3,6,1]=>001001
[4,5,7,2,6,1,3]=>001010
[4,5,7,2,6,3,1]=>001011
[4,5,7,3,1,2,6]=>001100
[4,5,7,3,1,6,2]=>001101
[4,5,7,3,2,1,6]=>001110
[4,5,7,3,2,6,1]=>001101
[4,5,7,3,6,1,2]=>001010
[4,5,7,3,6,2,1]=>001011
[4,5,7,6,1,2,3]=>001100
[4,5,7,6,1,3,2]=>001101
[4,5,7,6,2,1,3]=>001110
[4,5,7,6,2,3,1]=>001101
[4,5,7,6,3,1,2]=>001110
[4,5,7,6,3,2,1]=>001111
[4,6,1,2,3,5,7]=>010000
[4,6,1,2,3,7,5]=>010001
[4,6,1,2,5,3,7]=>010010
[4,6,1,2,5,7,3]=>010001
[4,6,1,2,7,3,5]=>010010
[4,6,1,2,7,5,3]=>010011
[4,6,1,3,2,5,7]=>010100
[4,6,1,3,2,7,5]=>010101
[4,6,1,3,5,2,7]=>010010
[4,6,1,3,5,7,2]=>010001
[4,6,1,3,7,2,5]=>010010
[4,6,1,3,7,5,2]=>010011
[4,6,1,5,2,3,7]=>010100
[4,6,1,5,2,7,3]=>010101
[4,6,1,5,3,2,7]=>010110
[4,6,1,5,3,7,2]=>010101
[4,6,1,5,7,2,3]=>010010
[4,6,1,5,7,3,2]=>010011
[4,6,1,7,2,3,5]=>010100
[4,6,1,7,2,5,3]=>010101
[4,6,1,7,3,2,5]=>010110
[4,6,1,7,3,5,2]=>010101
[4,6,1,7,5,2,3]=>010110
[4,6,1,7,5,3,2]=>010111
[4,6,2,1,3,5,7]=>011000
[4,6,2,1,3,7,5]=>011001
[4,6,2,1,5,3,7]=>011010
[4,6,2,1,5,7,3]=>011001
[4,6,2,1,7,3,5]=>011010
[4,6,2,1,7,5,3]=>011011
[4,6,2,3,1,5,7]=>010100
[4,6,2,3,1,7,5]=>010101
[4,6,2,3,5,1,7]=>010010
[4,6,2,3,5,7,1]=>010001
[4,6,2,3,7,1,5]=>010010
[4,6,2,3,7,5,1]=>010011
[4,6,2,5,1,3,7]=>010100
[4,6,2,5,1,7,3]=>010101
[4,6,2,5,3,1,7]=>010110
[4,6,2,5,3,7,1]=>010101
[4,6,2,5,7,1,3]=>010010
[4,6,2,5,7,3,1]=>010011
[4,6,2,7,1,3,5]=>010100
[4,6,2,7,1,5,3]=>010101
[4,6,2,7,3,1,5]=>010110
[4,6,2,7,3,5,1]=>010101
[4,6,2,7,5,1,3]=>010110
[4,6,2,7,5,3,1]=>010111
[4,6,3,1,2,5,7]=>011000
[4,6,3,1,2,7,5]=>011001
[4,6,3,1,5,2,7]=>011010
[4,6,3,1,5,7,2]=>011001
[4,6,3,1,7,2,5]=>011010
[4,6,3,1,7,5,2]=>011011
[4,6,3,2,1,5,7]=>011100
[4,6,3,2,1,7,5]=>011101
[4,6,3,2,5,1,7]=>011010
[4,6,3,2,5,7,1]=>011001
[4,6,3,2,7,1,5]=>011010
[4,6,3,2,7,5,1]=>011011
[4,6,3,5,1,2,7]=>010100
[4,6,3,5,1,7,2]=>010101
[4,6,3,5,2,1,7]=>010110
[4,6,3,5,2,7,1]=>010101
[4,6,3,5,7,1,2]=>010010
[4,6,3,5,7,2,1]=>010011
[4,6,3,7,1,2,5]=>010100
[4,6,3,7,1,5,2]=>010101
[4,6,3,7,2,1,5]=>010110
[4,6,3,7,2,5,1]=>010101
[4,6,3,7,5,1,2]=>010110
[4,6,3,7,5,2,1]=>010111
[4,6,5,1,2,3,7]=>011000
[4,6,5,1,2,7,3]=>011001
[4,6,5,1,3,2,7]=>011010
[4,6,5,1,3,7,2]=>011001
[4,6,5,1,7,2,3]=>011010
[4,6,5,1,7,3,2]=>011011
[4,6,5,2,1,3,7]=>011100
[4,6,5,2,1,7,3]=>011101
[4,6,5,2,3,1,7]=>011010
[4,6,5,2,3,7,1]=>011001
[4,6,5,2,7,1,3]=>011010
[4,6,5,2,7,3,1]=>011011
[4,6,5,3,1,2,7]=>011100
[4,6,5,3,1,7,2]=>011101
[4,6,5,3,2,1,7]=>011110
[4,6,5,3,2,7,1]=>011101
[4,6,5,3,7,1,2]=>011010
[4,6,5,3,7,2,1]=>011011
[4,6,5,7,1,2,3]=>010100
[4,6,5,7,1,3,2]=>010101
[4,6,5,7,2,1,3]=>010110
[4,6,5,7,2,3,1]=>010101
[4,6,5,7,3,1,2]=>010110
[4,6,5,7,3,2,1]=>010111
[4,6,7,1,2,3,5]=>001000
[4,6,7,1,2,5,3]=>001001
[4,6,7,1,3,2,5]=>001010
[4,6,7,1,3,5,2]=>001001
[4,6,7,1,5,2,3]=>001010
[4,6,7,1,5,3,2]=>001011
[4,6,7,2,1,3,5]=>001100
[4,6,7,2,1,5,3]=>001101
[4,6,7,2,3,1,5]=>001010
[4,6,7,2,3,5,1]=>001001
[4,6,7,2,5,1,3]=>001010
[4,6,7,2,5,3,1]=>001011
[4,6,7,3,1,2,5]=>001100
[4,6,7,3,1,5,2]=>001101
[4,6,7,3,2,1,5]=>001110
[4,6,7,3,2,5,1]=>001101
[4,6,7,3,5,1,2]=>001010
[4,6,7,3,5,2,1]=>001011
[4,6,7,5,1,2,3]=>001100
[4,6,7,5,1,3,2]=>001101
[4,6,7,5,2,1,3]=>001110
[4,6,7,5,2,3,1]=>001101
[4,6,7,5,3,1,2]=>001110
[4,6,7,5,3,2,1]=>001111
[4,7,1,2,3,5,6]=>010000
[4,7,1,2,3,6,5]=>010001
[4,7,1,2,5,3,6]=>010010
[4,7,1,2,5,6,3]=>010001
[4,7,1,2,6,3,5]=>010010
[4,7,1,2,6,5,3]=>010011
[4,7,1,3,2,5,6]=>010100
[4,7,1,3,2,6,5]=>010101
[4,7,1,3,5,2,6]=>010010
[4,7,1,3,5,6,2]=>010001
[4,7,1,3,6,2,5]=>010010
[4,7,1,3,6,5,2]=>010011
[4,7,1,5,2,3,6]=>010100
[4,7,1,5,2,6,3]=>010101
[4,7,1,5,3,2,6]=>010110
[4,7,1,5,3,6,2]=>010101
[4,7,1,5,6,2,3]=>010010
[4,7,1,5,6,3,2]=>010011
[4,7,1,6,2,3,5]=>010100
[4,7,1,6,2,5,3]=>010101
[4,7,1,6,3,2,5]=>010110
[4,7,1,6,3,5,2]=>010101
[4,7,1,6,5,2,3]=>010110
[4,7,1,6,5,3,2]=>010111
[4,7,2,1,3,5,6]=>011000
[4,7,2,1,3,6,5]=>011001
[4,7,2,1,5,3,6]=>011010
[4,7,2,1,5,6,3]=>011001
[4,7,2,1,6,3,5]=>011010
[4,7,2,1,6,5,3]=>011011
[4,7,2,3,1,5,6]=>010100
[4,7,2,3,1,6,5]=>010101
[4,7,2,3,5,1,6]=>010010
[4,7,2,3,5,6,1]=>010001
[4,7,2,3,6,1,5]=>010010
[4,7,2,3,6,5,1]=>010011
[4,7,2,5,1,3,6]=>010100
[4,7,2,5,1,6,3]=>010101
[4,7,2,5,3,1,6]=>010110
[4,7,2,5,3,6,1]=>010101
[4,7,2,5,6,1,3]=>010010
[4,7,2,5,6,3,1]=>010011
[4,7,2,6,1,3,5]=>010100
[4,7,2,6,1,5,3]=>010101
[4,7,2,6,3,1,5]=>010110
[4,7,2,6,3,5,1]=>010101
[4,7,2,6,5,1,3]=>010110
[4,7,2,6,5,3,1]=>010111
[4,7,3,1,2,5,6]=>011000
[4,7,3,1,2,6,5]=>011001
[4,7,3,1,5,2,6]=>011010
[4,7,3,1,5,6,2]=>011001
[4,7,3,1,6,2,5]=>011010
[4,7,3,1,6,5,2]=>011011
[4,7,3,2,1,5,6]=>011100
[4,7,3,2,1,6,5]=>011101
[4,7,3,2,5,1,6]=>011010
[4,7,3,2,5,6,1]=>011001
[4,7,3,2,6,1,5]=>011010
[4,7,3,2,6,5,1]=>011011
[4,7,3,5,1,2,6]=>010100
[4,7,3,5,1,6,2]=>010101
[4,7,3,5,2,1,6]=>010110
[4,7,3,5,2,6,1]=>010101
[4,7,3,5,6,1,2]=>010010
[4,7,3,5,6,2,1]=>010011
[4,7,3,6,1,2,5]=>010100
[4,7,3,6,1,5,2]=>010101
[4,7,3,6,2,1,5]=>010110
[4,7,3,6,2,5,1]=>010101
[4,7,3,6,5,1,2]=>010110
[4,7,3,6,5,2,1]=>010111
[4,7,5,1,2,3,6]=>011000
[4,7,5,1,2,6,3]=>011001
[4,7,5,1,3,2,6]=>011010
[4,7,5,1,3,6,2]=>011001
[4,7,5,1,6,2,3]=>011010
[4,7,5,1,6,3,2]=>011011
[4,7,5,2,1,3,6]=>011100
[4,7,5,2,1,6,3]=>011101
[4,7,5,2,3,1,6]=>011010
[4,7,5,2,3,6,1]=>011001
[4,7,5,2,6,1,3]=>011010
[4,7,5,2,6,3,1]=>011011
[4,7,5,3,1,2,6]=>011100
[4,7,5,3,1,6,2]=>011101
[4,7,5,3,2,1,6]=>011110
[4,7,5,3,2,6,1]=>011101
[4,7,5,3,6,1,2]=>011010
[4,7,5,3,6,2,1]=>011011
[4,7,5,6,1,2,3]=>010100
[4,7,5,6,1,3,2]=>010101
[4,7,5,6,2,1,3]=>010110
[4,7,5,6,2,3,1]=>010101
[4,7,5,6,3,1,2]=>010110
[4,7,5,6,3,2,1]=>010111
[4,7,6,1,2,3,5]=>011000
[4,7,6,1,2,5,3]=>011001
[4,7,6,1,3,2,5]=>011010
[4,7,6,1,3,5,2]=>011001
[4,7,6,1,5,2,3]=>011010
[4,7,6,1,5,3,2]=>011011
[4,7,6,2,1,3,5]=>011100
[4,7,6,2,1,5,3]=>011101
[4,7,6,2,3,1,5]=>011010
[4,7,6,2,3,5,1]=>011001
[4,7,6,2,5,1,3]=>011010
[4,7,6,2,5,3,1]=>011011
[4,7,6,3,1,2,5]=>011100
[4,7,6,3,1,5,2]=>011101
[4,7,6,3,2,1,5]=>011110
[4,7,6,3,2,5,1]=>011101
[4,7,6,3,5,1,2]=>011010
[4,7,6,3,5,2,1]=>011011
[4,7,6,5,1,2,3]=>011100
[4,7,6,5,1,3,2]=>011101
[4,7,6,5,2,1,3]=>011110
[4,7,6,5,2,3,1]=>011101
[4,7,6,5,3,1,2]=>011110
[4,7,6,5,3,2,1]=>011111
[5,1,2,3,4,6,7]=>100000
[5,1,2,3,4,7,6]=>100001
[5,1,2,3,6,4,7]=>100010
[5,1,2,3,6,7,4]=>100001
[5,1,2,3,7,4,6]=>100010
[5,1,2,3,7,6,4]=>100011
[5,1,2,4,3,6,7]=>100100
[5,1,2,4,3,7,6]=>100101
[5,1,2,4,6,3,7]=>100010
[5,1,2,4,6,7,3]=>100001
[5,1,2,4,7,3,6]=>100010
[5,1,2,4,7,6,3]=>100011
[5,1,2,6,3,4,7]=>100100
[5,1,2,6,3,7,4]=>100101
[5,1,2,6,4,3,7]=>100110
[5,1,2,6,4,7,3]=>100101
[5,1,2,6,7,3,4]=>100010
[5,1,2,6,7,4,3]=>100011
[5,1,2,7,3,4,6]=>100100
[5,1,2,7,3,6,4]=>100101
[5,1,2,7,4,3,6]=>100110
[5,1,2,7,4,6,3]=>100101
[5,1,2,7,6,3,4]=>100110
[5,1,2,7,6,4,3]=>100111
[5,1,3,2,4,6,7]=>101000
[5,1,3,2,4,7,6]=>101001
[5,1,3,2,6,4,7]=>101010
[5,1,3,2,6,7,4]=>101001
[5,1,3,2,7,4,6]=>101010
[5,1,3,2,7,6,4]=>101011
[5,1,3,4,2,6,7]=>100100
[5,1,3,4,2,7,6]=>100101
[5,1,3,4,6,2,7]=>100010
[5,1,3,4,6,7,2]=>100001
[5,1,3,4,7,2,6]=>100010
[5,1,3,4,7,6,2]=>100011
[5,1,3,6,2,4,7]=>100100
[5,1,3,6,2,7,4]=>100101
[5,1,3,6,4,2,7]=>100110
[5,1,3,6,4,7,2]=>100101
[5,1,3,6,7,2,4]=>100010
[5,1,3,6,7,4,2]=>100011
[5,1,3,7,2,4,6]=>100100
[5,1,3,7,2,6,4]=>100101
[5,1,3,7,4,2,6]=>100110
[5,1,3,7,4,6,2]=>100101
[5,1,3,7,6,2,4]=>100110
[5,1,3,7,6,4,2]=>100111
[5,1,4,2,3,6,7]=>101000
[5,1,4,2,3,7,6]=>101001
[5,1,4,2,6,3,7]=>101010
[5,1,4,2,6,7,3]=>101001
[5,1,4,2,7,3,6]=>101010
[5,1,4,2,7,6,3]=>101011
[5,1,4,3,2,6,7]=>101100
[5,1,4,3,2,7,6]=>101101
[5,1,4,3,6,2,7]=>101010
[5,1,4,3,6,7,2]=>101001
[5,1,4,3,7,2,6]=>101010
[5,1,4,3,7,6,2]=>101011
[5,1,4,6,2,3,7]=>100100
[5,1,4,6,2,7,3]=>100101
[5,1,4,6,3,2,7]=>100110
[5,1,4,6,3,7,2]=>100101
[5,1,4,6,7,2,3]=>100010
[5,1,4,6,7,3,2]=>100011
[5,1,4,7,2,3,6]=>100100
[5,1,4,7,2,6,3]=>100101
[5,1,4,7,3,2,6]=>100110
[5,1,4,7,3,6,2]=>100101
[5,1,4,7,6,2,3]=>100110
[5,1,4,7,6,3,2]=>100111
[5,1,6,2,3,4,7]=>101000
[5,1,6,2,3,7,4]=>101001
[5,1,6,2,4,3,7]=>101010
[5,1,6,2,4,7,3]=>101001
[5,1,6,2,7,3,4]=>101010
[5,1,6,2,7,4,3]=>101011
[5,1,6,3,2,4,7]=>101100
[5,1,6,3,2,7,4]=>101101
[5,1,6,3,4,2,7]=>101010
[5,1,6,3,4,7,2]=>101001
[5,1,6,3,7,2,4]=>101010
[5,1,6,3,7,4,2]=>101011
[5,1,6,4,2,3,7]=>101100
[5,1,6,4,2,7,3]=>101101
[5,1,6,4,3,2,7]=>101110
[5,1,6,4,3,7,2]=>101101
[5,1,6,4,7,2,3]=>101010
[5,1,6,4,7,3,2]=>101011
[5,1,6,7,2,3,4]=>100100
[5,1,6,7,2,4,3]=>100101
[5,1,6,7,3,2,4]=>100110
[5,1,6,7,3,4,2]=>100101
[5,1,6,7,4,2,3]=>100110
[5,1,6,7,4,3,2]=>100111
[5,1,7,2,3,4,6]=>101000
[5,1,7,2,3,6,4]=>101001
[5,1,7,2,4,3,6]=>101010
[5,1,7,2,4,6,3]=>101001
[5,1,7,2,6,3,4]=>101010
[5,1,7,2,6,4,3]=>101011
[5,1,7,3,2,4,6]=>101100
[5,1,7,3,2,6,4]=>101101
[5,1,7,3,4,2,6]=>101010
[5,1,7,3,4,6,2]=>101001
[5,1,7,3,6,2,4]=>101010
[5,1,7,3,6,4,2]=>101011
[5,1,7,4,2,3,6]=>101100
[5,1,7,4,2,6,3]=>101101
[5,1,7,4,3,2,6]=>101110
[5,1,7,4,3,6,2]=>101101
[5,1,7,4,6,2,3]=>101010
[5,1,7,4,6,3,2]=>101011
[5,1,7,6,2,3,4]=>101100
[5,1,7,6,2,4,3]=>101101
[5,1,7,6,3,2,4]=>101110
[5,1,7,6,3,4,2]=>101101
[5,1,7,6,4,2,3]=>101110
[5,1,7,6,4,3,2]=>101111
[5,2,1,3,4,6,7]=>110000
[5,2,1,3,4,7,6]=>110001
[5,2,1,3,6,4,7]=>110010
[5,2,1,3,6,7,4]=>110001
[5,2,1,3,7,4,6]=>110010
[5,2,1,3,7,6,4]=>110011
[5,2,1,4,3,6,7]=>110100
[5,2,1,4,3,7,6]=>110101
[5,2,1,4,6,3,7]=>110010
[5,2,1,4,6,7,3]=>110001
[5,2,1,4,7,3,6]=>110010
[5,2,1,4,7,6,3]=>110011
[5,2,1,6,3,4,7]=>110100
[5,2,1,6,3,7,4]=>110101
[5,2,1,6,4,3,7]=>110110
[5,2,1,6,4,7,3]=>110101
[5,2,1,6,7,3,4]=>110010
[5,2,1,6,7,4,3]=>110011
[5,2,1,7,3,4,6]=>110100
[5,2,1,7,3,6,4]=>110101
[5,2,1,7,4,3,6]=>110110
[5,2,1,7,4,6,3]=>110101
[5,2,1,7,6,3,4]=>110110
[5,2,1,7,6,4,3]=>110111
[5,2,3,1,4,6,7]=>101000
[5,2,3,1,4,7,6]=>101001
[5,2,3,1,6,4,7]=>101010
[5,2,3,1,6,7,4]=>101001
[5,2,3,1,7,4,6]=>101010
[5,2,3,1,7,6,4]=>101011
[5,2,3,4,1,6,7]=>100100
[5,2,3,4,1,7,6]=>100101
[5,2,3,4,6,1,7]=>100010
[5,2,3,4,6,7,1]=>100001
[5,2,3,4,7,1,6]=>100010
[5,2,3,4,7,6,1]=>100011
[5,2,3,6,1,4,7]=>100100
[5,2,3,6,1,7,4]=>100101
[5,2,3,6,4,1,7]=>100110
[5,2,3,6,4,7,1]=>100101
[5,2,3,6,7,1,4]=>100010
[5,2,3,6,7,4,1]=>100011
[5,2,3,7,1,4,6]=>100100
[5,2,3,7,1,6,4]=>100101
[5,2,3,7,4,1,6]=>100110
[5,2,3,7,4,6,1]=>100101
[5,2,3,7,6,1,4]=>100110
[5,2,3,7,6,4,1]=>100111
[5,2,4,1,3,6,7]=>101000
[5,2,4,1,3,7,6]=>101001
[5,2,4,1,6,3,7]=>101010
[5,2,4,1,6,7,3]=>101001
[5,2,4,1,7,3,6]=>101010
[5,2,4,1,7,6,3]=>101011
[5,2,4,3,1,6,7]=>101100
[5,2,4,3,1,7,6]=>101101
[5,2,4,3,6,1,7]=>101010
[5,2,4,3,6,7,1]=>101001
[5,2,4,3,7,1,6]=>101010
[5,2,4,3,7,6,1]=>101011
[5,2,4,6,1,3,7]=>100100
[5,2,4,6,1,7,3]=>100101
[5,2,4,6,3,1,7]=>100110
[5,2,4,6,3,7,1]=>100101
[5,2,4,6,7,1,3]=>100010
[5,2,4,6,7,3,1]=>100011
[5,2,4,7,1,3,6]=>100100
[5,2,4,7,1,6,3]=>100101
[5,2,4,7,3,1,6]=>100110
[5,2,4,7,3,6,1]=>100101
[5,2,4,7,6,1,3]=>100110
[5,2,4,7,6,3,1]=>100111
[5,2,6,1,3,4,7]=>101000
[5,2,6,1,3,7,4]=>101001
[5,2,6,1,4,3,7]=>101010
[5,2,6,1,4,7,3]=>101001
[5,2,6,1,7,3,4]=>101010
[5,2,6,1,7,4,3]=>101011
[5,2,6,3,1,4,7]=>101100
[5,2,6,3,1,7,4]=>101101
[5,2,6,3,4,1,7]=>101010
[5,2,6,3,4,7,1]=>101001
[5,2,6,3,7,1,4]=>101010
[5,2,6,3,7,4,1]=>101011
[5,2,6,4,1,3,7]=>101100
[5,2,6,4,1,7,3]=>101101
[5,2,6,4,3,1,7]=>101110
[5,2,6,4,3,7,1]=>101101
[5,2,6,4,7,1,3]=>101010
[5,2,6,4,7,3,1]=>101011
[5,2,6,7,1,3,4]=>100100
[5,2,6,7,1,4,3]=>100101
[5,2,6,7,3,1,4]=>100110
[5,2,6,7,3,4,1]=>100101
[5,2,6,7,4,1,3]=>100110
[5,2,6,7,4,3,1]=>100111
[5,2,7,1,3,4,6]=>101000
[5,2,7,1,3,6,4]=>101001
[5,2,7,1,4,3,6]=>101010
[5,2,7,1,4,6,3]=>101001
[5,2,7,1,6,3,4]=>101010
[5,2,7,1,6,4,3]=>101011
[5,2,7,3,1,4,6]=>101100
[5,2,7,3,1,6,4]=>101101
[5,2,7,3,4,1,6]=>101010
[5,2,7,3,4,6,1]=>101001
[5,2,7,3,6,1,4]=>101010
[5,2,7,3,6,4,1]=>101011
[5,2,7,4,1,3,6]=>101100
[5,2,7,4,1,6,3]=>101101
[5,2,7,4,3,1,6]=>101110
[5,2,7,4,3,6,1]=>101101
[5,2,7,4,6,1,3]=>101010
[5,2,7,4,6,3,1]=>101011
[5,2,7,6,1,3,4]=>101100
[5,2,7,6,1,4,3]=>101101
[5,2,7,6,3,1,4]=>101110
[5,2,7,6,3,4,1]=>101101
[5,2,7,6,4,1,3]=>101110
[5,2,7,6,4,3,1]=>101111
[5,3,1,2,4,6,7]=>110000
[5,3,1,2,4,7,6]=>110001
[5,3,1,2,6,4,7]=>110010
[5,3,1,2,6,7,4]=>110001
[5,3,1,2,7,4,6]=>110010
[5,3,1,2,7,6,4]=>110011
[5,3,1,4,2,6,7]=>110100
[5,3,1,4,2,7,6]=>110101
[5,3,1,4,6,2,7]=>110010
[5,3,1,4,6,7,2]=>110001
[5,3,1,4,7,2,6]=>110010
[5,3,1,4,7,6,2]=>110011
[5,3,1,6,2,4,7]=>110100
[5,3,1,6,2,7,4]=>110101
[5,3,1,6,4,2,7]=>110110
[5,3,1,6,4,7,2]=>110101
[5,3,1,6,7,2,4]=>110010
[5,3,1,6,7,4,2]=>110011
[5,3,1,7,2,4,6]=>110100
[5,3,1,7,2,6,4]=>110101
[5,3,1,7,4,2,6]=>110110
[5,3,1,7,4,6,2]=>110101
[5,3,1,7,6,2,4]=>110110
[5,3,1,7,6,4,2]=>110111
[5,3,2,1,4,6,7]=>111000
[5,3,2,1,4,7,6]=>111001
[5,3,2,1,6,4,7]=>111010
[5,3,2,1,6,7,4]=>111001
[5,3,2,1,7,4,6]=>111010
[5,3,2,1,7,6,4]=>111011
[5,3,2,4,1,6,7]=>110100
[5,3,2,4,1,7,6]=>110101
[5,3,2,4,6,1,7]=>110010
[5,3,2,4,6,7,1]=>110001
[5,3,2,4,7,1,6]=>110010
[5,3,2,4,7,6,1]=>110011
[5,3,2,6,1,4,7]=>110100
[5,3,2,6,1,7,4]=>110101
[5,3,2,6,4,1,7]=>110110
[5,3,2,6,4,7,1]=>110101
[5,3,2,6,7,1,4]=>110010
[5,3,2,6,7,4,1]=>110011
[5,3,2,7,1,4,6]=>110100
[5,3,2,7,1,6,4]=>110101
[5,3,2,7,4,1,6]=>110110
[5,3,2,7,4,6,1]=>110101
[5,3,2,7,6,1,4]=>110110
[5,3,2,7,6,4,1]=>110111
[5,3,4,1,2,6,7]=>101000
[5,3,4,1,2,7,6]=>101001
[5,3,4,1,6,2,7]=>101010
[5,3,4,1,6,7,2]=>101001
[5,3,4,1,7,2,6]=>101010
[5,3,4,1,7,6,2]=>101011
[5,3,4,2,1,6,7]=>101100
[5,3,4,2,1,7,6]=>101101
[5,3,4,2,6,1,7]=>101010
[5,3,4,2,6,7,1]=>101001
[5,3,4,2,7,1,6]=>101010
[5,3,4,2,7,6,1]=>101011
[5,3,4,6,1,2,7]=>100100
[5,3,4,6,1,7,2]=>100101
[5,3,4,6,2,1,7]=>100110
[5,3,4,6,2,7,1]=>100101
[5,3,4,6,7,1,2]=>100010
[5,3,4,6,7,2,1]=>100011
[5,3,4,7,1,2,6]=>100100
[5,3,4,7,1,6,2]=>100101
[5,3,4,7,2,1,6]=>100110
[5,3,4,7,2,6,1]=>100101
[5,3,4,7,6,1,2]=>100110
[5,3,4,7,6,2,1]=>100111
[5,3,6,1,2,4,7]=>101000
[5,3,6,1,2,7,4]=>101001
[5,3,6,1,4,2,7]=>101010
[5,3,6,1,4,7,2]=>101001
[5,3,6,1,7,2,4]=>101010
[5,3,6,1,7,4,2]=>101011
[5,3,6,2,1,4,7]=>101100
[5,3,6,2,1,7,4]=>101101
[5,3,6,2,4,1,7]=>101010
[5,3,6,2,4,7,1]=>101001
[5,3,6,2,7,1,4]=>101010
[5,3,6,2,7,4,1]=>101011
[5,3,6,4,1,2,7]=>101100
[5,3,6,4,1,7,2]=>101101
[5,3,6,4,2,1,7]=>101110
[5,3,6,4,2,7,1]=>101101
[5,3,6,4,7,1,2]=>101010
[5,3,6,4,7,2,1]=>101011
[5,3,6,7,1,2,4]=>100100
[5,3,6,7,1,4,2]=>100101
[5,3,6,7,2,1,4]=>100110
[5,3,6,7,2,4,1]=>100101
[5,3,6,7,4,1,2]=>100110
[5,3,6,7,4,2,1]=>100111
[5,3,7,1,2,4,6]=>101000
[5,3,7,1,2,6,4]=>101001
[5,3,7,1,4,2,6]=>101010
[5,3,7,1,4,6,2]=>101001
[5,3,7,1,6,2,4]=>101010
[5,3,7,1,6,4,2]=>101011
[5,3,7,2,1,4,6]=>101100
[5,3,7,2,1,6,4]=>101101
[5,3,7,2,4,1,6]=>101010
[5,3,7,2,4,6,1]=>101001
[5,3,7,2,6,1,4]=>101010
[5,3,7,2,6,4,1]=>101011
[5,3,7,4,1,2,6]=>101100
[5,3,7,4,1,6,2]=>101101
[5,3,7,4,2,1,6]=>101110
[5,3,7,4,2,6,1]=>101101
[5,3,7,4,6,1,2]=>101010
[5,3,7,4,6,2,1]=>101011
[5,3,7,6,1,2,4]=>101100
[5,3,7,6,1,4,2]=>101101
[5,3,7,6,2,1,4]=>101110
[5,3,7,6,2,4,1]=>101101
[5,3,7,6,4,1,2]=>101110
[5,3,7,6,4,2,1]=>101111
[5,4,1,2,3,6,7]=>110000
[5,4,1,2,3,7,6]=>110001
[5,4,1,2,6,3,7]=>110010
[5,4,1,2,6,7,3]=>110001
[5,4,1,2,7,3,6]=>110010
[5,4,1,2,7,6,3]=>110011
[5,4,1,3,2,6,7]=>110100
[5,4,1,3,2,7,6]=>110101
[5,4,1,3,6,2,7]=>110010
[5,4,1,3,6,7,2]=>110001
[5,4,1,3,7,2,6]=>110010
[5,4,1,3,7,6,2]=>110011
[5,4,1,6,2,3,7]=>110100
[5,4,1,6,2,7,3]=>110101
[5,4,1,6,3,2,7]=>110110
[5,4,1,6,3,7,2]=>110101
[5,4,1,6,7,2,3]=>110010
[5,4,1,6,7,3,2]=>110011
[5,4,1,7,2,3,6]=>110100
[5,4,1,7,2,6,3]=>110101
[5,4,1,7,3,2,6]=>110110
[5,4,1,7,3,6,2]=>110101
[5,4,1,7,6,2,3]=>110110
[5,4,1,7,6,3,2]=>110111
[5,4,2,1,3,6,7]=>111000
[5,4,2,1,3,7,6]=>111001
[5,4,2,1,6,3,7]=>111010
[5,4,2,1,6,7,3]=>111001
[5,4,2,1,7,3,6]=>111010
[5,4,2,1,7,6,3]=>111011
[5,4,2,3,1,6,7]=>110100
[5,4,2,3,1,7,6]=>110101
[5,4,2,3,6,1,7]=>110010
[5,4,2,3,6,7,1]=>110001
[5,4,2,3,7,1,6]=>110010
[5,4,2,3,7,6,1]=>110011
[5,4,2,6,1,3,7]=>110100
[5,4,2,6,1,7,3]=>110101
[5,4,2,6,3,1,7]=>110110
[5,4,2,6,3,7,1]=>110101
[5,4,2,6,7,1,3]=>110010
[5,4,2,6,7,3,1]=>110011
[5,4,2,7,1,3,6]=>110100
[5,4,2,7,1,6,3]=>110101
[5,4,2,7,3,1,6]=>110110
[5,4,2,7,3,6,1]=>110101
[5,4,2,7,6,1,3]=>110110
[5,4,2,7,6,3,1]=>110111
[5,4,3,1,2,6,7]=>111000
[5,4,3,1,2,7,6]=>111001
[5,4,3,1,6,2,7]=>111010
[5,4,3,1,6,7,2]=>111001
[5,4,3,1,7,2,6]=>111010
[5,4,3,1,7,6,2]=>111011
[5,4,3,2,1,6,7]=>111100
[5,4,3,2,1,7,6]=>111101
[5,4,3,2,6,1,7]=>111010
[5,4,3,2,6,7,1]=>111001
[5,4,3,2,7,1,6]=>111010
[5,4,3,2,7,6,1]=>111011
[5,4,3,6,1,2,7]=>110100
[5,4,3,6,1,7,2]=>110101
[5,4,3,6,2,1,7]=>110110
[5,4,3,6,2,7,1]=>110101
[5,4,3,6,7,1,2]=>110010
[5,4,3,6,7,2,1]=>110011
[5,4,3,7,1,2,6]=>110100
[5,4,3,7,1,6,2]=>110101
[5,4,3,7,2,1,6]=>110110
[5,4,3,7,2,6,1]=>110101
[5,4,3,7,6,1,2]=>110110
[5,4,3,7,6,2,1]=>110111
[5,4,6,1,2,3,7]=>101000
[5,4,6,1,2,7,3]=>101001
[5,4,6,1,3,2,7]=>101010
[5,4,6,1,3,7,2]=>101001
[5,4,6,1,7,2,3]=>101010
[5,4,6,1,7,3,2]=>101011
[5,4,6,2,1,3,7]=>101100
[5,4,6,2,1,7,3]=>101101
[5,4,6,2,3,1,7]=>101010
[5,4,6,2,3,7,1]=>101001
[5,4,6,2,7,1,3]=>101010
[5,4,6,2,7,3,1]=>101011
[5,4,6,3,1,2,7]=>101100
[5,4,6,3,1,7,2]=>101101
[5,4,6,3,2,1,7]=>101110
[5,4,6,3,2,7,1]=>101101
[5,4,6,3,7,1,2]=>101010
[5,4,6,3,7,2,1]=>101011
[5,4,6,7,1,2,3]=>100100
[5,4,6,7,1,3,2]=>100101
[5,4,6,7,2,1,3]=>100110
[5,4,6,7,2,3,1]=>100101
[5,4,6,7,3,1,2]=>100110
[5,4,6,7,3,2,1]=>100111
[5,4,7,1,2,3,6]=>101000
[5,4,7,1,2,6,3]=>101001
[5,4,7,1,3,2,6]=>101010
[5,4,7,1,3,6,2]=>101001
[5,4,7,1,6,2,3]=>101010
[5,4,7,1,6,3,2]=>101011
[5,4,7,2,1,3,6]=>101100
[5,4,7,2,1,6,3]=>101101
[5,4,7,2,3,1,6]=>101010
[5,4,7,2,3,6,1]=>101001
[5,4,7,2,6,1,3]=>101010
[5,4,7,2,6,3,1]=>101011
[5,4,7,3,1,2,6]=>101100
[5,4,7,3,1,6,2]=>101101
[5,4,7,3,2,1,6]=>101110
[5,4,7,3,2,6,1]=>101101
[5,4,7,3,6,1,2]=>101010
[5,4,7,3,6,2,1]=>101011
[5,4,7,6,1,2,3]=>101100
[5,4,7,6,1,3,2]=>101101
[5,4,7,6,2,1,3]=>101110
[5,4,7,6,2,3,1]=>101101
[5,4,7,6,3,1,2]=>101110
[5,4,7,6,3,2,1]=>101111
[5,6,1,2,3,4,7]=>010000
[5,6,1,2,3,7,4]=>010001
[5,6,1,2,4,3,7]=>010010
[5,6,1,2,4,7,3]=>010001
[5,6,1,2,7,3,4]=>010010
[5,6,1,2,7,4,3]=>010011
[5,6,1,3,2,4,7]=>010100
[5,6,1,3,2,7,4]=>010101
[5,6,1,3,4,2,7]=>010010
[5,6,1,3,4,7,2]=>010001
[5,6,1,3,7,2,4]=>010010
[5,6,1,3,7,4,2]=>010011
[5,6,1,4,2,3,7]=>010100
[5,6,1,4,2,7,3]=>010101
[5,6,1,4,3,2,7]=>010110
[5,6,1,4,3,7,2]=>010101
[5,6,1,4,7,2,3]=>010010
[5,6,1,4,7,3,2]=>010011
[5,6,1,7,2,3,4]=>010100
[5,6,1,7,2,4,3]=>010101
[5,6,1,7,3,2,4]=>010110
[5,6,1,7,3,4,2]=>010101
[5,6,1,7,4,2,3]=>010110
[5,6,1,7,4,3,2]=>010111
[5,6,2,1,3,4,7]=>011000
[5,6,2,1,3,7,4]=>011001
[5,6,2,1,4,3,7]=>011010
[5,6,2,1,4,7,3]=>011001
[5,6,2,1,7,3,4]=>011010
[5,6,2,1,7,4,3]=>011011
[5,6,2,3,1,4,7]=>010100
[5,6,2,3,1,7,4]=>010101
[5,6,2,3,4,1,7]=>010010
[5,6,2,3,4,7,1]=>010001
[5,6,2,3,7,1,4]=>010010
[5,6,2,3,7,4,1]=>010011
[5,6,2,4,1,3,7]=>010100
[5,6,2,4,1,7,3]=>010101
[5,6,2,4,3,1,7]=>010110
[5,6,2,4,3,7,1]=>010101
[5,6,2,4,7,1,3]=>010010
[5,6,2,4,7,3,1]=>010011
[5,6,2,7,1,3,4]=>010100
[5,6,2,7,1,4,3]=>010101
[5,6,2,7,3,1,4]=>010110
[5,6,2,7,3,4,1]=>010101
[5,6,2,7,4,1,3]=>010110
[5,6,2,7,4,3,1]=>010111
[5,6,3,1,2,4,7]=>011000
[5,6,3,1,2,7,4]=>011001
[5,6,3,1,4,2,7]=>011010
[5,6,3,1,4,7,2]=>011001
[5,6,3,1,7,2,4]=>011010
[5,6,3,1,7,4,2]=>011011
[5,6,3,2,1,4,7]=>011100
[5,6,3,2,1,7,4]=>011101
[5,6,3,2,4,1,7]=>011010
[5,6,3,2,4,7,1]=>011001
[5,6,3,2,7,1,4]=>011010
[5,6,3,2,7,4,1]=>011011
[5,6,3,4,1,2,7]=>010100
[5,6,3,4,1,7,2]=>010101
[5,6,3,4,2,1,7]=>010110
[5,6,3,4,2,7,1]=>010101
[5,6,3,4,7,1,2]=>010010
[5,6,3,4,7,2,1]=>010011
[5,6,3,7,1,2,4]=>010100
[5,6,3,7,1,4,2]=>010101
[5,6,3,7,2,1,4]=>010110
[5,6,3,7,2,4,1]=>010101
[5,6,3,7,4,1,2]=>010110
[5,6,3,7,4,2,1]=>010111
[5,6,4,1,2,3,7]=>011000
[5,6,4,1,2,7,3]=>011001
[5,6,4,1,3,2,7]=>011010
[5,6,4,1,3,7,2]=>011001
[5,6,4,1,7,2,3]=>011010
[5,6,4,1,7,3,2]=>011011
[5,6,4,2,1,3,7]=>011100
[5,6,4,2,1,7,3]=>011101
[5,6,4,2,3,1,7]=>011010
[5,6,4,2,3,7,1]=>011001
[5,6,4,2,7,1,3]=>011010
[5,6,4,2,7,3,1]=>011011
[5,6,4,3,1,2,7]=>011100
[5,6,4,3,1,7,2]=>011101
[5,6,4,3,2,1,7]=>011110
[5,6,4,3,2,7,1]=>011101
[5,6,4,3,7,1,2]=>011010
[5,6,4,3,7,2,1]=>011011
[5,6,4,7,1,2,3]=>010100
[5,6,4,7,1,3,2]=>010101
[5,6,4,7,2,1,3]=>010110
[5,6,4,7,2,3,1]=>010101
[5,6,4,7,3,1,2]=>010110
[5,6,4,7,3,2,1]=>010111
[5,6,7,1,2,3,4]=>001000
[5,6,7,1,2,4,3]=>001001
[5,6,7,1,3,2,4]=>001010
[5,6,7,1,3,4,2]=>001001
[5,6,7,1,4,2,3]=>001010
[5,6,7,1,4,3,2]=>001011
[5,6,7,2,1,3,4]=>001100
[5,6,7,2,1,4,3]=>001101
[5,6,7,2,3,1,4]=>001010
[5,6,7,2,3,4,1]=>001001
[5,6,7,2,4,1,3]=>001010
[5,6,7,2,4,3,1]=>001011
[5,6,7,3,1,2,4]=>001100
[5,6,7,3,1,4,2]=>001101
[5,6,7,3,2,1,4]=>001110
[5,6,7,3,2,4,1]=>001101
[5,6,7,3,4,1,2]=>001010
[5,6,7,3,4,2,1]=>001011
[5,6,7,4,1,2,3]=>001100
[5,6,7,4,1,3,2]=>001101
[5,6,7,4,2,1,3]=>001110
[5,6,7,4,2,3,1]=>001101
[5,6,7,4,3,1,2]=>001110
[5,6,7,4,3,2,1]=>001111
[5,7,1,2,3,4,6]=>010000
[5,7,1,2,3,6,4]=>010001
[5,7,1,2,4,3,6]=>010010
[5,7,1,2,4,6,3]=>010001
[5,7,1,2,6,3,4]=>010010
[5,7,1,2,6,4,3]=>010011
[5,7,1,3,2,4,6]=>010100
[5,7,1,3,2,6,4]=>010101
[5,7,1,3,4,2,6]=>010010
[5,7,1,3,4,6,2]=>010001
[5,7,1,3,6,2,4]=>010010
[5,7,1,3,6,4,2]=>010011
[5,7,1,4,2,3,6]=>010100
[5,7,1,4,2,6,3]=>010101
[5,7,1,4,3,2,6]=>010110
[5,7,1,4,3,6,2]=>010101
[5,7,1,4,6,2,3]=>010010
[5,7,1,4,6,3,2]=>010011
[5,7,1,6,2,3,4]=>010100
[5,7,1,6,2,4,3]=>010101
[5,7,1,6,3,2,4]=>010110
[5,7,1,6,3,4,2]=>010101
[5,7,1,6,4,2,3]=>010110
[5,7,1,6,4,3,2]=>010111
[5,7,2,1,3,4,6]=>011000
[5,7,2,1,3,6,4]=>011001
[5,7,2,1,4,3,6]=>011010
[5,7,2,1,4,6,3]=>011001
[5,7,2,1,6,3,4]=>011010
[5,7,2,1,6,4,3]=>011011
[5,7,2,3,1,4,6]=>010100
[5,7,2,3,1,6,4]=>010101
[5,7,2,3,4,1,6]=>010010
[5,7,2,3,4,6,1]=>010001
[5,7,2,3,6,1,4]=>010010
[5,7,2,3,6,4,1]=>010011
[5,7,2,4,1,3,6]=>010100
[5,7,2,4,1,6,3]=>010101
[5,7,2,4,3,1,6]=>010110
[5,7,2,4,3,6,1]=>010101
[5,7,2,4,6,1,3]=>010010
[5,7,2,4,6,3,1]=>010011
[5,7,2,6,1,3,4]=>010100
[5,7,2,6,1,4,3]=>010101
[5,7,2,6,3,1,4]=>010110
[5,7,2,6,3,4,1]=>010101
[5,7,2,6,4,1,3]=>010110
[5,7,2,6,4,3,1]=>010111
[5,7,3,1,2,4,6]=>011000
[5,7,3,1,2,6,4]=>011001
[5,7,3,1,4,2,6]=>011010
[5,7,3,1,4,6,2]=>011001
[5,7,3,1,6,2,4]=>011010
[5,7,3,1,6,4,2]=>011011
[5,7,3,2,1,4,6]=>011100
[5,7,3,2,1,6,4]=>011101
[5,7,3,2,4,1,6]=>011010
[5,7,3,2,4,6,1]=>011001
[5,7,3,2,6,1,4]=>011010
[5,7,3,2,6,4,1]=>011011
[5,7,3,4,1,2,6]=>010100
[5,7,3,4,1,6,2]=>010101
[5,7,3,4,2,1,6]=>010110
[5,7,3,4,2,6,1]=>010101
[5,7,3,4,6,1,2]=>010010
[5,7,3,4,6,2,1]=>010011
[5,7,3,6,1,2,4]=>010100
[5,7,3,6,1,4,2]=>010101
[5,7,3,6,2,1,4]=>010110
[5,7,3,6,2,4,1]=>010101
[5,7,3,6,4,1,2]=>010110
[5,7,3,6,4,2,1]=>010111
[5,7,4,1,2,3,6]=>011000
[5,7,4,1,2,6,3]=>011001
[5,7,4,1,3,2,6]=>011010
[5,7,4,1,3,6,2]=>011001
[5,7,4,1,6,2,3]=>011010
[5,7,4,1,6,3,2]=>011011
[5,7,4,2,1,3,6]=>011100
[5,7,4,2,1,6,3]=>011101
[5,7,4,2,3,1,6]=>011010
[5,7,4,2,3,6,1]=>011001
[5,7,4,2,6,1,3]=>011010
[5,7,4,2,6,3,1]=>011011
[5,7,4,3,1,2,6]=>011100
[5,7,4,3,1,6,2]=>011101
[5,7,4,3,2,1,6]=>011110
[5,7,4,3,2,6,1]=>011101
[5,7,4,3,6,1,2]=>011010
[5,7,4,3,6,2,1]=>011011
[5,7,4,6,1,2,3]=>010100
[5,7,4,6,1,3,2]=>010101
[5,7,4,6,2,1,3]=>010110
[5,7,4,6,2,3,1]=>010101
[5,7,4,6,3,1,2]=>010110
[5,7,4,6,3,2,1]=>010111
[5,7,6,1,2,3,4]=>011000
[5,7,6,1,2,4,3]=>011001
[5,7,6,1,3,2,4]=>011010
[5,7,6,1,3,4,2]=>011001
[5,7,6,1,4,2,3]=>011010
[5,7,6,1,4,3,2]=>011011
[5,7,6,2,1,3,4]=>011100
[5,7,6,2,1,4,3]=>011101
[5,7,6,2,3,1,4]=>011010
[5,7,6,2,3,4,1]=>011001
[5,7,6,2,4,1,3]=>011010
[5,7,6,2,4,3,1]=>011011
[5,7,6,3,1,2,4]=>011100
[5,7,6,3,1,4,2]=>011101
[5,7,6,3,2,1,4]=>011110
[5,7,6,3,2,4,1]=>011101
[5,7,6,3,4,1,2]=>011010
[5,7,6,3,4,2,1]=>011011
[5,7,6,4,1,2,3]=>011100
[5,7,6,4,1,3,2]=>011101
[5,7,6,4,2,1,3]=>011110
[5,7,6,4,2,3,1]=>011101
[5,7,6,4,3,1,2]=>011110
[5,7,6,4,3,2,1]=>011111
[6,1,2,3,4,5,7]=>100000
[6,1,2,3,4,7,5]=>100001
[6,1,2,3,5,4,7]=>100010
[6,1,2,3,5,7,4]=>100001
[6,1,2,3,7,4,5]=>100010
[6,1,2,3,7,5,4]=>100011
[6,1,2,4,3,5,7]=>100100
[6,1,2,4,3,7,5]=>100101
[6,1,2,4,5,3,7]=>100010
[6,1,2,4,5,7,3]=>100001
[6,1,2,4,7,3,5]=>100010
[6,1,2,4,7,5,3]=>100011
[6,1,2,5,3,4,7]=>100100
[6,1,2,5,3,7,4]=>100101
[6,1,2,5,4,3,7]=>100110
[6,1,2,5,4,7,3]=>100101
[6,1,2,5,7,3,4]=>100010
[6,1,2,5,7,4,3]=>100011
[6,1,2,7,3,4,5]=>100100
[6,1,2,7,3,5,4]=>100101
[6,1,2,7,4,3,5]=>100110
[6,1,2,7,4,5,3]=>100101
[6,1,2,7,5,3,4]=>100110
[6,1,2,7,5,4,3]=>100111
[6,1,3,2,4,5,7]=>101000
[6,1,3,2,4,7,5]=>101001
[6,1,3,2,5,4,7]=>101010
[6,1,3,2,5,7,4]=>101001
[6,1,3,2,7,4,5]=>101010
[6,1,3,2,7,5,4]=>101011
[6,1,3,4,2,5,7]=>100100
[6,1,3,4,2,7,5]=>100101
[6,1,3,4,5,2,7]=>100010
[6,1,3,4,5,7,2]=>100001
[6,1,3,4,7,2,5]=>100010
[6,1,3,4,7,5,2]=>100011
[6,1,3,5,2,4,7]=>100100
[6,1,3,5,2,7,4]=>100101
[6,1,3,5,4,2,7]=>100110
[6,1,3,5,4,7,2]=>100101
[6,1,3,5,7,2,4]=>100010
[6,1,3,5,7,4,2]=>100011
[6,1,3,7,2,4,5]=>100100
[6,1,3,7,2,5,4]=>100101
[6,1,3,7,4,2,5]=>100110
[6,1,3,7,4,5,2]=>100101
[6,1,3,7,5,2,4]=>100110
[6,1,3,7,5,4,2]=>100111
[6,1,4,2,3,5,7]=>101000
[6,1,4,2,3,7,5]=>101001
[6,1,4,2,5,3,7]=>101010
[6,1,4,2,5,7,3]=>101001
[6,1,4,2,7,3,5]=>101010
[6,1,4,2,7,5,3]=>101011
[6,1,4,3,2,5,7]=>101100
[6,1,4,3,2,7,5]=>101101
[6,1,4,3,5,2,7]=>101010
[6,1,4,3,5,7,2]=>101001
[6,1,4,3,7,2,5]=>101010
[6,1,4,3,7,5,2]=>101011
[6,1,4,5,2,3,7]=>100100
[6,1,4,5,2,7,3]=>100101
[6,1,4,5,3,2,7]=>100110
[6,1,4,5,3,7,2]=>100101
[6,1,4,5,7,2,3]=>100010
[6,1,4,5,7,3,2]=>100011
[6,1,4,7,2,3,5]=>100100
[6,1,4,7,2,5,3]=>100101
[6,1,4,7,3,2,5]=>100110
[6,1,4,7,3,5,2]=>100101
[6,1,4,7,5,2,3]=>100110
[6,1,4,7,5,3,2]=>100111
[6,1,5,2,3,4,7]=>101000
[6,1,5,2,3,7,4]=>101001
[6,1,5,2,4,3,7]=>101010
[6,1,5,2,4,7,3]=>101001
[6,1,5,2,7,3,4]=>101010
[6,1,5,2,7,4,3]=>101011
[6,1,5,3,2,4,7]=>101100
[6,1,5,3,2,7,4]=>101101
[6,1,5,3,4,2,7]=>101010
[6,1,5,3,4,7,2]=>101001
[6,1,5,3,7,2,4]=>101010
[6,1,5,3,7,4,2]=>101011
[6,1,5,4,2,3,7]=>101100
[6,1,5,4,2,7,3]=>101101
[6,1,5,4,3,2,7]=>101110
[6,1,5,4,3,7,2]=>101101
[6,1,5,4,7,2,3]=>101010
[6,1,5,4,7,3,2]=>101011
[6,1,5,7,2,3,4]=>100100
[6,1,5,7,2,4,3]=>100101
[6,1,5,7,3,2,4]=>100110
[6,1,5,7,3,4,2]=>100101
[6,1,5,7,4,2,3]=>100110
[6,1,5,7,4,3,2]=>100111
[6,1,7,2,3,4,5]=>101000
[6,1,7,2,3,5,4]=>101001
[6,1,7,2,4,3,5]=>101010
[6,1,7,2,4,5,3]=>101001
[6,1,7,2,5,3,4]=>101010
[6,1,7,2,5,4,3]=>101011
[6,1,7,3,2,4,5]=>101100
[6,1,7,3,2,5,4]=>101101
[6,1,7,3,4,2,5]=>101010
[6,1,7,3,4,5,2]=>101001
[6,1,7,3,5,2,4]=>101010
[6,1,7,3,5,4,2]=>101011
[6,1,7,4,2,3,5]=>101100
[6,1,7,4,2,5,3]=>101101
[6,1,7,4,3,2,5]=>101110
[6,1,7,4,3,5,2]=>101101
[6,1,7,4,5,2,3]=>101010
[6,1,7,4,5,3,2]=>101011
[6,1,7,5,2,3,4]=>101100
[6,1,7,5,2,4,3]=>101101
[6,1,7,5,3,2,4]=>101110
[6,1,7,5,3,4,2]=>101101
[6,1,7,5,4,2,3]=>101110
[6,1,7,5,4,3,2]=>101111
[6,2,1,3,4,5,7]=>110000
[6,2,1,3,4,7,5]=>110001
[6,2,1,3,5,4,7]=>110010
[6,2,1,3,5,7,4]=>110001
[6,2,1,3,7,4,5]=>110010
[6,2,1,3,7,5,4]=>110011
[6,2,1,4,3,5,7]=>110100
[6,2,1,4,3,7,5]=>110101
[6,2,1,4,5,3,7]=>110010
[6,2,1,4,5,7,3]=>110001
[6,2,1,4,7,3,5]=>110010
[6,2,1,4,7,5,3]=>110011
[6,2,1,5,3,4,7]=>110100
[6,2,1,5,3,7,4]=>110101
[6,2,1,5,4,3,7]=>110110
[6,2,1,5,4,7,3]=>110101
[6,2,1,5,7,3,4]=>110010
[6,2,1,5,7,4,3]=>110011
[6,2,1,7,3,4,5]=>110100
[6,2,1,7,3,5,4]=>110101
[6,2,1,7,4,3,5]=>110110
[6,2,1,7,4,5,3]=>110101
[6,2,1,7,5,3,4]=>110110
[6,2,1,7,5,4,3]=>110111
[6,2,3,1,4,5,7]=>101000
[6,2,3,1,4,7,5]=>101001
[6,2,3,1,5,4,7]=>101010
[6,2,3,1,5,7,4]=>101001
[6,2,3,1,7,4,5]=>101010
[6,2,3,1,7,5,4]=>101011
[6,2,3,4,1,5,7]=>100100
[6,2,3,4,1,7,5]=>100101
[6,2,3,4,5,1,7]=>100010
[6,2,3,4,5,7,1]=>100001
[6,2,3,4,7,1,5]=>100010
[6,2,3,4,7,5,1]=>100011
[6,2,3,5,1,4,7]=>100100
[6,2,3,5,1,7,4]=>100101
[6,2,3,5,4,1,7]=>100110
[6,2,3,5,4,7,1]=>100101
[6,2,3,5,7,1,4]=>100010
[6,2,3,5,7,4,1]=>100011
[6,2,3,7,1,4,5]=>100100
[6,2,3,7,1,5,4]=>100101
[6,2,3,7,4,1,5]=>100110
[6,2,3,7,4,5,1]=>100101
[6,2,3,7,5,1,4]=>100110
[6,2,3,7,5,4,1]=>100111
[6,2,4,1,3,5,7]=>101000
[6,2,4,1,3,7,5]=>101001
[6,2,4,1,5,3,7]=>101010
[6,2,4,1,5,7,3]=>101001
[6,2,4,1,7,3,5]=>101010
[6,2,4,1,7,5,3]=>101011
[6,2,4,3,1,5,7]=>101100
[6,2,4,3,1,7,5]=>101101
[6,2,4,3,5,1,7]=>101010
[6,2,4,3,5,7,1]=>101001
[6,2,4,3,7,1,5]=>101010
[6,2,4,3,7,5,1]=>101011
[6,2,4,5,1,3,7]=>100100
[6,2,4,5,1,7,3]=>100101
[6,2,4,5,3,1,7]=>100110
[6,2,4,5,3,7,1]=>100101
[6,2,4,5,7,1,3]=>100010
[6,2,4,5,7,3,1]=>100011
[6,2,4,7,1,3,5]=>100100
[6,2,4,7,1,5,3]=>100101
[6,2,4,7,3,1,5]=>100110
[6,2,4,7,3,5,1]=>100101
[6,2,4,7,5,1,3]=>100110
[6,2,4,7,5,3,1]=>100111
[6,2,5,1,3,4,7]=>101000
[6,2,5,1,3,7,4]=>101001
[6,2,5,1,4,3,7]=>101010
[6,2,5,1,4,7,3]=>101001
[6,2,5,1,7,3,4]=>101010
[6,2,5,1,7,4,3]=>101011
[6,2,5,3,1,4,7]=>101100
[6,2,5,3,1,7,4]=>101101
[6,2,5,3,4,1,7]=>101010
[6,2,5,3,4,7,1]=>101001
[6,2,5,3,7,1,4]=>101010
[6,2,5,3,7,4,1]=>101011
[6,2,5,4,1,3,7]=>101100
[6,2,5,4,1,7,3]=>101101
[6,2,5,4,3,1,7]=>101110
[6,2,5,4,3,7,1]=>101101
[6,2,5,4,7,1,3]=>101010
[6,2,5,4,7,3,1]=>101011
[6,2,5,7,1,3,4]=>100100
[6,2,5,7,1,4,3]=>100101
[6,2,5,7,3,1,4]=>100110
[6,2,5,7,3,4,1]=>100101
[6,2,5,7,4,1,3]=>100110
[6,2,5,7,4,3,1]=>100111
[6,2,7,1,3,4,5]=>101000
[6,2,7,1,3,5,4]=>101001
[6,2,7,1,4,3,5]=>101010
[6,2,7,1,4,5,3]=>101001
[6,2,7,1,5,3,4]=>101010
[6,2,7,1,5,4,3]=>101011
[6,2,7,3,1,4,5]=>101100
[6,2,7,3,1,5,4]=>101101
[6,2,7,3,4,1,5]=>101010
[6,2,7,3,4,5,1]=>101001
[6,2,7,3,5,1,4]=>101010
[6,2,7,3,5,4,1]=>101011
[6,2,7,4,1,3,5]=>101100
[6,2,7,4,1,5,3]=>101101
[6,2,7,4,3,1,5]=>101110
[6,2,7,4,3,5,1]=>101101
[6,2,7,4,5,1,3]=>101010
[6,2,7,4,5,3,1]=>101011
[6,2,7,5,1,3,4]=>101100
[6,2,7,5,1,4,3]=>101101
[6,2,7,5,3,1,4]=>101110
[6,2,7,5,3,4,1]=>101101
[6,2,7,5,4,1,3]=>101110
[6,2,7,5,4,3,1]=>101111
[6,3,1,2,4,5,7]=>110000
[6,3,1,2,4,7,5]=>110001
[6,3,1,2,5,4,7]=>110010
[6,3,1,2,5,7,4]=>110001
[6,3,1,2,7,4,5]=>110010
[6,3,1,2,7,5,4]=>110011
[6,3,1,4,2,5,7]=>110100
[6,3,1,4,2,7,5]=>110101
[6,3,1,4,5,2,7]=>110010
[6,3,1,4,5,7,2]=>110001
[6,3,1,4,7,2,5]=>110010
[6,3,1,4,7,5,2]=>110011
[6,3,1,5,2,4,7]=>110100
[6,3,1,5,2,7,4]=>110101
[6,3,1,5,4,2,7]=>110110
[6,3,1,5,4,7,2]=>110101
[6,3,1,5,7,2,4]=>110010
[6,3,1,5,7,4,2]=>110011
[6,3,1,7,2,4,5]=>110100
[6,3,1,7,2,5,4]=>110101
[6,3,1,7,4,2,5]=>110110
[6,3,1,7,4,5,2]=>110101
[6,3,1,7,5,2,4]=>110110
[6,3,1,7,5,4,2]=>110111
[6,3,2,1,4,5,7]=>111000
[6,3,2,1,4,7,5]=>111001
[6,3,2,1,5,4,7]=>111010
[6,3,2,1,5,7,4]=>111001
[6,3,2,1,7,4,5]=>111010
[6,3,2,1,7,5,4]=>111011
[6,3,2,4,1,5,7]=>110100
[6,3,2,4,1,7,5]=>110101
[6,3,2,4,5,1,7]=>110010
[6,3,2,4,5,7,1]=>110001
[6,3,2,4,7,1,5]=>110010
[6,3,2,4,7,5,1]=>110011
[6,3,2,5,1,4,7]=>110100
[6,3,2,5,1,7,4]=>110101
[6,3,2,5,4,1,7]=>110110
[6,3,2,5,4,7,1]=>110101
[6,3,2,5,7,1,4]=>110010
[6,3,2,5,7,4,1]=>110011
[6,3,2,7,1,4,5]=>110100
[6,3,2,7,1,5,4]=>110101
[6,3,2,7,4,1,5]=>110110
[6,3,2,7,4,5,1]=>110101
[6,3,2,7,5,1,4]=>110110
[6,3,2,7,5,4,1]=>110111
[6,3,4,1,2,5,7]=>101000
[6,3,4,1,2,7,5]=>101001
[6,3,4,1,5,2,7]=>101010
[6,3,4,1,5,7,2]=>101001
[6,3,4,1,7,2,5]=>101010
[6,3,4,1,7,5,2]=>101011
[6,3,4,2,1,5,7]=>101100
[6,3,4,2,1,7,5]=>101101
[6,3,4,2,5,1,7]=>101010
[6,3,4,2,5,7,1]=>101001
[6,3,4,2,7,1,5]=>101010
[6,3,4,2,7,5,1]=>101011
[6,3,4,5,1,2,7]=>100100
[6,3,4,5,1,7,2]=>100101
[6,3,4,5,2,1,7]=>100110
[6,3,4,5,2,7,1]=>100101
[6,3,4,5,7,1,2]=>100010
[6,3,4,5,7,2,1]=>100011
[6,3,4,7,1,2,5]=>100100
[6,3,4,7,1,5,2]=>100101
[6,3,4,7,2,1,5]=>100110
[6,3,4,7,2,5,1]=>100101
[6,3,4,7,5,1,2]=>100110
[6,3,4,7,5,2,1]=>100111
[6,3,5,1,2,4,7]=>101000
[6,3,5,1,2,7,4]=>101001
[6,3,5,1,4,2,7]=>101010
[6,3,5,1,4,7,2]=>101001
[6,3,5,1,7,2,4]=>101010
[6,3,5,1,7,4,2]=>101011
[6,3,5,2,1,4,7]=>101100
[6,3,5,2,1,7,4]=>101101
[6,3,5,2,4,1,7]=>101010
[6,3,5,2,4,7,1]=>101001
[6,3,5,2,7,1,4]=>101010
[6,3,5,2,7,4,1]=>101011
[6,3,5,4,1,2,7]=>101100
[6,3,5,4,1,7,2]=>101101
[6,3,5,4,2,1,7]=>101110
[6,3,5,4,2,7,1]=>101101
[6,3,5,4,7,1,2]=>101010
[6,3,5,4,7,2,1]=>101011
[6,3,5,7,1,2,4]=>100100
[6,3,5,7,1,4,2]=>100101
[6,3,5,7,2,1,4]=>100110
[6,3,5,7,2,4,1]=>100101
[6,3,5,7,4,1,2]=>100110
[6,3,5,7,4,2,1]=>100111
[6,3,7,1,2,4,5]=>101000
[6,3,7,1,2,5,4]=>101001
[6,3,7,1,4,2,5]=>101010
[6,3,7,1,4,5,2]=>101001
[6,3,7,1,5,2,4]=>101010
[6,3,7,1,5,4,2]=>101011
[6,3,7,2,1,4,5]=>101100
[6,3,7,2,1,5,4]=>101101
[6,3,7,2,4,1,5]=>101010
[6,3,7,2,4,5,1]=>101001
[6,3,7,2,5,1,4]=>101010
[6,3,7,2,5,4,1]=>101011
[6,3,7,4,1,2,5]=>101100
[6,3,7,4,1,5,2]=>101101
[6,3,7,4,2,1,5]=>101110
[6,3,7,4,2,5,1]=>101101
[6,3,7,4,5,1,2]=>101010
[6,3,7,4,5,2,1]=>101011
[6,3,7,5,1,2,4]=>101100
[6,3,7,5,1,4,2]=>101101
[6,3,7,5,2,1,4]=>101110
[6,3,7,5,2,4,1]=>101101
[6,3,7,5,4,1,2]=>101110
[6,3,7,5,4,2,1]=>101111
[6,4,1,2,3,5,7]=>110000
[6,4,1,2,3,7,5]=>110001
[6,4,1,2,5,3,7]=>110010
[6,4,1,2,5,7,3]=>110001
[6,4,1,2,7,3,5]=>110010
[6,4,1,2,7,5,3]=>110011
[6,4,1,3,2,5,7]=>110100
[6,4,1,3,2,7,5]=>110101
[6,4,1,3,5,2,7]=>110010
[6,4,1,3,5,7,2]=>110001
[6,4,1,3,7,2,5]=>110010
[6,4,1,3,7,5,2]=>110011
[6,4,1,5,2,3,7]=>110100
[6,4,1,5,2,7,3]=>110101
[6,4,1,5,3,2,7]=>110110
[6,4,1,5,3,7,2]=>110101
[6,4,1,5,7,2,3]=>110010
[6,4,1,5,7,3,2]=>110011
[6,4,1,7,2,3,5]=>110100
[6,4,1,7,2,5,3]=>110101
[6,4,1,7,3,2,5]=>110110
[6,4,1,7,3,5,2]=>110101
[6,4,1,7,5,2,3]=>110110
[6,4,1,7,5,3,2]=>110111
[6,4,2,1,3,5,7]=>111000
[6,4,2,1,3,7,5]=>111001
[6,4,2,1,5,3,7]=>111010
[6,4,2,1,5,7,3]=>111001
[6,4,2,1,7,3,5]=>111010
[6,4,2,1,7,5,3]=>111011
[6,4,2,3,1,5,7]=>110100
[6,4,2,3,1,7,5]=>110101
[6,4,2,3,5,1,7]=>110010
[6,4,2,3,5,7,1]=>110001
[6,4,2,3,7,1,5]=>110010
[6,4,2,3,7,5,1]=>110011
[6,4,2,5,1,3,7]=>110100
[6,4,2,5,1,7,3]=>110101
[6,4,2,5,3,1,7]=>110110
[6,4,2,5,3,7,1]=>110101
[6,4,2,5,7,1,3]=>110010
[6,4,2,5,7,3,1]=>110011
[6,4,2,7,1,3,5]=>110100
[6,4,2,7,1,5,3]=>110101
[6,4,2,7,3,1,5]=>110110
[6,4,2,7,3,5,1]=>110101
[6,4,2,7,5,1,3]=>110110
[6,4,2,7,5,3,1]=>110111
[6,4,3,1,2,5,7]=>111000
[6,4,3,1,2,7,5]=>111001
[6,4,3,1,5,2,7]=>111010
[6,4,3,1,5,7,2]=>111001
[6,4,3,1,7,2,5]=>111010
[6,4,3,1,7,5,2]=>111011
[6,4,3,2,1,5,7]=>111100
[6,4,3,2,1,7,5]=>111101
[6,4,3,2,5,1,7]=>111010
[6,4,3,2,5,7,1]=>111001
[6,4,3,2,7,1,5]=>111010
[6,4,3,2,7,5,1]=>111011
[6,4,3,5,1,2,7]=>110100
[6,4,3,5,1,7,2]=>110101
[6,4,3,5,2,1,7]=>110110
[6,4,3,5,2,7,1]=>110101
[6,4,3,5,7,1,2]=>110010
[6,4,3,5,7,2,1]=>110011
[6,4,3,7,1,2,5]=>110100
[6,4,3,7,1,5,2]=>110101
[6,4,3,7,2,1,5]=>110110
[6,4,3,7,2,5,1]=>110101
[6,4,3,7,5,1,2]=>110110
[6,4,3,7,5,2,1]=>110111
[6,4,5,1,2,3,7]=>101000
[6,4,5,1,2,7,3]=>101001
[6,4,5,1,3,2,7]=>101010
[6,4,5,1,3,7,2]=>101001
[6,4,5,1,7,2,3]=>101010
[6,4,5,1,7,3,2]=>101011
[6,4,5,2,1,3,7]=>101100
[6,4,5,2,1,7,3]=>101101
[6,4,5,2,3,1,7]=>101010
[6,4,5,2,3,7,1]=>101001
[6,4,5,2,7,1,3]=>101010
[6,4,5,2,7,3,1]=>101011
[6,4,5,3,1,2,7]=>101100
[6,4,5,3,1,7,2]=>101101
[6,4,5,3,2,1,7]=>101110
[6,4,5,3,2,7,1]=>101101
[6,4,5,3,7,1,2]=>101010
[6,4,5,3,7,2,1]=>101011
[6,4,5,7,1,2,3]=>100100
[6,4,5,7,1,3,2]=>100101
[6,4,5,7,2,1,3]=>100110
[6,4,5,7,2,3,1]=>100101
[6,4,5,7,3,1,2]=>100110
[6,4,5,7,3,2,1]=>100111
[6,4,7,1,2,3,5]=>101000
[6,4,7,1,2,5,3]=>101001
[6,4,7,1,3,2,5]=>101010
[6,4,7,1,3,5,2]=>101001
[6,4,7,1,5,2,3]=>101010
[6,4,7,1,5,3,2]=>101011
[6,4,7,2,1,3,5]=>101100
[6,4,7,2,1,5,3]=>101101
[6,4,7,2,3,1,5]=>101010
[6,4,7,2,3,5,1]=>101001
[6,4,7,2,5,1,3]=>101010
[6,4,7,2,5,3,1]=>101011
[6,4,7,3,1,2,5]=>101100
[6,4,7,3,1,5,2]=>101101
[6,4,7,3,2,1,5]=>101110
[6,4,7,3,2,5,1]=>101101
[6,4,7,3,5,1,2]=>101010
[6,4,7,3,5,2,1]=>101011
[6,4,7,5,1,2,3]=>101100
[6,4,7,5,1,3,2]=>101101
[6,4,7,5,2,1,3]=>101110
[6,4,7,5,2,3,1]=>101101
[6,4,7,5,3,1,2]=>101110
[6,4,7,5,3,2,1]=>101111
[6,5,1,2,3,4,7]=>110000
[6,5,1,2,3,7,4]=>110001
[6,5,1,2,4,3,7]=>110010
[6,5,1,2,4,7,3]=>110001
[6,5,1,2,7,3,4]=>110010
[6,5,1,2,7,4,3]=>110011
[6,5,1,3,2,4,7]=>110100
[6,5,1,3,2,7,4]=>110101
[6,5,1,3,4,2,7]=>110010
[6,5,1,3,4,7,2]=>110001
[6,5,1,3,7,2,4]=>110010
[6,5,1,3,7,4,2]=>110011
[6,5,1,4,2,3,7]=>110100
[6,5,1,4,2,7,3]=>110101
[6,5,1,4,3,2,7]=>110110
[6,5,1,4,3,7,2]=>110101
[6,5,1,4,7,2,3]=>110010
[6,5,1,4,7,3,2]=>110011
[6,5,1,7,2,3,4]=>110100
[6,5,1,7,2,4,3]=>110101
[6,5,1,7,3,2,4]=>110110
[6,5,1,7,3,4,2]=>110101
[6,5,1,7,4,2,3]=>110110
[6,5,1,7,4,3,2]=>110111
[6,5,2,1,3,4,7]=>111000
[6,5,2,1,3,7,4]=>111001
[6,5,2,1,4,3,7]=>111010
[6,5,2,1,4,7,3]=>111001
[6,5,2,1,7,3,4]=>111010
[6,5,2,1,7,4,3]=>111011
[6,5,2,3,1,4,7]=>110100
[6,5,2,3,1,7,4]=>110101
[6,5,2,3,4,1,7]=>110010
[6,5,2,3,4,7,1]=>110001
[6,5,2,3,7,1,4]=>110010
[6,5,2,3,7,4,1]=>110011
[6,5,2,4,1,3,7]=>110100
[6,5,2,4,1,7,3]=>110101
[6,5,2,4,3,1,7]=>110110
[6,5,2,4,3,7,1]=>110101
[6,5,2,4,7,1,3]=>110010
[6,5,2,4,7,3,1]=>110011
[6,5,2,7,1,3,4]=>110100
[6,5,2,7,1,4,3]=>110101
[6,5,2,7,3,1,4]=>110110
[6,5,2,7,3,4,1]=>110101
[6,5,2,7,4,1,3]=>110110
[6,5,2,7,4,3,1]=>110111
[6,5,3,1,2,4,7]=>111000
[6,5,3,1,2,7,4]=>111001
[6,5,3,1,4,2,7]=>111010
[6,5,3,1,4,7,2]=>111001
[6,5,3,1,7,2,4]=>111010
[6,5,3,1,7,4,2]=>111011
[6,5,3,2,1,4,7]=>111100
[6,5,3,2,1,7,4]=>111101
[6,5,3,2,4,1,7]=>111010
[6,5,3,2,4,7,1]=>111001
[6,5,3,2,7,1,4]=>111010
[6,5,3,2,7,4,1]=>111011
[6,5,3,4,1,2,7]=>110100
[6,5,3,4,1,7,2]=>110101
[6,5,3,4,2,1,7]=>110110
[6,5,3,4,2,7,1]=>110101
[6,5,3,4,7,1,2]=>110010
[6,5,3,4,7,2,1]=>110011
[6,5,3,7,1,2,4]=>110100
[6,5,3,7,1,4,2]=>110101
[6,5,3,7,2,1,4]=>110110
[6,5,3,7,2,4,1]=>110101
[6,5,3,7,4,1,2]=>110110
[6,5,3,7,4,2,1]=>110111
[6,5,4,1,2,3,7]=>111000
[6,5,4,1,2,7,3]=>111001
[6,5,4,1,3,2,7]=>111010
[6,5,4,1,3,7,2]=>111001
[6,5,4,1,7,2,3]=>111010
[6,5,4,1,7,3,2]=>111011
[6,5,4,2,1,3,7]=>111100
[6,5,4,2,1,7,3]=>111101
[6,5,4,2,3,1,7]=>111010
[6,5,4,2,3,7,1]=>111001
[6,5,4,2,7,1,3]=>111010
[6,5,4,2,7,3,1]=>111011
[6,5,4,3,1,2,7]=>111100
[6,5,4,3,1,7,2]=>111101
[6,5,4,3,2,1,7]=>111110
[6,5,4,3,2,7,1]=>111101
[6,5,4,3,7,1,2]=>111010
[6,5,4,3,7,2,1]=>111011
[6,5,4,7,1,2,3]=>110100
[6,5,4,7,1,3,2]=>110101
[6,5,4,7,2,1,3]=>110110
[6,5,4,7,2,3,1]=>110101
[6,5,4,7,3,1,2]=>110110
[6,5,4,7,3,2,1]=>110111
[6,5,7,1,2,3,4]=>101000
[6,5,7,1,2,4,3]=>101001
[6,5,7,1,3,2,4]=>101010
[6,5,7,1,3,4,2]=>101001
[6,5,7,1,4,2,3]=>101010
[6,5,7,1,4,3,2]=>101011
[6,5,7,2,1,3,4]=>101100
[6,5,7,2,1,4,3]=>101101
[6,5,7,2,3,1,4]=>101010
[6,5,7,2,3,4,1]=>101001
[6,5,7,2,4,1,3]=>101010
[6,5,7,2,4,3,1]=>101011
[6,5,7,3,1,2,4]=>101100
[6,5,7,3,1,4,2]=>101101
[6,5,7,3,2,1,4]=>101110
[6,5,7,3,2,4,1]=>101101
[6,5,7,3,4,1,2]=>101010
[6,5,7,3,4,2,1]=>101011
[6,5,7,4,1,2,3]=>101100
[6,5,7,4,1,3,2]=>101101
[6,5,7,4,2,1,3]=>101110
[6,5,7,4,2,3,1]=>101101
[6,5,7,4,3,1,2]=>101110
[6,5,7,4,3,2,1]=>101111
[6,7,1,2,3,4,5]=>010000
[6,7,1,2,3,5,4]=>010001
[6,7,1,2,4,3,5]=>010010
[6,7,1,2,4,5,3]=>010001
[6,7,1,2,5,3,4]=>010010
[6,7,1,2,5,4,3]=>010011
[6,7,1,3,2,4,5]=>010100
[6,7,1,3,2,5,4]=>010101
[6,7,1,3,4,2,5]=>010010
[6,7,1,3,4,5,2]=>010001
[6,7,1,3,5,2,4]=>010010
[6,7,1,3,5,4,2]=>010011
[6,7,1,4,2,3,5]=>010100
[6,7,1,4,2,5,3]=>010101
[6,7,1,4,3,2,5]=>010110
[6,7,1,4,3,5,2]=>010101
[6,7,1,4,5,2,3]=>010010
[6,7,1,4,5,3,2]=>010011
[6,7,1,5,2,3,4]=>010100
[6,7,1,5,2,4,3]=>010101
[6,7,1,5,3,2,4]=>010110
[6,7,1,5,3,4,2]=>010101
[6,7,1,5,4,2,3]=>010110
[6,7,1,5,4,3,2]=>010111
[6,7,2,1,3,4,5]=>011000
[6,7,2,1,3,5,4]=>011001
[6,7,2,1,4,3,5]=>011010
[6,7,2,1,4,5,3]=>011001
[6,7,2,1,5,3,4]=>011010
[6,7,2,1,5,4,3]=>011011
[6,7,2,3,1,4,5]=>010100
[6,7,2,3,1,5,4]=>010101
[6,7,2,3,4,1,5]=>010010
[6,7,2,3,4,5,1]=>010001
[6,7,2,3,5,1,4]=>010010
[6,7,2,3,5,4,1]=>010011
[6,7,2,4,1,3,5]=>010100
[6,7,2,4,1,5,3]=>010101
[6,7,2,4,3,1,5]=>010110
[6,7,2,4,3,5,1]=>010101
[6,7,2,4,5,1,3]=>010010
[6,7,2,4,5,3,1]=>010011
[6,7,2,5,1,3,4]=>010100
[6,7,2,5,1,4,3]=>010101
[6,7,2,5,3,1,4]=>010110
[6,7,2,5,3,4,1]=>010101
[6,7,2,5,4,1,3]=>010110
[6,7,2,5,4,3,1]=>010111
[6,7,3,1,2,4,5]=>011000
[6,7,3,1,2,5,4]=>011001
[6,7,3,1,4,2,5]=>011010
[6,7,3,1,4,5,2]=>011001
[6,7,3,1,5,2,4]=>011010
[6,7,3,1,5,4,2]=>011011
[6,7,3,2,1,4,5]=>011100
[6,7,3,2,1,5,4]=>011101
[6,7,3,2,4,1,5]=>011010
[6,7,3,2,4,5,1]=>011001
[6,7,3,2,5,1,4]=>011010
[6,7,3,2,5,4,1]=>011011
[6,7,3,4,1,2,5]=>010100
[6,7,3,4,1,5,2]=>010101
[6,7,3,4,2,1,5]=>010110
[6,7,3,4,2,5,1]=>010101
[6,7,3,4,5,1,2]=>010010
[6,7,3,4,5,2,1]=>010011
[6,7,3,5,1,2,4]=>010100
[6,7,3,5,1,4,2]=>010101
[6,7,3,5,2,1,4]=>010110
[6,7,3,5,2,4,1]=>010101
[6,7,3,5,4,1,2]=>010110
[6,7,3,5,4,2,1]=>010111
[6,7,4,1,2,3,5]=>011000
[6,7,4,1,2,5,3]=>011001
[6,7,4,1,3,2,5]=>011010
[6,7,4,1,3,5,2]=>011001
[6,7,4,1,5,2,3]=>011010
[6,7,4,1,5,3,2]=>011011
[6,7,4,2,1,3,5]=>011100
[6,7,4,2,1,5,3]=>011101
[6,7,4,2,3,1,5]=>011010
[6,7,4,2,3,5,1]=>011001
[6,7,4,2,5,1,3]=>011010
[6,7,4,2,5,3,1]=>011011
[6,7,4,3,1,2,5]=>011100
[6,7,4,3,1,5,2]=>011101
[6,7,4,3,2,1,5]=>011110
[6,7,4,3,2,5,1]=>011101
[6,7,4,3,5,1,2]=>011010
[6,7,4,3,5,2,1]=>011011
[6,7,4,5,1,2,3]=>010100
[6,7,4,5,1,3,2]=>010101
[6,7,4,5,2,1,3]=>010110
[6,7,4,5,2,3,1]=>010101
[6,7,4,5,3,1,2]=>010110
[6,7,4,5,3,2,1]=>010111
[6,7,5,1,2,3,4]=>011000
[6,7,5,1,2,4,3]=>011001
[6,7,5,1,3,2,4]=>011010
[6,7,5,1,3,4,2]=>011001
[6,7,5,1,4,2,3]=>011010
[6,7,5,1,4,3,2]=>011011
[6,7,5,2,1,3,4]=>011100
[6,7,5,2,1,4,3]=>011101
[6,7,5,2,3,1,4]=>011010
[6,7,5,2,3,4,1]=>011001
[6,7,5,2,4,1,3]=>011010
[6,7,5,2,4,3,1]=>011011
[6,7,5,3,1,2,4]=>011100
[6,7,5,3,1,4,2]=>011101
[6,7,5,3,2,1,4]=>011110
[6,7,5,3,2,4,1]=>011101
[6,7,5,3,4,1,2]=>011010
[6,7,5,3,4,2,1]=>011011
[6,7,5,4,1,2,3]=>011100
[6,7,5,4,1,3,2]=>011101
[6,7,5,4,2,1,3]=>011110
[6,7,5,4,2,3,1]=>011101
[6,7,5,4,3,1,2]=>011110
[6,7,5,4,3,2,1]=>011111
[7,1,2,3,4,5,6]=>100000
[7,1,2,3,4,6,5]=>100001
[7,1,2,3,5,4,6]=>100010
[7,1,2,3,5,6,4]=>100001
[7,1,2,3,6,4,5]=>100010
[7,1,2,3,6,5,4]=>100011
[7,1,2,4,3,5,6]=>100100
[7,1,2,4,3,6,5]=>100101
[7,1,2,4,5,3,6]=>100010
[7,1,2,4,5,6,3]=>100001
[7,1,2,4,6,3,5]=>100010
[7,1,2,4,6,5,3]=>100011
[7,1,2,5,3,4,6]=>100100
[7,1,2,5,3,6,4]=>100101
[7,1,2,5,4,3,6]=>100110
[7,1,2,5,4,6,3]=>100101
[7,1,2,5,6,3,4]=>100010
[7,1,2,5,6,4,3]=>100011
[7,1,2,6,3,4,5]=>100100
[7,1,2,6,3,5,4]=>100101
[7,1,2,6,4,3,5]=>100110
[7,1,2,6,4,5,3]=>100101
[7,1,2,6,5,3,4]=>100110
[7,1,2,6,5,4,3]=>100111
[7,1,3,2,4,5,6]=>101000
[7,1,3,2,4,6,5]=>101001
[7,1,3,2,5,4,6]=>101010
[7,1,3,2,5,6,4]=>101001
[7,1,3,2,6,4,5]=>101010
[7,1,3,2,6,5,4]=>101011
[7,1,3,4,2,5,6]=>100100
[7,1,3,4,2,6,5]=>100101
[7,1,3,4,5,2,6]=>100010
[7,1,3,4,5,6,2]=>100001
[7,1,3,4,6,2,5]=>100010
[7,1,3,4,6,5,2]=>100011
[7,1,3,5,2,4,6]=>100100
[7,1,3,5,2,6,4]=>100101
[7,1,3,5,4,2,6]=>100110
[7,1,3,5,4,6,2]=>100101
[7,1,3,5,6,2,4]=>100010
[7,1,3,5,6,4,2]=>100011
[7,1,3,6,2,4,5]=>100100
[7,1,3,6,2,5,4]=>100101
[7,1,3,6,4,2,5]=>100110
[7,1,3,6,4,5,2]=>100101
[7,1,3,6,5,2,4]=>100110
[7,1,3,6,5,4,2]=>100111
[7,1,4,2,3,5,6]=>101000
[7,1,4,2,3,6,5]=>101001
[7,1,4,2,5,3,6]=>101010
[7,1,4,2,5,6,3]=>101001
[7,1,4,2,6,3,5]=>101010
[7,1,4,2,6,5,3]=>101011
[7,1,4,3,2,5,6]=>101100
[7,1,4,3,2,6,5]=>101101
[7,1,4,3,5,2,6]=>101010
[7,1,4,3,5,6,2]=>101001
[7,1,4,3,6,2,5]=>101010
[7,1,4,3,6,5,2]=>101011
[7,1,4,5,2,3,6]=>100100
[7,1,4,5,2,6,3]=>100101
[7,1,4,5,3,2,6]=>100110
[7,1,4,5,3,6,2]=>100101
[7,1,4,5,6,2,3]=>100010
[7,1,4,5,6,3,2]=>100011
[7,1,4,6,2,3,5]=>100100
[7,1,4,6,2,5,3]=>100101
[7,1,4,6,3,2,5]=>100110
[7,1,4,6,3,5,2]=>100101
[7,1,4,6,5,2,3]=>100110
[7,1,4,6,5,3,2]=>100111
[7,1,5,2,3,4,6]=>101000
[7,1,5,2,3,6,4]=>101001
[7,1,5,2,4,3,6]=>101010
[7,1,5,2,4,6,3]=>101001
[7,1,5,2,6,3,4]=>101010
[7,1,5,2,6,4,3]=>101011
[7,1,5,3,2,4,6]=>101100
[7,1,5,3,2,6,4]=>101101
[7,1,5,3,4,2,6]=>101010
[7,1,5,3,4,6,2]=>101001
[7,1,5,3,6,2,4]=>101010
[7,1,5,3,6,4,2]=>101011
[7,1,5,4,2,3,6]=>101100
[7,1,5,4,2,6,3]=>101101
[7,1,5,4,3,2,6]=>101110
[7,1,5,4,3,6,2]=>101101
[7,1,5,4,6,2,3]=>101010
[7,1,5,4,6,3,2]=>101011
[7,1,5,6,2,3,4]=>100100
[7,1,5,6,2,4,3]=>100101
[7,1,5,6,3,2,4]=>100110
[7,1,5,6,3,4,2]=>100101
[7,1,5,6,4,2,3]=>100110
[7,1,5,6,4,3,2]=>100111
[7,1,6,2,3,4,5]=>101000
[7,1,6,2,3,5,4]=>101001
[7,1,6,2,4,3,5]=>101010
[7,1,6,2,4,5,3]=>101001
[7,1,6,2,5,3,4]=>101010
[7,1,6,2,5,4,3]=>101011
[7,1,6,3,2,4,5]=>101100
[7,1,6,3,2,5,4]=>101101
[7,1,6,3,4,2,5]=>101010
[7,1,6,3,4,5,2]=>101001
[7,1,6,3,5,2,4]=>101010
[7,1,6,3,5,4,2]=>101011
[7,1,6,4,2,3,5]=>101100
[7,1,6,4,2,5,3]=>101101
[7,1,6,4,3,2,5]=>101110
[7,1,6,4,3,5,2]=>101101
[7,1,6,4,5,2,3]=>101010
[7,1,6,4,5,3,2]=>101011
[7,1,6,5,2,3,4]=>101100
[7,1,6,5,2,4,3]=>101101
[7,1,6,5,3,2,4]=>101110
[7,1,6,5,3,4,2]=>101101
[7,1,6,5,4,2,3]=>101110
[7,1,6,5,4,3,2]=>101111
[7,2,1,3,4,5,6]=>110000
[7,2,1,3,4,6,5]=>110001
[7,2,1,3,5,4,6]=>110010
[7,2,1,3,5,6,4]=>110001
[7,2,1,3,6,4,5]=>110010
[7,2,1,3,6,5,4]=>110011
[7,2,1,4,3,5,6]=>110100
[7,2,1,4,3,6,5]=>110101
[7,2,1,4,5,3,6]=>110010
[7,2,1,4,5,6,3]=>110001
[7,2,1,4,6,3,5]=>110010
[7,2,1,4,6,5,3]=>110011
[7,2,1,5,3,4,6]=>110100
[7,2,1,5,3,6,4]=>110101
[7,2,1,5,4,3,6]=>110110
[7,2,1,5,4,6,3]=>110101
[7,2,1,5,6,3,4]=>110010
[7,2,1,5,6,4,3]=>110011
[7,2,1,6,3,4,5]=>110100
[7,2,1,6,3,5,4]=>110101
[7,2,1,6,4,3,5]=>110110
[7,2,1,6,4,5,3]=>110101
[7,2,1,6,5,3,4]=>110110
[7,2,1,6,5,4,3]=>110111
[7,2,3,1,4,5,6]=>101000
[7,2,3,1,4,6,5]=>101001
[7,2,3,1,5,4,6]=>101010
[7,2,3,1,5,6,4]=>101001
[7,2,3,1,6,4,5]=>101010
[7,2,3,1,6,5,4]=>101011
[7,2,3,4,1,5,6]=>100100
[7,2,3,4,1,6,5]=>100101
[7,2,3,4,5,1,6]=>100010
[7,2,3,4,5,6,1]=>100001
[7,2,3,4,6,1,5]=>100010
[7,2,3,4,6,5,1]=>100011
[7,2,3,5,1,4,6]=>100100
[7,2,3,5,1,6,4]=>100101
[7,2,3,5,4,1,6]=>100110
[7,2,3,5,4,6,1]=>100101
[7,2,3,5,6,1,4]=>100010
[7,2,3,5,6,4,1]=>100011
[7,2,3,6,1,4,5]=>100100
[7,2,3,6,1,5,4]=>100101
[7,2,3,6,4,1,5]=>100110
[7,2,3,6,4,5,1]=>100101
[7,2,3,6,5,1,4]=>100110
[7,2,3,6,5,4,1]=>100111
[7,2,4,1,3,5,6]=>101000
[7,2,4,1,3,6,5]=>101001
[7,2,4,1,5,3,6]=>101010
[7,2,4,1,5,6,3]=>101001
[7,2,4,1,6,3,5]=>101010
[7,2,4,1,6,5,3]=>101011
[7,2,4,3,1,5,6]=>101100
[7,2,4,3,1,6,5]=>101101
[7,2,4,3,5,1,6]=>101010
[7,2,4,3,5,6,1]=>101001
[7,2,4,3,6,1,5]=>101010
[7,2,4,3,6,5,1]=>101011
[7,2,4,5,1,3,6]=>100100
[7,2,4,5,1,6,3]=>100101
[7,2,4,5,3,1,6]=>100110
[7,2,4,5,3,6,1]=>100101
[7,2,4,5,6,1,3]=>100010
[7,2,4,5,6,3,1]=>100011
[7,2,4,6,1,3,5]=>100100
[7,2,4,6,1,5,3]=>100101
[7,2,4,6,3,1,5]=>100110
[7,2,4,6,3,5,1]=>100101
[7,2,4,6,5,1,3]=>100110
[7,2,4,6,5,3,1]=>100111
[7,2,5,1,3,4,6]=>101000
[7,2,5,1,3,6,4]=>101001
[7,2,5,1,4,3,6]=>101010
[7,2,5,1,4,6,3]=>101001
[7,2,5,1,6,3,4]=>101010
[7,2,5,1,6,4,3]=>101011
[7,2,5,3,1,4,6]=>101100
[7,2,5,3,1,6,4]=>101101
[7,2,5,3,4,1,6]=>101010
[7,2,5,3,4,6,1]=>101001
[7,2,5,3,6,1,4]=>101010
[7,2,5,3,6,4,1]=>101011
[7,2,5,4,1,3,6]=>101100
[7,2,5,4,1,6,3]=>101101
[7,2,5,4,3,1,6]=>101110
[7,2,5,4,3,6,1]=>101101
[7,2,5,4,6,1,3]=>101010
[7,2,5,4,6,3,1]=>101011
[7,2,5,6,1,3,4]=>100100
[7,2,5,6,1,4,3]=>100101
[7,2,5,6,3,1,4]=>100110
[7,2,5,6,3,4,1]=>100101
[7,2,5,6,4,1,3]=>100110
[7,2,5,6,4,3,1]=>100111
[7,2,6,1,3,4,5]=>101000
[7,2,6,1,3,5,4]=>101001
[7,2,6,1,4,3,5]=>101010
[7,2,6,1,4,5,3]=>101001
[7,2,6,1,5,3,4]=>101010
[7,2,6,1,5,4,3]=>101011
[7,2,6,3,1,4,5]=>101100
[7,2,6,3,1,5,4]=>101101
[7,2,6,3,4,1,5]=>101010
[7,2,6,3,4,5,1]=>101001
[7,2,6,3,5,1,4]=>101010
[7,2,6,3,5,4,1]=>101011
[7,2,6,4,1,3,5]=>101100
[7,2,6,4,1,5,3]=>101101
[7,2,6,4,3,1,5]=>101110
[7,2,6,4,3,5,1]=>101101
[7,2,6,4,5,1,3]=>101010
[7,2,6,4,5,3,1]=>101011
[7,2,6,5,1,3,4]=>101100
[7,2,6,5,1,4,3]=>101101
[7,2,6,5,3,1,4]=>101110
[7,2,6,5,3,4,1]=>101101
[7,2,6,5,4,1,3]=>101110
[7,2,6,5,4,3,1]=>101111
[7,3,1,2,4,5,6]=>110000
[7,3,1,2,4,6,5]=>110001
[7,3,1,2,5,4,6]=>110010
[7,3,1,2,5,6,4]=>110001
[7,3,1,2,6,4,5]=>110010
[7,3,1,2,6,5,4]=>110011
[7,3,1,4,2,5,6]=>110100
[7,3,1,4,2,6,5]=>110101
[7,3,1,4,5,2,6]=>110010
[7,3,1,4,5,6,2]=>110001
[7,3,1,4,6,2,5]=>110010
[7,3,1,4,6,5,2]=>110011
[7,3,1,5,2,4,6]=>110100
[7,3,1,5,2,6,4]=>110101
[7,3,1,5,4,2,6]=>110110
[7,3,1,5,4,6,2]=>110101
[7,3,1,5,6,2,4]=>110010
[7,3,1,5,6,4,2]=>110011
[7,3,1,6,2,4,5]=>110100
[7,3,1,6,2,5,4]=>110101
[7,3,1,6,4,2,5]=>110110
[7,3,1,6,4,5,2]=>110101
[7,3,1,6,5,2,4]=>110110
[7,3,1,6,5,4,2]=>110111
[7,3,2,1,4,5,6]=>111000
[7,3,2,1,4,6,5]=>111001
[7,3,2,1,5,4,6]=>111010
[7,3,2,1,5,6,4]=>111001
[7,3,2,1,6,4,5]=>111010
[7,3,2,1,6,5,4]=>111011
[7,3,2,4,1,5,6]=>110100
[7,3,2,4,1,6,5]=>110101
[7,3,2,4,5,1,6]=>110010
[7,3,2,4,5,6,1]=>110001
[7,3,2,4,6,1,5]=>110010
[7,3,2,4,6,5,1]=>110011
[7,3,2,5,1,4,6]=>110100
[7,3,2,5,1,6,4]=>110101
[7,3,2,5,4,1,6]=>110110
[7,3,2,5,4,6,1]=>110101
[7,3,2,5,6,1,4]=>110010
[7,3,2,5,6,4,1]=>110011
[7,3,2,6,1,4,5]=>110100
[7,3,2,6,1,5,4]=>110101
[7,3,2,6,4,1,5]=>110110
[7,3,2,6,4,5,1]=>110101
[7,3,2,6,5,1,4]=>110110
[7,3,2,6,5,4,1]=>110111
[7,3,4,1,2,5,6]=>101000
[7,3,4,1,2,6,5]=>101001
[7,3,4,1,5,2,6]=>101010
[7,3,4,1,5,6,2]=>101001
[7,3,4,1,6,2,5]=>101010
[7,3,4,1,6,5,2]=>101011
[7,3,4,2,1,5,6]=>101100
[7,3,4,2,1,6,5]=>101101
[7,3,4,2,5,1,6]=>101010
[7,3,4,2,5,6,1]=>101001
[7,3,4,2,6,1,5]=>101010
[7,3,4,2,6,5,1]=>101011
[7,3,4,5,1,2,6]=>100100
[7,3,4,5,1,6,2]=>100101
[7,3,4,5,2,1,6]=>100110
[7,3,4,5,2,6,1]=>100101
[7,3,4,5,6,1,2]=>100010
[7,3,4,5,6,2,1]=>100011
[7,3,4,6,1,2,5]=>100100
[7,3,4,6,1,5,2]=>100101
[7,3,4,6,2,1,5]=>100110
[7,3,4,6,2,5,1]=>100101
[7,3,4,6,5,1,2]=>100110
[7,3,4,6,5,2,1]=>100111
[7,3,5,1,2,4,6]=>101000
[7,3,5,1,2,6,4]=>101001
[7,3,5,1,4,2,6]=>101010
[7,3,5,1,4,6,2]=>101001
[7,3,5,1,6,2,4]=>101010
[7,3,5,1,6,4,2]=>101011
[7,3,5,2,1,4,6]=>101100
[7,3,5,2,1,6,4]=>101101
[7,3,5,2,4,1,6]=>101010
[7,3,5,2,4,6,1]=>101001
[7,3,5,2,6,1,4]=>101010
[7,3,5,2,6,4,1]=>101011
[7,3,5,4,1,2,6]=>101100
[7,3,5,4,1,6,2]=>101101
[7,3,5,4,2,1,6]=>101110
[7,3,5,4,2,6,1]=>101101
[7,3,5,4,6,1,2]=>101010
[7,3,5,4,6,2,1]=>101011
[7,3,5,6,1,2,4]=>100100
[7,3,5,6,1,4,2]=>100101
[7,3,5,6,2,1,4]=>100110
[7,3,5,6,2,4,1]=>100101
[7,3,5,6,4,1,2]=>100110
[7,3,5,6,4,2,1]=>100111
[7,3,6,1,2,4,5]=>101000
[7,3,6,1,2,5,4]=>101001
[7,3,6,1,4,2,5]=>101010
[7,3,6,1,4,5,2]=>101001
[7,3,6,1,5,2,4]=>101010
[7,3,6,1,5,4,2]=>101011
[7,3,6,2,1,4,5]=>101100
[7,3,6,2,1,5,4]=>101101
[7,3,6,2,4,1,5]=>101010
[7,3,6,2,4,5,1]=>101001
[7,3,6,2,5,1,4]=>101010
[7,3,6,2,5,4,1]=>101011
[7,3,6,4,1,2,5]=>101100
[7,3,6,4,1,5,2]=>101101
[7,3,6,4,2,1,5]=>101110
[7,3,6,4,2,5,1]=>101101
[7,3,6,4,5,1,2]=>101010
[7,3,6,4,5,2,1]=>101011
[7,3,6,5,1,2,4]=>101100
[7,3,6,5,1,4,2]=>101101
[7,3,6,5,2,1,4]=>101110
[7,3,6,5,2,4,1]=>101101
[7,3,6,5,4,1,2]=>101110
[7,3,6,5,4,2,1]=>101111
[7,4,1,2,3,5,6]=>110000
[7,4,1,2,3,6,5]=>110001
[7,4,1,2,5,3,6]=>110010
[7,4,1,2,5,6,3]=>110001
[7,4,1,2,6,3,5]=>110010
[7,4,1,2,6,5,3]=>110011
[7,4,1,3,2,5,6]=>110100
[7,4,1,3,2,6,5]=>110101
[7,4,1,3,5,2,6]=>110010
[7,4,1,3,5,6,2]=>110001
[7,4,1,3,6,2,5]=>110010
[7,4,1,3,6,5,2]=>110011
[7,4,1,5,2,3,6]=>110100
[7,4,1,5,2,6,3]=>110101
[7,4,1,5,3,2,6]=>110110
[7,4,1,5,3,6,2]=>110101
[7,4,1,5,6,2,3]=>110010
[7,4,1,5,6,3,2]=>110011
[7,4,1,6,2,3,5]=>110100
[7,4,1,6,2,5,3]=>110101
[7,4,1,6,3,2,5]=>110110
[7,4,1,6,3,5,2]=>110101
[7,4,1,6,5,2,3]=>110110
[7,4,1,6,5,3,2]=>110111
[7,4,2,1,3,5,6]=>111000
[7,4,2,1,3,6,5]=>111001
[7,4,2,1,5,3,6]=>111010
[7,4,2,1,5,6,3]=>111001
[7,4,2,1,6,3,5]=>111010
[7,4,2,1,6,5,3]=>111011
[7,4,2,3,1,5,6]=>110100
[7,4,2,3,1,6,5]=>110101
[7,4,2,3,5,1,6]=>110010
[7,4,2,3,5,6,1]=>110001
[7,4,2,3,6,1,5]=>110010
[7,4,2,3,6,5,1]=>110011
[7,4,2,5,1,3,6]=>110100
[7,4,2,5,1,6,3]=>110101
[7,4,2,5,3,1,6]=>110110
[7,4,2,5,3,6,1]=>110101
[7,4,2,5,6,1,3]=>110010
[7,4,2,5,6,3,1]=>110011
[7,4,2,6,1,3,5]=>110100
[7,4,2,6,1,5,3]=>110101
[7,4,2,6,3,1,5]=>110110
[7,4,2,6,3,5,1]=>110101
[7,4,2,6,5,1,3]=>110110
[7,4,2,6,5,3,1]=>110111
[7,4,3,1,2,5,6]=>111000
[7,4,3,1,2,6,5]=>111001
[7,4,3,1,5,2,6]=>111010
[7,4,3,1,5,6,2]=>111001
[7,4,3,1,6,2,5]=>111010
[7,4,3,1,6,5,2]=>111011
[7,4,3,2,1,5,6]=>111100
[7,4,3,2,1,6,5]=>111101
[7,4,3,2,5,1,6]=>111010
[7,4,3,2,5,6,1]=>111001
[7,4,3,2,6,1,5]=>111010
[7,4,3,2,6,5,1]=>111011
[7,4,3,5,1,2,6]=>110100
[7,4,3,5,1,6,2]=>110101
[7,4,3,5,2,1,6]=>110110
[7,4,3,5,2,6,1]=>110101
[7,4,3,5,6,1,2]=>110010
[7,4,3,5,6,2,1]=>110011
[7,4,3,6,1,2,5]=>110100
[7,4,3,6,1,5,2]=>110101
[7,4,3,6,2,1,5]=>110110
[7,4,3,6,2,5,1]=>110101
[7,4,3,6,5,1,2]=>110110
[7,4,3,6,5,2,1]=>110111
[7,4,5,1,2,3,6]=>101000
[7,4,5,1,2,6,3]=>101001
[7,4,5,1,3,2,6]=>101010
[7,4,5,1,3,6,2]=>101001
[7,4,5,1,6,2,3]=>101010
[7,4,5,1,6,3,2]=>101011
[7,4,5,2,1,3,6]=>101100
[7,4,5,2,1,6,3]=>101101
[7,4,5,2,3,1,6]=>101010
[7,4,5,2,3,6,1]=>101001
[7,4,5,2,6,1,3]=>101010
[7,4,5,2,6,3,1]=>101011
[7,4,5,3,1,2,6]=>101100
[7,4,5,3,1,6,2]=>101101
[7,4,5,3,2,1,6]=>101110
[7,4,5,3,2,6,1]=>101101
[7,4,5,3,6,1,2]=>101010
[7,4,5,3,6,2,1]=>101011
[7,4,5,6,1,2,3]=>100100
[7,4,5,6,1,3,2]=>100101
[7,4,5,6,2,1,3]=>100110
[7,4,5,6,2,3,1]=>100101
[7,4,5,6,3,1,2]=>100110
[7,4,5,6,3,2,1]=>100111
[7,4,6,1,2,3,5]=>101000
[7,4,6,1,2,5,3]=>101001
[7,4,6,1,3,2,5]=>101010
[7,4,6,1,3,5,2]=>101001
[7,4,6,1,5,2,3]=>101010
[7,4,6,1,5,3,2]=>101011
[7,4,6,2,1,3,5]=>101100
[7,4,6,2,1,5,3]=>101101
[7,4,6,2,3,1,5]=>101010
[7,4,6,2,3,5,1]=>101001
[7,4,6,2,5,1,3]=>101010
[7,4,6,2,5,3,1]=>101011
[7,4,6,3,1,2,5]=>101100
[7,4,6,3,1,5,2]=>101101
[7,4,6,3,2,1,5]=>101110
[7,4,6,3,2,5,1]=>101101
[7,4,6,3,5,1,2]=>101010
[7,4,6,3,5,2,1]=>101011
[7,4,6,5,1,2,3]=>101100
[7,4,6,5,1,3,2]=>101101
[7,4,6,5,2,1,3]=>101110
[7,4,6,5,2,3,1]=>101101
[7,4,6,5,3,1,2]=>101110
[7,4,6,5,3,2,1]=>101111
[7,5,1,2,3,4,6]=>110000
[7,5,1,2,3,6,4]=>110001
[7,5,1,2,4,3,6]=>110010
[7,5,1,2,4,6,3]=>110001
[7,5,1,2,6,3,4]=>110010
[7,5,1,2,6,4,3]=>110011
[7,5,1,3,2,4,6]=>110100
[7,5,1,3,2,6,4]=>110101
[7,5,1,3,4,2,6]=>110010
[7,5,1,3,4,6,2]=>110001
[7,5,1,3,6,2,4]=>110010
[7,5,1,3,6,4,2]=>110011
[7,5,1,4,2,3,6]=>110100
[7,5,1,4,2,6,3]=>110101
[7,5,1,4,3,2,6]=>110110
[7,5,1,4,3,6,2]=>110101
[7,5,1,4,6,2,3]=>110010
[7,5,1,4,6,3,2]=>110011
[7,5,1,6,2,3,4]=>110100
[7,5,1,6,2,4,3]=>110101
[7,5,1,6,3,2,4]=>110110
[7,5,1,6,3,4,2]=>110101
[7,5,1,6,4,2,3]=>110110
[7,5,1,6,4,3,2]=>110111
[7,5,2,1,3,4,6]=>111000
[7,5,2,1,3,6,4]=>111001
[7,5,2,1,4,3,6]=>111010
[7,5,2,1,4,6,3]=>111001
[7,5,2,1,6,3,4]=>111010
[7,5,2,1,6,4,3]=>111011
[7,5,2,3,1,4,6]=>110100
[7,5,2,3,1,6,4]=>110101
[7,5,2,3,4,1,6]=>110010
[7,5,2,3,4,6,1]=>110001
[7,5,2,3,6,1,4]=>110010
[7,5,2,3,6,4,1]=>110011
[7,5,2,4,1,3,6]=>110100
[7,5,2,4,1,6,3]=>110101
[7,5,2,4,3,1,6]=>110110
[7,5,2,4,3,6,1]=>110101
[7,5,2,4,6,1,3]=>110010
[7,5,2,4,6,3,1]=>110011
[7,5,2,6,1,3,4]=>110100
[7,5,2,6,1,4,3]=>110101
[7,5,2,6,3,1,4]=>110110
[7,5,2,6,3,4,1]=>110101
[7,5,2,6,4,1,3]=>110110
[7,5,2,6,4,3,1]=>110111
[7,5,3,1,2,4,6]=>111000
[7,5,3,1,2,6,4]=>111001
[7,5,3,1,4,2,6]=>111010
[7,5,3,1,4,6,2]=>111001
[7,5,3,1,6,2,4]=>111010
[7,5,3,1,6,4,2]=>111011
[7,5,3,2,1,4,6]=>111100
[7,5,3,2,1,6,4]=>111101
[7,5,3,2,4,1,6]=>111010
[7,5,3,2,4,6,1]=>111001
[7,5,3,2,6,1,4]=>111010
[7,5,3,2,6,4,1]=>111011
[7,5,3,4,1,2,6]=>110100
[7,5,3,4,1,6,2]=>110101
[7,5,3,4,2,1,6]=>110110
[7,5,3,4,2,6,1]=>110101
[7,5,3,4,6,1,2]=>110010
[7,5,3,4,6,2,1]=>110011
[7,5,3,6,1,2,4]=>110100
[7,5,3,6,1,4,2]=>110101
[7,5,3,6,2,1,4]=>110110
[7,5,3,6,2,4,1]=>110101
[7,5,3,6,4,1,2]=>110110
[7,5,3,6,4,2,1]=>110111
[7,5,4,1,2,3,6]=>111000
[7,5,4,1,2,6,3]=>111001
[7,5,4,1,3,2,6]=>111010
[7,5,4,1,3,6,2]=>111001
[7,5,4,1,6,2,3]=>111010
[7,5,4,1,6,3,2]=>111011
[7,5,4,2,1,3,6]=>111100
[7,5,4,2,1,6,3]=>111101
[7,5,4,2,3,1,6]=>111010
[7,5,4,2,3,6,1]=>111001
[7,5,4,2,6,1,3]=>111010
[7,5,4,2,6,3,1]=>111011
[7,5,4,3,1,2,6]=>111100
[7,5,4,3,1,6,2]=>111101
[7,5,4,3,2,1,6]=>111110
[7,5,4,3,2,6,1]=>111101
[7,5,4,3,6,1,2]=>111010
[7,5,4,3,6,2,1]=>111011
[7,5,4,6,1,2,3]=>110100
[7,5,4,6,1,3,2]=>110101
[7,5,4,6,2,1,3]=>110110
[7,5,4,6,2,3,1]=>110101
[7,5,4,6,3,1,2]=>110110
[7,5,4,6,3,2,1]=>110111
[7,5,6,1,2,3,4]=>101000
[7,5,6,1,2,4,3]=>101001
[7,5,6,1,3,2,4]=>101010
[7,5,6,1,3,4,2]=>101001
[7,5,6,1,4,2,3]=>101010
[7,5,6,1,4,3,2]=>101011
[7,5,6,2,1,3,4]=>101100
[7,5,6,2,1,4,3]=>101101
[7,5,6,2,3,1,4]=>101010
[7,5,6,2,3,4,1]=>101001
[7,5,6,2,4,1,3]=>101010
[7,5,6,2,4,3,1]=>101011
[7,5,6,3,1,2,4]=>101100
[7,5,6,3,1,4,2]=>101101
[7,5,6,3,2,1,4]=>101110
[7,5,6,3,2,4,1]=>101101
[7,5,6,3,4,1,2]=>101010
[7,5,6,3,4,2,1]=>101011
[7,5,6,4,1,2,3]=>101100
[7,5,6,4,1,3,2]=>101101
[7,5,6,4,2,1,3]=>101110
[7,5,6,4,2,3,1]=>101101
[7,5,6,4,3,1,2]=>101110
[7,5,6,4,3,2,1]=>101111
[7,6,1,2,3,4,5]=>110000
[7,6,1,2,3,5,4]=>110001
[7,6,1,2,4,3,5]=>110010
[7,6,1,2,4,5,3]=>110001
[7,6,1,2,5,3,4]=>110010
[7,6,1,2,5,4,3]=>110011
[7,6,1,3,2,4,5]=>110100
[7,6,1,3,2,5,4]=>110101
[7,6,1,3,4,2,5]=>110010
[7,6,1,3,4,5,2]=>110001
[7,6,1,3,5,2,4]=>110010
[7,6,1,3,5,4,2]=>110011
[7,6,1,4,2,3,5]=>110100
[7,6,1,4,2,5,3]=>110101
[7,6,1,4,3,2,5]=>110110
[7,6,1,4,3,5,2]=>110101
[7,6,1,4,5,2,3]=>110010
[7,6,1,4,5,3,2]=>110011
[7,6,1,5,2,3,4]=>110100
[7,6,1,5,2,4,3]=>110101
[7,6,1,5,3,2,4]=>110110
[7,6,1,5,3,4,2]=>110101
[7,6,1,5,4,2,3]=>110110
[7,6,1,5,4,3,2]=>110111
[7,6,2,1,3,4,5]=>111000
[7,6,2,1,3,5,4]=>111001
[7,6,2,1,4,3,5]=>111010
[7,6,2,1,4,5,3]=>111001
[7,6,2,1,5,3,4]=>111010
[7,6,2,1,5,4,3]=>111011
[7,6,2,3,1,4,5]=>110100
[7,6,2,3,1,5,4]=>110101
[7,6,2,3,4,1,5]=>110010
[7,6,2,3,4,5,1]=>110001
[7,6,2,3,5,1,4]=>110010
[7,6,2,3,5,4,1]=>110011
[7,6,2,4,1,3,5]=>110100
[7,6,2,4,1,5,3]=>110101
[7,6,2,4,3,1,5]=>110110
[7,6,2,4,3,5,1]=>110101
[7,6,2,4,5,1,3]=>110010
[7,6,2,4,5,3,1]=>110011
[7,6,2,5,1,3,4]=>110100
[7,6,2,5,1,4,3]=>110101
[7,6,2,5,3,1,4]=>110110
[7,6,2,5,3,4,1]=>110101
[7,6,2,5,4,1,3]=>110110
[7,6,2,5,4,3,1]=>110111
[7,6,3,1,2,4,5]=>111000
[7,6,3,1,2,5,4]=>111001
[7,6,3,1,4,2,5]=>111010
[7,6,3,1,4,5,2]=>111001
[7,6,3,1,5,2,4]=>111010
[7,6,3,1,5,4,2]=>111011
[7,6,3,2,1,4,5]=>111100
[7,6,3,2,1,5,4]=>111101
[7,6,3,2,4,1,5]=>111010
[7,6,3,2,4,5,1]=>111001
[7,6,3,2,5,1,4]=>111010
[7,6,3,2,5,4,1]=>111011
[7,6,3,4,1,2,5]=>110100
[7,6,3,4,1,5,2]=>110101
[7,6,3,4,2,1,5]=>110110
[7,6,3,4,2,5,1]=>110101
[7,6,3,4,5,1,2]=>110010
[7,6,3,4,5,2,1]=>110011
[7,6,3,5,1,2,4]=>110100
[7,6,3,5,1,4,2]=>110101
[7,6,3,5,2,1,4]=>110110
[7,6,3,5,2,4,1]=>110101
[7,6,3,5,4,1,2]=>110110
[7,6,3,5,4,2,1]=>110111
[7,6,4,1,2,3,5]=>111000
[7,6,4,1,2,5,3]=>111001
[7,6,4,1,3,2,5]=>111010
[7,6,4,1,3,5,2]=>111001
[7,6,4,1,5,2,3]=>111010
[7,6,4,1,5,3,2]=>111011
[7,6,4,2,1,3,5]=>111100
[7,6,4,2,1,5,3]=>111101
[7,6,4,2,3,1,5]=>111010
[7,6,4,2,3,5,1]=>111001
[7,6,4,2,5,1,3]=>111010
[7,6,4,2,5,3,1]=>111011
[7,6,4,3,1,2,5]=>111100
[7,6,4,3,1,5,2]=>111101
[7,6,4,3,2,1,5]=>111110
[7,6,4,3,2,5,1]=>111101
[7,6,4,3,5,1,2]=>111010
[7,6,4,3,5,2,1]=>111011
[7,6,4,5,1,2,3]=>110100
[7,6,4,5,1,3,2]=>110101
[7,6,4,5,2,1,3]=>110110
[7,6,4,5,2,3,1]=>110101
[7,6,4,5,3,1,2]=>110110
[7,6,4,5,3,2,1]=>110111
[7,6,5,1,2,3,4]=>111000
[7,6,5,1,2,4,3]=>111001
[7,6,5,1,3,2,4]=>111010
[7,6,5,1,3,4,2]=>111001
[7,6,5,1,4,2,3]=>111010
[7,6,5,1,4,3,2]=>111011
[7,6,5,2,1,3,4]=>111100
[7,6,5,2,1,4,3]=>111101
[7,6,5,2,3,1,4]=>111010
[7,6,5,2,3,4,1]=>111001
[7,6,5,2,4,1,3]=>111010
[7,6,5,2,4,3,1]=>111011
[7,6,5,3,1,2,4]=>111100
[7,6,5,3,1,4,2]=>111101
[7,6,5,3,2,1,4]=>111110
[7,6,5,3,2,4,1]=>111101
[7,6,5,3,4,1,2]=>111010
[7,6,5,3,4,2,1]=>111011
[7,6,5,4,1,2,3]=>111100
[7,6,5,4,1,3,2]=>111101
[7,6,5,4,2,1,3]=>111110
[7,6,5,4,2,3,1]=>111101
[7,6,5,4,3,1,2]=>111110
[7,6,5,4,3,2,1]=>111111
[8,7,6,5,4,3,2,1]=>1111111
[7,8,6,5,4,3,2,1]=>0111111
[8,6,7,5,4,3,2,1]=>1011111
[7,6,8,5,4,3,2,1]=>1011111
[6,7,8,5,4,3,2,1]=>0011111
[8,7,5,6,4,3,2,1]=>1101111
[7,8,5,6,4,3,2,1]=>0101111
[8,6,5,7,4,3,2,1]=>1101111
[8,5,6,7,4,3,2,1]=>1001111
[7,6,5,8,4,3,2,1]=>1101111
[6,7,5,8,4,3,2,1]=>0101111
[7,5,6,8,4,3,2,1]=>1001111
[6,5,7,8,4,3,2,1]=>1001111
[5,6,7,8,4,3,2,1]=>0001111
[8,7,6,4,5,3,2,1]=>1110111
[8,6,7,4,5,3,2,1]=>1010111
[7,6,8,4,5,3,2,1]=>1010111
[8,7,5,4,6,3,2,1]=>1110111
[8,6,5,4,7,3,2,1]=>1110111
[8,5,6,4,7,3,2,1]=>1010111
[8,6,4,5,7,3,2,1]=>1100111
[7,6,5,4,8,3,2,1]=>1110111
[6,7,5,4,8,3,2,1]=>0110111
[7,5,6,4,8,3,2,1]=>1010111
[6,5,7,4,8,3,2,1]=>1010111
[5,6,7,4,8,3,2,1]=>0010111
[7,6,4,5,8,3,2,1]=>1100111
[6,7,4,5,8,3,2,1]=>0100111
[7,5,4,6,8,3,2,1]=>1100111
[7,4,5,6,8,3,2,1]=>1000111
[6,5,4,7,8,3,2,1]=>1100111
[5,6,4,7,8,3,2,1]=>0100111
[6,4,5,7,8,3,2,1]=>1000111
[5,4,6,7,8,3,2,1]=>1000111
[4,5,6,7,8,3,2,1]=>0000111
[8,7,6,5,3,4,2,1]=>1111011
[7,8,6,5,3,4,2,1]=>0111011
[7,6,8,5,3,4,2,1]=>1011011
[8,7,5,6,3,4,2,1]=>1101011
[7,8,5,6,3,4,2,1]=>0101011
[8,5,6,7,3,4,2,1]=>1001011
[7,6,5,8,3,4,2,1]=>1101011
[6,7,5,8,3,4,2,1]=>0101011
[5,6,7,8,3,4,2,1]=>0001011
[8,7,6,4,3,5,2,1]=>1111011
[7,8,6,4,3,5,2,1]=>0111011
[7,6,8,4,3,5,2,1]=>1011011
[6,7,8,4,3,5,2,1]=>0011011
[8,7,6,3,4,5,2,1]=>1110011
[7,8,6,3,4,5,2,1]=>0110011
[8,6,7,3,4,5,2,1]=>1010011
[7,6,8,3,4,5,2,1]=>1010011
[6,7,8,3,4,5,2,1]=>0010011
[8,7,5,4,3,6,2,1]=>1111011
[7,8,5,4,3,6,2,1]=>0111011
[7,8,5,3,4,6,2,1]=>0110011
[8,7,4,3,5,6,2,1]=>1110011
[8,7,3,4,5,6,2,1]=>1100011
[7,6,5,4,3,8,2,1]=>1111011
[7,5,6,4,3,8,2,1]=>1011011
[7,4,5,6,3,8,2,1]=>1001011
[6,4,5,7,3,8,2,1]=>1001011
[5,4,6,7,3,8,2,1]=>1001011
[4,5,6,7,3,8,2,1]=>0001011
[7,6,3,4,5,8,2,1]=>1100011
[7,5,4,3,6,8,2,1]=>1110011
[7,5,3,4,6,8,2,1]=>1100011
[6,5,4,3,7,8,2,1]=>1110011
[8,7,6,5,4,2,3,1]=>1111101
[8,6,7,5,4,2,3,1]=>1011101
[7,6,8,5,4,2,3,1]=>1011101
[8,5,6,7,4,2,3,1]=>1001101
[7,6,5,8,4,2,3,1]=>1101101
[6,7,5,8,4,2,3,1]=>0101101
[7,5,6,8,4,2,3,1]=>1001101
[5,6,7,8,4,2,3,1]=>0001101
[8,7,6,4,5,2,3,1]=>1110101
[8,6,7,4,5,2,3,1]=>1010101
[7,6,8,4,5,2,3,1]=>1010101
[8,7,5,4,6,2,3,1]=>1110101
[8,7,4,5,6,2,3,1]=>1100101
[8,6,5,4,7,2,3,1]=>1110101
[8,5,6,4,7,2,3,1]=>1010101
[8,6,4,5,7,2,3,1]=>1100101
[7,5,6,4,8,2,3,1]=>1010101
[6,5,7,4,8,2,3,1]=>1010101
[4,5,6,7,8,2,3,1]=>0000101
[8,7,6,5,3,2,4,1]=>1111101
[7,8,6,5,3,2,4,1]=>0111101
[8,6,7,5,3,2,4,1]=>1011101
[7,6,8,5,3,2,4,1]=>1011101
[6,7,8,5,3,2,4,1]=>0011101
[8,6,5,7,3,2,4,1]=>1101101
[8,5,6,7,3,2,4,1]=>1001101
[7,6,5,8,3,2,4,1]=>1101101
[6,7,5,8,3,2,4,1]=>0101101
[5,6,7,8,3,2,4,1]=>0001101
[8,7,6,5,2,3,4,1]=>1111001
[8,6,7,5,2,3,4,1]=>1011001
[7,6,8,5,2,3,4,1]=>1011001
[6,7,8,5,2,3,4,1]=>0011001
[8,7,5,6,2,3,4,1]=>1101001
[7,8,5,6,2,3,4,1]=>0101001
[8,6,5,7,2,3,4,1]=>1101001
[8,5,6,7,2,3,4,1]=>1001001
[7,6,5,8,2,3,4,1]=>1101001
[6,7,5,8,2,3,4,1]=>0101001
[6,5,7,8,2,3,4,1]=>1001001
[5,6,7,8,2,3,4,1]=>0001001
[8,7,6,4,3,2,5,1]=>1111101
[7,8,6,4,3,2,5,1]=>0111101
[8,6,7,4,3,2,5,1]=>1011101
[7,6,8,4,3,2,5,1]=>1011101
[6,7,8,4,3,2,5,1]=>0011101
[8,7,6,3,4,2,5,1]=>1110101
[8,6,7,3,4,2,5,1]=>1010101
[7,6,8,3,4,2,5,1]=>1010101
[7,6,8,4,2,3,5,1]=>1011001
[6,7,8,4,2,3,5,1]=>0011001
[8,6,7,3,2,4,5,1]=>1011001
[6,7,8,3,2,4,5,1]=>0011001
[8,7,6,2,3,4,5,1]=>1110001
[7,8,6,2,3,4,5,1]=>0110001
[8,6,7,2,3,4,5,1]=>1010001
[7,6,8,2,3,4,5,1]=>1010001
[6,7,8,2,3,4,5,1]=>0010001
[8,7,5,3,4,2,6,1]=>1110101
[7,8,5,3,4,2,6,1]=>0110101
[8,7,5,3,2,4,6,1]=>1111001
[7,8,4,3,2,5,6,1]=>0111001
[7,8,3,4,2,5,6,1]=>0101001
[7,8,3,2,4,5,6,1]=>0110001
[8,6,5,4,3,2,7,1]=>1111101
[8,5,6,3,4,2,7,1]=>1010101
[8,6,4,3,5,2,7,1]=>1110101
[8,6,3,4,5,2,7,1]=>1100101
[8,4,5,3,6,2,7,1]=>1010101
[8,5,6,4,2,3,7,1]=>1011001
[8,6,4,2,3,5,7,1]=>1110001
[8,5,3,4,2,6,7,1]=>1101001
[8,5,4,2,3,6,7,1]=>1110001
[7,4,5,6,3,2,8,1]=>1001101
[6,4,5,7,3,2,8,1]=>1001101
[4,5,6,7,3,2,8,1]=>0001101
[7,5,6,3,4,2,8,1]=>1010101
[6,5,7,3,4,2,8,1]=>1010101
[7,4,5,3,6,2,8,1]=>1010101
[6,5,4,3,7,2,8,1]=>1110101
[6,4,5,3,7,2,8,1]=>1010101
[5,4,6,3,7,2,8,1]=>1010101
[4,5,6,3,7,2,8,1]=>0010101
[6,5,3,4,7,2,8,1]=>1100101
[5,6,3,4,7,2,8,1]=>0100101
[5,4,3,6,7,2,8,1]=>1100101
[6,7,5,4,2,3,8,1]=>0111001
[7,5,6,4,2,3,8,1]=>1011001
[6,5,7,4,2,3,8,1]=>1011001
[5,6,7,4,2,3,8,1]=>0011001
[6,7,4,5,2,3,8,1]=>0101001
[7,4,5,6,2,3,8,1]=>1001001
[6,5,4,7,2,3,8,1]=>1101001
[5,6,4,7,2,3,8,1]=>0101001
[6,4,5,7,2,3,8,1]=>1001001
[5,4,6,7,2,3,8,1]=>1001001
[4,5,6,7,2,3,8,1]=>0001001
[6,7,5,3,2,4,8,1]=>0111001
[6,5,7,3,2,4,8,1]=>1011001
[7,6,5,2,3,4,8,1]=>1110001
[5,6,7,2,3,4,8,1]=>0010001
[6,7,4,3,2,5,8,1]=>0111001
[7,6,4,2,3,5,8,1]=>1110001
[6,7,3,2,4,5,8,1]=>0110001
[6,7,2,3,4,5,8,1]=>0100001
[7,5,2,3,4,6,8,1]=>1100001
[6,5,4,3,2,7,8,1]=>1111001
[5,4,6,3,2,7,8,1]=>1011001
[5,4,3,6,2,7,8,1]=>1101001
[3,4,5,6,2,7,8,1]=>0001001
[6,5,4,2,3,7,8,1]=>1110001
[5,6,4,2,3,7,8,1]=>0110001
[6,4,5,2,3,7,8,1]=>1010001
[5,4,6,2,3,7,8,1]=>1010001
[6,5,2,3,4,7,8,1]=>1100001
[5,4,3,2,6,7,8,1]=>1110001
[4,3,5,2,6,7,8,1]=>1010001
[5,4,2,3,6,7,8,1]=>1100001
[4,5,2,3,6,7,8,1]=>0100001
[5,2,3,4,6,7,8,1]=>1000001
[4,3,2,5,6,7,8,1]=>1100001
[3,4,2,5,6,7,8,1]=>0100001
[3,2,4,5,6,7,8,1]=>1000001
[2,3,4,5,6,7,8,1]=>0000001
[8,7,6,5,4,3,1,2]=>1111110
[7,8,6,5,4,3,1,2]=>0111110
[8,7,5,6,4,3,1,2]=>1101110
[7,8,5,6,4,3,1,2]=>0101110
[7,6,5,8,4,3,1,2]=>1101110
[6,7,5,8,4,3,1,2]=>0101110
[7,5,6,8,4,3,1,2]=>1001110
[5,6,7,8,4,3,1,2]=>0001110
[7,8,6,4,5,3,1,2]=>0110110
[8,6,7,4,5,3,1,2]=>1010110
[8,7,5,4,6,3,1,2]=>1110110
[8,5,6,4,7,3,1,2]=>1010110
[6,7,4,5,8,3,1,2]=>0100110
[5,6,4,7,8,3,1,2]=>0100110
[4,5,6,7,8,3,1,2]=>0000110
[8,7,6,5,3,4,1,2]=>1111010
[7,8,6,5,3,4,1,2]=>0111010
[6,7,8,5,3,4,1,2]=>0011010
[8,7,5,6,3,4,1,2]=>1101010
[7,8,5,6,3,4,1,2]=>0101010
[8,5,6,7,3,4,1,2]=>1001010
[7,6,5,8,3,4,1,2]=>1101010
[6,7,5,8,3,4,1,2]=>0101010
[7,5,6,8,3,4,1,2]=>1001010
[6,5,7,8,3,4,1,2]=>1001010
[5,6,7,8,3,4,1,2]=>0001010
[7,8,5,4,3,6,1,2]=>0111010
[8,7,4,5,3,6,1,2]=>1101010
[7,8,4,5,3,6,1,2]=>0101010
[7,8,5,3,4,6,1,2]=>0110010
[8,7,4,3,5,6,1,2]=>1110010
[7,8,4,3,5,6,1,2]=>0110010
[7,8,3,4,5,6,1,2]=>0100010
[8,5,4,3,6,7,1,2]=>1110010
[8,5,3,4,6,7,1,2]=>1100010
[8,4,3,5,6,7,1,2]=>1100010
[7,6,5,4,3,8,1,2]=>1111010
[5,6,7,4,3,8,1,2]=>0011010
[6,7,4,5,3,8,1,2]=>0101010
[5,6,4,7,3,8,1,2]=>0101010
[5,4,6,7,3,8,1,2]=>1001010
[4,5,6,7,3,8,1,2]=>0001010
[7,5,6,3,4,8,1,2]=>1010010
[7,6,3,4,5,8,1,2]=>1100010
[7,5,4,3,6,8,1,2]=>1110010
[7,5,3,4,6,8,1,2]=>1100010
[6,5,4,3,7,8,1,2]=>1110010
[5,4,6,3,7,8,1,2]=>1010010
[4,5,6,3,7,8,1,2]=>0010010
[5,6,3,4,7,8,1,2]=>0100010
[6,4,3,5,7,8,1,2]=>1100010
[6,3,4,5,7,8,1,2]=>1000010
[5,4,3,6,7,8,1,2]=>1100010
[4,5,3,6,7,8,1,2]=>0100010
[5,3,4,6,7,8,1,2]=>1000010
[4,3,5,6,7,8,1,2]=>1000010
[3,4,5,6,7,8,1,2]=>0000010
[8,7,6,5,4,2,1,3]=>1111110
[7,6,8,5,4,2,1,3]=>1011110
[6,7,8,5,4,2,1,3]=>0011110
[8,7,5,6,4,2,1,3]=>1101110
[7,8,5,6,4,2,1,3]=>0101110
[7,6,5,8,4,2,1,3]=>1101110
[6,7,5,8,4,2,1,3]=>0101110
[7,5,6,8,4,2,1,3]=>1001110
[6,5,7,8,4,2,1,3]=>1001110
[5,6,7,8,4,2,1,3]=>0001110
[7,6,8,4,5,2,1,3]=>1010110
[8,7,4,5,6,2,1,3]=>1100110
[6,7,5,4,8,2,1,3]=>0110110
[7,5,6,4,8,2,1,3]=>1010110
[7,6,4,5,8,2,1,3]=>1100110
[4,5,6,7,8,2,1,3]=>0000110
[8,7,6,5,4,1,2,3]=>1111100
[6,7,8,5,4,1,2,3]=>0011100
[7,8,5,6,4,1,2,3]=>0101100
[8,5,6,7,4,1,2,3]=>1001100
[7,6,5,8,4,1,2,3]=>1101100
[6,7,5,8,4,1,2,3]=>0101100
[7,5,6,8,4,1,2,3]=>1001100
[6,5,7,8,4,1,2,3]=>1001100
[5,6,7,8,4,1,2,3]=>0001100
[8,7,5,4,6,1,2,3]=>1110100
[8,5,6,4,7,1,2,3]=>1010100
[8,6,4,5,7,1,2,3]=>1100100
[7,6,5,4,8,1,2,3]=>1110100
[6,7,5,4,8,1,2,3]=>0110100
[7,5,6,4,8,1,2,3]=>1010100
[6,5,7,4,8,1,2,3]=>1010100
[5,6,7,4,8,1,2,3]=>0010100
[7,6,4,5,8,1,2,3]=>1100100
[6,7,4,5,8,1,2,3]=>0100100
[7,5,4,6,8,1,2,3]=>1100100
[7,4,5,6,8,1,2,3]=>1000100
[6,5,4,7,8,1,2,3]=>1100100
[5,6,4,7,8,1,2,3]=>0100100
[6,4,5,7,8,1,2,3]=>1000100
[5,4,6,7,8,1,2,3]=>1000100
[4,5,6,7,8,1,2,3]=>0000100
[8,7,6,5,3,2,1,4]=>1111110
[7,8,6,5,3,2,1,4]=>0111110
[8,6,7,5,3,2,1,4]=>1011110
[7,6,8,5,3,2,1,4]=>1011110
[6,7,8,5,3,2,1,4]=>0011110
[8,7,5,6,3,2,1,4]=>1101110
[7,8,5,6,3,2,1,4]=>0101110
[8,6,5,7,3,2,1,4]=>1101110
[8,5,6,7,3,2,1,4]=>1001110
[7,6,5,8,3,2,1,4]=>1101110
[6,7,5,8,3,2,1,4]=>0101110
[7,5,6,8,3,2,1,4]=>1001110
[6,5,7,8,3,2,1,4]=>1001110
[5,6,7,8,3,2,1,4]=>0001110
[8,7,6,5,2,3,1,4]=>1111010
[7,8,6,5,2,3,1,4]=>0111010
[8,6,7,5,2,3,1,4]=>1011010
[7,6,8,5,2,3,1,4]=>1011010
[6,7,8,5,2,3,1,4]=>0011010
[8,7,5,6,2,3,1,4]=>1101010
[7,8,5,6,2,3,1,4]=>0101010
[8,6,5,7,2,3,1,4]=>1101010
[8,5,6,7,2,3,1,4]=>1001010
[7,6,5,8,2,3,1,4]=>1101010
[6,7,5,8,2,3,1,4]=>0101010
[7,5,6,8,2,3,1,4]=>1001010
[6,5,7,8,2,3,1,4]=>1001010
[5,6,7,8,2,3,1,4]=>0001010
[8,7,6,5,3,1,2,4]=>1111100
[7,8,6,5,3,1,2,4]=>0111100
[7,8,5,6,3,1,2,4]=>0101100
[7,6,5,8,3,1,2,4]=>1101100
[6,7,5,8,3,1,2,4]=>0101100
[7,5,6,8,3,1,2,4]=>1001100
[6,5,7,8,3,1,2,4]=>1001100
[5,6,7,8,3,1,2,4]=>0001100
[8,7,6,5,2,1,3,4]=>1111100
[7,6,8,5,2,1,3,4]=>1011100
[6,7,8,5,2,1,3,4]=>0011100
[7,8,5,6,2,1,3,4]=>0101100
[8,6,5,7,2,1,3,4]=>1101100
[8,5,6,7,2,1,3,4]=>1001100
[7,6,5,8,2,1,3,4]=>1101100
[6,7,5,8,2,1,3,4]=>0101100
[7,5,6,8,2,1,3,4]=>1001100
[6,5,7,8,2,1,3,4]=>1001100
[5,6,7,8,2,1,3,4]=>0001100
[8,7,6,5,1,2,3,4]=>1111000
[7,8,6,5,1,2,3,4]=>0111000
[8,6,7,5,1,2,3,4]=>1011000
[7,6,8,5,1,2,3,4]=>1011000
[6,7,8,5,1,2,3,4]=>0011000
[8,7,5,6,1,2,3,4]=>1101000
[7,8,5,6,1,2,3,4]=>0101000
[8,6,5,7,1,2,3,4]=>1101000
[8,5,6,7,1,2,3,4]=>1001000
[7,6,5,8,1,2,3,4]=>1101000
[6,7,5,8,1,2,3,4]=>0101000
[7,5,6,8,1,2,3,4]=>1001000
[6,5,7,8,1,2,3,4]=>1001000
[5,6,7,8,1,2,3,4]=>0001000
[8,7,6,4,3,2,1,5]=>1111110
[7,8,6,4,3,2,1,5]=>0111110
[8,6,7,4,3,2,1,5]=>1011110
[7,6,8,4,3,2,1,5]=>1011110
[6,7,8,4,3,2,1,5]=>0011110
[8,7,6,3,4,2,1,5]=>1110110
[7,8,6,3,4,2,1,5]=>0110110
[6,7,8,3,4,2,1,5]=>0010110
[8,7,6,4,2,3,1,5]=>1111010
[7,6,8,4,2,3,1,5]=>1011010
[6,7,8,4,2,3,1,5]=>0011010
[8,7,6,3,2,4,1,5]=>1111010
[8,6,7,3,2,4,1,5]=>1011010
[6,7,8,3,2,4,1,5]=>0011010
[8,7,6,2,3,4,1,5]=>1110010
[6,7,8,2,3,4,1,5]=>0010010
[8,7,6,4,3,1,2,5]=>1111100
[6,7,8,4,3,1,2,5]=>0011100
[8,7,6,3,4,1,2,5]=>1110100
[6,7,8,3,4,1,2,5]=>0010100
[8,7,6,4,2,1,3,5]=>1111100
[7,8,6,4,2,1,3,5]=>0111100
[8,6,7,4,2,1,3,5]=>1011100
[6,7,8,4,2,1,3,5]=>0011100
[8,7,6,4,1,2,3,5]=>1111000
[7,8,6,4,1,2,3,5]=>0111000
[7,6,8,4,1,2,3,5]=>1011000
[6,7,8,4,1,2,3,5]=>0011000
[8,7,6,3,2,1,4,5]=>1111100
[7,6,8,3,2,1,4,5]=>1011100
[6,7,8,3,2,1,4,5]=>0011100
[8,7,6,2,3,1,4,5]=>1110100
[7,6,8,2,3,1,4,5]=>1010100
[6,7,8,2,3,1,4,5]=>0010100
[8,7,6,3,1,2,4,5]=>1111000
[7,8,6,3,1,2,4,5]=>0111000
[6,7,8,3,1,2,4,5]=>0011000
[8,7,6,2,1,3,4,5]=>1111000
[7,8,6,2,1,3,4,5]=>0111000
[6,7,8,2,1,3,4,5]=>0011000
[8,7,6,1,2,3,4,5]=>1110000
[7,8,6,1,2,3,4,5]=>0110000
[8,6,7,1,2,3,4,5]=>1010000
[7,6,8,1,2,3,4,5]=>1010000
[6,7,8,1,2,3,4,5]=>0010000
[8,7,5,4,3,2,1,6]=>1111110
[7,8,5,4,3,2,1,6]=>0111110
[8,7,5,3,4,2,1,6]=>1110110
[8,7,3,4,5,2,1,6]=>1100110
[7,8,3,4,5,2,1,6]=>0100110
[8,7,4,5,2,3,1,6]=>1101010
[7,8,4,5,2,3,1,6]=>0101010
[8,7,5,3,2,4,1,6]=>1111010
[8,7,4,3,2,5,1,6]=>1111010
[7,8,4,3,2,5,1,6]=>0111010
[8,7,3,4,2,5,1,6]=>1101010
[7,8,3,4,2,5,1,6]=>0101010
[8,7,5,4,3,1,2,6]=>1111100
[7,8,5,4,3,1,2,6]=>0111100
[8,7,5,3,4,1,2,6]=>1110100
[7,8,5,3,4,1,2,6]=>0110100
[7,8,5,4,2,1,3,6]=>0111100
[7,8,5,4,1,2,3,6]=>0111000
[8,7,4,5,1,2,3,6]=>1101000
[8,7,5,3,2,1,4,6]=>1111100
[7,8,5,3,2,1,4,6]=>0111100
[8,7,5,2,3,1,4,6]=>1110100
[8,7,5,3,1,2,4,6]=>1111000
[7,8,5,3,1,2,4,6]=>0111000
[8,7,5,2,1,3,4,6]=>1111000
[7,8,5,2,1,3,4,6]=>0111000
[8,7,5,1,2,3,4,6]=>1110000
[7,8,5,1,2,3,4,6]=>0110000
[8,7,4,3,2,1,5,6]=>1111100
[7,8,4,3,2,1,5,6]=>0111100
[8,7,3,4,2,1,5,6]=>1101100
[7,8,3,4,2,1,5,6]=>0101100
[7,8,4,2,3,1,5,6]=>0110100
[8,7,3,2,4,1,5,6]=>1110100
[7,8,3,2,4,1,5,6]=>0110100
[7,8,2,3,4,1,5,6]=>0100100
[7,8,4,3,1,2,5,6]=>0111000
[8,7,3,4,1,2,5,6]=>1101000
[7,8,3,4,1,2,5,6]=>0101000
[7,8,4,2,1,3,5,6]=>0111000
[7,8,4,1,2,3,5,6]=>0110000
[8,7,3,2,1,4,5,6]=>1111000
[7,8,3,2,1,4,5,6]=>0111000
[7,8,2,3,1,4,5,6]=>0101000
[7,8,3,1,2,4,5,6]=>0110000
[7,8,2,1,3,4,5,6]=>0110000
[7,8,1,2,3,4,5,6]=>0100000
[8,6,5,4,3,2,1,7]=>1111110
[8,5,6,4,3,2,1,7]=>1011110
[8,4,5,6,3,2,1,7]=>1001110
[8,6,5,3,4,2,1,7]=>1110110
[8,5,6,3,4,2,1,7]=>1010110
[8,4,5,3,6,2,1,7]=>1010110
[8,6,5,4,2,3,1,7]=>1111010
[8,5,6,4,2,3,1,7]=>1011010
[8,6,5,3,2,4,1,7]=>1111010
[8,6,5,2,3,4,1,7]=>1110010
[8,5,6,2,3,4,1,7]=>1010010
[8,6,4,2,3,5,1,7]=>1110010
[8,6,3,2,4,5,1,7]=>1110010
[8,5,2,3,4,6,1,7]=>1100010
[8,6,4,5,3,1,2,7]=>1101100
[8,5,6,3,4,1,2,7]=>1010100
[8,6,3,4,5,1,2,7]=>1100100
[8,4,5,3,6,1,2,7]=>1010100
[8,4,3,5,6,1,2,7]=>1100100
[8,6,5,4,2,1,3,7]=>1111100
[8,5,6,4,2,1,3,7]=>1011100
[8,5,6,4,1,2,3,7]=>1011000
[8,4,5,6,1,2,3,7]=>1001000
[8,6,5,3,2,1,4,7]=>1111100
[8,5,6,3,2,1,4,7]=>1011100
[8,6,5,2,3,1,4,7]=>1110100
[8,5,6,2,3,1,4,7]=>1010100
[8,5,6,3,1,2,4,7]=>1011000
[8,6,5,2,1,3,4,7]=>1111000
[8,5,6,2,1,3,4,7]=>1011000
[8,6,5,1,2,3,4,7]=>1110000
[8,5,6,1,2,3,4,7]=>1010000
[8,6,4,3,2,1,5,7]=>1111100
[8,6,3,4,2,1,5,7]=>1101100
[8,6,4,2,3,1,5,7]=>1110100
[8,6,3,2,4,1,5,7]=>1110100
[8,6,3,4,1,2,5,7]=>1101000
[8,6,4,2,1,3,5,7]=>1111000
[8,6,4,1,2,3,5,7]=>1110000
[8,4,5,3,2,1,6,7]=>1011100
[8,4,3,5,2,1,6,7]=>1101100
[8,3,4,5,2,1,6,7]=>1001100
[8,4,5,2,3,1,6,7]=>1010100
[8,5,2,3,4,1,6,7]=>1100100
[8,4,2,3,5,1,6,7]=>1100100
[8,5,3,4,1,2,6,7]=>1101000
[8,5,4,2,1,3,6,7]=>1111000
[8,5,3,2,1,4,6,7]=>1111000
[8,5,3,1,2,4,6,7]=>1110000
[8,4,3,2,1,5,6,7]=>1111000
[8,3,4,1,2,5,6,7]=>1010000
[8,4,2,1,3,5,6,7]=>1110000
[8,3,2,1,4,5,6,7]=>1110000
[8,3,1,2,4,5,6,7]=>1100000
[8,1,2,3,4,5,6,7]=>1000000
[7,6,5,4,3,2,1,8]=>1111110
[6,7,5,4,3,2,1,8]=>0111110
[7,5,6,4,3,2,1,8]=>1011110
[6,5,7,4,3,2,1,8]=>1011110
[5,6,7,4,3,2,1,8]=>0011110
[7,6,4,5,3,2,1,8]=>1101110
[7,4,5,6,3,2,1,8]=>1001110
[6,5,4,7,3,2,1,8]=>1101110
[5,6,4,7,3,2,1,8]=>0101110
[4,5,6,7,3,2,1,8]=>0001110
[7,6,5,3,4,2,1,8]=>1110110
[6,7,5,3,4,2,1,8]=>0110110
[7,5,6,3,4,2,1,8]=>1010110
[6,5,7,3,4,2,1,8]=>1010110
[5,6,7,3,4,2,1,8]=>0010110
[7,6,3,4,5,2,1,8]=>1100110
[7,4,5,3,6,2,1,8]=>1010110
[7,3,4,5,6,2,1,8]=>1000110
[6,5,4,3,7,2,1,8]=>1110110
[5,4,6,3,7,2,1,8]=>1010110
[5,4,3,6,7,2,1,8]=>1100110
[7,5,6,4,2,3,1,8]=>1011010
[5,6,7,4,2,3,1,8]=>0011010
[7,6,4,5,2,3,1,8]=>1101010
[6,7,4,5,2,3,1,8]=>0101010
[7,4,5,6,2,3,1,8]=>1001010
[6,5,4,7,2,3,1,8]=>1101010
[5,6,4,7,2,3,1,8]=>0101010
[5,4,6,7,2,3,1,8]=>1001010
[4,5,6,7,2,3,1,8]=>0001010
[5,6,7,3,2,4,1,8]=>0011010
[7,6,5,2,3,4,1,8]=>1110010
[6,7,5,2,3,4,1,8]=>0110010
[7,5,6,2,3,4,1,8]=>1010010
[6,5,7,2,3,4,1,8]=>1010010
[5,6,7,2,3,4,1,8]=>0010010
[6,7,4,3,2,5,1,8]=>0111010
[6,7,3,4,2,5,1,8]=>0101010
[7,6,4,2,3,5,1,8]=>1110010
[7,6,3,2,4,5,1,8]=>1110010
[6,7,3,2,4,5,1,8]=>0110010
[7,6,2,3,4,5,1,8]=>1100010
[6,7,2,3,4,5,1,8]=>0100010
[7,4,5,3,2,6,1,8]=>1011010
[7,5,3,4,2,6,1,8]=>1101010
[7,4,3,5,2,6,1,8]=>1101010
[7,4,5,2,3,6,1,8]=>1010010
[7,5,3,2,4,6,1,8]=>1110010
[7,4,2,3,5,6,1,8]=>1100010
[5,4,6,3,2,7,1,8]=>1011010
[5,6,3,4,2,7,1,8]=>0101010
[6,3,4,5,2,7,1,8]=>1001010
[5,4,3,6,2,7,1,8]=>1101010
[4,5,3,6,2,7,1,8]=>0101010
[3,4,5,6,2,7,1,8]=>0001010
[6,5,3,2,4,7,1,8]=>1110010
[6,4,2,3,5,7,1,8]=>1100010
[6,3,2,4,5,7,1,8]=>1100010
[6,2,3,4,5,7,1,8]=>1000010
[5,4,3,2,6,7,1,8]=>1110010
[4,5,2,3,6,7,1,8]=>0100010
[7,4,5,6,3,1,2,8]=>1001100
[5,4,6,7,3,1,2,8]=>1001100
[4,5,6,7,3,1,2,8]=>0001100
[7,5,6,3,4,1,2,8]=>1010100
[7,5,3,4,6,1,2,8]=>1100100
[6,5,4,3,7,1,2,8]=>1110100
[3,4,5,6,7,1,2,8]=>0000100
[7,4,5,6,2,1,3,8]=>1001100
[4,5,6,7,2,1,3,8]=>0001100
[7,6,5,4,1,2,3,8]=>1111000
[7,5,6,4,1,2,3,8]=>1011000
[7,6,4,5,1,2,3,8]=>1101000
[7,5,4,6,1,2,3,8]=>1101000
[7,4,5,6,1,2,3,8]=>1001000
[4,5,6,7,1,2,3,8]=>0001000
[7,6,5,2,3,1,4,8]=>1110100
[6,7,5,2,3,1,4,8]=>0110100
[7,5,6,2,3,1,4,8]=>1010100
[6,5,7,2,3,1,4,8]=>1010100
[5,6,7,2,3,1,4,8]=>0010100
[7,5,6,3,1,2,4,8]=>1011000
[7,6,5,2,1,3,4,8]=>1111000
[7,6,5,1,2,3,4,8]=>1110000
[6,7,5,1,2,3,4,8]=>0110000
[7,5,6,1,2,3,4,8]=>1010000
[6,5,7,1,2,3,4,8]=>1010000
[5,6,7,1,2,3,4,8]=>0010000
[7,6,4,3,2,1,5,8]=>1111100
[6,7,4,3,2,1,5,8]=>0111100
[7,6,3,2,4,1,5,8]=>1110100
[7,6,2,3,4,1,5,8]=>1100100
[6,7,2,3,4,1,5,8]=>0100100
[7,6,4,2,1,3,5,8]=>1111000
[7,6,3,2,1,4,5,8]=>1111000
[6,7,3,2,1,4,5,8]=>0111000
[7,6,2,3,1,4,5,8]=>1101000
[6,7,3,1,2,4,5,8]=>0110000
[6,7,1,2,3,4,5,8]=>0100000
[7,5,2,3,4,1,6,8]=>1100100
[7,4,2,3,5,1,6,8]=>1100100
[7,2,3,4,5,1,6,8]=>1000100
[7,5,3,4,1,2,6,8]=>1101000
[7,4,5,1,2,3,6,8]=>1010000
[7,5,3,2,1,4,6,8]=>1111000
[7,5,3,1,2,4,6,8]=>1110000
[7,5,1,2,3,4,6,8]=>1100000
[7,4,3,2,1,5,6,8]=>1111000
[7,4,3,1,2,5,6,8]=>1110000
[7,3,4,1,2,5,6,8]=>1010000
[7,3,1,2,4,5,6,8]=>1100000
[7,1,2,3,4,5,6,8]=>1000000
[5,6,4,3,2,1,7,8]=>0111100
[5,4,6,3,2,1,7,8]=>1011100
[4,5,6,3,2,1,7,8]=>0011100
[6,5,3,4,2,1,7,8]=>1101100
[5,4,3,6,2,1,7,8]=>1101100
[3,4,5,6,2,1,7,8]=>0001100
[5,4,6,2,3,1,7,8]=>1010100
[5,6,3,2,4,1,7,8]=>0110100
[6,5,2,3,4,1,7,8]=>1100100
[5,6,2,3,4,1,7,8]=>0100100
[6,4,3,2,5,1,7,8]=>1110100
[5,4,3,2,6,1,7,8]=>1110100
[4,5,3,2,6,1,7,8]=>0110100
[5,3,2,4,6,1,7,8]=>1100100
[6,5,4,3,1,2,7,8]=>1111000
[5,6,4,2,1,3,7,8]=>0111000
[6,4,5,2,1,3,7,8]=>1011000
[6,4,3,2,1,5,7,8]=>1111000
[6,3,4,2,1,5,7,8]=>1011000
[6,4,3,1,2,5,7,8]=>1110000
[6,4,2,1,3,5,7,8]=>1110000
[5,4,3,2,1,6,7,8]=>1111000
[4,5,3,2,1,6,7,8]=>0111000
[5,3,4,2,1,6,7,8]=>1011000
[4,3,5,2,1,6,7,8]=>1011000
[3,4,5,2,1,6,7,8]=>0011000
[5,4,2,3,1,6,7,8]=>1101000
[4,5,2,3,1,6,7,8]=>0101000
[5,3,2,4,1,6,7,8]=>1101000
[5,2,3,4,1,6,7,8]=>1001000
[4,3,2,5,1,6,7,8]=>1101000
[3,4,2,5,1,6,7,8]=>0101000
[4,2,3,5,1,6,7,8]=>1001000
[3,2,4,5,1,6,7,8]=>1001000
[2,3,4,5,1,6,7,8]=>0001000
[5,4,3,1,2,6,7,8]=>1110000
[5,3,4,1,2,6,7,8]=>1010000
[5,4,2,1,3,6,7,8]=>1110000
[5,4,1,2,3,6,7,8]=>1100000
[4,5,1,2,3,6,7,8]=>0100000
[5,3,2,1,4,6,7,8]=>1110000
[5,2,3,1,4,6,7,8]=>1010000
[5,3,1,2,4,6,7,8]=>1100000
[5,2,1,3,4,6,7,8]=>1100000
[5,1,2,3,4,6,7,8]=>1000000
[4,3,2,1,5,6,7,8]=>1110000
[3,4,2,1,5,6,7,8]=>0110000
[4,2,3,1,5,6,7,8]=>1010000
[3,2,4,1,5,6,7,8]=>1010000
[2,3,4,1,5,6,7,8]=>0010000
[4,3,1,2,5,6,7,8]=>1100000
[3,4,1,2,5,6,7,8]=>0100000
[4,2,1,3,5,6,7,8]=>1100000
[4,1,2,3,5,6,7,8]=>1000000
[3,2,1,4,5,6,7,8]=>1100000
[2,3,1,4,5,6,7,8]=>0100000
[3,1,2,4,5,6,7,8]=>1000000
[2,1,3,4,5,6,7,8]=>1000000
[1,2,3,4,5,6,7,8]=>0000000
[6,8,7,5,4,3,2,1]=>0111111
[5,8,7,6,4,3,2,1]=>0111111
[5,7,8,6,4,3,2,1]=>0011111
[6,5,8,7,4,3,2,1]=>1011111
[5,6,8,7,4,3,2,1]=>0011111
[5,7,6,8,4,3,2,1]=>0101111
[4,8,7,6,5,3,2,1]=>0111111
[4,7,8,6,5,3,2,1]=>0011111
[4,6,8,7,5,3,2,1]=>0011111
[4,7,6,8,5,3,2,1]=>0101111
[4,6,7,8,5,3,2,1]=>0001111
[4,5,8,7,6,3,2,1]=>0011111
[4,5,7,8,6,3,2,1]=>0001111
[4,6,5,8,7,3,2,1]=>0101111
[4,5,6,8,7,3,2,1]=>0001111
[5,7,6,4,8,3,2,1]=>0110111
[4,7,6,5,8,3,2,1]=>0110111
[4,6,7,5,8,3,2,1]=>0010111
[5,4,7,6,8,3,2,1]=>1010111
[4,5,7,6,8,3,2,1]=>0010111
[4,6,5,7,8,3,2,1]=>0100111
[3,8,7,6,5,4,2,1]=>0111111
[3,5,8,7,6,4,2,1]=>0011111
[3,5,7,8,6,4,2,1]=>0001111
[3,5,6,8,7,4,2,1]=>0001111
[3,7,6,5,8,4,2,1]=>0110111
[3,6,7,5,8,4,2,1]=>0010111
[3,5,6,7,8,4,2,1]=>0000111
[3,4,8,7,6,5,2,1]=>0011111
[3,4,6,7,8,5,2,1]=>0000111
[5,4,3,7,8,6,2,1]=>1100111
[3,4,5,7,8,6,2,1]=>0000111
[4,5,6,3,8,7,2,1]=>0010111
[4,3,6,5,8,7,2,1]=>1010111
[5,4,3,6,8,7,2,1]=>1100111
[4,5,3,6,8,7,2,1]=>0100111
[5,7,6,4,3,8,2,1]=>0111011
[4,7,6,5,3,8,2,1]=>0111011
[3,4,7,6,5,8,2,1]=>0011011
[4,5,3,7,6,8,2,1]=>0101011
[4,3,5,7,6,8,2,1]=>1001011
[3,4,6,5,7,8,2,1]=>0010011
[2,8,7,6,5,4,3,1]=>0111111
[2,7,6,8,5,4,3,1]=>0101111
[2,5,6,7,8,4,3,1]=>0000111
[2,4,8,7,6,5,3,1]=>0011111
[2,4,6,8,7,5,3,1]=>0001111
[2,4,6,7,8,5,3,1]=>0000111
[2,5,4,8,7,6,3,1]=>0101111
[2,4,5,7,8,6,3,1]=>0000111
[2,5,6,4,8,7,3,1]=>0010111
[2,4,6,5,8,7,3,1]=>0010111
[2,7,6,5,4,8,3,1]=>0111011
[2,6,7,5,4,8,3,1]=>0011011
[2,4,7,6,5,8,3,1]=>0011011
[2,6,5,4,7,8,3,1]=>0110011
[3,2,8,7,6,5,4,1]=>1011111
[3,2,6,8,7,5,4,1]=>1001111
[3,2,5,7,6,8,4,1]=>1001011
[3,2,5,6,7,8,4,1]=>1000011
[2,3,8,7,6,5,4,1]=>0011111
[2,3,6,7,8,5,4,1]=>0000111
[2,3,5,7,8,6,4,1]=>0000111
[2,3,7,6,5,8,4,1]=>0011011
[2,3,5,6,7,8,4,1]=>0000011
[4,3,2,8,7,6,5,1]=>1101111
[3,4,2,8,7,6,5,1]=>0101111
[3,4,2,7,8,6,5,1]=>0100111
[2,4,3,8,7,6,5,1]=>0101111
[2,4,3,6,8,7,5,1]=>0100111
[3,2,4,8,7,6,5,1]=>1001111
[2,3,4,8,7,6,5,1]=>0001111
[2,3,4,6,7,8,5,1]=>0000011
[5,4,3,2,8,7,6,1]=>1110111
[5,4,3,2,7,8,6,1]=>1110011
[2,5,4,3,8,7,6,1]=>0110111
[2,5,4,3,7,8,6,1]=>0110011
[2,4,5,3,8,7,6,1]=>0010111
[2,3,5,4,8,7,6,1]=>0010111
[4,3,2,5,8,7,6,1]=>1100111
[2,4,3,5,8,7,6,1]=>0100111
[2,3,4,5,8,7,6,1]=>0000111
[6,5,4,3,2,8,7,1]=>1111011
[4,6,5,3,2,8,7,1]=>0111011
[5,4,6,3,2,8,7,1]=>1011011
[4,5,6,3,2,8,7,1]=>0011011
[3,6,5,4,2,8,7,1]=>0111011
[3,5,6,4,2,8,7,1]=>0011011
[4,3,6,5,2,8,7,1]=>1011011
[5,4,3,6,2,8,7,1]=>1101011
[2,6,5,4,3,8,7,1]=>0111011
[2,4,6,5,3,8,7,1]=>0011011
[4,3,2,6,5,8,7,1]=>1101011
[2,4,3,6,5,8,7,1]=>0101011
[2,3,4,6,5,8,7,1]=>0001011
[5,4,3,2,6,8,7,1]=>1110011
[2,5,4,3,6,8,7,1]=>0110011
[4,3,2,5,6,8,7,1]=>1100011
[3,4,2,5,6,8,7,1]=>0100011
[2,4,3,5,6,8,7,1]=>0100011
[2,3,4,5,6,8,7,1]=>0000011
[4,7,6,5,3,2,8,1]=>0111101
[4,6,5,7,3,2,8,1]=>0101101
[3,5,7,6,4,2,8,1]=>0011101
[3,5,6,7,4,2,8,1]=>0001101
[4,3,7,6,5,2,8,1]=>1011101
[4,3,6,7,5,2,8,1]=>1001101
[3,4,7,6,5,2,8,1]=>0011101
[5,4,3,7,6,2,8,1]=>1101101
[4,6,5,3,7,2,8,1]=>0110101
[3,6,5,4,7,2,8,1]=>0110101
[3,5,6,4,7,2,8,1]=>0010101
[4,3,6,5,7,2,8,1]=>1010101
[3,5,4,6,7,2,8,1]=>0100101
[2,5,4,7,6,3,8,1]=>0101101
[2,4,6,5,7,3,8,1]=>0010101
[2,4,5,6,7,3,8,1]=>0000101
[3,2,6,7,5,4,8,1]=>1001101
[3,2,6,5,7,4,8,1]=>1010101
[2,3,7,6,5,4,8,1]=>0011101
[4,3,2,7,6,5,8,1]=>1101101
[4,3,2,6,7,5,8,1]=>1100101
[3,4,2,7,6,5,8,1]=>0101101
[2,4,3,7,6,5,8,1]=>0101101
[3,2,4,7,6,5,8,1]=>1001101
[2,3,4,7,6,5,8,1]=>0001101
[5,4,3,2,7,6,8,1]=>1110101
[4,3,5,2,7,6,8,1]=>1010101
[2,5,4,3,7,6,8,1]=>0110101
[3,2,5,4,7,6,8,1]=>1010101
[2,3,5,4,7,6,8,1]=>0010101
[4,3,2,5,7,6,8,1]=>1100101
[2,4,3,5,7,6,8,1]=>0100101
[3,2,4,5,7,6,8,1]=>1000101
[2,3,4,5,7,6,8,1]=>0000101
[3,6,5,4,2,7,8,1]=>0111001
[3,5,6,4,2,7,8,1]=>0011001
[2,6,5,4,3,7,8,1]=>0111001
[2,5,4,6,3,7,8,1]=>0101001
[2,3,6,5,4,7,8,1]=>0011001
[2,3,5,6,4,7,8,1]=>0001001
[4,3,2,6,5,7,8,1]=>1101001
[3,4,2,6,5,7,8,1]=>0101001
[2,4,3,6,5,7,8,1]=>0101001
[2,3,4,6,5,7,8,1]=>0001001
[3,5,4,2,6,7,8,1]=>0110001
[2,5,4,3,6,7,8,1]=>0110001
[2,4,5,3,6,7,8,1]=>0010001
[3,2,5,4,6,7,8,1]=>1010001
[2,3,5,4,6,7,8,1]=>0010001
[2,4,3,5,6,7,8,1]=>0100001
[1,8,7,6,5,4,3,2]=>0111111
[1,7,8,6,5,4,3,2]=>0011111
[1,6,8,7,5,4,3,2]=>0011111
[1,7,6,8,5,4,3,2]=>0101111
[1,6,7,8,5,4,3,2]=>0001111
[1,7,6,5,8,4,3,2]=>0110111
[1,6,7,5,8,4,3,2]=>0010111
[1,5,7,6,8,4,3,2]=>0010111
[1,6,5,7,8,4,3,2]=>0100111
[1,5,6,7,8,4,3,2]=>0000111
[1,4,8,7,6,5,3,2]=>0011111
[1,4,7,8,6,5,3,2]=>0001111
[1,4,6,8,7,5,3,2]=>0001111
[1,4,6,7,8,5,3,2]=>0000111
[1,4,5,7,8,6,3,2]=>0000111
[1,4,6,5,8,7,3,2]=>0010111
[1,4,7,6,5,8,3,2]=>0011011
[1,6,5,4,7,8,3,2]=>0110011
[1,3,8,7,6,5,4,2]=>0011111
[1,3,6,8,7,5,4,2]=>0001111
[1,3,6,7,8,5,4,2]=>0000111
[1,3,5,8,7,6,4,2]=>0001111
[1,3,5,7,8,6,4,2]=>0000111
[1,3,5,7,6,8,4,2]=>0001011
[1,3,6,5,7,8,4,2]=>0010011
[1,3,5,6,7,8,4,2]=>0000011
[1,4,3,8,7,6,5,2]=>0101111
[1,4,3,7,8,6,5,2]=>0100111
[1,4,3,6,8,7,5,2]=>0100111
[1,4,3,7,6,8,5,2]=>0101011
[1,3,4,8,7,6,5,2]=>0001111
[1,3,4,7,6,8,5,2]=>0001011
[1,3,4,6,7,8,5,2]=>0000011
[1,5,4,3,8,7,6,2]=>0110111
[1,3,5,4,7,8,6,2]=>0010011
[1,4,3,5,8,7,6,2]=>0100111
[1,4,3,5,7,8,6,2]=>0100011
[1,3,4,5,8,7,6,2]=>0000111
[1,6,5,4,3,8,7,2]=>0111011
[1,5,6,4,3,8,7,2]=>0011011
[1,4,6,5,3,8,7,2]=>0011011
[1,3,6,5,4,8,7,2]=>0011011
[1,4,3,6,5,8,7,2]=>0101011
[1,5,4,3,6,8,7,2]=>0110011
[1,6,7,5,4,3,8,2]=>0011101
[1,3,5,7,6,4,8,2]=>0001101
[1,3,4,7,6,5,8,2]=>0001101
[1,3,5,4,7,6,8,2]=>0010101
[1,4,3,6,5,7,8,2]=>0101001
[1,5,4,3,6,7,8,2]=>0110001
[2,1,8,7,6,5,4,3]=>1011111
[2,1,7,8,6,5,4,3]=>1001111
[2,1,6,8,7,5,4,3]=>1001111
[2,1,7,6,8,5,4,3]=>1010111
[2,1,6,7,8,5,4,3]=>1000111
[2,1,5,7,8,6,4,3]=>1000111
[2,1,6,5,8,7,4,3]=>1010111
[2,1,7,6,5,8,4,3]=>1011011
[2,1,6,7,5,8,4,3]=>1001011
[2,1,6,5,7,8,4,3]=>1010011
[2,1,5,6,7,8,4,3]=>1000011
[2,1,4,8,7,6,5,3]=>1001111
[2,1,4,7,8,6,5,3]=>1000111
[2,1,4,6,8,7,5,3]=>1000111
[2,1,4,6,7,8,5,3]=>1000011
[2,1,4,5,8,7,6,3]=>1000111
[2,1,4,5,7,8,6,3]=>1000011
[2,1,4,6,5,8,7,3]=>1001011
[2,1,4,5,6,8,7,3]=>1000011
[2,1,5,7,6,4,8,3]=>1001101
[2,1,6,5,7,4,8,3]=>1010101
[2,1,5,6,7,4,8,3]=>1000101
[2,1,4,7,6,5,8,3]=>1001101
[2,1,4,6,7,5,8,3]=>1000101
[2,1,5,4,7,6,8,3]=>1010101
[2,1,5,6,4,7,8,3]=>1001001
[2,1,4,5,6,7,8,3]=>1000001
[1,2,8,7,6,5,4,3]=>0011111
[1,2,6,7,8,5,4,3]=>0000111
[1,2,6,5,8,7,4,3]=>0010111
[1,2,7,6,5,8,4,3]=>0011011
[1,2,5,7,6,8,4,3]=>0001011
[1,2,6,5,7,8,4,3]=>0010011
[1,2,5,6,7,8,4,3]=>0000011
[1,2,4,8,7,6,5,3]=>0001111
[1,2,4,7,8,6,5,3]=>0000111
[1,2,4,6,8,7,5,3]=>0000111
[1,2,4,6,7,8,5,3]=>0000011
[1,2,5,4,8,7,6,3]=>0010111
[1,2,4,5,7,8,6,3]=>0000011
[1,2,6,5,4,8,7,3]=>0011011
[1,2,5,7,6,4,8,3]=>0001101
[1,2,5,6,7,4,8,3]=>0000101
[1,2,4,7,6,5,8,3]=>0001101
[1,2,6,5,4,7,8,3]=>0011001
[3,2,1,8,7,6,5,4]=>1101111
[3,2,1,7,8,6,5,4]=>1100111
[3,2,1,6,8,7,5,4]=>1100111
[3,2,1,7,6,8,5,4]=>1101011
[3,2,1,6,7,8,5,4]=>1100011
[3,2,1,5,8,7,6,4]=>1100111
[3,2,1,5,7,8,6,4]=>1100011
[3,2,1,6,5,8,7,4]=>1101011
[3,2,1,5,6,8,7,4]=>1100011
[3,2,1,7,6,5,8,4]=>1101101
[3,2,1,6,7,5,8,4]=>1100101
[3,2,1,5,7,6,8,4]=>1100101
[3,2,1,6,5,7,8,4]=>1101001
[3,2,1,5,6,7,8,4]=>1100001
[2,3,1,8,7,6,5,4]=>0101111
[2,3,1,6,8,7,5,4]=>0100111
[2,3,1,7,6,8,5,4]=>0101011
[2,3,1,6,7,8,5,4]=>0100011
[2,3,1,6,5,8,7,4]=>0101011
[2,3,1,5,6,7,8,4]=>0100001
[1,3,2,8,7,6,5,4]=>0101111
[1,3,2,6,8,7,5,4]=>0100111
[1,3,2,5,7,8,6,4]=>0100011
[1,3,2,6,5,8,7,4]=>0101011
[1,3,2,7,6,5,8,4]=>0101101
[1,3,2,5,7,6,8,4]=>0100101
[1,3,2,6,5,7,8,4]=>0101001
[2,1,3,8,7,6,5,4]=>1001111
[2,1,3,7,8,6,5,4]=>1000111
[2,1,3,6,8,7,5,4]=>1000111
[1,2,3,8,7,6,5,4]=>0001111
[1,2,3,7,8,6,5,4]=>0000111
[1,2,3,6,8,7,5,4]=>0000111
[1,2,3,7,6,8,5,4]=>0001011
[1,2,3,6,7,8,5,4]=>0000011
[1,2,3,5,8,7,6,4]=>0000111
[1,2,3,5,7,8,6,4]=>0000011
[1,2,3,6,5,8,7,4]=>0001011
[1,2,3,5,6,8,7,4]=>0000011
[1,2,3,7,6,5,8,4]=>0001101
[1,2,3,6,7,5,8,4]=>0000101
[1,2,3,5,7,6,8,4]=>0000101
[1,2,3,6,5,7,8,4]=>0001001
[1,2,3,5,6,7,8,4]=>0000001
[4,3,2,1,8,7,6,5]=>1110111
[4,3,2,1,7,8,6,5]=>1110011
[4,3,2,1,6,8,7,5]=>1110011
[4,3,2,1,7,6,8,5]=>1110101
[4,3,2,1,6,7,8,5]=>1110001
[3,4,2,1,8,7,6,5]=>0110111
[3,4,2,1,7,8,6,5]=>0110011
[3,4,2,1,6,8,7,5]=>0110011
[3,4,2,1,7,6,8,5]=>0110101
[3,4,2,1,6,7,8,5]=>0110001
[2,4,3,1,8,7,6,5]=>0110111
[2,4,3,1,6,8,7,5]=>0110011
[2,4,3,1,7,6,8,5]=>0110101
[2,4,3,1,6,7,8,5]=>0110001
[3,2,4,1,8,7,6,5]=>1010111
[3,2,4,1,7,8,6,5]=>1010011
[3,2,4,1,6,8,7,5]=>1010011
[3,2,4,1,7,6,8,5]=>1010101
[3,2,4,1,6,7,8,5]=>1010001
[2,3,4,1,8,7,6,5]=>0010111
[2,3,4,1,7,8,6,5]=>0010011
[2,3,4,1,6,8,7,5]=>0010011
[2,3,4,1,7,6,8,5]=>0010101
[2,3,4,1,6,7,8,5]=>0010001
[1,4,3,2,8,7,6,5]=>0110111
[1,4,3,2,7,6,8,5]=>0110101
[1,4,3,2,6,7,8,5]=>0110001
[1,3,4,2,8,7,6,5]=>0010111
[1,3,4,2,7,8,6,5]=>0010011
[1,3,4,2,6,8,7,5]=>0010011
[1,3,4,2,7,6,8,5]=>0010101
[1,3,4,2,6,7,8,5]=>0010001
[2,1,4,3,8,7,6,5]=>1010111
[2,1,4,3,7,8,6,5]=>1010011
[2,1,4,3,6,8,7,5]=>1010011
[2,1,4,3,7,6,8,5]=>1010101
[2,1,4,3,6,7,8,5]=>1010001
[1,2,4,3,8,7,6,5]=>0010111
[1,2,4,3,7,8,6,5]=>0010011
[1,2,4,3,6,8,7,5]=>0010011
[1,2,4,3,7,6,8,5]=>0010101
[1,2,4,3,6,7,8,5]=>0010001
[3,2,1,4,8,7,6,5]=>1100111
[3,2,1,4,7,8,6,5]=>1100011
[3,2,1,4,6,8,7,5]=>1100011
[3,2,1,4,7,6,8,5]=>1100101
[3,2,1,4,6,7,8,5]=>1100001
[2,3,1,4,8,7,6,5]=>0100111
[2,3,1,4,7,8,6,5]=>0100011
[2,3,1,4,7,6,8,5]=>0100101
[2,3,1,4,6,7,8,5]=>0100001
[1,3,2,4,8,7,6,5]=>0100111
[1,3,2,4,6,8,7,5]=>0100011
[1,3,2,4,7,6,8,5]=>0100101
[1,3,2,4,6,7,8,5]=>0100001
[2,1,3,4,8,7,6,5]=>1000111
[2,1,3,4,7,6,8,5]=>1000101
[2,1,3,4,6,7,8,5]=>1000001
[1,2,3,4,8,7,6,5]=>0000111
[1,2,3,4,7,8,6,5]=>0000011
[1,2,3,4,6,8,7,5]=>0000011
[1,2,3,4,7,6,8,5]=>0000101
[1,2,3,4,6,7,8,5]=>0000001
[5,4,3,2,1,8,7,6]=>1111011
[5,4,3,2,1,7,8,6]=>1111001
[4,5,3,2,1,8,7,6]=>0111011
[3,5,4,2,1,8,7,6]=>0111011
[3,5,4,2,1,7,8,6]=>0111001
[4,3,5,2,1,8,7,6]=>1011011
[3,4,5,2,1,8,7,6]=>0011011
[3,4,5,2,1,7,8,6]=>0011001
[2,5,4,3,1,8,7,6]=>0111011
[2,5,4,3,1,7,8,6]=>0111001
[2,4,5,3,1,8,7,6]=>0011011
[3,2,5,4,1,8,7,6]=>1011011
[3,2,5,4,1,7,8,6]=>1011001
[2,3,5,4,1,8,7,6]=>0011011
[4,3,2,5,1,8,7,6]=>1101011
[3,4,2,5,1,8,7,6]=>0101011
[3,4,2,5,1,7,8,6]=>0101001
[2,4,3,5,1,8,7,6]=>0101011
[2,4,3,5,1,7,8,6]=>0101001
[3,2,4,5,1,8,7,6]=>1001011
[2,3,4,5,1,8,7,6]=>0001011
[1,3,5,4,2,7,8,6]=>0011001
[1,4,3,5,2,7,8,6]=>0101001
[1,3,4,5,2,8,7,6]=>0001011
[1,3,4,5,2,7,8,6]=>0001001
[1,2,5,4,3,7,8,6]=>0011001
[1,2,4,5,3,8,7,6]=>0001011
[1,2,4,5,3,7,8,6]=>0001001
[1,3,2,5,4,7,8,6]=>0101001
[2,1,3,5,4,8,7,6]=>1001011
[1,2,3,5,4,8,7,6]=>0001011
[1,2,3,5,4,7,8,6]=>0001001
[4,3,2,1,5,8,7,6]=>1110011
[4,3,2,1,5,7,8,6]=>1110001
[3,2,4,1,5,8,7,6]=>1010011
[3,2,4,1,5,7,8,6]=>1010001
[2,3,4,1,5,8,7,6]=>0010011
[2,3,4,1,5,7,8,6]=>0010001
[1,4,3,2,5,8,7,6]=>0110011
[1,4,3,2,5,7,8,6]=>0110001
[1,3,4,2,5,8,7,6]=>0010011
[1,3,4,2,5,7,8,6]=>0010001
[1,2,4,3,5,7,8,6]=>0010001
[3,2,1,4,5,8,7,6]=>1100011
[3,2,1,4,5,7,8,6]=>1100001
[2,3,1,4,5,7,8,6]=>0100001
[1,3,2,4,5,7,8,6]=>0100001
[1,2,3,4,5,8,7,6]=>0000011
[1,2,3,4,5,7,8,6]=>0000001
[6,5,4,3,2,1,8,7]=>1111101
[5,6,4,3,2,1,8,7]=>0111101
[4,6,5,3,2,1,8,7]=>0111101
[5,4,6,3,2,1,8,7]=>1011101
[4,5,6,3,2,1,8,7]=>0011101
[3,6,5,4,2,1,8,7]=>0111101
[3,5,6,4,2,1,8,7]=>0011101
[4,3,6,5,2,1,8,7]=>1011101
[5,4,3,6,2,1,8,7]=>1101101
[4,5,3,6,2,1,8,7]=>0101101
[3,4,5,6,2,1,8,7]=>0001101
[2,6,5,4,3,1,8,7]=>0111101
[2,5,6,4,3,1,8,7]=>0011101
[2,4,6,5,3,1,8,7]=>0011101
[2,3,6,5,4,1,8,7]=>0011101
[2,3,5,6,4,1,8,7]=>0001101
[2,4,3,6,5,1,8,7]=>0101101
[5,4,3,2,6,1,8,7]=>1110101
[4,5,3,2,6,1,8,7]=>0110101
[3,5,4,2,6,1,8,7]=>0110101
[4,3,5,2,6,1,8,7]=>1010101
[3,4,5,2,6,1,8,7]=>0010101
[2,5,4,3,6,1,8,7]=>0110101
[2,4,5,3,6,1,8,7]=>0010101
[3,2,5,4,6,1,8,7]=>1010101
[3,4,2,5,6,1,8,7]=>0100101
[2,3,4,5,6,1,8,7]=>0000101
[1,5,4,6,3,2,8,7]=>0101101
[1,3,6,5,4,2,8,7]=>0011101
[2,1,6,5,4,3,8,7]=>1011101
[2,1,5,6,4,3,8,7]=>1001101
[2,1,4,6,5,3,8,7]=>1001101
[2,1,5,4,6,3,8,7]=>1010101
[2,1,4,5,6,3,8,7]=>1000101
[2,3,1,6,5,4,8,7]=>0101101
[1,2,3,6,5,4,8,7]=>0001101
[1,2,3,5,6,4,8,7]=>0000101
[4,3,2,1,6,5,8,7]=>1110101
[3,4,2,1,6,5,8,7]=>0110101
[2,4,3,1,6,5,8,7]=>0110101
[3,2,4,1,6,5,8,7]=>1010101
[2,3,4,1,6,5,8,7]=>0010101
[2,1,4,3,6,5,8,7]=>1010101
[1,2,4,3,6,5,8,7]=>0010101
[1,3,2,4,6,5,8,7]=>0100101
[2,1,3,4,6,5,8,7]=>1000101
[1,2,3,4,6,5,8,7]=>0000101
[5,4,3,2,1,6,8,7]=>1111001
[4,5,3,2,1,6,8,7]=>0111001
[3,5,4,2,1,6,8,7]=>0111001
[2,5,4,3,1,6,8,7]=>0111001
[2,4,5,3,1,6,8,7]=>0011001
[3,2,5,4,1,6,8,7]=>1011001
[1,3,5,4,2,6,8,7]=>0011001
[1,3,4,5,2,6,8,7]=>0001001
[2,1,4,5,3,6,8,7]=>1001001
[1,2,5,4,3,6,8,7]=>0011001
[2,1,3,5,4,6,8,7]=>1001001
[4,3,2,1,5,6,8,7]=>1110001
[3,2,4,1,5,6,8,7]=>1010001
[2,3,4,1,5,6,8,7]=>0010001
[1,4,3,2,5,6,8,7]=>0110001
[1,3,4,2,5,6,8,7]=>0010001
[2,1,4,3,5,6,8,7]=>1010001
[1,2,4,3,5,6,8,7]=>0010001
[2,1,3,4,5,6,8,7]=>1000001
[1,2,3,4,5,6,8,7]=>0000001
[5,7,6,4,3,2,1,8]=>0111110
[4,7,6,5,3,2,1,8]=>0111110
[4,6,7,5,3,2,1,8]=>0011110
[4,5,7,6,3,2,1,8]=>0011110
[4,6,5,7,3,2,1,8]=>0101110
[3,5,7,6,4,2,1,8]=>0011110
[3,5,6,7,4,2,1,8]=>0001110
[3,4,7,6,5,2,1,8]=>0011110
[4,5,3,7,6,2,1,8]=>0101110
[3,5,4,7,6,2,1,8]=>0101110
[4,3,5,7,6,2,1,8]=>1001110
[2,5,6,7,4,3,1,8]=>0001110
[2,4,6,7,5,3,1,8]=>0001110
[3,2,7,6,5,4,1,8]=>1011110
[3,2,6,7,5,4,1,8]=>1001110
[3,2,5,7,6,4,1,8]=>1001110
[2,3,7,6,5,4,1,8]=>0011110
[2,3,6,7,5,4,1,8]=>0001110
[2,3,5,7,6,4,1,8]=>0001110
[2,3,6,5,7,4,1,8]=>0010110
[2,3,5,6,7,4,1,8]=>0000110
[3,2,4,6,7,5,1,8]=>1000110
[2,3,4,7,6,5,1,8]=>0001110
[5,4,3,2,7,6,1,8]=>1110110
[4,5,3,2,7,6,1,8]=>0110110
[3,5,4,2,7,6,1,8]=>0110110
[3,2,5,4,7,6,1,8]=>1010110
[4,3,2,5,7,6,1,8]=>1100110
[3,6,5,4,2,7,1,8]=>0111010
[3,4,6,5,2,7,1,8]=>0011010
[3,5,4,6,2,7,1,8]=>0101010
[2,5,4,6,3,7,1,8]=>0101010
[3,2,6,5,4,7,1,8]=>1011010
[3,4,2,6,5,7,1,8]=>0101010
[2,4,3,6,5,7,1,8]=>0101010
[3,5,4,2,6,7,1,8]=>0110010
[2,5,4,3,6,7,1,8]=>0110010
[1,5,6,7,4,3,2,8]=>0001110
[1,4,6,5,7,3,2,8]=>0010110
[1,3,5,7,6,4,2,8]=>0001110
[1,3,5,6,7,4,2,8]=>0000110
[1,3,5,4,7,6,2,8]=>0010110
[1,4,3,5,7,6,2,8]=>0100110
[1,5,4,6,3,7,2,8]=>0101010
[1,3,6,5,4,7,2,8]=>0011010
[1,4,3,6,5,7,2,8]=>0101010
[1,5,4,3,6,7,2,8]=>0110010
[1,3,4,5,6,7,2,8]=>0000010
[2,1,4,6,7,5,3,8]=>1000110
[1,2,5,7,6,4,3,8]=>0001110
[1,2,5,6,7,4,3,8]=>0000110
[1,2,5,6,4,7,3,8]=>0001010
[1,2,5,4,6,7,3,8]=>0010010
[3,2,1,5,7,6,4,8]=>1100110
[3,2,1,5,6,7,4,8]=>1100010
[2,3,1,6,7,5,4,8]=>0100110
[2,3,1,6,5,7,4,8]=>0101010
[2,3,1,5,6,7,4,8]=>0100010
[1,3,2,5,7,6,4,8]=>0100110
[1,3,2,6,5,7,4,8]=>0101010
[1,3,2,5,6,7,4,8]=>0100010
[2,1,3,6,7,5,4,8]=>1000110
[1,2,3,7,6,5,4,8]=>0001110
[1,2,3,6,7,5,4,8]=>0000110
[1,2,3,5,7,6,4,8]=>0000110
[1,2,3,6,5,7,4,8]=>0001010
[1,2,3,5,6,7,4,8]=>0000010
[4,3,2,1,7,6,5,8]=>1110110
[4,3,2,1,6,7,5,8]=>1110010
[3,2,4,1,7,6,5,8]=>1010110
[3,2,4,1,6,7,5,8]=>1010010
[2,3,4,1,7,6,5,8]=>0010110
[2,3,4,1,6,7,5,8]=>0010010
[1,4,3,2,7,6,5,8]=>0110110
[1,4,3,2,6,7,5,8]=>0110010
[1,3,4,2,6,7,5,8]=>0010010
[1,2,4,3,6,7,5,8]=>0010010
[2,3,1,4,6,7,5,8]=>0100010
[1,3,2,4,7,6,5,8]=>0100110
[1,2,3,4,7,6,5,8]=>0000110
[1,2,3,4,6,7,5,8]=>0000010
[5,4,3,2,1,7,6,8]=>1111010
[4,5,3,2,1,7,6,8]=>0111010
[3,5,4,2,1,7,6,8]=>0111010
[2,5,4,3,1,7,6,8]=>0111010
[2,4,5,3,1,7,6,8]=>0011010
[3,2,5,4,1,7,6,8]=>1011010
[3,4,2,5,1,7,6,8]=>0101010
[2,4,3,5,1,7,6,8]=>0101010
[1,3,5,4,2,7,6,8]=>0011010
[1,4,3,5,2,7,6,8]=>0101010
[1,3,4,5,2,7,6,8]=>0001010
[2,3,1,5,4,7,6,8]=>0101010
[1,3,2,5,4,7,6,8]=>0101010
[1,2,3,5,4,7,6,8]=>0001010
[4,3,2,1,5,7,6,8]=>1110010
[3,2,4,1,5,7,6,8]=>1010010
[2,3,4,1,5,7,6,8]=>0010010
[1,4,3,2,5,7,6,8]=>0110010
[1,3,4,2,5,7,6,8]=>0010010
[1,3,2,4,5,7,6,8]=>0100010
[1,2,3,4,5,7,6,8]=>0000010
[3,6,5,4,2,1,7,8]=>0111100
[4,3,6,5,2,1,7,8]=>1011100
[2,4,6,5,3,1,7,8]=>0011100
[2,4,5,6,3,1,7,8]=>0001100
[4,3,2,6,5,1,7,8]=>1101100
[3,5,4,2,6,1,7,8]=>0110100
[1,5,6,4,3,2,7,8]=>0011100
[1,4,6,5,3,2,7,8]=>0011100
[1,5,4,6,3,2,7,8]=>0101100
[1,4,5,6,3,2,7,8]=>0001100
[1,3,5,6,4,2,7,8]=>0001100
[1,4,3,6,5,2,7,8]=>0101100
[1,5,4,3,6,2,7,8]=>0110100
[2,1,5,6,4,3,7,8]=>1001100
[2,1,4,6,5,3,7,8]=>1001100
[1,2,6,5,4,3,7,8]=>0011100
[1,2,5,6,4,3,7,8]=>0001100
[1,2,4,5,6,3,7,8]=>0000100
[3,2,1,5,6,4,7,8]=>1100100
[1,3,2,5,6,4,7,8]=>0100100
[1,2,3,5,6,4,7,8]=>0000100
[4,3,2,1,6,5,7,8]=>1110100
[3,2,4,1,6,5,7,8]=>1010100
[2,3,4,1,6,5,7,8]=>0010100
[2,1,4,3,6,5,7,8]=>1010100
[1,2,4,3,6,5,7,8]=>0010100
[1,3,2,4,6,5,7,8]=>0100100
[2,1,3,4,6,5,7,8]=>1000100
[1,2,3,4,6,5,7,8]=>0000100
[3,5,4,2,1,6,7,8]=>0111000
[2,5,4,3,1,6,7,8]=>0111000
[2,4,5,3,1,6,7,8]=>0011000
[3,2,5,4,1,6,7,8]=>1011000
[2,3,5,4,1,6,7,8]=>0011000
[2,4,3,5,1,6,7,8]=>0101000
[1,3,5,4,2,6,7,8]=>0011000
[1,3,4,5,2,6,7,8]=>0001000
[1,3,2,5,4,6,7,8]=>0101000
[1,2,3,5,4,6,7,8]=>0001000
[2,4,3,1,5,6,7,8]=>0110000
[1,4,3,2,5,6,7,8]=>0110000
[1,3,4,2,5,6,7,8]=>0010000
[2,1,4,3,5,6,7,8]=>1010000
[1,2,4,3,5,6,7,8]=>0010000
[1,3,2,4,5,6,7,8]=>0100000
[1,2,3,4,8,6,7,5]=>0000101
[1,2,3,5,8,6,7,4]=>0000101
[1,2,3,7,5,6,4,8]=>0001010
[1,2,3,7,5,6,8,4]=>0001001
[1,2,3,8,5,6,7,4]=>0001001
[1,2,3,8,5,7,6,4]=>0001011
[1,2,3,8,6,5,7,4]=>0001101
[1,2,3,8,6,7,5,4]=>0001011
[1,2,4,5,8,6,7,3]=>0000101
[1,2,4,8,5,6,7,3]=>0001001
[1,2,4,8,6,5,7,3]=>0001101
[1,2,5,4,8,6,7,3]=>0010101
[1,2,6,4,5,3,7,8]=>0010100
[1,2,6,4,5,8,7,3]=>0010011
[1,2,8,4,5,6,7,3]=>0010001
[1,2,8,4,6,7,5,3]=>0010011
[1,2,8,4,7,6,5,3]=>0010111
[1,2,7,5,4,6,8,3]=>0011001
[1,2,8,5,4,6,7,3]=>0011001
[1,2,8,5,4,7,6,3]=>0011011
[1,2,8,6,5,4,7,3]=>0011101
[1,2,8,7,5,6,4,3]=>0011011
[1,3,2,7,5,6,8,4]=>0101001
[1,3,2,8,5,7,6,4]=>0101011
[1,3,4,5,8,6,7,2]=>0000101
[1,3,4,8,5,6,7,2]=>0001001
[1,3,6,4,5,2,8,7]=>0010101
[1,3,6,4,5,7,2,8]=>0010010
[1,3,6,4,5,8,7,2]=>0010011
[1,3,8,4,5,6,7,2]=>0010001
[1,3,8,4,6,5,7,2]=>0010101
[1,3,8,5,4,6,7,2]=>0011001
[1,3,8,5,4,7,6,2]=>0011011
[1,3,8,5,6,7,4,2]=>0010011
[1,3,8,5,7,6,4,2]=>0010111
[1,3,8,6,5,7,4,2]=>0011011
[1,3,8,7,5,6,4,2]=>0011011
[1,4,3,8,5,6,7,2]=>0101001
[1,4,3,8,5,7,6,2]=>0101011
[1,4,3,8,6,7,5,2]=>0101011
[1,5,3,4,2,7,8,6]=>0101001
[1,5,3,4,6,2,7,8]=>0100100
[1,5,3,4,6,7,2,8]=>0100010
[1,5,3,4,7,6,2,8]=>0100110
[1,5,3,4,8,6,7,2]=>0100101
[1,8,3,4,6,7,5,2]=>0100011
[1,6,3,5,4,2,7,8]=>0101100
[1,6,3,5,4,8,7,2]=>0101011
[1,8,3,5,4,7,6,2]=>0101011
[1,8,3,5,6,4,7,2]=>0100101
[1,8,3,5,7,6,4,2]=>0100111
[1,8,3,6,5,4,7,2]=>0101101
[1,8,3,7,5,6,4,2]=>0101011
[1,8,3,7,6,5,4,2]=>0101111
[1,6,4,3,5,2,7,8]=>0110100
[1,8,4,3,5,6,7,2]=>0110001
[1,8,4,3,5,7,6,2]=>0110011
[1,7,4,3,6,5,8,2]=>0110101
[1,8,4,3,6,7,5,2]=>0110011
[1,6,4,5,3,8,7,2]=>0101011
[1,8,4,5,6,3,7,2]=>0100101
[1,8,4,5,6,7,3,2]=>0100011
[1,8,4,6,5,7,3,2]=>0101011
[1,8,4,7,6,5,3,2]=>0101111
[1,7,5,4,3,6,8,2]=>0111001
[1,8,5,4,3,6,7,2]=>0111001
[1,8,5,4,3,7,6,2]=>0111011
[1,8,5,4,6,3,7,2]=>0110101
[1,8,5,4,6,7,3,2]=>0110011
[1,8,5,4,7,6,3,2]=>0110111
[1,8,6,4,5,7,3,2]=>0110011
[1,8,7,4,5,6,3,2]=>0110011
[1,8,7,4,6,5,3,2]=>0110111
[1,8,6,5,4,7,3,2]=>0111011
[1,8,7,5,4,6,3,2]=>0111011
[1,8,7,5,6,4,3,2]=>0110111
[2,1,3,4,8,6,7,5]=>1000101
[2,1,4,3,8,6,7,5]=>1010101
[2,1,4,5,8,6,7,3]=>1000101
[2,1,4,8,5,6,7,3]=>1001001
[2,1,4,8,5,7,6,3]=>1001011
[2,1,4,8,6,5,7,3]=>1001101
[2,1,4,8,6,7,5,3]=>1001011
[2,1,5,4,8,6,7,3]=>1010101
[2,1,6,4,5,3,8,7]=>1010101
[2,1,6,4,5,7,8,3]=>1010001
[2,1,6,4,5,8,7,3]=>1010011
[2,1,8,4,5,6,7,3]=>1010001
[2,1,8,4,5,7,6,3]=>1010011
[2,1,8,4,6,5,7,3]=>1010101
[2,1,8,4,6,7,5,3]=>1010011
[2,1,8,4,7,6,5,3]=>1010111
[2,1,7,5,4,6,8,3]=>1011001
[2,1,8,5,4,6,7,3]=>1011001
[2,1,8,5,4,7,6,3]=>1011011
[2,1,7,5,6,4,8,3]=>1010101
[2,1,8,5,6,4,7,3]=>1010101
[2,1,8,5,7,6,4,3]=>1010111
[2,1,8,7,5,6,4,3]=>1011011
[2,3,1,8,5,6,7,4]=>0101001
[2,3,1,8,6,7,5,4]=>0101011
[2,3,4,1,8,6,7,5]=>0010101
[2,3,4,5,8,6,7,1]=>0000101
[2,3,4,7,5,6,1,8]=>0001010
[2,3,4,7,5,6,8,1]=>0001001
[2,3,4,8,5,6,7,1]=>0001001
[2,3,4,8,5,7,6,1]=>0001011
[2,3,4,8,6,5,7,1]=>0001101
[2,3,4,8,6,7,5,1]=>0001011
[2,3,6,4,5,1,8,7]=>0010101
[2,3,6,4,5,7,8,1]=>0010001
[2,3,7,4,5,6,8,1]=>0010001
[2,3,8,4,5,6,7,1]=>0010001
[2,3,7,4,6,5,8,1]=>0010101
[2,3,7,5,4,6,1,8]=>0011010
[2,3,7,5,4,6,8,1]=>0011001
[2,3,7,5,6,4,1,8]=>0010110
[2,3,7,5,6,4,8,1]=>0010101
[2,3,8,5,7,6,4,1]=>0010111
[2,4,3,1,8,6,7,5]=>0110101
[2,4,3,5,8,6,7,1]=>0100101
[2,4,3,8,5,6,7,1]=>0101001
[2,4,3,8,6,7,5,1]=>0101011
[2,5,3,4,1,6,7,8]=>0101000
[2,5,3,4,1,8,7,6]=>0101011
[2,5,3,4,6,7,1,8]=>0100010
[2,5,3,4,8,7,6,1]=>0100111
[2,6,3,4,5,7,8,1]=>0100001
[2,6,3,4,5,8,7,1]=>0100011
[2,6,3,5,4,1,7,8]=>0101100
[2,6,3,5,4,1,8,7]=>0101101
[2,6,3,5,4,7,8,1]=>0101001
[2,7,3,5,4,6,8,1]=>0101001
[2,7,3,5,6,4,8,1]=>0100101
[2,8,3,5,7,6,4,1]=>0100111
[2,7,3,6,5,4,1,8]=>0101110
[2,8,3,7,5,6,4,1]=>0101011
[2,5,4,3,8,6,7,1]=>0110101
[2,6,4,3,5,7,8,1]=>0110001
[2,8,4,3,7,6,5,1]=>0110111
[2,6,4,5,3,1,7,8]=>0101100
[2,6,4,5,3,1,8,7]=>0101101
[2,6,4,5,3,7,8,1]=>0101001
[2,6,4,5,3,8,7,1]=>0101011
[2,7,4,5,6,3,1,8]=>0100110
[2,7,4,5,6,3,8,1]=>0100101
[2,7,5,4,3,6,8,1]=>0111001
[2,8,5,4,3,6,7,1]=>0111001
[2,8,5,4,3,7,6,1]=>0111011
[2,7,5,4,6,3,8,1]=>0110101
[2,8,5,4,7,6,3,1]=>0110111
[2,8,7,5,4,6,3,1]=>0111011
[2,8,7,5,6,4,3,1]=>0110111
[3,2,1,4,8,6,7,5]=>1100101
[3,2,1,5,8,6,7,4]=>1100101
[3,2,1,7,5,6,8,4]=>1101001
[3,2,1,8,5,6,7,4]=>1101001
[3,2,1,8,5,7,6,4]=>1101011
[3,2,1,8,6,5,7,4]=>1101101
[3,2,1,8,6,7,5,4]=>1101011
[3,2,4,1,8,6,7,5]=>1010101
[3,2,4,8,5,6,7,1]=>1001001
[3,2,5,4,8,6,7,1]=>1010101
[3,2,6,4,5,1,8,7]=>1010101
[3,2,6,4,5,7,1,8]=>1010010
[3,2,7,4,6,5,1,8]=>1010110
[3,2,7,4,6,5,8,1]=>1010101
[3,2,8,5,4,6,7,1]=>1011001
[3,2,7,5,6,4,1,8]=>1010110
[3,2,7,5,6,4,8,1]=>1010101
[3,2,8,5,6,4,7,1]=>1010101
[3,2,8,5,7,6,4,1]=>1010111
[4,2,3,1,6,5,8,7]=>1010101
[4,2,3,1,6,7,8,5]=>1010001
[4,2,3,1,6,8,7,5]=>1010011
[4,2,3,1,7,6,8,5]=>1010101
[4,2,3,1,8,6,7,5]=>1010101
[4,2,3,1,8,7,6,5]=>1010111
[4,2,3,5,1,7,8,6]=>1001001
[4,2,3,5,1,8,7,6]=>1001011
[4,2,3,5,6,1,8,7]=>1000101
[4,2,3,5,6,8,7,1]=>1000011
[4,2,3,6,5,1,7,8]=>1001100
[4,2,3,6,5,1,8,7]=>1001101
[4,2,3,6,5,8,7,1]=>1001011
[4,2,3,7,5,6,1,8]=>1001010
[4,2,3,8,5,6,7,1]=>1001001
[4,2,3,7,6,5,8,1]=>1001101
[4,2,3,8,6,7,5,1]=>1001011
[4,2,3,8,7,6,5,1]=>1001111
[5,2,3,4,1,8,7,6]=>1001011
[5,2,3,4,8,7,6,1]=>1000111
[8,2,3,4,7,6,5,1]=>1000111
[6,2,3,5,4,1,7,8]=>1001100
[6,2,3,5,4,1,8,7]=>1001101
[6,2,3,5,4,7,1,8]=>1001010
[8,2,3,5,4,7,6,1]=>1001011
[7,2,3,5,6,4,1,8]=>1000110
[8,2,3,5,6,7,4,1]=>1000011
[7,2,3,6,5,4,1,8]=>1001110
[8,2,3,7,5,6,4,1]=>1001011
[8,2,3,7,6,5,4,1]=>1001111
[5,2,4,3,1,6,7,8]=>1011000
[5,2,4,3,1,6,8,7]=>1011001
[5,2,4,3,1,7,6,8]=>1011010
[5,2,4,3,1,8,7,6]=>1011011
[5,2,4,3,6,1,7,8]=>1010100
[5,2,4,3,6,1,8,7]=>1010101
[5,2,4,3,7,6,1,8]=>1010110
[5,2,4,3,7,6,8,1]=>1010101
[6,2,4,3,5,1,8,7]=>1010101
[7,2,4,3,6,5,1,8]=>1010110
[7,2,4,3,6,5,8,1]=>1010101
[8,2,4,3,6,5,7,1]=>1010101
[8,2,4,3,7,6,5,1]=>1010111
[6,2,4,5,3,1,7,8]=>1001100
[6,2,4,5,3,1,8,7]=>1001101
[6,2,4,5,3,8,7,1]=>1001011
[7,2,4,5,3,6,1,8]=>1001010
[7,2,4,5,3,6,8,1]=>1001001
[8,2,4,7,5,6,3,1]=>1001011
[8,2,4,7,6,5,3,1]=>1001111
[6,2,5,4,3,1,8,7]=>1011101
[7,2,5,4,3,6,1,8]=>1011010
[8,2,5,4,3,7,6,1]=>1011011
[8,2,5,4,7,6,3,1]=>1010111
[8,2,6,4,5,3,7,1]=>1010101
[8,2,6,4,5,7,3,1]=>1010011
[8,2,7,4,5,6,3,1]=>1010011
[8,2,7,4,6,5,3,1]=>1010111
[7,2,6,5,4,3,1,8]=>1011110
[8,2,6,5,4,3,7,1]=>1011101
[8,2,7,5,4,6,3,1]=>1011011
[8,2,7,5,6,4,3,1]=>1010111
[8,2,7,6,5,4,3,1]=>1011111
[4,3,2,1,8,6,7,5]=>1110101
[4,3,2,7,5,6,8,1]=>1101001
[4,3,2,8,5,6,7,1]=>1101001
[4,3,2,8,6,7,5,1]=>1101011
[5,3,2,4,1,6,8,7]=>1101001
[5,3,2,4,1,8,7,6]=>1101011
[5,3,2,4,6,1,8,7]=>1100101
[6,3,2,5,4,1,7,8]=>1101100
[6,3,2,5,4,1,8,7]=>1101101
[6,3,2,5,4,7,1,8]=>1101010
[6,3,2,5,4,7,8,1]=>1101001
[8,3,2,5,4,7,6,1]=>1101011
[8,3,2,5,6,4,7,1]=>1100101
[8,3,2,5,7,6,4,1]=>1100111
[8,3,2,7,5,6,4,1]=>1101011
[8,3,2,7,6,5,4,1]=>1101111
[5,3,4,2,1,6,8,7]=>1011001
[5,3,4,2,1,7,8,6]=>1011001
[5,3,4,2,1,8,7,6]=>1011011
[5,3,4,2,6,1,8,7]=>1010101
[5,3,4,2,7,6,1,8]=>1010110
[5,3,4,2,7,6,8,1]=>1010101
[5,3,4,2,8,6,7,1]=>1010101
[6,3,4,2,5,1,8,7]=>1010101
[7,3,4,2,6,5,1,8]=>1010110
[7,3,4,2,6,5,8,1]=>1010101
[7,3,4,6,5,2,1,8]=>1001110
[6,3,5,4,2,1,8,7]=>1011101
[6,3,5,4,2,7,1,8]=>1011010
[6,3,5,4,2,7,8,1]=>1011001
[8,3,5,4,2,6,7,1]=>1011001
[7,3,5,4,6,2,1,8]=>1010110
[8,3,5,4,7,6,2,1]=>1010111
[7,3,6,4,5,2,1,8]=>1010110
[7,3,6,4,5,2,8,1]=>1010101
[8,3,6,4,5,2,7,1]=>1010101
[8,3,7,4,5,6,2,1]=>1010011
[7,3,6,5,4,2,1,8]=>1011110
[8,3,7,5,6,4,2,1]=>1010111
[5,4,3,2,8,6,7,1]=>1110101
[7,4,3,2,6,5,1,8]=>1110110
[7,4,3,2,6,5,8,1]=>1110101
[8,4,3,2,6,7,5,1]=>1110011
[8,4,3,2,7,6,5,1]=>1110111
[6,4,3,5,2,1,8,7]=>1101101
[8,4,3,5,7,6,2,1]=>1100111
[7,4,3,6,5,2,1,8]=>1101110
[7,4,3,6,5,2,8,1]=>1101101
[8,4,3,7,5,6,2,1]=>1101011
[6,5,3,4,2,1,8,7]=>1101101
[8,5,3,4,2,7,6,1]=>1101011
[8,5,3,4,7,6,2,1]=>1100111
[8,7,3,4,6,5,2,1]=>1100111
[7,6,3,5,4,2,1,8]=>1101110
[8,6,3,5,4,2,7,1]=>1101101
[8,7,3,5,4,6,2,1]=>1101011
[8,7,3,5,6,4,2,1]=>1100111
[8,7,3,6,5,4,2,1]=>1101111
[8,5,4,3,2,7,6,1]=>1111011
[8,5,4,3,7,6,2,1]=>1110111
[8,7,4,3,6,5,2,1]=>1110111
[2,4,1,3,6,5,8,7]=>0100101
[2,1,4,6,3,5,8,7]=>1001001
[2,4,1,6,3,5,8,7]=>0101001
[2,4,6,1,3,5,8,7]=>0010001
[2,1,4,3,6,8,5,7]=>1010010
[2,4,1,3,6,8,5,7]=>0100010
[2,1,4,6,3,8,5,7]=>1001010
[2,4,1,6,3,8,5,7]=>0101010
[2,4,6,1,3,8,5,7]=>0010010
[2,1,4,6,8,3,5,7]=>1000100
[2,4,1,6,8,3,5,7]=>0100100
[2,4,6,1,8,3,5,7]=>0010100
[2,4,6,8,1,3,5,7]=>0001000
[2,4,1,3,6,5,7,8]=>0100100
[2,4,1,6,3,7,5,8]=>0101010
[2,4,6,1,3,7,5,8]=>0010010
[2,4,6,7,1,3,5,8]=>0001000
[2,4,1,3,6,7,8,5]=>0100001
[2,1,4,6,3,7,8,5]=>1001001
[2,4,1,6,3,7,8,5]=>0101001
[2,4,6,1,3,7,8,5]=>0010001
[2,4,1,6,7,3,8,5]=>0100101
[2,4,6,1,7,3,8,5]=>0010101
[2,4,6,7,1,3,8,5]=>0001001
[2,4,1,6,7,8,3,5]=>0100010
[2,4,6,1,7,8,3,5]=>0010010
[2,4,6,7,1,8,3,5]=>0001010
[2,4,6,7,8,1,3,5]=>0000100
[2,1,4,3,7,5,8,6]=>1010101
[2,4,1,3,7,5,8,6]=>0100101
[2,4,1,7,3,5,8,6]=>0101001
[2,4,7,1,3,5,8,6]=>0010001
[2,1,4,3,7,8,5,6]=>1010010
[2,4,1,3,7,8,5,6]=>0100010
[2,4,1,7,3,8,5,6]=>0101010
[2,4,1,7,8,3,5,6]=>0100100
[2,4,7,1,8,3,5,6]=>0010100
[2,4,1,5,3,7,6,8]=>0101010
[2,4,5,1,7,3,6,8]=>0010100
[2,4,1,3,5,7,8,6]=>0100001
[2,4,1,5,3,7,8,6]=>0101001
[2,4,5,1,3,7,8,6]=>0010001
[2,1,4,5,7,3,8,6]=>1000101
[2,4,1,5,7,3,8,6]=>0100101
[2,4,5,1,7,3,8,6]=>0010101
[2,4,5,7,1,3,8,6]=>0001001
[2,4,5,7,8,1,3,6]=>0000100
[2,1,4,3,8,5,6,7]=>1010100
[2,4,1,3,8,5,6,7]=>0100100
[2,1,4,8,3,5,6,7]=>1001000
[2,4,1,8,3,5,6,7]=>0101000
[2,4,1,5,3,8,6,7]=>0101010
[2,1,4,5,8,3,6,7]=>1000100
[2,4,1,5,8,3,6,7]=>0100100
[2,4,5,8,1,3,6,7]=>0001000
[2,4,1,5,6,3,8,7]=>0100101
[2,1,4,5,6,8,3,7]=>1000010
[2,4,5,1,6,8,3,7]=>0010010
[2,4,5,6,1,8,3,7]=>0001010
[2,4,5,6,8,1,3,7]=>0000100
[2,4,1,3,5,6,7,8]=>0100000
[2,4,1,5,6,3,7,8]=>0100100
[2,4,5,1,6,3,7,8]=>0010100
[2,4,5,6,1,3,7,8]=>0001000
[2,4,5,6,7,1,3,8]=>0000100
[2,4,1,5,6,7,8,3]=>0100001
[2,4,5,6,7,1,8,3]=>0000101
[2,1,5,3,6,4,8,7]=>1010101
[2,1,5,6,3,4,8,7]=>1001001
[2,1,5,3,6,8,4,7]=>1010010
[2,5,1,3,6,8,4,7]=>0100010
[2,5,1,6,8,3,4,7]=>0100100
[2,1,5,6,3,4,7,8]=>1001000
[2,5,1,6,3,4,7,8]=>0101000
[2,1,5,3,6,7,4,8]=>1010010
[2,1,5,6,3,7,4,8]=>1001010
[2,5,1,6,3,7,4,8]=>0101010
[2,5,6,1,3,7,4,8]=>0010010
[2,1,5,6,7,3,4,8]=>1000100
[2,5,1,6,7,3,4,8]=>0100100
[2,1,5,3,6,7,8,4]=>1010001
[2,5,1,3,6,7,8,4]=>0100001
[2,1,5,6,3,7,8,4]=>1001001
[2,5,1,6,3,7,8,4]=>0101001
[2,5,6,1,3,7,8,4]=>0010001
[2,1,5,6,7,3,8,4]=>1000101
[2,5,1,6,7,3,8,4]=>0100101
[2,1,5,6,7,8,3,4]=>1000010
[2,5,1,6,7,8,3,4]=>0100010
[2,5,6,1,7,8,3,4]=>0010010
[2,5,6,7,8,1,3,4]=>0000100
[2,1,5,3,7,4,8,6]=>1010101
[2,5,1,3,7,4,8,6]=>0100101
[2,1,5,7,3,4,8,6]=>1001001
[2,5,1,7,3,4,8,6]=>0101001
[2,5,7,1,3,4,8,6]=>0010001
[2,1,5,3,7,8,4,6]=>1010010
[2,5,1,3,7,8,4,6]=>0100010
[2,1,5,7,3,8,4,6]=>1001010
[2,1,5,7,8,3,4,6]=>1000100
[2,5,1,7,8,3,4,6]=>0100100
[2,5,1,3,7,4,6,8]=>0100100
[2,1,5,7,3,4,6,8]=>1001000
[2,3,5,7,1,4,6,8]=>0001000
[2,3,5,1,7,4,8,6]=>0010101
[2,3,5,7,1,4,8,6]=>0001001
[2,3,5,7,1,8,4,6]=>0001010
[2,1,5,3,8,4,6,7]=>1010100
[2,1,5,8,3,4,6,7]=>1001000
[2,5,1,8,3,4,6,7]=>0101000
[2,3,5,1,4,8,6,7]=>0010010
[2,3,5,8,1,4,6,7]=>0001000
[2,1,5,3,4,6,8,7]=>1010001
[2,3,5,1,6,4,8,7]=>0010101
[2,3,5,6,1,4,8,7]=>0001001
[2,3,5,6,1,8,4,7]=>0001010
[2,3,5,6,8,1,4,7]=>0000100
[2,3,5,6,1,4,7,8]=>0001000
[2,3,5,6,1,7,4,8]=>0001010
[2,3,5,1,6,7,8,4]=>0010001
[2,3,5,6,1,7,8,4]=>0001001
[2,3,5,6,7,1,8,4]=>0000101
[2,3,5,6,7,8,1,4]=>0000010
[2,1,6,3,7,4,8,5]=>1010101
[2,6,1,3,7,4,8,5]=>0100101
[2,6,7,1,3,4,8,5]=>0010001
[2,1,6,3,7,8,4,5]=>1010010
[2,1,6,7,3,8,4,5]=>1001010
[2,6,1,7,3,8,4,5]=>0101010
[2,1,6,7,8,3,4,5]=>1000100
[2,6,1,7,8,3,4,5]=>0100100
[2,6,7,8,1,3,4,5]=>0001000
[2,6,1,7,3,4,5,8]=>0101000
[2,6,7,1,3,4,5,8]=>0010000
[2,3,1,6,4,7,5,8]=>0101010
[2,3,6,1,4,7,5,8]=>0010010
[2,3,6,7,1,4,5,8]=>0001000
[2,1,6,3,4,7,8,5]=>1010001
[2,3,6,1,4,7,8,5]=>0010001
[2,1,3,6,7,4,8,5]=>1000101
[2,3,6,7,1,4,8,5]=>0001001
[2,3,1,6,7,8,4,5]=>0100010
[2,3,6,1,7,8,4,5]=>0010010
[2,3,6,7,1,8,4,5]=>0001010
[2,3,6,7,8,1,4,5]=>0000100
[2,6,1,8,3,4,5,7]=>0101000
[2,6,8,1,3,4,5,7]=>0010000
[2,1,6,3,4,8,5,7]=>1010010
[2,3,1,6,4,8,5,7]=>0101010
[2,3,6,1,4,8,5,7]=>0010010
[2,3,1,6,8,4,5,7]=>0100100
[2,3,6,1,8,4,5,7]=>0010100
[2,3,6,8,1,4,5,7]=>0001000
[2,1,6,3,4,5,8,7]=>1010001
[2,6,1,3,4,5,8,7]=>0100001
[2,3,6,1,4,5,8,7]=>0010001
[2,3,4,1,6,8,5,7]=>0010010
[2,3,4,6,1,8,5,7]=>0001010
[2,3,6,1,4,5,7,8]=>0010000
[2,3,4,6,7,8,1,5]=>0000010
[2,7,1,3,8,4,5,6]=>0100100
[2,1,7,8,3,4,5,6]=>1001000
[2,7,1,8,3,4,5,6]=>0101000
[2,7,8,1,3,4,5,6]=>0010000
[2,1,7,3,4,8,5,6]=>1010010
[2,1,3,7,4,8,5,6]=>1001010
[2,3,1,7,4,8,5,6]=>0101010
[2,3,1,7,8,4,5,6]=>0100100
[2,3,7,8,1,4,5,6]=>0001000
[2,1,7,3,4,5,8,6]=>1010001
[2,3,1,7,4,5,8,6]=>0101001
[2,3,7,1,4,5,8,6]=>0010001
[2,3,4,1,7,5,8,6]=>0010101
[2,3,4,7,1,5,8,6]=>0001001
[2,1,3,4,7,8,5,6]=>1000010
[2,3,1,4,7,8,5,6]=>0100010
[2,3,4,1,7,8,5,6]=>0010010
[2,3,4,7,8,1,5,6]=>0000100
[2,3,4,1,7,5,6,8]=>0010100
[2,3,4,7,1,5,6,8]=>0001000
[2,1,8,3,4,5,6,7]=>1010000
[2,8,1,3,4,5,6,7]=>0100000
[2,3,8,1,4,5,6,7]=>0010000
[2,1,3,4,8,5,6,7]=>1000100
[2,3,1,4,8,5,6,7]=>0100100
[2,3,4,1,8,5,6,7]=>0010100
[2,3,4,8,1,5,6,7]=>0001000
[2,3,4,1,5,8,6,7]=>0010010
[2,3,4,5,8,1,6,7]=>0000100
[3,1,4,2,6,5,8,7]=>1010101
[3,4,1,2,6,5,8,7]=>0100101
[3,1,4,2,6,8,5,7]=>1010010
[3,4,1,2,6,8,5,7]=>0100010
[3,1,4,6,2,8,5,7]=>1001010
[3,1,4,6,8,2,5,7]=>1000100
[3,4,1,6,8,2,5,7]=>0100100
[3,1,4,2,6,5,7,8]=>1010100
[3,4,1,2,6,5,7,8]=>0100100
[3,1,4,2,6,7,5,8]=>1010010
[3,4,1,2,6,7,5,8]=>0100010
[3,4,1,6,2,7,5,8]=>0101010
[3,4,6,1,2,7,5,8]=>0010010
[3,1,4,2,6,7,8,5]=>1010001
[3,4,1,2,6,7,8,5]=>0100001
[3,4,6,1,2,7,8,5]=>0010001
[3,4,6,1,7,2,8,5]=>0010101
[3,1,4,6,7,8,2,5]=>1000010
[3,4,6,1,7,8,2,5]=>0010010
[3,4,6,7,1,8,2,5]=>0001010
[3,4,6,7,8,1,2,5]=>0000100
[3,1,4,2,7,5,8,6]=>1010101
[3,4,1,2,7,5,8,6]=>0100101
[3,4,7,1,2,5,8,6]=>0010001
[3,1,4,2,7,8,5,6]=>1010010
[3,4,1,2,7,8,5,6]=>0100010
[3,4,7,1,8,2,5,6]=>0010100
[3,1,4,2,7,5,6,8]=>1010100
[3,4,1,2,7,5,6,8]=>0100100
[3,4,1,2,5,7,6,8]=>0100010
[3,1,4,5,2,7,6,8]=>1001010
[3,4,1,5,2,7,6,8]=>0101010
[3,4,1,5,7,2,6,8]=>0100100
[3,1,4,2,5,7,8,6]=>1010001
[3,4,1,2,5,7,8,6]=>0100001
[3,1,4,5,2,7,8,6]=>1001001
[3,4,1,5,7,2,8,6]=>0100101
[3,4,5,7,1,2,8,6]=>0001001
[3,1,4,5,7,8,2,6]=>1000010
[3,4,1,5,7,8,2,6]=>0100010
[3,4,5,1,7,8,2,6]=>0010010
[3,1,4,2,8,5,6,7]=>1010100
[3,4,1,2,8,5,6,7]=>0100100
[3,1,4,8,2,5,6,7]=>1001000
[3,4,1,8,2,5,6,7]=>0101000
[3,4,8,1,2,5,6,7]=>0010000
[3,1,4,2,5,8,6,7]=>1010010
[3,4,1,2,5,8,6,7]=>0100010
[3,4,1,5,2,8,6,7]=>0101010
[3,4,5,1,2,8,6,7]=>0010010
[3,4,1,5,8,2,6,7]=>0100100
[3,4,5,8,1,2,6,7]=>0001000
[3,4,1,2,5,6,8,7]=>0100001
[3,1,4,5,6,2,8,7]=>1000101
[3,4,5,1,6,2,8,7]=>0010101
[3,4,5,6,1,2,8,7]=>0001001
[3,4,1,5,6,8,2,7]=>0100010
[3,4,5,6,1,8,2,7]=>0001010
[3,4,5,6,8,1,2,7]=>0000100
[3,1,4,2,5,6,7,8]=>1010000
[3,4,1,5,6,2,7,8]=>0100100
[3,4,5,1,6,2,7,8]=>0010100
[3,4,1,5,6,7,2,8]=>0100010
[3,4,5,6,1,7,2,8]=>0001010
[3,1,4,5,6,7,8,2]=>1000001
[3,4,5,1,6,7,8,2]=>0010001
[3,4,5,6,1,7,8,2]=>0001001
[3,1,5,2,6,4,8,7]=>1010101
[3,1,5,6,2,4,8,7]=>1001001
[3,5,1,6,2,4,8,7]=>0101001
[3,5,6,1,2,4,8,7]=>0010001
[3,5,1,2,6,8,4,7]=>0100010
[3,1,5,6,2,8,4,7]=>1001010
[3,5,6,1,2,8,4,7]=>0010010
[3,1,5,6,8,2,4,7]=>1000100
[3,5,6,1,8,2,4,7]=>0010100
[3,1,5,6,2,4,7,8]=>1001000
[3,5,1,6,2,4,7,8]=>0101000
[3,5,6,1,2,4,7,8]=>0010000
[3,5,1,6,2,7,4,8]=>0101010
[3,5,6,1,2,7,4,8]=>0010010
[3,5,6,1,7,2,4,8]=>0010100
[3,1,5,2,6,7,8,4]=>1010001
[3,5,1,2,6,7,8,4]=>0100001
[3,1,5,6,2,7,8,4]=>1001001
[3,5,1,6,2,7,8,4]=>0101001
[3,5,6,1,2,7,8,4]=>0010001
[3,1,5,6,7,2,8,4]=>1000101
[3,5,1,6,7,2,8,4]=>0100101
[3,5,6,1,7,2,8,4]=>0010101
[3,1,5,6,7,8,2,4]=>1000010
[3,5,1,6,7,8,2,4]=>0100010
[3,5,6,1,7,8,2,4]=>0010010
[3,5,6,7,8,1,2,4]=>0000100
[3,1,5,2,7,4,8,6]=>1010101
[3,5,1,2,7,4,8,6]=>0100101
[3,1,5,7,2,4,8,6]=>1001001
[3,5,1,7,2,4,8,6]=>0101001
[3,5,7,1,2,4,8,6]=>0010001
[3,1,5,2,7,8,4,6]=>1010010
[3,5,1,2,7,8,4,6]=>0100010
[3,1,5,7,2,8,4,6]=>1001010
[3,5,1,7,2,8,4,6]=>0101010
[3,1,5,7,8,2,4,6]=>1000100
[3,5,1,7,8,2,4,6]=>0100100
[3,5,7,8,1,2,4,6]=>0001000
[3,1,5,2,7,4,6,8]=>1010100
[3,5,1,2,7,4,6,8]=>0100100
[3,1,5,7,2,4,6,8]=>1001000
[3,5,1,7,2,4,6,8]=>0101000
[3,5,7,1,2,4,6,8]=>0010000
[3,1,5,2,4,7,6,8]=>1010010
[3,5,1,2,4,7,6,8]=>0100010
[3,1,2,5,4,7,6,8]=>1001010
[1,3,5,2,4,7,6,8]=>0010010
[3,1,2,5,7,4,6,8]=>1000100
[1,3,2,5,7,4,6,8]=>0100100
[1,3,5,2,7,4,6,8]=>0010100
[1,3,5,7,2,4,6,8]=>0001000
[3,5,1,2,4,7,8,6]=>0100001
[1,3,5,2,4,7,8,6]=>0010001
[3,1,2,5,7,4,8,6]=>1000101
[1,3,2,5,7,4,8,6]=>0100101
[1,3,5,2,7,4,8,6]=>0010101
[1,3,5,7,2,4,8,6]=>0001001
[1,3,2,5,7,8,4,6]=>0100010
[1,3,5,2,7,8,4,6]=>0010010
[1,3,5,7,2,8,4,6]=>0001010
[1,3,5,7,8,2,4,6]=>0000100
[3,1,5,2,8,4,6,7]=>1010100
[3,5,1,2,8,4,6,7]=>0100100
[3,1,5,8,2,4,6,7]=>1001000
[3,5,1,8,2,4,6,7]=>0101000
[3,1,5,2,4,8,6,7]=>1010010
[3,5,1,2,4,8,6,7]=>0100010
[1,3,2,5,4,8,6,7]=>0101010
[1,3,5,2,4,8,6,7]=>0010010
[3,1,2,5,8,4,6,7]=>1000100
[1,3,2,5,8,4,6,7]=>0100100
[1,3,5,2,8,4,6,7]=>0010100
[1,3,5,8,2,4,6,7]=>0001000
[3,5,1,2,4,6,8,7]=>0100001
[3,1,2,5,4,6,8,7]=>1001001
[1,3,5,2,4,6,8,7]=>0010001
[1,3,5,6,2,4,8,7]=>0001001
[3,1,2,5,6,8,4,7]=>1000010
[1,3,5,2,6,8,4,7]=>0010010
[3,5,1,2,4,6,7,8]=>0100000
[1,3,5,2,4,6,7,8]=>0010000
[1,3,5,2,6,4,7,8]=>0010100
[1,3,5,6,2,4,7,8]=>0001000
[3,1,2,5,6,7,4,8]=>1000010
[1,3,5,2,6,7,4,8]=>0010010
[1,3,5,6,2,7,4,8]=>0001010
[1,3,5,6,7,2,4,8]=>0000100
[3,1,2,5,6,7,8,4]=>1000001
[1,3,5,6,2,7,8,4]=>0001001
[1,3,5,6,7,8,2,4]=>0000010
[3,1,6,2,7,4,8,5]=>1010101
[3,6,1,2,7,4,8,5]=>0100101
[3,6,1,7,2,4,8,5]=>0101001
[3,6,7,1,2,4,8,5]=>0010001
[3,1,6,7,2,8,4,5]=>1001010
[3,6,1,7,2,8,4,5]=>0101010
[3,6,7,1,2,8,4,5]=>0010010
[3,6,1,7,8,2,4,5]=>0100100
[3,6,7,8,1,2,4,5]=>0001000
[3,1,6,7,2,4,5,8]=>1001000
[3,6,7,1,2,4,5,8]=>0010000
[3,1,6,2,4,7,5,8]=>1010010
[3,6,1,2,4,7,5,8]=>0100010
[3,1,2,6,4,7,5,8]=>1001010
[1,3,2,6,4,7,5,8]=>0101010
[1,3,6,2,4,7,5,8]=>0010010
[1,3,2,6,7,4,5,8]=>0100100
[3,1,6,2,4,7,8,5]=>1010001
[3,6,1,2,4,7,8,5]=>0100001
[3,1,2,6,4,7,8,5]=>1001001
[1,3,2,6,4,7,8,5]=>0101001
[1,3,6,2,4,7,8,5]=>0010001
[3,1,2,6,7,4,8,5]=>1000101
[1,3,6,2,7,4,8,5]=>0010101
[1,3,6,2,7,8,4,5]=>0010010
[3,1,6,2,8,4,5,7]=>1010100
[3,1,6,8,2,4,5,7]=>1001000
[3,6,8,1,2,4,5,7]=>0010000
[3,1,6,2,4,8,5,7]=>1010010
[3,6,1,2,4,8,5,7]=>0100010
[1,3,2,6,4,8,5,7]=>0101010
[1,3,6,2,4,8,5,7]=>0010010
[3,1,6,2,4,5,8,7]=>1010001
[3,1,2,6,4,5,8,7]=>1001001
[1,3,4,6,2,5,8,7]=>0001001
[3,1,2,4,6,8,5,7]=>1000010
[1,3,2,4,6,8,5,7]=>0100010
[1,3,4,6,8,2,5,7]=>0000100
[3,1,6,2,4,5,7,8]=>1010000
[1,3,2,6,4,5,7,8]=>0101000
[1,3,6,2,4,5,7,8]=>0010000
[3,1,2,4,6,7,5,8]=>1000010
[3,1,2,4,6,7,8,5]=>1000001
[1,3,4,6,7,2,8,5]=>0000101
[3,7,1,2,8,4,5,6]=>0100100
[3,1,7,8,2,4,5,6]=>1001000
[3,1,2,7,4,8,5,6]=>1001010
[1,3,2,7,4,8,5,6]=>0101010
[1,3,7,2,4,8,5,6]=>0010010
[3,1,2,7,8,4,5,6]=>1000100
[3,7,1,2,4,5,8,6]=>0100001
[1,3,7,2,4,5,8,6]=>0010001
[3,1,2,4,7,5,8,6]=>1000101
[1,3,2,4,7,5,8,6]=>0100101
[3,1,2,4,7,8,5,6]=>1000010
[1,3,2,4,7,8,5,6]=>0100010
[1,3,4,2,7,8,5,6]=>0010010
[3,7,1,2,4,5,6,8]=>0100000
[1,3,2,7,4,5,6,8]=>0101000
[3,1,2,4,7,5,6,8]=>1000100
[1,3,4,5,7,2,6,8]=>0000100
[1,3,4,5,7,2,8,6]=>0000101
[1,3,4,5,7,8,2,6]=>0000010
[3,1,8,2,4,5,6,7]=>1010000
[1,3,2,8,4,5,6,7]=>0101000
[1,3,8,2,4,5,6,7]=>0010000
[3,1,2,4,8,5,6,7]=>1000100
[1,3,2,4,8,5,6,7]=>0100100
[1,3,4,2,8,5,6,7]=>0010100
[1,3,4,8,2,5,6,7]=>0001000
[3,1,2,4,5,8,6,7]=>1000010
[1,3,2,4,5,8,6,7]=>0100010
[1,3,4,2,5,8,6,7]=>0010010
[1,3,4,5,2,8,6,7]=>0001010
[1,3,4,5,8,2,6,7]=>0000100
[4,1,5,2,6,3,8,7]=>1010101
[4,1,5,6,2,3,8,7]=>1001001
[4,5,1,6,2,3,8,7]=>0101001
[4,5,6,1,2,3,8,7]=>0010001
[4,1,5,2,6,8,3,7]=>1010010
[4,5,1,2,6,8,3,7]=>0100010
[4,1,5,6,2,8,3,7]=>1001010
[4,5,1,6,2,8,3,7]=>0101010
[4,1,5,6,8,2,3,7]=>1000100
[4,5,6,8,1,2,3,7]=>0001000
[4,1,5,6,2,3,7,8]=>1001000
[4,5,1,6,2,3,7,8]=>0101000
[4,5,1,6,2,7,3,8]=>0101010
[4,1,5,6,7,2,3,8]=>1000100
[4,5,1,6,7,2,3,8]=>0100100
[4,1,5,2,6,7,8,3]=>1010001
[4,5,1,2,6,7,8,3]=>0100001
[4,5,1,6,2,7,8,3]=>0101001
[4,1,5,6,7,2,8,3]=>1000101
[4,5,1,6,7,2,8,3]=>0100101
[4,5,6,1,7,2,8,3]=>0010101
[4,5,6,7,1,2,8,3]=>0001001
[4,1,5,6,7,8,2,3]=>1000010
[4,5,1,6,7,8,2,3]=>0100010
[4,5,6,7,1,8,2,3]=>0001010
[4,1,5,2,7,3,8,6]=>1010101
[4,5,1,7,2,3,8,6]=>0101001
[4,1,5,2,7,8,3,6]=>1010010
[4,5,1,2,7,8,3,6]=>0100010
[4,1,5,7,2,8,3,6]=>1001010
[4,5,1,7,2,8,3,6]=>0101010
[4,5,7,1,2,8,3,6]=>0010010
[4,5,1,7,8,2,3,6]=>0100100
[4,1,5,2,7,3,6,8]=>1010100
[4,5,1,2,7,3,6,8]=>0100100
[4,1,5,7,2,3,6,8]=>1001000
[4,5,1,7,2,3,6,8]=>0101000
[4,5,1,2,3,7,6,8]=>0100010
[1,4,2,5,3,7,6,8]=>0101010
[1,4,5,2,3,7,6,8]=>0010010
[4,1,2,5,7,3,6,8]=>1000100
[1,4,2,5,7,3,6,8]=>0100100
[1,4,5,2,7,3,6,8]=>0010100
[1,4,5,7,2,3,6,8]=>0001000
[4,1,5,2,3,7,8,6]=>1010001
[4,1,2,5,3,7,8,6]=>1001001
[1,4,2,5,3,7,8,6]=>0101001
[1,4,5,2,3,7,8,6]=>0010001
[4,1,2,5,7,3,8,6]=>1000101
[1,4,2,5,7,3,8,6]=>0100101
[1,4,5,2,7,3,8,6]=>0010101
[1,4,5,7,2,3,8,6]=>0001001
[4,1,2,5,7,8,3,6]=>1000010
[1,4,2,5,7,8,3,6]=>0100010
[1,4,5,2,7,8,3,6]=>0010010
[1,4,5,7,8,2,3,6]=>0000100
[4,1,5,2,8,3,6,7]=>1010100
[4,5,1,2,8,3,6,7]=>0100100
[4,1,5,8,2,3,6,7]=>1001000
[4,5,1,8,2,3,6,7]=>0101000
[4,5,8,1,2,3,6,7]=>0010000
[4,1,5,2,3,8,6,7]=>1010010
[4,5,1,2,3,8,6,7]=>0100010
[4,1,2,5,3,8,6,7]=>1001010
[1,4,2,5,3,8,6,7]=>0101010
[1,4,5,2,3,8,6,7]=>0010010
[4,1,2,5,8,3,6,7]=>1000100
[1,4,2,5,8,3,6,7]=>0100100
[1,4,5,2,8,3,6,7]=>0010100
[1,4,5,8,2,3,6,7]=>0001000
[1,4,2,5,3,6,8,7]=>0101001
[4,1,2,5,6,3,8,7]=>1000101
[1,4,5,2,6,3,8,7]=>0010101
[4,1,2,5,6,8,3,7]=>1000010
[1,4,5,2,6,8,3,7]=>0010010
[1,4,5,6,2,8,3,7]=>0001010
[1,4,5,6,8,2,3,7]=>0000100
[1,4,2,5,3,6,7,8]=>0101000
[1,4,5,2,3,6,7,8]=>0010000
[4,1,2,5,6,3,7,8]=>1000100
[1,4,5,2,6,3,7,8]=>0010100
[4,1,2,5,6,7,3,8]=>1000010
[1,4,2,5,6,7,3,8]=>0100010
[1,4,5,6,7,2,3,8]=>0000100
[4,1,2,5,6,7,8,3]=>1000001
[1,4,5,2,6,7,8,3]=>0010001
[1,4,5,6,7,2,8,3]=>0000101
[4,1,6,2,7,3,8,5]=>1010101
[4,1,6,7,2,3,8,5]=>1001001
[4,6,7,1,2,3,8,5]=>0010001
[4,6,7,1,2,8,3,5]=>0010010
[4,6,7,1,8,2,3,5]=>0010100
[4,6,7,8,1,2,3,5]=>0001000
[4,1,6,2,7,3,5,8]=>1010100
[4,6,1,2,7,3,5,8]=>0100100
[4,1,6,7,2,3,5,8]=>1001000
[4,6,1,7,2,3,5,8]=>0101000
[4,1,6,2,3,7,5,8]=>1010010
[4,6,1,2,3,7,5,8]=>0100010
[4,1,2,6,3,7,5,8]=>1001010
[1,4,2,6,3,7,5,8]=>0101010
[4,1,2,6,7,3,5,8]=>1000100
[1,4,2,6,7,3,5,8]=>0100100
[1,4,6,2,7,3,5,8]=>0010100
[4,1,6,2,3,7,8,5]=>1010001
[4,1,2,6,3,7,8,5]=>1001001
[1,4,6,2,3,7,8,5]=>0010001
[4,1,2,6,7,3,8,5]=>1000101
[1,4,6,2,7,3,8,5]=>0010101
[1,4,2,6,7,8,3,5]=>0100010
[1,4,6,2,7,8,3,5]=>0010010
[1,4,6,7,2,8,3,5]=>0001010
[4,1,6,2,8,3,5,7]=>1010100
[4,6,1,2,8,3,5,7]=>0100100
[4,1,6,8,2,3,5,7]=>1001000
[4,6,1,8,2,3,5,7]=>0101000
[4,6,8,1,2,3,5,7]=>0010000
[4,6,1,2,3,8,5,7]=>0100010
[4,1,2,6,3,8,5,7]=>1001010
[1,4,2,6,3,8,5,7]=>0101010
[1,4,6,2,3,8,5,7]=>0010010
[1,4,2,6,8,3,5,7]=>0100100
[1,4,6,2,8,3,5,7]=>0010100
[4,1,2,6,3,5,8,7]=>1001001
[1,4,2,6,3,5,8,7]=>0101001
[4,1,2,3,6,5,8,7]=>1000101
[1,4,2,3,6,5,8,7]=>0100101
[4,1,2,3,6,8,5,7]=>1000010
[1,2,4,3,6,8,5,7]=>0010010
[1,2,4,6,8,3,5,7]=>0000100
[1,4,2,6,3,5,7,8]=>0101000
[4,1,2,3,6,5,7,8]=>1000100
[1,4,2,3,6,5,7,8]=>0100100
[1,2,4,6,3,5,7,8]=>0001000
[4,1,2,3,6,7,5,8]=>1000010
[4,1,2,3,6,7,8,5]=>1000001
[1,4,2,3,6,7,8,5]=>0100001
[1,2,4,6,7,3,8,5]=>0000101
[4,1,7,2,8,3,5,6]=>1010100
[4,7,1,2,8,3,5,6]=>0100100
[4,7,1,8,2,3,5,6]=>0101000
[1,4,2,7,3,8,5,6]=>0101010
[4,1,2,7,8,3,5,6]=>1000100
[1,4,2,7,8,3,5,6]=>0100100
[4,1,7,2,3,5,8,6]=>1010001
[4,1,2,7,3,5,8,6]=>1001001
[1,4,2,7,3,5,8,6]=>0101001
[1,4,7,2,3,5,8,6]=>0010001
[4,1,2,3,7,5,8,6]=>1000101
[1,2,4,3,7,5,8,6]=>0010101
[4,1,2,3,7,8,5,6]=>1000010
[1,4,2,3,7,8,5,6]=>0100010
[1,2,4,3,7,8,5,6]=>0010010
[1,2,4,7,8,3,5,6]=>0000100
[1,4,2,7,3,5,6,8]=>0101000
[4,1,2,3,7,5,6,8]=>1000100
[1,4,2,3,7,5,6,8]=>0100100
[4,1,2,3,5,7,6,8]=>1000010
[1,4,2,3,5,7,6,8]=>0100010
[4,1,2,3,5,7,8,6]=>1000001
[1,4,2,3,5,7,8,6]=>0100001
[1,2,4,5,7,3,8,6]=>0000101
[4,8,1,2,3,5,6,7]=>0100000
[4,1,2,8,3,5,6,7]=>1001000
[1,4,2,8,3,5,6,7]=>0101000
[1,4,8,2,3,5,6,7]=>0010000
[4,1,2,3,8,5,6,7]=>1000100
[1,4,2,3,8,5,6,7]=>0100100
[1,2,4,3,8,5,6,7]=>0010100
[1,2,4,8,3,5,6,7]=>0001000
[4,1,2,3,5,8,6,7]=>1000010
[1,4,2,3,5,8,6,7]=>0100010
[1,2,4,3,5,8,6,7]=>0010010
[1,2,4,5,3,8,6,7]=>0001010
[1,2,4,5,8,3,6,7]=>0000100
[4,1,2,3,5,6,8,7]=>1000001
[1,4,2,3,5,6,8,7]=>0100001
[1,2,4,5,6,8,3,7]=>0000010
[1,4,2,3,5,6,7,8]=>0100000
[5,1,6,2,7,3,8,4]=>1010101
[5,6,1,2,7,3,8,4]=>0100101
[5,1,6,7,2,3,8,4]=>1001001
[5,6,1,7,2,3,8,4]=>0101001
[5,6,7,1,2,3,8,4]=>0010001
[5,1,6,7,2,8,3,4]=>1001010
[5,6,7,1,2,8,3,4]=>0010010
[5,1,6,7,8,2,3,4]=>1000100
[5,6,1,7,8,2,3,4]=>0100100
[5,6,7,1,8,2,3,4]=>0010100
[5,1,6,2,7,3,4,8]=>1010100
[5,1,6,2,3,7,4,8]=>1010010
[5,1,2,6,3,7,4,8]=>1001010
[1,5,2,6,3,7,4,8]=>0101010
[5,1,2,6,7,3,4,8]=>1000100
[1,5,2,6,7,3,4,8]=>0100100
[1,5,6,7,2,3,4,8]=>0001000
[5,1,6,2,3,7,8,4]=>1010001
[5,6,1,2,3,7,8,4]=>0100001
[5,1,2,6,3,7,8,4]=>1001001
[1,5,2,6,3,7,8,4]=>0101001
[1,5,6,2,3,7,8,4]=>0010001
[5,1,2,6,7,3,8,4]=>1000101
[1,5,6,7,2,3,8,4]=>0001001
[5,1,2,6,7,8,3,4]=>1000010
[1,5,6,7,8,2,3,4]=>0000100
[5,1,6,2,8,3,4,7]=>1010100
[5,6,1,2,8,3,4,7]=>0100100
[5,6,8,1,2,3,4,7]=>0010000
[5,1,6,2,3,8,4,7]=>1010010
[5,6,1,2,3,8,4,7]=>0100010
[5,1,2,6,3,8,4,7]=>1001010
[1,5,2,6,3,8,4,7]=>0101010
[1,5,6,2,3,8,4,7]=>0010010
[5,1,2,6,8,3,4,7]=>1000100
[1,5,2,6,8,3,4,7]=>0100100
[1,5,6,2,8,3,4,7]=>0010100
[1,5,6,8,2,3,4,7]=>0001000
[5,1,2,6,3,4,8,7]=>1001001
[1,5,2,6,3,4,8,7]=>0101001
[1,5,6,2,3,4,8,7]=>0010001
[1,2,5,3,6,4,8,7]=>0010101
[1,2,5,6,3,4,8,7]=>0001001
[5,1,2,3,6,8,4,7]=>1000010
[1,5,2,3,6,8,4,7]=>0100010
[1,2,5,6,3,8,4,7]=>0001010
[5,1,6,2,3,4,7,8]=>1010000
[5,1,2,6,3,4,7,8]=>1001000
[1,5,2,6,3,4,7,8]=>0101000
[1,2,5,6,3,4,7,8]=>0001000
[5,1,2,3,6,7,4,8]=>1000010
[1,2,5,6,3,7,4,8]=>0001010
[5,1,2,3,6,7,8,4]=>1000001
[1,5,2,3,6,7,8,4]=>0100001
[1,2,5,3,6,7,8,4]=>0010001
[1,2,5,6,3,7,8,4]=>0001001
[1,2,5,6,7,8,3,4]=>0000010
[5,1,7,2,8,3,4,6]=>1010100
[5,7,1,2,8,3,4,6]=>0100100
[5,7,8,1,2,3,4,6]=>0010000
[5,1,2,7,3,8,4,6]=>1001010
[1,5,2,7,3,8,4,6]=>0101010
[1,5,7,2,3,8,4,6]=>0010010
[5,1,2,7,8,3,4,6]=>1000100
[1,5,2,7,8,3,4,6]=>0100100
[1,5,7,2,8,3,4,6]=>0010100
[1,5,7,8,2,3,4,6]=>0001000
[5,1,7,2,3,4,8,6]=>1010001
[5,1,2,7,3,4,8,6]=>1001001
[1,5,2,7,3,4,8,6]=>0101001
[1,5,7,2,3,4,8,6]=>0010001
[5,1,2,3,7,4,8,6]=>1000101
[1,5,2,3,7,4,8,6]=>0100101
[1,2,5,3,7,4,8,6]=>0010101
[1,2,5,7,3,4,8,6]=>0001001
[5,1,2,3,7,8,4,6]=>1000010
[1,5,2,3,7,8,4,6]=>0100010
[1,2,5,7,3,8,4,6]=>0001010
[5,7,1,2,3,4,6,8]=>0100000
[5,1,2,7,3,4,6,8]=>1001000
[1,5,2,7,3,4,6,8]=>0101000
[1,2,5,7,3,4,6,8]=>0001000
[1,5,2,3,4,7,6,8]=>0100010
[1,2,3,5,7,4,6,8]=>0000100
[1,5,2,3,4,7,8,6]=>0100001
[1,2,5,3,4,7,8,6]=>0010001
[1,2,3,5,7,4,8,6]=>0000101
[1,2,3,5,7,8,4,6]=>0000010
[5,1,2,8,3,4,6,7]=>1001000
[1,5,2,8,3,4,6,7]=>0101000
[1,5,2,3,8,4,6,7]=>0100100
[1,2,5,3,8,4,6,7]=>0010100
[1,2,5,8,3,4,6,7]=>0001000
[1,5,2,3,4,8,6,7]=>0100010
[1,2,5,3,4,8,6,7]=>0010010
[1,2,3,5,4,8,6,7]=>0001010
[1,2,3,5,8,4,6,7]=>0000100
[1,5,2,3,4,6,8,7]=>0100001
[1,2,3,5,6,8,4,7]=>0000010
[1,5,2,3,4,6,7,8]=>0100000
[6,1,7,2,8,3,4,5]=>1010100
[6,1,7,8,2,3,4,5]=>1001000
[6,7,1,8,2,3,4,5]=>0101000
[6,1,7,2,3,8,4,5]=>1010010
[6,7,1,2,3,8,4,5]=>0100010
[6,1,2,7,3,8,4,5]=>1001010
[1,6,2,7,3,8,4,5]=>0101010
[1,6,7,2,3,8,4,5]=>0010010
[1,6,7,2,8,3,4,5]=>0010100
[1,6,7,8,2,3,4,5]=>0001000
[6,1,7,2,3,4,8,5]=>1010001
[6,7,1,2,3,4,8,5]=>0100001
[6,1,2,7,3,4,8,5]=>1001001
[1,6,2,7,3,4,8,5]=>0101001
[1,6,7,2,3,4,8,5]=>0010001
[1,6,2,3,7,4,8,5]=>0100101
[1,2,6,3,7,4,8,5]=>0010101
[6,1,2,3,7,8,4,5]=>1000010
[1,2,6,3,7,8,4,5]=>0010010
[1,2,6,7,3,8,4,5]=>0001010
[6,1,7,2,3,4,5,8]=>1010000
[1,6,2,7,3,4,5,8]=>0101000
[1,6,7,2,3,4,5,8]=>0010000
[1,6,2,3,4,7,5,8]=>0100010
[1,2,6,3,4,7,5,8]=>0010010
[1,2,3,6,4,7,5,8]=>0001010
[1,2,3,6,7,4,5,8]=>0000100
[6,1,2,3,4,7,8,5]=>1000001
[1,6,2,3,4,7,8,5]=>0100001
[1,2,6,3,4,7,8,5]=>0010001
[1,2,3,6,4,7,8,5]=>0001001
[1,2,3,6,7,4,8,5]=>0000101
[1,2,3,6,7,8,4,5]=>0000010
[6,1,8,2,3,4,5,7]=>1010000
[6,1,2,8,3,4,5,7]=>1001000
[1,6,2,8,3,4,5,7]=>0101000
[1,6,8,2,3,4,5,7]=>0010000
[1,6,2,3,8,4,5,7]=>0100100
[1,2,6,3,8,4,5,7]=>0010100
[1,2,6,8,3,4,5,7]=>0001000
[1,6,2,3,4,8,5,7]=>0100010
[1,2,6,3,4,8,5,7]=>0010010
[1,2,3,6,4,8,5,7]=>0001010
[6,1,2,3,4,5,8,7]=>1000001
[1,6,2,3,4,5,8,7]=>0100001
[1,2,6,3,4,5,8,7]=>0010001
[1,2,3,6,4,5,8,7]=>0001001
[1,2,3,4,6,8,5,7]=>0000010
[1,6,2,3,4,5,7,8]=>0100000
[1,2,6,3,4,5,7,8]=>0010000
[1,2,3,6,4,5,7,8]=>0001000
[7,1,2,8,3,4,5,6]=>1001000
[1,7,2,8,3,4,5,6]=>0101000
[1,7,8,2,3,4,5,6]=>0010000
[7,1,2,3,8,4,5,6]=>1000100
[1,2,7,8,3,4,5,6]=>0001000
[1,2,7,3,4,8,5,6]=>0010010
[1,2,3,7,4,8,5,6]=>0001010
[1,2,3,7,8,4,5,6]=>0000100
[1,2,7,3,4,5,8,6]=>0010001
[1,2,3,7,4,5,8,6]=>0001001
[1,2,3,4,7,5,8,6]=>0000101
[1,2,3,4,7,8,5,6]=>0000010
[1,7,2,3,4,5,6,8]=>0100000
[1,2,7,3,4,5,6,8]=>0010000
[1,2,3,7,4,5,6,8]=>0001000
[1,2,3,4,7,5,6,8]=>0000100
[1,8,2,3,4,5,6,7]=>0100000
[1,2,8,3,4,5,6,7]=>0010000
[1,2,3,8,4,5,6,7]=>0001000
[1,2,3,4,8,5,6,7]=>0000100
[1,2,3,4,5,8,6,7]=>0000010
[5,3,2,6,1,4,8,7]=>1101001
[7,3,2,5,4,8,1,6]=>1101010
[8,4,5,2,3,7,6,1]=>1010011
[7,4,5,2,3,8,1,6]=>1010010
[6,4,5,2,3,1,8,7]=>1010101
[5,4,6,2,1,3,8,7]=>1011001
[3,6,1,5,4,2,8,7]=>0101101
[4,6,5,1,3,2,8,7]=>0110101
[5,6,4,3,1,2,8,7]=>0111001
[7,5,4,3,2,8,1,6]=>1111010
[8,6,4,3,7,2,5,1]=>1110101
[7,6,4,3,8,2,1,5]=>1110110
[6,7,4,3,8,1,2,5]=>0110100
[5,7,4,3,1,8,2,6]=>0111010
[4,7,5,1,3,8,2,6]=>0110010
[3,7,1,5,4,8,2,6]=>0101010
[2,1,7,5,4,8,3,6]=>1011010
[3,8,1,5,4,7,6,2]=>0101011
[4,8,5,1,3,7,6,2]=>0110011
[5,8,4,3,1,7,6,2]=>0111011
[6,8,4,3,7,1,5,2]=>0110101
[7,8,4,3,6,5,1,2]=>0110110
[6,8,5,7,3,1,4,2]=>0101101
[5,8,6,7,1,3,4,2]=>0101001
[4,8,6,1,7,3,5,2]=>0110101
[3,8,1,6,7,4,5,2]=>0100101
[2,1,8,6,7,4,5,3]=>1010101
[2,1,7,6,8,4,3,5]=>1010110
[3,7,1,6,8,4,2,5]=>0100110
[4,7,6,1,8,3,2,5]=>0110110
[5,7,6,8,1,3,2,4]=>0101010
[5,4,7,2,1,8,3,6]=>1011010
[6,4,7,2,8,1,3,5]=>1010100
[7,4,6,2,8,3,1,5]=>1010110
[8,4,6,2,7,3,5,1]=>1010101
[8,3,2,6,7,4,5,1]=>1100101
[7,3,2,6,8,4,1,5]=>1100110
[6,3,2,7,8,1,4,5]=>1100100
[5,3,2,7,1,8,4,6]=>1101010
[4,3,2,1,7,8,5,6]=>1110010
[3,4,1,2,8,7,6,5]=>0100111
[5,3,2,8,1,7,6,4]=>1101011
[6,3,2,8,7,1,5,4]=>1101101
[7,3,2,8,6,5,1,4]=>1101110
[8,4,7,2,6,5,3,1]=>1010111
[7,4,8,2,6,5,1,3]=>1010110
[6,4,8,2,7,1,5,3]=>1010101
[5,4,8,2,1,7,6,3]=>1011011
[4,5,8,1,2,7,6,3]=>0010011
[3,5,1,8,2,7,6,4]=>0101011
[2,1,5,8,3,7,6,4]=>1001011
[2,1,6,8,7,3,5,4]=>1001101
[3,6,1,8,7,2,5,4]=>0101101
[4,6,8,1,7,2,5,3]=>0010101
[5,6,8,7,1,2,4,3]=>0011001
[6,5,8,7,2,1,4,3]=>1011101
[7,5,8,6,2,4,1,3]=>1011010
[8,5,7,6,2,4,3,1]=>1011011
[5,7,8,6,1,4,2,3]=>0011010
[4,7,8,1,6,5,2,3]=>0010110
[3,7,1,8,6,5,2,4]=>0101110
[2,1,7,8,6,5,3,4]=>1001110
[3,8,1,7,6,5,4,2]=>0101111
[4,8,7,1,6,5,3,2]=>0110111
[5,8,7,6,1,4,3,2]=>0111011
[6,8,7,5,4,1,3,2]=>0111101
[5,2,4,1,3,6,7,8]=>1010000
[3,2,6,1,4,5,7,8]=>1010000
[6,3,5,1,2,4,7,8]=>1010000
[5,2,7,1,3,4,6,8]=>1010000
[5,3,7,1,2,4,6,8]=>1010000
[5,4,7,1,2,3,6,8]=>1010000
[6,2,7,1,3,4,5,8]=>1010000
[6,3,7,1,2,4,5,8]=>1010000
[6,4,7,1,2,3,5,8]=>1010000
[7,3,5,1,2,4,6,8]=>1010000
[7,4,6,1,2,3,5,8]=>1010000
[3,2,8,1,4,5,6,7]=>1010000
[5,2,8,1,3,4,6,7]=>1010000
[5,4,8,1,2,3,6,7]=>1010000
[6,2,8,1,3,4,5,7]=>1010000
[6,5,8,1,2,3,4,7]=>1010000
[7,5,8,1,2,3,4,6]=>1010000
[8,3,5,1,2,4,6,7]=>1010000
[8,3,6,1,2,4,5,7]=>1010000
[8,4,7,1,2,3,5,6]=>1010000
[8,5,7,1,2,3,4,6]=>1010000
[3,2,5,7,1,4,6,8]=>1001000
[4,2,5,7,1,3,6,8]=>1001000
[4,3,5,7,1,2,6,8]=>1001000
[5,3,4,7,1,2,6,8]=>1001000
[4,2,6,7,1,3,5,8]=>1001000
[5,2,6,7,1,3,4,8]=>1001000
[7,3,5,6,1,2,4,8]=>1001000
[3,2,5,8,1,4,6,7]=>1001000
[4,2,5,8,1,3,6,7]=>1001000
[4,3,5,8,1,2,6,7]=>1001000
[5,2,4,8,1,3,6,7]=>1001000
[3,2,6,8,1,4,5,7]=>1001000
[4,2,6,8,1,3,5,7]=>1001000
[4,3,6,8,1,2,5,7]=>1001000
[5,2,6,8,1,3,4,7]=>1001000
[6,2,4,8,1,3,5,7]=>1001000
[6,2,5,8,1,3,4,7]=>1001000
[6,3,5,8,1,2,4,7]=>1001000
[3,2,7,8,1,4,5,6]=>1001000
[4,3,7,8,1,2,5,6]=>1001000
[6,2,7,8,1,3,4,5]=>1001000
[6,3,7,8,1,2,4,5]=>1001000
[6,4,7,8,1,2,3,5]=>1001000
[7,2,4,8,1,3,5,6]=>1001000
[7,3,5,8,1,2,4,6]=>1001000
[7,4,5,8,1,2,3,6]=>1001000
[8,2,5,6,1,3,4,7]=>1001000
[8,2,4,7,1,3,5,6]=>1001000
[8,2,5,7,1,3,4,6]=>1001000
[8,3,5,7,1,2,4,6]=>1001000
[8,2,6,7,1,3,4,5]=>1001000
[8,4,6,7,1,2,3,5]=>1001000
[4,6,2,5,1,3,7,8]=>0101000
[4,6,3,5,1,2,7,8]=>0101000
[4,7,3,5,1,2,6,8]=>0101000
[5,7,2,4,1,3,6,8]=>0101000
[5,7,3,4,1,2,6,8]=>0101000
[3,7,2,6,1,4,5,8]=>0101000
[5,7,2,6,1,3,4,8]=>0101000
[6,7,2,5,1,3,4,8]=>0101000
[4,8,2,5,1,3,6,7]=>0101000
[5,8,3,4,1,2,6,7]=>0101000
[5,8,3,6,1,2,4,7]=>0101000
[6,8,2,4,1,3,5,7]=>0101000
[6,8,3,4,1,2,5,7]=>0101000
[6,8,3,5,1,2,4,7]=>0101000
[6,8,4,5,1,2,3,7]=>0101000
[3,8,2,7,1,4,5,6]=>0101000
[4,8,2,7,1,3,5,6]=>0101000
[5,8,2,7,1,3,4,6]=>0101000
[5,8,3,7,1,2,4,6]=>0101000
[5,8,4,7,1,2,3,6]=>0101000
[6,8,2,7,1,3,4,5]=>0101000
[6,8,3,7,1,2,4,5]=>0101000
[6,8,5,7,1,2,3,4]=>0101000
[7,8,2,4,1,3,5,6]=>0101000
[7,8,2,5,1,3,4,6]=>0101000
[7,8,3,5,1,2,4,6]=>0101000
[7,8,4,6,1,2,3,5]=>0101000
[4,3,2,6,1,5,7,8]=>1101000
[5,3,2,6,1,4,7,8]=>1101000
[6,4,2,5,1,3,7,8]=>1101000
[6,5,2,4,1,3,7,8]=>1101000
[4,3,2,7,1,5,6,8]=>1101000
[5,3,2,7,1,4,6,8]=>1101000
[5,4,3,7,1,2,6,8]=>1101000
[6,3,2,7,1,4,5,8]=>1101000
[6,4,2,7,1,3,5,8]=>1101000
[6,4,3,7,1,2,5,8]=>1101000
[6,5,3,7,1,2,4,8]=>1101000
[7,3,2,5,1,4,6,8]=>1101000
[7,4,2,5,1,3,6,8]=>1101000
[7,3,2,6,1,4,5,8]=>1101000
[7,4,3,6,1,2,5,8]=>1101000
[7,5,2,6,1,3,4,8]=>1101000
[7,5,3,6,1,2,4,8]=>1101000
[7,6,3,5,1,2,4,8]=>1101000
[4,3,2,8,1,5,6,7]=>1101000
[5,3,2,8,1,4,6,7]=>1101000
[5,4,3,8,1,2,6,7]=>1101000
[6,3,2,8,1,4,5,7]=>1101000
[6,4,3,8,1,2,5,7]=>1101000
[6,5,2,8,1,3,4,7]=>1101000
[6,5,3,8,1,2,4,7]=>1101000
[6,5,4,8,1,2,3,7]=>1101000
[7,3,2,8,1,4,5,6]=>1101000
[7,4,2,8,1,3,5,6]=>1101000
[7,5,3,8,1,2,4,6]=>1101000
[7,6,2,8,1,3,4,5]=>1101000
[8,4,2,5,1,3,6,7]=>1101000
[8,3,2,6,1,4,5,7]=>1101000
[8,4,2,6,1,3,5,7]=>1101000
[8,5,3,6,1,2,4,7]=>1101000
[8,6,2,4,1,3,5,7]=>1101000
[8,6,2,5,1,3,4,7]=>1101000
[8,3,2,7,1,4,5,6]=>1101000
[8,4,2,7,1,3,5,6]=>1101000
[8,4,3,7,1,2,5,6]=>1101000
[8,5,2,7,1,3,4,6]=>1101000
[8,5,3,7,1,2,4,6]=>1101000
[8,5,4,7,1,2,3,6]=>1101000
[8,6,3,7,1,2,4,5]=>1101000
[8,7,2,4,1,3,5,6]=>1101000
[8,7,2,5,1,3,4,6]=>1101000
[8,7,3,5,1,2,4,6]=>1101000
[8,7,2,6,1,3,4,5]=>1101000
[8,7,3,6,1,2,4,5]=>1101000
[8,7,4,6,1,2,3,5]=>1101000
[4,6,3,5,8,1,2,7]=>0100100
[5,6,2,4,8,1,3,7]=>0100100
[4,7,2,5,8,1,3,6]=>0100100
[4,7,3,5,8,1,2,6]=>0100100
[5,7,3,4,8,1,2,6]=>0100100
[3,7,2,6,8,1,4,5]=>0100100
[4,7,3,6,8,1,2,5]=>0100100
[5,7,4,6,8,1,2,3]=>0100100
[6,7,3,5,8,1,2,4]=>0100100
[3,8,2,5,7,1,4,6]=>0100100
[4,8,2,5,7,1,3,6]=>0100100
[4,8,3,5,7,1,2,6]=>0100100
[3,8,2,6,7,1,4,5]=>0100100
[4,8,3,6,7,1,2,5]=>0100100
[6,8,2,5,7,1,3,4]=>0100100
[6,8,3,5,7,1,2,4]=>0100100
[6,8,4,5,7,1,2,3]=>0100100
[7,8,2,4,6,1,3,5]=>0100100
[7,8,2,5,6,1,3,4]=>0100100
[7,8,3,5,6,1,2,4]=>0100100
[4,3,2,6,8,1,5,7]=>1100100
[5,4,2,6,8,1,3,7]=>1100100
[5,4,3,6,8,1,2,7]=>1100100
[6,3,2,5,8,1,4,7]=>1100100
[6,4,3,5,8,1,2,7]=>1100100
[6,5,2,4,8,1,3,7]=>1100100
[4,3,2,7,8,1,5,6]=>1100100
[5,3,2,7,8,1,4,6]=>1100100
[5,4,2,7,8,1,3,6]=>1100100
[5,4,3,7,8,1,2,6]=>1100100
[6,4,2,7,8,1,3,5]=>1100100
[6,4,3,7,8,1,2,5]=>1100100
[6,5,2,7,8,1,3,4]=>1100100
[7,4,2,5,8,1,3,6]=>1100100
[7,3,2,6,8,1,4,5]=>1100100
[7,5,3,6,8,1,2,4]=>1100100
[7,6,3,5,8,1,2,4]=>1100100
[8,4,2,5,7,1,3,6]=>1100100
[8,5,2,6,7,1,3,4]=>1100100
[8,5,3,6,7,1,2,4]=>1100100
[8,6,3,5,7,1,2,4]=>1100100
[8,7,2,4,6,1,3,5]=>1100100
[8,7,3,4,6,1,2,5]=>1100100
[8,7,2,5,6,1,3,4]=>1100100
[8,7,3,5,6,1,2,4]=>1100100
[4,3,7,2,6,1,5,8]=>1010100
[5,3,7,2,6,1,4,8]=>1010100
[5,4,7,2,6,1,3,8]=>1010100
[6,3,7,2,5,1,4,8]=>1010100
[6,4,7,2,5,1,3,8]=>1010100
[7,3,6,2,5,1,4,8]=>1010100
[4,3,8,2,6,1,5,7]=>1010100
[5,3,8,2,6,1,4,7]=>1010100
[5,4,8,2,6,1,3,7]=>1010100
[6,4,8,2,5,1,3,7]=>1010100
[6,4,8,3,5,1,2,7]=>1010100
[6,5,8,3,4,1,2,7]=>1010100
[4,3,8,2,7,1,5,6]=>1010100
[5,3,8,2,7,1,4,6]=>1010100
[5,4,8,2,7,1,3,6]=>1010100
[6,4,8,2,7,1,3,5]=>1010100
[7,3,8,2,5,1,4,6]=>1010100
[7,4,8,3,5,1,2,6]=>1010100
[7,5,8,2,4,1,3,6]=>1010100
[7,5,8,3,4,1,2,6]=>1010100
[7,3,8,2,6,1,4,5]=>1010100
[7,4,8,2,6,1,3,5]=>1010100
[7,5,8,2,6,1,3,4]=>1010100
[7,5,8,3,6,1,2,4]=>1010100
[7,5,8,4,6,1,2,3]=>1010100
[8,3,6,2,5,1,4,7]=>1010100
[8,3,7,2,5,1,4,6]=>1010100
[8,3,7,2,6,1,4,5]=>1010100
[8,4,7,2,6,1,3,5]=>1010100
[8,4,7,3,6,1,2,5]=>1010100
[8,5,7,2,6,1,3,4]=>1010100
[8,6,7,2,5,1,3,4]=>1010100
[8,6,7,3,5,1,2,4]=>1010100
[5,4,3,2,7,1,6,8]=>1110100
[6,4,3,2,7,1,5,8]=>1110100
[6,5,3,2,7,1,4,8]=>1110100
[6,5,4,2,7,1,3,8]=>1110100
[7,5,3,2,6,1,4,8]=>1110100
[5,4,3,2,8,1,6,7]=>1110100
[6,5,3,2,8,1,4,7]=>1110100
[6,5,4,3,8,1,2,7]=>1110100
[7,5,3,2,8,1,4,6]=>1110100
[7,6,4,3,8,1,2,5]=>1110100
[8,5,3,2,6,1,4,7]=>1110100
[8,5,4,2,6,1,3,7]=>1110100
[8,6,5,2,4,1,3,7]=>1110100
[8,5,3,2,7,1,4,6]=>1110100
[8,6,3,2,7,1,4,5]=>1110100
[8,7,3,2,6,1,4,5]=>1110100
[8,7,4,2,6,1,3,5]=>1110100
[8,7,4,3,6,1,2,5]=>1110100
[8,7,5,2,6,1,3,4]=>1110100
[8,7,6,2,4,1,3,5]=>1110100
[8,7,6,2,5,1,3,4]=>1110100
[8,7,6,3,5,1,2,4]=>1110100
[4,8,3,7,2,6,1,5]=>0101010
[5,8,3,7,2,6,1,4]=>0101010
[5,8,4,7,2,6,1,3]=>0101010
[5,8,4,7,3,6,1,2]=>0101010
[6,8,3,7,2,5,1,4]=>0101010
[6,8,4,7,2,5,1,3]=>0101010
[6,8,4,7,3,5,1,2]=>0101010
[6,8,5,7,2,4,1,3]=>0101010
[6,8,5,7,3,4,1,2]=>0101010
[7,8,3,6,2,5,1,4]=>0101010
[7,8,4,6,2,5,1,3]=>0101010
[7,8,4,6,3,5,1,2]=>0101010
[7,8,5,6,2,4,1,3]=>0101010
[6,4,3,8,2,7,1,5]=>1101010
[6,5,3,8,2,7,1,4]=>1101010
[6,5,4,8,2,7,1,3]=>1101010
[7,4,3,8,2,6,1,5]=>1101010
[7,5,3,8,2,6,1,4]=>1101010
[7,5,4,8,2,6,1,3]=>1101010
[7,6,3,8,2,5,1,4]=>1101010
[7,6,4,8,2,5,1,3]=>1101010
[7,6,5,8,2,4,1,3]=>1101010
[8,4,3,7,2,6,1,5]=>1101010
[8,5,3,7,2,6,1,4]=>1101010
[8,6,3,7,2,5,1,4]=>1101010
[8,6,4,7,2,5,1,3]=>1101010
[8,6,5,7,2,4,1,3]=>1101010
[8,7,3,6,2,5,1,4]=>1101010
[8,7,4,6,3,5,1,2]=>1101010
[8,7,5,6,2,4,1,3]=>1101010
[6,5,4,3,2,8,1,7]=>1111010
[7,6,4,3,2,8,1,5]=>1111010
[8,5,4,3,2,7,1,6]=>1111010
[8,7,4,3,2,6,1,5]=>1111010
[8,7,5,3,2,6,1,4]=>1111010
[8,7,5,4,2,6,1,3]=>1111010
[8,7,6,3,2,5,1,4]=>1111010
[8,7,6,5,2,4,1,3]=>1111010
[8,1,2,3,7,4,5,6]=>1000100
[8,1,2,5,3,4,6,7]=>1001000
[6,1,2,5,3,8,4,7]=>1001010
[8,1,2,6,3,7,4,5]=>1001010
[4,1,2,8,7,3,5,6]=>1001100
[4,1,2,7,6,3,8,5]=>1001101
[8,1,2,5,6,3,4,7]=>1000100
[8,1,2,7,6,3,4,5]=>1001100
[7,1,2,5,6,3,8,4]=>1000101
[4,1,2,5,8,7,3,6]=>1000110
[8,1,2,5,6,7,3,4]=>1000010
[3,1,7,2,6,4,8,5]=>1010101
[3,1,5,2,8,7,4,6]=>1010110
[3,1,8,2,6,7,4,5]=>1010010
[8,1,4,2,3,5,6,7]=>1010000
[7,1,4,2,3,5,8,6]=>1010001
[6,1,4,2,3,8,5,7]=>1010010
[7,1,5,2,3,4,8,6]=>1010001
[6,1,5,2,3,8,4,7]=>1010010
[6,1,8,2,3,7,4,5]=>1010010
[6,1,5,2,3,7,8,4]=>1010001
[5,1,4,2,8,3,6,7]=>1010100
[5,1,4,2,7,3,8,6]=>1010101
[8,1,4,2,6,3,5,7]=>1010100
[7,1,4,2,6,3,8,5]=>1010101
[8,1,5,2,6,3,4,7]=>1010100
[8,1,5,2,7,3,4,6]=>1010100
[7,1,8,2,6,3,4,5]=>1010100
[7,1,5,2,6,3,8,4]=>1010101
[5,1,4,2,8,7,3,6]=>1010110
[8,1,4,2,6,7,3,5]=>1010010
[8,1,5,2,6,7,3,4]=>1010010
[5,1,4,2,6,7,8,3]=>1010001
[3,1,8,6,2,4,5,7]=>1011000
[3,1,6,5,2,8,4,7]=>1011010
[3,1,8,5,2,7,4,6]=>1011010
[3,1,8,6,2,7,4,5]=>1011010
[8,1,4,5,2,3,6,7]=>1001000
[7,1,8,5,2,3,4,6]=>1011000
[7,1,8,6,2,3,4,5]=>1011000
[7,1,6,5,2,3,8,4]=>1011001
[3,1,4,8,6,2,5,7]=>1001100
[3,1,8,5,7,2,4,6]=>1010100
[3,1,7,5,6,2,8,4]=>1010101
[8,1,4,5,7,2,3,6]=>1000100
[8,1,4,7,6,2,3,5]=>1001100
[3,1,4,5,8,7,2,6]=>1000110
[3,1,8,5,6,7,2,4]=>1010010
[8,1,4,5,6,7,2,3]=>1000010
[2,8,1,3,7,4,5,6]=>0100100
[2,8,1,3,6,7,4,5]=>0100010
[2,6,1,5,3,8,4,7]=>0101010
[2,6,1,5,3,7,8,4]=>0101001
[2,4,1,8,6,3,5,7]=>0101100
[2,8,1,5,7,3,4,6]=>0100100
[2,8,1,7,6,3,4,5]=>0101100
[2,4,1,5,8,7,3,6]=>0100110
[7,3,1,2,4,5,8,6]=>1100001
[6,3,1,2,4,8,5,7]=>1100010
[6,3,1,2,4,7,8,5]=>1100001
[5,3,1,2,8,4,6,7]=>1100100
[8,3,1,2,6,4,5,7]=>1100100
[8,3,1,2,7,4,5,6]=>1100100
[7,3,1,2,6,4,8,5]=>1100101
[5,3,1,2,8,7,4,6]=>1100110
[5,3,1,2,6,7,8,4]=>1100001
[8,4,1,2,3,7,5,6]=>1100010
[7,6,1,2,3,4,8,5]=>1100001
[8,6,1,2,3,7,4,5]=>1100010
[5,4,1,2,8,3,6,7]=>1100100
[8,4,1,2,7,3,5,6]=>1100100
[7,4,1,2,6,3,8,5]=>1100101
[5,8,1,2,7,3,4,6]=>0100100
[8,7,1,2,6,3,4,5]=>1100100
[5,7,1,2,6,3,8,4]=>0100101
[5,8,1,2,6,7,3,4]=>0100010
[5,4,1,2,6,7,8,3]=>1100001
[4,3,1,8,2,5,6,7]=>1101000
[4,3,1,7,2,5,8,6]=>1101001
[4,3,1,6,2,8,5,7]=>1101010
[4,3,1,6,2,7,8,5]=>1101001
[8,3,1,5,2,4,6,7]=>1101000
[8,3,1,6,2,4,5,7]=>1101000
[7,3,1,6,2,4,8,5]=>1101001
[8,3,1,5,2,7,4,6]=>1101010
[8,3,1,6,2,7,4,5]=>1101010
[6,3,1,5,2,7,8,4]=>1101001
[7,4,1,5,2,3,8,6]=>1101001
[8,4,1,6,2,3,5,7]=>1101000
[7,4,1,8,2,3,5,6]=>1101000
[7,4,1,6,2,3,8,5]=>1101001
[8,7,1,6,2,3,4,5]=>1101000
[6,7,1,5,2,3,8,4]=>0101001
[6,4,1,5,2,8,3,7]=>1101010
[8,4,1,6,2,7,3,5]=>1101010
[6,8,1,5,2,7,3,4]=>0101010
[6,4,1,5,2,7,8,3]=>1101001
[4,3,1,8,7,2,5,6]=>1101100
[4,3,1,7,6,2,8,5]=>1101101
[8,3,1,5,6,2,4,7]=>1100100
[8,3,1,5,7,2,4,6]=>1100100
[8,3,1,7,6,2,4,5]=>1101100
[7,3,1,5,6,2,8,4]=>1100101
[8,4,1,5,6,2,3,7]=>1100100
[7,8,1,5,6,2,3,4]=>0100100
[4,3,1,5,6,8,2,7]=>1100010
[8,4,1,5,6,7,2,3]=>1100010
[4,3,1,5,6,7,8,2]=>1100001
[2,3,7,1,6,4,8,5]=>0010101
[2,3,5,1,8,7,4,6]=>0010110
[2,3,8,1,6,7,4,5]=>0010010
[2,8,4,1,3,5,6,7]=>0110000
[2,6,4,1,3,8,5,7]=>0110010
[2,6,4,1,3,7,8,5]=>0110001
[2,8,4,1,7,3,5,6]=>0110100
[2,7,4,1,6,3,8,5]=>0110101
[2,8,5,1,7,3,4,6]=>0110100
[2,7,5,1,6,3,8,4]=>0110101
[2,8,4,1,6,7,3,5]=>0110010
[2,5,4,1,6,7,8,3]=>0110001
[6,3,4,1,2,7,8,5]=>1010001
[7,3,5,1,2,4,8,6]=>1010001
[6,3,7,1,2,4,8,5]=>1010001
[8,3,5,1,2,7,4,6]=>1010010
[6,3,8,1,2,7,4,5]=>1010010
[6,7,4,1,2,3,8,5]=>0110001
[6,8,5,1,2,3,4,7]=>0110000
[8,5,4,1,2,7,3,6]=>1110010
[6,8,4,1,2,7,3,5]=>0110010
[6,8,5,1,2,7,3,4]=>0110010
[8,3,4,1,7,2,5,6]=>1010100
[7,3,4,1,6,2,8,5]=>1010101
[8,3,5,1,6,2,4,7]=>1010100
[7,3,8,1,6,2,4,5]=>1010100
[7,3,5,1,6,2,8,4]=>1010101
[8,5,4,1,6,2,3,7]=>1110100
[7,8,4,1,6,2,3,5]=>0110100
[7,8,5,1,6,2,3,4]=>0110100
[7,5,4,1,6,2,8,3]=>1110101
[5,3,4,1,6,7,8,2]=>1010001
[2,3,4,8,1,7,5,6]=>0001010
[2,3,7,6,1,4,8,5]=>0011001
[2,3,6,5,1,8,4,7]=>0011010
[2,3,6,5,1,7,8,4]=>0011001
[2,8,4,5,1,3,6,7]=>0101000
[2,7,4,8,1,3,5,6]=>0101000
[2,7,4,6,1,3,8,5]=>0101001
[2,8,6,5,1,3,4,7]=>0111000
[2,7,8,5,1,3,4,6]=>0011000
[2,7,6,5,1,3,8,4]=>0111001
[2,6,4,5,1,8,3,7]=>0101010
[2,8,4,6,1,7,3,5]=>0101010
[7,3,8,5,1,2,4,6]=>1011000
[8,6,4,5,1,7,2,3]=>1101010
[2,3,4,8,6,1,5,7]=>0001100
[2,3,4,8,7,1,5,6]=>0001100
[2,3,4,7,6,1,8,5]=>0001101
[2,3,8,5,7,1,4,6]=>0010100
[2,3,7,5,6,1,8,4]=>0010101
[2,8,4,7,6,1,3,5]=>0101100
[2,8,7,5,6,1,3,4]=>0110100
[8,3,4,7,6,1,2,5]=>1001100
[8,3,7,5,6,1,2,4]=>1010100
[2,3,4,5,8,7,1,6]=>0000110
[2,3,4,8,6,7,1,5]=>0001010
[2,8,4,5,6,7,1,3]=>0100010
[6,5,8,7,3,4,1,2]=>1011010
[4,6,7,3,8,5,1,2]=>0010110
[3,6,7,4,5,8,1,2]=>0010010
[2,6,7,4,5,1,8,3]=>0010101
[1,6,7,4,5,2,3,8]=>0010100
[1,5,4,7,6,2,3,8]=>0101100
[2,5,4,7,6,1,8,3]=>0101101
[3,5,4,7,6,8,1,2]=>0101010
[4,5,3,7,8,6,1,2]=>0100110
[5,4,3,8,7,6,1,2]=>1101110
[6,4,8,3,7,5,1,2]=>1010110
[6,3,8,4,5,7,1,2]=>1010010
[5,3,4,8,6,7,1,2]=>1001010
[4,3,5,6,8,7,1,2]=>1000110
[3,2,5,6,1,8,7,4]=>1001011
[4,2,5,6,8,1,7,3]=>1000101
[5,2,4,8,6,1,7,3]=>1001101
[6,2,8,4,5,1,7,3]=>1010101
[7,8,2,4,5,1,6,3]=>0100101
[7,8,1,4,5,2,3,6]=>0100100
[6,1,8,4,5,2,3,7]=>1010100
[5,1,4,8,6,2,3,7]=>1001100
[4,1,3,2,8,6,5,7]=>1010110
[5,1,3,8,2,6,4,7]=>1001010
[6,1,8,3,2,5,4,7]=>1011010
[7,8,1,3,2,5,4,6]=>0101010
[7,8,2,3,1,5,6,4]=>0101001
[6,2,8,3,1,5,7,4]=>1011001
[5,2,3,8,1,6,7,4]=>1001001
[6,3,8,2,1,7,5,4]=>1011011
[7,8,3,2,1,6,5,4]=>0111011
[7,8,4,2,6,1,5,3]=>0110101
[5,4,2,8,7,1,6,3]=>1101101
[4,5,2,7,8,1,6,3]=>0100101
[3,5,2,7,1,8,6,4]=>0101011
[2,5,3,7,1,6,8,4]=>0101001
[1,5,3,7,2,6,4,8]=>0101010
[1,6,7,3,2,5,4,8]=>0011010
[2,6,7,3,1,5,8,4]=>0011001
[3,6,7,2,1,8,5,4]=>0011011
[4,6,7,2,8,1,5,3]=>0010101
[5,6,7,8,2,1,4,3]=>0001101
[7,8,5,6,2,1,4,3]=>0101101
[6,5,8,7,1,2,3,4]=>1011000
[5,4,1,8,7,2,3,6]=>1101100
[6,4,8,1,7,2,3,5]=>1010100
[7,8,3,1,2,6,4,5]=>0110010
[5,3,1,8,2,7,4,6]=>1101010
[4,3,1,2,8,7,5,6]=>1100110
[4,2,1,3,8,5,7,6]=>1100101
[5,2,1,8,3,4,7,6]=>1101001
[6,2,8,1,3,4,7,5]=>1010001
[7,8,2,1,3,4,6,5]=>0110001
[4,5,2,3,7,6,1,8]=>0100110
[6,4,3,7,2,5,1,8]=>1101010
[8,4,3,6,5,1,2,7]=>1101100
[1,5,6,3,4,8,7,2]=>0010011
[4,6,2,7,3,5,1,8]=>0101010
[3,2,6,7,4,5,1,8]=>1001010
[8,7,5,4,1,3,2,6]=>1111010
[5,8,6,2,4,1,3,7]=>0110100
[4,8,2,6,5,1,3,7]=>0101100
[4,1,2,6,5,8,7,3]=>1001011
[5,1,6,2,4,8,7,3]=>1010011
[6,1,5,4,2,8,7,3]=>1011011
[7,1,5,4,8,2,6,3]=>1010101
[8,1,5,4,7,6,2,3]=>1010110
[1,8,6,7,4,5,3,2]=>0101011
[8,1,6,7,4,5,2,3]=>1001010
[6,1,7,8,2,4,5,3]=>1001001
[5,1,7,2,8,4,6,3]=>1010101
[4,1,2,7,8,5,6,3]=>1000101
[3,2,1,7,8,5,6,4]=>1100101
[3,2,8,7,1,5,4,6]=>1011010
[4,8,2,7,1,5,3,6]=>0101010
[5,8,7,2,1,4,3,6]=>0111010
[6,8,7,1,2,4,3,5]=>0110010
[7,8,6,1,4,2,3,5]=>0110100
[8,7,6,1,4,3,2,5]=>1110110
[1,6,7,8,3,4,5,2]=>0001001
[8,6,7,1,3,4,2,5]=>1010010
[7,6,8,1,3,2,4,5]=>1010100
[5,7,8,2,1,3,4,6]=>0011000
[4,7,2,8,1,3,5,6]=>0101000
[3,2,6,8,4,1,5,7]=>1001100
[4,6,2,8,3,1,5,7]=>0101100
[5,6,8,2,3,1,4,7]=>0010100
[7,5,8,3,1,2,4,6]=>1011000
[8,5,7,3,1,4,2,6]=>1011010
[1,5,7,3,8,4,6,2]=>0010101
[1,4,3,7,8,5,6,2]=>0100101
[6,4,3,8,2,1,5,7]=>1101100
[4,5,2,3,8,1,6,7]=>0100100
[3,2,5,4,8,1,6,7]=>1010100
[4,5,2,3,1,8,7,6]=>0101011
[6,4,3,1,2,8,7,5]=>1110011
[7,4,3,1,8,2,6,5]=>1110101
[1,5,8,3,7,6,4,2]=>0010111
[7,5,1,3,8,2,6,4]=>1100101
[5,6,1,2,3,8,7,4]=>0100011
[4,6,2,1,3,8,7,5]=>0110011
[3,2,6,1,4,8,7,5]=>1010011
[3,2,7,1,8,4,6,5]=>1010101
[5,7,1,2,8,3,6,4]=>0100101
[6,7,1,8,2,3,5,4]=>0101001
[7,6,1,8,3,2,5,4]=>1101101
[8,7,1,6,5,3,2,4]=>1101110
[7,8,1,6,5,2,3,4]=>0101100
[6,8,1,7,2,5,3,4]=>0101010
[5,8,1,2,7,6,3,4]=>0100110
[4,8,2,1,7,6,3,5]=>0110110
[3,2,8,1,7,6,4,5]=>1010110
[4,1,2,8,7,6,5,3]=>1001111
[5,1,8,2,7,6,4,3]=>1010111
[6,1,8,7,2,5,4,3]=>1011011
[8,1,7,6,5,4,2,3]=>1011110
[3,2,5,1,6,4,8,7]=>1010101
[3,2,5,4,7,1,8,6]=>1010101
[4,2,5,3,7,6,8,1]=>1010101
[4,2,5,3,6,1,8,7]=>1010101
[4,1,5,3,6,2,8,7]=>1010101
[4,3,5,2,7,1,8,6]=>1010101
[4,3,5,1,7,2,8,6]=>1010101
[4,1,5,3,7,2,8,6]=>1010101
[2,1,5,4,7,3,8,6]=>1010101
[4,3,6,5,7,1,8,2]=>1010101
[5,3,6,4,7,1,8,2]=>1010101
[4,1,6,3,7,5,8,2]=>1010101
[2,1,6,4,7,5,8,3]=>1010101
[2,1,6,4,7,3,8,5]=>1010101
[3,1,6,4,7,2,8,5]=>1010101
[4,1,6,3,7,2,8,5]=>1010101
[5,3,6,2,7,4,8,1]=>1010101
[5,2,6,3,7,4,8,1]=>1010101
[5,2,6,3,7,1,8,4]=>1010101
[5,2,6,1,7,3,8,4]=>1010101
[4,2,6,1,7,3,8,5]=>1010101
[4,2,6,3,7,1,8,5]=>1010101
[4,2,6,3,7,5,8,1]=>1010101
[3,2,6,4,7,5,8,1]=>1010101
[3,2,6,4,7,1,8,5]=>1010101
[3,2,6,1,7,4,8,5]=>1010101
[3,2,5,1,7,4,8,6]=>1010101
[3,2,4,1,7,5,8,6]=>1010101
[3,1,4,2,7,6,8,5]=>1010101
[3,2,5,1,7,6,8,4]=>1010101
[3,2,6,1,7,5,8,4]=>1010101
[4,2,6,1,7,5,8,3]=>1010101
[3,1,5,2,7,6,8,4]=>1010101
[2,1,5,3,7,6,8,4]=>1010101
[2,1,6,3,7,5,8,4]=>1010101
[3,1,6,2,7,5,8,4]=>1010101
[4,1,6,2,7,5,8,3]=>1010101
[5,1,6,2,7,4,8,3]=>1010101
[5,2,6,1,7,4,8,3]=>1010101
[5,4,6,2,7,1,8,3]=>1010101
[5,1,6,4,7,2,8,3]=>1010101
[3,1,6,5,7,2,8,4]=>1010101
[3,1,6,5,7,4,8,2]=>1010101
[4,1,6,5,7,3,8,2]=>1010101
[5,1,6,4,7,3,8,2]=>1010101
[8,6,1,3,4,2,5,7]=>1100100
[8,3,5,2,1,6,4,7]=>1011010
[8,6,3,5,2,4,1,7]=>1101010
[8,3,7,5,2,4,6,1]=>1011001
[8,2,4,5,7,3,6,1]=>1000101
[2,4,5,7,3,1,8,6]=>0001101
[8,2,4,6,5,3,1,7]=>1001110
[8,1,2,4,5,6,3,7]=>1000010
[8,2,5,1,3,6,4,7]=>1010010
[8,6,1,4,5,3,2,7]=>1100110
[8,1,5,6,4,3,2,7]=>1001110
[8,5,7,4,3,2,6,1]=>1011101
[8,5,7,4,2,1,6,3]=>1011101
[4,6,3,8,7,1,5,2]=>0101101
[1,7,4,8,6,3,5,2]=>0101101
[8,4,7,6,3,5,2,1]=>1011011
[3,1,5,8,6,7,4,2]=>1001011
[4,8,1,6,7,3,5,2]=>0100101
[3,6,4,1,8,7,5,2]=>0110111
[8,2,6,1,4,7,5,3]=>1010011
[2,7,6,8,1,4,3,5]=>0101010
[1,7,3,5,6,8,2,4]=>0100010
[3,7,6,5,8,2,1,4]=>0110110
[3,6,8,5,7,2,4,1]=>0010101
[2,3,5,7,6,8,1,4]=>0001010
[2,1,6,5,7,8,3,4]=>1010010
[5,2,7,1,3,8,4,6]=>1010010
[5,3,1,7,8,2,4,6]=>1100100
[3,7,2,6,4,8,1,5]=>0101010
[3,2,6,1,4,7,8,5]=>1010001
[5,3,7,2,1,8,4,6]=>1011010
[4,7,3,2,1,5,8,6]=>0111001
[1,7,3,4,2,5,8,6]=>0101001
[4,7,2,1,3,5,8,6]=>0110001
[8,7,6,1,3,4,2,5]=>1110010
[8,5,7,3,2,1,6,4]=>1011101
[3,7,8,6,2,1,5,4]=>0011101
[8,7,6,3,5,2,4,1]=>1110101
[2,7,4,8,1,6,5,3]=>0101011
[4,6,8,2,1,7,5,3]=>0011011
[8,5,3,7,1,6,2,4]=>1101010
[8,5,7,2,1,3,6,4]=>1011001
[4,6,1,8,7,2,5,3]=>0101101
[8,1,2,5,6,7,4,3]=>1000011
[8,2,6,5,7,4,1,3]=>1010110
[2,1,7,8,5,6,4,3]=>1001011
[2,7,6,8,5,4,1,3]=>0101110
[3,7,8,1,6,5,2,4]=>0010110
[8,7,6,3,5,1,4,2]=>1110101
[8,4,7,6,5,1,3,2]=>1011101
[8,7,1,5,6,4,3,2]=>1100111
[8,1,6,7,5,4,3,2]=>1001111
[3,2,5,1,6,8,4,7]=>1010010
[3,6,2,5,4,8,1,7]=>0101010
[3,5,2,4,7,1,8,6]=>0100101
[3,5,8,2,4,7,6,1]=>0010011
[4,2,6,5,3,8,1,7]=>1011010
[5,3,1,6,8,2,4,7]=>1100100
[5,6,2,8,1,3,4,7]=>0101000
[5,4,3,2,7,1,8,6]=>1110101
[5,4,3,8,2,7,6,1]=>1101011
[4,3,7,6,2,1,8,5]=>1011101
[6,4,3,1,7,2,8,5]=>1110101
[1,4,7,5,8,3,2,6]=>0010110
[7,2,5,8,4,1,3,6]=>1001100
[2,8,5,7,4,6,1,3]=>0101010
[3,5,8,7,1,4,6,2]=>0011001
[4,3,7,1,8,6,5,2]=>1010111
[4,8,3,7,6,5,2,1]=>0101111
[7,5,3,1,8,6,4,2]=>1110111
[1,5,8,6,3,7,4,2]=>0011011
[6,2,8,7,4,5,1,3]=>1011010
[6,1,7,5,3,2,8,4]=>1011101
[5,2,6,3,8,7,4,1]=>1010111
[6,5,2,1,7,3,8,4]=>1110101
[6,1,7,4,2,8,3,5]=>1011010
[6,7,2,1,8,3,4,5]=>0110100
[7,5,8,2,1,3,4,6]=>1011000
[5,7,3,1,8,2,4,6]=>0110100
[4,7,1,5,2,8,3,6]=>0101010
[2,4,8,6,3,7,5,1]=>0011011
[3,8,6,2,4,7,5,1]=>0110011
[7,3,6,2,4,1,8,5]=>1010101
[3,5,2,7,1,8,4,6]=>0101010
[4,3,7,8,2,1,5,6]=>1001100
[8,3,7,1,4,6,2,5]=>1010010
[3,8,2,5,7,1,6,4]=>0100101
[7,8,3,6,2,1,5,4]=>0101101
[8,7,3,6,2,5,4,1]=>1101011
[4,2,6,8,1,7,5,3]=>1001011
[5,4,8,2,7,1,6,3]=>1010101
[5,8,3,7,1,6,2,4]=>0101010
[5,8,7,2,6,1,3,4]=>0110100
[6,4,8,1,7,2,5,3]=>1010101
[5,1,6,8,2,7,4,3]=>1001011
[6,5,2,8,1,7,4,3]=>1101011
[5,2,7,1,8,6,4,3]=>1010111
[5,8,2,7,6,4,3,1]=>0101111
[6,2,8,7,5,4,3,1]=>1011111
[6,1,7,2,8,5,4,3]=>1010111
[4,7,1,8,6,2,5,3]=>0101101
[7,8,3,1,6,5,2,4]=>0110110
[8,7,4,6,1,5,3,2]=>1101011
[8,5,7,1,6,4,3,2]=>1010111
[6,8,1,7,5,4,3,2]=>0101111
[7,1,8,6,5,4,3,2]=>1011111
[4,1,3,2,6,5,8,7]=>1010101
[6,3,5,1,2,4,8,7]=>1010001
[4,3,5,6,1,2,8,7]=>1001001
[8,3,7,5,2,1,4,6]=>1011100
[6,3,7,5,1,8,4,2]=>1011011
[6,5,2,7,1,8,3,4]=>1101010
[3,5,2,6,4,1,8,7]=>0101101
[6,1,2,4,5,3,8,7]=>1000101
[5,6,3,2,1,4,8,7]=>0111001
[2,1,6,3,5,4,8,7]=>1010101
[6,4,3,5,1,2,8,7]=>1101001
[5,3,1,4,6,2,8,7]=>1100101
[5,7,4,6,2,8,3,1]=>0101011
[3,4,7,8,5,2,1,6]=>0001110
[2,1,8,5,7,3,4,6]=>1010100
[8,6,3,5,1,7,4,2]=>1101011
[3,4,8,6,5,7,1,2]=>0011010
[5,1,4,6,8,2,7,3]=>1000101
[2,5,4,6,7,1,8,3]=>0100101
[2,4,6,3,7,5,8,1]=>0010101
[4,1,6,3,8,5,7,2]=>1010101
[3,7,4,2,8,6,5,1]=>0110111
[8,5,3,7,4,1,6,2]=>1101101
[2,1,5,7,4,8,6,3]=>1001011
[3,1,8,2,7,6,5,4]=>1010111
[2,3,8,1,6,7,5,4]=>0010011
[4,3,7,2,6,8,5,1]=>1010011
[2,8,1,3,6,5,7,4]=>0100101
[8,1,2,3,5,6,7,4]=>1000001
[7,8,2,4,3,6,1,5]=>0101010
[6,8,3,2,4,1,7,5]=>0110101
[2,1,8,3,4,6,7,5]=>1010001
[2,1,7,8,5,4,3,6]=>1001110
[5,7,3,8,1,4,2,6]=>0101010
[7,1,8,4,5,3,2,6]=>1010110
[8,7,1,6,3,4,2,5]=>1101010
[5,3,8,7,4,2,6,1]=>1011101
[8,3,6,1,4,2,7,5]=>1010101
[7,3,5,8,2,4,1,6]=>1001010
[2,3,4,1,8,5,7,6]=>0010101
[4,1,3,2,8,5,7,6]=>1010101
[2,1,4,3,8,5,7,6]=>1010101
[4,1,3,2,6,7,8,5]=>1010001
[8,3,5,6,2,7,1,4]=>1001010
[5,3,6,1,8,7,2,4]=>1010110
[5,6,2,8,7,4,1,3]=>0101110
[7,8,5,6,1,4,2,3]=>0101010
[8,1,6,4,5,7,2,3]=>1010010
[5,8,3,6,1,7,2,4]=>0101010
[2,1,8,6,5,7,3,4]=>1011010
[2,1,7,5,3,6,8,4]=>1011001
[7,1,4,2,5,6,8,3]=>1010001
[2,7,4,1,6,5,8,3]=>0110101
[7,3,5,4,6,1,8,2]=>1010101
[6,3,4,1,5,7,8,2]=>1010001
[3,1,4,5,6,8,7,2]=>1000011
[4,5,2,6,3,1,8,7]=>0101101
[6,5,2,1,4,3,8,7]=>1110101
[6,5,2,7,4,8,3,1]=>1101011
[8,5,2,7,4,1,6,3]=>1101101
[8,3,7,5,2,1,6,4]=>1011101
[6,3,7,5,2,8,4,1]=>1011011
[6,3,1,5,2,4,8,7]=>1101001
[3,1,6,5,4,2,8,7]=>1011101
[5,4,3,6,1,2,8,7]=>1101001
[5,6,3,2,4,1,8,7]=>0110101
[6,7,2,3,4,8,5,1]=>0100011
[8,7,2,3,4,1,6,5]=>1100101
[5,1,7,3,8,4,6,2]=>1010101
[2,5,7,3,8,6,4,1]=>0010111
[3,6,7,4,1,8,5,2]=>0011011
[5,6,3,7,4,8,1,2]=>0101010
[2,1,6,7,4,8,5,3]=>1001011
[2,1,8,7,4,3,6,5]=>1011101
[5,8,3,7,4,2,6,1]=>0101101
[7,8,1,3,5,2,6,4]=>0100101
[5,8,7,3,2,6,1,4]=>0111010
[2,8,6,3,1,5,7,4]=>0111001
[8,1,6,3,2,5,4,7]=>1011010
[2,8,4,1,6,3,7,5]=>0110101
[4,8,1,2,7,6,3,5]=>0100110
[6,8,3,5,2,7,4,1]=>0101011
[2,1,8,5,3,7,4,6]=>1011010
[6,5,3,2,8,7,1,4]=>1110110
[2,4,1,8,7,6,5,3]=>0101111
[4,1,2,8,7,5,6,3]=>1001101
[8,4,2,1,7,5,3,6]=>1110110
[4,3,1,8,6,7,5,2]=>1101011
[3,1,4,8,6,5,7,2]=>1001101
[7,3,5,4,8,6,1,2]=>1010110
[6,4,3,5,8,1,7,2]=>1100101
[2,1,7,6,5,8,3,4]=>1011010
[5,7,3,6,1,8,2,4]=>0101010
[2,7,6,4,5,8,1,3]=>0110010
[3,7,5,6,8,4,2,1]=>0100111
[5,7,1,6,8,2,4,3]=>0100101
[8,6,2,5,1,7,4,3]=>1101011
[7,5,2,6,3,8,1,4]=>1101010
[4,1,2,3,6,8,7,5]=>1000011
[2,4,3,1,8,5,6,7]=>0110100
[7,5,2,8,3,4,6,1]=>1101001
[4,7,2,8,1,5,3,6]=>0101010
[8,7,2,1,4,5,6,3]=>1110001
[3,6,8,7,1,5,4,2]=>0011011
[5,7,8,6,3,4,1,2]=>0011010
[5,7,3,8,1,4,6,2]=>0101001
[2,1,7,8,5,4,6,3]=>1001101
[7,5,8,4,3,6,2,1]=>1011011
[2,4,8,3,5,6,1,7]=>0010010
[4,1,8,3,6,5,2,7]=>1010110
[8,4,1,3,7,2,6,5]=>1100101
[4,3,8,2,5,1,7,6]=>1010101
[2,1,4,8,3,5,7,6]=>1001001
[6,8,2,4,3,5,1,7]=>0101010
[4,8,2,3,5,1,6,7]=>0100100
[7,8,5,6,1,4,3,2]=>0101011
[7,8,4,2,1,5,3,6]=>0111010
[7,8,2,1,6,5,3,4]=>0110110
[6,4,1,2,5,7,3,8]=>1100010
[4,3,8,1,7,2,5,6]=>1010100
[7,8,1,4,6,2,5,3]=>0100101
[7,8,3,5,4,2,1,6]=>0101110
[7,8,4,1,2,3,6,5]=>0110001
[7,8,3,6,5,4,1,2]=>0101110
[7,8,2,6,4,1,3,5]=>0101100
[7,8,1,6,5,4,3,2]=>0101111
[2,1,8,7,5,4,3,6]=>1011110
[1,3,8,2,6,4,7,5]=>0010101
[5,3,7,1,6,4,8,2]=>1010101
[6,1,2,5,8,7,4,3]=>1000111
[6,3,1,8,4,2,7,5]=>1101101
[6,4,2,1,5,3,8,7]=>1110101
[6,4,3,7,5,8,1,2]=>1101010
[4,3,8,7,5,6,1,2]=>1011010
[2,4,7,1,5,3,6,8]=>0010100
[3,7,2,8,6,4,1,5]=>0101110
[3,8,1,7,6,4,5,2]=>0101101
[1,8,5,7,3,6,4,2]=>0101011
[2,7,5,8,3,6,1,4]=>0101010
[1,5,6,8,2,4,7,3]=>0001001
[2,6,1,4,7,3,5,8]=>0100100
[3,6,8,4,7,5,1,2]=>0010110
[5,6,7,3,8,4,1,2]=>0010110
[4,5,6,7,2,8,1,3]=>0001010
[4,5,7,6,1,8,3,2]=>0011011
[1,5,8,6,2,7,3,4]=>0011010
[4,7,5,6,3,1,8,2]=>0101101
[5,1,6,3,4,2,8,7]=>1010101
[5,7,1,4,2,3,8,6]=>0101001
[5,7,6,4,3,8,1,2]=>0111010
[6,3,4,5,8,7,1,2]=>1000110
[6,2,4,1,8,3,7,5]=>1010101
[6,2,3,5,4,8,1,7]=>1001010
[5,1,4,2,7,6,8,3]=>1010101
[1,6,2,4,7,8,3,5]=>0100010
[5,7,2,4,1,6,3,8]=>0101010
[6,1,4,2,8,5,3,7]=>1010110
[6,7,5,8,1,4,3,2]=>0101011
[5,8,7,6,3,4,1,2]=>0111010
[5,8,7,6,2,3,1,4]=>0111010
[4,1,7,2,6,5,3,8]=>1010110
[4,8,2,1,5,6,3,7]=>0110010
[4,2,7,8,1,6,3,5]=>1001010
[2,1,8,7,6,5,3,4]=>1011110
[4,2,7,1,6,3,8,5]=>1010101
[4,3,7,5,6,8,1,2]=>1010010
[3,8,6,5,2,4,1,7]=>0111010
[3,8,5,6,1,4,7,2]=>0101001
[5,3,7,8,2,1,6,4]=>1001101
[5,2,8,7,1,6,4,3]=>1011011
[3,6,7,8,5,1,4,2]=>0001101
[3,7,8,5,1,2,4,6]=>0011000
[4,1,8,6,2,3,5,7]=>1011000
[4,7,8,6,3,5,1,2]=>0011010
[3,8,7,6,5,4,1,2]=>0111110
[2,8,6,7,5,1,3,4]=>0101100
[5,3,7,8,2,1,4,6]=>1001100
[7,6,1,2,5,8,3,4]=>1100010
[2,1,7,8,4,3,5,6]=>1001100
[7,8,1,2,5,4,6,3]=>0100101
[2,6,8,3,1,4,7,5]=>0011001
[8,4,1,3,7,6,2,5]=>1100110
[6,5,2,1,8,7,4,3]=>1110111
[4,7,2,8,1,3,6,5]=>0101001
[7,3,8,6,1,2,5,4]=>1011001
[3,4,7,1,8,2,6,5]=>0010101
[1,8,2,4,3,5,6,7]=>0101000
[1,7,2,4,3,5,6,8]=>0101000
[1,5,2,4,3,6,7,8]=>0101000
[1,7,2,5,3,4,6,8]=>0101000
[1,8,2,5,3,4,6,7]=>0101000
[1,8,2,6,3,4,5,7]=>0101000
[1,8,2,7,3,4,5,6]=>0101000
[1,8,2,7,3,5,4,6]=>0101010
[1,7,2,8,3,5,4,6]=>0101010
[1,6,2,8,3,5,4,7]=>0101010
[1,5,2,8,3,6,4,7]=>0101010
[1,4,2,8,3,6,5,7]=>0101010
[1,3,2,8,4,6,5,7]=>0101010
[1,2,3,8,4,6,5,7]=>0001010
[1,2,3,7,4,6,5,8]=>0001010
[1,3,2,7,4,6,5,8]=>0101010
[1,4,2,7,3,6,5,8]=>0101010
[1,5,2,7,3,6,4,8]=>0101010
[1,6,2,7,3,5,4,8]=>0101010
[1,7,2,6,3,5,4,8]=>0101010
[1,8,2,6,3,5,4,7]=>0101010
[1,8,2,5,3,6,4,7]=>0101010
[1,7,2,5,3,6,4,8]=>0101010
[1,6,2,5,3,7,4,8]=>0101010
[1,5,2,4,3,7,6,8]=>0101010
[1,6,2,4,3,7,5,8]=>0101010
[1,7,2,4,3,6,5,8]=>0101010
[1,8,2,4,3,6,5,7]=>0101010
[1,8,2,4,3,7,5,6]=>0101010
[1,7,2,4,3,8,5,6]=>0101010
[1,6,2,4,3,8,5,7]=>0101010
[1,5,2,4,3,8,6,7]=>0101010
[1,6,2,5,3,8,4,7]=>0101010
[1,7,2,5,3,8,4,6]=>0101010
[1,8,2,5,3,7,4,6]=>0101010
[1,8,2,6,3,7,4,5]=>0101010
[1,7,2,6,3,8,4,5]=>0101010
[1,2,3,8,4,7,5,6]=>0001010
[1,3,2,8,4,7,5,6]=>0101010
[1,4,2,8,3,7,5,6]=>0101010
[1,5,2,8,3,7,4,6]=>0101010
[1,6,2,8,3,7,4,5]=>0101010
[1,7,2,8,3,6,4,5]=>0101010
[1,8,2,7,3,6,4,5]=>0101010
[2,8,4,1,6,5,3,7]=>0110110
[2,8,4,1,5,6,7,3]=>0110001
[2,8,7,4,1,6,3,5]=>0111010
[7,2,8,5,1,6,4,3]=>1011011
[1,3,7,5,2,6,4,8]=>0011010
[1,3,7,5,4,2,6,8]=>0011100
[7,2,8,5,4,1,6,3]=>1011101
[2,8,5,3,4,1,6,7]=>0110100
[2,8,7,6,1,4,5,3]=>0111001
[2,8,6,5,7,3,1,4]=>0110110
[7,2,8,4,5,6,1,3]=>1010010
[6,2,3,8,5,1,7,4]=>1001101
[6,3,2,8,5,1,4,7]=>1101100
[7,4,8,5,2,1,3,6]=>1011100
[6,4,8,5,1,3,7,2]=>1011001
[4,3,7,5,1,2,8,6]=>1011001
[4,3,7,1,5,6,8,2]=>1010001
[3,6,1,7,5,2,8,4]=>0101101
[3,4,1,2,7,6,8,5]=>0100101
[6,5,2,7,4,1,8,3]=>1101101
[3,5,2,6,4,8,7,1]=>0101011
[4,3,2,1,8,6,5,7]=>1110110
[4,2,1,3,8,7,6,5]=>1100111
[7,1,6,8,4,3,5,2]=>1001101
[6,1,2,8,4,5,7,3]=>1001001
[5,6,8,2,3,1,7,4]=>0010101
[6,5,8,2,4,3,1,7]=>1010110
[6,5,8,4,2,3,7,1]=>1011001
[7,5,3,8,2,4,1,6]=>1101010
[1,6,5,7,3,4,2,8]=>0101010
[5,2,1,8,7,6,3,4]=>1101110
[7,1,3,8,4,6,2,5]=>1001010
[5,7,8,4,3,6,2,1]=>0011011
[4,1,8,3,5,6,7,2]=>1010001
[4,1,8,3,6,2,7,5]=>1010101
[2,3,4,8,6,1,7,5]=>0001101
[2,3,4,8,6,5,1,7]=>0001110
[2,7,3,5,8,6,1,4]=>0100110
[3,2,4,7,8,6,1,5]=>1000110
[1,5,4,6,2,7,3,8]=>0101010
[5,2,4,7,1,8,3,6]=>1001010
[5,3,6,4,1,8,7,2]=>1011011
[5,3,6,1,4,8,2,7]=>1010010
[7,3,5,6,8,4,2,1]=>1000111
[6,3,5,1,8,2,7,4]=>1010101
[5,7,1,6,3,8,4,2]=>0101011
[3,2,4,1,7,8,5,6]=>1010010
[2,5,4,6,1,7,8,3]=>0101001
[7,2,1,4,3,6,5,8]=>1101010
[7,3,4,1,2,6,5,8]=>1010010
[7,4,3,2,1,6,5,8]=>1111010
[6,7,3,2,5,4,8,1]=>0110101
[1,8,3,2,5,4,7,6]=>0110101
[1,8,4,5,2,3,7,6]=>0101001
[7,3,5,1,6,2,4,8]=>1010100
[7,2,1,5,6,3,4,8]=>1100100
[1,8,5,4,3,2,7,6]=>0111101
[6,4,7,5,1,3,8,2]=>1011001
[3,2,1,8,5,4,7,6]=>1101101
[2,3,8,1,5,4,7,6]=>0010101
[2,4,8,5,1,3,7,6]=>0011001
[2,6,8,4,3,7,1,5]=>0011010
[2,7,8,4,3,6,5,1]=>0011011
[1,8,7,5,6,3,4,2]=>0110101
[2,7,8,5,6,3,4,1]=>0010101
[2,5,8,6,7,1,3,4]=>0010100
[2,4,8,6,1,7,3,5]=>0011010
[3,2,1,8,6,7,4,5]=>1101010
[5,2,1,7,6,8,4,3]=>1101011
[5,3,7,1,6,8,4,2]=>1010011
[5,4,7,6,1,8,3,2]=>1011011
[4,5,7,6,8,1,3,2]=>0010101
[4,6,7,5,8,3,1,2]=>0010110
[1,8,5,6,7,2,3,4]=>0100100
[4,6,5,7,8,2,1,3]=>0100110
[5,4,6,7,1,8,2,3]=>1001010
[5,3,6,1,7,8,2,4]=>1010010
[5,2,1,6,7,8,3,4]=>1100010
[6,2,1,5,7,3,8,4]=>1100101
[6,3,5,1,7,2,8,4]=>1010101
[6,4,5,7,1,2,8,3]=>1001001
[5,6,4,7,2,8,1,3]=>0101010
[1,8,4,6,2,7,3,5]=>0101010
[1,8,3,2,6,7,4,5]=>0110010
[5,7,3,2,6,8,4,1]=>0110011
[6,5,3,2,7,1,8,4]=>1110101
[6,4,3,2,1,7,8,5]=>1111001
[6,2,1,4,3,7,8,5]=>1101001
[5,2,1,4,3,8,7,6]=>1101011
[5,3,4,1,2,8,7,6]=>1010011
[4,5,3,2,8,1,7,6]=>0110101
[4,6,3,2,8,7,1,5]=>0110110
[1,8,3,2,7,6,5,4]=>0110111
[1,8,4,7,2,6,5,3]=>0101011
[3,6,4,8,2,7,1,5]=>0101010
[3,4,5,8,1,2,7,6]=>0001001
[4,3,5,1,8,2,7,6]=>1010101
[4,2,1,5,8,3,7,6]=>1100101
[4,2,1,6,8,7,3,5]=>1100110
[3,4,6,8,1,7,2,5]=>0001010
[3,5,6,8,7,1,2,4]=>0001100
[3,6,5,8,7,2,1,4]=>0101110
[3,6,7,8,5,4,1,2]=>0001110
[3,5,7,8,6,1,4,2]=>0001101
[4,2,1,7,8,6,5,3]=>1100111
[2,3,8,1,7,6,5,4]=>0010111
[2,4,8,7,1,6,5,3]=>0011011
[8,1,6,7,3,2,5,4]=>1001101
[8,1,6,7,2,3,4,5]=>1001000
[8,1,2,4,3,6,5,7]=>1001010
[8,1,4,3,2,7,6,5]=>1011011
[8,1,5,3,7,2,6,4]=>1010101
[8,1,3,5,6,2,7,4]=>1000101
[6,3,2,1,4,5,8,7]=>1110001
[4,7,8,5,6,1,2,3]=>0010100
[3,7,8,5,6,2,1,4]=>0010110
[3,7,8,4,2,6,1,5]=>0011010
[3,7,8,2,4,5,1,6]=>0010010
[3,6,2,8,4,5,1,7]=>0101010
[2,3,6,7,4,5,8,1]=>0001001
[3,5,2,4,8,6,1,7]=>0100110
[3,5,4,2,8,7,1,6]=>0110110
[4,6,5,8,7,1,2,3]=>0101100
[6,4,5,1,7,8,2,3]=>1010010
[5,4,2,3,1,8,6,7]=>1101010
[6,5,3,1,8,2,7,4]=>1110101
[6,5,4,1,8,7,2,3]=>1110110
[7,5,1,4,8,6,2,3]=>1100110
[7,4,1,3,2,8,6,5]=>1101011
[7,4,1,2,3,8,5,6]=>1100010
[6,4,2,1,3,8,5,7]=>1110010
[2,6,4,8,3,7,5,1]=>0101011
[2,6,5,8,7,3,4,1]=>0101101
[6,5,2,1,8,3,4,7]=>1110100
[7,5,1,2,8,3,4,6]=>1100100
[7,6,1,8,2,3,4,5]=>1101000
[7,6,1,8,4,5,2,3]=>1101010
[6,7,8,1,4,5,2,3]=>0010010
[6,7,8,1,3,2,5,4]=>0010101
[2,5,6,7,8,3,4,1]=>0000101
[2,4,6,7,3,8,5,1]=>0001011
[4,2,6,7,3,1,5,8]=>1001100
[4,7,8,2,3,1,5,6]=>0010100
[4,7,8,3,2,1,6,5]=>0011101
[5,7,8,3,1,2,6,4]=>0011001
[5,7,8,4,1,6,2,3]=>0011010
[5,6,4,8,1,7,2,3]=>0101010
[4,6,3,8,2,1,7,5]=>0101101
[4,2,5,3,7,1,6,8]=>1010100
[5,3,6,7,1,2,8,4]=>1001001
[3,5,6,7,8,2,1,4]=>0000110
[3,4,6,7,2,8,1,5]=>0001010
[7,4,6,1,8,3,5,2]=>1010101
[7,3,5,1,8,4,6,2]=>1010101
[7,3,4,1,8,5,6,2]=>1010101
[4,5,7,3,1,8,6,2]=>0011011
[4,5,6,2,1,8,7,3]=>0011011
[1,6,5,2,7,4,3,8]=>0110110
[7,4,3,1,8,6,5,2]=>1110111
[3,6,7,5,1,8,4,2]=>0011011
[7,5,6,1,8,3,4,2]=>1010101
[7,6,5,1,8,4,3,2]=>1110111
[7,6,4,1,8,5,3,2]=>1110111
[6,4,2,1,8,7,5,3]=>1110111
[1,5,3,2,7,6,4,8]=>0110110
[2,6,5,1,7,8,4,3]=>0110011
[4,5,7,1,6,8,2,3]=>0010010
[4,5,7,1,3,8,2,6]=>0010010
[6,4,1,2,8,5,3,7]=>1100110
[5,3,1,2,8,6,4,7]=>1100110
[4,3,1,2,8,6,5,7]=>1100110
[6,1,2,5,8,3,4,7]=>1000100
[7,1,3,4,8,2,5,6]=>1000100
[2,6,1,5,7,8,3,4]=>0100010
[7,6,1,5,8,3,2,4]=>1100110
[3,6,7,1,5,8,2,4]=>0010010
[7,1,6,5,8,2,4,3]=>1010101
[7,5,1,6,8,4,2,3]=>1100110
[7,4,1,6,8,5,2,3]=>1100110
[5,2,3,1,8,6,7,4]=>1010101
[7,3,1,5,8,6,2,4]=>1100110
[6,2,4,1,8,5,7,3]=>1010101
[6,2,5,1,8,4,7,3]=>1010101
[7,1,6,4,8,2,5,3]=>1010101
[7,1,5,3,8,2,6,4]=>1010101
[6,1,5,2,8,3,7,4]=>1010101
[7,3,1,4,8,6,2,5]=>1100110
[6,2,1,4,8,7,3,5]=>1100110
[5,2,1,3,8,7,4,6]=>1100110
[7,4,1,3,8,5,2,6]=>1100110
[6,1,4,2,8,3,7,5]=>1010101
[7,1,4,3,8,2,6,5]=>1010101
[3,6,7,1,4,8,2,5]=>0010010
[7,6,1,4,8,3,2,5]=>1100110
[5,1,3,2,8,4,7,6]=>1010101
[4,2,1,3,8,7,5,6]=>1100110
[2,6,1,4,7,8,3,5]=>0100010
[7,1,3,5,8,2,4,6]=>1000100
[7,8,5,6,1,3,4,2]=>0101001
[7,8,1,3,6,2,5,4]=>0100101
[1,3,8,4,7,2,5,6]=>0010100
[4,6,1,2,5,7,3,8]=>0100010
[1,4,8,2,5,7,3,6]=>0010010
[7,8,4,2,5,1,3,6]=>0110100
[7,8,1,5,4,6,3,2]=>0101011
[7,8,2,1,6,3,4,5]=>0110100
[7,8,3,5,6,4,1,2]=>0100110
[7,8,4,5,3,1,6,2]=>0101101
[2,6,4,8,3,7,1,5]=>0101010
[1,4,6,8,3,7,5,2]=>0001011
[2,4,8,5,3,1,6,7]=>0011100
[2,5,8,1,4,7,6,3]=>0010011
[2,1,8,4,7,3,6,5]=>1010101
[3,5,8,4,7,6,1,2]=>0010110
[1,6,2,4,7,3,8,5]=>0100101
[4,6,2,5,3,1,8,7]=>0101101
[4,7,5,1,3,6,8,2]=>0110001
[7,5,3,6,2,4,1,8]=>1101010
[5,7,3,6,1,4,8,2]=>0101001
[5,3,6,7,2,1,8,4]=>1001101
[6,3,1,2,4,5,8,7]=>1100001
[1,4,7,2,5,3,8,6]=>0010101
[6,4,7,3,5,8,1,2]=>1010010
[3,5,6,7,8,1,4,2]=>0000101
[3,6,5,7,8,2,1,4]=>0100110
[5,2,7,6,1,4,3,8]=>1011010
[2,7,5,6,8,4,1,3]=>0100110
[2,1,6,8,4,5,3,7]=>1001010
[2,7,1,8,5,3,4,6]=>0101100
[3,7,6,8,5,4,1,2]=>0101110
[4,3,8,5,6,7,1,2]=>1010010
[4,2,8,1,6,3,7,5]=>1010101
[3,1,8,5,4,6,7,2]=>1011001
[3,4,2,8,6,1,7,5]=>0101101
[1,7,3,8,5,2,6,4]=>0101101
[4,1,8,3,6,2,5,7]=>1010100
[5,7,8,6,3,2,1,4]=>0011110
[5,7,8,6,1,3,4,2]=>0011001
[7,6,5,8,1,3,4,2]=>1101001
[1,6,4,3,8,2,5,7]=>0110100
[2,6,3,4,5,8,1,7]=>0100010
[2,6,4,1,8,3,7,5]=>0110101
[3,6,4,5,8,7,1,2]=>0100110
[7,1,6,5,3,8,4,2]=>1011011
[7,2,5,6,3,8,1,4]=>1001010
[5,6,2,7,3,1,4,8]=>0101100
[5,7,6,4,1,8,3,2]=>0111011
[6,7,1,5,2,8,3,4]=>0101010
[6,1,5,2,8,3,4,7]=>1010100
[7,5,2,4,3,1,6,8]=>1101100
[6,8,1,3,7,5,4,2]=>0100111
[7,4,2,6,5,1,3,8]=>1101100
[7,4,6,3,1,5,2,8]=>1011010
[7,2,3,5,4,1,6,8]=>1001100
[6,8,1,2,3,4,7,5]=>0100001
[2,5,1,7,8,3,6,4]=>0100101
[2,5,3,6,8,4,7,1]=>0100101
[2,1,4,7,8,5,6,3]=>1000101
[2,5,7,8,1,4,6,3]=>0001001
[3,5,7,4,1,6,2,8]=>0011010
[5,2,8,4,6,1,7,3]=>1010101
[4,2,8,5,7,6,3,1]=>1010111
[4,1,2,8,5,6,7,3]=>1001001
[1,4,2,7,5,8,6,3]=>0101011
[4,1,8,6,7,5,3,2]=>1010111
[5,3,8,7,6,2,4,1]=>1011101
[5,8,4,7,6,2,1,3]=>0101110
[5,8,7,4,3,6,1,2]=>0111010
[6,4,8,3,1,7,2,5]=>1011010
[6,4,2,8,7,1,3,5]=>1101100
[6,3,8,7,2,5,1,4]=>1011010
[6,3,1,8,7,2,4,5]=>1101100
[5,8,3,7,1,6,4,2]=>0101011
[5,1,8,4,6,2,7,3]=>1010101
[5,8,7,4,1,6,2,3]=>0111010
[6,8,5,2,4,3,7,1]=>0110101
[6,8,5,3,1,2,7,4]=>0111001
[4,5,1,2,7,6,3,8]=>0100110
[4,5,1,2,6,8,7,3]=>0100011
[3,5,6,1,8,4,7,2]=>0010101
[3,5,7,1,2,8,6,4]=>0010011
[4,2,6,1,7,3,5,8]=>1010100
[4,6,3,1,2,7,5,8]=>0110010
[3,5,2,7,8,1,6,4]=>0100101
[3,1,4,7,5,6,2,8]=>1001010
[4,2,5,6,1,8,7,3]=>1001011
[2,1,7,5,8,6,4,3]=>1010111
[1,2,7,5,3,8,6,4]=>0011011
[4,1,2,7,3,8,6,5]=>1001011
[7,1,4,2,5,3,8,6]=>1010101
[6,1,3,7,5,2,4,8]=>1001100
[3,1,2,6,8,5,4,7]=>1000110
[3,7,1,2,5,4,8,6]=>0100101
[1,3,7,2,4,8,6,5]=>0010011
[3,2,7,8,1,6,5,4]=>1001011
[2,4,1,7,8,6,5,3]=>0100111
[2,6,8,3,1,5,7,4]=>0011001
[3,6,4,8,5,1,7,2]=>0101101
[6,3,7,4,5,1,8,2]=>1010101
[6,4,7,5,2,8,1,3]=>1011010
[2,6,3,7,5,8,1,4]=>0101010
[5,2,1,7,8,3,4,6]=>1100100
[5,7,4,6,2,8,1,3]=>0101010
[5,7,3,4,6,1,8,2]=>0100101
[4,2,8,3,6,7,1,5]=>1010010
[4,8,3,1,7,2,5,6]=>0110100
[5,2,8,4,7,1,6,3]=>1010101
[5,8,4,7,3,1,6,2]=>0101101
[4,6,8,3,1,7,5,2]=>0011011
[6,3,8,2,7,1,5,4]=>1010101
[6,3,1,8,2,4,7,5]=>1101001
[3,5,1,8,2,7,4,6]=>0101010
[7,5,1,3,6,2,4,8]=>1100100
[8,5,4,1,2,6,3,7]=>1110010
[5,1,8,4,2,7,3,6]=>1011010
[4,1,6,2,8,3,7,5]=>1010101
[1,6,2,8,5,3,7,4]=>0101101
[6,8,5,3,1,7,4,2]=>0111011
[5,6,7,3,1,8,4,2]=>0011011
[5,6,2,1,7,8,4,3]=>0110011
[8,4,5,1,2,6,3,7]=>1010010
[1,6,3,7,2,8,4,5]=>0101010
[6,3,2,7,8,5,1,4]=>1100110
[6,4,7,2,8,1,5,3]=>1010101
[6,7,4,8,3,1,5,2]=>0101101
[4,5,7,8,3,1,6,2]=>0001101
[4,7,2,5,8,1,6,3]=>0100101
[5,7,3,8,2,6,1,4]=>0101010
[3,4,7,8,2,6,1,5]=>0001010
[8,1,3,4,6,2,5,7]=>1000100
[3,8,2,4,6,7,1,5]=>0100010
[2,4,5,6,8,1,7,3]=>0000101
[4,8,3,5,6,1,7,2]=>0100101
[8,4,3,6,5,1,7,2]=>1101101
[8,6,5,4,3,1,7,2]=>1111101
[1,8,6,5,2,7,3,4]=>0111010
[8,7,5,4,1,6,3,2]=>1111011
[7,8,5,4,1,3,6,2]=>0111001
[6,8,5,4,2,1,7,3]=>0111101
[5,8,6,2,4,1,7,3]=>0110101
[3,2,8,6,5,1,7,4]=>1011101
[5,1,7,3,6,2,4,8]=>1010100
[8,1,6,5,2,3,7,4]=>1011001
[1,2,8,3,7,4,5,6]=>0010100
[8,1,7,2,6,3,5,4]=>1010101
[7,1,8,2,6,4,3,5]=>1010110
[5,1,8,3,2,7,4,6]=>1011010
[3,2,1,8,4,7,5,6]=>1101010
[3,2,8,7,1,6,5,4]=>1011011
[4,8,2,7,1,6,5,3]=>0101011
[5,8,7,2,1,6,4,3]=>0111011
[8,7,6,1,5,4,3,2]=>1110111
[8,6,7,1,4,5,3,2]=>1010011
[7,6,8,1,4,3,5,2]=>1010101
[6,7,8,1,3,4,5,2]=>0010001
[5,7,8,2,1,4,6,3]=>0011001
[4,7,2,8,1,5,6,3]=>0101001
[3,2,7,8,1,5,6,4]=>1001001
[3,2,6,8,4,1,7,5]=>1001101
[4,6,2,8,3,1,7,5]=>0101101
[6,5,8,3,2,1,7,4]=>1011101
[7,5,8,3,1,4,6,2]=>1011001
[8,4,3,7,1,6,5,2]=>1101011
[6,4,3,8,2,1,7,5]=>1101101
[5,4,3,2,8,1,7,6]=>1110101
[4,5,2,3,8,1,7,6]=>0100101
[3,2,5,4,8,1,7,6]=>1010101
[6,4,3,1,5,2,7,8]=>1110100
[7,4,3,1,2,6,5,8]=>1110010
[1,5,4,2,3,6,7,8]=>0110000
[8,5,1,4,2,3,7,6]=>1101001
[7,5,1,4,2,6,3,8]=>1101010
[4,6,2,1,5,3,7,8]=>0110100
[3,2,6,1,5,4,7,8]=>1010100
[5,7,1,3,2,6,4,8]=>0101010
[6,7,1,2,4,5,3,8]=>0100010
[7,6,1,2,5,4,3,8]=>1100110
[7,8,1,2,3,5,6,4]=>0100001
[6,8,1,2,4,3,7,5]=>0100101
[4,8,2,1,3,5,7,6]=>0110001
[3,2,8,1,4,5,7,6]=>1010001
[4,1,3,2,5,6,7,8]=>1010000
[5,1,2,4,3,6,7,8]=>1001000
[5,8,7,3,4,1,2,6]=>0110100
[6,7,3,8,5,1,2,4]=>0101100
[6,7,4,5,1,8,3,2]=>0101011
[5,4,7,6,2,3,8,1]=>1011001
[5,4,7,6,8,1,2,3]=>1010100
[5,3,7,8,6,1,2,4]=>1001100
[4,3,8,7,6,1,2,5]=>1011100
[4,8,3,7,5,1,2,6]=>0101100
[4,5,6,7,1,8,3,2]=>0001011
[3,5,6,2,7,4,8,1]=>0010101
[3,5,6,1,7,8,4,2]=>0010011
[2,5,6,8,1,7,3,4]=>0001010
[8,2,4,5,1,6,3,7]=>1001010
[1,4,8,6,2,3,7,5]=>0011001
[1,5,6,8,2,3,7,4]=>0001001
[1,5,6,2,8,4,7,3]=>0010101
[1,4,2,6,8,5,7,3]=>0100101
[8,1,3,2,5,4,6,7]=>1010100
[2,4,1,6,8,7,5,3]=>0100111
[4,3,1,7,6,8,5,2]=>1101011
[3,8,2,1,7,5,4,6]=>0110110
[8,3,2,1,6,5,4,7]=>1110110
[8,4,2,6,1,5,3,7]=>1101010
[4,2,8,7,1,6,3,5]=>1011010
[5,2,7,8,1,6,3,4]=>1001010
[5,3,7,2,6,4,8,1]=>1010101
[6,7,3,1,5,8,4,2]=>0110011
[6,7,2,1,8,5,4,3]=>0110111
[6,7,2,8,1,5,3,4]=>0101010
[6,7,8,2,1,4,3,5]=>0011010
[8,5,6,2,1,4,3,7]=>1011010
[5,8,7,1,2,3,4,6]=>0110000
[6,7,1,2,8,4,5,3]=>0100101
[6,7,1,3,4,8,5,2]=>0100011
[5,1,7,3,4,8,6,2]=>1010011
[5,1,7,8,2,3,6,4]=>1001001
[4,8,1,7,2,3,5,6]=>0101000
[3,8,1,2,7,4,5,6]=>0100100
[3,1,8,2,7,4,6,5]=>1010101
[3,1,2,8,7,5,6,4]=>1001101
[4,1,3,7,5,8,6,2]=>1001011
[2,1,8,3,4,7,6,5]=>1010011
[1,8,2,3,4,5,7,6]=>0100001
[1,2,8,3,4,6,7,5]=>0010001
[6,3,8,5,2,7,4,1]=>1011011
[6,5,2,8,4,7,3,1]=>1101011
[6,3,4,5,8,7,2,1]=>1000111
[5,8,1,4,7,2,3,6]=>0100100
[3,6,4,8,5,7,1,2]=>0101010
[5,1,4,8,6,3,7,2]=>1001101
[3,4,7,1,8,6,5,2]=>0010111
[6,3,8,4,2,7,1,5]=>1011010
[3,6,8,7,1,4,2,5]=>0011010
[5,3,7,1,6,8,2,4]=>1010010
[4,6,1,2,7,8,5,3]=>0100011
[3,6,4,2,8,7,5,1]=>0110111
[6,3,7,5,2,8,1,4]=>1011010
[6,5,2,7,4,8,1,3]=>1101010
[5,8,1,4,6,7,2,3]=>0100010
[6,3,7,4,2,8,5,1]=>1011011
[8,7,1,6,2,4,5,3]=>1101001
[5,6,1,8,7,3,2,4]=>0101110
[3,6,4,5,7,2,8,1]=>0100101
[5,4,2,7,3,6,8,1]=>1101001
[6,4,1,5,3,8,2,7]=>1101010
[8,2,6,3,4,7,5,1]=>1010011
[4,2,5,7,3,6,8,1]=>1001001
[1,6,5,3,4,8,2,7]=>0110010
[6,8,3,1,7,2,5,4]=>0110101
[1,8,6,3,7,5,2,4]=>0110110
[8,7,5,2,6,4,3,1]=>1110111
[8,7,1,6,2,5,4,3]=>1101011
[2,8,1,7,3,5,6,4]=>0101001
[4,8,1,3,7,2,6,5]=>0100101
[4,2,8,5,7,3,6,1]=>1010101
[6,7,3,1,8,4,2,5]=>0110110
[1,7,3,8,4,5,2,6]=>0101010
[1,7,2,8,5,3,4,6]=>0101100
[7,6,1,8,4,3,2,5]=>1101110
[7,1,2,8,3,5,4,6]=>1001010
[6,3,7,2,1,8,4,5]=>1011010
[8,2,6,1,7,3,5,4]=>1010101
[4,2,1,5,8,3,6,7]=>1100100
[5,4,3,1,6,8,2,7]=>1110010
[1,5,3,4,6,8,2,7]=>0100010
[4,3,5,1,6,8,2,7]=>1010010
[4,7,5,6,8,3,2,1]=>0100111
[6,5,1,8,7,4,2,3]=>1101110
[8,6,4,7,5,3,2,1]=>1101111
[5,7,3,8,2,6,4,1]=>0101011
[2,3,8,7,4,5,6,1]=>0011001
[7,2,8,6,4,3,5,1]=>1011101
[2,1,8,7,5,6,3,4]=>1011010
[7,1,8,6,5,3,2,4]=>1011110
[4,7,1,8,6,5,2,3]=>0101110
[6,8,7,2,5,4,3,1]=>0110111
[6,7,4,8,3,5,1,2]=>0101010
[6,7,4,5,2,8,1,3]=>0101010
[5,7,4,6,2,3,1,8]=>0101010
[5,7,4,6,3,8,1,2]=>0101010
[5,7,4,8,3,6,1,2]=>0101010
[6,8,4,5,3,7,1,2]=>0101010
[5,8,4,6,3,7,1,2]=>0101010
[5,6,4,8,3,7,1,2]=>0101010
[5,6,3,7,2,4,1,8]=>0101010
[5,6,3,7,2,8,1,4]=>0101010
[5,6,3,8,2,7,1,4]=>0101010
[5,6,4,8,2,7,1,3]=>0101010
[5,8,4,6,2,7,1,3]=>0101010
[6,8,4,5,2,7,1,3]=>0101010
[7,8,4,5,2,6,1,3]=>0101010
[6,8,4,5,2,3,1,7]=>0101010
[5,8,4,6,2,3,1,7]=>0101010
[5,6,4,8,2,3,1,7]=>0101010
[5,6,3,8,2,4,1,7]=>0101010
[5,6,3,4,2,8,1,7]=>0101010
[4,6,3,5,2,7,1,8]=>0101010
[4,6,3,5,2,8,1,7]=>0101010
[4,6,3,8,2,5,1,7]=>0101010
[4,8,3,6,2,5,1,7]=>0101010
[5,8,3,6,2,4,1,7]=>0101010
[6,8,3,5,2,4,1,7]=>0101010
[7,8,3,5,2,4,1,6]=>0101010
[7,8,3,5,2,6,1,4]=>0101010
[6,8,3,5,2,7,1,4]=>0101010
[5,8,3,6,2,7,1,4]=>0101010
[4,8,3,6,2,7,1,5]=>0101010
[4,6,3,8,2,7,1,5]=>0101010
[4,6,3,7,2,8,1,5]=>0101010
[4,6,3,7,2,5,1,8]=>0101010
[4,7,3,6,2,5,1,8]=>0101010
[4,7,3,6,2,8,1,5]=>0101010
[4,7,3,8,2,6,1,5]=>0101010
[5,7,4,8,2,6,1,3]=>0101010
[5,7,3,6,2,8,1,4]=>0101010
[5,7,3,6,2,4,1,8]=>0101010
[6,7,3,5,2,4,1,8]=>0101010
[6,7,3,5,2,8,1,4]=>0101010
[6,7,3,8,2,5,1,4]=>0101010
[6,7,4,8,2,5,1,3]=>0101010
[6,7,5,8,2,4,1,3]=>0101010
[6,8,5,7,2,3,1,4]=>0101010
[6,7,4,8,2,3,1,5]=>0101010
[6,7,3,8,2,4,1,5]=>0101010
[6,7,3,4,2,8,1,5]=>0101010
[5,7,3,4,2,6,1,8]=>0101010
[5,7,3,4,2,8,1,6]=>0101010
[5,7,3,8,2,4,1,6]=>0101010
[5,7,4,8,2,3,1,6]=>0101010
[5,8,4,7,2,3,1,6]=>0101010
[6,8,4,7,2,3,1,5]=>0101010
[7,8,4,6,2,3,1,5]=>0101010
[7,8,3,6,2,4,1,5]=>0101010
[6,8,3,7,2,4,1,5]=>0101010
[5,8,3,7,2,4,1,6]=>0101010
[4,8,3,7,2,5,1,6]=>0101010
[4,7,3,8,2,5,1,6]=>0101010
[4,7,3,5,2,8,1,6]=>0101010
[4,7,3,5,2,6,1,8]=>0101010
[4,5,3,7,2,6,1,8]=>0101010
[4,5,3,7,2,8,1,6]=>0101010
[4,5,3,8,2,7,1,6]=>0101010
[4,8,3,5,2,7,1,6]=>0101010
[5,8,3,4,2,7,1,6]=>0101010
[6,8,3,4,2,7,1,5]=>0101010
[7,8,3,4,2,6,1,5]=>0101010
[6,8,3,4,2,5,1,7]=>0101010
[5,8,3,4,2,6,1,7]=>0101010
[4,8,3,5,2,6,1,7]=>0101010
[4,5,3,8,2,6,1,7]=>0101010
[4,5,3,6,2,8,1,7]=>0101010
[4,7,5,2,1,8,3,6]=>0111010
[4,6,5,2,1,3,8,7]=>0111001
[5,6,4,2,3,1,8,7]=>0110101
[6,4,5,3,1,2,8,7]=>1011001
[5,4,6,1,3,2,8,7]=>1010101
[4,6,8,1,7,3,2,5]=>0010110
[4,7,8,1,6,3,5,2]=>0010101
[7,4,8,1,6,5,3,2]=>1010111
[7,4,5,3,1,8,2,6]=>1011010
[6,4,8,1,7,5,2,3]=>1010110
[6,4,7,1,8,2,5,3]=>1010101
[8,5,7,6,4,2,1,3]=>1011110
[2,1,6,8,7,4,3,5]=>1001110
[2,1,7,8,6,4,5,3]=>1001101
[8,4,7,3,6,2,5,1]=>1010101
[7,6,8,5,2,4,3,1]=>1011011
[5,7,8,6,2,3,1,4]=>0011010
[5,8,7,6,3,2,1,4]=>0111110
[6,8,7,5,3,2,4,1]=>0111101
[7,8,4,2,6,5,3,1]=>0110111
[4,8,6,2,7,3,1,5]=>0110110
[3,6,1,8,7,4,2,5]=>0101110
[4,7,6,2,8,1,3,5]=>0110100
[6,7,4,2,8,1,5,3]=>0110101
[6,8,4,2,7,5,1,3]=>0110110
[5,7,4,2,3,8,1,6]=>0110010
[2,1,8,6,7,5,3,4]=>1010110
[8,6,4,3,7,5,1,2]=>1110110
[5,8,6,7,3,1,2,4]=>0101100
[6,7,5,8,1,3,4,2]=>0101001
[7,6,5,8,1,4,3,2]=>1101011
[8,6,5,7,4,1,3,2]=>1101101
[7,6,4,3,8,1,5,2]=>1110101
[2,1,7,6,8,3,5,4]=>1010101
[7,5,6,8,1,4,2,3]=>1001010
[4,1,7,3,6,5,8,2]=>1010101
[5,1,8,4,7,6,2,3]=>1010110
[8,1,3,7,4,6,5,2]=>1001011
[6,1,5,4,3,8,7,2]=>1011011
[6,1,4,5,3,7,8,2]=>1001001
[5,1,7,8,6,2,4,3]=>1001101
[6,1,8,3,4,5,7,2]=>1010001
[8,5,2,1,4,3,7,6]=>1110101
[5,6,2,1,4,8,3,7]=>0110010
[3,6,1,8,5,2,4,7]=>0101100
[3,4,1,2,8,6,5,7]=>0100110
[6,3,8,5,2,1,4,7]=>1011100
[8,5,2,7,3,1,6,4]=>1101101
[2,3,8,5,6,1,7,4]=>0010101
[7,4,5,6,3,1,8,2]=>1001101
[8,5,6,4,2,1,7,3]=>1011101
[7,5,3,6,2,8,1,4]=>1101010
[1,7,5,6,3,2,4,8]=>0101100
[8,7,5,4,1,6,2,3]=>1111010
[2,6,4,1,8,5,7,3]=>0110101
[6,1,2,3,8,5,7,4]=>1000101
[7,1,2,3,6,5,8,4]=>1000101
[7,2,1,3,8,6,4,5]=>1100110
[1,5,7,3,2,4,6,8]=>0011000
[5,2,7,3,1,8,4,6]=>1011010
[5,8,2,4,1,3,7,6]=>0101001
[8,7,2,6,3,4,1,5]=>1101010
[4,8,1,6,3,2,7,5]=>0101101
[3,1,8,6,4,2,7,5]=>1011101
[8,1,6,7,4,3,2,5]=>1001110
[3,5,8,7,2,4,1,6]=>0011010
[4,2,1,3,7,8,5,6]=>1100010
[8,6,1,3,7,2,4,5]=>1100100
[5,1,8,3,2,4,6,7]=>1011000
[5,2,7,8,6,4,1,3]=>1001110
[1,4,2,7,8,6,3,5]=>0100110
[1,6,2,4,8,5,3,7]=>0100110
[1,6,2,4,7,5,3,8]=>0100110
[1,7,3,8,5,2,4,6]=>0101100
[1,7,3,2,8,6,4,5]=>0110110
[7,8,3,6,5,2,1,4]=>0101110
[4,7,2,8,6,1,5,3]=>0101101
[4,2,5,7,8,6,1,3]=>1000110
[8,2,5,1,7,3,4,6]=>1010100
[1,3,6,4,8,5,7,2]=>0010101
[1,3,6,4,7,5,8,2]=>0010101
[6,2,4,7,5,8,1,3]=>1001010
[6,2,7,3,5,1,8,4]=>1010101
[6,2,1,3,7,8,4,5]=>1100010
[7,2,5,1,8,3,4,6]=>1010100
[7,8,2,1,4,3,5,6]=>0110100
[7,6,4,2,3,1,8,5]=>1110101
[7,5,4,2,6,8,1,3]=>1110010
[1,7,5,3,4,6,8,2]=>0110001
[8,2,5,4,6,7,1,3]=>1010010
[8,2,6,4,3,1,7,5]=>1011101
[8,2,7,4,1,3,5,6]=>1011000
[1,2,8,4,3,5,6,7]=>0011000
[1,8,7,4,3,2,5,6]=>0111100
[5,8,4,7,2,1,6,3]=>0101101
[1,8,7,5,4,3,6,2]=>0111101
[1,6,8,4,3,7,5,2]=>0011011
[6,8,7,3,2,5,1,4]=>0111010
[5,3,8,1,2,7,4,6]=>1010010
[5,1,8,3,2,6,4,7]=>1011010
[5,7,3,1,2,6,4,8]=>0110010
[1,4,6,2,8,3,7,5]=>0010101
[5,2,6,7,8,4,1,3]=>1000110
[5,3,6,1,2,8,4,7]=>1010010
[1,6,3,2,7,8,4,5]=>0110010
[6,7,3,8,5,2,1,4]=>0101110
[4,6,2,7,8,1,5,3]=>0100101
[1,6,4,7,8,3,5,2]=>0100101
[4,5,7,2,1,8,6,3]=>0011011
[7,8,3,4,2,1,6,5]=>0101101
[6,3,4,1,2,5,8,7]=>1010001
[6,3,1,4,2,7,5,8]=>1101010
[1,8,3,2,4,5,6,7]=>0110000
[8,6,3,2,4,1,7,5]=>1110101
[8,5,3,2,6,7,1,4]=>1110010
[4,5,2,6,8,1,7,3]=>0100101
[4,2,5,6,7,8,1,3]=>1000010
[7,2,3,1,4,5,8,6]=>1010001
[5,6,3,4,1,2,8,7]=>0101001
[7,8,3,5,4,6,1,2]=>0101010
[6,8,3,7,5,1,4,2]=>0101101
[2,1,7,8,5,6,3,4]=>1001010
[5,7,3,8,1,6,2,4]=>0101010
[7,5,8,4,2,6,1,3]=>1011010
[8,6,3,7,5,2,4,1]=>1101101
[8,5,3,7,2,6,4,1]=>1101011
[8,5,7,4,2,6,3,1]=>1011011
[7,8,4,6,1,5,2,3]=>0101010
[7,8,1,6,4,5,2,3]=>0101010
[6,8,1,7,4,5,2,3]=>0101010
[1,8,6,7,4,5,2,3]=>0101010
[1,8,6,7,3,5,2,4]=>0101010
[6,8,1,7,3,5,2,4]=>0101010
[7,8,1,6,3,5,2,4]=>0101010
[7,8,3,6,1,5,2,4]=>0101010
[7,8,3,6,4,5,1,2]=>0101010
[7,8,2,6,4,5,1,3]=>0101010
[7,8,2,6,3,5,1,4]=>0101010
[7,8,2,6,1,5,3,4]=>0101010
[7,8,1,6,2,5,3,4]=>0101010
[1,8,6,7,2,5,3,4]=>0101010
[1,8,5,7,2,6,3,4]=>0101010
[5,8,1,7,2,6,3,4]=>0101010
[5,8,2,7,1,6,3,4]=>0101010
[6,8,2,7,1,5,3,4]=>0101010
[6,8,2,7,3,5,1,4]=>0101010
[6,8,2,7,4,5,1,3]=>0101010
[6,8,3,7,4,5,1,2]=>0101010
[3,8,6,7,4,5,1,2]=>0101010
[2,8,6,7,4,5,1,3]=>0101010
[2,8,6,7,3,5,1,4]=>0101010
[2,8,6,7,1,5,3,4]=>0101010
[2,8,5,7,1,6,3,4]=>0101010
[2,8,1,7,5,6,3,4]=>0101010
[1,8,2,7,5,6,3,4]=>0101010
[1,8,2,7,4,6,3,5]=>0101010
[2,8,1,7,4,6,3,5]=>0101010
[2,8,4,7,1,6,3,5]=>0101010
[2,8,4,7,3,6,1,5]=>0101010
[2,8,5,7,3,6,1,4]=>0101010
[3,8,5,7,4,6,1,2]=>0101010
[5,8,3,7,4,6,1,2]=>0101010
[5,8,2,7,4,6,1,3]=>0101010
[5,8,2,7,3,6,1,4]=>0101010
[4,8,2,7,3,6,1,5]=>0101010
[4,8,2,7,1,6,3,5]=>0101010
[4,8,1,7,2,6,3,5]=>0101010
[1,8,4,7,2,6,3,5]=>0101010
[1,8,4,7,3,6,2,5]=>0101010
[4,8,1,7,3,6,2,5]=>0101010
[4,8,3,7,1,6,2,5]=>0101010
[6,8,3,7,1,5,2,4]=>0101010
[5,8,1,7,3,6,2,4]=>0101010
[1,8,5,7,3,6,2,4]=>0101010
[1,8,5,7,4,6,2,3]=>0101010
[5,8,1,7,4,6,2,3]=>0101010
[5,8,4,7,1,6,2,3]=>0101010
[6,8,4,7,1,5,2,3]=>0101010
[6,8,5,7,1,4,2,3]=>0101010
[5,8,6,7,3,4,1,2]=>0101010
[5,8,6,7,2,4,1,3]=>0101010
[5,8,6,7,1,4,2,3]=>0101010
[4,8,6,7,1,5,2,3]=>0101010
[4,8,5,7,1,6,2,3]=>0101010
[4,8,1,7,5,6,2,3]=>0101010
[1,8,4,7,5,6,2,3]=>0101010
[1,8,3,7,5,6,2,4]=>0101010
[3,8,1,7,5,6,2,4]=>0101010
[3,8,5,7,1,6,2,4]=>0101010
[3,8,6,7,1,5,2,4]=>0101010
[3,8,6,7,2,5,1,4]=>0101010
[4,8,6,7,2,5,1,3]=>0101010
[4,8,6,7,3,5,1,2]=>0101010
[4,8,5,7,3,6,1,2]=>0101010
[4,8,5,7,2,6,1,3]=>0101010
[3,8,5,7,2,6,1,4]=>0101010
[3,8,4,7,2,6,1,5]=>0101010
[3,8,4,7,1,6,2,5]=>0101010
[3,8,1,7,4,6,2,5]=>0101010
[1,8,3,7,4,6,2,5]=>0101010
[1,8,3,7,2,6,4,5]=>0101010
[3,8,1,7,2,6,4,5]=>0101010
[3,8,2,7,1,6,4,5]=>0101010
[3,8,2,7,4,6,1,5]=>0101010
[3,8,2,7,5,6,1,4]=>0101010
[4,8,2,7,5,6,1,3]=>0101010
[4,8,3,7,5,6,1,2]=>0101010
[3,8,4,7,5,6,1,2]=>0101010
[2,8,4,7,5,6,1,3]=>0101010
[2,8,3,7,5,6,1,4]=>0101010
[2,8,3,7,4,6,1,5]=>0101010
[2,8,3,7,1,6,4,5]=>0101010
[2,8,1,7,3,6,4,5]=>0101010
[7,5,2,8,6,4,1,3]=>1101110
[7,4,8,6,1,5,2,3]=>1011010
[7,1,8,4,5,2,6,3]=>1010101
[1,6,7,4,2,8,5,3]=>0011011
[1,6,7,3,8,5,2,4]=>0010110
[7,1,8,3,5,6,2,4]=>1010010
[7,3,8,6,2,5,1,4]=>1011010
[7,4,2,8,6,1,3,5]=>1101100
[6,8,1,7,2,3,4,5]=>0101000
[2,6,3,7,8,5,4,1]=>0100111
[2,5,3,7,8,1,6,4]=>0100101
[2,5,4,1,3,7,8,6]=>0110001
[3,1,5,4,7,8,2,6]=>1010010
[5,2,4,8,6,1,3,7]=>1001100
[4,8,1,3,6,7,2,5]=>0100010
[5,3,8,2,4,7,1,6]=>1010010
[5,4,3,8,1,2,7,6]=>1101001
[6,4,3,1,2,8,5,7]=>1110010
[6,4,2,8,1,3,7,5]=>1101001
[6,3,8,2,5,1,7,4]=>1010101
[6,3,8,1,4,7,2,5]=>1010010
[1,5,7,3,6,8,4,2]=>0010011
[1,5,7,4,2,6,8,3]=>0011001
[5,8,1,4,2,6,3,7]=>0101010
[6,5,1,2,8,7,3,4]=>1100110
[6,5,3,1,4,2,8,7]=>1110101
[5,3,1,6,4,2,7,8]=>1101100
[5,2,6,4,1,7,3,8]=>1011010
[4,6,1,7,5,2,8,3]=>0101101
[3,5,7,1,8,6,2,4]=>0010110
[3,6,2,7,5,1,8,4]=>0101101
[3,4,7,2,8,6,1,5]=>0010110
[3,4,5,8,2,7,1,6]=>0001010
[3,4,6,2,8,1,5,7]=>0010100
[3,5,2,6,8,1,7,4]=>0100101
[5,3,6,8,4,7,2,1]=>1001011
[3,7,2,5,4,8,6,1]=>0101011
[4,2,6,5,8,3,7,1]=>1010101
[4,1,6,5,8,3,2,7]=>1010110
[5,1,6,8,4,3,2,7]=>1001110
[6,7,8,1,4,3,2,5]=>0010110
[4,7,1,5,8,3,2,6]=>0100110
[8,3,1,5,4,7,2,6]=>1101010
[8,4,1,5,7,3,2,6]=>1100110
[8,4,6,1,7,3,2,5]=>1010110
[8,3,6,1,4,7,2,5]=>1010010
[8,2,6,1,4,3,7,5]=>1010101
[3,7,6,1,4,8,2,5]=>0110010
[6,7,8,5,1,3,2,4]=>0011010
[6,7,8,2,4,3,5,1]=>0010101
[4,7,6,2,8,3,5,1]=>0110101
[3,7,6,2,4,8,5,1]=>0110011
[5,7,3,8,4,6,2,1]=>0101011
[8,7,3,1,4,6,2,5]=>1110010
[8,7,6,3,2,5,4,1]=>1111011
[8,7,3,5,1,6,2,4]=>1101010
[8,7,2,5,1,3,6,4]=>1101001
[8,4,6,5,7,1,2,3]=>1010100
[4,7,6,5,8,1,2,3]=>0110100
[8,7,6,5,2,1,4,3]=>1111101
[3,6,4,8,7,5,1,2]=>0101110
[5,6,4,3,8,7,1,2]=>0110110
[1,6,2,4,7,8,5,3]=>0100011
[3,6,2,4,8,1,5,7]=>0100100
[3,4,7,2,8,1,6,5]=>0010101
[1,4,7,2,5,8,6,3]=>0010011
[3,8,7,5,4,6,1,2]=>0111010
[4,3,6,7,8,5,1,2]=>1000110
[3,5,6,4,8,7,1,2]=>0010110
[4,6,8,5,3,7,1,2]=>0011010
[4,2,7,5,1,8,6,3]=>1011011
[2,1,6,4,8,7,5,3]=>1010111
[7,8,1,4,2,6,5,3]=>0101011
[6,5,1,3,4,2,8,7]=>1100101
[4,8,5,3,1,7,2,6]=>0111010
[7,4,5,3,2,8,1,6]=>1011010
[5,8,3,6,1,4,2,7]=>0101010
[1,4,6,2,5,8,3,7]=>0010010
[1,6,8,7,4,2,3,5]=>0011100
[7,6,1,8,3,2,4,5]=>1101100
[7,1,8,6,3,4,2,5]=>1011010
[1,8,7,6,4,3,2,5]=>0111110
[2,1,7,5,6,3,8,4]=>1010101
[3,1,6,7,5,8,2,4]=>1001010
[7,8,1,6,5,3,2,4]=>0101110
[7,8,2,1,4,5,6,3]=>0110001
[4,2,6,1,8,5,7,3]=>1010101
[2,8,1,5,4,6,7,3]=>0101001
[1,2,8,3,6,5,7,4]=>0010101
[6,1,3,2,7,5,8,4]=>1010101
[2,6,4,1,7,5,8,3]=>0110101
[7,6,5,8,1,4,2,3]=>1101010
[5,8,6,7,3,2,1,4]=>0101110
[1,6,4,3,7,2,8,5]=>0110101
[4,6,3,8,1,2,7,5]=>0101001
[4,1,6,3,8,2,7,5]=>1010101
[7,8,1,3,4,2,6,5]=>0100101
[2,8,5,7,4,3,1,6]=>0101110
[7,2,5,8,3,4,1,6]=>1001010
[5,3,8,7,1,2,6,4]=>1011001
[6,5,3,8,2,1,7,4]=>1101101
[3,5,7,8,4,1,2,6]=>0001100
[5,4,7,3,6,8,1,2]=>1010010
[3,4,7,2,5,1,6,8]=>0010100
[1,4,7,2,5,8,3,6]=>0010010
[3,6,2,4,7,1,5,8]=>0100100
[7,6,3,5,4,8,1,2]=>1101010
[4,5,6,3,8,7,1,2]=>0010110
[6,3,7,5,8,4,1,2]=>1010110
[4,8,2,6,1,5,3,7]=>0101010
[4,3,6,2,5,1,8,7]=>1010101
[7,8,1,2,5,6,3,4]=>0100010
[4,1,6,2,5,7,3,8]=>1010010
[2,1,8,6,4,7,3,5]=>1011010
[7,1,3,6,8,4,2,5]=>1000110
[1,8,3,6,7,4,5,2]=>0100101
[7,1,5,8,3,6,2,4]=>1001010
[3,1,6,4,7,2,5,8]=>1010100
[5,8,7,1,2,4,3,6]=>0110010
[1,5,7,8,2,4,6,3]=>0001001
[6,8,5,1,3,4,2,7]=>0110010
[7,6,5,1,4,3,2,8]=>1110110
[2,6,4,5,1,3,8,7]=>0101001
[3,5,6,4,1,8,2,7]=>0011010
[7,8,5,4,1,3,2,6]=>0111010
[7,8,2,3,4,1,6,5]=>0100101
[4,2,6,3,8,1,7,5]=>1010101
[7,2,3,5,4,1,8,6]=>1001101
[6,2,4,3,1,5,7,8]=>1011000
[4,2,8,3,1,7,5,6]=>1011010
[1,3,7,4,8,2,5,6]=>0010100
[5,3,7,4,1,6,2,8]=>1011010
[2,4,7,3,6,1,8,5]=>0010101
[5,8,7,6,3,1,2,4]=>0111100
[7,5,6,8,1,4,3,2]=>1001011
[2,4,7,1,6,5,3,8]=>0010110
[5,2,7,1,8,4,6,3]=>1010101
[6,3,1,2,8,4,5,7]=>1100100
[4,2,1,3,6,5,8,7]=>1100101
[4,2,6,1,8,5,3,7]=>1010110
[7,8,2,1,4,5,3,6]=>0110010
[7,8,4,1,5,3,6,2]=>0110101
[7,5,1,6,4,3,8,2]=>1101101
[5,8,1,6,3,4,7,2]=>0101001
[6,8,1,7,5,2,3,4]=>0101100
[5,6,1,7,4,8,2,3]=>0101010
[7,8,5,1,6,4,2,3]=>0110110
[2,6,5,7,3,4,8,1]=>0101001
[1,6,4,7,5,8,2,3]=>0101010
[1,3,7,4,6,8,2,5]=>0010010
[5,2,4,7,3,6,8,1]=>1001001
[8,1,6,5,7,2,4,3]=>1010101
[7,1,6,5,8,3,2,4]=>1010110
[1,2,7,6,8,3,4,5]=>0010100
[3,8,6,4,2,7,5,1]=>0111011
[7,8,1,6,2,4,5,3]=>0101001
[2,8,1,7,4,3,6,5]=>0101101
[3,7,4,1,8,5,2,6]=>0110110
[6,7,1,4,8,3,2,5]=>0100110
[2,7,1,8,4,5,3,6]=>0101010
[6,1,2,8,4,3,5,7]=>1001100
[5,1,2,4,8,3,6,7]=>1000100
[4,1,3,2,8,5,6,7]=>1010100
[3,2,1,4,8,5,6,7]=>1100100
[4,3,6,1,5,8,2,7]=>1010010
[2,6,1,4,5,8,3,7]=>0100010
[1,6,2,5,8,3,4,7]=>0100100
[7,4,2,1,8,5,3,6]=>1110110
[1,5,4,2,8,3,6,7]=>0110100
[6,4,3,1,5,8,2,7]=>1110010
[5,4,3,2,1,8,6,7]=>1111010
[2,5,3,4,1,8,6,7]=>0101010
[4,3,5,2,1,8,6,7]=>1011010
[3,7,6,8,4,5,2,1]=>0101011
[1,7,6,8,5,4,2,3]=>0101110
[2,4,8,6,7,3,5,1]=>0010101
[3,4,8,5,6,7,2,1]=>0010011
[6,3,5,8,4,7,2,1]=>1001011
[5,4,3,8,6,7,2,1]=>1101011
[3,2,8,5,7,4,6,1]=>1010101
[2,1,8,7,4,6,3,5]=>1011010
[3,1,8,5,7,6,2,4]=>1010110
[6,1,5,8,7,4,2,3]=>1001110
[5,8,6,7,4,3,2,1]=>0101111
[4,8,7,5,6,3,2,1]=>0110111
[4,2,1,6,3,5,8,7]=>1101001
[6,2,1,4,3,8,5,7]=>1101010
[8,2,1,4,3,6,5,7]=>1101010
[6,2,4,1,3,8,5,7]=>1010010
[2,1,6,4,3,5,8,7]=>1011001
[6,4,2,1,3,5,8,7]=>1110001
[8,4,2,1,3,6,5,7]=>1110010
[8,4,2,1,6,3,5,7]=>1110100
[6,4,2,1,8,3,5,7]=>1110100
[4,6,2,1,3,8,5,7]=>0110010
[2,6,1,4,3,8,5,7]=>0101010
[2,1,6,4,3,8,5,7]=>1011010
[4,8,2,1,3,6,5,7]=>0110010
[6,8,2,1,4,3,5,7]=>0110100
[8,6,2,1,4,3,5,7]=>1110100
[2,8,1,4,6,3,5,7]=>0100100
[2,6,1,4,8,3,5,7]=>0100100
[2,6,4,1,8,3,5,7]=>0110100
[2,6,4,8,1,3,5,7]=>0101000
[4,2,6,1,8,3,5,7]=>1010100
[6,2,4,1,8,3,5,7]=>1010100
[4,2,1,6,8,3,5,7]=>1100100
[4,2,1,6,3,8,5,7]=>1101010
[4,2,1,3,6,8,5,7]=>1100010
[2,1,4,3,8,6,5,7]=>1010110
[2,4,1,3,8,6,5,7]=>0100110
[4,2,1,3,8,6,5,7]=>1100110
[4,2,1,8,3,6,5,7]=>1101010
[4,2,1,8,6,3,5,7]=>1101100
[8,2,1,6,4,3,5,7]=>1101100
[4,2,8,1,6,3,5,7]=>1010100
[2,4,1,8,3,6,5,7]=>0101010
[2,1,4,8,3,6,5,7]=>1001010
[2,4,8,1,6,3,5,7]=>0010100
[2,4,8,6,1,3,5,7]=>0011000
[4,2,8,6,1,3,5,7]=>1011000
[2,1,8,6,4,3,5,7]=>1011100
[2,8,6,1,4,3,5,7]=>0110100
[2,8,6,4,1,3,5,7]=>0111000
[4,8,6,2,1,3,5,7]=>0111000
[3,2,6,1,5,4,8,7]=>1010101
[6,1,5,2,4,3,8,7]=>1010101
[6,1,3,2,5,4,8,7]=>1010101
[4,3,6,1,5,2,8,7]=>1010101
[4,3,5,2,8,1,7,6]=>1010101
[4,3,7,2,6,5,8,1]=>1010101
[4,3,8,2,6,1,7,5]=>1010101
[4,3,8,1,5,2,7,6]=>1010101
[5,4,7,6,8,1,3,2]=>1010101
[4,3,7,1,8,5,6,2]=>1010101
[4,3,6,5,8,1,7,2]=>1010101
[6,3,5,4,7,2,8,1]=>1010101
[6,3,5,4,8,1,7,2]=>1010101
[7,1,6,3,8,4,5,2]=>1010101
[7,1,6,5,8,3,4,2]=>1010101
[7,4,6,5,8,1,3,2]=>1010101
[8,4,6,1,3,2,7,5]=>1010101
[8,1,6,3,4,2,7,5]=>1010101
[8,3,5,2,6,1,7,4]=>1010101
[7,3,5,2,6,4,8,1]=>1010101
[8,2,7,1,5,3,6,4]=>1010101
[8,1,7,2,4,3,6,5]=>1010101
[8,1,3,2,7,4,6,5]=>1010101
[2,1,8,3,7,4,6,5]=>1010101
[2,1,8,3,5,4,7,6]=>1010101
[8,1,3,2,5,4,7,6]=>1010101
[8,1,5,2,4,3,7,6]=>1010101
[8,2,4,1,5,3,7,6]=>1010101
[8,2,4,1,7,3,6,5]=>1010101
[3,2,8,4,6,1,7,5]=>1010101
[3,2,8,1,7,4,6,5]=>1010101
[3,2,8,1,5,4,7,6]=>1010101
[3,2,4,1,8,5,7,6]=>1010101
[4,1,3,2,7,6,8,5]=>1010101
[3,2,7,6,8,1,5,4]=>1010101
[3,2,7,1,8,5,6,4]=>1010101
[3,2,6,5,8,1,7,4]=>1010101
[7,2,4,1,8,5,6,3]=>1010101
[7,6,8,1,5,2,4,3]=>1010101
[7,6,8,1,3,2,5,4]=>1010101
[7,1,8,5,6,2,4,3]=>1010101
[7,1,8,2,6,4,5,3]=>1010101
[7,2,8,1,5,4,6,3]=>1010101
[5,4,7,2,6,3,8,1]=>1010101
[5,4,8,2,6,1,7,3]=>1010101
[6,1,8,4,7,2,5,3]=>1010101
[6,5,8,1,3,2,7,4]=>1010101
[6,5,7,4,8,1,3,2]=>1010101
[5,4,6,3,8,1,7,2]=>1010101
[3,2,1,5,8,4,6,7]=>1100100
[2,4,8,3,5,7,6,1]=>0010011
[4,2,5,3,1,8,6,7]=>1011010
[1,8,4,2,5,3,6,7]=>0110100
[8,1,5,3,2,4,6,7]=>1011000
[3,8,1,5,2,4,6,7]=>0101000
[5,4,1,3,8,2,6,7]=>1100100
[1,5,7,3,8,4,2,6]=>0010110
[5,1,4,7,8,3,2,6]=>1000110
[8,1,5,3,7,4,6,2]=>1010101
[1,4,3,8,7,5,6,2]=>0101101
[1,6,8,5,3,7,4,2]=>0011011
[6,4,8,1,7,3,5,2]=>1010101
[6,4,8,7,1,5,2,3]=>1011010
[7,1,6,8,4,3,2,5]=>1001110
[1,6,7,2,8,4,3,5]=>0010110
[6,7,1,4,2,8,3,5]=>0101010
[6,3,7,1,4,8,2,5]=>1010010
[3,7,8,1,5,2,4,6]=>0010100
[7,1,2,8,5,3,4,6]=>1001100
[1,7,2,8,4,5,3,6]=>0101010
[4,2,1,7,8,5,3,6]=>1100110
[6,2,4,8,3,7,5,1]=>1001011
[7,2,6,3,4,1,8,5]=>1010101
[2,7,1,8,3,5,4,6]=>0101010
[2,1,7,3,5,8,4,6]=>1010010
[1,2,7,5,8,3,4,6]=>0010100
[8,7,1,3,6,2,4,5]=>1100100
[8,2,1,7,3,5,6,4]=>1101001
[2,7,8,4,1,6,5,3]=>0011011
[2,8,4,1,6,7,5,3]=>0110011
[2,1,8,4,7,5,6,3]=>1010101
[8,3,7,1,5,6,2,4]=>1010010
[8,6,1,2,7,5,3,4]=>1100110
[8,1,6,2,7,4,5,3]=>1010101
[1,8,5,2,6,7,4,3]=>0110011
[5,2,1,8,6,7,4,3]=>1101011
[8,7,6,5,1,4,2,3]=>1111010
[8,7,6,1,5,3,4,2]=>1110101
[8,1,7,5,6,4,3,2]=>1010111
[1,8,6,7,5,4,3,2]=>0101111
[6,3,5,2,1,4,8,7]=>1011001
[8,3,5,7,2,4,1,6]=>1001010
[8,5,2,7,4,3,1,6]=>1101110
[6,5,3,1,2,4,8,7]=>1110001
[4,5,3,6,1,2,8,7]=>0101001
[3,5,1,4,6,2,8,7]=>0100101
[8,1,4,7,3,6,2,5]=>1001010
[8,5,1,4,7,3,2,6]=>1100110
[8,5,3,7,1,4,2,6]=>1101010
[6,3,4,7,5,8,1,2]=>1001010
[5,1,4,6,8,3,7,2]=>1000101
[4,7,1,3,5,8,6,2]=>0100011
[4,8,3,7,1,2,6,5]=>0101001
[8,7,1,4,2,6,3,5]=>1101010
[8,6,3,1,2,4,7,5]=>1110001
[2,1,8,7,5,3,4,6]=>1011100
[8,1,7,4,5,2,3,6]=>1010100
[2,8,7,5,4,1,3,6]=>0111100
[8,7,2,6,4,1,3,5]=>1101100
[5,3,7,8,2,4,6,1]=>1001001
[5,3,7,6,2,1,8,4]=>1011101
[5,7,8,6,4,2,1,3]=>0011110
[2,6,7,5,4,8,1,3]=>0011010
[6,7,3,5,1,8,2,4]=>0101010
[2,1,6,7,5,8,3,4]=>1001010
[2,1,5,7,3,6,8,4]=>1001001
[4,1,7,2,5,6,8,3]=>1010001
[2,4,7,1,6,5,8,3]=>0010101
[3,4,6,2,7,8,5,1]=>0010011
[4,6,1,2,5,8,7,3]=>0100011
[5,6,3,1,8,7,2,4]=>0110110
[3,5,6,4,7,1,8,2]=>0010101
[3,4,6,1,5,7,8,2]=>0010001
[3,4,1,5,7,6,8,2]=>0100101
[4,2,1,7,3,5,8,6]=>1101001
[7,3,1,5,4,2,8,6]=>1101101
[6,3,1,4,2,8,5,7]=>1101010
[8,4,1,5,2,7,6,3]=>1101011
[7,2,5,1,4,3,8,6]=>1010101
[3,6,2,7,1,4,8,5]=>0101001
[2,7,5,4,1,3,8,6]=>0111001
[6,4,3,2,1,8,5,7]=>1111010
[1,7,6,2,4,8,3,5]=>0110010
[2,7,3,6,4,8,1,5]=>0101010
[6,2,7,5,3,8,1,4]=>1011010
[7,1,8,5,3,6,4,2]=>1011011
[5,8,3,2,7,1,6,4]=>0110101
[8,7,2,6,1,5,4,3]=>1101011
[1,8,5,7,4,3,6,2]=>0101101
[1,8,5,7,2,4,6,3]=>0101001
[3,8,6,1,7,2,5,4]=>0110101
[7,2,8,5,6,1,4,3]=>1010101
[3,6,5,8,1,4,2,7]=>0101010
[4,3,6,8,2,1,5,7]=>1001100
[4,3,6,7,8,1,2,5]=>1000100
[5,4,6,7,2,8,1,3]=>1001010
[3,5,7,1,4,8,2,6]=>0010010
[8,1,5,2,7,4,6,3]=>1010101
[8,4,1,5,7,3,6,2]=>1100101
[6,4,2,5,8,3,1,7]=>1100110
[5,4,1,6,8,2,3,7]=>1100100
[5,3,1,7,2,8,4,6]=>1101010
[5,3,6,4,7,8,1,2]=>1010010
[6,3,7,4,8,5,2,1]=>1010111
[4,7,2,5,8,6,3,1]=>0100111
[6,3,1,8,4,7,5,2]=>1101011
[5,4,8,1,7,6,2,3]=>1010110
[5,2,8,1,7,3,6,4]=>1010101
[5,7,3,8,1,6,4,2]=>0101011
[6,4,7,8,1,5,3,2]=>1001011
[4,6,8,2,7,1,5,3]=>0010101
[2,5,8,7,1,3,6,4]=>0011001
[8,3,7,6,1,5,4,2]=>1011011
[8,2,7,6,5,1,4,3]=>1011101
[4,3,8,7,6,2,1,5]=>1011110
[2,4,8,7,6,1,3,5]=>0011100
[3,5,8,7,2,6,1,4]=>0011010
[4,7,3,8,6,5,1,2]=>0101110
[7,5,8,6,4,3,2,1]=>1011111
[5,8,7,3,6,4,2,1]=>0110111
[3,8,7,6,5,1,4,2]=>0111101
[2,8,7,6,5,4,1,3]=>0111110
[7,8,5,6,3,1,4,2]=>0101101
[7,8,5,3,6,1,2,4]=>0110100
[7,5,6,3,1,4,2,8]=>1011010
[7,5,8,3,1,4,2,6]=>1011010
[7,8,5,3,1,4,2,6]=>0111010
[7,8,5,3,1,6,2,4]=>0111010
[7,8,5,3,1,6,4,2]=>0111011
[7,8,5,3,6,1,4,2]=>0110101
[7,8,5,3,6,4,1,2]=>0110110
[7,8,5,3,4,1,6,2]=>0110101
[7,8,5,3,1,4,6,2]=>0111001
[7,5,8,3,1,2,6,4]=>1011001
[7,5,8,3,4,1,6,2]=>1010101
[7,5,8,3,4,6,1,2]=>1010010
[7,5,6,3,4,1,8,2]=>1010101
[7,5,6,3,1,4,8,2]=>1011001
[7,5,3,1,6,4,8,2]=>1110101
[7,5,3,6,1,4,8,2]=>1101001
[7,5,3,6,4,1,8,2]=>1101101
[7,5,3,6,4,8,1,2]=>1101010
[7,5,3,8,4,6,1,2]=>1101010
[7,5,3,8,4,1,6,2]=>1101101
[7,5,3,8,1,4,6,2]=>1101001
[7,5,3,1,8,4,6,2]=>1110101
[7,5,3,1,8,2,6,4]=>1110101
[7,5,3,1,6,2,4,8]=>1110100
[7,5,3,1,6,4,2,8]=>1110110
[7,5,3,1,8,4,2,6]=>1110110
[7,5,3,1,8,6,2,4]=>1110110
[7,5,3,8,1,6,4,2]=>1101011
[7,5,3,8,6,1,4,2]=>1101101
[7,5,3,8,6,4,1,2]=>1101110
[7,5,8,3,6,4,1,2]=>1010110
[7,5,8,3,6,1,4,2]=>1010101
[7,5,8,3,1,6,4,2]=>1011011
[7,5,8,3,1,6,2,4]=>1011010
[7,5,3,8,1,6,2,4]=>1101010
[7,5,3,8,1,4,2,6]=>1101010
[7,5,3,6,1,4,2,8]=>1101010
[7,5,3,6,4,1,2,8]=>1101100
[7,5,3,8,4,1,2,6]=>1101100
[7,5,3,8,6,1,2,4]=>1101100
[7,5,8,6,3,1,2,4]=>1011100
[7,5,8,6,3,1,4,2]=>1011101
[7,5,8,6,3,4,1,2]=>1011010
[7,5,6,8,3,1,4,2]=>1001101
[7,5,6,3,8,1,2,4]=>1010100
[7,5,3,6,1,8,2,4]=>1101010
[7,5,6,3,1,8,2,4]=>1011010
[7,5,6,3,1,8,4,2]=>1011011
[7,5,6,3,8,1,4,2]=>1010101
[7,5,6,3,8,4,1,2]=>1010110
[7,5,3,6,8,4,1,2]=>1100110
[7,5,3,6,8,1,4,2]=>1100101
[7,5,3,6,1,8,4,2]=>1101011
[7,5,3,1,6,8,4,2]=>1110011
[7,5,3,1,6,8,2,4]=>1110010
[7,5,3,1,2,8,6,4]=>1110011
[7,5,3,4,1,6,8,2]=>1101001
[4,6,8,3,5,7,1,2]=>0010010
[6,8,1,2,4,5,7,3]=>0100001
[3,6,8,2,5,7,1,4]=>0010010
[8,3,5,2,4,1,6,7]=>1010100
[3,5,7,2,4,6,1,8]=>0010010
[4,2,5,7,3,6,1,8]=>1001010
[4,5,2,8,3,1,6,7]=>0101100
[2,1,6,8,4,7,3,5]=>1001010
[1,2,5,8,3,6,7,4]=>0001001
[5,3,6,8,4,7,1,2]=>1001010
[3,1,2,6,8,5,7,4]=>1000101
[4,3,6,2,7,5,1,8]=>1010110
[4,3,1,7,8,2,6,5]=>1100101
[5,4,7,3,8,6,1,2]=>1010110
[5,8,4,7,6,3,1,2]=>0101110
[8,3,5,1,2,7,6,4]=>1010011
[4,7,3,6,5,2,1,8]=>0101110
[5,3,7,6,4,2,1,8]=>1011110
[5,3,1,6,4,2,8,7]=>1101101
[1,3,8,5,4,2,7,6]=>0011101
[1,8,3,6,2,7,5,4]=>0101011
[1,6,8,7,4,2,5,3]=>0011101
[6,4,8,7,5,3,1,2]=>1011110
[3,1,2,7,6,4,8,5]=>1001101
[5,2,6,3,7,4,1,8]=>1010110
[2,8,5,3,1,6,4,7]=>0111010
[2,1,7,3,8,5,4,6]=>1010110
[1,6,2,3,7,8,5,4]=>0100011
[1,6,7,2,8,4,5,3]=>0010101
[6,3,7,4,8,5,1,2]=>1010110
[5,7,1,8,2,4,6,3]=>0101001
[5,1,2,7,8,3,6,4]=>1000101
[4,2,1,7,3,8,5,6]=>1101010
[6,2,8,4,3,1,5,7]=>1011100
[6,4,2,7,3,5,1,8]=>1101010
[7,3,2,1,8,4,5,6]=>1110100
[3,7,2,8,6,1,4,5]=>0101100
[7,8,3,2,5,6,1,4]=>0110010
[7,1,8,2,4,5,6,3]=>1010001
[8,7,6,1,2,4,5,3]=>1110001
[8,3,6,5,2,1,4,7]=>1011100
[8,2,4,1,6,5,3,7]=>1010110
[8,2,4,1,7,6,3,5]=>1010110
[8,5,1,2,7,3,6,4]=>1100101
[6,1,8,2,3,7,5,4]=>1010011
[2,8,1,7,5,4,3,6]=>0101110
[1,7,2,8,3,6,5,4]=>0101011
[7,3,8,6,5,4,1,2]=>1011110
[1,8,7,6,5,2,4,3]=>0111101
[8,1,7,3,2,6,5,4]=>1011011
[4,3,1,2,8,7,6,5]=>1100111
[5,1,4,3,2,8,7,6]=>1011011
[8,6,4,3,1,5,7,2]=>1111001
[8,6,4,1,5,2,7,3]=>1110101
[8,6,5,3,2,1,7,4]=>1111101
[8,7,2,4,5,3,1,6]=>1100110
[8,5,1,2,6,7,3,4]=>1100010
[8,5,1,6,4,2,7,3]=>1101101
[8,5,1,3,6,4,7,2]=>1100101
[8,6,5,1,7,3,2,4]=>1110110
[7,4,8,3,1,6,2,5]=>1011010
[7,1,5,8,3,2,6,4]=>1001101
[5,7,4,1,8,2,6,3]=>0110101
[5,7,4,3,1,8,6,2]=>0111011
[8,5,7,4,6,1,3,2]=>1010101
[1,8,7,2,5,4,6,3]=>0110101
[4,3,1,8,7,5,2,6]=>1101110
[1,3,5,6,8,4,2,7]=>0000110
[3,1,4,6,8,7,2,5]=>1000110
[1,6,3,8,7,2,5,4]=>0101101
[1,6,2,4,8,7,5,3]=>0100111
[8,4,1,6,7,5,3,2]=>1100111
[7,3,6,8,5,1,2,4]=>1001100
[1,3,7,2,6,8,4,5]=>0010010
[3,6,5,2,8,1,4,7]=>0110100
[6,1,2,7,8,5,3,4]=>1000110
[6,1,2,7,4,8,5,3]=>1001011
[3,1,6,4,7,8,5,2]=>1010011
[5,7,1,3,8,4,6,2]=>0100101
[5,7,1,8,4,2,6,3]=>0101101
[5,7,1,2,8,6,3,4]=>0100110
[4,2,6,3,8,1,5,7]=>1010100
[4,2,6,7,3,5,1,8]=>1001010
[3,6,2,4,7,5,1,8]=>0100110
[3,6,2,4,1,8,5,7]=>0101010
[7,1,4,5,2,8,6,3]=>1001011
[4,7,3,1,5,8,6,2]=>0110011
[8,7,6,4,1,5,2,3]=>1111010
[3,8,2,7,1,5,4,6]=>0101010
[3,6,8,2,1,5,4,7]=>0011010
[2,4,8,1,6,5,3,7]=>0010110
[4,2,8,1,5,7,3,6]=>1010010
[8,5,7,6,1,4,2,3]=>1011010
[1,8,2,4,6,7,3,5]=>0100010
[2,1,5,8,6,4,3,7]=>1001110
[1,2,5,7,8,4,3,6]=>0000110
[1,2,7,4,8,6,3,5]=>0010110
[1,2,7,8,3,6,5,4]=>0001011
[1,8,5,7,4,3,2,6]=>0101110
[1,6,8,5,4,3,2,7]=>0011110
[7,1,5,8,3,4,6,2]=>1001001
[7,1,5,8,4,3,2,6]=>1001110
[7,1,2,5,8,3,6,4]=>1000101
[7,1,6,4,2,3,5,8]=>1011000
[2,7,1,4,8,3,5,6]=>0100100
[7,1,4,6,5,8,3,2]=>1001011
[7,1,2,3,8,5,4,6]=>1000110
[7,1,5,4,3,8,2,6]=>1011010
[7,1,3,4,2,6,8,5]=>1001001
[3,6,7,1,4,8,5,2]=>0010011
[3,5,1,4,8,6,2,7]=>0100110
[3,6,2,4,7,8,1,5]=>0100010
[5,6,2,4,8,7,1,3]=>0100110
[6,5,8,7,2,3,1,4]=>1011010
[3,4,7,2,5,8,1,6]=>0010010
[4,3,8,1,2,7,5,6]=>1010010
[5,6,7,8,1,3,4,2]=>0001001
[5,7,8,6,1,2,3,4]=>0011000
[2,8,3,1,5,6,4,7]=>0110010
[3,8,7,1,5,4,2,6]=>0110110
[4,3,1,7,6,8,2,5]=>1101010
[3,4,1,7,5,6,8,2]=>0101001
[3,4,1,5,7,6,2,8]=>0100110
[2,4,6,1,7,5,8,3]=>0010101
[4,7,8,1,2,3,6,5]=>0010001
[4,2,1,5,6,3,7,8]=>1100100
[5,8,1,6,4,3,2,7]=>0101110
[5,8,1,6,3,7,2,4]=>0101010
[7,6,5,1,3,8,2,4]=>1110010
[7,6,5,1,3,4,8,2]=>1110001
[7,2,6,4,1,3,8,5]=>1011001
[8,4,5,3,7,2,6,1]=>1010101
[4,7,5,2,8,1,6,3]=>0110101
[4,6,3,8,5,1,7,2]=>0101101
[2,6,4,3,1,5,7,8]=>0111000
[3,6,4,8,1,7,2,5]=>0101010
[7,3,8,4,1,5,2,6]=>1011010
[4,2,8,3,6,1,5,7]=>1010100
[6,7,5,8,2,1,4,3]=>0101101
[6,8,5,7,2,1,3,4]=>0101100
[4,8,5,2,7,1,3,6]=>0110100
[6,3,5,2,1,7,4,8]=>1011010
[3,6,5,4,2,8,1,7]=>0111010
[7,4,5,3,8,2,1,6]=>1010110
[1,6,4,7,2,5,3,8]=>0101010
[1,4,3,7,2,6,5,8]=>0101010
[1,5,7,2,4,8,3,6]=>0010010
[1,6,5,7,2,4,3,8]=>0101010
[1,7,6,2,8,3,4,5]=>0110100
[1,4,2,3,5,8,7,6]=>0100011
[1,5,2,3,4,8,7,6]=>0100011
[1,6,5,2,3,8,7,4]=>0110011
[1,7,6,5,2,8,4,3]=>0111011
[1,6,5,2,3,8,4,7]=>0110010
[1,6,7,5,2,3,8,4]=>0011001
[1,7,5,2,8,4,3,6]=>0110110
[1,7,5,6,2,8,3,4]=>0101010
[1,5,7,6,2,4,8,3]=>0011001
[1,4,7,6,2,5,8,3]=>0011001
[1,2,6,5,3,7,4,8]=>0011010
[1,3,7,5,2,6,8,4]=>0011001
[1,7,4,6,2,8,3,5]=>0101010
[1,7,3,5,2,8,4,6]=>0101010
[1,3,7,4,2,6,8,5]=>0011001
[1,4,7,3,2,5,8,6]=>0011001
[1,5,7,3,2,4,8,6]=>0011001
[1,7,3,4,2,8,5,6]=>0101010
[1,7,4,2,8,5,3,6]=>0110110
[1,6,7,4,2,3,8,5]=>0011001
[1,4,3,2,5,8,6,7]=>0110010
[1,5,3,2,4,8,6,7]=>0110010
[1,6,4,2,3,8,5,7]=>0110010
[1,7,6,4,2,8,5,3]=>0111011
[1,7,5,3,2,8,6,4]=>0111011
[1,6,4,2,3,8,7,5]=>0110011
[1,5,3,2,4,8,7,6]=>0110011
[6,8,5,4,3,2,1,7]=>0111110
[2,8,5,4,3,7,1,6]=>0111010
[7,6,1,4,3,8,5,2]=>1101011
[7,6,5,1,3,8,4,2]=>1110011
[7,3,5,4,8,1,6,2]=>1010101
[5,6,8,4,3,1,7,2]=>0011101
[6,8,5,4,1,2,7,3]=>0111001
[6,8,2,4,3,7,1,5]=>0101010
[1,8,3,4,7,2,6,5]=>0100101
[7,5,8,4,3,2,1,6]=>1011110
[4,8,5,7,3,2,1,6]=>0101110
[7,8,1,2,4,3,5,6]=>0100100
[7,8,2,1,4,3,6,5]=>0110101
[3,4,6,5,7,8,1,2]=>0010010
[4,3,6,5,8,7,1,2]=>1010110
[4,2,6,1,8,3,7,5]=>1010101
[6,7,3,8,4,5,1,2]=>0101010
[6,7,4,5,1,8,2,3]=>0101010
[4,5,3,8,6,7,1,2]=>0101010
[5,6,3,8,4,7,1,2]=>0101010
[5,6,4,7,1,8,2,3]=>0101010
[5,6,2,7,3,4,1,8]=>0101010
[4,5,1,8,6,7,2,3]=>0101010
[7,8,4,5,1,6,2,3]=>0101010
[4,5,2,3,1,8,6,7]=>0101010
[5,6,2,3,1,8,4,7]=>0101010
[5,6,3,4,1,8,2,7]=>0101010
[3,6,4,5,2,7,1,8]=>0101010
[3,6,4,5,1,8,2,7]=>0101010
[2,6,4,8,1,5,3,7]=>0101010
[2,8,3,6,1,5,4,7]=>0101010
[2,8,3,4,1,6,5,7]=>0101010
[7,8,1,5,3,6,2,4]=>0101010
[1,8,3,6,5,7,2,4]=>0101010
[1,6,4,7,3,8,2,5]=>0101010
[1,7,3,6,4,8,2,5]=>0101010
[1,7,2,8,4,6,3,5]=>0101010
[1,7,5,8,2,6,3,4]=>0101010
[6,7,1,5,3,8,2,4]=>0101010
[6,7,1,8,2,5,3,4]=>0101010
[6,7,1,8,4,5,2,3]=>0101010
[6,7,5,8,1,4,2,3]=>0101010
[5,8,6,7,2,3,1,4]=>0101010
[6,7,2,3,1,8,4,5]=>0101010
[6,7,2,8,1,4,3,5]=>0101010
[6,7,3,4,1,8,2,5]=>0101010
[3,4,2,7,5,6,1,8]=>0101010
[2,7,5,8,1,4,3,6]=>0101010
[2,3,1,8,4,7,5,6]=>0101010
[2,3,1,8,6,7,4,5]=>0101010
[7,8,2,3,1,6,4,5]=>0101010
[2,8,1,4,3,7,5,6]=>0101010
[2,8,1,7,3,5,4,6]=>0101010
[4,5,1,7,3,8,2,6]=>0101010
[3,8,1,5,2,7,4,6]=>0101010
[3,4,1,8,6,7,2,5]=>0101010
[7,8,3,4,1,6,2,5]=>0101010
[3,4,2,5,1,8,6,7]=>0101010
[3,4,2,8,1,6,5,7]=>0101010
[2,5,4,1,6,3,8,7]=>0110101
[3,6,5,1,2,4,8,7]=>0110001
[5,2,3,6,4,1,8,7]=>1001101
[6,1,4,5,3,2,8,7]=>1001101
[5,6,7,8,1,4,3,2]=>0001011
[4,2,6,8,5,7,3,1]=>1001011
[2,1,5,8,7,6,3,4]=>1001110
[2,1,4,7,6,3,8,5]=>1001101
[6,3,7,1,5,2,8,4]=>1010101
[4,2,8,6,7,3,1,5]=>1010110
[7,4,3,8,2,1,5,6]=>1101100
[2,4,1,5,8,3,7,6]=>0100101
[4,7,5,8,1,6,3,2]=>0101011
[2,1,5,8,7,3,4,6]=>1001100
[8,5,7,3,6,1,4,2]=>1010101
[4,2,5,1,6,7,8,3]=>1010001
[7,2,3,4,8,5,6,1]=>1000101
[6,1,8,5,2,7,4,3]=>1011011
[2,1,7,4,5,8,6,3]=>1010011
[2,1,8,3,6,7,5,4]=>1010011
[6,8,7,2,5,3,1,4]=>0110110
[8,2,1,6,4,7,5,3]=>1101011
[7,8,4,2,5,1,6,3]=>0110101
[6,1,2,3,7,5,8,4]=>1000101
[7,6,8,4,2,5,3,1]=>1011011
[8,5,7,1,6,3,2,4]=>1010110
[4,1,2,3,7,6,8,5]=>1000101
[3,2,4,1,8,5,6,7]=>1010100
[3,4,8,6,5,2,1,7]=>0011110
[4,1,6,3,5,8,7,2]=>1010011
[8,6,7,1,5,4,3,2]=>1010111
[2,1,6,5,8,4,7,3]=>1010101
[4,1,8,5,6,2,3,7]=>1010100
[2,6,4,8,7,3,5,1]=>0101101
[3,1,8,2,7,5,4,6]=>1010110
[8,2,3,1,7,4,6,5]=>1010101
[7,4,8,6,3,2,5,1]=>1011101
[5,8,4,7,2,1,3,6]=>0101100
[2,1,8,4,3,7,5,6]=>1011010
[6,3,8,2,4,5,7,1]=>1010001
[5,8,2,4,3,1,6,7]=>0101100
[7,3,5,8,1,4,2,6]=>1001010
[3,8,7,6,1,4,2,5]=>0111010
[5,1,8,3,6,7,2,4]=>1010010
[3,6,1,4,7,8,5,2]=>0100011
[1,6,8,4,7,5,2,3]=>0010110
[6,8,1,3,5,7,2,4]=>0100010
[7,6,1,4,3,8,2,5]=>1101010
[8,4,2,6,7,5,3,1]=>1100111
[7,4,1,6,8,2,5,3]=>1100101
[1,8,6,2,5,3,4,7]=>0110100
[4,7,1,2,5,3,8,6]=>0100101
[8,7,3,6,4,5,2,1]=>1101011
[5,7,8,6,2,1,4,3]=>0011101
[1,8,6,4,5,2,3,7]=>0110100
[1,4,7,2,6,8,3,5]=>0010010
[2,5,4,3,6,8,1,7]=>0110010
[3,8,5,4,6,2,1,7]=>0110110
[4,8,2,1,3,7,5,6]=>0110010
[1,8,3,2,5,6,7,4]=>0110001
[6,4,1,2,7,5,8,3]=>1100101
[4,3,7,8,5,1,6,2]=>1001101
[1,2,7,3,6,5,8,4]=>0010101
[2,8,7,6,3,4,1,5]=>0111010
[5,8,2,6,3,4,1,7]=>0101010
[4,1,7,5,8,6,2,3]=>1010110
[1,2,4,5,8,3,7,6]=>0000101
[4,8,1,5,2,3,7,6]=>0101001
[2,4,6,3,7,1,8,5]=>0010101
[6,5,8,7,1,3,4,2]=>1011001
[3,6,7,2,4,8,1,5]=>0010010
[1,5,2,7,4,3,8,6]=>0101101
[7,6,1,2,8,3,5,4]=>1100101
[6,7,8,1,5,2,4,3]=>0010101
[5,7,8,4,1,2,6,3]=>0011001
[4,7,8,5,6,1,3,2]=>0010101
[5,6,4,8,1,2,7,3]=>0101001
[6,5,4,1,2,3,8,7]=>1110001
[7,5,1,6,2,3,8,4]=>1101001
[4,5,6,7,8,1,3,2]=>0000101
[8,1,3,6,7,4,5,2]=>1000101
[4,2,6,7,3,1,8,5]=>1001101
[7,3,1,5,4,8,2,6]=>1101010
[4,5,3,2,8,1,6,7]=>0110100
[7,4,1,5,3,2,6,8]=>1101100
[8,1,5,4,3,2,6,7]=>1011100
[8,1,6,4,2,5,3,7]=>1011010
[6,5,3,1,2,7,4,8]=>1110010
[5,6,3,8,1,4,2,7]=>0101010
[4,6,3,8,2,1,5,7]=>0101100
[4,7,8,3,2,1,5,6]=>0011100
[5,7,8,3,1,4,2,6]=>0011010
[8,1,7,2,5,4,3,6]=>1010110
[8,1,7,2,4,5,6,3]=>1010001
[7,6,1,2,4,5,8,3]=>1100001
[4,7,8,2,3,1,6,5]=>0010101
[7,5,1,3,2,6,8,4]=>1101001
[8,1,6,3,2,5,7,4]=>1011001
[8,1,5,3,4,2,7,6]=>1010101
[5,4,2,3,1,6,8,7]=>1101001
[6,3,2,1,5,7,4,8]=>1110010
[8,1,4,3,5,6,2,7]=>1010010
[3,6,5,8,2,4,1,7]=>0101010
[6,2,4,5,8,3,1,7]=>1000110
[4,8,1,2,5,6,3,7]=>0100010
[8,1,3,5,2,6,4,7]=>1001010
[5,2,1,6,3,8,4,7]=>1101010
[6,1,4,5,8,3,2,7]=>1000110
[6,5,4,3,8,2,1,7]=>1110110
[4,6,8,3,7,2,5,1]=>0010101
[1,4,3,6,2,7,8,5]=>0101001
[4,7,8,5,3,1,2,6]=>0011100
[8,5,7,4,3,6,1,2]=>1011010
[4,7,8,3,6,1,5,2]=>0010101
[8,4,6,1,7,3,5,2]=>1010101
[1,3,8,6,4,7,5,2]=>0011011
[7,6,2,1,4,3,8,5]=>1110101
[7,6,8,1,4,3,2,5]=>1010110
[1,5,7,3,2,6,8,4]=>0011001
[3,2,6,8,5,7,4,1]=>1001011
[7,5,2,3,1,6,8,4]=>1101001
[1,6,4,7,2,3,8,5]=>0101001
[3,1,7,5,2,8,4,6]=>1011010
[1,7,4,5,2,8,3,6]=>0101010
[3,2,6,8,7,4,5,1]=>1001101
[6,3,2,1,7,8,4,5]=>1110010
[5,7,3,8,2,1,4,6]=>0101100
[3,7,1,8,4,2,5,6]=>0101100
[4,2,1,3,7,5,8,6]=>1100101
[8,4,3,7,6,2,1,5]=>1101110
[3,6,2,8,7,1,5,4]=>0101101
[7,3,2,8,1,6,5,4]=>1101011
[3,8,7,2,6,5,4,1]=>0110111
[4,2,7,8,6,1,5,3]=>1001101
[5,8,4,2,7,1,6,3]=>0110101
[8,5,3,1,7,2,6,4]=>1110101
[8,2,1,6,3,7,5,4]=>1101011
[1,4,6,8,2,7,5,3]=>0001011
[2,1,7,3,8,6,5,4]=>1010111
[8,2,1,7,6,5,4,3]=>1101111
[8,6,7,5,1,4,3,2]=>1011011
[6,4,7,3,2,1,8,5]=>1011101
[4,8,7,3,2,1,6,5]=>0111101
[6,5,3,7,2,1,4,8]=>1101100
[5,8,3,6,2,1,4,7]=>0101100
[6,4,3,7,2,1,8,5]=>1101101
[4,8,3,6,2,1,7,5]=>0101101
[6,3,7,8,2,1,4,5]=>1001100
[5,3,7,6,2,1,4,8]=>1011100
[3,8,7,6,2,1,4,5]=>0111100
[5,8,4,2,6,1,3,7]=>0110100
[4,8,7,2,5,1,3,6]=>0110100
[5,8,3,2,6,1,4,7]=>0110100
[4,8,3,2,5,1,7,6]=>0110101
[4,3,7,2,5,1,8,6]=>1010101
[6,4,2,7,5,1,3,8]=>1101100
[5,4,2,6,7,1,3,8]=>1100100
[6,2,7,8,5,1,3,4]=>1001100
[2,8,7,6,5,1,3,4]=>0111100
[6,4,7,3,1,5,8,2]=>1011001
[4,8,7,3,1,5,6,2]=>0111001
[6,5,3,7,1,4,8,2]=>1101001
[5,8,3,6,1,4,7,2]=>0101001
[6,4,3,7,1,5,8,2]=>1101001
[4,8,3,6,1,5,7,2]=>0101001
[5,3,7,6,1,4,8,2]=>1011001
[4,3,7,6,1,5,8,2]=>1011001
[3,8,7,6,1,4,5,2]=>0111001
[5,8,4,2,1,7,3,6]=>0111010
[6,4,7,2,1,5,3,8]=>1011010
[5,8,3,2,1,4,7,6]=>0111001
[6,3,7,2,1,4,5,8]=>1011000
[6,5,2,7,1,4,3,8]=>1101010
[5,8,2,6,1,4,3,7]=>0101010
[6,4,2,7,1,5,3,8]=>1101010
[2,8,7,6,1,4,3,5]=>0111010
[6,5,4,1,8,7,3,2]=>1110111
[6,4,7,1,5,8,3,2]=>1010011
[4,8,7,1,5,6,3,2]=>0110011
[6,5,3,1,8,4,7,2]=>1110101
[5,8,3,1,6,4,7,2]=>0110101
[6,4,3,1,5,8,7,2]=>1110011
[5,8,2,1,6,4,3,7]=>0110110
[6,4,2,1,5,8,3,7]=>1110010
[3,8,2,1,5,4,6,7]=>0110100
[6,2,7,1,5,4,3,8]=>1010110
[3,2,7,1,5,4,6,8]=>1010100
[2,8,7,1,5,4,3,6]=>0110110
[6,5,1,7,8,4,3,2]=>1100111
[5,4,1,6,7,8,3,2]=>1100011
[4,3,1,6,5,7,8,2]=>1101001
[4,2,1,6,5,7,3,8]=>1101010
[2,8,1,6,5,4,3,7]=>0101110
[6,1,7,8,5,4,3,2]=>1001111
[5,1,7,6,8,4,3,2]=>1010111
[4,1,7,6,5,8,3,2]=>1011011
[4,5,8,1,7,2,3,6]=>0010100
[4,5,8,1,2,6,3,7]=>0010010
[8,1,3,5,7,2,4,6]=>1000100
[3,6,8,1,7,2,4,5]=>0010100
[3,4,5,6,8,1,7,2]=>0000101
[8,2,3,5,6,7,1,4]=>1000010
[8,1,2,3,5,4,6,7]=>1000100
[4,5,8,1,7,6,3,2]=>0010111
[8,7,2,1,6,3,4,5]=>1110100
[8,7,2,1,3,5,4,6]=>1110010
[8,6,4,1,7,5,3,2]=>1110111
[2,3,6,7,8,1,5,4]=>0000101
[7,4,2,6,8,5,1,3]=>1100110
[7,3,2,5,8,6,1,4]=>1100110
[7,3,1,8,6,2,4,5]=>1101100
[3,1,7,2,5,4,8,6]=>1010101
[7,1,4,2,8,3,6,5]=>1010101
[7,1,8,2,5,3,6,4]=>1010101
[7,3,8,4,5,1,6,2]=>1010101
[8,3,7,4,6,1,5,2]=>1010101
[8,2,7,1,6,4,5,3]=>1010101
[8,1,7,5,4,2,3,6]=>1011100
[8,1,2,6,5,4,3,7]=>1001110
[8,1,7,6,3,2,4,5]=>1011100
[8,2,7,5,6,1,4,3]=>1010101
[3,6,8,1,7,5,4,2]=>0010111
[8,2,6,7,5,4,1,3]=>1001110
[8,6,7,2,3,1,5,4]=>1010101
[2,7,8,6,3,1,5,4]=>0011101
[7,3,1,8,6,5,4,2]=>1101111
[8,1,7,6,5,4,3,2]=>1011111
[2,1,8,6,3,7,4,5]=>1011010
[8,6,1,5,2,7,4,3]=>1101011
[8,5,1,7,4,2,6,3]=>1101101
[2,1,7,8,3,6,5,4]=>1001011
[2,1,4,8,5,7,3,6]=>1001010
[7,8,1,5,2,6,3,4]=>0101010
[6,4,1,5,2,3,8,7]=>1101001
[4,3,7,8,5,2,1,6]=>1001110
[5,3,7,4,6,8,1,2]=>1010010
[5,8,3,7,6,2,1,4]=>0101110
[4,2,6,3,8,5,1,7]=>1010110
[5,8,2,1,7,6,4,3]=>0110111
[8,3,2,4,1,7,5,6]=>1101010
[6,3,4,2,1,7,8,5]=>1011001
[7,2,8,1,4,6,5,3]=>1010011
[6,8,1,4,5,3,2,7]=>0100110
[8,2,6,1,4,7,3,5]=>1010010
[4,2,1,3,6,7,8,5]=>1100001
[2,3,4,1,8,6,5,7]=>0010110
[6,3,5,4,1,2,8,7]=>1011001
[8,7,3,6,5,1,4,2]=>1101101
[3,4,7,2,8,1,5,6]=>0010100
[3,8,4,7,1,6,5,2]=>0101011
[3,2,4,6,1,5,8,7]=>1001001
[6,8,5,4,3,7,2,1]=>0111011
[5,8,4,3,2,1,7,6]=>0111101
[6,5,4,3,1,8,7,2]=>1111011
[8,7,5,4,3,1,6,2]=>1111101
[3,4,6,2,8,5,1,7]=>0010110
[3,4,6,7,1,8,5,2]=>0001011
[3,4,6,8,1,5,2,7]=>0001010
[3,4,7,2,8,5,6,1]=>0010101
[3,4,8,2,1,5,6,7]=>0011000
[3,5,2,6,8,4,1,7]=>0100110
[3,5,2,7,4,8,6,1]=>0101011
[3,5,6,2,7,8,1,4]=>0010010
[3,5,6,2,8,4,1,7]=>0010110
[3,5,6,8,4,1,2,7]=>0001100
[3,5,7,2,4,8,6,1]=>0010011
[3,5,7,2,8,4,6,1]=>0010101
[3,5,7,8,4,1,6,2]=>0001101
[3,5,8,2,4,1,6,7]=>0010100
[3,6,2,1,7,8,5,4]=>0110011
[3,6,2,1,8,5,4,7]=>0110110
[3,6,2,7,4,8,5,1]=>0101011
[3,6,2,7,8,5,4,1]=>0100111
[3,6,8,2,4,5,1,7]=>0010010
[3,7,2,1,4,8,6,5]=>0110011
[3,7,2,8,4,5,6,1]=>0101001
[3,8,2,1,4,5,6,7]=>0110000
[4,1,5,6,7,8,3,2]=>1000011
[4,1,5,7,3,8,6,2]=>1001011
[4,1,5,7,8,2,6,3]=>1000101
[4,1,5,8,3,2,6,7]=>1001100
[4,1,6,3,7,8,5,2]=>1010011
[4,1,6,3,8,5,2,7]=>1010110
[4,1,6,7,3,8,5,2]=>1001011
[4,1,6,8,3,5,2,7]=>1001010
[4,1,7,3,8,5,6,2]=>1010101
[4,1,8,3,2,5,6,7]=>1011000
[4,5,2,7,3,8,6,1]=>0101011
[4,5,7,3,2,8,6,1]=>0011011
[4,5,8,3,2,1,6,7]=>0011100
[4,6,2,3,8,5,1,7]=>0100110
[4,6,2,8,3,5,1,7]=>0101010
[4,6,7,3,2,8,5,1]=>0011011
[4,7,2,8,3,5,6,1]=>0101001
[4,7,8,3,2,5,6,1]=>0011001
[4,8,2,3,1,5,6,7]=>0101000
[5,1,2,6,8,4,3,7]=>1000110
[5,1,2,8,4,3,6,7]=>1001100
[5,1,6,3,7,8,2,4]=>1010010
[5,1,6,3,8,4,2,7]=>1010110
[5,1,6,7,4,8,2,3]=>1001010
[5,6,2,3,8,4,1,7]=>0100110
[5,6,2,7,4,8,1,3]=>0101010
[5,6,2,7,8,4,1,3]=>0100110
[5,6,8,3,4,2,1,7]=>0010110
[5,7,8,3,4,2,6,1]=>0010101
[6,1,2,3,7,8,5,4]=>1000011
[6,1,2,3,8,5,4,7]=>1000110
[6,1,2,7,8,5,4,3]=>1000111
[6,1,7,8,4,5,3,2]=>1001011
[6,7,2,8,4,5,3,1]=>0101011
[7,1,2,3,4,8,6,5]=>1000011
[7,1,2,3,8,5,6,4]=>1000101
[7,1,2,8,4,5,6,3]=>1001001
[7,1,8,3,4,5,6,2]=>1010001
[2,4,6,1,8,5,7,3]=>0010101
[6,4,1,8,2,3,7,5]=>1101001
[5,8,1,2,4,3,7,6]=>0100101
[5,8,1,6,2,4,3,7]=>0101010
[1,3,5,7,2,6,4,8]=>0001010
[3,5,8,6,1,2,4,7]=>0011000
[3,5,1,8,2,4,7,6]=>0101001
[3,1,6,8,2,4,7,5]=>1001001
[2,3,5,6,8,1,7,4]=>0000101
[5,6,4,8,2,1,7,3]=>0101101
[7,1,8,6,3,4,5,2]=>1011001
[7,6,5,2,4,8,1,3]=>1110010
[6,7,4,5,2,1,8,3]=>0101101
[5,1,7,8,6,4,3,2]=>1001111
[2,5,7,8,6,3,1,4]=>0001110
[7,1,8,6,3,2,4,5]=>1011100
[7,8,1,6,4,2,3,5]=>0101100
[2,4,8,1,5,6,7,3]=>0010001
[8,4,1,2,5,6,3,7]=>1100010
[8,3,1,6,5,2,4,7]=>1101100
[2,5,3,8,7,6,1,4]=>0101110
[5,8,7,4,2,6,1,3]=>0111010
[5,1,8,4,7,6,3,2]=>1010111
[7,3,2,6,5,1,8,4]=>1101101
[8,2,3,6,5,1,7,4]=>1001101
[4,8,6,5,7,3,2,1]=>0110111
[4,8,5,6,7,3,2,1]=>0100111
[3,8,7,4,5,6,2,1]=>0110011
[2,8,7,6,3,4,5,1]=>0111001
[1,8,7,6,5,2,3,4]=>0111100
[7,2,8,6,5,4,1,3]=>1011110
[6,3,2,8,5,1,7,4]=>1101101
[8,4,7,2,5,6,3,1]=>1010011
[6,8,5,4,3,1,7,2]=>0111101
[5,8,6,4,1,3,7,2]=>0111001
[3,6,1,8,5,2,7,4]=>0101101
[3,4,1,2,8,6,7,5]=>0100101
[6,8,3,5,4,1,7,2]=>0101101
[7,6,3,8,5,2,1,4]=>1101110
[5,8,7,4,1,6,3,2]=>0111011
[4,2,3,1,7,8,5,6]=>1010010
[8,6,3,4,7,2,5,1]=>1100101
[5,2,8,4,1,6,7,3]=>1011001
[4,1,3,6,8,2,5,7]=>1000100
[1,6,3,2,5,8,4,7]=>0110010
[8,3,2,1,5,4,7,6]=>1110101
[5,3,6,2,4,8,1,7]=>1010010
[1,6,2,4,5,8,3,7]=>0100010
[5,3,2,1,6,8,4,7]=>1110010
[2,6,5,8,1,3,4,7]=>0101000
[4,3,1,6,5,8,2,7]=>1101010
[3,4,6,5,7,1,8,2]=>0010101
[8,2,6,4,1,7,3,5]=>1011010
[5,4,6,8,1,2,7,3]=>1001001
[3,4,7,8,6,2,5,1]=>0001101
[7,5,8,2,4,6,1,3]=>1010010
[8,2,7,4,6,1,3,5]=>1010100
[4,7,3,2,8,1,6,5]=>0110101
[3,8,1,7,2,5,6,4]=>0101001
[8,3,2,5,7,6,1,4]=>1100110
[2,8,6,1,5,7,3,4]=>0110010
[1,2,8,3,5,6,7,4]=>0010001
[4,2,3,7,1,8,6,5]=>1001011
[3,2,6,4,8,1,7,5]=>1010101
[8,2,1,6,7,3,4,5]=>1100100
[2,7,8,5,4,1,3,6]=>0011100
[1,7,5,3,8,4,2,6]=>0110110
[4,7,5,3,1,2,8,6]=>0111001
[5,6,7,3,8,4,2,1]=>0010111
[5,7,3,2,4,1,8,6]=>0110101
[8,4,1,3,7,2,5,6]=>1100100
[2,8,4,7,1,3,5,6]=>0101000
[3,5,2,8,6,1,7,4]=>0101101
[1,7,6,3,2,5,8,4]=>0111001
[3,8,1,5,6,2,7,4]=>0100101
[4,3,5,6,7,1,8,2]=>1000101
[7,1,5,2,8,6,4,3]=>1010111
[6,5,4,8,7,2,1,3]=>1101110
[1,8,5,3,6,2,7,4]=>0110101
[6,5,8,7,2,1,3,4]=>1011100
[3,6,2,1,7,5,8,4]=>0110101
[4,7,2,6,5,8,1,3]=>0101010
[6,8,1,4,2,7,3,5]=>0101010
[6,3,4,7,1,8,2,5]=>1001010
[3,4,7,8,2,5,6,1]=>0001001
[1,8,2,4,5,6,7,3]=>0100001
[2,1,4,6,8,5,7,3]=>1000101
[3,2,5,7,6,1,8,4]=>1001101
[3,1,4,6,5,7,8,2]=>1001001
[1,2,3,4,8,6,5,7]=>0000110
[1,2,3,8,5,4,6,7]=>0001100
[1,2,3,8,5,6,4,7]=>0001010
[1,2,3,8,6,5,4,7]=>0001110
[1,8,3,4,2,5,6,7]=>0101000
[1,2,8,5,4,3,6,7]=>0011100
[1,8,4,3,2,5,6,7]=>0111000
[8,5,7,6,4,3,2,1]=>1011111
[8,4,7,6,5,3,2,1]=>1011111
[8,4,7,5,6,3,2,1]=>1010111
[8,5,7,4,6,3,2,1]=>1010111
[8,7,6,3,5,4,2,1]=>1110111
[8,6,7,3,5,4,2,1]=>1010111
[8,5,7,3,6,4,2,1]=>1010111
[8,4,7,3,6,5,2,1]=>1010111
[8,1,7,4,6,5,3,2]=>1010111
[8,3,7,2,6,5,4,1]=>1010111
[8,5,7,2,6,4,3,1]=>1010111
[8,6,7,2,5,4,3,1]=>1010111
[8,7,6,2,5,4,3,1]=>1110111
[8,4,7,1,6,5,3,2]=>1010111
[8,3,7,1,6,5,4,2]=>1010111
[8,2,7,1,6,5,4,3]=>1010111
[8,1,7,2,6,5,4,3]=>1010111
[8,1,7,2,6,4,5,3]=>1010101
[8,3,7,1,6,4,5,2]=>1010101
[8,4,7,1,6,3,5,2]=>1010101
[8,5,7,1,6,3,4,2]=>1010101
[8,6,7,1,5,3,4,2]=>1010101
[8,7,6,2,5,3,4,1]=>1110101
[8,6,7,2,5,3,4,1]=>1010101
[8,5,7,2,6,3,4,1]=>1010101
[8,4,7,2,6,3,5,1]=>1010101
[8,3,7,2,6,4,5,1]=>1010101
[8,2,7,3,6,4,5,1]=>1010101
[8,1,7,3,6,4,5,2]=>1010101
[8,1,7,4,6,3,5,2]=>1010101
[8,2,7,4,6,3,5,1]=>1010101
[8,3,7,4,6,2,5,1]=>1010101
[8,5,7,3,6,2,4,1]=>1010101
[8,6,7,3,5,2,4,1]=>1010101
[8,5,7,4,6,2,3,1]=>1010101
[8,4,7,5,6,2,3,1]=>1010101
[8,3,7,5,6,2,4,1]=>1010101
[8,2,7,5,6,3,4,1]=>1010101
[8,1,7,5,6,3,4,2]=>1010101
[8,3,7,6,5,2,4,1]=>1011101
[8,4,7,6,5,2,3,1]=>1011101
[8,5,7,6,4,2,3,1]=>1011101
[8,7,6,5,4,1,3,2]=>1111101
[8,6,7,5,4,1,3,2]=>1011101
[8,5,7,6,4,1,3,2]=>1011101
[8,3,7,6,5,1,4,2]=>1011101
[8,1,7,5,6,2,4,3]=>1010101
[8,3,7,5,6,1,4,2]=>1010101
[8,4,7,5,6,1,3,2]=>1010101
[8,6,7,4,5,1,3,2]=>1010101
[8,7,6,4,5,1,3,2]=>1110101
[8,6,7,3,5,1,4,2]=>1010101
[8,4,7,3,6,1,5,2]=>1010101
[8,2,7,4,6,1,5,3]=>1010101
[8,1,7,4,6,2,5,3]=>1010101
[8,1,7,3,6,2,5,4]=>1010101
[8,2,7,3,6,1,5,4]=>1010101
[8,3,7,2,6,1,5,4]=>1010101
[8,4,7,2,6,1,5,3]=>1010101
[8,5,7,2,6,1,4,3]=>1010101
[8,6,7,2,5,1,4,3]=>1010101
[8,7,6,2,5,1,4,3]=>1110101
[8,7,6,1,5,2,4,3]=>1110101
[8,6,7,1,5,2,4,3]=>1010101
[8,5,7,1,6,2,4,3]=>1010101
[8,4,7,1,6,2,5,3]=>1010101
[8,3,7,1,6,2,5,4]=>1010101
[8,2,7,1,6,3,5,4]=>1010101
[4,6,7,3,8,5,2,1]=>0010111
[1,4,8,2,6,3,5,7]=>0010100
[1,6,2,4,8,3,5,7]=>0100100
[1,5,2,3,8,4,7,6]=>0100101
[1,7,2,3,5,4,8,6]=>0100101
[1,8,2,3,5,4,6,7]=>0100100
[1,7,8,2,4,5,3,6]=>0010010
[1,2,8,3,6,4,5,7]=>0010100
[1,5,8,2,3,7,4,6]=>0010010
[1,6,8,2,3,5,4,7]=>0010010
[5,7,2,6,3,8,1,4]=>0101010
[5,7,1,6,8,4,3,2]=>0100111
[4,8,1,2,5,7,3,6]=>0100010
[1,7,8,4,6,2,5,3]=>0010101
[3,7,4,8,5,1,6,2]=>0101101
[3,7,5,4,8,2,1,6]=>0110110
[4,7,1,3,2,8,6,5]=>0101011
[2,7,3,1,5,8,4,6]=>0110010
[2,7,5,8,6,4,1,3]=>0101110
[3,4,2,7,8,1,6,5]=>0100101
[4,3,2,1,5,8,6,7]=>1110010
[4,1,3,7,5,6,8,2]=>1001001
[3,4,6,1,5,8,2,7]=>0010010
[6,5,8,7,1,4,2,3]=>1011010
[4,1,7,3,8,5,2,6]=>1010110
[6,1,7,3,5,4,8,2]=>1010101
[5,6,8,7,2,4,1,3]=>0011010
[6,8,5,7,1,2,4,3]=>0101001
[7,1,3,4,2,8,5,6]=>1001010
[7,6,1,4,3,5,8,2]=>1101001
[3,5,4,1,6,7,8,2]=>0110001
[2,5,3,4,8,6,1,7]=>0100110
[2,4,8,3,6,1,7,5]=>0010101
[8,2,4,3,7,5,6,1]=>1010101
[6,8,2,1,5,7,3,4]=>0110010
[7,2,8,4,1,6,3,5]=>1011010
[1,2,4,8,6,5,3,7]=>0001110
[7,1,5,6,8,4,3,2]=>1000111
[7,3,5,6,1,4,8,2]=>1001001
[3,7,6,5,1,4,8,2]=>0111001
[2,7,6,5,3,8,1,4]=>0111010
[2,7,8,1,4,6,3,5]=>0010010
[4,8,2,5,7,1,6,3]=>0100101
[4,1,6,8,5,3,7,2]=>1001101
[5,2,6,4,8,3,1,7]=>1010110
[1,2,6,3,4,8,7,5]=>0010011
[5,3,6,1,4,7,8,2]=>1010001
[6,7,1,3,4,5,8,2]=>0100001
[1,7,3,2,4,8,5,6]=>0110010
[6,1,4,2,8,3,5,7]=>1010100
[5,8,6,7,2,1,4,3]=>0101101
[7,4,1,5,8,2,3,6]=>1100100
[6,3,4,2,8,7,5,1]=>1010111
[4,3,8,7,5,2,6,1]=>1011101
[6,8,7,4,2,3,5,1]=>0111001
[8,6,1,3,5,4,2,7]=>1100110
[2,7,6,3,4,5,8,1]=>0110001
[5,3,8,6,1,2,4,7]=>1011000
[2,4,8,7,3,5,6,1]=>0011001
[2,5,3,6,8,7,4,1]=>0100111
[3,8,7,2,6,4,5,1]=>0110101
[4,5,8,7,2,6,3,1]=>0011011
[8,5,2,7,1,4,3,6]=>1101010
[5,1,7,2,4,3,8,6]=>1010101
[4,5,2,8,3,7,6,1]=>0101011
[8,2,3,7,6,4,5,1]=>1001101
[3,7,5,8,2,6,1,4]=>0101010
[1,6,7,4,8,2,3,5]=>0010100
[8,2,1,3,5,6,7,4]=>1100001
[4,1,3,8,2,6,7,5]=>1001001
[3,6,1,4,7,2,8,5]=>0100101
[6,2,7,4,5,8,1,3]=>1010010
[2,1,8,4,5,7,3,6]=>1010010
[1,8,5,7,3,2,4,6]=>0101100
[3,2,1,6,4,8,5,7]=>1101010
[2,1,8,5,4,3,6,7]=>1011100
[2,7,4,1,5,3,8,6]=>0110101
[7,4,8,6,2,3,1,5]=>1011010
[7,3,2,4,8,6,1,5]=>1100110
[7,1,3,2,8,5,4,6]=>1010110
[5,1,7,4,2,3,8,6]=>1011001
[1,3,4,8,6,5,2,7]=>0001110
[4,1,8,6,5,3,2,7]=>1011110
[4,8,5,3,6,2,7,1]=>0110101
[5,7,4,3,6,2,8,1]=>0110101
[6,7,5,1,2,8,3,4]=>0110010
[7,5,1,4,2,6,8,3]=>1101001
[5,2,6,8,3,4,7,1]=>1001001
[7,6,2,4,5,8,3,1]=>1100011
[2,6,3,8,4,7,5,1]=>0101011
[6,2,7,5,8,3,1,4]=>1010110
[2,1,5,6,8,3,7,4]=>1000101
[1,2,7,4,8,3,6,5]=>0010101
[1,6,8,3,2,7,4,5]=>0011010
[1,6,7,5,2,8,3,4]=>0011010
[7,5,1,2,8,4,6,3]=>1100101
[5,4,8,3,6,2,7,1]=>1010101
[5,8,2,7,4,3,6,1]=>0101101
[5,7,3,8,2,4,6,1]=>0101001
[6,4,5,8,2,7,3,1]=>1001011
[5,7,3,6,4,8,2,1]=>0101011
[1,5,6,4,8,2,7,3]=>0010101
[3,6,2,4,7,1,8,5]=>0100101
[4,2,8,5,1,6,7,3]=>1011001
[2,1,6,4,8,5,3,7]=>1010110
[1,2,8,3,7,5,4,6]=>0010110
[1,6,3,8,7,4,2,5]=>0101110
[4,3,8,1,2,6,7,5]=>1010001
[6,4,5,8,1,2,7,3]=>1001001
[7,4,6,5,2,1,8,3]=>1011101
[5,1,8,6,7,4,3,2]=>1010111
[3,8,5,7,1,4,2,6]=>0101010
[4,7,2,5,1,3,8,6]=>0101001
[5,1,7,4,8,6,3,2]=>1010111
[3,6,5,2,1,8,7,4]=>0111011
[5,2,8,4,7,3,1,6]=>1010110
[5,2,7,4,1,3,6,8]=>1011000
[5,2,6,4,1,8,7,3]=>1011011
[6,3,2,1,4,8,7,5]=>1110011
[3,1,4,6,2,8,7,5]=>1001011
[6,3,5,1,7,4,2,8]=>1010110
[4,6,3,7,5,8,1,2]=>0101010
[5,7,4,3,8,1,2,6]=>0110100
[1,5,7,4,8,6,3,2]=>0010111
[1,8,2,7,6,5,4,3]=>0101111
[3,8,1,6,7,5,4,2]=>0100111
[3,7,2,6,8,5,1,4]=>0100110
[8,2,4,3,6,1,5,7]=>1010100
[1,7,8,5,4,3,6,2]=>0011101
[7,3,8,1,4,2,6,5]=>1010101
[1,8,4,5,3,2,6,7]=>0101100
[3,8,7,4,2,6,1,5]=>0111010
[3,7,8,1,2,6,5,4]=>0010011
[3,5,6,2,7,1,4,8]=>0010100
[3,7,1,6,8,2,4,5]=>0100100
[8,1,7,6,2,4,3,5]=>1011010
[1,6,4,5,7,2,3,8]=>0100100
[8,3,6,1,7,2,4,5]=>1010100
[1,7,5,3,6,8,4,2]=>0110011
[7,3,5,2,1,8,4,6]=>1011010
[7,4,1,6,5,8,3,2]=>1101011
[6,4,2,8,7,5,1,3]=>1101110
[4,2,1,5,8,7,3,6]=>1100110
[1,5,3,6,8,7,4,2]=>0100111
[3,5,4,6,1,8,2,7]=>0101010
[3,1,5,7,6,8,2,4]=>1001010
[6,4,5,7,2,8,1,3]=>1001010
[5,3,6,4,2,8,1,7]=>1011010
[4,1,5,3,8,2,7,6]=>1010101
[2,6,3,5,4,8,1,7]=>0101010
[3,7,4,5,6,8,1,2]=>0100010
[2,5,7,3,6,8,1,4]=>0010010
[7,6,4,5,2,8,1,3]=>1101010
[5,4,3,1,8,2,7,6]=>1110101
[8,2,6,4,7,3,1,5]=>1010110
[8,6,1,7,4,5,2,3]=>1101010
[1,2,8,3,5,4,6,7]=>0010100
[1,7,8,4,3,5,6,2]=>0011001
[3,1,6,8,4,5,7,2]=>1001001
[1,4,5,8,3,6,7,2]=>0001001
[2,5,7,1,8,3,6,4]=>0010101
[6,2,7,1,8,4,5,3]=>1010101
[4,7,1,3,8,5,6,2]=>0100101
[3,7,2,1,8,4,5,6]=>0110100
[2,1,5,8,3,6,7,4]=>1001001
[4,2,7,1,8,3,6,5]=>1010101
[4,3,1,6,8,2,7,5]=>1100101
[5,3,4,6,8,2,7,1]=>1000101
[3,5,1,6,8,2,7,4]=>0100101
[5,1,8,7,4,2,3,6]=>1011100
[5,8,3,2,6,4,1,7]=>0110110
[6,8,2,4,7,5,1,3]=>0100110
[7,3,8,2,6,4,1,5]=>1010110
[3,8,7,4,5,6,1,2]=>0110010
[2,7,6,3,5,4,1,8]=>0110110
[3,8,7,4,6,2,5,1]=>0110101
[5,8,3,7,6,2,4,1]=>0101101
[8,7,2,5,4,3,1,6]=>1101110
[6,8,3,2,5,4,7,1]=>0110101
[5,8,7,4,3,6,2,1]=>0111011
[5,8,6,4,3,7,1,2]=>0111010
[6,5,8,4,3,1,7,2]=>1011101
[2,6,4,7,1,5,3,8]=>0101010
[2,5,6,8,4,3,7,1]=>0001101
[5,3,8,1,7,6,4,2]=>1010111
[5,4,8,7,1,6,3,2]=>1011011
[4,8,6,7,5,3,1,2]=>0101110
[4,8,6,5,7,2,1,3]=>0110110
[4,8,5,6,7,1,2,3]=>0100100
[5,4,8,6,1,7,2,3]=>1011010
[5,3,8,1,6,7,2,4]=>1010010
[5,2,1,8,6,7,3,4]=>1101010
[6,2,1,5,8,3,7,4]=>1100101
[6,5,4,8,2,1,7,3]=>1101101
[5,8,4,7,2,6,3,1]=>0101011
[5,8,3,2,7,6,4,1]=>0110111
[5,8,3,2,6,7,1,4]=>0110010
[6,5,3,2,8,1,7,4]=>1110101
[6,4,3,2,1,8,7,5]=>1111011
[6,3,4,1,2,8,7,5]=>1010011
[6,2,1,4,3,8,7,5]=>1101011
[5,2,1,4,3,6,7,8]=>1101000
[4,6,3,2,5,1,7,8]=>0110100
[3,5,7,4,2,6,1,8]=>0011010
[4,3,6,1,5,2,7,8]=>1010100
[4,2,1,6,5,3,7,8]=>1101100
[4,2,1,5,7,6,3,8]=>1100110
[3,5,4,7,1,6,2,8]=>0101010
[3,4,7,5,6,1,2,8]=>0010100
[3,4,5,8,6,7,1,2]=>0001010
[3,4,6,5,8,1,7,2]=>0010101
[4,3,5,1,6,8,7,2]=>1010011
[2,1,5,3,8,4,7,6]=>1010101
[3,1,8,2,5,4,7,6]=>1010101
[8,1,3,2,6,4,7,5]=>1010101
[3,1,8,2,6,4,7,5]=>1010101
[2,1,8,3,6,4,7,5]=>1010101
[2,1,6,3,8,4,7,5]=>1010101
[2,1,7,3,5,4,8,6]=>1010101
[2,1,7,3,6,4,8,5]=>1010101
[2,1,7,3,8,4,6,5]=>1010101
[8,1,4,2,7,3,6,5]=>1010101
[4,1,8,2,7,3,6,5]=>1010101
[4,1,7,2,8,3,6,5]=>1010101
[3,1,7,2,8,4,6,5]=>1010101
[3,1,6,2,5,4,8,7]=>1010101
[7,1,3,2,5,4,8,6]=>1010101
[7,1,3,2,6,4,8,5]=>1010101
[7,1,3,2,8,4,6,5]=>1010101
[7,1,8,2,4,3,6,5]=>1010101
[8,1,7,2,5,3,6,4]=>1010101
[7,1,5,2,8,3,6,4]=>1010101
[6,1,4,2,5,3,8,7]=>1010101
[4,1,6,2,5,3,8,7]=>1010101
[4,1,7,2,5,3,8,6]=>1010101
[4,1,7,2,6,3,8,5]=>1010101
[5,1,7,2,6,3,8,4]=>1010101
[5,1,7,2,8,3,6,4]=>1010101
[5,1,8,2,7,3,6,4]=>1010101
[8,1,5,2,7,3,6,4]=>1010101
[8,1,5,2,6,3,7,4]=>1010101
[5,1,8,2,6,3,7,4]=>1010101
[5,1,6,2,8,3,7,4]=>1010101
[3,1,6,2,8,4,7,5]=>1010101
[4,1,8,2,6,3,7,5]=>1010101
[8,1,4,2,6,3,7,5]=>1010101
[8,1,4,2,5,3,7,6]=>1010101
[4,1,8,2,5,3,7,6]=>1010101
[4,1,5,2,8,3,7,6]=>1010101
[3,1,5,2,8,4,7,6]=>1010101
[3,1,4,2,8,5,7,6]=>1010101
[4,1,3,2,7,5,8,6]=>1010101
[5,1,4,2,8,3,7,6]=>1010101
[5,1,8,2,4,3,7,6]=>1010101
[8,1,6,2,4,3,7,5]=>1010101
[6,1,8,2,4,3,7,5]=>1010101
[6,1,3,2,8,4,7,5]=>1010101
[6,1,3,2,7,4,8,5]=>1010101
[5,1,3,2,7,4,8,6]=>1010101
[5,1,3,2,6,4,8,7]=>1010101
[5,1,4,2,6,3,8,7]=>1010101
[6,1,4,2,7,3,8,5]=>1010101
[6,1,5,2,7,3,8,4]=>1010101
[6,1,8,2,5,3,7,4]=>1010101
[8,1,6,2,5,3,7,4]=>1010101
[8,1,6,2,7,3,5,4]=>1010101
[6,1,8,2,7,3,5,4]=>1010101
[6,1,7,2,8,3,5,4]=>1010101
[6,1,7,2,5,3,8,4]=>1010101
[6,1,7,2,4,3,8,5]=>1010101
[5,1,6,2,4,3,8,7]=>1010101
[7,1,5,2,4,3,8,6]=>1010101
[7,1,6,2,4,3,8,5]=>1010101
[7,1,6,2,5,3,8,4]=>1010101
[7,1,6,2,8,3,5,4]=>1010101
[7,1,8,2,6,3,5,4]=>1010101
[7,8,3,1,2,5,6,4]=>0110001
[7,8,1,3,2,4,6,5]=>0101001
[6,2,8,1,3,5,4,7]=>1010010
[6,2,8,3,1,7,4,5]=>1011010
[3,2,5,7,1,8,4,6]=>1001010
[3,5,2,8,1,7,4,6]=>0101010
[4,3,1,2,7,8,6,5]=>1100011
[5,3,4,7,8,6,1,2]=>1000110
[4,1,3,2,6,8,7,5]=>1010011
[5,1,3,7,2,6,8,4]=>1001001
[5,2,4,7,8,1,6,3]=>1000101
[2,5,4,6,8,1,7,3]=>0100101
[4,3,5,7,6,8,1,2]=>1001010
[4,2,1,3,7,6,8,5]=>1100101
[2,4,3,1,8,5,7,6]=>0110101
[3,2,4,1,8,6,5,7]=>1010110
[3,4,2,1,8,7,5,6]=>0110110
[7,6,4,3,2,1,8,5]=>1111101
[7,6,5,8,2,1,4,3]=>1101101
[7,6,8,3,2,1,5,4]=>1011101
[7,8,4,3,2,1,6,5]=>0111101
[8,5,4,3,2,1,7,6]=>1111101
[7,6,3,8,2,1,5,4]=>1101101
[7,6,5,8,4,1,3,2]=>1101101
[7,4,8,3,2,1,6,5]=>1011101
[7,6,8,5,2,1,4,3]=>1011101
[4,8,6,1,7,5,2,3]=>0110110
[4,8,7,2,6,5,1,3]=>0110110
[4,7,8,2,6,1,5,3]=>0010101
[4,6,8,2,7,1,3,5]=>0010100
[8,6,4,2,7,5,3,1]=>1110111
[8,4,7,3,6,5,1,2]=>1010110
[6,4,7,1,8,3,2,5]=>1010110
[7,4,8,3,6,1,5,2]=>1010101
[7,8,4,3,6,2,5,1]=>0110101
[6,8,4,3,7,2,1,5]=>0110110
[6,7,4,2,8,3,1,5]=>0110110
[2,8,7,6,5,1,4,3]=>0111101
[7,3,2,5,4,1,6,8]=>1101100
[7,3,5,4,2,1,6,8]=>1011100
[2,7,6,3,1,5,8,4]=>0111001
[1,8,4,3,6,5,2,7]=>0110110
[1,8,4,6,5,3,2,7]=>0101110
[7,1,4,2,6,3,5,8]=>1010100
[7,3,4,1,5,6,2,8]=>1010010
[7,3,2,5,1,6,4,8]=>1101010
[7,4,1,3,5,2,6,8]=>1100100
[7,3,1,2,4,6,5,8]=>1100010
[3,6,2,1,4,8,5,7]=>0110010
[2,3,6,1,4,8,7,5]=>0010011
[3,6,7,4,1,5,8,2]=>0011001
[3,1,2,8,6,5,4,7]=>1001110
[5,4,8,6,1,2,3,7]=>1011000
[5,6,8,2,4,1,3,7]=>0010100
[5,6,8,7,4,3,1,2]=>0011110
[6,4,8,5,3,1,7,2]=>1011101
[5,7,8,6,1,3,2,4]=>0011010
[2,4,8,1,6,3,7,5]=>0010101
[1,8,4,5,2,6,7,3]=>0101001
[3,1,4,6,5,8,7,2]=>1001011
[3,7,5,4,6,8,2,1]=>0110011
[5,3,2,1,7,6,8,4]=>1110101
[5,6,1,4,7,2,8,3]=>0100101
[4,3,1,7,5,6,8,2]=>1101001
[1,8,4,3,6,2,7,5]=>0110101
[5,6,7,3,2,8,1,4]=>0011010
[5,3,2,1,4,8,6,7]=>1110010
[3,4,7,8,1,2,6,5]=>0001001
[3,6,7,8,1,4,5,2]=>0001001
[2,3,6,8,5,1,4,7]=>0001100
[3,1,6,4,8,2,5,7]=>1010100
[7,3,2,6,8,5,1,4]=>1100110
[7,3,5,8,4,6,1,2]=>1001010
[7,5,2,8,4,1,6,3]=>1101101
[1,8,4,2,3,5,7,6]=>0110001
[6,3,4,8,2,5,7,1]=>1001001
[7,5,4,8,3,6,2,1]=>1101011
[7,3,2,5,8,4,6,1]=>1100101
[5,7,8,3,1,4,6,2]=>0011001
[7,4,8,3,2,5,1,6]=>1011010
[7,3,8,2,4,5,6,1]=>1010001
[4,2,7,1,5,3,8,6]=>1010101
[2,7,1,3,5,4,8,6]=>0100101
[1,2,7,3,4,8,6,5]=>0010011
[4,7,2,1,5,8,6,3]=>0110011
[2,3,4,8,1,6,5,7]=>0001010
[3,1,4,8,2,6,7,5]=>1001001
[4,8,3,6,5,1,7,2]=>0101101
[6,4,7,3,5,1,8,2]=>1010101
[3,1,6,4,7,8,2,5]=>1010010
[7,3,1,6,8,2,4,5]=>1100100
[7,3,5,1,6,8,2,4]=>1010010
[4,7,3,5,6,1,8,2]=>0100101
[4,6,8,2,1,5,7,3]=>0011001
[1,8,2,3,5,7,4,6]=>0100010
[2,7,3,6,1,4,5,8]=>0101000
[1,2,5,8,3,7,4,6]=>0001010
[8,2,4,1,7,5,6,3]=>1010101
[3,8,4,7,5,1,6,2]=>0101101
[8,4,3,6,1,7,5,2]=>1101011
[2,1,8,6,7,3,5,4]=>1010101
[1,2,8,6,3,4,7,5]=>0011001
[7,3,2,5,6,1,4,8]=>1100100
[8,4,1,2,7,5,3,6]=>1100110
[1,5,2,8,6,3,7,4]=>0101101
[5,8,6,3,1,7,4,2]=>0111011
[7,8,1,4,2,5,3,6]=>0101010
[1,6,2,7,4,8,3,5]=>0101010
[6,2,1,7,8,5,3,4]=>1100110
[6,7,3,8,4,1,5,2]=>0101101
[2,7,1,8,5,6,3,4]=>0101010
[2,1,7,8,6,3,4,5]=>1001100
[7,8,6,2,1,3,5,4]=>0111001
[5,2,6,3,4,1,8,7]=>1010101
[4,1,2,6,5,3,8,7]=>1001101
[2,6,5,3,1,4,8,7]=>0111001
[6,1,3,4,2,8,7,5]=>1001011
[8,2,6,4,7,3,5,1]=>1010101
[3,8,5,1,7,2,4,6]=>0110100
[2,1,7,4,8,5,6,3]=>1010101
[2,5,1,8,7,4,6,3]=>0101101
[7,1,3,8,6,4,5,2]=>1001101
[2,3,5,8,6,7,4,1]=>0001011
[7,4,2,1,8,6,5,3]=>1110111
[2,1,6,3,4,8,7,5]=>1010011
[4,6,7,2,5,8,3,1]=>0010011
[7,6,2,5,3,8,1,4]=>1101010
[6,2,1,3,4,8,7,5]=>1100011
[8,1,4,2,5,6,7,3]=>1010001
[3,4,2,1,8,6,7,5]=>0110101
[2,7,6,8,1,5,3,4]=>0101010
[8,1,3,2,5,6,7,4]=>1010001
[3,2,8,7,4,5,1,6]=>1011010
[6,3,8,5,7,4,2,1]=>1010111
[7,4,6,8,5,1,2,3]=>1001100
[2,1,4,8,7,5,3,6]=>1001110
[7,1,5,8,2,6,3,4]=>1001010
[3,6,8,2,4,1,5,7]=>0010100
[6,2,8,1,7,5,4,3]=>1010111
[2,8,5,3,6,7,1,4]=>0110010
[3,8,1,4,5,6,2,7]=>0100010
[5,8,7,3,6,1,4,2]=>0110101
[5,8,3,7,6,1,4,2]=>0101101
[7,5,8,4,6,1,3,2]=>1010101
[6,5,8,4,7,1,3,2]=>1010101
[2,4,8,1,3,7,6,5]=>0010011
[2,5,1,3,8,4,7,6]=>0100101
[2,8,1,5,4,7,3,6]=>0101010
[3,1,8,2,5,7,4,6]=>1010010
[8,3,2,6,1,4,7,5]=>1101001
[2,6,1,3,8,7,5,4]=>0100111
[2,5,7,1,3,8,6,4]=>0010011
[2,8,1,7,6,5,4,3]=>0101111
[8,3,2,7,1,6,5,4]=>1101011
[7,4,2,8,1,6,5,3]=>1101011
[8,7,5,3,2,1,6,4]=>1111101
[7,5,2,6,3,1,4,8]=>1101100
[7,4,6,2,1,8,3,5]=>1011010
[7,4,5,8,6,2,1,3]=>1001110
[6,8,4,5,2,1,7,3]=>0101101
[4,6,8,5,1,7,3,2]=>0011011
[4,7,5,1,3,8,6,2]=>0110011
[5,1,7,6,4,2,8,3]=>1011101
[5,1,8,7,6,4,3,2]=>1011111
[8,5,2,1,6,3,7,4]=>1110101
[5,1,6,2,8,7,4,3]=>1010111
[4,5,6,1,8,7,2,3]=>0010110
[3,5,6,8,7,1,4,2]=>0001101
[3,6,1,7,4,8,2,5]=>0101010
[8,4,2,6,3,1,5,7]=>1101100
[4,1,8,5,7,3,6,2]=>1010101
[4,1,5,8,7,2,3,6]=>1001100
[3,4,8,7,1,2,6,5]=>0011001
[3,4,6,8,5,7,1,2]=>0001010
[4,6,8,3,5,7,2,1]=>0010011
[4,7,3,5,8,2,6,1]=>0100101
[5,4,8,2,7,3,6,1]=>1010101
[6,3,7,2,4,8,1,5]=>1010010
[5,6,8,3,7,2,1,4]=>0010110
[6,5,2,7,1,3,8,4]=>1101001
[6,5,4,1,7,2,8,3]=>1110101
[6,4,7,3,1,8,2,5]=>1011010
[6,8,5,7,4,3,2,1]=>0101111
[7,5,8,4,6,3,2,1]=>1010111
[5,6,3,7,4,2,1,8]=>0101110
[6,1,3,8,5,2,4,7]=>1001100
[7,4,2,6,3,5,1,8]=>1101010
[3,4,7,5,6,2,1,8]=>0010110
[8,1,3,4,5,2,6,7]=>1000100
[1,6,8,4,2,5,3,7]=>0011010
[3,6,8,4,1,7,5,2]=>0011011
[8,7,2,3,6,1,4,5]=>1100100
[6,7,4,8,5,1,2,3]=>0101100
[3,2,8,1,5,4,6,7]=>1010100
[6,1,4,8,5,3,7,2]=>1001101
[1,4,8,5,2,6,7,3]=>0011001
[8,1,2,3,6,5,7,4]=>1000101
[6,1,8,4,3,7,2,5]=>1011010
[3,2,6,4,1,8,7,5]=>1011011
[7,6,4,3,1,8,2,5]=>1111010
[8,4,6,5,1,7,2,3]=>1011010
[7,5,4,6,1,2,8,3]=>1101001
[3,2,5,6,1,7,8,4]=>1001001
[3,2,8,7,6,1,4,5]=>1011100
[6,8,4,7,2,1,3,5]=>0101100
[3,8,7,5,6,1,2,4]=>0110100
[8,2,7,6,5,1,3,4]=>1011100
[4,8,6,7,1,5,3,2]=>0101011
[1,8,6,7,2,3,4,5]=>0101000
[7,6,3,2,1,8,5,4]=>1111011
[3,5,4,2,7,1,8,6]=>0110101
[8,6,3,1,4,5,7,2]=>1110001
[3,2,6,1,5,7,4,8]=>1010010
[5,2,1,4,7,6,3,8]=>1100110
[4,2,1,3,5,8,7,6]=>1100011
[7,4,1,5,3,6,8,2]=>1101001
[6,8,2,4,5,1,3,7]=>0100100
[6,8,3,4,1,5,2,7]=>0101010
[5,8,4,1,7,2,6,3]=>0110101
[6,8,3,1,4,5,7,2]=>0110001
[5,3,8,4,2,6,7,1]=>1011001
[4,1,8,3,5,7,2,6]=>1010010
[2,4,6,3,5,8,1,7]=>0010010
[4,5,7,2,3,6,8,1]=>0010001
[2,6,3,4,7,5,8,1]=>0100101
[4,5,2,7,1,6,8,3]=>0101001
[2,3,1,7,6,4,8,5]=>0101101
[3,4,1,6,5,8,2,7]=>0101010
[7,3,1,4,8,5,6,2]=>1100101
[6,4,2,8,7,1,5,3]=>1101101
[3,1,8,2,7,6,4,5]=>1010110
[6,2,8,4,1,7,5,3]=>1011011
[3,6,4,7,2,5,1,8]=>0101010
[7,3,2,8,6,1,4,5]=>1101100
[4,3,8,7,1,2,5,6]=>1011000
[1,2,5,8,4,7,3,6]=>0001010
[1,3,6,8,5,2,7,4]=>0001101
[2,5,7,4,1,8,6,3]=>0011011
[2,4,6,1,8,3,7,5]=>0010101
[3,5,1,7,2,8,6,4]=>0101011
[4,6,3,1,7,8,5,2]=>0110011
[5,3,1,6,7,8,4,2]=>1100011
[4,1,6,2,7,8,5,3]=>1010011
[2,1,3,4,8,7,5,6]=>1000110
[4,8,7,3,6,5,1,2]=>0110110
[6,3,8,7,5,4,1,2]=>1011110
[4,3,8,7,6,5,1,2]=>1011110
[2,8,7,6,1,5,4,3]=>0111011
[5,2,8,7,6,1,4,3]=>1011101
[6,2,8,7,5,1,4,3]=>1011101
[7,8,2,6,5,1,4,3]=>0101101
[6,1,8,7,5,4,3,2]=>1011111
[4,1,8,7,6,5,3,2]=>1011111
[3,1,8,7,6,5,4,2]=>1011111
[7,8,2,6,1,5,4,3]=>0101011
[4,2,8,1,7,6,5,3]=>1010111
[3,2,8,1,7,6,5,4]=>1010111
[2,8,7,1,6,5,4,3]=>0110111
[3,8,2,1,7,6,5,4]=>0110111
[4,8,2,7,6,1,5,3]=>0101101
[3,8,2,7,1,6,5,4]=>0101011
[3,8,7,2,1,6,5,4]=>0111011
[4,8,7,2,6,1,5,3]=>0110101
[5,8,7,6,2,1,4,3]=>0111101
[6,5,8,7,1,4,3,2]=>1011011
[3,8,7,1,6,5,4,2]=>0110111
[4,8,1,7,6,5,3,2]=>0101111
[5,4,1,8,7,6,3,2]=>1101111
[6,4,8,1,7,5,3,2]=>1010111
[7,8,4,1,6,5,3,2]=>0110111
[7,8,3,1,6,5,4,2]=>0110111
[5,3,1,8,7,6,4,2]=>1101111
[4,3,1,8,7,6,5,2]=>1101111
[4,2,1,8,7,6,5,3]=>1101111
[6,5,3,1,8,7,4,2]=>1110111
[7,5,2,1,8,6,4,3]=>1110111
[5,4,2,1,8,7,6,3]=>1110111
[7,3,2,1,8,6,5,4]=>1110111
[6,1,4,2,3,5,8,7]=>1010001
[8,6,1,4,2,3,5,7]=>1101000
[6,8,1,4,2,3,5,7]=>0101000
[4,6,2,3,8,1,5,7]=>0100100
[8,2,3,6,4,1,5,7]=>1001100
[6,2,3,8,4,1,5,7]=>1001100
[8,4,2,3,6,1,5,7]=>1100100
[6,4,2,3,8,1,5,7]=>1100100
[2,8,4,3,6,1,5,7]=>0110100
[2,6,3,8,4,1,5,7]=>0101100
[6,3,8,4,2,1,5,7]=>1011100
[2,4,8,3,6,1,5,7]=>0010100
[2,4,6,3,8,1,5,7]=>0010100
[8,3,6,2,4,1,5,7]=>1010100
[8,3,6,2,1,4,5,7]=>1011000
[2,1,8,3,6,4,5,7]=>1010100
[6,3,8,2,1,4,5,7]=>1011000
[6,2,4,3,8,1,5,7]=>1010100
[3,6,4,7,8,5,1,2]=>0100110
[1,6,4,2,7,5,8,3]=>0110101
[3,4,6,8,7,5,1,2]=>0001110
[5,4,6,3,8,7,1,2]=>1010110
[6,4,8,5,3,7,1,2]=>1011010
[1,8,5,2,6,3,7,4]=>0110101
[1,4,6,2,8,5,7,3]=>0010101
[7,8,1,4,2,5,6,3]=>0101001
[3,6,5,2,4,1,8,7]=>0110101
[4,8,5,3,1,6,2,7]=>0111010
[5,1,6,2,8,7,3,4]=>1010110
[6,1,8,7,4,2,3,5]=>1011100
[1,2,8,5,7,3,6,4]=>0010101
[1,3,6,8,7,5,2,4]=>0001110
[7,8,1,2,4,6,5,3]=>0100011
[1,2,6,4,8,7,5,3]=>0010111
[1,8,2,5,4,7,6,3]=>0101011
[1,2,7,3,5,8,6,4]=>0010011
[4,6,2,1,7,5,3,8]=>0110110
[4,6,2,3,7,8,1,5]=>0100010
[4,2,1,3,5,7,8,6]=>1100001
[7,3,2,4,5,1,8,6]=>1100101
[7,8,3,2,4,1,6,5]=>0110101
[7,8,4,2,6,3,1,5]=>0110110
[4,2,6,3,8,7,1,5]=>1010110
[5,8,2,7,4,3,1,6]=>0101110
[7,5,2,8,3,4,1,6]=>1101010
[4,3,6,8,1,2,7,5]=>1001001
[6,4,3,5,2,8,1,7]=>1101010
[6,5,8,4,2,3,1,7]=>1011010
[4,1,3,6,5,8,7,2]=>1001011
[2,4,1,3,8,5,7,6]=>0100101
[2,4,1,3,5,8,7,6]=>0100011
[4,6,1,3,5,8,7,2]=>0100011
[1,4,6,3,5,8,7,2]=>0010011
[4,2,1,3,6,5,7,8]=>1100100
[4,2,1,6,3,5,7,8]=>1101000
[4,2,1,8,3,5,7,6]=>1101001
[6,2,1,8,3,5,7,4]=>1101001
[6,4,1,3,8,5,7,2]=>1100101
[6,1,4,3,8,5,7,2]=>1010101
[1,6,4,3,8,5,7,2]=>0110101
[8,1,4,3,6,5,7,2]=>1010101
[8,2,1,3,6,5,7,4]=>1100101
[8,2,1,4,3,5,7,6]=>1101001
[8,1,4,6,3,5,7,2]=>1001001
[6,1,4,8,3,5,7,2]=>1001001
[6,4,8,1,3,5,7,2]=>1010001
[2,4,8,1,3,5,7,6]=>0010001
[4,6,8,1,3,5,7,2]=>0010001
[4,6,1,8,3,5,7,2]=>0101001
[4,1,6,8,3,5,7,2]=>1001001
[1,4,6,8,3,5,7,2]=>0001001
[1,4,6,3,8,5,7,2]=>0010101
[4,6,1,3,8,5,7,2]=>0100101
[2,6,1,3,8,5,7,4]=>0100101
[2,1,6,3,8,5,7,4]=>1010101
[2,1,3,6,8,5,7,4]=>1000101
[4,1,3,6,8,5,7,2]=>1000101
[1,4,3,6,8,5,7,2]=>0100101
[2,1,8,3,6,5,7,4]=>1010101
[2,1,8,4,3,5,7,6]=>1011001
[4,1,8,3,6,5,7,2]=>1010101
[2,8,4,1,3,5,7,6]=>0110001
[6,8,1,4,3,5,7,2]=>0101001
[1,8,6,4,3,5,7,2]=>0111001
[8,6,1,4,3,5,7,2]=>1101001
[8,6,4,1,3,5,7,2]=>1110001
[8,4,2,1,3,5,7,6]=>1110001
[8,5,7,4,3,2,1,6]=>1011110
[8,7,6,5,1,4,3,2]=>1111011
[8,7,4,3,6,2,1,5]=>1110110
[8,7,3,6,5,2,1,4]=>1101110
[6,5,8,4,3,2,1,7]=>1011110
[8,4,7,6,3,2,1,5]=>1011110
[5,8,7,4,3,2,1,6]=>0111110
[4,5,2,7,3,1,8,6]=>0101101
[4,8,2,6,3,5,7,1]=>0101001
[8,6,1,2,7,4,3,5]=>1100110
[4,6,2,1,7,8,5,3]=>0110011
[2,3,8,7,4,1,6,5]=>0011101
[1,6,2,5,8,4,3,7]=>0100110
[1,5,8,6,2,3,7,4]=>0011001
[5,2,7,1,8,6,3,4]=>1010110
[1,2,8,3,7,6,5,4]=>0010111
[6,5,2,8,1,7,3,4]=>1101010
[2,8,3,5,1,7,4,6]=>0101010
[2,8,5,6,1,7,3,4]=>0101010
[5,4,2,8,6,1,7,3]=>1101101
[8,5,4,3,7,2,6,1]=>1110101
[8,3,7,4,2,6,5,1]=>1011011
[3,8,7,4,1,6,5,2]=>0111011
[6,3,2,8,4,1,7,5]=>1101101
[2,8,3,4,1,7,5,6]=>0101010
[5,4,2,8,3,1,7,6]=>1101101
[2,8,6,4,1,7,5,3]=>0111011
[8,4,7,6,2,5,3,1]=>1011011
[4,8,7,6,1,5,3,2]=>0111011
[7,3,8,5,2,1,6,4]=>1011101
[7,3,8,4,2,1,6,5]=>1011101
[7,5,4,3,8,2,1,6]=>1110110
[5,4,2,3,8,1,6,7]=>1100100
[3,7,8,4,1,2,6,5]=>0011001
[8,7,4,6,3,5,2,1]=>1101011
[7,3,4,8,2,1,5,6]=>1001100
[7,5,8,6,2,1,4,3]=>1011101
[6,5,8,7,3,1,4,2]=>1011101
[2,4,8,3,1,5,7,6]=>0011001
[6,3,2,4,8,1,5,7]=>1100100
[2,4,3,8,1,6,5,7]=>0101010
[2,3,8,4,1,6,7,5]=>0011001
[8,3,4,7,2,5,6,1]=>1001001
[3,4,8,7,1,5,6,2]=>0011001
[2,5,3,8,1,6,4,7]=>0101010
[3,7,4,8,1,5,2,6]=>0101010
[8,4,6,7,2,3,5,1]=>1001001
[2,6,8,5,1,3,7,4]=>0011001
[2,6,8,4,1,3,7,5]=>0011001
[3,7,5,8,1,4,2,6]=>0101010
[2,6,5,8,1,4,3,7]=>0101010
[2,5,8,3,1,4,7,6]=>0011001
[4,7,6,8,1,3,2,5]=>0101010
[5,6,8,7,1,3,4,2]=>0011001
[8,7,4,1,6,2,5,3]=>1110101
[6,3,7,4,5,8,2,1]=>1010011
[3,5,7,4,6,8,2,1]=>0010011
[6,8,4,1,7,2,5,3]=>0110101
[3,8,5,4,6,7,2,1]=>0110011
[6,8,3,4,5,7,2,1]=>0100011
[2,5,7,4,6,3,8,1]=>0010101
[5,4,2,7,8,3,6,1]=>1100101
[8,1,6,2,4,3,5,7]=>1010100
[8,7,1,2,4,3,5,6]=>1100100
[6,8,3,1,4,7,2,5]=>0110010
[6,4,7,2,8,5,1,3]=>1010110
[5,8,1,4,7,3,2,6]=>0100110
[8,7,1,4,5,3,2,6]=>1100110
[1,7,6,2,4,3,5,8]=>0110100
[8,7,4,2,6,5,1,3]=>1110110
[8,7,3,2,4,6,5,1]=>1110011
[1,7,2,5,4,3,6,8]=>0101100
[6,8,4,3,7,5,2,1]=>0110111
[6,4,7,3,8,5,2,1]=>1010111
[6,3,7,2,4,8,5,1]=>1010011
[8,1,2,5,4,3,6,7]=>1001100
[2,6,3,1,4,5,8,7]=>0110001
[4,7,3,2,5,6,1,8]=>0110010
[3,6,4,1,2,8,7,5]=>0110011
[3,6,5,1,8,2,7,4]=>0110101
[4,6,5,1,8,7,2,3]=>0110110
[5,7,1,4,8,6,2,3]=>0100110
[5,7,1,3,8,2,6,4]=>0100101
[6,3,7,2,8,4,5,1]=>1010101
[6,7,1,8,3,2,5,4]=>0101101
[8,7,6,1,4,5,2,3]=>1110010
[8,7,6,1,3,2,5,4]=>1110101
[8,7,3,5,1,2,6,4]=>1101001
[8,7,4,5,1,6,2,3]=>1101010
[8,5,6,4,1,7,2,3]=>1011010
[8,4,6,2,3,1,7,5]=>1010101
[8,3,5,4,2,1,7,6]=>1011101
[7,1,6,8,4,5,3,2]=>1001011
[7,5,1,6,4,2,3,8]=>1101100
[8,1,5,7,4,6,3,2]=>1001011
[1,8,4,6,7,5,3,2]=>0100111
[6,1,8,4,7,5,3,2]=>1010111
[8,4,1,5,6,7,3,2]=>1100011
[8,2,5,6,1,4,7,3]=>1001001
[4,8,5,2,1,6,7,3]=>0111001
[1,8,4,6,2,5,3,7]=>0101010
[8,5,6,1,2,4,3,7]=>1010010
[2,8,3,1,5,6,7,4]=>0110001
[8,2,4,3,6,7,1,5]=>1010010
[8,3,2,7,1,5,6,4]=>1101001
[3,2,8,5,7,1,6,4]=>1010101
[3,6,2,8,5,1,7,4]=>0101101
[6,2,1,8,4,7,5,3]=>1101011
[2,8,7,1,4,6,5,3]=>0110011
[8,2,7,1,5,4,6,3]=>1010101
[7,3,1,5,6,2,4,8]=>1100100
[2,7,3,6,5,8,1,4]=>0101010
[7,2,8,1,6,4,5,3]=>1010101
[7,8,2,6,4,1,5,3]=>0101101
[8,7,2,4,1,6,5,3]=>1101011
[1,2,8,6,3,7,5,4]=>0011011
[1,8,7,2,3,6,5,4]=>0110011
[1,7,8,2,6,4,3,5]=>0010110
[7,2,1,5,8,3,4,6]=>1100100
[7,1,5,8,3,2,4,6]=>1001100
[7,8,1,5,2,4,3,6]=>0101010
[8,7,1,2,5,4,3,6]=>1100110
[1,6,2,8,4,3,7,5]=>0101101
[1,8,3,7,2,5,4,6]=>0101010
[8,1,4,7,3,2,5,6]=>1001100
[4,7,8,1,3,2,5,6]=>0010100
[2,1,8,3,5,7,4,6]=>1010010
[1,2,3,4,8,5,7,6]=>0000101
[8,3,5,2,4,1,7,6]=>1010101
[8,6,2,5,3,1,7,4]=>1101101
[3,7,2,5,6,4,1,8]=>0100110
[7,6,2,5,4,3,1,8]=>1101110
[4,7,5,2,6,3,1,8]=>0110110
[5,6,7,2,4,3,1,8]=>0010110
[1,8,3,4,2,7,5,6]=>0101010
[2,8,3,4,1,6,7,5]=>0101001
[7,8,2,4,3,1,6,5]=>0101101
[6,1,3,5,7,2,4,8]=>1000100
[8,1,3,6,2,4,7,5]=>1001001
[2,1,8,3,7,5,4,6]=>1010110
[7,1,8,2,5,6,3,4]=>1010010
[6,1,5,8,2,7,3,4]=>1001010
[6,2,5,8,1,4,7,3]=>1001001
[2,3,8,1,5,6,7,4]=>0010001
[1,3,8,2,5,7,4,6]=>0010010
[2,8,7,1,6,4,5,3]=>0110101
[3,8,7,1,5,6,4,2]=>0110011
[4,8,7,5,1,6,3,2]=>0111011
[5,8,6,7,1,4,3,2]=>0101011
[6,7,8,5,1,4,3,2]=>0011011
[5,6,3,8,4,1,7,2]=>0101101
[7,3,8,5,4,1,6,2]=>1011101
[3,4,8,5,6,1,7,2]=>0010101
[8,3,7,4,1,6,5,2]=>1011011
[3,5,6,8,4,1,7,2]=>0001101
[5,6,4,7,8,1,3,2]=>0100101
[6,2,3,1,5,4,7,8]=>1010100
[8,5,1,3,2,4,7,6]=>1101001
[7,5,1,3,2,6,4,8]=>1101010
[3,6,4,1,5,2,7,8]=>0110100
[4,5,6,1,3,2,7,8]=>0010100
[6,7,1,4,2,5,3,8]=>0101010
[2,7,1,3,5,6,4,8]=>0100010
[8,6,1,2,4,3,7,5]=>1100101
[7,8,1,2,5,3,6,4]=>0100101
[6,8,1,4,2,3,7,5]=>0101001
[4,5,8,1,2,3,7,6]=>0010001
[1,8,2,7,5,4,6,3]=>0101101
[1,8,6,3,7,2,4,5]=>0110100
[1,8,5,3,4,7,2,6]=>0110010
[1,8,2,5,4,6,7,3]=>0101001
[7,4,3,8,2,5,6,1]=>1101001
[7,2,8,4,3,5,6,1]=>1011001
[7,2,8,1,3,6,4,5]=>1010010
[1,4,7,5,2,6,8,3]=>0011001
[4,6,5,3,7,1,8,2]=>0110101
[5,6,2,7,3,1,8,4]=>0101101
[1,6,3,7,5,8,2,4]=>0101010
[5,2,4,8,1,3,7,6]=>1001001
[6,2,5,4,8,3,7,1]=>1010101
[3,5,2,4,7,1,6,8]=>0100100
[6,4,5,3,8,2,1,7]=>1010110
[6,5,3,4,8,7,1,2]=>1100110
[7,6,3,8,5,4,1,2]=>1101110
[5,4,8,1,2,7,3,6]=>1010010
[6,2,4,8,5,1,3,7]=>1001100
[7,6,3,8,5,1,2,4]=>1101100
[6,3,8,1,7,2,4,5]=>1010100
[7,2,8,6,1,3,4,5]=>1011000
[7,2,8,6,1,5,3,4]=>1011010
[3,2,4,7,8,1,5,6]=>1000100
[1,5,7,4,2,8,6,3]=>0011011
[1,3,7,2,8,6,4,5]=>0010110
[1,5,3,6,8,2,7,4]=>0100101
[4,3,6,5,7,8,1,2]=>1010010
[4,2,3,5,6,8,1,7]=>1000010
[4,2,6,7,3,8,5,1]=>1001011
[3,2,5,6,8,1,7,4]=>1000101
[4,2,3,6,8,1,5,7]=>1000100
[2,6,1,5,4,8,3,7]=>0101010
[3,2,1,8,7,5,6,4]=>1101101
[3,1,6,2,5,8,4,7]=>1010010
[6,5,1,3,4,8,2,7]=>1100010
[6,2,4,5,8,1,3,7]=>1000100
[2,6,1,5,8,3,4,7]=>0100100
[2,3,4,8,1,7,6,5]=>0001011
[6,3,1,7,8,4,5,2]=>1100101
[6,2,7,8,4,5,1,3]=>1001010
[3,1,4,8,7,6,2,5]=>1001110
[2,3,6,5,8,7,1,4]=>0010110
[8,4,1,2,7,6,3,5]=>1100110
[3,4,8,2,7,5,1,6]=>0010110
[6,3,2,8,5,7,4,1]=>1101011
[3,2,6,8,5,1,7,4]=>1001101
[5,2,4,1,7,8,6,3]=>1010011
[3,8,4,7,2,5,6,1]=>0101001
[1,8,7,2,4,5,6,3]=>0110001
[5,3,4,7,1,8,6,2]=>1001011
[5,3,7,1,6,2,8,4]=>1010101
[4,7,6,5,8,2,1,3]=>0110110
[7,5,1,2,6,8,4,3]=>1100011
[1,2,5,3,8,7,6,4]=>0010111
[2,8,1,5,6,3,7,4]=>0100101
[4,8,2,3,6,7,1,5]=>0100010
[8,2,4,6,7,1,3,5]=>1000100
[3,7,5,1,8,4,6,2]=>0110101
[6,5,3,1,8,4,2,7]=>1110110
[5,7,4,3,8,6,2,1]=>0110111
[4,2,3,8,5,6,1,7]=>1001010
[3,6,4,2,8,5,7,1]=>0110101
[4,7,3,2,5,1,8,6]=>0110101
[2,4,8,7,1,3,5,6]=>0011000
[2,4,3,5,1,8,6,7]=>0101010
[8,6,1,2,4,3,5,7]=>1100100
[8,6,2,5,4,1,3,7]=>1101100
[8,3,5,7,6,2,1,4]=>1001110
[6,7,5,3,8,2,4,1]=>0110101
[8,2,6,3,4,5,1,7]=>1010010
[8,1,5,4,3,6,2,7]=>1011010
[8,6,4,2,1,5,3,7]=>1111010
[8,3,2,4,6,1,5,7]=>1100100
[8,2,3,4,7,6,1,5]=>1000110
[5,7,1,8,3,4,6,2]=>0101001
[1,5,6,7,3,4,8,2]=>0001001
[4,8,1,2,7,3,6,5]=>0100101
[2,5,7,8,4,1,3,6]=>0001100
[6,3,5,8,7,2,4,1]=>1001101
[5,2,8,7,1,3,4,6]=>1011000
[5,2,7,4,8,1,6,3]=>1010101
[8,3,7,4,2,5,6,1]=>1011001
[8,1,7,4,5,2,6,3]=>1010101
[1,7,8,3,5,4,6,2]=>0010101
[4,6,3,5,8,1,7,2]=>0100101
[8,2,4,1,5,6,7,3]=>1010001
[3,5,1,7,6,8,2,4]=>0101010
[2,1,7,6,4,5,8,3]=>1011001
[1,7,6,5,2,4,8,3]=>0111001
[5,1,7,6,2,8,4,3]=>1011011
[4,6,2,5,3,8,7,1]=>0101011
[8,6,4,2,3,1,7,5]=>1110101
[8,6,4,2,1,3,7,5]=>1111001
[4,2,8,3,1,5,6,7]=>1011000
[2,5,7,3,8,4,6,1]=>0010101
[4,2,7,1,8,5,3,6]=>1010110
[1,3,7,5,8,6,4,2]=>0010111
[2,7,4,5,8,3,6,1]=>0100101
[3,5,7,1,4,8,6,2]=>0010011
[3,4,1,2,8,5,7,6]=>0100101
[6,2,3,1,4,8,7,5]=>1010011
[8,4,3,2,5,7,1,6]=>1110010
[5,3,6,8,2,1,4,7]=>1001100
[3,2,6,8,5,4,1,7]=>1001110
[7,3,8,2,5,4,1,6]=>1010110
[7,4,2,5,8,3,1,6]=>1100110
[3,1,2,8,5,6,4,7]=>1001010
[5,2,1,6,8,3,4,7]=>1100100
[3,1,8,6,5,4,2,7]=>1011110
[5,6,8,1,4,3,2,7]=>0010110
[6,4,8,3,7,2,5,1]=>1010101
[4,7,3,6,2,1,8,5]=>0101101
[7,8,4,1,5,3,2,6]=>0110110
[7,3,8,5,1,4,2,6]=>1011010
[1,5,4,8,3,7,6,2]=>0101011
[4,7,8,3,1,6,5,2]=>0011011
[8,7,5,3,6,4,2,1]=>1110111
[4,6,1,3,8,7,5,2]=>0100111
[3,1,2,7,5,6,8,4]=>1001001
[3,6,1,2,7,5,8,4]=>0100101
[3,6,2,5,8,7,4,1]=>0100111
[8,5,2,3,6,7,4,1]=>1100011
[6,7,1,3,2,8,4,5]=>0101010
[6,2,7,1,3,4,8,5]=>1010001
[5,2,1,7,3,8,4,6]=>1101010
[4,7,2,6,3,8,1,5]=>0101010
[4,8,2,6,3,7,5,1]=>0101011
[3,7,2,4,6,1,8,5]=>0100101
[5,3,7,2,8,1,4,6]=>1010100
[7,1,8,3,4,2,5,6]=>1010100
[7,2,4,1,8,3,5,6]=>1010100
[4,8,7,6,3,2,1,5]=>0111110
[7,3,8,2,6,5,1,4]=>1010110
[7,8,2,4,6,1,5,3]=>0100101
[3,5,1,8,7,2,6,4]=>0101101
[5,2,8,1,7,6,3,4]=>1010110
[6,2,1,3,8,7,5,4]=>1100111
[6,7,8,1,2,5,4,3]=>0010011
[5,8,7,1,6,4,3,2]=>0110111
[6,8,7,5,1,4,3,2]=>0111011
[8,6,4,3,2,1,7,5]=>1111101
[6,5,4,3,8,2,7,1]=>1110101
[7,5,4,3,2,8,6,1]=>1111011
[8,5,4,3,7,2,1,6]=>1110110
[8,4,3,2,1,7,6,5]=>1111011
[3,7,5,8,1,4,6,2]=>0101001
[4,7,5,8,3,2,1,6]=>0101110
[5,7,2,3,6,1,8,4]=>0100101
[7,3,1,4,8,2,5,6]=>1100100
[7,4,1,2,5,8,3,6]=>1100010
[4,7,1,6,5,8,3,2]=>0101011
[2,7,5,4,3,8,1,6]=>0111010
[8,6,4,2,3,7,5,1]=>1110011
[7,6,4,2,3,8,1,5]=>1110010
[6,4,7,1,3,8,5,2]=>1010011
[3,1,2,4,8,7,6,5]=>1000111
[6,5,8,7,3,1,2,4]=>1011100
[5,6,7,8,1,4,2,3]=>0001010
[2,6,7,4,5,3,1,8]=>0010110
[1,3,7,4,2,8,5,6]=>0011010
[4,6,1,3,7,2,5,8]=>0100100
[6,5,7,8,3,1,4,2]=>1001101
[7,5,8,6,2,1,3,4]=>1011100
[2,8,1,3,6,5,4,7]=>0100110
[2,8,7,3,5,4,1,6]=>0110110
[3,4,2,6,8,7,1,5]=>0100110
[6,1,4,2,7,8,5,3]=>1010011
[7,3,8,4,1,2,6,5]=>1011001
[6,8,3,2,7,1,5,4]=>0110101
[5,1,4,3,6,2,7,8]=>1010100
[4,8,5,6,3,2,1,7]=>0101110
[2,8,5,6,3,7,1,4]=>0101010
[6,7,3,1,4,2,8,5]=>0110101
[3,2,6,7,4,8,1,5]=>1001010
[3,7,1,2,4,6,5,8]=>0100010
[4,1,8,2,6,3,5,7]=>1010100
[7,5,6,8,2,1,4,3]=>1001101
[5,8,6,7,1,2,3,4]=>0101000
[4,8,1,5,7,2,3,6]=>0100100
[3,5,1,4,7,6,8,2]=>0100101
[5,3,2,7,1,6,8,4]=>1101001
[8,4,3,7,5,1,6,2]=>1101101
[5,1,7,2,4,6,8,3]=>1010001
[4,5,7,1,2,6,8,3]=>0010001
[5,4,1,7,3,6,8,2]=>1101001
[3,6,4,7,5,2,8,1]=>0101101
[3,4,7,6,2,5,8,1]=>0011001
[4,8,3,6,5,2,1,7]=>0101110
[1,8,6,5,4,2,3,7]=>0111100
[8,1,7,4,2,5,6,3]=>1011001
[1,8,7,2,5,3,4,6]=>0110100
[4,8,1,5,2,6,3,7]=>0101010
[3,6,8,5,1,2,4,7]=>0011000
[1,5,2,7,8,4,6,3]=>0100101
[6,7,2,8,5,3,1,4]=>0101110
[6,7,2,8,3,1,5,4]=>0101101
[7,1,2,8,3,5,6,4]=>1001001
[6,7,5,2,8,1,4,3]=>0110101
[7,1,4,5,8,6,2,3]=>1000110
[3,1,4,6,7,8,5,2]=>1000011
[5,7,6,4,2,8,1,3]=>0111010
[7,4,6,1,8,2,3,5]=>1010100
[3,4,5,1,6,8,7,2]=>0010011
[5,1,6,8,4,2,7,3]=>1001101
[7,4,8,2,3,6,5,1]=>1010011
[7,5,8,6,3,4,2,1]=>1011011
[5,7,8,3,1,6,4,2]=>0011011
[7,5,8,3,2,4,1,6]=>1011010
[6,4,1,8,2,5,7,3]=>1101001
[5,8,2,6,3,1,4,7]=>0101100
[3,6,5,1,8,4,7,2]=>0110101
[8,2,7,5,4,1,3,6]=>1011100
[6,8,5,2,3,4,1,7]=>0110010
[2,6,8,7,1,5,3,4]=>0011010
[7,5,1,6,2,8,4,3]=>1101011
[6,2,7,3,8,4,1,5]=>1010110
[3,7,2,4,8,5,1,6]=>0100110
[1,5,2,6,3,8,7,4]=>0101011
[1,3,6,2,4,8,7,5]=>0010011
[7,3,5,2,4,1,6,8]=>1010100
[8,3,6,2,5,4,1,7]=>1010110
[3,5,8,2,4,6,1,7]=>0010010
[6,4,7,8,2,3,1,5]=>1001010
[7,4,8,5,3,2,1,6]=>1011110
[1,5,3,2,8,4,7,6]=>0110101
[2,8,7,3,5,1,4,6]=>0110100
[3,8,4,7,5,1,2,6]=>0101100
[6,1,2,7,3,8,5,4]=>1001011
[2,1,7,3,4,8,6,5]=>1010011
[8,3,1,6,7,2,5,4]=>1100101
[4,8,3,7,1,5,2,6]=>0101010
[1,3,5,8,2,4,7,6]=>0001001
[5,3,7,2,1,4,6,8]=>1011000
[6,4,2,8,3,1,5,7]=>1101100
[5,7,2,3,8,1,4,6]=>0100100
[6,4,7,5,8,1,2,3]=>1010100
[8,6,4,2,1,7,5,3]=>1111011
[7,4,2,1,5,8,6,3]=>1110011
[7,6,4,1,8,5,2,3]=>1110110
[1,6,4,8,7,5,3,2]=>0101111
[6,3,1,2,8,4,7,5]=>1100101
[3,6,1,8,2,4,7,5]=>0101001
[6,4,1,8,3,2,7,5]=>1101101
[1,4,8,7,2,6,5,3]=>0011011
[5,4,1,8,7,3,2,6]=>1101110
[5,8,4,1,7,6,2,3]=>0110110
[8,6,1,7,5,4,3,2]=>1101111
[3,1,8,7,6,5,2,4]=>1011110
[8,1,2,4,5,3,6,7]=>1000100
[1,8,7,6,4,5,3,2]=>0111011
[2,6,8,1,3,7,5,4]=>0010011
[2,4,8,1,5,7,6,3]=>0010011
[3,2,8,6,1,7,5,4]=>1011011
[6,2,8,3,1,7,5,4]=>1011011
[7,4,3,8,5,2,1,6]=>1101110
[6,5,2,8,4,3,1,7]=>1101110
[4,3,8,7,5,1,6,2]=>1011101
[4,2,3,8,5,1,6,7]=>1001100
[4,2,8,5,1,7,6,3]=>1011011
[3,4,2,8,5,6,1,7]=>0101010
[3,2,4,8,6,1,5,7]=>1001100
[3,2,5,8,6,1,4,7]=>1001100
[8,4,3,7,5,2,6,1]=>1101101
[4,3,7,8,5,1,2,6]=>1001100
[4,2,6,8,5,1,3,7]=>1001100
[3,5,2,8,4,6,1,7]=>0101010
[5,2,6,8,4,1,3,7]=>1001100
[5,3,7,8,4,1,2,6]=>1001100
[5,6,2,8,3,4,1,7]=>0101010
[5,3,8,7,4,1,6,2]=>1011101
[6,4,2,8,5,3,1,7]=>1101110
[8,7,5,3,6,2,4,1]=>1110101
[8,7,4,3,6,2,5,1]=>1110101
[8,6,5,3,7,2,4,1]=>1110101
[7,6,4,3,8,2,5,1]=>1110101
[6,4,5,3,8,2,7,1]=>1010101
[7,4,5,3,8,2,6,1]=>1010101
[7,5,6,3,8,2,4,1]=>1010101
[8,5,6,3,7,2,4,1]=>1010101
[8,4,6,3,7,2,5,1]=>1010101
[8,4,7,3,5,2,6,1]=>1010101
[8,5,7,3,4,2,6,1]=>1010101
[7,5,8,4,3,2,6,1]=>1011101
[6,5,8,3,4,2,7,1]=>1010101
[7,5,8,3,4,2,6,1]=>1010101
[7,6,8,3,5,2,4,1]=>1010101
[7,5,8,4,6,2,3,1]=>1010101
[7,5,8,3,6,2,4,1]=>1010101
[7,4,8,3,6,2,5,1]=>1010101
[7,4,8,3,5,2,6,1]=>1010101
[6,4,8,3,5,2,7,1]=>1010101
[5,4,7,3,6,2,8,1]=>1010101
[5,4,8,3,7,2,6,1]=>1010101
[6,5,8,3,7,2,4,1]=>1010101
[6,5,8,4,7,2,3,1]=>1010101
[6,5,8,4,7,3,2,1]=>1010111
[6,5,7,3,8,2,4,1]=>1010101
[5,4,6,3,8,2,7,1]=>1010101
[6,5,3,7,8,2,1,4]=>1100110
[6,5,4,2,8,7,1,3]=>1110110
[6,4,3,7,5,2,1,8]=>1101110
[6,3,7,8,5,2,1,4]=>1001110
[6,3,7,2,5,4,1,8]=>1010110
[6,3,2,7,5,4,1,8]=>1101110
[4,8,2,6,3,7,1,5]=>0101010
[5,8,4,1,2,7,3,6]=>0110010
[5,4,8,1,2,3,7,6]=>1010001
[1,4,7,6,3,2,5,8]=>0011100
[4,8,3,2,7,6,1,5]=>0110110
[5,8,1,7,4,2,3,6]=>0101100
[4,8,6,7,2,3,1,5]=>0101010
[4,8,7,3,6,2,1,5]=>0110110
[4,3,8,2,7,1,6,5]=>1010101
[4,1,8,7,3,2,5,6]=>1011100
[4,7,8,1,2,5,3,6]=>0010010
[4,7,5,1,2,8,3,6]=>0110010
[2,3,6,7,4,1,8,5]=>0001101
[2,6,3,4,7,8,1,5]=>0100010
[3,1,7,8,4,2,5,6]=>1001100
[4,3,1,2,8,5,7,6]=>1100101
[3,7,6,8,4,2,1,5]=>0101110
[4,7,1,8,5,2,3,6]=>0101100
[2,6,8,7,4,3,1,5]=>0011110
[3,7,8,6,2,4,1,5]=>0011010
[3,7,8,2,6,4,1,5]=>0010110
[4,2,3,8,1,6,7,5]=>1001001
[3,7,2,8,4,6,1,5]=>0101010
[4,2,8,3,6,1,7,5]=>1010101
[4,2,8,6,3,1,7,5]=>1011101
[2,6,8,4,7,3,1,5]=>0010110
[2,4,6,8,3,1,7,5]=>0001101
[3,7,2,4,8,6,1,5]=>0100110
[1,3,6,4,7,2,5,8]=>0010100
[2,4,6,3,8,1,7,5]=>0010101
[2,6,4,3,8,7,1,5]=>0110110
[2,4,3,6,1,8,7,5]=>0101011
[3,1,7,4,8,2,5,6]=>1010100
[2,6,3,7,4,8,1,5]=>0101010
[1,3,5,7,6,8,2,4]=>0001010
[1,3,5,7,6,2,8,4]=>0001101
[1,3,5,7,2,6,8,4]=>0001001
[1,3,5,2,7,6,8,4]=>0010101
[1,3,5,2,7,6,4,8]=>0010110
[1,3,5,7,6,2,4,8]=>0001100
[1,3,5,7,4,6,8,2]=>0001001
[1,3,5,7,4,6,2,8]=>0001010
[1,3,5,7,4,2,6,8]=>0001100
[1,3,5,4,7,2,6,8]=>0010100
[1,3,5,4,7,8,2,6]=>0010010
[1,3,5,4,7,2,8,6]=>0010101
[1,3,5,7,4,2,8,6]=>0001101
[1,3,5,7,4,8,2,6]=>0001010
[1,3,5,7,4,8,6,2]=>0001011
[1,3,5,7,8,4,6,2]=>0000101
[1,3,5,7,8,4,2,6]=>0000110
[1,3,5,2,7,8,6,4]=>0010011
[1,3,5,7,2,8,6,4]=>0001011
[1,3,5,7,8,2,6,4]=>0000101
[1,3,5,7,8,6,2,4]=>0000110
[2,3,6,1,7,8,5,4]=>0010011
[2,3,7,1,4,8,6,5]=>0010011
[2,6,1,3,7,8,5,4]=>0100011
[2,3,6,8,4,5,1,7]=>0001010
[2,5,7,3,4,8,6,1]=>0010011
[2,6,7,3,4,8,5,1]=>0010011
[6,5,2,4,3,7,1,8]=>1101010
[2,5,4,6,7,1,3,8]=>0100100
[1,7,6,3,5,4,8,2]=>0110101
[2,4,6,3,7,5,1,8]=>0010110
[4,7,2,3,5,6,1,8]=>0100010
[5,3,2,7,4,6,1,8]=>1101010
[1,6,8,5,7,3,4,2]=>0010101
[4,1,2,5,8,3,7,6]=>1000101
[4,6,1,2,5,8,3,7]=>0100010
[4,1,7,2,6,5,8,3]=>1010101
[5,6,7,2,1,4,8,3]=>0011001
[6,4,5,7,1,3,8,2]=>1001001
[6,8,5,2,4,1,7,3]=>0110101
[5,7,6,8,1,4,2,3]=>0101010
[4,1,6,2,8,5,7,3]=>1010101
[7,1,4,2,3,6,8,5]=>1010001
[6,4,2,1,3,8,7,5]=>1110011
[1,5,8,3,4,6,7,2]=>0010001
[8,1,2,3,4,6,7,5]=>1000001
[2,8,1,3,5,4,7,6]=>0100101
[8,7,1,4,3,5,2,6]=>1101010
[8,3,2,1,4,5,7,6]=>1110001
[4,3,2,8,1,6,5,7]=>1101010
[3,8,6,4,2,1,5,7]=>0111100
[3,8,2,1,5,6,4,7]=>0110010
[8,5,2,4,3,1,6,7]=>1101100
[8,3,2,5,4,1,6,7]=>1101100
[6,1,2,7,5,3,8,4]=>1001101
[2,6,1,4,7,3,8,5]=>0100101
[7,3,2,8,6,4,1,5]=>1101110
[7,8,2,5,3,6,1,4]=>0101010
[6,3,7,5,1,8,2,4]=>1011010
[8,1,6,3,5,7,2,4]=>1010010
[8,3,2,6,4,7,1,5]=>1101010
[5,8,4,6,1,7,2,3]=>0101010
[8,4,2,5,6,7,1,3]=>1100010
[2,3,8,7,6,5,1,4]=>0011110
[1,5,8,7,2,6,4,3]=>0011011
[2,5,8,7,3,6,1,4]=>0011010
[4,1,8,7,2,6,5,3]=>1011011
[1,2,8,7,3,6,5,4]=>0011011
[4,5,8,7,1,2,6,3]=>0011001
[1,5,8,7,3,2,6,4]=>0011101
[4,5,8,7,3,2,1,6]=>0011110
[2,6,8,1,7,5,4,3]=>0010111
[2,6,8,3,7,5,1,4]=>0010110
[1,6,8,4,7,2,5,3]=>0010101
[1,6,8,3,7,2,5,4]=>0010101
[2,5,8,1,7,6,4,3]=>0010111
[2,5,8,3,7,6,1,4]=>0010110
[3,2,8,4,7,6,1,5]=>1010110
[1,5,8,4,7,2,6,3]=>0010101
[1,5,8,3,7,2,6,4]=>0010101
[3,1,8,4,7,2,6,5]=>1010101
[5,6,8,1,2,7,4,3]=>0010011
[1,6,8,2,3,7,5,4]=>0010011
[1,5,8,4,2,7,6,3]=>0011011
[5,6,8,4,3,2,1,7]=>0011110
[7,1,4,8,6,2,5,3]=>1001101
[7,3,4,8,6,2,1,5]=>1001110
[7,1,5,8,2,6,4,3]=>1001011
[7,1,4,8,2,6,5,3]=>1001011
[7,4,5,8,1,2,6,3]=>1001001
[3,6,2,8,7,5,1,4]=>0101110
[1,6,4,8,7,2,5,3]=>0101101
[3,2,4,8,7,6,1,5]=>1001110
[1,4,5,8,7,2,6,3]=>0001101
[3,1,4,8,7,2,6,5]=>1001101
[1,6,5,8,2,7,4,3]=>0101011
[2,6,5,8,3,7,1,4]=>0101010
[1,6,4,8,2,7,5,3]=>0101011
[2,6,1,8,3,7,5,4]=>0101011
[1,4,5,8,3,2,7,6]=>0001101
[4,6,5,8,3,2,1,7]=>0101110
[7,6,2,3,8,5,1,4]=>1100110
[7,6,1,4,8,2,5,3]=>1100101
[7,6,3,4,8,2,1,5]=>1100110
[7,2,5,3,8,6,1,4]=>1010110
[7,2,1,4,8,6,5,3]=>1100111
[7,2,1,3,8,6,5,4]=>1100111
[2,6,5,3,8,7,1,4]=>0110110
[2,6,1,4,8,7,5,3]=>0100111
[1,3,5,4,8,2,7,6]=>0010101
[7,6,5,1,2,8,4,3]=>1110011
[7,1,5,2,3,8,6,4]=>1010011
[7,1,2,4,3,8,6,5]=>1001011
[7,2,5,4,3,8,1,6]=>1011010
[1,6,2,4,3,8,7,5]=>0101011
[2,6,5,4,3,8,1,7]=>0111010
[7,6,5,1,3,2,8,4]=>1110101
[8,2,7,6,5,4,1,3]=>1011110
[7,2,8,6,5,4,3,1]=>1011111
[3,2,8,7,6,5,1,4]=>1011110
[4,8,7,6,5,3,1,2]=>0111110
[7,8,6,1,5,4,3,2]=>0110111
[4,8,5,7,6,3,2,1]=>0101111
[3,2,4,6,8,1,5,7]=>1000100
[3,5,7,2,4,8,1,6]=>0010010
[3,5,7,2,4,6,8,1]=>0010001
[4,5,1,3,6,8,2,7]=>0100010
[4,3,5,7,2,6,8,1]=>1001001
[4,3,5,1,7,8,2,6]=>1010010
[4,6,3,5,1,7,8,2]=>0101001
[4,6,3,5,7,2,8,1]=>0100101
[5,1,6,7,3,4,8,2]=>1001001
[1,6,7,3,4,5,8,2]=>0010001
[2,6,7,4,5,8,1,3]=>0010010
[2,6,7,4,8,1,3,5]=>0010100
[1,4,6,7,3,8,2,5]=>0001010
[3,5,2,6,7,4,8,1]=>0100101
[6,3,1,7,8,2,4,5]=>1100100
[5,7,2,8,1,3,4,6]=>0101000
[6,3,7,2,8,1,4,5]=>1010100
[6,3,7,2,5,8,1,4]=>1010010
[6,2,4,5,7,3,8,1]=>1000101
[2,4,6,7,1,5,8,3]=>0001001
[2,4,7,1,5,6,8,3]=>0010001
[3,7,1,5,6,8,2,4]=>0100010
[4,6,7,1,2,5,8,3]=>0010001
[1,5,6,7,2,4,8,3]=>0001001
[5,6,2,4,1,7,8,3]=>0101001
[1,5,4,6,2,7,8,3]=>0101001
[5,6,4,7,1,3,8,2]=>0101001
[8,4,5,2,6,1,3,7]=>1010100
[6,4,3,7,2,5,8,1]=>1101001
[6,4,3,7,2,8,1,5]=>1101010
[7,4,5,3,1,6,8,2]=>1011001
[6,4,3,7,5,1,8,2]=>1101101
[5,6,3,7,4,1,8,2]=>0101101
[6,7,4,2,1,5,8,3]=>0111001
[6,7,4,2,1,8,3,5]=>0111010
[5,6,7,3,1,8,2,4]=>0011010
[5,6,3,7,8,1,2,4]=>0100100
[5,6,3,7,2,4,8,1]=>0101001
[5,6,7,2,3,8,1,4]=>0010010
[5,6,7,2,8,1,3,4]=>0010100
[6,7,3,8,1,2,4,5]=>0101000
[6,7,3,2,8,1,4,5]=>0110100
[7,6,4,2,1,3,8,5]=>1111001
[7,6,3,4,1,2,8,5]=>1101001
[7,6,3,2,4,1,8,5]=>1110101
[7,5,3,2,6,1,8,4]=>1110101
[6,5,3,2,7,8,1,4]=>1110010
[6,4,7,2,5,1,8,3]=>1010101
[6,4,7,5,1,2,8,3]=>1011001
[5,6,4,2,7,3,8,1]=>0110101
[6,5,3,7,1,8,2,4]=>1101010
[6,5,7,2,1,4,8,3]=>1011001
[5,4,6,7,3,1,8,2]=>1001101
[5,7,8,3,6,4,1,2]=>0010110
[3,7,8,5,6,4,1,2]=>0010110
[3,7,8,5,6,1,4,2]=>0010101
[1,7,8,5,6,3,4,2]=>0010101
[1,7,5,8,6,3,4,2]=>0101101
[3,7,5,8,6,1,4,2]=>0101101
[3,7,5,8,6,4,1,2]=>0101110
[5,7,3,8,6,4,1,2]=>0101110
[7,3,8,5,6,4,1,2]=>1010110
[7,3,5,8,6,4,1,2]=>1001110
[3,5,7,8,6,4,1,2]=>0001110
[1,5,7,8,6,3,4,2]=>0001101
[1,5,7,8,3,6,4,2]=>0001011
[5,3,7,8,1,6,4,2]=>1001011
[5,3,7,8,6,1,4,2]=>1001101
[7,3,5,8,6,1,4,2]=>1001101
[7,3,8,5,6,1,4,2]=>1010101
[7,8,3,5,6,1,4,2]=>0100101
[7,8,1,5,6,3,4,2]=>0100101
[7,1,8,5,6,3,4,2]=>1010101
[7,1,5,8,6,3,4,2]=>1001101
[5,1,7,8,6,3,4,2]=>1001101
[5,1,7,8,3,6,4,2]=>1001011
[3,1,7,8,5,6,4,2]=>1001011
[1,3,7,8,5,6,4,2]=>0001011
[3,1,7,5,8,6,4,2]=>1010111
[5,1,7,3,8,6,4,2]=>1010111
[7,1,5,3,8,6,4,2]=>1010111
[7,1,5,8,3,6,4,2]=>1001011
[7,8,1,5,3,6,4,2]=>0101011
[7,8,3,5,1,6,4,2]=>0101011
[7,3,8,5,1,6,4,2]=>1011011
[7,3,5,8,1,6,4,2]=>1001011
[7,3,5,1,8,6,4,2]=>1010111
[5,3,7,1,8,6,4,2]=>1010111
[3,5,7,1,8,6,4,2]=>0010111
[1,5,7,3,8,6,4,2]=>0010111
[1,7,5,3,8,6,4,2]=>0110111
[3,7,5,1,8,6,4,2]=>0110111
[5,7,3,1,8,6,4,2]=>0110111
[5,7,3,8,6,1,4,2]=>0101101
[3,7,5,8,1,6,4,2]=>0101011
[1,7,5,8,3,6,4,2]=>0101011
[1,7,8,5,3,6,4,2]=>0011011
[3,7,8,5,1,6,4,2]=>0011011
[5,7,8,3,6,1,4,2]=>0010101
[5,7,8,6,3,1,4,2]=>0011101
[7,5,8,6,1,3,4,2]=>1011001
[5,7,8,1,6,3,4,2]=>0010101
[5,7,8,1,3,6,4,2]=>0010011
[1,7,8,3,5,6,4,2]=>0010011
[1,7,3,8,5,6,4,2]=>0101011
[3,7,1,8,5,6,4,2]=>0101011
[5,7,1,8,3,6,4,2]=>0101011
[5,7,1,8,6,3,4,2]=>0101101
[7,5,1,8,6,3,4,2]=>1101101
[7,5,8,1,6,3,4,2]=>1010101
[7,8,5,1,6,3,4,2]=>0110101
[7,8,5,1,3,6,4,2]=>0110011
[7,5,8,1,3,6,4,2]=>1010011
[7,5,1,8,3,6,4,2]=>1101011
[7,5,1,3,8,6,4,2]=>1100111
[5,7,1,3,8,6,4,2]=>0100111
[3,7,1,5,8,6,4,2]=>0100111
[1,7,3,5,8,6,4,2]=>0100111
[1,5,3,7,8,6,4,2]=>0100111
[3,5,1,7,8,6,4,2]=>0100111
[5,3,1,7,8,6,4,2]=>1100111
[7,3,1,5,8,6,4,2]=>1100111
[7,3,1,8,5,6,4,2]=>1101011
[7,8,1,3,5,6,4,2]=>0100011
[7,1,8,3,5,6,4,2]=>1010011
[7,1,3,8,5,6,4,2]=>1001011
[7,1,3,5,8,6,4,2]=>1000111
[5,1,3,7,8,6,4,2]=>1000111
[3,1,5,7,8,6,4,2]=>1000111
[4,3,1,2,6,5,8,7]=>1100101
[6,1,4,3,5,2,8,7]=>1010101
[4,6,3,5,1,2,8,7]=>0101001
[6,2,4,5,1,3,8,7]=>1001001
[2,3,6,1,5,4,8,7]=>0010101
[2,1,6,5,3,4,8,7]=>1011001
[3,5,6,2,4,1,8,7]=>0010101
[8,7,6,1,3,2,4,5]=>1110100
[2,5,3,4,8,1,7,6]=>0100101
[5,1,8,2,3,4,7,6]=>1010001
[5,4,7,6,2,8,1,3]=>1011010
[2,1,6,8,5,7,3,4]=>1001010
[2,1,8,4,6,7,3,5]=>1010010
[3,1,8,6,2,7,5,4]=>1011011
[3,8,1,5,6,7,2,4]=>0100010
[8,2,3,5,7,1,6,4]=>1000101
[5,8,4,3,7,1,6,2]=>0110101
[2,8,3,6,7,5,1,4]=>0100110
[8,1,2,7,3,5,6,4]=>1001001
[6,8,4,2,1,3,7,5]=>0111001
[4,3,8,2,7,6,1,5]=>1010110
[2,1,4,5,8,3,7,6]=>1000101
[8,4,7,1,5,2,3,6]=>1010100
[7,3,5,8,4,2,1,6]=>1001110
[2,4,8,3,5,6,7,1]=>0010001
[6,4,7,5,2,3,8,1]=>1011001
[6,4,8,1,7,3,2,5]=>1010110
[2,1,4,3,8,7,5,6]=>1010110
[4,3,1,2,8,6,7,5]=>1100101
[5,1,6,7,8,4,3,2]=>1000111
[8,7,2,6,4,1,5,3]=>1101101
[2,1,5,7,8,4,6,3]=>1000101
[6,4,1,5,7,2,8,3]=>1100101
[7,4,8,1,2,5,6,3]=>1010001
[6,1,7,4,3,2,8,5]=>1011101
[6,8,3,4,2,1,7,5]=>0101101
[4,2,6,1,5,7,8,3]=>1010001
[7,1,4,8,3,5,6,2]=>1001001
[3,4,8,2,5,7,6,1]=>0010011
[3,7,1,4,5,6,8,2]=>0100001
[6,5,3,8,4,7,1,2]=>1101010
[8,6,4,7,5,3,1,2]=>1101110
[1,6,3,7,5,8,4,2]=>0101011
[1,3,7,4,5,8,6,2]=>0010011
[7,3,8,5,4,6,1,2]=>1011010
[3,4,8,5,6,7,1,2]=>0010010
[4,7,3,8,5,6,1,2]=>0101010
[6,8,4,7,5,3,1,2]=>0101110
[1,7,6,5,3,8,4,2]=>0111011
[2,7,6,3,1,4,5,8]=>0111000
[2,7,6,4,5,1,3,8]=>0110100
[5,7,2,6,4,1,3,8]=>0101100
[7,6,1,5,3,8,4,2]=>1101011
[1,8,2,7,3,6,5,4]=>0101011
[2,1,3,8,4,7,5,6]=>1001010
[3,1,2,8,4,6,7,5]=>1001001
[4,1,7,2,8,5,6,3]=>1010101
[5,1,2,4,8,3,7,6]=>1000101
[2,8,4,1,5,6,3,7]=>0110010
[1,7,2,8,5,3,6,4]=>0101101
[1,2,3,8,4,5,7,6]=>0001001
[2,4,8,3,1,5,6,7]=>0011000
[3,2,5,6,1,4,7,8]=>1001000
[4,7,3,8,2,1,5,6]=>0101100
[7,4,8,3,2,1,5,6]=>1011100
[7,6,8,5,1,4,3,2]=>1011011
[6,5,1,2,8,3,7,4]=>1100101
[6,8,4,1,3,7,5,2]=>0110011
[6,3,7,1,8,4,5,2]=>1010101
[5,8,3,1,7,4,6,2]=>0110101
[4,7,1,2,8,3,6,5]=>0100101
[3,4,1,8,5,6,7,2]=>0101001
[1,2,8,7,6,3,5,4]=>0011101
[2,3,1,8,7,4,5,6]=>0101100
[2,6,1,4,8,7,3,5]=>0100110
[5,8,2,1,7,6,3,4]=>0110110
[8,7,1,6,5,4,3,2]=>1101111
[3,1,8,7,6,4,5,2]=>1011101
[1,2,3,4,8,7,5,6]=>0000110
[1,2,3,8,6,4,5,7]=>0001100
[1,2,8,5,3,4,6,7]=>0011000
[1,8,4,2,3,5,6,7]=>0110000
[2,4,7,5,6,8,3,1]=>0010011
[2,5,3,8,7,4,6,1]=>0101101
[3,1,8,5,7,4,2,6]=>1010110
[8,3,5,7,4,2,6,1]=>1001101
[8,3,6,2,4,5,7,1]=>1010001
[2,7,6,4,5,8,3,1]=>0110011
[4,8,1,7,6,3,2,5]=>0101110
[3,7,1,8,6,2,5,4]=>0101101
[7,3,6,4,2,8,5,1]=>1011011
[5,8,7,1,4,3,2,6]=>0110110
[5,6,1,2,4,3,8,7]=>0100101
[3,6,8,1,2,7,5,4]=>0010011
[8,4,6,2,1,3,7,5]=>1011001
[4,8,1,5,3,7,2,6]=>0101010
[5,4,8,7,3,1,2,6]=>1011100
[6,4,3,8,1,5,2,7]=>1101010
[6,8,3,7,2,5,4,1]=>0101011
[5,3,6,8,7,2,4,1]=>1001101
[5,7,4,2,8,3,6,1]=>0110101
[6,4,7,2,1,8,3,5]=>1011010
[5,7,8,2,6,4,1,3]=>0010110
[2,6,8,4,5,7,1,3]=>0010010
[1,7,4,8,6,2,3,5]=>0101100
[2,7,4,8,5,6,1,3]=>0101010
[6,3,7,2,8,5,1,4]=>1010110
[3,6,2,5,7,8,1,4]=>0100010
[5,3,6,7,1,8,4,2]=>1001011
[8,1,3,6,7,2,4,5]=>1000100
[8,1,4,2,7,5,3,6]=>1010110
[6,1,3,8,2,7,4,5]=>1001010
[4,1,5,3,2,8,6,7]=>1011010
[2,7,1,4,3,8,5,6]=>0101010
[1,7,5,2,8,6,3,4]=>0110110
[7,4,2,5,1,8,6,3]=>1101011
[5,6,3,2,1,8,7,4]=>0111011
[4,5,3,2,7,1,8,6]=>0110101
[5,3,6,2,8,1,7,4]=>1010101
[6,4,2,8,5,1,7,3]=>1101101
[1,8,4,7,2,5,3,6]=>0101010
[1,5,8,4,2,6,3,7]=>0011010
[3,5,7,4,1,6,8,2]=>0011001
[4,5,8,3,1,7,6,2]=>0011011
[3,4,7,8,2,1,6,5]=>0001101
[4,6,3,5,2,1,8,7]=>0101101
[3,5,7,1,2,6,4,8]=>0010010
[7,4,1,2,8,6,3,5]=>1100110
[5,2,6,1,3,4,8,7]=>1010001
[3,8,2,6,5,4,1,7]=>0101110
[3,8,7,2,5,4,1,6]=>0110110
[7,5,1,6,8,4,3,2]=>1100111
[7,4,2,1,5,6,3,8]=>1110010
[7,3,8,1,5,4,6,2]=>1010101
[7,2,8,6,5,1,3,4]=>1011100
[6,2,7,8,5,4,1,3]=>1001110
[5,3,2,6,7,4,1,8]=>1100110
[4,8,2,6,5,7,1,3]=>0101010
[4,3,7,2,5,6,1,8]=>1010010
[3,8,7,6,2,4,1,5]=>0111010
[6,7,1,4,3,2,5,8]=>0101100
[3,5,6,2,4,7,1,8]=>0010010
[3,5,8,7,2,4,6,1]=>0011001
[1,7,8,2,5,4,3,6]=>0010110
[2,7,1,3,6,5,4,8]=>0100110
[5,7,1,4,6,3,2,8]=>0100110
[6,3,7,1,5,4,2,8]=>1010110
[4,7,1,6,3,5,2,8]=>0101010
[8,7,3,6,1,5,4,2]=>1101011
[5,7,8,3,2,1,4,6]=>0011100
[5,4,2,1,7,8,3,6]=>1110010
[4,7,8,3,5,2,1,6]=>0010110
[8,3,7,6,4,2,1,5]=>1011110
[8,3,2,1,4,7,6,5]=>1110011
[6,4,1,7,3,8,5,2]=>1101011
[1,7,5,3,8,2,6,4]=>0110101
[5,1,7,4,2,8,6,3]=>1011011
[8,6,3,2,7,5,1,4]=>1110110
[2,7,5,1,3,8,6,4]=>0110011
[8,7,4,2,6,1,5,3]=>1110101
[5,2,6,1,8,7,4,3]=>1010111
[1,7,6,4,3,8,2,5]=>0111010
[1,3,8,2,4,7,6,5]=>0010011
[3,7,5,1,8,6,2,4]=>0110110
[5,1,4,3,2,7,8,6]=>1011001
[3,7,6,2,4,1,8,5]=>0110101
[5,3,1,7,8,4,2,6]=>1100110
[4,1,7,8,5,3,2,6]=>1001110
[2,7,6,4,1,3,8,5]=>0111001
[8,4,2,7,6,3,1,5]=>1101110
[6,3,1,7,5,2,8,4]=>1101101
[6,2,7,5,3,1,8,4]=>1011101
[1,5,8,2,7,4,6,3]=>0010101
[8,4,7,3,1,6,5,2]=>1011011
[4,1,6,8,5,7,3,2]=>1001011
[1,8,6,7,3,4,2,5]=>0101010
[6,7,1,8,3,4,2,5]=>0101010
[7,8,1,6,3,4,2,5]=>0101010
[7,8,2,5,1,6,3,4]=>0101010
[1,8,5,6,2,7,3,4]=>0101010
[5,7,1,6,2,8,3,4]=>0101010
[5,6,2,7,1,8,3,4]=>0101010
[6,7,2,5,1,8,3,4]=>0101010
[6,7,2,4,3,8,1,5]=>0101010
[2,5,1,8,6,7,3,4]=>0101010
[2,6,5,8,1,7,3,4]=>0101010
[1,8,2,7,4,5,3,6]=>0101010
[2,4,3,8,5,6,1,7]=>0101010
[2,3,1,8,5,6,4,7]=>0101010
[4,6,2,7,1,5,3,8]=>0101010
[4,7,1,6,2,5,3,8]=>0101010
[4,6,3,5,1,7,2,8]=>0101010
[5,6,3,7,1,4,2,8]=>0101010
[1,8,5,6,3,4,2,7]=>0101010
[4,7,1,8,5,6,2,3]=>0101010
[3,4,2,6,5,8,1,7]=>0101010
[3,5,4,6,2,8,1,7]=>0101010
[3,7,1,6,2,8,4,5]=>0101010
[3,5,2,7,4,8,1,6]=>0101010
[4,7,2,3,1,8,5,6]=>0101010
[2,4,3,8,1,7,5,6]=>0101010
[6,1,2,7,4,5,8,3]=>1001001
[2,5,8,3,4,1,6,7]=>0010100
[5,6,2,7,4,3,8,1]=>0101101
[5,1,7,3,4,2,8,6]=>1010101
[4,6,7,3,2,5,8,1]=>0011001
[3,7,2,1,4,5,8,6]=>0110001
[2,7,1,3,4,8,6,5]=>0100011
[2,6,7,3,8,5,4,1]=>0010111
[2,6,1,8,4,5,3,7]=>0101010
[4,2,1,6,5,3,8,7]=>1101101
[6,2,4,3,1,5,8,7]=>1011001
[4,6,2,1,5,3,8,7]=>0110101
[8,4,2,1,6,5,3,7]=>1110110
[2,6,4,5,1,8,7,3]=>0101011
[6,8,7,2,1,4,3,5]=>0111010
[6,8,2,1,7,4,3,5]=>0110110
[6,8,2,1,4,3,7,5]=>0110101
[8,6,2,4,3,1,5,7]=>1101100
[6,8,2,4,3,1,7,5]=>0101101
[2,8,4,6,7,3,1,5]=>0100110
[2,8,6,7,4,3,1,5]=>0101110
[6,8,7,2,4,3,1,5]=>0110110
[4,6,5,2,8,3,7,1]=>0110101
[2,6,4,5,8,3,7,1]=>0100101
[6,4,2,8,3,5,7,1]=>1101001
[8,4,2,6,3,5,1,7]=>1101010
[4,2,6,3,8,7,5,1]=>1010111
[8,2,4,3,6,5,1,7]=>1010110
[4,2,1,6,8,7,5,3]=>1100111
[4,2,1,6,5,8,7,3]=>1101011
[4,2,1,3,6,8,7,5]=>1100011
[2,4,3,1,8,6,5,7]=>0110110
[6,2,1,8,7,4,3,5]=>1101110
[4,6,8,7,5,2,1,3]=>0011110
[4,6,5,8,7,2,1,3]=>0101110
[2,6,8,7,4,5,1,3]=>0011010
[2,4,8,6,7,5,1,3]=>0010110
[4,2,8,6,5,7,1,3]=>1011010
[6,4,8,2,1,5,7,3]=>1011001
[2,6,8,4,7,1,5,3]=>0010101
[4,6,5,8,2,1,7,3]=>0101101
[4,8,6,7,2,1,3,5]=>0101100
[6,2,3,5,1,4,8,7]=>1001001
[7,4,5,2,3,8,6,1]=>1010011
[7,3,2,5,4,8,6,1]=>1101011
[3,5,1,6,4,2,8,7]=>0101101
[3,6,2,4,5,1,8,7]=>0100101
[7,2,3,4,5,8,6,1]=>1000011
[8,2,3,4,5,7,1,6]=>1000010
[6,7,3,4,8,5,2,1]=>0100111
[5,7,1,3,8,6,2,4]=>0100110
[4,7,3,2,8,6,1,5]=>0110110
[3,8,2,6,7,4,5,1]=>0100101
[4,8,1,5,6,7,3,2]=>0100011
[6,8,2,5,1,7,3,4]=>0101010
[7,8,3,4,6,2,1,5]=>0100110
[4,8,2,5,1,6,7,3]=>0101001
[3,8,2,5,4,7,6,1]=>0101011
[3,7,6,1,8,5,2,4]=>0110110
[4,7,2,3,8,5,1,6]=>0100110
[4,6,7,1,8,5,3,2]=>0010111
[3,6,1,7,8,5,4,2]=>0100111
[2,1,5,7,3,8,6,4]=>1001011
[6,4,7,2,8,5,3,1]=>1010111
[7,6,1,4,8,5,2,3]=>1100110
[4,1,2,3,7,8,6,5]=>1000011
[3,4,2,1,8,5,6,7]=>0110100
[8,2,3,5,7,1,4,6]=>1000100
[8,1,3,6,4,7,2,5]=>1001010
[5,4,8,3,6,7,1,2]=>1010010
[4,5,8,3,6,7,2,1]=>0010011
[2,1,5,8,4,6,7,3]=>1001001
[4,6,8,3,5,2,7,1]=>0010101
[3,8,2,4,5,6,7,1]=>0100001
[6,8,2,3,1,4,5,7]=>0101000
[4,3,1,6,5,8,7,2]=>1101011
[8,2,7,4,1,3,6,5]=>1011001
[3,7,8,2,1,4,6,5]=>0011001
[3,7,5,2,8,4,1,6]=>0110110
[3,1,5,2,4,8,7,6]=>1010011
[3,6,4,5,1,8,7,2]=>0101011
[4,3,6,1,2,8,7,5]=>1010011
[6,1,3,5,4,8,7,2]=>1001011
[1,7,3,8,4,6,2,5]=>0101010
[1,6,7,4,8,5,3,2]=>0010111
[8,1,2,5,4,6,3,7]=>1001010
[6,8,3,1,4,7,5,2]=>0110011
[8,4,2,5,7,1,6,3]=>1100101
[1,8,5,3,7,4,6,2]=>0110101
[5,3,2,8,7,1,4,6]=>1101100
[1,2,8,7,5,6,3,4]=>0011010
[1,4,8,6,5,7,2,3]=>0011010
[3,5,4,8,6,1,2,7]=>0101100
[4,3,5,8,1,7,2,6]=>1001010
[1,4,5,8,6,7,3,2]=>0001011
[1,7,6,5,8,3,4,2]=>0110101
[7,3,6,1,8,2,4,5]=>1010100
[7,6,4,5,8,1,3,2]=>1100101
[1,6,5,4,8,2,3,7]=>0110100
[5,2,6,3,8,1,4,7]=>1010100
[4,3,1,6,8,7,5,2]=>1100111
[4,3,1,8,5,6,7,2]=>1101001
[6,2,8,4,3,1,7,5]=>1011101
[7,1,6,2,3,4,5,8]=>1010000
[3,8,6,1,2,5,4,7]=>0110010
[1,8,5,4,3,6,2,7]=>0111010
[5,3,8,4,1,2,7,6]=>1011001
[1,8,3,6,5,2,7,4]=>0101101
[4,7,1,8,2,6,5,3]=>0101011
[1,8,2,4,7,6,5,3]=>0100111
[1,4,8,3,5,7,6,2]=>0010011
[8,2,1,4,6,5,7,3]=>1100101
[6,1,5,2,4,7,8,3]=>1010001
[4,1,8,5,2,7,6,3]=>1011011
[4,3,8,5,1,2,6,7]=>1011000
[6,3,5,1,4,2,8,7]=>1010101
[4,1,8,2,3,7,5,6]=>1010010
[5,3,8,7,2,1,4,6]=>1011100
[7,6,5,4,1,3,2,8]=>1111010
[1,8,7,6,2,5,4,3]=>0111011
[4,6,3,1,5,2,7,8]=>0110100
[6,2,7,4,5,1,3,8]=>1010100
[5,2,7,4,1,6,3,8]=>1011010
[5,7,3,4,1,6,2,8]=>0101010
[4,2,8,1,5,6,7,3]=>1010001
[1,7,8,4,5,6,2,3]=>0010010
[1,6,8,4,5,2,7,3]=>0010101
[1,5,8,4,2,6,7,3]=>0011001
[1,5,3,8,2,6,7,4]=>0101001
[1,6,3,8,5,2,7,4]=>0101101
[1,7,3,8,5,6,2,4]=>0101010
[6,2,3,7,5,1,4,8]=>1001100
[4,2,6,1,5,3,7,8]=>1010100
[5,2,6,4,1,3,7,8]=>1011000
[1,2,7,8,5,6,3,4]=>0001010
[1,2,6,4,8,3,7,5]=>0010101
[8,7,3,2,1,6,5,4]=>1111011
[8,7,4,1,6,2,3,5]=>1110100
[8,5,1,7,2,3,4,6]=>1101000
[1,8,3,2,6,4,5,7]=>0110100
[7,3,8,1,5,2,4,6]=>1010100
[3,1,7,2,6,4,5,8]=>1010100
[1,8,4,2,3,6,7,5]=>0110001
[2,5,8,3,4,6,7,1]=>0010001
[4,1,7,2,3,6,8,5]=>1010001
[3,1,7,5,4,2,8,6]=>1011101
[4,6,2,1,5,7,8,3]=>0110001
[4,5,2,3,1,7,8,6]=>0101001
[3,2,6,7,4,1,8,5]=>1001101
[5,6,2,7,1,4,8,3]=>0101001
[6,4,2,8,1,5,7,3]=>1101001
[7,3,6,8,5,2,4,1]=>1001101
[2,7,8,3,6,5,1,4]=>0010110
[2,7,8,5,4,6,3,1]=>0011011
[2,6,8,3,4,7,1,5]=>0010010
[2,5,6,8,3,4,1,7]=>0001010
[2,7,8,3,6,1,4,5]=>0010100
[2,1,3,7,8,5,6,4]=>1000101
[5,1,2,4,8,7,3,6]=>1000110
[2,3,6,1,8,5,7,4]=>0010101
[5,2,6,1,7,8,4,3]=>1010011
[3,6,5,4,1,8,7,2]=>0111011
[5,4,2,3,7,8,6,1]=>1100011
[4,1,8,2,5,7,3,6]=>1010010
[3,1,8,4,7,2,5,6]=>1010100
[2,6,4,1,5,3,8,7]=>0110101
[1,5,8,2,4,7,3,6]=>0010010
[6,2,1,4,7,8,3,5]=>1100010
[3,8,1,4,2,6,5,7]=>0101010
[8,3,4,2,1,6,5,7]=>1011010
[5,3,2,8,1,6,4,7]=>1101010
[2,4,5,8,3,6,1,7]=>0001010
[3,5,8,1,2,6,4,7]=>0010010
[8,6,1,3,5,2,4,7]=>1100100
[5,7,4,3,6,1,8,2]=>0110101
[2,6,4,3,7,8,5,1]=>0110011
[7,4,1,8,3,2,5,6]=>1101100
[2,4,6,5,1,7,8,3]=>0011001
[5,6,1,7,4,2,8,3]=>0101101
[1,3,8,6,2,7,4,5]=>0011010
[6,4,7,8,2,1,3,5]=>1001100
[6,7,3,8,4,1,2,5]=>0101100
[2,7,8,3,4,6,1,5]=>0010010
[3,7,8,1,5,4,2,6]=>0010110
[7,5,8,4,1,3,2,6]=>1011010
[4,7,5,8,3,1,2,6]=>0101100
[5,7,3,1,6,8,4,2]=>0110011
[4,6,7,2,8,3,1,5]=>0010110
[4,8,1,2,3,5,7,6]=>0100001
[4,5,6,7,3,1,8,2]=>0001101
[8,5,3,2,7,6,1,4]=>1110110
[7,5,4,6,2,8,1,3]=>1101010
[2,5,1,3,6,8,7,4]=>0100011
[7,5,2,8,4,1,3,6]=>1101100
[7,3,8,5,2,1,4,6]=>1011100
[5,8,3,6,4,7,1,2]=>0101010
[3,7,8,4,1,5,6,2]=>0011001
[3,5,8,6,7,4,2,1]=>0010111
[3,7,6,8,1,2,5,4]=>0101001
[4,1,6,3,2,5,8,7]=>1011001
[8,6,1,7,2,5,4,3]=>1101011
[8,7,6,1,2,3,5,4]=>1110001
[5,4,1,6,2,3,8,7]=>1101001
[2,6,5,3,4,1,8,7]=>0110101
[5,8,7,6,1,2,3,4]=>0111000
[8,2,7,1,5,4,3,6]=>1010110
[2,1,6,3,8,5,4,7]=>1010110
[2,6,3,1,8,5,4,7]=>0110110
[4,6,2,8,5,1,3,7]=>0101100
[6,5,2,7,4,3,8,1]=>1101101
[4,6,5,2,7,3,8,1]=>0110101
[3,1,6,2,4,8,7,5]=>1010011
[8,7,5,1,2,6,4,3]=>1110011
[2,1,7,6,3,8,4,5]=>1011010
[8,2,3,4,6,7,1,5]=>1000010
[2,8,5,7,4,1,3,6]=>0101100
[7,8,5,3,6,4,2,1]=>0110111
[2,1,4,8,7,5,6,3]=>1001101
[7,4,6,8,5,1,3,2]=>1001101
[6,4,8,3,5,7,1,2]=>1010010
[8,5,7,4,6,2,1,3]=>1010110
[4,1,8,5,6,3,2,7]=>1010110
[5,8,3,2,4,6,1,7]=>0110010
[2,8,4,1,5,3,7,6]=>0110101
[4,8,7,6,5,2,3,1]=>0111101
[2,1,8,6,4,3,7,5]=>1011101
[3,6,7,1,8,5,2,4]=>0010110
[4,2,3,6,8,7,5,1]=>1000111
[6,5,7,3,1,8,4,2]=>1011011
[8,4,2,5,6,1,7,3]=>1100101
[6,1,5,7,2,4,8,3]=>1001001
[8,4,7,6,2,1,5,3]=>1011101
[3,5,7,6,4,1,8,2]=>0011101
[2,4,7,5,6,3,8,1]=>0010101
[5,4,1,7,6,2,8,3]=>1101101
[3,5,6,7,1,4,8,2]=>0001001
[4,7,5,2,1,3,8,6]=>0111001
[5,7,2,3,6,4,8,1]=>0100101
[7,1,2,3,5,8,4,6]=>1000010
[8,6,2,3,7,1,4,5]=>1100100
[6,1,8,2,7,3,4,5]=>1010100
[7,8,6,1,3,2,5,4]=>0110101
[8,1,5,7,2,3,6,4]=>1001001
[1,4,5,2,8,6,7,3]=>0010101
[2,3,1,7,8,6,4,5]=>0100110
[2,1,4,6,8,3,7,5]=>1000101
[3,5,7,6,2,8,1,4]=>0011010
[5,4,1,6,3,8,7,2]=>1101011
[4,5,6,1,2,8,7,3]=>0010011
[3,5,6,2,4,8,7,1]=>0010011
[5,4,1,2,8,7,6,3]=>1100111
[5,6,3,7,8,4,2,1]=>0100111
[4,3,2,6,8,1,7,5]=>1100101
[7,1,5,6,3,8,2,4]=>1001010
[1,5,4,2,7,8,3,6]=>0110010
[6,1,2,8,7,4,3,5]=>1001110
[5,1,6,8,4,7,2,3]=>1001010
[5,1,3,8,4,2,7,6]=>1001101
[3,1,6,8,7,4,2,5]=>1001110
[3,6,5,8,4,7,1,2]=>0101010
[6,5,8,4,3,1,2,7]=>1011100
[8,5,1,3,7,4,6,2]=>1100101
[3,2,8,1,4,7,6,5]=>1010011
[6,4,3,8,2,5,7,1]=>1101001
[3,2,5,8,4,1,7,6]=>1001101
[6,8,2,3,4,7,5,1]=>0100011
[2,1,7,8,3,4,6,5]=>1001001
[7,5,1,8,4,2,6,3]=>1101101
[5,6,1,8,2,7,4,3]=>0101011
[3,6,8,5,2,7,4,1]=>0011011
[2,1,6,5,4,8,3,7]=>1011010
[2,1,7,3,5,8,6,4]=>1010011
[7,8,1,2,4,5,6,3]=>0100001
[3,6,8,1,5,7,2,4]=>0010010
[3,5,7,8,4,6,1,2]=>0001010
[7,5,2,8,4,6,3,1]=>1101011
[7,8,2,4,3,1,5,6]=>0101100
[8,4,3,1,7,5,2,6]=>1110110
[7,6,2,8,5,1,4,3]=>1101101
[4,3,8,7,1,6,5,2]=>1011011
[4,7,1,8,5,2,6,3]=>0101101
[3,7,5,8,1,6,2,4]=>0101010
[3,7,6,4,5,1,8,2]=>0110101
[4,7,5,6,3,8,2,1]=>0101011
[4,2,7,5,8,3,6,1]=>1010101
[5,8,2,7,3,4,6,1]=>0101001
[5,7,2,1,8,3,6,4]=>0110101
[7,8,1,2,3,4,6,5]=>0100001
[5,6,2,4,3,1,8,7]=>0101101
[4,6,2,1,7,8,3,5]=>0110010
[6,3,2,1,4,8,5,7]=>1110010
[7,1,8,3,5,4,6,2]=>1010101
[7,1,2,4,8,5,6,3]=>1000101
[8,7,6,5,1,3,2,4]=>1111010
[8,7,6,2,4,3,1,5]=>1110110
[7,6,8,1,5,4,3,2]=>1010111
[7,6,1,8,5,4,3,2]=>1101111
[6,5,8,1,7,4,3,2]=>1010111
[4,3,8,7,6,1,5,2]=>1011101
[6,5,8,7,4,1,3,2]=>1011101
[5,4,8,7,6,3,1,2]=>1011110
[1,4,8,6,3,2,5,7]=>0011100
[7,4,1,6,3,8,5,2]=>1101011
[7,6,3,1,5,8,4,2]=>1110011
[1,6,3,8,5,2,4,7]=>0101100
[4,6,3,7,5,2,1,8]=>0101110
[3,7,2,6,5,4,1,8]=>0101110
[1,7,4,6,2,8,5,3]=>0101011
[6,2,5,1,7,4,8,3]=>1010101
[3,5,7,4,8,6,1,2]=>0010110
[5,2,7,4,1,6,8,3]=>1011001
[4,5,8,2,1,7,6,3]=>0011011
[1,6,4,8,5,2,7,3]=>0101101
[7,4,1,5,3,8,2,6]=>1101010
[3,4,1,2,7,8,6,5]=>0100011
[4,1,3,2,8,6,7,5]=>1010101
[3,1,2,4,7,6,8,5]=>1000101
[8,1,3,5,4,7,2,6]=>1001010
[7,1,4,3,5,2,8,6]=>1010101
[3,2,8,1,6,5,4,7]=>1010110
[6,8,4,1,2,5,3,7]=>0110010
[8,2,1,5,6,4,3,7]=>1100110
[4,7,1,8,2,5,3,6]=>0101010
[6,7,8,1,4,5,3,2]=>0010011
[3,2,5,4,7,8,1,6]=>1010010
[8,4,7,6,2,3,1,5]=>1011010
[6,1,2,8,7,3,5,4]=>1001101
[1,2,7,5,6,8,3,4]=>0010010
[5,7,2,3,8,1,6,4]=>0100101
[3,5,2,6,1,8,7,4]=>0101011
[3,2,5,6,7,8,1,4]=>1000010
[5,4,2,6,8,7,1,3]=>1100110
[6,4,1,2,8,7,3,5]=>1100110
[4,3,8,5,2,1,6,7]=>1011100
[3,6,4,5,2,1,8,7]=>0101101
[7,5,4,2,3,8,1,6]=>1110010
[5,6,3,1,8,2,7,4]=>0110101
[6,5,4,3,1,2,8,7]=>1111001
[4,5,2,1,6,8,3,7]=>0110010
[5,6,2,8,1,7,4,3]=>0101011
[2,1,4,5,8,6,3,7]=>1000110
[6,7,1,3,4,8,2,5]=>0100010
[6,7,8,2,3,5,4,1]=>0010011
[5,8,6,2,3,7,4,1]=>0110011
[1,8,3,4,7,6,2,5]=>0100110
[5,8,6,1,7,2,4,3]=>0110101
[3,1,2,8,6,4,5,7]=>1001100
[1,3,2,8,5,4,6,7]=>0101100
[3,2,1,8,6,5,4,7]=>1101110
[5,2,7,1,8,4,3,6]=>1010110
[6,7,2,1,8,4,3,5]=>0110110
[6,7,3,1,5,8,2,4]=>0110010
[2,4,1,6,8,5,3,7]=>0100110
[2,5,6,1,8,4,3,7]=>0010110
[5,4,7,6,1,8,2,3]=>1011010
[3,5,6,8,4,7,2,1]=>0001011
[2,5,6,8,7,3,4,1]=>0001101
[2,4,8,5,7,3,6,1]=>0010101
[5,3,7,8,4,6,2,1]=>1001011
[6,7,3,8,4,5,2,1]=>0101011
[4,2,8,6,7,3,5,1]=>1010101
[3,2,8,7,5,4,6,1]=>1011101
[2,1,8,7,6,4,3,5]=>1011110
[6,3,8,7,5,1,2,4]=>1011100
[2,8,7,4,1,3,5,6]=>0111000
[2,5,3,7,6,8,1,4]=>0101010
[2,8,7,1,4,5,3,6]=>0110010
[4,2,1,8,7,3,5,6]=>1101100
[8,7,4,6,2,3,1,5]=>1101010
[5,1,6,3,2,8,7,4]=>1011011
[8,7,2,3,5,4,1,6]=>1100110
[3,4,2,8,6,1,5,7]=>0101100
[8,1,4,2,3,6,7,5]=>1010001
[6,8,3,5,4,7,1,2]=>0101010
[1,8,2,5,7,6,3,4]=>0100110
[4,1,6,8,2,3,7,5]=>1001001
[1,4,6,3,7,2,8,5]=>0010101
[6,2,1,8,4,5,3,7]=>1101010
[4,7,3,8,5,2,1,6]=>0101110
[3,1,7,4,8,5,2,6]=>1010110
[7,4,1,6,3,2,8,5]=>1101101
[3,8,6,2,7,4,1,5]=>0110110
[7,3,1,4,5,2,8,6]=>1100101
[8,1,2,4,6,7,5,3]=>1000011
[8,1,3,6,7,5,4,2]=>1000111
[6,4,2,8,5,1,3,7]=>1101100
[8,6,2,4,1,3,7,5]=>1101001
[4,7,5,1,8,6,3,2]=>0110111
[6,7,5,1,4,2,8,3]=>0110101
[6,2,4,1,7,5,8,3]=>1010101
[3,6,5,8,4,1,7,2]=>0101101
[7,3,8,2,5,6,4,1]=>1010011
[5,7,3,1,6,4,8,2]=>0110101
[6,1,3,7,4,8,5,2]=>1001011
[3,2,1,7,4,8,5,6]=>1101010
[4,1,5,2,7,6,3,8]=>1010110
[6,2,7,1,4,8,5,3]=>1010011
[7,5,4,1,3,8,6,2]=>1110011
[4,3,2,1,8,5,7,6]=>1110101
[4,2,1,7,3,6,5,8]=>1101010
[7,4,3,2,8,1,6,5]=>1110101
[2,7,5,3,8,1,4,6]=>0110100
[1,8,5,3,6,4,2,7]=>0110110
[8,1,6,2,7,4,3,5]=>1010110
[7,3,1,6,5,4,2,8]=>1101110
[8,5,7,4,3,6,2,1]=>1011011
[2,8,5,6,1,4,3,7]=>0101010
[3,7,5,8,2,1,4,6]=>0101100
[5,4,8,3,2,1,7,6]=>1011101
[2,4,7,1,3,6,5,8]=>0010010
[5,7,4,8,1,3,6,2]=>0101001
[5,1,7,8,2,4,6,3]=>1001001
[3,6,7,8,1,2,5,4]=>0001001
[4,6,7,2,8,1,3,5]=>0010100
[6,3,7,1,8,2,5,4]=>1010101
[5,7,1,4,8,2,6,3]=>0100101
[2,7,4,1,8,3,6,5]=>0110101
[6,1,2,7,8,3,5,4]=>1000101
[3,6,4,7,8,1,2,5]=>0100100
[3,7,4,8,5,2,1,6]=>0101110
[7,2,5,8,6,3,1,4]=>1001110
[4,8,1,7,6,2,3,5]=>0101100
[4,8,2,1,7,5,3,6]=>0110110
[5,8,7,1,3,6,4,2]=>0110011
[2,8,7,1,6,3,5,4]=>0110101
[2,7,6,5,1,4,3,8]=>0111010
[3,8,7,6,2,1,5,4]=>0111101
[5,8,7,2,6,1,4,3]=>0110101
[7,3,8,6,5,1,2,4]=>1011100
[5,8,6,4,3,2,1,7]=>0111110
[8,7,6,2,5,3,1,4]=>1110110
[8,1,2,3,4,7,6,5]=>1000011
[3,8,2,7,6,5,4,1]=>0101111
[4,2,8,7,6,5,3,1]=>1011111
[8,3,1,7,6,5,4,2]=>1101111
[5,2,8,7,6,4,3,1]=>1011111
[8,3,2,1,7,6,5,4]=>1110111
[8,4,1,7,6,5,3,2]=>1101111
[6,4,1,3,2,8,5,7]=>1101010
[2,5,8,6,3,1,4,7]=>0011100
[3,2,7,4,5,8,1,6]=>1010010
[8,1,6,2,4,5,3,7]=>1010010
[5,8,1,6,2,3,4,7]=>0101000
[5,4,6,1,3,8,2,7]=>1010010
[2,4,1,7,5,8,3,6]=>0101010
[2,4,7,6,8,3,5,1]=>0010101
[4,8,6,5,7,1,2,3]=>0110100
[8,5,7,4,3,1,6,2]=>1011101
[8,1,7,4,2,3,6,5]=>1011001
[8,2,3,1,5,7,6,4]=>1010011
[1,4,8,2,3,6,7,5]=>0010001
[3,1,2,7,8,6,4,5]=>1000110
[7,5,1,8,2,4,3,6]=>1101010
[3,5,8,1,2,4,7,6]=>0010001
[8,4,1,5,2,3,7,6]=>1101001
[3,8,4,1,2,7,6,5]=>0110011
[2,7,5,8,3,4,1,6]=>0101010
[1,4,7,3,2,8,5,6]=>0011010
[6,4,1,3,2,7,8,5]=>1101001
[2,3,7,6,8,1,5,4]=>0010101
[2,6,3,5,1,8,7,4]=>0101011
[2,7,1,6,8,3,5,4]=>0100101
[6,7,5,4,2,1,8,3]=>0111101
[4,2,1,5,8,7,6,3]=>1100111
[8,5,3,2,6,1,7,4]=>1110101
[6,2,1,5,3,8,7,4]=>1101011
[7,8,4,1,2,5,3,6]=>0110010
[7,8,1,2,6,5,3,4]=>0100110
[6,1,4,2,7,5,3,8]=>1010110
[1,2,8,7,5,4,3,6]=>0011110
[1,2,8,3,6,4,7,5]=>0010101
[5,1,7,3,6,4,8,2]=>1010101
[6,2,3,7,4,1,5,8]=>1001100
[6,2,4,1,7,3,5,8]=>1010100
[3,4,8,7,5,6,1,2]=>0011010
[2,7,3,8,6,4,1,5]=>0101110
[1,8,3,7,6,4,5,2]=>0101101
[2,6,8,5,3,1,7,4]=>0011101
[5,6,2,1,7,3,8,4]=>0110101
[5,3,6,2,4,1,7,8]=>1010100
[5,7,4,2,1,3,6,8]=>0111000
[6,4,2,1,5,3,7,8]=>1110100
[5,3,1,4,6,2,7,8]=>1100100
[5,1,2,4,7,6,8,3]=>1000101
[1,6,4,2,8,7,3,5]=>0110110
[4,8,1,2,6,7,3,5]=>0100010
[3,1,2,4,6,8,7,5]=>1000011
[4,2,8,1,5,3,7,6]=>1010101
[4,3,8,5,7,6,1,2]=>1010110
[4,8,6,3,7,5,1,2]=>0110110
[3,8,6,5,2,7,1,4]=>0111010
[3,8,5,6,1,7,4,2]=>0101011
[3,7,8,5,2,1,6,4]=>0011101
[4,2,7,8,1,3,6,5]=>1001001
[2,1,8,7,6,3,5,4]=>1011101
[5,4,1,6,3,2,8,7]=>1101101
[6,8,1,5,4,7,3,2]=>0101011
[4,6,2,5,1,3,8,7]=>0101001
[2,6,4,3,1,5,8,7]=>0111001
[5,1,7,2,8,6,4,3]=>1010111
[6,8,2,7,4,3,1,5]=>0101110
[6,8,2,5,4,7,1,3]=>0101010
[2,1,7,6,3,8,5,4]=>1011011
[7,6,2,8,4,3,1,5]=>1101110
[2,6,5,1,8,4,3,7]=>0110110
[4,2,1,6,3,8,7,5]=>1101011
[5,8,3,2,7,6,1,4]=>0110110
[2,4,8,3,1,7,5,6]=>0011010
[4,8,3,2,1,7,6,5]=>0111011
[3,5,8,2,7,1,4,6]=>0010100
[4,5,8,2,6,1,3,7]=>0010100
[2,6,8,3,7,1,4,5]=>0010100
[6,8,3,7,2,1,5,4]=>0101101
[5,8,3,1,6,2,7,4]=>0110101
[5,1,7,3,6,2,8,4]=>1010101
[4,5,8,1,6,3,2,7]=>0010110
[6,8,4,7,1,5,3,2]=>0101011
[4,3,2,1,6,8,5,7]=>1110010
[2,4,1,3,8,7,6,5]=>0100111
[4,8,6,5,1,7,3,2]=>0111011
[6,5,3,1,7,2,8,4]=>1110101
[2,1,5,4,8,7,3,6]=>1010110
[3,8,5,4,2,1,7,6]=>0111101
[2,3,8,5,4,1,6,7]=>0011100
[2,1,4,8,6,5,3,7]=>1001110
[4,3,2,8,7,6,1,5]=>1101110
[3,2,8,7,5,4,1,6]=>1011110
[2,8,6,5,4,3,1,7]=>0111110
[5,4,2,6,3,1,8,7]=>1101101
[7,5,2,6,3,8,4,1]=>1101011
[7,3,6,5,2,8,4,1]=>1011011
[5,6,3,1,2,4,8,7]=>0110001
[7,1,5,3,8,4,6,2]=>1010101
[2,7,5,3,8,6,4,1]=>0110111
[3,7,6,4,2,8,5,1]=>0111011
[5,7,3,6,2,8,4,1]=>0101011
[2,1,8,7,4,3,5,6]=>1011100
[2,8,6,3,1,4,7,5]=>0111001
[3,5,7,4,8,6,2,1]=>0010111
[4,5,3,6,8,2,7,1]=>0100101
[5,6,3,7,4,8,2,1]=>0101011
[2,6,7,4,5,8,3,1]=>0010011
[6,3,7,5,8,4,2,1]=>1010111
[8,5,2,6,1,7,3,4]=>1101010
[5,4,2,6,8,3,7,1]=>1100101
[7,6,8,5,1,4,2,3]=>1011010
[7,1,8,5,4,2,3,6]=>1011100
[5,7,3,8,4,1,2,6]=>0101100
[2,1,7,8,5,3,4,6]=>1001100
[2,4,8,1,5,6,3,7]=>0010010
[4,1,8,2,6,5,3,7]=>1010110
[4,7,3,8,1,2,6,5]=>0101001
[4,8,1,2,5,3,6,7]=>0100100
[3,8,1,2,4,6,5,7]=>0100010
[4,8,7,6,3,5,2,1]=>0111011
[3,8,7,6,5,2,4,1]=>0111101
[4,8,7,3,6,5,2,1]=>0110111
[4,8,7,6,3,2,5,1]=>0111101
[3,8,7,6,5,2,1,4]=>0111110
[7,5,8,3,6,2,1,4]=>1010110
[7,5,8,3,2,6,1,4]=>1011010
[7,5,8,3,2,1,6,4]=>1011101
[2,3,7,8,4,1,6,5]=>0001101
[2,1,7,5,8,4,6,3]=>1010101
[2,5,6,8,1,7,4,3]=>0001011
[4,2,8,6,1,7,3,5]=>1011010
[8,6,4,1,3,2,5,7]=>1110100
[8,1,3,2,6,5,4,7]=>1010110
[8,5,3,6,2,4,1,7]=>1101010
[8,4,1,2,6,5,3,7]=>1100110
[8,3,5,6,2,1,4,7]=>1001100
[8,4,2,1,5,6,3,7]=>1110010
[5,4,7,6,8,2,3,1]=>1010101
[4,1,8,2,3,7,6,5]=>1010011
[3,7,4,5,8,2,1,6]=>0100110
[6,3,8,5,7,4,1,2]=>1010110
[7,4,1,8,3,5,6,2]=>1101001
[5,3,8,7,4,6,1,2]=>1011010
[7,5,8,2,1,4,6,3]=>1011001
[8,7,4,2,1,3,6,5]=>1111001
[7,4,8,3,2,6,1,5]=>1011010
[6,8,2,3,1,7,5,4]=>0101011
[7,4,3,2,6,8,5,1]=>1110011
[5,1,2,3,6,8,7,4]=>1000011
[2,4,7,3,8,1,6,5]=>0010101
[6,3,8,2,7,4,1,5]=>1010110
[8,2,1,3,6,4,7,5]=>1100101
[5,7,8,2,1,4,3,6]=>0011010
[3,5,1,7,8,4,2,6]=>0100110
[1,7,8,4,5,3,2,6]=>0010110
[3,2,4,8,6,7,1,5]=>1001010
[8,3,1,6,7,4,2,5]=>1100110
[3,2,5,7,4,8,1,6]=>1001010
[8,4,7,1,3,2,5,6]=>1010100
[8,4,7,2,1,3,5,6]=>1011000
[6,4,2,1,3,7,8,5]=>1110001
[7,1,6,3,5,8,2,4]=>1010010
[3,8,5,1,6,7,2,4]=>0110010
[5,3,6,7,8,4,2,1]=>1000111
[1,5,2,7,8,6,4,3]=>0100111
[1,4,2,8,6,5,7,3]=>0101101
[4,1,7,5,2,6,8,3]=>1011001
[7,6,2,4,5,1,8,3]=>1100101
[8,1,4,5,2,6,7,3]=>1001001
[8,4,6,5,2,1,7,3]=>1011101
[3,5,7,2,1,6,8,4]=>0011001
[4,2,1,5,6,7,8,3]=>1100001
[3,7,5,4,6,8,1,2]=>0110010
[8,3,4,1,5,6,7,2]=>1010001
[3,5,2,4,7,6,1,8]=>0100110
[7,3,5,2,4,6,1,8]=>1010010
[5,3,7,2,4,6,1,8]=>1010010
[3,5,2,7,4,6,1,8]=>0101010
[3,2,5,7,4,6,1,8]=>1001010
[3,7,5,2,4,6,1,8]=>0110010
[5,7,3,2,4,6,1,8]=>0110010
[1,5,3,2,4,7,6,8]=>0110010
[1,5,3,2,7,4,6,8]=>0110100
[3,7,2,5,4,1,6,8]=>0101100
[3,2,7,5,4,1,6,8]=>1011100
[5,1,3,2,4,7,6,8]=>1010010
[5,1,3,2,7,4,6,8]=>1010100
[7,1,3,2,5,4,6,8]=>1010100
[1,7,3,2,5,4,6,8]=>0110100
[1,7,3,5,2,4,6,8]=>0101000
[7,1,3,5,2,4,6,8]=>1001000
[5,1,3,7,2,4,6,8]=>1001000
[3,7,5,1,2,4,6,8]=>0110000
[5,7,3,1,2,4,6,8]=>0110000
[1,5,3,7,2,4,6,8]=>0101000
[3,5,7,2,1,4,6,8]=>0011000
[3,5,2,7,1,4,6,8]=>0101000
[3,2,5,7,4,1,6,8]=>1001100
[3,5,2,7,4,1,6,8]=>0101100
[3,5,7,2,4,1,6,8]=>0010100
[5,3,7,2,4,1,6,8]=>1010100
[7,3,5,2,1,4,6,8]=>1011000
[5,3,2,4,7,1,6,8]=>1100100
[3,2,5,4,7,1,6,8]=>1010100
[1,3,2,7,5,4,6,8]=>0101100
[1,3,7,2,5,4,6,8]=>0010100
[7,3,1,2,5,4,6,8]=>1100100
[5,3,1,2,7,4,6,8]=>1100100
[5,3,1,2,4,7,6,8]=>1100010
[3,5,2,1,4,7,6,8]=>0110010
[3,2,5,1,7,4,6,8]=>1010100
[3,5,2,1,7,4,6,8]=>0110100
[5,3,1,7,2,4,6,8]=>1101000
[7,3,1,5,2,4,6,8]=>1101000
[1,3,7,5,2,4,6,8]=>0011000
[7,5,1,3,2,4,6,8]=>1101000
[5,7,1,3,2,4,6,8]=>0101000
[3,7,1,5,2,4,6,8]=>0101000
[3,7,1,2,5,4,6,8]=>0100100
[3,1,2,7,5,4,6,8]=>1001100
[3,1,7,2,5,4,6,8]=>1010100
[3,1,7,5,2,4,6,8]=>1011000
[5,1,7,3,2,4,6,8]=>1011000
[7,1,5,3,2,4,6,8]=>1011000
[1,7,5,3,2,4,6,8]=>0111000
[5,8,7,1,2,6,4,3]=>0110011
[6,8,2,1,7,5,4,3]=>0110111
[1,8,7,6,3,2,5,4]=>0111101
[5,8,7,4,1,2,6,3]=>0111001
[2,8,7,4,3,6,1,5]=>0111010
[1,8,5,4,2,7,6,3]=>0111011
[7,6,4,2,8,5,3,1]=>1110111
[7,6,4,8,5,1,2,3]=>1101100
[1,6,7,5,3,8,4,2]=>0011011
[7,6,3,5,2,4,8,1]=>1101001
[7,6,4,2,5,1,8,3]=>1110101
[7,6,2,8,3,1,4,5]=>1101100
[1,6,7,5,8,2,3,4]=>0010100
[2,6,5,7,8,3,4,1]=>0100101
[3,2,5,1,7,8,4,6]=>1010010
[5,2,3,4,8,6,1,7]=>1000110
[5,3,4,8,2,7,6,1]=>1001011
[5,3,8,2,4,1,7,6]=>1010101
[5,2,8,4,1,7,3,6]=>1011010
[6,4,2,5,1,8,7,3]=>1101011
[6,4,3,5,8,2,1,7]=>1100110
[6,3,5,4,8,2,7,1]=>1010101
[6,3,5,8,7,1,2,4]=>1001100
[1,5,7,3,4,8,6,2]=>0010011
[5,8,4,1,3,7,6,2]=>0110011
[6,4,3,8,5,7,2,1]=>1101011
[5,4,2,6,3,1,7,8]=>1101100
[4,6,5,3,7,1,2,8]=>0110100
[3,5,6,1,4,8,7,2]=>0010011
[3,5,7,6,1,4,8,2]=>0011001
[3,6,5,7,4,8,1,2]=>0101010
[4,2,6,5,1,7,3,8]=>1011010
[4,3,5,7,2,1,6,8]=>1001100
[3,5,4,7,2,6,1,8]=>0101010
[3,4,7,6,8,1,2,5]=>0010100
[1,8,4,3,7,5,6,2]=>0110101
[5,2,8,6,4,7,3,1]=>1011011
[1,8,6,3,7,4,2,5]=>0110110
[1,8,6,5,7,2,3,4]=>0110100
[4,2,8,3,5,7,1,6]=>1010010
[4,3,8,6,5,7,1,2]=>1011010
[1,3,7,2,6,5,8,4]=>0010101
[1,5,7,2,4,6,8,3]=>0010001
[1,3,6,4,2,5,8,7]=>0011001
[5,6,3,4,7,1,8,2]=>0100101
[3,5,2,7,4,1,8,6]=>0101101
[5,2,3,8,4,1,7,6]=>1001101
[7,5,3,4,8,2,1,6]=>1100110
[7,6,3,8,4,2,1,5]=>1101110
[7,2,8,5,1,6,3,4]=>1011010
[7,4,3,8,5,2,6,1]=>1101101
[7,2,8,5,1,3,4,6]=>1011000
[7,6,8,1,2,5,3,4]=>1010010
[1,5,3,7,6,8,4,2]=>0101011
[1,2,6,4,5,8,3,7]=>0010010
[1,2,7,4,8,5,3,6]=>0010110
[1,6,3,7,8,2,4,5]=>0100100
[3,2,6,7,8,1,4,5]=>1000100
[1,4,7,3,5,2,6,8]=>0010100
[3,8,4,7,6,1,5,2]=>0101101
[5,7,4,2,6,3,1,8]=>0110110
[2,4,5,8,1,6,7,3]=>0001001
[6,1,3,7,4,2,5,8]=>1001100
[2,1,8,3,6,7,4,5]=>1010010
[5,1,8,6,2,7,3,4]=>1011010
[5,7,1,4,2,6,3,8]=>0101010
[3,2,6,8,1,5,7,4]=>1001001
[8,2,6,1,5,4,7,3]=>1010101
[7,8,5,4,1,6,3,2]=>0111011
[3,6,2,7,8,1,5,4]=>0100101
[2,7,3,8,1,5,6,4]=>0101001
[2,6,8,4,1,5,7,3]=>0011001
[5,7,8,4,1,6,3,2]=>0011011
[3,4,8,1,2,5,7,6]=>0010001
[6,3,1,7,5,2,4,8]=>1101100
[6,3,1,8,2,7,4,5]=>1101010
[7,8,1,2,4,3,6,5]=>0100101
[5,2,8,1,3,4,7,6]=>1010001
[3,2,1,6,4,7,8,5]=>1101001
[4,1,3,6,5,7,8,2]=>1001001
[5,1,3,4,2,7,8,6]=>1001001
[6,1,3,4,2,8,5,7]=>1001010
[8,1,4,3,5,7,6,2]=>1010011
[5,2,4,1,3,7,8,6]=>1010001
[3,2,6,1,5,7,8,4]=>1010001
[1,4,6,3,5,7,8,2]=>0010001
[3,5,1,6,4,7,8,2]=>0101001
[3,6,4,2,1,7,8,5]=>0111001
[3,8,6,1,4,7,5,2]=>0110011
[1,8,3,2,6,7,5,4]=>0110011
[8,7,1,3,6,5,4,2]=>1100111
[1,8,5,7,4,2,6,3]=>0101101
[4,7,5,3,8,2,1,6]=>0110110
[2,7,6,5,8,3,1,4]=>0110110
[1,4,7,6,8,2,3,5]=>0010100
[3,5,7,4,8,1,2,6]=>0010100
[4,6,1,7,5,8,2,3]=>0101010
[2,3,6,7,5,8,1,4]=>0001010
[1,3,7,5,6,8,2,4]=>0010010
[3,2,7,1,6,8,4,5]=>1010010
[8,1,5,4,7,2,6,3]=>1010101
[8,2,5,3,7,1,6,4]=>1010101
[2,1,4,7,5,8,3,6]=>1001010
[1,2,6,7,4,8,3,5]=>0001010
[3,6,4,7,8,5,2,1]=>0100111
[3,2,5,8,6,7,4,1]=>1001011
[6,3,5,8,7,4,1,2]=>1001110
[8,3,5,7,6,4,2,1]=>1001111
[4,1,8,3,7,5,6,2]=>1010101
[4,7,2,8,5,6,3,1]=>0101011
[1,4,8,7,3,5,6,2]=>0011001
[3,2,8,7,1,5,6,4]=>1011001
[1,5,8,7,4,6,2,3]=>0011010
[4,7,6,8,5,3,1,2]=>0101110
[4,8,6,7,5,3,2,1]=>0101111
[3,8,7,5,6,4,2,1]=>0110111
[8,1,5,6,3,2,4,7]=>1001100
[1,7,8,3,5,2,4,6]=>0010100
[8,2,5,3,1,6,4,7]=>1011010
[8,3,2,1,5,6,4,7]=>1110010
[8,6,5,1,3,4,2,7]=>1110010
[1,7,8,5,4,3,2,6]=>0011110
[2,6,8,7,4,3,5,1]=>0011101
[2,7,6,8,4,3,1,5]=>0101110
[1,2,6,7,8,4,3,5]=>0000110
[8,5,7,1,3,4,6,2]=>1010001
[3,5,8,6,7,4,1,2]=>0010110
[3,1,6,5,8,7,4,2]=>1010111
[3,7,6,4,8,1,2,5]=>0110100
[2,3,6,5,7,1,8,4]=>0010101
[2,3,6,4,1,7,8,5]=>0011001
[4,7,2,1,5,3,8,6]=>0110101
[3,1,7,4,5,2,8,6]=>1010101
[3,7,5,4,2,1,8,6]=>0111101
[1,3,6,7,4,2,8,5]=>0001101
[4,3,7,2,6,8,1,5]=>1010010
[5,4,2,1,3,7,8,6]=>1110001
[8,7,1,5,6,3,2,4]=>1100110
[8,7,2,5,4,6,1,3]=>1101010
[8,7,1,2,4,5,6,3]=>1100001
[8,7,2,5,3,1,6,4]=>1101101
[8,7,3,2,1,5,6,4]=>1111001
[8,7,6,5,1,3,4,2]=>1111001
[8,7,6,1,4,5,3,2]=>1110011
[8,7,5,6,1,4,3,2]=>1101011
[6,8,7,1,5,4,3,2]=>0110111
[8,5,7,6,1,4,3,2]=>1011011
[6,7,8,1,5,4,3,2]=>0010111
[8,7,4,6,5,1,3,2]=>1101101
[8,5,6,7,1,4,3,2]=>1001011
[8,7,6,3,5,4,1,2]=>1110110
[8,7,4,5,6,1,3,2]=>1100101
[8,7,6,5,2,4,3,1]=>1111011
[4,2,8,7,6,5,1,3]=>1011110
[7,5,8,1,6,4,3,2]=>1010111
[1,5,8,7,6,2,4,3]=>0011101
[7,5,8,4,1,6,3,2]=>1011011
[6,8,5,1,7,4,3,2]=>0110111
[1,6,8,7,2,5,4,3]=>0011011
[7,3,8,4,6,1,5,2]=>1010101
[4,8,5,7,1,6,3,2]=>0101011
[4,3,7,6,5,1,8,2]=>1011101
[5,4,3,6,7,1,8,2]=>1100101
[5,4,7,3,6,1,8,2]=>1010101
[4,8,7,6,3,1,5,2]=>0111101
[2,4,6,3,1,7,8,5]=>0011001
[6,8,5,7,3,2,1,4]=>0101110
[6,8,5,3,7,2,1,4]=>0110110
[6,8,5,7,4,2,1,3]=>0101110
[2,1,8,7,6,3,4,5]=>1011100
[5,8,7,6,2,4,1,3]=>0111010
[6,8,2,7,5,1,4,3]=>0101101
[5,8,7,2,6,4,1,3]=>0110110
[6,8,7,5,2,4,1,3]=>0111010
[5,8,7,6,4,2,3,1]=>0111101
[2,3,6,1,7,5,8,4]=>0010101
[2,3,6,1,8,5,4,7]=>0010110
[2,4,1,6,7,5,8,3]=>0100101
[2,4,1,7,3,8,6,5]=>0101011
[2,4,5,3,7,1,8,6]=>0010101
[2,4,5,7,3,8,6,1]=>0001011
[2,4,6,3,1,8,5,7]=>0011010
[2,4,6,3,8,5,1,7]=>0010110
[2,4,6,8,3,5,1,7]=>0001010
[2,4,7,3,1,5,8,6]=>0011001
[2,4,7,3,1,8,6,5]=>0011011
[2,4,7,8,3,5,6,1]=>0001001
[2,5,1,6,4,8,3,7]=>0101010
[2,5,1,6,7,4,8,3]=>0100101
[2,5,1,7,4,3,8,6]=>0101101
[2,5,6,3,4,8,1,7]=>0010010
[2,5,6,3,7,4,8,1]=>0010101
[2,5,6,3,8,4,1,7]=>0010110
[2,5,6,7,8,4,1,3]=>0000110
[2,5,6,8,4,3,1,7]=>0001110
[2,6,1,7,4,8,5,3]=>0101011
[6,8,4,3,2,1,7,5]=>0111101
[7,6,5,2,8,4,1,3]=>1110110
[7,6,3,8,2,4,1,5]=>1101010
[5,1,2,3,4,8,7,6]=>1000011
[4,1,2,3,7,6,5,8]=>1000110
[7,6,5,8,2,4,3,1]=>1101011
[6,8,7,4,5,2,3,1]=>0110101
[6,8,4,7,5,2,3,1]=>0101101
[6,8,4,7,2,5,3,1]=>0101011
[6,4,8,7,5,2,3,1]=>1011101
[6,8,4,2,7,5,3,1]=>0110111
[6,8,4,7,2,1,5,3]=>0101101
[6,8,4,7,3,5,2,1]=>0101011
[6,4,8,2,7,5,3,1]=>1010111
[6,8,4,2,7,1,5,3]=>0110101
[6,4,2,8,7,5,3,1]=>1101111
[6,8,4,7,3,2,5,1]=>0101101
[6,8,4,2,1,7,5,3]=>0111011
[6,8,4,7,3,2,1,5]=>0101110
[6,8,5,7,1,4,3,2]=>0101011
[1,8,7,3,6,2,5,4]=>0110101
[5,8,7,2,3,6,1,4]=>0110010
[6,8,2,7,5,4,1,3]=>0101110
[6,8,3,7,5,2,1,4]=>0101110
[6,8,1,7,3,5,4,2]=>0101011
[6,8,4,7,3,1,5,2]=>0101101
[6,8,1,7,3,2,5,4]=>0101101
[3,8,2,7,6,5,1,4]=>0101110
[1,8,4,7,6,2,5,3]=>0101101
[3,8,1,7,6,2,5,4]=>0101101
[1,8,4,7,3,6,5,2]=>0101011
[4,8,5,7,1,2,6,3]=>0101001
[1,8,4,7,3,2,6,5]=>0101101
[6,8,5,2,7,4,1,3]=>0110110
[6,8,3,4,7,1,5,2]=>0100101
[6,8,1,3,7,2,5,4]=>0100101
[2,8,1,3,7,6,5,4]=>0100111
[2,8,3,4,7,6,1,5]=>0100110
[6,8,5,4,2,7,1,3]=>0111010
[6,8,1,4,3,7,5,2]=>0101011
[6,8,1,4,2,7,5,3]=>0101011
[6,5,4,3,8,7,1,2]=>1110110
[3,1,7,2,8,5,6,4]=>1010101
[3,1,6,7,4,8,5,2]=>1001011
[3,1,5,7,8,4,6,2]=>1000101
[8,6,5,7,1,4,3,2]=>1101011
[8,6,4,2,7,5,1,3]=>1110110
[6,4,8,2,7,5,1,3]=>1010110
[8,4,7,6,2,5,1,3]=>1011010
[3,4,5,6,8,7,1,2]=>0000110
[3,4,5,7,8,6,1,2]=>0000110
[3,4,5,8,7,6,1,2]=>0001110
[3,4,6,7,8,5,1,2]=>0000110
[6,4,7,3,5,2,1,8]=>1010110
[5,4,7,3,6,2,1,8]=>1010110
[4,8,7,3,5,2,1,6]=>0110110
[7,5,3,6,8,2,1,4]=>1100110
[5,8,3,6,7,2,1,4]=>0100110
[5,8,7,3,2,4,1,6]=>0111010
[6,4,7,3,2,5,1,8]=>1011010
[6,5,3,7,2,4,1,8]=>1101010
[7,3,8,6,2,4,1,5]=>1011010
[6,3,7,8,2,4,1,5]=>1001010
[5,3,7,6,2,4,1,8]=>1011010
[7,5,8,2,6,4,1,3]=>1010110
[7,4,8,2,5,6,1,3]=>1010010
[5,4,7,2,6,8,1,3]=>1010010
[4,8,7,2,5,6,1,3]=>0110010
[5,4,3,2,6,8,1,7]=>1110010
[4,8,3,2,5,6,1,7]=>0110010
[5,3,7,2,6,4,1,8]=>1010110
[7,5,2,6,8,4,1,3]=>1100110
[6,4,2,7,5,8,1,3]=>1101010
[7,5,8,4,1,2,6,3]=>1011001
[7,1,8,2,3,6,5,4]=>1010011
[7,3,8,4,6,2,1,5]=>1010110
[7,1,8,4,2,6,5,3]=>1011011
[7,1,8,3,6,2,5,4]=>1010101
[7,2,3,4,5,1,8,6]=>1000101
[2,8,3,4,5,1,6,7]=>0100100
[2,7,3,4,1,5,6,8]=>0101000
[5,3,6,1,2,7,4,8]=>1010010
[2,8,5,3,4,6,7,1]=>0110001
[3,8,1,4,5,6,7,2]=>0100001
[4,5,3,1,2,8,7,6]=>0110011
[5,7,3,4,1,6,8,2]=>0101001
[4,5,3,1,2,6,8,7]=>0110001
[3,4,1,2,5,8,7,6]=>0100011
[6,5,3,2,1,8,7,4]=>1111011
[4,5,2,1,8,7,6,3]=>0110111
[3,4,1,8,7,6,5,2]=>0101111
[8,1,2,4,5,6,7,3]=>1000001
[7,1,2,3,4,6,8,5]=>1000001
[6,1,2,3,5,8,7,4]=>1000011
[5,1,2,4,8,6,7,3]=>1000101
[4,1,3,8,5,6,7,2]=>1001001
[7,1,2,3,5,8,6,4]=>1000011
[6,1,2,3,5,7,8,4]=>1000001
[5,1,3,8,4,6,7,2]=>1001001
[4,1,3,5,8,6,7,2]=>1000101
[8,6,3,5,2,7,4,1]=>1101011
[7,5,2,8,6,3,4,1]=>1101101
[5,2,8,6,7,3,4,1]=>1010101
[7,5,2,3,8,6,4,1]=>1100111
[5,2,3,8,6,7,4,1]=>1001011
[8,4,1,7,3,5,6,2]=>1101001
[7,4,1,2,6,8,5,3]=>1100011
[5,3,8,4,1,2,6,7]=>1011000
[6,3,5,8,4,1,2,7]=>1001100
[7,3,5,6,8,4,1,2]=>1000110
[7,4,5,1,2,8,6,3]=>1010011
[6,3,8,4,5,1,2,7]=>1010100
[8,5,1,7,4,6,2,3]=>1101010
[7,4,5,1,8,6,2,3]=>1010110
[8,4,5,1,7,3,6,2]=>1010101
[4,2,7,5,8,6,3,1]=>1010111
[4,2,8,5,6,3,1,7]=>1010110
[8,6,3,1,5,7,4,2]=>1110011
[7,4,2,8,5,6,3,1]=>1101011
[4,2,8,5,6,7,3,1]=>1010011
[7,4,8,5,6,1,2,3]=>1010100
[7,5,8,6,1,2,3,4]=>1011000
[7,3,4,8,5,6,1,2]=>1001010
[7,3,4,5,8,6,1,2]=>1000110
[6,4,8,5,2,3,1,7]=>1011010
[8,6,3,1,7,5,2,4]=>1110110
[7,2,8,3,4,5,6,1]=>1010001
[7,4,5,2,8,6,3,1]=>1010111
[8,5,2,7,4,6,3,1]=>1101011
[5,2,4,8,6,7,3,1]=>1001011
[7,5,8,6,2,3,1,4]=>1011010
[7,4,8,5,6,2,3,1]=>1010101
[7,3,1,8,4,5,6,2]=>1101001
[7,2,4,5,6,8,3,1]=>1000011
[3,4,5,7,6,8,1,2]=>0001010
[4,8,2,5,1,3,7,6]=>0101001
[2,1,8,7,3,4,6,5]=>1011001
[2,7,4,5,6,8,1,3]=>0100010
[4,1,2,8,7,5,3,6]=>1001110
[4,1,2,6,8,3,7,5]=>1000101
[3,1,7,6,8,2,4,5]=>1010100
[8,2,6,3,1,5,4,7]=>1011010
[7,3,5,1,8,2,4,6]=>1010100
[7,8,3,1,5,2,4,6]=>0110100
[1,5,6,7,8,3,4,2]=>0000101
[1,4,6,7,8,3,5,2]=>0000101
[1,5,6,3,7,8,4,2]=>0010011
[6,1,2,3,4,8,7,5]=>1000011
[5,1,2,3,8,7,6,4]=>1000111
[5,1,2,3,8,6,7,4]=>1000101
[2,8,5,3,1,4,6,7]=>0111000
[2,4,3,5,7,8,1,6]=>0100010
[2,6,3,7,8,1,4,5]=>0100100
[3,4,6,1,7,8,5,2]=>0010011
[3,4,6,1,8,5,7,2]=>0010101
[3,4,8,1,5,6,7,2]=>0010001
[3,5,1,7,4,8,6,2]=>0101011
[3,5,6,4,8,1,7,2]=>0010101
[3,5,8,4,1,6,7,2]=>0011001
[3,6,1,8,5,4,7,2]=>0101101
[3,6,7,4,8,5,1,2]=>0010110
[3,6,8,4,5,1,7,2]=>0010101
[4,1,5,6,8,3,7,2]=>1000101
[4,1,5,7,8,6,3,2]=>1000111
[4,1,7,3,5,8,6,2]=>1010011
[4,1,7,8,5,6,3,2]=>1001011
[4,5,7,3,8,6,1,2]=>0010110
[4,5,7,8,1,6,3,2]=>0001011
[4,5,8,3,1,6,7,2]=>0011001
[4,6,3,1,8,5,7,2]=>0110101
[4,6,7,3,5,8,1,2]=>0010010
[4,6,7,8,5,1,3,2]=>0001101
[4,6,8,3,5,1,7,2]=>0010101
[4,7,3,1,8,6,5,2]=>0110111
[4,7,8,3,5,6,1,2]=>0010010
[5,1,6,7,4,8,3,2]=>1001011
[5,1,6,7,8,3,4,2]=>1000101
[5,6,3,4,8,1,7,2]=>0100101
[5,6,7,8,4,1,3,2]=>0001101
[5,7,3,4,1,8,6,2]=>0101011
[5,7,3,4,8,6,1,2]=>0100110
[5,7,3,8,4,6,1,2]=>0101010
[5,7,8,4,3,6,1,2]=>0011010
[6,1,3,7,8,5,4,2]=>1000111
[6,1,7,4,5,8,3,2]=>1010011
[6,1,8,4,5,3,7,2]=>1010101
[6,7,3,8,5,4,1,2]=>0101110
[7,1,3,4,8,6,5,2]=>1000111
[8,4,1,3,2,5,6,7]=>1101000
[8,5,1,2,4,3,6,7]=>1100100
[8,6,1,2,3,5,4,7]=>1100010
[8,7,1,2,3,4,6,5]=>1100001
[8,5,1,4,2,3,6,7]=>1101000
[8,6,1,2,5,3,4,7]=>1100100
[8,7,1,2,3,6,4,5]=>1100010
[8,6,1,2,5,4,3,7]=>1100110
[2,5,8,6,1,7,3,4]=>0011010
[4,5,6,8,7,2,1,3]=>0001110
[5,6,8,7,2,3,1,4]=>0011010
[4,5,7,6,2,8,1,3]=>0011010
[4,8,2,5,6,1,3,7]=>0100100
[5,2,3,6,7,8,1,4]=>1000010
[4,2,8,7,5,3,1,6]=>1011110
[4,2,8,6,7,5,3,1]=>1010111
[1,3,2,4,8,5,7,6]=>0100101
[1,6,3,2,5,7,8,4]=>0110001
[2,5,6,1,8,7,3,4]=>0010110
[7,6,2,1,4,8,3,5]=>1110010
[2,6,5,1,8,7,3,4]=>0110110
[2,7,3,1,8,4,5,6]=>0110100
[1,4,2,7,3,8,6,5]=>0101011
[1,2,7,3,8,6,5,4]=>0010111
[3,1,8,4,6,2,7,5]=>1010101
[3,4,5,1,8,2,7,6]=>0010101
[3,8,1,6,5,2,7,4]=>0101101
[1,5,2,3,8,7,4,6]=>0100110
[2,8,7,6,3,1,4,5]=>0111100
[8,7,2,5,3,1,4,6]=>1101100
[7,6,2,3,4,8,1,5]=>1100010
[8,7,6,2,1,4,3,5]=>1111010
[8,2,7,4,1,5,3,6]=>1011010
[1,7,3,2,4,5,8,6]=>0110001
[1,3,8,6,2,4,7,5]=>0011001
[1,2,3,8,4,7,6,5]=>0001011
[1,6,2,3,7,5,8,4]=>0100101
[4,5,1,2,8,3,7,6]=>0100101
[1,4,8,2,6,3,7,5]=>0010101
[8,4,1,7,3,2,5,6]=>1101100
[1,8,7,3,2,4,6,5]=>0111001
[8,3,1,5,6,2,7,4]=>1100101
[3,4,1,6,5,7,2,8]=>0101010
[3,5,1,6,2,8,7,4]=>0101011
[5,4,3,6,1,7,2,8]=>1101010
[4,8,7,2,1,6,5,3]=>0111011
[6,2,1,8,7,5,4,3]=>1101111
[7,5,8,6,3,2,4,1]=>1011101
[5,8,7,6,3,2,4,1]=>0111101
[5,4,7,2,8,1,6,3]=>1010101
[8,1,5,4,6,3,7,2]=>1010101
[2,1,5,8,3,7,4,6]=>1001010
[2,1,7,4,8,3,6,5]=>1010101
[1,2,3,5,8,7,4,6]=>0000110
[6,1,2,7,8,4,3,5]=>1000110
[5,1,4,8,2,7,3,6]=>1001010
[3,4,1,2,8,7,5,6]=>0100110
[1,2,5,7,8,6,3,4]=>0000110
[2,1,3,4,8,5,7,6]=>1000101
[6,2,5,1,7,3,8,4]=>1010101
[1,5,4,8,6,2,7,3]=>0101101
[2,5,1,8,6,3,7,4]=>0101101
[2,1,3,7,4,8,6,5]=>1001011
[4,2,5,8,1,7,3,6]=>1001010
[2,6,8,5,1,7,3,4]=>0011010
[1,3,2,7,8,5,4,6]=>0100110
[7,1,2,3,6,8,4,5]=>1000010
[5,1,2,3,8,4,7,6]=>1000101
[3,4,5,1,8,7,2,6]=>0010110
[4,1,2,3,8,7,5,6]=>1000110
[2,3,1,8,5,4,7,6]=>0101101
[2,3,8,4,1,5,7,6]=>0011001
[5,3,1,8,7,2,4,6]=>1101100
[3,6,1,8,7,2,4,5]=>0101100
[1,3,8,4,2,7,6,5]=>0011011
[1,2,3,8,5,7,4,6]=>0001010
[6,1,7,2,5,8,3,4]=>1010010
[4,5,1,8,7,2,3,6]=>0101100
[1,4,2,8,5,3,7,6]=>0101101
[3,1,5,2,8,6,7,4]=>1010101
[7,8,6,5,2,1,4,3]=>0111101
[8,6,7,5,2,1,4,3]=>1011101
[6,7,8,2,1,5,4,3]=>0011011
[8,7,5,6,2,1,4,3]=>1101101
[3,2,8,5,6,7,1,4]=>1010010
[4,2,5,1,8,7,3,6]=>1010110
[5,2,7,8,6,3,1,4]=>1001110
[4,2,6,1,5,8,3,7]=>1010010
[7,2,4,5,8,3,6,1]=>1000101
[2,4,7,8,6,1,5,3]=>0001101
[4,2,7,1,5,6,8,3]=>1010001
[3,2,5,8,1,6,7,4]=>1001001
[8,1,4,3,2,5,6,7]=>1011000
[1,7,3,2,4,5,6,8]=>0110000
[1,6,3,2,4,5,7,8]=>0110000
[1,3,8,4,2,5,6,7]=>0011000
[6,2,5,1,8,3,4,7]=>1010100
[5,1,8,2,4,3,6,7]=>1010100
[8,2,3,1,5,6,7,4]=>1010001
[1,7,2,4,5,8,6,3]=>0100011
[1,5,7,8,4,6,2,3]=>0001010
[6,5,8,3,4,2,1,7]=>1010110
[6,5,8,2,3,4,1,7]=>1010010
[4,2,1,3,5,8,6,7]=>1100010
[1,3,8,2,6,4,5,7]=>0010100
[6,1,2,7,4,3,8,5]=>1001101
[5,4,1,2,3,8,6,7]=>1100010
[7,6,8,5,2,4,1,3]=>1011010
[6,7,8,5,2,4,1,3]=>0011010
[3,4,5,8,2,1,7,6]=>0001101
[3,4,6,2,7,1,5,8]=>0010100
[3,4,6,2,8,1,7,5]=>0010101
[3,4,6,8,1,5,7,2]=>0001001
[3,4,6,1,5,2,7,8]=>0010100
[3,4,7,2,1,6,5,8]=>0011010
[3,4,7,1,5,6,2,8]=>0010010
[3,5,2,6,1,4,7,8]=>0101000
[3,5,2,7,1,6,4,8]=>0101010
[3,5,6,4,8,2,1,7]=>0010110
[3,5,6,4,1,2,7,8]=>0011000
[3,5,6,8,4,2,1,7]=>0001110
[3,5,6,8,1,2,7,4]=>0001001
[3,5,6,1,4,2,7,8]=>0010100
[3,5,7,4,2,8,1,6]=>0011010
[3,5,7,4,2,1,6,8]=>0011100
[3,5,7,4,8,1,6,2]=>0010101
[3,5,7,8,1,6,2,4]=>0001010
[3,5,7,1,4,6,2,8]=>0010010
[3,5,8,4,2,6,1,7]=>0011010
[3,5,8,1,4,6,7,2]=>0010001
[3,6,2,4,8,1,7,5]=>0100101
[3,6,2,7,8,5,1,4]=>0100110
[3,6,2,7,8,1,4,5]=>0100100
[3,6,2,1,5,4,7,8]=>0110100
[3,6,7,8,5,1,2,4]=>0001100
[3,6,7,8,1,5,2,4]=>0001010
[3,7,2,4,5,8,1,6]=>0100010
[3,7,2,4,8,1,6,5]=>0100101
[3,7,2,4,1,6,5,8]=>0101010
[3,7,2,8,5,6,1,4]=>0101010
[3,7,8,4,5,1,6,2]=>0010101
[3,7,8,4,1,6,5,2]=>0011011
[3,8,2,4,1,6,7,5]=>0101001
[3,8,2,1,5,6,7,4]=>0110001
[8,1,5,4,3,6,7,2]=>1011001
[8,1,4,5,3,6,7,2]=>1001001
[4,1,6,3,5,7,8,2]=>1010001
[4,1,7,3,5,6,8,2]=>1010001
[4,1,3,6,7,8,5,2]=>1000011
[4,6,2,3,5,1,7,8]=>0100100
[3,5,2,4,1,6,7,8]=>0101000
[5,8,2,3,4,6,1,7]=>0100010
[4,7,2,3,5,1,6,8]=>0100100
[5,7,2,3,4,6,8,1]=>0100001
[4,6,2,3,5,7,1,8]=>0100010
[2,3,7,8,1,6,5,4]=>0001011
[2,7,6,1,4,8,3,5]=>0110010
[2,6,8,1,4,5,7,3]=>0010001
[2,6,5,8,1,3,7,4]=>0101001
[6,4,7,5,8,2,3,1]=>1010101
[6,7,4,1,8,2,3,5]=>0110100
[6,7,8,1,4,2,5,3]=>0010101
[5,2,6,1,4,8,3,7]=>1010010
[7,2,3,5,8,1,4,6]=>1000100
[2,4,7,5,8,1,3,6]=>0010100
[2,3,6,5,1,8,7,4]=>0011011
[2,3,4,8,1,5,7,6]=>0001001
[2,3,4,7,8,1,6,5]=>0000101
[2,7,8,5,1,4,6,3]=>0011001
[2,3,7,5,8,1,4,6]=>0010100
[2,3,6,8,5,1,7,4]=>0001101
[7,6,4,5,1,8,2,3]=>1101010
[7,4,6,8,1,5,2,3]=>1001010
[2,7,4,6,5,8,3,1]=>0101011
[2,6,7,8,5,3,1,4]=>0001110
[2,5,6,1,4,8,3,7]=>0010010
[2,6,4,8,5,7,3,1]=>0101011
[2,5,8,1,4,6,7,3]=>0010001
[7,2,3,4,8,1,6,5]=>1000101
[3,2,5,7,8,1,6,4]=>1000101
[6,4,1,7,8,2,3,5]=>1100100
[5,7,1,6,2,8,4,3]=>0101011
[5,6,1,8,2,3,7,4]=>0101001
[7,3,5,1,6,8,4,2]=>1010011
[6,3,4,5,8,2,1,7]=>1000110
[5,7,6,1,2,8,3,4]=>0110010
[5,6,8,1,2,4,7,3]=>0010001
[6,2,3,4,5,8,1,7]=>1000010
[4,7,1,3,8,2,6,5]=>0100101
[5,4,1,6,7,8,2,3]=>1100010
[7,4,1,5,8,2,6,3]=>1100101
[5,7,1,8,6,2,3,4]=>0101100
[7,3,5,1,8,2,6,4]=>1010101
[4,8,1,3,5,6,7,2]=>0100001
[8,1,2,3,7,5,6,4]=>1000101
[2,1,8,3,7,5,6,4]=>1010101
[5,6,7,3,8,2,1,4]=>0010110
[5,6,8,3,1,2,7,4]=>0011001
[5,7,3,2,8,6,1,4]=>0110110
[5,7,8,3,1,6,2,4]=>0011010
[5,8,3,2,1,6,7,4]=>0111001
[6,2,7,3,8,5,1,4]=>1010110
[6,2,3,7,8,5,1,4]=>1000110
[6,7,3,2,8,5,1,4]=>0110110
[6,7,8,3,5,1,2,4]=>0010100
[1,5,6,7,8,3,2,4]=>0000110
[1,5,8,3,2,6,7,4]=>0011001
[1,6,8,3,5,2,7,4]=>0010101
[1,7,3,2,8,6,5,4]=>0110111
[1,7,8,3,5,6,2,4]=>0010010
[1,6,7,8,4,2,3,5]=>0001100
[1,2,6,8,4,3,7,5]=>0001101
[1,8,3,4,2,6,7,5]=>0101001
[1,2,8,4,3,6,7,5]=>0011001
[6,2,7,8,4,1,3,5]=>1001100
[6,2,3,7,8,1,4,5]=>1000100
[4,5,7,1,8,6,2,3]=>0010110
[4,5,7,8,2,6,1,3]=>0001010
[4,6,2,8,5,1,7,3]=>0101101
[4,6,7,1,8,5,2,3]=>0010110
[4,7,2,8,5,6,1,3]=>0101010
[4,8,2,1,5,6,7,3]=>0110001
[1,2,8,4,5,3,7,6]=>0010101
[1,2,3,8,5,4,7,6]=>0001101
[1,7,3,8,5,4,2,6]=>0101110
[5,2,7,4,8,6,1,3]=>1010110
[5,2,7,8,4,6,1,3]=>1001010
[7,2,3,8,5,4,1,6]=>1001110
[5,6,2,7,8,1,4,3]=>0100101
[5,8,2,4,1,6,7,3]=>0101001
[6,2,1,7,8,5,4,3]=>1100111
[6,7,2,4,8,5,1,3]=>0100110
[6,7,2,8,5,4,1,3]=>0101110
[6,8,2,4,5,1,7,3]=>0100101
[3,2,5,6,8,1,4,7]=>1000100
[8,1,2,3,7,5,4,6]=>1000110
[4,1,8,2,7,5,3,6]=>1010110
[7,1,8,3,4,5,2,6]=>1010010
[7,1,6,3,8,2,4,5]=>1010100
[6,1,5,8,2,3,4,7]=>1001000
[8,1,6,7,4,2,3,5]=>1001100
[6,1,5,8,2,3,7,4]=>1001001
[4,1,7,2,5,8,3,6]=>1010010
[8,1,6,3,4,7,2,5]=>1010010
[7,1,6,8,2,5,3,4]=>1001010
[4,1,8,2,5,6,3,7]=>1010010
[4,1,8,2,5,6,7,3]=>1010001
[3,8,1,2,7,5,4,6]=>0100110
[3,8,1,7,4,5,2,6]=>0101010
[5,4,7,1,2,8,3,6]=>1010010
[8,4,7,1,3,2,6,5]=>1010101
[8,5,7,3,1,2,6,4]=>1011001
[3,8,1,2,4,5,7,6]=>0100001
[7,6,2,1,8,4,3,5]=>1110110
[8,5,2,3,6,1,4,7]=>1100100
[8,5,7,1,4,3,2,6]=>1010110
[3,6,1,4,2,8,5,7]=>0101010
[7,6,8,1,4,5,2,3]=>1010010
[3,7,1,4,2,8,6,5]=>0101011
[5,4,3,8,2,1,7,6]=>1101101
[5,8,7,3,2,1,6,4]=>0111101
[2,3,7,1,6,8,5,4]=>0010011
[2,6,1,5,7,4,8,3]=>0100101
[2,3,6,1,8,4,7,5]=>0010101
[3,5,1,4,6,7,8,2]=>0100001
[4,5,6,2,1,7,8,3]=>0011001
[5,2,4,7,6,3,8,1]=>1001101
[8,7,6,1,4,3,5,2]=>1110101
[8,7,6,1,3,4,5,2]=>1110001
[8,7,1,4,5,6,3,2]=>1100011
[8,1,5,6,7,4,3,2]=>1000111
[5,8,3,4,1,6,2,7]=>0101010
[4,2,6,1,7,8,5,3]=>1010011
[1,5,2,6,7,8,4,3]=>0100011
[4,5,2,7,8,6,1,3]=>0100110
[1,5,6,7,4,8,2,3]=>0001010
[4,2,6,8,5,1,7,3]=>1001101
[4,2,7,8,5,6,1,3]=>1001010
[3,5,2,7,4,6,8,1]=>0101001
[5,6,2,7,3,8,4,1]=>0101011
[3,5,2,8,4,6,7,1]=>0101001
[3,7,2,8,4,1,5,6]=>0101100
[3,5,2,4,7,8,6,1]=>0100011
[3,7,1,5,8,2,4,6]=>0100100
[5,1,3,8,2,4,6,7]=>1001000
[4,2,1,3,8,5,6,7]=>1100100
[1,8,7,6,3,4,5,2]=>0111001
[8,5,7,6,3,1,4,2]=>1011101
[8,5,7,6,3,2,1,4]=>1011110
[8,7,5,3,1,6,4,2]=>1111011
[4,2,8,3,1,6,7,5]=>1011001
[7,8,1,4,5,6,3,2]=>0100011
[4,2,8,3,5,1,7,6]=>1010101
[4,2,7,8,1,6,5,3]=>1001011
[6,8,1,4,5,3,7,2]=>0100101
[5,1,3,4,2,6,7,8]=>1001000
[4,2,7,3,1,6,5,8]=>1011010
[2,3,4,5,8,1,7,6]=>0000101
[4,1,5,3,6,7,8,2]=>1010001
[2,3,4,8,1,6,7,5]=>0001001
[5,1,4,6,3,7,8,2]=>1001001
[5,1,6,3,4,7,8,2]=>1010001
[2,1,7,5,3,8,6,4]=>1011011
[2,1,8,7,5,3,6,4]=>1011101
[7,5,3,2,1,8,6,4]=>1111011
[5,2,3,4,1,8,6,7]=>1001010
[3,8,1,2,5,4,7,6]=>0100101
[7,4,6,8,5,3,2,1]=>1001111
[7,5,8,6,3,2,1,4]=>1011110
[7,4,8,5,6,3,2,1]=>1010111
[7,5,8,6,4,2,1,3]=>1011110
[6,4,2,1,8,5,3,7]=>1110110
[5,3,8,7,4,2,1,6]=>1011110
[7,4,2,1,6,8,5,3]=>1110011
[5,3,8,4,2,1,6,7]=>1011100
[8,6,3,5,7,4,2,1]=>1100111
[6,3,5,8,4,2,1,7]=>1001110
[6,4,8,7,5,2,1,3]=>1011110
[7,5,2,1,3,8,6,4]=>1110011
[6,3,8,7,4,5,2,1]=>1011011
[7,4,5,2,1,8,6,3]=>1011011
[8,5,2,1,7,4,6,3]=>1110101
[6,3,8,4,5,2,1,7]=>1010110
[7,3,6,8,4,5,2,1]=>1001011
[7,3,4,5,8,6,2,1]=>1000111
[7,3,8,4,5,6,2,1]=>1010011
[1,8,7,2,6,5,4,3]=>0110111
[1,8,7,6,2,3,4,5]=>0111000
[1,8,2,5,7,6,4,3]=>0100111
[1,8,2,5,6,7,4,3]=>0100011
[1,2,8,3,4,5,7,6]=>0010001
[7,6,1,2,3,8,4,5]=>1100010
[1,6,2,3,4,8,7,5]=>0100011
[6,4,1,2,8,3,5,7]=>1100100
[4,8,1,2,3,7,5,6]=>0100010
[6,4,1,7,2,3,8,5]=>1101001
[7,1,6,2,3,8,4,5]=>1010010
[6,5,1,2,3,8,4,7]=>1100010
[1,8,5,2,3,7,4,6]=>0110010
[6,5,1,2,7,3,8,4]=>1100101
[7,6,4,1,8,2,3,5]=>1110100
[1,5,2,3,6,8,7,4]=>0100011
[7,3,1,2,8,4,5,6]=>1100100
[7,6,3,1,8,2,4,5]=>1110100
[5,3,6,1,2,4,8,7]=>1010001
[5,8,3,1,7,2,4,6]=>0110100
[7,5,4,1,8,2,3,6]=>1110100
[7,6,1,4,8,2,3,5]=>1100100
[1,2,8,5,3,7,4,6]=>0011010
[1,2,7,3,8,6,4,5]=>0010110
[7,5,1,6,8,2,3,4]=>1100100
[4,1,2,8,6,3,7,5]=>1001101
[6,3,4,1,7,2,8,5]=>1010101
[6,5,3,1,8,2,4,7]=>1110100
[3,8,1,6,7,2,4,5]=>0100100
[6,5,3,7,1,2,8,4]=>1101001
[7,1,4,2,8,5,3,6]=>1010110
[1,2,6,8,3,5,4,7]=>0001010
[1,2,3,7,8,6,4,5]=>0000110
[1,6,8,5,2,7,3,4]=>0011010
[7,6,3,4,1,8,2,5]=>1101010
[1,4,8,2,3,7,6,5]=>0010011
[1,2,8,3,5,7,6,4]=>0010011
[4,5,1,7,6,8,2,3]=>0101010
[3,4,8,1,2,6,7,5]=>0010001
[3,1,8,2,5,6,7,4]=>1010001
[1,4,2,5,6,8,7,3]=>0100011
[4,5,6,3,7,1,8,2]=>0010101
[4,2,5,6,7,8,3,1]=>1000011
[8,2,7,3,1,5,6,4]=>1011001
[7,2,1,8,4,5,6,3]=>1101001
[4,2,7,1,3,8,6,5]=>1010011
[8,2,6,3,4,7,1,5]=>1010010
[7,2,3,4,1,8,6,5]=>1001011
[6,1,8,2,7,5,3,4]=>1010110
[4,2,8,1,5,6,3,7]=>1010010
[8,2,7,3,1,4,5,6]=>1011000
[5,2,1,3,6,7,8,4]=>1100001
[6,4,8,7,3,2,1,5]=>1011110
[6,5,3,8,7,2,1,4]=>1101110
[5,4,8,7,3,2,1,6]=>1011110
[6,4,3,8,7,2,1,5]=>1101110
[6,3,8,7,5,2,1,4]=>1011110
[5,6,8,1,4,2,7,3]=>0010101
[5,6,3,1,4,2,7,8]=>0110100
[5,7,3,8,4,1,6,2]=>0101101
[5,7,3,1,4,6,2,8]=>0110010
[5,7,3,4,8,1,6,2]=>0100101
[5,2,6,1,4,3,7,8]=>1010100
[5,8,3,1,4,6,7,2]=>0110001
[6,2,7,4,1,5,3,8]=>1011010
[6,7,3,8,1,5,2,4]=>0101010
[6,7,3,4,1,5,2,8]=>0101010
[6,7,8,1,5,4,2,3]=>0010110
[4,5,6,7,1,3,2,8]=>0001010
[6,7,1,4,5,3,2,8]=>0100110
[4,5,7,8,2,1,6,3]=>0001101
[7,2,3,8,1,6,5,4]=>1001011
[7,2,3,8,5,1,6,4]=>1001101
[7,2,3,1,5,6,4,8]=>1010010
[7,2,8,4,1,6,5,3]=>1011011
[7,2,8,4,5,1,6,3]=>1010101
[4,6,3,8,1,5,7,2]=>0101001
[7,8,3,4,1,6,5,2]=>0101011
[4,6,7,3,8,1,2,5]=>0010100
[4,6,7,8,1,5,3,2]=>0001011
[4,6,7,1,5,2,3,8]=>0010100
[4,6,8,3,1,5,7,2]=>0011001
[4,6,1,3,5,2,7,8]=>0100100
[4,7,3,8,5,1,6,2]=>0101101
[4,7,3,8,1,6,5,2]=>0101011
[1,7,2,3,4,6,8,5]=>0100001
[8,1,2,3,5,6,4,7]=>1000010
[4,1,8,2,7,3,5,6]=>1010100
[1,8,4,2,7,3,5,6]=>0110100
[7,4,1,2,6,8,3,5]=>1100010
[8,7,1,2,4,5,3,6]=>1100010
[4,1,8,2,3,5,7,6]=>1010001
[6,1,2,8,3,4,7,5]=>1001001
[5,4,1,2,7,8,3,6]=>1100010
[1,5,2,8,3,4,7,6]=>0101001
[7,1,2,5,3,6,8,4]=>1001001
[1,8,2,5,6,3,7,4]=>0100101
[1,5,2,4,6,7,8,3]=>0100001
[6,8,1,3,4,2,5,7]=>0100100
[3,1,8,2,5,4,6,7]=>1010100
[3,1,7,5,8,2,4,6]=>1010100
[1,7,3,2,8,4,5,6]=>0110100
[6,3,5,1,8,2,4,7]=>1010100
[1,6,4,2,3,5,8,7]=>0110001
[1,7,4,2,3,5,8,6]=>0110001
[1,7,4,2,3,6,8,5]=>0110001
[1,2,7,3,8,4,6,5]=>0010101
[7,1,3,4,5,8,2,6]=>1000010
[7,6,1,3,4,8,2,5]=>1100010
[1,8,7,6,3,2,4,5]=>0111100
[1,8,2,7,5,3,6,4]=>0101101
[1,7,4,5,2,6,8,3]=>0101001
[1,4,8,5,6,2,7,3]=>0010101
[3,2,1,8,7,6,4,5]=>1101110
[3,2,1,8,7,5,4,6]=>1101110
[3,2,1,8,7,4,6,5]=>1101101
[3,2,1,8,7,4,5,6]=>1101100
[3,2,1,8,4,7,6,5]=>1101011
[3,2,8,7,6,1,5,4]=>1011101
[5,3,8,7,6,2,1,4]=>1011110
[6,5,8,7,3,2,1,4]=>1011110
[7,4,8,5,6,3,1,2]=>1010110
[4,5,3,8,6,2,7,1]=>0101101
[4,6,2,8,5,3,7,1]=>0101101
[5,3,8,4,6,2,7,1]=>1010101
[4,6,2,7,1,8,5,3]=>0101011
[4,7,1,6,2,8,5,3]=>0101011
[6,2,5,3,8,4,7,1]=>1010101
[4,6,5,3,8,2,7,1]=>0110101
[6,3,7,4,5,2,8,1]=>1010101
[5,7,8,4,3,2,1,6]=>0011110
[4,6,8,7,3,2,1,5]=>0011110
[2,4,8,7,6,5,1,3]=>0011110
[4,7,6,8,3,2,1,5]=>0101110
[3,6,8,5,7,2,1,4]=>0010110
[4,6,7,8,3,2,1,5]=>0001110
[3,5,6,8,7,2,1,4]=>0001110
[1,4,8,7,6,3,5,2]=>0011101
[2,4,5,8,7,6,1,3]=>0001110
[2,5,4,7,3,8,1,6]=>0101010
[2,6,4,7,8,3,1,5]=>0100110
[2,4,7,1,8,3,6,5]=>0010101
[2,4,6,1,5,8,3,7]=>0010010
[3,4,1,7,6,8,5,2]=>0101011
[3,6,1,7,8,4,2,5]=>0100110
[3,5,1,7,2,6,8,4]=>0101001
[4,3,6,2,8,1,7,5]=>1010101
[5,3,4,7,2,8,1,6]=>1001010
[4,5,7,2,1,8,3,6]=>0011010
[4,5,7,2,1,6,8,3]=>0011001
[4,6,5,2,8,7,3,1]=>0110111
[4,5,8,2,1,6,7,3]=>0011001
[3,4,1,5,6,8,7,2]=>0100011
[3,6,1,7,2,5,8,4]=>0101001
[7,3,4,5,8,2,1,6]=>1000110
[6,3,7,8,2,5,1,4]=>1001010
[6,7,4,8,2,5,3,1]=>0101011
[3,5,1,4,7,2,8,6]=>0100101
[4,3,7,5,6,2,8,1]=>1010101
[7,3,4,8,6,2,5,1]=>1001101
[4,7,8,5,6,2,1,3]=>0010110
[3,5,1,4,8,7,2,6]=>0100110
[4,5,6,3,8,2,1,7]=>0010110
[4,2,6,3,7,8,1,5]=>1010010
[4,2,7,3,5,8,1,6]=>1010010
[4,5,3,7,8,1,6,2]=>0100101
[4,2,6,8,5,3,1,7]=>1001110
[5,1,2,7,8,6,4,3]=>1000111
[4,1,2,7,8,6,3,5]=>1000110
[4,1,8,7,2,6,3,5]=>1011010
[4,1,5,8,7,3,2,6]=>1001110
[5,1,8,2,7,6,3,4]=>1010110
[7,1,6,2,8,3,4,5]=>1010100
[4,7,8,3,2,5,1,6]=>0011010
[4,5,2,8,7,3,1,6]=>0101110
[4,5,7,6,8,3,1,2]=>0010110
[8,2,1,7,4,6,3,5]=>1101010
[5,2,1,6,8,4,7,3]=>1100101
[4,5,2,8,7,1,6,3]=>0101101
[5,2,7,6,8,3,4,1]=>1010101
[4,2,5,7,3,1,8,6]=>1001101
[4,2,8,7,1,3,6,5]=>1011001
[8,2,1,7,3,5,4,6]=>1101010
[5,2,6,3,8,7,1,4]=>1010110
[5,2,8,6,4,1,7,3]=>1011101
[5,2,3,8,7,1,4,6]=>1001100
[5,1,8,3,7,4,2,6]=>1010110
[8,1,2,7,5,4,3,6]=>1001110
[6,1,2,8,3,7,4,5]=>1001010
[5,6,7,3,8,1,2,4]=>0010100
[4,1,7,6,8,3,2,5]=>1010110
[8,1,7,3,5,4,2,6]=>1010110
[7,1,6,3,4,2,8,5]=>1010101
[7,1,6,8,5,2,3,4]=>1001100
[8,1,7,3,5,2,6,4]=>1010101
[6,2,3,8,7,5,1,4]=>1001110
[3,8,5,7,2,4,1,6]=>0101010
[3,6,5,8,2,1,7,4]=>0101101
[4,7,1,8,3,5,2,6]=>0101010
[7,6,2,3,4,1,8,5]=>1100101
[4,8,6,7,1,2,3,5]=>0101000
[8,5,7,3,1,6,2,4]=>1011010
[3,4,7,2,1,5,8,6]=>0011001
[3,8,6,1,4,7,2,5]=>0110010
[3,7,6,8,2,5,1,4]=>0101010
[8,6,2,3,1,5,7,4]=>1101001
[3,8,7,1,2,5,6,4]=>0110001
[3,4,8,2,5,6,7,1]=>0010001
[4,2,1,3,7,6,5,8]=>1100110
[6,3,4,8,7,5,1,2]=>1001110
[8,3,5,7,6,1,4,2]=>1001101
[2,1,8,5,6,7,3,4]=>1010010
[6,8,4,5,7,2,3,1]=>0100101
[8,3,2,5,6,7,1,4]=>1100010
[7,3,2,6,8,5,4,1]=>1100111
[4,8,5,3,2,7,6,1]=>0111011
[7,3,5,6,8,1,4,2]=>1000101
[7,4,8,3,6,5,2,1]=>1010111
[7,5,6,3,8,4,2,1]=>1010111
[7,4,5,2,8,3,6,1]=>1010101
[4,8,6,7,3,5,2,1]=>0101011
[4,3,1,2,6,7,8,5]=>1100001
[7,4,6,5,8,3,2,1]=>1010111
[4,8,5,2,6,7,3,1]=>0110011
[2,5,8,6,7,3,1,4]=>0010110
[1,4,6,5,2,7,3,8]=>0011010
[3,7,4,8,6,2,5,1]=>0101101
[2,3,4,1,8,7,5,6]=>0010110
[4,2,6,5,1,8,7,3]=>1011011
[6,5,4,1,3,2,8,7]=>1110101
[6,5,4,2,1,3,8,7]=>1111001
[8,7,4,3,6,1,5,2]=>1110101
[7,8,4,2,1,5,6,3]=>0111001
[8,6,7,2,4,5,1,3]=>1010010
[7,8,2,3,6,1,5,4]=>0100101
[6,8,2,7,3,5,4,1]=>0101011
[2,1,7,8,4,5,6,3]=>1001001
[7,5,8,3,2,4,6,1]=>1011001
[8,6,7,3,4,1,5,2]=>1010101
[8,6,2,7,1,3,5,4]=>1101001
[8,3,2,7,6,4,1,5]=>1101110
[8,5,4,1,3,7,6,2]=>1110011
[5,8,2,3,4,7,6,1]=>0100011
[6,8,2,7,3,4,1,5]=>0101010
[5,6,1,4,7,2,3,8]=>0100100
[4,5,1,6,3,2,8,7]=>0101101
[3,6,7,4,1,2,5,8]=>0011000
[2,5,1,4,3,7,6,8]=>0101010
[1,4,5,3,7,2,8,6]=>0010101
[5,1,4,3,7,2,8,6]=>1010101
[1,6,7,4,3,2,8,5]=>0011101
[2,6,7,3,1,4,5,8]=>0011000
[5,1,4,6,7,2,3,8]=>1000100
[2,6,4,3,1,8,5,7]=>0111010
[1,6,5,2,3,4,8,7]=>0110001
[7,8,2,1,5,4,3,6]=>0110110
[7,8,1,2,3,6,4,5]=>0100010
[1,4,7,8,5,2,3,6]=>0001100
[1,3,2,6,5,8,4,7]=>0101010
[2,1,5,7,8,4,3,6]=>1000110
[3,1,7,2,6,5,8,4]=>1010101
[1,3,2,7,5,4,8,6]=>0101101
[1,4,5,8,6,2,3,7]=>0001100
[1,6,7,2,3,5,8,4]=>0010001
[2,4,1,8,6,5,3,7]=>0101110
[7,1,4,5,8,3,6,2]=>1000101
[3,7,8,5,4,6,1,2]=>0011010
[5,1,7,2,6,4,8,3]=>1010101
[2,3,4,6,8,5,7,1]=>0000101
[3,6,2,4,7,5,8,1]=>0100101
[3,7,2,8,4,6,5,1]=>0101011
[4,7,5,2,3,6,8,1]=>0110001
[4,3,5,8,7,2,6,1]=>1001101
[2,3,4,8,7,5,6,1]=>0001101
[5,1,6,3,7,8,4,2]=>1010011
[4,2,6,7,5,1,8,3]=>1001101
[5,7,6,3,4,8,1,2]=>0110010
[6,4,7,5,8,3,2,1]=>1010111
[3,6,7,5,8,1,4,2]=>0010101
[1,8,5,6,7,3,4,2]=>0100101
[3,2,7,4,6,1,8,5]=>1010101
[3,8,4,5,6,7,2,1]=>0100011
[8,2,4,1,6,7,5,3]=>1010011
[3,4,8,7,6,1,5,2]=>0011101
[4,3,8,7,6,2,5,1]=>1011101
[3,7,8,5,6,4,2,1]=>0010111
[3,4,7,5,8,6,1,2]=>0010110
[5,4,6,2,3,1,8,7]=>1010101
[6,3,1,5,4,2,8,7]=>1101101
[6,4,5,3,2,1,8,7]=>1011101
[7,8,3,4,6,5,1,2]=>0100110
[2,1,7,6,8,4,5,3]=>1010101
[2,5,4,8,6,3,7,1]=>0101101
[3,5,4,7,6,1,8,2]=>0101101
[2,6,5,3,7,4,8,1]=>0110101
[2,1,8,5,3,7,6,4]=>1011011
[6,5,4,2,7,8,3,1]=>1110011
[2,6,8,5,7,4,3,1]=>0010111
[2,1,8,6,7,5,4,3]=>1010111
[2,5,3,1,6,4,7,8]=>0110100
[7,5,4,2,3,1,8,6]=>1110101
[6,3,2,4,5,8,1,7]=>1100010
[3,5,4,2,8,6,1,7]=>0110110
[5,6,8,7,3,2,1,4]=>0011110
[6,4,5,3,2,8,1,7]=>1011010
[4,2,5,7,3,1,6,8]=>1001100
[7,4,1,3,2,6,8,5]=>1101001
[6,1,4,3,2,7,8,5]=>1011001
[1,6,4,2,3,7,8,5]=>0110001
[1,4,5,3,8,2,6,7]=>0010100
[2,5,4,3,8,1,6,7]=>0110100
[6,2,5,1,3,7,4,8]=>1010010
[7,6,5,8,1,2,4,3]=>1101001
[5,7,4,1,3,6,2,8]=>0110010
[4,3,8,1,6,7,2,5]=>1010010
[4,3,8,1,6,5,7,2]=>1010101
[4,3,8,2,5,6,7,1]=>1010001
[5,4,8,2,3,6,7,1]=>1010001
[3,2,8,1,6,7,4,5]=>1010010
[5,2,8,1,6,7,3,4]=>1010010
[7,2,6,3,8,1,5,4]=>1010101
[6,3,4,5,8,2,7,1]=>1000101
[7,3,8,1,4,5,6,2]=>1010001
[7,3,4,5,8,1,6,2]=>1000101
[7,4,8,1,5,6,2,3]=>1010010
[7,2,8,1,6,5,4,3]=>1010111
[8,1,3,4,6,5,2,7]=>1000110
[8,6,5,7,2,1,4,3]=>1101101
[1,8,6,3,7,4,5,2]=>0110101
[3,8,5,1,7,6,4,2]=>0110111
[2,8,1,3,5,6,7,4]=>0100001
[2,4,8,7,5,6,3,1]=>0011011
[3,8,7,5,2,6,4,1]=>0111011
[1,8,7,3,4,6,5,2]=>0110011
[2,8,1,4,5,7,6,3]=>0100011
[1,2,7,6,8,4,5,3]=>0010101
[1,2,5,3,7,6,8,4]=>0010101
[3,7,8,1,5,6,2,4]=>0010010
[1,2,4,8,3,6,5,7]=>0001010
[4,1,3,7,6,8,5,2]=>1001011
[6,5,7,8,1,4,3,2]=>1001011
[3,1,8,6,7,5,4,2]=>1010111
[2,8,3,1,7,5,4,6]=>0110110
[2,8,3,7,1,4,5,6]=>0101000
[4,8,2,7,5,1,3,6]=>0101100
[4,1,2,6,7,5,3,8]=>1000110
[1,2,5,3,8,6,4,7]=>0010110
[5,8,7,6,2,1,3,4]=>0111100
[6,4,8,3,7,5,2,1]=>1010111
[3,6,8,2,5,7,4,1]=>0010011
[4,8,7,5,2,6,3,1]=>0111011
[3,2,8,5,6,1,7,4]=>1010101
[3,4,8,1,5,7,6,2]=>0010011
[4,5,6,2,7,3,8,1]=>0010101
[4,7,5,6,2,3,8,1]=>0101001
[3,5,7,6,2,4,8,1]=>0011001
[1,6,8,7,4,5,3,2]=>0011011
[8,3,5,7,6,2,4,1]=>1001101
[6,4,5,2,8,7,3,1]=>1010111
[6,4,2,7,8,5,3,1]=>1100111
[2,4,5,8,6,7,1,3]=>0001010
[1,3,5,6,8,7,2,4]=>0000110
[5,7,4,1,6,2,8,3]=>0110101
[3,5,6,7,8,2,4,1]=>0000101
[5,2,4,1,6,7,8,3]=>1010001
[8,5,6,7,2,4,3,1]=>1001011
[7,8,4,5,1,6,3,2]=>0101011
[3,5,8,6,4,7,2,1]=>0011011
[4,5,6,8,3,7,2,1]=>0001011
[8,4,5,7,6,2,3,1]=>1001101
[4,8,6,7,5,2,3,1]=>0101101
[8,7,4,3,6,5,1,2]=>1110110
[8,1,4,3,6,5,2,7]=>1010110
[6,1,2,5,4,3,8,7]=>1001101
[2,8,6,3,4,7,1,5]=>0110010
[8,1,2,3,5,7,4,6]=>1000010
[8,1,2,3,6,5,4,7]=>1000110
[8,1,2,3,7,6,5,4]=>1000111
[2,8,1,6,7,5,3,4]=>0100110
[8,1,2,3,5,4,7,6]=>1000101
[4,8,5,2,7,1,6,3]=>0110101
[3,7,8,6,4,2,1,5]=>0011110
[3,7,8,4,6,2,1,5]=>0010110
[8,3,1,5,7,6,2,4]=>1100110
[4,5,2,8,6,7,1,3]=>0101010
[8,4,5,1,3,2,6,7]=>1010100
[8,1,2,3,6,7,5,4]=>1000011
[8,1,6,7,2,5,4,3]=>1001011
[5,4,1,3,2,8,7,6]=>1101011
[5,4,2,1,3,8,7,6]=>1110011
[3,2,7,4,1,6,5,8]=>1011010
[5,7,3,2,1,6,4,8]=>0111010
[7,6,5,1,3,4,2,8]=>1110010
[7,6,5,2,1,4,3,8]=>1111010
[8,6,2,4,3,5,1,7]=>1101010
[7,6,5,1,4,2,3,8]=>1110100
[1,7,6,3,2,4,5,8]=>0111000
[8,7,3,2,1,6,4,5]=>1111010
[1,5,7,2,4,3,6,8]=>0010100
[5,2,8,1,4,3,7,6]=>1010101
[7,1,6,8,2,4,5,3]=>1001001
[8,4,6,2,3,7,1,5]=>1010010
[8,6,1,3,7,5,2,4]=>1100110
[5,8,1,3,4,7,2,6]=>0100010
[5,8,6,2,3,1,4,7]=>0110100
[5,8,7,3,2,4,6,1]=>0111001
[7,6,2,8,3,5,4,1]=>1101011
[8,7,5,2,6,3,1,4]=>1110110
[8,4,7,3,1,5,2,6]=>1011010
[8,2,6,3,1,4,7,5]=>1011001
[8,3,2,7,6,1,4,5]=>1101100
[3,8,2,7,6,4,1,5]=>0101110
[3,6,7,5,8,2,1,4]=>0010110
[6,3,5,2,8,7,4,1]=>1010111
[5,8,4,3,2,7,6,1]=>0111011
[2,4,6,8,7,3,5,1]=>0001101
[6,3,5,7,8,2,4,1]=>1000101
[4,6,8,7,5,2,3,1]=>0011101
[3,5,6,8,7,2,4,1]=>0001101
[1,6,8,4,7,5,3,2]=>0010111
[3,8,6,5,1,7,2,4]=>0111010
[8,4,6,7,5,2,3,1]=>1001101
[8,4,5,7,2,6,3,1]=>1001011
[6,7,4,3,8,5,2,1]=>0110111
[2,6,8,5,4,7,3,1]=>0011011
[2,7,4,6,8,5,3,1]=>0100111
[6,4,7,8,3,5,2,1]=>1001011
[5,2,4,1,6,3,8,7]=>1010101
[6,3,5,2,7,4,8,1]=>1010101
[7,3,4,2,6,1,8,5]=>1010101
[2,3,7,4,6,1,8,5]=>0010101
[2,1,7,4,6,3,8,5]=>1010101
[7,5,4,2,6,3,8,1]=>1110101
[5,4,7,2,6,1,8,3]=>1010101
[5,2,7,4,6,1,8,3]=>1010101
[5,2,4,1,7,6,8,3]=>1010101
[4,2,7,5,6,1,8,3]=>1010101
[4,2,7,5,6,3,8,1]=>1010101
[6,2,4,3,7,5,8,1]=>1010101
[2,6,4,3,7,5,8,1]=>0110101
[2,7,5,4,8,6,3,1]=>0110111
[4,3,7,5,8,6,1,2]=>1010110
[6,7,4,8,3,5,2,1]=>0101011
[2,1,5,8,7,4,6,3]=>1001101
[5,8,3,4,6,7,2,1]=>0100011
[6,4,3,8,7,2,5,1]=>1101101
[3,6,8,5,4,7,1,2]=>0011010
[7,5,3,6,8,4,2,1]=>1100111
[8,4,3,5,7,2,6,1]=>1100101
[4,7,8,6,3,5,2,1]=>0011011
[6,7,5,8,2,4,3,1]=>0101011
[2,5,4,1,7,8,6,3]=>0110011
[4,3,1,5,6,8,7,2]=>1100011
[1,6,3,2,5,8,7,4]=>0110011
[8,1,5,3,2,6,7,4]=>1011001
[1,6,8,3,2,4,7,5]=>0011001
[1,8,7,6,4,2,3,5]=>0111100
[8,1,7,3,5,4,6,2]=>1010101
[7,1,3,8,4,6,5,2]=>1001011
[3,2,8,1,5,6,7,4]=>1010001
[8,6,1,2,4,5,7,3]=>1100001
[1,8,6,7,3,4,5,2]=>0101001
[1,7,3,8,2,4,6,5]=>0101001
[8,4,3,1,5,6,7,2]=>1110001
[1,8,7,6,3,4,2,5]=>0111010
[1,8,5,3,7,6,2,4]=>0110110
[3,5,2,6,1,4,8,7]=>0101001
[4,5,7,2,3,8,6,1]=>0010011
[4,5,7,2,3,8,1,6]=>0010010
[4,5,6,2,3,1,8,7]=>0010101
[4,5,6,2,1,3,8,7]=>0011001
[4,5,6,1,3,2,8,7]=>0010101
[4,5,6,3,1,2,8,7]=>0011001
[4,5,7,3,2,8,1,6]=>0011010
[4,6,7,3,8,2,5,1]=>0010101
[4,6,7,3,8,2,1,5]=>0010110
[4,5,7,3,1,8,2,6]=>0011010
[3,5,1,7,4,8,2,6]=>0101010
[2,1,5,7,4,8,3,6]=>1001010
[4,5,7,1,3,8,6,2]=>0010011
[4,6,7,3,8,1,5,2]=>0010101
[5,6,7,8,3,1,4,2]=>0001101
[4,6,7,1,8,3,5,2]=>0010101
[3,6,1,7,8,4,5,2]=>0100101
[2,1,6,7,8,4,5,3]=>1000101
[2,1,6,7,8,4,3,5]=>1000110
[4,6,7,1,8,3,2,5]=>0010110
[5,6,7,8,1,3,2,4]=>0001010
[4,6,7,2,8,3,5,1]=>0010101
[3,6,2,7,8,4,5,1]=>0100101
[3,6,2,7,8,4,1,5]=>0100110
[3,4,2,1,7,8,5,6]=>0110010
[4,6,7,2,8,5,3,1]=>0010111
[4,6,7,2,8,5,1,3]=>0010110
[4,5,7,1,2,8,6,3]=>0010011
[2,1,6,7,8,3,5,4]=>1000101
[3,6,1,7,8,2,5,4]=>0100101
[4,6,7,1,8,2,5,3]=>0010101
[5,6,7,8,1,2,4,3]=>0001001
[5,6,7,8,2,4,1,3]=>0001010
[5,6,7,8,2,4,3,1]=>0001011
[3,6,1,7,8,5,2,4]=>0100110
[2,1,6,7,8,5,3,4]=>1000110
[5,3,1,6,2,4,8,7]=>1101001
[7,3,1,5,2,8,4,6]=>1101010
[8,4,5,1,2,7,3,6]=>1010010
[7,4,5,1,2,8,3,6]=>1010010
[6,4,5,1,2,3,8,7]=>1010001
[5,4,6,1,2,3,8,7]=>1010001
[3,6,1,5,2,4,8,7]=>0101001
[4,6,5,1,2,3,8,7]=>0110001
[5,6,4,1,2,3,8,7]=>0110001
[7,5,4,1,2,8,3,6]=>1110010
[8,6,4,1,7,2,3,5]=>1110100
[5,7,4,1,2,8,3,6]=>0110010
[3,7,1,5,2,8,4,6]=>0101010
[2,1,7,5,3,8,4,6]=>1011010
[4,8,5,1,2,7,3,6]=>0110010
[6,8,4,1,7,2,3,5]=>0110100
[4,8,6,1,7,2,3,5]=>0110100
[2,1,8,6,7,3,4,5]=>1010100
[2,1,7,6,8,3,4,5]=>1010100
[4,7,6,1,8,2,3,5]=>0110100
[5,7,6,8,1,2,3,4]=>0101000
[6,4,7,1,8,2,3,5]=>1010100
[8,4,6,1,7,2,3,5]=>1010100
[8,3,1,6,7,2,4,5]=>1100100
[4,3,1,2,7,8,5,6]=>1100010
[8,4,7,1,6,2,3,5]=>1010100
[7,4,8,1,6,2,3,5]=>1010100
[4,5,8,1,2,7,3,6]=>0010010
[2,1,6,8,7,3,4,5]=>1001100
[4,6,8,1,7,2,3,5]=>0010100
[5,6,8,7,1,2,3,4]=>0011000
[8,5,7,6,1,2,3,4]=>1011000
[4,7,8,1,6,2,3,5]=>0010100
[3,7,1,8,6,2,4,5]=>0101100
[3,8,1,7,6,2,4,5]=>0101100
[4,8,7,1,6,2,3,5]=>0110100
[6,8,7,5,1,2,3,4]=>0111000
[6,4,7,3,8,5,1,2]=>1010110
[5,4,2,7,6,1,3,8]=>1101100
[5,4,2,7,6,1,8,3]=>1101101
[5,4,3,7,6,8,1,2]=>1101010
[5,4,3,7,8,6,1,2]=>1100110
[5,4,3,8,6,7,1,2]=>1101010
[5,4,3,6,8,7,1,2]=>1100110
[5,4,2,6,7,1,8,3]=>1100101
[5,3,2,6,1,7,4,8]=>1101010
[5,3,2,6,1,7,8,4]=>1101001
[5,3,2,6,1,8,7,4]=>1101011
[5,4,2,6,8,1,7,3]=>1100101
[6,4,8,2,5,1,7,3]=>1010101
[5,4,2,8,6,1,3,7]=>1101100
[5,3,2,6,1,8,4,7]=>1101010
[6,3,8,2,1,5,4,7]=>1011010
[7,8,3,2,1,5,4,6]=>0111010
[7,8,3,2,1,5,6,4]=>0111001
[6,3,8,2,1,5,7,4]=>1011001
[5,3,2,8,1,6,7,4]=>1101001
[5,4,2,7,8,1,6,3]=>1100101
[5,3,2,7,1,8,6,4]=>1101011
[5,3,2,7,1,6,4,8]=>1101010
[6,3,7,2,1,5,4,8]=>1011010
[6,3,7,2,1,5,8,4]=>1011001
[6,3,7,2,1,8,5,4]=>1011011
[6,5,7,8,2,1,4,3]=>1001101
[6,3,7,2,1,4,8,5]=>1011001
[5,3,2,7,1,4,8,6]=>1101001
[5,4,2,8,7,1,3,6]=>1101100
[7,8,4,2,6,1,3,5]=>0110100
[7,8,3,2,1,6,4,5]=>0111010
[6,3,8,2,1,7,4,5]=>1011010
[5,3,2,8,1,7,4,6]=>1101010
[4,3,2,1,8,7,5,6]=>1110110
[4,3,2,1,7,5,8,6]=>1110101
[4,3,2,1,7,5,6,8]=>1110100
[5,3,2,8,1,4,7,6]=>1101001
[6,3,8,2,1,4,7,5]=>1011001
[7,8,3,2,1,4,6,5]=>0111001
[4,3,2,1,8,5,6,7]=>1110100
[7,8,5,6,1,2,4,3]=>0101001
[7,8,4,1,6,2,5,3]=>0110101
[1,6,8,3,2,7,5,4]=>0011011
[6,1,8,3,2,7,5,4]=>1011011
[7,8,1,3,2,6,5,4]=>0101011
[7,8,3,1,2,6,5,4]=>0110011
[7,8,2,3,1,6,5,4]=>0101011
[7,8,2,1,3,6,5,4]=>0110011
[7,8,1,2,3,6,5,4]=>0100011
[1,5,2,8,3,7,6,4]=>0101011
[5,1,2,8,3,7,6,4]=>1001011
[5,2,1,8,3,7,6,4]=>1101011
[6,2,8,1,3,7,5,4]=>1010011
[6,2,8,4,7,1,5,3]=>1010101
[6,3,8,4,7,5,1,2]=>1010110
[2,6,8,3,1,7,5,4]=>0011011
[2,5,1,8,3,7,6,4]=>0101011
[1,2,5,8,3,7,6,4]=>0001011
[2,5,3,8,1,7,6,4]=>0101011
[2,5,4,8,7,1,6,3]=>0101101
[3,5,4,8,7,6,1,2]=>0101110
[5,3,4,8,7,6,1,2]=>1001110
[5,2,4,8,7,1,6,3]=>1001101
[5,2,3,8,1,7,6,4]=>1001011
[4,1,2,3,8,7,6,5]=>1000111
[1,4,2,3,8,7,6,5]=>0100111
[4,1,3,2,8,7,6,5]=>1010111
[6,3,8,1,2,7,5,4]=>1010011
[5,3,1,8,2,7,6,4]=>1101011
[5,1,3,8,2,7,6,4]=>1001011
[1,5,3,8,2,7,6,4]=>0101011
[1,5,4,8,7,2,6,3]=>0101101
[5,1,4,8,7,2,6,3]=>1001101
[5,4,1,8,7,2,6,3]=>1101101
[6,5,8,7,1,2,4,3]=>1011001
[5,6,8,7,3,4,1,2]=>0011010
[5,6,8,7,2,1,4,3]=>0011101
[4,5,1,8,7,2,6,3]=>0101101
[4,1,5,8,7,2,6,3]=>1001101
[1,3,5,8,2,7,6,4]=>0001011
[3,1,5,8,2,7,6,4]=>1001011
[3,6,8,2,1,7,5,4]=>0011011
[4,6,8,3,7,5,1,2]=>0010110
[4,5,3,8,7,6,1,2]=>0101110
[3,5,2,8,1,7,6,4]=>0101011
[3,1,4,2,8,7,6,5]=>1010111
[3,2,5,8,1,7,6,4]=>1001011
[4,2,5,8,7,1,6,3]=>1001101
[4,3,5,8,7,6,1,2]=>1001110
[2,4,5,8,7,1,6,3]=>0001101
[2,3,5,8,1,7,6,4]=>0001011
[6,2,5,1,4,3,8,7]=>1010101
[5,2,6,1,4,3,8,7]=>1010101
[5,2,7,1,4,3,8,6]=>1010101
[6,2,8,1,4,3,7,5]=>1010101
[6,2,7,1,4,3,8,5]=>1010101
[7,2,6,1,4,3,8,5]=>1010101
[8,2,5,1,4,3,7,6]=>1010101
[8,1,4,3,7,2,6,5]=>1010101
[8,2,6,1,5,3,7,4]=>1010101
[7,2,6,1,5,3,8,4]=>1010101
[6,2,7,1,5,3,8,4]=>1010101
[6,2,8,1,5,3,7,4]=>1010101
[7,4,8,1,3,2,6,5]=>1010101
[8,3,7,1,4,2,6,5]=>1010101
[8,3,7,1,5,2,6,4]=>1010101
[7,3,8,1,5,2,6,4]=>1010101
[6,2,7,3,8,1,5,4]=>1010101
[6,2,8,3,7,1,5,4]=>1010101
[5,1,8,3,7,2,6,4]=>1010101
[4,1,8,3,7,2,6,5]=>1010101
[3,1,7,4,8,2,6,5]=>1010101
[4,1,7,3,8,2,6,5]=>1010101
[5,1,7,3,8,2,6,4]=>1010101
[7,3,8,2,6,1,5,4]=>1010101
[8,2,6,3,7,1,5,4]=>1010101
[3,4,2,6,8,1,5,7]=>0100100
[5,3,6,2,8,1,4,7]=>1010100
[7,4,2,5,8,3,6,1]=>1100101
[4,5,2,6,3,8,1,7]=>0101010
[3,5,6,1,4,8,2,7]=>0010010
[4,1,5,6,3,8,2,7]=>1001010
[4,5,1,6,3,8,2,7]=>0101010
[4,5,6,3,2,8,1,7]=>0011010
[6,7,4,8,3,2,5,1]=>0101101
[6,7,4,8,3,2,1,5]=>0101110
[6,7,4,1,8,3,2,5]=>0110110
[5,3,7,8,1,4,2,6]=>1001010
[7,3,5,8,1,4,6,2]=>1001001
[4,5,1,7,8,3,6,2]=>0100101
[7,4,1,5,8,3,6,2]=>1100101
[6,7,4,3,8,1,5,2]=>0110101
[5,6,1,7,3,8,4,2]=>0101011
[5,1,6,7,3,8,4,2]=>1001011
[6,4,7,1,8,3,5,2]=>1010101
[6,7,8,3,1,4,5,2]=>0011001
[6,7,2,8,4,5,1,3]=>0101010
[6,7,2,8,4,1,3,5]=>0101100
[6,1,7,4,8,3,2,5]=>1010110
[5,1,6,7,3,2,8,4]=>1001101
[5,6,1,7,3,2,8,4]=>0101101
[5,6,7,3,2,1,8,4]=>0011101
[5,6,7,3,2,8,4,1]=>0011011
[7,4,2,5,1,8,3,6]=>1101010
[6,7,4,2,8,3,5,1]=>0110101
[3,6,7,2,8,4,5,1]=>0010101
[3,6,7,2,8,4,1,5]=>0010110
[3,6,7,2,1,8,4,5]=>0011010
[3,4,7,8,2,1,5,6]=>0001100
[3,7,8,1,4,6,2,5]=>0010010
[3,6,7,2,8,5,1,4]=>0010110
[3,6,7,8,5,2,1,4]=>0001110
[3,6,7,8,5,2,4,1]=>0001101
[6,4,7,8,2,5,3,1]=>1001011
[6,4,7,8,2,1,5,3]=>1001101
[5,3,7,8,1,6,2,4]=>1001010
[6,7,2,8,5,1,3,4]=>0101100
[6,4,1,7,8,2,5,3]=>1100101
[5,1,6,2,7,8,4,3]=>1010011
[5,6,2,7,1,8,4,3]=>0101011
[5,6,2,7,8,4,3,1]=>0100111
[5,6,7,2,8,4,3,1]=>0010111
[5,6,7,2,1,8,4,3]=>0011011
[5,6,1,7,2,8,4,3]=>0101011
[5,1,6,7,2,8,4,3]=>1001011
[6,7,8,3,5,1,4,2]=>0010101
[5,6,1,7,8,4,3,2]=>0100111
[5,6,7,1,8,4,3,2]=>0010111
[8,3,2,5,1,6,4,7]=>1101010
[5,3,2,7,4,1,8,6]=>1101101
[7,5,3,8,2,4,6,1]=>1101001
[8,2,4,5,6,3,1,7]=>1000110
[8,2,4,5,6,1,3,7]=>1000100
[8,5,3,6,4,1,2,7]=>1101100
[8,4,1,5,6,3,2,7]=>1100110
[8,1,4,5,6,3,2,7]=>1000110
[4,5,3,7,2,1,8,6]=>0101101
[7,4,5,8,3,2,6,1]=>1001101
[4,3,6,7,2,8,5,1]=>1001011
[4,3,6,7,2,8,1,5]=>1001010
[1,4,3,6,7,2,8,5]=>0100101
[4,5,3,7,1,8,2,6]=>0101010
[5,3,4,7,1,2,8,6]=>1001001
[7,4,5,8,3,6,1,2]=>1001010
[4,3,6,7,8,1,5,2]=>1000101
[3,5,6,7,8,4,1,2]=>0000110
[3,1,5,6,7,8,4,2]=>1000011
[4,6,1,7,8,3,5,2]=>0100101
[6,2,4,1,7,8,5,3]=>1010011
[2,6,7,1,4,8,3,5]=>0010010
[1,5,3,6,7,8,2,4]=>0100010
[4,5,2,7,8,1,3,6]=>0100100
[4,2,6,7,8,3,1,5]=>1000110
[4,2,6,7,8,3,5,1]=>1000101
[3,6,2,7,4,8,1,5]=>0101010
[3,7,4,2,1,5,8,6]=>0111001
[7,8,4,2,1,3,6,5]=>0111001
[6,3,2,7,1,8,5,4]=>1101011
[3,6,2,7,1,8,5,4]=>0101011
[6,7,3,8,2,5,4,1]=>0101011
[6,4,7,8,5,2,3,1]=>1001101
[2,6,4,7,8,1,5,3]=>0100101
[7,4,1,5,8,6,2,3]=>1100110
[7,5,8,2,1,6,3,4]=>1011010
[6,2,7,1,3,8,5,4]=>1010011
[6,3,1,7,8,2,5,4]=>1100101
[4,6,1,7,8,5,2,3]=>0100110
[5,1,2,6,7,8,4,3]=>1000011
[5,2,6,7,8,4,3,1]=>1000111
[1,6,4,7,8,5,2,3]=>0100110
[2,6,7,1,3,8,5,4]=>0010011
[6,7,3,8,5,1,4,2]=>0101101
[6,4,7,8,5,3,1,2]=>1001110
[3,1,2,6,5,8,7,4]=>1001011
[4,5,1,2,3,8,7,6]=>0100011
[4,6,1,2,3,8,7,5]=>0100011
[1,6,5,3,4,8,7,2]=>0110011
[6,1,5,2,4,8,7,3]=>1010011
[6,5,1,2,3,8,7,4]=>1100011
[6,4,1,2,3,8,7,5]=>1100011
[5,4,1,2,3,8,7,6]=>1100011
[5,4,1,2,7,3,6,8]=>1100100
[6,4,1,7,2,3,5,8]=>1101000
[6,4,1,8,2,3,5,7]=>1101000
[7,4,1,2,8,3,6,5]=>1100101
[7,5,1,2,8,3,6,4]=>1100101
[7,1,5,2,8,4,6,3]=>1010101
[1,7,5,3,8,4,6,2]=>0110101
[8,4,1,2,7,3,6,5]=>1100101
[8,4,1,7,2,3,5,6]=>1101000
[7,4,1,6,2,3,5,8]=>1101000
[8,6,1,7,2,3,5,4]=>1101001
[8,1,6,7,2,4,5,3]=>1001001
[1,7,6,8,3,4,5,2]=>0101001
[7,6,1,8,2,3,5,4]=>1101001
[3,1,2,7,8,5,6,4]=>1000101
[3,1,8,7,2,4,5,6]=>1011000
[3,1,7,6,2,4,5,8]=>1011000
[4,7,1,6,2,3,5,8]=>0101000
[4,8,1,6,2,3,5,7]=>0101000
[5,8,1,2,7,3,6,4]=>0100101
[5,1,8,2,7,4,6,3]=>1010101
[1,5,8,3,7,4,6,2]=>0010101
[1,6,8,7,3,4,5,2]=>0011001
[6,1,8,7,2,4,5,3]=>1011001
[6,8,1,7,2,3,5,4]=>0101001
[6,8,7,1,2,3,4,5]=>0110000
[5,8,6,1,2,3,4,7]=>0110000
[5,7,6,1,2,3,4,8]=>0110000
[7,8,1,6,2,3,5,4]=>0101001
[7,1,8,6,2,4,5,3]=>1011001
[1,7,8,6,3,4,5,2]=>0011001
[8,1,7,6,2,4,5,3]=>1011001
[8,7,1,6,2,3,5,4]=>1101001
[8,5,3,7,2,1,4,6]=>1101100
[6,8,1,4,5,7,3,2]=>0100011
[8,7,2,4,5,1,3,6]=>1100100
[2,6,1,4,5,3,8,7]=>0100101
[6,3,1,4,5,2,8,7]=>1100101
[3,1,6,4,5,2,8,7]=>1010101
[8,3,7,4,5,1,2,6]=>1010100
[5,8,7,4,2,6,3,1]=>0111011
[8,1,7,4,2,6,3,5]=>1011010
[3,7,8,4,5,1,2,6]=>0010100
[5,6,3,8,1,7,2,4]=>0101010
[7,6,1,4,5,8,3,2]=>1100011
[3,7,6,4,5,8,2,1]=>0110011
[8,5,7,4,1,6,3,2]=>1011011
[2,5,8,4,7,6,1,3]=>0010110
[3,8,4,2,5,6,7,1]=>0110001
[8,4,1,3,5,6,7,2]=>1100001
[7,5,8,4,3,6,1,2]=>1011010
[6,5,3,8,4,1,7,2]=>1101101
[2,1,4,8,3,6,7,5]=>1001001
[7,3,8,4,2,6,1,5]=>1011010
[8,3,1,2,5,6,7,4]=>1100001
[4,8,2,3,5,6,7,1]=>0100001
[2,7,8,4,5,3,1,6]=>0010110
[8,7,1,4,3,6,2,5]=>1101010
[5,6,3,8,4,2,7,1]=>0101101
[8,6,3,1,4,2,7,5]=>1110101
[8,6,3,5,1,2,7,4]=>1101001
[5,8,3,2,6,1,7,4]=>0110101
[3,5,8,4,7,6,2,1]=>0010111
[5,8,2,4,7,6,1,3]=>0100110
[7,1,6,4,5,8,2,3]=>1010010
[2,1,8,5,3,6,7,4]=>1011001
[6,8,3,5,2,1,7,4]=>0101101
[7,8,5,4,2,6,1,3]=>0111010
[4,8,1,2,5,6,7,3]=>0100001
[3,4,2,8,5,6,7,1]=>0101001
[2,4,1,8,5,6,7,3]=>0101001
[8,4,2,1,5,6,7,3]=>1110001
[7,5,2,4,8,6,1,3]=>1100110
[2,1,5,3,8,6,7,4]=>1010101
[3,1,4,8,5,6,7,2]=>1001001
[6,5,3,7,2,8,4,1]=>1101011
[6,7,2,4,5,8,3,1]=>0100011
[2,5,7,4,8,6,3,1]=>0010111
[5,6,3,7,1,8,4,2]=>0101011
[3,8,7,4,5,2,1,6]=>0110110
[3,7,5,4,8,6,2,1]=>0110111
[4,6,3,5,8,2,7,1]=>0100101
[3,7,8,4,1,6,2,5]=>0011010
[5,4,2,3,7,6,1,8]=>1100110
[3,2,7,6,4,5,1,8]=>1011010
[4,7,2,6,3,5,1,8]=>0101010
[5,7,6,2,3,4,1,8]=>0110010
[1,7,5,2,8,3,4,6]=>0110100
[6,8,5,2,3,1,4,7]=>0110100
[4,8,2,6,3,1,5,7]=>0101100
[3,2,8,6,4,1,5,7]=>1011100
[7,1,5,2,8,3,4,6]=>1010100
[1,8,5,2,7,3,4,6]=>0110100
[7,1,6,8,2,3,4,5]=>1001000
[3,2,1,7,8,4,5,6]=>1100100
[3,2,8,7,1,4,5,6]=>1011000
[5,8,7,2,1,3,4,6]=>0111000
[1,7,6,8,2,3,4,5]=>0101000
[6,5,8,2,3,1,4,7]=>1010100
[8,5,7,2,1,3,4,6]=>1011000
[3,2,5,4,1,8,6,7]=>1011010
[7,4,2,1,8,3,5,6]=>1110100
[8,4,2,1,7,3,5,6]=>1110100
[1,4,2,8,7,3,5,6]=>0101100
[1,5,8,2,7,3,4,6]=>0010100
[8,5,1,2,7,3,4,6]=>1100100
[3,2,6,1,4,8,5,7]=>1010010
[3,2,7,1,8,4,5,6]=>1010100
[4,7,2,1,8,3,5,6]=>0110100
[8,6,1,7,2,3,4,5]=>1101000
[1,6,8,7,2,3,4,5]=>0011000
[1,7,8,6,2,3,4,5]=>0011000
[7,8,1,6,2,3,4,5]=>0101000
[4,8,2,1,7,3,5,6]=>0110100
[3,2,8,1,7,4,5,6]=>1010100
[5,1,8,2,7,3,4,6]=>1010100
[6,1,8,7,2,3,4,5]=>1011000
[8,1,7,6,2,3,4,5]=>1011000
[2,8,4,1,6,5,7,3]=>0110101
[2,8,5,6,7,4,3,1]=>0100111
[7,5,8,6,1,4,2,3]=>1011010
[3,5,7,6,1,4,2,8]=>0011010
[7,5,8,2,4,1,6,3]=>1010101
[2,8,5,3,4,7,6,1]=>0110011
[2,8,5,3,4,1,7,6]=>0110101
[2,8,5,3,6,1,7,4]=>0110101
[2,8,5,6,7,4,1,3]=>0100110
[2,8,5,3,4,7,1,6]=>0110010
[2,8,5,3,4,6,1,7]=>0110010
[6,5,2,7,3,1,4,8]=>1101100
[6,5,2,8,3,1,7,4]=>1101101
[6,5,2,8,3,1,4,7]=>1101100
[7,5,8,2,4,6,3,1]=>1010011
[7,5,8,6,1,4,3,2]=>1011011
[6,5,8,2,1,3,7,4]=>1011001
[3,5,6,2,1,8,7,4]=>0011011
[3,5,7,2,4,1,8,6]=>0010101
[6,5,2,7,3,1,8,4]=>1101101
[4,5,2,6,3,1,7,8]=>0101100
[6,5,2,7,3,4,8,1]=>1101001
[5,1,6,7,4,3,8,2]=>1001101
[5,1,2,6,4,8,7,3]=>1001011
[5,1,2,8,6,4,7,3]=>1001101
[5,1,6,8,7,3,4,2]=>1001101
[6,5,2,8,3,7,4,1]=>1101011
[4,1,2,3,8,6,5,7]=>1000110
[4,1,2,3,8,6,7,5]=>1000101
[4,1,2,3,8,5,7,6]=>1000101
[6,5,8,2,4,3,7,1]=>1010101
[6,5,2,8,3,7,1,4]=>1101010
[6,5,2,7,3,4,1,8]=>1101010
[5,1,6,7,4,3,2,8]=>1001110
[5,1,6,8,7,3,2,4]=>1001110
[5,7,8,6,3,4,2,1]=>0011011
[3,1,4,8,6,2,7,5]=>1001101
[3,1,4,8,6,5,2,7]=>1001110
[4,1,6,7,8,3,2,5]=>1000110
[4,1,6,5,7,3,2,8]=>1010110
[4,5,2,6,3,7,1,8]=>0101010
[4,5,2,7,3,8,1,6]=>0101010
[3,5,6,2,4,8,1,7]=>0010010
[3,7,5,6,8,4,1,2]=>0100110
[3,6,5,2,8,1,7,4]=>0110101
[6,1,2,5,8,4,7,3]=>1000101
[4,1,2,3,5,8,7,6]=>1000011
[4,1,6,7,8,3,5,2]=>1000101
[4,1,2,6,8,5,7,3]=>1000101
[4,1,2,5,6,8,7,3]=>1000011
[4,5,2,6,3,7,8,1]=>0101001
[6,4,2,7,1,3,8,5]=>1101001
[7,4,2,5,1,3,8,6]=>1101001
[8,5,3,6,1,7,2,4]=>1101010
[7,3,6,2,4,8,1,5]=>1010010
[6,3,7,4,1,2,8,5]=>1011001
[3,7,5,1,2,4,8,6]=>0110001
[7,4,8,5,2,6,1,3]=>1011010
[5,8,2,6,3,7,1,4]=>0101010
[3,8,6,2,4,7,1,5]=>0110010
[3,8,5,7,1,2,4,6]=>0101000
[2,8,5,7,1,3,4,6]=>0101000
[4,8,6,2,7,1,3,5]=>0110100
[3,6,5,8,1,2,4,7]=>0101000
[5,4,7,3,8,1,2,6]=>1010100
[8,4,1,6,7,2,3,5]=>1100100
[6,5,1,2,7,8,3,4]=>1100010
[4,7,1,5,8,6,2,3]=>0100110
[7,6,1,8,5,2,3,4]=>1101100
[5,7,2,8,1,6,3,4]=>0101010
[6,3,7,8,5,1,2,4]=>1001100
[3,6,8,2,7,1,4,5]=>0010100
[5,3,8,7,1,2,4,6]=>1011000
[8,3,7,6,1,2,4,5]=>1011000
[8,4,7,6,1,2,3,5]=>1011000
[5,4,8,7,1,2,3,6]=>1011000
[3,5,8,7,1,2,4,6]=>0011000
[2,5,8,7,1,3,4,6]=>0011000
[6,8,4,7,5,1,2,3]=>0101100
[5,8,7,1,6,2,3,4]=>0110100
[2,8,7,6,1,3,4,5]=>0111000
[3,8,7,6,1,2,4,5]=>0111000
[4,8,7,6,1,2,3,5]=>0111000
[5,6,3,1,4,2,8,7]=>0110101
[7,5,3,8,2,1,6,4]=>1101101
[3,8,7,4,5,1,6,2]=>0110101
[6,7,1,4,5,8,2,3]=>0100010
[2,1,7,8,5,3,6,4]=>1001101
[5,7,3,8,1,2,6,4]=>0101001
[7,5,1,4,8,6,3,2]=>1100111
[6,4,3,8,1,5,7,2]=>1101001
[8,6,3,1,2,5,7,4]=>1110001
[8,7,1,4,2,6,5,3]=>1101011
[7,3,8,4,1,6,5,2]=>1011011
[5,3,2,7,4,6,8,1]=>1101001
[7,5,3,6,2,4,8,1]=>1101001
[6,3,2,5,1,8,4,7]=>1101010
[8,5,3,6,2,7,1,4]=>1101010
[7,2,6,3,4,5,8,1]=>1010001
[6,2,7,3,4,5,8,1]=>1010001
[6,7,3,5,2,4,8,1]=>0101001
[3,7,6,2,4,5,8,1]=>0110001
[6,5,3,1,2,8,4,7]=>1110010
[8,6,5,2,3,7,1,4]=>1110010
[8,5,2,1,7,3,4,6]=>1110100
[7,5,2,1,8,3,4,6]=>1110100
[1,6,3,2,8,4,5,7]=>0110100
[4,2,6,5,1,8,3,7]=>1011010
[5,4,8,6,2,7,1,3]=>1011010
[7,8,5,2,3,6,1,4]=>0110010
[6,8,2,1,7,3,4,5]=>0110100
[2,8,1,7,3,4,5,6]=>0101000
[3,8,6,1,7,2,4,5]=>0110100
[4,2,8,3,7,1,5,6]=>1010100
[8,1,2,7,3,4,5,6]=>1001000
[6,3,7,1,2,8,4,5]=>1010010
[7,2,6,1,8,3,4,5]=>1010100
[7,3,1,5,8,2,4,6]=>1100100
[5,4,1,3,6,8,2,7]=>1100010
[8,5,3,7,6,1,2,4]=>1101100
[6,1,8,3,7,2,4,5]=>1010100
[7,6,8,2,3,5,1,4]=>1010010
[3,7,8,2,4,6,1,5]=>0010010
[5,4,7,8,2,6,1,3]=>1001010
[4,2,5,8,7,1,3,6]=>1001100
[2,3,8,7,1,4,5,6]=>0011000
[2,1,8,7,3,4,5,6]=>1011000
[8,2,7,6,1,3,4,5]=>1011000
[1,2,8,7,3,4,5,6]=>0011000
[1,3,8,7,2,4,5,6]=>0011000
[1,7,8,3,6,2,4,5]=>0010100
[5,4,8,7,6,1,2,3]=>1011100
[6,8,3,7,5,1,2,4]=>0101100
[7,8,6,2,5,1,3,4]=>0110100
[8,1,6,7,3,2,4,5]=>1001100
[8,1,5,3,7,2,4,6]=>1010100
[8,1,5,3,6,2,4,7]=>1010100
[7,4,8,3,2,6,5,1]=>1011011
[7,4,1,3,2,6,5,8]=>1101010
[8,1,4,3,2,6,5,7]=>1011010
[8,1,4,3,2,7,5,6]=>1011010
[8,1,5,4,6,7,2,3]=>1010010
[8,1,5,3,6,2,7,4]=>1010101
[8,1,4,3,2,6,7,5]=>1011001
[8,1,4,3,2,5,7,6]=>1011001
[7,4,1,3,2,5,6,8]=>1101000
[7,4,8,3,2,5,6,1]=>1011001
[6,4,3,1,2,5,8,7]=>1110001
[7,4,1,3,2,5,8,6]=>1101001
[7,5,1,3,6,2,8,4]=>1100101
[7,5,1,4,6,8,2,3]=>1100010
[6,4,3,8,2,5,1,7]=>1101010
[5,4,3,2,8,6,1,7]=>1110110
[5,4,3,2,8,7,1,6]=>1110110
[6,5,4,8,7,1,2,3]=>1101100
[6,5,4,1,7,8,2,3]=>1110010
[6,4,3,1,2,7,8,5]=>1110001
[7,4,1,3,2,8,5,6]=>1101010
[6,4,3,1,2,7,5,8]=>1110010
[6,4,3,8,2,7,5,1]=>1101011
[6,5,3,8,7,2,4,1]=>1101101
[6,5,3,1,7,2,4,8]=>1110100
[7,5,1,3,8,2,4,6]=>1100100
[6,5,3,7,8,2,4,1]=>1100101
[6,4,3,7,2,8,5,1]=>1101011
[6,4,3,7,2,1,5,8]=>1101100
[7,5,8,4,1,6,2,3]=>1011010
[6,5,4,8,1,7,2,3]=>1101010
[6,5,3,8,1,2,7,4]=>1101001
[6,5,4,7,1,8,2,3]=>1101010
[5,4,3,2,7,8,1,6]=>1110010
[4,6,3,8,5,1,2,7]=>0101100
[5,6,8,3,4,1,2,7]=>0010100
[5,6,8,3,4,1,7,2]=>0010101
[4,6,2,7,5,3,1,8]=>0101110
[5,6,8,4,3,1,2,7]=>0011100
[5,7,8,4,1,3,6,2]=>0011001
[5,6,8,4,2,1,7,3]=>0011101
[5,6,8,2,4,1,7,3]=>0010101
[3,2,6,8,5,1,4,7]=>1001100
[5,6,8,4,2,1,3,7]=>0011100
[5,7,8,4,1,3,2,6]=>0011010
[5,7,8,4,1,2,3,6]=>0011000
[6,7,8,1,5,2,3,4]=>0010100
[6,7,8,1,5,3,2,4]=>0010110
[6,7,8,1,3,5,2,4]=>0010010
[5,7,8,2,1,6,3,4]=>0011010
[4,7,2,8,1,6,3,5]=>0101010
[3,2,7,8,1,6,4,5]=>1001010
[4,7,2,8,1,6,5,3]=>0101011
[5,7,8,2,1,6,4,3]=>0011011
[6,7,8,1,3,5,4,2]=>0010011
[6,7,8,1,5,3,4,2]=>0010101
[6,7,8,1,4,3,5,2]=>0010101
[5,6,8,3,2,1,7,4]=>0011101
[4,7,3,8,1,6,2,5]=>0101010
[4,7,3,8,1,5,6,2]=>0101001
[4,7,3,8,1,5,2,6]=>0101010
[4,7,3,8,1,2,5,6]=>0101000
[5,7,8,3,1,2,4,6]=>0011000
[5,6,8,3,2,1,4,7]=>0011100
[3,2,7,8,1,5,4,6]=>1001010
[6,7,8,1,3,4,2,5]=>0010010
[6,7,8,1,4,2,3,5]=>0010100
[6,7,8,1,2,5,3,4]=>0010010
[6,7,8,1,2,4,5,3]=>0010001
[5,7,8,2,1,3,6,4]=>0011001
[3,2,7,8,1,4,6,5]=>1001001
[6,7,8,1,3,2,4,5]=>0010100
[6,7,8,1,2,4,3,5]=>0010010
[6,7,8,1,2,3,5,4]=>0010001
[8,3,5,1,7,4,6,2]=>1010101
[8,3,4,1,7,5,6,2]=>1010101
[4,8,3,1,7,5,6,2]=>0110101
[4,6,2,1,7,5,8,3]=>0110101
[1,4,6,2,7,5,8,3]=>0010101
[1,7,5,2,6,8,4,3]=>0110011
[7,5,2,1,6,8,4,3]=>1110011
[6,8,4,3,1,7,5,2]=>0111011
[4,7,5,6,1,8,3,2]=>0101011
[6,7,5,1,8,4,3,2]=>0110111
[6,8,4,1,7,5,3,2]=>0110111
[6,7,5,3,1,8,4,2]=>0111011
[8,4,2,1,6,7,5,3]=>1110011
[1,8,4,2,6,7,5,3]=>0110011
[1,5,3,2,7,6,8,4]=>0110101
[2,5,3,1,7,6,8,4]=>0110101
[2,7,5,1,6,8,4,3]=>0110011
[4,7,1,6,5,8,2,3]=>0101010
[4,6,1,2,7,5,8,3]=>0100101
[8,4,1,2,6,7,5,3]=>1100011
[5,3,1,2,7,6,8,4]=>1100101
[4,3,1,2,7,6,8,5]=>1100101
[3,5,1,2,7,6,8,4]=>0100101
[6,7,1,5,8,2,3,4]=>0100100
[2,7,6,1,5,8,3,4]=>0110010
[2,3,5,1,7,6,8,4]=>0010101
[8,4,1,6,7,5,2,3]=>1100110
[5,2,3,1,7,6,8,4]=>1010101
[3,5,2,1,7,6,8,4]=>0110101
[1,7,6,2,5,8,3,4]=>0110010
[7,6,2,1,5,8,3,4]=>1110010
[8,2,6,4,7,1,5,3]=>1010101
[6,1,5,2,7,4,8,3]=>1010101
[7,6,2,5,8,3,1,4]=>1100110
[1,8,3,5,7,6,2,4]=>0100110
[1,5,2,3,7,6,8,4]=>0100101
[5,2,1,3,7,6,8,4]=>1100101
[8,4,2,6,7,5,1,3]=>1100110
[6,1,4,2,7,5,8,3]=>1010101
[8,2,6,5,7,1,4,3]=>1010101
[5,1,3,2,7,6,8,4]=>1010101
[1,4,2,3,7,6,8,5]=>0100101
[2,4,1,3,7,6,8,5]=>0100101
[2,5,1,3,7,6,8,4]=>0100101
[2,8,3,5,7,6,1,4]=>0100110
[6,8,2,3,5,7,1,4]=>0100010
[6,7,1,3,5,8,2,4]=>0100010
[8,3,5,7,6,1,2,4]=>1001100
[5,1,2,3,7,6,8,4]=>1000101
[4,7,1,2,8,6,5,3]=>0100111
[4,6,8,1,2,7,5,3]=>0010011
[6,8,7,1,5,3,2,4]=>0110110
[6,8,7,3,5,1,2,4]=>0110100
[7,8,1,3,6,5,2,4]=>0100110
[1,7,3,4,8,6,5,2]=>0100111
[4,2,7,1,8,6,5,3]=>1010111
[7,8,2,3,6,5,1,4]=>0100110
[8,5,7,1,6,2,3,4]=>1010100
[8,5,7,1,2,6,3,4]=>1010010
[6,8,2,7,1,3,5,4]=>0101001
[6,2,4,8,7,1,5,3]=>1001101
[1,6,8,3,7,4,5,2]=>0010101
[1,6,8,3,4,7,5,2]=>0010011
[6,2,4,8,1,7,5,3]=>1001011
[6,8,7,2,3,5,1,4]=>0110010
[6,8,2,1,7,3,5,4]=>0110101
[8,5,7,2,1,6,3,4]=>1011010
[8,5,7,1,2,3,6,4]=>1010001
[8,5,7,2,3,1,6,4]=>1010101
[1,8,7,5,3,4,6,2]=>0111001
[1,8,7,3,5,4,6,2]=>0110101
[8,2,5,4,7,1,6,3]=>1010101
[8,7,6,1,2,4,3,5]=>1110010
[8,7,6,1,4,2,3,5]=>1110100
[8,7,6,4,1,3,2,5]=>1111010
[8,5,7,1,3,2,6,4]=>1010101
[5,8,4,7,1,2,6,3]=>0101001
[8,1,2,6,5,7,4,3]=>1001011
[8,2,5,6,7,4,1,3]=>1000110
[4,8,5,1,7,2,6,3]=>0110101
[8,5,3,7,1,2,6,4]=>1101001
[4,6,2,8,1,7,5,3]=>0101011
[1,6,4,8,3,7,5,2]=>0101011
[1,8,7,4,5,3,6,2]=>0110101
[4,8,5,7,2,1,6,3]=>0101101
[8,5,3,7,2,1,6,4]=>1101101
[8,7,6,3,1,4,2,5]=>1111010
[8,5,3,2,7,1,6,4]=>1110101
[1,8,7,4,3,5,6,2]=>0111001
[1,8,7,3,4,5,6,2]=>0110001
[8,2,4,5,7,1,6,3]=>1000101
[8,5,2,3,7,1,6,4]=>1100101
[8,3,1,5,2,7,6,4]=>1101011
[8,5,4,2,1,7,3,6]=>1111010
[8,5,4,2,1,7,6,3]=>1111011
[6,5,4,2,3,1,8,7]=>1110101
[6,3,2,5,1,4,8,7]=>1101001
[8,5,4,1,2,7,6,3]=>1110011
[8,7,4,1,6,3,2,5]=>1110110
[8,7,4,1,6,3,5,2]=>1110101
[8,7,4,1,6,5,3,2]=>1110111
[8,5,4,3,1,7,6,2]=>1111011
[8,3,2,5,1,7,6,4]=>1101011
[8,3,2,5,1,7,4,6]=>1101010
[8,5,4,3,1,7,2,6]=>1111010
[8,5,4,1,3,7,2,6]=>1110010
[8,7,4,1,6,5,2,3]=>1110110
[2,1,8,7,6,4,5,3]=>1011101
[8,3,2,7,6,4,5,1]=>1101101
[8,5,4,2,3,7,6,1]=>1110011
[8,7,4,2,6,5,3,1]=>1110111
[8,7,4,2,6,3,5,1]=>1110101
[8,7,4,2,6,3,1,5]=>1110110
[8,3,1,7,6,4,2,5]=>1101110
[8,3,1,7,6,4,5,2]=>1101101
[8,3,1,5,4,7,6,2]=>1101011
[8,3,1,7,6,5,2,4]=>1101110
[8,3,1,7,6,2,5,4]=>1101101
[8,5,4,2,3,7,1,6]=>1110010
[8,3,2,5,4,7,1,6]=>1101010
[2,1,8,5,4,7,3,6]=>1011010
[8,3,2,7,6,5,1,4]=>1101110
[8,7,6,5,3,1,4,2]=>1111101
[8,3,2,7,6,1,5,4]=>1101101
[8,7,6,5,1,2,4,3]=>1111001
[5,2,3,1,6,4,8,7]=>1010101
[7,4,5,2,3,1,8,6]=>1010101
[7,3,5,2,4,1,8,6]=>1010101
[6,3,5,2,4,1,8,7]=>1010101
[4,1,6,3,5,2,8,7]=>1010101
[6,3,4,1,5,2,8,7]=>1010101
[5,2,7,3,4,1,8,6]=>1010101
[6,2,8,5,7,3,4,1]=>1010101
[6,2,7,3,4,1,8,5]=>1010101
[7,3,4,1,5,2,8,6]=>1010101
[4,1,7,3,5,2,8,6]=>1010101
[2,1,7,4,5,3,8,6]=>1010101
[3,1,8,6,7,4,5,2]=>1010101
[4,1,8,6,7,3,5,2]=>1010101
[8,5,7,3,4,1,6,2]=>1010101
[8,5,6,2,7,3,4,1]=>1010101
[8,4,7,3,5,1,6,2]=>1010101
[5,1,8,4,7,3,6,2]=>1010101
[3,1,8,5,7,4,6,2]=>1010101
[2,1,8,5,7,4,6,3]=>1010101
[3,1,7,4,6,2,8,5]=>1010101
[4,1,7,3,6,2,8,5]=>1010101
[6,2,8,4,7,3,5,1]=>1010101
[7,3,6,2,5,1,8,4]=>1010101
[5,2,4,1,7,3,8,6]=>1010101
[6,2,4,1,7,3,8,5]=>1010101
[7,4,6,2,3,1,8,5]=>1010101
[6,2,3,1,7,4,8,5]=>1010101
[5,2,3,1,7,4,8,6]=>1010101
[4,2,3,1,7,5,8,6]=>1010101
[3,1,4,2,8,6,7,5]=>1010101
[6,2,3,1,8,5,7,4]=>1010101
[8,5,6,2,3,1,7,4]=>1010101
[7,3,8,5,6,2,4,1]=>1010101
[8,5,6,2,4,1,7,3]=>1010101
[5,2,4,1,8,6,7,3]=>1010101
[4,1,5,2,8,6,7,3]=>1010101
[3,1,6,2,8,5,7,4]=>1010101
[5,1,6,2,8,4,7,3]=>1010101
[8,4,6,2,5,1,7,3]=>1010101
[7,3,8,4,6,2,5,1]=>1010101
[6,2,7,3,8,4,5,1]=>1010101
[8,4,5,1,6,2,7,3]=>1010101
[4,1,8,5,6,2,7,3]=>1010101
[3,1,8,5,6,2,7,4]=>1010101
[2,1,8,5,6,3,7,4]=>1010101
[3,1,7,4,8,5,6,2]=>1010101
[7,3,6,2,8,4,5,1]=>1010101
[6,8,7,3,4,1,2,5]=>0110100
[5,4,8,7,2,6,3,1]=>1011011
[5,3,8,7,6,1,2,4]=>1011100
[8,3,4,6,5,1,2,7]=>1001100
[3,4,8,7,6,1,2,5]=>0011100
[3,5,8,7,6,1,2,4]=>0011100
[4,5,8,7,6,1,2,3]=>0011100
[4,5,8,7,1,6,3,2]=>0011011
[3,5,8,2,7,6,4,1]=>0010111
[3,5,8,1,7,6,4,2]=>0010111
[2,5,8,7,1,6,3,4]=>0011010
[2,4,8,7,1,6,3,5]=>0011010
[2,8,4,7,1,5,3,6]=>0101010
[8,2,4,6,1,5,3,7]=>1001010
[8,1,4,6,2,5,3,7]=>1001010
[1,4,8,7,2,6,3,5]=>0011010
[1,5,8,7,2,6,3,4]=>0011010
[1,5,8,2,7,6,4,3]=>0010111
[2,5,8,3,7,6,4,1]=>0010111
[1,4,2,8,7,6,5,3]=>0101111
[1,3,8,2,7,6,4,5]=>0010110
[1,8,3,2,7,5,4,6]=>0110110
[8,2,3,1,6,5,4,7]=>1010110
[2,3,8,1,7,6,4,5]=>0010110
[5,2,8,7,1,6,3,4]=>1011010
[5,2,8,1,7,6,4,3]=>1010111
[5,3,8,2,7,6,4,1]=>1010111
[6,8,3,2,7,5,4,1]=>0110111
[6,8,3,1,7,5,4,2]=>0110111
[6,8,1,2,7,5,4,3]=>0100111
[6,8,2,3,7,5,4,1]=>0100111
[5,2,8,3,7,6,4,1]=>1010111
[5,1,8,3,7,6,4,2]=>1010111
[5,1,8,7,2,6,3,4]=>1011010
[4,8,1,7,2,5,3,6]=>0101010
[8,4,1,6,2,5,3,7]=>1101010
[8,3,1,2,6,5,4,7]=>1100110
[3,1,2,8,7,6,5,4]=>1001111
[4,1,3,8,7,6,5,2]=>1001111
[3,1,4,8,7,6,5,2]=>1001111
[2,1,8,3,7,6,4,5]=>1010110
[2,8,1,3,7,5,4,6]=>0100110
[8,2,1,3,6,5,4,7]=>1100110
[1,8,2,3,7,5,4,6]=>0100110
[1,2,8,3,7,6,4,5]=>0010110
[1,4,3,6,8,2,5,7]=>0100100
[1,4,5,2,8,3,7,6]=>0010101
[1,4,2,6,5,8,3,7]=>0101010
[1,5,4,2,6,8,3,7]=>0110010
[3,1,6,5,8,2,4,7]=>1010100
[1,6,4,2,5,8,3,7]=>0110010
[1,5,2,6,4,8,3,7]=>0101010
[1,2,6,5,4,8,3,7]=>0011010
[1,2,5,4,7,3,8,6]=>0010101
[4,1,2,6,3,8,7,5]=>1001011
[7,1,5,4,2,8,3,6]=>1011010
[1,4,7,5,2,8,3,6]=>0011010
[7,1,3,5,2,8,4,6]=>1001010
[1,4,5,2,8,7,3,6]=>0010110
[1,6,4,2,8,3,7,5]=>0110101
[1,4,2,8,3,7,6,5]=>0101011
[1,2,8,6,5,3,7,4]=>0011101
[6,2,1,8,7,3,4,5]=>1101100
[7,6,2,1,8,3,4,5]=>1110100
[7,3,1,6,2,8,4,5]=>1101010
[1,7,6,4,2,8,3,5]=>0111010
[1,7,5,2,6,3,8,4]=>0110101
[1,6,2,7,5,3,8,4]=>0101101
[1,2,7,6,5,3,8,4]=>0011101
[1,2,6,5,3,8,7,4]=>0011011
[1,5,2,7,6,3,8,4]=>0101101
[1,6,5,2,7,3,8,4]=>0110101
[1,5,7,4,2,8,3,6]=>0011010
[3,1,8,6,2,4,7,5]=>1011001
[4,3,7,1,8,2,5,6]=>1010100
[8,3,1,6,2,4,7,5]=>1101001
[7,1,8,3,2,4,6,5]=>1011001
[1,4,2,8,7,3,6,5]=>0101101
[1,7,4,2,8,3,6,5]=>0110101
[8,1,5,4,2,7,3,6]=>1011010
[1,4,8,5,2,7,3,6]=>0011010
[8,5,3,1,7,2,4,6]=>1110100
[8,6,2,1,7,3,4,5]=>1110100
[1,8,6,4,2,7,3,5]=>0111010
[1,5,2,7,3,8,6,4]=>0101011
[1,2,8,5,3,7,6,4]=>0011011
[1,2,6,3,8,7,5,4]=>0010111
[1,2,7,6,3,8,5,4]=>0011011
[1,6,2,7,3,8,5,4]=>0101011
[1,7,4,2,8,6,3,5]=>0110110
[7,1,8,3,2,6,4,5]=>1011010
[7,2,1,8,6,3,4,5]=>1101100
[1,8,7,3,2,6,4,5]=>0111010
[1,4,2,8,7,6,3,5]=>0101110
[1,2,8,7,5,3,6,4]=>0011101
[5,1,8,7,6,2,4,3]=>1011101
[8,1,7,6,3,4,5,2]=>1011001
[5,7,8,6,2,4,1,3]=>0011010
[5,7,1,6,2,4,3,8]=>0101010
[6,4,1,5,2,7,3,8]=>1101010
[8,1,4,5,3,7,6,2]=>1001011
[6,1,4,5,3,8,7,2]=>1001011
[7,1,4,5,3,8,6,2]=>1001011
[7,1,4,5,3,6,8,2]=>1001001
[7,4,1,5,2,6,3,8]=>1101010
[6,3,5,7,2,1,4,8]=>1001100
[6,3,5,8,2,1,7,4]=>1001101
[6,3,5,7,2,1,8,4]=>1001101
[8,4,5,7,3,6,1,2]=>1001010
[6,4,5,8,3,7,2,1]=>1001011
[5,4,8,6,3,1,7,2]=>1011101
[5,4,1,8,2,3,7,6]=>1101001
[8,4,1,5,2,6,3,7]=>1101010
[6,3,5,8,2,1,4,7]=>1001100
[2,3,8,5,1,4,7,6]=>0011001
[2,3,8,6,1,5,7,4]=>0011001
[2,8,6,7,1,3,5,4]=>0101001
[8,3,5,7,2,1,6,4]=>1001101
[8,4,5,6,3,1,7,2]=>1001101
[7,3,5,6,2,8,1,4]=>1001010
[7,3,5,8,2,1,6,4]=>1001101
[7,3,5,6,2,1,4,8]=>1001100
[2,7,6,5,1,3,4,8]=>0111000
[2,7,6,8,1,3,5,4]=>0101001
[8,7,5,6,1,4,2,3]=>1101010
[2,7,1,3,6,5,8,4]=>0100101
[2,7,6,1,8,3,4,5]=>0110100
[2,7,6,1,4,3,5,8]=>0110100
[7,3,5,1,2,8,4,6]=>1010010
[2,3,8,6,4,1,7,5]=>0011101
[2,8,6,1,7,3,4,5]=>0110100
[2,3,8,1,6,4,7,5]=>0010101
[2,3,8,1,4,5,7,6]=>0010001
[5,2,6,1,4,8,7,3]=>1010011
[5,7,2,3,8,6,1,4]=>0100110
[5,6,2,3,1,8,7,4]=>0101011
[5,6,2,1,3,8,7,4]=>0110011
[5,1,6,4,2,8,7,3]=>1011011
[5,6,1,3,2,8,7,4]=>0101011
[5,6,3,1,2,8,7,4]=>0110011
[5,7,3,2,8,1,6,4]=>0110101
[6,7,3,8,2,1,5,4]=>0101101
[6,7,3,8,1,2,5,4]=>0101001
[5,7,3,1,8,2,6,4]=>0110101
[5,1,7,4,8,2,6,3]=>1010101
[1,5,7,4,8,3,6,2]=>0010101
[5,1,7,4,8,6,2,3]=>1010110
[5,7,3,1,8,6,2,4]=>0110110
[6,7,8,3,1,4,2,5]=>0011010
[6,7,1,8,3,5,2,4]=>0101010
[6,1,7,8,4,5,2,3]=>1001010
[1,6,7,8,4,5,3,2]=>0001011
[1,6,7,8,4,3,5,2]=>0001101
[6,1,7,8,4,2,5,3]=>1001101
[6,7,2,8,1,3,5,4]=>0101001
[6,7,2,8,3,5,1,4]=>0101010
[6,2,7,8,4,1,5,3]=>1001101
[6,2,7,8,1,4,5,3]=>1001001
[4,2,1,7,8,5,6,3]=>1100101
[4,1,2,7,8,6,5,3]=>1000111
[6,2,7,8,1,5,4,3]=>1001011
[6,2,7,8,5,1,4,3]=>1001101
[5,7,2,1,8,6,3,4]=>0110110
[1,6,7,8,3,5,4,2]=>0001011
[6,1,7,8,2,5,4,3]=>1001011
[6,7,8,2,4,1,3,5]=>0010100
[6,7,8,2,4,3,1,5]=>0010110
[6,7,1,8,5,2,3,4]=>0101100
[6,1,7,8,5,2,4,3]=>1001101
[1,6,7,8,5,3,4,2]=>0001101
[6,1,7,8,5,4,2,3]=>1001110
[6,7,1,8,5,3,2,4]=>0101110
[6,7,8,4,1,3,2,5]=>0011010
[3,7,4,8,5,6,1,2]=>0101010
[3,7,1,8,5,6,2,4]=>0101010
[2,7,3,8,5,6,1,4]=>0101010
[1,7,4,8,5,6,2,3]=>0101010
[2,7,3,8,4,6,1,5]=>0101010
[3,7,1,8,4,6,2,5]=>0101010
[1,5,2,8,6,7,3,4]=>0101010
[2,6,1,8,5,7,3,4]=>0101010
[1,6,2,8,5,7,3,4]=>0101010
[1,6,2,8,4,7,3,5]=>0101010
[2,6,1,8,4,7,3,5]=>0101010
[3,7,2,6,1,8,4,5]=>0101010
[4,8,1,6,2,7,3,5]=>0101010
[5,8,1,6,2,7,3,4]=>0101010
[5,8,2,6,1,7,3,4]=>0101010
[4,8,2,6,1,7,3,5]=>0101010
[1,7,3,6,2,8,4,5]=>0101010
[2,7,3,6,1,8,4,5]=>0101010
[8,6,1,4,3,2,5,7]=>1101100
[3,7,5,1,8,2,4,6]=>0110100
[4,1,5,2,8,7,3,6]=>1010110
[8,1,2,4,6,5,3,7]=>1000110
[8,2,6,5,1,3,4,7]=>1011000
[8,3,1,6,2,5,4,7]=>1101010
[8,1,2,6,4,5,3,7]=>1001010
[8,1,2,5,6,4,3,7]=>1000110
[1,7,5,4,2,8,3,6]=>0111010
[1,4,6,8,2,7,3,5]=>0001010
[1,4,7,6,2,8,3,5]=>0011010
[5,1,4,7,2,8,3,6]=>1001010
[3,7,5,1,2,8,4,6]=>0110010
[4,1,5,8,2,7,3,6]=>1001010
[1,4,6,2,8,7,3,5]=>0010110
[1,4,2,8,6,7,3,5]=>0101010
[3,1,2,6,4,8,7,5]=>1001011
[2,1,7,6,3,4,8,5]=>1011001
[3,1,2,7,4,6,8,5]=>1001001
[1,2,3,6,8,5,7,4]=>0000101
[5,1,4,2,7,8,3,6]=>1010010
[1,4,2,7,6,8,3,5]=>0101010
[1,4,2,6,8,7,3,5]=>0100110
[5,3,7,1,8,2,4,6]=>1010100
[1,7,4,3,2,5,8,6]=>0111001
[4,8,7,2,1,3,5,6]=>0111000
[1,8,7,3,4,2,5,6]=>0110100
[3,1,7,8,2,6,4,5]=>1001010
[1,4,2,7,8,3,6,5]=>0100101
[2,1,8,6,3,4,7,5]=>1011001
[1,4,2,6,8,3,7,5]=>0100101
[1,2,3,7,8,5,6,4]=>0000101
[1,2,3,7,5,8,6,4]=>0001011
[3,1,7,2,8,6,4,5]=>1010110
[1,2,3,8,7,5,6,4]=>0001101
[5,7,8,4,2,6,1,3]=>0011010
[6,7,8,4,2,5,1,3]=>0011010
[8,6,3,7,2,1,5,4]=>1101101
[6,7,8,3,2,1,5,4]=>0011101
[5,7,8,3,2,1,6,4]=>0011101
[2,7,8,4,3,5,6,1]=>0011001
[3,7,8,4,2,5,1,6]=>0011010
[7,6,3,8,2,1,4,5]=>1101100
[8,6,3,7,2,1,4,5]=>1101100
[5,6,3,8,2,1,4,7]=>0101100
[3,6,4,8,2,5,1,7]=>0101010
[2,6,4,8,3,5,7,1]=>0101001
[2,6,4,7,3,5,8,1]=>0101001
[4,6,3,7,2,1,5,8]=>0101100
[5,6,3,7,2,1,4,8]=>0101100
[8,4,3,2,1,6,5,7]=>1111010
[6,4,3,2,1,7,5,8]=>1111010
[4,5,3,2,7,1,6,8]=>0110100
[7,4,3,2,1,8,5,6]=>1111010
[8,4,3,2,1,7,5,6]=>1111010
[7,4,3,2,1,8,6,5]=>1111011
[5,6,3,8,2,1,7,4]=>0101101
[7,5,3,2,8,1,6,4]=>1110101
[8,5,4,2,7,6,1,3]=>1110110
[7,5,4,2,8,6,1,3]=>1110110
[6,5,4,2,7,8,1,3]=>1110010
[8,5,4,2,6,7,1,3]=>1110010
[5,6,3,7,2,1,8,4]=>0101101
[4,6,3,7,2,1,8,5]=>0101101
[3,6,4,7,2,8,1,5]=>0101010
[2,6,4,7,3,8,5,1]=>0101011
[3,5,4,2,7,8,1,6]=>0110010
[7,4,3,2,1,6,8,5]=>1111001
[8,4,3,2,1,6,7,5]=>1111001
[8,4,3,2,1,5,7,6]=>1111001
[7,4,3,2,1,5,8,6]=>1111001
[6,4,3,2,1,5,8,7]=>1111001
[3,5,4,2,6,8,1,7]=>0110010
[3,2,6,4,8,5,1,7]=>1010110
[4,2,5,8,3,1,6,7]=>1001100
[4,3,2,7,5,1,6,8]=>1101100
[4,3,6,2,5,1,7,8]=>1010100
[4,5,1,7,3,2,6,8]=>0101100
[5,2,1,4,3,7,8,6]=>1101001
[5,3,6,4,1,2,7,8]=>1011000
[4,3,6,1,7,2,5,8]=>1010100
[6,2,4,1,3,7,8,5]=>1010001
[3,6,4,1,2,7,5,8]=>0110010
[4,6,3,1,7,2,5,8]=>0110100
[4,5,2,7,3,1,6,8]=>0101100
[4,6,2,1,7,3,5,8]=>0110100
[3,2,6,1,4,7,5,8]=>1010010
[7,3,1,4,6,8,2,5]=>1100010
[7,4,1,5,6,2,3,8]=>1100100
[7,3,1,5,2,6,4,8]=>1101010
[6,3,5,1,2,7,4,8]=>1010010
[3,6,5,1,2,7,4,8]=>0110010
[2,4,1,5,3,8,7,6]=>0101011
[3,4,5,1,2,8,7,6]=>0010011
[1,8,4,5,3,2,7,6]=>0101101
[2,4,8,5,3,1,7,6]=>0011101
[3,4,5,2,8,1,7,6]=>0010101
[3,4,6,2,1,7,8,5]=>0011001
[3,4,6,2,1,7,5,8]=>0011010
[3,5,6,2,7,1,8,4]=>0010101
[3,4,6,2,8,7,1,5]=>0010110
[3,4,6,8,2,7,1,5]=>0001010
[2,4,8,6,3,7,1,5]=>0011010
[1,8,4,6,3,7,2,5]=>0101010
[1,8,4,6,3,7,5,2]=>0101011
[3,4,6,8,2,7,5,1]=>0001011
[3,4,6,2,8,7,5,1]=>0010111
[3,5,6,2,7,8,4,1]=>0010011
[3,5,6,2,7,4,1,8]=>0010110
[4,5,6,7,2,8,3,1]=>0001011
[2,5,8,6,7,3,4,1]=>0010101
[1,8,5,6,7,3,2,4]=>0100110
[4,5,6,7,2,1,8,3]=>0001101
[3,4,6,1,8,7,2,5]=>0010110
[2,4,1,6,8,7,3,5]=>0100110
[2,5,1,6,7,8,4,3]=>0100011
[2,5,1,6,7,4,3,8]=>0100110
[3,5,6,1,7,4,2,8]=>0010110
[3,5,6,1,7,4,8,2]=>0010101
[3,4,6,1,8,7,5,2]=>0010111
[3,4,6,8,1,7,5,2]=>0001011
[2,4,8,6,1,7,5,3]=>0011011
[1,8,4,6,2,7,5,3]=>0101011
[1,8,5,6,7,2,4,3]=>0100101
[2,5,8,6,7,1,4,3]=>0010101
[4,5,6,7,1,3,8,2]=>0001001
[3,5,6,8,7,4,1,2]=>0001110
[2,5,8,6,7,4,1,3]=>0010110
[1,8,5,6,7,4,2,3]=>0100110
[1,8,5,6,7,4,3,2]=>0100111
[2,5,8,6,7,4,3,1]=>0010111
[8,2,4,3,7,1,6,5]=>1010101
[5,8,2,4,3,7,1,6]=>0101010
[4,2,5,6,1,8,3,7]=>1001010
[4,2,5,6,1,7,3,8]=>1001010
[6,1,5,7,3,2,4,8]=>1001100
[6,1,5,8,3,2,4,7]=>1001100
[3,8,2,4,7,1,5,6]=>0100100
[3,6,8,2,4,7,1,5]=>0010010
[7,3,2,4,6,1,5,8]=>1100100
[3,2,5,1,8,4,6,7]=>1010100
[7,8,3,2,4,6,1,5]=>0110010
[6,1,5,7,8,3,2,4]=>1000110
[4,2,5,6,1,7,8,3]=>1001001
[5,7,6,1,8,3,4,2]=>0110101
[5,8,6,1,7,3,4,2]=>0110101
[6,1,5,8,7,3,2,4]=>1001110
[8,7,3,2,4,6,1,5]=>1110010
[3,2,5,1,8,7,4,6]=>1010110
[3,2,5,1,6,4,7,8]=>1010100
[3,2,4,1,8,7,5,6]=>1010110
[3,2,5,1,6,8,7,4]=>1010011
[3,8,6,5,1,7,4,2]=>0111011
[3,7,6,5,1,8,4,2]=>0111011
[6,5,1,7,8,4,2,3]=>1100110
[3,2,5,1,6,7,8,4]=>1010001
[3,2,4,1,7,5,6,8]=>1010100
[3,2,4,1,6,8,5,7]=>1010010
[8,3,2,4,7,6,1,5]=>1100110
[3,2,5,1,8,4,7,6]=>1010101
[3,2,5,1,6,7,4,8]=>1010010
[6,5,1,7,4,2,3,8]=>1101100
[6,5,1,8,4,2,3,7]=>1101100
[8,4,2,3,7,5,1,6]=>1100110
[5,2,6,1,8,3,7,4]=>1010101
[5,2,6,1,8,4,7,3]=>1010101
[7,4,2,3,8,5,1,6]=>1100110
[8,5,1,6,4,2,3,7]=>1101100
[3,2,5,1,7,6,4,8]=>1010110
[3,2,5,1,8,6,4,7]=>1010110
[8,6,1,5,7,3,2,4]=>1100110
[8,5,6,1,7,3,4,2]=>1010101
[3,6,8,5,1,7,4,2]=>0011011
[8,5,1,6,7,4,2,3]=>1100110
[3,2,5,1,8,6,7,4]=>1010101
[3,2,4,1,5,8,6,7]=>1010010
[3,2,5,1,7,8,6,4]=>1010011
[8,7,5,1,6,4,2,3]=>1110110
[3,2,5,1,8,7,6,4]=>1010111
[4,6,3,7,1,8,5,2]=>0101011
[4,6,3,7,5,1,8,2]=>0101101
[4,2,6,1,7,5,3,8]=>1010110
[2,5,7,4,1,6,3,8]=>0011010
[2,5,7,4,1,6,8,3]=>0011001
[5,4,7,8,3,1,6,2]=>1001101
[4,3,7,5,1,8,6,2]=>1011011
[6,4,3,8,5,1,7,2]=>1101101
[5,8,4,3,6,1,7,2]=>0110101
[5,4,8,3,6,1,7,2]=>1010101
[2,5,4,6,1,7,3,8]=>0101010
[4,6,2,1,8,5,7,3]=>0110101
[2,4,1,7,5,8,6,3]=>0101011
[2,4,1,7,5,3,8,6]=>0101101
[2,6,4,1,8,5,3,7]=>0110110
[5,4,8,2,1,6,3,7]=>1011010
[2,5,8,4,1,6,3,7]=>0011010
[3,2,5,6,1,8,4,7]=>1001010
[4,8,3,2,6,1,5,7]=>0110100
[3,5,2,8,1,6,4,7]=>0101010
[3,2,1,6,8,5,4,7]=>1100110
[3,2,7,1,5,4,8,6]=>1010101
[3,2,7,1,5,8,6,4]=>1010011
[3,8,2,5,1,6,7,4]=>0101001
[4,8,3,2,6,7,1,5]=>0110010
[4,3,8,2,6,7,1,5]=>1010010
[4,3,2,6,7,8,1,5]=>1100010
[4,3,2,6,7,1,5,8]=>1100100
[4,3,7,8,2,6,1,5]=>1001010
[2,5,7,4,8,1,6,3]=>0010101
[3,2,5,7,1,6,8,4]=>1001001
[3,2,5,7,1,6,4,8]=>1001010
[6,3,2,7,1,5,4,8]=>1101010
[6,3,2,7,1,5,8,4]=>1101001
[6,3,2,7,8,1,5,4]=>1100101
[6,5,2,1,7,8,4,3]=>1110011
[6,2,1,8,5,3,7,4]=>1101101
[6,3,2,7,1,4,8,5]=>1101001
[6,3,2,1,4,7,8,5]=>1110001
[6,3,2,1,4,7,5,8]=>1110010
[3,5,2,1,7,8,4,6]=>0110010
[4,6,2,1,8,3,7,5]=>0110101
[3,2,7,1,4,8,6,5]=>1010011
[3,5,8,2,1,7,4,6]=>0011010
[4,8,3,7,2,1,5,6]=>0101100
[4,3,7,2,8,1,5,6]=>1010100
[4,3,7,2,1,5,6,8]=>1011000
[4,8,3,2,7,1,5,6]=>0110100
[6,3,2,8,1,4,7,5]=>1101001
[3,2,1,4,7,5,8,6]=>1100101
[5,3,2,1,8,4,6,7]=>1110100
[4,8,3,2,1,5,6,7]=>0111000
[4,3,8,2,1,5,6,7]=>1011000
[6,2,3,1,5,4,8,7]=>1010101
[8,4,5,2,3,1,7,6]=>1010101
[8,2,5,3,4,1,7,6]=>1010101
[6,2,5,3,4,1,8,7]=>1010101
[6,4,5,1,3,2,8,7]=>1010101
[6,1,5,3,4,2,8,7]=>1010101
[8,3,7,2,4,1,6,5]=>1010101
[8,3,5,1,4,2,7,6]=>1010101
[8,4,5,1,3,2,7,6]=>1010101
[2,1,8,4,5,3,7,6]=>1010101
[8,1,7,3,4,2,6,5]=>1010101
[8,2,7,1,4,3,6,5]=>1010101
[8,2,7,3,4,1,6,5]=>1010101
[8,4,7,2,3,1,6,5]=>1010101
[8,2,3,1,5,4,7,6]=>1010101
[4,2,3,1,8,5,7,6]=>1010101
[8,2,3,1,7,5,6,4]=>1010101
[8,6,7,1,3,2,5,4]=>1010101
[8,1,3,2,7,5,6,4]=>1010101
[2,1,8,5,7,3,6,4]=>1010101
[4,5,8,6,3,2,7,1]=>0011101
[1,5,8,7,3,6,2,4]=>0011010
[1,7,2,8,4,6,5,3]=>0101011
[6,7,2,8,4,1,5,3]=>0101101
[3,6,2,8,4,5,7,1]=>0101001
[2,6,1,8,4,5,7,3]=>0101001
[2,8,4,6,1,5,7,3]=>0101001
[6,3,1,8,4,5,7,2]=>1101001
[2,3,6,8,4,5,7,1]=>0001001
[6,3,7,8,4,1,5,2]=>1001101
[1,3,7,8,4,6,5,2]=>0001011
[3,6,7,8,4,2,5,1]=>0001101
[7,6,1,8,4,2,5,3]=>1101101
[2,8,3,7,1,6,5,4]=>0101011
[5,2,8,7,3,6,1,4]=>1011010
[7,2,1,8,4,6,5,3]=>1101011
[3,2,7,8,4,6,5,1]=>1001011
[5,2,7,8,1,4,6,3]=>1001001
[1,2,7,8,5,4,6,3]=>0001101
[7,2,5,8,3,4,6,1]=>1001001
[6,2,8,5,4,3,1,7]=>1011110
[2,8,3,5,4,1,6,7]=>0101100
[2,8,4,5,3,1,6,7]=>0101100
[7,3,5,8,2,4,6,1]=>1001001
[4,3,1,2,8,5,6,7]=>1100100
[2,7,6,8,4,3,5,1]=>0101101
[1,7,5,8,3,4,6,2]=>0101001
[4,6,8,5,1,3,2,7]=>0011010
[2,4,8,3,6,5,1,7]=>0010110
[4,1,8,3,5,6,2,7]=>1010010
[5,6,8,4,1,3,2,7]=>0011010
[4,6,8,1,5,3,2,7]=>0010110
[1,6,8,4,5,3,2,7]=>0010110
[1,7,3,8,5,4,6,2]=>0101101
[3,7,1,8,5,4,6,2]=>0101101
[2,7,3,8,4,6,5,1]=>0101011
[2,8,7,4,1,6,5,3]=>0111011
[2,8,5,4,3,1,6,7]=>0111100
[1,4,3,2,8,5,6,7]=>0110100
[7,3,2,8,5,4,6,1]=>1101101
[6,4,8,2,5,3,1,7]=>1010110
[2,8,4,3,5,1,6,7]=>0110100
[6,2,8,4,5,3,1,7]=>1010110
[7,2,3,8,5,4,6,1]=>1001101
[4,2,3,1,8,5,6,7]=>1010100
[5,1,3,2,4,8,6,7]=>1010010
[2,8,1,5,3,4,7,6]=>0101001
[1,4,2,8,5,3,6,7]=>0101100
[3,5,1,4,8,2,6,7]=>0100100
[1,5,2,8,4,3,6,7]=>0101100
[1,2,5,4,3,8,6,7]=>0011010
[1,2,4,8,5,3,7,6]=>0001101
[1,5,2,7,8,4,3,6]=>0100110
[5,1,2,7,4,8,3,6]=>1001010
[8,3,5,1,4,7,2,6]=>1010010
[1,2,8,5,7,4,3,6]=>0010110
[1,2,4,8,7,5,3,6]=>0001110
[2,8,1,4,3,7,6,5]=>0101011
[7,6,1,4,2,8,3,5]=>1101010
[7,1,6,2,8,4,3,5]=>1010110
[1,4,2,7,8,5,3,6]=>0100110
[6,1,2,8,4,3,7,5]=>1001101
[6,4,1,2,8,3,7,5]=>1100101
[7,6,1,3,2,4,8,5]=>1101001
[6,7,1,3,2,4,8,5]=>0101001
[1,2,7,3,5,8,4,6]=>0010010
[5,8,1,3,7,2,4,6]=>0100100
[1,2,5,8,7,3,4,6]=>0001100
[8,6,1,3,2,4,7,5]=>1101001
[4,2,8,1,7,3,6,5]=>1010101
[7,1,2,8,4,3,6,5]=>1001101
[1,2,8,4,7,5,3,6]=>0010110
[1,2,8,7,4,5,3,6]=>0011010
[2,8,1,7,5,3,4,6]=>0101100
[8,3,7,1,5,2,4,6]=>1010100
[8,6,1,4,2,7,3,5]=>1101010
[7,1,2,8,6,4,3,5]=>1001110
[3,7,4,8,1,6,2,5]=>0101010
[3,4,8,7,1,6,2,5]=>0011010
[4,2,8,1,7,6,3,5]=>1010110
[2,8,1,7,6,4,3,5]=>0101110
[7,8,3,4,1,5,2,6]=>0101010
[6,8,3,4,1,7,2,5]=>0101010
[5,7,3,4,1,8,2,6]=>0101010
[5,8,3,4,1,7,2,6]=>0101010
[4,7,3,5,1,6,2,8]=>0101010
[4,8,3,5,1,6,2,7]=>0101010
[4,8,3,5,1,7,2,6]=>0101010
[4,7,3,5,1,8,2,6]=>0101010
[5,6,2,3,1,7,4,8]=>0101010
[5,6,2,4,1,8,3,7]=>0101010
[5,6,2,4,1,7,3,8]=>0101010
[4,6,2,5,1,7,3,8]=>0101010
[4,6,2,5,1,8,3,7]=>0101010
[4,5,1,8,3,7,2,6]=>0101010
[4,6,2,7,3,8,1,5]=>0101010
[5,6,2,7,3,8,1,4]=>0101010
[5,6,2,8,4,7,1,3]=>0101010
[5,6,2,8,3,7,1,4]=>0101010
[4,6,2,8,3,7,1,5]=>0101010
[4,5,1,7,3,6,2,8]=>0101010
[4,5,1,8,3,6,2,7]=>0101010
[6,5,3,2,1,4,8,7]=>1111001
[8,7,3,5,2,4,1,6]=>1101010
[6,8,2,4,5,7,3,1]=>0100011
[3,6,1,4,5,2,8,7]=>0100101
[8,3,7,4,5,2,1,6]=>1010110
[6,3,8,4,5,7,2,1]=>1010011
[8,1,7,4,3,6,2,5]=>1011010
[8,7,3,5,1,4,2,6]=>1101010
[2,1,6,8,5,7,4,3]=>1001011
[6,8,3,5,1,7,4,2]=>0101011
[2,5,8,4,7,6,3,1]=>0010111
[4,3,8,1,5,6,7,2]=>1010001
[4,8,3,6,1,2,7,5]=>0101001
[3,8,7,4,1,6,2,5]=>0111010
[3,8,1,2,5,6,7,4]=>0100001
[2,8,7,4,5,1,3,6]=>0110100
[8,7,2,4,1,6,3,5]=>1101010
[5,8,3,6,2,4,7,1]=>0101001
[8,6,3,2,1,4,7,5]=>1111001
[8,7,3,5,2,1,4,6]=>1101100
[5,8,3,6,2,1,7,4]=>0101101
[6,1,8,4,5,7,2,3]=>1010010
[6,8,3,5,1,7,2,4]=>0101010
[5,8,3,6,1,2,7,4]=>0101001
[5,8,1,4,7,6,2,3]=>0100110
[4,5,3,8,6,1,7,2]=>0101101
[4,5,7,6,2,3,8,1]=>0011001
[3,5,7,2,6,4,8,1]=>0010101
[2,5,7,3,6,4,8,1]=>0010101
[8,4,3,7,6,1,5,2]=>1101101
[6,7,2,3,5,4,8,1]=>0100101
[5,2,7,3,6,4,8,1]=>1010101
[8,3,4,7,6,1,5,2]=>1001101
[8,2,4,7,1,6,5,3]=>1001011
[3,1,4,7,6,8,5,2]=>1001011
[5,1,7,3,6,8,4,2]=>1010011
[6,7,1,3,5,8,4,2]=>0100011
[4,8,3,7,6,1,5,2]=>0101101
[2,8,4,7,1,6,5,3]=>0101011
[8,1,4,7,2,6,5,3]=>1001011
[8,1,3,2,7,6,5,4]=>1010111
[2,8,3,1,7,6,5,4]=>0110111
[6,7,1,2,8,5,4,3]=>0100111
[8,2,3,1,7,6,5,4]=>1010111
[1,4,2,7,8,6,5,3]=>0100111
[8,4,2,7,1,6,5,3]=>1101011
[8,5,7,2,1,6,4,3]=>1011011
[1,5,7,2,8,6,4,3]=>0010111
[2,5,7,1,8,6,4,3]=>0010111
[3,5,7,1,6,8,4,2]=>0010011
[6,7,4,5,8,1,3,2]=>0100101
[2,5,7,8,1,6,4,3]=>0001011
[1,5,7,8,2,6,4,3]=>0001011
[8,5,7,1,2,6,4,3]=>1010011
[8,4,1,7,2,6,5,3]=>1101011
[6,7,2,8,1,5,4,3]=>0101011
[5,2,7,8,1,6,4,3]=>1001011
[4,2,8,7,1,6,5,3]=>1011011
[1,3,8,2,7,6,5,4]=>0010111
[8,3,1,2,7,6,5,4]=>1100111
[8,2,1,3,7,6,5,4]=>1100111
[2,1,8,3,7,6,5,4]=>1010111
[5,1,7,8,2,6,4,3]=>1001011
[6,7,1,8,2,5,4,3]=>0101011
[4,8,1,7,2,6,5,3]=>0101011
[3,8,1,2,7,6,5,4]=>0100111
[1,8,2,3,7,6,5,4]=>0100111
[3,7,1,5,8,2,6,4]=>0100101
[2,7,1,5,8,3,6,4]=>0100101
[2,6,5,1,8,3,7,4]=>0110101
[5,6,4,1,8,7,2,3]=>0110110
[8,1,4,5,7,6,2,3]=>1000110
[6,4,5,1,8,7,2,3]=>1010110
[5,4,6,1,8,7,2,3]=>1010110
[3,5,6,1,8,2,7,4]=>0010101
[2,5,6,1,8,3,7,4]=>0010101
[2,4,6,1,3,8,7,5]=>0010011
[3,4,6,1,2,8,7,5]=>0010011
[5,3,6,1,8,2,7,4]=>1010101
[7,3,1,5,8,2,6,4]=>1100101
[8,1,3,5,7,2,6,4]=>1000101
[8,1,2,5,7,3,6,4]=>1000101
[7,2,1,5,8,3,6,4]=>1100101
[6,2,5,1,8,3,7,4]=>1010101
[4,2,6,1,3,8,7,5]=>1010011
[4,2,5,3,1,8,7,6]=>1011011
[6,2,4,1,3,8,7,5]=>1010011
[7,2,1,4,3,8,6,5]=>1101011
[8,1,2,4,3,7,6,5]=>1001011
[8,1,3,4,2,7,6,5]=>1001011
[7,3,1,4,2,8,6,5]=>1101011
[4,6,3,1,2,8,7,5]=>0110011
[2,6,4,1,3,8,7,5]=>0110011
[2,7,1,4,3,8,6,5]=>0101011
[8,1,6,7,2,3,5,4]=>1001001
[4,7,1,2,3,8,6,5]=>0100011
[3,7,1,2,4,8,6,5]=>0100011
[2,6,3,1,4,8,7,5]=>0110011
[3,6,2,1,4,8,7,5]=>0110011
[5,6,2,1,8,3,7,4]=>0110101
[6,5,2,1,8,3,7,4]=>1110101
[8,1,4,2,3,7,6,5]=>1010011
[7,4,1,2,3,8,6,5]=>1100011
[5,4,2,3,1,8,7,6]=>1101011
[3,5,2,4,1,8,7,6]=>0101011
[7,3,1,2,4,8,6,5]=>1100011
[8,1,3,2,4,7,6,5]=>1010011
[7,2,1,3,4,8,6,5]=>1100011
[2,4,3,6,1,5,8,7]=>0101001
[2,4,3,6,5,8,1,7]=>0101010
[2,4,6,3,5,8,7,1]=>0010011
[2,4,6,3,5,1,8,7]=>0010101
[2,4,6,3,1,5,8,7]=>0011001
[2,4,1,6,5,3,8,7]=>0101101
[2,4,6,1,5,3,8,7]=>0010101
[4,2,6,5,3,1,8,7]=>1011101
[4,2,6,5,1,3,8,7]=>1011001
[4,2,6,5,8,1,7,3]=>1010101
[4,2,6,5,8,1,3,7]=>1010100
[4,2,6,5,8,3,1,7]=>1010110
[2,4,1,6,5,8,3,7]=>0101010
[2,1,4,6,5,8,3,7]=>1001010
[2,4,1,6,5,8,7,3]=>0101011
[2,4,6,1,5,8,7,3]=>0010011
[4,2,6,5,3,8,7,1]=>1011011
[2,6,4,3,8,7,5,1]=>0110111
[4,2,6,8,5,3,7,1]=>1001101
[2,4,6,8,1,5,7,3]=>0001001
[2,4,1,6,8,5,7,3]=>0100101
[2,1,4,6,8,5,3,7]=>1000110
[2,4,6,1,8,5,3,7]=>0010110
[2,4,6,8,1,5,3,7]=>0001010
[2,4,6,8,3,5,7,1]=>0001001
[2,4,6,8,3,1,5,7]=>0001100
[2,4,6,3,8,5,7,1]=>0010101
[2,4,3,6,8,5,7,1]=>0100101
[2,4,3,6,8,5,1,7]=>0100110
[2,4,3,6,8,1,5,7]=>0100100
[2,4,3,6,1,8,5,7]=>0101010
[2,4,3,1,6,8,5,7]=>0110010
[2,4,1,3,6,8,7,5]=>0100011
[2,4,3,6,8,1,7,5]=>0100101
[4,6,5,2,8,7,1,3]=>0110110
[4,6,2,5,8,7,1,3]=>0100110
[4,6,2,5,8,7,3,1]=>0100111
[2,4,6,3,1,8,7,5]=>0011011
[2,4,1,6,3,8,7,5]=>0101011
[2,1,4,6,3,8,7,5]=>1001011
[2,4,1,6,8,3,7,5]=>0100101
[2,4,6,8,1,3,7,5]=>0001001
[4,6,2,8,5,7,3,1]=>0101011
[4,6,2,8,5,7,1,3]=>0101010
[6,2,4,8,7,1,3,5]=>1001100
[2,6,4,8,1,7,5,3]=>0101011
[2,6,4,1,8,7,5,3]=>0110111
[2,1,6,4,8,7,3,5]=>1010110
[2,6,4,1,8,7,3,5]=>0110110
[2,6,4,8,1,7,3,5]=>0101010
[6,2,4,8,7,3,5,1]=>1001101
[6,2,4,8,7,3,1,5]=>1001110
[1,3,7,4,5,8,2,6]=>0010010
[1,7,6,3,4,8,2,5]=>0110010
[8,1,6,3,7,2,4,5]=>1010100
[1,2,7,4,8,3,5,6]=>0010100
[6,1,7,3,4,8,2,5]=>1010010
[2,1,7,4,5,8,3,6]=>1010010
[5,1,4,7,3,8,2,6]=>1001010
[4,3,1,7,5,8,2,6]=>1101010
[2,8,6,3,7,1,4,5]=>0110100
[6,8,1,3,7,2,4,5]=>0100100
[5,8,2,1,7,3,4,6]=>0110100
[5,7,2,1,8,3,4,6]=>0110100
[6,7,1,3,8,2,4,5]=>0100100
[8,5,1,3,7,2,4,6]=>1100100
[1,5,3,2,8,4,6,7]=>0110100
[2,6,4,8,7,1,3,5]=>0101100
[1,6,4,8,7,2,3,5]=>0101100
[4,3,2,8,7,1,5,6]=>1101100
[5,2,4,8,7,1,3,6]=>1001100
[6,2,8,3,7,1,4,5]=>1010100
[5,1,4,8,7,2,3,6]=>1001100
[3,7,2,1,5,4,8,6]=>0110101
[3,8,2,1,5,4,7,6]=>0110101
[8,3,2,1,5,4,6,7]=>1110100
[8,3,2,1,6,4,5,7]=>1110100
[8,4,2,5,1,6,3,7]=>1101010
[8,3,2,1,4,6,5,7]=>1110010
[3,8,2,1,4,5,7,6]=>0110001
[3,2,7,1,4,6,8,5]=>1010001
[3,2,8,1,4,6,7,5]=>1010001
[3,8,2,1,4,7,5,6]=>0110010
[3,8,2,1,5,7,4,6]=>0110010
[4,8,2,5,1,7,3,6]=>0101010
[4,7,2,5,1,8,3,6]=>0101010
[3,7,2,1,5,8,4,6]=>0110010
[3,7,2,1,4,8,5,6]=>0110010
[3,2,1,7,5,8,6,4]=>1101011
[4,2,7,6,1,8,3,5]=>1011010
[4,3,7,6,8,1,2,5]=>1010100
[4,3,8,6,7,1,2,5]=>1010100
[3,8,2,1,7,4,5,6]=>0110100
[3,2,8,1,6,4,7,5]=>1010101
[3,2,7,1,6,4,8,5]=>1010101
[4,2,7,6,1,3,8,5]=>1011001
[4,2,8,6,1,3,7,5]=>1011001
[5,7,8,3,4,1,2,6]=>0010100
[4,2,6,8,1,3,7,5]=>1001001
[4,2,6,7,1,3,8,5]=>1001001
[3,2,6,1,8,4,7,5]=>1010101
[3,7,2,1,8,5,4,6]=>0110110
[4,7,3,8,5,1,2,6]=>0101100
[4,3,7,8,6,1,2,5]=>1001100
[3,2,7,1,8,6,4,5]=>1010110
[3,2,1,6,8,5,7,4]=>1100101
[3,2,6,1,8,7,4,5]=>1010110
[4,2,6,8,1,7,3,5]=>1001010
[4,3,6,8,7,1,2,5]=>1001100
[4,2,6,7,1,8,3,5]=>1001010
[3,2,6,1,7,8,4,5]=>1010010
[5,3,6,4,8,7,1,2]=>1010110
[1,4,6,2,7,8,5,3]=>0010011
[3,1,8,5,4,2,6,7]=>1011100
[1,2,7,5,4,8,6,3]=>0011011
[6,3,7,5,4,8,1,2]=>1011010
[1,6,2,5,4,8,7,3]=>0101011
[1,8,2,5,7,3,6,4]=>0100101
[6,2,1,5,4,8,7,3]=>1101011
[4,1,6,2,8,7,5,3]=>1010111
[7,8,3,1,4,2,6,5]=>0110101
[4,3,6,1,8,2,7,5]=>1010101
[7,5,1,6,4,3,2,8]=>1101110
[6,1,5,7,4,3,2,8]=>1001110
[1,5,8,6,4,3,2,7]=>0011110
[7,8,5,1,6,3,2,4]=>0110110
[2,6,1,5,7,3,8,4]=>0100101
[1,6,8,7,4,3,2,5]=>0011110
[6,8,1,7,4,3,2,5]=>0101110
[5,6,1,7,4,3,2,8]=>0101110
[5,1,7,6,4,3,2,8]=>1011110
[6,1,7,8,4,3,2,5]=>1001110
[7,1,8,6,4,3,2,5]=>1011110
[7,2,1,5,4,6,8,3]=>1101001
[1,2,8,5,6,3,7,4]=>0010101
[6,1,2,5,7,3,8,4]=>1000101
[4,3,6,1,5,7,2,8]=>1010010
[1,3,6,8,5,7,2,4]=>0001010
[1,3,6,4,8,7,2,5]=>0010110
[4,1,6,7,3,8,2,5]=>1001010
[5,4,6,1,3,7,2,8]=>1010010
[6,4,1,5,2,3,7,8]=>1101000
[4,1,7,5,2,3,8,6]=>1011001
[2,8,3,5,4,1,7,6]=>0101101
[7,8,1,4,6,3,2,5]=>0100110
[5,1,8,7,4,3,2,6]=>1011110
[6,5,1,8,4,3,2,7]=>1101110
[6,5,7,1,4,3,2,8]=>1010110
[7,5,8,1,4,3,2,6]=>1010110
[1,5,7,8,4,3,2,6]=>0001110
[2,4,7,5,1,3,8,6]=>0011001
[7,8,4,6,1,3,2,5]=>0101010
[1,6,5,8,4,3,2,7]=>0101110
[6,8,5,1,4,3,2,7]=>0110110
[3,6,2,5,4,1,7,8]=>0101100
[4,3,6,2,8,1,5,7]=>1010100
[6,1,2,5,4,7,8,3]=>1001001
[6,2,4,5,1,3,7,8]=>1001000
[4,2,8,5,1,3,7,6]=>1011001
[4,3,6,8,1,7,2,5]=>1001010
[5,3,6,4,1,7,2,8]=>1011010
[1,6,7,4,8,3,5,2]=>0010101
[1,4,6,3,7,5,8,2]=>0010101
[4,6,7,2,5,8,1,3]=>0010010
[2,4,6,1,7,5,3,8]=>0010110
[2,7,5,4,1,6,3,8]=>0111010
[1,7,5,4,3,8,6,2]=>0111011
[1,5,8,4,3,6,7,2]=>0011001
[5,4,6,2,7,8,1,3]=>1010010
[2,5,4,1,6,7,3,8]=>0110010
[5,6,3,2,7,1,4,8]=>0110100
[5,6,3,2,7,1,8,4]=>0110101
[8,5,6,3,2,7,1,4]=>1011010
[5,4,6,2,8,1,7,3]=>1010101
[2,4,1,7,8,5,3,6]=>0100110
[5,6,3,2,1,8,4,7]=>0111010
[3,5,2,1,6,4,7,8]=>0110100
[6,8,4,3,2,1,5,7]=>0111100
[5,3,8,2,1,6,4,7]=>1011010
[7,3,2,8,5,1,6,4]=>1101101
[8,4,6,3,2,1,7,5]=>1011101
[5,4,7,2,1,8,6,3]=>1011011
[5,7,3,2,1,6,8,4]=>0111001
[6,3,7,2,5,1,8,4]=>1010101
[6,7,8,3,5,2,1,4]=>0010110
[6,2,5,7,8,4,1,3]=>1000110
[2,1,5,7,8,6,3,4]=>1000110
[3,6,7,2,8,1,4,5]=>0010100
[3,2,6,1,7,4,5,8]=>1010100
[2,5,8,4,1,3,7,6]=>0011001
[2,4,1,7,8,3,6,5]=>0100101
[3,6,8,2,1,7,4,5]=>0011010
[5,3,8,2,1,4,7,6]=>1011001
[4,8,7,3,2,1,5,6]=>0111100
[4,7,3,2,1,5,6,8]=>0111000
[8,4,7,3,2,1,5,6]=>1011100
[8,3,5,2,1,4,7,6]=>1011001
[3,5,2,1,4,6,8,7]=>0110001
[2,7,6,5,1,8,3,4]=>0111010
[2,7,6,5,1,8,4,3]=>0111011
[2,3,6,5,1,4,8,7]=>0011001
[2,3,6,4,1,5,8,7]=>0011001
[2,7,6,1,4,8,5,3]=>0110011
[7,3,5,1,8,4,2,6]=>1010110
[2,7,6,1,5,8,4,3]=>0110011
[2,7,6,4,1,8,5,3]=>0111011
[2,7,6,4,1,8,3,5]=>0111010
[7,3,5,1,8,6,2,4]=>1010110
[2,3,4,8,7,6,1,5]=>0001110
[2,3,4,8,5,7,1,6]=>0001010
[7,3,5,4,8,1,2,6]=>1010100
[6,4,3,5,8,7,2,1]=>1100111
[2,1,4,5,8,7,3,6]=>1000110
[6,4,3,5,8,7,1,2]=>1100110
[2,3,4,8,7,5,1,6]=>0001110
[2,7,6,5,4,8,1,3]=>0111010
[7,3,5,6,8,1,2,4]=>1000100
[6,4,1,5,8,7,2,3]=>1100110
[6,4,1,5,8,7,3,2]=>1100111
[6,4,1,5,8,3,7,2]=>1100101
[5,7,1,6,3,8,2,4]=>0101010
[6,4,1,5,8,3,2,7]=>1100110
[6,3,5,7,8,2,1,4]=>1000110
[5,7,3,6,1,8,4,2]=>0101011
[7,3,5,4,8,6,2,1]=>1010111
[2,3,4,8,5,6,1,7]=>0001010
[2,3,4,8,7,1,6,5]=>0001101
[2,3,4,8,5,1,7,6]=>0001101
[7,4,3,5,8,2,1,6]=>1100110
[7,4,3,5,8,2,6,1]=>1100101
[6,3,5,4,8,2,1,7]=>1010110
[2,3,4,8,5,1,6,7]=>0001100
[6,1,4,2,8,5,7,3]=>1010101
[4,8,6,5,3,2,7,1]=>0111101
[8,6,5,1,2,4,7,3]=>1110001
[1,7,5,8,2,6,4,3]=>0101011
[1,3,8,5,7,6,2,4]=>0010110
[6,3,8,5,7,1,2,4]=>1010100
[6,8,5,2,1,4,7,3]=>0111001
[3,8,2,5,6,1,7,4]=>0100101
[8,1,2,5,6,3,7,4]=>1000101
[8,6,1,5,7,2,3,4]=>1100100
[3,8,6,5,7,1,2,4]=>0110100
[5,1,7,6,8,4,2,3]=>1010110
[5,1,3,7,8,6,2,4]=>1000110
[7,2,5,8,1,6,4,3]=>1001011
[3,2,8,5,7,6,1,4]=>1010110
[8,2,1,5,7,6,3,4]=>1100110
[5,2,8,6,1,7,3,4]=>1011010
[1,2,8,6,5,7,3,4]=>0011010
[8,2,5,6,3,7,1,4]=>1001010
[7,2,6,5,4,1,8,3]=>1011101
[6,1,3,5,4,7,8,2]=>1001001
[6,1,5,3,4,7,8,2]=>1010001
[7,5,6,2,4,1,8,3]=>1010101
[8,5,2,6,3,7,1,4]=>1101010
[8,1,6,5,7,3,2,4]=>1010110
[3,5,8,6,2,7,1,4]=>0011010
[1,8,5,6,3,7,2,4]=>0101010
[1,7,6,5,4,2,8,3]=>0111101
[5,7,6,1,4,2,8,3]=>0110101
[7,1,4,2,6,5,8,3]=>1010101
[2,7,4,1,5,6,8,3]=>0110001
[5,7,6,4,1,2,8,3]=>0111001
[4,7,6,1,5,2,8,3]=>0110101
[1,7,6,4,5,2,8,3]=>0110101
[3,8,1,6,5,7,2,4]=>0101010
[8,1,3,5,7,6,2,4]=>1000110
[7,8,5,4,1,6,2,3]=>0111010
[6,1,5,4,3,7,8,2]=>1011001
[7,5,6,4,2,1,8,3]=>1011101
[8,3,2,6,5,7,1,4]=>1101010
[7,4,6,2,5,1,8,3]=>1010101
[6,1,4,3,5,7,8,2]=>1010001
[6,1,3,4,5,7,8,2]=>1000001
[7,2,6,4,5,1,8,3]=>1010101
[8,2,3,6,5,7,1,4]=>1001010
[3,8,2,7,6,1,5,4]=>0101101
[4,8,7,2,6,5,3,1]=>0110111
[4,8,7,3,1,6,5,2]=>0111011
[4,8,7,3,2,6,1,5]=>0111010
[4,8,7,3,2,6,5,1]=>0111011
[4,8,7,3,6,2,5,1]=>0110101
[4,8,7,3,6,1,5,2]=>0110101
[5,8,7,6,3,4,2,1]=>0111011
[5,8,7,6,3,1,4,2]=>0111101
[5,8,7,6,2,4,3,1]=>0111011
[5,8,7,6,4,2,1,3]=>0111110
[5,8,7,6,4,1,3,2]=>0111101
[5,8,7,6,4,3,1,2]=>0111110
[7,3,4,2,1,6,5,8]=>1011010
[7,3,5,2,6,1,4,8]=>1010100
[7,3,5,2,6,4,1,8]=>1010110
[7,2,1,5,6,4,3,8]=>1100110
[7,3,5,1,6,4,2,8]=>1010110
[7,4,5,6,1,3,2,8]=>1001010
[1,4,5,7,3,2,8,6]=>0001101
[6,4,5,7,3,1,8,2]=>1001101
[6,3,5,1,7,4,8,2]=>1010101
[6,2,1,5,7,4,8,3]=>1100101
[3,2,1,5,7,4,8,6]=>1100101
[2,4,6,7,3,8,1,5]=>0001010
[1,4,6,7,3,8,5,2]=>0001011
[2,5,6,7,8,3,1,4]=>0000110
[3,2,1,6,7,8,4,5]=>1100010
[5,2,1,6,7,8,4,3]=>1100011
[5,3,6,1,7,8,4,2]=>1010011
[5,4,6,7,1,8,3,2]=>1001011
[6,4,5,7,2,1,8,3]=>1001101
[5,4,6,7,2,8,3,1]=>1001011
[5,3,6,2,7,8,4,1]=>1010011
[5,3,6,2,7,8,1,4]=>1010010
[6,3,5,2,7,1,8,4]=>1010101
[5,3,4,1,2,7,8,6]=>1010001
[4,3,6,2,7,8,1,5]=>1010010
[4,3,6,2,7,8,5,1]=>1010011
[1,3,6,2,7,8,5,4]=>0010011
[1,4,6,7,2,8,5,3]=>0001011
[3,4,6,7,2,8,5,1]=>0001011
[3,4,5,7,2,1,8,6]=>0001101
[4,2,1,5,7,3,8,6]=>1100101
[4,2,1,6,7,8,3,5]=>1100010
[4,3,6,1,7,8,2,5]=>1010010
[1,5,6,7,8,2,4,3]=>0000101
[1,5,6,7,8,4,2,3]=>0000110
[4,3,6,1,7,8,5,2]=>1010011
[4,2,1,6,7,8,5,3]=>1100011
[2,4,6,7,1,8,5,3]=>0001011
[2,5,6,7,8,1,4,3]=>0000101
[1,4,3,6,2,5,7,8]=>0101000
[1,4,3,7,2,5,6,8]=>0101000
[1,4,3,7,6,8,2,5]=>0101010
[1,4,3,7,5,8,2,6]=>0101010
[1,5,3,7,4,8,2,6]=>0101010
[1,5,4,8,2,6,3,7]=>0101010
[1,5,4,8,3,7,2,6]=>0101010
[1,2,3,6,5,8,4,7]=>0001010
[6,8,2,4,5,7,1,3]=>0100010
[3,7,8,4,5,2,6,1]=>0010101
[7,8,1,4,5,3,6,2]=>0100101
[5,8,1,4,7,6,3,2]=>0100111
[7,5,1,8,6,2,4,3]=>1101101
[7,4,1,8,2,6,3,5]=>1101010
[7,1,8,4,2,6,3,5]=>1011010
[7,3,1,8,4,2,6,5]=>1101101
[7,2,8,3,6,5,1,4]=>1010110
[7,2,8,3,6,1,5,4]=>1010101
[6,1,2,8,3,5,4,7]=>1001010
[5,2,3,8,1,4,7,6]=>1001001
[6,2,4,1,8,7,3,5]=>1010110
[3,1,6,4,2,8,5,7]=>1011010
[2,6,3,8,7,1,5,4]=>0101101
[2,6,3,8,5,1,4,7]=>0101100
[2,5,1,8,3,4,7,6]=>0101001
[1,2,5,3,8,4,7,6]=>0010101
[1,2,4,8,3,7,6,5]=>0001011
[2,4,8,3,7,1,6,5]=>0010101
[2,4,8,3,7,6,1,5]=>0010110
[2,5,3,8,1,7,4,6]=>0101010
[2,5,4,1,3,8,7,6]=>0110011
[3,1,5,4,8,2,7,6]=>1010101
[5,3,1,4,8,2,7,6]=>1100101
[5,2,3,8,4,7,1,6]=>1001010
[4,8,2,3,7,6,1,5]=>0100110
[4,8,2,3,7,1,6,5]=>0100101
[4,8,1,2,3,7,6,5]=>0100011
[1,4,8,3,7,2,6,5]=>0010101
[6,3,8,1,5,2,4,7]=>1010100
[5,3,8,1,2,4,7,6]=>1010001
[5,1,3,8,2,4,7,6]=>1001001
[1,5,3,8,2,4,7,6]=>0101001
[1,5,4,8,2,7,6,3]=>0101011
[5,1,4,8,2,7,6,3]=>1001011
[5,4,8,1,2,7,6,3]=>1010011
[6,5,1,2,8,7,4,3]=>1100111
[4,1,5,8,2,7,6,3]=>1001011
[4,1,2,5,8,7,6,3]=>1000111
[1,4,2,5,8,7,6,3]=>0100111
[1,3,5,2,8,7,4,6]=>0010110
[3,5,1,2,8,7,4,6]=>0100110
[4,2,6,1,8,7,3,5]=>1010110
[4,3,1,5,8,2,7,6]=>1100101
[3,5,2,8,7,1,4,6]=>0101100
[3,4,8,7,2,6,1,5]=>0011010
[3,4,8,1,7,2,6,5]=>0010101
[1,3,4,8,7,2,6,5]=>0001101
[1,3,4,8,2,7,6,5]=>0001011
[3,4,8,1,2,7,6,5]=>0010011
[3,4,8,2,7,1,6,5]=>0010101
[3,4,8,2,7,6,1,5]=>0010110
[4,2,5,8,1,7,6,3]=>1001011
[4,3,1,2,5,8,7,6]=>1100011
[3,1,4,2,5,8,7,6]=>1010011
[2,3,5,1,8,7,6,4]=>0010111
[7,8,2,1,5,3,6,4]=>0110101
[6,4,1,2,7,3,5,8]=>1100100
[2,3,7,5,4,1,8,6]=>0011101
[6,3,1,5,4,2,7,8]=>1101100
[7,8,1,5,4,2,6,3]=>0101101
[7,8,3,5,4,1,6,2]=>0101101
[7,8,2,5,4,1,3,6]=>0101100
[7,8,2,5,4,6,1,3]=>0101010
[6,2,1,5,4,7,3,8]=>1101010
[5,3,6,2,4,7,1,8]=>1010010
[6,4,2,1,7,3,8,5]=>1110101
[2,7,6,5,3,1,4,8]=>0111100
[3,7,6,4,8,5,1,2]=>0110110
[5,7,6,3,8,4,1,2]=>0110110
[5,1,6,2,4,8,3,7]=>1010010
[4,7,6,5,2,1,3,8]=>0111100
[4,7,6,5,2,8,1,3]=>0111010
[4,7,6,5,1,8,3,2]=>0111011
[1,7,6,5,2,8,3,4]=>0111010
[1,7,6,5,3,2,8,4]=>0111101
[4,7,6,5,1,2,8,3]=>0111001
[4,7,6,5,3,1,8,2]=>0111101
[5,2,6,3,4,1,7,8]=>1010100
[5,1,6,2,4,7,8,3]=>1010001
[1,7,2,4,8,3,6,5]=>0100101
[4,7,2,1,5,3,6,8]=>0110100
[4,7,1,6,2,3,8,5]=>0101001
[1,7,2,6,8,3,5,4]=>0100101
[1,2,6,7,4,8,5,3]=>0001011
[3,1,6,7,4,2,8,5]=>1001101
[3,2,8,5,4,6,1,7]=>1011010
[4,7,6,3,5,8,1,2]=>0110010
[3,7,6,5,2,4,1,8]=>0111010
[3,7,6,5,2,1,8,4]=>0111101
[1,7,6,5,8,2,4,3]=>0110101
[3,7,6,5,8,1,4,2]=>0110101
[3,7,6,5,1,2,4,8]=>0111000
[3,1,6,8,4,2,5,7]=>1001100
[4,7,6,8,3,5,1,2]=>0101010
[2,7,6,5,8,1,3,4]=>0110100
[2,7,6,5,8,4,1,3]=>0110110
[3,7,5,8,2,4,1,6]=>0101010
[5,1,7,8,4,3,2,6]=>1001110
[5,1,2,6,4,3,8,7]=>1001101
[5,1,2,4,6,3,8,7]=>1000101
[4,1,5,7,8,3,2,6]=>1000110
[4,7,1,8,3,6,2,5]=>0101010
[4,1,7,8,5,2,3,6]=>1001100
[5,1,7,4,8,2,3,6]=>1010100
[5,1,8,4,7,2,3,6]=>1010100
[4,1,8,7,5,2,3,6]=>1011100
[4,7,1,6,3,2,8,5]=>0101101
[7,1,2,3,8,6,5,4]=>1000111
[6,8,1,4,3,7,2,5]=>0101010
[8,7,3,2,4,1,6,5]=>1110101
[6,7,1,4,3,8,2,5]=>0101010
[8,1,2,3,5,7,6,4]=>1000011
[7,1,2,3,6,8,5,4]=>1000011
[7,1,8,5,4,3,2,6]=>1011110
[7,8,2,6,3,4,1,5]=>0101010
[6,7,2,8,3,4,1,5]=>0101010
[3,8,7,1,4,2,6,5]=>0110101
[3,7,8,1,4,2,6,5]=>0010101
[3,6,8,1,4,2,7,5]=>0010101
[3,5,7,8,2,4,1,6]=>0001010
[3,6,7,1,4,2,8,5]=>0010101
[8,6,2,7,3,1,4,5]=>1101100
[8,1,7,5,4,3,2,6]=>1011110
[8,1,7,4,5,3,2,6]=>1010110
[5,8,3,7,1,4,2,6]=>0101010
[2,1,7,3,4,6,8,5]=>1010001
[6,7,3,2,4,1,8,5]=>0110101
[8,7,2,4,3,6,1,5]=>1101010
[7,1,2,3,5,6,8,4]=>1000001
[6,1,2,3,8,7,4,5]=>1000110
[5,1,2,3,7,8,6,4]=>1000011
[8,6,2,4,3,1,7,5]=>1101101
[7,6,3,2,4,8,1,5]=>1110010
[8,6,3,2,4,7,1,5]=>1110010
[7,6,2,4,3,1,8,5]=>1101101
[7,8,1,2,6,3,5,4]=>0100101
[1,4,8,2,7,3,5,6]=>0010100
[1,2,8,5,4,7,3,6]=>0011010
[2,3,6,8,4,7,1,5]=>0001010
[1,3,6,8,4,7,5,2]=>0001011
[2,4,8,1,7,3,6,5]=>0010101
[3,4,8,5,7,6,1,2]=>0010110
[1,2,6,8,4,5,7,3]=>0001001
[7,5,1,2,4,3,6,8]=>1100100
[7,4,6,1,5,2,3,8]=>1010100
[6,8,1,4,7,2,3,5]=>0100100
[1,6,4,2,8,3,5,7]=>0110100
[1,6,3,8,5,4,2,7]=>0101110
[7,1,3,6,5,4,2,8]=>1001110
[7,2,1,4,6,3,5,8]=>1100100
[7,2,3,6,5,1,4,8]=>1001100
[7,1,2,3,6,5,4,8]=>1000110
[6,8,1,2,7,3,5,4]=>0100101
[1,6,2,3,8,5,4,7]=>0100110
[1,5,8,2,7,6,3,4]=>0010110
[5,8,2,7,6,3,4,1]=>0101101
[6,2,8,1,7,3,5,4]=>1010101
[3,6,4,1,2,8,5,7]=>0110010
[2,5,1,8,7,6,3,4]=>0101110
[1,2,5,3,8,7,4,6]=>0010110
[2,5,3,8,7,1,6,4]=>0101101
[2,5,8,4,1,7,6,3]=>0011011
[3,5,8,7,1,4,2,6]=>0011010
[5,3,8,4,1,7,6,2]=>1011011
[4,2,8,7,6,3,5,1]=>1011101
[6,3,1,8,7,2,5,4]=>1101101
[5,1,3,8,7,6,2,4]=>1001110
[1,5,3,8,7,6,2,4]=>0101110
[5,1,8,4,7,2,6,3]=>1010101
[5,8,7,4,6,1,2,3]=>0110100
[6,8,5,1,2,4,7,3]=>0110001
[4,5,8,1,7,2,6,3]=>0010101
[1,3,2,5,8,7,4,6]=>0100110
[3,5,1,8,7,4,6,2]=>0101101
[4,3,6,1,2,8,5,7]=>1010010
[4,5,8,3,1,7,2,6]=>0011010
[4,5,2,8,7,1,3,6]=>0101100
[3,2,5,8,7,1,6,4]=>1001101
[3,4,8,7,6,2,1,5]=>0011110
[3,4,8,7,6,5,1,2]=>0011110
[1,3,4,8,7,6,2,5]=>0001110
[3,4,8,7,6,2,5,1]=>0011101
[3,2,5,8,7,4,6,1]=>1001101
[2,1,3,5,8,7,4,6]=>1000110
[1,2,7,5,8,6,4,3]=>0010111
[6,8,1,3,7,5,2,4]=>0100110
[1,3,7,8,2,6,5,4]=>0001011
[2,7,8,1,3,6,5,4]=>0010011
[8,1,2,6,7,3,5,4]=>1000101
[8,1,2,6,7,5,3,4]=>1000110
[8,2,5,7,1,3,6,4]=>1001001
[2,8,1,6,7,3,5,4]=>0100101
[2,6,8,3,7,1,5,4]=>0010101
[2,8,6,4,7,1,5,3]=>0110101
[6,8,3,4,1,7,5,2]=>0101011
[6,8,3,7,4,1,5,2]=>0101101
[8,2,5,7,1,6,3,4]=>1001010
[8,4,7,2,3,6,1,5]=>1010010
[8,5,7,4,2,6,1,3]=>1011010
[8,3,5,7,4,1,6,2]=>1001101
[8,5,2,4,7,1,6,3]=>1100101
[8,2,4,7,3,6,1,5]=>1001010
[8,2,7,1,4,6,3,5]=>1010010
[8,7,1,2,4,6,3,5]=>1100010
[8,7,1,4,6,2,3,5]=>1100100
[8,4,7,1,3,6,2,5]=>1010010
[8,3,5,7,1,2,6,4]=>1001001
[5,8,7,1,3,6,2,4]=>0110010
[8,5,4,7,1,6,2,3]=>1101010
[8,5,4,7,1,2,6,3]=>1101001
[8,5,1,4,7,2,6,3]=>1100101
[8,5,6,3,1,7,4,2]=>1011011
[1,8,4,5,7,2,6,3]=>0100101
[5,8,7,3,6,1,2,4]=>0110100
[8,3,5,7,1,6,2,4]=>1001010
[1,6,8,3,7,5,2,4]=>0010110
[6,3,8,2,7,5,1,4]=>1010110
[8,6,4,7,3,1,5,2]=>1101101
[8,4,5,7,3,1,6,2]=>1001101
[8,3,4,7,2,6,1,5]=>1001010
[8,7,1,3,4,6,2,5]=>1100010
[8,3,7,2,4,6,1,5]=>1010010
[2,8,4,5,7,1,6,3]=>0100101
[8,7,3,4,5,1,6,2]=>1100101
[8,7,4,5,2,6,1,3]=>1101010
[8,7,2,3,4,6,1,5]=>1100010
[8,6,5,1,3,2,7,4]=>1110101
[8,6,3,1,7,2,4,5]=>1110100
[8,7,3,1,5,2,4,6]=>1110100
[8,6,1,2,4,7,3,5]=>1100010
[8,6,1,5,3,4,7,2]=>1101001
[8,6,1,5,2,4,7,3]=>1101001
[8,6,1,2,5,7,3,4]=>1100010
[5,1,4,2,3,8,6,7]=>1010010
[5,1,4,2,7,3,6,8]=>1010100
[5,7,8,1,2,4,6,3]=>0010001
[5,7,8,1,3,4,6,2]=>0010001
[5,8,1,7,3,4,6,2]=>0101001
[8,1,5,7,2,4,6,3]=>1001001
[1,4,2,3,8,7,5,6]=>0100110
[1,4,2,7,6,3,5,8]=>0101100
[6,1,2,8,7,5,3,4]=>1001110
[6,1,2,4,8,7,5,3]=>1000111
[3,1,8,4,6,7,5,2]=>1010011
[3,1,7,6,4,8,5,2]=>1011011
[7,1,2,4,6,8,5,3]=>1000011
[7,1,2,6,8,5,3,4]=>1000110
[7,1,5,3,2,8,6,4]=>1011011
[8,1,7,5,3,2,6,4]=>1011101
[8,3,7,1,2,6,4,5]=>1010010
[3,1,2,8,4,7,5,6]=>1001010
[1,4,2,3,8,6,5,7]=>0100110
[1,4,2,3,8,5,7,6]=>0100101
[5,8,1,7,2,4,6,3]=>0101001
[5,8,1,3,4,7,6,2]=>0100011
[3,1,8,6,4,7,5,2]=>1011011
[8,1,2,6,7,4,5,3]=>1000101
[1,2,3,5,8,4,7,6]=>0000101
[1,2,3,5,8,6,4,7]=>0000110
[7,1,2,8,3,6,5,4]=>1001011
[7,1,2,8,6,4,5,3]=>1001101
[3,1,7,8,4,6,5,2]=>1001011
[8,1,2,7,4,6,5,3]=>1001011
[8,1,2,7,3,6,5,4]=>1001011
[1,2,3,6,8,5,4,7]=>0000110
[3,6,2,5,4,1,8,7]=>0101101
[3,5,2,8,4,7,6,1]=>0101011
[5,4,7,3,2,8,6,1]=>1011011
[5,4,8,3,2,7,6,1]=>1011011
[5,3,2,6,4,1,8,7]=>1101101
[4,5,8,3,2,7,6,1]=>0011011
[4,7,6,3,8,5,2,1]=>0110111
[4,8,6,3,7,5,2,1]=>0110111
[5,3,2,8,4,7,6,1]=>1101011
[2,1,5,8,4,7,6,3]=>1001011
[5,3,2,7,4,8,6,1]=>1101011
[5,7,4,3,2,8,6,1]=>0111011
[4,7,5,3,2,8,6,1]=>0111011
[4,7,8,3,6,5,2,1]=>0010111
[4,6,8,3,7,5,2,1]=>0010111
[7,6,4,3,8,5,2,1]=>1110111
[8,3,2,6,7,5,4,1]=>1100111
[8,6,4,3,7,5,2,1]=>1110111
[8,4,5,3,2,7,6,1]=>1011011
[8,4,6,3,7,5,2,1]=>1010111
[7,4,6,3,8,5,2,1]=>1010111
[3,7,2,6,8,5,4,1]=>0100111
[3,8,2,6,7,5,4,1]=>0100111
[3,7,2,8,6,5,4,1]=>0101111
[3,6,2,8,7,5,4,1]=>0101111
[7,4,5,3,2,8,6,1]=>1011011
[2,1,7,5,4,8,6,3]=>1011011
[7,3,2,8,6,5,4,1]=>1101111
[7,8,4,3,6,5,2,1]=>0110111
[6,3,2,8,7,5,4,1]=>1101111
[6,3,2,7,8,5,4,1]=>1100111
[1,6,4,8,2,5,3,7]=>0101010
[1,6,5,8,2,4,3,7]=>0101010
[1,6,8,2,4,3,7,5]=>0010101
[1,6,2,4,3,7,8,5]=>0101001
[1,5,6,2,4,7,3,8]=>0010010
[1,5,6,2,4,7,8,3]=>0010001
[1,6,7,2,4,3,8,5]=>0010101
[1,5,8,2,4,6,7,3]=>0010001
[1,5,7,8,3,2,4,6]=>0001100
[1,5,8,3,2,4,6,7]=>0011000
[1,5,6,2,4,8,3,7]=>0010010
[1,7,3,4,2,8,6,5]=>0101011
[1,5,6,2,4,8,7,3]=>0010011
[1,5,8,7,3,2,4,6]=>0011100
[1,7,4,2,8,6,5,3]=>0110111
[1,5,8,3,2,4,7,6]=>0011001
[1,6,5,2,3,7,4,8]=>0110010
[1,6,5,2,3,7,8,4]=>0110001
[1,6,8,4,2,3,7,5]=>0011001
[1,6,8,5,2,3,7,4]=>0011001
[1,6,4,2,3,7,5,8]=>0110010
[1,5,8,6,2,4,7,3]=>0011001
[1,7,5,2,8,6,4,3]=>0110111
[3,7,5,6,1,4,8,2]=>0101001
[8,6,1,4,2,7,5,3]=>1101011
[1,6,7,4,3,5,8,2]=>0011001
[6,7,1,4,3,5,8,2]=>0101001
[4,7,1,6,3,5,8,2]=>0101001
[3,1,4,7,6,5,8,2]=>1001101
[6,1,7,4,3,5,8,2]=>1011001
[7,1,6,4,3,5,8,2]=>1011001
[1,7,6,4,3,5,8,2]=>0111001
[8,1,6,4,2,7,5,3]=>1011011
[4,7,1,3,8,2,5,6]=>0100100
[7,4,1,3,8,2,5,6]=>1100100
[1,3,6,4,2,8,5,7]=>0011010
[4,7,3,1,2,8,5,6]=>0110010
[4,7,8,1,2,6,5,3]=>0010011
[1,8,6,4,2,7,5,3]=>0111011
[4,8,1,3,7,2,5,6]=>0100100
[8,7,1,3,6,2,5,4]=>1100101
[1,8,4,3,7,2,5,6]=>0110100
[3,7,4,6,8,2,1,5]=>0100110
[2,4,3,7,8,6,1,5]=>0100110
[1,4,7,3,8,2,5,6]=>0010100
[5,7,6,8,3,2,1,4]=>0101110
[6,1,4,3,8,2,5,7]=>1010100
[4,1,7,3,8,2,5,6]=>1010100
[8,1,4,3,7,2,5,6]=>1010100
[4,2,3,7,8,6,1,5]=>1000110
[2,7,5,6,3,8,1,4]=>0101010
[5,7,2,6,8,4,1,3]=>0100110
[7,2,5,6,8,4,1,3]=>1000110
[5,2,3,8,7,6,1,4]=>1001110
[8,2,3,7,5,6,1,4]=>1001010
[6,1,8,3,7,2,5,4]=>1010101
[1,7,8,4,2,6,5,3]=>0011011
[4,7,1,8,2,5,6,3]=>0101001
[1,4,8,3,6,2,5,7]=>0010100
[3,7,5,8,6,2,1,4]=>0101110
[3,7,8,6,5,2,1,4]=>0011110
[6,8,7,5,3,2,1,4]=>0111110
[5,7,6,8,3,4,1,2]=>0101010
[3,7,6,8,4,5,1,2]=>0101010
[1,5,4,7,6,8,2,3]=>0101010
[1,7,4,6,5,8,2,3]=>0101010
[3,7,4,6,5,8,1,2]=>0101010
[3,5,4,8,6,7,1,2]=>0101010
[3,8,4,6,5,7,1,2]=>0101010
[3,6,4,7,5,8,1,2]=>0101010
[1,6,2,7,5,8,3,4]=>0101010
[1,6,4,8,5,7,2,3]=>0101010
[1,8,4,6,5,7,2,3]=>0101010
[1,5,4,8,6,7,2,3]=>0101010
[7,8,1,5,4,6,2,3]=>0101010
[1,8,2,6,5,7,3,4]=>0101010
[1,7,2,8,5,6,3,4]=>0101010
[1,7,2,6,5,8,3,4]=>0101010
[1,5,2,7,6,8,3,4]=>0101010
[1,7,6,8,2,5,3,4]=>0101010
[1,7,6,8,4,5,2,3]=>0101010
[7,8,5,6,1,3,2,4]=>0101010
[5,8,6,7,1,3,2,4]=>0101010
[1,3,2,7,6,8,4,5]=>0101010
[1,7,6,8,2,4,3,5]=>0101010
[1,3,2,8,6,7,4,5]=>0101010
[7,8,1,3,2,6,4,5]=>0101010
[7,8,1,6,2,4,3,5]=>0101010
[1,8,6,7,2,4,3,5]=>0101010
[7,8,1,4,2,6,3,5]=>0101010
[6,4,8,5,2,7,1,3]=>1011010
[8,4,7,5,2,6,1,3]=>1011010
[5,4,6,8,2,1,7,3]=>1001101
[4,8,7,5,6,1,3,2]=>0110101
[2,7,5,1,8,4,3,6]=>0110110
[2,8,6,7,4,3,5,1]=>0101101
[3,8,7,1,4,6,5,2]=>0110011
[5,7,1,2,4,3,8,6]=>0100101
[4,3,7,6,8,2,5,1]=>1010101
[5,3,6,8,1,7,2,4]=>1001010
[3,2,6,8,5,7,1,4]=>1001010
[7,4,8,6,5,2,1,3]=>1011110
[7,1,8,2,5,4,3,6]=>1010110
[2,5,3,7,4,1,8,6]=>0101101
[3,6,4,7,5,1,8,2]=>0101101
[8,4,7,1,2,5,6,3]=>1010001
[4,2,8,7,3,5,6,1]=>1011001
[6,4,1,5,8,2,7,3]=>1100101
[8,3,5,6,7,4,1,2]=>1000110
[7,4,3,2,8,5,6,1]=>1110101
[4,2,7,1,8,5,6,3]=>1010101
[4,7,8,3,1,5,6,2]=>0011001
[3,7,1,4,8,5,6,2]=>0100101
[2,6,3,5,8,7,1,4]=>0100110
[7,6,2,1,5,8,4,3]=>1110011
[4,5,2,7,6,1,8,3]=>0101101
[3,6,8,7,5,2,1,4]=>0011110
[7,4,8,6,5,2,3,1]=>1011101
[8,1,6,4,7,3,2,5]=>1010110
[7,6,4,1,2,3,8,5]=>1110001
[2,6,4,8,5,3,7,1]=>0101101
[4,8,7,5,6,1,2,3]=>0110100
[6,1,4,8,7,3,5,2]=>1001101
[4,7,8,1,3,5,6,2]=>0010001
[8,7,3,4,1,5,6,2]=>1101001
[4,8,2,7,3,5,6,1]=>0101001
[3,1,8,7,2,5,6,4]=>1011001
[8,2,3,7,1,5,6,4]=>1001001
[6,4,8,7,1,3,2,5]=>1011010
[7,8,2,4,3,5,6,1]=>0101001
[2,8,3,7,1,5,6,4]=>0101001
[5,3,8,6,2,1,4,7]=>1011100
[4,6,5,2,8,3,1,7]=>0110110
[4,3,7,5,1,8,2,6]=>1011010
[6,8,5,2,7,4,3,1]=>0110111
[3,6,8,1,4,5,2,7]=>0010010
[6,8,1,2,4,5,3,7]=>0100010
[4,1,6,5,8,2,3,7]=>1010100
[4,3,8,6,2,5,1,7]=>1011010
[8,3,6,1,4,5,2,7]=>1010010
[6,3,8,7,4,2,5,1]=>1011101
[5,8,4,3,7,6,1,2]=>0110110
[8,7,4,3,1,6,2,5]=>1111010
[1,7,4,3,8,6,2,5]=>0110110
[7,1,5,3,4,8,2,6]=>1010010
[2,8,6,1,7,4,5,3]=>0110101
[4,7,6,8,2,1,5,3]=>0101101
[6,1,8,7,4,3,5,2]=>1011101
[8,5,4,3,1,6,7,2]=>1111001
[1,5,8,6,3,4,7,2]=>0011001
[2,5,8,6,3,4,7,1]=>0011001
[4,6,5,2,8,1,7,3]=>0110101
[1,8,5,2,3,6,7,4]=>0110001
[4,8,3,2,5,6,7,1]=>0110001
[2,1,8,3,5,6,7,4]=>1010001
[4,2,7,1,8,6,3,5]=>1010110
[3,8,4,1,2,6,7,5]=>0110001
[5,8,3,6,7,4,1,2]=>0100110
[2,3,1,6,8,4,7,5]=>0100101
[2,4,3,7,1,8,5,6]=>0101010
[2,4,1,8,6,3,7,5]=>0101101
[8,4,1,3,6,2,7,5]=>1100101
[6,8,5,1,7,2,3,4]=>0110100
[7,3,6,5,8,2,1,4]=>1010110
[7,6,3,5,8,2,1,4]=>1100110
[4,5,8,7,3,6,1,2]=>0011010
[8,6,5,4,1,2,7,3]=>1111001
[6,1,5,3,8,7,2,4]=>1010110
[2,8,6,3,7,1,5,4]=>0110101
[7,6,1,5,8,2,3,4]=>1100100
[3,6,8,5,1,2,7,4]=>0011001
[6,5,2,4,8,1,7,3]=>1100101
[5,1,4,8,2,6,7,3]=>1001001
[3,4,8,5,2,6,7,1]=>0011001
[4,2,1,8,5,6,7,3]=>1101001
[1,5,4,8,2,6,7,3]=>0101001
[7,2,1,5,8,6,3,4]=>1100110
[2,8,4,5,1,6,7,3]=>0101001
[5,4,8,3,7,6,1,2]=>1010110
[3,1,5,8,6,2,7,4]=>1001101
[6,3,4,8,5,1,7,2]=>1001101
[5,3,4,8,1,6,7,2]=>1001001
[6,5,4,8,7,1,3,2]=>1101101
[6,5,4,8,1,2,7,3]=>1101001
[7,5,1,6,8,2,4,3]=>1100101
[6,5,4,1,8,2,7,3]=>1110101
[6,5,4,7,1,2,8,3]=>1101001
[6,5,4,7,8,1,3,2]=>1100101
[6,5,3,7,1,4,2,8]=>1101010
[7,5,1,4,8,3,2,6]=>1100110
[8,1,6,4,7,3,5,2]=>1010101
[7,5,1,4,8,3,6,2]=>1100101
[7,4,1,5,3,8,6,2]=>1101011
[8,1,5,4,3,7,6,2]=>1011011
[8,1,5,4,3,7,2,6]=>1011010
[6,5,3,8,1,4,2,7]=>1101010
[8,1,7,2,5,4,6,3]=>1010101
[7,6,1,2,5,4,8,3]=>1100101
[6,5,3,8,1,4,7,2]=>1101001
[6,5,3,1,2,7,8,4]=>1110001
[8,1,6,4,2,5,7,3]=>1011001
[8,1,5,4,3,2,7,6]=>1011101
[7,4,1,5,3,2,8,6]=>1101101
[6,4,3,1,5,2,8,7]=>1110101
[6,4,3,1,5,7,2,8]=>1110010
[7,4,1,5,3,6,2,8]=>1101010
[6,4,3,1,5,7,8,2]=>1110001
[8,6,7,1,4,2,5,3]=>1010101
[8,6,3,7,5,1,2,4]=>1101100
[7,6,1,8,3,5,2,4]=>1101010
[7,6,2,8,3,5,1,4]=>1101010
[8,7,1,5,2,6,3,4]=>1101010
[8,7,1,5,2,3,6,4]=>1101001
[8,5,2,3,1,7,6,4]=>1101011
[8,6,2,3,7,1,5,4]=>1100101
[8,6,2,7,3,1,5,4]=>1101101
[8,7,2,5,1,6,3,4]=>1101010
[8,5,7,2,1,4,3,6]=>1011010
[5,8,7,3,1,4,2,6]=>0111010
[8,5,7,2,1,4,6,3]=>1011001
[8,6,1,3,7,2,5,4]=>1100101
[8,4,7,5,1,6,2,3]=>1011010
[8,4,7,5,1,2,3,6]=>1011000
[8,3,2,6,5,1,4,7]=>1101100
[4,8,7,3,1,5,2,6]=>0111010
[8,4,7,2,1,5,3,6]=>1011010
[8,7,3,1,2,4,6,5]=>1110001
[8,4,7,2,1,5,6,3]=>1011001
[1,2,7,3,5,4,8,6]=>0010101
[1,5,7,2,3,6,4,8]=>0010010
[1,3,8,2,4,5,7,6]=>0010001
[1,2,3,8,4,6,7,5]=>0001001
[1,7,8,2,3,6,4,5]=>0010010
[1,6,7,8,2,3,5,4]=>0001001
[1,7,8,2,5,3,6,4]=>0010101
[1,8,2,3,6,4,5,7]=>0100100
[1,2,7,8,3,6,4,5]=>0001010
[1,5,2,7,8,3,6,4]=>0100101
[1,3,2,8,4,6,7,5]=>0101001
[1,8,2,3,4,6,7,5]=>0100001
[1,7,8,2,4,3,6,5]=>0010101
[7,6,3,1,5,2,4,8]=>1110100
[6,7,3,1,5,2,8,4]=>0110101
[6,8,3,1,5,2,7,4]=>0110101
[6,8,4,5,1,2,7,3]=>0101001
[6,7,4,5,1,2,8,3]=>0101001
[7,2,1,6,5,3,4,8]=>1101100
[7,3,6,1,5,2,4,8]=>1010100
[7,4,6,5,1,2,3,8]=>1011000
[6,7,5,4,1,2,8,3]=>0111001
[5,8,6,4,1,7,2,3]=>0111010
[5,7,6,4,1,8,2,3]=>0111010
[5,6,7,4,1,8,2,3]=>0011010
[6,5,7,4,1,2,8,3]=>1011001
[6,2,1,7,5,3,8,4]=>1101101
[6,3,8,1,5,2,7,4]=>1010101
[6,4,8,5,1,2,7,3]=>1011001
[6,5,8,4,1,2,7,3]=>1011001
[5,6,8,4,1,7,2,3]=>0011010
[4,6,8,5,7,1,2,3]=>0010100
[4,5,8,6,7,1,2,3]=>0010100
[5,2,1,7,6,8,3,4]=>1101010
[4,5,7,6,8,1,2,3]=>0010100
[4,6,7,5,8,1,2,3]=>0010100
[4,7,5,6,8,1,2,3]=>0100100
[4,6,5,7,8,1,2,3]=>0100100
[5,7,4,6,1,8,2,3]=>0101010
[5,8,3,1,6,7,2,4]=>0110010
[5,7,3,1,6,8,2,4]=>0110010
[5,6,3,1,7,8,2,4]=>0110010
[5,8,3,1,7,6,2,4]=>0110110
[5,7,4,8,1,6,2,3]=>0101010
[5,2,1,6,8,7,3,4]=>1100110
[5,4,6,8,1,7,2,3]=>1001010
[4,5,6,8,7,1,2,3]=>0001100
[4,7,5,8,6,1,2,3]=>0101100
[4,8,5,7,6,1,2,3]=>0101100
[4,8,6,7,5,1,2,3]=>0101100
[4,7,6,8,5,1,2,3]=>0101100
[4,6,7,8,5,1,2,3]=>0001100
[4,5,7,8,6,1,2,3]=>0001100
[5,4,7,8,1,6,2,3]=>1001010
[5,3,7,1,8,6,2,4]=>1010110
[5,2,1,7,8,6,3,4]=>1100110
[5,3,8,1,7,6,2,4]=>1010110
[5,4,8,7,1,6,2,3]=>1011010
[4,6,8,7,5,1,2,3]=>0011100
[4,7,8,6,5,1,2,3]=>0011100
[4,8,7,6,5,1,2,3]=>0111100
[2,5,4,7,3,6,1,8]=>0101010
[4,2,7,3,6,5,1,8]=>1010110
[4,2,6,3,1,5,8,7]=>1011001
[2,5,3,1,6,4,8,7]=>0110101
[2,5,3,7,6,4,1,8]=>0101110
[2,6,5,3,7,4,1,8]=>0110110
[4,2,7,6,3,5,1,8]=>1011010
[2,7,5,3,6,4,1,8]=>0110110
[2,6,3,7,5,4,1,8]=>0101110
[1,7,5,2,3,8,4,6]=>0110010
[2,1,3,7,5,4,8,6]=>1001101
[2,3,1,8,6,5,4,7]=>0101110
[2,5,3,1,8,6,4,7]=>0110110
[4,2,8,3,1,6,5,7]=>1011010
[8,3,2,6,4,1,5,7]=>1101100
[3,6,8,2,1,4,5,7]=>0011000
[1,2,6,3,8,7,4,5]=>0010110
[1,2,7,6,3,4,8,5]=>0011001
[2,1,3,8,7,5,4,6]=>1001110
[1,2,3,8,6,4,7,5]=>0001101
[1,2,3,7,4,8,6,5]=>0001011
[1,2,7,6,3,8,4,5]=>0011010
[1,2,3,6,4,8,7,5]=>0001011
[1,2,3,7,6,4,8,5]=>0001101
[2,1,3,8,5,4,7,6]=>1001101
[7,1,8,4,2,3,5,6]=>1011000
[4,2,6,3,1,8,5,7]=>1011010
[5,4,2,8,3,1,6,7]=>1101100
[2,5,4,8,3,1,6,7]=>0101100
[1,8,7,4,2,3,5,6]=>0111000
[1,5,2,8,7,3,4,6]=>0101100
[1,2,7,3,6,4,8,5]=>0010101
[1,2,8,6,3,7,4,5]=>0011010
[1,2,6,3,8,4,7,5]=>0010101
[4,2,1,8,3,7,5,6]=>1101010
[8,3,2,1,7,4,5,6]=>1110100
[1,2,3,8,7,4,6,5]=>0001101
[1,2,3,8,7,6,4,5]=>0001110
[2,6,5,7,1,4,3,8]=>0101010
[2,6,5,7,1,3,8,4]=>0101001
[3,8,5,7,1,2,6,4]=>0101001
[3,8,5,7,2,6,4,1]=>0101011
[3,4,8,6,2,5,7,1]=>0011001
[3,4,8,6,1,2,5,7]=>0011000
[2,5,7,1,4,8,6,3]=>0010011
[2,8,1,7,5,6,4,3]=>0101011
[2,3,8,1,6,5,7,4]=>0010101
[3,5,7,6,1,2,4,8]=>0011000
[4,8,6,7,2,3,5,1]=>0101001
[4,8,6,7,1,3,5,2]=>0101001
[3,4,8,6,1,5,7,2]=>0011001
[3,8,5,7,1,6,4,2]=>0101011
[3,8,5,7,2,1,6,4]=>0101101
[3,4,8,6,2,1,5,7]=>0011100
[3,5,7,6,2,1,4,8]=>0011100
[5,8,6,7,3,4,2,1]=>0101011
[5,8,6,7,2,1,3,4]=>0101100
[4,8,6,7,2,1,5,3]=>0101101
[4,3,1,7,5,2,8,6]=>1101101
[4,3,2,8,5,1,7,6]=>1101101
[4,3,8,5,1,6,7,2]=>1011001
[5,8,6,7,2,3,4,1]=>0101001
[5,8,6,7,2,4,3,1]=>0101011
[5,8,6,7,1,2,4,3]=>0101001
[3,2,5,7,6,1,4,8]=>1001100
[4,8,6,7,1,3,2,5]=>0101010
[4,8,6,7,1,2,5,3]=>0101001
[4,8,6,7,2,5,3,1]=>0101011
[4,3,8,5,2,6,7,1]=>1011001
[4,2,6,7,5,1,3,8]=>1001100
[3,8,4,7,1,5,2,6]=>0101010
[3,5,1,7,4,6,2,8]=>0101010
[3,8,4,7,2,5,1,6]=>0101010
[4,1,3,8,5,2,6,7]=>1001100
[4,2,6,7,5,3,8,1]=>1001101
[4,8,6,7,3,2,5,1]=>0101101
[4,8,6,7,3,1,2,5]=>0101100
[3,1,5,7,6,2,4,8]=>1001100
[3,4,1,7,5,6,2,8]=>0101010
[4,1,7,5,2,8,6,3]=>1011011
[4,1,6,7,5,2,3,8]=>1001100
[5,8,6,7,3,2,4,1]=>0101101
[5,8,6,7,4,2,3,1]=>0101101
[5,8,6,7,4,1,2,3]=>0101100
[5,8,6,7,4,1,3,2]=>0101101
[5,8,6,7,3,1,4,2]=>0101101
[4,8,6,7,3,1,5,2]=>0101101
[4,1,6,7,5,3,8,2]=>1001101
[4,1,7,5,3,2,8,6]=>1011101
[4,2,8,5,3,1,7,6]=>1011101
[4,2,1,6,7,5,3,8]=>1100110
[4,8,6,7,3,2,1,5]=>0101110
[5,8,6,7,4,2,1,3]=>0101110
[5,8,6,7,4,3,1,2]=>0101110
[6,1,5,2,8,4,7,3]=>1010101
[4,6,1,8,5,7,2,3]=>0101010
[4,7,1,2,8,5,6,3]=>0100101
[1,4,7,2,8,5,6,3]=>0010101
[1,7,3,5,8,6,2,4]=>0100110
[7,3,5,8,6,1,2,4]=>1001100
[6,8,1,5,7,2,3,4]=>0100100
[7,1,2,5,8,6,3,4]=>1000110
[1,7,2,5,8,6,3,4]=>0100110
[1,7,6,8,2,3,5,4]=>0101001
[7,6,8,1,2,3,5,4]=>1010001
[2,7,1,5,8,6,3,4]=>0100110
[2,4,7,1,8,5,6,3]=>0010101
[4,7,5,8,3,1,6,2]=>0101101
[4,7,2,1,8,5,6,3]=>0110101
[7,3,5,8,6,2,1,4]=>1001110
[7,6,8,2,1,3,5,4]=>1011001
[1,2,7,6,8,3,5,4]=>0010101
[3,7,6,8,2,1,5,4]=>0101101
[6,7,4,1,8,5,3,2]=>0110111
[6,7,4,3,1,8,5,2]=>0111011
[2,7,4,1,6,8,5,3]=>0110011
[3,1,7,6,8,2,5,4]=>1010101
[1,3,7,6,8,2,5,4]=>0010101
[1,7,4,2,6,8,5,3]=>0110011
[7,1,4,2,8,5,6,3]=>1010101
[7,1,8,2,5,4,6,3]=>1010101
[7,1,6,8,5,4,2,3]=>1001110
[7,1,2,6,8,5,4,3]=>1000111
[1,7,2,6,8,5,4,3]=>0100111
[1,7,6,8,3,2,5,4]=>0101101
[7,6,8,3,1,2,5,4]=>1011001
[7,1,5,8,6,3,2,4]=>1001110
[3,6,7,1,8,5,4,2]=>0010111
[7,2,6,8,5,4,1,3]=>1001110
[7,6,8,2,3,1,5,4]=>1010101
[2,7,6,8,3,1,5,4]=>0101101
[2,7,1,6,8,5,4,3]=>0100111
[6,7,3,1,8,5,4,2]=>0110111
[6,7,1,8,5,4,3,2]=>0101111
[7,2,1,6,8,5,4,3]=>1100111
[7,8,4,2,1,6,5,3]=>0111011
[6,2,3,4,8,7,1,5]=>1000110
[6,2,3,4,7,8,1,5]=>1000010
[7,8,3,6,4,2,1,5]=>0101110
[7,8,3,5,6,2,1,4]=>0100110
[5,2,6,3,8,1,7,4]=>1010101
[6,3,2,5,8,7,1,4]=>1100110
[6,3,2,8,4,7,1,5]=>1101010
[6,4,3,8,7,5,1,2]=>1101110
[6,4,3,7,8,5,1,2]=>1100110
[6,3,2,7,4,8,1,5]=>1101010
[6,3,2,5,7,8,1,4]=>1100010
[5,8,2,3,6,1,7,4]=>0100101
[4,5,6,8,3,2,1,7]=>0001110
[4,6,8,5,3,2,1,7]=>0011110
[5,6,1,4,2,3,7,8]=>0101000
[5,6,8,4,3,7,1,2]=>0011010
[5,6,1,4,2,3,8,7]=>0101001
[5,2,8,3,4,1,7,6]=>1010101
[4,5,8,6,3,2,1,7]=>0011110
[4,7,5,6,3,2,1,8]=>0101110
[5,1,4,3,6,2,8,7]=>1010101
[5,1,4,3,8,2,7,6]=>1010101
[5,6,2,4,1,8,7,3]=>0101011
[5,7,2,4,1,8,6,3]=>0101011
[6,1,4,2,8,7,5,3]=>1010111
[5,8,2,4,1,7,6,3]=>0101011
[5,4,1,3,7,2,6,8]=>1100100
[5,8,1,4,2,3,7,6]=>0101001
[5,1,6,3,4,2,7,8]=>1010100
[4,8,6,5,3,2,1,7]=>0111110
[5,4,7,8,3,2,1,6]=>1001110
[4,7,8,5,3,2,1,6]=>0011110
[5,7,1,3,4,2,6,8]=>0100100
[5,1,8,4,2,3,6,7]=>1011000
[5,1,7,4,2,3,6,8]=>1011000
[5,8,1,3,4,2,6,7]=>0100100
[4,8,7,5,3,2,1,6]=>0111110
[4,7,8,6,3,2,1,5]=>0011110
[4,8,2,3,6,7,5,1]=>0100011
[4,8,3,1,6,7,5,2]=>0110011
[4,3,8,1,6,2,5,7]=>1010100
[1,4,8,7,3,5,2,6]=>0011010
[4,3,8,7,2,5,1,6]=>1011010
[5,8,1,4,7,2,6,3]=>0100101
[6,8,1,2,4,3,5,7]=>0100100
[5,8,7,1,3,4,2,6]=>0110010
[4,8,7,6,3,1,2,5]=>0111100
[5,8,4,7,3,1,2,6]=>0101100
[4,3,8,2,7,5,6,1]=>1010101
[1,4,8,3,7,5,6,2]=>0010101
[1,4,3,8,2,6,5,7]=>0101010
[4,1,3,8,2,6,5,7]=>1001010
[4,1,8,7,3,5,2,6]=>1011010
[3,4,8,1,6,2,5,7]=>0010100
[3,4,8,7,2,5,1,6]=>0011010
[3,4,8,2,7,5,6,1]=>0010101
[1,2,4,3,8,6,5,7]=>0010110
[3,4,2,1,8,6,5,7]=>0110110
[3,4,1,8,2,6,5,7]=>0101010
[3,6,7,8,4,1,2,5]=>0001100
[4,1,2,8,3,6,5,7]=>1001010
[1,4,3,2,8,6,5,7]=>0110110
[4,2,3,1,8,6,5,7]=>1010110
[3,7,8,2,6,4,5,1]=>0010101
[4,2,3,8,1,6,5,7]=>1001010
[4,3,1,8,2,6,5,7]=>1101010
[1,4,7,8,5,3,2,6]=>0001110
[4,2,8,6,3,1,5,7]=>1011100
[2,4,8,6,3,1,5,7]=>0011100
[7,3,6,8,4,2,1,5]=>1001110
[1,7,3,8,4,6,5,2]=>0101011
[1,3,4,8,2,6,5,7]=>0001010
[3,2,4,8,1,6,5,7]=>1001010
[7,3,8,2,6,4,5,1]=>1010101
[6,2,8,7,4,3,5,1]=>1011101
[7,4,1,8,5,2,6,3]=>1101101
[7,3,2,8,4,6,5,1]=>1101011
[1,3,4,2,8,6,5,7]=>0010110
[1,3,2,4,8,6,5,7]=>0100110
[3,2,1,4,8,6,5,7]=>1100110
[3,1,2,4,8,6,5,7]=>1000110
[3,1,4,2,8,6,5,7]=>1010110
[3,1,4,8,2,6,5,7]=>1001010
[7,3,4,8,5,1,6,2]=>1001101
[3,7,4,8,5,1,2,6]=>0101100
[6,7,2,8,3,5,4,1]=>0101011
[2,3,1,4,8,6,5,7]=>0100110
[2,1,3,4,8,6,5,7]=>1000110
[3,5,7,8,6,1,2,4]=>0001100
[3,1,5,6,8,2,7,4]=>1000101
[5,1,6,3,8,4,7,2]=>1010101
[2,5,1,6,8,3,7,4]=>0100101
[5,1,2,6,8,3,7,4]=>1000101
[1,5,2,7,8,6,3,4]=>0100110
[6,1,7,5,2,8,3,4]=>1011010
[2,6,7,5,1,8,3,4]=>0011010
[5,7,2,8,6,1,3,4]=>0101100
[3,5,7,8,6,2,1,4]=>0001110
[3,2,5,7,8,6,1,4]=>1000110
[6,2,7,5,1,8,3,4]=>1011010
[1,2,6,7,5,8,3,4]=>0001010
[6,2,7,5,4,1,8,3]=>1011101
[6,7,5,2,4,1,8,3]=>0110101
[6,7,2,5,3,8,1,4]=>0101010
[5,1,7,8,6,3,2,4]=>1001110
[1,6,7,5,3,8,2,4]=>0011010
[1,6,7,5,4,2,8,3]=>0011101
[5,7,8,6,4,1,2,3]=>0011100
[6,7,4,1,5,2,8,3]=>0110101
[1,6,7,4,5,2,8,3]=>0010101
[6,3,1,7,5,8,2,4]=>1101010
[2,5,3,7,8,6,1,4]=>0100110
[6,3,2,7,5,8,1,4]=>1101010
[6,7,4,2,5,1,8,3]=>0110101
[6,2,7,4,5,1,8,3]=>1010101
[6,2,3,7,5,8,1,4]=>1001010
[7,5,1,6,3,8,2,4]=>1101010
[7,5,1,6,3,8,4,2]=>1101011
[2,7,6,1,3,8,4,5]=>0110010
[2,7,6,1,3,8,5,4]=>0110011
[2,6,7,1,5,8,3,4]=>0010010
[2,6,7,4,1,8,3,5]=>0011010
[2,1,6,7,3,8,5,4]=>1001011
[2,6,7,4,1,8,5,3]=>0011011
[2,6,7,1,5,8,4,3]=>0010011
[3,6,5,1,8,4,2,7]=>0110110
[3,7,5,4,8,1,6,2]=>0110101
[3,7,5,4,8,1,2,6]=>0110100
[4,6,1,5,8,7,3,2]=>0100111
[4,6,1,5,8,7,2,3]=>0100110
[4,6,1,5,8,2,7,3]=>0100101
[7,5,1,6,2,8,3,4]=>1101010
[4,6,1,5,8,2,3,7]=>0100100
[4,7,1,5,8,3,6,2]=>0100101
[8,3,4,6,2,1,5,7]=>1001100
[3,5,6,2,1,8,4,7]=>0011010
[7,5,3,2,8,4,1,6]=>1110110
[7,5,3,2,8,4,6,1]=>1110101
[4,2,5,6,8,3,1,7]=>1000110
[5,3,6,8,1,4,2,7]=>1001010
[4,5,6,8,1,3,2,7]=>0001010
[1,4,5,6,8,3,2,7]=>0000110
[4,5,3,7,2,8,6,1]=>0101011
[6,4,7,3,2,8,5,1]=>1011011
[6,1,4,7,3,2,8,5]=>1001101
[5,1,7,3,8,4,2,6]=>1010110
[5,3,7,1,4,8,6,2]=>1010011
[6,4,3,1,7,8,5,2]=>1110011
[5,6,1,3,7,8,4,2]=>0100011
[5,6,1,7,8,3,4,2]=>0100101
[1,6,3,7,4,8,5,2]=>0101011
[6,7,2,4,1,8,5,3]=>0101011
[6,7,2,1,4,3,8,5]=>0110101
[6,4,7,3,1,2,8,5]=>1011001
[5,6,3,1,2,7,8,4]=>0110001
[5,6,1,3,2,7,8,4]=>0101001
[5,6,3,2,1,7,8,4]=>0111001
[5,6,3,2,7,8,4,1]=>0110011
[2,5,6,3,7,8,4,1]=>0010011
[2,5,6,3,1,7,8,4]=>0011001
[2,6,4,7,3,1,8,5]=>0101101
[6,3,7,2,8,4,1,5]=>1010110
[6,3,2,7,1,8,4,5]=>1101010
[7,5,3,2,1,8,4,6]=>1111010
[7,3,8,4,2,1,5,6]=>1011100
[4,7,2,1,3,8,6,5]=>0110011
[1,3,7,8,6,4,2,5]=>0001110
[5,7,3,8,2,1,6,4]=>0101101
[4,6,2,7,8,5,3,1]=>0100111
[2,5,1,7,3,8,6,4]=>0101011
[6,7,2,1,3,8,5,4]=>0110011
[5,1,6,7,8,2,4,3]=>1000101
[6,3,7,1,8,5,2,4]=>1010110
[6,2,1,7,3,8,5,4]=>1101011
[6,2,7,1,8,5,4,3]=>1010111
[6,3,1,7,8,5,4,2]=>1100111
[5,3,2,1,8,4,7,6]=>1110101
[4,5,2,1,3,8,7,6]=>0110011
[3,2,6,4,5,8,1,7]=>1010010
[2,4,6,5,8,1,3,7]=>0010100
[1,3,4,6,5,8,2,7]=>0001010
[1,6,3,4,5,8,2,7]=>0100010
[3,4,1,8,5,2,7,6]=>0101101
[2,8,4,1,7,6,3,5]=>0110110
[1,5,3,2,8,7,4,6]=>0110110
[8,2,1,7,5,3,4,6]=>1101100
[1,7,6,4,5,8,3,2]=>0110011
[5,8,7,4,6,2,1,3]=>0110110
[3,4,2,5,8,6,7,1]=>0100101
[4,1,3,5,6,8,7,2]=>1000011
[2,4,8,6,7,1,3,5]=>0010100
[3,7,4,8,2,1,6,5]=>0101101
[2,3,5,8,6,7,1,4]=>0001010
[3,2,5,6,8,7,1,4]=>1000110
[7,2,4,8,5,3,1,6]=>1001110
[4,8,3,1,2,7,6,5]=>0110011
[8,4,2,3,7,1,5,6]=>1100100
[3,5,2,7,6,1,8,4]=>0101101
[5,8,7,3,4,6,2,1]=>0110011
[5,8,2,7,4,1,6,3]=>0101101
[5,1,4,2,8,7,6,3]=>1010111
[5,2,6,8,7,1,3,4]=>1001100
[6,3,2,1,8,5,7,4]=>1110101
[2,7,5,4,1,8,6,3]=>0111011
[4,2,5,6,8,7,1,3]=>1000110
[1,8,4,2,5,6,7,3]=>0110001
[3,8,4,1,5,6,7,2]=>0110001
[4,2,8,5,6,7,1,3]=>1010010
[5,2,4,7,1,8,6,3]=>1001011
[8,1,3,6,5,2,4,7]=>1001100
[8,3,2,4,6,5,1,7]=>1100110
[8,3,6,4,1,5,2,7]=>1011010
[1,3,4,8,5,7,2,6]=>0001010
[5,8,4,7,6,2,3,1]=>0101101
[1,3,4,7,5,8,2,6]=>0001010
[1,3,5,2,4,8,7,6]=>0010011
[2,6,5,1,3,8,7,4]=>0110011
[2,8,5,1,4,7,6,3]=>0110011
[4,3,1,5,8,6,7,2]=>1100101
[5,4,2,1,6,8,7,3]=>1110011
[6,8,4,3,2,7,1,5]=>0111010
[5,1,3,2,8,6,7,4]=>1010101
[5,3,1,2,8,6,7,4]=>1100101
[5,2,3,1,6,8,7,4]=>1010011
[5,3,2,1,8,6,7,4]=>1110101
[5,2,1,3,6,8,7,4]=>1100011
[2,7,4,5,8,3,1,6]=>0100110
[1,8,4,3,7,2,6,5]=>0110101
[3,4,8,7,2,1,6,5]=>0011101
[5,4,7,8,3,6,2,1]=>1001011
[6,3,8,7,4,1,2,5]=>1011100
[8,4,7,2,3,1,5,6]=>1010100
[8,6,4,1,3,2,7,5]=>1110101
[3,5,7,2,6,1,8,4]=>0010101
[6,1,3,8,5,7,2,4]=>1001010
[2,8,1,5,4,7,6,3]=>0101011
[1,7,2,4,6,5,8,3]=>0100101
[5,8,2,6,1,3,7,4]=>0101001
[6,3,5,8,7,2,1,4]=>1001110
[2,5,7,8,4,1,6,3]=>0001101
[4,1,5,2,6,8,7,3]=>1010011
[4,1,8,5,2,6,7,3]=>1011001
[2,7,1,8,5,4,6,3]=>0101101
[5,8,6,2,1,3,7,4]=>0111001
[3,4,5,1,8,6,7,2]=>0010101
[1,3,2,7,5,8,6,4]=>0101011
[1,4,2,5,8,3,7,6]=>0100101
[4,1,2,6,8,5,3,7]=>1000110
[1,5,2,4,8,7,6,3]=>0100111
[1,2,7,4,8,6,5,3]=>0010111
[1,3,2,8,5,7,4,6]=>0101010
[1,2,6,4,8,7,3,5]=>0010110
[1,3,8,2,6,7,4,5]=>0010010
[1,6,7,8,2,5,3,4]=>0001010
[1,5,7,8,2,3,6,4]=>0001001
[1,2,8,4,7,3,6,5]=>0010101
[1,5,2,4,8,3,7,6]=>0100101
[1,8,3,5,2,7,4,6]=>0101010
[1,4,8,6,7,2,3,5]=>0010100
[1,5,7,8,6,2,3,4]=>0001100
[1,3,7,6,2,8,4,5]=>0011010
[1,2,5,8,7,6,3,4]=>0001110
[1,2,6,8,7,5,3,4]=>0001110
[1,2,7,8,6,5,3,4]=>0001110
[5,2,6,7,3,4,8,1]=>1001001
[5,6,2,1,7,8,3,4]=>0110010
[5,6,2,1,4,8,7,3]=>0110011
[2,6,1,4,5,8,7,3]=>0100011
[5,4,2,7,6,3,8,1]=>1101101
[2,3,7,6,4,5,8,1]=>0011001
[2,6,1,7,5,8,3,4]=>0101010
[5,1,2,7,8,4,3,6]=>1000110
[2,6,1,7,4,8,3,5]=>0101010
[3,6,4,1,7,8,2,5]=>0110010
[5,4,6,1,7,8,2,3]=>1010010
[5,4,6,1,3,8,7,2]=>1010011
[3,6,4,1,5,8,7,2]=>0110011
[2,6,1,5,4,8,7,3]=>0101011
[2,6,1,4,7,8,5,3]=>0100011
[5,1,2,4,8,7,6,3]=>1000111
[2,1,5,3,8,6,4,7]=>1010110
[5,1,2,4,8,6,3,7]=>1000110
[5,6,3,1,4,8,2,7]=>0110010
[2,5,4,3,1,8,6,7]=>0111010
[5,4,6,3,1,8,7,2]=>1011011
[2,1,3,7,8,6,4,5]=>1000110
[5,1,4,2,8,6,7,3]=>1010101
[1,2,3,8,6,7,4,5]=>0001010
[1,2,3,8,7,5,4,6]=>0001110
[1,2,3,8,7,4,5,6]=>0001100
[2,1,3,6,8,7,4,5]=>1000110
[3,1,6,2,8,7,5,4]=>1010111
[6,8,1,3,2,5,4,7]=>0101010
[6,8,1,4,2,5,3,7]=>0101010
[7,8,3,6,1,4,2,5]=>0101010
[7,8,2,5,1,4,3,6]=>0101010
[7,8,1,4,3,6,2,5]=>0101010
[5,8,1,4,3,7,2,6]=>0101010
[6,8,2,5,1,4,3,7]=>0101010
[6,8,2,5,3,7,1,4]=>0101010
[2,5,4,7,6,8,1,3]=>0101010
[2,6,1,4,3,7,5,8]=>0101010
[2,6,1,5,3,7,4,8]=>0101010
[2,6,4,7,5,8,1,3]=>0101010
[5,8,2,6,4,7,1,3]=>0101010
[6,8,3,7,1,4,2,5]=>0101010
[5,8,1,3,2,6,4,7]=>0101010
[5,8,4,7,1,3,2,6]=>0101010
[6,8,4,7,1,3,2,5]=>0101010
[6,8,5,7,1,3,2,4]=>0101010
[5,7,6,8,2,4,1,3]=>0101010
[4,7,5,8,1,3,2,6]=>0101010
[4,7,1,3,2,6,5,8]=>0101010
[3,7,1,4,2,6,5,8]=>0101010
[3,7,6,8,1,4,2,5]=>0101010
[4,7,6,8,2,5,1,3]=>0101010
[4,7,5,8,3,6,1,2]=>0101010
[4,7,5,8,2,6,1,3]=>0101010
[3,7,4,8,2,6,1,5]=>0101010
[3,7,1,5,2,6,4,8]=>0101010
[3,7,2,6,1,5,4,8]=>0101010
[3,7,2,6,5,8,1,4]=>0101010
[4,7,3,6,5,8,1,2]=>0101010
[2,6,5,8,4,7,1,3]=>0101010
[2,6,3,7,1,5,4,8]=>0101010
[7,6,4,8,5,2,3,1]=>1101101
[6,7,4,3,5,1,8,2]=>0110101
[6,7,3,5,4,8,2,1]=>0101011
[6,8,3,7,5,2,4,1]=>0101101
[7,6,3,5,8,2,4,1]=>1100101
[7,6,2,8,4,1,5,3]=>1101101
[7,6,3,4,8,2,5,1]=>1100101
[6,8,3,7,4,5,2,1]=>0101011
[6,7,3,5,8,4,2,1]=>0100111
[5,7,8,3,6,2,1,4]=>0010110
[6,3,4,8,7,2,5,1]=>1001101
[6,3,8,4,7,2,1,5]=>1010110
[6,3,4,7,5,8,2,1]=>1001011
[6,3,5,7,8,4,2,1]=>1000111
[5,7,3,6,8,2,1,4]=>0100110
[5,6,7,3,4,1,8,2]=>0010101
[4,6,7,8,3,5,2,1]=>0001011
[4,7,3,5,6,8,2,1]=>0100011
[5,3,4,7,8,2,1,6]=>1000110
[5,3,8,2,4,1,6,7]=>1010100
[5,3,4,8,2,6,1,7]=>1001010
[4,8,3,6,2,5,7,1]=>0101001
[4,8,3,5,7,2,6,1]=>0100101
[4,8,3,5,6,7,2,1]=>0100011
[4,7,8,3,5,6,2,1]=>0010011
[4,7,8,3,6,2,5,1]=>0010101
[4,8,3,6,7,2,5,1]=>0100101
[4,8,3,7,2,5,6,1]=>0101001
[5,8,3,7,2,6,4,1]=>0101011
[5,7,3,4,8,2,1,6]=>0100110
[5,8,4,2,3,1,6,7]=>0110100
[5,8,4,2,3,1,7,6]=>0110101
[6,4,8,5,3,7,2,1]=>1011011
[6,4,2,7,3,1,8,5]=>1101101
[6,4,3,7,8,5,2,1]=>1100111
[6,4,5,3,7,1,8,2]=>1010101
[5,7,4,2,3,1,6,8]=>0110100
[5,6,3,7,1,8,2,4]=>0101010
[5,6,3,4,8,2,1,7]=>0100110
[6,3,5,7,4,8,2,1]=>1001011
[6,3,5,4,7,8,2,1]=>1010011
[6,4,3,5,7,1,8,2]=>1100101
[6,4,2,5,1,7,3,8]=>1101010
[5,3,4,7,2,6,1,8]=>1001010
[4,7,3,6,2,5,8,1]=>0101001
[4,7,3,6,8,2,5,1]=>0100101
[4,6,7,3,5,8,2,1]=>0010011
[4,5,7,8,3,6,2,1]=>0001011
[4,5,8,3,7,2,6,1]=>0010101
[5,3,4,6,8,2,1,7]=>1000110
[5,3,6,7,1,8,2,4]=>1001010
[5,3,4,6,7,1,8,2]=>1000101
[4,6,3,5,7,8,2,1]=>0100011
[4,5,7,3,6,8,2,1]=>0010011
[7,1,5,8,4,2,3,6]=>1001100
[8,1,5,7,4,2,3,6]=>1001100
[7,1,4,5,8,2,3,6]=>1000100
[7,4,1,6,2,8,3,5]=>1101010
[8,4,1,7,2,6,3,5]=>1101010
[8,1,4,7,5,2,3,6]=>1001100
[8,1,5,4,7,2,3,6]=>1010100
[2,1,7,5,8,3,4,6]=>1010100
[7,1,5,4,8,2,3,6]=>1010100
[7,1,4,8,5,2,3,6]=>1001100
[7,8,3,1,2,4,6,5]=>0110001
[8,7,1,6,4,2,3,5]=>1101100
[8,6,1,7,4,2,3,5]=>1101100
[7,6,1,8,4,2,3,5]=>1101100
[7,3,8,1,2,4,6,5]=>1010001
[8,3,7,1,2,4,6,5]=>1010001
[8,3,6,1,2,4,7,5]=>1010001
[8,3,7,5,1,2,4,6]=>1011000
[7,3,6,1,2,4,8,5]=>1010001
[6,7,1,8,4,2,3,5]=>0101100
[6,8,1,7,4,2,3,5]=>0101100
[7,1,8,4,5,2,3,6]=>1010100
[7,6,3,1,2,4,8,5]=>1110001
[6,1,2,3,8,7,5,4]=>1000111
[6,8,3,1,2,7,4,5]=>0110010
[6,7,3,1,2,8,4,5]=>0110010
[6,7,1,4,2,3,8,5]=>0101001
[4,3,6,8,5,7,1,2]=>1001010
[6,1,2,5,4,8,3,7]=>1001010
[3,2,8,5,4,1,7,6]=>1011101
[7,8,2,1,4,6,3,5]=>0110010
[2,4,8,5,1,3,6,7]=>0011000
[3,5,6,1,8,4,2,7]=>0010110
[1,3,6,8,7,4,2,5]=>0001110
[1,2,8,5,7,3,4,6]=>0010100
[3,1,5,6,4,8,7,2]=>1001011
[1,3,6,2,5,7,8,4]=>0010001
[3,6,1,4,2,7,8,5]=>0101001
[1,3,6,5,2,7,8,4]=>0011001
[1,2,6,4,3,8,5,7]=>0011010
[1,2,6,3,5,8,7,4]=>0010011
[2,3,5,1,8,4,7,6]=>0010101
[1,2,7,4,6,8,3,5]=>0010010
[2,3,7,5,1,8,4,6]=>0011010
[4,7,2,5,3,8,6,1]=>0101011
[3,1,7,5,4,8,6,2]=>1011011
[1,2,7,6,4,8,5,3]=>0011011
[1,2,7,3,6,8,5,4]=>0010011
[3,1,5,4,8,7,6,2]=>1010111
[1,2,6,8,5,4,7,3]=>0001101
[3,5,7,4,8,2,1,6]=>0010110
[2,4,7,6,8,3,1,5]=>0010110
[1,4,6,8,3,5,2,7]=>0001010
[1,3,6,8,5,2,4,7]=>0001100
[1,2,6,8,5,4,3,7]=>0001110
[1,2,5,8,4,3,7,6]=>0001101
[1,3,6,8,2,5,4,7]=>0001010
[1,4,6,8,3,2,5,7]=>0001100
[2,3,6,5,8,1,7,4]=>0010101
[3,5,4,6,8,2,1,7]=>0100110
[3,5,4,6,8,1,2,7]=>0100100
[1,2,4,7,5,8,3,6]=>0001010
[3,6,4,7,1,8,5,2]=>0101011
[1,2,6,7,3,8,5,4]=>0001011
[1,2,5,7,3,8,6,4]=>0001011
[3,1,5,7,6,8,4,2]=>1001011
[3,5,4,6,8,2,7,1]=>0100101
[4,2,6,1,8,7,5,3]=>1010111
[1,2,7,4,6,8,5,3]=>0010011
[1,2,7,5,6,8,4,3]=>0010011
[3,1,6,7,5,8,4,2]=>1001011
[4,6,2,7,5,8,3,1]=>0101011
[3,5,7,4,8,2,6,1]=>0010101
[1,3,6,8,2,5,7,4]=>0001001
[1,3,5,8,2,7,4,6]=>0001010
[1,2,5,8,4,7,6,3]=>0001011
[1,2,4,8,7,3,6,5]=>0001101
[1,2,5,8,7,4,3,6]=>0001110
[1,3,5,8,7,2,4,6]=>0001100
[2,3,7,6,8,5,1,4]=>0010110
[5,7,1,2,8,6,4,3]=>0100111
[3,1,7,6,8,5,4,2]=>1010111
[1,2,6,8,5,7,4,3]=>0001011
[1,2,5,8,7,4,6,3]=>0001101
[1,2,4,8,7,6,3,5]=>0001110
[3,2,7,4,6,8,1,5]=>1010010
[5,3,6,2,7,1,4,8]=>1010100
[2,6,3,4,7,1,5,8]=>0100100
[2,7,3,4,5,8,1,6]=>0100010
[4,7,6,2,3,8,1,5]=>0110010
[7,3,5,2,4,8,1,6]=>1010010
[7,6,2,4,5,8,1,3]=>1100010
[6,5,2,3,4,8,1,7]=>1100010
[5,3,1,2,8,4,7,6]=>1100101
[6,5,2,3,7,1,4,8]=>1100100
[5,2,1,7,3,4,6,8]=>1101000
[5,2,1,8,3,4,6,7]=>1101000
[6,3,2,8,4,5,7,1]=>1101001
[7,3,1,2,8,4,6,5]=>1100101
[6,2,3,1,8,4,7,5]=>1010101
[8,3,5,2,7,1,4,6]=>1010100
[8,6,2,4,7,1,5,3]=>1100101
[8,2,1,7,3,4,5,6]=>1101000
[8,6,3,7,2,4,5,1]=>1101001
[8,2,7,3,4,5,6,1]=>1010001
[8,1,6,2,3,4,5,7]=>1010000
[8,1,7,3,4,5,6,2]=>1010001
[8,6,1,7,2,4,5,3]=>1101001
[1,7,5,8,2,3,6,4]=>0101001
[7,2,1,8,3,4,5,6]=>1101000
[1,7,8,3,4,5,6,2]=>0010001
[1,6,2,8,4,5,7,3]=>0101001
[4,1,3,6,8,2,7,5]=>1000101
[4,6,3,8,7,1,2,5]=>0101100
[6,4,5,8,7,1,2,3]=>1001100
[5,3,4,8,7,1,2,6]=>1001100
[3,2,8,7,1,4,6,5]=>1011001
[3,1,8,7,2,4,6,5]=>1011001
[5,3,7,6,1,2,4,8]=>1011000
[1,8,3,7,2,4,5,6]=>0101000
[3,8,1,7,2,4,5,6]=>0101000
[6,8,2,3,5,1,4,7]=>0100100
[4,7,8,2,6,1,3,5]=>0010100
[6,2,8,7,1,4,5,3]=>1011001
[3,8,7,1,4,5,6,2]=>0110001
[2,8,6,1,3,4,5,7]=>0110000
[2,7,6,1,3,4,5,8]=>0110000
[1,7,6,2,3,4,5,8]=>0110000
[1,8,6,2,3,4,5,7]=>0110000
[2,8,7,3,4,5,6,1]=>0110001
[3,8,7,2,4,5,6,1]=>0110001
[7,8,3,6,2,4,5,1]=>0101001
[1,5,8,7,2,3,6,4]=>0011001
[1,7,3,6,5,2,8,4]=>0101101
[8,6,2,5,4,1,7,3]=>1101101
[3,2,6,4,7,5,1,8]=>1010110
[6,2,3,7,5,4,1,8]=>1001110
[1,3,4,7,6,2,8,5]=>0001101
[2,8,3,6,1,7,5,4]=>0101011
[8,7,2,5,1,6,4,3]=>1101011
[3,8,2,6,5,1,7,4]=>0101101
[7,8,2,5,4,1,6,3]=>0101101
[4,8,5,2,6,1,7,3]=>0110101
[4,5,1,3,7,2,8,6]=>0100101
[6,1,3,7,5,2,8,4]=>1001101
[7,1,3,6,2,8,5,4]=>1001011
[8,1,3,6,2,7,5,4]=>1001011
[1,2,4,7,3,8,6,5]=>0001011
[7,1,8,2,6,5,4,3]=>1010111
[4,1,7,8,2,6,5,3]=>1001011
[3,4,8,6,5,1,7,2]=>0011101
[8,3,7,5,1,6,4,2]=>1011011
[1,4,8,6,2,7,5,3]=>0011011
[8,4,6,7,1,5,3,2]=>1001011
[3,4,6,5,1,2,8,7]=>0011001
[7,3,5,1,2,8,6,4]=>1010011
[1,4,6,2,3,8,7,5]=>0010011
[1,3,2,7,4,8,6,5]=>0101011
[7,2,1,6,3,8,5,4]=>1101011
[4,5,2,1,7,3,8,6]=>0110101
[5,6,7,1,2,8,4,3]=>0010011
[4,7,5,1,2,8,6,3]=>0110011
[3,7,1,6,2,8,5,4]=>0101011
[7,6,1,2,8,5,4,3]=>1100111
[2,7,1,3,8,6,5,4]=>0100111
[8,6,1,2,7,5,4,3]=>1100111
[1,7,2,3,8,6,5,4]=>0100111
[8,7,1,2,6,5,4,3]=>1100111
[7,8,1,2,6,5,4,3]=>0100111
[3,8,1,6,2,7,5,4]=>0101011
[4,8,5,1,2,7,6,3]=>0110011
[1,8,2,7,4,3,5,6]=>0101100
[1,8,6,4,7,2,3,5]=>0110100
[1,8,4,2,6,3,5,7]=>0110100
[7,4,8,1,5,2,3,6]=>1010100
[4,1,7,2,6,3,5,8]=>1010100
[5,1,7,4,3,6,2,8]=>1011010
[1,8,5,4,3,7,2,6]=>0111010
[1,8,4,2,5,3,7,6]=>0110101
[1,8,5,4,2,6,7,3]=>0111001
[7,4,8,2,1,3,5,6]=>1011000
[4,1,7,3,2,5,6,8]=>1011000
[7,5,4,8,2,3,6,1]=>1101001
[7,3,8,1,5,6,2,4]=>1010010
[3,1,7,2,6,8,4,5]=>1010010
[5,1,7,4,2,6,8,3]=>1011001
[4,3,1,6,2,5,7,8]=>1101000
[6,5,4,3,7,1,8,2]=>1110101
[6,3,2,8,5,7,1,4]=>1101010
[5,4,8,2,1,7,3,6]=>1011010
[7,2,8,6,3,1,4,5]=>1011100
[2,1,7,8,3,6,4,5]=>1001010
[4,2,1,6,7,3,5,8]=>1100100
[4,3,1,5,2,7,6,8]=>1101010
[5,4,2,7,3,8,1,6]=>1101010
[3,1,6,2,8,7,4,5]=>1010110
[6,3,1,7,8,5,2,4]=>1100110
[6,5,4,1,7,8,3,2]=>1110011
[5,4,3,1,6,7,2,8]=>1110010
[5,4,2,6,3,8,7,1]=>1101011
[4,3,1,5,2,6,8,7]=>1101001
[5,4,2,1,6,7,8,3]=>1110001
[5,4,3,1,6,7,8,2]=>1110001
[7,8,2,4,5,1,3,6]=>0100100
[4,6,7,2,5,1,3,8]=>0010100
[7,8,1,3,2,4,5,6]=>0101000
[7,8,4,1,5,2,3,6]=>0110100
[3,6,7,2,1,4,5,8]=>0011000
[5,2,3,6,1,4,7,8]=>1001000
[2,5,3,6,1,4,7,8]=>0101000
[6,4,7,1,5,2,3,8]=>1010100
[6,2,7,3,1,4,5,8]=>1011000
[3,5,4,6,7,8,1,2]=>0100010
[1,5,4,6,7,2,3,8]=>0100100
[1,6,7,3,2,4,5,8]=>0011000
[1,5,3,6,2,4,7,8]=>0101000
[5,1,3,6,2,4,7,8]=>1001000
[5,2,4,6,7,1,3,8]=>1000100
[2,6,7,4,5,1,3,8]=>0010100
[4,2,5,6,7,1,3,8]=>1000100
[4,5,2,6,7,1,3,8]=>0100100
[5,3,1,6,2,4,7,8]=>1101000
[6,1,7,3,2,4,5,8]=>1011000
[6,1,7,4,5,2,3,8]=>1010100
[6,3,7,4,5,8,1,2]=>1010010
[5,4,1,6,7,2,3,8]=>1100100
[5,2,1,6,3,4,7,8]=>1101000
[1,3,6,7,5,2,8,4]=>0001101
[7,3,4,1,6,2,5,8]=>1010100
[7,3,4,1,6,5,2,8]=>1010110
[7,3,4,1,5,2,6,8]=>1010100
[1,3,6,7,2,5,8,4]=>0001001
[4,3,1,7,2,6,8,5]=>1101001
[5,6,1,4,7,3,8,2]=>0100101
[5,3,2,1,7,4,8,6]=>1110101
[1,3,4,5,8,7,2,6]=>0000110
[6,3,4,5,8,1,7,2]=>1000101
[2,4,5,1,6,8,7,3]=>0010011
[3,1,2,5,6,8,7,4]=>1000011
[4,3,2,5,6,8,1,7]=>1100010
[3,1,4,6,5,8,2,7]=>1001010
[2,3,4,5,8,6,1,7]=>0000110
[4,3,1,7,6,5,8,2]=>1101101
[1,4,5,2,6,8,7,3]=>0010011
[3,7,5,2,6,8,1,4]=>0110010
[3,7,5,2,6,8,4,1]=>0110011
[5,6,1,2,7,4,8,3]=>0100101
[6,3,5,2,4,7,8,1]=>1010001
[5,3,2,1,4,7,8,6]=>1110001
[5,3,1,4,2,7,8,6]=>1101001
[5,3,1,2,4,7,8,6]=>1100001
[7,1,5,2,6,8,4,3]=>1010011
[7,1,5,2,6,8,3,4]=>1010010
[1,7,4,6,5,8,3,2]=>0101011
[2,7,4,6,1,8,3,5]=>0101010
[2,7,4,6,1,8,5,3]=>0101011
[2,3,6,7,1,5,8,4]=>0001001
[2,3,6,7,5,1,8,4]=>0001101
[4,3,2,6,7,1,8,5]=>1100101
[7,3,2,5,6,8,1,4]=>1100010
[7,1,5,4,6,8,2,3]=>1010010
[2,7,4,6,5,8,1,3]=>0101010
[7,3,4,5,8,1,2,6]=>1000100
[1,3,4,5,8,6,2,7]=>0000110
[1,3,4,5,8,2,7,6]=>0000101
[7,1,5,4,6,8,3,2]=>1010011
[7,3,2,5,6,8,4,1]=>1100011
[5,7,4,6,1,8,3,2]=>0101011
[6,3,4,5,8,1,2,7]=>1000100
[7,3,4,5,8,2,6,1]=>1000101
[4,2,1,8,3,6,7,5]=>1101001
[6,2,1,7,3,5,8,4]=>1101001
[2,7,3,1,4,8,5,6]=>0110010
[3,2,1,5,7,8,4,6]=>1100010
[4,3,6,8,5,1,7,2]=>1001101
[2,1,6,8,3,7,4,5]=>1001010
[3,2,1,5,6,8,4,7]=>1100010
[2,4,7,1,8,5,3,6]=>0010110
[2,4,8,5,1,6,3,7]=>0011010
[6,2,1,7,3,4,8,5]=>1101001
[6,2,1,7,8,3,5,4]=>1100101
[3,2,1,6,7,4,5,8]=>1100100
[2,4,8,5,1,6,7,3]=>0011001
[3,2,1,8,4,5,6,7]=>1101000
[1,6,8,3,7,2,4,5]=>0010100
[3,8,1,5,7,2,4,6]=>0100100
[1,2,6,8,4,7,3,5]=>0001010
[6,1,5,8,2,4,7,3]=>1001001
[1,2,4,8,3,6,7,5]=>0001001
[4,1,2,7,8,3,6,5]=>1000101
[5,3,8,4,7,6,1,2]=>1010110
[8,7,1,2,5,4,6,3]=>1100101
[5,8,1,2,3,7,6,4]=>0100011
[1,2,8,4,3,5,7,6]=>0011001
[1,2,5,3,7,6,4,8]=>0010110
[6,1,2,8,7,4,5,3]=>1001101
[7,1,6,2,8,4,5,3]=>1010101
[1,2,6,3,8,5,4,7]=>0010110
[1,2,8,5,3,6,4,7]=>0011010
[1,2,7,3,8,5,4,6]=>0010110
[1,6,2,8,4,3,5,7]=>0101100
[1,6,4,2,7,3,5,8]=>0110100
[1,8,6,3,2,4,5,7]=>0111000
[3,1,7,8,6,2,4,5]=>1001100
[1,8,7,3,5,6,2,4]=>0110010
[1,3,2,8,7,4,5,6]=>0101100
[1,2,8,4,3,7,5,6]=>0011010
[8,5,1,7,2,4,6,3]=>1101001
[3,8,6,4,7,5,1,2]=>0110110
[6,1,8,2,7,4,5,3]=>1010101
[1,2,7,5,3,6,4,8]=>0011010
[1,2,6,3,7,5,4,8]=>0010110
[1,2,3,7,5,4,8,6]=>0001101
[3,7,4,8,6,5,1,2]=>0101110
[1,8,2,7,6,4,5,3]=>0101101
[7,4,6,3,8,5,1,2]=>1010110
[8,4,6,2,7,5,3,1]=>1010111
[6,5,7,8,4,1,3,2]=>1001101
[7,5,6,8,2,4,1,3]=>1001010
[7,4,6,2,8,5,1,3]=>1010110
[4,3,2,6,8,5,1,7]=>1100110
[3,5,6,8,2,4,1,7]=>0001010
[2,6,7,8,1,4,5,3]=>0001001
[3,6,7,8,1,4,2,5]=>0001010
[3,5,7,8,2,1,4,6]=>0001100
[2,6,7,8,1,4,3,5]=>0001010
[2,5,7,8,3,1,4,6]=>0001100
[2,4,7,3,8,1,5,6]=>0010100
[6,4,7,3,8,1,5,2]=>1010101
[6,4,7,3,8,1,2,5]=>1010100
[7,4,6,3,8,2,1,5]=>1010110
[6,3,2,5,4,8,1,7]=>1101010
[6,4,5,2,3,8,1,7]=>1010010
[5,4,6,3,8,2,1,7]=>1010110
[5,4,7,3,8,1,6,2]=>1010101
[2,5,7,8,3,1,6,4]=>0001101
[4,5,7,8,3,1,2,6]=>0001100
[4,5,6,8,2,3,1,7]=>0001010
[5,4,6,2,8,3,1,7]=>1010110
[5,3,2,6,8,4,1,7]=>1100110
[5,4,7,2,8,1,3,6]=>1010100
[4,5,7,8,2,1,3,6]=>0001100
[4,6,7,8,1,3,2,5]=>0001010
[4,6,7,8,1,3,5,2]=>0001001
[2,6,7,8,1,3,5,4]=>0001001
[2,6,7,8,1,5,3,4]=>0001010
[4,6,7,8,1,5,2,3]=>0001010
[4,6,7,8,1,2,5,3]=>0001001
[5,3,2,7,8,1,6,4]=>1100101
[4,3,2,7,8,1,6,5]=>1100101
[3,5,7,8,2,1,6,4]=>0001101
[3,6,7,8,1,5,4,2]=>0001011
[2,6,7,8,1,5,4,3]=>0001011
[4,5,8,3,6,7,1,2]=>0010010
[4,5,8,3,7,6,1,2]=>0010110
[4,2,8,3,7,1,6,5]=>1010101
[7,2,3,4,8,1,5,6]=>1000100
[7,6,3,4,8,5,1,2]=>1100110
[7,6,3,5,8,4,1,2]=>1100110
[7,6,3,8,4,5,1,2]=>1101010
[7,2,3,8,5,1,4,6]=>1001100
[2,6,4,8,1,5,7,3]=>0101001
[7,2,3,8,4,1,5,6]=>1001100
[7,8,2,3,6,1,4,5]=>0100100
[4,2,6,3,7,1,5,8]=>1010100
[7,2,3,5,8,1,6,4]=>1000101
[7,2,3,8,4,1,6,5]=>1001101
[2,6,4,8,1,3,7,5]=>0101001
[3,6,4,8,1,7,5,2]=>0101011
[7,6,5,1,2,3,8,4]=>1110001
[7,6,5,1,4,2,8,3]=>1110101
[7,8,5,4,1,2,6,3]=>0111001
[3,5,6,4,1,2,8,7]=>0011001
[7,6,5,1,2,4,3,8]=>1110010
[7,6,5,1,2,4,8,3]=>1110001
[7,6,5,1,3,2,4,8]=>1110100
[2,6,4,3,1,8,7,5]=>0111011
[3,5,8,4,1,2,7,6]=>0011001
[3,5,8,4,1,2,6,7]=>0011000
[3,5,8,4,1,6,2,7]=>0011010
[2,5,8,4,1,7,3,6]=>0011010
[3,6,4,2,1,7,5,8]=>0111010
[3,5,6,4,1,8,7,2]=>0011011
[2,6,4,5,1,3,7,8]=>0101000
[7,6,5,1,4,3,8,2]=>1110101
[7,6,5,1,2,8,3,4]=>1110010
[7,6,5,1,8,2,4,3]=>1110101
[7,6,5,1,8,2,3,4]=>1110100
[7,6,5,1,8,3,2,4]=>1110110
[7,6,5,1,4,8,2,3]=>1110010
[3,6,4,5,1,7,2,8]=>0101010
[2,5,6,4,1,7,8,3]=>0011001
[2,5,6,4,1,7,3,8]=>0011010
[3,6,4,5,1,7,8,2]=>0101001
[7,6,5,1,4,8,3,2]=>1110011
[7,6,5,1,8,3,4,2]=>1110101
[7,6,5,1,8,4,2,3]=>1110110
[6,7,4,2,5,3,1,8]=>0110110
[7,6,4,8,3,1,5,2]=>1101101
[7,4,8,5,6,1,3,2]=>1010101
[7,4,2,5,6,3,1,8]=>1100110
[4,2,7,5,6,3,1,8]=>1010110
[4,7,3,5,6,2,1,8]=>0100110
[1,6,8,5,2,7,4,3]=>0011011
[6,2,8,5,1,7,4,3]=>1011011
[6,7,4,8,2,1,5,3]=>0101101
[3,2,7,8,6,1,5,4]=>1001101
[6,8,4,1,2,3,7,5]=>0110001
[1,8,2,5,6,4,3,7]=>0100110
[6,1,8,5,3,7,4,2]=>1011011
[3,8,1,5,2,7,6,4]=>0101011
[8,2,1,5,3,7,6,4]=>1101011
[8,1,6,5,3,7,2,4]=>1011010
[7,1,4,6,3,2,8,5]=>1001101
[3,2,6,4,1,7,8,5]=>1011001
[7,6,4,3,1,2,8,5]=>1111001
[8,6,3,5,1,7,2,4]=>1101010
[4,5,3,1,6,7,8,2]=>0110001
[3,5,2,1,6,7,8,4]=>0110001
[5,2,3,1,6,7,8,4]=>1010001
[1,5,3,2,6,7,8,4]=>0110001
[8,2,7,5,6,1,3,4]=>1010100
[1,7,4,6,2,3,8,5]=>0101001
[7,6,4,2,1,5,8,3]=>1111001
[5,7,4,6,1,3,8,2]=>0101001
[8,6,4,7,3,1,2,5]=>1101100
[5,2,4,3,7,1,8,6]=>1010101
[8,6,4,1,3,5,2,7]=>1110010
[6,7,4,1,5,3,8,2]=>0110101
[7,5,4,1,2,6,8,3]=>1110001
[1,8,2,5,3,7,6,4]=>0101011
[3,8,1,5,6,4,2,7]=>0100110
[7,6,4,1,5,2,8,3]=>1110101
[8,6,1,5,4,7,2,3]=>1101010
[5,2,1,4,6,7,8,3]=>1100001
[5,4,1,3,6,7,8,2]=>1100001
[8,4,1,5,3,7,2,6]=>1101010
[7,5,4,1,3,2,8,6]=>1110101
[3,2,5,1,4,7,8,6]=>1010001
[5,1,3,4,6,7,8,2]=>1000001
[3,8,1,7,5,6,4,2]=>0101011
[8,2,5,7,3,6,4,1]=>1001011
[1,8,6,7,5,3,4,2]=>0101101
[8,2,6,7,5,3,4,1]=>1001101
[5,4,8,6,2,3,7,1]=>1011001
[2,7,6,1,3,5,4,8]=>0110010
[2,8,6,1,3,5,4,7]=>0110010
[5,7,4,1,8,6,3,2]=>0110111
[5,6,4,2,8,3,7,1]=>0110101
[5,6,4,2,7,3,1,8]=>0110110
[5,8,1,4,6,3,7,2]=>0100101
[3,6,7,4,5,8,2,1]=>0010011
[5,4,6,1,7,8,3,2]=>1010011
[5,6,4,1,8,7,3,2]=>0110111
[3,5,8,4,6,7,2,1]=>0010011
[3,6,8,4,5,7,2,1]=>0010011
[3,7,8,4,5,6,2,1]=>0010011
[3,7,1,5,4,6,2,8]=>0101010
[3,8,1,5,4,6,7,2]=>0101001
[3,7,1,5,4,6,8,2]=>0101001
[6,7,1,4,5,3,8,2]=>0100101
[5,7,1,4,6,3,8,2]=>0100101
[5,4,7,2,8,3,1,6]=>1010110
[5,4,7,2,8,3,6,1]=>1010101
[5,6,4,2,8,3,1,7]=>0110110
[5,8,1,4,6,3,2,7]=>0100110
[3,8,1,5,4,6,2,7]=>0101010
[3,6,1,5,4,2,7,8]=>0101100
[3,6,1,5,4,8,2,7]=>0101010
[6,8,3,1,4,2,5,7]=>0110100
[7,3,8,1,4,2,5,6]=>1010100
[3,6,1,5,4,7,8,2]=>0101001
[3,4,1,2,7,6,5,8]=>0100110
[3,4,1,2,6,8,7,5]=>0100011
[7,8,1,4,5,3,2,6]=>0100110
[3,8,1,5,4,7,2,6]=>0101010
[3,6,1,5,4,8,7,2]=>0101011
[3,6,1,5,4,7,2,8]=>0101010
[6,7,3,1,4,2,5,8]=>0110100
[6,8,3,1,4,2,7,5]=>0110101
[7,8,3,1,4,6,2,5]=>0110010
[7,8,4,2,6,5,1,3]=>0110110
[6,5,8,7,3,4,2,1]=>1011011
[7,8,3,1,4,6,5,2]=>0110011
[6,7,3,1,4,5,2,8]=>0110010
[3,7,1,5,4,2,6,8]=>0101100
[3,8,1,5,4,2,7,6]=>0101101
[5,8,1,4,7,3,6,2]=>0100101
[6,3,7,1,4,8,5,2]=>1010011
[3,7,1,5,4,8,6,2]=>0101011
[3,7,1,5,4,2,8,6]=>0101101
[6,7,3,1,4,5,8,2]=>0110001
[7,3,8,1,4,5,2,6]=>1010010
[6,8,3,1,4,5,2,7]=>0110010
[3,8,1,5,4,2,6,7]=>0101100
[2,3,5,4,1,8,6,7]=>0011010
[2,3,6,4,8,1,5,7]=>0010100
[1,8,4,6,3,5,2,7]=>0101010
[5,4,8,6,2,1,3,7]=>1011100
[2,3,6,8,1,5,4,7]=>0001010
[2,5,6,1,4,7,8,3]=>0010001
[2,5,6,1,4,7,3,8]=>0010010
[2,7,6,1,8,5,4,3]=>0110111
[2,7,6,8,1,4,5,3]=>0101001
[5,7,8,6,2,3,4,1]=>0011001
[2,7,6,1,8,5,3,4]=>0110110
[6,3,5,1,7,2,4,8]=>1010100
[2,3,4,7,6,1,5,8]=>0001100
[7,3,5,8,4,1,2,6]=>1001100
[1,8,4,5,2,7,3,6]=>0101010
[1,8,4,5,2,7,6,3]=>0101011
[7,3,5,8,4,1,6,2]=>1001101
[2,7,6,4,8,5,1,3]=>0110110
[7,3,5,4,6,8,1,2]=>1010010
[6,3,5,4,7,1,8,2]=>1010101
[6,3,5,4,7,1,2,8]=>1010100
[3,7,1,6,8,5,2,4]=>0100110
[2,3,1,8,6,4,7,5]=>0101101
[1,8,4,3,6,2,5,7]=>0110100
[2,3,1,8,6,4,5,7]=>0101100
[3,7,1,6,8,5,4,2]=>0100111
[6,3,5,4,7,2,1,8]=>1010110
[7,3,5,4,6,8,2,1]=>1010011
[2,7,6,4,8,5,3,1]=>0110111
[1,8,4,5,2,6,3,7]=>0101010
[6,4,8,5,3,1,2,7]=>1011100
[7,3,5,8,4,6,2,1]=>1001011
[2,3,4,6,5,8,1,7]=>0001010
[2,3,4,7,5,1,8,6]=>0001101
[2,3,4,7,5,1,6,8]=>0001100
[2,3,4,7,1,6,5,8]=>0001010
[2,3,4,7,1,6,8,5]=>0001001
[2,3,4,6,1,8,7,5]=>0001011
[6,3,5,8,4,2,7,1]=>1001101
[1,8,4,5,2,3,6,7]=>0101000
[7,4,8,5,3,2,6,1]=>1011101
[3,4,8,7,5,2,6,1]=>0011101
[3,2,8,6,1,5,4,7]=>1011010
[8,7,3,6,4,2,5,1]=>1101101
[3,8,7,2,5,4,6,1]=>0110101
[8,7,2,4,5,6,3,1]=>1100011
[5,3,6,2,4,8,7,1]=>1010011
[3,5,2,8,6,1,4,7]=>0101100
[3,7,2,5,1,4,8,6]=>0101001
[5,1,8,6,2,3,4,7]=>1011000
[2,5,4,1,8,6,3,7]=>0110110
[3,7,6,1,8,2,5,4]=>0110101
[8,2,3,6,1,4,7,5]=>1001001
[1,8,2,6,3,4,7,5]=>0101001
[7,1,3,6,4,8,2,5]=>1001010
[8,2,1,3,5,7,4,6]=>1100010
[7,5,4,1,3,8,2,6]=>1110010
[7,3,8,5,4,1,2,6]=>1011100
[7,2,3,6,1,4,8,5]=>1001001
[1,3,7,2,5,8,4,6]=>0010010
[1,7,2,3,5,8,4,6]=>0100010
[7,4,8,1,3,6,2,5]=>1010010
[8,6,1,4,7,3,2,5]=>1100110
[2,6,3,7,1,4,8,5]=>0101001
[2,6,3,8,1,4,7,5]=>0101001
[7,5,4,8,1,3,2,6]=>1101010
[8,5,4,7,1,3,2,6]=>1101010
[2,3,1,8,5,4,6,7]=>0101100
[8,5,1,7,6,3,4,2]=>1101101
[3,4,7,6,1,8,5,2]=>0011011
[3,5,2,6,7,1,8,4]=>0100101
[3,2,8,4,7,5,1,6]=>1010110
[8,4,7,5,1,3,2,6]=>1011010
[6,8,3,1,7,2,4,5]=>0110100
[3,7,2,5,6,1,8,4]=>0100101
[6,8,4,2,5,1,7,3]=>0110101
[2,7,5,3,8,4,1,6]=>0110110
[8,3,1,4,7,2,6,5]=>1100101
[8,3,2,1,5,7,4,6]=>1110010
[2,8,3,6,4,7,1,5]=>0101010
[7,3,6,4,8,1,2,5]=>1010100
[8,3,6,4,7,1,2,5]=>1010100
[1,2,8,3,5,7,4,6]=>0010010
[1,8,3,2,5,7,4,6]=>0110010
[6,5,1,7,4,2,8,3]=>1101101
[7,3,6,4,8,2,1,5]=>1010110
[4,6,1,7,3,5,2,8]=>0101010
[5,6,1,7,3,4,2,8]=>0101010
[6,1,7,3,4,2,8,5]=>1010101
[7,3,8,1,6,5,2,4]=>1010110
[8,3,7,1,6,5,2,4]=>1010110
[2,8,1,7,6,5,3,4]=>0101110
[4,2,8,6,5,1,7,3]=>1011101
[8,6,4,7,1,5,2,3]=>1101010
[7,6,4,8,1,5,2,3]=>1101010
[5,1,6,4,2,3,8,7]=>1011001
[4,2,3,8,7,5,1,6]=>1001110
[3,8,7,1,6,5,2,4]=>0110110
[2,4,3,8,1,6,7,5]=>0101001
[2,4,3,7,1,6,8,5]=>0101001
[4,2,3,7,8,5,1,6]=>1000110
[5,1,6,4,2,3,7,8]=>1011000
[6,4,7,8,1,5,2,3]=>1001010
[8,7,4,6,1,5,2,3]=>1101010
[6,5,7,8,1,4,2,3]=>1001010
[4,7,8,6,1,5,2,3]=>0011010
[3,2,4,8,7,1,5,6]=>1001100
[4,8,7,6,1,5,2,3]=>0111010
[5,8,7,6,1,4,2,3]=>0111010
[8,6,5,7,1,4,2,3]=>1101010
[5,1,6,7,4,2,3,8]=>1001100
[6,7,4,8,1,5,2,3]=>0101010
[8,4,7,6,1,5,2,3]=>1011010
[8,3,2,4,7,1,5,6]=>1100100
[7,3,2,4,8,1,5,6]=>1100100
[2,5,3,7,1,6,4,8]=>0101010
[8,4,6,7,1,5,2,3]=>1001010
[5,1,6,8,4,2,3,7]=>1001100
[4,2,3,7,5,1,6,8]=>1001100
[2,4,3,7,1,6,5,8]=>0101010
[2,4,7,1,5,8,6,3]=>0010011
[3,2,4,7,6,1,5,8]=>1001100
[4,7,6,8,1,5,2,3]=>0101010
[8,5,6,7,1,4,2,3]=>1001010
[8,6,7,5,1,4,2,3]=>1011010
[6,8,7,5,1,4,2,3]=>0111010
[5,6,8,7,1,4,2,3]=>0011010
[4,6,8,7,1,5,2,3]=>0011010
[3,2,4,6,1,5,7,8]=>1001000
[6,7,8,5,1,4,2,3]=>0011010
[7,8,6,5,1,4,2,3]=>0111010
[2,1,8,5,4,6,3,7]=>1011010
[4,1,8,5,2,3,6,7]=>1011000
[5,4,1,3,6,7,2,8]=>1100010
[8,4,1,2,6,3,7,5]=>1100101
[8,2,7,1,5,3,4,6]=>1010100
[3,2,7,1,5,8,4,6]=>1010010
[7,3,8,1,5,4,2,6]=>1010110
[7,1,5,3,8,4,2,6]=>1010110
[3,6,8,1,5,4,2,7]=>0010110
[6,8,3,1,5,4,2,7]=>0110110
[7,6,3,1,5,4,2,8]=>1110110
[3,6,2,1,5,8,4,7]=>0110010
[8,6,2,1,5,3,4,7]=>1110100
[2,3,8,1,5,7,4,6]=>0010010
[7,1,3,2,8,6,4,5]=>1010110
[4,7,1,2,6,3,8,5]=>0100101
[2,7,8,1,5,3,4,6]=>0010100
[6,7,2,1,5,3,4,8]=>0110100
[4,7,2,1,8,5,3,6]=>0110110
[8,7,2,1,4,5,3,6]=>1110010
[5,7,8,6,1,4,3,2]=>0011011
[2,7,4,1,6,5,3,8]=>0110110
[7,1,6,4,5,8,3,2]=>1010011
[2,6,4,1,7,5,3,8]=>0110110
[5,6,8,7,1,4,3,2]=>0011011
[4,2,8,1,6,5,3,7]=>1010110
[6,2,4,1,8,5,3,7]=>1010110
[8,3,1,4,5,6,7,2]=>1100001
[5,3,1,4,8,6,7,2]=>1100101
[7,5,1,6,3,4,8,2]=>1101001
[7,1,5,8,4,3,6,2]=>1001101
[5,8,1,6,4,3,7,2]=>0101101
[5,3,1,8,4,6,7,2]=>1101001
[8,3,1,5,4,6,7,2]=>1101001
[8,2,6,1,4,5,3,7]=>1010010
[6,2,8,1,4,5,3,7]=>1010010
[7,2,6,1,5,3,4,8]=>1010100
[2,8,6,1,5,3,4,7]=>0110100
[4,2,1,5,6,3,8,7]=>1100101
[7,1,2,5,8,3,4,6]=>1000100
[7,1,4,5,6,8,3,2]=>1000011
[2,6,7,1,4,5,3,8]=>0010010
[3,5,1,7,4,6,8,2]=>0101001
[7,1,5,6,4,8,3,2]=>1001011
[7,1,6,5,4,8,3,2]=>1011011
[2,7,6,1,4,5,3,8]=>0110010
[5,7,6,8,1,4,3,2]=>0101011
[7,8,6,5,1,4,3,2]=>0111011
[5,3,1,2,4,8,7,6]=>1100011
[5,3,6,2,1,8,7,4]=>1011011
[5,3,7,2,8,4,1,6]=>1010110
[7,2,4,5,8,3,1,6]=>1000110
[7,2,4,5,1,3,6,8]=>1001000
[6,2,4,5,1,8,7,3]=>1001011
[3,1,4,5,2,8,7,6]=>1001011
[1,6,4,5,2,8,7,3]=>0101011
[3,7,4,5,1,2,6,8]=>0101000
[1,7,4,2,6,3,5,8]=>0110100
[8,7,4,5,2,1,6,3]=>1101101
[6,3,7,1,8,4,2,5]=>1010110
[5,7,4,1,6,3,2,8]=>0110110
[1,7,4,8,6,3,2,5]=>0101110
[5,7,4,8,6,3,1,2]=>0101110
[4,8,3,5,6,7,1,2]=>0100010
[1,8,3,5,6,7,2,4]=>0100010
[4,8,1,5,6,7,2,3]=>0100010
[4,1,3,5,6,7,2,8]=>1000010
[5,8,4,3,6,1,2,7]=>0110100
[5,3,8,4,1,7,2,6]=>1011010
[1,5,8,4,6,7,3,2]=>0010011
[1,4,8,3,6,7,5,2]=>0010011
[4,3,8,2,1,7,5,6]=>1011010
[3,8,4,2,6,1,5,7]=>0110100
[3,8,1,5,6,7,4,2]=>0100011
[3,8,2,5,6,7,1,4]=>0100010
[8,2,1,5,6,7,4,3]=>1100011
[8,1,3,5,6,7,4,2]=>1000011
[7,1,4,3,6,2,5,8]=>1010100
[7,8,4,3,6,2,1,5]=>0110110
[4,3,1,8,5,7,6,2]=>1101011
[6,3,5,8,2,7,1,4]=>1001010
[7,5,4,8,6,2,1,3]=>1101110
[7,1,4,8,6,2,3,5]=>1001100
[7,5,4,1,6,2,3,8]=>1110100
[1,6,4,5,8,2,3,7]=>0100100
[1,8,5,3,6,7,4,2]=>0110011
[8,3,5,2,1,7,4,6]=>1011010
[4,1,8,5,6,7,3,2]=>1010011
[1,2,8,5,6,7,3,4]=>0010010
[4,2,1,5,6,7,3,8]=>1100010
[1,5,3,8,6,7,4,2]=>0101011
[1,4,8,5,6,7,2,3]=>0010010
[6,2,4,3,8,7,5,1]=>1010111
[7,3,5,4,1,8,6,2]=>1011011
[5,2,7,1,3,4,8,6]=>1010001
[2,6,5,7,3,1,4,8]=>0101100
[2,6,5,7,3,1,8,4]=>0101101
[6,3,1,4,7,8,5,2]=>1100011
[6,8,2,1,3,4,5,7]=>0110000
[3,7,1,8,4,5,2,6]=>0101010
[6,3,2,4,7,5,8,1]=>1100101
[6,3,2,4,7,5,1,8]=>1100110
[4,2,1,6,3,7,5,8]=>1101010
[4,2,1,6,3,7,8,5]=>1101001
[7,4,3,5,8,6,1,2]=>1100110
[2,7,6,8,3,1,4,5]=>0101100
[7,4,3,5,8,6,2,1]=>1100111
[4,2,1,7,3,8,6,5]=>1101011
[4,2,1,3,7,8,6,5]=>1100011
[5,8,1,7,4,3,6,2]=>0101101
[5,8,1,7,4,3,2,6]=>0101110
[3,7,8,6,2,1,4,5]=>0011100
[4,2,1,8,3,5,6,7]=>1101000
[4,2,1,3,6,7,5,8]=>1100010
[4,2,1,3,7,5,6,8]=>1100100
[7,3,2,4,8,6,5,1]=>1100111
[4,2,1,7,3,5,6,8]=>1101000
[3,6,7,5,2,1,4,8]=>0011100
[3,6,7,5,2,1,8,4]=>0011101
[7,3,4,2,6,8,5,1]=>1010011
[4,8,6,2,7,3,5,1]=>0110101
[7,3,4,2,6,8,1,5]=>1010010
[3,6,7,5,2,4,8,1]=>0011001
[3,6,7,5,2,4,1,8]=>0011010
[4,2,1,7,3,6,8,5]=>1101001
[3,7,6,8,4,2,5,1]=>0101101
[5,8,1,7,4,2,6,3]=>0101101
[3,7,8,6,2,4,5,1]=>0011001
[4,2,1,3,8,6,7,5]=>1100101
[4,2,1,3,5,7,6,8]=>1100010
[4,8,1,7,3,6,5,2]=>0101011
[4,2,1,8,3,7,6,5]=>1101011
[4,2,1,3,5,6,8,7]=>1100001
[7,8,2,4,1,3,6,5]=>0101001
[2,6,1,5,4,7,8,3]=>0101001
[4,6,3,5,8,7,1,2]=>0100110
[2,3,6,8,4,1,5,7]=>0001100
[2,7,5,1,8,3,4,6]=>0110100
[4,7,5,2,1,3,6,8]=>0111000
[3,5,6,2,4,1,7,8]=>0010100
[3,1,8,5,2,7,6,4]=>1011011
[8,3,7,6,1,4,5,2]=>1011001
[3,1,7,8,2,5,6,4]=>1001001
[4,8,1,5,2,7,3,6]=>0101010
[4,1,2,5,3,8,7,6]=>1001011
[4,3,6,8,7,5,1,2]=>1001110
[6,4,8,1,2,5,3,7]=>1010010
[6,7,3,1,4,8,5,2]=>0110011
[6,5,1,2,3,4,8,7]=>1100001
[1,2,6,7,5,3,8,4]=>0001101
[1,7,5,3,2,8,4,6]=>0111010
[1,6,5,7,2,3,8,4]=>0101001
[1,3,8,2,6,5,7,4]=>0010101
[1,2,5,7,6,3,4,8]=>0001100
[1,3,4,8,2,5,7,6]=>0001001
[1,5,7,6,2,3,4,8]=>0011000
[1,5,3,8,2,6,4,7]=>0101010
[1,4,8,3,2,5,7,6]=>0011001
[1,2,4,8,3,5,7,6]=>0001001
[1,3,8,4,2,6,7,5]=>0011001
[1,4,8,2,3,5,7,6]=>0010001
[4,2,6,7,5,8,3,1]=>1001011
[6,7,5,2,1,8,4,3]=>0111011
[3,4,8,7,5,2,1,6]=>0011110
[1,7,5,2,8,4,6,3]=>0110101
[5,6,8,3,1,7,2,4]=>0011010
[6,1,4,8,3,2,7,5]=>1001101
[3,4,7,1,8,6,2,5]=>0010110
[3,4,6,8,2,1,5,7]=>0001100
[3,8,2,5,6,1,4,7]=>0100100
[3,5,2,8,6,4,1,7]=>0101110
[4,2,5,7,3,8,6,1]=>1001011
[7,4,2,5,3,8,1,6]=>1101010
[1,5,6,8,3,4,2,7]=>0001010
[4,5,1,6,8,3,2,7]=>0100110
[4,5,7,3,8,2,6,1]=>0010101
[6,4,3,7,8,2,5,1]=>1100101
[6,4,3,1,7,8,2,5]=>1110010
[4,5,3,1,7,8,2,6]=>0110010
[7,1,3,5,4,8,2,6]=>1001010
[7,5,2,8,1,4,3,6]=>1101010
[1,4,5,7,3,8,6,2]=>0001011
[4,6,3,7,8,5,2,1]=>0100111
[1,5,3,6,7,8,4,2]=>0100011
[4,6,1,7,3,8,5,2]=>0101011
[6,7,2,4,8,1,5,3]=>0100101
[5,2,3,6,7,8,4,1]=>1000011
[6,4,2,7,1,8,3,5]=>1101010
[4,2,6,3,7,8,5,1]=>1010011
[6,7,3,8,2,4,5,1]=>0101001
[3,6,2,7,4,1,8,5]=>0101101
[6,7,3,2,1,4,8,5]=>0111001
[7,2,4,8,6,1,3,5]=>1001100
[3,5,7,2,1,8,6,4]=>0011011
[6,7,8,3,2,5,1,4]=>0011010
[6,3,7,8,2,5,4,1]=>1001011
[2,6,7,4,8,5,3,1]=>0010111
[6,2,4,7,1,8,5,3]=>1001011
[1,7,4,8,5,2,6,3]=>0101101
[1,3,7,8,5,2,6,4]=>0001101
[2,5,7,8,1,6,3,4]=>0001010
[1,6,4,7,8,2,5,3]=>0100101
[2,5,6,1,7,8,4,3]=>0010011
[5,6,1,2,7,8,4,3]=>0100011
[6,7,2,1,8,5,3,4]=>0110110
[6,4,5,2,3,8,7,1]=>1010011
[4,6,5,2,3,1,8,7]=>0110101
[6,4,2,5,3,1,8,7]=>1101101
[6,4,2,5,3,8,7,1]=>1101011
[8,6,4,7,5,2,3,1]=>1101101
[8,6,2,7,4,5,3,1]=>1101011
[6,4,2,5,8,7,3,1]=>1100111
[4,6,5,2,3,8,7,1]=>0110011
[6,8,2,7,4,5,3,1]=>0101011
[8,6,4,7,2,5,3,1]=>1101011
[8,6,2,4,7,5,3,1]=>1100111
[6,8,2,4,7,5,3,1]=>0100111
[4,8,2,6,7,5,3,1]=>0100111
[2,8,4,6,7,5,3,1]=>0100111
[2,8,6,7,4,5,3,1]=>0101011
[6,8,7,2,4,5,3,1]=>0110011
[2,6,4,5,8,7,3,1]=>0100111
[2,6,4,8,7,5,3,1]=>0101111
[4,6,2,8,7,5,3,1]=>0101111
[8,2,4,6,7,5,3,1]=>1000111
[6,2,4,8,7,5,3,1]=>1001111
[4,2,6,8,7,5,3,1]=>1001111
[4,2,6,5,8,7,3,1]=>1010111
[6,2,4,5,8,7,3,1]=>1000111
[8,2,6,7,4,5,3,1]=>1001011
[8,6,7,2,4,5,3,1]=>1010011
[6,4,5,8,7,2,3,1]=>1001101
[8,6,7,4,2,5,3,1]=>1011011
[8,4,6,7,2,5,3,1]=>1001011
[6,4,8,7,2,5,3,1]=>1011011
[6,2,8,7,4,5,3,1]=>1011011
[4,6,5,8,7,2,3,1]=>0101101
[2,1,6,8,7,4,5,3]=>1001101
[2,6,8,7,4,5,3,1]=>0011011
[2,4,8,6,7,5,3,1]=>0010111
[6,2,8,4,7,5,3,1]=>1010111
[8,2,6,4,7,5,3,1]=>1010111
[4,6,8,2,7,5,3,1]=>0010111
[2,6,8,4,7,5,3,1]=>0010111
[4,6,8,7,2,5,3,1]=>0011011
[4,6,5,8,2,7,3,1]=>0101011
[2,1,6,8,4,7,5,3]=>1001011
[2,1,8,6,4,7,5,3]=>1011011
[6,8,7,4,2,5,3,1]=>0111011
[2,8,6,4,7,5,3,1]=>0110111
[4,8,6,2,7,5,3,1]=>0110111
[3,7,8,5,6,1,2,4]=>0010100
[3,6,1,8,4,7,2,5]=>0101010
[3,1,6,8,4,7,2,5]=>1001010
[4,1,6,8,3,2,7,5]=>1001101
[4,6,1,8,3,2,7,5]=>0101101
[4,7,8,1,3,2,6,5]=>0010101
[4,7,8,3,1,2,6,5]=>0011001
[2,7,8,3,4,6,5,1]=>0010011
[4,7,8,2,1,3,6,5]=>0011001
[4,6,1,8,2,3,7,5]=>0101001
[4,5,2,1,8,3,7,6]=>0110101
[4,6,2,8,1,3,7,5]=>0101001
[3,6,2,8,4,7,1,5]=>0101010
[2,3,6,8,4,7,5,1]=>0001011
[3,2,6,8,4,7,1,5]=>1001010
[4,2,6,8,3,1,7,5]=>1001101
[4,2,5,1,8,3,7,6]=>1010101
[5,1,2,4,3,8,7,6]=>1001011
[5,2,4,1,3,8,7,6]=>1010011
[4,2,5,3,8,1,7,6]=>1010101
[3,2,5,4,8,7,1,6]=>1010110
[3,5,2,4,8,7,1,6]=>0100110
[5,1,4,2,3,8,7,6]=>1010011
[5,4,3,1,2,8,7,6]=>1110011
[4,5,3,1,8,2,7,6]=>0110101
[4,5,1,3,8,2,7,6]=>0100101
[3,1,5,4,8,7,2,6]=>1010110
[3,5,4,1,8,7,2,6]=>0110110
[3,6,5,8,7,1,2,4]=>0101100
[3,4,1,5,8,7,2,6]=>0100110
[4,1,3,5,8,2,7,6]=>1000101
[4,3,6,8,2,1,7,5]=>1001101
[2,4,6,8,3,7,5,1]=>0001011
[3,4,5,2,8,7,1,6]=>0010110
[5,3,1,4,2,8,7,6]=>1101011
[5,1,3,4,2,8,7,6]=>1001011
[5,1,3,2,4,8,7,6]=>1010011
[5,3,2,1,4,8,7,6]=>1110011
[4,3,2,5,8,1,7,6]=>1100101
[3,4,2,5,8,7,1,6]=>0100110
[3,2,4,5,8,7,1,6]=>1000110
[4,2,3,5,8,1,7,6]=>1000101
[5,2,3,1,4,8,7,6]=>1010011
[5,2,1,3,4,8,7,6]=>1100011
[1,7,2,3,5,6,8,4]=>0100001
[3,7,4,2,1,5,6,8]=>0111000
[3,4,6,2,8,5,7,1]=>0010101
[4,2,1,7,5,8,3,6]=>1101010
[4,7,2,6,5,1,3,8]=>0101100
[3,7,4,1,2,5,8,6]=>0110001
[4,7,1,6,5,2,8,3]=>0101101
[4,7,3,6,5,1,8,2]=>0101101
[4,3,7,1,6,8,5,2]=>1010011
[4,2,1,7,5,6,8,3]=>1101001
[4,2,6,8,7,3,1,5]=>1001110
[3,4,6,1,8,5,2,7]=>0010110
[4,1,6,7,5,8,2,3]=>1001010
[4,3,6,7,5,1,2,8]=>1001100
[4,3,7,1,6,8,2,5]=>1010010
[4,3,7,5,6,8,2,1]=>1010011
[4,1,7,3,6,5,2,8]=>1010110
[2,8,7,4,5,3,1,6]=>0110110
[2,8,7,4,3,5,1,6]=>0111010
[4,1,7,3,6,2,5,8]=>1010100
[5,8,7,6,1,2,4,3]=>0111001
[4,1,7,2,6,8,5,3]=>1010011
[4,2,7,3,6,1,8,5]=>1010101
[4,2,7,3,6,5,8,1]=>1010101
[3,8,5,6,2,4,1,7]=>0101010
[2,8,6,5,3,7,1,4]=>0111010
[3,8,6,5,1,4,7,2]=>0111001
[3,8,2,1,4,6,7,5]=>0110001
[3,8,2,5,4,6,7,1]=>0101001
[4,2,6,7,5,3,1,8]=>1001110
[3,2,6,1,4,5,8,7]=>1010001
[2,8,7,3,4,5,1,6]=>0110010
[5,8,7,6,1,3,4,2]=>0111001
[5,8,7,6,2,3,4,1]=>0111001
[4,1,7,5,6,2,3,8]=>1010100
[3,8,1,5,2,6,4,7]=>0101010
[2,8,7,5,3,4,1,6]=>0111010
[2,8,7,5,4,3,1,6]=>0111110
[4,1,7,5,6,3,2,8]=>1010110
[5,8,7,6,1,3,2,4]=>0111010
[5,8,7,6,4,1,2,3]=>0111100
[8,1,7,2,4,5,3,6]=>1010010
[8,1,3,6,2,5,4,7]=>1001010
[7,2,1,6,3,5,4,8]=>1101010
[2,7,1,6,3,5,4,8]=>0101010
[2,7,1,5,4,3,6,8]=>0101100
[7,2,1,5,4,3,6,8]=>1101100
[8,1,3,5,4,2,6,7]=>1001100
[8,1,5,3,4,2,6,7]=>1010100
[8,1,5,6,2,3,7,4]=>1001001
[8,1,4,5,3,2,6,7]=>1001100
[8,1,4,3,5,2,6,7]=>1010100
[7,2,1,4,5,3,6,8]=>1100100
[2,7,1,4,5,3,6,8]=>0100100
[2,6,3,1,5,4,7,8]=>0110100
[6,3,2,1,5,4,7,8]=>1110100
[7,3,1,4,5,2,6,8]=>1100100
[7,3,1,5,4,2,6,8]=>1101100
[7,3,1,6,2,5,4,8]=>1101010
[3,7,1,6,2,5,4,8]=>0101010
[3,7,1,4,5,2,6,8]=>0100100
[2,3,6,1,5,4,7,8]=>0010100
[6,3,4,1,5,2,7,8]=>1010100
[6,2,4,1,5,3,7,8]=>1010100
[2,6,4,1,5,3,7,8]=>0110100
[2,6,5,1,3,7,4,8]=>0110010
[6,5,2,1,3,7,4,8]=>1110010
[7,6,1,2,4,5,3,8]=>1100010
[6,7,1,2,8,3,5,4]=>0100101
[6,7,1,2,5,4,3,8]=>0100110
[5,6,2,1,3,7,4,8]=>0110010
[5,2,6,1,3,7,4,8]=>1010010
[2,4,6,1,5,3,7,8]=>0010100
[4,7,1,3,5,2,6,8]=>0100100
[4,7,1,5,3,2,6,8]=>0101100
[5,7,1,6,2,3,8,4]=>0101001
[5,6,3,1,2,7,4,8]=>0110010
[4,2,5,3,1,6,7,8]=>1011000
[8,5,6,2,7,1,4,3]=>1010101
[6,5,1,2,7,8,4,3]=>1100011
[4,7,6,1,5,3,8,2]=>0110101
[5,7,6,4,1,3,8,2]=>0111001
[7,6,2,4,5,3,8,1]=>1100101
[6,1,7,5,3,8,4,2]=>1011011
[8,6,7,5,3,1,4,2]=>1011101
[8,5,2,7,1,6,4,3]=>1101011
[5,6,2,4,7,8,1,3]=>0100010
[3,4,8,6,7,1,5,2]=>0010101
[4,8,5,6,7,2,3,1]=>0100101
[5,8,6,4,1,2,7,3]=>0111001
[5,8,7,3,2,6,4,1]=>0111011
[5,8,1,7,2,6,4,3]=>0101011
[8,1,5,7,2,6,4,3]=>1001011
[8,1,7,2,5,6,3,4]=>1010010
[6,8,7,2,5,1,3,4]=>0110100
[5,8,7,2,1,6,3,4]=>0111010
[4,8,1,5,2,6,7,3]=>0101001
[3,7,8,5,1,6,2,4]=>0011010
[6,5,2,7,8,1,4,3]=>1100101
[7,1,2,8,5,6,3,4]=>1001010
[8,7,2,1,5,6,3,4]=>1110010
[8,6,7,1,5,2,3,4]=>1010100
[6,1,7,8,5,2,3,4]=>1001100
[7,5,6,2,1,8,4,3]=>1011011
[8,7,5,2,1,6,4,3]=>1111011
[7,1,3,5,8,6,2,4]=>1000110
[5,1,3,4,6,8,7,2]=>1000011
[8,4,3,1,2,6,7,5]=>1110001
[8,5,1,6,3,4,7,2]=>1101001
[5,1,8,6,3,4,7,2]=>1011001
[4,6,8,1,5,3,7,2]=>0010101
[6,4,5,8,3,2,7,1]=>1001101
[3,6,4,8,7,1,5,2]=>0101101
[6,5,8,1,3,4,7,2]=>1010001
[6,1,8,3,5,2,7,4]=>1010101
[7,6,8,3,5,2,1,4]=>1010110
[8,6,1,3,5,2,7,4]=>1100101
[8,7,1,3,5,6,2,4]=>1100010
[5,8,2,4,3,6,7,1]=>0101001
[5,8,2,3,1,6,7,4]=>0101001
[6,8,2,3,5,1,7,4]=>0100101
[7,8,2,3,5,6,1,4]=>0100010
[8,6,5,1,4,3,7,2]=>1110101
[2,4,8,6,1,3,7,5]=>0011001
[6,7,1,8,4,3,5,2]=>0101101
[2,7,8,6,1,4,3,5]=>0011010
[2,7,3,8,1,6,4,5]=>0101010
[7,5,1,8,2,4,6,3]=>1101001
[2,7,8,4,1,6,3,5]=>0011010
[2,6,5,4,1,3,8,7]=>0111001
[4,1,7,6,3,8,2,5]=>1011010
[4,8,2,5,7,6,3,1]=>0100111
[3,4,6,5,1,8,2,7]=>0011010
[4,6,1,5,2,3,8,7]=>0101001
[2,6,7,5,1,8,4,3]=>0011011
[7,6,5,2,8,3,4,1]=>1110101
[2,4,7,6,5,8,1,3]=>0011010
[2,1,4,8,7,6,3,5]=>1001110
[8,1,3,5,7,4,6,2]=>1000101
[3,2,8,7,5,1,6,4]=>1011101
[4,8,5,1,6,7,2,3]=>0110010
[7,8,6,1,3,5,2,4]=>0110010
[2,5,1,8,6,7,4,3]=>0101011
[3,5,1,8,6,7,4,2]=>0101011
[8,3,5,4,6,7,1,2]=>1010010
[5,1,3,8,6,7,4,2]=>1001011
[5,6,3,2,8,1,4,7]=>0110100
[8,1,6,3,5,2,7,4]=>1010101
[4,7,6,8,3,2,5,1]=>0101101
[2,7,5,8,1,3,4,6]=>0101000
[8,1,3,7,5,2,6,4]=>1001101
[3,4,8,7,5,1,6,2]=>0011101
[6,3,8,1,4,2,5,7]=>1010100
[3,6,8,2,4,1,7,5]=>0010101
[4,5,8,2,6,7,3,1]=>0010011
[2,5,8,4,6,7,3,1]=>0010011
[8,4,3,2,6,7,1,5]=>1110010
[4,2,8,1,6,7,3,5]=>1010010
[2,4,8,1,6,7,3,5]=>0010010
[5,1,8,2,6,7,3,4]=>1010010
[3,4,8,7,2,1,5,6]=>0011100
[5,8,4,1,6,7,2,3]=>0110010
[3,8,1,4,6,7,2,5]=>0100010
[1,6,4,5,2,3,7,8]=>0101000
[1,7,4,5,2,3,6,8]=>0101000
[1,6,3,5,2,4,7,8]=>0101000
[1,6,3,4,2,5,7,8]=>0101000
[1,7,3,4,2,5,6,8]=>0101000
[1,8,5,7,3,4,2,6]=>0101010
[1,7,3,4,2,6,5,8]=>0101010
[1,5,2,8,4,7,3,6]=>0101010
[1,4,2,8,5,7,3,6]=>0101010
[1,7,3,5,2,6,4,8]=>0101010
[1,8,4,7,3,5,2,6]=>0101010
[1,7,3,6,2,5,4,8]=>0101010
[1,7,3,6,2,4,5,8]=>0101000
[1,7,4,6,2,3,5,8]=>0101000
[1,8,5,6,2,3,4,7]=>0101000
[1,8,5,6,2,4,3,7]=>0101010
[1,3,2,8,5,6,4,7]=>0101010
[1,4,2,8,5,6,3,7]=>0101010
[1,5,2,8,4,6,3,7]=>0101010
[1,6,2,8,4,5,3,7]=>0101010
[8,6,4,7,2,1,3,5]=>1101100
[3,8,6,2,4,5,1,7]=>0110010
[1,7,6,4,8,2,3,5]=>0110100
[5,8,7,4,1,2,3,6]=>0111000
[6,8,3,7,2,1,4,5]=>0101100
[6,1,3,7,4,8,2,5]=>1001010
[7,1,6,4,8,2,3,5]=>1010100
[3,8,7,5,1,2,4,6]=>0111000
[3,7,6,1,2,4,5,8]=>0110000
[4,7,6,1,2,3,5,8]=>0110000
[8,5,7,4,1,2,3,6]=>1011000
[8,6,2,3,1,7,4,5]=>1101010
[1,7,2,8,6,3,4,5]=>0101100
[7,5,8,1,3,6,2,4]=>1010010
[5,4,1,8,2,3,6,7]=>1101000
[1,4,8,7,2,3,5,6]=>0011000
[1,5,8,7,2,3,4,6]=>0011000
[5,7,1,3,8,2,4,6]=>0100100
[7,1,5,8,6,2,3,4]=>1001100
[5,1,8,7,2,3,4,6]=>1011000
[7,1,5,8,3,4,2,6]=>1001010
[7,1,4,3,2,5,6,8]=>1011000
[6,4,2,3,8,5,7,1]=>1100101
[6,4,2,7,5,8,3,1]=>1101011
[7,1,4,6,5,2,3,8]=>1001100
[7,1,4,6,5,8,2,3]=>1001010
[7,1,4,6,3,8,2,5]=>1001010
[7,1,4,3,2,5,8,6]=>1011001
[7,1,4,6,5,2,8,3]=>1001101
[7,1,4,6,5,3,8,2]=>1001101
[7,1,4,6,5,3,2,8]=>1001110
[6,4,2,7,5,3,8,1]=>1101101
[3,4,7,2,6,8,5,1]=>0010011
[3,4,7,1,6,8,2,5]=>0010010
[3,4,7,1,6,8,5,2]=>0010011
[2,4,1,7,5,3,6,8]=>0101100
[3,4,1,7,8,6,2,5]=>0100110
[6,4,2,3,8,5,1,7]=>1100110
[6,4,2,7,5,3,1,8]=>1101110
[3,4,7,2,6,8,1,5]=>0010010
[5,4,7,3,6,8,2,1]=>1010011
[3,4,7,2,6,5,1,8]=>0010110
[4,8,7,3,5,1,2,6]=>0110100
[4,8,7,1,3,5,2,6]=>0110010
[4,8,3,1,2,6,5,7]=>0110010
[3,4,7,1,6,2,5,8]=>0010100
[3,4,7,1,6,2,8,5]=>0010101
[3,4,7,2,6,5,8,1]=>0010101
[4,8,3,1,2,6,7,5]=>0110001
[5,8,1,6,3,4,2,7]=>0101010
[6,8,5,1,3,7,2,4]=>0110010
[6,8,5,1,3,4,7,2]=>0110001
[5,8,3,4,2,6,7,1]=>0101001
[6,4,3,7,5,1,2,8]=>1101100
[3,8,7,4,1,5,2,6]=>0111010
[2,4,7,3,6,1,5,8]=>0010100
[5,8,3,2,1,6,4,7]=>0111010
[5,8,7,4,3,1,2,6]=>0111100
[5,3,6,2,4,7,8,1]=>1010001
[5,3,6,1,4,8,7,2]=>1010011
[5,3,7,2,4,6,8,1]=>1010001
[4,2,1,5,8,6,3,7]=>1100110
[4,2,1,5,8,6,7,3]=>1100101
[4,3,1,5,7,8,6,2]=>1100011
[4,3,1,7,5,8,6,2]=>1101011
[6,7,3,1,4,8,2,5]=>0110010
[5,3,7,1,4,8,2,6]=>1010010
[4,3,1,5,7,8,2,6]=>1100010
[3,2,1,8,5,4,6,7]=>1101100
[3,2,1,8,5,7,4,6]=>1101010
[6,7,2,1,8,4,5,3]=>0110101
[3,2,1,8,5,6,4,7]=>1101010
[4,3,1,6,7,8,5,2]=>1100011
[4,2,1,6,8,5,7,3]=>1100101
[4,2,1,6,8,5,3,7]=>1100110
[5,2,6,1,8,4,3,7]=>1010110
[5,2,6,1,8,7,3,4]=>1010110
[5,2,6,1,8,3,4,7]=>1010100
[4,2,1,6,8,3,7,5]=>1100101
[4,3,1,6,7,8,2,5]=>1100010
[4,2,1,7,8,6,3,5]=>1100110
[3,2,1,8,6,4,7,5]=>1101101
[3,2,1,8,6,4,5,7]=>1101100
[3,2,1,8,4,6,5,7]=>1101010
[3,2,1,8,4,6,7,5]=>1101001
[4,2,1,7,8,3,6,5]=>1100101
[5,2,7,1,8,3,6,4]=>1010101
[6,7,2,1,8,3,5,4]=>0110101
[5,2,7,1,8,3,4,6]=>1010100
[4,2,1,7,8,3,5,6]=>1100100
[3,2,1,8,4,5,7,6]=>1101001
[7,4,8,6,2,5,3,1]=>1011011
[7,3,8,6,2,4,5,1]=>1011001
[7,4,3,1,8,2,5,6]=>1110100
[7,4,2,8,5,6,1,3]=>1101010
[7,3,8,5,2,4,6,1]=>1011001
[6,3,8,2,4,5,1,7]=>1010010
[6,3,8,2,5,7,4,1]=>1010011
[5,6,7,3,8,2,4,1]=>0010101
[5,3,8,2,4,6,7,1]=>1010001
[6,3,8,2,4,7,5,1]=>1010011
[5,7,4,2,6,8,1,3]=>0110010
[6,5,3,1,4,2,7,8]=>1110100
[5,7,4,2,6,1,3,8]=>0110100
[5,6,4,2,3,8,1,7]=>0110010
[5,6,3,7,8,2,4,1]=>0100101
[5,6,3,8,2,4,7,1]=>0101001
[6,3,7,2,4,5,1,8]=>1010010
[6,3,7,2,5,8,4,1]=>1010011
[5,3,6,8,2,4,7,1]=>1001001
[5,4,6,2,3,8,1,7]=>1010010
[5,3,6,7,8,2,4,1]=>1000101
[3,6,4,2,1,5,8,7]=>0111001
[3,5,8,6,4,2,1,7]=>0011110
[5,8,6,3,4,2,1,7]=>0110110
[5,6,3,4,2,1,8,7]=>0101101
[6,3,4,2,1,5,8,7]=>1011001
[5,6,4,2,1,3,8,7]=>0111001
[2,7,8,5,4,1,6,3]=>0011101
[2,8,5,4,1,6,3,7]=>0111010
[2,6,3,8,5,4,1,7]=>0101110
[2,8,6,3,5,4,1,7]=>0110110
[5,8,6,4,2,1,3,7]=>0111100
[4,2,1,5,7,8,6,3]=>1100011
[2,7,8,6,3,5,4,1]=>0011011
[4,3,8,5,7,6,2,1]=>1010111
[2,1,8,5,6,4,3,7]=>1010110
[4,2,1,8,5,6,3,7]=>1101010
[6,3,4,2,1,8,5,7]=>1011010
[3,8,5,6,4,2,1,7]=>0101110
[3,6,4,2,1,8,5,7]=>0111010
[8,5,3,7,6,2,4,1]=>1101101
[7,6,2,4,1,8,5,3]=>1101011
[8,5,4,1,7,6,2,3]=>1110110
[7,6,2,3,8,5,4,1]=>1100111
[2,1,7,8,6,4,3,5]=>1001110
[2,1,6,4,3,7,8,5]=>1011001
[6,3,7,8,4,2,1,5]=>1001110
[7,8,4,2,1,6,3,5]=>0111010
[5,7,6,2,3,8,4,1]=>0110011
[2,6,1,8,4,3,7,5]=>0101101
[2,6,1,7,5,8,4,3]=>0101011
[8,4,2,3,7,5,6,1]=>1100101
[8,5,7,6,2,1,4,3]=>1011101
[4,8,5,7,6,2,1,3]=>0101110
[4,7,6,2,1,3,8,5]=>0111001
[7,5,6,1,8,4,2,3]=>1010110
[2,7,5,8,4,3,6,1]=>0101101
[2,8,4,3,6,1,7,5]=>0110101
[8,4,2,6,3,1,7,5]=>1101101
[1,5,3,7,4,2,8,6]=>0101101
[1,6,7,3,4,2,8,5]=>0010101
[8,6,5,2,3,1,7,4]=>1110101
[1,7,6,3,4,2,8,5]=>0110101
[1,8,6,3,2,5,7,4]=>0111001
[8,7,5,2,1,4,6,3]=>1111001
[7,8,5,2,1,4,6,3]=>0111001
[6,8,5,2,3,1,7,4]=>0110101
[5,8,6,2,3,1,7,4]=>0110101
[4,8,2,6,3,1,7,5]=>0101101
[3,2,8,6,4,1,7,5]=>1011101
[3,2,1,7,5,4,8,6]=>1101101
[4,1,3,7,5,2,8,6]=>1001101
[7,1,6,3,2,5,8,4]=>1011001
[1,2,7,4,3,6,8,5]=>0011001
[6,1,8,2,4,5,7,3]=>1010001
[5,1,8,3,2,6,7,4]=>1011001
[4,8,2,7,1,5,6,3]=>0101001
[5,8,7,2,1,4,6,3]=>0111001
[6,8,7,1,3,4,5,2]=>0110001
[7,8,6,1,3,4,5,2]=>0110001
[1,7,8,2,4,5,6,3]=>0010001
[8,6,7,1,3,4,5,2]=>1010001
[7,6,8,1,3,4,5,2]=>1010001
[6,5,8,2,3,1,7,4]=>1010101
[1,6,8,3,2,5,7,4]=>0011001
[8,4,2,7,1,5,6,3]=>1101001
[7,4,2,8,1,5,6,3]=>1101001
[6,4,2,8,3,1,7,5]=>1101101
[5,4,2,3,8,1,7,6]=>1100101
[4,5,2,3,1,6,8,7]=>0101001
[7,4,2,1,3,6,8,5]=>1110001
[8,4,2,1,3,6,7,5]=>1110001
[1,5,3,2,4,7,8,6]=>0110001
[8,5,1,3,2,6,7,4]=>1101001
[5,6,1,3,4,2,8,7]=>0100101
[4,7,2,1,3,6,8,5]=>0110001
[5,7,1,3,2,6,8,4]=>0101001
[6,7,1,2,4,5,8,3]=>0100001
[1,8,2,3,5,6,7,4]=>0100001
[5,8,1,3,2,6,7,4]=>0101001
[4,8,2,1,3,6,7,5]=>0110001
[4,1,3,2,5,7,8,6]=>1010001
[5,1,2,4,3,7,8,6]=>1001001
[8,7,5,2,6,3,4,1]=>1110101
[8,6,5,2,7,3,4,1]=>1110101
[1,2,6,4,7,5,8,3]=>0010101
[3,1,7,5,4,2,6,8]=>1011100
[6,3,8,5,4,7,1,2]=>1011010
[1,6,2,5,4,7,8,3]=>0101001
[1,2,6,4,8,5,7,3]=>0010101
[7,8,3,1,4,2,5,6]=>0110100
[4,8,1,5,2,3,6,7]=>0101000
[7,4,1,5,2,3,6,8]=>1101000
[5,6,1,8,4,3,2,7]=>0101110
[5,1,8,6,4,3,2,7]=>1011110
[5,1,6,3,8,7,2,4]=>1010110
[6,1,2,5,8,3,7,4]=>1000101
[6,1,8,7,4,3,2,5]=>1011110
[7,1,2,5,4,8,6,3]=>1001011
[1,2,7,5,8,3,6,4]=>0010101
[4,1,6,3,7,5,2,8]=>1010110
[1,3,6,7,8,5,2,4]=>0000110
[1,2,6,4,7,8,5,3]=>0010011
[4,1,6,3,7,8,2,5]=>1010010
[3,1,6,4,8,2,7,5]=>1010101
[7,8,4,1,6,3,2,5]=>0110110
[4,1,6,3,8,7,2,5]=>1010110
[7,5,1,8,4,3,2,6]=>1101110
[6,5,1,7,4,3,2,8]=>1101110
[4,1,8,5,2,3,7,6]=>1011001
[4,1,6,8,3,7,2,5]=>1001010
[6,5,8,1,4,3,2,7]=>1010110
[1,6,3,2,7,4,8,5]=>0110101
[1,3,7,2,5,4,8,6]=>0010101
[1,3,7,5,2,4,8,6]=>0011001
[2,5,3,7,4,8,1,6]=>0101010
[3,2,6,7,8,1,5,4]=>1000101
[3,5,2,7,8,4,1,6]=>0100110
[3,5,2,6,8,4,7,1]=>0100101
[2,5,7,4,3,8,6,1]=>0011011
[1,5,7,2,4,8,6,3]=>0010011
[4,6,3,7,2,8,5,1]=>0101011
[1,4,7,3,8,6,2,5]=>0010110
[5,1,6,8,2,4,3,7]=>1001010
[5,3,7,8,2,4,1,6]=>1001010
[8,5,3,7,2,4,1,6]=>1101010
[8,2,4,7,3,1,5,6]=>1001100
[2,4,7,8,3,1,5,6]=>0001100
[6,3,1,5,8,2,4,7]=>1100100
[6,5,3,4,2,8,1,7]=>1101010
[5,2,4,3,8,1,6,7]=>1010100
[3,2,4,8,1,5,6,7]=>1001000
[8,1,5,7,3,2,4,6]=>1001100
[8,4,6,7,2,3,1,5]=>1001010
[4,6,7,8,2,3,1,5]=>0001010
[7,4,6,8,2,3,1,5]=>1001010
[7,2,4,8,3,1,5,6]=>1001100
[5,3,8,7,2,4,1,6]=>1011010
[2,4,8,7,3,1,5,6]=>0011100
[4,6,8,7,2,3,1,5]=>0011010
[6,4,8,7,2,3,1,5]=>1011010
[3,1,7,4,2,8,6,5]=>1011011
[3,2,8,4,1,7,6,5]=>1011011
[7,6,4,8,2,3,1,5]=>1101010
[5,7,6,8,2,3,1,4]=>0101010
[4,7,6,8,2,3,1,5]=>0101010
[8,6,4,7,2,3,1,5]=>1101010
[8,2,3,7,4,1,6,5]=>1001101
[3,7,4,8,2,5,1,6]=>0101010
[2,3,7,4,1,6,8,5]=>0011001
[8,1,6,4,2,3,7,5]=>1011001
[4,7,8,6,2,3,1,5]=>0011010
[6,3,1,7,4,2,8,5]=>1101101
[8,5,7,6,2,3,1,4]=>1011010
[7,1,6,4,2,3,8,5]=>1011001
[3,1,7,6,4,2,8,5]=>1011101
[4,8,7,6,2,3,1,5]=>0111010
[6,8,7,5,2,3,1,4]=>0111010
[4,3,6,1,5,8,7,2]=>1010011
[4,3,6,5,1,8,7,2]=>1011011
[4,6,3,5,1,8,7,2]=>0101011
[4,6,3,1,5,8,7,2]=>0110011
[4,1,6,5,3,8,7,2]=>1011011
[4,6,1,5,3,8,7,2]=>0101011
[2,6,5,3,1,8,7,4]=>0111011
[2,6,5,8,3,1,7,4]=>0101101
[2,6,5,3,8,1,7,4]=>0110101
[4,6,1,5,8,3,7,2]=>0100101
[4,1,6,5,8,3,7,2]=>1010101
[1,4,6,5,8,3,7,2]=>0010101
[4,1,6,5,8,7,3,2]=>1010111
[6,4,3,8,7,1,5,2]=>1101101
[6,4,8,3,7,1,5,2]=>1010101
[2,6,8,5,3,7,1,4]=>0011010
[4,6,8,1,5,7,3,2]=>0010011
[4,6,1,8,5,7,3,2]=>0101011
[1,4,6,8,5,7,3,2]=>0001011
[1,4,6,8,5,3,7,2]=>0001101
[4,6,1,8,5,3,7,2]=>0101101
[4,6,3,8,5,7,1,2]=>0101010
[4,3,6,8,1,5,7,2]=>1001001
[4,3,6,1,8,5,7,2]=>1010101
[4,3,1,6,8,5,7,2]=>1100101
[4,1,3,6,8,7,5,2]=>1000111
[4,3,6,1,8,7,5,2]=>1010111
[4,3,6,8,1,7,5,2]=>1001011
[6,5,2,8,7,3,1,4]=>1101110
[6,5,2,8,7,1,3,4]=>1101100
[6,2,5,8,7,1,3,4]=>1001100
[6,2,5,8,7,3,1,4]=>1001110
[4,6,3,8,1,7,5,2]=>0101011
[4,6,3,1,8,7,5,2]=>0110111
[4,1,6,3,8,7,5,2]=>1010111
[1,4,6,3,8,7,5,2]=>0010111
[4,1,6,8,3,7,5,2]=>1001011
[4,6,1,8,3,7,5,2]=>0101011
[4,6,8,1,3,7,5,2]=>0010011
[6,2,8,5,7,3,1,4]=>1010110
[6,2,8,5,7,1,3,4]=>1010100
[2,4,8,7,1,5,3,6]=>0011010
[6,4,1,8,7,5,3,2]=>1101111
[6,1,4,8,7,5,3,2]=>1001111
[1,6,4,8,7,3,5,2]=>0101101
[6,4,1,8,7,3,5,2]=>1101101
[4,2,8,7,5,1,3,6]=>1011100
[2,4,8,7,3,5,1,6]=>0011010
[1,5,3,2,6,4,7,8]=>0110100
[1,5,3,2,6,7,4,8]=>0110010
[1,7,3,2,8,5,4,6]=>0110110
[1,7,3,2,5,8,4,6]=>0110010
[6,4,2,5,3,7,1,8]=>1101010
[5,4,7,6,2,3,1,8]=>1011010
[3,6,4,8,2,1,5,7]=>0101100
[1,6,2,8,5,3,4,7]=>0101100
[4,6,2,3,7,5,1,8]=>0100110
[4,7,2,3,6,5,1,8]=>0100110
[5,3,2,6,4,7,1,8]=>1101010
[3,5,2,1,6,8,4,7]=>0110010
[1,5,2,6,8,4,3,7]=>0100110
[1,5,7,2,8,4,3,6]=>0010110
[3,5,2,1,8,6,4,7]=>0110110
[3,6,8,4,2,1,5,7]=>0011100
[4,3,2,6,1,8,5,7]=>1101010
[1,5,8,2,7,4,3,6]=>0010110
[1,7,2,3,4,8,6,5]=>0100011
[6,8,2,3,4,1,7,5]=>0100101
[2,3,1,8,4,5,7,6]=>0101001
[7,3,2,1,4,5,8,6]=>1110001
[7,8,1,4,3,5,2,6]=>0101010
[1,8,2,3,4,7,6,5]=>0100011
[3,8,2,1,6,5,4,7]=>0110110
[1,7,8,3,5,4,2,6]=>0010110
[7,4,1,8,3,5,2,6]=>1101010
[8,4,1,7,3,5,2,6]=>1101010
[3,8,4,6,2,1,5,7]=>0101100
[8,4,2,5,3,1,6,7]=>1101100
[4,3,2,5,1,8,6,7]=>1101010
[3,5,2,4,1,8,6,7]=>0101010
[2,4,7,8,1,5,3,6]=>0001010
[1,8,7,3,5,4,2,6]=>0110110
[5,1,8,2,7,4,3,6]=>1010110
[5,1,7,2,8,4,3,6]=>1010110
[6,1,2,8,5,3,4,7]=>1001100
[6,3,2,1,8,4,5,7]=>1110100
[7,3,2,8,4,5,1,6]=>1101010
[2,7,8,4,3,5,1,6]=>0011010
[7,1,8,3,5,4,2,6]=>1010110
[7,8,2,3,4,6,1,5]=>0100010
[6,8,1,3,4,7,2,5]=>0100010
[8,6,2,3,4,1,7,5]=>1100101
[8,3,2,7,4,5,1,6]=>1101010
[6,7,2,3,4,1,8,5]=>0100101
[8,6,2,3,4,7,1,5]=>1100010
[4,8,7,3,5,6,1,2]=>0110010
[4,8,7,5,3,6,1,2]=>0111010
[5,8,7,3,4,6,1,2]=>0110010
[5,8,4,2,1,6,7,3]=>0111001
[5,8,4,1,2,6,7,3]=>0110001
[5,3,7,2,6,1,8,4]=>1010101
[5,2,8,1,6,3,7,4]=>1010101
[5,8,2,1,4,7,6,3]=>0110011
[4,8,2,5,1,7,6,3]=>0101011
[7,8,4,1,2,6,5,3]=>0110011
[4,8,1,5,2,7,6,3]=>0101011
[5,8,1,2,4,7,6,3]=>0100011
[5,2,8,3,6,7,1,4]=>1010010
[2,8,7,6,4,1,3,5]=>0111100
[7,8,2,6,5,1,3,4]=>0101100
[1,8,7,6,2,4,3,5]=>0111010
[2,8,1,4,5,6,7,3]=>0100001
[2,1,7,3,6,5,8,4]=>1010101
[3,2,7,1,6,5,8,4]=>1010101
[6,1,2,8,5,7,3,4]=>1001010
[6,2,1,8,5,7,3,4]=>1101010
[6,3,1,8,5,7,2,4]=>1101010
[6,4,2,1,7,5,8,3]=>1110101
[6,1,3,8,5,2,7,4]=>1001101
[1,3,7,2,6,8,5,4]=>0010011
[7,8,2,6,5,3,1,4]=>0101110
[3,2,6,7,5,8,1,4]=>1001010
[1,2,7,5,6,3,8,4]=>0010101
[2,8,7,6,4,3,1,5]=>0111110
[3,8,7,6,1,2,5,4]=>0111001
[4,8,7,6,2,1,3,5]=>0111100
[4,8,7,6,1,3,2,5]=>0111010
[3,8,7,6,4,1,2,5]=>0111100
[7,8,3,6,5,1,2,4]=>0101100
[2,3,7,5,6,8,1,4]=>0010010
[3,8,7,6,4,2,1,5]=>0111110
[3,4,2,6,7,8,1,5]=>0100010
[3,1,4,2,6,8,7,5]=>1010011
[8,3,4,2,6,1,7,5]=>1010101
[2,6,7,3,5,4,1,8]=>0010110
[2,7,8,3,5,4,1,6]=>0010110
[2,6,8,3,5,4,1,7]=>0010110
[4,7,1,2,8,5,3,6]=>0100110
[4,8,1,2,7,5,3,6]=>0100110
[2,1,6,3,7,5,4,8]=>1010110
[2,7,1,3,6,8,4,5]=>0100010
[7,4,1,2,8,5,3,6]=>1100110
[8,7,4,2,1,5,3,6]=>1111010
[7,4,1,2,6,5,3,8]=>1100110
[7,4,3,1,5,6,8,2]=>1110001
[6,7,4,1,5,8,3,2]=>0110011
[4,7,5,1,6,8,3,2]=>0110011
[4,5,3,1,7,6,8,2]=>0110101
[4,6,1,2,7,5,3,8]=>0100110
[4,6,1,2,8,5,3,7]=>0100110
[4,5,3,1,8,6,7,2]=>0110101
[4,8,5,6,3,1,7,2]=>0101101
[5,1,3,4,8,6,7,2]=>1000101
[5,4,3,8,1,6,7,2]=>1101001
[8,5,3,4,1,6,7,2]=>1101001
[6,4,8,2,1,5,3,7]=>1011010
[6,7,3,2,5,1,4,8]=>0110100
[6,8,3,2,5,1,4,7]=>0110100
[5,7,1,4,6,8,3,2]=>0100011
[5,1,3,4,7,6,8,2]=>1000101
[5,4,3,7,1,6,8,2]=>1101001
[6,7,5,4,1,8,3,2]=>0111011
[7,6,4,2,1,5,3,8]=>1111010
[8,5,6,1,3,2,4,7]=>1010100
[8,6,1,5,3,2,4,7]=>1101100
[7,8,1,5,3,2,4,6]=>0101100
[8,1,7,5,3,2,4,6]=>1011100
[8,6,1,4,5,2,3,7]=>1100100
[8,6,3,1,5,2,4,7]=>1110100
[8,4,6,1,5,2,3,7]=>1010100
[8,6,2,1,5,4,3,7]=>1110110
[8,5,2,6,1,4,3,7]=>1101010
[8,5,2,1,7,4,3,6]=>1110110
[8,2,7,5,1,3,4,6]=>1011000
[8,4,1,7,5,2,3,6]=>1101100
[8,2,6,1,7,4,3,5]=>1010110
[8,1,7,4,3,2,6,5]=>1011101
[8,1,5,7,3,2,6,4]=>1001101
[5,7,8,1,3,2,6,4]=>0010101
[8,2,6,1,5,7,3,4]=>1010010
[5,8,1,6,7,2,3,4]=>0100100
[5,7,6,1,8,2,3,4]=>0110100
[8,1,5,6,7,2,3,4]=>1000100
[6,5,7,1,8,2,3,4]=>1010100
[8,1,6,4,7,2,3,5]=>1010100
[7,5,8,1,3,2,4,6]=>1010100
[7,8,4,1,3,2,5,6]=>0110100
[8,3,7,4,1,2,5,6]=>1011000
[8,5,1,7,3,2,4,6]=>1101100
[6,8,1,7,3,2,4,5]=>0101100
[7,1,8,4,3,6,2,5]=>1011010
[7,3,1,8,6,4,2,5]=>1101110
[8,3,1,7,4,6,2,5]=>1101010
[8,4,5,1,7,2,3,6]=>1010100
[5,6,8,1,7,2,3,4]=>0010100
[6,5,8,1,2,7,3,4]=>1010010
[7,3,1,8,5,6,2,4]=>1101010
[6,2,7,8,3,1,5,4]=>1001101
[5,8,1,7,3,2,6,4]=>0101101
[8,4,1,7,3,2,6,5]=>1101101
[8,3,4,7,1,2,6,5]=>1001001
[7,4,8,2,1,3,6,5]=>1011001
[7,4,3,8,1,2,6,5]=>1101001
[8,2,3,6,7,1,5,4]=>1000101
[2,6,8,7,1,5,4,3]=>0011011
[7,8,5,2,3,6,4,1]=>0110011
[8,7,5,2,3,1,6,4]=>1110101
[6,8,5,2,3,4,7,1]=>0110001
[5,7,3,4,6,8,1,2]=>0100010
[5,7,3,4,6,1,2,8]=>0100100
[7,3,5,6,1,2,8,4]=>1001001
[5,7,3,1,4,6,8,2]=>0110001
[5,7,3,1,4,8,6,2]=>0110011
[5,7,3,1,4,8,2,6]=>0110010
[5,3,7,4,1,2,8,6]=>1011001
[5,3,7,4,1,2,6,8]=>1011000
[5,3,7,1,4,2,6,8]=>1010100
[5,3,7,1,4,2,8,6]=>1010101
[3,7,5,1,2,8,6,4]=>0110011
[7,8,3,5,1,2,6,4]=>0101001
[7,3,8,5,1,2,6,4]=>1011001
[7,3,5,8,1,2,6,4]=>1001001
[3,7,5,1,2,6,4,8]=>0110010
[3,7,5,1,2,6,8,4]=>0110001
[3,5,7,2,8,6,1,4]=>0010110
[2,5,7,4,8,6,1,3]=>0010110
[2,6,4,8,7,5,1,3]=>0101110
[3,6,2,5,8,7,1,4]=>0100110
[5,2,8,4,7,6,1,3]=>1010110
[6,2,4,8,7,5,1,3]=>1001110
[2,5,1,4,7,3,8,6]=>0100101
[3,1,5,6,2,8,7,4]=>1001011
[7,1,4,2,8,6,5,3]=>1010111
[4,1,5,3,2,8,7,6]=>1011011
[7,2,3,5,1,8,6,4]=>1001011
[1,6,4,2,8,7,5,3]=>0110111
[4,6,2,7,5,1,8,3]=>0101101
[1,5,3,6,2,8,7,4]=>0101011
[3,6,2,5,1,4,8,7]=>0101001
[5,2,8,4,1,3,7,6]=>1011001
[2,4,8,7,1,3,6,5]=>0011001
[6,3,1,7,2,8,5,4]=>1101011
[7,5,1,2,8,6,4,3]=>1100111
[1,5,2,3,8,7,6,4]=>0100111
[4,5,1,2,8,7,6,3]=>0100111
[3,5,8,7,2,6,4,1]=>0011011
[5,8,2,7,1,6,4,3]=>0101011
[2,1,6,4,5,8,3,7]=>1010010
[8,6,3,7,5,2,1,4]=>1101110
[4,6,3,8,5,2,1,7]=>0101110
[4,6,3,7,5,2,8,1]=>0101101
[3,5,7,8,2,6,1,4]=>0001010
[4,2,3,6,1,5,8,7]=>1001001
[3,8,6,4,5,1,2,7]=>0110100
[4,8,3,7,5,2,1,6]=>0101110
[8,7,3,6,5,1,2,4]=>1101100
[5,2,8,3,7,6,1,4]=>1010110
[8,2,7,3,1,6,4,5]=>1011010
[8,6,7,4,1,5,3,2]=>1011011
[4,8,6,7,5,1,3,2]=>0101101
[7,1,8,4,6,5,2,3]=>1010110
[8,7,1,5,4,6,2,3]=>1101010
[8,5,7,1,4,6,3,2]=>1010011
[6,4,8,5,1,7,3,2]=>1011011
[8,4,7,1,5,6,3,2]=>1010011
[8,7,5,1,4,6,2,3]=>1110010
[8,7,2,5,1,4,6,3]=>1101001
[4,8,7,2,5,1,6,3]=>0110101
[8,7,1,4,2,5,6,3]=>1101001
[8,7,5,1,2,4,6,3]=>1110001
[7,1,8,5,6,2,3,4]=>1010100
[3,5,8,7,1,2,6,4]=>0011001
[2,3,8,5,7,1,6,4]=>0010101
[3,8,7,1,5,6,2,4]=>0110010
[3,5,8,7,1,6,2,4]=>0011010
[2,3,8,6,7,5,1,4]=>0010110
[3,2,8,6,7,5,1,4]=>1010110
[4,1,8,6,2,7,5,3]=>1011011
[8,7,4,1,2,6,5,3]=>1110011
[1,3,8,6,7,5,2,4]=>0010110
[5,7,1,8,2,6,3,4]=>0101010
[2,8,7,1,5,6,3,4]=>0110010
[8,7,1,5,2,4,6,3]=>1101001
[7,1,8,2,4,6,5,3]=>1010011
[1,6,2,8,4,7,5,3]=>0101011
[1,3,8,5,7,2,6,4]=>0010101
[1,8,3,7,2,5,6,4]=>0101001
[2,8,7,1,3,5,6,4]=>0110001
[5,7,1,8,2,3,6,4]=>0101001
[7,1,8,2,3,5,6,4]=>1010001
[8,6,3,7,4,1,5,2]=>1101101
[4,2,8,6,7,5,1,3]=>1010110
[8,4,2,7,5,6,1,3]=>1101010
[4,8,3,6,1,7,5,2]=>0101011
[8,3,4,7,5,1,6,2]=>1001101
[8,3,7,4,5,1,6,2]=>1010101
[8,7,4,2,5,6,1,3]=>1110010
[8,7,5,1,6,2,3,4]=>1110100
[8,7,2,4,1,5,6,3]=>1101001
[4,8,6,1,7,2,5,3]=>0110101
[4,2,8,6,7,1,5,3]=>1010101
[8,7,4,1,2,5,6,3]=>1110001
[8,2,7,1,6,3,4,5]=>1010100
[8,2,7,1,3,6,4,5]=>1010010
[2,8,3,6,7,1,5,4]=>0100101
[8,7,2,1,3,5,6,4]=>1110001
[1,8,7,2,3,6,4,5]=>0110010
[1,8,7,2,6,3,4,5]=>0110100
[8,2,7,3,6,1,4,5]=>1010100
[1,8,7,3,6,2,4,5]=>0110100
[1,8,2,7,6,3,4,5]=>0101100
[8,2,7,4,1,5,6,3]=>1011001
[8,2,1,7,5,6,3,4]=>1101010
[8,7,3,1,5,6,2,4]=>1110010
[2,8,7,3,5,6,1,4]=>0110010
[8,3,1,6,7,5,2,4]=>1100110
[8,5,2,1,6,7,4,3]=>1110011
[1,5,2,8,6,7,4,3]=>0101011
[1,2,8,6,7,5,3,4]=>0010110
[1,8,3,6,7,5,2,4]=>0100110
[8,2,3,6,7,5,1,4]=>1000110
[8,3,7,2,5,6,1,4]=>1010010
[8,1,3,7,5,6,2,4]=>1001010
[8,4,1,2,7,5,6,3]=>1100101
[8,1,4,2,6,7,5,3]=>1010011
[1,2,8,6,7,3,5,4]=>0010101
[8,1,2,7,3,6,4,5]=>1001010
[8,1,7,3,6,2,4,5]=>1010100
[8,1,7,2,6,3,4,5]=>1010100
[8,1,7,2,3,6,4,5]=>1010010
[8,1,3,7,2,5,6,4]=>1001001
[1,8,3,6,7,2,5,4]=>0100101
[1,7,8,2,3,6,5,4]=>0010011
[8,3,7,1,2,5,6,4]=>1010001
[7,4,2,6,1,5,3,8]=>1101010
[7,4,2,5,6,1,3,8]=>1100100
[7,3,5,6,4,2,1,8]=>1001110
[7,4,3,1,5,6,2,8]=>1110010
[7,4,5,2,6,1,3,8]=>1010100
[5,3,7,2,8,6,4,1]=>1010111
[5,3,8,2,6,7,4,1]=>1010011
[6,3,8,2,5,4,7,1]=>1010101
[6,4,3,1,8,2,7,5]=>1110101
[5,3,7,8,2,6,4,1]=>1001011
[4,7,8,5,6,3,2,1]=>0010111
[5,3,7,6,8,2,4,1]=>1010101
[5,7,8,4,6,2,1,3]=>0010110
[5,8,4,3,6,7,1,2]=>0110010
[5,8,6,4,7,2,1,3]=>0110110
[5,3,8,6,2,7,4,1]=>1011011
[4,7,5,8,6,3,2,1]=>0101111
[6,3,8,7,2,4,1,5]=>1011010
[5,3,8,7,2,6,4,1]=>1011011
[5,3,8,6,7,2,4,1]=>1010101
[5,3,7,8,6,2,4,1]=>1001101
[5,7,6,4,8,2,1,3]=>0110110
[5,8,4,6,7,2,1,3]=>0100110
[6,4,2,8,1,7,3,5]=>1101010
[6,5,2,4,3,7,8,1]=>1101001
[5,4,6,2,8,7,1,3]=>1010110
[5,6,3,8,7,2,4,1]=>0101101
[6,7,4,3,1,8,2,5]=>0111010
[5,7,4,3,6,8,1,2]=>0110010
[5,7,3,8,6,2,4,1]=>0101101
[4,5,8,6,7,3,2,1]=>0010111
[4,6,8,5,7,3,2,1]=>0010111
[5,6,8,3,7,2,4,1]=>0010101
[5,4,6,8,2,7,1,3]=>1001010
[7,8,4,5,1,3,2,6]=>0101010
[6,7,1,3,2,5,4,8]=>0101010
[6,7,1,4,3,5,2,8]=>0101010
[7,8,2,3,1,5,4,6]=>0101010
[7,8,2,4,3,5,1,6]=>0101010
[7,8,2,4,1,5,3,6]=>0101010
[1,4,2,6,5,7,3,8]=>0101010
[5,6,1,4,2,7,3,8]=>0101010
[6,7,2,4,1,5,3,8]=>0101010
[6,7,2,4,3,5,1,8]=>0101010
[6,7,2,3,1,5,4,8]=>0101010
[6,7,3,5,4,8,1,2]=>0101010
[2,4,1,6,5,7,3,8]=>0101010
[1,5,2,6,4,7,3,8]=>0101010
[2,5,1,6,4,7,3,8]=>0101010
[5,6,2,4,3,7,1,8]=>0101010
[4,5,2,6,1,7,3,8]=>0101010
[4,5,1,6,3,7,2,8]=>0101010
[4,5,3,6,1,7,2,8]=>0101010
[5,6,3,4,1,7,2,8]=>0101010
[5,6,1,4,3,7,2,8]=>0101010
[5,6,1,3,2,7,4,8]=>0101010
[5,6,4,7,1,3,2,8]=>0101010
[6,7,4,5,1,3,2,8]=>0101010
[6,7,5,8,1,3,2,4]=>0101010
[4,5,1,3,2,7,6,8]=>0101010
[4,6,5,7,1,3,2,8]=>0101010
[4,6,1,3,2,7,5,8]=>0101010
[1,4,3,6,2,7,5,8]=>0101010
[4,5,2,3,1,7,6,8]=>0101010
[4,5,3,7,6,8,1,2]=>0101010
[4,6,5,7,3,8,1,2]=>0101010
[4,6,5,7,2,3,1,8]=>0101010
[3,5,4,6,1,7,2,8]=>0101010
[3,5,1,6,4,7,2,8]=>0101010
[1,5,3,6,4,7,2,8]=>0101010
[1,5,3,6,2,7,4,8]=>0101010
[3,5,2,6,1,7,4,8]=>0101010
[3,5,2,6,4,7,1,8]=>0101010
[3,4,2,6,1,7,5,8]=>0101010
[4,6,2,3,1,7,5,8]=>0101010
[2,4,3,6,1,7,5,8]=>0101010
[2,5,3,6,4,7,1,8]=>0101010
[2,5,3,6,1,7,4,8]=>0101010
[3,6,2,7,5,4,8,1]=>0101101
[5,2,6,7,4,3,8,1]=>1001101
[3,5,2,7,6,4,8,1]=>0101101
[1,3,7,2,8,5,6,4]=>0010101
[2,1,5,6,8,4,3,7]=>1000110
[1,3,7,2,8,5,4,6]=>0010110
[1,5,4,3,6,8,2,7]=>0110010
[1,6,4,5,7,8,3,2]=>0100011
[2,1,5,6,8,4,7,3]=>1000101
[2,1,5,6,8,7,3,4]=>1000110
[3,6,5,2,7,8,4,1]=>0110011
[6,2,4,7,5,8,3,1]=>1001011
[1,5,7,8,4,2,6,3]=>0001101
[3,7,4,1,8,6,2,5]=>0110110
[3,4,6,8,5,7,2,1]=>0001011
[4,5,6,2,8,7,3,1]=>0010111
[4,5,6,1,8,7,3,2]=>0010111
[4,5,6,3,1,8,7,2]=>0011011
[4,3,6,2,1,7,5,8]=>1011010
[4,6,3,2,1,7,5,8]=>0111010
[4,6,3,1,7,5,2,8]=>0110110
[4,5,3,7,6,1,8,2]=>0101101
[4,5,1,7,3,8,6,2]=>0101011
[2,5,7,1,4,3,8,6]=>0010101
[4,3,5,7,6,1,8,2]=>1001101
[4,3,6,1,7,5,2,8]=>1010110
[4,3,2,6,1,7,5,8]=>1101010
[5,3,2,1,6,4,7,8]=>1110100
[5,3,1,6,2,7,4,8]=>1101010
[5,1,6,3,2,7,4,8]=>1011010
[2,6,1,4,7,5,3,8]=>0100110
[3,6,1,7,4,2,5,8]=>0101100
[4,6,1,7,5,3,2,8]=>0101110
[5,1,6,3,7,4,2,8]=>1010110
[5,3,6,4,2,1,7,8]=>1011100
[5,3,2,6,4,1,7,8]=>1101100
[5,2,1,6,3,7,4,8]=>1101010
[5,2,6,3,1,7,4,8]=>1011010
[4,2,6,3,1,7,8,5]=>1011001
[3,6,2,1,7,4,5,8]=>0110100
[3,6,2,7,4,1,5,8]=>0101100
[3,5,7,2,8,6,4,1]=>0010111
[2,6,1,3,7,5,4,8]=>0100110
[3,6,1,7,5,2,4,8]=>0101100
[5,1,6,2,7,4,3,8]=>1010110
[5,2,6,4,3,1,7,8]=>1011100
[5,2,1,6,4,3,7,8]=>1101100
[5,4,2,1,6,3,7,8]=>1110100
[5,4,1,6,2,7,3,8]=>1101010
[5,1,6,4,2,7,3,8]=>1011010
[3,6,1,7,5,4,8,2]=>0101101
[2,6,1,5,4,3,7,8]=>0101100
[3,1,6,2,5,4,7,8]=>1010100
[4,1,6,3,2,7,8,5]=>1011001
[5,1,6,4,3,2,7,8]=>1011100
[5,4,1,6,3,2,7,8]=>1101100
[5,4,3,1,6,2,7,8]=>1110100
[1,2,8,7,4,6,3,5]=>0011010
[4,5,1,8,7,6,2,3]=>0101110
[4,1,5,8,7,6,2,3]=>1001110
[7,5,8,4,2,6,3,1]=>1011011
[6,8,4,5,2,7,3,1]=>0101011
[6,8,2,5,3,7,4,1]=>0101011
[6,3,8,4,2,7,5,1]=>1011011
[7,2,5,3,8,6,4,1]=>1010111
[3,4,7,5,8,6,2,1]=>0010111
[3,6,7,4,8,5,2,1]=>0010111
[6,7,4,2,8,5,3,1]=>0110111
[4,7,5,2,8,6,3,1]=>0110111
[5,6,2,8,3,7,4,1]=>0101011
[1,5,8,2,7,3,6,4]=>0010101
[5,8,4,7,2,3,6,1]=>0101001
[6,7,4,8,1,5,3,2]=>0101011
[6,8,5,3,7,2,4,1]=>0110101
[7,5,3,8,2,6,4,1]=>1101011
[3,7,4,5,8,6,2,1]=>0100111
[7,4,2,5,8,6,3,1]=>1100111
[6,8,4,2,5,7,3,1]=>0110011
[7,5,8,3,4,6,2,1]=>1010011
[7,4,5,8,1,6,3,2]=>1001011
[6,3,4,7,8,5,2,1]=>1000111
[3,6,8,4,5,7,1,2]=>0010010
[1,6,8,4,7,2,3,5]=>0010100
[1,4,5,7,8,2,6,3]=>0000101
[1,4,5,8,7,2,3,6]=>0001100
[1,2,5,8,3,6,4,7]=>0001010
[7,8,1,4,6,2,3,5]=>0100100
[1,6,7,4,8,2,5,3]=>0010101
[1,4,5,6,8,2,7,3]=>0000101
[1,4,5,8,6,2,7,3]=>0001101
[1,2,5,8,3,4,7,6]=>0001001
[7,8,1,2,3,5,4,6]=>0100010
[1,6,7,2,3,5,4,8]=>0010010
[1,4,5,7,6,2,3,8]=>0001100
[1,2,5,7,3,6,4,8]=>0001010
[1,2,5,7,3,6,8,4]=>0001001
[1,6,8,2,3,5,7,4]=>0010001
[1,6,8,4,5,2,3,7]=>0010100
[1,6,8,2,3,4,7,5]=>0010001
[1,6,8,2,3,7,4,5]=>0010010
[1,4,5,7,6,2,8,3]=>0001101
[7,8,1,4,5,2,6,3]=>0100101
[1,6,7,2,3,8,5,4]=>0010011
[1,2,5,6,3,8,7,4]=>0001011
[2,7,4,8,3,5,1,6]=>0101010
[2,7,4,8,3,5,6,1]=>0101001
[7,2,8,4,3,5,1,6]=>1011010
[8,4,2,1,5,3,6,7]=>1110100
[8,4,1,5,3,2,6,7]=>1101100
[6,7,3,8,4,2,5,1]=>0101101
[6,7,3,8,4,2,1,5]=>0101110
[7,1,8,4,3,5,2,6]=>1011010
[1,7,8,4,3,5,2,6]=>0011010
[7,1,4,8,3,5,2,6]=>1001010
[7,1,8,4,3,5,6,2]=>1011001
[6,7,3,1,8,4,5,2]=>0110101
[6,7,1,4,8,3,5,2]=>0100101
[6,7,4,1,3,8,2,5]=>0110010
[1,6,7,8,4,3,2,5]=>0001110
[7,2,1,8,4,5,3,6]=>1101010
[6,2,7,1,8,4,3,5]=>1010110
[6,2,7,8,4,3,1,5]=>1001110
[6,2,7,8,4,3,5,1]=>1001101
[2,6,7,4,8,3,5,1]=>0010101
[2,6,7,4,8,3,1,5]=>0010110
[7,8,1,3,6,2,4,5]=>0100100
[1,2,7,8,6,3,4,5]=>0001100
[2,6,7,1,8,5,3,4]=>0010110
[2,6,7,8,5,3,4,1]=>0001101
[6,2,7,8,4,5,3,1]=>1001011
[1,7,2,8,4,5,6,3]=>0101001
[6,3,7,8,1,5,2,4]=>1001010
[6,7,1,2,8,5,3,4]=>0100110
[1,6,7,8,4,2,5,3]=>0001101
[3,1,2,7,6,5,8,4]=>1001101
[6,1,2,4,7,3,8,5]=>1000101
[1,7,5,3,6,4,8,2]=>0110101
[5,1,2,6,7,4,8,3]=>1000101
[4,1,5,7,3,2,6,8]=>1001100
[4,6,1,7,3,2,5,8]=>0101100
[4,6,1,8,3,2,5,7]=>0101100
[4,1,7,8,6,2,3,5]=>1001100
[1,6,5,7,8,3,4,2]=>0100101
[1,6,5,8,7,3,4,2]=>0101101
[4,1,8,7,6,2,3,5]=>1011100
[4,8,1,7,3,5,2,6]=>0101010
[4,8,1,6,3,2,5,7]=>0101100
[4,7,1,6,3,2,5,8]=>0101100
[6,1,2,3,7,5,4,8]=>1000110
[6,8,1,5,3,7,2,4]=>0101010
[8,7,5,2,4,1,6,3]=>1110101
[1,5,8,3,4,7,6,2]=>0010011
[7,8,5,2,4,1,6,3]=>0110101
[7,1,2,3,5,6,4,8]=>1000010
[7,1,8,4,6,3,2,5]=>1010110
[6,8,2,4,3,1,5,7]=>0101100
[6,7,2,4,3,1,5,8]=>0101100
[3,7,1,8,6,4,2,5]=>0101110
[1,6,4,3,7,5,8,2]=>0110101
[3,1,2,6,7,5,8,4]=>1000101
[3,8,1,7,6,4,2,5]=>0101110
[7,6,2,4,3,1,5,8]=>1101100
[8,7,2,4,3,5,1,6]=>1101010
[8,1,7,4,6,3,2,5]=>1010110
[8,1,7,6,5,3,2,4]=>1011110
[1,5,7,3,4,6,8,2]=>0010001
[8,7,2,5,3,6,1,4]=>1101010
[7,1,2,3,5,4,8,6]=>1000101
[6,1,2,3,5,8,4,7]=>1000010
[6,1,2,3,5,7,4,8]=>1000010
[5,1,2,3,7,6,4,8]=>1000110
[5,1,2,3,8,6,4,7]=>1000110
[1,5,6,3,4,7,8,2]=>0010001
[8,6,5,2,4,7,1,3]=>1110010
[7,6,2,5,3,1,8,4]=>1101101
[6,7,3,5,1,4,8,2]=>0101001
[5,3,6,7,4,8,2,1]=>1001011
[5,3,2,8,6,7,4,1]=>1101011
[5,4,8,2,6,7,3,1]=>1010011
[5,4,8,6,2,7,3,1]=>1011011
[5,6,3,8,4,7,2,1]=>0101011
[6,7,3,8,5,2,4,1]=>0101101
[3,5,7,8,4,6,2,1]=>0001011
[5,7,8,2,4,6,3,1]=>0010011
[2,5,8,4,3,7,6,1]=>0011011
[3,7,4,8,6,2,1,5]=>0101110
[3,6,4,8,7,2,5,1]=>0101101
[3,5,4,8,2,7,6,1]=>0101011
[4,5,7,3,8,6,2,1]=>0010111
[6,3,1,8,7,5,4,2]=>1101111
[5,4,8,1,7,6,3,2]=>1010111
[5,8,4,1,7,6,3,2]=>0110111
[7,5,4,1,8,6,3,2]=>1110111
[8,5,4,1,7,6,3,2]=>1110111
[1,8,2,5,6,3,4,7]=>0100100
[7,2,8,4,5,1,3,6]=>1010100
[1,3,7,5,6,2,4,8]=>0010100
[1,6,7,4,3,5,2,8]=>0011010
[1,8,2,5,3,6,7,4]=>0101001
[2,6,8,4,3,5,7,1]=>0011001
[7,2,8,4,1,5,6,3]=>1011001
[7,5,8,1,2,6,3,4]=>1010010
[1,5,2,6,4,7,8,3]=>0101001
[1,5,4,6,2,3,7,8]=>0101000
[6,2,5,7,1,4,8,3]=>1001001
[6,5,4,3,8,1,7,2]=>1110101
[2,6,5,8,3,4,1,7]=>0101010
[2,6,5,7,3,4,1,8]=>0101010
[6,2,5,7,4,1,3,8]=>1001100
[6,2,5,8,4,1,3,7]=>1001100
[2,7,8,4,6,1,3,5]=>0010100
[6,1,2,8,5,4,7,3]=>1001101
[6,2,5,7,8,1,3,4]=>1000100
[1,5,4,2,6,7,3,8]=>0110010
[2,6,5,7,3,8,1,4]=>0101010
[1,6,2,7,5,8,4,3]=>0101011
[1,3,2,7,8,5,6,4]=>0100101
[1,6,2,4,8,7,3,5]=>0100110
[6,5,2,1,8,7,3,4]=>1110110
[2,6,5,3,7,8,4,1]=>0110011
[6,5,2,3,8,7,1,4]=>1100110
[5,1,4,2,3,7,8,6]=>1010001
[1,5,4,2,6,3,8,7]=>0110101
[5,1,6,3,8,2,7,4]=>1010101
[6,5,8,7,4,3,1,2]=>1011110
[6,4,2,7,8,5,1,3]=>1100110
[6,1,4,8,7,5,2,3]=>1001110
[1,6,4,8,7,5,2,3]=>0101110
[1,8,6,2,4,7,3,5]=>0110010
[8,1,6,2,4,7,3,5]=>1010010
[6,4,1,7,8,5,2,3]=>1100110
[7,6,1,2,4,8,3,5]=>1100010
[1,8,6,3,4,7,2,5]=>0110010
[1,7,2,5,4,8,3,6]=>0101010
[7,1,2,5,4,8,3,6]=>1001010
[2,7,1,5,4,8,3,6]=>0101010
[2,8,6,1,4,7,3,5]=>0110010
[7,2,1,5,4,8,3,6]=>1101010
[1,2,7,5,4,8,3,6]=>0011010
[3,2,7,5,4,8,1,6]=>1011010
[2,5,8,4,7,3,1,6]=>0010110
[2,3,7,5,4,8,1,6]=>0011010
[6,8,3,2,4,7,1,5]=>0110010
[3,7,2,5,4,8,1,6]=>0101010
[3,1,7,5,4,8,2,6]=>1011010
[1,3,7,5,4,8,2,6]=>0011010
[1,5,8,4,7,3,2,6]=>0010110
[5,1,8,4,7,3,2,6]=>1010110
[5,8,2,4,7,3,1,6]=>0100110
[6,8,4,3,7,5,1,2]=>0110110
[8,5,2,4,7,3,1,6]=>1100110
[8,1,5,4,7,3,2,6]=>1010110
[1,8,5,4,7,3,2,6]=>0110110
[1,7,3,5,4,8,2,6]=>0101010
[8,6,3,1,4,7,2,5]=>1110010
[8,6,4,1,7,2,5,3]=>1110101
[5,3,7,4,6,8,2,1]=>1010011
[4,1,3,2,7,8,5,6]=>1010010
[1,4,3,2,7,8,5,6]=>0110010
[2,4,3,1,7,8,5,6]=>0110010
[2,7,3,5,4,8,1,6]=>0101010
[2,8,5,4,7,3,1,6]=>0110110
[5,7,3,4,6,8,2,1]=>0100011
[8,2,5,4,7,3,1,6]=>1010110
[7,2,3,5,4,8,1,6]=>1001010
[3,2,1,4,7,8,5,6]=>1100010
[8,1,7,6,4,3,5,2]=>1011101
[8,6,4,5,2,7,1,3]=>1101010
[7,1,8,6,4,3,5,2]=>1011101
[7,4,2,5,1,6,3,8]=>1101010
[7,3,6,5,2,1,4,8]=>1011100
[8,3,6,5,2,1,7,4]=>1011101
[7,3,6,5,2,1,8,4]=>1011101
[5,4,2,8,1,3,7,6]=>1101001
[5,8,2,6,4,1,3,7]=>0101100
[6,4,2,5,1,8,3,7]=>1101010
[6,3,5,2,1,4,7,8]=>1011000
[2,3,5,8,1,4,7,6]=>0001001
[2,3,6,8,1,5,7,4]=>0001001
[6,3,8,5,2,7,1,4]=>1011010
[6,3,7,5,2,1,4,8]=>1011100
[2,5,7,6,3,1,4,8]=>0011100
[2,8,7,6,3,1,5,4]=>0111101
[2,5,8,7,6,3,1,4]=>0011110
[2,4,8,1,6,5,7,3]=>0010101
[2,8,7,3,6,1,4,5]=>0110100
[8,4,2,5,1,3,7,6]=>1101001
[2,3,6,8,1,4,7,5]=>0001001
[2,7,8,6,3,1,4,5]=>0011100
[2,8,6,3,1,4,5,7]=>0111000
[8,3,5,2,1,4,6,7]=>1011000
[2,5,8,1,7,3,6,4]=>0010101
[2,7,1,5,8,3,4,6]=>0100100
[3,7,5,8,1,2,6,4]=>0101001
[7,3,6,1,2,8,4,5]=>1010010
[7,4,8,1,6,5,2,3]=>1010110
[6,8,4,5,1,7,2,3]=>0101010
[5,1,8,7,6,2,3,4]=>1011100
[4,6,1,8,7,5,2,3]=>0101110
[3,4,8,7,1,2,5,6]=>0011000
[6,4,8,7,1,2,5,3]=>1011001
[6,5,1,8,2,7,3,4]=>1101010
[6,5,1,7,2,8,3,4]=>1101010
[6,5,1,7,2,3,8,4]=>1101001
[5,6,8,7,4,1,2,3]=>0011100
[6,8,3,1,5,2,4,7]=>0110100
[4,2,7,1,6,3,5,8]=>1010100
[5,1,7,4,2,6,3,8]=>1011010
[5,8,2,1,4,7,3,6]=>0110010
[6,8,4,3,1,5,7,2]=>0111001
[6,8,4,2,1,5,7,3]=>0111001
[6,8,3,2,1,4,5,7]=>0111000
[4,2,1,6,5,8,3,7]=>1101010
[6,3,2,1,7,4,5,8]=>1110100
[6,4,2,1,7,5,3,8]=>1110110
[5,3,2,7,6,1,4,8]=>1101100
[5,3,2,8,6,1,4,7]=>1101100
[6,3,2,8,7,1,4,5]=>1101100
[4,2,8,1,7,3,5,6]=>1010100
[4,3,8,7,2,1,5,6]=>1011100
[2,1,5,8,4,7,3,6]=>1001010
[4,3,2,5,8,1,6,7]=>1100100
[4,3,2,5,7,1,6,8]=>1100100
[4,3,1,6,2,7,5,8]=>1101010
[5,4,1,7,2,8,6,3]=>1101011
[3,2,1,4,8,7,5,6]=>1100110
[3,2,1,4,6,8,5,7]=>1100010
[8,6,1,4,5,7,2,3]=>1100010
[3,8,6,4,5,7,1,2]=>0110010
[5,2,8,3,7,4,6,1]=>1010101
[6,2,8,5,4,7,3,1]=>1011011
[5,2,8,4,3,6,7,1]=>1011001
[5,4,2,7,3,6,1,8]=>1101010
[5,4,2,8,3,6,1,7]=>1101010
[6,5,3,8,4,7,2,1]=>1101011
[5,2,8,4,3,7,1,6]=>1011010
[6,2,8,3,7,4,1,5]=>1010110
[5,4,2,7,3,1,8,6]=>1101101
[6,4,3,7,1,2,8,5]=>1101001
[6,4,3,8,1,2,7,5]=>1101001
[7,2,8,4,3,1,5,6]=>1011100
[7,5,3,8,4,2,6,1]=>1101101
[6,4,2,7,3,1,5,8]=>1101100
[7,6,4,8,2,3,5,1]=>1101001
[5,3,1,7,8,4,6,2]=>1100101
[5,3,2,7,8,4,6,1]=>1100101
[6,5,1,7,8,2,3,4]=>1100100
[6,3,1,7,8,4,2,5]=>1100110
[5,4,1,7,3,8,2,6]=>1101010
[6,3,2,7,8,4,1,5]=>1100110
[6,1,5,4,3,2,8,7]=>1011101
[8,7,6,1,3,5,2,4]=>1110010
[8,1,6,5,7,3,4,2]=>1010101
[8,4,1,5,7,6,2,3]=>1100110
[7,8,6,2,5,3,1,4]=>0110110
[6,1,3,5,2,8,4,7]=>1001010
[8,1,3,7,4,2,5,6]=>1001100
[4,3,8,7,5,2,1,6]=>1011110
[6,7,1,8,5,3,4,2]=>0101101
[2,7,6,4,8,3,5,1]=>0110101
[6,5,2,7,1,4,8,3]=>1101001
[7,4,6,1,3,2,8,5]=>1010101
[7,5,2,1,3,8,4,6]=>1110010
[8,4,7,6,3,1,5,2]=>1011101
[7,4,1,5,6,3,8,2]=>1100101
[3,4,7,5,6,1,8,2]=>0010101
[2,7,6,1,3,4,8,5]=>0110001
[5,7,2,1,6,3,8,4]=>0110101
[4,7,2,5,6,3,8,1]=>0100101
[8,6,2,5,7,1,4,3]=>1100101
[2,7,4,5,3,8,1,6]=>0101010
[6,8,7,1,3,2,5,4]=>0110101
[2,8,6,5,7,1,4,3]=>0110101
[5,8,4,3,2,6,7,1]=>0111001
[1,8,5,6,2,4,7,3]=>0101001
[8,1,5,6,2,4,7,3]=>1001001
[6,4,8,1,3,2,7,5]=>1010101
[5,4,1,2,8,6,7,3]=>1100101
[8,4,5,2,1,6,7,3]=>1011001
[3,1,2,6,8,4,7,5]=>1000101
[5,1,3,2,7,8,4,6]=>1010010
[4,6,7,8,3,1,5,2]=>0001101
[5,2,8,6,3,4,7,1]=>1011001
[5,6,8,4,3,2,7,1]=>0011101
[5,3,8,1,7,2,4,6]=>1010100
[3,6,7,8,4,2,1,5]=>0001110
[6,5,1,8,4,3,7,2]=>1101101
[6,3,8,4,2,1,7,5]=>1011101
[2,5,8,3,1,6,7,4]=>0011001
[3,5,8,1,2,6,7,4]=>0010001
[3,2,7,8,4,6,1,5]=>1001010
[5,1,8,3,4,6,7,2]=>1010001
[4,8,7,2,1,6,3,5]=>0111010
[2,8,1,6,3,4,7,5]=>0101001
[3,6,1,2,5,8,4,7]=>0100010
[1,4,5,8,2,3,7,6]=>0001001
[1,5,2,4,6,8,3,7]=>0100010
[3,6,1,5,8,2,4,7]=>0100100
[2,6,5,1,4,8,3,7]=>0110010
[2,5,1,8,4,7,3,6]=>0101010
[2,7,1,4,3,6,8,5]=>0101001
[1,3,7,5,8,2,4,6]=>0010100
[8,2,1,5,7,3,4,6]=>1100100
[2,5,4,8,1,3,7,6]=>0101001
[2,4,1,3,8,6,7,5]=>0100101
[8,4,3,7,1,2,6,5]=>1101001
[1,7,3,5,8,2,6,4]=>0100101
[1,8,4,2,6,7,3,5]=>0110010
[3,1,6,8,7,2,4,5]=>1001100
[7,2,1,6,8,3,4,5]=>1100100
[4,1,7,2,6,8,3,5]=>1010010
[5,1,7,2,3,6,8,4]=>1010001
[7,2,1,6,3,5,8,4]=>1101001
[2,6,1,7,3,5,8,4]=>0101001
[8,1,3,2,4,6,7,5]=>1010001
[7,3,1,2,4,6,8,5]=>1100001
[1,8,3,4,7,2,5,6]=>0100100
[3,5,8,1,2,7,4,6]=>0010010
[3,6,8,1,2,4,7,5]=>0010001
[4,1,3,8,7,2,6,5]=>1001101
[1,3,7,4,8,2,6,5]=>0010101
[1,4,6,8,2,3,7,5]=>0001001
[3,5,8,1,7,2,4,6]=>0010100
[2,6,8,1,7,3,4,5]=>0010100
[1,8,3,2,7,5,6,4]=>0110101
[2,6,7,3,8,1,5,4]=>0010101
[8,4,1,7,3,6,2,5]=>1101010
[3,7,2,8,6,1,5,4]=>0101101
[6,2,3,8,7,1,5,4]=>1001101
[5,1,7,8,4,2,6,3]=>1001101
[5,1,8,7,4,2,6,3]=>1011101
[4,7,2,8,3,6,5,1]=>0101011
[4,1,7,8,5,3,6,2]=>1001101
[5,1,7,4,8,3,6,2]=>1010101
[4,1,8,7,5,3,6,2]=>1011101
[4,8,2,7,3,6,5,1]=>0101011
[4,7,2,6,3,5,8,1]=>0101001
[6,8,2,4,3,7,5,1]=>0101011
[6,7,2,4,3,8,5,1]=>0101011
[3,8,7,2,4,1,5,6]=>0110100
[3,7,8,2,4,1,5,6]=>0010100
[3,6,8,2,4,5,7,1]=>0010001
[3,6,7,2,4,5,8,1]=>0010001
[1,7,5,3,8,2,4,6]=>0110100
[1,7,2,4,5,8,3,6]=>0100010
[1,7,4,5,8,3,2,6]=>0100110
[2,6,4,7,8,3,5,1]=>0100101
[1,2,6,4,7,8,3,5]=>0010010
[2,7,4,5,8,1,3,6]=>0100100
[2,7,5,3,1,8,4,6]=>0111010
[6,1,4,7,8,3,5,2]=>1000101
[3,6,4,7,8,1,5,2]=>0100101
[4,3,6,7,1,8,5,2]=>1001011
[4,3,6,7,1,8,2,5]=>1001010
[3,7,4,5,2,1,8,6]=>0101101
[1,3,6,4,7,2,8,5]=>0010101
[3,6,4,7,2,8,5,1]=>0101011
[6,1,7,3,8,2,5,4]=>1010101
[1,6,7,3,8,2,5,4]=>0010101
[6,1,4,7,8,5,2,3]=>1000110
[6,3,2,1,7,8,5,4]=>1110011
[6,2,7,3,1,8,5,4]=>1011011
[6,2,4,7,8,1,5,3]=>1000101
[2,6,7,3,1,8,5,4]=>0011011
[8,6,5,1,3,2,4,7]=>1110100
[6,4,7,8,3,2,5,1]=>1001101
[3,8,4,7,1,2,5,6]=>0101000
[4,8,6,1,5,3,2,7]=>0110110
[5,8,6,4,1,3,2,7]=>0111010
[8,3,6,4,5,2,1,7]=>1010110
[6,8,5,7,4,2,3,1]=>0101101
[2,3,8,7,1,6,4,5]=>0011010
[4,3,7,8,1,6,2,5]=>1001010
[3,5,8,7,4,1,2,6]=>0011100
[7,3,8,4,1,2,5,6]=>1011000
[4,8,1,2,7,3,5,6]=>0100100
[6,8,1,2,7,4,5,3]=>0100101
[5,6,8,4,1,3,7,2]=>0011001
[8,5,4,7,1,6,3,2]=>1101011
[2,5,8,7,3,6,4,1]=>0011011
[2,4,8,7,5,6,1,3]=>0011010
[3,7,4,8,5,6,2,1]=>0101011
[6,4,8,7,5,1,2,3]=>1011100
[3,8,5,2,4,6,7,1]=>0110001
[5,7,1,8,4,6,2,3]=>0101010
[6,3,8,7,2,1,4,5]=>1011100
[2,3,7,8,5,6,1,4]=>0001010
[3,7,6,8,5,1,2,4]=>0101100
[2,6,7,8,5,1,3,4]=>0001100
[2,4,7,8,1,6,3,5]=>0001010
[5,4,7,8,2,6,3,1]=>1001011
[2,8,3,4,1,5,7,6]=>0101001
[6,8,3,4,1,2,7,5]=>0101001
[6,8,7,1,5,2,3,4]=>0110100
[2,5,3,1,8,6,7,4]=>0110101
[4,5,3,2,8,6,7,1]=>0110101
[3,5,8,6,1,4,7,2]=>0011001
[2,8,5,6,1,4,7,3]=>0101001
[4,8,6,1,5,2,7,3]=>0110101
[5,8,2,3,7,6,1,4]=>0100110
[4,6,8,5,3,2,7,1]=>0011101
[2,6,4,8,5,1,7,3]=>0101101
[7,6,4,8,5,2,1,3]=>1101110
[3,4,8,6,5,2,7,1]=>0011101
[3,4,8,7,5,6,2,1]=>0011011
[7,5,3,2,8,6,1,4]=>1110110
[2,5,1,3,8,6,7,4]=>0100101
[4,5,1,2,8,6,7,3]=>0100101
[5,4,8,1,3,6,7,2]=>1010001
[8,3,5,4,1,6,7,2]=>1011001
[5,1,6,4,3,2,8,7]=>1011101
[8,3,7,1,4,6,5,2]=>1010011
[2,8,3,6,4,7,5,1]=>0101011
[6,2,1,7,5,8,3,4]=>1101010
[6,7,2,1,5,8,4,3]=>0110011
[1,6,4,8,3,2,5,7]=>0101100
[1,8,3,5,6,2,4,7]=>0100100
[1,4,8,5,6,2,3,7]=>0010100
[6,1,4,8,2,3,5,7]=>1001000
[8,7,2,5,6,1,4,3]=>1100101
[1,8,2,5,4,7,3,6]=>0101010
[5,7,4,1,2,3,8,6]=>0110001
[1,7,4,2,5,3,8,6]=>0110101
[6,7,4,2,1,3,8,5]=>0111001
[6,4,3,8,5,7,1,2]=>1101010
[6,8,4,2,3,1,5,7]=>0110100
[8,6,4,1,3,7,2,5]=>1110010
[5,3,6,1,8,2,4,7]=>1010100
[3,1,8,5,4,7,6,2]=>1011011
[4,1,5,8,3,7,6,2]=>1001011
[4,1,5,3,8,7,6,2]=>1010111
[4,5,1,8,2,7,6,3]=>0101011
[4,8,5,3,1,7,6,2]=>0111011
[4,5,2,8,1,7,6,3]=>0101011
[4,6,2,8,7,1,5,3]=>0101101
[4,8,6,3,7,1,5,2]=>0110101
[4,6,8,2,7,5,1,3]=>0010110
[4,6,2,8,7,5,1,3]=>0101110
[5,6,2,7,4,1,8,3]=>0101101
[5,6,7,2,3,1,8,4]=>0010101
[5,6,7,2,8,3,1,4]=>0010110
[5,6,7,2,1,8,3,4]=>0011010
[5,6,7,2,1,3,8,4]=>0011001
[5,6,1,7,8,2,4,3]=>0100101
[5,6,1,7,2,4,8,3]=>0101001
[4,1,6,8,7,3,5,2]=>1001101
[4,1,6,8,7,5,3,2]=>1001111
[5,6,1,7,8,4,2,3]=>0100110
[4,6,8,1,7,5,2,3]=>0010110
[4,8,6,1,7,5,3,2]=>0110111
[5,6,7,1,8,3,2,4]=>0010110
[5,6,7,1,3,8,2,4]=>0010010
[5,6,7,1,3,2,8,4]=>0010101
[5,6,7,3,1,2,8,4]=>0011001
[5,6,8,7,4,2,1,3]=>0011110
[7,8,1,3,5,6,2,4]=>0100010
[7,8,3,1,5,6,2,4]=>0110010
[7,1,3,8,5,6,2,4]=>1001010
[5,1,7,8,3,4,6,2]=>1001001
[1,5,7,8,3,4,6,2]=>0001001
[3,7,1,5,8,6,2,4]=>0100110
[1,3,7,8,2,5,6,4]=>0001001
[3,1,7,8,5,2,6,4]=>1001101
[1,3,7,5,8,2,6,4]=>0010101
[3,1,7,5,8,2,6,4]=>1010101
[3,5,7,1,8,4,6,2]=>0010101
[3,5,7,8,1,4,6,2]=>0001001
[5,3,7,8,4,6,1,2]=>1001010
[5,3,7,8,4,1,6,2]=>1001101
[5,3,7,8,1,4,6,2]=>1001001
[5,3,7,1,8,4,6,2]=>1010101
[1,5,3,7,8,4,2,6]=>0100110
[5,1,3,7,8,4,2,6]=>1000110
[3,6,2,1,4,5,8,7]=>0110001
[6,4,2,5,1,3,8,7]=>1101001
[8,6,1,7,3,2,4,5]=>1101100
[2,5,8,1,7,3,4,6]=>0010100
[6,8,2,7,3,1,4,5]=>0101100
[6,8,2,3,7,1,4,5]=>0100100
[8,6,2,7,4,5,1,3]=>1101010
[5,2,8,1,7,3,4,6]=>1010100
[4,2,3,8,1,5,6,7]=>1001000
[5,2,8,3,7,1,4,6]=>1010100
[5,2,8,4,6,1,3,7]=>1010100
[2,1,5,8,4,3,6,7]=>1001100
[5,8,3,2,7,1,4,6]=>0110100
[4,1,3,8,2,5,6,7]=>1001000
[5,1,8,3,7,2,4,6]=>1010100
[5,1,8,4,6,2,3,7]=>1010100
[5,8,4,1,6,2,3,7]=>0110100
[4,5,8,1,6,2,3,7]=>0010100
[5,4,8,1,6,2,3,7]=>1010100
[4,8,5,1,6,2,3,7]=>0110100
[2,1,5,4,8,3,6,7]=>1010100
[2,4,3,8,1,5,6,7]=>0101000
[3,1,8,4,2,5,6,7]=>1011000
[3,8,4,2,1,5,6,7]=>0111000
[2,3,8,4,1,5,6,7]=>0011000
[3,4,2,8,1,5,6,7]=>0101000
[3,8,5,2,7,1,4,6]=>0110100
[4,8,5,2,6,1,3,7]=>0110100
[2,1,4,8,5,3,6,7]=>1001100
[3,2,8,4,1,5,6,7]=>1011000
[2,8,4,3,1,5,6,7]=>0111000
[4,1,7,5,6,2,8,3]=>1010101
[5,7,4,3,8,1,6,2]=>0110101
[5,7,4,3,8,2,6,1]=>0110101
[3,8,4,2,6,7,5,1]=>0110011
[3,8,4,1,6,7,5,2]=>0110011
[6,1,7,5,2,8,4,3]=>1011011
[5,6,4,3,2,8,1,7]=>0111010
[2,6,7,5,3,8,4,1]=>0011011
[2,1,6,7,5,3,8,4]=>1001101
[3,8,4,2,1,6,7,5]=>0111001
[5,7,4,3,8,2,1,6]=>0110110
[6,7,4,8,1,2,5,3]=>0101001
[6,7,5,8,1,2,4,3]=>0101001
[6,7,4,8,3,1,2,5]=>0101100
[6,1,3,4,8,2,5,7]=>1000100
[6,2,3,4,8,1,5,7]=>1000100
[3,4,8,2,1,5,7,6]=>0011001
[6,7,5,8,3,1,4,2]=>0101101
[2,5,7,6,1,4,8,3]=>0011001
[6,7,4,8,2,3,5,1]=>0101001
[6,7,4,8,1,3,5,2]=>0101001
[2,6,7,5,1,3,8,4]=>0011001
[6,3,1,4,8,2,5,7]=>1100100
[6,7,4,8,1,3,2,5]=>0101010
[6,7,5,8,4,1,3,2]=>0101101
[6,7,4,8,2,1,3,5]=>0101100
[6,7,4,8,1,2,3,5]=>0101000
[7,8,3,2,6,1,4,5]=>0110100
[3,4,8,2,6,1,7,5]=>0010101
[7,8,4,1,5,6,3,2]=>0110011
[7,8,1,2,6,3,4,5]=>0100100
[7,8,5,1,4,6,3,2]=>0110011
[5,3,8,4,1,6,7,2]=>1011001
[6,2,4,8,1,5,3,7]=>1001010
[3,4,8,5,1,6,7,2]=>0011001
[5,3,8,1,4,6,7,2]=>1010001
[4,2,6,8,1,5,3,7]=>1001010
[7,4,2,8,1,5,3,6]=>1101010
[6,1,7,5,8,4,3,2]=>1010111
[1,2,7,8,5,3,4,6]=>0001100
[6,3,7,8,5,4,1,2]=>1001110
[6,1,5,7,8,4,3,2]=>1000111
[1,7,5,6,8,4,3,2]=>0100111
[3,1,8,4,5,6,7,2]=>1010001
[4,2,1,8,6,5,3,7]=>1101110
[3,2,7,8,5,1,4,6]=>1001100
[2,3,7,8,5,1,4,6]=>0001100
[2,7,3,8,5,1,4,6]=>0101100
[3,6,2,8,5,1,4,7]=>0101100
[1,4,2,8,7,5,3,6]=>0101110
[7,3,6,8,5,4,1,2]=>1001110
[7,2,1,8,5,3,4,6]=>1101100
[1,2,6,8,4,5,3,7]=>0001010
[7,1,6,5,8,4,3,2]=>1010111
[6,5,7,1,8,4,3,2]=>1010111
[5,7,6,1,8,4,3,2]=>0110111
[6,7,1,5,8,4,3,2]=>0100111
[7,1,2,8,4,5,3,6]=>1001010
[7,6,1,5,8,4,3,2]=>1100111
[7,5,6,1,8,4,3,2]=>1010111
[7,1,6,5,3,2,4,8]=>1011100
[1,8,7,5,3,2,4,6]=>0111100
[1,8,7,4,2,5,3,6]=>0111010
[8,7,4,2,5,3,6,1]=>1110101
[7,1,6,4,2,5,3,8]=>1011010
[2,6,5,4,7,1,3,8]=>0110100
[7,1,5,3,6,4,2,8]=>1010110
[5,3,7,1,6,4,2,8]=>1010110
[5,3,6,4,2,7,1,8]=>1011010
[1,5,3,8,7,4,2,6]=>0101110
[7,4,2,8,6,3,5,1]=>1101101
[5,3,6,1,8,7,4,2]=>1010111
[6,1,5,3,8,7,4,2]=>1010111
[2,8,7,5,4,6,1,3]=>0111010
[2,3,1,8,7,5,4,6]=>0101110
[7,4,2,1,8,6,3,5]=>1110110
[1,8,6,3,5,7,4,2]=>0110011
[6,3,8,5,2,1,7,4]=>1011101
[8,6,3,7,4,2,1,5]=>1101110
[2,8,6,4,7,5,1,3]=>0110110
[5,1,8,6,3,7,4,2]=>1011011
[6,3,7,4,1,8,5,2]=>1011011
[8,5,2,6,3,7,4,1]=>1101011
[6,1,8,7,4,2,5,3]=>1011101
[8,6,3,7,4,2,5,1]=>1101101
[1,8,6,3,2,4,7,5]=>0111001
[8,6,3,2,4,7,5,1]=>1110011
[7,5,1,8,6,3,2,4]=>1101110
[6,1,8,7,5,3,2,4]=>1011110
[2,4,5,1,3,8,7,6]=>0010011
[1,7,5,8,6,3,2,4]=>0101110
[1,7,4,2,5,8,6,3]=>0110011
[8,6,3,1,7,4,2,5]=>1110110
[8,7,4,2,5,3,1,6]=>1110110
[5,3,1,8,7,4,2,6]=>1101110
[4,1,8,7,5,3,2,6]=>1011110
[2,8,6,4,1,3,7,5]=>0111001
[4,1,8,6,3,2,7,5]=>1011101
[7,4,2,8,6,3,1,5]=>1101110
[6,3,1,8,5,2,7,4]=>1101101
[8,5,2,6,3,1,7,4]=>1101101
[7,4,8,5,2,6,3,1]=>1011011
[1,8,5,2,7,4,6,3]=>0110101
[7,4,6,3,1,8,5,2]=>1011011
[6,3,1,7,4,8,5,2]=>1101011
[4,1,7,5,8,6,3,2]=>1010111
[2,3,1,7,5,8,6,4]=>0101011
[7,4,8,5,2,1,6,3]=>1011101
[1,7,4,6,3,8,5,2]=>0101011
[3,6,5,2,1,4,8,7]=>0111001
[3,5,6,2,1,4,8,7]=>0011001
[3,5,7,8,1,4,2,6]=>0001010
[4,1,8,5,7,3,2,6]=>1010110
[4,1,7,5,8,3,2,6]=>1010110
[2,1,5,8,7,4,3,6]=>1001110
[5,1,7,4,8,3,2,6]=>1010110
[4,7,2,8,3,6,1,5]=>0101010
[4,6,2,7,3,1,8,5]=>0101101
[3,7,8,2,4,1,6,5]=>0010101
[3,8,7,2,4,1,6,5]=>0110101
[3,8,6,2,4,1,7,5]=>0110101
[6,2,8,4,1,7,3,5]=>1011010
[7,3,4,8,1,6,2,5]=>1001010
[6,3,4,8,1,7,2,5]=>1001010
[5,3,4,8,1,2,7,6]=>1001001
[4,3,5,8,1,2,7,6]=>1001001
[1,8,5,4,2,3,7,6]=>0111001
[3,5,4,8,1,2,7,6]=>0101001
[4,5,3,8,1,2,7,6]=>0101001
[6,4,3,8,1,7,2,5]=>1101010
[7,4,3,8,1,6,2,5]=>1101010
[6,5,3,8,7,1,2,4]=>1101100
[5,6,3,8,7,1,2,4]=>0101100
[4,6,3,8,1,7,2,5]=>0101010
[2,6,8,4,1,7,3,5]=>0011010
[1,8,7,4,2,6,3,5]=>0111010
[5,7,3,8,6,1,2,4]=>0101100
[3,7,5,8,6,1,2,4]=>0101100
[2,7,8,5,6,1,3,4]=>0010100
[1,8,7,5,6,2,3,4]=>0110100
[2,6,8,5,7,1,3,4]=>0010100
[5,3,6,8,7,1,2,4]=>1001100
[7,2,8,5,6,1,3,4]=>1010100
[5,2,8,6,7,1,3,4]=>1010100
[1,8,3,2,7,6,4,5]=>0110110
[5,2,8,7,6,1,3,4]=>1011100
[6,2,8,7,5,1,3,4]=>1011100
[3,4,7,8,1,6,2,5]=>0001010
[1,8,5,7,6,2,3,4]=>0101100
[2,5,8,7,6,1,3,4]=>0011100
[7,4,6,5,8,1,2,3]=>1010100
[2,6,8,7,5,1,3,4]=>0011100
[1,8,6,7,5,2,3,4]=>0101100
[2,7,8,6,5,1,3,4]=>0011100
[5,7,6,4,8,1,2,3]=>0110100
[6,1,3,2,4,8,7,5]=>1010011
[8,7,4,2,3,6,1,5]=>1110010
[8,7,1,5,4,2,3,6]=>1101100
[3,7,1,5,2,8,6,4]=>0101011
[8,7,2,5,4,1,3,6]=>1101100
[5,2,8,7,1,4,3,6]=>1011010
[7,1,8,6,2,4,3,5]=>1011010
[8,1,6,2,7,5,3,4]=>1010110
[7,1,6,2,8,5,3,4]=>1010110
[7,2,4,3,5,1,8,6]=>1010101
[5,1,7,2,3,8,6,4]=>1010011
[8,2,3,5,1,7,6,4]=>1001011
[7,6,3,1,4,8,2,5]=>1110010
[7,2,8,1,6,5,3,4]=>1010110
[7,2,6,4,3,8,1,5]=>1011010
[5,1,7,4,3,8,2,6]=>1011010
[5,3,1,7,4,8,2,6]=>1101010
[7,4,8,2,1,5,3,6]=>1011010
[8,2,4,1,6,3,7,5]=>1010101
[8,2,7,5,1,6,4,3]=>1011011
[6,1,7,3,2,8,5,4]=>1011011
[4,7,2,1,6,3,8,5]=>0110101
[6,2,1,5,3,8,4,7]=>1101010
[5,3,1,6,2,8,4,7]=>1101010
[6,1,5,2,8,4,3,7]=>1010110
[7,4,3,8,1,5,2,6]=>1101010
[7,4,8,1,5,3,2,6]=>1010110
[6,1,5,3,2,8,4,7]=>1011010
[6,3,2,8,4,1,5,7]=>1101100
[7,3,4,2,8,5,1,6]=>1010110
[8,5,1,3,7,4,2,6]=>1100110
[3,8,6,1,5,2,7,4]=>0110101
[4,8,5,6,1,7,3,2]=>0101011
[6,7,1,3,8,5,2,4]=>0100110
[3,6,7,1,5,2,8,4]=>0010101
[7,1,3,8,4,2,6,5]=>1001101
[5,6,2,7,1,3,8,4]=>0101001
[5,6,2,8,1,3,7,4]=>0101001
[6,1,8,3,7,5,2,4]=>1010110
[7,4,2,1,5,8,3,6]=>1110010
[7,4,1,5,8,3,2,6]=>1100110
[7,3,2,6,4,8,1,5]=>1101010
[6,4,2,7,3,8,1,5]=>1101010
[7,4,8,3,1,5,2,6]=>1011010
[5,2,1,7,4,8,3,6]=>1101010
[6,1,8,4,5,2,7,3]=>1010101
[7,1,6,4,5,2,8,3]=>1010101
[3,5,2,7,1,6,8,4]=>0101001
[4,5,7,3,1,6,8,2]=>0011001
[4,5,7,2,8,6,1,3]=>0010110
[4,5,7,2,8,1,3,6]=>0010100
[4,6,7,2,1,5,8,3]=>0011001
[4,6,7,1,3,8,5,2]=>0010011
[3,6,1,5,7,8,4,2]=>0100011
[4,6,7,1,5,8,3,2]=>0010011
[6,1,4,2,5,3,7,8]=>1010100
[1,3,7,5,4,2,8,6]=>0011101
[6,1,3,5,4,2,7,8]=>1001100
[6,1,2,5,4,7,3,8]=>1001010
[5,2,6,3,4,7,1,8]=>1010010
[2,4,7,1,5,3,8,6]=>0010101
[2,3,6,7,4,8,1,5]=>0001010
[1,3,6,7,4,8,5,2]=>0001011
[2,7,6,5,3,1,8,4]=>0111101
[5,2,6,1,4,7,8,3]=>1010001
[4,7,6,5,2,1,8,3]=>0111101
[6,3,1,5,4,7,8,2]=>1101001
[5,3,6,1,4,2,7,8]=>1010100
[1,7,4,2,6,3,8,5]=>0110101
[5,7,4,1,2,3,6,8]=>0110000
[6,4,1,2,5,3,7,8]=>1100100
[4,7,6,3,8,5,1,2]=>0110110
[3,7,6,5,2,8,1,4]=>0111010
[3,7,6,5,1,2,8,4]=>0111001
[4,7,2,6,1,3,8,5]=>0101001
[2,7,6,5,8,1,4,3]=>0110101
[4,2,6,8,3,1,5,7]=>1001100
[3,7,6,2,4,5,1,8]=>0110010
[2,3,6,5,8,1,4,7]=>0010100
[2,3,5,8,6,1,4,7]=>0001100
[4,2,3,8,6,1,5,7]=>1001100
[1,2,3,7,4,6,8,5]=>0001001
[3,2,7,1,4,5,8,6]=>1010001
[2,1,5,3,8,7,4,6]=>1010110
[5,8,3,2,4,1,6,7]=>0110100
[4,2,7,1,8,3,5,6]=>1010100
[1,2,7,5,3,8,4,6]=>0011010
[3,2,7,1,4,8,5,6]=>1010010
[1,2,3,7,6,8,4,5]=>0001010
[1,2,3,6,8,7,4,5]=>0000110
[1,2,3,7,8,4,6,5]=>0000101
[1,2,3,6,8,4,7,5]=>0000101
[6,2,8,3,7,5,1,4]=>1010110
[4,2,8,3,7,5,6,1]=>1010101
[7,3,4,8,6,5,1,2]=>1001110
[5,3,4,8,7,2,6,1]=>1001101
[4,6,3,8,5,7,2,1]=>0101011
[7,5,3,8,6,2,4,1]=>1101101
[2,6,8,3,7,4,5,1]=>0010101
[2,5,8,3,7,4,6,1]=>0010101
[7,4,3,8,6,2,5,1]=>1101101
[3,5,4,8,7,2,6,1]=>0101101
[4,5,3,8,6,7,2,1]=>0101011
[3,6,7,8,4,5,2,1]=>0001011
[1,8,5,6,4,7,3,2]=>0101011
[2,5,8,6,4,7,3,1]=>0011011
[6,3,7,8,4,5,2,1]=>1001011
[4,3,7,8,5,6,2,1]=>1001011
[4,2,8,6,5,7,3,1]=>1011011
[3,2,8,6,7,4,5,1]=>1010101
[2,3,8,7,5,4,6,1]=>0011101
[1,8,2,7,4,5,6,3]=>0101001
[7,2,8,6,3,4,5,1]=>1011001
[6,2,8,4,5,7,3,1]=>1010011
[5,2,8,4,6,7,3,1]=>1010011
[4,3,6,8,5,7,2,1]=>1001011
[3,4,6,8,7,2,5,1]=>0001101
[7,3,5,8,6,2,4,1]=>1001101
[1,8,3,5,7,4,6,2]=>0100101
[2,7,8,4,5,6,3,1]=>0010011
[3,7,5,8,4,6,2,1]=>0101011
[5,7,4,6,8,3,2,1]=>0100111
[3,6,5,8,4,7,2,1]=>0101011
[2,6,8,4,5,7,3,1]=>0010011
[4,2,7,1,3,8,5,6]=>1010010
[4,2,5,1,3,8,6,7]=>1010010
[5,3,6,1,7,2,4,8]=>1010100
[3,7,1,2,5,8,6,4]=>0100011
[3,7,4,1,2,8,5,6]=>0110010
[7,5,1,3,4,8,6,2]=>1100011
[7,5,1,2,4,8,6,3]=>1100011
[6,4,2,3,7,1,5,8]=>1100100
[7,6,3,8,1,2,5,4]=>1101001
[7,4,2,3,8,1,6,5]=>1100101
[4,7,5,2,8,1,3,6]=>0110100
[8,2,6,3,7,1,4,5]=>1010100
[8,6,1,2,7,4,5,3]=>1100101
[8,4,7,1,2,3,6,5]=>1010001
[8,5,7,1,2,4,6,3]=>1010001
[3,8,5,6,1,2,4,7]=>0101000
[3,7,5,8,1,2,4,6]=>0101000
[7,6,4,8,1,3,5,2]=>1101001
[6,5,8,1,2,4,7,3]=>1010001
[3,6,8,1,2,5,7,4]=>0010001
[4,6,3,8,1,2,5,7]=>0101000
[4,6,3,7,1,2,5,8]=>0101000
[4,1,7,8,2,3,6,5]=>1001001
[5,1,2,8,6,3,4,7]=>1001100
[5,3,8,1,6,2,4,7]=>1010100
[6,1,8,5,2,3,4,7]=>1011000
[6,1,7,5,2,3,4,8]=>1011000
[6,8,1,3,7,4,5,2]=>0100101
[7,2,8,1,6,3,4,5]=>1010100
[4,7,8,2,5,1,3,6]=>0010100
[6,8,2,7,1,4,5,3]=>0101001
[4,8,7,1,3,5,6,2]=>0110001
[3,8,7,1,2,4,6,5]=>0110001
[4,8,7,1,2,3,6,5]=>0110001
[5,8,7,1,2,4,6,3]=>0110001
[5,8,7,1,3,4,6,2]=>0110001
[7,1,8,6,2,3,5,4]=>1011001
[5,8,6,4,1,2,3,7]=>0111000
[5,1,3,4,6,7,2,8]=>1000010
[1,3,4,8,7,5,2,6]=>0001110
[8,2,4,1,7,3,5,6]=>1010100
[8,6,1,4,2,3,7,5]=>1101001
[3,6,1,4,2,8,7,5]=>0101011
[1,6,8,4,3,7,2,5]=>0011010
[3,1,4,7,8,5,2,6]=>1000110
[6,1,7,4,3,8,2,5]=>1011010
[1,8,7,4,3,6,2,5]=>0111010
[7,4,1,3,8,2,6,5]=>1100101
[4,8,2,3,1,5,7,6]=>0101001
[4,8,6,2,1,3,7,5]=>0111001
[2,7,4,1,8,3,5,6]=>0110100
[1,7,8,4,2,3,6,5]=>0011001
[8,7,1,3,4,2,6,5]=>1100101
[1,7,4,3,6,2,8,5]=>0110101
[3,8,6,4,5,2,1,7]=>0110110
[3,8,4,6,5,2,1,7]=>0101110
[2,4,3,7,5,8,1,6]=>0101010
[1,4,7,3,6,2,8,5]=>0010101
[6,4,1,3,7,2,8,5]=>1100101
[8,1,4,3,6,2,7,5]=>1010101
[4,2,3,8,5,7,1,6]=>1001010
[2,8,5,7,3,4,1,6]=>0101010
[5,8,2,6,4,3,1,7]=>0101110
[7,2,5,8,4,3,1,6]=>1001110
[4,2,3,5,8,7,1,6]=>1000110
[8,2,3,5,4,7,1,6]=>1001010
[6,1,8,3,4,2,7,5]=>1010101
[1,8,6,4,2,3,7,5]=>0111001
[3,8,4,5,6,2,1,7]=>0100110
[3,8,6,5,4,2,1,7]=>0111110
[6,3,1,4,2,8,7,5]=>1101011
[7,3,8,1,2,6,4,5]=>1010010
[7,1,4,5,3,2,6,8]=>1001100
[1,8,4,2,6,5,3,7]=>0110110
[5,1,4,8,6,3,2,7]=>1001110
[5,3,1,8,4,7,2,6]=>1101010
[4,3,8,1,5,7,2,6]=>1010010
[6,3,1,2,5,7,4,8]=>1100010
[7,1,4,2,6,5,3,8]=>1010110
[3,8,4,1,6,5,2,7]=>0110110
[7,5,3,6,4,8,2,1]=>1101011
[7,3,6,4,5,8,2,1]=>1010011
[8,7,2,4,5,1,6,3]=>1100101
[7,1,5,4,8,6,3,2]=>1010111
[5,8,3,7,4,1,6,2]=>0101101
[8,1,7,4,2,6,5,3]=>1011011
[5,6,3,1,8,4,7,2]=>0110101
[5,7,1,4,8,6,3,2]=>0100111
[5,3,7,4,8,6,2,1]=>1010111
[8,5,3,6,1,4,7,2]=>1101001
[5,4,3,6,8,2,7,1]=>1100101
[6,5,3,7,4,8,2,1]=>1101011
[2,7,8,4,5,1,6,3]=>0010101
[5,6,3,8,1,4,7,2]=>0101001
[8,4,1,2,5,6,7,3]=>1100001
[6,8,3,1,2,5,7,4]=>0110001
[8,7,1,4,5,2,6,3]=>1100101
[8,7,3,1,5,4,2,6]=>1110110
[3,5,4,7,6,1,2,8]=>0101100
[3,5,7,4,6,1,8,2]=>0010101
[3,5,7,4,6,1,2,8]=>0010100
[3,5,7,4,6,2,1,8]=>0010110
[3,5,2,7,6,4,1,8]=>0101110
[3,5,7,2,6,4,1,8]=>0010110
[5,3,7,6,1,2,8,4]=>1011001
[5,3,7,6,1,4,2,8]=>1011010
[5,3,7,6,4,1,2,8]=>1011100
[3,5,7,2,6,1,4,8]=>0010100
[3,5,2,7,6,1,4,8]=>0101100
[5,3,7,6,4,1,8,2]=>1011101
[3,7,5,4,1,8,2,6]=>0111010
[3,7,5,4,1,8,6,2]=>0111011
[3,7,5,1,4,8,6,2]=>0110011
[3,7,5,1,4,8,2,6]=>0110010
[3,5,7,1,2,6,8,4]=>0010001
[3,5,7,2,1,6,4,8]=>0011010
[5,3,7,1,6,2,4,8]=>1010100
[3,5,7,1,4,6,8,2]=>0010001
[3,5,7,1,4,2,6,8]=>0010100
[3,5,7,4,1,2,6,8]=>0011000
[3,5,4,7,1,6,8,2]=>0101001
[3,5,4,7,1,2,6,8]=>0101000
[3,5,4,7,2,1,6,8]=>0101100
[3,5,4,2,7,1,6,8]=>0110100
[3,5,4,7,2,1,8,6]=>0101101
[3,5,4,7,1,2,8,6]=>0101001
[5,7,6,3,1,8,4,2]=>0111011
[5,7,6,3,1,8,2,4]=>0111010
[3,5,7,4,1,2,8,6]=>0011001
[3,5,7,4,2,1,8,6]=>0011101
[3,2,5,7,4,1,8,6]=>1001101
[3,2,5,7,1,4,8,6]=>1001001
[3,5,2,7,1,4,8,6]=>0101001
[3,5,7,2,1,4,8,6]=>0011001
[3,5,7,1,4,2,8,6]=>0010101
[3,7,5,2,1,8,6,4]=>0111011
[3,7,2,5,1,8,6,4]=>0101011
[3,2,7,5,1,8,6,4]=>1011011
[3,2,7,5,1,8,4,6]=>1011010
[3,7,2,5,1,8,4,6]=>0101010
[3,7,5,2,1,8,4,6]=>0111010
[5,8,3,4,1,7,6,2]=>0101011
[5,8,7,2,4,1,6,3]=>0110101
[3,8,6,4,1,7,5,2]=>0111011
[4,3,5,6,8,1,7,2]=>1000101
[3,7,6,4,1,8,5,2]=>0111011
[3,7,4,1,8,6,5,2]=>0110111
[3,8,4,1,7,6,5,2]=>0110111
[3,2,7,6,1,5,4,8]=>1011010
[5,7,8,2,4,1,6,3]=>0010101
[4,2,5,8,1,6,7,3]=>1001001
[5,8,2,4,1,6,3,7]=>0101010
[8,4,2,6,5,1,3,7]=>1101100
[3,2,6,8,1,5,4,7]=>1001010
[8,3,2,5,6,1,4,7]=>1100100
[3,2,8,6,7,1,5,4]=>1010101
[3,2,6,8,7,1,5,4]=>1001101
[3,2,6,7,1,5,4,8]=>1001010
[8,7,3,2,5,6,1,4]=>1110010
[7,2,8,1,5,3,6,4]=>1010101
[8,4,2,7,5,1,3,6]=>1101100
[7,4,2,8,5,1,3,6]=>1101100
[7,2,4,1,8,3,6,5]=>1010101
[7,5,3,4,2,8,1,6]=>1101010
[8,5,3,6,2,4,7,1]=>1101001
[8,5,6,3,7,4,2,1]=>1010111
[8,5,6,2,7,4,3,1]=>1010111
[8,7,6,3,4,1,5,2]=>1110101
[1,7,2,3,6,8,5,4]=>0100011
[3,5,6,4,8,2,7,1]=>0010101
[3,5,1,4,8,2,7,6]=>0100101
[1,7,5,4,8,2,6,3]=>0110101
[3,7,5,1,6,4,8,2]=>0110101
[2,7,5,4,8,1,3,6]=>0110100
[2,7,5,4,8,6,1,3]=>0110110
[1,7,5,4,8,6,3,2]=>0110111
[2,5,1,4,8,7,3,6]=>0100110
[3,6,4,2,8,7,1,5]=>0110110
[3,5,2,4,8,1,6,7]=>0100100
[4,5,6,1,7,3,8,2]=>0010101
[3,5,6,4,8,1,2,7]=>0010100
[1,5,6,4,8,7,2,3]=>0010110
[3,6,4,1,8,7,2,5]=>0110110
[3,6,4,5,8,7,2,1]=>0100111
[1,6,4,3,8,5,2,7]=>0110110
[7,6,1,4,5,3,8,2]=>1100101
[7,6,1,3,5,4,8,2]=>1100101
[7,1,3,2,5,8,4,6]=>1010010
[1,6,4,2,8,5,3,7]=>0110110
[7,6,5,8,3,1,4,2]=>1101101
[2,6,4,3,8,1,7,5]=>0110101
[2,6,4,3,8,5,7,1]=>0110101
[7,2,3,1,5,8,6,4]=>1010011
[7,1,5,6,3,8,4,2]=>1001011
[7,3,6,5,1,4,8,2]=>1011001
[7,2,6,5,3,8,1,4]=>1011010
[7,2,3,1,4,8,6,5]=>1010011
[7,2,3,5,4,8,6,1]=>1001011
[2,6,4,5,8,1,7,3]=>0100101
[1,5,6,4,8,3,7,2]=>0010101
[2,5,6,4,8,3,1,7]=>0010110
[3,5,6,1,4,7,8,2]=>0010001
[7,6,1,3,4,5,8,2]=>1100001
[7,1,3,2,4,8,5,6]=>1010010
[7,6,1,5,3,4,8,2]=>1101001
[7,6,1,5,4,3,8,2]=>1101101
[1,6,4,5,8,3,2,7]=>0100110
[7,6,5,8,1,3,2,4]=>1101010
[3,4,6,8,7,2,1,5]=>0001110
[3,5,6,8,2,1,7,4]=>0001101
[4,2,1,5,3,7,8,6]=>1101001
[4,2,5,6,3,1,8,7]=>1001101
[3,5,6,8,1,7,2,4]=>0001010
[4,1,5,6,3,2,8,7]=>1001101
[4,5,3,1,7,2,8,6]=>0110101
[4,1,3,5,2,7,8,6]=>1001001
[2,5,4,7,3,8,6,1]=>0101011
[3,5,7,1,8,4,2,6]=>0010110
[4,1,5,3,2,7,8,6]=>1011001
[4,5,3,7,1,2,8,6]=>0101001
[4,3,6,1,2,7,5,8]=>1010010
[5,1,3,2,4,6,7,8]=>1010000
[3,6,1,7,4,5,2,8]=>0101010
[5,3,1,4,2,6,7,8]=>1101000
[4,5,2,3,7,1,8,6]=>0100101
[4,2,6,1,3,7,5,8]=>1010010
[4,6,2,1,3,7,5,8]=>0110010
[3,6,2,1,7,4,8,5]=>0110101
[3,1,4,7,6,5,2,8]=>1001110
[3,6,2,7,1,5,8,4]=>0101001
[4,6,2,7,1,3,5,8]=>0101000
[3,5,7,1,8,2,6,4]=>0010101
[5,1,4,2,3,6,7,8]=>1010000
[2,6,5,3,4,7,8,1]=>0110001
[3,6,1,7,5,4,2,8]=>0101110
[5,1,4,3,2,6,7,8]=>1011000
[5,4,1,3,2,6,7,8]=>1101000
[6,4,2,5,3,8,1,7]=>1101010
[4,6,2,3,5,1,8,7]=>0100101
[6,2,4,5,1,8,3,7]=>1001010
[8,2,6,7,1,4,5,3]=>1001001
[8,2,6,7,4,1,5,3]=>1001101
[4,6,2,3,5,8,1,7]=>0100010
[2,6,4,1,5,8,3,7]=>0110010
[2,8,1,6,7,4,5,3]=>0100101
[2,8,6,1,4,7,5,3]=>0110011
[2,8,1,6,4,7,5,3]=>0101011
[2,6,1,4,8,5,3,7]=>0100110
[6,4,5,2,8,3,1,7]=>1010110
[4,2,3,6,1,8,5,7]=>1001010
[4,2,3,1,6,8,5,7]=>1010010
[4,2,3,8,6,1,7,5]=>1001101
[6,4,5,8,2,3,7,1]=>1001001
[6,4,8,5,2,3,7,1]=>1011001
[2,4,8,1,3,6,7,5]=>0010001
[2,4,1,8,3,6,7,5]=>0101001
[2,1,4,8,6,3,7,5]=>1001101
[6,4,8,2,5,3,7,1]=>1010101
[8,6,2,4,7,5,1,3]=>1100110
[4,6,8,2,3,5,7,1]=>0010001
[2,1,6,8,4,5,7,3]=>1001001
[2,8,1,4,6,7,3,5]=>0100010
[4,8,6,2,3,7,5,1]=>0110011
[8,4,2,6,7,3,1,5]=>1100110
[5,1,8,3,6,4,7,2]=>1010101
[5,1,3,8,7,6,4,2]=>1001111
[3,8,5,6,1,7,2,4]=>0101010
[6,7,4,8,5,1,3,2]=>0101101
[3,6,5,8,7,1,4,2]=>0101101
[6,5,3,8,2,7,4,1]=>1101011
[6,4,8,1,3,7,5,2]=>1010011
[7,6,3,1,4,2,5,8]=>1110100
[1,5,4,3,7,8,2,6]=>0110010
[7,8,4,2,5,3,1,6]=>0110110
[4,2,7,8,5,3,1,6]=>1001110
[4,2,5,3,1,7,8,6]=>1011001
[4,2,8,7,6,3,1,5]=>1011110
[4,2,7,6,3,1,5,8]=>1011100
[6,3,1,8,7,5,2,4]=>1101110
[4,2,7,6,3,1,8,5]=>1011101
[7,6,3,1,8,4,2,5]=>1110110
[7,6,4,2,1,8,3,5]=>1111010
[1,8,2,7,6,4,3,5]=>0101110
[8,4,2,5,7,6,3,1]=>1100111
[7,5,2,4,8,6,3,1]=>1100111
[8,7,5,2,4,6,3,1]=>1110011
[7,5,2,4,6,3,1,8]=>1100110
[5,2,8,6,3,7,4,1]=>1011011
[8,4,7,5,2,6,3,1]=>1011011
[8,3,6,4,7,5,2,1]=>1010111
[7,5,2,1,8,3,6,4]=>1110101
[7,5,2,6,3,1,8,4]=>1101101
[5,2,7,4,1,8,6,3]=>1011011
[5,2,8,7,4,1,6,3]=>1011101
[8,7,4,1,5,2,6,3]=>1110101
[7,4,1,5,2,8,6,3]=>1101011
[7,6,3,1,4,2,8,5]=>1110101
[7,5,2,8,6,3,1,4]=>1101110
[7,5,2,1,3,6,4,8]=>1110010
[8,7,5,2,1,3,6,4]=>1111001
[1,3,7,6,5,8,2,4]=>0011010
[8,6,4,7,5,2,1,3]=>1101110
[6,4,7,5,2,1,3,8]=>1011100
[6,3,1,4,7,5,2,8]=>1100110
[6,3,1,4,8,7,5,2]=>1100111
[8,6,3,1,4,7,5,2]=>1110011
[1,8,2,6,4,7,5,3]=>0101011
[7,5,2,1,6,4,8,3]=>1110101
[6,3,8,7,4,1,5,2]=>1011101
[6,3,7,4,1,5,2,8]=>1011010
[7,4,1,6,3,5,2,8]=>1101010
[7,4,1,8,6,3,5,2]=>1101101
[8,4,6,3,1,7,5,2]=>1011011
[6,4,7,5,2,1,8,3]=>1011101
[1,6,4,7,5,3,8,2]=>0101101
[6,3,5,2,7,4,1,8]=>1010110
[4,6,7,2,5,3,1,8]=>0010110
[2,4,7,8,1,6,5,3]=>0001011
[4,2,6,8,7,1,5,3]=>1001101
[5,1,8,4,2,7,6,3]=>1011011
[4,6,7,1,2,8,5,3]=>0010011
[5,7,4,1,2,8,6,3]=>0110011
[6,3,7,1,2,8,5,4]=>1010011
[1,8,2,3,6,5,4,7]=>0100110
[3,5,8,4,7,2,6,1]=>0010101
[1,8,5,4,6,2,3,7]=>0110100
[3,8,5,4,6,1,2,7]=>0110100
[3,8,5,1,6,4,2,7]=>0110110
[2,8,5,4,6,1,3,7]=>0110100
[2,8,5,4,6,3,1,7]=>0110110
[1,8,5,4,6,3,2,7]=>0110110
[2,5,8,4,7,3,6,1]=>0010101
[3,6,4,2,7,8,5,1]=>0110011
[3,6,4,2,7,8,1,5]=>0110010
[3,5,4,1,6,2,7,8]=>0110100
[4,5,8,1,7,6,2,3]=>0010110
[3,5,8,4,7,1,6,2]=>0010101
[1,5,8,4,7,3,6,2]=>0010101
[3,6,4,1,7,8,5,2]=>0110011
[3,6,4,8,7,5,2,1]=>0101111
[1,6,4,3,7,8,5,2]=>0110011
[7,6,1,3,8,4,2,5]=>1100110
[1,6,4,2,7,8,3,5]=>0110010
[2,6,4,3,7,1,8,5]=>0110101
[2,6,4,1,7,8,3,5]=>0110010
[7,2,3,4,8,6,5,1]=>1000111
[7,2,3,1,8,6,4,5]=>1010110
[7,2,3,4,1,6,8,5]=>1001001
[1,2,4,3,8,5,7,6]=>0010101
[7,3,8,6,1,4,2,5]=>1011010
[7,2,8,6,3,4,1,5]=>1011010
[7,2,3,1,5,6,8,4]=>1010001
[7,2,3,8,5,6,4,1]=>1001011
[2,6,4,8,7,1,5,3]=>0101101
[1,5,8,4,7,6,2,3]=>0010110
[3,5,8,1,6,7,2,4]=>0010010
[7,6,1,3,5,8,2,4]=>1100010
[7,1,3,2,5,6,8,4]=>1010001
[7,1,3,8,2,6,5,4]=>1001011
[7,6,1,8,5,4,2,3]=>1101110
[3,2,6,5,8,4,7,1]=>1010101
[4,3,7,1,6,5,8,2]=>1010101
[5,2,6,4,8,3,7,1]=>1010101
[4,3,7,5,8,2,6,1]=>1010101
[5,3,7,4,8,2,6,1]=>1010101
[5,3,7,4,8,1,6,2]=>1010101
[5,4,8,2,6,3,7,1]=>1010101
[4,1,7,5,2,3,6,8]=>1011000
[4,1,7,8,6,3,2,5]=>1001110
[6,8,3,2,1,4,7,5]=>0111001
[6,8,2,4,1,3,7,5]=>0101001
[6,1,2,7,5,8,4,3]=>1001011
[4,2,7,3,8,5,6,1]=>1010101
[4,5,2,6,8,3,7,1]=>0100101
[4,8,3,2,5,7,6,1]=>0110011
[8,4,7,6,2,3,5,1]=>1011001
[6,8,4,1,5,3,7,2]=>0110101
[8,3,4,7,6,2,5,1]=>1001101
[1,8,3,5,2,6,7,4]=>0101001
[5,8,2,4,3,7,6,1]=>0101011
[6,5,3,8,4,2,7,1]=>1101101
[7,4,5,1,6,2,8,3]=>1010101
[4,7,3,5,6,2,8,1]=>0100101
[6,7,8,4,1,3,5,2]=>0011001
[3,1,6,8,4,7,5,2]=>1001011
[8,3,6,1,5,7,4,2]=>1010011
[3,2,7,5,8,6,1,4]=>1010110
[2,4,6,7,8,1,5,3]=>0000101
[2,4,6,8,1,7,5,3]=>0001011
[7,4,3,8,6,2,1,5]=>1101110
[4,3,6,2,1,8,5,7]=>1011010
[4,6,2,3,7,5,8,1]=>0100101
[5,8,4,2,3,6,7,1]=>0110001
[8,4,5,3,2,1,7,6]=>1011101
[6,8,4,2,3,7,5,1]=>0110011
[6,4,8,3,2,7,1,5]=>1011010
[5,8,3,7,2,1,6,4]=>0101101
[2,5,6,4,7,1,8,3]=>0010101
[2,5,4,8,1,6,7,3]=>0101001
[1,2,6,5,8,7,3,4]=>0010110
[5,6,3,4,8,7,2,1]=>0100111
[6,5,3,4,8,7,2,1]=>1100111
[7,5,3,8,4,6,2,1]=>1101011
[8,5,3,7,4,6,2,1]=>1101011
[5,8,1,2,3,4,7,6]=>0100001
[7,1,2,8,3,6,4,5]=>1001010
[6,1,8,2,3,5,7,4]=>1010001
[6,1,7,2,3,5,8,4]=>1010001
[4,3,8,7,5,6,2,1]=>1011011
[7,1,6,2,3,5,8,4]=>1010001
[8,1,6,2,3,5,7,4]=>1010001
[8,1,7,2,3,5,6,4]=>1010001
[5,8,3,7,4,6,2,1]=>0101011
[6,8,7,3,4,5,2,1]=>0110011
[8,6,1,2,3,4,7,5]=>1100001
[8,6,2,3,5,1,4,7]=>1100100
[8,2,4,5,7,3,1,6]=>1000110
[2,6,3,8,7,5,4,1]=>0101111
[8,2,3,7,5,4,1,6]=>1001110
[8,2,6,3,5,4,1,7]=>1010110
[8,6,1,5,2,4,3,7]=>1101010
[8,6,2,4,1,5,3,7]=>1101010
[8,4,1,6,5,3,2,7]=>1101110
[8,3,6,1,5,4,2,7]=>1010110
[8,3,2,6,5,4,1,7]=>1101110
[8,3,2,5,7,4,1,6]=>1100110
[8,3,1,7,5,4,2,6]=>1101110
[6,1,3,8,7,5,4,2]=>1001111
[3,6,1,8,7,5,4,2]=>0101111
[3,8,1,5,7,6,4,2]=>0100111
[3,5,2,8,7,6,4,1]=>0101111
[3,4,8,2,7,6,5,1]=>0010111
[3,4,8,7,1,6,5,2]=>0011011
[8,1,3,5,7,6,4,2]=>1000111
[4,1,8,5,7,6,3,2]=>1010111
[8,2,7,1,4,5,6,3]=>1010001
[8,1,7,3,4,6,2,5]=>1010010
[8,3,1,7,2,6,5,4]=>1101011
[3,8,2,4,7,6,5,1]=>0100111
[2,8,3,7,4,6,5,1]=>0101011
[8,2,3,7,1,6,5,4]=>1001011
[8,2,7,1,3,6,5,4]=>1010011
[8,1,7,2,6,4,3,5]=>1010110
[8,1,7,5,2,4,3,6]=>1011010
[8,2,3,7,4,6,1,5]=>1001010
[2,4,8,5,7,6,3,1]=>0010111
[8,2,4,3,7,6,1,5]=>1010110
[8,2,7,3,5,1,4,6]=>1010100
[8,2,7,4,3,1,5,6]=>1011100
[8,2,1,5,7,6,4,3]=>1100111
[6,1,8,2,7,5,4,3]=>1010111
[8,1,5,2,7,6,4,3]=>1010111
[8,1,7,2,4,6,5,3]=>1010011
[8,2,4,1,7,6,5,3]=>1010111
[4,2,8,3,7,6,5,1]=>1010111
[4,8,2,1,7,6,5,3]=>0110111
[5,1,8,7,2,6,4,3]=>1011011
[5,8,1,3,7,6,2,4]=>0100110
[8,2,5,4,1,7,6,3]=>1011011
[5,1,4,8,7,6,3,2]=>1001111
[8,1,4,3,7,6,5,2]=>1010111
[4,8,1,3,7,6,5,2]=>0100111
[4,3,8,1,7,6,5,2]=>1010111
[6,2,8,1,5,7,3,4]=>1010010
[7,2,5,4,1,8,6,3]=>1011011
[7,3,2,8,5,6,1,4]=>1101010
[5,4,6,8,7,2,1,3]=>1001110
[1,7,6,3,2,8,4,5]=>0111010
[6,5,8,3,4,1,7,2]=>1010101
[4,1,2,8,5,3,6,7]=>1001100
[3,5,8,2,6,1,7,4]=>0010101
[3,7,6,2,8,4,5,1]=>0110101
[4,3,6,8,5,1,2,7]=>1001100
[2,7,1,5,8,4,3,6]=>0100110
[2,7,6,1,8,4,3,5]=>0110110
[7,1,2,6,3,5,4,8]=>1001010
[7,2,6,3,4,5,1,8]=>1010010
[4,1,2,7,8,5,3,6]=>1000110
[4,7,3,1,2,6,8,5]=>0110001
[3,8,5,6,4,2,7,1]=>0101101
[3,2,6,4,7,8,5,1]=>1010011
[4,2,7,5,8,3,1,6]=>1010110
[5,2,1,4,7,8,3,6]=>1100010
[5,6,2,7,3,4,8,1]=>0101001
[1,5,8,6,4,2,3,7]=>0011100
[2,5,8,6,4,1,7,3]=>0011101
[4,7,2,3,1,6,8,5]=>0101001
[7,4,6,2,8,3,5,1]=>1010101
[3,4,6,5,1,2,7,8]=>0011000
[4,3,8,2,5,7,1,6]=>1010010
[4,1,6,2,5,3,7,8]=>1010100
[4,2,6,1,5,3,8,7]=>1010101
[6,7,2,3,1,5,8,4]=>0101001
[2,1,5,7,8,3,6,4]=>1000101
[4,7,5,8,6,3,1,2]=>0101110
[2,4,8,3,7,1,5,6]=>0010100
[5,2,8,4,1,6,3,7]=>1011010
[7,6,5,2,1,8,4,3]=>1111011
[2,7,5,1,8,3,6,4]=>0110101
[5,1,8,7,4,3,6,2]=>1011101
[3,8,7,2,4,6,1,5]=>0110010
[5,7,1,3,2,4,8,6]=>0101001
[4,2,7,6,3,5,8,1]=>1011001
[8,4,7,6,3,5,1,2]=>1011010
[8,1,7,4,2,3,5,6]=>1011000
[6,5,1,3,8,7,4,2]=>1100111
[6,1,8,5,3,7,2,4]=>1011010
[5,1,6,8,3,7,4,2]=>1001011
[8,6,5,1,7,4,3,2]=>1110111
[7,6,4,1,3,5,8,2]=>1110001
[8,2,3,7,1,4,5,6]=>1001000
[5,6,2,7,4,3,1,8]=>0101110
[3,7,8,2,6,1,4,5]=>0010100
[3,7,8,5,2,1,4,6]=>0011100
[4,8,6,5,1,2,7,3]=>0111001
[4,8,6,5,1,2,3,7]=>0111000
[3,8,7,6,5,1,2,4]=>0111100
[5,8,2,6,1,4,7,3]=>0101001
[3,8,7,5,6,1,4,2]=>0110101
[4,6,3,8,7,5,1,2]=>0101110
[2,8,4,1,5,7,6,3]=>0110011
[1,8,4,2,5,7,6,3]=>0110011
[2,8,5,4,1,7,6,3]=>0111011
[2,5,8,3,7,1,6,4]=>0010101
[1,8,5,2,4,7,6,3]=>0110011
[1,4,6,2,8,7,5,3]=>0010111
[7,8,2,4,1,6,5,3]=>0101011
[2,4,6,1,8,7,5,3]=>0010111
[2,8,4,5,1,7,6,3]=>0101011
[3,5,8,1,7,6,2,4]=>0010110
[3,5,8,2,7,6,1,4]=>0010110
[2,1,6,8,7,5,3,4]=>1001110
[1,8,2,4,5,7,6,3]=>0100011
[1,3,8,2,5,7,6,4]=>0010011
[2,3,8,1,5,7,6,4]=>0010011
[2,6,1,8,7,5,3,4]=>0101110
[1,6,2,8,7,5,3,4]=>0101110
[1,6,3,8,7,5,2,4]=>0101110
[2,6,3,8,7,5,1,4]=>0101110
[3,2,8,1,5,7,6,4]=>1010011
[3,1,8,2,5,7,6,4]=>1010011
[2,1,8,3,5,7,6,4]=>1010011
[7,8,2,1,4,6,5,3]=>0110011
[2,3,6,8,7,5,1,4]=>0001110
[3,1,6,8,7,2,5,4]=>1001101
[3,8,4,5,1,6,2,7]=>0101010
[6,1,4,5,7,2,3,8]=>1000100
[8,1,4,7,6,3,2,5]=>1001110
[8,3,1,6,4,7,2,5]=>1101010
[5,3,8,6,2,7,1,4]=>1011010
[8,3,6,1,5,7,2,4]=>1010010
[8,4,6,3,1,2,5,7]=>1011000
[6,8,1,4,5,2,3,7]=>0100100
[1,5,8,4,6,2,3,7]=>0010100
[5,6,8,1,4,2,3,7]=>0010100
[5,7,4,8,1,2,3,6]=>0101000
[4,7,8,1,2,6,3,5]=>0010010
[8,7,1,5,6,2,3,4]=>1100100
[1,6,5,8,7,2,3,4]=>0101100
[3,7,1,6,2,4,8,5]=>0101001
[5,1,2,7,6,8,3,4]=>1001010
[1,7,6,5,8,2,3,4]=>0110100
[1,6,8,5,7,2,3,4]=>0010100
[7,5,1,2,6,8,3,4]=>1100010
[6,1,5,2,7,8,3,4]=>1010010
[5,1,2,6,8,7,3,4]=>1000110
[1,8,6,2,5,7,3,4]=>0110010
[5,7,8,1,2,6,3,4]=>0010010
[8,1,5,7,6,2,3,4]=>1001100
[3,7,1,2,8,4,6,5]=>0100101
[1,5,8,7,6,2,3,4]=>0011100
[7,8,6,1,5,2,3,4]=>0110100
[4,5,7,2,3,1,8,6]=>0010101
[3,7,8,1,4,6,5,2]=>0010011
[2,5,8,7,4,1,3,6]=>0011100
[2,6,4,7,5,3,8,1]=>0101101
[6,2,4,7,1,3,8,5]=>1001001
[7,3,5,1,4,2,8,6]=>1010101
[5,4,7,1,3,2,8,6]=>1010101
[6,1,4,7,5,3,8,2]=>1001101
[8,7,4,3,1,5,6,2]=>1111001
[8,7,1,4,3,5,6,2]=>1101001
[6,1,8,4,7,3,2,5]=>1010110
[4,7,3,6,1,2,8,5]=>0101001
[5,2,1,7,4,3,8,6]=>1101101
[4,7,6,2,3,1,8,5]=>0110101
[7,6,8,2,5,3,4,1]=>1010101
[2,3,6,1,8,7,5,4]=>0010111
[2,6,8,7,5,3,1,4]=>0011110
[6,4,1,7,5,2,8,3]=>1101101
[5,7,8,2,3,6,1,4]=>0010010
[4,8,7,1,2,5,6,3]=>0110001
[2,8,7,4,1,5,6,3]=>0111001
[8,6,2,1,5,7,4,3]=>1110011
[3,8,6,7,5,2,1,4]=>0101110
[6,1,3,7,5,8,2,4]=>1001010
[4,7,3,1,8,5,6,2]=>0110101
[1,3,8,5,2,7,4,6]=>0011010
[1,3,8,6,7,2,4,5]=>0010100
[2,8,3,7,6,1,4,5]=>0101100
[1,3,8,7,6,2,4,5]=>0011100
[1,4,6,8,7,2,3,5]=>0001100
[7,6,4,8,5,1,3,2]=>1101101
[7,2,6,5,8,1,3,4]=>1010100
[3,6,7,5,2,8,4,1]=>0011011
[4,6,5,7,2,8,1,3]=>0101010
[5,3,6,7,8,1,4,2]=>1000101
[6,3,2,8,5,4,1,7]=>1101110
[3,8,4,1,5,2,6,7]=>0110100
[2,5,7,4,3,1,6,8]=>0011100
[5,3,4,2,7,1,6,8]=>1010100
[3,7,5,4,1,2,6,8]=>0111000
[4,2,5,1,3,8,7,6]=>1010011
[4,3,5,1,2,7,6,8]=>1010010
[5,3,4,1,7,2,6,8]=>1010100
[4,1,6,3,5,2,7,8]=>1010100
[3,1,7,2,5,6,4,8]=>1010010
[3,7,5,4,2,1,6,8]=>0111100
[7,3,2,1,6,4,5,8]=>1110100
[2,8,6,1,7,4,3,5]=>0110110
[2,5,4,6,1,3,7,8]=>0101000
[2,5,6,4,1,3,7,8]=>0011000
[8,5,2,6,1,3,7,4]=>1101001
[7,1,5,6,3,2,4,8]=>1001100
[7,1,2,5,4,6,3,8]=>1001010
[2,4,1,6,5,3,7,8]=>0101100
[4,1,2,7,5,6,3,8]=>1001010
[7,1,2,6,5,4,3,8]=>1001110
[8,2,1,5,6,3,7,4]=>1100101
[6,1,4,5,3,2,7,8]=>1001100
[3,1,6,5,4,2,7,8]=>1011100
[3,1,4,6,5,2,7,8]=>1001100
[5,6,3,8,7,4,1,2]=>0101110
[5,2,6,8,7,4,1,3]=>1001110
[5,2,3,1,4,8,6,7]=>1010010
[5,4,1,3,2,8,6,7]=>1101010
[5,1,3,4,2,8,6,7]=>1001010
[4,2,7,3,8,5,1,6]=>1010110
[4,3,7,2,8,5,6,1]=>1010101
[5,3,1,2,4,8,6,7]=>1100010
[1,3,2,6,4,8,7,5]=>0101011
[1,6,2,5,3,8,7,4]=>0101011
[1,8,2,6,3,7,5,4]=>0101011
[1,8,3,6,4,7,5,2]=>0101011
[1,7,2,6,3,8,5,4]=>0101011
[1,5,2,7,4,8,6,3]=>0101011
[1,4,2,8,5,7,6,3]=>0101011
[4,8,1,3,2,6,5,7]=>0101010
[1,5,3,8,4,7,6,2]=>0101011
[2,6,3,8,1,5,4,7]=>0101010
[8,3,1,4,2,6,5,7]=>1101010
[6,8,7,3,5,2,4,1]=>0110101
[8,3,5,1,2,6,4,7]=>1010010
[8,6,3,1,5,4,2,7]=>1110110
[8,6,4,1,5,3,2,7]=>1110110
[8,6,5,4,1,3,2,7]=>1111010
[5,3,8,7,4,6,2,1]=>1011011
[2,3,8,7,4,6,1,5]=>0011010
[8,3,5,7,4,1,2,6]=>1001100
[4,8,5,3,1,2,7,6]=>0111001
[6,8,7,3,1,5,4,2]=>0111011
[6,8,5,4,1,3,7,2]=>0111001
[2,5,8,7,4,6,3,1]=>0011011
[4,8,7,6,5,1,3,2]=>0111101
[3,8,7,5,1,6,2,4]=>0111010
[2,3,8,7,5,6,1,4]=>0011010
[2,8,7,1,3,6,4,5]=>0110010
[8,5,4,7,2,1,3,6]=>1101100
[6,8,7,3,5,2,1,4]=>0110110
[3,5,8,6,4,2,7,1]=>0011101
[6,8,4,1,5,2,7,3]=>0110101
[6,8,2,1,7,5,3,4]=>0110110
[5,8,4,6,1,2,7,3]=>0101001
[2,4,8,6,5,1,7,3]=>0011101
[4,8,7,6,5,2,1,3]=>0111110
[4,8,7,5,1,6,2,3]=>0111010
[4,5,2,1,8,6,7,3]=>0110101
[2,8,3,5,6,7,1,4]=>0100010
[5,6,2,4,7,1,8,3]=>0100101
[2,7,5,4,6,1,8,3]=>0110101
[3,7,5,4,6,2,8,1]=>0110101
[2,6,7,4,1,3,8,5]=>0011001
[6,5,7,4,1,3,8,2]=>1011001
[2,4,6,3,5,7,8,1]=>0010001
[3,6,4,2,5,7,8,1]=>0110001
[2,3,6,1,5,7,8,4]=>0010001
[4,3,6,2,5,7,8,1]=>1010001
[4,6,1,2,5,7,8,3]=>0100001
[2,6,4,1,5,7,8,3]=>0110001
[2,4,1,6,5,7,8,3]=>0101001
[7,8,4,1,6,3,5,2]=>0110101
[8,7,5,6,1,3,4,2]=>1101001
[1,4,5,8,6,3,2,7]=>0001110
[8,4,5,7,2,6,1,3]=>1001010
[8,1,7,5,3,6,2,4]=>1011010
[5,2,8,3,6,1,4,7]=>1010100
[5,2,6,3,1,7,8,4]=>1011001
[5,7,6,1,2,3,8,4]=>0110001
[5,3,2,1,8,6,4,7]=>1110110
[4,3,6,2,1,8,7,5]=>1011011
[5,3,6,4,8,2,1,7]=>1010110
[3,7,4,5,1,6,2,8]=>0101010
[3,6,4,5,8,2,1,7]=>0100110
[6,1,4,5,2,8,7,3]=>1001011
[7,2,4,5,1,6,3,8]=>1001010
[7,5,4,1,6,3,2,8]=>1110110
[1,5,4,8,6,3,2,7]=>0101110
[7,5,4,8,6,3,1,2]=>1101110
[1,8,7,5,3,6,4,2]=>0111011
[8,3,7,4,1,6,2,5]=>1011010
[8,5,4,1,6,3,2,7]=>1110110
[1,7,4,2,6,5,3,8]=>0110110
[8,2,1,5,6,7,3,4]=>1100010
[6,3,1,8,4,7,2,5]=>1101010
[7,1,4,8,6,3,2,5]=>1001110
[4,1,8,5,6,7,2,3]=>1010010
[5,7,4,8,6,2,1,3]=>0101110
[5,3,6,8,2,7,1,4]=>1001010
[6,3,7,4,8,2,1,5]=>1010110
[5,3,6,1,4,7,2,8]=>1010010
[4,3,6,8,2,7,1,5]=>1001010
[5,3,7,4,8,2,1,6]=>1010110
[5,3,8,4,1,6,2,7]=>1011010
[5,3,8,1,4,7,2,6]=>1010010
[5,8,4,1,6,3,2,7]=>0110110
[7,3,8,4,1,6,2,5]=>1011010
[1,5,8,3,6,7,4,2]=>0010011
[1,8,2,5,6,7,3,4]=>0100010
[7,8,4,1,6,5,2,3]=>0110110
[6,3,8,1,5,7,2,4]=>1010010
[8,3,1,2,5,7,4,6]=>1100010
[8,1,4,2,6,5,3,7]=>1010110
[3,8,5,6,2,7,1,4]=>0101010
[2,4,5,8,7,3,1,6]=>0001110
[4,3,1,5,6,2,8,7]=>1100101
[4,1,5,8,6,7,2,3]=>1001010
[4,3,7,6,1,2,8,5]=>1011001
[4,7,5,6,1,2,8,3]=>0101001
[4,5,1,8,6,7,3,2]=>0101011
[3,4,5,8,6,7,2,1]=>0001011
[2,1,5,8,6,7,4,3]=>1001011
[3,4,5,8,7,1,2,6]=>0001100
[4,7,1,5,6,2,8,3]=>0100101
[2,6,4,7,1,3,8,5]=>0101001
[5,3,8,6,4,7,2,1]=>1011011
[6,4,1,5,7,8,3,2]=>1100011
[3,6,4,7,2,1,8,5]=>0101101
[3,8,4,6,1,7,2,5]=>0101010
[3,8,5,6,4,7,2,1]=>0101011
[3,8,6,5,2,7,4,1]=>0111011
[3,8,7,5,2,1,4,6]=>0111100
[6,4,1,7,3,2,8,5]=>1101101
[5,1,4,6,7,2,8,3]=>1000101
[6,5,4,7,1,3,8,2]=>1101001
[2,1,6,5,3,7,8,4]=>1011001
[6,1,4,7,2,3,8,5]=>1001001
[1,6,2,5,4,8,3,7]=>0101010
[4,1,2,7,5,8,3,6]=>1001010
[6,1,3,5,8,2,4,7]=>1000100
[5,6,4,3,1,8,2,7]=>0111010
[6,2,3,5,8,1,4,7]=>1000100
[6,7,2,3,8,4,5,1]=>0100101
[6,7,2,1,3,8,4,5]=>0110010
[5,7,4,1,8,3,2,6]=>0110110
[4,1,7,5,8,3,6,2]=>1010101
[6,7,1,3,8,4,5,2]=>0100101
[1,6,7,4,3,8,5,2]=>0011011
[6,1,7,4,2,8,5,3]=>1011011
[2,1,6,7,4,3,8,5]=>1001101
[6,7,3,2,1,8,4,5]=>0111010
[2,5,7,3,1,4,8,6]=>0011001
[6,7,3,2,8,4,5,1]=>0110101
[2,6,7,4,3,8,5,1]=>0011011
[1,2,6,7,4,3,8,5]=>0001101
[1,7,5,8,2,4,3,6]=>0101010
[2,7,1,8,4,6,3,5]=>0101010
[2,7,5,8,1,6,3,4]=>0101010
[1,6,7,3,8,5,4,2]=>0010111
[6,7,1,8,4,5,3,2]=>0101011
[8,6,1,5,4,3,2,7]=>1101110
[2,4,3,8,5,1,6,7]=>0101100
[1,5,6,7,3,8,2,4]=>0001010
[1,6,5,4,8,3,2,7]=>0110110
[3,8,7,2,4,6,5,1]=>0110011
[1,3,7,6,4,8,5,2]=>0011011
[3,1,8,7,6,4,2,5]=>1011110
[3,1,8,7,5,4,2,6]=>1011110
[3,1,7,6,5,4,2,8]=>1011110
[4,7,1,6,5,3,2,8]=>0101110
[4,8,1,6,5,3,2,7]=>0101110
[4,8,1,7,5,3,2,6]=>0101110
[8,4,1,7,6,3,2,5]=>1101110
[5,4,1,8,6,3,2,7]=>1101110
[5,4,1,7,6,3,2,8]=>1101110
[6,4,1,7,5,3,2,8]=>1101110
[6,4,1,8,5,3,2,7]=>1101110
[8,4,1,7,5,3,2,6]=>1101110
[7,4,1,6,5,3,2,8]=>1101110
[7,5,6,1,4,3,2,8]=>1010110
[8,5,6,1,4,3,2,7]=>1010110
[5,7,6,1,4,3,2,8]=>0110110
[5,8,6,1,4,3,2,7]=>0110110
[6,7,5,1,4,3,2,8]=>0110110
[8,7,5,1,4,3,2,6]=>1110110
[8,6,5,1,4,3,2,7]=>1110110
[1,8,6,3,4,2,5,7]=>0110100
[3,1,6,4,5,7,2,8]=>1010010
[7,6,3,8,4,5,2,1]=>1101011
[8,2,7,6,1,4,3,5]=>1011010
[5,2,7,8,1,4,3,6]=>1001010
[8,2,7,6,1,4,5,3]=>1011001
[5,2,3,7,1,6,8,4]=>1001001
[1,7,5,2,6,4,8,3]=>0110101
[7,1,3,6,8,2,4,5]=>1000100
[1,2,5,7,8,4,6,3]=>0000101
[3,1,2,7,5,4,8,6]=>1001101
[6,7,4,1,3,2,8,5]=>0110101
[1,7,2,8,4,3,5,6]=>0101100
[4,1,6,5,7,8,2,3]=>1010010
[1,6,3,5,7,8,2,4]=>0100010
[8,6,1,7,5,2,4,3]=>1101101
[7,6,4,1,8,3,2,5]=>1110110
[8,4,1,6,5,2,7,3]=>1101101
[1,5,3,4,7,8,2,6]=>0100010
[4,2,1,5,7,8,3,6]=>1100010
[5,1,4,6,7,8,2,3]=>1000010
[4,1,5,3,7,8,2,6]=>1010010
[8,1,4,6,5,2,7,3]=>1001101
[7,1,5,4,6,3,2,8]=>1010110
[8,2,1,6,7,5,4,3]=>1100111
[1,2,4,7,6,3,8,5]=>0001101
[6,7,4,1,8,5,2,3]=>0110110
[8,6,4,1,5,7,3,2]=>1110011
[5,2,4,3,7,1,6,8]=>1010100
[6,1,5,4,8,3,2,7]=>1010110
[1,2,8,7,4,3,6,5]=>0011101
[3,2,1,7,5,8,4,6]=>1101010
[8,1,7,6,4,2,5,3]=>1011101
[1,3,6,4,7,8,2,5]=>0010010
[5,1,3,4,7,8,2,6]=>1000010
[4,5,1,3,7,8,2,6]=>0100010
[5,2,3,1,7,8,4,6]=>1010010
[1,6,4,3,7,8,2,5]=>0110010
[7,6,4,3,1,5,2,8]=>1111010
[3,2,6,4,1,8,5,7]=>1011010
[7,5,4,6,1,3,2,8]=>1101010
[8,4,6,5,1,2,7,3]=>1011001
[1,5,6,3,7,8,2,4]=>0010010
[4,2,5,1,7,8,3,6]=>1010010
[3,5,8,6,1,4,2,7]=>0011010
[1,8,4,2,7,6,3,5]=>0110110
[7,3,8,1,6,5,4,2]=>1010111
[2,4,1,8,7,3,6,5]=>0101101
[7,3,8,6,1,5,4,2]=>1011011
[3,5,1,7,8,2,6,4]=>0100101
[5,4,7,8,2,1,6,3]=>1001101
[5,3,6,1,8,4,2,7]=>1010110
[3,4,6,2,1,8,5,7]=>0011010
[5,6,4,8,3,2,1,7]=>0101110
[5,7,4,8,2,1,6,3]=>0101101
[4,7,5,8,2,1,6,3]=>0101101
[4,7,3,2,8,1,5,6]=>0110100
[7,1,2,6,3,8,5,4]=>1001011
[8,1,2,6,3,7,5,4]=>1001011
[8,1,2,7,6,3,5,4]=>1001101
[4,8,7,3,1,6,2,5]=>0111010
[4,7,8,3,1,6,2,5]=>0011010
[7,4,3,1,6,2,8,5]=>1110101
[7,4,3,1,8,6,2,5]=>1110110
[6,8,3,2,1,7,4,5]=>0111010
[3,7,6,2,4,8,1,5]=>0110010
[4,3,7,2,8,6,1,5]=>1010110
[5,1,2,6,3,8,7,4]=>1001011
[5,1,2,7,3,8,6,4]=>1001011
[6,1,2,7,3,5,8,4]=>1001001
[6,2,5,4,1,8,7,3]=>1011011
[4,6,3,2,1,8,7,5]=>0111011
[8,4,3,2,7,6,1,5]=>1110110
[1,5,8,4,7,6,3,2]=>0010111
[3,2,7,4,8,6,1,5]=>1010110
[7,4,3,2,8,6,1,5]=>1110110
[6,4,3,8,5,2,1,7]=>1101110
[8,2,5,4,7,6,1,3]=>1010110
[7,2,5,4,8,6,1,3]=>1010110
[6,2,8,7,5,4,1,3]=>1011110
[4,5,3,2,8,6,1,7]=>0110110
[3,2,5,4,8,6,1,7]=>1010110
[3,2,8,6,5,4,1,7]=>1011110
[8,4,3,6,5,2,1,7]=>1101110
[8,4,3,7,5,2,1,6]=>1101110
[3,2,7,8,5,4,1,6]=>1001110
[6,8,7,4,3,2,1,5]=>0111110
[6,3,2,1,8,7,4,5]=>1110110
[6,2,3,1,8,7,4,5]=>1010110
[7,2,1,5,8,4,6,3]=>1100101
[7,3,1,5,2,8,6,4]=>1101011
[7,1,6,4,2,8,5,3]=>1011011
[3,7,4,1,5,8,6,2]=>0110011
[6,7,1,4,3,8,5,2]=>0101011
[7,1,6,4,8,3,5,2]=>1010101
[8,5,3,6,1,7,4,2]=>1101011
[8,5,6,1,2,7,4,3]=>1010011
[3,6,4,1,5,2,8,7]=>0110101
[4,6,7,2,1,8,3,5]=>0011010
[3,7,1,8,2,5,4,6]=>0101010
[4,5,8,6,1,3,7,2]=>0011001
[4,5,8,6,2,7,3,1]=>0011011
[4,6,7,1,5,3,8,2]=>0010101
[4,6,7,2,1,8,5,3]=>0011011
[4,1,3,5,6,7,8,2]=>1000001
[4,6,8,3,2,7,1,5]=>0011010
[4,6,8,2,3,7,1,5]=>0010010
[4,5,8,3,7,1,2,6]=>0010100
[4,5,8,3,7,2,1,6]=>0010110
[3,7,8,4,6,2,5,1]=>0010101
[3,6,1,5,7,8,2,4]=>0100010
[3,8,2,5,4,7,1,6]=>0101010
[3,8,6,2,5,1,7,4]=>0110101
[4,5,8,6,2,1,7,3]=>0011101
[4,5,8,6,1,2,7,3]=>0011001
[2,1,5,8,6,3,7,4]=>1001101
[4,6,8,5,2,7,1,3]=>0011010
[3,7,8,5,2,6,1,4]=>0011010
[3,7,8,5,4,1,6,2]=>0011101
[4,6,8,5,3,1,7,2]=>0011101
[7,8,2,3,5,4,1,6]=>0100110
[4,6,5,1,7,3,8,2]=>0110101
[5,7,3,1,2,4,8,6]=>0110001
[6,3,2,5,1,7,4,8]=>1101010
[6,1,2,4,8,5,3,7]=>1000110
[6,3,1,7,2,5,8,4]=>1101001
[3,7,2,8,5,1,4,6]=>0101100
[3,6,5,2,4,7,1,8]=>0110010
[1,5,7,8,3,4,2,6]=>0001010
[6,8,4,3,1,7,2,5]=>0111010
[8,4,1,3,7,5,6,2]=>1100101
[4,8,1,3,7,5,6,2]=>0100101
[1,8,5,7,4,2,3,6]=>0101100
[2,1,6,8,5,3,4,7]=>1001100
[4,5,1,3,8,6,7,2]=>0100101
[1,2,6,8,5,3,4,7]=>0001100
[5,6,8,7,3,1,2,4]=>0011100
[1,5,6,8,4,2,3,7]=>0001100
[5,7,8,3,6,1,2,4]=>0010100
[1,5,8,6,2,4,3,7]=>0011010
[1,5,3,7,2,6,8,4]=>0101001
[1,5,2,4,8,6,7,3]=>0100101
[1,5,4,2,6,8,7,3]=>0110011
[5,7,6,8,3,1,2,4]=>0101100
[1,2,5,3,6,8,7,4]=>0010011
[7,1,5,6,2,3,8,4]=>1001001
[8,2,1,4,6,7,3,5]=>1100010
[7,2,6,1,3,4,8,5]=>1010001
[4,1,3,7,2,5,8,6]=>1001001
[6,2,7,5,1,3,8,4]=>1011001
[1,7,5,6,2,3,8,4]=>0101001
[3,7,6,1,2,4,8,5]=>0110001
[8,6,1,3,5,7,2,4]=>1100010
[1,7,4,3,8,2,5,6]=>0110100
[6,1,5,3,4,8,2,7]=>1010010
[3,6,7,5,2,8,1,4]=>0011010
[7,8,4,1,5,6,2,3]=>0110010
[5,8,1,3,6,7,2,4]=>0100010
[2,8,4,3,7,1,5,6]=>0110100
[3,8,4,6,7,1,2,5]=>0100100
[6,3,8,4,7,1,2,5]=>1010100
[1,2,5,4,8,3,6,7]=>0010100
[7,1,3,8,2,4,5,6]=>1001000
[8,1,3,7,2,4,5,6]=>1001000
[3,5,4,7,8,1,2,6]=>0100100
[8,3,1,4,7,2,5,6]=>1100100
[1,6,4,7,8,2,3,5]=>0100100
[1,3,7,8,5,6,2,4]=>0001010
[7,5,4,8,6,1,2,3]=>1101100
[8,2,6,7,5,1,3,4]=>1001100
[8,1,7,4,6,2,3,5]=>1010100
[2,5,8,4,7,1,3,6]=>0010100
[4,5,8,7,1,2,3,6]=>0011000
[4,1,8,5,7,2,3,6]=>1010100
[1,8,7,4,6,2,3,5]=>0110100
[2,6,5,4,1,8,3,7]=>0111010
[6,2,5,1,4,8,3,7]=>1010010
[6,5,4,1,3,8,2,7]=>1110010
[6,3,5,4,2,8,1,7]=>1011010
[1,3,8,7,4,2,6,5]=>0011101
[8,7,4,3,1,5,2,6]=>1111010
[8,2,5,1,4,6,7,3]=>1010001
[3,8,4,5,1,6,7,2]=>0101001
[8,5,4,1,3,6,7,2]=>1110001
[8,3,1,7,5,6,4,2]=>1101011
[8,4,7,6,5,3,1,2]=>1011110
[8,1,3,7,5,6,4,2]=>1001011
[8,1,4,5,7,6,3,2]=>1000111
[2,4,1,8,5,7,6,3]=>0101011
[8,2,1,4,7,6,3,5]=>1100110
[8,3,1,7,4,2,6,5]=>1101101
[8,2,7,3,1,6,5,4]=>1011011
[1,8,4,2,3,7,6,5]=>0110011
[3,1,2,8,7,4,6,5]=>1001101
[8,5,1,2,4,3,7,6]=>1100101
[2,8,3,7,4,1,6,5]=>0101101
[2,3,1,8,7,6,4,5]=>0101110
[4,2,8,7,3,1,5,6]=>1011100
[1,3,4,8,7,2,5,6]=>0001100
[8,1,3,4,6,7,2,5]=>1000010
[3,4,8,2,6,7,1,5]=>0010010
[3,6,8,2,5,1,7,4]=>0010101
[3,8,2,5,7,4,6,1]=>0100101
[8,4,2,1,7,5,6,3]=>1110101
[8,2,7,5,6,4,1,3]=>1010110
[6,2,8,5,4,1,7,3]=>1011101
[6,8,5,4,1,7,2,3]=>0111010
[2,8,1,5,7,6,3,4]=>0100110
[3,1,8,2,7,5,6,4]=>1010101
[8,5,7,1,6,4,2,3]=>1010110
[8,4,7,6,5,1,2,3]=>1011100
[2,8,4,7,3,6,5,1]=>0101011
[8,4,7,2,1,6,5,3]=>1011011
[1,8,4,7,6,5,2,3]=>0101110
[8,2,5,7,1,4,6,3]=>1001001
[3,5,8,1,7,4,6,2]=>0010101
[8,4,7,1,3,6,5,2]=>1010011
[5,1,7,8,3,4,2,6]=>1001010
[5,3,6,1,4,2,8,7]=>1010101
[5,7,2,1,4,3,8,6]=>0110101
[7,1,8,3,5,2,4,6]=>1010100
[7,2,4,8,1,5,6,3]=>1001001
[7,1,8,4,2,5,6,3]=>1011001
[6,4,2,5,8,1,7,3]=>1100101
[2,1,7,5,8,3,6,4]=>1010101
[7,3,8,5,6,2,1,4]=>1010110
[2,7,4,8,1,5,6,3]=>0101001
[7,4,8,3,1,5,6,2]=>1011001
[6,1,5,8,3,7,4,2]=>1001011
[2,6,3,5,8,7,4,1]=>0100111
[6,8,1,2,5,7,4,3]=>0100011
[8,6,5,3,7,2,1,4]=>1110110
[4,8,5,3,7,2,1,6]=>0110110
[7,4,8,6,5,3,2,1]=>1011111
[6,4,7,1,3,2,8,5]=>1010101
[7,8,4,1,3,5,6,2]=>0110001
[7,8,3,4,1,5,6,2]=>0101001
[7,3,1,8,2,5,6,4]=>1101001
[7,2,3,8,1,5,6,4]=>1001001
[2,7,4,8,6,3,1,5]=>0101110
[6,4,8,2,3,1,7,5]=>1010101
[7,2,1,8,3,5,6,4]=>1101001
[5,1,6,3,8,2,4,7]=>1010100
[3,5,6,8,1,4,2,7]=>0001010
[4,3,5,8,2,1,6,7]=>1001100
[6,4,7,2,3,1,5,8]=>1010100
[6,8,1,5,4,2,7,3]=>0101101
[7,8,6,3,1,4,2,5]=>0111010
[7,8,6,3,5,1,2,4]=>0110100
[7,2,8,5,4,6,3,1]=>1011011
[6,1,8,4,7,2,3,5]=>1010100
[6,5,3,7,2,4,8,1]=>1101001
[5,6,2,8,4,3,7,1]=>0101101
[4,6,2,7,8,3,5,1]=>0100101
[3,1,2,4,8,5,7,6]=>1000101
[5,1,2,4,6,7,8,3]=>1000001
[4,6,3,5,2,8,7,1]=>0101011
[5,3,2,6,8,4,7,1]=>1100101
[5,6,3,4,8,2,7,1]=>0100101
[5,2,6,4,1,7,8,3]=>1011001
[5,8,4,6,3,2,7,1]=>0101101
[5,4,3,8,6,2,7,1]=>1101101
[5,7,8,2,4,3,6,1]=>0010101
[5,6,2,4,8,3,7,1]=>0100101
[5,4,2,8,6,3,7,1]=>1101101
[5,7,4,2,6,3,8,1]=>0110101
[6,4,7,8,2,3,5,1]=>1001001
[3,7,5,2,4,8,1,6]=>0110010
[4,7,5,2,3,8,6,1]=>0110011
[6,4,7,3,2,5,8,1]=>1011001
[6,3,7,8,2,4,5,1]=>1001001
[5,7,3,2,8,4,6,1]=>0110101
[5,3,7,2,8,4,6,1]=>1010101
[4,3,7,2,5,8,6,1]=>1010011
[4,7,3,2,5,8,6,1]=>0110011
[4,7,3,2,6,8,5,1]=>0110011
[7,5,3,2,6,4,8,1]=>1110101
[5,7,3,2,6,4,8,1]=>0110101
[5,3,2,8,6,4,7,1]=>1101101
[8,5,2,6,7,3,4,1]=>1100101
[8,4,2,6,3,7,5,1]=>1101011
[7,4,6,2,3,8,5,1]=>1010011
[7,5,6,2,8,3,4,1]=>1010101
[6,3,7,5,2,4,8,1]=>1011001
[5,7,6,2,8,3,4,1]=>0110101
[4,7,6,2,3,8,5,1]=>0110011
[7,6,3,2,5,8,1,4]=>1110010
[7,6,4,2,5,8,3,1]=>1110011
[6,3,8,5,4,7,2,1]=>1011011
[4,8,3,7,1,6,5,2]=>0101011
[8,7,2,6,5,1,4,3]=>1101101
[5,8,3,2,1,7,6,4]=>0111011
[5,4,3,8,1,7,6,2]=>1101011
[6,5,3,8,7,1,4,2]=>1101101
[4,3,8,2,7,6,5,1]=>1010111
[4,8,2,7,6,5,3,1]=>0101111
[7,8,2,6,5,4,1,3]=>0101110
[3,8,7,6,2,5,1,4]=>0111010
[4,8,3,7,2,1,6,5]=>0101101
[8,6,3,1,7,5,4,2]=>1110111
[8,6,3,7,1,5,4,2]=>1101011
[4,8,3,7,6,2,5,1]=>0101101
[5,8,2,7,6,4,1,3]=>0101110
[8,4,2,1,7,6,5,3]=>1110111
[1,6,4,2,5,3,7,8]=>0110100
[1,6,7,2,5,3,4,8]=>0010100
[1,8,6,2,7,3,4,5]=>0110100
[1,5,2,6,4,3,7,8]=>0101100
[1,5,2,4,6,3,7,8]=>0100100
[1,8,6,2,3,7,4,5]=>0110010
[1,5,2,8,6,3,4,7]=>0101100
[1,7,3,2,6,8,4,5]=>0110010
[1,3,6,8,2,7,4,5]=>0001010
[1,4,3,8,2,5,6,7]=>0101000
[1,7,2,3,8,5,4,6]=>0100110
[1,6,2,8,5,4,3,7]=>0101110
[1,7,2,3,8,6,4,5]=>0100110
[1,5,3,8,2,7,4,6]=>0101010
[1,7,2,5,3,4,8,6]=>0101001
[1,4,8,2,5,6,3,7]=>0010010
[1,2,7,3,6,8,4,5]=>0010010
[1,7,2,3,6,8,4,5]=>0100010
[1,4,8,3,2,5,6,7]=>0011000
[1,7,2,5,8,3,4,6]=>0100100
[1,5,6,3,4,2,7,8]=>0010100
[1,5,6,3,4,7,2,8]=>0010010
[1,5,3,6,4,2,7,8]=>0101100
[1,7,5,6,8,3,4,2]=>0100101
[1,7,5,6,3,8,4,2]=>0101011
[1,3,7,5,2,8,6,4]=>0011011
[1,3,7,2,5,8,6,4]=>0010011
[1,5,3,7,4,6,2,8]=>0101010
[1,5,3,7,6,4,2,8]=>0101110
[1,5,3,6,7,4,2,8]=>0100110
[1,5,6,3,7,4,2,8]=>0010110
[1,5,7,6,3,4,8,2]=>0011001
[1,5,7,3,6,4,8,2]=>0010101
[1,3,7,2,5,6,8,4]=>0010001
[1,3,7,5,6,2,8,4]=>0010101
[2,5,7,4,1,3,8,6]=>0011001
[6,7,3,1,8,5,2,4]=>0110110
[8,3,5,1,7,6,2,4]=>1010110
[3,5,6,1,8,7,2,4]=>0010110
[2,4,6,8,7,3,1,5]=>0001110
[2,3,6,4,1,8,7,5]=>0011011
[4,7,5,2,1,8,6,3]=>0111011
[8,5,3,6,2,1,7,4]=>1101101
[4,5,7,3,1,2,8,6]=>0011001
[4,5,1,8,3,2,7,6]=>0101101
[3,6,1,2,4,8,7,5]=>0100011
[2,5,3,8,4,1,7,6]=>0101101
[8,6,2,3,1,7,5,4]=>1101011
[6,3,1,2,4,8,7,5]=>1100011
[2,6,4,5,8,1,3,7]=>0100100
[4,2,6,1,3,7,8,5]=>1010001
[8,5,4,2,7,6,3,1]=>1110111
[2,8,4,6,7,1,3,5]=>0100100
[5,8,2,1,4,6,7,3]=>0110001
[3,7,8,4,2,6,5,1]=>0011011
[7,1,3,8,4,5,6,2]=>1001001
[7,8,1,4,3,5,6,2]=>0101001
[3,6,7,1,8,2,5,4]=>0010101
[3,1,5,7,2,8,6,4]=>1001011
[4,1,8,3,2,7,6,5]=>1011011
[3,8,2,4,7,1,6,5]=>0100101
[3,2,4,8,7,1,6,5]=>1001101
[3,2,5,7,1,8,6,4]=>1001011
[4,2,8,3,1,7,6,5]=>1011011
[4,8,2,1,3,7,6,5]=>0110011
[4,2,8,1,3,7,6,5]=>1010011
[2,4,6,5,1,3,8,7]=>0011001
[2,3,4,6,8,7,1,5]=>0000110
[2,1,4,6,8,7,3,5]=>1000110
[4,5,7,1,6,8,3,2]=>0010011
[6,7,2,8,3,1,4,5]=>0101100
[7,8,5,2,4,1,3,6]=>0110100
[7,6,2,3,1,8,4,5]=>1101010
[4,1,3,7,8,5,2,6]=>1000110
[4,3,1,8,5,2,7,6]=>1101101
[3,1,8,5,4,2,7,6]=>1011101
[5,1,3,2,4,7,8,6]=>1010001
[2,4,8,5,6,1,7,3]=>0010101
[2,8,7,4,5,1,6,3]=>0110101
[1,3,8,5,2,6,7,4]=>0011001
[8,6,2,4,1,5,7,3]=>1101001
[1,6,4,3,2,7,8,5]=>0111001
[8,5,3,2,1,6,7,4]=>1111001
[1,7,5,2,3,6,8,4]=>0110001
[8,1,2,5,3,6,7,4]=>1001001
[8,2,6,4,3,5,1,7]=>1011010
[8,3,1,4,6,5,2,7]=>1100110
[5,8,3,1,2,6,4,7]=>0110010
[4,8,1,7,5,2,3,6]=>0101100
[4,8,1,7,5,2,6,3]=>0101101
[8,5,1,4,2,6,3,7]=>1101010
[8,4,1,3,5,6,2,7]=>1100010
[8,5,3,2,1,6,4,7]=>1111010
[8,1,5,4,2,6,3,7]=>1011010
[8,5,2,4,1,6,3,7]=>1101010
[4,8,7,1,5,2,6,3]=>0110101
[4,8,7,1,5,2,3,6]=>0110100
[7,6,8,4,1,3,2,5]=>1011010
[7,6,8,4,1,3,5,2]=>1011001
[8,4,2,7,5,1,6,3]=>1101101
[3,8,7,5,4,1,2,6]=>0111100
[7,6,8,4,1,5,2,3]=>1011010
[8,7,6,1,5,2,3,4]=>1110100
[7,1,4,8,6,3,5,2]=>1001101
[8,1,6,5,3,4,7,2]=>1011001
[8,6,2,5,3,4,7,1]=>1101001
[8,6,5,1,3,4,7,2]=>1110001
[8,7,5,1,3,6,2,4]=>1110010
[8,7,1,5,3,6,2,4]=>1101010
[8,6,1,3,5,4,7,2]=>1100101
[8,1,6,3,5,4,7,2]=>1010101
[7,1,4,8,3,6,5,2]=>1001011
[8,3,2,7,4,6,5,1]=>1101011
[7,8,5,2,4,3,6,1]=>0110101
[7,3,8,2,5,4,6,1]=>1010101
[8,4,2,5,3,7,6,1]=>1101011
[4,8,1,5,3,7,6,2]=>0101011
[7,4,8,2,6,3,5,1]=>1010101
[7,4,8,2,6,3,1,5]=>1010110
[8,7,3,1,6,4,2,5]=>1110110
[8,7,3,1,6,4,5,2]=>1110101
[8,7,3,1,4,6,5,2]=>1110011
[8,4,3,2,7,5,6,1]=>1110101
[6,4,1,7,8,5,3,2]=>1100111
[7,6,3,4,1,8,5,2]=>1101011
[8,7,3,1,6,2,5,4]=>1110101
[7,8,6,4,2,5,1,3]=>0111010
[7,8,2,4,6,5,1,3]=>0100110
[8,1,7,3,5,6,2,4]=>1010010
[8,7,1,6,5,2,3,4]=>1101100
[8,7,5,2,4,6,1,3]=>1110010
[8,1,7,5,4,6,2,3]=>1011010
[8,7,3,2,6,1,5,4]=>1110101
[8,1,7,6,5,2,3,4]=>1011100
[8,7,2,6,5,1,3,4]=>1101100
[1,4,8,6,7,5,3,2]=>0010111
[8,6,2,5,7,4,3,1]=>1100111
[7,1,3,6,8,5,4,2]=>1000111
[8,1,7,6,4,5,3,2]=>1011011
[7,1,8,6,4,5,3,2]=>1011011
[6,5,7,2,8,3,4,1]=>1010101
[6,7,2,5,8,1,4,3]=>0100101
[6,3,7,5,8,2,4,1]=>1010101
[6,5,7,3,8,1,4,2]=>1010101
[6,3,7,4,8,2,5,1]=>1010101
[6,3,7,4,8,1,5,2]=>1010101
[8,7,6,4,2,5,3,1]=>1111011
[8,7,4,6,2,3,5,1]=>1101001
[6,8,4,5,7,3,2,1]=>0100111
[6,7,5,1,4,3,8,2]=>0110101
[2,7,6,8,3,5,1,4]=>0101010
[7,2,1,5,3,8,6,4]=>1101011
[5,8,2,7,6,1,3,4]=>0101100
[4,2,3,1,5,8,6,7]=>1010010
[1,5,7,3,6,8,2,4]=>0010010
[8,4,6,2,5,7,1,3]=>1010010
[1,3,4,7,6,8,2,5]=>0001010
[8,1,3,6,7,4,2,5]=>1000110
[1,2,4,7,8,5,3,6]=>0000110
[2,1,4,7,8,5,3,6]=>1000110
[3,1,4,7,6,8,2,5]=>1001010
[4,1,3,7,6,8,2,5]=>1001010
[5,1,7,3,6,8,2,4]=>1010010
[6,7,8,2,4,5,1,3]=>0010010
[5,8,6,2,4,7,1,3]=>0110010
[3,8,2,6,5,7,1,4]=>0101010
[2,8,3,6,7,4,1,5]=>0100110
[1,8,3,6,7,4,2,5]=>0100110
[8,7,2,5,6,3,1,4]=>1100110
[8,7,1,6,4,3,2,5]=>1101110
[1,8,2,7,5,4,3,6]=>0101110
[3,8,1,7,5,4,2,6]=>0101110
[4,8,1,6,7,3,2,5]=>0100110
[5,8,6,1,7,3,2,4]=>0110110
[6,7,1,2,8,4,3,5]=>0100110
[2,1,3,8,6,5,4,7]=>1001110
[8,2,1,7,5,4,3,6]=>1101110
[1,3,2,8,6,5,4,7]=>0101110
[3,4,1,7,6,8,2,5]=>0101010
[2,5,7,1,8,4,3,6]=>0010110
[3,5,7,1,6,8,2,4]=>0010010
[4,5,7,6,1,8,2,3]=>0011010
[5,4,7,6,8,3,1,2]=>1010110
[1,5,7,8,6,3,2,4]=>0001110
[8,4,6,7,5,2,1,3]=>1001110
[8,3,7,5,6,2,1,4]=>1010110
[1,4,8,6,7,3,2,5]=>0010110
[2,4,8,6,7,3,1,5]=>0010110
[2,3,8,7,5,4,1,6]=>0011110
[1,3,8,7,5,4,2,6]=>0011110
[8,2,7,6,4,3,1,5]=>1011110
[8,1,7,6,4,3,2,5]=>1011110
[4,1,8,6,7,3,2,5]=>1010110
[4,8,7,5,6,2,1,3]=>0110110
[8,1,7,2,5,6,4,3]=>1010011
[8,1,3,5,2,7,6,4]=>1001011
[8,1,7,4,3,6,5,2]=>1011011
[2,7,1,5,4,8,6,3]=>0101011
[8,6,2,4,3,7,5,1]=>1101011
[8,1,4,5,6,3,7,2]=>1000101
[8,1,4,5,6,2,7,3]=>1000101
[8,1,4,7,6,2,5,3]=>1001101
[2,5,1,7,8,6,4,3]=>0100111
[3,5,6,2,8,7,4,1]=>0010111
[3,5,6,1,8,7,4,2]=>0010111
[2,4,5,1,7,6,3,8]=>0010110
[7,3,1,5,6,4,2,8]=>1100110
[8,6,2,4,7,3,1,5]=>1100110
[8,4,7,3,5,2,1,6]=>1010110
[8,4,5,3,7,6,2,1]=>1010111
[3,4,5,6,2,8,1,7]=>0001010
[3,7,4,2,8,5,1,6]=>0110110
[7,3,4,1,6,8,2,5]=>1010010
[2,6,3,1,4,7,5,8]=>0110010
[7,2,1,6,3,4,8,5]=>1101001
[7,3,4,1,6,5,8,2]=>1010101
[3,7,4,2,5,8,6,1]=>0110011
[2,3,5,1,4,8,7,6]=>0010011
[2,7,1,3,6,8,5,4]=>0100011
[2,7,1,3,8,4,6,5]=>0100101
[3,8,7,1,6,2,5,4]=>0110101
[3,8,7,1,4,5,2,6]=>0110010
[3,7,4,2,1,8,6,5]=>0111011
[4,8,5,7,2,6,3,1]=>0101011
[8,4,5,7,3,2,6,1]=>1001101
[8,3,7,2,4,1,5,6]=>1010100
[8,6,7,2,1,4,3,5]=>1011010
[8,3,7,5,1,2,6,4]=>1011001
[7,3,4,6,2,1,5,8]=>1001100
[3,7,4,6,1,5,2,8]=>0101010
[3,4,7,6,1,2,8,5]=>0011001
[4,5,8,7,6,1,3,2]=>0011101
[8,6,3,7,5,1,4,2]=>1101101
[8,7,3,5,6,1,4,2]=>1100101
[7,6,3,8,1,4,5,2]=>1101001
[8,5,2,7,6,1,3,4]=>1101100
[7,6,4,8,1,2,5,3]=>1101001
[8,7,3,1,4,5,2,6]=>1110010
[8,4,2,5,1,6,7,3]=>1101001
[8,5,3,1,6,4,7,2]=>1110101
[8,7,3,1,4,5,6,2]=>1110001
[8,7,4,1,5,6,2,3]=>1110010
[8,6,4,1,7,5,2,3]=>1110110
[8,6,3,1,7,4,5,2]=>1110101
[8,5,3,1,6,7,4,2]=>1110011
[8,5,3,7,1,6,4,2]=>1101011
[7,6,3,8,1,4,2,5]=>1101010
[7,4,8,2,6,1,5,3]=>1010101
[8,5,3,1,6,4,2,7]=>1110110
[8,7,4,1,5,2,3,6]=>1110100
[8,7,5,1,2,6,3,4]=>1110010
[8,6,4,1,2,7,5,3]=>1110011
[8,7,3,1,4,2,5,6]=>1110100
[8,7,4,1,2,5,3,6]=>1110010
[8,7,5,1,2,3,6,4]=>1110001
[1,6,7,3,2,8,4,5]=>0011010
[1,8,6,3,2,7,4,5]=>0111010
[1,5,3,7,2,8,4,6]=>0101010
[1,4,6,2,8,5,3,7]=>0010110
[1,5,6,2,8,4,3,7]=>0010110
[3,5,2,6,4,7,8,1]=>0101001
[1,2,5,3,8,6,7,4]=>0010101
[2,4,6,3,1,7,5,8]=>0011010
[3,4,8,6,5,7,2,1]=>0011011
[2,3,8,6,7,1,5,4]=>0010101
[1,2,5,7,4,6,8,3]=>0001001
[2,3,6,8,1,7,4,5]=>0001010
[2,4,8,5,6,7,1,3]=>0010010
[1,4,8,5,6,7,3,2]=>0010011
[6,1,3,5,4,2,8,7]=>1001101
[3,6,4,2,5,1,8,7]=>0110101
[2,1,5,8,6,4,7,3]=>1001101
[1,8,3,5,6,2,7,4]=>0100101
[8,3,2,5,6,1,7,4]=>1100101
[4,2,5,1,6,8,7,3]=>1010011
[5,4,2,7,8,6,1,3]=>1100110
[6,7,1,8,3,2,4,5]=>0101100
[6,7,2,8,1,3,4,5]=>0101000
[1,7,8,5,2,6,3,4]=>0011010
[5,8,7,2,6,3,4,1]=>0110101
[7,6,2,4,8,1,5,3]=>1100101
[4,8,3,1,7,6,5,2]=>0110111
[5,3,8,7,1,6,4,2]=>1011011
[5,8,7,3,1,6,4,2]=>0111011
[5,3,8,2,1,7,6,4]=>1011011
[3,8,7,2,6,5,1,4]=>0110110
[7,4,1,8,6,5,3,2]=>1101111
[5,4,2,8,1,7,6,3]=>1101011
[5,8,4,7,1,6,3,2]=>0101011
[8,5,6,1,4,7,2,3]=>1010010
[6,7,4,1,2,5,8,3]=>0110001
[3,6,7,5,8,1,2,4]=>0010100
[6,5,8,7,4,2,3,1]=>1011101
[5,7,6,2,8,3,1,4]=>0110110
[2,5,6,3,1,4,8,7]=>0011001
[3,8,7,2,1,5,4,6]=>0111010
[4,8,5,6,7,3,1,2]=>0100110
[3,7,6,2,8,5,1,4]=>0110110
[6,1,7,3,8,5,2,4]=>1010110
[4,8,5,6,7,2,1,3]=>0100110
[5,8,6,2,7,4,1,3]=>0110110
[4,6,5,8,7,3,1,2]=>0101110
[8,3,1,7,2,6,4,5]=>1101010
[8,4,5,1,7,6,2,3]=>1010110
[8,5,6,1,7,2,4,3]=>1010101
[7,5,6,1,3,8,4,2]=>1010011
[5,7,6,1,3,8,4,2]=>0110011
[6,7,1,4,2,8,5,3]=>0101011
[2,1,6,4,8,3,7,5]=>1010101
[5,8,7,4,6,2,3,1]=>0110101
[6,8,7,1,5,3,4,2]=>0110101
[2,7,8,4,6,5,1,3]=>0010110
[3,7,8,5,4,6,2,1]=>0011011
[2,8,7,5,3,6,4,1]=>0111011
[1,8,7,3,6,4,5,2]=>0110101
[2,8,7,4,6,1,5,3]=>0110101
[4,8,7,2,5,6,3,1]=>0110011
[4,7,8,5,3,6,2,1]=>0011011
[6,4,8,1,5,7,3,2]=>1010011
[4,5,8,6,3,7,2,1]=>0011011
[2,6,7,8,4,5,1,3]=>0001010
[6,1,2,8,4,7,5,3]=>1001011
[4,7,1,8,5,6,3,2]=>0101011
[5,7,1,8,2,6,4,3]=>0101011
[7,2,1,8,6,4,5,3]=>1101101
[5,3,8,4,7,6,2,1]=>1010111
[2,5,8,1,7,4,6,3]=>0010101
[4,5,8,3,7,6,2,1]=>0010111
[1,7,2,8,6,4,5,3]=>0101101
[2,4,7,8,5,6,1,3]=>0001010
[2,4,8,5,7,6,1,3]=>0010110
[2,6,3,8,5,1,7,4]=>0101101
[4,1,5,8,6,7,3,2]=>1001011
[3,4,6,8,2,1,7,5]=>0001101
[5,3,4,7,6,1,2,8]=>1001100
[1,2,7,8,4,3,6,5]=>0001101
[2,8,5,4,1,3,7,6]=>0111001
[4,2,8,7,1,3,5,6]=>1011000
[5,4,6,3,1,7,2,8]=>1011010
[4,3,6,5,1,8,2,7]=>1011010
[1,5,6,8,7,3,2,4]=>0001110
[1,4,8,3,6,5,2,7]=>0010110
[1,2,8,6,4,3,7,5]=>0011101
[6,5,1,8,7,3,2,4]=>1101110
[8,3,2,6,1,7,4,5]=>1101010
[6,5,1,8,7,4,3,2]=>1101111
[7,5,1,8,6,4,3,2]=>1101111
[8,5,1,7,6,4,3,2]=>1101111
[8,5,3,7,6,1,4,2]=>1101101
[3,8,7,6,1,5,4,2]=>0111011
[8,5,2,6,1,4,7,3]=>1101001
[2,7,5,8,1,4,6,3]=>0101001
[8,5,6,1,7,3,2,4]=>1010110
[3,2,6,7,1,8,5,4]=>1001011
[3,4,6,7,8,2,1,5]=>0000110
[6,7,1,3,8,5,4,2]=>0100111
[6,7,1,8,5,2,4,3]=>0101101
[1,6,2,7,8,5,3,4]=>0100110
[1,2,6,7,8,5,3,4]=>0000110
[1,6,7,4,8,3,2,5]=>0010110
[1,4,6,7,8,3,2,5]=>0000110
[8,6,1,2,7,3,4,5]=>1100100
[3,6,8,2,7,1,5,4]=>0010101
[2,8,6,1,4,5,7,3]=>0110001
[6,8,7,2,5,4,1,3]=>0110110
[3,7,2,1,8,4,6,5]=>0110101
[3,7,2,4,1,8,6,5]=>0101011
[3,2,6,4,8,7,5,1]=>1010111
[4,7,2,8,6,5,1,3]=>0101110
[4,7,1,8,6,5,3,2]=>0101111
[2,7,4,8,3,6,1,5]=>0101010
[4,7,3,8,6,1,5,2]=>0101101
[4,7,3,8,6,2,1,5]=>0101110
[4,3,6,8,7,2,5,1]=>1001101
[4,3,8,2,5,7,6,1]=>1010011
[4,3,8,1,5,7,6,2]=>1010011
[4,1,2,6,8,7,5,3]=>1000111
[2,4,3,6,8,7,1,5]=>0100110
[3,1,6,4,8,7,2,5]=>1010110
[4,1,6,8,7,5,2,3]=>1001110
[3,8,1,4,5,7,2,6]=>0100010
[3,8,1,4,2,5,7,6]=>0101001
[4,1,8,3,5,2,7,6]=>1010101
[4,2,3,6,8,7,1,5]=>1000110
[4,2,8,3,5,7,6,1]=>1010011
[3,8,2,4,5,7,6,1]=>0100011
[3,8,2,4,1,5,7,6]=>0101001
[3,8,2,5,1,4,7,6]=>0101001
[4,2,8,5,7,1,3,6]=>1010100
[3,8,1,5,2,4,7,6]=>0101001
[7,5,6,4,1,3,2,8]=>1011010
[7,8,6,4,1,3,2,5]=>0111010
[7,1,4,2,5,6,3,8]=>1010010
[7,3,2,1,4,6,5,8]=>1110010
[7,6,1,4,3,2,5,8]=>1101100
[7,4,1,3,5,6,2,8]=>1100010
[7,3,1,2,5,6,4,8]=>1100010
[2,7,1,3,5,6,8,4]=>0100001
[3,6,2,1,5,8,7,4]=>0110011
[2,3,6,1,5,8,7,4]=>0010011
[3,1,7,2,5,6,8,4]=>1010001
[3,4,7,1,5,6,8,2]=>0010001
[3,6,7,4,1,2,8,5]=>0011001
[4,3,2,7,1,6,8,5]=>1101001
[7,3,2,8,1,6,4,5]=>1101010
[7,4,8,1,5,6,3,2]=>1010011
[2,6,8,1,5,3,7,4]=>0010101
[6,8,2,1,5,3,7,4]=>0110101
[4,8,2,5,3,6,7,1]=>0101001
[4,5,8,2,3,6,7,1]=>0010001
[2,4,8,5,3,6,7,1]=>0011001
[4,1,8,6,5,3,7,2]=>1011101
[5,7,8,4,6,3,2,1]=>0010111
[5,3,2,6,4,8,7,1]=>1101011
[2,4,5,3,8,6,7,1]=>0010101
[4,3,5,2,8,6,7,1]=>1010101
[4,5,2,3,8,6,7,1]=>0100101
[4,8,5,3,2,6,7,1]=>0111001
[3,8,4,5,2,6,7,1]=>0101001
[3,5,4,2,8,6,7,1]=>0110101
[4,1,2,7,5,6,8,3]=>1001001
[4,8,1,6,5,2,7,3]=>0101101
[5,6,7,4,2,8,3,1]=>0011011
[2,5,7,4,6,8,3,1]=>0010011
[7,3,5,4,2,8,6,1]=>1011011
[7,5,2,4,3,8,6,1]=>1101011
[6,8,1,2,5,4,7,3]=>0100101
[6,4,1,8,5,2,7,3]=>1101101
[2,6,1,8,5,4,7,3]=>0101101
[7,1,2,8,5,6,4,3]=>1001011
[4,3,2,6,8,5,7,1]=>1100101
[3,7,6,4,8,5,2,1]=>0110111
[3,1,6,8,5,4,7,2]=>1001101
[2,3,5,8,4,6,7,1]=>0001001
[3,4,5,8,2,6,7,1]=>0001001
[5,4,2,8,3,6,7,1]=>1101001
[5,3,4,8,2,6,7,1]=>1001001
[2,5,4,8,3,6,7,1]=>0101001
[6,3,2,5,8,4,7,1]=>1100101
[6,1,8,3,5,4,7,2]=>1010101
[5,4,8,3,2,6,7,1]=>1011001
[5,8,2,3,4,6,7,1]=>0100001
[3,4,5,2,7,1,6,8]=>0010100
[7,5,6,1,2,3,8,4]=>1010001
[1,5,7,6,3,2,8,4]=>0011101
[8,4,6,7,3,2,5,1]=>1001101
[8,4,6,2,3,1,5,7]=>1010100
[7,5,2,1,4,3,8,6]=>1110101
[3,1,7,8,5,4,2,6]=>1001110
[3,4,5,2,1,8,6,7]=>0011010
[7,6,4,8,3,1,2,5]=>1101100
[6,2,8,5,1,3,4,7]=>1011000
[3,2,7,8,6,1,4,5]=>1001100
[6,8,2,5,1,3,7,4]=>0101001
[6,7,4,2,1,5,3,8]=>0111010
[5,6,8,1,3,7,2,4]=>0010010
[1,6,8,5,3,2,4,7]=>0011100
[7,2,8,4,6,1,3,5]=>1010100
[4,1,6,8,7,3,2,5]=>1001110
[5,1,4,6,7,3,8,2]=>1000101
[7,1,3,4,6,2,8,5]=>1000101
[5,8,7,4,2,1,3,6]=>0111100
[3,1,5,2,7,8,6,4]=>1010011
[1,8,7,3,2,5,4,6]=>0111010
[1,2,5,4,8,7,3,6]=>0010110
[1,2,4,8,6,3,5,7]=>0001100
[8,5,3,2,1,4,7,6]=>1111001
[1,2,7,6,8,4,3,5]=>0010110
[1,7,3,4,2,6,8,5]=>0101001
[1,6,3,5,8,4,2,7]=>0100110
[1,5,6,3,2,8,4,7]=>0011010
[1,2,5,8,4,6,3,7]=>0001010
[1,2,7,8,4,5,3,6]=>0001010
[1,5,3,2,7,8,4,6]=>0110010
[4,1,8,6,2,3,7,5]=>1011001
[1,7,6,4,3,8,5,2]=>0111011
[1,8,5,7,6,3,2,4]=>0101110
[1,6,3,5,7,8,4,2]=>0100011
[1,5,6,3,2,7,8,4]=>0011001
[1,8,4,7,5,3,2,6]=>0101110
[7,6,2,5,3,4,1,8]=>1101010
[7,6,2,4,5,3,1,8]=>1100110
[7,6,2,4,3,5,1,8]=>1101010
[7,6,2,3,5,4,1,8]=>1100110
[8,4,2,7,1,6,3,5]=>1101010
[8,7,6,1,5,3,2,4]=>1110110
[8,7,6,1,3,5,4,2]=>1110011
[8,7,6,1,5,4,2,3]=>1110110
[4,5,3,8,2,1,6,7]=>0101100
[8,3,5,4,2,1,6,7]=>1011100
[7,8,4,3,1,5,2,6]=>0111010
[7,5,8,2,1,4,3,6]=>1011010
[8,6,3,7,1,5,2,4]=>1101010
[8,7,6,1,2,5,3,4]=>1110010
[8,7,6,1,2,5,4,3]=>1110011
[8,7,6,1,4,2,5,3]=>1110101
[2,4,7,3,5,6,1,8]=>0010010
[5,7,6,4,2,3,1,8]=>0111010
[3,1,4,8,5,6,2,7]=>1001010
[5,8,2,4,6,1,3,7]=>0100100
[2,4,1,8,5,6,3,7]=>0101010
[6,1,4,8,5,2,7,3]=>1001101
[4,1,2,8,5,3,7,6]=>1001101
[2,4,6,8,5,1,7,3]=>0001101
[3,1,6,8,5,2,7,4]=>1001101
[2,3,8,1,5,6,4,7]=>0010010
[5,1,8,2,4,6,7,3]=>1010001
[4,1,8,2,3,6,7,5]=>1010001
[5,8,2,7,3,4,1,6]=>0101010
[3,8,7,5,2,6,1,4]=>0111010
[5,3,8,1,6,7,4,2]=>1010011
[5,8,2,1,3,7,6,4]=>0110011
[4,8,2,1,3,5,6,7]=>0110000
[5,1,8,3,6,7,4,2]=>1010011
[8,4,1,6,5,2,3,7]=>1101100
[6,8,7,3,2,4,1,5]=>0111010
[1,3,7,5,6,8,4,2]=>0010011
[3,2,4,7,5,8,1,6]=>1001010
[1,2,7,4,6,3,8,5]=>0010101
[2,8,7,6,4,5,1,3]=>0111010
[3,5,2,4,7,6,8,1]=>0100101
[3,5,2,4,6,7,8,1]=>0100001
[5,3,2,6,4,7,8,1]=>1101001
[5,3,2,6,7,4,8,1]=>1100101
[5,3,2,7,6,4,8,1]=>1101101
[7,3,5,2,8,4,6,1]=>1010101
[3,2,5,7,4,6,8,1]=>1001001
[2,3,5,7,4,6,8,1]=>0001001
[3,2,7,5,4,8,6,1]=>1011011
[3,7,5,2,4,8,6,1]=>0110011
[7,5,3,2,8,6,4,1]=>1110111
[2,3,7,5,4,8,6,1]=>0011011
[2,4,8,7,5,1,3,6]=>0011100
[3,5,7,6,1,8,4,2]=>0011011
[3,5,7,6,2,8,4,1]=>0011011
[2,4,6,3,8,7,5,1]=>0010111
[1,5,3,2,8,7,6,4]=>0110111
[6,3,1,8,7,4,2,5]=>1101110
[5,3,6,2,8,7,4,1]=>1010111
[5,8,3,1,7,6,4,2]=>0110111
[6,3,5,2,1,8,7,4]=>1011011
[3,8,1,4,7,6,5,2]=>0100111
[6,2,3,8,7,5,4,1]=>1001111
[4,1,3,5,8,7,6,2]=>1000111
[4,2,5,3,7,6,1,8]=>1010110
[6,2,4,3,7,5,1,8]=>1010110
[1,3,6,4,7,5,2,8]=>0010110
[8,2,5,3,6,4,1,7]=>1010110
[7,2,5,3,6,4,1,8]=>1010110
[6,2,5,3,7,4,1,8]=>1010110
[4,2,6,3,7,5,1,8]=>1010110
[5,2,7,3,6,4,1,8]=>1010110
[7,3,6,2,5,4,1,8]=>1010110
[6,3,8,2,5,4,1,7]=>1010110
[7,3,1,4,6,5,2,8]=>1100110
[8,3,7,2,5,4,1,6]=>1010110
[5,2,8,3,6,4,1,7]=>1010110
[4,2,8,3,6,5,1,7]=>1010110
[3,2,8,4,6,5,1,7]=>1010110
[1,4,7,3,6,5,2,8]=>0010110
[8,2,5,4,1,6,3,7]=>1011010
[1,3,6,5,2,7,4,8]=>0011010
[8,2,6,4,1,5,3,7]=>1011010
[1,4,8,3,7,5,2,6]=>0010110
[6,2,1,4,8,5,3,7]=>1100110
[5,2,1,4,8,6,3,7]=>1100110
[3,2,1,5,8,6,4,7]=>1100110
[4,2,8,3,7,5,1,6]=>1010110
[5,2,8,3,7,4,1,6]=>1010110
[8,3,7,2,6,4,1,5]=>1010110
[7,3,1,4,8,5,2,6]=>1100110
[1,3,7,4,8,5,2,6]=>0010110
[8,2,6,3,7,4,1,5]=>1010110
[7,2,6,3,8,4,1,5]=>1010110
[5,2,7,3,8,4,1,6]=>1010110
[3,2,7,4,8,5,1,6]=>1010110
[5,2,6,3,8,4,1,7]=>1010110
[6,2,5,3,8,4,1,7]=>1010110
[7,2,5,3,8,4,1,6]=>1010110
[8,2,5,3,7,4,1,6]=>1010110
[1,3,6,4,8,5,2,7]=>0010110
[1,3,5,4,8,6,2,7]=>0010110
[8,2,4,3,7,5,1,6]=>1010110
[7,2,4,3,8,5,1,6]=>1010110
[6,2,4,3,8,5,1,7]=>1010110
[5,2,4,3,8,6,1,7]=>1010110
[4,2,5,3,8,6,1,7]=>1010110
[4,2,5,3,1,7,6,8]=>1011010
[6,2,4,3,1,7,5,8]=>1011010
[7,2,4,3,1,6,5,8]=>1011010
[8,5,1,3,6,4,2,7]=>1100110
[8,4,1,3,6,5,2,7]=>1100110
[1,5,2,4,7,6,3,8]=>0100110
[7,2,5,3,1,6,4,8]=>1011010
[6,2,5,3,1,7,4,8]=>1011010
[4,2,6,3,1,7,5,8]=>1011010
[3,2,6,4,1,7,5,8]=>1011010
[5,2,7,3,1,6,4,8]=>1011010
[6,2,7,3,1,5,4,8]=>1011010
[7,2,6,3,1,5,4,8]=>1011010
[1,5,2,4,8,6,3,7]=>0100110
[8,4,1,3,7,5,2,6]=>1100110
[6,2,1,5,3,7,4,8]=>1101010
[3,2,1,6,4,7,5,8]=>1101010
[3,2,8,5,1,6,4,7]=>1011010
[4,2,8,5,1,6,3,7]=>1011010
[6,2,8,4,1,5,3,7]=>1011010
[1,4,8,5,2,6,3,7]=>0011010
[8,3,7,4,1,5,2,6]=>1011010
[7,1,3,2,5,6,4,8]=>1010010
[1,5,2,8,7,4,3,6]=>0101110
[5,7,2,8,1,4,3,6]=>0101010
[7,1,5,3,2,6,8,4]=>1011001
[1,7,3,4,5,2,8,6]=>0100101
[8,6,7,3,5,2,1,4]=>1010110
[3,2,1,7,8,5,4,6]=>1100110
[7,3,4,2,1,5,8,6]=>1011001
[1,7,6,3,2,4,8,5]=>0111001
[1,8,5,3,2,4,7,6]=>0111001
[1,2,8,4,6,3,5,7]=>0010100
[2,6,1,5,4,7,3,8]=>0101010
[1,2,8,5,4,6,3,7]=>0011010
[1,3,8,5,4,2,6,7]=>0011100
[1,3,6,8,4,5,7,2]=>0001001
[1,2,8,4,6,3,7,5]=>0010101
[4,6,3,5,7,8,1,2]=>0100010
[2,7,6,5,1,4,8,3]=>0111001
[2,7,4,8,1,3,6,5]=>0101001
[2,3,6,8,4,1,7,5]=>0001101
[1,2,6,8,4,7,5,3]=>0001011
[1,7,2,8,6,3,5,4]=>0101101
[2,3,8,5,4,7,1,6]=>0011010
[2,7,4,1,6,3,5,8]=>0110100
[1,2,8,4,7,3,5,6]=>0010100
[2,6,1,4,8,3,7,5]=>0100101
[3,7,6,5,2,1,4,8]=>0111100
[2,5,6,1,4,8,7,3]=>0010011
[7,1,5,2,6,4,3,8]=>1010110
[1,8,5,6,2,7,4,3]=>0101011
[4,2,7,6,1,8,5,3]=>1011011
[7,3,2,1,6,4,8,5]=>1110101
[6,7,2,4,3,5,8,1]=>0101001
[4,5,3,7,2,1,6,8]=>0101100
[4,3,8,2,1,5,7,6]=>1011001
[4,3,2,8,1,6,7,5]=>1101001
[4,5,8,3,2,7,1,6]=>0011010
[5,4,7,8,2,3,6,1]=>1001001
[4,3,8,2,1,6,7,5]=>1011001
[4,6,7,2,5,3,8,1]=>0010101
[6,4,7,8,3,1,5,2]=>1001101
[8,4,7,3,1,5,6,2]=>1011001
[5,6,7,1,8,3,4,2]=>0010101
[7,1,8,6,2,5,4,3]=>1011011
[8,5,1,7,6,4,2,3]=>1101110
[1,5,8,2,6,4,7,3]=>0010101
[1,5,7,4,6,8,3,2]=>0010011
[8,1,2,6,4,5,7,3]=>1001001
[3,1,8,6,5,2,7,4]=>1011101
[2,3,7,6,5,8,1,4]=>0011010
[2,3,7,6,5,1,8,4]=>0011101
[7,3,5,2,1,6,8,4]=>1011001
[3,7,2,6,8,1,5,4]=>0100101
[2,7,6,8,5,1,4,3]=>0101101
[1,5,4,7,8,6,2,3]=>0100110
[7,3,1,6,8,2,5,4]=>1100101
[7,1,6,8,5,2,4,3]=>1001101
[2,7,6,4,8,1,5,3]=>0110101
[3,6,2,1,4,7,8,5]=>0110001
[6,3,8,7,5,4,2,1]=>1011111
[6,8,2,7,5,4,3,1]=>0101111
[5,8,1,7,6,4,3,2]=>0101111
[4,2,6,3,8,5,7,1]=>1010101
[8,2,6,5,7,3,4,1]=>1010101
[5,1,8,3,7,4,6,2]=>1010101
[8,3,7,1,5,4,6,2]=>1010101
[8,4,7,1,5,3,6,2]=>1010101
[8,2,7,4,5,1,6,3]=>1010101
[5,8,7,1,4,2,3,6]=>0110100
[1,7,5,2,4,8,6,3]=>0110011
[2,6,3,7,1,4,5,8]=>0101000
[7,2,8,5,3,1,6,4]=>1011101
[7,2,4,1,3,8,5,6]=>1010010
[4,7,6,1,5,8,3,2]=>0110011
[4,7,3,8,6,2,5,1]=>0101101
[5,4,7,3,8,2,1,6]=>1010110
[4,3,5,7,2,6,1,8]=>1001010
[1,7,2,8,5,4,3,6]=>0101110
[5,4,8,3,6,2,1,7]=>1010110
[6,8,3,5,7,2,4,1]=>0100101
[3,8,6,2,7,5,1,4]=>0110110
[4,7,3,2,5,1,6,8]=>0110100
[4,2,5,3,8,7,1,6]=>1010110
[7,2,5,3,8,4,6,1]=>1010101
[6,7,3,2,5,4,1,8]=>0110110
[8,7,3,2,5,4,6,1]=>1110101
[4,5,6,2,7,3,1,8]=>0010110
[7,3,4,8,2,1,6,5]=>1001101
[3,8,1,7,5,2,4,6]=>0101100
[4,5,8,2,7,3,1,6]=>0010110
[6,5,8,2,7,3,1,4]=>1010110
[6,4,8,2,7,3,1,5]=>1010110
[4,3,8,2,7,5,1,6]=>1010110
[4,5,7,8,3,2,1,6]=>0001110
[8,1,5,4,6,2,7,3]=>1010101
[5,3,7,2,1,8,6,4]=>1011011
[5,4,8,3,2,7,1,6]=>1011010
[5,4,3,7,8,2,6,1]=>1100101
[5,4,3,8,2,6,7,1]=>1101001
[5,4,3,7,8,2,1,6]=>1100110
[2,3,8,7,5,1,6,4]=>0011101
[4,1,3,5,6,2,8,7]=>1000101
[6,4,8,7,3,5,2,1]=>1011011
[8,3,4,5,1,6,7,2]=>1001001
[7,8,1,5,6,3,2,4]=>0100110
[1,7,8,3,2,5,4,6]=>0011010
[7,8,1,3,5,4,2,6]=>0100110
[7,8,1,3,2,5,6,4]=>0101001
[7,8,1,3,5,4,6,2]=>0100101
[7,8,1,3,5,2,4,6]=>0100100
[1,3,7,8,5,2,4,6]=>0001100
[1,7,8,3,5,2,6,4]=>0010101
[1,7,8,3,2,5,6,4]=>0011001
[3,5,7,6,4,8,1,2]=>0011010
[1,3,7,8,5,4,6,2]=>0001101
[1,3,7,8,5,4,2,6]=>0001110
[1,3,7,8,2,5,4,6]=>0001010
[1,7,8,5,6,3,2,4]=>0010110
[5,7,6,8,1,3,4,2]=>0101001
[1,5,7,6,8,3,2,4]=>0010110
[3,5,4,7,8,6,1,2]=>0100110
[3,5,7,6,8,4,1,2]=>0010110
[1,5,7,6,8,3,4,2]=>0010101
[3,5,7,4,6,8,1,2]=>0010010
[7,2,8,6,5,1,4,3]=>1011101
[4,2,7,5,3,1,8,6]=>1011101
[7,3,2,5,4,1,8,6]=>1101101
[3,6,4,1,8,2,7,5]=>0110101
[4,6,3,8,7,2,1,5]=>0101110
[4,3,5,1,8,7,2,6]=>1010110
[8,4,3,2,7,5,1,6]=>1110110
[7,5,2,8,4,3,1,6]=>1101110
[1,7,2,4,5,3,6,8]=>0100100
[1,7,4,5,3,2,6,8]=>0101100
[1,6,4,7,3,5,2,8]=>0101010
[8,3,5,6,1,4,7,2]=>1001001
[1,6,4,7,5,2,3,8]=>0101100
[1,5,2,6,7,4,3,8]=>0100110
[8,5,6,1,4,3,7,2]=>1010101
[5,4,7,8,3,1,2,6]=>1001100
[2,5,4,7,8,3,1,6]=>0100110
[6,4,5,8,2,3,1,7]=>1001010
[8,6,1,3,2,5,7,4]=>1101001
[7,5,8,1,4,6,3,2]=>1010011
[4,2,6,7,8,1,5,3]=>1000101
[3,4,6,7,8,1,5,2]=>0000101
[4,3,2,7,5,8,1,6]=>1101010
[4,8,5,3,2,6,1,7]=>0111010
[2,8,4,5,3,6,1,7]=>0101010
[8,1,5,3,2,4,7,6]=>1011001
[8,1,2,4,5,3,7,6]=>1000101
[8,1,4,5,3,2,7,6]=>1001101
[7,8,4,1,3,6,5,2]=>0110011
[8,6,1,3,2,7,4,5]=>1101010
[7,3,8,2,4,1,6,5]=>1010101
[6,2,3,7,8,1,5,4]=>1000101
[6,3,7,8,1,5,4,2]=>1001011
[2,6,3,7,8,1,5,4]=>0100101
[7,5,8,1,6,4,2,3]=>1010110
[7,4,3,2,5,8,1,6]=>1110010
[7,2,4,3,5,8,1,6]=>1010010
[1,3,6,4,2,5,7,8]=>0011000
[1,7,6,4,2,3,5,8]=>0111000
[1,2,3,7,6,4,5,8]=>0001100
[1,3,2,5,8,6,4,7]=>0100110
[4,8,2,7,1,3,6,5]=>0101001
[1,7,4,6,8,3,5,2]=>0100101
[4,1,5,2,3,8,7,6]=>1010011
[6,3,5,8,2,4,7,1]=>1001001
[2,8,7,1,4,6,3,5]=>0110010
[3,1,2,8,5,7,4,6]=>1001010
[6,4,1,5,3,2,8,7]=>1101101
[6,3,8,1,2,5,4,7]=>1010010
[2,1,8,6,3,7,5,4]=>1011011
[1,6,5,3,2,4,7,8]=>0111000
[1,7,2,4,6,5,3,8]=>0100110
[1,4,7,2,6,5,3,8]=>0010110
[1,3,7,2,4,6,5,8]=>0010010
[1,7,2,6,4,3,5,8]=>0101100
[1,2,6,8,7,4,3,5]=>0001110
[1,2,7,4,3,5,8,6]=>0011001
[1,8,6,3,5,2,7,4]=>0110101
[1,6,2,8,7,4,3,5]=>0101110
[1,3,8,7,5,4,6,2]=>0011101
[1,2,8,6,3,5,7,4]=>0011001
[1,8,5,2,3,6,4,7]=>0110010
[1,7,4,8,5,2,3,6]=>0101100
[1,4,7,5,8,6,3,2]=>0010111
[1,4,7,5,2,8,6,3]=>0011011
[1,6,3,7,4,2,8,5]=>0101101
[1,8,5,2,7,4,3,6]=>0110110
[1,4,8,6,3,2,7,5]=>0011101
[1,4,8,7,5,3,2,6]=>0011110
[1,2,5,8,6,3,7,4]=>0001101
[1,2,4,7,5,8,6,3]=>0001011
[1,3,5,8,7,6,2,4]=>0001110
[1,5,2,4,3,6,8,7]=>0101001
[1,6,8,7,5,3,2,4]=>0011110
[1,2,5,7,4,3,8,6]=>0001101
[1,5,3,2,6,8,7,4]=>0110011
[1,4,2,6,8,7,5,3]=>0100111
[1,5,8,6,3,2,7,4]=>0011101
[1,8,5,2,6,3,4,7]=>0110100
[1,7,4,6,3,2,8,5]=>0101101
[1,6,3,2,8,5,4,7]=>0110110
[1,4,2,8,6,3,5,7]=>0101100
[1,3,8,6,4,2,5,7]=>0011100
[1,5,7,4,2,3,8,6]=>0011001
[8,2,7,3,1,5,4,6]=>1011010
[8,4,7,2,5,3,1,6]=>1010110
[8,3,4,5,2,1,7,6]=>1001101
[8,6,1,4,7,3,5,2]=>1100101
[5,3,6,7,2,8,4,1]=>1001011
[5,3,6,7,2,4,8,1]=>1001001
[1,3,8,2,5,6,7,4]=>0010001
[5,4,2,3,6,1,8,7]=>1100101
[5,1,7,4,3,6,8,2]=>1011001
[7,1,3,6,5,2,8,4]=>1001101
[6,1,8,5,2,7,3,4]=>1011010
[8,7,2,6,3,1,4,5]=>1101100
[5,4,1,3,7,2,8,6]=>1100101
[8,3,4,7,6,2,1,5]=>1001110
[3,1,8,7,5,2,4,6]=>1011100
[6,5,8,7,2,4,3,1]=>1011011
[4,3,6,5,8,2,1,7]=>1010110
[3,2,6,8,7,1,4,5]=>1001100
[4,7,3,1,8,5,2,6]=>0110110
[3,7,8,2,5,6,1,4]=>0010010
[3,1,2,5,7,8,6,4]=>1000011
[7,5,1,4,2,3,6,8]=>1101000
[7,8,6,1,2,4,5,3]=>0110001
[1,5,3,4,7,8,6,2]=>0100011
[5,1,2,4,7,8,6,3]=>1000011
[5,1,7,8,6,2,3,4]=>1001100
[8,5,1,6,7,2,3,4]=>1100100
[8,5,1,2,4,6,7,3]=>1100001
[1,8,5,3,4,6,7,2]=>0110001
[7,5,1,2,4,6,8,3]=>1100001
[6,1,5,2,7,3,4,8]=>1010100
[7,1,2,6,4,5,8,3]=>1001001
[1,7,3,6,4,5,8,2]=>0101001
[1,8,3,6,4,5,7,2]=>0101001
[8,1,6,2,7,3,4,5]=>1010100
[7,1,5,2,6,3,4,8]=>1010100
[7,1,6,2,5,3,4,8]=>1010100
[8,1,6,2,5,3,4,7]=>1010100
[8,1,7,2,5,3,4,6]=>1010100
[8,1,2,7,4,5,6,3]=>1001001
[1,8,3,7,4,5,6,2]=>0101001
[8,1,6,7,5,2,3,4]=>1001100
[8,1,6,4,2,3,5,7]=>1011000
[7,3,1,2,6,4,5,8]=>1100100
[8,3,1,2,4,6,7,5]=>1100001
[3,1,2,8,5,6,7,4]=>1001001
[6,3,1,2,7,4,5,8]=>1100100
[6,1,7,4,2,3,5,8]=>1011000
[6,1,8,4,2,3,5,7]=>1011000
[1,7,3,4,6,8,5,2]=>0100011
[1,7,3,8,4,5,6,2]=>0101001
[7,1,8,2,5,3,4,6]=>1010100
[6,1,8,2,5,3,4,7]=>1010100
[6,1,7,2,5,3,4,8]=>1010100
[5,1,7,2,6,3,4,8]=>1010100
[5,1,8,2,6,3,4,7]=>1010100
[1,6,3,8,4,5,7,2]=>0101001
[1,6,3,7,4,5,8,2]=>0101001
[2,7,4,3,8,5,1,6]=>0110110
[2,4,7,3,5,1,6,8]=>0010100
[2,5,8,4,6,3,1,7]=>0010110
[2,4,8,6,3,5,1,7]=>0011010
[2,3,7,5,4,1,6,8]=>0011100
[3,4,6,2,1,5,8,7]=>0011001
[2,6,8,3,5,1,4,7]=>0010100
[2,3,6,1,5,8,4,7]=>0010010
[2,3,7,1,6,5,8,4]=>0010101
[2,4,7,1,3,6,8,5]=>0010001
[5,4,7,8,1,3,2,6]=>1001010
[2,5,7,1,4,6,3,8]=>0010010
[2,4,7,1,6,3,5,8]=>0010100
[2,3,7,1,6,5,4,8]=>0010110
[2,5,7,1,4,3,6,8]=>0010100
[2,5,7,3,1,4,6,8]=>0011000
[3,4,7,2,1,6,8,5]=>0011001
[5,7,3,2,8,1,4,6]=>0110100
[3,6,8,5,4,1,7,2]=>0011101
[5,4,7,8,1,3,6,2]=>1001001
[2,5,7,1,4,6,8,3]=>0010001
[2,4,7,1,6,3,8,5]=>0010101
[2,4,7,1,6,8,3,5]=>0010010
[2,4,8,3,1,7,6,5]=>0011011
[8,6,5,1,2,4,3,7]=>1110010
[7,6,1,4,2,3,5,8]=>1101000
[7,5,4,8,3,2,6,1]=>1101101
[8,7,5,1,4,2,3,6]=>1110100
[8,4,1,2,5,3,6,7]=>1100100
[4,3,8,1,5,2,6,7]=>1010100
[8,6,1,4,2,5,3,7]=>1101010
[2,8,3,7,4,5,6,1]=>0101001
[8,7,5,2,4,3,6,1]=>1110101
[6,8,3,2,4,5,1,7]=>0110010
[3,8,5,2,4,6,1,7]=>0110010
[8,2,4,5,3,1,6,7]=>1001100
[4,8,2,5,3,1,6,7]=>0101100
[4,3,7,5,2,1,6,8]=>1011100
[1,6,7,4,3,2,5,8]=>0011100
[1,4,5,7,3,2,6,8]=>0001100
[3,5,1,4,7,2,6,8]=>0100100
[2,5,4,7,8,1,3,6]=>0100100
[2,5,1,4,7,8,3,6]=>0100010
[4,3,7,1,5,2,6,8]=>1010100
[3,5,1,6,4,2,7,8]=>0101100
[6,4,3,1,7,2,5,8]=>1110100
[6,2,7,4,3,1,5,8]=>1011100
[2,6,4,1,7,3,5,8]=>0110100
[6,3,2,7,4,5,1,8]=>1101010
[7,2,4,1,3,6,8,5]=>1010001
[6,3,2,5,7,1,4,8]=>1100100
[3,2,6,5,7,1,4,8]=>1010100
[1,7,3,2,5,6,4,8]=>0110010
[2,1,7,3,5,6,8,4]=>1010001
[2,1,6,3,5,7,8,4]=>1010001
[1,6,3,2,5,7,4,8]=>0110010
[5,6,2,1,4,3,7,8]=>0110100
[2,5,1,6,4,3,7,8]=>0101100
[2,5,4,1,6,3,7,8]=>0110100
[4,6,1,5,2,7,3,8]=>0101010
[1,6,5,3,7,2,4,8]=>0110100
[2,6,1,8,5,4,3,7]=>0101110
[5,8,6,2,3,4,1,7]=>0110010
[4,5,8,6,2,1,3,7]=>0011100
[6,3,7,4,2,5,8,1]=>1011001
[7,5,6,2,4,3,8,1]=>1010101
[6,2,5,7,4,3,8,1]=>1001101
[4,6,2,5,7,3,8,1]=>0100101
[4,2,8,5,3,6,1,7]=>1011010
[8,1,7,4,5,6,2,3]=>1010010
[8,4,6,2,5,3,7,1]=>1010101
[5,6,3,2,8,1,7,4]=>0110101
[8,2,6,3,1,5,7,4]=>1011001
[8,2,5,6,7,4,3,1]=>1000111
[8,2,5,3,4,7,6,1]=>1010011
[7,5,3,2,4,1,8,6]=>1110101
[6,5,3,2,4,8,1,7]=>1110010
[3,1,8,4,6,5,7,2]=>1010101
[3,4,7,5,8,2,6,1]=>0010101
[8,7,1,4,6,5,2,3]=>1100110
[8,3,7,6,4,5,1,2]=>1011010
[5,3,8,6,4,1,7,2]=>1011101
[6,4,7,1,8,5,2,3]=>1010110
[5,7,4,2,3,8,6,1]=>0110011
[3,8,2,5,1,7,4,6]=>0101010
[5,8,4,2,3,7,1,6]=>0110010
[4,8,5,2,1,7,3,6]=>0111010
[8,5,7,6,1,2,4,3]=>1011001
[7,8,6,5,2,4,3,1]=>0111011
[7,8,4,2,6,3,5,1]=>0110101
[5,7,6,8,4,1,3,2]=>0101101
[7,3,1,6,8,5,4,2]=>1100111
[5,3,1,7,4,8,6,2]=>1101011
[7,3,1,8,6,4,5,2]=>1101101
[8,6,4,1,7,3,2,5]=>1110110
[4,6,8,3,7,1,2,5]=>0010100
[3,5,2,8,4,7,1,6]=>0101010
[3,7,2,8,6,4,5,1]=>0101101
[8,6,5,7,1,3,2,4]=>1101010
[6,4,8,3,7,2,1,5]=>1010110
[3,6,2,8,7,4,1,5]=>0101110
[6,8,4,2,7,3,1,5]=>0110110
[3,4,7,8,5,1,2,6]=>0001100
[5,7,2,4,3,6,8,1]=>0101001
[4,7,3,2,5,6,8,1]=>0110001
[3,2,7,6,4,5,8,1]=>1011001
[1,7,3,6,8,4,2,5]=>0100110
[8,3,1,2,6,4,7,5]=>1100101
[1,7,8,2,4,3,5,6]=>0010100
[3,6,4,7,1,2,8,5]=>0101001
[2,4,7,8,5,1,3,6]=>0001100
[5,7,4,8,1,3,2,6]=>0101010
[4,3,7,8,1,5,2,6]=>1001010
[8,5,4,2,6,1,7,3]=>1110101
[3,2,6,8,7,4,1,5]=>1001110
[2,3,7,5,1,8,6,4]=>0011011
[6,3,1,2,8,7,4,5]=>1100110
[5,2,1,3,8,7,6,4]=>1100111
[7,2,1,5,3,8,4,6]=>1101010
[1,5,8,2,4,3,6,7]=>0010100
[4,3,6,8,1,5,2,7]=>1001010
[2,4,6,8,5,1,3,7]=>0001100
[1,6,8,2,4,3,5,7]=>0010100
[5,4,6,8,3,1,7,2]=>1001101
[8,6,1,7,2,4,3,5]=>1101010
[7,3,1,2,8,6,4,5]=>1100110
[2,3,7,6,1,8,5,4]=>0011011
[3,2,7,8,6,4,1,5]=>1001110
[6,2,8,3,1,4,7,5]=>1011001
[3,1,2,8,7,4,5,6]=>1001100
[2,1,3,8,7,4,6,5]=>1001101
[2,1,3,8,7,4,5,6]=>1001100
[8,5,1,7,2,4,3,6]=>1101010
[8,3,1,6,2,7,5,4]=>1101011
[1,3,2,8,7,6,4,5]=>0101110
[2,1,3,8,7,6,4,5]=>1001110
[5,7,2,8,4,1,3,6]=>0101100
[3,5,8,2,4,1,7,6]=>0010101
[2,4,8,3,1,6,7,5]=>0011001
[1,3,6,8,5,4,2,7]=>0001110
[1,4,2,5,7,6,3,8]=>0100110
[1,4,2,6,8,5,3,7]=>0100110
[1,5,3,2,6,8,4,7]=>0110010
[1,5,4,2,3,6,8,7]=>0110001
[1,6,8,3,5,4,2,7]=>0010110
[1,5,3,2,4,6,8,7]=>0110001
[1,5,8,7,6,3,2,4]=>0011110
[1,5,7,6,3,2,4,8]=>0011100
[1,6,3,2,4,7,5,8]=>0110010
[1,6,3,2,4,8,7,5]=>0110011
[1,2,7,6,4,3,5,8]=>0011100
[1,8,7,5,2,4,6,3]=>0111001
[1,7,5,2,4,6,3,8]=>0110010
[1,7,4,2,5,3,6,8]=>0110100
[1,8,4,7,5,2,6,3]=>0101101
[1,7,5,2,3,6,4,8]=>0110010
[1,7,5,2,6,3,4,8]=>0110100
[1,6,3,7,4,2,5,8]=>0101100
[1,6,3,2,7,5,4,8]=>0110110
[1,4,8,7,5,2,6,3]=>0011101
[1,4,7,5,2,6,3,8]=>0011010
[1,3,6,4,8,7,5,2]=>0010111
[1,3,7,6,4,2,5,8]=>0011100
[1,3,8,7,5,2,4,6]=>0011100
[1,4,6,3,2,7,5,8]=>0011010
[1,4,6,3,2,8,7,5]=>0011011
[1,5,7,6,4,2,3,8]=>0011100
[1,2,6,4,7,5,3,8]=>0010110
[1,6,3,2,8,4,7,5]=>0110101
[1,5,2,7,4,3,6,8]=>0101100
[1,6,3,5,2,7,4,8]=>0101010
[1,6,3,5,2,8,7,4]=>0101011
[1,8,3,7,5,2,4,6]=>0101100
[1,8,4,6,3,2,7,5]=>0101101
[6,4,7,1,5,3,8,2]=>1010101
[5,3,8,2,6,4,7,1]=>1010101
[4,3,8,2,6,5,7,1]=>1010101
[2,6,1,8,3,4,7,5]=>0101001
[6,5,7,1,4,3,8,2]=>1010101
[4,8,3,5,7,6,1,2]=>0100110
[5,7,6,1,2,4,8,3]=>0110001
[4,8,3,5,7,6,2,1]=>0100111
[5,7,6,2,4,8,3,1]=>0110011
[6,7,5,2,3,8,4,1]=>0110011
[6,7,5,3,8,4,2,1]=>0110111
[7,3,1,4,2,6,5,8]=>1101010
[7,4,1,6,2,5,3,8]=>1101010
[5,4,1,8,2,6,3,7]=>1101010
[4,7,1,5,2,6,3,8]=>0101010
[6,5,1,4,2,7,3,8]=>1101010
[5,4,1,6,2,8,3,7]=>1101010
[8,4,2,3,1,6,5,7]=>1101010
[4,8,6,2,3,1,7,5]=>0110101
[2,8,6,4,5,1,7,3]=>0110101
[8,2,4,6,7,1,5,3]=>1000101
[2,8,3,1,4,5,7,6]=>0110001
[8,7,4,5,1,6,3,2]=>1101011
[7,2,8,1,4,5,6,3]=>1010001
[8,2,3,7,4,5,6,1]=>1001001
[8,6,2,5,4,7,3,1]=>1101011
[8,5,7,2,3,6,4,1]=>1010011
[7,5,2,1,6,8,3,4]=>1110010
[7,6,1,5,4,8,2,3]=>1101010
[7,6,3,2,1,8,4,5]=>1111010
[2,8,7,3,4,6,1,5]=>0110010
[6,5,1,3,7,2,8,4]=>1100101
[1,8,7,3,4,5,2,6]=>0110010
[8,2,7,3,4,5,1,6]=>1010010
[1,7,8,3,4,5,2,6]=>0010010
[8,1,7,3,4,5,2,6]=>1010010
[6,8,7,3,4,2,1,5]=>0110110
[1,8,5,3,4,6,2,7]=>0110010
[7,1,6,5,4,3,8,2]=>1011101
[7,1,3,6,4,5,8,2]=>1001001
[7,1,5,3,6,4,8,2]=>1010101
[6,1,5,3,7,8,2,4]=>1010010
[5,7,1,3,2,8,6,4]=>0101011
[5,8,7,1,2,6,3,4]=>0110010
[6,8,2,3,4,7,1,5]=>0100010
[6,7,2,3,4,8,1,5]=>0100010
[5,1,7,3,8,6,2,4]=>1010110
[6,1,3,2,4,7,8,5]=>1010001
[6,2,1,3,4,7,8,5]=>1100001
[3,2,5,8,7,4,1,6]=>1001110
[4,2,5,8,7,3,1,6]=>1001110
[8,3,4,1,6,5,2,7]=>1010110
[3,4,8,5,7,2,1,6]=>0010110
[3,6,4,8,5,7,2,1]=>0101011
[5,8,4,7,3,6,2,1]=>0101011
[4,2,8,7,3,1,6,5]=>1011101
[6,5,8,2,1,7,4,3]=>1011011
[6,1,4,3,8,7,2,5]=>1010110
[5,1,3,2,6,8,7,4]=>1010011
[6,1,3,8,7,2,4,5]=>1001100
[1,2,8,4,5,7,3,6]=>0010010
[4,2,1,8,7,6,3,5]=>1101110
[3,2,5,8,7,1,4,6]=>1001100
[5,6,3,8,7,2,1,4]=>0101110
[2,5,8,4,7,1,6,3]=>0010101
[1,6,2,4,8,5,7,3]=>0100101
[3,1,6,5,8,7,2,4]=>1010110
[4,8,5,3,6,7,1,2]=>0110010
[1,8,5,3,4,7,6,2]=>0110011
[1,4,6,2,5,3,7,8]=>0010100
[4,3,6,5,1,2,7,8]=>1011000
[1,3,8,7,6,5,2,4]=>0011110
[1,8,7,2,6,3,5,4]=>0110101
[8,7,1,2,4,3,6,5]=>1100101
[2,8,7,1,6,3,4,5]=>0110100
[6,2,1,8,7,5,3,4]=>1101110
[3,2,1,4,5,8,6,7]=>1100010
[1,3,7,5,4,8,6,2]=>0011011
[5,2,1,4,3,6,8,7]=>1101001
[1,5,6,3,8,4,2,7]=>0010110
[2,6,5,3,8,4,1,7]=>0110110
[5,7,3,8,4,2,6,1]=>0101101
[2,3,6,5,4,8,1,7]=>0011010
[2,7,5,1,8,4,6,3]=>0110101
[1,7,6,4,8,2,5,3]=>0110101
[6,3,8,7,2,4,5,1]=>1011001
[2,4,3,8,7,1,6,5]=>0101101
[2,8,7,6,1,5,3,4]=>0111010
[5,4,7,6,3,1,2,8]=>1011100
[3,6,4,8,1,5,2,7]=>0101010
[3,6,8,4,1,5,2,7]=>0011010
[7,8,1,4,2,3,5,6]=>0101000
[8,7,1,4,2,3,5,6]=>1101000
[3,8,6,4,1,5,2,7]=>0111010
[3,8,4,6,1,5,2,7]=>0101010
[8,3,7,2,1,6,5,4]=>1011011
[8,4,7,3,6,2,1,5]=>1010110
[3,8,7,5,6,4,1,2]=>0110110
[3,8,7,5,6,2,1,4]=>0110110
[3,8,7,5,6,2,4,1]=>0110101
[2,8,7,5,6,4,1,3]=>0110110
[3,6,2,4,8,7,1,5]=>0100110
[1,5,6,3,8,2,7,4]=>0010101
[2,6,3,8,4,7,1,5]=>0101010
[2,6,3,5,7,8,1,4]=>0100010
[1,5,6,3,7,2,8,4]=>0010101
[1,7,5,3,6,2,8,4]=>0110101
[1,5,7,3,4,2,8,6]=>0010101
[1,5,8,3,4,2,7,6]=>0010101
[1,4,5,3,8,2,7,6]=>0010101
[6,5,1,4,2,7,8,3]=>1101001
[6,5,1,4,2,8,7,3]=>1101011
[1,7,5,4,2,8,6,3]=>0111011
[5,1,6,8,3,7,2,4]=>1001010
[3,8,5,2,1,4,7,6]=>0111001
[3,5,4,8,2,6,7,1]=>0101001
[1,4,8,2,6,5,3,7]=>0010110
[7,5,1,8,3,4,2,6]=>1101010
[1,4,8,2,6,7,3,5]=>0010010
[1,2,5,6,8,7,3,4]=>0000110
[1,5,6,8,2,7,4,3]=>0001011
[2,6,7,3,4,1,8,5]=>0010101
[1,6,5,7,8,2,4,3]=>0100101
[1,5,6,7,2,8,4,3]=>0001011
[1,3,7,2,6,4,8,5]=>0010101
[1,5,8,6,7,3,4,2]=>0010101
[1,6,5,8,7,2,4,3]=>0101101
[1,5,7,6,2,8,3,4]=>0011010
[1,2,5,8,6,7,4,3]=>0001011
[1,2,6,5,7,3,8,4]=>0010101
[1,7,5,8,6,4,2,3]=>0101110
[7,6,1,2,3,5,4,8]=>1100010
[8,5,2,6,4,3,1,7]=>1101110
[5,8,3,7,1,4,6,2]=>0101001
[3,8,7,4,2,6,5,1]=>0111011
[5,8,3,2,4,7,6,1]=>0110011
[6,1,3,4,2,5,7,8]=>1001000
[5,3,8,2,4,6,1,7]=>1010010
[4,1,5,6,3,2,7,8]=>1001100
[4,5,8,3,2,6,1,7]=>0011010
[5,8,2,1,4,6,3,7]=>0110010
[4,1,5,8,3,6,2,7]=>1001010
[4,5,8,3,6,1,2,7]=>0010100
[1,6,3,4,7,8,5,2]=>0100011
[8,1,3,4,2,6,5,7]=>1001010
[4,7,8,5,2,3,1,6]=>0011010
[4,1,5,8,6,2,3,7]=>1001100
[5,8,2,1,6,3,4,7]=>0110100
[2,7,1,3,8,5,4,6]=>0100110
[2,6,7,8,4,1,3,5]=>0001100
[2,6,7,8,4,3,1,5]=>0001110
[1,6,4,3,2,5,7,8]=>0111000
[1,7,4,3,2,5,6,8]=>0111000
[1,8,4,3,2,7,6,5]=>0111011
[1,7,4,3,6,2,5,8]=>0110100
[1,7,8,5,4,2,3,6]=>0011100
[8,1,5,3,6,4,7,2]=>1010101
[2,6,4,8,3,1,5,7]=>0101100
[3,6,4,5,2,8,1,7]=>0101010
[8,1,5,4,7,3,6,2]=>1010101
[3,6,4,1,5,7,2,8]=>0110010
[8,1,5,4,7,6,3,2]=>1010111
[2,5,1,4,6,7,3,8]=>0100010
[3,6,4,1,5,7,8,2]=>0110001
[8,6,3,5,4,1,2,7]=>1101100
[8,2,6,5,4,1,3,7]=>1011100
[8,2,6,5,4,3,1,7]=>1011110
[8,3,2,6,1,5,4,7]=>1101010
[8,1,6,5,4,3,2,7]=>1011110
[4,8,1,7,6,3,5,2]=>0101101
[8,5,1,7,4,3,6,2]=>1101101
[8,5,7,6,2,1,3,4]=>1011100
[5,4,8,3,1,7,2,6]=>1011010
[5,1,4,8,3,2,7,6]=>1001101
[4,8,1,7,6,5,2,3]=>0101110
[4,3,8,7,2,6,1,5]=>1011010
[3,8,7,2,6,4,1,5]=>0110110
[8,2,7,6,4,1,5,3]=>1011101
[4,3,8,7,2,6,5,1]=>1011011
[8,2,5,7,4,3,6,1]=>1001101
[3,8,7,4,6,1,2,5]=>0110100
[8,3,7,5,4,1,6,2]=>1011101
[2,8,4,7,6,1,5,3]=>0101101
[2,5,4,8,3,1,7,6]=>0101101
[5,4,8,2,1,3,7,6]=>1011001
[3,8,7,2,6,1,5,4]=>0110101
[1,8,4,7,6,3,5,2]=>0101101
[1,8,3,7,6,5,2,4]=>0101110
[1,4,3,8,7,2,6,5]=>0101101
[8,1,2,7,6,5,4,3]=>1001111
[7,8,3,1,6,2,5,4]=>0110101
[6,1,5,2,4,8,3,7]=>1010010
[1,5,6,3,8,2,4,7]=>0010100
[7,5,2,8,1,4,6,3]=>1101001
[7,2,8,1,6,4,3,5]=>1010110
[1,6,4,5,2,7,3,8]=>0101010
[1,4,7,3,2,5,6,8]=>0011000
[1,6,7,4,2,8,3,5]=>0011010
[1,5,8,7,4,3,2,6]=>0011110
[1,4,7,2,3,6,8,5]=>0010001
[3,1,2,6,7,8,5,4]=>1000011
[1,6,3,4,7,8,2,5]=>0100010
[3,1,5,7,6,2,8,4]=>1001101
[6,3,1,4,2,7,8,5]=>1101001
[2,4,3,7,6,1,8,5]=>0101101
[3,1,6,5,2,8,7,4]=>1011011
[3,1,7,6,5,2,8,4]=>1011101
[1,4,7,6,8,3,2,5]=>0010110
[7,2,1,5,6,3,8,4]=>1100101
[4,3,1,8,6,2,7,5]=>1101101
[3,1,5,2,8,7,6,4]=>1010111
[1,2,8,4,3,7,6,5]=>0011011
[1,8,5,4,2,7,3,6]=>0111010
[3,1,8,5,4,7,2,6]=>1011010
[2,6,1,8,7,4,3,5]=>0101110
[7,5,1,8,3,2,6,4]=>1101101
[4,7,6,3,1,8,2,5]=>0111010
[5,3,1,8,6,2,4,7]=>1101100
[5,1,8,6,3,2,4,7]=>1011100
[1,5,4,2,8,6,3,7]=>0110110
[8,3,1,6,4,2,5,7]=>1101100
[3,6,7,1,8,4,2,5]=>0010110
[1,7,4,8,3,5,2,6]=>0101010
[7,3,2,4,8,5,1,6]=>1100110
[6,3,4,7,1,8,5,2]=>1001011
[5,7,8,1,4,2,6,3]=>0010101
[5,7,1,2,3,8,6,4]=>0100011
[7,2,8,1,4,3,6,5]=>1010101
[2,6,3,8,1,7,5,4]=>0101011
[1,8,3,6,4,7,2,5]=>0101010
[2,8,6,4,1,7,3,5]=>0111010
[1,8,4,2,7,5,3,6]=>0110110
[6,5,1,7,2,8,4,3]=>1101011
[2,8,1,7,5,3,6,4]=>0101101
[1,2,8,7,6,4,3,5]=>0011110
[4,1,7,8,6,3,5,2]=>1001101
[1,6,5,7,8,4,2,3]=>0100110
[1,6,5,8,7,4,2,3]=>0101110
[4,1,8,7,6,3,5,2]=>1011101
[4,8,2,6,3,5,1,7]=>0101010
[6,7,2,5,3,8,4,1]=>0101011
[4,3,5,7,1,6,2,8]=>1001010
[4,2,8,5,3,6,7,1]=>1011001
[4,1,8,5,3,6,2,7]=>1011010
[6,4,2,5,3,1,7,8]=>1101100
[3,1,5,8,2,7,4,6]=>1001010
[6,4,1,5,3,2,7,8]=>1101100
[6,2,1,5,4,3,7,8]=>1101100
[3,1,8,5,4,6,2,7]=>1011010
[6,2,8,4,5,3,7,1]=>1010101
[6,1,8,4,5,3,2,7]=>1010110
[4,5,2,7,1,6,3,8]=>0101010
[4,3,5,7,1,6,8,2]=>1001001
[4,1,8,5,3,6,7,2]=>1011001
[6,3,8,4,5,1,7,2]=>1010101
[3,1,6,8,5,7,4,2]=>1001011
[2,6,1,8,5,7,4,3]=>0101011
[6,5,8,7,1,3,2,4]=>1011010
[6,5,8,7,2,3,4,1]=>1011001
[6,5,8,7,3,2,4,1]=>1011101
[6,3,8,4,5,2,7,1]=>1010101
[3,1,6,8,5,7,2,4]=>1001010
[2,1,6,8,5,3,7,4]=>1001101
[3,1,6,8,5,4,2,7]=>1001110
[3,2,6,8,5,4,7,1]=>1001101
[4,1,8,5,2,6,3,7]=>1011010
[3,1,6,8,5,2,4,7]=>1001100
[6,2,8,4,5,1,3,7]=>1010100
[6,5,8,7,4,1,2,3]=>1011100
[6,5,8,7,4,2,1,3]=>1011110
[6,5,8,7,2,4,1,3]=>1011010
[6,2,8,4,5,7,1,3]=>1010010
[6,1,8,4,5,7,3,2]=>1010011
[4,2,7,3,5,8,6,1]=>1010011
[3,6,2,4,8,5,7,1]=>0100101
[2,7,5,4,3,8,6,1]=>0111011
[3,5,1,8,4,7,6,2]=>0101011
[2,4,8,3,7,6,5,1]=>0010111
[3,6,8,5,2,4,7,1]=>0011001
[2,6,8,5,4,3,7,1]=>0011101
[3,6,8,2,5,4,7,1]=>0010101
[4,6,8,3,2,5,7,1]=>0011001
[4,6,2,8,3,5,7,1]=>0101001
[3,6,1,8,5,7,4,2]=>0101011
[4,6,3,8,7,2,5,1]=>0101101
[3,5,8,2,7,4,6,1]=>0010101
[2,4,8,7,3,6,5,1]=>0011011
[2,5,8,7,4,3,6,1]=>0011101
[2,4,8,7,6,3,5,1]=>0011101
[4,7,2,5,6,3,1,8]=>0100110
[6,1,2,8,7,3,4,5]=>1001100
[4,1,3,5,7,8,2,6]=>1000010
[6,1,5,8,4,3,2,7]=>1001110
[2,3,7,8,5,1,6,4]=>0001101
[8,1,3,2,5,6,4,7]=>1010010
[3,2,5,8,4,7,1,6]=>1001010
[8,6,4,1,5,2,3,7]=>1110100
[2,5,8,1,3,4,7,6]=>0010001
[3,5,1,8,7,4,2,6]=>0101110
[4,6,1,3,8,2,7,5]=>0100101
[6,2,1,8,5,7,4,3]=>1101011
[5,4,7,1,3,8,6,2]=>1010011
[6,5,7,8,1,3,4,2]=>1001001
[4,8,1,2,7,6,5,3]=>0100111
[3,7,4,8,5,2,6,1]=>0101101
[8,1,2,6,5,3,4,7]=>1001100
[3,4,2,8,6,7,5,1]=>0101011
[3,7,8,6,1,4,2,5]=>0011010
[3,6,1,5,2,7,8,4]=>0101001
[6,2,8,4,7,1,3,5]=>1010100
[1,8,4,3,7,6,2,5]=>0110110
[4,3,8,7,1,2,6,5]=>1011001
[1,8,3,6,7,2,4,5]=>0100100
[1,8,4,5,7,6,2,3]=>0100110
[4,3,8,5,7,1,6,2]=>1010101
[6,3,4,8,7,2,1,5]=>1001110
[5,3,8,4,7,1,6,2]=>1010101
[5,2,8,7,1,4,6,3]=>1011001
[3,2,8,7,1,6,4,5]=>1011010
[2,7,8,3,1,6,4,5]=>0011010
[3,5,8,7,4,1,6,2]=>0011101
[7,4,6,8,3,5,1,2]=>1001010
[7,2,8,4,1,3,6,5]=>1011001
[2,7,8,1,3,6,4,5]=>0010010
[2,7,8,1,5,4,6,3]=>0010101
[2,7,8,1,4,5,6,3]=>0010001
[3,6,7,8,2,4,1,5]=>0001010
[4,5,7,8,6,3,1,2]=>0001110
[5,4,6,8,7,3,1,2]=>1001110
[4,5,8,6,7,1,3,2]=>0010101
[5,7,6,8,2,1,3,4]=>0101100
[3,7,6,8,2,4,1,5]=>0101010
[5,4,7,8,6,3,1,2]=>1001110
[3,6,7,8,2,1,4,5]=>0001100
[4,5,6,8,7,3,1,2]=>0001110
[4,2,5,3,7,8,6,1]=>1010011
[5,3,6,2,4,1,8,7]=>1010101
[7,8,6,2,3,5,4,1]=>0110011
[5,8,2,6,3,7,4,1]=>0101011
[4,8,2,3,7,5,6,1]=>0100101
[7,5,6,2,3,8,4,1]=>1010011
[2,7,5,6,4,3,8,1]=>0101101
[2,8,4,3,7,5,6,1]=>0110101
[2,7,5,6,3,8,4,1]=>0101011
[7,6,3,8,5,4,2,1]=>1101111
[3,8,5,7,6,4,2,1]=>0101111
[7,8,6,3,5,4,2,1]=>0110111
[2,7,6,3,8,5,4,1]=>0110111
[4,2,8,5,3,7,6,1]=>1011011
[7,4,2,5,6,3,8,1]=>1100101
[6,2,7,5,3,8,4,1]=>1011011
[2,4,8,3,7,5,6,1]=>0010101
[4,8,3,7,5,6,2,1]=>0101011
[6,2,5,8,3,7,4,1]=>1001011
[7,6,2,5,3,8,4,1]=>1101011
[4,7,3,8,2,5,6,1]=>0101001
[8,2,5,6,3,7,4,1]=>1001011
[4,5,3,7,1,2,6,8]=>0101000
[6,7,2,8,4,3,1,5]=>0101110
[6,7,3,2,8,4,1,5]=>0110110
[4,5,8,1,3,2,6,7]=>0010100
[4,5,8,1,3,7,2,6]=>0010010
[2,6,7,4,3,8,1,5]=>0011010
[3,7,6,4,5,8,1,2]=>0110010
[5,7,2,8,3,4,6,1]=>0101001
[3,1,5,8,6,4,7,2]=>1001101
[3,6,2,8,7,4,5,1]=>0101101
[3,6,2,8,4,7,5,1]=>0101011
[8,3,5,1,6,4,2,7]=>1010110
[5,7,8,3,4,6,2,1]=>0010011
[3,1,5,8,6,2,4,7]=>1001100
[1,5,8,6,3,4,2,7]=>0011010
[3,7,8,5,2,6,4,1]=>0011011
[5,3,7,8,4,2,6,1]=>1001101
[5,1,6,4,3,8,7,2]=>1011011
[4,7,1,3,2,5,6,8]=>0101000
[4,7,6,8,3,1,5,2]=>0101101
[5,4,8,6,1,7,3,2]=>1011011
[3,5,4,7,1,8,6,2]=>0101011
[1,8,5,4,2,3,6,7]=>0111000
[7,1,5,4,2,3,6,8]=>1011000
[7,1,3,6,4,5,2,8]=>1001010
[6,1,3,8,4,5,2,7]=>1001010
[5,8,6,3,1,2,7,4]=>0111001
[5,8,2,7,1,3,6,4]=>0101001
[2,6,5,4,1,3,7,8]=>0111000
[4,1,5,7,6,3,2,8]=>1001110
[7,6,3,2,8,5,1,4]=>1110110
[5,3,8,2,7,1,6,4]=>1010101
[6,3,4,2,1,8,7,5]=>1011011
[4,5,1,7,6,3,2,8]=>0101110
[1,5,3,7,4,2,6,8]=>0101100
[1,2,7,4,3,8,6,5]=>0011011
[1,5,4,2,3,8,7,6]=>0110011
[1,5,4,2,3,8,6,7]=>0110010
[1,5,3,2,4,6,7,8]=>0110000
[1,5,4,2,3,7,8,6]=>0110001
[3,6,5,2,4,1,7,8]=>0110100
[4,6,7,2,5,1,8,3]=>0010101
[3,6,2,5,1,7,8,4]=>0101001
[3,4,2,7,8,6,1,5]=>0100110
[3,4,2,7,8,1,5,6]=>0100100
[3,8,5,2,4,7,1,6]=>0110010
[6,4,3,2,8,1,7,5]=>1110101
[6,2,4,3,8,1,7,5]=>1010101
[8,7,3,6,2,1,5,4]=>1101101
[3,7,5,4,6,1,2,8]=>0110100
[5,3,4,7,6,8,1,2]=>1001010
[5,3,7,4,6,1,2,8]=>1010100
[7,3,5,4,6,1,2,8]=>1010100
[7,8,3,5,4,1,2,6]=>0101100
[7,3,5,4,1,2,6,8]=>1011000
[5,7,6,3,1,2,4,8]=>0111000
[5,7,6,3,4,1,2,8]=>0110100
[7,5,6,8,1,3,2,4]=>1001010
[3,5,4,1,2,7,6,8]=>0110010
[5,7,6,1,3,2,4,8]=>0110100
[3,5,4,1,7,2,6,8]=>0110100
[5,3,4,1,2,7,6,8]=>1010010
[7,8,3,1,2,5,4,6]=>0110010
[7,8,5,1,3,2,4,6]=>0110100
[7,5,6,1,3,2,4,8]=>1010100
[7,1,3,8,2,5,4,6]=>1001010
[5,1,3,7,6,2,4,8]=>1001100
[6,7,1,8,3,4,5,2]=>0101001
[3,7,1,6,8,4,5,2]=>0100101
[8,7,1,5,3,2,6,4]=>1101101
[3,7,1,6,5,2,8,4]=>0101101
[8,6,7,2,5,3,1,4]=>1010110
[1,8,2,6,5,3,4,7]=>0101100
[8,6,1,5,2,3,4,7]=>1101000
[8,5,1,6,2,3,4,7]=>1101000
[8,1,4,2,3,5,7,6]=>1010001
[1,7,8,2,5,3,4,6]=>0010100
[2,7,8,4,1,3,5,6]=>0011000
[6,8,1,2,3,7,4,5]=>0100010
[1,2,8,6,4,5,3,7]=>0011010
[1,5,8,7,6,3,4,2]=>0011101
[1,2,7,8,4,3,5,6]=>0001100
[1,5,7,8,4,2,3,6]=>0001100
[1,6,8,5,4,2,3,7]=>0011100
[1,2,3,7,5,4,6,8]=>0001100
[4,6,5,2,1,7,8,3]=>0111001
[4,6,1,7,5,8,3,2]=>0101011
[3,5,6,2,1,4,7,8]=>0011000
[4,3,6,5,1,7,8,2]=>1011001
[4,6,5,3,1,7,8,2]=>0111001
[5,1,3,4,8,2,6,7]=>1000100
[5,8,1,4,2,3,6,7]=>0101000
[4,3,1,8,5,2,6,7]=>1101100
[4,5,8,2,3,1,6,7]=>0010100
[3,5,4,8,1,7,2,6]=>0101010
[5,3,6,8,1,4,7,2]=>1001001
[5,1,6,8,3,4,7,2]=>1001001
[3,5,1,8,6,4,7,2]=>0101101
[6,4,8,1,5,7,2,3]=>1010010
[4,7,2,8,3,1,6,5]=>0101101
[1,2,5,6,8,3,7,4]=>0000101
[5,1,6,8,7,2,3,4]=>1001100
[1,5,6,8,3,7,2,4]=>0001010
[5,6,8,1,2,3,7,4]=>0010001
[2,8,1,3,5,7,4,6]=>0100010
[7,4,8,1,5,2,6,3]=>1010101
[8,3,2,1,6,5,7,4]=>1110101
[4,1,5,6,8,7,2,3]=>1000110
[1,2,5,6,8,4,7,3]=>0000101
[1,5,6,8,4,7,2,3]=>0001010
[6,8,1,4,5,7,2,3]=>0100010
[4,3,5,1,8,6,7,2]=>1010101
[1,3,5,6,8,4,7,2]=>0000101
[5,6,8,1,3,4,7,2]=>0010001
[5,6,8,2,3,4,7,1]=>0010001
[5,7,8,3,2,6,1,4]=>0011010
[7,5,8,6,4,1,3,2]=>1011101
[5,1,8,6,4,2,7,3]=>1011101
[2,7,6,3,8,5,1,4]=>0110110
[2,3,1,8,4,6,5,7]=>0101010
[2,3,1,7,6,8,4,5]=>0101010
[2,3,1,8,4,6,7,5]=>0101001
[2,7,4,1,3,6,8,5]=>0110001
[6,3,2,8,1,7,5,4]=>1101011
[2,6,8,7,1,3,5,4]=>0011001
[3,7,6,1,4,5,2,8]=>0110010
[4,1,6,2,7,5,3,8]=>1010110
[7,6,2,5,3,1,4,8]=>1101100
[4,3,1,7,6,2,5,8]=>1101100
[4,5,3,1,2,8,6,7]=>0110010
[2,4,5,3,1,8,6,7]=>0011010
[5,7,6,2,3,1,4,8]=>0110100
[4,1,3,7,5,2,6,8]=>1001100
[4,1,6,3,2,7,5,8]=>1011010
[2,7,5,4,1,3,6,8]=>0111000
[7,5,4,1,3,2,6,8]=>1110100
[2,4,8,5,6,3,1,7]=>0010110
[2,5,7,4,1,3,6,8]=>0011000
[5,7,4,1,3,2,6,8]=>0110100
[6,2,4,5,7,3,1,8]=>1000110
[2,6,8,4,5,3,1,7]=>0010110
[2,5,3,8,4,1,6,7]=>0101100
[5,2,3,7,4,1,6,8]=>1001100
[4,5,1,6,3,2,7,8]=>0101100
[5,1,6,3,2,4,7,8]=>1011000
[4,2,5,1,6,3,7,8]=>1010100
[5,1,6,2,4,3,7,8]=>1010100
[4,3,5,1,6,2,7,8]=>1010100
[6,2,1,7,5,8,4,3]=>1101011
[1,5,7,8,6,4,2,3]=>0001110
[1,6,4,8,5,3,7,2]=>0101101
[1,6,5,3,4,7,8,2]=>0110001
[4,2,6,7,8,1,3,5]=>1000100
[4,5,1,7,6,3,8,2]=>0101101
[4,6,5,1,3,7,8,2]=>0110001
[5,2,1,7,6,4,8,3]=>1101101
[6,8,5,2,7,3,1,4]=>0110110
[6,1,2,4,3,7,8,5]=>1001001
[8,1,5,4,2,3,6,7]=>1011000
[7,1,2,4,6,3,8,5]=>1000101
[7,1,2,6,5,3,8,4]=>1001101
[7,5,6,1,2,4,8,3]=>1010001
[7,1,4,5,2,3,6,8]=>1001000
[6,1,4,8,7,2,3,5]=>1001100
[6,1,8,5,7,2,3,4]=>1010100
[1,6,7,5,8,3,4,2]=>0010101
[6,1,7,5,8,2,3,4]=>1010100
[6,1,4,7,8,2,3,5]=>1000100
[5,8,6,1,2,4,7,3]=>0110001
[1,6,8,7,5,3,4,2]=>0011101
[6,8,7,5,1,2,4,3]=>0111001
[6,1,8,7,5,2,3,4]=>1011100
[8,3,1,2,4,6,5,7]=>1100010
[8,3,1,2,4,5,7,6]=>1100001
[6,3,1,2,4,7,5,8]=>1100010
[6,7,1,4,2,3,5,8]=>0101000
[6,1,7,4,8,2,3,5]=>1010100
[6,7,8,5,1,2,4,3]=>0011001
[4,6,8,2,3,5,1,7]=>0010010
[6,8,2,1,3,5,4,7]=>0110010
[3,5,1,6,4,8,2,7]=>0101010
[3,5,8,6,2,1,4,7]=>0011100
[2,4,8,5,6,1,3,7]=>0010100
[5,3,8,4,2,7,6,1]=>1011011
[2,8,5,3,1,4,7,6]=>0111001
[3,7,8,5,1,4,2,6]=>0011010
[1,7,8,4,6,3,2,5]=>0010110
[8,7,2,4,6,3,1,5]=>1100110
[7,8,3,4,6,5,2,1]=>0100111
[8,7,3,6,5,2,4,1]=>1101101
[3,1,2,8,6,5,7,4]=>1001101
[3,8,2,7,5,4,6,1]=>0101101
[8,7,1,4,5,3,6,2]=>1100101
[2,8,7,4,6,3,5,1]=>0110101
[2,8,7,4,6,3,1,5]=>0110110
[8,3,4,1,2,5,7,6]=>1010001
[8,4,1,3,2,5,7,6]=>1101001
[7,4,8,2,3,5,1,6]=>1010010
[7,3,8,6,2,1,4,5]=>1011100
[7,2,8,4,6,5,1,3]=>1010110
[5,8,6,4,7,2,3,1]=>0110101
[4,7,2,6,5,8,3,1]=>0101011
[3,6,8,5,7,4,2,1]=>0010111
[6,7,5,2,4,8,3,1]=>0110011
[8,7,2,4,6,1,5,3]=>1100101
[8,1,2,7,5,6,3,4]=>1001010
[8,2,7,3,4,6,1,5]=>1010010
[6,7,5,4,8,1,3,2]=>0110101
[2,5,1,4,7,3,6,8]=>0100100
[3,1,6,5,7,2,4,8]=>1010100
[2,5,7,1,6,3,4,8]=>0010100
[2,5,7,1,6,3,8,4]=>0010101
[2,6,1,5,7,4,3,8]=>0100110
[3,1,6,5,2,4,7,8]=>1011000
[3,6,5,1,4,2,7,8]=>0110100
[3,5,6,2,8,1,7,4]=>0010101
[3,6,5,1,7,2,4,8]=>0110100
[3,6,5,2,1,4,7,8]=>0111000
[4,5,2,7,6,1,3,8]=>0101100
[4,6,5,3,1,2,7,8]=>0111000
[5,4,1,6,3,7,2,8]=>1101010
[5,4,2,6,3,7,8,1]=>1101001
[3,6,5,7,1,4,2,8]=>0101010
[3,6,5,1,4,7,2,8]=>0110010
[4,3,6,5,7,1,2,8]=>1010100
[4,2,6,5,1,3,7,8]=>1011000
[4,1,6,5,3,7,8,2]=>1011001
[4,1,5,7,6,3,8,2]=>1001101
[4,2,5,7,6,1,3,8]=>1001100
[3,4,7,6,1,2,5,8]=>0011000
[3,4,7,6,8,2,5,1]=>0010101
[4,2,5,7,6,3,8,1]=>1001101
[4,1,6,5,2,7,3,8]=>1011010
[4,2,6,5,7,3,1,8]=>1010110
[3,6,5,7,2,1,4,8]=>0101100
[3,5,7,6,2,4,1,8]=>0011010
[5,4,2,6,3,7,1,8]=>1101010
[4,6,5,2,7,3,1,8]=>0110110
[4,5,2,7,6,3,8,1]=>0101101
[4,6,5,2,1,7,3,8]=>0111010
[3,5,8,2,1,4,6,7]=>0011000
[3,5,8,2,4,6,7,1]=>0010001
[5,3,8,2,1,4,6,7]=>1011000
[5,3,1,8,2,4,6,7]=>1101000
[1,5,3,8,2,4,6,7]=>0101000
[1,5,8,4,2,3,6,7]=>0011000
[5,8,2,1,4,3,6,7]=>0110100
[5,8,2,4,6,3,1,7]=>0100110
[5,8,2,4,3,6,1,7]=>0101010
[5,8,1,4,6,2,3,7]=>0100100
[1,5,8,4,6,7,2,3]=>0010010
[5,1,8,4,6,7,2,3]=>1010010
[5,8,2,4,6,3,7,1]=>0100101
[3,8,4,6,7,2,1,5]=>0100110
[3,8,4,6,7,2,5,1]=>0100101
[8,4,3,6,7,2,5,1]=>1100101
[8,4,3,6,7,2,1,5]=>1100110
[8,6,2,4,5,3,7,1]=>1100101
[8,6,4,1,5,7,2,3]=>1110010
[1,8,6,4,5,7,2,3]=>0110010
[8,1,6,4,5,2,3,7]=>1010100
[8,6,2,4,5,3,1,7]=>1100110
[1,8,6,4,2,3,5,7]=>0111000
[3,8,1,6,2,4,5,7]=>0101000
[1,3,8,6,2,4,5,7]=>0011000
[3,8,6,2,1,4,5,7]=>0111000
[3,8,6,2,4,1,5,7]=>0110100
[3,8,6,2,4,5,7,1]=>0110001
[8,3,6,2,4,5,1,7]=>1010010
[1,8,3,6,2,4,5,7]=>0101000
[8,1,3,6,2,4,5,7]=>1001000
[8,3,6,7,2,1,4,5]=>1001100
[2,5,8,4,6,1,7,3]=>0010101
[3,8,6,7,2,1,4,5]=>0101100
[3,1,8,6,7,2,4,5]=>1010100
[8,2,6,4,5,1,7,3]=>1010101
[8,4,6,1,7,2,5,3]=>1010101
[1,8,4,6,7,5,2,3]=>0100110
[8,1,4,6,7,5,2,3]=>1000110
[8,4,6,1,3,7,2,5]=>1010010
[8,1,4,6,3,7,2,5]=>1001010
[8,4,1,6,3,7,2,5]=>1101010
[8,2,4,6,1,7,5,3]=>1001011
[8,4,6,2,3,7,5,1]=>1010011
[8,4,7,3,1,6,2,5]=>1011010
[8,4,7,2,1,3,6,5]=>1011001
[8,4,2,1,5,3,7,6]=>1110101
[8,2,1,4,7,3,6,5]=>1100101
[3,2,1,7,4,5,8,6]=>1101001
[2,8,4,1,7,5,3,6]=>0110110
[2,6,8,5,1,7,4,3]=>0011011
[4,7,3,1,8,6,2,5]=>0110110
[2,1,5,8,7,3,6,4]=>1001101
[3,2,1,6,7,4,8,5]=>1100101
[4,3,1,7,8,5,2,6]=>1100110
[5,6,8,2,4,3,7,1]=>0010101
[5,8,2,6,4,3,7,1]=>0101101
[2,8,5,3,6,4,7,1]=>0110101
[1,2,8,6,4,7,3,5]=>0011010
[4,2,7,8,3,5,6,1]=>1001001
[2,8,3,7,1,4,6,5]=>0101001
[2,8,7,1,5,3,6,4]=>0110101
[3,8,4,2,7,6,5,1]=>0110111
[3,8,4,2,5,1,7,6]=>0110101
[4,8,3,2,7,5,6,1]=>0110101
[3,2,4,8,7,5,6,1]=>1001101
[3,5,2,6,4,8,1,7]=>0101010
[2,6,8,1,5,3,4,7]=>0010100
[8,1,5,2,4,6,3,7]=>1010010
[3,8,1,6,4,5,2,7]=>0101010
[8,1,3,6,5,4,2,7]=>1001110
[7,4,3,6,2,1,8,5]=>1101101
[1,2,4,8,6,3,7,5]=>0001101
[7,2,1,5,3,4,8,6]=>1101001
[5,7,2,3,1,4,8,6]=>0101001
[7,1,5,2,4,6,8,3]=>1010001
[8,4,2,7,3,5,6,1]=>1101001
[1,8,6,4,7,5,3,2]=>0110111
[7,4,1,5,8,6,3,2]=>1100111
[8,6,3,2,7,4,1,5]=>1110110
[4,5,8,7,3,1,2,6]=>0011100
[1,3,8,7,6,4,2,5]=>0011110
[8,6,4,7,5,1,2,3]=>1101100
[2,8,5,1,7,4,6,3]=>0110101
[1,8,6,4,7,5,2,3]=>0110110
[2,7,4,6,3,8,5,1]=>0101011
[1,2,8,6,4,7,5,3]=>0011011
[8,6,2,1,5,7,3,4]=>1110010
[1,6,5,4,3,8,2,7]=>0111010
[6,4,2,1,5,7,3,8]=>1110010
[3,1,5,8,7,2,4,6]=>1001100
[3,2,5,7,8,4,1,6]=>1000110
[3,2,5,7,8,4,6,1]=>1000101
[5,3,7,4,2,6,8,1]=>1011001
[5,3,7,4,2,6,1,8]=>1011010
[5,2,8,4,3,1,6,7]=>1011100
[5,1,8,4,3,2,6,7]=>1011100
[5,2,7,4,3,6,1,8]=>1011010
[5,2,7,4,3,6,8,1]=>1011001
[5,3,7,4,1,6,8,2]=>1011001
[3,1,5,7,8,4,2,6]=>1000110
[1,2,8,6,4,5,7,3]=>0011001
[6,2,3,7,4,1,8,5]=>1001101
[5,2,7,4,1,3,8,6]=>1011001
[6,2,3,7,4,8,5,1]=>1001011
[6,2,3,7,4,8,1,5]=>1001010
[6,1,3,7,4,2,8,5]=>1001101
[6,2,3,7,4,5,1,8]=>1001010
[6,2,3,7,4,5,8,1]=>1001001
[6,1,3,7,4,5,8,2]=>1001001
[1,2,8,6,4,3,5,7]=>0011100
[6,1,3,7,4,5,2,8]=>1001010
[1,8,6,3,5,4,2,7]=>0110110
[1,8,2,7,5,3,4,6]=>0101100
[2,5,4,1,8,6,7,3]=>0110101
[1,8,5,3,2,6,7,4]=>0111001
[6,3,8,2,4,1,7,5]=>1010101
[5,1,7,8,2,4,3,6]=>1001010
[5,3,2,4,8,1,7,6]=>1100101
[5,3,2,4,8,1,6,7]=>1100100
[5,3,2,4,7,1,8,6]=>1100101
[4,8,1,7,3,5,6,2]=>0101001
[5,3,2,4,6,8,1,7]=>1100010
[7,6,4,2,8,3,1,5]=>1110110
[1,2,6,4,7,3,5,8]=>0010100
[8,5,2,4,3,7,1,6]=>1101010
[7,5,4,1,3,6,8,2]=>1110001
[4,2,5,7,8,6,3,1]=>1000111
[6,7,2,4,5,1,8,3]=>0100101
[5,2,7,8,3,6,1,4]=>1001010
[8,2,3,4,7,1,5,6]=>1000100
[2,4,7,8,1,3,6,5]=>0001001
[5,2,8,3,1,4,7,6]=>1011001
[8,7,2,5,1,4,3,6]=>1101010
[8,3,5,1,2,4,7,6]=>1010001
[8,6,5,1,7,4,2,3]=>1110110
[8,3,6,5,4,1,2,7]=>1011100
[8,7,4,5,1,2,6,3]=>1101001
[3,4,8,2,1,7,6,5]=>0011011
[8,3,5,2,7,4,6,1]=>1010101
[8,3,1,7,5,6,2,4]=>1101010
[8,4,1,7,5,2,6,3]=>1101101
[8,3,4,2,7,5,6,1]=>1010101
[8,3,2,7,5,6,1,4]=>1101010
[8,4,2,7,5,3,1,6]=>1101110
[8,2,6,5,7,1,3,4]=>1010100
[8,4,3,7,5,1,2,6]=>1101100
[8,5,7,6,4,3,1,2]=>1011110
[8,5,7,6,4,1,2,3]=>1011100
[8,2,4,7,1,5,6,3]=>1001001
[8,4,7,6,5,2,1,3]=>1011110
[8,3,1,4,7,6,2,5]=>1100110
[1,5,2,6,8,3,7,4]=>0100101
[7,2,8,4,1,3,5,6]=>1011000
[6,7,8,5,2,1,4,3]=>0011101
[1,6,2,7,8,4,3,5]=>0100110
[4,3,8,6,5,2,7,1]=>1011101
[2,3,8,6,5,1,7,4]=>0011101
[7,3,2,6,1,4,8,5]=>1101001
[3,2,5,6,8,4,1,7]=>1000110
[2,6,8,1,5,4,3,7]=>0010110
[8,4,7,1,2,5,3,6]=>1010010
[8,5,6,7,2,1,4,3]=>1001101
[8,5,6,7,3,1,4,2]=>1001101
[1,8,3,2,5,4,6,7]=>0110100
[5,1,7,3,2,8,4,6]=>1011010
[8,2,5,3,1,7,4,6]=>1011010
[1,4,8,5,3,2,6,7]=>0011100
[5,8,3,1,4,2,6,7]=>0110100
[1,5,4,8,2,3,6,7]=>0101000
[1,5,4,8,2,3,7,6]=>0101001
[5,7,8,1,3,2,4,6]=>0010100
[8,2,7,5,1,4,6,3]=>1011001
[8,2,4,1,6,7,3,5]=>1010010
[8,7,3,6,2,4,1,5]=>1101010
[1,7,4,8,3,6,2,5]=>0101010
[7,8,6,1,3,5,4,2]=>0110011
[1,7,5,8,4,3,2,6]=>0101110
[6,3,1,2,7,8,5,4]=>1100011
[7,1,8,5,3,4,2,6]=>1011010
[1,2,7,8,3,5,6,4]=>0001001
[8,2,7,5,3,4,1,6]=>1011010
[6,3,1,2,8,7,5,4]=>1100111
[8,4,7,2,6,3,1,5]=>1010110
[8,2,4,7,6,3,1,5]=>1001110
[7,6,3,4,2,1,8,5]=>1101101
[8,2,4,6,3,7,1,5]=>1001010
[3,4,5,8,1,7,2,6]=>0001010
[8,6,3,4,7,2,1,5]=>1100110
[4,3,8,6,7,5,1,2]=>1010110
[4,5,6,2,7,8,3,1]=>0010011
[4,5,6,2,7,1,8,3]=>0010101
[4,5,6,2,1,7,3,8]=>0011010
[4,5,6,1,7,8,3,2]=>0010011
[4,5,1,6,7,8,3,2]=>0100011
[4,5,1,6,7,3,8,2]=>0100101
[4,5,1,6,7,3,2,8]=>0100110
[4,5,6,1,7,3,2,8]=>0010110
[8,6,4,3,7,2,1,5]=>1110110
[5,8,1,4,3,2,7,6]=>0101101
[1,6,4,3,8,2,7,5]=>0110101
[7,8,1,4,3,2,5,6]=>0101100
[1,7,8,4,5,3,6,2]=>0010101
[2,7,6,3,4,1,8,5]=>0110101
[8,1,7,4,3,5,6,2]=>1011001
[7,1,8,4,5,3,6,2]=>1010101
[4,3,1,8,6,5,7,2]=>1101101
[4,3,2,7,5,1,8,6]=>1101101
[5,2,3,7,4,1,8,6]=>1001101
[2,1,7,4,3,6,8,5]=>1011001
[7,1,2,4,5,6,8,3]=>1000001
[2,8,7,1,4,5,6,3]=>0110001
[8,7,1,3,4,5,6,2]=>1100001
[7,8,1,3,4,5,6,2]=>0100001
[1,7,2,5,4,6,8,3]=>0101001
[2,5,3,8,1,6,7,4]=>0101001
[1,6,4,2,5,7,8,3]=>0110001
[8,5,3,1,4,6,7,2]=>1110001
[6,5,3,4,1,7,8,2]=>1101001
[5,6,3,4,1,7,8,2]=>0101001
[2,5,3,1,4,7,8,6]=>0110001
[2,6,1,4,3,7,8,5]=>0101001
[6,8,2,3,1,5,7,4]=>0101001
[6,1,3,4,2,7,8,5]=>1001001
[4,3,1,5,2,7,8,6]=>1101001
[5,2,3,1,4,7,8,6]=>1010001
[7,2,1,3,5,6,8,4]=>1100001
[5,2,4,7,8,6,3,1]=>1000111
[8,4,2,7,6,1,5,3]=>1101101
[5,3,7,6,1,8,4,2]=>1011011
[8,6,4,1,2,5,3,7]=>1110010
[8,6,1,4,2,5,7,3]=>1101001
[8,6,4,1,2,5,7,3]=>1110001
[8,6,1,4,7,2,5,3]=>1100101
[4,8,6,2,3,1,5,7]=>0110100
[2,5,3,7,6,4,8,1]=>0101101
[3,1,5,7,6,4,2,8]=>1001110
[3,1,6,5,4,7,2,8]=>1011010
[2,5,6,8,3,4,7,1]=>0001001
[4,1,3,6,5,2,7,8]=>1001100
[3,6,2,4,5,7,1,8]=>0100010
[3,6,2,5,4,7,1,8]=>0101010
[3,5,1,7,6,4,2,8]=>0101110
[3,6,1,4,5,7,2,8]=>0100010
[4,3,1,6,5,2,7,8]=>1101100
[4,1,2,6,5,3,7,8]=>1001100
[3,6,4,2,5,7,1,8]=>0110010
[4,2,6,3,5,1,7,8]=>1010100
[3,4,6,8,7,1,2,5]=>0001100
[3,4,7,6,5,1,2,8]=>0011100
[4,5,2,7,1,3,6,8]=>0101000
[4,6,1,2,5,3,7,8]=>0100100
[2,5,4,8,3,7,6,1]=>0101011
[1,3,6,2,5,8,7,4]=>0010011
[1,3,5,8,6,4,7,2]=>0001101
[5,8,7,1,4,6,3,2]=>0110011
[6,2,5,1,3,4,8,7]=>1010001
[2,6,5,1,3,4,8,7]=>0110001
[4,6,5,1,2,7,3,8]=>0110010
[5,6,4,1,2,7,3,8]=>0110010
[8,1,5,6,2,4,3,7]=>1001010
[6,4,5,1,2,7,3,8]=>1010010
[5,4,6,1,3,2,7,8]=>1010100
[5,7,1,4,3,2,6,8]=>0101100
[2,6,4,1,3,7,5,8]=>0110010
[6,3,2,5,7,4,8,1]=>1100101
[5,7,3,8,1,2,4,6]=>0101000
[4,5,2,7,6,3,1,8]=>0101110
[4,5,2,1,7,6,3,8]=>0110110
[5,4,1,6,7,2,8,3]=>1100101
[4,1,6,5,2,7,8,3]=>1011001
[5,4,6,2,7,8,3,1]=>1010011
[3,5,2,6,7,8,4,1]=>0100011
[6,3,2,5,1,7,8,4]=>1101001
[4,6,3,7,8,2,1,5]=>0100110
[5,6,7,1,8,4,2,3]=>0010110
[5,6,7,2,8,4,1,3]=>0010110
[1,7,8,4,6,5,2,3]=>0010110
[6,4,1,8,7,2,5,3]=>1101101
[3,7,2,8,6,5,1,4]=>0101110
[2,7,8,1,6,5,3,4]=>0010110
[2,5,8,1,7,6,3,4]=>0010110
[2,8,4,7,6,3,1,5]=>0101110
[4,5,8,7,1,6,2,3]=>0011010
[6,4,8,7,2,1,5,3]=>1011101
[3,2,8,7,6,4,1,5]=>1011110
[2,4,5,8,1,7,6,3]=>0001011
[2,6,8,1,4,3,7,5]=>0010101
[4,1,8,2,6,7,3,5]=>1010010
[8,1,7,3,5,2,4,6]=>1010100
[8,1,3,2,7,6,4,5]=>1010110
[7,5,8,1,6,2,3,4]=>1010100
[6,7,5,3,2,8,4,1]=>0111011
[6,2,5,3,8,1,4,7]=>1010100
[7,6,1,3,5,2,4,8]=>1100100
[6,2,4,5,3,8,1,7]=>1001010
[6,1,5,4,7,2,3,8]=>1010100
[1,2,5,4,7,8,3,6]=>0010010
[3,6,2,4,7,8,5,1]=>0100011
[1,8,5,4,6,7,2,3]=>0110010
[1,3,5,4,8,7,2,6]=>0010110
[1,6,2,4,8,3,7,5]=>0100101
[1,7,3,2,4,6,5,8]=>0110010
[8,1,3,2,6,5,7,4]=>1010101
[1,5,7,3,2,6,4,8]=>0011010
[5,1,3,7,2,6,4,8]=>1001010
[1,7,8,5,4,2,6,3]=>0011101
[8,1,7,5,4,2,6,3]=>1011101
[1,5,2,8,6,4,7,3]=>0101101
[1,6,5,2,7,4,8,3]=>0110101
[5,1,6,7,4,2,8,3]=>1001101
[1,5,4,2,8,6,7,3]=>0110101
[1,6,3,5,2,7,8,4]=>0101001
[5,8,4,1,6,2,7,3]=>0110101
[3,1,2,6,8,7,5,4]=>1000111
[6,4,8,2,3,5,7,1]=>1010001
[4,6,8,2,5,7,1,3]=>0010010
[6,4,8,2,5,7,1,3]=>1010010
[6,8,2,4,7,3,5,1]=>0100101
[8,6,2,4,5,1,3,7]=>1100100
[6,8,4,2,7,1,3,5]=>0110100
[6,8,2,4,1,7,3,5]=>0101010
[2,5,4,7,6,1,3,8]=>0101100
[5,2,3,7,6,1,4,8]=>1001100
[4,2,3,7,6,1,5,8]=>1001100
[4,2,7,3,5,1,6,8]=>1010100
[5,6,2,3,8,4,7,1]=>0100101
[5,6,2,3,1,7,8,4]=>0101001
[5,7,2,3,4,1,6,8]=>0100100
[6,2,7,3,5,1,4,8]=>1010100
[7,2,6,3,5,1,4,8]=>1010100
[6,5,2,3,1,7,8,4]=>1101001
[6,5,2,3,8,4,7,1]=>1100101
[7,5,2,1,4,6,8,3]=>1110001
[8,5,2,1,4,6,7,3]=>1110001
[8,5,2,3,1,6,4,7]=>1101010
[8,6,2,3,1,5,4,7]=>1101010
[8,2,6,3,1,7,4,5]=>1011010
[1,6,3,4,2,7,5,8]=>0101010
[8,5,2,7,3,4,6,1]=>1101001
[1,7,2,4,5,6,8,3]=>0100001
[1,8,3,2,5,6,4,7]=>0110010
[8,6,1,3,4,5,7,2]=>1100001
[6,8,1,3,4,5,7,2]=>0100001
[7,2,8,1,4,6,3,5]=>1010010
[2,7,8,1,5,6,3,4]=>0010010
[6,8,2,3,1,5,4,7]=>0101010
[5,8,2,3,1,6,4,7]=>0101010
[5,7,2,1,4,6,8,3]=>0110001
[4,2,3,8,1,7,5,6]=>1001010
[5,2,3,8,1,7,4,6]=>1001010
[2,5,4,8,1,7,3,6]=>0101010
[2,5,4,1,3,8,6,7]=>0110010
[4,2,1,5,3,7,6,8]=>1101010
[5,1,3,2,6,7,8,4]=>1010001
[5,1,3,4,2,7,6,8]=>1001010
[6,1,3,4,2,7,5,8]=>1001010
[7,2,1,3,5,8,4,6]=>1100010
[6,1,2,4,5,7,8,3]=>1000001
[6,8,7,2,3,4,5,1]=>0110001
[3,7,2,8,1,4,5,6]=>0101000
[5,2,3,7,4,6,1,8]=>1001010
[2,5,3,7,4,6,1,8]=>0101010
[2,6,7,3,4,5,1,8]=>0010010
[6,2,7,3,4,5,1,8]=>1010010
[6,2,8,3,5,1,4,7]=>1010100
[3,8,4,5,2,1,6,7]=>0101100
[8,2,6,3,5,1,4,7]=>1010100
[2,7,6,3,4,5,1,8]=>0110010
[2,8,6,3,5,1,4,7]=>0110100
[2,8,7,5,1,3,4,6]=>0111000
[1,5,7,3,6,2,8,4]=>0010101
[1,6,5,7,2,8,3,4]=>0101010
[7,5,2,6,1,8,4,3]=>1101011
[6,1,5,2,7,8,4,3]=>1010011
[1,6,5,7,2,8,4,3]=>0101011
[1,5,4,6,2,8,7,3]=>0101011
[1,5,4,6,2,8,3,7]=>0101010
[1,5,6,4,8,2,3,7]=>0010100
[6,2,1,5,8,4,7,3]=>1100101
[8,3,7,5,1,4,2,6]=>1011010
[8,3,7,1,6,4,2,5]=>1010110
[4,2,6,5,3,1,7,8]=>1011100
[4,3,7,5,1,6,2,8]=>1011010
[5,3,7,4,2,8,6,1]=>1011011
[5,3,1,4,6,7,8,2]=>1100001
[6,2,1,4,7,5,8,3]=>1100101
[4,5,7,2,3,6,1,8]=>0010010
[4,6,2,1,3,7,8,5]=>0110001
[6,5,2,7,4,1,3,8]=>1101100
[5,4,2,3,6,8,1,7]=>1100010
[6,4,1,2,7,8,3,5]=>1100010
[5,1,8,3,4,6,2,7]=>1010010
[4,5,8,2,3,7,1,6]=>0010010
[5,1,4,7,2,6,8,3]=>1001001
[2,6,5,3,8,1,4,7]=>0110100
[6,5,8,2,7,3,4,1]=>1010101
[5,2,6,8,3,7,1,4]=>1001010
[1,7,6,5,3,8,2,4]=>0111010
[1,7,2,4,3,5,8,6]=>0101001
[4,6,1,3,7,8,5,2]=>0100011
[8,4,1,5,2,6,7,3]=>1101001
[6,3,1,8,5,4,7,2]=>1101101
[6,1,3,8,7,4,5,2]=>1001101
[2,8,4,6,5,1,7,3]=>0101101
[7,4,1,3,6,5,2,8]=>1100110
[5,7,2,8,1,3,6,4]=>0101001
[2,3,8,4,1,7,6,5]=>0011011
[6,5,1,4,7,3,2,8]=>1100110
[2,7,8,4,1,3,6,5]=>0011001
[3,6,5,1,4,8,2,7]=>0110010
[3,6,4,1,2,7,8,5]=>0110001
[4,1,7,3,8,6,2,5]=>1010110
[4,8,2,7,6,5,1,3]=>0101110
[5,4,2,8,7,6,1,3]=>1101110
[7,4,2,8,6,5,1,3]=>1101110
[6,5,8,2,7,4,1,3]=>1010110
[8,6,5,2,7,1,4,3]=>1110101
[7,8,5,2,1,6,4,3]=>0111011
[6,8,5,2,7,1,4,3]=>0110101
[6,5,8,2,7,1,4,3]=>1010101
[7,5,8,2,1,6,4,3]=>1011011
[3,2,1,6,5,8,4,7]=>1101010
[6,3,1,4,5,8,2,7]=>1100010
[3,4,8,5,2,1,7,6]=>0011101
[4,8,7,1,3,2,6,5]=>0110101
[3,5,1,4,2,8,7,6]=>0101011
[5,8,7,4,6,1,3,2]=>0110101
[5,1,8,7,4,6,3,2]=>1011011
[3,4,1,8,7,6,2,5]=>0101110
[3,5,2,8,6,4,7,1]=>0101101
[2,8,7,5,4,1,6,3]=>0111101
[4,2,5,8,6,7,1,3]=>1001010
[8,1,5,7,4,2,6,3]=>1001101
[8,4,5,3,1,6,7,2]=>1011001
[5,8,7,3,4,1,6,2]=>0110101
[2,4,5,8,1,3,7,6]=>0001001
[7,1,4,3,8,5,6,2]=>1010101
[6,3,2,5,8,4,1,7]=>1100110
[8,7,1,4,6,3,2,5]=>1100110
[8,4,1,3,7,6,5,2]=>1100111
[2,7,8,6,5,3,1,4]=>0011110
[5,1,6,4,7,8,2,3]=>1010010
[2,8,3,5,6,1,4,7]=>0100100
[1,3,6,4,2,7,5,8]=>0011010
[3,2,8,5,6,1,4,7]=>1010100
[7,2,5,8,1,4,6,3]=>1001001
[4,7,5,8,1,2,6,3]=>0101001
[5,4,7,8,2,1,3,6]=>1001100
[4,7,5,8,1,2,3,6]=>0101000
[3,4,7,5,2,8,1,6]=>0011010
[4,3,2,5,7,8,1,6]=>1100010
[5,4,8,6,2,3,1,7]=>1011010
[2,4,7,5,8,3,1,6]=>0010110
[7,2,5,8,1,6,3,4]=>1001010
[3,7,8,4,2,1,6,5]=>0011101
[8,5,4,7,6,3,1,2]=>1101110
[1,5,4,8,7,6,2,3]=>0101110
[3,2,4,5,8,1,6,7]=>1000100
[2,4,6,8,3,7,1,5]=>0001010
[1,4,7,6,3,8,2,5]=>0011010
[3,6,5,1,7,2,8,4]=>0110101
[6,4,1,7,2,8,5,3]=>1101011
[7,4,1,6,2,8,5,3]=>1101011
[2,8,3,7,5,1,6,4]=>0101101
[1,3,6,8,2,4,7,5]=>0001001
[8,5,4,1,6,2,7,3]=>1110101
[4,7,2,8,5,1,6,3]=>0101101
[8,6,2,7,3,5,1,4]=>1101010
[5,7,3,2,4,8,6,1]=>0110011
[2,8,4,6,3,5,1,7]=>0101010
[2,7,8,3,6,4,5,1]=>0010101
[4,2,3,5,1,8,6,7]=>1001010
[4,5,2,6,7,1,8,3]=>0100101
[4,7,5,2,6,3,8,1]=>0110101
[3,5,6,2,8,1,4,7]=>0010100
[5,7,2,1,8,4,3,6]=>0110110
[6,1,8,2,4,3,5,7]=>1010100
[1,6,8,2,5,3,4,7]=>0010100
[8,7,6,2,4,5,1,3]=>1110010
[8,7,3,5,1,4,6,2]=>1101001
[8,6,3,5,2,1,4,7]=>1101100
[8,7,3,2,6,5,1,4]=>1110110
[8,4,2,7,6,5,1,3]=>1101110
[5,2,8,7,6,4,1,3]=>1011110
[8,7,1,4,5,6,2,3]=>1100010
[4,1,3,8,5,6,2,7]=>1001010
[3,2,4,8,5,7,1,6]=>1001010
[6,3,8,5,4,2,7,1]=>1011101
[7,4,6,1,3,5,2,8]=>1010010
[6,2,3,8,5,4,7,1]=>1001101
[1,5,3,8,7,4,6,2]=>0101101
[5,1,3,8,7,4,6,2]=>1001101
[2,5,3,8,7,4,1,6]=>0101110
[5,2,1,8,7,4,6,3]=>1101101
[6,8,3,5,1,2,7,4]=>0101001
[5,8,2,7,4,6,3,1]=>0101011
[6,8,7,3,1,2,4,5]=>0111000
[4,5,2,8,3,7,1,6]=>0101010
[4,5,8,1,3,7,6,2]=>0010011
[7,8,5,1,6,4,3,2]=>0110111
[8,7,5,1,6,4,3,2]=>1110111
[4,5,8,3,1,2,7,6]=>0011001
[4,6,8,3,2,1,7,5]=>0011101
[4,6,8,3,5,1,2,7]=>0010100
[7,1,6,8,5,4,3,2]=>1001111
[5,8,1,3,4,2,7,6]=>0100101
[1,4,6,3,7,5,2,8]=>0010110
[4,5,2,6,8,7,3,1]=>0100111
[3,2,8,7,4,5,6,1]=>1011001
[6,4,2,5,1,7,8,3]=>1101001
[1,3,2,8,7,4,6,5]=>0101101
[7,5,2,8,3,1,6,4]=>1101101
[5,4,2,7,3,8,6,1]=>1101011
[6,7,1,3,2,5,8,4]=>0101001
[8,3,5,4,7,1,2,6]=>1010100
[6,3,5,4,8,1,2,7]=>1010100
[6,2,5,4,1,7,8,3]=>1011001
[4,1,5,6,3,8,7,2]=>1001011
[6,8,7,4,3,2,5,1]=>0111101
[2,8,5,1,3,7,6,4]=>0110011
[5,6,4,1,8,2,7,3]=>0110101
[6,1,3,5,4,8,2,7]=>1001010
[1,3,8,7,2,5,6,4]=>0011001
[2,5,4,1,8,3,7,6]=>0110101
[6,1,5,4,3,8,2,7]=>1011010
[1,4,8,3,2,7,6,5]=>0011011
[5,1,4,8,3,7,6,2]=>1001011
[3,5,8,2,1,4,7,6]=>0011001
[8,4,1,2,7,6,5,3]=>1100111
[4,8,3,2,7,6,5,1]=>0110111
[2,4,8,1,7,6,5,3]=>0010111
[8,7,3,2,1,4,6,5]=>1111001
[1,4,8,5,2,3,6,7]=>0011000
[1,4,8,5,2,3,7,6]=>0011001
[6,1,4,2,8,7,3,5]=>1010110
[1,5,8,7,2,4,3,6]=>0011010
[1,2,8,7,3,5,4,6]=>0011010
[8,7,1,3,2,5,4,6]=>1101010
[6,7,4,2,8,1,3,5]=>0110100
[4,7,5,6,2,8,3,1]=>0101011
[8,4,3,6,7,5,2,1]=>1100111
[6,7,5,2,8,4,3,1]=>0110111
[6,8,4,3,2,7,5,1]=>0111011
[6,1,5,8,7,4,3,2]=>1001111
[8,5,1,4,7,6,3,2]=>1100111
[8,2,1,7,5,3,6,4]=>1101101
[8,1,3,7,2,4,6,5]=>1001001
[2,6,7,3,5,8,4,1]=>0010011
[2,6,7,3,5,8,1,4]=>0010010
[5,3,1,6,4,8,2,7]=>1101010
[2,5,6,7,1,4,8,3]=>0001001
[6,4,8,3,5,2,1,7]=>1010110
[4,7,5,2,8,6,1,3]=>0110110
[1,6,5,7,3,8,4,2]=>0101011
[5,8,1,2,7,4,3,6]=>0100110
[4,6,3,7,8,1,5,2]=>0100101
[2,1,4,7,5,8,6,3]=>1001011
[8,6,3,5,2,1,7,4]=>1101101
[6,8,3,1,2,5,4,7]=>0110010
[5,8,6,4,7,1,2,3]=>0110100
[2,5,1,8,7,3,4,6]=>0101100
[6,8,1,7,5,4,2,3]=>0101110
[4,8,2,7,5,3,6,1]=>0101101
[7,2,4,3,8,6,1,5]=>1010110
[5,8,4,3,1,6,7,2]=>0111001
[6,8,7,4,5,1,3,2]=>0110101
[1,4,7,3,6,8,2,5]=>0010010
[2,4,7,3,6,8,1,5]=>0010010
[2,8,3,1,4,7,5,6]=>0110010
[2,7,3,1,8,5,4,6]=>0110110
[2,3,1,6,8,7,4,5]=>0100110
[6,4,8,2,1,7,3,5]=>1011010
[2,3,1,7,8,5,6,4]=>0100101
[2,3,1,8,7,5,6,4]=>0101101
[8,7,4,5,1,3,2,6]=>1101010
[8,5,1,2,7,4,3,6]=>1100110
[1,3,7,6,8,4,2,5]=>0010110
[4,5,7,8,6,2,1,3]=>0001110
[2,1,5,7,4,6,8,3]=>1001001
[2,3,5,7,8,1,6,4]=>0000101
[1,6,4,2,3,5,7,8]=>0110000
[1,5,7,4,2,3,6,8]=>0011000
[1,5,7,2,3,6,8,4]=>0010001
[2,4,7,8,6,1,3,5]=>0001100
[1,3,6,2,5,8,4,7]=>0010010
[1,5,3,6,8,2,4,7]=>0100100
[2,8,5,1,4,3,7,6]=>0110101
[6,1,5,8,3,2,7,4]=>1001101
[1,8,6,2,4,3,7,5]=>0110101
[4,8,5,1,3,2,6,7]=>0110100
[5,4,3,1,2,7,6,8]=>1110010
[4,1,6,5,2,3,7,8]=>1011000
[7,1,5,2,3,6,4,8]=>1010010
[4,1,6,3,7,2,5,8]=>1010100
[4,6,1,2,8,3,7,5]=>0100101
[4,1,3,6,7,2,5,8]=>1000100
[2,6,5,1,3,4,7,8]=>0110000
[2,6,7,4,3,1,5,8]=>0011100
[2,6,3,1,7,4,5,8]=>0110100
[2,3,6,7,1,5,4,8]=>0001010
[3,7,5,6,2,1,4,8]=>0101100
[2,7,5,8,1,3,6,4]=>0101001
[5,1,6,7,3,2,4,8]=>1001100
[5,1,3,6,7,4,2,8]=>1000110
[2,5,6,3,8,4,7,1]=>0010101
[7,4,1,2,3,6,8,5]=>1100001
[8,5,6,2,1,4,7,3]=>1011001
[2,7,4,1,5,8,3,6]=>0110010
[6,1,7,3,4,2,5,8]=>1010100
[2,6,4,7,8,5,3,1]=>0100111
[5,2,8,4,6,7,1,3]=>1010010
[1,3,5,8,4,6,7,2]=>0001001
[8,2,7,6,3,4,5,1]=>1011001
[1,8,3,7,4,2,5,6]=>0101100
[8,5,7,2,4,3,6,1]=>1010101
[7,8,6,2,4,1,3,5]=>0110100
[6,8,7,3,2,1,4,5]=>0111100
[3,4,8,2,7,1,5,6]=>0010100
[7,2,6,1,4,8,3,5]=>1010010
[7,8,1,2,4,6,3,5]=>0100010
[7,2,8,3,4,5,1,6]=>1010010
[6,1,8,3,4,2,5,7]=>1010100
[6,8,4,3,1,5,2,7]=>0111010
[5,8,2,1,7,4,3,6]=>0110110
[1,7,2,6,3,4,8,5]=>0101001
[7,5,1,2,4,3,8,6]=>1100101
[7,6,8,1,4,2,3,5]=>1010100
[6,3,5,2,1,8,4,7]=>1011010
[3,2,4,8,6,1,7,5]=>1001101
[2,1,3,8,4,5,7,6]=>1001001
[1,4,7,5,2,3,8,6]=>0011001
[2,1,3,7,8,4,6,5]=>1000101
[2,1,3,8,4,7,6,5]=>1001011
[3,1,2,8,4,5,7,6]=>1001001
[1,2,8,7,5,4,6,3]=>0011101
[1,3,6,8,2,7,5,4]=>0001011
[3,2,7,5,6,8,1,4]=>1010010
[6,1,5,4,2,3,8,7]=>1011001
[6,4,5,1,2,8,3,7]=>1010010
[8,4,1,5,7,6,3,2]=>1100111
[8,1,6,3,5,2,4,7]=>1010100
[4,6,2,5,3,8,1,7]=>0101010
[4,6,5,2,1,8,3,7]=>0111010
[5,8,4,3,6,7,2,1]=>0110011
[6,8,2,1,5,3,4,7]=>0110100
[2,5,3,8,6,7,4,1]=>0101011
[3,2,6,5,1,8,4,7]=>1011010
[6,4,5,1,8,3,2,7]=>1010110
[3,6,8,2,5,1,4,7]=>0010100
[7,4,5,8,1,6,2,3]=>1001010
[4,5,8,1,6,7,3,2]=>0010011
[5,1,8,4,6,7,3,2]=>1010011
[4,8,3,1,6,7,2,5]=>0110010
[7,2,4,6,3,8,5,1]=>1001011
[2,8,3,7,6,1,5,4]=>0101101
[5,4,2,6,8,7,3,1]=>1100111
[3,7,2,5,8,6,4,1]=>0100111
[5,4,3,7,2,8,6,1]=>1101011
[2,4,8,7,6,1,5,3]=>0011101
[4,8,5,2,7,6,3,1]=>0110111
[2,8,6,5,7,1,3,4]=>0110100
[4,1,8,6,2,5,7,3]=>1011001
[3,8,4,7,2,1,6,5]=>0101101
[1,8,7,4,5,2,3,6]=>0110100
[5,8,1,7,6,2,3,4]=>0101100
[6,8,2,1,3,4,7,5]=>0110001
[4,8,1,3,7,6,2,5]=>0100110
[5,2,1,7,6,4,3,8]=>1101110
[7,4,8,3,6,5,1,2]=>1010110
[6,4,8,5,1,7,2,3]=>1011010
[5,2,8,1,3,6,7,4]=>1010001
[5,2,7,1,3,8,6,4]=>1010011
[6,3,7,2,5,4,8,1]=>1010101
[5,2,1,7,6,3,8,4]=>1101101
[6,3,2,7,4,5,8,1]=>1101001
[7,4,3,8,5,6,1,2]=>1101010
[7,3,2,8,4,6,1,5]=>1101010
[6,2,1,8,7,4,5,3]=>1101101
[6,2,1,8,7,3,5,4]=>1101101
[5,2,1,7,6,3,4,8]=>1101100
[7,4,3,8,5,6,2,1]=>1101011
[4,2,8,3,6,7,5,1]=>1010011
[4,2,6,8,5,7,1,3]=>1001010
[4,2,1,6,5,7,8,3]=>1101001
[8,6,1,4,3,5,2,7]=>1101010
[6,1,8,4,3,5,2,7]=>1011010
[5,1,6,4,8,2,3,7]=>1010100
[2,8,6,4,1,5,3,7]=>0111010
[8,1,4,2,5,3,6,7]=>1010100
[2,8,4,1,5,3,6,7]=>0110100
[8,4,1,3,5,2,6,7]=>1100100
[3,4,8,1,5,2,6,7]=>0010100
[4,1,8,3,5,2,6,7]=>1010100
[8,3,1,2,5,4,6,7]=>1100100
[2,8,1,3,5,4,6,7]=>0100100
[1,7,6,2,4,3,8,5]=>0110101
[1,4,5,8,3,2,6,7]=>0001100
[5,6,8,7,1,3,2,4]=>0011010
[2,8,6,5,7,4,3,1]=>0110111
[6,3,7,5,1,4,2,8]=>1011010
[2,8,6,5,7,4,1,3]=>0110110
[6,5,2,7,4,3,1,8]=>1101110
[6,5,2,8,4,3,7,1]=>1101101
[7,5,8,3,4,2,1,6]=>1010110
[6,3,7,5,1,4,8,2]=>1011001
[5,3,7,2,4,1,8,6]=>1010101
[5,1,2,8,6,3,7,4]=>1001101
[6,5,2,8,4,7,1,3]=>1101010
[6,5,8,3,1,2,7,4]=>1011001
[6,1,5,7,2,4,3,8]=>1001010
[7,1,6,8,2,5,4,3]=>1001011
[4,1,8,2,6,5,7,3]=>1010101
[6,1,4,7,8,5,3,2]=>1000111
[5,1,4,6,7,3,2,8]=>1000110
[6,1,5,7,8,4,2,3]=>1000110
[1,8,4,5,6,7,2,3]=>0100010
[4,2,8,6,7,1,3,5]=>1010100
[6,4,2,7,1,5,8,3]=>1101001
[5,6,2,7,4,8,3,1]=>0101011
[5,3,6,7,4,2,8,1]=>1001101
[2,6,3,7,5,4,8,1]=>0101101
[1,7,3,2,4,8,6,5]=>0110011
[6,4,1,3,8,7,5,2]=>1100111
[4,3,1,8,2,6,7,5]=>1101001
[4,8,1,3,2,5,7,6]=>0101001
[7,2,6,5,8,3,4,1]=>1010101
[1,7,5,3,8,6,2,4]=>0110110
[2,5,3,8,1,4,7,6]=>0101001
[4,2,5,8,1,3,7,6]=>1001001
[8,1,2,4,3,5,7,6]=>1001001
[2,4,3,8,1,5,7,6]=>0101001
[7,5,2,3,8,4,6,1]=>1100101
[2,7,5,1,4,8,3,6]=>0110010
[3,1,7,4,8,6,5,2]=>1010111
[6,4,5,3,2,8,7,1]=>1011011
[2,7,3,8,5,1,6,4]=>0101101
[8,7,3,2,5,6,4,1]=>1110011
[1,5,8,2,6,4,3,7]=>0010110
[3,1,8,2,6,5,4,7]=>1010110
[7,6,2,8,1,4,5,3]=>1101001
[8,4,2,3,1,5,7,6]=>1101001
[8,2,3,4,1,5,7,6]=>1001001
[7,1,6,2,4,8,3,5]=>1010010
[4,5,2,6,1,3,8,7]=>0101001
[2,7,8,1,4,3,6,5]=>0010101
[6,5,8,1,3,2,4,7]=>1010100
[5,7,2,1,8,4,6,3]=>0110101
[2,1,8,5,3,4,6,7]=>1011000
[7,8,1,5,2,4,6,3]=>0101001
[7,4,1,8,2,5,6,3]=>1101001
[2,1,6,7,4,8,3,5]=>1001010
[2,8,6,3,1,5,4,7]=>0111010
[5,8,6,3,2,1,4,7]=>0111100
[5,7,2,8,4,1,6,3]=>0101101
[2,5,6,3,8,1,4,7]=>0010100
[7,3,5,6,1,8,4,2]=>1001011
[7,4,5,6,8,1,3,2]=>1000101
[7,5,1,8,4,6,3,2]=>1101011
[2,8,1,7,4,5,3,6]=>0101010
[7,3,6,2,5,4,8,1]=>1010101
[6,1,5,3,8,4,7,2]=>1010101
[1,6,5,3,8,4,7,2]=>0110101
[7,6,2,3,5,4,8,1]=>1100101
[7,6,2,3,5,1,4,8]=>1100100
[6,1,5,2,3,4,8,7]=>1010001
[6,2,5,3,4,8,1,7]=>1010010
[6,2,5,3,4,8,7,1]=>1010011
[2,6,5,3,4,8,7,1]=>0110011
[2,6,5,3,4,8,1,7]=>0110010
[2,5,1,4,8,3,7,6]=>0100101
[1,2,5,4,8,3,7,6]=>0010101
[5,3,4,8,1,7,2,6]=>1001010
[5,1,3,4,8,7,2,6]=>1000110
[1,5,3,4,8,7,2,6]=>0100110
[5,1,3,8,4,7,6,2]=>1001011
[5,3,8,1,4,7,6,2]=>1010011
[4,3,5,8,1,7,6,2]=>1001011
[3,6,5,4,8,1,2,7]=>0110100
[3,6,5,4,8,2,7,1]=>0110101
[4,3,5,8,2,1,7,6]=>1001101
[3,5,2,4,8,7,6,1]=>0100111
[5,2,3,8,7,4,1,6]=>1001110
[2,3,1,7,4,8,6,5]=>0101011
[2,3,8,7,6,4,1,5]=>0011110
[7,5,2,3,1,6,4,8]=>1101010
[4,2,8,5,1,3,6,7]=>1011000
[7,4,1,3,6,2,5,8]=>1100100
[7,4,6,3,1,2,5,8]=>1011000
[8,2,5,3,6,1,4,7]=>1010100
[7,2,5,8,1,3,6,4]=>1001001
[1,2,6,5,3,4,7,8]=>0011000
[1,4,6,5,7,2,3,8]=>0010100
[2,4,6,5,7,1,8,3]=>0010101
[3,5,2,1,7,8,6,4]=>0110011
[1,2,7,8,6,4,5,3]=>0001101
[7,1,6,3,2,4,8,5]=>1011001
[8,5,1,2,3,6,7,4]=>1100001
[6,4,8,1,2,3,7,5]=>1010001
[4,3,5,1,7,8,6,2]=>1010011
[4,6,7,2,3,8,5,1]=>0010011
[4,5,3,7,8,1,2,6]=>0100100
[1,7,4,5,8,3,6,2]=>0100101
[7,3,6,8,5,2,1,4]=>1001110
[2,8,3,1,7,4,5,6]=>0110100
[4,5,7,6,3,1,8,2]=>0011101
[4,6,7,5,2,8,3,1]=>0011011
[4,6,7,5,1,3,8,2]=>0011001
[3,6,5,1,4,7,8,2]=>0110001
[4,6,7,3,1,5,8,2]=>0011001
[4,2,3,6,7,5,1,8]=>1000110
[6,2,3,5,7,4,1,8]=>1000110
[2,6,4,5,7,3,1,8]=>0100110
[7,1,5,2,4,8,3,6]=>1010010
[8,1,5,2,4,7,3,6]=>1010010
[7,5,8,1,4,2,3,6]=>1010100
[1,7,5,8,4,2,3,6]=>0101100
[1,3,4,8,5,6,2,7]=>0001010
[4,8,3,6,1,7,2,5]=>0101010
[4,6,3,1,2,5,7,8]=>0110000
[7,4,6,8,3,1,2,5]=>1001100
[8,5,4,7,3,1,2,6]=>1101100
[7,3,2,1,5,4,8,6]=>1110101
[2,5,6,4,8,1,3,7]=>0010100
[5,4,1,6,2,3,7,8]=>1101000
[1,5,6,4,2,3,7,8]=>0011000
[1,3,6,5,2,4,7,8]=>0011000
[1,5,6,3,2,4,7,8]=>0011000
[5,7,8,1,2,4,3,6]=>0010010
[6,5,1,2,4,3,8,7]=>1100101
[2,5,1,4,6,3,8,7]=>0100101
[5,8,7,3,1,2,4,6]=>0111000
[2,7,8,1,4,5,3,6]=>0010010
[4,3,7,1,2,6,8,5]=>1010001
[4,1,2,8,7,3,6,5]=>1001101
[8,7,5,1,2,4,3,6]=>1110010
[6,1,2,4,3,8,7,5]=>1001011
[3,7,8,1,2,4,6,5]=>0010001
[7,8,5,1,2,4,3,6]=>0110010
[8,3,4,1,2,6,7,5]=>1010001
[2,1,4,7,3,6,8,5]=>1001001
[7,3,4,1,2,6,8,5]=>1010001
[8,4,3,1,2,6,5,7]=>1110010
[3,8,2,7,4,5,1,6]=>0101010
[8,6,2,3,5,4,1,7]=>1100110
[8,2,6,1,3,5,4,7]=>1010010
[8,5,3,4,2,7,1,6]=>1101010
[8,4,3,7,2,5,6,1]=>1101001
[5,3,4,1,8,2,7,6]=>1010101
[8,3,1,7,4,5,2,6]=>1101010
[8,2,4,5,1,7,3,6]=>1001010
[4,3,8,1,7,5,6,2]=>1010101
[8,4,3,7,1,5,6,2]=>1101001
[8,3,4,7,2,6,5,1]=>1001011
[8,1,3,7,6,4,5,2]=>1001101
[8,1,4,3,7,5,6,2]=>1010101
[8,3,7,1,4,5,6,2]=>1010001
[8,7,3,6,1,2,5,4]=>1101001
[8,3,7,6,2,4,5,1]=>1011001
[8,7,2,3,6,1,5,4]=>1100101
[8,7,1,2,6,5,3,4]=>1100110
[8,2,7,1,3,4,6,5]=>1010001
[5,1,8,4,2,3,7,6]=>1011001
[8,2,4,7,3,1,6,5]=>1001101
[8,2,7,6,3,1,4,5]=>1011100
[6,8,1,4,7,3,2,5]=>0100110
[8,5,7,2,6,3,1,4]=>1010110
[5,8,2,7,3,1,6,4]=>0101101
[8,1,2,6,7,5,4,3]=>1000111
[6,2,8,5,1,7,3,4]=>1011010
[8,4,1,7,5,6,2,3]=>1101010
[8,1,2,4,7,6,5,3]=>1000111
[8,2,4,7,6,5,1,3]=>1001110
[8,2,7,6,4,5,1,3]=>1011010
[8,4,7,2,3,6,5,1]=>1010011
[8,2,4,7,3,6,5,1]=>1001011
[8,1,7,6,4,5,2,3]=>1011010
[8,1,2,7,6,4,5,3]=>1001101
[8,1,4,2,7,5,6,3]=>1010101
[8,1,5,7,3,6,4,2]=>1001011
[8,1,4,7,3,6,5,2]=>1001011
[1,7,3,8,6,2,5,4]=>0101101
[5,8,2,3,7,4,1,6]=>0100110
[4,2,8,3,7,6,1,5]=>1010110
[1,2,4,6,8,3,7,5]=>0000101
[1,3,5,6,4,8,2,7]=>0001010
[3,1,7,8,5,2,4,6]=>1001100
[6,3,5,2,8,4,7,1]=>1010101
[1,6,3,5,2,8,4,7]=>0101010
[1,5,4,8,6,3,7,2]=>0101101
[5,4,8,6,3,7,2,1]=>1011011
[5,4,8,6,3,7,1,2]=>1011010
[6,4,5,8,3,1,7,2]=>1001101
[6,4,5,8,1,3,7,2]=>1001001
[6,3,5,1,8,4,7,2]=>1010101
[2,6,3,1,5,8,4,7]=>0110010
[2,5,4,8,6,3,1,7]=>0101110
[1,2,5,4,8,6,3,7]=>0010110
[2,4,8,5,6,7,3,1]=>0010011
[4,8,5,6,7,1,3,2]=>0100101
[6,4,5,8,2,1,7,3]=>1001101
[5,3,8,2,6,7,1,4]=>1010010
[6,3,5,2,8,1,7,4]=>1010101
[5,3,4,1,2,6,8,7]=>1010001
[4,3,5,2,8,6,1,7]=>1010110
[1,4,3,5,2,8,6,7]=>0101010
[1,3,5,4,8,2,6,7]=>0010100
[3,5,4,8,2,6,1,7]=>0101010
[3,6,4,5,1,2,8,7]=>0101001
[4,3,5,1,8,6,2,7]=>1010110
[3,5,4,8,1,6,2,7]=>0101010
[3,4,8,5,6,1,2,7]=>0010100
[3,4,8,5,6,2,1,7]=>0010110
[3,4,8,5,6,2,7,1]=>0010101
[3,5,4,8,1,6,7,2]=>0101001
[2,4,3,1,5,8,6,7]=>0110010
[1,7,6,2,5,4,8,3]=>0110101
[8,1,6,4,3,5,2,7]=>1011010
[1,3,7,8,2,6,4,5]=>0001010
[3,8,6,4,5,2,7,1]=>0110101
[4,5,8,6,2,3,7,1]=>0011001
[4,5,8,1,6,7,2,3]=>0010010
[4,6,8,5,3,7,2,1]=>0011011
[4,5,7,2,8,6,3,1]=>0010111
[3,7,4,5,1,6,8,2]=>0101001
[4,6,8,1,2,5,7,3]=>0010001
[3,7,8,5,1,4,6,2]=>0011001
[4,6,8,5,1,3,7,2]=>0011001
[4,6,8,5,2,7,3,1]=>0011011
[3,8,6,2,7,4,5,1]=>0110101
[3,7,4,5,2,8,6,1]=>0101011
[3,7,8,4,6,1,5,2]=>0010101
[4,6,8,3,7,1,5,2]=>0010101
[3,5,1,7,8,4,6,2]=>0100101
[4,5,1,6,8,3,7,2]=>0100101
[4,3,1,8,5,7,2,6]=>1101010
[4,8,3,6,1,5,2,7]=>0101010
[8,3,2,4,7,1,6,5]=>1100101
[7,3,2,4,8,1,6,5]=>1100101
[8,3,2,4,6,1,7,5]=>1100101
[8,3,2,4,5,7,1,6]=>1100010
[8,3,6,2,4,1,7,5]=>1010101
[7,4,6,2,1,3,8,5]=>1011001
[3,2,4,5,7,8,1,6]=>1000010
[3,6,7,2,4,1,8,5]=>0010101
[5,3,2,8,7,6,4,1]=>1101111
[4,3,6,1,8,5,2,7]=>1010110
[4,3,7,5,8,2,1,6]=>1010110
[7,3,5,2,8,1,4,6]=>1010100
[2,6,8,4,5,1,7,3]=>0010101
[1,5,8,7,4,2,3,6]=>0011100
[1,5,2,7,6,4,8,3]=>0101101
[1,4,6,8,7,2,5,3]=>0001101
[1,3,6,8,7,2,5,4]=>0001101
[1,4,3,6,8,7,2,5]=>0100110
[1,6,2,7,5,3,4,8]=>0101100
[1,7,2,5,4,3,8,6]=>0101101
[1,6,3,7,2,4,5,8]=>0101000
[1,3,2,6,8,5,4,7]=>0100110
[1,6,3,2,7,4,5,8]=>0110100
[1,5,8,6,2,7,4,3]=>0011011
[1,3,7,2,6,4,5,8]=>0010100
[1,3,7,5,8,6,2,4]=>0010110
[1,7,3,2,8,5,6,4]=>0110101
[1,6,5,2,4,8,3,7]=>0110010
[1,4,7,6,2,3,5,8]=>0011000
[1,7,3,8,4,2,5,6]=>0101100
[1,6,2,4,7,5,8,3]=>0100101
[1,6,2,7,4,3,8,5]=>0101101
[1,5,8,2,3,6,4,7]=>0010010
[2,6,7,3,4,8,1,5]=>0010010
[4,1,3,8,7,5,2,6]=>1001110
[3,6,7,2,1,5,8,4]=>0011001
[2,5,6,1,3,8,7,4]=>0010011
[2,1,3,8,6,7,4,5]=>1001010
[3,8,5,2,1,6,4,7]=>0111010
[5,4,7,8,1,6,3,2]=>1001011
[7,2,8,5,6,3,4,1]=>1010101
[3,2,7,6,8,4,5,1]=>1010101
[4,3,8,6,7,2,5,1]=>1010101
[8,4,5,2,7,3,6,1]=>1010101
[4,3,8,5,6,2,7,1]=>1010101
[5,4,8,6,7,2,3,1]=>1010101
[7,3,4,2,8,5,6,1]=>1010101
[4,3,6,5,8,2,7,1]=>1010101
[8,2,7,4,5,3,6,1]=>1010101
[7,2,8,4,5,3,6,1]=>1010101
[6,3,8,2,7,4,5,1]=>1010101
[3,2,8,4,7,5,6,1]=>1010101
[3,2,7,4,8,5,6,1]=>1010101
[7,2,8,3,6,4,5,1]=>1010101
[8,3,6,2,7,4,5,1]=>1010101
[1,7,8,4,3,6,5,2]=>0011011
[1,7,8,3,6,5,4,2]=>0010111
[6,4,5,8,7,2,1,3]=>1001110
[1,8,4,2,3,7,5,6]=>0110010
[6,4,2,3,8,7,5,1]=>1100111
[6,1,4,2,7,8,3,5]=>1010010
[6,5,1,3,7,8,4,2]=>1100011
[6,4,2,3,7,8,5,1]=>1100011
[6,7,4,2,3,8,5,1]=>0110011
[5,1,3,2,6,8,4,7]=>1010010
[5,7,1,4,6,8,2,3]=>0100010
[5,7,8,3,2,4,6,1]=>0011001
[1,5,7,3,6,4,2,8]=>0010110
[1,6,3,5,7,4,8,2]=>0100101
[1,7,2,4,8,3,5,6]=>0100100
[1,6,7,2,4,8,3,5]=>0010010
[1,6,7,8,2,4,3,5]=>0001010
[3,1,6,7,8,4,2,5]=>1000110
[3,1,6,7,8,4,5,2]=>1000101
[1,6,7,8,2,4,5,3]=>0001001
[4,2,7,6,8,5,1,3]=>1010110
[5,3,4,1,7,8,6,2]=>1010011
[3,7,5,6,1,8,4,2]=>0101011
[1,2,6,8,4,3,5,7]=>0001100
[2,4,7,5,8,3,6,1]=>0010101
[6,8,7,4,2,5,1,3]=>0111010
[7,6,3,1,2,8,5,4]=>1110011
[3,1,8,6,4,7,2,5]=>1011010
[6,2,7,8,3,4,5,1]=>1001001
[8,1,3,5,6,4,7,2]=>1000101
[2,3,7,5,8,4,6,1]=>0010101
[2,5,7,4,6,1,3,8]=>0010100
[4,8,2,6,5,3,7,1]=>0101101
[5,8,6,4,7,3,2,1]=>0110111
[8,5,2,3,1,6,7,4]=>1101001
[8,5,4,2,1,6,7,3]=>1111001
[8,3,5,2,1,6,7,4]=>1011001
[2,8,6,3,5,1,7,4]=>0110101
[8,3,2,6,4,1,7,5]=>1101101
[8,4,1,5,3,6,7,2]=>1101001
[8,3,5,1,4,6,7,2]=>1010001
[8,5,1,3,4,6,7,2]=>1100001
[2,8,6,1,5,4,7,3]=>0110101
[8,3,2,6,1,5,7,4]=>1101001
[3,8,6,4,7,1,2,5]=>0110100
[3,8,6,2,5,4,7,1]=>0110101
[3,8,4,6,5,2,7,1]=>0101101
[2,8,6,4,7,3,1,5]=>0110110
[8,3,5,4,2,7,1,6]=>1011010
[8,1,7,4,2,5,3,6]=>1011010
[8,3,2,5,1,4,7,6]=>1101001
[8,4,1,3,2,6,7,5]=>1101001
[8,4,5,1,2,6,7,3]=>1010001
[8,1,5,2,4,6,7,3]=>1010001
[8,3,1,5,2,6,7,4]=>1101001
[2,8,1,6,5,3,7,4]=>0101101
[8,3,2,1,6,4,7,5]=>1110101
[5,2,6,4,1,3,8,7]=>1011001
[2,1,8,5,4,3,7,6]=>1011101
[6,2,8,5,4,1,3,7]=>1011100
[7,2,8,5,4,1,3,6]=>1011100
[3,7,5,8,4,1,2,6]=>0101100
[5,2,4,7,8,1,3,6]=>1000100
[1,7,6,2,8,5,3,4]=>0110110
[5,6,2,8,1,7,3,4]=>0101010
[3,1,2,4,8,6,7,5]=>1000101
[1,8,7,2,3,4,5,6]=>0110000
[8,6,3,2,5,4,7,1]=>1110101
[8,6,4,2,5,3,7,1]=>1110101
[8,6,5,2,4,3,7,1]=>1110101
[8,5,6,2,4,3,7,1]=>1010101
[6,2,5,3,7,4,8,1]=>1010101
[8,4,5,2,6,3,7,1]=>1010101
[8,5,4,2,6,3,7,1]=>1110101
[8,5,3,2,6,4,7,1]=>1110101
[7,4,6,5,8,2,3,1]=>1010101
[7,3,6,5,8,2,4,1]=>1010101
[7,3,6,4,8,2,5,1]=>1010101
[7,3,5,4,8,2,6,1]=>1010101
[3,7,5,2,8,1,4,6]=>0110100
[1,2,7,4,8,5,6,3]=>0010101
[2,6,7,1,8,4,5,3]=>0010101
[5,6,3,4,2,8,7,1]=>0101011
[3,2,7,5,8,1,6,4]=>1010101
[3,6,5,8,2,7,4,1]=>0101011
[2,7,1,8,5,6,4,3]=>0101011
[4,3,6,8,5,2,1,7]=>1001110
[4,3,6,8,5,2,7,1]=>1001101
[4,5,3,2,1,8,6,7]=>0111010
[3,6,5,8,1,7,4,2]=>0101011
[3,6,5,8,1,2,7,4]=>0101001
[4,1,6,8,5,2,3,7]=>1001100
[4,5,2,8,6,7,3,1]=>0101011
[3,5,8,6,2,4,7,1]=>0011001
[3,2,4,5,8,6,1,7]=>1000110
[3,4,5,8,6,2,1,7]=>0001110
[3,4,5,8,6,2,7,1]=>0001101
[4,5,2,1,3,8,6,7]=>0110010
[4,2,3,6,8,5,1,7]=>1000110
[4,1,3,6,8,5,2,7]=>1000110
[3,1,4,5,8,6,2,7]=>1000110
[4,5,1,3,2,8,6,7]=>0101010
[3,4,5,8,6,1,7,2]=>0001101
[3,4,5,8,6,1,2,7]=>0001100
[8,2,5,4,1,3,7,6]=>1011001
[8,2,6,4,1,3,7,5]=>1011001
[1,5,8,2,4,3,7,6]=>0010101
[4,3,7,8,2,6,5,1]=>1001011
[7,3,8,4,1,5,6,2]=>1011001
[8,6,7,1,4,3,2,5]=>1010110
[3,8,5,1,2,6,7,4]=>0110001
[3,7,8,2,5,4,6,1]=>0010101
[2,4,7,8,3,6,5,1]=>0001011
[5,4,7,8,3,6,1,2]=>1001010
[6,8,1,3,2,5,7,4]=>0101001
[2,4,8,3,5,7,1,6]=>0010010
[1,4,8,5,7,2,3,6]=>0010100
[1,8,7,3,2,4,5,6]=>0111000
[2,8,4,3,5,7,1,6]=>0110010
[5,6,2,7,8,3,1,4]=>0100110
[8,6,2,7,3,4,1,5]=>1101010
[8,6,2,7,3,4,5,1]=>1101001
[5,6,2,7,8,3,4,1]=>0100101
[5,6,3,2,8,7,1,4]=>0110110
[6,8,5,3,1,7,2,4]=>0111010
[8,6,1,7,3,4,2,5]=>1101010
[5,1,6,7,8,3,2,4]=>1000110
[1,5,6,3,7,2,4,8]=>0010100
[6,2,4,8,3,7,1,5]=>1001010
[1,6,8,7,5,2,3,4]=>0011100
[1,5,6,7,4,2,3,8]=>0001100
[5,1,6,7,3,4,2,8]=>1001010
[8,6,1,7,3,4,5,2]=>1101001
[6,1,8,7,4,5,2,3]=>1011010
[2,6,8,4,7,5,1,3]=>0010110
[6,8,5,1,7,4,2,3]=>0110110
[4,6,5,7,2,3,8,1]=>0101001
[5,3,7,4,6,2,8,1]=>1010101
[3,6,7,2,5,8,4,1]=>0010011
[3,5,7,6,8,2,1,4]=>0010110
[5,3,6,7,4,8,1,2]=>1001010
[3,5,7,6,8,1,4,2]=>0010101
[4,2,7,8,3,6,5,1]=>1001011
[5,4,3,7,8,1,6,2]=>1100101
[5,3,6,7,8,2,1,4]=>1000110
[3,5,7,8,4,2,1,6]=>0001110
[4,6,7,8,2,1,3,5]=>0001100
[4,6,7,3,2,8,1,5]=>0011010
[4,6,5,3,7,8,1,2]=>0110010
[4,6,5,2,7,8,3,1]=>0110011
[3,7,5,2,8,6,1,4]=>0110110
[5,6,2,4,7,8,3,1]=>0100011
[5,4,6,2,8,3,7,1]=>1010101
[5,6,3,2,8,4,7,1]=>0110101
[5,6,2,8,3,4,7,1]=>0101001
[3,7,4,8,1,6,5,2]=>0101011
[5,2,6,4,8,7,3,1]=>1010111
[2,4,7,8,6,5,1,3]=>0001110
[2,5,7,8,6,1,4,3]=>0001101
[1,3,6,4,8,2,7,5]=>0010101
[2,4,5,3,8,7,1,6]=>0010110
[8,6,3,7,2,4,1,5]=>1101010
[8,4,6,7,3,5,2,1]=>1001011
[4,8,5,3,2,7,1,6]=>0111010
[5,4,8,1,3,7,2,6]=>1010010
[8,4,5,3,1,7,2,6]=>1011010
[7,4,5,3,1,8,6,2]=>1011011
[5,6,8,7,2,4,3,1]=>0011011
[8,4,6,3,7,5,1,2]=>1010110
[5,7,8,6,4,2,3,1]=>0011101
[6,8,7,5,1,3,2,4]=>0111010
[3,8,2,6,7,5,1,4]=>0100110
[4,7,6,3,8,2,5,1]=>0110101
[6,7,4,1,8,2,5,3]=>0110101
[6,8,4,1,7,5,2,3]=>0110110
[7,5,4,2,1,8,6,3]=>1111011
[5,7,6,8,3,2,4,1]=>0101101
[7,6,4,2,8,1,5,3]=>1110101
[7,4,6,3,8,1,5,2]=>1010101
[3,4,6,8,2,5,7,1]=>0001001
[1,8,5,6,4,2,3,7]=>0101100
[1,8,4,5,6,2,3,7]=>0100100
[6,4,8,5,7,3,1,2]=>1010110
[1,7,6,2,3,5,8,4]=>0110001
[7,2,5,4,6,8,1,3]=>1010010
[7,2,4,5,6,8,1,3]=>1000010
[8,1,6,5,2,7,4,3]=>1011011
[2,7,1,5,3,8,6,4]=>0101011
[3,5,7,2,8,4,1,6]=>0010110
[7,3,2,1,4,8,6,5]=>1110011
[8,3,7,2,6,5,1,4]=>1010110
[7,8,6,1,4,5,2,3]=>0110010
[7,5,8,2,6,1,4,3]=>1010101
[4,5,7,2,8,3,1,6]=>0010110
[8,5,1,3,2,4,6,7]=>1101000
[3,8,5,1,2,4,6,7]=>0110000
[5,1,3,2,4,6,8,7]=>1010001
[5,3,8,1,4,2,6,7]=>1010100
[5,8,4,1,2,3,6,7]=>0110000
[5,1,7,8,4,2,3,6]=>1001100
[1,5,7,8,2,4,3,6]=>0001010
[3,5,8,1,4,2,7,6]=>0010101
[2,8,5,7,1,4,3,6]=>0101010
[4,8,7,5,1,2,3,6]=>0111000
[8,6,4,1,2,3,7,5]=>1110001
[8,1,2,4,6,3,7,5]=>1000101
[6,3,8,4,1,7,2,5]=>1011010
[7,6,1,4,2,3,8,5]=>1101001
[1,7,5,2,3,4,8,6]=>0110001
[7,8,1,2,5,3,4,6]=>0100100
[1,8,7,5,2,3,4,6]=>0111000
[7,1,4,8,2,3,6,5]=>1001001
[1,8,4,7,5,2,3,6]=>0101100
[7,3,4,1,8,6,2,5]=>1010110
[8,4,7,2,1,6,3,5]=>1011010
[7,1,5,3,6,8,2,4]=>1010010
[8,1,5,3,6,7,2,4]=>1010010
[3,6,5,2,4,7,8,1]=>0110001
[2,7,5,4,6,8,1,3]=>0110010
[1,7,5,4,6,8,2,3]=>0110010
[2,7,5,3,6,8,1,4]=>0110010
[4,7,8,2,5,6,1,3]=>0010010
[2,8,5,4,6,7,1,3]=>0110010
[4,7,5,3,8,1,2,6]=>0110100
[4,2,7,6,8,1,3,5]=>1010100
[3,1,7,8,5,6,2,4]=>1001010
[1,3,8,5,6,7,2,4]=>0010010
[3,4,7,8,6,1,2,5]=>0001100
[6,8,3,2,4,1,5,7]=>0110100
[7,6,1,8,2,5,4,3]=>1101011
[7,6,1,8,2,5,3,4]=>1101010
[5,8,4,2,1,6,3,7]=>0111010
[7,6,4,1,2,5,3,8]=>1110010
[8,7,2,6,4,5,3,1]=>1101011
[5,2,3,7,1,8,4,6]=>1001010
[1,7,5,4,8,6,2,3]=>0110110
[4,5,1,6,8,2,7,3]=>0100101
[1,6,3,7,2,4,8,5]=>0101001
[8,7,2,4,1,5,3,6]=>1101010
[5,2,4,1,8,3,6,7]=>1010100
[4,3,1,6,7,2,5,8]=>1100100
[6,3,1,5,7,2,4,8]=>1100100
[6,1,8,2,4,5,3,7]=>1010010
[4,5,2,1,3,7,6,8]=>0110010
[8,2,7,4,1,6,5,3]=>1011011
[3,7,6,4,1,5,8,2]=>0111001
[2,7,6,4,5,1,8,3]=>0110101
[4,6,8,1,7,3,5,2]=>0010101
[2,8,4,6,3,1,5,7]=>0101100
[2,8,3,1,6,7,4,5]=>0110010
[1,3,7,6,5,2,4,8]=>0011100
[1,3,6,7,5,2,4,8]=>0001100
[1,5,2,6,8,7,3,4]=>0100110
[4,8,5,7,1,2,3,6]=>0101000
[7,8,6,1,4,3,2,5]=>0110110
[7,4,8,3,6,2,1,5]=>1010110
[1,5,7,4,8,6,2,3]=>0010110
[4,8,7,5,2,3,1,6]=>0111010
[1,2,7,8,6,4,3,5]=>0001110
[3,5,1,7,8,6,2,4]=>0100110
[1,8,6,7,4,2,3,5]=>0101100
[7,1,3,2,6,5,8,4]=>1010101
[2,4,6,5,8,3,1,7]=>0010110
[2,4,6,5,8,1,7,3]=>0010101
[2,4,6,3,8,7,1,5]=>0010110
[1,5,4,7,3,8,6,2]=>0101011
[2,5,6,4,1,3,8,7]=>0011001
[7,2,3,1,6,8,4,5]=>1010010
[5,7,8,1,6,2,3,4]=>0010100
[1,4,8,3,2,7,5,6]=>0011010
[1,6,3,8,2,7,4,5]=>0101010
[1,6,4,2,7,3,8,5]=>0110101
[1,4,2,5,8,6,3,7]=>0100110
[4,8,2,1,5,7,3,6]=>0110010
[5,2,7,1,6,3,4,8]=>1010100
[4,8,2,5,1,6,3,7]=>0101010
[5,8,1,2,4,6,3,7]=>0100010
[5,1,7,3,6,4,2,8]=>1010110
[3,1,7,5,6,2,4,8]=>1010100
[3,2,7,5,6,1,4,8]=>1010100
[3,2,7,1,6,4,5,8]=>1010100
[6,3,1,7,5,4,2,8]=>1101110
[5,8,3,2,4,1,7,6]=>0110101
[6,1,4,3,7,5,8,2]=>1010101
[1,7,8,6,3,4,2,5]=>0011010
[3,7,8,1,6,4,2,5]=>0010110
[6,4,1,8,2,7,5,3]=>1101011
[1,5,6,8,4,2,7,3]=>0001101
[7,8,5,3,2,1,6,4]=>0111101
[4,7,2,6,1,8,3,5]=>0101010
[8,7,3,5,2,1,6,4]=>1101101
[3,8,6,2,1,7,4,5]=>0111010
[3,6,1,4,7,8,2,5]=>0100010
[2,5,7,1,3,6,4,8]=>0010010
[1,4,7,2,5,3,6,8]=>0010100
[4,5,1,3,8,2,6,7]=>0100100
[4,1,5,3,2,7,6,8]=>1011010
[7,3,5,1,4,2,6,8]=>1010100
[7,5,2,4,1,3,8,6]=>1101001
[6,2,1,7,4,3,8,5]=>1101101
[2,4,3,6,7,1,5,8]=>0100100
[3,1,7,4,2,6,8,5]=>1011001
[7,3,5,2,1,6,4,8]=>1011010
[4,6,5,2,1,3,7,8]=>0111000
[1,4,7,2,5,6,3,8]=>0010010
[7,2,5,6,1,3,8,4]=>1001001
[2,5,6,1,4,3,7,8]=>0010100
[6,1,5,3,7,2,4,8]=>1010100
[3,6,5,4,1,7,2,8]=>0111010
[1,7,4,5,6,8,2,3]=>0100010
[6,8,5,7,2,1,4,3]=>0101101
[1,6,8,7,3,4,2,5]=>0011010
[1,4,2,6,7,8,5,3]=>0100011
[5,6,4,2,1,8,3,7]=>0111010
[4,1,2,6,7,8,5,3]=>1000011
[3,7,8,1,5,2,6,4]=>0010101
[1,5,4,7,8,3,6,2]=>0100101
[5,1,4,7,8,3,6,2]=>1000101
[5,6,4,1,7,3,8,2]=>0110101
[8,3,7,5,4,2,6,1]=>1011101
[4,3,7,8,2,5,1,6]=>1001010
[3,7,8,5,4,2,1,6]=>0011110
[1,7,4,5,6,8,3,2]=>0100011
[2,7,4,5,6,8,3,1]=>0100011
[2,8,3,5,6,4,1,7]=>0100110
[2,4,7,8,3,1,6,5]=>0001101
[5,4,3,6,8,1,7,2]=>1100101
[3,7,4,5,8,1,2,6]=>0100100
[3,7,4,5,8,1,6,2]=>0100101
[1,4,3,5,6,8,2,7]=>0100010
[1,4,6,5,8,2,7,3]=>0010101
[2,4,3,5,8,1,6,7]=>0100100
[4,6,1,7,3,2,8,5]=>0101101
[1,7,3,6,4,2,8,5]=>0101101
[1,3,7,6,2,4,8,5]=>0011001
[4,7,3,5,1,2,8,6]=>0101001
[2,5,1,8,3,7,4,6]=>0101010
[5,1,2,4,3,6,8,7]=>1001001
[4,8,3,5,2,1,6,7]=>0101100
[8,7,3,1,5,2,6,4]=>1110101
[3,8,4,1,7,5,2,6]=>0110110
[7,8,5,3,6,2,1,4]=>0110110
[6,7,1,5,2,8,4,3]=>0101011
[2,7,6,4,8,3,1,5]=>0110110
[2,6,3,7,5,8,4,1]=>0101011
[4,7,3,2,6,5,1,8]=>0110110
[4,7,5,2,3,6,1,8]=>0110010
[4,3,7,8,2,1,6,5]=>1001101
[4,8,7,2,1,5,6,3]=>0111001
[7,3,8,2,5,1,6,4]=>1010101
[4,5,3,8,2,1,7,6]=>0101101
[4,5,3,8,6,1,2,7]=>0101100
[7,3,8,4,5,1,2,6]=>1010100
[4,8,7,5,1,3,2,6]=>0111010
[4,8,7,5,1,2,6,3]=>0111001
[7,8,4,6,1,3,5,2]=>0101001
[4,8,7,5,1,3,6,2]=>0111001
[4,5,3,6,8,1,2,7]=>0100100
[7,8,6,2,1,4,3,5]=>0111010
[4,7,5,8,2,1,3,6]=>0101100
[4,8,5,7,1,3,2,6]=>0101010
[7,8,6,3,1,2,5,4]=>0111001
[4,1,3,6,5,7,2,8]=>1001010
[4,1,3,5,7,2,8,6]=>1000101
[5,1,8,2,4,6,3,7]=>1010010
[6,8,2,1,4,5,3,7]=>0110010
[2,1,4,7,5,3,8,6]=>1001101
[6,8,1,3,5,7,4,2]=>0100011
[5,8,3,2,7,4,6,1]=>0110101
[4,1,3,7,5,6,2,8]=>1001010
[5,1,7,2,4,6,3,8]=>1010010
[4,2,7,3,6,8,5,1]=>1010011
[5,8,4,7,1,3,6,2]=>0101001
[3,1,5,8,6,7,2,4]=>1001010
[6,8,2,1,4,5,7,3]=>0110001
[5,3,1,2,4,6,8,7]=>1100001
[3,6,7,5,8,4,1,2]=>0010110
[6,1,5,2,8,7,4,3]=>1010111
[3,2,6,1,5,8,7,4]=>1010011
[4,5,2,1,6,7,8,3]=>0110001
[8,4,6,3,1,2,7,5]=>1011001
[3,7,6,4,1,5,2,8]=>0111010
[3,8,6,4,1,5,7,2]=>0111001
[8,7,1,4,5,2,3,6]=>1100100
[8,7,1,4,2,5,3,6]=>1101010
[4,8,7,3,1,2,6,5]=>0111001
[3,8,6,4,5,1,7,2]=>0110101
[3,7,6,4,5,1,2,8]=>0110100
[8,4,6,2,1,7,3,5]=>1011010
[7,4,6,3,1,2,8,5]=>1011001
[4,6,3,5,7,1,8,2]=>0100101
[4,6,2,5,7,8,1,3]=>0100010
[4,7,3,5,8,1,6,2]=>0100101
[4,6,3,5,7,1,2,8]=>0100100
[4,7,3,5,8,6,1,2]=>0100110
[4,7,3,5,6,1,2,8]=>0100100
[4,8,3,5,7,1,6,2]=>0100101
[4,8,3,5,6,1,2,7]=>0100100
[4,7,2,5,6,8,1,3]=>0100010
[4,8,2,5,6,7,1,3]=>0100010
[1,4,7,2,6,5,8,3]=>0010101
[1,2,7,8,3,5,4,6]=>0001010
[1,6,7,8,3,2,5,4]=>0001101
[1,7,6,2,8,5,4,3]=>0110111
[1,6,7,8,3,2,4,5]=>0001100
[1,2,7,8,3,4,6,5]=>0001001
[1,7,6,8,3,4,2,5]=>0101010
[8,4,7,3,1,2,6,5]=>1011001
[4,2,8,1,6,5,7,3]=>1010101
[3,1,8,2,6,5,7,4]=>1010101
[2,8,4,3,1,6,5,7]=>0111010
[2,4,3,8,6,5,1,7]=>0101110
[2,8,6,4,3,1,7,5]=>0111101
[7,4,5,8,1,3,6,2]=>1001001
[1,4,6,3,2,5,8,7]=>0011001
[4,2,5,7,1,6,8,3]=>1001001
[4,5,3,7,1,6,8,2]=>0101001
[6,8,4,1,5,7,3,2]=>0110011
[6,8,4,1,5,7,2,3]=>0110010
[5,2,6,7,4,1,8,3]=>1001101
[5,6,7,4,3,1,8,2]=>0011101
[8,5,6,4,1,7,3,2]=>1011011
[5,8,2,6,1,7,4,3]=>0101011
[7,8,3,1,6,4,5,2]=>0110101
[5,8,2,6,3,1,7,4]=>0101101
[4,5,8,1,6,3,7,2]=>0010101
[8,1,4,6,2,5,7,3]=>1001001
[4,8,1,3,6,2,7,5]=>0100101
[4,5,8,1,6,2,7,3]=>0010101
[5,2,6,8,1,4,3,7]=>1001010
[6,2,7,3,8,1,4,5]=>1010100
[6,7,3,8,2,1,4,5]=>0101100
[6,2,7,8,3,1,4,5]=>1001100
[8,7,3,1,2,5,6,4]=>1110001
[2,8,3,6,4,1,7,5]=>0101101
[6,1,3,7,2,8,5,4]=>1001011
[5,4,3,6,1,7,8,2]=>1101001
[4,8,3,2,1,7,5,6]=>0111010
[1,2,4,6,5,8,3,7]=>0001010
[2,4,8,6,3,1,7,5]=>0011101
[3,4,8,1,6,7,2,5]=>0010010
[3,6,7,8,4,1,5,2]=>0001101
[2,3,7,8,4,6,1,5]=>0001010
[1,3,7,8,4,6,2,5]=>0001010
[3,1,7,8,4,6,2,5]=>1001010
[4,8,7,3,6,1,2,5]=>0110100
[5,8,4,3,7,1,2,6]=>0110100
[4,1,8,3,7,5,2,6]=>1010110
[2,4,8,3,6,7,1,5]=>0010010
[2,4,8,6,5,7,1,3]=>0011010
[1,6,5,8,7,3,2,4]=>0101110
[5,6,4,8,7,2,1,3]=>0101110
[7,2,6,8,3,5,1,4]=>1001010
[7,2,8,6,5,3,1,4]=>1011110
[4,8,3,7,6,1,2,5]=>0101100
[4,1,7,8,6,5,2,3]=>1001110
[2,1,8,7,3,5,4,6]=>1011010
[1,7,6,2,3,8,5,4]=>0110011
[1,8,5,3,2,7,4,6]=>0111010
[4,5,1,3,7,6,2,8]=>0100110
[7,2,3,8,6,4,5,1]=>1001101
[3,5,8,1,7,4,2,6]=>0010110
[5,8,1,2,7,6,4,3]=>0100111
[8,7,1,3,2,6,4,5]=>1101010
[1,3,8,5,2,4,6,7]=>0011000
[7,8,6,1,3,2,4,5]=>0110100
[8,1,6,3,7,5,4,2]=>1010111
[8,5,1,3,7,6,4,2]=>1100111
[1,6,4,7,3,8,5,2]=>0101011
[1,6,7,5,8,4,2,3]=>0010110
[7,4,1,6,5,2,8,3]=>1101101
[5,3,8,2,7,6,1,4]=>1010110
[7,4,2,8,6,5,3,1]=>1101111
[5,8,2,7,6,1,4,3]=>0101101
[7,4,8,3,1,6,5,2]=>1011011
[5,8,7,2,6,4,3,1]=>0110111
[6,8,7,5,2,1,4,3]=>0111101
[6,8,7,3,5,1,4,2]=>0110101
[1,8,6,4,7,3,2,5]=>0110110
[7,2,5,4,1,3,8,6]=>1011001
[8,6,7,2,3,5,4,1]=>1010011
[5,4,8,6,7,3,1,2]=>1010110
[4,2,7,3,1,6,8,5]=>1011001
[7,2,6,8,5,1,3,4]=>1001100
[7,3,6,4,2,1,8,5]=>1011101
[4,8,5,2,7,3,1,6]=>0110110
[5,8,6,3,2,1,7,4]=>0111101
[6,4,3,1,8,5,2,7]=>1110110
[7,4,3,1,5,8,6,2]=>1110011
[7,4,8,6,5,3,1,2]=>1011110
[7,8,5,2,6,4,3,1]=>0110111
[7,3,2,1,8,5,6,4]=>1110101
[1,5,7,2,4,3,8,6]=>0010101
[1,2,7,5,8,4,3,6]=>0010110
[5,1,3,8,2,7,4,6]=>1001010
[5,7,1,3,2,8,4,6]=>0101010
[7,1,6,3,2,8,4,5]=>1011010
[8,1,7,2,3,6,5,4]=>1010011
[1,7,2,5,8,4,3,6]=>0100110
[7,1,2,6,4,3,8,5]=>1001101
[1,4,7,8,3,2,5,6]=>0001100
[8,7,1,3,2,4,6,5]=>1101001
[8,1,6,3,2,4,7,5]=>1011001
[1,8,2,7,6,3,5,4]=>0101101
[1,8,6,2,7,4,3,5]=>0110110
[8,1,6,3,2,7,4,5]=>1011010
[8,2,1,7,6,3,4,5]=>1101100
[6,8,4,3,5,1,2,7]=>0110100
[8,7,3,5,4,1,2,6]=>1101100
[8,5,3,6,4,2,1,7]=>1101110
[6,3,8,5,7,2,1,4]=>1010110
[8,7,3,6,4,1,2,5]=>1101100
[5,2,7,4,6,1,3,8]=>1010100
[8,7,2,3,5,1,4,6]=>1100100
[6,4,5,3,1,7,8,2]=>1011001
[6,4,5,3,1,8,7,2]=>1011011
[8,7,3,2,5,1,6,4]=>1110101
[6,3,5,2,8,1,4,7]=>1010100
[6,4,5,3,1,7,2,8]=>1011010
[8,7,2,4,3,1,5,6]=>1101100
[7,6,2,3,1,4,8,5]=>1101001
[4,7,6,2,3,1,5,8]=>0110100
[1,8,2,3,5,6,4,7]=>0100010
[2,8,1,3,5,6,4,7]=>0100010
[2,5,7,4,8,3,6,1]=>0010101
[2,6,3,4,7,8,5,1]=>0100011
[2,3,5,4,7,1,8,6]=>0010101
[7,4,1,3,6,8,5,2]=>1100011
[7,2,1,3,6,8,4,5]=>1100010
[7,4,2,3,6,8,5,1]=>1100011
[7,2,3,6,8,5,4,1]=>1000111
[7,6,3,1,8,5,2,4]=>1110110
[7,2,1,3,6,8,5,4]=>1100011
[7,6,3,8,1,5,2,4]=>1101010
[1,6,4,7,8,5,3,2]=>0100111
[1,2,4,6,8,5,7,3]=>0000101
[8,5,2,3,7,4,1,6]=>1100110
[2,6,3,7,4,1,8,5]=>0101101
[6,1,3,2,8,5,7,4]=>1010101
[3,8,5,1,2,4,7,6]=>0110001
[1,8,3,7,5,2,6,4]=>0101101
[8,1,3,6,5,2,7,4]=>1001101
[7,1,3,8,5,2,6,4]=>1001101
[4,7,1,5,2,6,8,3]=>0101001
[7,4,1,5,2,6,8,3]=>1101001
[3,1,6,7,5,2,8,4]=>1001101
[8,6,2,4,5,1,7,3]=>1100101
[4,6,2,5,3,1,7,8]=>0101100
[7,1,4,5,2,6,8,3]=>1001001
[5,7,6,8,2,1,4,3]=>0101101
[3,5,4,7,8,2,6,1]=>0100101
[5,1,4,7,6,8,3,2]=>1001011
[5,2,4,7,6,8,3,1]=>1001011
[5,6,4,7,1,8,3,2]=>0101011
[3,6,7,5,1,4,8,2]=>0011001
[6,3,7,1,2,5,8,4]=>1010001
[5,1,4,7,8,2,6,3]=>1000101
[6,3,7,5,1,2,8,4]=>1011001
[5,3,7,4,6,1,8,2]=>1010101
[5,4,1,7,6,8,3,2]=>1101011
[4,2,5,3,6,7,8,1]=>1010001
[4,5,1,3,6,7,8,2]=>0100001
[3,6,7,1,5,4,8,2]=>0010101
[3,6,4,7,5,8,2,1]=>0101011
[6,4,7,1,5,2,8,3]=>1010101
[3,5,6,2,1,7,8,4]=>0011001
[2,5,6,7,1,8,4,3]=>0001011
[8,1,4,3,5,2,7,6]=>1010101
[4,8,1,3,5,2,7,6]=>0100101
[4,5,1,6,2,8,7,3]=>0101011
[4,5,1,7,2,8,6,3]=>0101011
[7,1,4,3,6,8,2,5]=>1010010
[5,6,3,2,7,4,1,8]=>0110110
[5,2,6,7,4,3,1,8]=>1001110
[8,5,1,6,4,3,2,7]=>1101110
[8,5,1,6,4,3,7,2]=>1101101
[8,5,2,1,6,4,3,7]=>1110110
[8,6,3,5,2,7,1,4]=>1101010
[8,4,6,2,1,5,7,3]=>1011001
[5,6,2,1,8,4,7,3]=>0110101
[8,5,2,1,6,4,7,3]=>1110101
[1,7,2,8,5,4,6,3]=>0101101
[6,7,1,4,8,5,3,2]=>0100111
[7,4,8,2,1,5,6,3]=>1011001
[7,3,2,8,5,1,4,6]=>1101100
[6,7,1,4,3,2,8,5]=>0101101
[4,1,7,3,2,8,5,6]=>1011010
[8,3,5,2,4,7,1,6]=>1010010
[4,3,7,8,6,1,5,2]=>1001101
[6,2,8,4,3,7,1,5]=>1011010
[1,2,6,3,7,8,5,4]=>0010011
[6,1,3,2,7,8,5,4]=>1010011
[6,7,1,3,2,8,5,4]=>0101011
[2,6,4,7,5,3,1,8]=>0101110
[5,6,3,7,2,8,4,1]=>0101011
[4,5,1,8,6,2,7,3]=>0101101
[5,6,1,8,7,2,3,4]=>0101100
[4,5,1,6,8,7,3,2]=>0100111
[2,4,6,3,5,1,7,8]=>0010100
[4,1,6,2,5,8,3,7]=>1010010
[1,8,2,5,7,3,4,6]=>0100100
[3,8,2,5,4,1,6,7]=>0101100
[1,4,6,3,8,5,2,7]=>0010110
[4,5,6,3,1,7,2,8]=>0011010
[3,4,6,2,5,1,7,8]=>0010100
[6,2,1,5,8,3,4,7]=>1100100
[1,5,7,3,6,2,4,8]=>0010100
[1,4,7,5,2,3,6,8]=>0011000
[1,4,6,5,8,2,3,7]=>0010100
[1,5,8,6,2,3,4,7]=>0011000
[1,4,8,3,7,6,2,5]=>0010110
[1,4,5,3,7,2,6,8]=>0010100
[1,4,8,7,3,6,2,5]=>0011010
[8,3,5,1,6,4,7,2]=>1010101
[5,8,4,3,6,2,7,1]=>0110101
[4,6,5,8,3,2,7,1]=>0101101
[3,4,7,5,6,8,2,1]=>0010011
[3,4,7,8,5,2,6,1]=>0001101
[2,3,8,4,7,1,6,5]=>0010101
[1,8,7,5,2,6,3,4]=>0111010
[1,8,7,5,4,3,2,6]=>0111110
[1,7,6,3,4,5,8,2]=>0110001
[1,8,7,4,5,6,2,3]=>0110010
[1,8,7,3,6,4,2,5]=>0110110
[1,8,7,2,4,6,3,5]=>0110010
[1,4,7,8,6,2,5,3]=>0001101
[1,7,6,4,2,5,3,8]=>0111010
[1,4,7,5,8,2,3,6]=>0010100
[1,4,7,5,8,2,6,3]=>0010101
[1,6,8,3,4,2,5,7]=>0010100
[1,4,7,2,3,6,5,8]=>0010010
[1,3,2,6,8,4,7,5]=>0100101
[1,7,2,5,6,3,4,8]=>0100100
[1,5,8,3,6,4,7,2]=>0010101
[1,2,6,5,8,3,4,7]=>0010100
[1,6,8,2,7,3,4,5]=>0010100
[1,4,5,8,2,6,3,7]=>0001010
[3,5,6,7,2,4,1,8]=>0001010
[6,4,7,5,2,3,1,8]=>1011010
[1,5,6,4,8,3,2,7]=>0010110
[5,2,6,4,8,7,1,3]=>1010110
[2,1,5,6,4,8,3,7]=>1001010
[5,1,4,7,8,6,2,3]=>1000110
[2,5,7,1,8,6,3,4]=>0010110
[1,6,7,2,8,5,4,3]=>0010111
[4,6,1,7,8,5,3,2]=>0100111
[5,3,2,1,7,8,6,4]=>1110011
[7,4,3,8,6,1,5,2]=>1101101
[4,3,7,1,5,8,6,2]=>1010011
[8,2,4,5,3,1,7,6]=>1001101
[8,5,3,2,4,1,7,6]=>1110101
[1,4,3,2,7,5,8,6]=>0110101
[4,8,7,2,6,1,3,5]=>0110100
[4,5,8,2,1,7,3,6]=>0011010
[6,8,4,1,7,3,2,5]=>0110110
[7,6,2,8,4,5,3,1]=>1101011
[7,8,2,6,4,5,3,1]=>0101011
[2,8,3,1,7,5,6,4]=>0110101
[1,8,3,5,2,6,4,7]=>0101010
[2,5,8,4,6,1,3,7]=>0010100
[1,8,4,5,6,2,7,3]=>0100101
[2,3,8,7,4,5,1,6]=>0011010
[2,4,8,5,7,3,1,6]=>0010110
[1,8,3,5,7,4,2,6]=>0100110
[2,5,8,4,6,7,1,3]=>0010010
[3,5,6,8,4,7,1,2]=>0001010
[3,5,6,8,4,2,7,1]=>0001101
[2,5,8,4,6,3,7,1]=>0010101
[1,8,4,5,6,3,2,7]=>0100110
[7,2,5,3,4,6,1,8]=>1010010
[7,1,2,6,4,3,5,8]=>1001100
[7,1,2,6,3,4,5,8]=>1001000
[7,1,2,6,4,5,3,8]=>1001010
[7,1,2,6,5,3,4,8]=>1001100
[5,3,1,4,7,2,8,6]=>1100101
[7,1,3,8,2,6,4,5]=>1001010
[1,8,3,7,2,4,6,5]=>0101001
[2,7,5,6,4,8,1,3]=>0101010
[2,8,3,6,5,7,1,4]=>0101010
[7,4,3,1,6,5,2,8]=>1110110
[3,5,1,2,6,8,7,4]=>0100011
[1,5,2,4,3,8,7,6]=>0101011
[3,1,2,4,8,7,5,6]=>1000110
[5,2,1,6,3,8,7,4]=>1101011
[6,2,5,3,4,7,1,8]=>1010010
[5,2,7,3,4,6,1,8]=>1010010
[7,1,2,6,3,8,4,5]=>1001010
[8,1,2,7,5,3,4,6]=>1001100
[7,2,8,1,5,3,4,6]=>1010100
[4,2,8,1,3,7,5,6]=>1010010
[1,7,4,2,3,8,5,6]=>0110010
[7,5,1,8,2,3,4,6]=>1101000
[8,2,4,1,3,7,5,6]=>1010010
[8,1,7,5,2,3,4,6]=>1011000
[8,1,6,2,3,7,4,5]=>1010010
[7,1,8,2,3,6,4,5]=>1010010
[3,4,6,7,2,1,5,8]=>0001100
[2,5,7,4,6,8,1,3]=>0010010
[4,6,2,7,5,8,1,3]=>0101010
[4,7,2,5,3,8,1,6]=>0101010
[2,4,7,6,3,8,1,5]=>0011010
[5,8,3,6,4,1,7,2]=>0101101
[4,6,8,5,1,2,3,7]=>0011000
[4,6,5,7,1,2,3,8]=>0101000
[4,6,5,7,1,3,8,2]=>0101001
[3,4,7,6,1,8,2,5]=>0011010
[8,5,6,7,4,1,3,2]=>1001101
[1,6,5,7,3,8,2,4]=>0101010
[7,2,4,8,6,1,5,3]=>1001101
[7,1,4,8,6,5,2,3]=>1001110
[8,6,2,1,3,7,5,4]=>1110011
[8,1,4,6,7,2,5,3]=>1000101
[8,1,4,6,2,7,5,3]=>1001011
[8,6,1,3,2,7,5,4]=>1101011
[8,1,7,5,2,4,6,3]=>1011001
[8,6,2,7,5,3,1,4]=>1101110
[8,2,7,5,4,1,6,3]=>1011101
[8,2,1,6,7,4,5,3]=>1100101
[8,7,2,1,5,3,6,4]=>1110101
[8,6,1,2,7,3,5,4]=>1100101
[8,1,6,2,4,7,5,3]=>1010011
[5,2,6,7,4,8,3,1]=>1001011
[6,2,3,8,7,4,5,1]=>1001101
[8,5,7,1,4,2,6,3]=>1010101
[2,6,7,1,4,3,8,5]=>0010101
[4,5,2,1,6,3,8,7]=>0110101
[4,5,2,1,6,7,3,8]=>0110010
[5,3,8,6,2,4,7,1]=>1011001
[2,5,1,6,4,3,8,7]=>0101101
[3,6,2,8,5,7,1,4]=>0101010
[4,6,8,1,5,7,2,3]=>0010010
[4,1,2,5,7,6,3,8]=>1000110
[5,2,3,8,7,1,6,4]=>1001101
[3,2,8,1,7,5,4,6]=>1010110
[4,8,5,1,3,7,2,6]=>0110010
[4,6,5,8,1,7,3,2]=>0101011
[2,1,3,6,4,8,7,5]=>1001011
[4,8,2,1,6,7,5,3]=>0110011
[4,8,1,2,7,5,6,3]=>0100101
[5,2,8,1,7,4,6,3]=>1010101
[5,7,4,8,1,2,6,3]=>0101001
[4,5,1,6,8,7,2,3]=>0100110
[3,4,7,1,5,8,2,6]=>0010010
[6,2,7,4,5,3,1,8]=>1010110
[6,8,7,5,4,1,2,3]=>0111100
[4,3,8,6,1,2,5,7]=>1011000
[4,8,6,5,7,1,3,2]=>0110101
[4,8,1,5,3,6,7,2]=>0101001
[8,4,6,7,5,1,3,2]=>1001101
[8,3,4,2,7,6,1,5]=>1010110
[8,7,5,6,4,1,3,2]=>1101101
[8,7,4,2,3,6,5,1]=>1110011
[8,4,2,3,7,6,5,1]=>1100111
[8,6,4,7,5,1,3,2]=>1101101
[5,3,6,4,1,2,8,7]=>1011001
[5,4,1,7,8,6,2,3]=>1100110
[6,1,4,7,5,8,2,3]=>1001010
[2,1,7,5,8,6,3,4]=>1010110
[5,3,4,7,8,1,6,2]=>1000101
[5,1,4,8,2,3,7,6]=>1001001
[5,8,6,3,1,2,4,7]=>0111000
[7,4,8,6,3,5,1,2]=>1011010
[8,4,1,6,2,7,5,3]=>1101011
[4,2,7,1,5,8,3,6]=>1010010
[4,6,3,5,1,8,2,7]=>0101010
[8,5,7,6,2,3,4,1]=>1011001
[8,4,2,3,6,7,5,1]=>1100011
[4,1,7,6,2,8,3,5]=>1011010
[2,7,5,3,1,4,8,6]=>0111001
[4,1,7,2,8,5,3,6]=>1010110
[2,6,5,3,8,4,7,1]=>0110101
[7,1,4,3,6,5,8,2]=>1010101
[7,1,6,3,5,4,8,2]=>1010101
[5,7,3,2,8,4,1,6]=>0110110
[2,8,7,1,6,5,3,4]=>0110110
[2,8,6,1,7,5,3,4]=>0110110
[8,1,5,2,7,4,3,6]=>1010110
[2,6,8,1,7,5,3,4]=>0010110
[1,4,6,5,3,8,2,7]=>0011010
[2,4,5,8,7,1,3,6]=>0001100
[3,1,6,8,7,5,4,2]=>1001111
[3,1,8,7,5,6,4,2]=>1011011
[5,1,8,7,6,3,4,2]=>1011101
[1,3,8,4,7,2,6,5]=>0010101
[1,8,2,4,7,3,6,5]=>0100101
[8,2,7,5,3,6,4,1]=>1011011
[8,4,1,3,6,7,2,5]=>1100010
[8,7,2,3,1,5,6,4]=>1101001
[1,2,8,6,7,5,4,3]=>0010111
[2,8,5,7,6,1,3,4]=>0101100
[1,8,7,2,6,4,5,3]=>0110101
[8,7,2,1,6,4,5,3]=>1110101
[8,7,2,4,3,6,5,1]=>1101011
[4,2,8,7,3,6,5,1]=>1011011
[8,7,1,6,4,3,5,2]=>1101101
[8,4,1,7,3,6,5,2]=>1101011
[4,5,1,8,7,3,6,2]=>0101101
[4,3,8,5,2,7,1,6]=>1011010
[5,6,8,2,3,4,1,7]=>0010010
[3,6,4,7,5,2,1,8]=>0101110
[5,7,4,1,2,6,8,3]=>0110001
[2,8,6,7,5,3,1,4]=>0101110
[7,4,5,2,6,3,1,8]=>1010110
[8,4,5,3,6,1,7,2]=>1010101
[8,6,3,4,5,1,7,2]=>1100101
[8,6,3,5,4,1,7,2]=>1101101
[8,7,4,5,1,3,6,2]=>1101001
[8,4,5,2,6,1,7,3]=>1010101
[8,6,2,5,3,1,4,7]=>1101100
[8,4,7,3,1,2,5,6]=>1011000
[8,7,3,5,1,6,4,2]=>1101011
[8,6,2,3,5,1,7,4]=>1100101
[4,8,3,2,6,1,7,5]=>0110101
[5,2,6,3,7,8,4,1]=>1010011
[3,6,2,5,7,8,4,1]=>0100011
[2,7,4,6,8,3,5,1]=>0100101
[2,7,3,6,8,5,4,1]=>0100111
[3,7,6,8,1,5,4,2]=>0101011
[4,7,6,8,2,3,5,1]=>0101001
[3,7,5,6,8,2,4,1]=>0100101
[3,7,2,6,8,4,5,1]=>0100101
[1,5,7,6,8,4,2,3]=>0010110
[2,7,5,6,8,4,3,1]=>0100111
[3,7,6,8,5,1,4,2]=>0101101
[7,1,3,8,6,2,4,5]=>1001100
[2,7,1,8,6,5,3,4]=>0101110
[8,1,5,2,6,4,7,3]=>1010101
[5,3,4,7,6,2,1,8]=>1001110
[8,7,2,6,4,5,1,3]=>1101010
[3,1,2,8,7,5,4,6]=>1001110
[3,1,2,8,7,6,4,5]=>1001110
[4,5,2,6,7,3,8,1]=>0100101
[3,5,1,6,7,4,8,2]=>0100101
[6,5,8,1,4,3,7,2]=>1010101
[6,4,1,2,5,7,8,3]=>1100001
[6,1,5,4,2,7,3,8]=>1011010
[6,4,2,3,1,7,5,8]=>1101010
[4,6,1,3,5,7,2,8]=>0100010
[2,4,5,7,3,6,1,8]=>0001010
[3,4,6,1,8,2,7,5]=>0010101
[2,4,1,7,5,6,3,8]=>0101010
[5,3,1,4,7,6,2,8]=>1100110
[6,4,5,2,7,1,3,8]=>1010100
[7,4,3,5,1,6,2,8]=>1101010
[7,5,3,6,2,1,4,8]=>1101100
[6,4,3,7,1,8,2,5]=>1101010
[3,1,2,7,6,4,5,8]=>1001100
[5,1,2,7,6,3,4,8]=>1001100
[5,6,1,7,2,4,3,8]=>0101010
[2,6,5,7,1,3,4,8]=>0101000
[2,3,7,1,5,6,4,8]=>0010010
[5,6,1,3,2,4,7,8]=>0101000
[2,6,5,3,4,1,7,8]=>0110100
[2,6,1,3,5,4,7,8]=>0100100
[3,6,7,1,4,2,5,8]=>0010100
[3,6,5,2,7,1,4,8]=>0110100
[7,1,5,4,2,6,3,8]=>1011010
[4,6,1,5,2,8,7,3]=>0101011
[6,1,5,4,2,7,8,3]=>1011001
[4,6,1,5,2,7,8,3]=>0101001
[4,5,1,7,6,2,8,3]=>0101101
[2,8,6,5,1,3,7,4]=>0111001
[5,1,8,6,2,7,4,3]=>1011011
[3,6,8,2,7,5,1,4]=>0010110
[7,8,5,3,2,6,1,4]=>0111010
[6,8,3,2,7,5,1,4]=>0110110
[5,6,4,1,7,2,8,3]=>0110101
[1,6,7,2,4,3,5,8]=>0010100
[8,1,3,2,4,6,5,7]=>1010010
[1,6,2,7,8,4,5,3]=>0100101
[1,6,7,8,3,4,2,5]=>0001010
[7,2,1,8,3,6,4,5]=>1101010
[5,4,2,3,1,7,8,6]=>1101001
[2,1,3,8,6,4,7,5]=>1001101
[4,6,1,3,2,8,5,7]=>0101010
[4,6,5,3,8,2,1,7]=>0110110
[8,2,5,4,3,7,1,6]=>1011010
[5,8,4,3,7,6,2,1]=>0110111
[8,1,5,3,4,7,2,6]=>1010010
[6,1,8,7,4,5,3,2]=>1011011
[1,5,8,6,4,3,7,2]=>0011101
[2,5,8,6,4,3,7,1]=>0011101
[8,5,4,1,2,3,7,6]=>1110001
[8,5,2,4,1,3,7,6]=>1101001
[4,5,8,7,3,6,2,1]=>0011011
[5,8,6,4,2,1,7,3]=>0111101
[2,6,1,8,4,7,5,3]=>0101011
[5,3,8,6,1,2,7,4]=>1011001
[5,8,1,4,6,2,7,3]=>0100101
[6,3,2,8,4,5,1,7]=>1101010
[5,4,7,2,1,3,8,6]=>1011001
[8,4,6,5,2,7,3,1]=>1011011
[6,4,7,5,8,3,1,2]=>1010110
[4,6,7,5,1,8,3,2]=>0011011
[2,6,4,5,7,1,8,3]=>0100101
[4,1,7,6,5,2,8,3]=>1011101
[3,7,4,6,1,5,8,2]=>0101001
[3,4,6,5,2,8,1,7]=>0011010
[4,6,7,5,8,2,1,3]=>0010110
[6,4,7,1,2,3,8,5]=>1010001
[5,6,4,2,1,7,3,8]=>0111010
[6,5,7,1,2,8,3,4]=>1010010
[6,4,7,1,2,5,3,8]=>1010010
[5,7,6,3,1,2,8,4]=>0111001
[1,2,7,5,8,6,3,4]=>0010110
[7,4,5,1,6,8,2,3]=>1010010
[1,7,8,4,2,6,3,5]=>0011010
[6,3,2,5,7,4,1,8]=>1100110
[6,2,1,5,3,7,8,4]=>1101001
[7,5,6,1,4,3,8,2]=>1010101
[4,1,7,8,3,6,5,2]=>1001011
[6,3,2,4,8,5,1,7]=>1100110
[6,4,2,1,7,3,5,8]=>1110100
[5,7,4,2,1,6,3,8]=>0111010
[5,8,4,2,1,3,6,7]=>0111000
[2,7,3,8,5,6,4,1]=>0101011
[8,3,2,6,5,1,7,4]=>1101101
[1,8,5,6,4,3,7,2]=>0101101
[1,7,5,8,4,6,3,2]=>0101011
[8,3,5,6,1,7,2,4]=>1001010
[1,5,3,7,8,4,6,2]=>0100101
[1,4,7,3,5,8,6,2]=>0010011
[1,6,3,7,8,5,4,2]=>0100111
[8,5,6,1,7,4,2,3]=>1010110
[8,6,1,4,3,7,2,5]=>1101010
[3,7,8,2,5,1,6,4]=>0010101
[8,1,3,5,6,4,2,7]=>1000110
[8,6,1,4,3,2,7,5]=>1101101
[7,3,8,2,4,1,5,6]=>1010100
[6,3,7,8,1,2,5,4]=>1001001
[7,5,8,1,2,3,6,4]=>1010001
[8,6,1,5,3,7,2,4]=>1101010
[8,1,7,5,6,4,2,3]=>1010110
[8,1,4,7,6,5,2,3]=>1001110
[6,1,4,8,2,7,5,3]=>1001011
[4,6,8,5,1,2,7,3]=>0011001
[2,8,4,6,1,3,7,5]=>0101001
[5,2,7,8,4,1,3,6]=>1001100
[4,6,8,5,3,1,2,7]=>0011100
[8,6,4,2,7,3,5,1]=>1110101
[6,8,7,5,2,1,3,4]=>0111100
[7,6,1,5,2,3,8,4]=>1101001
[5,1,8,6,7,2,3,4]=>1010100
[5,7,1,6,8,2,3,4]=>0100100
[5,1,7,6,8,2,3,4]=>1010100
[6,1,5,7,2,8,3,4]=>1001010
[6,8,4,2,1,7,3,5]=>0111010
[5,8,6,1,7,2,3,4]=>0110100
[6,3,2,8,1,7,4,5]=>1101010
[1,4,7,8,3,5,2,6]=>0001010
[2,5,6,8,1,4,7,3]=>0001001
[8,4,5,1,6,7,2,3]=>1010010
[7,3,6,1,4,2,8,5]=>1010101
[7,4,1,6,5,2,3,8]=>1101100
[4,1,6,5,2,3,8,7]=>1011001
[4,5,1,7,8,6,2,3]=>0100110
[8,3,1,4,6,2,7,5]=>1100101
[2,5,3,4,6,8,1,7]=>0100010
[8,3,6,1,5,2,4,7]=>1010100
[4,7,1,2,5,6,3,8]=>0100010
[6,7,3,1,8,2,4,5]=>0110100
[7,3,1,4,6,2,8,5]=>1100101
[7,4,1,2,5,6,3,8]=>1100010
[4,5,1,3,6,8,7,2]=>0100011
[8,4,1,2,5,7,3,6]=>1100010
[8,4,1,3,6,7,5,2]=>1100011
[5,4,1,6,3,7,8,2]=>1101001
[6,7,3,1,5,2,4,8]=>0110100
[5,4,1,3,6,8,7,2]=>1100011
[6,4,1,2,5,8,3,7]=>1100010
[5,7,4,8,1,6,3,2]=>0101011
[7,5,3,6,4,2,1,8]=>1101110
[4,3,1,2,6,5,7,8]=>1100100
[4,3,1,2,5,7,6,8]=>1100010
[4,7,3,1,5,2,8,6]=>0110101
[8,3,6,5,7,4,2,1]=>1010111
[8,2,6,5,7,4,3,1]=>1010111
[8,1,4,2,6,5,7,3]=>1010101
[8,4,7,1,5,2,6,3]=>1010101
[8,2,6,3,7,4,5,1]=>1010101
[8,2,6,3,7,5,4,1]=>1010111
[8,2,5,3,7,6,4,1]=>1010111
[8,6,7,1,4,3,5,2]=>1010101
[8,5,7,1,4,3,6,2]=>1010101
[4,5,3,6,8,7,1,2]=>0100110
[6,5,1,2,7,4,8,3]=>1100101
[6,8,5,1,7,3,4,2]=>0110101
[5,3,8,1,4,2,7,6]=>1010101
[6,5,3,4,1,8,2,7]=>1101010
[3,1,8,4,2,7,6,5]=>1011011
[2,8,7,4,1,3,6,5]=>0111001
[8,2,3,1,7,6,4,5]=>1010110
[5,2,4,1,6,8,3,7]=>1010010
[8,7,2,3,1,6,4,5]=>1101010
[6,2,3,1,7,8,4,5]=>1010010
[7,2,5,8,3,1,4,6]=>1001100
[6,8,2,3,1,7,4,5]=>0101010
[8,2,5,7,3,1,4,6]=>1001100
[2,5,8,7,3,1,4,6]=>0011100
[2,8,7,3,1,4,5,6]=>0111000
[8,2,3,1,6,7,4,5]=>1010010
[2,8,4,1,3,6,7,5]=>0110001
[2,7,3,1,4,5,8,6]=>0110001
[7,2,8,3,1,4,5,6]=>1011000
[2,7,8,3,1,4,5,6]=>0011000
[5,3,2,8,7,1,6,4]=>1101101
[6,8,7,2,1,5,4,3]=>0111011
[8,2,5,4,1,6,7,3]=>1011001
[7,2,4,6,8,1,5,3]=>1000101
[6,2,5,4,7,8,1,3]=>1010010
[6,3,5,2,7,1,4,8]=>1010100
[8,5,6,3,7,2,1,4]=>1010110
[3,8,2,6,1,7,4,5]=>0101010
[5,7,1,3,6,2,4,8]=>0100100
[3,6,4,1,2,5,7,8]=>0110000
[3,6,4,1,2,5,8,7]=>0110001
[4,7,1,3,2,5,8,6]=>0101001
[4,7,1,3,2,6,8,5]=>0101001
[5,7,1,3,6,2,8,4]=>0100101
[6,8,2,5,7,3,1,4]=>0100110
[4,8,5,2,3,6,1,7]=>0110010
[5,8,6,3,4,7,2,1]=>0110011
[3,7,5,4,2,8,1,6]=>0111010
[4,6,5,1,7,8,2,3]=>0110010
[4,7,1,3,2,8,5,6]=>0101010
[3,6,5,1,8,2,4,7]=>0110100
[5,8,7,3,4,2,6,1]=>0110101
[3,8,5,4,2,1,6,7]=>0111100
[4,8,5,3,6,1,7,2]=>0110101
[6,3,1,5,4,8,2,7]=>1101010
[8,4,2,6,5,7,3,1]=>1101011
[4,7,6,3,5,2,8,1]=>0110101
[1,7,5,3,4,8,6,2]=>0110011
[4,8,6,2,5,7,3,1]=>0110011
[8,7,3,2,6,4,5,1]=>1110101
[8,3,1,4,7,5,2,6]=>1100110
[5,3,1,6,4,8,7,2]=>1101011
[3,4,8,5,7,2,6,1]=>0010101
[4,1,7,8,3,2,5,6]=>1001100
[8,5,1,2,7,6,4,3]=>1100111
[4,6,5,3,1,8,7,2]=>0111011
[8,1,6,7,4,5,3,2]=>1001011
[6,4,8,1,5,3,7,2]=>1010101
[6,4,7,2,5,3,1,8]=>1010110
[4,3,6,1,2,7,8,5]=>1010001
[2,7,4,6,3,8,1,5]=>0101010
[7,3,5,6,4,1,8,2]=>1001101
[5,7,6,3,4,2,1,8]=>0110110
[3,7,5,6,4,2,1,8]=>0101110
[5,7,3,6,4,2,1,8]=>0101110
[5,7,3,6,4,1,8,2]=>0101101
[3,7,5,6,4,1,8,2]=>0101101
[5,7,6,3,4,1,8,2]=>0110101
[3,2,7,5,6,1,8,4]=>1010101
[5,3,4,7,6,1,8,2]=>1001101
[5,3,4,2,7,1,8,6]=>1010101
[3,5,4,1,7,8,6,2]=>0110011
[2,4,6,5,1,8,7,3]=>0011011
[2,4,6,5,1,8,3,7]=>0011010
[2,4,6,1,8,7,3,5]=>0010110
[2,4,6,5,8,3,7,1]=>0010101
[2,4,6,8,5,3,1,7]=>0001110
[2,4,6,8,5,3,7,1]=>0001101
[2,4,6,8,5,7,3,1]=>0001011
[2,4,6,5,3,8,1,7]=>0011010
[2,4,6,5,8,7,1,3]=>0010110
[2,4,6,8,7,5,1,3]=>0001110
[2,4,6,8,5,7,1,3]=>0001010
[2,4,6,8,7,1,5,3]=>0001101
[2,4,6,8,7,1,3,5]=>0001100
[2,4,6,8,1,7,3,5]=>0001010
[2,7,6,4,3,8,5,1]=>0111011
[2,6,7,5,3,8,1,4]=>0011010
[3,6,7,5,8,2,4,1]=>0010101
[4,5,2,6,8,7,1,3]=>0100110
[4,5,2,6,8,3,1,7]=>0100110
[4,5,3,6,8,2,1,7]=>0100110
[3,1,2,7,5,8,4,6]=>1001010
[4,8,1,6,2,5,3,7]=>0101010
[1,5,8,3,4,6,2,7]=>0010010
[7,5,8,2,4,3,6,1]=>1010101
[8,1,5,3,4,6,2,7]=>1010010
[8,1,2,4,7,5,6,3]=>1000101
[2,7,3,8,4,5,6,1]=>0101001
[1,7,8,6,4,5,3,2]=>0011011
[5,8,7,2,4,3,6,1]=>0110101
[1,8,2,4,7,5,6,3]=>0100101
[1,7,2,4,8,5,6,3]=>0100101
[5,8,2,3,7,4,6,1]=>0100101
[7,8,2,3,5,4,6,1]=>0100101
[8,4,1,3,2,6,5,7]=>1101010
[2,8,3,1,4,6,5,7]=>0110010
[8,7,2,3,5,4,6,1]=>1100101
[1,7,6,8,4,5,3,2]=>0101011
[8,5,2,3,7,4,6,1]=>1100101
[7,4,1,3,8,5,6,2]=>1100101
[2,7,3,1,8,5,6,4]=>0110101
[2,8,6,1,5,7,4,3]=>0110011
[8,3,5,1,7,6,4,2]=>1010111
[8,3,5,4,7,1,6,2]=>1010101
[6,4,1,5,7,8,2,3]=>1100010
[8,4,1,5,6,2,7,3]=>1100101
[1,8,5,3,2,4,6,7]=>0111000
[4,8,5,1,2,3,6,7]=>0110000
[3,5,1,4,2,6,8,7]=>0101001
[4,8,7,1,2,5,3,6]=>0110010
[8,7,2,6,1,4,3,5]=>1101010
[1,7,6,8,4,2,3,5]=>0101100
[1,7,4,8,2,5,3,6]=>0101010
[6,1,7,3,8,2,4,5]=>1010100
[1,5,8,2,3,4,7,6]=>0010001
[8,4,2,7,1,3,6,5]=>1101001
[7,1,8,6,4,2,3,5]=>1011100
[1,7,8,6,4,2,3,5]=>0011100
[3,1,2,5,7,6,8,4]=>1000101
[7,1,3,2,4,6,8,5]=>1010001
[7,4,2,3,1,6,8,5]=>1101001
[5,1,7,3,2,6,8,4]=>1011001
[4,8,2,3,7,5,1,6]=>0100110
[6,8,5,3,4,2,1,7]=>0110110
[8,7,2,4,3,5,6,1]=>1101001
[8,1,3,6,4,5,2,7]=>1001010
[8,1,3,7,4,5,6,2]=>1001001
[8,1,3,2,7,5,4,6]=>1010110
[8,1,2,4,7,3,5,6]=>1000100
[7,1,2,4,8,3,5,6]=>1000100
[7,6,2,8,4,5,1,3]=>1101010
[8,7,5,3,2,6,4,1]=>1111011
[4,8,3,2,5,1,6,7]=>0110100
[4,3,8,5,1,2,7,6]=>1011001
[3,1,8,4,5,2,7,6]=>1010101
[8,3,6,2,1,5,4,7]=>1011010
[8,2,1,6,5,3,4,7]=>1101100
[2,3,7,6,1,8,4,5]=>0011010
[4,7,8,2,1,3,5,6]=>0011000
[4,8,5,2,1,3,7,6]=>0111001
[2,3,7,4,1,8,6,5]=>0011011
[5,8,4,2,1,3,7,6]=>0111001
[4,5,2,3,8,7,1,6]=>0100110
[4,6,7,5,2,3,1,8]=>0011010
[6,5,2,3,1,8,7,4]=>1101011
[6,2,5,3,1,8,7,4]=>1011011
[6,2,5,3,8,7,1,4]=>1010110
[6,4,5,3,8,7,1,2]=>1010110
[1,6,4,5,8,7,3,2]=>0100111
[8,4,7,5,2,3,1,6]=>1011010
[8,2,7,4,5,3,1,6]=>1010110
[6,2,4,7,5,3,1,8]=>1001110
[8,2,4,7,5,3,1,6]=>1001110
[8,2,6,7,5,3,1,4]=>1001110
[8,4,6,7,5,3,1,2]=>1001110
[6,4,5,8,7,3,1,2]=>1001110
[6,2,8,7,5,3,1,4]=>1011110
[2,4,8,7,5,3,1,6]=>0011110
[4,6,8,7,5,3,1,2]=>0011110
[4,6,5,3,8,7,1,2]=>0110110
[2,6,5,8,7,3,1,4]=>0101110
[6,7,2,4,5,3,1,8]=>0100110
[4,5,8,7,2,3,1,6]=>0011010
[4,8,7,2,5,3,1,6]=>0110110
[6,8,7,4,5,3,1,2]=>0110110
[2,8,4,7,5,3,1,6]=>0101110
[4,8,2,7,5,3,1,6]=>0101110
[6,8,2,7,5,3,1,4]=>0101110
[7,4,3,8,1,6,5,2]=>1101011
[1,3,6,7,4,5,8,2]=>0001001
[7,4,1,3,6,8,2,5]=>1100010
[5,1,7,3,4,6,8,2]=>1010001
[6,1,7,3,5,8,2,4]=>1010010
[6,8,1,2,7,3,4,5]=>0100100
[5,6,2,1,8,3,4,7]=>0110100
[6,4,1,3,7,8,2,5]=>1100010
[1,6,2,8,7,3,4,5]=>0101100
[5,2,8,4,7,1,3,6]=>1010100
[3,8,7,2,6,1,4,5]=>0110100
[2,5,1,8,3,6,4,7]=>0101010
[2,3,8,1,4,6,5,7]=>0010010
[1,3,8,2,5,4,7,6]=>0010101
[3,1,8,4,6,2,5,7]=>1010100
[6,3,2,4,8,7,1,5]=>1100110
[1,4,8,6,2,3,5,7]=>0011000
[3,1,8,4,5,6,2,7]=>1010010
[4,5,8,3,6,1,7,2]=>0010101
[3,5,4,8,6,1,7,2]=>0101101
[4,2,7,8,6,3,1,5]=>1001110
[7,1,4,2,8,6,3,5]=>1010110
[2,3,7,4,8,1,6,5]=>0010101
[1,6,2,7,4,5,3,8]=>0101010
[1,7,5,4,6,2,3,8]=>0110100
[5,2,8,6,3,1,4,7]=>1011100
[5,2,8,6,3,1,7,4]=>1011101
[7,1,5,6,3,2,8,4]=>1001101
[6,2,7,5,3,1,4,8]=>1011100
[6,1,7,4,8,5,2,3]=>1010110
[8,2,4,6,3,1,7,5]=>1001101
[7,4,8,3,5,6,2,1]=>1010011
[2,6,1,4,7,5,8,3]=>0100101
[5,1,4,3,7,8,6,2]=>1010011
[6,4,1,3,7,8,5,2]=>1100011
[3,1,5,7,2,6,8,4]=>1001001
[7,2,4,8,5,1,6,3]=>1001101
[3,1,7,5,2,6,8,4]=>1011001
[3,2,7,5,1,6,8,4]=>1011001
[5,2,7,3,1,6,8,4]=>1011001
[6,7,2,1,3,4,8,5]=>0110001
[4,6,3,1,2,7,8,5]=>0110001
[6,7,3,1,2,4,8,5]=>0110001
[3,8,5,2,1,6,7,4]=>0111001
[6,8,2,3,5,7,4,1]=>0100011
[5,3,8,4,6,7,2,1]=>1010011
[6,2,8,1,7,4,5,3]=>1010101
[4,2,6,7,8,5,3,1]=>1000111
[4,3,5,8,6,7,2,1]=>1001011
[6,2,4,7,8,5,3,1]=>1000111
[3,2,7,8,5,6,4,1]=>1001011
[4,7,3,8,5,6,2,1]=>0101011
[7,1,4,8,5,6,3,2]=>1001011
[4,3,8,7,2,5,6,1]=>1011001
[1,7,3,8,6,4,5,2]=>0101101
[3,4,8,2,6,7,5,1]=>0010011
[1,2,6,8,7,4,5,3]=>0001101
[1,6,3,8,7,4,5,2]=>0101101
[1,4,5,8,7,6,2,3]=>0001110
[6,4,7,8,3,5,1,2]=>1001010
[6,4,7,8,1,2,5,3]=>1001001
[3,5,6,7,1,8,4,2]=>0001011
[1,7,4,5,2,8,6,3]=>0101011
[1,7,3,8,2,5,4,6]=>0101010
[2,7,8,3,6,1,5,4]=>0010101
[1,7,8,3,6,2,5,4]=>0010101
[1,4,7,5,8,3,6,2]=>0010101
[3,4,7,5,8,2,1,6]=>0010110
[7,2,6,4,1,8,5,3]=>1011011
[7,4,3,5,8,1,6,2]=>1100101
[7,3,6,4,1,8,5,2]=>1011011
[7,8,4,3,6,1,5,2]=>0110101
[7,1,6,4,3,8,5,2]=>1011011
[8,7,3,4,1,5,2,6]=>1101010
[7,2,6,4,3,8,5,1]=>1011011
[1,7,5,4,3,8,2,6]=>0111010
[4,5,8,1,7,3,2,6]=>0010110
[4,6,7,1,3,8,2,5]=>0010010
[8,2,3,6,4,1,7,5]=>1001101
[2,7,3,6,4,1,8,5]=>0101101
[2,3,7,8,1,4,6,5]=>0001001
[2,7,3,5,4,1,8,6]=>0101101
[8,2,3,5,4,1,7,6]=>1001101
[7,1,3,8,2,4,6,5]=>1001001
[7,2,3,6,4,1,8,5]=>1001101
[6,5,2,4,1,8,3,7]=>1101010
[5,7,2,4,1,3,8,6]=>0101001
[6,2,5,4,1,8,3,7]=>1011010
[8,1,2,5,3,7,6,4]=>1001011
[1,6,4,3,7,5,2,8]=>0110110
[1,6,7,5,4,8,2,3]=>0011010
[1,8,5,4,2,6,3,7]=>0111010
[4,2,8,1,5,7,6,3]=>1010011
[6,7,3,5,4,1,2,8]=>0101100
[5,7,3,6,2,1,4,8]=>0101100
[5,6,8,4,2,7,1,3]=>0011010
[6,8,7,3,2,1,5,4]=>0111101
[3,6,8,7,2,4,1,5]=>0011010
[3,7,6,4,2,8,1,5]=>0111010
[2,8,6,4,7,3,5,1]=>0110101
[3,8,6,4,2,7,1,5]=>0111010
[5,7,3,6,2,1,8,4]=>0101101
[2,4,8,6,5,7,3,1]=>0011011
[3,6,5,2,4,8,1,7]=>0110010
[4,6,3,2,5,1,8,7]=>0110101
[8,3,6,5,4,2,1,7]=>1011110
[5,4,8,7,6,2,3,1]=>1011101
[6,8,4,7,5,1,3,2]=>0101101
[6,5,8,3,7,1,4,2]=>1010101
[7,4,6,1,5,3,8,2]=>1010101
[6,1,5,4,7,3,8,2]=>1010101
[7,1,5,4,6,3,8,2]=>1010101
[2,5,4,7,1,8,3,6]=>0101010
[1,5,4,7,3,8,2,6]=>0101010
[1,5,6,8,3,2,4,7]=>0001100
[1,2,6,7,3,5,4,8]=>0001010
[1,5,6,7,2,4,3,8]=>0001010
[4,5,8,2,3,7,6,1]=>0010011
[1,7,2,5,6,8,3,4]=>0100010
[4,1,7,5,6,8,2,3]=>1010010
[5,7,3,4,2,8,6,1]=>0101011
[5,8,3,4,2,7,6,1]=>0101011
[7,6,4,2,3,8,5,1]=>1110011
[7,3,8,4,2,6,5,1]=>1011011
[3,5,6,8,2,4,7,1]=>0001001
[8,4,7,3,2,5,6,1]=>1011001
[4,8,7,3,2,5,6,1]=>0111001
[8,5,7,3,2,4,6,1]=>1011001
[3,7,4,2,6,8,5,1]=>0110011
[7,2,8,4,5,6,3,1]=>1010011
[6,2,8,3,7,4,5,1]=>1010101
[4,3,7,8,6,2,5,1]=>1001101
[1,5,8,3,2,7,4,6]=>0011010
[8,1,4,3,6,7,2,5]=>1010010
[8,3,1,4,6,7,2,5]=>1100010
[7,8,5,1,2,6,3,4]=>0110010
[8,3,6,7,5,1,2,4]=>1001100
[7,6,4,2,5,3,1,8]=>1110110
[1,8,6,5,2,7,4,3]=>0111011
[8,2,6,5,1,7,4,3]=>1011011
[6,1,4,7,2,5,8,3]=>1001001
[6,8,2,5,1,7,4,3]=>0101011
[1,6,4,7,2,5,8,3]=>0101001
[7,6,4,1,2,5,8,3]=>1110001
[6,8,1,5,2,7,4,3]=>0101011
[8,6,5,2,1,7,4,3]=>1111011
[1,6,5,2,8,7,4,3]=>0110111
[1,8,5,2,7,6,4,3]=>0110111
[1,8,6,7,2,5,4,3]=>0101011
[1,7,6,8,2,5,4,3]=>0101011
[1,7,8,6,2,5,4,3]=>0011011
[8,1,7,6,2,5,4,3]=>1011011
[5,2,4,7,3,8,6,1]=>1001011
[1,5,6,3,2,8,7,4]=>0011011
[4,6,5,7,1,8,2,3]=>0101010
[6,7,5,3,8,2,1,4]=>0110110
[7,2,5,6,4,8,3,1]=>1001011
[7,4,6,2,8,5,3,1]=>1010111
[7,2,6,3,8,5,4,1]=>1010111
[1,2,6,5,3,8,4,7]=>0011010
[6,5,3,4,8,2,1,7]=>1100110
[1,7,8,6,3,5,4,2]=>0011011
[1,4,2,3,7,8,6,5]=>0100011
[1,8,4,2,3,6,5,7]=>0110010
[1,3,8,5,6,4,2,7]=>0010110
[1,6,3,7,8,4,2,5]=>0100110
[1,6,3,8,4,2,5,7]=>0101100
[1,7,8,4,2,3,5,6]=>0011000
[1,7,8,5,6,4,2,3]=>0010110
[1,6,3,4,2,5,8,7]=>0101001
[1,3,5,8,6,4,2,7]=>0001110
[1,7,6,2,3,8,4,5]=>0110010
[1,5,7,6,2,3,8,4]=>0011001
[1,3,7,6,2,4,5,8]=>0011000
[1,4,3,7,6,2,5,8]=>0101100
[1,5,8,4,3,7,6,2]=>0011011
[1,7,5,8,4,3,6,2]=>0101101
[4,1,5,7,3,8,2,6]=>1001010
[1,3,7,4,6,8,5,2]=>0010011
[1,5,2,6,8,7,4,3]=>0100111
[1,3,7,6,4,8,2,5]=>0011010
[6,5,1,4,3,8,7,2]=>1101011
[5,6,1,4,3,8,7,2]=>0101011
[5,8,6,4,3,1,7,2]=>0111101
[4,1,3,7,8,6,5,2]=>1000111
[8,5,6,4,3,1,7,2]=>1011101
[8,4,3,1,7,6,5,2]=>1110111
[3,2,7,1,8,6,5,4]=>1010111
[2,1,4,3,6,5,8,7,10,9]=>101010101
[2,4,6,8,10,1,3,5,7,9]=>000010000
[10,9,8,7,6,1,2,3,4,5]=>111110000
[9,10,7,8,5,6,3,4,1,2]=>010101010
[5,4,3,2,1,6,7,8,9,10]=>111100000
[6,4,3,2,7,1,5,8,9,10]=>111010000
[7,5,3,8,2,6,1,4,9,10]=>110101000
[8,6,9,4,7,2,5,1,3,10]=>101010100
[6,7,8,9,10,5,4,3,2,1]=>000011111
[5,7,8,9,4,10,6,3,2,1]=>000101111
[4,6,8,3,9,5,10,7,2,1]=>001010111
[3,5,2,7,4,9,6,10,8,1]=>010101011
[3,1,5,2,7,4,9,6,8,10]=>101010100
[1,2,3,4,5,10,9,8,7,6]=>000001111
[10,9,8,5,1,7,2,3,4,6]=>111101000
[10,9,4,1,6,2,8,3,5,7]=>111010100
[10,3,1,5,2,7,4,9,6,8]=>110101010
[1,4,2,6,3,8,5,10,7,9]=>010101010
[10,8,6,4,2,1,3,5,7,9]=>111110000
[6,5,4,3,7,8,9,10,1,2]=>111000010
[10,1,2,3,4,6,7,8,9,5]=>100000001
[2,1,7,8,9,10,6,5,4,3]=>100001111
[9,8,7,6,1,2,3,4,5,10]=>111100000
[3,2,5,4,7,6,9,8,1,10]=>101010110
[1,4,3,6,5,8,7,10,9,2]=>010101011
[3,4,2,1,6,5,8,7,10,9]=>011010101
[3,5,2,6,4,1,8,7,10,9]=>010110101
[3,5,2,7,4,8,6,1,10,9]=>010101101
[2,1,5,6,4,3,8,7,10,9]=>100110101
[4,5,6,3,2,1,8,7,10,9]=>001110101
[4,5,7,3,2,8,6,1,10,9]=>001101101
[4,5,7,3,2,9,6,10,8,1]=>001101011
[2,1,5,7,4,8,6,3,10,9]=>100101101
[4,6,7,3,8,5,2,1,10,9]=>001011101
[4,6,7,3,9,5,2,10,8,1]=>001011011
[2,1,5,7,4,9,6,10,8,3]=>100101011
[2,1,4,3,7,8,6,5,10,9]=>101001101
[3,4,2,1,7,8,6,5,10,9]=>011001101
[3,6,2,7,8,5,4,1,10,9]=>010011101
[3,6,2,7,9,5,4,10,8,1]=>010011011
[2,1,6,7,8,5,4,3,10,9]=>100011101
[5,6,7,8,4,3,2,1,10,9]=>000111101
[5,6,7,9,4,3,2,10,8,1]=>000111011
[2,1,6,7,9,5,4,10,8,3]=>100011011
[5,6,8,9,4,3,10,7,2,1]=>000110111
[2,1,4,3,7,9,6,10,8,5]=>101001011
[3,4,2,1,7,9,6,10,8,5]=>011001011
[3,6,2,8,9,5,10,7,4,1]=>010010111
[2,1,6,8,9,5,10,7,4,3]=>100010111
[2,1,4,3,6,5,9,10,8,7]=>101010011
[3,4,2,1,6,5,9,10,8,7]=>011010011
[3,5,2,6,4,1,9,10,8,7]=>010110011
[3,5,2,8,4,9,10,7,6,1]=>010100111
[2,1,5,6,4,3,9,10,8,7]=>100110011
[4,5,6,3,2,1,9,10,8,7]=>001110011
[4,5,8,3,2,9,10,7,6,1]=>001100111
[2,1,5,8,4,9,10,7,6,3]=>100100111
[4,7,8,3,9,10,6,5,2,1]=>001001111
[2,1,4,3,8,9,10,7,6,5]=>101000111
[3,4,2,1,8,9,10,7,6,5]=>011000111
[3,7,2,8,9,10,6,5,4,1]=>010001111
[7,8,10,9,5,6,3,4,1,2]=>001101010
[9,10,5,6,8,7,3,4,1,2]=>010011010
[5,8,10,6,9,7,3,4,1,2]=>001011010
[5,6,7,10,9,8,3,4,1,2]=>000111010
[9,10,7,8,3,4,6,5,1,2]=>010100110
[7,8,10,9,3,4,6,5,1,2]=>001100110
[9,10,3,6,8,4,7,5,1,2]=>010010110
[3,8,10,6,9,4,7,5,1,2]=>001010110
[3,6,7,10,9,4,8,5,1,2]=>000110110
[9,10,3,4,5,8,7,6,1,2]=>010001110
[3,8,10,4,5,9,7,6,1,2]=>001001110
[3,4,7,10,5,9,8,6,1,2]=>000101110
[3,4,5,6,10,9,8,7,1,2]=>000011110
[9,10,7,8,5,6,1,2,4,3]=>010101001
[7,8,10,9,5,6,1,2,4,3]=>001101001
[9,10,5,6,8,7,1,2,4,3]=>010011001
[5,8,10,6,9,7,1,2,4,3]=>001011001
[5,6,7,10,9,8,1,2,4,3]=>000111001
[9,10,7,8,1,4,6,2,5,3]=>010100101
[7,8,10,9,1,4,6,2,5,3]=>001100101
[9,10,1,6,8,4,7,2,5,3]=>010010101
[1,8,10,6,9,4,7,2,5,3]=>001010101
[1,6,7,10,9,4,8,2,5,3]=>000110101
[9,10,1,4,5,8,7,2,6,3]=>010001101
[1,8,10,4,5,9,7,2,6,3]=>001001101
[1,4,7,10,5,9,8,2,6,3]=>000101101
[1,4,5,6,10,9,8,2,7,3]=>000011101
[9,10,7,8,1,2,3,6,5,4]=>010100011
[7,8,10,9,1,2,3,6,5,4]=>001100011
[9,10,1,6,8,2,3,7,5,4]=>010010011
[1,8,10,6,9,2,3,7,5,4]=>001010011
[1,6,7,10,9,2,3,8,5,4]=>000110011
[9,10,1,2,5,8,3,7,6,4]=>010001011
[1,8,10,2,5,9,3,7,6,4]=>001001011
[1,2,7,10,5,9,3,8,6,4]=>000101011
[1,2,5,6,10,9,3,8,7,4]=>000011011
[9,10,1,2,3,4,8,7,6,5]=>010000111
[1,8,10,2,3,4,9,7,6,5]=>001000111
[1,2,7,10,3,4,9,8,6,5]=>000100111
[1,2,3,6,10,4,9,8,7,5]=>000010111
[2,1,4,3,6,5,10,9,7,8]=>101010110
[2,1,4,3,8,7,5,6,10,9]=>101011001
[2,1,4,3,10,7,5,9,6,8]=>101011010
[2,1,4,3,10,9,8,5,6,7]=>101011100
[2,1,6,5,3,4,8,7,10,9]=>101100101
[2,1,6,5,3,4,10,9,7,8]=>101100110
[2,1,8,5,3,7,4,6,10,9]=>101101001
[2,1,10,5,3,7,4,9,6,8]=>101101010
[2,1,10,5,3,9,8,4,6,7]=>101101100
[2,1,8,7,6,3,4,5,10,9]=>101110001
[2,1,10,7,6,3,4,9,5,8]=>101110010
[2,1,10,9,6,3,8,4,5,7]=>101110100
[2,1,10,9,8,7,3,4,5,6]=>101111000
[4,3,1,2,6,5,8,7,10,9]=>110010101
[4,3,1,2,6,5,10,9,7,8]=>110010110
[4,3,1,2,8,7,5,6,10,9]=>110011001
[4,3,1,2,10,7,5,9,6,8]=>110011010
[4,3,1,2,10,9,8,5,6,7]=>110011100
[6,3,1,5,2,4,8,7,10,9]=>110100101
[6,3,1,5,2,4,10,9,7,8]=>110100110
[8,3,1,5,2,7,4,6,10,9]=>110101001
[10,3,1,5,2,9,8,4,6,7]=>110101100
[8,3,1,7,6,2,4,5,10,9]=>110110001
[10,3,1,7,6,2,4,9,5,8]=>110110010
[10,3,1,9,6,2,8,4,5,7]=>110110100
[10,3,1,9,8,7,2,4,5,6]=>110111000
[6,5,4,1,2,3,8,7,10,9]=>111000101
[6,5,4,1,2,3,10,9,7,8]=>111000110
[8,5,4,1,2,7,3,6,10,9]=>111001001
[10,5,4,1,2,7,3,9,6,8]=>111001010
[10,5,4,1,2,9,8,3,6,7]=>111001100
[8,7,4,1,6,2,3,5,10,9]=>111010001
[10,7,4,1,6,2,3,9,5,8]=>111010010
[10,9,4,1,8,7,2,3,5,6]=>111011000
[8,7,6,5,1,2,3,4,10,9]=>111100001
[10,7,6,5,1,2,3,9,4,8]=>111100010
[10,9,6,5,1,2,8,3,4,7]=>111100100
[9,10,7,8,5,6,2,1,3,4]=>010101100
[9,10,7,8,4,3,5,6,1,2]=>010110010
[9,10,7,8,4,2,5,1,3,6]=>010110100
[9,10,7,8,3,2,1,4,5,6]=>010111000
[9,10,6,5,7,8,3,4,1,2]=>011001010
[9,10,6,5,7,8,2,1,3,4]=>011001100
[9,10,6,4,7,3,5,8,1,2]=>011010010
[9,10,6,4,7,2,5,1,3,8]=>011010100
[9,10,6,3,7,2,1,4,5,8]=>011011000
[9,10,5,4,3,6,7,8,1,2]=>011100010
[9,10,5,4,2,6,7,1,3,8]=>011100100
[9,10,5,3,2,6,1,4,7,8]=>011101000
[9,10,4,3,2,1,5,6,7,8]=>011110000
[8,7,9,10,5,6,3,4,1,2]=>100101010
[8,7,9,10,5,6,2,1,3,4]=>100101100
[8,7,9,10,4,3,5,6,1,2]=>100110010
[8,7,9,10,4,2,5,1,3,6]=>100110100
[8,7,9,10,3,2,1,4,5,6]=>100111000
[8,6,9,5,7,10,3,4,1,2]=>101001010
[8,6,9,5,7,10,2,1,3,4]=>101001100
[8,6,9,4,7,3,5,10,1,2]=>101010010
[8,6,9,3,7,2,1,4,5,10]=>101011000
[8,5,9,4,3,6,7,10,1,2]=>101100010
[8,5,9,4,2,6,7,1,3,10]=>101100100
[8,5,9,3,2,6,1,4,7,10]=>101101000
[8,4,9,3,2,1,5,6,7,10]=>101110000
[7,6,5,8,9,10,3,4,1,2]=>110001010
[7,6,5,8,9,10,2,1,3,4]=>110001100
[7,6,4,8,9,3,5,10,1,2]=>110010010
[7,6,4,8,9,2,5,1,3,10]=>110010100
[7,6,3,8,9,2,1,4,5,10]=>110011000
[7,5,4,8,3,6,9,10,1,2]=>110100010
[7,5,4,8,2,6,9,1,3,10]=>110100100
[7,4,3,8,2,1,5,6,9,10]=>110110000
[6,5,4,2,7,8,9,1,3,10]=>111000100
[6,5,3,2,7,8,1,4,9,10]=>111001000
[3,2,5,4,7,6,1,10,8,9]=>101011010
[3,2,5,4,9,8,6,7,1,10]=>101011010
[3,2,5,4,1,8,6,10,7,9]=>101101010
[3,2,5,4,1,10,9,6,7,8]=>101101100
[3,2,7,6,4,5,9,8,1,10]=>101100110
[3,2,7,6,4,5,1,10,8,9]=>101101010
[3,2,9,6,4,8,5,7,1,10]=>101101010
[3,2,1,6,4,8,5,10,7,9]=>110101010
[3,2,1,6,4,10,9,5,7,8]=>110101100
[3,2,9,8,7,4,5,6,1,10]=>101110010
[3,2,1,8,7,4,5,10,6,9]=>110110010
[3,2,1,10,7,4,9,5,6,8]=>110110100
[3,2,1,10,9,8,4,5,6,7]=>110111000
[5,4,2,3,7,6,9,8,1,10]=>110010110
[5,4,2,3,7,6,1,10,8,9]=>110011010
[5,4,2,3,9,8,6,7,1,10]=>110011010
[5,4,2,3,1,8,6,10,7,9]=>110101010
[5,4,2,3,1,10,9,6,7,8]=>110101100
[7,4,2,6,3,5,9,8,1,10]=>110100110
[7,4,2,6,3,5,1,10,8,9]=>110101010
[9,4,2,6,3,8,5,7,1,10]=>110101010
[1,4,2,6,3,10,9,5,7,8]=>010101100
[9,4,2,8,7,3,5,6,1,10]=>110110010
[1,4,2,8,7,3,5,10,6,9]=>010110010
[1,4,2,10,7,3,9,5,6,8]=>010110100
[1,4,2,10,9,8,3,5,6,7]=>010111000
[7,6,5,2,3,4,9,8,1,10]=>111000110
[7,6,5,2,3,4,1,10,8,9]=>111001010
[9,6,5,2,3,8,4,7,1,10]=>111001010
[1,6,5,2,3,8,4,10,7,9]=>011001010
[1,6,5,2,3,10,9,4,7,8]=>011001100
[9,8,5,2,7,3,4,6,1,10]=>111010010
[1,8,5,2,7,3,4,10,6,9]=>011010010
[1,10,5,2,7,3,9,4,6,8]=>011010100
[1,10,5,2,9,8,3,4,6,7]=>011011000
[9,8,7,6,2,3,4,5,1,10]=>111100010
[1,8,7,6,2,3,4,10,5,9]=>011100010
[1,10,7,6,2,3,9,4,5,8]=>011100100
[1,10,9,6,2,8,3,4,5,7]=>011101000
[1,10,9,8,7,2,3,4,5,6]=>011110000
[2,1,4,3,6,5,8,10,9,7]=>101010011
[2,1,4,3,6,8,7,5,10,9]=>101001101
[2,1,4,3,8,10,7,9,5,6]=>101001010
[2,1,4,3,6,7,10,8,9,5]=>101000101
[2,1,4,6,5,3,8,7,10,9]=>100110101
[2,1,4,6,5,3,8,10,9,7]=>100110011
[2,1,6,8,5,7,3,4,10,9]=>100101001
[2,1,8,7,5,10,4,9,3,6]=>101101010
[2,1,6,7,5,10,8,4,9,3]=>100101101
[2,1,4,5,8,6,7,3,10,9]=>100010101
[2,1,8,5,10,6,7,9,3,4]=>101010010
[2,1,4,7,10,6,9,8,3,5]=>100010110
[2,1,4,5,6,10,7,8,9,3]=>100001001
[2,4,3,1,6,5,8,7,10,9]=>011010101
[2,4,3,1,6,5,8,10,9,7]=>011010011
[2,4,3,1,6,8,7,5,10,9]=>011001101
[2,4,3,1,8,10,7,9,5,6]=>011001010
[2,4,3,1,6,7,10,8,9,5]=>011000101
[4,6,3,5,1,2,8,7,10,9]=>010100101
[4,6,3,5,1,2,8,10,9,7]=>010100011
[6,5,3,8,2,7,1,4,10,9]=>110101001
[8,5,3,7,2,10,4,9,1,6]=>110101010
[6,5,3,7,2,10,8,4,9,1]=>110101101
[4,5,3,8,6,2,7,1,10,9]=>010110101
[8,6,3,5,10,2,7,9,1,4]=>110010010
[4,7,3,6,10,1,9,8,2,5]=>010010110
[4,5,3,6,10,7,1,8,9,2]=>010011001
[2,3,6,4,5,1,8,7,10,9]=>001010101
[2,3,6,4,5,1,8,10,9,7]=>001010011
[6,3,8,4,5,7,1,2,10,9]=>101001001
[8,3,7,4,5,10,2,9,1,6]=>101001010
[6,3,7,4,5,10,8,2,9,1]=>101001101
[2,5,8,4,7,6,1,3,10,9]=>001011001
[8,5,10,4,7,6,2,9,1,3]=>101011010
[2,7,10,4,8,6,9,5,1,3]=>001010110
[2,5,6,4,10,8,7,3,9,1]=>001011101
[2,3,4,8,5,6,7,1,10,9]=>000100101
[8,3,4,10,5,6,7,9,1,2]=>100100010
[2,7,4,10,5,6,9,8,1,3]=>010100110
[2,3,6,10,5,9,7,8,1,4]=>000101010
[2,3,4,5,10,6,7,8,9,1]=>000010001
[1,4,3,6,5,10,9,7,8,2]=>010101101
[1,4,3,8,7,5,6,10,9,2]=>010110011
[1,4,3,10,7,5,9,6,8,2]=>010110101
[1,4,3,10,9,8,5,6,7,2]=>010111001
[1,6,5,3,4,8,7,10,9,2]=>011001011
[1,6,5,3,4,10,9,7,8,2]=>011001101
[1,8,5,3,7,4,6,10,9,2]=>011010011
[1,10,5,3,7,4,9,6,8,2]=>011010101
[1,10,5,3,9,8,4,6,7,2]=>011011001
[1,8,7,6,3,4,5,10,9,2]=>011100011
[1,10,7,6,3,4,9,5,8,2]=>011100101
[1,10,9,6,3,8,4,5,7,2]=>011101001
[1,10,9,8,7,3,4,5,6,2]=>011110001
[3,1,2,6,5,8,7,10,9,4]=>100101011
[3,1,2,6,5,10,9,7,8,4]=>100101101
[3,1,2,8,7,5,6,10,9,4]=>100110011
[3,1,2,10,7,5,9,6,8,4]=>100110101
[3,1,2,10,9,8,5,6,7,4]=>100111001
[3,1,5,2,4,8,7,10,9,6]=>101001011
[3,1,5,2,4,10,9,7,8,6]=>101001101
[3,1,5,2,7,4,6,10,9,8]=>101010011
[3,1,5,2,9,8,4,6,7,10]=>101011000
[3,1,7,6,2,4,5,10,9,8]=>101100011
[3,1,7,6,2,4,9,5,8,10]=>101100100
[3,1,9,6,2,8,4,5,7,10]=>101101000
[3,1,9,8,7,2,4,5,6,10]=>101110000
[5,4,1,2,3,8,7,10,9,6]=>110001011
[5,4,1,2,3,10,9,7,8,6]=>110001101
[5,4,1,2,7,3,6,10,9,8]=>110010011
[5,4,1,2,7,3,9,6,8,10]=>110010100
[5,4,1,2,9,8,3,6,7,10]=>110011000
[7,4,1,6,2,3,5,10,9,8]=>110100011
[7,4,1,6,2,3,9,5,8,10]=>110100100
[9,4,1,6,2,8,3,5,7,10]=>110101000
[9,4,1,8,7,2,3,5,6,10]=>110110000
[7,6,5,1,2,3,4,10,9,8]=>111000011
[7,6,5,1,2,3,9,4,8,10]=>111000100
[9,6,5,1,2,8,3,4,7,10]=>111001000
[9,8,5,1,7,2,3,4,6,10]=>111010000
[9,10,6,4,2,1,3,5,8,7]=>011110001
[10,7,8,4,2,1,3,6,5,9]=>101110010
[9,7,10,4,2,1,3,6,8,5]=>101110001
[8,9,10,4,2,1,3,7,6,5]=>001110011
[10,8,5,6,2,1,4,3,7,9]=>110110100
[9,10,5,6,2,1,4,3,8,7]=>010110101
[10,7,5,8,2,1,4,6,3,9]=>110110010
[9,7,5,10,2,1,4,6,8,3]=>110110001
[8,9,5,10,2,1,4,7,6,3]=>010110011
[10,6,7,8,2,1,5,4,3,9]=>100110110
[9,6,7,10,2,1,5,4,8,3]=>100110101
[8,6,9,10,2,1,5,7,4,3]=>100110011
[7,8,9,10,2,1,6,5,4,3]=>000110111
[10,8,6,3,4,2,1,5,7,9]=>111011000
[9,10,6,3,4,2,1,5,8,7]=>011011001
[10,7,8,3,4,2,1,6,5,9]=>101011010
[9,7,10,3,4,2,1,6,8,5]=>101011001
[8,9,10,3,4,2,1,7,6,5]=>001011011
[10,8,5,3,6,2,4,1,7,9]=>111010100
[9,10,5,3,6,2,4,1,8,7]=>011010101
[10,7,5,3,8,2,4,6,1,9]=>111010010
[9,7,5,3,10,2,4,6,8,1]=>111010001
[8,9,5,3,10,2,4,7,6,1]=>011010011
[10,6,7,3,8,2,5,4,1,9]=>101010110
[9,6,7,3,10,2,5,4,8,1]=>101010101
[8,6,9,3,10,2,5,7,4,1]=>101010011
[7,8,9,3,10,2,6,5,4,1]=>001010111
[10,8,4,5,6,3,2,1,7,9]=>110011100
[9,10,4,5,6,3,2,1,8,7]=>010011101
[10,7,4,5,8,3,2,6,1,9]=>110011010
[9,7,4,5,10,3,2,6,8,1]=>110011001
[8,9,4,5,10,3,2,7,6,1]=>010011011
[10,6,4,7,8,3,5,2,1,9]=>110010110
[9,6,4,7,10,3,5,2,8,1]=>110010101
[8,6,4,9,10,3,5,7,2,1]=>110010011
[7,8,4,9,10,3,6,5,2,1]=>010010111
[10,5,6,7,8,4,3,2,1,9]=>100011110
[9,5,6,7,10,4,3,2,8,1]=>100011101
[8,5,6,9,10,4,3,7,2,1]=>100011011
[7,5,8,9,10,4,6,3,2,1]=>100010111
[9,10,2,4,6,8,1,3,5,7]=>010001000
[7,8,2,4,6,10,1,3,5,9]=>010001000
[9,7,10,2,4,6,8,1,3,5]=>101000100
[8,9,10,7,2,4,6,1,3,5]=>001100100
[5,6,2,4,8,10,1,3,7,9]=>010001000
[5,6,9,10,2,4,8,1,3,7]=>000100100
[7,5,8,2,4,6,10,1,3,9]=>101000100
[7,9,5,10,2,4,6,8,1,3]=>010100010
[5,8,9,10,7,2,4,6,1,3]=>000110010
[6,7,8,5,2,4,10,1,3,9]=>001100100
[9,6,7,5,10,2,4,8,1,3]=>101010010
[8,9,6,10,5,7,2,4,1,3]=>010101010
[7,8,9,10,6,5,2,4,1,3]=>000111010
[3,4,2,6,8,10,1,5,7,9]=>010001000
[3,4,9,10,2,6,8,1,5,7]=>000100100
[3,4,7,8,2,6,10,1,5,9]=>000100100
[9,3,4,7,10,2,6,8,1,5]=>100010010
[8,9,10,3,4,7,2,6,1,5]=>001001010
[5,3,6,2,4,8,10,1,7,9]=>101000100
[5,3,6,9,10,2,4,8,1,7]=>100010010
[5,7,3,8,2,4,6,10,1,9]=>010100010
[5,7,9,3,10,2,4,6,8,1]=>001010001
[8,5,9,10,3,7,2,4,6,1]=>100101001
[3,6,7,8,5,2,4,10,1,9]=>000110010
[9,3,6,7,5,10,2,4,8,1]=>100101001
[6,8,3,9,10,5,7,2,4,1]=>010010101
[7,8,9,10,3,6,5,2,4,1]=>000101101
[4,5,6,3,2,8,10,1,7,9]=>001100100
[4,5,6,3,9,10,2,8,1,7]=>001001010
[7,4,5,3,8,2,6,10,1,9]=>101010010
[7,4,5,9,3,10,2,6,8,1]=>100101001
[4,8,5,9,10,3,7,2,6,1]=>010010101
[6,7,4,8,3,5,2,10,1,9]=>010101010
[6,7,9,4,3,5,10,2,8,1]=>001100101
[8,6,9,4,10,3,5,7,2,1]=>101010011
[7,4,8,9,10,6,3,5,2,1]=>100011011
[5,6,7,8,4,3,2,10,1,9]=>000111010
[9,5,6,7,4,3,10,2,8,1]=>100110101
[8,9,5,6,4,10,3,7,2,1]=>010101011
[7,8,9,5,10,4,6,3,2,1]=>001010111
[2,1,4,3,6,5,10,7,9,8]=>101010101
[2,1,4,3,8,5,7,6,10,9]=>101010101
[2,1,4,3,10,9,7,5,6,8]=>101011100
[2,1,4,3,10,5,6,8,9,7]=>101010001
[2,1,6,3,5,4,8,7,10,9]=>101010101
[2,1,6,3,5,4,10,7,9,8]=>101010101
[2,1,8,7,5,3,4,6,10,9]=>101110001
[2,1,10,7,5,9,4,3,6,8]=>101101100
[2,1,10,8,5,3,6,4,9,7]=>101110101
[2,1,8,3,4,6,7,5,10,9]=>101000101
[2,1,10,9,4,6,7,3,5,8]=>101100100
[2,1,10,3,9,6,4,8,5,7]=>101011010
[2,1,10,3,4,5,7,8,9,6]=>101000001
[4,1,3,2,6,5,8,7,10,9]=>101010101
[4,1,3,2,6,5,10,7,9,8]=>101010101
[4,1,3,2,8,5,7,6,10,9]=>101010101
[4,1,3,2,10,9,7,5,6,8]=>101011100
[4,1,3,2,10,5,6,8,9,7]=>101010001
[6,5,3,1,2,4,8,7,10,9]=>111000101
[6,5,3,1,2,4,10,7,9,8]=>111000101
[8,5,3,7,2,1,4,6,10,9]=>110110001
[10,5,3,7,2,9,4,1,6,8]=>110101100
[10,5,3,8,2,1,6,4,9,7]=>110110101
[8,6,3,1,4,2,7,5,10,9]=>111010101
[10,6,3,9,4,2,7,1,5,8]=>110110100
[10,6,3,1,9,2,4,8,5,7]=>111010010
[10,7,3,1,4,5,2,8,9,6]=>111001001
[6,1,2,4,5,3,8,7,10,9]=>100010101
[6,1,2,4,5,3,10,7,9,8]=>100010101
[8,7,2,4,5,1,3,6,10,9]=>110010001
[10,7,2,4,5,9,3,1,6,8]=>110001100
[10,8,2,4,5,1,6,3,9,7]=>110010101
[8,1,7,4,2,6,3,5,10,9]=>101101001
[10,9,7,4,2,6,3,1,5,8]=>111101100
[10,1,8,4,9,6,2,3,5,7]=>101011000
[10,1,8,4,2,5,7,3,9,6]=>101100101
[8,1,2,3,5,6,7,4,10,9]=>100000101
[10,9,2,3,5,6,7,1,4,8]=>110000100
[10,1,9,3,5,6,2,8,4,7]=>101001010
[10,1,2,9,5,3,7,8,4,6]=>100110010
[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101
[2,4,6,8,10,12,1,3,5,7,9,11]=>00000100000
[11,12,9,10,7,8,5,6,3,4,1,2]=>01010101010
[12,10,8,6,4,2,1,3,5,7,9,11]=>11111100000
[3,2,5,4,7,6,9,8,11,10,1,12]=>10101010110
[1,4,3,6,5,8,7,10,9,12,11,2]=>01010101011
[2,1,4,3,6,5,8,7,11,12,10,9]=>10101010011
[2,1,4,3,6,5,9,10,8,7,12,11]=>10101001101
[2,1,4,3,6,5,9,11,8,12,10,7]=>10101001011
[2,1,4,3,6,5,10,11,12,9,8,7]=>10101000111
[2,1,4,3,7,8,6,5,10,9,12,11]=>10100110101
[2,1,4,3,7,8,6,5,11,12,10,9]=>10100110011
[2,1,4,3,7,9,6,10,8,5,12,11]=>10100101101
[2,1,4,3,7,9,6,11,8,12,10,5]=>10100101011
[2,1,4,3,7,10,6,11,12,9,8,5]=>10100100111
[2,1,4,3,8,9,10,7,6,5,12,11]=>10100011101
[2,1,4,3,8,9,11,7,6,12,10,5]=>10100011011
[2,1,4,3,8,10,11,7,12,9,6,5]=>10100010111
[2,1,4,3,9,10,11,12,8,7,6,5]=>10100001111
[2,1,5,6,4,3,8,7,10,9,12,11]=>10011010101
[2,1,5,6,4,3,8,7,11,12,10,9]=>10011010011
[2,1,5,6,4,3,9,10,8,7,12,11]=>10011001101
[2,1,5,6,4,3,9,11,8,12,10,7]=>10011001011
[2,1,5,6,4,3,10,11,12,9,8,7]=>10011000111
[2,1,5,7,4,8,6,3,10,9,12,11]=>10010110101
[2,1,5,7,4,8,6,3,11,12,10,9]=>10010110011
[2,1,5,7,4,9,6,10,8,3,12,11]=>10010101101
[2,1,5,7,4,9,6,11,8,12,10,3]=>10010101011
[2,1,5,7,4,10,6,11,12,9,8,3]=>10010100111
[2,1,5,8,4,9,10,7,6,3,12,11]=>10010011101
[2,1,5,8,4,9,11,7,6,12,10,3]=>10010011011
[2,1,5,8,4,10,11,7,12,9,6,3]=>10010010111
[2,1,5,9,4,10,11,12,8,7,6,3]=>10010001111
[2,1,6,7,8,5,4,3,10,9,12,11]=>10001110101
[2,1,6,7,8,5,4,3,11,12,10,9]=>10001110011
[2,1,6,7,9,5,4,10,8,3,12,11]=>10001101101
[2,1,6,7,9,5,4,11,8,12,10,3]=>10001101011
[2,1,6,7,10,5,4,11,12,9,8,3]=>10001100111
[2,1,6,8,9,5,10,7,4,3,12,11]=>10001011101
[2,1,6,8,9,5,11,7,4,12,10,3]=>10001011011
[2,1,6,8,10,5,11,7,12,9,4,3]=>10001010111
[2,1,6,9,10,5,11,12,8,7,4,3]=>10001001111
[2,1,7,8,9,10,6,5,4,3,12,11]=>10000111101
[2,1,7,8,9,11,6,5,4,12,10,3]=>10000111011
[2,1,7,8,10,11,6,5,12,9,4,3]=>10000110111
[2,1,7,9,10,11,6,12,8,5,4,3]=>10000101111
[2,1,8,9,10,11,12,7,6,5,4,3]=>10000011111
[3,4,2,1,6,5,8,7,10,9,12,11]=>01101010101
[3,4,2,1,6,5,8,7,11,12,10,9]=>01101010011
[3,4,2,1,6,5,9,10,8,7,12,11]=>01101001101
[3,4,2,1,6,5,9,11,8,12,10,7]=>01101001011
[3,4,2,1,6,5,10,11,12,9,8,7]=>01101000111
[3,4,2,1,7,8,6,5,10,9,12,11]=>01100110101
[3,4,2,1,7,8,6,5,11,12,10,9]=>01100110011
[3,4,2,1,7,9,6,10,8,5,12,11]=>01100101101
[3,4,2,1,7,9,6,11,8,12,10,5]=>01100101011
[3,4,2,1,7,10,6,11,12,9,8,5]=>01100100111
[3,4,2,1,8,9,10,7,6,5,12,11]=>01100011101
[3,4,2,1,8,9,11,7,6,12,10,5]=>01100011011
[3,4,2,1,8,10,11,7,12,9,6,5]=>01100010111
[3,4,2,1,9,10,11,12,8,7,6,5]=>01100001111
[3,5,2,6,4,1,8,7,10,9,12,11]=>01011010101
[3,5,2,6,4,1,8,7,11,12,10,9]=>01011010011
[3,5,2,6,4,1,9,10,8,7,12,11]=>01011001101
[3,5,2,6,4,1,9,11,8,12,10,7]=>01011001011
[3,5,2,6,4,1,10,11,12,9,8,7]=>01011000111
[3,5,2,7,4,8,6,1,10,9,12,11]=>01010110101
[3,5,2,7,4,8,6,1,11,12,10,9]=>01010110011
[3,5,2,7,4,9,6,10,8,1,12,11]=>01010101101
[3,5,2,7,4,9,6,11,8,12,10,1]=>01010101011
[3,5,2,7,4,10,6,11,12,9,8,1]=>01010100111
[3,5,2,8,4,9,10,7,6,1,12,11]=>01010011101
[3,5,2,8,4,9,11,7,6,12,10,1]=>01010011011
[3,5,2,8,4,10,11,7,12,9,6,1]=>01010010111
[3,5,2,9,4,10,11,12,8,7,6,1]=>01010001111
[3,6,2,7,8,5,4,1,10,9,12,11]=>01001110101
[3,6,2,7,8,5,4,1,11,12,10,9]=>01001110011
[3,6,2,7,9,5,4,10,8,1,12,11]=>01001101101
[3,6,2,7,9,5,4,11,8,12,10,1]=>01001101011
[3,6,2,7,10,5,4,11,12,9,8,1]=>01001100111
[3,6,2,8,9,5,10,7,4,1,12,11]=>01001011101
[3,6,2,8,9,5,11,7,4,12,10,1]=>01001011011
[3,6,2,8,10,5,11,7,12,9,4,1]=>01001010111
[3,6,2,9,10,5,11,12,8,7,4,1]=>01001001111
[3,7,2,8,9,10,6,5,4,1,12,11]=>01000111101
[3,7,2,8,9,11,6,5,4,12,10,1]=>01000111011
[3,7,2,8,10,11,6,5,12,9,4,1]=>01000110111
[3,7,2,9,10,11,6,12,8,5,4,1]=>01000101111
[3,8,2,9,10,11,12,7,6,5,4,1]=>01000011111
[4,5,6,3,2,1,8,7,10,9,12,11]=>00111010101
[4,5,6,3,2,1,8,7,11,12,10,9]=>00111010011
[4,5,6,3,2,1,9,10,8,7,12,11]=>00111001101
[4,5,6,3,2,1,9,11,8,12,10,7]=>00111001011
[4,5,6,3,2,1,10,11,12,9,8,7]=>00111000111
[4,5,7,3,2,8,6,1,10,9,12,11]=>00110110101
[4,5,7,3,2,8,6,1,11,12,10,9]=>00110110011
[4,5,7,3,2,9,6,10,8,1,12,11]=>00110101101
[4,5,7,3,2,9,6,11,8,12,10,1]=>00110101011
[4,5,7,3,2,10,6,11,12,9,8,1]=>00110100111
[4,5,8,3,2,9,10,7,6,1,12,11]=>00110011101
[4,5,8,3,2,9,11,7,6,12,10,1]=>00110011011
[4,5,8,3,2,10,11,7,12,9,6,1]=>00110010111
[4,5,9,3,2,10,11,12,8,7,6,1]=>00110001111
[4,6,7,3,8,5,2,1,10,9,12,11]=>00101110101
[4,6,7,3,8,5,2,1,11,12,10,9]=>00101110011
[4,6,7,3,9,5,2,10,8,1,12,11]=>00101101101
[4,6,7,3,9,5,2,11,8,12,10,1]=>00101101011
[4,6,7,3,10,5,2,11,12,9,8,1]=>00101100111
[4,6,8,3,9,5,10,7,2,1,12,11]=>00101011101
[4,6,8,3,9,5,11,7,2,12,10,1]=>00101011011
[4,6,8,3,10,5,11,7,12,9,2,1]=>00101010111
[4,6,9,3,10,5,11,12,8,7,2,1]=>00101001111
[4,7,8,3,9,10,6,5,2,1,12,11]=>00100111101
[4,7,8,3,9,11,6,5,2,12,10,1]=>00100111011
[4,7,8,3,10,11,6,5,12,9,2,1]=>00100110111
[4,7,9,3,10,11,6,12,8,5,2,1]=>00100101111
[4,8,9,3,10,11,12,7,6,5,2,1]=>00100011111
[5,6,7,8,4,3,2,1,10,9,12,11]=>00011110101
[5,6,7,8,4,3,2,1,11,12,10,9]=>00011110011
[5,6,7,9,4,3,2,10,8,1,12,11]=>00011101101
[5,6,7,9,4,3,2,11,8,12,10,1]=>00011101011
[5,6,7,10,4,3,2,11,12,9,8,1]=>00011100111
[5,6,8,9,4,3,10,7,2,1,12,11]=>00011011101
[5,6,8,9,4,3,11,7,2,12,10,1]=>00011011011
[5,6,8,10,4,3,11,7,12,9,2,1]=>00011010111
[5,6,9,10,4,3,11,12,8,7,2,1]=>00011001111
[5,7,8,9,4,10,6,3,2,1,12,11]=>00010111101
[5,7,8,9,4,11,6,3,2,12,10,1]=>00010111011
[5,7,8,10,4,11,6,3,12,9,2,1]=>00010110111
[5,7,9,10,4,11,6,12,8,3,2,1]=>00010101111
[5,8,9,10,4,11,12,7,6,3,2,1]=>00010011111
[6,7,8,9,10,5,4,3,2,1,12,11]=>00001111101
[6,7,8,9,11,5,4,3,2,12,10,1]=>00001111011
[6,7,8,10,11,5,4,3,12,9,2,1]=>00001110111
[6,7,9,10,11,5,4,12,8,3,2,1]=>00001101111
[6,8,9,10,11,5,12,7,4,3,2,1]=>00001011111
[7,8,9,10,11,12,6,5,4,3,2,1]=>00000111111
[9,10,12,11,7,8,5,6,3,4,1,2]=>00110101010
[11,12,7,8,10,9,5,6,3,4,1,2]=>01001101010
[7,10,12,8,11,9,5,6,3,4,1,2]=>00101101010
[7,8,9,12,11,10,5,6,3,4,1,2]=>00011101010
[11,12,9,10,5,6,8,7,3,4,1,2]=>01010011010
[9,10,12,11,5,6,8,7,3,4,1,2]=>00110011010
[11,12,5,8,10,6,9,7,3,4,1,2]=>01001011010
[5,10,12,8,11,6,9,7,3,4,1,2]=>00101011010
[5,8,9,12,11,6,10,7,3,4,1,2]=>00011011010
[11,12,5,6,7,10,9,8,3,4,1,2]=>01000111010
[5,10,12,6,7,11,9,8,3,4,1,2]=>00100111010
[5,6,9,12,7,11,10,8,3,4,1,2]=>00010111010
[5,6,7,8,12,11,10,9,3,4,1,2]=>00001111010
[11,12,9,10,7,8,3,4,6,5,1,2]=>01010100110
[9,10,12,11,7,8,3,4,6,5,1,2]=>00110100110
[11,12,7,8,10,9,3,4,6,5,1,2]=>01001100110
[7,10,12,8,11,9,3,4,6,5,1,2]=>00101100110
[7,8,9,12,11,10,3,4,6,5,1,2]=>00011100110
[11,12,9,10,3,6,8,4,7,5,1,2]=>01010010110
[9,10,12,11,3,6,8,4,7,5,1,2]=>00110010110
[11,12,3,8,10,6,9,4,7,5,1,2]=>01001010110
[3,10,12,8,11,6,9,4,7,5,1,2]=>00101010110
[3,8,9,12,11,6,10,4,7,5,1,2]=>00011010110
[11,12,3,6,7,10,9,4,8,5,1,2]=>01000110110
[3,10,12,6,7,11,9,4,8,5,1,2]=>00100110110
[3,6,9,12,7,11,10,4,8,5,1,2]=>00010110110
[3,6,7,8,12,11,10,4,9,5,1,2]=>00001110110
[11,12,9,10,3,4,5,8,7,6,1,2]=>01010001110
[9,10,12,11,3,4,5,8,7,6,1,2]=>00110001110
[11,12,3,8,10,4,5,9,7,6,1,2]=>01001001110
[3,10,12,8,11,4,5,9,7,6,1,2]=>00101001110
[3,8,9,12,11,4,5,10,7,6,1,2]=>00011001110
[11,12,3,4,7,10,5,9,8,6,1,2]=>01000101110
[3,10,12,4,7,11,5,9,8,6,1,2]=>00100101110
[3,4,9,12,7,11,5,10,8,6,1,2]=>00010101110
[3,4,7,8,12,11,5,10,9,6,1,2]=>00001101110
[11,12,3,4,5,6,10,9,8,7,1,2]=>01000011110
[3,10,12,4,5,6,11,9,8,7,1,2]=>00100011110
[3,4,9,12,5,6,11,10,8,7,1,2]=>00010011110
[3,4,5,8,12,6,11,10,9,7,1,2]=>00001011110
[3,4,5,6,7,12,11,10,9,8,1,2]=>00000111110
[11,12,9,10,7,8,5,6,1,2,4,3]=>01010101001
[9,10,12,11,7,8,5,6,1,2,4,3]=>00110101001
[11,12,7,8,10,9,5,6,1,2,4,3]=>01001101001
[7,10,12,8,11,9,5,6,1,2,4,3]=>00101101001
[7,8,9,12,11,10,5,6,1,2,4,3]=>00011101001
[11,12,9,10,5,6,8,7,1,2,4,3]=>01010011001
[9,10,12,11,5,6,8,7,1,2,4,3]=>00110011001
[11,12,5,8,10,6,9,7,1,2,4,3]=>01001011001
[5,10,12,8,11,6,9,7,1,2,4,3]=>00101011001
[5,8,9,12,11,6,10,7,1,2,4,3]=>00011011001
[11,12,5,6,7,10,9,8,1,2,4,3]=>01000111001
[5,10,12,6,7,11,9,8,1,2,4,3]=>00100111001
[5,6,9,12,7,11,10,8,1,2,4,3]=>00010111001
[5,6,7,8,12,11,10,9,1,2,4,3]=>00001111001
[11,12,9,10,7,8,1,4,6,2,5,3]=>01010100101
[9,10,12,11,7,8,1,4,6,2,5,3]=>00110100101
[11,12,7,8,10,9,1,4,6,2,5,3]=>01001100101
[7,10,12,8,11,9,1,4,6,2,5,3]=>00101100101
[7,8,9,12,11,10,1,4,6,2,5,3]=>00011100101
[11,12,9,10,1,6,8,4,7,2,5,3]=>01010010101
[9,10,12,11,1,6,8,4,7,2,5,3]=>00110010101
[11,12,1,8,10,6,9,4,7,2,5,3]=>01001010101
[1,10,12,8,11,6,9,4,7,2,5,3]=>00101010101
[1,8,9,12,11,6,10,4,7,2,5,3]=>00011010101
[11,12,1,6,7,10,9,4,8,2,5,3]=>01000110101
[1,10,12,6,7,11,9,4,8,2,5,3]=>00100110101
[1,6,9,12,7,11,10,4,8,2,5,3]=>00010110101
[1,6,7,8,12,11,10,4,9,2,5,3]=>00001110101
[11,12,9,10,1,4,5,8,7,2,6,3]=>01010001101
[9,10,12,11,1,4,5,8,7,2,6,3]=>00110001101
[11,12,1,8,10,4,5,9,7,2,6,3]=>01001001101
[1,10,12,8,11,4,5,9,7,2,6,3]=>00101001101
[1,8,9,12,11,4,5,10,7,2,6,3]=>00011001101
[11,12,1,4,7,10,5,9,8,2,6,3]=>01000101101
[1,10,12,4,7,11,5,9,8,2,6,3]=>00100101101
[1,4,9,12,7,11,5,10,8,2,6,3]=>00010101101
[1,4,7,8,12,11,5,10,9,2,6,3]=>00001101101
[11,12,1,4,5,6,10,9,8,2,7,3]=>01000011101
[1,10,12,4,5,6,11,9,8,2,7,3]=>00100011101
[1,4,9,12,5,6,11,10,8,2,7,3]=>00010011101
[1,4,5,8,12,6,11,10,9,2,7,3]=>00001011101
[1,4,5,6,7,12,11,10,9,2,8,3]=>00000111101
[11,12,9,10,7,8,1,2,3,6,5,4]=>01010100011
[9,10,12,11,7,8,1,2,3,6,5,4]=>00110100011
[11,12,7,8,10,9,1,2,3,6,5,4]=>01001100011
[7,10,12,8,11,9,1,2,3,6,5,4]=>00101100011
[7,8,9,12,11,10,1,2,3,6,5,4]=>00011100011
[11,12,9,10,1,6,8,2,3,7,5,4]=>01010010011
[9,10,12,11,1,6,8,2,3,7,5,4]=>00110010011
[11,12,1,8,10,6,9,2,3,7,5,4]=>01001010011
[1,10,12,8,11,6,9,2,3,7,5,4]=>00101010011
[1,8,9,12,11,6,10,2,3,7,5,4]=>00011010011
[11,12,1,6,7,10,9,2,3,8,5,4]=>01000110011
[1,10,12,6,7,11,9,2,3,8,5,4]=>00100110011
[1,6,9,12,7,11,10,2,3,8,5,4]=>00010110011
[1,6,7,8,12,11,10,2,3,9,5,4]=>00001110011
[11,12,9,10,1,2,5,8,3,7,6,4]=>01010001011
[9,10,12,11,1,2,5,8,3,7,6,4]=>00110001011
[11,12,1,8,10,2,5,9,3,7,6,4]=>01001001011
[1,10,12,8,11,2,5,9,3,7,6,4]=>00101001011
[1,8,9,12,11,2,5,10,3,7,6,4]=>00011001011
[11,12,1,2,7,10,5,9,3,8,6,4]=>01000101011
[1,10,12,2,7,11,5,9,3,8,6,4]=>00100101011
[1,2,9,12,7,11,5,10,3,8,6,4]=>00010101011
[1,2,7,8,12,11,5,10,3,9,6,4]=>00001101011
[11,12,1,2,5,6,10,9,3,8,7,4]=>01000011011
[1,10,12,2,5,6,11,9,3,8,7,4]=>00100011011
[1,2,9,12,5,6,11,10,3,8,7,4]=>00010011011
[1,2,5,8,12,6,11,10,3,9,7,4]=>00001011011
[1,2,5,6,7,12,11,10,3,9,8,4]=>00000111011
[11,12,9,10,1,2,3,4,8,7,6,5]=>01010000111
[9,10,12,11,1,2,3,4,8,7,6,5]=>00110000111
[11,12,1,8,10,2,3,4,9,7,6,5]=>01001000111
[1,10,12,8,11,2,3,4,9,7,6,5]=>00101000111
[1,8,9,12,11,2,3,4,10,7,6,5]=>00011000111
[11,12,1,2,7,10,3,4,9,8,6,5]=>01000100111
[1,10,12,2,7,11,3,4,9,8,6,5]=>00100100111
[1,2,9,12,7,11,3,4,10,8,6,5]=>00010100111
[1,2,7,8,12,11,3,4,10,9,6,5]=>00001100111
[11,12,1,2,3,6,10,4,9,8,7,5]=>01000010111
[1,10,12,2,3,6,11,4,9,8,7,5]=>00100010111
[1,2,9,12,3,6,11,4,10,8,7,5]=>00010010111
[1,2,3,8,12,6,11,4,10,9,7,5]=>00001010111
[1,2,3,6,7,12,11,4,10,9,8,5]=>00000110111
[11,12,1,2,3,4,5,10,9,8,7,6]=>01000001111
[1,10,12,2,3,4,5,11,9,8,7,6]=>00100001111
[1,2,9,12,3,4,5,11,10,8,7,6]=>00010001111
[1,2,3,8,12,4,5,11,10,9,7,6]=>00001001111
[1,2,3,4,7,12,5,11,10,9,8,6]=>00000101111
[1,2,3,4,5,6,12,11,10,9,8,7]=>00000011111
[2,1,4,3,6,5,8,7,12,11,9,10]=>10101010110
[2,1,4,3,6,5,10,9,7,8,12,11]=>10101011001
[2,1,4,3,6,5,12,9,7,11,8,10]=>10101011010
[2,1,4,3,6,5,12,11,10,7,8,9]=>10101011100
[2,1,4,3,8,7,5,6,10,9,12,11]=>10101100101
[2,1,4,3,8,7,5,6,12,11,9,10]=>10101100110
[2,1,4,3,10,7,5,9,6,8,12,11]=>10101101001
[2,1,4,3,12,7,5,9,6,11,8,10]=>10101101010
[2,1,4,3,12,7,5,11,10,6,8,9]=>10101101100
[2,1,4,3,10,9,8,5,6,7,12,11]=>10101110001
[2,1,4,3,12,9,8,5,6,11,7,10]=>10101110010
[2,1,4,3,12,11,8,5,10,6,7,9]=>10101110100
[2,1,4,3,12,11,10,9,5,6,7,8]=>10101111000
[2,1,6,5,3,4,8,7,10,9,12,11]=>10110010101
[2,1,6,5,3,4,8,7,12,11,9,10]=>10110010110
[2,1,6,5,3,4,10,9,7,8,12,11]=>10110011001
[2,1,6,5,3,4,12,9,7,11,8,10]=>10110011010
[2,1,6,5,3,4,12,11,10,7,8,9]=>10110011100
[2,1,8,5,3,7,4,6,10,9,12,11]=>10110100101
[2,1,8,5,3,7,4,6,12,11,9,10]=>10110100110
[2,1,10,5,3,7,4,9,6,8,12,11]=>10110101001
[2,1,12,5,3,7,4,9,6,11,8,10]=>10110101010
[2,1,12,5,3,7,4,11,10,6,8,9]=>10110101100
[2,1,10,5,3,9,8,4,6,7,12,11]=>10110110001
[2,1,12,5,3,9,8,4,6,11,7,10]=>10110110010
[2,1,12,5,3,11,8,4,10,6,7,9]=>10110110100
[2,1,12,5,3,11,10,9,4,6,7,8]=>10110111000
[2,1,8,7,6,3,4,5,10,9,12,11]=>10111000101
[2,1,8,7,6,3,4,5,12,11,9,10]=>10111000110
[2,1,10,7,6,3,4,9,5,8,12,11]=>10111001001
[2,1,12,7,6,3,4,9,5,11,8,10]=>10111001010
[2,1,12,7,6,3,4,11,10,5,8,9]=>10111001100
[2,1,10,9,6,3,8,4,5,7,12,11]=>10111010001
[2,1,12,9,6,3,8,4,5,11,7,10]=>10111010010
[2,1,12,11,6,3,8,4,10,5,7,9]=>10111010100
[2,1,12,11,6,3,10,9,4,5,7,8]=>10111011000
[2,1,10,9,8,7,3,4,5,6,12,11]=>10111100001
[2,1,12,9,8,7,3,4,5,11,6,10]=>10111100010
[2,1,12,11,8,7,3,4,10,5,6,9]=>10111100100
[2,1,12,11,10,7,3,9,4,5,6,8]=>10111101000
[2,1,12,11,10,9,8,3,4,5,6,7]=>10111110000
[4,3,1,2,6,5,8,7,10,9,12,11]=>11001010101
[4,3,1,2,6,5,8,7,12,11,9,10]=>11001010110
[4,3,1,2,6,5,10,9,7,8,12,11]=>11001011001
[4,3,1,2,6,5,12,9,7,11,8,10]=>11001011010
[4,3,1,2,6,5,12,11,10,7,8,9]=>11001011100
[4,3,1,2,8,7,5,6,10,9,12,11]=>11001100101
[4,3,1,2,8,7,5,6,12,11,9,10]=>11001100110
[4,3,1,2,10,7,5,9,6,8,12,11]=>11001101001
[4,3,1,2,12,7,5,9,6,11,8,10]=>11001101010
[4,3,1,2,12,7,5,11,10,6,8,9]=>11001101100
[4,3,1,2,10,9,8,5,6,7,12,11]=>11001110001
[4,3,1,2,12,9,8,5,6,11,7,10]=>11001110010
[4,3,1,2,12,11,8,5,10,6,7,9]=>11001110100
[4,3,1,2,12,11,10,9,5,6,7,8]=>11001111000
[6,3,1,5,2,4,8,7,10,9,12,11]=>11010010101
[6,3,1,5,2,4,8,7,12,11,9,10]=>11010010110
[6,3,1,5,2,4,10,9,7,8,12,11]=>11010011001
[6,3,1,5,2,4,12,9,7,11,8,10]=>11010011010
[6,3,1,5,2,4,12,11,10,7,8,9]=>11010011100
[8,3,1,5,2,7,4,6,10,9,12,11]=>11010100101
[8,3,1,5,2,7,4,6,12,11,9,10]=>11010100110
[10,3,1,5,2,7,4,9,6,8,12,11]=>11010101001
[12,3,1,5,2,7,4,9,6,11,8,10]=>11010101010
[12,3,1,5,2,7,4,11,10,6,8,9]=>11010101100
[10,3,1,5,2,9,8,4,6,7,12,11]=>11010110001
[12,3,1,5,2,9,8,4,6,11,7,10]=>11010110010
[12,3,1,5,2,11,8,4,10,6,7,9]=>11010110100
[12,3,1,5,2,11,10,9,4,6,7,8]=>11010111000
[8,3,1,7,6,2,4,5,10,9,12,11]=>11011000101
[8,3,1,7,6,2,4,5,12,11,9,10]=>11011000110
[10,3,1,7,6,2,4,9,5,8,12,11]=>11011001001
[12,3,1,7,6,2,4,9,5,11,8,10]=>11011001010
[12,3,1,7,6,2,4,11,10,5,8,9]=>11011001100
[10,3,1,9,6,2,8,4,5,7,12,11]=>11011010001
[12,3,1,9,6,2,8,4,5,11,7,10]=>11011010010
[12,3,1,11,6,2,8,4,10,5,7,9]=>11011010100
[12,3,1,11,6,2,10,9,4,5,7,8]=>11011011000
[10,3,1,9,8,7,2,4,5,6,12,11]=>11011100001
[12,3,1,9,8,7,2,4,5,11,6,10]=>11011100010
[12,3,1,11,8,7,2,4,10,5,6,9]=>11011100100
[12,3,1,11,10,7,2,9,4,5,6,8]=>11011101000
[12,3,1,11,10,9,8,2,4,5,6,7]=>11011110000
[6,5,4,1,2,3,8,7,10,9,12,11]=>11100010101
[6,5,4,1,2,3,8,7,12,11,9,10]=>11100010110
[6,5,4,1,2,3,10,9,7,8,12,11]=>11100011001
[6,5,4,1,2,3,12,9,7,11,8,10]=>11100011010
[6,5,4,1,2,3,12,11,10,7,8,9]=>11100011100
[8,5,4,1,2,7,3,6,10,9,12,11]=>11100100101
[8,5,4,1,2,7,3,6,12,11,9,10]=>11100100110
[10,5,4,1,2,7,3,9,6,8,12,11]=>11100101001
[12,5,4,1,2,7,3,9,6,11,8,10]=>11100101010
[12,5,4,1,2,7,3,11,10,6,8,9]=>11100101100
[10,5,4,1,2,9,8,3,6,7,12,11]=>11100110001
[12,5,4,1,2,9,8,3,6,11,7,10]=>11100110010
[12,5,4,1,2,11,8,3,10,6,7,9]=>11100110100
[12,5,4,1,2,11,10,9,3,6,7,8]=>11100111000
[8,7,4,1,6,2,3,5,10,9,12,11]=>11101000101
[8,7,4,1,6,2,3,5,12,11,9,10]=>11101000110
[10,7,4,1,6,2,3,9,5,8,12,11]=>11101001001
[12,7,4,1,6,2,3,9,5,11,8,10]=>11101001010
[12,7,4,1,6,2,3,11,10,5,8,9]=>11101001100
[10,9,4,1,6,2,8,3,5,7,12,11]=>11101010001
[12,9,4,1,6,2,8,3,5,11,7,10]=>11101010010
[12,11,4,1,6,2,8,3,10,5,7,9]=>11101010100
[12,11,4,1,6,2,10,9,3,5,7,8]=>11101011000
[10,9,4,1,8,7,2,3,5,6,12,11]=>11101100001
[12,9,4,1,8,7,2,3,5,11,6,10]=>11101100010
[12,11,4,1,8,7,2,3,10,5,6,9]=>11101100100
[12,11,4,1,10,7,2,9,3,5,6,8]=>11101101000
[12,11,4,1,10,9,8,2,3,5,6,7]=>11101110000
[8,7,6,5,1,2,3,4,10,9,12,11]=>11110000101
[8,7,6,5,1,2,3,4,12,11,9,10]=>11110000110
[10,7,6,5,1,2,3,9,4,8,12,11]=>11110001001
[12,7,6,5,1,2,3,9,4,11,8,10]=>11110001010
[12,7,6,5,1,2,3,11,10,4,8,9]=>11110001100
[10,9,6,5,1,2,8,3,4,7,12,11]=>11110010001
[12,9,6,5,1,2,8,3,4,11,7,10]=>11110010010
[12,11,6,5,1,2,8,3,10,4,7,9]=>11110010100
[12,11,6,5,1,2,10,9,3,4,7,8]=>11110011000
[10,9,8,5,1,7,2,3,4,6,12,11]=>11110100001
[12,9,8,5,1,7,2,3,4,11,6,10]=>11110100010
[12,11,8,5,1,7,2,3,10,4,6,9]=>11110100100
[12,11,10,5,1,7,2,9,3,4,6,8]=>11110101000
[12,11,10,5,1,9,8,2,3,4,6,7]=>11110110000
[10,9,8,7,6,1,2,3,4,5,12,11]=>11111000001
[12,9,8,7,6,1,2,3,4,11,5,10]=>11111000010
[12,11,8,7,6,1,2,3,10,4,5,9]=>11111000100
[12,11,10,7,6,1,2,9,3,4,5,8]=>11111001000
[12,11,10,9,6,1,8,2,3,4,5,7]=>11111010000
[12,11,10,9,8,7,1,2,3,4,5,6]=>11111100000
[11,12,9,10,7,8,5,6,2,1,3,4]=>01010101100
[11,12,9,10,7,8,4,3,5,6,1,2]=>01010110010
[11,12,9,10,7,8,4,2,5,1,3,6]=>01010110100
[11,12,9,10,7,8,3,2,1,4,5,6]=>01010111000
[11,12,9,10,6,5,7,8,3,4,1,2]=>01011001010
[11,12,9,10,6,5,7,8,2,1,3,4]=>01011001100
[11,12,9,10,6,4,7,3,5,8,1,2]=>01011010010
[11,12,9,10,6,4,7,2,5,1,3,8]=>01011010100
[11,12,9,10,6,3,7,2,1,4,5,8]=>01011011000
[11,12,9,10,5,4,3,6,7,8,1,2]=>01011100010
[11,12,9,10,5,4,2,6,7,1,3,8]=>01011100100
[11,12,9,10,5,3,2,6,1,4,7,8]=>01011101000
[11,12,9,10,4,3,2,1,5,6,7,8]=>01011110000
[11,12,8,7,9,10,5,6,3,4,1,2]=>01100101010
[11,12,8,7,9,10,5,6,2,1,3,4]=>01100101100
[11,12,8,7,9,10,4,3,5,6,1,2]=>01100110010
[11,12,8,7,9,10,4,2,5,1,3,6]=>01100110100
[11,12,8,7,9,10,3,2,1,4,5,6]=>01100111000
[11,12,8,6,9,5,7,10,3,4,1,2]=>01101001010
[11,12,8,6,9,5,7,10,2,1,3,4]=>01101001100
[11,12,8,6,9,4,7,3,5,10,1,2]=>01101010010
[11,12,8,6,9,4,7,2,5,1,3,10]=>01101010100
[11,12,8,6,9,3,7,2,1,4,5,10]=>01101011000
[11,12,8,5,9,4,3,6,7,10,1,2]=>01101100010
[11,12,8,5,9,4,2,6,7,1,3,10]=>01101100100
[11,12,8,5,9,3,2,6,1,4,7,10]=>01101101000
[11,12,8,4,9,3,2,1,5,6,7,10]=>01101110000
[11,12,7,6,5,8,9,10,3,4,1,2]=>01110001010
[11,12,7,6,5,8,9,10,2,1,3,4]=>01110001100
[11,12,7,6,4,8,9,3,5,10,1,2]=>01110010010
[11,12,7,6,4,8,9,2,5,1,3,10]=>01110010100
[11,12,7,6,3,8,9,2,1,4,5,10]=>01110011000
[11,12,7,5,4,8,3,6,9,10,1,2]=>01110100010
[11,12,7,5,4,8,2,6,9,1,3,10]=>01110100100
[11,12,7,5,3,8,2,6,1,4,9,10]=>01110101000
[11,12,7,4,3,8,2,1,5,6,9,10]=>01110110000
[11,12,6,5,4,3,7,8,9,10,1,2]=>01111000010
[11,12,6,5,4,2,7,8,9,1,3,10]=>01111000100
[11,12,6,5,3,2,7,8,1,4,9,10]=>01111001000
[11,12,6,4,3,2,7,1,5,8,9,10]=>01111010000
[11,12,5,4,3,2,1,6,7,8,9,10]=>01111100000
[10,9,11,12,7,8,5,6,3,4,1,2]=>10010101010
[10,9,11,12,7,8,5,6,2,1,3,4]=>10010101100
[10,9,11,12,7,8,4,3,5,6,1,2]=>10010110010
[10,9,11,12,7,8,4,2,5,1,3,6]=>10010110100
[10,9,11,12,7,8,3,2,1,4,5,6]=>10010111000
[10,9,11,12,6,5,7,8,3,4,1,2]=>10011001010
[10,9,11,12,6,5,7,8,2,1,3,4]=>10011001100
[10,9,11,12,6,4,7,3,5,8,1,2]=>10011010010
[10,9,11,12,6,4,7,2,5,1,3,8]=>10011010100
[10,9,11,12,6,3,7,2,1,4,5,8]=>10011011000
[10,9,11,12,5,4,3,6,7,8,1,2]=>10011100010
[10,9,11,12,5,4,2,6,7,1,3,8]=>10011100100
[10,9,11,12,5,3,2,6,1,4,7,8]=>10011101000
[10,9,11,12,4,3,2,1,5,6,7,8]=>10011110000
[10,8,11,7,9,12,5,6,3,4,1,2]=>10100101010
[10,8,11,7,9,12,5,6,2,1,3,4]=>10100101100
[10,8,11,7,9,12,4,3,5,6,1,2]=>10100110010
[10,8,11,7,9,12,4,2,5,1,3,6]=>10100110100
[10,8,11,7,9,12,3,2,1,4,5,6]=>10100111000
[10,8,11,6,9,5,7,12,3,4,1,2]=>10101001010
[10,8,11,6,9,5,7,12,2,1,3,4]=>10101001100
[10,8,11,6,9,4,7,3,5,12,1,2]=>10101010010
[10,8,11,6,9,4,7,2,5,1,3,12]=>10101010100
[10,8,11,6,9,3,7,2,1,4,5,12]=>10101011000
[10,8,11,5,9,4,3,6,7,12,1,2]=>10101100010
[10,8,11,5,9,4,2,6,7,1,3,12]=>10101100100
[10,8,11,5,9,3,2,6,1,4,7,12]=>10101101000
[10,8,11,4,9,3,2,1,5,6,7,12]=>10101110000
[10,7,11,6,5,8,9,12,3,4,1,2]=>10110001010
[10,7,11,6,5,8,9,12,2,1,3,4]=>10110001100
[10,7,11,6,4,8,9,3,5,12,1,2]=>10110010010
[10,7,11,6,4,8,9,2,5,1,3,12]=>10110010100
[10,7,11,6,3,8,9,2,1,4,5,12]=>10110011000
[10,7,11,5,4,8,3,6,9,12,1,2]=>10110100010
[10,7,11,5,4,8,2,6,9,1,3,12]=>10110100100
[10,7,11,5,3,8,2,6,1,4,9,12]=>10110101000
[10,7,11,4,3,8,2,1,5,6,9,12]=>10110110000
[10,6,11,5,4,3,7,8,9,12,1,2]=>10111000010
[10,6,11,5,4,2,7,8,9,1,3,12]=>10111000100
[10,6,11,5,3,2,7,8,1,4,9,12]=>10111001000
[10,6,11,4,3,2,7,1,5,8,9,12]=>10111010000
[10,5,11,4,3,2,1,6,7,8,9,12]=>10111100000
[9,8,7,10,11,12,5,6,3,4,1,2]=>11000101010
[9,8,7,10,11,12,5,6,2,1,3,4]=>11000101100
[9,8,7,10,11,12,4,3,5,6,1,2]=>11000110010
[9,8,7,10,11,12,4,2,5,1,3,6]=>11000110100
[9,8,7,10,11,12,3,2,1,4,5,6]=>11000111000
[9,8,6,10,11,5,7,12,3,4,1,2]=>11001001010
[9,8,6,10,11,5,7,12,2,1,3,4]=>11001001100
[9,8,6,10,11,4,7,3,5,12,1,2]=>11001010010
[9,8,6,10,11,4,7,2,5,1,3,12]=>11001010100
[9,8,6,10,11,3,7,2,1,4,5,12]=>11001011000
[9,8,5,10,11,4,3,6,7,12,1,2]=>11001100010
[9,8,5,10,11,4,2,6,7,1,3,12]=>11001100100
[9,8,5,10,11,3,2,6,1,4,7,12]=>11001101000
[9,8,4,10,11,3,2,1,5,6,7,12]=>11001110000
[9,7,6,10,5,8,11,12,3,4,1,2]=>11010001010
[9,7,6,10,5,8,11,12,2,1,3,4]=>11010001100
[9,7,6,10,4,8,11,3,5,12,1,2]=>11010010010
[9,7,6,10,4,8,11,2,5,1,3,12]=>11010010100
[9,7,6,10,3,8,11,2,1,4,5,12]=>11010011000
[9,7,5,10,4,8,3,6,11,12,1,2]=>11010100010
[9,7,5,10,4,8,2,6,11,1,3,12]=>11010100100
[9,7,5,10,3,8,2,6,1,4,11,12]=>11010101000
[9,7,4,10,3,8,2,1,5,6,11,12]=>11010110000
[9,6,5,10,4,3,7,8,11,12,1,2]=>11011000010
[9,6,5,10,4,2,7,8,11,1,3,12]=>11011000100
[9,6,5,10,3,2,7,8,1,4,11,12]=>11011001000
[9,6,4,10,3,2,7,1,5,8,11,12]=>11011010000
[9,5,4,10,3,2,1,6,7,8,11,12]=>11011100000
[8,7,6,5,9,10,11,12,3,4,1,2]=>11100001010
[8,7,6,5,9,10,11,12,2,1,3,4]=>11100001100
[8,7,6,4,9,10,11,3,5,12,1,2]=>11100010010
[8,7,6,4,9,10,11,2,5,1,3,12]=>11100010100
[8,7,6,3,9,10,11,2,1,4,5,12]=>11100011000
[8,7,5,4,9,10,3,6,11,12,1,2]=>11100100010
[8,7,5,4,9,10,2,6,11,1,3,12]=>11100100100
[8,7,5,3,9,10,2,6,1,4,11,12]=>11100101000
[8,7,4,3,9,10,2,1,5,6,11,12]=>11100110000
[8,6,5,4,9,3,7,10,11,12,1,2]=>11101000010
[8,6,5,4,9,2,7,10,11,1,3,12]=>11101000100
[8,6,5,3,9,2,7,10,1,4,11,12]=>11101001000
[8,6,4,3,9,2,7,1,5,10,11,12]=>11101010000
[8,5,4,3,9,2,1,6,7,10,11,12]=>11101100000
[7,6,5,4,3,8,9,10,11,12,1,2]=>11110000010
[7,6,5,4,2,8,9,10,11,1,3,12]=>11110000100
[7,6,5,3,2,8,9,10,1,4,11,12]=>11110001000
[7,6,4,3,2,8,9,1,5,10,11,12]=>11110010000
[7,5,4,3,2,8,1,6,9,10,11,12]=>11110100000
[6,5,4,3,2,1,7,8,9,10,11,12]=>11111000000
[3,2,5,4,7,6,9,8,1,12,10,11]=>10101011010
[3,2,5,4,7,6,11,10,8,9,1,12]=>10101011010
[3,2,5,4,7,6,1,10,8,12,9,11]=>10101101010
[3,2,5,4,7,6,1,12,11,8,9,10]=>10101101100
[3,2,5,4,9,8,6,7,11,10,1,12]=>10101100110
[3,2,5,4,9,8,6,7,1,12,10,11]=>10101101010
[3,2,5,4,11,8,6,10,7,9,1,12]=>10101101010
[3,2,5,4,1,8,6,10,7,12,9,11]=>10110101010
[3,2,5,4,1,8,6,12,11,7,9,10]=>10110101100
[3,2,5,4,11,10,9,6,7,8,1,12]=>10101110010
[3,2,5,4,1,10,9,6,7,12,8,11]=>10110110010
[3,2,5,4,1,12,9,6,11,7,8,10]=>10110110100
[3,2,5,4,1,12,11,10,6,7,8,9]=>10110111000
[3,2,7,6,4,5,9,8,11,10,1,12]=>10110010110
[3,2,7,6,4,5,9,8,1,12,10,11]=>10110011010
[3,2,7,6,4,5,11,10,8,9,1,12]=>10110011010
[3,2,7,6,4,5,1,10,8,12,9,11]=>10110101010
[3,2,7,6,4,5,1,12,11,8,9,10]=>10110101100
[3,2,9,6,4,8,5,7,11,10,1,12]=>10110100110
[3,2,9,6,4,8,5,7,1,12,10,11]=>10110101010
[3,2,11,6,4,8,5,10,7,9,1,12]=>10110101010
[3,2,1,6,4,8,5,10,7,12,9,11]=>11010101010
[3,2,1,6,4,8,5,12,11,7,9,10]=>11010101100
[3,2,11,6,4,10,9,5,7,8,1,12]=>10110110010
[3,2,1,6,4,10,9,5,7,12,8,11]=>11010110010
[3,2,1,6,4,12,9,5,11,7,8,10]=>11010110100
[3,2,1,6,4,12,11,10,5,7,8,9]=>11010111000
[3,2,9,8,7,4,5,6,11,10,1,12]=>10111000110
[3,2,9,8,7,4,5,6,1,12,10,11]=>10111001010
[3,2,11,8,7,4,5,10,6,9,1,12]=>10111001010
[3,2,1,8,7,4,5,10,6,12,9,11]=>11011001010
[3,2,1,8,7,4,5,12,11,6,9,10]=>11011001100
[3,2,11,10,7,4,9,5,6,8,1,12]=>10111010010
[3,2,1,10,7,4,9,5,6,12,8,11]=>11011010010
[3,2,1,12,7,4,9,5,11,6,8,10]=>11011010100
[3,2,1,12,7,4,11,10,5,6,8,9]=>11011011000
[3,2,11,10,9,8,4,5,6,7,1,12]=>10111100010
[3,2,1,10,9,8,4,5,6,12,7,11]=>11011100010
[3,2,1,12,9,8,4,5,11,6,7,10]=>11011100100
[3,2,1,12,11,8,4,10,5,6,7,9]=>11011101000
[3,2,1,12,11,10,9,4,5,6,7,8]=>11011110000
[5,4,2,3,7,6,9,8,11,10,1,12]=>11001010110
[5,4,2,3,7,6,9,8,1,12,10,11]=>11001011010
[5,4,2,3,7,6,11,10,8,9,1,12]=>11001011010
[5,4,2,3,7,6,1,10,8,12,9,11]=>11001101010
[5,4,2,3,7,6,1,12,11,8,9,10]=>11001101100
[5,4,2,3,9,8,6,7,11,10,1,12]=>11001100110
[5,4,2,3,9,8,6,7,1,12,10,11]=>11001101010
[5,4,2,3,11,8,6,10,7,9,1,12]=>11001101010
[5,4,2,3,1,8,6,10,7,12,9,11]=>11010101010
[5,4,2,3,1,8,6,12,11,7,9,10]=>11010101100
[5,4,2,3,11,10,9,6,7,8,1,12]=>11001110010
[5,4,2,3,1,10,9,6,7,12,8,11]=>11010110010
[5,4,2,3,1,12,9,6,11,7,8,10]=>11010110100
[5,4,2,3,1,12,11,10,6,7,8,9]=>11010111000
[7,4,2,6,3,5,9,8,11,10,1,12]=>11010010110
[7,4,2,6,3,5,9,8,1,12,10,11]=>11010011010
[7,4,2,6,3,5,11,10,8,9,1,12]=>11010011010
[7,4,2,6,3,5,1,10,8,12,9,11]=>11010101010
[7,4,2,6,3,5,1,12,11,8,9,10]=>11010101100
[9,4,2,6,3,8,5,7,11,10,1,12]=>11010100110
[9,4,2,6,3,8,5,7,1,12,10,11]=>11010101010
[11,4,2,6,3,8,5,10,7,9,1,12]=>11010101010
[1,4,2,6,3,8,5,10,7,12,9,11]=>01010101010
[1,4,2,6,3,8,5,12,11,7,9,10]=>01010101100
[11,4,2,6,3,10,9,5,7,8,1,12]=>11010110010
[1,4,2,6,3,10,9,5,7,12,8,11]=>01010110010
[1,4,2,6,3,12,9,5,11,7,8,10]=>01010110100
[1,4,2,6,3,12,11,10,5,7,8,9]=>01010111000
[9,4,2,8,7,3,5,6,11,10,1,12]=>11011000110
[9,4,2,8,7,3,5,6,1,12,10,11]=>11011001010
[11,4,2,8,7,3,5,10,6,9,1,12]=>11011001010
[1,4,2,8,7,3,5,10,6,12,9,11]=>01011001010
[1,4,2,8,7,3,5,12,11,6,9,10]=>01011001100
[11,4,2,10,7,3,9,5,6,8,1,12]=>11011010010
[1,4,2,10,7,3,9,5,6,12,8,11]=>01011010010
[1,4,2,12,7,3,9,5,11,6,8,10]=>01011010100
[1,4,2,12,7,3,11,10,5,6,8,9]=>01011011000
[11,4,2,10,9,8,3,5,6,7,1,12]=>11011100010
[1,4,2,10,9,8,3,5,6,12,7,11]=>01011100010
[1,4,2,12,9,8,3,5,11,6,7,10]=>01011100100
[1,4,2,12,11,8,3,10,5,6,7,9]=>01011101000
[1,4,2,12,11,10,9,3,5,6,7,8]=>01011110000
[7,6,5,2,3,4,9,8,11,10,1,12]=>11100010110
[7,6,5,2,3,4,9,8,1,12,10,11]=>11100011010
[7,6,5,2,3,4,11,10,8,9,1,12]=>11100011010
[7,6,5,2,3,4,1,10,8,12,9,11]=>11100101010
[7,6,5,2,3,4,1,12,11,8,9,10]=>11100101100
[9,6,5,2,3,8,4,7,11,10,1,12]=>11100100110
[9,6,5,2,3,8,4,7,1,12,10,11]=>11100101010
[11,6,5,2,3,8,4,10,7,9,1,12]=>11100101010
[1,6,5,2,3,8,4,10,7,12,9,11]=>01100101010
[1,6,5,2,3,8,4,12,11,7,9,10]=>01100101100
[11,6,5,2,3,10,9,4,7,8,1,12]=>11100110010
[1,6,5,2,3,10,9,4,7,12,8,11]=>01100110010
[1,6,5,2,3,12,9,4,11,7,8,10]=>01100110100
[1,6,5,2,3,12,11,10,4,7,8,9]=>01100111000
[9,8,5,2,7,3,4,6,11,10,1,12]=>11101000110
[9,8,5,2,7,3,4,6,1,12,10,11]=>11101001010
[11,8,5,2,7,3,4,10,6,9,1,12]=>11101001010
[1,8,5,2,7,3,4,10,6,12,9,11]=>01101001010
[1,8,5,2,7,3,4,12,11,6,9,10]=>01101001100
[11,10,5,2,7,3,9,4,6,8,1,12]=>11101010010
[1,10,5,2,7,3,9,4,6,12,8,11]=>01101010010
[1,12,5,2,7,3,9,4,11,6,8,10]=>01101010100
[1,12,5,2,7,3,11,10,4,6,8,9]=>01101011000
[11,10,5,2,9,8,3,4,6,7,1,12]=>11101100010
[1,10,5,2,9,8,3,4,6,12,7,11]=>01101100010
[1,12,5,2,9,8,3,4,11,6,7,10]=>01101100100
[1,12,5,2,11,8,3,10,4,6,7,9]=>01101101000
[1,12,5,2,11,10,9,3,4,6,7,8]=>01101110000
[9,8,7,6,2,3,4,5,11,10,1,12]=>11110000110
[9,8,7,6,2,3,4,5,1,12,10,11]=>11110001010
[11,8,7,6,2,3,4,10,5,9,1,12]=>11110001010
[1,8,7,6,2,3,4,10,5,12,9,11]=>01110001010
[1,8,7,6,2,3,4,12,11,5,9,10]=>01110001100
[11,10,7,6,2,3,9,4,5,8,1,12]=>11110010010
[1,10,7,6,2,3,9,4,5,12,8,11]=>01110010010
[1,12,7,6,2,3,9,4,11,5,8,10]=>01110010100
[1,12,7,6,2,3,11,10,4,5,8,9]=>01110011000
[11,10,9,6,2,8,3,4,5,7,1,12]=>11110100010
[1,10,9,6,2,8,3,4,5,12,7,11]=>01110100010
[1,12,9,6,2,8,3,4,11,5,7,10]=>01110100100
[1,12,11,6,2,8,3,10,4,5,7,9]=>01110101000
[1,12,11,6,2,10,9,3,4,5,7,8]=>01110110000
[11,10,9,8,7,2,3,4,5,6,1,12]=>11111000010
[1,10,9,8,7,2,3,4,5,12,6,11]=>01111000010
[1,12,9,8,7,2,3,4,11,5,6,10]=>01111000100
[1,12,11,8,7,2,3,10,4,5,6,9]=>01111001000
[1,12,11,10,7,2,9,3,4,5,6,8]=>01111010000
[1,12,11,10,9,8,2,3,4,5,6,7]=>01111100000
[2,1,4,3,6,5,8,7,10,12,11,9]=>10101010011
[2,1,4,3,6,5,8,10,9,7,12,11]=>10101001101
[2,1,4,3,6,5,10,12,9,11,7,8]=>10101001010
[2,1,4,3,6,5,8,9,12,10,11,7]=>10101000101
[2,1,4,3,6,8,7,5,10,9,12,11]=>10100110101
[2,1,4,3,6,8,7,5,10,12,11,9]=>10100110011
[2,1,4,3,8,10,7,9,5,6,12,11]=>10100101001
[2,1,4,3,10,9,7,12,6,11,5,8]=>10101101010
[2,1,4,3,8,9,7,12,10,6,11,5]=>10100101101
[2,1,4,3,6,7,10,8,9,5,12,11]=>10100010101
[2,1,4,3,10,7,12,8,9,11,5,6]=>10101010010
[2,1,4,3,6,9,12,8,11,10,5,7]=>10100010110
[2,1,4,3,6,7,8,12,9,10,11,5]=>10100001001
[2,1,4,6,5,3,8,7,10,9,12,11]=>10011010101
[2,1,4,6,5,3,8,7,10,12,11,9]=>10011010011
[2,1,4,6,5,3,8,10,9,7,12,11]=>10011001101
[2,1,4,6,5,3,10,12,9,11,7,8]=>10011001010
[2,1,4,6,5,3,8,9,12,10,11,7]=>10011000101
[2,1,6,8,5,7,3,4,10,9,12,11]=>10010100101
[2,1,6,8,5,7,3,4,10,12,11,9]=>10010100011
[2,1,8,7,5,10,4,9,3,6,12,11]=>10110101001
[2,1,10,7,5,9,4,12,6,11,3,8]=>10110101010
[2,1,8,7,5,9,4,12,10,6,11,3]=>10110101101
[2,1,6,7,5,10,8,4,9,3,12,11]=>10010110101
[2,1,10,8,5,7,12,4,9,11,3,6]=>10110010010
[2,1,6,9,5,8,12,3,11,10,4,7]=>10010010110
[2,1,6,7,5,8,12,9,3,10,11,4]=>10010011001
[2,1,4,5,8,6,7,3,10,9,12,11]=>10001010101
[2,1,4,5,8,6,7,3,10,12,11,9]=>10001010011
[2,1,8,5,10,6,7,9,3,4,12,11]=>10101001001
[2,1,10,5,9,6,7,12,4,11,3,8]=>10101001010
[2,1,8,5,9,6,7,12,10,4,11,3]=>10101001101
[2,1,4,7,10,6,9,8,3,5,12,11]=>10001011001
[2,1,10,7,12,6,9,8,4,11,3,5]=>10101011010
[2,1,4,9,12,6,10,8,11,7,3,5]=>10001010110
[2,1,4,7,8,6,12,10,9,5,11,3]=>10001011101
[2,1,4,5,6,10,7,8,9,3,12,11]=>10000100101
[2,1,10,5,6,12,7,8,9,11,3,4]=>10100100010
[2,1,4,9,6,12,7,8,11,10,3,5]=>10010100110
[2,1,4,5,8,12,7,11,9,10,3,6]=>10000101010
[2,1,4,5,6,7,12,8,9,10,11,3]=>10000010001
[2,4,3,1,6,5,8,7,10,9,12,11]=>01101010101
[2,4,3,1,6,5,8,7,10,12,11,9]=>01101010011
[2,4,3,1,6,5,8,10,9,7,12,11]=>01101001101
[2,4,3,1,6,5,10,12,9,11,7,8]=>01101001010
[2,4,3,1,6,5,8,9,12,10,11,7]=>01101000101
[2,4,3,1,6,8,7,5,10,9,12,11]=>01100110101
[2,4,3,1,6,8,7,5,10,12,11,9]=>01100110011
[2,4,3,1,8,10,7,9,5,6,12,11]=>01100101001
[2,4,3,1,10,9,7,12,6,11,5,8]=>01101101010
[2,4,3,1,8,9,7,12,10,6,11,5]=>01100101101
[2,4,3,1,6,7,10,8,9,5,12,11]=>01100010101
[2,4,3,1,10,7,12,8,9,11,5,6]=>01101010010
[2,4,3,1,6,9,12,8,11,10,5,7]=>01100010110
[2,4,3,1,6,7,8,12,9,10,11,5]=>01100001001
[4,6,3,5,1,2,8,7,10,9,12,11]=>01010010101
[4,6,3,5,1,2,8,7,10,12,11,9]=>01010010011
[4,6,3,5,1,2,8,10,9,7,12,11]=>01010001101
[4,6,3,5,1,2,10,12,9,11,7,8]=>01010001010
[4,6,3,5,1,2,8,9,12,10,11,7]=>01010000101
[6,5,3,8,2,7,1,4,10,9,12,11]=>11010100101
[6,5,3,8,2,7,1,4,10,12,11,9]=>11010100011
[8,5,3,7,2,10,4,9,1,6,12,11]=>11010101001
[10,5,3,7,2,9,4,12,6,11,1,8]=>11010101010
[8,5,3,7,2,9,4,12,10,6,11,1]=>11010101101
[6,5,3,7,2,10,8,4,9,1,12,11]=>11010110101
[10,5,3,8,2,7,12,4,9,11,1,6]=>11010010010
[6,5,3,9,2,8,12,1,11,10,4,7]=>11010010110
[6,5,3,7,2,8,12,9,1,10,11,4]=>11010011001
[4,5,3,8,6,2,7,1,10,9,12,11]=>01011010101
[4,5,3,8,6,2,7,1,10,12,11,9]=>01011010011
[8,6,3,5,10,2,7,9,1,4,12,11]=>11001001001
[10,6,3,5,9,2,7,12,4,11,1,8]=>11001001010
[8,6,3,5,9,2,7,12,10,4,11,1]=>11001001101
[4,7,3,6,10,1,9,8,2,5,12,11]=>01001011001
[10,6,3,7,12,2,9,8,4,11,1,5]=>11001011010
[4,9,3,6,12,1,10,8,11,7,2,5]=>01001010110
[4,7,3,6,8,1,12,10,9,5,11,2]=>01001011101
[4,5,3,6,10,7,1,8,9,2,12,11]=>01001100101
[10,7,3,5,6,12,2,8,9,11,1,4]=>11000100010
[4,9,3,7,6,12,1,8,11,10,2,5]=>01010100110
[4,5,3,8,7,12,2,11,9,10,1,6]=>01010101010
[4,5,3,6,7,12,8,2,9,10,11,1]=>01000110001
[2,3,6,4,5,1,8,7,10,9,12,11]=>00101010101
[2,3,6,4,5,1,8,7,10,12,11,9]=>00101010011
[2,3,6,4,5,1,8,10,9,7,12,11]=>00101001101
[2,3,6,4,5,1,10,12,9,11,7,8]=>00101001010
[2,3,6,4,5,1,8,9,12,10,11,7]=>00101000101
[6,3,8,4,5,7,1,2,10,9,12,11]=>10100100101
[6,3,8,4,5,7,1,2,10,12,11,9]=>10100100011
[8,3,7,4,5,10,2,9,1,6,12,11]=>10100101001
[10,3,7,4,5,9,2,12,6,11,1,8]=>10100101010
[8,3,7,4,5,9,2,12,10,6,11,1]=>10100101101
[6,3,7,4,5,10,8,2,9,1,12,11]=>10100110101
[10,3,8,4,5,7,12,2,9,11,1,6]=>10100010010
[6,3,9,4,5,8,12,1,11,10,2,7]=>10100010110
[6,3,7,4,5,8,12,9,1,10,11,2]=>10100011001
[2,5,8,4,7,6,1,3,10,9,12,11]=>00101100101
[2,5,8,4,7,6,1,3,10,12,11,9]=>00101100011
[8,5,10,4,7,6,2,9,1,3,12,11]=>10101101001
[10,5,9,4,7,6,2,12,3,11,1,8]=>10101101010
[8,5,9,4,7,6,2,12,10,3,11,1]=>10101101101
[2,7,10,4,8,6,9,5,1,3,12,11]=>00101011001
[10,7,12,4,8,6,9,5,2,11,1,3]=>10101011010
[2,9,8,4,12,6,10,3,11,7,1,5]=>01101010110
[2,7,8,4,12,6,9,10,1,3,11,5]=>00101001001
[2,5,6,4,10,8,7,3,9,1,12,11]=>00101110101
[10,5,6,4,12,8,7,3,9,11,1,2]=>10101110010
[2,9,8,4,6,12,7,3,11,10,1,5]=>01100110110
[2,5,8,4,12,9,7,11,6,10,3,1]=>00101101011
[2,5,6,4,7,12,9,8,1,10,11,3]=>00100111001
[2,3,4,8,5,6,7,1,10,9,12,11]=>00010010101
[2,3,4,8,5,6,7,1,10,12,11,9]=>00010010011
[8,3,4,10,5,6,7,9,1,2,12,11]=>10010001001
[10,3,4,9,5,6,7,12,2,11,1,8]=>10010001010
[8,3,4,9,5,6,7,12,10,2,11,1]=>10010001101
[2,7,4,10,5,6,9,8,1,3,12,11]=>01010011001
[10,7,4,12,5,6,9,8,2,11,1,3]=>11010011010
[2,9,4,12,5,6,10,8,11,7,1,3]=>01010010110
[2,7,4,8,5,6,12,10,9,3,11,1]=>01010011101
[2,3,6,10,5,9,7,8,1,4,12,11]=>00010101001
[10,3,6,12,5,9,7,8,2,11,1,4]=>10010101010
[2,9,6,12,5,11,7,8,10,1,3,4]=>01010100100
[2,3,8,12,5,10,7,11,9,6,1,4]=>00010101110
[2,3,6,7,5,12,10,8,9,4,11,1]=>00010110101
[2,3,4,5,10,6,7,8,9,1,12,11]=>00001000101
[10,3,4,5,12,6,7,8,9,11,1,2]=>10001000010
[2,9,4,5,12,6,7,8,11,10,1,3]=>01001000110
[2,3,8,5,12,6,7,11,9,10,1,4]=>00101001010
[2,3,4,7,12,6,11,8,9,10,1,5]=>00001010010
[2,3,4,5,6,12,7,8,9,10,11,1]=>00000100001
[1,4,3,6,5,8,7,12,11,9,10,2]=>01010101101
[1,4,3,6,5,10,9,7,8,12,11,2]=>01010110011
[1,4,3,6,5,12,9,7,11,8,10,2]=>01010110101
[1,4,3,6,5,12,11,10,7,8,9,2]=>01010111001
[1,4,3,8,7,5,6,10,9,12,11,2]=>01011001011
[1,4,3,8,7,5,6,12,11,9,10,2]=>01011001101
[1,4,3,10,7,5,9,6,8,12,11,2]=>01011010011
[1,4,3,12,7,5,9,6,11,8,10,2]=>01011010101
[1,4,3,12,7,5,11,10,6,8,9,2]=>01011011001
[1,4,3,10,9,8,5,6,7,12,11,2]=>01011100011
[1,4,3,12,9,8,5,6,11,7,10,2]=>01011100101
[1,4,3,12,11,8,5,10,6,7,9,2]=>01011101001
[1,4,3,12,11,10,9,5,6,7,8,2]=>01011110001
[1,6,5,3,4,8,7,10,9,12,11,2]=>01100101011
[1,6,5,3,4,8,7,12,11,9,10,2]=>01100101101
[1,6,5,3,4,10,9,7,8,12,11,2]=>01100110011
[1,6,5,3,4,12,9,7,11,8,10,2]=>01100110101
[1,6,5,3,4,12,11,10,7,8,9,2]=>01100111001
[1,8,5,3,7,4,6,10,9,12,11,2]=>01101001011
[1,8,5,3,7,4,6,12,11,9,10,2]=>01101001101
[1,10,5,3,7,4,9,6,8,12,11,2]=>01101010011
[1,12,5,3,7,4,9,6,11,8,10,2]=>01101010101
[1,12,5,3,7,4,11,10,6,8,9,2]=>01101011001
[1,10,5,3,9,8,4,6,7,12,11,2]=>01101100011
[1,12,5,3,9,8,4,6,11,7,10,2]=>01101100101
[1,12,5,3,11,8,4,10,6,7,9,2]=>01101101001
[1,12,5,3,11,10,9,4,6,7,8,2]=>01101110001
[1,8,7,6,3,4,5,10,9,12,11,2]=>01110001011
[1,8,7,6,3,4,5,12,11,9,10,2]=>01110001101
[1,10,7,6,3,4,9,5,8,12,11,2]=>01110010011
[1,12,7,6,3,4,9,5,11,8,10,2]=>01110010101
[1,12,7,6,3,4,11,10,5,8,9,2]=>01110011001
[1,10,9,6,3,8,4,5,7,12,11,2]=>01110100011
[1,12,9,6,3,8,4,5,11,7,10,2]=>01110100101
[1,12,11,6,3,8,4,10,5,7,9,2]=>01110101001
[1,12,11,6,3,10,9,4,5,7,8,2]=>01110110001
[1,10,9,8,7,3,4,5,6,12,11,2]=>01111000011
[1,12,9,8,7,3,4,5,11,6,10,2]=>01111000101
[1,12,11,8,7,3,4,10,5,6,9,2]=>01111001001
[1,12,11,10,7,3,9,4,5,6,8,2]=>01111010001
[1,12,11,10,9,8,3,4,5,6,7,2]=>01111100001
[3,1,2,6,5,8,7,10,9,12,11,4]=>10010101011
[3,1,2,6,5,8,7,12,11,9,10,4]=>10010101101
[3,1,2,6,5,10,9,7,8,12,11,4]=>10010110011
[3,1,2,6,5,12,9,7,11,8,10,4]=>10010110101
[3,1,2,6,5,12,11,10,7,8,9,4]=>10010111001
[3,1,2,8,7,5,6,10,9,12,11,4]=>10011001011
[3,1,2,8,7,5,6,12,11,9,10,4]=>10011001101
[3,1,2,10,7,5,9,6,8,12,11,4]=>10011010011
[3,1,2,12,7,5,9,6,11,8,10,4]=>10011010101
[3,1,2,12,7,5,11,10,6,8,9,4]=>10011011001
[3,1,2,10,9,8,5,6,7,12,11,4]=>10011100011
[3,1,2,12,9,8,5,6,11,7,10,4]=>10011100101
[3,1,2,12,11,8,5,10,6,7,9,4]=>10011101001
[3,1,2,12,11,10,9,5,6,7,8,4]=>10011110001
[3,1,5,2,4,8,7,10,9,12,11,6]=>10100101011
[3,1,5,2,4,8,7,12,11,9,10,6]=>10100101101
[3,1,5,2,4,10,9,7,8,12,11,6]=>10100110011
[3,1,5,2,4,12,9,7,11,8,10,6]=>10100110101
[3,1,5,2,4,12,11,10,7,8,9,6]=>10100111001
[3,1,5,2,7,4,6,10,9,12,11,8]=>10101001011
[3,1,5,2,7,4,6,12,11,9,10,8]=>10101001101
[3,1,5,2,7,4,9,6,8,12,11,10]=>10101010011
[3,1,5,2,7,4,9,6,11,8,10,12]=>10101010100
[3,1,5,2,7,4,11,10,6,8,9,12]=>10101011000
[3,1,5,2,9,8,4,6,7,12,11,10]=>10101100011
[3,1,5,2,9,8,4,6,11,7,10,12]=>10101100100
[3,1,5,2,11,8,4,10,6,7,9,12]=>10101101000
[3,1,5,2,11,10,9,4,6,7,8,12]=>10101110000
[3,1,7,6,2,4,5,10,9,12,11,8]=>10110001011
[3,1,7,6,2,4,5,12,11,9,10,8]=>10110001101
[3,1,7,6,2,4,9,5,8,12,11,10]=>10110010011
[3,1,7,6,2,4,9,5,11,8,10,12]=>10110010100
[3,1,7,6,2,4,11,10,5,8,9,12]=>10110011000
[3,1,9,6,2,8,4,5,7,12,11,10]=>10110100011
[3,1,9,6,2,8,4,5,11,7,10,12]=>10110100100
[3,1,11,6,2,8,4,10,5,7,9,12]=>10110101000
[3,1,11,6,2,10,9,4,5,7,8,12]=>10110110000
[3,1,9,8,7,2,4,5,6,12,11,10]=>10111000011
[3,1,9,8,7,2,4,5,11,6,10,12]=>10111000100
[3,1,11,8,7,2,4,10,5,6,9,12]=>10111001000
[3,1,11,10,7,2,9,4,5,6,8,12]=>10111010000
[3,1,11,10,9,8,2,4,5,6,7,12]=>10111100000
[5,4,1,2,3,8,7,10,9,12,11,6]=>11000101011
[5,4,1,2,3,8,7,12,11,9,10,6]=>11000101101
[5,4,1,2,3,10,9,7,8,12,11,6]=>11000110011
[5,4,1,2,3,12,9,7,11,8,10,6]=>11000110101
[5,4,1,2,3,12,11,10,7,8,9,6]=>11000111001
[5,4,1,2,7,3,6,10,9,12,11,8]=>11001001011
[5,4,1,2,7,3,6,12,11,9,10,8]=>11001001101
[5,4,1,2,7,3,9,6,8,12,11,10]=>11001010011
[5,4,1,2,7,3,9,6,11,8,10,12]=>11001010100
[5,4,1,2,7,3,11,10,6,8,9,12]=>11001011000
[5,4,1,2,9,8,3,6,7,12,11,10]=>11001100011
[5,4,1,2,9,8,3,6,11,7,10,12]=>11001100100
[5,4,1,2,11,8,3,10,6,7,9,12]=>11001101000
[5,4,1,2,11,10,9,3,6,7,8,12]=>11001110000
[7,4,1,6,2,3,5,10,9,12,11,8]=>11010001011
[7,4,1,6,2,3,5,12,11,9,10,8]=>11010001101
[7,4,1,6,2,3,9,5,8,12,11,10]=>11010010011
[7,4,1,6,2,3,9,5,11,8,10,12]=>11010010100
[7,4,1,6,2,3,11,10,5,8,9,12]=>11010011000
[9,4,1,6,2,8,3,5,7,12,11,10]=>11010100011
[9,4,1,6,2,8,3,5,11,7,10,12]=>11010100100
[11,4,1,6,2,8,3,10,5,7,9,12]=>11010101000
[11,4,1,6,2,10,9,3,5,7,8,12]=>11010110000
[9,4,1,8,7,2,3,5,6,12,11,10]=>11011000011
[9,4,1,8,7,2,3,5,11,6,10,12]=>11011000100
[11,4,1,8,7,2,3,10,5,6,9,12]=>11011001000
[11,4,1,10,7,2,9,3,5,6,8,12]=>11011010000
[11,4,1,10,9,8,2,3,5,6,7,12]=>11011100000
[7,6,5,1,2,3,4,10,9,12,11,8]=>11100001011
[7,6,5,1,2,3,4,12,11,9,10,8]=>11100001101
[7,6,5,1,2,3,9,4,8,12,11,10]=>11100010011
[7,6,5,1,2,3,9,4,11,8,10,12]=>11100010100
[7,6,5,1,2,3,11,10,4,8,9,12]=>11100011000
[9,6,5,1,2,8,3,4,7,12,11,10]=>11100100011
[9,6,5,1,2,8,3,4,11,7,10,12]=>11100100100
[11,6,5,1,2,8,3,10,4,7,9,12]=>11100101000
[11,6,5,1,2,10,9,3,4,7,8,12]=>11100110000
[9,8,5,1,7,2,3,4,6,12,11,10]=>11101000011
[9,8,5,1,7,2,3,4,11,6,10,12]=>11101000100
[11,8,5,1,7,2,3,10,4,6,9,12]=>11101001000
[11,10,5,1,7,2,9,3,4,6,8,12]=>11101010000
[11,10,5,1,9,8,2,3,4,6,7,12]=>11101100000
[9,8,7,6,1,2,3,4,5,12,11,10]=>11110000011
[9,8,7,6,1,2,3,4,11,5,10,12]=>11110000100
[11,8,7,6,1,2,3,10,4,5,9,12]=>11110001000
[11,10,7,6,1,2,9,3,4,5,8,12]=>11110010000
[11,10,9,6,1,8,2,3,4,5,7,12]=>11110100000
[11,10,9,8,7,1,2,3,4,5,6,12]=>11111000000
[11,12,8,6,4,2,1,3,5,7,10,9]=>01111100001
[12,9,10,6,4,2,1,3,5,8,7,11]=>10111100010
[11,9,12,6,4,2,1,3,5,8,10,7]=>10111100001
[10,11,12,6,4,2,1,3,5,9,8,7]=>00111100011
[12,10,7,8,4,2,1,3,6,5,9,11]=>11011100100
[11,12,7,8,4,2,1,3,6,5,10,9]=>01011100101
[12,9,7,10,4,2,1,3,6,8,5,11]=>11011100010
[11,9,7,12,4,2,1,3,6,8,10,5]=>11011100001
[10,11,7,12,4,2,1,3,6,9,8,5]=>01011100011
[12,8,9,10,4,2,1,3,7,6,5,11]=>10011100110
[11,8,9,12,4,2,1,3,7,6,10,5]=>10011100101
[10,8,11,12,4,2,1,3,7,9,6,5]=>10011100011
[9,10,11,12,4,2,1,3,8,7,6,5]=>00011100111
[12,10,8,5,6,2,1,4,3,7,9,11]=>11101101000
[11,12,8,5,6,2,1,4,3,7,10,9]=>01101101001
[12,9,10,5,6,2,1,4,3,8,7,11]=>10101101010
[11,9,12,5,6,2,1,4,3,8,10,7]=>10101101001
[10,11,12,5,6,2,1,4,3,9,8,7]=>00101101011
[12,10,7,5,8,2,1,4,6,3,9,11]=>11101100100
[11,12,7,5,8,2,1,4,6,3,10,9]=>01101100101
[12,9,7,5,10,2,1,4,6,8,3,11]=>11101100010
[11,9,7,5,12,2,1,4,6,8,10,3]=>11101100001
[10,11,7,5,12,2,1,4,6,9,8,3]=>01101100011
[12,8,9,5,10,2,1,4,7,6,3,11]=>10101100110
[11,8,9,5,12,2,1,4,7,6,10,3]=>10101100101
[10,8,11,5,12,2,1,4,7,9,6,3]=>10101100011
[9,10,11,5,12,2,1,4,8,7,6,3]=>00101100111
[12,10,6,7,8,2,1,5,4,3,9,11]=>11001101100
[11,12,6,7,8,2,1,5,4,3,10,9]=>01001101101
[12,9,6,7,10,2,1,5,4,8,3,11]=>11001101010
[11,9,6,7,12,2,1,5,4,8,10,3]=>11001101001
[10,11,6,7,12,2,1,5,4,9,8,3]=>01001101011
[12,8,6,9,10,2,1,5,7,4,3,11]=>11001100110
[11,8,6,9,12,2,1,5,7,4,10,3]=>11001100101
[10,8,6,11,12,2,1,5,7,9,4,3]=>11001100011
[9,10,6,11,12,2,1,5,8,7,4,3]=>01001100111
[12,7,8,9,10,2,1,6,5,4,3,11]=>10001101110
[11,7,8,9,12,2,1,6,5,4,10,3]=>10001101101
[10,7,8,11,12,2,1,6,5,9,4,3]=>10001101011
[9,7,10,11,12,2,1,6,8,5,4,3]=>10001100111
[8,9,10,11,12,2,1,7,6,5,4,3]=>00001101111
[12,10,8,6,3,4,2,1,5,7,9,11]=>11110110000
[11,12,8,6,3,4,2,1,5,7,10,9]=>01110110001
[12,9,10,6,3,4,2,1,5,8,7,11]=>10110110010
[11,9,12,6,3,4,2,1,5,8,10,7]=>10110110001
[10,11,12,6,3,4,2,1,5,9,8,7]=>00110110011
[12,10,7,8,3,4,2,1,6,5,9,11]=>11010110100
[11,12,7,8,3,4,2,1,6,5,10,9]=>01010110101
[12,9,7,10,3,4,2,1,6,8,5,11]=>11010110010
[11,9,7,12,3,4,2,1,6,8,10,5]=>11010110001
[10,11,7,12,3,4,2,1,6,9,8,5]=>01010110011
[12,8,9,10,3,4,2,1,7,6,5,11]=>10010110110
[11,8,9,12,3,4,2,1,7,6,10,5]=>10010110101
[10,8,11,12,3,4,2,1,7,9,6,5]=>10010110011
[9,10,11,12,3,4,2,1,8,7,6,5]=>00010110111
[12,10,8,5,3,6,2,4,1,7,9,11]=>11110101000
[11,12,8,5,3,6,2,4,1,7,10,9]=>01110101001
[12,9,10,5,3,6,2,4,1,8,7,11]=>10110101010
[11,9,12,5,3,6,2,4,1,8,10,7]=>10110101001
[10,11,12,5,3,6,2,4,1,9,8,7]=>00110101011
[12,10,7,5,3,8,2,4,6,1,9,11]=>11110100100
[11,12,7,5,3,8,2,4,6,1,10,9]=>01110100101
[12,9,7,5,3,10,2,4,6,8,1,11]=>11110100010
[11,9,7,5,3,12,2,4,6,8,10,1]=>11110100001
[10,11,7,5,3,12,2,4,6,9,8,1]=>01110100011
[12,8,9,5,3,10,2,4,7,6,1,11]=>10110100110
[11,8,9,5,3,12,2,4,7,6,10,1]=>10110100101
[10,8,11,5,3,12,2,4,7,9,6,1]=>10110100011
[9,10,11,5,3,12,2,4,8,7,6,1]=>00110100111
[12,10,6,7,3,8,2,5,4,1,9,11]=>11010101100
[11,12,6,7,3,8,2,5,4,1,10,9]=>01010101101
[12,9,6,7,3,10,2,5,4,8,1,11]=>11010101010
[11,9,6,7,3,12,2,5,4,8,10,1]=>11010101001
[10,11,6,7,3,12,2,5,4,9,8,1]=>01010101011
[12,8,6,9,3,10,2,5,7,4,1,11]=>11010100110
[11,8,6,9,3,12,2,5,7,4,10,1]=>11010100101
[10,8,6,11,3,12,2,5,7,9,4,1]=>11010100011
[9,10,6,11,3,12,2,5,8,7,4,1]=>01010100111
[12,7,8,9,3,10,2,6,5,4,1,11]=>10010101110
[11,7,8,9,3,12,2,6,5,4,10,1]=>10010101101
[10,7,8,11,3,12,2,6,5,9,4,1]=>10010101011
[9,7,10,11,3,12,2,6,8,5,4,1]=>10010100111
[8,9,10,11,3,12,2,7,6,5,4,1]=>00010101111
[12,10,8,4,5,6,3,2,1,7,9,11]=>11100111000
[11,12,8,4,5,6,3,2,1,7,10,9]=>01100111001
[12,9,10,4,5,6,3,2,1,8,7,11]=>10100111010
[11,9,12,4,5,6,3,2,1,8,10,7]=>10100111001
[10,11,12,4,5,6,3,2,1,9,8,7]=>00100111011
[12,10,7,4,5,8,3,2,6,1,9,11]=>11100110100
[11,12,7,4,5,8,3,2,6,1,10,9]=>01100110101
[12,9,7,4,5,10,3,2,6,8,1,11]=>11100110010
[11,9,7,4,5,12,3,2,6,8,10,1]=>11100110001
[10,11,7,4,5,12,3,2,6,9,8,1]=>01100110011
[12,8,9,4,5,10,3,2,7,6,1,11]=>10100110110
[11,8,9,4,5,12,3,2,7,6,10,1]=>10100110101
[10,8,11,4,5,12,3,2,7,9,6,1]=>10100110011
[9,10,11,4,5,12,3,2,8,7,6,1]=>00100110111
[12,10,6,4,7,8,3,5,2,1,9,11]=>11100101100
[11,12,6,4,7,8,3,5,2,1,10,9]=>01100101101
[12,9,6,4,7,10,3,5,2,8,1,11]=>11100101010
[11,9,6,4,7,12,3,5,2,8,10,1]=>11100101001
[10,11,6,4,7,12,3,5,2,9,8,1]=>01100101011
[12,8,6,4,9,10,3,5,7,2,1,11]=>11100100110
[11,8,6,4,9,12,3,5,7,2,10,1]=>11100100101
[10,8,6,4,11,12,3,5,7,9,2,1]=>11100100011
[9,10,6,4,11,12,3,5,8,7,2,1]=>01100100111
[12,7,8,4,9,10,3,6,5,2,1,11]=>10100101110
[11,7,8,4,9,12,3,6,5,2,10,1]=>10100101101
[10,7,8,4,11,12,3,6,5,9,2,1]=>10100101011
[9,7,10,4,11,12,3,6,8,5,2,1]=>10100100111
[8,9,10,4,11,12,3,7,6,5,2,1]=>00100101111
[12,10,5,6,7,8,4,3,2,1,9,11]=>11000111100
[11,12,5,6,7,8,4,3,2,1,10,9]=>01000111101
[12,9,5,6,7,10,4,3,2,8,1,11]=>11000111010
[11,9,5,6,7,12,4,3,2,8,10,1]=>11000111001
[10,11,5,6,7,12,4,3,2,9,8,1]=>01000111011
[12,8,5,6,9,10,4,3,7,2,1,11]=>11000110110
[11,8,5,6,9,12,4,3,7,2,10,1]=>11000110101
[10,8,5,6,11,12,4,3,7,9,2,1]=>11000110011
[9,10,5,6,11,12,4,3,8,7,2,1]=>01000110111
[12,7,5,8,9,10,4,6,3,2,1,11]=>11000101110
[11,7,5,8,9,12,4,6,3,2,10,1]=>11000101101
[10,7,5,8,11,12,4,6,3,9,2,1]=>11000101011
[9,7,5,10,11,12,4,6,8,3,2,1]=>11000100111
[8,9,5,10,11,12,4,7,6,3,2,1]=>01000101111
[12,6,7,8,9,10,5,4,3,2,1,11]=>10000111110
[11,6,7,8,9,12,5,4,3,2,10,1]=>10000111101
[10,6,7,8,11,12,5,4,3,9,2,1]=>10000111011
[9,6,7,10,11,12,5,4,8,3,2,1]=>10000110111
[8,6,9,10,11,12,5,7,4,3,2,1]=>10000101111
[11,12,2,4,6,8,10,1,3,5,7,9]=>01000010000
[9,10,2,4,6,8,12,1,3,5,7,11]=>01000010000
[11,9,12,2,4,6,8,10,1,3,5,7]=>10100001000
[10,11,12,9,2,4,6,8,1,3,5,7]=>00110001000
[7,8,2,4,6,10,12,1,3,5,9,11]=>01000010000
[7,8,11,12,2,4,6,10,1,3,5,9]=>00010001000
[9,7,10,2,4,6,8,12,1,3,5,11]=>10100001000
[9,11,7,12,2,4,6,8,10,1,3,5]=>01010000100
[7,10,11,12,9,2,4,6,8,1,3,5]=>00011000100
[8,9,10,7,2,4,6,12,1,3,5,11]=>00110001000
[11,8,9,7,12,2,4,6,10,1,3,5]=>10101000100
[10,11,8,12,7,9,2,4,6,1,3,5]=>01010100100
[9,10,11,12,8,7,2,4,6,1,3,5]=>00011100100
[5,6,2,4,8,10,12,1,3,7,9,11]=>01000010000
[5,6,11,12,2,4,8,10,1,3,7,9]=>00010001000
[5,6,9,10,2,4,8,12,1,3,7,11]=>00010001000
[11,5,6,9,12,2,4,8,10,1,3,7]=>10001000100
[10,11,12,5,6,9,2,4,8,1,3,7]=>00100100100
[7,5,8,2,4,6,10,12,1,3,9,11]=>10100001000
[7,5,8,11,12,2,4,6,10,1,3,9]=>10001000100
[7,9,5,10,2,4,6,8,12,1,3,11]=>01010000100
[7,9,11,5,12,2,4,6,8,10,1,3]=>00101000010
[10,7,11,12,5,9,2,4,6,8,1,3]=>10010100010
[5,8,9,10,7,2,4,6,12,1,3,11]=>00011000100
[11,5,8,9,7,12,2,4,6,10,1,3]=>10010100010
[8,10,5,11,12,7,9,2,4,6,1,3]=>01001010010
[9,10,11,12,5,8,7,2,4,6,1,3]=>00010110010
[6,7,8,5,2,4,10,12,1,3,9,11]=>00110001000
[6,7,8,5,11,12,2,4,10,1,3,9]=>00100100100
[9,6,7,5,10,2,4,8,12,1,3,11]=>10101000100
[9,6,7,11,5,12,2,4,8,10,1,3]=>10010100010
[6,10,7,11,12,5,9,2,4,8,1,3]=>01001010010
[8,9,6,10,5,7,2,4,12,1,3,11]=>01010100100
[8,9,11,6,5,7,12,2,4,10,1,3]=>00110010010
[10,8,11,6,12,5,7,9,2,4,1,3]=>10101001010
[9,6,10,11,12,8,5,7,2,4,1,3]=>10001101010
[7,8,9,10,6,5,2,4,12,1,3,11]=>00011100100
[11,7,8,9,6,5,12,2,4,10,1,3]=>10011010010
[10,11,7,8,6,12,5,9,2,4,1,3]=>01010101010
[9,10,11,7,12,6,8,5,2,4,1,3]=>00101011010
[8,9,10,11,12,7,6,5,2,4,1,3]=>00001111010
[3,4,2,6,8,10,12,1,5,7,9,11]=>01000010000
[3,4,11,12,2,6,8,10,1,5,7,9]=>00010001000
[3,4,9,10,2,6,8,12,1,5,7,11]=>00010001000
[11,3,4,9,12,2,6,8,10,1,5,7]=>10001000100
[10,11,12,3,4,9,2,6,8,1,5,7]=>00100100100
[3,4,7,8,2,6,10,12,1,5,9,11]=>00010001000
[3,4,7,8,11,12,2,6,10,1,5,9]=>00000100100
[9,3,4,7,10,2,6,8,12,1,5,11]=>10001000100
[9,11,3,4,7,12,2,6,8,10,1,5]=>01000100010
[3,10,11,12,4,7,9,2,6,8,1,5]=>00010010010
[8,9,10,3,4,7,2,6,12,1,5,11]=>00100100100
[11,8,9,3,4,7,12,2,6,10,1,5]=>10100010010
[10,11,8,12,3,4,7,9,2,6,1,5]=>01010001010
[9,10,11,12,8,3,4,7,2,6,1,5]=>00011001010
[5,3,6,2,4,8,10,12,1,7,9,11]=>10100001000
[5,3,6,11,12,2,4,8,10,1,7,9]=>10001000100
[5,3,6,9,10,2,4,8,12,1,7,11]=>10001000100
[5,11,3,6,9,12,2,4,8,10,1,7]=>01000100010
[5,10,11,12,3,6,9,2,4,8,1,7]=>00010010010
[5,7,3,8,2,4,6,10,12,1,9,11]=>01010000100
[5,7,3,8,11,12,2,4,6,10,1,9]=>01000100010
[5,7,9,3,10,2,4,6,8,12,1,11]=>00101000010
[5,7,9,11,3,12,2,4,6,8,10,1]=>00010100001
[10,5,7,11,12,3,9,2,4,6,8,1]=>10001010001
[8,5,9,10,3,7,2,4,6,12,1,11]=>10010100010
[8,11,5,9,3,7,12,2,4,6,10,1]=>01010010001
[8,10,11,5,12,3,7,9,2,4,6,1]=>00101001001
[5,9,10,11,12,8,3,7,2,4,6,1]=>00001101001
[3,6,7,8,5,2,4,10,12,1,9,11]=>00011000100
[3,6,7,8,5,11,12,2,4,10,1,9]=>00010010010
[9,3,6,7,5,10,2,4,8,12,1,11]=>10010100010
[9,3,6,7,11,5,12,2,4,8,10,1]=>10001010001
[6,10,3,7,11,12,5,9,2,4,8,1]=>01000101001
[6,8,3,9,10,5,7,2,4,12,1,11]=>01001010010
[6,8,9,3,11,5,7,12,2,4,10,1]=>00101001001
[10,6,8,3,11,12,5,7,9,2,4,1]=>10100100101
[9,6,10,11,12,3,8,5,7,2,4,1]=>10001010101
[7,8,9,10,3,6,5,2,4,12,1,11]=>00010110010
[11,7,8,9,3,6,5,12,2,4,10,1]=>10010101001
[10,11,7,8,3,6,12,5,9,2,4,1]=>01010010101
[9,10,11,7,12,3,6,8,5,2,4,1]=>00101001101
[8,9,10,11,12,7,3,6,5,2,4,1]=>00001101101
[4,5,6,3,2,8,10,12,1,7,9,11]=>00110001000
[4,5,6,3,11,12,2,8,10,1,7,9]=>00100100100
[4,5,6,3,9,10,2,8,12,1,7,11]=>00100100100
[4,5,6,11,3,9,12,2,8,10,1,7]=>00010010010
[4,5,6,10,11,12,3,9,2,8,1,7]=>00000101010
[7,4,5,3,8,2,6,10,12,1,9,11]=>10101000100
[7,4,5,3,8,11,12,2,6,10,1,9]=>10100010010
[7,4,5,9,3,10,2,6,8,12,1,11]=>10010100010
[7,4,5,9,11,3,12,2,6,8,10,1]=>10001010001
[7,10,4,5,11,12,3,9,2,6,8,1]=>01000101001
[4,8,5,9,10,3,7,2,6,12,1,11]=>01001010010
[4,8,11,5,9,3,7,12,2,6,10,1]=>00101001001
[4,8,10,11,5,12,3,7,9,2,6,1]=>00010100101
[4,5,9,10,11,12,8,3,7,2,6,1]=>00000110101
[6,7,4,8,3,5,2,10,12,1,9,11]=>01010100100
[6,7,4,8,3,5,11,12,2,10,1,9]=>01010001010
[6,7,9,4,3,5,10,2,8,12,1,11]=>00110010010
[6,7,9,4,11,3,5,12,2,8,10,1]=>00101001001
[10,6,7,4,11,12,3,5,9,2,8,1]=>10100100101
[8,6,9,4,10,3,5,7,2,12,1,11]=>10101001010
[8,6,9,11,4,3,5,7,12,2,10,1]=>10011000101
[8,10,6,11,4,12,3,5,7,9,2,1]=>01010100011
[6,9,4,10,11,12,8,3,5,7,2,1]=>01000110011
[7,4,8,9,10,6,3,5,2,12,1,11]=>10001101010
[7,11,4,8,9,6,3,5,12,2,10,1]=>01001100101
[7,8,10,4,11,6,12,3,5,9,2,1]=>00101010011
[9,7,10,4,11,12,6,8,3,5,2,1]=>10100101011
[4,8,9,10,11,12,7,6,3,5,2,1]=>00000111011
[5,6,7,8,4,3,2,10,12,1,9,11]=>00011100100
[5,6,7,8,4,3,11,12,2,10,1,9]=>00011001010
[9,5,6,7,4,3,10,2,8,12,1,11]=>10011010010
[9,5,6,7,4,11,3,12,2,8,10,1]=>10010101001
[5,10,6,7,4,11,12,3,9,2,8,1]=>01010010101
[8,9,5,6,4,10,3,7,2,12,1,11]=>01010101010
[8,9,5,6,11,4,3,7,12,2,10,1]=>01001100101
[10,8,5,6,11,4,12,3,7,9,2,1]=>11001010011
[9,5,10,6,11,12,4,8,3,7,2,1]=>10100101011
[7,8,9,5,10,4,6,3,2,12,1,11]=>00101011010
[7,8,9,11,5,4,6,3,12,2,10,1]=>00011010101
[10,7,8,11,5,4,6,12,3,9,2,1]=>10011001011
[9,10,7,11,5,12,4,6,8,3,2,1]=>01010100111
[8,9,5,10,11,12,7,4,6,3,2,1]=>01000110111
[6,7,8,9,10,5,4,3,2,12,1,11]=>00001111010
[11,6,7,8,9,5,4,3,12,2,10,1]=>10001110101
[10,11,6,7,8,5,4,12,3,9,2,1]=>01001101011
[9,10,11,6,7,5,12,4,8,3,2,1]=>00101010111
[8,9,10,11,6,12,5,7,4,3,2,1]=>00010101111
[2,1,4,3,6,5,8,7,12,9,11,10]=>10101010101
[2,1,4,3,6,5,10,7,9,8,12,11]=>10101010101
[2,1,4,3,6,5,12,11,9,7,8,10]=>10101011100
[2,1,4,3,6,5,12,7,8,10,11,9]=>10101010001
[2,1,4,3,8,5,7,6,10,9,12,11]=>10101010101
[2,1,4,3,8,5,7,6,12,9,11,10]=>10101010101
[2,1,4,3,10,9,7,5,6,8,12,11]=>10101110001
[2,1,4,3,12,9,7,11,6,5,8,10]=>10101101100
[2,1,4,3,12,10,7,5,8,6,11,9]=>10101110101
[2,1,4,3,10,5,6,8,9,7,12,11]=>10101000101
[2,1,4,3,12,11,6,8,9,5,7,10]=>10101100100
[2,1,4,3,12,5,11,8,6,10,7,9]=>10101011010
[2,1,4,3,12,5,6,7,9,10,11,8]=>10101000001
[2,1,6,3,5,4,8,7,10,9,12,11]=>10101010101
[2,1,6,3,5,4,8,7,12,9,11,10]=>10101010101
[2,1,6,3,5,4,10,7,9,8,12,11]=>10101010101
[2,1,6,3,5,4,12,11,9,7,8,10]=>10101011100
[2,1,6,3,5,4,12,7,8,10,11,9]=>10101010001
[2,1,8,7,5,3,4,6,10,9,12,11]=>10111000101
[2,1,8,7,5,3,4,6,12,9,11,10]=>10111000101
[2,1,10,7,5,9,4,3,6,8,12,11]=>10110110001
[2,1,12,7,5,9,4,11,6,3,8,10]=>10110101100
[2,1,12,7,5,10,4,3,8,6,11,9]=>10110110101
[2,1,10,8,5,3,6,4,9,7,12,11]=>10111010101
[2,1,12,8,5,11,6,4,9,3,7,10]=>10110110100
[2,1,12,8,5,3,11,4,6,10,7,9]=>10111010010
[2,1,12,9,5,3,6,7,4,10,11,8]=>10111001001
[2,1,8,3,4,6,7,5,10,9,12,11]=>10100010101
[2,1,8,3,4,6,7,5,12,9,11,10]=>10100010101
[2,1,10,9,4,6,7,3,5,8,12,11]=>10110010001
[2,1,12,9,4,6,7,11,5,3,8,10]=>10110001100
[2,1,12,10,4,6,7,3,8,5,11,9]=>10110010101
[2,1,10,3,9,6,4,8,5,7,12,11]=>10101101001
[2,1,12,11,9,6,4,8,5,3,7,10]=>10111101100
[2,1,12,3,10,6,11,8,4,5,7,9]=>10101011000
[2,1,12,3,10,6,4,7,9,5,11,8]=>10101100101
[2,1,10,3,4,5,7,8,9,6,12,11]=>10100000101
[2,1,12,11,4,5,7,8,9,3,6,10]=>10110000100
[2,1,12,3,11,5,7,8,4,10,6,9]=>10101001010
[2,1,12,3,4,11,7,5,9,10,6,8]=>10100110010
[2,1,12,3,4,5,6,8,9,10,11,7]=>10100000001
[4,1,3,2,6,5,8,7,10,9,12,11]=>10101010101
[4,1,3,2,6,5,8,7,12,9,11,10]=>10101010101
[4,1,3,2,6,5,10,7,9,8,12,11]=>10101010101
[4,1,3,2,6,5,12,11,9,7,8,10]=>10101011100
[4,1,3,2,6,5,12,7,8,10,11,9]=>10101010001
[4,1,3,2,8,5,7,6,10,9,12,11]=>10101010101
[4,1,3,2,8,5,7,6,12,9,11,10]=>10101010101
[4,1,3,2,10,9,7,5,6,8,12,11]=>10101110001
[4,1,3,2,12,9,7,11,6,5,8,10]=>10101101100
[4,1,3,2,12,10,7,5,8,6,11,9]=>10101110101
[4,1,3,2,10,5,6,8,9,7,12,11]=>10101000101
[4,1,3,2,12,11,6,8,9,5,7,10]=>10101100100
[4,1,3,2,12,5,11,8,6,10,7,9]=>10101011010
[4,1,3,2,12,5,6,7,9,10,11,8]=>10101000001
[6,5,3,1,2,4,8,7,10,9,12,11]=>11100010101
[6,5,3,1,2,4,8,7,12,9,11,10]=>11100010101
[6,5,3,1,2,4,10,7,9,8,12,11]=>11100010101
[6,5,3,1,2,4,12,11,9,7,8,10]=>11100011100
[6,5,3,1,2,4,12,7,8,10,11,9]=>11100010001
[8,5,3,7,2,1,4,6,10,9,12,11]=>11011000101
[8,5,3,7,2,1,4,6,12,9,11,10]=>11011000101
[10,5,3,7,2,9,4,1,6,8,12,11]=>11010110001
[12,5,3,7,2,9,4,11,6,1,8,10]=>11010101100
[12,5,3,7,2,10,4,1,8,6,11,9]=>11010110101
[10,5,3,8,2,1,6,4,9,7,12,11]=>11011010101
[12,5,3,8,2,11,6,4,9,1,7,10]=>11010110100
[12,5,3,8,2,1,11,4,6,10,7,9]=>11011010010
[12,5,3,9,2,1,6,7,4,10,11,8]=>11011001001
[8,6,3,1,4,2,7,5,10,9,12,11]=>11101010101
[8,6,3,1,4,2,7,5,12,9,11,10]=>11101010101
[10,6,3,9,4,2,7,1,5,8,12,11]=>11011010001
[12,6,3,9,4,2,7,11,5,1,8,10]=>11011001100
[12,6,3,10,4,2,7,1,8,5,11,9]=>11011010101
[10,6,3,1,9,2,4,8,5,7,12,11]=>11101001001
[12,6,3,11,9,2,4,8,5,1,7,10]=>11011001100
[12,6,3,1,10,2,11,8,4,5,7,9]=>11101011000
[12,6,3,1,10,2,4,7,9,5,11,8]=>11101000101
[10,7,3,1,4,5,2,8,9,6,12,11]=>11100100101
[12,7,3,11,4,5,2,8,9,1,6,10]=>11010100100
[12,7,3,1,11,5,2,8,4,10,6,9]=>11101101010
[12,7,3,1,4,11,2,5,9,10,6,8]=>11100100010
[12,8,3,1,4,5,6,2,9,10,11,7]=>11100010001
[6,1,2,4,5,3,8,7,10,9,12,11]=>10001010101
[6,1,2,4,5,3,8,7,12,9,11,10]=>10001010101
[6,1,2,4,5,3,10,7,9,8,12,11]=>10001010101
[6,1,2,4,5,3,12,11,9,7,8,10]=>10001011100
[6,1,2,4,5,3,12,7,8,10,11,9]=>10001010001
[8,7,2,4,5,1,3,6,10,9,12,11]=>11001000101
[8,7,2,4,5,1,3,6,12,9,11,10]=>11001000101
[10,7,2,4,5,9,3,1,6,8,12,11]=>11000110001
[12,7,2,4,5,9,3,11,6,1,8,10]=>11000101100
[12,7,2,4,5,10,3,1,8,6,11,9]=>11000110101
[10,8,2,4,5,1,6,3,9,7,12,11]=>11001010101
[12,8,2,4,5,11,6,3,9,1,7,10]=>11000110100
[12,8,2,4,5,1,11,3,6,10,7,9]=>11001010010
[12,9,2,4,5,1,6,7,3,10,11,8]=>11001001001
[8,1,7,4,2,6,3,5,10,9,12,11]=>10110100101
[8,1,7,4,2,6,3,5,12,9,11,10]=>10110100101
[10,9,7,4,2,6,3,1,5,8,12,11]=>11110110001
[12,9,7,4,2,6,3,11,5,1,8,10]=>11110101100
[12,10,7,4,2,6,3,1,8,5,11,9]=>11110110101
[10,1,8,4,9,6,2,3,5,7,12,11]=>10101100001
[12,11,8,4,9,6,2,3,5,1,7,10]=>11101100100
[12,1,8,4,10,6,11,3,2,5,7,9]=>10101011000
[12,1,9,4,10,6,2,7,3,5,11,8]=>10101101001
[10,1,8,4,2,5,7,3,9,6,12,11]=>10110010101
[12,11,8,4,2,5,7,3,9,1,6,10]=>11110010100
[12,1,8,4,11,5,7,3,2,10,6,9]=>10101011010
[12,1,9,4,2,11,7,5,3,10,6,8]=>10110111010
[12,1,9,4,2,5,6,8,3,10,11,7]=>10110001001
[8,1,2,3,5,6,7,4,10,9,12,11]=>10000010101
[8,1,2,3,5,6,7,4,12,9,11,10]=>10000010101
[10,9,2,3,5,6,7,1,4,8,12,11]=>11000010001
[12,9,2,3,5,6,7,11,4,1,8,10]=>11000001100
[12,10,2,3,5,6,7,1,8,4,11,9]=>11000010101
[10,1,9,3,5,6,2,8,4,7,12,11]=>10100101001
[12,11,9,3,5,6,2,8,4,1,7,10]=>11100101100
[12,1,10,3,5,6,11,8,2,4,7,9]=>10100011000
[12,1,10,3,5,6,2,7,9,4,11,8]=>10100100101
[10,1,2,9,5,3,7,8,4,6,12,11]=>10011001001
[12,11,2,9,5,3,7,8,4,1,6,10]=>11011001100
[12,1,11,10,5,3,7,8,2,4,6,9]=>10111001000
[12,1,2,10,5,11,7,3,9,4,6,8]=>10010110100
[12,1,2,10,5,3,6,8,9,4,11,7]=>10011000101
[10,1,2,3,4,6,7,8,9,5,12,11]=>10000000101
[12,11,2,3,4,6,7,8,9,1,5,10]=>11000000100
[12,1,11,3,4,6,7,8,2,10,5,9]=>10100001010
[12,1,2,11,4,6,7,3,9,10,5,8]=>10010010010
[12,1,2,3,11,6,4,8,9,10,5,7]=>10001100010
[12,1,2,3,4,5,7,8,9,10,11,6]=>10000000001
          

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Description

The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.

Properties

surjective, graded

Sage code

def mapping(X):
    if X:
        D = X.descents(from_zero=True)
        w = [1 if i in D else 0 for i in range(len(X)-1)]
        return Words([0,1])(w)
    raise ValueError("The descent word is not defined for the empty permutation")

Weight

Created

Sep 22, 2020 at 11:07 by FindStatCrew

Updated

Sep 22, 2020 at 11:07 by Martin Rubey